diff --git a/CMakeLists.txt b/CMakeLists.txt
index 5106a0197dbe03a95bd81ca43a8489f7a117821c..fc24d6075c3a69fd8d0e3206d6c6c613ba945bdf 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -86,7 +86,6 @@ opt(SOLVER "Enable built-in finite element solvers (required for compounds)" ${D
opt(TAUCS "Enable Taucs linear solver" ${DEFAULT})
opt(TCMALLOC "Enable libtcmalloc, a fast malloc implementation but that does not release memory" OFF)
opt(TETGEN "Enable Tetgen 3D initial mesh generator" ${DEFAULT})
-opt(TETGEN_OLD "Enable older version of Tetgen" OFF)
opt(VORO3D "Enable Voro3D (for hex meshing, experimental)" ${DEFAULT})
opt(WRAP_JAVA "Enable generation of Java wrappers (experimental)" OFF)
opt(WRAP_PYTHON "Enable generation of Python wrappers" OFF)
@@ -795,11 +794,6 @@ if(HAVE_MESH)
include_directories(contrib/Tetgen1.5)
set_config_option(HAVE_TETGEN "Tetgen(1.5)")
add_definitions(-DTETLIBRARY)
- elseif(ENABLE_TETGEN_OLD AND EXISTS ${CMAKE_CURRENT_SOURCE_DIR}/contrib/Tetgen1.4/tetgen.h)
- add_subdirectory(contrib/Tetgen1.4)
- include_directories(contrib/Tetgen1.4)
- set_config_option(HAVE_TETGEN "Tetgen(1.4)")
- add_definitions(-DTETLIBRARY)
elseif(ENABLE_TETGEN)
find_library(TETGEN_LIB tet PATH_SUFFIXES lib)
find_path(TETGEN_INC "tetgen.h" PATH_SUFFIXES src include tetgen)
@@ -811,7 +805,7 @@ if(HAVE_MESH)
endif(ENABLE_TETGEN AND EXISTS ${CMAKE_CURRENT_SOURCE_DIR}/contrib/Tetgen1.5/tetgen.h)
if(HAVE_TETGEN)
message(STATUS "Note: By including Tetgen you have to comply with Tetgen's "
- "special licensing requirements stated in contrib/Tetgen*/LICENSE.")
+ "special licensing requirements stated in contrib/Tetgen1.5/LICENSE.")
endif(HAVE_TETGEN)
endif(HAVE_MESH)
diff --git a/contrib/Tetgen1.4/CMakeLists.txt b/contrib/Tetgen1.4/CMakeLists.txt
deleted file mode 100644
index 6b1004a40a334ed5756cee0e12197c49b1e05ee3..0000000000000000000000000000000000000000
--- a/contrib/Tetgen1.4/CMakeLists.txt
+++ /dev/null
@@ -1,12 +0,0 @@
-# Gmsh - Copyright (C) 1997-2016 C. Geuzaine, J.-F. Remacle
-#
-# See the LICENSE.txt file for license information. Please report all
-# bugs and problems to the public mailing list <gmsh@onelab.info>.
-
-set(SRC
- tetgen.cxx
- predicates.cxx
-)
-
-file(GLOB_RECURSE HDR RELATIVE ${CMAKE_CURRENT_SOURCE_DIR} *.h)
-append_gmsh_src(contrib/Tetgen1.4 "${SRC};${HDR}")
diff --git a/contrib/Tetgen1.4/LICENSE b/contrib/Tetgen1.4/LICENSE
deleted file mode 100644
index 65e5262522bd3faa6a85ec43002263fc1557455e..0000000000000000000000000000000000000000
--- a/contrib/Tetgen1.4/LICENSE
+++ /dev/null
@@ -1,66 +0,0 @@
-TetGen License
---------------
-
-The software (TetGen) is licensed under the terms of the MIT license
-with the following exceptions:
-
-Distribution of modified versions of this code is permissible UNDER
-THE CONDITION THAT THIS CODE AND ANY MODIFICATIONS MADE TO IT IN THE
-SAME SOURCE FILES tetgen.h AND tetgen.cxx REMAIN UNDER COPYRIGHT OF
-THE ORIGINAL AUTHOR, BOTH SOURCE AND OBJECT CODE ARE MADE FREELY
-AVAILABLE WITHOUT CHARGE, AND CLEAR NOTICE IS GIVEN OF THE
-MODIFICATIONS.
-
-Distribution of this code for any commercial purpose is permissible
-ONLY BY DIRECT ARRANGEMENT WITH THE COPYRIGHT OWNER.
-
-The full license text is reproduced below.
-
-This means that TetGen is no free software, but for private, research,
-and educational purposes it can be used at absolutely no cost and
-without further arrangements.
-
-
-For details, see http://tetgen.berlios.de
-
-==============================================================================
-
-TetGen
-A Quality Tetrahedral Mesh Generator and 3D Delaunay Triangulator
-Version 1.4 (Released on January 14, 2006).
-
-Copyright 2002, 2004, 2005, 2006
-Hang Si
-Rathausstr. 9, 10178 Berlin, Germany
-si@wias-berlin.de
-
-Permission is hereby granted, free of charge, to any person obtaining
-a copy of this software and associated documentation files (the
-"Software"), to deal in the Software without restriction, including
-without limitation the rights to use, copy, modify, merge, publish,
-distribute, sublicense and/or sell copies of the Software, and to
-permit persons to whom the Software is furnished to do so, subject to
-the following conditions:
-
-Distribution of modified versions of this code is permissible UNDER
-THE CONDITION THAT THIS CODE AND ANY MODIFICATIONS MADE TO IT IN THE
-SAME SOURCE FILES tetgen.h AND tetgen.cxx REMAIN UNDER COPYRIGHT OF
-THE ORIGINAL AUTHOR, BOTH SOURCE AND OBJECT CODE ARE MADE FREELY
-AVAILABLE WITHOUT CHARGE, AND CLEAR NOTICE IS GIVEN OF THE
-MODIFICATIONS.
-
-Distribution of this code for any commercial purpose is permissible
-ONLY BY DIRECT ARRANGEMENT WITH THE COPYRIGHT OWNER.
-
-The above copyright notice and this permission notice shall be
-included in all copies or substantial portions of the Software.
-
-THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
-EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
-MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
-IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
-CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
-TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
-SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
-
-==============================================================================
\ No newline at end of file
diff --git a/contrib/Tetgen1.4/README.txt b/contrib/Tetgen1.4/README.txt
deleted file mode 100644
index 125c22c4fa9ef24105952f8cbf5aa24e888af529..0000000000000000000000000000000000000000
--- a/contrib/Tetgen1.4/README.txt
+++ /dev/null
@@ -1,16 +0,0 @@
-This is TetGen version 1.4.2 (released on April 16, 2007)
-
-Please see the documentation of TetGen (available at the following link) for
-compiling and using TetGen.
-
- http://tetgen.berlios.de/index.html
-
-TetGen may be freely copied, modified, and redistributed under the
-copyright notices stated in the file LICENSE.
-
-Please send bugs/comments to Hang Si <si@wias-berlin.de>
-
-Thank you and enjoy!
-
-Hang Si
-April 16, 2007
diff --git a/contrib/Tetgen1.4/predicates.cxx b/contrib/Tetgen1.4/predicates.cxx
deleted file mode 100644
index bc0bd39f9e13f255295e81757db3889767a13196..0000000000000000000000000000000000000000
--- a/contrib/Tetgen1.4/predicates.cxx
+++ /dev/null
@@ -1,4187 +0,0 @@
-/*****************************************************************************/
-/* */
-/* Routines for Arbitrary Precision Floating-point Arithmetic */
-/* and Fast Robust Geometric Predicates */
-/* (predicates.c) */
-/* */
-/* May 18, 1996 */
-/* */
-/* Placed in the public domain by */
-/* Jonathan Richard Shewchuk */
-/* School of Computer Science */
-/* Carnegie Mellon University */
-/* 5000 Forbes Avenue */
-/* Pittsburgh, Pennsylvania 15213-3891 */
-/* jrs@cs.cmu.edu */
-/* */
-/* This file contains C implementation of algorithms for exact addition */
-/* and multiplication of floating-point numbers, and predicates for */
-/* robustly performing the orientation and incircle tests used in */
-/* computational geometry. The algorithms and underlying theory are */
-/* described in Jonathan Richard Shewchuk. "Adaptive Precision Floating- */
-/* Point Arithmetic and Fast Robust Geometric Predicates." Technical */
-/* Report CMU-CS-96-140, School of Computer Science, Carnegie Mellon */
-/* University, Pittsburgh, Pennsylvania, May 1996. (Submitted to */
-/* Discrete & Computational Geometry.) */
-/* */
-/* This file, the paper listed above, and other information are available */
-/* from the Web page http://www.cs.cmu.edu/~quake/robust.html . */
-/* */
-/*****************************************************************************/
-
-/*****************************************************************************/
-/* */
-/* Using this code: */
-/* */
-/* First, read the short or long version of the paper (from the Web page */
-/* above). */
-/* */
-/* Be sure to call exactinit() once, before calling any of the arithmetic */
-/* functions or geometric predicates. Also be sure to turn on the */
-/* optimizer when compiling this file. */
-/* */
-/* */
-/* Several geometric predicates are defined. Their parameters are all */
-/* points. Each point is an array of two or three floating-point */
-/* numbers. The geometric predicates, described in the papers, are */
-/* */
-/* orient2d(pa, pb, pc) */
-/* orient2dfast(pa, pb, pc) */
-/* orient3d(pa, pb, pc, pd) */
-/* orient3dfast(pa, pb, pc, pd) */
-/* incircle(pa, pb, pc, pd) */
-/* incirclefast(pa, pb, pc, pd) */
-/* insphere(pa, pb, pc, pd, pe) */
-/* inspherefast(pa, pb, pc, pd, pe) */
-/* */
-/* Those with suffix "fast" are approximate, non-robust versions. Those */
-/* without the suffix are adaptive precision, robust versions. There */
-/* are also versions with the suffices "exact" and "slow", which are */
-/* non-adaptive, exact arithmetic versions, which I use only for timings */
-/* in my arithmetic papers. */
-/* */
-/* */
-/* An expansion is represented by an array of floating-point numbers, */
-/* sorted from smallest to largest magnitude (possibly with interspersed */
-/* zeros). The length of each expansion is stored as a separate integer, */
-/* and each arithmetic function returns an integer which is the length */
-/* of the expansion it created. */
-/* */
-/* Several arithmetic functions are defined. Their parameters are */
-/* */
-/* e, f Input expansions */
-/* elen, flen Lengths of input expansions (must be >= 1) */
-/* h Output expansion */
-/* b Input scalar */
-/* */
-/* The arithmetic functions are */
-/* */
-/* grow_expansion(elen, e, b, h) */
-/* grow_expansion_zeroelim(elen, e, b, h) */
-/* expansion_sum(elen, e, flen, f, h) */
-/* expansion_sum_zeroelim1(elen, e, flen, f, h) */
-/* expansion_sum_zeroelim2(elen, e, flen, f, h) */
-/* fast_expansion_sum(elen, e, flen, f, h) */
-/* fast_expansion_sum_zeroelim(elen, e, flen, f, h) */
-/* linear_expansion_sum(elen, e, flen, f, h) */
-/* linear_expansion_sum_zeroelim(elen, e, flen, f, h) */
-/* scale_expansion(elen, e, b, h) */
-/* scale_expansion_zeroelim(elen, e, b, h) */
-/* compress(elen, e, h) */
-/* */
-/* All of these are described in the long version of the paper; some are */
-/* described in the short version. All return an integer that is the */
-/* length of h. Those with suffix _zeroelim perform zero elimination, */
-/* and are recommended over their counterparts. The procedure */
-/* fast_expansion_sum_zeroelim() (or linear_expansion_sum_zeroelim() on */
-/* processors that do not use the round-to-even tiebreaking rule) is */
-/* recommended over expansion_sum_zeroelim(). Each procedure has a */
-/* little note next to it (in the code below) that tells you whether or */
-/* not the output expansion may be the same array as one of the input */
-/* expansions. */
-/* */
-/* */
-/* If you look around below, you'll also find macros for a bunch of */
-/* simple unrolled arithmetic operations, and procedures for printing */
-/* expansions (commented out because they don't work with all C */
-/* compilers) and for generating random floating-point numbers whose */
-/* significand bits are all random. Most of the macros have undocumented */
-/* requirements that certain of their parameters should not be the same */
-/* variable; for safety, better to make sure all the parameters are */
-/* distinct variables. Feel free to send email to jrs@cs.cmu.edu if you */
-/* have questions. */
-/* */
-/*****************************************************************************/
-
-#include <stdio.h>
-#include <stdlib.h>
-#include <math.h>
-#ifdef CPU86
-#include <float.h>
-#endif /* CPU86 */
-#ifdef LINUX
-#include <fpu_control.h>
-#endif /* LINUX */
-
-#include "tetgen.h" // Defines the symbol REAL (float or double).
-
-/* On some machines, the exact arithmetic routines might be defeated by the */
-/* use of internal extended precision floating-point registers. Sometimes */
-/* this problem can be fixed by defining certain values to be volatile, */
-/* thus forcing them to be stored to memory and rounded off. This isn't */
-/* a great solution, though, as it slows the arithmetic down. */
-/* */
-/* To try this out, write "#define INEXACT volatile" below. Normally, */
-/* however, INEXACT should be defined to be nothing. ("#define INEXACT".) */
-
-#define INEXACT /* Nothing */
-/* #define INEXACT volatile */
-
-/* #define REAL double */ /* float or double */
-#define REALPRINT doubleprint
-#define REALRAND doublerand
-#define NARROWRAND narrowdoublerand
-#define UNIFORMRAND uniformdoublerand
-
-/* Which of the following two methods of finding the absolute values is */
-/* fastest is compiler-dependent. A few compilers can inline and optimize */
-/* the fabs() call; but most will incur the overhead of a function call, */
-/* which is disastrously slow. A faster way on IEEE machines might be to */
-/* mask the appropriate bit, but that's difficult to do in C. */
-
-#define Absolute(a) ((a) >= 0.0 ? (a) : -(a))
-/* #define Absolute(a) fabs(a) */
-
-/* Many of the operations are broken up into two pieces, a main part that */
-/* performs an approximate operation, and a "tail" that computes the */
-/* roundoff error of that operation. */
-/* */
-/* The operations Fast_Two_Sum(), Fast_Two_Diff(), Two_Sum(), Two_Diff(), */
-/* Split(), and Two_Product() are all implemented as described in the */
-/* reference. Each of these macros requires certain variables to be */
-/* defined in the calling routine. The variables `bvirt', `c', `abig', */
-/* `_i', `_j', `_k', `_l', `_m', and `_n' are declared `INEXACT' because */
-/* they store the result of an operation that may incur roundoff error. */
-/* The input parameter `x' (or the highest numbered `x_' parameter) must */
-/* also be declared `INEXACT'. */
-
-#define Fast_Two_Sum_Tail(a, b, x, y) \
- bvirt = x - a; \
- y = b - bvirt
-
-#define Fast_Two_Sum(a, b, x, y) \
- x = (REAL) (a + b); \
- Fast_Two_Sum_Tail(a, b, x, y)
-
-#define Fast_Two_Diff_Tail(a, b, x, y) \
- bvirt = a - x; \
- y = bvirt - b
-
-#define Fast_Two_Diff(a, b, x, y) \
- x = (REAL) (a - b); \
- Fast_Two_Diff_Tail(a, b, x, y)
-
-#define Two_Sum_Tail(a, b, x, y) \
- bvirt = (REAL) (x - a); \
- avirt = x - bvirt; \
- bround = b - bvirt; \
- around = a - avirt; \
- y = around + bround
-
-#define Two_Sum(a, b, x, y) \
- x = (REAL) (a + b); \
- Two_Sum_Tail(a, b, x, y)
-
-#define Two_Diff_Tail(a, b, x, y) \
- bvirt = (REAL) (a - x); \
- avirt = x + bvirt; \
- bround = bvirt - b; \
- around = a - avirt; \
- y = around + bround
-
-#define Two_Diff(a, b, x, y) \
- x = (REAL) (a - b); \
- Two_Diff_Tail(a, b, x, y)
-
-#define Split(a, ahi, alo) \
- c = (REAL) (splitter * a); \
- abig = (REAL) (c - a); \
- ahi = c - abig; \
- alo = a - ahi
-
-#define Two_Product_Tail(a, b, x, y) \
- Split(a, ahi, alo); \
- Split(b, bhi, blo); \
- err1 = x - (ahi * bhi); \
- err2 = err1 - (alo * bhi); \
- err3 = err2 - (ahi * blo); \
- y = (alo * blo) - err3
-
-#define Two_Product(a, b, x, y) \
- x = (REAL) (a * b); \
- Two_Product_Tail(a, b, x, y)
-
-/* Two_Product_Presplit() is Two_Product() where one of the inputs has */
-/* already been split. Avoids redundant splitting. */
-
-#define Two_Product_Presplit(a, b, bhi, blo, x, y) \
- x = (REAL) (a * b); \
- Split(a, ahi, alo); \
- err1 = x - (ahi * bhi); \
- err2 = err1 - (alo * bhi); \
- err3 = err2 - (ahi * blo); \
- y = (alo * blo) - err3
-
-/* Two_Product_2Presplit() is Two_Product() where both of the inputs have */
-/* already been split. Avoids redundant splitting. */
-
-#define Two_Product_2Presplit(a, ahi, alo, b, bhi, blo, x, y) \
- x = (REAL) (a * b); \
- err1 = x - (ahi * bhi); \
- err2 = err1 - (alo * bhi); \
- err3 = err2 - (ahi * blo); \
- y = (alo * blo) - err3
-
-/* Square() can be done more quickly than Two_Product(). */
-
-#define Square_Tail(a, x, y) \
- Split(a, ahi, alo); \
- err1 = x - (ahi * ahi); \
- err3 = err1 - ((ahi + ahi) * alo); \
- y = (alo * alo) - err3
-
-#define Square(a, x, y) \
- x = (REAL) (a * a); \
- Square_Tail(a, x, y)
-
-/* Macros for summing expansions of various fixed lengths. These are all */
-/* unrolled versions of Expansion_Sum(). */
-
-#define Two_One_Sum(a1, a0, b, x2, x1, x0) \
- Two_Sum(a0, b , _i, x0); \
- Two_Sum(a1, _i, x2, x1)
-
-#define Two_One_Diff(a1, a0, b, x2, x1, x0) \
- Two_Diff(a0, b , _i, x0); \
- Two_Sum( a1, _i, x2, x1)
-
-#define Two_Two_Sum(a1, a0, b1, b0, x3, x2, x1, x0) \
- Two_One_Sum(a1, a0, b0, _j, _0, x0); \
- Two_One_Sum(_j, _0, b1, x3, x2, x1)
-
-#define Two_Two_Diff(a1, a0, b1, b0, x3, x2, x1, x0) \
- Two_One_Diff(a1, a0, b0, _j, _0, x0); \
- Two_One_Diff(_j, _0, b1, x3, x2, x1)
-
-#define Four_One_Sum(a3, a2, a1, a0, b, x4, x3, x2, x1, x0) \
- Two_One_Sum(a1, a0, b , _j, x1, x0); \
- Two_One_Sum(a3, a2, _j, x4, x3, x2)
-
-#define Four_Two_Sum(a3, a2, a1, a0, b1, b0, x5, x4, x3, x2, x1, x0) \
- Four_One_Sum(a3, a2, a1, a0, b0, _k, _2, _1, _0, x0); \
- Four_One_Sum(_k, _2, _1, _0, b1, x5, x4, x3, x2, x1)
-
-#define Four_Four_Sum(a3, a2, a1, a0, b4, b3, b1, b0, x7, x6, x5, x4, x3, x2, \
- x1, x0) \
- Four_Two_Sum(a3, a2, a1, a0, b1, b0, _l, _2, _1, _0, x1, x0); \
- Four_Two_Sum(_l, _2, _1, _0, b4, b3, x7, x6, x5, x4, x3, x2)
-
-#define Eight_One_Sum(a7, a6, a5, a4, a3, a2, a1, a0, b, x8, x7, x6, x5, x4, \
- x3, x2, x1, x0) \
- Four_One_Sum(a3, a2, a1, a0, b , _j, x3, x2, x1, x0); \
- Four_One_Sum(a7, a6, a5, a4, _j, x8, x7, x6, x5, x4)
-
-#define Eight_Two_Sum(a7, a6, a5, a4, a3, a2, a1, a0, b1, b0, x9, x8, x7, \
- x6, x5, x4, x3, x2, x1, x0) \
- Eight_One_Sum(a7, a6, a5, a4, a3, a2, a1, a0, b0, _k, _6, _5, _4, _3, _2, \
- _1, _0, x0); \
- Eight_One_Sum(_k, _6, _5, _4, _3, _2, _1, _0, b1, x9, x8, x7, x6, x5, x4, \
- x3, x2, x1)
-
-#define Eight_Four_Sum(a7, a6, a5, a4, a3, a2, a1, a0, b4, b3, b1, b0, x11, \
- x10, x9, x8, x7, x6, x5, x4, x3, x2, x1, x0) \
- Eight_Two_Sum(a7, a6, a5, a4, a3, a2, a1, a0, b1, b0, _l, _6, _5, _4, _3, \
- _2, _1, _0, x1, x0); \
- Eight_Two_Sum(_l, _6, _5, _4, _3, _2, _1, _0, b4, b3, x11, x10, x9, x8, \
- x7, x6, x5, x4, x3, x2)
-
-/* Macros for multiplying expansions of various fixed lengths. */
-
-#define Two_One_Product(a1, a0, b, x3, x2, x1, x0) \
- Split(b, bhi, blo); \
- Two_Product_Presplit(a0, b, bhi, blo, _i, x0); \
- Two_Product_Presplit(a1, b, bhi, blo, _j, _0); \
- Two_Sum(_i, _0, _k, x1); \
- Fast_Two_Sum(_j, _k, x3, x2)
-
-#define Four_One_Product(a3, a2, a1, a0, b, x7, x6, x5, x4, x3, x2, x1, x0) \
- Split(b, bhi, blo); \
- Two_Product_Presplit(a0, b, bhi, blo, _i, x0); \
- Two_Product_Presplit(a1, b, bhi, blo, _j, _0); \
- Two_Sum(_i, _0, _k, x1); \
- Fast_Two_Sum(_j, _k, _i, x2); \
- Two_Product_Presplit(a2, b, bhi, blo, _j, _0); \
- Two_Sum(_i, _0, _k, x3); \
- Fast_Two_Sum(_j, _k, _i, x4); \
- Two_Product_Presplit(a3, b, bhi, blo, _j, _0); \
- Two_Sum(_i, _0, _k, x5); \
- Fast_Two_Sum(_j, _k, x7, x6)
-
-#define Two_Two_Product(a1, a0, b1, b0, x7, x6, x5, x4, x3, x2, x1, x0) \
- Split(a0, a0hi, a0lo); \
- Split(b0, bhi, blo); \
- Two_Product_2Presplit(a0, a0hi, a0lo, b0, bhi, blo, _i, x0); \
- Split(a1, a1hi, a1lo); \
- Two_Product_2Presplit(a1, a1hi, a1lo, b0, bhi, blo, _j, _0); \
- Two_Sum(_i, _0, _k, _1); \
- Fast_Two_Sum(_j, _k, _l, _2); \
- Split(b1, bhi, blo); \
- Two_Product_2Presplit(a0, a0hi, a0lo, b1, bhi, blo, _i, _0); \
- Two_Sum(_1, _0, _k, x1); \
- Two_Sum(_2, _k, _j, _1); \
- Two_Sum(_l, _j, _m, _2); \
- Two_Product_2Presplit(a1, a1hi, a1lo, b1, bhi, blo, _j, _0); \
- Two_Sum(_i, _0, _n, _0); \
- Two_Sum(_1, _0, _i, x2); \
- Two_Sum(_2, _i, _k, _1); \
- Two_Sum(_m, _k, _l, _2); \
- Two_Sum(_j, _n, _k, _0); \
- Two_Sum(_1, _0, _j, x3); \
- Two_Sum(_2, _j, _i, _1); \
- Two_Sum(_l, _i, _m, _2); \
- Two_Sum(_1, _k, _i, x4); \
- Two_Sum(_2, _i, _k, x5); \
- Two_Sum(_m, _k, x7, x6)
-
-/* An expansion of length two can be squared more quickly than finding the */
-/* product of two different expansions of length two, and the result is */
-/* guaranteed to have no more than six (rather than eight) components. */
-
-#define Two_Square(a1, a0, x5, x4, x3, x2, x1, x0) \
- Square(a0, _j, x0); \
- _0 = a0 + a0; \
- Two_Product(a1, _0, _k, _1); \
- Two_One_Sum(_k, _1, _j, _l, _2, x1); \
- Square(a1, _j, _1); \
- Two_Two_Sum(_j, _1, _l, _2, x5, x4, x3, x2)
-
-/* splitter = 2^ceiling(p / 2) + 1. Used to split floats in half. */
-static REAL splitter;
-static REAL epsilon; /* = 2^(-p). Used to estimate roundoff errors. */
-/* A set of coefficients used to calculate maximum roundoff errors. */
-static REAL resulterrbound;
-static REAL ccwerrboundA, ccwerrboundB, ccwerrboundC;
-static REAL o3derrboundA, o3derrboundB, o3derrboundC;
-static REAL iccerrboundA, iccerrboundB, iccerrboundC;
-static REAL isperrboundA, isperrboundB, isperrboundC;
-
-/*****************************************************************************/
-/* */
-/* doubleprint() Print the bit representation of a double. */
-/* */
-/* Useful for debugging exact arithmetic routines. */
-/* */
-/*****************************************************************************/
-
-/*
-void doubleprint(number)
-double number;
-{
- unsigned long long no;
- unsigned long long sign, expo;
- int exponent;
- int i, bottomi;
-
- no = *(unsigned long long *) &number;
- sign = no & 0x8000000000000000ll;
- expo = (no >> 52) & 0x7ffll;
- exponent = (int) expo;
- exponent = exponent - 1023;
- if (sign) {
- printf("-");
- } else {
- printf(" ");
- }
- if (exponent == -1023) {
- printf(
- "0.0000000000000000000000000000000000000000000000000000_ ( )");
- } else {
- printf("1.");
- bottomi = -1;
- for (i = 0; i < 52; i++) {
- if (no & 0x0008000000000000ll) {
- printf("1");
- bottomi = i;
- } else {
- printf("0");
- }
- no <<= 1;
- }
- printf("_%d (%d)", exponent, exponent - 1 - bottomi);
- }
-}
-*/
-
-/*****************************************************************************/
-/* */
-/* floatprint() Print the bit representation of a float. */
-/* */
-/* Useful for debugging exact arithmetic routines. */
-/* */
-/*****************************************************************************/
-
-/*
-void floatprint(number)
-float number;
-{
- unsigned no;
- unsigned sign, expo;
- int exponent;
- int i, bottomi;
-
- no = *(unsigned *) &number;
- sign = no & 0x80000000;
- expo = (no >> 23) & 0xff;
- exponent = (int) expo;
- exponent = exponent - 127;
- if (sign) {
- printf("-");
- } else {
- printf(" ");
- }
- if (exponent == -127) {
- printf("0.00000000000000000000000_ ( )");
- } else {
- printf("1.");
- bottomi = -1;
- for (i = 0; i < 23; i++) {
- if (no & 0x00400000) {
- printf("1");
- bottomi = i;
- } else {
- printf("0");
- }
- no <<= 1;
- }
- printf("_%3d (%3d)", exponent, exponent - 1 - bottomi);
- }
-}
-*/
-
-/*****************************************************************************/
-/* */
-/* expansion_print() Print the bit representation of an expansion. */
-/* */
-/* Useful for debugging exact arithmetic routines. */
-/* */
-/*****************************************************************************/
-
-/*
-void expansion_print(elen, e)
-int elen;
-REAL *e;
-{
- int i;
-
- for (i = elen - 1; i >= 0; i--) {
- REALPRINT(e[i]);
- if (i > 0) {
- printf(" +\n");
- } else {
- printf("\n");
- }
- }
-}
-*/
-
-/*****************************************************************************/
-/* */
-/* doublerand() Generate a double with random 53-bit significand and a */
-/* random exponent in [0, 511]. */
-/* */
-/*****************************************************************************/
-
-/*
-double doublerand()
-{
- double result;
- double expo;
- long a, b, c;
- long i;
-
- a = random();
- b = random();
- c = random();
- result = (double) (a - 1073741824) * 8388608.0 + (double) (b >> 8);
- for (i = 512, expo = 2; i <= 131072; i *= 2, expo = expo * expo) {
- if (c & i) {
- result *= expo;
- }
- }
- return result;
-}
-*/
-
-/*****************************************************************************/
-/* */
-/* narrowdoublerand() Generate a double with random 53-bit significand */
-/* and a random exponent in [0, 7]. */
-/* */
-/*****************************************************************************/
-
-/*
-double narrowdoublerand()
-{
- double result;
- double expo;
- long a, b, c;
- long i;
-
- a = random();
- b = random();
- c = random();
- result = (double) (a - 1073741824) * 8388608.0 + (double) (b >> 8);
- for (i = 512, expo = 2; i <= 2048; i *= 2, expo = expo * expo) {
- if (c & i) {
- result *= expo;
- }
- }
- return result;
-}
-*/
-
-/*****************************************************************************/
-/* */
-/* uniformdoublerand() Generate a double with random 53-bit significand. */
-/* */
-/*****************************************************************************/
-
-/*
-double uniformdoublerand()
-{
- double result;
- long a, b;
-
- a = random();
- b = random();
- result = (double) (a - 1073741824) * 8388608.0 + (double) (b >> 8);
- return result;
-}
-*/
-
-/*****************************************************************************/
-/* */
-/* floatrand() Generate a float with random 24-bit significand and a */
-/* random exponent in [0, 63]. */
-/* */
-/*****************************************************************************/
-
-/*
-float floatrand()
-{
- float result;
- float expo;
- long a, c;
- long i;
-
- a = random();
- c = random();
- result = (float) ((a - 1073741824) >> 6);
- for (i = 512, expo = 2; i <= 16384; i *= 2, expo = expo * expo) {
- if (c & i) {
- result *= expo;
- }
- }
- return result;
-}
-*/
-
-/*****************************************************************************/
-/* */
-/* narrowfloatrand() Generate a float with random 24-bit significand and */
-/* a random exponent in [0, 7]. */
-/* */
-/*****************************************************************************/
-
-/*
-float narrowfloatrand()
-{
- float result;
- float expo;
- long a, c;
- long i;
-
- a = random();
- c = random();
- result = (float) ((a - 1073741824) >> 6);
- for (i = 512, expo = 2; i <= 2048; i *= 2, expo = expo * expo) {
- if (c & i) {
- result *= expo;
- }
- }
- return result;
-}
-*/
-
-/*****************************************************************************/
-/* */
-/* uniformfloatrand() Generate a float with random 24-bit significand. */
-/* */
-/*****************************************************************************/
-
-/*
-float uniformfloatrand()
-{
- float result;
- long a;
-
- a = random();
- result = (float) ((a - 1073741824) >> 6);
- return result;
-}
-*/
-
-/*****************************************************************************/
-/* */
-/* exactinit() Initialize the variables used for exact arithmetic. */
-/* */
-/* `epsilon' is the largest power of two such that 1.0 + epsilon = 1.0 in */
-/* floating-point arithmetic. `epsilon' bounds the relative roundoff */
-/* error. It is used for floating-point error analysis. */
-/* */
-/* `splitter' is used to split floating-point numbers into two half- */
-/* length significands for exact multiplication. */
-/* */
-/* I imagine that a highly optimizing compiler might be too smart for its */
-/* own good, and somehow cause this routine to fail, if it pretends that */
-/* floating-point arithmetic is too much like real arithmetic. */
-/* */
-/* Don't change this routine unless you fully understand it. */
-/* */
-/*****************************************************************************/
-
-REAL exactinit()
-{
- REAL half;
- REAL check, lastcheck;
- int every_other;
-#ifdef LINUX
- int cword;
-#endif /* LINUX */
-
-#ifdef CPU86
-#ifdef SINGLE
- _control87(_PC_24, _MCW_PC); /* Set FPU control word for single precision. */
-#else /* not SINGLE */
- _control87(_PC_53, _MCW_PC); /* Set FPU control word for double precision. */
-#endif /* not SINGLE */
-#endif /* CPU86 */
-#ifdef LINUX
-#ifdef SINGLE
- /* cword = 4223; */
- cword = 4210; /* set FPU control word for single precision */
-#else /* not SINGLE */
- /* cword = 4735; */
- cword = 4722; /* set FPU control word for double precision */
-#endif /* not SINGLE */
- _FPU_SETCW(cword);
-#endif /* LINUX */
-
- every_other = 1;
- half = 0.5;
- epsilon = 1.0;
- splitter = 1.0;
- check = 1.0;
- /* Repeatedly divide `epsilon' by two until it is too small to add to */
- /* one without causing roundoff. (Also check if the sum is equal to */
- /* the previous sum, for machines that round up instead of using exact */
- /* rounding. Not that this library will work on such machines anyway. */
- do {
- lastcheck = check;
- epsilon *= half;
- if (every_other) {
- splitter *= 2.0;
- }
- every_other = !every_other;
- check = 1.0 + epsilon;
- } while ((check != 1.0) && (check != lastcheck));
- splitter += 1.0;
-
- /* Error bounds for orientation and incircle tests. */
- resulterrbound = (3.0 + 8.0 * epsilon) * epsilon;
- ccwerrboundA = (3.0 + 16.0 * epsilon) * epsilon;
- ccwerrboundB = (2.0 + 12.0 * epsilon) * epsilon;
- ccwerrboundC = (9.0 + 64.0 * epsilon) * epsilon * epsilon;
- o3derrboundA = (7.0 + 56.0 * epsilon) * epsilon;
- o3derrboundB = (3.0 + 28.0 * epsilon) * epsilon;
- o3derrboundC = (26.0 + 288.0 * epsilon) * epsilon * epsilon;
- iccerrboundA = (10.0 + 96.0 * epsilon) * epsilon;
- iccerrboundB = (4.0 + 48.0 * epsilon) * epsilon;
- iccerrboundC = (44.0 + 576.0 * epsilon) * epsilon * epsilon;
- isperrboundA = (16.0 + 224.0 * epsilon) * epsilon;
- isperrboundB = (5.0 + 72.0 * epsilon) * epsilon;
- isperrboundC = (71.0 + 1408.0 * epsilon) * epsilon * epsilon;
-
- return epsilon; /* Added by H. Si 30 Juli, 2004. */
-}
-
-/*****************************************************************************/
-/* */
-/* grow_expansion() Add a scalar to an expansion. */
-/* */
-/* Sets h = e + b. See the long version of my paper for details. */
-/* */
-/* Maintains the nonoverlapping property. If round-to-even is used (as */
-/* with IEEE 754), maintains the strongly nonoverlapping and nonadjacent */
-/* properties as well. (That is, if e has one of these properties, so */
-/* will h.) */
-/* */
-/*****************************************************************************/
-
-int grow_expansion(int elen, REAL *e, REAL b, REAL *h)
-/* e and h can be the same. */
-{
- REAL Q;
- INEXACT REAL Qnew;
- int eindex;
- REAL enow;
- INEXACT REAL bvirt;
- REAL avirt, bround, around;
-
- Q = b;
- for (eindex = 0; eindex < elen; eindex++) {
- enow = e[eindex];
- Two_Sum(Q, enow, Qnew, h[eindex]);
- Q = Qnew;
- }
- h[eindex] = Q;
- return eindex + 1;
-}
-
-/*****************************************************************************/
-/* */
-/* grow_expansion_zeroelim() Add a scalar to an expansion, eliminating */
-/* zero components from the output expansion. */
-/* */
-/* Sets h = e + b. See the long version of my paper for details. */
-/* */
-/* Maintains the nonoverlapping property. If round-to-even is used (as */
-/* with IEEE 754), maintains the strongly nonoverlapping and nonadjacent */
-/* properties as well. (That is, if e has one of these properties, so */
-/* will h.) */
-/* */
-/*****************************************************************************/
-
-int grow_expansion_zeroelim(int elen, REAL *e, REAL b, REAL *h)
-/* e and h can be the same. */
-{
- REAL Q, hh;
- INEXACT REAL Qnew;
- int eindex, hindex;
- REAL enow;
- INEXACT REAL bvirt;
- REAL avirt, bround, around;
-
- hindex = 0;
- Q = b;
- for (eindex = 0; eindex < elen; eindex++) {
- enow = e[eindex];
- Two_Sum(Q, enow, Qnew, hh);
- Q = Qnew;
- if (hh != 0.0) {
- h[hindex++] = hh;
- }
- }
- if ((Q != 0.0) || (hindex == 0)) {
- h[hindex++] = Q;
- }
- return hindex;
-}
-
-/*****************************************************************************/
-/* */
-/* expansion_sum() Sum two expansions. */
-/* */
-/* Sets h = e + f. See the long version of my paper for details. */
-/* */
-/* Maintains the nonoverlapping property. If round-to-even is used (as */
-/* with IEEE 754), maintains the nonadjacent property as well. (That is, */
-/* if e has one of these properties, so will h.) Does NOT maintain the */
-/* strongly nonoverlapping property. */
-/* */
-/*****************************************************************************/
-
-int expansion_sum(int elen, REAL *e, int flen, REAL *f, REAL *h)
-/* e and h can be the same, but f and h cannot. */
-{
- REAL Q;
- INEXACT REAL Qnew;
- int findex, hindex, hlast;
- REAL hnow;
- INEXACT REAL bvirt;
- REAL avirt, bround, around;
-
- Q = f[0];
- for (hindex = 0; hindex < elen; hindex++) {
- hnow = e[hindex];
- Two_Sum(Q, hnow, Qnew, h[hindex]);
- Q = Qnew;
- }
- h[hindex] = Q;
- hlast = hindex;
- for (findex = 1; findex < flen; findex++) {
- Q = f[findex];
- for (hindex = findex; hindex <= hlast; hindex++) {
- hnow = h[hindex];
- Two_Sum(Q, hnow, Qnew, h[hindex]);
- Q = Qnew;
- }
- h[++hlast] = Q;
- }
- return hlast + 1;
-}
-
-/*****************************************************************************/
-/* */
-/* expansion_sum_zeroelim1() Sum two expansions, eliminating zero */
-/* components from the output expansion. */
-/* */
-/* Sets h = e + f. See the long version of my paper for details. */
-/* */
-/* Maintains the nonoverlapping property. If round-to-even is used (as */
-/* with IEEE 754), maintains the nonadjacent property as well. (That is, */
-/* if e has one of these properties, so will h.) Does NOT maintain the */
-/* strongly nonoverlapping property. */
-/* */
-/*****************************************************************************/
-
-int expansion_sum_zeroelim1(int elen, REAL *e, int flen, REAL *f, REAL *h)
-/* e and h can be the same, but f and h cannot. */
-{
- REAL Q;
- INEXACT REAL Qnew;
- int index, findex, hindex, hlast;
- REAL hnow;
- INEXACT REAL bvirt;
- REAL avirt, bround, around;
-
- Q = f[0];
- for (hindex = 0; hindex < elen; hindex++) {
- hnow = e[hindex];
- Two_Sum(Q, hnow, Qnew, h[hindex]);
- Q = Qnew;
- }
- h[hindex] = Q;
- hlast = hindex;
- for (findex = 1; findex < flen; findex++) {
- Q = f[findex];
- for (hindex = findex; hindex <= hlast; hindex++) {
- hnow = h[hindex];
- Two_Sum(Q, hnow, Qnew, h[hindex]);
- Q = Qnew;
- }
- h[++hlast] = Q;
- }
- hindex = -1;
- for (index = 0; index <= hlast; index++) {
- hnow = h[index];
- if (hnow != 0.0) {
- h[++hindex] = hnow;
- }
- }
- if (hindex == -1) {
- return 1;
- } else {
- return hindex + 1;
- }
-}
-
-/*****************************************************************************/
-/* */
-/* expansion_sum_zeroelim2() Sum two expansions, eliminating zero */
-/* components from the output expansion. */
-/* */
-/* Sets h = e + f. See the long version of my paper for details. */
-/* */
-/* Maintains the nonoverlapping property. If round-to-even is used (as */
-/* with IEEE 754), maintains the nonadjacent property as well. (That is, */
-/* if e has one of these properties, so will h.) Does NOT maintain the */
-/* strongly nonoverlapping property. */
-/* */
-/*****************************************************************************/
-
-int expansion_sum_zeroelim2(int elen, REAL *e, int flen, REAL *f, REAL *h)
-/* e and h can be the same, but f and h cannot. */
-{
- REAL Q, hh;
- INEXACT REAL Qnew;
- int eindex, findex, hindex, hlast;
- REAL enow;
- INEXACT REAL bvirt;
- REAL avirt, bround, around;
-
- hindex = 0;
- Q = f[0];
- for (eindex = 0; eindex < elen; eindex++) {
- enow = e[eindex];
- Two_Sum(Q, enow, Qnew, hh);
- Q = Qnew;
- if (hh != 0.0) {
- h[hindex++] = hh;
- }
- }
- h[hindex] = Q;
- hlast = hindex;
- for (findex = 1; findex < flen; findex++) {
- hindex = 0;
- Q = f[findex];
- for (eindex = 0; eindex <= hlast; eindex++) {
- enow = h[eindex];
- Two_Sum(Q, enow, Qnew, hh);
- Q = Qnew;
- if (hh != 0) {
- h[hindex++] = hh;
- }
- }
- h[hindex] = Q;
- hlast = hindex;
- }
- return hlast + 1;
-}
-
-/*****************************************************************************/
-/* */
-/* fast_expansion_sum() Sum two expansions. */
-/* */
-/* Sets h = e + f. See the long version of my paper for details. */
-/* */
-/* If round-to-even is used (as with IEEE 754), maintains the strongly */
-/* nonoverlapping property. (That is, if e is strongly nonoverlapping, h */
-/* will be also.) Does NOT maintain the nonoverlapping or nonadjacent */
-/* properties. */
-/* */
-/*****************************************************************************/
-
-int fast_expansion_sum(int elen, REAL *e, int flen, REAL *f, REAL *h)
-/* h cannot be e or f. */
-{
- REAL Q;
- INEXACT REAL Qnew;
- INEXACT REAL bvirt;
- REAL avirt, bround, around;
- int eindex, findex, hindex;
- REAL enow, fnow;
-
- enow = e[0];
- fnow = f[0];
- eindex = findex = 0;
- if ((fnow > enow) == (fnow > -enow)) {
- Q = enow;
- enow = e[++eindex];
- } else {
- Q = fnow;
- fnow = f[++findex];
- }
- hindex = 0;
- if ((eindex < elen) && (findex < flen)) {
- if ((fnow > enow) == (fnow > -enow)) {
- Fast_Two_Sum(enow, Q, Qnew, h[0]);
- enow = e[++eindex];
- } else {
- Fast_Two_Sum(fnow, Q, Qnew, h[0]);
- fnow = f[++findex];
- }
- Q = Qnew;
- hindex = 1;
- while ((eindex < elen) && (findex < flen)) {
- if ((fnow > enow) == (fnow > -enow)) {
- Two_Sum(Q, enow, Qnew, h[hindex]);
- enow = e[++eindex];
- } else {
- Two_Sum(Q, fnow, Qnew, h[hindex]);
- fnow = f[++findex];
- }
- Q = Qnew;
- hindex++;
- }
- }
- while (eindex < elen) {
- Two_Sum(Q, enow, Qnew, h[hindex]);
- enow = e[++eindex];
- Q = Qnew;
- hindex++;
- }
- while (findex < flen) {
- Two_Sum(Q, fnow, Qnew, h[hindex]);
- fnow = f[++findex];
- Q = Qnew;
- hindex++;
- }
- h[hindex] = Q;
- return hindex + 1;
-}
-
-/*****************************************************************************/
-/* */
-/* fast_expansion_sum_zeroelim() Sum two expansions, eliminating zero */
-/* components from the output expansion. */
-/* */
-/* Sets h = e + f. See the long version of my paper for details. */
-/* */
-/* If round-to-even is used (as with IEEE 754), maintains the strongly */
-/* nonoverlapping property. (That is, if e is strongly nonoverlapping, h */
-/* will be also.) Does NOT maintain the nonoverlapping or nonadjacent */
-/* properties. */
-/* */
-/*****************************************************************************/
-
-int fast_expansion_sum_zeroelim(int elen, REAL *e, int flen, REAL *f, REAL *h)
-/* h cannot be e or f. */
-{
- REAL Q;
- INEXACT REAL Qnew;
- INEXACT REAL hh;
- INEXACT REAL bvirt;
- REAL avirt, bround, around;
- int eindex, findex, hindex;
- REAL enow, fnow;
-
- enow = e[0];
- fnow = f[0];
- eindex = findex = 0;
- if ((fnow > enow) == (fnow > -enow)) {
- Q = enow;
- enow = e[++eindex];
- } else {
- Q = fnow;
- fnow = f[++findex];
- }
- hindex = 0;
- if ((eindex < elen) && (findex < flen)) {
- if ((fnow > enow) == (fnow > -enow)) {
- Fast_Two_Sum(enow, Q, Qnew, hh);
- enow = e[++eindex];
- } else {
- Fast_Two_Sum(fnow, Q, Qnew, hh);
- fnow = f[++findex];
- }
- Q = Qnew;
- if (hh != 0.0) {
- h[hindex++] = hh;
- }
- while ((eindex < elen) && (findex < flen)) {
- if ((fnow > enow) == (fnow > -enow)) {
- Two_Sum(Q, enow, Qnew, hh);
- enow = e[++eindex];
- } else {
- Two_Sum(Q, fnow, Qnew, hh);
- fnow = f[++findex];
- }
- Q = Qnew;
- if (hh != 0.0) {
- h[hindex++] = hh;
- }
- }
- }
- while (eindex < elen) {
- Two_Sum(Q, enow, Qnew, hh);
- enow = e[++eindex];
- Q = Qnew;
- if (hh != 0.0) {
- h[hindex++] = hh;
- }
- }
- while (findex < flen) {
- Two_Sum(Q, fnow, Qnew, hh);
- fnow = f[++findex];
- Q = Qnew;
- if (hh != 0.0) {
- h[hindex++] = hh;
- }
- }
- if ((Q != 0.0) || (hindex == 0)) {
- h[hindex++] = Q;
- }
- return hindex;
-}
-
-/*****************************************************************************/
-/* */
-/* linear_expansion_sum() Sum two expansions. */
-/* */
-/* Sets h = e + f. See either version of my paper for details. */
-/* */
-/* Maintains the nonoverlapping property. (That is, if e is */
-/* nonoverlapping, h will be also.) */
-/* */
-/*****************************************************************************/
-
-int linear_expansion_sum(int elen, REAL *e, int flen, REAL *f, REAL *h)
-/* h cannot be e or f. */
-{
- REAL Q, q;
- INEXACT REAL Qnew;
- INEXACT REAL R;
- INEXACT REAL bvirt;
- REAL avirt, bround, around;
- int eindex, findex, hindex;
- REAL enow, fnow;
- REAL g0;
-
- enow = e[0];
- fnow = f[0];
- eindex = findex = 0;
- if ((fnow > enow) == (fnow > -enow)) {
- g0 = enow;
- enow = e[++eindex];
- } else {
- g0 = fnow;
- fnow = f[++findex];
- }
- if ((eindex < elen) && ((findex >= flen)
- || ((fnow > enow) == (fnow > -enow)))) {
- Fast_Two_Sum(enow, g0, Qnew, q);
- enow = e[++eindex];
- } else {
- Fast_Two_Sum(fnow, g0, Qnew, q);
- fnow = f[++findex];
- }
- Q = Qnew;
- for (hindex = 0; hindex < elen + flen - 2; hindex++) {
- if ((eindex < elen) && ((findex >= flen)
- || ((fnow > enow) == (fnow > -enow)))) {
- Fast_Two_Sum(enow, q, R, h[hindex]);
- enow = e[++eindex];
- } else {
- Fast_Two_Sum(fnow, q, R, h[hindex]);
- fnow = f[++findex];
- }
- Two_Sum(Q, R, Qnew, q);
- Q = Qnew;
- }
- h[hindex] = q;
- h[hindex + 1] = Q;
- return hindex + 2;
-}
-
-/*****************************************************************************/
-/* */
-/* linear_expansion_sum_zeroelim() Sum two expansions, eliminating zero */
-/* components from the output expansion. */
-/* */
-/* Sets h = e + f. See either version of my paper for details. */
-/* */
-/* Maintains the nonoverlapping property. (That is, if e is */
-/* nonoverlapping, h will be also.) */
-/* */
-/*****************************************************************************/
-
-int linear_expansion_sum_zeroelim(int elen, REAL *e, int flen, REAL *f,
- REAL *h)
-/* h cannot be e or f. */
-{
- REAL Q, q, hh;
- INEXACT REAL Qnew;
- INEXACT REAL R;
- INEXACT REAL bvirt;
- REAL avirt, bround, around;
- int eindex, findex, hindex;
- int count;
- REAL enow, fnow;
- REAL g0;
-
- enow = e[0];
- fnow = f[0];
- eindex = findex = 0;
- hindex = 0;
- if ((fnow > enow) == (fnow > -enow)) {
- g0 = enow;
- enow = e[++eindex];
- } else {
- g0 = fnow;
- fnow = f[++findex];
- }
- if ((eindex < elen) && ((findex >= flen)
- || ((fnow > enow) == (fnow > -enow)))) {
- Fast_Two_Sum(enow, g0, Qnew, q);
- enow = e[++eindex];
- } else {
- Fast_Two_Sum(fnow, g0, Qnew, q);
- fnow = f[++findex];
- }
- Q = Qnew;
- for (count = 2; count < elen + flen; count++) {
- if ((eindex < elen) && ((findex >= flen)
- || ((fnow > enow) == (fnow > -enow)))) {
- Fast_Two_Sum(enow, q, R, hh);
- enow = e[++eindex];
- } else {
- Fast_Two_Sum(fnow, q, R, hh);
- fnow = f[++findex];
- }
- Two_Sum(Q, R, Qnew, q);
- Q = Qnew;
- if (hh != 0) {
- h[hindex++] = hh;
- }
- }
- if (q != 0) {
- h[hindex++] = q;
- }
- if ((Q != 0.0) || (hindex == 0)) {
- h[hindex++] = Q;
- }
- return hindex;
-}
-
-/*****************************************************************************/
-/* */
-/* scale_expansion() Multiply an expansion by a scalar. */
-/* */
-/* Sets h = be. See either version of my paper for details. */
-/* */
-/* Maintains the nonoverlapping property. If round-to-even is used (as */
-/* with IEEE 754), maintains the strongly nonoverlapping and nonadjacent */
-/* properties as well. (That is, if e has one of these properties, so */
-/* will h.) */
-/* */
-/*****************************************************************************/
-
-int scale_expansion(int elen, REAL *e, REAL b, REAL *h)
-/* e and h cannot be the same. */
-{
- INEXACT REAL Q;
- INEXACT REAL sum;
- INEXACT REAL product1;
- REAL product0;
- int eindex, hindex;
- REAL enow;
- INEXACT REAL bvirt;
- REAL avirt, bround, around;
- INEXACT REAL c;
- INEXACT REAL abig;
- REAL ahi, alo, bhi, blo;
- REAL err1, err2, err3;
-
- Split(b, bhi, blo);
- Two_Product_Presplit(e[0], b, bhi, blo, Q, h[0]);
- hindex = 1;
- for (eindex = 1; eindex < elen; eindex++) {
- enow = e[eindex];
- Two_Product_Presplit(enow, b, bhi, blo, product1, product0);
- Two_Sum(Q, product0, sum, h[hindex]);
- hindex++;
- Two_Sum(product1, sum, Q, h[hindex]);
- hindex++;
- }
- h[hindex] = Q;
- return elen + elen;
-}
-
-/*****************************************************************************/
-/* */
-/* scale_expansion_zeroelim() Multiply an expansion by a scalar, */
-/* eliminating zero components from the */
-/* output expansion. */
-/* */
-/* Sets h = be. See either version of my paper for details. */
-/* */
-/* Maintains the nonoverlapping property. If round-to-even is used (as */
-/* with IEEE 754), maintains the strongly nonoverlapping and nonadjacent */
-/* properties as well. (That is, if e has one of these properties, so */
-/* will h.) */
-/* */
-/*****************************************************************************/
-
-int scale_expansion_zeroelim(int elen, REAL *e, REAL b, REAL *h)
-/* e and h cannot be the same. */
-{
- INEXACT REAL Q, sum;
- REAL hh;
- INEXACT REAL product1;
- REAL product0;
- int eindex, hindex;
- REAL enow;
- INEXACT REAL bvirt;
- REAL avirt, bround, around;
- INEXACT REAL c;
- INEXACT REAL abig;
- REAL ahi, alo, bhi, blo;
- REAL err1, err2, err3;
-
- Split(b, bhi, blo);
- Two_Product_Presplit(e[0], b, bhi, blo, Q, hh);
- hindex = 0;
- if (hh != 0) {
- h[hindex++] = hh;
- }
- for (eindex = 1; eindex < elen; eindex++) {
- enow = e[eindex];
- Two_Product_Presplit(enow, b, bhi, blo, product1, product0);
- Two_Sum(Q, product0, sum, hh);
- if (hh != 0) {
- h[hindex++] = hh;
- }
- Fast_Two_Sum(product1, sum, Q, hh);
- if (hh != 0) {
- h[hindex++] = hh;
- }
- }
- if ((Q != 0.0) || (hindex == 0)) {
- h[hindex++] = Q;
- }
- return hindex;
-}
-
-/*****************************************************************************/
-/* */
-/* compress() Compress an expansion. */
-/* */
-/* See the long version of my paper for details. */
-/* */
-/* Maintains the nonoverlapping property. If round-to-even is used (as */
-/* with IEEE 754), then any nonoverlapping expansion is converted to a */
-/* nonadjacent expansion. */
-/* */
-/*****************************************************************************/
-
-int compress(int elen, REAL *e, REAL *h)
-/* e and h may be the same. */
-{
- REAL Q, q;
- INEXACT REAL Qnew;
- int eindex, hindex;
- INEXACT REAL bvirt;
- REAL enow, hnow;
- int top, bottom;
-
- bottom = elen - 1;
- Q = e[bottom];
- for (eindex = elen - 2; eindex >= 0; eindex--) {
- enow = e[eindex];
- Fast_Two_Sum(Q, enow, Qnew, q);
- if (q != 0) {
- h[bottom--] = Qnew;
- Q = q;
- } else {
- Q = Qnew;
- }
- }
- top = 0;
- for (hindex = bottom + 1; hindex < elen; hindex++) {
- hnow = h[hindex];
- Fast_Two_Sum(hnow, Q, Qnew, q);
- if (q != 0) {
- h[top++] = q;
- }
- Q = Qnew;
- }
- h[top] = Q;
- return top + 1;
-}
-
-/*****************************************************************************/
-/* */
-/* estimate() Produce a one-word estimate of an expansion's value. */
-/* */
-/* See either version of my paper for details. */
-/* */
-/*****************************************************************************/
-
-REAL estimate(int elen, REAL *e)
-{
- REAL Q;
- int eindex;
-
- Q = e[0];
- for (eindex = 1; eindex < elen; eindex++) {
- Q += e[eindex];
- }
- return Q;
-}
-
-/*****************************************************************************/
-/* */
-/* orient2dfast() Approximate 2D orientation test. Nonrobust. */
-/* orient2dexact() Exact 2D orientation test. Robust. */
-/* orient2dslow() Another exact 2D orientation test. Robust. */
-/* orient2d() Adaptive exact 2D orientation test. Robust. */
-/* */
-/* Return a positive value if the points pa, pb, and pc occur */
-/* in counterclockwise order; a negative value if they occur */
-/* in clockwise order; and zero if they are collinear. The */
-/* result is also a rough approximation of twice the signed */
-/* area of the triangle defined by the three points. */
-/* */
-/* Only the first and last routine should be used; the middle two are for */
-/* timings. */
-/* */
-/* The last three use exact arithmetic to ensure a correct answer. The */
-/* result returned is the determinant of a matrix. In orient2d() only, */
-/* this determinant is computed adaptively, in the sense that exact */
-/* arithmetic is used only to the degree it is needed to ensure that the */
-/* returned value has the correct sign. Hence, orient2d() is usually quite */
-/* fast, but will run more slowly when the input points are collinear or */
-/* nearly so. */
-/* */
-/*****************************************************************************/
-
-REAL orient2dfast(REAL *pa, REAL *pb, REAL *pc)
-{
- REAL acx, bcx, acy, bcy;
-
- acx = pa[0] - pc[0];
- bcx = pb[0] - pc[0];
- acy = pa[1] - pc[1];
- bcy = pb[1] - pc[1];
- return acx * bcy - acy * bcx;
-}
-
-REAL orient2dexact(REAL *pa, REAL *pb, REAL *pc)
-{
- INEXACT REAL axby1, axcy1, bxcy1, bxay1, cxay1, cxby1;
- REAL axby0, axcy0, bxcy0, bxay0, cxay0, cxby0;
- REAL aterms[4], bterms[4], cterms[4];
- INEXACT REAL aterms3, bterms3, cterms3;
- REAL v[8], w[12];
- int vlength, wlength;
-
- INEXACT REAL bvirt;
- REAL avirt, bround, around;
- INEXACT REAL c;
- INEXACT REAL abig;
- REAL ahi, alo, bhi, blo;
- REAL err1, err2, err3;
- INEXACT REAL _i, _j;
- REAL _0;
-
- Two_Product(pa[0], pb[1], axby1, axby0);
- Two_Product(pa[0], pc[1], axcy1, axcy0);
- Two_Two_Diff(axby1, axby0, axcy1, axcy0,
- aterms3, aterms[2], aterms[1], aterms[0]);
- aterms[3] = aterms3;
-
- Two_Product(pb[0], pc[1], bxcy1, bxcy0);
- Two_Product(pb[0], pa[1], bxay1, bxay0);
- Two_Two_Diff(bxcy1, bxcy0, bxay1, bxay0,
- bterms3, bterms[2], bterms[1], bterms[0]);
- bterms[3] = bterms3;
-
- Two_Product(pc[0], pa[1], cxay1, cxay0);
- Two_Product(pc[0], pb[1], cxby1, cxby0);
- Two_Two_Diff(cxay1, cxay0, cxby1, cxby0,
- cterms3, cterms[2], cterms[1], cterms[0]);
- cterms[3] = cterms3;
-
- vlength = fast_expansion_sum_zeroelim(4, aterms, 4, bterms, v);
- wlength = fast_expansion_sum_zeroelim(vlength, v, 4, cterms, w);
-
- return w[wlength - 1];
-}
-
-REAL orient2dslow(REAL *pa, REAL *pb, REAL *pc)
-{
- INEXACT REAL acx, acy, bcx, bcy;
- REAL acxtail, acytail;
- REAL bcxtail, bcytail;
- REAL negate, negatetail;
- REAL axby[8], bxay[8];
- INEXACT REAL axby7, bxay7;
- REAL deter[16];
- int deterlen;
-
- INEXACT REAL bvirt;
- REAL avirt, bround, around;
- INEXACT REAL c;
- INEXACT REAL abig;
- REAL a0hi, a0lo, a1hi, a1lo, bhi, blo;
- REAL err1, err2, err3;
- INEXACT REAL _i, _j, _k, _l, _m, _n;
- REAL _0, _1, _2;
-
- Two_Diff(pa[0], pc[0], acx, acxtail);
- Two_Diff(pa[1], pc[1], acy, acytail);
- Two_Diff(pb[0], pc[0], bcx, bcxtail);
- Two_Diff(pb[1], pc[1], bcy, bcytail);
-
- Two_Two_Product(acx, acxtail, bcy, bcytail,
- axby7, axby[6], axby[5], axby[4],
- axby[3], axby[2], axby[1], axby[0]);
- axby[7] = axby7;
- negate = -acy;
- negatetail = -acytail;
- Two_Two_Product(bcx, bcxtail, negate, negatetail,
- bxay7, bxay[6], bxay[5], bxay[4],
- bxay[3], bxay[2], bxay[1], bxay[0]);
- bxay[7] = bxay7;
-
- deterlen = fast_expansion_sum_zeroelim(8, axby, 8, bxay, deter);
-
- return deter[deterlen - 1];
-}
-
-REAL orient2dadapt(REAL *pa, REAL *pb, REAL *pc, REAL detsum)
-{
- INEXACT REAL acx, acy, bcx, bcy;
- REAL acxtail, acytail, bcxtail, bcytail;
- INEXACT REAL detleft, detright;
- REAL detlefttail, detrighttail;
- REAL det, errbound;
- REAL B[4], C1[8], C2[12], D[16];
- INEXACT REAL B3;
- int C1length, C2length, Dlength;
- REAL u[4];
- INEXACT REAL u3;
- INEXACT REAL s1, t1;
- REAL s0, t0;
-
- INEXACT REAL bvirt;
- REAL avirt, bround, around;
- INEXACT REAL c;
- INEXACT REAL abig;
- REAL ahi, alo, bhi, blo;
- REAL err1, err2, err3;
- INEXACT REAL _i, _j;
- REAL _0;
-
- acx = (REAL) (pa[0] - pc[0]);
- bcx = (REAL) (pb[0] - pc[0]);
- acy = (REAL) (pa[1] - pc[1]);
- bcy = (REAL) (pb[1] - pc[1]);
-
- Two_Product(acx, bcy, detleft, detlefttail);
- Two_Product(acy, bcx, detright, detrighttail);
-
- Two_Two_Diff(detleft, detlefttail, detright, detrighttail,
- B3, B[2], B[1], B[0]);
- B[3] = B3;
-
- det = estimate(4, B);
- errbound = ccwerrboundB * detsum;
- if ((det >= errbound) || (-det >= errbound)) {
- return det;
- }
-
- Two_Diff_Tail(pa[0], pc[0], acx, acxtail);
- Two_Diff_Tail(pb[0], pc[0], bcx, bcxtail);
- Two_Diff_Tail(pa[1], pc[1], acy, acytail);
- Two_Diff_Tail(pb[1], pc[1], bcy, bcytail);
-
- if ((acxtail == 0.0) && (acytail == 0.0)
- && (bcxtail == 0.0) && (bcytail == 0.0)) {
- return det;
- }
-
- errbound = ccwerrboundC * detsum + resulterrbound * Absolute(det);
- det += (acx * bcytail + bcy * acxtail)
- - (acy * bcxtail + bcx * acytail);
- if ((det >= errbound) || (-det >= errbound)) {
- return det;
- }
-
- Two_Product(acxtail, bcy, s1, s0);
- Two_Product(acytail, bcx, t1, t0);
- Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
- u[3] = u3;
- C1length = fast_expansion_sum_zeroelim(4, B, 4, u, C1);
-
- Two_Product(acx, bcytail, s1, s0);
- Two_Product(acy, bcxtail, t1, t0);
- Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
- u[3] = u3;
- C2length = fast_expansion_sum_zeroelim(C1length, C1, 4, u, C2);
-
- Two_Product(acxtail, bcytail, s1, s0);
- Two_Product(acytail, bcxtail, t1, t0);
- Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
- u[3] = u3;
- Dlength = fast_expansion_sum_zeroelim(C2length, C2, 4, u, D);
-
- return(D[Dlength - 1]);
-}
-
-REAL orient2d(REAL *pa, REAL *pb, REAL *pc)
-{
- REAL detleft, detright, det;
- REAL detsum, errbound;
-
- detleft = (pa[0] - pc[0]) * (pb[1] - pc[1]);
- detright = (pa[1] - pc[1]) * (pb[0] - pc[0]);
- det = detleft - detright;
-
- if (detleft > 0.0) {
- if (detright <= 0.0) {
- return det;
- } else {
- detsum = detleft + detright;
- }
- } else if (detleft < 0.0) {
- if (detright >= 0.0) {
- return det;
- } else {
- detsum = -detleft - detright;
- }
- } else {
- return det;
- }
-
- errbound = ccwerrboundA * detsum;
- if ((det >= errbound) || (-det >= errbound)) {
- return det;
- }
-
- return orient2dadapt(pa, pb, pc, detsum);
-}
-
-/*****************************************************************************/
-/* */
-/* orient3dfast() Approximate 3D orientation test. Nonrobust. */
-/* orient3dexact() Exact 3D orientation test. Robust. */
-/* orient3dslow() Another exact 3D orientation test. Robust. */
-/* orient3d() Adaptive exact 3D orientation test. Robust. */
-/* */
-/* Return a positive value if the point pd lies below the */
-/* plane passing through pa, pb, and pc; "below" is defined so */
-/* that pa, pb, and pc appear in counterclockwise order when */
-/* viewed from above the plane. Returns a negative value if */
-/* pd lies above the plane. Returns zero if the points are */
-/* coplanar. The result is also a rough approximation of six */
-/* times the signed volume of the tetrahedron defined by the */
-/* four points. */
-/* */
-/* Only the first and last routine should be used; the middle two are for */
-/* timings. */
-/* */
-/* The last three use exact arithmetic to ensure a correct answer. The */
-/* result returned is the determinant of a matrix. In orient3d() only, */
-/* this determinant is computed adaptively, in the sense that exact */
-/* arithmetic is used only to the degree it is needed to ensure that the */
-/* returned value has the correct sign. Hence, orient3d() is usually quite */
-/* fast, but will run more slowly when the input points are coplanar or */
-/* nearly so. */
-/* */
-/*****************************************************************************/
-
-REAL orient3dfast(REAL *pa, REAL *pb, REAL *pc, REAL *pd)
-{
- REAL adx, bdx, cdx;
- REAL ady, bdy, cdy;
- REAL adz, bdz, cdz;
-
- adx = pa[0] - pd[0];
- bdx = pb[0] - pd[0];
- cdx = pc[0] - pd[0];
- ady = pa[1] - pd[1];
- bdy = pb[1] - pd[1];
- cdy = pc[1] - pd[1];
- adz = pa[2] - pd[2];
- bdz = pb[2] - pd[2];
- cdz = pc[2] - pd[2];
-
- return adx * (bdy * cdz - bdz * cdy)
- + bdx * (cdy * adz - cdz * ady)
- + cdx * (ady * bdz - adz * bdy);
-}
-
-REAL orient3dexact(REAL *pa, REAL *pb, REAL *pc, REAL *pd)
-{
- INEXACT REAL axby1, bxcy1, cxdy1, dxay1, axcy1, bxdy1;
- INEXACT REAL bxay1, cxby1, dxcy1, axdy1, cxay1, dxby1;
- REAL axby0, bxcy0, cxdy0, dxay0, axcy0, bxdy0;
- REAL bxay0, cxby0, dxcy0, axdy0, cxay0, dxby0;
- REAL ab[4], bc[4], cd[4], da[4], ac[4], bd[4];
- REAL temp8[8];
- int templen;
- REAL abc[12], bcd[12], cda[12], dab[12];
- int abclen, bcdlen, cdalen, dablen;
- REAL adet[24], bdet[24], cdet[24], ddet[24];
- int alen, blen, clen, dlen;
- REAL abdet[48], cddet[48];
- int ablen, cdlen;
- REAL deter[96];
- int deterlen;
- int i;
-
- INEXACT REAL bvirt;
- REAL avirt, bround, around;
- INEXACT REAL c;
- INEXACT REAL abig;
- REAL ahi, alo, bhi, blo;
- REAL err1, err2, err3;
- INEXACT REAL _i, _j;
- REAL _0;
-
- Two_Product(pa[0], pb[1], axby1, axby0);
- Two_Product(pb[0], pa[1], bxay1, bxay0);
- Two_Two_Diff(axby1, axby0, bxay1, bxay0, ab[3], ab[2], ab[1], ab[0]);
-
- Two_Product(pb[0], pc[1], bxcy1, bxcy0);
- Two_Product(pc[0], pb[1], cxby1, cxby0);
- Two_Two_Diff(bxcy1, bxcy0, cxby1, cxby0, bc[3], bc[2], bc[1], bc[0]);
-
- Two_Product(pc[0], pd[1], cxdy1, cxdy0);
- Two_Product(pd[0], pc[1], dxcy1, dxcy0);
- Two_Two_Diff(cxdy1, cxdy0, dxcy1, dxcy0, cd[3], cd[2], cd[1], cd[0]);
-
- Two_Product(pd[0], pa[1], dxay1, dxay0);
- Two_Product(pa[0], pd[1], axdy1, axdy0);
- Two_Two_Diff(dxay1, dxay0, axdy1, axdy0, da[3], da[2], da[1], da[0]);
-
- Two_Product(pa[0], pc[1], axcy1, axcy0);
- Two_Product(pc[0], pa[1], cxay1, cxay0);
- Two_Two_Diff(axcy1, axcy0, cxay1, cxay0, ac[3], ac[2], ac[1], ac[0]);
-
- Two_Product(pb[0], pd[1], bxdy1, bxdy0);
- Two_Product(pd[0], pb[1], dxby1, dxby0);
- Two_Two_Diff(bxdy1, bxdy0, dxby1, dxby0, bd[3], bd[2], bd[1], bd[0]);
-
- templen = fast_expansion_sum_zeroelim(4, cd, 4, da, temp8);
- cdalen = fast_expansion_sum_zeroelim(templen, temp8, 4, ac, cda);
- templen = fast_expansion_sum_zeroelim(4, da, 4, ab, temp8);
- dablen = fast_expansion_sum_zeroelim(templen, temp8, 4, bd, dab);
- for (i = 0; i < 4; i++) {
- bd[i] = -bd[i];
- ac[i] = -ac[i];
- }
- templen = fast_expansion_sum_zeroelim(4, ab, 4, bc, temp8);
- abclen = fast_expansion_sum_zeroelim(templen, temp8, 4, ac, abc);
- templen = fast_expansion_sum_zeroelim(4, bc, 4, cd, temp8);
- bcdlen = fast_expansion_sum_zeroelim(templen, temp8, 4, bd, bcd);
-
- alen = scale_expansion_zeroelim(bcdlen, bcd, pa[2], adet);
- blen = scale_expansion_zeroelim(cdalen, cda, -pb[2], bdet);
- clen = scale_expansion_zeroelim(dablen, dab, pc[2], cdet);
- dlen = scale_expansion_zeroelim(abclen, abc, -pd[2], ddet);
-
- ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
- cdlen = fast_expansion_sum_zeroelim(clen, cdet, dlen, ddet, cddet);
- deterlen = fast_expansion_sum_zeroelim(ablen, abdet, cdlen, cddet, deter);
-
- return deter[deterlen - 1];
-}
-
-REAL orient3dslow(REAL *pa, REAL *pb, REAL *pc, REAL *pd)
-{
- INEXACT REAL adx, ady, adz, bdx, bdy, bdz, cdx, cdy, cdz;
- REAL adxtail, adytail, adztail;
- REAL bdxtail, bdytail, bdztail;
- REAL cdxtail, cdytail, cdztail;
- REAL negate, negatetail;
- INEXACT REAL axby7, bxcy7, axcy7, bxay7, cxby7, cxay7;
- REAL axby[8], bxcy[8], axcy[8], bxay[8], cxby[8], cxay[8];
- REAL temp16[16], temp32[32], temp32t[32];
- int temp16len, temp32len, temp32tlen;
- REAL adet[64], bdet[64], cdet[64];
- int alen, blen, clen;
- REAL abdet[128];
- int ablen;
- REAL deter[192];
- int deterlen;
-
- INEXACT REAL bvirt;
- REAL avirt, bround, around;
- INEXACT REAL c;
- INEXACT REAL abig;
- REAL a0hi, a0lo, a1hi, a1lo, bhi, blo;
- REAL err1, err2, err3;
- INEXACT REAL _i, _j, _k, _l, _m, _n;
- REAL _0, _1, _2;
-
- Two_Diff(pa[0], pd[0], adx, adxtail);
- Two_Diff(pa[1], pd[1], ady, adytail);
- Two_Diff(pa[2], pd[2], adz, adztail);
- Two_Diff(pb[0], pd[0], bdx, bdxtail);
- Two_Diff(pb[1], pd[1], bdy, bdytail);
- Two_Diff(pb[2], pd[2], bdz, bdztail);
- Two_Diff(pc[0], pd[0], cdx, cdxtail);
- Two_Diff(pc[1], pd[1], cdy, cdytail);
- Two_Diff(pc[2], pd[2], cdz, cdztail);
-
- Two_Two_Product(adx, adxtail, bdy, bdytail,
- axby7, axby[6], axby[5], axby[4],
- axby[3], axby[2], axby[1], axby[0]);
- axby[7] = axby7;
- negate = -ady;
- negatetail = -adytail;
- Two_Two_Product(bdx, bdxtail, negate, negatetail,
- bxay7, bxay[6], bxay[5], bxay[4],
- bxay[3], bxay[2], bxay[1], bxay[0]);
- bxay[7] = bxay7;
- Two_Two_Product(bdx, bdxtail, cdy, cdytail,
- bxcy7, bxcy[6], bxcy[5], bxcy[4],
- bxcy[3], bxcy[2], bxcy[1], bxcy[0]);
- bxcy[7] = bxcy7;
- negate = -bdy;
- negatetail = -bdytail;
- Two_Two_Product(cdx, cdxtail, negate, negatetail,
- cxby7, cxby[6], cxby[5], cxby[4],
- cxby[3], cxby[2], cxby[1], cxby[0]);
- cxby[7] = cxby7;
- Two_Two_Product(cdx, cdxtail, ady, adytail,
- cxay7, cxay[6], cxay[5], cxay[4],
- cxay[3], cxay[2], cxay[1], cxay[0]);
- cxay[7] = cxay7;
- negate = -cdy;
- negatetail = -cdytail;
- Two_Two_Product(adx, adxtail, negate, negatetail,
- axcy7, axcy[6], axcy[5], axcy[4],
- axcy[3], axcy[2], axcy[1], axcy[0]);
- axcy[7] = axcy7;
-
- temp16len = fast_expansion_sum_zeroelim(8, bxcy, 8, cxby, temp16);
- temp32len = scale_expansion_zeroelim(temp16len, temp16, adz, temp32);
- temp32tlen = scale_expansion_zeroelim(temp16len, temp16, adztail, temp32t);
- alen = fast_expansion_sum_zeroelim(temp32len, temp32, temp32tlen, temp32t,
- adet);
-
- temp16len = fast_expansion_sum_zeroelim(8, cxay, 8, axcy, temp16);
- temp32len = scale_expansion_zeroelim(temp16len, temp16, bdz, temp32);
- temp32tlen = scale_expansion_zeroelim(temp16len, temp16, bdztail, temp32t);
- blen = fast_expansion_sum_zeroelim(temp32len, temp32, temp32tlen, temp32t,
- bdet);
-
- temp16len = fast_expansion_sum_zeroelim(8, axby, 8, bxay, temp16);
- temp32len = scale_expansion_zeroelim(temp16len, temp16, cdz, temp32);
- temp32tlen = scale_expansion_zeroelim(temp16len, temp16, cdztail, temp32t);
- clen = fast_expansion_sum_zeroelim(temp32len, temp32, temp32tlen, temp32t,
- cdet);
-
- ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
- deterlen = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, deter);
-
- return deter[deterlen - 1];
-}
-
-REAL orient3dadapt(REAL *pa, REAL *pb, REAL *pc, REAL *pd, REAL permanent)
-{
- INEXACT REAL adx, bdx, cdx, ady, bdy, cdy, adz, bdz, cdz;
- REAL det, errbound;
-
- INEXACT REAL bdxcdy1, cdxbdy1, cdxady1, adxcdy1, adxbdy1, bdxady1;
- REAL bdxcdy0, cdxbdy0, cdxady0, adxcdy0, adxbdy0, bdxady0;
- REAL bc[4], ca[4], ab[4];
- INEXACT REAL bc3, ca3, ab3;
- REAL adet[8], bdet[8], cdet[8];
- int alen, blen, clen;
- REAL abdet[16];
- int ablen;
- REAL *finnow, *finother, *finswap;
- REAL fin1[192], fin2[192];
- int finlength;
-
- ////////////////////////////////////////////////////////
- // To avoid uninitialized warnings reported by valgrind.
- int i;
- for (i = 0; i < 8; i++) {
- adet[i] = bdet[i] = cdet[i] = 0.0;
- }
- for (i = 0; i < 16; i++) {
- abdet[i] = 0.0;
- }
- ////////////////////////////////////////////////////////
-
- REAL adxtail, bdxtail, cdxtail;
- REAL adytail, bdytail, cdytail;
- REAL adztail, bdztail, cdztail;
- INEXACT REAL at_blarge, at_clarge;
- INEXACT REAL bt_clarge, bt_alarge;
- INEXACT REAL ct_alarge, ct_blarge;
- REAL at_b[4], at_c[4], bt_c[4], bt_a[4], ct_a[4], ct_b[4];
- int at_blen, at_clen, bt_clen, bt_alen, ct_alen, ct_blen;
- INEXACT REAL bdxt_cdy1, cdxt_bdy1, cdxt_ady1;
- INEXACT REAL adxt_cdy1, adxt_bdy1, bdxt_ady1;
- REAL bdxt_cdy0, cdxt_bdy0, cdxt_ady0;
- REAL adxt_cdy0, adxt_bdy0, bdxt_ady0;
- INEXACT REAL bdyt_cdx1, cdyt_bdx1, cdyt_adx1;
- INEXACT REAL adyt_cdx1, adyt_bdx1, bdyt_adx1;
- REAL bdyt_cdx0, cdyt_bdx0, cdyt_adx0;
- REAL adyt_cdx0, adyt_bdx0, bdyt_adx0;
- REAL bct[8], cat[8], abt[8];
- int bctlen, catlen, abtlen;
- INEXACT REAL bdxt_cdyt1, cdxt_bdyt1, cdxt_adyt1;
- INEXACT REAL adxt_cdyt1, adxt_bdyt1, bdxt_adyt1;
- REAL bdxt_cdyt0, cdxt_bdyt0, cdxt_adyt0;
- REAL adxt_cdyt0, adxt_bdyt0, bdxt_adyt0;
- REAL u[4], v[12], w[16];
- INEXACT REAL u3;
- int vlength, wlength;
- REAL negate;
-
- INEXACT REAL bvirt;
- REAL avirt, bround, around;
- INEXACT REAL c;
- INEXACT REAL abig;
- REAL ahi, alo, bhi, blo;
- REAL err1, err2, err3;
- INEXACT REAL _i, _j, _k;
- REAL _0;
-
- adx = (REAL) (pa[0] - pd[0]);
- bdx = (REAL) (pb[0] - pd[0]);
- cdx = (REAL) (pc[0] - pd[0]);
- ady = (REAL) (pa[1] - pd[1]);
- bdy = (REAL) (pb[1] - pd[1]);
- cdy = (REAL) (pc[1] - pd[1]);
- adz = (REAL) (pa[2] - pd[2]);
- bdz = (REAL) (pb[2] - pd[2]);
- cdz = (REAL) (pc[2] - pd[2]);
-
- Two_Product(bdx, cdy, bdxcdy1, bdxcdy0);
- Two_Product(cdx, bdy, cdxbdy1, cdxbdy0);
- Two_Two_Diff(bdxcdy1, bdxcdy0, cdxbdy1, cdxbdy0, bc3, bc[2], bc[1], bc[0]);
- bc[3] = bc3;
- alen = scale_expansion_zeroelim(4, bc, adz, adet);
-
- Two_Product(cdx, ady, cdxady1, cdxady0);
- Two_Product(adx, cdy, adxcdy1, adxcdy0);
- Two_Two_Diff(cdxady1, cdxady0, adxcdy1, adxcdy0, ca3, ca[2], ca[1], ca[0]);
- ca[3] = ca3;
- blen = scale_expansion_zeroelim(4, ca, bdz, bdet);
-
- Two_Product(adx, bdy, adxbdy1, adxbdy0);
- Two_Product(bdx, ady, bdxady1, bdxady0);
- Two_Two_Diff(adxbdy1, adxbdy0, bdxady1, bdxady0, ab3, ab[2], ab[1], ab[0]);
- ab[3] = ab3;
- clen = scale_expansion_zeroelim(4, ab, cdz, cdet);
-
- ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
- finlength = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, fin1);
-
- det = estimate(finlength, fin1);
- errbound = o3derrboundB * permanent;
- if ((det >= errbound) || (-det >= errbound)) {
- return det;
- }
-
- Two_Diff_Tail(pa[0], pd[0], adx, adxtail);
- Two_Diff_Tail(pb[0], pd[0], bdx, bdxtail);
- Two_Diff_Tail(pc[0], pd[0], cdx, cdxtail);
- Two_Diff_Tail(pa[1], pd[1], ady, adytail);
- Two_Diff_Tail(pb[1], pd[1], bdy, bdytail);
- Two_Diff_Tail(pc[1], pd[1], cdy, cdytail);
- Two_Diff_Tail(pa[2], pd[2], adz, adztail);
- Two_Diff_Tail(pb[2], pd[2], bdz, bdztail);
- Two_Diff_Tail(pc[2], pd[2], cdz, cdztail);
-
- if ((adxtail == 0.0) && (bdxtail == 0.0) && (cdxtail == 0.0)
- && (adytail == 0.0) && (bdytail == 0.0) && (cdytail == 0.0)
- && (adztail == 0.0) && (bdztail == 0.0) && (cdztail == 0.0)) {
- return det;
- }
-
- errbound = o3derrboundC * permanent + resulterrbound * Absolute(det);
- det += (adz * ((bdx * cdytail + cdy * bdxtail)
- - (bdy * cdxtail + cdx * bdytail))
- + adztail * (bdx * cdy - bdy * cdx))
- + (bdz * ((cdx * adytail + ady * cdxtail)
- - (cdy * adxtail + adx * cdytail))
- + bdztail * (cdx * ady - cdy * adx))
- + (cdz * ((adx * bdytail + bdy * adxtail)
- - (ady * bdxtail + bdx * adytail))
- + cdztail * (adx * bdy - ady * bdx));
- if ((det >= errbound) || (-det >= errbound)) {
- return det;
- }
-
- finnow = fin1;
- finother = fin2;
-
- if (adxtail == 0.0) {
- if (adytail == 0.0) {
- at_b[0] = 0.0;
- at_blen = 1;
- at_c[0] = 0.0;
- at_clen = 1;
- } else {
- negate = -adytail;
- Two_Product(negate, bdx, at_blarge, at_b[0]);
- at_b[1] = at_blarge;
- at_blen = 2;
- Two_Product(adytail, cdx, at_clarge, at_c[0]);
- at_c[1] = at_clarge;
- at_clen = 2;
- }
- } else {
- if (adytail == 0.0) {
- Two_Product(adxtail, bdy, at_blarge, at_b[0]);
- at_b[1] = at_blarge;
- at_blen = 2;
- negate = -adxtail;
- Two_Product(negate, cdy, at_clarge, at_c[0]);
- at_c[1] = at_clarge;
- at_clen = 2;
- } else {
- Two_Product(adxtail, bdy, adxt_bdy1, adxt_bdy0);
- Two_Product(adytail, bdx, adyt_bdx1, adyt_bdx0);
- Two_Two_Diff(adxt_bdy1, adxt_bdy0, adyt_bdx1, adyt_bdx0,
- at_blarge, at_b[2], at_b[1], at_b[0]);
- at_b[3] = at_blarge;
- at_blen = 4;
- Two_Product(adytail, cdx, adyt_cdx1, adyt_cdx0);
- Two_Product(adxtail, cdy, adxt_cdy1, adxt_cdy0);
- Two_Two_Diff(adyt_cdx1, adyt_cdx0, adxt_cdy1, adxt_cdy0,
- at_clarge, at_c[2], at_c[1], at_c[0]);
- at_c[3] = at_clarge;
- at_clen = 4;
- }
- }
- if (bdxtail == 0.0) {
- if (bdytail == 0.0) {
- bt_c[0] = 0.0;
- bt_clen = 1;
- bt_a[0] = 0.0;
- bt_alen = 1;
- } else {
- negate = -bdytail;
- Two_Product(negate, cdx, bt_clarge, bt_c[0]);
- bt_c[1] = bt_clarge;
- bt_clen = 2;
- Two_Product(bdytail, adx, bt_alarge, bt_a[0]);
- bt_a[1] = bt_alarge;
- bt_alen = 2;
- }
- } else {
- if (bdytail == 0.0) {
- Two_Product(bdxtail, cdy, bt_clarge, bt_c[0]);
- bt_c[1] = bt_clarge;
- bt_clen = 2;
- negate = -bdxtail;
- Two_Product(negate, ady, bt_alarge, bt_a[0]);
- bt_a[1] = bt_alarge;
- bt_alen = 2;
- } else {
- Two_Product(bdxtail, cdy, bdxt_cdy1, bdxt_cdy0);
- Two_Product(bdytail, cdx, bdyt_cdx1, bdyt_cdx0);
- Two_Two_Diff(bdxt_cdy1, bdxt_cdy0, bdyt_cdx1, bdyt_cdx0,
- bt_clarge, bt_c[2], bt_c[1], bt_c[0]);
- bt_c[3] = bt_clarge;
- bt_clen = 4;
- Two_Product(bdytail, adx, bdyt_adx1, bdyt_adx0);
- Two_Product(bdxtail, ady, bdxt_ady1, bdxt_ady0);
- Two_Two_Diff(bdyt_adx1, bdyt_adx0, bdxt_ady1, bdxt_ady0,
- bt_alarge, bt_a[2], bt_a[1], bt_a[0]);
- bt_a[3] = bt_alarge;
- bt_alen = 4;
- }
- }
- if (cdxtail == 0.0) {
- if (cdytail == 0.0) {
- ct_a[0] = 0.0;
- ct_alen = 1;
- ct_b[0] = 0.0;
- ct_blen = 1;
- } else {
- negate = -cdytail;
- Two_Product(negate, adx, ct_alarge, ct_a[0]);
- ct_a[1] = ct_alarge;
- ct_alen = 2;
- Two_Product(cdytail, bdx, ct_blarge, ct_b[0]);
- ct_b[1] = ct_blarge;
- ct_blen = 2;
- }
- } else {
- if (cdytail == 0.0) {
- Two_Product(cdxtail, ady, ct_alarge, ct_a[0]);
- ct_a[1] = ct_alarge;
- ct_alen = 2;
- negate = -cdxtail;
- Two_Product(negate, bdy, ct_blarge, ct_b[0]);
- ct_b[1] = ct_blarge;
- ct_blen = 2;
- } else {
- Two_Product(cdxtail, ady, cdxt_ady1, cdxt_ady0);
- Two_Product(cdytail, adx, cdyt_adx1, cdyt_adx0);
- Two_Two_Diff(cdxt_ady1, cdxt_ady0, cdyt_adx1, cdyt_adx0,
- ct_alarge, ct_a[2], ct_a[1], ct_a[0]);
- ct_a[3] = ct_alarge;
- ct_alen = 4;
- Two_Product(cdytail, bdx, cdyt_bdx1, cdyt_bdx0);
- Two_Product(cdxtail, bdy, cdxt_bdy1, cdxt_bdy0);
- Two_Two_Diff(cdyt_bdx1, cdyt_bdx0, cdxt_bdy1, cdxt_bdy0,
- ct_blarge, ct_b[2], ct_b[1], ct_b[0]);
- ct_b[3] = ct_blarge;
- ct_blen = 4;
- }
- }
-
- bctlen = fast_expansion_sum_zeroelim(bt_clen, bt_c, ct_blen, ct_b, bct);
- wlength = scale_expansion_zeroelim(bctlen, bct, adz, w);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
- finother);
- finswap = finnow; finnow = finother; finother = finswap;
-
- catlen = fast_expansion_sum_zeroelim(ct_alen, ct_a, at_clen, at_c, cat);
- wlength = scale_expansion_zeroelim(catlen, cat, bdz, w);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
- finother);
- finswap = finnow; finnow = finother; finother = finswap;
-
- abtlen = fast_expansion_sum_zeroelim(at_blen, at_b, bt_alen, bt_a, abt);
- wlength = scale_expansion_zeroelim(abtlen, abt, cdz, w);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
- finother);
- finswap = finnow; finnow = finother; finother = finswap;
-
- if (adztail != 0.0) {
- vlength = scale_expansion_zeroelim(4, bc, adztail, v);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v,
- finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- if (bdztail != 0.0) {
- vlength = scale_expansion_zeroelim(4, ca, bdztail, v);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v,
- finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- if (cdztail != 0.0) {
- vlength = scale_expansion_zeroelim(4, ab, cdztail, v);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v,
- finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
-
- if (adxtail != 0.0) {
- if (bdytail != 0.0) {
- Two_Product(adxtail, bdytail, adxt_bdyt1, adxt_bdyt0);
- Two_One_Product(adxt_bdyt1, adxt_bdyt0, cdz, u3, u[2], u[1], u[0]);
- u[3] = u3;
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
- finother);
- finswap = finnow; finnow = finother; finother = finswap;
- if (cdztail != 0.0) {
- Two_One_Product(adxt_bdyt1, adxt_bdyt0, cdztail, u3, u[2], u[1], u[0]);
- u[3] = u3;
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
- finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- }
- if (cdytail != 0.0) {
- negate = -adxtail;
- Two_Product(negate, cdytail, adxt_cdyt1, adxt_cdyt0);
- Two_One_Product(adxt_cdyt1, adxt_cdyt0, bdz, u3, u[2], u[1], u[0]);
- u[3] = u3;
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
- finother);
- finswap = finnow; finnow = finother; finother = finswap;
- if (bdztail != 0.0) {
- Two_One_Product(adxt_cdyt1, adxt_cdyt0, bdztail, u3, u[2], u[1], u[0]);
- u[3] = u3;
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
- finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- }
- }
- if (bdxtail != 0.0) {
- if (cdytail != 0.0) {
- Two_Product(bdxtail, cdytail, bdxt_cdyt1, bdxt_cdyt0);
- Two_One_Product(bdxt_cdyt1, bdxt_cdyt0, adz, u3, u[2], u[1], u[0]);
- u[3] = u3;
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
- finother);
- finswap = finnow; finnow = finother; finother = finswap;
- if (adztail != 0.0) {
- Two_One_Product(bdxt_cdyt1, bdxt_cdyt0, adztail, u3, u[2], u[1], u[0]);
- u[3] = u3;
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
- finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- }
- if (adytail != 0.0) {
- negate = -bdxtail;
- Two_Product(negate, adytail, bdxt_adyt1, bdxt_adyt0);
- Two_One_Product(bdxt_adyt1, bdxt_adyt0, cdz, u3, u[2], u[1], u[0]);
- u[3] = u3;
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
- finother);
- finswap = finnow; finnow = finother; finother = finswap;
- if (cdztail != 0.0) {
- Two_One_Product(bdxt_adyt1, bdxt_adyt0, cdztail, u3, u[2], u[1], u[0]);
- u[3] = u3;
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
- finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- }
- }
- if (cdxtail != 0.0) {
- if (adytail != 0.0) {
- Two_Product(cdxtail, adytail, cdxt_adyt1, cdxt_adyt0);
- Two_One_Product(cdxt_adyt1, cdxt_adyt0, bdz, u3, u[2], u[1], u[0]);
- u[3] = u3;
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
- finother);
- finswap = finnow; finnow = finother; finother = finswap;
- if (bdztail != 0.0) {
- Two_One_Product(cdxt_adyt1, cdxt_adyt0, bdztail, u3, u[2], u[1], u[0]);
- u[3] = u3;
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
- finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- }
- if (bdytail != 0.0) {
- negate = -cdxtail;
- Two_Product(negate, bdytail, cdxt_bdyt1, cdxt_bdyt0);
- Two_One_Product(cdxt_bdyt1, cdxt_bdyt0, adz, u3, u[2], u[1], u[0]);
- u[3] = u3;
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
- finother);
- finswap = finnow; finnow = finother; finother = finswap;
- if (adztail != 0.0) {
- Two_One_Product(cdxt_bdyt1, cdxt_bdyt0, adztail, u3, u[2], u[1], u[0]);
- u[3] = u3;
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
- finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- }
- }
-
- if (adztail != 0.0) {
- wlength = scale_expansion_zeroelim(bctlen, bct, adztail, w);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
- finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- if (bdztail != 0.0) {
- wlength = scale_expansion_zeroelim(catlen, cat, bdztail, w);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
- finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- if (cdztail != 0.0) {
- wlength = scale_expansion_zeroelim(abtlen, abt, cdztail, w);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
- finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
-
- return finnow[finlength - 1];
-}
-
-REAL orient3d(REAL *pa, REAL *pb, REAL *pc, REAL *pd)
-{
- REAL adx, bdx, cdx, ady, bdy, cdy, adz, bdz, cdz;
- REAL bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady;
- REAL det;
- REAL permanent, errbound;
-
- adx = pa[0] - pd[0];
- bdx = pb[0] - pd[0];
- cdx = pc[0] - pd[0];
- ady = pa[1] - pd[1];
- bdy = pb[1] - pd[1];
- cdy = pc[1] - pd[1];
- adz = pa[2] - pd[2];
- bdz = pb[2] - pd[2];
- cdz = pc[2] - pd[2];
-
- bdxcdy = bdx * cdy;
- cdxbdy = cdx * bdy;
-
- cdxady = cdx * ady;
- adxcdy = adx * cdy;
-
- adxbdy = adx * bdy;
- bdxady = bdx * ady;
-
- det = adz * (bdxcdy - cdxbdy)
- + bdz * (cdxady - adxcdy)
- + cdz * (adxbdy - bdxady);
-
- permanent = (Absolute(bdxcdy) + Absolute(cdxbdy)) * Absolute(adz)
- + (Absolute(cdxady) + Absolute(adxcdy)) * Absolute(bdz)
- + (Absolute(adxbdy) + Absolute(bdxady)) * Absolute(cdz);
- errbound = o3derrboundA * permanent;
- if ((det > errbound) || (-det > errbound)) {
- return det;
- }
-
- return orient3dadapt(pa, pb, pc, pd, permanent);
-}
-
-/*****************************************************************************/
-/* */
-/* incirclefast() Approximate 2D incircle test. Nonrobust. */
-/* incircleexact() Exact 2D incircle test. Robust. */
-/* incircleslow() Another exact 2D incircle test. Robust. */
-/* incircle() Adaptive exact 2D incircle test. Robust. */
-/* */
-/* Return a positive value if the point pd lies inside the */
-/* circle passing through pa, pb, and pc; a negative value if */
-/* it lies outside; and zero if the four points are cocircular.*/
-/* The points pa, pb, and pc must be in counterclockwise */
-/* order, or the sign of the result will be reversed. */
-/* */
-/* Only the first and last routine should be used; the middle two are for */
-/* timings. */
-/* */
-/* The last three use exact arithmetic to ensure a correct answer. The */
-/* result returned is the determinant of a matrix. In incircle() only, */
-/* this determinant is computed adaptively, in the sense that exact */
-/* arithmetic is used only to the degree it is needed to ensure that the */
-/* returned value has the correct sign. Hence, incircle() is usually quite */
-/* fast, but will run more slowly when the input points are cocircular or */
-/* nearly so. */
-/* */
-/*****************************************************************************/
-
-REAL incirclefast(REAL *pa, REAL *pb, REAL *pc, REAL *pd)
-{
- REAL adx, ady, bdx, bdy, cdx, cdy;
- REAL abdet, bcdet, cadet;
- REAL alift, blift, clift;
-
- adx = pa[0] - pd[0];
- ady = pa[1] - pd[1];
- bdx = pb[0] - pd[0];
- bdy = pb[1] - pd[1];
- cdx = pc[0] - pd[0];
- cdy = pc[1] - pd[1];
-
- abdet = adx * bdy - bdx * ady;
- bcdet = bdx * cdy - cdx * bdy;
- cadet = cdx * ady - adx * cdy;
- alift = adx * adx + ady * ady;
- blift = bdx * bdx + bdy * bdy;
- clift = cdx * cdx + cdy * cdy;
-
- return alift * bcdet + blift * cadet + clift * abdet;
-}
-
-REAL incircleexact(REAL *pa, REAL *pb, REAL *pc, REAL *pd)
-{
- INEXACT REAL axby1, bxcy1, cxdy1, dxay1, axcy1, bxdy1;
- INEXACT REAL bxay1, cxby1, dxcy1, axdy1, cxay1, dxby1;
- REAL axby0, bxcy0, cxdy0, dxay0, axcy0, bxdy0;
- REAL bxay0, cxby0, dxcy0, axdy0, cxay0, dxby0;
- REAL ab[4], bc[4], cd[4], da[4], ac[4], bd[4];
- REAL temp8[8];
- int templen;
- REAL abc[12], bcd[12], cda[12], dab[12];
- int abclen, bcdlen, cdalen, dablen;
- REAL det24x[24], det24y[24], det48x[48], det48y[48];
- int xlen, ylen;
- REAL adet[96], bdet[96], cdet[96], ddet[96];
- int alen, blen, clen, dlen;
- REAL abdet[192], cddet[192];
- int ablen, cdlen;
- REAL deter[384];
- int deterlen;
- int i;
-
- INEXACT REAL bvirt;
- REAL avirt, bround, around;
- INEXACT REAL c;
- INEXACT REAL abig;
- REAL ahi, alo, bhi, blo;
- REAL err1, err2, err3;
- INEXACT REAL _i, _j;
- REAL _0;
-
- Two_Product(pa[0], pb[1], axby1, axby0);
- Two_Product(pb[0], pa[1], bxay1, bxay0);
- Two_Two_Diff(axby1, axby0, bxay1, bxay0, ab[3], ab[2], ab[1], ab[0]);
-
- Two_Product(pb[0], pc[1], bxcy1, bxcy0);
- Two_Product(pc[0], pb[1], cxby1, cxby0);
- Two_Two_Diff(bxcy1, bxcy0, cxby1, cxby0, bc[3], bc[2], bc[1], bc[0]);
-
- Two_Product(pc[0], pd[1], cxdy1, cxdy0);
- Two_Product(pd[0], pc[1], dxcy1, dxcy0);
- Two_Two_Diff(cxdy1, cxdy0, dxcy1, dxcy0, cd[3], cd[2], cd[1], cd[0]);
-
- Two_Product(pd[0], pa[1], dxay1, dxay0);
- Two_Product(pa[0], pd[1], axdy1, axdy0);
- Two_Two_Diff(dxay1, dxay0, axdy1, axdy0, da[3], da[2], da[1], da[0]);
-
- Two_Product(pa[0], pc[1], axcy1, axcy0);
- Two_Product(pc[0], pa[1], cxay1, cxay0);
- Two_Two_Diff(axcy1, axcy0, cxay1, cxay0, ac[3], ac[2], ac[1], ac[0]);
-
- Two_Product(pb[0], pd[1], bxdy1, bxdy0);
- Two_Product(pd[0], pb[1], dxby1, dxby0);
- Two_Two_Diff(bxdy1, bxdy0, dxby1, dxby0, bd[3], bd[2], bd[1], bd[0]);
-
- templen = fast_expansion_sum_zeroelim(4, cd, 4, da, temp8);
- cdalen = fast_expansion_sum_zeroelim(templen, temp8, 4, ac, cda);
- templen = fast_expansion_sum_zeroelim(4, da, 4, ab, temp8);
- dablen = fast_expansion_sum_zeroelim(templen, temp8, 4, bd, dab);
- for (i = 0; i < 4; i++) {
- bd[i] = -bd[i];
- ac[i] = -ac[i];
- }
- templen = fast_expansion_sum_zeroelim(4, ab, 4, bc, temp8);
- abclen = fast_expansion_sum_zeroelim(templen, temp8, 4, ac, abc);
- templen = fast_expansion_sum_zeroelim(4, bc, 4, cd, temp8);
- bcdlen = fast_expansion_sum_zeroelim(templen, temp8, 4, bd, bcd);
-
- xlen = scale_expansion_zeroelim(bcdlen, bcd, pa[0], det24x);
- xlen = scale_expansion_zeroelim(xlen, det24x, pa[0], det48x);
- ylen = scale_expansion_zeroelim(bcdlen, bcd, pa[1], det24y);
- ylen = scale_expansion_zeroelim(ylen, det24y, pa[1], det48y);
- alen = fast_expansion_sum_zeroelim(xlen, det48x, ylen, det48y, adet);
-
- xlen = scale_expansion_zeroelim(cdalen, cda, pb[0], det24x);
- xlen = scale_expansion_zeroelim(xlen, det24x, -pb[0], det48x);
- ylen = scale_expansion_zeroelim(cdalen, cda, pb[1], det24y);
- ylen = scale_expansion_zeroelim(ylen, det24y, -pb[1], det48y);
- blen = fast_expansion_sum_zeroelim(xlen, det48x, ylen, det48y, bdet);
-
- xlen = scale_expansion_zeroelim(dablen, dab, pc[0], det24x);
- xlen = scale_expansion_zeroelim(xlen, det24x, pc[0], det48x);
- ylen = scale_expansion_zeroelim(dablen, dab, pc[1], det24y);
- ylen = scale_expansion_zeroelim(ylen, det24y, pc[1], det48y);
- clen = fast_expansion_sum_zeroelim(xlen, det48x, ylen, det48y, cdet);
-
- xlen = scale_expansion_zeroelim(abclen, abc, pd[0], det24x);
- xlen = scale_expansion_zeroelim(xlen, det24x, -pd[0], det48x);
- ylen = scale_expansion_zeroelim(abclen, abc, pd[1], det24y);
- ylen = scale_expansion_zeroelim(ylen, det24y, -pd[1], det48y);
- dlen = fast_expansion_sum_zeroelim(xlen, det48x, ylen, det48y, ddet);
-
- ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
- cdlen = fast_expansion_sum_zeroelim(clen, cdet, dlen, ddet, cddet);
- deterlen = fast_expansion_sum_zeroelim(ablen, abdet, cdlen, cddet, deter);
-
- return deter[deterlen - 1];
-}
-
-REAL incircleslow(REAL *pa, REAL *pb, REAL *pc, REAL *pd)
-{
- INEXACT REAL adx, bdx, cdx, ady, bdy, cdy;
- REAL adxtail, bdxtail, cdxtail;
- REAL adytail, bdytail, cdytail;
- REAL negate, negatetail;
- INEXACT REAL axby7, bxcy7, axcy7, bxay7, cxby7, cxay7;
- REAL axby[8], bxcy[8], axcy[8], bxay[8], cxby[8], cxay[8];
- REAL temp16[16];
- int temp16len;
- REAL detx[32], detxx[64], detxt[32], detxxt[64], detxtxt[64];
- int xlen, xxlen, xtlen, xxtlen, xtxtlen;
- REAL x1[128], x2[192];
- int x1len, x2len;
- REAL dety[32], detyy[64], detyt[32], detyyt[64], detytyt[64];
- int ylen, yylen, ytlen, yytlen, ytytlen;
- REAL y1[128], y2[192];
- int y1len, y2len;
- REAL adet[384], bdet[384], cdet[384], abdet[768], deter[1152];
- int alen, blen, clen, ablen, deterlen;
- int i;
-
- INEXACT REAL bvirt;
- REAL avirt, bround, around;
- INEXACT REAL c;
- INEXACT REAL abig;
- REAL a0hi, a0lo, a1hi, a1lo, bhi, blo;
- REAL err1, err2, err3;
- INEXACT REAL _i, _j, _k, _l, _m, _n;
- REAL _0, _1, _2;
-
- Two_Diff(pa[0], pd[0], adx, adxtail);
- Two_Diff(pa[1], pd[1], ady, adytail);
- Two_Diff(pb[0], pd[0], bdx, bdxtail);
- Two_Diff(pb[1], pd[1], bdy, bdytail);
- Two_Diff(pc[0], pd[0], cdx, cdxtail);
- Two_Diff(pc[1], pd[1], cdy, cdytail);
-
- Two_Two_Product(adx, adxtail, bdy, bdytail,
- axby7, axby[6], axby[5], axby[4],
- axby[3], axby[2], axby[1], axby[0]);
- axby[7] = axby7;
- negate = -ady;
- negatetail = -adytail;
- Two_Two_Product(bdx, bdxtail, negate, negatetail,
- bxay7, bxay[6], bxay[5], bxay[4],
- bxay[3], bxay[2], bxay[1], bxay[0]);
- bxay[7] = bxay7;
- Two_Two_Product(bdx, bdxtail, cdy, cdytail,
- bxcy7, bxcy[6], bxcy[5], bxcy[4],
- bxcy[3], bxcy[2], bxcy[1], bxcy[0]);
- bxcy[7] = bxcy7;
- negate = -bdy;
- negatetail = -bdytail;
- Two_Two_Product(cdx, cdxtail, negate, negatetail,
- cxby7, cxby[6], cxby[5], cxby[4],
- cxby[3], cxby[2], cxby[1], cxby[0]);
- cxby[7] = cxby7;
- Two_Two_Product(cdx, cdxtail, ady, adytail,
- cxay7, cxay[6], cxay[5], cxay[4],
- cxay[3], cxay[2], cxay[1], cxay[0]);
- cxay[7] = cxay7;
- negate = -cdy;
- negatetail = -cdytail;
- Two_Two_Product(adx, adxtail, negate, negatetail,
- axcy7, axcy[6], axcy[5], axcy[4],
- axcy[3], axcy[2], axcy[1], axcy[0]);
- axcy[7] = axcy7;
-
-
- temp16len = fast_expansion_sum_zeroelim(8, bxcy, 8, cxby, temp16);
-
- xlen = scale_expansion_zeroelim(temp16len, temp16, adx, detx);
- xxlen = scale_expansion_zeroelim(xlen, detx, adx, detxx);
- xtlen = scale_expansion_zeroelim(temp16len, temp16, adxtail, detxt);
- xxtlen = scale_expansion_zeroelim(xtlen, detxt, adx, detxxt);
- for (i = 0; i < xxtlen; i++) {
- detxxt[i] *= 2.0;
- }
- xtxtlen = scale_expansion_zeroelim(xtlen, detxt, adxtail, detxtxt);
- x1len = fast_expansion_sum_zeroelim(xxlen, detxx, xxtlen, detxxt, x1);
- x2len = fast_expansion_sum_zeroelim(x1len, x1, xtxtlen, detxtxt, x2);
-
- ylen = scale_expansion_zeroelim(temp16len, temp16, ady, dety);
- yylen = scale_expansion_zeroelim(ylen, dety, ady, detyy);
- ytlen = scale_expansion_zeroelim(temp16len, temp16, adytail, detyt);
- yytlen = scale_expansion_zeroelim(ytlen, detyt, ady, detyyt);
- for (i = 0; i < yytlen; i++) {
- detyyt[i] *= 2.0;
- }
- ytytlen = scale_expansion_zeroelim(ytlen, detyt, adytail, detytyt);
- y1len = fast_expansion_sum_zeroelim(yylen, detyy, yytlen, detyyt, y1);
- y2len = fast_expansion_sum_zeroelim(y1len, y1, ytytlen, detytyt, y2);
-
- alen = fast_expansion_sum_zeroelim(x2len, x2, y2len, y2, adet);
-
-
- temp16len = fast_expansion_sum_zeroelim(8, cxay, 8, axcy, temp16);
-
- xlen = scale_expansion_zeroelim(temp16len, temp16, bdx, detx);
- xxlen = scale_expansion_zeroelim(xlen, detx, bdx, detxx);
- xtlen = scale_expansion_zeroelim(temp16len, temp16, bdxtail, detxt);
- xxtlen = scale_expansion_zeroelim(xtlen, detxt, bdx, detxxt);
- for (i = 0; i < xxtlen; i++) {
- detxxt[i] *= 2.0;
- }
- xtxtlen = scale_expansion_zeroelim(xtlen, detxt, bdxtail, detxtxt);
- x1len = fast_expansion_sum_zeroelim(xxlen, detxx, xxtlen, detxxt, x1);
- x2len = fast_expansion_sum_zeroelim(x1len, x1, xtxtlen, detxtxt, x2);
-
- ylen = scale_expansion_zeroelim(temp16len, temp16, bdy, dety);
- yylen = scale_expansion_zeroelim(ylen, dety, bdy, detyy);
- ytlen = scale_expansion_zeroelim(temp16len, temp16, bdytail, detyt);
- yytlen = scale_expansion_zeroelim(ytlen, detyt, bdy, detyyt);
- for (i = 0; i < yytlen; i++) {
- detyyt[i] *= 2.0;
- }
- ytytlen = scale_expansion_zeroelim(ytlen, detyt, bdytail, detytyt);
- y1len = fast_expansion_sum_zeroelim(yylen, detyy, yytlen, detyyt, y1);
- y2len = fast_expansion_sum_zeroelim(y1len, y1, ytytlen, detytyt, y2);
-
- blen = fast_expansion_sum_zeroelim(x2len, x2, y2len, y2, bdet);
-
-
- temp16len = fast_expansion_sum_zeroelim(8, axby, 8, bxay, temp16);
-
- xlen = scale_expansion_zeroelim(temp16len, temp16, cdx, detx);
- xxlen = scale_expansion_zeroelim(xlen, detx, cdx, detxx);
- xtlen = scale_expansion_zeroelim(temp16len, temp16, cdxtail, detxt);
- xxtlen = scale_expansion_zeroelim(xtlen, detxt, cdx, detxxt);
- for (i = 0; i < xxtlen; i++) {
- detxxt[i] *= 2.0;
- }
- xtxtlen = scale_expansion_zeroelim(xtlen, detxt, cdxtail, detxtxt);
- x1len = fast_expansion_sum_zeroelim(xxlen, detxx, xxtlen, detxxt, x1);
- x2len = fast_expansion_sum_zeroelim(x1len, x1, xtxtlen, detxtxt, x2);
-
- ylen = scale_expansion_zeroelim(temp16len, temp16, cdy, dety);
- yylen = scale_expansion_zeroelim(ylen, dety, cdy, detyy);
- ytlen = scale_expansion_zeroelim(temp16len, temp16, cdytail, detyt);
- yytlen = scale_expansion_zeroelim(ytlen, detyt, cdy, detyyt);
- for (i = 0; i < yytlen; i++) {
- detyyt[i] *= 2.0;
- }
- ytytlen = scale_expansion_zeroelim(ytlen, detyt, cdytail, detytyt);
- y1len = fast_expansion_sum_zeroelim(yylen, detyy, yytlen, detyyt, y1);
- y2len = fast_expansion_sum_zeroelim(y1len, y1, ytytlen, detytyt, y2);
-
- clen = fast_expansion_sum_zeroelim(x2len, x2, y2len, y2, cdet);
-
- ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
- deterlen = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, deter);
-
- return deter[deterlen - 1];
-}
-
-REAL incircleadapt(REAL *pa, REAL *pb, REAL *pc, REAL *pd, REAL permanent)
-{
- INEXACT REAL adx, bdx, cdx, ady, bdy, cdy;
- REAL det, errbound;
-
- INEXACT REAL bdxcdy1, cdxbdy1, cdxady1, adxcdy1, adxbdy1, bdxady1;
- REAL bdxcdy0, cdxbdy0, cdxady0, adxcdy0, adxbdy0, bdxady0;
- REAL bc[4], ca[4], ab[4];
- INEXACT REAL bc3, ca3, ab3;
- REAL axbc[8], axxbc[16], aybc[8], ayybc[16], adet[32];
- int axbclen, axxbclen, aybclen, ayybclen, alen;
- REAL bxca[8], bxxca[16], byca[8], byyca[16], bdet[32];
- int bxcalen, bxxcalen, bycalen, byycalen, blen;
- REAL cxab[8], cxxab[16], cyab[8], cyyab[16], cdet[32];
- int cxablen, cxxablen, cyablen, cyyablen, clen;
- REAL abdet[64];
- int ablen;
- REAL fin1[1152], fin2[1152];
- REAL *finnow, *finother, *finswap;
- int finlength;
-
- REAL adxtail, bdxtail, cdxtail, adytail, bdytail, cdytail;
- INEXACT REAL adxadx1, adyady1, bdxbdx1, bdybdy1, cdxcdx1, cdycdy1;
- REAL adxadx0, adyady0, bdxbdx0, bdybdy0, cdxcdx0, cdycdy0;
- REAL aa[4], bb[4], cc[4];
- INEXACT REAL aa3, bb3, cc3;
- INEXACT REAL ti1, tj1;
- REAL ti0, tj0;
- REAL u[4], v[4];
- INEXACT REAL u3, v3;
- REAL temp8[8], temp16a[16], temp16b[16], temp16c[16];
- REAL temp32a[32], temp32b[32], temp48[48], temp64[64];
- int temp8len, temp16alen, temp16blen, temp16clen;
- int temp32alen, temp32blen, temp48len, temp64len;
- REAL axtbb[8], axtcc[8], aytbb[8], aytcc[8];
- int axtbblen, axtcclen, aytbblen, aytcclen;
- REAL bxtaa[8], bxtcc[8], bytaa[8], bytcc[8];
- int bxtaalen, bxtcclen, bytaalen, bytcclen;
- REAL cxtaa[8], cxtbb[8], cytaa[8], cytbb[8];
- int cxtaalen, cxtbblen, cytaalen, cytbblen;
- REAL axtbc[8], aytbc[8], bxtca[8], bytca[8], cxtab[8], cytab[8];
- int axtbclen, aytbclen, bxtcalen, bytcalen, cxtablen, cytablen;
- REAL axtbct[16], aytbct[16], bxtcat[16], bytcat[16], cxtabt[16], cytabt[16];
- int axtbctlen, aytbctlen, bxtcatlen, bytcatlen, cxtabtlen, cytabtlen;
- REAL axtbctt[8], aytbctt[8], bxtcatt[8];
- REAL bytcatt[8], cxtabtt[8], cytabtt[8];
- int axtbcttlen, aytbcttlen, bxtcattlen, bytcattlen, cxtabttlen, cytabttlen;
- REAL abt[8], bct[8], cat[8];
- int abtlen, bctlen, catlen;
- REAL abtt[4], bctt[4], catt[4];
- int abttlen, bcttlen, cattlen;
- INEXACT REAL abtt3, bctt3, catt3;
- REAL negate;
-
- INEXACT REAL bvirt;
- REAL avirt, bround, around;
- INEXACT REAL c;
- INEXACT REAL abig;
- REAL ahi, alo, bhi, blo;
- REAL err1, err2, err3;
- INEXACT REAL _i, _j;
- REAL _0;
-
- adx = (REAL) (pa[0] - pd[0]);
- bdx = (REAL) (pb[0] - pd[0]);
- cdx = (REAL) (pc[0] - pd[0]);
- ady = (REAL) (pa[1] - pd[1]);
- bdy = (REAL) (pb[1] - pd[1]);
- cdy = (REAL) (pc[1] - pd[1]);
-
- Two_Product(bdx, cdy, bdxcdy1, bdxcdy0);
- Two_Product(cdx, bdy, cdxbdy1, cdxbdy0);
- Two_Two_Diff(bdxcdy1, bdxcdy0, cdxbdy1, cdxbdy0, bc3, bc[2], bc[1], bc[0]);
- bc[3] = bc3;
- axbclen = scale_expansion_zeroelim(4, bc, adx, axbc);
- axxbclen = scale_expansion_zeroelim(axbclen, axbc, adx, axxbc);
- aybclen = scale_expansion_zeroelim(4, bc, ady, aybc);
- ayybclen = scale_expansion_zeroelim(aybclen, aybc, ady, ayybc);
- alen = fast_expansion_sum_zeroelim(axxbclen, axxbc, ayybclen, ayybc, adet);
-
- Two_Product(cdx, ady, cdxady1, cdxady0);
- Two_Product(adx, cdy, adxcdy1, adxcdy0);
- Two_Two_Diff(cdxady1, cdxady0, adxcdy1, adxcdy0, ca3, ca[2], ca[1], ca[0]);
- ca[3] = ca3;
- bxcalen = scale_expansion_zeroelim(4, ca, bdx, bxca);
- bxxcalen = scale_expansion_zeroelim(bxcalen, bxca, bdx, bxxca);
- bycalen = scale_expansion_zeroelim(4, ca, bdy, byca);
- byycalen = scale_expansion_zeroelim(bycalen, byca, bdy, byyca);
- blen = fast_expansion_sum_zeroelim(bxxcalen, bxxca, byycalen, byyca, bdet);
-
- Two_Product(adx, bdy, adxbdy1, adxbdy0);
- Two_Product(bdx, ady, bdxady1, bdxady0);
- Two_Two_Diff(adxbdy1, adxbdy0, bdxady1, bdxady0, ab3, ab[2], ab[1], ab[0]);
- ab[3] = ab3;
- cxablen = scale_expansion_zeroelim(4, ab, cdx, cxab);
- cxxablen = scale_expansion_zeroelim(cxablen, cxab, cdx, cxxab);
- cyablen = scale_expansion_zeroelim(4, ab, cdy, cyab);
- cyyablen = scale_expansion_zeroelim(cyablen, cyab, cdy, cyyab);
- clen = fast_expansion_sum_zeroelim(cxxablen, cxxab, cyyablen, cyyab, cdet);
-
- ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
- finlength = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, fin1);
-
- det = estimate(finlength, fin1);
- errbound = iccerrboundB * permanent;
- if ((det >= errbound) || (-det >= errbound)) {
- return det;
- }
-
- Two_Diff_Tail(pa[0], pd[0], adx, adxtail);
- Two_Diff_Tail(pa[1], pd[1], ady, adytail);
- Two_Diff_Tail(pb[0], pd[0], bdx, bdxtail);
- Two_Diff_Tail(pb[1], pd[1], bdy, bdytail);
- Two_Diff_Tail(pc[0], pd[0], cdx, cdxtail);
- Two_Diff_Tail(pc[1], pd[1], cdy, cdytail);
- if ((adxtail == 0.0) && (bdxtail == 0.0) && (cdxtail == 0.0)
- && (adytail == 0.0) && (bdytail == 0.0) && (cdytail == 0.0)) {
- return det;
- }
-
- errbound = iccerrboundC * permanent + resulterrbound * Absolute(det);
- det += ((adx * adx + ady * ady) * ((bdx * cdytail + cdy * bdxtail)
- - (bdy * cdxtail + cdx * bdytail))
- + 2.0 * (adx * adxtail + ady * adytail) * (bdx * cdy - bdy * cdx))
- + ((bdx * bdx + bdy * bdy) * ((cdx * adytail + ady * cdxtail)
- - (cdy * adxtail + adx * cdytail))
- + 2.0 * (bdx * bdxtail + bdy * bdytail) * (cdx * ady - cdy * adx))
- + ((cdx * cdx + cdy * cdy) * ((adx * bdytail + bdy * adxtail)
- - (ady * bdxtail + bdx * adytail))
- + 2.0 * (cdx * cdxtail + cdy * cdytail) * (adx * bdy - ady * bdx));
- if ((det >= errbound) || (-det >= errbound)) {
- return det;
- }
-
- finnow = fin1;
- finother = fin2;
-
- if ((bdxtail != 0.0) || (bdytail != 0.0)
- || (cdxtail != 0.0) || (cdytail != 0.0)) {
- Square(adx, adxadx1, adxadx0);
- Square(ady, adyady1, adyady0);
- Two_Two_Sum(adxadx1, adxadx0, adyady1, adyady0, aa3, aa[2], aa[1], aa[0]);
- aa[3] = aa3;
- }
- if ((cdxtail != 0.0) || (cdytail != 0.0)
- || (adxtail != 0.0) || (adytail != 0.0)) {
- Square(bdx, bdxbdx1, bdxbdx0);
- Square(bdy, bdybdy1, bdybdy0);
- Two_Two_Sum(bdxbdx1, bdxbdx0, bdybdy1, bdybdy0, bb3, bb[2], bb[1], bb[0]);
- bb[3] = bb3;
- }
- if ((adxtail != 0.0) || (adytail != 0.0)
- || (bdxtail != 0.0) || (bdytail != 0.0)) {
- Square(cdx, cdxcdx1, cdxcdx0);
- Square(cdy, cdycdy1, cdycdy0);
- Two_Two_Sum(cdxcdx1, cdxcdx0, cdycdy1, cdycdy0, cc3, cc[2], cc[1], cc[0]);
- cc[3] = cc3;
- }
-
- if (adxtail != 0.0) {
- axtbclen = scale_expansion_zeroelim(4, bc, adxtail, axtbc);
- temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, 2.0 * adx,
- temp16a);
-
- axtcclen = scale_expansion_zeroelim(4, cc, adxtail, axtcc);
- temp16blen = scale_expansion_zeroelim(axtcclen, axtcc, bdy, temp16b);
-
- axtbblen = scale_expansion_zeroelim(4, bb, adxtail, axtbb);
- temp16clen = scale_expansion_zeroelim(axtbblen, axtbb, -cdy, temp16c);
-
- temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
- temp16blen, temp16b, temp32a);
- temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
- temp32alen, temp32a, temp48);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
- temp48, finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- if (adytail != 0.0) {
- aytbclen = scale_expansion_zeroelim(4, bc, adytail, aytbc);
- temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, 2.0 * ady,
- temp16a);
-
- aytbblen = scale_expansion_zeroelim(4, bb, adytail, aytbb);
- temp16blen = scale_expansion_zeroelim(aytbblen, aytbb, cdx, temp16b);
-
- aytcclen = scale_expansion_zeroelim(4, cc, adytail, aytcc);
- temp16clen = scale_expansion_zeroelim(aytcclen, aytcc, -bdx, temp16c);
-
- temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
- temp16blen, temp16b, temp32a);
- temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
- temp32alen, temp32a, temp48);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
- temp48, finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- if (bdxtail != 0.0) {
- bxtcalen = scale_expansion_zeroelim(4, ca, bdxtail, bxtca);
- temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, 2.0 * bdx,
- temp16a);
-
- bxtaalen = scale_expansion_zeroelim(4, aa, bdxtail, bxtaa);
- temp16blen = scale_expansion_zeroelim(bxtaalen, bxtaa, cdy, temp16b);
-
- bxtcclen = scale_expansion_zeroelim(4, cc, bdxtail, bxtcc);
- temp16clen = scale_expansion_zeroelim(bxtcclen, bxtcc, -ady, temp16c);
-
- temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
- temp16blen, temp16b, temp32a);
- temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
- temp32alen, temp32a, temp48);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
- temp48, finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- if (bdytail != 0.0) {
- bytcalen = scale_expansion_zeroelim(4, ca, bdytail, bytca);
- temp16alen = scale_expansion_zeroelim(bytcalen, bytca, 2.0 * bdy,
- temp16a);
-
- bytcclen = scale_expansion_zeroelim(4, cc, bdytail, bytcc);
- temp16blen = scale_expansion_zeroelim(bytcclen, bytcc, adx, temp16b);
-
- bytaalen = scale_expansion_zeroelim(4, aa, bdytail, bytaa);
- temp16clen = scale_expansion_zeroelim(bytaalen, bytaa, -cdx, temp16c);
-
- temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
- temp16blen, temp16b, temp32a);
- temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
- temp32alen, temp32a, temp48);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
- temp48, finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- if (cdxtail != 0.0) {
- cxtablen = scale_expansion_zeroelim(4, ab, cdxtail, cxtab);
- temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, 2.0 * cdx,
- temp16a);
-
- cxtbblen = scale_expansion_zeroelim(4, bb, cdxtail, cxtbb);
- temp16blen = scale_expansion_zeroelim(cxtbblen, cxtbb, ady, temp16b);
-
- cxtaalen = scale_expansion_zeroelim(4, aa, cdxtail, cxtaa);
- temp16clen = scale_expansion_zeroelim(cxtaalen, cxtaa, -bdy, temp16c);
-
- temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
- temp16blen, temp16b, temp32a);
- temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
- temp32alen, temp32a, temp48);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
- temp48, finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- if (cdytail != 0.0) {
- cytablen = scale_expansion_zeroelim(4, ab, cdytail, cytab);
- temp16alen = scale_expansion_zeroelim(cytablen, cytab, 2.0 * cdy,
- temp16a);
-
- cytaalen = scale_expansion_zeroelim(4, aa, cdytail, cytaa);
- temp16blen = scale_expansion_zeroelim(cytaalen, cytaa, bdx, temp16b);
-
- cytbblen = scale_expansion_zeroelim(4, bb, cdytail, cytbb);
- temp16clen = scale_expansion_zeroelim(cytbblen, cytbb, -adx, temp16c);
-
- temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
- temp16blen, temp16b, temp32a);
- temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
- temp32alen, temp32a, temp48);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
- temp48, finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
-
- if ((adxtail != 0.0) || (adytail != 0.0)) {
- if ((bdxtail != 0.0) || (bdytail != 0.0)
- || (cdxtail != 0.0) || (cdytail != 0.0)) {
- Two_Product(bdxtail, cdy, ti1, ti0);
- Two_Product(bdx, cdytail, tj1, tj0);
- Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
- u[3] = u3;
- negate = -bdy;
- Two_Product(cdxtail, negate, ti1, ti0);
- negate = -bdytail;
- Two_Product(cdx, negate, tj1, tj0);
- Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
- v[3] = v3;
- bctlen = fast_expansion_sum_zeroelim(4, u, 4, v, bct);
-
- Two_Product(bdxtail, cdytail, ti1, ti0);
- Two_Product(cdxtail, bdytail, tj1, tj0);
- Two_Two_Diff(ti1, ti0, tj1, tj0, bctt3, bctt[2], bctt[1], bctt[0]);
- bctt[3] = bctt3;
- bcttlen = 4;
- } else {
- bct[0] = 0.0;
- bctlen = 1;
- bctt[0] = 0.0;
- bcttlen = 1;
- }
-
- if (adxtail != 0.0) {
- temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, adxtail, temp16a);
- axtbctlen = scale_expansion_zeroelim(bctlen, bct, adxtail, axtbct);
- temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, 2.0 * adx,
- temp32a);
- temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
- temp32alen, temp32a, temp48);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
- temp48, finother);
- finswap = finnow; finnow = finother; finother = finswap;
- if (bdytail != 0.0) {
- temp8len = scale_expansion_zeroelim(4, cc, adxtail, temp8);
- temp16alen = scale_expansion_zeroelim(temp8len, temp8, bdytail,
- temp16a);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
- temp16a, finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- if (cdytail != 0.0) {
- temp8len = scale_expansion_zeroelim(4, bb, -adxtail, temp8);
- temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail,
- temp16a);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
- temp16a, finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
-
- temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, adxtail,
- temp32a);
- axtbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adxtail, axtbctt);
- temp16alen = scale_expansion_zeroelim(axtbcttlen, axtbctt, 2.0 * adx,
- temp16a);
- temp16blen = scale_expansion_zeroelim(axtbcttlen, axtbctt, adxtail,
- temp16b);
- temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
- temp16blen, temp16b, temp32b);
- temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
- temp32blen, temp32b, temp64);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
- temp64, finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- if (adytail != 0.0) {
- temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, adytail, temp16a);
- aytbctlen = scale_expansion_zeroelim(bctlen, bct, adytail, aytbct);
- temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, 2.0 * ady,
- temp32a);
- temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
- temp32alen, temp32a, temp48);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
- temp48, finother);
- finswap = finnow; finnow = finother; finother = finswap;
-
-
- temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, adytail,
- temp32a);
- aytbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adytail, aytbctt);
- temp16alen = scale_expansion_zeroelim(aytbcttlen, aytbctt, 2.0 * ady,
- temp16a);
- temp16blen = scale_expansion_zeroelim(aytbcttlen, aytbctt, adytail,
- temp16b);
- temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
- temp16blen, temp16b, temp32b);
- temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
- temp32blen, temp32b, temp64);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
- temp64, finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- }
- if ((bdxtail != 0.0) || (bdytail != 0.0)) {
- if ((cdxtail != 0.0) || (cdytail != 0.0)
- || (adxtail != 0.0) || (adytail != 0.0)) {
- Two_Product(cdxtail, ady, ti1, ti0);
- Two_Product(cdx, adytail, tj1, tj0);
- Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
- u[3] = u3;
- negate = -cdy;
- Two_Product(adxtail, negate, ti1, ti0);
- negate = -cdytail;
- Two_Product(adx, negate, tj1, tj0);
- Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
- v[3] = v3;
- catlen = fast_expansion_sum_zeroelim(4, u, 4, v, cat);
-
- Two_Product(cdxtail, adytail, ti1, ti0);
- Two_Product(adxtail, cdytail, tj1, tj0);
- Two_Two_Diff(ti1, ti0, tj1, tj0, catt3, catt[2], catt[1], catt[0]);
- catt[3] = catt3;
- cattlen = 4;
- } else {
- cat[0] = 0.0;
- catlen = 1;
- catt[0] = 0.0;
- cattlen = 1;
- }
-
- if (bdxtail != 0.0) {
- temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, bdxtail, temp16a);
- bxtcatlen = scale_expansion_zeroelim(catlen, cat, bdxtail, bxtcat);
- temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, 2.0 * bdx,
- temp32a);
- temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
- temp32alen, temp32a, temp48);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
- temp48, finother);
- finswap = finnow; finnow = finother; finother = finswap;
- if (cdytail != 0.0) {
- temp8len = scale_expansion_zeroelim(4, aa, bdxtail, temp8);
- temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail,
- temp16a);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
- temp16a, finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- if (adytail != 0.0) {
- temp8len = scale_expansion_zeroelim(4, cc, -bdxtail, temp8);
- temp16alen = scale_expansion_zeroelim(temp8len, temp8, adytail,
- temp16a);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
- temp16a, finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
-
- temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, bdxtail,
- temp32a);
- bxtcattlen = scale_expansion_zeroelim(cattlen, catt, bdxtail, bxtcatt);
- temp16alen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, 2.0 * bdx,
- temp16a);
- temp16blen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, bdxtail,
- temp16b);
- temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
- temp16blen, temp16b, temp32b);
- temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
- temp32blen, temp32b, temp64);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
- temp64, finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- if (bdytail != 0.0) {
- temp16alen = scale_expansion_zeroelim(bytcalen, bytca, bdytail, temp16a);
- bytcatlen = scale_expansion_zeroelim(catlen, cat, bdytail, bytcat);
- temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, 2.0 * bdy,
- temp32a);
- temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
- temp32alen, temp32a, temp48);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
- temp48, finother);
- finswap = finnow; finnow = finother; finother = finswap;
-
-
- temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, bdytail,
- temp32a);
- bytcattlen = scale_expansion_zeroelim(cattlen, catt, bdytail, bytcatt);
- temp16alen = scale_expansion_zeroelim(bytcattlen, bytcatt, 2.0 * bdy,
- temp16a);
- temp16blen = scale_expansion_zeroelim(bytcattlen, bytcatt, bdytail,
- temp16b);
- temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
- temp16blen, temp16b, temp32b);
- temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
- temp32blen, temp32b, temp64);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
- temp64, finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- }
- if ((cdxtail != 0.0) || (cdytail != 0.0)) {
- if ((adxtail != 0.0) || (adytail != 0.0)
- || (bdxtail != 0.0) || (bdytail != 0.0)) {
- Two_Product(adxtail, bdy, ti1, ti0);
- Two_Product(adx, bdytail, tj1, tj0);
- Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
- u[3] = u3;
- negate = -ady;
- Two_Product(bdxtail, negate, ti1, ti0);
- negate = -adytail;
- Two_Product(bdx, negate, tj1, tj0);
- Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
- v[3] = v3;
- abtlen = fast_expansion_sum_zeroelim(4, u, 4, v, abt);
-
- Two_Product(adxtail, bdytail, ti1, ti0);
- Two_Product(bdxtail, adytail, tj1, tj0);
- Two_Two_Diff(ti1, ti0, tj1, tj0, abtt3, abtt[2], abtt[1], abtt[0]);
- abtt[3] = abtt3;
- abttlen = 4;
- } else {
- abt[0] = 0.0;
- abtlen = 1;
- abtt[0] = 0.0;
- abttlen = 1;
- }
-
- if (cdxtail != 0.0) {
- temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, cdxtail, temp16a);
- cxtabtlen = scale_expansion_zeroelim(abtlen, abt, cdxtail, cxtabt);
- temp32alen = scale_expansion_zeroelim(cxtabtlen, cxtabt, 2.0 * cdx,
- temp32a);
- temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
- temp32alen, temp32a, temp48);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
- temp48, finother);
- finswap = finnow; finnow = finother; finother = finswap;
- if (adytail != 0.0) {
- temp8len = scale_expansion_zeroelim(4, bb, cdxtail, temp8);
- temp16alen = scale_expansion_zeroelim(temp8len, temp8, adytail,
- temp16a);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
- temp16a, finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- if (bdytail != 0.0) {
- temp8len = scale_expansion_zeroelim(4, aa, -cdxtail, temp8);
- temp16alen = scale_expansion_zeroelim(temp8len, temp8, bdytail,
- temp16a);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
- temp16a, finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
-
- temp32alen = scale_expansion_zeroelim(cxtabtlen, cxtabt, cdxtail,
- temp32a);
- cxtabttlen = scale_expansion_zeroelim(abttlen, abtt, cdxtail, cxtabtt);
- temp16alen = scale_expansion_zeroelim(cxtabttlen, cxtabtt, 2.0 * cdx,
- temp16a);
- temp16blen = scale_expansion_zeroelim(cxtabttlen, cxtabtt, cdxtail,
- temp16b);
- temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
- temp16blen, temp16b, temp32b);
- temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
- temp32blen, temp32b, temp64);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
- temp64, finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- if (cdytail != 0.0) {
- temp16alen = scale_expansion_zeroelim(cytablen, cytab, cdytail, temp16a);
- cytabtlen = scale_expansion_zeroelim(abtlen, abt, cdytail, cytabt);
- temp32alen = scale_expansion_zeroelim(cytabtlen, cytabt, 2.0 * cdy,
- temp32a);
- temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
- temp32alen, temp32a, temp48);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
- temp48, finother);
- finswap = finnow; finnow = finother; finother = finswap;
-
-
- temp32alen = scale_expansion_zeroelim(cytabtlen, cytabt, cdytail,
- temp32a);
- cytabttlen = scale_expansion_zeroelim(abttlen, abtt, cdytail, cytabtt);
- temp16alen = scale_expansion_zeroelim(cytabttlen, cytabtt, 2.0 * cdy,
- temp16a);
- temp16blen = scale_expansion_zeroelim(cytabttlen, cytabtt, cdytail,
- temp16b);
- temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
- temp16blen, temp16b, temp32b);
- temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
- temp32blen, temp32b, temp64);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
- temp64, finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- }
-
- return finnow[finlength - 1];
-}
-
-REAL incircle(REAL *pa, REAL *pb, REAL *pc, REAL *pd)
-{
- REAL adx, bdx, cdx, ady, bdy, cdy;
- REAL bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady;
- REAL alift, blift, clift;
- REAL det;
- REAL permanent, errbound;
-
- adx = pa[0] - pd[0];
- bdx = pb[0] - pd[0];
- cdx = pc[0] - pd[0];
- ady = pa[1] - pd[1];
- bdy = pb[1] - pd[1];
- cdy = pc[1] - pd[1];
-
- bdxcdy = bdx * cdy;
- cdxbdy = cdx * bdy;
- alift = adx * adx + ady * ady;
-
- cdxady = cdx * ady;
- adxcdy = adx * cdy;
- blift = bdx * bdx + bdy * bdy;
-
- adxbdy = adx * bdy;
- bdxady = bdx * ady;
- clift = cdx * cdx + cdy * cdy;
-
- det = alift * (bdxcdy - cdxbdy)
- + blift * (cdxady - adxcdy)
- + clift * (adxbdy - bdxady);
-
- permanent = (Absolute(bdxcdy) + Absolute(cdxbdy)) * alift
- + (Absolute(cdxady) + Absolute(adxcdy)) * blift
- + (Absolute(adxbdy) + Absolute(bdxady)) * clift;
- errbound = iccerrboundA * permanent;
- if ((det > errbound) || (-det > errbound)) {
- return det;
- }
-
- return incircleadapt(pa, pb, pc, pd, permanent);
-}
-
-/*****************************************************************************/
-/* */
-/* inspherefast() Approximate 3D insphere test. Nonrobust. */
-/* insphereexact() Exact 3D insphere test. Robust. */
-/* insphereslow() Another exact 3D insphere test. Robust. */
-/* insphere() Adaptive exact 3D insphere test. Robust. */
-/* */
-/* Return a positive value if the point pe lies inside the */
-/* sphere passing through pa, pb, pc, and pd; a negative value */
-/* if it lies outside; and zero if the five points are */
-/* cospherical. The points pa, pb, pc, and pd must be ordered */
-/* so that they have a positive orientation (as defined by */
-/* orient3d()), or the sign of the result will be reversed. */
-/* */
-/* Only the first and last routine should be used; the middle two are for */
-/* timings. */
-/* */
-/* The last three use exact arithmetic to ensure a correct answer. The */
-/* result returned is the determinant of a matrix. In insphere() only, */
-/* this determinant is computed adaptively, in the sense that exact */
-/* arithmetic is used only to the degree it is needed to ensure that the */
-/* returned value has the correct sign. Hence, insphere() is usually quite */
-/* fast, but will run more slowly when the input points are cospherical or */
-/* nearly so. */
-/* */
-/*****************************************************************************/
-
-REAL inspherefast(REAL *pa, REAL *pb, REAL *pc, REAL *pd, REAL *pe)
-{
- REAL aex, bex, cex, dex;
- REAL aey, bey, cey, dey;
- REAL aez, bez, cez, dez;
- REAL alift, blift, clift, dlift;
- REAL ab, bc, cd, da, ac, bd;
- REAL abc, bcd, cda, dab;
-
- aex = pa[0] - pe[0];
- bex = pb[0] - pe[0];
- cex = pc[0] - pe[0];
- dex = pd[0] - pe[0];
- aey = pa[1] - pe[1];
- bey = pb[1] - pe[1];
- cey = pc[1] - pe[1];
- dey = pd[1] - pe[1];
- aez = pa[2] - pe[2];
- bez = pb[2] - pe[2];
- cez = pc[2] - pe[2];
- dez = pd[2] - pe[2];
-
- ab = aex * bey - bex * aey;
- bc = bex * cey - cex * bey;
- cd = cex * dey - dex * cey;
- da = dex * aey - aex * dey;
-
- ac = aex * cey - cex * aey;
- bd = bex * dey - dex * bey;
-
- abc = aez * bc - bez * ac + cez * ab;
- bcd = bez * cd - cez * bd + dez * bc;
- cda = cez * da + dez * ac + aez * cd;
- dab = dez * ab + aez * bd + bez * da;
-
- alift = aex * aex + aey * aey + aez * aez;
- blift = bex * bex + bey * bey + bez * bez;
- clift = cex * cex + cey * cey + cez * cez;
- dlift = dex * dex + dey * dey + dez * dez;
-
- return (dlift * abc - clift * dab) + (blift * cda - alift * bcd);
-}
-
-REAL insphereexact(REAL *pa, REAL *pb, REAL *pc, REAL *pd, REAL *pe)
-{
- INEXACT REAL axby1, bxcy1, cxdy1, dxey1, exay1;
- INEXACT REAL bxay1, cxby1, dxcy1, exdy1, axey1;
- INEXACT REAL axcy1, bxdy1, cxey1, dxay1, exby1;
- INEXACT REAL cxay1, dxby1, excy1, axdy1, bxey1;
- REAL axby0, bxcy0, cxdy0, dxey0, exay0;
- REAL bxay0, cxby0, dxcy0, exdy0, axey0;
- REAL axcy0, bxdy0, cxey0, dxay0, exby0;
- REAL cxay0, dxby0, excy0, axdy0, bxey0;
- REAL ab[4], bc[4], cd[4], de[4], ea[4];
- REAL ac[4], bd[4], ce[4], da[4], eb[4];
- REAL temp8a[8], temp8b[8], temp16[16];
- int temp8alen, temp8blen, temp16len;
- REAL abc[24], bcd[24], cde[24], dea[24], eab[24];
- REAL abd[24], bce[24], cda[24], deb[24], eac[24];
- int abclen, bcdlen, cdelen, dealen, eablen;
- int abdlen, bcelen, cdalen, deblen, eaclen;
- REAL temp48a[48], temp48b[48];
- int temp48alen, temp48blen;
- REAL abcd[96], bcde[96], cdea[96], deab[96], eabc[96];
- int abcdlen, bcdelen, cdealen, deablen, eabclen;
- REAL temp192[192];
- REAL det384x[384], det384y[384], det384z[384];
- int xlen, ylen, zlen;
- REAL detxy[768];
- int xylen;
- REAL adet[1152], bdet[1152], cdet[1152], ddet[1152], edet[1152];
- int alen, blen, clen, dlen, elen;
- REAL abdet[2304], cddet[2304], cdedet[3456];
- int ablen, cdlen;
- REAL deter[5760];
- int deterlen;
- int i;
-
- INEXACT REAL bvirt;
- REAL avirt, bround, around;
- INEXACT REAL c;
- INEXACT REAL abig;
- REAL ahi, alo, bhi, blo;
- REAL err1, err2, err3;
- INEXACT REAL _i, _j;
- REAL _0;
-
- Two_Product(pa[0], pb[1], axby1, axby0);
- Two_Product(pb[0], pa[1], bxay1, bxay0);
- Two_Two_Diff(axby1, axby0, bxay1, bxay0, ab[3], ab[2], ab[1], ab[0]);
-
- Two_Product(pb[0], pc[1], bxcy1, bxcy0);
- Two_Product(pc[0], pb[1], cxby1, cxby0);
- Two_Two_Diff(bxcy1, bxcy0, cxby1, cxby0, bc[3], bc[2], bc[1], bc[0]);
-
- Two_Product(pc[0], pd[1], cxdy1, cxdy0);
- Two_Product(pd[0], pc[1], dxcy1, dxcy0);
- Two_Two_Diff(cxdy1, cxdy0, dxcy1, dxcy0, cd[3], cd[2], cd[1], cd[0]);
-
- Two_Product(pd[0], pe[1], dxey1, dxey0);
- Two_Product(pe[0], pd[1], exdy1, exdy0);
- Two_Two_Diff(dxey1, dxey0, exdy1, exdy0, de[3], de[2], de[1], de[0]);
-
- Two_Product(pe[0], pa[1], exay1, exay0);
- Two_Product(pa[0], pe[1], axey1, axey0);
- Two_Two_Diff(exay1, exay0, axey1, axey0, ea[3], ea[2], ea[1], ea[0]);
-
- Two_Product(pa[0], pc[1], axcy1, axcy0);
- Two_Product(pc[0], pa[1], cxay1, cxay0);
- Two_Two_Diff(axcy1, axcy0, cxay1, cxay0, ac[3], ac[2], ac[1], ac[0]);
-
- Two_Product(pb[0], pd[1], bxdy1, bxdy0);
- Two_Product(pd[0], pb[1], dxby1, dxby0);
- Two_Two_Diff(bxdy1, bxdy0, dxby1, dxby0, bd[3], bd[2], bd[1], bd[0]);
-
- Two_Product(pc[0], pe[1], cxey1, cxey0);
- Two_Product(pe[0], pc[1], excy1, excy0);
- Two_Two_Diff(cxey1, cxey0, excy1, excy0, ce[3], ce[2], ce[1], ce[0]);
-
- Two_Product(pd[0], pa[1], dxay1, dxay0);
- Two_Product(pa[0], pd[1], axdy1, axdy0);
- Two_Two_Diff(dxay1, dxay0, axdy1, axdy0, da[3], da[2], da[1], da[0]);
-
- Two_Product(pe[0], pb[1], exby1, exby0);
- Two_Product(pb[0], pe[1], bxey1, bxey0);
- Two_Two_Diff(exby1, exby0, bxey1, bxey0, eb[3], eb[2], eb[1], eb[0]);
-
- temp8alen = scale_expansion_zeroelim(4, bc, pa[2], temp8a);
- temp8blen = scale_expansion_zeroelim(4, ac, -pb[2], temp8b);
- temp16len = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp8blen, temp8b,
- temp16);
- temp8alen = scale_expansion_zeroelim(4, ab, pc[2], temp8a);
- abclen = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp16len, temp16,
- abc);
-
- temp8alen = scale_expansion_zeroelim(4, cd, pb[2], temp8a);
- temp8blen = scale_expansion_zeroelim(4, bd, -pc[2], temp8b);
- temp16len = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp8blen, temp8b,
- temp16);
- temp8alen = scale_expansion_zeroelim(4, bc, pd[2], temp8a);
- bcdlen = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp16len, temp16,
- bcd);
-
- temp8alen = scale_expansion_zeroelim(4, de, pc[2], temp8a);
- temp8blen = scale_expansion_zeroelim(4, ce, -pd[2], temp8b);
- temp16len = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp8blen, temp8b,
- temp16);
- temp8alen = scale_expansion_zeroelim(4, cd, pe[2], temp8a);
- cdelen = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp16len, temp16,
- cde);
-
- temp8alen = scale_expansion_zeroelim(4, ea, pd[2], temp8a);
- temp8blen = scale_expansion_zeroelim(4, da, -pe[2], temp8b);
- temp16len = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp8blen, temp8b,
- temp16);
- temp8alen = scale_expansion_zeroelim(4, de, pa[2], temp8a);
- dealen = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp16len, temp16,
- dea);
-
- temp8alen = scale_expansion_zeroelim(4, ab, pe[2], temp8a);
- temp8blen = scale_expansion_zeroelim(4, eb, -pa[2], temp8b);
- temp16len = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp8blen, temp8b,
- temp16);
- temp8alen = scale_expansion_zeroelim(4, ea, pb[2], temp8a);
- eablen = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp16len, temp16,
- eab);
-
- temp8alen = scale_expansion_zeroelim(4, bd, pa[2], temp8a);
- temp8blen = scale_expansion_zeroelim(4, da, pb[2], temp8b);
- temp16len = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp8blen, temp8b,
- temp16);
- temp8alen = scale_expansion_zeroelim(4, ab, pd[2], temp8a);
- abdlen = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp16len, temp16,
- abd);
-
- temp8alen = scale_expansion_zeroelim(4, ce, pb[2], temp8a);
- temp8blen = scale_expansion_zeroelim(4, eb, pc[2], temp8b);
- temp16len = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp8blen, temp8b,
- temp16);
- temp8alen = scale_expansion_zeroelim(4, bc, pe[2], temp8a);
- bcelen = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp16len, temp16,
- bce);
-
- temp8alen = scale_expansion_zeroelim(4, da, pc[2], temp8a);
- temp8blen = scale_expansion_zeroelim(4, ac, pd[2], temp8b);
- temp16len = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp8blen, temp8b,
- temp16);
- temp8alen = scale_expansion_zeroelim(4, cd, pa[2], temp8a);
- cdalen = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp16len, temp16,
- cda);
-
- temp8alen = scale_expansion_zeroelim(4, eb, pd[2], temp8a);
- temp8blen = scale_expansion_zeroelim(4, bd, pe[2], temp8b);
- temp16len = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp8blen, temp8b,
- temp16);
- temp8alen = scale_expansion_zeroelim(4, de, pb[2], temp8a);
- deblen = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp16len, temp16,
- deb);
-
- temp8alen = scale_expansion_zeroelim(4, ac, pe[2], temp8a);
- temp8blen = scale_expansion_zeroelim(4, ce, pa[2], temp8b);
- temp16len = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp8blen, temp8b,
- temp16);
- temp8alen = scale_expansion_zeroelim(4, ea, pc[2], temp8a);
- eaclen = fast_expansion_sum_zeroelim(temp8alen, temp8a, temp16len, temp16,
- eac);
-
- temp48alen = fast_expansion_sum_zeroelim(cdelen, cde, bcelen, bce, temp48a);
- temp48blen = fast_expansion_sum_zeroelim(deblen, deb, bcdlen, bcd, temp48b);
- for (i = 0; i < temp48blen; i++) {
- temp48b[i] = -temp48b[i];
- }
- bcdelen = fast_expansion_sum_zeroelim(temp48alen, temp48a,
- temp48blen, temp48b, bcde);
- xlen = scale_expansion_zeroelim(bcdelen, bcde, pa[0], temp192);
- xlen = scale_expansion_zeroelim(xlen, temp192, pa[0], det384x);
- ylen = scale_expansion_zeroelim(bcdelen, bcde, pa[1], temp192);
- ylen = scale_expansion_zeroelim(ylen, temp192, pa[1], det384y);
- zlen = scale_expansion_zeroelim(bcdelen, bcde, pa[2], temp192);
- zlen = scale_expansion_zeroelim(zlen, temp192, pa[2], det384z);
- xylen = fast_expansion_sum_zeroelim(xlen, det384x, ylen, det384y, detxy);
- alen = fast_expansion_sum_zeroelim(xylen, detxy, zlen, det384z, adet);
-
- temp48alen = fast_expansion_sum_zeroelim(dealen, dea, cdalen, cda, temp48a);
- temp48blen = fast_expansion_sum_zeroelim(eaclen, eac, cdelen, cde, temp48b);
- for (i = 0; i < temp48blen; i++) {
- temp48b[i] = -temp48b[i];
- }
- cdealen = fast_expansion_sum_zeroelim(temp48alen, temp48a,
- temp48blen, temp48b, cdea);
- xlen = scale_expansion_zeroelim(cdealen, cdea, pb[0], temp192);
- xlen = scale_expansion_zeroelim(xlen, temp192, pb[0], det384x);
- ylen = scale_expansion_zeroelim(cdealen, cdea, pb[1], temp192);
- ylen = scale_expansion_zeroelim(ylen, temp192, pb[1], det384y);
- zlen = scale_expansion_zeroelim(cdealen, cdea, pb[2], temp192);
- zlen = scale_expansion_zeroelim(zlen, temp192, pb[2], det384z);
- xylen = fast_expansion_sum_zeroelim(xlen, det384x, ylen, det384y, detxy);
- blen = fast_expansion_sum_zeroelim(xylen, detxy, zlen, det384z, bdet);
-
- temp48alen = fast_expansion_sum_zeroelim(eablen, eab, deblen, deb, temp48a);
- temp48blen = fast_expansion_sum_zeroelim(abdlen, abd, dealen, dea, temp48b);
- for (i = 0; i < temp48blen; i++) {
- temp48b[i] = -temp48b[i];
- }
- deablen = fast_expansion_sum_zeroelim(temp48alen, temp48a,
- temp48blen, temp48b, deab);
- xlen = scale_expansion_zeroelim(deablen, deab, pc[0], temp192);
- xlen = scale_expansion_zeroelim(xlen, temp192, pc[0], det384x);
- ylen = scale_expansion_zeroelim(deablen, deab, pc[1], temp192);
- ylen = scale_expansion_zeroelim(ylen, temp192, pc[1], det384y);
- zlen = scale_expansion_zeroelim(deablen, deab, pc[2], temp192);
- zlen = scale_expansion_zeroelim(zlen, temp192, pc[2], det384z);
- xylen = fast_expansion_sum_zeroelim(xlen, det384x, ylen, det384y, detxy);
- clen = fast_expansion_sum_zeroelim(xylen, detxy, zlen, det384z, cdet);
-
- temp48alen = fast_expansion_sum_zeroelim(abclen, abc, eaclen, eac, temp48a);
- temp48blen = fast_expansion_sum_zeroelim(bcelen, bce, eablen, eab, temp48b);
- for (i = 0; i < temp48blen; i++) {
- temp48b[i] = -temp48b[i];
- }
- eabclen = fast_expansion_sum_zeroelim(temp48alen, temp48a,
- temp48blen, temp48b, eabc);
- xlen = scale_expansion_zeroelim(eabclen, eabc, pd[0], temp192);
- xlen = scale_expansion_zeroelim(xlen, temp192, pd[0], det384x);
- ylen = scale_expansion_zeroelim(eabclen, eabc, pd[1], temp192);
- ylen = scale_expansion_zeroelim(ylen, temp192, pd[1], det384y);
- zlen = scale_expansion_zeroelim(eabclen, eabc, pd[2], temp192);
- zlen = scale_expansion_zeroelim(zlen, temp192, pd[2], det384z);
- xylen = fast_expansion_sum_zeroelim(xlen, det384x, ylen, det384y, detxy);
- dlen = fast_expansion_sum_zeroelim(xylen, detxy, zlen, det384z, ddet);
-
- temp48alen = fast_expansion_sum_zeroelim(bcdlen, bcd, abdlen, abd, temp48a);
- temp48blen = fast_expansion_sum_zeroelim(cdalen, cda, abclen, abc, temp48b);
- for (i = 0; i < temp48blen; i++) {
- temp48b[i] = -temp48b[i];
- }
- abcdlen = fast_expansion_sum_zeroelim(temp48alen, temp48a,
- temp48blen, temp48b, abcd);
- xlen = scale_expansion_zeroelim(abcdlen, abcd, pe[0], temp192);
- xlen = scale_expansion_zeroelim(xlen, temp192, pe[0], det384x);
- ylen = scale_expansion_zeroelim(abcdlen, abcd, pe[1], temp192);
- ylen = scale_expansion_zeroelim(ylen, temp192, pe[1], det384y);
- zlen = scale_expansion_zeroelim(abcdlen, abcd, pe[2], temp192);
- zlen = scale_expansion_zeroelim(zlen, temp192, pe[2], det384z);
- xylen = fast_expansion_sum_zeroelim(xlen, det384x, ylen, det384y, detxy);
- elen = fast_expansion_sum_zeroelim(xylen, detxy, zlen, det384z, edet);
-
- ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
- cdlen = fast_expansion_sum_zeroelim(clen, cdet, dlen, ddet, cddet);
- cdelen = fast_expansion_sum_zeroelim(cdlen, cddet, elen, edet, cdedet);
- deterlen = fast_expansion_sum_zeroelim(ablen, abdet, cdelen, cdedet, deter);
-
- return deter[deterlen - 1];
-}
-
-REAL insphereslow(REAL *pa, REAL *pb, REAL *pc, REAL *pd, REAL *pe)
-{
- INEXACT REAL aex, bex, cex, dex, aey, bey, cey, dey, aez, bez, cez, dez;
- REAL aextail, bextail, cextail, dextail;
- REAL aeytail, beytail, ceytail, deytail;
- REAL aeztail, beztail, ceztail, deztail;
- REAL negate, negatetail;
- INEXACT REAL axby7, bxcy7, cxdy7, dxay7, axcy7, bxdy7;
- INEXACT REAL bxay7, cxby7, dxcy7, axdy7, cxay7, dxby7;
- REAL axby[8], bxcy[8], cxdy[8], dxay[8], axcy[8], bxdy[8];
- REAL bxay[8], cxby[8], dxcy[8], axdy[8], cxay[8], dxby[8];
- REAL ab[16], bc[16], cd[16], da[16], ac[16], bd[16];
- int ablen, bclen, cdlen, dalen, aclen, bdlen;
- REAL temp32a[32], temp32b[32], temp64a[64], temp64b[64], temp64c[64];
- int temp32alen, temp32blen, temp64alen, temp64blen, temp64clen;
- REAL temp128[128], temp192[192];
- int temp128len, temp192len;
- REAL detx[384], detxx[768], detxt[384], detxxt[768], detxtxt[768];
- int xlen, xxlen, xtlen, xxtlen, xtxtlen;
- REAL x1[1536], x2[2304];
- int x1len, x2len;
- REAL dety[384], detyy[768], detyt[384], detyyt[768], detytyt[768];
- int ylen, yylen, ytlen, yytlen, ytytlen;
- REAL y1[1536], y2[2304];
- int y1len, y2len;
- REAL detz[384], detzz[768], detzt[384], detzzt[768], detztzt[768];
- int zlen, zzlen, ztlen, zztlen, ztztlen;
- REAL z1[1536], z2[2304];
- int z1len, z2len;
- REAL detxy[4608];
- int xylen;
- REAL adet[6912], bdet[6912], cdet[6912], ddet[6912];
- int alen, blen, clen, dlen;
- REAL abdet[13824], cddet[13824], deter[27648];
- int deterlen;
- int i;
-
- INEXACT REAL bvirt;
- REAL avirt, bround, around;
- INEXACT REAL c;
- INEXACT REAL abig;
- REAL a0hi, a0lo, a1hi, a1lo, bhi, blo;
- REAL err1, err2, err3;
- INEXACT REAL _i, _j, _k, _l, _m, _n;
- REAL _0, _1, _2;
-
- Two_Diff(pa[0], pe[0], aex, aextail);
- Two_Diff(pa[1], pe[1], aey, aeytail);
- Two_Diff(pa[2], pe[2], aez, aeztail);
- Two_Diff(pb[0], pe[0], bex, bextail);
- Two_Diff(pb[1], pe[1], bey, beytail);
- Two_Diff(pb[2], pe[2], bez, beztail);
- Two_Diff(pc[0], pe[0], cex, cextail);
- Two_Diff(pc[1], pe[1], cey, ceytail);
- Two_Diff(pc[2], pe[2], cez, ceztail);
- Two_Diff(pd[0], pe[0], dex, dextail);
- Two_Diff(pd[1], pe[1], dey, deytail);
- Two_Diff(pd[2], pe[2], dez, deztail);
-
- Two_Two_Product(aex, aextail, bey, beytail,
- axby7, axby[6], axby[5], axby[4],
- axby[3], axby[2], axby[1], axby[0]);
- axby[7] = axby7;
- negate = -aey;
- negatetail = -aeytail;
- Two_Two_Product(bex, bextail, negate, negatetail,
- bxay7, bxay[6], bxay[5], bxay[4],
- bxay[3], bxay[2], bxay[1], bxay[0]);
- bxay[7] = bxay7;
- ablen = fast_expansion_sum_zeroelim(8, axby, 8, bxay, ab);
- Two_Two_Product(bex, bextail, cey, ceytail,
- bxcy7, bxcy[6], bxcy[5], bxcy[4],
- bxcy[3], bxcy[2], bxcy[1], bxcy[0]);
- bxcy[7] = bxcy7;
- negate = -bey;
- negatetail = -beytail;
- Two_Two_Product(cex, cextail, negate, negatetail,
- cxby7, cxby[6], cxby[5], cxby[4],
- cxby[3], cxby[2], cxby[1], cxby[0]);
- cxby[7] = cxby7;
- bclen = fast_expansion_sum_zeroelim(8, bxcy, 8, cxby, bc);
- Two_Two_Product(cex, cextail, dey, deytail,
- cxdy7, cxdy[6], cxdy[5], cxdy[4],
- cxdy[3], cxdy[2], cxdy[1], cxdy[0]);
- cxdy[7] = cxdy7;
- negate = -cey;
- negatetail = -ceytail;
- Two_Two_Product(dex, dextail, negate, negatetail,
- dxcy7, dxcy[6], dxcy[5], dxcy[4],
- dxcy[3], dxcy[2], dxcy[1], dxcy[0]);
- dxcy[7] = dxcy7;
- cdlen = fast_expansion_sum_zeroelim(8, cxdy, 8, dxcy, cd);
- Two_Two_Product(dex, dextail, aey, aeytail,
- dxay7, dxay[6], dxay[5], dxay[4],
- dxay[3], dxay[2], dxay[1], dxay[0]);
- dxay[7] = dxay7;
- negate = -dey;
- negatetail = -deytail;
- Two_Two_Product(aex, aextail, negate, negatetail,
- axdy7, axdy[6], axdy[5], axdy[4],
- axdy[3], axdy[2], axdy[1], axdy[0]);
- axdy[7] = axdy7;
- dalen = fast_expansion_sum_zeroelim(8, dxay, 8, axdy, da);
- Two_Two_Product(aex, aextail, cey, ceytail,
- axcy7, axcy[6], axcy[5], axcy[4],
- axcy[3], axcy[2], axcy[1], axcy[0]);
- axcy[7] = axcy7;
- negate = -aey;
- negatetail = -aeytail;
- Two_Two_Product(cex, cextail, negate, negatetail,
- cxay7, cxay[6], cxay[5], cxay[4],
- cxay[3], cxay[2], cxay[1], cxay[0]);
- cxay[7] = cxay7;
- aclen = fast_expansion_sum_zeroelim(8, axcy, 8, cxay, ac);
- Two_Two_Product(bex, bextail, dey, deytail,
- bxdy7, bxdy[6], bxdy[5], bxdy[4],
- bxdy[3], bxdy[2], bxdy[1], bxdy[0]);
- bxdy[7] = bxdy7;
- negate = -bey;
- negatetail = -beytail;
- Two_Two_Product(dex, dextail, negate, negatetail,
- dxby7, dxby[6], dxby[5], dxby[4],
- dxby[3], dxby[2], dxby[1], dxby[0]);
- dxby[7] = dxby7;
- bdlen = fast_expansion_sum_zeroelim(8, bxdy, 8, dxby, bd);
-
- temp32alen = scale_expansion_zeroelim(cdlen, cd, -bez, temp32a);
- temp32blen = scale_expansion_zeroelim(cdlen, cd, -beztail, temp32b);
- temp64alen = fast_expansion_sum_zeroelim(temp32alen, temp32a,
- temp32blen, temp32b, temp64a);
- temp32alen = scale_expansion_zeroelim(bdlen, bd, cez, temp32a);
- temp32blen = scale_expansion_zeroelim(bdlen, bd, ceztail, temp32b);
- temp64blen = fast_expansion_sum_zeroelim(temp32alen, temp32a,
- temp32blen, temp32b, temp64b);
- temp32alen = scale_expansion_zeroelim(bclen, bc, -dez, temp32a);
- temp32blen = scale_expansion_zeroelim(bclen, bc, -deztail, temp32b);
- temp64clen = fast_expansion_sum_zeroelim(temp32alen, temp32a,
- temp32blen, temp32b, temp64c);
- temp128len = fast_expansion_sum_zeroelim(temp64alen, temp64a,
- temp64blen, temp64b, temp128);
- temp192len = fast_expansion_sum_zeroelim(temp64clen, temp64c,
- temp128len, temp128, temp192);
- xlen = scale_expansion_zeroelim(temp192len, temp192, aex, detx);
- xxlen = scale_expansion_zeroelim(xlen, detx, aex, detxx);
- xtlen = scale_expansion_zeroelim(temp192len, temp192, aextail, detxt);
- xxtlen = scale_expansion_zeroelim(xtlen, detxt, aex, detxxt);
- for (i = 0; i < xxtlen; i++) {
- detxxt[i] *= 2.0;
- }
- xtxtlen = scale_expansion_zeroelim(xtlen, detxt, aextail, detxtxt);
- x1len = fast_expansion_sum_zeroelim(xxlen, detxx, xxtlen, detxxt, x1);
- x2len = fast_expansion_sum_zeroelim(x1len, x1, xtxtlen, detxtxt, x2);
- ylen = scale_expansion_zeroelim(temp192len, temp192, aey, dety);
- yylen = scale_expansion_zeroelim(ylen, dety, aey, detyy);
- ytlen = scale_expansion_zeroelim(temp192len, temp192, aeytail, detyt);
- yytlen = scale_expansion_zeroelim(ytlen, detyt, aey, detyyt);
- for (i = 0; i < yytlen; i++) {
- detyyt[i] *= 2.0;
- }
- ytytlen = scale_expansion_zeroelim(ytlen, detyt, aeytail, detytyt);
- y1len = fast_expansion_sum_zeroelim(yylen, detyy, yytlen, detyyt, y1);
- y2len = fast_expansion_sum_zeroelim(y1len, y1, ytytlen, detytyt, y2);
- zlen = scale_expansion_zeroelim(temp192len, temp192, aez, detz);
- zzlen = scale_expansion_zeroelim(zlen, detz, aez, detzz);
- ztlen = scale_expansion_zeroelim(temp192len, temp192, aeztail, detzt);
- zztlen = scale_expansion_zeroelim(ztlen, detzt, aez, detzzt);
- for (i = 0; i < zztlen; i++) {
- detzzt[i] *= 2.0;
- }
- ztztlen = scale_expansion_zeroelim(ztlen, detzt, aeztail, detztzt);
- z1len = fast_expansion_sum_zeroelim(zzlen, detzz, zztlen, detzzt, z1);
- z2len = fast_expansion_sum_zeroelim(z1len, z1, ztztlen, detztzt, z2);
- xylen = fast_expansion_sum_zeroelim(x2len, x2, y2len, y2, detxy);
- alen = fast_expansion_sum_zeroelim(z2len, z2, xylen, detxy, adet);
-
- temp32alen = scale_expansion_zeroelim(dalen, da, cez, temp32a);
- temp32blen = scale_expansion_zeroelim(dalen, da, ceztail, temp32b);
- temp64alen = fast_expansion_sum_zeroelim(temp32alen, temp32a,
- temp32blen, temp32b, temp64a);
- temp32alen = scale_expansion_zeroelim(aclen, ac, dez, temp32a);
- temp32blen = scale_expansion_zeroelim(aclen, ac, deztail, temp32b);
- temp64blen = fast_expansion_sum_zeroelim(temp32alen, temp32a,
- temp32blen, temp32b, temp64b);
- temp32alen = scale_expansion_zeroelim(cdlen, cd, aez, temp32a);
- temp32blen = scale_expansion_zeroelim(cdlen, cd, aeztail, temp32b);
- temp64clen = fast_expansion_sum_zeroelim(temp32alen, temp32a,
- temp32blen, temp32b, temp64c);
- temp128len = fast_expansion_sum_zeroelim(temp64alen, temp64a,
- temp64blen, temp64b, temp128);
- temp192len = fast_expansion_sum_zeroelim(temp64clen, temp64c,
- temp128len, temp128, temp192);
- xlen = scale_expansion_zeroelim(temp192len, temp192, bex, detx);
- xxlen = scale_expansion_zeroelim(xlen, detx, bex, detxx);
- xtlen = scale_expansion_zeroelim(temp192len, temp192, bextail, detxt);
- xxtlen = scale_expansion_zeroelim(xtlen, detxt, bex, detxxt);
- for (i = 0; i < xxtlen; i++) {
- detxxt[i] *= 2.0;
- }
- xtxtlen = scale_expansion_zeroelim(xtlen, detxt, bextail, detxtxt);
- x1len = fast_expansion_sum_zeroelim(xxlen, detxx, xxtlen, detxxt, x1);
- x2len = fast_expansion_sum_zeroelim(x1len, x1, xtxtlen, detxtxt, x2);
- ylen = scale_expansion_zeroelim(temp192len, temp192, bey, dety);
- yylen = scale_expansion_zeroelim(ylen, dety, bey, detyy);
- ytlen = scale_expansion_zeroelim(temp192len, temp192, beytail, detyt);
- yytlen = scale_expansion_zeroelim(ytlen, detyt, bey, detyyt);
- for (i = 0; i < yytlen; i++) {
- detyyt[i] *= 2.0;
- }
- ytytlen = scale_expansion_zeroelim(ytlen, detyt, beytail, detytyt);
- y1len = fast_expansion_sum_zeroelim(yylen, detyy, yytlen, detyyt, y1);
- y2len = fast_expansion_sum_zeroelim(y1len, y1, ytytlen, detytyt, y2);
- zlen = scale_expansion_zeroelim(temp192len, temp192, bez, detz);
- zzlen = scale_expansion_zeroelim(zlen, detz, bez, detzz);
- ztlen = scale_expansion_zeroelim(temp192len, temp192, beztail, detzt);
- zztlen = scale_expansion_zeroelim(ztlen, detzt, bez, detzzt);
- for (i = 0; i < zztlen; i++) {
- detzzt[i] *= 2.0;
- }
- ztztlen = scale_expansion_zeroelim(ztlen, detzt, beztail, detztzt);
- z1len = fast_expansion_sum_zeroelim(zzlen, detzz, zztlen, detzzt, z1);
- z2len = fast_expansion_sum_zeroelim(z1len, z1, ztztlen, detztzt, z2);
- xylen = fast_expansion_sum_zeroelim(x2len, x2, y2len, y2, detxy);
- blen = fast_expansion_sum_zeroelim(z2len, z2, xylen, detxy, bdet);
-
- temp32alen = scale_expansion_zeroelim(ablen, ab, -dez, temp32a);
- temp32blen = scale_expansion_zeroelim(ablen, ab, -deztail, temp32b);
- temp64alen = fast_expansion_sum_zeroelim(temp32alen, temp32a,
- temp32blen, temp32b, temp64a);
- temp32alen = scale_expansion_zeroelim(bdlen, bd, -aez, temp32a);
- temp32blen = scale_expansion_zeroelim(bdlen, bd, -aeztail, temp32b);
- temp64blen = fast_expansion_sum_zeroelim(temp32alen, temp32a,
- temp32blen, temp32b, temp64b);
- temp32alen = scale_expansion_zeroelim(dalen, da, -bez, temp32a);
- temp32blen = scale_expansion_zeroelim(dalen, da, -beztail, temp32b);
- temp64clen = fast_expansion_sum_zeroelim(temp32alen, temp32a,
- temp32blen, temp32b, temp64c);
- temp128len = fast_expansion_sum_zeroelim(temp64alen, temp64a,
- temp64blen, temp64b, temp128);
- temp192len = fast_expansion_sum_zeroelim(temp64clen, temp64c,
- temp128len, temp128, temp192);
- xlen = scale_expansion_zeroelim(temp192len, temp192, cex, detx);
- xxlen = scale_expansion_zeroelim(xlen, detx, cex, detxx);
- xtlen = scale_expansion_zeroelim(temp192len, temp192, cextail, detxt);
- xxtlen = scale_expansion_zeroelim(xtlen, detxt, cex, detxxt);
- for (i = 0; i < xxtlen; i++) {
- detxxt[i] *= 2.0;
- }
- xtxtlen = scale_expansion_zeroelim(xtlen, detxt, cextail, detxtxt);
- x1len = fast_expansion_sum_zeroelim(xxlen, detxx, xxtlen, detxxt, x1);
- x2len = fast_expansion_sum_zeroelim(x1len, x1, xtxtlen, detxtxt, x2);
- ylen = scale_expansion_zeroelim(temp192len, temp192, cey, dety);
- yylen = scale_expansion_zeroelim(ylen, dety, cey, detyy);
- ytlen = scale_expansion_zeroelim(temp192len, temp192, ceytail, detyt);
- yytlen = scale_expansion_zeroelim(ytlen, detyt, cey, detyyt);
- for (i = 0; i < yytlen; i++) {
- detyyt[i] *= 2.0;
- }
- ytytlen = scale_expansion_zeroelim(ytlen, detyt, ceytail, detytyt);
- y1len = fast_expansion_sum_zeroelim(yylen, detyy, yytlen, detyyt, y1);
- y2len = fast_expansion_sum_zeroelim(y1len, y1, ytytlen, detytyt, y2);
- zlen = scale_expansion_zeroelim(temp192len, temp192, cez, detz);
- zzlen = scale_expansion_zeroelim(zlen, detz, cez, detzz);
- ztlen = scale_expansion_zeroelim(temp192len, temp192, ceztail, detzt);
- zztlen = scale_expansion_zeroelim(ztlen, detzt, cez, detzzt);
- for (i = 0; i < zztlen; i++) {
- detzzt[i] *= 2.0;
- }
- ztztlen = scale_expansion_zeroelim(ztlen, detzt, ceztail, detztzt);
- z1len = fast_expansion_sum_zeroelim(zzlen, detzz, zztlen, detzzt, z1);
- z2len = fast_expansion_sum_zeroelim(z1len, z1, ztztlen, detztzt, z2);
- xylen = fast_expansion_sum_zeroelim(x2len, x2, y2len, y2, detxy);
- clen = fast_expansion_sum_zeroelim(z2len, z2, xylen, detxy, cdet);
-
- temp32alen = scale_expansion_zeroelim(bclen, bc, aez, temp32a);
- temp32blen = scale_expansion_zeroelim(bclen, bc, aeztail, temp32b);
- temp64alen = fast_expansion_sum_zeroelim(temp32alen, temp32a,
- temp32blen, temp32b, temp64a);
- temp32alen = scale_expansion_zeroelim(aclen, ac, -bez, temp32a);
- temp32blen = scale_expansion_zeroelim(aclen, ac, -beztail, temp32b);
- temp64blen = fast_expansion_sum_zeroelim(temp32alen, temp32a,
- temp32blen, temp32b, temp64b);
- temp32alen = scale_expansion_zeroelim(ablen, ab, cez, temp32a);
- temp32blen = scale_expansion_zeroelim(ablen, ab, ceztail, temp32b);
- temp64clen = fast_expansion_sum_zeroelim(temp32alen, temp32a,
- temp32blen, temp32b, temp64c);
- temp128len = fast_expansion_sum_zeroelim(temp64alen, temp64a,
- temp64blen, temp64b, temp128);
- temp192len = fast_expansion_sum_zeroelim(temp64clen, temp64c,
- temp128len, temp128, temp192);
- xlen = scale_expansion_zeroelim(temp192len, temp192, dex, detx);
- xxlen = scale_expansion_zeroelim(xlen, detx, dex, detxx);
- xtlen = scale_expansion_zeroelim(temp192len, temp192, dextail, detxt);
- xxtlen = scale_expansion_zeroelim(xtlen, detxt, dex, detxxt);
- for (i = 0; i < xxtlen; i++) {
- detxxt[i] *= 2.0;
- }
- xtxtlen = scale_expansion_zeroelim(xtlen, detxt, dextail, detxtxt);
- x1len = fast_expansion_sum_zeroelim(xxlen, detxx, xxtlen, detxxt, x1);
- x2len = fast_expansion_sum_zeroelim(x1len, x1, xtxtlen, detxtxt, x2);
- ylen = scale_expansion_zeroelim(temp192len, temp192, dey, dety);
- yylen = scale_expansion_zeroelim(ylen, dety, dey, detyy);
- ytlen = scale_expansion_zeroelim(temp192len, temp192, deytail, detyt);
- yytlen = scale_expansion_zeroelim(ytlen, detyt, dey, detyyt);
- for (i = 0; i < yytlen; i++) {
- detyyt[i] *= 2.0;
- }
- ytytlen = scale_expansion_zeroelim(ytlen, detyt, deytail, detytyt);
- y1len = fast_expansion_sum_zeroelim(yylen, detyy, yytlen, detyyt, y1);
- y2len = fast_expansion_sum_zeroelim(y1len, y1, ytytlen, detytyt, y2);
- zlen = scale_expansion_zeroelim(temp192len, temp192, dez, detz);
- zzlen = scale_expansion_zeroelim(zlen, detz, dez, detzz);
- ztlen = scale_expansion_zeroelim(temp192len, temp192, deztail, detzt);
- zztlen = scale_expansion_zeroelim(ztlen, detzt, dez, detzzt);
- for (i = 0; i < zztlen; i++) {
- detzzt[i] *= 2.0;
- }
- ztztlen = scale_expansion_zeroelim(ztlen, detzt, deztail, detztzt);
- z1len = fast_expansion_sum_zeroelim(zzlen, detzz, zztlen, detzzt, z1);
- z2len = fast_expansion_sum_zeroelim(z1len, z1, ztztlen, detztzt, z2);
- xylen = fast_expansion_sum_zeroelim(x2len, x2, y2len, y2, detxy);
- dlen = fast_expansion_sum_zeroelim(z2len, z2, xylen, detxy, ddet);
-
- ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
- cdlen = fast_expansion_sum_zeroelim(clen, cdet, dlen, ddet, cddet);
- deterlen = fast_expansion_sum_zeroelim(ablen, abdet, cdlen, cddet, deter);
-
- return deter[deterlen - 1];
-}
-
-REAL insphereadapt(REAL *pa, REAL *pb, REAL *pc, REAL *pd, REAL *pe,
- REAL permanent)
-{
- INEXACT REAL aex, bex, cex, dex, aey, bey, cey, dey, aez, bez, cez, dez;
- REAL det, errbound;
-
- INEXACT REAL aexbey1, bexaey1, bexcey1, cexbey1;
- INEXACT REAL cexdey1, dexcey1, dexaey1, aexdey1;
- INEXACT REAL aexcey1, cexaey1, bexdey1, dexbey1;
- REAL aexbey0, bexaey0, bexcey0, cexbey0;
- REAL cexdey0, dexcey0, dexaey0, aexdey0;
- REAL aexcey0, cexaey0, bexdey0, dexbey0;
- REAL ab[4], bc[4], cd[4], da[4], ac[4], bd[4];
- INEXACT REAL ab3, bc3, cd3, da3, ac3, bd3;
- REAL abeps, bceps, cdeps, daeps, aceps, bdeps;
- REAL temp8a[8], temp8b[8], temp8c[8], temp16[16], temp24[24], temp48[48];
- int temp8alen, temp8blen, temp8clen, temp16len, temp24len, temp48len;
- REAL xdet[96], ydet[96], zdet[96], xydet[192];
- int xlen, ylen, zlen, xylen;
- REAL adet[288], bdet[288], cdet[288], ddet[288];
- int alen, blen, clen, dlen;
- REAL abdet[576], cddet[576];
- int ablen, cdlen;
- REAL fin1[1152];
- int finlength;
-
- REAL aextail, bextail, cextail, dextail;
- REAL aeytail, beytail, ceytail, deytail;
- REAL aeztail, beztail, ceztail, deztail;
-
- INEXACT REAL bvirt;
- REAL avirt, bround, around;
- INEXACT REAL c;
- INEXACT REAL abig;
- REAL ahi, alo, bhi, blo;
- REAL err1, err2, err3;
- INEXACT REAL _i, _j;
- REAL _0;
-
- aex = (REAL) (pa[0] - pe[0]);
- bex = (REAL) (pb[0] - pe[0]);
- cex = (REAL) (pc[0] - pe[0]);
- dex = (REAL) (pd[0] - pe[0]);
- aey = (REAL) (pa[1] - pe[1]);
- bey = (REAL) (pb[1] - pe[1]);
- cey = (REAL) (pc[1] - pe[1]);
- dey = (REAL) (pd[1] - pe[1]);
- aez = (REAL) (pa[2] - pe[2]);
- bez = (REAL) (pb[2] - pe[2]);
- cez = (REAL) (pc[2] - pe[2]);
- dez = (REAL) (pd[2] - pe[2]);
-
- Two_Product(aex, bey, aexbey1, aexbey0);
- Two_Product(bex, aey, bexaey1, bexaey0);
- Two_Two_Diff(aexbey1, aexbey0, bexaey1, bexaey0, ab3, ab[2], ab[1], ab[0]);
- ab[3] = ab3;
-
- Two_Product(bex, cey, bexcey1, bexcey0);
- Two_Product(cex, bey, cexbey1, cexbey0);
- Two_Two_Diff(bexcey1, bexcey0, cexbey1, cexbey0, bc3, bc[2], bc[1], bc[0]);
- bc[3] = bc3;
-
- Two_Product(cex, dey, cexdey1, cexdey0);
- Two_Product(dex, cey, dexcey1, dexcey0);
- Two_Two_Diff(cexdey1, cexdey0, dexcey1, dexcey0, cd3, cd[2], cd[1], cd[0]);
- cd[3] = cd3;
-
- Two_Product(dex, aey, dexaey1, dexaey0);
- Two_Product(aex, dey, aexdey1, aexdey0);
- Two_Two_Diff(dexaey1, dexaey0, aexdey1, aexdey0, da3, da[2], da[1], da[0]);
- da[3] = da3;
-
- Two_Product(aex, cey, aexcey1, aexcey0);
- Two_Product(cex, aey, cexaey1, cexaey0);
- Two_Two_Diff(aexcey1, aexcey0, cexaey1, cexaey0, ac3, ac[2], ac[1], ac[0]);
- ac[3] = ac3;
-
- Two_Product(bex, dey, bexdey1, bexdey0);
- Two_Product(dex, bey, dexbey1, dexbey0);
- Two_Two_Diff(bexdey1, bexdey0, dexbey1, dexbey0, bd3, bd[2], bd[1], bd[0]);
- bd[3] = bd3;
-
- temp8alen = scale_expansion_zeroelim(4, cd, bez, temp8a);
- temp8blen = scale_expansion_zeroelim(4, bd, -cez, temp8b);
- temp8clen = scale_expansion_zeroelim(4, bc, dez, temp8c);
- temp16len = fast_expansion_sum_zeroelim(temp8alen, temp8a,
- temp8blen, temp8b, temp16);
- temp24len = fast_expansion_sum_zeroelim(temp8clen, temp8c,
- temp16len, temp16, temp24);
- temp48len = scale_expansion_zeroelim(temp24len, temp24, aex, temp48);
- xlen = scale_expansion_zeroelim(temp48len, temp48, -aex, xdet);
- temp48len = scale_expansion_zeroelim(temp24len, temp24, aey, temp48);
- ylen = scale_expansion_zeroelim(temp48len, temp48, -aey, ydet);
- temp48len = scale_expansion_zeroelim(temp24len, temp24, aez, temp48);
- zlen = scale_expansion_zeroelim(temp48len, temp48, -aez, zdet);
- xylen = fast_expansion_sum_zeroelim(xlen, xdet, ylen, ydet, xydet);
- alen = fast_expansion_sum_zeroelim(xylen, xydet, zlen, zdet, adet);
-
- temp8alen = scale_expansion_zeroelim(4, da, cez, temp8a);
- temp8blen = scale_expansion_zeroelim(4, ac, dez, temp8b);
- temp8clen = scale_expansion_zeroelim(4, cd, aez, temp8c);
- temp16len = fast_expansion_sum_zeroelim(temp8alen, temp8a,
- temp8blen, temp8b, temp16);
- temp24len = fast_expansion_sum_zeroelim(temp8clen, temp8c,
- temp16len, temp16, temp24);
- temp48len = scale_expansion_zeroelim(temp24len, temp24, bex, temp48);
- xlen = scale_expansion_zeroelim(temp48len, temp48, bex, xdet);
- temp48len = scale_expansion_zeroelim(temp24len, temp24, bey, temp48);
- ylen = scale_expansion_zeroelim(temp48len, temp48, bey, ydet);
- temp48len = scale_expansion_zeroelim(temp24len, temp24, bez, temp48);
- zlen = scale_expansion_zeroelim(temp48len, temp48, bez, zdet);
- xylen = fast_expansion_sum_zeroelim(xlen, xdet, ylen, ydet, xydet);
- blen = fast_expansion_sum_zeroelim(xylen, xydet, zlen, zdet, bdet);
-
- temp8alen = scale_expansion_zeroelim(4, ab, dez, temp8a);
- temp8blen = scale_expansion_zeroelim(4, bd, aez, temp8b);
- temp8clen = scale_expansion_zeroelim(4, da, bez, temp8c);
- temp16len = fast_expansion_sum_zeroelim(temp8alen, temp8a,
- temp8blen, temp8b, temp16);
- temp24len = fast_expansion_sum_zeroelim(temp8clen, temp8c,
- temp16len, temp16, temp24);
- temp48len = scale_expansion_zeroelim(temp24len, temp24, cex, temp48);
- xlen = scale_expansion_zeroelim(temp48len, temp48, -cex, xdet);
- temp48len = scale_expansion_zeroelim(temp24len, temp24, cey, temp48);
- ylen = scale_expansion_zeroelim(temp48len, temp48, -cey, ydet);
- temp48len = scale_expansion_zeroelim(temp24len, temp24, cez, temp48);
- zlen = scale_expansion_zeroelim(temp48len, temp48, -cez, zdet);
- xylen = fast_expansion_sum_zeroelim(xlen, xdet, ylen, ydet, xydet);
- clen = fast_expansion_sum_zeroelim(xylen, xydet, zlen, zdet, cdet);
-
- temp8alen = scale_expansion_zeroelim(4, bc, aez, temp8a);
- temp8blen = scale_expansion_zeroelim(4, ac, -bez, temp8b);
- temp8clen = scale_expansion_zeroelim(4, ab, cez, temp8c);
- temp16len = fast_expansion_sum_zeroelim(temp8alen, temp8a,
- temp8blen, temp8b, temp16);
- temp24len = fast_expansion_sum_zeroelim(temp8clen, temp8c,
- temp16len, temp16, temp24);
- temp48len = scale_expansion_zeroelim(temp24len, temp24, dex, temp48);
- xlen = scale_expansion_zeroelim(temp48len, temp48, dex, xdet);
- temp48len = scale_expansion_zeroelim(temp24len, temp24, dey, temp48);
- ylen = scale_expansion_zeroelim(temp48len, temp48, dey, ydet);
- temp48len = scale_expansion_zeroelim(temp24len, temp24, dez, temp48);
- zlen = scale_expansion_zeroelim(temp48len, temp48, dez, zdet);
- xylen = fast_expansion_sum_zeroelim(xlen, xdet, ylen, ydet, xydet);
- dlen = fast_expansion_sum_zeroelim(xylen, xydet, zlen, zdet, ddet);
-
- ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
- cdlen = fast_expansion_sum_zeroelim(clen, cdet, dlen, ddet, cddet);
- finlength = fast_expansion_sum_zeroelim(ablen, abdet, cdlen, cddet, fin1);
-
- det = estimate(finlength, fin1);
- errbound = isperrboundB * permanent;
- if ((det >= errbound) || (-det >= errbound)) {
- return det;
- }
-
- Two_Diff_Tail(pa[0], pe[0], aex, aextail);
- Two_Diff_Tail(pa[1], pe[1], aey, aeytail);
- Two_Diff_Tail(pa[2], pe[2], aez, aeztail);
- Two_Diff_Tail(pb[0], pe[0], bex, bextail);
- Two_Diff_Tail(pb[1], pe[1], bey, beytail);
- Two_Diff_Tail(pb[2], pe[2], bez, beztail);
- Two_Diff_Tail(pc[0], pe[0], cex, cextail);
- Two_Diff_Tail(pc[1], pe[1], cey, ceytail);
- Two_Diff_Tail(pc[2], pe[2], cez, ceztail);
- Two_Diff_Tail(pd[0], pe[0], dex, dextail);
- Two_Diff_Tail(pd[1], pe[1], dey, deytail);
- Two_Diff_Tail(pd[2], pe[2], dez, deztail);
- if ((aextail == 0.0) && (aeytail == 0.0) && (aeztail == 0.0)
- && (bextail == 0.0) && (beytail == 0.0) && (beztail == 0.0)
- && (cextail == 0.0) && (ceytail == 0.0) && (ceztail == 0.0)
- && (dextail == 0.0) && (deytail == 0.0) && (deztail == 0.0)) {
- return det;
- }
-
- errbound = isperrboundC * permanent + resulterrbound * Absolute(det);
- abeps = (aex * beytail + bey * aextail)
- - (aey * bextail + bex * aeytail);
- bceps = (bex * ceytail + cey * bextail)
- - (bey * cextail + cex * beytail);
- cdeps = (cex * deytail + dey * cextail)
- - (cey * dextail + dex * ceytail);
- daeps = (dex * aeytail + aey * dextail)
- - (dey * aextail + aex * deytail);
- aceps = (aex * ceytail + cey * aextail)
- - (aey * cextail + cex * aeytail);
- bdeps = (bex * deytail + dey * bextail)
- - (bey * dextail + dex * beytail);
- det += (((bex * bex + bey * bey + bez * bez)
- * ((cez * daeps + dez * aceps + aez * cdeps)
- + (ceztail * da3 + deztail * ac3 + aeztail * cd3))
- + (dex * dex + dey * dey + dez * dez)
- * ((aez * bceps - bez * aceps + cez * abeps)
- + (aeztail * bc3 - beztail * ac3 + ceztail * ab3)))
- - ((aex * aex + aey * aey + aez * aez)
- * ((bez * cdeps - cez * bdeps + dez * bceps)
- + (beztail * cd3 - ceztail * bd3 + deztail * bc3))
- + (cex * cex + cey * cey + cez * cez)
- * ((dez * abeps + aez * bdeps + bez * daeps)
- + (deztail * ab3 + aeztail * bd3 + beztail * da3))))
- + 2.0 * (((bex * bextail + bey * beytail + bez * beztail)
- * (cez * da3 + dez * ac3 + aez * cd3)
- + (dex * dextail + dey * deytail + dez * deztail)
- * (aez * bc3 - bez * ac3 + cez * ab3))
- - ((aex * aextail + aey * aeytail + aez * aeztail)
- * (bez * cd3 - cez * bd3 + dez * bc3)
- + (cex * cextail + cey * ceytail + cez * ceztail)
- * (dez * ab3 + aez * bd3 + bez * da3)));
- if ((det >= errbound) || (-det >= errbound)) {
- return det;
- }
-
- return insphereexact(pa, pb, pc, pd, pe);
-}
-
-REAL insphere(REAL *pa, REAL *pb, REAL *pc, REAL *pd, REAL *pe)
-{
- REAL aex, bex, cex, dex;
- REAL aey, bey, cey, dey;
- REAL aez, bez, cez, dez;
- REAL aexbey, bexaey, bexcey, cexbey, cexdey, dexcey, dexaey, aexdey;
- REAL aexcey, cexaey, bexdey, dexbey;
- REAL alift, blift, clift, dlift;
- REAL ab, bc, cd, da, ac, bd;
- REAL abc, bcd, cda, dab;
- REAL aezplus, bezplus, cezplus, dezplus;
- REAL aexbeyplus, bexaeyplus, bexceyplus, cexbeyplus;
- REAL cexdeyplus, dexceyplus, dexaeyplus, aexdeyplus;
- REAL aexceyplus, cexaeyplus, bexdeyplus, dexbeyplus;
- REAL det;
- REAL permanent, errbound;
-
- aex = pa[0] - pe[0];
- bex = pb[0] - pe[0];
- cex = pc[0] - pe[0];
- dex = pd[0] - pe[0];
- aey = pa[1] - pe[1];
- bey = pb[1] - pe[1];
- cey = pc[1] - pe[1];
- dey = pd[1] - pe[1];
- aez = pa[2] - pe[2];
- bez = pb[2] - pe[2];
- cez = pc[2] - pe[2];
- dez = pd[2] - pe[2];
-
- aexbey = aex * bey;
- bexaey = bex * aey;
- ab = aexbey - bexaey;
- bexcey = bex * cey;
- cexbey = cex * bey;
- bc = bexcey - cexbey;
- cexdey = cex * dey;
- dexcey = dex * cey;
- cd = cexdey - dexcey;
- dexaey = dex * aey;
- aexdey = aex * dey;
- da = dexaey - aexdey;
-
- aexcey = aex * cey;
- cexaey = cex * aey;
- ac = aexcey - cexaey;
- bexdey = bex * dey;
- dexbey = dex * bey;
- bd = bexdey - dexbey;
-
- abc = aez * bc - bez * ac + cez * ab;
- bcd = bez * cd - cez * bd + dez * bc;
- cda = cez * da + dez * ac + aez * cd;
- dab = dez * ab + aez * bd + bez * da;
-
- alift = aex * aex + aey * aey + aez * aez;
- blift = bex * bex + bey * bey + bez * bez;
- clift = cex * cex + cey * cey + cez * cez;
- dlift = dex * dex + dey * dey + dez * dez;
-
- det = (dlift * abc - clift * dab) + (blift * cda - alift * bcd);
-
- aezplus = Absolute(aez);
- bezplus = Absolute(bez);
- cezplus = Absolute(cez);
- dezplus = Absolute(dez);
- aexbeyplus = Absolute(aexbey);
- bexaeyplus = Absolute(bexaey);
- bexceyplus = Absolute(bexcey);
- cexbeyplus = Absolute(cexbey);
- cexdeyplus = Absolute(cexdey);
- dexceyplus = Absolute(dexcey);
- dexaeyplus = Absolute(dexaey);
- aexdeyplus = Absolute(aexdey);
- aexceyplus = Absolute(aexcey);
- cexaeyplus = Absolute(cexaey);
- bexdeyplus = Absolute(bexdey);
- dexbeyplus = Absolute(dexbey);
- permanent = ((cexdeyplus + dexceyplus) * bezplus
- + (dexbeyplus + bexdeyplus) * cezplus
- + (bexceyplus + cexbeyplus) * dezplus)
- * alift
- + ((dexaeyplus + aexdeyplus) * cezplus
- + (aexceyplus + cexaeyplus) * dezplus
- + (cexdeyplus + dexceyplus) * aezplus)
- * blift
- + ((aexbeyplus + bexaeyplus) * dezplus
- + (bexdeyplus + dexbeyplus) * aezplus
- + (dexaeyplus + aexdeyplus) * bezplus)
- * clift
- + ((bexceyplus + cexbeyplus) * aezplus
- + (cexaeyplus + aexceyplus) * bezplus
- + (aexbeyplus + bexaeyplus) * cezplus)
- * dlift;
- errbound = isperrboundA * permanent;
- if ((det > errbound) || (-det > errbound)) {
- return det;
- }
-
- return insphereadapt(pa, pb, pc, pd, pe, permanent);
-}
diff --git a/contrib/Tetgen1.4/tetgen.cxx b/contrib/Tetgen1.4/tetgen.cxx
deleted file mode 100644
index cd74509640b9c660d4692e5e2ee91432bede203a..0000000000000000000000000000000000000000
--- a/contrib/Tetgen1.4/tetgen.cxx
+++ /dev/null
@@ -1,35006 +0,0 @@
-///////////////////////////////////////////////////////////////////////////////
-// //
-// TetGen //
-// //
-// A Quality Tetrahedral Mesh Generator and 3D Delaunay Triangulator //
-// //
-// Version 1.4 //
-// April 16, 2007 //
-// //
-// Copyright (C) 2002--2007 //
-// Hang Si //
-// Research Group Numerical Mathematics and Scientific Computing //
-// Weierstrass Institute for Applied Analysis and Stochastics //
-// Mohrenstr. 39, 10117 Berlin, Germany //
-// si@wias-berlin.de //
-// //
-// TetGen is freely available through the website: http://tetgen.berlios.de. //
-// It may be copied, modified, and redistributed for non-commercial use. //
-// Please consult the file LICENSE for the detailed copyright notices. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// tetgen.cxx //
-// //
-// The TetGen library and program. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-#include "tetgen.h"
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// terminatetetgen() Terminate TetGen with a given exit code. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void terminatetetgen(int x)
-{
-#ifdef TETLIBRARY
- throw x;
-#else
- exit(x);
-#endif // #ifdef TETLIBRARY
-}
-
-//
-// Begin of class 'tetgenio' implementation
-//
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// initialize() Initialize all variables of 'tetgenio'. //
-// //
-// It is called by the only class constructor 'tetgenio()' implicitly. Thus, //
-// all variables are guaranteed to be initialized. Each array is initialized //
-// to be a 'NULL' pointer, and its length is equal zero. Some variables have //
-// their default value, 'firstnumber' equals zero, 'mesh_dim' equals 3, and //
-// 'numberofcorners' equals 4. Another possible use of this routine is to //
-// call it before to re-use an object. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenio::initialize()
-{
- firstnumber = 0; // Default item index is numbered from Zero.
- mesh_dim = 3; // Default mesh dimension is 3.
- useindex = true;
-
- pointlist = (REAL *) NULL;
- pointattributelist = (REAL *) NULL;
- pointmtrlist = (REAL *) NULL;
- pointmarkerlist = (int *) NULL;
- numberofpoints = 0;
- numberofpointattributes = 0;
- numberofpointmtrs = 0;
-
- tetrahedronlist = (int *) NULL;
- tetrahedronattributelist = (REAL *) NULL;
- tetrahedronvolumelist = (REAL *) NULL;
- neighborlist = (int *) NULL;
- numberoftetrahedra = 0;
- numberofcorners = 4; // Default is 4 nodes per element.
- numberoftetrahedronattributes = 0;
-
- trifacelist = (int *) NULL;
- adjtetlist = (int *) NULL;
- trifacemarkerlist = (int *) NULL;
- numberoftrifaces = 0;
-
- facetlist = (facet *) NULL;
- facetmarkerlist = (int *) NULL;
- numberoffacets = 0;
-
- edgelist = (int *) NULL;
- edgemarkerlist = (int *) NULL;
- numberofedges = 0;
-
- holelist = (REAL *) NULL;
- numberofholes = 0;
-
- regionlist = (REAL *) NULL;
- numberofregions = 0;
-
- facetconstraintlist = (REAL *) NULL;
- numberoffacetconstraints = 0;
- segmentconstraintlist = (REAL *) NULL;
- numberofsegmentconstraints = 0;
-
- pbcgrouplist = (pbcgroup *) NULL;
- numberofpbcgroups = 0;
-
- vpointlist = (REAL *) NULL;
- vedgelist = (voroedge *) NULL;
- vfacetlist = (vorofacet *) NULL;
- vcelllist = (int **) NULL;
- numberofvpoints = 0;
- numberofvedges = 0;
- numberofvfacets = 0;
- numberofvcells = 0;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// deinitialize() Free the memory allocated in 'tetgenio'. //
-// //
-// It is called by the class destructor '~tetgenio()' implicitly. Hence, the //
-// occupied memory by arrays of an object will be automatically released on //
-// the deletion of the object. However, this routine assumes that the memory //
-// is allocated by C++ memory allocation operator 'new', thus it is freed by //
-// the C++ array deletor 'delete []'. If one uses the C/C++ library function //
-// 'malloc()' to allocate memory for arrays, one has to free them with the //
-// 'free()' function, and call routine 'initialize()' once to disable this //
-// routine on deletion of the object. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenio::deinitialize()
-{
- facet *f;
- polygon *p;
- pbcgroup *pg;
- int i, j;
-
- if (pointlist != (REAL *) NULL) {
- delete [] pointlist;
- }
- if (pointattributelist != (REAL *) NULL) {
- delete [] pointattributelist;
- }
- if (pointmtrlist != (REAL *) NULL) {
- delete [] pointmtrlist;
- }
- if (pointmarkerlist != (int *) NULL) {
- delete [] pointmarkerlist;
- }
-
- if (tetrahedronlist != (int *) NULL) {
- delete [] tetrahedronlist;
- }
- if (tetrahedronattributelist != (REAL *) NULL) {
- delete [] tetrahedronattributelist;
- }
- if (tetrahedronvolumelist != (REAL *) NULL) {
- delete [] tetrahedronvolumelist;
- }
- if (neighborlist != (int *) NULL) {
- delete [] neighborlist;
- }
-
- if (trifacelist != (int *) NULL) {
- delete [] trifacelist;
- }
- if (adjtetlist != (int *) NULL) {
- delete [] adjtetlist;
- }
- if (trifacemarkerlist != (int *) NULL) {
- delete [] trifacemarkerlist;
- }
-
- if (edgelist != (int *) NULL) {
- delete [] edgelist;
- }
- if (edgemarkerlist != (int *) NULL) {
- delete [] edgemarkerlist;
- }
-
- if (facetlist != (facet *) NULL) {
- for (i = 0; i < numberoffacets; i++) {
- f = &facetlist[i];
- for (j = 0; j < f->numberofpolygons; j++) {
- p = &f->polygonlist[j];
- delete [] p->vertexlist;
- }
- delete [] f->polygonlist;
- if (f->holelist != (REAL *) NULL) {
- delete [] f->holelist;
- }
- }
- delete [] facetlist;
- }
- if (facetmarkerlist != (int *) NULL) {
- delete [] facetmarkerlist;
- }
-
- if (holelist != (REAL *) NULL) {
- delete [] holelist;
- }
- if (regionlist != (REAL *) NULL) {
- delete [] regionlist;
- }
- if (facetconstraintlist != (REAL *) NULL) {
- delete [] facetconstraintlist;
- }
- if (segmentconstraintlist != (REAL *) NULL) {
- delete [] segmentconstraintlist;
- }
- if (pbcgrouplist != (pbcgroup *) NULL) {
- for (i = 0; i < numberofpbcgroups; i++) {
- pg = &(pbcgrouplist[i]);
- if (pg->pointpairlist != (int *) NULL) {
- delete [] pg->pointpairlist;
- }
- }
- delete [] pbcgrouplist;
- }
- if (vpointlist != (REAL *) NULL) {
- delete [] vpointlist;
- }
- if (vedgelist != (voroedge *) NULL) {
- delete [] vedgelist;
- }
- if (vfacetlist != (vorofacet *) NULL) {
- for (i = 0; i < numberofvfacets; i++) {
- delete [] vfacetlist[i].elist;
- }
- delete [] vfacetlist;
- }
- if (vcelllist != (int **) NULL) {
- for (i = 0; i < numberofvcells; i++) {
- delete [] vcelllist[i];
- }
- delete [] vcelllist;
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// load_node_call() Load a list of nodes. //
-// //
-// It is a support routine for routines: 'load_nodes()', 'load_poly()', and //
-// 'load_tetmesh()'. 'infile' is the file handle contains the node list. It //
-// may point to a .node, or .poly or .smesh file. 'markers' indicates each //
-// node contains an additional marker (integer) or not. 'infilename' is the //
-// name of the file being read, it is only appeared in error message. //
-// //
-// The 'firstnumber' (0 or 1) is automatically determined by the number of //
-// the first index of the first point. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenio::load_node_call(FILE* infile, int markers, char* infilename)
-{
- char inputline[INPUTLINESIZE];
- char *stringptr;
- REAL x, y, z, attrib;
- int firstnode, currentmarker;
- int index, attribindex;
- int i, j;
-
- // Initialize 'pointlist', 'pointattributelist', and 'pointmarkerlist'.
- pointlist = new REAL[numberofpoints * 3];
- if (pointlist == (REAL *) NULL) {
- printf("Error: Out of memory.\n");
- terminatetetgen(1);
- }
- if (numberofpointattributes > 0) {
- pointattributelist = new REAL[numberofpoints * numberofpointattributes];
- if (pointattributelist == (REAL *) NULL) {
- printf("Error: Out of memory.\n");
- terminatetetgen(1);
- }
- }
- if (markers) {
- pointmarkerlist = new int[numberofpoints];
- if (pointmarkerlist == (int *) NULL) {
- printf("Error: Out of memory.\n");
- terminatetetgen(1);
- }
- }
-
- // Read the point section.
- index = 0;
- attribindex = 0;
- for (i = 0; i < numberofpoints; i++) {
- stringptr = readnumberline(inputline, infile, infilename);
- if (useindex) {
- if (i == 0) {
- firstnode = (int) strtol (stringptr, &stringptr, 0);
- if ((firstnode == 0) || (firstnode == 1)) {
- firstnumber = firstnode;
- }
- }
- stringptr = findnextnumber(stringptr);
- } // if (useindex)
- if (*stringptr == '\0') {
- printf("Error: Point %d has no x coordinate.\n", firstnumber + i);
- break;
- }
- x = (REAL) strtod(stringptr, &stringptr);
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- printf("Error: Point %d has no y coordinate.\n", firstnumber + i);
- break;
- }
- y = (REAL) strtod(stringptr, &stringptr);
- if (mesh_dim == 3) {
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- printf("Error: Point %d has no z coordinate.\n", firstnumber + i);
- break;
- }
- z = (REAL) strtod(stringptr, &stringptr);
- } else {
- z = 0.0; // mesh_dim == 2;
- }
- pointlist[index++] = x;
- pointlist[index++] = y;
- pointlist[index++] = z;
- // Read the point attributes.
- for (j = 0; j < numberofpointattributes; j++) {
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- attrib = 0.0;
- } else {
- attrib = (REAL) strtod(stringptr, &stringptr);
- }
- pointattributelist[attribindex++] = attrib;
- }
- if (markers) {
- // Read a point marker.
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- currentmarker = 0;
- } else {
- currentmarker = (int) strtol (stringptr, &stringptr, 0);
- }
- pointmarkerlist[i] = currentmarker;
- }
- }
- if (i < numberofpoints) {
- // Failed to read points due to some error.
- delete [] pointlist;
- pointlist = (REAL *) NULL;
- if (markers) {
- delete [] pointmarkerlist;
- pointmarkerlist = (int *) NULL;
- }
- if (numberofpointattributes > 0) {
- delete [] pointattributelist;
- pointattributelist = (REAL *) NULL;
- }
- numberofpoints = 0;
- return false;
- }
- return true;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// load_node() Load a list of nodes from a .node file. //
-// //
-// 'filename' is the inputfile without suffix. The node list is in 'filename.//
-// node'. On completion, the node list is returned in 'pointlist'. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenio::load_node(char* filename)
-{
- FILE *infile;
- char innodefilename[FILENAMESIZE];
- char inputline[INPUTLINESIZE];
- char *stringptr;
- int markers;
-
- // Assembling the actual file names we want to open.
- strcpy(innodefilename, filename);
- strcat(innodefilename, ".node");
-
- // Try to open a .node file.
- infile = fopen(innodefilename, "r");
- if (infile == (FILE *) NULL) {
- printf("File I/O Error: Cannot access file %s.\n", innodefilename);
- return false;
- }
- printf("Opening %s.\n", innodefilename);
- // Read the first line of the file.
- stringptr = readnumberline(inputline, infile, innodefilename);
- // Is this list of points generated from rbox?
- stringptr = strstr(inputline, "rbox");
- if (stringptr == NULL) {
- // Read number of points, number of dimensions, number of point
- // attributes, and number of boundary markers.
- stringptr = inputline;
- numberofpoints = (int) strtol (stringptr, &stringptr, 0);
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- mesh_dim = 3;
- } else {
- mesh_dim = (int) strtol (stringptr, &stringptr, 0);
- }
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- numberofpointattributes = 0;
- } else {
- numberofpointattributes = (int) strtol (stringptr, &stringptr, 0);
- }
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- markers = 0;
- } else {
- markers = (int) strtol (stringptr, &stringptr, 0);
- }
- } else {
- // It is a rbox (qhull) input file.
- stringptr = inputline;
- // Get the dimension.
- mesh_dim = (int) strtol (stringptr, &stringptr, 0);
- // Get the number of points.
- stringptr = readnumberline(inputline, infile, innodefilename);
- numberofpoints = (int) strtol (stringptr, &stringptr, 0);
- // There is no index column.
- useindex = 0;
- }
-
- // if ((mesh_dim != 3) && (mesh_dim != 2)) {
- // printf("Input error: TetGen only works for 2D & 3D point sets.\n");
- // fclose(infile);
- // return false;
- // }
- if (numberofpoints < (mesh_dim + 1)) {
- printf("Input error: TetGen needs at least %d points.\n", mesh_dim + 1);
- fclose(infile);
- return false;
- }
-
- // Load the list of nodes.
- if (!load_node_call(infile, markers, innodefilename)) {
- fclose(infile);
- return false;
- }
- fclose(infile);
- return true;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// load_pbc() Load a list of pbc groups into 'pbcgrouplist'. //
-// //
-// 'filename' is the filename of the original inputfile without suffix. The //
-// pbc groups are found in file 'filename.pbc'. //
-// //
-// This routine will be called both in load_poly() and load_tetmesh(). //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenio::load_pbc(char* filename)
-{
- FILE *infile;
- char pbcfilename[FILENAMESIZE];
- char inputline[INPUTLINESIZE];
- char *stringptr;
- pbcgroup *pg;
- int index, p1, p2;
- int i, j, k;
-
- // Pbc groups are saved in file "filename.pbc".
- strcpy(pbcfilename, filename);
- strcat(pbcfilename, ".pbc");
- infile = fopen(pbcfilename, "r");
- if (infile != (FILE *) NULL) {
- printf("Opening %s.\n", pbcfilename);
- } else {
- // No such file. Return.
- return false;
- }
-
- // Read the number of pbc groups.
- stringptr = readnumberline(inputline, infile, pbcfilename);
- numberofpbcgroups = (int) strtol (stringptr, &stringptr, 0);
- if (numberofpbcgroups == 0) {
- // It looks this file contains no point.
- fclose(infile);
- return false;
- }
- // Initialize 'pbcgrouplist';
- pbcgrouplist = new pbcgroup[numberofpbcgroups];
-
- // Read the list of pbc groups.
- for (i = 0; i < numberofpbcgroups; i++) {
- pg = &(pbcgrouplist[i]);
- // Initialize pbcgroup i;
- pg->numberofpointpairs = 0;
- pg->pointpairlist = (int *) NULL;
- // Read 'fmark1', 'fmark2'.
- stringptr = readnumberline(inputline, infile, pbcfilename);
- if (*stringptr == '\0') break;
- pg->fmark1 = (int) strtol(stringptr, &stringptr, 0);
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') break;
- pg->fmark2 = (int) strtol(stringptr, &stringptr, 0);
- // Read 'transmat'.
- do {
- stringptr = readline(inputline, infile, NULL);
- } while ((*stringptr != '[') && (*stringptr != '\0'));
- if (*stringptr == '\0') break;
- for (j = 0; j < 4; j++) {
- for (k = 0; k < 4; k++) {
- // Read the entry of [j, k].
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- // Try to read another line.
- stringptr = readnumberline(inputline, infile, pbcfilename);
- if (*stringptr == '\0') break;
- }
- pg->transmat[j][k] = (REAL) strtod(stringptr, &stringptr);
- }
- if (k < 4) break; // Not complete!
- }
- if (j < 4) break; // Not complete!
- // Read 'numberofpointpairs'.
- stringptr = readnumberline(inputline, infile, pbcfilename);
- if (*stringptr == '\0') break;
- pg->numberofpointpairs = (int) strtol(stringptr, &stringptr, 0);
- if (pg->numberofpointpairs > 0) {
- pg->pointpairlist = new int[pg->numberofpointpairs * 2];
- // Read the point pairs.
- index = 0;
- for (j = 0; j < pg->numberofpointpairs; j++) {
- stringptr = readnumberline(inputline, infile, pbcfilename);
- p1 = (int) strtol(stringptr, &stringptr, 0);
- stringptr = findnextnumber(stringptr);
- p2 = (int) strtol(stringptr, &stringptr, 0);
- pg->pointpairlist[index++] = p1;
- pg->pointpairlist[index++] = p2;
- }
- }
- }
- fclose(infile);
-
- if (i < numberofpbcgroups) {
- // Failed to read to additional points due to some error.
- delete [] pbcgrouplist;
- pbcgrouplist = (pbcgroup *) NULL;
- numberofpbcgroups = 0;
- return false;
- }
- return true;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// load_var() Load variant constraints applied on facets, segments, nodes.//
-// //
-// 'filename' is the filename of the original inputfile without suffix. The //
-// constraints are found in file 'filename.var'. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenio::load_var(char* filename)
-{
- FILE *infile;
- char varfilename[FILENAMESIZE];
- char inputline[INPUTLINESIZE];
- char *stringptr;
- int index;
- int i;
-
- // Variant constraints are saved in file "filename.var".
- strcpy(varfilename, filename);
- strcat(varfilename, ".var");
- infile = fopen(varfilename, "r");
- if (infile != (FILE *) NULL) {
- printf("Opening %s.\n", varfilename);
- } else {
- // No such file. Return.
- return false;
- }
-
- // Read the facet constraint section.
- stringptr = readnumberline(inputline, infile, varfilename);
- if (*stringptr != '\0') {
- numberoffacetconstraints = (int) strtol (stringptr, &stringptr, 0);
- } else {
- numberoffacetconstraints = 0;
- }
- if (numberoffacetconstraints > 0) {
- // Initialize 'facetconstraintlist'.
- facetconstraintlist = new REAL[numberoffacetconstraints * 2];
- index = 0;
- for (i = 0; i < numberoffacetconstraints; i++) {
- stringptr = readnumberline(inputline, infile, varfilename);
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- printf("Error: facet constraint %d has no facet marker.\n",
- firstnumber + i);
- break;
- } else {
- facetconstraintlist[index++] = (REAL) strtod(stringptr, &stringptr);
- }
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- printf("Error: facet constraint %d has no maximum area bound.\n",
- firstnumber + i);
- break;
- } else {
- facetconstraintlist[index++] = (REAL) strtod(stringptr, &stringptr);
- }
- }
- if (i < numberoffacetconstraints) {
- // This must be caused by an error.
- fclose(infile);
- return false;
- }
- }
-
- // Read the segment constraint section.
- stringptr = readnumberline(inputline, infile, varfilename);
- if (*stringptr != '\0') {
- numberofsegmentconstraints = (int) strtol (stringptr, &stringptr, 0);
- } else {
- numberofsegmentconstraints = 0;
- }
- if (numberofsegmentconstraints > 0) {
- // Initialize 'segmentconstraintlist'.
- segmentconstraintlist = new REAL[numberofsegmentconstraints * 3];
- index = 0;
- for (i = 0; i < numberofsegmentconstraints; i++) {
- stringptr = readnumberline(inputline, infile, varfilename);
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- printf("Error: segment constraint %d has no frist endpoint.\n",
- firstnumber + i);
- break;
- } else {
- segmentconstraintlist[index++] = (REAL) strtod(stringptr, &stringptr);
- }
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- printf("Error: segment constraint %d has no second endpoint.\n",
- firstnumber + i);
- break;
- } else {
- segmentconstraintlist[index++] = (REAL) strtod(stringptr, &stringptr);
- }
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- printf("Error: segment constraint %d has no maximum length bound.\n",
- firstnumber + i);
- break;
- } else {
- segmentconstraintlist[index++] = (REAL) strtod(stringptr, &stringptr);
- }
- }
- if (i < numberofsegmentconstraints) {
- // This must be caused by an error.
- fclose(infile);
- return false;
- }
- }
-
- fclose(infile);
- return true;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// load_mtr() Load a size specification map from file. //
-// //
-// 'filename' is the filename of the original inputfile without suffix. The //
-// size map is found in file 'filename.mtr'. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenio::load_mtr(char* filename)
-{
- FILE *infile;
- char mtrfilename[FILENAMESIZE];
- char inputline[INPUTLINESIZE];
- char *stringptr;
- REAL mtr;
- int mtrindex;
- int i, j;
-
- strcpy(mtrfilename, filename);
- strcat(mtrfilename, ".mtr");
- infile = fopen(mtrfilename, "r");
- if (infile != (FILE *) NULL) {
- printf("Opening %s.\n", mtrfilename);
- } else {
- // No such file. Return.
- return false;
- }
-
- // Read number of points, number of columns (1, 3, or 6).
- stringptr = readnumberline(inputline, infile, mtrfilename);
- stringptr = findnextnumber(stringptr); // Skip number of points.
- if (*stringptr != '\0') {
- numberofpointmtrs = (int) strtol (stringptr, &stringptr, 0);
- }
- if (numberofpointmtrs == 0) {
- // Column number doesn't match. Set a default number (1).
- numberofpointmtrs = 1;
- }
-
- // Allocate space for pointmtrlist.
- pointmtrlist = new REAL[numberofpoints * numberofpointmtrs];
- if (pointmtrlist == (REAL *) NULL) {
- printf("Error: Out of memory.\n");
- terminatetetgen(1);
- }
- mtrindex = 0;
- for (i = 0; i < numberofpoints; i++) {
- // Read metrics.
- stringptr = readnumberline(inputline, infile, mtrfilename);
- for (j = 0; j < numberofpointmtrs; j++) {
- if (*stringptr == '\0') {
- printf("Error: Metric %d is missing value #%d in %s.\n",
- i + firstnumber, j + 1, mtrfilename);
- terminatetetgen(1);
- }
- mtr = (REAL) strtod(stringptr, &stringptr);
- pointmtrlist[mtrindex++] = mtr;
- stringptr = findnextnumber(stringptr);
- }
- }
-
- fclose(infile);
- return true;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// load_poly() Load a piecewise linear complex from a .poly or .smesh. //
-// //
-// 'filename' is the inputfile without suffix. The PLC is in 'filename.poly' //
-// or 'filename.smesh', and possibly plus 'filename.node' (when the first //
-// line of the file starts with a zero). //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenio::load_poly(char* filename)
-{
- FILE *infile, *polyfile;
- char innodefilename[FILENAMESIZE];
- char inpolyfilename[FILENAMESIZE];
- char insmeshfilename[FILENAMESIZE];
- char inputline[INPUTLINESIZE];
- char *stringptr, *infilename;
- int smesh, markers, currentmarker;
- int readnodefile, index;
- int i, j, k;
-
- // Assembling the actual file names we want to open.
- strcpy(innodefilename, filename);
- strcpy(inpolyfilename, filename);
- strcpy(insmeshfilename, filename);
- strcat(innodefilename, ".node");
- strcat(inpolyfilename, ".poly");
- strcat(insmeshfilename, ".smesh");
-
- // First assume it is a .poly file.
- smesh = 0;
- // Try to open a .poly file.
- polyfile = fopen(inpolyfilename, "r");
- if (polyfile == (FILE *) NULL) {
- // .poly doesn't exist! Try to open a .smesh file.
- polyfile = fopen(insmeshfilename, "r");
- if (polyfile == (FILE *) NULL) {
- printf("File I/O Error: Cannot access file %s and %s.\n",
- inpolyfilename, insmeshfilename);
- return false;
- } else {
- printf("Opening %s.\n", insmeshfilename);
- }
- smesh = 1;
- } else {
- printf("Opening %s.\n", inpolyfilename);
- }
- // Initialize the default values.
- mesh_dim = 3; // Three-dimemsional accoordinates.
- numberofpointattributes = 0; // no point attribute.
- markers = 0; // no boundary marker.
- // Read number of points, number of dimensions, number of point
- // attributes, and number of boundary markers.
- stringptr = readnumberline(inputline, polyfile, inpolyfilename);
- numberofpoints = (int) strtol (stringptr, &stringptr, 0);
- stringptr = findnextnumber(stringptr);
- if (*stringptr != '\0') {
- mesh_dim = (int) strtol (stringptr, &stringptr, 0);
- }
- stringptr = findnextnumber(stringptr);
- if (*stringptr != '\0') {
- numberofpointattributes = (int) strtol (stringptr, &stringptr, 0);
- }
- stringptr = findnextnumber(stringptr);
- if (*stringptr != '\0') {
- markers = (int) strtol (stringptr, &stringptr, 0);
- }
- if (numberofpoints > 0) {
- readnodefile = 0;
- if (smesh) {
- infilename = insmeshfilename;
- } else {
- infilename = inpolyfilename;
- }
- infile = polyfile;
- } else {
- // If the .poly or .smesh file claims there are zero points, that
- // means the points should be read from a separate .node file.
- readnodefile = 1;
- infilename = innodefilename;
- }
-
- if (readnodefile) {
- // Read the points from the .node file.
- printf("Opening %s.\n", innodefilename);
- infile = fopen(innodefilename, "r");
- if (infile == (FILE *) NULL) {
- printf("File I/O Error: Cannot access file %s.\n", innodefilename);
- return false;
- }
- // Initialize the default values.
- mesh_dim = 3; // Three-dimemsional accoordinates.
- numberofpointattributes = 0; // no point attribute.
- markers = 0; // no boundary marker.
- // Read number of points, number of dimensions, number of point
- // attributes, and number of boundary markers.
- stringptr = readnumberline(inputline, infile, innodefilename);
- numberofpoints = (int) strtol (stringptr, &stringptr, 0);
- stringptr = findnextnumber(stringptr);
- if (*stringptr != '\0') {
- mesh_dim = (int) strtol (stringptr, &stringptr, 0);
- }
- stringptr = findnextnumber(stringptr);
- if (*stringptr != '\0') {
- numberofpointattributes = (int) strtol (stringptr, &stringptr, 0);
- }
- stringptr = findnextnumber(stringptr);
- if (*stringptr != '\0') {
- markers = (int) strtol (stringptr, &stringptr, 0);
- }
- }
-
- if ((mesh_dim != 3) && (mesh_dim != 2)) {
- printf("Input error: TetGen only works for 2D & 3D point sets.\n");
- fclose(infile);
- return false;
- }
- if (numberofpoints < (mesh_dim + 1)) {
- printf("Input error: TetGen needs at least %d points.\n", mesh_dim + 1);
- fclose(infile);
- return false;
- }
-
- // Load the list of nodes.
- if (!load_node_call(infile, markers, infilename)) {
- fclose(infile);
- return false;
- }
-
- if (readnodefile) {
- fclose(infile);
- }
-
- facet *f;
- polygon *p;
-
- if (mesh_dim == 3) {
-
- // Read number of facets and number of boundary markers.
- stringptr = readnumberline(inputline, polyfile, inpolyfilename);
- numberoffacets = (int) strtol (stringptr, &stringptr, 0);
- if (numberoffacets <= 0) {
- // No facet list, return.
- fclose(polyfile);
- return true;
- }
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- markers = 0; // no boundary marker.
- } else {
- markers = (int) strtol (stringptr, &stringptr, 0);
- }
-
- // Initialize the 'facetlist', 'facetmarkerlist'.
- facetlist = new facet[numberoffacets];
- if (markers == 1) {
- facetmarkerlist = new int[numberoffacets];
- }
-
- // Read data into 'facetlist', 'facetmarkerlist'.
- if (smesh == 0) {
- // Facets are in .poly file format.
- for (i = 1; i <= numberoffacets; i++) {
- f = &(facetlist[i - 1]);
- init(f);
- f->numberofholes = 0;
- currentmarker = 0;
- // Read number of polygons, number of holes, and a boundary marker.
- stringptr = readnumberline(inputline, polyfile, inpolyfilename);
- f->numberofpolygons = (int) strtol (stringptr, &stringptr, 0);
- stringptr = findnextnumber(stringptr);
- if (*stringptr != '\0') {
- f->numberofholes = (int) strtol (stringptr, &stringptr, 0);
- if (markers == 1) {
- stringptr = findnextnumber(stringptr);
- if (*stringptr != '\0') {
- currentmarker = (int) strtol(stringptr, &stringptr, 0);
- }
- }
- }
- // Initialize facetmarker if it needs.
- if (markers == 1) {
- facetmarkerlist[i - 1] = currentmarker;
- }
- // Each facet should has at least one polygon.
- if (f->numberofpolygons <= 0) {
- printf("Error: Wrong number of polygon in %d facet.\n", i);
- break;
- }
- // Initialize the 'f->polygonlist'.
- f->polygonlist = new polygon[f->numberofpolygons];
- // Go through all polygons, read in their vertices.
- for (j = 1; j <= f->numberofpolygons; j++) {
- p = &(f->polygonlist[j - 1]);
- init(p);
- // Read number of vertices of this polygon.
- stringptr = readnumberline(inputline, polyfile, inpolyfilename);
- p->numberofvertices = (int) strtol(stringptr, &stringptr, 0);
- if (p->numberofvertices < 1) {
- printf("Error: Wrong polygon %d in facet %d\n", j, i);
- break;
- }
- // Initialize 'p->vertexlist'.
- p->vertexlist = new int[p->numberofvertices];
- // Read all vertices of this polygon.
- for (k = 1; k <= p->numberofvertices; k++) {
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- // Try to load another non-empty line and continue to read the
- // rest of vertices.
- stringptr = readnumberline(inputline, polyfile, inpolyfilename);
- if (*stringptr == '\0') {
- printf("Error: Missing %d endpoints of polygon %d in facet %d",
- p->numberofvertices - k, j, i);
- break;
- }
- }
- p->vertexlist[k - 1] = (int) strtol (stringptr, &stringptr, 0);
- }
- }
- if (j <= f->numberofpolygons) {
- // This must be caused by an error. However, there're j - 1
- // polygons have been read. Reset the 'f->numberofpolygon'.
- if (j == 1) {
- // This is the first polygon.
- delete [] f->polygonlist;
- }
- f->numberofpolygons = j - 1;
- // No hole will be read even it exists.
- f->numberofholes = 0;
- break;
- }
- // If this facet has hole pints defined, read them.
- if (f->numberofholes > 0) {
- // Initialize 'f->holelist'.
- f->holelist = new REAL[f->numberofholes * 3];
- // Read the holes' coordinates.
- index = 0;
- for (j = 1; j <= f->numberofholes; j++) {
- stringptr = readnumberline(inputline, polyfile, inpolyfilename);
- for (k = 1; k <= 3; k++) {
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- printf("Error: Hole %d in facet %d has no coordinates", j, i);
- break;
- }
- f->holelist[index++] = (REAL) strtod (stringptr, &stringptr);
- }
- if (k <= 3) {
- // This must be caused by an error.
- break;
- }
- }
- if (j <= f->numberofholes) {
- // This must be caused by an error.
- break;
- }
- }
- }
- if (i <= numberoffacets) {
- // This must be caused by an error.
- numberoffacets = i - 1;
- fclose(polyfile);
- return false;
- }
- } else { // poly == 0
- // Read the facets from a .smesh file.
- for (i = 1; i <= numberoffacets; i++) {
- f = &(facetlist[i - 1]);
- init(f);
- // Initialize 'f->facetlist'. In a .smesh file, each facetlist only
- // contains exactly one polygon, no hole.
- f->numberofpolygons = 1;
- f->polygonlist = new polygon[f->numberofpolygons];
- p = &(f->polygonlist[0]);
- init(p);
- // Read number of vertices of this polygon.
- stringptr = readnumberline(inputline, polyfile, insmeshfilename);
- p->numberofvertices = (int) strtol (stringptr, &stringptr, 0);
- if (p->numberofvertices < 1) {
- printf("Error: Wrong number of vertex in facet %d\n", i);
- break;
- }
- // Initialize 'p->vertexlist'.
- p->vertexlist = new int[p->numberofvertices];
- for (k = 1; k <= p->numberofvertices; k++) {
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- // Try to load another non-empty line and continue to read the
- // rest of vertices.
- stringptr = readnumberline(inputline, polyfile, inpolyfilename);
- if (*stringptr == '\0') {
- printf("Error: Missing %d endpoints in facet %d",
- p->numberofvertices - k, i);
- break;
- }
- }
- p->vertexlist[k - 1] = (int) strtol (stringptr, &stringptr, 0);
- }
- if (k <= p->numberofvertices) {
- // This must be caused by an error.
- break;
- }
- // Read facet's boundary marker at last.
- if (markers == 1) {
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- currentmarker = 0;
- } else {
- currentmarker = (int) strtol(stringptr, &stringptr, 0);
- }
- facetmarkerlist[i - 1] = currentmarker;
- }
- }
- if (i <= numberoffacets) {
- // This must be caused by an error.
- numberoffacets = i - 1;
- fclose(polyfile);
- return false;
- }
- }
-
- // Read the hole section.
- stringptr = readnumberline(inputline, polyfile, inpolyfilename);
- if (*stringptr != '\0') {
- numberofholes = (int) strtol (stringptr, &stringptr, 0);
- } else {
- numberofholes = 0;
- }
- if (numberofholes > 0) {
- // Initialize 'holelist'.
- holelist = new REAL[numberofholes * 3];
- for (i = 0; i < 3 * numberofholes; i += 3) {
- stringptr = readnumberline(inputline, polyfile, inpolyfilename);
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- printf("Error: Hole %d has no x coord.\n", firstnumber + (i / 3));
- break;
- } else {
- holelist[i] = (REAL) strtod(stringptr, &stringptr);
- }
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- printf("Error: Hole %d has no y coord.\n", firstnumber + (i / 3));
- break;
- } else {
- holelist[i + 1] = (REAL) strtod(stringptr, &stringptr);
- }
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- printf("Error: Hole %d has no z coord.\n", firstnumber + (i / 3));
- break;
- } else {
- holelist[i + 2] = (REAL) strtod(stringptr, &stringptr);
- }
- }
- if (i < 3 * numberofholes) {
- // This must be caused by an error.
- fclose(polyfile);
- return false;
- }
- }
-
- // Read the region section. The 'region' section is optional, if we
- // don't reach the end-of-file, try read it in.
- stringptr = readnumberline(inputline, polyfile, NULL);
- if (stringptr != (char *) NULL && *stringptr != '\0') {
- numberofregions = (int) strtol (stringptr, &stringptr, 0);
- } else {
- numberofregions = 0;
- }
- if (numberofregions > 0) {
- // Initialize 'regionlist'.
- regionlist = new REAL[numberofregions * 5];
- index = 0;
- for (i = 0; i < numberofregions; i++) {
- stringptr = readnumberline(inputline, polyfile, inpolyfilename);
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- printf("Error: Region %d has no x coordinate.\n", firstnumber + i);
- break;
- } else {
- regionlist[index++] = (REAL) strtod(stringptr, &stringptr);
- }
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- printf("Error: Region %d has no y coordinate.\n", firstnumber + i);
- break;
- } else {
- regionlist[index++] = (REAL) strtod(stringptr, &stringptr);
- }
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- printf("Error: Region %d has no z coordinate.\n", firstnumber + i);
- break;
- } else {
- regionlist[index++] = (REAL) strtod(stringptr, &stringptr);
- }
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- printf("Error: Region %d has no region attrib.\n", firstnumber + i);
- break;
- } else {
- regionlist[index++] = (REAL) strtod(stringptr, &stringptr);
- }
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- regionlist[index] = regionlist[index - 1];
- } else {
- regionlist[index] = (REAL) strtod(stringptr, &stringptr);
- }
- index++;
- }
- if (i < numberofregions) {
- // This must be caused by an error.
- fclose(polyfile);
- return false;
- }
- }
-
- } else {
-
- // Read a PSLG from Triangle's poly file.
- assert(mesh_dim == 2);
- // A PSLG is a facet of a PLC.
- numberoffacets = 1;
- // Initialize the 'facetlist'.
- facetlist = new facet[numberoffacets];
- facetmarkerlist = (int *) NULL; // No facet markers.
- f = &(facetlist[0]);
- init(f);
- // Read number of segments.
- stringptr = readnumberline(inputline, polyfile, inpolyfilename);
- // Segments are degenerate polygons.
- f->numberofpolygons = (int) strtol (stringptr, &stringptr, 0);
- if (f->numberofpolygons > 0) {
- f->polygonlist = new polygon[f->numberofpolygons];
- }
- // Go through all segments, read in their vertices.
- for (j = 0; j < f->numberofpolygons; j++) {
- p = &(f->polygonlist[j]);
- init(p);
- // Read in a segment.
- stringptr = readnumberline(inputline, polyfile, inpolyfilename);
- stringptr = findnextnumber(stringptr); // Skip its index.
- p->numberofvertices = 2; // A segment always has two vertices.
- p->vertexlist = new int[p->numberofvertices];
- p->vertexlist[0] = (int) strtol (stringptr, &stringptr, 0);
- stringptr = findnextnumber(stringptr);
- p->vertexlist[1] = (int) strtol (stringptr, &stringptr, 0);
- }
- // Read number of holes.
- stringptr = readnumberline(inputline, polyfile, inpolyfilename);
- f->numberofholes = (int) strtol (stringptr, &stringptr, 0);
- if (f->numberofholes > 0) {
- // Initialize 'f->holelist'.
- f->holelist = new REAL[f->numberofholes * 3];
- // Read the holes' coordinates.
- for (j = 0; j < f->numberofholes; j++) {
- // Read a 2D hole point.
- stringptr = readnumberline(inputline, polyfile, inpolyfilename);
- stringptr = findnextnumber(stringptr); // Skip its index.
- f->holelist[j * 3] = (REAL) strtod (stringptr, &stringptr);
- stringptr = findnextnumber(stringptr);
- f->holelist[j * 3 + 1] = (REAL) strtod (stringptr, &stringptr);
- f->holelist[j * 3 + 2] = 0.0; // The z-coord.
- }
- }
- // The regions are skipped.
-
- }
-
- // End of reading poly/smesh file.
- fclose(polyfile);
-
- // Try to load a .var file if it exists.
- load_var(filename);
- // Try to load a .mtr file if it exists.
- load_mtr(filename);
- // Try to read a .pbc file if it exists.
- load_pbc(filename);
-
- return true;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// load_off() Load a polyhedron described in a .off file. //
-// //
-// The .off format is one of file formats of the Geomview, an interactive //
-// program for viewing and manipulating geometric objects. More information //
-// is available form: http://www.geomview.org. //
-// //
-// 'filename' is a input filename with extension .off or without extension ( //
-// the .off will be added in this case). On completion, the polyhedron is //
-// returned in 'pointlist' and 'facetlist'. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenio::load_off(char* filename)
-{
- FILE *fp;
- tetgenio::facet *f;
- tetgenio::polygon *p;
- char infilename[FILENAMESIZE];
- char buffer[INPUTLINESIZE];
- char *bufferp;
- double *coord;
- int nverts = 0, iverts = 0;
- int nfaces = 0, ifaces = 0;
- int nedges = 0;
- int line_count = 0, i;
-
- strncpy(infilename, filename, 1024 - 1);
- infilename[FILENAMESIZE - 1] = '\0';
- if (infilename[0] == '\0') {
- printf("Error: No filename.\n");
- return false;
- }
- if (strcmp(&infilename[strlen(infilename) - 4], ".off") != 0) {
- strcat(infilename, ".off");
- }
-
- if (!(fp = fopen(infilename, "r"))) {
- printf("File I/O Error: Unable to open file %s\n", infilename);
- return false;
- }
- printf("Opening %s.\n", infilename);
-
- // OFF requires the index starts from '0'.
- firstnumber = 0;
-
- while ((bufferp = readline(buffer, fp, &line_count)) != NULL) {
- // Check section
- if (nverts == 0) {
- // Read header
- bufferp = strstr(bufferp, "OFF");
- if (bufferp != NULL) {
- // Read mesh counts
- bufferp = findnextnumber(bufferp); // Skip field "OFF".
- if (*bufferp == '\0') {
- // Read a non-empty line.
- bufferp = readline(buffer, fp, &line_count);
- }
- if ((sscanf(bufferp, "%d%d%d", &nverts, &nfaces, &nedges) != 3)
- || (nverts == 0)) {
- printf("Syntax error reading header on line %d in file %s\n",
- line_count, infilename);
- fclose(fp);
- return false;
- }
- // Allocate memory for 'tetgenio'
- if (nverts > 0) {
- numberofpoints = nverts;
- pointlist = new REAL[nverts * 3];
- }
- if (nfaces > 0) {
- numberoffacets = nfaces;
- facetlist = new tetgenio::facet[nfaces];
- }
- }
- } else if (iverts < nverts) {
- // Read vertex coordinates
- coord = &pointlist[iverts * 3];
- for (i = 0; i < 3; i++) {
- if (*bufferp == '\0') {
- printf("Syntax error reading vertex coords on line %d in file %s\n",
- line_count, infilename);
- fclose(fp);
- return false;
- }
- coord[i] = (REAL) strtod(bufferp, &bufferp);
- bufferp = findnextnumber(bufferp);
- }
- iverts++;
- } else if (ifaces < nfaces) {
- // Get next face
- f = &facetlist[ifaces];
- init(f);
- // In .off format, each facet has one polygon, no hole.
- f->numberofpolygons = 1;
- f->polygonlist = new tetgenio::polygon[1];
- p = &f->polygonlist[0];
- init(p);
- // Read the number of vertices, it should be greater than 0.
- p->numberofvertices = (int) strtol(bufferp, &bufferp, 0);
- if (p->numberofvertices == 0) {
- printf("Syntax error reading polygon on line %d in file %s\n",
- line_count, infilename);
- fclose(fp);
- return false;
- }
- // Allocate memory for face vertices
- p->vertexlist = new int[p->numberofvertices];
- for (i = 0; i < p->numberofvertices; i++) {
- bufferp = findnextnumber(bufferp);
- if (*bufferp == '\0') {
- printf("Syntax error reading polygon on line %d in file %s\n",
- line_count, infilename);
- fclose(fp);
- return false;
- }
- p->vertexlist[i] = (int) strtol(bufferp, &bufferp, 0);
- }
- ifaces++;
- } else {
- // Should never get here
- printf("Found extra text starting at line %d in file %s\n", line_count,
- infilename);
- break;
- }
- }
-
- // Close file
- fclose(fp);
-
- // Check whether read all points
- if (iverts != nverts) {
- printf("Expected %d vertices, but read only %d vertices in file %s\n",
- nverts, iverts, infilename);
- return false;
- }
-
- // Check whether read all faces
- if (ifaces != nfaces) {
- printf("Expected %d faces, but read only %d faces in file %s\n",
- nfaces, ifaces, infilename);
- return false;
- }
-
- return true;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// load_ply() Load a polyhedron described in a .ply file. //
-// //
-// 'filename' is the file name with extension .ply or without extension (the //
-// .ply will be added in this case). //
-// //
-// This is a simplified version of reading .ply files, which only reads the //
-// set of vertices and the set of faces. Other informations (such as color, //
-// material, texture, etc) in .ply file are ignored. Complete routines for //
-// reading and writing ,ply files are available from: http://www.cc.gatech. //
-// edu/projects/large_models/ply.html. Except the header section, ply file //
-// format has exactly the same format for listing vertices and polygons as //
-// off file format. //
-// //
-// On completion, 'pointlist' and 'facetlist' together return the polyhedron.//
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenio::load_ply(char* filename)
-{
- FILE *fp;
- tetgenio::facet *f;
- tetgenio::polygon *p;
- char infilename[FILENAMESIZE];
- char buffer[INPUTLINESIZE];
- char *bufferp, *str;
- double *coord;
- int endheader = 0, format = 0;
- int nverts = 0, iverts = 0;
- int nfaces = 0, ifaces = 0;
- int line_count = 0, i;
-
- strncpy(infilename, filename, FILENAMESIZE - 1);
- infilename[FILENAMESIZE - 1] = '\0';
- if (infilename[0] == '\0') {
- printf("Error: No filename.\n");
- return false;
- }
- if (strcmp(&infilename[strlen(infilename) - 4], ".ply") != 0) {
- strcat(infilename, ".ply");
- }
-
- if (!(fp = fopen(infilename, "r"))) {
- printf("Error: Unable to open file %s\n", infilename);
- return false;
- }
- printf("Opening %s.\n", infilename);
-
- // PLY requires the index starts from '0'.
- firstnumber = 0;
-
- while ((bufferp = readline(buffer, fp, &line_count)) != NULL) {
- if (!endheader) {
- // Find if it is the keyword "end_header".
- str = strstr(bufferp, "end_header");
- // strstr() is case sensitive.
- if (!str) str = strstr(bufferp, "End_header");
- if (!str) str = strstr(bufferp, "End_Header");
- if (str) {
- // This is the end of the header section.
- endheader = 1;
- continue;
- }
- // Parse the number of vertices and the number of faces.
- if (nverts == 0 || nfaces == 0) {
- // Find if it si the keyword "element".
- str = strstr(bufferp, "element");
- if (!str) str = strstr(bufferp, "Element");
- if (str) {
- bufferp = findnextfield(str);
- if (*bufferp == '\0') {
- printf("Syntax error reading element type on line%d in file %s\n",
- line_count, infilename);
- fclose(fp);
- return false;
- }
- if (nverts == 0) {
- // Find if it is the keyword "vertex".
- str = strstr(bufferp, "vertex");
- if (!str) str = strstr(bufferp, "Vertex");
- if (str) {
- bufferp = findnextnumber(str);
- if (*bufferp == '\0') {
- printf("Syntax error reading vertex number on line");
- printf(" %d in file %s\n", line_count, infilename);
- fclose(fp);
- return false;
- }
- nverts = (int) strtol(bufferp, &bufferp, 0);
- // Allocate memory for 'tetgenio'
- if (nverts > 0) {
- numberofpoints = nverts;
- pointlist = new REAL[nverts * 3];
- }
- }
- }
- if (nfaces == 0) {
- // Find if it is the keyword "face".
- str = strstr(bufferp, "face");
- if (!str) str = strstr(bufferp, "Face");
- if (str) {
- bufferp = findnextnumber(str);
- if (*bufferp == '\0') {
- printf("Syntax error reading face number on line");
- printf(" %d in file %s\n", line_count, infilename);
- fclose(fp);
- return false;
- }
- nfaces = (int) strtol(bufferp, &bufferp, 0);
- // Allocate memory for 'tetgenio'
- if (nfaces > 0) {
- numberoffacets = nfaces;
- facetlist = new tetgenio::facet[nfaces];
- }
- }
- }
- } // It is not the string "element".
- }
- if (format == 0) {
- // Find the keyword "format".
- str = strstr(bufferp, "format");
- if (!str) str = strstr(bufferp, "Format");
- if (str) {
- format = 1;
- bufferp = findnextfield(str);
- // Find if it is the string "ascii".
- str = strstr(bufferp, "ascii");
- if (!str) str = strstr(bufferp, "ASCII");
- if (!str) {
- printf("This routine only reads ascii format of ply files.\n");
- printf("Hint: You can convert the binary to ascii format by\n");
- printf(" using the provided ply tools:\n");
- printf(" ply2ascii < %s > ascii_%s\n", infilename, infilename);
- fclose(fp);
- return false;
- }
- }
- }
- } else if (iverts < nverts) {
- // Read vertex coordinates
- coord = &pointlist[iverts * 3];
- for (i = 0; i < 3; i++) {
- if (*bufferp == '\0') {
- printf("Syntax error reading vertex coords on line %d in file %s\n",
- line_count, infilename);
- fclose(fp);
- return false;
- }
- coord[i] = (REAL) strtod(bufferp, &bufferp);
- bufferp = findnextnumber(bufferp);
- }
- iverts++;
- } else if (ifaces < nfaces) {
- // Get next face
- f = &facetlist[ifaces];
- init(f);
- // In .off format, each facet has one polygon, no hole.
- f->numberofpolygons = 1;
- f->polygonlist = new tetgenio::polygon[1];
- p = &f->polygonlist[0];
- init(p);
- // Read the number of vertices, it should be greater than 0.
- p->numberofvertices = (int) strtol(bufferp, &bufferp, 0);
- if (p->numberofvertices == 0) {
- printf("Syntax error reading polygon on line %d in file %s\n",
- line_count, infilename);
- fclose(fp);
- return false;
- }
- // Allocate memory for face vertices
- p->vertexlist = new int[p->numberofvertices];
- for (i = 0; i < p->numberofvertices; i++) {
- bufferp = findnextnumber(bufferp);
- if (*bufferp == '\0') {
- printf("Syntax error reading polygon on line %d in file %s\n",
- line_count, infilename);
- fclose(fp);
- return false;
- }
- p->vertexlist[i] = (int) strtol(bufferp, &bufferp, 0);
- }
- ifaces++;
- } else {
- // Should never get here
- printf("Found extra text starting at line %d in file %s\n", line_count,
- infilename);
- break;
- }
- }
-
- // Close file
- fclose(fp);
-
- // Check whether read all points
- if (iverts != nverts) {
- printf("Expected %d vertices, but read only %d vertices in file %s\n",
- nverts, iverts, infilename);
- return false;
- }
-
- // Check whether read all faces
- if (ifaces != nfaces) {
- printf("Expected %d faces, but read only %d faces in file %s\n",
- nfaces, ifaces, infilename);
- return false;
- }
-
- return true;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// load_stl() Load a surface mesh described in a .stl file. //
-// //
-// 'filename' is the file name with extension .stl or without extension (the //
-// .stl will be added in this case). //
-// //
-// The .stl or stereolithography format is an ASCII or binary file used in //
-// manufacturing. It is a list of the triangular surfaces that describe a //
-// computer generated solid model. This is the standard input for most rapid //
-// prototyping machines. //
-// //
-// On completion, 'pointlist' and 'facetlist' together return the polyhedron.//
-// Note: After load_stl(), there exist many duplicated points in 'pointlist'.//
-// They will be unified during the Delaunay tetrahedralization process. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenio::load_stl(char* filename)
-{
- FILE *fp;
- tetgenmesh::list *plist;
- tetgenio::facet *f;
- tetgenio::polygon *p;
- char infilename[FILENAMESIZE];
- char buffer[INPUTLINESIZE];
- char *bufferp, *str;
- double *coord;
- int solid = 0;
- int nverts = 0, iverts = 0;
- int nfaces = 0;
- int line_count = 0, i;
-
- strncpy(infilename, filename, FILENAMESIZE - 1);
- infilename[FILENAMESIZE - 1] = '\0';
- if (infilename[0] == '\0') {
- printf("Error: No filename.\n");
- return false;
- }
- if (strcmp(&infilename[strlen(infilename) - 4], ".stl") != 0) {
- strcat(infilename, ".stl");
- }
-
- if (!(fp = fopen(infilename, "r"))) {
- printf("Error: Unable to open file %s\n", infilename);
- return false;
- }
- printf("Opening %s.\n", infilename);
-
- // STL file has no number of points available. Use a list to read points.
- plist = new tetgenmesh::list(sizeof(double) * 3, NULL, 1024);
-
- while ((bufferp = readline(buffer, fp, &line_count)) != NULL) {
- // The ASCII .stl file must start with the lower case keyword solid and
- // end with endsolid.
- if (solid == 0) {
- // Read header
- bufferp = strstr(bufferp, "solid");
- if (bufferp != NULL) {
- solid = 1;
- }
- } else {
- // We're inside the block of the solid.
- str = bufferp;
- // Is this the end of the solid.
- bufferp = strstr(bufferp, "endsolid");
- if (bufferp != NULL) {
- solid = 0;
- } else {
- // Read the XYZ coordinates if it is a vertex.
- bufferp = str;
- bufferp = strstr(bufferp, "vertex");
- if (bufferp != NULL) {
- coord = (double *) plist->append(NULL);
- for (i = 0; i < 3; i++) {
- bufferp = findnextnumber(bufferp);
- if (*bufferp == '\0') {
- printf("Syntax error reading vertex coords on line %d\n",
- line_count);
- delete plist;
- fclose(fp);
- return false;
- }
- coord[i] = (REAL) strtod(bufferp, &bufferp);
- }
- }
- }
- }
- }
- fclose(fp);
-
- nverts = plist->len();
- // nverts should be an integer times 3 (every 3 vertices denote a face).
- if (nverts == 0 || (nverts % 3 != 0)) {
- printf("Error: Wrong number of vertices in file %s.\n", infilename);
- delete plist;
- return false;
- }
- numberofpoints = nverts;
- pointlist = new REAL[nverts * 3];
- for (i = 0; i < nverts; i++) {
- coord = (double *) (* plist)[i];
- iverts = i * 3;
- pointlist[iverts] = (REAL) coord[0];
- pointlist[iverts + 1] = (REAL) coord[1];
- pointlist[iverts + 2] = (REAL) coord[2];
- }
-
- nfaces = (int) (nverts / 3);
- numberoffacets = nfaces;
- facetlist = new tetgenio::facet[nfaces];
-
- // Default use '1' as the array starting index.
- firstnumber = 1;
- iverts = firstnumber;
- for (i = 0; i < nfaces; i++) {
- f = &facetlist[i];
- init(f);
- // In .stl format, each facet has one polygon, no hole.
- f->numberofpolygons = 1;
- f->polygonlist = new tetgenio::polygon[1];
- p = &f->polygonlist[0];
- init(p);
- // Each polygon has three vertices.
- p->numberofvertices = 3;
- p->vertexlist = new int[p->numberofvertices];
- p->vertexlist[0] = iverts;
- p->vertexlist[1] = iverts + 1;
- p->vertexlist[2] = iverts + 2;
- iverts += 3;
- }
-
- delete plist;
- return true;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// load_medit() Load a surface mesh described in .mesh file. //
-// //
-// 'filename' is the file name with extension .mesh or without entension ( //
-// the .mesh will be added in this case). .mesh is the file format of Medit, //
-// a user-friendly interactive mesh viewing program. //
-// //
-// This routine ONLY reads the sections containing vertices, triangles, and //
-// quadrilaters. Other sections (such as tetrahedra, edges, ...) are ignored.//
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenio::load_medit(char* filename)
-{
- FILE *fp;
- tetgenio::facet *tmpflist, *f;
- tetgenio::polygon *p;
- char infilename[FILENAMESIZE];
- char buffer[INPUTLINESIZE];
- char *bufferp, *str;
- double *coord;
- int *tmpfmlist;
- int dimension = 0;
- int nverts = 0;
- int nfaces = 0;
- int line_count = 0;
- int corners = 0; // 3 (triangle) or 4 (quad).
- int i, j;
-
- strncpy(infilename, filename, FILENAMESIZE - 1);
- infilename[FILENAMESIZE - 1] = '\0';
- if (infilename[0] == '\0') {
- printf("Error: No filename.\n");
- return false;
- }
- if (strcmp(&infilename[strlen(infilename) - 5], ".mesh") != 0) {
- strcat(infilename, ".mesh");
- }
-
- if (!(fp = fopen(infilename, "r"))) {
- printf("Error: Unable to open file %s\n", infilename);
- return false;
- }
- printf("Opening %s.\n", infilename);
-
- // Default uses the index starts from '1'.
- firstnumber = 1;
-
- while ((bufferp = readline(buffer, fp, &line_count)) != NULL) {
- if (*bufferp == '#') continue; // A comment line is skipped.
- if (dimension == 0) {
- // Find if it is the keyword "Dimension".
- str = strstr(bufferp, "Dimension");
- if (!str) str = strstr(bufferp, "dimension");
- if (!str) str = strstr(bufferp, "DIMENSION");
- if (str) {
- // Read the dimensions
- bufferp = findnextnumber(str); // Skip field "Dimension".
- if (*bufferp == '\0') {
- // Read a non-empty line.
- bufferp = readline(buffer, fp, &line_count);
- }
- dimension = (int) strtol(bufferp, &bufferp, 0);
- if (dimension != 2 && dimension != 3) {
- printf("Unknown dimension in file on line %d in file %s\n",
- line_count, infilename);
- fclose(fp);
- return false;
- }
- mesh_dim = dimension;
- }
- }
- if (nverts == 0) {
- // Find if it is the keyword "Vertices".
- str = strstr(bufferp, "Vertices");
- if (!str) str = strstr(bufferp, "vertices");
- if (!str) str = strstr(bufferp, "VERTICES");
- if (str) {
- // Read the number of vertices.
- bufferp = findnextnumber(str); // Skip field "Vertices".
- if (*bufferp == '\0') {
- // Read a non-empty line.
- bufferp = readline(buffer, fp, &line_count);
- }
- nverts = (int) strtol(bufferp, &bufferp, 0);
- // Allocate memory for 'tetgenio'
- if (nverts > 0) {
- numberofpoints = nverts;
- pointlist = new REAL[nverts * 3];
- }
- // Read the follwoing node list.
- for (i = 0; i < nverts; i++) {
- bufferp = readline(buffer, fp, &line_count);
- if (bufferp == NULL) {
- printf("Unexpected end of file on line %d in file %s\n",
- line_count, infilename);
- fclose(fp);
- return false;
- }
- // Read vertex coordinates
- coord = &pointlist[i * 3];
- for (j = 0; j < 3; j++) {
- if (*bufferp == '\0') {
- printf("Syntax error reading vertex coords on line");
- printf(" %d in file %s\n", line_count, infilename);
- fclose(fp);
- return false;
- }
- if ((j < 2) || (dimension == 3)) {
- coord[j] = (REAL) strtod(bufferp, &bufferp);
- } else {
- assert((j == 2) && (dimension == 2));
- coord[j] = 0.0;
- }
- bufferp = findnextnumber(bufferp);
- }
- }
- continue;
- }
- }
- if (nfaces == 0) {
- // Find if it is the keyword "Triangles" or "Quadrilaterals".
- corners = 0;
- str = strstr(bufferp, "Triangles");
- if (!str) str = strstr(bufferp, "triangles");
- if (!str) str = strstr(bufferp, "TRIANGLES");
- if (str) {
- corners = 3;
- } else {
- str = strstr(bufferp, "Quadrilaterals");
- if (!str) str = strstr(bufferp, "quadrilaterals");
- if (!str) str = strstr(bufferp, "QUADRILATERALS");
- if (str) {
- corners = 4;
- }
- }
- if (corners == 3 || corners == 4) {
- // Read the number of triangles (or quadrilaterals).
- bufferp = findnextnumber(str); // Skip field "Triangles".
- if (*bufferp == '\0') {
- // Read a non-empty line.
- bufferp = readline(buffer, fp, &line_count);
- }
- nfaces = strtol(bufferp, &bufferp, 0);
- // Allocate memory for 'tetgenio'
- if (nfaces > 0) {
- if (numberoffacets > 0) {
- // facetlist has already been allocated. Enlarge arrays.
- tmpflist = new tetgenio::facet[numberoffacets + nfaces];
- tmpfmlist = new int[numberoffacets + nfaces];
- // Copy the data of old arrays into new arrays.
- for (i = 0; i < numberoffacets; i++) {
- f = &(tmpflist[i]);
- tetgenio::init(f);
- *f = facetlist[i];
- tmpfmlist[i] = facetmarkerlist[i];
- }
- // Release old arrays.
- delete [] facetlist;
- delete [] facetmarkerlist;
- // Remember the new arrays.
- facetlist = tmpflist;
- facetmarkerlist = tmpfmlist;
- } else {
- // This is the first time to allocate facetlist.
- facetlist = new tetgenio::facet[nfaces];
- facetmarkerlist = new int[nfaces];
- }
- }
- // Read the following list of faces.
- for (i = numberoffacets; i < numberoffacets + nfaces; i++) {
- bufferp = readline(buffer, fp, &line_count);
- if (bufferp == NULL) {
- printf("Unexpected end of file on line %d in file %s\n",
- line_count, infilename);
- fclose(fp);
- return false;
- }
- f = &facetlist[i];
- tetgenio::init(f);
- // In .mesh format, each facet has one polygon, no hole.
- f->numberofpolygons = 1;
- f->polygonlist = new tetgenio::polygon[1];
- p = &f->polygonlist[0];
- tetgenio::init(p);
- p->numberofvertices = corners;
- // Allocate memory for face vertices
- p->vertexlist = new int[p->numberofvertices];
- // Read the vertices of the face.
- for (j = 0; j < corners; j++) {
- if (*bufferp == '\0') {
- printf("Syntax error reading face on line %d in file %s\n",
- line_count, infilename);
- fclose(fp);
- return false;
- }
- p->vertexlist[j] = (int) strtol(bufferp, &bufferp, 0);
- if (firstnumber == 1) {
- // Check if a '0' index appears.
- if (p->vertexlist[j] == 0) {
- // The first index is set to be 0.
- firstnumber = 0;
- }
- }
- bufferp = findnextnumber(bufferp);
- }
- // Read the marker of the face if it exists.
- facetmarkerlist[i] = 0;
- if (*bufferp != '\0') {
- facetmarkerlist[i] = (int) strtol(bufferp, &bufferp, 0);
- }
- }
- // Have read in a list of triangles/quads.
- numberoffacets += nfaces;
- nfaces = 0;
- }
- }
- // if (nverts > 0 && nfaces > 0) break; // Ignore other data.
- }
-
- // Close file
- fclose(fp);
-
- return true;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// load_plc() Load a piecewise linear complex from file. //
-// //
-// This is main entrance for loading plcs from different file formats into //
-// tetgenio. 'filename' is the input file name without extention. 'object' //
-// indicates which file format is used to describ the plc. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenio::load_plc(char* filename, int object)
-{
- enum tetgenbehavior::objecttype type;
-
- type = (enum tetgenbehavior::objecttype) object;
- switch (type) {
- case tetgenbehavior::NODES:
- return load_node(filename);
- case tetgenbehavior::POLY:
- return load_poly(filename);
- case tetgenbehavior::OFF:
- return load_off(filename);
- case tetgenbehavior::PLY:
- return load_ply(filename);
- case tetgenbehavior::STL:
- return load_stl(filename);
- case tetgenbehavior::MEDIT:
- return load_medit(filename);
- default:
- return load_poly(filename);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// load_tetmesh() Load a tetrahedral mesh from files. //
-// //
-// 'filename' is the inputfile without suffix. The nodes of the tetrahedral //
-// mesh is in "filename.node", the elements is in "filename.ele", if the //
-// "filename.face" and "filename.vol" exists, they will also be read. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenio::load_tetmesh(char* filename)
-{
- FILE *infile;
- char innodefilename[FILENAMESIZE];
- char inelefilename[FILENAMESIZE];
- char infacefilename[FILENAMESIZE];
- char inedgefilename[FILENAMESIZE];
- char involfilename[FILENAMESIZE];
- char inputline[INPUTLINESIZE];
- char *stringptr, *infilename;
- REAL attrib, volume;
- int volelements;
- int markers, corner;
- int index, attribindex;
- int i, j;
-
- // Assembling the actual file names we want to open.
- strcpy(innodefilename, filename);
- strcpy(inelefilename, filename);
- strcpy(infacefilename, filename);
- strcpy(inedgefilename, filename);
- strcpy(involfilename, filename);
- strcat(innodefilename, ".node");
- strcat(inelefilename, ".ele");
- strcat(infacefilename, ".face");
- strcat(inedgefilename, ".edge");
- strcat(involfilename, ".vol");
-
- // Read the points from a .node file.
- infilename = innodefilename;
- printf("Opening %s.\n", infilename);
- infile = fopen(infilename, "r");
- if (infile == (FILE *) NULL) {
- printf("File I/O Error: Cannot access file %s.\n", infilename);
- return false;
- }
- // Read the first line of the file.
- stringptr = readnumberline(inputline, infile, infilename);
- // Is this list of points generated from rbox?
- stringptr = strstr(inputline, "rbox");
- if (stringptr == NULL) {
- // Read number of points, number of dimensions, number of point
- // attributes, and number of boundary markers.
- stringptr = inputline;
- numberofpoints = (int) strtol (stringptr, &stringptr, 0);
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- mesh_dim = 3;
- } else {
- mesh_dim = (int) strtol (stringptr, &stringptr, 0);
- }
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- numberofpointattributes = 0;
- } else {
- numberofpointattributes = (int) strtol (stringptr, &stringptr, 0);
- }
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- markers = 0; // Default value.
- } else {
- markers = (int) strtol (stringptr, &stringptr, 0);
- }
- } else {
- // It is a rbox (qhull) input file.
- stringptr = inputline;
- // Get the dimension.
- mesh_dim = (int) strtol (stringptr, &stringptr, 0);
- // Get the number of points.
- stringptr = readnumberline(inputline, infile, infilename);
- numberofpoints = (int) strtol (stringptr, &stringptr, 0);
- // There is no index column.
- useindex = 0;
- }
-
- // Load the list of nodes.
- if (!load_node_call(infile, markers, infilename)) {
- fclose(infile);
- return false;
- }
- fclose(infile);
-
- // Read the elements from an .ele file.
- if (mesh_dim == 3) {
- infilename = inelefilename;
- infile = fopen(infilename, "r");
- if (infile != (FILE *) NULL) {
- printf("Opening %s.\n", infilename);
- // Read number of elements, number of corners (4 or 10), number of
- // element attributes.
- stringptr = readnumberline(inputline, infile, infilename);
- numberoftetrahedra = (int) strtol (stringptr, &stringptr, 0);
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- numberofcorners = 4; // Default read 4 nodes per element.
- } else {
- numberofcorners = (int) strtol(stringptr, &stringptr, 0);
- }
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- numberoftetrahedronattributes = 0; // Default no attribute.
- } else {
- numberoftetrahedronattributes = (int) strtol(stringptr, &stringptr, 0);
- }
- if (numberofcorners != 4 && numberofcorners != 10) {
- printf("Error: Wrong number of corners %d (should be 4 or 10).\n",
- numberofcorners);
- fclose(infile);
- return false;
- }
- // Allocate memory for tetrahedra.
- if (numberoftetrahedra > 0) {
- tetrahedronlist = new int[numberoftetrahedra * numberofcorners];
- if (tetrahedronlist == (int *) NULL) {
- printf("Error: Out of memory.\n");
- terminatetetgen(1);
- }
- // Allocate memory for output tetrahedron attributes if necessary.
- if (numberoftetrahedronattributes > 0) {
- tetrahedronattributelist = new REAL[numberoftetrahedra *
- numberoftetrahedronattributes];
- if (tetrahedronattributelist == (REAL *) NULL) {
- printf("Error: Out of memory.\n");
- terminatetetgen(1);
- }
- }
- }
- // Read the list of tetrahedra.
- index = 0;
- attribindex = 0;
- for (i = 0; i < numberoftetrahedra; i++) {
- // Read tetrahedron index and the tetrahedron's corners.
- stringptr = readnumberline(inputline, infile, infilename);
- for (j = 0; j < numberofcorners; j++) {
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- printf("Error: Tetrahedron %d is missing vertex %d in %s.\n",
- i + firstnumber, j + 1, infilename);
- terminatetetgen(1);
- }
- corner = (int) strtol(stringptr, &stringptr, 0);
- if (corner < firstnumber || corner >= numberofpoints + firstnumber) {
- printf("Error: Tetrahedron %d has an invalid vertex index.\n",
- i + firstnumber);
- terminatetetgen(1);
- }
- tetrahedronlist[index++] = corner;
- }
- // Read the tetrahedron's attributes.
- for (j = 0; j < numberoftetrahedronattributes; j++) {
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- attrib = 0.0;
- } else {
- attrib = (REAL) strtod(stringptr, &stringptr);
- }
- tetrahedronattributelist[attribindex++] = attrib;
- }
- }
- fclose(infile);
- }
- } // if (meshdim == 3)
-
- // Read the hullfaces or subfaces from a .face file if it exists.
- if (mesh_dim == 3) {
- infilename = infacefilename;
- } else {
- infilename = inelefilename;
- }
- infile = fopen(infilename, "r");
- if (infile != (FILE *) NULL) {
- printf("Opening %s.\n", infilename);
- // Read number of faces, boundary markers.
- stringptr = readnumberline(inputline, infile, infilename);
- numberoftrifaces = (int) strtol (stringptr, &stringptr, 0);
- stringptr = findnextnumber(stringptr);
- if (mesh_dim == 2) {
- // Skip a number.
- stringptr = findnextnumber(stringptr);
- }
- if (*stringptr == '\0') {
- markers = 0; // Default there is no marker per face.
- } else {
- markers = (int) strtol (stringptr, &stringptr, 0);
- }
- if (numberoftrifaces > 0) {
- trifacelist = new int[numberoftrifaces * 3];
- if (trifacelist == (int *) NULL) {
- printf("Error: Out of memory.\n");
- terminatetetgen(1);
- }
- if (markers) {
- trifacemarkerlist = new int[numberoftrifaces * 3];
- if (trifacemarkerlist == (int *) NULL) {
- printf("Error: Out of memory.\n");
- terminatetetgen(1);
- }
- }
- }
- // Read the list of faces.
- index = 0;
- for (i = 0; i < numberoftrifaces; i++) {
- // Read face index and the face's three corners.
- stringptr = readnumberline(inputline, infile, infilename);
- for (j = 0; j < 3; j++) {
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- printf("Error: Face %d is missing vertex %d in %s.\n",
- i + firstnumber, j + 1, infilename);
- terminatetetgen(1);
- }
- corner = (int) strtol(stringptr, &stringptr, 0);
- if (corner < firstnumber || corner >= numberofpoints + firstnumber) {
- printf("Error: Face %d has an invalid vertex index.\n",
- i + firstnumber);
- terminatetetgen(1);
- }
- trifacelist[index++] = corner;
- }
- // Read the boundary marker if it exists.
- if (markers) {
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- attrib = 0.0;
- } else {
- attrib = (REAL) strtod(stringptr, &stringptr);
- }
- trifacemarkerlist[i] = (int) attrib;
- }
- }
- fclose(infile);
- }
-
- // Read the boundary edges from a .edge file if it exists.
- infilename = inedgefilename;
- infile = fopen(infilename, "r");
- if (infile != (FILE *) NULL) {
- printf("Opening %s.\n", infilename);
- // Read number of boundary edges.
- stringptr = readnumberline(inputline, infile, infilename);
- numberofedges = (int) strtol (stringptr, &stringptr, 0);
- if (numberofedges > 0) {
- edgelist = new int[numberofedges * 2];
- if (edgelist == (int *) NULL) {
- printf("Error: Out of memory.\n");
- terminatetetgen(1);
- }
- }
- // Read the list of faces.
- index = 0;
- for (i = 0; i < numberofedges; i++) {
- // Read face index and the edge's two endpoints.
- stringptr = readnumberline(inputline, infile, infilename);
- for (j = 0; j < 2; j++) {
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- printf("Error: Edge %d is missing vertex %d in %s.\n",
- i + firstnumber, j + 1, infilename);
- terminatetetgen(1);
- }
- corner = (int) strtol(stringptr, &stringptr, 0);
- if (corner < firstnumber || corner >= numberofpoints + firstnumber) {
- printf("Error: Edge %d has an invalid vertex index.\n",
- i + firstnumber);
- terminatetetgen(1);
- }
- edgelist[index++] = corner;
- }
- }
- fclose(infile);
- }
-
- // Read the volume constraints from a .vol file if it exists.
- infilename = involfilename;
- infile = fopen(infilename, "r");
- if (infile != (FILE *) NULL) {
- printf("Opening %s.\n", infilename);
- // Read number of tetrahedra.
- stringptr = readnumberline(inputline, infile, infilename);
- volelements = (int) strtol (stringptr, &stringptr, 0);
- if (volelements != numberoftetrahedra) {
- printf("Warning: %s and %s disagree on number of tetrahedra.\n",
- inelefilename, involfilename);
- volelements = 0;
- }
- if (volelements > 0) {
- tetrahedronvolumelist = new REAL[volelements];
- if (tetrahedronvolumelist == (REAL *) NULL) {
- printf("Error: Out of memory.\n");
- terminatetetgen(1);
- }
- }
- // Read the list of volume constraints.
- for (i = 0; i < volelements; i++) {
- stringptr = readnumberline(inputline, infile, infilename);
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- volume = -1.0; // No constraint on this tetrahedron.
- } else {
- volume = (REAL) strtod(stringptr, &stringptr);
- }
- tetrahedronvolumelist[i] = volume;
- }
- fclose(infile);
- }
-
- // Try to load a .mtr file if it exists.
- load_mtr(filename);
- // Try to read a .pbc file if it exists.
- load_pbc(filename);
-
- return true;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// load_voronoi() Load a Voronoi diagram from files. //
-// //
-// 'filename' is the inputfile without suffix. The Voronoi diagram is read //
-// from files: filename.v.node, filename.v.edge, and filename.v.face. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenio::load_voronoi(char* filename)
-{
- FILE *infile;
- char innodefilename[FILENAMESIZE];
- char inedgefilename[FILENAMESIZE];
- char inputline[INPUTLINESIZE];
- char *stringptr, *infilename;
- voroedge *vedge;
- REAL x, y, z;
- int firstnode, corner;
- int index;
- int i, j;
-
- // Assembling the actual file names we want to open.
- strcpy(innodefilename, filename);
- strcpy(inedgefilename, filename);
- strcat(innodefilename, ".v.node");
- strcat(inedgefilename, ".v.edge");
-
- // Read the points from a .v.node file.
- infilename = innodefilename;
- printf("Opening %s.\n", infilename);
- infile = fopen(infilename, "r");
- if (infile == (FILE *) NULL) {
- printf("File I/O Error: Cannot access file %s.\n", infilename);
- return false;
- }
- // Read the first line of the file.
- stringptr = readnumberline(inputline, infile, infilename);
- // Is this list of points generated from rbox?
- stringptr = strstr(inputline, "rbox");
- if (stringptr == NULL) {
- // Read number of points, number of dimensions, number of point
- // attributes, and number of boundary markers.
- stringptr = inputline;
- numberofvpoints = (int) strtol (stringptr, &stringptr, 0);
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- mesh_dim = 3; // Default.
- } else {
- mesh_dim = (int) strtol (stringptr, &stringptr, 0);
- }
- useindex = 1; // There is an index column.
- } else {
- // It is a rbox (qhull) input file.
- stringptr = inputline;
- // Get the dimension.
- mesh_dim = (int) strtol (stringptr, &stringptr, 0);
- // Get the number of points.
- stringptr = readnumberline(inputline, infile, infilename);
- numberofvpoints = (int) strtol (stringptr, &stringptr, 0);
- useindex = 0; // No index column.
- }
- // Initialize 'vpointlist'.
- vpointlist = new REAL[numberofvpoints * 3];
- if (vpointlist == (REAL *) NULL) {
- printf("Error: Out of memory.\n");
- terminatetetgen(1);
- }
- // Read the point section.
- index = 0;
- for (i = 0; i < numberofvpoints; i++) {
- stringptr = readnumberline(inputline, infile, infilename);
- if (useindex) {
- if (i == 0) {
- firstnode = (int) strtol (stringptr, &stringptr, 0);
- if ((firstnode == 0) || (firstnode == 1)) {
- firstnumber = firstnode;
- }
- }
- stringptr = findnextnumber(stringptr);
- } // if (useindex)
- if (*stringptr == '\0') {
- printf("Error: Point %d has no x coordinate.\n", firstnumber + i);
- terminatetetgen(1);
- }
- x = (REAL) strtod(stringptr, &stringptr);
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- printf("Error: Point %d has no y coordinate.\n", firstnumber + i);
- terminatetetgen(1);
- }
- y = (REAL) strtod(stringptr, &stringptr);
- if (mesh_dim == 3) {
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- printf("Error: Point %d has no z coordinate.\n", firstnumber + i);
- terminatetetgen(1);
- }
- z = (REAL) strtod(stringptr, &stringptr);
- } else {
- z = 0.0; // mesh_dim == 2;
- }
- vpointlist[index++] = x;
- vpointlist[index++] = y;
- vpointlist[index++] = z;
- }
- fclose(infile);
-
- // Read the Voronoi edges from a .v.edge file if it exists.
- infilename = inedgefilename;
- infile = fopen(infilename, "r");
- if (infile != (FILE *) NULL) {
- printf("Opening %s.\n", infilename);
- // Read number of boundary edges.
- stringptr = readnumberline(inputline, infile, infilename);
- numberofvedges = (int) strtol (stringptr, &stringptr, 0);
- if (numberofvedges > 0) {
- vedgelist = new voroedge[numberofvedges];
- }
- // Read the list of faces.
- index = 0;
- for (i = 0; i < numberofvedges; i++) {
- // Read edge index and the edge's two endpoints.
- stringptr = readnumberline(inputline, infile, infilename);
- vedge = &(vedgelist[i]);
- for (j = 0; j < 2; j++) {
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- printf("Error: Edge %d is missing vertex %d in %s.\n",
- i + firstnumber, j + 1, infilename);
- terminatetetgen(1);
- }
- corner = (int) strtol(stringptr, &stringptr, 0);
- j == 0 ? vedge->v1 = corner : vedge->v2 = corner;
- }
- if (vedge->v2 < 0) {
- for (j = 0; j < mesh_dim; j++) {
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- printf("Error: Edge %d is missing normal in %s.\n",
- i + firstnumber, infilename);
- terminatetetgen(1);
- }
- vedge->vnormal[j] = (REAL) strtod(stringptr, &stringptr);
- }
- if (mesh_dim == 2) {
- vedge->vnormal[2] = 0.0;
- }
- } else {
- vedge->vnormal[0] = 0.0;
- vedge->vnormal[1] = 0.0;
- vedge->vnormal[2] = 0.0;
- }
- }
- fclose(infile);
- }
-
- return true;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// save_nodes() Save points to a .node file. //
-// //
-// 'filename' is a string containing the file name without suffix. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenio::save_nodes(char* filename)
-{
- FILE *fout;
- char outnodefilename[FILENAMESIZE];
- char outmtrfilename[FILENAMESIZE];
- int i, j;
-
- sprintf(outnodefilename, "%s.node", filename);
- printf("Saving nodes to %s\n", outnodefilename);
- fout = fopen(outnodefilename, "w");
- fprintf(fout, "%d %d %d %d\n", numberofpoints, mesh_dim,
- numberofpointattributes, pointmarkerlist != NULL ? 1 : 0);
- for (i = 0; i < numberofpoints; i++) {
- if (mesh_dim == 2) {
- fprintf(fout, "%d %.16g %.16g", i + firstnumber, pointlist[i * 2],
- pointlist[i * 2 + 1]);
- } else {
- fprintf(fout, "%d %.16g %.16g %.16g", i + firstnumber,
- pointlist[i * 3], pointlist[i * 3 + 1], pointlist[i * 3 + 2]);
- }
- for (j = 0; j < numberofpointattributes; j++) {
- fprintf(fout, " %.16g",
- pointattributelist[i * numberofpointattributes + j]);
- }
- if (pointmarkerlist != NULL) {
- fprintf(fout, " %d", pointmarkerlist[i]);
- }
- fprintf(fout, "\n");
- }
- fclose(fout);
-
- // If the point metrics exist, output them to a .mtr file.
- if ((numberofpointmtrs > 0) && (pointmtrlist != (REAL *) NULL)) {
- sprintf(outmtrfilename, "%s.mtr", filename);
- printf("Saving metrics to %s\n", outmtrfilename);
- fout = fopen(outmtrfilename, "w");
- fprintf(fout, "%d %d\n", numberofpoints, numberofpointmtrs);
- for (i = 0; i < numberofpoints; i++) {
- for (j = 0; j < numberofpointmtrs; j++) {
- fprintf(fout, "%.16g ", pointmtrlist[i * numberofpointmtrs + j]);
- }
- fprintf(fout, "\n");
- }
- fclose(fout);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// save_elements() Save elements to a .ele file. //
-// //
-// 'filename' is a string containing the file name without suffix. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenio::save_elements(char* filename)
-{
- FILE *fout;
- char outelefilename[FILENAMESIZE];
- int i, j;
-
- sprintf(outelefilename, "%s.ele", filename);
- printf("Saving elements to %s\n", outelefilename);
- fout = fopen(outelefilename, "w");
- fprintf(fout, "%d %d %d\n", numberoftetrahedra, numberofcorners,
- numberoftetrahedronattributes);
- for (i = 0; i < numberoftetrahedra; i++) {
- fprintf(fout, "%d", i + firstnumber);
- for (j = 0; j < numberofcorners; j++) {
- fprintf(fout, " %5d", tetrahedronlist[i * numberofcorners + j]);
- }
- for (j = 0; j < numberoftetrahedronattributes; j++) {
- fprintf(fout, " %g",
- tetrahedronattributelist[i * numberoftetrahedronattributes + j]);
- }
- fprintf(fout, "\n");
- }
-
- fclose(fout);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// save_faces() Save faces to a .face file. //
-// //
-// 'filename' is a string containing the file name without suffix. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenio::save_faces(char* filename)
-{
- FILE *fout;
- char outfacefilename[FILENAMESIZE];
- int i;
-
- sprintf(outfacefilename, "%s.face", filename);
- printf("Saving faces to %s\n", outfacefilename);
- fout = fopen(outfacefilename, "w");
- fprintf(fout, "%d %d\n", numberoftrifaces,
- trifacemarkerlist != NULL ? 1 : 0);
- for (i = 0; i < numberoftrifaces; i++) {
- fprintf(fout, "%d %5d %5d %5d", i + firstnumber, trifacelist[i * 3],
- trifacelist[i * 3 + 1], trifacelist[i * 3 + 2]);
- if (trifacemarkerlist != NULL) {
- fprintf(fout, " %d", trifacemarkerlist[i]);
- }
- fprintf(fout, "\n");
- }
-
- fclose(fout);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// save_edges() Save egdes to a .edge file. //
-// //
-// 'filename' is a string containing the file name without suffix. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenio::save_edges(char* filename)
-{
- FILE *fout;
- char outedgefilename[FILENAMESIZE];
- int i;
-
- sprintf(outedgefilename, "%s.edge", filename);
- printf("Saving edges to %s\n", outedgefilename);
- fout = fopen(outedgefilename, "w");
- fprintf(fout, "%d %d\n", numberofedges, edgemarkerlist != NULL ? 1 : 0);
- for (i = 0; i < numberofedges; i++) {
- fprintf(fout, "%d %4d %4d", i + firstnumber, edgelist[i * 2],
- edgelist[i * 2 + 1]);
- if (edgemarkerlist != NULL) {
- fprintf(fout, " %d", edgemarkerlist[i]);
- }
- fprintf(fout, "\n");
- }
-
- fclose(fout);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// save_neighbors() Save egdes to a .neigh file. //
-// //
-// 'filename' is a string containing the file name without suffix. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenio::save_neighbors(char* filename)
-{
- FILE *fout;
- char outneighborfilename[FILENAMESIZE];
- int i;
-
- sprintf(outneighborfilename, "%s.neigh", filename);
- printf("Saving neighbors to %s\n", outneighborfilename);
- fout = fopen(outneighborfilename, "w");
- fprintf(fout, "%d %d\n", numberoftetrahedra, mesh_dim + 1);
- for (i = 0; i < numberoftetrahedra; i++) {
- if (mesh_dim == 2) {
- fprintf(fout, "%d %5d %5d %5d", i + firstnumber, neighborlist[i * 3],
- neighborlist[i * 3 + 1], neighborlist[i * 3 + 2]);
- } else {
- fprintf(fout, "%d %5d %5d %5d %5d", i + firstnumber,
- neighborlist[i * 4], neighborlist[i * 4 + 1],
- neighborlist[i * 4 + 2], neighborlist[i * 4 + 3]);
- }
- fprintf(fout, "\n");
- }
-
- fclose(fout);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// save_poly() Save segments or facets to a .poly file. //
-// //
-// 'filename' is a string containing the file name without suffix. It only //
-// save the facets, holes and regions. The nodes are saved in a .node file //
-// by routine save_nodes(). //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenio::save_poly(char* filename)
-{
- FILE *fout;
- facet *f;
- polygon *p;
- char outpolyfilename[FILENAMESIZE];
- int i, j, k;
-
- sprintf(outpolyfilename, "%s.poly", filename);
- printf("Saving poly to %s\n", outpolyfilename);
- fout = fopen(outpolyfilename, "w");
-
- // The zero indicates that the vertices are in a separate .node file.
- // Followed by number of dimensions, number of vertex attributes,
- // and number of boundary markers (zero or one).
- fprintf(fout, "%d %d %d %d\n", 0, mesh_dim, numberofpointattributes,
- pointmarkerlist != NULL ? 1 : 0);
-
- // Save segments or facets.
- if (mesh_dim == 2) {
- // Number of segments, number of boundary markers (zero or one).
- fprintf(fout, "%d %d\n", numberofedges, edgemarkerlist != NULL ? 1 : 0);
- for (i = 0; i < numberofedges; i++) {
- fprintf(fout, "%d %4d %4d", i + firstnumber, edgelist[i * 2],
- edgelist[i * 2 + 1]);
- if (edgemarkerlist != NULL) {
- fprintf(fout, " %d", edgemarkerlist[i]);
- }
- fprintf(fout, "\n");
- }
- } else {
- // Number of facets, number of boundary markers (zero or one).
- fprintf(fout, "%d %d\n", numberoffacets, facetmarkerlist != NULL ? 1 : 0);
- for (i = 0; i < numberoffacets; i++) {
- f = &(facetlist[i]);
- fprintf(fout, "%d %d %d # %d\n", f->numberofpolygons,f->numberofholes,
- facetmarkerlist != NULL ? facetmarkerlist[i] : 0, i + firstnumber);
- // Output polygons of this facet.
- for (j = 0; j < f->numberofpolygons; j++) {
- p = &(f->polygonlist[j]);
- fprintf(fout, "%d ", p->numberofvertices);
- for (k = 0; k < p->numberofvertices; k++) {
- if (((k + 1) % 10) == 0) {
- fprintf(fout, "\n ");
- }
- fprintf(fout, " %d", p->vertexlist[k]);
- }
- fprintf(fout, "\n");
- }
- // Output holes of this facet.
- for (j = 0; j < f->numberofholes; j++) {
- fprintf(fout, "%d %.12g %.12g %.12g\n", j + firstnumber,
- f->holelist[j * 3], f->holelist[j * 3 + 1], f->holelist[j * 3 + 2]);
- }
- }
- }
-
- // Save holes.
- fprintf(fout, "%d\n", numberofholes);
- for (i = 0; i < numberofholes; i++) {
- // Output x, y coordinates.
- fprintf(fout, "%d %.12g %.12g", i + firstnumber, holelist[i * mesh_dim],
- holelist[i * mesh_dim + 1]);
- if (mesh_dim == 3) {
- // Output z coordinate.
- fprintf(fout, " %.12g", holelist[i * mesh_dim + 2]);
- }
- fprintf(fout, "\n");
- }
-
- // Save regions.
- fprintf(fout, "%d\n", numberofregions);
- for (i = 0; i < numberofregions; i++) {
- if (mesh_dim == 2) {
- // Output the index, x, y coordinates, attribute (region number)
- // and maximum area constraint (maybe -1).
- fprintf(fout, "%d %.12g %.12g %.12g %.12g\n", i + firstnumber,
- regionlist[i * 4], regionlist[i * 4 + 1],
- regionlist[i * 4 + 2], regionlist[i * 4 + 3]);
- } else {
- // Output the index, x, y, z coordinates, attribute (region number)
- // and maximum volume constraint (maybe -1).
- fprintf(fout, "%d %.12g %.12g %.12g %.12g %.12g\n", i + firstnumber,
- regionlist[i * 5], regionlist[i * 5 + 1],
- regionlist[i * 5 + 2], regionlist[i * 5 + 3],
- regionlist[i * 5 + 4]);
- }
- }
-
- fclose(fout);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// readline() Read a nonempty line from a file. //
-// //
-// A line is considered "nonempty" if it contains something more than white //
-// spaces. If a line is considered empty, it will be dropped and the next //
-// line will be read, this process ends until reaching the end-of-file or a //
-// non-empty line. Return NULL if it is the end-of-file, otherwise, return //
-// a pointer to the first non-whitespace character of the line. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-char* tetgenio::readline(char *string, FILE *infile, int *linenumber)
-{
- char *result;
-
- // Search for a non-empty line.
- do {
- result = fgets(string, INPUTLINESIZE - 1, infile);
- if (linenumber) (*linenumber)++;
- if (result == (char *) NULL) {
- return (char *) NULL;
- }
- // Skip white spaces.
- while ((*result == ' ') || (*result == '\t')) result++;
- // If it's end of line, read another line and try again.
- } while (*result == '\0');
- return result;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// findnextfield() Find the next field of a string. //
-// //
-// Jumps past the current field by searching for whitespace or a comma, then //
-// jumps past the whitespace or the comma to find the next field. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-char* tetgenio::findnextfield(char *string)
-{
- char *result;
-
- result = string;
- // Skip the current field. Stop upon reaching whitespace or a comma.
- while ((*result != '\0') && (*result != ' ') && (*result != '\t') &&
- (*result != ',') && (*result != ';')) {
- result++;
- }
- // Now skip the whitespace or the comma, stop at anything else that looks
- // like a character, or the end of a line.
- while ((*result == ' ') || (*result == '\t') || (*result == ',') ||
- (*result == ';')) {
- result++;
- }
- return result;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// readnumberline() Read a nonempty number line from a file. //
-// //
-// A line is considered "nonempty" if it contains something that looks like //
-// a number. Comments (prefaced by `#') are ignored. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-char* tetgenio::readnumberline(char *string, FILE *infile, char *infilename)
-{
- char *result;
-
- // Search for something that looks like a number.
- do {
- result = fgets(string, INPUTLINESIZE, infile);
- if (result == (char *) NULL) {
- if (infilename != (char *) NULL) {
- printf(" Error: Unexpected end of file in %s.\n", infilename);
- terminatetetgen(1);
- }
- return result;
- }
- // Skip anything that doesn't look like a number, a comment,
- // or the end of a line.
- while ((*result != '\0') && (*result != '#')
- && (*result != '.') && (*result != '+') && (*result != '-')
- && ((*result < '0') || (*result > '9'))) {
- result++;
- }
- // If it's a comment or end of line, read another line and try again.
- } while ((*result == '#') || (*result == '\0'));
- return result;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// findnextnumber() Find the next field of a number string. //
-// //
-// Jumps past the current field by searching for whitespace or a comma, then //
-// jumps past the whitespace or the comma to find the next field that looks //
-// like a number. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-char* tetgenio::findnextnumber(char *string)
-{
- char *result;
-
- result = string;
- // Skip the current field. Stop upon reaching whitespace or a comma.
- while ((*result != '\0') && (*result != '#') && (*result != ' ') &&
- (*result != '\t') && (*result != ',')) {
- result++;
- }
- // Now skip the whitespace and anything else that doesn't look like a
- // number, a comment, or the end of a line.
- while ((*result != '\0') && (*result != '#')
- && (*result != '.') && (*result != '+') && (*result != '-')
- && ((*result < '0') || (*result > '9'))) {
- result++;
- }
- // Check for a comment (prefixed with `#').
- if (*result == '#') {
- *result = '\0';
- }
- return result;
-}
-
-//
-// End of class 'tetgenio' implementation
-//
-
-static REAL PI = 3.14159265358979323846264338327950288419716939937510582;
-
-//
-// Begin of class 'tetgenbehavior' implementation
-//
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// tetgenbehavior() Initialize veriables of 'tetgenbehavior'. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-tetgenbehavior::tetgenbehavior()
-{
- // Initialize command line switches.
- plc = 0;
- quality = 0;
- refine = 0;
- coarse = 0;
- metric = 0;
- minratio = 2.0;
- goodratio = 0.0;
- minangle = 20.0;
- goodangle = 0.0;
- maxdihedral = 165.0;
- mindihedral = 5.0;
- varvolume = 0;
- fixedvolume = 0;
- maxvolume = -1.0;
- regionattrib = 0;
- insertaddpoints = 0;
- diagnose = 0;
- offcenter = 0;
- conformdel = 0;
- alpha1 = sqrt(2.0);
- alpha2 = 1.0;
- alpha3 = 0.6;
- zeroindex = 0;
- facesout = 0;
- edgesout = 0;
- neighout = 0;
- voroout = 0;
- meditview = 0;
- gidview = 0;
- geomview = 0;
- optlevel = 3;
- optpasses = 3;
- order = 1;
- nojettison = 0;
- nobound = 0;
- nonodewritten = 0;
- noelewritten = 0;
- nofacewritten = 0;
- noiterationnum = 0;
- nobisect = 0;
- noflip = 0;
- steiner = -1;
- fliprepair = 1;
- nomerge = 0;
- docheck = 0;
- quiet = 0;
- verbose = 0;
- useshelles = 0;
- epsilon = 1.0e-8;
- epsilon2 = 1.0e-5;
- object = NONE;
- // Initialize strings
- commandline[0] = '\0';
- infilename[0] = '\0';
- outfilename[0] = '\0';
- addinfilename[0] = '\0';
- bgmeshfilename[0] = '\0';
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// versioninfo() Print the version information of TetGen. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenbehavior::versioninfo()
-{
- printf("Version 1.4.2 (April 16, 2007).\n");
- printf("\n");
- printf("Copyright (C) 2002 - 2007\n");
- printf("Hang Si\n");
- printf("Mohrenstr. 39, 10117 Berlin, Germany\n");
- printf("si@wias-berlin.de\n");
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// syntax() Print list of command line switches and exit the program. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenbehavior::syntax()
-{
- printf(" tetgen [-prq_Ra_AiMYS_T_dzo_fenvgGOJBNEFICQVh] input_file\n");
- printf(" -p Tetrahedralizes a piecewise linear complex (PLC).\n");
- printf(" -r Reconstructs a previously generated mesh.\n");
- printf(" -q Quality mesh generation (adding new mesh points to ");
- printf("improve mesh quality).\n");
- printf(" -R Mesh coarsening (deleting redundant mesh points).\n");
- printf(" -a Applies a maximum tetrahedron volume constraint.\n");
- printf(" -A Assigns attributes to identify tetrahedra in different ");
- printf("regions.\n");
- printf(" -i Inserts a list of additional points into mesh.\n");
- printf(" -M Does not merge coplanar facets.\n");
- printf(" -Y Suppresses boundary facets/segments splitting.\n");
- printf(" -S Specifies maximum number of added points.\n");
- printf(" -T Sets a tolerance for coplanar test (default 1e-8).\n");
- printf(" -d Detects self-intersections of facets of the PLC.\n");
- printf(" -z Numbers all output items starting from zero.\n");
- printf(" -o2 Generates second-order subparametric elements.\n");
- printf(" -f Outputs all faces to .face file.");
- printf("file.\n");
- printf(" -e Outputs all edges to .edge file.\n");
- printf(" -n Outputs tetrahedra neighbors to .neigh file.\n");
- printf(" -v Outputs Voronoi diagram to files.\n");
- printf(" -g Outputs mesh to .mesh file for viewing by Medit.\n");
- printf(" -G Outputs mesh to .msh file for viewing by Gid.\n");
- printf(" -O Outputs mesh to .off file for viewing by Geomview.\n");
- printf(" -J No jettison of unused vertices from output .node file.\n");
- printf(" -B Suppresses output of boundary information.\n");
- printf(" -N Suppresses output of .node file.\n");
- printf(" -E Suppresses output of .ele file.\n");
- printf(" -F Suppresses output of .face file.\n");
- printf(" -I Suppresses mesh iteration numbers.\n");
- printf(" -C Checks the consistency of the final mesh.\n");
- printf(" -Q Quiet: No terminal output except errors.\n");
- printf(" -V Verbose: Detailed information, more terminal output.\n");
- printf(" -h Help: A brief instruction for using TetGen.\n");
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// usage() Print a brief instruction for using TetGen. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenbehavior::usage()
-{
- printf("TetGen\n");
- printf("A Quality Tetrahedral Mesh Generator and 3D Delaunay ");
- printf("Triangulator\n");
- versioninfo();
- printf("\n");
- printf("What Can TetGen Do?\n");
- printf("\n");
- printf(" TetGen generates exact Delaunay tetrahedralizations, exact\n");
- printf(" constrained Delaunay tetrahedralizations, and quality ");
- printf("tetrahedral\n meshes. The latter are nicely graded and whose ");
- printf("tetrahedra have\n radius-edge ratio bounded, thus are suitable ");
- printf("for finite element and\n finite volume analysis.\n");
- printf("\n");
- printf("Command Line Syntax:\n");
- printf("\n");
- printf(" Below is the command line syntax of TetGen with a list of ");
- printf("short\n");
- printf(" descriptions. Underscores indicate that numbers may optionally\n");
- printf(" follow certain switches. Do not leave any space between a ");
- printf("switch\n");
- printf(" and its numeric parameter. \'input_file\' contains input data\n");
- printf(" depending on the switches you supplied which may be a ");
- printf(" piecewise\n");
- printf(" linear complex or a list of nodes. File formats and detailed\n");
- printf(" description of command line switches are found in user's ");
- printf("manual.\n");
- printf("\n");
- syntax();
- printf("\n");
- printf("Examples of How to Use TetGen:\n");
- printf("\n");
- printf(" \'tetgen object\' reads vertices from object.node, and writes ");
- printf("their\n Delaunay tetrahedralization to object.1.node and ");
- printf("object.1.ele.\n");
- printf("\n");
- printf(" \'tetgen -p object\' reads a PLC from object.poly or object.");
- printf("smesh (and\n possibly object.node) and writes its constrained ");
- printf("Delaunay\n tetrahedralization to object.1.node, object.1.ele and ");
- printf("object.1.face.\n");
- printf("\n");
- printf(" \'tetgen -pq1.414a.1 object\' reads a PLC from object.poly or\n");
- printf(" object.smesh (and possibly object.node), generates a mesh ");
- printf("whose\n tetrahedra have radius-edge ratio smaller than 1.414 and ");
- printf("have volume\n of 0.1 or less, and writes the mesh to ");
- printf("object.1.node, object.1.ele\n and object.1.face.\n");
- printf("\n");
- printf("Please send bugs/comments to Hang Si <si@wias-berlin.de>\n");
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// parse_commandline() Read the command line, identify switches, and set //
-// up options and file names. //
-// //
-// 'argc' and 'argv' are the same parameters passed to the function main() //
-// of a C/C++ program. They together represent the command line user invoked //
-// from an environment in which TetGen is running. //
-// //
-// When TetGen is invoked from an environment. 'argc' is nonzero, switches //
-// and input filename should be supplied as zero-terminated strings in //
-// argv[0] through argv[argc - 1] and argv[0] shall be the name used to //
-// invoke TetGen, i.e. "tetgen". Switches are previously started with a //
-// dash '-' to identify them from the input filename. //
-// //
-// When TetGen is called from within another program. 'argc' is set to zero. //
-// switches are given in one zero-terminated string (no previous dash is //
-// required.), and 'argv' is a pointer points to this string. No input //
-// filename is required (usually the input data has been directly created by //
-// user in the 'tetgenio' structure). A default filename 'tetgen-tmpfile' //
-// will be created for debugging output purpose. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenbehavior::parse_commandline(int argc, char **argv)
-{
- int startindex;
- int increment;
- int meshnumber;
- int scount;
- int i, j, k;
- char workstring[1024];
-
- // First determine the input style of the switches.
- if (argc == 0) {
- startindex = 0; // Switches are given without a dash.
- argc = 1; // For running the following for-loop once.
- commandline[0] = '\0';
- } else {
- startindex = 1;
- strcpy(commandline, argv[0]);
- strcat(commandline, " ");
- }
-
- // Rcount used to count the number of '-R' be used.
- scount = 0;
-
- for (i = startindex; i < argc; i++) {
- // Remember the command line switches.
- strcat(commandline, argv[i]);
- strcat(commandline, " ");
- if (startindex == 1) {
- // Is this string a filename?
- if (argv[i][0] != '-') {
- strncpy(infilename, argv[i], 1024 - 1);
- infilename[1024 - 1] = '\0';
- // Go to the next string directly.
- continue;
- }
- }
- // Parse the individual switch from the string.
- for (j = startindex; argv[i][j] != '\0'; j++) {
- if (argv[i][j] == 'p') {
- plc = 1;
- } else if (argv[i][j] == 'r') {
- refine = 1;
- } else if (argv[i][j] == 'R') {
- coarse = 1;
- } else if (argv[i][j] == 'q') {
- quality++;
- if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
- (argv[i][j + 1] == '.')) {
- k = 0;
- while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
- (argv[i][j + 1] == '.')) {
- j++;
- workstring[k] = argv[i][j];
- k++;
- }
- workstring[k] = '\0';
- if (quality == 1) {
- minratio = (REAL) strtod(workstring, (char **) NULL);
- } else if (quality == 2) {
- mindihedral = (REAL) strtod(workstring, (char **) NULL);
- } else if (quality == 3) {
- maxdihedral = (REAL) strtod(workstring, (char **) NULL);
- } else if (quality == 4) {
- alpha2 = (REAL) strtod(workstring, (char **) NULL);
- } else if (quality == 5) {
- alpha1 = (REAL) strtod(workstring, (char **) NULL);
- }
- }
- } else if (argv[i][j] == 'm') {
- metric++;
- if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
- (argv[i][j + 1] == '.')) {
- k = 0;
- while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
- (argv[i][j + 1] == '.')) {
- j++;
- workstring[k] = argv[i][j];
- k++;
- }
- workstring[k] = '\0';
- if (metric == 1) {
- alpha1 = (REAL) strtod(workstring, (char **) NULL);
- } else if (metric == 2) {
- alpha2 = (REAL) strtod(workstring, (char **) NULL);
- }
- }
- } else if (argv[i][j] == 'a') {
- if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
- (argv[i][j + 1] == '.')) {
- fixedvolume = 1;
- k = 0;
- while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
- (argv[i][j + 1] == '.') || (argv[i][j + 1] == 'e') ||
- (argv[i][j + 1] == '-') || (argv[i][j + 1] == '+')) {
- j++;
- workstring[k] = argv[i][j];
- k++;
- }
- workstring[k] = '\0';
- maxvolume = (REAL) strtod(workstring, (char **) NULL);
- } else {
- varvolume = 1;
- }
- } else if (argv[i][j] == 'A') {
- regionattrib++;
- } else if (argv[i][j] == 'i') {
- insertaddpoints = 1;
- } else if (argv[i][j] == 'd') {
- diagnose = 1;
- } else if (argv[i][j] == 'z') {
- zeroindex = 1;
- } else if (argv[i][j] == 'f') {
- facesout = 1;
- } else if (argv[i][j] == 'e') {
- edgesout++;
- } else if (argv[i][j] == 'n') {
- neighout++;
- } else if (argv[i][j] == 'v') {
- voroout = 1;
- } else if (argv[i][j] == 'g') {
- meditview = 1;
- } else if (argv[i][j] == 'G') {
- gidview = 1;
- } else if (argv[i][j] == 'O') {
- geomview = 1;
- } else if (argv[i][j] == 'M') {
- nomerge = 1;
- } else if (argv[i][j] == 'Y') {
- nobisect++;
- } else if (argv[i][j] == 'J') {
- nojettison = 1;
- } else if (argv[i][j] == 'B') {
- nobound = 1;
- } else if (argv[i][j] == 'N') {
- nonodewritten = 1;
- } else if (argv[i][j] == 'E') {
- noelewritten = 1;
- } else if (argv[i][j] == 'F') {
- nofacewritten = 1;
- } else if (argv[i][j] == 'I') {
- noiterationnum = 1;
- } else if (argv[i][j] == 'o') {
- if (argv[i][j + 1] == '2') {
- j++;
- order = 2;
- }
- } else if (argv[i][j] == 'S') {
- if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
- (argv[i][j + 1] == '.')) {
- k = 0;
- while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
- (argv[i][j + 1] == '.') || (argv[i][j + 1] == 'e') ||
- (argv[i][j + 1] == '-') || (argv[i][j + 1] == '+')) {
- j++;
- workstring[k] = argv[i][j];
- k++;
- }
- workstring[k] = '\0';
- steiner = (int) strtol(workstring, (char **) NULL, 0);
- }
- } else if (argv[i][j] == 's') {
- scount++;
- if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
- (argv[i][j + 1] == '.')) {
- k = 0;
- while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
- (argv[i][j + 1] == '.') || (argv[i][j + 1] == 'e') ||
- (argv[i][j + 1] == '-') || (argv[i][j + 1] == '+')) {
- j++;
- workstring[k] = argv[i][j];
- k++;
- }
- workstring[k] = '\0';
- if (scount == 1) {
- optlevel = (int) strtol(workstring, (char **) NULL, 0);
- } else if (scount == 2) {
- optpasses = (int) strtol(workstring, (char **) NULL, 0);
- }
- }
- } else if (argv[i][j] == 'D') {
- conformdel++;
- } else if (argv[i][j] == 'T') {
- if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
- (argv[i][j + 1] == '.')) {
- k = 0;
- while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
- (argv[i][j + 1] == '.') || (argv[i][j + 1] == 'e') ||
- (argv[i][j + 1] == '-') || (argv[i][j + 1] == '+')) {
- j++;
- workstring[k] = argv[i][j];
- k++;
- }
- workstring[k] = '\0';
- epsilon = (REAL) strtod(workstring, (char **) NULL);
- }
- } else if (argv[i][j] == 'C') {
- docheck++;
- } else if (argv[i][j] == 'X') {
- fliprepair = 0;
- } else if (argv[i][j] == 'Q') {
- quiet = 1;
- } else if (argv[i][j] == 'V') {
- verbose++;
- // } else if (argv[i][j] == 'v') {
- // versioninfo();
- // terminatetetgen(0);
- } else if ((argv[i][j] == 'h') || (argv[i][j] == 'H') ||
- (argv[i][j] == '?')) {
- usage();
- terminatetetgen(0);
- } else {
- printf("Warning: Unknown switch -%c.\n", argv[i][j]);
- }
- }
- }
-
- if (startindex == 0) {
- // Set a temporary filename for debugging output.
- strcpy(infilename, "tetgen-tmpfile");
- } else {
- if (infilename[0] == '\0') {
- // No input file name. Print the syntax and exit.
- syntax();
- terminatetetgen(0);
- }
- // Recognize the object from file extension if it is available.
- if (!strcmp(&infilename[strlen(infilename) - 5], ".node")) {
- infilename[strlen(infilename) - 5] = '\0';
- object = NODES;
- } else if (!strcmp(&infilename[strlen(infilename) - 5], ".poly")) {
- infilename[strlen(infilename) - 5] = '\0';
- object = POLY;
- plc = 1;
- } else if (!strcmp(&infilename[strlen(infilename) - 6], ".smesh")) {
- infilename[strlen(infilename) - 6] = '\0';
- object = POLY;
- plc = 1;
- } else if (!strcmp(&infilename[strlen(infilename) - 4], ".off")) {
- infilename[strlen(infilename) - 4] = '\0';
- object = OFF;
- plc = 1;
- } else if (!strcmp(&infilename[strlen(infilename) - 4], ".ply")) {
- infilename[strlen(infilename) - 4] = '\0';
- object = PLY;
- plc = 1;
- } else if (!strcmp(&infilename[strlen(infilename) - 4], ".stl")) {
- infilename[strlen(infilename) - 4] = '\0';
- object = STL;
- plc = 1;
- } else if (!strcmp(&infilename[strlen(infilename) - 5], ".mesh")) {
- infilename[strlen(infilename) - 5] = '\0';
- object = MEDIT;
- plc = 1;
- } else if (!strcmp(&infilename[strlen(infilename) - 4], ".ele")) {
- infilename[strlen(infilename) - 4] = '\0';
- object = MESH;
- refine = 1;
- }
- }
- plc = plc || diagnose;
- useshelles = plc || refine || coarse || quality;
- goodratio = minratio;
- goodratio *= goodratio;
-
- // Detect improper combinations of switches.
- if (plc && refine) {
- printf("Error: Switch -r cannot use together with -p.\n");
- return false;
- }
- if (refine && (plc || noiterationnum)) {
- printf("Error: Switches %s cannot use together with -r.\n",
- "-p, -d, and -I");
- return false;
- }
- if (diagnose && (quality || insertaddpoints || (order == 2) || neighout
- || docheck)) {
- printf("Error: Switches %s cannot use together with -d.\n",
- "-q, -i, -o2, -n, and -C");
- return false;
- }
-
- // Be careful not to allocate space for element area constraints that
- // will never be assigned any value (other than the default -1.0).
- if (!refine && !plc) {
- varvolume = 0;
- }
- // Be careful not to add an extra attribute to each element unless the
- // input supports it (PLC in, but not refining a preexisting mesh).
- if (refine || !plc) {
- regionattrib = 0;
- }
- // If '-a' or '-aa' is in use, enable '-q' option too.
- if (fixedvolume || varvolume) {
- if (quality == 0) {
- quality = 1;
- }
- }
- // Calculate the goodangle for testing bad subfaces.
- goodangle = cos(minangle * PI / 180.0);
- goodangle *= goodangle;
-
- increment = 0;
- strcpy(workstring, infilename);
- j = 1;
- while (workstring[j] != '\0') {
- if ((workstring[j] == '.') && (workstring[j + 1] != '\0')) {
- increment = j + 1;
- }
- j++;
- }
- meshnumber = 0;
- if (increment > 0) {
- j = increment;
- do {
- if ((workstring[j] >= '0') && (workstring[j] <= '9')) {
- meshnumber = meshnumber * 10 + (int) (workstring[j] - '0');
- } else {
- increment = 0;
- }
- j++;
- } while (workstring[j] != '\0');
- }
- if (noiterationnum) {
- strcpy(outfilename, infilename);
- } else if (increment == 0) {
- strcpy(outfilename, infilename);
- strcat(outfilename, ".1");
- } else {
- workstring[increment] = '%';
- workstring[increment + 1] = 'd';
- workstring[increment + 2] = '\0';
- sprintf(outfilename, workstring, meshnumber + 1);
- }
- // Additional input file name has the end ".a".
- strcpy(addinfilename, infilename);
- strcat(addinfilename, ".a");
- // Background filename has the form "*.b.ele", "*.b.node", ...
- strcpy(bgmeshfilename, infilename);
- strcat(bgmeshfilename, ".b");
-
- return true;
-}
-
-//
-// End of class 'tetgenbehavior' implementation
-//
-
-//
-// Begin of class 'tetgenmesh' implementation
-//
-
-//
-// Begin of class 'list', 'memorypool' and 'link' implementation
-//
-
-// Following are predefined compare functions for primitive data types.
-// These functions take two pointers of the corresponding date type,
-// perform the comparation. Return -1, 0 or 1 indicating the default
-// linear order of two operators.
-
-// Compare two 'integers'.
-int tetgenmesh::compare_2_ints(const void* x, const void* y) {
- if (* (int *) x < * (int *) y) {
- return -1;
- } else if (* (int *) x > * (int *) y) {
- return 1;
- } else {
- return 0;
- }
-}
-
-// Compare two 'longs'. Note: in 64-bit machine the 'long' type is 64-bit
-// (8-byte) where the 'int' only 32-bit (4-byte).
-int tetgenmesh::compare_2_longs(const void* x, const void* y) {
- if (* (long *) x < * (long *) y) {
- return -1;
- } else if (* (long *) x > * (long *) y) {
- return 1;
- } else {
- return 0;
- }
-}
-
-// Compare two 'unsigned longs'.
-int tetgenmesh::compare_2_unsignedlongs(const void* x, const void* y) {
- if (* (unsigned long *) x < * (unsigned long *) y) {
- return -1;
- } else if (* (unsigned long *) x > * (unsigned long *) y) {
- return 1;
- } else {
- return 0;
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// set_compfunc() Determine the size of primitive data types and set the //
-// corresponding predefined linear order functions. //
-// //
-// 'str' is a zero-end string indicating a primitive data type, like 'int', //
-// 'long' or 'unsigned long'. Every string ending with a '*' is though as a //
-// type of pointer and the type 'unsign long' is used for it. //
-// //
-// When the type of 'str' is determined, the size of this type (in byte) is //
-// returned in 'itbytes', and the pointer of corresponding predefined linear //
-// order functions is returned in 'pcomp'. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::set_compfunc(char* str, int* itbytes, compfunc* pcomp)
-{
- // First figure out whether it is a pointer or not.
- if (str[strlen(str) - 1] == '*') {
- *itbytes = sizeof(unsigned long);
- *pcomp = &compare_2_unsignedlongs;
- return;
- }
- // Then determine other types.
- if (strcmp(str, "int") == 0) {
- *itbytes = sizeof(int);
- *pcomp = &compare_2_ints;
- } else if (strcmp(str, "long") == 0) {
- *itbytes = sizeof(long);
- *pcomp = &compare_2_longs;
- } else if (strcmp(str, "unsigned long") == 0) {
- *itbytes = sizeof(unsigned long);
- *pcomp = &compare_2_unsignedlongs;
- } else {
- // It is an unknown type.
- printf("Error in set_compfunc(): unknown type %s.\n", str);
- terminatetetgen(1);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// listinit() Initialize a list for storing a data type. //
-// //
-// Determine the size of each item, set the maximum size allocated at onece, //
-// set the expand size in case the list is full, and set the linear order //
-// function if it is provided (default is NULL). //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::list::
-listinit(int itbytes, compfunc pcomp, int mitems,int exsize)
-{
-#ifdef SELF_CHECK
- assert(itbytes > 0 && mitems > 0 && exsize > 0);
-#endif
- itembytes = itbytes;
- comp = pcomp;
- maxitems = mitems;
- expandsize = exsize;
- base = (char *) malloc(maxitems * itembytes);
- if (base == (char *) NULL) {
- printf("Error: Out of memory.\n");
- terminatetetgen(1);
- }
- items = 0;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// append() Add a new item at the end of the list. //
-// //
-// A new space at the end of this list will be allocated for storing the new //
-// item. If the memory is not sufficient, reallocation will be performed. If //
-// 'appitem' is not NULL, the contents of this pointer will be copied to the //
-// new allocated space. Returns the pointer to the new allocated space. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void* tetgenmesh::list::append(void *appitem)
-{
- // Do we have enough space?
- if (items == maxitems) {
- char* newbase = (char *) realloc(base, (maxitems + expandsize) *
- itembytes);
- if (newbase == (char *) NULL) {
- printf("Error: Out of memory.\n");
- terminatetetgen(1);
- }
- base = newbase;
- maxitems += expandsize;
- }
- if (appitem != (void *) NULL) {
- memcpy(base + items * itembytes, appitem, itembytes);
- }
- items++;
- return (void *) (base + (items - 1) * itembytes);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// insert() Insert an item before 'pos' (range from 0 to items - 1). //
-// //
-// A new space will be inserted at the position 'pos', that is, items lie //
-// after pos (including the item at pos) will be moved one space downwords. //
-// If 'insitem' is not NULL, its contents will be copied into the new //
-// inserted space. Return a pointer to the new inserted space. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void* tetgenmesh::list::insert(int pos, void* insitem)
-{
- if (pos >= items) {
- return append(insitem);
- }
- // Do we have enough space.
- if (items == maxitems) {
- char* newbase = (char *) realloc(base, (maxitems + expandsize) *
- itembytes);
- if (newbase == (char *) NULL) {
- printf("Error: Out of memory.\n");
- terminatetetgen(1);
- }
- base = newbase;
- maxitems += expandsize;
- }
- // Do block move.
- memmove(base + (pos + 1) * itembytes, // dest
- base + pos * itembytes, // src
- (items - pos) * itembytes); // size in bytes
- // Insert the item.
- if (insitem != (void *) NULL) {
- memcpy(base + pos * itembytes, insitem, itembytes);
- }
- items++;
- return (void *) (base + pos * itembytes);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// del() Delete an item at 'pos' (range from 0 to items - 1). //
-// //
-// The space at 'pos' will be overlapped by other item. If 'order' is 1, the //
-// remaining items of the list have the same order as usual, i.e., items lie //
-// after pos will be moved one space upwords. If 'order' is 0, the last item //
-// of the list will be moved up to pos. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::list::del(int pos, int order)
-{
- // If 'pos' is the last item of the list, nothing need to do.
- if (pos >= 0 && pos < items - 1) {
- if (order == 1) {
- // Do block move.
- memmove(base + pos * itembytes, // dest
- base + (pos + 1) * itembytes, // src
- (items - pos - 1) * itembytes);
- } else {
- // Use the last item to overlap the del item.
- memcpy(base + pos * itembytes, // item at pos
- base + (items - 1) * itembytes, // item at last
- itembytes);
- }
- }
- if (items > 0) {
- items--;
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// hasitem() Search in this list to find if 'checkitem' exists. //
-// //
-// This routine assumes that a linear order function has been set. It loops //
-// through the entire list, compares each item to 'checkitem'. If it exists, //
-// return its position (between 0 to items - 1), otherwise, return -1. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-int tetgenmesh::list::hasitem(void* checkitem)
-{
- int i;
-
- for (i = 0; i < items; i++) {
- if (comp != (compfunc) NULL) {
- if ((* comp)((void *)(base + i * itembytes), checkitem) == 0) {
- return i;
- }
- }
- }
- return -1;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// sort() Sort the items with respect to a linear order function. //
-// //
-// Uses QuickSort routines (qsort) of the standard C/C++ library (stdlib.h). //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::list::sort()
-{
- qsort((void *) base, (size_t) items, (size_t) itembytes, comp);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// memorypool() The constructors of memorypool. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-tetgenmesh::memorypool::memorypool()
-{
- firstblock = nowblock = (void **) NULL;
- nextitem = (void *) NULL;
- deaditemstack = (void *) NULL;
- pathblock = (void **) NULL;
- pathitem = (void *) NULL;
- itemwordtype = POINTER;
- alignbytes = 0;
- itembytes = itemwords = 0;
- itemsperblock = 0;
- items = maxitems = 0l;
- unallocateditems = 0;
- pathitemsleft = 0;
-}
-
-tetgenmesh::memorypool::
-memorypool(int bytecount, int itemcount, enum wordtype wtype, int alignment)
-{
- poolinit(bytecount, itemcount, wtype, alignment);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// ~memorypool() Free to the operating system all memory taken by a pool. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-tetgenmesh::memorypool::~memorypool()
-{
- while (firstblock != (void **) NULL) {
- nowblock = (void **) *(firstblock);
- free(firstblock);
- firstblock = nowblock;
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// poolinit() Initialize a pool of memory for allocation of items. //
-// //
-// A `pool' is created whose records have size at least `bytecount'. Items //
-// will be allocated in `itemcount'-item blocks. Each item is assumed to be //
-// a collection of words, and either pointers or floating-point values are //
-// assumed to be the "primary" word type. (The "primary" word type is used //
-// to determine alignment of items.) If `alignment' isn't zero, all items //
-// will be `alignment'-byte aligned in memory. `alignment' must be either a //
-// multiple or a factor of the primary word size; powers of two are safe. //
-// `alignment' is normally used to create a few unused bits at the bottom of //
-// each item's pointer, in which information may be stored. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::memorypool::
-poolinit(int bytecount, int itemcount, enum wordtype wtype, int alignment)
-{
- int wordsize;
-
- // Initialize values in the pool.
- itemwordtype = wtype;
- wordsize = (itemwordtype == POINTER) ? sizeof(void *) : sizeof(REAL);
- // Find the proper alignment, which must be at least as large as:
- // - The parameter `alignment'.
- // - The primary word type, to avoid unaligned accesses.
- // - sizeof(void *), so the stack of dead items can be maintained
- // without unaligned accesses.
- if (alignment > wordsize) {
- alignbytes = alignment;
- } else {
- alignbytes = wordsize;
- }
- if ((int) sizeof(void *) > alignbytes) {
- alignbytes = (int) sizeof(void *);
- }
- itemwords = ((bytecount + alignbytes - 1) / alignbytes)
- * (alignbytes / wordsize);
- itembytes = itemwords * wordsize;
- itemsperblock = itemcount;
-
- // Allocate a block of items. Space for `itemsperblock' items and one
- // pointer (to point to the next block) are allocated, as well as space
- // to ensure alignment of the items.
- firstblock = (void **) malloc(itemsperblock * itembytes + sizeof(void *)
- + alignbytes);
- if (firstblock == (void **) NULL) {
- printf("Error: Out of memory.\n");
- terminatetetgen(1);
- }
- // Set the next block pointer to NULL.
- *(firstblock) = (void *) NULL;
- restart();
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// restart() Deallocate all items in this pool. //
-// //
-// The pool is returned to its starting state, except that no memory is //
-// freed to the operating system. Rather, the previously allocated blocks //
-// are ready to be reused. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::memorypool::restart()
-{
- unsigned long alignptr;
-
- items = 0;
- maxitems = 0;
-
- // Set the currently active block.
- nowblock = firstblock;
- // Find the first item in the pool. Increment by the size of (void *).
- alignptr = (unsigned long) (nowblock + 1);
- // Align the item on an `alignbytes'-byte boundary.
- nextitem = (void *)
- (alignptr + (unsigned long) alignbytes -
- (alignptr % (unsigned long) alignbytes));
- // There are lots of unallocated items left in this block.
- unallocateditems = itemsperblock;
- // The stack of deallocated items is empty.
- deaditemstack = (void *) NULL;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// alloc() Allocate space for an item. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void* tetgenmesh::memorypool::alloc()
-{
- void *newitem;
- void **newblock;
- unsigned long alignptr;
-
- // First check the linked list of dead items. If the list is not
- // empty, allocate an item from the list rather than a fresh one.
- if (deaditemstack != (void *) NULL) {
- newitem = deaditemstack; // Take first item in list.
- deaditemstack = * (void **) deaditemstack;
- } else {
- // Check if there are any free items left in the current block.
- if (unallocateditems == 0) {
- // Check if another block must be allocated.
- if (*nowblock == (void *) NULL) {
- // Allocate a new block of items, pointed to by the previous block.
- newblock = (void **) malloc(itemsperblock * itembytes + sizeof(void *)
- + alignbytes);
- if (newblock == (void **) NULL) {
- printf("Error: Out of memory.\n");
- terminatetetgen(1);
- }
- *nowblock = (void *) newblock;
- // The next block pointer is NULL.
- *newblock = (void *) NULL;
- }
- // Move to the new block.
- nowblock = (void **) *nowblock;
- // Find the first item in the block.
- // Increment by the size of (void *).
- alignptr = (unsigned long) (nowblock + 1);
- // Align the item on an `alignbytes'-byte boundary.
- nextitem = (void *)
- (alignptr + (unsigned long) alignbytes -
- (alignptr % (unsigned long) alignbytes));
- // There are lots of unallocated items left in this block.
- unallocateditems = itemsperblock;
- }
- // Allocate a new item.
- newitem = nextitem;
- // Advance `nextitem' pointer to next free item in block.
- if (itemwordtype == POINTER) {
- nextitem = (void *) ((void **) nextitem + itemwords);
- } else {
- nextitem = (void *) ((REAL *) nextitem + itemwords);
- }
- unallocateditems--;
- maxitems++;
- }
- items++;
- return newitem;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// dealloc() Deallocate space for an item. //
-// //
-// The deallocated space is stored in a queue for later reuse. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::memorypool::dealloc(void *dyingitem)
-{
- // Push freshly killed item onto stack.
- *((void **) dyingitem) = deaditemstack;
- deaditemstack = dyingitem;
- items--;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// traversalinit() Prepare to traverse the entire list of items. //
-// //
-// This routine is used in conjunction with traverse(). //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::memorypool::traversalinit()
-{
- unsigned long alignptr;
-
- // Begin the traversal in the first block.
- pathblock = firstblock;
- // Find the first item in the block. Increment by the size of (void *).
- alignptr = (unsigned long) (pathblock + 1);
- // Align with item on an `alignbytes'-byte boundary.
- pathitem = (void *)
- (alignptr + (unsigned long) alignbytes -
- (alignptr % (unsigned long) alignbytes));
- // Set the number of items left in the current block.
- pathitemsleft = itemsperblock;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// traverse() Find the next item in the list. //
-// //
-// This routine is used in conjunction with traversalinit(). Be forewarned //
-// that this routine successively returns all items in the list, including //
-// deallocated ones on the deaditemqueue. It's up to you to figure out which //
-// ones are actually dead. It can usually be done more space-efficiently by //
-// a routine that knows something about the structure of the item. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void* tetgenmesh::memorypool::traverse()
-{
- void *newitem;
- unsigned long alignptr;
-
- // Stop upon exhausting the list of items.
- if (pathitem == nextitem) {
- return (void *) NULL;
- }
- // Check whether any untraversed items remain in the current block.
- if (pathitemsleft == 0) {
- // Find the next block.
- pathblock = (void **) *pathblock;
- // Find the first item in the block. Increment by the size of (void *).
- alignptr = (unsigned long) (pathblock + 1);
- // Align with item on an `alignbytes'-byte boundary.
- pathitem = (void *)
- (alignptr + (unsigned long) alignbytes -
- (alignptr % (unsigned long) alignbytes));
- // Set the number of items left in the current block.
- pathitemsleft = itemsperblock;
- }
- newitem = pathitem;
- // Find the next item in the block.
- if (itemwordtype == POINTER) {
- pathitem = (void *) ((void **) pathitem + itemwords);
- } else {
- pathitem = (void *) ((REAL *) pathitem + itemwords);
- }
- pathitemsleft--;
- return newitem;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// linkinit() Initialize a link for storing items. //
-// //
-// The input parameters are the size of each item, a pointer of a linear //
-// order function and the number of items allocating in one memory bulk. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::link::linkinit(int bytecount, compfunc pcomp, int itemcount)
-{
-#ifdef SELF_CHECK
- assert(bytecount > 0 && itemcount > 0);
-#endif
- // Remember the real size of each item.
- linkitembytes = bytecount;
- // Set the linear order function for this link.
- comp = pcomp;
-
- // Call the constructor of 'memorypool' to initialize its variables.
- // like: itembytes, itemwords, items, ... Each node has size
- // bytecount + 2 * sizeof(void **), and total 'itemcount + 2' (because
- // link has additional two nodes 'head' and 'tail').
- poolinit(bytecount + 2 * sizeof(void **), itemcount + 2, POINTER, 0);
-
- // Initial state of this link.
- head = (void **) alloc();
- tail = (void **) alloc();
- *head = (void *) tail;
- *(head + 1) = NULL;
- *tail = NULL;
- *(tail + 1) = (void *) head;
- nextlinkitem = *head;
- curpos = 1;
- linkitems = 0;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// clear() Deallocate all nodes in this link. //
-// //
-// The link is returned to its starting state, except that no memory is //
-// freed to the operating system. Rather, the previously allocated blocks //
-// are ready to be reused. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::link::clear()
-{
- // Reset the pool.
- restart();
-
- // Initial state of this link.
- head = (void **) alloc();
- tail = (void **) alloc();
- *head = (void *) tail;
- *(head + 1) = NULL;
- *tail = NULL;
- *(tail + 1) = (void *) head;
- nextlinkitem = *head;
- curpos = 1;
- linkitems = 0;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// move() Causes 'nextlinkitem' to traverse the specified number of nodes,//
-// updates 'curpos' to be the node to which 'nextlinkitem' points. //
-// //
-// 'numberofnodes' is a number indicating how many nodes need be traversed //
-// (not counter the current node) need be traversed. It may be positive(move //
-// forward) or negative (move backward). Return TRUE if it is successful. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::link::move(int numberofnodes)
-{
- void **nownode;
- int i;
-
- nownode = (void **) nextlinkitem;
- if (numberofnodes > 0) {
- // Move forward.
- i = 0;
- while ((i < numberofnodes) && *nownode) {
- nownode = (void **) *nownode;
- i++;
- }
- if (*nownode == NULL) return false;
- nextlinkitem = (void *) nownode;
- curpos += numberofnodes;
- } else if (numberofnodes < 0) {
- // Move backward.
- i = 0;
- numberofnodes = -numberofnodes;
- while ((i < numberofnodes) && *(nownode + 1)) {
- nownode = (void **) *(nownode + 1);
- i++;
- }
- if (*(nownode + 1) == NULL) return false;
- nextlinkitem = (void *) nownode;
- curpos -= numberofnodes;
- }
- return true;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// locate() Locates the node at the specified position. //
-// //
-// The number 'pos' (between 1 and 'linkitems') indicates the location. This //
-// routine first decides the shortest path traversing from 'curpos' to 'pos',//
-// i.e., from head, tail or 'curpos'. Routine 'move()' is called to really //
-// traverse the link. If success, 'nextlinkitem' points to the node, 'curpos'//
-// and 'pos' are equal. Otherwise, return FALSE. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::link::locate(int pos)
-{
- int headdist, taildist, curdist;
- int abscurdist, mindist;
-
- if (pos < 1 || pos > linkitems) return false;
-
- headdist = pos - 1;
- taildist = linkitems - pos;
- curdist = pos - curpos;
- abscurdist = curdist >= 0 ? curdist : -curdist;
-
- if (headdist > taildist) {
- if (taildist > abscurdist) {
- mindist = curdist;
- } else {
- // taildist <= abs(curdist)
- mindist = -taildist;
- goend();
- }
- } else {
- // headdist <= taildist
- if (headdist > abscurdist) {
- mindist = curdist;
- } else {
- // headdist <= abs(curdist)
- mindist = headdist;
- rewind();
- }
- }
-
- return move(mindist);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// add() Add a node at the end of this link. //
-// //
-// A new node is appended to the end of the link. If 'newitem' is not NULL, //
-// its conents will be copied to the data slot of the new node. Returns the //
-// pointer to the newest added node. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void* tetgenmesh::link::add(void* newitem)
-{
- void **newnode = tail;
- if (newitem != (void *) NULL) {
- memcpy((void *)(newnode + 2), newitem, linkitembytes);
- }
- tail = (void **) alloc();
- *tail = NULL;
- *newnode = (void*) tail;
- *(tail + 1) = (void*) newnode;
- linkitems++;
- return (void *)(newnode + 2);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// insert() Inserts a node before the specified position. //
-// //
-// 'pos' (between 1 and 'linkitems') indicates the inserting position. This //
-// routine inserts a new node before the node of 'pos'. If 'newitem' is not //
-// NULL, its conents will be copied into the data slot of the new node. If //
-// 'pos' is larger than 'linkitems', it is equal as 'add()'. A pointer to //
-// the newest inserted item is returned. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void* tetgenmesh::link::insert(int pos, void* insitem)
-{
- if (!locate(pos)) {
- return add(insitem);
- }
-
- void **nownode = (void **) nextlinkitem;
-
- // Insert a node before 'nownode'.
- void **newnode = (void **) alloc();
- if (insitem != (void *) NULL) {
- memcpy((void *)(newnode + 2), insitem, linkitembytes);
- }
-
- *(void **)(*(nownode + 1)) = (void *) newnode;
- *newnode = (void *) nownode;
- *(newnode + 1) = *(nownode + 1);
- *(nownode + 1) = (void *) newnode;
-
- linkitems++;
-
- nextlinkitem = (void *) newnode;
- return (void *)(newnode + 2);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// del() Delete a node. //
-// //
-// Returns a pointer of the deleted data. If you try to delete a non-existed //
-// node (e.g. link is empty or a wrong index is given) return NULL. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void* tetgenmesh::link::deletenode(void** deadnode)
-{
- void **nextnode = (void **) *deadnode;
- void **prevnode = (void **) *(deadnode + 1);
- *prevnode = (void *) nextnode;
- *(nextnode + 1) = (void *) prevnode;
-
- dealloc((void *) deadnode);
- linkitems--;
-
- nextlinkitem = (void *) nextnode;
- return (void *)(deadnode + 2);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// del() Delete a node at the specified position. //
-// //
-// 'pos' between 1 and 'linkitems'. Returns a pointer of the deleted data. //
-// If you try to delete a non-existed node (e.g. link is empty or a wrong //
-// index is given) return NULL. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void* tetgenmesh::link::del(int pos)
-{
- if (!locate(pos) || (linkitems == 0)) {
- return (void *) NULL;
- }
- return deletenode((void **) nextlinkitem);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// getitem() The link traversal routine. //
-// //
-// Returns the node to which 'nextlinkitem' points. Returns a 'NULL' if the //
-// end of the link is reaching. Both 'nextlinkitem' and 'curpos' will be //
-// updated after this operation. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void* tetgenmesh::link::getitem()
-{
- if (nextlinkitem == (void *) tail) return NULL;
- void **nownode = (void **) nextlinkitem;
- nextlinkitem = *nownode;
- curpos += 1;
- return (void *)(nownode + 2);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// getnitem() Returns the node at a specified position. //
-// //
-// 'pos' between 1 and 'linkitems'. After this operation, 'nextlinkitem' and //
-// 'curpos' will be updated to indicate this node. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void* tetgenmesh::link::getnitem(int pos)
-{
- if (!locate(pos)) return NULL;
- return (void *)((void **) nextlinkitem + 2);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// hasitem() Search in this link to find if 'checkitem' exists. //
-// //
-// If 'checkitem' exists, return its position (between 1 to 'linkitems'), //
-// otherwise, return -1. This routine requires the linear order function has //
-// been set. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-int tetgenmesh::link::hasitem(void* checkitem)
-{
- void *pathitem;
- int count;
-
- rewind();
- pathitem = getitem();
- count = 0;
- while (pathitem) {
- count ++;
- if (comp) {
- if ((* comp)(pathitem, checkitem) == 0) {
- return count;
- }
- }
- pathitem = getitem();
- }
- return -1;
-}
-
-//
-// End of class 'list', 'memorypool' and 'link' implementation
-//
-
-//
-// Begin of mesh manipulation primitives
-//
-
-//
-// Begin of tables initialization.
-//
-
-// For enumerating three edges of a triangle.
-
-int tetgenmesh::plus1mod3[3] = {1, 2, 0};
-int tetgenmesh::minus1mod3[3] = {2, 0, 1};
-
-// Table 've' takes an edge version as input, returns the next edge version
-// in the same edge ring.
-
-int tetgenmesh::ve[6] = { 2, 5, 4, 1, 0, 3 };
-
-// Tables 'vo', 'vd' and 'va' take an edge version, return the positions of
-// the origin, destination and apex in the triangle.
-
-int tetgenmesh::vo[6] = { 0, 1, 1, 2, 2, 0 };
-int tetgenmesh::vd[6] = { 1, 0, 2, 1, 0, 2 };
-int tetgenmesh::va[6] = { 2, 2, 0, 0, 1, 1 };
-
-// The following tables are for tetrahedron primitives (operate on trifaces).
-
-// For 'org()', 'dest()' and 'apex()'. Use 'loc' as the first index and
-// 'ver' as the second index.
-
-int tetgenmesh::locver2org[4][6] = {
- {0, 1, 1, 2, 2, 0},
- {0, 3, 3, 1, 1, 0},
- {1, 3, 3, 2, 2, 1},
- {2, 3, 3, 0, 0, 2}
-};
-int tetgenmesh::locver2dest[4][6] = {
- {1, 0, 2, 1, 0, 2},
- {3, 0, 1, 3, 0, 1},
- {3, 1, 2, 3, 1, 2},
- {3, 2, 0, 3, 2, 0}
-};
-int tetgenmesh::locver2apex[4][6] = {
- {2, 2, 0, 0, 1, 1},
- {1, 1, 0, 0, 3, 3},
- {2, 2, 1, 1, 3, 3},
- {0, 0, 2, 2, 3, 3}
-};
-
-// For oppo() primitives, use 'loc' as the index.
-
-int tetgenmesh::loc2oppo[4] = { 3, 2, 0, 1 };
-
-// For fnext() primitive. Use 'loc' as the first index and 'ver' as the
-// second index. Returns a new 'loc' and new 'ver' in an array. (It is
-// only valid for edge version equals one of {0, 2, 4}.)
-
-int tetgenmesh::locver2nextf[4][6][2] = {
- { {1, 5}, {-1, -1}, {2, 5}, {-1, -1}, {3, 5}, {-1, -1} },
- { {3, 3}, {-1, -1}, {2, 1}, {-1, -1}, {0, 1}, {-1, -1} },
- { {1, 3}, {-1, -1}, {3, 1}, {-1, -1}, {0, 3}, {-1, -1} },
- { {2, 3}, {-1, -1}, {1, 1}, {-1, -1}, {0, 5}, {-1, -1} }
-};
-
-// The edge number (from 0 to 5) of a tet is defined as follows:
-// 0 - (v0, v1), 1 - (v1, v2), 2 - (v2, v0)
-// 3 - (v3, v0), 4 - (v3, v1), 5 - (v3, v2).
-
-int tetgenmesh::locver2edge[4][6] = {
- {0, 0, 1, 1, 2, 2},
- {3, 3, 4, 4, 0, 0},
- {4, 4, 5, 5, 1, 1},
- {5, 5, 3, 3, 2, 2}
-};
-
-int tetgenmesh::edge2locver[6][2] = {
- {0, 0}, // 0 v0 -> v1
- {0, 2}, // 1 v1 -> v2
- {0, 4}, // 2 v2 -> v1
- {1, 0}, // 3 v0 -> v3
- {1, 2}, // 4 v1 -> v3
- {2, 2} // 5 v2 -> v3
-};
-
-//
-// End of tables initialization.
-//
-
-// Some macros for convenience
-
-#define Div2 >> 1
-#define Mod2 & 01
-
-// NOTE: These bit operators should only be used in macros below.
-
-// Get orient(Range from 0 to 2) from face version(Range from 0 to 5).
-
-#define Orient(V) ((V) Div2)
-
-// Determine edge ring(0 or 1) from face version(Range from 0 to 5).
-
-#define EdgeRing(V) ((V) Mod2)
-
-//
-// Begin of primitives for tetrahedra
-//
-
-// Each tetrahedron contains four pointers to its neighboring tetrahedra,
-// with face indices. To save memory, both information are kept in a
-// single pointer. To make this possible, all tetrahedra are aligned to
-// eight-byte boundaries, so that the last three bits of each pointer are
-// zeros. A face index (in the range 0 to 3) is compressed into the last
-// two bits of each pointer by the function 'encode()'. The function
-// 'decode()' decodes a pointer, extracting a face index and a pointer to
-// the beginning of a tetrahedron.
-
-inline void tetgenmesh::decode(tetrahedron ptr, triface& t) {
- t.loc = (int) ((unsigned long) (ptr) & (unsigned long) 3l);
- t.tet = (tetrahedron *) ((unsigned long) (ptr) & ~(unsigned long) 7l);
-}
-
-inline tetgenmesh::tetrahedron tetgenmesh::encode(triface& t) {
- return (tetrahedron) ((unsigned long) t.tet | (unsigned long) t.loc);
-}
-
-// sym() finds the abutting tetrahedron on the same face.
-
-inline void tetgenmesh::sym(triface& t1, triface& t2) {
- tetrahedron ptr = t1.tet[t1.loc];
- decode(ptr, t2);
-}
-
-inline void tetgenmesh::symself(triface& t) {
- tetrahedron ptr = t.tet[t.loc];
- decode(ptr, t);
-}
-
-// Bond two tetrahedra together at their faces.
-
-inline void tetgenmesh::bond(triface& t1, triface& t2) {
- t1.tet[t1.loc] = encode(t2);
- t2.tet[t2.loc] = encode(t1);
-}
-
-// Dissolve a bond (from one side). Note that the other tetrahedron will
-// still think it is connected to this tetrahedron. Usually, however,
-// the other tetrahedron is being deleted entirely, or bonded to another
-// tetrahedron, so it doesn't matter.
-
-inline void tetgenmesh::dissolve(triface& t) {
- t.tet[t.loc] = (tetrahedron) dummytet;
-}
-
-// These primitives determine or set the origin, destination, apex or
-// opposition of a tetrahedron with respect to 'loc' and 'ver'.
-
-inline tetgenmesh::point tetgenmesh::org(triface& t) {
- return (point) t.tet[locver2org[t.loc][t.ver] + 4];
-}
-
-inline tetgenmesh::point tetgenmesh::dest(triface& t) {
- return (point) t.tet[locver2dest[t.loc][t.ver] + 4];
-}
-
-inline tetgenmesh::point tetgenmesh::apex(triface& t) {
- return (point) t.tet[locver2apex[t.loc][t.ver] + 4];
-}
-
-inline tetgenmesh::point tetgenmesh::oppo(triface& t) {
- return (point) t.tet[loc2oppo[t.loc] + 4];
-}
-
-inline void tetgenmesh::setorg(triface& t, point pointptr) {
- t.tet[locver2org[t.loc][t.ver] + 4] = (tetrahedron) pointptr;
-}
-
-inline void tetgenmesh::setdest(triface& t, point pointptr) {
- t.tet[locver2dest[t.loc][t.ver] + 4] = (tetrahedron) pointptr;
-}
-
-inline void tetgenmesh::setapex(triface& t, point pointptr) {
- t.tet[locver2apex[t.loc][t.ver] + 4] = (tetrahedron) pointptr;
-}
-
-inline void tetgenmesh::setoppo(triface& t, point pointptr) {
- t.tet[loc2oppo[t.loc] + 4] = (tetrahedron) pointptr;
-}
-
-// These primitives were drived from Mucke's triangle-edge data structure
-// to change face-edge relation in a tetrahedron (esym, enext and enext2)
-// or between two tetrahedra (fnext).
-
-// If e0 = e(i, j), e1 = e(j, i), that is e0 and e1 are the two directions
-// of the same undirected edge of a face. e0.sym() = e1 and vice versa.
-
-inline void tetgenmesh::esym(triface& t1, triface& t2) {
- t2.tet = t1.tet;
- t2.loc = t1.loc;
- t2.ver = t1.ver + (EdgeRing(t1.ver) ? -1 : 1);
-}
-
-inline void tetgenmesh::esymself(triface& t) {
- t.ver += (EdgeRing(t.ver) ? -1 : 1);
-}
-
-// If e0 and e1 are both in the same edge ring of a face, e1 = e0.enext().
-
-inline void tetgenmesh::enext(triface& t1, triface& t2) {
- t2.tet = t1.tet;
- t2.loc = t1.loc;
- t2.ver = ve[t1.ver];
-}
-
-inline void tetgenmesh::enextself(triface& t) {
- t.ver = ve[t.ver];
-}
-
-// enext2() is equal to e2 = e0.enext().enext()
-
-inline void tetgenmesh::enext2(triface& t1, triface& t2) {
- t2.tet = t1.tet;
- t2.loc = t1.loc;
- t2.ver = ve[ve[t1.ver]];
-}
-
-inline void tetgenmesh::enext2self(triface& t) {
- t.ver = ve[ve[t.ver]];
-}
-
-// If f0 and f1 are both in the same face ring of a face, f1 = f0.fnext().
-// If f1 exists, return true. Otherwise, return false, i.e., f0 is a
-// boundary or hull face.
-
-inline bool tetgenmesh::fnext(triface& t1, triface& t2)
-{
- // Get the next face.
- t2.loc = locver2nextf[t1.loc][t1.ver][0];
- // Is the next face in the same tet?
- if (t2.loc != -1) {
- // It's in the same tet. Get the edge version.
- t2.ver = locver2nextf[t1.loc][t1.ver][1];
- t2.tet = t1.tet;
- } else {
- // The next face is in the neigbhour of 't1'.
- sym(t1, t2);
- if (t2.tet != dummytet) {
- // Find the corresponding edge in t2.
- point torg;
- int tloc, tver, i;
- t2.ver = 0;
- torg = org(t1);
- for (i = 0; (i < 3) && (org(t2) != torg); i++) {
- enextself(t2);
- }
- // Go to the next face in t2.
- tloc = t2.loc;
- tver = t2.ver;
- t2.loc = locver2nextf[tloc][tver][0];
- t2.ver = locver2nextf[tloc][tver][1];
- }
- }
- return t2.tet != dummytet;
-}
-
-inline bool tetgenmesh::fnextself(triface& t1)
-{
- triface t2;
-
- // Get the next face.
- t2.loc = locver2nextf[t1.loc][t1.ver][0];
- // Is the next face in the same tet?
- if (t2.loc != -1) {
- // It's in the same tet. Get the edge version.
- t2.ver = locver2nextf[t1.loc][t1.ver][1];
- t1.loc = t2.loc;
- t1.ver = t2.ver;
- } else {
- // The next face is in the neigbhour of 't1'.
- sym(t1, t2);
- if (t2.tet != dummytet) {
- // Find the corresponding edge in t2.
- point torg;
- int i;
- t2.ver = 0;
- torg = org(t1);
- for (i = 0; (i < 3) && (org(t2) != torg); i++) {
- enextself(t2);
- }
- t1.loc = locver2nextf[t2.loc][t2.ver][0];
- t1.ver = locver2nextf[t2.loc][t2.ver][1];
- t1.tet = t2.tet;
- }
- }
- return t2.tet != dummytet;
-}
-
-// enextfnext() and enext2fnext() are combination primitives of enext(),
-// enext2() and fnext().
-
-inline void tetgenmesh::enextfnext(triface& t1, triface& t2) {
- enext(t1, t2);
- fnextself(t2);
-}
-
-inline void tetgenmesh::enextfnextself(triface& t) {
- enextself(t);
- fnextself(t);
-}
-
-inline void tetgenmesh::enext2fnext(triface& t1, triface& t2) {
- enext2(t1, t2);
- fnextself(t2);
-}
-
-inline void tetgenmesh::enext2fnextself(triface& t) {
- enext2self(t);
- fnextself(t);
-}
-
-// Primitives to infect or cure a tetrahedron with the virus. The last
-// third bit of the pointer is marked for infection. These rely on the
-// assumption that all tetrahedron are aligned to eight-byte boundaries.
-
-inline void tetgenmesh::infect(triface& t) {
- t.tet[0] = (tetrahedron) ((unsigned long) t.tet[0] | (unsigned long) 4l);
-}
-
-inline void tetgenmesh::uninfect(triface& t) {
- t.tet[0] = (tetrahedron) ((unsigned long) t.tet[0] & ~ (unsigned long) 4l);
-}
-
-// Test a tetrahedron for viral infection.
-
-inline bool tetgenmesh::infected(triface& t) {
- return (((unsigned long) t.tet[0] & (unsigned long) 4l) != 0);
-}
-
-// Check or set a tetrahedron's attributes.
-
-inline REAL tetgenmesh::elemattribute(tetrahedron* ptr, int attnum) {
- return ((REAL *) (ptr))[elemattribindex + attnum];
-}
-
-inline void tetgenmesh::
-setelemattribute(tetrahedron* ptr, int attnum, REAL value){
- ((REAL *) (ptr))[elemattribindex + attnum] = value;
-}
-
-// Check or set a tetrahedron's maximum volume bound.
-
-inline REAL tetgenmesh::volumebound(tetrahedron* ptr) {
- return ((REAL *) (ptr))[volumeboundindex];
-}
-
-inline void tetgenmesh::setvolumebound(tetrahedron* ptr, REAL value) {
- ((REAL *) (ptr))[volumeboundindex] = value;
-}
-
-//
-// End of primitives for tetrahedra
-//
-
-//
-// Begin of primitives for subfaces/subsegments
-//
-
-// Each subface contains three pointers to its neighboring subfaces, with
-// edge versions. To save memory, both information are kept in a single
-// pointer. To make this possible, all subfaces are aligned to eight-byte
-// boundaries, so that the last three bits of each pointer are zeros. An
-// edge version (in the range 0 to 5) is compressed into the last three
-// bits of each pointer by 'sencode()'. 'sdecode()' decodes a pointer,
-// extracting an edge version and a pointer to the beginning of a subface.
-
-inline void tetgenmesh::sdecode(shellface sptr, face& s) {
- s.shver = (int) ((unsigned long) (sptr) & (unsigned long) 7l);
- s.sh = (shellface *) ((unsigned long) (sptr) & ~ (unsigned long) 7l);
-}
-
-inline tetgenmesh::shellface tetgenmesh::sencode(face& s) {
- return (shellface) ((unsigned long) s.sh | (unsigned long) s.shver);
-}
-
-// spivot() finds the other subface (from this subface) that shares the
-// same edge.
-
-inline void tetgenmesh::spivot(face& s1, face& s2) {
- shellface sptr = s1.sh[Orient(s1.shver)];
- sdecode(sptr, s2);
-}
-
-inline void tetgenmesh::spivotself(face& s) {
- shellface sptr = s.sh[Orient(s.shver)];
- sdecode(sptr, s);
-}
-
-// sbond() bonds two subfaces together, i.e., after bonding, both faces
-// are pointing to each other.
-
-inline void tetgenmesh::sbond(face& s1, face& s2) {
- s1.sh[Orient(s1.shver)] = sencode(s2);
- s2.sh[Orient(s2.shver)] = sencode(s1);
-}
-
-// sbond1() only bonds s2 to s1, i.e., after bonding, s1 is pointing to s2,
-// but s2 is not pointing to s1.
-
-inline void tetgenmesh::sbond1(face& s1, face& s2) {
- s1.sh[Orient(s1.shver)] = sencode(s2);
-}
-
-// Dissolve a subface bond (from one side). Note that the other subface
-// will still think it's connected to this subface.
-
-inline void tetgenmesh::sdissolve(face& s) {
- s.sh[Orient(s.shver)] = (shellface) dummysh;
-}
-
-// These primitives determine or set the origin, destination, or apex
-// of a subface with respect to the edge version.
-
-inline tetgenmesh::point tetgenmesh::sorg(face& s) {
- return (point) s.sh[3 + vo[s.shver]];
-}
-
-inline tetgenmesh::point tetgenmesh::sdest(face& s) {
- return (point) s.sh[3 + vd[s.shver]];
-}
-
-inline tetgenmesh::point tetgenmesh::sapex(face& s) {
- return (point) s.sh[3 + va[s.shver]];
-}
-
-inline void tetgenmesh::setsorg(face& s, point pointptr) {
- s.sh[3 + vo[s.shver]] = (shellface) pointptr;
-}
-
-inline void tetgenmesh::setsdest(face& s, point pointptr) {
- s.sh[3 + vd[s.shver]] = (shellface) pointptr;
-}
-
-inline void tetgenmesh::setsapex(face& s, point pointptr) {
- s.sh[3 + va[s.shver]] = (shellface) pointptr;
-}
-
-// These primitives were drived from Mucke[2]'s triangle-edge data structure
-// to change face-edge relation in a subface (sesym, senext and senext2).
-
-inline void tetgenmesh::sesym(face& s1, face& s2) {
- s2.sh = s1.sh;
- s2.shver = s1.shver + (EdgeRing(s1.shver) ? -1 : 1);
-}
-
-inline void tetgenmesh::sesymself(face& s) {
- s.shver += (EdgeRing(s.shver) ? -1 : 1);
-}
-
-inline void tetgenmesh::senext(face& s1, face& s2) {
- s2.sh = s1.sh;
- s2.shver = ve[s1.shver];
-}
-
-inline void tetgenmesh::senextself(face& s) {
- s.shver = ve[s.shver];
-}
-
-inline void tetgenmesh::senext2(face& s1, face& s2) {
- s2.sh = s1.sh;
- s2.shver = ve[ve[s1.shver]];
-}
-
-inline void tetgenmesh::senext2self(face& s) {
- s.shver = ve[ve[s.shver]];
-}
-
-// If f0 and f1 are both in the same face ring, then f1 = f0.fnext(),
-
-inline void tetgenmesh::sfnext(face& s1, face& s2) {
- getnextsface(&s1, &s2);
-}
-
-inline void tetgenmesh::sfnextself(face& s) {
- getnextsface(&s, NULL);
-}
-
-// These primitives read or set a pointer of the badface structure. The
-// pointer is stored sh[11].
-
-inline tetgenmesh::badface* tetgenmesh::shell2badface(face& s) {
- return (badface*) s.sh[11];
-}
-
-inline void tetgenmesh::setshell2badface(face& s, badface* value) {
- s.sh[11] = (shellface) value;
-}
-
-// Check or set a subface's maximum area bound.
-
-inline REAL tetgenmesh::areabound(face& s) {
- return ((REAL *) (s.sh))[areaboundindex];
-}
-
-inline void tetgenmesh::setareabound(face& s, REAL value) {
- ((REAL *) (s.sh))[areaboundindex] = value;
-}
-
-// These two primitives read or set a shell marker. Shell markers are used
-// to hold user boundary information.
-
-inline int tetgenmesh::shellmark(face& s) {
- return ((int *) (s.sh))[shmarkindex];
-}
-
-inline void tetgenmesh::setshellmark(face& s, int value) {
- ((int *) (s.sh))[shmarkindex] = value;
-}
-
-// These two primitives set or read the type of the subface or subsegment.
-
-inline enum tetgenmesh::shestype tetgenmesh::shelltype(face& s) {
- return (enum shestype) ((int *) (s.sh))[shmarkindex + 1];
-}
-
-inline void tetgenmesh::setshelltype(face& s, enum shestype value) {
- ((int *) (s.sh))[shmarkindex + 1] = (int) value;
-}
-
-// These two primitives set or read the pbc group of the subface.
-
-inline int tetgenmesh::shellpbcgroup(face& s) {
- return ((int *) (s.sh))[shmarkindex + 2];
-}
-
-inline void tetgenmesh::setshellpbcgroup(face& s, int value) {
- ((int *) (s.sh))[shmarkindex + 2] = value;
-}
-
-// Primitives to infect or cure a subface with the virus. These rely on the
-// assumption that all tetrahedra are aligned to eight-byte boundaries.
-
-inline void tetgenmesh::sinfect(face& s) {
- s.sh[6] = (shellface) ((unsigned long) s.sh[6] | (unsigned long) 4l);
-}
-
-inline void tetgenmesh::suninfect(face& s) {
- s.sh[6] = (shellface)((unsigned long) s.sh[6] & ~(unsigned long) 4l);
-}
-
-// Test a subface for viral infection.
-
-inline bool tetgenmesh::sinfected(face& s) {
- return (((unsigned long) s.sh[6] & (unsigned long) 4l) != 0);
-}
-
-//
-// End of primitives for subfaces/subsegments
-//
-
-//
-// Begin of primitives for interacting between tetrahedra and subfaces
-//
-
-// tspivot() finds a subface abutting on this tetrahdera.
-
-inline void tetgenmesh::tspivot(triface& t, face& s) {
- shellface sptr = (shellface) t.tet[8 + t.loc];
- sdecode(sptr, s);
-}
-
-// stpivot() finds a tetrahedron abutting a subface.
-
-inline void tetgenmesh::stpivot(face& s, triface& t) {
- tetrahedron ptr = (tetrahedron) s.sh[6 + EdgeRing(s.shver)];
- decode(ptr, t);
-}
-
-// tsbond() bond a tetrahedron to a subface.
-
-inline void tetgenmesh::tsbond(triface& t, face& s) {
- t.tet[8 + t.loc] = (tetrahedron) sencode(s);
- s.sh[6 + EdgeRing(s.shver)] = (shellface) encode(t);
-}
-
-// tsdissolve() dissolve a bond (from the tetrahedron side).
-
-inline void tetgenmesh::tsdissolve(triface& t) {
- t.tet[8 + t.loc] = (tetrahedron) dummysh;
-}
-
-// stdissolve() dissolve a bond (from the subface side).
-
-inline void tetgenmesh::stdissolve(face& s) {
- s.sh[6 + EdgeRing(s.shver)] = (shellface) dummytet;
-}
-
-//
-// End of primitives for interacting between tetrahedra and subfaces
-//
-
-//
-// Begin of primitives for interacting between subfaces and subsegs
-//
-
-// sspivot() finds a subsegment abutting a subface.
-
-inline void tetgenmesh::sspivot(face& s, face& edge) {
- shellface sptr = (shellface) s.sh[8 + Orient(s.shver)];
- sdecode(sptr, edge);
-}
-
-// ssbond() bond a subface to a subsegment.
-
-inline void tetgenmesh::ssbond(face& s, face& edge) {
- s.sh[8 + Orient(s.shver)] = sencode(edge);
- edge.sh[0] = sencode(s);
-}
-
-// ssdisolve() dissolve a bond (from the subface side)
-
-inline void tetgenmesh::ssdissolve(face& s) {
- s.sh[8 + Orient(s.shver)] = (shellface) dummysh;
-}
-
-//
-// End of primitives for interacting between subfaces and subsegs
-//
-
-//
-// Begin of primitives for interacting between tet and subsegs.
-//
-
-inline void tetgenmesh::tsspivot1(triface& t, face& seg)
-{
- shellface sptr = (shellface) t.tet[8 + locver2edge[t.loc][t.ver]];
- sdecode(sptr, seg);
-}
-
-// Only bond/dissolve at tet's side, but not vice versa.
-
-inline void tetgenmesh::tssbond1(triface& t, face& seg)
-{
- t.tet[8 + locver2edge[t.loc][t.ver]] = (tetrahedron) sencode(seg);
-}
-
-inline void tetgenmesh::tssdissolve1(triface& t)
-{
- t.tet[8 + locver2edge[t.loc][t.ver]] = (tetrahedron) dummysh;
-}
-
-//
-// End of primitives for interacting between tet and subsegs.
-//
-
-//
-// Begin of primitives for points
-//
-
-inline int tetgenmesh::pointmark(point pt) {
- return ((int *) (pt))[pointmarkindex];
-}
-
-inline void tetgenmesh::setpointmark(point pt, int value) {
- ((int *) (pt))[pointmarkindex] = value;
-}
-
-// These two primitives set and read the type of the point.
-
-inline enum tetgenmesh::verttype tetgenmesh::pointtype(point pt) {
- return (enum verttype) ((int *) (pt))[pointmarkindex + 1];
-}
-
-inline void tetgenmesh::setpointtype(point pt, enum verttype value) {
- ((int *) (pt))[pointmarkindex + 1] = (int) value;
-}
-
-// These following primitives set and read a pointer to a tetrahedron
-// a subface/subsegment, a point, or a tet of background mesh.
-
-inline tetgenmesh::tetrahedron tetgenmesh::point2tet(point pt) {
- return ((tetrahedron *) (pt))[point2simindex];
-}
-
-inline void tetgenmesh::setpoint2tet(point pt, tetrahedron value) {
- ((tetrahedron *) (pt))[point2simindex] = value;
-}
-
-inline tetgenmesh::shellface tetgenmesh::point2sh(point pt) {
- return (shellface) ((tetrahedron *) (pt))[point2simindex + 1];
-}
-
-inline void tetgenmesh::setpoint2sh(point pt, shellface value) {
- ((tetrahedron *) (pt))[point2simindex + 1] = (tetrahedron) value;
-}
-
-inline tetgenmesh::point tetgenmesh::point2ppt(point pt) {
- return (point) ((tetrahedron *) (pt))[point2simindex + 2];
-}
-
-inline void tetgenmesh::setpoint2ppt(point pt, point value) {
- ((tetrahedron *) (pt))[point2simindex + 2] = (tetrahedron) value;
-}
-
-inline tetgenmesh::tetrahedron tetgenmesh::point2bgmtet(point pt) {
- return ((tetrahedron *) (pt))[point2simindex + 3];
-}
-
-inline void tetgenmesh::setpoint2bgmtet(point pt, tetrahedron value) {
- ((tetrahedron *) (pt))[point2simindex + 3] = value;
-}
-
-// These primitives set and read a pointer to its pbc point.
-
-inline tetgenmesh::point tetgenmesh::point2pbcpt(point pt) {
- return (point) ((tetrahedron *) (pt))[point2pbcptindex];
-}
-
-inline void tetgenmesh::setpoint2pbcpt(point pt, point value) {
- ((tetrahedron *) (pt))[point2pbcptindex] = (tetrahedron) value;
-}
-
-//
-// End of primitives for points
-//
-
-//
-// Begin of advanced primitives
-//
-
-// adjustedgering() adjusts the edge version so that it belongs to the
-// indicated edge ring. The 'direction' only can be 0(CCW) or 1(CW).
-// If the edge is not in the wanted edge ring, reverse it.
-
-inline void tetgenmesh::adjustedgering(triface& t, int direction) {
- if (EdgeRing(t.ver) != direction) {
- esymself(t);
- }
-}
-
-inline void tetgenmesh::adjustedgering(face& s, int direction) {
- if (EdgeRing(s.shver) != direction) {
- sesymself(s);
- }
-}
-
-// isdead() returns TRUE if the tetrahedron or subface has been dealloced.
-
-inline bool tetgenmesh::isdead(triface* t) {
- if (t->tet == (tetrahedron *) NULL) return true;
- else return t->tet[4] == (tetrahedron) NULL;
-}
-
-inline bool tetgenmesh::isdead(face* s) {
- if (s->sh == (shellface *) NULL) return true;
- else return s->sh[3] == (shellface) NULL;
-}
-
-// isfacehaspoint() returns TRUE if the 'testpoint' is one of the vertices
-// of the tetface 't' subface 's'.
-
-inline bool tetgenmesh::isfacehaspoint(triface* t, point testpoint) {
- return ((org(*t) == testpoint) || (dest(*t) == testpoint) ||
- (apex(*t) == testpoint));
-}
-
-inline bool tetgenmesh::isfacehaspoint(face* s, point testpoint) {
- return (s->sh[3] == (shellface) testpoint) ||
- (s->sh[4] == (shellface) testpoint) ||
- (s->sh[5] == (shellface) testpoint);
-}
-
-// isfacehasedge() returns TRUE if the edge (given by its two endpoints) is
-// one of the three edges of the subface 's'.
-
-inline bool tetgenmesh::isfacehasedge(face* s, point tend1, point tend2) {
- return (isfacehaspoint(s, tend1) && isfacehaspoint(s, tend2));
-}
-
-// issymexist() returns TRUE if the adjoining tetrahedron is not 'duumytet'.
-
-inline bool tetgenmesh::issymexist(triface* t) {
- tetrahedron *ptr = (tetrahedron *)
- ((unsigned long)(t->tet[t->loc]) & ~(unsigned long)7l);
- return ptr != dummytet;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// getnextsface() Finds the next subface in the face ring. //
-// //
-// For saving space in the data structure of subface, there only exists one //
-// face ring around a segment (see programming manual). This routine imple- //
-// ments the double face ring as desired in Muecke's data structure. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::getnextsface(face* s1, face* s2)
-{
- face neighsh, spinsh;
- face testseg;
-
- sspivot(*s1, testseg);
- if (testseg.sh != dummysh) {
- testseg.shver = 0;
- if (sorg(testseg) == sorg(*s1)) {
- spivot(*s1, neighsh);
- } else {
- spinsh = *s1;
- do {
- neighsh = spinsh;
- spivotself(spinsh);
- } while (spinsh.sh != s1->sh);
- }
- } else {
- spivot(*s1, neighsh);
- }
- if (sorg(neighsh) != sorg(*s1)) {
- sesymself(neighsh);
- }
- if (s2 != (face *) NULL) {
- *s2 = neighsh;
- } else {
- *s1 = neighsh;
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// tsspivot() Finds a subsegment abutting on a tetrahderon's edge. //
-// //
-// The edge is represented in the primary edge of 'checkedge'. If there is a //
-// subsegment bonded at this edge, it is returned in handle 'checkseg', the //
-// edge direction of 'checkseg' is conformed to 'checkedge'. If there isn't, //
-// set 'checkseg.sh = dummysh' to indicate it is not a subsegment. //
-// //
-// To find whether an edge of a tetrahedron is a subsegment or not. First we //
-// need find a subface around this edge to see if it contains a subsegment. //
-// The reason is there is no direct connection between a tetrahedron and its //
-// adjoining subsegments. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::tsspivot(triface* checkedge, face* checkseg)
-{
- triface spintet;
- face parentsh;
- point tapex;
- int hitbdry;
-
- spintet = *checkedge;
- tapex = apex(*checkedge);
- hitbdry = 0;
- do {
- tspivot(spintet, parentsh);
- // Does spintet have a (non-fake) subface attached?
- if ((parentsh.sh != dummysh) && (sapex(parentsh) != NULL)) {
- // Find a subface! Find the edge in it.
- findedge(&parentsh, org(*checkedge), dest(*checkedge));
- sspivot(parentsh, *checkseg);
- if (checkseg->sh != dummysh) {
- // Find a subsegment! Correct its edge direction before return.
- if (sorg(*checkseg) != org(*checkedge)) {
- sesymself(*checkseg);
- }
- }
- return;
- }
- if (!fnextself(spintet)) {
- hitbdry++;
- if (hitbdry < 2) {
- esym(*checkedge, spintet);
- if (!fnextself(spintet)) {
- hitbdry++;
- }
- }
- }
- } while ((apex(spintet) != tapex) && (hitbdry < 2));
- // Not find.
- checkseg->sh = dummysh;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// sstpivot() Finds a tetrahedron abutting a subsegment. //
-// //
-// This is the inverse operation of 'tsspivot()'. One subsegment shared by //
-// arbitrary number of tetrahedron, the returned tetrahedron is not unique. //
-// The edge direction of the returned tetrahedron is conformed to the given //
-// subsegment. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::sstpivot(face* checkseg, triface* retedge)
-{
- face parentsh;
-
- // Get the subface which holds the subsegment.
- sdecode(checkseg->sh[0], parentsh);
-#ifdef SELF_CHECK
- assert(parentsh.sh != dummysh);
-#endif
- // Get a tetraheron to which the subface attches.
- stpivot(parentsh, *retedge);
- if (retedge->tet == dummytet) {
- sesymself(parentsh);
- stpivot(parentsh, *retedge);
-#ifdef SELF_CHECK
- assert(retedge->tet != dummytet);
-#endif
- }
- // Correct the edge direction before return.
- findedge(retedge, sorg(*checkseg), sdest(*checkseg));
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// findorg() Finds a point in the given handle (tetrahedron or subface). //
-// //
-// If 'dorg' is a one of vertices of the given handle, set the origin of //
-// this handle be that point and return TRUE. Otherwise, return FALSE and //
-// 'tface' remains unchanged. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::findorg(triface* tface, point dorg)
-{
- if (org(*tface) == dorg) {
- return true;
- } else {
- if (dest(*tface) == dorg) {
- enextself(*tface);
- return true;
- } else {
- if (apex(*tface) == dorg) {
- enext2self(*tface);
- return true;
- } else {
- if (oppo(*tface) == dorg) {
- // Keep 'tface' referring to the same tet after fnext().
- adjustedgering(*tface, CCW);
- fnextself(*tface);
- enext2self(*tface);
- return true;
- }
- }
- }
- }
- return false;
-}
-
-bool tetgenmesh::findorg(face* sface, point dorg)
-{
- if (sorg(*sface) == dorg) {
- return true;
- } else {
- if (sdest(*sface) == dorg) {
- senextself(*sface);
- return true;
- } else {
- if (sapex(*sface) == dorg) {
- senext2self(*sface);
- return true;
- }
- }
- }
- return false;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// findedge() Find an edge in the given handle (tetrahedron or subface). //
-// //
-// The edge is given in two points 'eorg' and 'edest'. It is assumed that //
-// the edge must exist in the given handle (tetrahedron or subface). This //
-// routine sets the right edge version for the input handle. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::findedge(triface* tface, point eorg, point edest)
-{
- int i;
-
- for (i = 0; i < 3; i++) {
- if (org(*tface) == eorg) {
- if (dest(*tface) == edest) {
- // Edge is found, return.
- return;
- }
- } else {
- if (org(*tface) == edest) {
- if (dest(*tface) == eorg) {
- // Edge is found, inverse the direction and return.
- esymself(*tface);
- return;
- }
- }
- }
- enextself(*tface);
- }
- // It should never be here.
- printf("Internalerror in findedge(): Unable to find an edge in tet.\n");
- internalerror();
-}
-
-void tetgenmesh::findedge(face* sface, point eorg, point edest)
-{
- int i;
-
- for (i = 0; i < 3; i++) {
- if (sorg(*sface) == eorg) {
- if (sdest(*sface) == edest) {
- // Edge is found, return.
- return;
- }
- } else {
- if (sorg(*sface) == edest) {
- if (sdest(*sface) == eorg) {
- // Edge is found, inverse the direction and return.
- sesymself(*sface);
- return;
- }
- }
- }
- senextself(*sface);
- }
- printf("Internalerror in findedge(): Unable to find an edge in subface.\n");
- internalerror();
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// findface() Find the face has the given origin, destination and apex. //
-// //
-// On input, 'fface' is a handle which may contain the three corners or may //
-// not or may be dead. On return, it represents exactly the face with the //
-// given origin, destination and apex. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::findface(triface *fface, point forg, point fdest, point fapex)
-{
- triface spintet;
- enum finddirectionresult collinear;
- int hitbdry;
-
- if (!isdead(fface)) {
- // First check the easiest case, that 'fface' is just the right one.
- if (org(*fface) == forg && dest(*fface) == fdest &&
- apex(*fface) == fapex) return;
- } else {
- // The input handle is dead, use the 'recenttet' if it is alive.
- if (!isdead(&recenttet)) *fface = recenttet;
- }
-
- if (!isdead(fface)) {
- if (!findorg(fface, forg)) {
- // 'forg' is not a corner of 'fface', locate it.
- preciselocate(forg, fface, tetrahedrons->items);
- }
- // It is possible that forg is not found in a non-convex mesh.
- if (org(*fface) == forg) {
- collinear = finddirection(fface, fdest, tetrahedrons->items);
- if (collinear == RIGHTCOLLINEAR) {
- // fdest is just the destination.
- } else if (collinear == LEFTCOLLINEAR) {
- enext2self(*fface);
- esymself(*fface);
- } else if (collinear == TOPCOLLINEAR) {
- fnextself(*fface);
- enext2self(*fface);
- esymself(*fface);
- }
- }
- // It is possible taht fdest is not found in a non-convex mesh.
- if ((org(*fface) == forg) && (dest(*fface) == fdest)) {
- // Find the apex of 'fapex'.
- spintet = *fface;
- hitbdry = 0;
- do {
- if (apex(spintet) == fapex) {
- // We have done. Be careful the edge direction of 'spintet',
- // it may reversed because of hitting boundary once.
- if (org(spintet) != org(*fface)) {
- esymself(spintet);
- }
- *fface = spintet;
- return;
- }
- if (!fnextself(spintet)) {
- hitbdry ++;
- if (hitbdry < 2) {
- esym(*fface, spintet);
- if (!fnextself(spintet)) {
- hitbdry ++;
- }
- }
- }
- } while (hitbdry < 2 && apex(spintet) != apex(*fface));
- // It is possible that fapex is not found in a non-convex mesh.
- }
- }
-
- if (isdead(fface) || (org(*fface) != forg) || (dest(*fface) != fdest) ||
- (apex(*fface) != fapex)) {
- // Too bad, the input handle is useless. We have to find a handle
- // for 'fface' contains the 'forg' and 'fdest'. Here a brute force
- // search is performed.
- if (b->verbose > 1) {
- printf("Warning in findface(): Perform a brute-force searching.\n");
- }
- enum verttype forgty, fdestty, fapexty;
- int share, i;
- forgty = pointtype(forg);
- fdestty = pointtype(fdest);
- fapexty = pointtype(fapex);
- setpointtype(forg, DEADVERTEX);
- setpointtype(fdest, DEADVERTEX);
- setpointtype(fapex, DEADVERTEX);
- tetrahedrons->traversalinit();
- fface->tet = tetrahedrontraverse();
- while (fface->tet != (tetrahedron *) NULL) {
- share = 0;
- for (i = 0; i < 4; i++) {
- if (pointtype((point) fface->tet[4 + i]) == DEADVERTEX) share ++;
- }
- if (share == 3) {
- // Found! Set the correct face and desired corners.
- if (pointtype((point) fface->tet[4]) != DEADVERTEX) {
- fface->loc = 2;
- } else if (pointtype((point) fface->tet[5]) != DEADVERTEX) {
- fface->loc = 3;
- } else if (pointtype((point) fface->tet[6]) != DEADVERTEX) {
- fface->loc = 1;
- } else { // pointtype((point) fface->tet[7]) != DEADVERTEX
- fface->loc = 0;
- }
- findedge(fface, forg, fdest);
- break;
- }
- fface->tet = tetrahedrontraverse();
- }
- setpointtype(forg, forgty);
- setpointtype(fdest, fdestty);
- setpointtype(fapex, fapexty);
- if (fface->tet == (tetrahedron *) NULL) {
- // It is impossible to reach here.
- printf("Internal error: Fail to find the indicated face.\n");
- internalerror();
- }
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// getonextseg() Get the next SEGMENT counterclockwise with the same org. //
-// //
-// 's' is a subface. This routine reteuns the segment which is counterclock- //
-// wise with the origin of s. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::getonextseg(face* s, face* lseg)
-{
- face checksh, checkseg;
- point forg;
-
- forg = sorg(*s);
- checksh = *s;
- do {
- // Go to the edge at forg's left side.
- senext2self(checksh);
- // Check if there is a segment attaching this edge.
- sspivot(checksh, checkseg);
- if (checkseg.sh != dummysh) break;
- // No segment! Go to the neighbor of this subface.
- spivotself(checksh);
-#ifdef SELF_CHECK
- // It should always meet a segment before come back.
- assert(checksh.sh != s->sh);
-#endif
- if (sorg(checksh) != forg) {
- sesymself(checksh);
-#ifdef SELF_CHECK
- assert(sorg(checksh) == forg);
-#endif
- }
- } while (true);
- if (sorg(checkseg) != forg) sesymself(checkseg);
- *lseg = checkseg;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// getseghasorg() Get the segment containing the given point. //
-// //
-// 'dorg' is an endpoint of a segment S. 'sseg' is a subsegment of S. This //
-// routine search a subsegment (along sseg) of S containing dorg. On return, //
-// 'sseg' contains 'dorg' as its origin. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::getseghasorg(face* sseg, point dorg)
-{
- face nextseg;
- point checkpt;
-
- nextseg = *sseg;
- checkpt = sorg(nextseg);
- while ((checkpt != dorg) && (pointtype(checkpt) == FREESEGVERTEX)) {
- // Search dorg along the original direction of sseg.
- senext2self(nextseg);
- spivotself(nextseg);
- nextseg.shver = 0;
- if (sdest(nextseg) != checkpt) sesymself(nextseg);
- checkpt = sorg(nextseg);
- }
- if (checkpt == dorg) {
- *sseg = nextseg;
- return;
- }
- nextseg = *sseg;
- checkpt = sdest(nextseg);
- while ((checkpt != dorg) && (pointtype(checkpt) == FREESEGVERTEX)) {
- // Search dorg along the destinational direction of sseg.
- senextself(nextseg);
- spivotself(nextseg);
- nextseg.shver = 0;
- if (sorg(nextseg) != checkpt) sesymself(nextseg);
- checkpt = sdest(nextseg);
- }
- if (checkpt == dorg) {
- sesym(nextseg, *sseg);
- return;
- }
- // Should never be here.
- printf("Internalerror in getseghasorg(): Unable to find the subseg.\n");
- internalerror();
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// getsubsegfarorg() Get the origin of the parent segment of a subseg. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-tetgenmesh::point tetgenmesh::getsubsegfarorg(face* sseg)
-{
- face prevseg;
- point checkpt;
-
- checkpt = sorg(*sseg);
- senext2(*sseg, prevseg);
- spivotself(prevseg);
- // Search dorg along the original direction of sseg.
- while (prevseg.sh != dummysh) {
- prevseg.shver = 0;
- if (sdest(prevseg) != checkpt) sesymself(prevseg);
- checkpt = sorg(prevseg);
- senext2self(prevseg);
- spivotself(prevseg);
- }
- return checkpt;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// getsubsegfardest() Get the dest. of the parent segment of a subseg. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-tetgenmesh::point tetgenmesh::getsubsegfardest(face* sseg)
-{
- face nextseg;
- point checkpt;
-
- checkpt = sdest(*sseg);
- senext(*sseg, nextseg);
- spivotself(nextseg);
- // Search dorg along the destinational direction of sseg.
- while (nextseg.sh != dummysh) {
- nextseg.shver = 0;
- if (sorg(nextseg) != checkpt) sesymself(nextseg);
- checkpt = sdest(nextseg);
- senextself(nextseg);
- spivotself(nextseg);
- }
- return checkpt;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// printtet() Print out the details of a tetrahedron on screen. //
-// //
-// It's also used when the highest level of verbosity (`-VVV') is specified. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::printtet(triface* tface)
-{
- triface tmpface, prtface;
- point tmppt;
- face tmpsh;
- int facecount;
-
- printf("Tetra x%lx with loc(%i) and ver(%i):",
- (unsigned long)(tface->tet), tface->loc, tface->ver);
- if (infected(*tface)) {
- printf(" (infected)");
- }
- printf("\n");
-
- tmpface = *tface;
- facecount = 0;
- while(facecount < 4) {
- tmpface.loc = facecount;
- sym(tmpface, prtface);
- if(prtface.tet == dummytet) {
- printf(" [%i] Outer space.\n", facecount);
- } else {
- printf(" [%i] x%lx loc(%i).", facecount,
- (unsigned long)(prtface.tet), prtface.loc);
- if (infected(prtface)) {
- printf(" (infected)");
- }
- printf("\n");
- }
- facecount ++;
- }
-
- tmppt = org(*tface);
- if(tmppt == (point) NULL) {
- printf(" Org [%i] NULL\n", locver2org[tface->loc][tface->ver]);
- } else {
- printf(" Org [%i] x%lx (%.12g,%.12g,%.12g) %d\n",
- locver2org[tface->loc][tface->ver], (unsigned long)(tmppt),
- tmppt[0], tmppt[1], tmppt[2], pointmark(tmppt));
- }
- tmppt = dest(*tface);
- if(tmppt == (point) NULL) {
- printf(" Dest[%i] NULL\n", locver2dest[tface->loc][tface->ver]);
- } else {
- printf(" Dest[%i] x%lx (%.12g,%.12g,%.12g) %d\n",
- locver2dest[tface->loc][tface->ver], (unsigned long)(tmppt),
- tmppt[0], tmppt[1], tmppt[2], pointmark(tmppt));
- }
- tmppt = apex(*tface);
- if(tmppt == (point) NULL) {
- printf(" Apex[%i] NULL\n", locver2apex[tface->loc][tface->ver]);
- } else {
- printf(" Apex[%i] x%lx (%.12g,%.12g,%.12g) %d\n",
- locver2apex[tface->loc][tface->ver], (unsigned long)(tmppt),
- tmppt[0], tmppt[1], tmppt[2], pointmark(tmppt));
- }
- tmppt = oppo(*tface);
- if(tmppt == (point) NULL) {
- printf(" Oppo[%i] NULL\n", loc2oppo[tface->loc]);
- } else {
- printf(" Oppo[%i] x%lx (%.12g,%.12g,%.12g) %d\n",
- loc2oppo[tface->loc], (unsigned long)(tmppt),
- tmppt[0], tmppt[1], tmppt[2], pointmark(tmppt));
- }
-
- if (b->useshelles) {
- tmpface = *tface;
- facecount = 0;
- while(facecount < 6) {
- tmpface.loc = facecount;
- tspivot(tmpface, tmpsh);
- if(tmpsh.sh != dummysh) {
- printf(" [%i] x%lx ID(%i) ", facecount,
- (unsigned long)(tmpsh.sh), shellmark(tmpsh));
- if (sorg(tmpsh) == (point) NULL) {
- printf("(fake)");
- }
- printf("\n");
- }
- facecount ++;
- }
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// printsh() Print out the details of a subface or subsegment on screen. //
-// //
-// It's also used when the highest level of verbosity (`-VVV') is specified. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::printsh(face* sface)
-{
- face prtsh;
- triface prttet;
- point printpoint;
-
- if (sapex(*sface) != NULL) {
- printf("subface x%lx, ver %d, mark %d:",
- (unsigned long)(sface->sh), sface->shver, shellmark(*sface));
- } else {
- printf("Subsegment x%lx, ver %d, mark %d:",
- (unsigned long)(sface->sh), sface->shver, shellmark(*sface));
- }
- if (sinfected(*sface)) {
- printf(" (infected)");
- }
- if (shell2badface(*sface)) {
- printf(" (queued)");
- }
- if (sapex(*sface) != NULL) {
- if (shelltype(*sface) == SHARP) {
- printf(" (sharp)");
- }
- } else {
- if (shelltype(*sface) == SHARP) {
- printf(" (sharp)");
- }
- }
- if (checkpbcs) {
- if (shellpbcgroup(*sface) >= 0) {
- printf(" (pbc %d)", shellpbcgroup(*sface));
- }
- }
- printf("\n");
-
- sdecode(sface->sh[0], prtsh);
- if (prtsh.sh == dummysh) {
- printf(" [0] = No shell\n");
- } else {
- printf(" [0] = x%lx %d\n", (unsigned long)(prtsh.sh), prtsh.shver);
- }
- sdecode(sface->sh[1], prtsh);
- if (prtsh.sh == dummysh) {
- printf(" [1] = No shell\n");
- } else {
- printf(" [1] = x%lx %d\n", (unsigned long)(prtsh.sh), prtsh.shver);
- }
- sdecode(sface->sh[2], prtsh);
- if (prtsh.sh == dummysh) {
- printf(" [2] = No shell\n");
- } else {
- printf(" [2] = x%lx %d\n", (unsigned long)(prtsh.sh), prtsh.shver);
- }
-
- printpoint = sorg(*sface);
- if (printpoint == (point) NULL)
- printf(" Org [%d] = NULL\n", vo[sface->shver]);
- else
- printf(" Org [%d] = x%lx (%.12g,%.12g,%.12g) %d\n",
- vo[sface->shver], (unsigned long)(printpoint), printpoint[0],
- printpoint[1], printpoint[2], pointmark(printpoint));
- printpoint = sdest(*sface);
- if (printpoint == (point) NULL)
- printf(" Dest[%d] = NULL\n", vd[sface->shver]);
- else
- printf(" Dest[%d] = x%lx (%.12g,%.12g,%.12g) %d\n",
- vd[sface->shver], (unsigned long)(printpoint), printpoint[0],
- printpoint[1], printpoint[2], pointmark(printpoint));
-
- if (sapex(*sface) != NULL) {
- printpoint = sapex(*sface);
- if (printpoint == (point) NULL)
- printf(" Apex[%d] = NULL\n", va[sface->shver]);
- else
- printf(" Apex[%d] = x%lx (%.12g,%.12g,%.12g) %d\n",
- va[sface->shver], (unsigned long)(printpoint), printpoint[0],
- printpoint[1], printpoint[2], pointmark(printpoint));
-
- decode(sface->sh[6], prttet);
- if (prttet.tet == dummytet) {
- printf(" [6] = Outer space\n");
- } else {
- printf(" [6] = x%lx %d\n",
- (unsigned long)(prttet.tet), prttet.loc);
- }
- decode(sface->sh[7], prttet);
- if (prttet.tet == dummytet) {
- printf(" [7] = Outer space\n");
- } else {
- printf(" [7] = x%lx %d\n",
- (unsigned long)(prttet.tet), prttet.loc);
- }
-
- sdecode(sface->sh[8], prtsh);
- if (prtsh.sh == dummysh) {
- printf(" [8] = No subsegment\n");
- } else {
- printf(" [8] = x%lx %d\n",
- (unsigned long)(prtsh.sh), prtsh.shver);
- }
- sdecode(sface->sh[9], prtsh);
- if (prtsh.sh == dummysh) {
- printf(" [9] = No subsegment\n");
- } else {
- printf(" [9] = x%lx %d\n",
- (unsigned long)(prtsh.sh), prtsh.shver);
- }
- sdecode(sface->sh[10], prtsh);
- if (prtsh.sh == dummysh) {
- printf(" [10]= No subsegment\n");
- } else {
- printf(" [10]= x%lx %d\n",
- (unsigned long)(prtsh.sh), prtsh.shver);
- }
- }
-}
-
-//
-// End of advanced primitives
-//
-
-//
-// End of mesh manipulation primitives
-//
-
-//
-// Begin of mesh items searching routines
-//
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// makepoint2tetmap() Construct a mapping from points to tetrahedra. //
-// //
-// Traverses all the tetrahedra, provides each corner of each tetrahedron //
-// with a pointer to that tetrahedera. Some pointers will be overwritten by //
-// other pointers because each point may be a corner of several tetrahedra, //
-// but in the end every point will point to a tetrahedron that contains it. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::makepoint2tetmap()
-{
- triface tetloop;
- point pointptr;
-
- if (b->verbose > 0) {
- printf(" Constructing mapping from points to tetrahedra.\n");
- }
-
- // Initialize the point2tet field of each point.
- points->traversalinit();
- pointptr = pointtraverse();
- while (pointptr != (point) NULL) {
- setpoint2tet(pointptr, (tetrahedron) NULL);
- pointptr = pointtraverse();
- }
-
- tetrahedrons->traversalinit();
- tetloop.tet = tetrahedrontraverse();
- while (tetloop.tet != (tetrahedron *) NULL) {
- // Check all four points of the tetrahedron.
- tetloop.loc = 0;
- pointptr = org(tetloop);
- setpoint2tet(pointptr, encode(tetloop));
- pointptr = dest(tetloop);
- setpoint2tet(pointptr, encode(tetloop));
- pointptr = apex(tetloop);
- setpoint2tet(pointptr, encode(tetloop));
- pointptr = oppo(tetloop);
- setpoint2tet(pointptr, encode(tetloop));
- // Get the next tetrahedron in the list.
- tetloop.tet = tetrahedrontraverse();
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// makeindex2pointmap() Create a map from index to vertices. //
-// //
-// 'idx2verlist' returns the created map. Traverse all vertices, a pointer //
-// to each vertex is set into the array. The pointer to the first vertex is //
-// saved in 'idx2verlist[0]'. Don't forget to minus 'in->firstnumber' when //
-// to get the vertex form its index. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::makeindex2pointmap(point*& idx2verlist)
-{
- point pointloop;
- int idx;
-
- if (b->verbose > 0) {
- printf(" Constructing mapping from indices to points.\n");
- }
-
- idx2verlist = new point[points->items];
-
- points->traversalinit();
- pointloop = pointtraverse();
- idx = 0;
- while (pointloop != (point) NULL) {
- idx2verlist[idx] = pointloop;
- idx++;
- pointloop = pointtraverse();
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// makesegmentmap() Create a map from vertices (their indices) to //
-// segments incident at the same vertices. //
-// //
-// Two arrays 'idx2seglist' and 'segsperverlist' together return the map. //
-// They form a sparse matrix structure with size (n + 1) x (n + 1), n is the //
-// number of segments. idx2seglist contains row information and //
-// segsperverlist contains all (non-zero) elements. The i-th entry of //
-// idx2seglist is the starting position of i-th row's (non-zero) elements in //
-// segsperverlist. The number of elements of i-th row is calculated by the //
-// (i+1)-th entry minus i-th entry of idx2seglist. //
-// //
-// NOTE: These two arrays will be created inside this routine, don't forget //
-// to free them after using. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::makesegmentmap(int*& idx2seglist, shellface**& segsperverlist)
-{
- shellface *shloop;
- int i, j, k;
-
- if (b->verbose > 0) {
- printf(" Constructing mapping from points to segments.\n");
- }
-
- // Create and initialize 'idx2seglist'.
- idx2seglist = new int[points->items + 1];
- for (i = 0; i < points->items + 1; i++) idx2seglist[i] = 0;
-
- // Loop the set of segments once, counter the number of segments sharing
- // each vertex.
- subsegs->traversalinit();
- shloop = shellfacetraverse(subsegs);
- while (shloop != (shellface *) NULL) {
- // Increment the number of sharing segments for each endpoint.
- for (i = 0; i < 2; i++) {
- j = pointmark((point) shloop[3 + i]) - in->firstnumber;
- idx2seglist[j]++;
- }
- shloop = shellfacetraverse(subsegs);
- }
-
- // Calculate the total length of array 'facesperverlist'.
- j = idx2seglist[0];
- idx2seglist[0] = 0; // Array starts from 0 element.
- for (i = 0; i < points->items; i++) {
- k = idx2seglist[i + 1];
- idx2seglist[i + 1] = idx2seglist[i] + j;
- j = k;
- }
- // The total length is in the last unit of idx2seglist.
- segsperverlist = new shellface*[idx2seglist[i]];
- // Loop the set of segments again, set the info. of segments per vertex.
- subsegs->traversalinit();
- shloop = shellfacetraverse(subsegs);
- while (shloop != (shellface *) NULL) {
- for (i = 0; i < 2; i++) {
- j = pointmark((point) shloop[3 + i]) - in->firstnumber;
- segsperverlist[idx2seglist[j]] = shloop;
- idx2seglist[j]++;
- }
- shloop = shellfacetraverse(subsegs);
- }
- // Contents in 'idx2seglist' are shifted, now shift them back.
- for (i = points->items - 1; i >= 0; i--) {
- idx2seglist[i + 1] = idx2seglist[i];
- }
- idx2seglist[0] = 0;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// makesubfacemap() Create a map from vertices (their indices) to //
-// subfaces incident at the same vertices. //
-// //
-// Two arrays 'idx2facelist' and 'facesperverlist' together return the map. //
-// They form a sparse matrix structure with size (n + 1) x (n + 1), n is the //
-// number of subfaces. idx2facelist contains row information and //
-// facesperverlist contains all (non-zero) elements. The i-th entry of //
-// idx2facelist is the starting position of i-th row's(non-zero) elements in //
-// facesperverlist. The number of elements of i-th row is calculated by the //
-// (i+1)-th entry minus i-th entry of idx2facelist. //
-// //
-// NOTE: These two arrays will be created inside this routine, don't forget //
-// to free them after using. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::
-makesubfacemap(int*& idx2facelist, shellface**& facesperverlist)
-{
- shellface *shloop;
- int i, j, k;
-
- if (b->verbose > 0) {
- printf(" Constructing mapping from points to subfaces.\n");
- }
-
- // Create and initialize 'idx2facelist'.
- idx2facelist = new int[points->items + 1];
- for (i = 0; i < points->items + 1; i++) idx2facelist[i] = 0;
-
- // Loop the set of subfaces once, counter the number of subfaces sharing
- // each vertex.
- subfaces->traversalinit();
- shloop = shellfacetraverse(subfaces);
- while (shloop != (shellface *) NULL) {
- // Increment the number of sharing segments for each endpoint.
- for (i = 0; i < 3; i++) {
- j = pointmark((point) shloop[3 + i]) - in->firstnumber;
- idx2facelist[j]++;
- }
- shloop = shellfacetraverse(subfaces);
- }
-
- // Calculate the total length of array 'facesperverlist'.
- j = idx2facelist[0];
- idx2facelist[0] = 0; // Array starts from 0 element.
- for (i = 0; i < points->items; i++) {
- k = idx2facelist[i + 1];
- idx2facelist[i + 1] = idx2facelist[i] + j;
- j = k;
- }
- // The total length is in the last unit of idx2facelist.
- facesperverlist = new shellface*[idx2facelist[i]];
- // Loop the set of segments again, set the info. of segments per vertex.
- subfaces->traversalinit();
- shloop = shellfacetraverse(subfaces);
- while (shloop != (shellface *) NULL) {
- for (i = 0; i < 3; i++) {
- j = pointmark((point) shloop[3 + i]) - in->firstnumber;
- facesperverlist[idx2facelist[j]] = shloop;
- idx2facelist[j]++;
- }
- shloop = shellfacetraverse(subfaces);
- }
- // Contents in 'idx2facelist' are shifted, now shift them back.
- for (i = points->items - 1; i >= 0; i--) {
- idx2facelist[i + 1] = idx2facelist[i];
- }
- idx2facelist[0] = 0;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// maketetrahedronmap() Create a map from vertices (their indices) to //
-// tetrahedra incident at the same vertices. //
-// //
-// Two arrays 'idx2tetlist' and 'tetsperverlist' together return the map. //
-// They form a sparse matrix structure with size (n + 1) x (n + 1), n is the //
-// number of tetrahedra. idx2tetlist contains row information and //
-// tetsperverlist contains all (non-zero) elements. The i-th entry of //
-// idx2tetlist is the starting position of i-th row's (non-zero) elements in //
-// tetsperverlist. The number of elements of i-th row is calculated by the //
-// (i+1)-th entry minus i-th entry of idx2tetlist. //
-// //
-// NOTE: These two arrays will be created inside this routine, don't forget //
-// to free them after using. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::
-maketetrahedronmap(int*& idx2tetlist, tetrahedron**& tetsperverlist)
-{
- tetrahedron *tetloop;
- int i, j, k;
-
- if (b->verbose > 0) {
- printf(" Constructing mapping from points to tetrahedra.\n");
- }
-
- // Create and initialize 'idx2tetlist'.
- idx2tetlist = new int[points->items + 1];
- for (i = 0; i < points->items + 1; i++) idx2tetlist[i] = 0;
-
- // Loop the set of tetrahedra once, counter the number of tetrahedra
- // sharing each vertex.
- tetrahedrons->traversalinit();
- tetloop = tetrahedrontraverse();
- while (tetloop != (tetrahedron *) NULL) {
- // Increment the number of sharing tetrahedra for each endpoint.
- for (i = 0; i < 4; i++) {
- j = pointmark((point) tetloop[4 + i]) - in->firstnumber;
- idx2tetlist[j]++;
- }
- tetloop = tetrahedrontraverse();
- }
-
- // Calculate the total length of array 'tetsperverlist'.
- j = idx2tetlist[0];
- idx2tetlist[0] = 0; // Array starts from 0 element.
- for (i = 0; i < points->items; i++) {
- k = idx2tetlist[i + 1];
- idx2tetlist[i + 1] = idx2tetlist[i] + j;
- j = k;
- }
- // The total length is in the last unit of idx2tetlist.
- tetsperverlist = new tetrahedron*[idx2tetlist[i]];
- // Loop the set of tetrahedra again, set the info. of tet. per vertex.
- tetrahedrons->traversalinit();
- tetloop = tetrahedrontraverse();
- while (tetloop != (tetrahedron *) NULL) {
- for (i = 0; i < 4; i++) {
- j = pointmark((point) tetloop[4 + i]) - in->firstnumber;
- tetsperverlist[idx2tetlist[j]] = tetloop;
- idx2tetlist[j]++;
- }
- tetloop = tetrahedrontraverse();
- }
- // Contents in 'idx2tetlist' are shifted, now shift them back.
- for (i = points->items - 1; i >= 0; i--) {
- idx2tetlist[i + 1] = idx2tetlist[i];
- }
- idx2tetlist[0] = 0;
-}
-
-//
-// End of mesh items searching routines
-//
-
-//
-// Begin of linear algebra functions
-//
-
-// dot() returns the dot product: v1 dot v2.
-
-inline REAL tetgenmesh::dot(REAL* v1, REAL* v2)
-{
- return v1[0] * v2[0] + v1[1] * v2[1] + v1[2] * v2[2];
-}
-
-// cross() computes the cross product: n = v1 cross v2.
-
-inline void tetgenmesh::cross(REAL* v1, REAL* v2, REAL* n)
-{
- n[0] = v1[1] * v2[2] - v2[1] * v1[2];
- n[1] = -(v1[0] * v2[2] - v2[0] * v1[2]);
- n[2] = v1[0] * v2[1] - v2[0] * v1[1];
-}
-
-// initm44() initializes a 4x4 matrix.
-static void initm44(REAL a00, REAL a01, REAL a02, REAL a03,
- REAL a10, REAL a11, REAL a12, REAL a13,
- REAL a20, REAL a21, REAL a22, REAL a23,
- REAL a30, REAL a31, REAL a32, REAL a33,
- REAL M[4][4])
-{
- M[0][0] = a00; M[0][1] = a01; M[0][2] = a02; M[0][3] = a03;
- M[1][0] = a10; M[1][1] = a11; M[1][2] = a12; M[1][3] = a13;
- M[2][0] = a20; M[2][1] = a21; M[2][2] = a22; M[2][3] = a23;
- M[3][0] = a30; M[3][1] = a31; M[3][2] = a32; M[3][3] = a33;
-}
-
-// m4xm4() multiplies 2 4x4 matrics: m1 = m1 * m2.
-static void m4xm4(REAL m1[4][4], REAL m2[4][4])
-{
- REAL tmp[4];
- int i, j;
-
- for (i = 0; i < 4; i++) { // i-th row
- for (j = 0; j < 4; j++) { // j-th col
- tmp[j] = m1[i][0] * m2[0][j] + m1[i][1] * m2[1][j]
- + m1[i][2] * m2[2][j] + m1[i][3] * m2[3][j];
- }
- for (j = 0; j < 4; j++)
- m1[i][j] = tmp[j];
- }
-}
-
-// m4xv4() multiplies a 4x4 matrix and 4x1 vector: v2 = m * v1
-static void m4xv4(REAL v2[4], REAL m[4][4], REAL v1[4])
-{
- v2[0] = m[0][0]*v1[0] + m[0][1]*v1[1] + m[0][2]*v1[2] + m[0][3]*v1[3];
- v2[1] = m[1][0]*v1[0] + m[1][1]*v1[1] + m[1][2]*v1[2] + m[1][3]*v1[3];
- v2[2] = m[2][0]*v1[0] + m[2][1]*v1[1] + m[2][2]*v1[2] + m[2][3]*v1[3];
- v2[3] = m[3][0]*v1[0] + m[3][1]*v1[1] + m[3][2]*v1[2] + m[3][3]*v1[3];
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// lu_decmp() Compute the LU decomposition of a matrix. //
-// //
-// Compute the LU decomposition of a (non-singular) square matrix A using //
-// partial pivoting and implicit row exchanges. The result is: //
-// A = P * L * U, //
-// where P is a permutation matrix, L is unit lower triangular, and U is //
-// upper triangular. The factored form of A is used in combination with //
-// 'lu_solve()' to solve linear equations: Ax = b, or invert a matrix. //
-// //
-// The inputs are a square matrix 'lu[N..n+N-1][N..n+N-1]', it's size is 'n'.//
-// On output, 'lu' is replaced by the LU decomposition of a rowwise permuta- //
-// tion of itself, 'ps[N..n+N-1]' is an output vector that records the row //
-// permutation effected by the partial pivoting, effectively, 'ps' array //
-// tells the user what the permutation matrix P is; 'd' is output as +1/-1 //
-// depending on whether the number of row interchanges was even or odd, //
-// respectively. //
-// //
-// Return true if the LU decomposition is successfully computed, otherwise, //
-// return false in case that A is a singular matrix. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::lu_decmp(REAL lu[4][4], int n, int* ps, REAL* d, int N)
-{
- REAL scales[4];
- REAL pivot, biggest, mult, tempf;
- int pivotindex = 0;
- int i, j, k;
-
- *d = 1.0; // No row interchanges yet.
-
- for (i = N; i < n + N; i++) { // For each row.
- // Find the largest element in each row for row equilibration
- biggest = 0.0;
- for (j = N; j < n + N; j++)
- if (biggest < (tempf = fabs(lu[i][j])))
- biggest = tempf;
- if (biggest != 0.0)
- scales[i] = 1.0 / biggest;
- else {
- scales[i] = 0.0;
- return false; // Zero row: singular matrix.
- }
- ps[i] = i; // Initialize pivot sequence.
- }
-
- for (k = N; k < n + N - 1; k++) { // For each column.
- // Find the largest element in each column to pivot around.
- biggest = 0.0;
- for (i = k; i < n + N; i++) {
- if (biggest < (tempf = fabs(lu[ps[i]][k]) * scales[ps[i]])) {
- biggest = tempf;
- pivotindex = i;
- }
- }
- if (biggest == 0.0) {
- return false; // Zero column: singular matrix.
- }
- if (pivotindex != k) { // Update pivot sequence.
- j = ps[k];
- ps[k] = ps[pivotindex];
- ps[pivotindex] = j;
- *d = -(*d); // ...and change the parity of d.
- }
-
- // Pivot, eliminating an extra variable each time
- pivot = lu[ps[k]][k];
- for (i = k + 1; i < n + N; i++) {
- lu[ps[i]][k] = mult = lu[ps[i]][k] / pivot;
- if (mult != 0.0) {
- for (j = k + 1; j < n + N; j++)
- lu[ps[i]][j] -= mult * lu[ps[k]][j];
- }
- }
- }
-
- // (lu[ps[n + N - 1]][n + N - 1] == 0.0) ==> A is singular.
- return lu[ps[n + N - 1]][n + N - 1] != 0.0;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// lu_solve() Solves the linear equation: Ax = b, after the matrix A //
-// has been decomposed into the lower and upper triangular //
-// matrices L and U, where A = LU. //
-// //
-// 'lu[N..n+N-1][N..n+N-1]' is input, not as the matrix 'A' but rather as //
-// its LU decomposition, computed by the routine 'lu_decmp'; 'ps[N..n+N-1]' //
-// is input as the permutation vector returned by 'lu_decmp'; 'b[N..n+N-1]' //
-// is input as the right-hand side vector, and returns with the solution //
-// vector. 'lu', 'n', and 'ps' are not modified by this routine and can be //
-// left in place for successive calls with different right-hand sides 'b'. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::lu_solve(REAL lu[4][4], int n, int* ps, REAL* b, int N)
-{
- int i, j;
- REAL X[4], dot;
-
- for (i = N; i < n + N; i++) X[i] = 0.0;
-
- // Vector reduction using U triangular matrix.
- for (i = N; i < n + N; i++) {
- dot = 0.0;
- for (j = N; j < i + N; j++)
- dot += lu[ps[i]][j] * X[j];
- X[i] = b[ps[i]] - dot;
- }
-
- // Back substitution, in L triangular matrix.
- for (i = n + N - 1; i >= N; i--) {
- dot = 0.0;
- for (j = i + 1; j < n + N; j++)
- dot += lu[ps[i]][j] * X[j];
- X[i] = (X[i] - dot) / lu[ps[i]][i];
- }
-
- for (i = N; i < n + N; i++) b[i] = X[i];
-}
-
-//
-// End of linear algebra functions
-//
-
-//
-// Begin of geometric tests
-//
-
-// All the following routines require the input objects are not degenerate.
-// i.e., a triangle must has three non-collinear corners; an edge must
-// has two identical endpoints. Degenerate cases should have to detect
-// first and then handled as special cases.
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// edge_vert_col_inter() Test whether an edge (ab) and a collinear vertex //
-// (p) are intersecting or not. //
-// //
-// Possible cases are p is coincident to a (p = a), or to b (p = b), or p is //
-// inside ab (a < p < b), or outside ab (p < a or p > b). These cases can be //
-// quickly determined by comparing the corresponding coords of a, b, and p //
-// (which are not all equal). //
-// //
-// The return value indicates one of the three cases: DISJOINT, SHAREVERTEX //
-// (p = a or p = b), and INTERSECT (a < p < b). //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-enum tetgenmesh::interresult tetgenmesh::edge_vert_col_inter(REAL* A, REAL* B,
- REAL* P)
-{
- int i = 0;
- do {
- if (A[i] < B[i]) {
- if (P[i] < A[i]) {
- return DISJOINT;
- } else if (P[i] > A[i]) {
- if (P[i] < B[i]) {
- return INTERSECT;
- } else if (P[i] > B[i]) {
- return DISJOINT;
- } else {
- // assert(P[i] == B[i]);
- return SHAREVERTEX;
- }
- } else {
- // assert(P[i] == A[i]);
- return SHAREVERTEX;
- }
- } else if (A[i] > B[i]) {
- if (P[i] < B[i]) {
- return DISJOINT;
- } else if (P[i] > B[i]) {
- if (P[i] < A[i]) {
- return INTERSECT;
- } else if (P[i] > A[i]) {
- return DISJOINT;
- } else {
- // assert(P[i] == A[i]);
- return SHAREVERTEX;
- }
- } else {
- // assert(P[i] == B[i]);
- return SHAREVERTEX;
- }
- }
- // i-th coordinates are equal, try i+1-th;
- i++;
- } while (i < 3);
- // Should never be here.
- return DISJOINT;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// edge_edge_cop_inter() Test whether two coplanar edges (ab, and pq) are //
-// intersecting or not. //
-// //
-// Possible cases are ab and pq are disjointed, or proper intersecting (int- //
-// ersect at a point other than their endpoints), or both collinear and int- //
-// ersecting, or sharing at a common endpoint, or are coincident. //
-// //
-// A reference point R is required, which is exactly not coplanar with these //
-// two edges. Since the caller knows these two edges are coplanar, it must //
-// be able to provide (or calculate) such a point. //
-// //
-// The return value indicates one of the four cases: DISJOINT, SHAREVERTEX, //
-// SHAREEDGE, and INTERSECT. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-enum tetgenmesh::interresult tetgenmesh:: edge_edge_cop_inter(REAL* A, REAL* B,
- REAL* P, REAL* Q, REAL* R)
-{
- REAL s1, s2, s3, s4;
-
-#ifdef SELF_CHECK
- assert(R != NULL);
-#endif
- s1 = orient3d(A, B, R, P);
- s2 = orient3d(A, B, R, Q);
- if (s1 * s2 > 0.0) {
- // Both p and q are at the same side of ab.
- return DISJOINT;
- }
- s3 = orient3d(P, Q, R, A);
- s4 = orient3d(P, Q, R, B);
- if (s3 * s4 > 0.0) {
- // Both a and b are at the same side of pq.
- return DISJOINT;
- }
-
- // Possible degenerate cases are:
- // (1) Only one of p and q is collinear with ab;
- // (2) Both p and q are collinear with ab;
- // (3) Only one of a and b is collinear with pq.
- enum interresult abp, abq;
- enum interresult pqa, pqb;
-
- if (s1 == 0.0) {
- // p is collinear with ab.
- abp = edge_vert_col_inter(A, B, P);
- if (abp == INTERSECT) {
- // p is inside ab.
- return INTERSECT;
- }
- if (s2 == 0.0) {
- // q is collinear with ab. Case (2).
- abq = edge_vert_col_inter(A, B, Q);
- if (abq == INTERSECT) {
- // q is inside ab.
- return INTERSECT;
- }
- if (abp == SHAREVERTEX && abq == SHAREVERTEX) {
- // ab and pq are identical.
- return SHAREEDGE;
- }
- pqa = edge_vert_col_inter(P, Q, A);
- if (pqa == INTERSECT) {
- // a is inside pq.
- return INTERSECT;
- }
- pqb = edge_vert_col_inter(P, Q, B);
- if (pqb == INTERSECT) {
- // b is inside pq.
- return INTERSECT;
- }
- if (abp == SHAREVERTEX || abq == SHAREVERTEX) {
- // either p or q is coincident with a or b.
-#ifdef SELF_CHECK
- // ONLY one case is possible, otherwise, shoule be SHAREEDGE.
- assert(abp ^ abq);
-#endif
- return SHAREVERTEX;
- }
- // The last case. They are disjointed.
-#ifdef SELF_CHECK
- assert((abp == DISJOINT) && (abp == abq && abq == pqa && pqa == pqb));
-#endif
- return DISJOINT;
- } else {
- // p is collinear with ab. Case (1).
-#ifdef SELF_CHECK
- assert(abp == SHAREVERTEX || abp == DISJOINT);
-#endif
- return abp;
- }
- }
- // p is NOT collinear with ab.
- if (s2 == 0.0) {
- // q is collinear with ab. Case (1).
- abq = edge_vert_col_inter(A, B, Q);
-#ifdef SELF_CHECK
- assert(abq == SHAREVERTEX || abq == DISJOINT || abq == INTERSECT);
-#endif
- return abq;
- }
-
- // We have found p and q are not collinear with ab. However, it is still
- // possible that a or b is collinear with pq (ONLY one of a and b).
- if (s3 == 0.0) {
- // a is collinear with pq. Case (3).
-#ifdef SELF_CHECK
- assert(s4 != 0.0);
-#endif
- pqa = edge_vert_col_inter(P, Q, A);
-#ifdef SELF_CHECK
- // This case should have been detected in above.
- assert(pqa != SHAREVERTEX);
- assert(pqa == INTERSECT || pqa == DISJOINT);
-#endif
- return pqa;
- }
- if (s4 == 0.0) {
- // b is collinear with pq. Case (3).
-#ifdef SELF_CHECK
- assert(s3 != 0.0);
-#endif
- pqb = edge_vert_col_inter(P, Q, B);
-#ifdef SELF_CHECK
- // This case should have been detected in above.
- assert(pqb != SHAREVERTEX);
- assert(pqb == INTERSECT || pqb == DISJOINT);
-#endif
- return pqb;
- }
-
- // ab and pq are intersecting properly.
- return INTERSECT;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// Notations //
-// //
-// Let ABC be the plane passes through a, b, and c; ABC+ be the halfspace //
-// including the set of all points x, such that orient3d(a, b, c, x) > 0; //
-// ABC- be the other halfspace, such that for each point x in ABC-, //
-// orient3d(a, b, c, x) < 0. For the set of x which are on ABC, orient3d(a, //
-// b, c, x) = 0. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// tri_vert_copl_inter() Test whether a triangle (abc) and a coplanar //
-// point (p) are intersecting or not. //
-// //
-// Possible cases are p is inside abc, or on an edge of, or coincident with //
-// a vertex of, or outside abc. //
-// //
-// A reference point R is required. R is exactly not coplanar with abc and p.//
-// Since the caller knows they are coplanar, it must be able to provide (or //
-// calculate) such a point. //
-// //
-// The return value indicates one of the four cases: DISJOINT, SHAREVERTEX, //
-// and INTERSECT. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-enum tetgenmesh::interresult tetgenmesh::tri_vert_cop_inter(REAL* A, REAL* B,
- REAL* C, REAL* P, REAL* R)
-{
- REAL s1, s2, s3;
- int sign;
-
-#ifdef SELF_CHECK
- assert(R != (REAL *) NULL);
-#endif
- // Adjust the orientation of a, b, c and r, so that we can assume that
- // r is strictly in ABC- (i.e., r is above ABC wrt. right-hand rule).
- s1 = orient3d(A, B, C, R);
-#ifdef SELF_CHECK
- assert(s1 != 0.0);
-#endif
- sign = s1 < 0.0 ? 1 : -1;
-
- // Test starts from here.
- s1 = orient3d(A, B, R, P) * sign;
- if (s1 < 0.0) {
- // p is in ABR-.
- return DISJOINT;
- }
- s2 = orient3d(B, C, R, P) * sign;
- if (s2 < 0.0) {
- // p is in BCR-.
- return DISJOINT;
- }
- s3 = orient3d(C, A, R, P) * sign;
- if (s3 < 0.0) {
- // p is in CAR-.
- return DISJOINT;
- }
- if (s1 == 0.0) {
- // p is on ABR.
- if (s2 == 0.0) {
- // p is on BCR.
-#ifdef SELF_CHECK
- assert(s3 > 0.0);
-#endif
- // p is coincident with b.
- return SHAREVERTEX;
- }
- if (s3 == 0.0) {
- // p is on CAR.
- // p is coincident with a.
- return SHAREVERTEX;
- }
- // p is on edge ab.
- return INTERSECT;
- }
- // p is in ABR+.
- if (s2 == 0.0) {
- // p is on BCR.
- if (s3 == 0.0) {
- // p is on CAR.
- // p is coincident with c.
- return SHAREVERTEX;
- }
- // p is on edge bc.
- return INTERSECT;
- }
- if (s3 == 0.0) {
- // p is on CAR.
- // p is on edge ca.
- return INTERSECT;
- }
-
- // p is strictly inside abc.
- return INTERSECT;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// tri_edge_cop_inter() Test whether a triangle (abc) and a coplanar edge //
-// (pq) are intersecting or not. //
-// //
-// A reference point R is required. R is exactly not coplanar with abc and //
-// pq. Since the caller knows they are coplanar, it must be able to provide //
-// (or calculate) such a point. //
-// //
-// The return value indicates one of the four cases: DISJOINT, SHAREVERTEX, //
-// SHAREEDGE, and INTERSECT. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-enum tetgenmesh::interresult tetgenmesh::tri_edge_cop_inter(REAL* A, REAL* B,
- REAL* C, REAL* P, REAL* Q, REAL* R)
-{
- enum interresult abpq, bcpq, capq;
- enum interresult abcp, abcq;
-
- // Test if pq is intersecting one of edges of abc.
- abpq = edge_edge_cop_inter(A, B, P, Q, R);
- if (abpq == INTERSECT || abpq == SHAREEDGE) {
- return abpq;
- }
- bcpq = edge_edge_cop_inter(B, C, P, Q, R);
- if (bcpq == INTERSECT || bcpq == SHAREEDGE) {
- return bcpq;
- }
- capq = edge_edge_cop_inter(C, A, P, Q, R);
- if (capq == INTERSECT || capq == SHAREEDGE) {
- return capq;
- }
-
- // Test if p and q is inside abc.
- abcp = tri_vert_cop_inter(A, B, C, P, R);
- if (abcp == INTERSECT) {
- return INTERSECT;
- }
- abcq = tri_vert_cop_inter(A, B, C, Q, R);
- if (abcq == INTERSECT) {
- return INTERSECT;
- }
-
- // Combine the test results of edge intersectings and triangle insides
- // to detect whether abc and pq are sharing vertex or disjointed.
- if (abpq == SHAREVERTEX) {
- // p or q is coincident with a or b.
-#ifdef SELF_CHECK
- assert(abcp ^ abcq);
-#endif
- return SHAREVERTEX;
- }
- if (bcpq == SHAREVERTEX) {
- // p or q is coincident with b or c.
-#ifdef SELF_CHECK
- assert(abcp ^ abcq);
-#endif
- return SHAREVERTEX;
- }
- if (capq == SHAREVERTEX) {
- // p or q is coincident with c or a.
-#ifdef SELF_CHECK
- assert(abcp ^ abcq);
-#endif
- return SHAREVERTEX;
- }
-
- // They are disjointed.
- return DISJOINT;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// tri_edge_inter_tail() Test whether a triangle (abc) and an edge (pq) //
-// are intersecting or not. //
-// //
-// s1 and s2 are results of pre-performed orientation tests. s1 = orient3d( //
-// a, b, c, p); s2 = orient3d(a, b, c, q). To separate this routine from //
-// tri_edge_inter() can save two orientation tests in tri_tri_inter(). //
-// //
-// The return value indicates one of the four cases: DISJOINT, SHAREVERTEX, //
-// SHAREEDGE, and INTERSECT. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-enum tetgenmesh::interresult tetgenmesh::tri_edge_inter_tail(REAL* A, REAL* B,
- REAL* C, REAL* P, REAL* Q, REAL s1, REAL s2)
-{
- REAL s3, s4, s5;
- int sign;
-
- if (s1 * s2 > 0.0) {
- // p, q are at the same halfspace of ABC, no intersection.
- return DISJOINT;
- }
-
- if (s1 * s2 < 0.0) {
- // p, q are both not on ABC (and not sharing vertices, edges of abc).
- // Adjust the orientation of a, b, c and p, so that we can assume that
- // p is strictly in ABC-, and q is strictly in ABC+.
- sign = s1 < 0.0 ? 1 : -1;
- s3 = orient3d(A, B, P, Q) * sign;
- if (s3 < 0.0) {
- // q is at ABP-.
- return DISJOINT;
- }
- s4 = orient3d(B, C, P, Q) * sign;
- if (s4 < 0.0) {
- // q is at BCP-.
- return DISJOINT;
- }
- s5 = orient3d(C, A, P, Q) * sign;
- if (s5 < 0.0) {
- // q is at CAP-.
- return DISJOINT;
- }
- if (s3 == 0.0) {
- // q is on ABP.
- if (s4 == 0.0) {
- // q is on BCP (and q must in CAP+).
-#ifdef SELF_CHECK
- assert(s5 > 0.0);
-#endif
- // pq intersects abc at vertex b.
- return SHAREVERTEX;
- }
- if (s5 == 0.0) {
- // q is on CAP (and q must in BCP+).
- // pq intersects abc at vertex a.
- return SHAREVERTEX;
- }
- // q in both BCP+ and CAP+.
- // pq crosses ab properly.
- return INTERSECT;
- }
- // q is in ABP+;
- if (s4 == 0.0) {
- // q is on BCP.
- if (s5 == 0.0) {
- // q is on CAP.
- // pq intersects abc at vertex c.
- return SHAREVERTEX;
- }
- // pq crosses bc properly.
- return INTERSECT;
- }
- // q is in BCP+;
- if (s5 == 0.0) {
- // q is on CAP.
- // pq crosses ca properly.
- return INTERSECT;
- }
- // q is in CAP+;
- // pq crosses abc properly.
- return INTERSECT;
- }
-
- if (s1 != 0.0 || s2 != 0.0) {
- // Either p or q is coplanar with abc. ONLY one of them is possible.
- if (s1 == 0.0) {
- // p is coplanar with abc, q can be used as reference point.
-#ifdef SELF_CHECK
- assert(s2 != 0.0);
-#endif
- return tri_vert_cop_inter(A, B, C, P, Q);
- } else {
- // q is coplanar with abc, p can be used as reference point.
-#ifdef SELF_CHECK
- assert(s2 == 0.0);
-#endif
- return tri_vert_cop_inter(A, B, C, Q, P);
- }
- }
-
- // pq is coplanar with abc. Calculate a point which is exactly not
- // coplanar with a, b, and c.
- REAL R[3], N[3];
- REAL ax, ay, az, bx, by, bz;
-
- ax = A[0] - B[0];
- ay = A[1] - B[1];
- az = A[2] - B[2];
- bx = A[0] - C[0];
- by = A[1] - C[1];
- bz = A[2] - C[2];
- N[0] = ay * bz - by * az;
- N[1] = az * bx - bz * ax;
- N[2] = ax * by - bx * ay;
- // The normal should not be a zero vector (otherwise, abc are collinear).
-#ifdef SELF_CHECK
- assert((fabs(N[0]) + fabs(N[1]) + fabs(N[2])) > 0.0);
-#endif
- // The reference point R is lifted from A to the normal direction with
- // a distance d = average edge length of the triangle abc.
- R[0] = N[0] + A[0];
- R[1] = N[1] + A[1];
- R[2] = N[2] + A[2];
- // Becareful the case: if the non-zero component(s) in N is smaller than
- // the machine epsilon (i.e., 2^(-16) for double), R will exactly equal
- // to A due to the round-off error. Do check if it is.
- if (R[0] == A[0] && R[1] == A[1] && R[2] == A[2]) {
- int i, j;
- for (i = 0; i < 3; i++) {
-#ifdef SELF_CHECK
- assert (R[i] == A[i]);
-#endif
- j = 2;
- do {
- if (N[i] > 0.0) {
- N[i] += (j * macheps);
- } else {
- N[i] -= (j * macheps);
- }
- R[i] = N[i] + A[i];
- j *= 2;
- } while (R[i] == A[i]);
- }
- }
-
- return tri_edge_cop_inter(A, B, C, P, Q, R);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// tri_edge_inter() Test whether a triangle (abc) and an edge (pq) are //
-// intersecting or not. //
-// //
-// The return value indicates one of the four cases: DISJOINT, SHAREVERTEX, //
-// SHAREEDGE, and INTERSECT. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-enum tetgenmesh::interresult tetgenmesh::tri_edge_inter(REAL* A, REAL* B,
- REAL* C, REAL* P, REAL* Q)
-{
- REAL s1, s2;
-
- // Test the locations of p and q with respect to ABC.
- s1 = orient3d(A, B, C, P);
- s2 = orient3d(A, B, C, Q);
-
- return tri_edge_inter_tail(A, B, C, P, Q, s1, s2);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// tri_tri_inter() Test whether two triangle (abc) and (opq) are //
-// intersecting or not. //
-// //
-// The return value indicates one of the five cases: DISJOINT, SHAREVERTEX, //
-// SHAREEDGE, SHAREFACE, and INTERSECT. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-enum tetgenmesh::interresult tetgenmesh::tri_tri_inter(REAL* A, REAL* B,
- REAL* C, REAL* O, REAL* P, REAL* Q)
-{
- REAL s_o, s_p, s_q;
- REAL s_a, s_b, s_c;
-
- s_o = orient3d(A, B, C, O);
- s_p = orient3d(A, B, C, P);
- s_q = orient3d(A, B, C, Q);
- if ((s_o * s_p > 0.0) && (s_o * s_q > 0.0)) {
- // o, p, q are all in the same halfspace of ABC.
- return DISJOINT;
- }
-
- s_a = orient3d(O, P, Q, A);
- s_b = orient3d(O, P, Q, B);
- s_c = orient3d(O, P, Q, C);
- if ((s_a * s_b > 0.0) && (s_a * s_c > 0.0)) {
- // a, b, c are all in the same halfspace of OPQ.
- return DISJOINT;
- }
-
- enum interresult abcop, abcpq, abcqo;
- int shareedge = 0;
-
- abcop = tri_edge_inter_tail(A, B, C, O, P, s_o, s_p);
- if (abcop == INTERSECT) {
- return INTERSECT;
- } else if (abcop == SHAREEDGE) {
- shareedge++;
- }
- abcpq = tri_edge_inter_tail(A, B, C, P, Q, s_p, s_q);
- if (abcpq == INTERSECT) {
- return INTERSECT;
- } else if (abcpq == SHAREEDGE) {
- shareedge++;
- }
- abcqo = tri_edge_inter_tail(A, B, C, Q, O, s_q, s_o);
- if (abcqo == INTERSECT) {
- return INTERSECT;
- } else if (abcqo == SHAREEDGE) {
- shareedge++;
- }
- if (shareedge == 3) {
- // opq are coincident with abc.
- return SHAREFACE;
- }
-#ifdef SELF_CHECK
- // It is only possible either no share edge or one.
- assert(shareedge == 0 || shareedge == 1);
-#endif
-
- // Continue to detect whether opq and abc are intersecting or not.
- enum interresult opqab, opqbc, opqca;
-
- opqab = tri_edge_inter_tail(O, P, Q, A, B, s_a, s_b);
- if (opqab == INTERSECT) {
- return INTERSECT;
- }
- opqbc = tri_edge_inter_tail(O, P, Q, B, C, s_b, s_c);
- if (opqbc == INTERSECT) {
- return INTERSECT;
- }
- opqca = tri_edge_inter_tail(O, P, Q, C, A, s_c, s_a);
- if (opqca == INTERSECT) {
- return INTERSECT;
- }
-
- // At this point, two triangles are not intersecting and not coincident.
- // They may be share an edge, or share a vertex, or disjoint.
- if (abcop == SHAREEDGE) {
-#ifdef SELF_CHECK
- assert(abcpq == SHAREVERTEX && abcqo == SHAREVERTEX);
-#endif
- // op is coincident with an edge of abc.
- return SHAREEDGE;
- }
- if (abcpq == SHAREEDGE) {
-#ifdef SELF_CHECK
- assert(abcop == SHAREVERTEX && abcqo == SHAREVERTEX);
-#endif
- // pq is coincident with an edge of abc.
- return SHAREEDGE;
- }
- if (abcqo == SHAREEDGE) {
-#ifdef SELF_CHECK
- assert(abcop == SHAREVERTEX && abcpq == SHAREVERTEX);
-#endif
- // qo is coincident with an edge of abc.
- return SHAREEDGE;
- }
-
- // They may share a vertex or disjoint.
- if (abcop == SHAREVERTEX) {
- // o or p is coincident with a vertex of abc.
- if (abcpq == SHAREVERTEX) {
- // p is the coincident vertex.
-#ifdef SELF_CHECK
- assert(abcqo != SHAREVERTEX);
-#endif
- } else {
- // o is the coincident vertex.
-#ifdef SELF_CHECK
- assert(abcqo == SHAREVERTEX);
-#endif
- }
- return SHAREVERTEX;
- }
- if (abcpq == SHAREVERTEX) {
- // q is the coincident vertex.
-#ifdef SELF_CHECK
- assert(abcqo == SHAREVERTEX);
-#endif
- return SHAREVERTEX;
- }
-
- // They are disjoint.
- return DISJOINT;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// insphere_sos() Insphere test with symbolic perturbation. //
-// //
-// The input points a, b, c, and d should be non-coplanar. They must be ord- //
-// ered so that they have a positive orientation (as defined by orient3d()), //
-// or the sign of the result will be reversed. //
-// //
-// Return a positive value if the point e lies inside the circumsphere of a, //
-// b, c, and d; a negative value if it lies outside. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-REAL tetgenmesh::insphere_sos(REAL* pa, REAL* pb, REAL* pc, REAL* pd, REAL* pe,
- int ia, int ib, int ic, int id, int ie)
-{
- REAL det;
-
- det = insphere(pa, pb, pc, pd, pe);
- if (det != 0.0) {
- return det;
- }
-
- // det = 0.0, use symbolic perturbation.
- REAL *p[5], *tmpp;
- REAL sign, det_c, det_d;
- int idx[5], perm, tmp;
- int n, i, j;
-
- p[0] = pa; idx[0] = ia;
- p[1] = pb; idx[1] = ib;
- p[2] = pc; idx[2] = ic;
- p[3] = pd; idx[3] = id;
- p[4] = pe; idx[4] = ie;
-
- // Bubble sort the points by the increasing order of the indices.
- n = 5;
- perm = 0; // The number of total swaps.
- for (i = 0; i < n - 1; i++) {
- for (j = 0; j < n - 1 - i; j++) {
- if (idx[j + 1] < idx[j]) { // compare the two neighbors.
- tmp = idx[j]; // swap idx[j] and idx[j + 1]
- idx[j] = idx[j + 1];
- idx[j + 1] = tmp;
- tmpp = p[j]; // swap p[j] and p[j + 1]
- p[j] = p[j + 1];
- p[j + 1] = tmpp;
- perm++;
- }
- }
- }
-
- sign = (perm % 2 == 0) ? 1.0 : -1.0;
- det_c = orient3d(p[1], p[2], p[3], p[4]); // orient3d(b, c, d, e)
- if (det_c != 0.0) {
- return sign * det_c;
- }
- det_d = orient3d(p[0], p[2], p[3], p[4]); // orient3d(a, c, d, e)
- return -sign * det_d;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// iscollinear() Check if three points are approximately collinear. //
-// //
-// 'eps' is a relative error tolerance. The collinearity is determined by //
-// the value q = cos(theta), where theta is the angle between two vectors //
-// A->B and A->C. They're collinear if 1.0 - q <= epspp. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::iscollinear(REAL* A, REAL* B, REAL* C, REAL eps)
-{
- REAL abx, aby, abz;
- REAL acx, acy, acz;
- REAL Lv, Lw, dd;
- REAL d, q;
-
- // Limit of two closed points.
- q = longest * eps;
- q *= q;
-
- abx = A[0] - B[0];
- aby = A[1] - B[1];
- abz = A[2] - B[2];
- acx = A[0] - C[0];
- acy = A[1] - C[1];
- acz = A[2] - C[2];
- Lv = abx * abx + aby * aby + abz * abz;
- // Is AB (nearly) indentical?
- if (Lv < q) return true;
- Lw = acx * acx + acy * acy + acz * acz;
- // Is AC (nearly) indentical?
- if (Lw < q) return true;
- dd = abx * acx + aby * acy + abz * acz;
-
- d = (dd * dd) / (Lv * Lw);
- if (d > 1.0) d = 1.0; // Rounding.
- q = 1.0 - sqrt(d); // Notice 0 < q < 1.0.
-
- return q <= eps;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// iscoplanar() Check if four points are approximately coplanar. //
-// //
-// 'vol6' is six times of the signed volume of the tetrahedron formed by the //
-// four points. 'eps' is the relative error tolerance. The coplanarity is //
-// determined by the value: q = fabs(vol6) / L^3, where L is the average //
-// edge length of the tet. They're coplanar if q <= eps. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::
-iscoplanar(REAL* k, REAL* l, REAL* m, REAL* n, REAL vol6, REAL eps)
-{
- REAL L, q;
- REAL x, y, z;
-
- if (vol6 == 0.0) return true;
-
- x = k[0] - l[0];
- y = k[1] - l[1];
- z = k[2] - l[2];
- L = sqrt(x * x + y * y + z * z);
- x = l[0] - m[0];
- y = l[1] - m[1];
- z = l[2] - m[2];
- L += sqrt(x * x + y * y + z * z);
- x = m[0] - k[0];
- y = m[1] - k[1];
- z = m[2] - k[2];
- L += sqrt(x * x + y * y + z * z);
- x = k[0] - n[0];
- y = k[1] - n[1];
- z = k[2] - n[2];
- L += sqrt(x * x + y * y + z * z);
- x = l[0] - n[0];
- y = l[1] - n[1];
- z = l[2] - n[2];
- L += sqrt(x * x + y * y + z * z);
- x = m[0] - n[0];
- y = m[1] - n[1];
- z = m[2] - n[2];
- L += sqrt(x * x + y * y + z * z);
-#ifdef SELF_CHECK
- assert(L > 0.0);
-#endif
- L /= 6.0;
- q = fabs(vol6) / (L * L * L);
-
- return q <= eps;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// iscospheric() Check if five points are approximately coplanar. //
-// //
-// 'vol24' is the 24 times of the signed volume of the 4-dimensional simplex //
-// formed by the five points. 'eps' is the relative tolerance. The cosphere //
-// case is determined by the value: q = fabs(vol24) / L^4, where L is the //
-// average edge length of the simplex. They're cosphere if q <= eps. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::
-iscospheric(REAL* k, REAL* l, REAL* m, REAL* n, REAL* o, REAL vol24, REAL eps)
-{
- REAL L, q;
-
- // A 4D simplex has 10 edges.
- L = distance(k, l);
- L += distance(l, m);
- L += distance(m, k);
- L += distance(k, n);
- L += distance(l, n);
- L += distance(m, n);
- L += distance(k, o);
- L += distance(l, o);
- L += distance(m, o);
- L += distance(n, o);
-#ifdef SELF_CHECK
- assert(L > 0.0);
-#endif
- L /= 10.0;
- q = fabs(vol24) / (L * L * L * L);
-
- return q < eps;
-}
-
-//
-// End of geometric tests
-//
-
-//
-// Begin of Geometric quantities calculators
-//
-
-// distance() computs the Euclidean distance between two points.
-inline REAL tetgenmesh::distance(REAL* p1, REAL* p2)
-{
- return sqrt((p2[0] - p1[0]) * (p2[0] - p1[0]) +
- (p2[1] - p1[1]) * (p2[1] - p1[1]) +
- (p2[2] - p1[2]) * (p2[2] - p1[2]));
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// shortdistance() Returns the shortest distance from point p to a line //
-// defined by two points e1 and e2. //
-// //
-// First compute the projection length l_p of the vector v1 = p - e1 along //
-// the vector v2 = e2 - e1. Then Pythagoras' Theorem is used to compute the //
-// shortest distance. //
-// //
-// This routine allows that p is collinear with the line. In this case, the //
-// return value is zero. The two points e1 and e2 should not be identical. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-REAL tetgenmesh::shortdistance(REAL* p, REAL* e1, REAL* e2)
-{
- REAL v1[3], v2[3];
- REAL len, l_p;
-
- v1[0] = e2[0] - e1[0];
- v1[1] = e2[1] - e1[1];
- v1[2] = e2[2] - e1[2];
- v2[0] = p[0] - e1[0];
- v2[1] = p[1] - e1[1];
- v2[2] = p[2] - e1[2];
-
- len = sqrt(dot(v1, v1));
-#ifdef SELF_CHECK
- assert(len != 0.0);
-#endif
- v1[0] /= len;
- v1[1] /= len;
- v1[2] /= len;
- l_p = dot(v1, v2);
-
- return sqrt(dot(v2, v2) - l_p * l_p);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// shortdistance() Returns the shortest distance from point p to a face. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-REAL tetgenmesh::shortdistance(REAL* p, REAL* e1, REAL* e2, REAL* e3)
-{
- REAL prj[3];
-
- projpt2face(p, e1, e2, e3, prj);
- return distance(p, prj);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// interiorangle() Return the interior angle (0 - 2 * PI) between vectors //
-// o->p1 and o->p2. //
-// //
-// 'n' is the normal of the plane containing face (o, p1, p2). The interior //
-// angle is the total angle rotating from o->p1 around n to o->p2. Exchange //
-// the position of p1 and p2 will get the complement angle of the other one. //
-// i.e., interiorangle(o, p1, p2) = 2 * PI - interiorangle(o, p2, p1). Set //
-// 'n' be NULL if you only want the interior angle between 0 - PI. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-REAL tetgenmesh::interiorangle(REAL* o, REAL* p1, REAL* p2, REAL* n)
-{
- REAL v1[3], v2[3], np[3];
- REAL theta, costheta, lenlen;
- REAL ori, len1, len2;
-
- // Get the interior angle (0 - PI) between o->p1, and o->p2.
- v1[0] = p1[0] - o[0];
- v1[1] = p1[1] - o[1];
- v1[2] = p1[2] - o[2];
- v2[0] = p2[0] - o[0];
- v2[1] = p2[1] - o[1];
- v2[2] = p2[2] - o[2];
- len1 = sqrt(dot(v1, v1));
- len2 = sqrt(dot(v2, v2));
- lenlen = len1 * len2;
-#ifdef SELF_CHECK
- assert(lenlen != 0.0);
-#endif
- costheta = dot(v1, v2) / lenlen;
- if (costheta > 1.0) {
- costheta = 1.0; // Roundoff.
- } else if (costheta < -1.0) {
- costheta = -1.0; // Roundoff.
- }
- theta = acos(costheta);
- if (n != NULL) {
- // Get a point above the face (o, p1, p2);
- np[0] = o[0] + n[0];
- np[1] = o[1] + n[1];
- np[2] = o[2] + n[2];
- // Adjust theta (0 - 2 * PI).
- ori = orient3d(p1, o, np, p2);
- if (ori > 0.0) {
- theta = 2 * PI - theta;
- }
- }
-
- return theta;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// projpt2edge() Return the projection point from a point to an edge. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::projpt2edge(REAL* p, REAL* e1, REAL* e2, REAL* prj)
-{
- REAL v1[3], v2[3];
- REAL len, l_p;
-
- v1[0] = e2[0] - e1[0];
- v1[1] = e2[1] - e1[1];
- v1[2] = e2[2] - e1[2];
- v2[0] = p[0] - e1[0];
- v2[1] = p[1] - e1[1];
- v2[2] = p[2] - e1[2];
-
- len = sqrt(dot(v1, v1));
-#ifdef SELF_CHECK
- assert(len != 0.0);
-#endif
- v1[0] /= len;
- v1[1] /= len;
- v1[2] /= len;
- l_p = dot(v1, v2);
-
- prj[0] = e1[0] + l_p * v1[0];
- prj[1] = e1[1] + l_p * v1[1];
- prj[2] = e1[2] + l_p * v1[2];
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// projpt2face() Return the projection point from a point to a face. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::projpt2face(REAL* p, REAL* f1, REAL* f2, REAL* f3, REAL* prj)
-{
- REAL fnormal[3], v1[3];
- REAL len, dist;
-
- // Get the unit face normal.
- facenormal(f1, f2, f3, fnormal, &len);
-#ifdef SELF_CHECK
- assert(len > 0.0);
-#endif
- fnormal[0] /= len;
- fnormal[1] /= len;
- fnormal[2] /= len;
- // Get the vector v1 = |p - f1|.
- v1[0] = p[0] - f1[0];
- v1[1] = p[1] - f1[1];
- v1[2] = p[2] - f1[2];
- // Get the project distance.
- dist = dot(fnormal, v1);
-
- // Get the project point.
- prj[0] = p[0] - dist * fnormal[0];
- prj[1] = p[1] - dist * fnormal[1];
- prj[2] = p[2] - dist * fnormal[2];
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// facenormal() Calculate the normal of a face given by three points. //
-// //
-// In general, the face normal can be calculate by the cross product of any //
-// pair of the three edge vectors. However, if the three points are nearly //
-// collinear, the rounding error may harm the result. To choose a good pair //
-// of vectors is helpful to reduce the error. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::facenormal(REAL* pa, REAL* pb, REAL* pc, REAL* n, REAL* nlen)
-{
- REAL v1[3], v2[3];
-
- v1[0] = pb[0] - pa[0];
- v1[1] = pb[1] - pa[1];
- v1[2] = pb[2] - pa[2];
- v2[0] = pc[0] - pa[0];
- v2[1] = pc[1] - pa[1];
- v2[2] = pc[2] - pa[2];
-
- cross(v1, v2, n);
- if (nlen != (REAL *) NULL) {
- *nlen = sqrt(dot(n, n));
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// edgeorthonormal() Return the unit normal of an edge in a given plane. //
-// //
-// The edge is from e1 to e2, the plane is defined by given an additional //
-// point op, which is non-collinear with the edge. In addition, the side of //
-// the edge in which op lies defines the positive position of the normal. //
-// //
-// Let v1 be the unit vector from e1 to e2, v2 be the unit edge vector from //
-// e1 to op, fn be the unit face normal calculated by fn = v1 x v2. Then the //
-// unit edge normal of e1e2 pointing to op is n = fn x v1. Note, we should //
-// not change the position of fn and v1, otherwise, we get the edge normal //
-// pointing to the other side of op. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::edgeorthonormal(REAL* e1, REAL* e2, REAL* op, REAL* n)
-{
- REAL v1[3], v2[3], fn[3];
- REAL len;
-
- // Get the edge vector v1.
- v1[0] = e2[0] - e1[0];
- v1[1] = e2[1] - e1[1];
- v1[2] = e2[2] - e1[2];
- // Get the edge vector v2.
- v2[0] = op[0] - e1[0];
- v2[1] = op[1] - e1[1];
- v2[2] = op[2] - e1[2];
- // Get the face normal fn = v1 x v2.
- cross(v1, v2, fn);
- // Get the edge normal n pointing to op. n = fn x v1.
- cross(fn, v1, n);
- // Normalize the vector.
- len = sqrt(dot(n, n));
- n[0] /= len;
- n[1] /= len;
- n[2] /= len;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// facedihedral() Return the dihedral angle (in radian) between two //
-// adjoining faces. //
-// //
-// 'pa', 'pb' are the shared edge of these two faces, 'pc1', and 'pc2' are //
-// apexes of these two faces. Return the angle (between 0 to 2*pi) between //
-// the normal of face (pa, pb, pc1) and normal of face (pa, pb, pc2). //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-REAL tetgenmesh::facedihedral(REAL* pa, REAL* pb, REAL* pc1, REAL* pc2)
-{
- REAL n1[3], n2[3];
- REAL n1len, n2len;
- REAL costheta, ori;
- REAL theta;
-
- facenormal(pa, pb, pc1, n1, &n1len);
- facenormal(pa, pb, pc2, n2, &n2len);
- costheta = dot(n1, n2) / (n1len * n2len);
- // Be careful rounding error!
- if (costheta > 1.0) {
- costheta = 1.0;
- } else if (costheta < -1.0) {
- costheta = -1.0;
- }
- theta = acos(costheta);
- ori = orient3d(pa, pb, pc1, pc2);
- if (ori > 0.0) {
- theta = 2 * PI - theta;
- }
-
- return theta;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// tetalldihedral() Get all (six) dihedral angles of a tet. //
-// //
-// The tet is given by its four corners a, b, c, and d. If 'cosdd' is not //
-// NULL, it returns the cosines of the 6 dihedral angles, the corresponding //
-// edges are: ab, bc, ca, ad, bd, and cd. If 'cosmaxd' (or 'cosmind') is not //
-// NULL, it returns the cosine of the maximal (or minimal) dihedral angle. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::tetalldihedral(point pa, point pb, point pc, point pd,
- REAL* cosdd, REAL* cosmaxd, REAL* cosmind)
-{
- REAL N[4][3], cosd, len;
- int f1, f2, i, j;
-
- // Get four normals of faces of the tet.
- tetallnormal(pa, pb, pc, pd, N, NULL);
- // Normalize the normals.
- for (i = 0; i < 4; i++) {
- len = sqrt(dot(N[i], N[i]));
- if (len != 0.0) {
- for (j = 0; j < 3; j++) N[i][j] /= len;
- }
- }
-
- for (i = 0; i < 6; i++) {
- switch (i) {
- case 0: f1 = 2; f2 = 3; break; // edge ab.
- case 1: f1 = 0; f2 = 3; break; // edge bc.
- case 2: f1 = 1; f2 = 3; break; // edge ca.
- case 3: f1 = 1; f2 = 2; break; // edge ad.
- case 4: f1 = 2; f2 = 0; break; // edge bd.
- case 5: f1 = 0; f2 = 1; break; // edge cd.
- }
- cosd = -dot(N[f1], N[f2]);
- if (cosdd) cosdd[i] = cosd;
- if (i == 0) {
- if (cosmaxd) *cosmaxd = cosd;
- if (cosmind) *cosmind = cosd;
- } else {
- if (cosmaxd) *cosmaxd = cosd < *cosmaxd ? cosd : *cosmaxd;
- if (cosmind) *cosmind = cosd > *cosmind ? cosd : *cosmind;
- }
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// tetallnormal() Get the in-noramls of the four faces of a given tet. //
-// //
-// Let tet be abcd. N[4][3] returns the four normals, which are: N[0] cbd, //
-// N[1] acd, N[2] bad, N[3] abc. These normals are unnormalized. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::tetallnormal(point pa, point pb, point pc, point pd,
- REAL N[4][3], REAL* volume)
-{
- REAL A[4][4], rhs[4], D;
- int indx[4];
- int i, j;
-
- // get the entries of A[3][3].
- for (i = 0; i < 3; i++) A[0][i] = pa[i] - pd[i]; // d->a vec
- for (i = 0; i < 3; i++) A[1][i] = pb[i] - pd[i]; // d->b vec
- for (i = 0; i < 3; i++) A[2][i] = pc[i] - pd[i]; // d->c vec
- // Compute the inverse of matrix A, to get 3 normals of the 4 faces.
- lu_decmp(A, 3, indx, &D, 0); // Decompose the matrix just once.
- if (volume != NULL) {
- // Get the volume of the tet.
- *volume = fabs((A[indx[0]][0] * A[indx[1]][1] * A[indx[2]][2])) / 6.0;
- }
- for (j = 0; j < 3; j++) {
- for (i = 0; i < 3; i++) rhs[i] = 0.0;
- rhs[j] = 1.0; // Positive means the inside direction
- lu_solve(A, 3, indx, rhs, 0);
- for (i = 0; i < 3; i++) N[j][i] = rhs[i];
- }
- // Get the fourth normal by summing up the first three.
- for (i = 0; i < 3; i++) N[3][i] = - N[0][i] - N[1][i] - N[2][i];
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// tetaspectratio() Calculate the aspect ratio of the tetrahedron. //
-// //
-// The aspect ratio of a tet is R/h, where R is the circumradius and h is //
-// the shortest height of the tet. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-REAL tetgenmesh::tetaspectratio(point pa, point pb, point pc, point pd)
-{
- REAL vda[3], vdb[3], vdc[3];
- REAL N[4][3], A[4][4], rhs[4], D;
- REAL H[4], volume, radius2, minheightinv;
- int indx[4];
- int i, j;
-
- // Set the matrix A = [vda, vdb, vdc]^T.
- for (i = 0; i < 3; i++) A[0][i] = vda[i] = pa[i] - pd[i];
- for (i = 0; i < 3; i++) A[1][i] = vdb[i] = pb[i] - pd[i];
- for (i = 0; i < 3; i++) A[2][i] = vdc[i] = pc[i] - pd[i];
- // Lu-decompose the matrix A.
- lu_decmp(A, 3, indx, &D, 0);
- // Get the volume of abcd.
- volume = (A[indx[0]][0] * A[indx[1]][1] * A[indx[2]][2]) / 6.0;
- // Check if it is zero.
- if (volume == 0.0) return 1.0e+200; // A degenerate tet.
- // if (volume < 0.0) volume = -volume;
- // Check the radiu-edge ratio of the tet.
- rhs[0] = 0.5 * dot(vda, vda);
- rhs[1] = 0.5 * dot(vdb, vdb);
- rhs[2] = 0.5 * dot(vdc, vdc);
- lu_solve(A, 3, indx, rhs, 0);
- // Get the circumcenter.
- // for (i = 0; i < 3; i++) circumcent[i] = pd[i] + rhs[i];
- // Get the square of the circumradius.
- radius2 = dot(rhs, rhs);
-
- // Compute the 4 face normals (N[0], ..., N[3]).
- for (j = 0; j < 3; j++) {
- for (i = 0; i < 3; i++) rhs[i] = 0.0;
- rhs[j] = 1.0; // Positive means the inside direction
- lu_solve(A, 3, indx, rhs, 0);
- for (i = 0; i < 3; i++) N[j][i] = rhs[i];
- }
- // Get the fourth normal by summing up the first three.
- for (i = 0; i < 3; i++) N[3][i] = - N[0][i] - N[1][i] - N[2][i];
- // Normalized the normals.
- for (i = 0; i < 4; i++) {
- // H[i] is the inverse of the height of its corresponding face.
- H[i] = sqrt(dot(N[i], N[i]));
- // if (H[i] > 0.0) {
- // for (j = 0; j < 3; j++) N[i][j] /= H[i];
- // }
- }
- // Get the radius of the inscribed sphere.
- // insradius = 1.0 / (H[0] + H[1] + H[2] + H[3]);
- // Get the biggest H[i] (corresponding to the smallest height).
- minheightinv = H[0];
- for (i = 1; i < 3; i++) {
- if (H[i] > minheightinv) minheightinv = H[i];
- }
-
- return sqrt(radius2) * minheightinv;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// circumsphere() Calculate the smallest circumsphere (center and radius) //
-// of the given three or four points. //
-// //
-// The circumsphere of four points (a tetrahedron) is unique if they are not //
-// degenerate. If 'pd = NULL', the smallest circumsphere of three points is //
-// the diametral sphere of the triangle if they are not degenerate. //
-// //
-// Return TRUE if the input points are not degenerate and the circumcenter //
-// and circumradius are returned in 'cent' and 'radius' respectively if they //
-// are not NULLs. Otherwise, return FALSE indicated the points are degenrate.//
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::
-circumsphere(REAL* pa, REAL* pb, REAL* pc, REAL* pd, REAL* cent, REAL* radius)
-{
- REAL A[4][4], rhs[4], D;
- int indx[4];
-
- // Compute the coefficient matrix A (3x3).
- A[0][0] = pb[0] - pa[0];
- A[0][1] = pb[1] - pa[1];
- A[0][2] = pb[2] - pa[2];
- A[1][0] = pc[0] - pa[0];
- A[1][1] = pc[1] - pa[1];
- A[1][2] = pc[2] - pa[2];
- if (pd != NULL) {
- A[2][0] = pd[0] - pa[0];
- A[2][1] = pd[1] - pa[1];
- A[2][2] = pd[2] - pa[2];
- } else {
- cross(A[0], A[1], A[2]);
- }
-
- // Compute the right hand side vector b (3x1).
- rhs[0] = 0.5 * dot(A[0], A[0]);
- rhs[1] = 0.5 * dot(A[1], A[1]);
- if (pd != NULL) {
- rhs[2] = 0.5 * dot(A[2], A[2]);
- } else {
- rhs[2] = 0.0;
- }
-
- // Solve the 3 by 3 equations use LU decomposition with partial pivoting
- // and backward and forward substitute..
- if (!lu_decmp(A, 3, indx, &D, 0)) {
- if (radius != (REAL *) NULL) *radius = 0.0;
- return false;
- }
- lu_solve(A, 3, indx, rhs, 0);
- if (cent != (REAL *) NULL) {
- cent[0] = pa[0] + rhs[0];
- cent[1] = pa[1] + rhs[1];
- cent[2] = pa[2] + rhs[2];
- }
- if (radius != (REAL *) NULL) {
- *radius = sqrt(rhs[0] * rhs[0] + rhs[1] * rhs[1] + rhs[2] * rhs[2]);
- }
- return true;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// inscribedsphere() Compute the radius and center of the biggest //
-// inscribed sphere of a given tetrahedron. //
-// //
-// The tetrahedron is given by its four points, it must not be degenerate. //
-// The center and radius are returned in 'cent' and 'radius' respectively if //
-// they are not NULLs. //
-// //
-// Geometrical fact. For any simplex in d dimension, //
-// r/h1 + r/h2 + ... r/hn = 1 (n <= d + 1); //
-// where r is the radius of inscribed ball, and h is the height of each side //
-// of the simplex. The value of 'r/h' is just the barycenter coordinates of //
-// each vertex of the simplex. Therefore, we can compute the radius and //
-// center of the smallest inscribed ball as following equations: //
-// r = 1.0 / (1/h1 + 1/h2 + ... + 1/hn); (1) //
-// C = r/h1 * P1 + r/h2 * P2 + ... + r/hn * Pn; (2) //
-// where C is the vector of center, P1, P2, .. Pn are vectors of vertices. //
-// Here (2) contains n linear equations with n variables. (h, P) must be a //
-// pair, h is the height from P to its opposite face. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::inscribedsphere(REAL* pa, REAL* pb, REAL* pc, REAL* pd,
- REAL* cent, REAL* radius)
-{
- REAL N[4][3], H[4]; // Normals (colume vectors) and heights of each face.
- REAL rd;
- int i;
-
- // Get the all normals of the tet.
- tetallnormal(pa, pb, pc, pd, N, NULL);
- for (i = 0; i < 4; i++) {
- // H[i] is the inverse of height of its corresponding face.
- H[i] = sqrt(dot(N[i], N[i]));
- }
- // Compute the radius use eq. (1).
- rd = 1.0 / (H[0] + H[1] + H[2] + H[3]);
- if (radius != (REAL*) NULL) *radius = rd;
- if (cent != (REAL*) NULL) {
- // Compute the center use eq. (2).
- cent[0] = rd * (H[0] * pa[0] + H[1] * pb[0] + H[2] * pc[0] + H[3] * pd[0]);
- cent[1] = rd * (H[0] * pa[1] + H[1] * pb[1] + H[2] * pc[1] + H[3] * pd[1]);
- cent[2] = rd * (H[0] * pa[2] + H[1] * pb[2] + H[2] * pc[2] + H[3] * pd[2]);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// rotatepoint() Create a point by rotating an existing point. //
-// //
-// Create a 3D point by rotating point 'p' with an angle 'rotangle' (in arc //
-// degree) around a rotating axis given by a vector from point 'p1' to 'p2'. //
-// The rotation is according with right-hand rule, i.e., use your right-hand //
-// to grab the axis with your thumber pointing to its positive direction, //
-// your fingers indicate the rotating direction. //
-// //
-// The rotating steps are the following: //
-// 1. Translate vector 'p1->p2' to origin, M1; //
-// 2. Rotate vector around the Y-axis until it lies in the YZ plane, M2; //
-// 3. Rotate vector around the X-axis until it lies on the Z axis, M3; //
-// 4. Perform the rotation of 'p' around the z-axis, M4; //
-// 5. Undo Step 3, M5; //
-// 6. Undo Step 2, M6; //
-// 7. Undo Step 1, M7; //
-// Use matrix multiplication to combine the above sequences, we get: //
-// p0' = T * p0, where T = M7 * M6 * M5 * M4 * M3 * M2 * M1 //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::rotatepoint(REAL* p, REAL rotangle, REAL* p1, REAL* p2)
-{
- REAL T[4][4], pp0[4], p0t[4], p2t[4];
- REAL roty, rotx, alphaR, projlen;
- REAL dx, dy, dz;
-
- initm44(1, 0, 0, -p1[0],
- 0, 1, 0, -p1[1],
- 0, 0, 1, -p1[2],
- 0, 0, 0, 1, T);
- pp0[0] = p[0]; pp0[1] = p[1]; pp0[2] = p[2]; pp0[3] = 1.0;
- m4xv4(p0t, T, pp0); // Step 1
- pp0[0] = p2[0]; pp0[1] = p2[1]; pp0[2] = p2[2]; pp0[3] = 1.0;
- m4xv4(p2t, T, pp0); // Step 1
-
- // Get the rotation angle around y-axis;
- dx = p2t[0];
- dz = p2t[2];
- projlen = sqrt(dx * dx + dz * dz);
- if (projlen <= (b->epsilon * 1e-2) * longest) {
- roty = 0;
- } else {
- roty = acos(dz / projlen);
- if (dx < 0) {
- roty = -roty;
- }
- }
-
- initm44(cos(-roty), 0, sin(-roty), 0,
- 0, 1, 0, 0,
- -sin(-roty), 0, cos(-roty), 0,
- 0, 0, 0, 1, T);
- pp0[0] = p0t[0]; pp0[1] = p0t[1]; pp0[2] = p0t[2]; pp0[3] = 1.0;
- m4xv4(p0t, T, pp0); // Step 2
- pp0[0] = p2t[0]; pp0[1] = p2t[1]; pp0[2] = p2t[2]; pp0[3] = 1.0;
- m4xv4(p2t, T, pp0); // Step 2
-
- // Get the rotation angle around x-axis
- dy = p2t[1];
- dz = p2t[2];
- projlen = sqrt(dy * dy + dz * dz);
- if (projlen <= (b->epsilon * 1e-2) * longest) {
- rotx = 0;
- } else {
- rotx = acos(dz / projlen);
- if (dy < 0) {
- rotx = -rotx;
- }
- }
-
- initm44(1, 0, 0, 0,
- 0, cos(rotx), -sin(rotx), 0,
- 0, sin(rotx), cos(rotx), 0,
- 0, 0, 0, 1, T);
- pp0[0] = p0t[0]; pp0[1] = p0t[1]; pp0[2] = p0t[2]; pp0[3] = 1.0;
- m4xv4(p0t, T, pp0); // Step 3
- // pp0[0] = p2t[0]; pp0[1] = p2t[1]; pp0[2] = p2t[2]; pp0[3] = 1.0;
- // m4xv4(p2t, T, pp0); // Step 3
-
- alphaR = rotangle;
- initm44(cos(alphaR), -sin(alphaR), 0, 0,
- sin(alphaR), cos(alphaR), 0, 0,
- 0, 0, 1, 0,
- 0, 0, 0, 1, T);
- pp0[0] = p0t[0]; pp0[1] = p0t[1]; pp0[2] = p0t[2]; pp0[3] = 1.0;
- m4xv4(p0t, T, pp0); // Step 4
-
- initm44(1, 0, 0, 0,
- 0, cos(-rotx), -sin(-rotx), 0,
- 0, sin(-rotx), cos(-rotx), 0,
- 0, 0, 0, 1, T);
- pp0[0] = p0t[0]; pp0[1] = p0t[1]; pp0[2] = p0t[2]; pp0[3] = 1.0;
- m4xv4(p0t, T, pp0); // Step 5
-
- initm44(cos(roty), 0, sin(roty), 0,
- 0, 1, 0, 0,
- -sin(roty), 0, cos(roty), 0,
- 0, 0, 0, 1, T);
- pp0[0] = p0t[0]; pp0[1] = p0t[1]; pp0[2] = p0t[2]; pp0[3] = 1.0;
- m4xv4(p0t, T, pp0); // Step 6
-
- initm44(1, 0, 0, p1[0],
- 0, 1, 0, p1[1],
- 0, 0, 1, p1[2],
- 0, 0, 0, 1, T);
- pp0[0] = p0t[0]; pp0[1] = p0t[1]; pp0[2] = p0t[2]; pp0[3] = 1.0;
- m4xv4(p0t, T, pp0); // Step 7
-
- p[0] = p0t[0];
- p[1] = p0t[1];
- p[2] = p0t[2];
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// spherelineint() 3D line sphere (or circle) intersection. //
-// //
-// The line is given by two points p1, and p2, the sphere is centered at c //
-// with radius r. This function returns a pointer array p which first index //
-// indicates the number of intersection point, followed by coordinate pairs. //
-// //
-// The following code are adapted from: http://astronomy.swin.edu.au/pbourke //
-// /geometry/sphereline. Paul Bourke pbourke@swin.edu.au //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::spherelineint(REAL* p1, REAL* p2, REAL* C, REAL R, REAL p[7])
-{
- REAL x1, y1, z1; // P1 coordinates (point of line)
- REAL x2, y2, z2; // P2 coordinates (point of line)
- REAL x3, y3, z3, r; // P3 coordinates and radius (sphere)
- REAL a, b, c, mu, i ;
-
- x1 = p1[0]; y1 = p1[1]; z1 = p1[2];
- x2 = p2[0]; y2 = p2[1]; z2 = p2[2];
- x3 = C[0]; y3 = C[1]; z3 = C[2];
- r = R;
-
- a = (x2 - x1) * (x2 - x1)
- + (y2 - y1) * (y2 - y1)
- + (z2 - z1) * (z2 - z1);
- b = 2 * ( (x2 - x1) * (x1 - x3)
- + (y2 - y1) * (y1 - y3)
- + (z2 - z1) * (z1 - z3) ) ;
- c = (x3 * x3) + (y3 * y3) + (z3 * z3)
- + (x1 * x1) + (y1 * y1) + (z1 * z1)
- - 2 * (x3 * x1 + y3 * y1 + z3 * z1) - (r * r) ;
- i = b * b - 4 * a * c ;
-
- if (i < 0.0) {
- // no intersection
- p[0] = 0.0;
- } else if (i == 0.0) {
- // one intersection
- p[0] = 1.0;
- mu = -b / (2 * a) ;
- p[1] = x1 + mu * (x2 - x1);
- p[2] = y1 + mu * (y2 - y1);
- p[3] = z1 + mu * (z2 - z1);
- } else {
- // two intersections
- p[0] = 2.0;
- // first intersection
- mu = (-b + sqrt((b * b) - 4 * a * c)) / (2 * a);
- p[1] = x1 + mu * (x2 - x1);
- p[2] = y1 + mu * (y2 - y1);
- p[3] = z1 + mu * (z2 - z1);
- // second intersection
- mu = (-b - sqrt((b * b) - 4 * a * c)) / (2 * a);
- p[4] = x1 + mu * (x2 - x1);
- p[5] = y1 + mu * (y2 - y1);
- p[6] = z1 + mu * (z2 - z1);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// linelineint() Calculate the shortest line between two lines in 3D. //
-// //
-// Two 3D lines generally don't intersect at a point, they may be parallel ( //
-// no intersections), or coincident (infinite intersections) but most often //
-// only their projections onto a plane intersect. If they don't exactly int- //
-// ersect at a point they can be connected by a line segment, the shortest //
-// segment is unique and is often considered to be their intersection in 3D. //
-// //
-// The following code are adapted from: http://astronomy.swin.edu.au/pbourke //
-// /geometry/lineline3d. Paul Bourke pbourke@swin.edu.au //
-// //
-// Calculate the line segment PaPb that is the shortest route between two //
-// lines P1P2 and P3P4. This function returns a pointer array p which first //
-// index indicates there exists solution or not, 0 means no solution, 1 meas //
-// has solution followed by two coordinate pairs. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::linelineint(REAL *p1,REAL *p2, REAL *p3, REAL *p4, REAL p[7])
-{
- REAL p13[3], p43[3], p21[3];
- REAL d1343, d4321, d1321, d4343, d2121;
- REAL numer, denom;
- REAL mua, mub;
-
- p13[0] = p1[0] - p3[0];
- p13[1] = p1[1] - p3[1];
- p13[2] = p1[2] - p3[2];
- p43[0] = p4[0] - p3[0];
- p43[1] = p4[1] - p3[1];
- p43[2] = p4[2] - p3[2];
- if (p43[0] == 0.0 && p43[1] == 0.0 && p43[2] == 0.0) {
- p[0] = 0.0;
- return;
- }
-
- p21[0] = p2[0] - p1[0];
- p21[1] = p2[1] - p1[1];
- p21[2] = p2[2] - p1[2];
- if (p21[0] == 0.0 && p21[1] == 0.0 && p21[2] == 0.0) {
- p[0] = 0.0;
- return;
- }
-
- d1343 = p13[0] * p43[0] + p13[1] * p43[1] + p13[2] * p43[2];
- d4321 = p43[0] * p21[0] + p43[1] * p21[1] + p43[2] * p21[2];
- d1321 = p13[0] * p21[0] + p13[1] * p21[1] + p13[2] * p21[2];
- d4343 = p43[0] * p43[0] + p43[1] * p43[1] + p43[2] * p43[2];
- d2121 = p21[0] * p21[0] + p21[1] * p21[1] + p21[2] * p21[2];
-
- denom = d2121 * d4343 - d4321 * d4321;
- if (denom == 0.0) {
- p[0] = 0.0;
- return;
- }
- numer = d1343 * d4321 - d1321 * d4343;
- mua = numer / denom;
- mub = (d1343 + d4321 * mua) / d4343;
-
- p[0] = 1.0;
- p[1] = p1[0] + mua * p21[0];
- p[2] = p1[1] + mua * p21[1];
- p[3] = p1[2] + mua * p21[2];
- p[4] = p3[0] + mub * p43[0];
- p[5] = p3[1] + mub * p43[1];
- p[6] = p3[2] + mub * p43[2];
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// planelineint() Calculate the intersection of a line and a plane. //
-// //
-// The equation of a plane (points P are on the plane with normal N and P3 //
-// on the plane) can be written as: N dot (P - P3) = 0. The equation of the //
-// line (points P on the line passing through P1 and P2) can be written as: //
-// P = P1 + u (P2 - P1). The intersection of these two occurs when: //
-// N dot (P1 + u (P2 - P1)) = N dot P3. //
-// Solving for u gives: //
-// N dot (P3 - P1) //
-// u = ------------------. //
-// N dot (P2 - P1) //
-// If the denominator is 0 then N (the normal to the plane) is perpendicular //
-// to the line. Thus the line is either parallel to the plane and there are //
-// no solutions or the line is on the plane in which case there are an infi- //
-// nite number of solutions. //
-// //
-// The plane is given by three points pa, pb, and pc, e1 and e2 defines the //
-// line. If u is non-zero, The intersection point (if exists) returns in ip. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::planelineint(REAL* pa, REAL* pb, REAL* pc, REAL* e1, REAL* e2,
- REAL* ip, REAL* u)
-{
- REAL n[3], det, det1;
-
- // Calculate N.
- facenormal(pa, pb, pc, n, NULL);
- // Calculate N dot (e2 - e1).
- det = n[0] * (e2[0] - e1[0]) + n[1] * (e2[1] - e1[1])
- + n[2] * (e2[2] - e1[2]);
- if (det != 0.0) {
- // Calculate N dot (pa - e1)
- det1 = n[0] * (pa[0] - e1[0]) + n[1] * (pa[1] - e1[1])
- + n[2] * (pa[2] - e1[2]);
- *u = det1 / det;
- ip[0] = e1[0] + *u * (e2[0] - e1[0]);
- ip[1] = e1[1] + *u * (e2[1] - e1[1]);
- ip[2] = e1[2] + *u * (e2[2] - e1[2]);
- } else {
- *u = 0.0;
- }
-}
-
-//
-// End of Geometric quantities calculators
-//
-
-//
-// Begin of memory management routines
-//
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// dummyinit() Initialize the tetrahedron that fills "outer space" and //
-// the omnipresent subface. //
-// //
-// The tetrahedron that fills "outer space" called 'dummytet', is pointed to //
-// by every tetrahedron and subface on a boundary (be it outer or inner) of //
-// the tetrahedralization. Also, 'dummytet' points to one of the tetrahedron //
-// on the convex hull(until the holes and concavities are carved), making it //
-// possible to find a starting tetrahedron for point location. //
-// //
-// The omnipresent subface,'dummysh', is pointed to by every tetrahedron or //
-// subface that doesn't have a full complement of real subface to point to. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::dummyinit(int tetwords, int shwords)
-{
- unsigned long alignptr;
-
- // Set up 'dummytet', the 'tetrahedron' that occupies "outer space".
- dummytetbase = (tetrahedron *) new char[tetwords * sizeof(tetrahedron)
- + tetrahedrons->alignbytes];
- // Align 'dummytet' on a 'tetrahedrons->alignbytes'-byte boundary.
- alignptr = (unsigned long) dummytetbase;
- dummytet = (tetrahedron *)
- (alignptr + (unsigned long) tetrahedrons->alignbytes
- - (alignptr % (unsigned long) tetrahedrons->alignbytes));
- // Initialize the four adjoining tetrahedra to be "outer space". These
- // will eventually be changed by various bonding operations, but their
- // values don't really matter, as long as they can legally be
- // dereferenced.
- dummytet[0] = (tetrahedron) dummytet;
- dummytet[1] = (tetrahedron) dummytet;
- dummytet[2] = (tetrahedron) dummytet;
- dummytet[3] = (tetrahedron) dummytet;
- // Four null vertex points.
- dummytet[4] = (tetrahedron) NULL;
- dummytet[5] = (tetrahedron) NULL;
- dummytet[6] = (tetrahedron) NULL;
- dummytet[7] = (tetrahedron) NULL;
-
- if (b->useshelles) {
- // Set up 'dummysh', the omnipresent "subface" pointed to by any
- // tetrahedron side or subface end that isn't attached to a real
- // subface.
- dummyshbase = (shellface *) new char[shwords * sizeof(shellface)
- + subfaces->alignbytes];
- // Align 'dummysh' on a 'subfaces->alignbytes'-byte boundary.
- alignptr = (unsigned long) dummyshbase;
- dummysh = (shellface *)
- (alignptr + (unsigned long) subfaces->alignbytes
- - (alignptr % (unsigned long) subfaces->alignbytes));
- // Initialize the three adjoining subfaces to be the omnipresent
- // subface. These will eventually be changed by various bonding
- // operations, but their values don't really matter, as long as they
- // can legally be dereferenced.
- dummysh[0] = (shellface) dummysh;
- dummysh[1] = (shellface) dummysh;
- dummysh[2] = (shellface) dummysh;
- // Three null vertex points.
- dummysh[3] = (shellface) NULL;
- dummysh[4] = (shellface) NULL;
- dummysh[5] = (shellface) NULL;
- // Initialize the two adjoining tetrahedra to be "outer space".
- dummysh[6] = (shellface) dummytet;
- dummysh[7] = (shellface) dummytet;
- // Initialize the three adjoining subsegments to be "out boundary".
- dummysh[8] = (shellface) dummysh;
- dummysh[9] = (shellface) dummysh;
- dummysh[10] = (shellface) dummysh;
- // Initialize the pointer to badface structure.
- dummysh[11] = (shellface) NULL;
- // Initialize the four adjoining subfaces of 'dummytet' to be the
- // omnipresent subface.
- dummytet[8 ] = (tetrahedron) dummysh;
- dummytet[9 ] = (tetrahedron) dummysh;
- dummytet[10] = (tetrahedron) dummysh;
- dummytet[11] = (tetrahedron) dummysh;
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// initializepools() Calculate the sizes of the point, tetrahedron, and //
-// subface. Initialize their memory pools. //
-// //
-// This routine also computes the indices 'pointmarkindex', 'point2simindex',//
-// and 'point2pbcptindex' used to find values within each point; computes //
-// indices 'highorderindex', 'elemattribindex', and 'volumeboundindex' used //
-// to find values within each tetrahedron. //
-// //
-// There are two types of boundary elements, which are subfaces and subsegs, //
-// they are stored in seperate pools. However, the data structures of them //
-// are the same. A subsegment can be regarded as a degenerate subface, i.e.,//
-// one of its three corners is not used. We set the apex of it be 'NULL' to //
-// distinguish it's a subsegment. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::initializepools()
-{
- enum wordtype wtype;
- int pointsize, elesize, shsize;
-
- // Default checkpbc = 0;
- if ((b->plc || b->refine) && (in->pbcgrouplist != NULL)) {
- checkpbcs = 1;
- }
- // Default varconstraint = 0;
- if (in->segmentconstraintlist || in->facetconstraintlist) {
- varconstraint = 1;
- }
-
- // The index within each point at which its metric tensor is found. It is
- // saved directly after the list of point attributes.
- pointmtrindex = 3 + in->numberofpointattributes;
- // Decide the size (1, 3, or 6) of the metric tensor.
- if (b->metric) {
- // For '-m' option. A tensor field is provided (*.mtr or *.b.mtr file).
- if (bgm != (tetgenmesh *) NULL) {
- // A background mesh is allocated. It may not exist though.
- sizeoftensor = (bgm->in != (tetgenio *) NULL) ?
- bgm->in->numberofpointmtrs : in->numberofpointmtrs;
- } else {
- // No given background mesh - Itself is a background mesh.
- sizeoftensor = in->numberofpointmtrs;
- }
- // Make sure sizeoftensor is at least 1.
- sizeoftensor = (sizeoftensor > 0) ? sizeoftensor : 1;
- } else {
- // For '-q' option. Make sure to have space for saving a scalar value.
- sizeoftensor = b->quality ? 1 : 0;
- }
- // The index within each point at which an element pointer is found, where
- // the index is measured in pointers. Ensure the index is aligned to a
- // sizeof(tetrahedron)-byte address.
- point2simindex = ((pointmtrindex + sizeoftensor) * sizeof(REAL)
- + sizeof(tetrahedron) - 1) / sizeof(tetrahedron);
- if (b->plc || b->refine) {
- // Increase the point size by three pointers, which are:
- // - a pointer to a tet, read by point2tet();
- // - a pointer to a subface/subsegment , read by point2sh();
- // - a pointer to a parent point, read by point2ppt()).
- if (b->metric) {
- // Increase one pointer to a tet of the background mesh.
- pointsize = (point2simindex + 4) * sizeof(tetrahedron);
- } else {
- pointsize = (point2simindex + 3) * sizeof(tetrahedron);
- }
- // The index within each point at which a pbc point is found.
- point2pbcptindex = (pointsize + sizeof(tetrahedron) - 1)
- / sizeof(tetrahedron);
- if (checkpbcs) {
- // Increase the size by one pointer to a corresponding pbc point,
- // read by point2pbcpt().
- pointsize = (point2pbcptindex + 1) * sizeof(tetrahedron);
- }
- } else {
- pointsize = point2simindex * sizeof(tetrahedron);
- }
- // The index within each point at which the boundary marker is found,
- // Ensure the point marker is aligned to a sizeof(int)-byte address.
- pointmarkindex = (pointsize + sizeof(int) - 1) / sizeof(int);
- // Now point size is the ints (inidcated by pointmarkindex) plus:
- // - an integer for boundary marker;
- // - an integer for vertex type;
- pointsize = (pointmarkindex + 2) * sizeof(int);
- // Decide the wordtype used in vertex pool.
- wtype = (sizeof(REAL) >= sizeof(tetrahedron)) ? FLOATINGPOINT : POINTER;
- // Initialize the pool of vertices.
- points = new memorypool(pointsize, VERPERBLOCK, wtype, 0);
-
- // The number of bytes occupied by a tetrahedron. There are four pointers
- // to other tetrahedra, four pointers to corners, and possibly four
- // pointers to subfaces.
- elesize = (8 + b->useshelles * 6) * sizeof(tetrahedron);
- // If Voronoi diagram is wanted, make sure we have additional space.
- if (b->voroout && (b->useshelles == 0)) {
- elesize = (8 + 4) * sizeof(tetrahedron);
- }
- // The index within each element at which its attributes are found, where
- // the index is measured in REALs.
- elemattribindex = (elesize + sizeof(REAL) - 1) / sizeof(REAL);
- // The index within each element at which the maximum voulme bound is
- // found, where the index is measured in REALs. Note that if the
- // `b->regionattrib' flag is set, an additional attribute will be added.
- volumeboundindex = elemattribindex + in->numberoftetrahedronattributes
- + (b->regionattrib > 0);
- // If element attributes or an constraint are needed, increase the number
- // of bytes occupied by an element.
- if (b->varvolume) {
- elesize = (volumeboundindex + 1) * sizeof(REAL);
- } else if (in->numberoftetrahedronattributes + b->regionattrib > 0) {
- elesize = volumeboundindex * sizeof(REAL);
- }
- // If element neighbor graph is requested (-n switch), an additional
- // integer is allocated for each element.
- elemmarkerindex = (elesize + sizeof(int) - 1) / sizeof(int);
- if (b->neighout || b->voroout) {
- elesize = (elemmarkerindex + 1) * sizeof(int);
- }
- // If -o2 switch is used, an additional pointer pointed to the list of
- // higher order nodes is allocated for each element.
- highorderindex = (elesize + sizeof(tetrahedron) - 1) / sizeof(tetrahedron);
- if (b->order == 2) {
- elesize = (highorderindex + 1) * sizeof(tetrahedron);
- }
- // Having determined the memory size of an element, initialize the pool.
- tetrahedrons = new memorypool(elesize, ELEPERBLOCK, POINTER, 8);
-
- if (b->useshelles) {
- // The number of bytes occupied by a subface. The list of pointers
- // stored in a subface are: three to other subfaces, three to corners,
- // three to subsegments, two to tetrahedra, and one to a badface.
- shsize = 12 * sizeof(shellface);
- // The index within each subface at which the maximum area bound is
- // found, where the index is measured in REALs.
- areaboundindex = (shsize + sizeof(REAL) - 1) / sizeof(REAL);
- // If -q switch is in use, increase the number of bytes occupied by
- // a subface for saving maximum area bound.
- if (b->quality && varconstraint) {
- shsize = (areaboundindex + 1) * sizeof(REAL);
- } else {
- shsize = areaboundindex * sizeof(REAL);
- }
- // The index within subface at which the facet marker is found. Ensure
- // the marker is aligned to a sizeof(int)-byte address.
- shmarkindex = (shsize + sizeof(int) - 1) / sizeof(int);
- // Increase the number of bytes by two or three integers, one for facet
- // marker, one for shellface type, and optionally one for pbc group.
- shsize = (shmarkindex + 2 + checkpbcs) * sizeof(int);
- // Initialize the pool of subfaces. Each subface record is eight-byte
- // aligned so it has room to store an edge version (from 0 to 5) in
- // the least three bits.
- subfaces = new memorypool(shsize, SUBPERBLOCK, POINTER, 8);
- // Initialize the pool of subsegments. The subsegment's record is same
- // with subface.
- subsegs = new memorypool(shsize, SUBPERBLOCK, POINTER, 8);
- // Initialize the "outer space" tetrahedron and omnipresent subface.
- dummyinit(tetrahedrons->itemwords, subfaces->itemwords);
- } else {
- // Initialize the "outer space" tetrahedron.
- dummyinit(tetrahedrons->itemwords, 0);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// tetrahedrondealloc() Deallocate space for a tet., marking it dead. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::tetrahedrondealloc(tetrahedron *dyingtetrahedron)
-{
- // Set tetrahedron's vertices to NULL. This makes it possible to detect
- // dead tetrahedra when traversing the list of all tetrahedra.
- dyingtetrahedron[4] = (tetrahedron) NULL;
- dyingtetrahedron[5] = (tetrahedron) NULL;
- dyingtetrahedron[6] = (tetrahedron) NULL;
- dyingtetrahedron[7] = (tetrahedron) NULL;
- tetrahedrons->dealloc((void *) dyingtetrahedron);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// tetrahedrontraverse() Traverse the tetrahedra, skipping dead ones. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-tetgenmesh::tetrahedron* tetgenmesh::tetrahedrontraverse()
-{
- tetrahedron *newtetrahedron;
-
- do {
- newtetrahedron = (tetrahedron *) tetrahedrons->traverse();
- if (newtetrahedron == (tetrahedron *) NULL) {
- return (tetrahedron *) NULL;
- }
- } while (newtetrahedron[7] == (tetrahedron) NULL); // Skip dead ones.
- return newtetrahedron;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// shellfacedealloc() Deallocate space for a shellface, marking it dead. //
-// Used both for dealloc a subface and subsegment. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::shellfacedealloc(memorypool *pool, shellface *dyingsh)
-{
- // Set shellface's vertices to NULL. This makes it possible to detect dead
- // shellfaces when traversing the list of all shellfaces.
- dyingsh[3] = (shellface) NULL;
- dyingsh[4] = (shellface) NULL;
- dyingsh[5] = (shellface) NULL;
- pool->dealloc((void *) dyingsh);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// shellfacetraverse() Traverse the subfaces, skipping dead ones. Used //
-// for both subfaces and subsegments pool traverse. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-tetgenmesh::shellface* tetgenmesh::shellfacetraverse(memorypool *pool)
-{
- shellface *newshellface;
-
- do {
- newshellface = (shellface *) pool->traverse();
- if (newshellface == (shellface *) NULL) {
- return (shellface *) NULL;
- }
- } while (newshellface[3] == (shellface) NULL); // Skip dead ones.
- return newshellface;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// badfacedealloc() Deallocate space for a badface, marking it dead. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::badfacedealloc(memorypool *pool, badface *dying)
-{
- // Set badface's forg to NULL. This makes it possible to detect dead
- // ones when traversing the list of all items.
- dying->forg = (point) NULL;
- pool->dealloc((void *) dying);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// badfacetraverse() Traverse the pools, skipping dead ones. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-tetgenmesh::badface* tetgenmesh::badfacetraverse(memorypool *pool)
-{
- badface *newsh;
-
- do {
- newsh = (badface *) pool->traverse();
- if (newsh == (badface *) NULL) {
- return (badface *) NULL;
- }
- } while (newsh->forg == (point) NULL); // Skip dead ones.
- return newsh;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// pointdealloc() Deallocate space for a point, marking it dead. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::pointdealloc(point dyingpoint)
-{
- // Mark the point as dead. This makes it possible to detect dead points
- // when traversing the list of all points.
- setpointtype(dyingpoint, DEADVERTEX);
- points->dealloc((void *) dyingpoint);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// pointtraverse() Traverse the points, skipping dead ones. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-tetgenmesh::point tetgenmesh::pointtraverse()
-{
- point newpoint;
-
- do {
- newpoint = (point) points->traverse();
- if (newpoint == (point) NULL) {
- return (point) NULL;
- }
- } while (pointtype(newpoint) == DEADVERTEX); // Skip dead ones.
- return newpoint;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// maketetrahedron() Create a new tetrahedron. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::maketetrahedron(triface *newtet)
-{
- newtet->tet = (tetrahedron *) tetrahedrons->alloc();
- // Initialize the four adjoining tetrahedra to be "outer space".
- newtet->tet[0] = (tetrahedron) dummytet;
- newtet->tet[1] = (tetrahedron) dummytet;
- newtet->tet[2] = (tetrahedron) dummytet;
- newtet->tet[3] = (tetrahedron) dummytet;
- // Four NULL vertices.
- newtet->tet[4] = (tetrahedron) NULL;
- newtet->tet[5] = (tetrahedron) NULL;
- newtet->tet[6] = (tetrahedron) NULL;
- newtet->tet[7] = (tetrahedron) NULL;
- // Initialize the four adjoining subfaces to be the omnipresent subface.
- if (b->useshelles) {
- newtet->tet[8 ] = (tetrahedron) dummysh;
- newtet->tet[9 ] = (tetrahedron) dummysh;
- newtet->tet[10] = (tetrahedron) dummysh;
- newtet->tet[11] = (tetrahedron) dummysh;
- newtet->tet[12] = (tetrahedron) dummysh;
- newtet->tet[13] = (tetrahedron) dummysh;
- }
- for (int i = 0; i < in->numberoftetrahedronattributes; i++) {
- setelemattribute(newtet->tet, i, 0.0);
- }
- if (b->varvolume) {
- setvolumebound(newtet->tet, -1.0);
- }
- // Initialize the location and version to be Zero.
- newtet->loc = 0;
- newtet->ver = 0;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// makeshellface() Create a new shellface with version zero. Used for //
-// both subfaces and seusegments. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::makeshellface(memorypool *pool, face *newface)
-{
- newface->sh = (shellface *) pool->alloc();
- //Initialize the three adjoining subfaces to be the omnipresent subface.
- newface->sh[0] = (shellface) dummysh;
- newface->sh[1] = (shellface) dummysh;
- newface->sh[2] = (shellface) dummysh;
- // Three NULL vertices.
- newface->sh[3] = (shellface) NULL;
- newface->sh[4] = (shellface) NULL;
- newface->sh[5] = (shellface) NULL;
- // Initialize the two adjoining tetrahedra to be "outer space".
- newface->sh[6] = (shellface) dummytet;
- newface->sh[7] = (shellface) dummytet;
- // Initialize the three adjoining subsegments to be the omnipresent
- // subsegments.
- newface->sh [8] = (shellface) dummysh;
- newface->sh [9] = (shellface) dummysh;
- newface->sh[10] = (shellface) dummysh;
- // Initialize the pointer to badface structure.
- newface->sh[11] = (shellface) NULL;
- if (b->quality && varconstraint) {
- // Initialize the maximum area bound.
- setareabound(*newface, 0.0);
- }
- // Set the boundary marker to zero.
- setshellmark(*newface, 0);
- // Set the type.
- setshelltype(*newface, NSHARP);
- if (checkpbcs) {
- // Set the pbcgroup be ivalid.
- setshellpbcgroup(*newface, -1);
- }
- // Initialize the version to be Zero.
- newface->shver = 0;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// makepoint() Create a new point. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::makepoint(point* pnewpoint)
-{
- int ptmark, i;
-
- *pnewpoint = (point) points->alloc();
- // Initialize three coordinates.
- (*pnewpoint)[0] = 0.0;
- (*pnewpoint)[1] = 0.0;
- (*pnewpoint)[2] = 0.0;
- // Initialize the list of user-defined attributes.
- for (i = 0; i < in->numberofpointattributes; i++) {
- (*pnewpoint)[3 + i] = 0.0;
- }
- // Initialize the metric tensor.
- for (i = 0; i < sizeoftensor; i++) {
- (*pnewpoint)[pointmtrindex + i] = 0.0;
- }
- if (b->plc || b->refine) {
- // Initialize the point-to-simplex filed.
- setpoint2tet(*pnewpoint, NULL);
- setpoint2sh(*pnewpoint, NULL);
- setpoint2ppt(*pnewpoint, NULL);
- if (b->metric) {
- setpoint2bgmtet(*pnewpoint, NULL);
- }
- if (checkpbcs) {
- // Initialize the other pointer to its pbc point.
- setpoint2pbcpt(*pnewpoint, NULL);
- }
- }
- // Initialize the point marker (starting from in->firstnumber).
- ptmark = (int) points->items - (in->firstnumber == 1 ? 0 : 1);
- setpointmark(*pnewpoint, ptmark);
- // Initialize the point type.
- setpointtype(*pnewpoint, UNUSEDVERTEX);
-}
-
-//
-// End of memory management routines
-//
-
-//
-// Begin of point location routines
-//
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// randomnation() Generate a random number between 0 and 'choices' - 1. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-unsigned long tetgenmesh::randomnation(unsigned int choices)
-{
- unsigned long newrandom;
-
- if (choices >= 714025l) {
- newrandom = (randomseed * 1366l + 150889l) % 714025l;
- randomseed = (newrandom * 1366l + 150889l) % 714025l;
- newrandom = newrandom * (choices / 714025l) + randomseed;
- if (newrandom >= choices) {
- return newrandom - choices;
- } else {
- return newrandom;
- }
- } else {
- randomseed = (randomseed * 1366l + 150889l) % 714025l;
- return randomseed % choices;
- }
- // Old function.
- // randomseed = (randomseed * 1366l + 150889l) % 714025l;
- // return randomseed / (714025l / choices + 1);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// distance2() Returns the square "distance" of a tetrahedron to point p. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-REAL tetgenmesh::distance2(tetrahedron* tetptr, point p)
-{
- point p1, p2, p3, p4;
- REAL dx, dy, dz;
-
- p1 = (point) tetptr[4];
- p2 = (point) tetptr[5];
- p3 = (point) tetptr[6];
- p4 = (point) tetptr[7];
-
- dx = p[0] - 0.25 * (p1[0] + p2[0] + p3[0] + p4[0]);
- dy = p[1] - 0.25 * (p1[1] + p2[1] + p3[1] + p4[1]);
- dz = p[2] - 0.25 * (p1[2] + p2[2] + p3[2] + p4[2]);
-
- return dx * dx + dy * dy + dz * dz;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// preciselocate() Find a simplex containing a given point. //
-// //
-// This routine implements the simple Walk-through point location algorithm. //
-// Begins its search from 'searchtet', assume there is a line segment L from //
-// a vertex of 'searchtet' to the query point 'searchpt', and simply walk //
-// towards 'searchpt' by traversing all faces intersected by L. //
-// //
-// On completion, 'searchtet' is a tetrahedron that contains 'searchpt'. The //
-// returned value indicates one of the following cases: //
-// - Returns ONVERTEX if the point lies on an existing vertex. 'searchtet' //
-// is a handle whose origin is the existing vertex. //
-// - Returns ONEDGE if the point lies on a mesh edge. 'searchtet' is a //
-// handle whose primary edge is the edge on which the point lies. //
-// - Returns ONFACE if the point lies strictly within a face. 'searchtet' //
-// is a handle whose primary face is the face on which the point lies. //
-// - Returns INTETRAHEDRON if the point lies strictly in a tetrahededron. //
-// 'searchtet' is a handle on the tetrahedron that contains the point. //
-// - Returns OUTSIDE if the point lies outside the mesh. 'searchtet' is a //
-// handle whose location is the face the point is to 'above' of. //
-// //
-// WARNING: This routine is designed for convex triangulations, and will not //
-// generally work after the holes and concavities have been carved. //
-// //
-// If 'maxtetnumber' > 0, stop the searching process if the number of passed //
-// tets is larger than it and return OUTSIDE. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-enum tetgenmesh::locateresult tetgenmesh::preciselocate(point searchpt,
- triface* searchtet, long maxtetnumber)
-{
- triface backtracetet;
- triface walkthroface;
- point forg, fdest, fapex, toppo;
- REAL ori1, ori2, ori3, ori4;
- long tetnumber;
- int side;
-
- if (isdead(searchtet)) searchtet->tet = dummytet;
- if (searchtet->tet == dummytet) {
- searchtet->loc = 0;
- symself(*searchtet);
- }
- // 'searchtet' should be a valid tetrahedron now.
-#ifdef SELF_CHECK
- // assert(!isdead(searchtet) && (searchtet->tet != dummytet));
-#endif
- if (isdead(searchtet)) {
- printf("Warning: Point location failed.\n");
- return OUTSIDE;
- }
-
- searchtet->ver = 0; // Keep in CCW edge ring.
- // Find a face of 'searchtet' such that the 'searchpt' lies strictly
- // above it. Such face should always exist.
- for (searchtet->loc = 0; searchtet->loc < 4; searchtet->loc++) {
- forg = org(*searchtet);
- fdest = dest(*searchtet);
- fapex = apex(*searchtet);
- ori1 = orient3d(forg, fdest, fapex, searchpt);
- if (ori1 < 0.0) break;
- }
-#ifdef SELF_CHECK
- assert(searchtet->loc < 4);
-#endif
-
- // Define 'tetnumber' for exit the loop when it's running endless.
- tetnumber = 0l;
- while ((maxtetnumber > 0l) && (tetnumber <= maxtetnumber)) {
- // Check if we are reaching the boundary of the triangulation.
- if (searchtet->tet == dummytet) {
- *searchtet = backtracetet;
- return OUTSIDE;
- }
- // Initialize the face for returning the walk-through face.
- walkthroface.tet = (tetrahedron *) NULL;
- // Adjust the edge ring, so that 'ori1 < 0.0' holds.
- searchtet->ver = 0;
- // 'toppo' remains unchange for the following orientation tests.
- toppo = oppo(*searchtet);
- // Check the three sides of 'searchtet' to find the face through which
- // we can walk next.
- for (side = 0; side < 3; side++) {
- forg = org(*searchtet);
- fdest = dest(*searchtet);
- ori2 = orient3d(forg, fdest, toppo, searchpt);
- if (ori2 == 0.0) {
- // They are coplanar, check if 'searchpt' lies inside, or on an edge,
- // or coindice with a vertex of face (forg, fdest, toppo).
- fapex = apex(*searchtet);
- ori3 = orient3d(fdest, fapex, toppo, searchpt);
- if (ori3 < 0.0) {
- // Outside the face (fdest, fapex, toppo), walk through it.
- enextself(*searchtet);
- fnext(*searchtet, walkthroface);
- break;
- }
- ori4 = orient3d(fapex, forg, toppo, searchpt);
- if (ori4 < 0.0) {
- // Outside the face (fapex, forg, toppo), walk through it.
- enext2self(*searchtet);
- fnext(*searchtet, walkthroface);
- break;
- }
- // Remember, ori1 < 0.0, which means 'searchpt' will not on edge
- // (forg, fdest) or on vertex forg or fdest.
-#ifdef SELF_CHECK
- assert(ori1 < 0.0);
-#endif
- // The rest possible cases are:
- // (1) 'searchpt' lies on edge (fdest, toppo);
- // (2) 'searchpt' lies on edge (toppo, forg);
- // (3) 'searchpt' coincident with toppo;
- // (4) 'searchpt' lies inside face (forg, fdest, toppo).
- fnextself(*searchtet);
- if (ori3 == 0.0) {
- if (ori4 == 0.0) {
- // Case (4).
- enext2self(*searchtet);
- return ONVERTEX;
- } else {
- // Case (1).
- enextself(*searchtet);
- return ONEDGE;
- }
- }
- if (ori4 == 0.0) {
- // Case (2).
- enext2self(*searchtet);
- return ONEDGE;
- }
- // Case (4).
- return ONFACE;
- } else if (ori2 < 0.0) {
- // Outside the face (forg, fdest, toppo), walk through it.
- fnext(*searchtet, walkthroface);
- break;
- }
- // Go to check next side.
- enextself(*searchtet);
- }
- if (side >= 3) {
- // Found! Inside tetrahedron.
- return INTETRAHEDRON;
- }
- // We walk through the face 'walkthroface' and continue the searching.
-#ifdef SELF_CHECK
- assert(walkthroface.tet != (tetrahedron *) NULL);
-#endif
- // Store the face handle in 'backtracetet' before we take the real walk.
- // So we are able to restore the handle to 'searchtet' if we are
- // reaching the outer boundary.
- backtracetet = walkthroface;
- sym(walkthroface, *searchtet);
- tetnumber++;
- }
-
- // Should never be here.
- // printf("Internal error in preciselocate(): Point location failed.\n");
- // internalerror();
- return OUTSIDE;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// locate() Find a simplex containing a given point. //
-// //
-// This routine implements Muecke's Jump-and-walk point location algorithm. //
-// It improves the simple walk-through by "jumping" to a good starting point //
-// via random sampling. Searching begins from one of handles: the input //
-// 'searchtet', a recently encountered tetrahedron 'recenttet', or from one //
-// chosen from a random sample. The choice is made by determining which one //
-// 's barycenter is closest to the point we are searcing for. Having chosen //
-// the starting tetrahedron, the simple Walk-through algorithm is used to do //
-// the real walking. //
-// //
-// The return value indicates the location of the 'searchpt' (INTETRAHEDRON, //
-// or ONFACE, ...). 'searchtet' is adjusted to a tetrahedron corresponding //
-// to that value. See the introduction part of preciselocate() for detail. //
-// //
-// WARNING: This routine is designed for convex triangulations, and will not //
-// generally work after the holes and concavities have been carved. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-enum tetgenmesh::locateresult tetgenmesh::locate(point searchpt,
- triface *searchtet)
-{
- tetrahedron *firsttet, *tetptr;
- void **sampleblock;
- long sampleblocks, samplesperblock, samplenum;
- long tetblocks, i, j;
- unsigned long alignptr;
- REAL searchdist, dist;
-
- // 'searchtet' should be a valid tetrahedron.
- if (isdead(searchtet)) {
- searchtet->tet = dummytet;
- }
- if (searchtet->tet == dummytet) {
- // This is an 'Outer Space' handle, get a hull tetrahedron.
- searchtet->loc = 0;
- symself(*searchtet);
- }
-#ifdef SELF_CHECK
- // assert(!isdead(searchtet));
-#endif
- if (isdead(searchtet)) {
- printf("Warning: Point location failed.\n");
- return OUTSIDE;
- }
-
- // Get the distance from the suggested starting tet to the point we seek.
- searchdist = distance2(searchtet->tet, searchpt);
-
- // If a recently encountered tetrahedron has been recorded and has not
- // been deallocated, test it as a good starting point.
- if (!isdead(&recenttet) && (recenttet.tet != searchtet->tet)) {
- dist = distance2(recenttet.tet, searchpt);
- if (dist < searchdist) {
- *searchtet = recenttet;
- searchdist = dist;
- }
- }
-
- // Select "good" candidate using k random samples, taking the closest one.
- // The number of random samples taken is proportional to the fourth root
- // of the number of tetrahedra in the mesh. The next bit of code assumes
- // that the number of tetrahedra increases monotonically.
- while (SAMPLEFACTOR * samples * samples * samples * samples <
- tetrahedrons->items) {
- samples++;
- }
- // Find how much blocks in current tet pool.
- tetblocks = (tetrahedrons->maxitems + ELEPERBLOCK - 1) / ELEPERBLOCK;
- // Find the average samles per block. Each block at least have 1 sample.
- samplesperblock = 1 + (samples / tetblocks);
- sampleblocks = samples / samplesperblock;
- sampleblock = tetrahedrons->firstblock;
- for (i = 0; i < sampleblocks; i++) {
- alignptr = (unsigned long) (sampleblock + 1);
- firsttet = (tetrahedron *)
- (alignptr + (unsigned long) tetrahedrons->alignbytes
- - (alignptr % (unsigned long) tetrahedrons->alignbytes));
- for (j = 0; j < samplesperblock; j++) {
- if (i == tetblocks - 1) {
- // This is the last block.
- samplenum = randomnation((int)
- (tetrahedrons->maxitems - (i * ELEPERBLOCK)));
- } else {
- samplenum = randomnation(ELEPERBLOCK);
- }
- tetptr = (tetrahedron *)
- (firsttet + (samplenum * tetrahedrons->itemwords));
- if (tetptr[4] != (tetrahedron) NULL) {
- dist = distance2(tetptr, searchpt);
- if (dist < searchdist) {
- searchtet->tet = tetptr;
- searchdist = dist;
- }
- }
- }
- sampleblock = (void **) *sampleblock;
- }
-
- // Call simple walk-through to locate the point.
- return preciselocate(searchpt, searchtet, tetrahedrons->items);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// adjustlocate() Adjust the precise location of a vertex. //
-// //
-// 'precise' is the value returned from preciselocate(). It indicates the //
-// exact location of the point 'searchpt' with respect to the tetrahedron //
-// 'searchtet'. 'epspp' is a given relative tolerance. //
-// //
-// This routine re-evaluates the orientations of searchpt with respect to //
-// the four sides of searchtet. Detects the coplanarities by additinal tests //
-// which are based on the given tolerance. If 'precise' is ONFACE or ONEDGE, //
-// we can save one or two orientation tests. //
-// //
-// The return value indicates the location of the 'searchpt' (INTETRAHEDRON, //
-// or ONFACE, ...). 'searchtet' is adjusted to a tetrahedron corresponding //
-// to that value. See the introduction part of preciselocate() for detail. //
-// //
-// WARNING: This routine detect degenerate case using relative tolerance. //
-// It is better used after locate() or preciselocate(). For general inputs, //
-// it may not able to tell the correct location. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-enum tetgenmesh::locateresult tetgenmesh::adjustlocate(point searchpt,
- triface* searchtet, enum locateresult precise, REAL epspp)
-{
- point torg, tdest, tapex, toppo;
- REAL s1, s2, s3, s4;
-
- // For the given 'searchtet', the orientations tests are:
- // s1: (tdest, torg, tapex, searchpt);
- // s2: (torg, tdest, toppo, searchpt);
- // s3: (tdest, tapex, toppo, searchpt);
- // s4: (tapex, torg, toppo, searchpt);
- adjustedgering(*searchtet, CCW);
- torg = org(*searchtet);
- tdest = dest(*searchtet);
- tapex = apex(*searchtet);
- toppo = oppo(*searchtet);
-
- switch (precise) {
- case ONVERTEX:
- // This case we don't need do any further test.
- return ONVERTEX;
- case ONEDGE:
- // (torg, tdest);
- s1 = 0.0;
- s2 = 0.0;
- break;
- case ONFACE:
- // (tdest, torg, tapex);
- s1 = 0.0;
- s2 = orient3d(torg, tdest, toppo, searchpt);
- break;
- default: // INTETRAHEDRON or OUTSIDE
- s1 = orient3d(tdest, torg, tapex, searchpt);
- s2 = orient3d(torg, tdest, toppo, searchpt);
- }
-
- if (s1 != 0.0) {
- if (iscoplanar(tdest, torg, tapex, searchpt, s1, epspp)) {
- s1 = 0.0;
- }
- }
- if (s1 < 0.0) {
- return OUTSIDE;
- }
-
- if (s2 != 0.0) {
- if (iscoplanar(torg, tdest, toppo, searchpt, s2, epspp)) {
- s2 = 0.0;
- }
- }
- if (s2 < 0.0) {
- fnextself(*searchtet);
- return OUTSIDE;
- }
-
- s3 = orient3d(tdest, tapex, toppo, searchpt);
- if (s3 != 0.0) {
- if (iscoplanar(tdest, tapex, toppo, searchpt, s3, epspp)) {
- s3 = 0.0;
- }
- }
- if (s3 < 0.0) {
- enextfnextself(*searchtet);
- return OUTSIDE;
- }
-
- s4 = orient3d(tapex, torg, toppo, searchpt);
- if (s4 != 0.0) {
- if (iscoplanar(tapex, torg, toppo, searchpt, s4, epspp)) {
- s4 = 0.0;
- }
- }
- if (s4 < 0.0) {
- enext2fnextself(*searchtet);
- return OUTSIDE;
- }
-
- // Determine degenerate cases.
- if (s1 == 0.0) {
- if (s2 == 0.0) {
- if (s3 == 0.0) {
- // On tdest.
- enextself(*searchtet);
- return ONVERTEX;
- }
- if (s4 == 0.0) {
- // On torg.
- return ONVERTEX;
- }
- // On edge (torg, tdest).
- return ONEDGE;
- }
- if (s3 == 0.0) {
- if (s4 == 0.0) {
- // On tapex.
- enext2self(*searchtet);
- return ONVERTEX;
- }
- // On edge (tdest, tapex).
- enextself(*searchtet);
- return ONEDGE;
- }
- if (s4 == 0.0) {
- // On edge (tapex, torg).
- enext2self(*searchtet);
- return ONEDGE;
- }
- // On face (torg, tdest, tapex).
- return ONFACE;
- }
- if (s2 == 0.0) {
- fnextself(*searchtet);
- if (s3 == 0.0) {
- if (s4 == 0.0) {
- // On toppo.
- enext2self(*searchtet);
- return ONVERTEX;
- }
- // On edge (tdest, toppo).
- enextself(*searchtet);
- return ONEDGE;
- }
- if (s4 == 0.0) {
- // On edge (toppo, torg).
- enext2self(*searchtet);
- return ONEDGE;
- }
- // On face (torg, tdest, toppo).
- return ONFACE;
- }
- if (s3 == 0.0) {
- enextfnextself(*searchtet);
- if (s4 == 0.0) {
- // On edge (tapex, toppo).
- enextself(*searchtet);
- return ONEDGE;
- }
- // On face (tdest, tapex, toppo).
- return ONFACE;
- }
- if (s4 == 0.0) {
- enext2fnextself(*searchtet);
- // On face (tapex, torg, toppo).
- return ONFACE;
- }
-
- // Inside tetrahedron.
- return INTETRAHEDRON;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// hullwalk() Find a tetrahedron on the hull to continue search. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-enum tetgenmesh::locateresult tetgenmesh::hullwalk(point searchpt,
- triface *hulltet)
-{
- list* travtetlist;
- triface travtet, neightet;
- point pa, pb, pc;
- enum locateresult loc;
- REAL ori;
- int i;
-
- travtetlist = new list(sizeof(triface), NULL, 256);
- travtet = *hulltet;
- infect(travtet);
- travtetlist->append(&travtet);
-
- loc = OUTSIDE;
- for (i = 0; i < travtetlist->len(); i++) {
- travtet = * (triface *)(* travtetlist)[i];
- // Choose the CCW-edgering in face.
- travtet.ver = 0;
- // Look for a side where pt lies below it.
- for (travtet.loc = 0; travtet.loc < 4; travtet.loc++) {
- pa = org(travtet);
- pb = dest(travtet);
- pc = apex(travtet);
- ori = orient3d(pa, pb, pc, searchpt);
- if (ori > 0.0) break;
- }
- // Is pt above all (or coplanar with some of) the four sides?
- if (travtet.loc == 4) {
- hulltet->tet = travtet.tet;
- loc = adjustlocate(searchpt, hulltet, INTETRAHEDRON, b->epsilon);
- assert(loc != OUTSIDE);
- } else { // ori > 0.0
- // pt is below (behind) this side. We want to walk through it.
- sym(travtet, neightet);
- if (neightet.tet == dummytet) {
- // This is a hull side. Is p approximately on this side.
- loc = adjustlocate(searchpt, &travtet, OUTSIDE, b->epsilon);
- }
- if (loc == OUTSIDE) {
- // Let's collect all the neighbors for next searching.
- for (travtet.loc = 0; travtet.loc < 4; travtet.loc++) {
- sym(travtet, neightet);
- if ((neightet.tet != dummytet) && !infected(neightet)) {
- // Neighbor exists and not visited.
- infect(neightet);
- travtetlist->append(&neightet);
- }
- } // for (travtet.loc = 0;
- } // if (loc == OUTSIDE)
- } // if (travtet.loc == 4)
- if (loc != OUTSIDE) break;
- } // for (i = 0; i < travtetlist->len(); i++)
-
- // Uninfect traversed tets.
- for (i = 0; i < travtetlist->len(); i++) {
- travtet = * (triface *)(* travtetlist)[i];
- uninfect(travtet);
- }
-
- delete travtetlist;
- return loc;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// locatesub() Find a point in the surface mesh of a facet. //
-// //
-// Searching begins from the input 'searchsh', it should be a handle on the //
-// convex hull of the facet triangulation. //
-// //
-// If 'stopatseg' is nonzero, the search will stop if it tries to walk //
-// through a subsegment, and will return OUTSIDE. //
-// //
-// On completion, 'searchsh' is a subface that contains 'searchpt'. //
-// - Returns ONVERTEX if the point lies on an existing vertex. 'searchsh' //
-// is a handle whose origin is the existing vertex. //
-// - Returns ONEDGE if the point lies on a mesh edge. 'searchsh' is a //
-// handle whose primary edge is the edge on which the point lies. //
-// - Returns ONFACE if the point lies strictly within a subface. //
-// 'searchsh' is a handle on which the point lies. //
-// - Returns OUTSIDE if the point lies outside the triangulation. //
-// //
-// WARNING: This routine is designed for convex triangulations, and will not //
-// not generally work after the holes and concavities have been carved. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-enum tetgenmesh::locateresult tetgenmesh::locatesub(point searchpt,
- face* searchsh, int stopatseg, REAL epspp)
-{
- face backtracksh, spinsh, checkedge;
- point forg, fdest, fapex;
- REAL orgori, destori;
- REAL ori, sign;
- int moveleft, i;
-
- if (searchsh->sh == dummysh) {
- searchsh->shver = 0;
- spivotself(*searchsh);
-#ifdef SELF_CHECK
- assert(searchsh->sh != dummysh);
-#endif
- }
- // Find the sign to simulate that abovepoint is 'above' the facet.
- adjustedgering(*searchsh, CCW);
- forg = sorg(*searchsh);
- fdest = sdest(*searchsh);
- fapex = sapex(*searchsh);
- ori = orient3d(forg, fdest, fapex, abovepoint);
- sign = ori > 0.0 ? -1 : 1;
-
- // Orient 'searchsh' so that 'searchpt' is below it (i.e., searchpt has
- // CCW orientation with respect to searchsh in plane). Such edge
- // should always exist. Save it as (forg, fdest).
- for (i = 0; i < 3; i++) {
- forg = sorg(*searchsh);
- fdest = sdest(*searchsh);
- ori = orient3d(forg, fdest, abovepoint, searchpt) * sign;
- if (ori > 0.0) break;
- senextself(*searchsh);
- }
-#ifdef SELF_CHECK
- assert(i < 3);
-#endif
-
- while (1) {
- fapex = sapex(*searchsh);
- // Check whether the apex is the point we seek.
- if (fapex[0] == searchpt[0] && fapex[1] == searchpt[1] &&
- fapex[2] == searchpt[2]) {
- senext2self(*searchsh);
- return ONVERTEX;
- }
- // Does the point lie on the other side of the line defined by the
- // triangle edge opposite the triangle's destination?
- destori = orient3d(forg, fapex, abovepoint, searchpt) * sign;
- if (epspp > 0.0) {
- if (iscoplanar(forg, fapex, abovepoint, searchpt, destori, epspp)) {
- destori = 0.0;
- }
- }
- // Does the point lie on the other side of the line defined by the
- // triangle edge opposite the triangle's origin?
- orgori = orient3d(fapex, fdest, abovepoint, searchpt) * sign;
- if (epspp > 0.0) {
- if (iscoplanar(fapex, fdest, abovepoint, searchpt, orgori, epspp)) {
- orgori = 0.0;
- }
- }
- if (destori > 0.0) {
- moveleft = 1;
- } else {
- if (orgori > 0.0) {
- moveleft = 0;
- } else {
- // The point must be on the boundary of or inside this triangle.
- if (destori == 0.0) {
- senext2self(*searchsh);
- return ONEDGE;
- }
- if (orgori == 0.0) {
- senextself(*searchsh);
- return ONEDGE;
- }
- return ONFACE;
- }
- }
- // Move to another triangle. Leave a trace `backtracksh' in case
- // walking off a boundary of the triangulation.
- if (moveleft) {
- senext2(*searchsh, backtracksh);
- fdest = fapex;
- } else {
- senext(*searchsh, backtracksh);
- forg = fapex;
- }
- // Check if we meet a segment.
- sspivot(backtracksh, checkedge);
- if (checkedge.sh != dummysh) {
- if (stopatseg) {
- // The flag indicates we should not cross a segment. Stop.
- *searchsh = backtracksh;
- return OUTSIDE;
- }
- // Try to walk through a segment. We need to find a coplanar subface
- // sharing this segment to get into.
- spinsh = backtracksh;
- do {
- spivotself(spinsh);
- if (spinsh.sh == backtracksh.sh) {
- // Turn back, no coplanar subface is found.
- break;
- }
- // Are they belong to the same facet.
- if (shellmark(spinsh) == shellmark(backtracksh)) {
- // Find a coplanar subface. Walk into it.
- *searchsh = spinsh;
- break;
- }
- // Are they (nearly) coplanar?
- ori = orient3d(forg, fdest, sapex(backtracksh), sapex(spinsh));
- if (iscoplanar(forg, fdest, sapex(backtracksh), sapex(spinsh), ori,
- b->epsilon)) {
- // Find a coplanar subface. Walk into it.
- *searchsh = spinsh;
- break;
- }
- } while (spinsh.sh != backtracksh.sh);
- } else {
- spivot(backtracksh, *searchsh);
- }
- // Check for walking right out of the triangulation.
- if ((searchsh->sh == dummysh) || (searchsh->sh == backtracksh.sh)) {
- // Go back to the last triangle.
- *searchsh = backtracksh;
- return OUTSIDE;
- }
- // To keep the same orientation wrt abovepoint.
- if (sorg(*searchsh) != forg) sesymself(*searchsh);
-#ifdef SELF_CHECK
- assert((sorg(*searchsh) == forg) && (sdest(*searchsh) == fdest));
-#endif
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// adjustlocatesub() Adjust the precise location of a vertex. //
-// //
-// 'precise' is the precise location (returned from locatesub()) of 'searcht'//
-// with respect to 'searchsh'. 'epspp' is the given relative tolerance. //
-// //
-// This routine re-evaluates the orientations of 'searchpt' with respect to //
-// the three edges of 'searchsh'. Detects the collinearities by additinal //
-// tests based on the given tolerance. If 'precise' is ONEDGE, one can save //
-// one orientation test for the current edge of 'searchsh'. //
-// //
-// On completion, 'searchsh' is a subface contains 'searchpt'. The returned //
-// value indicates one of the following cases: //
-// - Returns ONVERTEX if the point lies on an existing vertex. 'searchsh' //
-// is a handle whose origin is the existing vertex. //
-// - Returns ONEDGE if the point lies on a mesh edge. 'searchsh' is a //
-// handle whose primary edge is the edge on which the point lies. //
-// - Returns ONFACE if the point lies strictly within a subface. //
-// 'searchsh' is a handle on which the point lies. //
-// - Returns OUTSIDE if the point lies outside 'searchsh'. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-enum tetgenmesh::locateresult tetgenmesh::
-adjustlocatesub(point searchpt, face* searchsh, enum locateresult precise,
- REAL epspp)
-{
- point pa, pb, pc;
- bool s1, s2, s3;
-
- pa = sorg(*searchsh);
- pb = sdest(*searchsh);
- pc = sapex(*searchsh);
-
- if (precise == ONEDGE) {
- s1 = true;
- } else {
- s1 = iscollinear(pa, pb, searchpt, epspp);
- }
- s2 = iscollinear(pb, pc, searchpt, epspp);
- s3 = iscollinear(pc, pa, searchpt, epspp);
- if (s1) {
- if (s2) {
- // on vertex pb.
-#ifdef SELF_CHECK
- assert(!s3);
-#endif
- senextself(*searchsh);
- return ONVERTEX;
- } else if (s3) {
- // on vertex pa.
- return ONVERTEX;
- } else {
- // on edge pa->pb.
- return ONEDGE;
- }
- } else if (s2) {
- if (s3) {
- // on vertex pc.
- senext2self(*searchsh);
- return ONVERTEX;
- } else {
- // on edge pb->pc.
- senextself(*searchsh);
- return ONEDGE;
- }
- } else if (s3) {
- // on edge pc->pa.
- senext2self(*searchsh);
- return ONEDGE;
- } else {
- return precise;
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// locateseg() Find a point in subsegments. //
-// //
-// Searching begins from the input 'searchseg', it should be a subsegment of //
-// the whole segment. //
-// //
-// On completion, 'searchseg' is a subsegment that contains 'searchpt'. //
-// - Returns ONVERTEX if the point lies on an existing vertex. 'searchseg' //
-// is a handle whose origin is the existing vertex. //
-// - Returns ONEDGE if the point lies inside 'searchseg'. //
-// - Returns OUTSIDE if the point lies outside the segment. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-enum tetgenmesh::locateresult tetgenmesh::
-locateseg(point searchpt, face* searchseg)
-{
- face backtraceseg;
- point pa, pb;
- REAL dx, dy, dz;
- int moveleft;
- int i;
-
- moveleft = 0;
- while (1) {
- searchseg->shver = 0;
- pa = sorg(*searchseg);
- pb = sdest(*searchseg);
- // Find the biggest difference in x, y, and z coordinates of a and b.
- dx = fabs(pb[0] - pa[0]);
- dy = fabs(pb[1] - pa[1]);
- dz = fabs(pb[2] - pa[2]);
- if (dx > dy) {
- if (dx > dz) {
- i = 0;
- } else {
- i = 2;
- }
- } else {
- if (dy > dz) {
- i = 1;
- } else {
- i = 2;
- }
- }
- if (pa[i] < pb[i]) {
- if (searchpt[i] < pa[i]) {
- moveleft = 1;
- } else if (searchpt[i] > pa[i]) {
- if (searchpt[i] < pb[i]) {
- return ONEDGE;
- } else if (searchpt[i] > pb[i]) {
- moveleft = 0;
- } else {
-#ifdef SELF_CHECK
- assert(searchpt[i] == pb[i]);
-#endif
- sesymself(*searchseg);
- return ONVERTEX;
- }
- } else {
-#ifdef SELF_CHECK
- assert(searchpt[i] == pa[i]);
-#endif
- return ONVERTEX;
- }
- } else if (pa[i] > pb[i]) {
- if (searchpt[i] < pb[i]) {
- moveleft = 0;
- } else if (searchpt[i] > pb[i]) {
- if (searchpt[i] < pa[i]) {
- return ONEDGE;
- } else if (searchpt[i] > pa[i]) {
- moveleft = 1;
- } else {
-#ifdef SELF_CHECK
- assert(searchpt[i] == pa[i]);
-#endif
- return ONVERTEX;
- }
- } else {
-#ifdef SELF_CHECK
- assert(searchpt[i] == pb[i]);
-#endif
- sesymself(*searchseg);
- return ONVERTEX;
- }
- }
- backtraceseg = *searchseg;
- if (moveleft) {
- senext2self(*searchseg);
- } else {
- senextself(*searchseg);
- }
- spivotself(*searchseg);
- if (searchseg->sh == dummysh) {
- *searchseg = backtraceseg;
- break;
- }
- }
-
- return OUTSIDE;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// adjustlocateseg() Adjust the precise location of a vertex on segment. //
-// //
-// 'searchpt' is either inside or ouside the segment 'searchseg'. It will be //
-// adjusted to on vertex if it is very close to an endpoint of 'searchseg'. //
-// 'epspp' is the given relative tolerance. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-enum tetgenmesh::locateresult tetgenmesh::
-adjustlocateseg(point searchpt, face* searchseg, enum locateresult precise,
- REAL epspp)
-{
- point pa, pb;
- REAL L, d, r;
-
- pa = sorg(*searchseg);
- pb = sdest(*searchseg);
- L = distance(pa, pb);
-
- // Is searchpt approximate to pa?
- d = distance(pa, searchpt);
- r = d / L;
- if (r <= epspp) {
- return ONVERTEX;
- }
- // Is searchpt approximate to pb?
- d = distance(pb, searchpt);
- r = d / L;
- if (r <= epspp) {
- sesymself(*searchseg);
- return ONVERTEX;
- }
-
- return precise;
-}
-
-//
-// End of point location routines
-//
-
-//
-// Begin of mesh transformation routines
-//
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// Flip operations //
-// //
-// If abc is a hull face, it is unflipable, and is locally Delaunay. In the //
-// following, we assume abc is an interior face, and the other tetrahedron //
-// adjoining at abc is bace. //
-// //
-// If the convex hull CH of the set {a, b, c, d, e} only has four vertices, //
-// i.e., one vertex lies inside CH, then abc is unflipable, and is locally //
-// Delaunay. If CH is the vertex set itself, we have the following cases to //
-// determine whether abc is flipable or not. //
-// //
-// If no four points of {a, b, c, d, e} are coplanar, a 2-to-3 flip can be //
-// applied to abc if the edge de crosses the triangle abc; a 3-to-2 flip can //
-// be applied to abc if ab crosses cde, and abde exists, otherwise, face abc //
-// is unflipable, i.e., the tetrahedron abde is not present. //
-// //
-// If four points of {a, b, c, d, e} are coplanar (two faces are coplanar). //
-// Assume faces abd and abe are coplanar (it is impossible be abc). If a, b, //
-// d, e form a non-convex quadrilateral, then abc is unflipable, furthermore,//
-// it is locally Delaunay. Assume they are convex quadrilateral, if abd and //
-// abe are hull faces, a 2-to-2 flip can be applied to abc; if abd and abe //
-// are interior faces, assume two tetrahedra adjoining abd and abe at the //
-// opposite sides are abdg and abef, respectively. If g = f, a 4-to-4 flip //
-// can be applied to abc, otherwise, abc is unflipable. //
-// //
-// There are other cases which can cause abc unflipable. If abc is a subface,//
-// a 2-to-3 flip is forbidden; if ab is a subsegment, flips 3-to-2, 2-to-2, //
-// and 4-to-4 are forbidden. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// categorizeface() Determine the flip type of a given face. //
-// //
-// On input, 'horiz' represents the face abc we want to flip (imagine it is //
-// parallel to the horizon). Let the tet above it be abcd. //
-// //
-// This routine determines the suitable type of flip operation for 'horiz'. //
-// - Returns T23 if a 2-to-3 flip is applicable. 'horiz' is same as input. //
-// - Returns T32 if a 3-to-2 flip is applicable. 'horiz' returns the edge //
-// of abc which is the flipable. //
-// - Returns T22 if a 2-to-2 or 4-to-4 flip is applicable. 'horiz' returns //
-// the edge of abc which is flipable. //
-// - Returns N32 indicates it is unflipable due to the absence of a tet. //
-// 'horize' returns the unflipable edge. //
-// - Returns N40 indicates it is unflipable and is locally Delaunay. //
-// - Returns FORBIDDENFACE indicates abc is a subface. //
-// - Returns FORBIDDENEDGE indicates the flipable edge of abc is a segment.//
-// 'horize' returns the flipable edge. //
-// //
-// Given a face abc, with two adjoining tetrahedra abcd and bace. If abc is //
-// flipable, i.e., T23, T32, T22 or T44, its flip type can be determined by //
-// doing five orientation tests: two tests for determining that d, e lie on //
-// the different sides of abc, three tests for determining if the edge de //
-// intersects the face abc. However, if we use the neighbor information of //
-// the mesh data structure, we can reduce the five orientation tests to at //
-// most three tests, that is, the two tests for determining whether d and e //
-// lie on the different sides of abc can be saved. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-enum tetgenmesh::fliptype tetgenmesh::categorizeface(triface& horiz)
-{
- triface symhoriz, casing;
- face checksh, checkseg;
- face cassh1, cassh2;
- point pa, pb, pc, pd, pe, pf, pg;
- point abdoppo, bcdoppo, cadoppo;
- REAL ori1, ori2, ori3;
- int adjtet;
-
- sym(horiz, symhoriz);
- if (symhoriz.tet == dummytet) {
- // A hull face is unflipable and locally Delaunay.
- return N40;
- }
-
- adjustedgering(horiz, CCW);
- findedge(&symhoriz, dest(horiz), org(horiz));
- pa = org(horiz);
- pb = dest(horiz);
- pc = apex(horiz);
- pd = oppo(horiz);
- pe = oppo(symhoriz);
-
- // Find the number of adjacent tetrahedra of abc, which have d, e, and one
- // of corners of abc as their corners. This number can be 0, 1 and 2.
- abdoppo = bcdoppo = cadoppo = (point) NULL;
- adjtet = 0;
- fnext(horiz, casing); // at edge 'ab'.
- symself(casing);
- if (casing.tet != dummytet) {
- abdoppo = oppo(casing);
- if (abdoppo == pe) adjtet++;
- }
- enextfnext(horiz, casing); // at edge 'bc'.
- symself(casing);
- if (casing.tet != dummytet) {
- bcdoppo = oppo(casing);
- if (bcdoppo == pe) adjtet++;
- }
- enext2fnext(horiz, casing); // at edge 'ca'.
- symself(casing);
- if (casing.tet != dummytet) {
- cadoppo = oppo(casing);
- if (cadoppo == pe) adjtet++;
- }
-
- if (adjtet == 0) {
- // No adjacent tetrahedron. Types T23, T22 and T44 are possible.
- ori1 = orient3d(pa, pb, pd, pe);
- if (checksubfaces && ori1 != 0.0) {
- // Check if abd and abe are both boundary faces?
- fnext(horiz, casing);
- tspivot(casing, cassh1);
- fnext(symhoriz, casing);
- tspivot(casing, cassh2);
- if ((cassh1.sh != dummysh) && (cassh2.sh != dummysh)) {
- // abd and abe are both boundary faces. Check if ab is a segment.
- findedge(&cassh1, pa, pb);
- sspivot(cassh1, checkseg);
- if (checkseg.sh == dummysh) {
- // ab is not a segment - abd and abe belong to the same facet.
- // The four points are forced to be coplanar.
- ori1 = 0.0;
- } else {
- // ab is a segment - abd and abe belong to two different facets.
- // In principle, a, b, c and d can form a tetrahedron (since
- // ori1 != 0.0). However, we should avoid to create a very
- // flat one which may form a sequence of extremely badly-shaped
- // or even wrong orientational tets. Test with a larger epsilon.
- if (iscoplanar(pa, pb, pd, pe, ori1, b->epsilon * 1e+2)) ori1 = 0.0;
- }
- } else {
- // abd and abe are not both boundary faces. Check if abd and bae
- // are approximately coplanar with respect to the epsilon.
- if (iscoplanar(pa, pb, pd, pe, ori1, b->epsilon)) ori1 = 0.0;
- }
- }
- if (ori1 < 0.0) {
- // e lies above abd, unflipable, tet abde is not present.
-#ifdef SELF_CHECK
- if (!nonconvex) {
- // abd and abe should not be hull faces, check it.
- fnext(horiz, casing);
- symself(casing);
- assert(casing.tet != dummytet);
- fnext(symhoriz, casing);
- symself(casing);
- assert(casing.tet != dummytet);
- }
-#endif
- if (checksubfaces) {
- // The nonconvexbility may be casued by existing an subsegment.
- tsspivot(&horiz, &checkseg);
- if (checkseg.sh != dummysh) {
- return FORBIDDENEDGE;
- }
- }
- return N32;
- }
- ori2 = orient3d(pb, pc, pd, pe);
- if (checksubfaces && ori2 != 0.0) {
- // Check if bcd and cbe are both boundary faces.
- enextfnext(horiz, casing);
- tspivot(casing, cassh1);
- enext2fnext(symhoriz, casing);
- tspivot(casing, cassh2);
- if (cassh1.sh != dummysh && cassh2.sh != dummysh) {
- // bcd and cbe are both boundary faces. Check if bc is a segment.
- findedge(&cassh1, pb, pc);
- sspivot(cassh1, checkseg);
- if (checkseg.sh == dummysh) {
- // bc is not a segment - bcd and cbe belong to the same facet.
- // The four points are forced to be coplanar.
- ori2 = 0.0;
- } else {
- if (iscoplanar(pb, pc, pd, pe, ori2, b->epsilon * 1e+2)) ori2 = 0.0;
- }
- } else {
- // bcd and cbe are not both boundary faces. Check if bcd and cbe
- // are approximately coplanar with respect to the epsilon.
- if (iscoplanar(pb, pc, pd, pe, ori2, b->epsilon)) ori2 = 0.0;
- }
- }
- if (ori2 < 0.0) {
- // e lies above bcd, unflipable, tet bcde is not present.
-#ifdef SELF_CHECK
- if (!nonconvex) {
- // bcd and cbe should not be hull faces, check it.
- enextfnext(horiz, casing);
- symself(casing);
- assert(casing.tet != dummytet);
- enext2fnext(symhoriz, casing);
- symself(casing);
- assert(casing.tet != dummytet);
- }
-#endif
- enextself(horiz);
- if (checksubfaces) {
- // The nonconvexbility may be casued by existing an subsegment.
- tsspivot(&horiz, &checkseg);
- if (checkseg.sh != dummysh) {
- return FORBIDDENEDGE;
- }
- }
- return N32;
- }
- ori3 = orient3d(pc, pa, pd, pe);
- if (checksubfaces && ori3 != 0.0) {
- // Check if cad and ace are both boundary faces.
- enext2fnext(horiz, casing);
- tspivot(casing, cassh1);
- enextfnext(symhoriz, casing);
- tspivot(casing, cassh2);
- if (cassh1.sh != dummysh && cassh2.sh != dummysh) {
- // cad and ace are both boundary faces. Check if ca is a segment.
- findedge(&cassh1, pc, pa);
- sspivot(cassh1, checkseg);
- if (checkseg.sh == dummysh) {
- // ca is not a segment - cad and ace belong to the same facet.
- // The four points are forced to be coplanar.
- ori3 = 0.0;
- } else {
- // ca is a segment - cad and ace belong to two different facets.
- // In principle, c, a, d and e can form a tetrahedron (since
- // ori3 != 0.0). Use a larger eps to test if they're coplanar.
- if (iscoplanar(pc, pa, pd, pe, ori3, b->epsilon * 1e+2)) ori3 = 0.0;
- }
- } else {
- // cad and ace are not both boundary faces. Check if cad and ace
- // are approximately coplanar with respect to the epsilon.
- if (iscoplanar(pc, pa, pd, pe, ori3, b->epsilon)) ori3 = 0.0;
- }
- }
- if (ori3 < 0.0) {
- // e lies above cad, unflipable, tet cade is not present.
-#ifdef SELF_CHECK
- if (!nonconvex) {
- // cad and ace should not be hull faces, check it.
- enext2fnext(horiz, casing);
- symself(casing);
- assert(casing.tet != dummytet);
- enextfnext(symhoriz, casing);
- symself(casing);
- assert(casing.tet != dummytet);
- }
-#endif
- enext2self(horiz);
- if (checksubfaces) {
- // The nonconvexbility may be casued by existing an subsegment.
- tsspivot(&horiz, &checkseg);
- if (checkseg.sh != dummysh) {
- return FORBIDDENEDGE;
- }
- }
- return N32;
- }
- if (ori1 == 0.0) {
- // e is coplanar with abd.
- if (ori2 * ori3 == 0.0) {
- // only one zero is possible.
- // assert(!(ori2 == 0.0 && ori3 == 0.0));
- // Three points (d, e, and a or b) are collinear, abc is unflipable
- // and locally Delaunay.
- return N40;
- }
- } else if (ori2 == 0.0) {
- // e is coplanar with bcd.
- if (ori1 * ori3 == 0.0) {
- // only one zero is possible.
- // assert(!(ori1 == 0.0 && ori3 == 0.0));
- // Three points (d, e, and b or c) are collinear, abc is unflipable
- // and locally Delaunay.
- return N40;
- }
- // Adjust 'horiz' and 'symhoriz' be the edge bc.
- enextself(horiz);
- enext2self(symhoriz);
- } else if (ori3 == 0.0) {
- // e is coplanar with cad.
- if (ori1 * ori2 == 0.0) {
- // only one zero is possible.
- // assert(!(ori1 == 0.0 && ori2 == 0.0));
- // Three points (d, e, and c or a) are collinear, abc is unflipable
- // and locally Delaunay.
- return N40;
- }
- // Adjust 'horiz' and 'symhoriz' be the edge ca.
- enext2self(horiz);
- enextself(symhoriz);
- } else {
- // e lies below all three faces, flipable.
- if (checksubfaces) {
- tspivot(horiz, checksh);
- if (checksh.sh != dummysh) {
- // To flip a subface is forbidden.
- return FORBIDDENFACE;
- }
- }
- return T23;
- }
- // Four points are coplanar, T22 or T44 is possible.
- if (checksubfaces) {
- tsspivot(&horiz, &checkseg);
- if (checkseg.sh != dummysh) {
- // To flip a subsegment is forbidden.
- return FORBIDDENEDGE;
- }
- tspivot(horiz, checksh);
- if (checksh.sh != dummysh) {
- // To flip a subface is forbidden.
- return FORBIDDENFACE;
- }
- }
- // Assume the four coplanar points are a, b, d, e, abd and abe are two
- // coplanar faces. If both abd and abe are hull faces, flipable(T22).
- // If they are interior faces, get the opposite tetrahedra abdf and
- // abeg, if f = g, flipable (T44). Otherwise, unflipable.
- pf = pg = (point) NULL;
- fnext(horiz, casing);
- symself(casing);
- if (casing.tet != dummytet) {
- pf = oppo(casing);
- }
- fnext(symhoriz, casing);
- symself(casing);
- if (casing.tet != dummytet) {
- pg = oppo(casing);
- }
- if (pf == pg) {
- // Either T22 (pf == pg == NULL) or T44 (pf and pg) is possible.
- if (checksubfaces) {
- // Retreat the corner points a, b, and c.
- pa = org(horiz);
- pb = dest(horiz);
- pc = apex(horiz);
- // Be careful not to create an inverted tetrahedron. Check the case.
- ori1 = orient3d(pc, pd, pe, pa);
- if (ori1 <= 0) return N40;
- ori1 = orient3d(pd, pc, pe, pb);
- if (ori1 <= 0) return N40;
- if (pf != (point) NULL) {
- ori1 = orient3d(pd, pf, pe, pa);
- if (ori1 <= 0) return N40;
- ori1 = orient3d(pf, pd, pe, pb);
- if (ori1 <= 0) return N40;
- }
- }
- if (pf == (point) NULL) {
- // abd and abe are hull faces, flipable.
- return T22;
- } else {
- // abd and abe are interior faces, flipable.
-#ifdef SELF_CHECK
- assert(pf != (point) NULL);
-#endif
- return T44;
- }
- } else {
- // ab has more than four faces around it, unflipable.
- return N32;
- }
- } else if (adjtet == 1) {
- // One of its three edges is locally non-convex. Type T32 is possible.
- // Adjust current configuration so that edge ab is non-convex.
- if (bcdoppo == pe) {
- // Edge bc is non-convex. Adjust 'horiz' and 'symhoriz' be edge bc.
- enextself(horiz);
- enext2self(symhoriz);
- pa = org(horiz);
- pb = dest(horiz);
- pc = apex(horiz);
- } else if (cadoppo == pe) {
- // Edge ca is non-convex. Adjust 'horiz' and 'symhoriz' be edge ca.
- enext2self(horiz);
- enextself(symhoriz);
- pa = org(horiz);
- pb = dest(horiz);
- pc = apex(horiz);
- } else {
- // Edge ab is non-convex.
-#ifdef SELF_CHECK
- assert(abdoppo == pe);
-#endif
- } // Now ab is the non-convex edge.
- // In order to be flipable, ab should cross face cde. Check it.
- ori1 = orient3d(pc, pd, pe, pa);
- if (checksubfaces && ori1 != 0.0) {
- // Check if cad and ace are both boundary faces.
- enext2fnext(horiz, casing);
- tspivot(casing, cassh1);
- enextfnext(symhoriz, casing);
- tspivot(casing, cassh2);
- if (cassh1.sh != dummysh && cassh2.sh != dummysh) {
- // cad and ace are both boundary faces. Check if ca is a segment.
- findedge(&cassh1, pc, pa);
- sspivot(cassh1, checkseg);
- if (checkseg.sh == dummysh) {
- // ca is not a segment. cad and ace belong to the same facet.
- // The four points are forced to be coplanar.
- ori1 = 0.0;
- } else {
- // ca is a segment. cad and ace belong to different facets.
- // In principle, c, d, e, and a can form a tetrahedron (since
- // ori1 != 0.0). However, we should avoid to create a very
- // flat tet. Use a larger epsilon to test if they're coplanar.
- if (iscoplanar(pc, pd, pe, pa, ori1, b->epsilon * 1e+2)) ori1 = 0.0;
- }
- } else {
- // Check if c, d, e, and a are approximately coplanar.
- if (iscoplanar(pc, pd, pe, pa, ori1, b->epsilon)) ori1 = 0.0;
- }
- }
- if (ori1 <= 0.0) {
- // a lies above or is coplanar cde, abc is locally Delaunay.
- return N40;
- }
- ori2 = orient3d(pd, pc, pe, pb);
- if (checksubfaces && ori2 != 0.0) {
- // Check if bcd and cbe are both boundary faces.
- enextfnext(horiz, casing);
- tspivot(casing, cassh1);
- enext2fnext(symhoriz, casing);
- tspivot(casing, cassh2);
- if (cassh1.sh != dummysh && cassh2.sh != dummysh) {
- // bcd and cbe are both boundary faces. Check if bc is a segment.
- findedge(&cassh1, pb, pc);
- sspivot(cassh1, checkseg);
- if (checkseg.sh == dummysh) {
- // bc is not a segment. bcd and cbe belong to the same facet.
- // The four points are forced to be coplanar.
- ori2 = 0.0;
- } else {
- // bc is a segment. bcd and cbe belong to different facets.
- // In principle, d, c, e, and b can form a tetrahedron (since
- // ori2 != 0.0). However, we should avoid to create a very
- // flat tet. Use a larger epsilon to test if they're coplanar.
- if (iscoplanar(pd, pc, pe, pb, ori2, b->epsilon * 1e+2)) ori2 = 0.0;
- }
- } else {
- // Check if d, c, e, and b are approximately coplanar.
- if (iscoplanar(pd, pc, pe, pb, ori2, b->epsilon)) ori2 = 0.0;
- }
- }
- if (ori2 <= 0.0) {
- // b lies above dce, unflipable, and abc is locally Delaunay.
- return N40;
- }
- // Edge ab crosses face cde properly.
- if (checksubfaces) {
- // If abc is subface, then ab must be a subsegment (because abde is
- // a tetrahedron and ab crosses cde properly).
- tsspivot(&horiz, &checkseg);
- if (checkseg.sh != dummysh) {
- // To flip a subsegment is forbidden.
- return FORBIDDENEDGE;
- }
- // Both abd and bae should not be subfaces (because they're not
- // coplanar and ab is not a subsegment). However, they may be
- // subfaces and belong to a facet (created during facet recovery),
- // that is, abde is an invalid tetrahedron. Find this case out.
- fnext(horiz, casing);
- tspivot(casing, cassh1);
- fnext(symhoriz, casing);
- tspivot(casing, cassh2);
- if (cassh1.sh != dummysh || cassh2.sh != dummysh) {
- if (!b->quiet) {
- // Unfortunately, they're subfaces. Corrections need be done here.
- printf("Warning: A tetrahedron spans two subfaces of a facet.\n");
- }
- // Temporarily, let it be there.
- return N32;
- }
- }
- return T32;
- } else {
- // The convex hull of {a, b, c, d, e} has only four vertices, abc is
- // unflipable, furthermore, it is locally Delaunay.
- return N40;
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// enqueueflipface(), enqueueflipedge() Queue a face (or an edge). //
-// //
-// The face (or edge) may be non-locally Delaunay. It is queued for process- //
-// ing in flip() (or flipsub()). The vertices of the face (edge) are stored //
-// seperatly to ensure the face (or edge) is still the same one when we save //
-// it since other flips will cause this face (or edge) be changed or dead. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::enqueueflipface(triface& checkface, queue* flipqueue)
-{
- badface *queface;
- triface symface;
-
- sym(checkface, symface);
- if (symface.tet != dummytet) {
- queface = (badface *) flipqueue->push((void *) NULL);
- queface->tt = checkface;
- queface->foppo = oppo(symface);
- }
-}
-
-void tetgenmesh::enqueueflipedge(face& checkedge, queue* flipqueue)
-{
- badface *queface;
-
- queface = (badface *) flipqueue->push((void *) NULL);
- queface->ss = checkedge;
- queface->forg = sorg(checkedge);
- queface->fdest = sdest(checkedge);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// flip23() Perform a 2-to-3 flip. //
-// //
-// On input, 'flipface' represents the face will be flipped. Let it is abc, //
-// the two tetrahedra sharing abc are abcd, bace. abc is not a subface. //
-// //
-// A 2-to-3 flip is to change two tetrahedra abcd, bace to three tetrahedra //
-// edab, edbc, and edca. As a result, face abc has been removed and three //
-// new faces eda, edb and edc have been created. //
-// //
-// On completion, 'flipface' returns edab. If 'flipqueue' is not NULL, all //
-// possibly non-Delaunay faces are added into it. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::flip23(triface* flipface, queue* flipqueue)
-{
- triface abcd, bace; // Old configuration.
- triface oldabd, oldbcd, oldcad;
- triface abdcasing, bcdcasing, cadcasing;
- triface oldbae, oldcbe, oldace;
- triface baecasing, cbecasing, acecasing;
- triface worktet;
- face abdsh, bcdsh, cadsh; // The six subfaces on the CH.
- face baesh, cbesh, acesh;
- face abseg, bcseg, caseg; // The nine segs on the CH.
- face adseg, bdseg, cdseg;
- face aeseg, beseg, ceseg;
- triface edab, edbc, edca; // New configuration.
- point pa, pb, pc, pd, pe;
- REAL attrib, volume;
- int i;
-
- abcd = *flipface;
- adjustedgering(abcd, CCW); // abcd represents edge ab.
- pa = org(abcd);
- pb = dest(abcd);
- pc = apex(abcd);
- pd = oppo(abcd);
- // sym(abcd, bace);
- // findedge(&bace, dest(abcd), org(abcd)); // bace represents edge ba.
- sym(abcd, bace);
- bace.ver = 0; // CCW.
- for (i = 0; (i < 3) && (org(bace) != pb); i++) {
- enextself(bace);
- }
- pe = oppo(bace);
-
- if (b->verbose > 2) {
- printf(" Do T23 on face (%d, %d, %d) %d, %d.\n", pointmark(pa),
- pointmark(pb), pointmark(pc), pointmark(pd), pointmark(pe));
- }
- flip23s++;
-
- // Storing the old configuration outside the convex hull.
- fnext(abcd, oldabd);
- enextfnext(abcd, oldbcd);
- enext2fnext(abcd, oldcad);
- fnext(bace, oldbae);
- enext2fnext(bace, oldcbe);
- enextfnext(bace, oldace);
- sym(oldabd, abdcasing);
- sym(oldbcd, bcdcasing);
- sym(oldcad, cadcasing);
- sym(oldbae, baecasing);
- sym(oldcbe, cbecasing);
- sym(oldace, acecasing);
- if (checksubfaces) {
- tspivot(oldabd, abdsh);
- tspivot(oldbcd, bcdsh);
- tspivot(oldcad, cadsh);
- tspivot(oldbae, baesh);
- tspivot(oldcbe, cbesh);
- tspivot(oldace, acesh);
- } else if (checksubsegs) {
- tsspivot1(abcd, abseg);
- enext(abcd, worktet);
- tsspivot1(worktet, bcseg);
- enext2(abcd, worktet);
- tsspivot1(worktet, caseg);
- enext2(oldabd, worktet);
- tsspivot1(worktet, adseg);
- enext2(oldbcd, worktet);
- tsspivot1(worktet, bdseg);
- enext2(oldcad, worktet);
- tsspivot1(worktet, cdseg);
- enext(oldbae, worktet);
- tsspivot1(worktet, aeseg);
- enext(oldcbe, worktet);
- tsspivot1(worktet, beseg);
- enext(oldace, worktet);
- tsspivot1(worktet, ceseg);
- }
-
- // Creating the new configuration inside the convex hull.
- edab.tet = abcd.tet; // Update abcd to be edab.
- setorg (edab, pe);
- setdest(edab, pd);
- setapex(edab, pa);
- setoppo(edab, pb);
- edbc.tet = bace.tet; // Update bace to be edbc.
- setorg (edbc, pe);
- setdest(edbc, pd);
- setapex(edbc, pb);
- setoppo(edbc, pc);
- maketetrahedron(&edca); // Create edca.
- setorg (edca, pe);
- setdest(edca, pd);
- setapex(edca, pc);
- setoppo(edca, pa);
- // Set the element attributes of the new tetrahedron 'edca'.
- for (i = 0; i < in->numberoftetrahedronattributes; i++) {
- attrib = elemattribute(abcd.tet, i);
- setelemattribute(edca.tet, i, attrib);
- }
- // Set the volume constraint of the new tetrahedron 'edca' if the -ra
- // switches are not used together. In -ra case, the various volume
- // constraints can be spreaded very far.
- if (b->varvolume && !b->refine) {
- volume = volumebound(abcd.tet);
- setvolumebound(edca.tet, volume);
- }
-
- // Clear old bonds in edab(was abcd) and edbc(was bace).
- for (i = 0; i < 4; i ++) {
- edab.tet[i] = (tetrahedron) dummytet;
- }
- for (i = 0; i < 4; i ++) {
- edbc.tet[i] = (tetrahedron) dummytet;
- }
- // Bond the faces inside the convex hull.
- edab.loc = 0;
- edca.loc = 1;
- bond(edab, edca);
- edab.loc = 1;
- edbc.loc = 0;
- bond(edab, edbc);
- edbc.loc = 1;
- edca.loc = 0;
- bond(edbc, edca);
- // Bond the faces on the convex hull.
- edab.loc = 2;
- bond(edab, abdcasing);
- edab.loc = 3;
- bond(edab, baecasing);
- edbc.loc = 2;
- bond(edbc, bcdcasing);
- edbc.loc = 3;
- bond(edbc, cbecasing);
- edca.loc = 2;
- bond(edca, cadcasing);
- edca.loc = 3;
- bond(edca, acecasing);
- // There may exist subfaces that need to be bonded to new configuarton.
- if (checksubfaces) {
- // Clear old flags in edab(was abcd) and edbc(was bace).
- for (i = 0; i < 4; i ++) {
- edab.loc = i;
- tsdissolve(edab);
- edbc.loc = i;
- tsdissolve(edbc);
- }
- if (abdsh.sh != dummysh) {
- edab.loc = 2;
- tsbond(edab, abdsh);
- }
- if (baesh.sh != dummysh) {
- edab.loc = 3;
- tsbond(edab, baesh);
- }
- if (bcdsh.sh != dummysh) {
- edbc.loc = 2;
- tsbond(edbc, bcdsh);
- }
- if (cbesh.sh != dummysh) {
- edbc.loc = 3;
- tsbond(edbc, cbesh);
- }
- if (cadsh.sh != dummysh) {
- edca.loc = 2;
- tsbond(edca, cadsh);
- }
- if (acesh.sh != dummysh) {
- edca.loc = 3;
- tsbond(edca, acesh);
- }
- } else if (checksubsegs) {
- for (i = 0; i < 6; i++) {
- edab.tet[8 + i] = (tetrahedron) dummysh;
- }
- for (i = 0; i < 6; i++) {
- edbc.tet[8 + i] = (tetrahedron) dummysh;
- }
- edab.loc = edab.ver = 0;
- edbc.loc = edab.ver = 0;
- edca.loc = edab.ver = 0;
- // Operate in tet edab (5 edges).
- enext(edab, worktet);
- tssbond1(worktet, adseg);
- enext2(edab, worktet);
- tssbond1(worktet, aeseg);
- fnext(edab, worktet);
- enextself(worktet);
- tssbond1(worktet, bdseg);
- enextself(worktet);
- tssbond1(worktet, beseg);
- enextfnext(edab, worktet);
- enextself(worktet);
- tssbond1(worktet, abseg);
- // Operate in tet edbc (5 edges)
- enext(edbc, worktet);
- tssbond1(worktet, bdseg);
- enext2(edbc, worktet);
- tssbond1(worktet, beseg);
- fnext(edbc, worktet);
- enextself(worktet);
- tssbond1(worktet, cdseg);
- enextself(worktet);
- tssbond1(worktet, ceseg);
- enextfnext(edbc, worktet);
- enextself(worktet);
- tssbond1(worktet, bcseg);
- // Operate in tet edca (5 edges)
- enext(edca, worktet);
- tssbond1(worktet, cdseg);
- enext2(edca, worktet);
- tssbond1(worktet, ceseg);
- fnext(edca, worktet);
- enextself(worktet);
- tssbond1(worktet, adseg);
- enextself(worktet);
- tssbond1(worktet, aeseg);
- enextfnext(edca, worktet);
- enextself(worktet);
- tssbond1(worktet, caseg);
- }
-
- edab.loc = 0;
- edbc.loc = 0;
- edca.loc = 0;
- if (b->verbose > 3) {
- printf(" Updating edab ");
- printtet(&edab);
- printf(" Updating edbc ");
- printtet(&edbc);
- printf(" Creating edca ");
- printtet(&edca);
- }
-
- if (flipqueue != (queue *) NULL) {
- enextfnext(edab, abdcasing);
- enqueueflipface(abdcasing, flipqueue);
- enext2fnext(edab, baecasing);
- enqueueflipface(baecasing, flipqueue);
- enextfnext(edbc, bcdcasing);
- enqueueflipface(bcdcasing, flipqueue);
- enext2fnext(edbc, cbecasing);
- enqueueflipface(cbecasing, flipqueue);
- enextfnext(edca, cadcasing);
- enqueueflipface(cadcasing, flipqueue);
- enext2fnext(edca, acecasing);
- enqueueflipface(acecasing, flipqueue);
- }
-
- // Save a live handle in 'recenttet'.
- recenttet = edbc;
- // Set the return handle be edab.
- *flipface = edab;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// flip32() Perform a 3-to-2 flip. //
-// //
-// On input, 'flipface' represents the face will be flipped. Let it is eda, //
-// where edge ed is locally non-convex. Three tetrahedra sharing ed are edab,//
-// edbc, and edca. ed is not a subsegment. //
-// //
-// A 3-to-2 flip is to change the three tetrahedra edab, edbc, and edca into //
-// another two tetrahedra abcd and bace. As a result, the edge ed has been //
-// removed and the face abc has been created. //
-// //
-// On completion, 'flipface' returns abcd. If 'flipqueue' is not NULL, all //
-// possibly non-Delaunay faces are added into it. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::flip32(triface* flipface, queue* flipqueue)
-{
- triface edab, edbc, edca; // Old configuration.
- triface oldabd, oldbcd, oldcad;
- triface abdcasing, bcdcasing, cadcasing;
- triface oldbae, oldcbe, oldace;
- triface baecasing, cbecasing, acecasing;
- triface worktet;
- face abdsh, bcdsh, cadsh;
- face baesh, cbesh, acesh;
- face abseg, bcseg, caseg; // The nine segs on the CH.
- face adseg, bdseg, cdseg;
- face aeseg, beseg, ceseg;
- triface abcd, bace; // New configuration.
- point pa, pb, pc, pd, pe;
- int i;
-
- edab = *flipface;
- adjustedgering(edab, CCW);
- pa = apex(edab);
- pb = oppo(edab);
- pd = dest(edab);
- pe = org(edab);
- fnext(edab, edbc);
- symself(edbc);
- edbc.ver = 0;
- for (i = 0; (i < 3) && (org(edbc) != pe); i++) {
- enextself(edbc);
- }
- pc = oppo(edbc);
- fnext(edbc, edca);
- symself(edca);
- edca.ver = 0;
- for (i = 0; (i < 3) && (org(edca) != pe); i++) {
- enextself(edca);
- }
-
- if (b->verbose > 2) {
- printf(" Do T32 on edge (%d, %d) %d, %d, %d.\n", pointmark(pe),
- pointmark(pd), pointmark(pa), pointmark(pb), pointmark(pc));
- }
- flip32s++;
-
- // Storing the old configuration outside the convex hull.
- enextfnext(edab, oldabd);
- enext2fnext(edab, oldbae);
- enextfnext(edbc, oldbcd);
- enext2fnext(edbc, oldcbe);
- enextfnext(edca, oldcad);
- enext2fnext(edca, oldace);
- sym(oldabd, abdcasing);
- sym(oldbcd, bcdcasing);
- sym(oldcad, cadcasing);
- sym(oldbae, baecasing);
- sym(oldcbe, cbecasing);
- sym(oldace, acecasing);
- if (checksubfaces) {
- tspivot(oldabd, abdsh);
- tspivot(oldbcd, bcdsh);
- tspivot(oldcad, cadsh);
- tspivot(oldbae, baesh);
- tspivot(oldcbe, cbesh);
- tspivot(oldace, acesh);
- } else if (checksubsegs) {
- enext(edab, worktet);
- tsspivot1(worktet, adseg);
- enext2(edab, worktet);
- tsspivot1(worktet, aeseg);
- enext(edbc, worktet);
- tsspivot1(worktet, bdseg);
- enext2(edbc, worktet);
- tsspivot1(worktet, beseg);
- enext(edca, worktet);
- tsspivot1(worktet, cdseg);
- enext2(edca, worktet);
- tsspivot1(worktet, ceseg);
- enextfnext(edab, worktet);
- enextself(worktet);
- tsspivot1(worktet, abseg);
- enextfnext(edbc, worktet);
- enextself(worktet);
- tsspivot1(worktet, bcseg);
- enextfnext(edca, worktet);
- enextself(worktet);
- tsspivot1(worktet, caseg);
- }
-
- // Creating the new configuration inside the convex hull.
- abcd.tet = edab.tet; // Update edab to be abcd.
- setorg (abcd, pa);
- setdest(abcd, pb);
- setapex(abcd, pc);
- setoppo(abcd, pd);
- bace.tet = edbc.tet; // Update edbc to be bace.
- setorg (bace, pb);
- setdest(bace, pa);
- setapex(bace, pc);
- setoppo(bace, pe);
- // Dealloc a redundant tetrahedron (edca).
- tetrahedrondealloc(edca.tet);
-
- // Clear the old bonds in abcd (was edab) and bace (was edbc).
- for (i = 0; i < 4; i ++) {
- abcd.tet[i] = (tetrahedron) dummytet;
- }
- for (i = 0; i < 4; i ++) {
- bace.tet[i] = (tetrahedron) dummytet;
- }
- // Bond the inside face of the convex hull.
- abcd.loc = 0;
- bace.loc = 0;
- bond(abcd, bace);
- // Bond the outside faces of the convex hull.
- abcd.loc = 1;
- bond(abcd, abdcasing);
- abcd.loc = 2;
- bond(abcd, bcdcasing);
- abcd.loc = 3;
- bond(abcd, cadcasing);
- bace.loc = 1;
- bond(bace, baecasing);
- bace.loc = 3;
- bond(bace, cbecasing);
- bace.loc = 2;
- bond(bace, acecasing);
- if (checksubfaces) {
- // Clear old bonds in abcd(was edab) and bace(was edbc).
- for (i = 0; i < 4; i ++) {
- abcd.tet[8 + i] = (tetrahedron) dummysh;
- }
- for (i = 0; i < 4; i ++) {
- bace.tet[8 + i] = (tetrahedron) dummysh;
- }
- if (abdsh.sh != dummysh) {
- abcd.loc = 1;
- tsbond(abcd, abdsh);
- }
- if (bcdsh.sh != dummysh) {
- abcd.loc = 2;
- tsbond(abcd, bcdsh);
- }
- if (cadsh.sh != dummysh) {
- abcd.loc = 3;
- tsbond(abcd, cadsh);
- }
- if (baesh.sh != dummysh) {
- bace.loc = 1;
- tsbond(bace, baesh);
- }
- if (cbesh.sh != dummysh) {
- bace.loc = 3;
- tsbond(bace, cbesh);
- }
- if (acesh.sh != dummysh) {
- bace.loc = 2;
- tsbond(bace, acesh);
- }
- } else if (checksubsegs) {
- for (i = 0; i < 6; i++) {
- abcd.tet[8 + i] = (tetrahedron) dummysh;
- }
- for (i = 0; i < 6; i++) {
- bace.tet[8 + i] = (tetrahedron) dummysh;
- }
- abcd.loc = abcd.ver = 0;
- bace.loc = bace.ver = 0;
- tssbond1(abcd, abseg); // 1
- enext(abcd, worktet);
- tssbond1(worktet, bcseg); // 2
- enext2(abcd, worktet);
- tssbond1(worktet, caseg); // 3
- fnext(abcd, worktet);
- enext2self(worktet);
- tssbond1(worktet, adseg); // 4
- enextfnext(abcd, worktet);
- enext2self(worktet);
- tssbond1(worktet, bdseg); // 5
- enext2fnext(abcd, worktet);
- enext2self(worktet);
- tssbond1(worktet, cdseg); // 6
- tssbond1(bace, abseg);
- enext2(bace, worktet);
- tssbond1(worktet, bcseg);
- enext(bace, worktet);
- tssbond1(worktet, caseg);
- fnext(bace, worktet);
- enextself(worktet);
- tssbond1(worktet, aeseg); // 7
- enext2fnext(bace, worktet);
- enextself(worktet);
- tssbond1(worktet, beseg); // 8
- enextfnext(bace, worktet);
- enextself(worktet);
- tssbond1(worktet, ceseg); // 9
- }
-
- abcd.loc = 0;
- bace.loc = 0;
- if (b->verbose > 3) {
- printf(" Updating abcd ");
- printtet(&abcd);
- printf(" Updating bace ");
- printtet(&bace);
- printf(" Deleting edca ");
- // printtet(&edca);
- }
-
- if (flipqueue != (queue *) NULL) {
- fnext(abcd, abdcasing);
- enqueueflipface(abdcasing, flipqueue);
- fnext(bace, baecasing);
- enqueueflipface(baecasing, flipqueue);
- enextfnext(abcd, bcdcasing);
- enqueueflipface(bcdcasing, flipqueue);
- enextfnext(bace, cbecasing);
- enqueueflipface(cbecasing, flipqueue);
- enext2fnext(abcd, cadcasing);
- enqueueflipface(cadcasing, flipqueue);
- enext2fnext(bace, acecasing);
- enqueueflipface(acecasing, flipqueue);
- }
-
- // Save a live handle in 'recenttet'.
- recenttet = abcd;
- // Set the return handle be abcd.
- *flipface = abcd;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// flip22() Perform a 2-to-2 (or 4-to-4) flip. //
-// //
-// On input, 'flipface' represents the face will be flipped. Let it is abe, //
-// ab is the flipable edge, the two tetrahedra sharing abe are abce and bade,//
-// hence a, b, c and d are coplanar. If abc, bad are interior faces, the two //
-// tetrahedra opposite to e are bacf and abdf. ab is not a subsegment. //
-// //
-// A 2-to-2 flip is to change two tetrahedra abce and bade into another two //
-// tetrahedra dcae and cdbe. If bacf and abdf exist, they're changed to cdaf //
-// and dcbf, thus a 4-to-4 flip. As a result, two or four tetrahedra have //
-// rotated counterclockwise (using right-hand rule with thumb points to e): //
-// abce->dcae, bade->cdbe, and bacf->cdaf, abdf->dcbf. //
-// //
-// If abc and bad are subfaces, a 2-to-2 flip is performed simultaneously by //
-// calling routine flip22sub(), hence abc->dca, bad->cdb. The edge rings of //
-// the flipped subfaces dca and cdb have the same orientation as abc and bad.//
-// Hence, they have the same orientation as other subfaces of the facet with //
-// respect to the lift point of this facet. //
-// //
-// On completion, 'flipface' holds edge dc of tetrahedron dcae. 'flipqueue' //
-// contains all possibly non-Delaunay faces if it is not NULL. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::flip22(triface* flipface, queue* flipqueue)
-{
- triface abce, bade;
- triface oldbce, oldcae, oldade, olddbe;
- triface bcecasing, caecasing, adecasing, dbecasing;
- face bcesh, caesh, adesh, dbesh;
- triface bacf, abdf;
- triface oldacf, oldcbf, oldbdf, olddaf;
- triface acfcasing, cbfcasing, bdfcasing, dafcasing;
- triface worktet;
- face acfsh, cbfsh, bdfsh, dafsh;
- face abc, bad;
- face adseg, dbseg, bcseg, caseg; // Coplanar segs.
- face aeseg, deseg, beseg, ceseg; // Above segs.
- face afseg, dfseg, bfseg, cfseg; // Below segs.
- point pa, pb, pc, pd, pe, pf;
- int mirrorflag, i;
-
- adjustedgering(*flipface, CCW); // 'flipface' is bae.
- fnext(*flipface, abce);
- esymself(abce);
- adjustedgering(*flipface, CW); // 'flipface' is abe.
- fnext(*flipface, bade);
-#ifdef SELF_CHECK
- assert(bade.tet != dummytet);
-#endif
- esymself(bade);
- pa = org(abce);
- pb = dest(abce);
- pc = apex(abce);
- pd = apex(bade);
- pe = oppo(bade);
-#ifdef SELF_CHECK
- assert(oppo(abce) == pe);
-#endif
- sym(abce, bacf);
- mirrorflag = bacf.tet != dummytet;
- if (mirrorflag) {
- // findedge(&bacf, pb, pa);
- bacf.ver = 0;
- for (i = 0; (i < 3) && (org(bacf) != pb); i++) {
- enextself(bacf);
- }
- sym(bade, abdf);
-#ifdef SELF_CHECK
- assert(abdf.tet != dummytet);
-#endif
- // findedge(&abdf, pa, pb);
- abdf.ver = 0;
- for (i = 0; (i < 3) && (org(abdf) != pa); i++) {
- enextself(abdf);
- }
- pf = oppo(bacf);
-#ifdef SELF_CHECK
- assert(oppo(abdf) == pf);
-#endif
- }
-
- if (b->verbose > 2) {
- printf(" Do %s on edge (%d, %d).\n", mirrorflag ? "T44" : "T22",
- pointmark(pa), pointmark(pb));
- }
- mirrorflag ? flip44s++ : flip22s++;
-
- // Save the old configuration at the convex hull.
- enextfnext(abce, oldbce);
- enext2fnext(abce, oldcae);
- enextfnext(bade, oldade);
- enext2fnext(bade, olddbe);
- sym(oldbce, bcecasing);
- sym(oldcae, caecasing);
- sym(oldade, adecasing);
- sym(olddbe, dbecasing);
- if (checksubfaces) {
- tspivot(oldbce, bcesh);
- tspivot(oldcae, caesh);
- tspivot(oldade, adesh);
- tspivot(olddbe, dbesh);
- tspivot(abce, abc);
- tspivot(bade, bad);
- } else if (checksubsegs) {
- // Coplanar segs: a->d->b->c.
- enext(bade, worktet);
- tsspivot1(worktet, adseg);
- enext2(bade, worktet);
- tsspivot1(worktet, dbseg);
- enext(abce, worktet);
- tsspivot1(worktet, bcseg);
- enext2(abce, worktet);
- tsspivot1(worktet, caseg);
- // Above segs: a->e, d->e, b->e, c->e.
- fnext(bade, worktet);
- enextself(worktet);
- tsspivot1(worktet, aeseg);
- enextfnext(bade, worktet);
- enextself(worktet);
- tsspivot1(worktet, deseg);
- enext2fnext(bade, worktet);
- enextself(worktet);
- tsspivot1(worktet, beseg);
- enextfnext(abce, worktet);
- enextself(worktet);
- tsspivot1(worktet, ceseg);
- }
- if (mirrorflag) {
- enextfnext(bacf, oldacf);
- enext2fnext(bacf, oldcbf);
- enextfnext(abdf, oldbdf);
- enext2fnext(abdf, olddaf);
- sym(oldacf, acfcasing);
- sym(oldcbf, cbfcasing);
- sym(oldbdf, bdfcasing);
- sym(olddaf, dafcasing);
- if (checksubfaces) {
- tspivot(oldacf, acfsh);
- tspivot(oldcbf, cbfsh);
- tspivot(oldbdf, bdfsh);
- tspivot(olddaf, dafsh);
- } else if (checksubsegs) {
- // Below segs: a->f, d->f, b->f, c->f.
- fnext(abdf, worktet);
- enext2self(worktet);
- tsspivot1(worktet, afseg);
- enext2fnext(abdf, worktet);
- enext2self(worktet);
- tsspivot1(worktet, dfseg);
- enextfnext(abdf, worktet);
- enext2self(worktet);
- tsspivot1(worktet, bfseg);
- enextfnext(bacf, worktet);
- enextself(worktet);
- tsspivot1(worktet, cfseg);
- }
- }
-
- // Rotate abce, bade one-quarter turn counterclockwise.
- bond(oldbce, caecasing);
- bond(oldcae, adecasing);
- bond(oldade, dbecasing);
- bond(olddbe, bcecasing);
- if (checksubfaces) {
- // Check for subfaces and rebond them to the rotated tets.
- if (caesh.sh == dummysh) {
- tsdissolve(oldbce);
- } else {
- tsbond(oldbce, caesh);
- }
- if (adesh.sh == dummysh) {
- tsdissolve(oldcae);
- } else {
- tsbond(oldcae, adesh);
- }
- if (dbesh.sh == dummysh) {
- tsdissolve(oldade);
- } else {
- tsbond(oldade, dbesh);
- }
- if (bcesh.sh == dummysh) {
- tsdissolve(olddbe);
- } else {
- tsbond(olddbe, bcesh);
- }
- } else if (checksubsegs) {
- // 5 edges in abce are changed.
- enext(abce, worktet); // fit b->c into c->a.
- if (caseg.sh == dummysh) {
- tssdissolve1(worktet);
- } else {
- tssbond1(worktet, caseg);
- }
- enext2(abce, worktet); // fit c->a into a->d.
- if (adseg.sh == dummysh) {
- tssdissolve1(worktet);
- } else {
- tssbond1(worktet, adseg);
- }
- fnext(abce, worktet); // fit b->e into c->e.
- enextself(worktet);
- if (ceseg.sh == dummysh) {
- tssdissolve1(worktet);
- } else {
- tssbond1(worktet, ceseg);
- }
- enextfnext(abce, worktet); // fit c->e into a->e.
- enextself(worktet);
- if (aeseg.sh == dummysh) {
- tssdissolve1(worktet);
- } else {
- tssbond1(worktet, aeseg);
- }
- enext2fnext(abce, worktet); // fit a->e into d->e.
- enextself(worktet);
- if (deseg.sh == dummysh) {
- tssdissolve1(worktet);
- } else {
- tssbond1(worktet, deseg);
- }
- // 5 edges in bade are changed.
- enext(bade, worktet); // fit a->d into d->b.
- if (dbseg.sh == dummysh) {
- tssdissolve1(worktet);
- } else {
- tssbond1(worktet, dbseg);
- }
- enext2(bade, worktet); // fit d->b into b->c.
- if (bcseg.sh == dummysh) {
- tssdissolve1(worktet);
- } else {
- tssbond1(worktet, bcseg);
- }
- fnext(bade, worktet); // fit a->e into d->e.
- enextself(worktet);
- if (deseg.sh == dummysh) {
- tssdissolve1(worktet);
- } else {
- tssbond1(worktet, deseg);
- }
- enextfnext(bade, worktet); // fit d->e into b->e.
- enextself(worktet);
- if (beseg.sh == dummysh) {
- tssdissolve1(worktet);
- } else {
- tssbond1(worktet, beseg);
- }
- enext2fnext(bade, worktet); // fit b->e into c->e.
- enextself(worktet);
- if (ceseg.sh == dummysh) {
- tssdissolve1(worktet);
- } else {
- tssbond1(worktet, ceseg);
- }
- }
- if (mirrorflag) {
- // Rotate bacf, abdf one-quarter turn counterclockwise.
- bond(oldcbf, acfcasing);
- bond(oldacf, dafcasing);
- bond(olddaf, bdfcasing);
- bond(oldbdf, cbfcasing);
- if (checksubfaces) {
- // Check for subfaces and rebond them to the rotated tets.
- if (acfsh.sh == dummysh) {
- tsdissolve(oldcbf);
- } else {
- tsbond(oldcbf, acfsh);
- }
- if (dafsh.sh == dummysh) {
- tsdissolve(oldacf);
- } else {
- tsbond(oldacf, dafsh);
- }
- if (bdfsh.sh == dummysh) {
- tsdissolve(olddaf);
- } else {
- tsbond(olddaf, bdfsh);
- }
- if (cbfsh.sh == dummysh) {
- tsdissolve(oldbdf);
- } else {
- tsbond(oldbdf, cbfsh);
- }
- } else if (checksubsegs) {
- // 5 edges in bacf are changed.
- enext2(bacf, worktet); // fit b->c into c->a.
- if (caseg.sh == dummysh) {
- tssdissolve1(worktet);
- } else {
- tssbond1(worktet, caseg);
- }
- enext(bacf, worktet); // fit c->a into a->d.
- if (adseg.sh == dummysh) {
- tssdissolve1(worktet);
- } else {
- tssbond1(worktet, adseg);
- }
- fnext(bacf, worktet); // fit b->f into c->f.
- enext2self(worktet);
- if (cfseg.sh == dummysh) {
- tssdissolve1(worktet);
- } else {
- tssbond1(worktet, cfseg);
- }
- enext2fnext(bacf, worktet); // fit c->f into a->f.
- enext2self(worktet);
- if (afseg.sh == dummysh) {
- tssdissolve1(worktet);
- } else {
- tssbond1(worktet, afseg);
- }
- enextfnext(bacf, worktet); // fit a->f into d->f.
- enext2self(worktet);
- if (dfseg.sh == dummysh) {
- tssdissolve1(worktet);
- } else {
- tssbond1(worktet, dfseg);
- }
- // 5 edges in abdf are changed.
- enext2(abdf, worktet); // fit a->d into d->b.
- if (dbseg.sh == dummysh) {
- tssdissolve1(worktet);
- } else {
- tssbond1(worktet, dbseg);
- }
- enext(abdf, worktet); // fit d->b into b->c.
- if (bcseg.sh == dummysh) {
- tssdissolve1(worktet);
- } else {
- tssbond1(worktet, bcseg);
- }
- fnext(abdf, worktet); // fit a->f into d->f.
- enext2self(worktet);
- if (dfseg.sh == dummysh) {
- tssdissolve1(worktet);
- } else {
- tssbond1(worktet, dfseg);
- }
- enext2fnext(abdf, worktet); // fit d->f into b->f.
- enext2self(worktet);
- if (bfseg.sh == dummysh) {
- tssdissolve1(worktet);
- } else {
- tssbond1(worktet, bfseg);
- }
- enextfnext(abdf, worktet); // fit b->f into c->f.
- enext2self(worktet);
- if (cfseg.sh == dummysh) {
- tssdissolve1(worktet);
- } else {
- tssbond1(worktet, cfseg);
- }
- }
- }
-
- // New vertex assignments for the rotated tetrahedra.
- setorg(abce, pd); // Update abce to dcae
- setdest(abce, pc);
- setapex(abce, pa);
- setorg(bade, pc); // Update bade to cdbe
- setdest(bade, pd);
- setapex(bade, pb);
- if (mirrorflag) {
- setorg(bacf, pc); // Update bacf to cdaf
- setdest(bacf, pd);
- setapex(bacf, pa);
- setorg(abdf, pd); // Update abdf to dcbf
- setdest(abdf, pc);
- setapex(abdf, pb);
- }
-
- // Are there subfaces need to be flipped?
- if (checksubfaces && abc.sh != dummysh) {
-#ifdef SELF_CHECK
- assert(bad.sh != dummysh);
-#endif
- // Adjust the edge be ab, so the rotation of subfaces is according with
- // the rotation of tetrahedra.
- findedge(&abc, pa, pb);
- // Flip an edge of two subfaces, ignore non-Delaunay edges.
- flip22sub(&abc, NULL);
- }
-
- if (b->verbose > 3) {
- printf(" Updating abce ");
- printtet(&abce);
- printf(" Updating bade ");
- printtet(&bade);
- if (mirrorflag) {
- printf(" Updating bacf ");
- printtet(&bacf);
- printf(" Updating abdf ");
- printtet(&abdf);
- }
- }
-
- if (flipqueue != (queue *) NULL) {
- enextfnext(abce, bcecasing);
- enqueueflipface(bcecasing, flipqueue);
- enext2fnext(abce, caecasing);
- enqueueflipface(caecasing, flipqueue);
- enextfnext(bade, adecasing);
- enqueueflipface(adecasing, flipqueue);
- enext2fnext(bade, dbecasing);
- enqueueflipface(dbecasing, flipqueue);
- if (mirrorflag) {
- enextfnext(bacf, acfcasing);
- enqueueflipface(acfcasing, flipqueue);
- enext2fnext(bacf, cbfcasing);
- enqueueflipface(cbfcasing, flipqueue);
- enextfnext(abdf, bdfcasing);
- enqueueflipface(bdfcasing, flipqueue);
- enext2fnext(abdf, dafcasing);
- enqueueflipface(dafcasing, flipqueue);
- }
- // The two new faces dcae (abce), cdbe (bade) may still not be locally
- // Delaunay, and may need be flipped (flip23). On the other hand, in
- // conforming Delaunay algorithm, two new subfaces dca (abc), and cdb
- // (bad) may be non-conforming Delaunay, they need be queued if they
- // are locally Delaunay but non-conforming Delaunay.
- enqueueflipface(abce, flipqueue);
- enqueueflipface(bade, flipqueue);
- }
-
- // Save a live handle in 'recenttet'.
- recenttet = abce;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// flip22sub() Perform a 2-to-2 flip on a subface edge. //
-// //
-// The flip edge is given by subface 'flipedge'. Let it is abc, where ab is //
-// the flipping edge. The other subface is bad, where a, b, c, d form a //
-// convex quadrilateral. ab is not a subsegment. //
-// //
-// A 2-to-2 subface flip is to change two subfaces abc and bad to another //
-// two subfaces dca and cdb. Hence, edge ab has been removed and dc becomes //
-// an edge. If a point e is above abc, this flip is equal to rotate abc and //
-// bad counterclockwise using right-hand rule with thumb points to e. It is //
-// important to know that the edge rings of the flipped subfaces dca and cdb //
-// are keeping the same orientation as their original subfaces. So they have //
-// the same orientation with respect to the lift point of this facet. //
-// //
-// During rotating, the face rings of the four edges bc, ca, ad, and de need //
-// be re-connected. If the edge is not a subsegment, then its face ring has //
-// only two faces, a sbond() will bond them together. If it is a subsegment, //
-// one should use sbond1() twice to bond two different handles to the rotat- //
-// ing subface, one is predecssor (-casin), another is successor (-casout). //
-// //
-// If 'flipqueue' is not NULL, it returns four edges bc, ca, ad, de, which //
-// may be non-Delaunay. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::flip22sub(face* flipedge, queue* flipqueue)
-{
- face abc, bad;
- face oldbc, oldca, oldad, olddb;
- face bccasin, bccasout, cacasin, cacasout;
- face adcasin, adcasout, dbcasin, dbcasout;
- face bc, ca, ad, db;
- face spinsh;
- point pa, pb, pc, pd;
-
- abc = *flipedge;
- spivot(abc, bad);
- if (sorg(bad) != sdest(abc)) {
- sesymself(bad);
- }
- pa = sorg(abc);
- pb = sdest(abc);
- pc = sapex(abc);
- pd = sapex(bad);
-
- if (b->verbose > 2) {
- printf(" Flip sub edge (%d, %d).\n", pointmark(pa), pointmark(pb));
- }
-
- // Save the old configuration outside the quadrilateral.
- senext(abc, oldbc);
- senext2(abc, oldca);
- senext(bad, oldad);
- senext2(bad, olddb);
- // Get the outside connection. Becareful if there is a subsegment on the
- // quadrilateral, two casings (casin and casout) are needed to save for
- // keeping the face link.
- spivot(oldbc, bccasout);
- sspivot(oldbc, bc);
- if (bc.sh != dummysh) {
- // 'bc' is a subsegment.
- if (bccasout.sh != dummysh) {
- if (oldbc.sh != bccasout.sh) {
- // 'oldbc' is not self-bonded.
- spinsh = bccasout;
- do {
- bccasin = spinsh;
- spivotself(spinsh);
- } while (spinsh.sh != oldbc.sh);
- } else {
- bccasout.sh = dummysh;
- }
- }
- ssdissolve(oldbc);
- }
- spivot(oldca, cacasout);
- sspivot(oldca, ca);
- if (ca.sh != dummysh) {
- // 'ca' is a subsegment.
- if (cacasout.sh != dummysh) {
- if (oldca.sh != cacasout.sh) {
- // 'oldca' is not self-bonded.
- spinsh = cacasout;
- do {
- cacasin = spinsh;
- spivotself(spinsh);
- } while (spinsh.sh != oldca.sh);
- } else {
- cacasout.sh = dummysh;
- }
- }
- ssdissolve(oldca);
- }
- spivot(oldad, adcasout);
- sspivot(oldad, ad);
- if (ad.sh != dummysh) {
- // 'ad' is a subsegment.
- if (adcasout.sh != dummysh) {
- if (oldad.sh != adcasout.sh) {
- // 'adcasout' is not self-bonded.
- spinsh = adcasout;
- do {
- adcasin = spinsh;
- spivotself(spinsh);
- } while (spinsh.sh != oldad.sh);
- } else {
- adcasout.sh = dummysh;
- }
- }
- ssdissolve(oldad);
- }
- spivot(olddb, dbcasout);
- sspivot(olddb, db);
- if (db.sh != dummysh) {
- // 'db' is a subsegment.
- if (dbcasout.sh != dummysh) {
- if (olddb.sh != dbcasout.sh) {
- // 'dbcasout' is not self-bonded.
- spinsh = dbcasout;
- do {
- dbcasin = spinsh;
- spivotself(spinsh);
- } while (spinsh.sh != olddb.sh);
- } else {
- dbcasout.sh = dummysh;
- }
- }
- ssdissolve(olddb);
- }
-
- // Rotate abc and bad one-quarter turn counterclockwise.
- if (ca.sh != dummysh) {
- if (cacasout.sh != dummysh) {
- sbond1(cacasin, oldbc);
- sbond1(oldbc, cacasout);
- } else {
- // Bond 'oldbc' to itself.
- sbond(oldbc, oldbc);
- // Make sure that dummysh always correctly bonded.
- dummysh[0] = sencode(oldbc);
- }
- ssbond(oldbc, ca);
- } else {
- sbond(oldbc, cacasout);
- }
- if (ad.sh != dummysh) {
- if (adcasout.sh != dummysh) {
- sbond1(adcasin, oldca);
- sbond1(oldca, adcasout);
- } else {
- // Bond 'oldca' to itself.
- sbond(oldca, oldca);
- // Make sure that dummysh always correctly bonded.
- dummysh[0] = sencode(oldca);
- }
- ssbond(oldca, ad);
- } else {
- sbond(oldca, adcasout);
- }
- if (db.sh != dummysh) {
- if (dbcasout.sh != dummysh) {
- sbond1(dbcasin, oldad);
- sbond1(oldad, dbcasout);
- } else {
- // Bond 'oldad' to itself.
- sbond(oldad, oldad);
- // Make sure that dummysh always correctly bonded.
- dummysh[0] = sencode(oldad);
- }
- ssbond(oldad, db);
- } else {
- sbond(oldad, dbcasout);
- }
- if (bc.sh != dummysh) {
- if (bccasout.sh != dummysh) {
- sbond1(bccasin, olddb);
- sbond1(olddb, bccasout);
- } else {
- // Bond 'olddb' to itself.
- sbond(olddb, olddb);
- // Make sure that dummysh always correctly bonded.
- dummysh[0] = sencode(olddb);
- }
- ssbond(olddb, bc);
- } else {
- sbond(olddb, bccasout);
- }
-
- // New vertex assignments for the rotated subfaces.
- setsorg(abc, pd); // Update abc to dca.
- setsdest(abc, pc);
- setsapex(abc, pa);
- setsorg(bad, pc); // Update bad to cdb.
- setsdest(bad, pd);
- setsapex(bad, pb);
-
- if (flipqueue != (queue *) NULL) {
- enqueueflipedge(bccasout, flipqueue);
- enqueueflipedge(cacasout, flipqueue);
- enqueueflipedge(adcasout, flipqueue);
- enqueueflipedge(dbcasout, flipqueue);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// flip() Flips non-locally Delaunay faces in flipqueue until it is empty.//
-// //
-// Assumpation: Current tetrahedralization is non-Delaunay after inserting //
-// a point or performing a flip operation, all possibly non-Delaunay faces //
-// are in 'flipqueue'. //
-// //
-// If 'plastflip' is not NULL, it is used to return a stack of recently //
-// flipped faces. This stack will be used to reverse the flips done in this //
-// routine later for removing a newly inserted point because it encroaches //
-// any subfaces or subsegments. //
-// //
-// The return value is the total number of flips done during this invocation.//
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-long tetgenmesh::flip(queue* flipqueue, badface **plastflip)
-{
- badface *qface, *newflip;
- triface flipface, symface;
- point pa, pb, pc, pd, pe;
- enum fliptype fc;
- REAL sign, bakepsilon;
- long flipcount, maxfaces;
- int epscount, fcount;
- int ia, ib, ic, id, ie;
-
- if (b->verbose > 1) {
- printf(" Do flipface queue: %ld faces.\n", flipqueue->len());
- }
-
- flipcount = flip23s + flip32s + flip22s + flip44s;
- if (checksubfaces) {
- maxfaces = (4l * tetrahedrons->items + hullsize) / 2l;
- fcount = 0;
- }
-
- if (plastflip != (badface **) NULL) {
- // Initialize the stack of the flip sequence.
- flipstackers->restart();
- *plastflip = (badface *) NULL;
- }
-
- // Loop until the queue is empty.
- while (!flipqueue->empty()) {
- qface = (badface *) flipqueue->pop();
- flipface = qface->tt;
- if (isdead(&flipface)) continue;
- sym(flipface, symface);
- // Only do check when the adjacent tet exists and it's not a "fake" tet.
- if ((symface.tet != dummytet) && (oppo(symface) == qface->foppo)) {
- // For positive orientation that insphere() test requires.
- adjustedgering(flipface, CW);
- pa = org(flipface);
- pb = dest(flipface);
- pc = apex(flipface);
- pd = oppo(flipface);
- pe = oppo(symface);
- if (symbolic) {
- ia = pointmark(pa);
- ib = pointmark(pb);
- ic = pointmark(pc);
- id = pointmark(pd);
- ie = pointmark(pe);
- sign = insphere_sos(pa, pb, pc, pd, pe, ia, ib, ic, id, ie);
- assert(sign != 0.0);
- } else {
- sign = insphere(pa, pb, pc, pd, pe);
- }
- } else {
- sign = -1.0; // A hull face is locally Delaunay.
- }
- if (sign > 0.0) {
- // 'flipface' is non-locally Delaunay, try to flip it.
- if (checksubfaces) {
- fcount++;
- bakepsilon = b->epsilon;
- epscount = 0;
- while (epscount < 32) {
- fc = categorizeface(flipface);
- if (fc == N40) {
- b->epsilon *= 1e-1;
- epscount++;
- continue;
- }
- break;
- }
- b->epsilon = bakepsilon;
- if (epscount >= 32) {
- if (b->verbose > 0) {
- printf("Warning: Can't flip a degenerate tetrahedron.\n");
- }
- fc = N40;
- }
- } else {
- fc = categorizeface(flipface);
-#ifdef SELF_CHECK
- assert(fc != N40);
-#endif
- }
- switch (fc) {
- // The following face types are flipable.
- case T44:
- case T22:
- flip22(&flipface, flipqueue);
- break;
- case T23:
- flip23(&flipface, flipqueue);
- break;
- case T32:
- flip32(&flipface, flipqueue);
- break;
- // The following face types are unflipable.
- case N32:
- break;
- case FORBIDDENFACE:
- break;
- case FORBIDDENEDGE:
- break;
- // This case is only possible when the domain is nonconvex.
- case N40:
- // assert(nonconvex);
- break;
- }
- if (plastflip != (badface **) NULL) {
- if ((fc == T44) || (fc == T22) || (fc == T23) || (fc == T32)) {
- // Push the flipped face into stack.
- newflip = (badface *) flipstackers->alloc();
- newflip->tt = flipface;
- newflip->key = (REAL) fc;
- newflip->forg = org(flipface);
- newflip->fdest = dest(flipface);
- newflip->fapex = apex(flipface);
- newflip->previtem = *plastflip;
- *plastflip = newflip;
- }
- }
- }
- }
-
- flipcount = flip23s + flip32s + flip22s + flip44s - flipcount;
- if (b->verbose > 1) {
- printf(" %ld flips.\n", flipcount);
- }
-
- return flipcount;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// lawson() Flip locally non-Delaunay faces by Lawson's algorithm. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-long tetgenmesh::lawson(list *misseglist, queue* flipqueue)
-{
- badface *qface, *misseg;
- triface flipface, symface;
- triface starttet, spintet;
- face checksh, checkseg;
- point pa, pb, pc, pd, pe;
- point swappt;
- REAL sign, ori;
- long flipcount;
- int ia, ib, ic, id, ie;
- int hitbdry, i;
-
- if (b->verbose > 1) {
- printf(" Do flipface queue: %ld faces.\n", flipqueue->len());
- }
- flipcount = flip23s + flip32s + flip22s + flip44s;
-
- // Go through the stack of possible flips and decide whether to do them.
- // Note that during the loop new possible flips will be pushed onto
- // this stack, while they popped in this loop.
- while (!flipqueue->empty()) {
- qface = (badface *) flipqueue->pop();
- flipface = qface->tt;
- // Check if tet has already been flipped out of existence.
- if (!isdead(&flipface)) {
- sym(flipface, symface);
- // Check if this tet is the same as the one which was stacked.
- if ((symface.tet != dummytet) && (oppo(symface) == qface->foppo)) {
- flipface.ver = 0; // Select the CCW ring.
- pa = org(flipface);
- pb = dest(flipface);
- pc = apex(flipface);
- pd = oppo(flipface);
- pe = oppo(symface);
- if (symbolic) {
- ia = pointmark(pa);
- ib = pointmark(pb);
- ic = pointmark(pc);
- id = pointmark(pd);
- ie = pointmark(pe);
- sign = insphere_sos(pb, pa, pc, pd, pe, ib, ia, ic, id, ie);
- } else {
- sign = insphere(pb, pa, pc, pd, pe);
- }
- if (sign > 0.0) {
- for (i = 0; i < 3; i++) {
- ori = orient3d(pa, pb, pd, pe);
- if (ori > 0.0) {
- // Goto and check the next edge.
- swappt = pa;
- pa = pb;
- pb = pc;
- pc = swappt;
- enextself(flipface);
- } else {
- break; // either (ori < 0.0) or (ori == 0.0)
- }
- } // for (i = 0; ....)
- if (ori > 0.0) {
- // All three edges are convex, a 2-3 flip is possible.
- if (checksubfaces) {
- tspivot(flipface, checksh);
- if (checksh.sh != dummysh) {
- // A subface is not flipable.
- continue;
- }
- }
- flip23(&flipface, flipqueue);
- } else if (ori < 0.0) {
- // The edge (a, b) is non-convex, check for a 3-2 flip.
- fnext(flipface, symface);
- symself(symface);
- if (oppo(symface) == pe) {
- // Only three tets adjoining this edge.
- if (checksubfaces) {
- tsspivot(&flipface, &checkseg);
- if (checkseg.sh != dummysh) {
- // A subsegment is not flipable.
- continue;
- }
- } else if (checksubsegs) {
- tsspivot1(flipface, checkseg);
- if (checkseg.sh != dummysh) {
- if (b->verbose > 2) {
- printf(" Queuing missing segment (%d, %d).\n",
- pointmark(org(flipface)), pointmark(dest(flipface)));
- }
- misseg = (badface *) misseglist->append(NULL);
- misseg->ss = checkseg;
- misseg->forg = sorg(checkseg);
- misseg->fdest = sdest(checkseg);
- // Detach all tets having this seg.
- starttet = flipface;
- adjustedgering(starttet, CCW);
- fnextself(starttet);
- spintet = starttet;
- hitbdry = 0;
- do {
- tssdissolve1(spintet);
- if (!fnextself(spintet)) {
- hitbdry++;
- if (hitbdry < 2) {
- esym(starttet, spintet);
- if (!fnextself(spintet)) {
- hitbdry++;
- }
- }
- }
- } while ((apex(spintet) != apex(starttet)) && (hitbdry < 2));
- }
- } // if (checksubfaces)
- flip32(&flipface, flipqueue);
- }
- } else {
- // Four points (a, b, d, e) are coplanar.
- fnext(flipface, symface);
- if (fnextself(symface)) {
- // Check for a 4-4 flip.
- fnextself(symface);
- if (apex(symface) == pe) {
- if (checksubfaces) {
- tsspivot(&flipface, &checkseg);
- if (checkseg.sh != dummysh) {
- // A subsegment is not flippable.
- continue;
- }
- } else if (checksubsegs) {
- tsspivot1(flipface, checkseg);
- if (checkseg.sh != dummysh) {
- if (b->verbose > 2) {
- printf(" Queuing missing segment (%d, %d).\n",
- pointmark(org(flipface)), pointmark(dest(flipface)));
- }
- misseg = (badface *) misseglist->append(NULL);
- misseg->ss = checkseg;
- misseg->forg = sorg(checkseg);
- misseg->fdest = sdest(checkseg);
- // Detach all tets having this seg.
- starttet = flipface;
- adjustedgering(starttet, CCW);
- fnextself(starttet);
- spintet = starttet;
- hitbdry = 0;
- do {
- tssdissolve1(spintet);
- if (!fnextself(spintet)) {
- hitbdry++;
- if (hitbdry < 2) {
- esym(starttet, spintet);
- if (!fnextself(spintet)) {
- hitbdry++;
- }
- }
- }
- } while ((apex(spintet) != apex(starttet)) &&
- (hitbdry < 2));
- }
- } // if (checksubfaces)
- flip22(&flipface, flipqueue);
- }
- } else {
- // Check for a 2-2 flip.
- esym(flipface, symface);
- fnextself(symface);
- symself(symface);
- if (symface.tet == dummytet) {
- if (checksubfaces) {
- tsspivot(&flipface, &checkseg);
- if (checkseg.sh != dummysh) {
- // A subsegment is not flipable.
- continue;
- }
- } else if (checksubsegs) {
- tsspivot1(flipface, checkseg);
- if (checkseg.sh != dummysh) {
- if (b->verbose > 2) {
- printf(" Queuing missing segment (%d, %d).\n",
- pointmark(org(flipface)), pointmark(dest(flipface)));
- }
- misseg = (badface *) misseglist->append(NULL);
- misseg->ss = checkseg;
- misseg->forg = sorg(checkseg);
- misseg->fdest = sdest(checkseg);
- // Detach all tets having this seg.
- starttet = flipface;
- adjustedgering(starttet, CCW);
- fnextself(starttet);
- spintet = starttet;
- hitbdry = 0;
- do {
- tssdissolve1(spintet);
- if (!fnextself(spintet)) {
- hitbdry++;
- if (hitbdry < 2) {
- esym(starttet, spintet);
- if (!fnextself(spintet)) {
- hitbdry++;
- }
- }
- }
- } while ((apex(spintet) != apex(starttet)) &&
- (hitbdry < 2));
- }
- } // if (checksubfaces)
- flip22(&flipface, flipqueue);
- }
- }
- } // if (ori > 0.0)
- } // if (sign > 0.0)
- }
- } // !isdead(&qface->tt)
- } // while (!flipqueue->empty())
-
- flipcount = flip23s + flip32s + flip22s + flip44s - flipcount;
- if (b->verbose > 1) {
- printf(" %ld flips.\n", flipcount);
- }
- return flipcount;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// undoflip() Undo the most recent flip sequence induced by flip(). //
-// //
-// 'lastflip' is the stack of recently flipped faces. Walks through the list //
-// of flips, in the reverse of the order in which they were done, and undoes //
-// them. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::undoflip(badface *lastflip)
-{
- enum fliptype fc;
-
- while (lastflip != (badface *) NULL) {
- // Get the right flipped face.
- findface(&lastflip->tt, lastflip->forg, lastflip->fdest, lastflip->fapex);
- fc = (enum fliptype) (int) lastflip->key;
- switch (fc) {
- case T23:
- // The reverse operation of T23 is T32.
- flip32(&lastflip->tt, NULL);
- break;
- case T32:
- // The reverse operation of T32 is T23.
- flip23(&lastflip->tt, NULL);
- break;
- case T22:
- case T44:
- // The reverse operation of T22 or T44 is again T22 or T44.
- flip22(&lastflip->tt, NULL);
- break;
- default: // To omit compile warnings.
- break;
- }
- // Go on and process the next transformation.
- lastflip = lastflip->previtem;
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// flipsub() Flip non-Delaunay edges in a queue of (coplanar) subfaces. //
-// //
-// Assumpation: Current triangulation T contains non-Delaunay edges (after //
-// inserting a point or performing a flip). Non-Delaunay edges are queued in //
-// 'facequeue'. Returns the total number of flips done during this call. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-long tetgenmesh::flipsub(queue* flipqueue)
-{
- badface *qedge;
- face flipedge, symedge;
- face checkseg;
- point pa, pb, pc, pd;
- REAL vab[3], vac[3], vad[3];
- REAL dot1, dot2, lac, lad;
- REAL sign, ori;
- int edgeflips;
- int i;
-
- if (b->verbose > 1) {
- printf(" Start do edge queue: %ld edges.\n", flipqueue->len());
- }
-
- edgeflips = 0;
-
- while (!flipqueue->empty()) {
- qedge = (badface *) flipqueue->pop();
- flipedge = qedge->ss;
- if (flipedge.sh == dummysh) continue;
- if ((sorg(flipedge) != qedge->forg) ||
- (sdest(flipedge) != qedge->fdest)) continue;
- sspivot(flipedge, checkseg);
- if (checkseg.sh != dummysh) continue; // Can't flip a subsegment.
- spivot(flipedge, symedge);
- if (symedge.sh == dummysh) continue; // Can't flip a hull edge.
- pa = sorg(flipedge);
- pb = sdest(flipedge);
- pc = sapex(flipedge);
- pd = sapex(symedge);
- // Choose the triangle abc or abd as the base depending on the angle1
- // (Vac, Vab) and angle2 (Vad, Vab).
- for (i = 0; i < 3; i++) vab[i] = pb[i] - pa[i];
- for (i = 0; i < 3; i++) vac[i] = pc[i] - pa[i];
- for (i = 0; i < 3; i++) vad[i] = pd[i] - pa[i];
- dot1 = dot(vac, vab);
- dot2 = dot(vad, vab);
- dot1 *= dot1;
- dot2 *= dot2;
- lac = dot(vac, vac);
- lad = dot(vad, vad);
- if (lad * dot1 <= lac * dot2) {
- // angle1 is closer to 90 than angle2, choose abc (flipedge).
- abovepoint = facetabovepointarray[shellmark(flipedge)];
- if (abovepoint == (point) NULL) {
- getfacetabovepoint(&flipedge);
- }
- sign = insphere(pa, pb, pc, abovepoint, pd);
- ori = orient3d(pa, pb, pc, abovepoint);
- } else {
- // angle2 is closer to 90 than angle1, choose abd (symedge).
- abovepoint = facetabovepointarray[shellmark(symedge)];
- if (abovepoint == (point) NULL) {
- getfacetabovepoint(&symedge);
- }
- sign = insphere(pa, pb, pd, abovepoint, pc);
- ori = orient3d(pa, pb, pd, abovepoint);
- }
- // Correct the sign.
- sign = ori > 0.0 ? sign : -sign;
- if (sign > 0.0) {
- // Flip the non-Delaunay edge.
- flip22sub(&flipedge, flipqueue);
- edgeflips++;
- }
- }
-
- if (b->verbose > 1) {
- printf(" Total %d flips.\n", edgeflips);
- }
-
- return edgeflips;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// removetetbypeeloff() Remove a boundary tet by peeling it off. //
-// //
-// 'striptet' (abcd) is on boundary and can be removed by stripping it off. //
-// Let abc and bad are the external boundary faces. //
-// //
-// To strip 'abcd' from the mesh is to detach its two interal faces (dca and //
-// cdb) from their adjoining tets together with a 2-to-2 flip to transform //
-// two subfaces (abc and bad) into another two (dca and cdb). //
-// //
-// In mesh optimization. It is possible that ab is a segment and abcd is a //
-// sliver on the hull. Strip abcd will also delete the segment ab. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::removetetbypeeloff(triface *striptet)
-{
- triface abcd, badc;
- triface dcacasing, cdbcasing;
- face abc, bad;
- face abseg;
- REAL ang;
-
- abcd = *striptet;
- adjustedgering(abcd, CCW);
- // Get the casing tets at the internal sides.
- enextfnext(abcd, cdbcasing);
- enext2fnext(abcd, dcacasing);
- symself(cdbcasing);
- symself(dcacasing);
- // Do the neighboring tets exist? During optimization. It is possible
- // that the neighboring tets are already dead.
- if ((cdbcasing.tet == dummytet) || (dcacasing.tet == dummytet)) {
- // Do not strip this tet.
- return false;
- }
-
- // Are there subfaces?
- if (checksubfaces) {
- // Get the external subfaces abc, bad.
- fnext(abcd, badc);
- esymself(badc);
- tspivot(abcd, abc);
- tspivot(badc, bad);
- if (abc.sh != dummysh) {
- assert(bad.sh != dummysh);
- findedge(&abc, org(abcd), dest(abcd));
- findedge(&bad, org(badc), dest(badc));
- // Is ab a segment?
- sspivot(abc, abseg);
- if (abseg.sh != dummysh) {
- // Does a segment allow to be removed?
- if ((b->optlevel > 3) && (b->nobisect == 0)) {
- // Only remove this segment if the dihedal angle at ab is between
- // [b->maxdihedral-9, 180] (deg). This avoids mistakely fliping
- // ab when it has actually no big dihedral angle while cd has.
- ang = facedihedral(org(abcd), dest(abcd), apex(abcd), oppo(abcd));
- ang = ang * 180.0 / PI;
- if ((ang + 9.0) > b->maxdihedral) {
- if (b->verbose > 1) {
- printf(" Remove a segment during peeling.\n");
- }
- face prevseg, nextseg;
- // It is only shared by abc and bad (abcd is a tet).
- ssdissolve(abc);
- ssdissolve(bad);
- abseg.shver = 0;
- senext(abseg, nextseg);
- spivotself(nextseg);
- if (nextseg.sh != dummysh) {
- ssdissolve(nextseg);
- }
- senext2(abseg, prevseg);
- spivotself(prevseg);
- if (prevseg.sh != dummysh) {
- ssdissolve(prevseg);
- }
- shellfacedealloc(subsegs, abseg.sh);
- optcount[1]++;
- } else {
- return false;
- }
- } else {
- return false;
- }
- }
- // Do a 2-to-2 flip on abc and bad, transform abc->dca, bad->cdb.
- flip22sub(&abc, NULL);
- // The two internal faces become boundary faces.
- tsbond(cdbcasing, bad);
- tsbond(dcacasing, abc);
- }
- }
-
- // Detach abcd from the two internal faces.
- dissolve(cdbcasing);
- dissolve(dcacasing);
- // Delete abcd.
- tetrahedrondealloc(abcd.tet);
- return true;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// removeedgebyflip22() Remove an edge by a 2-to-2 (or 4-to-4) flip. //
-// //
-// 'abtetlist' contains n tets (n is 2 or 4) sharing edge ab, abtetlist[0] //
-// and abtetlist[1] are tets abec and abde, respectively (NOTE, both are in //
-// CW edge ring), where a, b, c, and d are coplanar. If n = 4, abtetlist[2] //
-// and abtetlist[3] are tets abfd and abcf, respectively. This routine uses //
-// flip22() to replace edge ab with cd, the surrounding tets are rotated. //
-// //
-// If 'key' != NULL. The old tets are replaced by the new tets only if the //
-// local mesh quality is improved. Current 'key' = cos(\theta), where \theta //
-// is the maximum dihedral angle in the old tets. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::removeedgebyflip22(REAL *key, int n, triface *abtetlist,
- queue *flipque)
-{
- point pa, pb, pc, pd, pe, pf;
- REAL cosmaxd, d1, d2, d3;
- bool doflip;
-
- doflip = true;
- adjustedgering(abtetlist[0], CW);
- pa = org(abtetlist[0]);
- pb = dest(abtetlist[0]);
- pe = apex(abtetlist[0]);
- pc = oppo(abtetlist[0]);
- pd = apex(abtetlist[1]);
- if (n == 4) {
- pf = apex(abtetlist[2]);
- }
- if (key && (*key > -1.0)) {
- tetalldihedral(pc, pd, pe, pa, NULL, &d1, NULL);
- tetalldihedral(pd, pc, pe, pb, NULL, &d2, NULL);
- cosmaxd = d1 < d2 ? d1 : d2; // Choose the bigger angle.
- if (n == 4) {
- tetalldihedral(pd, pc, pf, pa, NULL, &d1, NULL);
- tetalldihedral(pc, pd, pf, pb, NULL, &d2, NULL);
- d3 = d1 < d2 ? d1 : d2; // Choose the bigger angle.
- cosmaxd = cosmaxd < d3 ? cosmaxd : d3; // Choose the bigger angle.
- }
- doflip = (*key < cosmaxd); // Can local quality be improved?
- }
-
- if (doflip) {
- flip22(&abtetlist[0], NULL);
- // Return the improved quality value.
- if (key) *key = cosmaxd;
- }
-
- return doflip;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// removefacebyflip23() Remove a face by a 2-to-3 flip. //
-// //
-// 'abctetlist' contains 2 tets sharing abc, which are [0]abcd and [1]bace. //
-// This routine forms three new tets that abc is not a face anymore. Save //
-// them in 'newtetlist': [0]edab, [1]edbc, and [2]edca. Note that the new //
-// tets may not valid if one of them get inverted. return false if so. //
-// //
-// If 'key' != NULL. The old tets are replaced by the new tets only if the //
-// local mesh quality is improved. Current 'key' = cos(\theta), where \theta //
-// is the maximum dihedral angle in the old tets. //
-// //
-// If the face is flipped, 'newtetlist' returns the three new tets. The two //
-// tets in 'abctetlist' are NOT deleted. The caller has the right to either //
-// delete them or reverse the operation. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::removefacebyflip23(REAL *key, triface *abctetlist,
- triface *newtetlist, queue *flipque)
-{
- triface edab, edbc, edca; // new configuration.
- triface newfront, oldfront, adjfront;
- face checksh;
- point pa, pb, pc, pd, pe;
- REAL ori, cosmaxd, d1, d2, d3;
- REAL attrib, volume;
- bool doflip;
- int i;
-
- adjustedgering(abctetlist[0], CCW);
- pa = org(abctetlist[0]);
- pb = dest(abctetlist[0]);
- pc = apex(abctetlist[0]);
- pd = oppo(abctetlist[0]);
- pe = oppo(abctetlist[1]);
-
- // Check if the flip creates valid new tets.
- ori = orient3d(pe, pd, pa, pb);
- if (ori < 0.0) {
- ori = orient3d(pe, pd, pb, pc);
- if (ori < 0.0) {
- ori = orient3d(pe, pd, pc, pa);
- }
- }
- doflip = (ori < 0.0); // Can abc be flipped away?
- if (doflip && (key != (REAL *) NULL)) {
- if (*key > -1.0) {
- // Test if the new tets reduce the maximal dihedral angle.
- tetalldihedral(pe, pd, pa, pb, NULL, &d1, NULL);
- tetalldihedral(pe, pd, pb, pc, NULL, &d2, NULL);
- tetalldihedral(pe, pd, pc, pa, NULL, &d3, NULL);
- cosmaxd = d1 < d2 ? d1 : d2; // Choose the bigger angle.
- cosmaxd = cosmaxd < d3 ? cosmaxd : d3; // Choose the bigger angle.
- doflip = (*key < cosmaxd); // Can local quality be improved?
- }
- }
-
- if (doflip) {
- // A valid (2-to-3) flip is found.
- flip23s++;
- // Create the new tets.
- maketetrahedron(&edab);
- setorg(edab, pe);
- setdest(edab, pd);
- setapex(edab, pa);
- setoppo(edab, pb);
- maketetrahedron(&edbc);
- setorg(edbc, pe);
- setdest(edbc, pd);
- setapex(edbc, pb);
- setoppo(edbc, pc);
- maketetrahedron(&edca);
- setorg(edca, pe);
- setdest(edca, pd);
- setapex(edca, pc);
- setoppo(edca, pa);
- // Transfer the element attributes.
- for (i = 0; i < in->numberoftetrahedronattributes; i++) {
- attrib = elemattribute(abctetlist[0].tet, i);
- setelemattribute(edab.tet, i, attrib);
- setelemattribute(edbc.tet, i, attrib);
- setelemattribute(edca.tet, i, attrib);
- }
- // Transfer the volume constraints.
- if (b->varvolume && !b->refine) {
- volume = volumebound(abctetlist[0].tet);
- setvolumebound(edab.tet, volume);
- setvolumebound(edbc.tet, volume);
- setvolumebound(edca.tet, volume);
- }
- // Return two new tets.
- newtetlist[0] = edab;
- newtetlist[1] = edbc;
- newtetlist[2] = edca;
- // Glue the three new tets.
- for (i = 0; i < 3; i++) {
- fnext(newtetlist[i], newfront);
- bond(newfront, newtetlist[(i + 1) % 3]);
- }
- // Substitute the three new tets into the old cavity.
- for (i = 0; i < 3; i++) {
- fnext(abctetlist[0], oldfront);
- sym(oldfront, adjfront); // may be outside.
- enextfnext(newtetlist[i], newfront);
- bond(newfront, adjfront);
- if (checksubfaces) {
- tspivot(oldfront, checksh);
- if (checksh.sh != dummysh) {
- tsbond(newfront, checksh);
- }
- }
- if (flipque != (queue *) NULL) {
- enqueueflipface(newfront, flipque);
- }
- enextself(abctetlist[0]);
- }
- findedge(&(abctetlist[1]), pb, pa);
- for (i = 0; i < 3; i++) {
- fnext(abctetlist[1], oldfront);
- sym(oldfront, adjfront); // may be outside.
- enext2fnext(newtetlist[i], newfront);
- bond(newfront, adjfront);
- if (checksubfaces) {
- tspivot(oldfront, checksh);
- if (checksh.sh != dummysh) {
- tsbond(newfront, checksh);
- }
- }
- if (flipque != (queue *) NULL) {
- enqueueflipface(newfront, flipque);
- }
- enext2self(abctetlist[1]);
- }
- // Do not delete the old tets.
- // for (i = 0; i < 2; i++) {
- // tetrahedrondealloc(abctetlist[i].tet);
- // }
- // Return the improved quality value.
- if (key != (REAL *) NULL) *key = cosmaxd;
- return true;
- }
-
- return false;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// removeedgebyflip32() Remove an edge by a 3-to-2 flip. //
-// //
-// 'abtetlist' contains 3 tets sharing ab. Imaging that ab is perpendicular //
-// to the screen, where a lies in front of and b lies behind it. The 3 tets //
-// of the list are: [0]abce, [1]abdc, and [2]abed, respectively. //
-// //
-// This routine forms two new tets that ab is not an edge of them. Save them //
-// in 'newtetlist', [0]dcea, [1]cdeb. Note that the new tets may not valid //
-// if one of them get inverted. return false if so. //
-// //
-// If 'key' != NULL. The old tets are replaced by the new tets only if the //
-// local mesh quality is improved. Current 'key' = cos(\theta), where \theta //
-// is the maximum dihedral angle in the old tets. //
-// //
-// If the edge is flipped, 'newtetlist' returns the two new tets. The three //
-// tets in 'abtetlist' are NOT deleted. The caller has the right to either //
-// delete them or reverse the operation. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::removeedgebyflip32(REAL *key, triface *abtetlist,
- triface *newtetlist, queue *flipque)
-{
- triface dcea, cdeb; // new configuration.
- triface newfront, oldfront, adjfront;
- face checksh;
- point pa, pb, pc, pd, pe;
- REAL ori, cosmaxd, d1, d2;
- REAL attrib, volume;
- bool doflip;
- int i;
-
- pa = org(abtetlist[0]);
- pb = dest(abtetlist[0]);
- pc = apex(abtetlist[0]);
- pd = apex(abtetlist[1]);
- pe = apex(abtetlist[2]);
-
- ori = orient3d(pd, pc, pe, pa);
- if (ori < 0.0) {
- ori = orient3d(pc, pd, pe, pb);
- }
- doflip = (ori < 0.0); // Can ab be flipped away?
-
- // Does the caller ensure a valid configuration?
- if (doflip && (key != (REAL *) NULL)) {
- if (*key > -1.0) {
- // Test if the new tets reduce the maximal dihedral angle.
- tetalldihedral(pd, pc, pe, pa, NULL, &d1, NULL);
- tetalldihedral(pc, pd, pe, pb, NULL, &d2, NULL);
- cosmaxd = d1 < d2 ? d1 : d2; // Choose the bigger angle.
- doflip = (*key < cosmaxd); // Can local quality be improved?
- // Return the key
- *key = cosmaxd;
- }
- }
-
- if (doflip) {
- // Create the new tets.
- maketetrahedron(&dcea);
- setorg(dcea, pd);
- setdest(dcea, pc);
- setapex(dcea, pe);
- setoppo(dcea, pa);
- maketetrahedron(&cdeb);
- setorg(cdeb, pc);
- setdest(cdeb, pd);
- setapex(cdeb, pe);
- setoppo(cdeb, pb);
- // Transfer the element attributes.
- for (i = 0; i < in->numberoftetrahedronattributes; i++) {
- attrib = elemattribute(abtetlist[0].tet, i);
- setelemattribute(dcea.tet, i, attrib);
- setelemattribute(cdeb.tet, i, attrib);
- }
- // Transfer the volume constraints.
- if (b->varvolume && !b->refine) {
- volume = volumebound(abtetlist[0].tet);
- setvolumebound(dcea.tet, volume);
- setvolumebound(cdeb.tet, volume);
- }
- // Return two new tets.
- newtetlist[0] = dcea;
- newtetlist[1] = cdeb;
- // Glue the two new tets.
- bond(dcea, cdeb);
- // Substitute the two new tets into the old three-tets cavity.
- for (i = 0; i < 3; i++) {
- fnext(dcea, newfront); // face dca, cea, eda.
- esym(abtetlist[(i + 1) % 3], oldfront);
- enextfnextself(oldfront);
- // Get the adjacent tet at the face (may be a dummytet).
- sym(oldfront, adjfront);
- bond(newfront, adjfront);
- if (checksubfaces) {
- tspivot(oldfront, checksh);
- if (checksh.sh != dummysh) {
- tsbond(newfront, checksh);
- }
- }
- if (flipque != (queue *) NULL) {
- enqueueflipface(newfront, flipque);
- }
- enext2self(dcea);
- }
- for (i = 0; i < 3; i++) {
- fnext(cdeb, newfront); // face cdb, deb, ecb.
- esym(abtetlist[(i + 1) % 3], oldfront);
- enext2fnextself(oldfront);
- // Get the adjacent tet at the face (may be a dummytet).
- sym(oldfront, adjfront);
- bond(newfront, adjfront);
- if (checksubfaces) {
- tspivot(oldfront, checksh);
- if (checksh.sh != dummysh) {
- tsbond(newfront, checksh);
- }
- }
- if (flipque != (queue *) NULL) {
- enqueueflipface(newfront, flipque);
- }
- enextself(cdeb);
- }
- // Do not delete the old tets.
- // for (i = 0; i < 3; i++) {
- // tetrahedrondealloc(abtetlist[i].tet);
- // }
- return true;
- } // if (doflip)
-
- return false;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// removeedgebytranNM() Remove an edge by transforming n-to-m tets. //
-// //
-// This routine attempts to remove a given edge (ab) by transforming the set //
-// T of tets surrounding ab into another set T' of tets. T and T' have the //
-// same outer faces and ab is not an edge of T' anymore. Let |T|=n, and |T'| //
-// =m, it is actually a n-to-m flip for n > 3. The relation between n and m //
-// depends on the method, ours is found below. //
-// //
-// 'abtetlist' contains n tets sharing ab. Imaging that ab is perpendicular //
-// to the screen, where a lies in front of and b lies behind it. Let the //
-// projections of the n apexes onto screen in clockwise order are: p_0, ... //
-// p_n-1, respectively. The tets in the list are: [0]abp_0p_n-1,[1]abp_1p_0, //
-// ..., [n-1]abp_n-1p_n-2, respectively. //
-// //
-// The principle of the approach is: Recursively reduce the link of ab by //
-// using flip23 until only three faces remain, hence a flip32 can be applied //
-// to remove ab. For a given face a.b.p_0, check a flip23 can be applied on //
-// it, i.e, edge p_1.p_n-1 crosses it. NOTE*** We do the flip even p_1.p_n-1 //
-// intersects with a.b (they are coplanar). If so, a degenerate tet (a.b.p_1.//
-// p_n-1) is temporarily created, but it will be eventually removed by the //
-// final flip32. This relaxation splits a flip44 into flip23 + flip32. *NOTE //
-// Now suppose a.b.p_0 gets flipped, p_0 is not on the link of ab anymore. //
-// The link is then reduced (by 1). 2 of the 3 new tets, p_n-1.p_1.p_0.a and //
-// p_1.p_n-1.p_0.b, will be part of the new configuration. The left new tet,//
-// a.b.p_1.p_n-1, goes into the new link of ab. A recurrence can be applied. //
-// //
-// If 'e1' and 'e2' are not NULLs, they specify an wanted edge to appear in //
-// the new tet configuration. In such case, only do flip23 if edge e1<->e2 //
-// can be recovered. It is used in removeedgebycombNM(). //
-// //
-// If ab gets removed. 'newtetlist' contains m new tets. By using the above //
-// approach, the pairs (n, m) can be easily enumerated. For example, (3, 2),//
-// (4, 4), (5, 6), (6, 8), (7, 10), (8, 12), (9, 14), (10, 16), and so on. //
-// It is easy to deduce, that m = (n - 2) * 2, when n >= 3. The n tets in //
-// 'abtetlist' are NOT deleted in this routine. The caller has the right to //
-// either delete them or reverse this operation. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::removeedgebytranNM(REAL *key, int n, triface *abtetlist,
- triface *newtetlist, point e1, point e2, queue *flipque)
-{
- triface tmpabtetlist[9]; // Temporary max 9 tets configuration.
- triface newfront, oldfront, adjfront;
- face checksh;
- point pa, pb, p[10];
- REAL ori, cosmaxd, d1, d2;
- REAL tmpkey;
- REAL attrib, volume;
- bool doflip, copflag, success;
- int i, j, k;
-
- // Maximum 10 tets.
- assert(n <= 10);
- // Two points a and b are fixed.
- pa = org(abtetlist[0]);
- pb = dest(abtetlist[0]);
- // The points p_0, p_1, ..., p_n-1 are permuted in each new configuration.
- // These permutations can be easily done in the following loop.
- // Loop through all the possible new tets configurations. Stop on finding
- // a valid new tet configuration which also immproves the quality value.
- for (i = 0; i < n; i++) {
- // Get other n points for the current configuration.
- for (j = 0; j < n; j++) {
- p[j] = apex(abtetlist[(i + j) % n]);
- }
- // Is there a wanted edge?
- if ((e1 != (point) NULL) && (e2 != (point) NULL)) {
- // Yes. Skip this face if p[1]<->p[n-1] is not the edge.
- if (!(((p[1] == e1) && (p[n - 1] == e2)) ||
- ((p[1] == e2) && (p[n - 1] == e1)))) continue;
- }
- // Test if face a.b.p_0 can be flipped (by flip23), ie, to check if the
- // edge p_n-1.p_1 crosses face a.b.p_0 properly.
- // Note. It is possible that face a.b.p_0 has type flip44, ie, a,b,p_1,
- // and p_n-1 are coplanar. A trick is to split the flip44 into two
- // steps: frist a flip23, then a flip32. The first step creates a
- // degenerate tet (vol=0) which will be removed by the second flip.
- ori = orient3d(pa, pb, p[1], p[n - 1]);
- copflag = (ori == 0.0); // Are they coplanar?
- if (ori >= 0.0) {
- // Accept the coplanar case which supports flip44.
- ori = orient3d(pb, p[0], p[1], p[n - 1]);
- if (ori > 0.0) {
- ori = orient3d(p[0], pa, p[1], p[n - 1]);
- }
- }
- // Is face abc flipable?
- if (ori > 0.0) {
- // A valid (2-to-3) flip (or 4-to-4 flip) is found.
- copflag ? flip44s++ : flip23s++;
- doflip = true;
- if (key != (REAL *) NULL) {
- if (*key > -1.0) {
- // Test if the new tets reduce the maximal dihedral angle. Only 2
- // tets, p_n-1.p_1.p_0.a and p_1.p_n-1.p_0.b, need to be tested
- // The left one a.b.p_n-1.p_1 goes into the new link of ab.
- tetalldihedral(p[n - 1], p[1], p[0], pa, NULL, &d1, NULL);
- tetalldihedral(p[1], p[n - 1], p[0], pb, NULL, &d2, NULL);
- cosmaxd = d1 < d2 ? d1 : d2; // Choose the bigger angle.
- doflip = *key < cosmaxd; // Can the local quality be improved?
- }
- }
- if (doflip) {
- tmpkey = key != NULL ? *key : -1.0;
- // Create the two new tets.
- maketetrahedron(&(newtetlist[0]));
- setorg(newtetlist[0], p[n - 1]);
- setdest(newtetlist[0], p[1]);
- setapex(newtetlist[0], p[0]);
- setoppo(newtetlist[0], pa);
- maketetrahedron(&(newtetlist[1]));
- setorg(newtetlist[1], p[1]);
- setdest(newtetlist[1], p[n - 1]);
- setapex(newtetlist[1], p[0]);
- setoppo(newtetlist[1], pb);
- // Create the n - 1 temporary new tets (the new Star(ab)).
- maketetrahedron(&(tmpabtetlist[0]));
- setorg(tmpabtetlist[0], pa);
- setdest(tmpabtetlist[0], pb);
- setapex(tmpabtetlist[0], p[n - 1]);
- setoppo(tmpabtetlist[0], p[1]);
- for (j = 1; j < n - 1; j++) {
- maketetrahedron(&(tmpabtetlist[j]));
- setorg(tmpabtetlist[j], pa);
- setdest(tmpabtetlist[j], pb);
- setapex(tmpabtetlist[j], p[j]);
- setoppo(tmpabtetlist[j], p[j + 1]);
- }
- // Transfer the element attributes.
- for (j = 0; j < in->numberoftetrahedronattributes; j++) {
- attrib = elemattribute(abtetlist[0].tet, j);
- setelemattribute(newtetlist[0].tet, j, attrib);
- setelemattribute(newtetlist[1].tet, j, attrib);
- for (k = 0; k < n - 1; k++) {
- setelemattribute(tmpabtetlist[k].tet, j, attrib);
- }
- }
- // Transfer the volume constraints.
- if (b->varvolume && !b->refine) {
- volume = volumebound(abtetlist[0].tet);
- setvolumebound(newtetlist[0].tet, volume);
- setvolumebound(newtetlist[1].tet, volume);
- for (k = 0; k < n - 1; k++) {
- setvolumebound(tmpabtetlist[k].tet, volume);
- }
- }
- // Glue the new tets at their internal faces: 2 + (n - 1).
- bond(newtetlist[0], newtetlist[1]); // p_n-1.p_1.p_0.
- fnext(newtetlist[0], newfront);
- enext2fnext(tmpabtetlist[0], adjfront);
- bond(newfront, adjfront); // p_n-1.p_1.a.
- fnext(newtetlist[1], newfront);
- enextfnext(tmpabtetlist[0], adjfront);
- bond(newfront, adjfront); // p_n-1.p_1.b.
- // Glue n - 1 internal faces around ab.
- for (j = 0; j < n - 1; j++) {
- fnext(tmpabtetlist[j], newfront);
- bond(newfront, tmpabtetlist[(j + 1) % (n - 1)]); // a.b.p_j+1
- }
- // Substitute the old tets with the new tets by connecting the new
- // tets to the adjacent tets in the mesh. There are n * 2 (outer)
- // faces of the new tets need to be operated.
- // Note, after the substitution, the old tets still have pointers to
- // their adjacent tets in the mesh. These pointers can be re-used
- // to inverse the substitution.
- for (j = 0; j < n; j++) {
- // Get an old tet: [0]a.b.p_0.p_n-1 or [j]a.b.p_j.p_j-1, (j > 0).
- oldfront = abtetlist[(i + j) % n];
- esymself(oldfront);
- enextfnextself(oldfront);
- // Get an adjacent tet at face: [0]a.p_0.p_n-1 or [j]a.p_j.p_j-1.
- sym(oldfront, adjfront); // adjfront may be dummy.
- // Get the corresponding face from the new tets.
- if (j == 0) {
- enext2fnext(newtetlist[0], newfront); // a.p_0.n_n-1
- } else if (j == 1) {
- enextfnext(newtetlist[0], newfront); // a.p_1.p_0
- } else { // j >= 2.
- enext2fnext(tmpabtetlist[j - 1], newfront); // a.p_j.p_j-1
- }
- bond(newfront, adjfront);
- if (checksubfaces) {
- tspivot(oldfront, checksh);
- if (checksh.sh != dummysh) {
- tsbond(newfront, checksh);
- }
- }
- if (flipque != (queue *) NULL) {
- // Only queue the faces of the two new tets.
- if (j < 2) enqueueflipface(newfront, flipque);
- }
- }
- for (j = 0; j < n; j++) {
- // Get an old tet: [0]a.b.p_0.p_n-1 or [j]a.b.p_j.p_j-1, (j > 0).
- oldfront = abtetlist[(i + j) % n];
- esymself(oldfront);
- enext2fnextself(oldfront);
- // Get an adjacent tet at face: [0]b.p_0.p_n-1 or [j]b.p_j.p_j-1.
- sym(oldfront, adjfront); // adjfront may be dummy.
- // Get the corresponding face from the new tets.
- if (j == 0) {
- enextfnext(newtetlist[1], newfront); // b.p_0.n_n-1
- } else if (j == 1) {
- enext2fnext(newtetlist[1], newfront); // b.p_1.p_0
- } else { // j >= 2.
- enextfnext(tmpabtetlist[j - 1], newfront); // b.p_j.p_j-1
- }
- bond(newfront, adjfront);
- if (checksubfaces) {
- tspivot(oldfront, checksh);
- if (checksh.sh != dummysh) {
- tsbond(newfront, checksh);
- }
- }
- if (flipque != (queue *) NULL) {
- // Only queue the faces of the two new tets.
- if (j < 2) enqueueflipface(newfront, flipque);
- }
- }
- // Adjust the faces in the temporary new tets at ab for recursively
- // processing on the n-1 tets.(See the description at beginning)
- for (j = 0; j < n - 1; j++) {
- fnextself(tmpabtetlist[j]);
- }
- if (n > 4) {
- success = removeedgebytranNM(&tmpkey, n-1, tmpabtetlist,
- &(newtetlist[2]), NULL, NULL, flipque);
- } else { // assert(n == 4);
- success = removeedgebyflip32(&tmpkey, tmpabtetlist,
- &(newtetlist[2]), flipque);
- }
- // No matter it was success or not, delete the temporary tets.
- for (j = 0; j < n - 1; j++) {
- tetrahedrondealloc(tmpabtetlist[j].tet);
- }
- if (success) {
- // The new configuration is good.
- // Do not delete the old tets.
- // for (j = 0; j < n; j++) {
- // tetrahedrondealloc(abtetlist[j].tet);
- // }
- // Save the minimal improved quality value.
- if (key != (REAL *) NULL) {
- *key = (tmpkey < cosmaxd ? tmpkey : cosmaxd);
- }
- return true;
- } else {
- // The new configuration is bad, substitue back the old tets.
- for (j = 0; j < n; j++) {
- oldfront = abtetlist[(i + j) % n];
- esymself(oldfront);
- enextfnextself(oldfront); // [0]a.p_0.p_n-1, [j]a.p_j.p_j-1.
- sym(oldfront, adjfront); // adjfront may be dummy.
- bond(oldfront, adjfront);
- if (checksubfaces) {
- tspivot(oldfront, checksh);
- if (checksh.sh != dummysh) {
- tsbond(oldfront, checksh);
- }
- }
- }
- for (j = 0; j < n; j++) {
- oldfront = abtetlist[(i + j) % n];
- esymself(oldfront);
- enext2fnextself(oldfront); // [0]b.p_0.p_n-1, [j]b.p_j.p_j-1.
- sym(oldfront, adjfront); // adjfront may be dummy
- bond(oldfront, adjfront);
- if (checksubfaces) {
- tspivot(oldfront, checksh);
- if (checksh.sh != dummysh) {
- tsbond(oldfront, checksh);
- }
- }
- }
- // Delete the new tets.
- tetrahedrondealloc(newtetlist[0].tet);
- tetrahedrondealloc(newtetlist[1].tet);
- // If tmpkey has been modified, then the failure was not due to
- // unflipable configuration, but the non-improvement.
- if (key && (tmpkey < *key)) {
- *key = tmpkey;
- return false;
- }
- } // if (success)
- } // if (doflip)
- } // if (ori > 0.0)
- } // for (i = 0; i < n; i++)
-
- return false;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// removeedgebycombNM() Remove an edge by combining two flipNMs. //
-// //
-// Given a set T of tets surrounding edge ab. The premise is that ab can not //
-// be removed by a flipNM. This routine attempts to remove ab by two flipNMs,//
-// i.e., first find and flip an edge af (or bf) by flipNM, then flip ab by //
-// flipNM. If it succeeds, two sets T(ab) and T(af) of tets are replaced by //
-// a new set T' and both ab and af are not edges in T' anymore. //
-// //
-// 'abtetlist' contains n tets sharing ab. Imaging that ab is perpendicular //
-// to the screen, such that a lies in front of and b lies behind it. Let the //
-// projections of the n apexes on the screen in clockwise order are: p_0,...,//
-// p_n-1, respectively. So the list of tets are: [0]abp_0p_n-1, [1]abp_1p_0, //
-// ..., [n-1]abp_n-1p_n-2, respectively. //
-// //
-// The principle of the approach is: for a face a.b.p_0, check if edge b.p_0 //
-// is of type N32 (or N44). If it is, then try to do a flipNM on it. If the //
-// flip is successful, then try to do another flipNM on a.b. If one of the //
-// two flipNMs fails, restore the old tets as they have never been flipped. //
-// Then try the next face a.b.p_1. The process can be looped for all faces //
-// having ab. Stop if ab is removed or all faces have been visited. Note in //
-// the above description only b.p_0 is considered, a.p_0 is done by swapping //
-// the position of a and b. //
-// //
-// Similar operations have been described in [Joe,1995]. My approach checks //
-// more cases for finding flips than Joe's. For instance, the cases (1)-(7) //
-// of Joe only consider abf for finding a flip (T23/T32). My approach looks //
-// all faces at ab for finding flips. Moreover, the flipNM can flip an edge //
-// whose star may have more than 3 tets while Joe's only works on 3-tet case.//
-// //
-// If ab is removed, 'newtetlist' contains the new tets. Two sets 'abtetlist'//
-// (n tets) and 'bftetlist' (n1 tets) have been replaced. The number of new //
-// tets can be calculated by follows: the 1st flip transforms n1 tets into //
-// (n1 - 2) * 2 new tets, however,one of the new tets goes into the new link //
-// of ab, i.e., the reduced tet number in Star(ab) is n - 1; the 2nd flip //
-// transforms n - 1 tets into (n - 3) * 2 new tets. Hence the number of new //
-// tets are: m = ((n1 - 2) * 2 - 1) + (n - 3) * 2. The old tets are NOT del-//
-// eted. The caller has the right to delete them or reverse the operation. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::removeedgebycombNM(REAL *key, int n, triface *abtetlist,
- int *n1, triface *bftetlist, triface *newtetlist, queue *flipque)
-{
- triface tmpabtetlist[11];
- triface newfront, oldfront, adjfront;
- face checksh;
- point pa, pb, p[10];
- REAL ori, tmpkey, tmpkey2;
- REAL attrib, volume;
- bool doflip, success;
- int twice, count;
- int i, j, k, m;
-
- // Maximal 10 tets in Star(ab).
- assert(n <= 10);
-
- // Do the following procedure twice, one for flipping edge b.p_0 and the
- // other for p_0.a which is symmetric to the first.
- twice = 0;
- do {
- // Two points a and b are fixed.
- pa = org(abtetlist[0]);
- pb = dest(abtetlist[0]);
- // The points p_0, ..., p_n-1 are permuted in the following loop.
- for (i = 0; i < n; i++) {
- // Get the n points for the current configuration.
- for (j = 0; j < n; j++) {
- p[j] = apex(abtetlist[(i + j) % n]);
- }
- // Check if b.p_0 is of type N32 or N44.
- ori = orient3d(pb, p[0], p[1], p[n - 1]);
- if ((ori > 0) && (key != (REAL *) NULL)) {
- // b.p_0 is not N32. However, it is possible that the tet b.p_0.p_1.
- // p_n-1 has worse quality value than the key. In such case, also
- // try to flip b.p_0.
- tetalldihedral(pb, p[0], p[n - 1], p[1], NULL, &tmpkey, NULL);
- if (tmpkey < *key) ori = 0.0;
- }
- if (ori <= 0.0) {
- // b.p_0 is either N32 or N44. Try the 1st flipNM.
- bftetlist[0] = abtetlist[i];
- enextself(bftetlist[0]);// go to edge b.p_0.
- adjustedgering(bftetlist[0], CW); // edge p_0.b.
- assert(apex(bftetlist[0]) == pa);
- // Form Star(b.p_0).
- doflip = true;
- *n1 = 0;
- do {
- // Is the list full?
- if (*n1 == 10) break;
- if (checksubfaces) {
- // Stop if a subface appears.
- tspivot(bftetlist[*n1], checksh);
- if (checksh.sh != dummysh) {
- doflip = false; break;
- }
- }
- // Get the next tet at p_0.b.
- fnext(bftetlist[*n1], bftetlist[(*n1) + 1]);
- (*n1)++;
- } while (apex(bftetlist[*n1]) != pa);
- // 2 <= n1 <= 10.
- if (doflip) {
- success = false;
- tmpkey = -1.0; // = acos(pi).
- if (key != (REAL *) NULL) tmpkey = *key;
- m = 0;
- if (*n1 == 3) {
- // Three tets case. Try flip32.
- success = removeedgebyflip32(&tmpkey,bftetlist,newtetlist,flipque);
- m = 2;
- } else if ((*n1 > 3) && (*n1 < 7)) {
- // Four or more tets case. Try flipNM.
- success = removeedgebytranNM(&tmpkey, *n1, bftetlist, newtetlist,
- p[1], p[n - 1], flipque);
- // If success, the number of new tets.
- m = ((*n1) - 2) * 2;
- } else {
- if (b->verbose > 1) {
- printf(" !! Unhandled case: n1 = %d.\n", *n1);
- }
- }
- if (success) {
- // b.p_0 is flipped. The link of ab is reduced (by 1), i.e., p_0
- // is not on the link of ab. Two old tets a.b.p_0.p_n-1 and
- // a.b.p_1.p_0 have been removed from the Star(ab) and one new
- // tet t = a.b.p_1.p_n-1 belongs to Star(ab).
- // Find t in the 'newtetlist' and remove it from the list.
- setpointmark(pa, -pointmark(pa) - 1);
- setpointmark(pb, -pointmark(pb) - 1);
- assert(m > 0);
- for (j = 0; j < m; j++) {
- tmpabtetlist[0] = newtetlist[j];
- // Does it has ab?
- count = 0;
- for (k = 0; k < 4; k++) {
- if (pointmark((point)(tmpabtetlist[0].tet[4+k])) < 0) count++;
- }
- if (count == 2) {
- // It is. Adjust t to be the edge ab.
- for (tmpabtetlist[0].loc = 0; tmpabtetlist[0].loc < 4;
- tmpabtetlist[0].loc++) {
- if ((oppo(tmpabtetlist[0]) != pa) &&
- (oppo(tmpabtetlist[0]) != pb)) break;
- }
- // The face of t must contain ab.
- assert(tmpabtetlist[0].loc < 4);
- findedge(&(tmpabtetlist[0]), pa, pb);
- break;
- }
- }
- assert(j < m); // The tet must exist.
- // Remove t from list. Fill t's position by the last tet.
- newtetlist[j] = newtetlist[m - 1];
- setpointmark(pa, -(pointmark(pa) + 1));
- setpointmark(pb, -(pointmark(pb) + 1));
- // Create the temporary Star(ab) for the next flipNM.
- adjustedgering(tmpabtetlist[0], CCW);
- if (org(tmpabtetlist[0]) != pa) {
- fnextself(tmpabtetlist[0]);
- esymself(tmpabtetlist[0]);
- }
-#ifdef SELF_CHECK
- // Make sure current edge is a->b.
- assert(org(tmpabtetlist[0]) == pa);
- assert(dest(tmpabtetlist[0]) == pb);
- assert(apex(tmpabtetlist[0]) == p[n - 1]);
- assert(oppo(tmpabtetlist[0]) == p[1]);
-#endif // SELF_CHECK
- // There are n - 2 left temporary tets.
- for (j = 1; j < n - 1; j++) {
- maketetrahedron(&(tmpabtetlist[j]));
- setorg(tmpabtetlist[j], pa);
- setdest(tmpabtetlist[j], pb);
- setapex(tmpabtetlist[j], p[j]);
- setoppo(tmpabtetlist[j], p[j + 1]);
- }
- // Transfer the element attributes.
- for (j = 0; j < in->numberoftetrahedronattributes; j++) {
- attrib = elemattribute(abtetlist[0].tet, j);
- for (k = 0; k < n - 1; k++) {
- setelemattribute(tmpabtetlist[k].tet, j, attrib);
- }
- }
- // Transfer the volume constraints.
- if (b->varvolume && !b->refine) {
- volume = volumebound(abtetlist[0].tet);
- for (k = 0; k < n - 1; k++) {
- setvolumebound(tmpabtetlist[k].tet, volume);
- }
- }
- // Glue n - 1 internal faces of Star(ab).
- for (j = 0; j < n - 1; j++) {
- fnext(tmpabtetlist[j], newfront);
- bond(newfront, tmpabtetlist[(j + 1) % (n - 1)]); // a.b.p_j+1
- }
- // Substitute the old tets with the new tets by connecting the
- // new tets to the adjacent tets in the mesh. There are (n-2)
- // * 2 (outer) faces of the new tets need to be operated.
- // Note that the old tets still have the pointers to their
- // adjacent tets in the mesh. These pointers can be re-used
- // to inverse the substitution.
- for (j = 2; j < n; j++) {
- // Get an old tet: [j]a.b.p_j.p_j-1, (j > 1).
- oldfront = abtetlist[(i + j) % n];
- esymself(oldfront);
- enextfnextself(oldfront);
- // Get an adjacent tet at face: [j]a.p_j.p_j-1.
- sym(oldfront, adjfront); // adjfront may be dummy.
- // Get the corresponding face from the new tets.
- // j >= 2.
- enext2fnext(tmpabtetlist[j - 1], newfront); // a.p_j.p_j-1
- bond(newfront, adjfront);
- if (checksubfaces) {
- tspivot(oldfront, checksh);
- if (checksh.sh != dummysh) {
- tsbond(newfront, checksh);
- }
- }
- }
- for (j = 2; j < n; j++) {
- // Get an old tet: [j]a.b.p_j.p_j-1, (j > 2).
- oldfront = abtetlist[(i + j) % n];
- esymself(oldfront);
- enext2fnextself(oldfront);
- // Get an adjacent tet at face: [j]b.p_j.p_j-1.
- sym(oldfront, adjfront); // adjfront may be dummy.
- // Get the corresponding face from the new tets.
- // j >= 2.
- enextfnext(tmpabtetlist[j - 1], newfront); // b.p_j.p_j-1
- bond(newfront, adjfront);
- if (checksubfaces) {
- tspivot(oldfront, checksh);
- if (checksh.sh != dummysh) {
- tsbond(newfront, checksh);
- }
- }
- }
- // Adjust the faces in the temporary new tets at ab for
- // recursively processing on the n-1 tets.
- for (j = 0; j < n - 1; j++) {
- fnextself(tmpabtetlist[j]);
- }
- tmpkey2 = -1;
- if (key) tmpkey2 = *key;
- if ((n - 1) == 3) {
- success = removeedgebyflip32(&tmpkey2, tmpabtetlist,
- &(newtetlist[m - 1]), flipque);
- } else { // assert((n - 1) >= 4);
- success = removeedgebytranNM(&tmpkey2, n - 1, tmpabtetlist,
- &(newtetlist[m - 1]), NULL, NULL, flipque);
- }
- // No matter it was success or not, delete the temporary tets.
- for (j = 0; j < n - 1; j++) {
- tetrahedrondealloc(tmpabtetlist[j].tet);
- }
- if (success) {
- // The new configuration is good.
- // Do not delete the old tets.
- // for (j = 0; j < n; j++) {
- // tetrahedrondealloc(abtetlist[j].tet);
- // }
- // Return the bigger dihedral in the two sets of new tets.
- if (key != (REAL *) NULL) {
- *key = tmpkey2 < tmpkey ? tmpkey2 : tmpkey;
- }
- return true;
- } else {
- // The new configuration is bad, substitue back the old tets.
- for (j = 0; j < n; j++) {
- oldfront = abtetlist[(i + j) % n];
- esymself(oldfront);
- enextfnextself(oldfront); // [0]a.p_0.p_n-1, [j]a.p_j.p_j-1.
- sym(oldfront, adjfront); // adjfront may be dummy.
- bond(oldfront, adjfront);
- if (checksubfaces) {
- tspivot(oldfront, checksh);
- if (checksh.sh != dummysh) {
- tsbond(oldfront, checksh);
- }
- }
- }
- for (j = 0; j < n; j++) {
- oldfront = abtetlist[(i + j) % n];
- esymself(oldfront);
- enext2fnextself(oldfront); // [0]b.p_0.p_n-1, [j]b.p_j.p_j-1.
- sym(oldfront, adjfront); // adjfront may be dummy
- bond(oldfront, adjfront);
- if (checksubfaces) {
- tspivot(oldfront, checksh);
- if (checksh.sh != dummysh) {
- tsbond(oldfront, checksh);
- }
- }
- }
- // Substitute back the old tets of the first flip.
- for (j = 0; j < *n1; j++) {
- oldfront = bftetlist[j];
- esymself(oldfront);
- enextfnextself(oldfront);
- sym(oldfront, adjfront); // adjfront may be dummy.
- bond(oldfront, adjfront);
- if (checksubfaces) {
- tspivot(oldfront, checksh);
- if (checksh.sh != dummysh) {
- tsbond(oldfront, checksh);
- }
- }
- }
- for (j = 0; j < *n1; j++) {
- oldfront = bftetlist[j];
- esymself(oldfront);
- enext2fnextself(oldfront); // [0]b.p_0.p_n-1, [j]b.p_j.p_j-1.
- sym(oldfront, adjfront); // adjfront may be dummy
- bond(oldfront, adjfront);
- if (checksubfaces) {
- tspivot(oldfront, checksh);
- if (checksh.sh != dummysh) {
- tsbond(oldfront, checksh);
- }
- }
- }
- // Delete the new tets of the first flip. Note that one new
- // tet has already been removed from the list.
- for (j = 0; j < m - 1; j++) {
- tetrahedrondealloc(newtetlist[j].tet);
- }
- } // if (success)
- } // if (success)
- } // if (doflip)
- } // if (ori <= 0.0)
- } // for (i = 0; i < n; i++)
- // Inverse a and b and the tets configuration.
- for (i = 0; i < n; i++) newtetlist[i] = abtetlist[i];
- for (i = 0; i < n; i++) {
- oldfront = newtetlist[n - i - 1];
- esymself(oldfront);
- fnextself(oldfront);
- abtetlist[i] = oldfront;
- }
- twice++;
- } while (twice < 2);
-
- return false;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// splittetrahedron() Insert a point into a tetrahedron, split it into //
-// four tetrahedra. //
-// //
-// The tetrahedron is given by 'splittet'. Let it is abcd. The inserting //
-// point 'newpoint' v should lie strictly inside abcd. //
-// //
-// Splitting a tetrahedron is to shrink abcd to abcv, and create three new //
-// tetrahedra badv, cbdv, and acdv. //
-// //
-// On completion, 'splittet' returns abcv. If 'flipqueue' is not NULL, it //
-// contains all possibly non-locally Delaunay faces. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::splittetrahedron(point newpoint, triface* splittet,
- queue* flipqueue)
-{
- triface oldabd, oldbcd, oldcad; // Old configuration.
- triface abdcasing, bcdcasing, cadcasing;
- face abdsh, bcdsh, cadsh;
- triface abcv, badv, cbdv, acdv; // New configuration.
- triface worktet;
- face abseg, bcseg, caseg;
- face adseg, bdseg, cdseg;
- point pa, pb, pc, pd;
- REAL attrib, volume;
- int i;
-
- abcv = *splittet;
- abcv.ver = 0;
- // Set the changed vertices and new tetrahedron.
- pa = org(abcv);
- pb = dest(abcv);
- pc = apex(abcv);
- pd = oppo(abcv);
-
- if (b->verbose > 1) {
- printf(" Inserting point %d in tetrahedron (%d, %d, %d, %d).\n",
- pointmark(newpoint), pointmark(pa), pointmark(pb), pointmark(pc),
- pointmark(pd));
- }
-
- fnext(abcv, oldabd);
- enextfnext(abcv, oldbcd);
- enext2fnext(abcv, oldcad);
- sym(oldabd, abdcasing);
- sym(oldbcd, bcdcasing);
- sym(oldcad, cadcasing);
- maketetrahedron(&badv);
- maketetrahedron(&cbdv);
- maketetrahedron(&acdv);
-
- // Set 'badv' vertices.
- setorg (badv, pb);
- setdest(badv, pa);
- setapex(badv, pd);
- setoppo(badv, newpoint);
- // Set 'cbdv' vertices.
- setorg (cbdv, pc);
- setdest(cbdv, pb);
- setapex(cbdv, pd);
- setoppo(cbdv, newpoint);
- // Set 'acdv' vertices.
- setorg (acdv, pa);
- setdest(acdv, pc);
- setapex(acdv, pd);
- setoppo(acdv, newpoint);
- // Set 'abcv' vertices
- setoppo(abcv, newpoint);
-
- // Set the element attributes of the new tetrahedra.
- for (i = 0; i < in->numberoftetrahedronattributes; i++) {
- attrib = elemattribute(abcv.tet, i);
- setelemattribute(badv.tet, i, attrib);
- setelemattribute(cbdv.tet, i, attrib);
- setelemattribute(acdv.tet, i, attrib);
- }
- // Set the volume constraint of the new tetrahedra.
- if (b->varvolume) {
- volume = volumebound(abcv.tet);
- setvolumebound(badv.tet, volume);
- setvolumebound(cbdv.tet, volume);
- setvolumebound(acdv.tet, volume);
- }
-
- // Bond the new triangles to the surrounding tetrahedron.
- bond(badv, abdcasing);
- bond(cbdv, bcdcasing);
- bond(acdv, cadcasing);
- // There may exist subfaces need to be bonded to the new tetrahedra.
- if (checksubfaces) {
- tspivot(oldabd, abdsh);
- if (abdsh.sh != dummysh) {
- tsdissolve(oldabd);
- tsbond(badv, abdsh);
- }
- tspivot(oldbcd, bcdsh);
- if (bcdsh.sh != dummysh) {
- tsdissolve(oldbcd);
- tsbond(cbdv, bcdsh);
- }
- tspivot(oldcad, cadsh);
- if (cadsh.sh != dummysh) {
- tsdissolve(oldcad);
- tsbond(acdv, cadsh);
- }
- } else if (checksubsegs) {
- tsspivot1(abcv, abseg);
- if (abseg.sh != dummysh) {
- tssbond1(badv, abseg);
- }
- enext(abcv, worktet);
- tsspivot1(worktet, bcseg);
- if (bcseg.sh != dummysh) {
- tssbond1(cbdv, bcseg);
- }
- enext2(abcv, worktet);
- tsspivot1(worktet, caseg);
- if (caseg.sh != dummysh) {
- tssbond1(acdv, caseg);
- }
- fnext(abcv, worktet);
- enext2self(worktet);
- tsspivot1(worktet, adseg);
- if (adseg.sh != dummysh) {
- tssdissolve1(worktet);
- enext(badv, worktet);
- tssbond1(worktet, adseg);
- enext2(acdv, worktet);
- tssbond1(worktet, adseg);
- }
- enextfnext(abcv, worktet);
- enext2self(worktet);
- tsspivot1(worktet, bdseg);
- if (bdseg.sh != dummysh) {
- tssdissolve1(worktet);
- enext(cbdv, worktet);
- tssbond1(worktet, bdseg);
- enext2(badv, worktet);
- tssbond1(worktet, bdseg);
- }
- enext2fnext(abcv, worktet);
- enext2self(worktet);
- tsspivot1(worktet, cdseg);
- if (cdseg.sh != dummysh) {
- tssdissolve1(worktet);
- enext(acdv, worktet);
- tssbond1(worktet, cdseg);
- enext2(cbdv, worktet);
- tssbond1(worktet, cdseg);
- }
- }
- badv.loc = 3;
- cbdv.loc = 2;
- bond(badv, cbdv);
- cbdv.loc = 3;
- acdv.loc = 2;
- bond(cbdv, acdv);
- acdv.loc = 3;
- badv.loc = 2;
- bond(acdv, badv);
- badv.loc = 1;
- bond(badv, oldabd);
- cbdv.loc = 1;
- bond(cbdv, oldbcd);
- acdv.loc = 1;
- bond(acdv, oldcad);
-
- badv.loc = 0;
- cbdv.loc = 0;
- acdv.loc = 0;
- if (b->verbose > 3) {
- printf(" Updating abcv ");
- printtet(&abcv);
- printf(" Creating badv ");
- printtet(&badv);
- printf(" Creating cbdv ");
- printtet(&cbdv);
- printf(" Creating acdv ");
- printtet(&acdv);
- }
-
- if (flipqueue != (queue *) NULL) {
- enqueueflipface(abcv, flipqueue);
- enqueueflipface(badv, flipqueue);
- enqueueflipface(cbdv, flipqueue);
- enqueueflipface(acdv, flipqueue);
- }
-
- // Save a handle for quick point location.
- recenttet = abcv;
- // Set the return handle be abcv.
- *splittet = abcv;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// unsplittetrahedron() Reverse the operation of inserting a point into a //
-// tetrahedron, so as to remove the newly inserted //
-// point from the mesh. //
-// //
-// Assume the origional tetrahedron is abcd, it was split by v into four //
-// tetrahedra abcv, badv, cbdv, and acdv. 'splittet' represents face abc of //
-// abcv (i.e., its opposite is v). //
-// //
-// Point v is removed by expanding abcv to abcd, deleting three tetrahedra //
-// badv, cbdv and acdv. On return, point v is not deleted in this routine. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::unsplittetrahedron(triface* splittet)
-{
- triface abcv, badv, cbdv, acdv;
- triface oldabv, oldbcv, oldcav;
- triface badcasing, cbdcasing, acdcasing;
- face badsh, cbdsh, acdsh;
-
- abcv = *splittet;
- adjustedgering(abcv, CCW); // for sure.
- fnext(abcv, oldabv);
- fnext(oldabv, badv);
- esymself(badv);
- enextfnext(abcv, oldbcv);
- fnext(oldbcv, cbdv);
- esymself(cbdv);
- enext2fnext(abcv, oldcav);
- fnext(oldcav, acdv);
- esymself(acdv);
-
- if (b->verbose > 1) {
- printf(" Removing point %d in tetrahedron (%d, %d, %d, %d).\n",
- pointmark(oppo(abcv)), pointmark(org(abcv)), pointmark(dest(abcv)),
- pointmark(apex(abcv)), pointmark(apex(badv)));
- }
-
- sym(badv, badcasing);
- tspivot(badv, badsh);
- sym(cbdv, cbdcasing);
- tspivot(cbdv, cbdsh);
- sym(acdv, acdcasing);
- tspivot(acdv, acdsh);
-
- // Expanding abcv to abcd.
- setoppo(abcv, apex(badv));
- bond(oldabv, badcasing);
- if (badsh.sh != dummysh) {
- tsbond(oldabv, badsh);
- }
- bond(oldbcv, cbdcasing);
- if (cbdsh.sh != dummysh) {
- tsbond(oldbcv, cbdsh);
- }
- bond(oldcav, acdcasing);
- if (acdsh.sh != dummysh) {
- tsbond(oldcav, acdsh);
- }
-
- // Delete the three split-out tetrahedra.
- tetrahedrondealloc(badv.tet);
- tetrahedrondealloc(cbdv.tet);
- tetrahedrondealloc(acdv.tet);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// splittetface() Insert a point on a face of a mesh. //
-// //
-// 'splittet' is the splitting face. Let it is abcd, where abc is the face //
-// will be split. If abc is not a hull face, abce is the tetrahedron at the //
-// opposite of d. //
-// //
-// To split face abc by a point v is to shrink the tetrahedra abcd to abvd, //
-// create two new tetrahedra bcvd, cavd. If abc is not a hull face, shrink //
-// the tetrahedra bace to bave, create two new tetrahedra cbve, acve. //
-// //
-// If abc is a subface, it is split into three subfaces simultaneously by //
-// calling routine splitsubface(), hence, abv, bcv, cav. The edge rings of //
-// the split subfaces have the same orientation as abc's. //
-// //
-// On completion, 'splittet' returns abvd. If 'flipqueue' is not NULL, it //
-// contains all possibly non-locally Delaunay faces. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::splittetface(point newpoint, triface* splittet,
- queue* flipqueue)
-{
- triface abcd, bace; // Old configuration.
- triface oldbcd, oldcad, oldace, oldcbe;
- triface bcdcasing, cadcasing, acecasing, cbecasing;
- face abcsh, bcdsh, cadsh, acesh, cbesh;
- triface abvd, bcvd, cavd, bave, cbve, acve; // New configuration.
- triface worktet;
- face bcseg, caseg;
- face adseg, bdseg, cdseg;
- face aeseg, beseg, ceseg;
- point pa, pb, pc, pd, pe;
- REAL attrib, volume;
- bool mirrorflag;
- int i;
-
- abcd = *splittet;
- // abcd.ver = 0; // Adjust to be CCW edge ring.
- adjustedgering(abcd, CCW);
- pa = org(abcd);
- pb = dest(abcd);
- pc = apex(abcd);
- pd = oppo(abcd);
- pe = (point) NULL; // avoid a compile warning.
- // Is there a second tetrahderon?
- mirrorflag = issymexist(&abcd);
- if (mirrorflag) {
- // This is an interior face.
- sym(abcd, bace);
- findedge(&bace, dest(abcd), org(abcd));
- pe = oppo(bace);
- }
- if (checksubfaces) {
- // Is there a subface need to be split together?
- tspivot(abcd, abcsh);
- if (abcsh.sh != dummysh) {
- // Exists! Keep the edge ab of both handles be the same.
- findedge(&abcsh, org(abcd), dest(abcd));
- }
- }
-
- if (b->verbose > 1) {
- printf(" Inserting point %d on face (%d, %d, %d).\n", pointmark(newpoint),
- pointmark(pa), pointmark(pb), pointmark(pc));
- }
-
- // Save the old configuration at faces bcd and cad.
- enextfnext(abcd, oldbcd);
- enext2fnext(abcd, oldcad);
- sym(oldbcd, bcdcasing);
- sym(oldcad, cadcasing);
- // Create two new tetrahedra.
- maketetrahedron(&bcvd);
- maketetrahedron(&cavd);
- if (mirrorflag) {
- // Save the old configuration at faces bce and cae.
- enextfnext(bace, oldace);
- enext2fnext(bace, oldcbe);
- sym(oldace, acecasing);
- sym(oldcbe, cbecasing);
- // Create two new tetrahedra.
- maketetrahedron(&acve);
- maketetrahedron(&cbve);
- } else {
- // Splitting a boundary face increases the number of boundary faces.
- hullsize += 2;
- }
-
- // Set vertices to the changed tetrahedron and new tetrahedra.
- abvd = abcd; // Update 'abcd' to 'abvd'.
- setapex(abvd, newpoint);
- setorg (bcvd, pb); // Set 'bcvd'.
- setdest(bcvd, pc);
- setapex(bcvd, newpoint);
- setoppo(bcvd, pd);
- setorg (cavd, pc); // Set 'cavd'.
- setdest(cavd, pa);
- setapex(cavd, newpoint);
- setoppo(cavd, pd);
- // Set the element attributes of the new tetrahedra.
- for (i = 0; i < in->numberoftetrahedronattributes; i++) {
- attrib = elemattribute(abvd.tet, i);
- setelemattribute(bcvd.tet, i, attrib);
- setelemattribute(cavd.tet, i, attrib);
- }
- if (b->varvolume) {
- // Set the area constraint of the new tetrahedra.
- volume = volumebound(abvd.tet);
- setvolumebound(bcvd.tet, volume);
- setvolumebound(cavd.tet, volume);
- }
- if (mirrorflag) {
- bave = bace; // Update 'bace' to 'bave'.
- setapex(bave, newpoint);
- setorg (acve, pa); // Set 'acve'.
- setdest(acve, pc);
- setapex(acve, newpoint);
- setoppo(acve, pe);
- setorg (cbve, pc); // Set 'cbve'.
- setdest(cbve, pb);
- setapex(cbve, newpoint);
- setoppo(cbve, pe);
- // Set the element attributes of the new tetrahedra.
- for (i = 0; i < in->numberoftetrahedronattributes; i++) {
- attrib = elemattribute(bave.tet, i);
- setelemattribute(acve.tet, i, attrib);
- setelemattribute(cbve.tet, i, attrib);
- }
- if (b->varvolume) {
- // Set the area constraint of the new tetrahedra.
- volume = volumebound(bave.tet);
- setvolumebound(acve.tet, volume);
- setvolumebound(cbve.tet, volume);
- }
- }
-
- // Bond the new tetrahedra to the surrounding tetrahedra.
- bcvd.loc = 1;
- bond(bcvd, bcdcasing);
- cavd.loc = 1;
- bond(cavd, cadcasing);
- bcvd.loc = 3;
- bond(bcvd, oldbcd);
- cavd.loc = 2;
- bond(cavd, oldcad);
- bcvd.loc = 2;
- cavd.loc = 3;
- bond(bcvd, cavd);
- if (mirrorflag) {
- acve.loc = 1;
- bond(acve, acecasing);
- cbve.loc = 1;
- bond(cbve, cbecasing);
- acve.loc = 3;
- bond(acve, oldace);
- cbve.loc = 2;
- bond(cbve, oldcbe);
- acve.loc = 2;
- cbve.loc = 3;
- bond(acve, cbve);
- // Bond two new coplanar facets.
- bcvd.loc = 0;
- cbve.loc = 0;
- bond(bcvd, cbve);
- cavd.loc = 0;
- acve.loc = 0;
- bond(cavd, acve);
- }
-
- // There may exist subface needed to be bonded to the new tetrahedra.
- if (checksubfaces) {
- tspivot(oldbcd, bcdsh);
- if (bcdsh.sh != dummysh) {
- tsdissolve(oldbcd);
- bcvd.loc = 1;
- tsbond(bcvd, bcdsh);
- }
- tspivot(oldcad, cadsh);
- if (cadsh.sh != dummysh) {
- tsdissolve(oldcad);
- cavd.loc = 1;
- tsbond(cavd, cadsh);
- }
- if (mirrorflag) {
- tspivot(oldace, acesh);
- if (acesh.sh != dummysh) {
- tsdissolve(oldace);
- acve.loc = 1;
- tsbond(acve, acesh);
- }
- tspivot(oldcbe, cbesh);
- if (cbesh.sh != dummysh) {
- tsdissolve(oldcbe);
- cbve.loc = 1;
- tsbond(cbve, cbesh);
- }
- }
- // Is there a subface needs to be split together?
- if (abcsh.sh != dummysh) {
- // Split this subface 'abc' into three i.e, abv, bcv, cav.
- splitsubface(newpoint, &abcsh, (queue *) NULL);
- }
- } else if (checksubsegs) {
- // abvd.loc = abvd.ver = 0;
- bcvd.loc = bcvd.ver = 0;
- cavd.loc = cavd.ver = 0;
- if (mirrorflag) {
- // bave.loc = bave.ver = 0;
- cbve.loc = cbve.ver = 0;
- acve.loc = acve.ver = 0;
- }
- enext(abvd, worktet);
- tsspivot1(worktet, bcseg);
- if (bcseg.sh != dummysh) {
- tssdissolve1(worktet);
- tssbond1(bcvd, bcseg);
- if (mirrorflag) {
- enext2(bave, worktet);
- tssdissolve1(worktet);
- tssbond1(cbve, bcseg);
- }
- }
- enext2(abvd, worktet);
- tsspivot1(worktet, caseg);
- if (caseg.sh != dummysh) {
- tssdissolve1(worktet);
- tssbond1(cavd, caseg);
- if (mirrorflag) {
- enext(bave, worktet);
- tssdissolve1(worktet);
- tssbond1(acve, caseg);
- }
- }
- fnext(abvd, worktet);
- enext2self(worktet);
- tsspivot1(worktet, adseg);
- if (adseg.sh != dummysh) {
- fnext(cavd, worktet);
- enextself(worktet);
- tssbond1(worktet, adseg);
- }
- fnext(abvd, worktet);
- enextself(worktet);
- tsspivot1(worktet, bdseg);
- if (bdseg.sh != dummysh) {
- fnext(bcvd, worktet);
- enext2self(worktet);
- tssbond1(worktet, bdseg);
- }
- enextfnext(abvd, worktet);
- enextself(worktet);
- tsspivot1(worktet, cdseg);
- if (cdseg.sh != dummysh) {
- tssdissolve1(worktet);
- fnext(bcvd, worktet);
- enextself(worktet);
- tssbond1(worktet, cdseg);
- fnext(cavd, worktet);
- enext2self(worktet);
- tssbond1(worktet, cdseg);
- }
- if (mirrorflag) {
- fnext(bave, worktet);
- enextself(worktet);
- tsspivot1(worktet, aeseg);
- if (aeseg.sh != dummysh) {
- fnext(acve, worktet);
- enext2self(worktet);
- tssbond1(worktet, aeseg);
- }
- fnext(bave, worktet);
- enext2self(worktet);
- tsspivot1(worktet, beseg);
- if (beseg.sh != dummysh) {
- fnext(cbve, worktet);
- enextself(worktet);
- tssbond1(worktet, beseg);
- }
- enextfnext(bave, worktet);
- enextself(worktet);
- tsspivot1(worktet, ceseg);
- if (ceseg.sh != dummysh) {
- tssdissolve1(worktet);
- fnext(cbve, worktet);
- enext2self(worktet);
- tssbond1(worktet, ceseg);
- fnext(acve, worktet);
- enextself(worktet);
- tssbond1(worktet, ceseg);
- }
- }
- }
-
- // Save a handle for quick point location.
- recenttet = abvd;
- // Set the return handle be abvd.
- *splittet = abvd;
-
- bcvd.loc = 0;
- cavd.loc = 0;
- if (mirrorflag) {
- cbve.loc = 0;
- acve.loc = 0;
- }
- if (b->verbose > 3) {
- printf(" Updating abvd ");
- printtet(&abvd);
- printf(" Creating bcvd ");
- printtet(&bcvd);
- printf(" Creating cavd ");
- printtet(&cavd);
- if (mirrorflag) {
- printf(" Updating bave ");
- printtet(&bave);
- printf(" Creating cbve ");
- printtet(&cbve);
- printf(" Creating acve ");
- printtet(&acve);
- }
- }
-
- if (flipqueue != (queue *) NULL) {
- fnextself(abvd);
- enqueueflipface(abvd, flipqueue);
- fnextself(bcvd);
- enqueueflipface(bcvd, flipqueue);
- fnextself(cavd);
- enqueueflipface(cavd, flipqueue);
- if (mirrorflag) {
- fnextself(bave);
- enqueueflipface(bave, flipqueue);
- fnextself(cbve);
- enqueueflipface(cbve, flipqueue);
- fnextself(acve);
- enqueueflipface(acve, flipqueue);
- }
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// unsplittetface() Reverse the operation of inserting a point on a face, //
-// so as to remove the newly inserted point. //
-// //
-// Assume the original face is abc, the tetrahedron containing abc is abcd. //
-// If abc is not a hull face, bace is the tetrahedron at the opposite of d. //
-// After face abc was split by a point v, tetrahedron abcd had been split //
-// into three tetrahedra, abvd, bcvd, cavd, and bace (if it exists) had been //
-// split into bave, cbve, acve. 'splittet' represents abvd (its apex is v). //
-// //
-// Point v is removed by expanding abvd to abcd, deleting two tetrahedra //
-// bcvd, cavd. Expanding bave(if it exists) to bace, deleting two tetrahedra //
-// cbve, acve. If abv is a subface, routine unsplitsubface() will be called //
-// to reverse the operation of splitting a subface. On completion, point v //
-// is not deleted in this routine. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::unsplittetface(triface* splittet)
-{
- triface abvd, bcvd, cavd, bave, cbve, acve;
- triface oldbvd, oldvad, oldvbe, oldave;
- triface bcdcasing, cadcasing, cbecasing, acecasing;
- face bcdsh, cadsh, cbesh, acesh;
- face abvsh;
- bool mirrorflag;
-
- abvd = *splittet;
- adjustedgering(abvd, CCW); // for sure.
- enextfnext(abvd, oldbvd);
- fnext(oldbvd, bcvd);
- esymself(bcvd);
- enextself(bcvd);
- enext2fnext(abvd, oldvad);
- fnext(oldvad, cavd);
- esymself(cavd);
- enext2self(cavd);
- // Is there a second tetrahedron?
- sym(abvd, bave);
- mirrorflag = bave.tet != dummytet;
- if (mirrorflag) {
- findedge(&bave, dest(abvd), org(abvd));
- enextfnext(bave, oldave);
- fnext(oldave, acve);
- esymself(acve);
- enextself(acve);
- enext2fnext(bave, oldvbe);
- fnext(oldvbe, cbve);
- esymself(cbve);
- enext2self(cbve);
- } else {
- // Unsplit a hull face decrease the number of boundary faces.
- hullsize -= 2;
- }
- // Is there a subface at abv.
- tspivot(abvd, abvsh);
- if (abvsh.sh != dummysh) {
- // Exists! Keep the edge ab of both handles be the same.
- findedge(&abvsh, org(abvd), dest(abvd));
- }
-
- if (b->verbose > 1) {
- printf(" Removing point %d on face (%d, %d, %d).\n",
- pointmark(apex(abvd)), pointmark(org(abvd)), pointmark(dest(abvd)),
- pointmark(dest(bcvd)));
- }
-
- fnextself(bcvd); // bcvd has changed to bcdv.
- sym(bcvd, bcdcasing);
- tspivot(bcvd, bcdsh);
- fnextself(cavd); // cavd has changed to cadv.
- sym(cavd, cadcasing);
- tspivot(cavd, cadsh);
- if (mirrorflag) {
- fnextself(acve); // acve has changed to acev.
- sym(acve, acecasing);
- tspivot(acve, acesh);
- fnextself(cbve); // cbve has changed to cbev.
- sym(cbve, cbecasing);
- tspivot(cbve, cbesh);
- }
-
- // Expand abvd to abcd.
- setapex(abvd, dest(bcvd));
- bond(oldbvd, bcdcasing);
- if (bcdsh.sh != dummysh) {
- tsbond(oldbvd, bcdsh);
- }
- bond(oldvad, cadcasing);
- if (cadsh.sh != dummysh) {
- tsbond(oldvad, cadsh);
- }
- if (mirrorflag) {
- // Expanding bave to bace.
- setapex(bave, dest(acve));
- bond(oldave, acecasing);
- if (acesh.sh != dummysh) {
- tsbond(oldave, acesh);
- }
- bond(oldvbe, cbecasing);
- if (cbesh.sh != dummysh) {
- tsbond(oldvbe, cbesh);
- }
- }
-
- // Unsplit a subface if there exists.
- if (abvsh.sh != dummysh) {
- unsplitsubface(&abvsh);
- }
-
- // Delete the split-out tetrahedra.
- tetrahedrondealloc(bcvd.tet);
- tetrahedrondealloc(cavd.tet);
- if (mirrorflag) {
- tetrahedrondealloc(acve.tet);
- tetrahedrondealloc(cbve.tet);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// splitsubface() Insert a point on a subface, split it into three. //
-// //
-// The subface is 'splitface'. Let it is abc. The inserting point 'newpoint'//
-// v should lie inside abc. If the neighbor tetrahedra of abc exist, i.e., //
-// abcd and bace, they should have been split by routine splittetface() //
-// before calling this routine, so the connection between the new tetrahedra //
-// and new subfaces can be correctly set. //
-// //
-// To split subface abc by point v is to shrink abc to abv, create two new //
-// subfaces bcv and cav. Set the connection between updated and new created //
-// subfaces. If there is a subsegment at edge bc or ca, connection of new //
-// subface (bcv or cav) to its casing subfaces is a face link, 'casingin' is //
-// the predecessor and 'casingout' is the successor. It is important to keep //
-// the orientations of the edge rings of the updated and created subfaces be //
-// the same as abc's. So they have the same orientation as other subfaces of //
-// this facet with respect to the lift point of this facet. //
-// //
-// On completion, 'splitface' returns abv. If 'flipqueue' is not NULL, it //
-// returns all possibly non-Delaunay edges. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::splitsubface(point newpoint, face* splitface,
- queue* flipqueue)
-{
- triface abvd, bcvd, cavd, bave, cbve, acve;
- face abc, oldbc, oldca, bc, ca, spinsh;
- face bccasin, bccasout, cacasin, cacasout;
- face abv, bcv, cav;
- point pa, pb, pc;
-
- abc = *splitface;
- // The newly created subfaces will have the same edge ring as abc.
- adjustedgering(abc, CCW);
- pa = sorg(abc);
- pb = sdest(abc);
- pc = sapex(abc);
-
- if (b->verbose > 1) {
- printf(" Inserting point %d on subface (%d, %d, %d).\n",
- pointmark(newpoint), pointmark(pa), pointmark(pb), pointmark(pc));
- }
-
- // Save the old configuration at edge bc and ca. Subsegments may appear
- // at both sides, save the face links and dissolve them.
- senext(abc, oldbc);
- senext2(abc, oldca);
- spivot(oldbc, bccasout);
- sspivot(oldbc, bc);
- if (bc.sh != dummysh) {
- if (oldbc.sh != bccasout.sh) {
- // 'oldbc' is not self-bonded.
- spinsh = bccasout;
- do {
- bccasin = spinsh;
- spivotself(spinsh);
- } while (spinsh.sh != oldbc.sh);
- } else {
- bccasout.sh = dummysh;
- }
- ssdissolve(oldbc);
- }
- spivot(oldca, cacasout);
- sspivot(oldca, ca);
- if (ca.sh != dummysh) {
- if (oldca.sh != cacasout.sh) {
- // 'oldca' is not self-bonded.
- spinsh = cacasout;
- do {
- cacasin = spinsh;
- spivotself(spinsh);
- } while (spinsh.sh != oldca.sh);
- } else {
- cacasout.sh = dummysh;
- }
- ssdissolve(oldca);
- }
- // Create two new subfaces.
- makeshellface(subfaces, &bcv);
- makeshellface(subfaces, &cav);
-
- // Set the vertices of changed and new subfaces.
- abv = abc; // Update 'abc' to 'abv'.
- setsapex(abv, newpoint);
- setsorg(bcv, pb); // Set 'bcv'.
- setsdest(bcv, pc);
- setsapex(bcv, newpoint);
- setsorg(cav, pc); // Set 'cav'.
- setsdest(cav, pa);
- setsapex(cav, newpoint);
- if (b->quality && varconstraint) {
- // Copy yhr area bound into the new subfaces.
- setareabound(bcv, areabound(abv));
- setareabound(cav, areabound(abv));
- }
- // Copy the boundary mark into the new subfaces.
- setshellmark(bcv, shellmark(abv));
- setshellmark(cav, shellmark(abv));
- // Copy the subface type into the new subfaces.
- setshelltype(bcv, shelltype(abv));
- setshelltype(cav, shelltype(abv));
- if (checkpbcs) {
- // Copy the pbcgroup into the new subfaces.
- setshellpbcgroup(bcv, shellpbcgroup(abv));
- setshellpbcgroup(cav, shellpbcgroup(abv));
- }
- // Bond the new subfaces to the surrounding subfaces.
- if (bc.sh != dummysh) {
- if (bccasout.sh != dummysh) {
- sbond1(bccasin, bcv);
- sbond1(bcv, bccasout);
- } else {
- // Bond 'bcv' to itsself.
- sbond(bcv, bcv);
- }
- ssbond(bcv, bc);
- } else {
- sbond(bcv, bccasout);
- }
- if (ca.sh != dummysh) {
- if (cacasout.sh != dummysh) {
- sbond1(cacasin, cav);
- sbond1(cav, cacasout);
- } else {
- // Bond 'cav' to itself.
- sbond(cav, cav);
- }
- ssbond(cav, ca);
- } else {
- sbond(cav, cacasout);
- }
- senext2self(bcv);
- sbond(bcv, oldbc);
- senextself(cav);
- sbond(cav, oldca);
- senext2self(bcv);
- senextself(cav);
- sbond(bcv, cav);
-
- // Bond the new subfaces to the new tetrahedra if they exist.
- stpivot(abv, abvd);
- if (abvd.tet != dummytet) {
- // Get two new tetrahedra and their syms.
- findedge(&abvd, sorg(abv), sdest(abv));
- enextfnext(abvd, bcvd);
-#ifdef SELF_CHECK
- assert(bcvd.tet != dummytet);
-#endif
- fnextself(bcvd);
- enext2fnext(abvd, cavd);
-#ifdef SELF_CHECK
- assert(cavd.tet != dummytet);
-#endif
- fnextself(cavd);
- // Bond two new subfaces to the two new tetrahedra.
- tsbond(bcvd, bcv);
- tsbond(cavd, cav);
- }
- // Set the connection at the other sides if the tetrahedra exist.
- sesymself(abv); // bav
- stpivot(abv, bave);
- if (bave.tet != dummytet) {
- sesymself(bcv); // cbv
- sesymself(cav); // acv
- // Get two new tetrahedra and their syms.
- findedge(&bave, sorg(abv), sdest(abv));
- enextfnext(bave, acve);
-#ifdef SELF_CHECK
- assert(acve.tet != dummytet);
-#endif
- fnextself(acve);
- enext2fnext(bave, cbve);
-#ifdef SELF_CHECK
- assert(cbve.tet != dummytet);
-#endif
- fnextself(cbve);
- // Bond two new subfaces to the two new tetrahedra.
- tsbond(acve, cav);
- tsbond(cbve, bcv);
- }
-
- bcv.shver = 0;
- cav.shver = 0;
- if (b->verbose > 3) {
- printf(" Updating abv ");
- printsh(&abv);
- printf(" Creating bcv ");
- printsh(&bcv);
- printf(" Creating cav ");
- printsh(&cav);
- }
-
- if (flipqueue != (queue *) NULL) {
- enqueueflipedge(abv, flipqueue);
- enqueueflipedge(bcv, flipqueue);
- enqueueflipedge(cav, flipqueue);
- }
-
- // Set the return handle be abv.
- *splitface = abv;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// unsplitsubface() Reverse the operation of inserting a point on a //
-// subface, so as to remove the newly inserted point. //
-// //
-// Assume the original subface is abc, it was split by a point v into three //
-// subfaces abv, bcv and cav. 'splitsh' represents abv. //
-// //
-// To remove point v is to expand abv to abc, delete bcv and cav. If edge bc //
-// or ca is a subsegment, the connection at a subsegment is a subface link, //
-// '-casin' and '-casout' are used to save the predecessor and successor of //
-// bcv or cav. On completion, point v is not deleted in this routine. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::unsplitsubface(face* splitsh)
-{
- face abv, bcv, cav;
- face oldbv, oldva, bc, ca, spinsh;
- face bccasin, bccasout, cacasin, cacasout;
-
- abv = *splitsh;
- senext(abv, oldbv);
- spivot(oldbv, bcv);
- if (sorg(bcv) != sdest(oldbv)) {
- sesymself(bcv);
- }
- senextself(bcv);
- senext2(abv, oldva);
- spivot(oldva, cav);
- if (sorg(cav) != sdest(oldva)) {
- sesymself(cav);
- }
- senext2self(cav);
-
- if (b->verbose > 1) {
- printf(" Removing point %d on subface (%d, %d, %d).\n",
- pointmark(sapex(abv)), pointmark(sorg(abv)), pointmark(sdest(abv)),
- pointmark(sdest(bcv)));
- }
-
- spivot(bcv, bccasout);
- sspivot(bcv, bc);
- if (bc.sh != dummysh) {
- if (bcv.sh != bccasout.sh) {
- // 'bcv' is not self-bonded.
- spinsh = bccasout;
- do {
- bccasin = spinsh;
- spivotself(spinsh);
- } while (spinsh.sh != bcv.sh);
- } else {
- bccasout.sh = dummysh;
- }
- }
- spivot(cav, cacasout);
- sspivot(cav, ca);
- if (ca.sh != dummysh) {
- if (cav.sh != cacasout.sh) {
- // 'cav' is not self-bonded.
- spinsh = cacasout;
- do {
- cacasin = spinsh;
- spivotself(spinsh);
- } while (spinsh.sh != cav.sh);
- } else {
- cacasout.sh = dummysh;
- }
- }
-
- // Expand abv to abc.
- setsapex(abv, sdest(bcv));
- if (bc.sh != dummysh) {
- if (bccasout.sh != dummysh) {
- sbond1(bccasin, oldbv);
- sbond1(oldbv, bccasout);
- } else {
- // Bond 'oldbv' to itself.
- sbond(oldbv, oldbv);
- }
- ssbond(oldbv, bc);
- } else {
- sbond(oldbv, bccasout);
- }
- if (ca.sh != dummysh) {
- if (cacasout.sh != dummysh) {
- sbond1(cacasin, oldva);
- sbond1(oldva, cacasout);
- } else {
- // Bond 'oldva' to itself.
- sbond(oldva, oldva);
- }
- ssbond(oldva, ca);
- } else {
- sbond(oldva, cacasout);
- }
-
- // Delete two split-out subfaces.
- shellfacedealloc(subfaces, bcv.sh);
- shellfacedealloc(subfaces, cav.sh);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// splittetedge() Insert a point on an edge of the mesh. //
-// //
-// The edge is given by 'splittet'. Assume its four corners are a, b, n1 and //
-// n2, where ab is the edge will be split. Around ab may exist any number of //
-// tetrahedra. For convenience, they're ordered in a sequence following the //
-// right-hand rule with your thumb points from a to b. Let the vertex set of //
-// these tetrahedra be {a, b, n1, n2, ..., n(i)}. NOTE the tetrahedra around //
-// ab may not connect to each other (can only happen when ab is a subsegment,//
-// hence some faces abn(i) are subfaces). If ab is a subsegment, abn1 must //
-// be a subface. //
-// //
-// To split edge ab by a point v is to split all tetrahedra containing ab by //
-// v. More specifically, for each such tetrahedron, an1n2b, it is shrunk to //
-// an1n2v, and a new tetrahedra bn2n1v is created. If ab is a subsegment, or //
-// some faces of the splitting tetrahedra are subfaces, they must be split //
-// either by calling routine 'splitsubedge()'. //
-// //
-// On completion, 'splittet' returns avn1n2. If 'flipqueue' is not NULL, it //
-// returns all faces which may become non-Delaunay after this operation. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::splittetedge(point newpoint, triface* splittet,
- queue* flipqueue)
-{
- triface *bots, *newtops;
- triface oldtop, topcasing;
- triface spintet, tmpbond0, tmpbond1;
- face abseg, splitsh, topsh, spinsh;
- triface worktet;
- face n1n2seg, n2vseg, n1vseg;
- point pa, pb, n1, n2;
- REAL attrib, volume;
- int wrapcount, hitbdry;
- int i, j;
-
- if (checksubfaces) {
- // Is there a subsegment need to be split together?
- tsspivot(splittet, &abseg);
- if (abseg.sh != dummysh) {
- abseg.shver = 0;
- // Orient the edge direction of 'splittet' be abseg.
- if (org(*splittet) != sorg(abseg)) {
- esymself(*splittet);
- }
- }
- }
- spintet = *splittet;
- pa = org(spintet);
- pb = dest(spintet);
-
- if (b->verbose > 1) {
- printf(" Inserting point %d on edge (%d, %d).\n",
- pointmark(newpoint), pointmark(pa), pointmark(pb));
- }
-
- // Collect the tetrahedra containing the splitting edge (ab).
- n1 = apex(spintet);
- hitbdry = 0;
- wrapcount = 1;
- if (checksubfaces && abseg.sh != dummysh) {
- // It may happen that some tetrahedra containing ab (a subsegment) are
- // completely disconnected with others. If it happens, use the face
- // link of ab to cross the boundary.
- while (true) {
- if (!fnextself(spintet)) {
- // Meet a boundary, walk through it.
- hitbdry ++;
- tspivot(spintet, spinsh);
-#ifdef SELF_CHECK
- assert(spinsh.sh != dummysh);
-#endif
- findedge(&spinsh, pa, pb);
- sfnextself(spinsh);
- stpivot(spinsh, spintet);
-#ifdef SELF_CHECK
- assert(spintet.tet != dummytet);
-#endif
- findedge(&spintet, pa, pb);
- // Remember this position (hull face) in 'splittet'.
- *splittet = spintet;
- // Split two hull faces increase the hull size;
- hullsize += 2;
- }
- if (apex(spintet) == n1) break;
- wrapcount ++;
- }
- if (hitbdry > 0) {
- wrapcount -= hitbdry;
- }
- } else {
- // All the tetrahedra containing ab are connected together. If there
- // are subfaces, 'splitsh' keeps one of them.
- splitsh.sh = dummysh;
- while (hitbdry < 2) {
- if (checksubfaces && splitsh.sh == dummysh) {
- tspivot(spintet, splitsh);
- }
- if (fnextself(spintet)) {
- if (apex(spintet) == n1) break;
- wrapcount++;
- } else {
- hitbdry ++;
- if (hitbdry < 2) {
- esym(*splittet, spintet);
- }
- }
- }
- if (hitbdry > 0) {
- // ab is on the hull.
- wrapcount -= 1;
- // 'spintet' now is a hull face, inverse its edge direction.
- esym(spintet, *splittet);
- // Split two hull faces increases the number of hull faces.
- hullsize += 2;
- }
- }
-
- // Make arrays of updating (bot, oldtop) and new (newtop) tetrahedra.
- bots = new triface[wrapcount];
- newtops = new triface[wrapcount];
- // Spin around ab, gather tetrahedra and set up new tetrahedra.
- spintet = *splittet;
- for (i = 0; i < wrapcount; i++) {
- // Get 'bots[i] = an1n2b'.
- enext2fnext(spintet, bots[i]);
- esymself(bots[i]);
- // Create 'newtops[i]'.
- maketetrahedron(&(newtops[i]));
- // Go to the next.
- fnextself(spintet);
- if (checksubfaces && abseg.sh != dummysh) {
- if (!issymexist(&spintet)) {
- // We meet a hull face, walk through it.
- tspivot(spintet, spinsh);
-#ifdef SELF_CHECK
- assert(spinsh.sh != dummysh);
-#endif
- findedge(&spinsh, pa, pb);
- sfnextself(spinsh);
- stpivot(spinsh, spintet);
-#ifdef SELF_CHECK
- assert(spintet.tet != dummytet);
-#endif
- findedge(&spintet, pa, pb);
- }
- }
- }
-
- // Set the vertices of updated and new tetrahedra.
- for (i = 0; i < wrapcount; i++) {
- // Update 'bots[i] = an1n2v'.
- setoppo(bots[i], newpoint);
- // Set 'newtops[i] = bn2n1v'.
- n1 = dest(bots[i]);
- n2 = apex(bots[i]);
- // Set 'newtops[i]'.
- setorg(newtops[i], pb);
- setdest(newtops[i], n2);
- setapex(newtops[i], n1);
- setoppo(newtops[i], newpoint);
- // Set the element attributes of a new tetrahedron.
- for (j = 0; j < in->numberoftetrahedronattributes; j++) {
- attrib = elemattribute(bots[i].tet, j);
- setelemattribute(newtops[i].tet, j, attrib);
- }
- if (b->varvolume) {
- // Set the area constraint of a new tetrahedron.
- volume = volumebound(bots[i].tet);
- setvolumebound(newtops[i].tet, volume);
- }
-#ifdef SELF_CHECK
- // Make sure no inversed tetrahedron has been created.
- // volume = orient3d(pa, n1, n2, newpoint);
- // if (volume >= 0.0) {
- // printf("Internal error in splittetedge(): volume = %.12g.\n", volume);
- // }
- // volume = orient3d(pb, n2, n1, newpoint);
- // if (volume >= 0.0) {
- // printf("Internal error in splittetedge(): volume = %.12g.\n", volume);
- // }
-#endif
- }
-
- // Bond newtops to topcasings and bots.
- for (i = 0; i < wrapcount; i++) {
- // Get 'oldtop = n1n2va' from 'bots[i]'.
- enextfnext(bots[i], oldtop);
- sym(oldtop, topcasing);
- bond(newtops[i], topcasing);
- if (checksubfaces) {
- tspivot(oldtop, topsh);
- if (topsh.sh != dummysh) {
- tsdissolve(oldtop);
- tsbond(newtops[i], topsh);
- }
- }
- enextfnext(newtops[i], tmpbond0);
- bond(oldtop, tmpbond0);
- }
- // Bond between newtops.
- fnext(newtops[0], tmpbond0);
- enext2fnext(bots[0], spintet);
- for (i = 1; i < wrapcount; i ++) {
- if (issymexist(&spintet)) {
- enext2fnext(newtops[i], tmpbond1);
- bond(tmpbond0, tmpbond1);
- }
- fnext(newtops[i], tmpbond0);
- enext2fnext(bots[i], spintet);
- }
- // Bond the last to the first if no boundary.
- if (issymexist(&spintet)) {
- enext2fnext(newtops[0], tmpbond1);
- bond(tmpbond0, tmpbond1);
- }
- if (checksubsegs) {
- for (i = 0; i < wrapcount; i++) {
- enextfnext(bots[i], worktet); // edge n1->n2.
- tsspivot1(worktet, n1n2seg);
- if (n1n2seg.sh != dummysh) {
- enext(newtops[i], tmpbond0);
- tssbond1(tmpbond0, n1n2seg);
- }
- enextself(worktet); // edge n2->v ==> n2->b
- tsspivot1(worktet, n2vseg);
- if (n2vseg.sh != dummysh) {
- tssdissolve1(worktet);
- tssbond1(newtops[i], n2vseg);
- }
- enextself(worktet); // edge v->n1 ==> b->n1
- tsspivot1(worktet, n1vseg);
- if (n1vseg.sh != dummysh) {
- tssdissolve1(worktet);
- enext2(newtops[i], tmpbond0);
- tssbond1(tmpbond0, n1vseg);
- }
- }
- }
-
- // Is there exist subfaces and subsegment need to be split?
- if (checksubfaces) {
- if (abseg.sh != dummysh) {
- // A subsegment needs be split.
- spivot(abseg, splitsh);
-#ifdef SELF_CHECK
- assert(splitsh.sh != dummysh);
-#endif
- }
- if (splitsh.sh != dummysh) {
- // Split subfaces (and subsegment).
- findedge(&splitsh, pa, pb);
- splitsubedge(newpoint, &splitsh, (queue *) NULL);
- }
- }
-
- if (b->verbose > 3) {
- for (i = 0; i < wrapcount; i++) {
- printf(" Updating bots[%i] ", i);
- printtet(&(bots[i]));
- printf(" Creating newtops[%i] ", i);
- printtet(&(newtops[i]));
- }
- }
-
- if (flipqueue != (queue *) NULL) {
- for (i = 0; i < wrapcount; i++) {
- enqueueflipface(bots[i], flipqueue);
- enqueueflipface(newtops[i], flipqueue);
- }
- }
-
- // Set the return handle be avn1n2. It is got by transforming from
- // 'bots[0]' (which is an1n2v).
- fnext(bots[0], spintet); // spintet is an1vn2.
- esymself(spintet); // spintet is n1avn2.
- enextself(spintet); // spintet is avn1n2.
- *splittet = spintet;
-
- delete [] bots;
- delete [] newtops;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// unsplittetedge() Reverse the operation of splitting an edge, so as to //
-// remove the newly inserted point. //
-// //
-// Assume the original edge is ab, the tetrahedron containing ab is abn1n2. //
-// After ab was split by a point v, every tetrahedron containing ab (e.g., //
-// abn1n2) has been split into two (e.g., an1n2v and bn2n1v). 'splittet' //
-// represents avn1n2 (i.e., its destination is v). //
-// //
-// To remove point v is to expand each split tetrahedron containing ab (e.g.,//
-// (avn1n2 to abn1n2), then delete the redundant one(e.g., vbn1n2). If there //
-// exists any subface around ab, routine unsplitsubedge() will be called to //
-// reverse the operation of splitting a edge (or a subsegment) of subfaces. //
-// On completion, point v is not deleted in this routine. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::unsplittetedge(triface* splittet)
-{
- triface *bots, *newtops;
- triface oldtop, topcasing;
- triface spintet;
- face avseg, splitsh, topsh, spinsh;
- point pa, pv, n1;
- int wrapcount, hitbdry;
- int i;
-
- spintet = *splittet;
- pa = org(spintet);
- pv = dest(spintet);
- if (checksubfaces) {
- // Is there a subsegment need to be unsplit together?
- tsspivot(splittet, &avseg);
- if (avseg.sh != dummysh) {
- // The subsegment's direction should conform to 'splittet'.
- if (sorg(avseg) != pa) {
- sesymself(avseg);
- }
- }
- }
-
- n1 = apex(spintet);
- hitbdry = 0;
- wrapcount = 1;
- if (checksubfaces && avseg.sh != dummysh) {
- // It may happen that some tetrahedra containing ab (a subsegment) are
- // completely disconnected with others. If it happens, use the face
- // link of ab to cross the boundary.
- while (true) {
- if (!fnextself(spintet)) {
- // Meet a boundary, walk through it.
- hitbdry ++;
- tspivot(spintet, spinsh);
-#ifdef SELF_CHECK
- assert(spinsh.sh != dummysh);
-#endif
- findedge(&spinsh, pa, pv);
- sfnextself(spinsh);
- stpivot(spinsh, spintet);
-#ifdef SELF_CHECK
- assert(spintet.tet != dummytet);
-#endif
- findedge(&spintet, pa, pv);
- // Remember this position (hull face) in 'splittet'.
- *splittet = spintet;
- // Split two hull faces increase the hull size;
- hullsize += 2;
- }
- if (apex(spintet) == n1) break;
- wrapcount ++;
- }
- if (hitbdry > 0) {
- wrapcount -= hitbdry;
- }
- } else {
- // All the tetrahedra containing ab are connected together. If there
- // are subfaces, 'splitsh' keeps one of them.
- splitsh.sh = dummysh;
- while (hitbdry < 2) {
- if (checksubfaces && splitsh.sh == dummysh) {
- tspivot(spintet, splitsh);
- }
- if (fnextself(spintet)) {
- if (apex(spintet) == n1) break;
- wrapcount++;
- } else {
- hitbdry ++;
- if (hitbdry < 2) {
- esym(*splittet, spintet);
- }
- }
- }
- if (hitbdry > 0) {
- // ab is on the hull.
- wrapcount -= 1;
- // 'spintet' now is a hull face, inverse its edge direction.
- esym(spintet, *splittet);
- // Split two hull faces increases the number of hull faces.
- hullsize += 2;
- }
- }
-
- // Make arrays of updating (bot, oldtop) and new (newtop) tetrahedra.
- bots = new triface[wrapcount];
- newtops = new triface[wrapcount];
- // Spin around av, gather tetrahedra and set up new tetrahedra.
- spintet = *splittet;
- for (i = 0; i < wrapcount; i++) {
- // Get 'bots[i] = an1n2v'.
- enext2fnext(spintet, bots[i]);
- esymself(bots[i]);
- // Get 'oldtop = n1n2va'.
- enextfnext(bots[i], oldtop);
- // Get 'newtops[i] = 'bn1n2v'
- fnext(oldtop, newtops[i]); // newtop = n1n2bv
- esymself(newtops[i]); // newtop = n2n1bv
- enext2self(newtops[i]); // newtop = bn2n1v
- // Go to the next.
- fnextself(spintet);
- if (checksubfaces && avseg.sh != dummysh) {
- if (!issymexist(&spintet)) {
- // We meet a hull face, walk through it.
- tspivot(spintet, spinsh);
-#ifdef SELF_CHECK
- assert(spinsh.sh != dummysh);
-#endif
- findedge(&spinsh, pa, pv);
- sfnextself(spinsh);
- stpivot(spinsh, spintet);
-#ifdef SELF_CHECK
- assert(spintet.tet != dummytet);
-#endif
- findedge(&spintet, pa, pv);
- }
- }
- }
-
- if (b->verbose > 1) {
- printf(" Removing point %d from edge (%d, %d).\n",
- pointmark(oppo(bots[0])), pointmark(org(bots[0])),
- pointmark(org(newtops[0])));
- }
-
- for (i = 0; i < wrapcount; i++) {
- // Expand an1n2v to an1n2b.
- setoppo(bots[i], org(newtops[i]));
- // Get 'oldtop = n1n2va' from 'bot[i]'.
- enextfnext(bots[i], oldtop);
- // Get 'topcasing' from 'newtop[i]'
- sym(newtops[i], topcasing);
- // Bond them.
- bond(oldtop, topcasing);
- if (checksubfaces) {
- tspivot(newtops[i], topsh);
- if (topsh.sh != dummysh) {
- tsbond(oldtop, topsh);
- }
- }
- // Delete the tetrahedron above an1n2v.
- tetrahedrondealloc(newtops[i].tet);
- }
-
- // If there exists any subface, unsplit them.
- if (checksubfaces) {
- if (avseg.sh != dummysh) {
- spivot(avseg, splitsh);
-#ifdef SELF_CHECK
- assert(splitsh.sh != dummysh);
-#endif
- }
- if (splitsh.sh != dummysh) {
- findedge(&splitsh, pa, pv);
- unsplitsubedge(&splitsh);
- }
- }
-
- delete [] bots;
- delete [] newtops;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// splitsubedge() Insert a point on an edge of the surface mesh. //
-// //
-// The splitting edge is given by 'splitsh'. Assume its three corners are a, //
-// b, c, where ab is the edge will be split. ab may be a subsegment. //
-// //
-// To split edge ab is to split all subfaces conatining ab. If ab is not a //
-// subsegment, there are only two subfaces need be split, otherwise, there //
-// may have any number of subfaces need be split. Each splitting subface abc //
-// is shrunk to avc, a new subface vbc is created. It is important to keep //
-// the orientations of edge rings of avc and vbc be the same as abc's. If ab //
-// is a subsegment, it is shrunk to av and a new subsegment vb is created. //
-// //
-// If there are tetrahedra adjoining to the splitting subfaces, they should //
-// be split before calling this routine, so the connection between the new //
-// tetrahedra and the new subfaces can be correctly set. //
-// //
-// On completion, 'splitsh' returns avc. If 'flipqueue' is not NULL, it //
-// returns all edges which may be non-Delaunay. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::splitsubedge(point newpoint, face* splitsh, queue* flipqueue)
-{
- triface abcd, bace, vbcd, bvce;
- face startabc, spinabc, spinsh;
- face oldbc, bccasin, bccasout;
- face ab, bc;
- face avc, vbc, vbc1;
- face av, vb;
- point pa, pb;
-
- startabc = *splitsh;
- // Is there a subsegment?
- sspivot(startabc, ab);
- if (ab.sh != dummysh) {
- ab.shver = 0;
- if (sorg(startabc) != sorg(ab)) {
- sesymself(startabc);
- }
- }
- pa = sorg(startabc);
- pb = sdest(startabc);
-
- if (b->verbose > 1) {
- printf(" Inserting point %d on subedge (%d, %d) %s.\n",
- pointmark(newpoint), pointmark(pa), pointmark(pb),
- (ab.sh != dummysh ? "(seg)" : " "));
- }
-
- // Spin arround ab, split every subface containing ab.
- spinabc = startabc;
- do {
- // Adjust spinabc be edge ab.
- if (sorg(spinabc) != pa) {
- sesymself(spinabc);
- }
- // Save old configuration at edge bc, if bc has a subsegment, save the
- // face link of it and dissolve it from bc.
- senext(spinabc, oldbc);
- spivot(oldbc, bccasout);
- sspivot(oldbc, bc);
- if (bc.sh != dummysh) {
- if (spinabc.sh != bccasout.sh) {
- // 'spinabc' is not self-bonded.
- spinsh = bccasout;
- do {
- bccasin = spinsh;
- spivotself(spinsh);
- } while (spinsh.sh != oldbc.sh);
- } else {
- bccasout.sh = dummysh;
- }
- ssdissolve(oldbc);
- }
- // Create a new subface.
- makeshellface(subfaces, &vbc);
- // Split abc.
- avc = spinabc; // Update 'abc' to 'avc'.
- setsdest(avc, newpoint);
- // Make 'vbc' be in the same edge ring as 'avc'.
- vbc.shver = avc.shver;
- setsorg(vbc, newpoint); // Set 'vbc'.
- setsdest(vbc, pb);
- setsapex(vbc, sapex(avc));
- if (b->quality && varconstraint) {
- // Copy the area bound into the new subface.
- setareabound(vbc, areabound(avc));
- }
- // Copy the shell marker and shell type into the new subface.
- setshellmark(vbc, shellmark(avc));
- setshelltype(vbc, shelltype(avc));
- if (checkpbcs) {
- // Copy the pbcgroup into the new subface.
- setshellpbcgroup(vbc, shellpbcgroup(avc));
- }
- // Set the connection between updated and new subfaces.
- senext2self(vbc);
- sbond(vbc, oldbc);
- // Set the connection between new subface and casings.
- senext2self(vbc);
- if (bc.sh != dummysh) {
- if (bccasout.sh != dummysh) {
- // Insert 'vbc' into face link.
- sbond1(bccasin, vbc);
- sbond1(vbc, bccasout);
- } else {
- // Bond 'vbc' to itself.
- sbond(vbc, vbc);
- }
- ssbond(vbc, bc);
- } else {
- sbond(vbc, bccasout);
- }
- // Go to next subface at edge ab.
- spivotself(spinabc);
- if (spinabc.sh == dummysh) {
- break; // 'ab' is a hull edge.
- }
- } while (spinabc.sh != startabc.sh);
-
- // Get the new subface vbc above the updated subface avc (= startabc).
- senext(startabc, oldbc);
- spivot(oldbc, vbc);
- if (sorg(vbc) == newpoint) {
- sesymself(vbc);
- }
-#ifdef SELF_CHECK
- assert(sorg(vbc) == sdest(oldbc) && sdest(vbc) == sorg(oldbc));
-#endif
- senextself(vbc);
- // Set the face link for the new created subfaces around edge vb.
- spinabc = startabc;
- do {
- // Go to the next subface at edge av.
- spivotself(spinabc);
- if (spinabc.sh == dummysh) {
- break; // 'ab' is a hull edge.
- }
- if (sorg(spinabc) != pa) {
- sesymself(spinabc);
- }
- // Get the new subface vbc1 above the updated subface avc (= spinabc).
- senext(spinabc, oldbc);
- spivot(oldbc, vbc1);
- if (sorg(vbc1) == newpoint) {
- sesymself(vbc1);
- }
-#ifdef SELF_CHECK
- assert(sorg(vbc1) == sdest(oldbc) && sdest(vbc1) == sorg(oldbc));
-#endif
- senextself(vbc1);
- // Set the connection: vbc->vbc1.
- sbond1(vbc, vbc1);
- // For the next connection.
- vbc = vbc1;
- } while (spinabc.sh != startabc.sh);
-
- // Split ab if it is a subsegment.
- if (ab.sh != dummysh) {
- // Update subsegment ab to av.
- av = ab;
- setsdest(av, newpoint);
- // Create a new subsegment vb.
- makeshellface(subsegs, &vb);
- setsorg(vb, newpoint);
- setsdest(vb, pb);
- // vb gets the same mark and segment type as av.
- setshellmark(vb, shellmark(av));
- setshelltype(vb, shelltype(av));
- if (b->quality && varconstraint) {
- // Copy the area bound into the new subsegment.
- setareabound(vb, areabound(av));
- }
- // Save the old connection at ab (re-use the handles oldbc, bccasout).
- senext(av, oldbc);
- spivot(oldbc, bccasout);
- // Bond av and vb (bonded at their "fake" edges).
- senext2(vb, bccasin);
- sbond(bccasin, oldbc);
- if (bccasout.sh != dummysh) {
- // There is a subsegment connecting with ab at b. It will connect
- // to vb at b after splitting.
- bccasout.shver = 0;
- if (sorg(bccasout) != pb) sesymself(bccasout);
-#ifdef SELF_CHECK
- assert(sorg(bccasout) == pb);
-#endif
- senext2self(bccasout);
- senext(vb, bccasin);
- sbond(bccasin, bccasout);
- }
- // Bond all new subfaces (vbc) to vb.
- spinabc = startabc;
- do {
- // Adjust spinabc be edge av.
- if (sorg(spinabc) != pa) {
- sesymself(spinabc);
- }
- // Get new subface vbc above the updated subface avc (= spinabc).
- senext(spinabc, oldbc);
- spivot(oldbc, vbc);
- if (sorg(vbc) == newpoint) {
- sesymself(vbc);
- }
- senextself(vbc);
- // Bond the new subface and the new subsegment.
- ssbond(vbc, vb);
- // Go to the next.
- spivotself(spinabc);
-#ifdef SELF_CHECK
- assert(spinabc.sh != dummysh);
-#endif
- } while (spinabc.sh != startabc.sh);
- }
-
- // Bond the new subfaces to new tetrahedra if they exist. New tetrahedra
- // should have been created before calling this routine.
- spinabc = startabc;
- do {
- // Adjust spinabc be edge av.
- if (sorg(spinabc) != pa) {
- sesymself(spinabc);
- }
- // Get new subface vbc above the updated subface avc (= spinabc).
- senext(spinabc, oldbc);
- spivot(oldbc, vbc);
- if (sorg(vbc) == newpoint) {
- sesymself(vbc);
- }
- senextself(vbc);
- // Get the adjacent tetrahedra at 'spinabc'.
- stpivot(spinabc, abcd);
- if (abcd.tet != dummytet) {
- findedge(&abcd, sorg(spinabc), sdest(spinabc));
- enextfnext(abcd, vbcd);
- fnextself(vbcd);
-#ifdef SELF_CHECK
- assert(vbcd.tet != dummytet);
-#endif
- tsbond(vbcd, vbc);
- sym(vbcd, bvce);
- sesymself(vbc);
- tsbond(bvce, vbc);
- } else {
- // One side is empty, check the other side.
- sesymself(spinabc);
- stpivot(spinabc, bace);
- if (bace.tet != dummytet) {
- findedge(&bace, sorg(spinabc), sdest(spinabc));
- enext2fnext(bace, bvce);
- fnextself(bvce);
-#ifdef SELF_CHECK
- assert(bvce.tet != dummytet);
-#endif
- sesymself(vbc);
- tsbond(bvce, vbc);
- }
- }
- // Go to the next.
- spivotself(spinabc);
- if (spinabc.sh == dummysh) {
- break; // 'ab' is a hull edge.
- }
- } while (spinabc.sh != startabc.sh);
-
- if (b->verbose > 3) {
- spinabc = startabc;
- do {
- // Adjust spinabc be edge av.
- if (sorg(spinabc) != pa) {
- sesymself(spinabc);
- }
- printf(" Updating abc:\n");
- printsh(&spinabc);
- // Get new subface vbc above the updated subface avc (= spinabc).
- senext(spinabc, oldbc);
- spivot(oldbc, vbc);
- if (sorg(vbc) == newpoint) {
- sesymself(vbc);
- }
- senextself(vbc);
- printf(" Creating vbc:\n");
- printsh(&vbc);
- // Go to the next.
- spivotself(spinabc);
- if (spinabc.sh == dummysh) {
- break; // 'ab' is a hull edge.
- }
- } while (spinabc.sh != startabc.sh);
- }
-
- if (flipqueue != (queue *) NULL) {
- spinabc = startabc;
- do {
- // Adjust spinabc be edge av.
- if (sorg(spinabc) != pa) {
- sesymself(spinabc);
- }
- senext2(spinabc, oldbc); // Re-use oldbc.
- enqueueflipedge(oldbc, flipqueue);
- // Get new subface vbc above the updated subface avc (= spinabc).
- senext(spinabc, oldbc);
- spivot(oldbc, vbc);
- if (sorg(vbc) == newpoint) {
- sesymself(vbc);
- }
- senextself(vbc);
- senext(vbc, oldbc); // Re-use oldbc.
- enqueueflipedge(oldbc, flipqueue);
- // Go to the next.
- spivotself(spinabc);
- if (spinabc.sh == dummysh) {
- break; // 'ab' is a hull edge.
- }
- } while (spinabc.sh != startabc.sh);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// unsplitsubedge() Reverse the operation of splitting an edge of subface,//
-// so as to remove a point from the edge. //
-// //
-// Assume the original edge is ab, the subface containing it is abc. It was //
-// split by a point v into avc, and vbc. 'splitsh' represents avc, further- //
-// more, if av is a subsegment, av should be the zero version of the split //
-// subsegment (i.e., av.shver = 0), so we are sure that the destination (v) //
-// of both avc and av is the deleting point. //
-// //
-// To remove point v is to expand avc to abc, delete vbc, do the same for //
-// other subfaces containing av and vb. If av and vb are subsegments, expand //
-// av to ab, delete vb. On completion, point v is not deleted. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::unsplitsubedge(face* splitsh)
-{
- face startavc, spinavc, spinbcv;
- face oldvc, bccasin, bccasout, spinsh;
- face av, vb, bc;
- point pa, pv, pb;
-
- startavc = *splitsh;
- sspivot(startavc, av);
- if (av.sh != dummysh) {
- // Orient the direction of subsegment to conform the subface.
- if (sorg(av) != sorg(startavc)) {
- sesymself(av);
- }
-#ifdef SELF_CHECK
- assert(av.shver == 0);
-#endif
- }
- senext(startavc, oldvc);
- spivot(oldvc, vb); // vb is subface vbc
- if (sorg(vb) != sdest(oldvc)) {
- sesymself(vb);
- }
- senextself(vb);
- pa = sorg(startavc);
- pv = sdest(startavc);
- pb = sdest(vb);
-
- if (b->verbose > 1) {
- printf(" Removing point %d from subedge (%d, %d).\n",
- pointmark(pv), pointmark(pa), pointmark(pb));
- }
-
- // Spin arround av, unsplit every subface containing av.
- spinavc = startavc;
- do {
- // Adjust spinavc be edge av.
- if (sorg(spinavc) != pa) {
- sesymself(spinavc);
- }
- // Save old configuration at edge bc, if bc has a subsegment, save the
- // face link of it.
- senext(spinavc, oldvc);
- spivot(oldvc, spinbcv);
- if (sorg(spinbcv) != sdest(oldvc)) {
- sesymself(spinbcv);
- }
- senext2self(spinbcv);
- spivot(spinbcv, bccasout);
- sspivot(spinbcv, bc);
- if (bc.sh != dummysh) {
- if (spinbcv.sh != bccasout.sh) {
- // 'spinbcv' is not self-bonded.
- spinsh = bccasout;
- do {
- bccasin = spinsh;
- spivotself(spinsh);
- } while (spinsh.sh != spinbcv.sh);
- } else {
- bccasout.sh = dummysh;
- }
- }
- // Expand avc to abc.
- setsdest(spinavc, pb);
- if (bc.sh != dummysh) {
- if (bccasout.sh != dummysh) {
- sbond1(bccasin, oldvc);
- sbond1(oldvc, bccasout);
- } else {
- // Bond 'oldbc' to itself.
- sbond(oldvc, oldvc);
- }
- ssbond(oldvc, bc);
- } else {
- sbond(oldvc, bccasout);
- }
- // Delete bcv.
- shellfacedealloc(subfaces, spinbcv.sh);
- // Go to next subface at edge av.
- spivotself(spinavc);
- if (spinavc.sh == dummysh) {
- break; // 'av' is a hull edge.
- }
- } while (spinavc.sh != startavc.sh);
-
- // Is there a subsegment need to be unsplit?
- if (av.sh != dummysh) {
- senext(av, oldvc); // Re-use oldvc.
- spivot(oldvc, vb);
- vb.shver = 0;
-#ifdef SELF_CHECK
- assert(sdest(av) == sorg(vb));
-#endif
- senext(vb, spinbcv); // Re-use spinbcv.
- spivot(spinbcv, bccasout);
- // Expand av to ab.
- setsdest(av, pb);
- sbond(oldvc, bccasout);
- // Delete vb.
- shellfacedealloc(subsegs, vb.sh);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// insertsite() Insert a point into the mesh. //
-// //
-// The 'newpoint' is located. If 'searchtet->tet' is not NULL, the search //
-// for the containing tetrahedron begins from 'searchtet', otherwise, a full //
-// point location procedure is called. If 'newpoint' is found inside a //
-// tetrahedron, the tetrahedron is split into four (by splittetrahedron()); //
-// if 'newpoint' lies on a face, the face is split into three, thereby //
-// splitting the two adjacent tetrahedra into six (by splittetface()); if //
-// 'newpoint' lies on an edge, the edge is split into two, thereby, every //
-// tetrahedron containing this edge is split into two. If 'newpoint' lies on //
-// an existing vertex, no action is taken, and the value DUPLICATEPOINT is //
-// returned and 'searchtet' is set to a handle whose origin is the vertex. //
-// //
-// If 'flipqueue' is not NULL, after 'newpoint' is inserted, it returns all //
-// faces which may become non-Delaunay due to the newly inserted point. Flip //
-// operations can be performed as necessary on them to maintain the Delaunay //
-// property. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-enum tetgenmesh::insertsiteresult tetgenmesh::insertsite(point newpoint,
- triface* searchtet, bool approx, queue* flipqueue)
-{
- enum locateresult intersect, exactloc;
- point checkpt;
- REAL epspp, checklen;
- int count;
-
- if (b->verbose > 1) {
- printf(" Insert point to mesh: (%.12g, %.12g, %.12g) %d.\n",
- newpoint[0], newpoint[1], newpoint[2], pointmark(newpoint));
- }
-
- if (searchtet->tet == (tetrahedron *) NULL) {
- // Search for a tetrahedron containing 'newpoint'.
- searchtet->tet = dummytet;
- exactloc = locate(newpoint, searchtet);
- } else {
- // Start searching from the tetrahedron provided by the caller.
- exactloc = preciselocate(newpoint, searchtet, tetrahedrons->items);
- }
- intersect = exactloc;
- if (approx && (exactloc != ONVERTEX)) {
- // Adjust the exact location to an approx. location wrt. epsilon.
- epspp = b->epsilon;
- count = 0;
- while (count < 16) {
- intersect = adjustlocate(newpoint, searchtet, exactloc, epspp);
- if (intersect == ONVERTEX) {
- checkpt = org(*searchtet);
- checklen = distance(checkpt, newpoint);
- if (checklen / longest > b->epsilon) {
- epspp *= 1e-2;
- count++;
- continue;
- }
- }
- break;
- }
- }
- // Keep current search state for next searching.
- recenttet = *searchtet;
-
- // Insert the point using the right routine
- switch (intersect) {
- case ONVERTEX:
- // There's already a vertex there. Return in 'searchtet' a tetrahedron
- // whose origin is the existing vertex.
- if (b->verbose > 1) {
- printf(" Not insert for duplicating point.\n");
- }
- return DUPLICATEPOINT;
-
- case OUTSIDE:
- if (b->verbose > 1) {
- printf(" Not insert for locating outside the mesh.\n");
- }
- return OUTSIDEPOINT;
-
- case ONEDGE:
- // 'newpoint' falls on an edge.
- splittetedge(newpoint, searchtet, flipqueue);
- return SUCCESSONEDGE;
-
- case ONFACE:
- // 'newpoint' falls on a face.
- splittetface(newpoint, searchtet, flipqueue);
- return SUCCESSONFACE;
-
- case INTETRAHEDRON:
- // 'newpoint' falls inside a tetrahedron.
- splittetrahedron(newpoint, searchtet, flipqueue);
- return SUCCESSINTET;
-
- default:
- // Impossible case.
- return OUTSIDEPOINT;
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// undosite() Undo the most recently point insertion. //
-// //
-// 'insresult' indicates in where the newpoint has been inserted, i.e., in a //
-// tetrahedron, on a face, or on an edge. A correspoding routine will be //
-// called to undo the point insertion. 'splittet' is a handle represent one //
-// of the resulting tetrahedra, but it may be changed after transformation, //
-// even may be dead. Four points 'torg', ... 'toppo' are the corners which //
-// 'splittet' should have. On finish, 'newpoint' is not removed. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::undosite(enum insertsiteresult insresult, triface* splittet,
- point torg, point tdest, point tapex, point toppo)
-{
- // Set the four corners of 'splittet' exactly be 'torg', ... 'toppo'.
- findface(splittet, torg, tdest, tapex);
- if (oppo(*splittet) != toppo) {
- symself(*splittet);
-#ifdef SELF_CHECK
- assert(oppo(*splittet) == toppo);
-#endif
- // The sym() operation may inverse the edge, correct it if so.
- findedge(splittet, torg, tdest);
- }
-
- // Unsplit the tetrahedron according to 'insresult'.
- switch (insresult) {
- case SUCCESSINTET:
- // 'splittet' should be the face with 'newpoint' as its opposite.
- unsplittetrahedron(splittet);
- break;
- case SUCCESSONFACE:
- // 'splittet' should be the one of three splitted face with 'newpoint'
- // as its apex.
- unsplittetface(splittet);
- break;
- case SUCCESSONEDGE:
- // 'splittet' should be the tet with destination is 'newpoint'.
- unsplittetedge(splittet);
- break;
- default: // To omit compile warnings.
- break;
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// closeopenface() Close "open" faces recursively. //
-// //
-// This is the support routine of inserthullsite(). A point p which lies out-//
-// side of CH(T). p is inserted to T by forming a tet t from p and a visible //
-// CH face f. The three sides of f which have p as a vertex is called "open" //
-// face. Each open face will be closed by either creating a tet on top of it //
-// or become a new CH face. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::closeopenface(triface* openface, queue* flipque)
-{
- triface newtet, oldhull;
- triface newopenface, closeface;
- point inspoint, pa, pb, pc;
- REAL attrib, volume;
- int i;
-
- // Get the new point p.
- inspoint = apex(*openface);
- // Find the old CH face f_o (f and f_o share the same edge).
- esym(*openface, oldhull);
- while (fnextself(oldhull)) ;
- if (apex(oldhull) != inspoint) {
- // Is f_o visible by p?
- pa = org(oldhull);
- pb = dest(oldhull);
- pc = apex(oldhull);
- if (orient3d(pa, pb, pc, inspoint) < 0.0) {
- // Yes. Create a new tet t above f_o.
- maketetrahedron(&newtet);
- setorg(newtet, pa);
- setdest(newtet, pb);
- setapex(newtet, pc);
- setoppo(newtet, inspoint);
- for (i = 0; i < in->numberoftetrahedronattributes; i++) {
- attrib = elemattribute(oldhull.tet, i);
- setelemattribute(newtet.tet, i, attrib);
- }
- if (b->varvolume) {
- volume = volumebound(oldhull.tet);
- setvolumebound(newtet.tet, volume);
- }
- // Connect t to T.
- bond(newtet, oldhull);
- // Close f.
- fnext(newtet, newopenface);
- bond(newopenface, *openface);
- // f_o becomes an interior face.
- enqueueflipface(oldhull, flipque);
- // Hull face number decreases.
- hullsize--;
- // Two faces of t become open face.
- enextself(newtet);
- for (i = 0; i < 2; i++) {
- fnext(newtet, newopenface);
- sym(newopenface, closeface);
- if (closeface.tet == dummytet) {
- closeopenface(&newopenface, flipque);
- }
- enextself(newtet);
- }
- } else {
- // Inivisible. f becomes a new CH face.
- hullsize++;
- // Let 'dummytet' holds f for the next point location.
- dummytet[0] = encode(*openface);
- }
- } else {
- // f_o is co-incident with f --> f is closed by f_o.
- bond(*openface, oldhull);
- // f is an interior face.
- enqueueflipface(*openface, flipque);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// inserthullsite() Insert a point which lies outside the convex hull. //
-// //
-// The 'inspoint' p lies outside the tetrahedralization T. The 'horiz' f is //
-// on the convex hull of T, CH(T), which is visible by p (Imagine f is para- //
-// llel to the horizon). To insert p into T we have to enlarge the CH(T) and //
-// update T so that p is on the new CH(T). //
-// //
-// To enlarge the CH(T). We need to find the set F of faces which are on CH //
-// (T) and visible by p (F can be formed by a depth-first search from f). p //
-// is then inserted into T by mounting new tets formed by p and these faces. //
-// Faces of F become interior faces and may non-locally Delaunay. They are //
-// queued in 'flipqueue' for flip tests. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::inserthullsite(point inspoint, triface* horiz, queue* flipque)
-{
- triface firstnewtet;
- triface openface, closeface;
- REAL attrib, volume;
- int i;
-
- // Let f face to p.
- adjustedgering(*horiz, CW);
- // Create the first tet t (from f and p).
- maketetrahedron(&firstnewtet);
- setorg (firstnewtet, org(*horiz));
- setdest(firstnewtet, dest(*horiz));
- setapex(firstnewtet, apex(*horiz));
- setoppo(firstnewtet, inspoint);
- for (i = 0; i < in->numberoftetrahedronattributes; i++) {
- attrib = elemattribute(horiz->tet, i);
- setelemattribute(firstnewtet.tet, i, attrib);
- }
- if (b->varvolume) {
- volume = volumebound(horiz->tet);
- setvolumebound(firstnewtet.tet, volume);
- }
- // Connect t to T.
- bond(firstnewtet, *horiz);
- // f is not on CH(T) anymore.
- enqueueflipface(*horiz, flipque);
- // Hull face number decreases.
- hullsize--;
-
- // Call the faces of t which have p as a vertex "open" face.
- for (i = 0; i < 3; i++) {
- // Get an open face f_i of t.
- fnext(firstnewtet, openface);
- // Close f_i if it is still open.
- sym(openface, closeface);
- if (closeface.tet == dummytet) {
- closeopenface(&openface, flipque);
- }
- // Go to the next open face of t.
- enextself(firstnewtet);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// Terminology: BC(p) and CBC(p), B(p) and C(p). //
-// //
-// Given an arbitrary point p, the Bowyer-Watson cavity BC(p) is formed by //
-// tets whose circumspheres containing p. The outer faces of BC(p) form a //
-// polyhedron B(p). //
-// //
-// If p is on a facet F, the constrained Bowyer-Watson cavity CBC(p) on F is //
-// formed by subfaces of F whose circumspheres containing p. The outer edges //
-// of CBC(p) form a polygon C(p). B(p) is separated into two parts by C(p), //
-// denoted as B_1(p) and B_2(p), one of them may be empty (F is on the hull).//
-// //
-// If p is on a segment S which is shared by n facets. There exist n C(p)s, //
-// each one is a non-closed polygon (without S). B(p) is split into n parts, //
-// each of them is denoted as B_i(p), some B_i(p) may be empty. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// formbowatcavitysub() Form CBC(p) and C(p) on a facet F. //
-// //
-// Parameters: bp = p, bpseg = S, sublist = CBC(p), subceillist = C(p). //
-// //
-// CBC(p) contains at least one subface on input; S may be NULL which means //
-// that p is inside a facet. On output, all subfaces of CBC(p) are infected, //
-// and the edge rings are oriented to the same halfspace. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::formbowatcavitysub(point bp, face* bpseg, list* sublist,
- list* subceillist)
-{
- triface adjtet;
- face startsh, neighsh;
- face checkseg;
- point pa, pb, pc, pd;
- REAL sign;
- int i, j;
-
- // Form CBC(p) and C(p) by a broadth-first searching.
- for (i = 0; i < sublist->len(); i++) {
- startsh = * (face *)(* sublist)[i]; // startsh = f.
- // Look for three neighbors of f.
- for (j = 0; j < 3; j++) {
- sspivot(startsh, checkseg);
- if (checkseg.sh == dummysh) {
- // Get its neighbor n.
- spivot(startsh, neighsh);
- // Is n already in CBC(p)?
- if (!sinfected(neighsh)) {
- stpivot(neighsh, adjtet);
- if (adjtet.tet == dummytet) {
- sesymself(neighsh);
- stpivot(neighsh, adjtet);
- }
- // For positive orientation that insphere() test requires.
- adjustedgering(adjtet, CW);
- pa = org(adjtet);
- pb = dest(adjtet);
- pc = apex(adjtet);
- pd = oppo(adjtet);
- sign = insphere(pa, pb, pc, pd, bp);
- if (sign >= 0.0) {
- // Orient edge ring of n according to that of f.
- if (sorg(neighsh) != sdest(startsh)) sesymself(neighsh);
- // Collect it into CBC(p).
- sinfect(neighsh);
- sublist->append(&neighsh);
- } else {
- subceillist->append(&startsh); // Found an edge of C(p).
- }
- }
- } else {
- // Do not cross a segment.
- if (bpseg != (face *) NULL) {
- if (checkseg.sh != bpseg->sh) {
- subceillist->append(&startsh); // Found an edge of C(p).
- }
- } else {
- subceillist->append(&startsh); // Found an edge of C(p).
- }
- }
- senextself(startsh);
- }
- }
-
- if (b->verbose > 2) {
- printf(" Collect CBC(%d): %d subfaces, %d edges.\n", pointmark(bp),
- sublist->len(), subceillist->len());
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// formbowatcavityquad() Form BC_i(p) and B_i(p) in a quadrant. //
-// //
-// Parameters: bp = p, tetlist = BC_i(p), ceillist = B_i(p). //
-// //
-// BC_i(p) contains at least one tet on input. On finish, all tets collected //
-// in BC_i(p) are infected. B_i(p) may not closed when p is on segment or in //
-// facet. C(p) must be formed before this routine. Check the infect flag of //
-// a subface to identify the unclosed side of B_i(p). These sides will be //
-// closed by new subfaces of C(p)s. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::formbowatcavityquad(point bp, list* tetlist, list* ceillist)
-{
- triface starttet, neightet;
- face checksh;
- point pa, pb, pc, pd;
- REAL sign;
- int i;
-
- // Form BC_i(p) and B_i(p) by a broadth-first searching.
- for (i = 0; i < tetlist->len(); i++) {
- starttet = * (triface *)(* tetlist)[i];
- for (starttet.loc = 0; starttet.loc < 4; starttet.loc++) {
- // Try to collect the neighbor of the face (f).
- tspivot(starttet, checksh);
- if (checksh.sh == dummysh) {
- // Get its neighbor n.
- sym(starttet, neightet);
- // Is n already in BC_i(p)?
- if (!infected(neightet)) {
- // For positive orientation that insphere() test requires.
- adjustedgering(neightet, CW);
- pa = org(neightet);
- pb = dest(neightet);
- pc = apex(neightet);
- pd = oppo(neightet);
- sign = insphere(pa, pb, pc, pd, bp);
- if (sign >= 0.0) {
- // Collect it into BC_i(p).
- infect(neightet);
- tetlist->append(&neightet);
- } else {
- ceillist->append(&starttet); // Found a face of B_i(p).
- }
- }
- } else {
- // Do not cross a boundary face.
- if (!sinfected(checksh)) {
- ceillist->append(&starttet); // Found a face of B_i(p).
- }
- }
- }
- }
-
- if (b->verbose > 2) {
- printf(" Collect BC_i(%d): %d tets, %d faces.\n", pointmark(bp),
- tetlist->len(), ceillist->len());
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// formbowatcavitysegquad() Form BC_i(p) and B_i(p) in a segment quadrant.//
-// //
-// Parameters: bp = p, tetlist = BC_i(p), ceillist = B_i(p). //
-// //
-// BC_i(p) contains at least one tet on input. On finish, all tets collected //
-// in BC_i(p) are infected. B_i(p) is not closed. C(p) must be formed before //
-// this routine. Check the infect flag of a subface to identify the unclosed //
-// sides of B_i(p). These sides will be closed by new subfaces of C(p)s. //
-// //
-// During the repair of encroaching subsegments, there may exist locally non-//
-// Delaunay faces. These faces are collected in BC_i(p) either. B_i(p) has //
-// to be formed later than BC_i(p). //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::formbowatcavitysegquad(point bp, list* tetlist,list* ceillist)
-{
- triface starttet, neightet, cavtet;
- face checksh;
- point pa, pb, pc, pd, pe;
- REAL sign;
- int i;
-
- // Form BC_i(p) by a broadth-first searching.
- for (i = 0; i < tetlist->len(); i++) {
- starttet = * (triface *)(* tetlist)[i];
- for (starttet.loc = 0; starttet.loc < 4; starttet.loc++) {
- // Try to collect the neighbor of the face f.
- tspivot(starttet, checksh);
- if (checksh.sh == dummysh) {
- // Get its neighbor n.
- sym(starttet, neightet);
- // Is n already in BC_i(p)?
- if (!infected(neightet)) {
- // For positive orientation that insphere() test requires.
- adjustedgering(neightet, CW);
- pa = org(neightet);
- pb = dest(neightet);
- pc = apex(neightet);
- pd = oppo(neightet);
- sign = insphere(pa, pb, pc, pd, bp);
- if (sign >= 0.0) {
- // Collect it into BC_i(p).
- infect(neightet);
- tetlist->append(&neightet);
- } else {
- // Check if the face is locally non-Delaunay.
- pe = oppo(starttet);
- sign = insphere(pa, pb, pc, pd, pe);
- if (sign >= 0.0) {
- // Collect it into BC_i(p).
- infect(neightet);
- tetlist->append(&neightet);
- }
- }
- }
- }
- }
- }
-
- // Generate B_i(p).
- for (i = 0; i < tetlist->len(); i++) {
- cavtet = * (triface *)(* tetlist)[i];
- for (cavtet.loc = 0; cavtet.loc < 4; cavtet.loc++) {
- tspivot(cavtet, checksh);
- if (checksh.sh == dummysh) {
- sym(cavtet, neightet);
- if (!infected(neightet)) {
- ceillist->append(&cavtet); // Found a face of B(p).
- }
- } else {
- // Do not cross a boundary face.
- if (!sinfected(checksh)) {
- ceillist->append(&cavtet); // Found a face of B(p).
- }
- }
- }
- }
-
- if (b->verbose > 2) {
- printf(" Collect BC_i(%d): %d tets, %d faces.\n", pointmark(bp),
- tetlist->len(), ceillist->len());
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// formbowatcavity() Form BC(p), B(p), CBC(p)s, and C(p)s. //
-// //
-// If 'bpseg'(S) != NULL, p is on segment S, else, p is on facet containing //
-// 'bpsh' (F). 'n' returns the number of quadrants in BC(p). 'nmax' is the //
-// maximum pre-allocated array length for the lists. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::formbowatcavity(point bp, face* bpseg, face* bpsh, int* n,
- int* nmax, list** sublists, list** subceillists, list** tetlists,
- list** ceillists)
-{
- list *sublist;
- triface adjtet;
- face startsh, spinsh;
- point pa, pb;
- int i, j;
-
- *n = 0;
- if (bpseg != (face *) NULL) {
- // p is on segment S.
- bpseg->shver = 0;
- pa = sorg(*bpseg);
- pb = sdest(*bpseg);
- // Count the number of facets sharing at S.
- spivot(*bpseg, startsh);
- spinsh = startsh;
- do {
- (*n)++; // spinshlist->append(&spinsh);
- spivotself(spinsh);
- } while (spinsh.sh != startsh.sh);
- // *n is the number of quadrants around S.
- if (*n > *nmax) {
- // Reallocate arrays. Should not happen very often.
- delete [] tetlists;
- delete [] ceillists;
- delete [] sublists;
- delete [] subceillists;
- tetlists = new list*[*n];
- ceillists = new list*[*n];
- sublists = new list*[*n];
- subceillists = new list*[*n];
- *nmax = *n;
- }
- // Form CBC(p)s and C(p)s.
- spinsh = startsh;
- for (i = 0; i < *n; i++) {
- sublists[i] = new list(sizeof(face), NULL, 256);
- subceillists[i] = new list(sizeof(face), NULL, 256);
- // Set a subface f to start search.
- startsh = spinsh;
- // Let f face to the quadrant of interest (used in forming BC(p)).
- findedge(&startsh, pa, pb);
- sinfect(startsh);
- sublists[i]->append(&startsh);
- formbowatcavitysub(bp, bpseg, sublists[i], subceillists[i]);
- // Go to the next facet.
- spivotself(spinsh);
- }
- } else if (sublists != (list **) NULL) {
- // p is on a facet.
- *n = 2;
- // Form CBC(p) and C(p).
- sublists[0] = new list(sizeof(face), NULL, 256);
- subceillists[0] = new list(sizeof(face), NULL, 256);
- sinfect(*bpsh);
- sublists[0]->append(bpsh);
- formbowatcavitysub(bp, NULL, sublists[0], subceillists[0]);
- } else {
- // p is inside a tet.
- *n = 1;
- }
-
- // Form BC_i(p) and B_i(p).
- for (i = 0; i < *n; i++) {
- tetlists[i] = new list(sizeof(triface), NULL, 256);
- ceillists[i] = new list(sizeof(triface), NULL, 256);
- if (sublists != (list **) NULL) {
- // There are C(p)s.
- sublist = ((bpseg == (face *) NULL) ? sublists[0] : sublists[i]);
- // Add all adjacent tets of C_i(p) into BC_i(p).
- for (j = 0; j < sublist->len(); j++) {
- startsh = * (face *)(* sublist)[j];
- // Adjust the side facing to the right quadrant for C(p).
- if ((bpseg == (face *) NULL) && (i == 1)) sesymself(startsh);
- stpivot(startsh, adjtet);
- if (adjtet.tet != dummytet) {
- if (!infected(adjtet)) {
- infect(adjtet);
- tetlists[i]->append(&adjtet);
- }
- }
- }
- if (bpseg != (face *) NULL) {
- // The quadrant is bounded by another facet.
- sublist = ((i < *n - 1) ? sublists[i + 1] : sublists[0]);
- for (j = 0; j < sublist->len(); j++) {
- startsh = * (face *)(* sublist)[j];
- // Adjust the side facing to the right quadrant for C(p).
- sesymself(startsh);
- stpivot(startsh, adjtet);
- if (adjtet.tet != dummytet) {
- if (!infected(adjtet)) {
- infect(adjtet);
- tetlists[i]->append(&adjtet);
- }
- }
- }
- }
- }
- // It is possible that BC_i(p) is empty.
- if (tetlists[i]->len() == 0) continue;
- // Collect the rest of tets of BC_i(p) and form B_i(p).
- // if (b->conformdel) {
- // formbowatcavitysegquad(bp, tetlists[i], ceillists[i]);
- // } else {
- formbowatcavityquad(bp, tetlists[i], ceillists[i]);
- // }
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// releasebowatcavity() Undo and free the memory allocated in routine //
-// formbowatcavity(). //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::releasebowatcavity(face* bpseg, int n, list** sublists,
- list** subceillist, list** tetlists, list** ceillists)
-{
- triface oldtet;
- face oldsh;
- int i, j;
-
- if (sublists != (list **) NULL) {
- // Release CBC(p)s.
- for (i = 0; i < n; i++) {
- // Uninfect subfaces of CBC(p).
- for (j = 0; j < sublists[i]->len(); j++) {
- oldsh = * (face *)(* (sublists[i]))[j];
-#ifdef SELF_CHECK
- assert(sinfected(oldsh));
-#endif
- suninfect(oldsh);
- }
- delete sublists[i];
- delete subceillist[i];
- sublists[i] = (list *) NULL;
- subceillist[i] = (list *) NULL;
- if (bpseg == (face *) NULL) break;
- }
- }
- // Release BC(p).
- for (i = 0; i < n; i++) {
- // Uninfect tets of BC_i(p).
- for (j = 0; j < tetlists[i]->len(); j++) {
- oldtet = * (triface *)(* (tetlists[i]))[j];
-#ifdef SELF_CHECK
- assert(infected(oldtet));
-#endif
- uninfect(oldtet);
- }
- delete tetlists[i];
- delete ceillists[i];
- tetlists[i] = (list *) NULL;
- ceillists[i] = (list *) NULL;
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// validatebowatcavityquad() Valid B_i(p). //
-// //
-// B_i(p) is valid if all faces of B_i(p) are visible by p, else B_i(p) is //
-// invalid. Each tet of BC_i(p) which has such a face is marked (uninfect). //
-// They will be removed in updatebowatcavityquad(). //
-// //
-// Return TRUE if B(p) is valid, else, return FALSE. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::validatebowatcavityquad(point bp,list* ceillist,REAL maxcosd)
-{
- triface ceiltet;
- point pa, pb, pc;
- REAL ori, cosd;
- int remcount, i;
-
- // Check the validate of B(p), cut tets having invisible faces.
- remcount = 0;
- for (i = 0; i < ceillist->len(); i++) {
- ceiltet = * (triface *)(* ceillist)[i];
- if (infected(ceiltet)) {
- adjustedgering(ceiltet, CCW);
- pa = org(ceiltet);
- pb = dest(ceiltet);
- pc = apex(ceiltet);
- ori = orient3d(pa, pb, pc, bp);
- if (ori >= 0.0) {
- // Found an invisible face.
- uninfect(ceiltet);
- remcount++;
- continue;
- }
- // If a non-trival 'maxcosd' is given.
- if (maxcosd > -1.0) {
- // Get the maximal dihedral angle of tet abcp.
- tetalldihedral(pa, pb, pc, bp, NULL, &cosd, NULL);
- // Do not form the tet if the maximal dihedral angle is not reduced.
- if (cosd < maxcosd) {
- uninfect(ceiltet);
- remcount++;
- }
- }
- }
- }
- return remcount == 0;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// updatebowatcavityquad() Update BC_i(p) and reform B_i(p). //
-// //
-// B_i(p) is invalid and some tets in BC_i(p) have been marked to be removed //
-// in validatebowatcavityquad(). This routine actually remove the cut tets //
-// of BC_i(p) and re-form the B_i(p). //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::updatebowatcavityquad(list* tetlist, list* ceillist)
-{
- triface cavtet, neightet;
- face checksh;
- int remcount, i;
-
- remcount = 0;
- for (i = 0; i < tetlist->len(); i++) {
- cavtet = * (triface *)(* tetlist)[i];
- if (!infected(cavtet)) {
- tetlist->del(i, 1);
- remcount++;
- i--;
- }
- }
-
- // Are there tets have been cut in BC_i(p)?
- if (remcount > 0) {
- // Re-form B_i(p).
- ceillist->clear();
- for (i = 0; i < tetlist->len(); i++) {
- cavtet = * (triface *)(* tetlist)[i];
- for (cavtet.loc = 0; cavtet.loc < 4; cavtet.loc++) {
- tspivot(cavtet, checksh);
- if (checksh.sh == dummysh) {
- sym(cavtet, neightet);
- if (!infected(neightet)) {
- ceillist->append(&cavtet); // Found a face of B_i(p).
- }
- } else {
- // Do not cross a boundary face.
- if (!sinfected(checksh)) {
- ceillist->append(&cavtet); // Found a face of B_i(p).
- }
- }
- }
- }
- if (b->verbose > 2) {
- printf(" Update BC_i(p): %d tets, %d faces.\n", tetlist->len(),
- ceillist->len());
- }
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// updatebowatcavitysub() Check and update CBC(p) and C(p). //
-// //
-// A CBC(p) is valid if all its subfaces are inside or on the hull of BC(p). //
-// A subface s of CBC(p) is invalid if it is in one of the two cases: //
-// (1) s is completely outside BC(p); //
-// (2) s has two adjacent tets but only one of them is in BC(p); //
-// s is removed from CBC(p) if it is invalid. If there is an adjacent tet of //
-// s which is in BC(p), it gets removed from BC(p) too. If CBC(p) is updated,//
-// C(p) is re-formed. //
-// //
-// A C(p) is valid if all its edges are on the hull of BC(p). An edge e of //
-// C(p) may be inside BC(p) if e is a segment and belongs to only one facet. //
-// To correct C(p), a tet of BC(p) which shields e gets removed. //
-// //
-// If BC(p) is formed with locally non-Delaunay check (b->conformdel > 0). //
-// A boundary-consistent check is needed for non-segment edges of C(p). Let //
-// e be such an edge, the subface f contains e and outside C(p) may belong //
-// to B(p) due to the non-coplanarity of the facet definition. The tet of //
-// BC(p) containing f gets removed to avoid creating a degenerate new tet. //
-// //
-// 'cutcount' accumulates the total number of cuttets(not only by this call).//
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::updatebowatcavitysub(list* sublist, list* subceillist,
- int* cutcount)
-{
- triface adjtet, rotface;
- face checksh, neighsh;
- face checkseg;
- point pa, pb, pc;
- REAL ori1, ori2;
- int remcount;
- int i, j;
-
- remcount = 0;
- // Check the validity of CBC(p).
- for (i = 0; i < sublist->len(); i++) {
- checksh = * (face *)(* sublist)[i];
- // Check two adjacent tets of s.
- for (j = 0; j < 2; j++) {
- stpivot(checksh, adjtet);
- if (adjtet.tet != dummytet) {
- if (!infected(adjtet)) {
- // Could be either case (1) or (2).
- suninfect(checksh); // s survives.
- // If the sym. adjtet exists, it should remove from BC(p) too.
- sesymself(checksh);
- stpivot(checksh, adjtet);
- if (adjtet.tet != dummytet) {
- if (infected(adjtet)) {
- // Found an adj. tet in BC(p), remove it.
- uninfect(adjtet);
- (*cutcount)++;
- }
- }
- // Remove s from C(p).
- sublist->del(i, 1);
- i--;
- remcount++;
- break;
- }
- }
- sesymself(checksh);
- }
- }
- if (remcount > 0) {
- if (b->verbose > 2) {
- printf(" Removed %d subfaces from CBC(p).\n", remcount);
- }
- // Re-generate C(p).
- subceillist->clear();
- for (i = 0; i < sublist->len(); i++) {
- checksh = * (face *)(* sublist)[i];
- for (j = 0; j < 3; j++) {
- spivot(checksh, neighsh);
- if (!sinfected(neighsh)) {
- subceillist->append(&checksh);
- }
- senextself(checksh);
- }
- }
- if (b->verbose > 2) {
- printf(" Update CBC(p): %d subs, %d edges.\n", sublist->len(),
- subceillist->len());
- }
- }
-
- // Check the validity of C(p).
- for (i = 0; i < subceillist->len(); i++) {
- checksh = * (face *)(* subceillist)[i];
- sspivot(checksh, checkseg);
- if (checkseg.sh != dummysh) {
- // A segment. Check if it is inside BC(p).
- stpivot(checksh, adjtet);
- if (adjtet.tet == dummytet) {
- sesym(checksh, neighsh);
- stpivot(neighsh, adjtet);
- }
- findedge(&adjtet, sorg(checkseg), sdest(checkseg));
- adjustedgering(adjtet, CCW);
- fnext(adjtet, rotface); // It's the same tet.
- // Rotate rotface (f), stop on either of the following cases:
- // (a) meet a subface, or
- // (b) enter an uninfected tet, or
- // (c) rewind back to adjtet.
- do {
- if (!infected(rotface)) break; // case (b)
- tspivot(rotface, neighsh);
- if (neighsh.sh != dummysh) break; // case (a)
- // Go to the next tet of the facing ring.
- fnextself(rotface);
- } while (apex(rotface) != apex(adjtet));
- // Is it case (c)?
- if (apex(rotface) == apex(adjtet)) {
- // The segment is enclosed by BC(p), invalid cavity.
- pa = org(adjtet);
- pb = dest(adjtet);
- pc = apex(adjtet);
- // Find the shield tet and cut it. Notice that the shield tet may
- // not be unique when there are four coplanar points, ie.,
- // ori1 * ori2 == 0.0. In such case, choose either of them.
- fnext(adjtet, rotface);
- do {
- fnextself(rotface);
- assert(infected(rotface));
- ori1 = orient3d(pa, pb, pc, apex(rotface));
- ori2 = orient3d(pa, pb, pc, oppo(rotface));
- } while (ori1 * ori2 > 0.0);
- // Cut this tet from BC(p).
- uninfect(rotface);
- (*cutcount)++;
- }
- } else {
- /*// An edge. Check if boundary-consistency should be enforced.
- if (b->conformdel > 0) {
- // Get the adj-sub n at e, it must be outside C(p).
- spivot(checksh, neighsh);
- assert(!sinfected(neighsh));
- // Check if n is on B(p).
- for (j = 0; j < 2; j++) {
- stpivot(neighsh, adjtet);
- if (adjtet.tet != dummytet) {
- if (infected(adjtet)) {
- uninfect(adjtet);
- (*cutcount)++;
- }
- }
- sesymself(neighsh);
- }
- } */
- }
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// trimbowatcavity() Validate B(p), CBC(p)s and C(p)s, update BC(p). //
-// //
-// A B(p) is valid if all its faces are visible by p. If a face f of B(p) is //
-// found invisible by p, the tet of BC(p) containing f gets removed and B(p) //
-// is refromed. The new B(p) may still contain invisible faces by p. Iterat- //
-// ively do the above procedure until B(p) is satisfied. //
-// //
-// A CBC(p) is valid if each subface of CBC(p) is either on the hull of BC(p)//
-// or completely inside BC(p). If a subface s of CBC(p) is not valid, it is //
-// removed from CBC(p) and C(p) is reformed. If there exists a tet t of BC(p)//
-// containg s, t is removed from BC(p). The process for validating BC(p) and //
-// B(p) is re-excuted. //
-// //
-// A C(p) is valid if each edge of C(p) is on the hull of BC(p). If an edge //
-// e of C(p) is invalid (e should be a subsegment which only belong to one //
-// facet), a tet of BC(p) which contains e and has two other faces shielding //
-// e is removed. The process for validating BC(p) and B(p) is re-excuted. //
-// //
-// If either BC(p) or CBC(p) becomes empty. No valid BC(p) is found, return //
-// FALSE. else, return TRUE. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::trimbowatcavity(point bp, face* bpseg, int n, list** sublists,
- list** subceillists, list** tetlists, list** ceillists, REAL maxcosd)
-{
- bool valflag;
- int oldnum, cutnum, cutcount;
- int i;
-
- cutnum = 0; // Count the total number of cut-off tets of BC(p).
- valflag = true;
-
- do {
- // Validate BC(p), B(p).
- for (i = 0; i < n && valflag; i++) {
- oldnum = tetlists[i]->len();
- // Iteratively validate BC_i(p) and B_i(p).
- while (!validatebowatcavityquad(bp, ceillists[i], maxcosd)) {
- // Update BC_i(p) and B_i(p).
- updatebowatcavityquad(tetlists[i], ceillists[i]);
- valflag = tetlists[i]->len() > 0;
- }
- cutnum += (oldnum - tetlists[i]->len());
- }
- if (valflag && (sublists != (list **) NULL)) {
- // Validate CBC(p), C(p).
- cutcount = 0;
- for (i = 0; i < n; i++) {
- updatebowatcavitysub(sublists[i], subceillists[i], &cutcount);
- // Only do once if p is on a facet.
- if (bpseg == (face *) NULL) break;
- }
- // Are there cut tets?
- if (cutcount > 0) {
- // Squeeze all cut tets in BC(p), keep valflag once it gets FLASE.
- for (i = 0; i < n; i++) {
- if (tetlists[i]->len() > 0) {
- updatebowatcavityquad(tetlists[i], ceillists[i]);
- if (valflag) {
- valflag = tetlists[i]->len() > 0;
- }
- }
- }
- cutnum += cutcount;
- // Go back to valid the updated BC(p).
- continue;
- }
- }
- break; // Leave the while-loop.
- } while (true);
-
- // Check if any CBC(p) becomes non-empty.
- if (valflag && (sublists != (list **) NULL)) {
- for (i = 0; i < n && valflag; i++) {
- valflag = (sublists[i]->len() > 0);
- if (bpseg == (face *) NULL) break;
- }
- }
-
- if (valflag && (cutnum > 0)) {
- // Accumulate counters.
- if (bpseg != (face *) NULL) {
- updsegcount++;
- } else if (sublists != (list **) NULL) {
- updsubcount++;
- } else {
- updvolcount++;
- }
- }
-
- if (!valflag) {
- // Accumulate counters.
- if (bpseg != (face *) NULL) {
- failsegcount++;
- } else if (sublists != (list **) NULL) {
- failsubcount++;
- } else {
- failvolcount++;
- }
- }
-
- return valflag;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// bowatinsertsite() Insert a point using the Bowyer-Watson method. //
-// //
-// Parameters: 'bp' = p, 'splitseg' = S, 'n' = the number of quadrants, //
-// 'sublists', an array of CBC_i(p)s, 'subceillists', an array of C_i(p)s, //
-// 'tetlists', an array of BC_i(p)s, 'ceillists', an array of B_i(p)s. //
-// //
-// If p is inside the mesh domain, then S = NULL, n = 1, CBC(p) and C(p) are //
-// NULLs. 'tetlists[0]' = BC(p), 'ceillists[0]' = B(p). //
-// If p is on a facet F, then S = NULL, n = 2, and 'subceillists[0]' = C(p), //
-// 'subceillists[1]' is not needed (set it to NULL). B_1(p) and B_2(p) are //
-// in 'ceillists[0]' and 'ceillists[1]'. //
-// If p is on a segment S, then F(S) is a list of subfaces around S, and n = //
-// len(F(S)), there are n C_i(p)s and B_i(p)s supplied in 'subceillists[i]'//
-// and 'ceillists[i]'. //
-// //
-// If 'verlist' != NULL, it returns a list of vertices which connect to p. //
-// This vertices are used for interpolating size of p. //
-// //
-// If 'flipque' != NULL, it returns a list of internal faces of new tets in //
-// BC(p), faces on C(p)s are excluded. These faces may be locally non- //
-// Delaunay and will be flipped if they are flippable. Such non-Delaunay //
-// faces may exist when p is inserted to split an encroaching segment. //
-// //
-// 'chkencseg', 'chkencsub', and 'chkbadtet' are flags that indicate whether //
-// or not there should be checks for the creation of encroached subsegments, //
-// subfaces, or bad quality tets. If 'chkencseg' = TRUE, the encroached sub- //
-// segments are added to the list of subsegments to be split. //
-// //
-// On return, 'ceillists' returns Star(p). //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::bowatinsertsite(point bp,face* splitseg,int n,list** sublists,
- list** subceillists, list** tetlists, list** ceillists, list* verlist,
- queue* flipque, bool chkencseg, bool chkencsub, bool chkbadtet)
-{
- list *ceillist, *subceillist;
- triface oldtet, newtet, newface, rotface, neightet;
- face oldsh, newsh, newedge, checksh;
- face spinsh, casingin, casingout;
- face *apsegshs, *pbsegshs;
- face apseg, pbseg, checkseg;
- point pa, pb, pc;
- REAL attrib, volume;
- int idx, i, j, k;
-
- if (b->verbose > 1) {
- printf(" Insert point %d (%.12g, %.12g, %.12g)", pointmark(bp), bp[0],
- bp[1], bp[2]);
- }
- if (splitseg != (face *) NULL) {
- if (b->verbose > 1) {
- printf(" on segment.\n");
- }
- bowatsegcount++;
- } else {
- if (subceillists != (list **) NULL) {
- if (b->verbose > 1) {
- printf(" on facet.\n");
- }
- bowatsubcount++;
- } else {
- if (b->verbose > 1) {
- printf(" in volume.\n");
- }
- bowatvolcount++;
- }
- }
-
- // Create new tets to fill B(p).
- for (k = 0; k < n; k++) {
- // Create new tets from each B_i(p).
- ceillist = ceillists[k];
- for (i = 0; i < ceillist->len(); i++) {
- oldtet = * (triface *)(* ceillist)[i];
- adjustedgering(oldtet, CCW);
- pa = org(oldtet);
- pb = dest(oldtet);
- pc = apex(oldtet);
- maketetrahedron(&newtet);
- setorg(newtet, pa);
- setdest(newtet, pb);
- setapex(newtet, pc);
- setoppo(newtet, bp);
- for (j = 0; j < in->numberoftetrahedronattributes; j++) {
- attrib = elemattribute(oldtet.tet, j);
- setelemattribute(newtet.tet, j, attrib);
- }
- if (b->varvolume) {
- volume = volumebound(oldtet.tet);
- if (volume > 0.0) {
- if (!b->fixedvolume && b->refine) {
- // '-r -a' switches and a .vol file case. Enlarge the maximum
- // volume constraint for the new tets. Hence the new points
- // only spread near the original constrained tet.
- volume *= 1.2;
- }
- }
- setvolumebound(newtet.tet, volume);
- }
- sym(oldtet, neightet);
- tspivot(oldtet, checksh);
- if (neightet.tet != dummytet) {
- bond(newtet, neightet);
- }
- if (checksh.sh != dummysh) {
- tsbond(newtet, checksh);
- }
- if (verlist != (list *) NULL) {
- // Collect vertices connecting to p.
- idx = pointmark(pa);
- if (idx >= 0) {
- setpointmark(pa, -idx - 1);
- verlist->append(&pa);
- }
- idx = pointmark(pb);
- if (idx >= 0) {
- setpointmark(pb, -idx - 1);
- verlist->append(&pb);
- }
- idx = pointmark(pc);
- if (idx >= 0) {
- setpointmark(pc, -idx - 1);
- verlist->append(&pc);
- }
- }
- // Replace the tet by the newtet for checking the quality.
- * (triface *)(* ceillist)[i] = newtet;
- }
- }
- if (verlist != (list *) NULL) {
- // Uninfect collected vertices.
- for (i = 0; i < verlist->len(); i++) {
- pa = * (point *)(* verlist)[i];
- idx = pointmark(pa);
- setpointmark(pa, -(idx + 1));
- }
- }
-
- // Connect new tets of B(p). Not all faces of new tets can be connected,
- // e.g., if there are empty B_i(p)s.
- for (k = 0; k < n; k++) {
- ceillist = ceillists[k];
- for (i = 0; i < ceillist->len(); i++) {
- newtet = * (triface *)(* ceillist)[i];
- newtet.ver = 0;
- for (j = 0; j < 3; j++) {
- fnext(newtet, newface);
- sym(newface, neightet);
- if (neightet.tet == dummytet) {
- // Find the neighbor face by rotating the faces at edge ab.
- esym(newtet, rotface);
- pa = org(rotface);
- pb = dest(rotface);
- while (fnextself(rotface));
- // Do we meet a boundary face?
- tspivot(rotface, checksh);
- if (checksh.sh != dummysh) {
- // Walk through the boundary and continue to rotate faces.
- do {
- findedge(&checksh, pa, pb);
- sfnextself(checksh);
- assert((sorg(checksh) == pa) && (sdest(checksh) == pb));
- stpivot(checksh, rotface);
- if (infected(rotface)) {
- // Meet an old tet of B_i(p). This side is on the hull and
- // will be connected to a new subface created in C(p).
- break;
- }
- findedge(&rotface, pa, pb);
- while (fnextself(rotface));
- tspivot(rotface, checksh);
- } while (checksh.sh != dummysh);
- }
- // The rotface has edge ab, but it may not have newpt.
- if (apex(rotface) == apex(newface)) {
- // Bond the two tets together.
- bond(newface, rotface);
- // Queue (uniquely) this face if 'flipque' is given.
- if (flipque != (queue *) NULL) {
- enqueueflipface(newface, flipque);
- }
- }
- }
- enextself(newtet);
- }
- }
- }
-
- if (subceillists != (list **) NULL) {
- // There are C(p)s.
- if (splitseg != (face *) NULL) {
- // S (ab) is split by p.
- splitseg->shver = 0;
- pa = sorg(*splitseg);
- pb = sdest(*splitseg);
- // Allcate two arrays for saving the subface rings of the two new
- // segments a->p and p->b.
- apsegshs = new face[n];
- pbsegshs = new face[n];
- }
-
- // For each C_k(p), do the following:
- // (1) Create new subfaces to fill C_k(p), insert them into B(p);
- // (2) Connect new subfaces to each other;
- for (k = 0; k < n; k++) {
- subceillist = subceillists[k];
-
- // Check if 'hullsize' should be updated.
- oldsh = * (face *)(* subceillist)[0];
- stpivot(oldsh, neightet);
- if (neightet.tet != dummytet) {
- sesymself(oldsh);
- stpivot(oldsh, neightet);
- }
- if (neightet.tet == dummytet) {
- // The hull size changes.
- hullsize += (subceillist->len() - sublists[k]->len());
- }
-
- // (1) Create new subfaces to fill C_k(p), insert them into B(p).
- for (i = 0; i < subceillist->len(); i++) {
- oldsh = * (face *)(* subceillist)[i];
- makeshellface(subfaces, &newsh);
- setsorg(newsh, sorg(oldsh));
- setsdest(newsh, sdest(oldsh));
- setsapex(newsh, bp);
- if (b->quality && varconstraint) {
- setareabound(newsh, areabound(oldsh));
- }
- setshellmark(newsh, shellmark(oldsh));
- setshelltype(newsh, shelltype(oldsh));
- if (checkpbcs) {
- setshellpbcgroup(newsh, shellpbcgroup(oldsh));
- }
- // Replace oldsh by newsh at the edge.
- spivot(oldsh, casingout);
- sspivot(oldsh, checkseg);
- if (checkseg.sh != dummysh) {
- // A segment. Insert s into the face ring, ie, s_in -> s -> s_out.
- if (oldsh.sh != casingout.sh) {
- // s is not bonded to itself.
- spinsh = casingout;
- do {
- casingin = spinsh;
- spivotself(spinsh);
- } while (sapex(spinsh) != sapex(oldsh));
- assert(casingin.sh != oldsh.sh);
- // Bond s_in -> s -> s_out (and dissolve s_in -> s_old -> s_out).
- sbond1(casingin, newsh);
- sbond1(newsh, casingout);
- } else {
- // Bond newsh -> newsh.
- sbond(newsh, newsh);
- }
- // Bond the segment.
- ssbond(newsh, checkseg);
- } else {
- // Bond s <-> s_out (and dissolve s_out -> s_old).
- sbond(newsh, casingout);
- }
-
- // Insert newsh into B(p). Use the coonections of oldsh.
- stpivot(oldsh, neightet);
- if (neightet.tet == dummytet) {
- sesymself(oldsh);
- sesymself(newsh); // Keep the same orientation as oldsh.
- stpivot(oldsh, neightet);
- }
- assert(infected(neightet));
- // Set on the rotating edge.
- findedge(&neightet, sorg(oldsh), sdest(oldsh));
- // Choose the rotating direction (to the inside of B(p)).
- adjustedgering(neightet, CCW);
- rotface = neightet;
- // Rotate face. Stop at a non-infected tet t (not in B(p)) or a
- // hull face f (on B(p)). Get the neighbor n of t or f. n is
- // a new tet that has just been created to fill B(p).
- do {
- fnextself(rotface);
- sym(rotface, neightet);
- if (neightet.tet == dummytet) {
- tspivot(rotface, checksh);
- assert(checksh.sh != dummysh);
- stpivot(checksh, newtet);
- break;
- } else if (!infected(neightet)) {
- sym(neightet, newtet);
- break;
- }
- } while (true);
- assert(newtet.tet != rotface.tet);
- // Set the rotating edge of n.
- findedge(&newtet, sorg(oldsh), sdest(oldsh));
- // Choose the rotating direction (to the inside of B(p)).
- adjustedgering(newtet, CCW);
- fnext(newtet, newface);
- assert(apex(newface) == bp);
- // newsh has already been oriented toward n.
- tsbond(newface, newsh);
- sym(newface, neightet); // 'neightet' maybe outside.
- sesymself(newsh);
- tsbond(neightet, newsh); // Bond them anyway.
-
- // Replace oldsh by newsh in list.
- * (face *)(* subceillist)[i] = newsh;
- }
-
- // (2) Connect new subfaces to each other.
- for (i = 0; i < subceillist->len(); i++) {
- // Get a face cdp.
- newsh = * (face *)(* subceillist)[i];
- // Get a new tet containing cdp.
- stpivot(newsh, newtet);
- if (newtet.tet == dummytet) {
- sesymself(newsh);
- stpivot(newsh, newtet);
- }
- for (j = 0; j < 2; j++) {
- if (j == 0) {
- senext(newsh, newedge); // edge dp.
- } else {
- senext2(newsh, newedge); // edge pc.
- sesymself(newedge); // edge cp.
- }
- if (splitseg != (face *) NULL) {
- // Don not operate on newedge if it is ap or pb.
- if (sorg(newedge) == pa) {
- apsegshs[k] = newedge;
- continue;
- } else if (sorg(newedge) == pb) {
- pbsegshs[k] = newedge;
- continue;
- }
- }
- // There should no segment inside the cavity. Check it.
- sspivot(newedge, checkseg);
- assert(checkseg.sh == dummysh);
- spivot(newedge, casingout);
- if (casingout.sh == dummysh) {
- rotface = newtet;
- findedge(&rotface, sorg(newedge), sdest(newedge));
- // Rotate newtet until meeting a new subface which contains
- // newedge. It must exist since newedge is not a seg.
- adjustedgering(rotface, CCW);
- do {
- fnextself(rotface);
- tspivot(rotface, checksh);
- if (checksh.sh != dummysh) break;
- } while (true);
- findedge(&checksh, sorg(newedge), sdest(newedge));
- sbond(newedge, checksh);
- }
- }
- }
- // Only do once if p is on a facet.
- if (splitseg == (face *) NULL) break;
- } // for (k = 0; k < n; k++)
-
- if (splitseg != (face *) NULL) {
- // Update a->b to be a->p.
- apseg = *splitseg;
- setsdest(apseg, bp);
- // Create a new subsegment p->b.
- makeshellface(subsegs, &pbseg);
- setsorg(pbseg, bp);
- setsdest(pbseg, pb);
- // p->b gets the same mark and segment type as a->p.
- setshellmark(pbseg, shellmark(apseg));
- setshelltype(pbseg, shelltype(apseg));
- if (b->quality && varconstraint) {
- // Copy the area bound into the new subsegment.
- setareabound(pbseg, areabound(apseg));
- }
- senext(apseg, checkseg);
- // Get the old connection at b of a->b.
- spivot(checkseg, casingout);
- // Bond a->p and p->b together.
- senext2(pbseg, casingin);
- sbond(casingin, checkseg);
- if (casingout.sh != dummysh) {
- // There is a subsegment connect at b of p->b.
- casingout.shver = 0;
-#ifdef SELF_CHECK
- assert(sorg(casingout) == pb);
-#endif
- senext2self(casingout);
- senext(pbseg, casingin);
- sbond(casingin, casingout);
- }
-
- // Bond all new subfaces to a->p and p->b.
- for (i = 0; i < n; i++) {
- spinsh = apsegshs[i];
- findedge(&spinsh, pa, bp);
- ssbond(spinsh, apseg);
- spinsh = pbsegshs[i];
- findedge(&spinsh, bp, pb);
- ssbond(spinsh, pbseg);
- }
- // Bond all subfaces share at a->p together.
- for (i = 0; i < n; i++) {
- spinsh = apsegshs[i];
- if (i < (n - 1)) {
- casingout = apsegshs[i + 1];
- } else {
- casingout = apsegshs[0];
- }
- sbond1(spinsh, casingout);
- }
- // Bond all subfaces share at p->b together.
- for (i = 0; i < n; i++) {
- spinsh = pbsegshs[i];
- if (i < (n - 1)) {
- casingout = pbsegshs[i + 1];
- } else {
- casingout = pbsegshs[0];
- }
- sbond1(spinsh, casingout);
- }
- delete [] apsegshs;
- delete [] pbsegshs;
-
- // Check for newly encroached subsegments if the flag is set.
- if (chkencseg) {
- // Check if a->p and p->b are encroached by other vertices.
- checkseg4encroach(&apseg, NULL, NULL, true);
- checkseg4encroach(&pbseg, NULL, NULL, true);
- // Check if the adjacent segments are encroached by p.
- tallencsegs(bp, n, ceillists);
- }
- } // if (splitseg != (face *) NULL)
-
- // Delete subfaces of old CBC_i(p)s.
- for (k = 0; k < n; k++) {
- for (i = 0; i < sublists[k]->len(); i++) {
- oldsh = * (face *)(* (sublists[k]))[i];
- shellfacedealloc(subfaces, oldsh.sh);
- }
- // Clear the list so that the subs will not get unmarked later in
- // routine releasebowatcavity() which only frees the memory.
- sublists[k]->clear();
- // Only do once if p is on a facet.
- if (splitseg == (face *) NULL) break;
- }
-
- // Check for newly encroached subfaces if the flag is set.
- if (chkencsub) {
- // Check if new subfaces of C_i(p) are encroached by other vertices.
- for (k = 0; k < n; k++) {
- subceillist = subceillists[k];
- for (i = 0; i < subceillist->len(); i++) {
- newsh = * (face *)(* subceillist)[i];
- checksub4encroach(&newsh, NULL, true);
- }
- // Only do once if p is on a facet.
- if (splitseg == (face *) NULL) break;
- }
- // Check if the adjacent subfaces are encroached by p.
- tallencsubs(bp, n, ceillists);
- }
- } // if (subceillists != (list **) NULL)
-
- // Delete tets of old BC_i(p)s.
- for (k = 0; k < n; k++) {
- for (i = 0; i < tetlists[k]->len(); i++) {
- oldtet = * (triface *)(* (tetlists[k]))[i];
- tetrahedrondealloc(oldtet.tet);
- }
- // Clear the list so that the tets will not get unmarked later in
- // routine releasebowatcavity() which only frees the memory.
- tetlists[k]->clear();
- }
-
- // check for bad quality tets if the flags is set.
- if (chkbadtet) {
- for (k = 0; k < n; k++) {
- ceillist = ceillists[k];
- for (i = 0; i < ceillist->len(); i++) {
- newtet = * (triface *)(* ceillist)[i];
- checktet4badqual(&newtet, true);
- }
- }
- }
-
- if (flipque != (queue *) NULL) {
- // Newly created internal faces of BC(p) (excluding faces on C(p)s) are
- // in 'flipque'. Some of these faces may be locally non-Delaunay due,
- // to the existence of non-constrained tets. check and fix them.
- repairflipcount += flip(flipque, NULL);
- }
-}
-
-//
-// End of mesh transformation routines
-//
-
-//
-// Begin Delaunay tetrahedralization routines
-//
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// formstarpolyhedron() Get the star ployhedron of a point 'pt'. //
-// //
-// The polyhedron P is formed by faces of tets having 'pt' as a vertex. If //
-// 'complete' is TRUE, P is the complete star of 'pt'. Otherwise, P is boun- //
-// ded by subfaces, i.e. P is only part of the star of 'pt'. //
-// //
-// 'tetlist' T returns the tets, it has one of such tets on input. Moreover, //
-// if t is in T, then oppo(t) = p. Topologically, T is the star of p; and //
-// the faces of T is the link of p. 'verlist' V returns the vertices of T. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::formstarpolyhedron(point pt, list* tetlist, list* verlist,
- bool complete)
-{
- triface starttet, neightet;
- face checksh;
- point ver[3];
- int idx, i, j;
-
- // Get a tet t containing p.
- starttet = * (triface *)(* tetlist)[0];
- // Let oppo(t) = p.
- for (starttet.loc = 0; starttet.loc < 4; starttet.loc++) {
- if (oppo(starttet) == pt) break;
- }
- assert(starttet.loc < 4);
- // Add t into T.
- * (triface *)(* tetlist)[0] = starttet;
- infect(starttet);
- if (verlist != (list *) NULL) {
- // Add three verts of t into V.
- ver[0] = org(starttet);
- ver[1] = dest(starttet);
- ver[2] = apex(starttet);
- for (i = 0; i < 3; i++) {
- // Mark the vert by inversing the index of the vert.
- idx = pointmark(ver[i]);
- setpointmark(ver[i], -idx - 1); // -1 to distinguish the zero.
- verlist->append(&(ver[i]));
- }
- }
-
- // Find other tets by a broadth-first search.
- for (i = 0; i < tetlist->len(); i++) {
- starttet = * (triface *)(* tetlist)[i];
- starttet.ver = 0;
- for (j = 0; j < 3; j++) {
- fnext(starttet, neightet);
- tspivot(neightet, checksh);
- // Should we cross a subface.
- if ((checksh.sh == dummysh) || complete) {
- // Get the neighbor n.
- symself(neightet);
- if ((neightet.tet != dummytet) && !infected(neightet)) {
- // Let oppo(n) = p.
- for (neightet.loc = 0; neightet.loc < 4; neightet.loc++) {
- if (oppo(neightet) == pt) break;
- }
- assert(neightet.loc < 4);
- // Add n into T.
- infect(neightet);
- tetlist->append(&neightet);
- if (verlist != (list *) NULL) {
- // Add the apex vertex in n into V.
- ver[0] = org(starttet);
- ver[1] = dest(starttet);
- findedge(&neightet, ver[0], ver[1]);
- ver[2] = apex(neightet);
- idx = pointmark(ver[2]);
- if (idx >= 0) {
- setpointmark(ver[2], -idx - 1);
- verlist->append(&(ver[2]));
- }
- }
- }
- }
- enextself(starttet);
- }
- }
-
- // Uninfect tets.
- for (i = 0; i < tetlist->len(); i++) {
- starttet = * (triface *)(* tetlist)[i];
- uninfect(starttet);
- }
- if (verlist != (list *) NULL) {
- // Uninfect vertices.
- for (i = 0; i < verlist->len(); i++) {
- ver[0] = * (point *)(* verlist)[i];
- idx = pointmark(ver[0]);
- setpointmark(ver[0], -(idx + 1));
- }
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// unifypoint() Unify two distinct points if they're very close. //
-// //
-// This function is used for dealing with inputs from CAD tools. Two points //
-// p and q are unified if: dist(p, q) / longest < eps. Where dist() is the //
-// Euclidean distance between p and q, longest is the maximum edge size of //
-// the input point set, eps is the tolerrence specified by user, default is //
-// 1e-6, it can be adjusted by '-T' switch. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::unifypoint(point testpt, triface *starttet, enum locateresult
- loc, REAL eps)
-{
- triface symtet, spintet;
- point checkpt, tapex;
- REAL tol;
- bool merged;
- int hitbdry;
- int i;
-
- merged = false;
- tol = longest * eps;
- if ((loc == OUTSIDE) || (loc == INTETRAHEDRON) || (loc == ONFACE)) {
- // Check p is close to the four corners of the tet.
- for (i = 0; i < 4; i++) {
- checkpt = (point) starttet->tet[4 + i];
- if (distance(testpt, checkpt) < tol) {
- merged = true; // Found a merge point p'.
- break;
- }
- }
- if (!merged && (loc == ONFACE)) {
- // Check the opposite point of the neighbor tet if it exists.
- sym(*starttet, symtet);
- if (symtet.tet != dummytet) {
- checkpt = oppo(symtet);
- if (distance(testpt, checkpt) < tol) {
- merged = true; // Found a merge point p'.
- }
- }
- }
- } else if (loc == ONEDGE) {
- // Check two endpoints of the edge.
- checkpt = org(*starttet);
- if (distance(testpt, checkpt) < tol) {
- merged = true; // Found a merge point p'.
- }
- if (!merged) {
- checkpt = dest(*starttet);
- if (distance(testpt, checkpt) < tol) {
- merged = true; // Found a merge point p'.
- }
- }
- if (!merged) {
- // Check apexes of the faces having the edge.
- spintet = *starttet;
- tapex = apex(*starttet);
- hitbdry = 0;
- do {
- checkpt = apex(spintet);
- if (distance(testpt, checkpt) < tol) {
- merged = true; // Found a merge point p'.
- break;
- }
- if (!fnextself(spintet)) {
- hitbdry++;
- if (hitbdry < 2) {
- esym(*starttet, spintet);
- if (!fnextself(spintet)) {
- hitbdry++;
- }
- }
- }
- } while ((apex(spintet) != tapex) && (hitbdry < 2));
- }
- }
- if (merged) {
- if (b->object != tetgenbehavior::STL) {
- if (!b->quiet) {
- printf("Warning: Point %d is unified to point %d.\n",
- pointmark(testpt), pointmark(checkpt));
- }
- // Count the number of duplicated points.
- dupverts++;
- }
- // Remember it is a duplicated point.
- setpointtype(testpt, DUPLICATEDVERTEX);
- // Set a pointer to the point it duplicates.
- setpoint2ppt(testpt, checkpt);
- }
- return merged;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// incrflipdelaunay() Construct a delaunay tetrahedrization from a set of //
-// 3D points by the incremental flip algorithm. //
-// //
-// The incremental flip algorithm (by Edelsbrunner and Shah) can be describ- //
-// ed as follows: //
-// //
-// S be a set of points in 3D, Let 4 <= i <= n and assume that the //
-// Delaunay tetrahedralization of the first i-1 points in S is already //
-// constructed; call it D(i-1). Add the i-th point p_i (belong to S) to //
-// D(i-1), and restore Delaunayhood by flipping; this result in D(i). //
-// Repeat this procedure until i = n. //
-// //
-// This strategy always leads to the Delaunay triangulation of a point set. //
-// The return value is the number of convex hull faces of D. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::incrflipdelaunay(triface* oldtet, point* insertarray,
- long arraysize, bool jump, bool merge, REAL eps, queue* flipque)
-{
- triface newtet, searchtet;
- point swappt, lastpt;
- enum locateresult loc;
- REAL det, n[3];
- REAL attrib, volume;
- int i, j;
- clock_t loc_start, loc_end;
-
- if (b->verbose > 0) {
- printf(" Creating initial tetrahedralization.\n");
- }
-
- // The initial tetrahedralization T only has one tet formed by 4 affinely
- // linear independent vertices of the point set V = 'insertarray'. The
- // first point a = insertarray[0].
-
- // Get the second point b, that is not identical or very close to a.
- for (i = 1; i < arraysize; i++) {
- det = distance(insertarray[0], insertarray[i]);
- if (det > (longest * eps)) break;
- }
- if (i == arraysize) {
- printf("\nAll points seem to be identical.\n");
- return;
- } else {
- // Swap to move b from index i to index 1.
- swappt = insertarray[i];
- insertarray[i] = insertarray[1];
- insertarray[1] = swappt;
- }
- // Get the third point c, that is not collinear with a and b.
- for (i++; i < arraysize; i++) {
- if (!iscollinear(insertarray[0], insertarray[1], insertarray[i], eps))
- break;
- }
- if (i == arraysize) {
- printf("\nAll points seem to be collinear.\n");
- return;
- } else {
- // Swap to move c from index i to index 2.
- swappt = insertarray[i];
- insertarray[i] = insertarray[2];
- insertarray[2] = swappt;
- }
- // Get the fourth point d, that is not coplanar with a, b, and c.
- for (i++; i < arraysize; i++) {
- det = orient3d(insertarray[0], insertarray[1], insertarray[2],
- insertarray[i]);
- if (det == 0.0) continue;
- if (!iscoplanar(insertarray[0], insertarray[1], insertarray[2],
- insertarray[i], det, eps)) break;
- }
- if (i == arraysize) {
- // It's a 2D problem.
- in->mesh_dim = 2;
- // All points are coplanar.
- if (b->plc) {
- // Create an abovepoint. Maybe a surface triangulation can be formed.
- facenormal(insertarray[0], insertarray[1], insertarray[2], n, &det);
- if (det != 0.0) for (j = 0; j < 3; j++) n[j] /= det;
- // Take the average edge length of the bounding box.
- det = (0.5*(xmax - xmin) + 0.5*(ymax - ymin) + 0.5*(zmax - zmin)) / 3.0;
- // Temporarily create a point. It will be removed by jettison();
- makepoint(&lastpt);
- for (j = 0; j < 3; j++) lastpt[j] = insertarray[0][j] + det * n[j];
- abovepoint = lastpt;
- det = orient3d(insertarray[0], insertarray[1], insertarray[2], lastpt);
- // The index of the next inserting point is 3.
- i = 3;
- } else {
- printf("\nAll points seem to be coplanar.\n");
- return;
- }
- } else {
- // Swap to move d from index i to index 3.
- swappt = insertarray[i];
- insertarray[i] = insertarray[3];
- insertarray[3] = swappt;
- lastpt = insertarray[3];
- // The index of the next inserting point is 4.
- i = 4;
- }
-
- // Create the initial tet.
- maketetrahedron(&newtet);
- if (det > 0.0) {
- // For keeping the positive orientation.
- swappt = insertarray[0];
- insertarray[0] = insertarray[1];
- insertarray[1] = swappt;
- }
- if (b->verbose > 2) {
- printf(" Create the first tet (%d, %d, %d, %d).\n",
- pointmark(insertarray[0]), pointmark(insertarray[1]),
- pointmark(insertarray[2]), pointmark(lastpt));
- }
- setorg(newtet, insertarray[0]);
- setdest(newtet, insertarray[1]);
- setapex(newtet, insertarray[2]);
- setoppo(newtet, lastpt);
- if (oldtet != (triface *) NULL) {
- for (j = 0; j < in->numberoftetrahedronattributes; j++) {
- attrib = elemattribute(oldtet->tet, j);
- setelemattribute(newtet.tet, j, attrib);
- }
- if (b->varvolume) {
- volume = volumebound(oldtet->tet);
- setvolumebound(newtet.tet, volume);
- }
- }
- // Set vertex type be FREEVOLVERTEX if it has no type yet.
- if (pointtype(insertarray[0]) == UNUSEDVERTEX) {
- setpointtype(insertarray[0], FREEVOLVERTEX);
- }
- if (pointtype(insertarray[1]) == UNUSEDVERTEX) {
- setpointtype(insertarray[1], FREEVOLVERTEX);
- }
- if (pointtype(insertarray[2]) == UNUSEDVERTEX) {
- setpointtype(insertarray[2], FREEVOLVERTEX);
- }
- if (pointtype(lastpt) == UNUSEDVERTEX) {
- setpointtype(lastpt, FREEVOLVERTEX);
- }
- // Bond to 'dummytet' for point location.
- dummytet[0] = encode(newtet);
- if (b->verbose > 3) {
- printf(" Creating tetra ");
- printtet(&newtet);
- }
- // At init, all faces of this tet are hull faces.
- hullsize = 4;
-
- if (b->verbose > 0) {
- printf(" Incrementally inserting points.\n");
- }
-
- flip23s = flip32s = flip22s = flip44s = 0;
- searchtet.tet = (tetrahedron *) NULL;
-
- // Insert the rest of points, one by one.
- for (; i < arraysize; i++) {
- // Locate p_i in T.
-#ifdef SELF_CHECK
- loc_start = clock();
-#endif
- if (jump) {
- loc = locate(insertarray[i], &searchtet);
- } else {
- loc = preciselocate(insertarray[i], &searchtet, tetrahedrons->items);
- }
-#ifdef SELF_CHECK
- loc_end = clock();
- tloctime += ((REAL) (loc_end - loc_start)) / CLOCKS_PER_SEC;
-#endif
- // Keep current search state for next searching.
- recenttet = searchtet;
- if (loc == ONVERTEX) {
- if (b->object != tetgenbehavior::STL) {
- if (!b->quiet) {
- printf("Warning: Point %d is identical with point %d.\n",
- pointmark(insertarray[i]), pointmark(org(searchtet)));
- }
- }
- // Count the number of duplicated points.
- dupverts++;
- // Remember it is a duplicated point.
- setpointtype(insertarray[i], DUPLICATEDVERTEX);
- if (b->plc || b->refine) {
- // Set a pointer to the point it duplicates.
- setpoint2ppt(insertarray[i], org(searchtet));
- }
- continue; // p_i is not inserted.
- }
- if (merge) {
- // Unify p_i if it is too close to a point of T.
- if (unifypoint(insertarray[i], &searchtet, loc, eps)) {
- continue; // p_i is not inserted.
- }
- }
- // Insert p_i in T.
- if (loc != OUTSIDE) {
- if (b->verbose > 1) {
- printf(" Insert point %d in tetrahedralization.\n",
- pointmark(insertarray[i]));
- }
- if (loc == INTETRAHEDRON) {
- splittetrahedron(insertarray[i], &searchtet, flipque);
- } else if (loc == ONFACE) {
- splittetface(insertarray[i], &searchtet, flipque);
- } else if (loc == ONEDGE) {
- splittetedge(insertarray[i], &searchtet, flipque);
- }
- } else {
- if (b->verbose > 1) {
- printf(" Insert point %d on convex hull.\n",
- pointmark(insertarray[i]));
- }
- inserthullsite(insertarray[i], &searchtet, flipque);
- }
- if (pointtype(insertarray[i]) == UNUSEDVERTEX) {
- // p_i becomes a (volume) vertex of T.
- setpointtype(insertarray[i], FREEVOLVERTEX);
- }
-#ifdef SELF_CHECK
- loc_start = clock();
-#endif
- if (!b->noflip) {
- // Recover Delaunayness of T by flipping.
- flip(flipque, NULL);
- } else {
- lawson(NULL, flipque);
- // T remains regular.
- // flipque->clear();
- }
-#ifdef SELF_CHECK
- loc_end = clock();
- tfliptime += ((REAL) (loc_end - loc_start)) / CLOCKS_PER_SEC;
-#endif
- }
-
- if (b->verbose > 0) {
- printf(" %ld Flips (T23 %ld, T32 %ld, T22 %ld, T44 %ld)\n",
- flip23s+flip32s+flip22s+flip44s, flip23s, flip32s, flip22s, flip44s);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// delaunizevertices() Form a Delaunay tetrahedralization. //
-// //
-// Given a point set V (saved in 'points'). The Delaunay tetrahedralization //
-// D of V is created by incrementally inserting vertices. Returns the number //
-// of triangular faces bounding the convex hull of D. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-long tetgenmesh::delaunizevertices()
-{
- queue *flipque;
- point *insertarray;
- long arraysize;
- int i, j;
-
- if (!b->quiet) {
- if (!b->noflip) {
- printf("Constructing Delaunay tetrahedralization.\n");
- } else {
- printf("Constructing regular tetrahedralization.\n");
- }
- }
-
- flipque = new queue(sizeof(badface));
- // Prepare the array of points for inserting.
- arraysize = points->items;
- insertarray = new point[arraysize];
- points->traversalinit();
-
- // Randomize the point order.
- // randomseed = b->srandseed;
- for (i = 0; i < arraysize; i++) {
- j = (int) randomnation(i + 1); // 0 <= j <= i;
- insertarray[i] = insertarray[j];
- insertarray[j] = pointtraverse();
- }
-
- // Use lawson flip.
- b->noflip = 1;
-
- // Form the DT by incremental flip Delaunay algorithm.
- incrflipdelaunay(NULL, insertarray, arraysize, true, b->plc, b->epsilon,
- flipque);
-
- b->noflip = 0;
-
- delete [] insertarray;
- delete flipque;
- return hullsize;
-}
-
-//
-// End Delaunay tetrahedralization routines
-//
-
-//
-// Begin of surface triangulation routines
-//
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// formstarpolygon() Form the star polygon of a point in facet. //
-// //
-// The polygon P is formed by all coplanar subfaces having 'pt' as a vertex. //
-// P is bounded by segments, e.g, if no segments, P is the full star of pt. //
-// //
-// 'trilist' T returns the subfaces, it has one of such subfaces on input. //
-// In addition, if f is in T, then sapex(f) = p. 'vertlist' V are verts of P.//
-// Topologically, T is the star of p; V and the edges of T are the link of p.//
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::formstarpolygon(point pt, list* trilist, list* vertlist)
-{
- face steinsh, lnextsh, rnextsh;
- face checkseg;
- point pa, pb, pc, pd;
- int i;
-
- // Get a subface f containing p.
- steinsh = * (face *)(* trilist)[0];
- steinsh.shver = 0; // CCW
- // Let sapex(f) be p.
- for (i = 0; i < 3; i++) {
- if (sapex(steinsh) == pt) break;
- senextself(steinsh);
- }
- assert(i < 3);
- // Add the edge f into list.
- * (face *)(* trilist)[0] = steinsh;
- pa = sorg(steinsh);
- pb = sdest(steinsh);
- if (vertlist != (list *) NULL) {
- // Add two verts a, b into V,
- vertlist->append(&pa);
- vertlist->append(&pb);
- }
-
- // Rotate edge pa to the left (CW) until meet pb or a segment.
- lnextsh = steinsh;
- pc = pa;
- do {
- senext2self(lnextsh);
- assert(sorg(lnextsh) == pt);
- sspivot(lnextsh, checkseg);
- if (checkseg.sh != dummysh) break; // Do not cross a segment.
- // Get neighbor subface n (must exist).
- spivotself(lnextsh);
- if (lnextsh.sh == dummysh) break; // It's a hull edge.
- // Go to the edge ca opposite to p.
- if (sdest(lnextsh) != pt) sesymself(lnextsh);
- assert(sdest(lnextsh) == pt);
- senext2self(lnextsh);
- // Add n (at edge ca) to T.
- trilist->append(&lnextsh);
- // Add edge ca to E.
- pc = sorg(lnextsh);
- if (pc == pb) break; // Rotate back.
- if (vertlist != (list *) NULL) {
- // Add vert c into V.
- vertlist->append(&pc);
- }
- } while (true);
-
- if (pc != pb) {
- // Rotate edge bp to the right (CCW) until meet a segment.
- rnextsh = steinsh;
- do {
- senextself(rnextsh);
- assert(sdest(rnextsh) == pt);
- sspivot(rnextsh, checkseg);
- if (checkseg.sh != dummysh) break; // Do not cross a segment.
- // Get neighbor subface n (must exist).
- spivotself(rnextsh);
- if (rnextsh.sh == dummysh) break; // It's a hull edge.
- // Go to the edge bd opposite to p.
- if (sorg(rnextsh) != pt) sesymself(rnextsh);
- assert(sorg(rnextsh) == pt);
- senextself(rnextsh);
- // Add n (at edge bd) to T.
- trilist->append(&rnextsh);
- // Add edge bd to E.
- pd = sdest(rnextsh);
- if (pd == pa) break; // Rotate back.
- if (vertlist != (list *) NULL) {
- // Add vert d into V.
- vertlist->append(&pd);
- }
- } while (true);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// About the 'abovepoint' //
-// //
-// The 'abovepoint' of a facet is a point which is exactly non-coplanar with //
-// the plane containing that facet. With such an point, the 3D predicates: //
-// orient3d(), and insphere() can be used to substitute the corresponding 2D //
-// siblings, e.g. orient2d(), and incircle(). Its location is not critical, //
-// but floating-point accuracy is improved if it is nicely placed over the //
-// facet, not too close or too far away. //
-// //
-// We take the convention that the abovepoint of a facet always lies above //
-// the facet. By this convention, given three points a, b, and c in a facet, //
-// we say c has the counterclockwise order with ab is corresponding to say //
-// that c is below the plane abp, where p is the lift point. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// getfacetabovepoint() Get a point above a plane pass through a facet. //
-// //
-// The calculcated point is saved in 'facetabovepointarray'. The 'abovepoint'//
-// is set on return. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::getfacetabovepoint(face* facetsh)
-{
- list *verlist, *trilist, *tetlist;
- triface adjtet;
- face symsh;
- point p1, p2, p3, pa;
- enum locateresult loc;
- REAL smallcos, cosa;
- REAL largevol, volume;
- REAL v1[3], v2[3], len;
- int smallidx, largeidx;
- int shmark;
- int i, j;
-
- abovecount++;
- // Initialize working lists.
- verlist = new list(sizeof(point *), NULL);
- trilist = new list(sizeof(face), NULL);
- tetlist = new list(sizeof(triface), NULL);
-
- // Get three pivotal points p1, p2, and p3 in the facet as a base triangle
- // which is non-trivil and has good base angle (close to 90 degree).
-
- // p1 is chosen as the one which has the smallest index in pa, pb, pc.
- p1 = sorg(*facetsh);
- pa = sdest(*facetsh);
- if (pointmark(pa) < pointmark(p1)) p1 = pa;
- pa = sapex(*facetsh);
- if (pointmark(pa) < pointmark(p1)) p1 = pa;
- // Form the star polygon of p1.
- trilist->append(facetsh);
- formstarpolygon(p1, trilist, verlist);
-
- // Get the second pivotal point p2.
- p2 = * (point *)(* verlist)[0];
- // Get vector v1 = p1->p2.
- for (i = 0; i < 3; i++) v1[i] = p2[i] - p1[i];
- len = sqrt(dot(v1, v1));
- assert(len > 0.0); // p2 != p1.
- for (i = 0; i < 3; i++) v1[i] /= len;
-
- // Get the third pivotal point p3. p3 is chosen as the one in 'verlist'
- // which forms an angle with v1 closer to 90 degree than others do.
- smallcos = 1.0; // The cosine value of 0 degree.
- smallidx = 1; // Default value.
- for (i = 1; i < verlist->len(); i++) {
- p3 = * (point *)(* verlist)[i];
- for (j = 0; j < 3; j++) v2[j] = p3[j] - p1[j];
- len = sqrt(dot(v2, v2));
- if (len > 0.0) { // v2 is not too small.
- cosa = fabs(dot(v1, v2)) / len;
- if (cosa < smallcos) {
- smallidx = i;
- smallcos = cosa;
- }
- }
- }
- assert(smallcos < 1.0); // p1->p3 != p1->p2.
- p3 = * (point *)(* verlist)[smallidx];
- verlist->clear();
-
- if (tetrahedrons->items > 0l) {
- // Get a tet having p1 as a vertex.
- stpivot(*facetsh, adjtet);
- if (adjtet.tet == dummytet) {
- sesym(*facetsh, symsh);
- stpivot(symsh, adjtet);
- }
- if (adjtet.tet == dummytet) {
- decode(point2tet(p1), adjtet);
- if (isdead(&adjtet)) {
- adjtet.tet = dummytet;
- } else {
- if (!findorg(&adjtet, p1)) {
- adjtet.tet = dummytet;
- }
- }
- }
- if (adjtet.tet == dummytet) {
- loc = locate(p1, &adjtet);
- if (loc == ONVERTEX) {
- setpoint2tet(p1, encode(adjtet));
- } else {
- adjtet.tet = dummytet;
- }
- }
- if (adjtet.tet != dummytet) {
- // Get the star polyhedron of p1.
- tetlist->append(&adjtet);
- formstarpolyhedron(p1, tetlist, verlist, false);
- }
- }
-
- // Get the abovepoint in 'verlist'. It is the one form the largest valid
- // volumw with the base triangle over other points in 'verlist.
- largevol = 0.0;
- largeidx = 0;
- for (i = 0; i < verlist->len(); i++) {
- pa = * (point *)(* verlist)[i];
- volume = orient3d(p1, p2, p3, pa);
- if (!iscoplanar(p1, p2, p3, pa, volume, b->epsilon * 1e+2)) {
- if (fabs(volume) > largevol) {
- largevol = fabs(volume);
- largeidx = i;
- }
- }
- }
-
- // Do we have the abovepoint?
- if (largevol > 0.0) {
- abovepoint = * (point *)(* verlist)[largeidx];
- if (b->verbose > 1) {
- printf(" Chosen abovepoint %d for facet %d.\n", pointmark(abovepoint),
- shellmark(*facetsh));
- }
- } else {
- // Calculate an abovepoint for this facet.
- facenormal(p1, p2, p3, v1, &len);
- if (len != 0.0) for (i = 0; i < 3; i++) v1[i] /= len;
- // Take the average edge length of the bounding box.
- len = (0.5*(xmax - xmin) + 0.5*(ymax - ymin) + 0.5*(zmax - zmin)) / 3.0;
- // Temporarily create a point. It will be removed by jettison();
- makepoint(&abovepoint);
- setpointtype(abovepoint, UNUSEDVERTEX);
- unuverts++;
- for (i = 0; i < 3; i++) abovepoint[i] = p1[i] + len * v1[i];
- if (b->verbose > 1) {
- printf(" Calculated abovepoint %d for facet %d.\n",
- pointmark(abovepoint), shellmark(*facetsh));
- }
- }
- // Save the abovepoint in 'facetabovepointarray'.
- shmark = shellmark(*facetsh);
- facetabovepointarray[shmark] = abovepoint;
-
- delete trilist;
- delete tetlist;
- delete verlist;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// collectcavsubs() Collect non-locally Delaunay subfaces wrt a point. //
-// //
-// 'cavsublist' returns the list of subfaces. On input, it conatins at least //
-// one subface. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::collectcavsubs(point newpoint, list* cavsublist)
-{
- face startsub, neighsub;
- face checkseg;
- point pa, pb, pc;
- REAL sign, ori;
- int i, j;
-
- // First infect subfaces in 'cavsublist'.
- for (i = 0; i < cavsublist->len(); i++) {
- startsub = * (face *)(* cavsublist)[i];
- sinfect(startsub);
- }
- // Find the other subfaces by a broadth-first searching.
- for (i = 0; i < cavsublist->len(); i++) {
- startsub = * (face *)(* cavsublist)[i];
- for (j = 0; j < 3; j++) {
- sspivot(startsub, checkseg);
- // Is there a segment?
- if (checkseg.sh == dummysh) {
- // No segment. Get the neighbor.
- spivot(startsub, neighsub);
- if (!sinfected(neighsub)) {
- pa = sorg(neighsub);
- pb = sdest(neighsub);
- pc = sapex(neighsub);
- sign = insphere(pa, pb, pc, abovepoint, newpoint);
- ori = orient3d(pa, pb, pc, abovepoint);
- if (sign != 0.0) {
- // Correct the sign.
- sign = ori > 0.0 ? sign : -sign;
- }
- if (sign > 0.0) {
- // neighsub is encroached by newpoint.
- sinfect(neighsub);
- cavsublist->append(&neighsub);
- }
- }
- }
- senextself(startsub);
- }
- }
- // Having found all subfaces, uninfect them before return.
- for (i = 0; i < cavsublist->len(); i++) {
- startsub = * (face *)(* cavsublist)[i];
- suninfect(startsub);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// collectvisiblesubs() Collect convex hull edges which are visible from //
-// the inserting point. Construct new subfaces from //
-// these edges and the point. //
-// //
-// Let T be the current Delaunay triangulation (of vertices of a facet F). //
-// 'shmark', the index of F in 'in->facetlist' (starts from 1); 'inspoint' //
-// lies outside of T; 'horiz' is a hull edge of T which is visible by it. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::collectvisiblesubs(int shmark, point inspoint, face* horiz,
- queue* flipqueue)
-{
- face newsh, hullsh;
- face rightsh, leftsh, spinedge;
- point horg, hdest;
- bool aboveflag;
- REAL ori, sign;
-
- // Get the sign of abovepoint (so we can assume it is above the plane).
- adjustedgering(*horiz, CCW);
- horg = sorg(*horiz);
- hdest = sdest(*horiz);
- ori = orient3d(horg, hdest, sapex(*horiz), abovepoint);
- sign = ori > 0.0 ? -1 : 1;
-
- // Create a new subface above 'horiz'.
- makeshellface(subfaces, &newsh);
- setsorg(newsh, hdest);
- setsdest(newsh, horg);
- setsapex(newsh, inspoint);
- setshellmark(newsh, shmark);
- if (b->quality && varconstraint) {
- setareabound(newsh, areabound(*horiz));
- }
- if (checkpbcs) {
- setshellpbcgroup(newsh, shellpbcgroup(*horiz));
- }
- // Make the connection.
- sbond(newsh, *horiz);
- // 'horiz' becomes interior edge.
- enqueueflipedge(*horiz, flipqueue);
-
- // Finish the hull edges at the right side of the newsh.
- hullsh = *horiz;
- while (1) {
- senext(newsh, rightsh);
- // Get the right hull edge of 'horiz' by spinning inside edges around
- // 'horg' until reaching the 'dummysh'.
- spinedge = hullsh;
- do {
- hullsh = spinedge;
- senext2self(hullsh);
- spivot(hullsh, spinedge);
- if (spinedge.sh == dummysh) break;
- if (sorg(spinedge) != horg) sesymself(spinedge);
- assert(sorg(spinedge) == horg);
- } while (true);
- horg = sorg(hullsh);
- // Test whether 'inspoint' is visible by 'hullsh'.
- ori = orient3d(horg, sdest(hullsh), abovepoint, inspoint);
- ori *= sign;
- aboveflag = ori < 0.0;
- if (aboveflag) {
- // It's visible.
- makeshellface(subfaces, &newsh);
- setsorg(newsh, sdest(hullsh));
- setsdest(newsh, horg);
- setsapex(newsh, inspoint);
- setshellmark(newsh, shmark);
- if (b->quality && varconstraint) {
- setareabound(newsh, areabound(hullsh));
- }
- if (checkpbcs) {
- setshellpbcgroup(newsh, shellpbcgroup(hullsh));
- }
- // Make the connection.
- sbond(newsh, hullsh);
- senext2(newsh, leftsh);
- sbond(leftsh, rightsh);
- // 'hullsh' becomes interior edge.
- enqueueflipedge(hullsh, flipqueue);
- } else {
- // 'rightsh' is a new hull edge.
- dummysh[0] = sencode(rightsh);
- break;
- }
- }
-
- // Finish the hull edges at the left side of the newsh.
- hullsh = *horiz;
- spivot(*horiz, newsh);
- while (1) {
- senext2(newsh, leftsh);
- // Get the left hull edge of 'horiz' by spinning edges around 'hdest'.
- spinedge = hullsh;
- do {
- hullsh = spinedge;
- senextself(hullsh);
- spivot(hullsh, spinedge);
- if (spinedge.sh == dummysh) break;
- if (sdest(spinedge) != hdest) sesymself(spinedge);
- assert(sdest(spinedge) == hdest);
- } while (true);
- // Update 'hdest'.
- hdest = sdest(hullsh);
- // Test whether 'inspoint' is visible from 'hullsh'.
- ori = orient3d(sorg(hullsh), hdest, abovepoint, inspoint);
- ori *= sign;
- aboveflag = ori < 0.0;
- if (aboveflag) {
- // It's a visible hull edge.
- makeshellface(subfaces, &newsh);
- setsorg(newsh, hdest);
- setsdest(newsh, sorg(hullsh));
- setsapex(newsh, inspoint);
- setshellmark(newsh, shmark);
- if (b->quality && varconstraint) {
- setareabound(newsh, areabound(hullsh));
- }
- if (checkpbcs) {
- setshellpbcgroup(newsh, shellpbcgroup(hullsh));
- }
- // Make the connection.
- sbond(newsh, hullsh);
- senext(newsh, rightsh);
- sbond(rightsh, leftsh);
- // 'horiz' becomes interior edge.
- enqueueflipedge(hullsh, flipqueue);
- } else {
- // 'leftsh' is a new hull edge.
- dummysh[0] = sencode(leftsh);
- break;
- }
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// incrflipdelaunaysub() Create a DT from a 3D coplanar point set using //
-// the incremental flip algorithm. //
-// //
-// Let T be the current Delaunay triangulation (of vertices of a facet F). //
-// 'shmark', the index of F in 'in->facetlist' (starts from 1). //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::incrflipdelaunaysub(int shmark, REAL eps, list* ptlist,
- int holes, REAL* holelist, queue* flipque)
-{
- face newsh, startsh;
- point *insertarray;
- point swappt;
- pbcdata *pd;
- enum locateresult loc;
- REAL det, area;
- bool aboveflag;
- int arraysize;
- int epscount;
- int fmarker;
- int idx, i, j, k;
-
- // Get the point array (saved in 'ptlist').
- insertarray = (point *) ptlist->base;
- arraysize = ptlist->len();
- if (arraysize < 3) return;
-
- // Do calculation of 'abovepoint' if number of points > 3.
- aboveflag = (arraysize > 3);
-
- // The initial triangulation T only has one triangle formed by 3 not
- // cillinear points of the set V = 'insertarray'. The first point:
- // a = insertarray[0].
-
- epscount = 0;
- while (true) {
- for (i = 1; i < arraysize; i++) {
- det = distance(insertarray[0], insertarray[i]);
- if (det > (longest * eps)) break;
- }
- if (i < arraysize) {
- // Swap to move b from index i to index 1.
- swappt = insertarray[i];
- insertarray[i] = insertarray[1];
- insertarray[1] = swappt;
- }
- // Get the third point c, that is not collinear with a and b.
- for (i++; i < arraysize; i++) {
- if (!iscollinear(insertarray[0], insertarray[1], insertarray[i], eps))
- break;
- }
- if (i < arraysize) {
- // Swap to move c from index i to index 2.
- swappt = insertarray[i];
- insertarray[i] = insertarray[2];
- insertarray[2] = swappt;
- i = 3; // The next inserting point.
- } else {
- // The set of vertices is not good (or nearly degenerate). However,
- // a trivial triangulation can be formed (using 3 vertices). It may
- // be corrected (or deleted) by mergefacet().
- if ((eps == 0.0) || (epscount > 16)) {
- printf("Error: Invalid PLC.\n");
- printf(" Facet (%d, %d, %d", pointmark(insertarray[0]),
- pointmark(insertarray[1]), pointmark(insertarray[2]));
- if (ptlist->len() > 3) {
- printf(", ...");
- }
- printf(") (%d) is not a valid polygon.\n", shmark);
- terminatetetgen(1);
- }
- // Decrease the eps, and continue to try.
- eps *= 1e-2;
- epscount++;
- continue;
- }
- break;
- } // while (true);
-
- // Create the initial triangle.
- makeshellface(subfaces, &newsh);
- setsorg(newsh, insertarray[0]);
- setsdest(newsh, insertarray[1]);
- setsapex(newsh, insertarray[2]);
- // Remeber the facet it belongs to.
- setshellmark(newsh, shmark);
- // Set vertex type be FREESUBVERTEX if it has no type yet.
- if (pointtype(insertarray[0]) == FREEVOLVERTEX) {
- setpointtype(insertarray[0], FREESUBVERTEX);
- }
- if (pointtype(insertarray[1]) == FREEVOLVERTEX) {
- setpointtype(insertarray[1], FREESUBVERTEX);
- }
- if (pointtype(insertarray[2]) == FREEVOLVERTEX) {
- setpointtype(insertarray[2], FREESUBVERTEX);
- }
- // Let 'dummysh' point to it (for point location).
- dummysh[0] = sencode(newsh);
-
- // Are there area constraints?
- if (b->quality && (in->facetconstraintlist != (REAL *) NULL)) {
- idx = in->facetmarkerlist[shmark - 1]; // The actual facet marker.
- for (k = 0; k < in->numberoffacetconstraints; k++) {
- fmarker = (int) in->facetconstraintlist[k * 2];
- if (fmarker == idx) {
- area = in->facetconstraintlist[k * 2 + 1];
- setareabound(newsh, area);
- break;
- }
- }
- }
-
- // Are there pbc conditions?
- if (checkpbcs) {
- idx = in->facetmarkerlist[shmark - 1]; // The actual facet marker.
- for (k = 0; k < in->numberofpbcgroups; k++) {
- pd = &subpbcgrouptable[k];
- for (j = 0; j < 2; j++) {
- if (pd->fmark[j] == idx) {
- setshellpbcgroup(newsh, k);
- pd->ss[j] = newsh;
- }
- }
- }
- }
-
- if (aboveflag) {
- // Compute the 'abovepoint' for orient3d().
- abovepoint = facetabovepointarray[shmark];
- if (abovepoint == (point) NULL) {
- getfacetabovepoint(&newsh);
- }
- }
-
- if (holes > 0) {
- // Project hole points onto the plane containing the facet.
- REAL prj[3];
- for (k = 0; k < holes; k++) {
- projpt2face(&(holelist[k * 3]), insertarray[0], insertarray[1],
- insertarray[2], prj);
- for (j = 0; j < 3; j++) holelist[k * 3 + j] = prj[j];
- }
- }
-
- // Incrementally insert the rest of points into T.
- for (; i < arraysize; i++) {
- // Insert p_i.
- startsh.sh = dummysh;
- loc = locatesub(insertarray[i], &startsh, 0, 0.0);
- if (loc == ONFACE) {
- splitsubface(insertarray[i], &startsh, flipque);
- } else if (loc == ONEDGE) {
- splitsubedge(insertarray[i], &startsh, flipque);
- } else if (loc == OUTSIDE) {
- collectvisiblesubs(shmark, insertarray[i], &startsh, flipque);
- } else if (loc == ONVERTEX) {
- // !should not happen!
- }
- // Set p_i's type FREESUBVERTEX if it has no type yet.
- if (pointtype(insertarray[i]) == FREEVOLVERTEX) {
- setpointtype(insertarray[i], FREESUBVERTEX);
- }
- flipsub(flipque);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// finddirectionsub() Find the first subface in a facet on the path from //
-// one point to another. //
-// //
-// Finds the subface in the facet that intersects a line segment drawn from //
-// the origin of `searchsh' to the point `tend', and returns the result in //
-// `searchsh'. The origin of `searchsh' does not change, even though the //
-// subface returned may differ from the one passed in. //
-// //
-// The return value notes whether the destination or apex of the found face //
-// is collinear with the two points in question. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-enum tetgenmesh::finddirectionresult tetgenmesh::finddirectionsub(
- face* searchsh, point tend)
-{
- face checksh;
- point startpoint, leftpoint, rightpoint;
- REAL leftccw, rightccw;
- REAL ori, sign;
- int leftflag, rightflag;
-
- startpoint = sorg(*searchsh);
- // Find the sign to simulate that abovepoint is 'above' the facet.
- adjustedgering(*searchsh, CCW);
- // Make sure 'startpoint' is the origin.
- if (sorg(*searchsh) != startpoint) senextself(*searchsh);
- rightpoint = sdest(*searchsh);
- leftpoint = sapex(*searchsh);
- ori = orient3d(startpoint, rightpoint, leftpoint, abovepoint);
- sign = ori > 0.0 ? -1 : 1;
-
- // Is `tend' to the left?
- ori = orient3d(tend, startpoint, abovepoint, leftpoint);
- leftccw = ori * sign;
- leftflag = leftccw > 0.0;
- // Is `tend' to the right?
- ori = orient3d(startpoint, tend, abovepoint, rightpoint);
- rightccw = ori * sign;
- rightflag = rightccw > 0.0;
- if (leftflag && rightflag) {
- // `searchsh' faces directly away from `tend'. We could go left or
- // right. Ask whether it's a triangle or a boundary on the left.
- senext2(*searchsh, checksh);
- spivotself(checksh);
- if (checksh.sh == dummysh) {
- leftflag = 0;
- } else {
- rightflag = 0;
- }
- }
- while (leftflag) {
- // Turn left until satisfied.
- senext2self(*searchsh);
- spivotself(*searchsh);
- if (searchsh->sh == dummysh) {
- printf("Internal error in finddirectionsub(): Unable to find a\n");
- printf(" subface leading from %d to %d.\n", pointmark(startpoint),
- pointmark(tend));
- internalerror();
- }
- if (sorg(*searchsh) != startpoint) sesymself(*searchsh);
- assert(sorg(*searchsh) == startpoint);
- leftpoint = sapex(*searchsh);
- rightccw = leftccw;
- ori = orient3d(tend, startpoint, abovepoint, leftpoint);
- leftccw = ori * sign;
- leftflag = leftccw > 0.0;
- }
- while (rightflag) {
- // Turn right until satisfied.
- spivotself(*searchsh);
- if (searchsh->sh == dummysh) {
- printf("Internal error in finddirectionsub(): Unable to find a\n");
- printf(" subface leading from %d to %d.\n", pointmark(startpoint),
- pointmark(tend));
- internalerror();
- }
- if (sdest(*searchsh) != startpoint) sesymself(*searchsh);
- assert(sdest(*searchsh) == startpoint);
- senextself(*searchsh);
- rightpoint = sdest(*searchsh);
- leftccw = rightccw;
- ori = orient3d(startpoint, tend, abovepoint, rightpoint);
- rightccw = ori * sign;
- rightflag = rightccw > 0.0;
- }
- if (leftccw == 0.0) {
- return LEFTCOLLINEAR;
- } else if (rightccw == 0.0) {
- return RIGHTCOLLINEAR;
- } else {
- return ACROSSEDGE;
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// insertsubseg() Create a subsegment and insert it between two subfaces. //
-// //
-// The new subsegment ab is inserted at the edge of subface 'tri'. If ab is //
-// not a hull edge, it is inserted between two subfaces. If 'tri' is a hull //
-// face, the initial face ring of ab will be set only one face which is self-//
-// bonded. The final face ring will be constructed in 'unifysegments()'. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::insertsubseg(face* tri)
-{
- face oppotri;
- face newsubseg;
- point pa, pb;
- REAL len;
- int e1, e2;
- int i;
-
- // Check if there's already a subsegment here.
- sspivot(*tri, newsubseg);
- if (newsubseg.sh == dummysh) {
- // Make new subsegment and initialize its vertices.
- makeshellface(subsegs, &newsubseg);
- pa = sorg(*tri);
- pb = sdest(*tri);
- setsorg(newsubseg, pa);
- setsdest(newsubseg, pb);
- // Are there length constraints?
- if (b->quality && (in->segmentconstraintlist != (REAL *) NULL)) {
- for (i = 0; i < in->numberofsegmentconstraints; i++) {
- e1 = (int) in->segmentconstraintlist[i * 3];
- e2 = (int) in->segmentconstraintlist[i * 3 + 1];
- if (((pointmark(pa) == e1) && (pointmark(pb) == e2)) ||
- ((pointmark(pa) == e2) && (pointmark(pb) == e1))) {
- len = in->segmentconstraintlist[i * 3 + 2];
- setareabound(newsubseg, len);
- break;
- }
- }
- }
- // Bond new subsegment to the two subfaces it is sandwiched between.
- ssbond(*tri, newsubseg);
- spivot(*tri, oppotri);
- // 'oppotri' might be "out space".
- if (oppotri.sh != dummysh) {
- ssbond(oppotri, newsubseg);
- } /* else {
- // Outside! Bond '*tri' to itself.
- sbond(*tri, *tri);
- } */
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// scoutsegmentsub() Scout the first triangle on the path from one point //
-// to another, and check for completion (reaching the //
-// second point), a collinear point,or the intersection //
-// of two segments. //
-// //
-// Returns true if the entire segment is successfully inserted, and false if //
-// the job must be finished by constrainededge(). //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::scoutsegmentsub(face* searchsh, point tend)
-{
- face newsubseg;
- face crosssub, crosssubseg;
- point leftpoint, rightpoint;
- enum finddirectionresult collinear;
-
- collinear = finddirectionsub(searchsh, tend);
- rightpoint = sdest(*searchsh);
- leftpoint = sapex(*searchsh);
- if (rightpoint == tend || leftpoint == tend) {
- // The segment is already an edge.
- if (leftpoint == tend) {
- senext2self(*searchsh);
- }
- // Insert a subsegment.
- insertsubseg(searchsh);
- return true;
- } else if (collinear == LEFTCOLLINEAR) {
- // We've collided with a vertex between the segment's endpoints.
- // Make the collinear vertex be the triangle's origin.
- senextself(*searchsh); // lprevself(*searchtri);
- // Insert a subsegment.
- insertsubseg(searchsh);
- // Insert the remainder of the segment.
- return scoutsegmentsub(searchsh, tend);
- } else if (collinear == RIGHTCOLLINEAR) {
- // We've collided with a vertex between the segment's endpoints.
- // Insert a subsegment.
- insertsubseg(searchsh);
- // Make the collinear vertex be the triangle's origin.
- senextself(*searchsh); // lnextself(*searchtri);
- // Insert the remainder of the segment.
- return scoutsegmentsub(searchsh, tend);
- } else {
- senext(*searchsh, crosssub); // lnext(*searchtri, crosstri);
- // Check for a crossing segment.
- sspivot(crosssub, crosssubseg);
-#ifdef SELF_CHECK
- assert(crosssubseg.sh == dummysh);
-#endif
- return false;
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// flipedgerecursive() Flip an edge. //
-// //
-// This is a support routine for inserting segments into a CDT. //
-// //
-// Let 'flipedge' be ab, and two triangles abc, abd share at it. ab may not //
-// flipable if the four vertices a, b, c, and d are non-convex. If it is the //
-// case, recursively flip ad or bd. Return when ab is flipped. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::flipedgerecursive(face* flipedge, queue* flipqueue)
-{
- face fixupsh;
- point pa, pb, pc, pd;
- REAL oria, orib;
- bool doflip;
-
- pa = sorg(*flipedge);
- pb = sdest(*flipedge);
- pc = sapex(*flipedge);
- do {
- spivot(*flipedge, fixupsh);
- pd = sapex(fixupsh);
- oria = orient3d(pc, pd, abovepoint, pa);
- orib = orient3d(pc, pd, abovepoint, pb);
- doflip = (oria * orib < 0.0);
- if (doflip) {
- // Flip the edge (a, b) away.
- flip22sub(flipedge, flipqueue);
- // Fix flipedge on edge e (c, d).
- findedge(flipedge, pc, pd);
- } else {
- // ab is unflipable. Get the next edge (bd, or da) to flip.
- if (sorg(fixupsh) != pb) sesymself(fixupsh);
- assert(sdest(fixupsh) == pa);
- if (fabs(oria) > fabs(orib)) {
- // acd has larger area. Choose da.
- senextself(fixupsh);
- } else {
- // bcd has larger area. Choose bd.
- senext2self(fixupsh);
- }
- // Flip the edge.
- flipedgerecursive(&fixupsh, flipqueue);
- }
- } while (!doflip);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// constrainededge() Force a segment into a CDT. //
-// //
-// The segment s is recovered by flipping away the edges it intersects, and //
-// triangulating the polygons that form on each side of it. //
-// //
-// Generates a single subsegment connecting `tstart' to `tend'. The triangle //
-// `startsh' has `tstart' as its origin. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::constrainededge(face* startsh, point tend, queue* flipqueue)
-{
- point tstart, tright, tleft;
- REAL rori, lori;
- bool collision;
-
- tstart = sorg(*startsh);
- do {
- // Loop edges oppo to tstart until find one crosses the segment.
- do {
- tright = sdest(*startsh);
- tleft = sapex(*startsh);
- // Is edge (tright, tleft) corss the segment.
- rori = orient3d(tstart, tright, abovepoint, tend);
- collision = (rori == 0.0);
- if (collision) break; // tright is on the segment.
- lori = orient3d(tstart, tleft, abovepoint, tend);
- collision = (lori == 0.0);
- if (collision) { // tleft is on the segment.
- senext2self(*startsh);
- break;
- }
- if (rori * lori < 0.0) break; // Find the crossing edge.
- // Both points are at one side of the segment.
- finddirectionsub(startsh, tend);
- } while (true);
- if (collision) break;
- // Get the neighbor face at edge e (tright, tleft).
- senextself(*startsh);
- // Flip the crossing edge.
- flipedgerecursive(startsh, flipqueue);
- // After flip, sorg(*startsh) == tstart.
- assert(sorg(*startsh) == tstart);
- } while (sdest(*startsh) != tend);
-
- // Insert a subsegment to make the segment permanent.
- insertsubseg(startsh);
- // If there was a collision with an interceding vertex, install another
- // segment connecting that vertex with endpoint2.
- if (collision) {
- // Insert the remainder of the segment.
- if (!scoutsegmentsub(startsh, tend)) {
- constrainededge(startsh, tend, flipqueue);
- }
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// recoversegment() Recover a segment in the surface triangulation. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::recoversegment(point tstart, point tend, queue* flipqueue)
-{
- face searchsh;
-
- if (b->verbose > 2) {
- printf(" Insert seg (%d, %d).\n", pointmark(tstart), pointmark(tend));
- }
-
- // Find a triangle whose origin is the segment's first endpoint.
- searchsh.sh = dummysh;
- // Search for the segment's first endpoint by point location.
- if (locatesub(tstart, &searchsh, 0, 0.0) != ONVERTEX) {
- // Possibly caused by a degenerate subface. Do a brute-force search.
- list *newshlist;
- int i, j;
- newshlist = new list(sizeof(face), NULL, 256);
- // Get new subfaces, do not remove protected segments.
- retrievenewsubs(newshlist, false);
- // Search for a sub contain tstart.
- for (i = 0; i < newshlist->len(); i++) {
- searchsh = * (face *)(* newshlist)[i];
- for (j = 0; j < 3; j++) {
- if (sorg(searchsh) == tstart) break;
- senextself(searchsh);
- }
- if (j < 3) break;
- }
- delete newshlist;
- if (sorg(searchsh) != tstart) {
- printf("Internal error in recoversegment(): Vertex location failed.\n");
- internalerror();
- }
- }
- // Scout the segment and insert it if it is found.
- if (scoutsegmentsub(&searchsh, tend)) {
- // The segment was easily inserted.
- return;
- }
- // Insert the segment into the triangulation by flips.
- constrainededge(&searchsh, tend, flipqueue);
- // Some edges may need flipping.
- flipsub(flipqueue);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// infecthullsub() Virally infect all of the triangles of the convex hull //
-// that are not protected by subsegments. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::infecthullsub(memorypool* viri)
-{
- face hulltri, nexttri, starttri;
- face hullsubseg;
- shellface **deadshellface;
-
- // Find a triangle handle on the hull.
- hulltri.sh = dummysh;
- hulltri.shver = 0;
- spivotself(hulltri);
- adjustedgering(hulltri, CCW);
- // Remember where we started so we know when to stop.
- starttri = hulltri;
- // Go once counterclockwise around the convex hull.
- do {
- // Ignore triangles that are already infected.
- if (!sinfected(hulltri)) {
- // Is the triangle protected by a subsegment?
- sspivot(hulltri, hullsubseg);
- if (hullsubseg.sh == dummysh) {
- // The triangle is not protected; infect it.
- if (!sinfected(hulltri)) {
- sinfect(hulltri);
- deadshellface = (shellface **) viri->alloc();
- *deadshellface = hulltri.sh;
- }
- }
- }
- // To find the next hull edge, go clockwise around the next vertex.
- senextself(hulltri); // lnextself(hulltri);
- spivot(hulltri, nexttri); // oprev(hulltri, nexttri);
- if (nexttri.sh == hulltri.sh) {
- nexttri.sh = dummysh; // 'hulltri' is self-bonded.
- } else {
- adjustedgering(nexttri, CCW);
- senextself(nexttri);
- }
- while (nexttri.sh != dummysh) {
- hulltri = nexttri;
- spivot(hulltri, nexttri); // oprev(hulltri, nexttri);
- if (nexttri.sh == hulltri.sh) {
- nexttri.sh = dummysh; // 'hulltri' is self-bonded.
- } else {
- adjustedgering(nexttri, CCW);
- senextself(nexttri);
- }
- }
- } while (hulltri != starttri);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// plaguesub() Spread the virus from all infected triangles to any //
-// neighbors not protected by subsegments. Delete all //
-// infected triangles. //
-// //
-// This is the procedure that actually creates holes and concavities. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::plaguesub(memorypool* viri)
-{
- face testtri, neighbor, ghostsh;
- face neighborsubseg;
- shellface **virusloop;
- shellface **deadshellface;
- int i;
-
- // Loop through all the infected triangles, spreading the virus to
- // their neighbors, then to their neighbors' neighbors.
- viri->traversalinit();
- virusloop = (shellface **) viri->traverse();
- while (virusloop != (shellface **) NULL) {
- testtri.sh = *virusloop;
- // Check each of the triangle's three neighbors.
- for (i = 0; i < 3; i++) {
- // Find the neighbor.
- spivot(testtri, neighbor);
- // Check for a subsegment between the triangle and its neighbor.
- sspivot(testtri, neighborsubseg);
- // Check if the neighbor is nonexistent or already infected.
- if ((neighbor.sh == dummysh) || sinfected(neighbor)) {
- if (neighborsubseg.sh != dummysh) {
- // There is a subsegment separating the triangle from its
- // neighbor, but both triangles are dying, so the subsegment
- // dies too.
- shellfacedealloc(subsegs, neighborsubseg.sh);
- if (neighbor.sh != dummysh) {
- // Make sure the subsegment doesn't get deallocated again
- // later when the infected neighbor is visited.
- ssdissolve(neighbor);
- }
- }
- } else { // The neighbor exists and is not infected.
- if (neighborsubseg.sh == dummysh) {
- // There is no subsegment protecting the neighbor, so the
- // neighbor becomes infected.
- sinfect(neighbor);
- // Ensure that the neighbor's neighbors will be infected.
- deadshellface = (shellface **) viri->alloc();
- *deadshellface = neighbor.sh;
- } else { // The neighbor is protected by a subsegment.
- // Remove this triangle from the subsegment.
- ssbond(neighbor, neighborsubseg);
- }
- }
- senextself(testtri);
- }
- virusloop = (shellface **) viri->traverse();
- }
-
- ghostsh.sh = dummysh; // A handle of outer space.
- viri->traversalinit();
- virusloop = (shellface **) viri->traverse();
- while (virusloop != (shellface **) NULL) {
- testtri.sh = *virusloop;
- // Record changes in the number of boundary edges, and disconnect
- // dead triangles from their neighbors.
- for (i = 0; i < 3; i++) {
- spivot(testtri, neighbor);
- if (neighbor.sh != dummysh) {
- // Disconnect the triangle from its neighbor.
- // sdissolve(neighbor);
- sbond(neighbor, ghostsh);
- }
- senextself(testtri);
- }
- // Return the dead triangle to the pool of triangles.
- shellfacedealloc(subfaces, testtri.sh);
- virusloop = (shellface **) viri->traverse();
- }
- // Empty the virus pool.
- viri->restart();
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// carveholessub() Find the holes and infect them. Find the area //
-// constraints and infect them. Infect the convex hull. //
-// Spread the infection and kill triangles. Spread the //
-// area constraints. //
-// //
-// This routine mainly calls other routines to carry out all these functions.//
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::carveholessub(int holes, REAL* holelist, memorypool *viri)
-{
- face searchtri, triangleloop;
- shellface **holetri;
- enum locateresult intersect;
- int i;
-
- // Mark as infected any unprotected triangles on the boundary.
- // This is one way by which concavities are created.
- infecthullsub(viri);
-
- if (holes > 0) {
- // Infect each triangle in which a hole lies.
- for (i = 0; i < 3 * holes; i += 3) {
- // Ignore holes that aren't within the bounds of the mesh.
- if ((holelist[i] >= xmin) && (holelist[i] <= xmax)
- && (holelist[i + 1] >= ymin) && (holelist[i + 1] <= ymax)
- && (holelist[i + 2] >= zmin) && (holelist[i + 2] <= zmax)) {
- // Start searching from some triangle on the outer boundary.
- searchtri.sh = dummysh;
- // Find a triangle that contains the hole.
- intersect = locatesub(&holelist[i], &searchtri, 0, 0.0);
- if ((intersect != OUTSIDE) && (!sinfected(searchtri))) {
- // Infect the triangle. This is done by marking the triangle
- // as infected and including the triangle in the virus pool.
- sinfect(searchtri);
- holetri = (shellface **) viri->alloc();
- *holetri = searchtri.sh;
- }
- }
- }
- }
-
- if (viri->items > 0) {
- // Carve the holes and concavities.
- plaguesub(viri);
- }
- // The virus pool should be empty now.
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// triangulate() Triangulate a PSLG into a CDT. //
-// //
-// A Planar Straight Line Graph (PSLG) P is actually a 2D polygonal region, //
-// possibly contains holes, segments and vertices in its interior. P is tri- //
-// angulated into a set of _subfaces_ forming a CDT of P. //
-// //
-// The vertices and segments of P are found in 'ptlist' and 'conlist', resp- //
-// ectively. 'holelist' contains a list of hole points. 'shmark' will be set //
-// to all subfaces of P. //
-// //
-// The CDT is created directly in the pools 'subfaces' and 'subsegs'. It can //
-// be retrived by a broadth-first searching starting from 'dummysh[0]'(debug //
-// function 'outsurfmesh()' does it). //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::triangulate(int shmark, REAL eps, list* ptlist, list* conlist,
- int holes, REAL* holelist, memorypool* viri, queue* flipqueue)
-{
- face newsh;
- point *cons;
- int i;
-
- if (b->verbose > 1) {
- printf(" %d vertices, %d segments", ptlist->len(), conlist->len());
- if (holes > 0) {
- printf(", %d holes", holes);
- }
- printf(", shmark: %d.\n", shmark);
- }
-
- // Create the DT of V by the 2D incremental flip algorithm.
- incrflipdelaunaysub(shmark, eps, ptlist, holes, holelist, flipqueue);
- // Recover boundary edges.
- if (ptlist->len() > 3) {
- // Insert segments into the DT.
- for (i = 0; i < conlist->len(); i++) {
- cons = (point *)(* conlist)[i];
- recoversegment(cons[0], cons[1], flipqueue);
- }
- // Carve holes and concavities.
- carveholessub(holes, holelist, viri);
- } else if (ptlist->len() == 3) {
- // Insert 3 segments directly.
- newsh.sh = dummysh;
- newsh.shver = 0;
- spivotself(newsh);
- for (i = 0; i < 3; i++) {
- insertsubseg(&newsh);
- senextself(newsh);
- }
- } else if (ptlist->len() == 2) {
- // This facet is actually a segment. It is not support by the mesh data
- // strcuture. Hence the segment will not be maintained in the mesh.
- // However, during segment recovery, the segment can be processed.
- cons = (point *)(* conlist)[0];
- makeshellface(subsegs, &newsh);
- setsorg(newsh, cons[0]);
- setsdest(newsh, cons[1]);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// retrievenewsubs() Retrieve newly created subfaces. //
-// //
-// The new subfaces created by triangulate() can be found by a broadth-first //
-// searching starting from 'dummysh[0]'. //
-// //
-// 'newshlist' (empty on input) returns the retrieved subfaces. Each edge on //
-// the hull is bound to 'dummysh' and protected by a segment. If 'removeseg' //
-// is TRUE, the segment is removed. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::retrievenewsubs(list* newshlist, bool removeseg)
-{
- face startsh, neighsh;
- face deadseg;
- int i, j;
-
- // The first new subface is found at dummysh[0].
- startsh.sh = dummysh;
- startsh.shver = 0;
- spivotself(startsh);
- assert(startsh.sh != dummysh);
- sinfect(startsh);
- newshlist->append(&startsh);
-
- // Find the rest of new subfaces by a broadth-first searching.
- for (i = 0; i < newshlist->len(); i++) {
- // Get a new subface s.
- startsh = * (face *)(* newshlist)[i];
- for (j = 0; j < 3; j++) {
- spivot(startsh, neighsh);
- if (neighsh.sh != dummysh) {
- if (!sinfected(neighsh)) {
- // Discovered a new subface.
- sinfect(neighsh);
- newshlist->append(&neighsh);
- }
- } else {
- // Found a boundary edge.
- if (removeseg) {
- // This side of s may be protected by a segment.
- sspivot(startsh, deadseg);
- if (deadseg.sh != dummysh) {
- // Detach it from s.
- ssdissolve(startsh);
- // Delete the segment.
- shellfacedealloc(subsegs, deadseg.sh);
- }
- }
- }
- senextself(startsh);
- }
- }
- for (i = 0; i < newshlist->len(); i++) {
- startsh = * (face *)(* newshlist)[i];
- suninfect(startsh);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// unifysegments() Unify identical segments and build facet connections. //
-// //
-// After creating the surface mesh. Each facet has its own segments. There //
-// are duplicated segments between adjacent facets. This routine has three //
-// purposes: //
-// (1) identify the set of segments which have the same endpoints and //
-// unify them into one segment, remove redundant ones; //
-// (2) create the face rings of the unified segments, hence setup the //
-// connections between facets; and //
-// (3) set a unique marker (1-based) for each segment. //
-// On finish, each segment is unique and the face ring around it (right-hand //
-// rule) is constructed. The connections between facets-facets are setup. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::unifysegments()
-{
- list *sfacelist;
- shellface **facesperverlist;
- face subsegloop, testseg;
- face sface, sface1, sface2;
- point torg, tdest;
- REAL da1, da2;
- int *idx2facelist;
- int segmarker;
- int idx, k, m;
-
- if (b->verbose > 0) {
- printf(" Unifying segments.\n");
- }
-
- // Compute a mapping from indices of vertices to subfaces.
- makesubfacemap(idx2facelist, facesperverlist);
- // Initialize 'sfacelist' for constructing the face link of each segment.
- sfacelist = new list(sizeof(face), NULL);
-
- segmarker = 1;
- subsegs->traversalinit();
- subsegloop.sh = shellfacetraverse(subsegs);
- while (subsegloop.sh != (shellface *) NULL) {
- subsegloop.shver = 0; // For sure.
- torg = sorg(subsegloop);
- tdest = sdest(subsegloop);
- idx = pointmark(torg) - in->firstnumber;
- // Loop through the set of subfaces containing 'torg'. Get all the
- // subfaces containing the edge (torg, tdest). Save and order them
- // in 'sfacelist', the ordering is defined by the right-hand rule
- // with thumb points from torg to tdest.
- for (k = idx2facelist[idx]; k < idx2facelist[idx + 1]; k++) {
- sface.sh = facesperverlist[k];
- sface.shver = 0;
- // sface may be died due to the removing of duplicated subfaces.
- if (!isdead(&sface) && isfacehasedge(&sface, torg, tdest)) {
- // 'sface' contains this segment.
- findedge(&sface, torg, tdest);
- // Save it in 'sfacelist'.
- if (sfacelist->len() < 2) {
- sfacelist->append(&sface);
- } else {
- for (m = 0; m < sfacelist->len() - 1; m++) {
- sface1 = * (face *)(* sfacelist)[m];
- sface2 = * (face *)(* sfacelist)[m + 1];
- da1 = facedihedral(torg, tdest, sapex(sface1), sapex(sface));
- da2 = facedihedral(torg, tdest, sapex(sface1), sapex(sface2));
- if (da1 < da2) {
- break; // Insert it after m.
- }
- }
- sfacelist->insert(m + 1, &sface);
- }
- }
- }
- if (b->verbose > 1) {
- printf(" Identifying %d segments of (%d %d).\n", sfacelist->len(),
- pointmark(torg), pointmark(tdest));
- }
- // Set the connection between this segment and faces containing it,
- // at the same time, remove redundant segments.
- for (k = 0; k < sfacelist->len(); k++) {
- sface = *(face *)(* sfacelist)[k];
- sspivot(sface, testseg);
- // If 'testseg' is not 'subsegloop', it is a redundant segment that
- // needs be removed. BE CAREFUL it may already be removed. Do not
- // remove it twice, i.e., do test 'isdead()' together.
- if ((testseg.sh != subsegloop.sh) && !isdead(&testseg)) {
- shellfacedealloc(subsegs, testseg.sh);
- }
- // 'ssbond' bonds the subface and the segment together, and dissloves
- // the old bond as well.
- ssbond(sface, subsegloop);
- }
- // Set connection between these faces.
- sface = *(face *)(* sfacelist)[0];
- for (k = 1; k <= sfacelist->len(); k++) {
- if (k < sfacelist->len()) {
- sface1 = *(face *)(* sfacelist)[k];
- } else {
- sface1 = *(face *)(* sfacelist)[0]; // Form a face loop.
- }
- /*
- // Check if these two subfaces are the same. It is possible when user
- // defines one facet (or polygon) two or more times. If they are,
- // they should not be bonded together, instead of that, one of them
- // should be delete from the surface mesh.
- if ((sfacelist->len() > 1) && sapex(sface) == sapex(sface1)) {
- // They are duplicated faces.
- if (b->verbose > 0) {
- printf(" A duplicated subface (%d, %d, %d) is removed.\n",
- pointmark(torg), pointmark(tdest), pointmark(sapex(sface)));
- }
- if (k == sfacelist->len()) {
- // 'sface' is the last face, however, it is same as the first one.
- // In order to form the ring, we have to let the second last
- // face bond to the first one 'sface1'.
- shellfacedealloc(subfaces, sface.sh);
- assert(sfacelist->len() >= 2);
- assert(k == sfacelist->len());
- sface = *(face *)(* sfacelist)[k - 2];
- } else {
- // 'sface1' is in the middle and may be the last one.
- shellfacedealloc(subfaces, sface1.sh);
- // Skip this face and go to the next one.
- continue;
- }
- }
- */
- if (b->verbose > 2) {
- printf(" Bond subfaces (%d, %d, %d) and (%d, %d, %d).\n",
- pointmark(torg), pointmark(tdest), pointmark(sapex(sface)),
- pointmark(torg), pointmark(tdest), pointmark(sapex(sface1)));
- }
- sbond1(sface, sface1);
- sface = sface1;
- }
- // Set the unique segment marker into the unified segment.
- setshellmark(subsegloop, segmarker);
- // Increase the marker.
- segmarker++;
- // Clear the working list.
- sfacelist->clear();
- subsegloop.sh = shellfacetraverse(subsegs);
- }
-
- delete [] idx2facelist;
- delete [] facesperverlist;
- delete sfacelist;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// mergefacets() Merge adjacent facets to be one facet if they are //
-// coplanar and have the same boundary marker. //
-// //
-// Segments between two merged facets will be removed from the mesh. If all //
-// segments around a vertex have been removed, change its vertex type to be //
-// FREESUBVERTEX. Edge flips will be performed to ensure the Delaunayness of //
-// the triangulation of merged facets. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::mergefacets(queue* flipqueue)
-{
- face parentsh, neighsh, neineighsh;
- face segloop;
- point eorg, edest;
- REAL ori;
- bool mergeflag, pbcflag;
- int* segspernodelist;
- int fidx1, fidx2;
- int i, j;
-
- if (b->verbose > 0) {
- printf(" Merging coplanar facets.\n");
- }
- // Create and initialize 'segspernodelist'.
- segspernodelist = new int[points->items + 1];
- for (i = 0; i < points->items + 1; i++) segspernodelist[i] = 0;
-
- // Loop the segments, counter the number of segments sharing each vertex.
- subsegs->traversalinit();
- segloop.sh = shellfacetraverse(subsegs);
- while (segloop.sh != (shellface *) NULL) {
- // Increment the number of sharing segments for each endpoint.
- for (i = 0; i < 2; i++) {
- j = pointmark((point) segloop.sh[3 + i]);
- segspernodelist[j]++;
- }
- segloop.sh = shellfacetraverse(subsegs);
- }
-
- // Loop the segments, find out dead segments.
- subsegs->traversalinit();
- segloop.sh = shellfacetraverse(subsegs);
- while (segloop.sh != (shellface *) NULL) {
- eorg = sorg(segloop);
- edest = sdest(segloop);
- spivot(segloop, parentsh);
- spivot(parentsh, neighsh);
- spivot(neighsh, neineighsh);
- if (parentsh.sh != neighsh.sh && parentsh.sh == neineighsh.sh) {
- // Exactly two subfaces at this segment.
- fidx1 = shellmark(parentsh) - 1;
- fidx2 = shellmark(neighsh) - 1;
- pbcflag = false;
- if (checkpbcs) {
- pbcflag = (shellpbcgroup(parentsh) >= 0)
- || (shellpbcgroup(neighsh) >= 0);
- }
- // Possibly merge them if they are not in the same facet.
- if ((fidx1 != fidx2) && !pbcflag) {
- // Test if they are coplanar.
- ori = orient3d(eorg, edest, sapex(parentsh), sapex(neighsh));
- if (ori != 0.0) {
- if (iscoplanar(eorg, edest, sapex(parentsh), sapex(neighsh), ori,
- b->epsilon)) {
- ori = 0.0; // They are assumed as coplanar.
- }
- }
- if (ori == 0.0) {
- mergeflag = (in->facetmarkerlist == (int *) NULL ||
- in->facetmarkerlist[fidx1] == in->facetmarkerlist[fidx2]);
- if (mergeflag) {
- // This segment becomes dead.
- if (b->verbose > 1) {
- printf(" Removing segment (%d, %d).\n", pointmark(eorg),
- pointmark(edest));
- }
- ssdissolve(parentsh);
- ssdissolve(neighsh);
- shellfacedealloc(subsegs, segloop.sh);
- j = pointmark(eorg);
- segspernodelist[j]--;
- if (segspernodelist[j] == 0) {
- setpointtype(eorg, FREESUBVERTEX);
- }
- j = pointmark(edest);
- segspernodelist[j]--;
- if (segspernodelist[j] == 0) {
- setpointtype(edest, FREESUBVERTEX);
- }
- // Add 'parentsh' to queue checking for flip.
- enqueueflipedge(parentsh, flipqueue);
- }
- }
- }
- }
- segloop.sh = shellfacetraverse(subsegs);
- }
-
- if (!flipqueue->empty()) {
- // Restore the Delaunay property in the facet triangulation.
- flipsub(flipqueue);
- }
-
- delete [] segspernodelist;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// meshsurface() Create the surface mesh of a PLC. //
-// //
-// Let X be the PLC, the surface mesh S of X consists of triangulated facets.//
-// S is created mainly in the following steps: //
-// //
-// (1) Form the CDT of each facet of X separately (by routine triangulate()).//
-// After it is done, the subfaces of each facet are connected to each other, //
-// however there is no connection between facets yet. Notice each facet has //
-// its own segments, some of them are duplicated. //
-// //
-// (2) Remove the redundant segments created in step (1) (by routine unify- //
-// segment()). The subface ring of each segment is created, the connection //
-// between facets are established as well. //
-// //
-// The return value indicates the number of segments of X. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-long tetgenmesh::meshsurface()
-{
- list *ptlist, *conlist;
- queue *flipqueue;
- tetgenio::facet *f;
- tetgenio::polygon *p;
- memorypool *viri;
- point *idx2verlist;
- point tstart, tend, *cons;
- int *worklist;
- int end1, end2;
- int shmark, i, j;
-
- if (!b->quiet) {
- printf("Creating surface mesh.\n");
- }
-
- // Compute a mapping from indices to points.
- makeindex2pointmap(idx2verlist);
- // Compute a mapping from points to tets for computing abovepoints.
- makepoint2tetmap();
- // Initialize 'facetabovepointarray'.
- facetabovepointarray = new point[in->numberoffacets + 1];
- for (i = 0; i < in->numberoffacets + 1; i++) {
- facetabovepointarray[i] = (point) NULL;
- }
- if (checkpbcs) {
- // Initialize the global array 'subpbcgrouptable'.
- createsubpbcgrouptable();
- }
-
- // Initialize working lists.
- viri = new memorypool(sizeof(shellface *), 1024, POINTER, 0);
- flipqueue = new queue(sizeof(badface));
- ptlist = new list(sizeof(point *), NULL, 256);
- conlist = new list(sizeof(point *) * 2, NULL, 256);
- worklist = new int[points->items + 1];
- for (i = 0; i < points->items + 1; i++) worklist[i] = 0;
-
- // Loop the facet list, triangulate each facet. On finish, all subfaces
- // are in 'subfaces', all segments are in 'subsegs'. Notice: there're
- // redundant segments. Remember: All facet indices count from 1.
- for (shmark = 1; shmark <= in->numberoffacets; shmark++) {
- // Get a facet F.
- f = &in->facetlist[shmark - 1];
-
- // Process the duplicated points first, they are marked with type
- // DUPLICATEDVERTEX by incrflipdelaunay(). Let p and q are dup.
- // and the index of p is larger than q's, p is substituted by q.
- // In a STL mesh, duplicated points are implicitly included.
- if ((b->object == tetgenbehavior::STL) || dupverts) {
- // Loop all polygons of this facet.
- for (i = 0; i < f->numberofpolygons; i++) {
- p = &(f->polygonlist[i]);
- // Loop other vertices of this polygon.
- for (j = 0; j < p->numberofvertices; j++) {
- end1 = p->vertexlist[j];
- tstart = idx2verlist[end1 - in->firstnumber];
- if (pointtype(tstart) == DUPLICATEDVERTEX) {
- // Reset the index of vertex-j.
- tend = point2ppt(tstart);
- end2 = pointmark(tend);
- p->vertexlist[j] = end2;
- }
- }
- }
- }
-
- // Loop polygons of F, get the set V of vertices and S of segments.
- for (i = 0; i < f->numberofpolygons; i++) {
- // Get a polygon.
- p = &(f->polygonlist[i]);
- // Get the first vertex.
- end1 = p->vertexlist[0];
- if ((end1 < in->firstnumber) ||
- (end1 >= in->firstnumber + in->numberofpoints)) {
- if (!b->quiet) {
- printf("Warning: Invalid the 1st vertex %d of polygon", end1);
- printf(" %d in facet %d.\n", i + 1, shmark);
- }
- continue; // Skip this polygon.
- }
- tstart = idx2verlist[end1 - in->firstnumber];
- // Add tstart to V if it haven't been added yet.
- if (worklist[end1] == 0) {
- ptlist->append(&tstart);
- worklist[end1] = 1;
- }
- // Loop other vertices of this polygon.
- for (j = 1; j <= p->numberofvertices; j++) {
- // get a vertex.
- if (j < p->numberofvertices) {
- end2 = p->vertexlist[j];
- } else {
- end2 = p->vertexlist[0]; // Form a loop from last to first.
- }
- if ((end2 < in->firstnumber) ||
- (end2 >= in->firstnumber + in->numberofpoints)) {
- if (!b->quiet) {
- printf("Warning: Invalid vertex %d in polygon %d", end2, i + 1);
- printf(" in facet %d.\n", shmark);
- }
- } else {
- if (end1 != end2) {
- // 'end1' and 'end2' form a segment.
- tend = idx2verlist[end2 - in->firstnumber];
- // Add tstart to V if it haven't been added yet.
- if (worklist[end2] == 0) {
- ptlist->append(&tend);
- worklist[end2] = 1;
- }
- // Save the segment in S (conlist).
- cons = (point *) conlist->append(NULL);
- cons[0] = tstart;
- cons[1] = tend;
- // Set the start for next continuous segment.
- end1 = end2;
- tstart = tend;
- } else {
- // Two identical vertices represent an isolated vertex of F.
- if (p->numberofvertices > 2) {
- // This may be an error in the input, anyway, we can continue
- // by simply skipping this segment.
- if (!b->quiet) {
- printf("Warning: Polygon %d has two identical verts", i + 1);
- printf(" in facet %d.\n", shmark);
- }
- }
- // Ignore this vertex.
- }
- }
- // Is the polygon degenerate (a segment or a vertex)?
- if (p->numberofvertices == 2) break;
- }
- }
- // Unmark vertices.
- for (i = 0; i < ptlist->len(); i++) {
- tstart = * (point *)(* ptlist)[i];
- end1 = pointmark(tstart);
- assert(worklist[end1] == 1);
- worklist[end1] = 0;
- }
-
- // Create a CDT of F.
- triangulate(shmark, b->epsilon * 1e+2, ptlist, conlist, f->numberofholes,
- f->holelist, viri, flipqueue);
- // Clear working lists.
- ptlist->clear();
- conlist->clear();
- viri->restart();
- }
-
- // Unify segments in 'subsegs', remove redundant segments. Face links
- // of segments are also built.
- unifysegments();
- // Remember the number of input segments (for output).
- insegments = subsegs->items;
-
- if (checkpbcs) {
- // Create the global array 'segpbcgrouptable'.
- createsegpbcgrouptable();
- }
-
- if (b->object == tetgenbehavior::STL) {
- // Remove redundant vertices (for .stl input mesh).
- jettisonnodes();
- }
-
- if (!b->nomerge && !b->nobisect && !checkpbcs) {
- // No '-M' switch - merge adjacent facets if they are coplanar.
- mergefacets(flipqueue);
- }
-
- delete [] idx2verlist;
- delete [] worklist;
- delete ptlist;
- delete conlist;
- delete flipqueue;
- delete viri;
-
- return subsegs->items;
-}
-
-//
-// End of surface triangulation routines
-//
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// interecursive() Recursively do intersection test on a set of triangles.//
-// //
-// Recursively split the set 'subfacearray' of subfaces into two sets using //
-// a cut plane parallel to x-, or, y-, or z-axies. The split criteria are //
-// follows. Assume the cut plane is H, and H+ denotes the left halfspace of //
-// H, and H- denotes the right halfspace of H; and s be a subface: //
-// //
-// (1) If all points of s lie at H+, put it into left array; //
-// (2) If all points of s lie at H-, put it into right array; //
-// (3) If some points of s lie at H+ and some of lie at H-, or some //
-// points lie on H, put it into both arraies. //
-// //
-// Partitions by x-axis if axis == '0'; by y-axis if axis == '1'; by z-axis //
-// if axis == '2'. If current cut plane is parallel to the x-axis, the next //
-// one will be parallel to y-axis, and the next one after the next is z-axis,//
-// and then alternately return back to x-axis. //
-// //
-// Stop splitting when the number of triangles of the input array is not //
-// decreased anymore. Do tests on the current set. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::
-interecursive(shellface** subfacearray, int arraysize, int axis, REAL bxmin,
- REAL bxmax, REAL bymin, REAL bymax, REAL bzmin, REAL bzmax,
- int* internum)
-{
- shellface **leftarray, **rightarray;
- face sface1, sface2;
- point p1, p2, p3;
- point p4, p5, p6;
- enum interresult intersect;
- REAL split;
- bool toleft, toright;
- int leftsize, rightsize;
- int i, j;
-
- if (b->verbose > 1) {
- printf(" Recur %d faces. Bbox (%g, %g, %g),(%g, %g, %g). %s-axis\n",
- arraysize, bxmin, bymin, bzmin, bxmax, bymax, bzmax,
- axis == 0 ? "x" : (axis == 1 ? "y" : "z"));
- }
-
- leftarray = new shellface*[arraysize];
- if (leftarray == NULL) {
- printf("Error in interecursive(): Insufficient memory.\n");
- terminatetetgen(1);
- }
- rightarray = new shellface*[arraysize];
- if (rightarray == NULL) {
- printf("Error in interecursive(): Insufficient memory.\n");
- terminatetetgen(1);
- }
- leftsize = rightsize = 0;
-
- if (axis == 0) {
- // Split along x-axis.
- split = 0.5 * (bxmin + bxmax);
- } else if (axis == 1) {
- // Split along y-axis.
- split = 0.5 * (bymin + bymax);
- } else {
- // Split along z-axis.
- split = 0.5 * (bzmin + bzmax);
- }
-
- for (i = 0; i < arraysize; i++) {
- sface1.sh = subfacearray[i];
- p1 = (point) sface1.sh[3];
- p2 = (point) sface1.sh[4];
- p3 = (point) sface1.sh[5];
- toleft = toright = false;
- if (p1[axis] < split) {
- toleft = true;
- if (p2[axis] >= split || p3[axis] >= split) {
- toright = true;
- }
- } else if (p1[axis] > split) {
- toright = true;
- if (p2[axis] <= split || p3[axis] <= split) {
- toleft = true;
- }
- } else {
- // p1[axis] == split;
- toleft = true;
- toright = true;
- }
- // At least one is true;
-#ifdef SELF_CHECK
- assert(!(toleft == false && toright == false));
-#endif
- if (toleft) {
- leftarray[leftsize] = sface1.sh;
- leftsize++;
- }
- if (toright) {
- rightarray[rightsize] = sface1.sh;
- rightsize++;
- }
- }
-
- if (leftsize < arraysize && rightsize < arraysize) {
- // Continue to partition the input set. Now 'subfacearray' has been
- // split into two sets, it's memory can be freed. 'leftarray' and
- // 'rightarray' will be freed in the next recursive (after they're
- // partitioned again or performing tests).
- delete [] subfacearray;
- // Continue to split these two sets.
- if (axis == 0) {
- interecursive(leftarray, leftsize, 1, bxmin, split, bymin, bymax,
- bzmin, bzmax, internum);
- interecursive(rightarray, rightsize, 1, split, bxmax, bymin, bymax,
- bzmin, bzmax, internum);
- } else if (axis == 1) {
- interecursive(leftarray, leftsize, 2, bxmin, bxmax, bymin, split,
- bzmin, bzmax, internum);
- interecursive(rightarray, rightsize, 2, bxmin, bxmax, split, bymax,
- bzmin, bzmax, internum);
- } else {
- interecursive(leftarray, leftsize, 0, bxmin, bxmax, bymin, bymax,
- bzmin, split, internum);
- interecursive(rightarray, rightsize, 0, bxmin, bxmax, bymin, bymax,
- split, bzmax, internum);
- }
- } else {
- if (b->verbose > 1) {
- printf(" Checking intersecting faces.\n");
- }
- // Perform a brute-force compare on the set.
- for (i = 0; i < arraysize; i++) {
- sface1.sh = subfacearray[i];
- p1 = (point) sface1.sh[3];
- p2 = (point) sface1.sh[4];
- p3 = (point) sface1.sh[5];
- for (j = i + 1; j < arraysize; j++) {
- sface2.sh = subfacearray[j];
- p4 = (point) sface2.sh[3];
- p5 = (point) sface2.sh[4];
- p6 = (point) sface2.sh[5];
- intersect = tri_tri_inter(p1, p2, p3, p4, p5, p6);
- if (intersect == INTERSECT || intersect == SHAREFACE) {
- if (!b->quiet) {
- if (intersect == INTERSECT) {
- printf(" Facet #%d intersects facet #%d at triangles:\n",
- shellmark(sface1), shellmark(sface2));
- printf(" (%4d, %4d, %4d) and (%4d, %4d, %4d)\n",
- pointmark(p1), pointmark(p2), pointmark(p3),
- pointmark(p4), pointmark(p5), pointmark(p6));
- } else {
- printf(" Facet #%d duplicates facet #%d at triangle:\n",
- shellmark(sface1), shellmark(sface2));
- printf(" (%4d, %4d, %4d)\n", pointmark(p1), pointmark(p2),
- pointmark(p3));
- }
- }
- // Increase the number of intersecting pairs.
- (*internum)++;
- // Infect these two faces (although they may already be infected).
- sinfect(sface1);
- sinfect(sface2);
- }
- }
- }
- // Don't forget to free all three arrays. No further partition.
- delete [] leftarray;
- delete [] rightarray;
- delete [] subfacearray;
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// detectinterfaces() Detect intersecting triangles. //
-// //
-// Given a set of triangles, find the pairs of intersecting triangles from //
-// them. Here the set of triangles is in 'subfaces' which is a surface mesh //
-// of a PLC (.poly or .smesh). //
-// //
-// To detect whether two triangles are intersecting is done by the routine //
-// 'tri_tri_inter()'. The algorithm for the test is very simple and stable. //
-// It is based on geometric orientation test which uses exact arithmetics. //
-// //
-// Use divide-and-conquer algorithm for reducing the number of intersection //
-// tests. Start from the bounding box of the input point set, recursively //
-// partition the box into smaller boxes, until the number of triangles in a //
-// box is not decreased anymore. Then perform triangle-triangle tests on the //
-// remaining set of triangles. The memory allocated in the input set is //
-// freed immediately after it has been partitioned into two arrays. So it //
-// can be re-used for the consequent partitions. //
-// //
-// On return, the pool 'subfaces' will be cleared, and only the intersecting //
-// triangles remain for output (to a .face file). //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::detectinterfaces()
-{
- shellface **subfacearray;
- face shloop;
- int internum;
- int i;
-
- if (!b->quiet) {
- printf("Detecting intersecting facets.\n");
- }
-
- // Construct a map from indices to subfaces;
- subfacearray = new shellface*[subfaces->items];
- subfaces->traversalinit();
- shloop.sh = shellfacetraverse(subfaces);
- i = 0;
- while (shloop.sh != (shellface *) NULL) {
- subfacearray[i] = shloop.sh;
- shloop.sh = shellfacetraverse(subfaces);
- i++;
- }
-
- internum = 0;
- // Recursively split the set of triangles into two sets using a cut plane
- // parallel to x-, or, y-, or z-axies. Stop splitting when the number
- // of subfaces is not decreasing anymore. Do tests on the current set.
- interecursive(subfacearray, subfaces->items, 0, xmin, xmax, ymin, ymax,
- zmin, zmax, &internum);
-
- if (!b->quiet) {
- if (internum > 0) {
- printf("\n!! Found %d pairs of faces are intersecting.\n\n", internum);
- } else {
- printf("\nNo faces are intersecting.\n\n");
- }
- }
-
- if (internum > 0) {
- // Traverse all subfaces, deallocate those have not been infected (they
- // are not intersecting faces). Uninfect those have been infected.
- // After this loop, only intersecting faces remain.
- subfaces->traversalinit();
- shloop.sh = shellfacetraverse(subfaces);
- while (shloop.sh != (shellface *) NULL) {
- if (sinfected(shloop)) {
- suninfect(shloop);
- } else {
- shellfacedealloc(subfaces, shloop.sh);
- }
- shloop.sh = shellfacetraverse(subfaces);
- }
- } else {
- // Deallocate all subfaces.
- subfaces->restart();
- }
-}
-
-//
-// Begin of periodic boundary condition routines
-//
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// createsubpbcgrouptable() Create the 'subpbcgrouptable'. //
-// //
-// Allocate the memory for 'subpbcgrouptable'. Each entry i (a pbcdata) of //
-// the table represents a pbcgroup. Most of the fields of a group-i are set //
-// in this routine. 'fmark[0]', 'fmark[1]', and 'transmat[0]' are directly //
-// copied from the corresponding data of 'in->numberofpbcgroups'. 'transmat //
-// [1]' is calculated as the inverse matrix of 'transmat[0]'. 'ss[0]' and //
-// 'ss[1]' are initilized be 'dummysh'. They are set in 'trangulatefacet()' //
-// (when -p is in use) or 'reconstructmesh()' (when -r is in use). //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::createsubpbcgrouptable()
-{
- tetgenio::pbcgroup *pg;
- pbcdata *pd;
- REAL A[4][4], rhs[4], D;
- int indx[4];
- int i, j, k;
-
- subpbcgrouptable = new pbcdata[in->numberofpbcgroups];
- for (i = 0; i < in->numberofpbcgroups; i++) {
- pg = &(in->pbcgrouplist[i]);
- pd = &(subpbcgrouptable[i]);
- // Copy data from pg to pd.
- pd->fmark[0] = pg->fmark1;
- pd->fmark[1] = pg->fmark2;
- // Initialize array 'pd->ss'.
- pd->ss[0].sh = dummysh;
- pd->ss[1].sh = dummysh;
- // Copy the transform matrix from pg to pd->transmat[0].
- for (j = 0; j < 4; j++) {
- for (k = 0; k < 4; k++) {
- pd->transmat[0][j][k] = pg->transmat[j][k];
- // Prepare for inverting the matrix.
- A[j][k] = pg->transmat[j][k];
- }
- }
- // Calculate the inverse matrix (pd->transmat[1]) of pd->transmat[0].
- lu_decmp(A, 4, indx, &D, 0);
- for (j = 0; j < 4; j++) {
- for (k = 0; k < 4; k++) rhs[k] = 0.0;
- rhs[j] = 1.0;
- lu_solve(A, 4, indx, rhs, 0);
- for (k = 0; k < 4; k++) pd->transmat[1][k][j] = rhs[k];
- }
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// getsubpbcgroup() Get the pbcgroup of a subface. //
-// //
-// 'pbcsub' has pbc defined. Its pbcgroup is returned in 'pd'. In addition, //
-// 'f1' (0 or 1) indicates the position of 'pbcsub' in 'pd'; 'f2' (= 1 - f1) //
-// is the position where the symmetric subface of 'pbcsub' is found. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::getsubpbcgroup(face* pbcsub, pbcdata** pd, int *f1, int *f2)
-{
- int groupid, fmark, idx;
-
- groupid = shellpbcgroup(*pbcsub);
- *pd = &subpbcgrouptable[groupid];
-
- // Get the facet index (1 - based).
- idx = shellmark(*pbcsub);
- // Get the facet marker from array (0 - based).
- fmark = in->facetmarkerlist[idx - 1];
- if ((*pd)->fmark[0] == fmark) {
- *f1 = 0;
- } else {
-#ifdef SELF_CHECK
- assert((*pd)->fmark[1] == fmark);
-#endif
- *f1 = 1;
- }
- *f2 = 1 - (*f1);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// getsubpbcsympoint() Compute the symmetric point for a subface point. //
-// //
-// 'newpoint' lies on 'splitsub'. This routine calculates a 'sympoint' which //
-// locates on 'symsplitsub' and symmtric to 'newpoint'. Return the location //
-// of sympoint wrt. symsplitsub. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-enum tetgenmesh::locateresult tetgenmesh:: getsubpbcsympoint(point newpoint,
- face* splitsub, point sympoint, face* symsplitsub)
-{
- pbcdata *pd;
- face subloop;
- point pa, pb, pc;
- enum locateresult symloc;
- REAL ori;
- int f1, f2, i;
-
- // Get the pbcgroup of 'splitsub'.
- getsubpbcgroup(splitsub, &pd, &f1, &f2);
-
- // Transform newpoint from f1 -> f2.
- for (i = 0; i < 3; i++) {
- sympoint[i] = pd->transmat[f1][i][0] * newpoint[0]
- + pd->transmat[f1][i][1] * newpoint[1]
- + pd->transmat[f1][i][2] * newpoint[2]
- + pd->transmat[f1][i][3] * 1.0;
- }
- // Locate sympoint in f2.
- symloc = OUTSIDE;
- *symsplitsub = pd->ss[f2];
- // Is the stored subface valid? Hole removal may delete the subface.
- if ((symsplitsub->sh != dummysh) && !isdead(symsplitsub)) {
- // 'symsplitsub' should lie on the symmetric facet. Check it.
- i = shellmark(*symsplitsub);
- if (in->facetmarkerlist[i - 1] == pd->fmark[f2]) {
- // 'symsplitsub' has the symmetric boundary marker.
- pa = sorg(*symsplitsub);
- pb = sdest(*symsplitsub);
- pc = sapex(*symsplitsub);
- // Test if they are (nearly) coplanar. Some facets may have the
- // same boundary marker but not coplanar with this point.
- ori = orient3d(pa, pb, pc, sympoint);
- if (iscoplanar(pa, pb, pc, sympoint, ori, b->epsilon * 1e+2)) {
- // Locate sympoint in facet. Don't stop at subsegment.
- abovepoint = facetabovepointarray[shellmark(*symsplitsub)];
- if (abovepoint == (point) NULL) {
- getfacetabovepoint(symsplitsub);
- }
- symloc = locatesub(sympoint, symsplitsub, 0, b->epsilon * 1e+2);
- }
- }
- }
- if (symloc == OUTSIDE) {
- // Do a brute-force searching for the symmetric subface.
- REAL epspp = b->epsilon * 1e+2;
- int lcount = 0;
- do {
- // Locate sympoint in the pool of subfaces (with fmark pd->fmark[f2]).
- subfaces->traversalinit();
- subloop.sh = shellfacetraverse(subfaces);
- while (subloop.sh != (shellface *) NULL) {
- i = shellmark(subloop);
- if (in->facetmarkerlist[i - 1] == pd->fmark[f2]) {
- // Found a facet have the symmetric boundary marker.
- pa = sorg(subloop);
- pb = sdest(subloop);
- pc = sapex(subloop);
- // Test if they are (nearly) coplanar. Some facets may have the
- // same boundary marker but not coplanar with this point.
- ori = orient3d(pa, pb, pc, sympoint);
- if (iscoplanar(pa, pb, pc, sympoint, ori, epspp)) {
- // Test if sympoint is (nearly) inside this facet.
- // Get the abovepoint of the facet.
- abovepoint = facetabovepointarray[shellmark(subloop)];
- // Do we need to calculate the abovepoint?
- if (abovepoint == (point) NULL) {
- getfacetabovepoint(&subloop);
- }
- // subloop is on the facet, search sympoint.
- symloc = locatesub(sympoint, &subloop, 0, epspp);
- if (symloc != OUTSIDE) break;
- }
- }
- subloop.sh = shellfacetraverse(subfaces);
- }
- lcount++;
- epspp *= 10.0;
- } while ((symloc == OUTSIDE) && (lcount < 3));
-#ifdef SELF_CHECK
- // sympoint should be inside the facet.
- assert(symloc != OUTSIDE);
-#endif
- // Set the returning subface.
- *symsplitsub = subloop;
- // Update the stored subface for next searching.
- pd->ss[f2] = *symsplitsub;
- }
-
- return adjustlocatesub(sympoint, symsplitsub, symloc, b->epsilon);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// createsegpbcgrouptable() Create the 'segpbcgrouptable'. //
-// //
-// Each segment may belong to more than one pbcgroups. For example, segment //
-// ab may need to be symmteric to both segments cd, and ef, then ab and cd, //
-// cd and ef, ef and ab form three pbcgroups. //
-// //
-// 'segpbcgrouptable' is implemented as a list of pbcdatas. Each item i is //
-// a pbcgroup. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::createsegpbcgrouptable()
-{
- shellface** segsperverlist;
- pbcdata *pd, *ppd, pd1, pd2;
- face segloop, symseg;
- face startsh, spinsh, symsh;
- point pa, pb, syma, symb;
- enum locateresult symloc;
- REAL testpt[3], sympt[3];
- bool inflag;
- int *idx2seglist;
- int segid1, segid2;
- int f1, f2;
- int i, j, k, l;
-
- // Allocate memory for 'subpbcgrouptable'.
- segpbcgrouptable = new list(sizeof(pbcdata), NULL, 256);
-
- if (b->refine) {
- // Create a point-to-seg map for quickly finding PBC seg pairs.
- makesegmentmap(idx2seglist, segsperverlist);
- }
-
- // Loop through the segment list.
- subsegs->traversalinit();
- segloop.sh = shellfacetraverse(subsegs);
- while (segloop.sh != (shellface *) NULL) {
- // Loop the subface ring of segloop ab.
- pa = sorg(segloop);
- pb = sdest(segloop);
- segid1 = shellmark(segloop);
- spivot(segloop, startsh);
- spinsh = startsh;
- do {
- // Adjust spinsh be edge ab.
- if (sorg(spinsh) != pa) {
- sesymself(spinsh);
- }
- // Does spinsh belong to a pbcgroup?
- if (shellpbcgroup(spinsh) != -1) {
- // Yes! There exists a segment cd. ab and cd form a pbcgroup.
- if (b->refine) {
- getsubpbcgroup(&spinsh, &pd, &f1, &f2);
- // Transform pa from f1 -> f2.
- for (i = 0; i < 3; i++) {
- sympt[i] = pd->transmat[f1][i][0] * pa[0]
- + pd->transmat[f1][i][1] * pa[1]
- + pd->transmat[f1][i][2] * pa[2]
- + pd->transmat[f1][i][3] * 1.0;
- }
- syma = point2pbcpt(pa);
- // Is 'sympt == syma'?
- if (distance(sympt, syma) > (longest * b->epsilon)) {
- // No. Search the symmetric vertex of pa.
- symloc = getsubpbcsympoint(pa, &spinsh, sympt, &symsh);
- syma = sorg(symsh);
- if (symloc != ONVERTEX) {
- // Do a brute force search. Not done yet.
- assert(0);
- }
- }
- // Transform pb from f1 -> f2.
- for (i = 0; i < 3; i++) {
- sympt[i] = pd->transmat[f1][i][0] * pb[0]
- + pd->transmat[f1][i][1] * pb[1]
- + pd->transmat[f1][i][2] * pb[2]
- + pd->transmat[f1][i][3] * 1.0;
- }
- // Search sym subface from the point-to-subface map.
- symseg.shver = 0;
- j = pointmark(syma) - in->firstnumber;
- for (i = idx2seglist[j]; i < idx2seglist[j + 1]; i++) {
- symseg.sh = segsperverlist[i];
- if (sorg(symseg) == syma) symb = sdest(symseg);
- else symb = sorg(symseg);
- if (distance(sympt, symb) <= (longest * b->epsilon)) break;
- }
- assert(i < idx2seglist[j + 1]);
- } else {
- // 'testpt' is the midpoint of ab used to find cd.
- for (i = 0; i < 3; i++) testpt[i] = 0.5 * (pa[i] + pb[i]);
- symloc = getsubpbcsympoint(testpt, &spinsh, sympt, &symsh);
-#ifdef SELF_CHECK
- assert(symloc == ONEDGE);
-#endif
- sspivot(symsh, symseg);
- }
-#ifdef SELF_CHECK
- assert(symseg.sh != dummysh);
-#endif
- // Check whether this group has already been created in list.
- segid2 = shellmark(symseg);
- inflag = false;
- for (i = 0; i < segpbcgrouptable->len() && !inflag; i++) {
- pd = (pbcdata *)(* segpbcgrouptable)[i];
- if (pd->segid[0] == segid1) {
- if (pd->segid[1] == segid2) inflag = true;
- } else if (pd->segid[0] == segid2) {
- if (pd->segid[1] == segid1) inflag = true;
- }
- }
- if (!inflag) {
- // Create a segment pbcgroup in list for ab and cd.
- pd = (pbcdata *) segpbcgrouptable->append(NULL);
- // Save the markers of ab and cd.
- pd->segid[0] = segid1;
- pd->segid[1] = segid2;
- // Save the handles of ab and cd.
- pd->ss[0] = segloop;
- pd->ss[1] = symseg;
- // Find the map from ab to cd.
- getsubpbcgroup(&spinsh, &ppd, &f1, &f2);
- pd->fmark[0] = ppd->fmark[f1];
- pd->fmark[1] = ppd->fmark[f2];
- // Set the map from ab to cd.
- for (i = 0; i < 4; i++) {
- for (j = 0; j < 4; j++) {
- pd->transmat[0][i][j] = ppd->transmat[f1][i][j];
- }
- }
- // Set the map from cd to ab.
- for (i = 0; i < 4; i++) {
- for (j = 0; j < 4; j++) {
- pd->transmat[1][i][j] = ppd->transmat[f2][i][j];
- }
- }
- }
- }
- // Go to the next subface in the ring of ab.
- spivotself(spinsh);
- } while (spinsh.sh != startsh.sh);
- segloop.sh = shellfacetraverse(subsegs);
- }
-
- if (b->refine) {
- delete [] segsperverlist;
- delete [] idx2seglist;
- }
-
- // Create the indirect segment pbcgroups.
- // Bug-fixed (08 Sept. 2006). The total size of 'segpbcgrouptable' may get
- // increased. Do not use pointers for 'pd1' and 'pd2'. The addresses may
- // be invaild after realloc().
- for (i = 0; i < segpbcgrouptable->len(); i++) {
- pd1 = * (pbcdata *)(* segpbcgrouptable)[i];
- for (f1 = 0; f1 < 2; f1++) {
- // Search for a group (except i) contains pd1.segid[f1].
- for (j = 0; j < segpbcgrouptable->len(); j++) {
- if (j == i) continue;
- pd2 = * (pbcdata *)(* segpbcgrouptable)[j];
- f2 = -1;
- if (pd1.segid[f1] == pd2.segid[0]) {
- f2 = 0;
- } else if (pd1.segid[f1] == pd2.segid[1]) {
- f2 = 1;
- }
- if (f2 != -1) {
-#ifdef SELF_CHECK
- assert(pd1.segid[f1] == pd2.segid[f2]);
-#endif
- segid1 = pd1.segid[1 - f1];
- segid2 = pd2.segid[1 - f2];
- // Search for the existence of segment pbcgroup (segid1, segid2).
- inflag = false;
- for (k = 0; k < segpbcgrouptable->len() && !inflag; k++) {
- pd = (pbcdata *)(* segpbcgrouptable)[k];
- if (pd->segid[0] == segid1) {
- if (pd->segid[1] == segid2) inflag = true;
- } else if (pd->segid[0] == segid2) {
- if (pd->segid[1] == segid1) inflag = true;
- }
- }
- if (!inflag) {
- pd = (pbcdata *) segpbcgrouptable->append(NULL);
- pd->segid[0] = pd1.segid[1 - f1];
- pd->segid[1] = pd2.segid[1 - f2];
- pd->ss[0] = pd1.ss[1 - f1];
- pd->ss[1] = pd2.ss[1 - f2];
- // Invalid the fmark[0] == fmark[1].
- pd->fmark[0] = pd->fmark[1] = 0;
- // Translate matrix pd->transmat[0] = m2 * m1, where m1 =
- // pd1.transmat[1 - f1], m2 = pd2.transmat[f2].
- for (k = 0; k < 4; k++) {
- for (l = 0; l < 4; l++) {
- pd->transmat[0][k][l] = pd2.transmat[f2][k][l];
- }
- }
- m4xm4(pd->transmat[0], pd1.transmat[1 - f1]);
- // Translate matrix pd->transmat[1] = m4 * m3, where m3 =
- // pd2.transmat[1 - f2], m4 = pd1.transmat[f1].
- for (k = 0; k < 4; k++) {
- for (l = 0; l < 4; l++) {
- pd->transmat[1][k][l] = pd1.transmat[f1][k][l];
- }
- }
- m4xm4(pd->transmat[1], pd2.transmat[1 - f2]);
- }
- }
- }
- }
- }
-
- // Form a map from segment index to pbcgroup list of this segment.
- idx2segpglist = new int[subsegs->items + 1];
- for (i = 0; i < subsegs->items + 1; i++) idx2segpglist[i] = 0;
- // Loop through 'segpbcgrouptable', counter the number of pbcgroups of
- // each segment.
- for (i = 0; i < segpbcgrouptable->len(); i++) {
- pd = (pbcdata *)(* segpbcgrouptable)[i];
- for (j = 0; j < 2; j++) {
- k = pd->segid[j] - 1;
- idx2segpglist[k]++;
- }
- }
- // Calculate the total length of array 'segpglist'.
- j = idx2segpglist[0];
- idx2segpglist[0] = 0; // Array starts from 0 element.
- for (i = 0; i < subsegs->items; i++) {
- k = idx2segpglist[i + 1];
- idx2segpglist[i + 1] = idx2segpglist[i] + j;
- j = k;
- }
- // The total length is in the last unit of idx2segpglist.
- segpglist = new int[idx2segpglist[i]];
- // Loop the set of pbcgroups again, set the data into segpglist.
- for (i = 0; i < segpbcgrouptable->len(); i++) {
- pd = (pbcdata *)(* segpbcgrouptable)[i];
- for (j = 0; j < 2; j++) {
- k = pd->segid[j] - 1;
- segpglist[idx2segpglist[k]] = i;
- idx2segpglist[k]++;
- }
- }
- // Contents in 'idx2segpglist' are shifted, now shift them back.
- for (i = subsegs->items - 1; i >= 0; i--) {
- idx2segpglist[i + 1] = idx2segpglist[i];
- }
- idx2segpglist[0] = 0;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// getsegpbcsympoint() Compute the symmetric point for a segment point. //
-// //
-// 'newpoint' lies on 'splitseg'. This routine calculates a 'sympoint' which //
-// locates on 'symsplitseg' and symmtric to 'newpoint'. Return the location //
-// of sympoint wrt. symsplitseg. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-enum tetgenmesh::locateresult tetgenmesh::
-getsegpbcsympoint(point newpoint, face* splitseg, point sympoint,
- face* symsplitseg, int groupid)
-{
- pbcdata *pd;
- enum locateresult symloc;
- int segid, f1, f2, i;
-
- pd = (pbcdata *)(* segpbcgrouptable)[groupid];
- segid = shellmark(*splitseg);
- if (pd->segid[0] == segid) {
- f1 = 0;
- } else {
-#ifdef SELF_CHECK
- assert(pd->segid[1] == segid);
-#endif
- f1 = 1;
- }
- f2 = 1 - f1;
-
- // Transform newpoint from f1 -> f2.
- for (i = 0; i < 3; i++) {
- sympoint[i] = pd->transmat[f1][i][0] * newpoint[0]
- + pd->transmat[f1][i][1] * newpoint[1]
- + pd->transmat[f1][i][2] * newpoint[2]
- + pd->transmat[f1][i][3] * 1.0;
- }
- // Locate sympoint in f2.
- *symsplitseg = pd->ss[f2];
-#ifdef SELF_CHECK
- assert(symsplitseg->sh != dummysh);
-#endif
- // Locate sympoint in facet. Stop at subsegment.
- symloc = locateseg(sympoint, symsplitseg);
- symloc = adjustlocateseg(sympoint, symsplitseg, symloc, b->epsilon * 1e+2);
- return symloc;
-}
-
-//
-// End of periodic boundary condition routines
-//
-
-//
-// Begin of vertex perturbation routines
-//
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// randgenerator() Generate a random REAL number between (0, |range|). //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-REAL tetgenmesh::randgenerator(REAL range)
-{
- REAL worknumber, result;
- int expo;
-
- if (range == 0.0) return 0.0;
-
- expo = 0;
- worknumber = fabs(range);
- // Normalize worknumber (i.e., 1.xxxExx)
- if (worknumber > 10.0) {
- while (worknumber > 10.0) {
- worknumber /= 10.0;
- expo++;
- }
- } else if (worknumber < 1.0) {
- while (worknumber < 1.0) {
- worknumber *= 10.0;
- expo--;
- }
- }
-#ifdef SELF_CHECK
- assert(worknumber >= 1.0 && worknumber <= 10.0);
-#endif
-
- // Enlarge worknumber 1000 times.
- worknumber *= 1e+3;
- expo -= 3;
- // Generate a randome number between (0, worknumber).
- result = (double) randomnation((int) worknumber);
-
- // Scale result back into the original size.
- if (expo > 0) {
- while (expo != 0) {
- result *= 10.0;
- expo--;
- }
- } else if (expo < 0) {
- while (expo != 0) {
- result /= 10.0;
- expo++;
- }
- }
-#ifdef SELF_CHECK
- assert((result >= 0.0) && (result <= fabs(range)));
-#endif
-
- return result;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// checksub4cocir() Test a subface to find co-circular pair of subfaces. //
-// //
-// 'eps' is a relative tolerance for testing approximately cospherical case. //
-// Set it to zero if only exact test is desired. //
-// //
-// An edge(not a segment) of 'testsub' is locally degenerate if the opposite //
-// vertex of the adjacent subface is cocircular with the vertices of testsub.//
-// If 'once' is TRUE, operate on the edge only if the pointer 'testsub->sh' //
-// is smaller than its neighbor (for each edge is considered only once). //
-// //
-// Return TRUE if find an edge of testsub is locally degenerate. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::checksub4cocir(face* testsub, REAL eps, bool once,
- bool enqflag)
-{
- badface *cocirsub;
- face subloop, neighsub;
- face checkseg;
- point pa, pb, pc, pd;
- REAL sign;
- int i;
-
- subloop = *testsub;
- subloop.shver = 0; // Keep the CCW orientation.
- // Get the abovepoint of the facet.
- abovepoint = facetabovepointarray[shellmark(subloop)];
- // Do we need to calculate the abovepoint?
- if (abovepoint == (point) NULL) {
- getfacetabovepoint(&subloop);
- }
- // Check the three edges of subloop.
- for (i = 0; i < 3; i++) {
- sspivot(subloop, checkseg);
- if (checkseg.sh == dummysh) {
- // It is not a segment, get the adjacent subface.
- spivot(subloop, neighsub);
- // assert(neighsub.sh != dummysh);
- if (!once || (once && (neighsub.sh > subloop.sh))) {
- pa = sorg(subloop);
- pb = sdest(subloop);
- pc = sapex(subloop);
- pd = sapex(neighsub);
- sign = insphere(pa, pb, pc, abovepoint, pd);
- if ((sign != 0.0) && (eps > 0.0)) {
- if (iscospheric(pa, pb, pc, abovepoint, pd, sign, eps)) sign = 0.0;
- }
- if (sign == 0.0) {
- // It's locally degenerate!
- if (enqflag && badsubfaces != (memorypool *) NULL) {
- // Save it.
- cocirsub = (badface *) badsubfaces->alloc();
- cocirsub->ss = subloop;
- cocirsub->forg = pa;
- cocirsub->fdest = pb;
- cocirsub->fapex = pc;
- cocirsub->foppo = pd;
- setshell2badface(cocirsub->ss, cocirsub);
- }
- if (b->verbose > 1) {
- printf(" Found set (%d, %d, %d, %d).\n", pointmark(pa),
- pointmark(pb), pointmark(pc), pointmark(pd));
- }
- return true;
- }
- }
- }
- senextself(subloop);
- }
-
- return false;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// tallcocirsubs() Find all co-circular subfaces and save them in list. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::tallcocirsubs(REAL eps, bool enqflag)
-{
- face subloop;
-
- // Loop over all subfaces.
- subfaces->traversalinit();
- subloop.sh = shellfacetraverse(subfaces);
- while (subloop.sh != (shellface *) NULL) {
- checksub4cocir(&subloop, eps, true, enqflag);
- subloop.sh = shellfacetraverse(subfaces);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// tallencsegsfsubs() Check for encroached segs from a list of subfaces. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::tallencsegsfsubs(point testpt, list* cavsublist)
-{
- face startsub, checkseg;
- long oldencnum;
- int i, j;
-
- // Remember the current number of encroached segments.
- oldencnum = badsubsegs->items;
-
- // Check segments in the list of subfaces.
- for (i = 0; i < cavsublist->len(); i++) {
- startsub = * (face *)(* cavsublist)[i];
- // Test all three edges of startsub.
- for (j = 0; j < 3; j++) {
- sspivot(startsub, checkseg);
- if (checkseg.sh != dummysh) {
- if (!shell2badface(checkseg)) {
- checkseg4encroach(&checkseg, testpt, NULL, true);
- }
- }
- senextself(startsub);
- }
- }
-
- return (badsubsegs->items > oldencnum);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// collectflipedges() Collect edges of split subfaces for flip checking. //
-// //
-// 'inspoint' is a newly inserted segment point (inserted by insertsite()). //
-// 'splitseg' is one of the two split subsegments. Some subfaces may be non- //
-// Delaunay since they're still not bonded to CDT. This routine collect all //
-// such possible subfaces in 'flipqueue'. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::
-collectflipedges(point inspoint, face* splitseg, queue* flipqueue)
-{
- face startsh, spinsh, checksh;
- face nextseg;
- point pa, pb;
-
- // Let the dest of splitseg be inspoint.
- splitseg->shver = 0;
- if (sdest(*splitseg) != inspoint) {
- sesymself(*splitseg);
- }
-#ifdef SELF_CHECK
- assert(sdest(*splitseg) == inspoint);
-#endif
- pa = sorg(*splitseg);
- spivot(*splitseg, startsh);
- spinsh = startsh;
- do {
- findedge(&spinsh, pa, inspoint);
- senext2(spinsh, checksh);
- enqueueflipedge(checksh, flipqueue);
- spivotself(spinsh);
- } while (spinsh.sh != startsh.sh);
-
- // Get the next subsegment.
- senext(*splitseg, nextseg);
- spivotself(nextseg);
-#ifdef SELF_CHECK
- assert(nextseg.sh != (shellface *) NULL);
-#endif
-
- // Let the org of nextseg be inspoint.
- nextseg.shver = 0;
- if (sorg(nextseg) != inspoint) {
- sesymself(nextseg);
- }
-#ifdef SELF_CHECK
- assert(sorg(nextseg) == inspoint);
-#endif
- pb = sdest(nextseg);
- spivot(nextseg, startsh);
- spinsh = startsh;
- do {
- findedge(&spinsh, inspoint, pb);
- senext(spinsh, checksh);
- enqueueflipedge(checksh, flipqueue);
- spivotself(spinsh);
- } while (spinsh.sh != startsh.sh);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// perturbrepairencsegs() Repair all encroached segments. //
-// //
-// All encroached segments are stored in 'badsubsegs'. Each segment will be //
-// split by adding a perturbed point near its circumcenter. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::perturbrepairencsegs(queue* flipqueue)
-{
- badface *encloop;
- tetrahedron encodedtet;
- triface splittet;
- face splitsub, symsplitsub;
- face splitseg, symsplitseg;
- point newpoint, sympoint;
- point pa, pb, pc;
- enum insertsiteresult success;
- enum locateresult loc, symloc;
- REAL cent[3], d1, ps, rs;
- int i, j;
-
- // Note that steinerleft == -1 if an unlimited number of Steiner points
- // is allowed. Loop until 'badsubsegs' is empty.
- badsubsegs->traversalinit();
- encloop = badfacetraverse(badsubsegs);
- while ((encloop != (badface *) NULL) && (steinerleft != 0)) {
- splitseg = encloop->ss;
-#ifdef SELF_CHECK
- assert(shell2badface(splitseg) == encloop);
-#endif
- setshell2badface(splitseg, NULL);
- pa = sorg(splitseg);
- pb = sdest(splitseg);
- if ((pa == encloop->forg) && (pb == encloop->fdest)) {
- if (b->verbose > 1) {
- printf(" Get seg (%d, %d).\n", pointmark(pa), pointmark(pb));
- }
- // Create the newpoint.
- makepoint(&newpoint);
- // Get the circumcenter and radius of ab.
- for (i = 0; i < 3; i++) cent[i] = 0.5 * (pa[i] + pb[i]);
- d1 = 0.5 * distance(pa, pb);
- // Add a random perturbation to newpoint along the vector ab.
- ps = randgenerator(d1 * 1.0e-3);
- rs = ps / d1;
- // Set newpoint (be at the perturbed circumcenter of ab).
- for (i = 0; i < 3; i++) newpoint[i] = cent[i] + rs * (cent[i] - pa[i]);
- setpointtype(newpoint, FREESEGVERTEX);
- // Set splitseg into the newpoint.
- setpoint2sh(newpoint, sencode(splitseg));
-
- // Is there periodic boundary condition?
- if (checkpbcs) {
- // Insert points on other segments of incident pbcgroups.
- i = shellmark(splitseg) - 1;
- for (j = idx2segpglist[i]; j < idx2segpglist[i + 1]; j++) {
- makepoint(&sympoint);
- symloc = getsegpbcsympoint(newpoint, &splitseg, sympoint,
- &symsplitseg, segpglist[j]);
-#ifdef SELF_CHECK
- assert(symloc != OUTSIDE);
-#endif
- // Note: the symsplitseg and splitseg may be identical, in case
- // when the the splitseg is the axis of the rotational sym.
- if ((symloc == ONEDGE) && (symsplitseg.sh != splitseg.sh)) {
- setpointtype(sympoint, FREESEGVERTEX);
- setpoint2sh(sympoint, sencode(symsplitseg));
- // Insert sympoint into DT.
- pc = sorg(symsplitseg);
- splittet.tet = dummytet;
- // Find a good start point to search.
- encodedtet = point2tet(pc);
- if (encodedtet != (tetrahedron) NULL) {
- decode(encodedtet, splittet);
- if (isdead(&splittet)) {
- splittet.tet = dummytet;
- }
- }
- // Locate sympoint in DT. Do exact location.
- success = insertsite(sympoint, &splittet, false, flipqueue);
-#ifdef SELF_CHECK
- assert(success != DUPLICATEPOINT);
-#endif
- if (success == OUTSIDEPOINT) {
- inserthullsite(sympoint, &splittet, flipqueue);
- }
- if (steinerleft > 0) steinerleft--;
- // Let sympoint remember splittet.
- setpoint2tet(sympoint, encode(splittet));
- // Do flip in DT.
- flip(flipqueue, NULL);
- // Insert sympoint into F.
- symloc = locateseg(sympoint, &symsplitseg);
- if (symloc == ONEDGE) {
- symsplitseg.shver = 0;
- spivot(symsplitseg, symsplitsub);
- // sympoint should on the edge of symsplitsub.
- splitsubedge(sympoint, &symsplitsub, flipqueue);
- } else {
- // insertsite() has done the whole job.
-#ifdef SELF_CHECK
- assert(symloc == ONVERTEX);
- assert(checksubfaces);
-#endif
- // Some edges may need to be flipped.
- collectflipedges(sympoint, &symsplitseg, flipqueue);
- }
- // Do flip in facet.
- flipsub(flipqueue);
- } else { // if (symloc == ONVERTEX) {
- // The symmtric point already exists. It is possible when two
- // pbc group are idebtical. Omit sympoint.
- pointdealloc(sympoint);
- }
- }
- }
-
- // Insert newpoint into DT.
- splittet.tet = dummytet;
- // Find a good start point to search.
- encodedtet = point2tet(pa);
- if (encodedtet != (tetrahedron) NULL) {
- decode(encodedtet, splittet);
- if (isdead(&splittet)) {
- splittet.tet = dummytet;
- }
- }
- if (splittet.tet == dummytet) { // Try pb.
- encodedtet = point2tet(pb);
- if (encodedtet != (tetrahedron) NULL) {
- decode(encodedtet, splittet);
- if (isdead(&splittet)) {
- splittet.tet = dummytet;
- }
- }
- }
- // Locate the newpoint in DT. Do exact location.
- success = insertsite(newpoint, &splittet, false, flipqueue);
-#ifdef SELF_CHECK
- assert(success != DUPLICATEPOINT);
-#endif
- if (success == OUTSIDEPOINT) {
- // A convex hull edge is mssing, and the inserting point lies
- // (slightly) outside the convex hull due to the significant
- // digits lost in the calculation. Enlarge the convex hull.
- inserthullsite(newpoint, &splittet, flipqueue);
- }
- if (steinerleft > 0) steinerleft--;
- // Let newpoint remember splittet.
- setpoint2tet(newpoint, encode(splittet));
- // Do flip in DT.
- flip(flipqueue, NULL);
- // Insert newpoint into F.
- loc = locateseg(newpoint, &splitseg);
- if (loc == ONEDGE) {
- splitseg.shver = 0;
- spivot(splitseg, splitsub);
- // newpoint should on the edge of splitsub.
- splitsubedge(newpoint, &splitsub, flipqueue);
- } else {
- // insertsite() has done the whole job.
-#ifdef SELF_CHECK
- assert(loc == ONVERTEX);
- assert(checksubfaces);
-#endif
- // Some edges may need to be flipped.
- collectflipedges(newpoint, &splitseg, flipqueue);
- }
- // Do flip in facet.
- flipsub(flipqueue);
- }
- // Remove this entry from list.
- badfacedealloc(badsubsegs, encloop);
- // Get the next encroached segments.
- encloop = badfacetraverse(badsubsegs);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// perturbrepairencsubs() Repair all encroached subfaces. //
-// //
-// All encroached subfaces are stored in 'badsubfaces'. Each subface will be //
-// split by adding a perturbed point near its circumcenter. However, if the //
-// point encroaches some segments, it will not be inserted. Instead, the //
-// encroached segments are split. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::perturbrepairencsubs(list* cavsublist, queue* flipqueue)
-{
- badface *encloop, *encsubseg;
- tetrahedron encodedtet;
- triface splittet;
- face splitsub, symsplitsub;
- face checkseg, symsplitseg;
- point newpoint, sympoint;
- point pa, pb, pc, pd;
- enum insertsiteresult success;
- enum locateresult loc, symloc;
- REAL cent[3], d1, ps, rs;
- bool reject;
- int i;
-
- // Note that steinerleft == -1 if an unlimited number of Steiner points
- // is allowed. Loop until the list 'badsubfaces' is empty.
- while ((badsubfaces->items > 0) && (steinerleft != 0)) {
- badsubfaces->traversalinit();
- encloop = badfacetraverse(badsubfaces);
- while ((encloop != (badface *) NULL) && (steinerleft != 0)) {
- splitsub = encloop->ss;
-#ifdef SELF_CHECK
- assert(shell2badface(splitsub) == encloop);
-#endif
- setshell2badface(splitsub, NULL);
- pa = sorg(splitsub);
- pb = sdest(splitsub);
- pc = sapex(splitsub);
- // The subface may be not the same one when it was determined to be
- // encroached. If its adjacent encroached subface was split, the
- // consequent flips may change it into another subface.
- if ((pa == encloop->forg) && (pb == encloop->fdest) &&
- (pc == encloop->fapex)) {
- if (b->verbose > 1) {
- printf(" Get subface (%d, %d, %d).\n", pointmark(pa),
- pointmark(pb), pointmark(pc));
- }
- // Create the newpoint.
- makepoint(&newpoint);
- // Get the circumcenter of abc.
- circumsphere(pa, pb, pc, NULL, cent, &d1);
-#ifdef SELF_CHECK
- assert(d1 > 0.0);
-#endif
- // Add a random perturbation to newpoint along the vector a->cent.
- // This way, the perturbed point still lies in the plane of abc.
- ps = randgenerator(d1 * 1.0e-3);
- rs = ps / d1;
- // Set newpoint (be at the perturbed circumcenter of abc).
- for (i = 0; i < 3; i++) newpoint[i] = cent[i] + rs * (cent[i] - pa[i]);
- // Get the abovepoint of the facet.
- abovepoint = facetabovepointarray[shellmark(splitsub)];
- // Do we need to calculate the abovepoint?
- if (abovepoint == (point) NULL) {
- getfacetabovepoint(&splitsub);
- }
- loc = locatesub(newpoint, &splitsub, 1, 0.0);
-#ifdef SELF_CHECK
- assert(loc != ONVERTEX);
-#endif
- if (loc != OUTSIDE) {
- // Add 'splitsub' into 'cavsublist'.
- cavsublist->append(&splitsub);
- // Collect all subfaces that encroached by newpoint.
- collectcavsubs(newpoint, cavsublist);
- // Find if there are encroached segments.
- reject = tallencsegsfsubs(newpoint, cavsublist);
- // Clear cavsublist for the next use.
- cavsublist->clear();
- } else {
- // newpoint lies outside. splitsub contains the boundary segment.
- sspivot(splitsub, checkseg);
-#ifdef SELF_CHECK
- assert(checkseg.sh != dummysh);
-#endif
- // Add this segment into list for splitting.
- if (b->verbose > 2) {
- printf(" Queuing boundary segment (%d, %d).\n",
- pointmark(sorg(checkseg)), pointmark(sdest(checkseg)));
- }
- encsubseg = (badface *) badsubsegs->alloc();
- encsubseg->ss = checkseg;
- encsubseg->forg = sorg(checkseg);
- encsubseg->fdest = sdest(checkseg);
- encsubseg->foppo = (point) NULL;
- setshell2badface(encsubseg->ss, encsubseg);
- // Reject newpoint.
- reject = true;
- }
-
- if (!reject) {
- // newpoint is going to be inserted.
-
- // Is there periodic boundary condition?
- if (checkpbcs) {
- if (shellpbcgroup(splitsub) >= 0) {
- // Insert a point on another facet of the pbcgroup.
- makepoint(&sympoint);
- // Note: 'abovepoint' will be changed.
- symloc = getsubpbcsympoint(newpoint, &splitsub, sympoint,
- &symsplitsub);
-#ifdef SELF_CHECK
- assert(symloc != ONVERTEX);
-#endif
- setpoint2pbcpt(newpoint, sympoint);
- setpoint2pbcpt(sympoint, newpoint);
- setpointtype(sympoint, FREESUBVERTEX);
- // setpoint2sh(sympoint, sencode(symsplitsub));
- // Insert sympoint into DT.
- pd = sorg(symsplitsub);
- splittet.tet = dummytet;
- // Find a good start point to search.
- encodedtet = point2tet(pd);
- if (encodedtet != (tetrahedron) NULL) {
- decode(encodedtet, splittet);
- if (isdead(&splittet)) {
- splittet.tet = dummytet;
- }
- }
- // Locate sympoint in DT. Do exact location.
- success = insertsite(sympoint, &splittet, false, flipqueue);
-#ifdef SELF_CHECK
- assert(success != DUPLICATEPOINT);
-#endif
- if (success == OUTSIDEPOINT) {
- inserthullsite(sympoint, &splittet, flipqueue);
- }
- if (steinerleft > 0) steinerleft--;
- // Let sympoint remember splittet.
- setpoint2tet(sympoint, encode(splittet));
- // Do flip in DT.
- flip(flipqueue, NULL);
- // Insert sympoint into F.
- // getabovepoint(&symsplitsub);
- // symloc = locatesub(sympoint, &symsplitsub, 1, 0.0);
- if (symloc == ONFACE) {
- splitsubface(sympoint, &symsplitsub, flipqueue);
- } else if (symloc == ONEDGE) {
- splitsubedge(sympoint, &symsplitsub, flipqueue);
- } else {
- // 'insertsite()' has done the whole job.
-#ifdef SELF_CHECK
- assert(symloc == ONVERTEX);
- assert(checksubfaces);
-#endif
- // Split subfaces have been flipped.
- flipqueue->clear();
- }
- // Do flip in facet.
- flipsub(flipqueue);
- }
- }
-
- // Insert newpoint into DT.
- splittet.tet = dummytet;
- // Find a good start point to search.
- encodedtet = point2tet(pa);
- if (encodedtet != (tetrahedron) NULL) {
- decode(encodedtet, splittet);
- if (isdead(&splittet)) {
- splittet.tet = dummytet;
- }
- }
- if (splittet.tet == dummytet) { // Try pb.
- encodedtet = point2tet(pb);
- if (encodedtet != (tetrahedron) NULL) {
- decode(encodedtet, splittet);
- if (isdead(&splittet)) {
- splittet.tet = dummytet;
- }
- }
- }
- // Locate the newpoint in DT. Do exact location.
- success = insertsite(newpoint, &splittet, false, flipqueue);
-#ifdef SELF_CHECK
- assert(success != DUPLICATEPOINT);
-#endif
- if (success == OUTSIDEPOINT) {
- inserthullsite(newpoint, &splittet, flipqueue);
- }
- if (steinerleft > 0) steinerleft--;
- // Let newpoint remember splittet.
- setpoint2tet(newpoint, encode(splittet));
- // Do flip in DT.
- flip(flipqueue, NULL);
- // Insert newpoint into F.
- // if (checkpbcs) {
- // 'abovepoint' has been changed.
- // getabovepoint(&splitsub);
- // loc = locatesub(newpoint, &splitsub, 1, 0.0);
- // }
- if (loc == ONFACE) {
- // Insert the newpoint in facet.
- splitsubface(newpoint, &splitsub, flipqueue);
- } else if (loc == ONEDGE) {
- // Insert the newpoint in facet.
- splitsubedge(newpoint, &splitsub, flipqueue);
- } else {
- // 'insertsite()' has done the whole job.
-#ifdef SELF_CHECK
- assert(loc == ONVERTEX);
- assert(checksubfaces);
-#endif
- // Split subfaces have been flipped.
- flipqueue->clear();
- }
- // Set the type of the newpoint.
- setpointtype(newpoint, FREESUBVERTEX);
- // Set splitsub into the newpoint.
- // setpoint2sh(newpoint, sencode(splitsub));
- // Do flip in the facet.
- flipsub(flipqueue);
-
- // Remove this entry from list.
- badfacedealloc(badsubfaces, encloop);
- } else {
- // newpoint is rejected. Remove it from points.
- pointdealloc(newpoint);
- // Repair all encroached segments.
- perturbrepairencsegs(flipqueue);
- // Do not remove 'encloop'. Later it will be tested again.
- setshell2badface(encloop->ss, encloop);
- }
- } else {
- // This subface has been changed. Remove this entry from list.
- badfacedealloc(badsubfaces, encloop);
- // It may be co-circular with its neighbors.
- // checksub4cocir(&splitsub, eps, false, true);
- }
- // Get the next encroached subfaces.
- encloop = badfacetraverse(badsubfaces);
- }
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// incrperturbvertices() Remove the local degeneracies in DT. //
-// //
-// A local degeneracy of a DT D is a set of 5 or more vertices which share a //
-// common sphere S and no other vertex of D in S. D is not unique if it has //
-// local degeneracies. This routine removes the local degeneracies from D by //
-// inserting break points (as described in reference [2]). //
-// //
-// 'eps' is a user-provided error tolerance. It is used to detect whether or //
-// not five points are approximate cospherical (evaluated in iscospheric()). //
-// Set it to 0.0 to disable it, i.e., only test pure degenerate point set. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::incrperturbvertices(REAL eps)
-{
- queue *flipqueue;
- list *cavsublist;
- long vertcount;
-
- if (!b->quiet) {
- printf("Perturbing vertices.\n");
- }
-
- vertcount = points->items;
- // Create a map from points to tets for fastening search.
- // makepoint2tetmap(); // This has been done in meshsurface().
-
- // Initialize working queues, lists.
- flipqueue = new queue(sizeof(badface));
- cavsublist = new list(sizeof(face), NULL, 256);
- // Initialize the pool of encroached subfaces and subsegments.
- badsubsegs = new memorypool(sizeof(badface), SUBPERBLOCK, POINTER, 0);
- badsubfaces = new memorypool(sizeof(badface), SUBPERBLOCK, POINTER, 0);
- // Find all pairs of co-circular subfaces.
- tallcocirsubs(eps, true);
- if (b->verbose && badsubfaces->items > 0) {
- printf(" Removing degenerate subfaces.\n");
- }
- perturbrepairencsubs(cavsublist, flipqueue);
-
- if (b->verbose > 0) {
- printf(" %ld break points.\n", points->items - vertcount);
- }
-
- delete cavsublist;
- delete flipqueue;
- delete badsubfaces;
- delete badsubsegs;
- badsubsegs = (memorypool *) NULL;
- badsubfaces = (memorypool *) NULL;
-}
-
-//
-// End of vertex perturbation routines
-//
-
-//
-// Begin of segment recovery routines
-//
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// markacutevertices() Mark acute vertices. //
-// //
-// A vertex v is called acute if there are two segments sharing at v forming //
-// an acute angle (i.e. smaller than 90 degree). //
-// //
-// This routine finds all acute vertices in the PLC and marks them as point- //
-// type ACUTEVERTEX. The other vertices of segments which are non-acute will //
-// be marked as NACUTEVERTEX. Vertices which are not endpoints of segments //
-// (such as DUPLICATEDVERTEX, UNUSEDVERTEX, etc) are not infected. //
-// //
-// NOTE: This routine should be called before Steiner points are introduced. //
-// That is, no point has type like FREESEGVERTEX, etc. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::markacutevertices(REAL acuteangle)
-{
- shellface **segsperverlist;
- face segloop, nextseg;
- point pointloop, edest, eapex;
- REAL cosbound, anglearc;
- REAL v1[3], v2[3], L, D;
- bool isacute;
- int *idx2seglist;
- int acutecount;
- int idx, i, j, k;
-
- if (b->verbose > 0) {
- printf(" Marking acute vertices.\n");
- }
-
- anglearc = acuteangle * PI / 180.0;
- cosbound = cos(anglearc);
- acutecount = 0;
- // Constructing a map from vertex to segments.
- makesegmentmap(idx2seglist, segsperverlist);
-
- // Loop over the set of vertices.
- points->traversalinit();
- pointloop = pointtraverse();
- while (pointloop != (point) NULL) {
- idx = pointmark(pointloop) - in->firstnumber;
- // Only do test if p is an endpoint of some segments.
- if (idx2seglist[idx + 1] > idx2seglist[idx]) {
- // Init p to be non-acute.
- setpointtype(pointloop, NACUTEVERTEX);
- isacute = false;
- // Loop through all segments sharing at p.
- for (i = idx2seglist[idx]; i < idx2seglist[idx + 1] && !isacute; i++) {
- segloop.sh = segsperverlist[i];
- // segloop.shver = 0;
- if (sorg(segloop) != pointloop) sesymself(segloop);
- edest = sdest(segloop);
- for (j = i + 1; j < idx2seglist[idx + 1] && !isacute; j++) {
- nextseg.sh = segsperverlist[j];
- // nextseg.shver = 0;
- if (sorg(nextseg) != pointloop) sesymself(nextseg);
- eapex = sdest(nextseg);
- // Check the angle formed by segs (p, edest) and (p, eapex).
- for (k = 0; k < 3; k++) {
- v1[k] = edest[k] - pointloop[k];
- v2[k] = eapex[k] - pointloop[k];
- }
- L = sqrt(v1[0] * v1[0] + v1[1] * v1[1] + v1[2] * v1[2]);
- for (k = 0; k < 3; k++) v1[k] /= L;
- L = sqrt(v2[0] * v2[0] + v2[1] * v2[1] + v2[2] * v2[2]);
- for (k = 0; k < 3; k++) v2[k] /= L;
- D = v1[0] * v2[0] + v1[1] * v2[1] + v1[2] * v2[2];
- // Is D acute?
- isacute = (D >= cosbound);
- }
- }
- if (isacute) {
- // Mark p to be acute.
- setpointtype(pointloop, ACUTEVERTEX);
- acutecount++;
- }
- }
- pointloop = pointtraverse();
- }
-
- delete [] idx2seglist;
- delete [] segsperverlist;
-
- if ((b->verbose > 0) && (acutecount > 0)) {
- printf(" %d acute vertices.\n", acutecount);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// finddirection() Find the first tetrahedron on the path from one point //
-// to another. //
-// //
-// Find the tetrahedron that intersects a line segment L (from the origin of //
-// 'searchtet' to the point 'tend'), and returns the result in 'searchtet'. //
-// The origin of 'searchtet' does not change, even though the tetrahedron //
-// returned may differ from the one passed in. This routine is used to find //
-// the direction to move in to get from one point to another. //
-// //
-// The return value notes the location of the line segment L with respect to //
-// 'searchtet': //
-// - Returns RIGHTCOLLINEAR indicates L is collinear with the line segment //
-// from the origin to the destination of 'searchtet'. //
-// - Returns LEFTCOLLINEAR indicates L is collinear with the line segment //
-// from the origin to the apex of 'searchtet'. //
-// - Returns TOPCOLLINEAR indicates L is collinear with the line segment //
-// from the origin to the opposite of 'searchtet'. //
-// - Returns ACROSSEDGE indicates L intersects with the line segment from //
-// the destination to the apex of 'searchtet'. //
-// - Returns ACROSSFACE indicates L intersects with the face opposite to //
-// the origin of 'searchtet'. //
-// - Returns BELOWHULL indicates L crosses outside the mesh domain. This //
-// can only happen when the domain is non-convex. //
-// //
-// NOTE: This routine only works correctly when the mesh is exactly Delaunay.//
-// //
-// If 'maxtetnumber' > 0, stop the searching process if the number of passed //
-// tets is larger than it. Return BELOWHULL. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-enum tetgenmesh::finddirectionresult tetgenmesh::
-finddirection(triface *searchtet, point tend, long maxtetnumber)
-{
- triface neightet;
- point tstart, tdest, tapex, toppo;
- REAL ori1, ori2, ori3;
- long tetnumber;
-
- tstart = org(*searchtet);
-#ifdef SELF_CHECK
- assert(tstart != tend);
-#endif
- adjustedgering(*searchtet, CCW);
- if (tstart != org(*searchtet)) {
- enextself(*searchtet); // For keeping the same origin.
- }
- tdest = dest(*searchtet);
- if (tdest == tend) {
- return RIGHTCOLLINEAR;
- }
- tapex = apex(*searchtet);
- if (tapex == tend) {
- return LEFTCOLLINEAR;
- }
-
- ori1 = orient3d(tstart, tdest, tapex, tend);
- if (ori1 > 0.0) {
- // 'tend' is below the face, get the neighbor of this side.
- sym(*searchtet, neightet);
- if (neightet.tet != dummytet) {
- findorg(&neightet, tstart);
- adjustedgering(neightet, CCW);
- if (org(neightet) != tstart) {
- enextself(neightet); // keep the same origin.
- }
- // Set the changed configuratiuon.
- *searchtet = neightet;
- ori1 = -1.0;
- tdest = dest(*searchtet);
- tapex = apex(*searchtet);
- } else {
- // A hull face. Only possible for a nonconvex mesh.
-#ifdef SELF_CHECK
- assert(nonconvex);
-#endif
- return BELOWHULL;
- }
- }
-
- // Repeatedly change the 'searchtet', remain 'tstart' be its origin, until
- // find a tetrahedron contains 'tend' or is crossed by the line segment
- // from 'tstart' to 'tend'.
- tetnumber = 0l;
- while ((maxtetnumber > 0) && (tetnumber <= maxtetnumber)) {
- tetnumber++;
- toppo = oppo(*searchtet);
- if (toppo == tend) {
- return TOPCOLLINEAR;
- }
- ori2 = orient3d(tstart, toppo, tdest, tend);
- if (ori2 > 0.0) {
- // 'tend' is below the face, get the neighbor at this side.
- fnext(*searchtet, neightet);
- symself(neightet);
- if (neightet.tet != dummytet) {
- findorg(&neightet, tstart);
- adjustedgering(neightet, CCW);
- if (org(neightet) != tstart) {
- enextself(neightet); // keep the same origin.
- }
- // Set the changed configuration.
- *searchtet = neightet;
- ori1 = -1.0;
- tdest = dest(*searchtet);
- tapex = apex(*searchtet);
- // Continue the search from the changed 'searchtet'.
- continue;
- } else {
- // A hull face. Only possible for a nonconvex mesh.
-#ifdef SELF_CHECK
- assert(nonconvex);
-#endif
- return BELOWHULL;
- }
- }
- ori3 = orient3d(tapex, toppo, tstart, tend);
- if (ori3 > 0.0) {
- // 'tend' is below the face, get the neighbor at this side.
- enext2fnext(*searchtet, neightet);
- symself(neightet);
- if (neightet.tet != dummytet) {
- findorg(&neightet, tstart);
- adjustedgering(neightet, CCW);
- if (org(neightet) != tstart) {
- enextself(neightet); // keep the same origin.
- }
- // Set the changed configuration.
- *searchtet = neightet;
- ori1 = -1.0;
- tdest = dest(*searchtet);
- tapex = apex(*searchtet);
- // Continue the search from the changed 'searchtet'.
- continue;
- } else {
- // A hull face. Only possible for a nonconvex mesh.
-#ifdef SELF_CHECK
- assert(nonconvex);
-#endif
- return BELOWHULL;
- }
- }
- // Now 'ori1', 'ori2' and 'ori3' are possible be 0.0 or all < 0.0;
- if (ori1 < 0.0) {
- // Possible cases are: ACROSSFACE, ACROSSEDGE, TOPCOLLINEAR.
- if (ori2 < 0.0) {
- if (ori3 < 0.0) {
- return ACROSSFACE;
- } else { // ori3 == 0.0;
- // Cross edge (apex, oppo)
- enext2fnextself(*searchtet);
- esymself(*searchtet); // org(*searchtet) == tstart;
- return ACROSSEDGE;
- }
- } else { // ori2 == 0.0;
- if (ori3 < 0.0) {
- // Cross edge (dest, oppo)
- fnextself(*searchtet);
- esymself(*searchtet);
- enextself(*searchtet); // org(*searchtet) == tstart;
- return ACROSSEDGE;
- } else { // ori3 == 0.0;
- // Collinear with edge (org, oppo)
- return TOPCOLLINEAR;
- }
- }
- } else { // ori1 == 0.0;
- // Possible cases are: RIGHTCOLLINEAR, LEFTCOLLINEAR, ACROSSEDGE.
- if (ori2 < 0.0) {
- if (ori3 < 0.0) {
- // Cross edge (tdest, tapex)
- return ACROSSEDGE;
- } else { // ori3 == 0.0
- // Collinear with edge (torg, tapex)
- return LEFTCOLLINEAR;
- }
- } else { // ori2 == 0.0;
-#ifdef SELF_CHECK
- assert(ori3 != 0.0);
-#endif
- // Collinear with edge (torg, tdest)
- return RIGHTCOLLINEAR;
- }
- }
- }
- // Loop breakout. It may happen when the mesh is non-Delaunay.
- return BELOWHULL;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// getsearchtet() Find a tetrahedron whose origin is either 'p1' or 'p2'. //
-// //
-// On return, the origin of 'searchtet' is either 'p1' or 'p2', and 'tend' //
-// returns the other point. 'searchtet' serves as the starting tetrahedron //
-// for searching of the line segment from 'p1' to 'p2' or vice versa. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::getsearchtet(point p1, point p2, triface* searchtet,
- point* tend)
-{
- tetrahedron encodedtet1, encodedtet2;
-
- // Is there a valid handle provided by the user?
- if ((searchtet->tet != (tetrahedron *) NULL) && !isdead(searchtet)) {
- // Find which endpoint the handle holds.
- if (findorg(searchtet, p1)) {
- *tend = p2;
- return;
- } else {
- if (findorg(searchtet, p2)) {
- *tend = p1;
- return;
- }
- }
- }
- // If not, search the tet handle stored in 'p1' or 'p2'.
- *tend = (point) NULL;
- encodedtet1 = point2tet(p1);
- encodedtet2 = point2tet(p2);
- if (encodedtet1 != (tetrahedron) NULL) {
- decode(encodedtet1, *searchtet);
- // Be careful, here 'searchtet' may be dead.
- if (findorg(searchtet, p1)) {
- *tend = p2;
- }
- } else if (encodedtet2 != (tetrahedron) NULL) {
- decode(encodedtet2, *searchtet);
- // Be careful, here 'searchtet' may be dead.
- if (findorg(searchtet, p2)) {
- *tend = p1;
- }
- }
- // If still not, perform a full point location. The starting tet is
- // chosen as follows: Use the handle stored in 'p1' or 'p2' if it is
- // alive; otherwise, start from a tet on the convex hull.
- if (*tend == (point) NULL) {
- if (encodedtet1 != (tetrahedron) NULL) {
- decode(encodedtet1, *searchtet);
- // Be careful, here 'searchtet' may be dead.
- }
- if (isdead(searchtet)) {
- if (encodedtet2 != (tetrahedron) NULL) {
- decode(encodedtet2, *searchtet);
- // Be careful, here 'searchtet' may be dead.
- }
- if (isdead(searchtet)) {
- searchtet->tet = dummytet;
- searchtet->loc = 0;
- symself(*searchtet);
- }
-#ifdef SELF_CHECK
- assert(!isdead(searchtet));
-#endif
- }
- if (locate(p1, searchtet) != ONVERTEX) {
- printf("Internal error in getsearchtet(): Failed to locate point\n");
- internalerror();
- }
- // Remember this handle in 'p1' to enhance the search speed.
- setpoint2tet(p1, encode(*searchtet));
- *tend = p2;
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// isedgeencroached() Check whether or not a subsegment is encroached. //
-// //
-// A segment with endpoints 'p1' and 'p2' is encroached by the point 'testpt'//
-// if it lies in the diametral sphere of this segment. The degenerate case //
-// that 'testpt' lies on the sphere is treated as encroached if 'degflag' is //
-// set to be TRUE. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::isedgeencroached(point p1, point p2, point testpt,
- bool degflag)
-{
- REAL dotproduct;
-
- // Check if the segment is facing an angle larger than 90 degree?
- dotproduct = (p1[0] - testpt[0]) * (p2[0] - testpt[0])
- + (p1[1] - testpt[1]) * (p2[1] - testpt[1])
- + (p1[2] - testpt[2]) * (p2[2] - testpt[2]);
- if (dotproduct < 0) {
- return true;
- } else if (dotproduct == 0 && degflag) {
- return true;
- } else {
- return false;
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// scoutrefpoint() Search the reference point of a missing segment. //
-// //
-// A segment S is missing in current Delaunay tetrahedralization DT and will //
-// be split by inserting a point V in it. The two end points of S are the //
-// origin of 'searchtet' and 'tend'. And we know that S is crossing the face //
-// of 'searchtet' opposite to its origin (may be intersecting with the edge //
-// from the destination to the apex of the 'searchtet'). The search of P is //
-// completed by walking through all faces of DT across by S. //
-// //
-// Warning: This routine is correct when the tetrahedralization is Delaunay //
-// and convex. Otherwise, the search loop may not terminate. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-tetgenmesh::point tetgenmesh::scoutrefpoint(triface* searchtet, point tend)
-{
- triface checkface;
- point tstart, testpt, refpoint;
- REAL cent[3], radius, largest;
- REAL ahead;
- bool ncollinear;
- int sides;
-
- if (b->verbose > 2) {
- printf(" Scout the reference point of segment (%d, %d).\n",
- pointmark(org(*searchtet)), pointmark(tend));
- }
-
- tstart = org(*searchtet);
- refpoint = (point) NULL;
- largest = 0; // avoid compile warning.
-
- // Check the three vertices of the crossing face.
- testpt = apex(*searchtet);
- if (isedgeencroached(tstart, tend, testpt, true)) {
- ncollinear = circumsphere(tstart, tend, testpt, NULL, cent, &radius);
-#ifdef SELF_CHECK
- assert(ncollinear);
-#endif
- refpoint = testpt;
- largest = radius;
- }
- testpt = dest(*searchtet);
- if (isedgeencroached(tstart, tend, testpt, true)) {
- ncollinear = circumsphere(tstart, tend, testpt, NULL, cent, &radius);
-#ifdef SELF_CHECK
- assert(ncollinear);
-#endif
- if (refpoint == (point) NULL) {
- refpoint = testpt;
- largest = radius;
- } else {
- if (radius > largest) {
- refpoint = testpt;
- largest = radius;
- }
- }
- }
- testpt = oppo(*searchtet);
- if (isedgeencroached(tstart, tend, testpt, true)) {
- ncollinear = circumsphere(tstart, tend, testpt, NULL, cent, &radius);
-#ifdef SELF_CHECK
- assert(ncollinear);
-#endif
- if (refpoint == (point) NULL) {
- refpoint = testpt;
- largest = radius;
- } else {
- if (radius > largest) {
- refpoint = testpt;
- largest = radius;
- }
- }
- }
- // Check the opposite vertex of the neighboring tet in case the segment
- // crosses the edge (leftpoint, rightpoint) of the crossing face.
- sym(*searchtet, checkface);
- if (checkface.tet != dummytet) {
- testpt = oppo(checkface);
- if (isedgeencroached(tstart, tend, testpt, true)) {
- ncollinear = circumsphere(tstart, tend, testpt, NULL, cent, &radius);
-#ifdef SELF_CHECK
- assert(ncollinear);
-#endif
- if (refpoint == (point) NULL) {
- refpoint = testpt;
- largest = radius;
- } else {
- if (radius > largest) {
- refpoint = testpt;
- largest = radius;
- }
- }
- }
- }
-
- // Walk through all crossing faces.
- enextfnext(*searchtet, checkface);
- sym(checkface, *searchtet);
- while (true) {
- // Check if we are reaching the boundary of the triangulation.
-#ifdef SELF_CHECK
- assert(searchtet->tet != dummytet);
-#endif
- // Search for an adjoining tetrahedron we can walk through.
- searchtet->ver = 0;
- // 'testpt' is the shared vertex for the following orientation tests.
- testpt = oppo(*searchtet);
- if (testpt == tend) {
- // The searching is finished.
- break;
- } else {
- // 'testpt' may encroach the segment.
- if ((testpt != tstart) && (testpt != refpoint)) {
- if (isedgeencroached(tstart, tend, testpt, true)) {
- ncollinear = circumsphere(tstart, tend, testpt, NULL, cent, &radius);
- if (!ncollinear) {
- // 'testpt' is collinear with the segment. It may happen when a
- // set of collinear and continuous segments is defined by two
- // extreme endpoints. In this case, we should choose 'testpt'
- // as the splitting point immediately. No new point should be
- // created.
- refpoint = testpt;
- break;
- }
- if (refpoint == (point) NULL) {
- refpoint = testpt;
- largest = radius;
- } else {
- if (radius > largest) {
- refpoint = testpt;
- largest = radius;
- }
- }
- }
- }
- }
- // Check three side-faces of 'searchtet' to find the one through
- // which we can walk next.
- for (sides = 0; sides < 3; sides++) {
- fnext(*searchtet, checkface);
- ahead = orient3d(org(checkface), dest(checkface), testpt, tend);
- if (ahead < 0.0) {
- // We can walk through this face and continue the searching.
- sym(checkface, *searchtet);
- break;
- }
- enextself(*searchtet);
- }
-#ifdef SELF_CHECK
- assert (sides < 3);
-#endif
- }
-
-#ifdef SELF_CHECK
- assert(refpoint != (point) NULL);
-#endif
- return refpoint;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// getsegmentorigin() Return the origin of the (unsplit) segment. //
-// //
-// After a segment (or a subsegment) is split. Two resulting subsegments are //
-// connecting each other through the pointers saved in their data fields. //
-// With these pointers, the whole (unsplit) segment can be found. 'splitseg' //
-// may be a split subsegment. Returns the origin of the unsplit segment. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-tetgenmesh::point tetgenmesh::getsegmentorigin(face* splitseg)
-{
- face workseg;
- point farorg;
-
- farorg = sorg(*splitseg);
- if ((pointtype(farorg) != ACUTEVERTEX) &&
- (pointtype(farorg) != NACUTEVERTEX)) {
- workseg = *splitseg;
- do {
- senext2self(workseg);
- spivotself(workseg);
- if (workseg.sh != dummysh) {
- workseg.shver = 0; // It's a subsegment.
- if (sdest(workseg) != farorg) {
- sesymself(workseg);
-#ifdef SELF_CHECK
- assert(sdest(workseg) == farorg);
-#endif
- }
- farorg = sorg(workseg);
- if ((pointtype(farorg) == ACUTEVERTEX) ||
- (pointtype(farorg) == NACUTEVERTEX)) break;
- }
- } while (workseg.sh != dummysh);
- }
-#ifdef SELF_CHECK
- assert((pointtype(farorg) == ACUTEVERTEX) ||
- (pointtype(farorg) == NACUTEVERTEX));
-#endif
- return farorg;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// getsplitpoint() Get a point for splitting a segment. //
-// //
-// 'splitseg' is the segment will be split. 'refpoint' is a reference point //
-// for splitting this segment. Moreover, it should not collinear with the //
-// splitting segment. (The collinear case will be detected by iscollinear() //
-// before entering this routine.) The calculation of the splitting point is //
-// governed by three rules introduced in my paper. //
-// //
-// After the position is calculated, a new point is created at this location.//
-// The new point has one of the two pointtypes: FREESEGVERTEX indicating it //
-// is an inserting vertex on segment, and NACUTEVERTEX indicating it is an //
-// endpoint of a segment which original has type-3 now becomes type-2. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-tetgenmesh::point tetgenmesh::getsplitpoint(face* splitseg, point refpoint)
-{
- point splitpoint;
- point farorg, fardest;
- point ei, ej, ek, c;
- REAL v[3], r, split;
- REAL d1, d2, ps, rs;
- bool acuteorg, acutedest;
- int stype, rule;
- int i;
-
- // First determine the type of the segment (type-1, type-2, or type-3).
- farorg = getsegmentorigin(splitseg);
- acuteorg = (pointtype(farorg) == ACUTEVERTEX);
- sesymself(*splitseg);
- fardest = getsegmentorigin(splitseg);
- acutedest = (pointtype(fardest) == ACUTEVERTEX);
- sesymself(*splitseg);
-
- ek = (point) NULL; // avoid a compilation warning.
-
- if (acuteorg) {
- if (acutedest) {
- stype = 3;
- } else {
- stype = 2;
- ek = farorg;
- }
- } else {
- if (acutedest) {
- stype = 2;
- // Adjust splitseg, so that its origin is acute.
- sesymself(*splitseg);
- ek = fardest;
- } else {
- stype = 1;
- }
- }
- ei = sorg(*splitseg);
- ej = sdest(*splitseg);
-
- if (b->verbose > 1) {
- printf(" Splitting segment (%d, %d) type-%d with refpoint %d.\n",
- pointmark(ei), pointmark(ej), stype, pointmark(refpoint));
- }
-
- if (stype == 1 || stype == 3) {
- // Use rule-1.
- REAL eij, eip, ejp;
- eij = distance(ei, ej);
- eip = distance(ei, refpoint);
- ejp = distance(ej, refpoint);
- if ((eip < ejp) && (eip < 0.5 * eij)) {
- c = ei;
- r = eip;
- } else if ((eip > ejp) && (ejp < 0.5 * eij)) {
- c = ej;
- ej = ei;
- r = ejp;
- } else {
- c = ei;
- r = 0.5 * eij;
- }
- split = r / eij;
- for (i = 0; i < 3; i++) {
- v[i] = c[i] + split * (ej[i] - c[i]);
- }
- rule = 1;
- } else {
- // Use rule-2 or rule-3.
- REAL eki, ekj, ekp, evj, evp, eiv;
- c = ek;
- eki = distance(ek, ei); // eki may equal zero.
- ekj = distance(ek, ej);
- ekp = distance(ek, refpoint);
- // Calculate v (the going to split position between ei, ej).
- r = ekp;
- // Check the validity of the position.
- if (!(eki < r && r < ekj)) {
- printf("Error: Invalid PLC.\n");
- printf(" Hint: Use -d switch to check it.\n");
- terminatetetgen(1);
- }
- split = r / ekj;
- for (i = 0; i < 3; i++) {
- v[i] = c[i] + split * (ej[i] - c[i]);
- }
- rule = 2;
- evj = ekj - r; // distance(v, ej);
- evp = distance(v, refpoint);
- if (evj < evp) {
- // v is rejected, use rule-3.
- eiv = distance(ei, v);
- if (evp <= 0.5 * eiv) {
- r = eki + eiv - evp;
- } else {
- r = eki + 0.5 * eiv;
- }
-#ifdef SELF_CHECK
- assert(eki < r && r < ekj);
-#endif
- split = r / ekj;
- for (i = 0; i < 3; i++) {
- v[i] = c[i] + split * (ej[i] - c[i]);
- }
- if (b->verbose > 1) {
- printf(" Using rule-3.\n");
- }
- rule = 3;
- }
- }
-
- // Accumulate the corresponding counters.
- if (rule == 1) r1count++;
- else if (rule == 2) r2count++;
- else if (rule == 3) r3count++;
-
- if (b->verbose > 1) {
- if (stype == 2) {
- printf(" Split = %.12g.\n", distance(ei, v) / distance(ei, ej));
- } else {
- printf(" Split = %.12g.\n", distance(c, v) / distance(c, ej));
- }
- }
-
- // Create the newpoint.
- makepoint(&splitpoint);
- // Add a random perturbation on splitpoint.
- d1 = distance(c, v);
- d2 = distance(refpoint, v);
- if (stype == 1 || stype == 3) {
- ps = randgenerator(d1 * 1.0e-3);
- } else {
- // For type-2 segment, add a smaller perturbation.
- // ps = randgenerator(d1 * 1.0e-5);
- // REAL d2 = distance(refpoint, v);
- ps = randgenerator(d2 * 1.0e-5);
- }
- rs = ps / d1;
- // Perturb splitpoint away from c.
- for (i = 0; i < 3; i++) {
- splitpoint[i] = c[i] + (1.0 + rs) * (v[i] - c[i]);
- }
- // for (i = 0; i < in->numberofpointattributes; i++) {
- // splitpoint[i + 3] = c[i + 3] + (split + rs) * (ej[i + 3] - c[i + 3]);
- // }
- if (stype == 3) {
- // Change a type-3 segment into two type-2 segments.
- setpointtype(splitpoint, NACUTEVERTEX);
- } else {
- // Set it's type be FREESEGVERTEX.
- setpointtype(splitpoint, FREESEGVERTEX);
- }
- setpoint2sh(splitpoint, sencode(*splitseg));
-
- return splitpoint;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// insertsegment() Insert segment into DT. Queue it if it does not exist. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::insertsegment(face *insseg, list *misseglist)
-{
- badface *misseg;
- triface searchtet, spintet;
- point tend, checkpoint;
- point p1, p2;
- enum finddirectionresult collinear;
- int hitbdry;
-
- // Search segment ab in DT.
- p1 = (point) insseg->sh[3];
- p2 = (point) insseg->sh[4];
- getsearchtet(p1, p2, &searchtet, &tend);
- collinear = finddirection(&searchtet, tend, tetrahedrons->items);
- if (collinear == LEFTCOLLINEAR) {
- checkpoint = apex(searchtet);
- enext2self(searchtet);
- esymself(searchtet);
- } else if (collinear == RIGHTCOLLINEAR) {
- checkpoint = dest(searchtet);
- } else if (collinear == TOPCOLLINEAR) {
- checkpoint = oppo(searchtet);
- fnextself(searchtet);
- enext2self(searchtet);
- esymself(searchtet);
- } else {
- // assert(collinear == ACROSSFACE || collinear == ACROSSEDGE);
- checkpoint = (point) NULL;
- }
- if (checkpoint == tend) {
- // Segment exist. Bond it to all tets containing it.
- hitbdry = 0;
- adjustedgering(searchtet, CCW);
- fnextself(searchtet);
- spintet = searchtet;
- do {
- tssbond1(spintet, *insseg);
- if (!fnextself(spintet)) {
- hitbdry++;
- if (hitbdry < 2) {
- esym(searchtet, spintet);
- if (!fnextself(spintet)) {
- hitbdry++;
- }
- }
- }
- } while ((apex(spintet) != apex(searchtet)) && (hitbdry < 2));
- return true;
- } else {
- // Segment is missing.
- if (misseglist != (list *) NULL) {
- if (b->verbose > 2) {
- printf(" Queuing missing segment (%d, %d).\n", pointmark(p1),
- pointmark(p2));
- }
- misseg = (badface *) misseglist->append(NULL);
- misseg->ss = *insseg;
- misseg->forg = p1;
- misseg->fdest = p2;
- misseg->foppo = (point) NULL; // Not used.
- // setshell2badface(misseg->ss, misseg);
- }
- return false;
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// tallmissegs() Find and queue all missing segments in DT. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::tallmissegs(list *misseglist)
-{
- face segloop;
-
- if (b->verbose) {
- printf(" Queuing missing segments.\n");
- }
-
- subsegs->traversalinit();
- segloop.sh = shellfacetraverse(subsegs);
- while (segloop.sh != (shellface *) NULL) {
- insertsegment(&segloop, misseglist);
- segloop.sh = shellfacetraverse(subsegs);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// delaunizesegments() Split segments repeatedly until they appear in a //
-// Delaunay tetrahedralization. //
-// //
-// Given a PLC X, which has a set V of vertices and a set of segments. Start //
-// from a Delaunay tetrahedralization D of V, this routine recovers segments //
-// of X in D by incrementally inserting points on missing segments, updating //
-// D with the newly inserted points into D', which remains to be a Delaunay //
-// tetrahedralization and respects the segments of X. Hence, each segment of //
-// X appears as a union of edges in D'. //
-// //
-// This routine dynamically maintains two meshes, one is DT, another is the //
-// surface mesh F of X. DT and F have exactly the same vertices. They are //
-// updated simultaneously with the newly inserted points. //
-// //
-// Missing segments are found by looping the set S of segments, checking the //
-// existence of each segment in DT. Once a segment is found missing in DT, //
-// it is split into two subsegments by inserting a point into both DT and F, //
-// and S is updated accordingly. However, the inserted point may cause some //
-// other existing segments be non-Delaunay, hence are missing from the DT. //
-// In order to force all segments to appear in DT, we have to loop S again //
-// after some segments are split. (A little ugly method) Use a handle to //
-// remember the last segment be split in one loop, hence all segments after //
-// it are existing and need not be checked. //
-// //
-// In priciple, a segment on the convex hull should exist in DT. However, if //
-// there are four coplanar points on the convex hull, and the DT only can //
-// contain one diagonal edge which is unfortunately not the segment, then it //
-// is missing. During the recovery of the segment, it is possible that the //
-// calculated inserting point for recovering this convex hull segment is not //
-// exact enough and lies (slightly) outside the DT. In order to insert the //
-// point, we enlarge the convex hull of the DT, so it can contain the point //
-// and remains convex. 'inserthullsite()' is called for this case. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::delaunizesegments()
-{
- list *misseglist;
- queue *flipqueue;
- badface *misloop;
- tetrahedron encodedtet;
- triface searchtet, splittet;
- face splitsh, symsplitsub;
- face segloop, symsplitseg;
- point refpoint, splitpoint, sympoint;
- point tend, checkpoint;
- point p1, p2, pa;
- enum finddirectionresult collinear;
- enum insertsiteresult success;
- enum locateresult symloc;
- bool coll;
- long vertcount;
- int i, j;
-
- if (!b->quiet) {
- printf("Delaunizing segments.\n");
- }
-
- // Construct a map from points to tets for speeding point location.
- makepoint2tetmap();
- // Initialize a flipqueue.
- flipqueue = new queue(sizeof(badface));
- // Initialize the pool of missing segments.
- misseglist = new list(sizeof(badface), NULL, SUBPERBLOCK);
- // Looking for missing segments.
- tallmissegs(misseglist);
- // The DT contains segments now.
- checksubsegs = 1;
- // Remember the current number of points.
- vertcount = points->items;
- // Initialize the counters.
- r1count = r2count = r3count = 0l;
-
- // Loop until 'misseglist' is empty.
- while (misseglist->items > 0) {
- // Randomly pick a missing segment to recover.
- i = randomnation(misseglist->items);
- misloop = (badface *)(* misseglist)[i];
- segloop = misloop->ss;
- // Fill the "hole" in the list by filling the last one.
- *misloop = *(badface *)(* misseglist)[misseglist->items - 1];
- misseglist->items--;
- // Now recover the segment.
- p1 = (point) segloop.sh[3];
- p2 = (point) segloop.sh[4];
- if (b->verbose > 1) {
- printf(" Recover segment (%d, %d).\n", pointmark(p1), pointmark(p2));
- }
- getsearchtet(p1, p2, &searchtet, &tend);
- collinear = finddirection(&searchtet, tend, tetrahedrons->items);
- if (collinear == LEFTCOLLINEAR) {
- checkpoint = apex(searchtet);
- } else if (collinear == RIGHTCOLLINEAR) {
- checkpoint = dest(searchtet);
- } else if (collinear == TOPCOLLINEAR) {
- checkpoint = oppo(searchtet);
- } else {
-#ifdef SELF_CHECK
- assert(collinear == ACROSSFACE || collinear == ACROSSEDGE);
-#endif
- checkpoint = (point) NULL;
- }
- if (checkpoint != tend) {
- // ab is missing.
- splitpoint = (point) NULL;
- if (checkpoint != (point) NULL) {
- // An existing point c is found on the segment. It can happen when
- // ab is defined by a long segment with c inside it. Use c to
- // split ab. No new point is created.
- splitpoint = checkpoint;
- if (pointtype(checkpoint) == FREEVOLVERTEX) {
- // c is not a segment vertex yet. It becomes NACUTEVERTEX.
- setpointtype(splitpoint, NACUTEVERTEX);
- } else if (pointtype(checkpoint) == ACUTEVERTEX) {
- // c is an acute vertex. The definition of PLC is wrong.
- } else if (pointtype(checkpoint) == NACUTEVERTEX) {
- // c is an nonacute vertex. The definition of PLC is wrong.
- } else {
- // assert(0);
- }
- } else {
- // Find a reference point p of ab.
- refpoint = scoutrefpoint(&searchtet, tend);
- if (pointtype(refpoint) == FREEVOLVERTEX) {
- // p is an input point, check if it is nearly collinear with ab.
- coll = iscollinear(p1, p2, refpoint, b->epsilon);
- if (coll) {
- // a, b, and p are collinear. We insert p into ab. p becomes
- // a segment vertex with type NACUTEVERTEX.
- splitpoint = refpoint;
- setpointtype(splitpoint, NACUTEVERTEX);
- }
- }
- if (splitpoint == (point) NULL) {
- // Calculate a split point v using rule 1, or 2, or 3.
- splitpoint = getsplitpoint(&segloop, refpoint);
-
- // Is there periodic boundary conditions?
- if (checkpbcs) {
- // Yes! Insert points on other segments of incident pbcgroups.
- i = shellmark(segloop) - 1;
- for (j = idx2segpglist[i]; j < idx2segpglist[i + 1]; j++) {
- makepoint(&sympoint);
- symloc = getsegpbcsympoint(splitpoint, &segloop, sympoint,
- &symsplitseg, segpglist[j]);
-#ifdef SELF_CHECK
- assert(symloc != OUTSIDE);
-#endif
- if ((symloc == ONEDGE) && (symsplitseg.sh != segloop.sh)) {
-#ifdef SELF_CHECK
- assert(symsplitseg.sh != dummysh);
-#endif
- setpointtype(sympoint, FREESEGVERTEX);
- setpoint2sh(sympoint, sencode(symsplitseg));
- // Insert sympoint into DT.
- pa = sorg(symsplitseg);
- splittet.tet = dummytet;
- // Find a good start point to search.
- encodedtet = point2tet(pa);
- if (encodedtet != (tetrahedron) NULL) {
- decode(encodedtet, splittet);
- if (isdead(&splittet)) {
- splittet.tet = dummytet;
- }
- }
- // Locate sympoint in DT. Do exact location.
- success = insertsite(sympoint, &splittet, false, flipqueue);
-#ifdef SELF_CHECK
- assert(success != DUPLICATEPOINT);
-#endif
- if (success == OUTSIDEPOINT) {
- inserthullsite(sympoint, &splittet, flipqueue);
- }
- if (steinerleft > 0) steinerleft--;
- // Let sympoint remember splittet.
- setpoint2tet(sympoint, encode(splittet));
- // Do flip in DT.
- lawson(misseglist, flipqueue);
- // Insert sympoint into F.
- symsplitseg.shver = 0;
- spivot(symsplitseg, symsplitsub);
- // sympoint should on the edge of symsplitsub.
- splitsubedge(sympoint, &symsplitsub, flipqueue);
- // Do flip in facet.
- flipsub(flipqueue);
- // Insert the two subsegments.
- symsplitseg.shver = 0;
- insertsegment(&symsplitseg, misseglist);
- senextself(symsplitseg);
- spivotself(symsplitseg);
- symsplitseg.shver = 0;
- insertsegment(&symsplitseg, misseglist);
- } else { // if (symloc == ONVERTEX) {
- // The sympoint already exists. It is possible when two
- // pbc groups are exactly the same. Omit this point.
- pointdealloc(sympoint);
- }
- }
- }
-
- // Insert 'splitpoint' into DT.
- if (isdead(&searchtet)) searchtet.tet = dummytet;
- success = insertsite(splitpoint, &searchtet, false, flipqueue);
- if (success == OUTSIDEPOINT) {
- // A convex hull edge is missing, and the inserting point lies
- // (slightly) outside the convex hull due to the significant
- // digits lost in the calculation. Enlarge the convex hull.
- inserthullsite(splitpoint, &searchtet, flipqueue);
- }
- if (steinerleft > 0) steinerleft--;
- // Remember a handle in 'splitpoint' to enhance the speed of
- // consequent point location.
- setpoint2tet(splitpoint, encode(searchtet));
- // Maintain Delaunayness in DT.
- lawson(misseglist, flipqueue);
- }
- }
- // Insert 'splitpoint' into F.
- spivot(segloop, splitsh);
- splitsubedge(splitpoint, &splitsh, flipqueue);
- flipsub(flipqueue);
- // Insert the two subsegments.
- segloop.shver = 0;
- insertsegment(&segloop, misseglist);
- senextself(segloop);
- spivotself(segloop);
- segloop.shver = 0;
- insertsegment(&segloop, misseglist);
- }
- }
-
- // Detach all segments from tets.
- tetrahedrons->traversalinit();
- searchtet.tet = tetrahedrontraverse();
- while (searchtet.tet != (tetrahedron *) NULL) {
- for (i = 0; i < 6; i++) {
- searchtet.tet[8 + i] = (tetrahedron) dummysh;
- }
- searchtet.tet = tetrahedrontraverse();
- }
- // No segments now.
- checksubsegs = 0;
-
- if (b->verbose > 0) {
- printf(" %ld protect points.\n", points->items - vertcount);
- printf(" R1: %ld, R2: %ld, R3: %ld.\n", r1count, r2count, r3count);
- }
-
- delete flipqueue;
- delete misseglist;
-}
-
-//
-// End of segments recovery routines
-//
-
-//
-// Begin of facet recovery routines
-//
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// insertsubface() Fix a subface in place. //
-// //
-// Search a subface s in current tetrahedralization T. If s is found a face //
-// face of T, it is inserted into T. Return FALSE if s is not found in T. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::insertsubface(face* insertsh, triface* searchtet)
-{
- triface spintet, symtet;
- face testsh, testseg;
- face spinsh, casin, casout;
- point tapex, checkpoint;
- enum finddirectionresult collinear;
- int hitbdry;
-
- // Search an edge of s.
- getsearchtet(sorg(*insertsh), sdest(*insertsh), searchtet, &checkpoint);
- collinear = finddirection(searchtet, checkpoint, tetrahedrons->items);
- if (collinear == LEFTCOLLINEAR) {
- enext2self(*searchtet);
- esymself(*searchtet);
- } else if (collinear == TOPCOLLINEAR) {
- fnextself(*searchtet);
- enext2self(*searchtet);
- esymself(*searchtet);
- }
- if (dest(*searchtet) != checkpoint) {
- // The edge doesn't exist => s is missing.
- return false;
- }
-
- // Search s by spinning faces around the edge.
- tapex = sapex(*insertsh);
- spintet = *searchtet;
- hitbdry = 0;
- do {
- if (apex(spintet) == tapex) {
- // Found s in T. Check if s has already been inserted.
- tspivot(spintet, testsh);
- if (testsh.sh == dummysh) {
- adjustedgering(spintet, CCW);
- findedge(insertsh, org(spintet), dest(spintet));
- tsbond(spintet, *insertsh);
- sym(spintet, symtet); // 'symtet' maybe outside, use it anyway.
- sesymself(*insertsh);
- tsbond(symtet, *insertsh);
- } else {
- // Found a duplicated subface (due to the redundant input).
- if (!b->quiet) {
- printf("Warning: Two subfaces are found duplicated at ");
- printf("(%d, %d, %d)\n", pointmark(sorg(testsh)),
- pointmark(sdest(testsh)), pointmark(sapex(testsh)));
- printf(" Subface of facet #%d is deleted.\n", shellmark(*insertsh));
- // printf(" Hint: -d switch can find all duplicated facets.\n");
- }
- shellfacedealloc(subfaces, insertsh->sh);
- }
- return true;
- }
- if (!fnextself(spintet)) {
- hitbdry ++;
- if (hitbdry < 2) {
- esym(*searchtet, spintet);
- if (!fnextself(spintet)) {
- hitbdry ++;
- }
- }
- }
- } while (hitbdry < 2 && apex(spintet) != apex(*searchtet));
-
- // s is missing.
- return false;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// tritritest() Test if two triangles are intersecting in their interior. //
-// //
-// One triangle t1 is the face of 'checktet', the other t2 is given by three //
-// corners 'p1', 'p2' and 'p3'. This routine calls tri_tri_inter() to detect //
-// whether t1 and t2 exactly intersect in their interior. Cases like share a //
-// vertex, share an edge, or coincidence are considered not intersect. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::tritritest(triface* checktet, point p1, point p2, point p3)
-{
- point forg, fdest, fapex;
- enum interresult intersect;
-
- forg = org(*checktet);
- fdest = dest(*checktet);
- fapex = apex(*checktet);
-
-#ifdef SELF_CHECK
- REAL ax, ay, az, bx, by, bz;
- REAL n[3];
- // face (torg, tdest, tapex) should not be degenerate. However p1, p2,
- // and p3 may be collinear. Check it.
- ax = forg[0] - fdest[0];
- ay = forg[1] - fdest[1];
- az = forg[2] - fdest[2];
- bx = forg[0] - fapex[0];
- by = forg[1] - fapex[1];
- bz = forg[2] - fapex[2];
- n[0] = ay * bz - by * az;
- n[1] = az * bx - bz * ax;
- n[2] = ax * by - bx * ay;
- assert(fabs(n[0]) + fabs(n[1]) + fabs(n[2]) > 0.0);
- // The components of n should not smaller than the machine epsilon.
-
- ax = p1[0] - p2[0];
- ay = p1[1] - p2[1];
- az = p1[2] - p2[2];
- bx = p1[0] - p3[0];
- by = p1[1] - p3[1];
- bz = p1[2] - p3[2];
- n[0] = ay * bz - by * az;
- n[1] = az * bx - bz * ax;
- n[2] = ax * by - bx * ay;
- assert(fabs(n[0]) + fabs(n[1]) + fabs(n[2]) > 0.0);
- // The components of n should not smaller than the machine epsilon.
-#endif
-
- intersect = tri_tri_inter(forg, fdest, fapex, p1, p2, p3);
- return intersect == INTERSECT;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// initializecavity() Initialize the cavity. //
-// //
-// A cavity C is bounded by a list of faces, called fronts. Each front f is //
-// hold by a tet t adjacent to C, t is not in C (uninfected). If f is a hull //
-// face, t does't exist, a fake tet t' is created to hold f. t' has the same //
-// vertices as f but no opposite. t' will be removed automatically after C //
-// is filled with new tets (by carvecavity()). //
-// //
-// The faces of C are given in two lists. 'floorlist' is a set of subfaces, //
-// each subface has been oriented to face to the inside of C. 'ceillist' is //
-// a set of tetrahedral faces. 'frontlist' returns the initialized fronts. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::initializecavity(list* floorlist, list* ceillist,
- list* frontlist)
-{
- triface neightet, casingtet;
- triface faketet;
- face worksh;
- int i;
-
- // Initialize subfaces of C.
- for (i = 0; i < floorlist->len(); i++) {
- // Get a subface s.
- worksh = * (face *)(* floorlist)[i];
-#ifdef SELF_CHECK
- // Current side of s should be empty.
- stpivot(worksh, neightet);
- assert(neightet.tet == dummytet);
-#endif
- // Get the adjacent tet t.
- sesymself(worksh);
- stpivot(worksh, casingtet);
- // Does t exist?
- if (casingtet.tet == dummytet) {
- // Create a fake tet t' to hold f temporarily.
- maketetrahedron(&faketet);
- setorg(faketet, sorg(worksh));
- setdest(faketet, sdest(worksh));
- setapex(faketet, sapex(worksh));
- setoppo(faketet, (point) NULL); // Indicates it is 'fake'.
- tsbond(faketet, worksh);
- frontlist->append(&faketet);
- } else {
- frontlist->append(&casingtet);
- }
- }
- // Initialize tet faces of C.
- for (i = 0; i < ceillist->len(); i++) {
- // Get a tet face c.
- neightet = * (triface *) (* ceillist)[i];
-#ifdef SELF_CHECK
- // The tet of c must be inside C (going to be deleted).
- assert(infected(neightet));
-#endif
- // Get the adjacent tet t.
- sym(neightet, casingtet);
- // Does t exist?
- if (casingtet.tet == dummytet) {
- // No. Create a fake tet t' to hold f temporarily.
- maketetrahedron(&faketet);
- // Be sure that the vertices of t' are CCW oriented.
- adjustedgering(neightet, CW); // CW edge ring.
- setorg(faketet, org(neightet));
- setdest(faketet, dest(neightet));
- setapex(faketet, apex(neightet));
- setoppo(faketet, (point) NULL); // Indicates it is 'fake'.
- // Bond t' to a subface if it exists.
- tspivot(neightet, worksh);
- if (worksh.sh != dummysh) {
- sesymself(worksh);
- tsbond(faketet, worksh);
- }
- // Bond c <--> t'. So we're able to find t' and remove it.
- bond(faketet, neightet);
- // c may become uninfected due to the bond().
- infect(neightet);
- frontlist->append(&faketet);
- } else {
- frontlist->append(&casingtet);
- }
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// retrievenewtets() Retrieve the newly created tets. //
-// //
-// On input, 'newtetlist' contains at least one alive new tet. From this tet,//
-// other new tets can be found by a broadth-first searching. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::retrievenewtets(list* newtetlist)
-{
- triface searchtet, casingtet;
- int i;
-
- // There may be dead tets due to flip32(). Delete them first.
- for (i = 0; i < newtetlist->len(); i++) {
- searchtet = * (triface *)(* newtetlist)[i];
- if (isdead(&searchtet)) {
- newtetlist->del(i, 0); i--;
- continue;
- }
- infect(searchtet);
- }
- // Find all new tets.
- for (i = 0; i < newtetlist->len(); i++) {
- searchtet = * (triface *)(* newtetlist)[i];
- for (searchtet.loc = 0; searchtet.loc < 4; searchtet.loc++) {
- sym(searchtet, casingtet);
- if ((casingtet.tet != dummytet) && !infected(casingtet)) {
- infect(casingtet);
- newtetlist->append(&casingtet);
- }
- }
- }
- // Uninfect new tets.
- for (i = 0; i < newtetlist->len(); i++) {
- searchtet = * (triface *)(* newtetlist)[i];
- uninfect(searchtet);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// delaunizecavvertices() Form a DT of the vertices of a cavity. //
-// //
-// 'floorptlist' and 'ceilptlist' are the vertices of the cavity. //
-// //
-// The tets of the DT are created directly in the pool 'tetrahedrons', i.e., //
-// no auxiliary data structure and memory are required. The trick is at the //
-// time they're created, there are no connections between them to the other //
-// tets in the pool. You can imagine they form an ioslated island. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::delaunizecavvertices(triface* oldtet, list* floorptlist,
- list* ceilptlist, list* newtetlist, queue* flipque)
-{
- point *insertarray;
- triface bakhulltet, newtet;
- long bakhullsize;
- long arraysize;
- int bakchksub;
- int i, j;
-
- // Prepare the array of points for inserting.
- arraysize = floorptlist->len();
- if (ceilptlist != (list *) NULL) {
- arraysize += ceilptlist->len();
- }
- insertarray = new point[arraysize];
- for (i = 0; i < floorptlist->len(); i++) {
- insertarray[i] = * (point *)(* floorptlist)[i];
- }
- if (ceilptlist != (list *) NULL) {
- for (j = 0; j < ceilptlist->len(); j++) {
- insertarray[i + j] = * (point *)(* ceilptlist)[j];
- }
- }
-
- // The incrflipdelaunay() is re-used. Backup global variables.
- decode(dummytet[0], bakhulltet);
- bakhullsize = hullsize;
- bakchksub = checksubfaces;
- checksubfaces = 0;
- b->verbose--;
-
- // Form the DT by incremental flip Delaunay algorithm. Do not jump for
- // point location, do not merge points.
- incrflipdelaunay(oldtet, insertarray, arraysize, false, false, 0.0, flipque);
-
- // Get a tet in D.
- decode(dummytet[0], newtet);
- newtetlist->append(&newtet);
- // Get all tets of D.
- retrievenewtets(newtetlist);
-
- // Restore global variables.
- dummytet[0] = encode(bakhulltet);
- hullsize = bakhullsize;
- checksubfaces = bakchksub;
- b->verbose++;
-
- delete [] insertarray;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// insertauxsubface() Fix an auxilary subface in place. //
-// //
-// An auxilary subface s is fixed in D as it is a real subface, but s has no //
-// vertices and neighbors. It has two uses: (1) it protects an identfied //
-// front f in D; (2) it serves the link to bond a tet in C and f later. The //
-// first neighbor of s (s->sh[0]) stores a pointer to f. //
-// //
-// 'front' is a front f of C. idfront' t is a tet in D where f is identified //
-// be a face of it. s will be fixed between t and its neighbor. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::insertauxsubface(triface* front, triface* idfront)
-{
- triface neightet;
- face auxsh;
-
- // Create the aux subface s.
- makeshellface(subfaces, &auxsh);
- // Bond s <--> t.
- tsbond(*idfront, auxsh);
- // Does t's neighbor n exist?
- sym(*idfront, neightet);
- if (neightet.tet != dummytet) {
- // Bond s <--> n.
- sesymself(auxsh);
- tsbond(neightet, auxsh);
- }
- // Let s remember f.
- auxsh.sh[0] = (shellface) encode(*front);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// scoutfront() Scout a face in D. //
-// //
-// Search a 'front' f in D. If f is found, return TRUE and the face of D is //
-// returned in 'idfront'. Otherwise, return FALSE. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::scoutfront(triface* front, triface* idfront, list* newtetlist)
-{
- triface spintet;
- point pa, pb, pc;
- enum locateresult loc;
- enum finddirectionresult col;
- int hitbdry;
- int i;
-
- // Let the front we're searching is abc.
- pa = org(*front);
- pb = dest(*front);
- // Get a tet in D for searching.
- *idfront = recenttet;
- // Make sure the tet is valid (it may be killed by flips).
- if (isdead(idfront)) {
- // The tet is dead. Search a live tet in D. !!!
- for (i = 0; i < newtetlist->len(); i++) {
- recenttet = * (triface *)(* newtetlist)[i];
- if (!isdead(&recenttet)) break;
- }
- assert(i < newtetlist->len());
- }
-
- // Search a tet having vertex a.
- loc = preciselocate(pa, idfront, (long) newtetlist->len());
- assert(loc == ONVERTEX);
- recenttet = *idfront;
- // Search a tet having edge ab.
- col = finddirection(idfront, pb, (long) newtetlist->len());
- if (col == RIGHTCOLLINEAR) {
- // b is just the destination.
- } else if (col == LEFTCOLLINEAR) {
- enext2self(*idfront);
- esymself(*idfront);
- } else if (col == TOPCOLLINEAR) {
- fnextself(*idfront);
- enext2self(*idfront);
- esymself(*idfront);
- }
-
- if (dest(*idfront) == pb) {
- // Search a tet having face abc
- pc = apex(*front);
- spintet = *idfront;
- hitbdry = 0;
- do {
- if (apex(spintet) == pc) {
- // Found abc. Insert an auxilary subface s at idfront.
- // insertauxsubface(front, &spintet);
- *idfront = spintet;
- return true;
- }
- if (!fnextself(spintet)) {
- hitbdry ++;
- if (hitbdry < 2) {
- esym(*idfront, spintet);
- if (!fnextself(spintet)) {
- hitbdry ++;
- }
- }
- }
- if (apex(spintet) == apex(*idfront)) break;
- } while (hitbdry < 2);
- }
-
- // f is missing in D.
- if (b->verbose > 2) {
- printf(" Front (%d, %d, %d) is missing.\n", pointmark(pa),
- pointmark(pb), pointmark(apex(*front)));
- }
- return false;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// gluefronts() Glue two fronts together. //
-// //
-// This is a support routine for identifyfront(). Two fronts f and f1 are //
-// found indentical. This is caused by the non-coplanarity of vertices of a //
-// facet. Hence f and f1 are a subface and a tet. They are not fronts of the //
-// cavity anymore. This routine glues f and f1 together. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::gluefronts(triface* front, triface* front1)
-{
- face consh;
-
- // Glue f and f1 together. There're four cases:
- // (1) both f and f1 are not fake;
- // (2) f is not fake, f1 is fake;
- // (3) f is fake and f1 is not fake;
- // (4) both f and f1 are fake.
- // Case (4) should be not possible.
-
- // Is there a concrete subface c at f.
- tspivot(*front, consh);
- if (consh.sh != dummysh) {
- sesymself(consh);
- tsbond(*front1, consh); // Bond: f1 <--> c.
- sesymself(consh);
- }
- // Does f hold by a fake tet.
- if (oppo(*front) == (point) NULL) {
- // f is fake. Case (3) or (4).
- assert(oppo(*front1) != (point) NULL); // Eliminate (4).
- // Case (3).
- if (consh.sh != dummysh) {
- stdissolve(consh); // Dissolve: c -x-> f.
- }
- // Dealloc f.
- tetrahedrondealloc(front->tet);
- // f1 becomes a hull. let 'dummytet' bond to it.
- dummytet[0] = encode(*front1);
- } else {
- // Case (1) or (2).
- bond(*front, *front1); // Bond f1 <--> f.
- }
- // Is f a fake tet?
- if (!isdead(front)) {
- // No. Check for case (2).
- tspivot(*front1, consh);
- // Is f1 fake?
- if (oppo(*front1) == (point) NULL) {
- // Case (2) or (4)
- assert(oppo(*front) != (point) NULL); // Eliminate (4).
- // Case (2).
- if (consh.sh != dummysh) {
- stdissolve(consh); // Dissolve: c -x-> f1.
- sesymself(consh); // Bond: f <--> c.
- tsbond(*front, consh);
- }
- // Dissolve: f -x->f1.
- dissolve(*front);
- // Dealloc f1.
- tetrahedrondealloc(front1->tet);
- // f becomes a hull. let 'dummytet' bond to it.
- dummytet[0] = encode(*front);
- } else {
- // Case (1).
- if (consh.sh != dummysh) {
- sesymself(consh);
- tsbond(*front, consh); // Bond: f <--> c.
- }
- }
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// identifyfronts() Identify cavity faces in D. //
-// //
-// 'frontlist' are fronts of C need indentfying. This routine searches each //
-// front f in D. Once f is found, an auxilary subface s is inserted in D at //
-// the face. If f is not found in D, remove it from frontlist and save it in //
-// 'misfrontlist'. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::identifyfronts(list* frontlist, list* misfrontlist,
- list* newtetlist)
-{
- triface front, front1, tfront;
- triface idfront, neightet;
- face auxsh;
- int len, i, j;
-
- misfrontlist->clear();
- // Set a new tet in D for searching.
- recenttet = * (triface *)(* newtetlist)[0];
-
- // Identify all fronts in D.
- for (i = 0; i < frontlist->len(); i++) {
- // Get a front f.
- front = * (triface *)( *frontlist)[i];
- if (scoutfront(&front, &idfront, newtetlist)) {
- // Found f. Insert an aux subface s.
- assert((idfront.tet != dummytet) && !isdead(&idfront));
- // Does s already exist?
- tspivot(idfront, auxsh);
- if (auxsh.sh != dummysh) {
- // There're two identical fronts, f (front) and f1 (s.sh[0])!
- decode((tetrahedron) auxsh.sh[0], front1);
- assert((front1.tet != dummytet) && !infected(front1));
- // Detach s in D.
- tsdissolve(idfront);
- sym(idfront, neightet);
- if (neightet.tet != dummytet) {
- tsdissolve(neightet);
- }
- // s has fulfilled its duty. Can be deleted.
- shellfacedealloc(subfaces, auxsh.sh);
- // Remove f from frontlist.
- frontlist->del(i, 1); i--;
- // Remove f1 from frontlist.
- len = frontlist->len();
- for (j = 0; j < frontlist->len(); j++) {
- tfront = * (triface *)(* frontlist)[j];
- if ((tfront.tet == front1.tet) && (tfront.loc == front1.loc)) {
- // Found f1 in list. Check f1 != f.
- assert((tfront.tet != front.tet) || (tfront.loc != front.loc));
- frontlist->del(j, 1); i--;
- break;
- }
- }
- assert((frontlist->len() + 1) == len);
- // Glue f and f1 together.
- gluefronts(&front, &front1);
- } else {
- // Insert an aux subface to protect f in D.
- insertauxsubface(&front, &idfront);
- }
- } else {
- // f is missing.
- frontlist->del(i, 1); i--;
- // Are there two identical fronts, f (front) and f1 (front1)?
- for (j = 0; j < misfrontlist->len(); j++) {
- front1 = * (triface *)(* misfrontlist)[j];
- if (isfacehaspoint(&front1, org(front)) &&
- isfacehaspoint(&front1, dest(front)) &&
- isfacehaspoint(&front1, apex(front))) break;
- }
- if (j < misfrontlist->len()) {
- // Found an identical front f1. Remove f1 from the list.
- misfrontlist->del(j, 1);
- // Glue f and f1 together.
- gluefronts(&front, &front1);
- } else {
- // Add f into misfrontlist.
- misfrontlist->append(&front);
- }
- }
- }
- return misfrontlist->len() == 0;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// detachauxsubfaces() Detach auxilary subfaces in D. //
-// //
-// This is a reverse routine of identifyfronts(). Some fronts are missing in //
-// D. C can not be easily tetrahedralized. It needs remediation (expansion, //
-// or constrained flips, or adding a Steiner point). This routine detaches //
-// the auxilary subfaces have been inserted in D and delete them. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::detachauxsubfaces(list* newtetlist)
-{
- triface newtet, neightet;
- face auxsh;
- int i;
-
- for (i = 0; i < newtetlist->len(); i++) {
- // Get a new tet t.
- newtet = * (triface *)(* newtetlist)[i];
- // t may e dead due to flips.
- if (isdead(&newtet)) continue;
- assert(!infected(newtet));
- // Check the four faces of t.
- for (newtet.loc = 0; newtet.loc < 4; newtet.loc++) {
- tspivot(newtet, auxsh);
- if (auxsh.sh != dummysh) {
- // An auxilary subface s.
- assert(sorg(auxsh) == (point) NULL);
- tsdissolve(newtet); // t -x-> s.
- sym(newtet, neightet);
- if (neightet.tet != dummytet) {
- assert(!isdead(&neightet));
- tsdissolve(neightet); // n -x-> s.
- }
- // Delete s.
- shellfacedealloc(subfaces, auxsh.sh);
- }
- }
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// expandcavity() Expand the cavity by adding new fronts. //
-// //
-// This is the support routine for delaunizecavity(). Some fronts of C are //
-// missing in D since they're not strongly Delaunay. Such fronts are removed //
-// and the faces of the tets abutting to them are added. C is then expanded. //
-// Some removed faces may be subfaces, they're queued to recover later. D is //
-// expanded simultaneously with the new vertices of the new fronts. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::expandcavity(list* frontlist, list* misfrontlist,
- list* newtetlist, list* crosstetlist, queue* missingshqueue, queue* flipque)
-{
- triface misfront, newfront, casingtet, crosstet;
- triface searchtet, faketet, bakhulltet;
- face checksh;
- point pd;
- enum insertsiteresult success;
- long bakhullsize;
- int bakchksub;
- int i, j, k;
-
- if (b->verbose > 1) {
- printf(" Expand cavity (%d missing fronts).\n", misfrontlist->len());
- }
- // Increase the number of expanded times.
- expcavcount++;
- // The incrflipdelaunay() is re-used. Backup global variables.
- decode(dummytet[0], bakhulltet);
- bakhullsize = hullsize;
- bakchksub = checksubfaces;
- checksubfaces = 0;
- b->verbose--;
-
- // Choose a tet in D for searching.
- recenttet = * (triface *)(* newtetlist)[0];
- assert((recenttet.tet != dummytet) && !isdead(&recenttet));
-
- // Loop through 'misfrontlist'.
- for (i = 0; i < misfrontlist->len(); i++) {
- // Get a missing front f.
- misfront = * (triface *)(* misfrontlist)[i];
- // C will be expanded at f.
- if (b->verbose > 1) {
- printf(" Get misfront (%d, %d, %d).\n", pointmark(org(misfront)),
- pointmark(dest(misfront)), pointmark(apex(misfront)));
- }
- // Is f has a subface s?
- tspivot(misfront, checksh);
- if (checksh.sh != dummysh) {
- // A subface s is found. Check whether f is expandable at s.
- sym(misfront, crosstet);
- if (!infected(crosstet)) {
- // f is not expandable. In principle is should not happen. However,
- // it can happen when PBC is in use.
- assert(checkpbcs);
- // Skip expanding f. It will be processed later.
- continue;
- }
- // Temporarily remove s. Queue and recover it later.
- if (b->verbose > 1) {
- printf(" Queuing subface (%d, %d, %d).\n",
- pointmark(sorg(checksh)), pointmark(sdest(checksh)),
- pointmark(sapex(checksh)));
- }
- // Detach s from tets at its both sides.
- tsdissolve(misfront);
- tsdissolve(crosstet);
- // Detach tets at from s.
- stdissolve(checksh);
- sesymself(checksh);
- stdissolve(checksh);
- // Mark and queue it.
- sinfect(checksh);
- missingshqueue->push(&checksh);
- }
- // f may already be processed (become a cross tet of C).
- if (infected(misfront)) continue;
- // Get the point p = oppo(t), t is the tet holds f.
- pd = oppo(misfront);
-#ifdef SELF_CHECK
- // t must not be fake.
- assert(pd != (point) NULL);
-#endif
- // Insert p in D. p may not be inserted if it is one of the two cases:
- // (1) p is already a vertex of D;
- // (2) p lies outside the CH of D;
- searchtet = recenttet;
- // Make sure the tet is valid (it may be killed by flips).
- if (isdead(&searchtet)) {
- // The tet is dead. Get a live tet in D. !!!
- for (j = 0; j < newtetlist->len(); j++) {
- recenttet = * (triface *)(* newtetlist)[j];
- if (!isdead(&recenttet)) break;
- }
- assert(j < newtetlist->len());
- searchtet = recenttet;
- }
- success = insertsite(pd, &searchtet, false, flipque);
- if (success == OUTSIDEPOINT) {
- // case (2). Insert p onto CH of D.
- inserthullsite(pd, &searchtet, flipque);
- }
- if (success != DUPLICATEPOINT) {
- // p is inserted. Recover Delaunness of D by flips.
- flip(flipque, NULL);
- }
- // Expand C by adding new fronts. The three faces of t which have p as a
- // vertex become new fronts. However, if a new front is coincident with
- // an old front of C, it is not added and the old front is removed.
- adjustedgering(misfront, CCW);
- for (j = 0; j < 3; j++) {
- // Notice: Below I mis-used the names. 'newfront' is not exactly a new
- // front, instead the 'casingtet' should be called new front.
- // Get a new front f_n.
- fnext(misfront, newfront);
- // Get the neighbor tet n at f_n.
- sym(newfront, casingtet);
- // Is n a cross tet?
- if (!infected(casingtet)) {
- // f_n becomes a new front of C.
- // Does n exist?
- if (casingtet.tet == dummytet) {
- // Create a fake tet n' to hold f_n temporarily.
- maketetrahedron(&faketet);
- // Be sure that the vertices of fake tet are CCW oriented.
- adjustedgering(newfront, CW); // CW edge ring.
- setorg(faketet, org(newfront));
- setdest(faketet, dest(newfront));
- setapex(faketet, apex(newfront));
- setoppo(faketet, (point) NULL); // Indicates it is 'fake'.
- // Bond n' to a subface if it exists.
- tspivot(newfront, checksh);
- if (checksh.sh != dummysh) {
- sesymself(checksh);
- tsbond(faketet, checksh);
- }
- // Bond f_n <--> n'. So we're able to find n' and remove it.
- bond(faketet, newfront);
- frontlist->append(&faketet);
- } else {
- // Add n to frontlist.
- frontlist->append(&casingtet);
- }
- } else {
- // f_n is coincident with an existing front f' of C. f' is no longer
- // a front, remove it from frontlist. Use the inverse order to
- // search f' (most likely, a newly added front may be f').
- for (k = frontlist->len() - 1; k >= 0; k--) {
- searchtet = * (triface *)(* frontlist)[k];
- if ((newfront.tet == searchtet.tet) &&
- (newfront.loc == searchtet.loc)) {
- frontlist->del(k, 0);
- break;
- }
- }
- // Is f_n a subface?
- tspivot(newfront, checksh);
- if (checksh.sh != dummysh) {
- // Temporarily remove checksh. Make it missing. recover it later.
- if (b->verbose > 2) {
- printf(" Queuing subface (%d, %d, %d).\n",
- pointmark(sorg(checksh)), pointmark(sdest(checksh)),
- pointmark(sapex(checksh)));
- }
- tsdissolve(newfront);
- tsdissolve(casingtet);
- // Detach tets at the both sides of checksh.
- stdissolve(checksh);
- sesymself(checksh);
- stdissolve(checksh);
- sinfect(checksh);
- missingshqueue->push(&checksh);
- }
- }
- enextself(misfront);
- }
- // C has been expanded at f. t becomes a cross tet.
- if (!infected(misfront)) {
- // t will be deleted, queue it.
- infect(misfront);
- crosstetlist->append(&misfront);
- }
- }
-
- // Loop through misfrontlist, remove infected misfronts.
- for (i = 0; i < misfrontlist->len(); i++) {
- misfront = * (triface *)(* misfrontlist)[i];
- if (infected(misfront)) {
- // Remove f, keep original list order.
- misfrontlist->del(i, 1);
- i--;
- }
- }
-
- // Are we done?
- if (misfrontlist->len() > 0) {
- // No. There are unexpandable fronts.
- // expandcavity_sos(misfrontlist);
- assert(0); // Not done yet.
- }
-
- // D has been updated (by added new tets or dead tets) (due to flips).
- retrievenewtets(newtetlist);
-
- // Restore global variables.
- dummytet[0] = encode(bakhulltet);
- hullsize = bakhullsize;
- checksubfaces = bakchksub;
- b->verbose++;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// carvecavity() Remove redundant (outside) tetrahedra from D. //
-// //
-// The fronts of C have been identified in D. Hence C can be tetrahedralized //
-// by removing the tets outside C. The CDT is then updated by filling C with //
-// the remaining tets (inside C) of D. //
-// //
-// Each front is protected by an auxilary subface s in D. s has a pointer to //
-// f (s.sh[0]). f can be used to classified the in- and out- tets of C (the //
-// CW orientation of f faces to the inside of C). The classified out-tets of //
-// C are marked (infected) for removing. //
-// //
-// Notice that the out-tets may not only the tets on the CH of C, but also //
-// tets completely inside D, eg., there is a "hole" in D. Such tets must be //
-// marked during classification. The hole tets are poped up and removed too. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::carvecavity(list* newtetlist, list* outtetlist,
- queue* flipque)
-{
- triface newtet, neightet, front, outtet;
- face auxsh, consh;
- point pointptr;
- REAL ori;
- int i;
-
- // Clear work list.
- outtetlist->clear();
-
- // Classify in- and out- tets in D. Mark and queue classified out-tets.
- for (i = 0; i < newtetlist->len(); i++) {
- // Get a new tet t.
- newtet = * (triface *)(* newtetlist)[i];
- assert(!isdead(&newtet));
- // Look for aux subfaces attached at t.
- for (newtet.loc = 0; newtet.loc < 4; newtet.loc++) {
- tspivot(newtet, auxsh);
- if (auxsh.sh != dummysh) {
- // Has this side a neighbor n?
- sym(newtet, neightet);
- if (neightet.tet != dummytet) {
- // Classify t and n (one is "in" and another is "out").
- // Get the front f.
- decode((tetrahedron) auxsh.sh[0], front);
- // Let f face to the inside of C.
- adjustedgering(front, CW);
- ori = orient3d(org(front), dest(front), apex(front), oppo(newtet));
- assert(ori != 0.0);
- if (ori < 0.0) {
- // t is in-tet. n is out-tet.
- outtet = neightet;
- } else {
- // n is in-tet. t is out-tet.
- outtet = newtet;
- }
- // Add the out-tet into list.
- if (!infected(outtet)) {
- infect(outtet);
- outtetlist->append(&outtet);
- }
- }
- }
- }
- }
-
- // Find and mark all out-tets.
- for (i = 0; i < outtetlist->len(); i++) {
- outtet = * (triface *)(* outtetlist)[i];
- for (outtet.loc = 0; outtet.loc < 4; outtet.loc++) {
- sym(outtet, neightet);
- // Does the neighbor exist and unmarked?
- if ((neightet.tet != dummytet) && !infected(neightet)) {
- // Is it protected by an aux subface?
- tspivot(outtet, auxsh);
- if (auxsh.sh == dummysh) {
- // It's an out-tet.
- infect(neightet);
- outtetlist->append(&neightet);
- }
- }
- }
- }
-
- // Remove the out- (and hole) tets.
- for (i = 0; i < outtetlist->len(); i++) {
- // Get an out-tet t.
- outtet = * (triface *)(* outtetlist)[i];
- // Detach t from the in-tets.
- for (outtet.loc = 0; outtet.loc < 4; outtet.loc++) {
- // Is there an aux subface s?
- tspivot(outtet, auxsh);
- if (auxsh.sh != dummysh) {
- // Get the neighbor n.
- sym(outtet, neightet);
- assert(!infected(neightet)); // t must be in-tet.
- // Detach n -x-> t.
- dissolve(neightet);
- }
- }
- // Dealloc the tet.
- tetrahedrondealloc(outtet.tet);
- }
-
- // Connect the in-tets of C to fronts. Remove aux subfaces and fake tets.
- for (i = 0; i < newtetlist->len(); i++) {
- // Get a new tet t.
- newtet = * (triface *)(* newtetlist)[i];
- // t may be an out-tet and has got deleted.
- if (isdead(&newtet)) continue;
- // t is an in-tet. Look for aux subfaces attached at t.
- for (newtet.loc = 0; newtet.loc < 4; newtet.loc++) {
- // Is there an aux subface s?
- tspivot(newtet, auxsh);
- if (auxsh.sh != dummysh) {
- // Get the front f.
- decode((tetrahedron) auxsh.sh[0], front);
- assert((front.tet != dummytet) && !infected(front));
- // s has fulfilled its duty. Can be deleted.
- tsdissolve(newtet); // dissolve: t -x-> s.
- // Delete s.
- shellfacedealloc(subfaces, auxsh.sh);
- // Connect the newtet t and front f.
- // Is there a concrete subface c at f.
- tspivot(front, consh);
- if (consh.sh != dummysh) {
- sesymself(consh);
- // Bond: t <--> c.
- tsbond(newtet, consh);
- }
- // Does f hold by a fake tet.
- if (oppo(front) == (point) NULL) {
- // f is fake.
- if (consh.sh != dummysh) {
- sesymself(consh);
- // Dissolve: c -x-> f.
- stdissolve(consh);
- }
- // Dealloc f.
- tetrahedrondealloc(front.tet);
- // f becomes a hull. let 'dummytet' bond to it.
- dummytet[0] = encode(newtet);
- } else {
- // Bond t <--> f.
- bond(newtet, front);
- }
- // t may be non-locally Delaunay and flipable.
- if (flipque != (queue *) NULL) {
- enqueueflipface(newtet, flipque);
- }
- }
- }
- // Let the corners of t2 point to it for fast searching.
- pointptr = org(newtet);
- setpoint2tet(pointptr, encode(newtet));
- pointptr = dest(newtet);
- setpoint2tet(pointptr, encode(newtet));
- pointptr = apex(newtet);
- setpoint2tet(pointptr, encode(newtet));
- pointptr = oppo(newtet);
- setpoint2tet(pointptr, encode(newtet));
- }
- // The cavity has been re-tetrahedralized.
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// delaunizecavity() Tetrahedralize a cavity by Delaunay tetrahedra. //
-// //
-// The cavity C is bounded by a set of triangles in 'floorlist' (a list of //
-// coplanar subfaces) and 'ceillist' (a list of tetrahedral faces lie above //
-// the subfaces). 'floorptlist' and 'ceilptlist' are the vertices of C. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::delaunizecavity(list* floorlist, list* ceillist,
- list* ceilptlist, list* floorptlist, list* frontlist, list* misfrontlist,
- list* newtetlist, list* crosstetlist, queue* missingshqueue, queue* flipque)
-{
- int vertnum;
-
- vertnum = floorptlist->len();
- vertnum += (ceilptlist != (list *) NULL ? ceilptlist->len() : 0);
- if (b->verbose > 1) {
- printf(" Delaunizing cavity (%d floors, %d ceilings, %d vertices).\n",
- floorlist->len(), ceillist->len(), vertnum);
- }
- // Save the size of the largest cavity.
- if ((floorlist->len() + ceillist->len()) > maxcavfaces) {
- maxcavfaces = floorlist->len() + ceillist->len();
- }
- if (vertnum > maxcavverts) {
- maxcavverts = vertnum;
- }
-
- // Clear these lists.
- frontlist->clear();
- misfrontlist->clear();
- newtetlist->clear();
-
- // Initialize the cavity C.
- initializecavity(floorlist, ceillist, frontlist);
- // Form the D of the vertices of C.
- delaunizecavvertices(NULL, floorptlist, ceilptlist, newtetlist, flipque);
- // Identify faces of C in D.
- while (!identifyfronts(frontlist, misfrontlist, newtetlist)) {
- // Remove protecting subfaces, keep new tets.
- detachauxsubfaces(newtetlist);
- // Expand C and updateing D.
- expandcavity(frontlist, misfrontlist, newtetlist, crosstetlist,
- missingshqueue, flipque);
- }
- // All fronts have identified in D. Get the shape of C by removing out
- // tets of C. 'misfrontlist' is reused for removing out tets.
- carvecavity(newtetlist, misfrontlist, NULL);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// formmissingregion() Form the missing region. //
-// //
-// 'missingsh' is a missing subface. Start from it we can form the missing //
-// region R (a set of connected missing subfaces). Because all missing sub- //
-// faces have been marked (infected) before. R can be formed by checking the //
-// neighbors of 'missingsh', and the neighbors of the neighbors, and so on. //
-// Stop checking further at either a segment or an unmarked subface. //
-// //
-// 'missingshlist' returns R. The edge ring of subfaces of R are oriented in //
-// the same direction. 'equatptlist' returns the vertices of R, each vertex //
-// is marked with '1' (in 'worklist'). //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::formmissingregion(face* missingsh, list* missingshlist,
- list* equatptlist, int* worklist)
-{
- face neighsh, worksh, workseg;
- point workpt[3];
- int idx, i, j;
-
- // Add 'missingsh' into 'missingshlist'.
- missingshlist->append(missingsh);
- // Save and mark its three vertices.
- workpt[0] = sorg(*missingsh);
- workpt[1] = sdest(*missingsh);
- workpt[2] = sapex(*missingsh);
- for (i = 0; i < 3; i++) {
- idx = pointmark(workpt[i]) - in->firstnumber;
- worklist[idx] = 1;
- equatptlist->append(&workpt[i]);
- }
- // Temporarily uninfect it (avoid to save it again).
- suninfect(*missingsh);
-
- // Find the other missing subfaces.
- for (i = 0; i < missingshlist->len(); i++) {
- // Get a missing subface.
- worksh = * (face *)(* missingshlist)[i];
- // Check three neighbors of this face.
- for (j = 0; j < 3; j++) {
- sspivot(worksh, workseg);
- if (workseg.sh == dummysh) {
- spivot(worksh, neighsh);
- if (sinfected(neighsh)) {
- // Find a missing subface, adjust the face orientation.
- if (sorg(neighsh) != sdest(worksh)) {
- sesymself(neighsh);
- }
- if (b->verbose > 2) {
- printf(" Add missing subface (%d, %d, %d).\n",
- pointmark(sorg(neighsh)), pointmark(sdest(neighsh)),
- pointmark(sapex(neighsh)));
- }
- missingshlist->append(&neighsh);
- // Save and mark its apex.
- workpt[0] = sapex(neighsh);
- idx = pointmark(workpt[0]) - in->firstnumber;
- // Has workpt[0] been added?
- if (worklist[idx] == 0) {
- worklist[idx] = 1;
- equatptlist->append(&workpt[0]);
- }
- // Temporarily uninfect it (avoid to save it again).
- suninfect(neighsh);
- }
- }
- senextself(worksh);
- }
- }
-
- // R has been formed. Infect missing subfaces again.
- for (i = 0; i < missingshlist->len(); i++) {
- worksh = * (face *)(* missingshlist)[i];
- sinfect(worksh);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// rearrangesubfaces() Rearrange the set of subfaces of a missing region //
-// so that they conform to the faces of DT. //
-// //
-// The missing region formed by subfaces of 'missingshlist' contains a set //
-// of degenerate vertices, hence the set of subfaces don't match the set of //
-// faces in DT. Instead of forcing them to present in DT, we re-arrange the //
-// connection of them so that the new subfaces conform to the faces of DT. //
-// 'boundedgelist' is a set of boundary edges of the region, these edges(may //
-// be subsegments) must exist in DT. //
-// //
-// On completion, we have created and inserted a set of new subfaces which //
-// conform to faces of DT. The set of old subfaces in 'missingshlist' are //
-// deleted. The region vertices in 'equatptlist' are unmarked. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::rearrangesubfaces(list* missingshlist, list* boundedgelist,
- list* equatptlist, int* worklist)
-{
- link *boundedgelink;
- link *newshlink;
- triface starttet, spintet, neightet, worktet;
- face shloop, newsh, neighsh, spinsh, worksh;
- face workseg, casingin, casingout;
- point torg, tdest, workpt;
- point spt1, spt2, spt3;
- enum finddirectionresult collinear;
- enum shestype shtype;
- REAL area;
- bool matchflag, finishflag;
- int shmark, pbcgp, idx, hitbdry;
- int i, j;
-
- // Initialize the boundary edge link.
- boundedgelink = new link(sizeof(face), NULL, 256);
- // Initialize the new subface link.
- newshlink = new link(sizeof(face), NULL, 256);
- // Remember the type (skinny or not) of replaced subfaces. They should
- // all have the same type since there is no segment inside the region.
- worksh = * (face *)(* missingshlist)[0];
- shtype = shelltype(worksh);
- // The following loop is only for checking purpose.
- for (i = 1; i < missingshlist->len(); i++) {
- worksh = * (face *)(* missingshlist)[i];
- assert(shelltype(worksh) == shtype);
- }
- // To avoid compilation warnings.
- shmark = pbcgp = 0;
- area = 0.0;
-
- // Create an initial boundary link.
- for (i = 0; i < boundedgelist->len(); i++) {
- shloop = * (face *)(* boundedgelist)[i];
- if (i == 0) {
- // 'shmark' will be set to all new created subfaces.
- shmark = shellmark(shloop);
- if (b->quality && varconstraint) {
- // area will be copied to all new created subfaces.
- area = areabound(shloop);
- }
- if (checkpbcs) {
- // pbcgp will be copied to all new created subfaces.
- pbcgp = shellpbcgroup(shloop);
- }
- // Get the abovepoint of this facet.
- abovepoint = facetabovepointarray[shellmark(shloop)];
- if (abovepoint == (point) NULL) {
- getfacetabovepoint(&shloop);
- }
- }
- sspivot(shloop, workseg);
- if (workseg.sh == dummysh) {
- // This edge is an interior edge.
- spivot(shloop, neighsh);
- boundedgelink->add(&neighsh);
- } else {
- // This side has a segment, the edge exists.
- boundedgelink->add(&shloop);
- }
- }
-
- // Each edge ab of boundedgelink will be finished by finding a vertex c
- // which is a vertex of the missing region, such that:
- // (1) abc is inside the missing region, i.e., abc intersects at least
- // one of missing subfaces (saved in missingshlist);
- // (2) abc is not intersect with any previously created new subfaces
- // in the missing region (saved in newshlink).
- // After abc is created, it will be inserted into both the surface mesh
- // and the DT. The boundedgelink will be updated, ab is removed, bc and
- // ca will be added if they are open.
-
- while (boundedgelink->len() > 0) {
- // Remove an edge (ab) from the link.
- shloop = * (face *) boundedgelink->del(1);
- // 'workseg' indicates it is a segment or not.
- sspivot(shloop, workseg);
- torg = sorg(shloop); // torg = a;
- tdest = sdest(shloop); // tdest = b;
- // Find a tetrahedron containing ab.
- getsearchtet(torg, tdest, &starttet, &workpt);
- collinear = finddirection(&starttet, workpt, tetrahedrons->items);
- if (collinear == LEFTCOLLINEAR) {
- enext2self(starttet);
- esymself(starttet);
- } else if (collinear == TOPCOLLINEAR) {
- fnextself(starttet);
- enext2self(starttet);
- esymself(starttet);
- }
- assert(dest(starttet) == workpt);
- // Checking faces around ab until a valid face is found.
- matchflag = false;
- spintet = starttet;
- hitbdry = 0;
- do {
- workpt = apex(spintet);
- idx = pointmark(workpt) - in->firstnumber;
- if (worklist[idx] == 1) {
- // (trog, tdest, workpt) is on the facet. Check if it satisfies (1).
- finishflag = false;
- for (i = 0; i < missingshlist->len(); i++) {
- worksh = * (face *)(* missingshlist)[i];
- spt1 = sorg(worksh);
- spt2 = sdest(worksh);
- spt3 = sapex(worksh);
- // Does bc intersect the face?
- if (tri_edge_cop_inter(spt1, spt2, spt3, tdest, workpt, abovepoint)
- == INTERSECT) {
- finishflag = true; break;
- }
- // Does ca intersect the face?
- if (tri_edge_cop_inter(spt1, spt2, spt3, workpt, torg, abovepoint)
- == INTERSECT) {
- finishflag = true; break;
- }
- // Does c inside the face?
- if (tri_vert_cop_inter(spt1, spt2, spt3, workpt, abovepoint)
- == INTERSECT) {
- finishflag = true; break;
- }
- }
- if (finishflag) {
- // Satisfying (1). Check if it satisfies (2).
- matchflag = true;
- for (i = 0; i < newshlink->len() && matchflag; i++) {
- worksh = * (face *) newshlink->getnitem(i + 1);
- spt1 = sorg(worksh);
- spt2 = sdest(worksh);
- spt3 = sapex(worksh);
- // Does bc intersect the face?
- if (tri_edge_cop_inter(spt1, spt2, spt3, tdest, workpt, abovepoint)
- == INTERSECT) {
- matchflag = false; break;
- }
- // Does ca intersect the face?
- if (tri_edge_cop_inter(spt1, spt2, spt3, workpt, torg, abovepoint)
- == INTERSECT) {
- matchflag = false; break;
- }
- // Does c inside the face?
- if (tri_vert_cop_inter(spt1, spt2, spt3, workpt, abovepoint)
- == INTERSECT) {
- matchflag = false; break;
- }
- }
- }
- if (matchflag == true) {
- // Satisfying both (1) and (2). Find abc.
- break;
- }
- }
- if (!fnextself(spintet)) {
- hitbdry ++;
- if (hitbdry < 2) {
- esym(starttet, spintet);
- if (!fnextself(spintet)) {
- hitbdry ++;
- }
- }
- }
- } while (hitbdry < 2 && apex(spintet) != apex(starttet));
-#ifdef SELF_CHECK //GMSH
- assert(matchflag == true);
-#endif //GMSH
- tspivot(spintet, neighsh);
- if (neighsh.sh != dummysh) {
- printf("Error: Invalid PLC.\n");
- printf(" Facet #%d and facet #%d overlap each other.\n",
- shellmark(neighsh), shellmark(shloop));
- printf(" It might be caused by a facet is defined more than once.\n");
- printf(" Hint: Use -d switch to find all overlapping facets.\n");
- terminatetetgen(1);
- //GMSH exit(1);
- }
- // The side of 'spintet' is at which a new subface will be attached.
- adjustedgering(spintet, CCW);
- // Create the new subface.
- makeshellface(subfaces, &newsh);
- setsorg(newsh, org(spintet));
- setsdest(newsh, dest(spintet));
- setsapex(newsh, apex(spintet));
- if (b->quality && varconstraint) {
- setareabound(newsh, area);
- }
- if (checkpbcs) {
- setshellpbcgroup(newsh, pbcgp);
- }
- setshellmark(newsh, shmark);
- setshelltype(newsh, shtype); // It may be a skinny subface.
- // Add newsh into newshlink for intersecting checking.
- newshlink->add(&newsh);
- // Insert it into the current mesh.
- tsbond(spintet, newsh);
- sym(spintet, neightet);
- if (neightet.tet != dummytet) {
- sesym(newsh, neighsh);
- tsbond(neightet, neighsh);
- }
- // Insert it into the surface mesh.
- sspivot(shloop, workseg);
- if (workseg.sh == dummysh) {
- sbond(shloop, newsh);
- } else {
- // There is a subsegment, 'shloop' is the subface which is going to
- // die. Insert the 'newsh' at the place of 'shloop' into its face
- // link, so as to dettach 'shloop'. The original connection is:
- // -> casingin -> shloop -> casingout ->, it will be changed with:
- // -> casingin -> newsh -> casingout ->. Pay attention to the
- // case when this subsegment is dangling in the mesh, i.e., 'shloop'
- // is bonded to itself.
- spivot(shloop, casingout);
- if (shloop.sh != casingout.sh) {
- // 'shloop' is not bonded to itself.
- spinsh = casingout;
- do {
- casingin = spinsh;
- spivotself(spinsh);
- } while (sapex(spinsh) != sapex(shloop));
- assert(casingin.sh != shloop.sh);
- // Bond casingin -> newsh -> casingout.
- sbond1(casingin, newsh);
- sbond1(newsh, casingout);
- } else {
- // Bond newsh -> newsh.
- sbond(newsh, newsh);
- }
- // Bond the segment.
- ssbond(newsh, workseg);
- }
- // Check other two sides of this new subface. If a side is not bonded
- // to any edge in the link, it will be added to the link.
- for (i = 0; i < 2; i++) {
- if (i == 0) {
- senext(newsh, worksh);
- } else {
- senext2(newsh, worksh);
- }
- torg = sorg(worksh);
- tdest = sdest(worksh);
- finishflag = false;
- for (j = 0; j < boundedgelink->len() && !finishflag; j++) {
- neighsh = * (face *) boundedgelink->getnitem(j + 1);
- if ((sorg(neighsh) == torg && sdest(neighsh) == tdest) ||
- (sorg(neighsh) == tdest && sdest(neighsh) == torg)) {
- // Find a boundary edge. Bond them and exit the loop.
- sspivot(neighsh, workseg);
- if (workseg.sh == dummysh) {
- sbond(neighsh, worksh);
- } else {
- // There is a subsegment, 'neighsh' is the subface which is
- // going to die. Do the same as above for 'worksh'.
- spivot(neighsh, casingout);
- if (neighsh.sh != casingout.sh) {
- // 'neighsh' is not bonded to itself.
- spinsh = casingout;
- do {
- casingin = spinsh;
- spivotself(spinsh);
- } while (sapex(spinsh) != sapex(neighsh));
- assert(casingin.sh != neighsh.sh);
- // Bond casingin -> worksh -> casingout.
- sbond1(casingin, worksh);
- sbond1(worksh, casingout);
- } else {
- // Bond worksh -> worksh.
- sbond(worksh, worksh);
- }
- // Bond the segment.
- ssbond(worksh, workseg);
- }
- // Remove this boundary edge from the link.
- boundedgelink->del(j + 1);
- finishflag = true;
- }
- }
- if (!finishflag) {
- // It's a new boundary edge, add it to link.
- boundedgelink->add(&worksh);
- }
- }
- }
-
- // Deallocate the set of old missing subfaces.
- for (i = 0; i < missingshlist->len(); i++) {
- worksh = * (face *)(* missingshlist)[i];
- shellfacedealloc(subfaces, worksh.sh);
- }
- // Unmark region vertices in 'worklist'.
- for (i = 0; i < equatptlist->len(); i++) {
- workpt = * (point *)(* equatptlist)[i];
- idx = pointmark(workpt) - in->firstnumber;
- worklist[idx] = 0;
- }
-
- delete boundedgelink;
- delete newshlink;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// scoutcrossingedge() Search an edge crossing the missing region. //
-// //
-// 'missingshlist' forms the missing region R. This routine searches for an //
-// edge crossing R. It first forms a 'boundedgelist' consisting of the //
-// boundary edges of R. Such edges are existing in CDT. A crossing edge is //
-// found by rotating faces around one of the boundary edges. It is possible //
-// there is no edge crosses R (e.g. R has a degenerate point set). //
-// //
-// If find a croosing edge, return TRUE, 'crossedgelist' contains this edge. //
-// Otherwise, return FALSE. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::scoutcrossingedge(list* missingshlist, list* boundedgelist,
- list* crossedgelist, int* worklist)
-{
- triface starttet, spintet, worktet;
- face startsh, neighsh, worksh, workseg;
- point torg, tdest, tapex;
- point workpt[3], pa, pb, pc;
- enum finddirectionresult collinear;
- REAL ori1, ori2;
- bool crossflag;
- int hitbdry;
- int i, j, k;
-
- // Form the 'boundedgelist'. Loop through 'missingshlist', check each
- // edge of these subfaces. If an edge is a segment or the neighbor
- // subface is uninfected, add it to 'boundedgelist'.
- for (i = 0; i < missingshlist->len(); i++) {
- worksh = * (face *)(* missingshlist)[i];
- for (j = 0; j < 3; j++) {
- sspivot(worksh, workseg);
- if (workseg.sh == dummysh) {
- spivot(worksh, neighsh);
- if (!sinfected(neighsh)) {
- boundedgelist->append(&worksh);
- }
- } else {
- boundedgelist->append(&worksh);
- }
- senextself(worksh);
- }
- }
-
- crossflag = false;
- // Find a crossing edge. It is possible there is no such edge. We need to
- // loop through all edges of 'boundedgelist' for sure we don't miss any.
- for (i = 0; i < boundedgelist->len() && !crossflag; i++) {
- startsh = * (face *)(* boundedgelist)[i];
- // 'startsh' (abc) holds an existing edge of the DT, find it.
- torg = sorg(startsh);
- tdest = sdest(startsh);
- tapex = sapex(startsh);
- getsearchtet(torg, tdest, &starttet, &workpt[0]);
- collinear = finddirection(&starttet, workpt[0], tetrahedrons->items);
- if (collinear == LEFTCOLLINEAR) {
- enext2self(starttet);
- esymself(starttet);
- } else if (collinear == TOPCOLLINEAR) {
- fnextself(starttet);
- enext2self(starttet);
- esymself(starttet);
- }
-#ifdef SELF_CHECK
- assert(dest(starttet) == workpt[0]);
-#endif
- // Now starttet holds edge ab. Find is edge de crossing R.
- spintet = starttet;
- hitbdry = 0;
- do {
- if (fnextself(spintet)) {
- // splittet = abde. Check if de crosses abc.
- workpt[1] = apex(spintet); // workpt[1] = d.
- workpt[2] = oppo(spintet); // workpt[2] = e.
- j = pointmark(workpt[1]) - in->firstnumber;
- k = pointmark(workpt[2]) - in->firstnumber;
- if (worklist[j] == 1) {
- ori1 = 0.0; // d is a vertex of the missing region.
- } else {
- // Get the orientation of d wrt. abc.
- ori1 = orient3d(torg, tdest, tapex, workpt[1]);
- }
- if (worklist[k] == 1) {
- ori2 = 0.0; // e is a vertex of the missing region.
- } else {
- // Get the orientation of e wrt. abc.
- ori2 = orient3d(torg, tdest, tapex, workpt[2]);
- }
- // Only do check if d and e locate on different sides of abc.
- if (ori1 * ori2 < 0.0) {
- // Check if de crosses any subface of R.
- for (j = 0; j < missingshlist->len(); j++) {
- worksh = * (face *)(* missingshlist)[j];
- pa = sorg(worksh);
- pb = sdest(worksh);
- pc = sapex(worksh);
- crossflag = (tri_tri_inter(pa, pb, pc, workpt[0], workpt[1],
- workpt[2]) == INTERSECT);
- if (crossflag) {
- // Find a crossing edge. We're done.
- worktet = spintet;
- adjustedgering(worktet, CCW);
- enextfnextself(worktet);
- enextself(worktet);
- // Add this edge (worktet) into 'crossedgelist'.
- crossedgelist->append(&worktet);
- break;
- }
- }
- if (crossflag) break;
- }
- if (apex(spintet) == apex(starttet)) break;
- } else {
- hitbdry++;
- // It is only possible to hit boundary once.
- if (hitbdry < 2) {
- esym(starttet, spintet);
- }
- }
- } while (hitbdry < 2);
- }
-
- return crossflag;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// formcavity() Form the cavity for recovering the missing region. //
-// //
-// The cavity C is bounded by faces of current CDT. All tetrahedra inside C //
-// will be removed, intead a set of constrained Delaunay tetrahedra will be //
-// filled in and the missing region are recovered. //
-// //
-// 'missingshlist' contains a set of subfaces forming the missing region R. //
-// C is formed by first finding all the tetrahedra in CDT that intersect the //
-// relative interior of R; then deleting them from the CDT, this will form C //
-// inside the CDT. At the beginning, 'crossedgelist' contains an edge which //
-// is crossing R. All tets containing this edge must cross R. Start from it, //
-// other crossing edges can be found incrementally. The discovered crossing //
-// tets are saved in 'crosstetlist'. //
-// //
-// Notice that not all tets in 'crosstetlist' are crossing R. The discovered //
-// tets are connected each other. However, there may be other tets crossing //
-// R but disjoint with the found tets. Due to this fact we need to check the //
-// 'missingshlist' once more. Only recover those subfaces which are crossed //
-// by the set of discovered tets, i.e., R may be shrinked to conform the set //
-// of discovered tets. The extra subfaces of R will be recovered later. //
-// //
-// Notice that some previous recovered subfaces may completely included in C.//
-// This can happen when R is very big and these subfaces lie above R and so //
-// close to it. Such subfaces have to be queued (and sinfected()) to recover //
-// them later. Otherwise, we lost the connection to these subfaces forever. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::formcavity(list* missingshlist, list* crossedgelist,
- list* equatptlist, list* crossshlist, list* crosstetlist,
- list* belowfacelist, list* abovefacelist, list* horizptlist,
- list* belowptlist, list* aboveptlist, queue* missingshqueue, int* worklist)
-{
- triface starttet, spintet, neightet, worktet;
- face startsh, neighsh, worksh, workseg;
- point torg, tdest, tapex, workpt[3];
- REAL checksign, orgori, destori;
- bool crossflag, inlistflag;
- bool belowflag, aboveflag;
- int idx, share;
- int i, j, k;
-
- // Get a face at horizon.
- startsh = * (face *)(* missingshlist)[0];
- torg = sorg(startsh);
- tdest = sdest(startsh);
- tapex = sapex(startsh);
-
- // Collect the set of crossing tetrahedra by rotating crossing edges.
- for (i = 0; i < crossedgelist->len(); i++) {
- // Get a tet abcd, ab is a crossing edge.
- starttet = * (triface *)(* crossedgelist)[i];
- adjustedgering(starttet, CCW);
- if (b->verbose > 2) {
- printf(" Collect tets containing edge (%d, %d).\n",
- pointmark(org(starttet)), pointmark(dest(starttet)));
- }
- orgori = orient3d(torg, tdest, tapex, org(starttet));
- destori = orient3d(torg, tdest, tapex, dest(starttet));
-#ifdef SELF_CHECK
- assert(orgori * destori < 0.0);
-#endif
- spintet = starttet;
- do {
- // The face rotation should not meet boundary.
- fnextself(spintet);
- // Check the validity of the PLC.
- tspivot(spintet, worksh);
- if (worksh.sh != dummysh) {
- printf("Error: Invalid PLC.\n");
- printf(" Two subfaces (%d, %d, %d) and (%d, %d, %d)\n",
- pointmark(torg), pointmark(tdest), pointmark(tapex),
- pointmark(sorg(worksh)), pointmark(sdest(worksh)),
- pointmark(sapex(worksh)));
- printf(" are found intersecting each other.\n");
- printf(" Hint: Use -d switch to find all intersecting facets.\n");
- terminatetetgen(1);
- }
- if (!infected(spintet)) {
- if (b->verbose > 2) {
- printf(" Add crossing tet (%d, %d, %d, %d).\n",
- pointmark(org(spintet)), pointmark(dest(spintet)),
- pointmark(apex(spintet)), pointmark(oppo(spintet)));
- }
- infect(spintet);
- crosstetlist->append(&spintet);
- }
- // Check whether other two edges of 'spintet' is a crossing edge.
- // It can be quickly checked from the apex of 'spintet', if it is
- // not on the facet, then there exists a crossing edge.
- workpt[0] = apex(spintet);
- idx = pointmark(workpt[0]) - in->firstnumber;
- if (worklist[idx] != 1) {
- // Either edge (dest, apex) or edge (apex, org) crosses.
- checksign = orient3d(torg, tdest, tapex, workpt[0]);
-#ifdef SELF_CHECK
- assert(checksign != 0.0);
-#endif
- if (checksign * orgori < 0.0) {
- enext2(spintet, worktet); // edge (apex, org).
- workpt[1] = org(spintet);
- } else {
-#ifdef SELF_CHECK
- assert(checksign * destori < 0.0);
-#endif
- enext(spintet, worktet); // edge (dest, apex).
- workpt[1] = dest(spintet);
- }
- // 'worktet' represents the crossing edge. Add it into list only
- // it doesn't exist in 'crossedgelist'.
- inlistflag = false;
- for (j = 0; j < crossedgelist->len() && !inlistflag; j++) {
- neightet = * (triface *)(* crossedgelist)[j];
- if (org(neightet) == workpt[0]) {
- if (dest(neightet) == workpt[1]) inlistflag = true;
- } else if (org(neightet) == workpt[1]) {
- if (dest(neightet) == workpt[0]) inlistflag = true;
- }
- }
- if (!inlistflag) {
- crossedgelist->append(&worktet);
- }
- }
- } while (apex(spintet) != apex(starttet));
- }
-
- // Identifying the boundary faces and vertices of C. Sort them into
- // 'abovefacelist', 'aboveptlist, 'belowfacelist', and 'belowptlist',
- // respectively. "above" and "below" are wrt.(torg, tdest, tapex).
- for (i = 0; i < crosstetlist->len(); i++) {
- // Get a tet abcd, ab is the crossing edge.
- starttet = * (triface *)(* crosstetlist)[i];
-#ifdef SELF_CHECK
- assert(infected(starttet));
-#endif
- adjustedgering(starttet, CCW);
- // abc and abd are sharing the crossing edge, the two neighbors must
- // be crossing tetrahedra too. They can't be boundaries of C.
- for (j = 0; j < 2; j++) {
- if (j == 0) {
- enextfnext(starttet, worktet); // Check bcd.
- } else {
- enext2fnext(starttet, worktet); // Check acd.
- }
- sym(worktet, neightet);
- // If the neighbor doesn't exist or exists but doesn't be infected,
- // it's a boundary face of C, save it.
- if ((neightet.tet == dummytet) || !infected(neightet)) {
- workpt[0] = org(worktet);
- workpt[1] = dest(worktet);
- workpt[2] = apex(worktet);
- belowflag = aboveflag = false;
- share = 0;
- for (k = 0; k < 3; k++) {
- idx = pointmark(workpt[k]) - in->firstnumber;
- if (worklist[idx] == 0) {
- // It's not a vertices of facet, find which side it lies.
- checksign = orient3d(torg, tdest, tapex, workpt[k]);
-#ifdef SELF_CHECK
- assert(checksign != 0.0);
-#endif
- if (checksign > 0.0) {
- // It lies "below" the facet wrt. 'startsh'.
- worklist[idx] = 2;
- belowptlist->append(&workpt[k]);
- } else if (checksign < 0.0) {
- // It lies "above" the facet wrt. 'startsh'.
- worklist[idx] = 3;
- aboveptlist->append(&workpt[k]);
- }
- }
- if (worklist[idx] == 2) {
- // This face lies "below" the facet wrt. 'startsh'.
- belowflag = true;
- } else if (worklist[idx] == 3) {
- // This face lies "above" the facet wrt. 'startsh'.
- aboveflag = true;
- } else {
-#ifdef SELF_CHECK
- // In degenerate case, this face may just be the equator.
- assert(worklist[idx] == 1);
-#endif
- share++;
- }
- }
-#ifdef SELF_CHECK
- // The degenerate case has been ruled out.
- assert(share < 3);
- // Only one flag is possible for a cavity face.
- assert(belowflag ^ aboveflag);
-#endif
- if (belowflag) {
- belowfacelist->append(&worktet);
- } else if (aboveflag) {
- abovefacelist->append(&worktet);
- }
- }
- }
- }
-
- // Shrink R if not all its subfaces are crossing by the discovered tets.
- // 'crossshlist' and 'horizptlist' represent the set of subfaces and
- // vertices of the shrinked missing region, respectively.
- for (i = 0; i < missingshlist->len(); i++) {
- worksh = * (face *)(* missingshlist)[i];
-#ifdef SELF_CHECK
- assert(sinfected(worksh));
-#endif
- workpt[0] = sorg(worksh);
- workpt[1] = sdest(worksh);
- workpt[2] = sapex(worksh);
- crossflag = false;
- for (j = 0; j < crosstetlist->len() && !crossflag; j++) {
- // Get a tet abcd, ab is a crossing edge.
- starttet = * (triface *)(* crosstetlist)[j];
- adjustedgering(starttet, CCW);
- // Only need to check two sides of worktet.
- for (k = 0; k < 2 && !crossflag; k++) {
- if (k == 0) {
- worktet = starttet; // Check abc.
- } else {
- fnext(starttet, worktet); // Check abd.
- }
- crossflag = tritritest(&worktet, workpt[0], workpt[1], workpt[2]);
- }
- }
- if (crossflag) {
- // 'worksh' is crossed by 'worktet', uninfect it.
- suninfect(worksh);
- crossshlist->append(&worksh);
- // Add its corners into 'horizptlist'.
- for (k = 0; k < 3; k++) {
- idx = pointmark(workpt[k]) - in->firstnumber;
- if (worklist[idx] != 4) {
- worklist[idx] = 4;
- horizptlist->append(&workpt[k]);
- }
- }
- }
- }
-
- // Check 'crossingtetlist'. Queue subfaces inside them.
- for (i = 0; i < crosstetlist->len(); i++) {
- starttet = * (triface *)(* crosstetlist)[i];
- for (starttet.loc = 0; starttet.loc < 4; starttet.loc++) {
- sym(starttet, neightet);
- // If the neighbor exist and is infected, check it.
- if ((neightet.tet != dummytet) && infected(neightet)) {
- tspivot(starttet, worksh);
- if (worksh.sh != dummysh) {
- // Temporarily remove worksh. Make it missing. recover it later.
- if (b->verbose > 2) {
- printf(" Queuing subface (%d, %d, %d).\n",
- pointmark(sorg(worksh)), pointmark(sdest(worksh)),
- pointmark(sapex(worksh)));
- }
- tsdissolve(neightet);
- tsdissolve(starttet);
- // Detach tets at the both sides of this subface.
- stdissolve(worksh);
- sesymself(worksh);
- stdissolve(worksh);
- sinfect(worksh);
- missingshqueue->push(&worksh);
- }
- }
- }
- }
-
- // Clear flags set in 'worklist'.
- for (i = 0; i < equatptlist->len(); i++) {
- workpt[0] = * (point *)(* equatptlist)[i];
- idx = pointmark(workpt[0]) - in->firstnumber;
-#ifdef SELF_CHECK
- assert((worklist[idx] == 1) || (worklist[idx] == 4));
-#endif
- worklist[idx] = 0;
- }
- for (i = 0; i < belowptlist->len(); i++) {
- workpt[0] = * (point *)(* belowptlist)[i];
- idx = pointmark(workpt[0]) - in->firstnumber;
-#ifdef SELF_CHECK
- assert(worklist[idx] == 2);
-#endif
- worklist[idx] = 0;
- }
- for (i = 0; i < aboveptlist->len(); i++) {
- workpt[0] = * (point *)(* aboveptlist)[i];
- idx = pointmark(workpt[0]) - in->firstnumber;
-#ifdef SELF_CHECK
- assert(worklist[idx] == 3);
-#endif
- worklist[idx] = 0;
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// insertallsubfaces() Insert all subfaces, queue missing subfaces. //
-// //
-// Loop through all subfaces, insert each into the DT. If one already exists,//
-// bond it to the tetrahedra having it. Otherwise, it is missing, infect it //
-// and save it in 'missingshqueue'. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::insertallsubfaces(queue* missingshqueue)
-{
- triface searchtet;
- face subloop;
-
- searchtet.tet = (tetrahedron *) NULL;
- subfaces->traversalinit();
- subloop.sh = shellfacetraverse(subfaces);
- while (subloop.sh != (shellface *) NULL) {
- if (!insertsubface(&subloop, &searchtet)) {
- if (b->verbose > 1) {
- printf(" Queuing subface (%d, %d, %d).\n", pointmark(sorg(subloop)),
- pointmark(sdest(subloop)), pointmark(sapex(subloop)));
- }
- sinfect(subloop);
- missingshqueue->push(&subloop);
- }
- subloop.sh = shellfacetraverse(subfaces);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// constrainedfacets() Recover subfaces in a Delaunay tetrahedralization. //
-// //
-// This routine creates a CDT by incrementally updating a DT D into a CDT T. //
-// The process of recovering facets can be imagined by "merging" the surface //
-// mesh F into D. At the beginning, F and D are completely seperated. Some //
-// faces of them are matching some are not because they are crossed by some //
-// tetrahedra of D. The non-matching subfaces will be forced to appear in T //
-// by locally retetrahedralizing the regions where F and D are intersecting. //
-// //
-// When a subface s of F is found missing in D, probably some other subfaces //
-// near to s are missing too. The set of adjoining coplanar missing faces //
-// forms a missing region R (R may not simply connected). //
-// //
-// There are two possibilities can result a mssing region R: (1) Some edges //
-// of D cross R; (2) No edge of D crosses R, but some faces of D spans R, ie,//
-// D is locally degenerate at R. In case (1), D is modified so that it resp- //
-// ects R (done by a cavity retetrahedralization algorithm). In case (2), F //
-// is modified so that the set of subfaces of R matches faces in D (done by //
-// a face rearrangment algorithm). //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::constrainedfacets()
-{
- queue *missingshqueue, *flipque;
- list *missingshlist, *equatptlist;
- list *boundedgelist, *crossedgelist, *crosstetlist;
- list *crossshlist, *belowfacelist, *abovefacelist;
- list *horizptlist, *belowptlist, *aboveptlist;
- list *frontlist, *misfrontlist, *newtetlist;
- triface searchtet, worktet;
- face subloop, worksh;
- int *worklist;
- int i;
-
- if (!b->quiet) {
- printf("Constraining facets.\n");
- }
-
- // Initialize queues.
- missingshqueue = new queue(sizeof(face));
- flipque = new queue(sizeof(badface));
- // Initialize the working lists.
- missingshlist = new list(sizeof(face), NULL);
- boundedgelist = new list(sizeof(face), NULL);
- crossedgelist = new list(sizeof(triface), NULL);
- equatptlist = new list("point *");
- crossshlist = new list(sizeof(face), NULL);
- crosstetlist = new list(sizeof(triface), NULL);
- belowfacelist = new list(sizeof(triface), NULL);
- abovefacelist = new list(sizeof(triface), NULL);
- horizptlist = new list("point *");
- belowptlist = new list("point *");
- aboveptlist = new list("point *");
- frontlist = new list(sizeof(triface), NULL);
- misfrontlist = new list(sizeof(triface), NULL);
- newtetlist = new list(sizeof(triface), NULL);
- // Initialize the array for marking vertices.
- worklist = new int[points->items + 1];
- for (i = 0; i < points->items + 1; i++) worklist[i] = 0;
-
- // Compute a mapping from points to tetrahedra for fast searching.
- makepoint2tetmap();
-
- // Match subfaces in D, queue all missing subfaces.
- insertallsubfaces(missingshqueue);
-
- // Recover all missing subfaces.
- while (!missingshqueue->empty()) {
- // Get a queued face s.
- subloop = * (face *) missingshqueue->pop();
- // s may have been deleted in a face rearrangment operation.
- if (isdead(&subloop)) continue;
- // s may have been recovered in a previous missing region.
- if (!sinfected(subloop)) continue;
- // s may match a face in D now due to previous transformations.
- if (insertsubface(&subloop, &searchtet)) {
- suninfect(subloop);
- continue;
- }
- if (b->verbose > 1) {
- printf(" Recover subface (%d, %d, %d).\n", pointmark(sorg(subloop)),
- pointmark(sdest(subloop)), pointmark(sapex(subloop)));
- }
- // Form the missing region R containing s.
- formmissingregion(&subloop, missingshlist, equatptlist, worklist);
- // Is R crossing by any tetrahedron?
- if (scoutcrossingedge(missingshlist, boundedgelist, crossedgelist,
- worklist)) {
- // Form the cavity C containing R.
- formcavity(missingshlist, crossedgelist, equatptlist, crossshlist,
- crosstetlist, belowfacelist, abovefacelist, horizptlist,
- belowptlist, aboveptlist, missingshqueue, worklist);
- // Recover the above part of C.
- delaunizecavity(crossshlist, abovefacelist, aboveptlist, horizptlist,
- frontlist, misfrontlist, newtetlist, crosstetlist,
- missingshqueue, flipque);
- // Inverse the direction of subfaces in R.
- for (i = 0; i < crossshlist->len(); i++) {
- worksh = * (face *)(* crossshlist)[i];
- sesymself(worksh);
- * (face *)(* crossshlist)[i] = worksh;
- }
- // Recover the below part of C.
- delaunizecavity(crossshlist, belowfacelist, belowptlist, horizptlist,
- frontlist, misfrontlist, newtetlist, crosstetlist,
- missingshqueue, flipque);
- // Delete tetrahedra in C.
- for (i = 0; i < crosstetlist->len(); i++) {
- worktet = * (triface *)(* crosstetlist)[i];
- tetrahedrondealloc(worktet.tet);
- }
- // There may have some un-recovered subfaces of R. Put them back into
- // queue. Otherwise, they will be missing on the boundary.
- for (i = 0; i < missingshlist->len(); i++) {
- worksh = * (face *)(* missingshlist)[i];
- if (sinfected(worksh)) {
- // An unrecovered subface, put it back into queue.
- missingshqueue->push(&worksh);
- }
- }
- crossshlist->clear();
- belowfacelist->clear();
- abovefacelist->clear();
- horizptlist->clear();
- belowptlist->clear();
- aboveptlist->clear();
- crosstetlist->clear();
- } else {
- // No. Rearrange subfaces of F conforming to that of D in R. It can
- // happen when the facet has non-coplanar vertices.
- rearrangesubfaces(missingshlist, boundedgelist, equatptlist, worklist);
- }
- // Clear all working lists.
- missingshlist->clear();
- boundedgelist->clear();
- crossedgelist->clear();
- equatptlist->clear();
- }
-
- // Subfaces have been merged into D.
- checksubfaces = 1;
-
- if (b->verbose > 0) {
- printf(" The biggest cavity: %d faces, %d vertices\n", maxcavfaces,
- maxcavverts);
- printf(" Enlarged %d times\n", expcavcount);
- }
-
- delete missingshqueue;
- delete flipque;
- delete missingshlist;
- delete boundedgelist;
- delete crossedgelist;
- delete equatptlist;
- delete crossshlist;
- delete crosstetlist;
- delete belowfacelist;
- delete abovefacelist;
- delete horizptlist;
- delete belowptlist;
- delete aboveptlist;
- delete frontlist;
- delete misfrontlist;
- delete newtetlist;
- delete [] worklist;
-}
-
-//
-// End of facet recovery routines
-//
-
-//
-// Begin of carving out holes and concavities routines
-//
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// infecthull() Virally infect all of the tetrahedra of the convex hull //
-// that are not protected by subfaces. Where there are //
-// subfaces, set boundary markers as appropriate. //
-// //
-// Memorypool 'viri' is used to return all the infected tetrahedra. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::infecthull(memorypool *viri)
-{
- triface tetloop, tsymtet;
- tetrahedron **deadtet;
- face hullface;
- // point horg, hdest, hapex;
-
- if (b->verbose > 0) {
- printf(" Marking concavities for elimination.\n");
- }
- tetrahedrons->traversalinit();
- tetloop.tet = tetrahedrontraverse();
- while (tetloop.tet != (tetrahedron *) NULL) {
- // Is this tetrahedron on the hull?
- for (tetloop.loc = 0; tetloop.loc < 4; tetloop.loc++) {
- sym(tetloop, tsymtet);
- if (tsymtet.tet == dummytet) {
- // Is the tetrahedron protected by a subface?
- tspivot(tetloop, hullface);
- if (hullface.sh == dummysh) {
- // The tetrahedron is not protected; infect it.
- if (!infected(tetloop)) {
- infect(tetloop);
- deadtet = (tetrahedron **) viri->alloc();
- *deadtet = tetloop.tet;
- break; // Go and get next tet.
- }
- } else {
- // The tetrahedron is protected; set boundary markers if appropriate.
- if (shellmark(hullface) == 0) {
- setshellmark(hullface, 1);
- /*
- horg = sorg(hullface);
- hdest = sdest(hullface);
- hapex = sapex(hullface);
- if (pointmark(horg) == 0) {
- setpointmark(horg, 1);
- }
- if (pointmark(hdest) == 0) {
- setpointmark(hdest, 1);
- }
- if (pointmark(hapex) == 0) {
- setpointmark(hapex, 1);
- }
- */
- }
- }
- }
- }
- tetloop.tet = tetrahedrontraverse();
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// plague() Spread the virus from all infected tets to any neighbors not //
-// protected by subfaces. //
-// //
-// This routine identifies all the tetrahedra that will die, and marks them //
-// as infected. They are marked to ensure that each tetrahedron is added to //
-// the virus pool only once, so the procedure will terminate. 'viri' returns //
-// all infected tetrahedra which are outside the domian. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::plague(memorypool *viri)
-{
- tetrahedron **virusloop;
- tetrahedron **deadtet;
- triface testtet, neighbor;
- face neighsh, testseg;
- face spinsh, casingin, casingout;
- int firstdadsub;
- int i;
-
- if (b->verbose > 0) {
- printf(" Marking neighbors of marked tetrahedra.\n");
- }
- firstdadsub = 0;
- // Loop through all the infected tetrahedra, spreading the virus to
- // their neighbors, then to their neighbors' neighbors.
- viri->traversalinit();
- virusloop = (tetrahedron **) viri->traverse();
- while (virusloop != (tetrahedron **) NULL) {
- testtet.tet = *virusloop;
- // Temporarily uninfect this tetrahedron, not necessary.
- uninfect(testtet);
- // Check each of the tetrahedron's four neighbors.
- for (testtet.loc = 0; testtet.loc < 4; testtet.loc++) {
- // Find the neighbor.
- sym(testtet, neighbor);
- // Check for a shell between the tetrahedron and its neighbor.
- tspivot(testtet, neighsh);
- // Check if the neighbor is nonexistent or already infected.
- if ((neighbor.tet == dummytet) || infected(neighbor)) {
- if (neighsh.sh != dummysh) {
- // There is a subface separating the tetrahedron from its neighbor,
- // but both tetrahedra are dying, so the subface dies too.
- // Before deallocte this subface, dissolve the connections between
- // other subfaces, subsegments and tetrahedra.
- neighsh.shver = 0;
- if (!firstdadsub) {
- firstdadsub = 1; // Report the problem once.
- if (!b->quiet) {
- printf("Warning: Detecting an open face (%d, %d, %d).\n",
- pointmark(sorg(neighsh)), pointmark(sdest(neighsh)),
- pointmark(sapex(neighsh)));
- }
- }
- // For keep the same enext() direction.
- findedge(&testtet, sorg(neighsh), sdest(neighsh));
- for (i = 0; i < 3; i++) {
- sspivot(neighsh, testseg);
- if (testseg.sh != dummysh) {
- // A subsegment is found at this side, dissolve this subface
- // from the face link of this subsegment.
- testseg.shver = 0;
- spinsh = neighsh;
- if (sorg(spinsh) != sorg(testseg)) {
- sesymself(spinsh);
- }
- spivot(spinsh, casingout);
- if (casingout.sh == spinsh.sh) {
- // This is a trivial face link, only 'neighsh' itself,
- // the subsegment at this side is also died.
- shellfacedealloc(subsegs, testseg.sh);
- } else {
- spinsh = casingout;
- do {
- casingin = spinsh;
- spivotself(spinsh);
- } while (spinsh.sh != neighsh.sh);
- // Set the link casingin->casingout.
- sbond1(casingin, casingout);
- // Bond the subsegment anyway.
- ssbond(casingin, testseg);
- }
- }
- senextself(neighsh);
- enextself(testtet);
- }
- if (neighbor.tet != dummytet) {
- // Make sure the subface doesn't get deallocated again later
- // when the infected neighbor is visited.
- tsdissolve(neighbor);
- }
- // This subface has been separated.
- if (in->mesh_dim > 2) {
- shellfacedealloc(subfaces, neighsh.sh);
- } else {
- // Dimension is 2. keep it for output.
- // Dissolve tets at both sides of this subface.
- stdissolve(neighsh);
- sesymself(neighsh);
- stdissolve(neighsh);
- }
- }
- } else { // The neighbor exists and is not infected.
- if (neighsh.sh == dummysh) {
- // There is no subface protecting the neighbor, infect it.
- infect(neighbor);
- // Ensure that the neighbor's neighbors will be infected.
- deadtet = (tetrahedron **) viri->alloc();
- *deadtet = neighbor.tet;
- } else { // The neighbor is protected by a subface.
- // Remove this tetrahedron from the subface.
- stdissolve(neighsh);
- // The subface becomes a boundary. Set markers accordingly.
- if (shellmark(neighsh) == 0) {
- setshellmark(neighsh, 1);
- }
- // This side becomes hull. Update the handle in dummytet.
- dummytet[0] = encode(neighbor);
- }
- }
- }
- // Remark the tetrahedron as infected, so it doesn't get added to the
- // virus pool again.
- infect(testtet);
- virusloop = (tetrahedron **) viri->traverse();
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// regionplague() Spread regional attributes and/or volume constraints //
-// (from a .poly file) throughout the mesh. //
-// //
-// This procedure operates in two phases. The first phase spreads an attri- //
-// bute and/or a volume constraint through a (facet-bounded) region. The //
-// second phase uninfects all infected tetrahedra, returning them to normal. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::
-regionplague(memorypool *regionviri, REAL attribute, REAL volume)
-{
- tetrahedron **virusloop;
- tetrahedron **regiontet;
- triface testtet, neighbor;
- face neighsh;
-
- if (b->verbose > 1) {
- printf(" Marking neighbors of marked tetrahedra.\n");
- }
- // Loop through all the infected tetrahedra, spreading the attribute
- // and/or volume constraint to their neighbors, then to their neighbors'
- // neighbors.
- regionviri->traversalinit();
- virusloop = (tetrahedron **) regionviri->traverse();
- while (virusloop != (tetrahedron **) NULL) {
- testtet.tet = *virusloop;
- // Temporarily uninfect this tetrahedron, not necessary.
- uninfect(testtet);
- if (b->regionattrib) {
- // Set an attribute.
- setelemattribute(testtet.tet, in->numberoftetrahedronattributes,
- attribute);
- }
- if (b->varvolume) {
- // Set a volume constraint.
- setvolumebound(testtet.tet, volume);
- }
- // Check each of the tetrahedron's four neighbors.
- for (testtet.loc = 0; testtet.loc < 4; testtet.loc++) {
- // Find the neighbor.
- sym(testtet, neighbor);
- // Check for a subface between the tetrahedron and its neighbor.
- tspivot(testtet, neighsh);
- // Make sure the neighbor exists, is not already infected, and
- // isn't protected by a subface, or is protected by a nonsolid
- // subface.
- if ((neighbor.tet != dummytet) && !infected(neighbor)
- && (neighsh.sh == dummysh)) {
- // Infect the neighbor.
- infect(neighbor);
- // Ensure that the neighbor's neighbors will be infected.
- regiontet = (tetrahedron **) regionviri->alloc();
- *regiontet = neighbor.tet;
- }
- }
- // Remark the tetrahedron as infected, so it doesn't get added to the
- // virus pool again.
- infect(testtet);
- virusloop = (tetrahedron **) regionviri->traverse();
- }
-
- // Uninfect all tetrahedra.
- if (b->verbose > 1) {
- printf(" Unmarking marked tetrahedra.\n");
- }
- regionviri->traversalinit();
- virusloop = (tetrahedron **) regionviri->traverse();
- while (virusloop != (tetrahedron **) NULL) {
- testtet.tet = *virusloop;
- uninfect(testtet);
- virusloop = (tetrahedron **) regionviri->traverse();
- }
- // Empty the virus pool.
- regionviri->restart();
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// removeholetets() Remove tetrahedra which are outside the domain. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::removeholetets(memorypool* viri)
-{
- tetrahedron **virusloop;
- triface testtet, neighbor;
- point checkpt;
- int *tetspernodelist;
- int i, j;
-
- if (b->verbose > 0) {
- printf(" Deleting marked tetrahedra.\n");
- }
-
- // Create and initialize 'tetspernodelist'.
- tetspernodelist = new int[points->items + 1];
- for (i = 0; i < points->items + 1; i++) tetspernodelist[i] = 0;
-
- // Loop the tetrahedra list, counter the number of tets sharing each node.
- tetrahedrons->traversalinit();
- testtet.tet = tetrahedrontraverse();
- while (testtet.tet != (tetrahedron *) NULL) {
- // Increment the number of sharing tets for each endpoint.
- for (i = 0; i < 4; i++) {
- j = pointmark((point) testtet.tet[4 + i]);
- tetspernodelist[j]++;
- }
- testtet.tet = tetrahedrontraverse();
- }
-
- viri->traversalinit();
- virusloop = (tetrahedron **) viri->traverse();
- while (virusloop != (tetrahedron **) NULL) {
- testtet.tet = *virusloop;
- // Record changes in the number of boundary faces, and disconnect
- // dead tetrahedra from their neighbors.
- for (testtet.loc = 0; testtet.loc < 4; testtet.loc++) {
- sym(testtet, neighbor);
- if (neighbor.tet == dummytet) {
- // There is no neighboring tetrahedron on this face, so this face
- // is a boundary face. This tetrahedron is being deleted, so this
- // boundary face is deleted.
- hullsize--;
- } else {
- // Disconnect the tetrahedron from its neighbor.
- dissolve(neighbor);
- // There is a neighboring tetrahedron on this face, so this face
- // becomes a boundary face when this tetrahedron is deleted.
- hullsize++;
- }
- }
- // Check the four corners of this tet if they're isolated.
- for (i = 0; i < 4; i++) {
- checkpt = (point) testtet.tet[4 + i];
- j = pointmark(checkpt);
- tetspernodelist[j]--;
- if (tetspernodelist[j] == 0) {
- // If it is added volume vertex or '-j' is not used, delete it.
- if ((pointtype(checkpt) == FREEVOLVERTEX) || !b->nojettison) {
- setpointtype(checkpt, UNUSEDVERTEX);
- unuverts++;
- }
- }
- }
- // Return the dead tetrahedron to the pool of tetrahedra.
- tetrahedrondealloc(testtet.tet);
- virusloop = (tetrahedron **) viri->traverse();
- }
-
- delete [] tetspernodelist;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// assignregionattribs() Assign each tetrahedron a region number. //
-// //
-// This routine is called when '-AA' switch is specified. Every tetrahedron //
-// of a (bounded) region will get a integer number to that region. Default, //
-// regions are numbered as 1, 2, 3, etc. However, if a number has already //
-// been used (set by user in the region section in .poly or .smesh), it is //
-// skipped and the next available number will be used. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::assignregionattribs()
-{
- list *regionnumlist;
- list *regiontetlist;
- triface tetloop, regiontet, neightet;
- face checksh;
- bool flag;
- int regionnum, num;
- int attridx, count;
- int i;
-
- if (b->verbose > 0) {
- printf(" Assign region numbers.\n");
- }
-
- regionnumlist = new list(sizeof(int), NULL, 256);
- regiontetlist = new list(sizeof(triface), NULL, 1024);
- attridx = in->numberoftetrahedronattributes;
-
- // Loop through all tets. Infect tets which already have a region number,
- // and save the used numbers in 'regionnumlist'.
- tetrahedrons->traversalinit();
- tetloop.tet = tetrahedrontraverse();
- while (tetloop.tet != (tetrahedron *) NULL) {
- if (!infected(tetloop)) {
- regionnum = (int) elemattribute(tetloop.tet, attridx);
- if (regionnum != 0.0) {
- // Found a numbered region tet.
- infect(tetloop);
- regiontetlist->append(&tetloop);
- // Found and infect all tets in this region.
- for (i = 0; i < regiontetlist->len(); i++) {
- regiontet = * (triface *)(* regiontetlist)[i];
- for (regiontet.loc = 0; regiontet.loc < 4; regiontet.loc++) {
- // Is there a boundary face?
- tspivot(regiontet, checksh);
- if (checksh.sh == dummysh) {
- sym(regiontet, neightet);
- if ((neightet.tet != dummytet) && !infected(neightet)) {
-#ifdef SELF_CHECK
- // neightet should have the same region number. Check it.
- num = (int) elemattribute(neightet.tet, attridx);
- assert(num == regionnum);
-#endif
- infect(neightet);
- regiontetlist->append(&neightet);
- }
- }
- }
- }
- // Add regionnum to list if it is not exist.
- flag = false;
- for (i = 0; i < regionnumlist->len() && !flag; i++) {
- num = * (int *)(* regionnumlist)[i];
- flag = (num == regionnum);
- }
- if (!flag) regionnumlist->append(®ionnum);
- // Clear list for the next region.
- regiontetlist->clear();
- }
- }
- tetloop.tet = tetrahedrontraverse();
- }
-
- if (b->verbose > 0) {
- printf(" %d user-specified regions.\n", regionnumlist->len());
- }
-
- // Now loop the tets again. Assign region numbers to uninfected tets.
- tetrahedrons->traversalinit();
- tetloop.tet = tetrahedrontraverse();
- regionnum = 1; // Start region number.
- count = 0;
- while (tetloop.tet != (tetrahedron *) NULL) {
- if (!infected(tetloop)) {
- // An unassigned region tet.
- count++;
- do {
- flag = false;
- // Check if the region number has been used.
- for (i = 0; i < regionnumlist->len() && !flag; i++) {
- num = * (int *)(* regionnumlist)[i];
- flag = (num == regionnum);
- }
- if (flag) regionnum++;
- } while (flag);
- setelemattribute(tetloop.tet, attridx, (REAL) regionnum);
- infect(tetloop);
- regiontetlist->append(&tetloop);
- // Found and infect all tets in this region.
- for (i = 0; i < regiontetlist->len(); i++) {
- regiontet = * (triface *)(* regiontetlist)[i];
- for (regiontet.loc = 0; regiontet.loc < 4; regiontet.loc++) {
- // Is there a boundary face?
- tspivot(regiontet, checksh);
- if (checksh.sh == dummysh) {
- sym(regiontet, neightet);
- if ((neightet.tet != dummytet) && !infected(neightet)) {
-#ifdef SELF_CHECK
- // neightet should have not been assigned yet. Check it.
- num = (int) elemattribute(neightet.tet, attridx);
- assert(num == 0);
-#endif
- setelemattribute(neightet.tet, attridx, (REAL) regionnum);
- infect(neightet);
- regiontetlist->append(&neightet);
- }
- }
- }
- }
- regiontetlist->clear();
- regionnum++; // The next region number.
- }
- tetloop.tet = tetrahedrontraverse();
- }
-
- // Uninfect all tets.
- tetrahedrons->traversalinit();
- tetloop.tet = tetrahedrontraverse();
- while (tetloop.tet != (tetrahedron *) NULL) {
-#ifdef SELF_CHECK
- assert(infected(tetloop));
-#endif
- uninfect(tetloop);
- tetloop.tet = tetrahedrontraverse();
- }
-
- if (b->verbose > 0) {
- printf(" %d regions are numbered.\n", count);
- }
-
- delete regionnumlist;
- delete regiontetlist;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// carveholes() Find the holes and infect them. Find the volume //
-// constraints and infect them. Infect the convex hull. //
-// Spread the infection and kill tetrahedra. Spread the //
-// volume constraints. //
-// //
-// This routine mainly calls other routines to carry out all these functions.//
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::carveholes()
-{
- memorypool *holeviri, *regionviri;
- tetrahedron *tptr, **holetet, **regiontet;
- triface searchtet, *holetets, *regiontets;
- enum locateresult intersect;
- int i;
-
- if (!b->quiet) {
- printf("Removing unwanted tetrahedra.\n");
- if (b->verbose && (in->numberofholes > 0)) {
- printf(" Marking holes for elimination.\n");
- }
- }
-
- // Initialize a pool of viri to be used for holes, concavities.
- holeviri = new memorypool(sizeof(tetrahedron *), 1024, POINTER, 0);
- // Mark as infected any unprotected tetrahedra on the boundary.
- infecthull(holeviri);
-
- if (in->numberofholes > 0) {
- // Allocate storage for the tetrahedra in which hole points fall.
- holetets = (triface *) new triface[in->numberofholes];
- // Infect each tetrahedron in which a hole lies.
- for (i = 0; i < 3 * in->numberofholes; i += 3) {
- // Ignore holes that aren't within the bounds of the mesh.
- if ((in->holelist[i] >= xmin) && (in->holelist[i] <= xmax)
- && (in->holelist[i + 1] >= ymin)
- && (in->holelist[i + 1] <= ymax)
- && (in->holelist[i + 2] >= zmin)
- && (in->holelist[i + 2] <= zmax)) {
- searchtet.tet = dummytet;
- // Find a tetrahedron that contains the hole.
- intersect = locate(&in->holelist[i], &searchtet);
- if ((intersect != OUTSIDE) && (!infected(searchtet))) {
- // Record the tetrahedron for processing carve hole.
- holetets[i / 3] = searchtet;
- }
- }
- }
- // Infect the hole tetrahedron. This is done by marking the tet as
- // infected and including the tetrahedron in the virus pool.
- for (i = 0; i < in->numberofholes; i++) {
- infect(holetets[i]);
- holetet = (tetrahedron **) holeviri->alloc();
- *holetet = holetets[i].tet;
- }
- // Free up memory.
- delete [] holetets;
- }
-
- // Mark as infected all tets of the holes and concavities.
- plague(holeviri);
- // The virus pool contains all outside tets now.
-
- // Is -A switch in use.
- if (b->regionattrib) {
- // Assign every tetrahedron a regional attribute of zero.
- tetrahedrons->traversalinit();
- tptr = tetrahedrontraverse();
- while (tptr != (tetrahedron *) NULL) {
- setelemattribute(tptr, in->numberoftetrahedronattributes, 0.0);
- tptr = tetrahedrontraverse();
- }
- }
-
- if (in->numberofregions > 0) {
- if (!b->quiet) {
- if (b->regionattrib) {
- if (b->varvolume) {
- printf("Spreading regional attributes and volume constraints.\n");
- } else {
- printf("Spreading regional attributes.\n");
- }
- } else {
- printf("Spreading regional volume constraints.\n");
- }
- }
- // Allocate storage for the tetrahedra in which region points fall.
- regiontets = (triface *) new triface[in->numberofregions];
- // Find the starting tetrahedron for each region.
- for (i = 0; i < in->numberofregions; i++) {
- regiontets[i].tet = dummytet;
- // Ignore region points that aren't within the bounds of the mesh.
- if ((in->regionlist[5 * i] >= xmin)
- && (in->regionlist[5 * i] <= xmax)
- && (in->regionlist[5 * i + 1] >= ymin)
- && (in->regionlist[5 * i + 1] <= ymax)
- && (in->regionlist[5 * i + 2] >= zmin)
- && (in->regionlist[5 * i + 2] <= zmax)) {
- searchtet.tet = dummytet;
- // Find a tetrahedron that contains the region point.
- intersect = locate(&in->regionlist[5 * i], &searchtet);
- if ((intersect != OUTSIDE) && (!infected(searchtet))) {
- // Record the tetrahedron for processing after the
- // holes have been carved.
- regiontets[i] = searchtet;
- }
- }
- }
- // Initialize a pool to be used for regional attrs, and/or regional
- // volume constraints.
- regionviri = new memorypool(sizeof(tetrahedron *), 1024, POINTER, 0);
- // Find and set all regions.
- for (i = 0; i < in->numberofregions; i++) {
- if (regiontets[i].tet != dummytet) {
- // Make sure the tetrahedron under consideration still exists.
- // It may have been eaten by the virus.
- if (!isdead(&(regiontets[i]))) {
- // Put one tetrahedron in the virus pool.
- infect(regiontets[i]);
- regiontet = (tetrahedron **) regionviri->alloc();
- *regiontet = regiontets[i].tet;
- // Apply one region's attribute and/or volume constraint.
- regionplague(regionviri, in->regionlist[5 * i + 3],
- in->regionlist[5 * i + 4]);
- // The virus pool should be empty now.
- }
- }
- }
- // Free up memory.
- delete [] regiontets;
- delete regionviri;
- }
-
- // Now acutually remove the outside and hole tets.
- removeholetets(holeviri);
- // The mesh is nonconvex now.
- nonconvex = 1;
-
- if (b->regionattrib) {
- if (b->regionattrib > 1) {
- // -AA switch. Assign each tet a region number (> 0).
- assignregionattribs();
- }
- // Note the fact that each tetrahedron has an additional attribute.
- in->numberoftetrahedronattributes++;
- }
-
- // Free up memory.
- delete holeviri;
-}
-
-//
-// End of carving out holes and concavities routines
-//
-
-//
-// Begin of boundary Steiner points removing routines
-//
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// replacepolygonsubs() Substitute the subfaces of a polygon. //
-// //
-// 'oldshlist' (T_old) contains the old subfaces of P. It will be replaced //
-// by 'newshlist' (T_new) of new subfaces. Each boundary edge of P is bonded //
-// to 'dummysh' in T_new. //
-// //
-// Notice that Not every boundary edge of T_new is able to bond to a subface,//
-// e.g., when it is a segment recovered by removing a Steiner point in it. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::replacepolygonsubs(list* oldshlist, list* newshlist)
-{
- face newsh, oldsh, spinsh;
- face casingout, casingin;
- face checkseg;
- point pa, pb;
- int i, j, k, l;
-
- for (i = 0; i < newshlist->len(); i++) {
- // Get a new subface s.
- newsh = * (face *)(* newshlist)[i];
- // Check the three edges of s.
- for (k = 0; k < 3; k++) {
- spivot(newsh, casingout);
- // Is it a boundary edge?
- if (casingout.sh == dummysh) {
- // Find the old subface s_o having the same edge as s.
- pa = sorg(newsh);
- pb = sdest(newsh);
- for (j = 0; j < oldshlist->len(); j++) {
- oldsh = * (face *)(* oldshlist)[j];
- for (l = 0; l < 3; l++) {
- if (((sorg(oldsh) == pa) && (sdest(oldsh) == pb)) ||
- ((sorg(oldsh) == pb) && (sdest(oldsh) == pa))) break;
- senextself(oldsh);
- }
- if (l < 3) break;
- }
- // Is there a matched edge?
- if (j < oldshlist->len()) {
- // Get the neighbor subface s_out.
- spivot(oldsh, casingout);
- sspivot(oldsh, checkseg);
- if (checkseg.sh != dummysh) {
- // A segment. Insert s into the face ring, ie, s_in -> s -> s_out.
- if (oldsh.sh != casingout.sh) {
- // s is not bonded to itself.
- spinsh = casingout;
- do {
- casingin = spinsh;
- spivotself(spinsh);
- } while (sapex(spinsh) != sapex(oldsh));
- assert(casingin.sh != oldsh.sh);
- // Bond s_in -> s -> s_out (and dissolve s_in -> s_old -> s_out).
- sbond1(casingin, newsh);
- sbond1(newsh, casingout);
- } else {
- // Bond newsh -> newsh.
- sbond(newsh, newsh);
- }
- // Bond the segment.
- ssbond(newsh, checkseg);
- } else {
- // Bond s <-> s_out (and dissolve s_out -> s_old).
- sbond(newsh, casingout);
- }
- // Unbound oldsh to indicate it's neighbor has been replaced.
- // It will be used to indentfy the edge in the inverse.
- sdissolve(oldsh);
- ssdissolve(oldsh);
- }
- }
- // Go to the next edge of s.
- senextself(newsh);
- }
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// orientnewsubs() Orient new subfaces facing to the inside of cavity. //
-// //
-// 'newshlist' contains new subfaces of the cavity C (created by re-triangu- //
-// lation the polygon P). They're not necessary facing to the inside of C. //
-// 'orientsh', faces to the inside of C, is used to adjust new subfaces. The //
-// normal of the new subfaces is returned in 'norm'. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::orientnewsubs(list* newshlist, face* orientsh, REAL* norm)
-{
- face *newsh;
- point pa, pb, pc;
- REAL ref[3], ori, len;
- int i;
-
- // Calculate the normal of 'orientsh'.
- pa = sorg(*orientsh);
- pb = sdest(*orientsh);
- pc = sapex(*orientsh);
- facenormal(pa, pb, pc, norm, &len);
- for (i = 0; i < 3; i++) ref[i] = pa[i] + norm[i];
- for (i = 0; i < 3; i++) norm[i] /= len;
-
- // Orient new subfaces. Let the normal above each one.
- for (i = 0; i < newshlist->len(); i++) {
- newsh = (face *)(* newshlist)[i];
- pa = sorg(*newsh);
- pb = sdest(*newsh);
- pc = sapex(*newsh);
- ori = orient3d(pa, pb, pc, ref);
- assert(ori != 0.0);
- if (ori > 0.0) {
- sesymself(*newsh);
- }
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// constrainedflip() Flip a non-constrained face. //
-// //
-// 'flipface' f (abc) is a face we want to flip. In addition, if 'front' is //
-// given (not a NULL), f is a crossface. f may not be flippable if it is one //
-// of the following cases: //
-// (1) f has an aux subface attached; //
-// (2) f is on the convex hull; //
-// (3) f is not locally Delaunay (f must be recovered by a previous flip, //
-// we should keep it, otherwise, we may fall into a flip loop); //
-// (4) f is T32 at ab, but abd or abe has an aux subface attached; //
-// (5) f is T22 or T44 at ab, but abd, or abe, or abf has an aux subface //
-// attached; //
-// (6) f is unflipable at ab, and abd, abe, ... are all unflippable due to //
-// the cases (1) - (5). //
-// If f is a crssface ('front' != NULL) and it is unflipable due to case (3),//
-// (4), (5) and (6). Try to flip the next crossing face of front first. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::constrainedflip(triface* flipface, triface* front,
- queue* flipque)
-{
- triface symface, spintet;
- face checksh;
- point pa, pb, pc, pd, pe;
- enum fliptype fc;
- REAL sign;
- bool doflip;
- int ia, ib, ic, id, ie;
- int i;
-
- // (1) Is f protected by an (auxilary) subface?
- tspivot(*flipface, checksh);
- if (checksh.sh != dummysh) return false;
- // (2) Is f on the convex hull?
- sym(*flipface, symface);
- if (symface.tet == dummytet) return false;
- // (3) Is f not locally Delaunay?
- adjustedgering(*flipface, CCW);
- pa = dest(*flipface);
- pb = org(*flipface);
- pc = apex(*flipface);
- pd = oppo(*flipface);
- pe = oppo(symface);
- // if (symbolic) {
- ia = pointmark(pa);
- ib = pointmark(pb);
- ic = pointmark(pc);
- id = pointmark(pd);
- ie = pointmark(pe);
- sign = insphere_sos(pa, pb, pc, pd, pe, ia, ib, ic, id, ie);
- assert(sign != 0.0);
- // } else {
- // sign = insphere(pa, pb, pc, pd, pe);
- // }
- if (sign <= 0.0) {
- // Get the fliptype of f.
- checksubfaces = 0; // switch off subface test.
- fc = categorizeface(*flipface);
- checksubfaces = 1; // switch on subface test.
- if (fc == T23) {
- doflip = true;
- // Avoid one tet created by the 2-3 flip is nearly degenerate.
- /* pc = oppo(*flipface);
- pd = oppo(symface);
- adjustedgering(*flipface, CCW);
- for (i = 0; i < 3; i++) {
- pa = org(*flipface);
- pb = dest(*flipface);
- ori = orient3d(pa, pb, pc, pd);
- if (iscoplanar(pa, pb, pc, pd, ori, b->epsilon)) {
- doflip = false; break;
- }
- enextself(*flipface);
- } */
- if (doflip) {
- flip23(flipface, flipque);
- return true;
- }
- } else if (fc == T32) {
- // (4) Is abd, or abe protected?
- doflip = true;
- spintet = *flipface;
- for (i = 0; i < 2; i++) {
- fnextself(spintet);
- tspivot(spintet, checksh);
- if (checksh.sh != dummysh) {
- doflip = false; break; // f is protected. Unflipable.
- }
- }
- if (doflip) {
- flip32(flipface, flipque);
- return true;
- }
- } else if (fc == T22 || fc == T44) {
- // (5) Is abd, abe, or abf protected?
- doflip = true;
- if (fc == T22) {
- for (i = 0; i < 2; i++) {
- spintet = *flipface;
- if (i == 1) {
- esymself(spintet);
- }
- fnextself(spintet);
- tspivot(spintet, checksh);
- if (checksh.sh != dummysh) {
- doflip = false; break; // f is protected. Unflipable.
- }
- }
- } else if (fc == T44) {
- spintet = *flipface;
- for (i = 0; i < 3; i++) {
- fnextself(spintet);
- tspivot(spintet, checksh);
- if (checksh.sh != dummysh) {
- doflip = false; break; // f is protected. Unflipable.
- }
- }
- }
- if (doflip) {
- flip22(flipface, flipque);
- return true;
- }
- } else if (fc == N32) {
- // Is f a crossface?
- if (front != (triface *) NULL) {
- // (6) Is any obstacle face (abd, or abe, ...) flipable?
- spintet = *flipface;
- while (fnextself(spintet)) {
- if (apex(spintet) == apex(*flipface)) break;
- // Check if spintet is flipable, no recursive.
- if (constrainedflip(&spintet, NULL, flipque)) {
- // One obstacle face has been flipped.
- return true;
- }
- // Unflipable. Go to the next obstacle face.
- findedge(&spintet, org(*flipface), dest(*flipface));
- }
- }
- }
- }
-
- // f is unflipable. Is f a crossface?
- if (front != (triface *) NULL) {
- // Look if there is another crossface.
- pa = org(*front);
- pb = dest(*front);
- pc = apex(*front);
- // sym(*flipface, symface);
- // Have we reach the end of abc (We've started from edge ab).
- if (oppo(symface) != pc) {
- adjustedgering(symface, CCW);
- for (i = 0; i < 3; i++) {
- fnext(symface, spintet);
- // Is c ahead of this face?
- sign = orient3d(org(spintet), dest(spintet), apex(spintet), pc);
- if (sign < 0.0) {
- if (tritritest(&spintet, pa, pb, pc)) {
- if (b->verbose > 2) {
- printf(" Next crossface (%d, %d, %d).\n",
- pointmark(org(spintet)), pointmark(dest(spintet)),
- pointmark(apex(spintet)));
- }
- return constrainedflip(&spintet, front, flipque);
- // return constrainedflip(&spintet, NULL, flipque);
- }
- }
- enextself(symface);
- }
- }
- }
- return false;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// recoverfront() Recover a missing front by flips. //
-// //
-// 'front' f is missing in D - it was crossed by faces of D. The cross faces //
-// may be flippable, so f can be recovered by flipping them away. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::recoverfront(triface* front, list* newtetlist, queue* flipque)
-{
- triface idfront, starttet, spintet;
- point pa, pb, pc, pd, ref;
- enum locateresult loc;
- enum finddirectionresult col;
- REAL ori, ori1, ori2, sign;
- int hitbdry;
- int i, j;
-
- // Find an existing edge of f in D to start with.
- for (i = 0; i < 3; i++) {
- pa = org(*front);
- pb = dest(*front);
- // Get a tet for searching.
- idfront = recenttet;
- // Make sure the tet is valid (flip32() may kill a tet).
- if (isdead(&idfront)) {
- // The tet is dead. Get a live tet in D. !!!
- for (j = 0; j < newtetlist->len(); j++) {
- recenttet = * (triface *)(* newtetlist)[j];
- if (!isdead(&recenttet)) break;
- }
- assert(j < newtetlist->len());
- }
- loc = preciselocate(pa, &idfront, (long) newtetlist->len());
- if (loc != ONVERTEX) {
- // Do a brute-force search in D.
- for (j = 0; j < newtetlist->len(); j++) {
- idfront = * (triface *)(* newtetlist)[j];
- if (isdead(&idfront)) continue;
- if (findorg(&idfront, pa)) break;
- }
- assert(j < newtetlist->len()); // a must belong to one tet.
- }
- recenttet = idfront;
- // Search for a tet having edge ab.
- col = finddirection(&idfront, pb, (long) newtetlist->len());
- if (col == BELOWHULL) {
- // Do a brute-force search in D.
- for (j = 0; j < newtetlist->len(); j++) {
- idfront = * (triface *)(* newtetlist)[j];
- if (isdead(&idfront)) continue;
- if (findorg(&idfront, pa)) {
- assert(org(idfront) == pa);
- if (dest(idfront) == pb) {
- col = RIGHTCOLLINEAR; break;
- } else if (apex(idfront) == pb) {
- col = LEFTCOLLINEAR; break;
- } else if (oppo(idfront) == pb) {
- col = TOPCOLLINEAR; break;
- }
- }
- }
- }
- if (col == RIGHTCOLLINEAR) {
- // b is just the destination.
- } else if (col == LEFTCOLLINEAR) {
- enext2self(idfront);
- esymself(idfront);
- } else if (col == TOPCOLLINEAR) {
- fnextself(idfront);
- enext2self(idfront);
- esymself(idfront);
- }
- if (dest(idfront) == pb) break; // Found.
- // Missing. Go to the next edge of f.
- enextself(*front);
- }
- if (i == 3) {
- // All three edges of f are missing - unrecoverable.
- return false;
- }
-
- // Search for a tet having f (abc).
- pc = apex(*front);
- spintet = idfront;
- hitbdry = 0;
- do {
- if (apex(spintet) == pc) {
- // Found abc. Insert an auxilary subface s at idfront.
- insertauxsubface(front, &spintet);
- return true;
- }
- if (!fnextself(spintet)) {
- hitbdry ++;
- if (hitbdry < 2) {
- esym(idfront, spintet);
- if (!fnextself(spintet)) {
- hitbdry ++;
- }
- }
- }
- if (apex(spintet) == apex(idfront)) break;
- } while (hitbdry < 2);
-
- // Search for a crossing face to flip.
- pd = apex(idfront);
- assert(pd != pc);
- // Decide the orientation of d with abc.
- ori = orient3d(pa, pb, pc, pd);
- if (ori < 0.0) {
- // d is above abc. Rotate downwards.
- esym(idfront, starttet);
- sign = -1.0;
- } else if (ori > 0.0) {
- // d is below abc. Rotate upwards.
- starttet = idfront;
- sign = 1.0;
- } else {
- assert(ori == 0.0);
- // d is coplanar with abc. Do abc and abd intersect?
- ref = oppo(idfront);
- ori1 = orient3d(pa, pb, ref, pc);
- ori2 = orient3d(pa, pb, ref, pd);
- assert(ori1 * ori2 != 0.0);
- if (ori1 * ori2 > 0) {
- // abc and abd intersect. There're two possible intersections:
- // ad and bc, or ac and bd. Find it out.
- ori1 = orient3d(pb, pc, ref, pd);
- ori2 = orient3d(pb, pc, ref, pa);
- assert(ori1 * ori2 != 0.0);
- if (ori1 * ori2 > 0) {
- // ac intersects bd.
- enextself(idfront); // go to edge bd.
- } else {
- // ad intersects bc.
- enext2self(idfront); // go to edge ad.
- }
- adjustedgering(idfront, CCW);
- fnextself(idfront); // face ade or bce need a 4-to-4 flip.
- if (b->verbose > 2) {
- printf(" Get crossface (%d, %d, %d).\n", pointmark(org(idfront)),
- pointmark(dest(idfront)), pointmark(apex(idfront)));
- }
- if (constrainedflip(&idfront, front, flipque)) {
- // A crossface has been flipped. Continue to recover f.
- return recoverfront(front, newtetlist, flipque);
- }
- // Unable to recover f.
- return false; // sign = 0.0;
- } else {
- // Not intersect. We can go either direction.
- starttet = idfront;
- if (fnextself(starttet)) {
- // Choose to rotate upwards.
- sign = 1.0;
- } else {
- // Hit convex hull. Choose to rotate downwrads.
- esym(idfront, starttet);
- sign = -1.0;
- }
- }
- }
-
- assert(sign != 0.0);
- if (sign == -1) {
- // The edge ab has be changed. Reverse it.
- pa = org(starttet);
- pb = dest(starttet);
- // The sign has been reversed as well.
- sign = -sign;
- }
- // Rotate face abd around edge ab. Moreover, we've chosen the rotate
- // direction such that no convex hull face will be reach.
- spintet = starttet;
- while (fnextself(spintet)) {
- pd = apex(spintet);
- assert(pd != pc);
- // Check if the orientation of d (with abc) has changed.
- ori = orient3d(pa, pb, pc, pd);
- if (ori == 0.0) {
- // abc and abd must coplanar intersect (4-to-4 flip is needed).
- ref = oppo(spintet);
- ori1 = orient3d(pb, pc, ref, pd);
- ori2 = orient3d(pb, pc, ref, pa);
- assert(ori1 * ori2 != 0.0);
- if (ori1 * ori2 > 0) {
- // ac intersects bd.
- enextself(spintet); // go to edge bd.
- } else {
- // ad intersects bc.
- enext2self(spintet); // go to edge ad.
- }
- adjustedgering(spintet, CCW);
- fnextself(spintet); // face ade or bce need a 4-to-4 flip.
- if (b->verbose > 2) {
- printf(" Get crossface (%d, %d, %d).\n", pointmark(org(spintet)),
- pointmark(dest(spintet)), pointmark(apex(spintet)));
- }
- if (constrainedflip(&spintet, front, flipque)) {
- // A crossface has been flipped. Continue to recover f.
- return recoverfront(front, newtetlist, flipque);
- }
- // Unable to recover f.
- return false; // sign = 0.0;
- } else if (ori * sign < 0.0) {
- // Sign has changed. The face dea or deb must cross abc.
- adjustedgering(spintet, CCW);
- enextself(spintet);
- for (i = 0; i < 2; i++) {
- // Get the face dea or deb.
- fnext(spintet, starttet);
- if (tritritest(&starttet, pa, pb, pc)) {
- if (b->verbose > 2) {
- printf(" Get crossface (%d, %d, %d).\n",
- pointmark(org(starttet)), pointmark(dest(starttet)),
- pointmark(apex(starttet)));
- }
- if (constrainedflip(&starttet, front, flipque)) {
- // A crossface has been flipped. Continue to recover f.
- return recoverfront(front, newtetlist, flipque);
- }
- }
- enextself(spintet);
- }
- // Unable to recover f.
- return false;
- }
- }
- // Impossible to be here.
- assert(0);
- return false;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// repairflips() Flip non-Delaunay and non-constrained faces. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::repairflips(queue* flipque)
-{
- badface *qface;
- triface flipface, symface, spintet;
- face checksh;
- point pa, pb, pc, pd, pe;
- enum fliptype fc;
- REAL sign;
- long flipcount;
- bool doflip;
- int ia, ib, ic, id, ie;
- int i;
-
- if (b->verbose > 1) {
- printf(" Repair flip %ld faces.\n", flipque->len());
- }
- flipcount = flip23s + flip32s + flip22s + flip44s;
- // Loop until the queue is empty.
- while (!flipque->empty()) {
- qface = (badface *) flipque->pop();
- flipface = qface->tt;
- // Check the validity of this face.
- if (isdead(&flipface) || flipface.tet == dummytet ||
- (org(flipface) != qface->forg) ||
- (dest(flipface) != qface->fdest) ||
- (apex(flipface) != qface->fapex) ||
- (oppo(flipface) == (point) NULL)) continue;
- // (1) Is f protected by an (auxilary) subface?
- tspivot(flipface, checksh);
- if (checksh.sh != dummysh) continue;
- // (2) Is f on the convex hull?
- sym(flipface, symface);
- if (symface.tet == dummytet) continue;
- // For positive orientation that insphere() test requires.
- adjustedgering(flipface, CW);
- pa = org(flipface);
- pb = dest(flipface);
- pc = apex(flipface);
- pd = oppo(flipface);
- pe = oppo(symface);
- // if (symbolic) {
- ia = pointmark(pa);
- ib = pointmark(pb);
- ic = pointmark(pc);
- id = pointmark(pd);
- ie = pointmark(pe);
- sign = insphere_sos(pa, pb, pc, pd, pe, ia, ib, ic, id, ie);
- assert(sign != 0.0);
- // } else {
- // sign = insphere(pa, pb, pc, pd, pe);
- // }
- if (sign > 0.0) {
- // f is non-lcally Delaunay. Get the fliptype of f.
- checksubfaces = 0; // switch off subface test.
- fc = categorizeface(flipface);
- checksubfaces = 1; // switch on subface test.
- if (fc == T23) {
- doflip = true;
- // Avoid to create a nearly degenerate tet.
- /* pc = oppo(flipface);
- pd = oppo(symface);
- adjustedgering(flipface, CCW);
- for (i = 0; i < 3; i++) {
- pa = org(flipface);
- pb = dest(flipface);
- ori = orient3d(pa, pb, pc, pd);
- if (iscoplanar(pa, pb, pc, pd, ori, b->epsilon)) {
- doflip = false; break;
- }
- enextself(flipface);
- } */
- if (doflip) {
- flip23(&flipface, flipque);
- }
- } else if (fc == T32) {
- // (4) Is abd, or abe protected?
- doflip = true;
- spintet = flipface;
- for (i = 0; i < 2; i++) {
- fnextself(spintet);
- tspivot(spintet, checksh);
- if (checksh.sh != dummysh) {
- doflip = false; break; // f is protected. Unflipable.
- }
- }
- if (doflip) {
- flip32(&flipface, flipque);
- }
- } else if (fc == T22 || fc == T44) {
- // (5) Is abd, abe, or abf protected?
- doflip = true;
- if (fc == T22) {
- for (i = 0; i < 2; i++) {
- spintet = flipface;
- if (i == 1) {
- esymself(spintet);
- }
- fnextself(spintet);
- tspivot(spintet, checksh);
- if (checksh.sh != dummysh) {
- doflip = false; break; // f is protected. Unflipable.
- }
- }
- } else if (fc == T44) {
- spintet = flipface;
- for (i = 0; i < 3; i++) {
- fnextself(spintet);
- tspivot(spintet, checksh);
- if (checksh.sh != dummysh) {
- doflip = false; break; // f is protected. Unflipable.
- }
- }
- }
- if (doflip) {
- flip22(&flipface, flipque);
- }
- }
- }
- }
- flipcount = flip23s + flip32s + flip22s + flip44s - flipcount;
- if (b->verbose > 1) {
- printf(" %ld flips.\n", flipcount);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// constrainedcavity() Tetrahedralize a cavity by constrained tetrahedra. //
-// //
-// The cavity C is bounded by faces F in 'floorlist' and 'ceillist'. 'ptlist'//
-// V is the set of vertices of C. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::constrainedcavity(triface* oldtet, list* floorlist,
- list* ceillist, list* ptlist, list* frontlist, list* misfrontlist,
- list* newtetlist, queue* flipque)
-{
- triface misfront, newtet;
- long facenum;
- int i;
-
- if (b->verbose > 1) {
- printf(" Constrained cavity (%d floors, %d ceilings, %d vertices).\n",
- floorlist->len(), ceillist->len(), ptlist->len());
- }
-
- // symbolic = 1;
-
- // Initialize the cavity C.
- initializecavity(floorlist, ceillist, frontlist);
- // Form the D of the vertices of C.
- delaunizecavvertices(oldtet, ptlist, NULL, newtetlist, flipque);
-
- // Identify faces of C in D.
- if (!identifyfronts(frontlist, misfrontlist, newtetlist)) {
- // Some faces are missing.
- recenttet = * (triface *)(* newtetlist)[0];
- assert((recenttet.tet != dummytet) && !isdead(&recenttet));
- // Try to recover missing faces by flips.
- do {
- facenum = misfrontlist->len();
- for (i = 0; i < misfrontlist->len(); i++) {
- // Get a missing front f.
- misfront = * (triface *)(* misfrontlist)[i];
- // Let f face toward the inside of C.
- adjustedgering(misfront, CW);
- if (b->verbose > 1) {
- printf(" Recover face (%d, %d, %d).\n", pointmark(org(misfront)),
- pointmark(dest(misfront)), pointmark(apex(misfront)));
- }
- if (recoverfront(&misfront, newtetlist, flipque)) {
- // f has been recovered.
- frontlist->append(&misfront);
- misfrontlist->del(i, 0); i--;
- }
- // Flip non-locally non-constrained Delaunay faces.
- repairflips(flipque);
- }
- // Have all faces been recovered?
- if (misfrontlist->len() == 0) break;
- // No! There are still un-recovered faces. Continue the loop if any
- // face has been recovered.
- } while (misfrontlist->len() < facenum);
- // Retrieve new tets and purge dead tets in D.
- retrievenewtets(newtetlist);
- }
-
- // symbolic = 0;
-
- if (misfrontlist->len() == 0) {
- // All fronts have identified in D. Get the shape of C by removing out
- // tets of C. 'misfrontlist' is reused for removing out tets.
- // Don't do flip since the new tets may get deleted later.
- carvecavity(newtetlist, misfrontlist, NULL);
- // Recover locally Delaunay faces.
- // flip(flipque, NULL);
- return true;
- } else {
- // Fail to tetrahedralize C.
- // Remove aux subfaces.
- detachauxsubfaces(newtetlist);
- // Remove new tets.
- for (i = 0; i < newtetlist->len(); i++) {
- newtet = * (triface *)(* newtetlist)[i];
- assert(!isdead(&newtet));
- tetrahedrondealloc(newtet.tet);
- }
- newtetlist->clear();
- // Restore faces of C in frontlist.
- for (i = 0; i < misfrontlist->len(); i++) {
- misfront = * (triface *)(* misfrontlist)[i];
- frontlist->append(&misfront);
- }
- return false;
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// expandsteinercavity() Expand the cavity of a Steiner point. //
-// //
-// Expand the cavity C if there fronts (except fronts having subfaces) which //
-// are either (nearly) coplanar or invisible by the Steiner point. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::expandsteinercavity(point steinpt, REAL eps, list* frontlist,
- list* oldtetlist)
-{
- triface front, symfront, newfront, oldfront;
- face frontsh;
- point pa, pb, pc;
- REAL ori;
- bool expflag, newflag;
- int i, j;
-
- do {
- expflag = false;
- for (i = 0; i < frontlist->len(); i++) {
- // Get a front f.
- front = * (triface *)(* frontlist)[i];
- // f can be expanded if it is not a subface.
- tspivot(front, frontsh);
- if (frontsh.sh == dummysh) {
- // Let f face to the inside of C.
- adjustedgering(front, CW);
- pa = org(front);
- pb = dest(front);
- pc = apex(front);
- ori = orient3d(pa, pb, pc, steinpt);
- if (ori != 0.0) {
- if (iscoplanar(pa, pb, pc, steinpt, ori, eps)) {
- ori = 0.0; // f is nearly coplanar with p.
- }
- }
- if (ori >= 0.0) {
- // f is either invisible or coplanar with p.
- if (b->verbose > 2) {
- printf(" Remove front (%d, %d, %d).\n", pointmark(pa),
- pointmark(pb), pointmark(pc));
- }
- frontlist->del(i, 1);
- expflag = true;
- break;
- }
- }
- }
- if (expflag) {
- assert(!infected(front) && (oppo(front) != NULL));
- // Expand C at f by including new fronts.
- adjustedgering(front, CCW);
- for (i = 0; i < 3; i++) {
- newflag = true;
- // Get a new boundary n of the cavity.
- fnext(front, symfront);
- tspivot(symfront, frontsh);
- sym(symfront, newfront);
- if (frontsh.sh == dummysh) {
- assert(newfront.tet != dummytet);
- // Is n a front of the unexp. cavity?
- if (infected(newfront)) {
- for (j = 0; j < frontlist->len(); j++) {
- oldfront = * (triface *)(* frontlist)[j];
- if ((oldfront.tet == symfront.tet) &&
- (oldfront.loc == symfront.loc)) {
- // n is not a front anymore.
- if (b->verbose > 2) {
- printf(" Remove front (%d, %d, %d).\n",
- pointmark(org(oldfront)), pointmark(dest(oldfront)),
- pointmark(apex(oldfront)));
- }
- frontlist->del(j, 1);
- newflag = false;
- break;
- }
- }
- }
- } else {
- // n is a subface.
- if (newfront.tet == dummytet) {
- sesymself(frontsh);
- // Create a fake tet to hold n.
- maketetrahedron(&newfront);
- setorg(newfront, sorg(frontsh));
- setdest(newfront, sdest(frontsh));
- setapex(newfront, sapex(frontsh));
- setoppo(newfront, (point) NULL);
- tsbond(newfront, frontsh);
- } else {
- // n should not be a front of cavity yet.
- assert(!infected(newfront));
- }
- }
- if (newflag) {
- if (b->verbose > 2) {
- printf(" Add front (%d, %d, %d).\n", pointmark(org(newfront)),
- pointmark(dest(newfront)), pointmark(apex(newfront)));
- }
- frontlist->append(&newfront);
- }
- enextself(front);
- }
- // Add f into oldtetlist (to be deleted).
- infect(front);
- oldtetlist->append(&front);
- expcavcount++;
- }
- } while (expflag);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// findrelocatepoint() Find new location for relocating a point. //
-// //
-// 'frontlist' contains the boundary faces of the cavity C. Some fronts are //
-// visible by 'stpt' p, some are coplanar with p. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::findrelocatepoint(point sp, point np, REAL* n,
- list* frontlist, list* oldtetlist)
-{
- triface front;
- point pa, pb, pc;
- REAL tp[3], tvol, mvol;
- REAL ori, eps;
- bool visible;
- int i, j, k;
-
- if (b->verbose > 1) {
- printf(" Find new location for point %d.\n", pointmark(sp));
- }
-
- // Avoid compilation warnings.
- tvol = mvol = 0.0;
- visible = false;
-
- eps = b->epsilon;
- // Initialize np far enough from p (outside C).
- for (i = 0; i < 3; i++) np[i] = sp[i] + longest * n[i];
- // Let tp = np;
- for (i = 0; i < 3; i++) tp[i] = np[i];
- // Interation to adjust np until it is visible by all fronts.
- j = 0;
- do {
- for (i = 0; i < frontlist->len(); i++) {
- // Get a front face f.
- front = * (triface *)(* frontlist)[i];
- // Let f face to the interior of C.
- adjustedgering(front, CW);
- pa = org(front);
- pb = dest(front);
- pc = apex(front);
- ori = orient3d(pa, pb, pc, np);
- visible = (ori < 0.0);
- if (!visible) {
- // A front is invisible by np. Move it towards p along the normal.
- for (i = 0; i < 3; i++) np[i] = sp[i] + 0.5 * (sp[i] - np[i]);
- // Failed if tp = np.
- if ((tp[0] == np[0]) && (tp[1] == np[1]) && (tp[2] == np[2])) {
- // Try to expand the cavity.
- expandsteinercavity(sp, eps, frontlist, oldtetlist);
- eps *= 10.0;
- if (eps > b->epsilon * 1000.0) {
- // printf("Internal error: Fail to relocate pt %d.\n",pointmark(sp));
- // internalerror();
- return false;
- }
- // Restart the point relocation.
- for (i = 0; i < 3; i++) np[i] = sp[i] + longest * n[i];
- }
- if (j % 2) {
- // Set tp = np (at every 2 steps) to catch the stop state.
- for (i = 0; i < 3; i++) tp[i] = np[i];
- }
- break;
- } else {
- // Save the smallest volume.
- if (i == 0) {
- mvol = fabs(ori);
- } else {
- mvol = fabs(ori) < mvol ? fabs(ori) : mvol;
- }
- }
- }
- j++;
- } while (!visible);
-
- if (b->verbose > 1) {
- printf(" %d iterations. minvol = %.12g.\n", j, mvol);
- }
-
- // Continue to adjust np until the minimal volume of tets formed by
- // fronts and np doesn't increase (all fronts are visible by np).
- k = 0;
- do {
- j = 0;
- do {
- if (k == 0) {
- // Initial tp := np + 0.9 * (p - np). Move toward p.
- for (i = 0; i < 3; i++) tp[i] = sp[i] + 0.9 * (np[i] - sp[i]);
- } else {
- // Initial tp := np + 1.1 * (p - np). Move away from p.
- for (i = 0; i < 3; i++) tp[i] = sp[i] + 1.1 * (np[i] - sp[i]);
- }
- // Get the minial volume formed by tp with one of the fronts.
- for (i = 0; i < frontlist->len(); i++) {
- // Get a front face f.
- front = * (triface *)(* frontlist)[i];
- // Let f face to the interior of C.
- adjustedgering(front, CW);
- pa = org(front);
- pb = dest(front);
- pc = apex(front);
- ori = orient3d(pa, pb, pc, tp);
- visible = (ori < 0.0);
- if (visible) {
- // Save the smallest volume.
- if (i == 0) {
- tvol = fabs(ori);
- } else {
- tvol = fabs(ori) < tvol ? fabs(ori) : tvol;
- }
- } else {
- // A front is invisible by tp. Stop.
- tvol = 0.0;
- break;
- }
- }
- if (tvol > mvol) {
- // Get a larger minimal volume.
- for (i = 0; i < 3; i++) np[i] = tp[i];
- mvol = tvol;
- } else {
- // Minimal volume decreases. Stop.
- break;
- }
- // Continue to adjust np.
- j++;
- } while (true);
- // Has np been adjusted?
- if (j > 0) break;
- // Try to move np to anoter direction.
- k++;
- } while (k < 2);
-
- if (b->verbose > 1) {
- printf(" %d adjust iterations. minvol = %.12g.\n", j, mvol);
- }
- return true;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// relocatepoint() Relocate a point into the cavity. //
-// //
-// 'frontlist' contains the boundary faces of the cavity C. All fronts must //
-// be visible by 'steinpt'. Some fronts may hold by 'fake' tets (they are //
-// hull faces). Fake tets will be removed when they're finished. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::relocatepoint(point steinpt, triface* oldtet, list* frontlist,
- list* newtetlist, queue* flipque)
-{
- triface front, newtet, newface, neightet;
- face checksh;
- point pa, pb;
- REAL attrib, volume;
- bool bdflag;
- int i, j, k, l;
-
- if (b->verbose > 1) {
- printf(" Insert Steiner point (%.12g, %.12g, %.12g) %d.\n",
- steinpt[0], steinpt[1], steinpt[2], pointmark(steinpt));
- }
- // Clear the list first.
- newtetlist->clear();
-
- // Create the tets formed by fronts and 'steinpt'.
- for (i = 0; i < frontlist->len(); i++) {
- // Get a front f.
- front = * (triface *)(* frontlist)[i];
- // Let f face inside C. (f is a face of tet adjacent to C).
- adjustedgering(front, CW);
- if (b->verbose > 2) {
- printf(" Get front (%d, %d, %d).\n", pointmark(org(front)),
- pointmark(dest(front)), pointmark(apex(front)));
- }
- maketetrahedron(&newtet);
- newtetlist->append(&newtet);
- setorg(newtet, org(front));
- setdest(newtet, dest(front));
- setapex(newtet, apex(front));
- setoppo(newtet, steinpt);
- if (oldtet != (triface *) NULL) {
- for (j = 0; j < in->numberoftetrahedronattributes; j++) {
- attrib = elemattribute(oldtet->tet, j);
- setelemattribute(newtet.tet, j, attrib);
- }
- if (b->varvolume) {
- volume = volumebound(oldtet->tet);
- setvolumebound(newtet.tet, volume);
- }
- }
- // 'front' may be a 'fake' tet.
- tspivot(front, checksh);
- if (oppo(front) == (point) NULL) {
- if (checksh.sh != dummysh) {
- stdissolve(checksh);
- }
- // Dealloc the 'fake' tet.
- tetrahedrondealloc(front.tet);
- // This side (newtet) is a boundary face, let 'dummytet' bond to it.
- // Otherwise, 'dummytet' may point to a dead tetrahedron after the
- // old cavity tets are removed.
- dummytet[0] = encode(newtet);
- } else {
- // Bond two tetrahedra, also dissolve the old bond at 'front'.
- bond(newtet, front);
- }
- if (checksh.sh != dummysh) {
- sesymself(checksh);
- tsbond(newtet, checksh);
- }
- if (flipque != (queue *) NULL) {
- // f may be non-locally Delaunay and flipable.
- enqueueflipface(newtet, flipque);
- }
- // The three neighbors are open. Will be finished later.
- }
-
- // Connect new tets in C. All connecting faces must contain 'steinpt'.
- for (i = 0; i < newtetlist->len(); i++) {
- newtet = * (triface *)(* newtetlist)[i];
- newtet.ver = 0;
- for (j = 0; j < 3; j++) {
- fnext(newtet, newface);
- sym(newface, neightet);
- if (neightet.tet == dummytet) {
- // Find a neightet to connect it.
- bdflag = false;
- pa = org(newface);
- pb = dest(newface);
- assert(apex(newface) == steinpt);
- for (k = i + 1; k < newtetlist->len() && !bdflag; k++) {
- neightet = * (triface *)(* newtetlist)[k];
- neightet.ver = 0;
- for (l = 0; l < 3; l++) {
- if ((org(neightet) == pa && dest(neightet) == pb) ||
- (org(neightet) == pb && dest(neightet) == pa)) {
- // Find the neighbor.
- fnextself(neightet);
- assert(apex(neightet) == steinpt);
- // Now neightet is a face same as newface, bond them.
- bond(newface, neightet);
- bdflag = true;
- break;
- }
- enextself(neightet);
- }
- }
- assert(bdflag);
- }
- enextself(newtet);
- }
- // Let the corners of newtet point to it for fast searching.
- pa = org(newtet);
- setpoint2tet(pa, encode(newtet));
- pa = dest(newtet);
- setpoint2tet(pa, encode(newtet));
- pa = apex(newtet);
- setpoint2tet(pa, encode(newtet));
- pa = oppo(newtet);
- setpoint2tet(pa, encode(newtet));
- }
-
- if (flipque != (queue *) NULL) {
- // Recover locally Delaunay faces.
- flip(flipque, NULL);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// findcollapseedge() Find collapseable edge to suppress an endpoint. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::findcollapseedge(point suppt, point *conpt, list* oldtetlist,
- list* ptlist)
-{
- triface front;
- point pt, pa, pb, pc;
- REAL *lenarray, ltmp, ori;
- bool visflag;
- int *idxarray, itmp;
- int n, i, j;
-
- if (b->verbose > 2) {
- printf(" Search an edge (in %d edges) for collapse %d.\n",
- ptlist->len(), pointmark(suppt));
- }
-
- // Candidate edges are p to the points of B(p) (in 'ptlist').
- n = ptlist->len();
- lenarray = new REAL[n];
- idxarray = new int[n];
- // Sort the points of B(p) by distance to p.
- for (i = 0; i < n; i++) {
- pt = * (point *)(* ptlist)[i];
- lenarray[i] = distance(suppt, pt);
- idxarray[i] = i;
- }
- // Bubble sort.
- for (i = 0; i < n - 1; i++) {
- for (j = 0; j < n - 1 - i; j++) {
- if (lenarray[j + 1] < lenarray[j]) { // compare the two neighbors
- ltmp = lenarray[j]; // swap a[j] and a[j + 1]
- lenarray[j] = lenarray[j + 1];
- lenarray[j + 1] = ltmp;
- itmp = idxarray[j]; // swap a[j] and a[j + 1]
- idxarray[j] = idxarray[j + 1];
- idxarray[j + 1] = itmp;
- }
- }
- }
- // For each point q of B(p), test if the edge (p, q) can be collapseed.
- for (i = 0; i < n; i++) {
- pt = * (point *)(* ptlist)[idxarray[i]];
- // Is q visible by faces of B(p) not with q as a vertex.
- lenarray[i] = 0.0; // zero volume.
- visflag = true;
- for (j = 0; j < oldtetlist->len() && visflag; j++) {
- front = * (triface *)(* oldtetlist)[j];
- // Let f face to inside of B(p).
- adjustedgering(front, CCW);
- pa = org(front);
- pb = dest(front);
- pc = apex(front);
- // Is f contains q?
- if ((pa != pt) && (pb != pt) && (pc != pt)) {
- ori = orient3d(pa, pb, pc, pt);
- if (ori != 0.0) {
- if (iscoplanar(pa, pb, pc, pt, ori, b->epsilon * 1e+2)) ori = 0.0;
- }
- visflag = ori < 0.0;
- if (visflag) {
- // Visible, set the smallest volume.
- if (j == 0) {
- lenarray[i] = fabs(ori);
- } else {
- lenarray[i] = fabs(ori) < lenarray[i] ? fabs(ori) : lenarray[i];
- }
- } else {
- // Invisible. Do not collapse (p, q).
- lenarray[i] = 0.0;
- }
- }
- }
- if ((b->verbose > 2) && visflag) {
- printf(" Got candidate %d vol(%g).\n", pointmark(pt), lenarray[i]);
- }
- }
-
- // Select the largest non-zero volume (result in ltmp).
- ltmp = lenarray[0];
- itmp = idxarray[0];
- for (i = 1; i < n; i++) {
- if (lenarray[i] != 0.0) {
- if (lenarray[i] > ltmp) {
- ltmp = lenarray[i];
- itmp = idxarray[i]; // The index to find the point.
- }
- }
- }
-
- delete [] lenarray;
- delete [] idxarray;
-
- if (ltmp == 0.0) {
- // No edge can be collapseed.
- *conpt = (point) NULL;
- return false;
- } else {
- pt = * (point *)(* ptlist)[itmp];
- *conpt = pt;
- return true;
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// collapseedge() Remove a point by edge collapse. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::collapseedge(point suppt, point conpt, list* oldtetlist,
- list* deadtetlist)
-{
- triface oldtet, deadtet;
- triface adjtet1, adjtet2;
- face adjsh;
- point pa, pb, pc;
- int i, j;
-
- if (b->verbose > 2) {
- printf(" Collapse edge (%d,%d).\n", pointmark(suppt), pointmark(conpt));
- }
-
- // Loop in B(p), replace p with np, queue dead tets, uninfect old tets.
- for (i = 0; i < oldtetlist->len(); i++) {
- oldtet = * (triface *)(* oldtetlist)[i]; // assert(infected(oldtet));
- uninfect(oldtet);
- pa = org(oldtet);
- pb = dest(oldtet);
- pc = apex(oldtet);
- assert(oppo(oldtet) == suppt);
- setoppo(oldtet, conpt);
- if ((pa == conpt) || (pb == conpt) || (pc == conpt)) {
- deadtetlist->append(&oldtet); // a collpased tet.
- }
- }
- // Loop in deadtetlist, glue adjacent tets of dead tets.
- for (i = 0; i < deadtetlist->len(); i++) {
- deadtet = * (triface *)(* deadtetlist)[i];
- // Get the adjacent tet n1 (outside B(p)).
- sym(deadtet, adjtet1);
- tspivot(deadtet, adjsh);
- // Find the edge in deadtet opposite to conpt.
- adjustedgering(deadtet, CCW);
- for (j = 0; j < 3; j++) {
- if (apex(deadtet) == conpt) break;
- enextself(deadtet);
- }
- assert(j < 3);
- // Get another adjacent tet n2.
- fnext(deadtet, adjtet2);
- symself(adjtet2);
- assert(adjtet2.tet != dummytet); // n2 is inside B(p).
- if (adjtet1.tet != dummytet) {
- bond(adjtet1, adjtet2); // Bond n1 <--> n2.
- } else {
- dissolve(adjtet2); // Dissolve at n2.
- dummytet[0] = encode(adjtet2); // Let dummytet holds n2.
- }
- if (adjsh.sh != dummysh) {
- tsbond(adjtet2, adjsh); // Bond s <--> n2.
- }
- // Collapse deadtet.
- tetrahedrondealloc(deadtet.tet);
- }
- deadtetlist->clear();
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// deallocfaketets() Deleted fake tets at fronts. //
-// //
-// This routine is only called when the findrelocatepoint() routine fails. //
-// In other cases, the fake tets are removed automatically in carvecavity() //
-// or relocatepoint(). //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::deallocfaketets(list* frontlist)
-{
- triface front, neightet;
- face checksh;
- bool infectflag;
- int i;
-
- for (i = 0; i < frontlist->len(); i++) {
- // Get a front f.
- front = * (triface *)(* frontlist)[i];
- // Let f face inside C. (f is a face of tet adjacent to C).
- adjustedgering(front, CW);
- sym(front, neightet);
- tspivot(front, checksh);
- if (oppo(front) == (point) NULL) {
- if (b->verbose > 2) {
- printf(" Get fake tet (%d, %d, %d).\n", pointmark(org(front)),
- pointmark(dest(front)), pointmark(apex(front)));
- }
- if (neightet.tet != dummytet) {
- // The neightet may be infected. After dissolve it, the infect flag
- // will be lost. Save the flag and restore it later.
- infectflag = infected(neightet);
- dissolve(neightet);
- if (infectflag) {
- infect(neightet);
- }
- }
- if (checksh.sh != dummysh) {
- infectflag = sinfected(checksh);
- stdissolve(checksh);
- if (infectflag) {
- sinfect(checksh);
- }
- }
- // Dealloc the 'fake' tet.
- tetrahedrondealloc(front.tet);
- // If 'neightet' is a hull face, let 'dummytet' bond to it. It is
- // a 'dummytet' when this front was created from a new subface.
- // In such case, it should not be bounded.
- if (neightet.tet != dummytet) {
- dummytet[0] = encode(neightet);
- }
- }
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// restorepolyhedron() Restore the tetrahedralization in a polyhedron. //
-// //
-// This routine is only called when the operation of suppressing a point is //
-// aborted (eg., findrelocatepoint() routine fails). The polyhedron has been //
-// remeshed by new tets. This routine restore the old tets in it. //
-// //
-// 'oldtetlist' contains the list of old tets. Each old tet t_o assumes that //
-// it still connects to a tet t_b of the mesh, however, t_b does not connect //
-// to t_o, this routine resets the connection such that t_b <--> t_o. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::restorepolyhedron(list* oldtetlist)
-{
- triface oldtet, neightet, neineitet;
- face checksh;
- int i;
-
- for (i = 0; i < oldtetlist->len(); i++) {
- // Get an old tet t_o.
- oldtet = * (triface *)(* oldtetlist)[i];
- // Check the four sides of t_o.
- for (oldtet.loc = 0; oldtet.loc < 4; oldtet.loc++) {
- sym(oldtet, neightet);
- tspivot(oldtet, checksh);
- if (neightet.tet != dummytet) {
- sym(neightet, neineitet);
- if (neineitet.tet != oldtet.tet) {
- // This face of t_o is a boundary of P.
- bond(neightet, oldtet);
- if (checksh.sh != dummysh) {
- tsbond(oldtet, checksh);
- }
- }
- } else {
- // t_o has a hull face. It should be the boundary of P.
-#ifdef SELF_CHECK
- assert(checksh.sh != dummysh);
- stpivot(checksh, neineitet);
- assert(neineitet.tet != oldtet.tet);
-#endif
- tsbond(oldtet, checksh);
- // Let dummytet[0] points to it.
- dummytet[0] = encode(oldtet);
- }
- }
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// suppressfacetpoint() Suppress a point inside a facet. //
-// //
-// The point p inside a facet F will be suppressed from F by either being //
-// deleted from the mesh or being relocated into the volume. //
-// //
-// 'supsh' is a subface f of F, and p = sapex(f); the other parameters are //
-// working lists which are empty at the beginning and the end. //
-// //
-// 'optflag' is used for mesh optimization. If it is set, after removing p, //
-// test the object function on each new tet, queue bad tets. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::suppressfacetpoint(face* supsh, list* frontlist,
- list* misfrontlist, list* ptlist, list* conlist, memorypool* viri,
- queue* flipque, bool noreloc, bool optflag)
-{
- list *oldtetlist[2], *newtetlist[2];
- list *oldshlist, *newshlist;
- triface oldtet, newtet;
- face oldsh, newsh;
- point suppt, newpt[2];
- point *cons;
- REAL norm[3];
- bool success;
- int shmark;
- int i, j;
-
- suppt = sapex(*supsh);
- if (b->verbose > 1) {
- printf(" Suppress point %d in facet.\n", pointmark(suppt));
- }
-
- // Initialize working lists, variables.
- for (i = 0; i < 2; i++) {
- oldtetlist[i] = (list *) NULL;
- newtetlist[i] = (list *) NULL;
- newpt[i] = (point) NULL;
- }
- oldshlist = new list(sizeof(face), NULL, 256);
- newshlist = new list(sizeof(face), NULL, 256);
- success = true; // Assume p can be suppressed.
-
- // Find subs of C(p).
- oldshlist->append(supsh);
- formstarpolygon(suppt, oldshlist, ptlist);
- // Get the edges of C(p). They form a closed polygon.
- for (i = 0; i < oldshlist->len(); i++) {
- oldsh = * (face *)(* oldshlist)[i];
- cons = (point *) conlist->append(NULL);
- cons[0] = sorg(oldsh);
- cons[1] = sdest(oldsh);
- }
- // Re-triangulate the old C(p).
- shmark = shellmark(*supsh);
- triangulate(shmark, b->epsilon, ptlist, conlist, 0, NULL, viri, flipque);
- // Get new subs of C(p), remove protected segments.
- retrievenewsubs(newshlist, true);
- // Substitute the old C(p) with the new C(p)
- replacepolygonsubs(oldshlist, newshlist);
- // Clear work lists.
- ptlist->clear();
- conlist->clear();
- flipque->clear();
- viri->restart();
-
- // B(p) (tets with p as a vertex) has been separated into two parts
- // (B_0(p) and B_1(p)) by F. Process them individually.
- for (i = 0; i < 2 && success; i++) {
- if (i == 1) sesymself(*supsh);
- // Get a tet containing p.
- stpivot(*supsh, oldtet);
- // Is this part empty?
- if (oldtet.tet == dummytet) continue;
- // Allocate spaces for storing (old and new) B_i(p).
- oldtetlist[i] = new list(sizeof(triface), NULL, 256);
- newtetlist[i] = new list(sizeof(triface), NULL, 256);
- // Form old B_i(p) in oldtetlist[i].
- assert(!isdead(&oldtet));
- oldtetlist[i]->append(&oldtet);
- formstarpolyhedron(suppt, oldtetlist[i], ptlist, false);
- // Infect the tets in old B_i(p) (they're going to be delete).
- for (j = 0; j < oldtetlist[i]->len(); j++) {
- oldtet = * (triface *)(* (oldtetlist[i]))[j];
- infect(oldtet);
- }
- // Preparation for re-tetrahedralzing old B_i(p).
- orientnewsubs(newshlist, supsh, norm);
- // Tetrahedralize old B_i(p).
- success = constrainedcavity(&oldtet, newshlist, oldtetlist[i], ptlist,
- frontlist, misfrontlist, newtetlist[i], flipque);
- // If p is not suppressed, do relocation if 'noreloc' is not set.
- if (!success && !noreloc) {
- // Try to relocate p into the old B_i(p).
- makepoint(&(newpt[i]));
- success = findrelocatepoint(suppt, newpt[i], norm, frontlist,
- oldtetlist[i]);
- // Initialize newpt = suppt.
- // for (j = 0; j < 3; j++) newpt[i][j] = suppt[j];
- // success = smoothvolpoint(newpt[i], frontlist, true);
- if (success) {
- // p is relocated by newpt[i]. Now insert it. Don't do flip since
- // the new tets may get deleted again.
- relocatepoint(newpt[i], &oldtet, frontlist, newtetlist[i], NULL);
- setpointtype(newpt[i], FREEVOLVERTEX);
- relverts++;
- } else {
- // Fail to relocate p. Clean fake tets and quit this option.
- deallocfaketets(frontlist);
- pointdealloc(newpt[i]);
- newpt[i] = (point) NULL;
- assert(newtetlist[i]->len() == 0);
- }
- }
- if (!success && noreloc) {
- // Failed and no point relocation. Clean fake tets.
- deallocfaketets(frontlist);
- }
- // Clear work lists.
- ptlist->clear();
- frontlist->clear();
- misfrontlist->clear();
- flipque->clear();
- }
-
- if (success) {
- // p has been removed! (Still in the pool).
- setpointtype(suppt, UNUSEDVERTEX);
- unuverts++;
- // Delete old C(p).
- for (i = 0; i < oldshlist->len(); i++) {
- oldsh = * (face *)(* oldshlist)[i];
- if (i == 0) {
- // Update the 'hullsize' if C(p) is on the hull.
- stpivot(oldsh, oldtet);
- if (oldtet.tet != dummytet) {
- sesymself(oldsh);
- stpivot(oldsh, oldtet);
- }
- if (oldtet.tet == dummytet) {
- // A boundary face. Update the 'hullsize'.
- j = oldshlist->len() - newshlist->len();
- assert(j > 0);
- hullsize -= j;
- }
- }
- shellfacedealloc(subfaces, oldsh.sh);
- }
- // Delete old B_i(p).
- for (i = 0; i < 2; i++) {
- if (oldtetlist[i] != (list *) NULL) {
- // Delete tets of the old B_i(p).
- for (j = 0; j < oldtetlist[i]->len(); j++) {
- oldtet = * (triface *)(* (oldtetlist[i]))[j];
- assert(!isdead(&oldtet));
- tetrahedrondealloc(oldtet.tet);
- }
- }
- }
- if (optflag) {
- // Check for new bad-quality tets.
- for (i = 0; i < 2; i++) {
- if (newtetlist[i] != (list *) NULL) {
- for (j = 0; j < newtetlist[i]->len(); j++) {
- newtet = * (triface *)(* (newtetlist[i]))[j];
- if (!isdead(&newtet)) checktet4opt(&newtet, true);
- }
- }
- }
- }
- } else {
- // p is not suppressed. Recover the original state.
- unsupverts++;
- // Restore the old C(p).
- replacepolygonsubs(newshlist, oldshlist);
- // Delete subs of the new C(p)
- for (i = 0; i < newshlist->len(); i++) {
- newsh = * (face *)(* newshlist)[i];
- shellfacedealloc(subfaces, newsh.sh);
- }
- // Restore old B_i(p).
- for (i = 0; i < 2; i++) {
- if (oldtetlist[i] != (list *) NULL) {
- // Uninfect tets of old B_i(p).
- for (j = 0; j < oldtetlist[i]->len(); j++) {
- oldtet = * (triface *)(* (oldtetlist[i]))[j];
- assert(infected(oldtet));
- uninfect(oldtet);
- }
- // Has it been re-meshed?
- if (newtetlist[i]->len() > 0) {
- // Restore the old B_i(p).
- restorepolyhedron(oldtetlist[i]);
- // Delete tets of the new B_i(p);
- for (j = 0; j < newtetlist[i]->len(); j++) {
- newtet = * (triface *)(* (newtetlist[i]))[j];
- // Some new tets may already be deleted (by carvecavity()).
- if (!isdead(&newtet)) {
- tetrahedrondealloc(newtet.tet);
- }
- }
- }
- // Dealloc newpt[i] if it exists.
- if (newpt[i] != (point) NULL) {
- pointdealloc(newpt[i]);
- relverts--;
- }
- }
- }
- }
-
- // Delete work lists.
- delete oldshlist;
- delete newshlist;
- for (i = 0; i < 2; i++) {
- if (oldtetlist[i] != (list *) NULL) {
- delete oldtetlist[i];
- delete newtetlist[i];
- }
- }
-
- return success;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// suppresssegpoint() Suppress a point on a segment. //
-// //
-// The point p on a segment S will be suppressed from S by either being //
-// deleted from the mesh or being relocated into the volume. //
-// //
-// 'supseg' is the segment S, and p = sdest(S); the other parameters are //
-// working lists which are empty at the beginning and the end. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::suppresssegpoint(face* supseg, list* spinshlist,
- list* newsegshlist, list* frontlist, list* misfrontlist, list* ptlist,
- list* conlist, memorypool* viri, queue* flipque, bool noreloc, bool optflag)
-{
- list **oldtetlist, **newtetlist;
- list **oldshlist, **newshlist;
- list *pnewshlist, *dnewshlist;
- triface oldtet, newtet;
- face oldsh, newsh;
- face startsh, spinsh, segsh1, segsh2;
- face nsupseg, newseg, prevseg, nextseg;
- point suppt, *newpt;
- point pa, pb, *cons;
- REAL pnorm[2][3], norm[3];
- bool success;
- int shmark;
- int n, i, j, k;
-
- // Get the Steiner point p.
- assert(supseg->shver < 2);
- suppt = sdest(*supseg);
- // Find the segment ab split by p.
- senext(*supseg, nsupseg);
- spivotself(nsupseg);
- assert(nsupseg.sh != dummysh);
- nsupseg.shver = 0;
- if (sorg(nsupseg) != suppt) sesymself(nsupseg);
- assert(sorg(nsupseg) == suppt);
- pa = sorg(*supseg);
- pb = sdest(nsupseg);
- if (b->verbose > 1) {
- printf(" Remove point %d on segment (%d, %d).\n",
- pointmark(suppt), pointmark(pa), pointmark(pb));
- }
-
- // Let startsh s containing p.
- spivot(*supseg, startsh);
- spinsh = startsh;
- do {
- // Save it in list.
- spinshlist->append(&spinsh);
- // Go to the next facet.
- spivotself(spinsh);
- } while (spinsh.sh != startsh.sh);
- if (spinshlist->len() == 1) {
- // This case has not handled yet.
- // printf("Unhandled case: segment only belongs to one facet.\n");
- spinshlist->clear();
- unsupverts++;
- return false;
- }
-
- // Suppose ab is shared by n facets (n > 1), then there are n B(p) (tets
- // with p as a vertex). Some B(p) may be empty, eg, outside.
- n = spinshlist->len();
- oldtetlist = new list*[n];
- newtetlist = new list*[n];
- oldshlist = new list*[n];
- newshlist = new list*[n];
- newpt = new point[n];
- for (i = 0; i < n; i++) {
- oldtetlist[i] = (list *) NULL;
- newtetlist[i] = (list *) NULL;
- oldshlist[i] = (list *) NULL;
- newshlist[i] = (list *) NULL;
- newpt[i] = (point) NULL;
- }
-
- // Create a new segment ab (result in newseg).
- makeshellface(subsegs, &newseg);
- setsorg(newseg, pa);
- setsdest(newseg, pb);
- // ab gets the same mark and segment type as ap.
- setshellmark(newseg, shellmark(*supseg));
- setshelltype(newseg, shelltype(*supseg));
- if (b->quality && varconstraint) {
- // Copy the areabound into the new subsegment.
- setareabound(newseg, areabound(*supseg));
- }
- // Save the old connection at a.
- senext2(*supseg, prevseg);
- spivotself(prevseg);
- if (prevseg.sh != dummysh) {
- prevseg.shver = 0;
- if (sdest(prevseg) != pa) sesymself(prevseg);
- assert(sdest(prevseg) == pa);
- senextself(prevseg);
- senext2self(newseg);
- sbond(newseg, prevseg);
- newseg.shver = 0;
- }
- // Save the old connection at b.
- senext(nsupseg, nextseg);
- spivotself(nextseg);
- if (nextseg.sh != dummysh) {
- nextseg.shver = 0;
- if (sorg(nextseg) != pb) sesymself(nextseg);
- assert(sorg(nextseg) == pb);
- senext2self(nextseg);
- senextself(newseg);
- sbond(newseg, nextseg);
- newseg.shver = 0;
- }
-
- // Re-triangulate C(p) (subs with p as a vertex) to remove p.
- for (i = 0; i < spinshlist->len(); i++) {
- spinsh = * (face *)(* spinshlist)[i];
- // Allocate spaces for C_i(p).
- oldshlist[i] = new list(sizeof(face), NULL, 256);
- newshlist[i] = new list(sizeof(face), NULL, 256);
- // Get the subs of C_i(p).
- oldshlist[i]->append(&spinsh);
- formstarpolygon(suppt, oldshlist[i], ptlist);
- // Find the edges of C_i(p). It DOES NOT form a closed polygon.
- for (j = 0; j < oldshlist[i]->len(); j++) {
- oldsh = * (face *)(* (oldshlist[i]))[j];
- cons = (point *) conlist->append(NULL);
- cons[0] = sorg(oldsh);
- cons[1] = sdest(oldsh);
- }
- // The C_i(p) isn't closed without ab. Add it to it.
- cons = (point *) conlist->append(NULL);
- cons[0] = pa;
- cons[1] = pb;
- // Re-triangulate C_i(p).
- shmark = shellmark(spinsh);
- triangulate(shmark, b->epsilon, ptlist, conlist, 0, NULL, viri, flipque);
- // Get new subs of C_i(p), remove protected segments.
- retrievenewsubs(newshlist[i], true);
- // Substitute old C_i(p) with the new C_i(p). !IT IS NOT COMPLETE!
- replacepolygonsubs(oldshlist[i], newshlist[i]);
- // Find the new subface s having edge ab.
- for (j = 0; j < newshlist[i]->len(); j++) {
- segsh1 = * (face *)(* (newshlist[i]))[j];
- for (k = 0; k < 3; k++) {
- if (((sorg(segsh1) == pa) && (sdest(segsh1) == pb)) ||
- ((sorg(segsh1) == pb) && (sdest(segsh1) == pa))) break;
- senextself(segsh1);
- }
- if (k < 3) break; // Found.
- }
- assert(j < newshlist[i]->len()); // ab must exist.
- // Bond s and ab together. The C_i(p) is completedly substituted.
- ssbond(segsh1, newseg);
- // Save s for forming the face ring of ab.
- newsegshlist->append(&segsh1);
- // Clear work lists.
- ptlist->clear();
- conlist->clear();
- flipque->clear();
- viri->restart();
- }
- // Form the face ring of ab.
- for (i = 0; i < newsegshlist->len(); i++) {
- segsh1 = * (face *)(* newsegshlist)[i];
- if ((i + 1) == newsegshlist->len()) {
- segsh2 = * (face *)(* newsegshlist)[0];
- } else {
- segsh2 = * (face *)(* newsegshlist)[i + 1];
- }
- sbond1(segsh1, segsh2);
- }
-
- // A work list for keeping subfaces from two facets.
- dnewshlist = new list(sizeof(face), NULL, 256);
- success = true; // Assume p is suppressable.
-
- // Suppress p in all B(p). B_i(p) is looped wrt the right-hand rule of ab.
- for (i = 0; i < spinshlist->len() && success; i++) {
- // Get an old subface s (ap) of a facet.
- spinsh = * (face *)(* spinshlist)[i];
- // Let the edge direction of s be a->b. Hence all subfaces follow
- // the right-hand rule of ab.
- if (sorg(spinsh) != pa) sesymself(spinsh);
- // Get a tet t of B_i(p).
- stpivot(spinsh, oldtet);
- // Is B_i(p) empty?
- if (oldtet.tet == dummytet) continue;
- // Allocate spaces for B_i(p).
- oldtetlist[i] = new list(sizeof(triface), NULL, 256);
- newtetlist[i] = new list(sizeof(triface), NULL, 256);
- // Find all tets of old B_i(p).
- oldtetlist[i]->append(&oldtet);
- formstarpolyhedron(suppt, oldtetlist[i], ptlist, false);
- // Infect tets of old B_i(p) (they're going to be deleted).
- for (j = 0; j < oldtetlist[i]->len(); j++) {
- oldtet = * (triface *)(* (oldtetlist[i]))[j];
- infect(oldtet);
- }
- // Collect new subfaces (of two facets) bounded B_i(p).
- for (k = 0; k < 2; k++) {
- if ((i + k) < spinshlist->len()) {
- pnewshlist = newshlist[i + k];
- segsh1 = * (face *)(* spinshlist)[i + k];
- } else {
- pnewshlist = newshlist[0];
- segsh1 = * (face *)(* spinshlist)[0];
- }
- // Adjust the orientation of segsh1 to face to the inside of C.
- if (k == 0) {
- if (sorg(segsh1) != pa) sesymself(segsh1);
- assert(sorg(segsh1) == pa);
- } else {
- if (sdest(segsh1) != pa) sesymself(segsh1);
- assert(sdest(segsh1) == pa);
- }
- // Preparation for re-tetrahedralzing old B_i(p).
- orientnewsubs(pnewshlist, &segsh1, pnorm[k]);
- for (j = 0; j < pnewshlist->len(); j++) {
- dnewshlist->append((face *)(* pnewshlist)[j]);
- }
- }
- // Tetrahedralize B_i(p).
- success = constrainedcavity(&oldtet, dnewshlist, oldtetlist[i], ptlist,
- frontlist, misfrontlist, newtetlist[i], flipque);
- if (!success && !noreloc) {
- // C must be finished by re-locating the steiner point.
- makepoint(&(newpt[i]));
- for (j = 0; j < 3; j++) norm[j] = 0.5 * (pnorm[0][j] + pnorm[1][j]);
- success = findrelocatepoint(suppt, newpt[i], norm, frontlist,
- oldtetlist[i]);
- // for (j = 0; j < 3; j++) newpt[i][j] = suppt[j];
- // success = smoothvolpoint(newpt[i], frontlist, true);
- if (success) {
- // p is relocated by newpt[i]. Now insert it. Don't do flip since
- // the new tets may get deleted again.
- relocatepoint(newpt[i], &oldtet, frontlist, newtetlist[i], NULL);
- setpointtype(newpt[i], FREEVOLVERTEX);
- relverts++;
- } else {
- // Fail to relocate p. Clean fake tets and quit this option.
- deallocfaketets(frontlist);
- pointdealloc(newpt[i]);
- newpt[i] = (point) NULL;
- assert(newtetlist[i]->len() == 0);
- }
- }
- if (!success && noreloc) {
- // Failed and no point relocation. Clean fake tets.
- deallocfaketets(frontlist);
- }
- // Clear work lists.
- dnewshlist->clear();
- ptlist->clear();
- frontlist->clear();
- misfrontlist->clear();
- flipque->clear();
- }
-
- if (success) {
- // p has been suppressed. (Still in the pool).
- setpointtype(suppt, UNUSEDVERTEX);
- unuverts++;
- // Update the segmnet pointers saved in a and b.
- setpoint2sh(pa, sencode(newseg));
- setpoint2sh(pb, sencode(newseg));
- // Delete old segments ap, pb.
- shellfacedealloc(subsegs, supseg->sh);
- shellfacedealloc(subsegs, nsupseg.sh);
- // Delete subs of old C_i(p).
- for (i = 0; i < spinshlist->len(); i++) {
- for (j = 0; j < oldshlist[i]->len(); j++) {
- oldsh = * (face *)(* (oldshlist[i]))[j];
- if (j == 0) {
- // Update 'hullsize' if C_i(p) is on the hull.
- stpivot(oldsh, oldtet);
- if (oldtet.tet != dummytet) {
- sesymself(oldsh);
- stpivot(oldsh, oldtet);
- }
- if (oldtet.tet == dummytet) {
- // Update 'hullsize'.
- k = oldshlist[i]->len() - newshlist[i]->len();
- assert(k > 0);
- hullsize -= k;
- }
- }
- shellfacedealloc(subfaces, oldsh.sh);
- }
- }
- // Delete tets old B_i(p).
- for (i = 0; i < spinshlist->len(); i++) {
- // Delete them if it is not empty.
- if (oldtetlist[i] != (list *) NULL) {
- for (j = 0; j < oldtetlist[i]->len(); j++) {
- oldtet = * (triface *)(* (oldtetlist[i]))[j];
- assert(!isdead(&oldtet));
- tetrahedrondealloc(oldtet.tet);
- }
- }
- }
- if (optflag) {
- for (i = 0; i < spinshlist->len(); i++) {
- // Check for new bad-quality tets.
- if (newtetlist[i] != (list *) NULL) {
- for (j = 0; j < newtetlist[i]->len(); j++) {
- newtet = * (triface *)(* (newtetlist[i]))[j];
- if (!isdead(&newtet)) checktet4opt(&newtet, true);
- }
- }
- }
- }
- } else {
- // p is not suppressed. Recover the original state.
- unsupverts++;
- // Restore old connection at a.
- senext2(*supseg, prevseg);
- spivotself(prevseg);
- if (prevseg.sh != dummysh) {
- prevseg.shver = 0;
- if (sdest(prevseg) != pa) sesymself(prevseg);
- assert(sdest(prevseg) == pa);
- senextself(prevseg);
- senext2self(*supseg);
- sbond(*supseg, prevseg);
- senextself(*supseg); // Restore original state.
- assert(supseg->shver < 2);
- }
- // Restore old connection at b.
- senext(nsupseg, nextseg);
- spivotself(nextseg);
- if (nextseg.sh != dummysh) {
- nextseg.shver = 0;
- if (sorg(nextseg) != pb) sesymself(nextseg);
- assert(sorg(nextseg) == pb);
- senext2self(nextseg);
- senextself(nsupseg);
- sbond(nsupseg, nextseg);
- // nsupseg.shver = 0;
- senext2self(nsupseg); // Restore original state
- assert(nsupseg.shver < 2);
- }
- // Delete the new segment ab.
- shellfacedealloc(subsegs, newseg.sh);
- // Restore old C_i(p).
- for (i = 0; i < spinshlist->len(); i++) {
- replacepolygonsubs(newshlist[i], oldshlist[i]);
- // Delete subs of the new C_i(p)
- for (j = 0; j < newshlist[i]->len(); j++) {
- newsh = * (face *)(* (newshlist[i]))[j];
- shellfacedealloc(subfaces, newsh.sh);
- }
- }
- // Restore old B_i(p).
- for (i = 0; i < spinshlist->len(); i++) {
- if (oldtetlist[i] != (list *) NULL) {
- // Uninfect tets of old B_i(p).
- for (j = 0; j < oldtetlist[i]->len(); j++) {
- oldtet = * (triface *)(* (oldtetlist[i]))[j];
- assert(infected(oldtet));
- uninfect(oldtet);
- }
- // Has it been re-meshed?
- if (newtetlist[i]->len() > 0) {
- // Restore the old B_i(p).
- restorepolyhedron(oldtetlist[i]);
- // Delete tets of the new B_i(p);
- for (j = 0; j < newtetlist[i]->len(); j++) {
- newtet = * (triface *)(* (newtetlist[i]))[j];
- // Some new tets may already be deleted (by carvecavity()).
- if (!isdead(&newtet)) {
- tetrahedrondealloc(newtet.tet);
- }
- }
- }
- // Dealloc newpt[i] if it exists.
- if (newpt[i] != (point) NULL) {
- pointdealloc(newpt[i]);
- relverts--;
- }
- }
- }
- }
-
- // Delete work lists.
- delete dnewshlist;
- for (i = 0; i < spinshlist->len(); i++) {
- delete oldshlist[i];
- delete newshlist[i];
- }
- delete [] oldshlist;
- delete [] newshlist;
- for (i = 0; i < spinshlist->len(); i++) {
- if (oldtetlist[i] != (list *) NULL) {
- delete oldtetlist[i];
- delete newtetlist[i];
- }
- }
- delete [] oldtetlist;
- delete [] newtetlist;
- // Clear work lists.
- newsegshlist->clear();
- spinshlist->clear();
-
- return success;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// suppressvolpoint() Suppress a point inside mesh. //
-// //
-// The point p = org(suptet) is inside the mesh and will be suppressed from //
-// the mesh. Note that p may not be suppressed. //
-// //
-// 'optflag' is used for mesh optimization. If it is set, after removing p, //
-// test the object function on each new tet, queue bad tets. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::suppressvolpoint(triface* suptet, list* frontlist,
- list* misfrontlist, list* ptlist, queue* flipque, bool optflag)
-{
- list *myfrontlist, *mymisfrontlist, *myptlist;
- list *oldtetlist, *newtetlist;
- list *newshlist; // a dummy list.
- queue *myflipque;
- triface oldtet, newtet;
- point suppt, conpt;
- bool success;
- int j;
-
- // Allocate spaces for storing (old and new) B(p).
- oldtetlist = new list(sizeof(triface), NULL, 256);
- newtetlist = new list(sizeof(triface), NULL, 256);
- newshlist = new list(sizeof(face), NULL, 256);
- // Allocate work lists if user doesn't supply them.
- myfrontlist = mymisfrontlist = myptlist = (list *) NULL;
- myflipque = (queue *) NULL;
- if (frontlist == (list *) NULL) {
- myfrontlist = new list(sizeof(triface), NULL, 256);
- frontlist = myfrontlist;
- mymisfrontlist = new list(sizeof(triface), NULL, 256);
- misfrontlist = mymisfrontlist;
- myptlist = new list(sizeof(point *), NULL, 256);
- ptlist = myptlist;
- myflipque = new queue(sizeof(badface));
- flipque = myflipque;
- }
-
- suppt = org(*suptet);
- oldtet = *suptet;
- success = true; // Assume p can be suppressed.
-
- if (b->verbose > 1) {
- printf(" Remove point %d in mesh.\n", pointmark(suppt));
- }
-
- // Form old B(p) in oldtetlist.
- oldtetlist->append(&oldtet);
- formstarpolyhedron(suppt, oldtetlist, ptlist, false);
- // Infect the tets in old B(p) (they're going to be delete).
- for (j = 0; j < oldtetlist->len(); j++) {
- oldtet = * (triface *)(* oldtetlist)[j];
- infect(oldtet);
- }
- // Tetrahedralize old B(p).
- success = constrainedcavity(&oldtet, newshlist, oldtetlist, ptlist,
- frontlist, misfrontlist, newtetlist, flipque);
- if (!success) {
- // Unable to suppress p.
- deallocfaketets(frontlist);
- // Try to collapse an edge at p.
- conpt = (point) NULL;
- assert(newtetlist->len() == 0);
- if (findcollapseedge(suppt, &conpt, oldtetlist, ptlist)) {
- // Collapse the edge suppt->conpt. Re-use newtetlist.
- collapseedge(suppt, conpt, oldtetlist, newtetlist);
- // The oldtetlist contains newtetlist.
- if (optflag) {
- assert(newtetlist->len() == 0);
- for (j = 0; j < oldtetlist->len(); j++) {
- newtet = * (triface *)(* oldtetlist)[j];
- newtetlist->append(&newtet);
- }
- }
- oldtetlist->clear(); // Do not delete them.
- collapverts++;
- success = true;
- }
- }
- if (success) {
- // p has been removed! (Still in the pool).
- setpointtype(suppt, UNUSEDVERTEX);
- unuverts++;
- suprelverts++;
- // Delete old B(p).
- for (j = 0; j < oldtetlist->len(); j++) {
- oldtet = * (triface *)(* oldtetlist)[j];
- assert(!isdead(&oldtet));
- tetrahedrondealloc(oldtet.tet);
- }
- if (optflag) {
- // Check for new bad tets.
- for (j = 0; j < newtetlist->len(); j++) {
- newtet = * (triface *)(* newtetlist)[j];
- if (!isdead(&newtet)) checktet4opt(&newtet, true);
- }
- }
- } else {
- // p is not suppressed. Recover the original state.
- // Uninfect tets of old B(p).
- for (j = 0; j < oldtetlist->len(); j++) {
- oldtet = * (triface *)(* oldtetlist)[j];
- assert(infected(oldtet));
- uninfect(oldtet);
- }
- }
-
- // Clear work lists.
- ptlist->clear();
- frontlist->clear();
- misfrontlist->clear();
- flipque->clear();
- // Deallocate work lists.
- if (myfrontlist != (list *) NULL) {
- delete myfrontlist;
- delete mymisfrontlist;
- delete myptlist;
- delete myflipque;
- }
- delete oldtetlist;
- delete newtetlist;
- delete newshlist;
-
- return success;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// smoothpoint() Smooth a volume/segment point. //
-// //
-// 'smthpt' (p) is inside the polyhedron (C) bounded by faces in 'starlist'. //
-// This routine moves p inside C until an object function is maximized. //
-// //
-// Default, the CCW edge ring of the faces on C points to p. If 'invtori' is //
-// TRUE, the orientation is inversed. //
-// //
-// If 'key' != NULL, it contains an object value to be improved. Current it //
-// means the cosine of the largest dihedral angle. In such case, the point //
-// is smoothed only if the final configuration improves the object value, it //
-// is returned by the 'key'. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::smoothpoint(point smthpt, point e1, point e2, list *starlist,
- bool invtori, REAL *key)
-{
- triface starttet;
- point pa, pb, pc;
- REAL fcent[3], startpt[3], nextpt[3], bestpt[3];
- REAL iniTmax, oldTmax, newTmax;
- REAL ori, aspT, aspTmax, imprate;
- REAL cosd, maxcosd;
- bool segflag, randflag; //, subflag;
- int numdirs;
- int iter, i, j;
-
- // Is p a segment vertex?
- segflag = (e1 != (point) NULL);
- // Decide the number of moving directions.
- numdirs = segflag ? 2 : starlist->len();
- randflag = numdirs > 10;
- if (randflag) {
- numdirs = 10; // Maximum 10 directions.
- }
-
- // Calculate the initial object value (the largest aspect ratio).
- for (i = 0; i < starlist->len(); i++) {
- starttet = * (triface *)(* starlist)[i];
- adjustedgering(starttet, !invtori ? CCW : CW);
- pa = org(starttet);
- pb = dest(starttet);
- pc = apex(starttet);
- aspT = tetaspectratio(pa, pb, pc, smthpt);
- if (i == 0) {
- aspTmax = aspT;
- } else {
- aspTmax = aspT > aspTmax ? aspT : aspTmax;
- }
- }
- iniTmax = aspTmax;
-
- if (b->verbose > 1) {
- printf(" Smooth %s point %d (%g, %g, %g).\n", segflag ? "seg" : "vol",
- pointmark(smthpt), smthpt[0], smthpt[1], smthpt[2]);
- printf(" Initial max L/h = %g.\n", iniTmax);
- }
- for (i = 0; i < 3; i++) {
- bestpt[i] = startpt[i] = smthpt[i];
- }
-
- // Do iteration until the new aspTmax does not decrease.
- newTmax = iniTmax;
- iter = 0;
- while (true) {
- // Find the best next location.
- oldTmax = newTmax;
- for (i = 0; i < numdirs; i++) {
- // Calculate the moved point (saved in 'nextpt').
- if (!segflag) {
- if (randflag) {
- // Randomly pick a direction.
- j = (int) randomnation(starlist->len());
- } else {
- j = i;
- }
- starttet = * (triface *)(* starlist)[j];
- adjustedgering(starttet, !invtori ? CCW : CW);
- pa = org(starttet);
- pb = dest(starttet);
- pc = apex(starttet);
- for (j = 0; j < 3; j++) {
- fcent[j] = (pa[j] + pb[j] + pc[j]) / 3.0;
- }
- } else {
- for (j = 0; j < 3; j++) {
- fcent[j] = (i == 0 ? e1[j] : e2[j]);
- }
- }
- for (j = 0; j < 3; j++) {
- nextpt[j] = startpt[j] + 0.01 * (fcent[j] - startpt[j]);
- }
- // Get the largest object value for the new location.
- for (j = 0; j < starlist->len(); j++) {
- starttet = * (triface *)(* starlist)[j];
- adjustedgering(starttet, !invtori ? CCW : CW);
- pa = org(starttet);
- pb = dest(starttet);
- pc = apex(starttet);
- ori = orient3d(pa, pb, pc, nextpt);
- if (ori < 0.0) {
- aspT = tetaspectratio(pa, pb, pc, nextpt);
- if (j == 0) {
- aspTmax = aspT;
- } else {
- aspTmax = aspT > aspTmax ? aspT : aspTmax;
- }
- } else {
- // An invalid new tet. Discard this point.
- aspTmax = newTmax;
- } // if (ori < 0.0)
- // Stop looping when the object value is bigger than before.
- if (aspTmax >= newTmax) break;
- } // for (j = 0; j < starlist->len(); j++)
- if (aspTmax < newTmax) {
- // Save the improved object value and the location.
- newTmax = aspTmax;
- for (j = 0; j < 3; j++) bestpt[j] = nextpt[j];
- }
- } // for (i = 0; i < starlist->len(); i++)
- // Does the object value improved much?
- imprate = fabs(oldTmax - newTmax) / oldTmax;
- if (imprate < 1e-3) break;
- // Yes, move p to the new location and continue.
- for (j = 0; j < 3; j++) startpt[j] = bestpt[j];
- iter++;
- } // while (true)
-
- if (iter > 0) {
- // The point is moved.
- if (key) {
- // Check if the quality is improved by the smoothed point.
- maxcosd = 0.0; // = cos(90).
- for (j = 0; j < starlist->len(); j++) {
- starttet = * (triface *)(* starlist)[j];
- adjustedgering(starttet, !invtori ? CCW : CW);
- pa = org(starttet);
- pb = dest(starttet);
- pc = apex(starttet);
- tetalldihedral(pa, pb, pc, startpt, NULL, &cosd, NULL);
- if (cosd < *key) {
- // This quality will not be improved. Stop.
- iter = 0; break;
- } else {
- // Remeber the worst quality value (of the new configuration).
- maxcosd = maxcosd < cosd ? maxcosd : cosd;
- }
- }
- if (iter > 0) *key = maxcosd;
- }
- }
-
- if (iter > 0) {
- segflag ? smoothsegverts++ : smoothvolverts++;
- for (i = 0; i < 3; i++) smthpt[i] = startpt[i];
- if (b->verbose > 1) {
- printf(" Move to new location (%g, %g, %g).\n", smthpt[0], smthpt[1],
- smthpt[2]);
- printf(" Final max L/h = %g. (%d iterations)\n", newTmax, iter);
- if (key) {
- printf(" Max. dihed = %g (degree).\n", acos(*key) / PI * 180.0);
- }
- }
- return true;
- } else {
- if (b->verbose > 1) {
- printf(" Not smoothed.\n");
- }
- return false;
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// removesteiners() Delete or relocate Steiner points on facets. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::removesteiners(bool coarseflag)
-{
- list *frontlist, *misfrontlist;
- list *spinshlist, *newsegshlist;
- list *ptlist, *conlist;
- memorypool *viri;
- queue *flipque;
- triface checktet;
- face shloop;
- face segloop, nextseg;
- point pa, neipt;
- REAL len;
- bool remflag;
- int *worklist;
- int oldnum, rmstein;
- int i, j;
-
- if (!b->quiet) {
- if (!coarseflag) {
- printf("Removing Steiner points.\n");
- } else {
- printf("Coarsening mesh.\n");
- }
- }
-
- // Initialize work lists.
- frontlist = new list(sizeof(triface), NULL);
- misfrontlist = new list(sizeof(triface), NULL);
- spinshlist = new list(sizeof(face), NULL);
- newsegshlist = new list(sizeof(face), NULL);
- ptlist = new list(sizeof(point *), NULL);
- conlist = new list(sizeof(point *) * 2, NULL);
- flipque = new queue(sizeof(badface));
- viri = new memorypool(sizeof(shellface *), 1024, POINTER, 0);
- oldnum = unuverts;
- relverts = suprelverts = collapverts = unsupverts;
- smoothvolverts = 0;
- expcavcount = 0;
-
- // Suppress Steiner points inside facets.
- do {
- rmstein = unuverts;
- subfaces->traversalinit();
- shloop.sh = shellfacetraverse(subfaces);
- while (shloop.sh != (shellface *) NULL) {
- remflag = false;
- // Is s contains a Steiner point?
- shloop.shver = 0;
- for (i = 0; i < 3; i++) {
- pa = sapex(shloop);
- if (pointtype(pa) == FREESUBVERTEX) {
- if (!coarseflag) {
- // Remove it if it is not an input point.
- j = pointmark(pa) - in->firstnumber;
- if (j >= in->numberofpoints) {
- if (b->nobisect == 1) {
- // '-Y'. Remove p if s is a hull face.
- stpivot(shloop, checktet);
- if (checktet.tet != dummytet) {
- sesymself(shloop);
- stpivot(shloop, checktet);
- }
- remflag = (checktet.tet == dummytet);
- } else {
- // '-YY'. Remove p whatever s is a hull face or not.
- remflag = true;
- }
- }
- } else {
- // Check if this vertex can be coarsed.
- if (b->nobisect == 0) {
- // Is a background mesh available?
- if (b->metric) {
- // assert(pa[pointmtrindex] > 0.0);
- // Form the star of pa.
- spinshlist->append(&shloop);
- formstarpolygon(pa, spinshlist, ptlist);
- len = 0.0;
- for (j = 0; j < ptlist->len(); j++) {
- neipt = * (point *)(* ptlist)[j];
- len += distance(pa, neipt);
- }
- len /= ptlist->len();
- // Carse it if the average edge length is small.
- remflag = len < pa[pointmtrindex];
- spinshlist->clear();
- ptlist->clear();
- } else {
- // Coarse it if (1) it is an input point and its pointmarker
- // is zero, or (2) it is a Steiner point.
- remflag = true;
- j = pointmark(pa) - in->firstnumber;
- if (j < in->numberofpoints) {
- remflag = (in->pointmarkerlist[j] == 0);
- }
- } // if (b->metric)
- } // if (b->nobisect == 0)
- } // if (!coarseflag)
- if (remflag) break;
- } // if (pointtype(pa) == FREESUBVERTEX)
- senextself(shloop);
- } // for (i = 0; i < 3; i++)
- if (remflag) {
- suppressfacetpoint(&shloop, frontlist, misfrontlist, ptlist, conlist,
- viri, flipque, coarseflag, false);
- }
- shloop.sh = shellfacetraverse(subfaces);
- }
- // Continue if any Steiner point has been removed.
- } while (unuverts > rmstein);
-
- if (coarseflag) {
- shellface **segsperverlist;
- int *idx2seglist;
- face seg1, seg2;
- point e1, e2;
- // Connecting collinear segments. Hence the segment vertices may be
- // removed. In fact, this should be done by reconstructmesh().
- makesegmentmap(idx2seglist, segsperverlist);
- subsegs->traversalinit();
- segloop.sh = shellfacetraverse(subsegs);
- while (segloop.sh != (shellface *) NULL) {
- for (i = 0; i < 2; i++) {
- segloop.shver = i;
- senext(segloop, nextseg);
- spivotself(nextseg);
- if ((nextseg.sh == dummysh) || (nextseg.sh > segloop.sh)) {
- // No neighbor segment connection or haven't been processed yet.
- pa = sdest(segloop);
- j = pointmark(pa) - in->firstnumber;
- if (idx2seglist[j + 1] - idx2seglist[j] == 2) {
- // pa is shared by only two segments. Get the other one.
- nextseg.sh = segsperverlist[idx2seglist[j]];
- if (nextseg.sh == segloop.sh) {
- nextseg.sh = segsperverlist[idx2seglist[j] + 1];
- }
- nextseg.shver = 0;
- if (sorg(nextseg) != pa) sesymself(nextseg);
- // Check if the two segments are collinear.
- e1 = sorg(segloop);
- e2 = sdest(nextseg);
- if (iscollinear(e1, pa, e2, b->epsilon)) {
- // Connect the two segments together.
- if (b->verbose > 1) {
- printf(" Glue two insegs (%d, %d) at %d.\n", pointmark(e1),
- pointmark(e2), pointmark(pa));
- }
- senext(segloop, seg1);
- senext2(nextseg, seg2);
- sbond(seg1, seg2);
- }
- }
- } // if (nextseg.sh == dummysh)
- } // for (i = 0;
- segloop.sh = shellfacetraverse(subsegs);
- }
- delete [] segsperverlist;
- delete [] idx2seglist;
- }
-
- // Suppress Steiner points on segments.
- do {
- rmstein = unuverts;
- subsegs->traversalinit();
- segloop.sh = shellfacetraverse(subsegs);
- while (segloop.sh != (shellface *) NULL) {
- remflag = false;
- // for (i = 0; i < 2; i++) {
- // Don't check the poinytype of pa, it may be a Steiner point but
- // has type NACUTEVERTEX due to splitting a type-3 segment.
- segloop.shver = 0; // segloop.shver = i;
- senext(segloop, nextseg);
- spivotself(nextseg);
- if (nextseg.sh != dummysh) {
- pa = sdest(segloop); // p is going to be checked for removal.
- nextseg.shver = 0;
- if (sorg(nextseg) != pa) sesymself(nextseg);
- assert(sorg(nextseg) == pa);
- if (!coarseflag) {
- // try to remove it if it is not an input point.
- j = pointmark(pa) - in->firstnumber;
- if (j >= in->numberofpoints) {
- if (b->nobisect == 1) {
- // '-Y'. Remove p if it is on the hull.
- sstpivot(&segloop, &checktet);
- assert(checktet.tet != dummytet);
- pa = apex(checktet);
- do {
- if (!fnextself(checktet)) {
- // Meet a boundary face - p is on the hull.
- remflag = true; break;
- }
- } while (pa != apex(checktet));
- } else {
- // '-YY'. Remove p whatever it is on the hull or not.
- remflag = true;
- }
- }
- } else {
- // Check if this vertex can be coarsed.
- if (b->nobisect == 0) {
- if (b->metric) {
- // assert(pa[pointmtrindex] > 0.0);
- len = 0.0;
- neipt = sorg(segloop);
- for (j = 0; j < 2; j++) {
- len += distance(pa, neipt);
- /*// Is neipt inside the sparse ball of pa?
- if (len < pa[pointmtrindex]) {
- // Yes, the local of pa is too dense, corse it.
- remflag = true; break;
- } */
- neipt = sdest(nextseg);
- }
- len /= 2.0;
- // Carse it if the average edge lengh is small.
- remflag = len < pa[pointmtrindex];
- } else {
- // Coarse it if (1) it is an input point and its pointmarker
- // is zero, or (2) it is a Steiner point.
- remflag = true;
- j = pointmark(pa) - in->firstnumber;
- if (j < in->numberofpoints) {
- remflag = (in->pointmarkerlist[j] == 0);
- }
- } // if (b->metric)
- } // if (b->nobisect == 0)
- } // if (!coarseflag)
- } // if (nextseg.sh != dummysh)
- // if (remflag) break;
- // } // for (i = 0; i < 2; i++)
- if (remflag) {
- suppresssegpoint(&segloop, spinshlist, newsegshlist, frontlist,
- misfrontlist, ptlist, conlist, viri, flipque, coarseflag, false);
- }
- segloop.sh = shellfacetraverse(subsegs);
- }
- // Continue if any Steiner point has been removed.
- } while (unuverts > rmstein);
-
- if ((relverts > 0) || coarseflag) {
- worklist = new int[points->items + 1];
- // Suppress relocated points & coarse free mesh points.
- do {
- // Initialize the work list. Each entry of the list counts how many
- // times the point has been processed.
- for (i = 0; i < points->items + 1; i++) worklist[i] = 0;
- rmstein = unuverts;
- tetrahedrons->traversalinit();
- checktet.tet = tetrahedrontraverse();
- while (checktet.tet != (tetrahedron *) NULL) {
- remflag = false;
- for (i = 0; i < 4; i++) {
- pa = (point) checktet.tet[4 + i];
- if (pointtype(pa) == FREEVOLVERTEX) {
- // NOTE. Chenge the number 3 will change the number n of removed
- // Steiner points. In my test, n is larger when it is 1. 3
- // reduces n in a reasonable way (see example, mech_part,
- // thepart), 5 results a larger n than 3 does. While the best
- // result is no limit of this number, but it makes the code
- // extremely slow.
- if (worklist[pointmark(pa)] < 3) {
- worklist[pointmark(pa)]++;
- if (!coarseflag) {
- // Remove p if it is a Steiner point.
- if (pointmark(pa) >= (in->numberofpoints + in->firstnumber)) {
- remflag = true;
- }
- } else {
- if (b->metric) {
- // assert(pa[pointmtrindex] > 0.0);
- // Form the star of pa.
- frontlist->append(&checktet);
- formstarpolyhedron(pa, frontlist, ptlist, true);
- len = 0.0;
- for (j = 0; j < ptlist->len(); j++) {
- neipt = * (point *)(* ptlist)[j];
- len += distance(pa, neipt);
- }
- len /= ptlist->len();
- // Carse it if the average edge length is small.
- remflag = len < pa[pointmtrindex];
- frontlist->clear();
- ptlist->clear();
- } else {
- // Coarse it if (1) it is an input point and its pointmarker
- // is zero, or (2) it is a Steiner point.
- remflag = true;
- j = pointmark(pa) - in->firstnumber;
- if (j < in->numberofpoints) {
- remflag = (in->pointmarkerlist[j] == 0);
- }
- } // if (b->metric)
- } // if (!coarseflag)
- if (remflag) break;
- } // if (worklist[pointmark(pa)] == 0)
- } // if (pointtype(pa) == FREEVOLVERTEX)
- } // for (i = 0; i < 4; i++)
- if (remflag) {
- findorg(&checktet, pa);
- assert(org(checktet) == pa);
- suppressvolpoint(&checktet, frontlist, misfrontlist, ptlist, flipque,
- false);
- }
- checktet.tet = tetrahedrontraverse();
- }
- // Continue if any relocated point has been suppressed.
- } while (unuverts > rmstein);
-
-
- // Smooth the unsuppressed points if it is not coarse mesh.
- if (!coarseflag && (relverts > suprelverts)) {
- if (b->verbose) {
- printf(" Smoothing relocated points.\n");
- }
- for (i = 0; i < points->items + 1; i++) worklist[i] = 0;
- tetrahedrons->traversalinit();
- checktet.tet = tetrahedrontraverse();
- while (checktet.tet != (tetrahedron *) NULL) {
- for (i = 0; i < 4; i++) {
- pa = (point) checktet.tet[4 + i];
- if (pointtype(pa) == FREEVOLVERTEX) {
- if (worklist[pointmark(pa)] == 0) {
- worklist[pointmark(pa)] = 1;
- if (pointmark(pa) >= (in->numberofpoints + in->firstnumber)) {
- // Smooth pa.
- findorg(&checktet, pa);
- frontlist->append(&checktet);
- formstarpolyhedron(pa, frontlist, NULL, false);
- smoothpoint(pa, NULL, NULL, frontlist, false, NULL);
- frontlist->clear();
- }
- } // if (worklist[pointmark(pa)] == 0)
- } // if (pointtype(pa) == FREEVOLVERTEX)
- } // for (i = 0; i < 4; i++)
- checktet.tet = tetrahedrontraverse();
- }
- }
- delete [] worklist;
- }
-
- if (b->verbose > 0) {
- if (!coarseflag) {
- printf(" %d points removed from boundary", unuverts - oldnum);
- if (expcavcount > 0) {
- printf(" (%d cavity corrections)", expcavcount);
- }
- printf("\n");
- if (relverts > 0) {
- printf(" %d points relocated (%d suppressed, %d collapsed).\n",
- relverts, suprelverts - collapverts, collapverts);
- if (smoothvolverts > 0) {
- printf(" %d points are smoothed.\n", smoothvolverts);
- }
- }
- if (unsupverts > 0) {
- printf(" !! %d points are unsuppressed.\n", unsupverts);
- }
- } else {
- printf(" %d points are removed.\n", unuverts - oldnum);
- }
- }
-
- // Delete work lists.
- delete frontlist;
- delete misfrontlist;
- delete spinshlist;
- delete newsegshlist;
- delete ptlist;
- delete conlist;
- delete flipque;
- delete viri;
-}
-
-//
-// End of boundary Steiner points removing routines
-//
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// reconstructmesh() Reconstruct a tetrahedral mesh from a list of //
-// tetrahedra and possibly a list of boundary faces. //
-// //
-// The list of tetrahedra is stored in 'in->tetrahedronlist', the list of //
-// boundary faces is stored in 'in->trifacelist'. The tetrahedral mesh is //
-// reconstructed in memorypool 'tetrahedrons', its boundary faces (subfaces) //
-// are reconstructed in 'subfaces', its boundary edges (subsegments) are //
-// reconstructed in 'subsegs'. If the -a switch is used, this procedure will //
-// also read a list of REALs from 'in->tetrahedronvolumelist' and set a //
-// maximum volume constraint on each tetrahedron. //
-// //
-// If the user has provided the boundary faces in 'in->trifacelist', they //
-// will be inserted the mesh. Otherwise subfaces will be identified from the //
-// mesh. All hull faces (including faces of the internal holes) will be //
-// recognized as subfaces, internal faces between two tetrahedra which have //
-// different attributes will also be recognized as subfaces. //
-// //
-// Subsegments will be identified after subfaces are reconstructed. Edges at //
-// the intersections of non-coplanar subfaces are recognized as subsegments. //
-// Edges between two coplanar subfaces with different boundary markers are //
-// also recognized as subsegments. //
-// //
-// The facet index of each subface will be set automatically after we have //
-// recovered subfaces and subsegments. That is, the set of subfaces, which //
-// are coplanar and have the same boundary marker will be recognized as a //
-// facet and has a unique index, stored as the facet marker in each subface //
-// of the set, the real boundary marker of each subface will be found in //
-// 'in->facetmarkerlist' by the index. Facet index will be used in Delaunay //
-// refinement for detecting two incident facets. //
-// //
-// Points which are not corners of tetrahedra will be inserted into the mesh.//
-// Return the number of faces on the hull after the reconstruction. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-long tetgenmesh::reconstructmesh()
-{
- tetrahedron **tetsperverlist;
- shellface **facesperverlist;
- triface tetloop, neightet, neineightet, spintet;
- face subloop, neighsh, neineighsh, subseg;
- face sface1, sface2;
- point *idx2verlist;
- point torg, tdest, tapex, toppo;
- point norg, ndest, napex;
- list *neighshlist, *markerlist;
- REAL sign, attrib, volume;
- REAL da1, da2;
- bool bondflag, insertsegflag;
- int *idx2tetlist;
- int *idx2facelist;
- int *worklist;
- int facetidx, marker;
- int iorg, idest, iapex, ioppo;
- int inorg, indest, inapex;
- int index, i, j;
-
- if (!b->quiet) {
- printf("Reconstructing mesh.\n");
- }
-
- // Create a map from index to points.
- makeindex2pointmap(idx2verlist);
-
- // Create the tetrahedra.
- for (i = 0; i < in->numberoftetrahedra; i++) {
- // Create a new tetrahedron and set its four corners, make sure that
- // four corners form a positive orientation.
- maketetrahedron(&tetloop);
- index = i * in->numberofcorners;
- // Although there may be 10 nodes, we only read the first 4.
- iorg = in->tetrahedronlist[index] - in->firstnumber;
- idest = in->tetrahedronlist[index + 1] - in->firstnumber;
- iapex = in->tetrahedronlist[index + 2] - in->firstnumber;
- ioppo = in->tetrahedronlist[index + 3] - in->firstnumber;
- torg = idx2verlist[iorg];
- tdest = idx2verlist[idest];
- tapex = idx2verlist[iapex];
- toppo = idx2verlist[ioppo];
- sign = orient3d(torg, tdest, tapex, toppo);
- if (sign > 0.0) {
- norg = torg; torg = tdest; tdest = norg;
- } else if (sign == 0.0) {
- if (!b->quiet) {
- printf("Warning: Tet %d is degenerate.\n", i + in->firstnumber);
- }
- }
- setorg(tetloop, torg);
- setdest(tetloop, tdest);
- setapex(tetloop, tapex);
- setoppo(tetloop, toppo);
- // Temporarily set the vertices be type FREEVOLVERTEX, to indicate that
- // they belong to the mesh. These types may be changed later.
- setpointtype(torg, FREEVOLVERTEX);
- setpointtype(tdest, FREEVOLVERTEX);
- setpointtype(tapex, FREEVOLVERTEX);
- setpointtype(toppo, FREEVOLVERTEX);
- // Set element attributes if they exist.
- for (j = 0; j < in->numberoftetrahedronattributes; j++) {
- index = i * in->numberoftetrahedronattributes;
- attrib = in->tetrahedronattributelist[index + j];
- setelemattribute(tetloop.tet, j, attrib);
- }
- // If -a switch is used (with no number follows) Set a volume
- // constraint if it exists.
- if (b->varvolume) {
- if (in->tetrahedronvolumelist != (REAL *) NULL) {
- volume = in->tetrahedronvolumelist[i];
- } else {
- volume = -1.0;
- }
- setvolumebound(tetloop.tet, volume);
- }
- }
-
- // Set the connection between tetrahedra.
- hullsize = 0l;
- // Create a map from nodes to tetrahedra.
- maketetrahedronmap(idx2tetlist, tetsperverlist);
- // Initialize the worklist.
- worklist = new int[points->items];
- for (i = 0; i < points->items; i++) worklist[i] = 0;
-
- // Loop all tetrahedra, bond two tetrahedra if they share a common face.
- tetrahedrons->traversalinit();
- tetloop.tet = tetrahedrontraverse();
- while (tetloop.tet != (tetrahedron *) NULL) {
- // Loop the four sides of the tetrahedron.
- for (tetloop.loc = 0; tetloop.loc < 4; tetloop.loc++) {
- sym(tetloop, neightet);
- if (neightet.tet != dummytet) continue; // This side has finished.
- torg = org(tetloop);
- tdest = dest(tetloop);
- tapex = apex(tetloop);
- iorg = pointmark(torg) - in->firstnumber;
- idest = pointmark(tdest) - in->firstnumber;
- iapex = pointmark(tapex) - in->firstnumber;
- worklist[iorg] = 1;
- worklist[idest] = 1;
- worklist[iapex] = 1;
- bondflag = false;
- // Search its neighbor in the adjacent tets of torg.
- for (j = idx2tetlist[iorg]; j < idx2tetlist[iorg + 1] && !bondflag;
- j++) {
- if (tetsperverlist[j] == tetloop.tet) continue; // Skip myself.
- neightet.tet = tetsperverlist[j];
- for (neightet.loc = 0; neightet.loc < 4; neightet.loc++) {
- sym(neightet, neineightet);
- if (neineightet.tet == dummytet) {
- norg = org(neightet);
- ndest = dest(neightet);
- napex = apex(neightet);
- inorg = pointmark(norg) - in->firstnumber;
- indest = pointmark(ndest) - in->firstnumber;
- inapex = pointmark(napex) - in->firstnumber;
- if ((worklist[inorg] + worklist[indest] + worklist[inapex]) == 3) {
- // Find! Bond them together and break the loop.
- bond(tetloop, neightet);
- bondflag = true;
- break;
- }
- }
- }
- }
- if (!bondflag) {
- hullsize++; // It's a hull face.
- // Bond this side to outer space.
- dummytet[0] = encode(tetloop);
- if ((in->pointmarkerlist != (int *) NULL) && !b->coarse) {
- // Set its three corners's markers be boundary (hull) vertices.
- if (in->pointmarkerlist[iorg] == 0) {
- in->pointmarkerlist[iorg] = 1;
- }
- if (in->pointmarkerlist[idest] == 0) {
- in->pointmarkerlist[idest] = 1;
- }
- if (in->pointmarkerlist[iapex] == 0) {
- in->pointmarkerlist[iapex] = 1;
- }
- }
- }
- worklist[iorg] = 0;
- worklist[idest] = 0;
- worklist[iapex] = 0;
- }
- tetloop.tet = tetrahedrontraverse();
- }
-
- // Subfaces will be inserted into the mesh. It has two phases:
- // (1) Insert subfaces provided by user (in->trifacelist);
- // (2) Create subfaces for hull faces (if they're not subface yet) and
- // interior faces which separate two different materials.
-
- // Phase (1). Is there a list of user-provided subfaces?
- if (in->trifacelist != (int *) NULL) {
- // Recover subfaces from 'in->trifacelist'.
- for (i = 0; i < in->numberoftrifaces; i++) {
- index = i * 3;
- iorg = in->trifacelist[index] - in->firstnumber;
- idest = in->trifacelist[index + 1] - in->firstnumber;
- iapex = in->trifacelist[index + 2] - in->firstnumber;
- // Look for the location of this subface.
- worklist[iorg] = 1;
- worklist[idest] = 1;
- worklist[iapex] = 1;
- bondflag = false;
- // Search its neighbor in the adjacent tets of torg.
- for (j = idx2tetlist[iorg]; j < idx2tetlist[iorg + 1] && !bondflag;
- j++) {
- neightet.tet = tetsperverlist[j];
- for (neightet.loc = 0; neightet.loc < 4; neightet.loc++) {
- norg = org(neightet);
- ndest = dest(neightet);
- napex = apex(neightet);
- inorg = pointmark(norg) - in->firstnumber;
- indest = pointmark(ndest) - in->firstnumber;
- inapex = pointmark(napex) - in->firstnumber;
- if ((worklist[inorg] + worklist[indest] + worklist[inapex]) == 3) {
- bondflag = true; // Find!
- break;
- }
- }
- }
- if (bondflag) {
- // Create a new subface and insert it into the mesh.
- makeshellface(subfaces, &subloop);
- torg = idx2verlist[iorg];
- tdest = idx2verlist[idest];
- tapex = idx2verlist[iapex];
- setsorg(subloop, torg);
- setsdest(subloop, tdest);
- setsapex(subloop, tapex);
- // Set the vertices be FREESUBVERTEX to indicate they belong to a
- // facet of the domain. They may be changed later.
- setpointtype(torg, FREESUBVERTEX);
- setpointtype(tdest, FREESUBVERTEX);
- setpointtype(tapex, FREESUBVERTEX);
- if (in->trifacemarkerlist != (int *) NULL) {
- setshellmark(subloop, in->trifacemarkerlist[i]);
- }
- adjustedgering(neightet, CCW);
- findedge(&subloop, org(neightet), dest(neightet));
- tsbond(neightet, subloop);
- sym(neightet, neineightet);
- if (neineightet.tet != dummytet) {
- sesymself(subloop);
- tsbond(neineightet, subloop);
- }
- } else {
- if (!b->quiet) {
- printf("Warning: Subface %d is discarded.\n", i + in->firstnumber);
- }
- }
- worklist[iorg] = 0;
- worklist[idest] = 0;
- worklist[iapex] = 0;
- }
- }
-
- // Phase (2). Indentify subfaces from the mesh.
- tetrahedrons->traversalinit();
- tetloop.tet = tetrahedrontraverse();
- while (tetloop.tet != (tetrahedron *) NULL) {
- // Loop the four sides of the tetrahedron.
- for (tetloop.loc = 0; tetloop.loc < 4; tetloop.loc++) {
- tspivot(tetloop, subloop);
- if (subloop.sh != dummysh) continue;
- bondflag = false;
- sym(tetloop, neightet);
- if (neightet.tet == dummytet) {
- // It's a hull face. Insert a subface at here.
- bondflag = true;
- } else {
- // It's an interior face. Insert a subface if two tetrahedra have
- // different attributes (i.e., they belong to two regions).
- if (in->numberoftetrahedronattributes > 0) {
- if (elemattribute(neightet.tet,
- in->numberoftetrahedronattributes - 1) !=
- elemattribute(tetloop.tet,
- in->numberoftetrahedronattributes - 1)) {
- bondflag = true;
- }
- }
- }
- if (bondflag) {
- adjustedgering(tetloop, CCW);
- makeshellface(subfaces, &subloop);
- torg = org(tetloop);
- tdest = dest(tetloop);
- tapex = apex(tetloop);
- setsorg(subloop, torg);
- setsdest(subloop, tdest);
- setsapex(subloop, tapex);
- // Set the vertices be FREESUBVERTEX to indicate they belong to a
- // facet of the domain. They may be changed later.
- setpointtype(torg, FREESUBVERTEX);
- setpointtype(tdest, FREESUBVERTEX);
- setpointtype(tapex, FREESUBVERTEX);
- tsbond(tetloop, subloop);
- if (neightet.tet != dummytet) {
- sesymself(subloop);
- tsbond(neightet, subloop);
- }
- }
- }
- tetloop.tet = tetrahedrontraverse();
- }
-
- // Set the connection between subfaces. A subsegment may have more than
- // two subfaces sharing it, 'neighshlist' stores all subfaces sharing
- // one edge.
- neighshlist = new list(sizeof(face), NULL);
- // Create a map from nodes to subfaces.
- makesubfacemap(idx2facelist, facesperverlist);
-
- // Loop over the set of subfaces, setup the connection between subfaces.
- subfaces->traversalinit();
- subloop.sh = shellfacetraverse(subfaces);
- while (subloop.sh != (shellface *) NULL) {
- for (i = 0; i < 3; i++) {
- spivot(subloop, neighsh);
- if (neighsh.sh == dummysh) {
- // This side is 'empty', operate on it.
- torg = sorg(subloop);
- tdest = sdest(subloop);
- tapex = sapex(subloop);
- neighshlist->append(&subloop);
- iorg = pointmark(torg) - in->firstnumber;
- // Search its neighbor in the adjacent list of torg.
- for (j = idx2facelist[iorg]; j < idx2facelist[iorg + 1]; j++) {
- neighsh.sh = facesperverlist[j];
- if (neighsh.sh == subloop.sh) continue;
- neighsh.shver = 0;
- if (isfacehasedge(&neighsh, torg, tdest)) {
- findedge(&neighsh, torg, tdest);
- // Insert 'neighsh' into 'neighshlist'.
- if (neighshlist->len() < 2) {
- neighshlist->append(&neighsh);
- } else {
- for (index = 0; index < neighshlist->len() - 1; index++) {
- sface1 = * (face *)(* neighshlist)[index];
- sface2 = * (face *)(* neighshlist)[index + 1];
- da1 = facedihedral(torg, tdest, sapex(sface1), sapex(neighsh));
- da2 = facedihedral(torg, tdest, sapex(sface1), sapex(sface2));
- if (da1 < da2) {
- break; // Insert it after index.
- }
- }
- neighshlist->insert(index + 1, &neighsh);
- }
- }
- }
- // Bond the subfaces in 'neighshlist'.
- if (neighshlist->len() > 1) {
- neighsh = * (face *)(* neighshlist)[0];
- for (j = 1; j <= neighshlist->len(); j++) {
- if (j < neighshlist->len()) {
- neineighsh = * (face *)(* neighshlist)[j];
- } else {
- neineighsh = * (face *)(* neighshlist)[0];
- }
- sbond1(neighsh, neineighsh);
- neighsh = neineighsh;
- }
- } else {
- // No neighbor subface be found, bond 'subloop' to itself.
- sbond(subloop, subloop);
- }
- neighshlist->clear();
- }
- senextself(subloop);
- }
- subloop.sh = shellfacetraverse(subfaces);
- }
-
- // Segments will be introudced. Each segment has a unique marker (1-based).
- marker = 1;
- subfaces->traversalinit();
- subloop.sh = shellfacetraverse(subfaces);
- while (subloop.sh != (shellface *) NULL) {
- for (i = 0; i < 3; i++) {
- sspivot(subloop, subseg);
- if (subseg.sh == dummysh) {
- // This side has no subsegment bonded, check it.
- torg = sorg(subloop);
- tdest = sdest(subloop);
- tapex = sapex(subloop);
- spivot(subloop, neighsh);
- spivot(neighsh, neineighsh);
- insertsegflag = false;
- if (subloop.sh == neighsh.sh || subloop.sh != neineighsh.sh) {
- // This side is either self-bonded or more than two subfaces,
- // insert a subsegment at this side.
- insertsegflag = true;
- } else {
- // Only two subfaces case.
-#ifdef SELF_CHECK
- assert(subloop.sh != neighsh.sh);
-#endif
- napex = sapex(neighsh);
- sign = orient3d(torg, tdest, tapex, napex);
- if (iscoplanar(torg, tdest, tapex, napex, sign, b->epsilon)) {
- // Although they are coplanar, we still need to check if they
- // have the same boundary marker.
- insertsegflag = (shellmark(subloop) != shellmark(neighsh));
- } else {
- // Non-coplanar.
- insertsegflag = true;
- }
- }
- if (insertsegflag) {
- // Create a subsegment at this side.
- makeshellface(subsegs, &subseg);
- setsorg(subseg, torg);
- setsdest(subseg, tdest);
- // The two vertices have been marked as FREESUBVERTEX. Now mark
- // them as NACUTEVERTEX.
- setpointtype(torg, NACUTEVERTEX);
- setpointtype(tdest, NACUTEVERTEX);
- setshellmark(subseg, marker);
- marker++;
- // Bond all subfaces to this subsegment.
- neighsh = subloop;
- do {
- ssbond(neighsh, subseg);
- spivotself(neighsh);
- } while (neighsh.sh != subloop.sh);
- }
- }
- senextself(subloop);
- }
- subloop.sh = shellfacetraverse(subfaces);
- }
- // Remember the number of input segments.
- insegments = subsegs->items;
- // Find the acute vertices and set them be type ACUTEVERTEX.
-
- // Indentify facets and set the facet marker (1-based) for subfaces.
- markerlist = new list("int");
-
- subfaces->traversalinit();
- subloop.sh = shellfacetraverse(subfaces);
- while (subloop.sh != (shellface *) NULL) {
- // Only operate on uninfected subface, after operating, infect it.
- if (!sinfected(subloop)) {
- // A new facet is found.
- marker = shellmark(subloop);
- markerlist->append(&marker);
- facetidx = markerlist->len(); // 'facetidx' starts from 1.
- setshellmark(subloop, facetidx);
- sinfect(subloop);
- neighshlist->append(&subloop);
- // Find out all subfaces of this facet (bounded by subsegments).
- for (i = 0; i < neighshlist->len(); i++) {
- neighsh = * (face *) (* neighshlist)[i];
- for (j = 0; j < 3; j++) {
- sspivot(neighsh, subseg);
- if (subseg.sh == dummysh) {
- spivot(neighsh, neineighsh);
- if (!sinfected(neineighsh)) {
- // 'neineighsh' is in the same facet as 'subloop'.
-#ifdef SELF_CHECK
- assert(shellmark(neineighsh) == marker);
-#endif
- setshellmark(neineighsh, facetidx);
- sinfect(neineighsh);
- neighshlist->append(&neineighsh);
- }
- }
- senextself(neighsh);
- }
- }
- neighshlist->clear();
- }
- subloop.sh = shellfacetraverse(subfaces);
- }
- // Uninfect all subfaces.
- subfaces->traversalinit();
- subloop.sh = shellfacetraverse(subfaces);
- while (subloop.sh != (shellface *) NULL) {
-#ifdef SELF_CHECK
- assert(sinfected(subloop));
-#endif
- suninfect(subloop);
- subloop.sh = shellfacetraverse(subfaces);
- }
- // Save the facet markers in 'in->facetmarkerlist'.
- in->numberoffacets = markerlist->len();
- in->facetmarkerlist = new int[in->numberoffacets];
- for (i = 0; i < in->numberoffacets; i++) {
- marker = * (int *) (* markerlist)[i];
- in->facetmarkerlist[i] = marker;
- }
- // Initialize the 'facetabovepointlist'.
- facetabovepointarray = new point[in->numberoffacets + 1];
- for (i = 0; i < in->numberoffacets + 1; i++) {
- facetabovepointarray[i] = (point) NULL;
- }
-
- // The mesh contains boundary now.
- checksubfaces = 1;
- // The mesh is nonconvex now.
- nonconvex = 1;
-
- // Is there periodic boundary confitions?
- if (checkpbcs) {
- tetgenio::pbcgroup *pg;
- pbcdata *pd;
- // Initialize the global array 'subpbcgrouptable'.
- createsubpbcgrouptable();
- // Loop for each pbcgroup i.
- for (i = 0; i < in->numberofpbcgroups; i++) {
- pg = &(in->pbcgrouplist[i]);
- pd = &(subpbcgrouptable[i]);
- // Find all subfaces of pd, set each subface's group id be i.
- for (j = 0; j < 2; j++) {
- subfaces->traversalinit();
- subloop.sh = shellfacetraverse(subfaces);
- while (subloop.sh != (shellface *) NULL) {
- facetidx = shellmark(subloop);
- marker = in->facetmarkerlist[facetidx - 1];
- if (marker == pd->fmark[j]) {
- setshellpbcgroup(subloop, i);
- pd->ss[j] = subloop;
- }
- subloop.sh = shellfacetraverse(subfaces);
- }
- }
- if (pg->pointpairlist != (int *) NULL) {
- // Set the connections between pbc point pairs.
- for (j = 0; j < pg->numberofpointpairs; j++) {
- iorg = pg->pointpairlist[j * 2] - in->firstnumber;
- idest = pg->pointpairlist[j * 2 + 1] - in->firstnumber;
- torg = idx2verlist[iorg];
- tdest = idx2verlist[idest];
- setpoint2pbcpt(torg, tdest);
- setpoint2pbcpt(tdest, torg);
- }
- }
- }
- // Create the global array 'segpbcgrouptable'.
- createsegpbcgrouptable();
- }
-
- delete markerlist;
- delete neighshlist;
- delete [] worklist;
- delete [] idx2tetlist;
- delete [] tetsperverlist;
- delete [] idx2facelist;
- delete [] facesperverlist;
- delete [] idx2verlist;
-
- return hullsize;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// insertconstrainedpoints() Insert a list of constrained points. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::insertconstrainedpoints(tetgenio *addio)
-{
- queue *flipqueue;
- triface searchtet;
- face checksh, checkseg;
- point newpoint;
- enum locateresult loc;
- REAL *attr;
- bool insertflag;
- int covertices, outvertices;
- int index;
- int i, j;
-
- if (!b->quiet) {
- printf("Insert additional points into mesh.\n");
- }
- // Initialize 'flipqueue'.
- flipqueue = new queue(sizeof(badface));
- recenttet.tet = dummytet;
- covertices = outvertices = 0;
-
- index = 0;
- for (i = 0; i < addio->numberofpoints; i++) {
- // Create a newpoint.
- makepoint(&newpoint);
- newpoint[0] = addio->pointlist[index++];
- newpoint[1] = addio->pointlist[index++];
- newpoint[2] = addio->pointlist[index++];
- // Read the add point attributes if current points have attributes.
- if ((addio->numberofpointattributes > 0) &&
- (in->numberofpointattributes > 0)) {
- attr = addio->pointattributelist + addio->numberofpointattributes * i;
- for (j = 0; j < in->numberofpointattributes; j++) {
- if (j < addio->numberofpointattributes) {
- newpoint[3 + j] = attr[j];
- }
- }
- }
- // Find the location of the inserted point.
- searchtet = recenttet;
- loc = locate(newpoint, &searchtet);
- if (loc != ONVERTEX) {
- loc = adjustlocate(newpoint, &searchtet, loc, b->epsilon2);
- }
- if (loc == OUTSIDE) {
- loc = hullwalk(newpoint, &searchtet);
- if (loc == OUTSIDE) {
- // Perform a brute-force search.
- tetrahedrons->traversalinit();
- searchtet.tet = tetrahedrontraverse();
- while (searchtet.tet != (tetrahedron *) NULL) {
- loc = adjustlocate(newpoint, &searchtet, OUTSIDE, b->epsilon2);
- if (loc != OUTSIDE) break;
- searchtet.tet = tetrahedrontraverse();
- }
- }
- }
- // Insert the point if it not lies outside or on a vertex.
- insertflag = true;
- switch (loc) {
- case INTETRAHEDRON:
- setpointtype(newpoint, FREEVOLVERTEX);
- splittetrahedron(newpoint, &searchtet, flipqueue);
- break;
- case ONFACE:
- tspivot(searchtet, checksh);
- if (checksh.sh != dummysh) {
- // It is a boundary face. Don't insert it if -Y option is used.
- if (b->nobisect) {
- insertflag = false;
- } else {
- setpointtype(newpoint, FREESUBVERTEX);
- }
- } else {
- setpointtype(newpoint, FREEVOLVERTEX);
- }
- if (insertflag) {
- splittetface(newpoint, &searchtet, flipqueue);
- }
- break;
- case ONEDGE:
- tsspivot(&searchtet, &checkseg);
- if (checkseg.sh != dummysh) {
- if (b->nobisect) {
- insertflag = false;
- } else {
- setpointtype(newpoint, FREESEGVERTEX);
- setpoint2sh(newpoint, sencode(checkseg));
- }
- } else {
- tspivot(searchtet, checksh);
- if (checksh.sh != dummysh) {
- if (b->nobisect) {
- insertflag = false;
- } else {
- setpointtype(newpoint, FREESUBVERTEX);
- }
- } else {
- setpointtype(newpoint, FREEVOLVERTEX);
- }
- }
- if (insertflag) {
- splittetedge(newpoint, &searchtet, flipqueue);
- }
- break;
- case ONVERTEX:
- insertflag = false;
- covertices++;
- break;
- case OUTSIDE:
- insertflag = false;
- outvertices++;
- break;
- }
- // Remember the tetrahedron for next point searching.
- recenttet = searchtet;
- if (!insertflag) {
- pointdealloc(newpoint);
- } else {
- flip(flipqueue, NULL);
- }
- }
-
- if (b->verbose) {
- if (covertices > 0) {
- printf(" %d constrained points already exist.\n", covertices);
- }
- if (outvertices > 0) {
- printf(" %d constrained points lie outside the mesh.\n", outvertices);
- }
- printf(" %d constrained points have been inserted.\n",
- addio->numberofpoints - covertices - outvertices);
- }
-
- delete flipqueue;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// p1interpolatebgm() Set pt size by p^1 interpolation in background mesh.//
-// //
-// On input, 'bgmtet' is a suggesting tet in background mesh for searching //
-// 'pt'. It returns the tet containing 'pt'. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::p1interpolatebgm(point pt, triface* bgmtet, long *scount)
-{
- point bgmpt[4];
- enum locateresult loc;
- REAL vol, volpt[4], weights[4];
- int i;
-
- loc = bgm->preciselocate(pt, bgmtet, bgm->tetrahedrons->items);
- if (loc == OUTSIDE) {
- loc = bgm->hullwalk(pt, bgmtet);
- if (loc == OUTSIDE) {
- // Perform a brute-force search.
- if (b->verbose) {
- printf("Warning: Global point location.\n");
- }
- if (scount) (*scount)++;
- bgm->tetrahedrons->traversalinit(); // in bgm
- bgmtet->tet = bgm->tetrahedrontraverse(); // in bgm
- while (bgmtet->tet != (tetrahedron *) NULL) {
- loc = bgm->adjustlocate(pt, bgmtet, OUTSIDE, b->epsilon);
- if (loc != OUTSIDE) break;
- bgmtet->tet = bgm->tetrahedrontraverse(); // in bgm
- }
- }
- }
- if (loc != OUTSIDE) {
- // Let p remember t.
- setpoint2bgmtet(pt, encode(*bgmtet)); // in m
- // get the corners of t.
- for (i = 0; i < 4; i++) bgmpt[i] = (point) bgmtet->tet[4 + i];
- // Calculate the weighted coordinates of p in t.
- vol = orient3d(bgmpt[0], bgmpt[1], bgmpt[2], bgmpt[3]);
- volpt[0] = orient3d(pt, bgmpt[1], bgmpt[2], bgmpt[3]);
- volpt[1] = orient3d(bgmpt[0], pt, bgmpt[2], bgmpt[3]);
- volpt[2] = orient3d(bgmpt[0], bgmpt[1], pt, bgmpt[3]);
- volpt[3] = orient3d(bgmpt[0], bgmpt[1], bgmpt[2], pt);
- for (i = 0; i < 4; i++) weights[i] = fabs(volpt[i] / vol);
- // Interpolate the solution for p.
- for (i = 0; i < bgm->in->numberofpointmtrs; i++) {
- pt[pointmtrindex + i] = weights[0] * bgmpt[0][bgm->pointmtrindex + i]
- + weights[1] * bgmpt[1][bgm->pointmtrindex + i]
- + weights[2] * bgmpt[2][bgm->pointmtrindex + i]
- + weights[3] * bgmpt[3][bgm->pointmtrindex + i];
- }
- } else {
- setpoint2bgmtet(pt, (tetrahedron) NULL); // in m
- }
- return loc != OUTSIDE;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// interpolatesizemap() Interpolate the point sizes in the given size map.//
-// //
-// The size map is specified on each node of the background mesh. The points //
-// of current mesh get their sizes by interpolating. //
-// //
-// This function operation on two meshes simultaneously, the current mesh m, //
-// and the background mesh bgm. After this function, each point p in m will //
-// have a pointer to a tet of bgm. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::interpolatesizemap()
-{
- list *adjtetlist;
- triface tetloop, neightet, bgmtet;
- point searchpt;
- long scount;
- int *worklist;
- int sepcount;
- int i;
-
- if (b->verbose) {
- printf(" Interpolating size map.\n");
- }
-
- worklist = new int[points->items + 1];
- for (i = 0; i < points->items + 1; i++) worklist[i] = 0;
- sepcount = 0;
- scount = 0l;
-
- tetrahedrons->traversalinit();
- tetloop.tet = tetrahedrontraverse();
- while (tetloop.tet != (tetrahedron *) NULL) {
- if (!infected(tetloop)) {
- // Find a new subdomain.
- adjtetlist = new list(sizeof(triface), NULL, 1024);
- infect(tetloop);
- // Search the four corners in background mesh.
- for (i = 0; i < 4; i++) {
- searchpt = (point) tetloop.tet[4 + i];
- // Mark the point for avoiding multiple searchings.
- // assert(worklist[pointmark(searchpt)] == 0);
- worklist[pointmark(searchpt)] = 1;
- // Does it contain a pointer to bgm tet?
- bgm->decode(point2bgmtet(searchpt), bgmtet);
- if (bgm->isdead(&bgmtet)) {
- bgmtet = bgm->recenttet;
- }
- if (p1interpolatebgm(searchpt, &bgmtet, &scount)) {
- bgm->recenttet = bgmtet;
- }
- } // for (i = 0; i < 4; i++)
- // Collect all tets in this region.
- adjtetlist->append(&tetloop);
- // Collect the tets in the subdomain.
- for (i = 0; i < adjtetlist->len(); i++) {
- tetloop = * (triface *)(* adjtetlist)[i];
- for (tetloop.loc = 0; tetloop.loc < 4; tetloop.loc++) {
- sym(tetloop, neightet);
- if ((neightet.tet != dummytet) && !infected(neightet)) {
- // Only need to search for the opposite point.
- searchpt = oppo(neightet);
- if (worklist[pointmark(searchpt)] == 0) {
- worklist[pointmark(searchpt)] = 1;
- decode(point2bgmtet(searchpt), bgmtet);
- if (bgm->isdead(&bgmtet)) {
- bgmtet = bgm->recenttet;
- }
- if (p1interpolatebgm(searchpt, &bgmtet, &scount)) {
- bgm->recenttet = bgmtet;
- }
- }
- infect(neightet);
- adjtetlist->append(&neightet);
- }
- }
- }
- // Increase the number of separated domains.
- sepcount++;
- delete adjtetlist;
- } // if (!infect())
- tetloop.tet = tetrahedrontraverse();
- }
-
- // Unmark all tets.
- tetrahedrons->traversalinit();
- tetloop.tet = tetrahedrontraverse();
- while (tetloop.tet != (tetrahedron *) NULL) {
- assert(infected(tetloop));
- uninfect(tetloop);
- tetloop.tet = tetrahedrontraverse();
- }
- delete [] worklist;
-
-#ifdef SELF_CHECK
- if (b->verbose && scount > 0l) {
- printf(" %ld brute-force searches.\n", scount);
- }
- if (b->verbose && sepcount > 0) {
- printf(" %d separate domains.\n", sepcount);
- }
-#endif
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// duplicatebgmesh() Duplicate current mesh to background mesh. //
-// //
-// Current mesh 'this' is copied into 'this->bgm'.Both meshes share the same //
-// input tetgenio object, 'this->in', same tetgenbehavior object 'this->b'. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::duplicatebgmesh()
-{
- triface tetloop, btetloop;
- triface symtet, bsymtet;
- face bhullsh, bneighsh;
- point *idx2bplist, *tetptbaklist;
- point ploop, bploop;
- int idx, i;
-
- if (!b->quiet) {
- printf("Duplicating background mesh.\n");
- }
-
- // The background mesh itself has no background mesh.
- // assert(bgm->bgm == (tetgenmesh *) NULL);
- // The space for metric tensor should be allocated.
- // assert(bgm->sizeoftensor > 0);
-
- // Copy point list.
- idx2bplist = new point[points->items + 1];
- idx = in->firstnumber;
- points->traversalinit();
- ploop = pointtraverse();
- while (ploop != (point) NULL) {
- bgm->makepoint(&bploop);
- // Copy coordinates, attributes.
- for (i = 0; i < 3 + in->numberofpointattributes; i++) {
- bploop[i] = ploop[i];
- }
- // Transfer the metric tensor.
- for (i = 0; i < bgm->sizeoftensor; i++) {
- bploop[bgm->pointmtrindex + i] = ploop[pointmtrindex + i];
- // Metric tensor should have a positive value.
- if (bploop[bgm->pointmtrindex + i] <= 0.0) {
- printf("Error: Point %d has non-positive size %g (-m option).\n",
- bgm->pointmark(bploop), bploop[bgm->pointmtrindex + i]);
- terminatetetgen(1);
- }
- }
- // Remember the point for searching.
- idx2bplist[idx++] = bploop;
- ploop = pointtraverse();
- }
-
- // Copy tetrahedra list.
- tetptbaklist = new point[tetrahedrons->items + 1];
- idx = in->firstnumber;
- tetrahedrons->traversalinit();
- tetloop.tet = tetrahedrontraverse();
- while (tetloop.tet != (tetrahedron *) NULL) {
- bgm->maketetrahedron(&btetloop);
- // Set the four corners.
- for (i = 0; i < 4; i++) {
- ploop = (point) tetloop.tet[4 + i];
- bploop = idx2bplist[pointmark(ploop)];
- btetloop.tet[4 + i] = (tetrahedron) bploop;
- }
- // Remember the tet for setting neighbor connections.
- tetptbaklist[idx++] = (point) tetloop.tet[4];
- tetloop.tet[4] = (tetrahedron) btetloop.tet;
- tetloop.tet = tetrahedrontraverse();
- }
-
- // Set the connections between background tetrahedra. Create background
- // hull subfaces. Create the map of point-to-bgmtet.
- idx = in->firstnumber;
- tetrahedrons->traversalinit();
- tetloop.tet = tetrahedrontraverse();
- while (tetloop.tet != (tetrahedron *) NULL) {
- // Get the corresponding background tet.
- btetloop.tet = (tetrahedron *) tetloop.tet[4];
- // Set the four neighbors.
- for (tetloop.loc = 0; tetloop.loc < 4; tetloop.loc++) {
- btetloop.loc = tetloop.loc;
- sym(tetloop, symtet);
- if ((symtet.tet != dummytet) && (symtet.tet > tetloop.tet)) {
- // Operate on the un-connected interior face.
- bsymtet.tet = (tetrahedron *) symtet.tet[4]; // The saved bgm tet.
- bsymtet.loc = symtet.loc;
- bgm->bond(btetloop, bsymtet);
- } else if (symtet.tet == dummytet) {
- // Create a subface in background mesh.
- bgm->makeshellface(bgm->subfaces, &bhullsh);
- bgm->adjustedgering(btetloop, CCW); // face to inside.
- bgm->setsorg(bhullsh, bgm->org(btetloop));
- bgm->setsdest(bhullsh, bgm->dest(btetloop));
- bgm->setsapex(bhullsh, bgm->apex(btetloop));
- bgm->tsbond(btetloop, bhullsh);
- // Remember a hull face for point location.
- bgm->dummytet[0] = bgm->encode(btetloop);
- }
- }
- // Restore the backup tet point.
- tetloop.tet[4] = (tetrahedron) tetptbaklist[idx++];
- // Make the point-to-bgmtet map for size interpolation.
- btetloop.loc = 0;
- for (i = 0; i < 4; i++) {
- ploop = (point) tetloop.tet[4 + i];
- setpoint2bgmtet(ploop, bgm->encode(btetloop));
- }
- // Go to the next tet, btet.
- tetloop.tet = tetrahedrontraverse();
- }
-
- // Connect bgm hull subfaces. Note: all hull subfaces form a 2-manifold.
- bgm->subfaces->traversalinit();
- bhullsh.sh = bgm->shellfacetraverse(bgm->subfaces);
- while (bhullsh.sh != (shellface *) NULL) {
- bhullsh.shver = 0;
- bgm->stpivot(bhullsh, btetloop);
- assert(btetloop.tet != bgm->dummytet);
- bgm->adjustedgering(btetloop, CCW);
- for (i = 0; i < 3; i++) {
- bgm->spivot(bhullsh, bneighsh);
- if (bneighsh.sh == bgm->dummysh) {
- // This side is open, operate on it.
- bsymtet = btetloop;
- while (bgm->fnextself(bsymtet));
- bgm->tspivot(bsymtet, bneighsh);
- bgm->findedge(&bneighsh, bgm->sdest(bhullsh), bgm->sorg(bhullsh));
- bgm->sbond(bhullsh, bneighsh);
- }
- bgm->enextself(btetloop);
- bgm->senextself(bhullsh);
- }
- bhullsh.sh = bgm->shellfacetraverse(bgm->subfaces);
- }
-
- delete [] tetptbaklist;
- delete [] idx2bplist;
-}
-
-//
-// Begin of Delaunay refinement routines
-//
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// marksharpsegments() Mark sharp segments. //
-// //
-// A segment s is called sharp if it is in one of the two cases: //
-// (1) There is a segment s' intersecting with s. The internal angle (*) //
-// between s and s' is acute. //
-// (2) There are two facets f1 and f2 intersecting at s. The internal //
-// dihedral angle (*) between f1 and f2 is acute. //
-// This routine finds the sharp segments and marked them as type SHARP. //
-// The minimum angle between segments (minfaceang) and the minimum dihedral //
-// angle between facets (minfacetdihed) are calulcated. //
-// //
-// (*) The internal angle (or dihedral) bewteen two features means the angle //
-// inside the mesh domain. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::marksharpsegments(REAL sharpangle)
-{
- triface adjtet;
- face startsh, spinsh, neighsh;
- face segloop, prevseg, nextseg;
- point eorg, edest;
- REAL ang, smallang;
- bool issharp;
- int sharpsegcount;
-
- if (b->verbose > 0) {
- printf(" Marking sharp segments.\n");
- }
-
- smallang = sharpangle * PI / 180.;
- sharpsegcount = 0;
- eorg = edest = (point) NULL; // To avoid compiler warnings.
-
- // A segment s may have been split into many subsegments. Operate the one
- // which contains the origin of s. Then mark the rest of subsegments.
- subsegs->traversalinit();
- segloop.sh = shellfacetraverse(subsegs);
- while (segloop.sh != (shellface *) NULL) {
- segloop.shver = 0;
- senext2(segloop, prevseg);
- spivotself(prevseg);
- if (prevseg.sh == dummysh) {
- // Operate on this seg s.
- assert(shelltype(segloop) != SHARP); // It should be unmarked.
- issharp = false;
- spivot(segloop, startsh);
- if (startsh.sh != dummysh) {
- // First check if two facets form an acute dihedral angle at s.
- eorg = sorg(segloop);
- edest = sdest(segloop);
- spinsh = startsh;
- do {
- if (sorg(spinsh) != eorg) {
- sesymself(spinsh);
- }
- // Only do test when the spinsh is faceing inward.
- stpivot(spinsh, adjtet);
- if (adjtet.tet != dummytet) {
- // Get the subface on the adjacent facet.
- spivot(spinsh, neighsh);
- // Do not calculate if it is self-bonded.
- if (neighsh.sh != spinsh.sh) {
- // Calculate the dihedral angle between the two subfaces.
- ang = facedihedral(eorg, edest, sapex(spinsh), sapex(neighsh));
- // Only do check if a sharp angle has not been found.
- if (!issharp) issharp = (ang < smallang);
- // Remember the smallest facet dihedral angle.
- minfacetdihed = minfacetdihed < ang ? minfacetdihed : ang;
- }
- }
- // Go to the next facet.
- spivotself(spinsh);
- } while (spinsh.sh != startsh.sh);
- // if (!issharp) {
- // Second check if s forms an acute angle with another seg.
- spinsh = startsh;
- do {
- if (sorg(spinsh) != eorg) {
- sesymself(spinsh);
- }
- // Calculate the angle between s and s' of this facet.
- neighsh = spinsh;
- // Rotate edges around 'eorg' until meeting another seg s'. Such
- // seg (s') must exist since the facet is segment-bounded.
- // The sum of the angles of faces at 'eorg' gives the internal
- // angle between the two segments.
- ang = 0.0;
- do {
- ang += interiorangle(eorg, sdest(neighsh), sapex(neighsh), NULL);
- senext2self(neighsh);
- sspivot(neighsh, nextseg);
- if (nextseg.sh != dummysh) break;
- // Go to the next coplanar subface.
- spivotself(neighsh);
- assert(neighsh.sh != dummysh);
- if (sorg(neighsh) != eorg) {
- sesymself(neighsh);
- }
- } while (true);
- // Only do check if a sharp angle has not been found.
- if (!issharp) issharp = (ang < smallang);
- // Remember the smallest input face angle.
- minfaceang = minfaceang < ang ? minfaceang : ang;
- // Go to the next facet.
- spivotself(spinsh);
- } while (spinsh.sh != startsh.sh);
- // }
- }
- if (issharp) {
- setshelltype(segloop, SHARP);
- // Set the type for all subsegments at forwards.
- senext(segloop, nextseg);
- spivotself(nextseg);
- while (nextseg.sh != dummysh) {
- nextseg.shver = 0;
- setshelltype(nextseg, SHARP);
- senextself(nextseg);
- spivotself(nextseg);
- }
- sharpsegcount++;
- }
- }
- segloop.sh = shellfacetraverse(subsegs);
- }
-
- // So far we have marked all segments which have an acute dihedral angle
- // or whose ORIGINs have an acute angle. In the un-marked subsegments,
- // there are possible ones whose DESTINATIONs have an acute angle.
- subsegs->traversalinit();
- segloop.sh = shellfacetraverse(subsegs);
- while (segloop.sh != (shellface *) NULL) {
- // Only operate if s is non-sharp and contains the dest.
- segloop.shver = 0;
- senext(segloop, nextseg);
- spivotself(nextseg);
- // if ((nextseg.sh == dummysh) && (shelltype(segloop) != SHARP)) {
- if (nextseg.sh == dummysh) {
- // issharp = false;
- issharp = (shelltype(segloop) == SHARP);
- spivot(segloop, startsh);
- if (startsh.sh != dummysh) {
- // Check if s forms an acute angle with another seg.
- eorg = sdest(segloop);
- spinsh = startsh;
- do {
- if (sorg(spinsh) != eorg) {
- sesymself(spinsh);
- }
- // Calculate the angle between s and s' of this facet.
- neighsh = spinsh;
- ang = 0.0;
- do {
- ang += interiorangle(eorg, sdest(neighsh), sapex(neighsh), NULL);
- senext2self(neighsh);
- sspivot(neighsh, nextseg);
- if (nextseg.sh != dummysh) break;
- // Go to the next coplanar subface.
- spivotself(neighsh);
- assert(neighsh.sh != dummysh);
- if (sorg(neighsh) != eorg) {
- sesymself(neighsh);
- }
- } while (true);
- // Only do check if a sharp angle has not been found.
- if (!issharp) issharp = (ang < smallang);
- // Remember the smallest input face angle.
- minfaceang = minfaceang < ang ? minfaceang : ang;
- // Go to the next facet.
- spivotself(spinsh);
- } while (spinsh.sh != startsh.sh);
- }
- if (issharp) {
- setshelltype(segloop, SHARP);
- // Set the type for all subsegments at backwards.
- senext2(segloop, prevseg);
- spivotself(prevseg);
- while (prevseg.sh != dummysh) {
- prevseg.shver = 0;
- setshelltype(prevseg, SHARP);
- senext2self(prevseg);
- spivotself(prevseg);
- }
- sharpsegcount++;
- }
- }
- segloop.sh = shellfacetraverse(subsegs);
- }
-
- if ((b->verbose > 0) && (sharpsegcount > 0)) {
- printf(" %d sharp segments.\n", sharpsegcount);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// decidefeaturepointsizes() Decide the sizes for all feature points. //
-// //
-// A feature point is a point on a sharp segment. Every feature point p will //
-// be assigned a positive size which is the radius of the protecting ball. //
-// //
-// The size of a feature point may be specified by one of the following ways://
-// (1) directly specifying on an input vertex (by using .mtr file); //
-// (2) imposing a fixed maximal volume constraint ('-a__' option); //
-// (3) imposing a maximal volume constraint in a region ('-a' option); //
-// (4) imposing a maximal area constraint on a facet (in .var file); //
-// (5) imposing a maximal length constraint on a segment (in .var file); //
-// (6) combining (1) - (5). //
-// (7) automatically deriving a size if none of (1) - (6) is available. //
-// In case (7),the size of p is set to be the smallest edge length among all //
-// edges connecting at p. The final size of p is the minimum of (1) - (7). //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::decidefeaturepointsizes()
-{
- list *tetlist, *verlist;
- shellface **segsperverlist;
- triface starttet;
- face shloop;
- face checkseg, prevseg, nextseg, testseg;
- point ploop, adjpt, e1, e2;
- REAL lfs_0, len, vol, maxlen, varlen;
- bool isfeature;
- int *idx2seglist;
- int featurecount;
- int idx, i, j;
-
- if (b->verbose > 0) {
- printf(" Deciding feature-point sizes.\n");
- }
-
- // Constructing a map from vertices to segments.
- makesegmentmap(idx2seglist, segsperverlist);
- // Initialize working lists.
- tetlist = new list(sizeof(triface), NULL, 256);
- verlist = new list(sizeof(point *), NULL, 256);
-
- if (b->fixedvolume) {
- // A fixed volume constraint is imposed. This gives an upper bound of
- // the maximal radius of the protect ball of a vertex.
- maxlen = pow(6.0 * b->maxvolume, 1.0/3.0);
- }
-
- if (!b->refine) {
- // Initially correct types for Steiner points.
- featurecount = 0;
- points->traversalinit();
- ploop = pointtraverse();
- while (ploop != (point) NULL) {
- if (pointtype(ploop) == NACUTEVERTEX) {
- if (point2sh(ploop) != (shellface) NULL) {
- setpointtype(ploop, FREESEGVERTEX);
- featurecount++;
- }
- }
- ploop = pointtraverse();
- }
-#ifdef SELF_CHECK
- if ((b->verbose > 0) && (featurecount > 0)) {
- printf(" %d Steiner points correction.\n", featurecount);
- }
-#endif
- }
-
- // First only assign a size of p if p is not a Steiner point. The size of
- // a Steiner point will be interpolated later from the endpoints of the
- // segment on which it lies.
- featurecount = 0;
- points->traversalinit();
- ploop = pointtraverse();
- while (ploop != (point) NULL) {
- if (pointtype(ploop) != FREESEGVERTEX) {
- // Is p a feature point?
- isfeature = false;
- idx = pointmark(ploop) - in->firstnumber;
- for (i = idx2seglist[idx]; i < idx2seglist[idx + 1] && !isfeature; i++) {
- checkseg.sh = segsperverlist[i];
- isfeature = (shelltype(checkseg) == SHARP);
- }
- // Decide the size of p if it is on a sharp segment.
- if (isfeature) {
- // Find a tet containing p (checkseg is a sharp seg which contains p).
- sstpivot(&checkseg, &starttet);
- // Form star(p).
- tetlist->append(&starttet);
- formstarpolyhedron(ploop, tetlist, verlist, true);
- // Decide the size for p if no input size is given on input.
- if (ploop[pointmtrindex] == 0.0) {
- // Calculate lfs_0(p).
- lfs_0 = longest;
- for (i = 0; i < verlist->len(); i++) {
- adjpt = * (point *)(* verlist)[i];
- if (pointtype(adjpt) == FREESEGVERTEX) {
- // A Steiner point q. Find the seg it lies on.
- sdecode(point2sh(adjpt), checkseg);
- assert(checkseg.sh != dummysh);
- checkseg.shver = 0;
- // Find the origin of this seg.
- prevseg = checkseg;
- do {
- senext2(prevseg, testseg);
- spivotself(testseg);
- if (testseg.sh == dummysh) break;
- prevseg = testseg; // Go to the previous subseg.
- prevseg.shver = 0;
- } while (true);
- // Find the dest of this seg.
- nextseg = checkseg;
- do {
- senext(nextseg, testseg);
- spivotself(testseg);
- if (testseg.sh == dummysh) break;
- nextseg = testseg; // Go to the next subseg.
- nextseg.shver = 0;
- } while (true);
- e1 = sorg(prevseg);
- e2 = sdest(nextseg);
- // Check if p is the origin or the dest of this seg.
- if (ploop == e1) {
- // Set q to be the dest of this seg.
- adjpt = e2;
- } else if (ploop == e2) {
- // Set q to be the org of this seg.
- adjpt = e1;
- }
- }
- len = distance(ploop, adjpt);
- if (lfs_0 > len) lfs_0 = len;
- }
- ploop[pointmtrindex] = lfs_0;
- }
- if (b->fixedvolume) {
- // A fixed volume constraint is imposed. Adjust H(p) <= maxlen.
- if (ploop[pointmtrindex] > maxlen) {
- ploop[pointmtrindex] = maxlen;
- }
- }
- if (b->varvolume) {
- // Variant volume constraints are imposed. Adjust H(p) <= varlen.
- for (i = 0; i < tetlist->len(); i++) {
- starttet = * (triface *)(* tetlist)[i];
- vol = volumebound(starttet.tet);
- if (vol > 0.0) {
- varlen = pow(6 * vol, 1.0/3.0);
- if (ploop[pointmtrindex] > varlen) {
- ploop[pointmtrindex] = varlen;
- }
- }
- }
- }
- // Clear working lists.
- tetlist->clear();
- verlist->clear();
- featurecount++;
- } else {
- // NO feature point, set the size of p be zero.
- ploop[pointmtrindex] = 0.0;
- }
- } // if (pointtype(ploop) != FREESEGVERTEX) {
- ploop = pointtraverse();
- }
-
- if (b->verbose > 0) {
- printf(" %d feature points.\n", featurecount);
- }
-
- if (!b->refine) {
- // Second only assign sizes for all Steiner points. A Steiner point p
- // inserted on a sharp segment s is assigned a size by interpolating
- // the sizes of the original endpoints of s.
- featurecount = 0;
- points->traversalinit();
- ploop = pointtraverse();
- while (ploop != (point) NULL) {
- if (pointtype(ploop) == FREESEGVERTEX) {
- if (ploop[pointmtrindex] == 0.0) {
- sdecode(point2sh(ploop), checkseg);
- assert(checkseg.sh != dummysh);
- if (shelltype(checkseg) == SHARP) {
- checkseg.shver = 0;
- // Find the origin of this seg.
- prevseg = checkseg;
- do {
- senext2(prevseg, testseg);
- spivotself(testseg);
- if (testseg.sh == dummysh) break;
- prevseg = testseg; // Go the previous subseg.
- prevseg.shver = 0;
- } while (true);
- // Find the dest of this seg.
- nextseg = checkseg;
- do {
- senext(nextseg, testseg);
- spivotself(testseg);
- if (testseg.sh == dummysh) break;
- nextseg = testseg; // Go the next subseg.
- nextseg.shver = 0;
- } while (true);
- e1 = sorg(prevseg);
- e2 = sdest(nextseg);
- len = distance(e1, e2);
- lfs_0 = distance(e1, ploop);
- // The following assert() happens when -Y option is used.
- if (b->nobisect == 0) {
- assert(lfs_0 < len);
- }
- ploop[pointmtrindex] = e1[pointmtrindex]
- + (lfs_0 / len) * (e2[pointmtrindex] - e1[pointmtrindex]);
- featurecount++;
- } else {
- // NO feature point, set the size of p be zero.
- ploop[pointmtrindex] = 0.0;
- } // if (shelltype(checkseg) == SHARP)
- } // if (ploop[pointmtrindex] == 0.0)
- } // if (pointtype(ploop) != FREESEGVERTEX)
- ploop = pointtraverse();
- }
- if ((b->verbose > 0) && (featurecount > 0)) {
- printf(" %d Steiner feature points.\n", featurecount);
- }
- }
-
- if (varconstraint) {
- // A .var file exists. Adjust feature sizes.
- if (in->facetconstraintlist) {
- // Have facet area constrains.
- subfaces->traversalinit();
- shloop.sh = shellfacetraverse(subfaces);
- while (shloop.sh != (shellface *) NULL) {
- varlen = areabound(shloop);
- if (varlen > 0.0) {
- // Check if the three corners are feature points.
- varlen = sqrt(varlen);
- for (j = 0; j < 3; j++) {
- ploop = (point) shloop.sh[3 + j];
- isfeature = false;
- idx = pointmark(ploop) - in->firstnumber;
- for (i = idx2seglist[idx]; i < idx2seglist[idx + 1] && !isfeature;
- i++) {
- checkseg.sh = segsperverlist[i];
- isfeature = (shelltype(checkseg) == SHARP);
- }
- if (isfeature) {
- assert(ploop[pointmtrindex] > 0.0);
- if (ploop[pointmtrindex] > varlen) {
- ploop[pointmtrindex] = varlen;
- }
- }
- } // for (j = 0; j < 3; j++)
- }
- shloop.sh = shellfacetraverse(subfaces);
- }
- }
- if (in->segmentconstraintlist) {
- // Have facet area constrains.
- subsegs->traversalinit();
- shloop.sh = shellfacetraverse(subsegs);
- while (shloop.sh != (shellface *) NULL) {
- varlen = areabound(shloop);
- if (varlen > 0.0) {
- // Check if the two endpoints are feature points.
- for (j = 0; j < 2; j++) {
- ploop = (point) shloop.sh[3 + j];
- isfeature = false;
- idx = pointmark(ploop) - in->firstnumber;
- for (i = idx2seglist[idx]; i < idx2seglist[idx + 1] && !isfeature;
- i++) {
- checkseg.sh = segsperverlist[i];
- isfeature = (shelltype(checkseg) == SHARP);
- }
- if (isfeature) {
- assert(ploop[pointmtrindex] > 0.0);
- if (ploop[pointmtrindex] > varlen) {
- ploop[pointmtrindex] = varlen;
- }
- }
- } // for (j = 0; j < 2; j++)
- }
- shloop.sh = shellfacetraverse(subsegs);
- }
- }
- } // if (varconstraint)
-
- delete [] segsperverlist;
- delete [] idx2seglist;
- delete tetlist;
- delete verlist;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// enqueueencsub() Add an encroached subface into the queue. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::enqueueencsub(face* testsub, point encpt, int quenumber,
- REAL* cent)
-{
- badface *encsub;
- int i;
-
- encsub = (badface *) badsubfaces->alloc();
- encsub->ss = *testsub;
- encsub->forg = sorg(*testsub);
- encsub->fdest = sdest(*testsub);
- encsub->fapex = sapex(*testsub);
- encsub->foppo = (point) encpt;
- for (i = 0; i < 3; i++) encsub->cent[i] = cent[i];
- encsub->nextitem = (badface *) NULL;
- // Set the pointer of 'encsubseg' into 'testsub'. It has two purposes:
- // (1) We can regonize it is encroached; (2) It is uniquely queued.
- setshell2badface(encsub->ss, encsub);
- // Add the subface to the end of a queue (quenumber = 2, high priority).
- *subquetail[quenumber] = encsub;
- // Maintain a pointer to the NULL pointer at the end of the queue.
- subquetail[quenumber] = &encsub->nextitem;
- if (b->verbose > 2) {
- printf(" Queuing subface (%d, %d, %d) [%d].\n", pointmark(encsub->forg),
- pointmark(encsub->fdest), pointmark(encsub->fapex), quenumber);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// dequeueencsub() Remove an enc-subface from the front of the queue. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-tetgenmesh::badface* tetgenmesh::dequeueencsub(int* pquenumber)
-{
- badface *result;
- int quenumber;
-
- // Look for a nonempty queue.
- for (quenumber = 2; quenumber >= 0; quenumber--) {
- result = subquefront[quenumber];
- if (result != (badface *) NULL) {
- // Remove the badface from the queue.
- subquefront[quenumber] = result->nextitem;
- // Maintain a pointer to the NULL pointer at the end of the queue.
- if (subquefront[quenumber] == (badface *) NULL) {
- subquetail[quenumber] = &subquefront[quenumber];
- }
- *pquenumber = quenumber;
- return result;
- }
- }
- return (badface *) NULL;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// enqueuebadtet() Add a tetrahedron into the queue. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::enqueuebadtet(triface* testtet, REAL ratio2, REAL* cent)
-{
- badface *newbadtet;
- int queuenumber;
- int i;
-
- // Allocate space for the bad tetrahedron.
- newbadtet = (badface *) badtetrahedrons->alloc();
- newbadtet->tt = *testtet;
- newbadtet->key = ratio2;
- if (cent != NULL) {
- for (i = 0; i < 3; i++) newbadtet->cent[i] = cent[i];
- } else {
- for (i = 0; i < 3; i++) newbadtet->cent[i] = 0.0;
- }
- newbadtet->forg = org(*testtet);
- newbadtet->fdest = dest(*testtet);
- newbadtet->fapex = apex(*testtet);
- newbadtet->foppo = oppo(*testtet);
- newbadtet->nextitem = (badface *) NULL;
- // Determine the appropriate queue to put the bad tetrahedron into.
- if (ratio2 > b->goodratio) {
- // queuenumber = (int) ((ratio2 - b->goodratio) / 0.5);
- queuenumber = (int) (64.0 - 64.0 / ratio2);
- // 'queuenumber' may overflow (negative) caused by a very large ratio.
- if ((queuenumber > 63) || (queuenumber < 0)) {
- queuenumber = 63;
- }
- } else {
- // It's not a bad ratio; put the tet in the lowest-priority queue.
- queuenumber = 0;
- }
-
- // Are we inserting into an empty queue?
- if (tetquefront[queuenumber] == (badface *) NULL) {
- // Yes. Will this become the highest-priority queue?
- if (queuenumber > firstnonemptyq) {
- // Yes, this is the highest-priority queue.
- nextnonemptyq[queuenumber] = firstnonemptyq;
- firstnonemptyq = queuenumber;
- } else {
- // No. Find the queue with next higher priority.
- i = queuenumber + 1;
- while (tetquefront[i] == (badface *) NULL) {
- i++;
- }
- // Mark the newly nonempty queue as following a higher-priority queue.
- nextnonemptyq[queuenumber] = nextnonemptyq[i];
- nextnonemptyq[i] = queuenumber;
- }
- // Put the bad tetrahedron at the beginning of the (empty) queue.
- tetquefront[queuenumber] = newbadtet;
- } else {
- // Add the bad tetrahedron to the end of an already nonempty queue.
- tetquetail[queuenumber]->nextitem = newbadtet;
- }
- // Maintain a pointer to the last tetrahedron of the queue.
- tetquetail[queuenumber] = newbadtet;
-
- if (b->verbose > 2) {
- printf(" Queueing bad tet: (%d, %d, %d, %d), ratio %g, qnum %d.\n",
- pointmark(newbadtet->forg), pointmark(newbadtet->fdest),
- pointmark(newbadtet->fapex), pointmark(newbadtet->foppo),
- sqrt(ratio2), queuenumber);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// dequeuebadtet() Remove a tetrahedron from the front of the queue. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-tetgenmesh::badface* tetgenmesh::topbadtetra()
-{
- // Keep a record of which queue was accessed in case dequeuebadtetra()
- // is called later.
- recentq = firstnonemptyq;
- // If no queues are nonempty, return NULL.
- if (firstnonemptyq < 0) {
- return (badface *) NULL;
- } else {
- // Return the first tetrahedron of the highest-priority queue.
- return tetquefront[firstnonemptyq];
- }
-}
-
-void tetgenmesh::dequeuebadtet()
-{
- badface *deadbadtet;
- int i;
-
- // If queues were empty last time topbadtetra() was called, do nothing.
- if (recentq >= 0) {
- // Find the tetrahedron last returned by topbadtetra().
- deadbadtet = tetquefront[recentq];
- // Remove the tetrahedron from the queue.
- tetquefront[recentq] = deadbadtet->nextitem;
- // If this queue is now empty, update the list of nonempty queues.
- if (deadbadtet == tetquetail[recentq]) {
- // Was this the highest-priority queue?
- if (firstnonemptyq == recentq) {
- // Yes; find the queue with next lower priority.
- firstnonemptyq = nextnonemptyq[firstnonemptyq];
- } else {
- // No; find the queue with next higher priority.
- i = recentq + 1;
- while (tetquefront[i] == (badface *) NULL) {
- i++;
- }
- nextnonemptyq[i] = nextnonemptyq[recentq];
- }
- }
- // Return the bad tetrahedron to the pool.
- badfacedealloc(badtetrahedrons, deadbadtet);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// checkseg4encroach() Check a subsegment to see if it is encroached. //
-// //
-// A segment s is encroached if there is a vertex lies inside or on its dia- //
-// metral circumsphere, i.e., s faces an angle theta >= 90 degrees. //
-// //
-// If 'testpt' (p) != NULL, only test if 'testseg' (s) is encroached by it, //
-// else, check all apexes of faces around s. Return TRUE if s is encroached. //
-// If and 'enqflag' is TRUE, add it into 'badsubsegs' if s is encroached. //
-// //
-// If 'prefpt' != NULL, it returns the reference point (defined in my paper) //
-// if it exists. This point is will be used to split s. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::checkseg4encroach(face* testseg, point testpt, point* prefpt,
- bool enqflag)
-{
- badface *encsubseg;
- triface starttet, spintet;
- point eorg, edest, eapex, encpt;
- REAL cent[3], radius, dist, diff;
- REAL maxradius;
- bool enq;
- int hitbdry;
-
- enq = false;
- eorg = sorg(*testseg);
- edest = sdest(*testseg);
- cent[0] = 0.5 * (eorg[0] + edest[0]);
- cent[1] = 0.5 * (eorg[1] + edest[1]);
- cent[2] = 0.5 * (eorg[2] + edest[2]);
- radius = distance(cent, eorg);
-
- if (varconstraint && (areabound(*testseg) > 0.0)) {
- enq = (2.0 * radius) > areabound(*testseg);
- }
-
- if (!enq) {
- maxradius = 0.0;
- if (testpt == (point) NULL) {
- // Check if it is encroached by traversing all faces containing it.
- sstpivot(testseg, &starttet);
- eapex = apex(starttet);
- spintet = starttet;
- hitbdry = 0;
- do {
- dist = distance(cent, apex(spintet));
- diff = dist - radius;
- if (fabs(diff) / radius <= b->epsilon) diff = 0.0; // Rounding.
- if (diff <= 0.0) {
- // s is encroached.
- enq = true;
- if (prefpt != (point *) NULL) {
- // Find the reference point.
- encpt = apex(spintet);
- circumsphere(eorg, edest, encpt, NULL, NULL, &dist);
- if (dist > maxradius) {
- // Rememebr this point.
- *prefpt = encpt;
- maxradius = dist;
- }
- } else {
- break;
- }
- }
- if (!fnextself(spintet)) {
- hitbdry++;
- if (hitbdry < 2) {
- esym(starttet, spintet);
- if (!fnextself(spintet)) {
- hitbdry++;
- }
- }
- }
- } while (apex(spintet) != eapex && (hitbdry < 2));
- } else {
- // Only check if 'testseg' is encroached by 'testpt'.
- dist = distance(cent, testpt);
- diff = dist - radius;
- if (fabs(diff) / radius <= b->epsilon) diff = 0.0; // Rounding.
- enq = (diff <= 0.0);
- }
- }
-
- if (enq && enqflag) {
- if (b->verbose > 2) {
- printf(" Queuing encroaching subsegment (%d, %d).\n",
- pointmark(eorg), pointmark(edest));
- }
- encsubseg = (badface *) badsubsegs->alloc();
- encsubseg->ss = *testseg;
- encsubseg->forg = eorg;
- encsubseg->fdest = edest;
- encsubseg->foppo = (point) NULL; // Not used.
- // Set the pointer of 'encsubseg' into 'testseg'. It has two purposes:
- // (1) We can regonize it is encroached; (2) It is uniquely queued.
- setshell2badface(encsubseg->ss, encsubseg);
- }
-
- return enq;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// checksub4encroach() Check a subface to see if it is encroached. //
-// //
-// A subface f is encroached if there is a vertex inside or on its diametral //
-// circumsphere. //
-// //
-// If 'testpt (p) != NULL', test if 'testsub' (f) is encroached by it, else, //
-// test if f is encroached by one of the two opposites of the adjacent tets. //
-// Return TRUE if f is encroached and queue it if 'enqflag' is set. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::checksub4encroach(face* testsub, point testpt, bool enqflag)
-{
- triface abuttet;
- point pa, pb, pc, encpt;
- REAL A[4][4], rhs[4], D;
- REAL cent[3], area;
- REAL radius, dist, diff;
- bool enq;
- int indx[4];
- int quenumber;
-
- enq = false;
- radius = 0.0;
- encpt = (point) NULL;
-
- pa = sorg(*testsub);
- pb = sdest(*testsub);
- pc = sapex(*testsub);
-
- // Compute the coefficient matrix A (3x3).
- A[0][0] = pb[0] - pa[0];
- A[0][1] = pb[1] - pa[1];
- A[0][2] = pb[2] - pa[2]; // vector V1 (pa->pb)
- A[1][0] = pc[0] - pa[0];
- A[1][1] = pc[1] - pa[1];
- A[1][2] = pc[2] - pa[2]; // vector V2 (pa->pc)
- cross(A[0], A[1], A[2]); // vector V3 (V1 X V2)
-
- if (varconstraint && (areabound(*testsub) > 0.0)) {
- // Check if the subface has too big area.
- area = 0.5 * sqrt(dot(A[2], A[2]));
- enq = area > areabound(*testsub);
- if (enq) {
- quenumber = 2; // A queue of subfaces having too big area.
- }
- }
-
- // Compute the right hand side vector b (3x1).
- rhs[0] = 0.5 * dot(A[0], A[0]);
- rhs[1] = 0.5 * dot(A[1], A[1]);
- rhs[2] = 0.0;
- // Solve the 3 by 3 equations use LU decomposition with partial pivoting
- // and backward and forward substitute..
- if (lu_decmp(A, 3, indx, &D, 0)) {
- lu_solve(A, 3, indx, rhs, 0);
- cent[0] = pa[0] + rhs[0];
- cent[1] = pa[1] + rhs[1];
- cent[2] = pa[2] + rhs[2];
- radius = sqrt(rhs[0] * rhs[0] + rhs[1] * rhs[1] + rhs[2] * rhs[2]);
- }
-
- if (!enq) {
- // Check if the subface is encroached.
- if (testpt == (point) NULL) {
- stpivot(*testsub, abuttet);
- if (abuttet.tet != dummytet) {
- dist = distance(cent, oppo(abuttet));
- diff = dist - radius;
- if (fabs(diff) / radius <= b->epsilon) diff = 0.0; // Rounding.
- enq = (diff <= 0.0);
- if (enq) encpt = oppo(abuttet);
- }
- if (!enq) {
- sesymself(*testsub);
- stpivot(*testsub, abuttet);
- if (abuttet.tet != dummytet) {
- dist = distance(cent, oppo(abuttet));
- diff = dist - radius;
- if (fabs(diff) / radius <= b->epsilon) diff = 0.0; // Rounding.
- enq = (diff <= 0.0);
- if (enq) encpt = oppo(abuttet);
- }
- }
- } else {
- dist = distance(cent, testpt);
- diff = dist - radius;
- if (fabs(diff) / radius <= b->epsilon) diff = 0.0; // Rounding.
- enq = (diff <= 0.0);
- }
- if (enq) {
- quenumber = 0; // A queue of encroached subfaces.
- }
- }
-
- if (enq && enqflag) {
- enqueueencsub(testsub, encpt, quenumber, cent);
- }
-
- return enq;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// checktet4badqual() Test a tetrahedron for quality measures. //
-// //
-// Tests a tetrahedron to see if it satisfies the minimum ratio condition //
-// and the maximum volume condition. Tetrahedra that aren't upto spec are //
-// added to the bad tetrahedron queue. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::checktet4badqual(triface* testtet, bool enqflag)
-{
- point pa, pb, pc, pd, pe1, pe2;
- REAL vda[3], vdb[3], vdc[3];
- REAL vab[3], vbc[3], vca[3];
- REAL N[4][3], A[4][4], rhs[4], D;
- REAL elen[6], circumcent[3];
- REAL bicent[3], offcent[3];
- REAL volume, L, cosd;
- REAL radius2, smlen2, ratio2;
- REAL dist, sdist, split;
- bool enq;
- int indx[4];
- int sidx, i, j;
-
- pa = (point) testtet->tet[4];
- pb = (point) testtet->tet[5];
- pc = (point) testtet->tet[6];
- pd = (point) testtet->tet[7];
-
- // Get the edge vectors vda: d->a, vdb: d->b, vdc: d->c.
- // Set the matrix A = [vda, vdb, vdc]^T.
- for (i = 0; i < 3; i++) A[0][i] = vda[i] = pa[i] - pd[i];
- for (i = 0; i < 3; i++) A[1][i] = vdb[i] = pb[i] - pd[i];
- for (i = 0; i < 3; i++) A[2][i] = vdc[i] = pc[i] - pd[i];
- // Get the rest edge vectors
- for (i = 0; i < 3; i++) vab[i] = pb[i] - pa[i];
- for (i = 0; i < 3; i++) vbc[i] = pc[i] - pb[i];
- for (i = 0; i < 3; i++) vca[i] = pa[i] - pc[i];
-
- // Lu-decompose the matrix A.
- lu_decmp(A, 3, indx, &D, 0);
- // Get the volume of abcd.
- volume = (A[indx[0]][0] * A[indx[1]][1] * A[indx[2]][2]) / 6.0;
- if (volume < 0.0) volume = -volume;
- // Check the radiu-edge ratio of the tet.
- rhs[0] = 0.5 * dot(vda, vda);
- rhs[1] = 0.5 * dot(vdb, vdb);
- rhs[2] = 0.5 * dot(vdc, vdc);
- lu_solve(A, 3, indx, rhs, 0);
- // Get the circumcenter.
- for (i = 0; i < 3; i++) circumcent[i] = pd[i] + rhs[i];
- // Get the square of the circumradius.
- radius2 = dot(rhs, rhs);
- // Find the square of the shortest edge length.
- elen[0] = dot(vda, vda);
- elen[1] = dot(vdb, vdb);
- elen[2] = dot(vdc, vdc);
- elen[3] = dot(vab, vab);
- elen[4] = dot(vbc, vbc);
- elen[5] = dot(vca, vca);
- smlen2 = elen[0]; sidx = 0;
- for (i = 1; i < 6; i++) {
- if (smlen2 > elen[i]) { smlen2 = elen[i]; sidx = i; }
- }
- // Calculate the square of radius-edge ratio.
- ratio2 = radius2 / smlen2;
- // Check whether the ratio is smaller than permitted.
- enq = ratio2 > b->goodratio;
- if (!enq) {
- // abcd has good ratio.
- // ratio2 = 0.0;
- // if (b->offcenter) {
- // Test if it is a sliver.
- // Compute the 4 face normals (N[0], ..., N[3]).
- for (j = 0; j < 3; j++) {
- for (i = 0; i < 3; i++) rhs[i] = 0.0;
- rhs[j] = 1.0; // Positive means the inside direction
- lu_solve(A, 3, indx, rhs, 0);
- for (i = 0; i < 3; i++) N[j][i] = rhs[i];
- }
- // Get the fourth normal by summing up the first three.
- for (i = 0; i < 3; i++) N[3][i] = - N[0][i] - N[1][i] - N[2][i];
- // Normalized the normals.
- for (i = 0; i < 4; i++) {
- L = sqrt(dot(N[i], N[i]));
- if (L > 0.0) {
- for (j = 0; j < 3; j++) N[i][j] /= L;
- }
- }
- // N[0] is the normal of face bcd. Test the dihedral angles at edge
- // cd, bd, and bc to see if they are too small or too big.
- for (i = 1; i < 4 && !enq; i++) {
- cosd = -dot(N[0], N[i]); // Edge cd, bd, bc.
- enq = cosd > cosmindihed;
- }
- if (!enq) {
- for (i = 2; i < 4 && !enq; i++) {
- cosd = -dot(N[1], N[i]); // Edge ad, ac
- enq = cosd > cosmindihed;
- }
- if (!enq) {
- cosd = -dot(N[2], N[3]); // Edge ab
- enq = cosd > cosmindihed;
- }
- }
- // }
- } else if (b->offcenter) {
- // abcd has bad-quality. Use off-center instead of circumcenter.
- switch (sidx) {
- case 0: // edge da.
- pe1 = pd; pe2 = pa; break;
- case 1: // edge db.
- pe1 = pd; pe2 = pb; break;
- case 2: // edge dc.
- pe1 = pd; pe2 = pc; break;
- case 3: // edge ab.
- pe1 = pa; pe2 = pb; break;
- case 4: // edge bc.
- pe1 = pb; pe2 = pc; break;
- case 5: // edge ca.
- pe1 = pc; pe2 = pa; break;
- default:
- pe1 = pe2 = (point) NULL; // Avoid a compile warning.
- }
- // The shortest edge is e1->e2.
- for (i = 0; i < 3; i++) bicent[i] = 0.5 * (pe1[i] + pe2[i]);
- dist = distance(bicent, circumcent);
- // sdist = sqrt(smlen2) * sin(PI / 3.0); // A icoso-triangle.
- // The following formulae is from
- sdist = b->alpha3 * (b->minratio+sqrt(b->goodratio-0.25))* sqrt(smlen2);
- split = sdist / dist;
- if (split > 1.0) split = 1.0;
- // Get the off-center.
- for (i = 0; i < 3; i++) {
- offcent[i] = bicent[i] + split * (circumcent[i] - bicent[i]);
- }
- }
-
- if (!enq && (b->varvolume || b->fixedvolume)) {
- // Check if the tet has too big volume.
- enq = b->fixedvolume && (volume > b->maxvolume);
- if (!enq && b->varvolume) {
- enq = (volume > volumebound(testtet->tet)) &&
- (volumebound(testtet->tet) > 0.0);
- }
- }
-
- if (!enq) {
- // Check if the user-defined sizing function is satisfied.
- if (b->metric) {
- // assert(b->alpha1 > 0.0);
- sdist = sqrt(radius2) / b->alpha1;
- for (i = 0; i < 4; i++) {
- pa = (point) testtet->tet[4 + i];
- // Get the indicated size of p.
- dist = pa[pointmtrindex]; // dist = b->alpha1 * pa[pointmtrindex];
- enq = ((dist < sdist) && (dist > 0.0));
- if (enq) break; // It is bad wrt. a node constraint.
- // *** Experiment ! Stop test if c is inside H(a).
- // if ((dist > 0.0) && (dist > sdist)) break;
- }
- // *** Experiment !
- // enq = (i == 4); // Does c lies outside all sparse-ball?
- } // if (b->metric)
- }
-
- if (enq && enqflag) {
- if (b->offcenter && (ratio2 > b->goodratio)) {
- for (i = 0; i < 3; i++) circumcent[i] = offcent[i];
- }
- enqueuebadtet(testtet, ratio2, circumcent);
- }
-
- return enq;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// acceptsegpt() Check if a segment point can be inserted or not. //
-// //
-// Segment(ab) is indicated to be split by a point p (\in ab). This routine //
-// decides whether p can be inserted or not. //
-// //
-// p can not be inserted either the '-Y' option is used and ab is a hull //
-// segment or '-YY' option is used. //
-// //
-// p can be inserted if it is in one of the following cases: //
-// (1) if L = |a - b| is too long wrt the edge constraint; or //
-// (2) if |x - p| > \alpha_2 H(x) for x = a, b; or //
-// (3) if 'refpt' != NULL. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::acceptsegpt(point segpt, point refpt, face* splitseg)
-{
- point p[2];
- REAL L, lfs;
- int i, j;
-
- if (b->nobisect == 1) {
- // '-Y'. It can not be split if it is on the hull.
- triface spintet;
- point pc;
- sstpivot(splitseg, &spintet);
- assert(spintet.tet != dummytet);
- pc = apex(spintet);
- do {
- if (!fnextself(spintet)) {
- // Meet a boundary face - s is on the hull.
- return false;
- }
- } while (pc != apex(spintet));
- } else if (b->nobisect > 1) {
- // '-YY'. Do not split it.
- return false;
- }
-
- p[0] = sorg(*splitseg);
- p[1] = sdest(*splitseg);
- if (varconstraint && (areabound(*splitseg) > 0)) {
- lfs = areabound(*splitseg);
- L = distance(p[0], p[1]);
- if (L > lfs) {
- return true; // case (1)
- }
- }
-
- j = 0; // Use j to count the number of inside balls.
- for (i = 0; i < 2; i++) {
- // Check if p is inside the protect ball of q.
- if (p[i][pointmtrindex] > 0.0) {
- lfs = b->alpha2 * p[i][pointmtrindex];
- L = distance(p[i], segpt);
- if (L < lfs) j++; // p is inside ball.
- }
- }
- if (j == 0) return true; // case (3).
-
- // If 'refpt' != NULL, force p to be inserted.
- if (refpt != (point) NULL) {
- cdtenforcesegpts++;
- return true;
- }
-
- // Do not split it.
- rejsegpts++;
- return false;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// acceptfacpt() Check if a facet point can be inserted or not. //
-// //
-// 'subceillist' is CBC(p). 'verlist' (V) is empty on input, it returns the //
-// set of vertices of CBC(p). //
-// //
-// p can not be inserted either the '-Y' option is used and the facet is on //
-// the hull or '-YY' option is used. //
-// //
-// p can be inserted if |p - v| > \alpha_2 H(v), for all v \in V. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::acceptfacpt(point facpt, list* subceillist, list* verlist)
-{
- face *testsh;
- point p[2], ploop;
- REAL L, lfs;
- int idx, i, j;
-
- if (b->nobisect == 1) {
- // '-Y'. p can not be inserted if CBC(p) is on the hull.
- triface testtet;
- testsh = (face *)(* subceillist)[0];
- stpivot(*testsh, testtet);
- if (testtet.tet != dummytet) {
- sesymself(*testsh);
- stpivot(*testsh, testtet);
- }
- if (testtet.tet == dummytet) return false;
- } else if (b->nobisect > 1) {
- // '-YY'. Do not split s.
- return false;
- }
-
- // Collect the vertices of CBC(p), save them in V.
- for (i = 0; i < subceillist->len(); i++) {
- testsh = (face *)(* subceillist)[i];
- p[0] = sorg(*testsh);
- p[1] = sdest(*testsh);
- for (j = 0; j < 2; j++) {
- idx = pointmark(p[j]);
- if (idx >= 0) {
- setpointmark(p[j], -idx - 1);
- verlist->append(&(p[j]));
- }
- }
- }
-
- j = 0; // Use j to count the number of inside balls.
- for (i = 0; i < verlist->len(); i++) {
- ploop = * (point *)(* verlist)[i];
- // Uninfect q.
- idx = pointmark(ploop);
- setpointmark(ploop, -(idx + 1));
- // Check if p is inside the protect ball of q.
- if (ploop[pointmtrindex] > 0.0) {
- lfs = b->alpha2 * ploop[pointmtrindex];
- L = distance(ploop, facpt);
- if (L < lfs) j++; // p is inside ball.
- }
- }
- verlist->clear();
-
- if (j == 0) return true; // case (3).
-
- rejsubpts++;
- return false;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// acceptvolpt() Check if a volume point can be inserted or not. //
-// //
-// 'ceillist' is B(p). 'verlist' (V) is empty on input, it returns the set //
-// of vertices of B(p). //
-// //
-// p can be split if |p - v| > \alpha_2 H(v), for all v \in V. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::acceptvolpt(point volpt, list* ceillist, list* verlist)
-{
- triface* testtet;
- point p[3], ploop;
- REAL L, lfs;
- int idx, i, j;
-
- // Collect the vertices of CBC(p), save them in V.
- for (i = 0; i < ceillist->len(); i++) {
- testtet = (triface *)(* ceillist)[i];
- p[0] = org(*testtet);
- p[1] = dest(*testtet);
- p[2] = apex(*testtet);
- for (j = 0; j < 3; j++) {
- idx = pointmark(p[j]);
- if (idx >= 0) {
- setpointmark(p[j], -idx - 1);
- verlist->append(&(p[j]));
- }
- }
- }
-
- j = 0; // Use j to counte the number of inside balls.
- for (i = 0; i < verlist->len(); i++) {
- ploop = * (point *)(* verlist)[i];
- // Uninfect q.
- idx = pointmark(ploop);
- setpointmark(ploop, -(idx + 1));
- // Check if p is inside the protect ball of q.
- if (ploop[pointmtrindex] > 0.0) {
- lfs = b->alpha2 * ploop[pointmtrindex];
- L = distance(ploop, volpt);
- if (L < lfs) j++; // p is inside the protect ball.
- }
- }
- verlist->clear();
-
- if (j == 0) return true; // case (2).
-
- rejtetpts++;
- return false;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// getsplitpoint() Get the inserting point in a segment. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::getsplitpoint(point e1, point e2, point refpt, point newpt)
-{
- point ei, ej;
- REAL split, L, d1, d2, ps, rs;
- bool acutea, acuteb;
- int i;
-
- if (refpt != (point) NULL) {
- // Use the CDT rules to split the segment.
- acutea = (pointtype(e1) == ACUTEVERTEX);
- acuteb = (pointtype(e2) == ACUTEVERTEX);
- if (acutea ^ acuteb) {
- // Only one endpoint is acute. Use rule-2 or rule-3.
- ei = acutea ? e1 : e2;
- ej = acutea ? e2 : e1;
- L = distance(ei, ej);
- // Apply rule-2.
- d1 = distance(ei, refpt);
- split = d1 / L;
- for (i = 0; i < 3; i++) newpt[i] = ei[i] + split * (ej[i] - ei[i]);
- // Check if rule-3 is needed.
- d2 = distance(refpt, newpt);
- if (d2 > (L - d1)) {
- // Apply rule-3.
- if ((d1 - d2) > (0.5 * d1)) {
- split = (d1 - d2) / L;
- } else {
- split = 0.5 * d1 / L;
- }
- for (i = 0; i < 3; i++) newpt[i] = ei[i] + split * (ej[i] - ei[i]);
- if (b->verbose > 1) {
- printf(" Found by rule-3:");
- }
- r3count++;
- } else {
- if (b->verbose > 1) {
- printf(" Found by rule-2:");
- }
- r2count++;
- }
- if (b->verbose > 1) {
- printf(" center %d, split = %.12g.\n", pointmark(ei), split);
- }
- // Add a random perturbation on newpt.
- d1 = distance(ei, newpt);
- d2 = distance(newpt, refpt);
- ps = randgenerator(d2 * b->epsilon2 * 1e+2);
- rs = ps / d1;
- // Perturb newpt away from ei.
- for (i = 0; i < 3; i++) newpt[i] = ei[i] + (1.0+rs) * (newpt[i] - ei[i]);
- } else {
- // Both endpoints are acute or not. Split it at the middle.
- for (i = 0; i < 3; i++) newpt[i] = 0.5 * (e1[i] + e2[i]);
- // Add a random perturbation on newpt.
- d1 = 0.5 * distance(e1, e2);
- ps = randgenerator(d1 * b->epsilon2 * 1e+2);
- rs = ps / d1;
- for (i = 0; i < 3; i++) newpt[i] = e1[i] + (1.0+rs) * (newpt[i] - e1[i]);
- }
- } else {
- // Split the segment at its midpoint.
- for (i = 0; i < 3; i++) newpt[i] = 0.5 * (e1[i] + e2[i]);
- // Add a random perturbation on newpt.
- d1 = 0.5 * distance(e1, e2);
- ps = randgenerator(d1 * b->epsilon2 * 1e+2);
- rs = ps / d1;
- for (i = 0; i < 3; i++) newpt[i] = e1[i] + (1.0+rs) * (newpt[i] - e1[i]);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// shepardinterpolation() Interpolate the local size of a newpoint. //
-// //
-// The classical Shepard interoplation (inversed weighted distance) is used. //
-// (With the choice p = 2). //
-// //
-// 'verlist' contains a list vertices neighboring to 'newpt'. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::shepardinterpolate(point newpt, list *verlist)
-{
- point neipt;
- REAL *weights, sumweight;
- REAL vec[3];
- int i, j;
-
- weights = new REAL[verlist->len()];
- sumweight = 0.0;
-
- // Calculate the weight of each point.
- for (i = 0; i < verlist->len(); i++) {
- neipt = * (point *)(* verlist)[i];
- for (j = 0; j < 3; j++) vec[j] = neipt[j] - newpt[j];
- weights[i] = 1.0 / dot(vec, vec);
- sumweight += weights[i];
- }
- // Interpolate.
- newpt[pointmtrindex] = 0.0;
- for (i = 0; i < verlist->len(); i++) {
- neipt = * (point *)(* verlist)[i];
- newpt[pointmtrindex] += (weights[i] * neipt[pointmtrindex]) / sumweight;
- }
-
- delete [] weights;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// setnewpointsize() Set the size for a new point. //
-// //
-// The size of the new point p is interpolated either from a background mesh //
-// (b->bgmesh) or from the two input endpoints. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::setnewpointsize(point newpt, point e1, point e2)
-{
- if (b->metric) {
- // Interpolate the point size in a background mesh.
- triface bgmtet;
- // Get a tet in background mesh for locating p.
- decode(point2bgmtet(e1), bgmtet);
- p1interpolatebgm(newpt, &bgmtet, NULL);
- } else {
- if (e2 != (point) NULL) {
- // Interpolate the size between the two endpoints.
- REAL split, l, d;
- l = distance(e1, e2);
- d = distance(e1, newpt);
- split = d / l;
-#ifdef SELF_CHECK
- // Check if e1 and e2 are endpoints of a sharp segment.
- assert(e1[pointmtrindex] > 0.0);
- assert(e2[pointmtrindex] > 0.0);
-#endif
- newpt[pointmtrindex] = (1.0 - split) * e1[pointmtrindex]
- + split * e2[pointmtrindex];
- }
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// splitencseg() Split an enc-seg and recover the Delaunayness by flips. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::splitencseg(point newpt, face* splitseg, list* tetlist,
- list* sublist, list* verlist, queue* flipque, bool chkencsub, bool chkbadtet,
- bool optflag)
-{
- list *mytetlist;
- queue *myflipque;
- triface starttet;
- face startsh, spinsh, checksh;
- int i;
-
- if (optflag) {
- mytetlist = new list(sizeof(triface), NULL, 1024);
- myflipque = new queue(sizeof(badface));
- tetlist = mytetlist;
- flipque = myflipque;
- }
-
- // Use the base orientation (important in this routine).
- splitseg->shver = 0;
- // Insert p, this should always success.
- sstpivot(splitseg, &starttet);
- splittetedge(newpt, &starttet, flipque);
- // Remove locally non-Delaunay faces by flipping.
- flip(flipque, NULL); // lawson(NULL, flipque);
-
- if (!optflag) {
- // Check the two new subsegs to see if they're encroached (not by p).
- for (i = 0; i < 2; i++) {
- if (!shell2badface(*splitseg)) {
- checkseg4encroach(splitseg, NULL, NULL, true);
- }
- if (i == 1) break; // Two new segs have been checked.
- senextself(*splitseg);
- spivotself(*splitseg);
-#ifdef SELF_CHECK
- assert(splitseg->sh != (shellface *) NULL);
-#endif
- splitseg->shver = 0;
- }
- // Check the new subfaces to see if they're encroached (not by p).
- if (chkencsub) {
- spivot(*splitseg, startsh);
- spinsh = startsh;
- do {
- sublist->append(&spinsh);
- formstarpolygon(newpt, sublist, verlist);
- for (i = 0; i < sublist->len(); i++) {
- checksh = * (face *)(* sublist)[i];
- if (!shell2badface(checksh)) {
- checksub4encroach(&checksh, NULL, true);
- }
- }
- sublist->clear();
- if (verlist) verlist->clear();
- spivotself(spinsh);
- } while (spinsh.sh != startsh.sh);
- }
- } // if (!optflag)
-
- // Collect the new tets connecting at p.
- sstpivot(splitseg, &starttet);
- tetlist->append(&starttet);
- formstarpolyhedron(newpt, tetlist, verlist, true);
-
- if (!optflag) {
- // Check if p encroaches adjacent segments.
- tallencsegs(newpt, 1, &tetlist);
- if (chkencsub) {
- // Check if p encroaches adjacent subfaces.
- tallencsubs(newpt, 1, &tetlist);
- }
- if (chkbadtet) {
- // Check if there are new bad quality tets at p.
- for (i = 0; i < tetlist->len(); i++) {
- starttet = * (triface *)(* tetlist)[i];
- checktet4badqual(&starttet, true);
- }
- }
- tetlist->clear();
- } else {
- // Check if new tets are non-optimal.
- for (i = 0; i < tetlist->len(); i++) {
- starttet = * (triface *)(* tetlist)[i];
- checktet4opt(&starttet, true);
- }
- delete mytetlist;
- delete myflipque;
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// tallencsegs() Check for encroached segments and save them in list. //
-// //
-// If 'testpt' (p) != NULL, only check if segments are encroached by p, else,//
-// check all the nearby mesh vertices. //
-// //
-// If 'ceillists' (B_i(p)) != NULL, there are 'n' B_i(p)s, only check the //
-// segments which are on B_i(p)s, else, check the entire list of segments //
-// (in the pool 'this->subsegs'). //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::tallencsegs(point testpt, int n, list **ceillists)
-{
- list *ceillist;
- triface ceiltet;
- face checkseg;
- long oldencnum;
- int i, j, k;
-
- // Remember the current number of encroached segments.
- oldencnum = badsubsegs->items;
-
- if (ceillists != (list **) NULL) {
- for (k = 0; k < n; k++) {
- ceillist = ceillists[k];
- // Check the segments on B_i(p).
- for (i = 0; i < ceillist->len(); i++) {
- ceiltet = * (triface *)(* ceillist)[i];
- ceiltet.ver = 0;
- for (j = 0; j < 3; j++) {
- tsspivot(&ceiltet, &checkseg);
- if (checkseg.sh != dummysh) {
- // Found a segment. Test it if it isn't in enc-list.
- if (!shell2badface(checkseg)) {
- checkseg4encroach(&checkseg, testpt, NULL, true);
- }
- }
- enextself(ceiltet);
- }
- }
- }
- } else {
- // Check the entire list of segments.
- subsegs->traversalinit();
- checkseg.sh = shellfacetraverse(subsegs);
- while (checkseg.sh != (shellface *) NULL) {
- // Test it if it isn't in enc-list.
- if (!shell2badface(checkseg)) {
- checkseg4encroach(&checkseg, testpt, NULL, true);
- }
- checkseg.sh = shellfacetraverse(subsegs);
- }
- }
-
- return (badsubsegs->items > oldencnum);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// tallencsubs() Find all encroached subfaces and save them in list. //
-// //
-// If 'testpt' (p) != NULL, only check if subfaces are encroached by p, else,//
-// check the adjacent vertices of subfaces. //
-// //
-// If 'ceillists' (B_i(p)) != NULL, there are 'n' B_i(p)s, only check the //
-// subfaces which are on B_i(p)s, else, check the entire list of subfaces //
-// (in the pool 'this->subfaces'). //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::tallencsubs(point testpt, int n, list** ceillists)
-{
- list *ceillist;
- triface ceiltet;
- face checksh;
- long oldencnum;
- int i, k;
-
- // Remember the current number of encroached segments.
- oldencnum = badsubfaces->items;
-
- if (ceillists != (list **) NULL) {
- for (k = 0; k < n; k++) {
- ceillist = ceillists[k];
- // Check the subfaces on B_i(p).
- for (i = 0; i < ceillist->len(); i++) {
- ceiltet = * (triface *)(* ceillist)[i];
- tspivot(ceiltet, checksh);
- if (checksh.sh != dummysh) {
- // Found a subface. Test it if it isn't in enc-list.
- if (!shell2badface(checksh)) {
- checksub4encroach(&checksh, testpt, true);
- }
- }
- }
- }
- } else {
- // Check the entire list of subfaces.
- subfaces->traversalinit();
- checksh.sh = shellfacetraverse(subfaces);
- while (checksh.sh != (shellface *) NULL) {
- // Test it if it isn't in enc-list.
- if (!shell2badface(checksh)) {
- checksub4encroach(&checksh, testpt, true);
- }
- checksh.sh = shellfacetraverse(subfaces);
- }
- }
-
- return (badsubfaces->items > oldencnum);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// tallbadtetrahedrons() Queue all the bad-quality tetrahedra in the mesh.//
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::tallbadtetrahedrons()
-{
- triface tetloop;
-
- tetrahedrons->traversalinit();
- tetloop.tet = tetrahedrontraverse();
- while (tetloop.tet != (tetrahedron *) NULL) {
- checktet4badqual(&tetloop, true);
- tetloop.tet = tetrahedrontraverse();
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// repairencsegs() Repair (split) all the encroached segments. //
-// //
-// Each encroached segment is repaired by splitting it - inserting a vertex //
-// at or near its midpoint. Newly inserted vertices may encroach upon other //
-// subsegments, these are also repaired. //
-// //
-// 'chkencsub' and 'chkbadtet' are two flags that specify whether one should //
-// take note of new encroaced subfaces and bad quality tets that result from //
-// inserting vertices to repair encroached subsegments. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::repairencsegs(bool chkencsub, bool chkbadtet)
-{
- list **tetlists, **ceillists;
- list **sublists, **subceillists;
- list *tetlist, *sublist;
- queue *flipque;
- badface *encloop;
- face splitseg, symsplitseg;
- point newpt, sympt, refpt;
- point e1, e2;
- enum locateresult symloc;
- int nmax, n, i, j;
-
- n = 0;
- nmax = 128;
- if (!b->fliprepair) {
- tetlists = new list*[nmax];
- ceillists = new list*[nmax];
- sublists = new list*[nmax];
- subceillists = new list*[nmax];
- } else {
- tetlist = new list(sizeof(triface), NULL, 1024);
- sublist = new list(sizeof(face), NULL, 256);
- flipque = new queue(sizeof(badface));
- }
-
- // Loop until the pool 'badsubsegs' is empty. Note that steinerleft == -1
- // if an unlimited number of Steiner points is allowed.
- while ((badsubsegs->items > 0) && (steinerleft != 0)) {
- badsubsegs->traversalinit();
- encloop = badfacetraverse(badsubsegs);
- while ((encloop != (badface *) NULL) && (steinerleft != 0)) {
- // Get an encroached subsegment s.
- splitseg = encloop->ss;
- // Clear the in-queue flag in s.
- setshell2badface(splitseg, NULL);
- if ((sorg(splitseg) == encloop->forg) &&
- (sdest(splitseg) == encloop->fdest)) {
- if (b->verbose > 1) {
- printf(" Get an enc-seg (%d, %d)\n", pointmark(encloop->forg),
- pointmark(encloop->fdest));
- }
- refpt = (point) NULL;
- if (b->conformdel) {
- // Look for a reference point.
- checkseg4encroach(&splitseg, NULL, &refpt, false);
- }
- // Create the new point p (at the middle of s).
- makepoint(&newpt);
- getsplitpoint(encloop->forg, encloop->fdest, refpt, newpt);
- setpointtype(newpt, FREESEGVERTEX);
- setpoint2sh(newpt, sencode(splitseg));
- // Decide whether p can be inserted or not.
- if (acceptsegpt(newpt, refpt, &splitseg)) {
- // Is there periodic boundary condition?
- if (checkpbcs) {
- // Insert points on other segments of incident pbcgroups.
- i = shellmark(splitseg) - 1;
- for (j = idx2segpglist[i]; j < idx2segpglist[i + 1]; j++) {
- makepoint(&sympt);
- symloc = getsegpbcsympoint(newpt, &splitseg, sympt, &symsplitseg,
- segpglist[j]);
- if (symloc == ONEDGE) {
- if (symsplitseg.sh != splitseg.sh) {
- // Insert sympt.
- setpointtype(sympt, FREESEGVERTEX);
- setpoint2sh(sympt, sencode(symsplitseg));
- // Save the endpoints of the seg for size interpolation.
- e1 = sorg(symsplitseg);
- if (shelltype(symsplitseg) == SHARP) {
- e2 = sdest(symsplitseg);
- } else {
- e2 = (point) NULL; // No need to do size interpolation.
- }
- if (!b->fliprepair) {
- // Form BC(symp), B(symp), CBC(symp)s, C(symp)s.
- formbowatcavity(sympt, &symsplitseg, NULL, &n, &nmax,
- sublists, subceillists, tetlists, ceillists);
- // Validate BC(symp), B(symp), CBC(symp)s, C(symp)s.
- if (trimbowatcavity(sympt, &symsplitseg, n, sublists,
- subceillists, tetlists, ceillists, -1.0)) {
- bowatinsertsite(sympt, &symsplitseg, n, sublists,
- subceillists, tetlists, ceillists, NULL, flipque,
- true, chkencsub, chkbadtet);
- setnewpointsize(sympt, e1, e2);
- if (steinerleft > 0) steinerleft--;
- } else {
- // p did not insert for invalid BC(symp).
- pointdealloc(sympt);
- }
- // Free the memory allocated in formbowatcavity().
- releasebowatcavity(&symsplitseg, n, sublists, subceillists,
- tetlists, ceillists);
- } else {
- splitencseg(sympt, &symsplitseg, tetlist, sublist, NULL,
- flipque, chkencsub, chkbadtet, false);
- setnewpointsize(sympt, e1, e2);
- if (steinerleft > 0) steinerleft--;
- }
- } else {
- // The sympt are on the same segment. It is possible when
- // splitseg is the symmetric rotating axes.
- pointdealloc(sympt);
- }
- } else if (symloc == ONVERTEX) {
- // The sympt already exists. It is possible when two pbc
- // groups are exactly the same. Omit this point.
- pointdealloc(sympt);
- } else {
- // Do not isnert symp for unknown cases: ONFACE, OUTSIDE.
- // assert(0);
- pointdealloc(sympt);
- }
- } // for (j = idx2segpglist[i]; j < idx2segpglist[i + 1]; j++)
- } // if (checkpbcs)
- // Save the endpoints of the seg for size interpolation.
- e1 = sorg(splitseg);
- if (shelltype(splitseg) == SHARP) {
- e2 = sdest(splitseg);
- } else {
- e2 = (point) NULL; // No need to do size interoplation.
- }
- if (!b->fliprepair) {
- // Form BC(p), B(p), CBC(p)s, and C(p)s.
- formbowatcavity(newpt, &splitseg, NULL, &n, &nmax, sublists,
- subceillists, tetlists, ceillists);
- // Validate/update BC(p), B(p), CBC(p)s, and C(p)s.
- if (trimbowatcavity(newpt, &splitseg, n, sublists, subceillists,
- tetlists, ceillists, -1.0)) {
- bowatinsertsite(newpt, &splitseg, n, sublists, subceillists,
- tetlists, ceillists, NULL, flipque, true,
- chkencsub, chkbadtet);
- setnewpointsize(newpt, e1, e2);
- if (steinerleft > 0) steinerleft--;
- } else {
- // p did not insert for invalid B(p).
- pointdealloc(newpt);
- }
- // Free the memory allocated in formbowatcavity().
- releasebowatcavity(&splitseg, n, sublists, subceillists, tetlists,
- ceillists);
- } else {
- splitencseg(newpt, &splitseg, tetlist, sublist, NULL, flipque,
- chkencsub, chkbadtet, false);
- setnewpointsize(newpt, e1, e2);
- if (steinerleft > 0) steinerleft--;
- }
- } else {
- // p did not accept for insertion.
- pointdealloc(newpt);
- } // if (checkseg4splitting(newpt, &splitseg))
- } // if ((encloop->forg == pa) && (encloop->fdest == pb))
- badfacedealloc(badsubsegs, encloop); // Remove this entry from list.
- encloop = badfacetraverse(badsubsegs); // Get the next enc-segment.
- } // while ((encloop != (badface *) NULL) && (steinerleft != 0))
- } // while ((badsubsegs->items > 0) && (steinerleft != 0))
-
- if (!b->fliprepair) {
- delete [] tetlists;
- delete [] ceillists;
- delete [] sublists;
- delete [] subceillists;
- } else {
- delete tetlist;
- delete sublist;
- delete flipque;
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// repairencsubs() Repair (split) all the encroached subfaces. //
-// //
-// Each encroached subface is repaired by splitting it - inserting a vertex //
-// at or near its circumcenter. Newly inserted vertices may encroach upon //
-// other subfaces, these are also repaired. //
-// //
-// 'chkbadtet' is a flag that specifies whether one should take note of new //
-// bad quality tets that result from inserted vertices. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::repairencsubs(bool chkbadtet)
-{
- list *tetlists[2], *ceillists[2];
- list *sublist, *subceillist;
- list *verlist;
- badface *encloop;
- face splitsub, symsplitsub;
- point newpt, sympt, e1;
- enum locateresult loc, symloc;
- bool reject;
- long oldptnum;
- int quenumber, n, i;
-
- n = 0;
- sublist = (list *) NULL;
- subceillist = (list *) NULL;
- verlist = new list(sizeof(point *), NULL, 256);
-
- // Loop until the pool 'badsubfaces' is empty. Note that steinerleft == -1
- // if an unlimited number of Steiner points is allowed.
- while ((badsubfaces->items > 0) && (steinerleft != 0)) {
- // Get an encroached subface f.
- encloop = dequeueencsub(&quenumber);
- splitsub = encloop->ss;
- // Clear the in-queue flag of f.
- setshell2badface(splitsub, NULL);
- // f may not be the same one when it was determined to be encroached.
- if (!isdead(&splitsub)
- && (sorg(splitsub) == encloop->forg)
- && (sdest(splitsub) == encloop->fdest)
- && (sapex(splitsub) == encloop->fapex)) {
- if (b->verbose > 1) {
- printf(" Dequeuing ensub (%d, %d, %d) [%d].\n",
- pointmark(encloop->forg), pointmark(encloop->fdest),
- pointmark(encloop->fapex), quenumber);
- }
- // Create a new point p at the circumcenter of f.
- makepoint(&newpt);
- for (i = 0; i < 3; i++) newpt[i] = encloop->cent[i];
- setpointtype(newpt, FREESUBVERTEX);
- setpoint2sh(newpt, sencode(splitsub));
- // Set the abovepoint of f for point location.
- abovepoint = facetabovepointarray[shellmark(splitsub)];
- if (abovepoint == (point) NULL) {
- getfacetabovepoint(&splitsub);
- }
- // Locate p, start from f, stop at segment (1), use a tolerance to
- // detect ONVERTEX or OUTSIDE case. Update f on return.
- loc = locatesub(newpt, &splitsub, 1, b->epsilon * 1e+2);
- if ((loc != ONVERTEX) && (loc != OUTSIDE)) {
- // Form BC(p), B(p), CBC(p) and C(p).
- formbowatcavity(newpt, NULL, &splitsub, &n, NULL, &sublist,
- &subceillist, tetlists, ceillists);
- // Check for encroached subsegments (on B(p)).
- reject = tallencsegs(newpt, 2, ceillists);
- // Execute point accept rule if p does not encroach upon any segment.
- if (!reject) {
- reject = !acceptfacpt(newpt, subceillist, verlist);
- }
- if (!reject) {
- // Validate/update cavity.
- reject = !trimbowatcavity(newpt, NULL, n, &sublist, &subceillist,
- tetlists, ceillists, -1.0);
- }
- if (!reject) {
- // CBC(p) should include s, so that s can be removed after CBC(p)
- // is remeshed. However, if there are locally non-Delaunay faces
- // and encroached subsegments, s may not be collected in CBC(p).
- // p should not be inserted in such case.
- reject = !sinfected(encloop->ss);
- }
- if (!reject) {
- if (checkpbcs) {
- if (shellpbcgroup(splitsub) >= 0) {
- // Check for splitting of the symmetric subface of f.
- makepoint(&sympt);
- symloc = getsubpbcsympoint(newpt,&splitsub,sympt,&symsplitsub);
- if (symloc != ONVERTEX) {
- // Release CBC(p) and BC(p) and free the memory..
- releasebowatcavity(NULL, 2, &sublist, &subceillist, tetlists,
- ceillists);
- // Form CBC(symp), C(symp), BC(sympt) and B(sympt).
- formbowatcavity(sympt, NULL, &symsplitsub, &n, NULL, &sublist,
- &subceillist, tetlists, ceillists);
- reject = tallencsegs(sympt, 2, ceillists);
- if (!reject) {
- reject = !acceptfacpt(sympt, subceillist, verlist);
- }
- if (!reject) {
- reject = !trimbowatcavity(sympt,NULL,n,&sublist,&subceillist,
- tetlists, ceillists, -1.0);
- }
- if (!reject) {
- // Insert sympt.
- setpoint2pbcpt(newpt, sympt);
- setpoint2pbcpt(sympt, newpt);
- setpointtype(sympt, FREESUBVERTEX);
- setpoint2sh(sympt, sencode(symsplitsub));
- // Save a point for size interpolation.
- e1 = sorg(symsplitsub);
- bowatinsertsite(sympt, NULL, n, &sublist, &subceillist,
- tetlists,ceillists,NULL,NULL,false,true,chkbadtet);
- setnewpointsize(sympt, e1, NULL);
- if (steinerleft > 0) steinerleft--;
- // Release CBC(symp) and BC(symp) and free the memory..
- releasebowatcavity(NULL, n, &sublist, &subceillist, tetlists,
- ceillists);
- } else {
- // symp is rejected for one of the following reasons:
- // (1) BC(symp) is not valid; or
- // (2) symp encroaches upon some subsegments (queued); or
- // (3) symp is rejected by point accepting rule.
- pointdealloc(sympt);
- // Cavity will be released by the following code.
- }
- } else {
- // Do not insert sympt for invalid PBC data.
- pointdealloc(sympt);
- // p is rejected due to symp.
- reject = true;
- }
- }
- } // if (checkpbcs)
- }
- if (!reject) {
- // Insert p.
- if (checkpbcs) {
- if (shellpbcgroup(splitsub) >= 0) {
- // Form CBC(p), C(p), BC(p) and B(p).
- formbowatcavity(newpt, NULL, &splitsub, &n, NULL, &sublist,
- &subceillist, tetlists, ceillists);
- trimbowatcavity(newpt, NULL, n, &sublist, &subceillist, tetlists,
- ceillists, -1.0);
- }
- }
- // Save a point for size interpolation.
- e1 = sorg(splitsub);
- bowatinsertsite(newpt, NULL, n, &sublist, &subceillist, tetlists,
- ceillists, NULL, NULL, true, true, chkbadtet);
- setnewpointsize(newpt, e1, NULL);
- if (steinerleft > 0) steinerleft--;
- } else {
- // p is rejected for the one of the following reasons:
- // (1) BC(p) is not valid.
- // (2) s does not in CBC(p).
- // (3) p encroaches upon some segments (queued); or
- // (4) p is rejected by point accepting rule, or
- // (5) due to the rejection of symp (the PBC).
- pointdealloc(newpt);
- } // if (!reject)
- // Release the cavity and free the memory.
- releasebowatcavity(NULL,n,&sublist,&subceillist,tetlists,ceillists);
- if (reject) {
- // Are there queued encroached subsegments.
- if (badsubsegs->items > 0) {
- // Repair enc-subsegments.
- oldptnum = points->items;
- repairencsegs(true, chkbadtet);
- if (points->items > oldptnum) {
- // Some enc-subsegments got split. Try to repair f later.
- splitsub = encloop->ss;
- if (!isdead(&splitsub)) {
- if (!shell2badface(splitsub)) {
- checksub4encroach(&splitsub, NULL, true);
- }
- }
- }
- }
- }
- } else {
- // Don't insert p for one of the following reasons:
- // (1) Locate on an existing vertex; or
- // (2) locate outside the domain.
- // Case (1) should not be possible. If such vertex v exists, it is
- // the circumcenter of f, ie., f is non-Delaunay. Either f was got
- // split before by v, but survived after v was inserted, or the
- // same for a f' which is nearly co-circular with f. Whatsoever,
- // there are encroached segs by v, but the routine tallencsegs()
- // did not find them out.
- if (loc == ONVERTEX) {
- printf("Internal error in repairencsubs():\n");
- printf(" During repairing encroached subface (%d, %d, %d)\n",
- pointmark(encloop->forg), pointmark(encloop->fdest),
- pointmark(encloop->fapex));
- printf(" New point %d is coincident with an existing vertex %d\n",
- pointmark(newpt), pointmark(sorg(splitsub)));
- internalerror();
- }
- // Case (2) can happen when thers is a segment s which is close to f
- // and is non-conforming Delaunay. The circumcenter of f encroaches
- // upon s, but the circumcenter of s is rejected for insertion.
- pointdealloc(newpt);
- } // if ((loc != ONVERTEX) && (loc != OUTSIDE))
- } else {
- if (!isdead(&splitsub)) {
- // The subface has been changed, re-check it.
- checksub4encroach(&splitsub, NULL, true);
- }
- } // if (!isdead(&splitsub) && (sorg(splitsub) == encloop->forg) &&
- // Remove this entry from list.
- badfacedealloc(badsubfaces, encloop);
- } // while ((badsubfaces->items > 0) && (steinerleft != 0))
-
- delete verlist;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// repairbadtets() Repair all bad-quality tetrahedra. //
-// //
-// All bad-quality tets are stored in pool 'badtetrahedrons'. Each bad tet //
-// is repaired by inserting a point at or near its circumcenter. However, if //
-// this point encroaches any subsegment or subface, it is not inserted. Ins- //
-// tead the encroached segment and subface are split. Newly inserted points //
-// may create other bad-quality tets, these are also repaired. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::repairbadtets()
-{
- list *tetlist, *ceillist;
- list *verlist;
- badface *badtet;
- triface starttet;
- point newpt, e1;
- enum locateresult loc;
- bool reject;
- long oldptnum;
- int i;
-
- tetlist = new list(sizeof(triface), NULL, 1024);
- ceillist = new list(sizeof(triface), NULL, 1024);
- verlist = new list(sizeof(point *), NULL, 256);
-
- // Loop until pool 'badtetrahedrons' is empty. Note that steinerleft == -1
- // if an unlimited number of Steiner points is allowed.
- while ((badtetrahedrons->items > 0) && (steinerleft != 0)) {
- // Get a bad-quality tet t.
- badtet = topbadtetra();
- // Make sure that the tet is still the same one when it was tested.
- // Subsequent transformations may have made it a different tet.
- if ((badtet != (badface *) NULL) && !isdead(&badtet->tt)
- && org(badtet->tt) == badtet->forg
- && dest(badtet->tt) == badtet->fdest
- && apex(badtet->tt) == badtet->fapex
- && oppo(badtet->tt) == badtet->foppo) {
- if (b->verbose > 1) {
- printf(" Dequeuing btet (%d, %d, %d, %d).\n",
- pointmark(badtet->forg), pointmark(badtet->fdest),
- pointmark(badtet->fapex), pointmark(badtet->foppo));
- }
- // Create the new point p (at the circumcenter of t).
- makepoint(&newpt);
- for (i = 0; i < 3; i++) newpt[i] = badtet->cent[i];
- setpointtype(newpt, FREEVOLVERTEX);
- // Locate p.
- starttet = badtet->tt;
- loc = preciselocate(newpt, &starttet, tetrahedrons->items);
- if ((loc != ONVERTEX) && (loc != OUTSIDE)) {
- // For BC(p) and B(p).
- infect(starttet);
- tetlist->append(&starttet);
- formbowatcavityquad(newpt, tetlist, ceillist);
- // Check for encroached subsegments.
- reject = tallencsegs(newpt, 1, &ceillist);
- if (!reject) {
- // Check for encroached subfaces.
- reject = tallencsubs(newpt, 1, &ceillist);
- }
- // Execute point accepting rule if p does not encroach upon any
- // subsegment and subface.
- if (!reject) {
- reject = !acceptvolpt(newpt, ceillist, verlist);
- }
- if (!reject) {
- reject = !trimbowatcavity(newpt, NULL, 1, NULL, NULL, &tetlist,
- &ceillist, -1.0);
- }
- if (!reject) {
- // BC(p) should include t, so that t can be removed after BC(p) is
- // remeshed. However, if there are locally non-Delaunay faces
- // and encroached subsegments/subfaces, t may not be collected
- // in BC(p). p should not be inserted in such case.
- reject = !infected(badtet->tt);
- if (reject) outbowatcircumcount++;
- }
- if (!reject) {
- // Save a point for size interpolation.
- e1 = org(starttet);
- // Insert p.
- bowatinsertsite(newpt, NULL, 1, NULL, NULL, &tetlist, &ceillist,
- NULL, NULL, false, false, true);
- setnewpointsize(newpt, e1, NULL);
- if (steinerleft > 0) steinerleft--;
- } else {
- // p is rejected for one of the following reasons:
- // (1) BC(p) is not valid.
- // (2) t does not in BC(p).
- // (3) p encroaches upon some segments;
- // (4) p encroaches upon some subfaces;
- // (5) p is rejected by the point accepting rule.
- pointdealloc(newpt);
- // Uninfect tets of BC(p).
- for (i = 0; i < tetlist->len(); i++) {
- starttet = * (triface *)(* tetlist)[i];
- uninfect(starttet);
- }
- }
- tetlist->clear();
- ceillist->clear();
- // Split encroached subsegments/subfaces if there are.
- if (reject) {
- oldptnum = points->items;
- if (badsubsegs->items > 0) {
- repairencsegs(true, true);
- }
- if (badsubfaces->items > 0) {
- repairencsubs(true);
- }
- if (points->items > oldptnum) {
- // Some encroaching subsegments/subfaces got split. Re-queue the
- // tet if it is still alive.
- starttet = badtet->tt;
- if (!isdead(&starttet)) {
- checktet4badqual(&starttet, true);
- }
- }
- }
- } else {
- // Do not insert p. The reason may be one of:
- // (1) p is coincident (ONVERTEX) with an existing vertex; or
- // (2) p is outside (OUTSIDE) the mesh.
- // Case (1) should not be possible. If such vertex v exists, it is
- // the circumcenter of t, ie., t is non-Delaunay. Either t was got
- // split before by v, but survived after v was inserted, or the
- // same for a t' which is nearly co-spherical with t. Whatsoever,
- // there are encroached segments or subfaces by v but the routines
- // tallencsegs() or tallencsubs() did not find them out.
- if (loc == ONVERTEX) {
- printf("Internal error in repairbadtets():\n");
- printf(" During repairing bad tet (%d, %d, %d, %d)\n",
- pointmark(badtet->forg), pointmark(badtet->fdest),
- pointmark(badtet->fapex), pointmark(badtet->foppo));
- printf(" New point %d is coincident with an existing vertex %d\n",
- pointmark(newpt), pointmark(org(starttet)));
- internalerror();
- }
- // Case (2) can happen when there is a segment s (or subface f) which
- // is close to f and is non-conforming Delaunay. The circumcenter
- // of t encroaches upon s (or f), but the circumcenter of s (or f)
- // is rejected for insertion.
- pointdealloc(newpt);
- } // if ((loc != ONVERTEX) && (loc != OUTSIDE))
- } // if (!isdead(&badtet->tt) && org(badtet->tt) == badtet->forg &&
- // Remove the tet from the queue.
- dequeuebadtet();
- } // while ((badtetrahedrons->items > 0) && (steinerleft != 0))
-
- delete tetlist;
- delete ceillist;
- delete verlist;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// enforcequality() Refine the mesh. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::enforcequality()
-{
- long total, vertcount;
- int i;
-
- if (!b->quiet) {
- printf("Adding Steiner points to enforce quality.\n");
- }
-
- total = vertcount = 0l;
- if (b->conformdel) {
- r2count = r3count = 0l;
- }
-
- // If both '-D' and '-r' options are used.
- if (b->conformdel && b->refine) {
- markacutevertices(65.0);
- }
- // If '-m' is not used.
- if (!b->metric) {
- // Find and mark all sharp segments.
- marksharpsegments(65.0);
- // Decide the sizes for feature points.
- decidefeaturepointsizes();
- }
-
- // Initialize the pool of encroached subsegments.
- badsubsegs = new memorypool(sizeof(badface), SUBPERBLOCK, POINTER, 0);
- // Looking for encroached subsegments.
- tallencsegs(NULL, 0, NULL);
- if (b->verbose && badsubsegs->items > 0) {
- printf(" Splitting encroached subsegments.\n");
- }
- vertcount = points->items;
- // Fix encroached segments without noting any enc subfaces.
- repairencsegs(false, false);
- if (b->verbose > 0) {
- printf(" %ld split points.\n", points->items - vertcount);
- }
- total += points->items - vertcount;
-
- // Initialize the pool of encroached subfaces.
- badsubfaces = new memorypool(sizeof(badface), SUBPERBLOCK, POINTER, 0);
- // Initialize the priority queues of badfaces.
- for (i = 0; i < 3; i++) subquefront[i] = (badface *) NULL;
- for (i = 0; i < 3; i++) subquetail[i] = &subquefront[i];
- // Looking for encroached subfaces.
- tallencsubs(NULL, 0, NULL);
- if (b->verbose && badsubfaces->items > 0) {
- printf(" Splitting encroached subfaces.\n");
- }
- vertcount = points->items;
- // Fix encroached subfaces without noting bad tetrahedra.
- repairencsubs(false);
- if (b->verbose > 0) {
- printf(" %ld split points.\n", points->items - vertcount);
- }
- total += points->items - vertcount;
- // At this point, the mesh should be conforming Delaunay if no input
- // angle is smaller than 90 degree.
-
- // Next, fix bad quality tetrahedra.
- if ((b->minratio > 0.0) || b->varvolume || b->fixedvolume) {
- // Initialize the pool of bad tets
- badtetrahedrons = new memorypool(sizeof(badface), ELEPERBLOCK, POINTER, 0);
- // Initialize the priority queues of bad tets.
- for (i = 0; i < 64; i++) tetquefront[i] = (badface *) NULL;
- firstnonemptyq = -1;
- recentq = -1;
- // Looking for bad quality tets.
- cosmaxdihed = cos(b->maxdihedral * PI / 180.0);
- cosmindihed = cos(b->mindihedral * PI / 180.0);
- tallbadtetrahedrons();
- if (b->verbose && badtetrahedrons->items > 0) {
- printf(" Splitting bad tetrahedra.\n");
- }
- vertcount = points->items;
- repairbadtets();
- if (b->verbose > 0) {
- printf(" %ld refinement points.\n", points->items - vertcount);
- }
- total += points->items - vertcount;
- delete badtetrahedrons;
- }
-
- if (b->verbose > 0) {
- printf(" Totally added %ld points.\n", total);
- }
-
- delete badsubfaces;
- delete badsubsegs;
-}
-
-//
-// End of Delaunay refinement routines
-//
-
-//
-// Begin of mesh optimization routines
-//
-
-void tetgenmesh::dumpbadtets()
-{
- FILE *fout;
- badface *remtet;
-
- // Write out a file of remaining bad tets.
- printf(" Writing bad tets to file bad-dump.lua.\n");
- fout = fopen("bad-dump.lua", "w");
- fprintf(fout, "-- %ld remaining bad tets (> %g degree).\n",
- badtetrahedrons->items, b->maxdihedral);
- badtetrahedrons->traversalinit();
- remtet = badfacetraverse(badtetrahedrons);
- while (remtet != (badface *) NULL) {
- if (!isdead(&remtet->tt) && org(remtet->tt) == remtet->forg &&
- dest(remtet->tt) == remtet->fdest &&
- apex(remtet->tt) == remtet->fapex &&
- oppo(remtet->tt) == remtet->foppo) {
- fprintf(fout, "p:draw_tet(%d, %d, %d, %d) -- %g\n",
- pointmark(remtet->forg), pointmark(remtet->fdest),
- pointmark(remtet->fapex), pointmark(remtet->foppo),
- acos(remtet->key) * 180.0 / PI);
- }
- remtet = badfacetraverse(badtetrahedrons);
- }
- fclose(fout);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// checktet4ill() Check a tet to see if it is illegal. //
-// //
-// A tet is "illegal" if it spans on one input facet. Save the tet in queue //
-// if it is illegal and the flag 'enqflag' is set. //
-// //
-// Note: Such case can happen when the input facet has non-coplanar vertices //
-// and the Delaunay tetrahedralization of the vertices may creat such tets. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::checktet4ill(triface* testtet, bool enqflag)
-{
- badface *newbadtet;
- triface checktet;
- face checksh1, checksh2;
- face checkseg;
- bool illflag;
- int i;
-
- illflag = false;
- for (testtet->loc = 0; testtet->loc < 4; testtet->loc++) {
- tspivot(*testtet, checksh1);
- if (checksh1.sh != dummysh) {
- testtet->ver = 0;
- findedge(&checksh1, org(*testtet), dest(*testtet));
- for (i = 0; i < 3; i++) {
- fnext(*testtet, checktet);
- tspivot(checktet, checksh2);
- if (checksh2.sh != dummysh) {
- // Two subfaces share this edge.
- sspivot(checksh1, checkseg);
- if (checkseg.sh == dummysh) {
- // The four corners of the tet are on one facet. Illegal! Try to
- // flip the opposite edge of the current one.
- enextfnextself(*testtet);
- enextself(*testtet);
- illflag = true;
- break;
- }
- }
- enextself(*testtet);
- senextself(checksh1);
- }
- }
- if (illflag) break;
- }
-
- if (illflag && enqflag) {
- // Allocate space for the bad tetrahedron.
- newbadtet = (badface *) badtetrahedrons->alloc();
- newbadtet->tt = *testtet;
- newbadtet->key = -1.0; // = 180 degree.
- for (i = 0; i < 3; i++) newbadtet->cent[i] = 0.0;
- newbadtet->forg = org(*testtet);
- newbadtet->fdest = dest(*testtet);
- newbadtet->fapex = apex(*testtet);
- newbadtet->foppo = oppo(*testtet);
- newbadtet->nextitem = (badface *) NULL;
- if (b->verbose > 2) {
- printf(" Queueing illtet: (%d, %d, %d, %d).\n",
- pointmark(newbadtet->forg), pointmark(newbadtet->fdest),
- pointmark(newbadtet->fapex), pointmark(newbadtet->foppo));
- }
- }
-
- return illflag;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// checktet4opt() Check a tet to see if it needs to be optimized. //
-// //
-// A tet t needs to be optimized if it fails to certain quality measures. //
-// The only quality measure currently used is the maximal dihedral angle at //
-// edges. The desired maximal dihedral angle is b->maxdihed (set by the '-s' //
-// option. //
-// //
-// A tet may have one, two, or three big dihedral angles. Examples: Let the //
-// tet t = abcd, and its four corners are nearly co-planar. Then t has one //
-// big dihedral angle if d is very close to the edge ab; t has three big //
-// dihedral angles if d's projection on the face abc is also inside abc, i.e.//
-// the shape of t likes a hat; finally, t has two big dihedral angles if d's //
-// projection onto abc is outside abc. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::checktet4opt(triface* testtet, bool enqflag)
-{
- badface *newbadtet;
- point pa, pb, pc, pd;
- REAL N[4][3], len;
- REAL cosd;
- bool enq;
- int i, j;
-
- enq = false;
- pa = (point) testtet->tet[4];
- pb = (point) testtet->tet[5];
- pc = (point) testtet->tet[6];
- pd = (point) testtet->tet[7];
- // Compute the 4 face normals: N[0] cbd, N[1] acd, N[2] bad, N[3] abc.
- tetallnormal(pa, pb, pc, pd, N, NULL);
- // Normalize the normals.
- for (i = 0; i < 4; i++) {
- len = sqrt(dot(N[i], N[i]));
- if (len != 0.0) {
- for (j = 0; j < 3; j++) N[i][j] /= len;
- }
- }
- // Find all large dihedral angles.
- for (i = 0; i < 6; i++) {
- // Locate the edge i and calculate the dihedral angle at the edge.
- testtet->loc = 0;
- testtet->ver = 0;
- switch (i) {
- case 0: // edge ab
- cosd = -dot(N[2], N[3]);
- break;
- case 1: // edge cd
- enextfnextself(*testtet);
- enextself(*testtet);
- cosd = -dot(N[0], N[1]);
- break;
- case 2: // edge bd
- enextfnextself(*testtet);
- enext2self(*testtet);
- cosd = -dot(N[0], N[2]);
- break;
- case 3: // edge bc
- enextself(*testtet);
- cosd = -dot(N[0], N[3]);
- break;
- case 4: // edge ad
- enext2fnextself(*testtet);
- enextself(*testtet);
- cosd = -dot(N[1], N[2]);
- break;
- case 5: // edge ac
- enext2self(*testtet);
- cosd = -dot(N[1], N[3]);
- break;
- }
- if (cosd < cosmaxdihed) {
- // A bigger dihedral angle.
- if (enqflag) {
- // Allocate space for the bad tetrahedron.
- newbadtet = (badface *) badtetrahedrons->alloc();
- newbadtet->tt = *testtet;
- newbadtet->key = cosd;
- for (j = 0; j < 3; j++) newbadtet->cent[j] = 0.0;
- newbadtet->forg = org(*testtet);
- newbadtet->fdest = dest(*testtet);
- newbadtet->fapex = apex(*testtet);
- newbadtet->foppo = oppo(*testtet);
- newbadtet->nextitem = (badface *) NULL;
- if (b->verbose > 2) {
- printf(" Queueing tet: (%d, %d, %d, %d), dihed %g (degree).\n",
- pointmark(newbadtet->forg), pointmark(newbadtet->fdest),
- pointmark(newbadtet->fapex), pointmark(newbadtet->foppo),
- acos(cosd) * 180.0 / PI);
- }
- }
- enq = true;
- }
- }
-
- return enq;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// removeedge() Remove an edge //
-// //
-// 'remedge' is a tet (abcd) having the edge ab wanted to be removed. Local //
-// reconnecting operations are used to remove edge ab. The following opera- //
-// tion will be tryed. //
-// //
-// If ab is on the hull, and abc and abd are both hull faces. Then ab can be //
-// removed by stripping abcd from the mesh. However, if ab is a segemnt, do //
-// the operation only if 'b->optlevel' > 1 and 'b->nobisect == 0'. //
-// //
-// If ab is an internal edge, there are n tets contains it. Then ab can be //
-// removed if there exists another m tets which can replace the n tets with- //
-// out changing the boundary of the n tets. //
-// //
-// If 'optflag' is set. The value 'remedge->key' means cos(theta), where //
-// 'theta' is the maximal dishedral angle at ab. In this case, even if the //
-// n-to-m flip exists, it will not be performed if the maximum dihedral of //
-// the new tets is larger than 'theta'. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::removeedge(badface* remedge, bool optflag)
-{
- triface abcd, badc; // Tet configuration at edge ab.
- triface baccasing, abdcasing;
- triface abtetlist[11]; // Old configuration at ab, save maximum 10 tets.
- triface bftetlist[11]; // Old configuration at bf, save maximum 10 tets.
- triface newtetlist[33]; // New configuration after removing ab.
- face checksh;
- enum fliptype fty;
- REAL key;
- bool remflag, subflag;
- int n, n1, m, i, j;
-
- // First try to strip abcd from the mesh. This needs to check either ab
- // or cd is on the hull. Try to strip it whichever is true.
- abcd = remedge->tt;
- adjustedgering(abcd, CCW);
- i = 0;
- do {
- sym(abcd, baccasing);
- // Is the tet on the hull?
- if (baccasing.tet == dummytet) {
- fnext(abcd, badc);
- sym(badc, abdcasing);
- if (abdcasing.tet == dummytet) {
- // Strip the tet from the mesh -> ab is removed as well.
- if (removetetbypeeloff(&abcd)) {
- if (b->verbose > 1) {
- printf(" Stripped tet from the mesh.\n");
- }
- optcount[0]++;
- return true;
- }
- }
- }
- // Check if the oppsite edge cd is on the hull.
- enext2fnextself(abcd);
- enext2self(abcd);
- esymself(abcd); // --> cdab
- i++;
- } while (i < 2);
-
- // Get the tets configuration at ab. Collect maximum 10 tets.
- subflag = false;
- abcd = remedge->tt;
- adjustedgering(abcd, CW);
- n = 0;
- abtetlist[n] = abcd;
- do {
- // Is the list full?
- if (n == 10) break;
- // Stop if a subface appears.
- tspivot(abtetlist[n], checksh);
- if (checksh.sh != dummysh) {
- // ab is either a segment or a facet edge. The latter case is not
- // handled yet! An edge flip is needed.
- subflag = true; break; // return false;
- }
- // Get the next tet at ab.
- fnext(abtetlist[n], abtetlist[n + 1]);
- n++;
- } while (apex(abtetlist[n]) != apex(abcd));
-
- remflag = false;
- key = remedge->key;
-
- if (subflag && optflag) {
- abcd = remedge->tt;
- adjustedgering(abcd, CCW);
- // Try to flip face cda or cdb to improve quality.
- for (j = 0; j < 2; j++) {
- if (j == 0) {
- enext2fnext(abcd, abtetlist[0]); // Goto cda.
- } else {
- enextfnext(abcd, abtetlist[0]); // Goto cdb.
- }
- fty = categorizeface(abtetlist[0]);
- if (fty == T23) {
- // A 2-to-3 flip is possible.
- sym(abtetlist[0], abtetlist[1]);
- assert(abtetlist[1].tet != dummytet);
- n = 2;
- m = 3;
- remflag = removefacebyflip23(&key, abtetlist, newtetlist, NULL);
- } else if (fty == T22) {
- // A 2-to-2 or 4-to-4 flip is possible.
- n = 2;
- newtetlist[0] = abtetlist[0];
- adjustedgering(newtetlist[0], CW);
- fnext(newtetlist[0], newtetlist[1]);
- assert(newtetlist[1].tet != dummytet);
- // May it is 4-to-4 flip.
- if (fnext(newtetlist[1], newtetlist[2])) {
- fnext(newtetlist[2], newtetlist[3]);
- assert(newtetlist[3].tet != dummytet);
- n = 4;
- }
- m = n;
- remflag = removeedgebyflip22(&key, n, newtetlist, NULL);
- }
- // Has quality been improved?
- if (remflag) {
- if (b->verbose > 1) {
- printf(" Done flip %d-to-%d. Qual: %g -> %g.\n", n, m,
- acos(remedge->key) / PI * 180.0, acos(key) / PI * 180.0);
- }
- // Delete the old tets. Note, flip22() does not create new tets.
- if (m == 3) {
- for (i = 0; i < n; i++) {
- tetrahedrondealloc(abtetlist[i].tet);
- }
- }
- for (i = 0; i < m; i++) {
- checktet4opt(&(newtetlist[i]), true);
- }
- optcount[1]++;
- return true;
- }
- } // if (j = 0; j < 2; j++)
- // Faces are not flipable. Return.
- return false;
- }
-
- // 2 <= n <= 10.
- if (n == 3) {
- // There are three tets at ab. Try to do a flip32 at ab.
- remflag = removeedgebyflip32(&key, abtetlist, newtetlist, NULL);
- } else if ((n == 4) || (n == 5) || (n == 6)) {
- // Four tets case. Try to do edge transformation.
- remflag = removeedgebytranNM(&key,n,abtetlist,newtetlist,NULL,NULL,NULL);
- } else {
- if (b->verbose > 1) {
- printf(" !! Unhandled case: n = %d.\n", n);
- }
- }
- if (remflag) {
- optcount[n]++;
- // Delete the old tets.
- for (i = 0; i < n; i++) {
- tetrahedrondealloc(abtetlist[i].tet);
- }
- m = (n - 2) * 2; // The numebr of new tets.
- if (b->verbose > 1) {
- printf(" Done flip %d-to-%d. ", n, m);
- if (optflag) {
- printf("Qual: %g -> %g.", acos(remedge->key) / PI * 180.0,
- acos(key) / PI * 180.0);
- }
- printf("\n");
- }
- }
-
- if (!remflag && (key == remedge->key) && (n < 7)) {
- // Try to do a combination of flips.
- n1 = 0;
- remflag = removeedgebycombNM(&key, n, abtetlist, &n1, bftetlist,
- newtetlist, NULL);
- if (remflag) {
- optcount[9]++;
- // Delete the old tets.
- for (i = 0; i < n; i++) {
- tetrahedrondealloc(abtetlist[i].tet);
- }
- for (i = 0; i < n1; i++) {
- if (!isdead(&(bftetlist[i]))) {
- tetrahedrondealloc(bftetlist[i].tet);
- }
- }
- m = ((n1 - 2) * 2 - 1) + (n - 3) * 2; // The number of new tets.
- if (b->verbose > 1) {
- printf(" Done flip %d-to-%d (n-1=%d, n1=%d). ", n+n1-2, m, n-1,n1);
- if (optflag) {
- printf("Qual: %g -> %g.", acos(remedge->key) / PI * 180.0,
- acos(key) / PI * 180.0);
- }
- printf("\n");
- }
- }
- }
-
- if (remflag) {
- // edge is removed. Test new tets for further optimization.
- for (i = 0; i < m; i++) {
- if (optflag) {
- checktet4opt(&(newtetlist[i]), true);
- } else {
- checktet4ill(&(newtetlist[i]), true);
- }
- }
- }
-
- return remflag;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// smoothsliver() Remove a sliver by smoothing a vertex of it. //
-// //
-// The 'slivtet' represents a sliver abcd, and ab is the current edge which //
-// has a large dihedral angle (close to 180 degree). //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::smoothsliver(badface* remedge, list *starlist)
-{
- triface checktet;
- point smthpt;
- bool smthed;
- int idx, i, j;
-
- // Find a Steiner volume point and smooth it.
- smthed = false;
- for (i = 0; i < 4 && !smthed; i++) {
- smthpt = (point) remedge->tt.tet[4 + i];
- // Is it a volume point?
- if (pointtype(smthpt) == FREEVOLVERTEX) {
- // Is it a Steiner point?
- idx = pointmark(smthpt) - in->firstnumber;
- if (!(idx < in->numberofpoints)) {
- // Smooth a Steiner volume point.
- starlist->append(&(remedge->tt.tet));
- formstarpolyhedron(smthpt, starlist, NULL, false);
- smthed = smoothpoint(smthpt,NULL,NULL,starlist,false,&remedge->key);
- // If it is smoothed. Queue new bad tets.
- if (smthed) {
- for (j = 0; j < starlist->len(); j++) {
- checktet = * (triface *)(* starlist)[j];
- checktet4opt(&checktet, true);
- }
- }
- starlist->clear();
- }
- }
- }
-
- /* Omit to smooth segment points. This may cause infinite loop.
- if (smthed) {
- return true;
- }
- face abseg, nextseg, prevseg;
- point pt[2];
- // Check if ab is a segment.
- tsspivot(slivtet, &abseg);
- if (abseg.sh == dummysh) {
- // ab is not a segment. Check if a or b is a Steiner segment point.
- for (i = 0; i < 2 && !smthed; i++) {
- smthpt = (i == 0 ? org(*slivtet) : dest(*slivtet));
- if (pointtype(smthpt) == FREESEGVERTEX) {
- // Is it a Steiner point?
- idx = pointmark(smthpt) - in->firstnumber;
- if (!(idx < in->numberofpoints)) {
- // Smooth a Steiner segment point. Get the segment.
- sdecode(point2sh(smthpt), nextseg);
- locateseg(smthpt, &nextseg);
- assert(sorg(nextseg) == smthpt);
- pt[0] = sdest(nextseg);
- senext2(nextseg, prevseg);
- spivotself(prevseg);
- prevseg.shver = 0;
- if (sorg(prevseg) == smthpt) sesymself(prevseg);
- assert(sdest(prevseg) == smthpt);
- pt[1] = sorg(prevseg);
- starlist->append(slivtet);
- formstarpolyhedron(smthpt, starlist, NULL, true);
- smthed = smoothpoint(smthpt, pt[0], pt[1], starlist, false);
- // If it is smoothed. Check if the tet is still a sliver.
- if (smthed) checktet4opt(slivtet, true);
- starlist->clear();
- }
- }
- }
- }
- */
-
- return smthed;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// splitsliver() Remove a sliver by inserting a point. //
-// //
-// The 'remedge->tt' represents a sliver abcd, ab is the current edge which //
-// has a large dihedral angle (close to 180 degree). //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::splitsliver(badface *remedge, list *tetlist, list *ceillist)
-{
- triface starttet;
- face checkseg;
- point newpt, pt[4];
- bool remflag;
- int i;
-
- starttet = remedge->tt;
-
- // Check if cd is a segment.
- adjustedgering(starttet, CCW);
- enextfnextself(starttet);
- enextself(starttet);
- tsspivot(&starttet, &checkseg);
- if (b->nobisect == 0) {
- if (checkseg.sh != dummysh) {
- // cd is a segment. The seg will be split. BUT do not flip! Due to the
- // exact predicates, lot of slivers ay be rsulted and hard to remove.
- checkseg.shver = 0;
- pt[0] = sorg(checkseg);
- pt[1] = sdest(checkseg);
- makepoint(&newpt);
- getsplitpoint(pt[0], pt[1], NULL, newpt);
- setpointtype(newpt, FREESEGVERTEX);
- setpoint2sh(newpt, sencode(checkseg));
- // Insert p, this should always success.
- sstpivot(&checkseg, &starttet);
- splittetedge(newpt, &starttet, NULL);
- // Collect the new tets connecting at p.
- sstpivot(&checkseg, &starttet);
- ceillist->append(&starttet);
- formstarpolyhedron(newpt, ceillist, NULL, true);
- setnewpointsize(newpt, pt[0], NULL);
- if (steinerleft > 0) steinerleft--;
- // Smooth p.
- smoothpoint(newpt, pt[0], pt[1], ceillist, false, NULL);
- // Queue new slivers.
- for (i = 0; i < ceillist->len(); i++) {
- starttet = * (triface *)(* ceillist)[i];
- checktet4opt(&starttet, true);
- }
- ceillist->clear();
- return true;
- }
- }
-
- // Get the four corners.
- for (i = 0; i < 4; i++) {
- pt[i] = (point) starttet.tet[4 + i];
- }
- // Create the new point p (at the circumcenter of t).
- makepoint(&newpt);
- for (i = 0; i < 3; i++) {
- newpt[i] = 0.25 * (pt[0][i] + pt[1][i] + pt[2][i] + pt[3][i]);
- }
- setpointtype(newpt, FREEVOLVERTEX);
-
- // Form the Bowyer-Watson cavity of p.
- remflag = false;
- infect(starttet);
- tetlist->append(&starttet);
- formbowatcavityquad(newpt, tetlist, ceillist);
- if (trimbowatcavity(newpt, NULL, 1, NULL, NULL, &tetlist, &ceillist, -1.0)) {
- // Smooth p.
- if (smoothpoint( newpt, NULL, NULL, ceillist, false, &remedge->key)) {
- // Insert p.
- bowatinsertsite(newpt, NULL, 1, NULL, NULL, &tetlist, &ceillist, NULL,
- NULL, false, false, false);
- setnewpointsize(newpt, pt[0], NULL);
- if (steinerleft > 0) steinerleft--;
- // Queue new slivers.
- for (i = 0; i < ceillist->len(); i++) {
- starttet = * (triface *)(* ceillist)[i];
- checktet4opt(&starttet, true);
- }
- remflag = true;
- } // if (smoothpoint)
- } // if (trimbowatcavity)
-
- if (!remflag) {
- // p is rejected for BC(p) is not valid.
- pointdealloc(newpt);
- // Uninfect tets of BC(p).
- for (i = 0; i < tetlist->len(); i++) {
- starttet = * (triface *)(* tetlist)[i];
- uninfect(starttet);
- }
- }
- tetlist->clear();
- ceillist->clear();
-
- return remflag;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// tallslivers() Queue all the slivers in the mesh. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::tallslivers(bool optflag)
-{
- triface tetloop;
-
- tetrahedrons->traversalinit();
- tetloop.tet = tetrahedrontraverse();
- while (tetloop.tet != (tetrahedron *) NULL) {
- if (optflag) {
- checktet4opt(&tetloop, true);
- } else {
- checktet4ill(&tetloop, true);
- }
- tetloop.tet = tetrahedrontraverse();
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// optimizemesh() Improve mesh quality by mesh optimizations. //
-// //
-// Available mesh optimizing operations are: (1) multiple edge flips (3-to-2,//
-// 4-to-4, 5-to-6, etc), (2) free vertex deletion, (3) new vertex insertion. //
-// (1) is mandatory, while (2) and (3) are optionally. //
-// //
-// The variable 'b->optlevel' (set after '-s') determines the use of these //
-// operations. If it is: 0, do no optimization; 1, only do (1) operation; 2, //
-// do (1) and (2) operations; 3, do all operations. Deault, b->optlvel = 2. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::optimizemesh(bool optflag)
-{
- list *splittetlist, *tetlist, *ceillist;
- badface *remtet, *lastentry;
- REAL maxdihed, objdihed, curdihed;
- long oldnum;
- int iter, i;
-
- if (!b->quiet) {
- if (optflag) {
- printf("Optimizing mesh.\n");
- } else {
- printf("Repairing mesh.\n");
- }
- }
-
-#ifdef SELF_CHECK
- if (optflag && (b->verbose)) {
- printf(" level = %d.\n", b->optlevel);
- }
-#endif
-
- // Initialize the pool of bad tets.
- badtetrahedrons = new memorypool(sizeof(badface), ELEPERBLOCK, POINTER, 0);
- if (optflag) {
- cosmaxdihed = cos(b->maxdihedral * PI / 180.0);
- cosmindihed = cos(b->mindihedral * PI / 180.0);
- // The radian of the maximum dihedral angle.
- maxdihed = b->maxdihedral / 180.0 * PI;
- // A sliver has an angle large than 'objdihed' will be split.
- objdihed = b->maxdihedral + 5.0;
- if (objdihed < 170.0) objdihed = 170.0;
- objdihed = objdihed / 180.0 * PI;
- }
- // Looking for non-optimal tets.
- tallslivers(optflag);
-
- optcount[0] = 0l; // tet strip count.
- optcount[1] = 0l; // face (2-3) and edge (2-2) flip count.
- optcount[3] = optcount[4] = optcount[5] = optcount[6] = 0l; // edge flips.
- optcount[9] = 0l; // combined flip count.
-
- // Perform edge flip to improve quality.
- lastentry = (badface *) NULL;
- // Loop until pool 'badtetrahedrons' is empty.
- while (badtetrahedrons->items > 0) {
- badtetrahedrons->traversalinit();
- remtet = badfacetraverse(badtetrahedrons);
- while (remtet != (badface *) NULL) {
- // Make sure that the tet is still the same one when it was tested.
- // Subsequent transformations may have made it a different tet.
- if (!isdead(&remtet->tt) && org(remtet->tt) == remtet->forg &&
- dest(remtet->tt) == remtet->fdest &&
- apex(remtet->tt) == remtet->fapex &&
- oppo(remtet->tt) == remtet->foppo) {
- if (b->verbose > 1) {
- printf(" Repair tet (%d, %d, %d, %d) %g (degree).\n",
- pointmark(remtet->forg), pointmark(remtet->fdest),
- pointmark(remtet->fapex), pointmark(remtet->foppo),
- acos(remtet->key) / PI * 180.0);
- }
- if (!removeedge(remtet, optflag)) {
- // An unremoveable tet. Check if it forms a loop.
- if (lastentry != (badface *) NULL) {
- if (remtet == lastentry) break;
- } else {
- // Remember this tet as a breakpoint.
- lastentry = remtet;
- }
- } else {
- // Clear the breakpoint.
- lastentry = (badface *) NULL;
- // Remove the entry from the queue.
- badfacedealloc(badtetrahedrons, remtet);
- }
- } else {
- // Remove the entry from the queue.
- badfacedealloc(badtetrahedrons, remtet);
- }
- remtet = badfacetraverse(badtetrahedrons);
- }
- // Stop if the above loop was out by force.
- if (remtet != (badface *) NULL) break;
- }
-
- if (b->verbose) {
- if (optcount[0] > 0l) {
- printf(" %ld tets are peeled off.\n", optcount[0]);
- }
- if (optcount[1] > 0l) {
- printf(" %ld faces are flipped.\n", optcount[1]);
- }
- if (optcount[3] + optcount[4] + optcount[5] + optcount[6] +
- optcount[9] > 0l) {
- printf(" %ld edges are flipped.\n", optcount[3] + optcount[4] +
- optcount[5] + optcount[6] + optcount[9]);
- }
- // if (badtetrahedrons->items > 0l) {
- // printf(" %ld edges remain.\n", badtetrahedrons->items);
- // }
- }
-
- if ((badtetrahedrons->items > 0l) && optflag && (b->optlevel > 2)) {
- splittetlist = new list(sizeof(badface), NULL, 256);
- tetlist = new list(sizeof(triface), NULL, 256);
- ceillist = new list(sizeof(triface), NULL, 256);
- oldnum = points->items;
- smoothsegverts = smoothvolverts = 0;
- optcount[1] = 0l;
- optcount[3] = optcount[4] = optcount[5] = optcount[6] = 0l; // edge flips.
- optcount[9] = 0l; // combined flip count.
- iter = 0;
-
- do {
- // Form a list of slivers to be split and clean the pool.
- badtetrahedrons->traversalinit();
- remtet = badfacetraverse(badtetrahedrons);
- while (remtet != (badface *) NULL) {
- splittetlist->append(remtet);
- // Remove the entry from the queue.
- badfacedealloc(badtetrahedrons, remtet);
- remtet = badfacetraverse(badtetrahedrons);
- }
- for (i = 0; i < splittetlist->len(); i++) {
- remtet = (badface *)(* splittetlist)[i];
- // Make sure that the tet is still the same one when it was tested.
- // Subsequent transformations may have made it a different tet.
- if (!isdead(&remtet->tt) && org(remtet->tt) == remtet->forg &&
- dest(remtet->tt) == remtet->fdest &&
- apex(remtet->tt) == remtet->fapex &&
- oppo(remtet->tt) == remtet->foppo) {
- // The sliver may get smoothed due to a neighboring tet.
- curdihed = facedihedral(remtet->forg, remtet->fdest, remtet->fapex,
- remtet->foppo);
- // The dihedral angle of a tet must less than PI, correct it.
- if (curdihed > PI) curdihed = 2 * PI - curdihed;
- // Is it a large angle?
- if (curdihed > objdihed) {
- remtet->key = cos(curdihed);
- if (b->verbose > 1) {
- printf(" Get sliver (%d, %d, %d, %d) %g (degree).\n",
- pointmark(remtet->forg), pointmark(remtet->fdest),
- pointmark(remtet->fapex), pointmark(remtet->foppo),
- acos(remtet->key) / PI * 180.0);
- }
- if (!removeedge(remtet, optflag)) {
- if (!smoothsliver(remtet, tetlist)) {
- splitsliver(remtet, tetlist, ceillist);
- }
- }
- }
- }
- }
- iter++;
- } while ((badtetrahedrons->items > 0l) && (iter < b->optpasses));
-
- if (b->verbose) {
- printf(" %d passes.\n", iter);
- if ((points->items - oldnum) > 0l) {
- printf(" %ld points are inserted (%d on segment).\n",
- points->items - oldnum, smoothsegverts);
- }
- if (optcount[1] > 0l) {
- printf(" %ld faces are flipped.\n", optcount[1]);
- }
- if (optcount[3] + optcount[4] + optcount[5] + optcount[6] +
- optcount[9] > 0l) {
- printf(" %ld edges are flipped.\n", optcount[3] + optcount[4] +
- optcount[5] + optcount[6] + optcount[9]);
- }
- // if (badtetrahedrons->items > 0l) {
- // printf(" %ld edges remain.\n", badtetrahedrons->items);
- // }
- }
- delete tetlist;
- delete ceillist;
- delete splittetlist;
- }
-
- delete badtetrahedrons;
- badtetrahedrons = (memorypool *) NULL;
-}
-
-//
-// End of mesh optimization routines
-//
-
-//
-// Begin of I/O rouitnes
-//
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// transfernodes() Transfer nodes from 'io->pointlist' to 'this->points'. //
-// //
-// Initializing 'this->points'. Transferring all points from 'in->pointlist'//
-// into it. All points are indexed (start from in->firstnumber). Each point //
-// is initialized be UNUSEDVERTEX. The bounding box (xmin, xmax, ymin, ymax,//
-// zmin, zmax) and the diameter (longest) of the point set are calculated. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::transfernodes()
-{
- point pointloop;
- REAL x, y, z;
- int coordindex;
- int attribindex;
- int mtrindex;
- int i, j;
-
- // Read the points.
- coordindex = 0;
- attribindex = 0;
- mtrindex = 0;
- for (i = 0; i < in->numberofpoints; i++) {
- makepoint(&pointloop);
- // Read the point coordinates.
- x = pointloop[0] = in->pointlist[coordindex++];
- y = pointloop[1] = in->pointlist[coordindex++];
- z = pointloop[2] = in->pointlist[coordindex++];
- // Read the point attributes.
- for (j = 0; j < in->numberofpointattributes; j++) {
- pointloop[3 + j] = in->pointattributelist[attribindex++];
- }
- // Read the point metric tensor.
- for (j = 0; j < in->numberofpointmtrs; j++) {
- pointloop[pointmtrindex + j] = in->pointmtrlist[mtrindex++];
- }
- // Determine the smallest and largests x, y and z coordinates.
- if (i == 0) {
- xmin = xmax = x;
- ymin = ymax = y;
- zmin = zmax = z;
- } else {
- xmin = (x < xmin) ? x : xmin;
- xmax = (x > xmax) ? x : xmax;
- ymin = (y < ymin) ? y : ymin;
- ymax = (y > ymax) ? y : ymax;
- zmin = (z < zmin) ? z : zmin;
- zmax = (z > zmax) ? z : zmax;
- }
- }
- // 'longest' is the largest possible edge length formed by input vertices.
- x = xmax - xmin;
- y = ymax - ymin;
- z = zmax - zmin;
- longest = sqrt(x * x + y * y + z * z);
- if (longest == 0.0) {
- printf("Error: The point set is trivial.\n");
- terminatetetgen(1);
- }
- // Two identical points are distinguished by 'lengthlimit'.
- lengthlimit = longest * b->epsilon * 1e+2;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// jettisonnodes() Jettison unused or duplicated vertices. //
-// //
-// Unused points are those input points which are outside the mesh domain or //
-// have no connection (isolated) to the mesh. Duplicated points exist for //
-// example if the input PLC is read from a .stl mesh file (marked during the //
-// Delaunay tetrahedralization step. This routine remove these points from //
-// points list. All existing points are reindexed. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::jettisonnodes()
-{
- point pointloop;
- bool jetflag;
- int oldidx, newidx;
- int remcount;
-
- if (!b->quiet) {
- printf("Jettisoning redundants points.\n");
- }
-
- points->traversalinit();
- pointloop = pointtraverse();
- oldidx = newidx = 0; // in->firstnumber;
- remcount = 0;
- while (pointloop != (point) NULL) {
- jetflag = (pointtype(pointloop) == DUPLICATEDVERTEX) ||
- (pointtype(pointloop) == UNUSEDVERTEX);
- if (jetflag) {
- // It is a duplicated point, delete it.
- pointdealloc(pointloop);
- remcount++;
- } else {
- // Re-index it.
- setpointmark(pointloop, newidx + in->firstnumber);
- if (in->pointmarkerlist != (int *) NULL) {
- if (oldidx < in->numberofpoints) {
- // Re-index the point marker as well.
- in->pointmarkerlist[newidx] = in->pointmarkerlist[oldidx];
- }
- }
- newidx++;
- }
- oldidx++;
- if (oldidx == in->numberofpoints) {
- // Update the numbe of input points (Because some were removed).
- in->numberofpoints -= remcount;
- // Remember this number for output original input nodes.
- jettisoninverts = remcount;
- }
- pointloop = pointtraverse();
- }
- if (b->verbose) {
- printf(" %d duplicated vertices have been removed.\n", dupverts);
- printf(" %d unused vertices have been removed.\n", unuverts);
- }
- dupverts = 0;
- unuverts = 0;
-
- // The following line ensures that dead items in the pool of nodes cannot
- // be allocated for the new created nodes. This ensures that the input
- // nodes will occur earlier in the output files, and have lower indices.
- points->deaditemstack = (void *) NULL;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// highorder() Create extra nodes for quadratic subparametric elements. //
-// //
-// 'highordertable' is an array (size = numberoftetrahedra * 6) for storing //
-// high-order nodes of each tetrahedron. This routine is used only when -o2 //
-// switch is used. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::highorder()
-{
- triface tetloop, worktet;
- triface spintet, adjtet;
- point torg, tdest, tapex;
- point *extralist, *adjextralist;
- point newpoint;
- int hitbdry, ptmark;
- int i, j;
-
- if (!b->quiet) {
- printf("Adding vertices for second-order tetrahedra.\n");
- }
-
- // Initialize the 'highordertable'.
- highordertable = new point[tetrahedrons->items * 6];
- if (highordertable == (point *) NULL) {
- printf("Error: Out of memory.\n");
- terminatetetgen(1);
- }
-
- // The following line ensures that dead items in the pool of nodes cannot
- // be allocated for the extra nodes associated with high order elements.
- // This ensures that the primary nodes (at the corners of elements) will
- // occur earlier in the output files, and have lower indices, than the
- // extra nodes.
- points->deaditemstack = (void *) NULL;
-
- // Assign an entry for each tetrahedron to find its extra nodes. At the
- // mean while, initialize all extra nodes be NULL.
- i = 0;
- tetrahedrons->traversalinit();
- tetloop.tet = tetrahedrontraverse();
- while (tetloop.tet != (tetrahedron *) NULL) {
- tetloop.tet[highorderindex] = (tetrahedron) &highordertable[i];
- for (j = 0; j < 6; j++) {
- highordertable[i + j] = (point) NULL;
- }
- i += 6;
- tetloop.tet = tetrahedrontraverse();
- }
-
- // To create a unique node on each edge. Loop over all tetrahedra, and
- // look at the six edges of each tetrahedron. If the extra node in
- // the tetrahedron corresponding to this edge is NULL, create a node
- // for this edge, at the same time, set the new node into the extra
- // node lists of all other tetrahedra sharing this edge.
- tetrahedrons->traversalinit();
- tetloop.tet = tetrahedrontraverse();
- while (tetloop.tet != (tetrahedron *) NULL) {
- // Get the list of extra nodes.
- extralist = (point *) tetloop.tet[highorderindex];
- worktet.tet = tetloop.tet;
- for (i = 0; i < 6; i++) {
- if (extralist[i] == (point) NULL) {
- // Operate on this edge.
- worktet.loc = edge2locver[i][0];
- worktet.ver = edge2locver[i][1];
- // Create a new node on this edge.
- torg = org(worktet);
- tdest = dest(worktet);
- // Create a new node in the middle of the edge.
- newpoint = (point) points->alloc();
- // Interpolate its attributes.
- for (j = 0; j < 3 + in->numberofpointattributes; j++) {
- newpoint[j] = 0.5 * (torg[j] + tdest[j]);
- }
- ptmark = (int) points->items - (in->firstnumber == 1 ? 0 : 1);
- setpointmark(newpoint, ptmark);
- // Add this node to its extra node list.
- extralist[i] = newpoint;
- // Set 'newpoint' into extra node lists of other tetrahedra
- // sharing this edge.
- tapex = apex(worktet);
- spintet = worktet;
- hitbdry = 0;
- while (hitbdry < 2) {
- if (fnextself(spintet)) {
- // Get the extra node list of 'spintet'.
- adjextralist = (point *) spintet.tet[highorderindex];
- // Find the index of its extra node list.
- j = locver2edge[spintet.loc][spintet.ver];
- // Only set 'newpoint' into 'adjextralist' if it is a NULL.
- // Because two faces can belong to the same tetrahedron.
- if (adjextralist[j] == (point) NULL) {
- adjextralist[j] = newpoint;
- }
- if (apex(spintet) == tapex) {
- break;
- }
- } else {
- hitbdry++;
- if (hitbdry < 2) {
- esym(worktet, spintet);
- }
- }
- }
- }
- }
- tetloop.tet = tetrahedrontraverse();
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// outnodes() Output the points to a .node file or a tetgenio structure. //
-// //
-// Note: each point has already been numbered on input (the first index is //
-// 'in->firstnumber'). //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::outnodes(tetgenio* out)
-{
- FILE *outfile;
- char outnodefilename[FILENAMESIZE];
- shellface subptr;
- triface adjtet;
- face subloop;
- point pointloop;
- point *extralist, ep[3];
- int nextras, bmark, shmark, marker;
- int coordindex, attribindex;
- int pointnumber, firstindex;
- int index, i;
-
- if (out == (tetgenio *) NULL) {
- strcpy(outnodefilename, b->outfilename);
- strcat(outnodefilename, ".node");
- }
-
- if (!b->quiet) {
- if (out == (tetgenio *) NULL) {
- printf("Writing %s.\n", outnodefilename);
- } else {
- printf("Writing nodes.\n");
- }
- }
-
- nextras = in->numberofpointattributes;
- bmark = !b->nobound && in->pointmarkerlist;
-
- // Avoid compile warnings.
- outfile = (FILE *) NULL;
- marker = coordindex = 0;
-
- if (out == (tetgenio *) NULL) {
- outfile = fopen(outnodefilename, "w");
- if (outfile == (FILE *) NULL) {
- printf("File I/O Error: Cannot create file %s.\n", outnodefilename);
- terminatetetgen(1);
- }
- // Number of points, number of dimensions, number of point attributes,
- // and number of boundary markers (zero or one).
- fprintf(outfile, "%ld %d %d %d\n", points->items, 3, nextras, bmark);
- } else {
- // Allocate space for 'pointlist';
- out->pointlist = new REAL[points->items * 3];
- if (out->pointlist == (REAL *) NULL) {
- printf("Error: Out of memory.\n");
- terminatetetgen(1);
- }
- // Allocate space for 'pointattributelist' if necessary;
- if (nextras > 0) {
- out->pointattributelist = new REAL[points->items * nextras];
- if (out->pointattributelist == (REAL *) NULL) {
- printf("Error: Out of memory.\n");
- terminatetetgen(1);
- }
- }
- // Allocate space for 'pointmarkerlist' if necessary;
- if (bmark) {
- out->pointmarkerlist = new int[points->items];
- if (out->pointmarkerlist == (int *) NULL) {
- printf("Error: Out of memory.\n");
- terminatetetgen(1);
- }
- }
- out->numberofpoints = points->items;
- out->numberofpointattributes = nextras;
- coordindex = 0;
- attribindex = 0;
- }
-
- if (bmark && (b->plc || b->refine)) {
- // Initialize the point2tet field of each point.
- points->traversalinit();
- pointloop = pointtraverse();
- while (pointloop != (point) NULL) {
- setpoint2tet(pointloop, (tetrahedron) NULL);
- pointloop = pointtraverse();
- }
- // Make a map point-to-subface. Hence a boundary point will get the
- // facet marker from that facet where it lies on.
- subfaces->traversalinit();
- subloop.sh = shellfacetraverse(subfaces);
- while (subloop.sh != (shellface *) NULL) {
- subloop.shver = 0;
- // Check all three points of the subface.
- for (i = 0; i < 3; i++) {
- pointloop = (point) subloop.sh[3 + i];
- setpoint2tet(pointloop, (tetrahedron) sencode(subloop));
- }
- if (b->order == 2) {
- // '-o2' switch. Set markers for quadratic nodes of this subface.
- stpivot(subloop, adjtet);
- if (adjtet.tet == dummytet) {
- sesymself(subloop);
- stpivot(subloop, adjtet);
- }
- assert(adjtet.tet != dummytet);
- extralist = (point *) adjtet.tet[highorderindex];
- switch (adjtet.loc) {
- case 0:
- ep[0] = extralist[0];
- ep[1] = extralist[1];
- ep[2] = extralist[2];
- break;
- case 1:
- ep[0] = extralist[0];
- ep[1] = extralist[4];
- ep[2] = extralist[3];
- break;
- case 2:
- ep[0] = extralist[1];
- ep[1] = extralist[5];
- ep[2] = extralist[4];
- break;
- case 3:
- ep[0] = extralist[2];
- ep[1] = extralist[3];
- ep[2] = extralist[5];
- break;
- default: break;
- }
- for (i = 0; i < 3; i++) {
- setpoint2tet(ep[i], (tetrahedron) sencode(subloop));
- }
- }
- subloop.sh = shellfacetraverse(subfaces);
- }
- }
-
- // Determine the first index (0 or 1).
- firstindex = b->zeroindex ? 0 : in->firstnumber;
-
- points->traversalinit();
- pointloop = pointtraverse();
- pointnumber = firstindex; // in->firstnumber;
- index = 0;
- while (pointloop != (point) NULL) {
- if (bmark) {
- // Default the vertex has a zero marker.
- marker = 0;
- // Is it an input vertex?
- if (index < in->numberofpoints) {
- // Input point's marker is directly copied to output.
- marker = in->pointmarkerlist[index];
- }
- // Is it a boundary vertex has marker zero?
- if ((marker == 0) && (b->plc || b->refine)) {
- subptr = (shellface) point2tet(pointloop);
- if (subptr != (shellface) NULL) {
- // Default a boundary vertex has marker 1.
- marker = 1;
- if (in->facetmarkerlist != (int *) NULL) {
- // The vertex gets the marker from the facet it lies on.
- sdecode(subptr, subloop);
- shmark = shellmark(subloop);
- marker = in->facetmarkerlist[shmark - 1];
- }
- }
- }
- }
- if (out == (tetgenio *) NULL) {
- // Point number, x, y and z coordinates.
- fprintf(outfile, "%4d %.17g %.17g %.17g", pointnumber,
- pointloop[0], pointloop[1], pointloop[2]);
- for (i = 0; i < nextras; i++) {
- // Write an attribute.
- fprintf(outfile, " %.17g", pointloop[3 + i]);
- }
- if (bmark) {
- // Write the boundary marker.
- fprintf(outfile, " %d", marker);
- }
- fprintf(outfile, "\n");
- } else {
- // X, y, and z coordinates.
- out->pointlist[coordindex++] = pointloop[0];
- out->pointlist[coordindex++] = pointloop[1];
- out->pointlist[coordindex++] = pointloop[2];
- // Point attributes.
- for (i = 0; i < nextras; i++) {
- // Output an attribute.
- out->pointattributelist[attribindex++] = pointloop[3 + i];
- }
- if (bmark) {
- // Output the boundary marker.
- out->pointmarkerlist[index] = marker;
- }
- }
- pointloop = pointtraverse();
- pointnumber++;
- index++;
- }
-
- if (out == (tetgenio *) NULL) {
- fprintf(outfile, "# Generated by %s\n", b->commandline);
- fclose(outfile);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// outmetrics() Output the metric to a file (*.mtr) or a tetgenio obj. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::outmetrics(tetgenio* out)
-{
- FILE *outfile;
- char outmtrfilename[FILENAMESIZE];
- list *tetlist, *ptlist;
- triface tetloop;
- point ptloop, neipt;
- REAL lave, len; // lmin, lmax,
- int mtrindex;
- int i;
-
- if (out == (tetgenio *) NULL) {
- strcpy(outmtrfilename, b->outfilename);
- strcat(outmtrfilename, ".mtr");
- }
-
- if (!b->quiet) {
- if (out == (tetgenio *) NULL) {
- printf("Writing %s.\n", outmtrfilename);
- } else {
- printf("Writing metrics.\n");
- }
- }
-
- // Avoid compile warnings.
- outfile = (FILE *) NULL;
- mtrindex = 0;
-
- if (out == (tetgenio *) NULL) {
- outfile = fopen(outmtrfilename, "w");
- if (outfile == (FILE *) NULL) {
- printf("File I/O Error: Cannot create file %s.\n", outmtrfilename);
- terminatetetgen(1);
- }
- // Number of points, number of point metrices,
- // fprintf(outfile, "%ld %d\n", points->items, sizeoftensor + 3);
- fprintf(outfile, "%ld %d\n", points->items, 1);
- } else {
- // Allocate space for 'pointmtrlist' if necessary;
- // out->pointmtrlist = new REAL[points->items * (sizeoftensor + 3)];
- out->pointmtrlist = new REAL[points->items];
- if (out->pointmtrlist == (REAL *) NULL) {
- printf("Error: Out of memory.\n");
- terminatetetgen(1);
- }
- out->numberofpointmtrs = 1; // (sizeoftensor + 3);
- mtrindex = 0;
- }
-
- // Initialize the point2tet field of each point.
- points->traversalinit();
- ptloop = pointtraverse();
- while (ptloop != (point) NULL) {
- setpoint2tet(ptloop, (tetrahedron) NULL);
- ptloop = pointtraverse();
- }
- // Create the point-to-tet map.
- tetrahedrons->traversalinit();
- tetloop.tet = tetrahedrontraverse();
- while (tetloop.tet != (tetrahedron *) NULL) {
- for (i = 0; i < 4; i++) {
- ptloop = (point) tetloop.tet[4 + i];
- setpoint2tet(ptloop, encode(tetloop));
- }
- tetloop.tet = tetrahedrontraverse();
- }
-
- tetlist = new list(sizeof(triface), NULL, 256);
- ptlist = new list(sizeof(point *), NULL, 256);
-
- points->traversalinit();
- ptloop = pointtraverse();
- while (ptloop != (point) NULL) {
- decode(point2tet(ptloop), tetloop);
- if (!isdead(&tetloop)) {
- // Form the star of p.
- tetlist->append(&tetloop);
- formstarpolyhedron(ptloop, tetlist, ptlist, true);
- // lmin = longest;
- // lmax = 0.0;
- lave = 0.0;
- for (i = 0; i < ptlist->len(); i++) {
- neipt = * (point *)(* ptlist)[i];
- len = distance(ptloop, neipt);
- // lmin = lmin < len ? lmin : len;
- // lmax = lmax > len ? lmax : len;
- lave += len;
- }
- lave /= ptlist->len();
- }
- if (out == (tetgenio *) NULL) {
- // for (i = 0; i < sizeoftensor; i++) {
- // fprintf(outfile, "%-16.8e ", ptloop[pointmtrindex + i]);
- // }
- if (ptlist->len() > 0) {
- // fprintf(outfile, "%-16.8e %-16.8e %-16.8e", lmin, lmax, lave);
- fprintf(outfile, "%-16.8e ", lave);
- } else {
- fprintf(outfile, "0.0 "); // fprintf(outfile, "0.0 0.0 0.0");
- }
- fprintf(outfile, "\n");
- } else {
- // for (i = 0; i < sizeoftensor; i++) {
- // out->pointmtrlist[mtrindex++] = ptloop[pointmtrindex + i];
- // }
- if (ptlist->len() > 0) {
- // out->pointmtrlist[mtrindex++] = lmin;
- // out->pointmtrlist[mtrindex++] = lmax;
- out->pointmtrlist[mtrindex++] = lave;
- } else {
- // out->pointmtrlist[mtrindex++] = 0.0;
- // out->pointmtrlist[mtrindex++] = 0.0;
- out->pointmtrlist[mtrindex++] = 0.0;
- }
- }
- tetlist->clear();
- ptlist->clear();
- ptloop = pointtraverse();
- }
-
- delete tetlist;
- delete ptlist;
-
- if (out == (tetgenio *) NULL) {
- fprintf(outfile, "# Generated by %s\n", b->commandline);
- fclose(outfile);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// outelements() Output the tetrahedra to an .ele file or a tetgenio //
-// structure. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::outelements(tetgenio* out)
-{
- FILE *outfile;
- char outelefilename[FILENAMESIZE];
- tetrahedron* tptr;
- int *tlist;
- REAL *talist;
- int firstindex, shift;
- int pointindex;
- int attribindex;
- point p1, p2, p3, p4;
- point *extralist;
- int elementnumber;
- int eextras;
- int i;
-
- if (out == (tetgenio *) NULL) {
- strcpy(outelefilename, b->outfilename);
- strcat(outelefilename, ".ele");
- }
-
- if (!b->quiet) {
- if (out == (tetgenio *) NULL) {
- printf("Writing %s.\n", outelefilename);
- } else {
- printf("Writing elements.\n");
- }
- }
-
- // Avoid compile warnings.
- outfile = (FILE *) NULL;
- tlist = (int *) NULL;
- talist = (double *) NULL;
- pointindex = attribindex = 0;
-
- eextras = in->numberoftetrahedronattributes;
- if (out == (tetgenio *) NULL) {
- outfile = fopen(outelefilename, "w");
- if (outfile == (FILE *) NULL) {
- printf("File I/O Error: Cannot create file %s.\n", outelefilename);
- terminatetetgen(1);
- }
- // Number of tetras, points per tetra, attributes per tetra.
- fprintf(outfile, "%ld %d %d\n", tetrahedrons->items,
- b->order == 1 ? 4 : 10, eextras);
- } else {
- // Allocate memory for output tetrahedra.
- out->tetrahedronlist = new int[tetrahedrons->items *
- (b->order == 1 ? 4 : 10)];
- if (out->tetrahedronlist == (int *) NULL) {
- printf("Error: Out of memory.\n");
- terminatetetgen(1);
- }
- // Allocate memory for output tetrahedron attributes if necessary.
- if (eextras > 0) {
- out->tetrahedronattributelist = new REAL[tetrahedrons->items * eextras];
- if (out->tetrahedronattributelist == (REAL *) NULL) {
- printf("Error: Out of memory.\n");
- terminatetetgen(1);
- }
- }
- out->numberoftetrahedra = tetrahedrons->items;
- out->numberofcorners = b->order == 1 ? 4 : 10;
- out->numberoftetrahedronattributes = eextras;
- tlist = out->tetrahedronlist;
- talist = out->tetrahedronattributelist;
- pointindex = 0;
- attribindex = 0;
- }
-
- // Determine the first index (0 or 1).
- firstindex = b->zeroindex ? 0 : in->firstnumber;
- shift = 0; // Default no shiftment.
- if ((in->firstnumber == 1) && (firstindex == 0)) {
- shift = 1; // Shift the output indices by 1.
- }
-
- tetrahedrons->traversalinit();
- tptr = tetrahedrontraverse();
- elementnumber = firstindex; // in->firstnumber;
- while (tptr != (tetrahedron *) NULL) {
- p1 = (point) tptr[4];
- p2 = (point) tptr[5];
- p3 = (point) tptr[6];
- p4 = (point) tptr[7];
- if (out == (tetgenio *) NULL) {
- // Tetrahedron number, indices for four points.
- fprintf(outfile, "%5d %5d %5d %5d %5d", elementnumber,
- pointmark(p1) - shift, pointmark(p2) - shift,
- pointmark(p3) - shift, pointmark(p4) - shift);
- if (b->order == 2) {
- extralist = (point *) tptr[highorderindex];
- // Tetrahedron number, indices for four points plus six extra points.
- fprintf(outfile, " %5d %5d %5d %5d %5d %5d",
- pointmark(extralist[0]) - shift, pointmark(extralist[1]) - shift,
- pointmark(extralist[2]) - shift, pointmark(extralist[3]) - shift,
- pointmark(extralist[4]) - shift, pointmark(extralist[5]) - shift);
- }
- for (i = 0; i < eextras; i++) {
- fprintf(outfile, " %.17g", elemattribute(tptr, i));
- }
- fprintf(outfile, "\n");
- } else {
- tlist[pointindex++] = pointmark(p1) - shift;
- tlist[pointindex++] = pointmark(p2) - shift;
- tlist[pointindex++] = pointmark(p3) - shift;
- tlist[pointindex++] = pointmark(p4) - shift;
- if (b->order == 2) {
- extralist = (point *) tptr[highorderindex];
- tlist[pointindex++] = pointmark(extralist[0]) - shift;
- tlist[pointindex++] = pointmark(extralist[1]) - shift;
- tlist[pointindex++] = pointmark(extralist[2]) - shift;
- tlist[pointindex++] = pointmark(extralist[3]) - shift;
- tlist[pointindex++] = pointmark(extralist[4]) - shift;
- tlist[pointindex++] = pointmark(extralist[5]) - shift;
- }
- for (i = 0; i < eextras; i++) {
- talist[attribindex++] = elemattribute(tptr, i);
- }
- }
- if (b->neighout) {
- // Remember the index of this element.
- * (int *) (tptr + elemmarkerindex) = elementnumber;
- }
- tptr = tetrahedrontraverse();
- elementnumber++;
- }
- if (b->neighout) {
- // Set the outside element marker.
- * (int *) (dummytet + elemmarkerindex) = -1;
- }
-
- if (out == (tetgenio *) NULL) {
- fprintf(outfile, "# Generated by %s\n", b->commandline);
- fclose(outfile);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// outfaces() Output all faces to a .face file or a tetgenio structure. //
-// //
-// This routines outputs all triangular faces (including outer boundary //
-// faces and inner faces) of this mesh. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::outfaces(tetgenio* out)
-{
- FILE *outfile;
- char facefilename[FILENAMESIZE];
- int *elist;
- int *emlist;
- int neigh1, neigh2;
- int index;
- triface tface, tsymface;
- face checkmark;
- point torg, tdest, tapex;
- long faces;
- int bmark, faceid, marker;
- int firstindex, shift;
- int facenumber;
-
- if (out == (tetgenio *) NULL) {
- strcpy(facefilename, b->outfilename);
- strcat(facefilename, ".face");
- }
-
- if (!b->quiet) {
- if (out == (tetgenio *) NULL) {
- printf("Writing %s.\n", facefilename);
- } else {
- printf("Writing faces.\n");
- }
- }
-
- // Avoid compile warnings.
- outfile = (FILE *) NULL;
- elist = (int *) NULL;
- emlist = (int *) NULL;
- index = marker = 0;
-
- faces = (4l * tetrahedrons->items + hullsize) / 2l;
- bmark = !b->nobound && in->facetmarkerlist;
-
- if (out == (tetgenio *) NULL) {
- outfile = fopen(facefilename, "w");
- if (outfile == (FILE *) NULL) {
- printf("File I/O Error: Cannot create file %s.\n", facefilename);
- terminatetetgen(1);
- }
- fprintf(outfile, "%ld %d\n", faces, bmark);
- } else {
- // Allocate memory for 'trifacelist'.
- out->trifacelist = new int[faces * 3];
- if (out->trifacelist == (int *) NULL) {
- printf("Error: Out of memory.\n");
- terminatetetgen(1);
- }
- // Allocate memory for 'trifacemarkerlist' if necessary.
- if (bmark) {
- out->trifacemarkerlist = new int[faces];
- if (out->trifacemarkerlist == (int *) NULL) {
- printf("Error: Out of memory.\n");
- terminatetetgen(1);
- }
- }
- if (b->neighout > 1) {
- // '-nn' switch.
- out->adjtetlist = new int[subfaces->items * 2];
- if (out->adjtetlist == (int *) NULL) {
- printf("Error: Out of memory.\n");
- terminatetetgen(1);
- }
- }
- out->numberoftrifaces = faces;
- elist = out->trifacelist;
- emlist = out->trifacemarkerlist;
- index = 0;
- }
-
- // Determine the first index (0 or 1).
- firstindex = b->zeroindex ? 0 : in->firstnumber;
- shift = 0; // Default no shiftment.
- if ((in->firstnumber == 1) && (firstindex == 0)) {
- shift = 1; // Shift the output indices by 1.
- }
-
- tetrahedrons->traversalinit();
- tface.tet = tetrahedrontraverse();
- facenumber = firstindex; // in->firstnumber;
- // To loop over the set of faces, loop over all tetrahedra, and look at
- // the four faces of each one. If there isn't another tetrahedron
- // adjacent to this face, operate on the face. If there is another
- // adjacent tetrahedron, operate on the face only if the current
- // tetrahedron has a smaller pointer than its neighbor. This way, each
- // face is considered only once.
- while (tface.tet != (tetrahedron *) NULL) {
- for (tface.loc = 0; tface.loc < 4; tface.loc ++) {
- sym(tface, tsymface);
- if ((tsymface.tet == dummytet) || (tface.tet < tsymface.tet)) {
- torg = org(tface);
- tdest = dest(tface);
- tapex = apex(tface);
- if (bmark) {
- // Get the boundary marker of this face. If it is an inner face,
- // it has no boundary marker, set it be zero.
- if (b->useshelles) {
- // Shell face is used.
- tspivot(tface, checkmark);
- if (checkmark.sh == dummysh) {
- marker = 0; // It is an inner face.
- } else {
- faceid = shellmark(checkmark) - 1;
- marker = in->facetmarkerlist[faceid];
- }
- } else {
- // Shell face is not used, only distinguish outer and inner face.
- marker = tsymface.tet != dummytet ? 1 : 0;
- }
- }
- if (b->neighout > 1) {
- // '-nn' switch. Output adjacent tets indices.
- neigh1 = * (int *)(tface.tet + elemmarkerindex);
- if (tsymface.tet != dummytet) {
- neigh2 = * (int *)(tsymface.tet + elemmarkerindex);
- } else {
- neigh2 = -1;
- }
- }
- if (out == (tetgenio *) NULL) {
- // Face number, indices of three vertices.
- fprintf(outfile, "%5d %4d %4d %4d", facenumber,
- pointmark(torg) - shift, pointmark(tdest) - shift,
- pointmark(tapex) - shift);
- if (bmark) {
- // Output a boundary marker.
- fprintf(outfile, " %d", marker);
- }
- if (b->neighout > 1) {
- fprintf(outfile, " %5d %5d", neigh1, neigh2);
- }
- fprintf(outfile, "\n");
- } else {
- // Output indices of three vertices.
- elist[index++] = pointmark(torg) - shift;
- elist[index++] = pointmark(tdest) - shift;
- elist[index++] = pointmark(tapex) - shift;
- if (bmark) {
- emlist[facenumber - in->firstnumber] = marker;
- }
- if (b->neighout > 1) {
- out->adjtetlist[(facenumber - in->firstnumber) * 2] = neigh1;
- out->adjtetlist[(facenumber - in->firstnumber) * 2 + 1] = neigh2;
- }
- }
- facenumber++;
- }
- }
- tface.tet = tetrahedrontraverse();
- }
-
- if (out == (tetgenio *) NULL) {
- fprintf(outfile, "# Generated by %s\n", b->commandline);
- fclose(outfile);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// outhullfaces() Output outer boundary faces to a .face file or a //
-// tetgenio structure. //
-// //
-// The normal of each face is arranged to point inside of the domain (use //
-// right-hand rule). This routines will outputs convex hull faces if the //
-// mesh is a Delaunay tetrahedralization. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::outhullfaces(tetgenio* out)
-{
- FILE *outfile;
- char facefilename[FILENAMESIZE];
- int *elist;
- int index;
- triface tface, tsymface;
- face checkmark;
- point torg, tdest, tapex;
- int firstindex, shift;
- int facenumber;
-
- if (out == (tetgenio *) NULL) {
- strcpy(facefilename, b->outfilename);
- strcat(facefilename, ".face");
- }
-
- if (!b->quiet) {
- if (out == (tetgenio *) NULL) {
- printf("Writing %s.\n", facefilename);
- } else {
- printf("Writing faces.\n");
- }
- }
-
- // Avoid compile warnings.
- outfile = (FILE *) NULL;
- elist = (int *) NULL;
- index = 0;
-
- if (out == (tetgenio *) NULL) {
- outfile = fopen(facefilename, "w");
- if (outfile == (FILE *) NULL) {
- printf("File I/O Error: Cannot create file %s.\n", facefilename);
- terminatetetgen(1);
- }
- fprintf(outfile, "%ld 0\n", hullsize);
- } else {
- // Allocate memory for 'trifacelist'.
- out->trifacelist = new int[hullsize * 3];
- if (out->trifacelist == (int *) NULL) {
- printf("Error: Out of memory.\n");
- terminatetetgen(1);
- }
- out->numberoftrifaces = hullsize;
- elist = out->trifacelist;
- index = 0;
- }
-
- // Determine the first index (0 or 1).
- firstindex = b->zeroindex ? 0 : in->firstnumber;
- shift = 0; // Default no shiftment.
- if ((in->firstnumber == 1) && (firstindex == 0)) {
- shift = 1; // Shift the output indices by 1.
- }
-
- tetrahedrons->traversalinit();
- tface.tet = tetrahedrontraverse();
- facenumber = firstindex; // in->firstnumber;
- // To loop over the set of hull faces, loop over all tetrahedra, and look
- // at the four faces of each one. If there isn't another tetrahedron
- // adjacent to this face, operate on the face.
- while (tface.tet != (tetrahedron *) NULL) {
- for (tface.loc = 0; tface.loc < 4; tface.loc ++) {
- sym(tface, tsymface);
- if (tsymface.tet == dummytet) {
- torg = org(tface);
- tdest = dest(tface);
- tapex = apex(tface);
- if (out == (tetgenio *) NULL) {
- // Face number, indices of three vertices.
- fprintf(outfile, "%5d %4d %4d %4d", facenumber,
- pointmark(torg) - shift, pointmark(tdest) - shift,
- pointmark(tapex) - shift);
- fprintf(outfile, "\n");
- } else {
- // Output indices of three vertices.
- elist[index++] = pointmark(torg) - shift;
- elist[index++] = pointmark(tdest) - shift;
- elist[index++] = pointmark(tapex) - shift;
- }
- facenumber++;
- }
- }
- tface.tet = tetrahedrontraverse();
- }
-
- if (out == (tetgenio *) NULL) {
- fprintf(outfile, "# Generated by %s\n", b->commandline);
- fclose(outfile);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// outsubfaces() Output subfaces (i.e. boundary faces) to a .face file or //
-// a tetgenio structure. //
-// //
-// The boundary faces are exist in 'subfaces'. For listing triangle vertices //
-// in the same sense for all triangles in the mesh, the direction determined //
-// by right-hand rule is pointer to the inside of the volume. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::outsubfaces(tetgenio* out)
-{
- FILE *outfile;
- char facefilename[FILENAMESIZE];
- int *elist;
- int *emlist;
- int index, index1, index2;
- triface abuttingtet;
- face faceloop;
- point torg, tdest, tapex;
- int bmark, faceid, marker;
- int firstindex, shift;
- int neigh1, neigh2;
- int facenumber;
-
- if (out == (tetgenio *) NULL) {
- strcpy(facefilename, b->outfilename);
- strcat(facefilename, ".face");
- }
-
- if (!b->quiet) {
- if (out == (tetgenio *) NULL) {
- printf("Writing %s.\n", facefilename);
- } else {
- printf("Writing subfaces.\n");
- }
- }
-
- // Avoid compile warnings.
- outfile = (FILE *) NULL;
- elist = (int *) NULL;
- emlist = (int *) NULL;
- index = index1 = index2 = 0;
- faceid = marker = 0;
- neigh1 = neigh2 = 0;
-
- bmark = !b->nobound && in->facetmarkerlist;
-
- if (out == (tetgenio *) NULL) {
- outfile = fopen(facefilename, "w");
- if (outfile == (FILE *) NULL) {
- printf("File I/O Error: Cannot create file %s.\n", facefilename);
- terminatetetgen(1);
- }
- // Number of subfaces.
- fprintf(outfile, "%ld %d\n", subfaces->items, bmark);
- } else {
- // Allocate memory for 'trifacelist'.
- out->trifacelist = new int[subfaces->items * 3];
- if (out->trifacelist == (int *) NULL) {
- printf("Error: Out of memory.\n");
- terminatetetgen(1);
- }
- if (bmark) {
- // Allocate memory for 'trifacemarkerlist'.
- out->trifacemarkerlist = new int[subfaces->items];
- if (out->trifacemarkerlist == (int *) NULL) {
- printf("Error: Out of memory.\n");
- terminatetetgen(1);
- }
- }
- if (b->neighout > 1) {
- // '-nn' switch.
- out->adjtetlist = new int[subfaces->items * 2];
- if (out->adjtetlist == (int *) NULL) {
- printf("Error: Out of memory.\n");
- terminatetetgen(1);
- }
- }
- out->numberoftrifaces = subfaces->items;
- elist = out->trifacelist;
- emlist = out->trifacemarkerlist;
- }
-
- // Determine the first index (0 or 1).
- firstindex = b->zeroindex ? 0 : in->firstnumber;
- shift = 0; // Default no shiftment.
- if ((in->firstnumber == 1) && (firstindex == 0)) {
- shift = 1; // Shift the output indices by 1.
- }
-
- subfaces->traversalinit();
- faceloop.sh = shellfacetraverse(subfaces);
- facenumber = firstindex; // in->firstnumber;
- while (faceloop.sh != (shellface *) NULL) {
- stpivot(faceloop, abuttingtet);
- if (abuttingtet.tet == dummytet) {
- sesymself(faceloop);
- stpivot(faceloop, abuttingtet);
- }
- if (abuttingtet.tet != dummytet) {
- // If there is a tetrahedron containing this subface, orient it so
- // that the normal of this face points to inside of the volume by
- // right-hand rule.
- adjustedgering(abuttingtet, CCW);
- torg = org(abuttingtet);
- tdest = dest(abuttingtet);
- tapex = apex(abuttingtet);
- } else {
- // This may happen when only a surface mesh be generated.
- torg = sorg(faceloop);
- tdest = sdest(faceloop);
- tapex = sapex(faceloop);
- }
- if (bmark) {
- faceid = shellmark(faceloop) - 1;
- marker = in->facetmarkerlist[faceid];
- }
- if (b->neighout > 1) {
- // '-nn' switch. Output adjacent tets indices.
- neigh1 = -1;
- stpivot(faceloop, abuttingtet);
- if (abuttingtet.tet != dummytet) {
- neigh1 = * (int *)(abuttingtet.tet + elemmarkerindex);
- }
- neigh2 = -1;
- sesymself(faceloop);
- stpivot(faceloop, abuttingtet);
- if (abuttingtet.tet != dummytet) {
- neigh2 = * (int *)(abuttingtet.tet + elemmarkerindex);
- }
- }
- if (out == (tetgenio *) NULL) {
- fprintf(outfile, "%5d %4d %4d %4d", facenumber,
- pointmark(torg) - shift, pointmark(tdest) - shift,
- pointmark(tapex) - shift);
- if (bmark) {
- fprintf(outfile, " %d", marker);
- }
- if (b->neighout > 1) {
- fprintf(outfile, " %5d %5d", neigh1, neigh2);
- }
- fprintf(outfile, "\n");
- } else {
- // Output three vertices of this face;
- elist[index++] = pointmark(torg) - shift;
- elist[index++] = pointmark(tdest) - shift;
- elist[index++] = pointmark(tapex) - shift;
- if (bmark) {
- emlist[index1++] = marker;
- }
- if (b->neighout > 1) {
- out->adjtetlist[index2++] = neigh1;
- out->adjtetlist[index2++] = neigh2;
- }
- }
- facenumber++;
- faceloop.sh = shellfacetraverse(subfaces);
- }
-
- if (out == (tetgenio *) NULL) {
- fprintf(outfile, "# Generated by %s\n", b->commandline);
- fclose(outfile);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// outedges() Output all edges to a .edge file or a structure. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::outedges(tetgenio* out)
-{
- FILE *outfile;
- char edgefilename[FILENAMESIZE];
- int *elist, *emlist;
- int index, index1;
- triface tetloop, worktet, spintet;
- face checksh;
- point torg, tdest;
- long faces, edges;
- int firstindex, shift;
- int edgenumber, faceid, marker;
- int hitbdry, i;
-
- if (out == (tetgenio *) NULL) {
- strcpy(edgefilename, b->outfilename);
- strcat(edgefilename, ".edge");
- }
-
- if (!b->quiet) {
- if (out == (tetgenio *) NULL) {
- printf("Writing %s.\n", edgefilename);
- } else {
- printf("Writing edges.\n");
- }
- }
-
- // Avoid compile warnings.
- outfile = (FILE *) NULL;
- elist = (int *) NULL;
- emlist = (int *) NULL;
- index = index1 = 0;
- faceid = marker = 0;
-
- // Using the Euler formula (V-E+F-T=1) to get the total number of edges.
- faces = (4l * tetrahedrons->items + hullsize) / 2l;
- edges = points->items + faces - tetrahedrons->items - 1l;
-
- if (out == (tetgenio *) NULL) {
- outfile = fopen(edgefilename, "w");
- if (outfile == (FILE *) NULL) {
- printf("File I/O Error: Cannot create file %s.\n", edgefilename);
- terminatetetgen(1);
- }
- // Write the number of edges, boundary markers (0 or 1).
- fprintf(outfile, "%ld %d\n", edges, !b->nobound);
- } else {
- // Allocate memory for 'edgelist'.
- out->edgelist = new int[edges * 2];
- if (out->edgelist == (int *) NULL) {
- printf("Error: Out of memory.\n");
- terminatetetgen(1);
- }
- if (!b->nobound) {
- out->edgemarkerlist = new int[edges];
- }
- out->numberofedges = edges;
- elist = out->edgelist;
- emlist = out->edgemarkerlist;
- }
-
- // Determine the first index (0 or 1).
- firstindex = b->zeroindex ? 0 : in->firstnumber;
- shift = 0; // Default no shiftment.
- if ((in->firstnumber == 1) && (firstindex == 0)) {
- shift = 1; // Shift (reduce) the output indices by 1.
- }
-
- tetrahedrons->traversalinit();
- tetloop.tet = tetrahedrontraverse();
- edgenumber = firstindex; // in->firstnumber;
- while (tetloop.tet != (tetrahedron *) NULL) {
- // Count the number of Voronoi faces. Look at the six edges of each
- // tetrahedron. Count the edge only if the tetrahedron's pointer is
- // smaller than those of all other tetrahedra that share the edge.
- worktet.tet = tetloop.tet;
- for (i = 0; i < 6; i++) {
- worktet.loc = edge2locver[i][0];
- worktet.ver = edge2locver[i][1];
- adjustedgering(worktet, CW);
- spintet = worktet;
- hitbdry = 0;
- while (hitbdry < 2) {
- if (fnextself(spintet)) {
- if (apex(spintet) == apex(worktet)) break;
- if (spintet.tet < worktet.tet) break;
- } else {
- hitbdry++;
- if (hitbdry < 2) {
- esym(worktet, spintet);
- fnextself(spintet); // In the same tet.
- }
- }
- }
- // Count this edge if no adjacent tets are smaller than this tet.
- if (spintet.tet >= worktet.tet) {
- torg = org(worktet);
- tdest = dest(worktet);
- if (out == (tetgenio *) NULL) {
- fprintf(outfile, "%5d %4d %4d", edgenumber,
- pointmark(torg) - shift, pointmark(tdest) - shift);
- } else {
- // Output three vertices of this face;
- elist[index++] = pointmark(torg) - shift;
- elist[index++] = pointmark(tdest) - shift;
- }
- if (!b->nobound) {
- if (hitbdry > 0) {
- // It is a boundary edge. Get the boundary marker of the facet
- // containing this edge. Note there may have more than one
- // facet, choose one arbitrarily.
- if ((b->plc || b->refine) && in->facetmarkerlist) {
- tspivot(spintet, checksh);
- faceid = shellmark(checksh) - 1;
- marker = in->facetmarkerlist[faceid];
- } else {
- marker = 1; // Indicate it's a boundary edge.
- }
- } else {
- marker = 0;
- }
- if (out == (tetgenio *) NULL) {
- fprintf(outfile, " %d", marker);
- } else {
- emlist[index1++] = marker;
- }
- }
- if (out == (tetgenio *) NULL) {
- fprintf(outfile, "\n");
- }
- edgenumber++;
- }
- }
- tetloop.tet = tetrahedrontraverse();
- }
-
- if (out == (tetgenio *) NULL) {
- fprintf(outfile, "# Generated by %s\n", b->commandline);
- fclose(outfile);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// outsubsegments() Output segments to a .edge file or a structure. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::outsubsegments(tetgenio* out)
-{
- FILE *outfile;
- char edgefilename[FILENAMESIZE];
- int *elist;
- int index;
- face edgeloop;
- point torg, tdest;
- int firstindex, shift;
- int edgenumber;
-
- if (out == (tetgenio *) NULL) {
- strcpy(edgefilename, b->outfilename);
- strcat(edgefilename, ".edge");
- }
-
- if (!b->quiet) {
- if (out == (tetgenio *) NULL) {
- printf("Writing %s.\n", edgefilename);
- } else {
- printf("Writing edges.\n");
- }
- }
-
- // Avoid compile warnings.
- outfile = (FILE *) NULL;
- elist = (int *) NULL;
- index = 0;
-
- if (out == (tetgenio *) NULL) {
- outfile = fopen(edgefilename, "w");
- if (outfile == (FILE *) NULL) {
- printf("File I/O Error: Cannot create file %s.\n", edgefilename);
- terminatetetgen(1);
- }
- // Number of subsegments.
- fprintf(outfile, "%ld\n", subsegs->items);
- } else {
- // Allocate memory for 'edgelist'.
- out->edgelist = new int[subsegs->items * 2];
- if (out->edgelist == (int *) NULL) {
- printf("Error: Out of memory.\n");
- terminatetetgen(1);
- }
- out->numberofedges = subsegs->items;
- elist = out->edgelist;
- }
-
- // Determine the first index (0 or 1).
- firstindex = b->zeroindex ? 0 : in->firstnumber;
- shift = 0; // Default no shiftment.
- if ((in->firstnumber == 1) && (firstindex == 0)) {
- shift = 1; // Shift the output indices by 1.
- }
-
- subsegs->traversalinit();
- edgeloop.sh = shellfacetraverse(subsegs);
- edgenumber = firstindex; // in->firstnumber;
- while (edgeloop.sh != (shellface *) NULL) {
- torg = sorg(edgeloop);
- tdest = sdest(edgeloop);
- if (out == (tetgenio *) NULL) {
- fprintf(outfile, "%5d %4d %4d\n", edgenumber,
- pointmark(torg) - shift, pointmark(tdest) - shift);
- } else {
- // Output three vertices of this face;
- elist[index++] = pointmark(torg) - shift;
- elist[index++] = pointmark(tdest) - shift;
- }
- edgenumber++;
- edgeloop.sh = shellfacetraverse(subsegs);
- }
-
- if (out == (tetgenio *) NULL) {
- fprintf(outfile, "# Generated by %s\n", b->commandline);
- fclose(outfile);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// outneighbors() Output tet neighbors to a .neigh file or a structure. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::outneighbors(tetgenio* out)
-{
- FILE *outfile;
- char neighborfilename[FILENAMESIZE];
- int *nlist;
- int index;
- triface tetloop, tetsym;
- int neighbor1, neighbor2, neighbor3, neighbor4;
- int firstindex;
- int elementnumber;
-
- if (out == (tetgenio *) NULL) {
- strcpy(neighborfilename, b->outfilename);
- strcat(neighborfilename, ".neigh");
- }
-
- if (!b->quiet) {
- if (out == (tetgenio *) NULL) {
- printf("Writing %s.\n", neighborfilename);
- } else {
- printf("Writing neighbors.\n");
- }
- }
-
- // Avoid compile warnings.
- outfile = (FILE *) NULL;
- nlist = (int *) NULL;
- index = 0;
-
- if (out == (tetgenio *) NULL) {
- outfile = fopen(neighborfilename, "w");
- if (outfile == (FILE *) NULL) {
- printf("File I/O Error: Cannot create file %s.\n", neighborfilename);
- terminatetetgen(1);
- }
- // Number of tetrahedra, four faces per tetrahedron.
- fprintf(outfile, "%ld %d\n", tetrahedrons->items, 4);
- } else {
- // Allocate memory for 'neighborlist'.
- out->neighborlist = new int[tetrahedrons->items * 4];
- if (out->neighborlist == (int *) NULL) {
- printf("Error: Out of memory.\n");
- terminatetetgen(1);
- }
- nlist = out->neighborlist;
- }
-
- // Determine the first index (0 or 1).
- firstindex = b->zeroindex ? 0 : in->firstnumber;
-
- tetrahedrons->traversalinit();
- tetloop.tet = tetrahedrontraverse();
- elementnumber = firstindex; // in->firstnumber;
- while (tetloop.tet != (tetrahedron *) NULL) {
- tetloop.loc = 2;
- sym(tetloop, tetsym);
- neighbor1 = * (int *) (tetsym.tet + elemmarkerindex);
- tetloop.loc = 3;
- sym(tetloop, tetsym);
- neighbor2 = * (int *) (tetsym.tet + elemmarkerindex);
- tetloop.loc = 1;
- sym(tetloop, tetsym);
- neighbor3 = * (int *) (tetsym.tet + elemmarkerindex);
- tetloop.loc = 0;
- sym(tetloop, tetsym);
- neighbor4 = * (int *) (tetsym.tet + elemmarkerindex);
- if (out == (tetgenio *) NULL) {
- // Tetrahedra number, neighboring tetrahedron numbers.
- fprintf(outfile, "%4d %4d %4d %4d %4d\n", elementnumber,
- neighbor1, neighbor2, neighbor3, neighbor4);
- } else {
- nlist[index++] = neighbor1;
- nlist[index++] = neighbor2;
- nlist[index++] = neighbor3;
- nlist[index++] = neighbor4;
- }
- tetloop.tet = tetrahedrontraverse();
- elementnumber++;
- }
-
- if (out == (tetgenio *) NULL) {
- fprintf(outfile, "# Generated by %s\n", b->commandline);
- fclose(outfile);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// outvoronoi() Output the Voronoi diagram to .v.node, .v.edge, v.face, //
-// and .v.cell. //
-// //
-// The Voronoi diagram is the geometric dual of the Delaunay triangulation. //
-// The Voronoi vertices are the circumcenters of Delaunay tetrahedra. Each //
-// Voronoi edge connects two Voronoi vertices at two sides of a common Dela- //
-// unay face. At a face of convex hull, it becomes a ray (goto the infinity).//
-// A Voronoi face is the convex hull of all Voronoi vertices around a common //
-// Delaunay edge. It is a closed polygon for any interal Delaunay edge. At a //
-// ridge, it is unbounded. Each Voronoi cell is the convex hull of all Vor- //
-// onoi vertices around a common Delaunay vertex. It is a polytope for any //
-// internal Delaunay vertex. It is an unbounded polyhedron for a Delaunay //
-// vertex belonging to the convex hull. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::outvoronoi(tetgenio* out)
-{
- FILE *outfile;
- char outfilename[FILENAMESIZE];
- tetgenio::voroedge *vedge;
- tetgenio::vorofacet *vfacet;
- list *tetlist, *ptlist;
- triface tetloop, worktet, spintet;
- point pt[4], ptloop, neipt;
- REAL ccent[3], infvec[3], vec1[3], vec2[3], L;
- long faces, edges;
- int *tetfaceindexarray, *tetedgeindexarray;
- int arraysize, *vertarray;
- int vpointcount, vedgecount, vfacecount, tcount;
- int index, shift;
- int end1, end2;
- int hitbdry, i, j, k;
-
-
- //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- //NODES
- //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
- // Output Voronoi vertices to .v.node file.
- if (out == (tetgenio *) NULL) {
- strcpy(outfilename, b->outfilename);
- strcat(outfilename, ".v.node");
- }
-
- if (!b->quiet) {
- if (out == (tetgenio *) NULL) {
- printf("Writing %s.\n", outfilename);
- } else {
- printf("Writing Voronoi vertices.\n");
- }
- }
-
- // Determine the first index (0 or 1).
- shift = (b->zeroindex ? 0 : in->firstnumber);
- // The number of Delaunay faces (= the number of Voronoi edges).
- faces = (4l * tetrahedrons->items + hullsize) / 2l;
- // The number of Delaunay edges (= the number of Voronoi faces).
- edges = points->items + faces - tetrahedrons->items - 1;
- outfile = (FILE *) NULL; // Avoid compile warnings.
-
- if (out == (tetgenio *) NULL) {
- outfile = fopen(outfilename, "w");
- if (outfile == (FILE *) NULL) {
- printf("File I/O Error: Cannot create file %s.\n", outfilename);
- terminatetetgen(1);
- }
- // Number of voronoi points, 3 dim, no attributes, no marker.
- //fprintf(outfile, "%ld 3 0 0\n", tetrahedrons->items);
- fprintf(outfile, "View \"voronoi nodes\" {\n");//EMI
- } else {
- // Allocate space for 'vpointlist'.
- out->numberofvpoints = (int) tetrahedrons->items;
- out->vpointlist = new REAL[out->numberofvpoints * 3];
- if (out->vpointlist == (REAL *) NULL) {
- printf("Error: Out of memory.\n");
- terminatetetgen(1);
- }
- }
-
- // Loop the tetrahedronlist once, do the following:
- // (1) Output Voronoi vertices (the circumcenter of the tetrahedron).
- // (2) Make a map from points-to-tetrahedra (for Voronoi cells).
- tetrahedrons->traversalinit();
- tetloop.tet = tetrahedrontraverse();
- vpointcount = 0;
- index = 0;
- REAL *vlist;
- REAL *radlist;
- vlist = new REAL[(int)tetrahedrons->items * 3]; //for coords of circumcenters
- radlist = new REAL[(int)tetrahedrons->items ]; //for radii of circumcenters
-
- while (tetloop.tet != (tetrahedron *) NULL) {
- // Calculate the circumcenter.
- for (i = 0; i < 4; i++) {
- pt[i] = (point) tetloop.tet[4 + i];
- setpoint2tet(pt[i], encode(tetloop));
- }
- REAL radius;
- circumsphere(pt[0], pt[1], pt[2], pt[3], ccent, &radius);
- if (out == (tetgenio *) NULL) {
- //fprintf(outfile, "%4d %16.8e %16.8e %16.8e\n", vpointcount + shift,
- // ccent[0], ccent[1], ccent[2]);
- fprintf(outfile,"SP(%g,%g,%g) {%g};\n", ccent[0], ccent[1], ccent[2], (double)radius);//EMI
- int indexCenter = (vpointcount+shift);//EMI
- vlist[indexCenter*3+0] = ccent[0];//EMI
- vlist[indexCenter*3+1] = ccent[1];//EMI
- vlist[indexCenter*3+2] = ccent[2];//EMI
- radlist[indexCenter] = radius;//EMI
-
- } else {
- out->vpointlist[index++] = ccent[0];
- out->vpointlist[index++] = ccent[1];
- out->vpointlist[index++] = ccent[2];
- }
- // Remember the index of this element.
- * (int *) (tetloop.tet + elemmarkerindex) = vpointcount;
- vpointcount++;
- tetloop.tet = tetrahedrontraverse();
- }
-
- // Set the outside element marker.
- * (int *) (dummytet + elemmarkerindex) = -1;
-
- if (out == (tetgenio *) NULL) {
- //fprintf(outfile, "# Generated by %s\n", b->commandline);
- fprintf(outfile,"};\n"); //EMI
- fclose(outfile);
- }
-
- //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- //EDGES
- //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
- // Output Voronoi edges to .v.edge file.
- if (out == (tetgenio *) NULL) {
- strcpy(outfilename, b->outfilename);
- strcat(outfilename, ".v.edge");
- }
-
- if (!b->quiet) {
- if (out == (tetgenio *) NULL) {
- printf("Writing %s.\n", outfilename);
- } else {
- printf("Writing Voronoi edges.\n");
- }
- }
-
- if (out == (tetgenio *) NULL) {
- outfile = fopen(outfilename, "w");
- if (outfile == (FILE *) NULL) {
- printf("File I/O Error: Cannot create file %s.\n", outfilename);
- terminatetetgen(1);
- }
- // Number of Voronoi edges, no marker.
- //sfprintf(outfile, "%ld 0\n", faces);
- fprintf(outfile, "View \"voronoi edges\" {\n");//EMI
- } else {
- // Allocate space for 'vpointlist'.
- out->numberofedges = (int) faces;
- out->vedgelist = new tetgenio::voroedge[out->numberofvedges];
- }
-
- // Loop the tetrahedronlist once, output the Voronoi edges. The index of
- // each Voronoi edge corresponding to the index of the Delaunay face.
- // The four faces' indices of each tetrahedron are saved in the list
- // 'tetfaceindexarray', in the entry of i, where i (0-based) is the
- // index of this tetrahedron (= vpointcount).
- tetfaceindexarray = new int[tetrahedrons->items * 4];
- tetrahedrons->traversalinit();
- tetloop.tet = tetrahedrontraverse();
- vedgecount = 0;
- index = 0;
- while (tetloop.tet != (tetrahedron *) NULL) {
- // Count the number of Voronoi edges. Look at the four faces of each
- // tetrahedron. Count the face if the tetrahedron's pointer is
- // smaller than its neighbor's or the neighbor is outside.
- end1 = * (int *) (tetloop.tet + elemmarkerindex);
- for (i = 0; i < 4; i++) {
- decode(tetloop.tet[i], worktet);
- if ((worktet.tet == dummytet) || (tetloop.tet < worktet.tet)) {
- if (out == (tetgenio *) NULL) {
- //fprintf(outfile, "%4d %4d", vedgecount + shift, end1 + shift); //EMI
- } else {
- vedge = &(out->vedgelist[index++]);
- vedge->v1 = end1 + shift;
- }
- end2 = * (int *) (worktet.tet + elemmarkerindex);
- // Note that end2 may be -1 (worktet.tet is outside).
- if (end2 == -1) {
- // Calculate the out normal of this hull face.
- worktet.tet = tetloop.tet;
- worktet.loc = i;
- worktet.ver = 1; // The CW edge ring.
- pt[0] = org(worktet);
- pt[1] = dest(worktet);
- pt[2] = apex(worktet);
- for (j = 0; j < 3; j++) vec1[j] = pt[1][j] - pt[0][j];
- for (j = 0; j < 3; j++) vec2[j] = pt[2][j] - pt[0][j];
- cross(vec1, vec2, infvec);
- // Normalize it.
- L = sqrt(infvec[0] * infvec[0] + infvec[1] * infvec[1]
- + infvec[2] * infvec[2]);
- if (L > 0) for (j = 0; j < 3; j++) infvec[j] /= L;
- if (out == (tetgenio *) NULL) {
- //fprintf(outfile, " -1");//EMI
- //fprintf(outfile, " %g %g %g\n", infvec[0], infvec[1], infvec[2]);//EMI
- } else {
- vedge->v2 = -1;
- vedge->vnormal[0] = infvec[0];
- vedge->vnormal[1] = infvec[1];
- vedge->vnormal[2] = infvec[2];
- }
- } else {
- if (out == (tetgenio *) NULL) {
- //fprintf(outfile, " %4d\n", end2 + shift);//EMI
- int v1 = (end1+shift);
- int v2 = (end2+shift);
- fprintf(outfile,"SL(%g,%g,%g,%g,%g,%g) {%g,%g};\n",
- vlist[v1*3+0], vlist[v1*3+1], vlist[v1*3+2],
- vlist[v2*3+0], vlist[v2*3+1], vlist[v2*3+2],
- radlist[v1], radlist[v2]);
- } else {
- vedge->v2 = end2 + shift;
- vedge->vnormal[0] = 0.0;
- vedge->vnormal[1] = 0.0;
- vedge->vnormal[2] = 0.0;
- }
- }
- // Save the face index in this tet and its neighbor if exists.
- tetfaceindexarray[end1 * 4 + i] = vedgecount;
- if (end2 != -1) {
- tetfaceindexarray[end2 * 4 + worktet.loc] = vedgecount;
- }
- vedgecount++;
- }
- }
- tetloop.tet = tetrahedrontraverse();
- }
-
- if (out == (tetgenio *) NULL) {
- //fprintf(outfile, "# Generated by %s\n", b->commandline);
- fprintf(outfile,"};\n"); //EMI
- fclose(outfile);
- }
-
- //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- // FACES
- //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
- // Output Voronoi faces to .v.face file.
- if (out == (tetgenio *) NULL) {
- strcpy(outfilename, b->outfilename);
- strcat(outfilename, ".v.face");
- }
-
- if (!b->quiet) {
- if (out == (tetgenio *) NULL) {
- printf("Writing %s.\n", outfilename);
- } else {
- printf("Writing Voronoi faces.\n");
- }
- }
-
- if (out == (tetgenio *) NULL) {
- outfile = fopen(outfilename, "w");
- if (outfile == (FILE *) NULL) {
- printf("File I/O Error: Cannot create file %s.\n", outfilename);
- terminatetetgen(1);
- }
- // Number of Voronoi faces.
- fprintf(outfile, "%ld 0\n", edges);
- } else {
- out->numberofvfacets = edges;
- out->vfacetlist = new tetgenio::vorofacet[out->numberofvfacets];
- if (out->vfacetlist == (tetgenio::vorofacet *) NULL) {
- printf("Error: Out of memory.\n");
- terminatetetgen(1);
- }
- }
-
- // Loop the tetrahedronlist once, Output Voronoi facets. The index of each
- // Voronoi facet corresponding to the index of the Delaunay edge. The
- // six edges' indices of each tetrahedron are saved in the list 'tetedge-
- // indexarray', in the entry of i, where i (0-based) is the index of
- // this tetrahedron (= vpointcount).
- tetedgeindexarray = new int[tetrahedrons->items * 6];
- tetrahedrons->traversalinit();
- tetloop.tet = tetrahedrontraverse();
- vfacecount = 0;
- while (tetloop.tet != (tetrahedron *) NULL) {
- // Count the number of Voronoi faces. Look at the six edges of each
- // tetrahedron. Count the edge only if the tetrahedron's pointer is
- // smaller than those of all other tetrahedra that share the edge.
- worktet = tetloop;
- for (i = 0; i < 6; i++) {
- worktet.loc = edge2locver[i][0];
- worktet.ver = edge2locver[i][1];
- // Now count the number of tets surrounding this edge.
- tcount = 1;
- adjustedgering(worktet, CW);
- spintet = worktet;
- hitbdry = 0;
- while (hitbdry < 2) {
- if (fnextself(spintet)) {
- if (apex(spintet) == apex(worktet)) break;
- if (spintet.tet < worktet.tet) break;
- tcount++;
- } else {
- hitbdry++;
- if (hitbdry < 2) {
- esym(worktet, spintet);
- fnextself(spintet); // In the same tet.
- }
- }
- }
- // Count this edge if no adjacent tets are smaller than this tet.
- if (spintet.tet >= worktet.tet) {
- // Get the two endpoints of this edge.
- pt[0] = org(worktet);
- pt[1] = dest(worktet);
- end1 = pointmark(pt[0]) - in->firstnumber;
- end2 = pointmark(pt[1]) - in->firstnumber;
- if (out == (tetgenio *) NULL) {
- fprintf(outfile, "%4d %4d %4d %-2d ", vfacecount + shift,
- end1 + shift, end2 + shift, tcount + (hitbdry > 0));
- } else {
- vfacet = &(out->vfacetlist[vfacecount]);
- vfacet->c1 = end1 + shift;
- vfacet->c2 = end2 + shift;
- vfacet->elist = new int[tcount + (hitbdry > 0) + 1];
- vfacet->elist[0] = tcount + (hitbdry > 0);
- index = 1;
- }
- // If hitbdry > 0, then spintet is a hull face.
- if (hitbdry > 0) {
- // The edge list starts with a ray.
- vpointcount = * (int *) (spintet.tet + elemmarkerindex);
- vedgecount = tetfaceindexarray[vpointcount * 4 + spintet.loc];
- if (out == (tetgenio *) NULL) {
- fprintf(outfile, " %d", vedgecount + shift);
- } else {
- vfacet->elist[index++] = vedgecount + shift;
- }
- // Save this facet number in tet.
- tetedgeindexarray[vpointcount * 6 +
- locver2edge[spintet.loc][spintet.ver]] = vfacecount;
- esymself(spintet);
- fnextself(spintet); // In the same tet.
- }
- // Output internal Voronoi edges.
- for (j = 0; j < tcount; j++) {
- vpointcount = * (int *) (spintet.tet + elemmarkerindex);
- vedgecount = tetfaceindexarray[vpointcount * 4 + spintet.loc];
- if (out == (tetgenio *) NULL) {
- fprintf(outfile, " %d", vedgecount + shift);
- } else {
- vfacet->elist[index++] = vedgecount + shift;
- }
- // Save this facet number in tet.
- tetedgeindexarray[vpointcount * 6 +
- locver2edge[spintet.loc][spintet.ver]] = vfacecount;
- fnextself(spintet);
- }
- if (out == (tetgenio *) NULL) {
- fprintf(outfile, "\n");
- }
- vfacecount++;
- }
- } // if (i = 0; i < 6; i++)
- tetloop.tet = tetrahedrontraverse();
- }
-
- if (out == (tetgenio *) NULL) {
- fprintf(outfile, "# Generated by %s\n", b->commandline);
- fclose(outfile);
- }
-
- //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- // CELLS
- //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
- // Output Voronoi cells to .v.cell file.
- if (out == (tetgenio *) NULL) {
- strcpy(outfilename, b->outfilename);
- strcat(outfilename, ".v.cell");
- }
-
- if (!b->quiet) {
- if (out == (tetgenio *) NULL) {
- printf("Writing %s.\n", outfilename);
- } else {
- printf("Writing Voronoi cells.\n");
- }
- }
-
- if (out == (tetgenio *) NULL) {
- outfile = fopen(outfilename, "w");
- if (outfile == (FILE *) NULL) {
- printf("File I/O Error: Cannot create file %s.\n", outfilename);
- terminatetetgen(1);
- }
- // Number of Voronoi cells.
- fprintf(outfile, "%ld\n", points->items);
- } else {
- out->numberofvcells = points->items;
- out->vcelllist = new int*[out->numberofvcells];
- if (out->vcelllist == (int **) NULL) {
- printf("Error: Out of memory.\n");
- terminatetetgen(1);
- }
- }
-
- // Loop through point list, for each point, output a Voronoi cell.
- tetlist = new list(sizeof(triface), NULL, 256);
- ptlist = new list(sizeof(point *), NULL, 256);
- points->traversalinit();
- ptloop = pointtraverse();
- vpointcount = 0;
- while (ptloop != (point) NULL) {
- decode(point2tet(ptloop), tetloop);
- // assert(!isdead(&tetloop));
- if (!isdead(&tetloop)) {
- // Form the star of p.
- tetlist->append(&tetloop);
- formstarpolyhedron(ptloop, tetlist, ptlist, true);
- tcount = ptlist->len();
- if (out == (tetgenio *) NULL) {
- fprintf(outfile, "%4d %-2d ", vpointcount + shift, tcount);
- } else {
- arraysize = tcount;
- vertarray = out->vcelllist[vpointcount];
- vertarray = new int[arraysize + 1];
- vertarray[0] = arraysize;
- index = 1;
- }
- // List Voronoi facets bounding this cell.
- for (i = 0; i < ptlist->len(); i++) {
- neipt = * (point *)(* ptlist)[i];
- // Find a tet in tetlist having edge (ptloop, neipt) -- Very Slow.
- for (j = 0; j < tetlist->len(); j++) {
- tetloop = * (triface *)(* tetlist)[j];
- for (k = 0; k < 6; k++) {
- tetloop.loc = edge2locver[k][0];
- tetloop.ver = edge2locver[k][1];
- if (org(tetloop) == ptloop) {
- if (dest(tetloop) == neipt) break;
- } else if (org(tetloop) == neipt) {
- if (dest(tetloop) == ptloop) break;
- }
- }
- if (k < 6) break; // Found this edge.
- }
- assert(j < tetlist->len());
- // k is the right edge number.
- end1 = * (int *) (tetloop.tet + elemmarkerindex);
- vfacecount = tetedgeindexarray[end1 * 6 + k];
- if (out == (tetgenio *) NULL) {
- fprintf(outfile, " %d", vfacecount + shift);
- } else {
- vertarray[index++] = vfacecount + shift;
- }
- } // for (i = 0; i < ptlist->len(); i++) {
- if (out == (tetgenio *) NULL) {
- fprintf(outfile, "\n");
- }
- vpointcount++;
- }
- tetlist->clear();
- ptlist->clear();
- ptloop = pointtraverse();
- }
- delete tetlist;
- delete ptlist;
- delete [] tetfaceindexarray;
- delete [] tetedgeindexarray;
-
- if (out == (tetgenio *) NULL) {
- fprintf(outfile, "# Generated by %s\n", b->commandline);
- fclose(outfile);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// outpbcnodes() Output pbc node pairs to a .pbc file or a structure. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::outpbcnodes(tetgenio* out)
-{
- FILE *outfile;
- char pbcfilename[FILENAMESIZE];
- list *ptpairlist;
- tetgenio::pbcgroup *pgi, *pgo;
- pbcdata *pd;
- face faceloop;
- face checkseg, symseg;
- point *ptpair, pa, pb;
- enum locateresult loc;
- REAL sympt[3], d1, d2;
- int *worklist;
- int firstindex, shift;
- int index, idx;
- int i, j, k, l;
-
- if (out == (tetgenio *) NULL) {
- strcpy(pbcfilename, b->outfilename);
- strcat(pbcfilename, ".pbc");
- }
-
- if (!b->quiet) {
- if (out == (tetgenio *) NULL) {
- printf("Writing %s.\n", pbcfilename);
- } else {
- printf("Writing pbc nodes.\n");
- }
- }
-
- // Avoid compilation warnings.
- outfile = (FILE *) NULL;
- pgo = (tetgenio::pbcgroup *) NULL;
- index = 0;
-
- if (out == (tetgenio *) NULL) {
- outfile = fopen(pbcfilename, "w");
- if (outfile == (FILE *) NULL) {
- printf("File I/O Error: Cannot create file %s.\n", pbcfilename);
- terminatetetgen(1);
- }
- // Number of pbc groups.
- fprintf(outfile, "# number of PBCs.\n");
- fprintf(outfile, "%d\n\n", in->numberofpbcgroups);
- } else {
- out->numberofpbcgroups = in->numberofpbcgroups;
- // Allocate memory for 'out->pbcgrouplist'.
- out->pbcgrouplist = new tetgenio::pbcgroup[in->numberofpbcgroups];
- // (Next line was a bug, reported by Murry Nigel).
- if (out->pbcgrouplist == (tetgenio::pbcgroup *) NULL) {
- printf("Error: Out of memory.\n");
- terminatetetgen(1);
- }
- }
-
- ptpairlist = new list(2 * sizeof(point *), NULL, 256);
- worklist = new int[points->items + 1];
- for (i = 0; i < points->items + 1; i++) worklist[i] = 0;
-
- // Determine the first index (0 or 1).
- firstindex = b->zeroindex ? 0 : in->firstnumber;
- shift = 0; // Default no shiftment.
- if ((in->firstnumber == 1) && (firstindex == 0)) {
- shift = 1; // Shift the output indices by 1.
- }
-
- for (i = 0; i < in->numberofpbcgroups; i++) {
- // Group i.
- pgi = &(in->pbcgrouplist[i]);
- if (out == (tetgenio *) NULL) {
- fprintf(outfile, "# PBC %d\n", in->firstnumber + i);
- // Output facet markers.
- fprintf(outfile, "%d %d\n", pgi->fmark1, pgi->fmark2);
- // Output transformation matrix.
- fprintf(outfile, "[\n");
- for (j = 0; j < 4; j++) {
- fprintf(outfile, " %.12g %.12g %.12g %.12g\n", pgi->transmat[j][0],
- pgi->transmat[j][1], pgi->transmat[j][2], pgi->transmat[j][3]);
- }
- fprintf(outfile, "]\n");
- } else {
- pgo = &(out->pbcgrouplist[i]);
- // Copy data from pgi to pgo.
- pgo->fmark1 = pgi->fmark1;
- pgo->fmark2 = pgi->fmark2;
- for (j = 0; j < 4; j++) {
- for (k = 0; k < 4; k++) pgo->transmat[j][k] = pgi->transmat[j][k];
- }
- }
-
- // Find the point pairs of group i.
- subfaces->traversalinit();
- faceloop.sh = shellfacetraverse(subfaces);
- while (faceloop.sh != (shellface *) NULL) {
- if (shellpbcgroup(faceloop) == i) {
- // It is in group i. Operate on it if it has pgi->fmark1.
- idx = shellmark(faceloop) - 1;
- if (in->facetmarkerlist[idx] == pgi->fmark1) {
- // Loop three edges of the subface.
- for (j = 0; j < 3; j++) {
- sspivot(faceloop, checkseg);
- // Loop two vertices of the edge.
- for (k = 0; k < 2; k++) {
- if (k == 0) pa = sorg(faceloop);
- else pa = sdest(faceloop);
- if (worklist[pointmark(pa)] == 0) {
- pb = (point) NULL;
- if (checkseg.sh != dummysh) {
- // pa is on a segment. Find pb.
- // Find the incident pbcgroup of checkseg.
- idx = shellmark(checkseg) - 1;
- for (l = idx2segpglist[idx]; l < idx2segpglist[idx + 1];
- l++) {
- pd = (pbcdata *)(* segpbcgrouptable)[segpglist[l]];
- if (((pd->fmark[0] == pgi->fmark1) &&
- (pd->fmark[1] == pgi->fmark2)) ||
- ((pd->fmark[0] == pgi->fmark2) &&
- (pd->fmark[1] == pgi->fmark1))) break;
- }
-#ifdef SELF_CHECK
- assert(l < idx2segpglist[idx + 1]);
-#endif
- loc = getsegpbcsympoint(pa, &checkseg, sympt, &symseg,
- segpglist[l]);
- if (loc != ONVERTEX) {
- // Not found a match point! It may be caused by the
- // pair of input vertices don't have enough digits.
- // Choose a near vertex.
- d1 = distance(sympt, sorg(symseg));
- d2 = distance(sympt, sdest(symseg));
- if (d1 > d2) sesymself(symseg);
- }
- pb = sorg(symseg);
- } else {
- // Operate on pa if it is inside the facet.
- if (pointtype(pa) == FREESUBVERTEX) {
- pb = point2pbcpt(pa);
- }
- }
- if (pb != (point) NULL) {
- // Add the pair (pa, pb) into list.
- ptpair = (point *) ptpairlist->append(NULL);
- ptpair[0] = pa;
- ptpair[1] = pb;
- // Mark pa (avoid to operate on it later).
- worklist[pointmark(pa)] = 1;
- }
- }
- }
- // Get the next edge.
- senextself(faceloop);
- }
- }
- }
- faceloop.sh = shellfacetraverse(subfaces);
- }
-
- // Output the list of pbc points.
- if (out == (tetgenio *) NULL) {
- fprintf(outfile, "%d\n", ptpairlist->len());
- } else {
- pgo->numberofpointpairs = ptpairlist->len();
- pgo->pointpairlist = new int[pgo->numberofpointpairs * 2];
- index = 0;
- }
- for (j = 0; j < ptpairlist->len(); j++) {
- ptpair = (point *)(* ptpairlist)[j];
- pa = ptpair[0];
- pb = ptpair[1];
- if (out == (tetgenio *) NULL) {
- fprintf(outfile, " %4d %4d\n", pointmark(pa) - shift,
- pointmark(pb) - shift);
- } else {
- pgo->pointpairlist[index++] = pointmark(pa) - shift;
- pgo->pointpairlist[index++] = pointmark(pb) - shift;
- }
- // Unmark pa.
- worklist[pointmark(pa)] = 0;
- }
- if (out == (tetgenio *) NULL) {
- fprintf(outfile, "\n");
- }
- ptpairlist->clear();
- }
-
- delete [] worklist;
- delete ptpairlist;
-
- if (out == (tetgenio *) NULL) {
- fprintf(outfile, "# Generated by %s\n", b->commandline);
- fclose(outfile);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// outsmesh() Write surface mesh to a .smesh file, which can be read and //
-// tetrahedralized by TetGen. //
-// //
-// You can specify a filename (without suffix) in 'smfilename'. If you don't //
-// supply a filename (let smfilename be NULL), the default name stored in //
-// 'tetgenbehavior' will be used. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::outsmesh(char* smfilename)
-{
- FILE *outfile;
- char nodfilename[FILENAMESIZE];
- char smefilename[FILENAMESIZE];
- face faceloop;
- point p1, p2, p3;
- int firstindex, shift;
- int bmark;
- int faceid, marker;
- int i;
-
- if (smfilename != (char *) NULL && smfilename[0] != '\0') {
- strcpy(smefilename, smfilename);
- } else if (b->outfilename[0] != '\0') {
- strcpy(smefilename, b->outfilename);
- } else {
- strcpy(smefilename, "unnamed");
- }
- strcpy(nodfilename, smefilename);
- strcat(smefilename, ".smesh");
- strcat(nodfilename, ".node");
-
- if (!b->quiet) {
- printf("Writing %s.\n", smefilename);
- }
- outfile = fopen(smefilename, "w");
- if (outfile == (FILE *) NULL) {
- printf("File I/O Error: Cannot create file %s.\n", smefilename);
- return;
- }
-
- // Determine the first index (0 or 1).
- firstindex = b->zeroindex ? 0 : in->firstnumber;
- shift = 0; // Default no shiftment.
- if ((in->firstnumber == 1) && (firstindex == 0)) {
- shift = 1; // Shift the output indices by 1.
- }
-
- fprintf(outfile, "# %s. TetGen's input file.\n", smefilename);
- fprintf(outfile, "\n# part 1: node list.\n");
- fprintf(outfile, "0 3 0 0 # nodes are found in %s.\n", nodfilename);
-
- marker = 0; // avoid compile warning.
- bmark = !b->nobound && in->facetmarkerlist;
-
- fprintf(outfile, "\n# part 2: facet list.\n");
- // Number of facets, boundary marker.
- fprintf(outfile, "%ld %d\n", subfaces->items, bmark);
-
- subfaces->traversalinit();
- faceloop.sh = shellfacetraverse(subfaces);
- while (faceloop.sh != (shellface *) NULL) {
- p1 = sorg(faceloop);
- p2 = sdest(faceloop);
- p3 = sapex(faceloop);
- if (bmark) {
- faceid = shellmark(faceloop) - 1;
- if (faceid >= 0) {
- marker = in->facetmarkerlist[faceid];
- } else {
- marker = 0; // This subface must be added manually later.
- }
- }
- fprintf(outfile, "3 %4d %4d %4d", pointmark(p1) - shift,
- pointmark(p2) - shift, pointmark(p3) - shift);
- if (bmark) {
- fprintf(outfile, " %d", marker);
- }
- fprintf(outfile, "\n");
- faceloop.sh = shellfacetraverse(subfaces);
- }
-
- // Copy input holelist.
- fprintf(outfile, "\n# part 3: hole list.\n");
- fprintf(outfile, "%d\n", in->numberofholes);
- for (i = 0; i < in->numberofholes; i++) {
- fprintf(outfile, "%d %g %g %g\n", i + in->firstnumber,
- in->holelist[i * 3], in->holelist[i * 3 + 1],
- in->holelist[i * 3 + 2]);
- }
-
- // Copy input regionlist.
- fprintf(outfile, "\n# part 4: region list.\n");
- fprintf(outfile, "%d\n", in->numberofregions);
- for (i = 0; i < in->numberofregions; i++) {
- fprintf(outfile, "%d %g %g %g %d %g\n", i + in->firstnumber,
- in->regionlist[i * 5], in->regionlist[i * 5 + 1],
- in->regionlist[i * 5 + 2], (int) in->regionlist[i * 5 + 3],
- in->regionlist[i * 5 + 4]);
- }
-
- fprintf(outfile, "# Generated by %s\n", b->commandline);
- fclose(outfile);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// outmesh2medit() Write mesh to a .mesh file, which can be read and //
-// rendered by Medit (a free mesh viewer from INRIA). //
-// //
-// You can specify a filename (without suffix) in 'mfilename'. If you don't //
-// supply a filename (let mfilename be NULL), the default name stored in //
-// 'tetgenbehavior' will be used. The output file will have the suffix .mesh.//
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::outmesh2medit(char* mfilename)
-{
- FILE *outfile;
- char mefilename[FILENAMESIZE];
- tetrahedron* tetptr;
- triface tface, tsymface;
- face segloop, checkmark;
- point ptloop, p1, p2, p3, p4;
- long faces;
- int pointnumber;
- int i;
-
- if (mfilename != (char *) NULL && mfilename[0] != '\0') {
- strcpy(mefilename, mfilename);
- } else if (b->outfilename[0] != '\0') {
- strcpy(mefilename, b->outfilename);
- } else {
- strcpy(mefilename, "unnamed");
- }
- strcat(mefilename, ".mesh");
-
- if (!b->quiet) {
- printf("Writing %s.\n", mefilename);
- }
- outfile = fopen(mefilename, "w");
- if (outfile == (FILE *) NULL) {
- printf("File I/O Error: Cannot create file %s.\n", mefilename);
- return;
- }
-
- fprintf(outfile, "MeshVersionFormatted 1\n");
- fprintf(outfile, "\n");
- fprintf(outfile, "Dimension\n");
- fprintf(outfile, "3\n");
- fprintf(outfile, "\n");
-
- fprintf(outfile, "\n# Set of mesh vertices\n");
- fprintf(outfile, "Vertices\n");
- fprintf(outfile, "%ld\n", points->items);
-
- points->traversalinit();
- ptloop = pointtraverse();
- pointnumber = 1; // Medit need start number form 1.
- while (ptloop != (point) NULL) {
- // Point coordinates.
- fprintf(outfile, "%.17g %.17g %.17g", ptloop[0], ptloop[1], ptloop[2]);
- if (in->numberofpointattributes > 0) {
- // Write an attribute, ignore others if more than one.
- fprintf(outfile, " %.17g\n", ptloop[3]);
- } else {
- fprintf(outfile, " 0\n");
- }
- setpointmark(ptloop, pointnumber);
- ptloop = pointtraverse();
- pointnumber++;
- }
-
- // Compute the number of edges.
- faces = (4l * tetrahedrons->items + hullsize) / 2l;
-
- fprintf(outfile, "\n# Set of Triangles\n");
- fprintf(outfile, "Triangles\n");
- fprintf(outfile, "%ld\n", faces);
-
- tetrahedrons->traversalinit();
- tface.tet = tetrahedrontraverse();
- // To loop over the set of faces, loop over all tetrahedra, and look at
- // the four faces of each tetrahedron. If there isn't another tetrahedron
- // adjacent to the face, operate on the face. If there is another adj-
- // acent tetrahedron, operate on the face only if the current tetrahedron
- // has a smaller pointer than its neighbor. This way, each face is
- // considered only once.
- while (tface.tet != (tetrahedron *) NULL) {
- for (tface.loc = 0; tface.loc < 4; tface.loc ++) {
- sym(tface, tsymface);
- if (tface.tet < tsymface.tet || tsymface.tet == dummytet) {
- p1 = org (tface);
- p2 = dest(tface);
- p3 = apex(tface);
- fprintf(outfile, "%5d %5d %5d",
- pointmark(p1), pointmark(p2), pointmark(p3));
- fprintf(outfile, " 0\n");
- }
- }
- tface.tet = tetrahedrontraverse();
- }
-
- fprintf(outfile, "\n# Set of Tetrahedra\n");
- fprintf(outfile, "Tetrahedra\n");
- fprintf(outfile, "%ld\n", tetrahedrons->items);
-
- tetrahedrons->traversalinit();
- tetptr = tetrahedrontraverse();
- while (tetptr != (tetrahedron *) NULL) {
- p1 = (point) tetptr[4];
- p2 = (point) tetptr[5];
- p3 = (point) tetptr[6];
- p4 = (point) tetptr[7];
- fprintf(outfile, "%5d %5d %5d %5d",
- pointmark(p1), pointmark(p2), pointmark(p3), pointmark(p4));
- if (in->numberoftetrahedronattributes > 0) {
- fprintf(outfile, " %.17g", elemattribute(tetptr, 0));
- } else {
- fprintf(outfile, " 0");
- }
- fprintf(outfile, "\n");
- tetptr = tetrahedrontraverse();
- }
-
- fprintf(outfile, "\nCorners\n");
- fprintf(outfile, "%d\n", in->numberofpoints);
-
- for (i = 0; i < in->numberofpoints; i++) {
- fprintf(outfile, "%4d\n", i + 1);
- }
-
- if (b->useshelles) {
- fprintf(outfile, "\nEdges\n");
- fprintf(outfile, "%ld\n", subsegs->items);
-
- subsegs->traversalinit();
- segloop.sh = shellfacetraverse(subsegs);
- while (segloop.sh != (shellface *) NULL) {
- p1 = sorg(segloop);
- p2 = sdest(segloop);
- fprintf(outfile, "%5d %5d", pointmark(p1), pointmark(p2));
- fprintf(outfile, " 0\n");
- segloop.sh = shellfacetraverse(subsegs);
- }
- }
-
- fprintf(outfile, "\nEnd\n");
- fclose(outfile);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// outmesh2gid() Write mesh to a .ele.msh file and a .face.msh file, //
-// which can be imported and rendered by Gid. //
-// //
-// You can specify a filename (without suffix) in 'gfilename'. If you don't //
-// supply a filename (let gfilename be NULL), the default name stored in //
-// 'tetgenbehavior' will be used. The suffixes (.ele.msh and .face.msh) will //
-// be automatically added. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::outmesh2gid(char* gfilename)
-{
- FILE *outfile;
- char gidfilename[FILENAMESIZE];
- tetrahedron* tetptr;
- triface tface, tsymface;
- face sface;
- point ptloop, p1, p2, p3, p4;
- int pointnumber;
- int elementnumber;
-
- if (gfilename != (char *) NULL && gfilename[0] != '\0') {
- strcpy(gidfilename, gfilename);
- } else if (b->outfilename[0] != '\0') {
- strcpy(gidfilename, b->outfilename);
- } else {
- strcpy(gidfilename, "unnamed");
- }
- strcat(gidfilename, ".ele.msh");
-
- if (!b->quiet) {
- printf("Writing %s.\n", gidfilename);
- }
- outfile = fopen(gidfilename, "w");
- if (outfile == (FILE *) NULL) {
- printf("File I/O Error: Cannot create file %s.\n", gidfilename);
- return;
- }
-
- fprintf(outfile, "mesh dimension = 3 elemtype tetrahedron nnode = 4\n");
- fprintf(outfile, "coordinates\n");
-
- points->traversalinit();
- ptloop = pointtraverse();
- pointnumber = 1; // Gid need start number form 1.
- while (ptloop != (point) NULL) {
- // Point coordinates.
- fprintf(outfile, "%4d %.17g %.17g %.17g", pointnumber,
- ptloop[0], ptloop[1], ptloop[2]);
- if (in->numberofpointattributes > 0) {
- // Write an attribute, ignore others if more than one.
- fprintf(outfile, " %.17g", ptloop[3]);
- }
- fprintf(outfile, "\n");
- setpointmark(ptloop, pointnumber);
- ptloop = pointtraverse();
- pointnumber++;
- }
-
- fprintf(outfile, "end coordinates\n");
- fprintf(outfile, "elements\n");
-
- tetrahedrons->traversalinit();
- tetptr = tetrahedrontraverse();
- elementnumber = 1;
- while (tetptr != (tetrahedron *) NULL) {
- p1 = (point) tetptr[4];
- p2 = (point) tetptr[5];
- p3 = (point) tetptr[6];
- p4 = (point) tetptr[7];
- fprintf(outfile, "%5d %5d %5d %5d %5d", elementnumber,
- pointmark(p1), pointmark(p2), pointmark(p3), pointmark(p4));
- if (in->numberoftetrahedronattributes > 0) {
- fprintf(outfile, " %.17g", elemattribute(tetptr, 0));
- }
- fprintf(outfile, "\n");
- tetptr = tetrahedrontraverse();
- elementnumber++;
- }
-
- fprintf(outfile, "end elements\n");
- fclose(outfile);
-
- if (gfilename != (char *) NULL && gfilename[0] != '\0') {
- strcpy(gidfilename, gfilename);
- } else if (b->outfilename[0] != '\0') {
- strcpy(gidfilename, b->outfilename);
- } else {
- strcpy(gidfilename, "unnamed");
- }
- strcat(gidfilename, ".face.msh");
-
- if (!b->quiet) {
- printf("Writing %s.\n", gidfilename);
- }
- outfile = fopen(gidfilename, "w");
- if (outfile == (FILE *) NULL) {
- printf("File I/O Error: Cannot create file %s.\n", gidfilename);
- return;
- }
-
- fprintf(outfile, "mesh dimension = 3 elemtype triangle nnode = 3\n");
- fprintf(outfile, "coordinates\n");
-
- points->traversalinit();
- ptloop = pointtraverse();
- pointnumber = 1; // Gid need start number form 1.
- while (ptloop != (point) NULL) {
- // Point coordinates.
- fprintf(outfile, "%4d %.17g %.17g %.17g", pointnumber,
- ptloop[0], ptloop[1], ptloop[2]);
- if (in->numberofpointattributes > 0) {
- // Write an attribute, ignore others if more than one.
- fprintf(outfile, " %.17g", ptloop[3]);
- }
- fprintf(outfile, "\n");
- setpointmark(ptloop, pointnumber);
- ptloop = pointtraverse();
- pointnumber++;
- }
-
- fprintf(outfile, "end coordinates\n");
- fprintf(outfile, "elements\n");
-
- tetrahedrons->traversalinit();
- tface.tet = tetrahedrontraverse();
- elementnumber = 1;
- while (tface.tet != (tetrahedron *) NULL) {
- for (tface.loc = 0; tface.loc < 4; tface.loc ++) {
- sym(tface, tsymface);
- if ((tface.tet < tsymface.tet) || (tsymface.tet == dummytet)) {
- p1 = org(tface);
- p2 = dest(tface);
- p3 = apex(tface);
- if (tsymface.tet == dummytet) {
- // It's a hull face, output it.
- fprintf(outfile, "%5d %d %d %d\n", elementnumber,
- pointmark(p1), pointmark(p2), pointmark(p3));
- elementnumber++;
- } else if (b->useshelles) {
- // Only output it if it's a subface.
- tspivot(tface, sface);
- if (sface.sh != dummysh) {
- fprintf(outfile, "%5d %d %d %d\n", elementnumber,
- pointmark(p1), pointmark(p2), pointmark(p3));
- elementnumber++;
- }
- }
- }
- }
- tface.tet = tetrahedrontraverse();
- }
-
- fprintf(outfile, "end elements\n");
- fclose(outfile);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// outmesh2off() Write the mesh to an .off file. //
-// //
-// .off, the Object File Format, is one of the popular file formats from the //
-// Geometry Center's Geomview package (http://www.geomview.org). //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::outmesh2off(char* ofilename)
-{
- FILE *outfile;
- char offfilename[FILENAMESIZE];
- triface tface, tsymface;
- point ptloop, p1, p2, p3;
- long faces;
- int shift;
-
- if (ofilename != (char *) NULL && ofilename[0] != '\0') {
- strcpy(offfilename, ofilename);
- } else if (b->outfilename[0] != '\0') {
- strcpy(offfilename, b->outfilename);
- } else {
- strcpy(offfilename, "unnamed");
- }
- strcat(offfilename, ".off");
-
- if (!b->quiet) {
- printf("Writing %s.\n", offfilename);
- }
- outfile = fopen(offfilename, "w");
- if (outfile == (FILE *) NULL) {
- printf("File I/O Error: Cannot create file %s.\n", offfilename);
- return;
- }
-
- // Calculate the number of triangular faces in the tetrahedral mesh.
- faces = (4l * tetrahedrons->items + hullsize) / 2l;
-
- // Number of points, faces, and edges(not used, here show hullsize).
- fprintf(outfile, "OFF\n%ld %ld %ld\n", points->items, faces, hullsize);
-
- // Write the points.
- points->traversalinit();
- ptloop = pointtraverse();
- while (ptloop != (point) NULL) {
- fprintf(outfile, " %.17g %.17g %.17g\n",ptloop[0], ptloop[1], ptloop[2]);
- ptloop = pointtraverse();
- }
-
- // OFF always use zero as the first index.
- shift = in->firstnumber == 1 ? 1 : 0;
-
- tetrahedrons->traversalinit();
- tface.tet = tetrahedrontraverse();
- // To loop over the set of faces, loop over all tetrahedra, and look at
- // the four faces of each tetrahedron. If there isn't another tetrahedron
- // adjacent to the face, operate on the face. If there is another adj-
- // acent tetrahedron, operate on the face only if the current tetrahedron
- // has a smaller pointer than its neighbor. This way, each face is
- // considered only once.
- while (tface.tet != (tetrahedron *) NULL) {
- for (tface.loc = 0; tface.loc < 4; tface.loc ++) {
- sym(tface, tsymface);
- if ((tface.tet < tsymface.tet) || (tsymface.tet == dummytet)) {
- p1 = org(tface);
- p2 = dest(tface);
- p3 = apex(tface);
- // Face number, indices of three vertexs.
- fprintf(outfile, "3 %4d %4d %4d\n", pointmark(p1) - shift,
- pointmark(p2) - shift, pointmark(p3) - shift);
- }
- }
- tface.tet = tetrahedrontraverse();
- }
-
- fprintf(outfile, "# Generated by %s\n", b->commandline);
- fclose(outfile);
-}
-
-//
-// End of I/O rouitnes
-//
-
-//
-// Begin of user interaction routines
-//
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// internalerror() Ask the user to send me the defective product. Exit. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::internalerror()
-{
- printf(" Please report this bug to sihang@mail.berlios.de. Include the\n");
- printf(" message above, your input data set, and the exact command\n");
- printf(" line you used to run this program, thank you.\n");
- terminatetetgen(2);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// checkmesh() Test the mesh for topological consistency. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::checkmesh()
-{
- triface tetraloop;
- triface oppotet, oppooppotet;
- point tetorg, tetdest, tetapex, tetoppo;
- REAL oritest;
- int horrors;
-
- if (!b->quiet) {
- printf(" Checking consistency of mesh...\n");
- }
-
- horrors = 0;
- // Run through the list of tetrahedra, checking each one.
- tetrahedrons->traversalinit();
- tetraloop.tet = tetrahedrontraverse();
- while (tetraloop.tet != (tetrahedron *) NULL) {
- // Check all four faces of the tetrahedron.
- for (tetraloop.loc = 0; tetraloop.loc < 4; tetraloop.loc++) {
- tetorg = org(tetraloop);
- tetdest = dest(tetraloop);
- tetapex = apex(tetraloop);
- tetoppo = oppo(tetraloop);
- if (tetraloop.loc == 0) { // Only test for inversion once.
- oritest = orient3d(tetorg, tetdest, tetapex, tetoppo);
- if (oritest >= 0.0) {
- printf(" !! !! %s ", oritest > 0.0 ? "Inverted" : "Degenerated");
- printtet(&tetraloop);
- printf(" orient3d = %.17g.\n", oritest);
- horrors++;
- }
- }
- // Find the neighboring tetrahedron on this face.
- sym(tetraloop, oppotet);
- if (oppotet.tet != dummytet) {
- // Check that the tetrahedron's neighbor knows it's a neighbor.
- sym(oppotet, oppooppotet);
- if ((tetraloop.tet != oppooppotet.tet)
- || (tetraloop.loc != oppooppotet.loc)) {
- printf(" !! !! Asymmetric tetra-tetra bond:\n");
- if (tetraloop.tet == oppooppotet.tet) {
- printf(" (Right tetrahedron, wrong orientation)\n");
- }
- printf(" First ");
- printtet(&tetraloop);
- printf(" Second (nonreciprocating) ");
- printtet(&oppotet);
- horrors++;
- }
- }
- }
- tetraloop.tet = tetrahedrontraverse();
- }
- if (horrors == 0) {
- if (!b->quiet) {
- printf(" In my studied opinion, the mesh appears to be consistent.\n");
- }
- } else if (horrors == 1) {
- printf(" !! !! !! !! Precisely one festering wound discovered.\n");
- } else {
- printf(" !! !! !! !! %d abominations witnessed.\n", horrors);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// checkshells() Test the boundary mesh for topological consistency. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::checkshells()
-{
- triface oppotet, oppooppotet, testtet;
- face shloop, segloop, spin;
- face testsh, testseg, testshsh;
- point shorg, shdest, segorg, segdest;
- REAL checksign;
- bool same;
- int horrors;
- int i;
-
- if (!b->quiet) {
- printf(" Checking consistency of the mesh boundary...\n");
- }
- horrors = 0;
-
- // Run through the list of subfaces, checking each one.
- subfaces->traversalinit();
- shloop.sh = shellfacetraverse(subfaces);
- while (shloop.sh != (shellface *) NULL) {
- // Check two connected tetrahedra if they exist.
- shloop.shver = 0;
- stpivot(shloop, oppotet);
- if (oppotet.tet != dummytet) {
- tspivot(oppotet, testsh);
- if (testsh.sh != shloop.sh) {
- printf(" !! !! Wrong tetra-subface connection.\n");
- printf(" Tetra: ");
- printtet(&oppotet);
- printf(" Subface: ");
- printsh(&shloop);
- horrors++;
- }
- if (oppo(oppotet) != (point) NULL) {
- adjustedgering(oppotet, CCW);
- checksign = orient3d(sorg(shloop), sdest(shloop), sapex(shloop),
- oppo(oppotet));
- if (checksign >= 0.0) {
- printf(" !! !! Wrong subface orientation.\n");
- printf(" Subface: ");
- printsh(&shloop);
- horrors++;
- }
- }
- }
- sesymself(shloop);
- stpivot(shloop, oppooppotet);
- if (oppooppotet.tet != dummytet) {
- tspivot(oppooppotet, testsh);
- if (testsh.sh != shloop.sh) {
- printf(" !! !! Wrong tetra-subface connection.\n");
- printf(" Tetra: ");
- printtet(&oppooppotet);
- printf(" Subface: ");
- printsh(&shloop);
- horrors++;
- }
- if (oppotet.tet != dummytet) {
- sym(oppotet, testtet);
- if (testtet.tet != oppooppotet.tet) {
- printf(" !! !! Wrong tetra-subface-tetra connection.\n");
- printf(" Tetra 1: ");
- printtet(&oppotet);
- printf(" Subface: ");
- printsh(&shloop);
- printf(" Tetra 2: ");
- printtet(&oppooppotet);
- horrors++;
- }
- }
- if (oppo(oppooppotet) != (point) NULL) {
- adjustedgering(oppooppotet, CCW);
- checksign = orient3d(sorg(shloop), sdest(shloop), sapex(shloop),
- oppo(oppooppotet));
- if (checksign >= 0.0) {
- printf(" !! !! Wrong subface orientation.\n");
- printf(" Subface: ");
- printsh(&shloop);
- horrors++;
- }
- }
- }
- // Check connection between subfaces.
- shloop.shver = 0;
- for (i = 0; i < 3; i++) {
- shorg = sorg(shloop);
- shdest = sdest(shloop);
- sspivot(shloop, testseg);
- if (testseg.sh != dummysh) {
- segorg = sorg(testseg);
- segdest = sdest(testseg);
- same = ((shorg == segorg) && (shdest == segdest))
- || ((shorg == segdest) && (shdest == segorg));
- if (!same) {
- printf(" !! !! Wrong subface-subsegment connection.\n");
- printf(" Subface: ");
- printsh(&shloop);
- printf(" Subsegment: ");
- printsh(&testseg);
- horrors++;
- }
- }
- spivot(shloop, testsh);
- if (testsh.sh != dummysh) {
- segorg = sorg(testsh);
- segdest = sdest(testsh);
- same = ((shorg == segorg) && (shdest == segdest))
- || ((shorg == segdest) && (shdest == segorg));
- if (!same) {
- printf(" !! !! Wrong subface-subface connection.\n");
- printf(" Subface 1: ");
- printsh(&shloop);
- printf(" Subface 2: ");
- printsh(&testsh);
- horrors++;
- }
- spivot(testsh, testshsh);
- shorg = sorg(testshsh);
- shdest = sdest(testshsh);
- same = ((shorg == segorg) && (shdest == segdest))
- || ((shorg == segdest) && (shdest == segorg));
- if (!same) {
- printf(" !! !! Wrong subface-subface connection.\n");
- printf(" Subface 1: ");
- printsh(&testsh);
- printf(" Subface 2: ");
- printsh(&testshsh);
- horrors++;
- }
- if (testseg.sh == dummysh) {
- if (testshsh.sh != shloop.sh) {
- printf(" !! !! Wrong subface-subface connection.\n");
- printf(" Subface 1: ");
- printsh(&shloop);
- printf(" Subface 2: ");
- printsh(&testsh);
- horrors++;
- }
- }
- }
- senextself(shloop);
- }
- shloop.sh = shellfacetraverse(subfaces);
- }
-
- // Run through the list of subsegs, checking each one.
- subsegs->traversalinit();
- segloop.sh = shellfacetraverse(subsegs);
- while (segloop.sh != (shellface *) NULL) {
- segorg = sorg(segloop);
- segdest = sdest(segloop);
- spivot(segloop, testsh);
- if (testsh.sh == dummysh) {
- printf(" !! !! Wrong subsegment-subface connection.\n");
- printf(" Subsegment: ");
- printsh(&segloop);
- horrors++;
- segloop.sh = shellfacetraverse(subsegs);
- continue;
- }
- shorg = sorg(testsh);
- shdest = sdest(testsh);
- same = ((shorg == segorg) && (shdest == segdest))
- || ((shorg == segdest) && (shdest == segorg));
- if (!same) {
- printf(" !! !! Wrong subsegment-subface connection.\n");
- printf(" Subsegment : ");
- printsh(&segloop);
- printf(" Subface : ");
- printsh(&testsh);
- horrors++;
- segloop.sh = shellfacetraverse(subsegs);
- continue;
- }
- // Check the connection of face loop around this subsegment.
- spin = testsh;
- i = 0;
- do {
- spivotself(spin);
- shorg = sorg(spin);
- shdest = sdest(spin);
- same = ((shorg == segorg) && (shdest == segdest))
- || ((shorg == segdest) && (shdest == segorg));
- if (!same) {
- printf(" !! !! Wrong subsegment-subface connection.\n");
- printf(" Subsegment : ");
- printsh(&segloop);
- printf(" Subface : ");
- printsh(&testsh);
- horrors++;
- break;
- }
- i++;
- } while (spin.sh != testsh.sh && i < 1000);
- if (i >= 1000) {
- printf(" !! !! Wrong subsegment-subface connection.\n");
- printf(" Subsegment : ");
- printsh(&segloop);
- horrors++;
- }
- segloop.sh = shellfacetraverse(subsegs);
- }
- if (horrors == 0) {
- if (!b->quiet) {
- printf(" Mesh boundaries connected correctly.\n");
- }
- } else {
- printf(" !! !! !! !! %d boundary connection viewed with horror.\n",
- horrors);
- return;
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// checkdelaunay() Ensure that the mesh is constrained Delaunay. //
-// //
-// If 'flipqueue' is not NULL, non-locally Delaunay faces are saved in it. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::checkdelaunay(REAL eps, queue* flipqueue)
-{
- triface tetraloop;
- triface oppotet;
- face opposhelle;
- point tetorg, tetdest, tetapex, tetoppo;
- point oppooppo;
- enum fliptype fc;
- REAL sign;
- int shouldbedelaunay;
- int horrors;
-
- if (!b->quiet) {
- printf(" Checking Delaunay property of the mesh...\n");
- }
- horrors = 0;
- // Run through the list of triangles, checking each one.
- tetrahedrons->traversalinit();
- tetraloop.tet = tetrahedrontraverse();
- while (tetraloop.tet != (tetrahedron *) NULL) {
- // Check all four faces of the tetrahedron.
- for (tetraloop.loc = 0; tetraloop.loc < 4; tetraloop.loc++) {
- tetorg = org(tetraloop);
- tetdest = dest(tetraloop);
- tetapex = apex(tetraloop);
- tetoppo = oppo(tetraloop);
- sym(tetraloop, oppotet);
- oppooppo = oppo(oppotet);
- // Only do testif there is an adjoining tetrahedron whose pointer is
- // larger (to ensure that each pair isn't tested twice).
- shouldbedelaunay = (oppotet.tet != dummytet)
- && (tetoppo != (point) NULL)
- && (oppooppo != (point) NULL)
- && (tetraloop.tet < oppotet.tet);
- if (checksubfaces && shouldbedelaunay) {
- // If a shell face separates the tetrahedra, then the face is
- // constrained, so no local Delaunay test should be done.
- tspivot(tetraloop, opposhelle);
- if (opposhelle.sh != dummysh){
- shouldbedelaunay = 0;
- }
- }
- if (shouldbedelaunay) {
- sign = insphere(tetdest, tetorg, tetapex, tetoppo, oppooppo);
- if ((sign > 0.0) && (eps > 0.0)) {
- if (iscospheric(tetdest, tetorg, tetapex, tetoppo, oppooppo, sign,
- eps)) sign = 0.0;
- }
- if (sign > 0.0) {
- if (flipqueue) {
- enqueueflipface(tetraloop, flipqueue);
- } else {
- printf(" !! Non-locally Delaunay face (%d, %d, %d) ",
- pointmark(tetorg), pointmark(tetdest), pointmark(tetapex));
- fc = categorizeface(tetraloop);
- switch (fc) {
- case T23: printf("\"T23\""); break;
- case T32: printf("\"T32\""); break;
- case T22: printf("\"T22\""); break;
- case T44: printf("\"T44\""); break;
- case N32: printf("\"N32\""); break;
- case N40: printf("\"N40\""); break;
- case FORBIDDENFACE:printf("\"FORBIDDENFACE\""); break;
- case FORBIDDENEDGE:printf("\"FORBIDDENEDGE\""); break;
- }
- printf("\n");
- }
- horrors++;
- }
- }
- }
- tetraloop.tet = tetrahedrontraverse();
- }
- if (flipqueue == (queue *) NULL) {
- if (horrors == 0) {
- if (!b->quiet) {
- printf(" The mesh is %s.\n",
- checksubfaces ? "constrained Delaunay" : "Delaunay");
- }
- } else {
- printf(" !! !! !! !! %d obscenities viewed with horror.\n", horrors);
- }
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// checkconforming() Ensure that the mesh is conforming Delaunay. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::checkconforming()
-{
- face segloop, shloop;
- int encsubsegs, encsubfaces;
-
- if (!b->quiet) {
- printf(" Checking conforming Delaunay property of mesh...\n");
- }
- encsubsegs = encsubfaces = 0;
- // Run through the list of subsegments, check each one.
- subsegs->traversalinit();
- segloop.sh = shellfacetraverse(subsegs);
- while (segloop.sh != (shellface *) NULL) {
- if (checkseg4encroach(&segloop, NULL, NULL, false)) {
- printf(" !! !! Non-conforming subsegment: (%d, %d)\n",
- pointmark(sorg(segloop)), pointmark(sdest(segloop)));
- encsubsegs++;
- }
- segloop.sh = shellfacetraverse(subsegs);
- }
- // Run through the list of subfaces, check each one.
- subfaces->traversalinit();
- shloop.sh = shellfacetraverse(subfaces);
- while (shloop.sh != (shellface *) NULL) {
- if (checksub4encroach(&shloop, NULL, false)) {
- printf(" !! !! Non-conforming subface: (%d, %d, %d)\n",
- pointmark(sorg(shloop)), pointmark(sdest(shloop)),
- pointmark(sapex(shloop)));
- encsubfaces++;
- }
- shloop.sh = shellfacetraverse(subfaces);
- }
- if (encsubsegs == 0 && encsubfaces == 0) {
- if (!b->quiet) {
- printf(" The mesh is conforming Delaunay.\n");
- }
- } else {
- if (encsubsegs > 0) {
- printf(" !! !! %d subsegments are non-conforming.\n", encsubsegs);
- }
- if (encsubfaces > 0) {
- printf(" !! !! %d subfaces are non-conforming.\n", encsubfaces);
- }
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// algorithmicstatistics() Print statistics about the mesh algorithms. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-#ifdef SELF_CHECK
-
-void tetgenmesh::algorithmicstatistics()
-{
- /*
- printf("Algorithmic statistics:\n\n");
- printf(" Point location millisecond: %g\n", (REAL) tloctime * 1e+3);
- printf(" Flip millisecond: %g\n", (REAL) tfliptime * 1e+3);
- if (b->plc || b->refine) {
- printf(" Number of facet above points calculations: %ld\n", abovecount);
- }
- if (b->plc) {
- printf(" Segment split rules: R1 %ld, R2 %ld, R3 %ld\n", r1count, r2count,
- r3count);
- }
- if (b->quality) {
- printf(" Bowyer-Watson insertions: seg %ld, sub %ld, vol %ld.\n",
- bowatsegcount, bowatsubcount, bowatvolcount);
- printf(" Bowyer-Watson corrections: seg %ld, sub %ld, vol %ld\n",
- updsegcount, updsubcount, updvolcount);
- printf(" Bowyer-Watson failures: seg %ld, sub %ld, vol %ld\n",
- failsegcount, failsubcount, failvolcount);
- printf(" Number of repair flips: %ld.\n", repairflipcount);
- printf(" Number of circumcenters outside Bowat-cav.: %ld.\n",
- outbowatcircumcount);
- if (b->conformdel) {
- printf(" Segment split rules: R2 %ld, R3 %ld\n", r2count, r3count);
- printf(" Number of CDT enforcement points: %ld.\n", cdtenforcesegpts);
- }
- printf(" Number of Rejections: seg %ld, sub %ld, tet %ld.\n", rejsegpts,
- rejsubpts, rejtetpts);
- if (b->optlevel) {
- printf(
- " Optimization flips: f32 %ld, f44 %ld, f56 %ld, f68 %ld, fnm %ld.\n",
- optcount[3], optcount[4], optcount[5], optcount[6], optcount[9]);
- printf(" Optimization segment deletions: %ld.\n", optcount[1]);
- }
- }
- printf("\n");
- */
-}
-
-#endif // #ifdef SELF_CHECK
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// qualitystatistics() Print statistics about the quality of the mesh. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::qualitystatistics()
-{
- triface tetloop, neightet;
- point p[4];
- char sbuf[128];
- REAL radiusratiotable[12];
- REAL aspectratiotable[12];
- REAL A[4][4], rhs[4], D;
- REAL V[6][3], N[4][3], H[4]; // edge-vectors, face-normals, face-heights.
- REAL edgelength[6], alldihed[6], faceangle[3];
- REAL shortest, longest;
- REAL smallestvolume, biggestvolume;
- REAL smallestdiangle, biggestdiangle;
- REAL smallestfaangle, biggestfaangle;
- REAL tetvol, minaltitude;
- REAL cirradius, minheightinv; // insradius;
- REAL shortlen, longlen;
- REAL tetaspect, tetradius;
- REAL smalldiangle, bigdiangle;
- REAL smallfaangle, bigfaangle;
- int radiustable[12];
- int aspecttable[16];
- int dihedangletable[18];
- int faceangletable[18];
- int indx[4];
- int radiusindex;
- int aspectindex;
- int tendegree;
- int i, j;
-
- printf("Mesh quality statistics:\n\n");
-
- // Avoid compile warnings.
- shortlen = longlen = 0.0;
- smalldiangle = bigdiangle = 0.0;
-
- radiusratiotable[0] = 0.707; radiusratiotable[1] = 1.0;
- radiusratiotable[2] = 1.1; radiusratiotable[3] = 1.2;
- radiusratiotable[4] = 1.4; radiusratiotable[5] = 1.6;
- radiusratiotable[6] = 1.8; radiusratiotable[7] = 2.0;
- radiusratiotable[8] = 2.5; radiusratiotable[9] = 3.0;
- radiusratiotable[10] = 10.0; radiusratiotable[11] = 0.0;
-
- aspectratiotable[0] = 1.5; aspectratiotable[1] = 2.0;
- aspectratiotable[2] = 2.5; aspectratiotable[3] = 3.0;
- aspectratiotable[4] = 4.0; aspectratiotable[5] = 6.0;
- aspectratiotable[6] = 10.0; aspectratiotable[7] = 15.0;
- aspectratiotable[8] = 25.0; aspectratiotable[9] = 50.0;
- aspectratiotable[10] = 100.0; aspectratiotable[11] = 0.0;
-
- for (i = 0; i < 12; i++) radiustable[i] = 0;
- for (i = 0; i < 12; i++) aspecttable[i] = 0;
- for (i = 0; i < 18; i++) dihedangletable[i] = 0;
- for (i = 0; i < 18; i++) faceangletable[i] = 0;
-
- minaltitude = xmax - xmin + ymax - ymin + zmax - zmin;
- minaltitude = minaltitude * minaltitude;
- shortest = minaltitude;
- longest = 0.0;
- smallestvolume = minaltitude;
- biggestvolume = 0.0;
- smallestdiangle = smallestfaangle = 180.0;
- biggestdiangle = biggestfaangle = 0.0;
-
- // Loop all elements, calculate quality parameters for each element.
- tetrahedrons->traversalinit();
- tetloop.tet = tetrahedrontraverse();
- while (tetloop.tet != (tetrahedron *) NULL) {
-
- // Get four vertices: p0, p1, p2, p3.
- for (i = 0; i < 4; i++) p[i] = (point) tetloop.tet[4 + i];
- // Set the edge vectors: V[0], ..., V[5]
- for (i = 0; i < 3; i++) V[0][i] = p[0][i] - p[3][i]; // V[0]: p3->p0.
- for (i = 0; i < 3; i++) V[1][i] = p[1][i] - p[3][i]; // V[1]: p3->p1.
- for (i = 0; i < 3; i++) V[2][i] = p[2][i] - p[3][i]; // V[2]: p3->p2.
- for (i = 0; i < 3; i++) V[3][i] = p[1][i] - p[0][i]; // V[3]: p0->p1.
- for (i = 0; i < 3; i++) V[4][i] = p[2][i] - p[1][i]; // V[4]: p1->p2.
- for (i = 0; i < 3; i++) V[5][i] = p[0][i] - p[2][i]; // V[5]: p2->p0.
- // Set the matrix A = [V[0], V[1], V[2]]^T.
- for (j = 0; j < 3; j++) {
- for (i = 0; i < 3; i++) A[j][i] = V[j][i];
- }
- // Decompose A just once.
- lu_decmp(A, 3, indx, &D, 0);
- // Get the tet volume.
- tetvol = fabs(A[indx[0]][0] * A[indx[1]][1] * A[indx[2]][2]) / 6.0;
- // Get the three faces normals.
- for (j = 0; j < 3; j++) {
- for (i = 0; i < 3; i++) rhs[i] = 0.0;
- rhs[j] = 1.0; // Positive means the inside direction
- lu_solve(A, 3, indx, rhs, 0);
- for (i = 0; i < 3; i++) N[j][i] = rhs[i];
- }
- // Get the fourth face normal by summing up the first three.
- for (i = 0; i < 3; i++) N[3][i] = - N[0][i] - N[1][i] - N[2][i];
- // Get the radius of the circumsphere.
- for (i = 0; i < 3; i++) rhs[i] = 0.5 * dot(V[i], V[i]);
- lu_solve(A, 3, indx, rhs, 0);
- cirradius = sqrt(dot(rhs, rhs));
- // Normalize the face normals.
- for (i = 0; i < 4; i++) {
- // H[i] is the inverse of height of its corresponding face.
- H[i] = sqrt(dot(N[i], N[i]));
- for (j = 0; j < 3; j++) N[i][j] /= H[i];
- }
- // Get the radius of the inscribed sphere.
- // insradius = 1.0 / (H[0] + H[1] + H[2] + H[3]);
- // Get the biggest H[i] (corresponding to the smallest height).
- minheightinv = H[0];
- for (i = 1; i < 3; i++) {
- if (H[i] > minheightinv) minheightinv = H[i];
- }
- // Get the squares of the edge lengthes.
- for (i = 0; i < 6; i++) edgelength[i] = dot(V[i], V[i]);
- // Get the dihedrals (in degree) at each edges.
- j = 0;
- for (i = 1; i < 4; i++) {
- alldihed[j] = -dot(N[0], N[i]); // Edge cd, bd, bc.
- if (alldihed[j] < -1.0) alldihed[j] = -1; // Rounding.
- else if (alldihed[j] > 1.0) alldihed[j] = 1;
- alldihed[j] = acos(alldihed[j]) / PI * 180.0;
- j++;
- }
- for (i = 2; i < 4; i++) {
- alldihed[j] = -dot(N[1], N[i]); // Edge ad, ac.
- if (alldihed[j] < -1.0) alldihed[j] = -1; // Rounding.
- else if (alldihed[j] > 1.0) alldihed[j] = 1;
- alldihed[j] = acos(alldihed[j]) / PI * 180.0;
- j++;
- }
- alldihed[j] = -dot(N[2], N[3]); // Edge ab.
- if (alldihed[j] < -1.0) alldihed[j] = -1; // Rounding.
- else if (alldihed[j] > 1.0) alldihed[j] = 1;
- alldihed[j] = acos(alldihed[j]) / PI * 180.0;
-
- // Calculate the longest and shortest edge length.
- for (i = 0; i < 6; i++) {
- if (i == 0) {
- shortlen = longlen = edgelength[i];
- } else {
- shortlen = edgelength[i] < shortlen ? edgelength[i] : shortlen;
- longlen = edgelength[i] > longlen ? edgelength[i] : longlen;
- }
- if (edgelength[i] > longest) {
- longest = edgelength[i];
- }
- if (edgelength[i] < shortest) {
- shortest = edgelength[i];
- }
- }
-
- // Calculate the largest and smallest volume.
- if (tetvol < smallestvolume) {
- smallestvolume = tetvol;
- }
- if (tetvol > biggestvolume) {
- biggestvolume = tetvol;
- }
-
- // Calculate the largest and smallest dihedral angles.
- for (i = 0; i < 6; i++) {
- if (i == 0) {
- smalldiangle = bigdiangle = alldihed[i];
- } else {
- smalldiangle = alldihed[i] < smalldiangle ? alldihed[i] : smalldiangle;
- bigdiangle = alldihed[i] > bigdiangle ? alldihed[i] : bigdiangle;
- }
- if (alldihed[i] < smallestdiangle) {
- smallestdiangle = alldihed[i];
- }
- if (alldihed[i] > biggestdiangle) {
- biggestdiangle = alldihed[i];
- }
- }
- // Accumulate the corresponding number in the dihedral angle histogram.
- if (smalldiangle < 5.0) {
- tendegree = 0;
- } else if (smalldiangle >= 5.0 && smalldiangle < 10.0) {
- tendegree = 1;
- } else if (smalldiangle >= 80.0 && smalldiangle < 110.0) {
- tendegree = 9; // Angles between 80 to 110 degree are in one entry.
- } else {
- tendegree = (int) (smalldiangle / 10.);
- if (smalldiangle < 80.0) {
- tendegree++; // In the left column.
- } else {
- tendegree--; // In the right column.
- }
- }
- dihedangletable[tendegree]++;
- if (bigdiangle >= 80.0 && bigdiangle < 110.0) {
- tendegree = 9; // Angles between 80 to 110 degree are in one entry.
- } else if (bigdiangle >= 170.0 && bigdiangle < 175.0) {
- tendegree = 16;
- } else if (bigdiangle >= 175.0) {
- tendegree = 17;
- } else {
- tendegree = (int) (bigdiangle / 10.);
- if (bigdiangle < 80.0) {
- tendegree++; // In the left column.
- } else {
- tendegree--; // In the right column.
- }
- }
- dihedangletable[tendegree]++;
-
- // Calulate the largest and smallest face angles.
- tetloop.ver = 0;
- for (tetloop.loc = 0; tetloop.loc < 4; tetloop.loc++) {
- sym(tetloop, neightet);
- // Only do the calulation once for a face.
- if ((neightet.tet == dummytet) || (tetloop.tet < neightet.tet)) {
- p[0] = org(tetloop);
- p[1] = dest(tetloop);
- p[2] = apex(tetloop);
- faceangle[0] = interiorangle(p[0], p[1], p[2], NULL);
- faceangle[1] = interiorangle(p[1], p[2], p[0], NULL);
- faceangle[2] = PI - (faceangle[0] + faceangle[1]);
- // Translate angles into degrees.
- for (i = 0; i < 3; i++) {
- faceangle[i] = (faceangle[i] * 180.0) / PI;
- }
- // Calculate the largest and smallest face angles.
- for (i = 0; i < 3; i++) {
- if (i == 0) {
- smallfaangle = bigfaangle = faceangle[i];
- } else {
- smallfaangle = faceangle[i] < smallfaangle ?
- faceangle[i] : smallfaangle;
- bigfaangle = faceangle[i] > bigfaangle ? faceangle[i] : bigfaangle;
- }
- if (faceangle[i] < smallestfaangle) {
- smallestfaangle = faceangle[i];
- }
- if (faceangle[i] > biggestfaangle) {
- biggestfaangle = faceangle[i];
- }
- }
- tendegree = (int) (smallfaangle / 10.);
- faceangletable[tendegree]++;
- tendegree = (int) (bigfaangle / 10.);
- faceangletable[tendegree]++;
- }
- }
-
- // Calculate aspect ratio and radius-edge ratio for this element.
- tetradius = cirradius / sqrt(shortlen);
- // tetaspect = sqrt(longlen) / (2.0 * insradius);
- tetaspect = sqrt(longlen) * minheightinv;
- aspectindex = 0;
- while ((tetaspect > aspectratiotable[aspectindex]) && (aspectindex < 11)) {
- aspectindex++;
- }
- aspecttable[aspectindex]++;
- radiusindex = 0;
- while ((tetradius > radiusratiotable[radiusindex]) && (radiusindex < 11)) {
- radiusindex++;
- }
- radiustable[radiusindex]++;
-
- tetloop.tet = tetrahedrontraverse();
- }
-
- shortest = sqrt(shortest);
- longest = sqrt(longest);
- minaltitude = sqrt(minaltitude);
-
- printf(" Smallest volume: %16.5g | Largest volume: %16.5g\n",
- smallestvolume, biggestvolume);
- printf(" Shortest edge: %16.5g | Longest edge: %16.5g\n",
- shortest, longest);
- sprintf(sbuf, "%.17g", biggestfaangle);
- if (strlen(sbuf) > 8) {
- sbuf[8] = '\0';
- }
- printf(" Smallest facangle: %14.5g | Largest facangle: %s\n",
- smallestfaangle, sbuf);
- sprintf(sbuf, "%.17g", biggestdiangle);
- if (strlen(sbuf) > 8) {
- sbuf[8] = '\0';
- }
- printf(" Smallest dihedral: %14.5g | Largest dihedral: %s\n\n",
- smallestdiangle, sbuf);
-
- /*
- printf(" Radius-edge ratio histogram:\n");
- printf(" < %-6.6g : %8d | %6.6g - %-6.6g : %8d\n",
- radiusratiotable[0], radiustable[0], radiusratiotable[5],
- radiusratiotable[6], radiustable[6]);
- for (i = 1; i < 5; i++) {
- printf(" %6.6g - %-6.6g : %8d | %6.6g - %-6.6g : %8d\n",
- radiusratiotable[i - 1], radiusratiotable[i], radiustable[i],
- radiusratiotable[i + 5], radiusratiotable[i + 6],
- radiustable[i + 6]);
- }
- printf(" %6.6g - %-6.6g : %8d | %6.6g - : %8d\n",
- radiusratiotable[4], radiusratiotable[5], radiustable[5],
- radiusratiotable[10], radiustable[11]);
- printf(" (A tetrahedron's radius-edge ratio is its radius of ");
- printf("circumsphere divided\n");
- printf(" by its shortest edge length)\n\n");
- */
-
- printf(" Aspect ratio histogram:\n");
- printf(" < %-6.6g : %8d | %6.6g - %-6.6g : %8d\n",
- aspectratiotable[0], aspecttable[0], aspectratiotable[5],
- aspectratiotable[6], aspecttable[6]);
- for (i = 1; i < 5; i++) {
- printf(" %6.6g - %-6.6g : %8d | %6.6g - %-6.6g : %8d\n",
- aspectratiotable[i - 1], aspectratiotable[i], aspecttable[i],
- aspectratiotable[i + 5], aspectratiotable[i + 6],
- aspecttable[i + 6]);
- }
- printf(" %6.6g - %-6.6g : %8d | %6.6g - : %8d\n",
- aspectratiotable[4], aspectratiotable[5], aspecttable[5],
- aspectratiotable[10], aspecttable[11]);
- printf(" (A tetrahedron's aspect ratio is its longest edge length");
- printf(" divided by its\n");
- printf(" smallest side height)\n\n");
-
- printf(" Face angle histogram:\n");
- for (i = 0; i < 9; i++) {
- printf(" %3d - %3d degrees: %8d | %3d - %3d degrees: %8d\n",
- i * 10, i * 10 + 10, faceangletable[i],
- i * 10 + 90, i * 10 + 100, faceangletable[i + 9]);
- }
- if (minfaceang != PI) {
- printf(" Minimum input face angle is %g (degree).\n",
- minfaceang / PI * 180.0);
- }
- printf("\n");
-
- printf(" Dihedral angle histogram:\n");
- // Print the three two rows:
- printf(" %3d - %2d degrees: %8d | %3d - %3d degrees: %8d\n",
- 0, 5, dihedangletable[0], 80, 110, dihedangletable[9]);
- printf(" %3d - %2d degrees: %8d | %3d - %3d degrees: %8d\n",
- 5, 10, dihedangletable[1], 110, 120, dihedangletable[10]);
- // Print the third to seventh rows.
- for (i = 2; i < 7; i++) {
- printf(" %3d - %2d degrees: %8d | %3d - %3d degrees: %8d\n",
- (i - 1) * 10, (i - 1) * 10 + 10, dihedangletable[i],
- (i - 1) * 10 + 110, (i - 1) * 10 + 120, dihedangletable[i + 9]);
- }
- // Print the last two rows.
- printf(" %3d - %2d degrees: %8d | %3d - %3d degrees: %8d\n",
- 60, 70, dihedangletable[7], 170, 175, dihedangletable[16]);
- printf(" %3d - %2d degrees: %8d | %3d - %3d degrees: %8d\n",
- 70, 80, dihedangletable[8], 175, 180, dihedangletable[17]);
- if (minfacetdihed != PI) {
- printf(" Minimum input facet dihedral angle is %g (degree).\n",
- minfacetdihed / PI * 180.0);
- }
- printf("\n");
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// statistics() Print all sorts of cool facts. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::statistics()
-{
- printf("\nStatistics:\n\n");
- printf(" Input points: %d\n", in->numberofpoints + jettisoninverts);
- if (b->refine) {
- printf(" Input tetrahedra: %d\n", in->numberoftetrahedra);
- }
- if (b->plc) {
- printf(" Input facets: %d\n", in->numberoffacets);
- printf(" Input segments: %ld\n", insegments);
- printf(" Input holes: %d\n", in->numberofholes);
- printf(" Input regions: %d\n", in->numberofregions);
- }
-
- printf("\n Mesh points: %ld\n", points->items);
- printf(" Mesh tetrahedra: %ld\n", tetrahedrons->items);
- if (b->plc || b->refine) {
- printf(" Mesh triangles: %ld\n", (4l*tetrahedrons->items+hullsize)/2l);
- }
- if (b->plc || b->refine) {
- printf(" Mesh subfaces: %ld\n", subfaces->items);
- printf(" Mesh subsegments: %ld\n\n", subsegs->items);
- } else {
- printf(" Convex hull triangles: %ld\n\n", hullsize);
- }
- if (b->verbose > 0) {
- qualitystatistics();
- unsigned long totalmeshbytes;
- printf("Memory allocation statistics:\n\n");
- printf(" Maximum number of vertices: %ld\n", points->maxitems);
- totalmeshbytes = points->maxitems * points->itembytes;
- printf(" Maximum number of tetrahedra: %ld\n", tetrahedrons->maxitems);
- totalmeshbytes += tetrahedrons->maxitems * tetrahedrons->itembytes;
- if (subfaces != (memorypool *) NULL) {
- printf(" Maximum number of subfaces: %ld\n", subfaces->maxitems);
- totalmeshbytes += subfaces->maxitems * subfaces->itembytes;
- }
- if (subsegs != (memorypool *) NULL) {
- printf(" Maximum number of segments: %ld\n", subsegs->maxitems);
- totalmeshbytes += subsegs->maxitems * subsegs->itembytes;
- }
- printf(" Approximate heap memory used by the mesh (K bytes): %g\n\n",
- (double) totalmeshbytes / 1024.0);
-#ifdef SELF_CHECK
- algorithmicstatistics();
-#endif
- }
-}
-
-//
-// End of user interaction routines
-//
-
-//
-// Begin of constructor and destructor of tetgenmesh
-//
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// ~tetgenmesh() Deallocte memory occupied by a tetgenmesh object. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-tetgenmesh::~tetgenmesh()
-{
- bgm = (tetgenmesh *) NULL;
- in = (tetgenio *) NULL;
- b = (tetgenbehavior *) NULL;
-
- if (tetrahedrons != (memorypool *) NULL) {
- delete tetrahedrons;
- }
- if (subfaces != (memorypool *) NULL) {
- delete subfaces;
- }
- if (subsegs != (memorypool *) NULL) {
- delete subsegs;
- }
- if (points != (memorypool *) NULL) {
- delete points;
- }
- if (dummytetbase != (tetrahedron *) NULL) {
- delete [] dummytetbase;
- }
- if (dummyshbase != (shellface *) NULL) {
- delete [] dummyshbase;
- }
- if (facetabovepointarray != (point *) NULL) {
- delete [] facetabovepointarray;
- }
- if (highordertable != (point *) NULL) {
- delete [] highordertable;
- }
- if (subpbcgrouptable != (pbcdata *) NULL) {
- delete [] subpbcgrouptable;
- }
- if (segpbcgrouptable != (list *) NULL) {
- delete segpbcgrouptable;
- delete [] idx2segpglist;
- delete [] segpglist;
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// tetgenmesh() Initialize a tetgenmesh object. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-tetgenmesh::tetgenmesh()
-{
- bgm = (tetgenmesh *) NULL;
- in = (tetgenio *) NULL;
- b = (tetgenbehavior *) NULL;
-
- tetrahedrons = (memorypool *) NULL;
- subfaces = (memorypool *) NULL;
- subsegs = (memorypool *) NULL;
- points = (memorypool *) NULL;
- badsubsegs = (memorypool *) NULL;
- badsubfaces = (memorypool *) NULL;
- badtetrahedrons = (memorypool *) NULL;
- flipstackers = (memorypool *) NULL;
-
- dummytet = (tetrahedron *) NULL;
- dummytetbase = (tetrahedron *) NULL;
- dummysh = (shellface *) NULL;
- dummyshbase = (shellface *) NULL;
-
- facetabovepointarray = (point *) NULL;
- abovepoint = (point) NULL;
- highordertable = (point *) NULL;
- subpbcgrouptable = (pbcdata *) NULL;
- segpbcgrouptable = (list *) NULL;
- idx2segpglist = (int *) NULL;
- segpglist = (int *) NULL;
-
- xmax = xmin = ymax = ymin = zmax = zmin = 0.0;
- longest = 0.0;
- hullsize = 0l;
- insegments = 0l;
- pointmtrindex = 0;
- pointmarkindex = 0;
- point2simindex = 0;
- point2pbcptindex = 0;
- highorderindex = 0;
- elemattribindex = 0;
- volumeboundindex = 0;
- shmarkindex = 0;
- areaboundindex = 0;
- checksubfaces = 0;
- checksubsegs = 0;
- checkpbcs = 0;
- varconstraint = 0;
- nonconvex = 0;
- dupverts = 0;
- unuverts = 0;
- relverts = 0;
- suprelverts = 0;
- collapverts = 0;
- unsupverts = 0;
- jettisoninverts = 0;
- symbolic = 1;
- samples = 0l;
- randomseed = 1l;
- macheps = 0.0;
- minfaceang = minfacetdihed = PI;
- maxcavfaces = maxcavverts = 0;
- expcavcount = 0;
- abovecount = 0l;
- bowatvolcount = bowatsubcount = bowatsegcount = 0l;
- updvolcount = updsubcount = updsegcount = 0l;
- repairflipcount = 0l;
- outbowatcircumcount = 0l;
- failvolcount = failsubcount = failsegcount = 0l;
- r1count = r2count = r3count = 0l;
- cdtenforcesegpts = 0l;
- rejsegpts = rejsubpts = rejtetpts = 0l;
- flip23s = flip32s = flip22s = flip44s = 0l;
- tloctime = tfliptime = 0.0;
-}
-
-//
-// End of constructor and destructor of tetgenmesh
-//
-
-//
-// End of class 'tetgenmesh' implementation.
-//
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// tetrahedralize() The interface for users using TetGen library to //
-// generate tetrahedral meshes with all features. //
-// //
-// The sequence is roughly as follows. Many of these steps can be skipped, //
-// depending on the command line switches. //
-// //
-// - Initialize constants and parse the command line. //
-// - Read the vertices from a file and either //
-// - tetrahedralize them (no -r), or //
-// - read an old mesh from files and reconstruct it (-r). //
-// - Insert the PLC segments and facets (-p). //
-// - Read the holes (-p), regional attributes (-pA), and regional volume //
-// constraints (-pa). Carve the holes and concavities, and spread the //
-// regional attributes and volume constraints. //
-// - Enforce the constraints on minimum quality bound (-q) and maximum //
-// volume (-a). Also enforce the conforming Delaunay property (-q and -a). //
-// - Promote the mesh's linear tetrahedra to higher order elements (-o). //
-// - Write the output files and print the statistics. //
-// - Check the consistency and Delaunay property of the mesh (-C). //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetrahedralize(tetgenbehavior *b, tetgenio *in, tetgenio *out,
- tetgenio *addin, tetgenio *bgmin)
-{
- tetgenmesh m;
- // Variables for timing the performance of TetGen (defined in time.h).
- clock_t tv[14];
-
- tv[0] = clock();
-
- m.b = b;
- m.in = in;
- m.macheps = exactinit();
- m.steinerleft = b->steiner;
- if (b->metric) {
- m.bgm = new tetgenmesh();
- m.bgm->b = b;
- m.bgm->in = bgmin;
- m.bgm->macheps = exactinit();
- }
- m.initializepools();
- m.transfernodes();
-
- tv[1] = clock();
-
- if (b->refine) {
- m.reconstructmesh();
- } else {
- m.delaunizevertices();
- }
-
- tv[2] = clock();
-
- if (!b->quiet) {
- if (b->refine) {
- printf("Mesh reconstruction seconds:");
- } else {
- printf("Delaunay seconds:");
- }
- printf(" %g\n", (tv[2] - tv[1]) / (REAL) CLOCKS_PER_SEC);
- }
-
- if (b->metric) {
- if (bgmin != (tetgenio *) NULL) {
- m.bgm->initializepools();
- m.bgm->transfernodes();
- m.bgm->reconstructmesh();
- } else {
- m.bgm->in = in;
- m.bgm->initializepools();
- m.duplicatebgmesh();
- }
- }
-
- tv[3] = clock();
-
- if (!b->quiet) {
- if (b->metric) {
- printf("Background mesh reconstruct seconds: %g\n",
- (tv[3] - tv[2]) / (REAL) CLOCKS_PER_SEC);
- }
- }
-
- if (b->useshelles && !b->refine) {
- m.meshsurface();
- if (b->diagnose != 1) {
- m.markacutevertices(89.0);
- m.incrperturbvertices(b->epsilon);
- m.delaunizesegments();
- if (m.checkpbcs) {
- long oldnum;
- do {
- oldnum = m.points->items;
- m.incrperturbvertices(b->epsilon);
- if (m.points->items > oldnum) {
- oldnum = m.points->items;
- m.delaunizesegments();
- }
- } while (oldnum < m.points->items);
- }
- m.constrainedfacets();
- } else {
- m.detectinterfaces();
- }
- }
-
- tv[4] = clock();
-
- if (!b->quiet) {
- if (b->useshelles && !b->refine) {
- if (b->diagnose != 1) {
- printf("Segment and facet ");
- } else {
- printf("Intersection ");
- }
- printf("seconds: %g\n", (tv[4] - tv[3]) / (REAL) CLOCKS_PER_SEC);
- }
- }
-
- if (b->plc && !(b->diagnose == 1)) {
- m.carveholes();
- }
-
- tv[5] = clock();
-
- if (!b->quiet) {
- if (b->plc && !(b->diagnose == 1)) {
- printf("Hole seconds: %g\n", (tv[5] - tv[4]) / (REAL) CLOCKS_PER_SEC);
- }
- }
-
- if ((b->plc || b->refine) && !(b->diagnose == 1)) {
- m.optimizemesh(false);
- }
-
- tv[6] = clock();
-
- if (!b->quiet) {
- if ((b->plc || b->refine) && !(b->diagnose == 1)) {
- printf("Repair seconds: %g\n", (tv[6] - tv[5]) / (REAL) CLOCKS_PER_SEC);
- }
- }
-
- if ((b->plc && b->nobisect) && !(b->diagnose == 1)) {
- m.removesteiners(false);
- }
-
- tv[7] = clock();
-
- if (!b->quiet) {
- if ((b->plc && b->nobisect) && !(b->diagnose == 1)) {
- printf("Steiner removal seconds: %g\n",
- (tv[7] - tv[6]) / (REAL) CLOCKS_PER_SEC);
- }
- }
-
- if (b->insertaddpoints && (addin != (tetgenio *) NULL)) {
- if (addin->numberofpoints > 0) {
- m.insertconstrainedpoints(addin);
- }
- }
-
- tv[8] = clock();
-
- if (!b->quiet) {
- if ((b->plc || b->refine) && (b->insertaddpoints)) {
- printf("Constrained points seconds: %g\n",
- (tv[8] - tv[7]) / (REAL) CLOCKS_PER_SEC);
- }
- }
-
- if (b->metric) {
- m.interpolatesizemap();
- }
-
- tv[9] = clock();
-
- if (!b->quiet) {
- if (b->metric) {
- printf("Size interpolating seconds: %g\n",
- (tv[9] - tv[8]) / (REAL) CLOCKS_PER_SEC);
- }
- }
-
- if (b->coarse) {
- m.removesteiners(true);
- }
-
- tv[10] = clock();
-
- if (!b->quiet) {
- if (b->coarse) {
- printf("Mesh coarsening seconds: %g\n",
- (tv[10] - tv[9]) / (REAL) CLOCKS_PER_SEC);
- }
- }
-
- if (b->quality) {
- m.enforcequality();
- }
-
- tv[11] = clock();
-
- if (!b->quiet) {
- if (b->quality) {
- printf("Quality seconds: %g\n",
- (tv[11] - tv[10]) / (REAL) CLOCKS_PER_SEC);
- }
- }
-
- if (b->quality && (b->optlevel > 0)) {
- m.optimizemesh(true);
- }
-
- tv[12] = clock();
-
- if (!b->quiet) {
- if (b->quality && (b->optlevel > 0)) {
- printf("Optimize seconds: %g\n",
- (tv[12] - tv[11]) / (REAL) CLOCKS_PER_SEC);
- }
- }
-
- if (!b->nojettison && ((m.dupverts > 0) || (m.unuverts > 0)
- || (b->refine && (in->numberofcorners == 10)))) {
- m.jettisonnodes();
- }
-
- if (b->order > 1) {
- m.highorder();
- }
-
- if (!b->quiet) {
- printf("\n");
- }
-
- if (out != (tetgenio *) NULL) {
- out->firstnumber = in->firstnumber;
- out->mesh_dim = in->mesh_dim;
- }
-
- if (b->nonodewritten || b->noiterationnum) {
- if (!b->quiet) {
- printf("NOT writing a .node file.\n");
- }
- } else {
- if (b->diagnose == 1) {
- if (m.subfaces->items > 0l) {
- m.outnodes(out); // Only output when self-intersecting faces exist.
- }
- } else {
- m.outnodes(out);
- if (b->quality || b->metric) {
- // m.outmetrics(out);
- }
- }
- }
-
- if (b->noelewritten) {
- if (!b->quiet) {
- printf("NOT writing an .ele file.\n");
- }
- } else {
- if (!(b->diagnose == 1)) {
- if (m.tetrahedrons->items > 0l) {
- m.outelements(out);
- }
- }
- }
-
- if (b->nofacewritten) {
- if (!b->quiet) {
- printf("NOT writing an .face file.\n");
- }
- } else {
- if (b->facesout) {
- if (m.tetrahedrons->items > 0l) {
- m.outfaces(out); // Output all faces.
- }
- } else {
- if (b->diagnose == 1) {
- if (m.subfaces->items > 0l) {
- m.outsubfaces(out); // Only output self-intersecting faces.
- }
- } else if (b->plc || b->refine) {
- if (m.subfaces->items > 0l) {
- m.outsubfaces(out); // Output boundary faces.
- }
- } else {
- if (m.tetrahedrons->items > 0l) {
- m.outhullfaces(out); // Output convex hull faces.
- }
- }
- }
- }
-
- if (m.checkpbcs) {
- m.outpbcnodes(out);
- }
-
- if (b->edgesout) {
- if (b->edgesout > 1) {
- m.outedges(out); // -ee, output all mesh edges.
- } else {
- m.outsubsegments(out); // -e, only output subsegments.
- }
- }
-
- if (!out && b->plc &&
- ((b->object == tetgenbehavior::OFF) ||
- (b->object == tetgenbehavior::PLY) ||
- (b->object == tetgenbehavior::STL))) {
- m.outsmesh(b->outfilename);
- }
-
- if (!out && b->meditview) {
- m.outmesh2medit(b->outfilename);
- }
-
- if (!out && b->gidview) {
- m.outmesh2gid(b->outfilename);
- }
-
- if (!out && b->geomview) {
- m.outmesh2off(b->outfilename);
- }
-
- if (b->neighout) {
- m.outneighbors(out);
- }
-
- if (b->voroout) {
- m.outvoronoi(NULL);
- //m.outvoronoi(out);
- }
-
- tv[13] = clock();
-
- if (!b->quiet) {
- printf("\nOutput seconds: %g\n",
- (tv[13] - tv[12]) / (REAL) CLOCKS_PER_SEC);
- printf("Total running seconds: %g\n",
- (tv[13] - tv[0]) / (REAL) CLOCKS_PER_SEC);
- }
-
- if (b->docheck) {
- m.checkmesh();
- if (m.checksubfaces) {
- m.checkshells();
- }
- if (b->docheck > 1) {
- m.checkdelaunay(0.0, NULL);
- if (b->docheck > 2) {
- if (b->quality || b->refine) {
- m.checkconforming();
- }
- }
- }
- }
-
- if (!b->quiet) {
- m.statistics();
- }
-
- if (b->metric) {
- delete m.bgm;
- }
-}
-
-#ifndef TETLIBRARY
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// main() The entrance for running TetGen from command line. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-int main(int argc, char *argv[])
-
-#else // with TETLIBRARY
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// tetrahedralize() The entrance for calling TetGen from another program. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetrahedralize(char *switches, tetgenio *in, tetgenio *out,
- tetgenio *addin, tetgenio *bgmin)
-
-#endif // not TETLIBRARY
-
-{
- tetgenbehavior b;
-
-#ifndef TETLIBRARY
-
- tetgenio in, addin, bgmin;
-
- if (!b.parse_commandline(argc, argv)) {
- terminatetetgen(1);
- }
- if (b.refine) {
- if (!in.load_tetmesh(b.infilename)) {
- terminatetetgen(1);
- }
- } else {
- if (!in.load_plc(b.infilename, (int) b.object)) {
- terminatetetgen(1);
- }
- }
- if (b.insertaddpoints) {
- if (!addin.load_node(b.addinfilename)) {
- addin.numberofpoints = 0l;
- }
- }
- if (b.metric) {
- if (!bgmin.load_tetmesh(b.bgmeshfilename)) {
- bgmin.numberoftetrahedra = 0l;
- }
- }
-
- if (bgmin.numberoftetrahedra > 0l) {
- tetrahedralize(&b, &in, NULL, &addin, &bgmin);
- } else {
- tetrahedralize(&b, &in, NULL, &addin, NULL);
- }
-
- return 0;
-
-#else // with TETLIBRARY
-
- if (!b.parse_commandline(switches)) {
- terminatetetgen(1);
- }
- tetrahedralize(&b, in, out, addin, bgmin);
-
-#endif // not TETLIBRARY
-}
diff --git a/contrib/Tetgen1.4/tetgen.h b/contrib/Tetgen1.4/tetgen.h
deleted file mode 100644
index 74106f92601af6ca5b6458882f7f7c1802d0aae5..0000000000000000000000000000000000000000
--- a/contrib/Tetgen1.4/tetgen.h
+++ /dev/null
@@ -1,1916 +0,0 @@
-///////////////////////////////////////////////////////////////////////////////
-// //
-// TetGen //
-// //
-// A Quality Tetrahedral Mesh Generator and 3D Delaunay Triangulator //
-// //
-// Version 1.4 //
-// April 16, 2007 //
-// //
-// Copyright (C) 2002--2007 //
-// Hang Si //
-// Research Group Numerical Mathematics and Scientific Computing //
-// Weierstrass Institute for Applied Analysis and Stochastics //
-// Mohrenstr. 39, 10117 Berlin, Germany //
-// si@wias-berlin.de //
-// //
-// TetGen is freely available through the website: http://tetgen.berlios.de. //
-// It may be copied, modified, and redistributed for non-commercial use. //
-// Please consult the file LICENSE for the detailed copyright notices. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// TetGen computes Delaunay tetrahedralizations, constrained Delaunay tetra- //
-// hedralizations, and quality Delaunay tetrahedral meshes. The latter are //
-// nicely graded and whose tetrahedra have radius-edge ratio bounded. Such //
-// meshes are suitable for finite element and finite volume methods. //
-// //
-// TetGen incorporates a suit of geometrical and mesh generation algorithms. //
-// A brief description of algorithms used in TetGen is found in the first //
-// section of the user's manual. References are given for users who are //
-// interesting in these approaches. The main references are given below: //
-// //
-// The efficient Delaunay tetrahedralization algorithm is: H. Edelsbrunner //
-// and N. R. Shah, "Incremental Topological Flipping Works for Regular //
-// Triangulations". Algorithmica 15: 223--241, 1996. //
-// //
-// The constrained Delaunay tetrahedralization algorithm is described in: //
-// H. Si and K. Gaertner, "Meshing Piecewise Linear Complexes by Constr- //
-// ained Delaunay Tetrahedralizations". In Proceeding of the 14th Inter- //
-// national Meshing Roundtable. September 2005. //
-// //
-// The mesh refinement algorithm is from: Hang Si, "Adaptive Tetrahedral //
-// Mesh Generation by Constrained Delaunay Refinement". WIAS Preprint No. //
-// 1176, Berlin 2006. //
-// //
-// The mesh data structure of TetGen is a combination of two types of mesh //
-// data structures. The tetrahedron-based mesh data structure introduced //
-// by Shewchuk is eligible for tetrahedralization algorithms. The triangle //
-// -edge data structure developed by Muecke is adopted for representing //
-// boundary elements: subfaces and subsegments. //
-// //
-// J. R. Shewchuk, "Delaunay Refinement Mesh Generation". PhD thesis, //
-// Carnegie Mellon University, Pittsburgh, PA, 1997. //
-// //
-// E. P. Muecke, "Shapes and Implementations in Three-Dimensional //
-// Geometry". PhD thesis, Univ. of Illinois, Urbana, Illinois, 1993. //
-// //
-// The research of mesh generation is definitly on the move. Many State-of- //
-// the-art algorithms need implementing and evaluating. I heartily welcome //
-// any new algorithm especially for generating quality conforming Delaunay //
-// meshes and anisotropic conforming Delaunay meshes. //
-// //
-// TetGen is supported by the "pdelib" project of Weierstrass Institute for //
-// Applied Analysis and Stochastics (WIAS) in Berlin. It is a collection //
-// of software components for solving non-linear partial differential //
-// equations including 2D and 3D mesh generators, sparse matrix solvers, //
-// and scientific visualization tools, etc. For more information please //
-// visit: http://www.wias-berlin.de/software/pdelib. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// tetgen.h //
-// //
-// Header file of the TetGen library. Also is the user-level header file. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-// Here are the most general used head files for C/C++ programs.
-
-#include <stdio.h> // Standard IO: FILE, NULL, EOF, printf(), ...
-#include <stdlib.h> // Standard lib: abort(), system(), getenv(), ...
-#include <string.h> // String lib: strcpy(), strcat(), strcmp(), ...
-#include <math.h> // Math lib: sin(), sqrt(), pow(), ...
-#include <time.h> // Defined type clock_t, constant CLOCKS_PER_SEC.
-#include <assert.h>
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// TetGen Library Overview //
-// //
-// TetGen library is comprised by several data types and global functions. //
-// //
-// There are three main data types: tetgenio, tetgenbehavior, and tetgenmesh.//
-// Tetgenio is used to pass data into and out of TetGen library; tetgenbeha- //
-// vior keeps the runtime options and thus controls the behaviors of TetGen; //
-// tetgenmesh, the biggest data type I've ever defined, contains mesh data //
-// structures and mesh traversing and transformation operators. The meshing //
-// algorithms are implemented on top of it. These data types are defined as //
-// C++ classes. //
-// //
-// There are few global functions. tetrahedralize() is provided for calling //
-// TetGen from another program. Two functions: orient3d() and insphere() are //
-// incorporated from a public C code provided by Shewchuk. They performing //
-// exact geometrical tests. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-#ifndef tetgenH
-#define tetgenH
-
-// To compile TetGen as a library instead of an executable program, define
-// the TETLIBRARY symbol.
-
-// #define TETLIBRARY
-
-// Uncomment the following line to disable assert macros. These macros are
-// inserted in places where I hope to catch bugs.
-
-// #define NDEBUG
-
-// To insert lots of self-checks for internal errors, define the SELF_CHECK
-// symbol. This will slow down the program significantly.
-
-// #define SELF_CHECK
-
-// For single precision ( which will save some memory and reduce paging ),
-// define the symbol SINGLE by using the -DSINGLE compiler switch or by
-// writing "#define SINGLE" below.
-//
-// For double precision ( which will allow you to refine meshes to a smaller
-// edge length), leave SINGLE undefined.
-
-// #define SINGLE
-
-#ifdef SINGLE
- #define REAL float
-#else
- #define REAL double
-#endif // not defined SINGLE
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// tetgenio Passing data into and out of the library of TetGen. //
-// //
-// The tetgenio data structure is actually a collection of arrays of points, //
-// facets, tetrahedra, and so forth. The library will read and write these //
-// arrays according to the options specified in tetgenbehavior structure. //
-// //
-// If you want to program with the library of TetGen, it's necessary for you //
-// to understand this data type,while the other two structures can be hidden //
-// through calling the global function "tetrahedralize()". Each array corre- //
-// sponds to a list of data in the file formats of TetGen. It is necessary //
-// to understand TetGen's input/output file formats (see user's manual). //
-// //
-// Once an object of tetgenio is declared, no array is created. One has to //
-// allocate enough memory for them, e.g., use the "new" operator in C++. On //
-// deletion of the object, the memory occupied by these arrays needs to be //
-// freed. Routine deinitialize() will be automatically called. It will de- //
-// allocate the memory for an array if it is not a NULL. However, it assumes //
-// that the memory is allocated by the C++ "new" operator. If you use malloc //
-// (), you should free() them and set the pointers to NULLs before reaching //
-// deinitialize(). //
-// //
-// In all cases, the first item in an array is stored starting at index [0]. //
-// However, that item is item number `firstnumber' which may be '0' or '1'. //
-// Be sure to set the 'firstnumber' be '1' if your indices pointing into the //
-// pointlist is starting from '1'. Default, it is initialized be '0'. //
-// //
-// Tetgenio also contains routines for reading and writing TetGen's files as //
-// well. Both the library of TetGen and TetView use these routines to parse //
-// input files, i.e., .node, .poly, .smesh, .ele, .face, and .edge files. //
-// Other routines are provided mainly for debugging purpose. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-class tetgenio {
-
- public:
-
- // Maximum number of characters in a file name (including the null).
- enum {FILENAMESIZE = 1024};
-
- // Maxi. numbers of chars in a line read from a file (incl. the null).
- enum {INPUTLINESIZE = 1024};
-
- // The polygon data structure. A "polygon" is a planar polygon. It can
- // be arbitrary shaped (convex or non-convex) and bounded by non-
- // crossing segments, i.e., the number of vertices it has indictes the
- // same number of edges.
- // 'vertexlist' is a list of vertex indices (integers), its length is
- // indicated by 'numberofvertices'. The vertex indices are odered in
- // either counterclockwise or clockwise way.
- typedef struct {
- int *vertexlist;
- int numberofvertices;
- } polygon;
-
- static void init(polygon* p) {
- p->vertexlist = (int *) NULL;
- p->numberofvertices = 0;
- }
-
- // The facet data structure. A "facet" is a planar facet. It is used
- // to represent a planar straight line graph (PSLG) in two dimension.
- // A PSLG contains a list of polygons. It also may conatin holes in it,
- // indicated by a list of hole points (their coordinates).
- typedef struct {
- polygon *polygonlist;
- int numberofpolygons;
- REAL *holelist;
- int numberofholes;
- } facet;
-
- static void init(facet* f) {
- f->polygonlist = (polygon *) NULL;
- f->numberofpolygons = 0;
- f->holelist = (REAL *) NULL;
- f->numberofholes = 0;
- }
-
- // A 'voroedge' is an edge of the Voronoi diagram. It corresponds to a
- // Delaunay face. Each voroedge is either a line segment connecting
- // two Voronoi vertices or a ray starting from a Voronoi vertex to an
- // "infinite vertex". 'v1' and 'v2' are two indices pointing to the
- // list of Voronoi vertices. 'v1' must be non-negative, while 'v2' may
- // be -1 if it is a ray, in this case, the unit normal of this ray is
- // given in 'vnormal'.
- typedef struct {
- int v1, v2;
- REAL vnormal[3];
- } voroedge;
-
- // A 'vorofacet' is an facet of the Voronoi diagram. It corresponds to a
- // Delaunay edge. Each Voronoi facet is a convex polygon formed by a
- // list of Voronoi edges, it may not be closed. 'c1' and 'c2' are two
- // indices pointing into the list of Voronoi cells, i.e., the two cells
- // share this facet. 'elist' is an array of indices pointing into the
- // list of Voronoi edges, 'elist[0]' saves the number of Voronoi edges
- // (including rays) of this facet.
- typedef struct {
- int c1, c2;
- int *elist;
- } vorofacet;
-
- // The periodic boundary condition group data structure. A "pbcgroup"
- // contains the definition of a pbc and the list of pbc point pairs.
- // 'fmark1' and 'fmark2' are the facetmarkers of the two pbc facets f1
- // and f2, respectively. 'transmat' is the transformation matrix which
- // maps a point in f1 into f2. An array of pbc point pairs are saved
- // in 'pointpairlist'. The first point pair is at indices [0] and [1],
- // followed by remaining pairs. Two integers per pair.
- typedef struct {
- int fmark1, fmark2;
- REAL transmat[4][4];
- int numberofpointpairs;
- int *pointpairlist;
- } pbcgroup;
-
- public:
-
- // Items are numbered starting from 'firstnumber' (0 or 1), default is 0.
- int firstnumber;
- // Dimension of the mesh (2 or 3), default is 3.
- int mesh_dim;
- // Does the lines in .node file contain index or not, default is TRUE.
- bool useindex;
-
- // 'pointlist': An array of point coordinates. The first point's x
- // coordinate is at index [0] and its y coordinate at index [1], its
- // z coordinate is at index [2], followed by the coordinates of the
- // remaining points. Each point occupies three REALs.
- // 'pointattributelist': An array of point attributes. Each point's
- // attributes occupy 'numberofpointattributes' REALs.
- // 'pointmtrlist': An array of metric tensors at points. Each point's
- // tensor occupies 'numberofpointmtr' REALs.
- // `pointmarkerlist': An array of point markers; one int per point.
- REAL *pointlist;
- REAL *pointattributelist;
- REAL *pointmtrlist;
- int *pointmarkerlist;
- int numberofpoints;
- int numberofpointattributes;
- int numberofpointmtrs;
-
- // `elementlist': An array of element (triangle or tetrahedron) corners.
- // The first element's first corner is at index [0], followed by its
- // other corners in counterclockwise order, followed by any other
- // nodes if the element represents a nonlinear element. Each element
- // occupies `numberofcorners' ints.
- // `elementattributelist': An array of element attributes. Each
- // element's attributes occupy `numberofelementattributes' REALs.
- // `elementconstraintlist': An array of constraints, i.e. triangle's
- // area or tetrahedron's volume; one REAL per element. Input only.
- // `neighborlist': An array of element neighbors; 3 or 4 ints per
- // element. Output only.
- int *tetrahedronlist;
- REAL *tetrahedronattributelist;
- REAL *tetrahedronvolumelist;
- int *neighborlist;
- int numberoftetrahedra;
- int numberofcorners;
- int numberoftetrahedronattributes;
-
- // `facetlist': An array of facets. Each entry is a structure of facet.
- // `facetmarkerlist': An array of facet markers; one int per facet.
- facet *facetlist;
- int *facetmarkerlist;
- int numberoffacets;
-
- // `holelist': An array of holes. The first hole's x, y and z
- // coordinates are at indices [0], [1] and [2], followed by the
- // remaining holes. Three REALs per hole.
- REAL *holelist;
- int numberofholes;
-
- // `regionlist': An array of regional attributes and volume constraints.
- // The first constraint's x, y and z coordinates are at indices [0],
- // [1] and [2], followed by the regional attribute at index [3], foll-
- // owed by the maximum volume at index [4]. Five REALs per constraint.
- // Note that each regional attribute is used only if you select the `A'
- // switch, and each volume constraint is used only if you select the
- // `a' switch (with no number following).
- REAL *regionlist;
- int numberofregions;
-
- // `facetconstraintlist': An array of facet maximal area constraints.
- // Two REALs per constraint. The first one is the facet marker (cast
- // it to int), the second is its maximum area bound.
- // Note the 'facetconstraintlist' is used only for the 'q' switch.
- REAL *facetconstraintlist;
- int numberoffacetconstraints;
-
- // `segmentconstraintlist': An array of segment max. length constraints.
- // Three REALs per constraint. The first two are the indices (pointing
- // into 'pointlist') of the endpoints of the segment, the third is its
- // maximum length bound.
- // Note the 'segmentconstraintlist' is used only for the 'q' switch.
- REAL *segmentconstraintlist;
- int numberofsegmentconstraints;
-
- // 'pbcgrouplist': An array of periodic boundary condition groups.
- pbcgroup *pbcgrouplist;
- int numberofpbcgroups;
-
- // `trifacelist': An array of triangular face endpoints. The first
- // face's endpoints are at indices [0], [1] and [2], followed by the
- // remaining faces. Three ints per face.
- // `adjtetlist': An array of adjacent tetrahedra to the faces of
- // trifacelist. Each face has at most two adjacent tets, the first
- // face's adjacent tets are at [0], [1]. Two ints per face. A '-1'
- // indicates outside (no adj. tet). This list is output when '-nn'
- // switch is used.
- // `trifacemarkerlist': An array of face markers; one int per face.
- int *trifacelist;
- int *adjtetlist;
- int *trifacemarkerlist;
- int numberoftrifaces;
-
- // `edgelist': An array of edge endpoints. The first edge's endpoints
- // are at indices [0] and [1], followed by the remaining edges. Two
- // ints per edge.
- // `edgemarkerlist': An array of edge markers; one int per edge.
- int *edgelist;
- int *edgemarkerlist;
- int numberofedges;
-
- // 'vpointlist': An array of Voronoi vertex coordinates (like pointlist).
- // 'vedgelist': An array of Voronoi edges. Each entry is a 'voroedge'.
- // 'vfacetlist': An array of Voronoi facets. Each entry is a 'vorofacet'.
- // 'vcelllist': An array of Voronoi cells. Each entry is an array of
- // indices pointing into 'vfacetlist'. The 0th entry is used to store
- // the length of this array.
- REAL *vpointlist;
- voroedge *vedgelist;
- vorofacet *vfacetlist;
- int **vcelllist;
- int numberofvpoints;
- int numberofvedges;
- int numberofvfacets;
- int numberofvcells;
-
- public:
-
- // Initialize routine.
- void initialize();
- void deinitialize();
-
- // Input & output routines.
- bool load_node_call(FILE* infile, int markers, char* nodefilename);
- bool load_node(char* filename);
- bool load_pbc(char* filename);
- bool load_var(char* filename);
- bool load_mtr(char* filename);
- bool load_poly(char* filename);
- bool load_off(char* filename);
- bool load_ply(char* filename);
- bool load_stl(char* filename);
- bool load_medit(char* filename);
- bool load_plc(char* filename, int object);
- bool load_tetmesh(char* filename);
- bool load_voronoi(char* filename);
- void save_nodes(char* filename);
- void save_elements(char* filename);
- void save_faces(char* filename);
- void save_edges(char* filename);
- void save_neighbors(char* filename);
- void save_poly(char* filename);
-
- // Read line and parse string functions.
- char *readline(char* string, FILE* infile, int *linenumber);
- char *findnextfield(char* string);
- char *readnumberline(char* string, FILE* infile, char* infilename);
- char *findnextnumber(char* string);
-
- // Constructor and destructor.
- tetgenio() {initialize();}
- ~tetgenio() {deinitialize();}
-};
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// tetgenbehavior Parsing command line switches and file names. //
-// //
-// It includes a list of variables corresponding to the commandline switches //
-// for control the behavior of TetGen. These varibales are all initialized //
-// to their default values. //
-// //
-// parse_commandline() provides an simple interface to set the vaules of the //
-// variables. It accepts the standard parameters (e.g., 'argc' and 'argv') //
-// that pass to C/C++ main() function. Alternatively a string which contains //
-// the command line options can be used as its parameter. //
-// //
-// You don't need to understand this data type. It can be implicitly called //
-// by the global function "tetrahedralize()" defined below. The necessary //
-// thing you need to know is the meaning of command line switches of TetGen. //
-// They are described in the third section of the user's manual. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-class tetgenbehavior {
-
- public:
-
- // Labels define the objects which are acceptable by TetGen. They are
- // recognized by the file extensions.
- // - NODES, a list of nodes (.node);
- // - POLY, a piecewise linear complex (.poly or .smesh);
- // - OFF, a polyhedron (.off, Geomview's file format);
- // - PLY, a polyhedron (.ply, file format from gatech);
- // - STL, a surface mesh (.stl, stereolithography format);
- // - MEDIT, a surface mesh (.mesh, Medit's file format);
- // - MESH, a tetrahedral mesh (.ele).
- // If no extension is available, the imposed commandline switch
- // (-p or -r) implies the object.
-
- enum objecttype {NONE, NODES, POLY, OFF, PLY, STL, MEDIT, MESH};
-
- // Variables of command line switches. Each variable corresponds to a
- // switch and will be initialized. The meanings of these switches
- // are explained in the user's manul.
-
- int plc; // '-p' switch, 0.
- int quality; // '-q' switch, 0.
- int refine; // '-r' switch, 0.
- int coarse; // '-R' switch, 0.
- int metric; // '-m' switch, 0.
- int varvolume; // '-a' switch without number, 0.
- int fixedvolume; // '-a' switch with number, 0.
- int insertaddpoints; // '-i' switch, 0.
- int regionattrib; // '-A' switch, 0.
- int conformdel; // '-D' switch, 0.
- int diagnose; // '-d' switch, 0.
- int zeroindex; // '-z' switch, 0.
- int optlevel; // number specified after '-s' switch, 3.
- int optpasses; // number specified after '-ss' switch, 5.
- int order; // element order, specified after '-o' switch, 1.
- int facesout; // '-f' switch, 0.
- int edgesout; // '-e' switch, 0.
- int neighout; // '-n' switch, 0.
- int voroout; // '-v',switch, 0.
- int meditview; // '-g' switch, 0.
- int gidview; // '-G' switch, 0.
- int geomview; // '-O' switch, 0.
- int nobound; // '-B' switch, 0.
- int nonodewritten; // '-N' switch, 0.
- int noelewritten; // '-E' switch, 0.
- int nofacewritten; // '-F' switch, 0.
- int noiterationnum; // '-I' switch, 0.
- int nomerge; // '-M',switch, 0.
- int nobisect; // count of how often '-Y' switch is selected, 0.
- int noflip; // do not perform flips. '-X' switch. 0.
- int nojettison; // do not jettison redundants nodes. '-J' switch. 0.
- int steiner; // number after '-S' switch. 0.
- int fliprepair; // '-X' switch, 1.
- int offcenter; // '-R' switch, 0.
- int docheck; // '-C' switch, 0.
- int quiet; // '-Q' switch, 0.
- int verbose; // count of how often '-V' switch is selected, 0.
- int useshelles; // '-p', '-r', '-q', '-d', or '-R' switch, 0.
- REAL minratio; // number after '-q' switch, 2.0.
- REAL goodratio; // number calculated from 'minratio', 0.0.
- REAL minangle; // minimum angle bound, 20.0.
- REAL goodangle; // cosine squared of minangle, 0.0.
- REAL maxvolume; // number after '-a' switch, -1.0.
- REAL mindihedral; // number after '-qq' switch, 5.0.
- REAL maxdihedral; // number after '-qqq' switch, 165.0.
- REAL alpha1; // number after '-m' switch, sqrt(2).
- REAL alpha2; // number after '-mm' switch, 1.0.
- REAL alpha3; // number after '-mmm' switch, 0.6.
- REAL epsilon; // number after '-T' switch, 1.0e-8.
- REAL epsilon2; // number after '-TT' switch, 1.0e-5.
- enum objecttype object; // determined by -p, or -r switch. NONE.
-
- // Variables used to save command line switches and in/out file names.
- char commandline[1024];
- char infilename[1024];
- char outfilename[1024];
- char addinfilename[1024];
- char bgmeshfilename[1024];
-
- tetgenbehavior();
- ~tetgenbehavior() {}
-
- void versioninfo();
- void syntax();
- void usage();
-
- // Command line parse routine.
- bool parse_commandline(int argc, char **argv);
- bool parse_commandline(char *switches) {
- return parse_commandline(0, &switches);
- }
-};
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// Geometric predicates //
-// //
-// Return one of the values +1, 0, and -1 on basic geometric questions such //
-// as the orientation of point sets, in-circle, and in-sphere tests. They //
-// are basic units for implmenting geometric algorithms. TetGen uses two 3D //
-// geometric predicates: the orientation and in-sphere tests. //
-// //
-// Orientation test: let a, b, c be a sequence of 3 non-collinear points in //
-// R^3. They defines a unique hypeplane H. Let H+ and H- be the two spaces //
-// separated by H, which are defined as follows (using the left-hand rule): //
-// make a fist using your left hand in such a way that your fingers follow //
-// the order of a, b and c, then your thumb is pointing to H+. Given any //
-// point d in R^3, the orientation test returns +1 if d lies in H+, -1 if d //
-// lies in H-, or 0 if d lies on H. //
-// //
-// In-sphere test: let a, b, c, d be 4 non-coplanar points in R^3. They //
-// defines a unique circumsphere S. Given any point e in R^3, the in-sphere //
-// test returns +1 if e lies inside S, or -1 if e lies outside S, or 0 if e //
-// lies on S. //
-// //
-// The correctness of geometric predicates is crucial for the control flow //
-// and hence for the correctness and robustness of an implementation of a //
-// geometric algorithm. The following routines use arbitrary precision //
-// floating-point arithmetic. They are fast and robust. It is provided by J. //
-// Schewchuk in public domain (http://www.cs.cmu.edu/~quake/robust.html). //
-// The source code are found in a separate file "predicates.cxx". //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-REAL exactinit();
-REAL orient3d(REAL *pa, REAL *pb, REAL *pc, REAL *pd);
-REAL insphere(REAL *pa, REAL *pb, REAL *pc, REAL *pd, REAL *pe);
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// The tetgenmesh data type //
-// //
-// Includes data types and mesh routines for creating tetrahedral meshes and //
-// Delaunay tetrahedralizations, mesh input & output, and so on. //
-// //
-// An object of tetgenmesh can be used to store a triangular or tetrahedral //
-// mesh and its settings. TetGen's functions operates on one mesh each time. //
-// This type allows reusing of the same function for different meshes. //
-// //
-// The mesh data structure (tetrahedron-based and triangle-edge data struct- //
-// ures) are declared. There are other accessary data type defined as well, //
-// for efficient memory management and link list operations, etc. //
-// //
-// All algorithms TetGen used are implemented in this data type as member //
-// functions. References of these algorithms can be found in user's manual. //
-// //
-// It's not necessary to understand this type. There is a global function //
-// "tetrahedralize()" (defined at the end of this file) implicitly creates //
-// the object and calls its member functions according to the command line //
-// switches you specified. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-class tetgenmesh {
-
- public:
-
- // Maximum number of characters in a file name (including the null).
- enum {FILENAMESIZE = 1024};
-
- // For efficiency, a variety of data structures are allocated in bulk.
- // The following constants determine how many of each structure is
- // allocated at once.
- enum {VERPERBLOCK = 4092, SUBPERBLOCK = 4092, ELEPERBLOCK = 8188};
-
- // Used for the point location scheme of Mucke, Saias, and Zhu, to
- // decide how large a random sample of tetrahedra to inspect.
- enum {SAMPLEFACTOR = 11};
-
- // Labels that signify two edge rings of a triangle defined in Muecke's
- // triangle-edge data structure, one (CCW) traversing edges in count-
- // erclockwise direction and one (CW) in clockwise direction.
- enum {CCW = 0, CW = 1};
-
- // Labels that signify whether a record consists primarily of pointers
- // or of floating-point words. Used to make decisions about data
- // alignment.
- enum wordtype {POINTER, FLOATINGPOINT};
-
- // Labels that signify the type of a vertex. An UNUSEDVERTEX is a vertex
- // read from input (.node file or tetgenio structure) or an isolated
- // vertex (outside the mesh). It is the default type for a newpoint.
- enum verttype {UNUSEDVERTEX, DUPLICATEDVERTEX, NACUTEVERTEX, ACUTEVERTEX,
- FREESEGVERTEX, FREESUBVERTEX, FREEVOLVERTEX, DEADVERTEX = -32768};
-
- // Labels that signify the type of a subface/subsegment.
- enum shestype {NSHARP, SHARP};
-
- // Labels that signify the type of flips can be applied on a face.
- // A flipable face has the one of the types T23, T32, T22, and T44.
- // Types N32, N40 are unflipable.
- enum fliptype {T23, T32, T22, T44, N32, N40, FORBIDDENFACE, FORBIDDENEDGE};
-
- // Labels that signify the result of triangle-triangle intersection test.
- // Two triangles are DISJOINT, or adjoint at a vertex SHAREVERTEX, or
- // adjoint at an edge SHAREEDGE, or coincident SHAREFACE or INTERSECT.
- enum interresult {DISJOINT, SHAREVERTEX, SHAREEDGE, SHAREFACE, INTERSECT};
-
- // Labels that signify the result of point location. The result of a
- // search indicates that the point falls inside a tetrahedron, inside
- // a triangle, on an edge, on a vertex, or outside the mesh.
- enum locateresult {INTETRAHEDRON, ONFACE, ONEDGE, ONVERTEX, OUTSIDE};
-
- // Labels that signify the result of vertex insertion. The result
- // indicates that the vertex was inserted with complete success, was
- // inserted but encroaches upon a subsegment, was not inserted because
- // it lies on a segment, or was not inserted because another vertex
- // occupies the same location.
- enum insertsiteresult {SUCCESSINTET, SUCCESSONFACE, SUCCESSONEDGE,
- DUPLICATEPOINT, OUTSIDEPOINT};
-
- // Labels that signify the result of direction finding. The result
- // indicates that a segment connecting the two query points accross
- // an edge of the direction triangle/tetrahedron, across a face of
- // the direction tetrahedron, along the left edge of the direction
- // triangle/tetrahedron, along the right edge of the direction
- // triangle/tetrahedron, or along the top edge of the tetrahedron.
- enum finddirectionresult {ACROSSEDGE, ACROSSFACE, LEFTCOLLINEAR,
- RIGHTCOLLINEAR, TOPCOLLINEAR, BELOWHULL};
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// The basic mesh element data structures //
-// //
-// There are four types of mesh elements: tetrahedra, subfaces, subsegments, //
-// and points, where subfaces and subsegments are triangles and edges which //
-// appear on boundaries. A tetrahedralization of a 3D point set comprises //
-// tetrahedra and points; a surface mesh of a 3D domain comprises subfaces //
-// subsegments and points. The elements of all the four types consist of a //
-// tetrahedral mesh of a 3D domain. However, TetGen uses three data types: //
-// 'tetrahedron', 'shellface', and 'point'. A 'tetrahedron' is a tetrahedron;//
-// while a 'shellface' can be either a subface or a subsegment; and a 'point'//
-// is a point. These three data types, linked by pointers comprise a mesh. //
-// //
-// A tetrahedron primarily consists of a list of 4 pointers to its corners, //
-// a list of 4 pointers to its adjoining tetrahedra, a list of 4 pointers to //
-// its adjoining subfaces (when subfaces are needed). Optinoally, (depending //
-// on the selected switches), it may contain an arbitrary number of user- //
-// defined floating-point attributes, an optional maximum volume constraint //
-// (for -a switch), and a pointer to a list of high-order nodes (-o2 switch).//
-// Since the size of a tetrahedron is not determined until running time, it //
-// is not simply declared as a structure. //
-// //
-// The data structure of tetrahedron also stores the geometrical information.//
-// Let t be a tetrahedron, v0, v1, v2, and v3 be the 4 nodes corresponding //
-// to the order of their storage in t. v3 always has a negative orientation //
-// with respect to v0, v1, v2 (ie,, v3 lies above the oriented plane passes //
-// through v0, v1, v2). Let the 4 faces of t be f0, f1, f2, and f3. Vertices //
-// of each face are stipulated as follows: f0 (v0, v1, v2), f1 (v0, v3, v1), //
-// f2 (v1, v3, v2), f3 (v2, v3, v0). //
-// //
-// A subface has 3 pointers to vertices, 3 pointers to adjoining subfaces, 3 //
-// pointers to adjoining subsegments, 2 pointers to adjoining tetrahedra, a //
-// boundary marker(an integer). Like a tetrahedron, the pointers to vertices,//
-// subfaces, and subsegments are ordered in a way that indicates their geom- //
-// etric relation. Let s be a subface, v0, v1 and v2 be the 3 nodes corres- //
-// ponding to the order of their storage in s, e0, e1 and e2 be the 3 edges,//
-// then we have: e0 (v0, v1), e1 (v1, v2), e2 (v2, v0). //
-// //
-// A subsegment has exactly the same data fields as a subface has, but only //
-// uses some of them. It has 2 pointers to its endpoints, 2 pointers to its //
-// adjoining (and collinear) subsegments, a pointer to a subface containing //
-// it (there may exist any number of subfaces having it, choose one of them //
-// arbitrarily). The geometric relation between its endpoints and adjoining //
-// subsegments is kept with respect to the storing order of its endpoints. //
-// //
-// The data structure of point is relatively simple. A point is a list of //
-// floating-point numbers, starting with the x, y, and z coords, followed by //
-// an arbitrary number of optional user-defined floating-point attributes, //
-// an integer boundary marker, an integer for the point type, and a pointer //
-// to a tetrahedron (used for speeding up point location). //
-// //
-// For a tetrahedron on a boundary (or a hull) of the mesh, some or all of //
-// the adjoining tetrahedra may not be present. For an interior tetrahedron, //
-// often no neighboring subfaces are present, Such absent tetrahedra and //
-// subfaces are never represented by the NULL pointers; they are represented //
-// by two special records: `dummytet', the tetrahedron fills "outer space", //
-// and `dummysh', the vacuous subfaces which are omnipresent. //
-// //
-// Tetrahedra and adjoining subfaces are glued together through the pointers //
-// saved in each data fields of them. Subfaces and adjoining subsegments are //
-// connected in the same fashion. However, there are no pointers directly //
-// gluing tetrahedra and adjoining subsegments. For the purpose of saving //
-// space, the connections between tetrahedra and subsegments are entirely //
-// mediated through subfaces. The following part explains how subfaces are //
-// connected in TetGen. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// The subface-subface and subface-subsegment connections //
-// //
-// Adjoining subfaces sharing a common edge are connected in such a way that //
-// they form a face ring around the edge. It is indeed a single linked list //
-// which is cyclic, e.g., one can start from any subface in it and traverse //
-// back. When the edge is not a subsegment, the ring only has two coplanar //
-// subfaces which are pointing to each other. Otherwise, the face ring may //
-// have any number of subfaces (and are not all coplanar). //
-// //
-// How is the face ring formed? Let s be a subsegment, f is one of subfaces //
-// containing s as an edge. The direction of s is stipulated from its first //
-// endpoint to its second (according to their storage in s). Once the dir of //
-// s is determined, the other two edges of f are oriented to follow this dir.//
-// The "directional normal" N_f is a vector formed from any point in f and a //
-// points orthogonally above f. //
-// //
-// The face ring of s is a cyclic ordered set of subfaces containing s, i.e.,//
-// F(s) = {f1, f2, ..., fn}, n >= 1. Where the order is defined as follows: //
-// let fi, fj be two faces in F(s), the "normal-angle", NAngle(i,j) (range //
-// from 0 to 360 degree) is the angle between the N_fi and N_fj; then fi is //
-// in front of fj (or symbolically, fi < fj) if there exists another fk in //
-// F(s), and NAangle(k, i) < NAngle(k, j). The face ring of s is: f1 < f2 < //
-// ... < fn < f1. //
-// //
-// The easiest way to imagine how a face ring is formed is to use the right- //
-// hand rule. Make a fist using your right hand with the thumb pointing to //
-// the direction of the subsegment. The face ring is connected following the //
-// direction of your fingers. //
-// //
-// The subface and subsegment are also connected through pointers stored in //
-// their own data fields. Every subface has a pointer to its adjoining sub- //
-// segment. However, a subsegment only has one pointer to a subface which is //
-// containing it. Such subface can be chosen arbitrarily, other subfaces are //
-// found through the face ring. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
- // The tetrahedron data structure. Fields of a tetrahedron contains:
- // - a list of four adjoining tetrahedra;
- // - a list of four vertices;
- // - a list of four subfaces (optional, used for -p switch);
- // - a list of user-defined floating-point attributes (optional);
- // - a volume constraint (optional, used for -a switch);
- // - an integer of element marker (optional, used for -n switch);
- // - a pointer to a list of high-ordered nodes (optional, -o2 switch);
-
- typedef REAL **tetrahedron;
-
- // The shellface data structure. Fields of a shellface contains:
- // - a list of three adjoining subfaces;
- // - a list of three vertices;
- // - a list of two adjoining tetrahedra;
- // - a list of three adjoining subsegments;
- // - a pointer to a badface containing it (used for -q);
- // - an area constraint (optional, used for -q);
- // - an integer for boundary marker;
- // - an integer for type: SHARPSEGMENT, NONSHARPSEGMENT, ...;
- // - an integer for pbc group (optional, if in->pbcgrouplist exists);
-
- typedef REAL **shellface;
-
- // The point data structure. It is actually an array of REALs:
- // - x, y and z coordinates;
- // - a list of user-defined point attributes (optional);
- // - a list of REALs of a user-defined metric tensor (optional);
- // - a pointer to a simplex (tet, tri, edge, or vertex);
- // - a pointer to a parent (or duplicate) point;
- // - a pointer to a tet in background mesh (optional);
- // - a pointer to another pbc point (optional);
- // - an integer for boundary marker;
- // - an integer for verttype: INPUTVERTEX, FREEVERTEX, ...;
-
- typedef REAL *point;
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// The mesh handle (triface, face) data types //
-// //
-// Two special data types, 'triface' and 'face' are defined for maintaining //
-// and updating meshes. They are like pointers (or handles), which allow you //
-// to hold one particular part of the mesh, i.e., a tetrahedron, a triangle, //
-// an edge and a vertex. However, these data types do not themselves store //
-// any part of the mesh. The mesh is made of the data types defined above. //
-// //
-// Muecke's "triangle-edge" data structure is the prototype for these data //
-// types. It allows a universal representation for every tetrahedron, //
-// triangle, edge and vertex. For understanding the following descriptions //
-// of these handle data structures, readers are required to read both the //
-// introduction and implementation detail of "triangle-edge" data structure //
-// in Muecke's thesis. //
-// //
-// A 'triface' represents a face of a tetrahedron and an oriented edge of //
-// the face simultaneously. It has a pointer 'tet' to a tetrahedron, an //
-// integer 'loc' (range from 0 to 3) as the face index, and an integer 'ver' //
-// (range from 0 to 5) as the edge version. A face of the tetrahedron can be //
-// uniquly determined by the pair (tet, loc), and an oriented edge of this //
-// face can be uniquly determined by the triple (tet, loc, ver). Therefore, //
-// different usages of one triface are possible. If we only use the pair //
-// (tet, loc), it refers to a face, and if we add the 'ver' additionally to //
-// the pair, it is an oriented edge of this face. //
-// //
-// A 'face' represents a subface and an oriented edge of it simultaneously. //
-// It has a pointer 'sh' to a subface, an integer 'shver'(range from 0 to 5) //
-// as the edge version. The pair (sh, shver) determines a unique oriented //
-// edge of this subface. A 'face' is also used to represent a subsegment, //
-// in this case, 'sh' points to the subsegment, and 'shver' indicates the //
-// one of two orientations of this subsegment, hence, it only can be 0 or 1. //
-// //
-// Mesh navigation and updating are accomplished through a set of mesh //
-// manipulation primitives which operate on trifaces and faces. They are //
-// introduced below. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
- class triface {
-
- public:
-
- tetrahedron* tet;
- int loc, ver;
-
- // Constructors;
- triface() : tet(0), loc(0), ver(0) {}
- // Operators;
- triface& operator=(const triface& t) {
- tet = t.tet; loc = t.loc; ver = t.ver;
- return *this;
- }
- bool operator==(triface& t) {
- return tet == t.tet && loc == t.loc && ver == t.ver;
- }
- bool operator!=(triface& t) {
- return tet != t.tet || loc != t.loc || ver != t.ver;
- }
- };
-
- class face {
-
- public:
-
- shellface *sh;
- int shver;
-
- // Constructors;
- face() : sh(0), shver(0) {}
- // Operators;
- face& operator=(const face& s) {
- sh = s.sh; shver = s.shver;
- return *this;
- }
- bool operator==(face& s) {return (sh == s.sh) && (shver == s.shver);}
- bool operator!=(face& s) {return (sh != s.sh) || (shver != s.shver);}
- };
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// The badface structure //
-// //
-// A multiple usages structure. Despite of its name, a 'badface' can be used //
-// to represent the following objects: //
-// - a face of a tetrahedron which is (possibly) non-Delaunay; //
-// - an encroached subsegment or subface; //
-// - a bad-quality tetrahedron, i.e, has too large radius-edge ratio; //
-// - a sliver, i.e., has good radius-edge ratio but nearly zero volume; //
-// - a degenerate tetrahedron (see routine checkdegetet()). //
-// - a recently flipped face (saved for undoing the flip later). //
-// //
-// It has the following fields: 'tt' holds a tetrahedron; 'ss' holds a sub- //
-// segment or subface; 'cent' is the circumcent of 'tt' or 'ss', 'key' is a //
-// special value depending on the use, it can be either the square of the //
-// radius-edge ratio of 'tt' or the flipped type of 'tt'; 'forg', 'fdest', //
-// 'fapex', and 'foppo' are vertices saved for checking the object in 'tt' //
-// or 'ss' is still the same when it was stored; 'noppo' is the fifth vertex //
-// of a degenerate point set. 'previtem' and 'nextitem' implement a double //
-// link for managing many basfaces. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
- struct badface {
- triface tt;
- face ss;
- REAL key;
- REAL cent[3];
- point forg, fdest, fapex, foppo;
- point noppo;
- struct badface *previtem, *nextitem;
- };
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// The pbcdata structure //
-// //
-// A pbcdata stores data of a periodic boundary condition defined on a pair //
-// of facets or segments. Let f1 and f2 define a pbcgroup. 'fmark' saves the //
-// facet markers of f1 and f2; 'ss' contains two subfaces belong to f1 and //
-// f2, respectively. Let s1 and s2 define a segment pbcgroup. 'segid' are //
-// the segment ids of s1 and s2; 'ss' contains two segments belong to s1 and //
-// s2, respectively. 'transmat' are two transformation matrices. transmat[0] //
-// transforms a point of f1 (or s1) into a point of f2 (or s2), transmat[1] //
-// does the inverse. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
- struct pbcdata {
- int fmark[2];
- int segid[2];
- face ss[2];
- REAL transmat[2][4][4];
- };
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// The list, link and queue data structures //
-// //
-// These data types are used to manipulate a set of (same-typed) data items. //
-// For a given set S = {a, b, c, ...}, a list stores the elements of S in a //
-// piece of continuous memory. It allows quickly accessing each element of S,//
-// thus is suitable for storing a fix-sized set. While a link stores its //
-// elements incontinuously. It allows quickly inserting or deleting an item, //
-// thus is suitable for storing a size-variable set. A queue is basically a //
-// special case of a link where one data element joins the link at the end //
-// and leaves in an ordered fashion at the other end. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
- // The compfunc data type. "compfunc" is a pointer to a linear-order
- // function, which takes two 'void*' arguments and returning an 'int'.
- //
- // A function: int cmp(const T &, const T &), is said to realize a
- // linear order on the type T if there is a linear order <= on T such
- // that for all x and y in T satisfy the following relation:
- // -1 if x < y.
- // comp(x, y) = 0 if x is equivalent to y.
- // +1 if x > y.
- typedef int (*compfunc) (const void *, const void *);
-
- // The predefined compare functions for primitive data types. They
- // take two pointers of the corresponding date type, perform the
- // comparation, and return -1, 0 or 1 indicating the default linear
- // order of them.
- static int compare_2_ints(const void* x, const void* y);
- static int compare_2_longs(const void* x, const void* y);
- static int compare_2_unsignedlongs(const void* x, const void* y);
-
- // The function used to determine the size of primitive data types and
- // set the corresponding predefined linear order functions for them.
- static void set_compfunc(char* str, int* itembytes, compfunc* pcomp);
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// List data structure. //
-// //
-// A 'list' is an array of items with automatically reallocation of memory. //
-// It behaves like an array. //
-// //
-// 'base' is the starting address of the array; The memory unit in list is //
-// byte, i.e., sizeof(char). 'itembytes' is the size of each item in byte, //
-// so that the next item in list will be found at the next 'itembytes' //
-// counted from the current position. //
-// //
-// 'items' is the number of items stored in list. 'maxitems' indicates how //
-// many items can be stored in this list. 'expandsize' is the increasing //
-// size (items) when the list is full. //
-// //
-// 'comp' is a pointer pointing to a linear order function for the list. //
-// default it is set to 'NULL'. //
-// //
-// The index of list always starts from zero, i.e., for a list L contains //
-// n elements, the first element is L[0], and the last element is L[n-1]. //
-// This feature lets lists like C/C++ arrays. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
- class list {
-
- public:
-
- char *base;
- int itembytes;
- int items, maxitems, expandsize;
- compfunc comp;
-
- public:
-
- list(int itbytes, compfunc pcomp, int mitems = 256, int exsize = 128) {
- listinit(itbytes, pcomp, mitems, exsize);
- }
- list(char* str, int mitems = 256, int exsize = 128) {
- set_compfunc(str, &itembytes, &comp);
- listinit(itembytes, comp, mitems, exsize);
- }
- ~list() { free(base); }
-
- void *operator[](int i) { return (void *) (base + i * itembytes); }
-
- void listinit(int itbytes, compfunc pcomp, int mitems, int exsize);
- void setcomp(compfunc compf) { comp = compf; }
- void clear() { items = 0; }
- int len() { return items; }
- void *append(void* appitem);
- void *insert(int pos, void* insitem);
- void del(int pos, int order);
- int hasitem(void* checkitem);
- void sort();
- };
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// Memorypool data structure. //
-// //
-// A type used to allocate memory. (It is incorporated from Shewchuk's //
-// Triangle program) //
-// //
-// firstblock is the first block of items. nowblock is the block from which //
-// items are currently being allocated. nextitem points to the next slab //
-// of free memory for an item. deaditemstack is the head of a linked list //
-// (stack) of deallocated items that can be recycled. unallocateditems is //
-// the number of items that remain to be allocated from nowblock. //
-// //
-// Traversal is the process of walking through the entire list of items, and //
-// is separate from allocation. Note that a traversal will visit items on //
-// the "deaditemstack" stack as well as live items. pathblock points to //
-// the block currently being traversed. pathitem points to the next item //
-// to be traversed. pathitemsleft is the number of items that remain to //
-// be traversed in pathblock. //
-// //
-// itemwordtype is set to POINTER or FLOATINGPOINT, and is used to suggest //
-// what sort of word the record is primarily made up of. alignbytes //
-// determines how new records should be aligned in memory. itembytes and //
-// itemwords are the length of a record in bytes (after rounding up) and //
-// words. itemsperblock is the number of items allocated at once in a //
-// single block. items is the number of currently allocated items. //
-// maxitems is the maximum number of items that have been allocated at //
-// once; it is the current number of items plus the number of records kept //
-// on deaditemstack. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
- class memorypool {
-
- public:
-
- void **firstblock, **nowblock;
- void *nextitem;
- void *deaditemstack;
- void **pathblock;
- void *pathitem;
- wordtype itemwordtype;
- int alignbytes;
- int itembytes, itemwords;
- int itemsperblock;
- long items, maxitems;
- int unallocateditems;
- int pathitemsleft;
-
- public:
-
- memorypool();
- memorypool(int, int, enum wordtype, int);
- ~memorypool();
-
- void poolinit(int, int, enum wordtype, int);
- void restart();
- void *alloc();
- void dealloc(void*);
- void traversalinit();
- void *traverse();
- };
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// Link data structure. //
-// //
-// A 'link' is a double linked nodes. It uses the memorypool data structure //
-// for memory management. Following is an image of a link. //
-// //
-// head-> ____0____ ____1____ ____2____ _________<-tail //
-// |__next___|--> |__next___|--> |__next___|--> |__NULL___| //
-// |__NULL___|<-- |__prev___|<-- |__prev___|<-- |__prev___| //
-// | | |_ _| |_ _| | | //
-// | | |_ Data1 _| |_ Data2 _| | | //
-// |_________| |_________| |_________| |_________| //
-// //
-// The unit size for storage is size of pointer, which may be 4-byte (in 32- //
-// bit machine) or 8-byte (in 64-bit machine). The real size of an item is //
-// stored in 'linkitembytes'. //
-// //
-// 'head' and 'tail' are pointers pointing to the first and last nodes. They //
-// do not conatin data (See above). //
-// //
-// 'nextlinkitem' is a pointer pointing to a node which is the next one will //
-// be traversed. 'curpos' remembers the position (1-based) of the current //
-// traversing node. //
-// //
-// 'linkitems' indicates how many items in link. Note it is different with //
-// 'items' of memorypool. //
-// //
-// The index of link starts from 1, i.e., for a link K contains n elements, //
-// the first element of the link is K[1], and the last element is K[n]. //
-// See the above figure. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
- class link : public memorypool {
-
- public:
-
- void **head, **tail;
- void *nextlinkitem;
- int linkitembytes;
- int linkitems;
- int curpos;
- compfunc comp;
-
- public:
-
- link(int _itembytes, compfunc _comp, int itemcount) {
- linkinit(_itembytes, _comp, itemcount);
- }
- link(char* str, int itemcount) {
- set_compfunc(str, &linkitembytes, &comp);
- linkinit(linkitembytes, comp, itemcount);
- }
-
- void linkinit(int _itembytes, compfunc _comp, int itemcount);
- void setcomp(compfunc compf) { comp = compf; }
- void rewind() { nextlinkitem = *head; curpos = 1; }
- void goend() { nextlinkitem = *(tail + 1); curpos = linkitems; }
- long len() { return linkitems; }
- void clear();
- bool move(int numberofnodes);
- bool locate(int pos);
- void *add(void* newitem);
- void *insert(int pos, void* insitem);
- void *deletenode(void** delnode);
- void *del(int pos);
- void *getitem();
- void *getnitem(int pos);
- int hasitem(void* checkitem);
- };
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// Queue data structure. //
-// //
-// A 'queue' is basically a link. Following is an image of a queue. //
-// ___________ ___________ ___________ //
-// Pop() <-- |_ _|<--|_ _|<--|_ _| <-- Push() //
-// |_ Data0 _| |_ Data1 _| |_ Data2 _| //
-// |___________| |___________| |___________| //
-// queue head queue tail //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
- class queue : public link {
-
- public:
-
- queue(int bytes, int count = 256) : link(bytes, NULL, count) {}
- bool empty() { return linkitems == 0; }
- void *push(void* newitem) {return link::add(newitem);}
- void *pop() {return link::deletenode((void **) *head);}
- // Stack is implemented as a single link list.
- void *stackpush() {
- void **newnode = (void **) alloc();
- // if (newitem != (void *) NULL) {
- // memcpy((void *)(newnode + 2), newitem, linkitembytes);
- // }
- void **nextnode = (void **) *head;
- *head = (void *) newnode;
- *newnode = (void *) nextnode;
- linkitems++;
- return (void *)(newnode + 2);
- }
- void *stackpop() {
- void **deadnode = (void **) *head;
- *head = *deadnode;
- linkitems--;
- return (void *)(deadnode + 2);
- }
- };
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// Global variables used for miscellaneous purposes. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
- // Pointer to the input data (a set of nodes, a PLC, or a mesh).
- tetgenio *in;
- // Pointer to the options (and filenames).
- tetgenbehavior *b;
- // Pointer to a background mesh (contains size specification map).
- tetgenmesh *bgm;
-
- // Variables used to allocate and access memory for tetrahedra, subfaces
- // subsegments, points, encroached subfaces, encroached subsegments,
- // bad-quality tetrahedra, and so on.
- memorypool *tetrahedrons;
- memorypool *subfaces;
- memorypool *subsegs;
- memorypool *points;
- memorypool *badsubsegs;
- memorypool *badsubfaces;
- memorypool *badtetrahedrons;
- memorypool *flipstackers;
-
- // Pointer to the 'tetrahedron' that occupies all of "outer space".
- tetrahedron *dummytet;
- tetrahedron *dummytetbase; // Keep base address so we can free it later.
-
- // Pointer to the omnipresent subface. Referenced by any tetrahedron,
- // or subface that isn't connected to a subface at that location.
- shellface *dummysh;
- shellface *dummyshbase; // Keep base address so we can free it later.
-
- // A point above the plane in which the facet currently being used lies.
- // It is used as a reference point for orient3d().
- point *facetabovepointarray, abovepoint;
-
- // Array (size = numberoftetrahedra * 6) for storing high-order nodes of
- // tetrahedra (only used when -o2 switch is selected).
- point *highordertable;
-
- // Arrays for storing and searching pbc data. 'subpbcgrouptable', (size
- // is numberofpbcgroups) for pbcgroup of subfaces. 'segpbcgrouptable',
- // a list for pbcgroup of segments. Because a segment can have several
- // pbcgroup incident on it, its size is unknown on input, it will be
- // found in 'createsegpbcgrouptable()'.
- pbcdata *subpbcgrouptable;
- list *segpbcgrouptable;
- // A map for searching the pbcgroups of a given segment. 'idx2segpglist'
- // (size = number of input segments + 1), and 'segpglist'.
- int *idx2segpglist, *segpglist;
-
- // Queues that maintain the bad (badly-shaped or too large) tetrahedra.
- // The tails are pointers to the pointers that have to be filled in to
- // enqueue an item. The queues are ordered from 63 (highest priority)
- // to 0 (lowest priority).
- badface *subquefront[3], **subquetail[3];
- badface *tetquefront[64], *tetquetail[64];
- int nextnonemptyq[64];
- int firstnonemptyq, recentq;
-
- // Pointer to a recently visited tetrahedron. Improves point location
- // if proximate points are inserted sequentially.
- triface recenttet;
-
- REAL xmax, xmin, ymax, ymin, zmax, zmin; // Bounding box of points.
- REAL longest; // The longest possible edge length.
- REAL lengthlimit; // The limiting length of a new edge.
- long hullsize; // Number of faces of convex hull.
- long insegments; // Number of input segments.
- int steinerleft; // Number of Steiner points not yet used.
- int sizeoftensor; // Number of REALs per metric tensor.
- int pointmtrindex; // Index to find the metric tensor of a point.
- int point2simindex; // Index to find a simplex adjacent to a point.
- int pointmarkindex; // Index to find boundary marker of a point.
- int point2pbcptindex; // Index to find a pbc point to a point.
- int highorderindex; // Index to find extra nodes for highorder elements.
- int elemattribindex; // Index to find attributes of a tetrahedron.
- int volumeboundindex; // Index to find volume bound of a tetrahedron.
- int elemmarkerindex; // Index to find marker of a tetrahedron.
- int shmarkindex; // Index to find boundary marker of a subface.
- int areaboundindex; // Index to find area bound of a subface.
- int checksubfaces; // Are there subfaces in the mesh yet?
- int checksubsegs; // Are there subsegs in the mesh yet?
- int checkpbcs; // Are there periodic boundary conditions?
- int varconstraint; // Are there variant (node, seg, facet) constraints?
- int nonconvex; // Is current mesh non-convex?
- int dupverts; // Are there duplicated vertices?
- int unuverts; // Are there unused vertices?
- int relverts; // The number of relocated vertices.
- int suprelverts; // The number of suppressed relocated vertices.
- int collapverts; // The number of collapsed relocated vertices.
- int unsupverts; // The number of unsuppressed vertices.
- int smoothsegverts; // The number of smoothed vertices.
- int smoothvolverts; // The number of smoothed vertices.
- int jettisoninverts; // The number of jettisoned input vertices.
- int symbolic; // Use symbolic insphere test.
- long samples; // Number of random samples for point location.
- unsigned long randomseed; // Current random number seed.
- REAL macheps; // The machine epsilon.
- REAL cosmaxdihed, cosmindihed; // The cosine values of max/min dihedral.
- REAL minfaceang, minfacetdihed; // The minimum input (dihedral) angles.
- int maxcavfaces, maxcavverts; // The size of the largest cavity.
- int expcavcount; // The times of expanding cavitys.
- long abovecount; // Number of abovepoints calculation.
- long bowatvolcount, bowatsubcount, bowatsegcount; // Bowyer-Watsons.
- long updvolcount, updsubcount, updsegcount; // Bow-Wat cavities updates.
- long failvolcount, failsubcount, failsegcount; // Bow-Wat fails.
- long repairflipcount; // Number of flips for repairing segments.
- long outbowatcircumcount; // Number of circumcenters outside Bowat-cav.
- long r1count, r2count, r3count; // Numbers of edge splitting rules.
- long cdtenforcesegpts; // Number of CDT enforcement points.
- long rejsegpts, rejsubpts, rejtetpts; // Number of rejected points.
- long optcount[10]; // Numbers of various optimizing operations.
- long flip23s, flip32s, flip22s, flip44s; // Number of flips performed.
- REAL tloctime, tfliptime; // Time (microseconds) of point location.
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// Fast lookup tables for mesh manipulation primitives. //
-// //
-// Mesh manipulation primitives (given below) are basic operations on mesh //
-// data structures. They answer basic queries on mesh handles, such as "what //
-// is the origin (or destination, or apex) of the face?", "what is the next //
-// (or previous) edge in the edge ring?", and "what is the next face in the //
-// face ring?", and so on. //
-// //
-// The implementation of teste basic queries can take advangtage of the fact //
-// that the mesh data structures additionally store geometric informations. //
-// For example, we have ordered the 4 vertices (from 0 to 3) and the 4 faces //
-// (from 0 to 3) of a tetrahedron, and for each face of the tetrahedron, a //
-// sequence of vertices has stipulated, therefore the origin of any face of //
-// the tetrahedron can be quickly determined by a table 'locver2org', which //
-// takes the index of the face and the edge version as inputs. A list of //
-// fast lookup tables are defined below. They're just like global variables. //
-// These tables are initialized at the runtime. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
- // For enext() primitive, uses 'ver' as the index.
- static int ve[6];
-
- // For org(), dest() and apex() primitives, uses 'ver' as the index.
- static int vo[6], vd[6], va[6];
-
- // For org(), dest() and apex() primitives, uses 'loc' as the first
- // index and 'ver' as the second index.
- static int locver2org[4][6];
- static int locver2dest[4][6];
- static int locver2apex[4][6];
-
- // For oppo() primitives, uses 'loc' as the index.
- static int loc2oppo[4];
-
- // For fnext() primitives, uses 'loc' as the first index and 'ver' as
- // the second index, returns an array containing a new 'loc' and a
- // new 'ver'. Note: Only valid for 'ver' equals one of {0, 2, 4}.
- static int locver2nextf[4][6][2];
-
- // The edge number (from 0 to 5) of a tet is defined as follows:
- static int locver2edge[4][6];
- static int edge2locver[6][2];
-
- // For enumerating three edges of a triangle.
- static int plus1mod3[3];
- static int minus1mod3[3];
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// Mesh manipulation primitives //
-// //
-// A serial of mesh operations such as topological maintenance, navigation, //
-// local modification, etc., is accomplished through a set of mesh manipul- //
-// ation primitives. These primitives are indeed very simple functions which //
-// take one or two handles ('triface's and 'face's) as parameters, perform //
-// basic operations such as "glue two tetrahedra at a face", "return the //
-// origin of a tetrahedron", "return the subface adjoining at the face of a //
-// tetrahedron", and so on. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
- // Primitives for tetrahedra.
- inline void decode(tetrahedron ptr, triface& t);
- inline tetrahedron encode(triface& t);
- inline void sym(triface& t1, triface& t2);
- inline void symself(triface& t);
- inline void bond(triface& t1, triface& t2);
- inline void dissolve(triface& t);
- inline point org(triface& t);
- inline point dest(triface& t);
- inline point apex(triface& t);
- inline point oppo(triface& t);
- inline void setorg(triface& t, point pointptr);
- inline void setdest(triface& t, point pointptr);
- inline void setapex(triface& t, point pointptr);
- inline void setoppo(triface& t, point pointptr);
- inline void esym(triface& t1, triface& t2);
- inline void esymself(triface& t);
- inline void enext(triface& t1, triface& t2);
- inline void enextself(triface& t);
- inline void enext2(triface& t1, triface& t2);
- inline void enext2self(triface& t);
- inline bool fnext(triface& t1, triface& t2);
- inline bool fnextself(triface& t);
- inline void enextfnext(triface& t1, triface& t2);
- inline void enextfnextself(triface& t);
- inline void enext2fnext(triface& t1, triface& t2);
- inline void enext2fnextself(triface& t);
- inline void infect(triface& t);
- inline void uninfect(triface& t);
- inline bool infected(triface& t);
- inline REAL elemattribute(tetrahedron* ptr, int attnum);
- inline void setelemattribute(tetrahedron* ptr, int attnum, REAL value);
- inline REAL volumebound(tetrahedron* ptr);
- inline void setvolumebound(tetrahedron* ptr, REAL value);
-
- // Primitives for subfaces and subsegments.
- inline void sdecode(shellface sptr, face& s);
- inline shellface sencode(face& s);
- inline void spivot(face& s1, face& s2);
- inline void spivotself(face& s);
- inline void sbond(face& s1, face& s2);
- inline void sbond1(face& s1, face& s2);
- inline void sdissolve(face& s);
- inline point sorg(face& s);
- inline point sdest(face& s);
- inline point sapex(face& s);
- inline void setsorg(face& s, point pointptr);
- inline void setsdest(face& s, point pointptr);
- inline void setsapex(face& s, point pointptr);
- inline void sesym(face& s1, face& s2);
- inline void sesymself(face& s);
- inline void senext(face& s1, face& s2);
- inline void senextself(face& s);
- inline void senext2(face& s1, face& s2);
- inline void senext2self(face& s);
- inline void sfnext(face&, face&);
- inline void sfnextself(face&);
- inline badface* shell2badface(face& s);
- inline void setshell2badface(face& s, badface* value);
- inline REAL areabound(face& s);
- inline void setareabound(face& s, REAL value);
- inline int shellmark(face& s);
- inline void setshellmark(face& s, int value);
- inline enum shestype shelltype(face& s);
- inline void setshelltype(face& s, enum shestype value);
- inline int shellpbcgroup(face& s);
- inline void setshellpbcgroup(face& s, int value);
- inline void sinfect(face& s);
- inline void suninfect(face& s);
- inline bool sinfected(face& s);
-
- // Primitives for interacting tetrahedra and subfaces.
- inline void tspivot(triface& t, face& s);
- inline void stpivot(face& s, triface& t);
- inline void tsbond(triface& t, face& s);
- inline void tsdissolve(triface& t);
- inline void stdissolve(face& s);
-
- // Primitives for interacting subfaces and subsegs.
- inline void sspivot(face& s, face& edge);
- inline void ssbond(face& s, face& edge);
- inline void ssdissolve(face& s);
-
- inline void tsspivot1(triface& t, face& seg);
- inline void tssbond1(triface& t, face& seg);
- inline void tssdissolve1(triface& t);
-
- // Primitives for points.
- inline int pointmark(point pt);
- inline void setpointmark(point pt, int value);
- inline enum verttype pointtype(point pt);
- inline void setpointtype(point pt, enum verttype value);
- inline tetrahedron point2tet(point pt);
- inline void setpoint2tet(point pt, tetrahedron value);
- inline shellface point2sh(point pt);
- inline void setpoint2sh(point pt, shellface value);
- inline point point2ppt(point pt);
- inline void setpoint2ppt(point pt, point value);
- inline tetrahedron point2bgmtet(point pt);
- inline void setpoint2bgmtet(point pt, tetrahedron value);
- inline point point2pbcpt(point pt);
- inline void setpoint2pbcpt(point pt, point value);
-
- // Advanced primitives.
- inline void adjustedgering(triface& t, int direction);
- inline void adjustedgering(face& s, int direction);
- inline bool isdead(triface* t);
- inline bool isdead(face* s);
- inline bool isfacehaspoint(triface* t, point testpoint);
- inline bool isfacehaspoint(face* t, point testpoint);
- inline bool isfacehasedge(face* s, point tend1, point tend2);
- inline bool issymexist(triface* t);
- void getnextsface(face*, face*);
- void tsspivot(triface*, face*);
- void sstpivot(face*, triface*);
- bool findorg(triface* t, point dorg);
- bool findorg(face* s, point dorg);
- void findedge(triface* t, point eorg, point edest);
- void findedge(face* s, point eorg, point edest);
- void findface(triface *fface, point forg, point fdest, point fapex);
- void getonextseg(face* s, face* lseg);
- void getseghasorg(face* sseg, point dorg);
- point getsubsegfarorg(face* sseg);
- point getsubsegfardest(face* sseg);
- void printtet(triface*);
- void printsh(face*);
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// Triangle-triangle intersection test //
-// //
-// The triangle-triangle intersection test is implemented with exact arithm- //
-// etic. It exactly tells whether or not two triangles in three dimensions //
-// intersect. Before implementing this test myself, I tried two C codes //
-// (implemented by Thomas Moeller and Philippe Guigue, respectively), which //
-// are all public available. However both of them failed frequently. Another //
-// unconvenience is both codes only tell whether or not the two triangles //
-// intersect without distinguishing the cases whether they exactly intersect //
-// in interior or they just share a vertex or share an edge. The two latter //
-// cases are acceptable and should return not intersection in TetGen. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
- enum interresult edge_vert_col_inter(REAL*, REAL*, REAL*);
- enum interresult edge_edge_cop_inter(REAL*, REAL*, REAL*, REAL*, REAL*);
- enum interresult tri_vert_cop_inter(REAL*, REAL*, REAL*, REAL*, REAL*);
- enum interresult tri_edge_cop_inter(REAL*, REAL*, REAL*,REAL*,REAL*,REAL*);
- enum interresult tri_edge_inter_tail(REAL*, REAL*, REAL*, REAL*, REAL*,
- REAL, REAL);
- enum interresult tri_edge_inter(REAL*, REAL*, REAL*, REAL*, REAL*);
- enum interresult tri_tri_inter(REAL*, REAL*, REAL*, REAL*, REAL*, REAL*);
-
- // Geometric predicates
- REAL insphere_sos(REAL*, REAL*, REAL*, REAL*, REAL*, int, int,int,int,int);
- bool iscollinear(REAL*, REAL*, REAL*, REAL eps);
- bool iscoplanar(REAL*, REAL*, REAL*, REAL*, REAL vol6, REAL eps);
- bool iscospheric(REAL*, REAL*, REAL*, REAL*, REAL*, REAL vol24, REAL eps);
-
- // Linear algebra functions
- inline REAL dot(REAL* v1, REAL* v2);
- inline void cross(REAL* v1, REAL* v2, REAL* n);
- bool lu_decmp(REAL lu[4][4], int n, int* ps, REAL* d, int N);
- void lu_solve(REAL lu[4][4], int n, int* ps, REAL* b, int N);
-
- // Geometric quantities calculators.
- inline REAL distance(REAL* p1, REAL* p2);
- REAL shortdistance(REAL* p, REAL* e1, REAL* e2);
- REAL shortdistance(REAL* p, REAL* e1, REAL* e2, REAL* e3);
- REAL interiorangle(REAL* o, REAL* p1, REAL* p2, REAL* n);
- void projpt2edge(REAL* p, REAL* e1, REAL* e2, REAL* prj);
- void projpt2face(REAL* p, REAL* f1, REAL* f2, REAL* f3, REAL* prj);
- void facenormal(REAL* pa, REAL* pb, REAL* pc, REAL* n, REAL* nlen);
- void edgeorthonormal(REAL* e1, REAL* e2, REAL* op, REAL* n);
- REAL facedihedral(REAL* pa, REAL* pb, REAL* pc1, REAL* pc2);
- void tetalldihedral(point, point, point, point, REAL*, REAL*, REAL*);
- void tetallnormal(point, point, point, point, REAL N[4][3], REAL* volume);
- REAL tetaspectratio(point, point, point, point);
- bool circumsphere(REAL*, REAL*, REAL*, REAL*, REAL* cent, REAL* radius);
- void inscribedsphere(REAL*, REAL*, REAL*, REAL*, REAL* cent, REAL* radius);
- void rotatepoint(REAL* p, REAL rotangle, REAL* p1, REAL* p2);
- void spherelineint(REAL* p1, REAL* p2, REAL* C, REAL R, REAL p[7]);
- void linelineint(REAL *p1,REAL *p2, REAL *p3, REAL *p4, REAL p[7]);
- void planelineint(REAL*, REAL*, REAL*, REAL*, REAL*, REAL*, REAL*);
-
- // Memory managment routines.
- void dummyinit(int, int);
- void initializepools();
- void tetrahedrondealloc(tetrahedron*);
- tetrahedron *tetrahedrontraverse();
- void shellfacedealloc(memorypool*, shellface*);
- shellface *shellfacetraverse(memorypool*);
- void badfacedealloc(memorypool*, badface*);
- badface *badfacetraverse(memorypool*);
- void pointdealloc(point);
- point pointtraverse();
- void maketetrahedron(triface*);
- void makeshellface(memorypool*, face*);
- void makepoint(point*);
-
- // Mesh items searching routines.
- void makepoint2tetmap();
- void makeindex2pointmap(point*& idx2verlist);
- void makesegmentmap(int*& idx2seglist, shellface**& segsperverlist);
- void makesubfacemap(int*& idx2facelist, shellface**& facesperverlist);
- void maketetrahedronmap(int*& idx2tetlist, tetrahedron**& tetsperverlist);
-
- // Point location routines.
- unsigned long randomnation(unsigned int choices);
- REAL distance2(tetrahedron* tetptr, point p);
- enum locateresult preciselocate(point searchpt, triface* searchtet, long);
- enum locateresult locate(point searchpt, triface* searchtet);
- enum locateresult adjustlocate(point, triface*, enum locateresult, REAL);
- enum locateresult hullwalk(point searchpt, triface* hulltet);
- enum locateresult locatesub(point searchpt, face* searchsh, int, REAL);
- enum locateresult adjustlocatesub(point, face*, enum locateresult, REAL);
- enum locateresult locateseg(point searchpt, face* searchseg);
- enum locateresult adjustlocateseg(point, face*, enum locateresult, REAL);
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// Mesh Local Transformation Operators //
-// //
-// These operators (including flips, insert & remove vertices and so on) are //
-// used to transform (or replace) a set of mesh elements into another set of //
-// mesh elements. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
- // Mesh transformation routines.
- enum fliptype categorizeface(triface& horiz);
- void enqueueflipface(triface& checkface, queue* flipqueue);
- void enqueueflipedge(face& checkedge, queue* flipqueue);
- void flip23(triface* flipface, queue* flipqueue);
- void flip32(triface* flipface, queue* flipqueue);
- void flip22(triface* flipface, queue* flipqueue);
- void flip22sub(face* flipedge, queue* flipqueue);
- long flip(queue* flipqueue, badface **plastflip);
- long lawson(list *misseglist, queue* flipqueue);
- void undoflip(badface *lastflip);
- long flipsub(queue* flipqueue);
- bool removetetbypeeloff(triface *striptet);
- bool removefacebyflip23(REAL *key, triface*, triface*, queue*);
- bool removeedgebyflip22(REAL *key, int, triface*, queue*);
- bool removeedgebyflip32(REAL *key, triface*, triface*, queue*);
- bool removeedgebytranNM(REAL*,int,triface*,triface*,point,point,queue*);
- bool removeedgebycombNM(REAL*,int,triface*,int*,triface*,triface*,queue*);
-
- void splittetrahedron(point newpoint, triface* splittet, queue* flipqueue);
- void unsplittetrahedron(triface* splittet);
- void splittetface(point newpoint, triface* splittet, queue* flipqueue);
- void unsplittetface(triface* splittet);
- void splitsubface(point newpoint, face* splitface, queue* flipqueue);
- void unsplitsubface(face* splitsh);
- void splittetedge(point newpoint, triface* splittet, queue* flipqueue);
- void unsplittetedge(triface* splittet);
- void splitsubedge(point newpoint, face* splitsh, queue* flipqueue);
- void unsplitsubedge(face* splitsh);
- enum insertsiteresult insertsite(point newpoint, triface* searchtet,
- bool approx, queue* flipqueue);
- void undosite(enum insertsiteresult insresult, triface* splittet,
- point torg, point tdest, point tapex, point toppo);
- void closeopenface(triface* openface, queue* flipque);
- void inserthullsite(point inspoint, triface* horiz, queue* flipque);
-
- void formbowatcavitysub(point, face*, list*, list*);
- void formbowatcavityquad(point, list*, list*);
- void formbowatcavitysegquad(point, list*, list*);
- void formbowatcavity(point bp, face* bpseg, face* bpsh, int* n, int* nmax,
- list** sublists, list** subceillists, list** tetlists,
- list** ceillists);
- void releasebowatcavity(face*, int, list**, list**, list**, list**);
- bool validatebowatcavityquad(point bp, list* ceillist, REAL maxcosd);
- void updatebowatcavityquad(list* tetlist, list* ceillist);
- void updatebowatcavitysub(list* sublist, list* subceillist, int* cutcount);
- bool trimbowatcavity(point bp, face* bpseg, int n, list** sublists,
- list** subceillists, list** tetlists,list** ceillists,
- REAL maxcosd);
- void bowatinsertsite(point bp, face* splitseg, int n, list** sublists,
- list** subceillists, list** tetlists,
- list** ceillists, list* verlist, queue* flipque,
- bool chkencseg, bool chkencsub, bool chkbadtet);
-
- // Delaunay tetrahedralization routines.
- void formstarpolyhedron(point pt, list* tetlist, list* verlist, bool);
- bool unifypoint(point testpt, triface*, enum locateresult, REAL);
- void incrflipdelaunay(triface*, point*, long, bool, bool, REAL, queue*);
- long delaunizevertices();
-
- // Surface triangulation routines.
- void formstarpolygon(point pt, list* trilist, list* verlist);
- void getfacetabovepoint(face* facetsh);
- void collectcavsubs(point newpoint, list* cavsublist);
- void collectvisiblesubs(int shmark, point inspoint, face* horiz, queue*);
- void incrflipdelaunaysub(int shmark, REAL eps, list*, int, REAL*, queue*);
- enum finddirectionresult finddirectionsub(face* searchsh, point tend);
- void insertsubseg(face* tri);
- bool scoutsegmentsub(face* searchsh, point tend);
- void flipedgerecursive(face* flipedge, queue* flipqueue);
- void constrainededge(face* startsh, point tend, queue* flipqueue);
- void recoversegment(point tstart, point tend, queue* flipqueue);
- void infecthullsub(memorypool* viri);
- void plaguesub(memorypool* viri);
- void carveholessub(int holes, REAL* holelist, memorypool* viri);
- void triangulate(int shmark, REAL eps, list* ptlist, list* conlist,
- int holes, REAL* holelist, memorypool* viri, queue*);
- void retrievenewsubs(list* newshlist, bool removeseg);
- void unifysegments();
- void mergefacets(queue* flipqueue);
- long meshsurface();
-
- // Detect intersecting facets of PLC.
- void interecursive(shellface** subfacearray, int arraysize, int axis,
- REAL bxmin, REAL bxmax, REAL bymin, REAL bymax,
- REAL bzmin, REAL bzmax, int* internum);
- void detectinterfaces();
-
- // Periodic boundary condition supporting routines.
- void createsubpbcgrouptable();
- void getsubpbcgroup(face* pbcsub, pbcdata** pd, int *f1, int *f2);
- enum locateresult getsubpbcsympoint(point, face*, point, face*);
- void createsegpbcgrouptable();
- enum locateresult getsegpbcsympoint(point, face*, point, face*, int);
-
- // Vertex perturbation routines.
- REAL randgenerator(REAL range);
- bool checksub4cocir(face* testsub, REAL eps, bool once, bool enqflag);
- void tallcocirsubs(REAL eps, bool enqflag);
- bool tallencsegsfsubs(point testpt, list* cavsublist);
- void collectflipedges(point inspoint, face* splitseg, queue* flipqueue);
- void perturbrepairencsegs(queue* flipqueue);
- void perturbrepairencsubs(list* cavsublist, queue* flipqueue);
- void incrperturbvertices(REAL eps);
-
- // Segment recovery routines.
- void markacutevertices(REAL acuteangle);
- enum finddirectionresult finddirection(triface* searchtet, point, long);
- void getsearchtet(point p1, point p2, triface* searchtet, point* tend);
- bool isedgeencroached(point p1, point p2, point testpt, bool degflag);
- point scoutrefpoint(triface* searchtet, point tend);
- point getsegmentorigin(face* splitseg);
- point getsplitpoint(face* splitseg, point refpoint);
- bool insertsegment(face *insseg, list *misseglist);
- void tallmissegs(list *misseglist);
- void delaunizesegments();
-
- // Facets recovery routines.
- bool insertsubface(face* insertsh, triface* searchtet);
- bool tritritest(triface* checktet, point p1, point p2, point p3);
- void initializecavity(list* floorlist, list* ceillist, list* frontlist);
- void delaunizecavvertices(triface*, list*, list*, list*, queue*);
- void retrievenewtets(list* newtetlist);
- void insertauxsubface(triface* front, triface* idfront);
- bool scoutfront(triface* front, triface* idfront, list* newtetlist);
- void gluefronts(triface* front, triface* front1);
- bool identifyfronts(list* frontlist, list* misfrontlist, list* newtetlist);
- void detachauxsubfaces(list* newtetlist);
- void expandcavity(list* frontlist, list* misfrontlist, list* newtetlist,
- list* crosstetlist, queue* missingshqueue, queue*);
- void carvecavity(list* newtetlist, list* outtetlist, queue* flipque);
- void delaunizecavity(list* floorlist, list* ceillist, list* ceilptlist,
- list* floorptlist, list* frontlist,list* misfrontlist,
- list* newtetlist, list* crosstetlist, queue*, queue*);
- void formmissingregion(face* missingsh, list* missingshlist,
- list* equatptlist, int* worklist);
- void formcavity(list* missingshlist, list* crossedgelist,
- list* equatptlist, list* crossshlist, list* crosstetlist,
- list* belowfacelist, list* abovefacelist,
- list* horizptlist, list* belowptlist, list* aboveptlist,
- queue* missingshqueue, int* worklist);
- bool scoutcrossingedge(list* missingshlist, list* boundedgelist,
- list* crossedgelist, int* worklist);
- void rearrangesubfaces(list* missingshlist, list* boundedgelist,
- list* equatptlist, int* worklist);
- void insertallsubfaces(queue* missingshqueue);
- void constrainedfacets();
-
- // Carving out holes and concavities routines.
- void infecthull(memorypool *viri);
- void plague(memorypool *viri);
- void regionplague(memorypool *viri, REAL attribute, REAL volume);
- void removeholetets(memorypool *viri);
- void assignregionattribs();
- void carveholes();
-
- // Steiner points removing routines.
- void replacepolygonsubs(list* oldshlist, list* newshlist);
- void orientnewsubs(list* newshlist, face* orientsh, REAL* norm);
- bool constrainedflip(triface* flipface, triface* front, queue* flipque);
- bool recoverfront(triface* front, list* newtetlist, queue* flipque);
- void repairflips(queue* flipque);
- bool constrainedcavity(triface* oldtet, list* floorlist, list* ceillist,
- list* ptlist, list* frontlist, list* misfrontlist,
- list* newtetlist, queue* flipque);
- void expandsteinercavity(point steinpt, REAL eps, list* frontlist, list*);
- bool findrelocatepoint(point sp, point np, REAL* n, list*, list*);
- void relocatepoint(point steinpt, triface* oldtet, list*, list*, queue*);
- bool findcollapseedge(point suppt, point* conpt, list* oldtetlist, list*);
- void collapseedge(point suppt, point conpt, list* oldtetlist, list*);
- void deallocfaketets(list* frontlist);
- void restorepolyhedron(list* oldtetlist);
- bool suppressfacetpoint(face* supsh, list* frontlist, list* misfrontlist,
- list* ptlist, list* conlist, memorypool* viri,
- queue* flipque, bool noreloc, bool optflag);
- bool suppresssegpoint(face* supseg, list* spinshlist, list* newsegshlist,
- list* frontlist, list* misfrontlist, list* ptlist,
- list* conlist, memorypool* viri, queue* flipque,
- bool noreloc, bool optflag);
- bool suppressvolpoint(triface* suptet, list* frontlist, list* misfrontlist,
- list* ptlist, queue* flipque, bool optflag);
- bool smoothpoint(point smthpt, point, point, list *starlist, bool, REAL*);
- void removesteiners(bool coarseflag);
-
- // Mesh reconstruction routines.
- long reconstructmesh();
- // Constrained points insertion routines.
- void insertconstrainedpoints(tetgenio *addio);
- // Background mesh operations.
- bool p1interpolatebgm(point pt, triface* bgmtet, long *scount);
- void interpolatesizemap();
- void duplicatebgmesh();
-
- // Delaunay refinement routines.
- void marksharpsegments(REAL sharpangle);
- void decidefeaturepointsizes();
- void enqueueencsub(face* ss, point encpt, int quenumber, REAL* cent);
- badface* dequeueencsub(int* quenumber);
- void enqueuebadtet(triface* tt, REAL key, REAL* cent);
- badface* topbadtetra();
- void dequeuebadtet();
- bool checkseg4encroach(face* testseg, point testpt, point*, bool enqflag);
- bool checksub4encroach(face* testsub, point testpt, bool enqflag);
- bool checktet4badqual(triface* testtet, bool enqflag);
- bool acceptsegpt(point segpt, point refpt, face* splitseg);
- bool acceptfacpt(point facpt, list* subceillist, list* verlist);
- bool acceptvolpt(point volpt, list* ceillist, list* verlist);
- void getsplitpoint(point e1, point e2, point refpt, point newpt);
- void shepardinterpolate(point newpt, list* verlist);
- void setnewpointsize(point newpt, point e1, point e2);
- void splitencseg(point, face*, list*, list*, list*,queue*,bool,bool,bool);
- bool tallencsegs(point testpt, int n, list** ceillists);
- bool tallencsubs(point testpt, int n, list** ceillists);
- void tallbadtetrahedrons();
- void repairencsegs(bool chkencsub, bool chkbadtet);
- void repairencsubs(bool chkbadtet);
- void repairbadtets();
- void enforcequality();
-
- // Mesh optimization routines.
- void dumpbadtets();
- bool checktet4ill(triface* testtet, bool enqflag);
- bool checktet4opt(triface* testtet, bool enqflag);
- bool removeedge(badface* remedge, bool optflag);
- bool smoothsliver(badface* remedge, list *starlist);
- bool splitsliver(badface* remedge, list *tetlist, list *ceillist);
- void tallslivers(bool optflag);
- void optimizemesh(bool optflag);
-
- // I/O routines
- void transfernodes();
- void jettisonnodes();
- void highorder();
- void outnodes(tetgenio* out);
- void outmetrics(tetgenio* out);
- void outelements(tetgenio* out);
- void outfaces(tetgenio* out);
- void outhullfaces(tetgenio* out);
- void outsubfaces(tetgenio* out);
- void outedges(tetgenio* out);
- void outsubsegments(tetgenio* out);
- void outneighbors(tetgenio* out);
- void outvoronoi(tetgenio* out);
- void outpbcnodes(tetgenio* out);
- void outsmesh(char* smfilename);
- void outmesh2medit(char* mfilename);
- void outmesh2gid(char* gfilename);
- void outmesh2off(char* ofilename);
-
- // User interaction routines.
- void internalerror();
- void checkmesh();
- void checkshells();
- void checkdelaunay(REAL eps, queue* flipqueue);
- void checkconforming();
- void algorithmicstatistics();
- void qualitystatistics();
- void statistics();
-
- public:
-
- // Constructor and destructor.
- tetgenmesh();
- ~tetgenmesh();
-
-}; // End of class tetgenmesh.
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// tetrahedralize() Interface for using TetGen's library to generate //
-// Delaunay tetrahedralizations, constrained Delaunay //
-// tetrahedralizations, quality tetrahedral meshes. //
-// //
-// 'in' is an object of 'tetgenio' which contains a PLC you want to tetrahed-//
-// ralize or a previously generated tetrahedral mesh you want to refine. It //
-// must not be a NULL. 'out' is another object of 'tetgenio' for storing the //
-// generated tetrahedral mesh. It can be a NULL. If so, the output will be //
-// saved to file(s). If 'bgmin' != NULL, it contains a background mesh which //
-// defines a mesh size distruction function. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetrahedralize(tetgenbehavior *b, tetgenio *in, tetgenio *out,
- tetgenio *addin = NULL, tetgenio *bgmin = NULL);
-void tetrahedralize(char *switches, tetgenio *in, tetgenio *out,
- tetgenio *addin = NULL, tetgenio *bgmin = NULL);
-
-#endif // #ifndef tetgenH