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/*****************************************************************************/
/* */
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/* "8oo8D */
/* */
/* A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator. */
/* (triangle.c) */
/* */
/* Version 1.6 */
/* July 28, 2005 */
/* */
/* Copyright 1993, 1995, 1997, 1998, 2002, 2005 */
/* Jonathan Richard Shewchuk */
/* 2360 Woolsey #H */
/* Berkeley, California 94705-1927 */
/* jrs@cs.berkeley.edu */
/* */
/* This program may be freely redistributed under the condition that the */
/* copyright notices (including this entire header and the copyright */
/* notice printed when the `-h' switch is selected) are not removed, and */
/* no compensation is received. Private, research, and institutional */
/* use is free. You may distribute modified versions of this code UNDER */
/* THE CONDITION THAT THIS CODE AND ANY MODIFICATIONS MADE TO IT IN THE */
/* SAME FILE 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 as */
/* part of a commercial system is permissible ONLY BY DIRECT ARRANGEMENT */
/* WITH THE AUTHOR. (If you are not directly supplying this code to a */
/* customer, and you are instead telling them how they can obtain it for */
/* free, then you are not required to make any arrangement with me.) */
/* */
/* Hypertext instructions for Triangle are available on the Web at */
/* */
/* http://www.cs.cmu.edu/~quake/triangle.html */
/* */
/* Disclaimer: Neither I nor Carnegie Mellon warrant this code in any way */
/* whatsoever. This code is provided "as-is". Use at your own risk. */
/* */
/* Some of the references listed below are marked with an asterisk. [*] */
/* These references are available for downloading from the Web page */
/* */
/* http://www.cs.cmu.edu/~quake/triangle.research.html */
/* */
/* Three papers discussing aspects of Triangle are available. A short */
/* overview appears in "Triangle: Engineering a 2D Quality Mesh */
/* Generator and Delaunay Triangulator," in Applied Computational */
/* Geometry: Towards Geometric Engineering, Ming C. Lin and Dinesh */
/* Manocha, editors, Lecture Notes in Computer Science volume 1148, */
/* pages 203-222, Springer-Verlag, Berlin, May 1996 (from the First ACM */
/* Workshop on Applied Computational Geometry). [*] */
/* */
/* The algorithms are discussed in the greatest detail in "Delaunay */
/* Refinement Algorithms for Triangular Mesh Generation," Computational */
/* Geometry: Theory and Applications 22(1-3):21-74, May 2002. [*] */
/* */
/* More detail about the data structures may be found in my dissertation: */
/* "Delaunay Refinement Mesh Generation," Ph.D. thesis, Technical Report */
/* CMU-CS-97-137, School of Computer Science, Carnegie Mellon University, */
/* Pittsburgh, Pennsylvania, 18 May 1997. [*] */
/* */
/* Triangle was created as part of the Quake Project in the School of */
/* Computer Science at Carnegie Mellon University. For further */
/* information, see Hesheng Bao, Jacobo Bielak, Omar Ghattas, Loukas F. */
/* Kallivokas, David R. O'Hallaron, Jonathan R. Shewchuk, and Jifeng Xu, */
/* "Large-scale Simulation of Elastic Wave Propagation in Heterogeneous *//* Media on Parallel Computers," Computer Methods in Applied Mechanics */
/* and Engineering 152(1-2):85-102, 22 January 1998. */
/* */
/* Triangle's Delaunay refinement algorithm for quality mesh generation is */
/* a hybrid of one due to Jim Ruppert, "A Delaunay Refinement Algorithm */
/* for Quality 2-Dimensional Mesh Generation," Journal of Algorithms */
/* 18(3):548-585, May 1995 [*], and one due to L. Paul Chew, "Guaranteed- */
/* Quality Mesh Generation for Curved Surfaces," Proceedings of the Ninth */
/* Annual Symposium on Computational Geometry (San Diego, California), */
/* pages 274-280, Association for Computing Machinery, May 1993, */
/* http://portal.acm.org/citation.cfm?id=161150 . */
/* */
/* The Delaunay refinement algorithm has been modified so that it meshes */
/* domains with small input angles well, as described in Gary L. Miller, */
/* Steven E. Pav, and Noel J. Walkington, "When and Why Ruppert's */
/* Algorithm Works," Twelfth International Meshing Roundtable, pages */
/* 91-102, Sandia National Laboratories, September 2003. [*] */
/* */
/* My implementation of the divide-and-conquer and incremental Delaunay */
/* triangulation algorithms follows closely the presentation of Guibas */
/* and Stolfi, even though I use a triangle-based data structure instead */
/* of their quad-edge data structure. (In fact, I originally implemented */
/* Triangle using the quad-edge data structure, but the switch to a */
/* triangle-based data structure sped Triangle by a factor of two.) The */
/* mesh manipulation primitives and the two aforementioned Delaunay */
/* triangulation algorithms are described by Leonidas J. Guibas and Jorge */
/* Stolfi, "Primitives for the Manipulation of General Subdivisions and */
/* the Computation of Voronoi Diagrams," ACM Transactions on Graphics */
/* 4(2):74-123, April 1985, http://portal.acm.org/citation.cfm?id=282923 .*/
/* */
/* Their O(n log n) divide-and-conquer algorithm is adapted from Der-Tsai */
/* Lee and Bruce J. Schachter, "Two Algorithms for Constructing the */
/* Delaunay Triangulation," International Journal of Computer and */
/* Information Science 9(3):219-242, 1980. Triangle's improvement of the */
/* divide-and-conquer algorithm by alternating between vertical and */
/* horizontal cuts was introduced by Rex A. Dwyer, "A Faster Divide-and- */
/* Conquer Algorithm for Constructing Delaunay Triangulations," */
/* Algorithmica 2(2):137-151, 1987. */
/* */
/* The incremental insertion algorithm was first proposed by C. L. Lawson, */
/* "Software for C1 Surface Interpolation," in Mathematical Software III, */
/* John R. Rice, editor, Academic Press, New York, pp. 161-194, 1977. */
/* For point location, I use the algorithm of Ernst P. Mucke, Isaac */
/* Saias, and Binhai Zhu, "Fast Randomized Point Location Without */
/* Preprocessing in Two- and Three-Dimensional Delaunay Triangulations," */
/* Proceedings of the Twelfth Annual Symposium on Computational Geometry, */
/* ACM, May 1996. [*] If I were to randomize the order of vertex */
/* insertion (I currently don't bother), their result combined with the */
/* result of Kenneth L. Clarkson and Peter W. Shor, "Applications of */
/* Random Sampling in Computational Geometry II," Discrete & */
/* Computational Geometry 4(1):387-421, 1989, would yield an expected */
/* O(n^{4/3}) bound on running time. */
/* */
/* The O(n log n) sweepline Delaunay triangulation algorithm is taken from */
/* Steven Fortune, "A Sweepline Algorithm for Voronoi Diagrams", */
/* Algorithmica 2(2):153-174, 1987. A random sample of edges on the */
/* boundary of the triangulation are maintained in a splay tree for the */
/* purpose of point location. Splay trees are described by Daniel */
/* Dominic Sleator and Robert Endre Tarjan, "Self-Adjusting Binary Search */
/* Trees," Journal of the ACM 32(3):652-686, July 1985, */
/* http://portal.acm.org/citation.cfm?id=3835 . */
/* */
/* The algorithms for exact computation of the signs of determinants are */
/* described in Jonathan Richard Shewchuk, "Adaptive Precision Floating- */
/* Point Arithmetic and Fast Robust Geometric Predicates," Discrete & */
/* Computational Geometry 18(3):305-363, October 1997. (Also available */
/* as Technical Report CMU-CS-96-140, School of Computer Science, */
/* Carnegie Mellon University, Pittsburgh, Pennsylvania, May 1996.) [*] */
/* An abbreviated version appears as Jonathan Richard Shewchuk, "Robust */
/* Adaptive Floating-Point Geometric Predicates," Proceedings of the *//* Twelfth Annual Symposium on Computational Geometry, ACM, May 1996. [*] */
/* Many of the ideas for my exact arithmetic routines originate with */
/* Douglas M. Priest, "Algorithms for Arbitrary Precision Floating Point */
/* Arithmetic," Tenth Symposium on Computer Arithmetic, pp. 132-143, IEEE */
/* Computer Society Press, 1991. [*] Many of the ideas for the correct */
/* evaluation of the signs of determinants are taken from Steven Fortune */
/* and Christopher J. Van Wyk, "Efficient Exact Arithmetic for Computa- */
/* tional Geometry," Proceedings of the Ninth Annual Symposium on */
/* Computational Geometry, ACM, pp. 163-172, May 1993, and from Steven */
/* Fortune, "Numerical Stability of Algorithms for 2D Delaunay Triangu- */
/* lations," International Journal of Computational Geometry & Applica- */
/* tions 5(1-2):193-213, March-June 1995. */
/* */
/* The method of inserting new vertices off-center (not precisely at the */
/* circumcenter of every poor-quality triangle) is from Alper Ungor, */
/* "Off-centers: A New Type of Steiner Points for Computing Size-Optimal */
/* Quality-Guaranteed Delaunay Triangulations," Proceedings of LATIN */
/* 2004 (Buenos Aires, Argentina), April 2004. */
/* */
/* For definitions of and results involving Delaunay triangulations, */
/* constrained and conforming versions thereof, and other aspects of */
/* triangular mesh generation, see the excellent survey by Marshall Bern */
/* and David Eppstein, "Mesh Generation and Optimal Triangulation," in */
/* Computing and Euclidean Geometry, Ding-Zhu Du and Frank Hwang, */
/* editors, World Scientific, Singapore, pp. 23-90, 1992. [*] */
/* */
/* The time for incrementally adding PSLG (planar straight line graph) */
/* segments to create a constrained Delaunay triangulation is probably */
/* O(t^2) per segment in the worst case and O(t) per segment in the */
/* common case, where t is the number of triangles that intersect the */
/* segment before it is inserted. This doesn't count point location, */
/* which can be much more expensive. I could improve this to O(d log d) */
/* time, but d is usually quite small, so it's not worth the bother. */
/* (This note does not apply when the -s switch is used, invoking a */
/* different method is used to insert segments.) */
/* */
/* The time for deleting a vertex from a Delaunay triangulation is O(d^2) */
/* in the worst case and O(d) in the common case, where d is the degree */
/* of the vertex being deleted. I could improve this to O(d log d) time, */
/* but d is usually quite small, so it's not worth the bother. */
/* */
/* Ruppert's Delaunay refinement algorithm typically generates triangles */
/* at a linear rate (constant time per triangle) after the initial */
/* triangulation is formed. There may be pathological cases where */
/* quadratic time is required, but these never arise in practice. */
/* */
/* The geometric predicates (circumcenter calculations, segment */
/* intersection formulae, etc.) appear in my "Lecture Notes on Geometric */
/* Robustness" at http://www.cs.berkeley.edu/~jrs/mesh . */
/* */
/* If you make any improvements to this code, please please please let me */
/* know, so that I may obtain the improvements. Even if you don't change */
/* the code, I'd still love to hear what it's being used for. */
/* */
/*****************************************************************************/
/* 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. */
/* */
/* Double precision uses more memory, but improves the resolution of the */
/* meshes you can generate with Triangle. It also reduces the likelihood */
/* of a floating exception due to overflow. Finally, it is much faster */
/* than single precision on 64-bit architectures like the DEC Alpha. I */
/* recommend double precision unless you want to generate a mesh for which */
/* you do not have enough memory. */
/* #define SINGLE */
#ifdef SINGLE
#define REAL float
#else /* not SINGLE */
#define REAL double
#endif /* not SINGLE */
/* If yours is not a Unix system, define the NO_TIMER compiler switch to */
/* remove the Unix-specific timing code. */
/* #define NO_TIMER */
/* To insert lots of self-checks for internal errors, define the SELF_CHECK */
/* symbol. This will slow down the program significantly. It is best to */
/* define the symbol using the -DSELF_CHECK compiler switch, but you could */
/* write "#define SELF_CHECK" below. If you are modifying this code, I */
/* recommend you turn self-checks on until your work is debugged. */
/* #define SELF_CHECK */
/* To compile Triangle as a callable object library (triangle.o), define the */
/* TRILIBRARY symbol. Read the file triangle.h for details on how to call */
/* the procedure triangulate() that results. */
/* #define TRILIBRARY */
/* It is possible to generate a smaller version of Triangle using one or */
/* both of the following symbols. Define the REDUCED symbol to eliminate */
/* all features that are primarily of research interest; specifically, the */
/* -i, -F, -s, and -C switches. Define the CDT_ONLY symbol to eliminate */
/* all meshing algorithms above and beyond constrained Delaunay */
/* triangulation; specifically, the -r, -q, -a, -u, -D, -S, and -s */
/* switches. These reductions are most likely to be useful when */
/* generating an object library (triangle.o) by defining the TRILIBRARY */
/* symbol. */
/* #define REDUCED */
/* #define CDT_ONLY */
/* On some machines, my exact arithmetic routines might be defeated by the */
/* use of internal extended precision floating-point registers. The best */
/* way to solve this problem is to set the floating-point registers to use */
/* single or double precision internally. On 80x86 processors, this may */
/* be accomplished by setting the CPU86 symbol for the Microsoft C */
/* compiler, or the LINUX symbol for the gcc compiler running on Linux. */
/* */
/* An inferior solution is to declare certain values as `volatile', thus */
/* forcing them to be stored to memory and rounded off. Unfortunately, */
/* this solution might slow Triangle down quite a bit. To use volatile */
/* values, write "#define INEXACT volatile" below. Normally, however, */
/* INEXACT should be defined to be nothing. ("#define INEXACT".) */
/* */
/* For more discussion, see http://www.cs.cmu.edu/~quake/robust.pc.html . */
/* For yet more discussion, see Section 5 of my paper, "Adaptive Precision */
/* Floating-Point Arithmetic and Fast Robust Geometric Predicates" (also */
/* available as Section 6.6 of my dissertation). */
/* #define CPU86 */
/* #define LINUX */
#define INEXACT /* Nothing */
/* #define INEXACT volatile */
/* Maximum number of characters in a file name (including the null). */
#define FILENAMESIZE 2048
/* Maximum number of characters in a line read from a file (including the */
/* null). */
#define INPUTLINESIZE 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. */
#define TRIPERBLOCK 4092 /* Number of triangles allocated at once. */
#define SUBSEGPERBLOCK 508 /* Number of subsegments allocated at once. */
#define VERTEXPERBLOCK 4092 /* Number of vertices allocated at once. */
#define VIRUSPERBLOCK 1020 /* Number of virus triangles allocated at once. */
/* Number of encroached subsegments allocated at once. */
#define BADSUBSEGPERBLOCK 252
/* Number of skinny triangles allocated at once. */
#define BADTRIPERBLOCK 4092
/* Number of flipped triangles allocated at once. */
#define FLIPSTACKERPERBLOCK 252
/* Number of splay tree nodes allocated at once. */
#define SPLAYNODEPERBLOCK 508
/* The vertex types. A DEADVERTEX has been deleted entirely. An */
/* UNDEADVERTEX is not part of the mesh, but is written to the output */
/* .node file and affects the node indexing in the other output files. */
#define INPUTVERTEX 0
#define SEGMENTVERTEX 1
#define FREEVERTEX 2
#define DEADVERTEX -32768
#define UNDEADVERTEX -32767
/* The next line is used to outsmart some very stupid compilers. If your */
/* compiler is smarter, feel free to replace the "int" with "void". */
/* Not that it matters. */
#define VOID int
/* Two constants for algorithms based on random sampling. Both constants */
/* have been chosen empirically to optimize their respective algorithms. */
/* Used for the point location scheme of Mucke, Saias, and Zhu, to decide */
/* how large a random sample of triangles to inspect. */
#define SAMPLEFACTOR 11
/* Used in Fortune's sweepline Delaunay algorithm to determine what fraction */
/* of boundary edges should be maintained in the splay tree for point */
/* location on the front. */
#define SAMPLERATE 10
/* A number that speaks for itself, every kissable digit. */
#define PI 3.141592653589793238462643383279502884197169399375105820974944592308
/* Another fave. */
#define SQUAREROOTTWO 1.4142135623730950488016887242096980785696718753769480732
/* And here's one for those of you who are intimidated by math. */
#define ONETHIRD 0.333333333333333333333333333333333333333333333333333333333333
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#ifndef NO_TIMER
#include <sys/time.h>
#endif /* not NO_TIMER */
#ifdef CPU86#include <float.h>
#endif /* CPU86 */
#ifdef LINUX
#include <fpu_control.h>
#endif /* LINUX */
#ifdef TRILIBRARY
#include "triangle.h"
#endif /* TRILIBRARY */
/* A few forward declarations. */
#ifndef TRILIBRARY
char *readline();
char *findfield();
#endif /* not TRILIBRARY */
/* Labels that signify the result of point location. The result of a */
/* search indicates that the point falls in the interior of a triangle, on */
/* an edge, on a vertex, or outside the mesh. */
enum locateresult {INTRIANGLE, 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 insertvertexresult {SUCCESSFULVERTEX, ENCROACHINGVERTEX, VIOLATINGVERTEX,
DUPLICATEVERTEX};
/* Labels that signify the result of direction finding. The result */
/* indicates that a segment connecting the two query points falls within */
/* the direction triangle, along the left edge of the direction triangle, */
/* or along the right edge of the direction triangle. */
enum finddirectionresult {WITHIN, LEFTCOLLINEAR, RIGHTCOLLINEAR};
/*****************************************************************************/
/* */
/* The basic mesh data structures */
/* */
/* There are three: vertices, triangles, and subsegments (abbreviated */
/* `subseg'). These three data structures, linked by pointers, comprise */
/* the mesh. A vertex simply represents a mesh vertex and its properties. */
/* A triangle is a triangle. A subsegment is a special data structure used */
/* to represent an impenetrable edge of the mesh (perhaps on the outer */
/* boundary, on the boundary of a hole, or part of an internal boundary */
/* separating two triangulated regions). Subsegments represent boundaries, */
/* defined by the user, that triangles may not lie across. */
/* */
/* A triangle consists of a list of three vertices, a list of three */
/* adjoining triangles, a list of three adjoining subsegments (when */
/* segments exist), an arbitrary number of optional user-defined */
/* floating-point attributes, and an optional area constraint. The latter */
/* is an upper bound on the permissible area of each triangle in a region, */
/* used for mesh refinement. */
/* */
/* For a triangle on a boundary of the mesh, some or all of the neighboring */
/* triangles may not be present. For a triangle in the interior of the */
/* mesh, often no neighboring subsegments are present. Such absent */
/* triangles and subsegments are never represented by NULL pointers; they */
/* are represented by two special records: `dummytri', the triangle that */
/* fills "outer space", and `dummysub', the omnipresent subsegment. */
/* `dummytri' and `dummysub' are used for several reasons; for instance, */
/* they can be dereferenced and their contents examined without violating */
/* protected memory. */
/* */
/* However, it is important to understand that a triangle includes other */
/* information as well. The pointers to adjoining vertices, triangles, and *//* subsegments are ordered in a way that indicates their geometric relation */
/* to each other. Furthermore, each of these pointers contains orientation */
/* information. Each pointer to an adjoining triangle indicates which face */
/* of that triangle is contacted. Similarly, each pointer to an adjoining */
/* subsegment indicates which side of that subsegment is contacted, and how */
/* the subsegment is oriented relative to the triangle. */
/* */
/* The data structure representing a subsegment may be thought to be */
/* abutting the edge of one or two triangle data structures: either */
/* sandwiched between two triangles, or resting against one triangle on an */
/* exterior boundary or hole boundary. */
/* */
/* A subsegment consists of a list of four vertices--the vertices of the */
/* subsegment, and the vertices of the segment it is a part of--a list of */
/* two adjoining subsegments, and a list of two adjoining triangles. One */
/* of the two adjoining triangles may not be present (though there should */
/* always be one), and neighboring subsegments might not be present. */
/* Subsegments also store a user-defined integer "boundary marker". */
/* Typically, this integer is used to indicate what boundary conditions are */
/* to be applied at that location in a finite element simulation. */
/* */
/* Like triangles, subsegments maintain information about the relative */
/* orientation of neighboring objects. */
/* */
/* Vertices are relatively simple. A vertex is a list of floating-point */
/* numbers, starting with the x, and y coordinates, followed by an */
/* arbitrary number of optional user-defined floating-point attributes, */
/* followed by an integer boundary marker. During the segment insertion */
/* phase, there is also a pointer from each vertex to a triangle that may */
/* contain it. Each pointer is not always correct, but when one is, it */
/* speeds up segment insertion. These pointers are assigned values once */
/* at the beginning of the segment insertion phase, and are not used or */
/* updated except during this phase. Edge flipping during segment */
/* insertion will render some of them incorrect. Hence, don't rely upon */
/* them for anything. */
/* */
/* Other than the exception mentioned above, vertices have no information */
/* about what triangles, subfacets, or subsegments they are linked to. */
/* */
/*****************************************************************************/
/*****************************************************************************/
/* */
/* Handles */
/* */
/* The oriented triangle (`otri') and oriented subsegment (`osub') data */
/* structures defined below do not themselves store any part of the mesh. */
/* The mesh itself is made of `triangle's, `subseg's, and `vertex's. */
/* */
/* Oriented triangles and oriented subsegments will usually be referred to */
/* as "handles." A handle is essentially a pointer into the mesh; it */
/* allows you to "hold" one particular part of the mesh. Handles are used */
/* to specify the regions in which one is traversing and modifying the mesh.*/
/* A single `triangle' may be held by many handles, or none at all. (The */
/* latter case is not a memory leak, because the triangle is still */
/* connected to other triangles in the mesh.) */
/* */
/* An `otri' is a handle that holds a triangle. It holds a specific edge */
/* of the triangle. An `osub' is a handle that holds a subsegment. It */
/* holds either the left or right side of the subsegment. */
/* */
/* Navigation about the mesh is accomplished through a set of mesh */
/* manipulation primitives, further below. Many of these primitives take */
/* a handle and produce a new handle that holds the mesh near the first */
/* handle. Other primitives take two handles and glue the corresponding */
/* parts of the mesh together. The orientation of the handles is */
/* important. For instance, when two triangles are glued together by the */
/* bond() primitive, they are glued at the edges on which the handles lie. */
/* */
/* Because vertices have no information about which triangles they are *//* attached to, I commonly represent a vertex by use of a handle whose */
/* origin is the vertex. A single handle can simultaneously represent a */
/* triangle, an edge, and a vertex. */
/* */
/*****************************************************************************/
/* The triangle data structure. Each triangle contains three pointers to */
/* adjoining triangles, plus three pointers to vertices, plus three */
/* pointers to subsegments (declared below; these pointers are usually */
/* `dummysub'). It may or may not also contain user-defined attributes */
/* and/or a floating-point "area constraint." It may also contain extra */
/* pointers for nodes, when the user asks for high-order elements. */
/* Because the size and structure of a `triangle' is not decided until */
/* runtime, I haven't simply declared the type `triangle' as a struct. */
typedef REAL **triangle; /* Really: typedef triangle *triangle */
/* An oriented triangle: includes a pointer to a triangle and orientation. */
/* The orientation denotes an edge of the triangle. Hence, there are */
/* three possible orientations. By convention, each edge always points */
/* counterclockwise about the corresponding triangle. */
struct otri {
triangle *tri;
int orient; /* Ranges from 0 to 2. */
};
/* The subsegment data structure. Each subsegment contains two pointers to */
/* adjoining subsegments, plus four pointers to vertices, plus two */
/* pointers to adjoining triangles, plus one boundary marker, plus one */
/* segment number. */
typedef REAL **subseg; /* Really: typedef subseg *subseg */
/* An oriented subsegment: includes a pointer to a subsegment and an */
/* orientation. The orientation denotes a side of the edge. Hence, there */
/* are two possible orientations. By convention, the edge is always */
/* directed so that the "side" denoted is the right side of the edge. */
struct osub {
subseg *ss;
int ssorient; /* Ranges from 0 to 1. */
};
/* The vertex data structure. Each vertex is actually an array of REALs. */
/* The number of REALs is unknown until runtime. An integer boundary */
/* marker, and sometimes a pointer to a triangle, is appended after the */
/* REALs. */
typedef REAL *vertex;
/* A queue used to store encroached subsegments. Each subsegment's vertices */
/* are stored so that we can check whether a subsegment is still the same. */
struct badsubseg {
subseg encsubseg; /* An encroached subsegment. */
vertex subsegorg, subsegdest; /* Its two vertices. */
};
/* A queue used to store bad triangles. The key is the square of the cosine */
/* of the smallest angle of the triangle. Each triangle's vertices are */
/* stored so that one can check whether a triangle is still the same. */
struct badtriang {
triangle poortri; /* A skinny or too-large triangle. */
REAL key; /* cos^2 of smallest (apical) angle. */
vertex triangorg, triangdest, triangapex; /* Its three vertices. */
struct badtriang *nexttriang; /* Pointer to next bad triangle. */
};
/* A stack of triangles flipped during the most recent vertex insertion. */
/* The stack is used to undo the vertex insertion if the vertex encroaches */
/* upon a subsegment. */
struct flipstacker {
triangle flippedtri; /* A recently flipped triangle. */
struct flipstacker *prevflip; /* Previous flip in the stack. */
};
/* A node in a heap used to store events for the sweepline Delaunay */
/* algorithm. Nodes do not point directly to their parents or children in */
/* the heap. Instead, each node knows its position in the heap, and can */
/* look up its parent and children in a separate array. The `eventptr' */
/* points either to a `vertex' or to a triangle (in encoded format, so */
/* that an orientation is included). In the latter case, the origin of */
/* the oriented triangle is the apex of a "circle event" of the sweepline */
/* algorithm. To distinguish site events from circle events, all circle */
/* events are given an invalid (smaller than `xmin') x-coordinate `xkey'. */
struct event {
REAL xkey, ykey; /* Coordinates of the event. */
VOID *eventptr; /* Can be a vertex or the location of a circle event. */
int heapposition; /* Marks this event's position in the heap. */
};
/* A node in the splay tree. Each node holds an oriented ghost triangle */
/* that represents a boundary edge of the growing triangulation. When a */
/* circle event covers two boundary edges with a triangle, so that they */
/* are no longer boundary edges, those edges are not immediately deleted */
/* from the tree; rather, they are lazily deleted when they are next */
/* encountered. (Since only a random sample of boundary edges are kept */
/* in the tree, lazy deletion is faster.) `keydest' is used to verify */
/* that a triangle is still the same as when it entered the splay tree; if */
/* it has been rotated (due to a circle event), it no longer represents a */
/* boundary edge and should be deleted. */
struct splaynode {
struct otri keyedge; /* Lprev of an edge on the front. */
vertex keydest; /* Used to verify that splay node is still live. */
struct splaynode *lchild, *rchild; /* Children in splay tree. */
};
/* A type used to allocate memory. 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. */
/* */
/* alignbytes determines how new records should be aligned in memory. */
/* itembytes is the length of a record in bytes (after rounding up). */
/* itemsperblock is the number of items allocated at once in a single */
/* block. itemsfirstblock is the number of items in the first block, */
/* which can vary from the others. 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. */
struct memorypool {
VOID **firstblock, **nowblock;
VOID *nextitem;
VOID *deaditemstack;
VOID **pathblock; VOID *pathitem;
int alignbytes;
int itembytes;
int itemsperblock;
int itemsfirstblock;
long items, maxitems;
int unallocateditems;
int pathitemsleft;
};
/* Global constants. */
REAL splitter; /* Used to split REAL factors for exact multiplication. */
REAL epsilon; /* Floating-point machine epsilon. */
REAL resulterrbound;
REAL ccwerrboundA, ccwerrboundB, ccwerrboundC;
REAL iccerrboundA, iccerrboundB, iccerrboundC;
REAL o3derrboundA, o3derrboundB, o3derrboundC;
/* Random number seed is not constant, but I've made it global anyway. */
unsigned long randomseed; /* Current random number seed. */
/* Mesh data structure. Triangle operates on only one mesh, but the mesh */
/* structure is used (instead of global variables) to allow reentrancy. */
struct mesh {
/* Variables used to allocate memory for triangles, subsegments, vertices, */
/* viri (triangles being eaten), encroached segments, bad (skinny or too */
/* large) triangles, and splay tree nodes. */
struct memorypool triangles;
struct memorypool subsegs;
struct memorypool vertices;
struct memorypool viri;
struct memorypool badsubsegs;
struct memorypool badtriangles;
struct memorypool flipstackers;
struct memorypool splaynodes;
/* Variables that maintain the bad triangle queues. The queues are */
/* ordered from 4095 (highest priority) to 0 (lowest priority). */
struct badtriang *queuefront[4096];
struct badtriang *queuetail[4096];
int nextnonemptyq[4096];
int firstnonemptyq;
/* Variable that maintains the stack of recently flipped triangles. */
struct flipstacker *lastflip;
/* Other variables. */
REAL xmin, xmax, ymin, ymax; /* x and y bounds. */
REAL xminextreme; /* Nonexistent x value used as a flag in sweepline. */
int invertices; /* Number of input vertices. */
int inelements; /* Number of input triangles. */
int insegments; /* Number of input segments. */
int holes; /* Number of input holes. */
int regions; /* Number of input regions. */
int undeads; /* Number of input vertices that don't appear in the mesh. */
long edges; /* Number of output edges. */
int mesh_dim; /* Dimension (ought to be 2). */
int nextras; /* Number of attributes per vertex. */
int eextras; /* Number of attributes per triangle. */
long hullsize; /* Number of edges in convex hull. */ int steinerleft; /* Number of Steiner points not yet used. */
int vertexmarkindex; /* Index to find boundary marker of a vertex. */
int vertex2triindex; /* Index to find a triangle adjacent to a vertex. */
int highorderindex; /* Index to find extra nodes for high-order elements. */
int elemattribindex; /* Index to find attributes of a triangle. */
int areaboundindex; /* Index to find area bound of a triangle. */
int checksegments; /* Are there segments in the triangulation yet? */
int checkquality; /* Has quality triangulation begun yet? */
int readnodefile; /* Has a .node file been read? */
long samples; /* Number of random samples for point location. */
long incirclecount; /* Number of incircle tests performed. */
long counterclockcount; /* Number of counterclockwise tests performed. */
long orient3dcount; /* Number of 3D orientation tests performed. */
long hyperbolacount; /* Number of right-of-hyperbola tests performed. */
long circumcentercount; /* Number of circumcenter calculations performed. */
long circletopcount; /* Number of circle top calculations performed. */
/* Triangular bounding box vertices. */
vertex infvertex1, infvertex2, infvertex3;
/* Pointer to the `triangle' that occupies all of "outer space." */
triangle *dummytri;
triangle *dummytribase; /* Keep base address so we can free() it later. */
/* Pointer to the omnipresent subsegment. Referenced by any triangle or */
/* subsegment that isn't really connected to a subsegment at that */
/* location. */
subseg *dummysub;
subseg *dummysubbase; /* Keep base address so we can free() it later. */
/* Pointer to a recently visited triangle. Improves point location if */
/* proximate vertices are inserted sequentially. */
struct otri recenttri;
}; /* End of `struct mesh'. */
/* Data structure for command line switches and file names. This structure */
/* is used (instead of global variables) to allow reentrancy. */
struct behavior {
/* Switches for the triangulator. */
/* poly: -p switch. refine: -r switch. */
/* quality: -q switch. */
/* minangle: minimum angle bound, specified after -q switch. */
/* goodangle: cosine squared of minangle. */
/* offconstant: constant used to place off-center Steiner points. */
/* vararea: -a switch without number. */
/* fixedarea: -a switch with number. */
/* maxarea: maximum area bound, specified after -a switch. */
/* usertest: -u switch. */
/* regionattrib: -A switch. convex: -c switch. */
/* weighted: 1 for -w switch, 2 for -W switch. jettison: -j switch */
/* firstnumber: inverse of -z switch. All items are numbered starting */
/* from `firstnumber'. */
/* edgesout: -e switch. voronoi: -v switch. */
/* neighbors: -n switch. geomview: -g switch. */
/* nobound: -B switch. nopolywritten: -P switch. */
/* nonodewritten: -N switch. noelewritten: -E switch. */
/* noiterationnum: -I switch. noholes: -O switch. */
/* noexact: -X switch. */
/* order: element order, specified after -o switch. */
/* nobisect: count of how often -Y switch is selected. */
/* steiner: maximum number of Steiner points, specified after -S switch. *//* incremental: -i switch. sweepline: -F switch. */
/* dwyer: inverse of -l switch. */
/* splitseg: -s switch. */
/* conformdel: -D switch. docheck: -C switch. */
/* quiet: -Q switch. verbose: count of how often -V switch is selected. */
/* usesegments: -p, -r, -q, or -c switch; determines whether segments are */
/* used at all. */
/* */
/* Read the instructions to find out the meaning of these switches. */
int poly, refine, quality, vararea, fixedarea, usertest;
int regionattrib, convex, weighted, jettison;
int firstnumber;
int edgesout, voronoi, neighbors, geomview;
int nobound, nopolywritten, nonodewritten, noelewritten, noiterationnum;
int noholes, noexact, conformdel;
int incremental, sweepline, dwyer;
int splitseg;
int docheck;
int quiet, verbose;
int usesegments;
int order;
int nobisect;
int steiner;
REAL minangle, goodangle, offconstant;
REAL maxarea;
/* Variables for file names. */
#ifndef TRILIBRARY
char innodefilename[FILENAMESIZE];
char inelefilename[FILENAMESIZE];
char inpolyfilename[FILENAMESIZE];
char areafilename[FILENAMESIZE];
char outnodefilename[FILENAMESIZE];
char outelefilename[FILENAMESIZE];
char outpolyfilename[FILENAMESIZE];
char edgefilename[FILENAMESIZE];
char vnodefilename[FILENAMESIZE];
char vedgefilename[FILENAMESIZE];
char neighborfilename[FILENAMESIZE];
char offfilename[FILENAMESIZE];
#endif /* not TRILIBRARY */
}; /* End of `struct behavior'. */
/*****************************************************************************/
/* */
/* Mesh manipulation primitives. Each triangle contains three pointers to */
/* other triangles, with orientations. Each pointer points not to the */
/* first byte of a triangle, but to one of the first three bytes of a */
/* triangle. It is necessary to extract both the triangle itself and the */
/* orientation. To save memory, I keep both pieces of information in one */
/* pointer. To make this possible, I assume that all triangles are aligned */
/* to four-byte boundaries. The decode() routine below decodes a pointer, */
/* extracting an orientation (in the range 0 to 2) and a pointer to the */
/* beginning of a triangle. The encode() routine compresses a pointer to a */
/* triangle and an orientation into a single pointer. My assumptions that */
/* triangles are four-byte-aligned and that the `unsigned long' type is */
/* long enough to hold a pointer are two of the few kludges in this program.*/
/* */
/* Subsegments are manipulated similarly. A pointer to a subsegment */
/* carries both an address and an orientation in the range 0 to 1. */
/* */
/* The other primitives take an oriented triangle or oriented subsegment, */
/* and return an oriented triangle or oriented subsegment or vertex; or */
/* they change the connections in the data structure. */
/* */
/* Below, triangles and subsegments are denoted by their vertices. The *//* triangle abc has origin (org) a, destination (dest) b, and apex (apex) */
/* c. These vertices occur in counterclockwise order about the triangle. */
/* The handle abc may simultaneously denote vertex a, edge ab, and triangle */
/* abc. */
/* */
/* Similarly, the subsegment ab has origin (sorg) a and destination (sdest) */
/* b. If ab is thought to be directed upward (with b directly above a), */
/* then the handle ab is thought to grasp the right side of ab, and may */
/* simultaneously denote vertex a and edge ab. */
/* */
/* An asterisk (*) denotes a vertex whose identity is unknown. */
/* */
/* Given this notation, a partial list of mesh manipulation primitives */
/* follows. */
/* */
/* */
/* For triangles: */
/* */
/* sym: Find the abutting triangle; same edge. */
/* sym(abc) -> ba* */
/* */
/* lnext: Find the next edge (counterclockwise) of a triangle. */
/* lnext(abc) -> bca */
/* */
/* lprev: Find the previous edge (clockwise) of a triangle. */
/* lprev(abc) -> cab */
/* */
/* onext: Find the next edge counterclockwise with the same origin. */
/* onext(abc) -> ac* */
/* */
/* oprev: Find the next edge clockwise with the same origin. */
/* oprev(abc) -> a*b */
/* */
/* dnext: Find the next edge counterclockwise with the same destination. */
/* dnext(abc) -> *ba */
/* */
/* dprev: Find the next edge clockwise with the same destination. */
/* dprev(abc) -> cb* */
/* */
/* rnext: Find the next edge (counterclockwise) of the adjacent triangle. */
/* rnext(abc) -> *a* */
/* */
/* rprev: Find the previous edge (clockwise) of the adjacent triangle. */
/* rprev(abc) -> b** */
/* */
/* org: Origin dest: Destination apex: Apex */
/* org(abc) -> a dest(abc) -> b apex(abc) -> c */
/* */
/* bond: Bond two triangles together at the resepective handles. */
/* bond(abc, bad) */
/* */
/* */
/* For subsegments: */
/* */
/* ssym: Reverse the orientation of a subsegment. */
/* ssym(ab) -> ba */
/* */
/* spivot: Find adjoining subsegment with the same origin. */
/* spivot(ab) -> a* */
/* */
/* snext: Find next subsegment in sequence. */
/* snext(ab) -> b* */
/* */
/* sorg: Origin sdest: Destination */
/* sorg(ab) -> a sdest(ab) -> b */
/* */
/* sbond: Bond two subsegments together at the respective origins. */
/* sbond(ab, ac) */
/* */
/* *//* For interacting tetrahedra and subfacets: */
/* */
/* tspivot: Find a subsegment abutting a triangle. */
/* tspivot(abc) -> ba */
/* */
/* stpivot: Find a triangle abutting a subsegment. */
/* stpivot(ab) -> ba* */
/* */
/* tsbond: Bond a triangle to a subsegment. */
/* tsbond(abc, ba) */
/* */
/*****************************************************************************/
/********* Mesh manipulation primitives begin here *********/
/** **/
/** **/
/* Fast lookup arrays to speed some of the mesh manipulation primitives. */
int plus1mod3[3] = {1, 2, 0};
int minus1mod3[3] = {2, 0, 1};
/********* Primitives for triangles *********/
/* */
/* */
/* decode() converts a pointer to an oriented triangle. The orientation is */
/* extracted from the two least significant bits of the pointer. */
#define decode(ptr, otri) \
(otri).orient = (int) ((unsigned long) (ptr) & (unsigned long) 3l); \
(otri).tri = (triangle *) \
((unsigned long) (ptr) ^ (unsigned long) (otri).orient)
/* encode() compresses an oriented triangle into a single pointer. It */
/* relies on the assumption that all triangles are aligned to four-byte */
/* boundaries, so the two least significant bits of (otri).tri are zero. */
#define encode(otri) \
(triangle) ((unsigned long) (otri).tri | (unsigned long) (otri).orient)
/* The following handle manipulation primitives are all described by Guibas */
/* and Stolfi. However, Guibas and Stolfi use an edge-based data */
/* structure, whereas I use a triangle-based data structure. */
/* sym() finds the abutting triangle, on the same edge. Note that the edge */
/* direction is necessarily reversed, because the handle specified by an */
/* oriented triangle is directed counterclockwise around the triangle. */
#define sym(otri1, otri2) \
ptr = (otri1).tri[(otri1).orient]; \
decode(ptr, otri2);
#define symself(otri) \
ptr = (otri).tri[(otri).orient]; \
decode(ptr, otri);
/* lnext() finds the next edge (counterclockwise) of a triangle. */
#define lnext(otri1, otri2) \
(otri2).tri = (otri1).tri; \
(otri2).orient = plus1mod3[(otri1).orient]
#define lnextself(otri) \
(otri).orient = plus1mod3[(otri).orient]
/* lprev() finds the previous edge (clockwise) of a triangle. */
#define lprev(otri1, otri2) \
(otri2).tri = (otri1).tri; \ (otri2).orient = minus1mod3[(otri1).orient]
#define lprevself(otri) \
(otri).orient = minus1mod3[(otri).orient]
/* onext() spins counterclockwise around a vertex; that is, it finds the */
/* next edge with the same origin in the counterclockwise direction. This */
/* edge is part of a different triangle. */
#define onext(otri1, otri2) \
lprev(otri1, otri2); \
symself(otri2);
#define onextself(otri) \
lprevself(otri); \
symself(otri);
/* oprev() spins clockwise around a vertex; that is, it finds the next edge */
/* with the same origin in the clockwise direction. This edge is part of */
/* a different triangle. */
#define oprev(otri1, otri2) \
sym(otri1, otri2); \
lnextself(otri2);
#define oprevself(otri) \
symself(otri); \
lnextself(otri);
/* dnext() spins counterclockwise around a vertex; that is, it finds the */
/* next edge with the same destination in the counterclockwise direction. */
/* This edge is part of a different triangle. */
#define dnext(otri1, otri2) \
sym(otri1, otri2); \
lprevself(otri2);
#define dnextself(otri) \
symself(otri); \
lprevself(otri);
/* dprev() spins clockwise around a vertex; that is, it finds the next edge */
/* with the same destination in the clockwise direction. This edge is */
/* part of a different triangle. */
#define dprev(otri1, otri2) \
lnext(otri1, otri2); \
symself(otri2);
#define dprevself(otri) \
lnextself(otri); \
symself(otri);
/* rnext() moves one edge counterclockwise about the adjacent triangle. */
/* (It's best understood by reading Guibas and Stolfi. It involves */
/* changing triangles twice.) */
#define rnext(otri1, otri2) \
sym(otri1, otri2); \
lnextself(otri2); \
symself(otri2);
#define rnextself(otri) \
symself(otri); \
lnextself(otri); \
symself(otri);
/* rprev() moves one edge clockwise about the adjacent triangle. */
/* (It's best understood by reading Guibas and Stolfi. It involves */
/* changing triangles twice.) */
#define rprev(otri1, otri2) \
sym(otri1, otri2); \
lprevself(otri2); \
symself(otri2);
#define rprevself(otri) \
symself(otri); \
lprevself(otri); \
symself(otri);
/* These primitives determine or set the origin, destination, or apex of a */
/* triangle. */
#define org(otri, vertexptr) \
vertexptr = (vertex) (otri).tri[plus1mod3[(otri).orient] + 3]
#define dest(otri, vertexptr) \
vertexptr = (vertex) (otri).tri[minus1mod3[(otri).orient] + 3]
#define apex(otri, vertexptr) \
vertexptr = (vertex) (otri).tri[(otri).orient + 3]
#define setorg(otri, vertexptr) \
(otri).tri[plus1mod3[(otri).orient] + 3] = (triangle) vertexptr
#define setdest(otri, vertexptr) \
(otri).tri[minus1mod3[(otri).orient] + 3] = (triangle) vertexptr
#define setapex(otri, vertexptr) \
(otri).tri[(otri).orient + 3] = (triangle) vertexptr
/* Bond two triangles together. */
#define bond(otri1, otri2) \
(otri1).tri[(otri1).orient] = encode(otri2); \
(otri2).tri[(otri2).orient] = encode(otri1)
/* Dissolve a bond (from one side). Note that the other triangle will still */
/* think it's connected to this triangle. Usually, however, the other */
/* triangle is being deleted entirely, or bonded to another triangle, so */
/* it doesn't matter. */
#define dissolve(otri) \
(otri).tri[(otri).orient] = (triangle) m->dummytri
/* Copy an oriented triangle. */
#define otricopy(otri1, otri2) \
(otri2).tri = (otri1).tri; \
(otri2).orient = (otri1).orient
/* Test for equality of oriented triangles. */
#define otriequal(otri1, otri2) \
(((otri1).tri == (otri2).tri) && \
((otri1).orient == (otri2).orient))
/* Primitives to infect or cure a triangle with the virus. These rely on */
/* the assumption that all subsegments are aligned to four-byte boundaries.*/
#define infect(otri) \
(otri).tri[6] = (triangle) \
((unsigned long) (otri).tri[6] | (unsigned long) 2l)
#define uninfect(otri) \
(otri).tri[6] = (triangle) \
((unsigned long) (otri).tri[6] & ~ (unsigned long) 2l)
/* Test a triangle for viral infection. */
#define infected(otri) \
(((unsigned long) (otri).tri[6] & (unsigned long) 2l) != 0l)
/* Check or set a triangle's attributes. */
#define elemattribute(otri, attnum) \
((REAL *) (otri).tri)[m->elemattribindex + (attnum)]
#define setelemattribute(otri, attnum, value) \
((REAL *) (otri).tri)[m->elemattribindex + (attnum)] = value
/* Check or set a triangle's maximum area bound. */
#define areabound(otri) ((REAL *) (otri).tri)[m->areaboundindex]
#define setareabound(otri, value) \
((REAL *) (otri).tri)[m->areaboundindex] = value
/* Check or set a triangle's deallocation. Its second pointer is set to */
/* NULL to indicate that it is not allocated. (Its first pointer is used */
/* for the stack of dead items.) Its fourth pointer (its first vertex) */
/* is set to NULL in case a `badtriang' structure points to it. */
#define deadtri(tria) ((tria)[1] == (triangle) NULL)
#define killtri(tria) \
(tria)[1] = (triangle) NULL; \
(tria)[3] = (triangle) NULL
/********* Primitives for subsegments *********/
/* */
/* */
/* sdecode() converts a pointer to an oriented subsegment. The orientation */
/* is extracted from the least significant bit of the pointer. The two */
/* least significant bits (one for orientation, one for viral infection) */
/* are masked out to produce the real pointer. */
#define sdecode(sptr, osub) \
(osub).ssorient = (int) ((unsigned long) (sptr) & (unsigned long) 1l); \
(osub).ss = (subseg *) \
((unsigned long) (sptr) & ~ (unsigned long) 3l)
/* sencode() compresses an oriented subsegment into a single pointer. It */
/* relies on the assumption that all subsegments are aligned to two-byte */
/* boundaries, so the least significant bit of (osub).ss is zero. */
#define sencode(osub) \
(subseg) ((unsigned long) (osub).ss | (unsigned long) (osub).ssorient)
/* ssym() toggles the orientation of a subsegment. */
#define ssym(osub1, osub2) \
(osub2).ss = (osub1).ss; \
(osub2).ssorient = 1 - (osub1).ssorient
#define ssymself(osub) \
(osub).ssorient = 1 - (osub).ssorient
/* spivot() finds the other subsegment (from the same segment) that shares */
/* the same origin. */
#define spivot(osub1, osub2) \
sptr = (osub1).ss[(osub1).ssorient]; \
sdecode(sptr, osub2)
#define spivotself(osub) \
sptr = (osub).ss[(osub).ssorient]; \
sdecode(sptr, osub)
/* snext() finds the next subsegment (from the same segment) in sequence; */
/* one whose origin is the input subsegment's destination. */
#define snext(osub1, osub2) \
sptr = (osub1).ss[1 - (osub1).ssorient]; \
sdecode(sptr, osub2)
#define snextself(osub) \
sptr = (osub).ss[1 - (osub).ssorient]; \
sdecode(sptr, osub)
/* These primitives determine or set the origin or destination of a */
/* subsegment or the segment that includes it. */
#define sorg(osub, vertexptr) \
vertexptr = (vertex) (osub).ss[2 + (osub).ssorient]
#define sdest(osub, vertexptr) \
vertexptr = (vertex) (osub).ss[3 - (osub).ssorient]
#define setsorg(osub, vertexptr) \
(osub).ss[2 + (osub).ssorient] = (subseg) vertexptr
#define setsdest(osub, vertexptr) \
(osub).ss[3 - (osub).ssorient] = (subseg) vertexptr
#define segorg(osub, vertexptr) \
vertexptr = (vertex) (osub).ss[4 + (osub).ssorient]
#define segdest(osub, vertexptr) \
vertexptr = (vertex) (osub).ss[5 - (osub).ssorient]
#define setsegorg(osub, vertexptr) \
(osub).ss[4 + (osub).ssorient] = (subseg) vertexptr
#define setsegdest(osub, vertexptr) \
(osub).ss[5 - (osub).ssorient] = (subseg) vertexptr
/* These primitives read or set a boundary marker. Boundary markers are */
/* used to hold user-defined tags for setting boundary conditions in */
/* finite element solvers. */
#define mark(osub) (* (int *) ((osub).ss + 8))
#define setmark(osub, value) \
* (int *) ((osub).ss + 8) = value
/* Bond two subsegments together. */
#define sbond(osub1, osub2) \
(osub1).ss[(osub1).ssorient] = sencode(osub2); \
(osub2).ss[(osub2).ssorient] = sencode(osub1)
/* Dissolve a subsegment bond (from one side). Note that the other */
/* subsegment will still think it's connected to this subsegment. */
#define sdissolve(osub) \
(osub).ss[(osub).ssorient] = (subseg) m->dummysub
/* Copy a subsegment. */
#define subsegcopy(osub1, osub2) \
(osub2).ss = (osub1).ss; \
(osub2).ssorient = (osub1).ssorient
/* Test for equality of subsegments. */
#define subsegequal(osub1, osub2) \
(((osub1).ss == (osub2).ss) && \ ((osub1).ssorient == (osub2).ssorient))
/* Check or set a subsegment's deallocation. Its second pointer is set to */
/* NULL to indicate that it is not allocated. (Its first pointer is used */
/* for the stack of dead items.) Its third pointer (its first vertex) */
/* is set to NULL in case a `badsubseg' structure points to it. */
#define deadsubseg(sub) ((sub)[1] == (subseg) NULL)
#define killsubseg(sub) \
(sub)[1] = (subseg) NULL; \
(sub)[2] = (subseg) NULL
/********* Primitives for interacting triangles and subsegments *********/
/* */
/* */
/* tspivot() finds a subsegment abutting a triangle. */
#define tspivot(otri, osub) \
sptr = (subseg) (otri).tri[6 + (otri).orient]; \
sdecode(sptr, osub)
/* stpivot() finds a triangle abutting a subsegment. It requires that the */
/* variable `ptr' of type `triangle' be defined. */
#define stpivot(osub, otri) \
ptr = (triangle) (osub).ss[6 + (osub).ssorient]; \
decode(ptr, otri)
/* Bond a triangle to a subsegment. */
#define tsbond(otri, osub) \
(otri).tri[6 + (otri).orient] = (triangle) sencode(osub); \
(osub).ss[6 + (osub).ssorient] = (subseg) encode(otri)
/* Dissolve a bond (from the triangle side). */
#define tsdissolve(otri) \
(otri).tri[6 + (otri).orient] = (triangle) m->dummysub
/* Dissolve a bond (from the subsegment side). */
#define stdissolve(osub) \
(osub).ss[6 + (osub).ssorient] = (subseg) m->dummytri
/********* Primitives for vertices *********/
/* */
/* */
#define vertexmark(vx) ((int *) (vx))[m->vertexmarkindex]
#define setvertexmark(vx, value) \
((int *) (vx))[m->vertexmarkindex] = value
#define vertextype(vx) ((int *) (vx))[m->vertexmarkindex + 1]
#define setvertextype(vx, value) \
((int *) (vx))[m->vertexmarkindex + 1] = value
#define vertex2tri(vx) ((triangle *) (vx))[m->vertex2triindex]
#define setvertex2tri(vx, value) \
((triangle *) (vx))[m->vertex2triindex] = value
/** **/
/** **/
/********* Mesh manipulation primitives end here *********/
/********* User-defined triangle evaluation routine begins here *********//** **/
/** **/
/*****************************************************************************/
/* */
/* triunsuitable() Determine if a triangle is unsuitable, and thus must */
/* be further refined. */
/* */
/* You may write your own procedure that decides whether or not a selected */
/* triangle is too big (and needs to be refined). There are two ways to do */
/* this. */
/* */
/* (1) Modify the procedure `triunsuitable' below, then recompile */
/* Triangle. */
/* */
/* (2) Define the symbol EXTERNAL_TEST (either by adding the definition */
/* to this file, or by using the appropriate compiler switch). This way, */
/* you can compile triangle.c separately from your test. Write your own */
/* `triunsuitable' procedure in a separate C file (using the same prototype */
/* as below). Compile it and link the object code with triangle.o. */
/* */
/* This procedure returns 1 if the triangle is too large and should be */
/* refined; 0 otherwise. */
/* */
/*****************************************************************************/
#ifdef EXTERNAL_TEST
int triunsuitable();
#else /* not EXTERNAL_TEST */
#ifdef ANSI_DECLARATORS
int triunsuitable(vertex triorg, vertex tridest, vertex triapex, REAL area)
#else /* not ANSI_DECLARATORS */
int triunsuitable(triorg, tridest, triapex, area)
vertex triorg; /* The triangle's origin vertex. */
vertex tridest; /* The triangle's destination vertex. */
vertex triapex; /* The triangle's apex vertex. */
REAL area; /* The area of the triangle. */
#endif /* not ANSI_DECLARATORS */
{
REAL dxoa, dxda, dxod;
REAL dyoa, dyda, dyod;
REAL oalen, dalen, odlen;
REAL maxlen;
dxoa = triorg[0] - triapex[0];
dyoa = triorg[1] - triapex[1];
dxda = tridest[0] - triapex[0];
dyda = tridest[1] - triapex[1];
dxod = triorg[0] - tridest[0];
dyod = triorg[1] - tridest[1];
/* Find the squares of the lengths of the triangle's three edges. */
oalen = dxoa * dxoa + dyoa * dyoa;
dalen = dxda * dxda + dyda * dyda;
odlen = dxod * dxod + dyod * dyod;
/* Find the square of the length of the longest edge. */
maxlen = (dalen > oalen) ? dalen : oalen;
maxlen = (odlen > maxlen) ? odlen : maxlen;
if (maxlen > 0.05 * (triorg[0] * triorg[0] + triorg[1] * triorg[1]) + 0.02) {
return 1;
} else {
return 0;
}
}
#endif /* not EXTERNAL_TEST */
/** **/
/** **/
/********* User-defined triangle evaluation routine ends here *********/
/********* Memory allocation and program exit wrappers begin here *********/
/** **/
/** **/
#ifdef ANSI_DECLARATORS
void triexit(int status)
#else /* not ANSI_DECLARATORS */
void triexit(status)
int status;
#endif /* not ANSI_DECLARATORS */
{
exit(status);
}
#ifdef ANSI_DECLARATORS
VOID *trimalloc(int size)
#else /* not ANSI_DECLARATORS */
VOID *trimalloc(size)
int size;
#endif /* not ANSI_DECLARATORS */
{
VOID *memptr;
memptr = (VOID *) malloc((unsigned int) size);
if (memptr == (VOID *) NULL) {
printf("Error: Out of memory.\n");
triexit(1);
}
return(memptr);
}
#ifdef ANSI_DECLARATORS
void trifree(VOID *memptr)
#else /* not ANSI_DECLARATORS */
void trifree(memptr)
VOID *memptr;
#endif /* not ANSI_DECLARATORS */
{
free(memptr);
}
/** **/
/** **/
/********* Memory allocation and program exit wrappers end here *********/
/********* User interaction routines begin here *********/
/** **/
/** **/
/*****************************************************************************/
/* */
/* syntax() Print list of command line switches. */
/* */
/*****************************************************************************/
#ifndef TRILIBRARY
void syntax()
{
#ifdef CDT_ONLY
#ifdef REDUCED
printf("triangle [-pAcjevngBPNEIOXzo_lQVh] input_file\n");#else /* not REDUCED */
printf("triangle [-pAcjevngBPNEIOXzo_iFlCQVh] input_file\n");
#endif /* not REDUCED */
#else /* not CDT_ONLY */
#ifdef REDUCED
printf("triangle [-prq__a__uAcDjevngBPNEIOXzo_YS__lQVh] input_file\n");
#else /* not REDUCED */
printf("triangle [-prq__a__uAcDjevngBPNEIOXzo_YS__iFlsCQVh] input_file\n");
#endif /* not REDUCED */
#endif /* not CDT_ONLY */
printf(" -p Triangulates a Planar Straight Line Graph (.poly file).\n");
#ifndef CDT_ONLY
printf(" -r Refines a previously generated mesh.\n");
printf(
" -q Quality mesh generation. A minimum angle may be specified.\n");
printf(" -a Applies a maximum triangle area constraint.\n");
printf(" -u Applies a user-defined triangle constraint.\n");
#endif /* not CDT_ONLY */
printf(
" -A Applies attributes to identify triangles in certain regions.\n");
printf(" -c Encloses the convex hull with segments.\n");
#ifndef CDT_ONLY
printf(" -D Conforming Delaunay: all triangles are truly Delaunay.\n");
#endif /* not CDT_ONLY */
/*
printf(" -w Weighted Delaunay triangulation.\n");
printf(" -W Regular triangulation (lower hull of a height field).\n");
*/
printf(" -j Jettison unused vertices from output .node file.\n");
printf(" -e Generates an edge list.\n");
printf(" -v Generates a Voronoi diagram.\n");
printf(" -n Generates a list of triangle neighbors.\n");
printf(" -g Generates an .off file for Geomview.\n");
printf(" -B Suppresses output of boundary information.\n");
printf(" -P Suppresses output of .poly file.\n");
printf(" -N Suppresses output of .node file.\n");
printf(" -E Suppresses output of .ele file.\n");
printf(" -I Suppresses mesh iteration numbers.\n");
printf(" -O Ignores holes in .poly file.\n");
printf(" -X Suppresses use of exact arithmetic.\n");
printf(" -z Numbers all items starting from zero (rather than one).\n");
printf(" -o2 Generates second-order subparametric elements.\n");
#ifndef CDT_ONLY
printf(" -Y Suppresses boundary segment splitting.\n");
printf(" -S Specifies maximum number of added Steiner points.\n");
#endif /* not CDT_ONLY */
#ifndef REDUCED
printf(" -i Uses incremental method, rather than divide-and-conquer.\n");
printf(" -F Uses Fortune's sweepline algorithm, rather than d-and-c.\n");
#endif /* not REDUCED */
printf(" -l Uses vertical cuts only, rather than alternating cuts.\n");
#ifndef REDUCED
#ifndef CDT_ONLY
printf(
" -s Force segments into mesh by splitting (instead of using CDT).\n");
#endif /* not CDT_ONLY */
printf(" -C Check consistency of final mesh.\n");
#endif /* not REDUCED */
printf(" -Q Quiet: No terminal output except errors.\n");
printf(" -V Verbose: Detailed information on what I'm doing.\n");
printf(" -h Help: Detailed instructions for Triangle.\n");
triexit(0);
}
#endif /* not TRILIBRARY */
/*****************************************************************************/
/* */
/* info() Print out complete instructions. *//* */
/*****************************************************************************/
#ifndef TRILIBRARY
void info()
{
printf("Triangle\n");
printf(
"A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator.\n");
printf("Version 1.6\n\n");
printf(
"Copyright 1993, 1995, 1997, 1998, 2002, 2005 Jonathan Richard Shewchuk\n");
printf("2360 Woolsey #H / Berkeley, California 94705-1927\n");
printf("Bugs/comments to jrs@cs.berkeley.edu\n");
printf(
"Created as part of the Quake project (tools for earthquake simulation).\n");
printf(
"Supported in part by NSF Grant CMS-9318163 and an NSERC 1967 Scholarship.\n");
printf("There is no warranty whatsoever. Use at your own risk.\n");
#ifdef SINGLE
printf("This executable is compiled for single precision arithmetic.\n\n\n");
#else /* not SINGLE */
printf("This executable is compiled for double precision arithmetic.\n\n\n");
#endif /* not SINGLE */
printf(
"Triangle generates exact Delaunay triangulations, constrained Delaunay\n");
printf(
"triangulations, conforming Delaunay triangulations, Voronoi diagrams, and\n");
printf(
"high-quality triangular meshes. The latter can be generated with no small\n"
);
printf(
"or large angles, and are thus suitable for finite element analysis. If no\n"
);
printf(
"command line switch is specified, your .node input file is read, and the\n");
printf(
"Delaunay triangulation is returned in .node and .ele output files. The\n");
printf("command syntax is:\n\n");
printf("triangle [-prq__a__uAcDjevngBPNEIOXzo_YS__iFlsCQVh] input_file\n\n");
printf(
"Underscores indicate that numbers may optionally follow certain switches.\n");
printf(
"Do not leave any space between a switch and its numeric parameter.\n");
printf(
"input_file must be a file with extension .node, or extension .poly if the\n");
printf(
"-p switch is used. If -r is used, you must supply .node and .ele files,\n");
printf(
"and possibly a .poly file and an .area file as well. The formats of these\n"
);
printf("files are described below.\n\n");
printf("Command Line Switches:\n\n");
printf(
" -p Reads a Planar Straight Line Graph (.poly file), which can specify\n"
);
printf(
" vertices, segments, holes, regional attributes, and regional area\n");
printf(
" constraints. Generates a constrained Delaunay triangulation (CDT)\n"
);
printf(
" fitting the input; or, if -s, -q, -a, or -u is used, a conforming\n");
printf(
" constrained Delaunay triangulation (CCDT). If you want a truly\n");
printf(
" Delaunay (not just constrained Delaunay) triangulation, use -D as\n");
printf(
" well. When -p is not used, Triangle reads a .node file by default.\n");
printf(
" -r Refines a previously generated mesh. The mesh is read from a .node\n"
);
printf(
" file and an .ele file. If -p is also used, a .poly file is read\n");
printf(
" and used to constrain segments in the mesh. If -a is also used\n");
printf(
" (with no number following), an .area file is read and used to\n");
printf(
" impose area constraints on the mesh. Further details on refinement\n"
);
printf(" appear below.\n");
printf(
" -q Quality mesh generation by Delaunay refinement (a hybrid of Paul\n");
printf(
" Chew's and Jim Ruppert's algorithms). Adds vertices to the mesh to\n"
);
printf(
" ensure that all angles are between 20 and 140 degrees. An\n");
printf(
" alternative bound on the minimum angle, replacing 20 degrees, may\n");
printf(
" be specified after the `q'. The specified angle may include a\n");
printf(
" decimal point, but not exponential notation. Note that a bound of\n"
);
printf(
" theta degrees on the smallest angle also implies a bound of\n");
printf(
" (180 - 2 theta) on the largest angle. If the minimum angle is 28.6\n"
);
printf(
" degrees or smaller, Triangle is mathematically guaranteed to\n");
printf(
" terminate (assuming infinite precision arithmetic--Triangle may\n");
printf(
" fail to terminate if you run out of precision). In practice,\n");
printf(
" Triangle often succeeds for minimum angles up to 34 degrees. For\n");
printf(
" some meshes, however, you might need to reduce the minimum angle to\n"
);
printf(
" avoid problems associated with insufficient floating-point\n");
printf(" precision.\n");
printf(
" -a Imposes a maximum triangle area. If a number follows the `a', no\n");
printf(
" triangle is generated whose area is larger than that number. If no\n"
);
printf(
" number is specified, an .area file (if -r is used) or .poly file\n");
printf(
" (if -r is not used) specifies a set of maximum area constraints.\n");
printf(
" An .area file contains a separate area constraint for each\n");
printf(
" triangle, and is useful for refining a finite element mesh based on\n"
);
printf(
" a posteriori error estimates. A .poly file can optionally contain\n"
);
printf(
" an area constraint for each segment-bounded region, thereby\n");
printf(
" controlling triangle densities in a first triangulation of a PSLG.\n"
);
printf(" You can impose both a fixed area constraint and a varying area\n");
printf(
" constraint by invoking the -a switch twice, once with and once\n");
printf(
" without a number following. Each area specified may include a\n");
printf(" decimal point.\n");
printf(
" -u Imposes a user-defined constraint on triangle size. There are two\n"
);
printf(
" ways to use this feature. One is to edit the triunsuitable()\n");
printf(
" procedure in triangle.c to encode any constraint you like, then\n");
printf(
" recompile Triangle. The other is to compile triangle.c with the\n");
printf(
" EXTERNAL_TEST symbol set (compiler switch -DEXTERNAL_TEST), then\n");
printf(
" link Triangle with a separate object file that implements\n");
printf(
" triunsuitable(). In either case, the -u switch causes the user-\n");
printf(" defined test to be applied to every triangle.\n");
printf(
" -A Assigns an additional floating-point attribute to each triangle\n");
printf(
" that identifies what segment-bounded region each triangle belongs\n");
printf(
" to. Attributes are assigned to regions by the .poly file. If a\n");
printf(
" region is not explicitly marked by the .poly file, triangles in\n");
printf(
" that region are assigned an attribute of zero. The -A switch has\n");
printf(
" an effect only when the -p switch is used and the -r switch is not.\n"
);
printf(
" -c Creates segments on the convex hull of the triangulation. If you\n");
printf(
" are triangulating a vertex set, this switch causes a .poly file to\n"
);
printf(
" be written, containing all edges of the convex hull. If you are\n");
printf(
" triangulating a PSLG, this switch specifies that the whole convex\n");
printf(
" hull of the PSLG should be triangulated, regardless of what\n");
printf(
" segments the PSLG has. If you do not use this switch when\n");
printf(
" triangulating a PSLG, Triangle assumes that you have identified the\n"
);
printf(
" region to be triangulated by surrounding it with segments of the\n");
printf(
" input PSLG. Beware: if you are not careful, this switch can cause\n"
);
printf(
" the introduction of an extremely thin angle between a PSLG segment\n"
);
printf(
" and a convex hull segment, which can cause overrefinement (and\n");
printf(
" possibly failure if Triangle runs out of precision). If you are\n");
printf(
" refining a mesh, the -c switch works differently: it causes a\n");
printf(
" .poly file to be written containing the boundary edges of the mesh\n"
);
printf(" (useful if no .poly file was read).\n");
printf(" -D Conforming Delaunay triangulation: use this switch if you want to\n"
);
printf(
" ensure that all the triangles in the mesh are Delaunay, and not\n");
printf(
" merely constrained Delaunay; or if you want to ensure that all the\n"
);
printf(
" Voronoi vertices lie within the triangulation. (Some finite volume\n"
);
printf(
" methods have this requirement.) This switch invokes Ruppert's\n");
printf(
" original algorithm, which splits every subsegment whose diametral\n");
printf(
" circle is encroached. It usually increases the number of vertices\n"
);
printf(" and triangles.\n");
printf(
" -j Jettisons vertices that are not part of the final triangulation\n");
printf(
" from the output .node file. By default, Triangle copies all\n");
printf(
" vertices in the input .node file to the output .node file, in the\n");
printf(
" same order, so their indices do not change. The -j switch prevents\n"
);
printf(
" duplicated input vertices, or vertices `eaten' by holes, from\n");
printf(
" appearing in the output .node file. Thus, if two input vertices\n");
printf(
" have exactly the same coordinates, only the first appears in the\n");
printf(
" output. If any vertices are jettisoned, the vertex numbering in\n");
printf(
" the output .node file differs from that of the input .node file.\n");
printf(
" -e Outputs (to an .edge file) a list of edges of the triangulation.\n");
printf(
" -v Outputs the Voronoi diagram associated with the triangulation.\n");
printf(
" Does not attempt to detect degeneracies, so some Voronoi vertices\n");
printf(
" may be duplicated. See the discussion of Voronoi diagrams below.\n");
printf(
" -n Outputs (to a .neigh file) a list of triangles neighboring each\n");
printf(" triangle.\n");
printf(
" -g Outputs the mesh to an Object File Format (.off) file, suitable for\n"
);
printf(" viewing with the Geometry Center's Geomview package.\n");
printf(
" -B No boundary markers in the output .node, .poly, and .edge output\n");
printf(
" files. See the detailed discussion of boundary markers below.\n");
printf(
" -P No output .poly file. Saves disk space, but you lose the ability\n");
printf(
" to maintain constraining segments on later refinements of the mesh.\n"
);
printf(" -N No output .node file.\n");
printf(" -E No output .ele file.\n");
printf(
" -I No iteration numbers. Suppresses the output of .node and .poly\n");
printf(
" files, so your input files won't be overwritten. (If your input is\n"
);
printf(
" a .poly file only, a .node file is written.) Cannot be used with\n"); printf(
" the -r switch, because that would overwrite your input .ele file.\n");
printf(
" Shouldn't be used with the -q, -a, -u, or -s switch if you are\n");
printf(
" using a .node file for input, because no .node file is written, so\n"
);
printf(" there is no record of any added Steiner points.\n");
printf(" -O No holes. Ignores the holes in the .poly file.\n");
printf(
" -X No exact arithmetic. Normally, Triangle uses exact floating-point\n"
);
printf(
" arithmetic for certain tests if it thinks the inexact tests are not\n"
);
printf(
" accurate enough. Exact arithmetic ensures the robustness of the\n");
printf(
" triangulation algorithms, despite floating-point roundoff error.\n");
printf(
" Disabling exact arithmetic with the -X switch causes a small\n");
printf(
" improvement in speed and creates the possibility that Triangle will\n"
);
printf(" fail to produce a valid mesh. Not recommended.\n");
printf(
" -z Numbers all items starting from zero (rather than one). Note that\n"
);
printf(
" this switch is normally overridden by the value used to number the\n"
);
printf(
" first vertex of the input .node or .poly file. However, this\n");
printf(
" switch is useful when calling Triangle from another program.\n");
printf(
" -o2 Generates second-order subparametric elements with six nodes each.\n"
);
printf(
" -Y No new vertices on the boundary. This switch is useful when the\n");
printf(
" mesh boundary must be preserved so that it conforms to some\n");
printf(
" adjacent mesh. Be forewarned that you will probably sacrifice much\n"
);
printf(
" of the quality of the mesh; Triangle will try, but the resulting\n");
printf(
" mesh may contain poorly shaped triangles. Works well if all the\n");
printf(
" boundary vertices are closely spaced. Specify this switch twice\n");
printf(
" (`-YY') to prevent all segment splitting, including internal\n");
printf(" boundaries.\n");
printf(
" -S Specifies the maximum number of Steiner points (vertices that are\n");
printf(
" not in the input, but are added to meet the constraints on minimum\n"
);
printf(
" angle and maximum area). The default is to allow an unlimited\n");
printf(
" number. If you specify this switch with no number after it,\n");
printf(
" the limit is set to zero. Triangle always adds vertices at segment\n"
);
printf(
" intersections, even if it needs to use more vertices than the limit\n"
);
printf(" you set. When Triangle inserts segments by splitting (-s), it\n");
printf(
" always adds enough vertices to ensure that all the segments of the\n"
);
printf(" PLSG are recovered, ignoring the limit if necessary.\n");
printf(
" -i Uses an incremental rather than a divide-and-conquer algorithm to\n");
printf(
" construct a Delaunay triangulation. Try it if the divide-and-\n");
printf(" conquer algorithm fails.\n");
printf(
" -F Uses Steven Fortune's sweepline algorithm to construct a Delaunay\n");
printf(
" triangulation. Warning: does not use exact arithmetic for all\n");
printf(" calculations. An exact result is not guaranteed.\n");
printf(
" -l Uses only vertical cuts in the divide-and-conquer algorithm. By\n");
printf(
" default, Triangle alternates between vertical and horizontal cuts,\n"
);
printf(
" which usually improve the speed except with vertex sets that are\n");
printf(
" small or short and wide. This switch is primarily of theoretical\n");
printf(" interest.\n");
printf(
" -s Specifies that segments should be forced into the triangulation by\n"
);
printf(
" recursively splitting them at their midpoints, rather than by\n");
printf(
" generating a constrained Delaunay triangulation. Segment splitting\n"
);
printf(
" is true to Ruppert's original algorithm, but can create needlessly\n"
);
printf(
" small triangles. This switch is primarily of theoretical interest.\n"
);
printf(
" -C Check the consistency of the final mesh. Uses exact arithmetic for\n"
);
printf(
" checking, even if the -X switch is used. Useful if you suspect\n");
printf(" Triangle is buggy.\n");
printf(
" -Q Quiet: Suppresses all explanation of what Triangle is doing,\n");
printf(" unless an error occurs.\n");
printf(
" -V Verbose: Gives detailed information about what Triangle is doing.\n"
);
printf(
" Add more `V's for increasing amount of detail. `-V' is most\n");
printf(
" useful; itgives information on algorithmic progress and much more\n");
printf(
" detailed statistics. `-VV' gives vertex-by-vertex details, and\n");
printf(
" prints so much that Triangle runs much more slowly. `-VVVV' gives\n"
);
printf(" information only a debugger could love.\n");
printf(" -h Help: Displays these instructions.\n");
printf("\n");
printf("Definitions:\n");
printf("\n");
printf(
" A Delaunay triangulation of a vertex set is a triangulation whose\n");
printf(
" vertices are the vertex set, that covers the convex hull of the vertex\n");
printf(" set. A Delaunay triangulation has the property that no vertex lies\n");
printf(
" inside the circumscribing circle (circle that passes through all three\n");
printf(" vertices) of any triangle in the triangulation.\n\n");
printf(
" A Voronoi diagram of a vertex set is a subdivision of the plane into\n");
printf(
" polygonal cells (some of which may be unbounded, meaning infinitely\n");
printf(
" large), where each cell is the set of points in the plane that are closer\n"
);
printf(
" to some input vertex than to any other input vertex. The Voronoi diagram\n"
);
printf(" is a geometric dual of the Delaunay triangulation.\n\n");
printf(
" A Planar Straight Line Graph (PSLG) is a set of vertices and segments.\n");
printf(
" Segments are simply edges, whose endpoints are all vertices in the PSLG.\n"
);
printf(
" Segments may intersect each other only at their endpoints. The file\n");
printf(" format for PSLGs (.poly files) is described below.\n\n");
printf(
" A constrained Delaunay triangulation (CDT) of a PSLG is similar to a\n");
printf(
" Delaunay triangulation, but each PSLG segment is present as a single edge\n"
);
printf(
" of the CDT. (A constrained Delaunay triangulation is not truly a\n");
printf(
" Delaunay triangulation, because some of its triangles might not be\n");
printf(
" Delaunay.) By definition, a CDT does not have any vertices other than\n");
printf(
" those specified in the input PSLG. Depending on context, a CDT might\n");
printf(
" cover the convex hull of the PSLG, or it might cover only a segment-\n");
printf(" bounded region (e.g. a polygon).\n\n");
printf(
" A conforming Delaunay triangulation of a PSLG is a triangulation in which\n"
);
printf(
" each triangle is truly Delaunay, and each PSLG segment is represented by\n"
);
printf(
" a linear contiguous sequence of edges of the triangulation. New vertices\n"
);
printf(
" (not part of the PSLG) may appear, and each input segment may have been\n");
printf(
" subdivided into shorter edges (subsegments) by these additional vertices.\n"
);
printf(
" The new vertices are frequently necessary to maintain the Delaunay\n");
printf(" property while ensuring that every segment is represented.\n\n");
printf(
" A conforming constrained Delaunay triangulation (CCDT) of a PSLG is a\n");
printf(
" triangulation of a PSLG whose triangles are constrained Delaunay. New\n");
printf(" vertices may appear, and input segments may be subdivided into\n");
printf(
" subsegments, but not to guarantee that segments are respected; rather, to\n"
);
printf(
" improve the quality of the triangles. The high-quality meshes produced\n");
printf(
" by the -q switch are usually CCDTs, but can be made conforming Delaunay\n");
printf(" with the -D switch.\n\n");
printf("File Formats:\n\n"); printf(
" All files may contain comments prefixed by the character '#'. Vertices,\n"
);
printf(
" triangles, edges, holes, and maximum area constraints must be numbered\n");
printf(
" consecutively, starting from either 1 or 0. Whichever you choose, all\n");
printf(
" input files must be consistent; if the vertices are numbered from 1, so\n");
printf(
" must be all other objects. Triangle automatically detects your choice\n");
printf(
" while reading the .node (or .poly) file. (When calling Triangle from\n");
printf(
" another program, use the -z switch if you wish to number objects from\n");
printf(" zero.) Examples of these file formats are given below.\n\n");
printf(" .node files:\n");
printf(
" First line: <# of vertices> <dimension (must be 2)> <# of attributes>\n"
);
printf(
" <# of boundary markers (0 or 1)>\n"
);
printf(
" Remaining lines: <vertex #> <x> <y> [attributes] [boundary marker]\n");
printf("\n");
printf(
" The attributes, which are typically floating-point values of physical\n");
printf(
" quantities (such as mass or conductivity) associated with the nodes of\n"
);
printf(
" a finite element mesh, are copied unchanged to the output mesh. If -q,\n"
);
printf(
" -a, -u, -D, or -s is selected, each new Steiner point added to the mesh\n"
);
printf(" has attributes assigned to it by linear interpolation.\n\n");
printf(
" If the fourth entry of the first line is `1', the last column of the\n");
printf(
" remainder of the file is assumed to contain boundary markers. Boundary\n"
);
printf(
" markers are used to identify boundary vertices and vertices resting on\n"
);
printf(
" PSLG segments; a complete description appears in a section below. The\n"
);
printf(
" .node file produced by Triangle contains boundary markers in the last\n");
printf(" column unless they are suppressed by the -B switch.\n\n");
printf(" .ele files:\n");
printf(
" First line: <# of triangles> <nodes per triangle> <# of attributes>\n");
printf(
" Remaining lines: <triangle #> <node> <node> <node> ... [attributes]\n");
printf("\n");
printf(
" Nodes are indices into the corresponding .node file. The first three\n");
printf(
" nodes are the corner vertices, and are listed in counterclockwise order\n"
);
printf(
" around each triangle. (The remaining nodes, if any, depend on the type\n"
);
printf(" of finite element used.)\n\n");
printf(
" The attributes are just like those of .node files. Because there is no\n"
); printf(
" simple mapping from input to output triangles, Triangle attempts to\n");
printf(
" interpolate attributes, and may cause a lot of diffusion of attributes\n"
);
printf(
" among nearby triangles as the triangulation is refined. Attributes do\n"
);
printf(" not diffuse across segments, so attributes used to identify\n");
printf(" segment-bounded regions remain intact.\n\n");
printf(
" In .ele files produced by Triangle, each triangular element has three\n");
printf(
" nodes (vertices) unless the -o2 switch is used, in which case\n");
printf(
" subparametric quadratic elements with six nodes each are generated.\n");
printf(
" The first three nodes are the corners in counterclockwise order, and\n");
printf(
" the fourth, fifth, and sixth nodes lie on the midpoints of the edges\n");
printf(
" opposite the first, second, and third vertices, respectively.\n");
printf("\n");
printf(" .poly files:\n");
printf(
" First line: <# of vertices> <dimension (must be 2)> <# of attributes>\n"
);
printf(
" <# of boundary markers (0 or 1)>\n"
);
printf(
" Following lines: <vertex #> <x> <y> [attributes] [boundary marker]\n");
printf(" One line: <# of segments> <# of boundary markers (0 or 1)>\n");
printf(
" Following lines: <segment #> <endpoint> <endpoint> [boundary marker]\n");
printf(" One line: <# of holes>\n");
printf(" Following lines: <hole #> <x> <y>\n");
printf(
" Optional line: <# of regional attributes and/or area constraints>\n");
printf(
" Optional following lines: <region #> <x> <y> <attribute> <max area>\n");
printf("\n");
printf(
" A .poly file represents a PSLG, as well as some additional information.\n"
);
printf(
" The first section lists all the vertices, and is identical to the\n");
printf(
" format of .node files. <# of vertices> may be set to zero to indicate\n"
);
printf(
" that the vertices are listed in a separate .node file; .poly files\n");
printf(
" produced by Triangle always have this format. A vertex set represented\n"
);
printf(
" this way has the advantage that it may easily be triangulated with or\n");
printf(
" without segments (depending on whether the -p switch is invoked).\n");
printf("\n");
printf(
" The second section lists the segments. Segments are edges whose\n");
printf(
" presence in the triangulation is enforced. (Depending on the choice of\n"
);
printf(
" switches, segment might be subdivided into smaller edges). Each\n");
printf(
" segment is specified by listing the indices of its two endpoints. This\n"
); printf(
" means that you must include its endpoints in the vertex list. Each\n");
printf(" segment, like each point, may have a boundary marker.\n\n");
printf(
" If -q, -a, -u, and -s are not selected, Triangle produces a constrained\n"
);
printf(
" Delaunay triangulation (CDT), in which each segment appears as a single\n"
);
printf(
" edge in the triangulation. If -q, -a, -u, or -s is selected, Triangle\n"
);
printf(
" produces a conforming constrained Delaunay triangulation (CCDT), in\n");
printf(
" which segments may be subdivided into smaller edges. If -D is\n");
printf(
" selected, Triangle produces a conforming Delaunay triangulation, so\n");
printf(
" that every triangle is Delaunay, and not just constrained Delaunay.\n");
printf("\n");
printf(
" The third section lists holes (and concavities, if -c is selected) in\n");
printf(
" the triangulation. Holes are specified by identifying a point inside\n");
printf(
" each hole. After the triangulation is formed, Triangle creates holes\n");
printf(
" by eating triangles, spreading out from each hole point until its\n");
printf(
" progress is blocked by segments in the PSLG. You must be careful to\n");
printf(
" enclose each hole in segments, or your whole triangulation might be\n");
printf(
" eaten away. If the two triangles abutting a segment are eaten, the\n");
printf(
" segment itself is also eaten. Do not place a hole directly on a\n");
printf(" segment; if you do, Triangle chooses one side of the segment\n");
printf(" arbitrarily.\n\n");
printf(
" The optional fourth section lists regional attributes (to be assigned\n");
printf(
" to all triangles in a region) and regional constraints on the maximum\n");
printf(
" triangle area. Triangle reads this section only if the -A switch is\n");
printf(
" used or the -a switch is used without a number following it, and the -r\n"
);
printf(
" switch is not used. Regional attributes and area constraints are\n");
printf(
" propagated in the same manner as holes: you specify a point for each\n");
printf(
" attribute and/or constraint, and the attribute and/or constraint\n");
printf(
" affects the whole region (bounded by segments) containing the point.\n");
printf(
" If two values are written on a line after the x and y coordinate, the\n");
printf(
" first such value is assumed to be a regional attribute (but is only\n");
printf(
" applied if the -A switch is selected), and the second value is assumed\n"
);
printf(
" to be a regional area constraint (but is only applied if the -a switch\n"
);
printf(
" is selected). You may specify just one value after the coordinates,\n");
printf(
" which can serve as both an attribute and an area constraint, depending\n");
printf(
" on the choice of switches. If you are using the -A and -a switches\n");
printf(
" simultaneously and wish to assign an attribute to some region without\n");
printf(" imposing an area constraint, use a negative maximum area.\n\n");
printf(
" When a triangulation is created from a .poly file, you must either\n");
printf(
" enclose the entire region to be triangulated in PSLG segments, or\n");
printf(
" use the -c switch, which automatically creates extra segments that\n");
printf(
" enclose the convex hull of the PSLG. If you do not use the -c switch,\n"
);
printf(
" Triangle eats all triangles that are not enclosed by segments; if you\n");
printf(
" are not careful, your whole triangulation may be eaten away. If you do\n"
);
printf(
" use the -c switch, you can still produce concavities by the appropriate\n"
);
printf(
" placement of holes just inside the boundary of the convex hull.\n");
printf("\n");
printf(
" An ideal PSLG has no intersecting segments, nor any vertices that lie\n");
printf(
" upon segments (except, of course, the endpoints of each segment). You\n"
);
printf(
" aren't required to make your .poly files ideal, but you should be aware\n"
);
printf(
" of what can go wrong. Segment intersections are relatively safe--\n");
printf(
" Triangle calculates the intersection points for you and adds them to\n");
printf(
" the triangulation--as long as your machine's floating-point precision\n");
printf(
" doesn't become a problem. You are tempting the fates if you have three\n"
);
printf(
" segments that cross at the same location, and expect Triangle to figure\n"
);
printf(
" out where the intersection point is. Thanks to floating-point roundoff\n"
);
printf(
" error, Triangle will probably decide that the three segments intersect\n"
);
printf(
" at three different points, and you will find a minuscule triangle in\n");
printf(
" your output--unless Triangle tries to refine the tiny triangle, uses\n");
printf(
" up the last bit of machine precision, and fails to terminate at all.\n");
printf(
" You're better off putting the intersection point in the input files,\n");
printf(
" and manually breaking up each segment into two. Similarly, if you\n");
printf(
" place a vertex at the middle of a segment, and hope that Triangle will\n"
);
printf(
" break up the segment at that vertex, you might get lucky. On the other\n"
);
printf(
" hand, Triangle might decide that the vertex doesn't lie precisely on\n"); printf(
" the segment, and you'll have a needle-sharp triangle in your output--or\n"
);
printf(" a lot of tiny triangles if you're generating a quality mesh.\n");
printf("\n");
printf(
" When Triangle reads a .poly file, it also writes a .poly file, which\n");
printf(
" includes all the subsegments--the edges that are parts of input\n");
printf(
" segments. If the -c switch is used, the output .poly file also\n");
printf(
" includes all of the edges on the convex hull. Hence, the output .poly\n"
);
printf(
" file is useful for finding edges associated with input segments and for\n"
);
printf(
" setting boundary conditions in finite element simulations. Moreover,\n");
printf(
" you will need the output .poly file if you plan to refine the output\n");
printf(
" mesh, and don't want segments to be missing in later triangulations.\n");
printf("\n");
printf(" .area files:\n");
printf(" First line: <# of triangles>\n");
printf(" Following lines: <triangle #> <maximum area>\n");
printf("\n");
printf(
" An .area file associates with each triangle a maximum area that is used\n"
);
printf(
" for mesh refinement. As with other file formats, every triangle must\n");
printf(
" be represented, and the triangles must be numbered consecutively. A\n");
printf(
" triangle may be left unconstrained by assigning it a negative maximum\n");
printf(" area.\n\n");
printf(" .edge files:\n");
printf(" First line: <# of edges> <# of boundary markers (0 or 1)>\n");
printf(
" Following lines: <edge #> <endpoint> <endpoint> [boundary marker]\n");
printf("\n");
printf(
" Endpoints are indices into the corresponding .node file. Triangle can\n"
);
printf(
" produce .edge files (use the -e switch), but cannot read them. The\n");
printf(
" optional column of boundary markers is suppressed by the -B switch.\n");
printf("\n");
printf(
" In Voronoi diagrams, one also finds a special kind of edge that is an\n");
printf(
" infinite ray with only one endpoint. For these edges, a different\n");
printf(" format is used:\n\n");
printf(" <edge #> <endpoint> -1 <direction x> <direction y>\n\n");
printf(
" The `direction' is a floating-point vector that indicates the direction\n"
);
printf(" of the infinite ray.\n\n");
printf(" .neigh files:\n");
printf(
" First line: <# of triangles> <# of neighbors per triangle (always 3)>\n"
);
printf(
" Following lines: <triangle #> <neighbor> <neighbor> <neighbor>\n");
printf("\n");
printf(
" Neighbors are indices into the corresponding .ele file. An index of -1\n");
printf(
" indicates no neighbor (because the triangle is on an exterior\n");
printf(
" boundary). The first neighbor of triangle i is opposite the first\n");
printf(" corner of triangle i, and so on.\n\n");
printf(
" Triangle can produce .neigh files (use the -n switch), but cannot read\n"
);
printf(" them.\n\n");
printf("Boundary Markers:\n\n");
printf(
" Boundary markers are tags used mainly to identify which output vertices\n");
printf(
" and edges are associated with which PSLG segment, and to identify which\n");
printf(
" vertices and edges occur on a boundary of the triangulation. A common\n");
printf(
" use is to determine where boundary conditions should be applied to a\n");
printf(
" finite element mesh. You can prevent boundary markers from being written\n"
);
printf(" into files produced by Triangle by using the -B switch.\n\n");
printf(
" The boundary marker associated with each segment in an output .poly file\n"
);
printf(" and each edge in an output .edge file is chosen as follows:\n");
printf(
" - If an output edge is part or all of a PSLG segment with a nonzero\n");
printf(
" boundary marker, then the edge is assigned the same marker.\n");
printf(
" - Otherwise, if the edge lies on a boundary of the triangulation\n");
printf(
" (even the boundary of a hole), then the edge is assigned the marker\n");
printf(" one (1).\n");
printf(" - Otherwise, the edge is assigned the marker zero (0).\n");
printf(
" The boundary marker associated with each vertex in an output .node file\n");
printf(" is chosen as follows:\n");
printf(
" - If a vertex is assigned a nonzero boundary marker in the input file,\n"
);
printf(
" then it is assigned the same marker in the output .node file.\n");
printf(
" - Otherwise, if the vertex lies on a PSLG segment (even if it is an\n");
printf(
" endpoint of the segment) with a nonzero boundary marker, then the\n");
printf(
" vertex is assigned the same marker. If the vertex lies on several\n");
printf(" such segments, one of the markers is chosen arbitrarily.\n");
printf(
" - Otherwise, if the vertex occurs on a boundary of the triangulation,\n");
printf(" then the vertex is assigned the marker one (1).\n");
printf(" - Otherwise, the vertex is assigned the marker zero (0).\n");
printf("\n");
printf(
" If you want Triangle to determine for you which vertices and edges are on\n"
);
printf(
" the boundary, assign them the boundary marker zero (or use no markers at\n"
);
printf(
" all) in your input files. In the output files, all boundary vertices,\n");
printf(" edges, and segments will be assigned the value one.\n\n");
printf("Triangulation Iteration Numbers:\n\n");
printf(
" Because Triangle can read and refine its own triangulations, input\n");
printf(" and output files have iteration numbers. For instance, Triangle might\n");
printf(
" read the files mesh.3.node, mesh.3.ele, and mesh.3.poly, refine the\n");
printf(
" triangulation, and output the files mesh.4.node, mesh.4.ele, and\n");
printf(" mesh.4.poly. Files with no iteration number are treated as if\n");
printf(
" their iteration number is zero; hence, Triangle might read the file\n");
printf(
" points.node, triangulate it, and produce the files points.1.node and\n");
printf(" points.1.ele.\n\n");
printf(
" Iteration numbers allow you to create a sequence of successively finer\n");
printf(
" meshes suitable for multigrid methods. They also allow you to produce a\n"
);
printf(
" sequence of meshes using error estimate-driven mesh refinement.\n");
printf("\n");
printf(
" If you're not using refinement or quality meshing, and you don't like\n");
printf(
" iteration numbers, use the -I switch to disable them. This switch also\n");
printf(
" disables output of .node and .poly files to prevent your input files from\n"
);
printf(
" being overwritten. (If the input is a .poly file that contains its own\n");
printf(
" points, a .node file is written. This can be quite convenient for\n");
printf(" computing CDTs or quality meshes.)\n\n");
printf("Examples of How to Use Triangle:\n\n");
printf(
" `triangle dots' reads vertices from dots.node, and writes their Delaunay\n"
);
printf(
" triangulation to dots.1.node and dots.1.ele. (dots.1.node is identical\n");
printf(
" to dots.node.) `triangle -I dots' writes the triangulation to dots.ele\n");
printf(
" instead. (No additional .node file is needed, so none is written.)\n");
printf("\n");
printf(
" `triangle -pe object.1' reads a PSLG from object.1.poly (and possibly\n");
printf(
" object.1.node, if the vertices are omitted from object.1.poly) and writes\n"
);
printf(
" its constrained Delaunay triangulation to object.2.node and object.2.ele.\n"
);
printf(
" The segments are copied to object.2.poly, and all edges are written to\n");
printf(" object.2.edge.\n\n");
printf(
" `triangle -pq31.5a.1 object' reads a PSLG from object.poly (and possibly\n"
);
printf(
" object.node), generates a mesh whose angles are all between 31.5 and 117\n"
);
printf(
" degrees and whose triangles all have areas of 0.1 or less, and writes the\n"
);
printf(
" mesh to object.1.node and object.1.ele. Each segment may be broken up\n");
printf(" into multiple subsegments; these are written to object.1.poly.\n");
printf("\n");
printf(
" Here is a sample file `box.poly' describing a square with a square hole:\n"
);
printf("\n"); printf(
" # A box with eight vertices in 2D, no attributes, one boundary marker.\n"
);
printf(" 8 2 0 1\n");
printf(" # Outer box has these vertices:\n");
printf(" 1 0 0 0\n");
printf(" 2 0 3 0\n");
printf(" 3 3 0 0\n");
printf(" 4 3 3 33 # A special marker for this vertex.\n");
printf(" # Inner square has these vertices:\n");
printf(" 5 1 1 0\n");
printf(" 6 1 2 0\n");
printf(" 7 2 1 0\n");
printf(" 8 2 2 0\n");
printf(" # Five segments with boundary markers.\n");
printf(" 5 1\n");
printf(" 1 1 2 5 # Left side of outer box.\n");
printf(" # Square hole has these segments:\n");
printf(" 2 5 7 0\n");
printf(" 3 7 8 0\n");
printf(" 4 8 6 10\n");
printf(" 5 6 5 0\n");
printf(" # One hole in the middle of the inner square.\n");
printf(" 1\n");
printf(" 1 1.5 1.5\n");
printf("\n");
printf(
" Note that some segments are missing from the outer square, so you must\n");
printf(
" use the `-c' switch. After `triangle -pqc box.poly', here is the output\n"
);
printf(
" file `box.1.node', with twelve vertices. The last four vertices were\n");
printf(
" added to meet the angle constraint. Vertices 1, 2, and 9 have markers\n");
printf(
" from segment 1. Vertices 6 and 8 have markers from segment 4. All the\n");
printf(
" other vertices but 4 have been marked to indicate that they lie on a\n");
printf(" boundary.\n\n");
printf(" 12 2 0 1\n");
printf(" 1 0 0 5\n");
printf(" 2 0 3 5\n");
printf(" 3 3 0 1\n");
printf(" 4 3 3 33\n");
printf(" 5 1 1 1\n");
printf(" 6 1 2 10\n");
printf(" 7 2 1 1\n");
printf(" 8 2 2 10\n");
printf(" 9 0 1.5 5\n");
printf(" 10 1.5 0 1\n");
printf(" 11 3 1.5 1\n");
printf(" 12 1.5 3 1\n");
printf(" # Generated by triangle -pqc box.poly\n");
printf("\n");
printf(" Here is the output file `box.1.ele', with twelve triangles.\n");
printf("\n");
printf(" 12 3 0\n");
printf(" 1 5 6 9\n");
printf(" 2 10 3 7\n");
printf(" 3 6 8 12\n");
printf(" 4 9 1 5\n");
printf(" 5 6 2 9\n");
printf(" 6 7 3 11\n");
printf(" 7 11 4 8\n");
printf(" 8 7 5 10\n");
printf(" 9 12 2 6\n");
printf(" 10 8 7 11\n");
printf(" 11 5 1 10\n");
printf(" 12 8 4 12\n"); printf(" # Generated by triangle -pqc box.poly\n\n");
printf(
" Here is the output file `box.1.poly'. Note that segments have been added\n"
);
printf(
" to represent the convex hull, and some segments have been subdivided by\n");
printf(
" newly added vertices. Note also that <# of vertices> is set to zero to\n");
printf(" indicate that the vertices should be read from the .node file.\n");
printf("\n");
printf(" 0 2 0 1\n");
printf(" 12 1\n");
printf(" 1 1 9 5\n");
printf(" 2 5 7 1\n");
printf(" 3 8 7 1\n");
printf(" 4 6 8 10\n");
printf(" 5 5 6 1\n");
printf(" 6 3 10 1\n");
printf(" 7 4 11 1\n");
printf(" 8 2 12 1\n");
printf(" 9 9 2 5\n");
printf(" 10 10 1 1\n");
printf(" 11 11 3 1\n");
printf(" 12 12 4 1\n");
printf(" 1\n");
printf(" 1 1.5 1.5\n");
printf(" # Generated by triangle -pqc box.poly\n");
printf("\n");
printf("Refinement and Area Constraints:\n");
printf("\n");
printf(
" The -r switch causes a mesh (.node and .ele files) to be read and\n");
printf(
" refined. If the -p switch is also used, a .poly file is read and used to\n"
);
printf(
" specify edges that are constrained and cannot be eliminated (although\n");
printf(
" they can be subdivided into smaller edges) by the refinement process.\n");
printf("\n");
printf(
" When you refine a mesh, you generally want to impose tighter constraints.\n"
);
printf(
" One way to accomplish this is to use -q with a larger angle, or -a\n");
printf(
" followed by a smaller area than you used to generate the mesh you are\n");
printf(
" refining. Another way to do this is to create an .area file, which\n");
printf(
" specifies a maximum area for each triangle, and use the -a switch\n");
printf(
" (without a number following). Each triangle's area constraint is applied\n"
);
printf(
" to that triangle. Area constraints tend to diffuse as the mesh is\n");
printf(
" refined, so if there are large variations in area constraint between\n");
printf(
" adjacent triangles, you may not get the results you want. In that case,\n"
);
printf(
" consider instead using the -u switch and writing a C procedure that\n");
printf(" determines which triangles are too large.\n\n");
printf(
" If you are refining a mesh composed of linear (three-node) elements, the\n"
);
printf(
" output mesh contains all the nodes present in the input mesh, in the same\n"
); printf(
" order, with new nodes added at the end of the .node file. However, the\n");
printf(
" refinement is not hierarchical: there is no guarantee that each output\n");
printf(
" element is contained in a single input element. Often, an output element\n"
);
printf(
" can overlap two or three input elements, and some input edges are not\n");
printf(
" present in the output mesh. Hence, a sequence of refined meshes forms a\n"
);
printf(
" hierarchy of nodes, but not a hierarchy of elements. If you refine a\n");
printf(
" mesh of higher-order elements, the hierarchical property applies only to\n"
);
printf(
" the nodes at the corners of an element; the midpoint nodes on each edge\n");
printf(" are discarded before the mesh is refined.\n\n");
printf(
" Maximum area constraints in .poly files operate differently from those in\n"
);
printf(
" .area files. A maximum area in a .poly file applies to the whole\n");
printf(
" (segment-bounded) region in which a point falls, whereas a maximum area\n");
printf(
" in an .area file applies to only one triangle. Area constraints in .poly\n"
);
printf(
" files are used only when a mesh is first generated, whereas area\n");
printf(
" constraints in .area files are used only to refine an existing mesh, and\n"
);
printf(
" are typically based on a posteriori error estimates resulting from a\n");
printf(" finite element simulation on that mesh.\n\n");
printf(
" `triangle -rq25 object.1' reads object.1.node and object.1.ele, then\n");
printf(
" refines the triangulation to enforce a 25 degree minimum angle, and then\n"
);
printf(
" writes the refined triangulation to object.2.node and object.2.ele.\n");
printf("\n");
printf(
" `triangle -rpaa6.2 z.3' reads z.3.node, z.3.ele, z.3.poly, and z.3.area.\n"
);
printf(
" After reconstructing the mesh and its subsegments, Triangle refines the\n");
printf(
" mesh so that no triangle has area greater than 6.2, and furthermore the\n");
printf(
" triangles satisfy the maximum area constraints in z.3.area. No angle\n");
printf(
" bound is imposed at all. The output is written to z.4.node, z.4.ele, and\n"
);
printf(" z.4.poly.\n\n");
printf(
" The sequence `triangle -qa1 x', `triangle -rqa.3 x.1', `triangle -rqa.1\n");
printf(
" x.2' creates a sequence of successively finer meshes x.1, x.2, and x.3,\n");
printf(" suitable for multigrid.\n\n");
printf("Convex Hulls and Mesh Boundaries:\n\n");
printf(
" If the input is a vertex set (not a PSLG), Triangle produces its convex\n");
printf(
" hull as a by-product in the output .poly file if you use the -c switch.\n");
printf(" There are faster algorithms for finding a two-dimensional convex hull\n");
printf(" than triangulation, of course, but this one comes for free.\n\n");
printf(
" If the input is an unconstrained mesh (you are using the -r switch but\n");
printf(
" not the -p switch), Triangle produces a list of its boundary edges\n");
printf(
" (including hole boundaries) as a by-product when you use the -c switch.\n");
printf(
" If you also use the -p switch, the output .poly file contains all the\n");
printf(" segments from the input .poly file as well.\n\n");
printf("Voronoi Diagrams:\n\n");
printf(
" The -v switch produces a Voronoi diagram, in files suffixed .v.node and\n");
printf(
" .v.edge. For example, `triangle -v points' reads points.node, produces\n");
printf(
" its Delaunay triangulation in points.1.node and points.1.ele, and\n");
printf(
" produces its Voronoi diagram in points.1.v.node and points.1.v.edge. The\n"
);
printf(
" .v.node file contains a list of all Voronoi vertices, and the .v.edge\n");
printf(
" file contains a list of all Voronoi edges, some of which may be infinite\n"
);
printf(
" rays. (The choice of filenames makes it easy to run the set of Voronoi\n");
printf(" vertices through Triangle, if so desired.)\n\n");
printf(
" This implementation does not use exact arithmetic to compute the Voronoi\n"
);
printf(
" vertices, and does not check whether neighboring vertices are identical.\n"
);
printf(
" Be forewarned that if the Delaunay triangulation is degenerate or\n");
printf(
" near-degenerate, the Voronoi diagram may have duplicate vertices or\n");
printf(" crossing edges.\n\n");
printf(
" The result is a valid Voronoi diagram only if Triangle's output is a true\n"
);
printf(
" Delaunay triangulation. The Voronoi output is usually meaningless (and\n");
printf(
" may contain crossing edges and other pathology) if the output is a CDT or\n"
);
printf(
" CCDT, or if it has holes or concavities. If the triangulated domain is\n");
printf(
" convex and has no holes, you can use -D switch to force Triangle to\n");
printf(
" construct a conforming Delaunay triangulation instead of a CCDT, so the\n");
printf(" Voronoi diagram will be valid.\n\n");
printf("Mesh Topology:\n\n");
printf(
" You may wish to know which triangles are adjacent to a certain Delaunay\n");
printf(
" edge in an .edge file, which Voronoi cells are adjacent to a certain\n");
printf(
" Voronoi edge in a .v.edge file, or which Voronoi cells are adjacent to\n");
printf(
" each other. All of this information can be found by cross-referencing\n");
printf(
" output files with the recollection that the Delaunay triangulation and\n");
printf(" the Voronoi diagram are planar duals.\n\n");
printf(
" Specifically, edge i of an .edge file is the dual of Voronoi edge i of\n");
printf(" the corresponding .v.edge file, and is rotated 90 degrees counterclock-\n");
printf(
" wise from the Voronoi edge. Triangle j of an .ele file is the dual of\n");
printf(
" vertex j of the corresponding .v.node file. Voronoi cell k is the dual\n");
printf(" of vertex k of the corresponding .node file.\n\n");
printf(
" Hence, to find the triangles adjacent to a Delaunay edge, look at the\n");
printf(
" vertices of the corresponding Voronoi edge. If the endpoints of a\n");
printf(
" Voronoi edge are Voronoi vertices 2 and 6 respectively, then triangles 2\n"
);
printf(
" and 6 adjoin the left and right sides of the corresponding Delaunay edge,\n"
);
printf(
" respectively. To find the Voronoi cells adjacent to a Voronoi edge, look\n"
);
printf(
" at the endpoints of the corresponding Delaunay edge. If the endpoints of\n"
);
printf(
" a Delaunay edge are input vertices 7 and 12, then Voronoi cells 7 and 12\n"
);
printf(
" adjoin the right and left sides of the corresponding Voronoi edge,\n");
printf(
" respectively. To find which Voronoi cells are adjacent to each other,\n");
printf(" just read the list of Delaunay edges.\n\n");
printf(
" Triangle does not write a list of the edges adjoining each Voronoi cell,\n"
);
printf(
" but you can reconstructed it straightforwardly. For instance, to find\n");
printf(
" all the edges of Voronoi cell 1, search the output .edge file for every\n");
printf(
" edge that has input vertex 1 as an endpoint. The corresponding dual\n");
printf(
" edges in the output .v.edge file form the boundary of Voronoi cell 1.\n");
printf("\n");
printf(
" For each Voronoi vertex, the .neigh file gives a list of the three\n");
printf(
" Voronoi vertices attached to it. You might find this more convenient\n");
printf(" than the .v.edge file.\n\n");
printf("Quadratic Elements:\n\n");
printf(
" Triangle generates meshes with subparametric quadratic elements if the\n");
printf(
" -o2 switch is specified. Quadratic elements have six nodes per element,\n"
);
printf(
" rather than three. `Subparametric' means that the edges of the triangles\n"
);
printf(
" are always straight, so that subparametric quadratic elements are\n");
printf(
" geometrically identical to linear elements, even though they can be used\n"
);
printf(
" with quadratic interpolating functions. The three extra nodes of an\n");
printf(
" element fall at the midpoints of the three edges, with the fourth, fifth,\n"
);
printf(
" and sixth nodes appearing opposite the first, second, and third corners\n");
printf(" respectively.\n\n");
printf("Domains with Small Angles:\n\n"); printf(
" If two input segments adjoin each other at a small angle, clearly the -q\n"
);
printf(
" switch cannot remove the small angle. Moreover, Triangle may have no\n");
printf(
" choice but to generate additional triangles whose smallest angles are\n");
printf(
" smaller than the specified bound. However, these triangles only appear\n");
printf(
" between input segments separated by small angles. Moreover, if you\n");
printf(
" request a minimum angle of theta degrees, Triangle will generally produce\n"
);
printf(
" no angle larger than 180 - 2 theta, even if it is forced to compromise on\n"
);
printf(" the minimum angle.\n\n");
printf("Statistics:\n\n");
printf(
" After generating a mesh, Triangle prints a count of entities in the\n");
printf(
" output mesh, including the number of vertices, triangles, edges, exterior\n"
);
printf(
" boundary edges (i.e. subsegments on the boundary of the triangulation,\n");
printf(
" including hole boundaries), interior boundary edges (i.e. subsegments of\n"
);
printf(
" input segments not on the boundary), and total subsegments. If you've\n");
printf(
" forgotten the statistics for an existing mesh, run Triangle on that mesh\n"
);
printf(
" with the -rNEP switches to read the mesh and print the statistics without\n"
);
printf(
" writing any files. Use -rpNEP if you've got a .poly file for the mesh.\n");
printf("\n");
printf(
" The -V switch produces extended statistics, including a rough estimate\n");
printf(
" of memory use, the number of calls to geometric predicates, and\n");
printf(
" histograms of the angles and the aspect ratios of the triangles in the\n");
printf(" mesh.\n\n");
printf("Exact Arithmetic:\n\n");
printf(
" Triangle uses adaptive exact arithmetic to perform what computational\n");
printf(
" geometers call the `orientation' and `incircle' tests. If the floating-\n"
);
printf(
" point arithmetic of your machine conforms to the IEEE 754 standard (as\n");
printf(
" most workstations do), and does not use extended precision internal\n");
printf(
" floating-point registers, then your output is guaranteed to be an\n");
printf(
" absolutely true Delaunay or constrained Delaunay triangulation, roundoff\n"
);
printf(
" error notwithstanding. The word `adaptive' implies that these arithmetic\n"
);
printf(
" routines compute the result only to the precision necessary to guarantee\n"
);
printf(
" correctness, so they are usually nearly as fast as their approximate\n"); printf(" counterparts.\n\n");
printf(
" May CPUs, including Intel x86 processors, have extended precision\n");
printf(
" floating-point registers. These must be reconfigured so their precision\n"
);
printf(
" is reduced to memory precision. Triangle does this if it is compiled\n");
printf(" correctly. See the makefile for details.\n\n");
printf(
" The exact tests can be disabled with the -X switch. On most inputs, this\n"
);
printf(
" switch reduces the computation time by about eight percent--it's not\n");
printf(
" worth the risk. There are rare difficult inputs (having many collinear\n");
printf(
" and cocircular vertices), however, for which the difference in speed\n");
printf(
" could be a factor of two. Be forewarned that these are precisely the\n");
printf(
" inputs most likely to cause errors if you use the -X switch. Hence, the\n"
);
printf(" -X switch is not recommended.\n\n");
printf(
" Unfortunately, the exact tests don't solve every numerical problem.\n");
printf(
" Exact arithmetic is not used to compute the positions of new vertices,\n");
printf(
" because the bit complexity of vertex coordinates would grow without\n");
printf(
" bound. Hence, segment intersections aren't computed exactly; in very\n");
printf(
" unusual cases, roundoff error in computing an intersection point might\n");
printf(
" actually lead to an inverted triangle and an invalid triangulation.\n");
printf(
" (This is one reason to specify your own intersection points in your .poly\n"
);
printf(
" files.) Similarly, exact arithmetic is not used to compute the vertices\n"
);
printf(" of the Voronoi diagram.\n\n");
printf(
" Another pair of problems not solved by the exact arithmetic routines is\n");
printf(
" underflow and overflow. If Triangle is compiled for double precision\n");
printf(
" arithmetic, I believe that Triangle's geometric predicates work correctly\n"
);
printf(
" if the exponent of every input coordinate falls in the range [-148, 201].\n"
);
printf(
" Underflow can silently prevent the orientation and incircle tests from\n");
printf(
" being performed exactly, while overflow typically causes a floating\n");
printf(" exception.\n\n");
printf("Calling Triangle from Another Program:\n\n");
printf(" Read the file triangle.h for details.\n\n");
printf("Troubleshooting:\n\n");
printf(" Please read this section before mailing me bugs.\n\n");
printf(" `My output mesh has no triangles!'\n\n");
printf(
" If you're using a PSLG, you've probably failed to specify a proper set\n"
);
printf(
" of bounding segments, or forgotten to use the -c switch. Or you may\n");
printf(
" have placed a hole badly, thereby eating all your triangles. To test\n"); printf(" these possibilities, try again with the -c and -O switches.\n");
printf(
" Alternatively, all your input vertices may be collinear, in which case\n"
);
printf(" you can hardly expect to triangulate them.\n\n");
printf(" `Triangle doesn't terminate, or just crashes.'\n\n");
printf(
" Bad things can happen when triangles get so small that the distance\n");
printf(
" between their vertices isn't much larger than the precision of your\n");
printf(
" machine's arithmetic. If you've compiled Triangle for single-precision\n"
);
printf(
" arithmetic, you might do better by recompiling it for double-precision.\n"
);
printf(
" Then again, you might just have to settle for more lenient constraints\n"
);
printf(
" on the minimum angle and the maximum area than you had planned.\n");
printf("\n");
printf(
" You can minimize precision problems by ensuring that the origin lies\n");
printf(
" inside your vertex set, or even inside the densest part of your\n");
printf(
" mesh. If you're triangulating an object whose x-coordinates all fall\n");
printf(
" between 6247133 and 6247134, you're not leaving much floating-point\n");
printf(" precision for Triangle to work with.\n\n");
printf(
" Precision problems can occur covertly if the input PSLG contains two\n");
printf(
" segments that meet (or intersect) at an extremely small angle, or if\n");
printf(
" such an angle is introduced by the -c switch. If you don't realize\n");
printf(
" that a tiny angle is being formed, you might never discover why\n");
printf(
" Triangle is crashing. To check for this possibility, use the -S switch\n"
);
printf(
" (with an appropriate limit on the number of Steiner points, found by\n");
printf(
" trial-and-error) to stop Triangle early, and view the output .poly file\n"
);
printf(
" with Show Me (described below). Look carefully for regions where dense\n"
);
printf(
" clusters of vertices are forming and for small angles between segments.\n"
);
printf(
" Zoom in closely, as such segments might look like a single segment from\n"
);
printf(" a distance.\n\n");
printf(
" If some of the input values are too large, Triangle may suffer a\n");
printf(
" floating exception due to overflow when attempting to perform an\n");
printf(
" orientation or incircle test. (Read the section on exact arithmetic\n");
printf(
" above.) Again, I recommend compiling Triangle for double (rather\n");
printf(" than single) precision arithmetic.\n\n");
printf(
" Unexpected problems can arise if you use quality meshing (-q, -a, or\n");
printf(
" -u) with an input that is not segment-bounded--that is, if your input\n"); printf(
" is a vertex set, or you're using the -c switch. If the convex hull of\n"
);
printf(
" your input vertices has collinear vertices on its boundary, an input\n");
printf(
" vertex that you think lies on the convex hull might actually lie just\n");
printf(
" inside the convex hull. If so, the vertex and the nearby convex hull\n");
printf(
" edge form an extremely thin triangle. When Triangle tries to refine\n");
printf(
" the mesh to enforce angle and area constraints, Triangle might generate\n"
);
printf(
" extremely tiny triangles, or it might fail because of insufficient\n");
printf(" floating-point precision.\n\n");
printf(
" `The numbering of the output vertices doesn't match the input vertices.'\n"
);
printf("\n");
printf(
" You may have had duplicate input vertices, or you may have eaten some\n");
printf(
" of your input vertices with a hole, or by placing them outside the area\n"
);
printf(
" enclosed by segments. In any case, you can solve the problem by not\n");
printf(" using the -j switch.\n\n");
printf(
" `Triangle executes without incident, but when I look at the resulting\n");
printf(
" mesh, it has overlapping triangles or other geometric inconsistencies.'\n");
printf("\n");
printf(
" If you select the -X switch, Triangle occasionally makes mistakes due\n");
printf(
" to floating-point roundoff error. Although these errors are rare,\n");
printf(
" don't use the -X switch. If you still have problems, please report the\n"
);
printf(" bug.\n\n");
printf(
" `Triangle executes without incident, but when I look at the resulting\n");
printf(" Voronoi diagram, it has overlapping edges or other geometric\n");
printf(" inconsistencies.'\n");
printf("\n");
printf(
" If your input is a PSLG (-p), you can only expect a meaningful Voronoi\n"
);
printf(
" diagram if the domain you are triangulating is convex and free of\n");
printf(
" holes, and you use the -D switch to construct a conforming Delaunay\n");
printf(" triangulation (instead of a CDT or CCDT).\n\n");
printf(
" Strange things can happen if you've taken liberties with your PSLG. Do\n");
printf(
" you have a vertex lying in the middle of a segment? Triangle sometimes\n");
printf(
" copes poorly with that sort of thing. Do you want to lay out a collinear\n"
);
printf(
" row of evenly spaced, segment-connected vertices? Have you simply\n");
printf(
" defined one long segment connecting the leftmost vertex to the rightmost\n"
);
printf(
" vertex, and a bunch of vertices lying along it? This method occasionally\n"
); printf(
" works, especially with horizontal and vertical lines, but often it\n");
printf(
" doesn't, and you'll have to connect each adjacent pair of vertices with a\n"
);
printf(" separate segment. If you don't like it, tough.\n\n");
printf(
" Furthermore, if you have segments that intersect other than at their\n");
printf(
" endpoints, try not to let the intersections fall extremely close to PSLG\n"
);
printf(" vertices or each other.\n\n");
printf(
" If you have problems refining a triangulation not produced by Triangle:\n");
printf(
" Are you sure the triangulation is geometrically valid? Is it formatted\n");
printf(
" correctly for Triangle? Are the triangles all listed so the first three\n"
);
printf(
" vertices are their corners in counterclockwise order? Are all of the\n");
printf(
" triangles constrained Delaunay? Triangle's Delaunay refinement algorithm\n"
);
printf(" assumes that it starts with a CDT.\n\n");
printf("Show Me:\n\n");
printf(
" Triangle comes with a separate program named `Show Me', whose primary\n");
printf(
" purpose is to draw meshes on your screen or in PostScript. Its secondary\n"
);
printf(
" purpose is to check the validity of your input files, and do so more\n");
printf(
" thoroughly than Triangle does. Unlike Triangle, Show Me requires that\n");
printf(
" you have the X Windows system. Sorry, Microsoft Windows users.\n");
printf("\n");
printf("Triangle on the Web:\n");
printf("\n");
printf(" To see an illustrated version of these instructions, check out\n");
printf("\n");
printf(" http://www.cs.cmu.edu/~quake/triangle.html\n");
printf("\n");
printf("A Brief Plea:\n");
printf("\n");
printf(
" If you use Triangle, and especially if you use it to accomplish real\n");
printf(
" work, I would like very much to hear from you. A short letter or email\n");
printf(
" (to jrs@cs.berkeley.edu) describing how you use Triangle will mean a lot\n"
);
printf(
" to me. The more people I know are using this program, the more easily I\n"
);
printf(
" can justify spending time on improvements, which in turn will benefit\n");
printf(
" you. Also, I can put you on a list to receive email whenever a new\n");
printf(" version of Triangle is available.\n\n");
printf(
" If you use a mesh generated by Triangle in a publication, please include\n"
);
printf(
" an acknowledgment as well. And please spell Triangle with a capital `T'!\n"
);
printf(
" If you want to include a citation, use `Jonathan Richard Shewchuk,\n");
printf(" ``Triangle: Engineering a 2D Quality Mesh Generator and Delaunay\n");
printf(
" Triangulator,'' in Applied Computational Geometry: Towards Geometric\n");
printf(
" Engineering (Ming C. Lin and Dinesh Manocha, editors), volume 1148 of\n");
printf(
" Lecture Notes in Computer Science, pages 203-222, Springer-Verlag,\n");
printf(
" Berlin, May 1996. (From the First ACM Workshop on Applied Computational\n"
);
printf(" Geometry.)'\n\n");
printf("Research credit:\n\n");
printf(
" Of course, I can take credit for only a fraction of the ideas that made\n");
printf(
" this mesh generator possible. Triangle owes its existence to the efforts\n"
);
printf(
" of many fine computational geometers and other researchers, including\n");
printf(
" Marshall Bern, L. Paul Chew, Kenneth L. Clarkson, Boris Delaunay, Rex A.\n"
);
printf(
" Dwyer, David Eppstein, Steven Fortune, Leonidas J. Guibas, Donald E.\n");
printf(
" Knuth, Charles L. Lawson, Der-Tsai Lee, Gary L. Miller, Ernst P. Mucke,\n");
printf(
" Steven E. Pav, Douglas M. Priest, Jim Ruppert, Isaac Saias, Bruce J.\n");
printf(
" Schachter, Micha Sharir, Peter W. Shor, Daniel D. Sleator, Jorge Stolfi,\n"
);
printf(" Robert E. Tarjan, Alper Ungor, Christopher J. Van Wyk, Noel J.\n");
printf(
" Walkington, and Binhai Zhu. See the comments at the beginning of the\n");
printf(" source code for references.\n\n");
triexit(0);
}
#endif /* not TRILIBRARY */
/*****************************************************************************/
/* */
/* internalerror() Ask the user to send me the defective product. Exit. */
/* */
/*****************************************************************************/
void internalerror()
{
printf(" Please report this bug to jrs@cs.berkeley.edu\n");
printf(" Include the message above, your input data set, and the exact\n");
printf(" command line you used to run Triangle.\n");
triexit(1);
}
/*****************************************************************************/
/* */
/* parsecommandline() Read the command line, identify switches, and set */
/* up options and file names. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
void parsecommandline(int argc, char **argv, struct behavior *b)
#else /* not ANSI_DECLARATORS */
void parsecommandline(argc, argv, b)
int argc;
char **argv;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */
{
#ifdef TRILIBRARY
#define STARTINDEX 0
#else /* not TRILIBRARY */
#define STARTINDEX 1
int increment;
int meshnumber;
#endif /* not TRILIBRARY */
int i, j, k;
char workstring[FILENAMESIZE];
b->poly = b->refine = b->quality = 0;
b->vararea = b->fixedarea = b->usertest = 0;
b->regionattrib = b->convex = b->weighted = b->jettison = 0;
b->firstnumber = 1;
b->edgesout = b->voronoi = b->neighbors = b->geomview = 0;
b->nobound = b->nopolywritten = b->nonodewritten = b->noelewritten = 0;
b->noiterationnum = 0;
b->noholes = b->noexact = 0;
b->incremental = b->sweepline = 0;
b->dwyer = 1;
b->splitseg = 0;
b->docheck = 0;
b->nobisect = 0;
b->conformdel = 0;
b->steiner = -1;
b->order = 1;
b->minangle = 0.0;
b->maxarea = -1.0;
b->quiet = b->verbose = 0;
#ifndef TRILIBRARY
b->innodefilename[0] = '\0';
#endif /* not TRILIBRARY */
for (i = STARTINDEX; i < argc; i++) {
#ifndef TRILIBRARY
if (argv[i][0] == '-') {
#endif /* not TRILIBRARY */
for (j = STARTINDEX; argv[i][j] != '\0'; j++) {
if (argv[i][j] == 'p') {
b->poly = 1;
}
#ifndef CDT_ONLY
if (argv[i][j] == 'r') {
b->refine = 1;
}
if (argv[i][j] == 'q') {
b->quality = 1;
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';
b->minangle = (REAL) strtod(workstring, (char **) NULL);
} else {
b->minangle = 20.0;
}
}
if (argv[i][j] == 'a') {
b->quality = 1;
if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
(argv[i][j + 1] == '.')) {
b->fixedarea = 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';
b->maxarea = (REAL) strtod(workstring, (char **) NULL);
if (b->maxarea <= 0.0) {
printf("Error: Maximum area must be greater than zero.\n");
triexit(1);
}
} else {
b->vararea = 1;
}
}
if (argv[i][j] == 'u') {
b->quality = 1;
b->usertest = 1;
}
#endif /* not CDT_ONLY */
if (argv[i][j] == 'A') {
b->regionattrib = 1;
}
if (argv[i][j] == 'c') {
b->convex = 1;
}
if (argv[i][j] == 'w') {
b->weighted = 1;
}
if (argv[i][j] == 'W') {
b->weighted = 2;
}
if (argv[i][j] == 'j') {
b->jettison = 1;
}
if (argv[i][j] == 'z') {
b->firstnumber = 0;
}
if (argv[i][j] == 'e') {
b->edgesout = 1;
}
if (argv[i][j] == 'v') {
b->voronoi = 1;
}
if (argv[i][j] == 'n') {
b->neighbors = 1;
}
if (argv[i][j] == 'g') {
b->geomview = 1;
}
if (argv[i][j] == 'B') {
b->nobound = 1;
}
if (argv[i][j] == 'P') {
b->nopolywritten = 1;
}
if (argv[i][j] == 'N') {
b->nonodewritten = 1;
}
if (argv[i][j] == 'E') {
b->noelewritten = 1;
}
#ifndef TRILIBRARY
if (argv[i][j] == 'I') {
b->noiterationnum = 1;
}
#endif /* not TRILIBRARY */
if (argv[i][j] == 'O') {
b->noholes = 1;
} if (argv[i][j] == 'X') {
b->noexact = 1;
}
if (argv[i][j] == 'o') {
if (argv[i][j + 1] == '2') {
j++;
b->order = 2;
}
}
#ifndef CDT_ONLY
if (argv[i][j] == 'Y') {
b->nobisect++;
}
if (argv[i][j] == 'S') {
b->steiner = 0;
while ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) {
j++;
b->steiner = b->steiner * 10 + (int) (argv[i][j] - '0');
}
}
#endif /* not CDT_ONLY */
#ifndef REDUCED
if (argv[i][j] == 'i') {
b->incremental = 1;
}
if (argv[i][j] == 'F') {
b->sweepline = 1;
}
#endif /* not REDUCED */
if (argv[i][j] == 'l') {
b->dwyer = 0;
}
#ifndef REDUCED
#ifndef CDT_ONLY
if (argv[i][j] == 's') {
b->splitseg = 1;
}
if ((argv[i][j] == 'D') || (argv[i][j] == 'L')) {
b->quality = 1;
b->conformdel = 1;
}
#endif /* not CDT_ONLY */
if (argv[i][j] == 'C') {
b->docheck = 1;
}
#endif /* not REDUCED */
if (argv[i][j] == 'Q') {
b->quiet = 1;
}
if (argv[i][j] == 'V') {
b->verbose++;
}
#ifndef TRILIBRARY
if ((argv[i][j] == 'h') || (argv[i][j] == 'H') ||
(argv[i][j] == '?')) {
info();
}
#endif /* not TRILIBRARY */
}
#ifndef TRILIBRARY
} else {
strncpy(b->innodefilename, argv[i], FILENAMESIZE - 1);
b->innodefilename[FILENAMESIZE - 1] = '\0';
}
#endif /* not TRILIBRARY */
}
#ifndef TRILIBRARY
if (b->innodefilename[0] == '\0') {
syntax();
} if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 5], ".node")) {
b->innodefilename[strlen(b->innodefilename) - 5] = '\0';
}
if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 5], ".poly")) {
b->innodefilename[strlen(b->innodefilename) - 5] = '\0';
b->poly = 1;
}
#ifndef CDT_ONLY
if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 4], ".ele")) {
b->innodefilename[strlen(b->innodefilename) - 4] = '\0';
b->refine = 1;
}
if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 5], ".area")) {
b->innodefilename[strlen(b->innodefilename) - 5] = '\0';
b->refine = 1;
b->quality = 1;
b->vararea = 1;
}
#endif /* not CDT_ONLY */
#endif /* not TRILIBRARY */
b->usesegments = b->poly || b->refine || b->quality || b->convex;
b->goodangle = cos(b->minangle * PI / 180.0);
if (b->goodangle == 1.0) {
b->offconstant = 0.0;
} else {
b->offconstant = 0.475 * sqrt((1.0 + b->goodangle) / (1.0 - b->goodangle));
}
b->goodangle *= b->goodangle;
if (b->refine && b->noiterationnum) {
printf(
"Error: You cannot use the -I switch when refining a triangulation.\n");
triexit(1);
}
/* Be careful not to allocate space for element area constraints that */
/* will never be assigned any value (other than the default -1.0). */
if (!b->refine && !b->poly) {
b->vararea = 0;
}
/* Be careful not to add an extra attribute to each element unless the */
/* input supports it (PSLG in, but not refining a preexisting mesh). */
if (b->refine || !b->poly) {
b->regionattrib = 0;
}
/* Regular/weighted triangulations are incompatible with PSLGs */
/* and meshing. */
if (b->weighted && (b->poly || b->quality)) {
b->weighted = 0;
if (!b->quiet) {
printf("Warning: weighted triangulations (-w, -W) are incompatible\n");
printf(" with PSLGs (-p) and meshing (-q, -a, -u). Weights ignored.\n"
);
}
}
if (b->jettison && b->nonodewritten && !b->quiet) {
printf("Warning: -j and -N switches are somewhat incompatible.\n");
printf(" If any vertices are jettisoned, you will need the output\n");
printf(" .node file to reconstruct the new node indices.");
}
#ifndef TRILIBRARY
strcpy(b->inpolyfilename, b->innodefilename);
strcpy(b->inelefilename, b->innodefilename);
strcpy(b->areafilename, b->innodefilename);
increment = 0;
strcpy(workstring, b->innodefilename);
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 (b->noiterationnum) {
strcpy(b->outnodefilename, b->innodefilename);
strcpy(b->outelefilename, b->innodefilename);
strcpy(b->edgefilename, b->innodefilename);
strcpy(b->vnodefilename, b->innodefilename);
strcpy(b->vedgefilename, b->innodefilename);
strcpy(b->neighborfilename, b->innodefilename);
strcpy(b->offfilename, b->innodefilename);
strcat(b->outnodefilename, ".node");
strcat(b->outelefilename, ".ele");
strcat(b->edgefilename, ".edge");
strcat(b->vnodefilename, ".v.node");
strcat(b->vedgefilename, ".v.edge");
strcat(b->neighborfilename, ".neigh");
strcat(b->offfilename, ".off");
} else if (increment == 0) {
strcpy(b->outnodefilename, b->innodefilename);
strcpy(b->outpolyfilename, b->innodefilename);
strcpy(b->outelefilename, b->innodefilename);
strcpy(b->edgefilename, b->innodefilename);
strcpy(b->vnodefilename, b->innodefilename);
strcpy(b->vedgefilename, b->innodefilename);
strcpy(b->neighborfilename, b->innodefilename);
strcpy(b->offfilename, b->innodefilename);
strcat(b->outnodefilename, ".1.node");
strcat(b->outpolyfilename, ".1.poly");
strcat(b->outelefilename, ".1.ele");
strcat(b->edgefilename, ".1.edge");
strcat(b->vnodefilename, ".1.v.node");
strcat(b->vedgefilename, ".1.v.edge");
strcat(b->neighborfilename, ".1.neigh");
strcat(b->offfilename, ".1.off");
} else {
workstring[increment] = '%';
workstring[increment + 1] = 'd';
workstring[increment + 2] = '\0';
sprintf(b->outnodefilename, workstring, meshnumber + 1);
strcpy(b->outpolyfilename, b->outnodefilename);
strcpy(b->outelefilename, b->outnodefilename);
strcpy(b->edgefilename, b->outnodefilename);
strcpy(b->vnodefilename, b->outnodefilename);
strcpy(b->vedgefilename, b->outnodefilename);
strcpy(b->neighborfilename, b->outnodefilename);
strcpy(b->offfilename, b->outnodefilename);
strcat(b->outnodefilename, ".node");
strcat(b->outpolyfilename, ".poly");
strcat(b->outelefilename, ".ele");
strcat(b->edgefilename, ".edge");
strcat(b->vnodefilename, ".v.node");
strcat(b->vedgefilename, ".v.edge");
strcat(b->neighborfilename, ".neigh");
strcat(b->offfilename, ".off");
}
strcat(b->innodefilename, ".node");
strcat(b->inpolyfilename, ".poly");
strcat(b->inelefilename, ".ele"); strcat(b->areafilename, ".area");
#endif /* not TRILIBRARY */
}
/** **/
/** **/
/********* User interaction routines begin here *********/
/********* Debugging routines begin here *********/
/** **/
/** **/
/*****************************************************************************/
/* */
/* printtriangle() Print out the details of an oriented triangle. */
/* */
/* I originally wrote this procedure to simplify debugging; it can be */
/* called directly from the debugger, and presents information about an */
/* oriented triangle in digestible form. It's also used when the */
/* highest level of verbosity (`-VVV') is specified. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
void printtriangle(struct mesh *m, struct behavior *b, struct otri *t)
#else /* not ANSI_DECLARATORS */
void printtriangle(m, b, t)
struct mesh *m;
struct behavior *b;
struct otri *t;
#endif /* not ANSI_DECLARATORS */
{
struct otri printtri;
struct osub printsh;
vertex printvertex;
printf("triangle x%lx with orientation %d:\n", (unsigned long) t->tri,
t->orient);
decode(t->tri[0], printtri);
if (printtri.tri == m->dummytri) {
printf(" [0] = Outer space\n");
} else {
printf(" [0] = x%lx %d\n", (unsigned long) printtri.tri,
printtri.orient);
}
decode(t->tri[1], printtri);
if (printtri.tri == m->dummytri) {
printf(" [1] = Outer space\n");
} else {
printf(" [1] = x%lx %d\n", (unsigned long) printtri.tri,
printtri.orient);
}
decode(t->tri[2], printtri);
if (printtri.tri == m->dummytri) {
printf(" [2] = Outer space\n");
} else {
printf(" [2] = x%lx %d\n", (unsigned long) printtri.tri,
printtri.orient);
}
org(*t, printvertex);
if (printvertex == (vertex) NULL)
printf(" Origin[%d] = NULL\n", (t->orient + 1) % 3 + 3);
else
printf(" Origin[%d] = x%lx (%.12g, %.12g)\n",
(t->orient + 1) % 3 + 3, (unsigned long) printvertex,
printvertex[0], printvertex[1]);
dest(*t, printvertex);
if (printvertex == (vertex) NULL) printf(" Dest [%d] = NULL\n", (t->orient + 2) % 3 + 3);
else
printf(" Dest [%d] = x%lx (%.12g, %.12g)\n",
(t->orient + 2) % 3 + 3, (unsigned long) printvertex,
printvertex[0], printvertex[1]);
apex(*t, printvertex);
if (printvertex == (vertex) NULL)
printf(" Apex [%d] = NULL\n", t->orient + 3);
else
printf(" Apex [%d] = x%lx (%.12g, %.12g)\n",
t->orient + 3, (unsigned long) printvertex,
printvertex[0], printvertex[1]);
if (b->usesegments) {
sdecode(t->tri[6], printsh);
if (printsh.ss != m->dummysub) {
printf(" [6] = x%lx %d\n", (unsigned long) printsh.ss,
printsh.ssorient);
}
sdecode(t->tri[7], printsh);
if (printsh.ss != m->dummysub) {
printf(" [7] = x%lx %d\n", (unsigned long) printsh.ss,
printsh.ssorient);
}
sdecode(t->tri[8], printsh);
if (printsh.ss != m->dummysub) {
printf(" [8] = x%lx %d\n", (unsigned long) printsh.ss,
printsh.ssorient);
}
}
if (b->vararea) {
printf(" Area constraint: %.4g\n", areabound(*t));
}
}
/*****************************************************************************/
/* */
/* printsubseg() Print out the details of an oriented subsegment. */
/* */
/* I originally wrote this procedure to simplify debugging; it can be */
/* called directly from the debugger, and presents information about an */
/* oriented subsegment in digestible form. It's also used when the highest */
/* level of verbosity (`-VVV') is specified. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
void printsubseg(struct mesh *m, struct behavior *b, struct osub *s)
#else /* not ANSI_DECLARATORS */
void printsubseg(m, b, s)
struct mesh *m;
struct behavior *b;
struct osub *s;
#endif /* not ANSI_DECLARATORS */
{
struct osub printsh;
struct otri printtri;
vertex printvertex;
printf("subsegment x%lx with orientation %d and mark %d:\n",
(unsigned long) s->ss, s->ssorient, mark(*s));
sdecode(s->ss[0], printsh);
if (printsh.ss == m->dummysub) {
printf(" [0] = No subsegment\n");
} else {
printf(" [0] = x%lx %d\n", (unsigned long) printsh.ss,
printsh.ssorient);
} sdecode(s->ss[1], printsh);
if (printsh.ss == m->dummysub) {
printf(" [1] = No subsegment\n");
} else {
printf(" [1] = x%lx %d\n", (unsigned long) printsh.ss,
printsh.ssorient);
}
sorg(*s, printvertex);
if (printvertex == (vertex) NULL)
printf(" Origin[%d] = NULL\n", 2 + s->ssorient);
else
printf(" Origin[%d] = x%lx (%.12g, %.12g)\n",
2 + s->ssorient, (unsigned long) printvertex,
printvertex[0], printvertex[1]);
sdest(*s, printvertex);
if (printvertex == (vertex) NULL)
printf(" Dest [%d] = NULL\n", 3 - s->ssorient);
else
printf(" Dest [%d] = x%lx (%.12g, %.12g)\n",
3 - s->ssorient, (unsigned long) printvertex,
printvertex[0], printvertex[1]);
decode(s->ss[6], printtri);
if (printtri.tri == m->dummytri) {
printf(" [6] = Outer space\n");
} else {
printf(" [6] = x%lx %d\n", (unsigned long) printtri.tri,
printtri.orient);
}
decode(s->ss[7], printtri);
if (printtri.tri == m->dummytri) {
printf(" [7] = Outer space\n");
} else {
printf(" [7] = x%lx %d\n", (unsigned long) printtri.tri,
printtri.orient);
}
segorg(*s, printvertex);
if (printvertex == (vertex) NULL)
printf(" Segment origin[%d] = NULL\n", 4 + s->ssorient);
else
printf(" Segment origin[%d] = x%lx (%.12g, %.12g)\n",
4 + s->ssorient, (unsigned long) printvertex,
printvertex[0], printvertex[1]);
segdest(*s, printvertex);
if (printvertex == (vertex) NULL)
printf(" Segment dest [%d] = NULL\n", 5 - s->ssorient);
else
printf(" Segment dest [%d] = x%lx (%.12g, %.12g)\n",
5 - s->ssorient, (unsigned long) printvertex,
printvertex[0], printvertex[1]);
}
/** **/
/** **/
/********* Debugging routines end here *********/
/********* Memory management routines begin here *********/
/** **/
/** **/
/*****************************************************************************/
/* */
/* poolzero() Set all of a pool's fields to zero. */
/* */
/* This procedure should never be called on a pool that has any memory */
/* allocated to it, as that memory would leak. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
void poolzero(struct memorypool *pool)
#else /* not ANSI_DECLARATORS */
void poolzero(pool)
struct memorypool *pool;
#endif /* not ANSI_DECLARATORS */
{
pool->firstblock = (VOID **) NULL;
pool->nowblock = (VOID **) NULL;
pool->nextitem = (VOID *) NULL;
pool->deaditemstack = (VOID *) NULL;
pool->pathblock = (VOID **) NULL;
pool->pathitem = (VOID *) NULL;
pool->alignbytes = 0;
pool->itembytes = 0;
pool->itemsperblock = 0;
pool->itemsfirstblock = 0;
pool->items = 0;
pool->maxitems = 0;
pool->unallocateditems = 0;
pool->pathitemsleft = 0;
}
/*****************************************************************************/
/* */
/* poolrestart() Deallocate all items in a 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. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
void poolrestart(struct memorypool *pool)
#else /* not ANSI_DECLARATORS */
void poolrestart(pool)
struct memorypool *pool;
#endif /* not ANSI_DECLARATORS */
{
unsigned long alignptr;
pool->items = 0;
pool->maxitems = 0;
/* Set the currently active block. */
pool->nowblock = pool->firstblock;
/* Find the first item in the pool. Increment by the size of (VOID *). */
alignptr = (unsigned long) (pool->nowblock + 1);
/* Align the item on an `alignbytes'-byte boundary. */
pool->nextitem = (VOID *)
(alignptr + (unsigned long) pool->alignbytes -
(alignptr % (unsigned long) pool->alignbytes));
/* There are lots of unallocated items left in this block. */
pool->unallocateditems = pool->itemsfirstblock;
/* The stack of deallocated items is empty. */
pool->deaditemstack = (VOID *) NULL;
}
/*****************************************************************************/
/* */
/* poolinit() Initialize a pool of memory for allocation of items. */
/* */
/* This routine initializes the machinery for allocating 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. */
/* */
/* Don't change this routine unless you understand it. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
void poolinit(struct memorypool *pool, int bytecount, int itemcount,
int firstitemcount, int alignment)
#else /* not ANSI_DECLARATORS */
void poolinit(pool, bytecount, itemcount, firstitemcount, alignment)
struct memorypool *pool;
int bytecount;
int itemcount;
int firstitemcount;
int alignment;
#endif /* not ANSI_DECLARATORS */
{
/* Find the proper alignment, which must be at least as large as: */
/* - The parameter `alignment'. */
/* - sizeof(VOID *), so the stack of dead items can be maintained */
/* without unaligned accesses. */
if (alignment > sizeof(VOID *)) {
pool->alignbytes = alignment;
} else {
pool->alignbytes = sizeof(VOID *);
}
pool->itembytes = ((bytecount - 1) / pool->alignbytes + 1) *
pool->alignbytes;
pool->itemsperblock = itemcount;
if (firstitemcount == 0) {
pool->itemsfirstblock = itemcount;
} else {
pool->itemsfirstblock = firstitemcount;
}
/* Allocate a block of items. Space for `itemsfirstblock' items and one */
/* pointer (to point to the next block) are allocated, as well as space */
/* to ensure alignment of the items. */
pool->firstblock = (VOID **)
trimalloc(pool->itemsfirstblock * pool->itembytes + (int) sizeof(VOID *) +
pool->alignbytes);
/* Set the next block pointer to NULL. */
*(pool->firstblock) = (VOID *) NULL;
poolrestart(pool);
}
/*****************************************************************************/
/* */
/* pooldeinit() Free to the operating system all memory taken by a pool. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
void pooldeinit(struct memorypool *pool)
#else /* not ANSI_DECLARATORS */
void pooldeinit(pool)
struct memorypool *pool;
#endif /* not ANSI_DECLARATORS */
{
while (pool->firstblock != (VOID **) NULL) {
pool->nowblock = (VOID **) *(pool->firstblock);
trifree((VOID *) pool->firstblock); pool->firstblock = pool->nowblock;
}
}
/*****************************************************************************/
/* */
/* poolalloc() Allocate space for an item. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
VOID *poolalloc(struct memorypool *pool)
#else /* not ANSI_DECLARATORS */
VOID *poolalloc(pool)
struct memorypool *pool;
#endif /* not ANSI_DECLARATORS */
{
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 (pool->deaditemstack != (VOID *) NULL) {
newitem = pool->deaditemstack; /* Take first item in list. */
pool->deaditemstack = * (VOID **) pool->deaditemstack;
} else {
/* Check if there are any free items left in the current block. */
if (pool->unallocateditems == 0) {
/* Check if another block must be allocated. */
if (*(pool->nowblock) == (VOID *) NULL) {
/* Allocate a new block of items, pointed to by the previous block. */
newblock = (VOID **) trimalloc(pool->itemsperblock * pool->itembytes +
(int) sizeof(VOID *) +
pool->alignbytes);
*(pool->nowblock) = (VOID *) newblock;
/* The next block pointer is NULL. */
*newblock = (VOID *) NULL;
}
/* Move to the new block. */
pool->nowblock = (VOID **) *(pool->nowblock);
/* Find the first item in the block. */
/* Increment by the size of (VOID *). */
alignptr = (unsigned long) (pool->nowblock + 1);
/* Align the item on an `alignbytes'-byte boundary. */
pool->nextitem = (VOID *)
(alignptr + (unsigned long) pool->alignbytes -
(alignptr % (unsigned long) pool->alignbytes));
/* There are lots of unallocated items left in this block. */
pool->unallocateditems = pool->itemsperblock;
}
/* Allocate a new item. */
newitem = pool->nextitem;
/* Advance `nextitem' pointer to next free item in block. */
pool->nextitem = (VOID *) ((char *) pool->nextitem + pool->itembytes);
pool->unallocateditems--;
pool->maxitems++;
}
pool->items++;
return newitem;
}
/*****************************************************************************/
/* */
/* pooldealloc() Deallocate space for an item. */
/* */
/* The deallocated space is stored in a queue for later reuse. *//* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
void pooldealloc(struct memorypool *pool, VOID *dyingitem)
#else /* not ANSI_DECLARATORS */
void pooldealloc(pool, dyingitem)
struct memorypool *pool;
VOID *dyingitem;
#endif /* not ANSI_DECLARATORS */
{
/* Push freshly killed item onto stack. */
*((VOID **) dyingitem) = pool->deaditemstack;
pool->deaditemstack = dyingitem;
pool->items--;
}
/*****************************************************************************/
/* */
/* traversalinit() Prepare to traverse the entire list of items. */
/* */
/* This routine is used in conjunction with traverse(). */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
void traversalinit(struct memorypool *pool)
#else /* not ANSI_DECLARATORS */
void traversalinit(pool)
struct memorypool *pool;
#endif /* not ANSI_DECLARATORS */
{
unsigned long alignptr;
/* Begin the traversal in the first block. */
pool->pathblock = pool->firstblock;
/* Find the first item in the block. Increment by the size of (VOID *). */
alignptr = (unsigned long) (pool->pathblock + 1);
/* Align with item on an `alignbytes'-byte boundary. */
pool->pathitem = (VOID *)
(alignptr + (unsigned long) pool->alignbytes -
(alignptr % (unsigned long) pool->alignbytes));
/* Set the number of items left in the current block. */
pool->pathitemsleft = pool->itemsfirstblock;
}
/*****************************************************************************/
/* */
/* 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. Why? I don't want to allocate extra */
/* space just to demarcate dead items. It can usually be done more */
/* space-efficiently by a routine that knows something about the structure */
/* of the item. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
VOID *traverse(struct memorypool *pool)
#else /* not ANSI_DECLARATORS */
VOID *traverse(pool)
struct memorypool *pool;
#endif /* not ANSI_DECLARATORS */
{ VOID *newitem;
unsigned long alignptr;
/* Stop upon exhausting the list of items. */
if (pool->pathitem == pool->nextitem) {
return (VOID *) NULL;
}
/* Check whether any untraversed items remain in the current block. */
if (pool->pathitemsleft == 0) {
/* Find the next block. */
pool->pathblock = (VOID **) *(pool->pathblock);
/* Find the first item in the block. Increment by the size of (VOID *). */
alignptr = (unsigned long) (pool->pathblock + 1);
/* Align with item on an `alignbytes'-byte boundary. */
pool->pathitem = (VOID *)
(alignptr + (unsigned long) pool->alignbytes -
(alignptr % (unsigned long) pool->alignbytes));
/* Set the number of items left in the current block. */
pool->pathitemsleft = pool->itemsperblock;
}
newitem = pool->pathitem;
/* Find the next item in the block. */
pool->pathitem = (VOID *) ((char *) pool->pathitem + pool->itembytes);
pool->pathitemsleft--;
return newitem;
}
/*****************************************************************************/
/* */
/* dummyinit() Initialize the triangle that fills "outer space" and the */
/* omnipresent subsegment. */
/* */
/* The triangle that fills "outer space," called `dummytri', is pointed to */
/* by every triangle and subsegment on a boundary (be it outer or inner) of */
/* the triangulation. Also, `dummytri' points to one of the triangles on */
/* the convex hull (until the holes and concavities are carved), making it */
/* possible to find a starting triangle for point location. */
/* */
/* The omnipresent subsegment, `dummysub', is pointed to by every triangle */
/* or subsegment that doesn't have a full complement of real subsegments */
/* to point to. */
/* */
/* `dummytri' and `dummysub' are generally required to fulfill only a few */
/* invariants: their vertices must remain NULL and `dummytri' must always */
/* be bonded (at offset zero) to some triangle on the convex hull of the */
/* mesh, via a boundary edge. Otherwise, the connections of `dummytri' and */
/* `dummysub' may change willy-nilly. This makes it possible to avoid */
/* writing a good deal of special-case code (in the edge flip, for example) */
/* for dealing with the boundary of the mesh, places where no subsegment is */
/* present, and so forth. Other entities are frequently bonded to */
/* `dummytri' and `dummysub' as if they were real mesh entities, with no */
/* harm done. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
void dummyinit(struct mesh *m, struct behavior *b, int trianglebytes,
int subsegbytes)
#else /* not ANSI_DECLARATORS */
void dummyinit(m, b, trianglebytes, subsegbytes)
struct mesh *m;
struct behavior *b;
int trianglebytes;
int subsegbytes;
#endif /* not ANSI_DECLARATORS */
{
unsigned long alignptr;
/* Set up `dummytri', the `triangle' that occupies "outer space." */
m->dummytribase = (triangle *) trimalloc(trianglebytes +
m->triangles.alignbytes);
/* Align `dummytri' on a `triangles.alignbytes'-byte boundary. */
alignptr = (unsigned long) m->dummytribase;
m->dummytri = (triangle *)
(alignptr + (unsigned long) m->triangles.alignbytes -
(alignptr % (unsigned long) m->triangles.alignbytes));
/* Initialize the three adjoining triangles 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. */
m->dummytri[0] = (triangle) m->dummytri;
m->dummytri[1] = (triangle) m->dummytri;
m->dummytri[2] = (triangle) m->dummytri;
/* Three NULL vertices. */
m->dummytri[3] = (triangle) NULL;
m->dummytri[4] = (triangle) NULL;
m->dummytri[5] = (triangle) NULL;
if (b->usesegments) {
/* Set up `dummysub', the omnipresent subsegment pointed to by any */
/* triangle side or subsegment end that isn't attached to a real */
/* subsegment. */
m->dummysubbase = (subseg *) trimalloc(subsegbytes +
m->subsegs.alignbytes);
/* Align `dummysub' on a `subsegs.alignbytes'-byte boundary. */
alignptr = (unsigned long) m->dummysubbase;
m->dummysub = (subseg *)
(alignptr + (unsigned long) m->subsegs.alignbytes -
(alignptr % (unsigned long) m->subsegs.alignbytes));
/* Initialize the two adjoining subsegments to be the omnipresent */
/* subsegment. These will eventually be changed by various bonding */
/* operations, but their values don't really matter, as long as they */
/* can legally be dereferenced. */
m->dummysub[0] = (subseg) m->dummysub;
m->dummysub[1] = (subseg) m->dummysub;
/* Four NULL vertices. */
m->dummysub[2] = (subseg) NULL;
m->dummysub[3] = (subseg) NULL;
m->dummysub[4] = (subseg) NULL;
m->dummysub[5] = (subseg) NULL;
/* Initialize the two adjoining triangles to be "outer space." */
m->dummysub[6] = (subseg) m->dummytri;
m->dummysub[7] = (subseg) m->dummytri;
/* Set the boundary marker to zero. */
* (int *) (m->dummysub + 8) = 0;
/* Initialize the three adjoining subsegments of `dummytri' to be */
/* the omnipresent subsegment. */
m->dummytri[6] = (triangle) m->dummysub;
m->dummytri[7] = (triangle) m->dummysub;
m->dummytri[8] = (triangle) m->dummysub;
}
}
/*****************************************************************************/
/* */
/* initializevertexpool() Calculate the size of the vertex data structure */
/* and initialize its memory pool. */
/* */
/* This routine also computes the `vertexmarkindex' and `vertex2triindex' */
/* indices used to find values within each vertex. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
void initializevertexpool(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */void initializevertexpool(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */
{
int vertexsize;
/* The index within each vertex at which the boundary marker is found, */
/* followed by the vertex type. Ensure the vertex marker is aligned to */
/* a sizeof(int)-byte address. */
m->vertexmarkindex = ((m->mesh_dim + m->nextras) * sizeof(REAL) +
sizeof(int) - 1) /
sizeof(int);
vertexsize = (m->vertexmarkindex + 2) * sizeof(int);
if (b->poly) {
/* The index within each vertex at which a triangle pointer is found. */
/* Ensure the pointer is aligned to a sizeof(triangle)-byte address. */
m->vertex2triindex = (vertexsize + sizeof(triangle) - 1) /
sizeof(triangle);
vertexsize = (m->vertex2triindex + 1) * sizeof(triangle);
}
/* Initialize the pool of vertices. */
poolinit(&m->vertices, vertexsize, VERTEXPERBLOCK,
m->invertices > VERTEXPERBLOCK ? m->invertices : VERTEXPERBLOCK,
sizeof(REAL));
}
/*****************************************************************************/
/* */
/* initializetrisubpools() Calculate the sizes of the triangle and */
/* subsegment data structures and initialize */
/* their memory pools. */
/* */
/* This routine also computes the `highorderindex', `elemattribindex', and */
/* `areaboundindex' indices used to find values within each triangle. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
void initializetrisubpools(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
void initializetrisubpools(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */
{
int trisize;
/* The index within each triangle at which the extra nodes (above three) */
/* associated with high order elements are found. There are three */
/* pointers to other triangles, three pointers to corners, and possibly */
/* three pointers to subsegments before the extra nodes. */
m->highorderindex = 6 + (b->usesegments * 3);
/* The number of bytes occupied by a triangle. */
trisize = ((b->order + 1) * (b->order + 2) / 2 + (m->highorderindex - 3)) *
sizeof(triangle);
/* The index within each triangle at which its attributes are found, */
/* where the index is measured in REALs. */
m->elemattribindex = (trisize + sizeof(REAL) - 1) / sizeof(REAL);
/* The index within each triangle at which the maximum area constraint */
/* is found, where the index is measured in REALs. Note that if the */
/* `regionattrib' flag is set, an additional attribute will be added. */
m->areaboundindex = m->elemattribindex + m->eextras + b->regionattrib;
/* If triangle attributes or an area bound are needed, increase the number */
/* of bytes occupied by a triangle. */
if (b->vararea) {
trisize = (m->areaboundindex + 1) * sizeof(REAL); } else if (m->eextras + b->regionattrib > 0) {
trisize = m->areaboundindex * sizeof(REAL);
}
/* If a Voronoi diagram or triangle neighbor graph is requested, make */
/* sure there's room to store an integer index in each triangle. This */
/* integer index can occupy the same space as the subsegment pointers */
/* or attributes or area constraint or extra nodes. */
if ((b->voronoi || b->neighbors) &&
(trisize < 6 * sizeof(triangle) + sizeof(int))) {
trisize = 6 * sizeof(triangle) + sizeof(int);
}
/* Having determined the memory size of a triangle, initialize the pool. */
poolinit(&m->triangles, trisize, TRIPERBLOCK,
(2 * m->invertices - 2) > TRIPERBLOCK ? (2 * m->invertices - 2) :
TRIPERBLOCK, 4);
if (b->usesegments) {
/* Initialize the pool of subsegments. Take into account all eight */
/* pointers and one boundary marker. */
poolinit(&m->subsegs, 8 * sizeof(triangle) + sizeof(int),
SUBSEGPERBLOCK, SUBSEGPERBLOCK, 4);
/* Initialize the "outer space" triangle and omnipresent subsegment. */
dummyinit(m, b, m->triangles.itembytes, m->subsegs.itembytes);
} else {
/* Initialize the "outer space" triangle. */
dummyinit(m, b, m->triangles.itembytes, 0);
}
}
/*****************************************************************************/
/* */
/* triangledealloc() Deallocate space for a triangle, marking it dead. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
void triangledealloc(struct mesh *m, triangle *dyingtriangle)
#else /* not ANSI_DECLARATORS */
void triangledealloc(m, dyingtriangle)
struct mesh *m;
triangle *dyingtriangle;
#endif /* not ANSI_DECLARATORS */
{
/* Mark the triangle as dead. This makes it possible to detect dead */
/* triangles when traversing the list of all triangles. */
killtri(dyingtriangle);
pooldealloc(&m->triangles, (VOID *) dyingtriangle);
}
/*****************************************************************************/
/* */
/* triangletraverse() Traverse the triangles, skipping dead ones. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
triangle *triangletraverse(struct mesh *m)
#else /* not ANSI_DECLARATORS */
triangle *triangletraverse(m)
struct mesh *m;
#endif /* not ANSI_DECLARATORS */
{
triangle *newtriangle;
do {
newtriangle = (triangle *) traverse(&m->triangles); if (newtriangle == (triangle *) NULL) {
return (triangle *) NULL;
}
} while (deadtri(newtriangle)); /* Skip dead ones. */
return newtriangle;
}
/*****************************************************************************/
/* */
/* subsegdealloc() Deallocate space for a subsegment, marking it dead. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
void subsegdealloc(struct mesh *m, subseg *dyingsubseg)
#else /* not ANSI_DECLARATORS */
void subsegdealloc(m, dyingsubseg)
struct mesh *m;
subseg *dyingsubseg;
#endif /* not ANSI_DECLARATORS */
{
/* Mark the subsegment as dead. This makes it possible to detect dead */
/* subsegments when traversing the list of all subsegments. */
killsubseg(dyingsubseg);
pooldealloc(&m->subsegs, (VOID *) dyingsubseg);
}
/*****************************************************************************/
/* */
/* subsegtraverse() Traverse the subsegments, skipping dead ones. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
subseg *subsegtraverse(struct mesh *m)
#else /* not ANSI_DECLARATORS */
subseg *subsegtraverse(m)
struct mesh *m;
#endif /* not ANSI_DECLARATORS */
{
subseg *newsubseg;
do {
newsubseg = (subseg *) traverse(&m->subsegs);
if (newsubseg == (subseg *) NULL) {
return (subseg *) NULL;
}
} while (deadsubseg(newsubseg)); /* Skip dead ones. */
return newsubseg;
}
/*****************************************************************************/
/* */
/* vertexdealloc() Deallocate space for a vertex, marking it dead. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
void vertexdealloc(struct mesh *m, vertex dyingvertex)
#else /* not ANSI_DECLARATORS */
void vertexdealloc(m, dyingvertex)
struct mesh *m;
vertex dyingvertex;
#endif /* not ANSI_DECLARATORS */
{
/* Mark the vertex as dead. This makes it possible to detect dead */
/* vertices when traversing the list of all vertices. */ setvertextype(dyingvertex, DEADVERTEX);
pooldealloc(&m->vertices, (VOID *) dyingvertex);
}
/*****************************************************************************/
/* */
/* vertextraverse() Traverse the vertices, skipping dead ones. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
vertex vertextraverse(struct mesh *m)
#else /* not ANSI_DECLARATORS */
vertex vertextraverse(m)
struct mesh *m;
#endif /* not ANSI_DECLARATORS */
{
vertex newvertex;
do {
newvertex = (vertex) traverse(&m->vertices);
if (newvertex == (vertex) NULL) {
return (vertex) NULL;
}
} while (vertextype(newvertex) == DEADVERTEX); /* Skip dead ones. */
return newvertex;
}
/*****************************************************************************/
/* */
/* badsubsegdealloc() Deallocate space for a bad subsegment, marking it */
/* dead. */
/* */
/*****************************************************************************/
#ifndef CDT_ONLY
#ifdef ANSI_DECLARATORS
void badsubsegdealloc(struct mesh *m, struct badsubseg *dyingseg)
#else /* not ANSI_DECLARATORS */
void badsubsegdealloc(m, dyingseg)
struct mesh *m;
struct badsubseg *dyingseg;
#endif /* not ANSI_DECLARATORS */
{
/* Set subsegment's origin to NULL. This makes it possible to detect dead */
/* badsubsegs when traversing the list of all badsubsegs . */
dyingseg->subsegorg = (vertex) NULL;
pooldealloc(&m->badsubsegs, (VOID *) dyingseg);
}
#endif /* not CDT_ONLY */
/*****************************************************************************/
/* */
/* badsubsegtraverse() Traverse the bad subsegments, skipping dead ones. */
/* */
/*****************************************************************************/
#ifndef CDT_ONLY
#ifdef ANSI_DECLARATORS
struct badsubseg *badsubsegtraverse(struct mesh *m)
#else /* not ANSI_DECLARATORS */
struct badsubseg *badsubsegtraverse(m)
struct mesh *m;
#endif /* not ANSI_DECLARATORS */
{
struct badsubseg *newseg;
do {
newseg = (struct badsubseg *) traverse(&m->badsubsegs);
if (newseg == (struct badsubseg *) NULL) {
return (struct badsubseg *) NULL;
}
} while (newseg->subsegorg == (vertex) NULL); /* Skip dead ones. */
return newseg;
}
#endif /* not CDT_ONLY */
/*****************************************************************************/
/* */
/* getvertex() Get a specific vertex, by number, from the list. */
/* */
/* The first vertex is number 'firstnumber'. */
/* */
/* Note that this takes O(n) time (with a small constant, if VERTEXPERBLOCK */
/* is large). I don't care to take the trouble to make it work in constant */
/* time. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
vertex getvertex(struct mesh *m, struct behavior *b, int number)
#else /* not ANSI_DECLARATORS */
vertex getvertex(m, b, number)
struct mesh *m;
struct behavior *b;
int number;
#endif /* not ANSI_DECLARATORS */
{
VOID **getblock;
char *foundvertex;
unsigned long alignptr;
int current;
getblock = m->vertices.firstblock;
current = b->firstnumber;
/* Find the right block. */
if (current + m->vertices.itemsfirstblock <= number) {
getblock = (VOID **) *getblock;
current += m->vertices.itemsfirstblock;
while (current + m->vertices.itemsperblock <= number) {
getblock = (VOID **) *getblock;
current += m->vertices.itemsperblock;
}
}
/* Now find the right vertex. */
alignptr = (unsigned long) (getblock + 1);
foundvertex = (char *) (alignptr + (unsigned long) m->vertices.alignbytes -
(alignptr % (unsigned long) m->vertices.alignbytes));
return (vertex) (foundvertex + m->vertices.itembytes * (number - current));
}
/*****************************************************************************/
/* */
/* triangledeinit() Free all remaining allocated memory. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
void triangledeinit(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */void triangledeinit(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */
{
pooldeinit(&m->triangles);
trifree((VOID *) m->dummytribase);
if (b->usesegments) {
pooldeinit(&m->subsegs);
trifree((VOID *) m->dummysubbase);
}
pooldeinit(&m->vertices);
#ifndef CDT_ONLY
if (b->quality) {
pooldeinit(&m->badsubsegs);
if ((b->minangle > 0.0) || b->vararea || b->fixedarea || b->usertest) {
pooldeinit(&m->badtriangles);
pooldeinit(&m->flipstackers);
}
}
#endif /* not CDT_ONLY */
}
/** **/
/** **/
/********* Memory management routines end here *********/
/********* Constructors begin here *********/
/** **/
/** **/
/*****************************************************************************/
/* */
/* maketriangle() Create a new triangle with orientation zero. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
void maketriangle(struct mesh *m, struct behavior *b, struct otri *newotri)
#else /* not ANSI_DECLARATORS */
void maketriangle(m, b, newotri)
struct mesh *m;
struct behavior *b;
struct otri *newotri;
#endif /* not ANSI_DECLARATORS */
{
int i;
newotri->tri = (triangle *) poolalloc(&m->triangles);
/* Initialize the three adjoining triangles to be "outer space". */
newotri->tri[0] = (triangle) m->dummytri;
newotri->tri[1] = (triangle) m->dummytri;
newotri->tri[2] = (triangle) m->dummytri;
/* Three NULL vertices. */
newotri->tri[3] = (triangle) NULL;
newotri->tri[4] = (triangle) NULL;
newotri->tri[5] = (triangle) NULL;
if (b->usesegments) {
/* Initialize the three adjoining subsegments to be the omnipresent */
/* subsegment. */
newotri->tri[6] = (triangle) m->dummysub;
newotri->tri[7] = (triangle) m->dummysub;
newotri->tri[8] = (triangle) m->dummysub;
}
for (i = 0; i < m->eextras; i++) {
setelemattribute(*newotri, i, 0.0);
}
if (b->vararea) { setareabound(*newotri, -1.0);
}
newotri->orient = 0;
}
/*****************************************************************************/
/* */
/* makesubseg() Create a new subsegment with orientation zero. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
void makesubseg(struct mesh *m, struct osub *newsubseg)
#else /* not ANSI_DECLARATORS */
void makesubseg(m, newsubseg)
struct mesh *m;
struct osub *newsubseg;
#endif /* not ANSI_DECLARATORS */
{
newsubseg->ss = (subseg *) poolalloc(&m->subsegs);
/* Initialize the two adjoining subsegments to be the omnipresent */
/* subsegment. */
newsubseg->ss[0] = (subseg) m->dummysub;
newsubseg->ss[1] = (subseg) m->dummysub;
/* Four NULL vertices. */
newsubseg->ss[2] = (subseg) NULL;
newsubseg->ss[3] = (subseg) NULL;
newsubseg->ss[4] = (subseg) NULL;
newsubseg->ss[5] = (subseg) NULL;
/* Initialize the two adjoining triangles to be "outer space." */
newsubseg->ss[6] = (subseg) m->dummytri;
newsubseg->ss[7] = (subseg) m->dummytri;
/* Set the boundary marker to zero. */
setmark(*newsubseg, 0);
newsubseg->ssorient = 0;
}
/** **/
/** **/
/********* Constructors end here *********/
/********* Geometric primitives begin here *********/
/** **/
/** **/
/* The adaptive exact arithmetic geometric predicates implemented herein are */
/* described in detail in my paper, "Adaptive Precision Floating-Point */
/* Arithmetic and Fast Robust Geometric Predicates." See the header for a */
/* full citation. */
/* 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 without */
/* forcing the value to be stored to memory (rather than be kept in the */
/* register to which the optimizer assigned it). */
#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 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
/* 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)
/* Macro for multiplying a two-component expansion by a single component. */
#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)
/*****************************************************************************/
/* */
/* 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. */
/* */
/*****************************************************************************/
void 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 these routines will work on such machines.) */
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;
iccerrboundA = (10.0 + 96.0 * epsilon) * epsilon;
iccerrboundB = (4.0 + 48.0 * epsilon) * epsilon;
iccerrboundC = (44.0 + 576.0 * 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;
}
/*****************************************************************************/
/* */
/* fast_expansion_sum_zeroelim() Sum two expansions, eliminating zero */
/* components from the output expansion. */
/* */
/* Sets h = e + f. See my Robust Predicates 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. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
int fast_expansion_sum_zeroelim(int elen, REAL *e, int flen, REAL *f, REAL *h)
#else /* not ANSI_DECLARATORS */
int fast_expansion_sum_zeroelim(elen, e, flen, f, h) /* h cannot be e or f. */
int elen;
REAL *e;
int flen;
REAL *f;
REAL *h;
#endif /* not ANSI_DECLARATORS */
{ 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;
}
/*****************************************************************************/
/* */
/* scale_expansion_zeroelim() Multiply an expansion by a scalar, *//* eliminating zero components from the */
/* output expansion. */
/* */
/* Sets h = be. See my Robust Predicates 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.) */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
int scale_expansion_zeroelim(int elen, REAL *e, REAL b, REAL *h)
#else /* not ANSI_DECLARATORS */
int scale_expansion_zeroelim(elen, e, b, h) /* e and h cannot be the same. */
int elen;
REAL *e;
REAL b;
REAL *h;
#endif /* not ANSI_DECLARATORS */
{
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;
}
/*****************************************************************************/
/* */
/* estimate() Produce a one-word estimate of an expansion's value. */
/* */
/* See my Robust Predicates paper for details. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
REAL estimate(int elen, REAL *e)#else /* not ANSI_DECLARATORS */
REAL estimate(elen, e)
int elen;
REAL *e;
#endif /* not ANSI_DECLARATORS */
{
REAL Q;
int eindex;
Q = e[0];
for (eindex = 1; eindex < elen; eindex++) {
Q += e[eindex];
}
return Q;
}
/*****************************************************************************/
/* */
/* counterclockwise() 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. */
/* */
/* Uses exact arithmetic if necessary to ensure a correct answer. The */
/* result returned is the determinant of a matrix. 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, this function is usually quite fast, but will run */
/* more slowly when the input points are collinear or nearly so. */
/* */
/* See my Robust Predicates paper for details. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
REAL counterclockwiseadapt(vertex pa, vertex pb, vertex pc, REAL detsum)
#else /* not ANSI_DECLARATORS */
REAL counterclockwiseadapt(pa, pb, pc, detsum)
vertex pa;
vertex pb;
vertex pc;
REAL detsum;
#endif /* not ANSI_DECLARATORS */
{
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]);
}
#ifdef ANSI_DECLARATORS
REAL counterclockwise(struct mesh *m, struct behavior *b,
vertex pa, vertex pb, vertex pc)
#else /* not ANSI_DECLARATORS */
REAL counterclockwise(m, b, pa, pb, pc)
struct mesh *m;
struct behavior *b;
vertex pa;
vertex pb;
vertex pc;
#endif /* not ANSI_DECLARATORS */
{
REAL detleft, detright, det; REAL detsum, errbound;
m->counterclockcount++;
detleft = (pa[0] - pc[0]) * (pb[1] - pc[1]);
detright = (pa[1] - pc[1]) * (pb[0] - pc[0]);
det = detleft - detright;
if (b->noexact) {
return det;
}
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 counterclockwiseadapt(pa, pb, pc, detsum);
}
/*****************************************************************************/
/* */
/* incircle() 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. */
/* */
/* Uses exact arithmetic if necessary to ensure a correct answer. The */
/* result returned is the determinant of a matrix. 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, this function is usually quite fast, but will run */
/* more slowly when the input points are cocircular or nearly so. */
/* */
/* See my Robust Predicates paper for details. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
REAL incircleadapt(vertex pa, vertex pb, vertex pc, vertex pd, REAL permanent)
#else /* not ANSI_DECLARATORS */
REAL incircleadapt(pa, pb, pc, pd, permanent)
vertex pa;
vertex pb;
vertex pc;
vertex pd;
REAL permanent;
#endif /* not ANSI_DECLARATORS */
{
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];
}
#ifdef ANSI_DECLARATORS
REAL incircle(struct mesh *m, struct behavior *b,
vertex pa, vertex pb, vertex pc, vertex pd)
#else /* not ANSI_DECLARATORS */
REAL incircle(m, b, pa, pb, pc, pd)
struct mesh *m;
struct behavior *b;
vertex pa;
vertex pb;
vertex pc;
vertex pd;
#endif /* not ANSI_DECLARATORS */
{
REAL adx, bdx, cdx, ady, bdy, cdy;
REAL bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady;
REAL alift, blift, clift;
REAL det;
REAL permanent, errbound;
m->incirclecount++;
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);
if (b->noexact) {
return det;
}
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);
}
/*****************************************************************************/
/* */
/* orient3d() 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. */
/* */
/* Uses exact arithmetic if necessary to ensure a correct answer. The */
/* result returned is the determinant of a matrix. 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, this function is usually quite fast, but will run */
/* more slowly when the input points are coplanar or nearly so. */
/* */
/* See my Robust Predicates paper for details. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
REAL orient3dadapt(vertex pa, vertex pb, vertex pc, vertex pd,
REAL aheight, REAL bheight, REAL cheight, REAL dheight,
REAL permanent)
#else /* not ANSI_DECLARATORS */
REAL orient3dadapt(pa, pb, pc, pd,
aheight, bheight, cheight, dheight, permanent)
vertex pa;
vertex pb;
vertex pc;
vertex pd;
REAL aheight;
REAL bheight;
REAL cheight;
REAL dheight;
REAL permanent;
#endif /* not ANSI_DECLARATORS */
{
INEXACT REAL adx, bdx, cdx, ady, bdy, cdy, adheight, bdheight, cdheight;
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;
REAL adxtail, bdxtail, cdxtail;
REAL adytail, bdytail, cdytail;
REAL adheighttail, bdheighttail, cdheighttail;
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]);
adheight = (REAL) (aheight - dheight);
bdheight = (REAL) (bheight - dheight);
cdheight = (REAL) (cheight - dheight);
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, adheight, 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, bdheight, 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, cdheight, 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(aheight, dheight, adheight, adheighttail);
Two_Diff_Tail(bheight, dheight, bdheight, bdheighttail);
Two_Diff_Tail(cheight, dheight, cdheight, cdheighttail);
if ((adxtail == 0.0) && (bdxtail == 0.0) && (cdxtail == 0.0) &&
(adytail == 0.0) && (bdytail == 0.0) && (cdytail == 0.0) &&
(adheighttail == 0.0) &&
(bdheighttail == 0.0) &&
(cdheighttail == 0.0)) {
return det;
}
errbound = o3derrboundC * permanent + resulterrbound * Absolute(det);
det += (adheight * ((bdx * cdytail + cdy * bdxtail) -
(bdy * cdxtail + cdx * bdytail)) +
adheighttail * (bdx * cdy - bdy * cdx)) +
(bdheight * ((cdx * adytail + ady * cdxtail) -
(cdy * adxtail + adx * cdytail)) +
bdheighttail * (cdx * ady - cdy * adx)) +
(cdheight * ((adx * bdytail + bdy * adxtail) -
(ady * bdxtail + bdx * adytail)) +
cdheighttail * (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, adheight, 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, bdheight, 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, cdheight, w);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
finother);
finswap = finnow; finnow = finother; finother = finswap;
if (adheighttail != 0.0) {
vlength = scale_expansion_zeroelim(4, bc, adheighttail, v);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v,
finother);
finswap = finnow; finnow = finother; finother = finswap;
}
if (bdheighttail != 0.0) {
vlength = scale_expansion_zeroelim(4, ca, bdheighttail, v);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v,
finother);
finswap = finnow; finnow = finother; finother = finswap;
}
if (cdheighttail != 0.0) {
vlength = scale_expansion_zeroelim(4, ab, cdheighttail, 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, cdheight, 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 (cdheighttail != 0.0) {
Two_One_Product(adxt_bdyt1, adxt_bdyt0, cdheighttail,
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, bdheight, 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 (bdheighttail != 0.0) {
Two_One_Product(adxt_cdyt1, adxt_cdyt0, bdheighttail,
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, adheight, 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 (adheighttail != 0.0) {
Two_One_Product(bdxt_cdyt1, bdxt_cdyt0, adheighttail,
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, cdheight, 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 (cdheighttail != 0.0) {
Two_One_Product(bdxt_adyt1, bdxt_adyt0, cdheighttail,
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, bdheight, 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 (bdheighttail != 0.0) {
Two_One_Product(cdxt_adyt1, cdxt_adyt0, bdheighttail,
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, adheight, 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 (adheighttail != 0.0) {
Two_One_Product(cdxt_bdyt1, cdxt_bdyt0, adheighttail,
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 (adheighttail != 0.0) { wlength = scale_expansion_zeroelim(bctlen, bct, adheighttail, w);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
finother);
finswap = finnow; finnow = finother; finother = finswap;
}
if (bdheighttail != 0.0) {
wlength = scale_expansion_zeroelim(catlen, cat, bdheighttail, w);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
finother);
finswap = finnow; finnow = finother; finother = finswap;
}
if (cdheighttail != 0.0) {
wlength = scale_expansion_zeroelim(abtlen, abt, cdheighttail, w);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
finother);
finswap = finnow; finnow = finother; finother = finswap;
}
return finnow[finlength - 1];
}
#ifdef ANSI_DECLARATORS
REAL orient3d(struct mesh *m, struct behavior *b,
vertex pa, vertex pb, vertex pc, vertex pd,
REAL aheight, REAL bheight, REAL cheight, REAL dheight)
#else /* not ANSI_DECLARATORS */
REAL orient3d(m, b, pa, pb, pc, pd, aheight, bheight, cheight, dheight)
struct mesh *m;
struct behavior *b;
vertex pa;
vertex pb;
vertex pc;
vertex pd;
REAL aheight;
REAL bheight;
REAL cheight;
REAL dheight;
#endif /* not ANSI_DECLARATORS */
{
REAL adx, bdx, cdx, ady, bdy, cdy, adheight, bdheight, cdheight;
REAL bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady;
REAL det;
REAL permanent, errbound;
m->orient3dcount++;
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];
adheight = aheight - dheight;
bdheight = bheight - dheight;
cdheight = cheight - dheight;
bdxcdy = bdx * cdy;
cdxbdy = cdx * bdy;
cdxady = cdx * ady;
adxcdy = adx * cdy;
adxbdy = adx * bdy;
bdxady = bdx * ady;
det = adheight * (bdxcdy - cdxbdy)
+ bdheight * (cdxady - adxcdy)
+ cdheight * (adxbdy - bdxady);
if (b->noexact) {
return det;
}
permanent = (Absolute(bdxcdy) + Absolute(cdxbdy)) * Absolute(adheight)
+ (Absolute(cdxady) + Absolute(adxcdy)) * Absolute(bdheight)
+ (Absolute(adxbdy) + Absolute(bdxady)) * Absolute(cdheight);
errbound = o3derrboundA * permanent;
if ((det > errbound) || (-det > errbound)) {
return det;
}
return orient3dadapt(pa, pb, pc, pd, aheight, bheight, cheight, dheight,
permanent);
}
/*****************************************************************************/
/* */
/* nonregular() Return a positive value if the point pd is incompatible */
/* with the circle or plane passing through pa, pb, and pc */
/* (meaning that pd is inside the circle or below the */
/* plane); a negative value if it is compatible; and zero if */
/* the four points are cocircular/coplanar. The points pa, */
/* pb, and pc must be in counterclockwise order, or the sign */
/* of the result will be reversed. */
/* */
/* If the -w switch is used, the points are lifted onto the parabolic */
/* lifting map, then they are dropped according to their weights, then the */
/* 3D orientation test is applied. If the -W switch is used, the points' */
/* heights are already provided, so the 3D orientation test is applied */
/* directly. If neither switch is used, the incircle test is applied. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
REAL nonregular(struct mesh *m, struct behavior *b,
vertex pa, vertex pb, vertex pc, vertex pd)
#else /* not ANSI_DECLARATORS */
REAL nonregular(m, b, pa, pb, pc, pd)
struct mesh *m;
struct behavior *b;
vertex pa;
vertex pb;
vertex pc;
vertex pd;
#endif /* not ANSI_DECLARATORS */
{
if (b->weighted == 0) {
return incircle(m, b, pa, pb, pc, pd);
} else if (b->weighted == 1) {
return orient3d(m, b, pa, pb, pc, pd,
pa[0] * pa[0] + pa[1] * pa[1] - pa[2],
pb[0] * pb[0] + pb[1] * pb[1] - pb[2],
pc[0] * pc[0] + pc[1] * pc[1] - pc[2],
pd[0] * pd[0] + pd[1] * pd[1] - pd[2]);
} else {
return orient3d(m, b, pa, pb, pc, pd, pa[2], pb[2], pc[2], pd[2]);
}
}
/*****************************************************************************/
/* */
/* findcircumcenter() Find the circumcenter of a triangle. */
/* */
/* The result is returned both in terms of x-y coordinates and xi-eta */
/* (barycentric) coordinates. The xi-eta coordinate system is defined in */
/* terms of the triangle: the origin of the triangle is the origin of the */
/* coordinate system; the destination of the triangle is one unit along the */
/* xi axis; and the apex of the triangle is one unit along the eta axis. *//* This procedure also returns the square of the length of the triangle's */
/* shortest edge. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
void findcircumcenter(struct mesh *m, struct behavior *b,
vertex torg, vertex tdest, vertex tapex,
vertex circumcenter, REAL *xi, REAL *eta, int offcenter)
#else /* not ANSI_DECLARATORS */
void findcircumcenter(m, b, torg, tdest, tapex, circumcenter, xi, eta,
offcenter)
struct mesh *m;
struct behavior *b;
vertex torg;
vertex tdest;
vertex tapex;
vertex circumcenter;
REAL *xi;
REAL *eta;
int offcenter;
#endif /* not ANSI_DECLARATORS */
{
REAL xdo, ydo, xao, yao;
REAL dodist, aodist, dadist;
REAL denominator;
REAL dx, dy, dxoff, dyoff;
m->circumcentercount++;
/* Compute the circumcenter of the triangle. */
xdo = tdest[0] - torg[0];
ydo = tdest[1] - torg[1];
xao = tapex[0] - torg[0];
yao = tapex[1] - torg[1];
dodist = xdo * xdo + ydo * ydo;
aodist = xao * xao + yao * yao;
dadist = (tdest[0] - tapex[0]) * (tdest[0] - tapex[0]) +
(tdest[1] - tapex[1]) * (tdest[1] - tapex[1]);
if (b->noexact) {
denominator = 0.5 / (xdo * yao - xao * ydo);
} else {
/* Use the counterclockwise() routine to ensure a positive (and */
/* reasonably accurate) result, avoiding any possibility of */
/* division by zero. */
denominator = 0.5 / counterclockwise(m, b, tdest, tapex, torg);
/* Don't count the above as an orientation test. */
m->counterclockcount--;
}
dx = (yao * dodist - ydo * aodist) * denominator;
dy = (xdo * aodist - xao * dodist) * denominator;
/* Find the (squared) length of the triangle's shortest edge. This */
/* serves as a conservative estimate of the insertion radius of the */
/* circumcenter's parent. The estimate is used to ensure that */
/* the algorithm terminates even if very small angles appear in */
/* the input PSLG. */
if ((dodist < aodist) && (dodist < dadist)) {
if (offcenter && (b->offconstant > 0.0)) {
/* Find the position of the off-center, as described by Alper Ungor. */
dxoff = 0.5 * xdo - b->offconstant * ydo;
dyoff = 0.5 * ydo + b->offconstant * xdo;
/* If the off-center is closer to the origin than the */
/* circumcenter, use the off-center instead. */
if (dxoff * dxoff + dyoff * dyoff < dx * dx + dy * dy) {
dx = dxoff;
dy = dyoff;
}
} } else if (aodist < dadist) {
if (offcenter && (b->offconstant > 0.0)) {
dxoff = 0.5 * xao + b->offconstant * yao;
dyoff = 0.5 * yao - b->offconstant * xao;
/* If the off-center is closer to the origin than the */
/* circumcenter, use the off-center instead. */
if (dxoff * dxoff + dyoff * dyoff < dx * dx + dy * dy) {
dx = dxoff;
dy = dyoff;
}
}
} else {
if (offcenter && (b->offconstant > 0.0)) {
dxoff = 0.5 * (tapex[0] - tdest[0]) -
b->offconstant * (tapex[1] - tdest[1]);
dyoff = 0.5 * (tapex[1] - tdest[1]) +
b->offconstant * (tapex[0] - tdest[0]);
/* If the off-center is closer to the destination than the */
/* circumcenter, use the off-center instead. */
if (dxoff * dxoff + dyoff * dyoff <
(dx - xdo) * (dx - xdo) + (dy - ydo) * (dy - ydo)) {
dx = xdo + dxoff;
dy = ydo + dyoff;
}
}
}
circumcenter[0] = torg[0] + dx;
circumcenter[1] = torg[1] + dy;
/* To interpolate vertex attributes for the new vertex inserted at */
/* the circumcenter, define a coordinate system with a xi-axis, */
/* directed from the triangle's origin to its destination, and */
/* an eta-axis, directed from its origin to its apex. */
/* Calculate the xi and eta coordinates of the circumcenter. */
*xi = (yao * dx - xao * dy) * (2.0 * denominator);
*eta = (xdo * dy - ydo * dx) * (2.0 * denominator);
}
/** **/
/** **/
/********* Geometric primitives end here *********/
/*****************************************************************************/
/* */
/* triangleinit() Initialize some variables. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
void triangleinit(struct mesh *m)
#else /* not ANSI_DECLARATORS */
void triangleinit(m)
struct mesh *m;
#endif /* not ANSI_DECLARATORS */
{
poolzero(&m->vertices);
poolzero(&m->triangles);
poolzero(&m->subsegs);
poolzero(&m->viri);
poolzero(&m->badsubsegs);
poolzero(&m->badtriangles);
poolzero(&m->flipstackers);
poolzero(&m->splaynodes);
m->recenttri.tri = (triangle *) NULL; /* No triangle has been visited yet. */
m->undeads = 0; /* No eliminated input vertices yet. */
m->samples = 1; /* Point location should take at least one sample. */
m->checksegments = 0; /* There are no segments in the triangulation yet. */ m->checkquality = 0; /* The quality triangulation stage has not begun. */
m->incirclecount = m->counterclockcount = m->orient3dcount = 0;
m->hyperbolacount = m->circletopcount = m->circumcentercount = 0;
randomseed = 1;
exactinit(); /* Initialize exact arithmetic constants. */
}
/*****************************************************************************/
/* */
/* randomnation() Generate a random number between 0 and `choices' - 1. */
/* */
/* This is a simple linear congruential random number generator. Hence, it */
/* is a bad random number generator, but good enough for most randomized */
/* geometric algorithms. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
unsigned long randomnation(unsigned int choices)
#else /* not ANSI_DECLARATORS */
unsigned long randomnation(choices)
unsigned int choices;
#endif /* not ANSI_DECLARATORS */
{
randomseed = (randomseed * 1366l + 150889l) % 714025l;
return randomseed / (714025l / choices + 1);
}
/********* Mesh quality testing routines begin here *********/
/** **/
/** **/
/*****************************************************************************/
/* */
/* checkmesh() Test the mesh for topological consistency. */
/* */
/*****************************************************************************/
#ifndef REDUCED
#ifdef ANSI_DECLARATORS
void checkmesh(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
void checkmesh(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */
{
struct otri triangleloop;
struct otri oppotri, oppooppotri;
vertex triorg, tridest, triapex;
vertex oppoorg, oppodest;
int horrors;
int saveexact;
triangle ptr; /* Temporary variable used by sym(). */
/* Temporarily turn on exact arithmetic if it's off. */
saveexact = b->noexact;
b->noexact = 0;
if (!b->quiet) {
printf(" Checking consistency of mesh...\n");
}
horrors = 0;
/* Run through the list of triangles, checking each one. */
traversalinit(&m->triangles);
triangleloop.tri = triangletraverse(m);
while (triangleloop.tri != (triangle *) NULL) { /* Check all three edges of the triangle. */
for (triangleloop.orient = 0; triangleloop.orient < 3;
triangleloop.orient++) {
org(triangleloop, triorg);
dest(triangleloop, tridest);
if (triangleloop.orient == 0) { /* Only test for inversion once. */
/* Test if the triangle is flat or inverted. */
apex(triangleloop, triapex);
if (counterclockwise(m, b, triorg, tridest, triapex) <= 0.0) {
printf(" !! !! Inverted ");
printtriangle(m, b, &triangleloop);
horrors++;
}
}
/* Find the neighboring triangle on this edge. */
sym(triangleloop, oppotri);
if (oppotri.tri != m->dummytri) {
/* Check that the triangle's neighbor knows it's a neighbor. */
sym(oppotri, oppooppotri);
if ((triangleloop.tri != oppooppotri.tri)
|| (triangleloop.orient != oppooppotri.orient)) {
printf(" !! !! Asymmetric triangle-triangle bond:\n");
if (triangleloop.tri == oppooppotri.tri) {
printf(" (Right triangle, wrong orientation)\n");
}
printf(" First ");
printtriangle(m, b, &triangleloop);
printf(" Second (nonreciprocating) ");
printtriangle(m, b, &oppotri);
horrors++;
}
/* Check that both triangles agree on the identities */
/* of their shared vertices. */
org(oppotri, oppoorg);
dest(oppotri, oppodest);
if ((triorg != oppodest) || (tridest != oppoorg)) {
printf(" !! !! Mismatched edge coordinates between two triangles:\n"
);
printf(" First mismatched ");
printtriangle(m, b, &triangleloop);
printf(" Second mismatched ");
printtriangle(m, b, &oppotri);
horrors++;
}
}
}
triangleloop.tri = triangletraverse(m);
}
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);
}
/* Restore the status of exact arithmetic. */
b->noexact = saveexact;
}
#endif /* not REDUCED */
/*****************************************************************************/
/* */
/* checkdelaunay() Ensure that the mesh is (constrained) Delaunay. */
/* */
/*****************************************************************************/
#ifndef REDUCED
#ifdef ANSI_DECLARATORS
void checkdelaunay(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
void checkdelaunay(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */
{
struct otri triangleloop;
struct otri oppotri;
struct osub opposubseg;
vertex triorg, tridest, triapex;
vertex oppoapex;
int shouldbedelaunay;
int horrors;
int saveexact;
triangle ptr; /* Temporary variable used by sym(). */
subseg sptr; /* Temporary variable used by tspivot(). */
/* Temporarily turn on exact arithmetic if it's off. */
saveexact = b->noexact;
b->noexact = 0;
if (!b->quiet) {
printf(" Checking Delaunay property of mesh...\n");
}
horrors = 0;
/* Run through the list of triangles, checking each one. */
traversalinit(&m->triangles);
triangleloop.tri = triangletraverse(m);
while (triangleloop.tri != (triangle *) NULL) {
/* Check all three edges of the triangle. */
for (triangleloop.orient = 0; triangleloop.orient < 3;
triangleloop.orient++) {
org(triangleloop, triorg);
dest(triangleloop, tridest);
apex(triangleloop, triapex);
sym(triangleloop, oppotri);
apex(oppotri, oppoapex);
/* Only test that the edge is locally Delaunay if there is an */
/* adjoining triangle whose pointer is larger (to ensure that */
/* each pair isn't tested twice). */
shouldbedelaunay = (oppotri.tri != m->dummytri) &&
!deadtri(oppotri.tri) && (triangleloop.tri < oppotri.tri) &&
(triorg != m->infvertex1) && (triorg != m->infvertex2) &&
(triorg != m->infvertex3) &&
(tridest != m->infvertex1) && (tridest != m->infvertex2) &&
(tridest != m->infvertex3) &&
(triapex != m->infvertex1) && (triapex != m->infvertex2) &&
(triapex != m->infvertex3) &&
(oppoapex != m->infvertex1) && (oppoapex != m->infvertex2) &&
(oppoapex != m->infvertex3);
if (m->checksegments && shouldbedelaunay) {
/* If a subsegment separates the triangles, then the edge is */
/* constrained, so no local Delaunay test should be done. */
tspivot(triangleloop, opposubseg);
if (opposubseg.ss != m->dummysub){
shouldbedelaunay = 0;
}
}
if (shouldbedelaunay) {
if (nonregular(m, b, triorg, tridest, triapex, oppoapex) > 0.0) {
if (!b->weighted) {
printf(" !! !! Non-Delaunay pair of triangles:\n");
printf(" First non-Delaunay ");
printtriangle(m, b, &triangleloop);
printf(" Second non-Delaunay ");
} else {
printf(" !! !! Non-regular pair of triangles:\n"); printf(" First non-regular ");
printtriangle(m, b, &triangleloop);
printf(" Second non-regular ");
}
printtriangle(m, b, &oppotri);
horrors++;
}
}
}
triangleloop.tri = triangletraverse(m);
}
if (horrors == 0) {
if (!b->quiet) {
printf(
" By virtue of my perceptive intelligence, I declare the mesh Delaunay.\n");
}
} else if (horrors == 1) {
printf(
" !! !! !! !! Precisely one terrifying transgression identified.\n");
} else {
printf(" !! !! !! !! %d obscenities viewed with horror.\n", horrors);
}
/* Restore the status of exact arithmetic. */
b->noexact = saveexact;
}
#endif /* not REDUCED */
/*****************************************************************************/
/* */
/* enqueuebadtriang() Add a bad triangle data structure to the end of a */
/* queue. */
/* */
/* The queue is actually a set of 4096 queues. I use multiple queues to */
/* give priority to smaller angles. I originally implemented a heap, but */
/* the queues are faster by a larger margin than I'd suspected. */
/* */
/*****************************************************************************/
#ifndef CDT_ONLY
#ifdef ANSI_DECLARATORS
void enqueuebadtriang(struct mesh *m, struct behavior *b,
struct badtriang *badtri)
#else /* not ANSI_DECLARATORS */
void enqueuebadtriang(m, b, badtri)
struct mesh *m;
struct behavior *b;
struct badtriang *badtri;
#endif /* not ANSI_DECLARATORS */
{
REAL length, multiplier;
int exponent, expincrement;
int queuenumber;
int posexponent;
int i;
if (b->verbose > 2) {
printf(" Queueing bad triangle:\n");
printf(" (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
badtri->triangorg[0], badtri->triangorg[1],
badtri->triangdest[0], badtri->triangdest[1],
badtri->triangapex[0], badtri->triangapex[1]);
}
/* Determine the appropriate queue to put the bad triangle into. */
/* Recall that the key is the square of its shortest edge length. */
if (badtri->key >= 1.0) {
length = badtri->key; posexponent = 1;
} else {
/* `badtri->key' is 2.0 to a negative exponent, so we'll record that */
/* fact and use the reciprocal of `badtri->key', which is > 1.0. */
length = 1.0 / badtri->key;
posexponent = 0;
}
/* `length' is approximately 2.0 to what exponent? The following code */
/* determines the answer in time logarithmic in the exponent. */
exponent = 0;
while (length > 2.0) {
/* Find an approximation by repeated squaring of two. */
expincrement = 1;
multiplier = 0.5;
while (length * multiplier * multiplier > 1.0) {
expincrement *= 2;
multiplier *= multiplier;
}
/* Reduce the value of `length', then iterate if necessary. */
exponent += expincrement;
length *= multiplier;
}
/* `length' is approximately squareroot(2.0) to what exponent? */
exponent = 2.0 * exponent + (length > SQUAREROOTTWO);
/* `exponent' is now in the range 0...2047 for IEEE double precision. */
/* Choose a queue in the range 0...4095. The shortest edges have the */
/* highest priority (queue 4095). */
if (posexponent) {
queuenumber = 2047 - exponent;
} else {
queuenumber = 2048 + exponent;
}
/* Are we inserting into an empty queue? */
if (m->queuefront[queuenumber] == (struct badtriang *) NULL) {
/* Yes, we are inserting into an empty queue. */
/* Will this become the highest-priority queue? */
if (queuenumber > m->firstnonemptyq) {
/* Yes, this is the highest-priority queue. */
m->nextnonemptyq[queuenumber] = m->firstnonemptyq;
m->firstnonemptyq = queuenumber;
} else {
/* No, this is not the highest-priority queue. */
/* Find the queue with next higher priority. */
i = queuenumber + 1;
while (m->queuefront[i] == (struct badtriang *) NULL) {
i++;
}
/* Mark the newly nonempty queue as following a higher-priority queue. */
m->nextnonemptyq[queuenumber] = m->nextnonemptyq[i];
m->nextnonemptyq[i] = queuenumber;
}
/* Put the bad triangle at the beginning of the (empty) queue. */
m->queuefront[queuenumber] = badtri;
} else {
/* Add the bad triangle to the end of an already nonempty queue. */
m->queuetail[queuenumber]->nexttriang = badtri;
}
/* Maintain a pointer to the last triangle of the queue. */
m->queuetail[queuenumber] = badtri;
/* Newly enqueued bad triangle has no successor in the queue. */
badtri->nexttriang = (struct badtriang *) NULL;
}
#endif /* not CDT_ONLY */
/*****************************************************************************/
/* */
/* enqueuebadtri() Add a bad triangle to the end of a queue. */
/* *//* Allocates a badtriang data structure for the triangle, then passes it to */
/* enqueuebadtriang(). */
/* */
/*****************************************************************************/
#ifndef CDT_ONLY
#ifdef ANSI_DECLARATORS
void enqueuebadtri(struct mesh *m, struct behavior *b, struct otri *enqtri,
REAL minedge, vertex enqapex, vertex enqorg, vertex enqdest)
#else /* not ANSI_DECLARATORS */
void enqueuebadtri(m, b, enqtri, minedge, enqapex, enqorg, enqdest)
struct mesh *m;
struct behavior *b;
struct otri *enqtri;
REAL minedge;
vertex enqapex;
vertex enqorg;
vertex enqdest;
#endif /* not ANSI_DECLARATORS */
{
struct badtriang *newbad;
/* Allocate space for the bad triangle. */
newbad = (struct badtriang *) poolalloc(&m->badtriangles);
newbad->poortri = encode(*enqtri);
newbad->key = minedge;
newbad->triangapex = enqapex;
newbad->triangorg = enqorg;
newbad->triangdest = enqdest;
enqueuebadtriang(m, b, newbad);
}
#endif /* not CDT_ONLY */
/*****************************************************************************/
/* */
/* dequeuebadtriang() Remove a triangle from the front of the queue. */
/* */
/*****************************************************************************/
#ifndef CDT_ONLY
#ifdef ANSI_DECLARATORS
struct badtriang *dequeuebadtriang(struct mesh *m)
#else /* not ANSI_DECLARATORS */
struct badtriang *dequeuebadtriang(m)
struct mesh *m;
#endif /* not ANSI_DECLARATORS */
{
struct badtriang *result;
/* If no queues are nonempty, return NULL. */
if (m->firstnonemptyq < 0) {
return (struct badtriang *) NULL;
}
/* Find the first triangle of the highest-priority queue. */
result = m->queuefront[m->firstnonemptyq];
/* Remove the triangle from the queue. */
m->queuefront[m->firstnonemptyq] = result->nexttriang;
/* If this queue is now empty, note the new highest-priority */
/* nonempty queue. */
if (result == m->queuetail[m->firstnonemptyq]) {
m->firstnonemptyq = m->nextnonemptyq[m->firstnonemptyq];
}
return result;
}
#endif /* not CDT_ONLY */
/*****************************************************************************/
/* */
/* checkseg4encroach() Check a subsegment to see if it is encroached; add */
/* it to the list if it is. */
/* */
/* A subsegment is encroached if there is a vertex in its diametral lens. */
/* For Ruppert's algorithm (-D switch), the "diametral lens" is the */
/* diametral circle. For Chew's algorithm (default), the diametral lens is */
/* just big enough to enclose two isosceles triangles whose bases are the */
/* subsegment. Each of the two isosceles triangles has two angles equal */
/* to `b->minangle'. */
/* */
/* Chew's algorithm does not require diametral lenses at all--but they save */
/* time. Any vertex inside a subsegment's diametral lens implies that the */
/* triangle adjoining the subsegment will be too skinny, so it's only a */
/* matter of time before the encroaching vertex is deleted by Chew's */
/* algorithm. It's faster to simply not insert the doomed vertex in the */
/* first place, which is why I use diametral lenses with Chew's algorithm. */
/* */
/* Returns a nonzero value if the subsegment is encroached. */
/* */
/*****************************************************************************/
#ifndef CDT_ONLY
#ifdef ANSI_DECLARATORS
int checkseg4encroach(struct mesh *m, struct behavior *b,
struct osub *testsubseg)
#else /* not ANSI_DECLARATORS */
int checkseg4encroach(m, b, testsubseg)
struct mesh *m;
struct behavior *b;
struct osub *testsubseg;
#endif /* not ANSI_DECLARATORS */
{
struct otri neighbortri;
struct osub testsym;
struct badsubseg *encroachedseg;
REAL dotproduct;
int encroached;
int sides;
vertex eorg, edest, eapex;
triangle ptr; /* Temporary variable used by stpivot(). */
encroached = 0;
sides = 0;
sorg(*testsubseg, eorg);
sdest(*testsubseg, edest);
/* Check one neighbor of the subsegment. */
stpivot(*testsubseg, neighbortri);
/* Does the neighbor exist, or is this a boundary edge? */
if (neighbortri.tri != m->dummytri) {
sides++;
/* Find a vertex opposite this subsegment. */
apex(neighbortri, eapex);
/* Check whether the apex is in the diametral lens of the subsegment */
/* (the diametral circle if `conformdel' is set). A dot product */
/* of two sides of the triangle is used to check whether the angle */
/* at the apex is greater than (180 - 2 `minangle') degrees (for */
/* lenses; 90 degrees for diametral circles). */
dotproduct = (eorg[0] - eapex[0]) * (edest[0] - eapex[0]) +
(eorg[1] - eapex[1]) * (edest[1] - eapex[1]);
if (dotproduct < 0.0) {
if (b->conformdel ||
(dotproduct * dotproduct >=
(2.0 * b->goodangle - 1.0) * (2.0 * b->goodangle - 1.0) * ((eorg[0] - eapex[0]) * (eorg[0] - eapex[0]) +
(eorg[1] - eapex[1]) * (eorg[1] - eapex[1])) *
((edest[0] - eapex[0]) * (edest[0] - eapex[0]) +
(edest[1] - eapex[1]) * (edest[1] - eapex[1])))) {
encroached = 1;
}
}
}
/* Check the other neighbor of the subsegment. */
ssym(*testsubseg, testsym);
stpivot(testsym, neighbortri);
/* Does the neighbor exist, or is this a boundary edge? */
if (neighbortri.tri != m->dummytri) {
sides++;
/* Find the other vertex opposite this subsegment. */
apex(neighbortri, eapex);
/* Check whether the apex is in the diametral lens of the subsegment */
/* (or the diametral circle, if `conformdel' is set). */
dotproduct = (eorg[0] - eapex[0]) * (edest[0] - eapex[0]) +
(eorg[1] - eapex[1]) * (edest[1] - eapex[1]);
if (dotproduct < 0.0) {
if (b->conformdel ||
(dotproduct * dotproduct >=
(2.0 * b->goodangle - 1.0) * (2.0 * b->goodangle - 1.0) *
((eorg[0] - eapex[0]) * (eorg[0] - eapex[0]) +
(eorg[1] - eapex[1]) * (eorg[1] - eapex[1])) *
((edest[0] - eapex[0]) * (edest[0] - eapex[0]) +
(edest[1] - eapex[1]) * (edest[1] - eapex[1])))) {
encroached += 2;
}
}
}
if (encroached && (!b->nobisect || ((b->nobisect == 1) && (sides == 2)))) {
if (b->verbose > 2) {
printf(
" Queueing encroached subsegment (%.12g, %.12g) (%.12g, %.12g).\n",
eorg[0], eorg[1], edest[0], edest[1]);
}
/* Add the subsegment to the list of encroached subsegments. */
/* Be sure to get the orientation right. */
encroachedseg = (struct badsubseg *) poolalloc(&m->badsubsegs);
if (encroached == 1) {
encroachedseg->encsubseg = sencode(*testsubseg);
encroachedseg->subsegorg = eorg;
encroachedseg->subsegdest = edest;
} else {
encroachedseg->encsubseg = sencode(testsym);
encroachedseg->subsegorg = edest;
encroachedseg->subsegdest = eorg;
}
}
return encroached;
}
#endif /* not CDT_ONLY */
/*****************************************************************************/
/* */
/* testtriangle() Test a triangle for quality and size. */
/* */
/* Tests a triangle to see if it satisfies the minimum angle condition and */
/* the maximum area condition. Triangles that aren't up to spec are added */
/* to the bad triangle queue. */
/* */
/*****************************************************************************/
#ifndef CDT_ONLY
#ifdef ANSI_DECLARATORS
void testtriangle(struct mesh *m, struct behavior *b, struct otri *testtri)
#else /* not ANSI_DECLARATORS */
void testtriangle(m, b, testtri)
struct mesh *m;
struct behavior *b;
struct otri *testtri;
#endif /* not ANSI_DECLARATORS */
{
struct otri tri1, tri2;
struct osub testsub;
vertex torg, tdest, tapex;
vertex base1, base2;
vertex org1, dest1, org2, dest2;
vertex joinvertex;
REAL dxod, dyod, dxda, dyda, dxao, dyao;
REAL dxod2, dyod2, dxda2, dyda2, dxao2, dyao2;
REAL apexlen, orglen, destlen, minedge;
REAL angle;
REAL area;
REAL dist1, dist2;
subseg sptr; /* Temporary variable used by tspivot(). */
triangle ptr; /* Temporary variable used by oprev() and dnext(). */
org(*testtri, torg);
dest(*testtri, tdest);
apex(*testtri, tapex);
dxod = torg[0] - tdest[0];
dyod = torg[1] - tdest[1];
dxda = tdest[0] - tapex[0];
dyda = tdest[1] - tapex[1];
dxao = tapex[0] - torg[0];
dyao = tapex[1] - torg[1];
dxod2 = dxod * dxod;
dyod2 = dyod * dyod;
dxda2 = dxda * dxda;
dyda2 = dyda * dyda;
dxao2 = dxao * dxao;
dyao2 = dyao * dyao;
/* Find the lengths of the triangle's three edges. */
apexlen = dxod2 + dyod2;
orglen = dxda2 + dyda2;
destlen = dxao2 + dyao2;
if ((apexlen < orglen) && (apexlen < destlen)) {
/* The edge opposite the apex is shortest. */
minedge = apexlen;
/* Find the square of the cosine of the angle at the apex. */
angle = dxda * dxao + dyda * dyao;
angle = angle * angle / (orglen * destlen);
base1 = torg;
base2 = tdest;
otricopy(*testtri, tri1);
} else if (orglen < destlen) {
/* The edge opposite the origin is shortest. */
minedge = orglen;
/* Find the square of the cosine of the angle at the origin. */
angle = dxod * dxao + dyod * dyao;
angle = angle * angle / (apexlen * destlen);
base1 = tdest;
base2 = tapex;
lnext(*testtri, tri1);
} else {
/* The edge opposite the destination is shortest. */
minedge = destlen;
/* Find the square of the cosine of the angle at the destination. */
angle = dxod * dxda + dyod * dyda;
angle = angle * angle / (apexlen * orglen);
base1 = tapex; base2 = torg;
lprev(*testtri, tri1);
}
if (b->vararea || b->fixedarea || b->usertest) {
/* Check whether the area is larger than permitted. */
area = 0.5 * (dxod * dyda - dyod * dxda);
if (b->fixedarea && (area > b->maxarea)) {
/* Add this triangle to the list of bad triangles. */
enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest);
return;
}
/* Nonpositive area constraints are treated as unconstrained. */
if ((b->vararea) && (area > areabound(*testtri)) &&
(areabound(*testtri) > 0.0)) {
/* Add this triangle to the list of bad triangles. */
enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest);
return;
}
if (b->usertest) {
/* Check whether the user thinks this triangle is too large. */
if (triunsuitable(torg, tdest, tapex, area)) {
enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest);
return;
}
}
}
/* Check whether the angle is smaller than permitted. */
if (angle > b->goodangle) {
/* Use the rules of Miller, Pav, and Walkington to decide that certain */
/* triangles should not be split, even if they have bad angles. */
/* A skinny triangle is not split if its shortest edge subtends a */
/* small input angle, and both endpoints of the edge lie on a */
/* concentric circular shell. For convenience, I make a small */
/* adjustment to that rule: I check if the endpoints of the edge */
/* both lie in segment interiors, equidistant from the apex where */
/* the two segments meet. */
/* First, check if both points lie in segment interiors. */
if ((vertextype(base1) == SEGMENTVERTEX) &&
(vertextype(base2) == SEGMENTVERTEX)) {
/* Check if both points lie in a common segment. If they do, the */
/* skinny triangle is enqueued to be split as usual. */
tspivot(tri1, testsub);
if (testsub.ss == m->dummysub) {
/* No common segment. Find a subsegment that contains `torg'. */
otricopy(tri1, tri2);
do {
oprevself(tri1);
tspivot(tri1, testsub);
} while (testsub.ss == m->dummysub);
/* Find the endpoints of the containing segment. */
segorg(testsub, org1);
segdest(testsub, dest1);
/* Find a subsegment that contains `tdest'. */
do {
dnextself(tri2);
tspivot(tri2, testsub);
} while (testsub.ss == m->dummysub);
/* Find the endpoints of the containing segment. */
segorg(testsub, org2);
segdest(testsub, dest2);
/* Check if the two containing segments have an endpoint in common. */
joinvertex = (vertex) NULL;
if ((dest1[0] == org2[0]) && (dest1[1] == org2[1])) {
joinvertex = dest1;
} else if ((org1[0] == dest2[0]) && (org1[1] == dest2[1])) {
joinvertex = org1; }
if (joinvertex != (vertex) NULL) {
/* Compute the distance from the common endpoint (of the two */
/* segments) to each of the endpoints of the shortest edge. */
dist1 = ((base1[0] - joinvertex[0]) * (base1[0] - joinvertex[0]) +
(base1[1] - joinvertex[1]) * (base1[1] - joinvertex[1]));
dist2 = ((base2[0] - joinvertex[0]) * (base2[0] - joinvertex[0]) +
(base2[1] - joinvertex[1]) * (base2[1] - joinvertex[1]));
/* If the two distances are equal, don't split the triangle. */
if ((dist1 < 1.001 * dist2) && (dist1 > 0.999 * dist2)) {
/* Return now to avoid enqueueing the bad triangle. */
return;
}
}
}
}
/* Add this triangle to the list of bad triangles. */
enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest);
}
}
#endif /* not CDT_ONLY */
/** **/
/** **/
/********* Mesh quality testing routines end here *********/
/********* Point location routines begin here *********/
/** **/
/** **/
/*****************************************************************************/
/* */
/* makevertexmap() Construct a mapping from vertices to triangles to */
/* improve the speed of point location for segment */
/* insertion. */
/* */
/* Traverses all the triangles, and provides each corner of each triangle */
/* with a pointer to that triangle. Of course, pointers will be */
/* overwritten by other pointers because (almost) each vertex is a corner */
/* of several triangles, but in the end every vertex will point to some */
/* triangle that contains it. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
void makevertexmap(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
void makevertexmap(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */
{
struct otri triangleloop;
vertex triorg;
if (b->verbose) {
printf(" Constructing mapping from vertices to triangles.\n");
}
traversalinit(&m->triangles);
triangleloop.tri = triangletraverse(m);
while (triangleloop.tri != (triangle *) NULL) {
/* Check all three vertices of the triangle. */
for (triangleloop.orient = 0; triangleloop.orient < 3;
triangleloop.orient++) {
org(triangleloop, triorg);
setvertex2tri(triorg, encode(triangleloop));
} triangleloop.tri = triangletraverse(m);
}
}
/*****************************************************************************/
/* */
/* preciselocate() Find a triangle or edge containing a given point. */
/* */
/* Begins its search from `searchtri'. It is important that `searchtri' */
/* be a handle with the property that `searchpoint' is strictly to the left */
/* of the edge denoted by `searchtri', or is collinear with that edge and */
/* does not intersect that edge. (In particular, `searchpoint' should not */
/* be the origin or destination of that edge.) */
/* */
/* These conditions are imposed because preciselocate() is normally used in */
/* one of two situations: */
/* */
/* (1) To try to find the location to insert a new point. Normally, we */
/* know an edge that the point is strictly to the left of. In the */
/* incremental Delaunay algorithm, that edge is a bounding box edge. */
/* In Ruppert's Delaunay refinement algorithm for quality meshing, */
/* that edge is the shortest edge of the triangle whose circumcenter */
/* is being inserted. */
/* */
/* (2) To try to find an existing point. In this case, any edge on the */
/* convex hull is a good starting edge. You must screen out the */
/* possibility that the vertex sought is an endpoint of the starting */
/* edge before you call preciselocate(). */
/* */
/* On completion, `searchtri' is a triangle that contains `searchpoint'. */
/* */
/* This implementation differs from that given by Guibas and Stolfi. It */
/* walks from triangle to triangle, crossing an edge only if `searchpoint' */
/* is on the other side of the line containing that edge. After entering */
/* a triangle, there are two edges by which one can leave that triangle. */
/* If both edges are valid (`searchpoint' is on the other side of both */
/* edges), one of the two is chosen by drawing a line perpendicular to */
/* the entry edge (whose endpoints are `forg' and `fdest') passing through */
/* `fapex'. Depending on which side of this perpendicular `searchpoint' */
/* falls on, an exit edge is chosen. */
/* */
/* This implementation is empirically faster than the Guibas and Stolfi */
/* point location routine (which I originally used), which tends to spiral */
/* in toward its target. */
/* */
/* Returns ONVERTEX if the point lies on an existing vertex. `searchtri' */
/* is a handle whose origin is the existing vertex. */
/* */
/* Returns ONEDGE if the point lies on a mesh edge. `searchtri' is a */
/* handle whose primary edge is the edge on which the point lies. */
/* */
/* Returns INTRIANGLE if the point lies strictly within a triangle. */
/* `searchtri' is a handle on the triangle that contains the point. */
/* */
/* Returns OUTSIDE if the point lies outside the mesh. `searchtri' is a */
/* handle whose primary edge the point is to the right of. This might */
/* occur when the circumcenter of a triangle falls just slightly outside */
/* the mesh due to floating-point roundoff error. It also occurs when */
/* seeking a hole or region point that a foolish user has placed outside */
/* the mesh. */
/* */
/* If `stopatsubsegment' is nonzero, the search will stop if it tries to */
/* walk through a subsegment, and will return OUTSIDE. */
/* */
/* WARNING: This routine is designed for convex triangulations, and will */
/* not generally work after the holes and concavities have been carved. */
/* However, it can still be used to find the circumcenter of a triangle, as */
/* long as the search is begun from the triangle in question. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
enum locateresult preciselocate(struct mesh *m, struct behavior *b,
vertex searchpoint, struct otri *searchtri,
int stopatsubsegment)
#else /* not ANSI_DECLARATORS */
enum locateresult preciselocate(m, b, searchpoint, searchtri, stopatsubsegment)
struct mesh *m;
struct behavior *b;
vertex searchpoint;
struct otri *searchtri;
int stopatsubsegment;
#endif /* not ANSI_DECLARATORS */
{
struct otri backtracktri;
struct osub checkedge;
vertex forg, fdest, fapex;
REAL orgorient, destorient;
int moveleft;
triangle ptr; /* Temporary variable used by sym(). */
subseg sptr; /* Temporary variable used by tspivot(). */
if (b->verbose > 2) {
printf(" Searching for point (%.12g, %.12g).\n",
searchpoint[0], searchpoint[1]);
}
/* Where are we? */
org(*searchtri, forg);
dest(*searchtri, fdest);
apex(*searchtri, fapex);
while (1) {
if (b->verbose > 2) {
printf(" At (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
forg[0], forg[1], fdest[0], fdest[1], fapex[0], fapex[1]);
}
/* Check whether the apex is the point we seek. */
if ((fapex[0] == searchpoint[0]) && (fapex[1] == searchpoint[1])) {
lprevself(*searchtri);
return ONVERTEX;
}
/* Does the point lie on the other side of the line defined by the */
/* triangle edge opposite the triangle's destination? */
destorient = counterclockwise(m, b, forg, fapex, searchpoint);
/* Does the point lie on the other side of the line defined by the */
/* triangle edge opposite the triangle's origin? */
orgorient = counterclockwise(m, b, fapex, fdest, searchpoint);
if (destorient > 0.0) {
if (orgorient > 0.0) {
/* Move left if the inner product of (fapex - searchpoint) and */
/* (fdest - forg) is positive. This is equivalent to drawing */
/* a line perpendicular to the line (forg, fdest) and passing */
/* through `fapex', and determining which side of this line */
/* `searchpoint' falls on. */
moveleft = (fapex[0] - searchpoint[0]) * (fdest[0] - forg[0]) +
(fapex[1] - searchpoint[1]) * (fdest[1] - forg[1]) > 0.0;
} else {
moveleft = 1;
}
} else {
if (orgorient > 0.0) {
moveleft = 0;
} else {
/* The point we seek must be on the boundary of or inside this */
/* triangle. */
if (destorient == 0.0) {
lprevself(*searchtri);
return ONEDGE;
}
if (orgorient == 0.0) { lnextself(*searchtri);
return ONEDGE;
}
return INTRIANGLE;
}
}
/* Move to another triangle. Leave a trace `backtracktri' in case */
/* floating-point roundoff or some such bogey causes us to walk */
/* off a boundary of the triangulation. */
if (moveleft) {
lprev(*searchtri, backtracktri);
fdest = fapex;
} else {
lnext(*searchtri, backtracktri);
forg = fapex;
}
sym(backtracktri, *searchtri);
if (m->checksegments && stopatsubsegment) {
/* Check for walking through a subsegment. */
tspivot(backtracktri, checkedge);
if (checkedge.ss != m->dummysub) {
/* Go back to the last triangle. */
otricopy(backtracktri, *searchtri);
return OUTSIDE;
}
}
/* Check for walking right out of the triangulation. */
if (searchtri->tri == m->dummytri) {
/* Go back to the last triangle. */
otricopy(backtracktri, *searchtri);
return OUTSIDE;
}
apex(*searchtri, fapex);
}
}
/*****************************************************************************/
/* */
/* locate() Find a triangle or edge containing a given point. */
/* */
/* Searching begins from one of: the input `searchtri', a recently */
/* encountered triangle `recenttri', or from a triangle chosen from a */
/* random sample. The choice is made by determining which triangle's */
/* origin is closest to the point we are searching for. Normally, */
/* `searchtri' should be a handle on the convex hull of the triangulation. */
/* */
/* Details on the random sampling method can be found in the Mucke, Saias, */
/* and Zhu paper cited in the header of this code. */
/* */
/* On completion, `searchtri' is a triangle that contains `searchpoint'. */
/* */
/* Returns ONVERTEX if the point lies on an existing vertex. `searchtri' */
/* is a handle whose origin is the existing vertex. */
/* */
/* Returns ONEDGE if the point lies on a mesh edge. `searchtri' is a */
/* handle whose primary edge is the edge on which the point lies. */
/* */
/* Returns INTRIANGLE if the point lies strictly within a triangle. */
/* `searchtri' is a handle on the triangle that contains the point. */
/* */
/* Returns OUTSIDE if the point lies outside the mesh. `searchtri' is a */
/* handle whose primary edge the point is to the right of. This might */
/* occur when the circumcenter of a triangle falls just slightly outside */
/* the mesh due to floating-point roundoff error. It also occurs when */
/* seeking a hole or region point that a foolish user has placed outside */
/* the mesh. */
/* *//* WARNING: This routine is designed for convex triangulations, and will */
/* not generally work after the holes and concavities have been carved. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
enum locateresult locate(struct mesh *m, struct behavior *b,
vertex searchpoint, struct otri *searchtri)
#else /* not ANSI_DECLARATORS */
enum locateresult locate(m, b, searchpoint, searchtri)
struct mesh *m;
struct behavior *b;
vertex searchpoint;
struct otri *searchtri;
#endif /* not ANSI_DECLARATORS */
{
VOID **sampleblock;
char *firsttri;
struct otri sampletri;
vertex torg, tdest;
unsigned long alignptr;
REAL searchdist, dist;
REAL ahead;
long samplesperblock, totalsamplesleft, samplesleft;
long population, totalpopulation;
triangle ptr; /* Temporary variable used by sym(). */
if (b->verbose > 2) {
printf(" Randomly sampling for a triangle near point (%.12g, %.12g).\n",
searchpoint[0], searchpoint[1]);
}
/* Record the distance from the suggested starting triangle to the */
/* point we seek. */
org(*searchtri, torg);
searchdist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) +
(searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]);
if (b->verbose > 2) {
printf(" Boundary triangle has origin (%.12g, %.12g).\n",
torg[0], torg[1]);
}
/* If a recently encountered triangle has been recorded and has not been */
/* deallocated, test it as a good starting point. */
if (m->recenttri.tri != (triangle *) NULL) {
if (!deadtri(m->recenttri.tri)) {
org(m->recenttri, torg);
if ((torg[0] == searchpoint[0]) && (torg[1] == searchpoint[1])) {
otricopy(m->recenttri, *searchtri);
return ONVERTEX;
}
dist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) +
(searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]);
if (dist < searchdist) {
otricopy(m->recenttri, *searchtri);
searchdist = dist;
if (b->verbose > 2) {
printf(" Choosing recent triangle with origin (%.12g, %.12g).\n",
torg[0], torg[1]);
}
}
}
}
/* The number of random samples taken is proportional to the cube root of */
/* the number of triangles in the mesh. The next bit of code assumes */
/* that the number of triangles increases monotonically (or at least */
/* doesn't decrease enough to matter). */
while (SAMPLEFACTOR * m->samples * m->samples * m->samples <
m->triangles.items) { m->samples++;
}
/* We'll draw ceiling(samples * TRIPERBLOCK / maxitems) random samples */
/* from each block of triangles (except the first)--until we meet the */
/* sample quota. The ceiling means that blocks at the end might be */
/* neglected, but I don't care. */
samplesperblock = (m->samples * TRIPERBLOCK - 1) / m->triangles.maxitems + 1;
/* We'll draw ceiling(samples * itemsfirstblock / maxitems) random samples */
/* from the first block of triangles. */
samplesleft = (m->samples * m->triangles.itemsfirstblock - 1) /
m->triangles.maxitems + 1;
totalsamplesleft = m->samples;
population = m->triangles.itemsfirstblock;
totalpopulation = m->triangles.maxitems;
sampleblock = m->triangles.firstblock;
sampletri.orient = 0;
while (totalsamplesleft > 0) {
/* If we're in the last block, `population' needs to be corrected. */
if (population > totalpopulation) {
population = totalpopulation;
}
/* Find a pointer to the first triangle in the block. */
alignptr = (unsigned long) (sampleblock + 1);
firsttri = (char *) (alignptr +
(unsigned long) m->triangles.alignbytes -
(alignptr %
(unsigned long) m->triangles.alignbytes));
/* Choose `samplesleft' randomly sampled triangles in this block. */
do {
sampletri.tri = (triangle *) (firsttri +
(randomnation((unsigned int) population) *
m->triangles.itembytes));
if (!deadtri(sampletri.tri)) {
org(sampletri, torg);
dist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) +
(searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]);
if (dist < searchdist) {
otricopy(sampletri, *searchtri);
searchdist = dist;
if (b->verbose > 2) {
printf(" Choosing triangle with origin (%.12g, %.12g).\n",
torg[0], torg[1]);
}
}
}
samplesleft--;
totalsamplesleft--;
} while ((samplesleft > 0) && (totalsamplesleft > 0));
if (totalsamplesleft > 0) {
sampleblock = (VOID **) *sampleblock;
samplesleft = samplesperblock;
totalpopulation -= population;
population = TRIPERBLOCK;
}
}
/* Where are we? */
org(*searchtri, torg);
dest(*searchtri, tdest);
/* Check the starting triangle's vertices. */
if ((torg[0] == searchpoint[0]) && (torg[1] == searchpoint[1])) {
return ONVERTEX;
}
if ((tdest[0] == searchpoint[0]) && (tdest[1] == searchpoint[1])) {
lnextself(*searchtri);
return ONVERTEX; }
/* Orient `searchtri' to fit the preconditions of calling preciselocate(). */
ahead = counterclockwise(m, b, torg, tdest, searchpoint);
if (ahead < 0.0) {
/* Turn around so that `searchpoint' is to the left of the */
/* edge specified by `searchtri'. */
symself(*searchtri);
} else if (ahead == 0.0) {
/* Check if `searchpoint' is between `torg' and `tdest'. */
if (((torg[0] < searchpoint[0]) == (searchpoint[0] < tdest[0])) &&
((torg[1] < searchpoint[1]) == (searchpoint[1] < tdest[1]))) {
return ONEDGE;
}
}
return preciselocate(m, b, searchpoint, searchtri, 0);
}
/** **/
/** **/
/********* Point location routines end here *********/
/********* Mesh transformation routines begin here *********/
/** **/
/** **/
/*****************************************************************************/
/* */
/* insertsubseg() Create a new subsegment and insert it between two */
/* triangles. */
/* */
/* The new subsegment is inserted at the edge described by the handle */
/* `tri'. Its vertices are properly initialized. The marker `subsegmark' */
/* is applied to the subsegment and, if appropriate, its vertices. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
void insertsubseg(struct mesh *m, struct behavior *b, struct otri *tri,
int subsegmark)
#else /* not ANSI_DECLARATORS */
void insertsubseg(m, b, tri, subsegmark)
struct mesh *m;
struct behavior *b;
struct otri *tri; /* Edge at which to insert the new subsegment. */
int subsegmark; /* Marker for the new subsegment. */
#endif /* not ANSI_DECLARATORS */
{
struct otri oppotri;
struct osub newsubseg;
vertex triorg, tridest;
triangle ptr; /* Temporary variable used by sym(). */
subseg sptr; /* Temporary variable used by tspivot(). */
org(*tri, triorg);
dest(*tri, tridest);
/* Mark vertices if possible. */
if (vertexmark(triorg) == 0) {
setvertexmark(triorg, subsegmark);
}
if (vertexmark(tridest) == 0) {
setvertexmark(tridest, subsegmark);
}
/* Check if there's already a subsegment here. */
tspivot(*tri, newsubseg);
if (newsubseg.ss == m->dummysub) {
/* Make new subsegment and initialize its vertices. */
makesubseg(m, &newsubseg);
setsorg(newsubseg, tridest);
setsdest(newsubseg, triorg); setsegorg(newsubseg, tridest);
setsegdest(newsubseg, triorg);
/* Bond new subsegment to the two triangles it is sandwiched between. */
/* Note that the facing triangle `oppotri' might be equal to */
/* `dummytri' (outer space), but the new subsegment is bonded to it */
/* all the same. */
tsbond(*tri, newsubseg);
sym(*tri, oppotri);
ssymself(newsubseg);
tsbond(oppotri, newsubseg);
setmark(newsubseg, subsegmark);
if (b->verbose > 2) {
printf(" Inserting new ");
printsubseg(m, b, &newsubseg);
}
} else {
if (mark(newsubseg) == 0) {
setmark(newsubseg, subsegmark);
}
}
}
/*****************************************************************************/
/* */
/* Terminology */
/* */
/* A "local transformation" replaces a small set of triangles with another */
/* set of triangles. This may or may not involve inserting or deleting a */
/* vertex. */
/* */
/* The term "casing" is used to describe the set of triangles that are */
/* attached to the triangles being transformed, but are not transformed */
/* themselves. Think of the casing as a fixed hollow structure inside */
/* which all the action happens. A "casing" is only defined relative to */
/* a single transformation; each occurrence of a transformation will */
/* involve a different casing. */
/* */
/*****************************************************************************/
/*****************************************************************************/
/* */
/* flip() Transform two triangles to two different triangles by flipping */
/* an edge counterclockwise within a quadrilateral. */
/* */
/* Imagine the original triangles, abc and bad, oriented so that the */
/* shared edge ab lies in a horizontal plane, with the vertex b on the left */
/* and the vertex a on the right. The vertex c lies below the edge, and */
/* the vertex d lies above the edge. The `flipedge' handle holds the edge */
/* ab of triangle abc, and is directed left, from vertex a to vertex b. */
/* */
/* The triangles abc and bad are deleted and replaced by the triangles cdb */
/* and dca. The triangles that represent abc and bad are NOT deallocated; */
/* they are reused for dca and cdb, respectively. Hence, any handles that */
/* may have held the original triangles are still valid, although not */
/* directed as they were before. */
/* */
/* Upon completion of this routine, the `flipedge' handle holds the edge */
/* dc of triangle dca, and is directed down, from vertex d to vertex c. */
/* (Hence, the two triangles have rotated counterclockwise.) */
/* */
/* WARNING: This transformation is geometrically valid only if the */
/* quadrilateral adbc is convex. Furthermore, this transformation is */
/* valid only if there is not a subsegment between the triangles abc and */
/* bad. This routine does not check either of these preconditions, and */
/* it is the responsibility of the calling routine to ensure that they are */
/* met. If they are not, the streets shall be filled with wailing and */
/* gnashing of teeth. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
void flip(struct mesh *m, struct behavior *b, struct otri *flipedge)
#else /* not ANSI_DECLARATORS */
void flip(m, b, flipedge)
struct mesh *m;
struct behavior *b;
struct otri *flipedge; /* Handle for the triangle abc. */
#endif /* not ANSI_DECLARATORS */
{
struct otri botleft, botright;
struct otri topleft, topright;
struct otri top;
struct otri botlcasing, botrcasing;
struct otri toplcasing, toprcasing;
struct osub botlsubseg, botrsubseg;
struct osub toplsubseg, toprsubseg;
vertex leftvertex, rightvertex, botvertex;
vertex farvertex;
triangle ptr; /* Temporary variable used by sym(). */
subseg sptr; /* Temporary variable used by tspivot(). */
/* Identify the vertices of the quadrilateral. */
org(*flipedge, rightvertex);
dest(*flipedge, leftvertex);
apex(*flipedge, botvertex);
sym(*flipedge, top);
#ifdef SELF_CHECK
if (top.tri == m->dummytri) {
printf("Internal error in flip(): Attempt to flip on boundary.\n");
lnextself(*flipedge);
return;
}
if (m->checksegments) {
tspivot(*flipedge, toplsubseg);
if (toplsubseg.ss != m->dummysub) {
printf("Internal error in flip(): Attempt to flip a segment.\n");
lnextself(*flipedge);
return;
}
}
#endif /* SELF_CHECK */
apex(top, farvertex);
/* Identify the casing of the quadrilateral. */
lprev(top, topleft);
sym(topleft, toplcasing);
lnext(top, topright);
sym(topright, toprcasing);
lnext(*flipedge, botleft);
sym(botleft, botlcasing);
lprev(*flipedge, botright);
sym(botright, botrcasing);
/* Rotate the quadrilateral one-quarter turn counterclockwise. */
bond(topleft, botlcasing);
bond(botleft, botrcasing);
bond(botright, toprcasing);
bond(topright, toplcasing);
if (m->checksegments) {
/* Check for subsegments and rebond them to the quadrilateral. */
tspivot(topleft, toplsubseg);
tspivot(botleft, botlsubseg);
tspivot(botright, botrsubseg);
tspivot(topright, toprsubseg);
if (toplsubseg.ss == m->dummysub) {
tsdissolve(topright);
} else {
tsbond(topright, toplsubseg);
} if (botlsubseg.ss == m->dummysub) {
tsdissolve(topleft);
} else {
tsbond(topleft, botlsubseg);
}
if (botrsubseg.ss == m->dummysub) {
tsdissolve(botleft);
} else {
tsbond(botleft, botrsubseg);
}
if (toprsubseg.ss == m->dummysub) {
tsdissolve(botright);
} else {
tsbond(botright, toprsubseg);
}
}
/* New vertex assignments for the rotated quadrilateral. */
setorg(*flipedge, farvertex);
setdest(*flipedge, botvertex);
setapex(*flipedge, rightvertex);
setorg(top, botvertex);
setdest(top, farvertex);
setapex(top, leftvertex);
if (b->verbose > 2) {
printf(" Edge flip results in left ");
printtriangle(m, b, &top);
printf(" and right ");
printtriangle(m, b, flipedge);
}
}
/*****************************************************************************/
/* */
/* unflip() Transform two triangles to two different triangles by */
/* flipping an edge clockwise within a quadrilateral. Reverses */
/* the flip() operation so that the data structures representing */
/* the triangles are back where they were before the flip(). */
/* */
/* Imagine the original triangles, abc and bad, oriented so that the */
/* shared edge ab lies in a horizontal plane, with the vertex b on the left */
/* and the vertex a on the right. The vertex c lies below the edge, and */
/* the vertex d lies above the edge. The `flipedge' handle holds the edge */
/* ab of triangle abc, and is directed left, from vertex a to vertex b. */
/* */
/* The triangles abc and bad are deleted and replaced by the triangles cdb */
/* and dca. The triangles that represent abc and bad are NOT deallocated; */
/* they are reused for cdb and dca, respectively. Hence, any handles that */
/* may have held the original triangles are still valid, although not */
/* directed as they were before. */
/* */
/* Upon completion of this routine, the `flipedge' handle holds the edge */
/* cd of triangle cdb, and is directed up, from vertex c to vertex d. */
/* (Hence, the two triangles have rotated clockwise.) */
/* */
/* WARNING: This transformation is geometrically valid only if the */
/* quadrilateral adbc is convex. Furthermore, this transformation is */
/* valid only if there is not a subsegment between the triangles abc and */
/* bad. This routine does not check either of these preconditions, and */
/* it is the responsibility of the calling routine to ensure that they are */
/* met. If they are not, the streets shall be filled with wailing and */
/* gnashing of teeth. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
void unflip(struct mesh *m, struct behavior *b, struct otri *flipedge)
#else /* not ANSI_DECLARATORS */
void unflip(m, b, flipedge)
struct mesh *m;struct behavior *b;
struct otri *flipedge; /* Handle for the triangle abc. */
#endif /* not ANSI_DECLARATORS */
{
struct otri botleft, botright;
struct otri topleft, topright;
struct otri top;
struct otri botlcasing, botrcasing;
struct otri toplcasing, toprcasing;
struct osub botlsubseg, botrsubseg;
struct osub toplsubseg, toprsubseg;
vertex leftvertex, rightvertex, botvertex;
vertex farvertex;
triangle ptr; /* Temporary variable used by sym(). */
subseg sptr; /* Temporary variable used by tspivot(). */
/* Identify the vertices of the quadrilateral. */
org(*flipedge, rightvertex);
dest(*flipedge, leftvertex);
apex(*flipedge, botvertex);
sym(*flipedge, top);
#ifdef SELF_CHECK
if (top.tri == m->dummytri) {
printf("Internal error in unflip(): Attempt to flip on boundary.\n");
lnextself(*flipedge);
return;
}
if (m->checksegments) {
tspivot(*flipedge, toplsubseg);
if (toplsubseg.ss != m->dummysub) {
printf("Internal error in unflip(): Attempt to flip a subsegment.\n");
lnextself(*flipedge);
return;
}
}
#endif /* SELF_CHECK */
apex(top, farvertex);
/* Identify the casing of the quadrilateral. */
lprev(top, topleft);
sym(topleft, toplcasing);
lnext(top, topright);
sym(topright, toprcasing);
lnext(*flipedge, botleft);
sym(botleft, botlcasing);
lprev(*flipedge, botright);
sym(botright, botrcasing);
/* Rotate the quadrilateral one-quarter turn clockwise. */
bond(topleft, toprcasing);
bond(botleft, toplcasing);
bond(botright, botlcasing);
bond(topright, botrcasing);
if (m->checksegments) {
/* Check for subsegments and rebond them to the quadrilateral. */
tspivot(topleft, toplsubseg);
tspivot(botleft, botlsubseg);
tspivot(botright, botrsubseg);
tspivot(topright, toprsubseg);
if (toplsubseg.ss == m->dummysub) {
tsdissolve(botleft);
} else {
tsbond(botleft, toplsubseg);
}
if (botlsubseg.ss == m->dummysub) {
tsdissolve(botright);
} else {
tsbond(botright, botlsubseg);
} if (botrsubseg.ss == m->dummysub) {
tsdissolve(topright);
} else {
tsbond(topright, botrsubseg);
}
if (toprsubseg.ss == m->dummysub) {
tsdissolve(topleft);
} else {
tsbond(topleft, toprsubseg);
}
}
/* New vertex assignments for the rotated quadrilateral. */
setorg(*flipedge, botvertex);
setdest(*flipedge, farvertex);
setapex(*flipedge, leftvertex);
setorg(top, farvertex);
setdest(top, botvertex);
setapex(top, rightvertex);
if (b->verbose > 2) {
printf(" Edge unflip results in left ");
printtriangle(m, b, flipedge);
printf(" and right ");
printtriangle(m, b, &top);
}
}
/*****************************************************************************/
/* */
/* insertvertex() Insert a vertex into a Delaunay triangulation, */
/* performing flips as necessary to maintain the Delaunay */
/* property. */
/* */
/* The point `insertvertex' is located. If `searchtri.tri' is not NULL, */
/* the search for the containing triangle begins from `searchtri'. If */
/* `searchtri.tri' is NULL, a full point location procedure is called. */
/* If `insertvertex' is found inside a triangle, the triangle is split into */
/* three; if `insertvertex' lies on an edge, the edge is split in two, */
/* thereby splitting the two adjacent triangles into four. Edge flips are */
/* used to restore the Delaunay property. If `insertvertex' lies on an */
/* existing vertex, no action is taken, and the value DUPLICATEVERTEX is */
/* returned. On return, `searchtri' is set to a handle whose origin is the */
/* existing vertex. */
/* */
/* Normally, the parameter `splitseg' is set to NULL, implying that no */
/* subsegment should be split. In this case, if `insertvertex' is found to */
/* lie on a segment, no action is taken, and the value VIOLATINGVERTEX is */
/* returned. On return, `searchtri' is set to a handle whose primary edge */
/* is the violated subsegment. */
/* */
/* If the calling routine wishes to split a subsegment by inserting a */
/* vertex in it, the parameter `splitseg' should be that subsegment. In */
/* this case, `searchtri' MUST be the triangle handle reached by pivoting */
/* from that subsegment; no point location is done. */
/* */
/* `segmentflaws' and `triflaws' are flags that indicate whether or not */
/* there should be checks for the creation of encroached subsegments or bad */
/* quality triangles. If a newly inserted vertex encroaches upon */
/* subsegments, these subsegments are added to the list of subsegments to */
/* be split if `segmentflaws' is set. If bad triangles are created, these */
/* are added to the queue if `triflaws' is set. */
/* */
/* If a duplicate vertex or violated segment does not prevent the vertex */
/* from being inserted, the return value will be ENCROACHINGVERTEX if the */
/* vertex encroaches upon a subsegment (and checking is enabled), or */
/* SUCCESSFULVERTEX otherwise. In either case, `searchtri' is set to a */
/* handle whose origin is the newly inserted vertex. */
/* */
/* insertvertex() does not use flip() for reasons of speed; some */
/* information can be reused from edge flip to edge flip, like the *//* locations of subsegments. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
enum insertvertexresult insertvertex(struct mesh *m, struct behavior *b,
vertex newvertex, struct otri *searchtri,
struct osub *splitseg,
int segmentflaws, int triflaws)
#else /* not ANSI_DECLARATORS */
enum insertvertexresult insertvertex(m, b, newvertex, searchtri, splitseg,
segmentflaws, triflaws)
struct mesh *m;
struct behavior *b;
vertex newvertex;
struct otri *searchtri;
struct osub *splitseg;
int segmentflaws;
int triflaws;
#endif /* not ANSI_DECLARATORS */
{
struct otri horiz;
struct otri top;
struct otri botleft, botright;
struct otri topleft, topright;
struct otri newbotleft, newbotright;
struct otri newtopright;
struct otri botlcasing, botrcasing;
struct otri toplcasing, toprcasing;
struct otri testtri;
struct osub botlsubseg, botrsubseg;
struct osub toplsubseg, toprsubseg;
struct osub brokensubseg;
struct osub checksubseg;
struct osub rightsubseg;
struct osub newsubseg;
struct badsubseg *encroached;
struct flipstacker *newflip;
vertex first;
vertex leftvertex, rightvertex, botvertex, topvertex, farvertex;
vertex segmentorg, segmentdest;
REAL attrib;
REAL area;
enum insertvertexresult success;
enum locateresult intersect;
int doflip;
int mirrorflag;
int enq;
int i;
triangle ptr; /* Temporary variable used by sym(). */
subseg sptr; /* Temporary variable used by spivot() and tspivot(). */
if (b->verbose > 1) {
printf(" Inserting (%.12g, %.12g).\n", newvertex[0], newvertex[1]);
}
if (splitseg == (struct osub *) NULL) {
/* Find the location of the vertex to be inserted. Check if a good */
/* starting triangle has already been provided by the caller. */
if (searchtri->tri == m->dummytri) {
/* Find a boundary triangle. */
horiz.tri = m->dummytri;
horiz.orient = 0;
symself(horiz);
/* Search for a triangle containing `newvertex'. */
intersect = locate(m, b, newvertex, &horiz);
} else {
/* Start searching from the triangle provided by the caller. */
otricopy(*searchtri, horiz); intersect = preciselocate(m, b, newvertex, &horiz, 1);
}
} else {
/* The calling routine provides the subsegment in which */
/* the vertex is inserted. */
otricopy(*searchtri, horiz);
intersect = ONEDGE;
}
if (intersect == ONVERTEX) {
/* There's already a vertex there. Return in `searchtri' a triangle */
/* whose origin is the existing vertex. */
otricopy(horiz, *searchtri);
otricopy(horiz, m->recenttri);
return DUPLICATEVERTEX;
}
if ((intersect == ONEDGE) || (intersect == OUTSIDE)) {
/* The vertex falls on an edge or boundary. */
if (m->checksegments && (splitseg == (struct osub *) NULL)) {
/* Check whether the vertex falls on a subsegment. */
tspivot(horiz, brokensubseg);
if (brokensubseg.ss != m->dummysub) {
/* The vertex falls on a subsegment, and hence will not be inserted. */
if (segmentflaws) {
enq = b->nobisect != 2;
if (enq && (b->nobisect == 1)) {
/* This subsegment may be split only if it is an */
/* internal boundary. */
sym(horiz, testtri);
enq = testtri.tri != m->dummytri;
}
if (enq) {
/* Add the subsegment to the list of encroached subsegments. */
encroached = (struct badsubseg *) poolalloc(&m->badsubsegs);
encroached->encsubseg = sencode(brokensubseg);
sorg(brokensubseg, encroached->subsegorg);
sdest(brokensubseg, encroached->subsegdest);
if (b->verbose > 2) {
printf(
" Queueing encroached subsegment (%.12g, %.12g) (%.12g, %.12g).\n",
encroached->subsegorg[0], encroached->subsegorg[1],
encroached->subsegdest[0], encroached->subsegdest[1]);
}
}
}
/* Return a handle whose primary edge contains the vertex, */
/* which has not been inserted. */
otricopy(horiz, *searchtri);
otricopy(horiz, m->recenttri);
return VIOLATINGVERTEX;
}
}
/* Insert the vertex on an edge, dividing one triangle into two (if */
/* the edge lies on a boundary) or two triangles into four. */
lprev(horiz, botright);
sym(botright, botrcasing);
sym(horiz, topright);
/* Is there a second triangle? (Or does this edge lie on a boundary?) */
mirrorflag = topright.tri != m->dummytri;
if (mirrorflag) {
lnextself(topright);
sym(topright, toprcasing);
maketriangle(m, b, &newtopright);
} else {
/* Splitting a boundary edge increases the number of boundary edges. */
m->hullsize++;
}
maketriangle(m, b, &newbotright);
/* Set the vertices of changed and new triangles. */
org(horiz, rightvertex);
dest(horiz, leftvertex);
apex(horiz, botvertex);
setorg(newbotright, botvertex);
setdest(newbotright, rightvertex);
setapex(newbotright, newvertex);
setorg(horiz, newvertex);
for (i = 0; i < m->eextras; i++) {
/* Set the element attributes of a new triangle. */
setelemattribute(newbotright, i, elemattribute(botright, i));
}
if (b->vararea) {
/* Set the area constraint of a new triangle. */
setareabound(newbotright, areabound(botright));
}
if (mirrorflag) {
dest(topright, topvertex);
setorg(newtopright, rightvertex);
setdest(newtopright, topvertex);
setapex(newtopright, newvertex);
setorg(topright, newvertex);
for (i = 0; i < m->eextras; i++) {
/* Set the element attributes of another new triangle. */
setelemattribute(newtopright, i, elemattribute(topright, i));
}
if (b->vararea) {
/* Set the area constraint of another new triangle. */
setareabound(newtopright, areabound(topright));
}
}
/* There may be subsegments that need to be bonded */
/* to the new triangle(s). */
if (m->checksegments) {
tspivot(botright, botrsubseg);
if (botrsubseg.ss != m->dummysub) {
tsdissolve(botright);
tsbond(newbotright, botrsubseg);
}
if (mirrorflag) {
tspivot(topright, toprsubseg);
if (toprsubseg.ss != m->dummysub) {
tsdissolve(topright);
tsbond(newtopright, toprsubseg);
}
}
}
/* Bond the new triangle(s) to the surrounding triangles. */
bond(newbotright, botrcasing);
lprevself(newbotright);
bond(newbotright, botright);
lprevself(newbotright);
if (mirrorflag) {
bond(newtopright, toprcasing);
lnextself(newtopright);
bond(newtopright, topright);
lnextself(newtopright);
bond(newtopright, newbotright);
}
if (splitseg != (struct osub *) NULL) {
/* Split the subsegment into two. */
setsdest(*splitseg, newvertex);
segorg(*splitseg, segmentorg);
segdest(*splitseg, segmentdest);
ssymself(*splitseg);
spivot(*splitseg, rightsubseg);
insertsubseg(m, b, &newbotright, mark(*splitseg)); tspivot(newbotright, newsubseg);
setsegorg(newsubseg, segmentorg);
setsegdest(newsubseg, segmentdest);
sbond(*splitseg, newsubseg);
ssymself(newsubseg);
sbond(newsubseg, rightsubseg);
ssymself(*splitseg);
/* Transfer the subsegment's boundary marker to the vertex */
/* if required. */
if (vertexmark(newvertex) == 0) {
setvertexmark(newvertex, mark(*splitseg));
}
}
if (m->checkquality) {
poolrestart(&m->flipstackers);
m->lastflip = (struct flipstacker *) poolalloc(&m->flipstackers);
m->lastflip->flippedtri = encode(horiz);
m->lastflip->prevflip = (struct flipstacker *) &insertvertex;
}
#ifdef SELF_CHECK
if (counterclockwise(m, b, rightvertex, leftvertex, botvertex) < 0.0) {
printf("Internal error in insertvertex():\n");
printf(
" Clockwise triangle prior to edge vertex insertion (bottom).\n");
}
if (mirrorflag) {
if (counterclockwise(m, b, leftvertex, rightvertex, topvertex) < 0.0) {
printf("Internal error in insertvertex():\n");
printf(" Clockwise triangle prior to edge vertex insertion (top).\n");
}
if (counterclockwise(m, b, rightvertex, topvertex, newvertex) < 0.0) {
printf("Internal error in insertvertex():\n");
printf(
" Clockwise triangle after edge vertex insertion (top right).\n");
}
if (counterclockwise(m, b, topvertex, leftvertex, newvertex) < 0.0) {
printf("Internal error in insertvertex():\n");
printf(
" Clockwise triangle after edge vertex insertion (top left).\n");
}
}
if (counterclockwise(m, b, leftvertex, botvertex, newvertex) < 0.0) {
printf("Internal error in insertvertex():\n");
printf(
" Clockwise triangle after edge vertex insertion (bottom left).\n");
}
if (counterclockwise(m, b, botvertex, rightvertex, newvertex) < 0.0) {
printf("Internal error in insertvertex():\n");
printf(
" Clockwise triangle after edge vertex insertion (bottom right).\n");
}
#endif /* SELF_CHECK */
if (b->verbose > 2) {
printf(" Updating bottom left ");
printtriangle(m, b, &botright);
if (mirrorflag) {
printf(" Updating top left ");
printtriangle(m, b, &topright);
printf(" Creating top right ");
printtriangle(m, b, &newtopright);
}
printf(" Creating bottom right ");
printtriangle(m, b, &newbotright);
}
/* Position `horiz' on the first edge to check for */
/* the Delaunay property. */
lnextself(horiz); } else {
/* Insert the vertex in a triangle, splitting it into three. */
lnext(horiz, botleft);
lprev(horiz, botright);
sym(botleft, botlcasing);
sym(botright, botrcasing);
maketriangle(m, b, &newbotleft);
maketriangle(m, b, &newbotright);
/* Set the vertices of changed and new triangles. */
org(horiz, rightvertex);
dest(horiz, leftvertex);
apex(horiz, botvertex);
setorg(newbotleft, leftvertex);
setdest(newbotleft, botvertex);
setapex(newbotleft, newvertex);
setorg(newbotright, botvertex);
setdest(newbotright, rightvertex);
setapex(newbotright, newvertex);
setapex(horiz, newvertex);
for (i = 0; i < m->eextras; i++) {
/* Set the element attributes of the new triangles. */
attrib = elemattribute(horiz, i);
setelemattribute(newbotleft, i, attrib);
setelemattribute(newbotright, i, attrib);
}
if (b->vararea) {
/* Set the area constraint of the new triangles. */
area = areabound(horiz);
setareabound(newbotleft, area);
setareabound(newbotright, area);
}
/* There may be subsegments that need to be bonded */
/* to the new triangles. */
if (m->checksegments) {
tspivot(botleft, botlsubseg);
if (botlsubseg.ss != m->dummysub) {
tsdissolve(botleft);
tsbond(newbotleft, botlsubseg);
}
tspivot(botright, botrsubseg);
if (botrsubseg.ss != m->dummysub) {
tsdissolve(botright);
tsbond(newbotright, botrsubseg);
}
}
/* Bond the new triangles to the surrounding triangles. */
bond(newbotleft, botlcasing);
bond(newbotright, botrcasing);
lnextself(newbotleft);
lprevself(newbotright);
bond(newbotleft, newbotright);
lnextself(newbotleft);
bond(botleft, newbotleft);
lprevself(newbotright);
bond(botright, newbotright);
if (m->checkquality) {
poolrestart(&m->flipstackers);
m->lastflip = (struct flipstacker *) poolalloc(&m->flipstackers);
m->lastflip->flippedtri = encode(horiz);
m->lastflip->prevflip = (struct flipstacker *) NULL;
}
#ifdef SELF_CHECK
if (counterclockwise(m, b, rightvertex, leftvertex, botvertex) < 0.0) {
printf("Internal error in insertvertex():\n");
printf(" Clockwise triangle prior to vertex insertion.\n"); }
if (counterclockwise(m, b, rightvertex, leftvertex, newvertex) < 0.0) {
printf("Internal error in insertvertex():\n");
printf(" Clockwise triangle after vertex insertion (top).\n");
}
if (counterclockwise(m, b, leftvertex, botvertex, newvertex) < 0.0) {
printf("Internal error in insertvertex():\n");
printf(" Clockwise triangle after vertex insertion (left).\n");
}
if (counterclockwise(m, b, botvertex, rightvertex, newvertex) < 0.0) {
printf("Internal error in insertvertex():\n");
printf(" Clockwise triangle after vertex insertion (right).\n");
}
#endif /* SELF_CHECK */
if (b->verbose > 2) {
printf(" Updating top ");
printtriangle(m, b, &horiz);
printf(" Creating left ");
printtriangle(m, b, &newbotleft);
printf(" Creating right ");
printtriangle(m, b, &newbotright);
}
}
/* The insertion is successful by default, unless an encroached */
/* subsegment is found. */
success = SUCCESSFULVERTEX;
/* Circle around the newly inserted vertex, checking each edge opposite */
/* it for the Delaunay property. Non-Delaunay edges are flipped. */
/* `horiz' is always the edge being checked. `first' marks where to */
/* stop circling. */
org(horiz, first);
rightvertex = first;
dest(horiz, leftvertex);
/* Circle until finished. */
while (1) {
/* By default, the edge will be flipped. */
doflip = 1;
if (m->checksegments) {
/* Check for a subsegment, which cannot be flipped. */
tspivot(horiz, checksubseg);
if (checksubseg.ss != m->dummysub) {
/* The edge is a subsegment and cannot be flipped. */
doflip = 0;
#ifndef CDT_ONLY
if (segmentflaws) {
/* Does the new vertex encroach upon this subsegment? */
if (checkseg4encroach(m, b, &checksubseg)) {
success = ENCROACHINGVERTEX;
}
}
#endif /* not CDT_ONLY */
}
}
if (doflip) {
/* Check if the edge is a boundary edge. */
sym(horiz, top);
if (top.tri == m->dummytri) {
/* The edge is a boundary edge and cannot be flipped. */
doflip = 0;
} else {
/* Find the vertex on the other side of the edge. */
apex(top, farvertex);
/* In the incremental Delaunay triangulation algorithm, any of */
/* `leftvertex', `rightvertex', and `farvertex' could be vertices */
/* of the triangular bounding box. These vertices must be */
/* treated as if they are infinitely distant, even though their */
/* "coordinates" are not. */ if ((leftvertex == m->infvertex1) || (leftvertex == m->infvertex2) ||
(leftvertex == m->infvertex3)) {
/* `leftvertex' is infinitely distant. Check the convexity of */
/* the boundary of the triangulation. 'farvertex' might be */
/* infinite as well, but trust me, this same condition should */
/* be applied. */
doflip = counterclockwise(m, b, newvertex, rightvertex, farvertex)
> 0.0;
} else if ((rightvertex == m->infvertex1) ||
(rightvertex == m->infvertex2) ||
(rightvertex == m->infvertex3)) {
/* `rightvertex' is infinitely distant. Check the convexity of */
/* the boundary of the triangulation. 'farvertex' might be */
/* infinite as well, but trust me, this same condition should */
/* be applied. */
doflip = counterclockwise(m, b, farvertex, leftvertex, newvertex)
> 0.0;
} else if ((farvertex == m->infvertex1) ||
(farvertex == m->infvertex2) ||
(farvertex == m->infvertex3)) {
/* `farvertex' is infinitely distant and cannot be inside */
/* the circumcircle of the triangle `horiz'. */
doflip = 0;
} else {
/* Test whether the edge is locally Delaunay. */
doflip = incircle(m, b, leftvertex, newvertex, rightvertex,
farvertex) > 0.0;
}
if (doflip) {
/* We made it! Flip the edge `horiz' by rotating its containing */
/* quadrilateral (the two triangles adjacent to `horiz'). */
/* Identify the casing of the quadrilateral. */
lprev(top, topleft);
sym(topleft, toplcasing);
lnext(top, topright);
sym(topright, toprcasing);
lnext(horiz, botleft);
sym(botleft, botlcasing);
lprev(horiz, botright);
sym(botright, botrcasing);
/* Rotate the quadrilateral one-quarter turn counterclockwise. */
bond(topleft, botlcasing);
bond(botleft, botrcasing);
bond(botright, toprcasing);
bond(topright, toplcasing);
if (m->checksegments) {
/* Check for subsegments and rebond them to the quadrilateral. */
tspivot(topleft, toplsubseg);
tspivot(botleft, botlsubseg);
tspivot(botright, botrsubseg);
tspivot(topright, toprsubseg);
if (toplsubseg.ss == m->dummysub) {
tsdissolve(topright);
} else {
tsbond(topright, toplsubseg);
}
if (botlsubseg.ss == m->dummysub) {
tsdissolve(topleft);
} else {
tsbond(topleft, botlsubseg);
}
if (botrsubseg.ss == m->dummysub) {
tsdissolve(botleft);
} else {
tsbond(botleft, botrsubseg);
}
if (toprsubseg.ss == m->dummysub) {
tsdissolve(botright);
} else {
tsbond(botright, toprsubseg); }
}
/* New vertex assignments for the rotated quadrilateral. */
setorg(horiz, farvertex);
setdest(horiz, newvertex);
setapex(horiz, rightvertex);
setorg(top, newvertex);
setdest(top, farvertex);
setapex(top, leftvertex);
for (i = 0; i < m->eextras; i++) {
/* Take the average of the two triangles' attributes. */
attrib = 0.5 * (elemattribute(top, i) + elemattribute(horiz, i));
setelemattribute(top, i, attrib);
setelemattribute(horiz, i, attrib);
}
if (b->vararea) {
if ((areabound(top) <= 0.0) || (areabound(horiz) <= 0.0)) {
area = -1.0;
} else {
/* Take the average of the two triangles' area constraints. */
/* This prevents small area constraints from migrating a */
/* long, long way from their original location due to flips. */
area = 0.5 * (areabound(top) + areabound(horiz));
}
setareabound(top, area);
setareabound(horiz, area);
}
if (m->checkquality) {
newflip = (struct flipstacker *) poolalloc(&m->flipstackers);
newflip->flippedtri = encode(horiz);
newflip->prevflip = m->lastflip;
m->lastflip = newflip;
}
#ifdef SELF_CHECK
if (newvertex != (vertex) NULL) {
if (counterclockwise(m, b, leftvertex, newvertex, rightvertex) <
0.0) {
printf("Internal error in insertvertex():\n");
printf(" Clockwise triangle prior to edge flip (bottom).\n");
}
/* The following test has been removed because constrainededge() */
/* sometimes generates inverted triangles that insertvertex() */
/* removes. */
/*
if (counterclockwise(m, b, rightvertex, farvertex, leftvertex) <
0.0) {
printf("Internal error in insertvertex():\n");
printf(" Clockwise triangle prior to edge flip (top).\n");
}
*/
if (counterclockwise(m, b, farvertex, leftvertex, newvertex) <
0.0) {
printf("Internal error in insertvertex():\n");
printf(" Clockwise triangle after edge flip (left).\n");
}
if (counterclockwise(m, b, newvertex, rightvertex, farvertex) <
0.0) {
printf("Internal error in insertvertex():\n");
printf(" Clockwise triangle after edge flip (right).\n");
}
}
#endif /* SELF_CHECK */
if (b->verbose > 2) {
printf(" Edge flip results in left ");
lnextself(topleft);
printtriangle(m, b, &topleft);
printf(" and right ");
printtriangle(m, b, &horiz); }
/* On the next iterations, consider the two edges that were */
/* exposed (this is, are now visible to the newly inserted */
/* vertex) by the edge flip. */
lprevself(horiz);
leftvertex = farvertex;
}
}
}
if (!doflip) {
/* The handle `horiz' is accepted as locally Delaunay. */
#ifndef CDT_ONLY
if (triflaws) {
/* Check the triangle `horiz' for quality. */
testtriangle(m, b, &horiz);
}
#endif /* not CDT_ONLY */
/* Look for the next edge around the newly inserted vertex. */
lnextself(horiz);
sym(horiz, testtri);
/* Check for finishing a complete revolution about the new vertex, or */
/* falling outside of the triangulation. The latter will happen */
/* when a vertex is inserted at a boundary. */
if ((leftvertex == first) || (testtri.tri == m->dummytri)) {
/* We're done. Return a triangle whose origin is the new vertex. */
lnext(horiz, *searchtri);
lnext(horiz, m->recenttri);
return success;
}
/* Finish finding the next edge around the newly inserted vertex. */
lnext(testtri, horiz);
rightvertex = leftvertex;
dest(horiz, leftvertex);
}
}
}
/*****************************************************************************/
/* */
/* triangulatepolygon() Find the Delaunay triangulation of a polygon that */
/* has a certain "nice" shape. This includes the */
/* polygons that result from deletion of a vertex or */
/* insertion of a segment. */
/* */
/* This is a conceptually difficult routine. The starting assumption is */
/* that we have a polygon with n sides. n - 1 of these sides are currently */
/* represented as edges in the mesh. One side, called the "base", need not */
/* be. */
/* */
/* Inside the polygon is a structure I call a "fan", consisting of n - 1 */
/* triangles that share a common origin. For each of these triangles, the */
/* edge opposite the origin is one of the sides of the polygon. The */
/* primary edge of each triangle is the edge directed from the origin to */
/* the destination; note that this is not the same edge that is a side of */
/* the polygon. `firstedge' is the primary edge of the first triangle. */
/* From there, the triangles follow in counterclockwise order about the */
/* polygon, until `lastedge', the primary edge of the last triangle. */
/* `firstedge' and `lastedge' are probably connected to other triangles */
/* beyond the extremes of the fan, but their identity is not important, as */
/* long as the fan remains connected to them. */
/* */
/* Imagine the polygon oriented so that its base is at the bottom. This */
/* puts `firstedge' on the far right, and `lastedge' on the far left. */
/* The right vertex of the base is the destination of `firstedge', and the */
/* left vertex of the base is the apex of `lastedge'. */
/* */
/* The challenge now is to find the right sequence of edge flips to */
/* transform the fan into a Delaunay triangulation of the polygon. Each */
/* edge flip effectively removes one triangle from the fan, committing it */
/* to the polygon. The resulting polygon has one fewer edge. If `doflip' *//* is set, the final flip will be performed, resulting in a fan of one */
/* (useless?) triangle. If `doflip' is not set, the final flip is not */
/* performed, resulting in a fan of two triangles, and an unfinished */
/* triangular polygon that is not yet filled out with a single triangle. */
/* On completion of the routine, `lastedge' is the last remaining triangle, */
/* or the leftmost of the last two. */
/* */
/* Although the flips are performed in the order described above, the */
/* decisions about what flips to perform are made in precisely the reverse */
/* order. The recursive triangulatepolygon() procedure makes a decision, */
/* uses up to two recursive calls to triangulate the "subproblems" */
/* (polygons with fewer edges), and then performs an edge flip. */
/* */
/* The "decision" it makes is which vertex of the polygon should be */
/* connected to the base. This decision is made by testing every possible */
/* vertex. Once the best vertex is found, the two edges that connect this */
/* vertex to the base become the bases for two smaller polygons. These */
/* are triangulated recursively. Unfortunately, this approach can take */
/* O(n^2) time not only in the worst case, but in many common cases. It's */
/* rarely a big deal for vertex deletion, where n is rarely larger than */
/* ten, but it could be a big deal for segment insertion, especially if */
/* there's a lot of long segments that each cut many triangles. I ought to */
/* code a faster algorithm some day. */
/* */
/* The `edgecount' parameter is the number of sides of the polygon, */
/* including its base. `triflaws' is a flag that determines whether the */
/* new triangles should be tested for quality, and enqueued if they are */
/* bad. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
void triangulatepolygon(struct mesh *m, struct behavior *b,
struct otri *firstedge, struct otri *lastedge,
int edgecount, int doflip, int triflaws)
#else /* not ANSI_DECLARATORS */
void triangulatepolygon(m, b, firstedge, lastedge, edgecount, doflip, triflaws)
struct mesh *m;
struct behavior *b;
struct otri *firstedge;
struct otri *lastedge;
int edgecount;
int doflip;
int triflaws;
#endif /* not ANSI_DECLARATORS */
{
struct otri testtri;
struct otri besttri;
struct otri tempedge;
vertex leftbasevertex, rightbasevertex;
vertex testvertex;
vertex bestvertex;
int bestnumber;
int i;
triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */
/* Identify the base vertices. */
apex(*lastedge, leftbasevertex);
dest(*firstedge, rightbasevertex);
if (b->verbose > 2) {
printf(" Triangulating interior polygon at edge\n");
printf(" (%.12g, %.12g) (%.12g, %.12g)\n", leftbasevertex[0],
leftbasevertex[1], rightbasevertex[0], rightbasevertex[1]);
}
/* Find the best vertex to connect the base to. */
onext(*firstedge, besttri);
dest(besttri, bestvertex);
otricopy(besttri, testtri);
bestnumber = 1; for (i = 2; i <= edgecount - 2; i++) {
onextself(testtri);
dest(testtri, testvertex);
/* Is this a better vertex? */
if (incircle(m, b, leftbasevertex, rightbasevertex, bestvertex,
testvertex) > 0.0) {
otricopy(testtri, besttri);
bestvertex = testvertex;
bestnumber = i;
}
}
if (b->verbose > 2) {
printf(" Connecting edge to (%.12g, %.12g)\n", bestvertex[0],
bestvertex[1]);
}
if (bestnumber > 1) {
/* Recursively triangulate the smaller polygon on the right. */
oprev(besttri, tempedge);
triangulatepolygon(m, b, firstedge, &tempedge, bestnumber + 1, 1,
triflaws);
}
if (bestnumber < edgecount - 2) {
/* Recursively triangulate the smaller polygon on the left. */
sym(besttri, tempedge);
triangulatepolygon(m, b, &besttri, lastedge, edgecount - bestnumber, 1,
triflaws);
/* Find `besttri' again; it may have been lost to edge flips. */
sym(tempedge, besttri);
}
if (doflip) {
/* Do one final edge flip. */
flip(m, b, &besttri);
#ifndef CDT_ONLY
if (triflaws) {
/* Check the quality of the newly committed triangle. */
sym(besttri, testtri);
testtriangle(m, b, &testtri);
}
#endif /* not CDT_ONLY */
}
/* Return the base triangle. */
otricopy(besttri, *lastedge);
}
/*****************************************************************************/
/* */
/* deletevertex() Delete a vertex from a Delaunay triangulation, ensuring */
/* that the triangulation remains Delaunay. */
/* */
/* The origin of `deltri' is deleted. The union of the triangles adjacent */
/* to this vertex is a polygon, for which the Delaunay triangulation is */
/* found. Two triangles are removed from the mesh. */
/* */
/* Only interior vertices that do not lie on segments or boundaries may be */
/* deleted. */
/* */
/*****************************************************************************/
#ifndef CDT_ONLY
#ifdef ANSI_DECLARATORS
void deletevertex(struct mesh *m, struct behavior *b, struct otri *deltri)
#else /* not ANSI_DECLARATORS */
void deletevertex(m, b, deltri)
struct mesh *m;
struct behavior *b;
struct otri *deltri;
#endif /* not ANSI_DECLARATORS */
{ struct otri countingtri;
struct otri firstedge, lastedge;
struct otri deltriright;
struct otri lefttri, righttri;
struct otri leftcasing, rightcasing;
struct osub leftsubseg, rightsubseg;
vertex delvertex;
vertex neworg;
int edgecount;
triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */
subseg sptr; /* Temporary variable used by tspivot(). */
org(*deltri, delvertex);
if (b->verbose > 1) {
printf(" Deleting (%.12g, %.12g).\n", delvertex[0], delvertex[1]);
}
vertexdealloc(m, delvertex);
/* Count the degree of the vertex being deleted. */
onext(*deltri, countingtri);
edgecount = 1;
while (!otriequal(*deltri, countingtri)) {
#ifdef SELF_CHECK
if (countingtri.tri == m->dummytri) {
printf("Internal error in deletevertex():\n");
printf(" Attempt to delete boundary vertex.\n");
internalerror();
}
#endif /* SELF_CHECK */
edgecount++;
onextself(countingtri);
}
#ifdef SELF_CHECK
if (edgecount < 3) {
printf("Internal error in deletevertex():\n Vertex has degree %d.\n",
edgecount);
internalerror();
}
#endif /* SELF_CHECK */
if (edgecount > 3) {
/* Triangulate the polygon defined by the union of all triangles */
/* adjacent to the vertex being deleted. Check the quality of */
/* the resulting triangles. */
onext(*deltri, firstedge);
oprev(*deltri, lastedge);
triangulatepolygon(m, b, &firstedge, &lastedge, edgecount, 0,
!b->nobisect);
}
/* Splice out two triangles. */
lprev(*deltri, deltriright);
dnext(*deltri, lefttri);
sym(lefttri, leftcasing);
oprev(deltriright, righttri);
sym(righttri, rightcasing);
bond(*deltri, leftcasing);
bond(deltriright, rightcasing);
tspivot(lefttri, leftsubseg);
if (leftsubseg.ss != m->dummysub) {
tsbond(*deltri, leftsubseg);
}
tspivot(righttri, rightsubseg);
if (rightsubseg.ss != m->dummysub) {
tsbond(deltriright, rightsubseg);
}
/* Set the new origin of `deltri' and check its quality. */
org(lefttri, neworg);
setorg(*deltri, neworg);
if (!b->nobisect) { testtriangle(m, b, deltri);
}
/* Delete the two spliced-out triangles. */
triangledealloc(m, lefttri.tri);
triangledealloc(m, righttri.tri);
}
#endif /* not CDT_ONLY */
/*****************************************************************************/
/* */
/* undovertex() Undo the most recent vertex insertion. */
/* */
/* Walks through the list of transformations (flips and a vertex insertion) */
/* in the reverse of the order in which they were done, and undoes them. */
/* The inserted vertex is removed from the triangulation and deallocated. */
/* Two triangles (possibly just one) are also deallocated. */
/* */
/*****************************************************************************/
#ifndef CDT_ONLY
#ifdef ANSI_DECLARATORS
void undovertex(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
void undovertex(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */
{
struct otri fliptri;
struct otri botleft, botright, topright;
struct otri botlcasing, botrcasing, toprcasing;
struct otri gluetri;
struct osub botlsubseg, botrsubseg, toprsubseg;
vertex botvertex, rightvertex;
triangle ptr; /* Temporary variable used by sym(). */
subseg sptr; /* Temporary variable used by tspivot(). */
/* Walk through the list of transformations (flips and a vertex insertion) */
/* in the reverse of the order in which they were done, and undo them. */
while (m->lastflip != (struct flipstacker *) NULL) {
/* Find a triangle involved in the last unreversed transformation. */
decode(m->lastflip->flippedtri, fliptri);
/* We are reversing one of three transformations: a trisection of one */
/* triangle into three (by inserting a vertex in the triangle), a */
/* bisection of two triangles into four (by inserting a vertex in an */
/* edge), or an edge flip. */
if (m->lastflip->prevflip == (struct flipstacker *) NULL) {
/* Restore a triangle that was split into three triangles, */
/* so it is again one triangle. */
dprev(fliptri, botleft);
lnextself(botleft);
onext(fliptri, botright);
lprevself(botright);
sym(botleft, botlcasing);
sym(botright, botrcasing);
dest(botleft, botvertex);
setapex(fliptri, botvertex);
lnextself(fliptri);
bond(fliptri, botlcasing);
tspivot(botleft, botlsubseg);
tsbond(fliptri, botlsubseg);
lnextself(fliptri);
bond(fliptri, botrcasing);
tspivot(botright, botrsubseg); tsbond(fliptri, botrsubseg);
/* Delete the two spliced-out triangles. */
triangledealloc(m, botleft.tri);
triangledealloc(m, botright.tri);
} else if (m->lastflip->prevflip == (struct flipstacker *) &insertvertex) {
/* Restore two triangles that were split into four triangles, */
/* so they are again two triangles. */
lprev(fliptri, gluetri);
sym(gluetri, botright);
lnextself(botright);
sym(botright, botrcasing);
dest(botright, rightvertex);
setorg(fliptri, rightvertex);
bond(gluetri, botrcasing);
tspivot(botright, botrsubseg);
tsbond(gluetri, botrsubseg);
/* Delete the spliced-out triangle. */
triangledealloc(m, botright.tri);
sym(fliptri, gluetri);
if (gluetri.tri != m->dummytri) {
lnextself(gluetri);
dnext(gluetri, topright);
sym(topright, toprcasing);
setorg(gluetri, rightvertex);
bond(gluetri, toprcasing);
tspivot(topright, toprsubseg);
tsbond(gluetri, toprsubseg);
/* Delete the spliced-out triangle. */
triangledealloc(m, topright.tri);
}
/* This is the end of the list, sneakily encoded. */
m->lastflip->prevflip = (struct flipstacker *) NULL;
} else {
/* Undo an edge flip. */
unflip(m, b, &fliptri);
}
/* Go on and process the next transformation. */
m->lastflip = m->lastflip->prevflip;
}
}
#endif /* not CDT_ONLY */
/** **/
/** **/
/********* Mesh transformation routines end here *********/
/********* Divide-and-conquer Delaunay triangulation begins here *********/
/** **/
/** **/
/*****************************************************************************/
/* */
/* The divide-and-conquer bounding box */
/* */
/* I originally implemented the divide-and-conquer and incremental Delaunay */
/* triangulations using the edge-based data structure presented by Guibas */
/* and Stolfi. Switching to a triangle-based data structure doubled the */
/* speed. However, I had to think of a few extra tricks to maintain the */
/* elegance of the original algorithms. */
/* */
/* The "bounding box" used by my variant of the divide-and-conquer *//* algorithm uses one triangle for each edge of the convex hull of the */
/* triangulation. These bounding triangles all share a common apical */
/* vertex, which is represented by NULL and which represents nothing. */
/* The bounding triangles are linked in a circular fan about this NULL */
/* vertex, and the edges on the convex hull of the triangulation appear */
/* opposite the NULL vertex. You might find it easiest to imagine that */
/* the NULL vertex is a point in 3D space behind the center of the */
/* triangulation, and that the bounding triangles form a sort of cone. */
/* */
/* This bounding box makes it easy to represent degenerate cases. For */
/* instance, the triangulation of two vertices is a single edge. This edge */
/* is represented by two bounding box triangles, one on each "side" of the */
/* edge. These triangles are also linked together in a fan about the NULL */
/* vertex. */
/* */
/* The bounding box also makes it easy to traverse the convex hull, as the */
/* divide-and-conquer algorithm needs to do. */
/* */
/*****************************************************************************/
/*****************************************************************************/
/* */
/* vertexsort() Sort an array of vertices by x-coordinate, using the */
/* y-coordinate as a secondary key. */
/* */
/* Uses quicksort. Randomized O(n log n) time. No, I did not make any of */
/* the usual quicksort mistakes. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
void vertexsort(vertex *sortarray, int arraysize)
#else /* not ANSI_DECLARATORS */
void vertexsort(sortarray, arraysize)
vertex *sortarray;
int arraysize;
#endif /* not ANSI_DECLARATORS */
{
int left, right;
int pivot;
REAL pivotx, pivoty;
vertex temp;
if (arraysize == 2) {
/* Recursive base case. */
if ((sortarray[0][0] > sortarray[1][0]) ||
((sortarray[0][0] == sortarray[1][0]) &&
(sortarray[0][1] > sortarray[1][1]))) {
temp = sortarray[1];
sortarray[1] = sortarray[0];
sortarray[0] = temp;
}
return;
}
/* Choose a random pivot to split the array. */
pivot = (int) randomnation((unsigned int) arraysize);
pivotx = sortarray[pivot][0];
pivoty = sortarray[pivot][1];
/* Split the array. */
left = -1;
right = arraysize;
while (left < right) {
/* Search for a vertex whose x-coordinate is too large for the left. */
do {
left++;
} while ((left <= right) && ((sortarray[left][0] < pivotx) ||
((sortarray[left][0] == pivotx) &&
(sortarray[left][1] < pivoty))));
/* Search for a vertex whose x-coordinate is too small for the right. */ do {
right--;
} while ((left <= right) && ((sortarray[right][0] > pivotx) ||
((sortarray[right][0] == pivotx) &&
(sortarray[right][1] > pivoty))));
if (left < right) {
/* Swap the left and right vertices. */
temp = sortarray[left];
sortarray[left] = sortarray[right];
sortarray[right] = temp;
}
}
if (left > 1) {
/* Recursively sort the left subset. */
vertexsort(sortarray, left);
}
if (right < arraysize - 2) {
/* Recursively sort the right subset. */
vertexsort(&sortarray[right + 1], arraysize - right - 1);
}
}
/*****************************************************************************/
/* */
/* vertexmedian() An order statistic algorithm, almost. Shuffles an */
/* array of vertices so that the first `median' vertices */
/* occur lexicographically before the remaining vertices. */
/* */
/* Uses the x-coordinate as the primary key if axis == 0; the y-coordinate */
/* if axis == 1. Very similar to the vertexsort() procedure, but runs in */
/* randomized linear time. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
void vertexmedian(vertex *sortarray, int arraysize, int median, int axis)
#else /* not ANSI_DECLARATORS */
void vertexmedian(sortarray, arraysize, median, axis)
vertex *sortarray;
int arraysize;
int median;
int axis;
#endif /* not ANSI_DECLARATORS */
{
int left, right;
int pivot;
REAL pivot1, pivot2;
vertex temp;
if (arraysize == 2) {
/* Recursive base case. */
if ((sortarray[0][axis] > sortarray[1][axis]) ||
((sortarray[0][axis] == sortarray[1][axis]) &&
(sortarray[0][1 - axis] > sortarray[1][1 - axis]))) {
temp = sortarray[1];
sortarray[1] = sortarray[0];
sortarray[0] = temp;
}
return;
}
/* Choose a random pivot to split the array. */
pivot = (int) randomnation((unsigned int) arraysize);
pivot1 = sortarray[pivot][axis];
pivot2 = sortarray[pivot][1 - axis];
/* Split the array. */
left = -1;
right = arraysize;
while (left < right) {
/* Search for a vertex whose x-coordinate is too large for the left. */ do {
left++;
} while ((left <= right) && ((sortarray[left][axis] < pivot1) ||
((sortarray[left][axis] == pivot1) &&
(sortarray[left][1 - axis] < pivot2))));
/* Search for a vertex whose x-coordinate is too small for the right. */
do {
right--;
} while ((left <= right) && ((sortarray[right][axis] > pivot1) ||
((sortarray[right][axis] == pivot1) &&
(sortarray[right][1 - axis] > pivot2))));
if (left < right) {
/* Swap the left and right vertices. */
temp = sortarray[left];
sortarray[left] = sortarray[right];
sortarray[right] = temp;
}
}
/* Unlike in vertexsort(), at most one of the following */
/* conditionals is true. */
if (left > median) {
/* Recursively shuffle the left subset. */
vertexmedian(sortarray, left, median, axis);
}
if (right < median - 1) {
/* Recursively shuffle the right subset. */
vertexmedian(&sortarray[right + 1], arraysize - right - 1,
median - right - 1, axis);
}
}
/*****************************************************************************/
/* */
/* alternateaxes() Sorts the vertices as appropriate for the divide-and- */
/* conquer algorithm with alternating cuts. */
/* */
/* Partitions by x-coordinate if axis == 0; by y-coordinate if axis == 1. */
/* For the base case, subsets containing only two or three vertices are */
/* always sorted by x-coordinate. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
void alternateaxes(vertex *sortarray, int arraysize, int axis)
#else /* not ANSI_DECLARATORS */
void alternateaxes(sortarray, arraysize, axis)
vertex *sortarray;
int arraysize;
int axis;
#endif /* not ANSI_DECLARATORS */
{
int divider;
divider = arraysize >> 1;
if (arraysize <= 3) {
/* Recursive base case: subsets of two or three vertices will be */
/* handled specially, and should always be sorted by x-coordinate. */
axis = 0;
}
/* Partition with a horizontal or vertical cut. */
vertexmedian(sortarray, arraysize, divider, axis);
/* Recursively partition the subsets with a cross cut. */
if (arraysize - divider >= 2) {
if (divider >= 2) {
alternateaxes(sortarray, divider, 1 - axis);
}
alternateaxes(&sortarray[divider], arraysize - divider, 1 - axis);
}
}
/*****************************************************************************/
/* */
/* mergehulls() Merge two adjacent Delaunay triangulations into a */
/* single Delaunay triangulation. */
/* */
/* This is similar to the algorithm given by Guibas and Stolfi, but uses */
/* a triangle-based, rather than edge-based, data structure. */
/* */
/* The algorithm walks up the gap between the two triangulations, knitting */
/* them together. As they are merged, some of their bounding triangles */
/* are converted into real triangles of the triangulation. The procedure */
/* pulls each hull's bounding triangles apart, then knits them together */
/* like the teeth of two gears. The Delaunay property determines, at each */
/* step, whether the next "tooth" is a bounding triangle of the left hull */
/* or the right. When a bounding triangle becomes real, its apex is */
/* changed from NULL to a real vertex. */
/* */
/* Only two new triangles need to be allocated. These become new bounding */
/* triangles at the top and bottom of the seam. They are used to connect */
/* the remaining bounding triangles (those that have not been converted */
/* into real triangles) into a single fan. */
/* */
/* On entry, `farleft' and `innerleft' are bounding triangles of the left */
/* triangulation. The origin of `farleft' is the leftmost vertex, and */
/* the destination of `innerleft' is the rightmost vertex of the */
/* triangulation. Similarly, `innerright' and `farright' are bounding */
/* triangles of the right triangulation. The origin of `innerright' and */
/* destination of `farright' are the leftmost and rightmost vertices. */
/* */
/* On completion, the origin of `farleft' is the leftmost vertex of the */
/* merged triangulation, and the destination of `farright' is the rightmost */
/* vertex. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
void mergehulls(struct mesh *m, struct behavior *b, struct otri *farleft,
struct otri *innerleft, struct otri *innerright,
struct otri *farright, int axis)
#else /* not ANSI_DECLARATORS */
void mergehulls(m, b, farleft, innerleft, innerright, farright, axis)
struct mesh *m;
struct behavior *b;
struct otri *farleft;
struct otri *innerleft;
struct otri *innerright;
struct otri *farright;
int axis;
#endif /* not ANSI_DECLARATORS */
{
struct otri leftcand, rightcand;
struct otri baseedge;
struct otri nextedge;
struct otri sidecasing, topcasing, outercasing;
struct otri checkedge;
vertex innerleftdest;
vertex innerrightorg;
vertex innerleftapex, innerrightapex;
vertex farleftpt, farrightpt;
vertex farleftapex, farrightapex;
vertex lowerleft, lowerright;
vertex upperleft, upperright;
vertex nextapex;
vertex checkvertex;
int changemade;
int badedge;
int leftfinished, rightfinished;
triangle ptr; /* Temporary variable used by sym(). */
dest(*innerleft, innerleftdest);
apex(*innerleft, innerleftapex);
org(*innerright, innerrightorg);
apex(*innerright, innerrightapex);
/* Special treatment for horizontal cuts. */
if (b->dwyer && (axis == 1)) {
org(*farleft, farleftpt);
apex(*farleft, farleftapex);
dest(*farright, farrightpt);
apex(*farright, farrightapex);
/* The pointers to the extremal vertices are shifted to point to the */
/* topmost and bottommost vertex of each hull, rather than the */
/* leftmost and rightmost vertices. */
while (farleftapex[1] < farleftpt[1]) {
lnextself(*farleft);
symself(*farleft);
farleftpt = farleftapex;
apex(*farleft, farleftapex);
}
sym(*innerleft, checkedge);
apex(checkedge, checkvertex);
while (checkvertex[1] > innerleftdest[1]) {
lnext(checkedge, *innerleft);
innerleftapex = innerleftdest;
innerleftdest = checkvertex;
sym(*innerleft, checkedge);
apex(checkedge, checkvertex);
}
while (innerrightapex[1] < innerrightorg[1]) {
lnextself(*innerright);
symself(*innerright);
innerrightorg = innerrightapex;
apex(*innerright, innerrightapex);
}
sym(*farright, checkedge);
apex(checkedge, checkvertex);
while (checkvertex[1] > farrightpt[1]) {
lnext(checkedge, *farright);
farrightapex = farrightpt;
farrightpt = checkvertex;
sym(*farright, checkedge);
apex(checkedge, checkvertex);
}
}
/* Find a line tangent to and below both hulls. */
do {
changemade = 0;
/* Make innerleftdest the "bottommost" vertex of the left hull. */
if (counterclockwise(m, b, innerleftdest, innerleftapex, innerrightorg) >
0.0) {
lprevself(*innerleft);
symself(*innerleft);
innerleftdest = innerleftapex;
apex(*innerleft, innerleftapex);
changemade = 1;
}
/* Make innerrightorg the "bottommost" vertex of the right hull. */
if (counterclockwise(m, b, innerrightapex, innerrightorg, innerleftdest) >
0.0) {
lnextself(*innerright);
symself(*innerright);
innerrightorg = innerrightapex;
apex(*innerright, innerrightapex);
changemade = 1;
}
} while (changemade);
/* Find the two candidates to be the next "gear tooth." */
sym(*innerleft, leftcand);
sym(*innerright, rightcand); /* Create the bottom new bounding triangle. */
maketriangle(m, b, &baseedge);
/* Connect it to the bounding boxes of the left and right triangulations. */
bond(baseedge, *innerleft);
lnextself(baseedge);
bond(baseedge, *innerright);
lnextself(baseedge);
setorg(baseedge, innerrightorg);
setdest(baseedge, innerleftdest);
/* Apex is intentionally left NULL. */
if (b->verbose > 2) {
printf(" Creating base bounding ");
printtriangle(m, b, &baseedge);
}
/* Fix the extreme triangles if necessary. */
org(*farleft, farleftpt);
if (innerleftdest == farleftpt) {
lnext(baseedge, *farleft);
}
dest(*farright, farrightpt);
if (innerrightorg == farrightpt) {
lprev(baseedge, *farright);
}
/* The vertices of the current knitting edge. */
lowerleft = innerleftdest;
lowerright = innerrightorg;
/* The candidate vertices for knitting. */
apex(leftcand, upperleft);
apex(rightcand, upperright);
/* Walk up the gap between the two triangulations, knitting them together. */
while (1) {
/* Have we reached the top? (This isn't quite the right question, */
/* because even though the left triangulation might seem finished now, */
/* moving up on the right triangulation might reveal a new vertex of */
/* the left triangulation. And vice-versa.) */
leftfinished = counterclockwise(m, b, upperleft, lowerleft, lowerright) <=
0.0;
rightfinished = counterclockwise(m, b, upperright, lowerleft, lowerright)
<= 0.0;
if (leftfinished && rightfinished) {
/* Create the top new bounding triangle. */
maketriangle(m, b, &nextedge);
setorg(nextedge, lowerleft);
setdest(nextedge, lowerright);
/* Apex is intentionally left NULL. */
/* Connect it to the bounding boxes of the two triangulations. */
bond(nextedge, baseedge);
lnextself(nextedge);
bond(nextedge, rightcand);
lnextself(nextedge);
bond(nextedge, leftcand);
if (b->verbose > 2) {
printf(" Creating top bounding ");
printtriangle(m, b, &nextedge);
}
/* Special treatment for horizontal cuts. */
if (b->dwyer && (axis == 1)) {
org(*farleft, farleftpt);
apex(*farleft, farleftapex);
dest(*farright, farrightpt);
apex(*farright, farrightapex);
sym(*farleft, checkedge);
apex(checkedge, checkvertex);
/* The pointers to the extremal vertices are restored to the */
/* leftmost and rightmost vertices (rather than topmost and */
/* bottommost). */
while (checkvertex[0] < farleftpt[0]) {
lprev(checkedge, *farleft);
farleftapex = farleftpt;
farleftpt = checkvertex; sym(*farleft, checkedge);
apex(checkedge, checkvertex);
}
while (farrightapex[0] > farrightpt[0]) {
lprevself(*farright);
symself(*farright);
farrightpt = farrightapex;
apex(*farright, farrightapex);
}
}
return;
}
/* Consider eliminating edges from the left triangulation. */
if (!leftfinished) {
/* What vertex would be exposed if an edge were deleted? */
lprev(leftcand, nextedge);
symself(nextedge);
apex(nextedge, nextapex);
/* If nextapex is NULL, then no vertex would be exposed; the */
/* triangulation would have been eaten right through. */
if (nextapex != (vertex) NULL) {
/* Check whether the edge is Delaunay. */
badedge = incircle(m, b, lowerleft, lowerright, upperleft, nextapex) >
0.0;
while (badedge) {
/* Eliminate the edge with an edge flip. As a result, the */
/* left triangulation will have one more boundary triangle. */
lnextself(nextedge);
sym(nextedge, topcasing);
lnextself(nextedge);
sym(nextedge, sidecasing);
bond(nextedge, topcasing);
bond(leftcand, sidecasing);
lnextself(leftcand);
sym(leftcand, outercasing);
lprevself(nextedge);
bond(nextedge, outercasing);
/* Correct the vertices to reflect the edge flip. */
setorg(leftcand, lowerleft);
setdest(leftcand, NULL);
setapex(leftcand, nextapex);
setorg(nextedge, NULL);
setdest(nextedge, upperleft);
setapex(nextedge, nextapex);
/* Consider the newly exposed vertex. */
upperleft = nextapex;
/* What vertex would be exposed if another edge were deleted? */
otricopy(sidecasing, nextedge);
apex(nextedge, nextapex);
if (nextapex != (vertex) NULL) {
/* Check whether the edge is Delaunay. */
badedge = incircle(m, b, lowerleft, lowerright, upperleft,
nextapex) > 0.0;
} else {
/* Avoid eating right through the triangulation. */
badedge = 0;
}
}
}
}
/* Consider eliminating edges from the right triangulation. */
if (!rightfinished) {
/* What vertex would be exposed if an edge were deleted? */
lnext(rightcand, nextedge);
symself(nextedge);
apex(nextedge, nextapex);
/* If nextapex is NULL, then no vertex would be exposed; the */
/* triangulation would have been eaten right through. */
if (nextapex != (vertex) NULL) {
/* Check whether the edge is Delaunay. */ badedge = incircle(m, b, lowerleft, lowerright, upperright, nextapex) >
0.0;
while (badedge) {
/* Eliminate the edge with an edge flip. As a result, the */
/* right triangulation will have one more boundary triangle. */
lprevself(nextedge);
sym(nextedge, topcasing);
lprevself(nextedge);
sym(nextedge, sidecasing);
bond(nextedge, topcasing);
bond(rightcand, sidecasing);
lprevself(rightcand);
sym(rightcand, outercasing);
lnextself(nextedge);
bond(nextedge, outercasing);
/* Correct the vertices to reflect the edge flip. */
setorg(rightcand, NULL);
setdest(rightcand, lowerright);
setapex(rightcand, nextapex);
setorg(nextedge, upperright);
setdest(nextedge, NULL);
setapex(nextedge, nextapex);
/* Consider the newly exposed vertex. */
upperright = nextapex;
/* What vertex would be exposed if another edge were deleted? */
otricopy(sidecasing, nextedge);
apex(nextedge, nextapex);
if (nextapex != (vertex) NULL) {
/* Check whether the edge is Delaunay. */
badedge = incircle(m, b, lowerleft, lowerright, upperright,
nextapex) > 0.0;
} else {
/* Avoid eating right through the triangulation. */
badedge = 0;
}
}
}
}
if (leftfinished || (!rightfinished &&
(incircle(m, b, upperleft, lowerleft, lowerright, upperright) >
0.0))) {
/* Knit the triangulations, adding an edge from `lowerleft' */
/* to `upperright'. */
bond(baseedge, rightcand);
lprev(rightcand, baseedge);
setdest(baseedge, lowerleft);
lowerright = upperright;
sym(baseedge, rightcand);
apex(rightcand, upperright);
} else {
/* Knit the triangulations, adding an edge from `upperleft' */
/* to `lowerright'. */
bond(baseedge, leftcand);
lnext(leftcand, baseedge);
setorg(baseedge, lowerright);
lowerleft = upperleft;
sym(baseedge, leftcand);
apex(leftcand, upperleft);
}
if (b->verbose > 2) {
printf(" Connecting ");
printtriangle(m, b, &baseedge);
}
}
}
/*****************************************************************************/
/* */
/* divconqrecurse() Recursively form a Delaunay triangulation by the */
/* divide-and-conquer method. *//* */
/* Recursively breaks down the problem into smaller pieces, which are */
/* knitted together by mergehulls(). The base cases (problems of two or */
/* three vertices) are handled specially here. */
/* */
/* On completion, `farleft' and `farright' are bounding triangles such that */
/* the origin of `farleft' is the leftmost vertex (breaking ties by */
/* choosing the highest leftmost vertex), and the destination of */
/* `farright' is the rightmost vertex (breaking ties by choosing the */
/* lowest rightmost vertex). */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
void divconqrecurse(struct mesh *m, struct behavior *b, vertex *sortarray,
int vertices, int axis,
struct otri *farleft, struct otri *farright)
#else /* not ANSI_DECLARATORS */
void divconqrecurse(m, b, sortarray, vertices, axis, farleft, farright)
struct mesh *m;
struct behavior *b;
vertex *sortarray;
int vertices;
int axis;
struct otri *farleft;
struct otri *farright;
#endif /* not ANSI_DECLARATORS */
{
struct otri midtri, tri1, tri2, tri3;
struct otri innerleft, innerright;
REAL area;
int divider;
if (b->verbose > 2) {
printf(" Triangulating %d vertices.\n", vertices);
}
if (vertices == 2) {
/* The triangulation of two vertices is an edge. An edge is */
/* represented by two bounding triangles. */
maketriangle(m, b, farleft);
setorg(*farleft, sortarray[0]);
setdest(*farleft, sortarray[1]);
/* The apex is intentionally left NULL. */
maketriangle(m, b, farright);
setorg(*farright, sortarray[1]);
setdest(*farright, sortarray[0]);
/* The apex is intentionally left NULL. */
bond(*farleft, *farright);
lprevself(*farleft);
lnextself(*farright);
bond(*farleft, *farright);
lprevself(*farleft);
lnextself(*farright);
bond(*farleft, *farright);
if (b->verbose > 2) {
printf(" Creating ");
printtriangle(m, b, farleft);
printf(" Creating ");
printtriangle(m, b, farright);
}
/* Ensure that the origin of `farleft' is sortarray[0]. */
lprev(*farright, *farleft);
return;
} else if (vertices == 3) {
/* The triangulation of three vertices is either a triangle (with */
/* three bounding triangles) or two edges (with four bounding */
/* triangles). In either case, four triangles are created. */
maketriangle(m, b, &midtri);
maketriangle(m, b, &tri1); maketriangle(m, b, &tri2);
maketriangle(m, b, &tri3);
area = counterclockwise(m, b, sortarray[0], sortarray[1], sortarray[2]);
if (area == 0.0) {
/* Three collinear vertices; the triangulation is two edges. */
setorg(midtri, sortarray[0]);
setdest(midtri, sortarray[1]);
setorg(tri1, sortarray[1]);
setdest(tri1, sortarray[0]);
setorg(tri2, sortarray[2]);
setdest(tri2, sortarray[1]);
setorg(tri3, sortarray[1]);
setdest(tri3, sortarray[2]);
/* All apices are intentionally left NULL. */
bond(midtri, tri1);
bond(tri2, tri3);
lnextself(midtri);
lprevself(tri1);
lnextself(tri2);
lprevself(tri3);
bond(midtri, tri3);
bond(tri1, tri2);
lnextself(midtri);
lprevself(tri1);
lnextself(tri2);
lprevself(tri3);
bond(midtri, tri1);
bond(tri2, tri3);
/* Ensure that the origin of `farleft' is sortarray[0]. */
otricopy(tri1, *farleft);
/* Ensure that the destination of `farright' is sortarray[2]. */
otricopy(tri2, *farright);
} else {
/* The three vertices are not collinear; the triangulation is one */
/* triangle, namely `midtri'. */
setorg(midtri, sortarray[0]);
setdest(tri1, sortarray[0]);
setorg(tri3, sortarray[0]);
/* Apices of tri1, tri2, and tri3 are left NULL. */
if (area > 0.0) {
/* The vertices are in counterclockwise order. */
setdest(midtri, sortarray[1]);
setorg(tri1, sortarray[1]);
setdest(tri2, sortarray[1]);
setapex(midtri, sortarray[2]);
setorg(tri2, sortarray[2]);
setdest(tri3, sortarray[2]);
} else {
/* The vertices are in clockwise order. */
setdest(midtri, sortarray[2]);
setorg(tri1, sortarray[2]);
setdest(tri2, sortarray[2]);
setapex(midtri, sortarray[1]);
setorg(tri2, sortarray[1]);
setdest(tri3, sortarray[1]);
}
/* The topology does not depend on how the vertices are ordered. */
bond(midtri, tri1);
lnextself(midtri);
bond(midtri, tri2);
lnextself(midtri);
bond(midtri, tri3);
lprevself(tri1);
lnextself(tri2);
bond(tri1, tri2);
lprevself(tri1);
lprevself(tri3);
bond(tri1, tri3);
lnextself(tri2);
lprevself(tri3); bond(tri2, tri3);
/* Ensure that the origin of `farleft' is sortarray[0]. */
otricopy(tri1, *farleft);
/* Ensure that the destination of `farright' is sortarray[2]. */
if (area > 0.0) {
otricopy(tri2, *farright);
} else {
lnext(*farleft, *farright);
}
}
if (b->verbose > 2) {
printf(" Creating ");
printtriangle(m, b, &midtri);
printf(" Creating ");
printtriangle(m, b, &tri1);
printf(" Creating ");
printtriangle(m, b, &tri2);
printf(" Creating ");
printtriangle(m, b, &tri3);
}
return;
} else {
/* Split the vertices in half. */
divider = vertices >> 1;
/* Recursively triangulate each half. */
divconqrecurse(m, b, sortarray, divider, 1 - axis, farleft, &innerleft);
divconqrecurse(m, b, &sortarray[divider], vertices - divider, 1 - axis,
&innerright, farright);
if (b->verbose > 1) {
printf(" Joining triangulations with %d and %d vertices.\n", divider,
vertices - divider);
}
/* Merge the two triangulations into one. */
mergehulls(m, b, farleft, &innerleft, &innerright, farright, axis);
}
}
#ifdef ANSI_DECLARATORS
long removeghosts(struct mesh *m, struct behavior *b, struct otri *startghost)
#else /* not ANSI_DECLARATORS */
long removeghosts(m, b, startghost)
struct mesh *m;
struct behavior *b;
struct otri *startghost;
#endif /* not ANSI_DECLARATORS */
{
struct otri searchedge;
struct otri dissolveedge;
struct otri deadtriangle;
vertex markorg;
long hullsize;
triangle ptr; /* Temporary variable used by sym(). */
if (b->verbose) {
printf(" Removing ghost triangles.\n");
}
/* Find an edge on the convex hull to start point location from. */
lprev(*startghost, searchedge);
symself(searchedge);
m->dummytri[0] = encode(searchedge);
/* Remove the bounding box and count the convex hull edges. */
otricopy(*startghost, dissolveedge);
hullsize = 0;
do {
hullsize++;
lnext(dissolveedge, deadtriangle);
lprevself(dissolveedge);
symself(dissolveedge);
/* If no PSLG is involved, set the boundary markers of all the vertices */ /* on the convex hull. If a PSLG is used, this step is done later. */
if (!b->poly) {
/* Watch out for the case where all the input vertices are collinear. */
if (dissolveedge.tri != m->dummytri) {
org(dissolveedge, markorg);
if (vertexmark(markorg) == 0) {
setvertexmark(markorg, 1);
}
}
}
/* Remove a bounding triangle from a convex hull triangle. */
dissolve(dissolveedge);
/* Find the next bounding triangle. */
sym(deadtriangle, dissolveedge);
/* Delete the bounding triangle. */
triangledealloc(m, deadtriangle.tri);
} while (!otriequal(dissolveedge, *startghost));
return hullsize;
}
/*****************************************************************************/
/* */
/* divconqdelaunay() Form a Delaunay triangulation by the divide-and- */
/* conquer method. */
/* */
/* Sorts the vertices, calls a recursive procedure to triangulate them, and */
/* removes the bounding box, setting boundary markers as appropriate. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
long divconqdelaunay(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
long divconqdelaunay(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */
{
vertex *sortarray;
struct otri hullleft, hullright;
int divider;
int i, j;
if (b->verbose) {
printf(" Sorting vertices.\n");
}
/* Allocate an array of pointers to vertices for sorting. */
sortarray = (vertex *) trimalloc(m->invertices * (int) sizeof(vertex));
traversalinit(&m->vertices);
for (i = 0; i < m->invertices; i++) {
sortarray[i] = vertextraverse(m);
}
/* Sort the vertices. */
vertexsort(sortarray, m->invertices);
/* Discard duplicate vertices, which can really mess up the algorithm. */
i = 0;
for (j = 1; j < m->invertices; j++) {
if ((sortarray[i][0] == sortarray[j][0])
&& (sortarray[i][1] == sortarray[j][1])) {
if (!b->quiet) {
printf(
"Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n",
sortarray[j][0], sortarray[j][1]);
}
setvertextype(sortarray[j], UNDEADVERTEX);
m->undeads++;
} else {
i++; sortarray[i] = sortarray[j];
}
}
i++;
if (b->dwyer) {
/* Re-sort the array of vertices to accommodate alternating cuts. */
divider = i >> 1;
if (i - divider >= 2) {
if (divider >= 2) {
alternateaxes(sortarray, divider, 1);
}
alternateaxes(&sortarray[divider], i - divider, 1);
}
}
if (b->verbose) {
printf(" Forming triangulation.\n");
}
/* Form the Delaunay triangulation. */
divconqrecurse(m, b, sortarray, i, 0, &hullleft, &hullright);
trifree((VOID *) sortarray);
return removeghosts(m, b, &hullleft);
}
/** **/
/** **/
/********* Divide-and-conquer Delaunay triangulation ends here *********/
/********* Incremental Delaunay triangulation begins here *********/
/** **/
/** **/
/*****************************************************************************/
/* */
/* boundingbox() Form an "infinite" bounding triangle to insert vertices */
/* into. */
/* */
/* The vertices at "infinity" are assigned finite coordinates, which are */
/* used by the point location routines, but (mostly) ignored by the */
/* Delaunay edge flip routines. */
/* */
/*****************************************************************************/
#ifndef REDUCED
#ifdef ANSI_DECLARATORS
void boundingbox(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
void boundingbox(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */
{
struct otri inftri; /* Handle for the triangular bounding box. */
REAL width;
if (b->verbose) {
printf(" Creating triangular bounding box.\n");
}
/* Find the width (or height, whichever is larger) of the triangulation. */
width = m->xmax - m->xmin;
if (m->ymax - m->ymin > width) {
width = m->ymax - m->ymin;
}
if (width == 0.0) {
width = 1.0;
} /* Create the vertices of the bounding box. */
m->infvertex1 = (vertex) trimalloc(m->vertices.itembytes);
m->infvertex2 = (vertex) trimalloc(m->vertices.itembytes);
m->infvertex3 = (vertex) trimalloc(m->vertices.itembytes);
m->infvertex1[0] = m->xmin - 50.0 * width;
m->infvertex1[1] = m->ymin - 40.0 * width;
m->infvertex2[0] = m->xmax + 50.0 * width;
m->infvertex2[1] = m->ymin - 40.0 * width;
m->infvertex3[0] = 0.5 * (m->xmin + m->xmax);
m->infvertex3[1] = m->ymax + 60.0 * width;
/* Create the bounding box. */
maketriangle(m, b, &inftri);
setorg(inftri, m->infvertex1);
setdest(inftri, m->infvertex2);
setapex(inftri, m->infvertex3);
/* Link dummytri to the bounding box so we can always find an */
/* edge to begin searching (point location) from. */
m->dummytri[0] = (triangle) inftri.tri;
if (b->verbose > 2) {
printf(" Creating ");
printtriangle(m, b, &inftri);
}
}
#endif /* not REDUCED */
/*****************************************************************************/
/* */
/* removebox() Remove the "infinite" bounding triangle, setting boundary */
/* markers as appropriate. */
/* */
/* The triangular bounding box has three boundary triangles (one for each */
/* side of the bounding box), and a bunch of triangles fanning out from */
/* the three bounding box vertices (one triangle for each edge of the */
/* convex hull of the inner mesh). This routine removes these triangles. */
/* */
/* Returns the number of edges on the convex hull of the triangulation. */
/* */
/*****************************************************************************/
#ifndef REDUCED
#ifdef ANSI_DECLARATORS
long removebox(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
long removebox(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */
{
struct otri deadtriangle;
struct otri searchedge;
struct otri checkedge;
struct otri nextedge, finaledge, dissolveedge;
vertex markorg;
long hullsize;
triangle ptr; /* Temporary variable used by sym(). */
if (b->verbose) {
printf(" Removing triangular bounding box.\n");
}
/* Find a boundary triangle. */
nextedge.tri = m->dummytri;
nextedge.orient = 0;
symself(nextedge);
/* Mark a place to stop. */
lprev(nextedge, finaledge);
lnextself(nextedge); symself(nextedge);
/* Find a triangle (on the boundary of the vertex set) that isn't */
/* a bounding box triangle. */
lprev(nextedge, searchedge);
symself(searchedge);
/* Check whether nextedge is another boundary triangle */
/* adjacent to the first one. */
lnext(nextedge, checkedge);
symself(checkedge);
if (checkedge.tri == m->dummytri) {
/* Go on to the next triangle. There are only three boundary */
/* triangles, and this next triangle cannot be the third one, */
/* so it's safe to stop here. */
lprevself(searchedge);
symself(searchedge);
}
/* Find a new boundary edge to search from, as the current search */
/* edge lies on a bounding box triangle and will be deleted. */
m->dummytri[0] = encode(searchedge);
hullsize = -2l;
while (!otriequal(nextedge, finaledge)) {
hullsize++;
lprev(nextedge, dissolveedge);
symself(dissolveedge);
/* If not using a PSLG, the vertices should be marked now. */
/* (If using a PSLG, markhull() will do the job.) */
if (!b->poly) {
/* Be careful! One must check for the case where all the input */
/* vertices are collinear, and thus all the triangles are part of */
/* the bounding box. Otherwise, the setvertexmark() call below */
/* will cause a bad pointer reference. */
if (dissolveedge.tri != m->dummytri) {
org(dissolveedge, markorg);
if (vertexmark(markorg) == 0) {
setvertexmark(markorg, 1);
}
}
}
/* Disconnect the bounding box triangle from the mesh triangle. */
dissolve(dissolveedge);
lnext(nextedge, deadtriangle);
sym(deadtriangle, nextedge);
/* Get rid of the bounding box triangle. */
triangledealloc(m, deadtriangle.tri);
/* Do we need to turn the corner? */
if (nextedge.tri == m->dummytri) {
/* Turn the corner. */
otricopy(dissolveedge, nextedge);
}
}
triangledealloc(m, finaledge.tri);
trifree((VOID *) m->infvertex1); /* Deallocate the bounding box vertices. */
trifree((VOID *) m->infvertex2);
trifree((VOID *) m->infvertex3);
return hullsize;
}
#endif /* not REDUCED */
/*****************************************************************************/
/* */
/* incrementaldelaunay() Form a Delaunay triangulation by incrementally */
/* inserting vertices. */
/* */
/* Returns the number of edges on the convex hull of the triangulation. */
/* */
/*****************************************************************************/
#ifndef REDUCED
#ifdef ANSI_DECLARATORS
long incrementaldelaunay(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
long incrementaldelaunay(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */
{
struct otri starttri;
vertex vertexloop;
/* Create a triangular bounding box. */
boundingbox(m, b);
if (b->verbose) {
printf(" Incrementally inserting vertices.\n");
}
traversalinit(&m->vertices);
vertexloop = vertextraverse(m);
while (vertexloop != (vertex) NULL) {
starttri.tri = m->dummytri;
if (insertvertex(m, b, vertexloop, &starttri, (struct osub *) NULL, 0, 0)
== DUPLICATEVERTEX) {
if (!b->quiet) {
printf(
"Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n",
vertexloop[0], vertexloop[1]);
}
setvertextype(vertexloop, UNDEADVERTEX);
m->undeads++;
}
vertexloop = vertextraverse(m);
}
/* Remove the bounding box. */
return removebox(m, b);
}
#endif /* not REDUCED */
/** **/
/** **/
/********* Incremental Delaunay triangulation ends here *********/
/********* Sweepline Delaunay triangulation begins here *********/
/** **/
/** **/
#ifndef REDUCED
#ifdef ANSI_DECLARATORS
void eventheapinsert(struct event **heap, int heapsize, struct event *newevent)
#else /* not ANSI_DECLARATORS */
void eventheapinsert(heap, heapsize, newevent)
struct event **heap;
int heapsize;
struct event *newevent;
#endif /* not ANSI_DECLARATORS */
{
REAL eventx, eventy;
int eventnum;
int parent;
int notdone;
eventx = newevent->xkey;
eventy = newevent->ykey;
eventnum = heapsize;
notdone = eventnum > 0; while (notdone) {
parent = (eventnum - 1) >> 1;
if ((heap[parent]->ykey < eventy) ||
((heap[parent]->ykey == eventy)
&& (heap[parent]->xkey <= eventx))) {
notdone = 0;
} else {
heap[eventnum] = heap[parent];
heap[eventnum]->heapposition = eventnum;
eventnum = parent;
notdone = eventnum > 0;
}
}
heap[eventnum] = newevent;
newevent->heapposition = eventnum;
}
#endif /* not REDUCED */
#ifndef REDUCED
#ifdef ANSI_DECLARATORS
void eventheapify(struct event **heap, int heapsize, int eventnum)
#else /* not ANSI_DECLARATORS */
void eventheapify(heap, heapsize, eventnum)
struct event **heap;
int heapsize;
int eventnum;
#endif /* not ANSI_DECLARATORS */
{
struct event *thisevent;
REAL eventx, eventy;
int leftchild, rightchild;
int smallest;
int notdone;
thisevent = heap[eventnum];
eventx = thisevent->xkey;
eventy = thisevent->ykey;
leftchild = 2 * eventnum + 1;
notdone = leftchild < heapsize;
while (notdone) {
if ((heap[leftchild]->ykey < eventy) ||
((heap[leftchild]->ykey == eventy)
&& (heap[leftchild]->xkey < eventx))) {
smallest = leftchild;
} else {
smallest = eventnum;
}
rightchild = leftchild + 1;
if (rightchild < heapsize) {
if ((heap[rightchild]->ykey < heap[smallest]->ykey) ||
((heap[rightchild]->ykey == heap[smallest]->ykey)
&& (heap[rightchild]->xkey < heap[smallest]->xkey))) {
smallest = rightchild;
}
}
if (smallest == eventnum) {
notdone = 0;
} else {
heap[eventnum] = heap[smallest];
heap[eventnum]->heapposition = eventnum;
heap[smallest] = thisevent;
thisevent->heapposition = smallest;
eventnum = smallest;
leftchild = 2 * eventnum + 1;
notdone = leftchild < heapsize; }
}
}
#endif /* not REDUCED */
#ifndef REDUCED
#ifdef ANSI_DECLARATORS
void eventheapdelete(struct event **heap, int heapsize, int eventnum)
#else /* not ANSI_DECLARATORS */
void eventheapdelete(heap, heapsize, eventnum)
struct event **heap;
int heapsize;
int eventnum;
#endif /* not ANSI_DECLARATORS */
{
struct event *moveevent;
REAL eventx, eventy;
int parent;
int notdone;
moveevent = heap[heapsize - 1];
if (eventnum > 0) {
eventx = moveevent->xkey;
eventy = moveevent->ykey;
do {
parent = (eventnum - 1) >> 1;
if ((heap[parent]->ykey < eventy) ||
((heap[parent]->ykey == eventy)
&& (heap[parent]->xkey <= eventx))) {
notdone = 0;
} else {
heap[eventnum] = heap[parent];
heap[eventnum]->heapposition = eventnum;
eventnum = parent;
notdone = eventnum > 0;
}
} while (notdone);
}
heap[eventnum] = moveevent;
moveevent->heapposition = eventnum;
eventheapify(heap, heapsize - 1, eventnum);
}
#endif /* not REDUCED */
#ifndef REDUCED
#ifdef ANSI_DECLARATORS
void createeventheap(struct mesh *m, struct event ***eventheap,
struct event **events, struct event **freeevents)
#else /* not ANSI_DECLARATORS */
void createeventheap(m, eventheap, events, freeevents)
struct mesh *m;
struct event ***eventheap;
struct event **events;
struct event **freeevents;
#endif /* not ANSI_DECLARATORS */
{
vertex thisvertex;
int maxevents;
int i;
maxevents = (3 * m->invertices) / 2;
*eventheap = (struct event **) trimalloc(maxevents *
(int) sizeof(struct event *)); *events = (struct event *) trimalloc(maxevents * (int) sizeof(struct event));
traversalinit(&m->vertices);
for (i = 0; i < m->invertices; i++) {
thisvertex = vertextraverse(m);
(*events)[i].eventptr = (VOID *) thisvertex;
(*events)[i].xkey = thisvertex[0];
(*events)[i].ykey = thisvertex[1];
eventheapinsert(*eventheap, i, *events + i);
}
*freeevents = (struct event *) NULL;
for (i = maxevents - 1; i >= m->invertices; i--) {
(*events)[i].eventptr = (VOID *) *freeevents;
*freeevents = *events + i;
}
}
#endif /* not REDUCED */
#ifndef REDUCED
#ifdef ANSI_DECLARATORS
int rightofhyperbola(struct mesh *m, struct otri *fronttri, vertex newsite)
#else /* not ANSI_DECLARATORS */
int rightofhyperbola(m, fronttri, newsite)
struct mesh *m;
struct otri *fronttri;
vertex newsite;
#endif /* not ANSI_DECLARATORS */
{
vertex leftvertex, rightvertex;
REAL dxa, dya, dxb, dyb;
m->hyperbolacount++;
dest(*fronttri, leftvertex);
apex(*fronttri, rightvertex);
if ((leftvertex[1] < rightvertex[1]) ||
((leftvertex[1] == rightvertex[1]) &&
(leftvertex[0] < rightvertex[0]))) {
if (newsite[0] >= rightvertex[0]) {
return 1;
}
} else {
if (newsite[0] <= leftvertex[0]) {
return 0;
}
}
dxa = leftvertex[0] - newsite[0];
dya = leftvertex[1] - newsite[1];
dxb = rightvertex[0] - newsite[0];
dyb = rightvertex[1] - newsite[1];
return dya * (dxb * dxb + dyb * dyb) > dyb * (dxa * dxa + dya * dya);
}
#endif /* not REDUCED */
#ifndef REDUCED
#ifdef ANSI_DECLARATORS
REAL circletop(struct mesh *m, vertex pa, vertex pb, vertex pc, REAL ccwabc)
#else /* not ANSI_DECLARATORS */
REAL circletop(m, pa, pb, pc, ccwabc)
struct mesh *m;
vertex pa;
vertex pb;
vertex pc;
REAL ccwabc;
#endif /* not ANSI_DECLARATORS */
{
REAL xac, yac, xbc, ybc, xab, yab;
REAL aclen2, bclen2, ablen2;
m->circletopcount++;
xac = pa[0] - pc[0];
yac = pa[1] - pc[1];
xbc = pb[0] - pc[0];
ybc = pb[1] - pc[1];
xab = pa[0] - pb[0];
yab = pa[1] - pb[1];
aclen2 = xac * xac + yac * yac;
bclen2 = xbc * xbc + ybc * ybc;
ablen2 = xab * xab + yab * yab;
return pc[1] + (xac * bclen2 - xbc * aclen2 + sqrt(aclen2 * bclen2 * ablen2))
/ (2.0 * ccwabc);
}
#endif /* not REDUCED */
#ifndef REDUCED
#ifdef ANSI_DECLARATORS
void check4deadevent(struct otri *checktri, struct event **freeevents,
struct event **eventheap, int *heapsize)
#else /* not ANSI_DECLARATORS */
void check4deadevent(checktri, freeevents, eventheap, heapsize)
struct otri *checktri;
struct event **freeevents;
struct event **eventheap;
int *heapsize;
#endif /* not ANSI_DECLARATORS */
{
struct event *deadevent;
vertex eventvertex;
int eventnum;
org(*checktri, eventvertex);
if (eventvertex != (vertex) NULL) {
deadevent = (struct event *) eventvertex;
eventnum = deadevent->heapposition;
deadevent->eventptr = (VOID *) *freeevents;
*freeevents = deadevent;
eventheapdelete(eventheap, *heapsize, eventnum);
(*heapsize)--;
setorg(*checktri, NULL);
}
}
#endif /* not REDUCED */
#ifndef REDUCED
#ifdef ANSI_DECLARATORS
struct splaynode *splay(struct mesh *m, struct splaynode *splaytree,
vertex searchpoint, struct otri *searchtri)
#else /* not ANSI_DECLARATORS */
struct splaynode *splay(m, splaytree, searchpoint, searchtri)
struct mesh *m;
struct splaynode *splaytree;
vertex searchpoint;
struct otri *searchtri;
#endif /* not ANSI_DECLARATORS */
{
struct splaynode *child, *grandchild;
struct splaynode *lefttree, *righttree;
struct splaynode *leftright; vertex checkvertex;
int rightofroot, rightofchild;
if (splaytree == (struct splaynode *) NULL) {
return (struct splaynode *) NULL;
}
dest(splaytree->keyedge, checkvertex);
if (checkvertex == splaytree->keydest) {
rightofroot = rightofhyperbola(m, &splaytree->keyedge, searchpoint);
if (rightofroot) {
otricopy(splaytree->keyedge, *searchtri);
child = splaytree->rchild;
} else {
child = splaytree->lchild;
}
if (child == (struct splaynode *) NULL) {
return splaytree;
}
dest(child->keyedge, checkvertex);
if (checkvertex != child->keydest) {
child = splay(m, child, searchpoint, searchtri);
if (child == (struct splaynode *) NULL) {
if (rightofroot) {
splaytree->rchild = (struct splaynode *) NULL;
} else {
splaytree->lchild = (struct splaynode *) NULL;
}
return splaytree;
}
}
rightofchild = rightofhyperbola(m, &child->keyedge, searchpoint);
if (rightofchild) {
otricopy(child->keyedge, *searchtri);
grandchild = splay(m, child->rchild, searchpoint, searchtri);
child->rchild = grandchild;
} else {
grandchild = splay(m, child->lchild, searchpoint, searchtri);
child->lchild = grandchild;
}
if (grandchild == (struct splaynode *) NULL) {
if (rightofroot) {
splaytree->rchild = child->lchild;
child->lchild = splaytree;
} else {
splaytree->lchild = child->rchild;
child->rchild = splaytree;
}
return child;
}
if (rightofchild) {
if (rightofroot) {
splaytree->rchild = child->lchild;
child->lchild = splaytree;
} else {
splaytree->lchild = grandchild->rchild;
grandchild->rchild = splaytree;
}
child->rchild = grandchild->lchild;
grandchild->lchild = child;
} else {
if (rightofroot) {
splaytree->rchild = grandchild->lchild;
grandchild->lchild = splaytree;
} else {
splaytree->lchild = child->rchild;
child->rchild = splaytree;
}
child->lchild = grandchild->rchild;
grandchild->rchild = child;
} return grandchild;
} else {
lefttree = splay(m, splaytree->lchild, searchpoint, searchtri);
righttree = splay(m, splaytree->rchild, searchpoint, searchtri);
pooldealloc(&m->splaynodes, (VOID *) splaytree);
if (lefttree == (struct splaynode *) NULL) {
return righttree;
} else if (righttree == (struct splaynode *) NULL) {
return lefttree;
} else if (lefttree->rchild == (struct splaynode *) NULL) {
lefttree->rchild = righttree->lchild;
righttree->lchild = lefttree;
return righttree;
} else if (righttree->lchild == (struct splaynode *) NULL) {
righttree->lchild = lefttree->rchild;
lefttree->rchild = righttree;
return lefttree;
} else {
/* printf("Holy Toledo!!!\n"); */
leftright = lefttree->rchild;
while (leftright->rchild != (struct splaynode *) NULL) {
leftright = leftright->rchild;
}
leftright->rchild = righttree;
return lefttree;
}
}
}
#endif /* not REDUCED */
#ifndef REDUCED
#ifdef ANSI_DECLARATORS
struct splaynode *splayinsert(struct mesh *m, struct splaynode *splayroot,
struct otri *newkey, vertex searchpoint)
#else /* not ANSI_DECLARATORS */
struct splaynode *splayinsert(m, splayroot, newkey, searchpoint)
struct mesh *m;
struct splaynode *splayroot;
struct otri *newkey;
vertex searchpoint;
#endif /* not ANSI_DECLARATORS */
{
struct splaynode *newsplaynode;
newsplaynode = (struct splaynode *) poolalloc(&m->splaynodes);
otricopy(*newkey, newsplaynode->keyedge);
dest(*newkey, newsplaynode->keydest);
if (splayroot == (struct splaynode *) NULL) {
newsplaynode->lchild = (struct splaynode *) NULL;
newsplaynode->rchild = (struct splaynode *) NULL;
} else if (rightofhyperbola(m, &splayroot->keyedge, searchpoint)) {
newsplaynode->lchild = splayroot;
newsplaynode->rchild = splayroot->rchild;
splayroot->rchild = (struct splaynode *) NULL;
} else {
newsplaynode->lchild = splayroot->lchild;
newsplaynode->rchild = splayroot;
splayroot->lchild = (struct splaynode *) NULL;
}
return newsplaynode;
}
#endif /* not REDUCED */
#ifndef REDUCED
#ifdef ANSI_DECLARATORS
struct splaynode *circletopinsert(struct mesh *m, struct behavior *b,
struct splaynode *splayroot,
struct otri *newkey,
vertex pa, vertex pb, vertex pc, REAL topy)
#else /* not ANSI_DECLARATORS */
struct splaynode *circletopinsert(m, b, splayroot, newkey, pa, pb, pc, topy)
struct mesh *m;
struct behavior *b;
struct splaynode *splayroot;
struct otri *newkey;
vertex pa;
vertex pb;
vertex pc;
REAL topy;
#endif /* not ANSI_DECLARATORS */
{
REAL ccwabc;
REAL xac, yac, xbc, ybc;
REAL aclen2, bclen2;
REAL searchpoint[2];
struct otri dummytri;
ccwabc = counterclockwise(m, b, pa, pb, pc);
xac = pa[0] - pc[0];
yac = pa[1] - pc[1];
xbc = pb[0] - pc[0];
ybc = pb[1] - pc[1];
aclen2 = xac * xac + yac * yac;
bclen2 = xbc * xbc + ybc * ybc;
searchpoint[0] = pc[0] - (yac * bclen2 - ybc * aclen2) / (2.0 * ccwabc);
searchpoint[1] = topy;
return splayinsert(m, splay(m, splayroot, (vertex) searchpoint, &dummytri),
newkey, (vertex) searchpoint);
}
#endif /* not REDUCED */
#ifndef REDUCED
#ifdef ANSI_DECLARATORS
struct splaynode *frontlocate(struct mesh *m, struct splaynode *splayroot,
struct otri *bottommost, vertex searchvertex,
struct otri *searchtri, int *farright)
#else /* not ANSI_DECLARATORS */
struct splaynode *frontlocate(m, splayroot, bottommost, searchvertex,
searchtri, farright)
struct mesh *m;
struct splaynode *splayroot;
struct otri *bottommost;
vertex searchvertex;
struct otri *searchtri;
int *farright;
#endif /* not ANSI_DECLARATORS */
{
int farrightflag;
triangle ptr; /* Temporary variable used by onext(). */
otricopy(*bottommost, *searchtri);
splayroot = splay(m, splayroot, searchvertex, searchtri);
farrightflag = 0;
while (!farrightflag && rightofhyperbola(m, searchtri, searchvertex)) {
onextself(*searchtri);
farrightflag = otriequal(*searchtri, *bottommost);
}
*farright = farrightflag;
return splayroot;}
#endif /* not REDUCED */
#ifndef REDUCED
#ifdef ANSI_DECLARATORS
long sweeplinedelaunay(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
long sweeplinedelaunay(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */
{
struct event **eventheap;
struct event *events;
struct event *freeevents;
struct event *nextevent;
struct event *newevent;
struct splaynode *splayroot;
struct otri bottommost;
struct otri searchtri;
struct otri fliptri;
struct otri lefttri, righttri, farlefttri, farrighttri;
struct otri inserttri;
vertex firstvertex, secondvertex;
vertex nextvertex, lastvertex;
vertex connectvertex;
vertex leftvertex, midvertex, rightvertex;
REAL lefttest, righttest;
int heapsize;
int check4events, farrightflag;
triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */
poolinit(&m->splaynodes, sizeof(struct splaynode), SPLAYNODEPERBLOCK,
SPLAYNODEPERBLOCK, 0);
splayroot = (struct splaynode *) NULL;
if (b->verbose) {
printf(" Placing vertices in event heap.\n");
}
createeventheap(m, &eventheap, &events, &freeevents);
heapsize = m->invertices;
if (b->verbose) {
printf(" Forming triangulation.\n");
}
maketriangle(m, b, &lefttri);
maketriangle(m, b, &righttri);
bond(lefttri, righttri);
lnextself(lefttri);
lprevself(righttri);
bond(lefttri, righttri);
lnextself(lefttri);
lprevself(righttri);
bond(lefttri, righttri);
firstvertex = (vertex) eventheap[0]->eventptr;
eventheap[0]->eventptr = (VOID *) freeevents;
freeevents = eventheap[0];
eventheapdelete(eventheap, heapsize, 0);
heapsize--;
do {
if (heapsize == 0) {
printf("Error: Input vertices are all identical.\n");
triexit(1);
}
secondvertex = (vertex) eventheap[0]->eventptr;
eventheap[0]->eventptr = (VOID *) freeevents;
freeevents = eventheap[0]; eventheapdelete(eventheap, heapsize, 0);
heapsize--;
if ((firstvertex[0] == secondvertex[0]) &&
(firstvertex[1] == secondvertex[1])) {
if (!b->quiet) {
printf(
"Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n",
secondvertex[0], secondvertex[1]);
}
setvertextype(secondvertex, UNDEADVERTEX);
m->undeads++;
}
} while ((firstvertex[0] == secondvertex[0]) &&
(firstvertex[1] == secondvertex[1]));
setorg(lefttri, firstvertex);
setdest(lefttri, secondvertex);
setorg(righttri, secondvertex);
setdest(righttri, firstvertex);
lprev(lefttri, bottommost);
lastvertex = secondvertex;
while (heapsize > 0) {
nextevent = eventheap[0];
eventheapdelete(eventheap, heapsize, 0);
heapsize--;
check4events = 1;
if (nextevent->xkey < m->xmin) {
decode(nextevent->eventptr, fliptri);
oprev(fliptri, farlefttri);
check4deadevent(&farlefttri, &freeevents, eventheap, &heapsize);
onext(fliptri, farrighttri);
check4deadevent(&farrighttri, &freeevents, eventheap, &heapsize);
if (otriequal(farlefttri, bottommost)) {
lprev(fliptri, bottommost);
}
flip(m, b, &fliptri);
setapex(fliptri, NULL);
lprev(fliptri, lefttri);
lnext(fliptri, righttri);
sym(lefttri, farlefttri);
if (randomnation(SAMPLERATE) == 0) {
symself(fliptri);
dest(fliptri, leftvertex);
apex(fliptri, midvertex);
org(fliptri, rightvertex);
splayroot = circletopinsert(m, b, splayroot, &lefttri, leftvertex,
midvertex, rightvertex, nextevent->ykey);
}
} else {
nextvertex = (vertex) nextevent->eventptr;
if ((nextvertex[0] == lastvertex[0]) &&
(nextvertex[1] == lastvertex[1])) {
if (!b->quiet) {
printf(
"Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n",
nextvertex[0], nextvertex[1]);
}
setvertextype(nextvertex, UNDEADVERTEX);
m->undeads++;
check4events = 0;
} else {
lastvertex = nextvertex;
splayroot = frontlocate(m, splayroot, &bottommost, nextvertex,
&searchtri, &farrightflag);
/*
otricopy(bottommost, searchtri);
farrightflag = 0;
while (!farrightflag && rightofhyperbola(m, &searchtri, nextvertex)) { onextself(searchtri);
farrightflag = otriequal(searchtri, bottommost);
}
*/
check4deadevent(&searchtri, &freeevents, eventheap, &heapsize);
otricopy(searchtri, farrighttri);
sym(searchtri, farlefttri);
maketriangle(m, b, &lefttri);
maketriangle(m, b, &righttri);
dest(farrighttri, connectvertex);
setorg(lefttri, connectvertex);
setdest(lefttri, nextvertex);
setorg(righttri, nextvertex);
setdest(righttri, connectvertex);
bond(lefttri, righttri);
lnextself(lefttri);
lprevself(righttri);
bond(lefttri, righttri);
lnextself(lefttri);
lprevself(righttri);
bond(lefttri, farlefttri);
bond(righttri, farrighttri);
if (!farrightflag && otriequal(farrighttri, bottommost)) {
otricopy(lefttri, bottommost);
}
if (randomnation(SAMPLERATE) == 0) {
splayroot = splayinsert(m, splayroot, &lefttri, nextvertex);
} else if (randomnation(SAMPLERATE) == 0) {
lnext(righttri, inserttri);
splayroot = splayinsert(m, splayroot, &inserttri, nextvertex);
}
}
}
nextevent->eventptr = (VOID *) freeevents;
freeevents = nextevent;
if (check4events) {
apex(farlefttri, leftvertex);
dest(lefttri, midvertex);
apex(lefttri, rightvertex);
lefttest = counterclockwise(m, b, leftvertex, midvertex, rightvertex);
if (lefttest > 0.0) {
newevent = freeevents;
freeevents = (struct event *) freeevents->eventptr;
newevent->xkey = m->xminextreme;
newevent->ykey = circletop(m, leftvertex, midvertex, rightvertex,
lefttest);
newevent->eventptr = (VOID *) encode(lefttri);
eventheapinsert(eventheap, heapsize, newevent);
heapsize++;
setorg(lefttri, newevent);
}
apex(righttri, leftvertex);
org(righttri, midvertex);
apex(farrighttri, rightvertex);
righttest = counterclockwise(m, b, leftvertex, midvertex, rightvertex);
if (righttest > 0.0) {
newevent = freeevents;
freeevents = (struct event *) freeevents->eventptr;
newevent->xkey = m->xminextreme;
newevent->ykey = circletop(m, leftvertex, midvertex, rightvertex,
righttest);
newevent->eventptr = (VOID *) encode(farrighttri);
eventheapinsert(eventheap, heapsize, newevent);
heapsize++;
setorg(farrighttri, newevent);
} }
}
pooldeinit(&m->splaynodes);
lprevself(bottommost);
return removeghosts(m, b, &bottommost);
}
#endif /* not REDUCED */
/** **/
/** **/
/********* Sweepline Delaunay triangulation ends here *********/
/********* General mesh construction routines begin here *********/
/** **/
/** **/
/*****************************************************************************/
/* */
/* delaunay() Form a Delaunay triangulation. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
long delaunay(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
long delaunay(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */
{
long hulledges;
m->eextras = 0;
initializetrisubpools(m, b);
#ifdef REDUCED
if (!b->quiet) {
printf(
"Constructing Delaunay triangulation by divide-and-conquer method.\n");
}
hulledges = divconqdelaunay(m, b);
#else /* not REDUCED */
if (!b->quiet) {
printf("Constructing Delaunay triangulation ");
if (b->incremental) {
printf("by incremental method.\n");
} else if (b->sweepline) {
printf("by sweepline method.\n");
} else {
printf("by divide-and-conquer method.\n");
}
}
if (b->incremental) {
hulledges = incrementaldelaunay(m, b);
} else if (b->sweepline) {
hulledges = sweeplinedelaunay(m, b);
} else {
hulledges = divconqdelaunay(m, b);
}
#endif /* not REDUCED */
if (m->triangles.items == 0) {
/* The input vertices were all collinear, so there are no triangles. */
return 0l;
} else {
return hulledges;
}}
/*****************************************************************************/
/* */
/* reconstruct() Reconstruct a triangulation from its .ele (and possibly */
/* .poly) file. Used when the -r switch is used. */
/* */
/* Reads an .ele file and reconstructs the original mesh. If the -p switch */
/* is used, this procedure will also read a .poly file and reconstruct the */
/* subsegments of the original mesh. If the -a switch is used, this */
/* procedure will also read an .area file and set a maximum area constraint */
/* on each triangle. */
/* */
/* Vertices that are not corners of triangles, such as nodes on edges of */
/* subparametric elements, are discarded. */
/* */
/* This routine finds the adjacencies between triangles (and subsegments) */
/* by forming one stack of triangles for each vertex. Each triangle is on */
/* three different stacks simultaneously. Each triangle's subsegment */
/* pointers are used to link the items in each stack. This memory-saving */
/* feature makes the code harder to read. The most important thing to keep */
/* in mind is that each triangle is removed from a stack precisely when */
/* the corresponding pointer is adjusted to refer to a subsegment rather */
/* than the next triangle of the stack. */
/* */
/*****************************************************************************/
#ifndef CDT_ONLY
#ifdef TRILIBRARY
#ifdef ANSI_DECLARATORS
int reconstruct(struct mesh *m, struct behavior *b, int *trianglelist,
REAL *triangleattriblist, REAL *trianglearealist,
int elements, int corners, int attribs,
int *segmentlist,int *segmentmarkerlist, int numberofsegments)
#else /* not ANSI_DECLARATORS */
int reconstruct(m, b, trianglelist, triangleattriblist, trianglearealist,
elements, corners, attribs, segmentlist, segmentmarkerlist,
numberofsegments)
struct mesh *m;
struct behavior *b;
int *trianglelist;
REAL *triangleattriblist;
REAL *trianglearealist;
int elements;
int corners;
int attribs;
int *segmentlist;
int *segmentmarkerlist;
int numberofsegments;
#endif /* not ANSI_DECLARATORS */
#else /* not TRILIBRARY */
#ifdef ANSI_DECLARATORS
long reconstruct(struct mesh *m, struct behavior *b, char *elefilename,
char *areafilename, char *polyfilename, FILE *polyfile)
#else /* not ANSI_DECLARATORS */
long reconstruct(m, b, elefilename, areafilename, polyfilename, polyfile)
struct mesh *m;
struct behavior *b;
char *elefilename;
char *areafilename;
char *polyfilename;
FILE *polyfile;
#endif /* not ANSI_DECLARATORS */
#endif /* not TRILIBRARY */
{
#ifdef TRILIBRARY
int vertexindex;
int attribindex;
#else /* not TRILIBRARY */
FILE *elefile;
FILE *areafile;
char inputline[INPUTLINESIZE];
char *stringptr;
int areaelements;
#endif /* not TRILIBRARY */
struct otri triangleloop;
struct otri triangleleft;
struct otri checktri;
struct otri checkleft;
struct otri checkneighbor;
struct osub subsegloop;
triangle *vertexarray;
triangle *prevlink;
triangle nexttri;
vertex tdest, tapex;
vertex checkdest, checkapex;
vertex shorg;
vertex killvertex;
vertex segmentorg, segmentdest;
REAL area;
int corner[3];
int end[2];
int killvertexindex;
int incorners;
int segmentmarkers;
int boundmarker;
int aroundvertex;
long hullsize;
int notfound;
long elementnumber, segmentnumber;
int i, j;
triangle ptr; /* Temporary variable used by sym(). */
#ifdef TRILIBRARY
m->inelements = elements;
incorners = corners;
if (incorners < 3) {
printf("Error: Triangles must have at least 3 vertices.\n");
triexit(1);
}
m->eextras = attribs;
#else /* not TRILIBRARY */
/* Read the triangles from an .ele file. */
if (!b->quiet) {
printf("Opening %s.\n", elefilename);
}
elefile = fopen(elefilename, "r");
if (elefile == (FILE *) NULL) {
printf(" Error: Cannot access file %s.\n", elefilename);
triexit(1);
}
/* Read number of triangles, number of vertices per triangle, and */
/* number of triangle attributes from .ele file. */
stringptr = readline(inputline, elefile, elefilename);
m->inelements = (int) strtol(stringptr, &stringptr, 0);
stringptr = findfield(stringptr);
if (*stringptr == '\0') {
incorners = 3;
} else {
incorners = (int) strtol(stringptr, &stringptr, 0);
if (incorners < 3) {
printf("Error: Triangles in %s must have at least 3 vertices.\n",
elefilename);
triexit(1); }
}
stringptr = findfield(stringptr);
if (*stringptr == '\0') {
m->eextras = 0;
} else {
m->eextras = (int) strtol(stringptr, &stringptr, 0);
}
#endif /* not TRILIBRARY */
initializetrisubpools(m, b);
/* Create the triangles. */
for (elementnumber = 1; elementnumber <= m->inelements; elementnumber++) {
maketriangle(m, b, &triangleloop);
/* Mark the triangle as living. */
triangleloop.tri[3] = (triangle) triangleloop.tri;
}
segmentmarkers = 0;
if (b->poly) {
#ifdef TRILIBRARY
m->insegments = numberofsegments;
segmentmarkers = segmentmarkerlist != (int *) NULL;
#else /* not TRILIBRARY */
/* Read number of segments and number of segment */
/* boundary markers from .poly file. */
stringptr = readline(inputline, polyfile, b->inpolyfilename);
m->insegments = (int) strtol(stringptr, &stringptr, 0);
stringptr = findfield(stringptr);
if (*stringptr != '\0') {
segmentmarkers = (int) strtol(stringptr, &stringptr, 0);
}
#endif /* not TRILIBRARY */
/* Create the subsegments. */
for (segmentnumber = 1; segmentnumber <= m->insegments; segmentnumber++) {
makesubseg(m, &subsegloop);
/* Mark the subsegment as living. */
subsegloop.ss[2] = (subseg) subsegloop.ss;
}
}
#ifdef TRILIBRARY
vertexindex = 0;
attribindex = 0;
#else /* not TRILIBRARY */
if (b->vararea) {
/* Open an .area file, check for consistency with the .ele file. */
if (!b->quiet) {
printf("Opening %s.\n", areafilename);
}
areafile = fopen(areafilename, "r");
if (areafile == (FILE *) NULL) {
printf(" Error: Cannot access file %s.\n", areafilename);
triexit(1);
}
stringptr = readline(inputline, areafile, areafilename);
areaelements = (int) strtol(stringptr, &stringptr, 0);
if (areaelements != m->inelements) {
printf("Error: %s and %s disagree on number of triangles.\n",
elefilename, areafilename);
triexit(1);
}
}
#endif /* not TRILIBRARY */
if (!b->quiet) {
printf("Reconstructing mesh.\n");
} /* Allocate a temporary array that maps each vertex to some adjacent */
/* triangle. I took care to allocate all the permanent memory for */
/* triangles and subsegments first. */
vertexarray = (triangle *) trimalloc(m->vertices.items *
(int) sizeof(triangle));
/* Each vertex is initially unrepresented. */
for (i = 0; i < m->vertices.items; i++) {
vertexarray[i] = (triangle) m->dummytri;
}
if (b->verbose) {
printf(" Assembling triangles.\n");
}
/* Read the triangles from the .ele file, and link */
/* together those that share an edge. */
traversalinit(&m->triangles);
triangleloop.tri = triangletraverse(m);
elementnumber = b->firstnumber;
while (triangleloop.tri != (triangle *) NULL) {
#ifdef TRILIBRARY
/* Copy the triangle's three corners. */
for (j = 0; j < 3; j++) {
corner[j] = trianglelist[vertexindex++];
if ((corner[j] < b->firstnumber) ||
(corner[j] >= b->firstnumber + m->invertices)) {
printf("Error: Triangle %ld has an invalid vertex index.\n",
elementnumber);
triexit(1);
}
}
#else /* not TRILIBRARY */
/* Read triangle number and the triangle's three corners. */
stringptr = readline(inputline, elefile, elefilename);
for (j = 0; j < 3; j++) {
stringptr = findfield(stringptr);
if (*stringptr == '\0') {
printf("Error: Triangle %ld is missing vertex %d in %s.\n",
elementnumber, j + 1, elefilename);
triexit(1);
} else {
corner[j] = (int) strtol(stringptr, &stringptr, 0);
if ((corner[j] < b->firstnumber) ||
(corner[j] >= b->firstnumber + m->invertices)) {
printf("Error: Triangle %ld has an invalid vertex index.\n",
elementnumber);
triexit(1);
}
}
}
#endif /* not TRILIBRARY */
/* Find out about (and throw away) extra nodes. */
for (j = 3; j < incorners; j++) {
#ifdef TRILIBRARY
killvertexindex = trianglelist[vertexindex++];
#else /* not TRILIBRARY */
stringptr = findfield(stringptr);
if (*stringptr != '\0') {
killvertexindex = (int) strtol(stringptr, &stringptr, 0);
#endif /* not TRILIBRARY */
if ((killvertexindex >= b->firstnumber) &&
(killvertexindex < b->firstnumber + m->invertices)) {
/* Delete the non-corner vertex if it's not already deleted. */
killvertex = getvertex(m, b, killvertexindex);
if (vertextype(killvertex) != DEADVERTEX) {
vertexdealloc(m, killvertex);
}
}
#ifndef TRILIBRARY
}#endif /* not TRILIBRARY */
}
/* Read the triangle's attributes. */
for (j = 0; j < m->eextras; j++) {
#ifdef TRILIBRARY
setelemattribute(triangleloop, j, triangleattriblist[attribindex++]);
#else /* not TRILIBRARY */
stringptr = findfield(stringptr);
if (*stringptr == '\0') {
setelemattribute(triangleloop, j, 0);
} else {
setelemattribute(triangleloop, j,
(REAL) strtod(stringptr, &stringptr));
}
#endif /* not TRILIBRARY */
}
if (b->vararea) {
#ifdef TRILIBRARY
area = trianglearealist[elementnumber - b->firstnumber];
#else /* not TRILIBRARY */
/* Read an area constraint from the .area file. */
stringptr = readline(inputline, areafile, areafilename);
stringptr = findfield(stringptr);
if (*stringptr == '\0') {
area = -1.0; /* No constraint on this triangle. */
} else {
area = (REAL) strtod(stringptr, &stringptr);
}
#endif /* not TRILIBRARY */
setareabound(triangleloop, area);
}
/* Set the triangle's vertices. */
triangleloop.orient = 0;
setorg(triangleloop, getvertex(m, b, corner[0]));
setdest(triangleloop, getvertex(m, b, corner[1]));
setapex(triangleloop, getvertex(m, b, corner[2]));
/* Try linking the triangle to others that share these vertices. */
for (triangleloop.orient = 0; triangleloop.orient < 3;
triangleloop.orient++) {
/* Take the number for the origin of triangleloop. */
aroundvertex = corner[triangleloop.orient];
/* Look for other triangles having this vertex. */
nexttri = vertexarray[aroundvertex - b->firstnumber];
/* Link the current triangle to the next one in the stack. */
triangleloop.tri[6 + triangleloop.orient] = nexttri;
/* Push the current triangle onto the stack. */
vertexarray[aroundvertex - b->firstnumber] = encode(triangleloop);
decode(nexttri, checktri);
if (checktri.tri != m->dummytri) {
dest(triangleloop, tdest);
apex(triangleloop, tapex);
/* Look for other triangles that share an edge. */
do {
dest(checktri, checkdest);
apex(checktri, checkapex);
if (tapex == checkdest) {
/* The two triangles share an edge; bond them together. */
lprev(triangleloop, triangleleft);
bond(triangleleft, checktri);
}
if (tdest == checkapex) {
/* The two triangles share an edge; bond them together. */
lprev(checktri, checkleft);
bond(triangleloop, checkleft);
}
/* Find the next triangle in the stack. */
nexttri = checktri.tri[6 + checktri.orient]; decode(nexttri, checktri);
} while (checktri.tri != m->dummytri);
}
}
triangleloop.tri = triangletraverse(m);
elementnumber++;
}
#ifdef TRILIBRARY
vertexindex = 0;
#else /* not TRILIBRARY */
fclose(elefile);
if (b->vararea) {
fclose(areafile);
}
#endif /* not TRILIBRARY */
hullsize = 0; /* Prepare to count the boundary edges. */
if (b->poly) {
if (b->verbose) {
printf(" Marking segments in triangulation.\n");
}
/* Read the segments from the .poly file, and link them */
/* to their neighboring triangles. */
boundmarker = 0;
traversalinit(&m->subsegs);
subsegloop.ss = subsegtraverse(m);
segmentnumber = b->firstnumber;
while (subsegloop.ss != (subseg *) NULL) {
#ifdef TRILIBRARY
end[0] = segmentlist[vertexindex++];
end[1] = segmentlist[vertexindex++];
if (segmentmarkers) {
boundmarker = segmentmarkerlist[segmentnumber - b->firstnumber];
}
#else /* not TRILIBRARY */
/* Read the endpoints of each segment, and possibly a boundary marker. */
stringptr = readline(inputline, polyfile, b->inpolyfilename);
/* Skip the first (segment number) field. */
stringptr = findfield(stringptr);
if (*stringptr == '\0') {
printf("Error: Segment %ld has no endpoints in %s.\n", segmentnumber,
polyfilename);
triexit(1);
} else {
end[0] = (int) strtol(stringptr, &stringptr, 0);
}
stringptr = findfield(stringptr);
if (*stringptr == '\0') {
printf("Error: Segment %ld is missing its second endpoint in %s.\n",
segmentnumber, polyfilename);
triexit(1);
} else {
end[1] = (int) strtol(stringptr, &stringptr, 0);
}
if (segmentmarkers) {
stringptr = findfield(stringptr);
if (*stringptr == '\0') {
boundmarker = 0;
} else {
boundmarker = (int) strtol(stringptr, &stringptr, 0);
}
}
#endif /* not TRILIBRARY */
for (j = 0; j < 2; j++) {
if ((end[j] < b->firstnumber) ||
(end[j] >= b->firstnumber + m->invertices)) {
printf("Error: Segment %ld has an invalid vertex index.\n",
segmentnumber);
triexit(1); }
}
/* set the subsegment's vertices. */
subsegloop.ssorient = 0;
segmentorg = getvertex(m, b, end[0]);
segmentdest = getvertex(m, b, end[1]);
setsorg(subsegloop, segmentorg);
setsdest(subsegloop, segmentdest);
setsegorg(subsegloop, segmentorg);
setsegdest(subsegloop, segmentdest);
setmark(subsegloop, boundmarker);
/* Try linking the subsegment to triangles that share these vertices. */
for (subsegloop.ssorient = 0; subsegloop.ssorient < 2;
subsegloop.ssorient++) {
/* Take the number for the destination of subsegloop. */
aroundvertex = end[1 - subsegloop.ssorient];
/* Look for triangles having this vertex. */
prevlink = &vertexarray[aroundvertex - b->firstnumber];
nexttri = vertexarray[aroundvertex - b->firstnumber];
decode(nexttri, checktri);
sorg(subsegloop, shorg);
notfound = 1;
/* Look for triangles having this edge. Note that I'm only */
/* comparing each triangle's destination with the subsegment; */
/* each triangle's apex is handled through a different vertex. */
/* Because each triangle appears on three vertices' lists, each */
/* occurrence of a triangle on a list can (and does) represent */
/* an edge. In this way, most edges are represented twice, and */
/* every triangle-subsegment bond is represented once. */
while (notfound && (checktri.tri != m->dummytri)) {
dest(checktri, checkdest);
if (shorg == checkdest) {
/* We have a match. Remove this triangle from the list. */
*prevlink = checktri.tri[6 + checktri.orient];
/* Bond the subsegment to the triangle. */
tsbond(checktri, subsegloop);
/* Check if this is a boundary edge. */
sym(checktri, checkneighbor);
if (checkneighbor.tri == m->dummytri) {
/* The next line doesn't insert a subsegment (because there's */
/* already one there), but it sets the boundary markers of */
/* the existing subsegment and its vertices. */
insertsubseg(m, b, &checktri, 1);
hullsize++;
}
notfound = 0;
}
/* Find the next triangle in the stack. */
prevlink = &checktri.tri[6 + checktri.orient];
nexttri = checktri.tri[6 + checktri.orient];
decode(nexttri, checktri);
}
}
subsegloop.ss = subsegtraverse(m);
segmentnumber++;
}
}
/* Mark the remaining edges as not being attached to any subsegment. */
/* Also, count the (yet uncounted) boundary edges. */
for (i = 0; i < m->vertices.items; i++) {
/* Search the stack of triangles adjacent to a vertex. */
nexttri = vertexarray[i];
decode(nexttri, checktri);
while (checktri.tri != m->dummytri) {
/* Find the next triangle in the stack before this */
/* information gets overwritten. */
nexttri = checktri.tri[6 + checktri.orient];
/* No adjacent subsegment. (This overwrites the stack info.) */ tsdissolve(checktri);
sym(checktri, checkneighbor);
if (checkneighbor.tri == m->dummytri) {
insertsubseg(m, b, &checktri, 1);
hullsize++;
}
decode(nexttri, checktri);
}
}
trifree((VOID *) vertexarray);
return hullsize;
}
#endif /* not CDT_ONLY */
/** **/
/** **/
/********* General mesh construction routines end here *********/
/********* Segment insertion begins here *********/
/** **/
/** **/
/*****************************************************************************/
/* */
/* finddirection() Find the first triangle on the path from one point */
/* to another. */
/* */
/* Finds the triangle that intersects a line segment drawn from the */
/* origin of `searchtri' to the point `searchpoint', and returns the result */
/* in `searchtri'. The origin of `searchtri' does not change, even though */
/* the triangle 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 whether the destination or apex of the found */
/* triangle is collinear with the two points in question. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
enum finddirectionresult finddirection(struct mesh *m, struct behavior *b,
struct otri *searchtri,
vertex searchpoint)
#else /* not ANSI_DECLARATORS */
enum finddirectionresult finddirection(m, b, searchtri, searchpoint)
struct mesh *m;
struct behavior *b;
struct otri *searchtri;
vertex searchpoint;
#endif /* not ANSI_DECLARATORS */
{
struct otri checktri;
vertex startvertex;
vertex leftvertex, rightvertex;
REAL leftccw, rightccw;
int leftflag, rightflag;
triangle ptr; /* Temporary variable used by onext() and oprev(). */
org(*searchtri, startvertex);
dest(*searchtri, rightvertex);
apex(*searchtri, leftvertex);
/* Is `searchpoint' to the left? */
leftccw = counterclockwise(m, b, searchpoint, startvertex, leftvertex);
leftflag = leftccw > 0.0;
/* Is `searchpoint' to the right? */
rightccw = counterclockwise(m, b, startvertex, searchpoint, rightvertex);
rightflag = rightccw > 0.0; if (leftflag && rightflag) {
/* `searchtri' faces directly away from `searchpoint'. We could go left */
/* or right. Ask whether it's a triangle or a boundary on the left. */
onext(*searchtri, checktri);
if (checktri.tri == m->dummytri) {
leftflag = 0;
} else {
rightflag = 0;
}
}
while (leftflag) {
/* Turn left until satisfied. */
onextself(*searchtri);
if (searchtri->tri == m->dummytri) {
printf("Internal error in finddirection(): Unable to find a\n");
printf(" triangle leading from (%.12g, %.12g) to", startvertex[0],
startvertex[1]);
printf(" (%.12g, %.12g).\n", searchpoint[0], searchpoint[1]);
internalerror();
}
apex(*searchtri, leftvertex);
rightccw = leftccw;
leftccw = counterclockwise(m, b, searchpoint, startvertex, leftvertex);
leftflag = leftccw > 0.0;
}
while (rightflag) {
/* Turn right until satisfied. */
oprevself(*searchtri);
if (searchtri->tri == m->dummytri) {
printf("Internal error in finddirection(): Unable to find a\n");
printf(" triangle leading from (%.12g, %.12g) to", startvertex[0],
startvertex[1]);
printf(" (%.12g, %.12g).\n", searchpoint[0], searchpoint[1]);
internalerror();
}
dest(*searchtri, rightvertex);
leftccw = rightccw;
rightccw = counterclockwise(m, b, startvertex, searchpoint, rightvertex);
rightflag = rightccw > 0.0;
}
if (leftccw == 0.0) {
return LEFTCOLLINEAR;
} else if (rightccw == 0.0) {
return RIGHTCOLLINEAR;
} else {
return WITHIN;
}
}
/*****************************************************************************/
/* */
/* segmentintersection() Find the intersection of an existing segment */
/* and a segment that is being inserted. Insert */
/* a vertex at the intersection, splitting an */
/* existing subsegment. */
/* */
/* The segment being inserted connects the apex of splittri to endpoint2. */
/* splitsubseg is the subsegment being split, and MUST adjoin splittri. */
/* Hence, endpoints of the subsegment being split are the origin and */
/* destination of splittri. */
/* */
/* On completion, splittri is a handle having the newly inserted */
/* intersection point as its origin, and endpoint1 as its destination. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
void segmentintersection(struct mesh *m, struct behavior *b,
struct otri *splittri, struct osub *splitsubseg,
vertex endpoint2)#else /* not ANSI_DECLARATORS */
void segmentintersection(m, b, splittri, splitsubseg, endpoint2)
struct mesh *m;
struct behavior *b;
struct otri *splittri;
struct osub *splitsubseg;
vertex endpoint2;
#endif /* not ANSI_DECLARATORS */
{
struct osub opposubseg;
vertex endpoint1;
vertex torg, tdest;
vertex leftvertex, rightvertex;
vertex newvertex;
enum insertvertexresult success;
enum finddirectionresult collinear;
REAL ex, ey;
REAL tx, ty;
REAL etx, ety;
REAL split, denom;
int i;
triangle ptr; /* Temporary variable used by onext(). */
subseg sptr; /* Temporary variable used by snext(). */
/* Find the other three segment endpoints. */
apex(*splittri, endpoint1);
org(*splittri, torg);
dest(*splittri, tdest);
/* Segment intersection formulae; see the Antonio reference. */
tx = tdest[0] - torg[0];
ty = tdest[1] - torg[1];
ex = endpoint2[0] - endpoint1[0];
ey = endpoint2[1] - endpoint1[1];
etx = torg[0] - endpoint2[0];
ety = torg[1] - endpoint2[1];
denom = ty * ex - tx * ey;
if (denom == 0.0) {
printf("Internal error in segmentintersection():");
printf(" Attempt to find intersection of parallel segments.\n");
internalerror();
}
split = (ey * etx - ex * ety) / denom;
/* Create the new vertex. */
newvertex = (vertex) poolalloc(&m->vertices);
/* Interpolate its coordinate and attributes. */
for (i = 0; i < 2 + m->nextras; i++) {
newvertex[i] = torg[i] + split * (tdest[i] - torg[i]);
}
setvertexmark(newvertex, mark(*splitsubseg));
setvertextype(newvertex, INPUTVERTEX);
if (b->verbose > 1) {
printf(
" Splitting subsegment (%.12g, %.12g) (%.12g, %.12g) at (%.12g, %.12g).\n",
torg[0], torg[1], tdest[0], tdest[1], newvertex[0], newvertex[1]);
}
/* Insert the intersection vertex. This should always succeed. */
success = insertvertex(m, b, newvertex, splittri, splitsubseg, 0, 0);
if (success != SUCCESSFULVERTEX) {
printf("Internal error in segmentintersection():\n");
printf(" Failure to split a segment.\n");
internalerror();
}
/* Record a triangle whose origin is the new vertex. */
setvertex2tri(newvertex, encode(*splittri));
if (m->steinerleft > 0) {
m->steinerleft--;
}
/* Divide the segment into two, and correct the segment endpoints. */ ssymself(*splitsubseg);
spivot(*splitsubseg, opposubseg);
sdissolve(*splitsubseg);
sdissolve(opposubseg);
do {
setsegorg(*splitsubseg, newvertex);
snextself(*splitsubseg);
} while (splitsubseg->ss != m->dummysub);
do {
setsegorg(opposubseg, newvertex);
snextself(opposubseg);
} while (opposubseg.ss != m->dummysub);
/* Inserting the vertex may have caused edge flips. We wish to rediscover */
/* the edge connecting endpoint1 to the new intersection vertex. */
collinear = finddirection(m, b, splittri, endpoint1);
dest(*splittri, rightvertex);
apex(*splittri, leftvertex);
if ((leftvertex[0] == endpoint1[0]) && (leftvertex[1] == endpoint1[1])) {
onextself(*splittri);
} else if ((rightvertex[0] != endpoint1[0]) ||
(rightvertex[1] != endpoint1[1])) {
printf("Internal error in segmentintersection():\n");
printf(" Topological inconsistency after splitting a segment.\n");
internalerror();
}
/* `splittri' should have destination endpoint1. */
}
/*****************************************************************************/
/* */
/* scoutsegment() Scout the first triangle on the path from one endpoint */
/* to another, and check for completion (reaching the */
/* second endpoint), a collinear vertex, or the */
/* intersection of two segments. */
/* */
/* Returns one if the entire segment is successfully inserted, and zero if */
/* the job must be finished by conformingedge() or constrainededge(). */
/* */
/* If the first triangle on the path has the second endpoint as its */
/* destination or apex, a subsegment is inserted and the job is done. */
/* */
/* If the first triangle on the path has a destination or apex that lies on */
/* the segment, a subsegment is inserted connecting the first endpoint to */
/* the collinear vertex, and the search is continued from the collinear */
/* vertex. */
/* */
/* If the first triangle on the path has a subsegment opposite its origin, */
/* then there is a segment that intersects the segment being inserted. */
/* Their intersection vertex is inserted, splitting the subsegment. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
int scoutsegment(struct mesh *m, struct behavior *b, struct otri *searchtri,
vertex endpoint2, int newmark)
#else /* not ANSI_DECLARATORS */
int scoutsegment(m, b, searchtri, endpoint2, newmark)
struct mesh *m;
struct behavior *b;
struct otri *searchtri;
vertex endpoint2;
int newmark;
#endif /* not ANSI_DECLARATORS */
{
struct otri crosstri;
struct osub crosssubseg;
vertex leftvertex, rightvertex;
enum finddirectionresult collinear; subseg sptr; /* Temporary variable used by tspivot(). */
collinear = finddirection(m, b, searchtri, endpoint2);
dest(*searchtri, rightvertex);
apex(*searchtri, leftvertex);
if (((leftvertex[0] == endpoint2[0]) && (leftvertex[1] == endpoint2[1])) ||
((rightvertex[0] == endpoint2[0]) && (rightvertex[1] == endpoint2[1]))) {
/* The segment is already an edge in the mesh. */
if ((leftvertex[0] == endpoint2[0]) && (leftvertex[1] == endpoint2[1])) {
lprevself(*searchtri);
}
/* Insert a subsegment, if there isn't already one there. */
insertsubseg(m, b, searchtri, newmark);
return 1;
} else if (collinear == LEFTCOLLINEAR) {
/* We've collided with a vertex between the segment's endpoints. */
/* Make the collinear vertex be the triangle's origin. */
lprevself(*searchtri);
insertsubseg(m, b, searchtri, newmark);
/* Insert the remainder of the segment. */
return scoutsegment(m, b, searchtri, endpoint2, newmark);
} else if (collinear == RIGHTCOLLINEAR) {
/* We've collided with a vertex between the segment's endpoints. */
insertsubseg(m, b, searchtri, newmark);
/* Make the collinear vertex be the triangle's origin. */
lnextself(*searchtri);
/* Insert the remainder of the segment. */
return scoutsegment(m, b, searchtri, endpoint2, newmark);
} else {
lnext(*searchtri, crosstri);
tspivot(crosstri, crosssubseg);
/* Check for a crossing segment. */
if (crosssubseg.ss == m->dummysub) {
return 0;
} else {
/* Insert a vertex at the intersection. */
segmentintersection(m, b, &crosstri, &crosssubseg, endpoint2);
otricopy(crosstri, *searchtri);
insertsubseg(m, b, searchtri, newmark);
/* Insert the remainder of the segment. */
return scoutsegment(m, b, searchtri, endpoint2, newmark);
}
}
}
/*****************************************************************************/
/* */
/* conformingedge() Force a segment into a conforming Delaunay */
/* triangulation by inserting a vertex at its midpoint, */
/* and recursively forcing in the two half-segments if */
/* necessary. */
/* */
/* Generates a sequence of subsegments connecting `endpoint1' to */
/* `endpoint2'. `newmark' is the boundary marker of the segment, assigned */
/* to each new splitting vertex and subsegment. */
/* */
/* Note that conformingedge() does not always maintain the conforming */
/* Delaunay property. Once inserted, segments are locked into place; */
/* vertices inserted later (to force other segments in) may render these */
/* fixed segments non-Delaunay. The conforming Delaunay property will be */
/* restored by enforcequality() by splitting encroached subsegments. */
/* */
/*****************************************************************************/
#ifndef REDUCED
#ifndef CDT_ONLY
#ifdef ANSI_DECLARATORS
void conformingedge(struct mesh *m, struct behavior *b,
vertex endpoint1, vertex endpoint2, int newmark)#else /* not ANSI_DECLARATORS */
void conformingedge(m, b, endpoint1, endpoint2, newmark)
struct mesh *m;
struct behavior *b;
vertex endpoint1;
vertex endpoint2;
int newmark;
#endif /* not ANSI_DECLARATORS */
{
struct otri searchtri1, searchtri2;
struct osub brokensubseg;
vertex newvertex;
vertex midvertex1, midvertex2;
enum insertvertexresult success;
int i;
subseg sptr; /* Temporary variable used by tspivot(). */
if (b->verbose > 2) {
printf("Forcing segment into triangulation by recursive splitting:\n");
printf(" (%.12g, %.12g) (%.12g, %.12g)\n", endpoint1[0], endpoint1[1],
endpoint2[0], endpoint2[1]);
}
/* Create a new vertex to insert in the middle of the segment. */
newvertex = (vertex) poolalloc(&m->vertices);
/* Interpolate coordinates and attributes. */
for (i = 0; i < 2 + m->nextras; i++) {
newvertex[i] = 0.5 * (endpoint1[i] + endpoint2[i]);
}
setvertexmark(newvertex, newmark);
setvertextype(newvertex, SEGMENTVERTEX);
/* No known triangle to search from. */
searchtri1.tri = m->dummytri;
/* Attempt to insert the new vertex. */
success = insertvertex(m, b, newvertex, &searchtri1, (struct osub *) NULL,
0, 0);
if (success == DUPLICATEVERTEX) {
if (b->verbose > 2) {
printf(" Segment intersects existing vertex (%.12g, %.12g).\n",
newvertex[0], newvertex[1]);
}
/* Use the vertex that's already there. */
vertexdealloc(m, newvertex);
org(searchtri1, newvertex);
} else {
if (success == VIOLATINGVERTEX) {
if (b->verbose > 2) {
printf(" Two segments intersect at (%.12g, %.12g).\n",
newvertex[0], newvertex[1]);
}
/* By fluke, we've landed right on another segment. Split it. */
tspivot(searchtri1, brokensubseg);
success = insertvertex(m, b, newvertex, &searchtri1, &brokensubseg,
0, 0);
if (success != SUCCESSFULVERTEX) {
printf("Internal error in conformingedge():\n");
printf(" Failure to split a segment.\n");
internalerror();
}
}
/* The vertex has been inserted successfully. */
if (m->steinerleft > 0) {
m->steinerleft--;
}
}
otricopy(searchtri1, searchtri2);
/* `searchtri1' and `searchtri2' are fastened at their origins to */
/* `newvertex', and will be directed toward `endpoint1' and `endpoint2' */
/* respectively. First, we must get `searchtri2' out of the way so it */
/* won't be invalidated during the insertion of the first half of the */ /* segment. */
finddirection(m, b, &searchtri2, endpoint2);
if (!scoutsegment(m, b, &searchtri1, endpoint1, newmark)) {
/* The origin of searchtri1 may have changed if a collision with an */
/* intervening vertex on the segment occurred. */
org(searchtri1, midvertex1);
conformingedge(m, b, midvertex1, endpoint1, newmark);
}
if (!scoutsegment(m, b, &searchtri2, endpoint2, newmark)) {
/* The origin of searchtri2 may have changed if a collision with an */
/* intervening vertex on the segment occurred. */
org(searchtri2, midvertex2);
conformingedge(m, b, midvertex2, endpoint2, newmark);
}
}
#endif /* not CDT_ONLY */
#endif /* not REDUCED */
/*****************************************************************************/
/* */
/* delaunayfixup() Enforce the Delaunay condition at an edge, fanning out */
/* recursively from an existing vertex. Pay special */
/* attention to stacking inverted triangles. */
/* */
/* This is a support routine for inserting segments into a constrained */
/* Delaunay triangulation. */
/* */
/* The origin of fixuptri is treated as if it has just been inserted, and */
/* the local Delaunay condition needs to be enforced. It is only enforced */
/* in one sector, however, that being the angular range defined by */
/* fixuptri. */
/* */
/* This routine also needs to make decisions regarding the "stacking" of */
/* triangles. (Read the description of constrainededge() below before */
/* reading on here, so you understand the algorithm.) If the position of */
/* the new vertex (the origin of fixuptri) indicates that the vertex before */
/* it on the polygon is a reflex vertex, then "stack" the triangle by */
/* doing nothing. (fixuptri is an inverted triangle, which is how stacked */
/* triangles are identified.) */
/* */
/* Otherwise, check whether the vertex before that was a reflex vertex. */
/* If so, perform an edge flip, thereby eliminating an inverted triangle */
/* (popping it off the stack). The edge flip may result in the creation */
/* of a new inverted triangle, depending on whether or not the new vertex */
/* is visible to the vertex three edges behind on the polygon. */
/* */
/* If neither of the two vertices behind the new vertex are reflex */
/* vertices, fixuptri and fartri, the triangle opposite it, are not */
/* inverted; hence, ensure that the edge between them is locally Delaunay. */
/* */
/* `leftside' indicates whether or not fixuptri is to the left of the */
/* segment being inserted. (Imagine that the segment is pointing up from */
/* endpoint1 to endpoint2.) */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
void delaunayfixup(struct mesh *m, struct behavior *b,
struct otri *fixuptri, int leftside)
#else /* not ANSI_DECLARATORS */
void delaunayfixup(m, b, fixuptri, leftside)
struct mesh *m;
struct behavior *b;
struct otri *fixuptri;
int leftside;
#endif /* not ANSI_DECLARATORS */
{
struct otri neartri; struct otri fartri;
struct osub faredge;
vertex nearvertex, leftvertex, rightvertex, farvertex;
triangle ptr; /* Temporary variable used by sym(). */
subseg sptr; /* Temporary variable used by tspivot(). */
lnext(*fixuptri, neartri);
sym(neartri, fartri);
/* Check if the edge opposite the origin of fixuptri can be flipped. */
if (fartri.tri == m->dummytri) {
return;
}
tspivot(neartri, faredge);
if (faredge.ss != m->dummysub) {
return;
}
/* Find all the relevant vertices. */
apex(neartri, nearvertex);
org(neartri, leftvertex);
dest(neartri, rightvertex);
apex(fartri, farvertex);
/* Check whether the previous polygon vertex is a reflex vertex. */
if (leftside) {
if (counterclockwise(m, b, nearvertex, leftvertex, farvertex) <= 0.0) {
/* leftvertex is a reflex vertex too. Nothing can */
/* be done until a convex section is found. */
return;
}
} else {
if (counterclockwise(m, b, farvertex, rightvertex, nearvertex) <= 0.0) {
/* rightvertex is a reflex vertex too. Nothing can */
/* be done until a convex section is found. */
return;
}
}
if (counterclockwise(m, b, rightvertex, leftvertex, farvertex) > 0.0) {
/* fartri is not an inverted triangle, and farvertex is not a reflex */
/* vertex. As there are no reflex vertices, fixuptri isn't an */
/* inverted triangle, either. Hence, test the edge between the */
/* triangles to ensure it is locally Delaunay. */
if (incircle(m, b, leftvertex, farvertex, rightvertex, nearvertex) <=
0.0) {
return;
}
/* Not locally Delaunay; go on to an edge flip. */
} /* else fartri is inverted; remove it from the stack by flipping. */
flip(m, b, &neartri);
lprevself(*fixuptri); /* Restore the origin of fixuptri after the flip. */
/* Recursively process the two triangles that result from the flip. */
delaunayfixup(m, b, fixuptri, leftside);
delaunayfixup(m, b, &fartri, leftside);
}
/*****************************************************************************/
/* */
/* constrainededge() Force a segment into a constrained Delaunay */
/* triangulation by deleting the triangles it */
/* intersects, and triangulating the polygons that */
/* form on each side of it. */
/* */
/* Generates a single subsegment connecting `endpoint1' to `endpoint2'. */
/* The triangle `starttri' has `endpoint1' as its origin. `newmark' is the */
/* boundary marker of the segment. */
/* */
/* To insert a segment, every triangle whose interior intersects the */
/* segment is deleted. The union of these deleted triangles is a polygon */
/* (which is not necessarily monotone, but is close enough), which is */
/* divided into two polygons by the new segment. This routine's task is */
/* to generate the Delaunay triangulation of these two polygons. */
/* *//* You might think of this routine's behavior as a two-step process. The */
/* first step is to walk from endpoint1 to endpoint2, flipping each edge */
/* encountered. This step creates a fan of edges connected to endpoint1, */
/* including the desired edge to endpoint2. The second step enforces the */
/* Delaunay condition on each side of the segment in an incremental manner: */
/* proceeding along the polygon from endpoint1 to endpoint2 (this is done */
/* independently on each side of the segment), each vertex is "enforced" */
/* as if it had just been inserted, but affecting only the previous */
/* vertices. The result is the same as if the vertices had been inserted */
/* in the order they appear on the polygon, so the result is Delaunay. */
/* */
/* In truth, constrainededge() interleaves these two steps. The procedure */
/* walks from endpoint1 to endpoint2, and each time an edge is encountered */
/* and flipped, the newly exposed vertex (at the far end of the flipped */
/* edge) is "enforced" upon the previously flipped edges, usually affecting */
/* only one side of the polygon (depending upon which side of the segment */
/* the vertex falls on). */
/* */
/* The algorithm is complicated by the need to handle polygons that are not */
/* convex. Although the polygon is not necessarily monotone, it can be */
/* triangulated in a manner similar to the stack-based algorithms for */
/* monotone polygons. For each reflex vertex (local concavity) of the */
/* polygon, there will be an inverted triangle formed by one of the edge */
/* flips. (An inverted triangle is one with negative area - that is, its */
/* vertices are arranged in clockwise order - and is best thought of as a */
/* wrinkle in the fabric of the mesh.) Each inverted triangle can be */
/* thought of as a reflex vertex pushed on the stack, waiting to be fixed */
/* later. */
/* */
/* A reflex vertex is popped from the stack when a vertex is inserted that */
/* is visible to the reflex vertex. (However, if the vertex behind the */
/* reflex vertex is not visible to the reflex vertex, a new inverted */
/* triangle will take its place on the stack.) These details are handled */
/* by the delaunayfixup() routine above. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
void constrainededge(struct mesh *m, struct behavior *b,
struct otri *starttri, vertex endpoint2, int newmark)
#else /* not ANSI_DECLARATORS */
void constrainededge(m, b, starttri, endpoint2, newmark)
struct mesh *m;
struct behavior *b;
struct otri *starttri;
vertex endpoint2;
int newmark;
#endif /* not ANSI_DECLARATORS */
{
struct otri fixuptri, fixuptri2;
struct osub crosssubseg;
vertex endpoint1;
vertex farvertex;
REAL area;
int collision;
int done;
triangle ptr; /* Temporary variable used by sym() and oprev(). */
subseg sptr; /* Temporary variable used by tspivot(). */
org(*starttri, endpoint1);
lnext(*starttri, fixuptri);
flip(m, b, &fixuptri);
/* `collision' indicates whether we have found a vertex directly */
/* between endpoint1 and endpoint2. */
collision = 0;
done = 0;
do {
org(fixuptri, farvertex);
/* `farvertex' is the extreme point of the polygon we are "digging" */ /* to get from endpoint1 to endpoint2. */
if ((farvertex[0] == endpoint2[0]) && (farvertex[1] == endpoint2[1])) {
oprev(fixuptri, fixuptri2);
/* Enforce the Delaunay condition around endpoint2. */
delaunayfixup(m, b, &fixuptri, 0);
delaunayfixup(m, b, &fixuptri2, 1);
done = 1;
} else {
/* Check whether farvertex is to the left or right of the segment */
/* being inserted, to decide which edge of fixuptri to dig */
/* through next. */
area = counterclockwise(m, b, endpoint1, endpoint2, farvertex);
if (area == 0.0) {
/* We've collided with a vertex between endpoint1 and endpoint2. */
collision = 1;
oprev(fixuptri, fixuptri2);
/* Enforce the Delaunay condition around farvertex. */
delaunayfixup(m, b, &fixuptri, 0);
delaunayfixup(m, b, &fixuptri2, 1);
done = 1;
} else {
if (area > 0.0) { /* farvertex is to the left of the segment. */
oprev(fixuptri, fixuptri2);
/* Enforce the Delaunay condition around farvertex, on the */
/* left side of the segment only. */
delaunayfixup(m, b, &fixuptri2, 1);
/* Flip the edge that crosses the segment. After the edge is */
/* flipped, one of its endpoints is the fan vertex, and the */
/* destination of fixuptri is the fan vertex. */
lprevself(fixuptri);
} else { /* farvertex is to the right of the segment. */
delaunayfixup(m, b, &fixuptri, 0);
/* Flip the edge that crosses the segment. After the edge is */
/* flipped, one of its endpoints is the fan vertex, and the */
/* destination of fixuptri is the fan vertex. */
oprevself(fixuptri);
}
/* Check for two intersecting segments. */
tspivot(fixuptri, crosssubseg);
if (crosssubseg.ss == m->dummysub) {
flip(m, b, &fixuptri); /* May create inverted triangle at left. */
} else {
/* We've collided with a segment between endpoint1 and endpoint2. */
collision = 1;
/* Insert a vertex at the intersection. */
segmentintersection(m, b, &fixuptri, &crosssubseg, endpoint2);
done = 1;
}
}
}
} while (!done);
/* Insert a subsegment to make the segment permanent. */
insertsubseg(m, b, &fixuptri, newmark);
/* 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 (!scoutsegment(m, b, &fixuptri, endpoint2, newmark)) {
constrainededge(m, b, &fixuptri, endpoint2, newmark);
}
}
}
/*****************************************************************************/
/* */
/* insertsegment() Insert a PSLG segment into a triangulation. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORSvoid insertsegment(struct mesh *m, struct behavior *b,
vertex endpoint1, vertex endpoint2, int newmark)
#else /* not ANSI_DECLARATORS */
void insertsegment(m, b, endpoint1, endpoint2, newmark)
struct mesh *m;
struct behavior *b;
vertex endpoint1;
vertex endpoint2;
int newmark;
#endif /* not ANSI_DECLARATORS */
{
struct otri searchtri1, searchtri2;
triangle encodedtri;
vertex checkvertex;
triangle ptr; /* Temporary variable used by sym(). */
if (b->verbose > 1) {
printf(" Connecting (%.12g, %.12g) to (%.12g, %.12g).\n",
endpoint1[0], endpoint1[1], endpoint2[0], endpoint2[1]);
}
/* Find a triangle whose origin is the segment's first endpoint. */
checkvertex = (vertex) NULL;
encodedtri = vertex2tri(endpoint1);
if (encodedtri != (triangle) NULL) {
decode(encodedtri, searchtri1);
org(searchtri1, checkvertex);
}
if (checkvertex != endpoint1) {
/* Find a boundary triangle to search from. */
searchtri1.tri = m->dummytri;
searchtri1.orient = 0;
symself(searchtri1);
/* Search for the segment's first endpoint by point location. */
if (locate(m, b, endpoint1, &searchtri1) != ONVERTEX) {
printf(
"Internal error in insertsegment(): Unable to locate PSLG vertex\n");
printf(" (%.12g, %.12g) in triangulation.\n",
endpoint1[0], endpoint1[1]);
internalerror();
}
}
/* Remember this triangle to improve subsequent point location. */
otricopy(searchtri1, m->recenttri);
/* Scout the beginnings of a path from the first endpoint */
/* toward the second. */
if (scoutsegment(m, b, &searchtri1, endpoint2, newmark)) {
/* The segment was easily inserted. */
return;
}
/* The first endpoint may have changed if a collision with an intervening */
/* vertex on the segment occurred. */
org(searchtri1, endpoint1);
/* Find a triangle whose origin is the segment's second endpoint. */
checkvertex = (vertex) NULL;
encodedtri = vertex2tri(endpoint2);
if (encodedtri != (triangle) NULL) {
decode(encodedtri, searchtri2);
org(searchtri2, checkvertex);
}
if (checkvertex != endpoint2) {
/* Find a boundary triangle to search from. */
searchtri2.tri = m->dummytri;
searchtri2.orient = 0;
symself(searchtri2);
/* Search for the segment's second endpoint by point location. */
if (locate(m, b, endpoint2, &searchtri2) != ONVERTEX) {
printf( "Internal error in insertsegment(): Unable to locate PSLG vertex\n");
printf(" (%.12g, %.12g) in triangulation.\n",
endpoint2[0], endpoint2[1]);
internalerror();
}
}
/* Remember this triangle to improve subsequent point location. */
otricopy(searchtri2, m->recenttri);
/* Scout the beginnings of a path from the second endpoint */
/* toward the first. */
if (scoutsegment(m, b, &searchtri2, endpoint1, newmark)) {
/* The segment was easily inserted. */
return;
}
/* The second endpoint may have changed if a collision with an intervening */
/* vertex on the segment occurred. */
org(searchtri2, endpoint2);
#ifndef REDUCED
#ifndef CDT_ONLY
if (b->splitseg) {
/* Insert vertices to force the segment into the triangulation. */
conformingedge(m, b, endpoint1, endpoint2, newmark);
} else {
#endif /* not CDT_ONLY */
#endif /* not REDUCED */
/* Insert the segment directly into the triangulation. */
constrainededge(m, b, &searchtri1, endpoint2, newmark);
#ifndef REDUCED
#ifndef CDT_ONLY
}
#endif /* not CDT_ONLY */
#endif /* not REDUCED */
}
/*****************************************************************************/
/* */
/* markhull() Cover the convex hull of a triangulation with subsegments. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
void markhull(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
void markhull(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */
{
struct otri hulltri;
struct otri nexttri;
struct otri starttri;
triangle ptr; /* Temporary variable used by sym() and oprev(). */
/* Find a triangle handle on the hull. */
hulltri.tri = m->dummytri;
hulltri.orient = 0;
symself(hulltri);
/* Remember where we started so we know when to stop. */
otricopy(hulltri, starttri);
/* Go once counterclockwise around the convex hull. */
do {
/* Create a subsegment if there isn't already one here. */
insertsubseg(m, b, &hulltri, 1);
/* To find the next hull edge, go clockwise around the next vertex. */
lnextself(hulltri);
oprev(hulltri, nexttri);
while (nexttri.tri != m->dummytri) {
otricopy(nexttri, hulltri); oprev(hulltri, nexttri);
}
} while (!otriequal(hulltri, starttri));
}
/*****************************************************************************/
/* */
/* formskeleton() Create the segments of a triangulation, including PSLG */
/* segments and edges on the convex hull. */
/* */
/* The PSLG segments are read from a .poly file. The return value is the */
/* number of segments in the file. */
/* */
/*****************************************************************************/
#ifdef TRILIBRARY
#ifdef ANSI_DECLARATORS
void formskeleton(struct mesh *m, struct behavior *b, int *segmentlist,
int *segmentmarkerlist, int numberofsegments)
#else /* not ANSI_DECLARATORS */
void formskeleton(m, b, segmentlist, segmentmarkerlist, numberofsegments)
struct mesh *m;
struct behavior *b;
int *segmentlist;
int *segmentmarkerlist;
int numberofsegments;
#endif /* not ANSI_DECLARATORS */
#else /* not TRILIBRARY */
#ifdef ANSI_DECLARATORS
void formskeleton(struct mesh *m, struct behavior *b,
FILE *polyfile, char *polyfilename)
#else /* not ANSI_DECLARATORS */
void formskeleton(m, b, polyfile, polyfilename)
struct mesh *m;
struct behavior *b;
FILE *polyfile;
char *polyfilename;
#endif /* not ANSI_DECLARATORS */
#endif /* not TRILIBRARY */
{
#ifdef TRILIBRARY
char polyfilename[6];
int index;
#else /* not TRILIBRARY */
char inputline[INPUTLINESIZE];
char *stringptr;
#endif /* not TRILIBRARY */
vertex endpoint1, endpoint2;
int segmentmarkers;
int end1, end2;
int boundmarker;
int i;
if (b->poly) {
if (!b->quiet) {
printf("Recovering segments in Delaunay triangulation.\n");
}
#ifdef TRILIBRARY
strcpy(polyfilename, "input");
m->insegments = numberofsegments;
segmentmarkers = segmentmarkerlist != (int *) NULL;
index = 0;
#else /* not TRILIBRARY */
/* Read the segments from a .poly file. */
/* Read number of segments and number of boundary markers. */ stringptr = readline(inputline, polyfile, polyfilename);
m->insegments = (int) strtol(stringptr, &stringptr, 0);
stringptr = findfield(stringptr);
if (*stringptr == '\0') {
segmentmarkers = 0;
} else {
segmentmarkers = (int) strtol(stringptr, &stringptr, 0);
}
#endif /* not TRILIBRARY */
/* If the input vertices are collinear, there is no triangulation, */
/* so don't try to insert segments. */
if (m->triangles.items == 0) {
return;
}
/* If segments are to be inserted, compute a mapping */
/* from vertices to triangles. */
if (m->insegments > 0) {
makevertexmap(m, b);
if (b->verbose) {
printf(" Recovering PSLG segments.\n");
}
}
boundmarker = 0;
/* Read and insert the segments. */
for (i = 0; i < m->insegments; i++) {
#ifdef TRILIBRARY
end1 = segmentlist[index++];
end2 = segmentlist[index++];
if (segmentmarkers) {
boundmarker = segmentmarkerlist[i];
}
#else /* not TRILIBRARY */
stringptr = readline(inputline, polyfile, b->inpolyfilename);
stringptr = findfield(stringptr);
if (*stringptr == '\0') {
printf("Error: Segment %d has no endpoints in %s.\n",
b->firstnumber + i, polyfilename);
triexit(1);
} else {
end1 = (int) strtol(stringptr, &stringptr, 0);
}
stringptr = findfield(stringptr);
if (*stringptr == '\0') {
printf("Error: Segment %d is missing its second endpoint in %s.\n",
b->firstnumber + i, polyfilename);
triexit(1);
} else {
end2 = (int) strtol(stringptr, &stringptr, 0);
}
if (segmentmarkers) {
stringptr = findfield(stringptr);
if (*stringptr == '\0') {
boundmarker = 0;
} else {
boundmarker = (int) strtol(stringptr, &stringptr, 0);
}
}
#endif /* not TRILIBRARY */
if ((end1 < b->firstnumber) ||
(end1 >= b->firstnumber + m->invertices)) {
if (!b->quiet) {
printf("Warning: Invalid first endpoint of segment %d in %s.\n",
b->firstnumber + i, polyfilename);
}
} else if ((end2 < b->firstnumber) ||
(end2 >= b->firstnumber + m->invertices)) {
if (!b->quiet) {
printf("Warning: Invalid second endpoint of segment %d in %s.\n", b->firstnumber + i, polyfilename);
}
} else {
/* Find the vertices numbered `end1' and `end2'. */
endpoint1 = getvertex(m, b, end1);
endpoint2 = getvertex(m, b, end2);
if ((endpoint1[0] == endpoint2[0]) && (endpoint1[1] == endpoint2[1])) {
if (!b->quiet) {
printf("Warning: Endpoints of segment %d are coincident in %s.\n",
b->firstnumber + i, polyfilename);
}
} else {
insertsegment(m, b, endpoint1, endpoint2, boundmarker);
}
}
}
} else {
m->insegments = 0;
}
if (b->convex || !b->poly) {
/* Enclose the convex hull with subsegments. */
if (b->verbose) {
printf(" Enclosing convex hull with segments.\n");
}
markhull(m, b);
}
}
/** **/
/** **/
/********* Segment insertion ends here *********/
/********* Carving out holes and concavities begins here *********/
/** **/
/** **/
/*****************************************************************************/
/* */
/* infecthull() Virally infect all of the triangles of the convex hull */
/* that are not protected by subsegments. Where there are */
/* subsegments, set boundary markers as appropriate. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
void infecthull(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
void infecthull(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */
{
struct otri hulltri;
struct otri nexttri;
struct otri starttri;
struct osub hullsubseg;
triangle **deadtriangle;
vertex horg, hdest;
triangle ptr; /* Temporary variable used by sym(). */
subseg sptr; /* Temporary variable used by tspivot(). */
if (b->verbose) {
printf(" Marking concavities (external triangles) for elimination.\n");
}
/* Find a triangle handle on the hull. */
hulltri.tri = m->dummytri;
hulltri.orient = 0;
symself(hulltri);
/* Remember where we started so we know when to stop. */ otricopy(hulltri, starttri);
/* Go once counterclockwise around the convex hull. */
do {
/* Ignore triangles that are already infected. */
if (!infected(hulltri)) {
/* Is the triangle protected by a subsegment? */
tspivot(hulltri, hullsubseg);
if (hullsubseg.ss == m->dummysub) {
/* The triangle is not protected; infect it. */
if (!infected(hulltri)) {
infect(hulltri);
deadtriangle = (triangle **) poolalloc(&m->viri);
*deadtriangle = hulltri.tri;
}
} else {
/* The triangle is protected; set boundary markers if appropriate. */
if (mark(hullsubseg) == 0) {
setmark(hullsubseg, 1);
org(hulltri, horg);
dest(hulltri, hdest);
if (vertexmark(horg) == 0) {
setvertexmark(horg, 1);
}
if (vertexmark(hdest) == 0) {
setvertexmark(hdest, 1);
}
}
}
}
/* To find the next hull edge, go clockwise around the next vertex. */
lnextself(hulltri);
oprev(hulltri, nexttri);
while (nexttri.tri != m->dummytri) {
otricopy(nexttri, hulltri);
oprev(hulltri, nexttri);
}
} while (!otriequal(hulltri, starttri));
}
/*****************************************************************************/
/* */
/* plague() 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. */
/* */
/* This procedure operates in two phases. The first phase identifies all */
/* the triangles that will die, and marks them as infected. They are */
/* marked to ensure that each triangle is added to the virus pool only */
/* once, so the procedure will terminate. */
/* */
/* The second phase actually eliminates the infected triangles. It also */
/* eliminates orphaned vertices. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
void plague(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
void plague(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */
{
struct otri testtri;
struct otri neighbor;
triangle **virusloop;
triangle **deadtriangle;
struct osub neighborsubseg; vertex testvertex;
vertex norg, ndest;
vertex deadorg, deaddest, deadapex;
int killorg;
triangle ptr; /* Temporary variable used by sym() and onext(). */
subseg sptr; /* Temporary variable used by tspivot(). */
if (b->verbose) {
printf(" Marking neighbors of marked triangles.\n");
}
/* Loop through all the infected triangles, spreading the virus to */
/* their neighbors, then to their neighbors' neighbors. */
traversalinit(&m->viri);
virusloop = (triangle **) traverse(&m->viri);
while (virusloop != (triangle **) NULL) {
testtri.tri = *virusloop;
/* A triangle is marked as infected by messing with one of its pointers */
/* to subsegments, setting it to an illegal value. Hence, we have to */
/* temporarily uninfect this triangle so that we can examine its */
/* adjacent subsegments. */
uninfect(testtri);
if (b->verbose > 2) {
/* Assign the triangle an orientation for convenience in */
/* checking its vertices. */
testtri.orient = 0;
org(testtri, deadorg);
dest(testtri, deaddest);
apex(testtri, deadapex);
printf(" Checking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
deadorg[0], deadorg[1], deaddest[0], deaddest[1],
deadapex[0], deadapex[1]);
}
/* Check each of the triangle's three neighbors. */
for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
/* Find the neighbor. */
sym(testtri, neighbor);
/* Check for a subsegment between the triangle and its neighbor. */
tspivot(testtri, neighborsubseg);
/* Check if the neighbor is nonexistent or already infected. */
if ((neighbor.tri == m->dummytri) || infected(neighbor)) {
if (neighborsubseg.ss != m->dummysub) {
/* There is a subsegment separating the triangle from its */
/* neighbor, but both triangles are dying, so the subsegment */
/* dies too. */
subsegdealloc(m, neighborsubseg.ss);
if (neighbor.tri != m->dummytri) {
/* Make sure the subsegment doesn't get deallocated again */
/* later when the infected neighbor is visited. */
uninfect(neighbor);
tsdissolve(neighbor);
infect(neighbor);
}
}
} else { /* The neighbor exists and is not infected. */
if (neighborsubseg.ss == m->dummysub) {
/* There is no subsegment protecting the neighbor, so */
/* the neighbor becomes infected. */
if (b->verbose > 2) {
org(neighbor, deadorg);
dest(neighbor, deaddest);
apex(neighbor, deadapex);
printf(
" Marking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
deadorg[0], deadorg[1], deaddest[0], deaddest[1],
deadapex[0], deadapex[1]);
}
infect(neighbor);
/* Ensure that the neighbor's neighbors will be infected. */
deadtriangle = (triangle **) poolalloc(&m->viri);
*deadtriangle = neighbor.tri; } else { /* The neighbor is protected by a subsegment. */
/* Remove this triangle from the subsegment. */
stdissolve(neighborsubseg);
/* The subsegment becomes a boundary. Set markers accordingly. */
if (mark(neighborsubseg) == 0) {
setmark(neighborsubseg, 1);
}
org(neighbor, norg);
dest(neighbor, ndest);
if (vertexmark(norg) == 0) {
setvertexmark(norg, 1);
}
if (vertexmark(ndest) == 0) {
setvertexmark(ndest, 1);
}
}
}
}
/* Remark the triangle as infected, so it doesn't get added to the */
/* virus pool again. */
infect(testtri);
virusloop = (triangle **) traverse(&m->viri);
}
if (b->verbose) {
printf(" Deleting marked triangles.\n");
}
traversalinit(&m->viri);
virusloop = (triangle **) traverse(&m->viri);
while (virusloop != (triangle **) NULL) {
testtri.tri = *virusloop;
/* Check each of the three corners of the triangle for elimination. */
/* This is done by walking around each vertex, checking if it is */
/* still connected to at least one live triangle. */
for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
org(testtri, testvertex);
/* Check if the vertex has already been tested. */
if (testvertex != (vertex) NULL) {
killorg = 1;
/* Mark the corner of the triangle as having been tested. */
setorg(testtri, NULL);
/* Walk counterclockwise about the vertex. */
onext(testtri, neighbor);
/* Stop upon reaching a boundary or the starting triangle. */
while ((neighbor.tri != m->dummytri) &&
(!otriequal(neighbor, testtri))) {
if (infected(neighbor)) {
/* Mark the corner of this triangle as having been tested. */
setorg(neighbor, NULL);
} else {
/* A live triangle. The vertex survives. */
killorg = 0;
}
/* Walk counterclockwise about the vertex. */
onextself(neighbor);
}
/* If we reached a boundary, we must walk clockwise as well. */
if (neighbor.tri == m->dummytri) {
/* Walk clockwise about the vertex. */
oprev(testtri, neighbor);
/* Stop upon reaching a boundary. */
while (neighbor.tri != m->dummytri) {
if (infected(neighbor)) {
/* Mark the corner of this triangle as having been tested. */
setorg(neighbor, NULL);
} else {
/* A live triangle. The vertex survives. */
killorg = 0; }
/* Walk clockwise about the vertex. */
oprevself(neighbor);
}
}
if (killorg) {
if (b->verbose > 1) {
printf(" Deleting vertex (%.12g, %.12g)\n",
testvertex[0], testvertex[1]);
}
setvertextype(testvertex, UNDEADVERTEX);
m->undeads++;
}
}
}
/* Record changes in the number of boundary edges, and disconnect */
/* dead triangles from their neighbors. */
for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
sym(testtri, neighbor);
if (neighbor.tri == m->dummytri) {
/* There is no neighboring triangle on this edge, so this edge */
/* is a boundary edge. This triangle is being deleted, so this */
/* boundary edge is deleted. */
m->hullsize--;
} else {
/* Disconnect the triangle from its neighbor. */
dissolve(neighbor);
/* There is a neighboring triangle on this edge, so this edge */
/* becomes a boundary edge when this triangle is deleted. */
m->hullsize++;
}
}
/* Return the dead triangle to the pool of triangles. */
triangledealloc(m, testtri.tri);
virusloop = (triangle **) traverse(&m->viri);
}
/* Empty the virus pool. */
poolrestart(&m->viri);
}
/*****************************************************************************/
/* */
/* regionplague() Spread regional attributes and/or area constraints */
/* (from a .poly file) throughout the mesh. */
/* */
/* This procedure operates in two phases. The first phase spreads an */
/* attribute and/or an area constraint through a (segment-bounded) region. */
/* The triangles are marked to ensure that each triangle is added to the */
/* virus pool only once, so the procedure will terminate. */
/* */
/* The second phase uninfects all infected triangles, returning them to */
/* normal. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
void regionplague(struct mesh *m, struct behavior *b,
REAL attribute, REAL area)
#else /* not ANSI_DECLARATORS */
void regionplague(m, b, attribute, area)
struct mesh *m;
struct behavior *b;
REAL attribute;
REAL area;
#endif /* not ANSI_DECLARATORS */
{
struct otri testtri;
struct otri neighbor; triangle **virusloop;
triangle **regiontri;
struct osub neighborsubseg;
vertex regionorg, regiondest, regionapex;
triangle ptr; /* Temporary variable used by sym() and onext(). */
subseg sptr; /* Temporary variable used by tspivot(). */
if (b->verbose > 1) {
printf(" Marking neighbors of marked triangles.\n");
}
/* Loop through all the infected triangles, spreading the attribute */
/* and/or area constraint to their neighbors, then to their neighbors' */
/* neighbors. */
traversalinit(&m->viri);
virusloop = (triangle **) traverse(&m->viri);
while (virusloop != (triangle **) NULL) {
testtri.tri = *virusloop;
/* A triangle is marked as infected by messing with one of its pointers */
/* to subsegments, setting it to an illegal value. Hence, we have to */
/* temporarily uninfect this triangle so that we can examine its */
/* adjacent subsegments. */
uninfect(testtri);
if (b->regionattrib) {
/* Set an attribute. */
setelemattribute(testtri, m->eextras, attribute);
}
if (b->vararea) {
/* Set an area constraint. */
setareabound(testtri, area);
}
if (b->verbose > 2) {
/* Assign the triangle an orientation for convenience in */
/* checking its vertices. */
testtri.orient = 0;
org(testtri, regionorg);
dest(testtri, regiondest);
apex(testtri, regionapex);
printf(" Checking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
regionorg[0], regionorg[1], regiondest[0], regiondest[1],
regionapex[0], regionapex[1]);
}
/* Check each of the triangle's three neighbors. */
for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
/* Find the neighbor. */
sym(testtri, neighbor);
/* Check for a subsegment between the triangle and its neighbor. */
tspivot(testtri, neighborsubseg);
/* Make sure the neighbor exists, is not already infected, and */
/* isn't protected by a subsegment. */
if ((neighbor.tri != m->dummytri) && !infected(neighbor)
&& (neighborsubseg.ss == m->dummysub)) {
if (b->verbose > 2) {
org(neighbor, regionorg);
dest(neighbor, regiondest);
apex(neighbor, regionapex);
printf(" Marking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
regionorg[0], regionorg[1], regiondest[0], regiondest[1],
regionapex[0], regionapex[1]);
}
/* Infect the neighbor. */
infect(neighbor);
/* Ensure that the neighbor's neighbors will be infected. */
regiontri = (triangle **) poolalloc(&m->viri);
*regiontri = neighbor.tri;
}
}
/* Remark the triangle as infected, so it doesn't get added to the */
/* virus pool again. */
infect(testtri);
virusloop = (triangle **) traverse(&m->viri); }
/* Uninfect all triangles. */
if (b->verbose > 1) {
printf(" Unmarking marked triangles.\n");
}
traversalinit(&m->viri);
virusloop = (triangle **) traverse(&m->viri);
while (virusloop != (triangle **) NULL) {
testtri.tri = *virusloop;
uninfect(testtri);
virusloop = (triangle **) traverse(&m->viri);
}
/* Empty the virus pool. */
poolrestart(&m->viri);
}
/*****************************************************************************/
/* */
/* carveholes() 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. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
void carveholes(struct mesh *m, struct behavior *b, REAL *holelist, int holes,
REAL *regionlist, int regions)
#else /* not ANSI_DECLARATORS */
void carveholes(m, b, holelist, holes, regionlist, regions)
struct mesh *m;
struct behavior *b;
REAL *holelist;
int holes;
REAL *regionlist;
int regions;
#endif /* not ANSI_DECLARATORS */
{
struct otri searchtri;
struct otri triangleloop;
struct otri *regiontris;
triangle **holetri;
triangle **regiontri;
vertex searchorg, searchdest;
enum locateresult intersect;
int i;
triangle ptr; /* Temporary variable used by sym(). */
if (!(b->quiet || (b->noholes && b->convex))) {
printf("Removing unwanted triangles.\n");
if (b->verbose && (holes > 0)) {
printf(" Marking holes for elimination.\n");
}
}
if (regions > 0) {
/* Allocate storage for the triangles in which region points fall. */
regiontris = (struct otri *) trimalloc(regions *
(int) sizeof(struct otri));
} else {
regiontris = (struct otri *) NULL;
}
if (((holes > 0) && !b->noholes) || !b->convex || (regions > 0)) {
/* Initialize a pool of viri to be used for holes, concavities, */ /* regional attributes, and/or regional area constraints. */
poolinit(&m->viri, sizeof(triangle *), VIRUSPERBLOCK, VIRUSPERBLOCK, 0);
}
if (!b->convex) {
/* Mark as infected any unprotected triangles on the boundary. */
/* This is one way by which concavities are created. */
infecthull(m, b);
}
if ((holes > 0) && !b->noholes) {
/* Infect each triangle in which a hole lies. */
for (i = 0; i < 2 * holes; i += 2) {
/* Ignore holes that aren't within the bounds of the mesh. */
if ((holelist[i] >= m->xmin) && (holelist[i] <= m->xmax)
&& (holelist[i + 1] >= m->ymin) && (holelist[i + 1] <= m->ymax)) {
/* Start searching from some triangle on the outer boundary. */
searchtri.tri = m->dummytri;
searchtri.orient = 0;
symself(searchtri);
/* Ensure that the hole is to the left of this boundary edge; */
/* otherwise, locate() will falsely report that the hole */
/* falls within the starting triangle. */
org(searchtri, searchorg);
dest(searchtri, searchdest);
if (counterclockwise(m, b, searchorg, searchdest, &holelist[i]) >
0.0) {
/* Find a triangle that contains the hole. */
intersect = locate(m, b, &holelist[i], &searchtri);
if ((intersect != OUTSIDE) && (!infected(searchtri))) {
/* Infect the triangle. This is done by marking the triangle */
/* as infected and including the triangle in the virus pool. */
infect(searchtri);
holetri = (triangle **) poolalloc(&m->viri);
*holetri = searchtri.tri;
}
}
}
}
}
/* Now, we have to find all the regions BEFORE we carve the holes, because */
/* locate() won't work when the triangulation is no longer convex. */
/* (Incidentally, this is the reason why regional attributes and area */
/* constraints can't be used when refining a preexisting mesh, which */
/* might not be convex; they can only be used with a freshly */
/* triangulated PSLG.) */
if (regions > 0) {
/* Find the starting triangle for each region. */
for (i = 0; i < regions; i++) {
regiontris[i].tri = m->dummytri;
/* Ignore region points that aren't within the bounds of the mesh. */
if ((regionlist[4 * i] >= m->xmin) && (regionlist[4 * i] <= m->xmax) &&
(regionlist[4 * i + 1] >= m->ymin) &&
(regionlist[4 * i + 1] <= m->ymax)) {
/* Start searching from some triangle on the outer boundary. */
searchtri.tri = m->dummytri;
searchtri.orient = 0;
symself(searchtri);
/* Ensure that the region point is to the left of this boundary */
/* edge; otherwise, locate() will falsely report that the */
/* region point falls within the starting triangle. */
org(searchtri, searchorg);
dest(searchtri, searchdest);
if (counterclockwise(m, b, searchorg, searchdest, ®ionlist[4 * i]) >
0.0) {
/* Find a triangle that contains the region point. */
intersect = locate(m, b, ®ionlist[4 * i], &searchtri);
if ((intersect != OUTSIDE) && (!infected(searchtri))) {
/* Record the triangle for processing after the */ /* holes have been carved. */
otricopy(searchtri, regiontris[i]);
}
}
}
}
}
if (m->viri.items > 0) {
/* Carve the holes and concavities. */
plague(m, b);
}
/* The virus pool should be empty now. */
if (regions > 0) {
if (!b->quiet) {
if (b->regionattrib) {
if (b->vararea) {
printf("Spreading regional attributes and area constraints.\n");
} else {
printf("Spreading regional attributes.\n");
}
} else {
printf("Spreading regional area constraints.\n");
}
}
if (b->regionattrib && !b->refine) {
/* Assign every triangle a regional attribute of zero. */
traversalinit(&m->triangles);
triangleloop.orient = 0;
triangleloop.tri = triangletraverse(m);
while (triangleloop.tri != (triangle *) NULL) {
setelemattribute(triangleloop, m->eextras, 0.0);
triangleloop.tri = triangletraverse(m);
}
}
for (i = 0; i < regions; i++) {
if (regiontris[i].tri != m->dummytri) {
/* Make sure the triangle under consideration still exists. */
/* It may have been eaten by the virus. */
if (!deadtri(regiontris[i].tri)) {
/* Put one triangle in the virus pool. */
infect(regiontris[i]);
regiontri = (triangle **) poolalloc(&m->viri);
*regiontri = regiontris[i].tri;
/* Apply one region's attribute and/or area constraint. */
regionplague(m, b, regionlist[4 * i + 2], regionlist[4 * i + 3]);
/* The virus pool should be empty now. */
}
}
}
if (b->regionattrib && !b->refine) {
/* Note the fact that each triangle has an additional attribute. */
m->eextras++;
}
}
/* Free up memory. */
if (((holes > 0) && !b->noholes) || !b->convex || (regions > 0)) {
pooldeinit(&m->viri);
}
if (regions > 0) {
trifree((VOID *) regiontris);
}
}
/** **/
/** **/
/********* Carving out holes and concavities ends here *********/
/********* Mesh quality maintenance begins here *********/
/** **/
/** **/
/*****************************************************************************/
/* */
/* tallyencs() Traverse the entire list of subsegments, and check each */
/* to see if it is encroached. If so, add it to the list. */
/* */
/*****************************************************************************/
#ifndef CDT_ONLY
#ifdef ANSI_DECLARATORS
void tallyencs(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
void tallyencs(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */
{
struct osub subsegloop;
int dummy;
traversalinit(&m->subsegs);
subsegloop.ssorient = 0;
subsegloop.ss = subsegtraverse(m);
while (subsegloop.ss != (subseg *) NULL) {
/* If the segment is encroached, add it to the list. */
dummy = checkseg4encroach(m, b, &subsegloop);
subsegloop.ss = subsegtraverse(m);
}
}
#endif /* not CDT_ONLY */
/*****************************************************************************/
/* */
/* precisionerror() Print an error message for precision problems. */
/* */
/*****************************************************************************/
#ifndef CDT_ONLY
void precisionerror()
{
printf("Try increasing the area criterion and/or reducing the minimum\n");
printf(" allowable angle so that tiny triangles are not created.\n");
#ifdef SINGLE
printf("Alternatively, try recompiling me with double precision\n");
printf(" arithmetic (by removing \"#define SINGLE\" from the\n");
printf(" source file or \"-DSINGLE\" from the makefile).\n");
#endif /* SINGLE */
}
#endif /* not CDT_ONLY */
/*****************************************************************************/
/* */
/* splitencsegs() Split all the encroached subsegments. */
/* */
/* Each encroached subsegment 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. */
/* */
/* `triflaws' is a flag that specifies whether one should take note of new */
/* bad triangles that result from inserting vertices to repair encroached */
/* subsegments. */
/* *//*****************************************************************************/
#ifndef CDT_ONLY
#ifdef ANSI_DECLARATORS
void splitencsegs(struct mesh *m, struct behavior *b, int triflaws)
#else /* not ANSI_DECLARATORS */
void splitencsegs(m, b, triflaws)
struct mesh *m;
struct behavior *b;
int triflaws;
#endif /* not ANSI_DECLARATORS */
{
struct otri enctri;
struct otri testtri;
struct osub testsh;
struct osub currentenc;
struct badsubseg *encloop;
vertex eorg, edest, eapex;
vertex newvertex;
enum insertvertexresult success;
REAL segmentlength, nearestpoweroftwo;
REAL split;
REAL multiplier, divisor;
int acuteorg, acuteorg2, acutedest, acutedest2;
int dummy;
int i;
triangle ptr; /* Temporary variable used by stpivot(). */
subseg sptr; /* Temporary variable used by snext(). */
/* Note that steinerleft == -1 if an unlimited number */
/* of Steiner points is allowed. */
while ((m->badsubsegs.items > 0) && (m->steinerleft != 0)) {
traversalinit(&m->badsubsegs);
encloop = badsubsegtraverse(m);
while ((encloop != (struct badsubseg *) NULL) && (m->steinerleft != 0)) {
sdecode(encloop->encsubseg, currentenc);
sorg(currentenc, eorg);
sdest(currentenc, edest);
/* Make sure that this segment is still the same segment it was */
/* when it was determined to be encroached. If the segment was */
/* enqueued multiple times (because several newly inserted */
/* vertices encroached it), it may have already been split. */
if (!deadsubseg(currentenc.ss) &&
(eorg == encloop->subsegorg) && (edest == encloop->subsegdest)) {
/* To decide where to split a segment, we need to know if the */
/* segment shares an endpoint with an adjacent segment. */
/* The concern is that, if we simply split every encroached */
/* segment in its center, two adjacent segments with a small */
/* angle between them might lead to an infinite loop; each */
/* vertex added to split one segment will encroach upon the */
/* other segment, which must then be split with a vertex that */
/* will encroach upon the first segment, and so on forever. */
/* To avoid this, imagine a set of concentric circles, whose */
/* radii are powers of two, about each segment endpoint. */
/* These concentric circles determine where the segment is */
/* split. (If both endpoints are shared with adjacent */
/* segments, split the segment in the middle, and apply the */
/* concentric circles for later splittings.) */
/* Is the origin shared with another segment? */
stpivot(currentenc, enctri);
lnext(enctri, testtri);
tspivot(testtri, testsh);
acuteorg = testsh.ss != m->dummysub;
/* Is the destination shared with another segment? */
lnextself(testtri);
tspivot(testtri, testsh);
acutedest = testsh.ss != m->dummysub;
/* If we're using Chew's algorithm (rather than Ruppert's) */
/* to define encroachment, delete free vertices from the */
/* subsegment's diametral circle. */
if (!b->conformdel && !acuteorg && !acutedest) {
apex(enctri, eapex);
while ((vertextype(eapex) == FREEVERTEX) &&
((eorg[0] - eapex[0]) * (edest[0] - eapex[0]) +
(eorg[1] - eapex[1]) * (edest[1] - eapex[1]) < 0.0)) {
deletevertex(m, b, &testtri);
stpivot(currentenc, enctri);
apex(enctri, eapex);
lprev(enctri, testtri);
}
}
/* Now, check the other side of the segment, if there's a triangle */
/* there. */
sym(enctri, testtri);
if (testtri.tri != m->dummytri) {
/* Is the destination shared with another segment? */
lnextself(testtri);
tspivot(testtri, testsh);
acutedest2 = testsh.ss != m->dummysub;
acutedest = acutedest || acutedest2;
/* Is the origin shared with another segment? */
lnextself(testtri);
tspivot(testtri, testsh);
acuteorg2 = testsh.ss != m->dummysub;
acuteorg = acuteorg || acuteorg2;
/* Delete free vertices from the subsegment's diametral circle. */
if (!b->conformdel && !acuteorg2 && !acutedest2) {
org(testtri, eapex);
while ((vertextype(eapex) == FREEVERTEX) &&
((eorg[0] - eapex[0]) * (edest[0] - eapex[0]) +
(eorg[1] - eapex[1]) * (edest[1] - eapex[1]) < 0.0)) {
deletevertex(m, b, &testtri);
sym(enctri, testtri);
apex(testtri, eapex);
lprevself(testtri);
}
}
}
/* Use the concentric circles if exactly one endpoint is shared */
/* with another adjacent segment. */
if (acuteorg || acutedest) {
segmentlength = sqrt((edest[0] - eorg[0]) * (edest[0] - eorg[0]) +
(edest[1] - eorg[1]) * (edest[1] - eorg[1]));
/* Find the power of two that most evenly splits the segment. */
/* The worst case is a 2:1 ratio between subsegment lengths. */
nearestpoweroftwo = 1.0;
while (segmentlength > 3.0 * nearestpoweroftwo) {
nearestpoweroftwo *= 2.0;
}
while (segmentlength < 1.5 * nearestpoweroftwo) {
nearestpoweroftwo *= 0.5;
}
/* Where do we split the segment? */
split = nearestpoweroftwo / segmentlength;
if (acutedest) {
split = 1.0 - split;
}
} else {
/* If we're not worried about adjacent segments, split */
/* this segment in the middle. */
split = 0.5;
}
/* Create the new vertex. */
newvertex = (vertex) poolalloc(&m->vertices);
/* Interpolate its coordinate and attributes. */
for (i = 0; i < 2 + m->nextras; i++) {
newvertex[i] = eorg[i] + split * (edest[i] - eorg[i]);
}
if (!b->noexact) {
/* Roundoff in the above calculation may yield a `newvertex' */
/* that is not precisely collinear with `eorg' and `edest'. */
/* Improve collinearity by one step of iterative refinement. */
multiplier = counterclockwise(m, b, eorg, edest, newvertex);
divisor = ((eorg[0] - edest[0]) * (eorg[0] - edest[0]) +
(eorg[1] - edest[1]) * (eorg[1] - edest[1]));
if ((multiplier != 0.0) && (divisor != 0.0)) {
multiplier = multiplier / divisor;
/* Watch out for NANs. */
if (multiplier == multiplier) {
newvertex[0] += multiplier * (edest[1] - eorg[1]);
newvertex[1] += multiplier * (eorg[0] - edest[0]);
}
}
}
setvertexmark(newvertex, mark(currentenc));
setvertextype(newvertex, SEGMENTVERTEX);
if (b->verbose > 1) {
printf(
" Splitting subsegment (%.12g, %.12g) (%.12g, %.12g) at (%.12g, %.12g).\n",
eorg[0], eorg[1], edest[0], edest[1],
newvertex[0], newvertex[1]);
}
/* Check whether the new vertex lies on an endpoint. */
if (((newvertex[0] == eorg[0]) && (newvertex[1] == eorg[1])) ||
((newvertex[0] == edest[0]) && (newvertex[1] == edest[1]))) {
printf("Error: Ran out of precision at (%.12g, %.12g).\n",
newvertex[0], newvertex[1]);
printf("I attempted to split a segment to a smaller size than\n");
printf(" can be accommodated by the finite precision of\n");
printf(" floating point arithmetic.\n");
precisionerror();
triexit(1);
}
/* Insert the splitting vertex. This should always succeed. */
success = insertvertex(m, b, newvertex, &enctri, ¤tenc,
1, triflaws);
if ((success != SUCCESSFULVERTEX) && (success != ENCROACHINGVERTEX)) {
printf("Internal error in splitencsegs():\n");
printf(" Failure to split a segment.\n");
internalerror();
}
if (m->steinerleft > 0) {
m->steinerleft--;
}
/* Check the two new subsegments to see if they're encroached. */
dummy = checkseg4encroach(m, b, ¤tenc);
snextself(currentenc);
dummy = checkseg4encroach(m, b, ¤tenc);
}
badsubsegdealloc(m, encloop);
encloop = badsubsegtraverse(m);
}
}
}
#endif /* not CDT_ONLY */
/*****************************************************************************/
/* *//* tallyfaces() Test every triangle in the mesh for quality measures. */
/* */
/*****************************************************************************/
#ifndef CDT_ONLY
#ifdef ANSI_DECLARATORS
void tallyfaces(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
void tallyfaces(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */
{
struct otri triangleloop;
if (b->verbose) {
printf(" Making a list of bad triangles.\n");
}
traversalinit(&m->triangles);
triangleloop.orient = 0;
triangleloop.tri = triangletraverse(m);
while (triangleloop.tri != (triangle *) NULL) {
/* If the triangle is bad, enqueue it. */
testtriangle(m, b, &triangleloop);
triangleloop.tri = triangletraverse(m);
}
}
#endif /* not CDT_ONLY */
/*****************************************************************************/
/* */
/* splittriangle() Inserts a vertex at the circumcenter of a triangle. */
/* Deletes the newly inserted vertex if it encroaches */
/* upon a segment. */
/* */
/*****************************************************************************/
#ifndef CDT_ONLY
#ifdef ANSI_DECLARATORS
void splittriangle(struct mesh *m, struct behavior *b,
struct badtriang *badtri)
#else /* not ANSI_DECLARATORS */
void splittriangle(m, b, badtri)
struct mesh *m;
struct behavior *b;
struct badtriang *badtri;
#endif /* not ANSI_DECLARATORS */
{
struct otri badotri;
vertex borg, bdest, bapex;
vertex newvertex;
REAL xi, eta;
enum insertvertexresult success;
int errorflag;
int i;
decode(badtri->poortri, badotri);
org(badotri, borg);
dest(badotri, bdest);
apex(badotri, bapex);
/* Make sure that this triangle is still the same triangle it was */
/* when it was tested and determined to be of bad quality. */
/* Subsequent transformations may have made it a different triangle. */
if (!deadtri(badotri.tri) && (borg == badtri->triangorg) &&
(bdest == badtri->triangdest) && (bapex == badtri->triangapex)) { if (b->verbose > 1) {
printf(" Splitting this triangle at its circumcenter:\n");
printf(" (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", borg[0],
borg[1], bdest[0], bdest[1], bapex[0], bapex[1]);
}
errorflag = 0;
/* Create a new vertex at the triangle's circumcenter. */
newvertex = (vertex) poolalloc(&m->vertices);
findcircumcenter(m, b, borg, bdest, bapex, newvertex, &xi, &eta, 1);
/* Check whether the new vertex lies on a triangle vertex. */
if (((newvertex[0] == borg[0]) && (newvertex[1] == borg[1])) ||
((newvertex[0] == bdest[0]) && (newvertex[1] == bdest[1])) ||
((newvertex[0] == bapex[0]) && (newvertex[1] == bapex[1]))) {
if (!b->quiet) {
printf(
"Warning: New vertex (%.12g, %.12g) falls on existing vertex.\n",
newvertex[0], newvertex[1]);
errorflag = 1;
}
vertexdealloc(m, newvertex);
} else {
for (i = 2; i < 2 + m->nextras; i++) {
/* Interpolate the vertex attributes at the circumcenter. */
newvertex[i] = borg[i] + xi * (bdest[i] - borg[i])
+ eta * (bapex[i] - borg[i]);
}
/* The new vertex must be in the interior, and therefore is a */
/* free vertex with a marker of zero. */
setvertexmark(newvertex, 0);
setvertextype(newvertex, FREEVERTEX);
/* Ensure that the handle `badotri' does not represent the longest */
/* edge of the triangle. This ensures that the circumcenter must */
/* fall to the left of this edge, so point location will work. */
/* (If the angle org-apex-dest exceeds 90 degrees, then the */
/* circumcenter lies outside the org-dest edge, and eta is */
/* negative. Roundoff error might prevent eta from being */
/* negative when it should be, so I test eta against xi.) */
if (eta < xi) {
lprevself(badotri);
}
/* Insert the circumcenter, searching from the edge of the triangle, */
/* and maintain the Delaunay property of the triangulation. */
success = insertvertex(m, b, newvertex, &badotri, (struct osub *) NULL,
1, 1);
if (success == SUCCESSFULVERTEX) {
if (m->steinerleft > 0) {
m->steinerleft--;
}
} else if (success == ENCROACHINGVERTEX) {
/* If the newly inserted vertex encroaches upon a subsegment, */
/* delete the new vertex. */
undovertex(m, b);
if (b->verbose > 1) {
printf(" Rejecting (%.12g, %.12g).\n", newvertex[0], newvertex[1]);
}
vertexdealloc(m, newvertex);
} else if (success == VIOLATINGVERTEX) {
/* Failed to insert the new vertex, but some subsegment was */
/* marked as being encroached. */
vertexdealloc(m, newvertex);
} else { /* success == DUPLICATEVERTEX */
/* Couldn't insert the new vertex because a vertex is already there. */
if (!b->quiet) {
printf(
"Warning: New vertex (%.12g, %.12g) falls on existing vertex.\n",
newvertex[0], newvertex[1]); errorflag = 1;
}
vertexdealloc(m, newvertex);
}
}
if (errorflag) {
if (b->verbose) {
printf(" The new vertex is at the circumcenter of triangle\n");
printf(" (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
borg[0], borg[1], bdest[0], bdest[1], bapex[0], bapex[1]);
}
printf("This probably means that I am trying to refine triangles\n");
printf(" to a smaller size than can be accommodated by the finite\n");
printf(" precision of floating point arithmetic. (You can be\n");
printf(" sure of this if I fail to terminate.)\n");
precisionerror();
}
}
}
#endif /* not CDT_ONLY */
/*****************************************************************************/
/* */
/* enforcequality() Remove all the encroached subsegments and bad */
/* triangles from the triangulation. */
/* */
/*****************************************************************************/
#ifndef CDT_ONLY
#ifdef ANSI_DECLARATORS
void enforcequality(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
void enforcequality(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */
{
struct badtriang *badtri;
int i;
if (!b->quiet) {
printf("Adding Steiner points to enforce quality.\n");
}
/* Initialize the pool of encroached subsegments. */
poolinit(&m->badsubsegs, sizeof(struct badsubseg), BADSUBSEGPERBLOCK,
BADSUBSEGPERBLOCK, 0);
if (b->verbose) {
printf(" Looking for encroached subsegments.\n");
}
/* Test all segments to see if they're encroached. */
tallyencs(m, b);
if (b->verbose && (m->badsubsegs.items > 0)) {
printf(" Splitting encroached subsegments.\n");
}
/* Fix encroached subsegments without noting bad triangles. */
splitencsegs(m, b, 0);
/* At this point, if we haven't run out of Steiner points, the */
/* triangulation should be (conforming) Delaunay. */
/* Next, we worry about enforcing triangle quality. */
if ((b->minangle > 0.0) || b->vararea || b->fixedarea || b->usertest) {
/* Initialize the pool of bad triangles. */
poolinit(&m->badtriangles, sizeof(struct badtriang), BADTRIPERBLOCK,
BADTRIPERBLOCK, 0);
/* Initialize the queues of bad triangles. */
for (i = 0; i < 4096; i++) {
m->queuefront[i] = (struct badtriang *) NULL; }
m->firstnonemptyq = -1;
/* Test all triangles to see if they're bad. */
tallyfaces(m, b);
/* Initialize the pool of recently flipped triangles. */
poolinit(&m->flipstackers, sizeof(struct flipstacker), FLIPSTACKERPERBLOCK,
FLIPSTACKERPERBLOCK, 0);
m->checkquality = 1;
if (b->verbose) {
printf(" Splitting bad triangles.\n");
}
while ((m->badtriangles.items > 0) && (m->steinerleft != 0)) {
/* Fix one bad triangle by inserting a vertex at its circumcenter. */
badtri = dequeuebadtriang(m);
splittriangle(m, b, badtri);
if (m->badsubsegs.items > 0) {
/* Put bad triangle back in queue for another try later. */
enqueuebadtriang(m, b, badtri);
/* Fix any encroached subsegments that resulted. */
/* Record any new bad triangles that result. */
splitencsegs(m, b, 1);
} else {
/* Return the bad triangle to the pool. */
pooldealloc(&m->badtriangles, (VOID *) badtri);
}
}
}
/* At this point, if the "-D" switch was selected and we haven't run out */
/* of Steiner points, the triangulation should be (conforming) Delaunay */
/* and have no low-quality triangles. */
/* Might we have run out of Steiner points too soon? */
if (!b->quiet && b->conformdel && (m->badsubsegs.items > 0) &&
(m->steinerleft == 0)) {
printf("\nWarning: I ran out of Steiner points, but the mesh has\n");
if (m->badsubsegs.items == 1) {
printf(" one encroached subsegment, and therefore might not be truly\n"
);
} else {
printf(" %ld encroached subsegments, and therefore might not be truly\n"
, m->badsubsegs.items);
}
printf(" Delaunay. If the Delaunay property is important to you,\n");
printf(" try increasing the number of Steiner points (controlled by\n");
printf(" the -S switch) slightly and try again.\n\n");
}
}
#endif /* not CDT_ONLY */
/** **/
/** **/
/********* Mesh quality maintenance ends here *********/
/*****************************************************************************/
/* */
/* highorder() Create extra nodes for quadratic subparametric elements. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
void highorder(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
void highorder(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */
{
struct otri triangleloop, trisym; struct osub checkmark;
vertex newvertex;
vertex torg, tdest;
int i;
triangle ptr; /* Temporary variable used by sym(). */
subseg sptr; /* Temporary variable used by tspivot(). */
if (!b->quiet) {
printf("Adding vertices for second-order triangles.\n");
}
/* 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. */
m->vertices.deaditemstack = (VOID *) NULL;
traversalinit(&m->triangles);
triangleloop.tri = triangletraverse(m);
/* To loop over the set of edges, loop over all triangles, and look at */
/* the three edges of each triangle. If there isn't another triangle */
/* adjacent to the edge, operate on the edge. If there is another */
/* adjacent triangle, operate on the edge only if the current triangle */
/* has a smaller pointer than its neighbor. This way, each edge is */
/* considered only once. */
while (triangleloop.tri != (triangle *) NULL) {
for (triangleloop.orient = 0; triangleloop.orient < 3;
triangleloop.orient++) {
sym(triangleloop, trisym);
if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) {
org(triangleloop, torg);
dest(triangleloop, tdest);
/* Create a new node in the middle of the edge. Interpolate */
/* its attributes. */
newvertex = (vertex) poolalloc(&m->vertices);
for (i = 0; i < 2 + m->nextras; i++) {
newvertex[i] = 0.5 * (torg[i] + tdest[i]);
}
/* Set the new node's marker to zero or one, depending on */
/* whether it lies on a boundary. */
setvertexmark(newvertex, trisym.tri == m->dummytri);
setvertextype(newvertex,
trisym.tri == m->dummytri ? FREEVERTEX : SEGMENTVERTEX);
if (b->usesegments) {
tspivot(triangleloop, checkmark);
/* If this edge is a segment, transfer the marker to the new node. */
if (checkmark.ss != m->dummysub) {
setvertexmark(newvertex, mark(checkmark));
setvertextype(newvertex, SEGMENTVERTEX);
}
}
if (b->verbose > 1) {
printf(" Creating (%.12g, %.12g).\n", newvertex[0], newvertex[1]);
}
/* Record the new node in the (one or two) adjacent elements. */
triangleloop.tri[m->highorderindex + triangleloop.orient] =
(triangle) newvertex;
if (trisym.tri != m->dummytri) {
trisym.tri[m->highorderindex + trisym.orient] = (triangle) newvertex;
}
}
}
triangleloop.tri = triangletraverse(m);
}
}
/********* File I/O routines begin here *********/
/** **/
/** **/
/*****************************************************************************/
/* */
/* readline() Read a nonempty line from a file. */
/* */
/* A line is considered "nonempty" if it contains something that looks like */
/* a number. Comments (prefaced by `#') are ignored. */
/* */
/*****************************************************************************/
#ifndef TRILIBRARY
#ifdef ANSI_DECLARATORS
char *readline(char *string, FILE *infile, char *infilename)
#else /* not ANSI_DECLARATORS */
char *readline(string, infile, infilename)
char *string;
FILE *infile;
char *infilename;
#endif /* not ANSI_DECLARATORS */
{
char *result;
/* Search for something that looks like a number. */
do {
result = fgets(string, INPUTLINESIZE, infile);
if (result == (char *) NULL) {
printf(" Error: Unexpected end of file in %s.\n", infilename);
triexit(1);
}
/* 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;
}
#endif /* not TRILIBRARY */
/*****************************************************************************/
/* */
/* findfield() Find the next field of a string. */
/* */
/* Jumps past the current field by searching for whitespace, then jumps */
/* past the whitespace to find the next field. */
/* */
/*****************************************************************************/
#ifndef TRILIBRARY
#ifdef ANSI_DECLARATORS
char *findfield(char *string)
#else /* not ANSI_DECLARATORS */
char *findfield(string)
char *string;
#endif /* not ANSI_DECLARATORS */
{
char *result;
result = string;
/* Skip the current field. Stop upon reaching whitespace. */
while ((*result != '\0') && (*result != '#')
&& (*result != ' ') && (*result != '\t')) {
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;
}
#endif /* not TRILIBRARY */
/*****************************************************************************/
/* */
/* readnodes() Read the vertices from a file, which may be a .node or */
/* .poly file. */
/* */
/*****************************************************************************/
#ifndef TRILIBRARY
#ifdef ANSI_DECLARATORS
void readnodes(struct mesh *m, struct behavior *b, char *nodefilename,
char *polyfilename, FILE **polyfile)
#else /* not ANSI_DECLARATORS */
void readnodes(m, b, nodefilename, polyfilename, polyfile)
struct mesh *m;
struct behavior *b;
char *nodefilename;
char *polyfilename;
FILE **polyfile;
#endif /* not ANSI_DECLARATORS */
{
FILE *infile;
vertex vertexloop;
char inputline[INPUTLINESIZE];
char *stringptr;
char *infilename;
REAL x, y;
int firstnode;
int nodemarkers;
int currentmarker;
int i, j;
if (b->poly) {
/* Read the vertices from a .poly file. */
if (!b->quiet) {
printf("Opening %s.\n", polyfilename);
}
*polyfile = fopen(polyfilename, "r");
if (*polyfile == (FILE *) NULL) {
printf(" Error: Cannot access file %s.\n", polyfilename);
triexit(1);
}
/* Read number of vertices, number of dimensions, number of vertex */
/* attributes, and number of boundary markers. */
stringptr = readline(inputline, *polyfile, polyfilename);
m->invertices = (int) strtol(stringptr, &stringptr, 0);
stringptr = findfield(stringptr);
if (*stringptr == '\0') {
m->mesh_dim = 2;
} else {
m->mesh_dim = (int) strtol(stringptr, &stringptr, 0);
} stringptr = findfield(stringptr);
if (*stringptr == '\0') {
m->nextras = 0;
} else {
m->nextras = (int) strtol(stringptr, &stringptr, 0);
}
stringptr = findfield(stringptr);
if (*stringptr == '\0') {
nodemarkers = 0;
} else {
nodemarkers = (int) strtol(stringptr, &stringptr, 0);
}
if (m->invertices > 0) {
infile = *polyfile;
infilename = polyfilename;
m->readnodefile = 0;
} else {
/* If the .poly file claims there are zero vertices, that means that */
/* the vertices should be read from a separate .node file. */
m->readnodefile = 1;
infilename = nodefilename;
}
} else {
m->readnodefile = 1;
infilename = nodefilename;
*polyfile = (FILE *) NULL;
}
if (m->readnodefile) {
/* Read the vertices from a .node file. */
if (!b->quiet) {
printf("Opening %s.\n", nodefilename);
}
infile = fopen(nodefilename, "r");
if (infile == (FILE *) NULL) {
printf(" Error: Cannot access file %s.\n", nodefilename);
triexit(1);
}
/* Read number of vertices, number of dimensions, number of vertex */
/* attributes, and number of boundary markers. */
stringptr = readline(inputline, infile, nodefilename);
m->invertices = (int) strtol(stringptr, &stringptr, 0);
stringptr = findfield(stringptr);
if (*stringptr == '\0') {
m->mesh_dim = 2;
} else {
m->mesh_dim = (int) strtol(stringptr, &stringptr, 0);
}
stringptr = findfield(stringptr);
if (*stringptr == '\0') {
m->nextras = 0;
} else {
m->nextras = (int) strtol(stringptr, &stringptr, 0);
}
stringptr = findfield(stringptr);
if (*stringptr == '\0') {
nodemarkers = 0;
} else {
nodemarkers = (int) strtol(stringptr, &stringptr, 0);
}
}
if (m->invertices < 3) {
printf("Error: Input must have at least three input vertices.\n");
triexit(1);
}
if (m->mesh_dim != 2) {
printf("Error: Triangle only works with two-dimensional meshes.\n");
triexit(1);
} if (m->nextras == 0) {
b->weighted = 0;
}
initializevertexpool(m, b);
/* Read the vertices. */
for (i = 0; i < m->invertices; i++) {
vertexloop = (vertex) poolalloc(&m->vertices);
stringptr = readline(inputline, infile, infilename);
if (i == 0) {
firstnode = (int) strtol(stringptr, &stringptr, 0);
if ((firstnode == 0) || (firstnode == 1)) {
b->firstnumber = firstnode;
}
}
stringptr = findfield(stringptr);
if (*stringptr == '\0') {
printf("Error: Vertex %d has no x coordinate.\n", b->firstnumber + i);
triexit(1);
}
x = (REAL) strtod(stringptr, &stringptr);
stringptr = findfield(stringptr);
if (*stringptr == '\0') {
printf("Error: Vertex %d has no y coordinate.\n", b->firstnumber + i);
triexit(1);
}
y = (REAL) strtod(stringptr, &stringptr);
vertexloop[0] = x;
vertexloop[1] = y;
/* Read the vertex attributes. */
for (j = 2; j < 2 + m->nextras; j++) {
stringptr = findfield(stringptr);
if (*stringptr == '\0') {
vertexloop[j] = 0.0;
} else {
vertexloop[j] = (REAL) strtod(stringptr, &stringptr);
}
}
if (nodemarkers) {
/* Read a vertex marker. */
stringptr = findfield(stringptr);
if (*stringptr == '\0') {
setvertexmark(vertexloop, 0);
} else {
currentmarker = (int) strtol(stringptr, &stringptr, 0);
setvertexmark(vertexloop, currentmarker);
}
} else {
/* If no markers are specified in the file, they default to zero. */
setvertexmark(vertexloop, 0);
}
setvertextype(vertexloop, INPUTVERTEX);
/* Determine the smallest and largest x and y coordinates. */
if (i == 0) {
m->xmin = m->xmax = x;
m->ymin = m->ymax = y;
} else {
m->xmin = (x < m->xmin) ? x : m->xmin;
m->xmax = (x > m->xmax) ? x : m->xmax;
m->ymin = (y < m->ymin) ? y : m->ymin;
m->ymax = (y > m->ymax) ? y : m->ymax;
}
}
if (m->readnodefile) {
fclose(infile);
}
/* Nonexistent x value used as a flag to mark circle events in sweepline */
/* Delaunay algorithm. */ m->xminextreme = 10 * m->xmin - 9 * m->xmax;
}
#endif /* not TRILIBRARY */
/*****************************************************************************/
/* */
/* transfernodes() Read the vertices from memory. */
/* */
/*****************************************************************************/
#ifdef TRILIBRARY
#ifdef ANSI_DECLARATORS
void transfernodes(struct mesh *m, struct behavior *b, REAL *pointlist,
REAL *pointattriblist, int *pointmarkerlist,
int numberofpoints, int numberofpointattribs)
#else /* not ANSI_DECLARATORS */
void transfernodes(m, b, pointlist, pointattriblist, pointmarkerlist,
numberofpoints, numberofpointattribs)
struct mesh *m;
struct behavior *b;
REAL *pointlist;
REAL *pointattriblist;
int *pointmarkerlist;
int numberofpoints;
int numberofpointattribs;
#endif /* not ANSI_DECLARATORS */
{
vertex vertexloop;
REAL x, y;
int i, j;
int coordindex;
int attribindex;
m->invertices = numberofpoints;
m->mesh_dim = 2;
m->nextras = numberofpointattribs;
m->readnodefile = 0;
if (m->invertices < 3) {
printf("Error: Input must have at least three input vertices.\n");
triexit(1);
}
if (m->nextras == 0) {
b->weighted = 0;
}
initializevertexpool(m, b);
/* Read the vertices. */
coordindex = 0;
attribindex = 0;
for (i = 0; i < m->invertices; i++) {
vertexloop = (vertex) poolalloc(&m->vertices);
/* Read the vertex coordinates. */
x = vertexloop[0] = pointlist[coordindex++];
y = vertexloop[1] = pointlist[coordindex++];
/* Read the vertex attributes. */
for (j = 0; j < numberofpointattribs; j++) {
vertexloop[2 + j] = pointattriblist[attribindex++];
}
if (pointmarkerlist != (int *) NULL) {
/* Read a vertex marker. */
setvertexmark(vertexloop, pointmarkerlist[i]);
} else {
/* If no markers are specified, they default to zero. */
setvertexmark(vertexloop, 0);
}
setvertextype(vertexloop, INPUTVERTEX); /* Determine the smallest and largest x and y coordinates. */
if (i == 0) {
m->xmin = m->xmax = x;
m->ymin = m->ymax = y;
} else {
m->xmin = (x < m->xmin) ? x : m->xmin;
m->xmax = (x > m->xmax) ? x : m->xmax;
m->ymin = (y < m->ymin) ? y : m->ymin;
m->ymax = (y > m->ymax) ? y : m->ymax;
}
}
/* Nonexistent x value used as a flag to mark circle events in sweepline */
/* Delaunay algorithm. */
m->xminextreme = 10 * m->xmin - 9 * m->xmax;
}
#endif /* TRILIBRARY */
/*****************************************************************************/
/* */
/* readholes() Read the holes, and possibly regional attributes and area */
/* constraints, from a .poly file. */
/* */
/*****************************************************************************/
#ifndef TRILIBRARY
#ifdef ANSI_DECLARATORS
void readholes(struct mesh *m, struct behavior *b,
FILE *polyfile, char *polyfilename, REAL **hlist, int *holes,
REAL **rlist, int *regions)
#else /* not ANSI_DECLARATORS */
void readholes(m, b, polyfile, polyfilename, hlist, holes, rlist, regions)
struct mesh *m;
struct behavior *b;
FILE *polyfile;
char *polyfilename;
REAL **hlist;
int *holes;
REAL **rlist;
int *regions;
#endif /* not ANSI_DECLARATORS */
{
REAL *holelist;
REAL *regionlist;
char inputline[INPUTLINESIZE];
char *stringptr;
int index;
int i;
/* Read the holes. */
stringptr = readline(inputline, polyfile, polyfilename);
*holes = (int) strtol(stringptr, &stringptr, 0);
if (*holes > 0) {
holelist = (REAL *) trimalloc(2 * *holes * (int) sizeof(REAL));
*hlist = holelist;
for (i = 0; i < 2 * *holes; i += 2) {
stringptr = readline(inputline, polyfile, polyfilename);
stringptr = findfield(stringptr);
if (*stringptr == '\0') {
printf("Error: Hole %d has no x coordinate.\n",
b->firstnumber + (i >> 1));
triexit(1);
} else {
holelist[i] = (REAL) strtod(stringptr, &stringptr);
}
stringptr = findfield(stringptr);
if (*stringptr == '\0') { printf("Error: Hole %d has no y coordinate.\n",
b->firstnumber + (i >> 1));
triexit(1);
} else {
holelist[i + 1] = (REAL) strtod(stringptr, &stringptr);
}
}
} else {
*hlist = (REAL *) NULL;
}
#ifndef CDT_ONLY
if ((b->regionattrib || b->vararea) && !b->refine) {
/* Read the area constraints. */
stringptr = readline(inputline, polyfile, polyfilename);
*regions = (int) strtol(stringptr, &stringptr, 0);
if (*regions > 0) {
regionlist = (REAL *) trimalloc(4 * *regions * (int) sizeof(REAL));
*rlist = regionlist;
index = 0;
for (i = 0; i < *regions; i++) {
stringptr = readline(inputline, polyfile, polyfilename);
stringptr = findfield(stringptr);
if (*stringptr == '\0') {
printf("Error: Region %d has no x coordinate.\n",
b->firstnumber + i);
triexit(1);
} else {
regionlist[index++] = (REAL) strtod(stringptr, &stringptr);
}
stringptr = findfield(stringptr);
if (*stringptr == '\0') {
printf("Error: Region %d has no y coordinate.\n",
b->firstnumber + i);
triexit(1);
} else {
regionlist[index++] = (REAL) strtod(stringptr, &stringptr);
}
stringptr = findfield(stringptr);
if (*stringptr == '\0') {
printf(
"Error: Region %d has no region attribute or area constraint.\n",
b->firstnumber + i);
triexit(1);
} else {
regionlist[index++] = (REAL) strtod(stringptr, &stringptr);
}
stringptr = findfield(stringptr);
if (*stringptr == '\0') {
regionlist[index] = regionlist[index - 1];
} else {
regionlist[index] = (REAL) strtod(stringptr, &stringptr);
}
index++;
}
}
} else {
/* Set `*regions' to zero to avoid an accidental free() later. */
*regions = 0;
*rlist = (REAL *) NULL;
}
#endif /* not CDT_ONLY */
fclose(polyfile);
}
#endif /* not TRILIBRARY */
/*****************************************************************************/
/* *//* finishfile() Write the command line to the output file so the user */
/* can remember how the file was generated. Close the file. */
/* */
/*****************************************************************************/
#ifndef TRILIBRARY
#ifdef ANSI_DECLARATORS
void finishfile(FILE *outfile, int argc, char **argv)
#else /* not ANSI_DECLARATORS */
void finishfile(outfile, argc, argv)
FILE *outfile;
int argc;
char **argv;
#endif /* not ANSI_DECLARATORS */
{
int i;
fprintf(outfile, "# Generated by");
for (i = 0; i < argc; i++) {
fprintf(outfile, " ");
fputs(argv[i], outfile);
}
fprintf(outfile, "\n");
fclose(outfile);
}
#endif /* not TRILIBRARY */
/*****************************************************************************/
/* */
/* writenodes() Number the vertices and write them to a .node file. */
/* */
/* To save memory, the vertex numbers are written over the boundary markers */
/* after the vertices are written to a file. */
/* */
/*****************************************************************************/
#ifdef TRILIBRARY
#ifdef ANSI_DECLARATORS
void writenodes(struct mesh *m, struct behavior *b, REAL **pointlist,
REAL **pointattriblist, int **pointmarkerlist)
#else /* not ANSI_DECLARATORS */
void writenodes(m, b, pointlist, pointattriblist, pointmarkerlist)
struct mesh *m;
struct behavior *b;
REAL **pointlist;
REAL **pointattriblist;
int **pointmarkerlist;
#endif /* not ANSI_DECLARATORS */
#else /* not TRILIBRARY */
#ifdef ANSI_DECLARATORS
void writenodes(struct mesh *m, struct behavior *b, char *nodefilename,
int argc, char **argv)
#else /* not ANSI_DECLARATORS */
void writenodes(m, b, nodefilename, argc, argv)
struct mesh *m;
struct behavior *b;
char *nodefilename;
int argc;
char **argv;
#endif /* not ANSI_DECLARATORS */
#endif /* not TRILIBRARY */
{#ifdef TRILIBRARY
REAL *plist;
REAL *palist;
int *pmlist;
int coordindex;
int attribindex;
#else /* not TRILIBRARY */
FILE *outfile;
#endif /* not TRILIBRARY */
vertex vertexloop;
long outvertices;
int vertexnumber;
int i;
if (b->jettison) {
outvertices = m->vertices.items - m->undeads;
} else {
outvertices = m->vertices.items;
}
#ifdef TRILIBRARY
if (!b->quiet) {
printf("Writing vertices.\n");
}
/* Allocate memory for output vertices if necessary. */
if (*pointlist == (REAL *) NULL) {
*pointlist = (REAL *) trimalloc((int) (outvertices * 2 * sizeof(REAL)));
}
/* Allocate memory for output vertex attributes if necessary. */
if ((m->nextras > 0) && (*pointattriblist == (REAL *) NULL)) {
*pointattriblist = (REAL *) trimalloc((int) (outvertices * m->nextras *
sizeof(REAL)));
}
/* Allocate memory for output vertex markers if necessary. */
if (!b->nobound && (*pointmarkerlist == (int *) NULL)) {
*pointmarkerlist = (int *) trimalloc((int) (outvertices * sizeof(int)));
}
plist = *pointlist;
palist = *pointattriblist;
pmlist = *pointmarkerlist;
coordindex = 0;
attribindex = 0;
#else /* not TRILIBRARY */
if (!b->quiet) {
printf("Writing %s.\n", nodefilename);
}
outfile = fopen(nodefilename, "w");
if (outfile == (FILE *) NULL) {
printf(" Error: Cannot create file %s.\n", nodefilename);
triexit(1);
}
/* Number of vertices, number of dimensions, number of vertex attributes, */
/* and number of boundary markers (zero or one). */
fprintf(outfile, "%ld %d %d %d\n", outvertices, m->mesh_dim,
m->nextras, 1 - b->nobound);
#endif /* not TRILIBRARY */
traversalinit(&m->vertices);
vertexnumber = b->firstnumber;
vertexloop = vertextraverse(m);
while (vertexloop != (vertex) NULL) {
if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) {
#ifdef TRILIBRARY
/* X and y coordinates. */
plist[coordindex++] = vertexloop[0];
plist[coordindex++] = vertexloop[1];
/* Vertex attributes. */
for (i = 0; i < m->nextras; i++) {
palist[attribindex++] = vertexloop[2 + i];
} if (!b->nobound) {
/* Copy the boundary marker. */
pmlist[vertexnumber - b->firstnumber] = vertexmark(vertexloop);
}
#else /* not TRILIBRARY */
/* Vertex number, x and y coordinates. */
fprintf(outfile, "%4d %.17g %.17g", vertexnumber, vertexloop[0],
vertexloop[1]);
for (i = 0; i < m->nextras; i++) {
/* Write an attribute. */
fprintf(outfile, " %.17g", vertexloop[i + 2]);
}
if (b->nobound) {
fprintf(outfile, "\n");
} else {
/* Write the boundary marker. */
fprintf(outfile, " %d\n", vertexmark(vertexloop));
}
#endif /* not TRILIBRARY */
setvertexmark(vertexloop, vertexnumber);
vertexnumber++;
}
vertexloop = vertextraverse(m);
}
#ifndef TRILIBRARY
finishfile(outfile, argc, argv);
#endif /* not TRILIBRARY */
}
/*****************************************************************************/
/* */
/* numbernodes() Number the vertices. */
/* */
/* Each vertex is assigned a marker equal to its number. */
/* */
/* Used when writenodes() is not called because no .node file is written. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
void numbernodes(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
void numbernodes(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */
{
vertex vertexloop;
int vertexnumber;
traversalinit(&m->vertices);
vertexnumber = b->firstnumber;
vertexloop = vertextraverse(m);
while (vertexloop != (vertex) NULL) {
setvertexmark(vertexloop, vertexnumber);
if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) {
vertexnumber++;
}
vertexloop = vertextraverse(m);
}
}
/*****************************************************************************/
/* */
/* writeelements() Write the triangles to an .ele file. */
/* */
/*****************************************************************************/
#ifdef TRILIBRARY
#ifdef ANSI_DECLARATORS
void writeelements(struct mesh *m, struct behavior *b,
int **trianglelist, REAL **triangleattriblist)
#else /* not ANSI_DECLARATORS */
void writeelements(m, b, trianglelist, triangleattriblist)
struct mesh *m;
struct behavior *b;
int **trianglelist;
REAL **triangleattriblist;
#endif /* not ANSI_DECLARATORS */
#else /* not TRILIBRARY */
#ifdef ANSI_DECLARATORS
void writeelements(struct mesh *m, struct behavior *b, char *elefilename,
int argc, char **argv)
#else /* not ANSI_DECLARATORS */
void writeelements(m, b, elefilename, argc, argv)
struct mesh *m;
struct behavior *b;
char *elefilename;
int argc;
char **argv;
#endif /* not ANSI_DECLARATORS */
#endif /* not TRILIBRARY */
{
#ifdef TRILIBRARY
int *tlist;
REAL *talist;
int vertexindex;
int attribindex;
#else /* not TRILIBRARY */
FILE *outfile;
#endif /* not TRILIBRARY */
struct otri triangleloop;
vertex p1, p2, p3;
vertex mid1, mid2, mid3;
long elementnumber;
int i;
#ifdef TRILIBRARY
if (!b->quiet) {
printf("Writing triangles.\n");
}
/* Allocate memory for output triangles if necessary. */
if (*trianglelist == (int *) NULL) {
*trianglelist = (int *) trimalloc((int) (m->triangles.items *
((b->order + 1) * (b->order + 2) /
2) * sizeof(int)));
}
/* Allocate memory for output triangle attributes if necessary. */
if ((m->eextras > 0) && (*triangleattriblist == (REAL *) NULL)) {
*triangleattriblist = (REAL *) trimalloc((int) (m->triangles.items *
m->eextras *
sizeof(REAL)));
}
tlist = *trianglelist;
talist = *triangleattriblist;
vertexindex = 0;
attribindex = 0;
#else /* not TRILIBRARY */
if (!b->quiet) {
printf("Writing %s.\n", elefilename);
}
outfile = fopen(elefilename, "w"); if (outfile == (FILE *) NULL) {
printf(" Error: Cannot create file %s.\n", elefilename);
triexit(1);
}
/* Number of triangles, vertices per triangle, attributes per triangle. */
fprintf(outfile, "%ld %d %d\n", m->triangles.items,
(b->order + 1) * (b->order + 2) / 2, m->eextras);
#endif /* not TRILIBRARY */
traversalinit(&m->triangles);
triangleloop.tri = triangletraverse(m);
triangleloop.orient = 0;
elementnumber = b->firstnumber;
while (triangleloop.tri != (triangle *) NULL) {
org(triangleloop, p1);
dest(triangleloop, p2);
apex(triangleloop, p3);
if (b->order == 1) {
#ifdef TRILIBRARY
tlist[vertexindex++] = vertexmark(p1);
tlist[vertexindex++] = vertexmark(p2);
tlist[vertexindex++] = vertexmark(p3);
#else /* not TRILIBRARY */
/* Triangle number, indices for three vertices. */
fprintf(outfile, "%4ld %4d %4d %4d", elementnumber,
vertexmark(p1), vertexmark(p2), vertexmark(p3));
#endif /* not TRILIBRARY */
} else {
mid1 = (vertex) triangleloop.tri[m->highorderindex + 1];
mid2 = (vertex) triangleloop.tri[m->highorderindex + 2];
mid3 = (vertex) triangleloop.tri[m->highorderindex];
#ifdef TRILIBRARY
tlist[vertexindex++] = vertexmark(p1);
tlist[vertexindex++] = vertexmark(p2);
tlist[vertexindex++] = vertexmark(p3);
tlist[vertexindex++] = vertexmark(mid1);
tlist[vertexindex++] = vertexmark(mid2);
tlist[vertexindex++] = vertexmark(mid3);
#else /* not TRILIBRARY */
/* Triangle number, indices for six vertices. */
fprintf(outfile, "%4ld %4d %4d %4d %4d %4d %4d", elementnumber,
vertexmark(p1), vertexmark(p2), vertexmark(p3), vertexmark(mid1),
vertexmark(mid2), vertexmark(mid3));
#endif /* not TRILIBRARY */
}
#ifdef TRILIBRARY
for (i = 0; i < m->eextras; i++) {
talist[attribindex++] = elemattribute(triangleloop, i);
}
#else /* not TRILIBRARY */
for (i = 0; i < m->eextras; i++) {
fprintf(outfile, " %.17g", elemattribute(triangleloop, i));
}
fprintf(outfile, "\n");
#endif /* not TRILIBRARY */
triangleloop.tri = triangletraverse(m);
elementnumber++;
}
#ifndef TRILIBRARY
finishfile(outfile, argc, argv);
#endif /* not TRILIBRARY */
}
/*****************************************************************************/
/* */
/* writepoly() Write the segments and holes to a .poly file. */
/* *//*****************************************************************************/
#ifdef TRILIBRARY
#ifdef ANSI_DECLARATORS
void writepoly(struct mesh *m, struct behavior *b,
int **segmentlist, int **segmentmarkerlist)
#else /* not ANSI_DECLARATORS */
void writepoly(m, b, segmentlist, segmentmarkerlist)
struct mesh *m;
struct behavior *b;
int **segmentlist;
int **segmentmarkerlist;
#endif /* not ANSI_DECLARATORS */
#else /* not TRILIBRARY */
#ifdef ANSI_DECLARATORS
void writepoly(struct mesh *m, struct behavior *b, char *polyfilename,
REAL *holelist, int holes, REAL *regionlist, int regions,
int argc, char **argv)
#else /* not ANSI_DECLARATORS */
void writepoly(m, b, polyfilename, holelist, holes, regionlist, regions,
argc, argv)
struct mesh *m;
struct behavior *b;
char *polyfilename;
REAL *holelist;
int holes;
REAL *regionlist;
int regions;
int argc;
char **argv;
#endif /* not ANSI_DECLARATORS */
#endif /* not TRILIBRARY */
{
#ifdef TRILIBRARY
int *slist;
int *smlist;
int index;
#else /* not TRILIBRARY */
FILE *outfile;
long holenumber, regionnumber;
#endif /* not TRILIBRARY */
struct osub subsegloop;
vertex endpoint1, endpoint2;
long subsegnumber;
#ifdef TRILIBRARY
if (!b->quiet) {
printf("Writing segments.\n");
}
/* Allocate memory for output segments if necessary. */
if (*segmentlist == (int *) NULL) {
*segmentlist = (int *) trimalloc((int) (m->subsegs.items * 2 *
sizeof(int)));
}
/* Allocate memory for output segment markers if necessary. */
if (!b->nobound && (*segmentmarkerlist == (int *) NULL)) {
*segmentmarkerlist = (int *) trimalloc((int) (m->subsegs.items *
sizeof(int)));
}
slist = *segmentlist;
smlist = *segmentmarkerlist;
index = 0;
#else /* not TRILIBRARY */
if (!b->quiet) {
printf("Writing %s.\n", polyfilename); }
outfile = fopen(polyfilename, "w");
if (outfile == (FILE *) NULL) {
printf(" Error: Cannot create file %s.\n", polyfilename);
triexit(1);
}
/* 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(outfile, "%d %d %d %d\n", 0, m->mesh_dim, m->nextras,
1 - b->nobound);
/* Number of segments, number of boundary markers (zero or one). */
fprintf(outfile, "%ld %d\n", m->subsegs.items, 1 - b->nobound);
#endif /* not TRILIBRARY */
traversalinit(&m->subsegs);
subsegloop.ss = subsegtraverse(m);
subsegloop.ssorient = 0;
subsegnumber = b->firstnumber;
while (subsegloop.ss != (subseg *) NULL) {
sorg(subsegloop, endpoint1);
sdest(subsegloop, endpoint2);
#ifdef TRILIBRARY
/* Copy indices of the segment's two endpoints. */
slist[index++] = vertexmark(endpoint1);
slist[index++] = vertexmark(endpoint2);
if (!b->nobound) {
/* Copy the boundary marker. */
smlist[subsegnumber - b->firstnumber] = mark(subsegloop);
}
#else /* not TRILIBRARY */
/* Segment number, indices of its two endpoints, and possibly a marker. */
if (b->nobound) {
fprintf(outfile, "%4ld %4d %4d\n", subsegnumber,
vertexmark(endpoint1), vertexmark(endpoint2));
} else {
fprintf(outfile, "%4ld %4d %4d %4d\n", subsegnumber,
vertexmark(endpoint1), vertexmark(endpoint2), mark(subsegloop));
}
#endif /* not TRILIBRARY */
subsegloop.ss = subsegtraverse(m);
subsegnumber++;
}
#ifndef TRILIBRARY
#ifndef CDT_ONLY
fprintf(outfile, "%d\n", holes);
if (holes > 0) {
for (holenumber = 0; holenumber < holes; holenumber++) {
/* Hole number, x and y coordinates. */
fprintf(outfile, "%4ld %.17g %.17g\n", b->firstnumber + holenumber,
holelist[2 * holenumber], holelist[2 * holenumber + 1]);
}
}
if (regions > 0) {
fprintf(outfile, "%d\n", regions);
for (regionnumber = 0; regionnumber < regions; regionnumber++) {
/* Region number, x and y coordinates, attribute, maximum area. */
fprintf(outfile, "%4ld %.17g %.17g %.17g %.17g\n",
b->firstnumber + regionnumber,
regionlist[4 * regionnumber], regionlist[4 * regionnumber + 1],
regionlist[4 * regionnumber + 2],
regionlist[4 * regionnumber + 3]);
}
}
#endif /* not CDT_ONLY */
finishfile(outfile, argc, argv);
#endif /* not TRILIBRARY */}
/*****************************************************************************/
/* */
/* writeedges() Write the edges to an .edge file. */
/* */
/*****************************************************************************/
#ifdef TRILIBRARY
#ifdef ANSI_DECLARATORS
void writeedges(struct mesh *m, struct behavior *b,
int **edgelist, int **edgemarkerlist)
#else /* not ANSI_DECLARATORS */
void writeedges(m, b, edgelist, edgemarkerlist)
struct mesh *m;
struct behavior *b;
int **edgelist;
int **edgemarkerlist;
#endif /* not ANSI_DECLARATORS */
#else /* not TRILIBRARY */
#ifdef ANSI_DECLARATORS
void writeedges(struct mesh *m, struct behavior *b, char *edgefilename,
int argc, char **argv)
#else /* not ANSI_DECLARATORS */
void writeedges(m, b, edgefilename, argc, argv)
struct mesh *m;
struct behavior *b;
char *edgefilename;
int argc;
char **argv;
#endif /* not ANSI_DECLARATORS */
#endif /* not TRILIBRARY */
{
#ifdef TRILIBRARY
int *elist;
int *emlist;
int index;
#else /* not TRILIBRARY */
FILE *outfile;
#endif /* not TRILIBRARY */
struct otri triangleloop, trisym;
struct osub checkmark;
vertex p1, p2;
long edgenumber;
triangle ptr; /* Temporary variable used by sym(). */
subseg sptr; /* Temporary variable used by tspivot(). */
#ifdef TRILIBRARY
if (!b->quiet) {
printf("Writing edges.\n");
}
/* Allocate memory for edges if necessary. */
if (*edgelist == (int *) NULL) {
*edgelist = (int *) trimalloc((int) (m->edges * 2 * sizeof(int)));
}
/* Allocate memory for edge markers if necessary. */
if (!b->nobound && (*edgemarkerlist == (int *) NULL)) {
*edgemarkerlist = (int *) trimalloc((int) (m->edges * sizeof(int)));
}
elist = *edgelist;
emlist = *edgemarkerlist;
index = 0;
#else /* not TRILIBRARY */
if (!b->quiet) {
printf("Writing %s.\n", edgefilename); }
outfile = fopen(edgefilename, "w");
if (outfile == (FILE *) NULL) {
printf(" Error: Cannot create file %s.\n", edgefilename);
triexit(1);
}
/* Number of edges, number of boundary markers (zero or one). */
fprintf(outfile, "%ld %d\n", m->edges, 1 - b->nobound);
#endif /* not TRILIBRARY */
traversalinit(&m->triangles);
triangleloop.tri = triangletraverse(m);
edgenumber = b->firstnumber;
/* To loop over the set of edges, loop over all triangles, and look at */
/* the three edges of each triangle. If there isn't another triangle */
/* adjacent to the edge, operate on the edge. If there is another */
/* adjacent triangle, operate on the edge only if the current triangle */
/* has a smaller pointer than its neighbor. This way, each edge is */
/* considered only once. */
while (triangleloop.tri != (triangle *) NULL) {
for (triangleloop.orient = 0; triangleloop.orient < 3;
triangleloop.orient++) {
sym(triangleloop, trisym);
if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) {
org(triangleloop, p1);
dest(triangleloop, p2);
#ifdef TRILIBRARY
elist[index++] = vertexmark(p1);
elist[index++] = vertexmark(p2);
#endif /* TRILIBRARY */
if (b->nobound) {
#ifndef TRILIBRARY
/* Edge number, indices of two endpoints. */
fprintf(outfile, "%4ld %d %d\n", edgenumber,
vertexmark(p1), vertexmark(p2));
#endif /* not TRILIBRARY */
} else {
/* Edge number, indices of two endpoints, and a boundary marker. */
/* If there's no subsegment, the boundary marker is zero. */
if (b->usesegments) {
tspivot(triangleloop, checkmark);
if (checkmark.ss == m->dummysub) {
#ifdef TRILIBRARY
emlist[edgenumber - b->firstnumber] = 0;
#else /* not TRILIBRARY */
fprintf(outfile, "%4ld %d %d %d\n", edgenumber,
vertexmark(p1), vertexmark(p2), 0);
#endif /* not TRILIBRARY */
} else {
#ifdef TRILIBRARY
emlist[edgenumber - b->firstnumber] = mark(checkmark);
#else /* not TRILIBRARY */
fprintf(outfile, "%4ld %d %d %d\n", edgenumber,
vertexmark(p1), vertexmark(p2), mark(checkmark));
#endif /* not TRILIBRARY */
}
} else {
#ifdef TRILIBRARY
emlist[edgenumber - b->firstnumber] = trisym.tri == m->dummytri;
#else /* not TRILIBRARY */
fprintf(outfile, "%4ld %d %d %d\n", edgenumber,
vertexmark(p1), vertexmark(p2), trisym.tri == m->dummytri);
#endif /* not TRILIBRARY */
}
}
edgenumber++;
}
}
triangleloop.tri = triangletraverse(m);
}
#ifndef TRILIBRARY
finishfile(outfile, argc, argv);
#endif /* not TRILIBRARY */
}
/*****************************************************************************/
/* */
/* writevoronoi() Write the Voronoi diagram to a .v.node and .v.edge */
/* file. */
/* */
/* The Voronoi diagram is the geometric dual of the Delaunay triangulation. */
/* Hence, the Voronoi vertices are listed by traversing the Delaunay */
/* triangles, and the Voronoi edges are listed by traversing the Delaunay */
/* edges. */
/* */
/* WARNING: In order to assign numbers to the Voronoi vertices, this */
/* procedure messes up the subsegments or the extra nodes of every */
/* element. Hence, you should call this procedure last. */
/* */
/*****************************************************************************/
#ifdef TRILIBRARY
#ifdef ANSI_DECLARATORS
void writevoronoi(struct mesh *m, struct behavior *b, REAL **vpointlist,
REAL **vpointattriblist, int **vpointmarkerlist,
int **vedgelist, int **vedgemarkerlist, REAL **vnormlist)
#else /* not ANSI_DECLARATORS */
void writevoronoi(m, b, vpointlist, vpointattriblist, vpointmarkerlist,
vedgelist, vedgemarkerlist, vnormlist)
struct mesh *m;
struct behavior *b;
REAL **vpointlist;
REAL **vpointattriblist;
int **vpointmarkerlist;
int **vedgelist;
int **vedgemarkerlist;
REAL **vnormlist;
#endif /* not ANSI_DECLARATORS */
#else /* not TRILIBRARY */
#ifdef ANSI_DECLARATORS
void writevoronoi(struct mesh *m, struct behavior *b, char *vnodefilename,
char *vedgefilename, int argc, char **argv)
#else /* not ANSI_DECLARATORS */
void writevoronoi(m, b, vnodefilename, vedgefilename, argc, argv)
struct mesh *m;
struct behavior *b;
char *vnodefilename;
char *vedgefilename;
int argc;
char **argv;
#endif /* not ANSI_DECLARATORS */
#endif /* not TRILIBRARY */
{
#ifdef TRILIBRARY
REAL *plist;
REAL *palist;
int *elist;
REAL *normlist;
int coordindex;
int attribindex;
#else /* not TRILIBRARY */
FILE *outfile;
#endif /* not TRILIBRARY */
struct otri triangleloop, trisym; vertex torg, tdest, tapex;
REAL circumcenter[2];
REAL xi, eta;
long vnodenumber, vedgenumber;
int p1, p2;
int i;
triangle ptr; /* Temporary variable used by sym(). */
#ifdef TRILIBRARY
if (!b->quiet) {
printf("Writing Voronoi vertices.\n");
}
/* Allocate memory for Voronoi vertices if necessary. */
if (*vpointlist == (REAL *) NULL) {
*vpointlist = (REAL *) trimalloc((int) (m->triangles.items * 2 *
sizeof(REAL)));
}
/* Allocate memory for Voronoi vertex attributes if necessary. */
if (*vpointattriblist == (REAL *) NULL) {
*vpointattriblist = (REAL *) trimalloc((int) (m->triangles.items *
m->nextras * sizeof(REAL)));
}
*vpointmarkerlist = (int *) NULL;
plist = *vpointlist;
palist = *vpointattriblist;
coordindex = 0;
attribindex = 0;
#else /* not TRILIBRARY */
if (!b->quiet) {
printf("Writing %s.\n", vnodefilename);
}
outfile = fopen(vnodefilename, "w");
if (outfile == (FILE *) NULL) {
printf(" Error: Cannot create file %s.\n", vnodefilename);
triexit(1);
}
/* Number of triangles, two dimensions, number of vertex attributes, */
/* no markers. */
fprintf(outfile, "%ld %d %d %d\n", m->triangles.items, 2, m->nextras, 0);
#endif /* not TRILIBRARY */
traversalinit(&m->triangles);
triangleloop.tri = triangletraverse(m);
triangleloop.orient = 0;
vnodenumber = b->firstnumber;
while (triangleloop.tri != (triangle *) NULL) {
org(triangleloop, torg);
dest(triangleloop, tdest);
apex(triangleloop, tapex);
findcircumcenter(m, b, torg, tdest, tapex, circumcenter, &xi, &eta, 0);
#ifdef TRILIBRARY
/* X and y coordinates. */
plist[coordindex++] = circumcenter[0];
plist[coordindex++] = circumcenter[1];
for (i = 2; i < 2 + m->nextras; i++) {
/* Interpolate the vertex attributes at the circumcenter. */
palist[attribindex++] = torg[i] + xi * (tdest[i] - torg[i])
+ eta * (tapex[i] - torg[i]);
}
#else /* not TRILIBRARY */
/* Voronoi vertex number, x and y coordinates. */
fprintf(outfile, "%4ld %.17g %.17g", vnodenumber, circumcenter[0],
circumcenter[1]);
for (i = 2; i < 2 + m->nextras; i++) {
/* Interpolate the vertex attributes at the circumcenter. */
fprintf(outfile, " %.17g", torg[i] + xi * (tdest[i] - torg[i])
+ eta * (tapex[i] - torg[i]));
}
fprintf(outfile, "\n");
#endif /* not TRILIBRARY */
* (int *) (triangleloop.tri + 6) = (int) vnodenumber;
triangleloop.tri = triangletraverse(m);
vnodenumber++;
}
#ifndef TRILIBRARY
finishfile(outfile, argc, argv);
#endif /* not TRILIBRARY */
#ifdef TRILIBRARY
if (!b->quiet) {
printf("Writing Voronoi edges.\n");
}
/* Allocate memory for output Voronoi edges if necessary. */
if (*vedgelist == (int *) NULL) {
*vedgelist = (int *) trimalloc((int) (m->edges * 2 * sizeof(int)));
}
*vedgemarkerlist = (int *) NULL;
/* Allocate memory for output Voronoi norms if necessary. */
if (*vnormlist == (REAL *) NULL) {
*vnormlist = (REAL *) trimalloc((int) (m->edges * 2 * sizeof(REAL)));
}
elist = *vedgelist;
normlist = *vnormlist;
coordindex = 0;
#else /* not TRILIBRARY */
if (!b->quiet) {
printf("Writing %s.\n", vedgefilename);
}
outfile = fopen(vedgefilename, "w");
if (outfile == (FILE *) NULL) {
printf(" Error: Cannot create file %s.\n", vedgefilename);
triexit(1);
}
/* Number of edges, zero boundary markers. */
fprintf(outfile, "%ld %d\n", m->edges, 0);
#endif /* not TRILIBRARY */
traversalinit(&m->triangles);
triangleloop.tri = triangletraverse(m);
vedgenumber = b->firstnumber;
/* To loop over the set of edges, loop over all triangles, and look at */
/* the three edges of each triangle. If there isn't another triangle */
/* adjacent to the edge, operate on the edge. If there is another */
/* adjacent triangle, operate on the edge only if the current triangle */
/* has a smaller pointer than its neighbor. This way, each edge is */
/* considered only once. */
while (triangleloop.tri != (triangle *) NULL) {
for (triangleloop.orient = 0; triangleloop.orient < 3;
triangleloop.orient++) {
sym(triangleloop, trisym);
if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) {
/* Find the number of this triangle (and Voronoi vertex). */
p1 = * (int *) (triangleloop.tri + 6);
if (trisym.tri == m->dummytri) {
org(triangleloop, torg);
dest(triangleloop, tdest);
#ifdef TRILIBRARY
/* Copy an infinite ray. Index of one endpoint, and -1. */
elist[coordindex] = p1;
normlist[coordindex++] = tdest[1] - torg[1];
elist[coordindex] = -1;
normlist[coordindex++] = torg[0] - tdest[0];
#else /* not TRILIBRARY */
/* Write an infinite ray. Edge number, index of one endpoint, -1, */
/* and x and y coordinates of a vector representing the */
/* direction of the ray. */
fprintf(outfile, "%4ld %d %d %.17g %.17g\n", vedgenumber,
p1, -1, tdest[1] - torg[1], torg[0] - tdest[0]);#endif /* not TRILIBRARY */
} else {
/* Find the number of the adjacent triangle (and Voronoi vertex). */
p2 = * (int *) (trisym.tri + 6);
/* Finite edge. Write indices of two endpoints. */
#ifdef TRILIBRARY
elist[coordindex] = p1;
normlist[coordindex++] = 0.0;
elist[coordindex] = p2;
normlist[coordindex++] = 0.0;
#else /* not TRILIBRARY */
fprintf(outfile, "%4ld %d %d\n", vedgenumber, p1, p2);
#endif /* not TRILIBRARY */
}
vedgenumber++;
}
}
triangleloop.tri = triangletraverse(m);
}
#ifndef TRILIBRARY
finishfile(outfile, argc, argv);
#endif /* not TRILIBRARY */
}
#ifdef TRILIBRARY
#ifdef ANSI_DECLARATORS
void writeneighbors(struct mesh *m, struct behavior *b, int **neighborlist)
#else /* not ANSI_DECLARATORS */
void writeneighbors(m, b, neighborlist)
struct mesh *m;
struct behavior *b;
int **neighborlist;
#endif /* not ANSI_DECLARATORS */
#else /* not TRILIBRARY */
#ifdef ANSI_DECLARATORS
void writeneighbors(struct mesh *m, struct behavior *b, char *neighborfilename,
int argc, char **argv)
#else /* not ANSI_DECLARATORS */
void writeneighbors(m, b, neighborfilename, argc, argv)
struct mesh *m;
struct behavior *b;
char *neighborfilename;
int argc;
char **argv;
#endif /* not ANSI_DECLARATORS */
#endif /* not TRILIBRARY */
{
#ifdef TRILIBRARY
int *nlist;
int index;
#else /* not TRILIBRARY */
FILE *outfile;
#endif /* not TRILIBRARY */
struct otri triangleloop, trisym;
long elementnumber;
int neighbor1, neighbor2, neighbor3;
triangle ptr; /* Temporary variable used by sym(). */
#ifdef TRILIBRARY
if (!b->quiet) {
printf("Writing neighbors.\n");
}
/* Allocate memory for neighbors if necessary. */
if (*neighborlist == (int *) NULL) { *neighborlist = (int *) trimalloc((int) (m->triangles.items * 3 *
sizeof(int)));
}
nlist = *neighborlist;
index = 0;
#else /* not TRILIBRARY */
if (!b->quiet) {
printf("Writing %s.\n", neighborfilename);
}
outfile = fopen(neighborfilename, "w");
if (outfile == (FILE *) NULL) {
printf(" Error: Cannot create file %s.\n", neighborfilename);
triexit(1);
}
/* Number of triangles, three neighbors per triangle. */
fprintf(outfile, "%ld %d\n", m->triangles.items, 3);
#endif /* not TRILIBRARY */
traversalinit(&m->triangles);
triangleloop.tri = triangletraverse(m);
triangleloop.orient = 0;
elementnumber = b->firstnumber;
while (triangleloop.tri != (triangle *) NULL) {
* (int *) (triangleloop.tri + 6) = (int) elementnumber;
triangleloop.tri = triangletraverse(m);
elementnumber++;
}
* (int *) (m->dummytri + 6) = -1;
traversalinit(&m->triangles);
triangleloop.tri = triangletraverse(m);
elementnumber = b->firstnumber;
while (triangleloop.tri != (triangle *) NULL) {
triangleloop.orient = 1;
sym(triangleloop, trisym);
neighbor1 = * (int *) (trisym.tri + 6);
triangleloop.orient = 2;
sym(triangleloop, trisym);
neighbor2 = * (int *) (trisym.tri + 6);
triangleloop.orient = 0;
sym(triangleloop, trisym);
neighbor3 = * (int *) (trisym.tri + 6);
#ifdef TRILIBRARY
nlist[index++] = neighbor1;
nlist[index++] = neighbor2;
nlist[index++] = neighbor3;
#else /* not TRILIBRARY */
/* Triangle number, neighboring triangle numbers. */
fprintf(outfile, "%4ld %d %d %d\n", elementnumber,
neighbor1, neighbor2, neighbor3);
#endif /* not TRILIBRARY */
triangleloop.tri = triangletraverse(m);
elementnumber++;
}
#ifndef TRILIBRARY
finishfile(outfile, argc, argv);
#endif /* not TRILIBRARY */
}
/*****************************************************************************/
/* */
/* writeoff() Write the triangulation to an .off file. */
/* */
/* OFF stands for the Object File Format, a format used by the Geometry */
/* Center's Geomview package. */
/* */
/*****************************************************************************/
#ifndef TRILIBRARY
#ifdef ANSI_DECLARATORS
void writeoff(struct mesh *m, struct behavior *b, char *offfilename,
int argc, char **argv)
#else /* not ANSI_DECLARATORS */
void writeoff(m, b, offfilename, argc, argv)
struct mesh *m;
struct behavior *b;
char *offfilename;
int argc;
char **argv;
#endif /* not ANSI_DECLARATORS */
{
FILE *outfile;
struct otri triangleloop;
vertex vertexloop;
vertex p1, p2, p3;
long outvertices;
if (!b->quiet) {
printf("Writing %s.\n", offfilename);
}
if (b->jettison) {
outvertices = m->vertices.items - m->undeads;
} else {
outvertices = m->vertices.items;
}
outfile = fopen(offfilename, "w");
if (outfile == (FILE *) NULL) {
printf(" Error: Cannot create file %s.\n", offfilename);
triexit(1);
}
/* Number of vertices, triangles, and edges. */
fprintf(outfile, "OFF\n%ld %ld %ld\n", outvertices, m->triangles.items,
m->edges);
/* Write the vertices. */
traversalinit(&m->vertices);
vertexloop = vertextraverse(m);
while (vertexloop != (vertex) NULL) {
if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) {
/* The "0.0" is here because the OFF format uses 3D coordinates. */
fprintf(outfile, " %.17g %.17g %.17g\n", vertexloop[0], vertexloop[1],
0.0);
}
vertexloop = vertextraverse(m);
}
/* Write the triangles. */
traversalinit(&m->triangles);
triangleloop.tri = triangletraverse(m);
triangleloop.orient = 0;
while (triangleloop.tri != (triangle *) NULL) {
org(triangleloop, p1);
dest(triangleloop, p2);
apex(triangleloop, p3);
/* The "3" means a three-vertex polygon. */
fprintf(outfile, " 3 %4d %4d %4d\n", vertexmark(p1) - b->firstnumber,
vertexmark(p2) - b->firstnumber, vertexmark(p3) - b->firstnumber);
triangleloop.tri = triangletraverse(m);
}
finishfile(outfile, argc, argv);
}
#endif /* not TRILIBRARY */
/** **/
/** **/
/********* File I/O routines end here *********/
/*****************************************************************************/
/* */
/* quality_statistics() Print statistics about the quality of the mesh. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
void quality_statistics(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
void quality_statistics(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */
{
struct otri triangleloop;
vertex p[3];
REAL cossquaretable[8];
REAL ratiotable[16];
REAL dx[3], dy[3];
REAL edgelength[3];
REAL dotproduct;
REAL cossquare;
REAL triarea;
REAL shortest, longest;
REAL trilongest2;
REAL smallestarea, biggestarea;
REAL triminaltitude2;
REAL minaltitude;
REAL triaspect2;
REAL worstaspect;
REAL smallestangle, biggestangle;
REAL radconst, degconst;
int angletable[18];
int aspecttable[16];
int aspectindex;
int tendegree;
int acutebiggest;
int i, ii, j, k;
printf("Mesh quality statistics:\n\n");
radconst = PI / 18.0;
degconst = 180.0 / PI;
for (i = 0; i < 8; i++) {
cossquaretable[i] = cos(radconst * (REAL) (i + 1));
cossquaretable[i] = cossquaretable[i] * cossquaretable[i];
}
for (i = 0; i < 18; i++) {
angletable[i] = 0;
}
ratiotable[0] = 1.5; ratiotable[1] = 2.0;
ratiotable[2] = 2.5; ratiotable[3] = 3.0;
ratiotable[4] = 4.0; ratiotable[5] = 6.0;
ratiotable[6] = 10.0; ratiotable[7] = 15.0;
ratiotable[8] = 25.0; ratiotable[9] = 50.0;
ratiotable[10] = 100.0; ratiotable[11] = 300.0;
ratiotable[12] = 1000.0; ratiotable[13] = 10000.0;
ratiotable[14] = 100000.0; ratiotable[15] = 0.0;
for (i = 0; i < 16; i++) {
aspecttable[i] = 0;
}
worstaspect = 0.0;
minaltitude = m->xmax - m->xmin + m->ymax - m->ymin;
minaltitude = minaltitude * minaltitude; shortest = minaltitude;
longest = 0.0;
smallestarea = minaltitude;
biggestarea = 0.0;
worstaspect = 0.0;
smallestangle = 0.0;
biggestangle = 2.0;
acutebiggest = 1;
traversalinit(&m->triangles);
triangleloop.tri = triangletraverse(m);
triangleloop.orient = 0;
while (triangleloop.tri != (triangle *) NULL) {
org(triangleloop, p[0]);
dest(triangleloop, p[1]);
apex(triangleloop, p[2]);
trilongest2 = 0.0;
for (i = 0; i < 3; i++) {
j = plus1mod3[i];
k = minus1mod3[i];
dx[i] = p[j][0] - p[k][0];
dy[i] = p[j][1] - p[k][1];
edgelength[i] = dx[i] * dx[i] + dy[i] * dy[i];
if (edgelength[i] > trilongest2) {
trilongest2 = edgelength[i];
}
if (edgelength[i] > longest) {
longest = edgelength[i];
}
if (edgelength[i] < shortest) {
shortest = edgelength[i];
}
}
triarea = counterclockwise(m, b, p[0], p[1], p[2]);
if (triarea < smallestarea) {
smallestarea = triarea;
}
if (triarea > biggestarea) {
biggestarea = triarea;
}
triminaltitude2 = triarea * triarea / trilongest2;
if (triminaltitude2 < minaltitude) {
minaltitude = triminaltitude2;
}
triaspect2 = trilongest2 / triminaltitude2;
if (triaspect2 > worstaspect) {
worstaspect = triaspect2;
}
aspectindex = 0;
while ((triaspect2 > ratiotable[aspectindex] * ratiotable[aspectindex])
&& (aspectindex < 15)) {
aspectindex++;
}
aspecttable[aspectindex]++;
for (i = 0; i < 3; i++) {
j = plus1mod3[i];
k = minus1mod3[i];
dotproduct = dx[j] * dx[k] + dy[j] * dy[k];
cossquare = dotproduct * dotproduct / (edgelength[j] * edgelength[k]);
tendegree = 8;
for (ii = 7; ii >= 0; ii--) {
if (cossquare > cossquaretable[ii]) {
tendegree = ii;
}
}
if (dotproduct <= 0.0) {
angletable[tendegree]++; if (cossquare > smallestangle) {
smallestangle = cossquare;
}
if (acutebiggest && (cossquare < biggestangle)) {
biggestangle = cossquare;
}
} else {
angletable[17 - tendegree]++;
if (acutebiggest || (cossquare > biggestangle)) {
biggestangle = cossquare;
acutebiggest = 0;
}
}
}
triangleloop.tri = triangletraverse(m);
}
shortest = sqrt(shortest);
longest = sqrt(longest);
minaltitude = sqrt(minaltitude);
worstaspect = sqrt(worstaspect);
smallestarea *= 0.5;
biggestarea *= 0.5;
if (smallestangle >= 1.0) {
smallestangle = 0.0;
} else {
smallestangle = degconst * acos(sqrt(smallestangle));
}
if (biggestangle >= 1.0) {
biggestangle = 180.0;
} else {
if (acutebiggest) {
biggestangle = degconst * acos(sqrt(biggestangle));
} else {
biggestangle = 180.0 - degconst * acos(sqrt(biggestangle));
}
}
printf(" Smallest area: %16.5g | Largest area: %16.5g\n",
smallestarea, biggestarea);
printf(" Shortest edge: %16.5g | Longest edge: %16.5g\n",
shortest, longest);
printf(" Shortest altitude: %12.5g | Largest aspect ratio: %8.5g\n\n",
minaltitude, worstaspect);
printf(" Triangle aspect ratio histogram:\n");
printf(" 1.1547 - %-6.6g : %8d | %6.6g - %-6.6g : %8d\n",
ratiotable[0], aspecttable[0], ratiotable[7], ratiotable[8],
aspecttable[8]);
for (i = 1; i < 7; i++) {
printf(" %6.6g - %-6.6g : %8d | %6.6g - %-6.6g : %8d\n",
ratiotable[i - 1], ratiotable[i], aspecttable[i],
ratiotable[i + 7], ratiotable[i + 8], aspecttable[i + 8]);
}
printf(" %6.6g - %-6.6g : %8d | %6.6g - : %8d\n",
ratiotable[6], ratiotable[7], aspecttable[7], ratiotable[14],
aspecttable[15]);
printf(" (Aspect ratio is longest edge divided by shortest altitude)\n\n");
printf(" Smallest angle: %15.5g | Largest angle: %15.5g\n\n",
smallestangle, biggestangle);
printf(" Angle histogram:\n");
for (i = 0; i < 9; i++) {
printf(" %3d - %3d degrees: %8d | %3d - %3d degrees: %8d\n",
i * 10, i * 10 + 10, angletable[i],
i * 10 + 90, i * 10 + 100, angletable[i + 9]);
}
printf("\n");
}
/*****************************************************************************/
/* */
/* statistics() Print all sorts of cool facts. */
/* */
/*****************************************************************************/
#ifdef ANSI_DECLARATORS
void statistics(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
void statistics(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */
{
printf("\nStatistics:\n\n");
printf(" Input vertices: %d\n", m->invertices);
if (b->refine) {
printf(" Input triangles: %d\n", m->inelements);
}
if (b->poly) {
printf(" Input segments: %d\n", m->insegments);
if (!b->refine) {
printf(" Input holes: %d\n", m->holes);
}
}
printf("\n Mesh vertices: %ld\n", m->vertices.items - m->undeads);
printf(" Mesh triangles: %ld\n", m->triangles.items);
printf(" Mesh edges: %ld\n", m->edges);
printf(" Mesh exterior boundary edges: %ld\n", m->hullsize);
if (b->poly || b->refine) {
printf(" Mesh interior boundary edges: %ld\n",
m->subsegs.items - m->hullsize);
printf(" Mesh subsegments (constrained edges): %ld\n",
m->subsegs.items);
}
printf("\n");
if (b->verbose) {
quality_statistics(m, b);
printf("Memory allocation statistics:\n\n");
printf(" Maximum number of vertices: %ld\n", m->vertices.maxitems);
printf(" Maximum number of triangles: %ld\n", m->triangles.maxitems);
if (m->subsegs.maxitems > 0) {
printf(" Maximum number of subsegments: %ld\n", m->subsegs.maxitems);
}
if (m->viri.maxitems > 0) {
printf(" Maximum number of viri: %ld\n", m->viri.maxitems);
}
if (m->badsubsegs.maxitems > 0) {
printf(" Maximum number of encroached subsegments: %ld\n",
m->badsubsegs.maxitems);
}
if (m->badtriangles.maxitems > 0) {
printf(" Maximum number of bad triangles: %ld\n",
m->badtriangles.maxitems);
}
if (m->flipstackers.maxitems > 0) {
printf(" Maximum number of stacked triangle flips: %ld\n",
m->flipstackers.maxitems);
}
if (m->splaynodes.maxitems > 0) {
printf(" Maximum number of splay tree nodes: %ld\n",
m->splaynodes.maxitems);
}
printf(" Approximate heap memory use (bytes): %ld\n\n",
m->vertices.maxitems * m->vertices.itembytes +
m->triangles.maxitems * m->triangles.itembytes + m->subsegs.maxitems * m->subsegs.itembytes +
m->viri.maxitems * m->viri.itembytes +
m->badsubsegs.maxitems * m->badsubsegs.itembytes +
m->badtriangles.maxitems * m->badtriangles.itembytes +
m->flipstackers.maxitems * m->flipstackers.itembytes +
m->splaynodes.maxitems * m->splaynodes.itembytes);
printf("Algorithmic statistics:\n\n");
if (!b->weighted) {
printf(" Number of incircle tests: %ld\n", m->incirclecount);
} else {
printf(" Number of 3D orientation tests: %ld\n", m->orient3dcount);
}
printf(" Number of 2D orientation tests: %ld\n", m->counterclockcount);
if (m->hyperbolacount > 0) {
printf(" Number of right-of-hyperbola tests: %ld\n",
m->hyperbolacount);
}
if (m->circletopcount > 0) {
printf(" Number of circle top computations: %ld\n",
m->circletopcount);
}
if (m->circumcentercount > 0) {
printf(" Number of triangle circumcenter computations: %ld\n",
m->circumcentercount);
}
printf("\n");
}
}
/*****************************************************************************/
/* */
/* main() or triangulate() Gosh, do everything. */
/* */
/* 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 */
/* - triangulate them (no -r), or */
/* - read an old mesh from files and reconstruct it (-r). */
/* - Insert the PSLG segments (-p), and possibly segments on the convex */
/* hull (-c). */
/* - Read the holes (-p), regional attributes (-pA), and regional area */
/* constraints (-pa). Carve the holes and concavities, and spread the */
/* regional attributes and area constraints. */
/* - Enforce the constraints on minimum angle (-q) and maximum area (-a). */
/* Also enforce the conforming Delaunay property (-q and -a). */
/* - Compute the number of edges in the resulting mesh. */
/* - Promote the mesh's linear triangles to higher order elements (-o). */
/* - Write the output files and print the statistics. */
/* - Check the consistency and Delaunay property of the mesh (-C). */
/* */
/*****************************************************************************/
#ifdef TRILIBRARY
#ifdef ANSI_DECLARATORS
void triangulate(char *triswitches, struct triangulateio *in,
struct triangulateio *out, struct triangulateio *vorout)
#else /* not ANSI_DECLARATORS */
void triangulate(triswitches, in, out, vorout)
char *triswitches;
struct triangulateio *in;
struct triangulateio *out;
struct triangulateio *vorout;
#endif /* not ANSI_DECLARATORS */
#else /* not TRILIBRARY */
#ifdef ANSI_DECLARATORS
int main(int argc, char **argv)
#else /* not ANSI_DECLARATORS */
int main(argc, argv)
int argc;
char **argv;
#endif /* not ANSI_DECLARATORS */
#endif /* not TRILIBRARY */
{
struct mesh m;
struct behavior b;
REAL *holearray; /* Array of holes. */
REAL *regionarray; /* Array of regional attributes and area constraints. */
#ifndef TRILIBRARY
FILE *polyfile;
#endif /* not TRILIBRARY */
#ifndef NO_TIMER
/* Variables for timing the performance of Triangle. The types are */
/* defined in sys/time.h. */
struct timeval tv0, tv1, tv2, tv3, tv4, tv5, tv6;
struct timezone tz;
#endif /* not NO_TIMER */
#ifndef NO_TIMER
gettimeofday(&tv0, &tz);
#endif /* not NO_TIMER */
triangleinit(&m);
#ifdef TRILIBRARY
parsecommandline(1, &triswitches, &b);
#else /* not TRILIBRARY */
parsecommandline(argc, argv, &b);
#endif /* not TRILIBRARY */
m.steinerleft = b.steiner;
#ifdef TRILIBRARY
transfernodes(&m, &b, in->pointlist, in->pointattributelist,
in->pointmarkerlist, in->numberofpoints,
in->numberofpointattributes);
#else /* not TRILIBRARY */
readnodes(&m, &b, b.innodefilename, b.inpolyfilename, &polyfile);
#endif /* not TRILIBRARY */
#ifndef NO_TIMER
if (!b.quiet) {
gettimeofday(&tv1, &tz);
}
#endif /* not NO_TIMER */
#ifdef CDT_ONLY
m.hullsize = delaunay(&m, &b); /* Triangulate the vertices. */
#else /* not CDT_ONLY */
if (b.refine) {
/* Read and reconstruct a mesh. */
#ifdef TRILIBRARY
m.hullsize = reconstruct(&m, &b, in->trianglelist,
in->triangleattributelist, in->trianglearealist,
in->numberoftriangles, in->numberofcorners,
in->numberoftriangleattributes,
in->segmentlist, in->segmentmarkerlist,
in->numberofsegments);
#else /* not TRILIBRARY */
m.hullsize = reconstruct(&m, &b, b.inelefilename, b.areafilename,
b.inpolyfilename, polyfile);
#endif /* not TRILIBRARY */
} else {
m.hullsize = delaunay(&m, &b); /* Triangulate the vertices. */
}#endif /* not CDT_ONLY */
#ifndef NO_TIMER
if (!b.quiet) {
gettimeofday(&tv2, &tz);
if (b.refine) {
printf("Mesh reconstruction");
} else {
printf("Delaunay");
}
printf(" milliseconds: %ld\n", 1000l * (tv2.tv_sec - tv1.tv_sec) +
(tv2.tv_usec - tv1.tv_usec) / 1000l);
}
#endif /* not NO_TIMER */
/* Ensure that no vertex can be mistaken for a triangular bounding */
/* box vertex in insertvertex(). */
m.infvertex1 = (vertex) NULL;
m.infvertex2 = (vertex) NULL;
m.infvertex3 = (vertex) NULL;
if (b.usesegments) {
m.checksegments = 1; /* Segments will be introduced next. */
if (!b.refine) {
/* Insert PSLG segments and/or convex hull segments. */
#ifdef TRILIBRARY
formskeleton(&m, &b, in->segmentlist,
in->segmentmarkerlist, in->numberofsegments);
#else /* not TRILIBRARY */
formskeleton(&m, &b, polyfile, b.inpolyfilename);
#endif /* not TRILIBRARY */
}
}
#ifndef NO_TIMER
if (!b.quiet) {
gettimeofday(&tv3, &tz);
if (b.usesegments && !b.refine) {
printf("Segment milliseconds: %ld\n",
1000l * (tv3.tv_sec - tv2.tv_sec) +
(tv3.tv_usec - tv2.tv_usec) / 1000l);
}
}
#endif /* not NO_TIMER */
if (b.poly && (m.triangles.items > 0)) {
#ifdef TRILIBRARY
holearray = in->holelist;
m.holes = in->numberofholes;
regionarray = in->regionlist;
m.regions = in->numberofregions;
#else /* not TRILIBRARY */
readholes(&m, &b, polyfile, b.inpolyfilename, &holearray, &m.holes,
®ionarray, &m.regions);
#endif /* not TRILIBRARY */
if (!b.refine) {
/* Carve out holes and concavities. */
carveholes(&m, &b, holearray, m.holes, regionarray, m.regions);
}
} else {
/* Without a PSLG, there can be no holes or regional attributes */
/* or area constraints. The following are set to zero to avoid */
/* an accidental free() later. */
m.holes = 0;
m.regions = 0;
}
#ifndef NO_TIMER
if (!b.quiet) {
gettimeofday(&tv4, &tz); if (b.poly && !b.refine) {
printf("Hole milliseconds: %ld\n", 1000l * (tv4.tv_sec - tv3.tv_sec) +
(tv4.tv_usec - tv3.tv_usec) / 1000l);
}
}
#endif /* not NO_TIMER */
#ifndef CDT_ONLY
if (b.quality && (m.triangles.items > 0)) {
enforcequality(&m, &b); /* Enforce angle and area constraints. */
}
#endif /* not CDT_ONLY */
#ifndef NO_TIMER
if (!b.quiet) {
gettimeofday(&tv5, &tz);
#ifndef CDT_ONLY
if (b.quality) {
printf("Quality milliseconds: %ld\n",
1000l * (tv5.tv_sec - tv4.tv_sec) +
(tv5.tv_usec - tv4.tv_usec) / 1000l);
}
#endif /* not CDT_ONLY */
}
#endif /* not NO_TIMER */
/* Calculate the number of edges. */
m.edges = (3l * m.triangles.items + m.hullsize) / 2l;
if (b.order > 1) {
highorder(&m, &b); /* Promote elements to higher polynomial order. */
}
if (!b.quiet) {
printf("\n");
}
#ifdef TRILIBRARY
if (b.jettison) {
out->numberofpoints = m.vertices.items - m.undeads;
} else {
out->numberofpoints = m.vertices.items;
}
out->numberofpointattributes = m.nextras;
out->numberoftriangles = m.triangles.items;
out->numberofcorners = (b.order + 1) * (b.order + 2) / 2;
out->numberoftriangleattributes = m.eextras;
out->numberofedges = m.edges;
if (b.usesegments) {
out->numberofsegments = m.subsegs.items;
} else {
out->numberofsegments = m.hullsize;
}
if (vorout != (struct triangulateio *) NULL) {
vorout->numberofpoints = m.triangles.items;
vorout->numberofpointattributes = m.nextras;
vorout->numberofedges = m.edges;
}
#endif /* TRILIBRARY */
/* If not using iteration numbers, don't write a .node file if one was */
/* read, because the original one would be overwritten! */
if (b.nonodewritten || (b.noiterationnum && m.readnodefile)) {
if (!b.quiet) {
#ifdef TRILIBRARY
printf("NOT writing vertices.\n");
#else /* not TRILIBRARY */
printf("NOT writing a .node file.\n");
#endif /* not TRILIBRARY */
}
numbernodes(&m, &b); /* We must remember to number the vertices. */
} else { /* writenodes() numbers the vertices too. */
#ifdef TRILIBRARY
writenodes(&m, &b, &out->pointlist, &out->pointattributelist,
&out->pointmarkerlist);
#else /* not TRILIBRARY */
writenodes(&m, &b, b.outnodefilename, argc, argv);
#endif /* TRILIBRARY */
}
if (b.noelewritten) {
if (!b.quiet) {
#ifdef TRILIBRARY
printf("NOT writing triangles.\n");
#else /* not TRILIBRARY */
printf("NOT writing an .ele file.\n");
#endif /* not TRILIBRARY */
}
} else {
#ifdef TRILIBRARY
writeelements(&m, &b, &out->trianglelist, &out->triangleattributelist);
#else /* not TRILIBRARY */
writeelements(&m, &b, b.outelefilename, argc, argv);
#endif /* not TRILIBRARY */
}
/* The -c switch (convex switch) causes a PSLG to be written */
/* even if none was read. */
if (b.poly || b.convex) {
/* If not using iteration numbers, don't overwrite the .poly file. */
if (b.nopolywritten || b.noiterationnum) {
if (!b.quiet) {
#ifdef TRILIBRARY
printf("NOT writing segments.\n");
#else /* not TRILIBRARY */
printf("NOT writing a .poly file.\n");
#endif /* not TRILIBRARY */
}
} else {
#ifdef TRILIBRARY
writepoly(&m, &b, &out->segmentlist, &out->segmentmarkerlist);
out->numberofholes = m.holes;
out->numberofregions = m.regions;
if (b.poly) {
out->holelist = in->holelist;
out->regionlist = in->regionlist;
} else {
out->holelist = (REAL *) NULL;
out->regionlist = (REAL *) NULL;
}
#else /* not TRILIBRARY */
writepoly(&m, &b, b.outpolyfilename, holearray, m.holes, regionarray,
m.regions, argc, argv);
#endif /* not TRILIBRARY */
}
}
#ifndef TRILIBRARY
#ifndef CDT_ONLY
if (m.regions > 0) {
trifree((VOID *) regionarray);
}
#endif /* not CDT_ONLY */
if (m.holes > 0) {
trifree((VOID *) holearray);
}
if (b.geomview) {
writeoff(&m, &b, b.offfilename, argc, argv);
}
#endif /* not TRILIBRARY */
if (b.edgesout) {
#ifdef TRILIBRARY
writeedges(&m, &b, &out->edgelist, &out->edgemarkerlist);
#else /* not TRILIBRARY */ writeedges(&m, &b, b.edgefilename, argc, argv);
#endif /* not TRILIBRARY */
}
if (b.voronoi) {
#ifdef TRILIBRARY
writevoronoi(&m, &b, &vorout->pointlist, &vorout->pointattributelist,
&vorout->pointmarkerlist, &vorout->edgelist,
&vorout->edgemarkerlist, &vorout->normlist);
#else /* not TRILIBRARY */
writevoronoi(&m, &b, b.vnodefilename, b.vedgefilename, argc, argv);
#endif /* not TRILIBRARY */
}
if (b.neighbors) {
#ifdef TRILIBRARY
writeneighbors(&m, &b, &out->neighborlist);
#else /* not TRILIBRARY */
writeneighbors(&m, &b, b.neighborfilename, argc, argv);
#endif /* not TRILIBRARY */
}
if (!b.quiet) {
#ifndef NO_TIMER
gettimeofday(&tv6, &tz);
printf("\nOutput milliseconds: %ld\n",
1000l * (tv6.tv_sec - tv5.tv_sec) +
(tv6.tv_usec - tv5.tv_usec) / 1000l);
printf("Total running milliseconds: %ld\n",
1000l * (tv6.tv_sec - tv0.tv_sec) +
(tv6.tv_usec - tv0.tv_usec) / 1000l);
#endif /* not NO_TIMER */
statistics(&m, &b);
}
#ifndef REDUCED
if (b.docheck) {
checkmesh(&m, &b);
checkdelaunay(&m, &b);
}
#endif /* not REDUCED */
triangledeinit(&m, &b);
#ifndef TRILIBRARY
return 0;
#endif /* not TRILIBRARY */
}