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/*****************************************************************************/
/* */
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/* 888 888 888 88b 888 888 888 888 888 d888 88b */
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/* "8oo8D */
/* */
/* A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator. */
/* (triangle.c) */
/* */
/* Version 1.3 */
/* July 19, 1996 */
/* */
/* Copyright 1996 */
/* Jonathan Richard Shewchuk */
/* School of Computer Science */
/* Carnegie Mellon University */
/* 5000 Forbes Avenue */
/* Pittsburgh, Pennsylvania 15213-3891 */
/* jrs@cs.cmu.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 */
/* */
/* Some of the references listed below are marked [*]. These are available */
/* for downloading from the Web page */
/* */
/* http://www.cs.cmu.edu/~quake/triangle.research.html */
/* */
/* A paper discussing some aspects of Triangle is available. See Jonathan */
/* Richard Shewchuk, "Triangle: Engineering a 2D Quality Mesh Generator */
/* and Delaunay Triangulator," First Workshop on Applied Computational */
/* Geometry, ACM, May 1996. [*] */
/* */
/* Triangle was created as part of the Archimedes project in the School of */
/* Computer Science at Carnegie Mellon University. Archimedes is a */
/* system for compiling parallel finite element solvers. For further */
/* information, see Anja Feldmann, Omar Ghattas, John R. Gilbert, Gary L. */
/* Miller, David R. O'Hallaron, Eric J. Schwabe, Jonathan R. Shewchuk, */
/* and Shang-Hua Teng, "Automated Parallel Solution of Unstructured PDE */
/* Problems." To appear in Communications of the ACM, we hope. */
/* */
/* The quality mesh generation algorithm is due to Jim Ruppert, "A */
/* Delaunay Refinement Algorithm for Quality 2-Dimensional Mesh */
/* Generation," Journal of Algorithms 18(3):548-585, May 1995. [*] */
/* */
/* 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 switching 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. */
/* */
/* 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. The idea to improve 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 point */
/* insertion (I currently don't bother), their result combined with the */
/* result of Leonidas J. Guibas, Donald E. Knuth, and Micha Sharir, */
/* "Randomized Incremental Construction of Delaunay and Voronoi */
/* Diagrams," Algorithmica 7(4):381-413, 1992, 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. */
/* */
/* 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," Technical */
/* Report CMU-CS-96-140, School of Computer Science, Carnegie Mellon */
/* University, Pittsburgh, Pennsylvania, May 1996. [*] (Submitted to */
/* Discrete & Computational Geometry.) An abbreviated version appears as */
/* Jonathan Richard Shewchuk, "Robust Adaptive Floating-Point Geometric */
/* Predicates," Proceedings of the Twelfth Annual Symposium on Computa- */
/* tional 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, 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 Computational 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 Triangulations," International Journal */
/* of Computational Geometry & Applications 5(1-2):193-213, March-June */
/* 1995. */
/* */
/* 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(n^2) per segment in the worst case and O(n) per edge in the common */
/* case, where n 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. (This note does not apply to conforming */
/* Delaunay triangulations, for which a different method is used to */
/* insert segments.) */
/* */
/* The time for adding segments to a conforming Delaunay triangulation is */
/* not clear, but does not depend upon n alone. In some cases, very */
/* small features (like a point lying next to a segment) can cause a */
/* single segment to be split an arbitrary number of times. Of course, */
/* floating-point precision is a practical barrier to how much this can */
/* happen. */
/* */
/* The time for deleting a point from a Delaunay triangulation is O(n^2) in */
/* the worst case and O(n) in the common case, where n is the degree of */
/* the point being deleted. I could improve this to expected O(n) time */
/* by "inserting" the neighboring vertices in random order, but n is */
/* usually quite small, so it's not worth the bother. (The O(n) time */
/* for random insertion follows from L. Paul Chew, "Building Voronoi */
/* Diagrams for Convex Polygons in Linear Expected Time," Technical */
/* Report PCS-TR90-147, Department of Mathematics and Computer Science, */
/* Dartmouth College, 1990. */
/* */
/* 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 more */
/* time is required, but these never arise in practice. */
/* */
/* The segment intersection formulae are straightforward. If you want to */
/* see them derived, see Franklin Antonio. "Faster Line Segment */
/* Intersection." In Graphics Gems III (David Kirk, editor), pp. 199- */
/* 202. Academic Press, Boston, 1992. */
/* */
/* 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. */
/* */
/* Disclaimer: Neither I nor Carnegie Mellon warrant this code in any way */
/* whatsoever. This code is provided "as-is". Use at your own risk. */
/* */
/*****************************************************************************/
/* 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. */
/* #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, -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, the exact arithmetic routines might be defeated by the */
/* use of internal extended precision floating-point registers. Sometimes */
/* this problem can be fixed by defining certain values to be volatile, */
/* thus forcing them to be stored to memory and rounded off. This isn't */
/* a great solution, though, as it slows Triangle down. */
/* */
/* To try this out, write "#define INEXACT volatile" below. Normally, */
/* however, INEXACT should be defined to be nothing. ("#define INEXACT".) */
#define INEXACT /* Nothing */
/* #define INEXACT volatile */
/* Maximum number of characters in a file name (including the null). */
#define FILENAMESIZE 512
/* Maximum number of characters in a line read from a file (including the */
/* null). */
#define INPUTLINESIZE 512
/* 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 SHELLEPERBLOCK 508 /* Number of shell edges allocated at once. */
#define POINTPERBLOCK 4092 /* Number of points allocated at once. */
#define VIRUSPERBLOCK 1020 /* Number of virus triangles allocated at once. */
/* Number of encroached segments allocated at once. */
#define BADSEGMENTPERBLOCK 252
/* Number of skinny triangles allocated at once. */
#define BADTRIPERBLOCK 4092
/* Number of splay tree nodes allocated at once. */
#define SPLAYNODEPERBLOCK 508
/* The point marker DEADPOINT is an arbitrary number chosen large enough to */
/* (hopefully) not conflict with user boundary markers. Make sure that it */
/* is small enough to fit into your machine's integer size. */
#define DEADPOINT -1073741824
/* 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 <string.h>
#include <math.h>
#ifndef NO_TIMER
#include <sys/time.h>
#endif /* NO_TIMER */
#ifdef TRILIBRARY
#include "triangle.h"
#endif /* TRILIBRARY */
/* The following obscenity seems to be necessary to ensure that this program */
/* will port to Dec Alphas running OSF/1, because their stdio.h file commits */
/* the unpardonable sin of including stdlib.h. Hence, malloc(), free(), and */
/* exit() may or may not already be defined at this point. I declare these */
/* functions explicitly because some non-ANSI C compilers lack stdlib.h. */
#ifndef _STDLIB_H_
extern void *malloc();
extern void free();
extern void exit();
extern double strtod();
extern long strtol();
#endif /* _STDLIB_H_ */
/* A few forward declarations. */
void poolrestart();
#ifndef TRILIBRARY
char *readline();
char *findfield();
#endif /* not TRILIBRARY */
/* Labels that signify whether a record consists primarily of pointers or of */
/* floating-point words. Used to make decisions about data alignment. */
enum wordtype {POINTER, FLOATINGPOINT};
/* Labels that signify the 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 site insertion. The result indicates */
/* that the point was inserted with complete success, was inserted but */
/* encroaches on a segment, was not inserted because it lies on a segment, *//* or was not inserted because another point occupies the same location. */
enum insertsiteresult {SUCCESSFULPOINT, ENCROACHINGPOINT, VIOLATINGPOINT,
DUPLICATEPOINT};
/* 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};
/* Labels that signify the result of the circumcenter computation routine. */
/* The return value indicates which edge of the triangle is shortest. */
enum circumcenterresult {OPPOSITEORG, OPPOSITEDEST, OPPOSITEAPEX};
/*****************************************************************************/
/* */
/* The basic mesh data structures */
/* */
/* There are three: points, triangles, and shell edges (abbreviated */
/* `shelle'). These three data structures, linked by pointers, comprise */
/* the mesh. A point simply represents a point in space and its properties.*/
/* A triangle is a triangle. A shell edge is a special data structure used */
/* to represent impenetrable segments in the mesh (including the outer */
/* boundary, boundaries of holes, and internal boundaries separating two */
/* triangulated regions). Shell edges 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 shell edges (when shell */
/* edges are used), 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 shell edges are present. Such absent */
/* triangles and shell edges are never represented by NULL pointers; they */
/* are represented by two special records: `dummytri', the triangle that */
/* fills "outer space", and `dummysh', the omnipresent shell edge. */
/* `dummytri' and `dummysh' are used for several reasons; for instance, */
/* they can be dereferenced and their contents examined without causing the */
/* memory protection exception that would occur if NULL were dereferenced. */
/* */
/* However, it is important to understand that a triangle includes other */
/* information as well. The pointers to adjoining vertices, triangles, and */
/* shell edges 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 */
/* shell edge indicates which side of that shell edge is contacted, and how */
/* the shell edge is oriented relative to the triangle. */
/* */
/* Shell edges are found abutting edges of triangles; either sandwiched */
/* between two triangles, or resting against one triangle on an exterior */
/* boundary or hole boundary. */
/* */
/* A shell edge consists of a list of two vertices, a list of two */
/* adjoining shell edges, 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 shell edges might not be present. */
/* Shell edges also store a user-defined integer "boundary marker". */
/* Typically, this integer is used to indicate what sort of boundary */
/* conditions are to be applied at that location in a finite element */
/* simulation. */
/* */
/* Like triangles, shell edges maintain information about the relative *//* orientation of neighboring objects. */
/* */
/* Points are relatively simple. A point 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 point 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 at any other time. Edge swapping during segment insertion will */
/* render some of them incorrect. Hence, don't rely upon them for */
/* anything. For the most part, points do not have any information about */
/* what triangles or shell edges they are linked to. */
/* */
/*****************************************************************************/
/*****************************************************************************/
/* */
/* Handles */
/* */
/* The oriented triangle (`triedge') and oriented shell edge (`edge') data */
/* structures defined below do not themselves store any part of the mesh. */
/* The mesh itself is made of `triangle's, `shelle's, and `point's. */
/* */
/* Oriented triangles and oriented shell edges 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.) */
/* */
/* A `triedge' is a handle that holds a triangle. It holds a specific side */
/* of the triangle. An `edge' is a handle that holds a shell edge. It */
/* holds either the left or right side of the edge. */
/* */
/* 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 exact position of the handles is */
/* important. For instance, when two triangles are glued together by the */
/* bond() primitive, they are glued by the sides on which the handles lie. */
/* */
/* Because points have no information about which triangles they are */
/* attached to, I commonly represent a point by use of a handle whose */
/* origin is the point. A single handle can simultaneously represent a */
/* triangle, an edge, and a point. */
/* */
/*****************************************************************************/
/* The triangle data structure. Each triangle contains three pointers to */
/* adjoining triangles, plus three pointers to vertex points, plus three */
/* pointers to shell edges (defined below; these pointers are usually */
/* `dummysh'). 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 defined the type `triangle' to be 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 is always */
/* directed to point counterclockwise about the corresponding triangle. */
struct triedge {
triangle *tri; int orient; /* Ranges from 0 to 2. */
};
/* The shell data structure. Each shell edge contains two pointers to */
/* adjoining shell edges, plus two pointers to vertex points, plus two */
/* pointers to adjoining triangles, plus one shell marker. */
typedef REAL **shelle; /* Really: typedef shelle *shelle */
/* An oriented shell edge: includes a pointer to a shell edge 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 edge {
shelle *sh;
int shorient; /* Ranges from 0 to 1. */
};
/* The point data structure. Each point 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 *point;
/* A queue used to store encroached segments. Each segment's vertices are */
/* stored so that one can check whether a segment is still the same. */
struct badsegment {
struct edge encsegment; /* An encroached segment. */
point segorg, segdest; /* The two vertices. */
struct badsegment *nextsegment; /* Pointer to next encroached segment. */
};
/* 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 badface {
struct triedge badfacetri; /* A bad triangle. */
REAL key; /* cos^2 of smallest (apical) angle. */
point faceorg, facedest, faceapex; /* The three vertices. */
struct badface *nextface; /* Pointer to next bad triangle. */
};
/* 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 `point' 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 point 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 triedge keyedge; /* Lprev of an edge on the front. */
point 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. */
/* */
/* itemwordtype is set to POINTER or FLOATINGPOINT, and is used to suggest */
/* what sort of word the record is primarily made up of. alignbytes */
/* determines how new records should be aligned in memory. itembytes and */
/* itemwords are the length of a record in bytes (after rounding up) and */
/* words. itemsperblock is the number of items allocated at once in a */
/* single block. items is the number of currently allocated items. */
/* maxitems is the maximum number of items that have been allocated at */
/* once; it is the current number of items plus the number of records kept */
/* on deaditemstack. */
struct memorypool {
VOID **firstblock, **nowblock;
VOID *nextitem;
VOID *deaditemstack;
VOID **pathblock;
VOID *pathitem;
enum wordtype itemwordtype;
int alignbytes;
int itembytes, itemwords;
int itemsperblock;
long items, maxitems;
int unallocateditems;
int pathitemsleft;
};
/* Variables used to allocate memory for triangles, shell edges, points, */
/* viri (triangles being eaten), bad (encroached) segments, bad (skinny */
/* or too large) triangles, and splay tree nodes. */
struct memorypool triangles;
struct memorypool shelles;
struct memorypool points;
struct memorypool viri;
struct memorypool badsegments;
struct memorypool badtriangles;
struct memorypool splaynodes;
/* Variables that maintain the bad triangle queues. The tails are pointers */
/* to the pointers that have to be filled in to enqueue an item. */
struct badface *queuefront[64];
struct badface **queuetail[64];
REAL xmin, xmax, ymin, ymax; /* x and y bounds. */
REAL xminextreme; /* Nonexistent x value used as a flag in sweepline. */
int inpoints; /* Number of input points. */
int inelements; /* Number of input triangles. */int insegments; /* Number of input segments. */
int holes; /* Number of input holes. */
int regions; /* Number of input regions. */
long edges; /* Number of output edges. */
int mesh_dim; /* Dimension (ought to be 2). */
int nextras; /* Number of attributes per point. */
int eextras; /* Number of attributes per triangle. */
long hullsize; /* Number of edges of convex hull. */
int triwords; /* Total words per triangle. */
int shwords; /* Total words per shell edge. */
int pointmarkindex; /* Index to find boundary marker of a point. */
int point2triindex; /* Index to find a triangle adjacent to a point. */
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 readnodefile; /* Has a .node file been read? */
long samples; /* Number of random samples for point location. */
unsigned long randomseed; /* Current random number seed. */
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;
long incirclecount; /* Number of incircle tests performed. */
long counterclockcount; /* Number of counterclockwise 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. */
/* 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. */
/* vararea: -a switch without number. */
/* fixedarea: -a switch with number. */
/* maxarea: maximum area bound, specified after -a switch. */
/* regionattrib: -A switch. convex: -c 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. */
/* steinerleft: number of Steiner points not yet used. */
/* incremental: -i switch. sweepline: -F switch. */
/* dwyer: inverse of -l switch. */
/* splitseg: -s switch. */
/* docheck: -C switch. */
/* quiet: -Q switch. verbose: count of how often -V switch is selected. */
/* useshelles: -p, -r, -q, or -c switch; determines whether shell edges */
/* are used at all. */
/* */
/* Read the instructions to find out the meaning of these switches. */
int poly, refine, quality, vararea, fixedarea, regionattrib, convex;
int firstnumber;
int edgesout, voronoi, neighbors, geomview;
int nobound, nopolywritten, nonodewritten, noelewritten, noiterationnum;
int noholes, noexact;
int incremental, sweepline, dwyer;
int splitseg;int docheck;
int quiet, verbose;
int useshelles;
int order;
int nobisect;
int steiner, steinerleft;
REAL minangle, goodangle;
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 */
/* Triangular bounding box points. */
point infpoint1, infpoint2, infpoint3;
/* 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 shell edge. Referenced by any triangle or */
/* shell edge that isn't really connected to a shell edge at that */
/* location. */
shelle *dummysh;
shelle *dummyshbase; /* Keep base address so we can free() it later. */
/* Pointer to a recently visited triangle. Improves point location if */
/* proximate points are inserted sequentially. */
struct triedge recenttri;
/*****************************************************************************/
/* */
/* 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.*/
/* */
/* Shell edges are manipulated similarly. A pointer to a shell edge */
/* carries both an address and an orientation in the range 0 to 1. */
/* */
/* The other primitives take an oriented triangle or oriented shell edge, */
/* and return an oriented triangle or oriented shell edge or point; or they */
/* change the connections in the data structure. */
/* */
/*****************************************************************************/
/********* 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, triedge) \
(triedge).orient = (int) ((unsigned long) (ptr) & (unsigned long) 3l); \
(triedge).tri = (triangle *) \
((unsigned long) (ptr) ^ (unsigned long) (triedge).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 (triedge).tri are zero.*/
#define encode(triedge) \
(triangle) ((unsigned long) (triedge).tri | (unsigned long) (triedge).orient)
/* The following edge manipulation primitives are all described by Guibas */
/* and Stolfi. However, they use an edge-based data structure, whereas I */
/* am using a triangle-based data structure. */
/* sym() finds the abutting triangle, on the same edge. Note that the */
/* edge direction is necessarily reversed, because triangle/edge handles */
/* are always directed counterclockwise around the triangle. */
#define sym(triedge1, triedge2) \
ptr = (triedge1).tri[(triedge1).orient]; \
decode(ptr, triedge2);
#define symself(triedge) \
ptr = (triedge).tri[(triedge).orient]; \
decode(ptr, triedge);
/* lnext() finds the next edge (counterclockwise) of a triangle. */
#define lnext(triedge1, triedge2) \
(triedge2).tri = (triedge1).tri; \
(triedge2).orient = plus1mod3[(triedge1).orient]
#define lnextself(triedge) \
(triedge).orient = plus1mod3[(triedge).orient]
/* lprev() finds the previous edge (clockwise) of a triangle. */
#define lprev(triedge1, triedge2) \
(triedge2).tri = (triedge1).tri; \
(triedge2).orient = minus1mod3[(triedge1).orient]
#define lprevself(triedge) \
(triedge).orient = minus1mod3[(triedge).orient]
/* onext() spins counterclockwise around a point; that is, it finds the next */
/* edge with the same origin in the counterclockwise direction. This edge */
/* will be part of a different triangle. */
#define onext(triedge1, triedge2) \
lprev(triedge1, triedge2); \
symself(triedge2);
#define onextself(triedge) \
lprevself(triedge); \
symself(triedge);
/* oprev() spins clockwise around a point; that is, it finds the next edge */
/* with the same origin in the clockwise direction. This edge will be */
/* part of a different triangle. */
#define oprev(triedge1, triedge2) \
sym(triedge1, triedge2); \
lnextself(triedge2);
#define oprevself(triedge) \
symself(triedge); \
lnextself(triedge);
/* dnext() spins counterclockwise around a point; that is, it finds the next */
/* edge with the same destination in the counterclockwise direction. This */
/* edge will be part of a different triangle. */
#define dnext(triedge1, triedge2) \
sym(triedge1, triedge2); \
lprevself(triedge2);
#define dnextself(triedge) \
symself(triedge); \
lprevself(triedge);
/* dprev() spins clockwise around a point; that is, it finds the next edge */
/* with the same destination in the clockwise direction. This edge will */
/* be part of a different triangle. */
#define dprev(triedge1, triedge2) \
lnext(triedge1, triedge2); \
symself(triedge2);
#define dprevself(triedge) \
lnextself(triedge); \
symself(triedge);
/* 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(triedge1, triedge2) \
sym(triedge1, triedge2); \
lnextself(triedge2); \
symself(triedge2);
#define rnextself(triedge) \
symself(triedge); \
lnextself(triedge); \
symself(triedge);
/* rnext() moves one edge clockwise about the adjacent triangle. */
/* (It's best understood by reading Guibas and Stolfi. It involves */
/* changing triangles twice.) */
#define rprev(triedge1, triedge2) \
sym(triedge1, triedge2); \
lprevself(triedge2); \
symself(triedge2);
#define rprevself(triedge) \
symself(triedge); \
lprevself(triedge); \
symself(triedge);
/* These primitives determine or set the origin, destination, or apex of a *//* triangle. */
#define org(triedge, pointptr) \
pointptr = (point) (triedge).tri[plus1mod3[(triedge).orient] + 3]
#define dest(triedge, pointptr) \
pointptr = (point) (triedge).tri[minus1mod3[(triedge).orient] + 3]
#define apex(triedge, pointptr) \
pointptr = (point) (triedge).tri[(triedge).orient + 3]
#define setorg(triedge, pointptr) \
(triedge).tri[plus1mod3[(triedge).orient] + 3] = (triangle) pointptr
#define setdest(triedge, pointptr) \
(triedge).tri[minus1mod3[(triedge).orient] + 3] = (triangle) pointptr
#define setapex(triedge, pointptr) \
(triedge).tri[(triedge).orient + 3] = (triangle) pointptr
#define setvertices2null(triedge) \
(triedge).tri[3] = (triangle) NULL; \
(triedge).tri[4] = (triangle) NULL; \
(triedge).tri[5] = (triangle) NULL;
/* Bond two triangles together. */
#define bond(triedge1, triedge2) \
(triedge1).tri[(triedge1).orient] = encode(triedge2); \
(triedge2).tri[(triedge2).orient] = encode(triedge1)
/* 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(triedge) \
(triedge).tri[(triedge).orient] = (triangle) dummytri
/* Copy a triangle/edge handle. */
#define triedgecopy(triedge1, triedge2) \
(triedge2).tri = (triedge1).tri; \
(triedge2).orient = (triedge1).orient
/* Test for equality of triangle/edge handles. */
#define triedgeequal(triedge1, triedge2) \
(((triedge1).tri == (triedge2).tri) && \
((triedge1).orient == (triedge2).orient))
/* Primitives to infect or cure a triangle with the virus. These rely on */
/* the assumption that all shell edges are aligned to four-byte boundaries.*/
#define infect(triedge) \
(triedge).tri[6] = (triangle) \
((unsigned long) (triedge).tri[6] | (unsigned long) 2l)
#define uninfect(triedge) \
(triedge).tri[6] = (triangle) \
((unsigned long) (triedge).tri[6] & ~ (unsigned long) 2l)
/* Test a triangle for viral infection. */
#define infected(triedge) \
(((unsigned long) (triedge).tri[6] & (unsigned long) 2l) != 0)
/* Check or set a triangle's attributes. */
#define elemattribute(triedge, attnum) \ ((REAL *) (triedge).tri)[elemattribindex + (attnum)]
#define setelemattribute(triedge, attnum, value) \
((REAL *) (triedge).tri)[elemattribindex + (attnum)] = value
/* Check or set a triangle's maximum area bound. */
#define areabound(triedge) ((REAL *) (triedge).tri)[areaboundindex]
#define setareabound(triedge, value) \
((REAL *) (triedge).tri)[areaboundindex] = value
/********* Primitives for shell edges *********/
/* */
/* */
/* sdecode() converts a pointer to an oriented shell edge. 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, edge) \
(edge).shorient = (int) ((unsigned long) (sptr) & (unsigned long) 1l); \
(edge).sh = (shelle *) \
((unsigned long) (sptr) & ~ (unsigned long) 3l)
/* sencode() compresses an oriented shell edge into a single pointer. It */
/* relies on the assumption that all shell edges are aligned to two-byte */
/* boundaries, so the least significant bit of (edge).sh is zero. */
#define sencode(edge) \
(shelle) ((unsigned long) (edge).sh | (unsigned long) (edge).shorient)
/* ssym() toggles the orientation of a shell edge. */
#define ssym(edge1, edge2) \
(edge2).sh = (edge1).sh; \
(edge2).shorient = 1 - (edge1).shorient
#define ssymself(edge) \
(edge).shorient = 1 - (edge).shorient
/* spivot() finds the other shell edge (from the same segment) that shares */
/* the same origin. */
#define spivot(edge1, edge2) \
sptr = (edge1).sh[(edge1).shorient]; \
sdecode(sptr, edge2)
#define spivotself(edge) \
sptr = (edge).sh[(edge).shorient]; \
sdecode(sptr, edge)
/* snext() finds the next shell edge (from the same segment) in sequence; */
/* one whose origin is the input shell edge's destination. */
#define snext(edge1, edge2) \
sptr = (edge1).sh[1 - (edge1).shorient]; \
sdecode(sptr, edge2)
#define snextself(edge) \
sptr = (edge).sh[1 - (edge).shorient]; \
sdecode(sptr, edge)
/* These primitives determine or set the origin or destination of a shell */
/* edge. */
#define sorg(edge, pointptr) \
pointptr = (point) (edge).sh[2 + (edge).shorient]
#define sdest(edge, pointptr) \
pointptr = (point) (edge).sh[3 - (edge).shorient]
#define setsorg(edge, pointptr) \
(edge).sh[2 + (edge).shorient] = (shelle) pointptr
#define setsdest(edge, pointptr) \
(edge).sh[3 - (edge).shorient] = (shelle) pointptr
/* These primitives read or set a shell marker. Shell markers are used to */
/* hold user boundary information. */
#define mark(edge) (* (int *) ((edge).sh + 6))
#define setmark(edge, value) \
* (int *) ((edge).sh + 6) = value
/* Bond two shell edges together. */
#define sbond(edge1, edge2) \
(edge1).sh[(edge1).shorient] = sencode(edge2); \
(edge2).sh[(edge2).shorient] = sencode(edge1)
/* Dissolve a shell edge bond (from one side). Note that the other shell */
/* edge will still think it's connected to this shell edge. */
#define sdissolve(edge) \
(edge).sh[(edge).shorient] = (shelle) dummysh
/* Copy a shell edge. */
#define shellecopy(edge1, edge2) \
(edge2).sh = (edge1).sh; \
(edge2).shorient = (edge1).shorient
/* Test for equality of shell edges. */
#define shelleequal(edge1, edge2) \
(((edge1).sh == (edge2).sh) && \
((edge1).shorient == (edge2).shorient))
/********* Primitives for interacting triangles and shell edges *********/
/* */
/* */
/* tspivot() finds a shell edge abutting a triangle. */
#define tspivot(triedge, edge) \
sptr = (shelle) (triedge).tri[6 + (triedge).orient]; \
sdecode(sptr, edge)
/* stpivot() finds a triangle abutting a shell edge. It requires that the */
/* variable `ptr' of type `triangle' be defined. */
#define stpivot(edge, triedge) \
ptr = (triangle) (edge).sh[4 + (edge).shorient]; \
decode(ptr, triedge)
/* Bond a triangle to a shell edge. */
#define tsbond(triedge, edge) \
(triedge).tri[6 + (triedge).orient] = (triangle) sencode(edge); \
(edge).sh[4 + (edge).shorient] = (shelle) encode(triedge)
/* Dissolve a bond (from the triangle side). */
#define tsdissolve(triedge) \
(triedge).tri[6 + (triedge).orient] = (triangle) dummysh
/* Dissolve a bond (from the shell edge side). */
#define stdissolve(edge) \
(edge).sh[4 + (edge).shorient] = (shelle) dummytri
/********* Primitives for points *********/
/* */
/* */
#define pointmark(pt) ((int *) (pt))[pointmarkindex]
#define setpointmark(pt, value) \
((int *) (pt))[pointmarkindex] = value
#define point2tri(pt) ((triangle *) (pt))[point2triindex]
#define setpoint2tri(pt, value) \
((triangle *) (pt))[point2triindex] = value
/** **/
/** **/
/********* Mesh manipulation primitives 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 [-pAcevngBPNEIOXzo_lQVh] input_file\n");
#else /* not REDUCED */
printf("triangle [-pAcevngBPNEIOXzo_iFlCQVh] input_file\n");
#endif /* not REDUCED */
#else /* not CDT_ONLY */
#ifdef REDUCED
printf("triangle [-prq__a__AcevngBPNEIOXzo_YS__lQVh] input_file\n");
#else /* not REDUCED */
printf("triangle [-prq__a__AcevngBPNEIOXzo_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");
#endif /* not CDT_ONLY */
printf(
" -A Applies attributes to identify elements in certain regions.\n");
printf(" -c Encloses the convex hull with segments.\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");
exit(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 1.3\n\n");
printf(
"Copyright 1996 Jonathan Richard Shewchuk (bugs/comments to jrs@cs.cmu.edu)\n"
);
printf("School of Computer Science / Carnegie Mellon University\n");
printf("5000 Forbes Avenue / Pittsburgh, Pennsylvania 15213-3891\n");
printf(
"Created as part of the Archimedes project (tools for parallel FEM).\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, and quality conforming Delaunay triangulations. The latter\n"
);
printf(
"can be generated with no small angles, and are thus suitable for finite\n");
printf(
"element analysis. If no command line switches are specified, your .node\n");
printf(
"input file will be read, and the Delaunay triangulation will be returned in\n"
);
printf(".node and .ele output files. The command syntax is:\n\n");
#ifdef CDT_ONLY#ifdef REDUCED
printf("triangle [-pAcevngBPNEIOXzo_lQVh] input_file\n\n");
#else /* not REDUCED */
printf("triangle [-pAcevngBPNEIOXzo_iFlCQVh] input_file\n\n");
#endif /* not REDUCED */
#else /* not CDT_ONLY */
#ifdef REDUCED
printf("triangle [-prq__a__AcevngBPNEIOXzo_YS__lQVh] input_file\n\n");
#else /* not REDUCED */
printf("triangle [-prq__a__AcevngBPNEIOXzo_YS__iFlsCQVh] input_file\n\n");
#endif /* not REDUCED */
#endif /* not CDT_ONLY */
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 .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(
" points, segments, holes, and regional attributes and area\n");
printf(
" constraints. Will generate a constrained Delaunay triangulation\n");
printf(
" fitting the input; or, if -s, -q, or -a is used, a conforming\n");
printf(
" Delaunay triangulation. If -p is not used, Triangle reads a .node\n"
);
printf(" 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 edges in the mesh. Further details on\n");
printf(" refinement are given below.\n");
printf(
" -q Quality mesh generation by Jim Ruppert's Delaunay refinement\n");
printf(
" algorithm. Adds points to the mesh to ensure that no angles\n");
printf(
" smaller than 20 degrees occur. An alternative minimum angle may be\n"
);
printf(
" specified after the `q'. If the minimum angle is 20.7 degrees or\n");
printf(
" smaller, the triangulation algorithm is theoretically guaranteed to\n"
);
printf(
" terminate (assuming infinite precision arithmetic - Triangle may\n");
printf(
" fail to terminate if you run out of precision). In practice, the\n");
printf(
" algorithm often succeeds for minimum angles up to 33.8 degrees.\n");
printf(
" For highly refined meshes, however, it may be necessary to reduce\n");
printf(
" the minimum angle to well below 20 to avoid problems associated\n");
printf(
" with insufficient floating-point precision. The specified angle\n");
printf(" may include a decimal point.\n"); printf(
" -a Imposes a maximum triangle area. If a number follows the `a', no\n");
printf(
" triangle will be generated whose area is larger than that number.\n");
printf(
" If no number is specified, an .area file (if -r is used) or .poly\n");
printf(
" file (if -r is not used) specifies a number of maximum area\n");
printf(
" constraints. An .area file contains a separate area constraint for\n"
);
printf(
" each triangle, and is useful for refining a finite element mesh\n");
printf(
" based on a posteriori error estimates. A .poly file can optionally\n"
);
printf(
" contain an area constraint for each segment-bounded region, thereby\n"
);
printf(
" enforcing triangle densities in a first triangulation. You can\n");
printf(
" impose both a fixed area constraint and a varying area constraint\n");
printf(
" by invoking the -a switch twice, once with and once without a\n");
printf(
" number following. Each area specified may include a decimal point.\n"
);
printf(
" -A Assigns an additional attribute to each triangle that identifies\n");
printf(
" what segment-bounded region each triangle belongs to. Attributes\n");
printf(
" are assigned to regions by the .poly file. If a region is not\n");
printf(
" explicitly marked by the .poly file, triangles in that region are\n");
printf(
" assigned an attribute of zero. The -A switch has an effect only\n");
printf(" 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 point set, this switch causes a .poly file to\n");
printf(
" be written, containing all edges in the convex hull. (By default,\n"
);
printf(
" a .poly file is written only if a .poly file is read.) If you are\n"
);
printf(
" triangulating a PSLG, this switch specifies that the interior of\n");
printf(
" the convex hull of the PSLG should be triangulated. If you do not\n"
);
printf(
" use this switch when triangulating a PSLG, it is assumed that you\n");
printf(
" have identified the region to be triangulated by surrounding it\n");
printf(
" with segments of the input PSLG. Beware: if you are not careful,\n"
);
printf(
" this switch can cause the introduction of an extremely thin angle\n");
printf(
" between a PSLG segment and a convex hull segment, which can cause\n");
printf(
" overrefinement or failure if Triangle runs out of precision. If\n");
printf(
" you are refining a mesh, the -c switch works differently; it\n");
printf(" generates the set of boundary edges of the mesh, rather than the\n");
printf(" convex hull.\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.\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 impose segment constraints 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 will be written.) Cannot be used\n");
printf(
" with the -r switch, because that would overwrite your input .ele\n");
printf(
" file. Shouldn't be used with the -s, -q, or -a switch if you are\n");
printf(
" using a .node file for input, because no .node file will be\n");
printf(" written, so there will be no record of any added 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 will cause a small\n");
printf(
" improvement in speed and create the possibility (albeit small) that\n"
);
printf(
" Triangle will 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 overrided by the value used to number the\n");
printf(
" first point of the input .node or .poly file. However, this switch\n"
);
printf(" 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 points on the boundary. This switch is useful when the mesh\n");
printf(
" boundary must be preserved so that it conforms to some adjacent\n");
printf(
" mesh. Be forewarned that you will probably sacrifice some of the\n");
printf(
" quality of the mesh; Triangle will try, but the resulting mesh may\n"
);
printf(
" contain triangles of poor aspect ratio. Works well if all the\n");
printf(
" boundary points 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 (points that are not\n"
);
printf(
" in the input, but are added to meet the constraints of 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 points at segment\n");
printf(
" intersections, even if it needs to use more points than the limit\n");
printf(
" you set. When Triangle inserts segments by splitting (-s), it\n");
printf(
" always adds enough points to ensure that all the segments appear in\n"
);
printf(
" the triangulation, again ignoring the limit. Be forewarned that\n");
printf(
" the -S switch may result in a conforming triangulation that is not\n"
);
printf(
" truly Delaunay, because Triangle may be forced to stop adding\n");
printf(
" points when the mesh is in a state where a segment is non-Delaunay\n"
);
printf(
" and needs to be split. If so, Triangle will print a warning.\n");
printf(
" -i Uses an incremental rather than divide-and-conquer algorithm to\n");
printf(
" form a Delaunay triangulation. Try it if the divide-and-conquer\n");
printf(" algorithm fails.\n");
printf(
" -F Uses Steven Fortune's sweepline algorithm to form 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 uses alternating vertical and horizontal cuts,\n");
printf(
" which usually improve the speed except with point 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 near external small features.\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, unless\n"
);
printf(" 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' gives\n");
printf(
" information on algorithmic progress and more detailed statistics.\n");
printf(
" `-VV' gives point-by-point details, and will print so much that\n");
printf(
" Triangle will run much more slowly. `-VVV' gives information only\n"
);
printf(" 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 point set is a triangulation whose vertices\n"
);
printf(
" are the point set, having the property that no point in the point set\n");
printf(
" falls in the interior of the circumcircle (circle that passes through all\n"
);
printf(" three vertices) of any triangle in the triangulation.\n\n");
printf(
" A Voronoi diagram of a point set is a subdivision of the plane into\n");
printf(
" polygonal regions (some of which may be infinite), where each region is\n");
printf(
" the set of points in the plane that are closer to some input point than\n");
printf(
" to any other input point. (The Voronoi diagram is the geometric dual of\n"
);
printf(" the Delaunay triangulation.)\n\n");
printf(
" A Planar Straight Line Graph (PSLG) is a collection of points and\n");
printf(
" segments. Segments are simply edges, whose endpoints are points in the\n");
printf(
" PSLG. The file format for PSLGs (.poly files) is described below.\n");
printf("\n");
printf(
" A constrained Delaunay triangulation of a PSLG is similar to a Delaunay\n");
printf(
" triangulation, but each PSLG segment is present as a single edge in the\n");
printf(
" triangulation. (A constrained Delaunay triangulation is not truly a\n");
printf(" Delaunay triangulation.)\n\n");
printf(
" A conforming Delaunay triangulation of a PSLG is a true Delaunay\n");
printf(
" triangulation in which each PSLG segment may have been subdivided into\n");
printf(" several edges by the insertion of additional points. These inserted\n");
printf(
" points are necessary to allow the segments to exist in the mesh while\n");
printf(" maintaining the Delaunay property.\n\n");
printf("File Formats:\n\n");
printf(
" All files may contain comments prefixed by the character '#'. Points,\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 nodes are numbered from 1, so must\n"
);
printf(
" be all other objects. Triangle automatically detects your choice while\n");
printf(
" reading the .node (or .poly) file. (When calling Triangle from another\n");
printf(
" program, use the -z switch if you wish to number objects from zero.)\n");
printf(" Examples of these file formats are given below.\n\n");
printf(" .node files:\n");
printf(
" First line: <# of points> <dimension (must be 2)> <# of attributes>\n");
printf(
" <# of boundary markers (0 or 1)>\n"
);
printf(
" Remaining lines: <point #> <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 -s,\n"
);
printf(
" -q, or -a is selected, each new Steiner point added to the mesh will\n");
printf(" have 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 points and points resting on PSLG\n"
);
printf(
" segments; a complete description appears in a section below. The .node\n"
);
printf(
" file produced by Triangle will contain 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> <points per triangle> <# of attributes>\n");
printf(
" Remaining lines: <triangle #> <point> <point> <point> ... [attributes]\n"
);
printf("\n");
printf(
" Points are indices into the corresponding .node file. The first three\n"
);
printf(
" points are the corners, and are listed in counterclockwise order around\n"
);
printf(
" each triangle. (The remaining points, if any, depend on the type of\n"); printf(
" finite element used.) The attributes are just like those of .node\n");
printf(
" files. Because there is no simple mapping from input to output\n");
printf(
" triangles, an attempt is made to interpolate attributes, which may\n");
printf(
" result in a good deal of diffusion of attributes among nearby triangles\n"
);
printf(
" as the triangulation is refined. Diffusion does not occur across\n");
printf(
" segments, so attributes used to identify segment-bounded regions remain\n"
);
printf(
" intact. In output .ele files, all triangles have three points each\n");
printf(
" unless the -o2 switch is used, in which case they have six, and the\n");
printf(
" fourth, fifth, and sixth points lie on the midpoints of the edges\n");
printf(" opposite the first, second, and third corners.\n\n");
printf(" .poly files:\n");
printf(
" First line: <# of points> <dimension (must be 2)> <# of attributes>\n");
printf(
" <# of boundary markers (0 or 1)>\n"
);
printf(
" Following lines: <point #> <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: <constraint #> <x> <y> <attrib> <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 points, and is identical to the format\n"
);
printf(
" of .node files. <# of points> may be set to zero to indicate that the\n"
);
printf(
" points are listed in a separate .node file; .poly files produced by\n");
printf(
" Triangle always have this format. This has the advantage that a point\n"
);
printf(
" set may easily be triangulated with or without segments. (The same\n");
printf(
" effect can be achieved, albeit using more disk space, by making a copy\n"
);
printf(
" of the .poly file with the extension .node; all sections of the file\n");
printf(" but the first are ignored.)\n\n");
printf(
" The second section lists the segments. Segments are edges whose\n");
printf(
" presence in the triangulation is enforced. Each segment is specified\n");
printf(
" by listing the indices of its two endpoints. This means that you must\n"
);
printf(
" include its endpoints in the point list. If -s, -q, and -a are not\n"); printf(
" selected, Triangle will produce a constrained Delaunay triangulation,\n");
printf(
" in which each segment appears as a single edge in the triangulation.\n");
printf(
" If -q or -a is selected, Triangle will produce a conforming Delaunay\n");
printf(
" triangulation, in which segments may be subdivided into smaller edges.\n"
);
printf(" Each segment, like each point, may have a boundary marker.\n\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 PSLG segments; you must be careful to enclose\n");
printf(
" each hole in segments, or your whole triangulation may be eaten away.\n");
printf(
" If the two triangles abutting a segment are eaten, the segment itself\n");
printf(
" is also eaten. Do not place a hole directly on a segment; if you do,\n");
printf(" Triangle will choose one side of the segment 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 will read this section only if the -A switch\n");
printf(
" is used or the -a switch is used without a number following it, and the\n"
);
printf(
" -r 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 will\n");
printf(
" affect the whole region (bounded by segments) containing the point. If\n"
);
printf(
" two values are written on a line after the x and y coordinate, the\n");
printf(
" former is assumed to be a regional attribute (but will only be applied\n"
);
printf(
" if the -A switch is selected), and the latter is assumed to be a\n");
printf(
" regional area constraint (but will only be applied if the -a switch is\n"
);
printf(
" selected). You may also 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 encloses the convex hull of the input point\n");
printf(
" set. If you do not use the -c switch, Triangle will eat all triangles\n"
);
printf(
" on the outer boundary that are not protected by segments; if you are\n");
printf(
" not careful, your whole triangulation may be eaten away. If you do\n");
printf(
" use the -c switch, you can still produce concavities by appropriate\n");
printf(" placement of holes just inside the convex hull.\n\n");
printf(
" An ideal PSLG has no intersecting segments, nor any points 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 will calculate the intersection points for you and add 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 point at the middle of a segment, and hope that Triangle will\n");
printf(
" break up the segment at that point, you might get lucky. On the other\n"
);
printf(
" hand, Triangle might decide that the point doesn't lie precisely on the\n"
);
printf(
" line, and you'll have a needle-sharp triangle in your output - or a lot\n"
);
printf(" of tiny triangles if you're generating a quality mesh.\n\n");
printf(
" When Triangle reads a .poly file, it also writes a .poly file, which\n");
printf(
" includes all edges that are part of input segments. If the -c switch\n");
printf(
" is used, the output .poly file will also include all of the edges on\n");
printf(
" the convex hull. Hence, the output .poly file is useful for finding\n"); printf(
" edges associated with input segments and setting boundary conditions in\n"
);
printf(
" finite element simulations. More importantly, you will need it if you\n"
);
printf(
" plan to refine the output mesh, and don't want segments to be missing\n");
printf(" in later triangulations.\n\n");
printf(" .area files:\n");
printf(" First line: <# of triangles>\n");
printf(" Following lines: <triangle #> <maximum area>\n\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 they must be numbered consecutively. A triangle\n");
printf(
" may be left unconstrained by assigning it a negative maximum area.\n");
printf("\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 a mesh boundary, and therefore no neighbor. Triangle can\n");
printf(
" produce .neigh files (use the -n switch), but cannot read them.\n");
printf("\n");
printf(
" The first neighbor of triangle i is opposite the first corner of\n");
printf(" triangle i, and so on.\n\n");
printf("Boundary Markers:\n\n");
printf(
" Boundary markers are tags used mainly to identify which output points and\n"
);
printf(
" edges are associated with which PSLG segment, and to identify which\n");
printf(" points and edges occur on a boundary of the triangulation. A common use\n"
);
printf(
" is to determine where boundary conditions should be applied to a finite\n");
printf(
" element mesh. You can prevent boundary markers from being written into\n");
printf(" 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(" or 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 occurs on a boundary of the triangulation\n");
printf(
" (including boundaries of holes), 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 point in an output .node file is\n"
);
printf(" chosen as follows:\n");
printf(
" - If a point 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 point lies on a PSLG segment (including the\n");
printf(
" segment's endpoints) with a nonzero boundary marker, then the point\n");
printf(
" is assigned the same marker. If the point lies on several such\n");
printf(" segments, one of the markers is chosen arbitrarily.\n");
printf(
" - Otherwise, if the point occurs on a boundary of the triangulation,\n");
printf(" then the point is assigned the marker one (1).\n");
printf(" - Otherwise, the point is assigned the marker zero (0).\n");
printf("\n");
printf(
" If you want Triangle to determine for you which points 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. Alternatively, you can mark some of them and\n");
printf(" leave others marked zero, allowing Triangle to label them.\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 will\n");
printf(
" also disable output of .node and .poly files to prevent your input files\n"
);
printf(
" from being overwritten. (If the input is a .poly file that contains its\n"
);
printf(" own points, a .node file will be written.)\n\n");
printf("Examples of How to Use Triangle:\n\n");
printf(
" `triangle dots' will read points from dots.node, and write their Delaunay\n"
);
printf(
" triangulation to dots.1.node and dots.1.ele. (dots.1.node will be\n");
printf(
" identical to dots.node.) `triangle -I dots' writes the triangulation to\n"
);
printf(
" dots.ele instead. (No additional .node file is needed, so none is\n");
printf(" written.)\n\n");
printf(
" `triangle -pe object.1' will read a PSLG from object.1.poly (and possibly\n"
);
printf(
" object.1.node, if the points are omitted from object.1.poly) and write\n");
printf(" their constrained Delaunay triangulation to object.2.node and\n");
printf(
" object.2.ele. The segments will be copied to object.2.poly, and all\n");
printf(" edges will be written to object.2.edge.\n\n");
printf(
" `triangle -pq31.5a.1 object' will read a PSLG from object.poly (and\n");
printf(
" possibly object.node), generate a mesh whose angles are all greater than\n"
);
printf(
" 31.5 degrees and whose triangles all have area smaller than 0.1, and\n");
printf(
" write the mesh to object.1.node and object.1.ele. Each segment may have\n"
);
printf(
" been broken up into multiple edges; the resulting constrained edges are\n");
printf(" written to object.1.poly.\n\n");
printf(
" Here is a sample file `box.poly' describing a square with a square hole:\n"
);
printf("\n");
printf(
" # A box with eight points 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 point.\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(" 2 5 7 0 # Segments 2 through 5 enclose the hole.\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\n");
printf(
" Note that some segments are missing from the outer square, so one must\n");
printf(
" use the `-c' switch. After `triangle -pqc box.poly', here is the output\n"
);
printf(
" file `box.1.node', with twelve points. The last four points were added\n");
printf(
" to meet the angle constraint. Points 1, 2, and 9 have markers from\n");
printf(
" segment 1. Points 6 and 8 have markers from segment 4. All the other\n");
printf(
" points but 4 have been marked to indicate that they lie on a boundary.\n");
printf("\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\n");
printf(" Here is the output file `box.1.ele', with twelve triangles.\n\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 split by newly\n"
);
printf(
" added points. Note also that <# of points> is set to zero to indicate\n");
printf(" that the points should be read from the .node file.\n\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\n");
printf("Refinement and Area Constraints:\n\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 divided into smaller edges) by the refinement process.\n");
printf("\n");
printf(
" When you refine a mesh, you generally want to impose tighter quality\n");
printf(
" constraints. One way to accomplish this is to use -q with a larger\n");
printf(
" angle, or -a followed by a smaller area than you used to generate the\n");
printf(
" mesh you are refining. Another way to do this is to create an .area\n");
printf(
" file, which specifies a maximum area for each triangle, and use the -a\n");
printf(
" switch (without a number following). Each triangle's area constraint is\n"
);
printf(
" applied to that triangle. Area constraints tend to diffuse as the mesh\n");
printf(
" is refined, so if there are large variations in area constraint between\n");
printf(" adjacent triangles, you may not get the results you want.\n\n");
printf(
" If you are refining a mesh composed of linear (three-node) elements, the\n"
);
printf(
" output mesh will contain all the nodes present in the input mesh, in the\n"
);
printf(
" same order, with new nodes added at the end of the .node file. However,\n"
);
printf(
" there is no guarantee that each output element is contained in a single\n");
printf(
" input element. Often, output elements will overlap two input elements,\n");
printf(
" and input edges are not present in the output mesh. Hence, a sequence of\n"
);
printf(
" refined meshes will form a hierarchy of nodes, but not a hierarchy of\n");
printf(
" elements. If you a refining a mesh of higher-order elements, the\n");
printf(
" hierarchical property applies only to the nodes at the corners of an\n");
printf(" element; other nodes may not be present in the refined mesh.\n\n");
printf(
" It is important to understand that maximum area constraints in .poly\n");
printf(
" files are handled differently from those in .area files. A maximum area\n"
);
printf(
" in a .poly file applies to the whole (segment-bounded) region in which a\n"
);
printf(
" point falls, whereas a maximum area in an .area file applies to only one\n"
);
printf(
" triangle. Area constraints in .poly files are used only when a mesh is\n");
printf(" first generated, whereas area constraints in .area files are used only to\n"
);
printf(
" refine an existing mesh, and are typically based on a posteriori error\n");
printf(
" estimates resulting from a finite element simulation on that mesh.\n");
printf("\n");
printf(
" `triangle -rq25 object.1' will read object.1.node and object.1.ele, then\n"
);
printf(
" refine the triangulation to enforce a 25 degree minimum angle, and then\n");
printf(
" write the refined triangulation to object.2.node and object.2.ele.\n");
printf("\n");
printf(
" `triangle -rpaa6.2 z.3' will read z.3.node, z.3.ele, z.3.poly, and\n");
printf(
" z.3.area. After reconstructing the mesh and its segments, Triangle will\n"
);
printf(
" refine the mesh so that no triangle has area greater than 6.2, and\n");
printf(
" furthermore the triangles satisfy the maximum area constraints in\n");
printf(
" z.3.area. The output is written to z.4.node, z.4.ele, and z.4.poly.\n");
printf("\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 point set (rather than a PSLG), Triangle produces its\n");
printf(
" convex hull as a by-product in the output .poly file if you use the -c\n");
printf(
" switch. There are faster algorithms for finding a two-dimensional convex\n"
);
printf(
" hull than triangulation, of course, but this one comes for free. If the\n"
);
printf(
" input is an unconstrained mesh (you are using the -r switch but not the\n");
printf(
" -p switch), Triangle produces a list of its boundary edges (including\n");
printf(" hole boundaries) as a by-product if you use the -c switch.\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' will read points.node,\n");
printf(
" produce its Delaunay triangulation in points.1.node and points.1.ele,\n");
printf(
" and produce its Voronoi diagram in points.1.v.node and points.1.v.edge.\n");
printf(
" The .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 points, crossing\n"
);
printf(
" edges, or infinite rays whose direction vector is zero. Also, if you\n");
printf(
" generate a constrained (as opposed to conforming) Delaunay triangulation,\n"
);
printf(
" or if the triangulation has holes, the corresponding Voronoi diagram is\n");
printf(" likely to have crossing edges and unlikely to make sense.\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 regions are adjacent to a certain\n");
printf(
" Voronoi edge in a .v.edge file, or which Voronoi regions 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 diagrams 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; and Voronoi region k is the\n");
printf(" dual of point 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; their dual triangles are on\n");
printf(
" the left and right of the Delaunay edge, respectively. To find the\n");
printf(
" Voronoi regions adjacent to a Voronoi edge, look at the endpoints of the\n"
);
printf(
" corresponding Delaunay edge; their dual regions are on the right and left\n"
);
printf(
" of the Voronoi edge, respectively. To find which Voronoi regions are\n");
printf(" adjacent to each other, just read the list of Delaunay edges.\n");
printf("\n");
printf("Statistics:\n");
printf("\n");
printf(
" After generating a mesh, Triangle prints a count of the number of points,\n"
);
printf(
" triangles, edges, boundary edges, and segments in the output mesh. If\n");
printf(
" you've forgotten the statistics for an existing mesh, the -rNEP switches\n"
);
printf(
" (or -rpNEP if you've got a .poly file for the existing mesh) will\n");
printf(" regenerate these statistics without writing any output.\n\n");
printf(
" The -V switch produces extended statistics, including a rough estimate\n");
printf(
" of memory use and a histogram of triangle aspect ratios and angles 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(
" registers, then your output is guaranteed to be an absolutely true\n");
printf(" Delaunay or conforming Delaunay triangulation, roundoff error\n");
printf(
" 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. The exact tests can be disabled with the -X switch. On\n");
printf(
" most inputs, this switch will reduce the computation time by about eight\n"
);
printf(
" percent - it's not worth the risk. There are rare difficult inputs\n");
printf(
" (having many collinear and cocircular points), however, for which the\n");
printf(
" difference could be a factor of two. These are precisely the inputs most\n"
);
printf(" likely to cause errors if you use the -X switch.\n\n");
printf(
" Unfortunately, these routines don't solve every numerical problem. Exact\n"
);
printf(
" arithmetic is not used to compute the positions of points, because the\n");
printf(
" bit complexity of point coordinates would grow without bound. Hence,\n");
printf(
" segment intersections aren't computed exactly; in very unusual cases,\n");
printf(
" roundoff error in computing an intersection point might actually lead to\n"
);
printf(
" an inverted triangle and an invalid triangulation. (This is one reason\n");
printf(
" to compute your own intersection points in your .poly files.) Similarly,\n"
);
printf(
" exact arithmetic is not used to compute the vertices of the Voronoi\n");
printf(" diagram.\n\n");
printf(
" Underflow and overflow can also cause difficulties; the exact arithmetic\n"
);
printf(
" routines do not ameliorate out-of-bounds exponents, which can arise\n");
printf(
" during the orientation and incircle tests. As a rule of thumb, you\n");
printf(
" should ensure that your input values are within a range such that their\n");
printf(
" third powers can be taken without underflow or overflow. Underflow can\n");
printf(
" silently prevent the tests from being performed exactly, while overflow\n");
printf(" will typically cause a floating 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. To test these possibilities, try again with\n"
);
printf(
" the -c and -O switches. Alternatively, all your input points may be\n");
printf(
" collinear, in which case you can hardly expect to triangulate them.\n");
printf("\n");
printf(" `Triangle doesn't terminate, or just crashes.'\n");
printf("\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 point set, or even inside the densest part of your\n");
printf(
" mesh. On the other hand, if you're triangulating an object whose x\n");
printf(
" coordinates all fall between 6247133 and 6247134, you're not leaving\n");
printf(" much floating-point 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 a very small angle, or if such an\n"
);
printf(
" angle is introduced by the -c switch, which may occur if a point lies\n");
printf(
" ever-so-slightly inside the convex hull, and is connected by a PSLG\n");
printf(
" segment to a point on the convex hull. If you don't realize that a\n");
printf(
" small angle is being formed, you might never discover why Triangle is\n");
printf(
" crashing. To check for this possibility, use the -S switch (with an\n");
printf(
" appropriate limit on the number of Steiner points, found by trial-and-\n"
);
printf(
" error) to stop Triangle early, and view the output .poly file with\n");
printf(
" Show Me (described below). Look carefully for small angles between\n");
printf(
" segments; zoom in closely, as such segments might look like a single\n");
printf(" segment from 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(
" `The numbering of the output points doesn't match the input points.'\n");
printf("\n");
printf(
" You may have eaten some of your input points with a hole, or by placing\n"
);
printf(" them outside the area enclosed by segments.\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's divide-and-conquer Delaunay\n");
printf(
" triangulation algorithm occasionally makes mistakes due to floating-\n");
printf(
" point roundoff error. Although these errors are rare, don't use the -X\n"
);
printf(" switch. If you still have problems, please report the bug.\n");
printf("\n");
printf(
" Strange things can happen if you've taken liberties with your PSLG. Do\n");
printf(
" you have a point 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 points? Have you simply defined\n"
);
printf(
" one long segment connecting the leftmost point to the rightmost point,\n");
printf(
" and a bunch of points lying along it? This method occasionally works,\n");
printf(
" especially with horizontal and vertical lines, but often it doesn't, and\n"
);
printf(
" you'll have to connect each adjacent pair of points with a separate\n");
printf(" 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(" points 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(" points are their corners in counterclockwise order?\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. Show Me requires that you have the X\n");
printf(
" Windows system. If you didn't receive Show Me with Triangle, complain to\n"
);
printf(" whomever you obtained Triangle from, then send me mail.\n\n");
printf("Triangle on the Web:\n\n");
printf(
" To see an illustrated, updated 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.cmu.edu) describing how you use Triangle will mean a lot to\n");
printf(
" me. The more people I know are using this program, the more easily I can\n"
);
printf(
" justify spending time on improvements and on the three-dimensional\n");
printf(
" successor to Triangle, which in turn will benefit you. Also, I can put\n");
printf(
" you on a list to receive email whenever a new version of Triangle is\n");
printf(" available.\n\n");
printf(
" If you use a mesh generated by Triangle in a publication, please include\n"
);
printf(" an acknowledgment as well.\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, Boris Delaunay, Rex A. Dwyer, David\n");
printf(
" Eppstein, Steven Fortune, Leonidas J. Guibas, Donald E. Knuth, C. L.\n");
printf(
" Lawson, Der-Tsai Lee, Ernst P. Mucke, Douglas M. Priest, Jim Ruppert,\n");
printf(
" Isaac Saias, Bruce J. Schachter, Micha Sharir, Jorge Stolfi, Christopher\n"
);
printf(
" J. Van Wyk, David F. Watson, and Binhai Zhu. See the comments at the\n");
printf(" beginning of the source code for references.\n\n");
exit(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.cmu.edu\n");
printf(" Include the message above, your input data set, and the exact\n"); printf(" command line you used to run Triangle.\n");
exit(1);
}
/*****************************************************************************/
/* */
/* parsecommandline() Read the command line, identify switches, and set */
/* up options and file names. */
/* */
/* The effects of this routine are felt entirely through global variables. */
/* */
/*****************************************************************************/
void parsecommandline(argc, argv)
int argc;
char **argv;
{
#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];
poly = refine = quality = vararea = fixedarea = regionattrib = convex = 0;
firstnumber = 1;
edgesout = voronoi = neighbors = geomview = 0;
nobound = nopolywritten = nonodewritten = noelewritten = noiterationnum = 0;
noholes = noexact = 0;
incremental = sweepline = 0;
dwyer = 1;
splitseg = 0;
docheck = 0;
nobisect = 0;
steiner = -1;
order = 1;
minangle = 0.0;
maxarea = -1.0;
quiet = verbose = 0;
#ifndef TRILIBRARY
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') {
poly = 1;
}
#ifndef CDT_ONLY
if (argv[i][j] == 'r') {
refine = 1;
}
if (argv[i][j] == 'q') {
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'; minangle = (REAL) strtod(workstring, (char **) NULL);
} else {
minangle = 20.0;
}
}
if (argv[i][j] == 'a') {
quality = 1;
if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
(argv[i][j + 1] == '.')) {
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';
maxarea = (REAL) strtod(workstring, (char **) NULL);
if (maxarea <= 0.0) {
printf("Error: Maximum area must be greater than zero.\n");
exit(1);
}
} else {
vararea = 1;
}
}
#endif /* not CDT_ONLY */
if (argv[i][j] == 'A') {
regionattrib = 1;
}
if (argv[i][j] == 'c') {
convex = 1;
}
if (argv[i][j] == 'z') {
firstnumber = 0;
}
if (argv[i][j] == 'e') {
edgesout = 1;
}
if (argv[i][j] == 'v') {
voronoi = 1;
}
if (argv[i][j] == 'n') {
neighbors = 1;
}
if (argv[i][j] == 'g') {
geomview = 1;
}
if (argv[i][j] == 'B') {
nobound = 1;
}
if (argv[i][j] == 'P') {
nopolywritten = 1;
}
if (argv[i][j] == 'N') {
nonodewritten = 1;
}
if (argv[i][j] == 'E') {
noelewritten = 1;
}
#ifndef TRILIBRARY
if (argv[i][j] == 'I') {
noiterationnum = 1;
}
#endif /* not TRILIBRARY */
if (argv[i][j] == 'O') {
noholes = 1;
}
if (argv[i][j] == 'X') { noexact = 1;
}
if (argv[i][j] == 'o') {
if (argv[i][j + 1] == '2') {
j++;
order = 2;
}
}
#ifndef CDT_ONLY
if (argv[i][j] == 'Y') {
nobisect++;
}
if (argv[i][j] == 'S') {
steiner = 0;
while ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) {
j++;
steiner = steiner * 10 + (int) (argv[i][j] - '0');
}
}
#endif /* not CDT_ONLY */
#ifndef REDUCED
if (argv[i][j] == 'i') {
incremental = 1;
}
if (argv[i][j] == 'F') {
sweepline = 1;
}
#endif /* not REDUCED */
if (argv[i][j] == 'l') {
dwyer = 0;
}
#ifndef REDUCED
#ifndef CDT_ONLY
if (argv[i][j] == 's') {
splitseg = 1;
}
#endif /* not CDT_ONLY */
if (argv[i][j] == 'C') {
docheck = 1;
}
#endif /* not REDUCED */
if (argv[i][j] == 'Q') {
quiet = 1;
}
if (argv[i][j] == 'V') {
verbose++;
}
#ifndef TRILIBRARY
if ((argv[i][j] == 'h') || (argv[i][j] == 'H') ||
(argv[i][j] == '?')) {
info();
}
#endif /* not TRILIBRARY */
}
#ifndef TRILIBRARY
} else {
strncpy(innodefilename, argv[i], FILENAMESIZE - 1);
innodefilename[FILENAMESIZE - 1] = '\0';
}
#endif /* not TRILIBRARY */
}
#ifndef TRILIBRARY
if (innodefilename[0] == '\0') {
syntax();
}
if (!strcmp(&innodefilename[strlen(innodefilename) - 5], ".node")) {
innodefilename[strlen(innodefilename) - 5] = '\0';
}
if (!strcmp(&innodefilename[strlen(innodefilename) - 5], ".poly")) {
innodefilename[strlen(innodefilename) - 5] = '\0'; poly = 1;
}
#ifndef CDT_ONLY
if (!strcmp(&innodefilename[strlen(innodefilename) - 4], ".ele")) {
innodefilename[strlen(innodefilename) - 4] = '\0';
refine = 1;
}
if (!strcmp(&innodefilename[strlen(innodefilename) - 5], ".area")) {
innodefilename[strlen(innodefilename) - 5] = '\0';
refine = 1;
quality = 1;
vararea = 1;
}
#endif /* not CDT_ONLY */
#endif /* not TRILIBRARY */
steinerleft = steiner;
useshelles = poly || refine || quality || convex;
goodangle = cos(minangle * PI / 180.0);
goodangle *= goodangle;
if (refine && noiterationnum) {
printf(
"Error: You cannot use the -I switch when refining a triangulation.\n");
exit(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 (!refine && !poly) {
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 (refine || !poly) {
regionattrib = 0;
}
#ifndef TRILIBRARY
strcpy(inpolyfilename, innodefilename);
strcpy(inelefilename, innodefilename);
strcpy(areafilename, innodefilename);
increment = 0;
strcpy(workstring, 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 (noiterationnum) {
strcpy(outnodefilename, innodefilename);
strcpy(outelefilename, innodefilename);
strcpy(edgefilename, innodefilename);
strcpy(vnodefilename, innodefilename);
strcpy(vedgefilename, innodefilename);
strcpy(neighborfilename, innodefilename);
strcpy(offfilename, innodefilename);
strcat(outnodefilename, ".node");
strcat(outelefilename, ".ele"); strcat(edgefilename, ".edge");
strcat(vnodefilename, ".v.node");
strcat(vedgefilename, ".v.edge");
strcat(neighborfilename, ".neigh");
strcat(offfilename, ".off");
} else if (increment == 0) {
strcpy(outnodefilename, innodefilename);
strcpy(outpolyfilename, innodefilename);
strcpy(outelefilename, innodefilename);
strcpy(edgefilename, innodefilename);
strcpy(vnodefilename, innodefilename);
strcpy(vedgefilename, innodefilename);
strcpy(neighborfilename, innodefilename);
strcpy(offfilename, innodefilename);
strcat(outnodefilename, ".1.node");
strcat(outpolyfilename, ".1.poly");
strcat(outelefilename, ".1.ele");
strcat(edgefilename, ".1.edge");
strcat(vnodefilename, ".1.v.node");
strcat(vedgefilename, ".1.v.edge");
strcat(neighborfilename, ".1.neigh");
strcat(offfilename, ".1.off");
} else {
workstring[increment] = '%';
workstring[increment + 1] = 'd';
workstring[increment + 2] = '\0';
sprintf(outnodefilename, workstring, meshnumber + 1);
strcpy(outpolyfilename, outnodefilename);
strcpy(outelefilename, outnodefilename);
strcpy(edgefilename, outnodefilename);
strcpy(vnodefilename, outnodefilename);
strcpy(vedgefilename, outnodefilename);
strcpy(neighborfilename, outnodefilename);
strcpy(offfilename, outnodefilename);
strcat(outnodefilename, ".node");
strcat(outpolyfilename, ".poly");
strcat(outelefilename, ".ele");
strcat(edgefilename, ".edge");
strcat(vnodefilename, ".v.node");
strcat(vedgefilename, ".v.edge");
strcat(neighborfilename, ".neigh");
strcat(offfilename, ".off");
}
strcat(innodefilename, ".node");
strcat(inpolyfilename, ".poly");
strcat(inelefilename, ".ele");
strcat(areafilename, ".area");
#endif /* not TRILIBRARY */
}
/** **/
/** **/
/********* User interaction routines begin here *********/
/********* Debugging routines begin here *********/
/** **/
/** **/
/*****************************************************************************/
/* */
/* printtriangle() Print out the details of a triangle/edge handle. */
/* */
/* I originally wrote this procedure to simplify debugging; it can be */
/* called directly from the debugger, and presents information about a */
/* triangle/edge handle in digestible form. It's also used when the */
/* highest level of verbosity (`-VVV') is specified. */
/* */
/*****************************************************************************/
void printtriangle(t)struct triedge *t;
{
struct triedge printtri;
struct edge printsh;
point printpoint;
printf("triangle x%lx with orientation %d:\n", (unsigned long) t->tri,
t->orient);
decode(t->tri[0], printtri);
if (printtri.tri == 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 == 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 == dummytri) {
printf(" [2] = Outer space\n");
} else {
printf(" [2] = x%lx %d\n", (unsigned long) printtri.tri,
printtri.orient);
}
org(*t, printpoint);
if (printpoint == (point) 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) printpoint,
printpoint[0], printpoint[1]);
dest(*t, printpoint);
if (printpoint == (point) 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) printpoint,
printpoint[0], printpoint[1]);
apex(*t, printpoint);
if (printpoint == (point) NULL)
printf(" Apex [%d] = NULL\n", t->orient + 3);
else
printf(" Apex [%d] = x%lx (%.12g, %.12g)\n",
t->orient + 3, (unsigned long) printpoint,
printpoint[0], printpoint[1]);
if (useshelles) {
sdecode(t->tri[6], printsh);
if (printsh.sh != dummysh) {
printf(" [6] = x%lx %d\n", (unsigned long) printsh.sh,
printsh.shorient);
}
sdecode(t->tri[7], printsh);
if (printsh.sh != dummysh) {
printf(" [7] = x%lx %d\n", (unsigned long) printsh.sh,
printsh.shorient);
}
sdecode(t->tri[8], printsh);
if (printsh.sh != dummysh) {
printf(" [8] = x%lx %d\n", (unsigned long) printsh.sh,
printsh.shorient);
}
}
if (vararea) {
printf(" Area constraint: %.4g\n", areabound(*t));
}}
/*****************************************************************************/
/* */
/* printshelle() Print out the details of a shell edge handle. */
/* */
/* I originally wrote this procedure to simplify debugging; it can be */
/* called directly from the debugger, and presents information about a */
/* shell edge handle in digestible form. It's also used when the highest */
/* level of verbosity (`-VVV') is specified. */
/* */
/*****************************************************************************/
void printshelle(s)
struct edge *s;
{
struct edge printsh;
struct triedge printtri;
point printpoint;
printf("shell edge x%lx with orientation %d and mark %d:\n",
(unsigned long) s->sh, s->shorient, mark(*s));
sdecode(s->sh[0], printsh);
if (printsh.sh == dummysh) {
printf(" [0] = No shell\n");
} else {
printf(" [0] = x%lx %d\n", (unsigned long) printsh.sh,
printsh.shorient);
}
sdecode(s->sh[1], printsh);
if (printsh.sh == dummysh) {
printf(" [1] = No shell\n");
} else {
printf(" [1] = x%lx %d\n", (unsigned long) printsh.sh,
printsh.shorient);
}
sorg(*s, printpoint);
if (printpoint == (point) NULL)
printf(" Origin[%d] = NULL\n", 2 + s->shorient);
else
printf(" Origin[%d] = x%lx (%.12g, %.12g)\n",
2 + s->shorient, (unsigned long) printpoint,
printpoint[0], printpoint[1]);
sdest(*s, printpoint);
if (printpoint == (point) NULL)
printf(" Dest [%d] = NULL\n", 3 - s->shorient);
else
printf(" Dest [%d] = x%lx (%.12g, %.12g)\n",
3 - s->shorient, (unsigned long) printpoint,
printpoint[0], printpoint[1]);
decode(s->sh[4], printtri);
if (printtri.tri == dummytri) {
printf(" [4] = Outer space\n");
} else {
printf(" [4] = x%lx %d\n", (unsigned long) printtri.tri,
printtri.orient);
}
decode(s->sh[5], printtri);
if (printtri.tri == dummytri) {
printf(" [5] = Outer space\n");
} else {
printf(" [5] = x%lx %d\n", (unsigned long) printtri.tri,
printtri.orient);
}
}
/** **/
/** **/
/********* Debugging routines end here *********/
/********* Memory management routines begin here *********/
/** **/
/** **/
/*****************************************************************************/
/* */
/* 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. */
/* */
/*****************************************************************************/
void poolinit(pool, bytecount, itemcount, wtype, alignment)
struct memorypool *pool;
int bytecount;
int itemcount;
enum wordtype wtype;
int alignment;
{
int wordsize;
/* Initialize values in the pool. */
pool->itemwordtype = wtype;
wordsize = (pool->itemwordtype == POINTER) ? sizeof(VOID *) : sizeof(REAL);
/* Find the proper alignment, which must be at least as large as: */
/* - The parameter `alignment'. */
/* - The primary word type, to avoid unaligned accesses. */
/* - sizeof(VOID *), so the stack of dead items can be maintained */
/* without unaligned accesses. */
if (alignment > wordsize) {
pool->alignbytes = alignment;
} else {
pool->alignbytes = wordsize;
}
if (sizeof(VOID *) > pool->alignbytes) {
pool->alignbytes = sizeof(VOID *);
}
pool->itemwords = ((bytecount + pool->alignbytes - 1) / pool->alignbytes)
* (pool->alignbytes / wordsize);
pool->itembytes = pool->itemwords * wordsize;
pool->itemsperblock = itemcount;
/* Allocate a block of items. Space for `itemsperblock' items and one */
/* pointer (to point to the next block) are allocated, as well as space */
/* to ensure alignment of the items. */
pool->firstblock = (VOID **) malloc(pool->itemsperblock * pool->itembytes
+ sizeof(VOID *) + pool->alignbytes);
if (pool->firstblock == (VOID **) NULL) {
printf("Error: Out of memory.\n");
exit(1);
}
/* Set the next block pointer to NULL. */
*(pool->firstblock) = (VOID *) NULL;
poolrestart(pool);
}
/*****************************************************************************/
/* */
/* 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. */
/* */
/*****************************************************************************/
void poolrestart(pool)
struct memorypool *pool;
{
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->itemsperblock;
/* The stack of deallocated items is empty. */
pool->deaditemstack = (VOID *) NULL;
}
/*****************************************************************************/
/* */
/* pooldeinit() Free to the operating system all memory taken by a pool. */
/* */
/*****************************************************************************/
void pooldeinit(pool)
struct memorypool *pool;
{
while (pool->firstblock != (VOID **) NULL) {
pool->nowblock = (VOID **) *(pool->firstblock);
free(pool->firstblock);
pool->firstblock = pool->nowblock;
}
}
/*****************************************************************************/
/* */
/* poolalloc() Allocate space for an item. */
/* */
/*****************************************************************************/
VOID *poolalloc(pool)
struct memorypool *pool;
{
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 **) malloc(pool->itemsperblock * pool->itembytes + sizeof(VOID *) + pool->alignbytes);
if (newblock == (VOID **) NULL) {
printf("Error: Out of memory.\n");
exit(1);
}
*(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. */
if (pool->itemwordtype == POINTER) {
pool->nextitem = (VOID *) ((VOID **) pool->nextitem + pool->itemwords);
} else {
pool->nextitem = (VOID *) ((REAL *) pool->nextitem + pool->itemwords);
}
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. */
/* */
/*****************************************************************************/
void pooldealloc(pool, dyingitem)
struct memorypool *pool;
VOID *dyingitem;
{
/* 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(). */
/* */
/*****************************************************************************/
void traversalinit(pool)
struct memorypool *pool;
{
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->itemsperblock;
}
/*****************************************************************************/
/* */
/* traverse() Find the next item in the list. */
/* */
/* This routine is used in conjunction with traversalinit(). Be forewarned */
/* that this routine successively returns all items in the list, including */
/* deallocated ones on the deaditemqueue. It's up to you to figure out */
/* which ones are actually dead. 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. */
/* */
/*****************************************************************************/
VOID *traverse(pool)
struct memorypool *pool;
{
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. */
if (pool->itemwordtype == POINTER) {
pool->pathitem = (VOID *) ((VOID **) pool->pathitem + pool->itemwords);
} else {
pool->pathitem = (VOID *) ((REAL *) pool->pathitem + pool->itemwords);
}
pool->pathitemsleft--;
return newitem;
}
/*****************************************************************************/
/* */
/* dummyinit() Initialize the triangle that fills "outer space" and the */
/* omnipresent shell edge. */
/* */
/* The triangle that fills "outer space", called `dummytri', is pointed to */
/* by every triangle and shell edge 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 shell edge, `dummysh', is pointed to by every triangle */
/* or shell edge that doesn't have a full complement of real shell edges *//* to point to. */
/* */
/*****************************************************************************/
void dummyinit(trianglewords, shellewords)
int trianglewords;
int shellewords;
{
unsigned long alignptr;
/* `triwords' and `shwords' are used by the mesh manipulation primitives */
/* to extract orientations of triangles and shell edges from pointers. */
triwords = trianglewords; /* Initialize `triwords' once and for all. */
shwords = shellewords; /* Initialize `shwords' once and for all. */
/* Set up `dummytri', the `triangle' that occupies "outer space". */
dummytribase = (triangle *) malloc(triwords * sizeof(triangle)
+ triangles.alignbytes);
if (dummytribase == (triangle *) NULL) {
printf("Error: Out of memory.\n");
exit(1);
}
/* Align `dummytri' on a `triangles.alignbytes'-byte boundary. */
alignptr = (unsigned long) dummytribase;
dummytri = (triangle *)
(alignptr + (unsigned long) triangles.alignbytes
- (alignptr % (unsigned long) 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. */
dummytri[0] = (triangle) dummytri;
dummytri[1] = (triangle) dummytri;
dummytri[2] = (triangle) dummytri;
/* Three NULL vertex points. */
dummytri[3] = (triangle) NULL;
dummytri[4] = (triangle) NULL;
dummytri[5] = (triangle) NULL;
if (useshelles) {
/* Set up `dummysh', the omnipresent "shell edge" pointed to by any */
/* triangle side or shell edge end that isn't attached to a real shell */
/* edge. */
dummyshbase = (shelle *) malloc(shwords * sizeof(shelle)
+ shelles.alignbytes);
if (dummyshbase == (shelle *) NULL) {
printf("Error: Out of memory.\n");
exit(1);
}
/* Align `dummysh' on a `shelles.alignbytes'-byte boundary. */
alignptr = (unsigned long) dummyshbase;
dummysh = (shelle *)
(alignptr + (unsigned long) shelles.alignbytes
- (alignptr % (unsigned long) shelles.alignbytes));
/* Initialize the two adjoining shell edges to be the omnipresent shell */
/* edge. These will eventually be changed by various bonding */
/* operations, but their values don't really matter, as long as they */
/* can legally be dereferenced. */
dummysh[0] = (shelle) dummysh;
dummysh[1] = (shelle) dummysh;
/* Two NULL vertex points. */
dummysh[2] = (shelle) NULL;
dummysh[3] = (shelle) NULL;
/* Initialize the two adjoining triangles to be "outer space". */
dummysh[4] = (shelle) dummytri;
dummysh[5] = (shelle) dummytri;
/* Set the boundary marker to zero. */
* (int *) (dummysh + 6) = 0;
/* Initialize the three adjoining shell edges of `dummytri' to be */ /* the omnipresent shell edge. */
dummytri[6] = (triangle) dummysh;
dummytri[7] = (triangle) dummysh;
dummytri[8] = (triangle) dummysh;
}
}
/*****************************************************************************/
/* */
/* initializepointpool() Calculate the size of the point data structure */
/* and initialize its memory pool. */
/* */
/* This routine also computes the `pointmarkindex' and `point2triindex' */
/* indices used to find values within each point. */
/* */
/*****************************************************************************/
void initializepointpool()
{
int pointsize;
/* The index within each point at which the boundary marker is found. */
/* Ensure the point marker is aligned to a sizeof(int)-byte address. */
pointmarkindex = ((mesh_dim + nextras) * sizeof(REAL) + sizeof(int) - 1)
/ sizeof(int);
pointsize = (pointmarkindex + 1) * sizeof(int);
if (poly) {
/* The index within each point at which a triangle pointer is found. */
/* Ensure the pointer is aligned to a sizeof(triangle)-byte address. */
point2triindex = (pointsize + sizeof(triangle) - 1) / sizeof(triangle);
pointsize = (point2triindex + 1) * sizeof(triangle);
}
/* Initialize the pool of points. */
poolinit(&points, pointsize, POINTPERBLOCK,
(sizeof(REAL) >= sizeof(triangle)) ? FLOATINGPOINT : POINTER, 0);
}
/*****************************************************************************/
/* */
/* initializetrisegpools() Calculate the sizes of the triangle and shell */
/* edge data structures and initialize their */
/* memory pools. */
/* */
/* This routine also computes the `highorderindex', `elemattribindex', and */
/* `areaboundindex' indices used to find values within each triangle. */
/* */
/*****************************************************************************/
void initializetrisegpools()
{
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 shell edges before the extra nodes. */
highorderindex = 6 + (useshelles * 3);
/* The number of bytes occupied by a triangle. */
trisize = ((order + 1) * (order + 2) / 2 + (highorderindex - 3)) *
sizeof(triangle);
/* The index within each triangle at which its attributes are found, */
/* where the index is measured in REALs. */
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. */
areaboundindex = elemattribindex + eextras + regionattrib;
/* If triangle attributes or an area bound are needed, increase the number */
/* of bytes occupied by a triangle. */
if (vararea) { trisize = (areaboundindex + 1) * sizeof(REAL);
} else if (eextras + regionattrib > 0) {
trisize = 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 shell edges or */
/* attributes or area constraint or extra nodes. */
if ((voronoi || 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(&triangles, trisize, TRIPERBLOCK, POINTER, 4);
if (useshelles) {
/* Initialize the pool of shell edges. */
poolinit(&shelles, 6 * sizeof(triangle) + sizeof(int), SHELLEPERBLOCK,
POINTER, 4);
/* Initialize the "outer space" triangle and omnipresent shell edge. */
dummyinit(triangles.itemwords, shelles.itemwords);
} else {
/* Initialize the "outer space" triangle. */
dummyinit(triangles.itemwords, 0);
}
}
/*****************************************************************************/
/* */
/* triangledealloc() Deallocate space for a triangle, marking it dead. */
/* */
/*****************************************************************************/
void triangledealloc(dyingtriangle)
triangle *dyingtriangle;
{
/* Set triangle's vertices to NULL. This makes it possible to */
/* detect dead triangles when traversing the list of all triangles. */
dyingtriangle[3] = (triangle) NULL;
dyingtriangle[4] = (triangle) NULL;
dyingtriangle[5] = (triangle) NULL;
pooldealloc(&triangles, (VOID *) dyingtriangle);
}
/*****************************************************************************/
/* */
/* triangletraverse() Traverse the triangles, skipping dead ones. */
/* */
/*****************************************************************************/
triangle *triangletraverse()
{
triangle *newtriangle;
do {
newtriangle = (triangle *) traverse(&triangles);
if (newtriangle == (triangle *) NULL) {
return (triangle *) NULL;
}
} while (newtriangle[3] == (triangle) NULL); /* Skip dead ones. */
return newtriangle;
}
/*****************************************************************************/
/* */
/* shelledealloc() Deallocate space for a shell edge, marking it dead. */
/* */
/*****************************************************************************/
void shelledealloc(dyingshelle)
shelle *dyingshelle;
{
/* Set shell edge's vertices to NULL. This makes it possible to */
/* detect dead shells when traversing the list of all shells. */
dyingshelle[2] = (shelle) NULL;
dyingshelle[3] = (shelle) NULL;
pooldealloc(&shelles, (VOID *) dyingshelle);
}
/*****************************************************************************/
/* */
/* shelletraverse() Traverse the shell edges, skipping dead ones. */
/* */
/*****************************************************************************/
shelle *shelletraverse()
{
shelle *newshelle;
do {
newshelle = (shelle *) traverse(&shelles);
if (newshelle == (shelle *) NULL) {
return (shelle *) NULL;
}
} while (newshelle[2] == (shelle) NULL); /* Skip dead ones. */
return newshelle;
}
/*****************************************************************************/
/* */
/* pointdealloc() Deallocate space for a point, marking it dead. */
/* */
/*****************************************************************************/
void pointdealloc(dyingpoint)
point dyingpoint;
{
/* Mark the point as dead. This makes it possible to detect dead points */
/* when traversing the list of all points. */
setpointmark(dyingpoint, DEADPOINT);
pooldealloc(&points, (VOID *) dyingpoint);
}
/*****************************************************************************/
/* */
/* pointtraverse() Traverse the points, skipping dead ones. */
/* */
/*****************************************************************************/
point pointtraverse()
{
point newpoint;
do {
newpoint = (point) traverse(&points);
if (newpoint == (point) NULL) {
return (point) NULL;
}
} while (pointmark(newpoint) == DEADPOINT); /* Skip dead ones. */
return newpoint;
}
/*****************************************************************************/
/* */
/* badsegmentdealloc() Deallocate space for a bad segment, marking it */
/* dead. */
/* */
/*****************************************************************************/
#ifndef CDT_ONLY
void badsegmentdealloc(dyingseg)
struct edge *dyingseg;
{
/* Set segment's orientation to -1. This makes it possible to */
/* detect dead segments when traversing the list of all segments. */
dyingseg->shorient = -1;
pooldealloc(&badsegments, (VOID *) dyingseg);
}
#endif /* not CDT_ONLY */
/*****************************************************************************/
/* */
/* badsegmenttraverse() Traverse the bad segments, skipping dead ones. */
/* */
/*****************************************************************************/
#ifndef CDT_ONLY
struct edge *badsegmenttraverse()
{
struct edge *newseg;
do {
newseg = (struct edge *) traverse(&badsegments);
if (newseg == (struct edge *) NULL) {
return (struct edge *) NULL;
}
} while (newseg->shorient == -1); /* Skip dead ones. */
return newseg;
}
#endif /* not CDT_ONLY */
/*****************************************************************************/
/* */
/* getpoint() Get a specific point, by number, from the list. */
/* */
/* The first point is number 'firstnumber'. */
/* */
/* Note that this takes O(n) time (with a small constant, if POINTPERBLOCK */
/* is large). I don't care to take the trouble to make it work in constant */
/* time. */
/* */
/*****************************************************************************/
point getpoint(number)
int number;
{
VOID **getblock;
point foundpoint;
unsigned long alignptr;
int current;
getblock = points.firstblock;
current = firstnumber;
/* Find the right block. */
while (current + points.itemsperblock <= number) {
getblock = (VOID **) *getblock;
current += points.itemsperblock;
}
/* Now find the right point. */
alignptr = (unsigned long) (getblock + 1);
foundpoint = (point) (alignptr + (unsigned long) points.alignbytes
- (alignptr % (unsigned long) points.alignbytes));
while (current < number) {
foundpoint += points.itemwords;
current++; }
return foundpoint;
}
/*****************************************************************************/
/* */
/* triangledeinit() Free all remaining allocated memory. */
/* */
/*****************************************************************************/
void triangledeinit()
{
pooldeinit(&triangles);
free(dummytribase);
if (useshelles) {
pooldeinit(&shelles);
free(dummyshbase);
}
pooldeinit(&points);
#ifndef CDT_ONLY
if (quality) {
pooldeinit(&badsegments);
if ((minangle > 0.0) || vararea || fixedarea) {
pooldeinit(&badtriangles);
}
}
#endif /* not CDT_ONLY */
}
/** **/
/** **/
/********* Memory management routines end here *********/
/********* Constructors begin here *********/
/** **/
/** **/
/*****************************************************************************/
/* */
/* maketriangle() Create a new triangle with orientation zero. */
/* */
/*****************************************************************************/
void maketriangle(newtriedge)
struct triedge *newtriedge;
{
int i;
newtriedge->tri = (triangle *) poolalloc(&triangles);
/* Initialize the three adjoining triangles to be "outer space". */
newtriedge->tri[0] = (triangle) dummytri;
newtriedge->tri[1] = (triangle) dummytri;
newtriedge->tri[2] = (triangle) dummytri;
/* Three NULL vertex points. */
newtriedge->tri[3] = (triangle) NULL;
newtriedge->tri[4] = (triangle) NULL;
newtriedge->tri[5] = (triangle) NULL;
/* Initialize the three adjoining shell edges to be the omnipresent */
/* shell edge. */
if (useshelles) {
newtriedge->tri[6] = (triangle) dummysh;
newtriedge->tri[7] = (triangle) dummysh;
newtriedge->tri[8] = (triangle) dummysh;
}
for (i = 0; i < eextras; i++) {
setelemattribute(*newtriedge, i, 0.0);
}
if (vararea) {
setareabound(*newtriedge, -1.0);
}
newtriedge->orient = 0;
}
/*****************************************************************************/
/* */
/* makeshelle() Create a new shell edge with orientation zero. */
/* */
/*****************************************************************************/
void makeshelle(newedge)
struct edge *newedge;
{
newedge->sh = (shelle *) poolalloc(&shelles);
/* Initialize the two adjoining shell edges to be the omnipresent */
/* shell edge. */
newedge->sh[0] = (shelle) dummysh;
newedge->sh[1] = (shelle) dummysh;
/* Two NULL vertex points. */
newedge->sh[2] = (shelle) NULL;
newedge->sh[3] = (shelle) NULL;
/* Initialize the two adjoining triangles to be "outer space". */
newedge->sh[4] = (shelle) dummytri;
newedge->sh[5] = (shelle) dummytri;
/* Set the boundary marker to zero. */
setmark(*newedge, 0);
newedge->shorient = 0;
}
/** **/
/** **/
/********* Constructors end here *********/
/********* Determinant evaluation routines begin here *********/
/** **/
/** **/
/* The adaptive exact arithmetic geometric predicates implemented herein are */
/* described in detail in my Technical Report CMU-CS-96-140. The complete */
/* reference is given in the header. */
/* Which of the following two methods of finding the absolute values is */
/* fastest is compiler-dependent. A few compilers can inline and optimize */
/* the fabs() call; but most will incur the overhead of a function call, */
/* which is disastrously slow. A faster way on IEEE machines might be to */
/* mask the appropriate bit, but that's difficult to do in C. */
#define Absolute(a) ((a) >= 0.0 ? (a) : -(a))
/* #define Absolute(a) fabs(a) */
/* Many of the operations are broken up into two pieces, a main part that */
/* performs an approximate operation, and a "tail" that computes the */
/* roundoff error of that operation. */
/* */
/* The operations Fast_Two_Sum(), Fast_Two_Diff(), Two_Sum(), Two_Diff(), */
/* Split(), and Two_Product() are all implemented as described in the */
/* reference. Each of these macros requires certain variables to be */
/* defined in the calling routine. The variables `bvirt', `c', `abig', */
/* `_i', `_j', `_k', `_l', `_m', and `_n' are declared `INEXACT' because */
/* they store the result of an operation that may incur roundoff error. */
/* The input parameter `x' (or the highest numbered `x_' parameter) must */
/* also be declared `INEXACT'. */
#define Fast_Two_Sum_Tail(a, b, x, y) \
bvirt = x - a; \
y = b - bvirt
#define Fast_Two_Sum(a, b, x, y) \
x = (REAL) (a + b); \ Fast_Two_Sum_Tail(a, b, x, y)
#define 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)
/*****************************************************************************/
/* */
/* 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;
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 anyway. */
do {
lastcheck = check;
epsilon *= half;
if (every_other) {
splitter *= 2.0;
}
every_other = !every_other;
check = 1.0 + epsilon;
} while ((check != 1.0) && (check != lastcheck));
splitter += 1.0;
if (verbose > 1) {
printf("Floating point roundoff is of magnitude %.17g\n", epsilon);
printf("Floating point splitter is %.17g\n", splitter);
}
/* 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;}
/*****************************************************************************/
/* */
/* 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. */
/* */
/*****************************************************************************/
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;
{
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.) */
/* */
/*****************************************************************************/
int scale_expansion_zeroelim(elen, e, b, h) /* e and h cannot be the same. */
int elen;
REAL *e;
REAL b;
REAL *h;
{
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. */
/* */
/*****************************************************************************/
REAL estimate(elen, e)
int elen;
REAL *e;
{
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. */
/* */
/*****************************************************************************/
REAL counterclockwiseadapt(pa, pb, pc, detsum)
point pa;
point pb;
point pc;
REAL detsum;
{
INEXACT REAL acx, acy, bcx, bcy;
REAL acxtail, acytail, bcxtail, bcytail;
INEXACT REAL detleft, detright;
REAL detlefttail, detrighttail;
REAL det, errbound;
REAL B[4], C1[8], C2[12], D[16];
INEXACT REAL B3;
int C1length, C2length, Dlength;
REAL u[4];
INEXACT REAL u3;
INEXACT REAL s1, t1;
REAL s0, t0;
INEXACT REAL bvirt; REAL avirt, bround, around;
INEXACT REAL c;
INEXACT REAL abig;
REAL ahi, alo, bhi, blo;
REAL err1, err2, err3;
INEXACT REAL _i, _j;
REAL _0;
acx = (REAL) (pa[0] - pc[0]);
bcx = (REAL) (pb[0] - pc[0]);
acy = (REAL) (pa[1] - pc[1]);
bcy = (REAL) (pb[1] - pc[1]);
Two_Product(acx, bcy, detleft, detlefttail);
Two_Product(acy, bcx, detright, detrighttail);
Two_Two_Diff(detleft, detlefttail, detright, detrighttail,
B3, B[2], B[1], B[0]);
B[3] = B3;
det = estimate(4, B);
errbound = ccwerrboundB * detsum;
if ((det >= errbound) || (-det >= errbound)) {
return det;
}
Two_Diff_Tail(pa[0], pc[0], acx, acxtail);
Two_Diff_Tail(pb[0], pc[0], bcx, bcxtail);
Two_Diff_Tail(pa[1], pc[1], acy, acytail);
Two_Diff_Tail(pb[1], pc[1], bcy, bcytail);
if ((acxtail == 0.0) && (acytail == 0.0)
&& (bcxtail == 0.0) && (bcytail == 0.0)) {
return det;
}
errbound = ccwerrboundC * detsum + resulterrbound * Absolute(det);
det += (acx * bcytail + bcy * acxtail)
- (acy * bcxtail + bcx * acytail);
if ((det >= errbound) || (-det >= errbound)) {
return det;
}
Two_Product(acxtail, bcy, s1, s0);
Two_Product(acytail, bcx, t1, t0);
Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
u[3] = u3;
C1length = fast_expansion_sum_zeroelim(4, B, 4, u, C1);
Two_Product(acx, bcytail, s1, s0);
Two_Product(acy, bcxtail, t1, t0);
Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
u[3] = u3;
C2length = fast_expansion_sum_zeroelim(C1length, C1, 4, u, C2);
Two_Product(acxtail, bcytail, s1, s0);
Two_Product(acytail, bcxtail, t1, t0);
Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
u[3] = u3;
Dlength = fast_expansion_sum_zeroelim(C2length, C2, 4, u, D);
return(D[Dlength - 1]);
}
REAL counterclockwise(pa, pb, pc)
point pa;
point pb;
point pc;
{
REAL detleft, detright, det; REAL detsum, errbound;
counterclockcount++;
detleft = (pa[0] - pc[0]) * (pb[1] - pc[1]);
detright = (pa[1] - pc[1]) * (pb[0] - pc[0]);
det = detleft - detright;
if (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. */
/* */
/*****************************************************************************/
REAL incircleadapt(pa, pb, pc, pd, permanent)
point pa;
point pb;
point pc;
point pd;
REAL permanent;
{
INEXACT REAL adx, bdx, cdx, ady, bdy, cdy;
REAL det, errbound;
INEXACT REAL bdxcdy1, cdxbdy1, cdxady1, adxcdy1, adxbdy1, bdxady1;
REAL bdxcdy0, cdxbdy0, cdxady0, adxcdy0, adxbdy0, bdxady0;
REAL bc[4], ca[4], ab[4];
INEXACT REAL bc3, ca3, ab3;
REAL axbc[8], axxbc[16], aybc[8], ayybc[16], adet[32]; int axbclen, axxbclen, aybclen, ayybclen, alen;
REAL bxca[8], bxxca[16], byca[8], byyca[16], bdet[32];
int bxcalen, bxxcalen, bycalen, byycalen, blen;
REAL cxab[8], cxxab[16], cyab[8], cyyab[16], cdet[32];
int cxablen, cxxablen, cyablen, cyyablen, clen;
REAL abdet[64];
int ablen;
REAL fin1[1152], fin2[1152];
REAL *finnow, *finother, *finswap;
int finlength;
REAL adxtail, bdxtail, cdxtail, adytail, bdytail, cdytail;
INEXACT REAL adxadx1, adyady1, bdxbdx1, bdybdy1, cdxcdx1, cdycdy1;
REAL adxadx0, adyady0, bdxbdx0, bdybdy0, cdxcdx0, cdycdy0;
REAL aa[4], bb[4], cc[4];
INEXACT REAL aa3, bb3, cc3;
INEXACT REAL ti1, tj1;
REAL ti0, tj0;
REAL u[4], v[4];
INEXACT REAL u3, v3;
REAL temp8[8], temp16a[16], temp16b[16], temp16c[16];
REAL temp32a[32], temp32b[32], temp48[48], temp64[64];
int temp8len, temp16alen, temp16blen, temp16clen;
int temp32alen, temp32blen, temp48len, temp64len;
REAL axtbb[8], axtcc[8], aytbb[8], aytcc[8];
int axtbblen, axtcclen, aytbblen, aytcclen;
REAL bxtaa[8], bxtcc[8], bytaa[8], bytcc[8];
int bxtaalen, bxtcclen, bytaalen, bytcclen;
REAL cxtaa[8], cxtbb[8], cytaa[8], cytbb[8];
int cxtaalen, cxtbblen, cytaalen, cytbblen;
REAL axtbc[8], aytbc[8], bxtca[8], bytca[8], cxtab[8], cytab[8];
int axtbclen, aytbclen, bxtcalen, bytcalen, cxtablen, cytablen;
REAL axtbct[16], aytbct[16], bxtcat[16], bytcat[16], cxtabt[16], cytabt[16];
int axtbctlen, aytbctlen, bxtcatlen, bytcatlen, cxtabtlen, cytabtlen;
REAL axtbctt[8], aytbctt[8], bxtcatt[8];
REAL bytcatt[8], cxtabtt[8], cytabtt[8];
int axtbcttlen, aytbcttlen, bxtcattlen, bytcattlen, cxtabttlen, cytabttlen;
REAL abt[8], bct[8], cat[8];
int abtlen, bctlen, catlen;
REAL abtt[4], bctt[4], catt[4];
int abttlen, bcttlen, cattlen;
INEXACT REAL abtt3, bctt3, catt3;
REAL negate;
INEXACT REAL bvirt;
REAL avirt, bround, around;
INEXACT REAL c;
INEXACT REAL abig;
REAL ahi, alo, bhi, blo;
REAL err1, err2, err3;
INEXACT REAL _i, _j;
REAL _0;
adx = (REAL) (pa[0] - pd[0]);
bdx = (REAL) (pb[0] - pd[0]);
cdx = (REAL) (pc[0] - pd[0]);
ady = (REAL) (pa[1] - pd[1]);
bdy = (REAL) (pb[1] - pd[1]);
cdy = (REAL) (pc[1] - pd[1]);
Two_Product(bdx, cdy, bdxcdy1, bdxcdy0);
Two_Product(cdx, bdy, cdxbdy1, cdxbdy0);
Two_Two_Diff(bdxcdy1, bdxcdy0, cdxbdy1, cdxbdy0, bc3, bc[2], bc[1], bc[0]);
bc[3] = bc3;
axbclen = scale_expansion_zeroelim(4, bc, adx, axbc);
axxbclen = scale_expansion_zeroelim(axbclen, axbc, adx, axxbc);
aybclen = scale_expansion_zeroelim(4, bc, ady, aybc);
ayybclen = scale_expansion_zeroelim(aybclen, aybc, ady, ayybc);
alen = fast_expansion_sum_zeroelim(axxbclen, axxbc, ayybclen, ayybc, adet);
Two_Product(cdx, ady, cdxady1, cdxady0);
Two_Product(adx, cdy, adxcdy1, adxcdy0);
Two_Two_Diff(cdxady1, cdxady0, adxcdy1, adxcdy0, ca3, ca[2], ca[1], ca[0]);
ca[3] = ca3;
bxcalen = scale_expansion_zeroelim(4, ca, bdx, bxca);
bxxcalen = scale_expansion_zeroelim(bxcalen, bxca, bdx, bxxca);
bycalen = scale_expansion_zeroelim(4, ca, bdy, byca);
byycalen = scale_expansion_zeroelim(bycalen, byca, bdy, byyca);
blen = fast_expansion_sum_zeroelim(bxxcalen, bxxca, byycalen, byyca, bdet);
Two_Product(adx, bdy, adxbdy1, adxbdy0);
Two_Product(bdx, ady, bdxady1, bdxady0);
Two_Two_Diff(adxbdy1, adxbdy0, bdxady1, bdxady0, ab3, ab[2], ab[1], ab[0]);
ab[3] = ab3;
cxablen = scale_expansion_zeroelim(4, ab, cdx, cxab);
cxxablen = scale_expansion_zeroelim(cxablen, cxab, cdx, cxxab);
cyablen = scale_expansion_zeroelim(4, ab, cdy, cyab);
cyyablen = scale_expansion_zeroelim(cyablen, cyab, cdy, cyyab);
clen = fast_expansion_sum_zeroelim(cxxablen, cxxab, cyyablen, cyyab, cdet);
ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
finlength = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, fin1);
det = estimate(finlength, fin1);
errbound = iccerrboundB * permanent;
if ((det >= errbound) || (-det >= errbound)) {
return det;
}
Two_Diff_Tail(pa[0], pd[0], adx, adxtail);
Two_Diff_Tail(pa[1], pd[1], ady, adytail);
Two_Diff_Tail(pb[0], pd[0], bdx, bdxtail);
Two_Diff_Tail(pb[1], pd[1], bdy, bdytail);
Two_Diff_Tail(pc[0], pd[0], cdx, cdxtail);
Two_Diff_Tail(pc[1], pd[1], cdy, cdytail);
if ((adxtail == 0.0) && (bdxtail == 0.0) && (cdxtail == 0.0)
&& (adytail == 0.0) && (bdytail == 0.0) && (cdytail == 0.0)) {
return det;
}
errbound = iccerrboundC * permanent + resulterrbound * Absolute(det);
det += ((adx * adx + ady * ady) * ((bdx * cdytail + cdy * bdxtail)
- (bdy * cdxtail + cdx * bdytail))
+ 2.0 * (adx * adxtail + ady * adytail) * (bdx * cdy - bdy * cdx))
+ ((bdx * bdx + bdy * bdy) * ((cdx * adytail + ady * cdxtail)
- (cdy * adxtail + adx * cdytail))
+ 2.0 * (bdx * bdxtail + bdy * bdytail) * (cdx * ady - cdy * adx))
+ ((cdx * cdx + cdy * cdy) * ((adx * bdytail + bdy * adxtail)
- (ady * bdxtail + bdx * adytail))
+ 2.0 * (cdx * cdxtail + cdy * cdytail) * (adx * bdy - ady * bdx));
if ((det >= errbound) || (-det >= errbound)) {
return det;
}
finnow = fin1;
finother = fin2;
if ((bdxtail != 0.0) || (bdytail != 0.0)
|| (cdxtail != 0.0) || (cdytail != 0.0)) {
Square(adx, adxadx1, adxadx0);
Square(ady, adyady1, adyady0);
Two_Two_Sum(adxadx1, adxadx0, adyady1, adyady0, aa3, aa[2], aa[1], aa[0]);
aa[3] = aa3;
}
if ((cdxtail != 0.0) || (cdytail != 0.0)
|| (adxtail != 0.0) || (adytail != 0.0)) {
Square(bdx, bdxbdx1, bdxbdx0);
Square(bdy, bdybdy1, bdybdy0);
Two_Two_Sum(bdxbdx1, bdxbdx0, bdybdy1, bdybdy0, bb3, bb[2], bb[1], bb[0]);
bb[3] = bb3; }
if ((adxtail != 0.0) || (adytail != 0.0)
|| (bdxtail != 0.0) || (bdytail != 0.0)) {
Square(cdx, cdxcdx1, cdxcdx0);
Square(cdy, cdycdy1, cdycdy0);
Two_Two_Sum(cdxcdx1, cdxcdx0, cdycdy1, cdycdy0, cc3, cc[2], cc[1], cc[0]);
cc[3] = cc3;
}
if (adxtail != 0.0) {
axtbclen = scale_expansion_zeroelim(4, bc, adxtail, axtbc);
temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, 2.0 * adx,
temp16a);
axtcclen = scale_expansion_zeroelim(4, cc, adxtail, axtcc);
temp16blen = scale_expansion_zeroelim(axtcclen, axtcc, bdy, temp16b);
axtbblen = scale_expansion_zeroelim(4, bb, adxtail, axtbb);
temp16clen = scale_expansion_zeroelim(axtbblen, axtbb, -cdy, temp16c);
temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
temp16blen, temp16b, temp32a);
temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
temp32alen, temp32a, temp48);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
temp48, finother);
finswap = finnow; finnow = finother; finother = finswap;
}
if (adytail != 0.0) {
aytbclen = scale_expansion_zeroelim(4, bc, adytail, aytbc);
temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, 2.0 * ady,
temp16a);
aytbblen = scale_expansion_zeroelim(4, bb, adytail, aytbb);
temp16blen = scale_expansion_zeroelim(aytbblen, aytbb, cdx, temp16b);
aytcclen = scale_expansion_zeroelim(4, cc, adytail, aytcc);
temp16clen = scale_expansion_zeroelim(aytcclen, aytcc, -bdx, temp16c);
temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
temp16blen, temp16b, temp32a);
temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
temp32alen, temp32a, temp48);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
temp48, finother);
finswap = finnow; finnow = finother; finother = finswap;
}
if (bdxtail != 0.0) {
bxtcalen = scale_expansion_zeroelim(4, ca, bdxtail, bxtca);
temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, 2.0 * bdx,
temp16a);
bxtaalen = scale_expansion_zeroelim(4, aa, bdxtail, bxtaa);
temp16blen = scale_expansion_zeroelim(bxtaalen, bxtaa, cdy, temp16b);
bxtcclen = scale_expansion_zeroelim(4, cc, bdxtail, bxtcc);
temp16clen = scale_expansion_zeroelim(bxtcclen, bxtcc, -ady, temp16c);
temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
temp16blen, temp16b, temp32a);
temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
temp32alen, temp32a, temp48);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
temp48, finother);
finswap = finnow; finnow = finother; finother = finswap;
}
if (bdytail != 0.0) {
bytcalen = scale_expansion_zeroelim(4, ca, bdytail, bytca);
temp16alen = scale_expansion_zeroelim(bytcalen, bytca, 2.0 * bdy,
temp16a);
bytcclen = scale_expansion_zeroelim(4, cc, bdytail, bytcc);
temp16blen = scale_expansion_zeroelim(bytcclen, bytcc, adx, temp16b);
bytaalen = scale_expansion_zeroelim(4, aa, bdytail, bytaa);
temp16clen = scale_expansion_zeroelim(bytaalen, bytaa, -cdx, temp16c);
temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
temp16blen, temp16b, temp32a);
temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
temp32alen, temp32a, temp48);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
temp48, finother);
finswap = finnow; finnow = finother; finother = finswap;
}
if (cdxtail != 0.0) {
cxtablen = scale_expansion_zeroelim(4, ab, cdxtail, cxtab);
temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, 2.0 * cdx,
temp16a);
cxtbblen = scale_expansion_zeroelim(4, bb, cdxtail, cxtbb);
temp16blen = scale_expansion_zeroelim(cxtbblen, cxtbb, ady, temp16b);
cxtaalen = scale_expansion_zeroelim(4, aa, cdxtail, cxtaa);
temp16clen = scale_expansion_zeroelim(cxtaalen, cxtaa, -bdy, temp16c);
temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
temp16blen, temp16b, temp32a);
temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
temp32alen, temp32a, temp48);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
temp48, finother);
finswap = finnow; finnow = finother; finother = finswap;
}
if (cdytail != 0.0) {
cytablen = scale_expansion_zeroelim(4, ab, cdytail, cytab);
temp16alen = scale_expansion_zeroelim(cytablen, cytab, 2.0 * cdy,
temp16a);
cytaalen = scale_expansion_zeroelim(4, aa, cdytail, cytaa);
temp16blen = scale_expansion_zeroelim(cytaalen, cytaa, bdx, temp16b);
cytbblen = scale_expansion_zeroelim(4, bb, cdytail, cytbb);
temp16clen = scale_expansion_zeroelim(cytbblen, cytbb, -adx, temp16c);
temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
temp16blen, temp16b, temp32a);
temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
temp32alen, temp32a, temp48);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
temp48, finother);
finswap = finnow; finnow = finother; finother = finswap;
}
if ((adxtail != 0.0) || (adytail != 0.0)) {
if ((bdxtail != 0.0) || (bdytail != 0.0)
|| (cdxtail != 0.0) || (cdytail != 0.0)) {
Two_Product(bdxtail, cdy, ti1, ti0);
Two_Product(bdx, cdytail, tj1, tj0);
Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
u[3] = u3;
negate = -bdy;
Two_Product(cdxtail, negate, ti1, ti0);
negate = -bdytail;
Two_Product(cdx, negate, tj1, tj0);
Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
v[3] = v3;
bctlen = fast_expansion_sum_zeroelim(4, u, 4, v, bct);
Two_Product(bdxtail, cdytail, ti1, ti0); Two_Product(cdxtail, bdytail, tj1, tj0);
Two_Two_Diff(ti1, ti0, tj1, tj0, bctt3, bctt[2], bctt[1], bctt[0]);
bctt[3] = bctt3;
bcttlen = 4;
} else {
bct[0] = 0.0;
bctlen = 1;
bctt[0] = 0.0;
bcttlen = 1;
}
if (adxtail != 0.0) {
temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, adxtail, temp16a);
axtbctlen = scale_expansion_zeroelim(bctlen, bct, adxtail, axtbct);
temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, 2.0 * adx,
temp32a);
temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
temp32alen, temp32a, temp48);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
temp48, finother);
finswap = finnow; finnow = finother; finother = finswap;
if (bdytail != 0.0) {
temp8len = scale_expansion_zeroelim(4, cc, adxtail, temp8);
temp16alen = scale_expansion_zeroelim(temp8len, temp8, bdytail,
temp16a);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
temp16a, finother);
finswap = finnow; finnow = finother; finother = finswap;
}
if (cdytail != 0.0) {
temp8len = scale_expansion_zeroelim(4, bb, -adxtail, temp8);
temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail,
temp16a);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
temp16a, finother);
finswap = finnow; finnow = finother; finother = finswap;
}
temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, adxtail,
temp32a);
axtbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adxtail, axtbctt);
temp16alen = scale_expansion_zeroelim(axtbcttlen, axtbctt, 2.0 * adx,
temp16a);
temp16blen = scale_expansion_zeroelim(axtbcttlen, axtbctt, adxtail,
temp16b);
temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
temp16blen, temp16b, temp32b);
temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
temp32blen, temp32b, temp64);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
temp64, finother);
finswap = finnow; finnow = finother; finother = finswap;
}
if (adytail != 0.0) {
temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, adytail, temp16a);
aytbctlen = scale_expansion_zeroelim(bctlen, bct, adytail, aytbct);
temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, 2.0 * ady,
temp32a);
temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
temp32alen, temp32a, temp48);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
temp48, finother);
finswap = finnow; finnow = finother; finother = finswap;
temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, adytail,
temp32a);
aytbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adytail, aytbctt);
temp16alen = scale_expansion_zeroelim(aytbcttlen, aytbctt, 2.0 * ady,
temp16a); temp16blen = scale_expansion_zeroelim(aytbcttlen, aytbctt, adytail,
temp16b);
temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
temp16blen, temp16b, temp32b);
temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
temp32blen, temp32b, temp64);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
temp64, finother);
finswap = finnow; finnow = finother; finother = finswap;
}
}
if ((bdxtail != 0.0) || (bdytail != 0.0)) {
if ((cdxtail != 0.0) || (cdytail != 0.0)
|| (adxtail != 0.0) || (adytail != 0.0)) {
Two_Product(cdxtail, ady, ti1, ti0);
Two_Product(cdx, adytail, tj1, tj0);
Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
u[3] = u3;
negate = -cdy;
Two_Product(adxtail, negate, ti1, ti0);
negate = -cdytail;
Two_Product(adx, negate, tj1, tj0);
Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
v[3] = v3;
catlen = fast_expansion_sum_zeroelim(4, u, 4, v, cat);
Two_Product(cdxtail, adytail, ti1, ti0);
Two_Product(adxtail, cdytail, tj1, tj0);
Two_Two_Diff(ti1, ti0, tj1, tj0, catt3, catt[2], catt[1], catt[0]);
catt[3] = catt3;
cattlen = 4;
} else {
cat[0] = 0.0;
catlen = 1;
catt[0] = 0.0;
cattlen = 1;
}
if (bdxtail != 0.0) {
temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, bdxtail, temp16a);
bxtcatlen = scale_expansion_zeroelim(catlen, cat, bdxtail, bxtcat);
temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, 2.0 * bdx,
temp32a);
temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
temp32alen, temp32a, temp48);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
temp48, finother);
finswap = finnow; finnow = finother; finother = finswap;
if (cdytail != 0.0) {
temp8len = scale_expansion_zeroelim(4, aa, bdxtail, temp8);
temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail,
temp16a);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
temp16a, finother);
finswap = finnow; finnow = finother; finother = finswap;
}
if (adytail != 0.0) {
temp8len = scale_expansion_zeroelim(4, cc, -bdxtail, temp8);
temp16alen = scale_expansion_zeroelim(temp8len, temp8, adytail,
temp16a);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
temp16a, finother);
finswap = finnow; finnow = finother; finother = finswap;
}
temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, bdxtail,
temp32a);
bxtcattlen = scale_expansion_zeroelim(cattlen, catt, bdxtail, bxtcatt);
temp16alen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, 2.0 * bdx,
temp16a); temp16blen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, bdxtail,
temp16b);
temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
temp16blen, temp16b, temp32b);
temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
temp32blen, temp32b, temp64);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
temp64, finother);
finswap = finnow; finnow = finother; finother = finswap;
}
if (bdytail != 0.0) {
temp16alen = scale_expansion_zeroelim(bytcalen, bytca, bdytail, temp16a);
bytcatlen = scale_expansion_zeroelim(catlen, cat, bdytail, bytcat);
temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, 2.0 * bdy,
temp32a);
temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
temp32alen, temp32a, temp48);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
temp48, finother);
finswap = finnow; finnow = finother; finother = finswap;
temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, bdytail,
temp32a);
bytcattlen = scale_expansion_zeroelim(cattlen, catt, bdytail, bytcatt);
temp16alen = scale_expansion_zeroelim(bytcattlen, bytcatt, 2.0 * bdy,
temp16a);
temp16blen = scale_expansion_zeroelim(bytcattlen, bytcatt, bdytail,
temp16b);
temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
temp16blen, temp16b, temp32b);
temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
temp32blen, temp32b, temp64);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
temp64, finother);
finswap = finnow; finnow = finother; finother = finswap;
}
}
if ((cdxtail != 0.0) || (cdytail != 0.0)) {
if ((adxtail != 0.0) || (adytail != 0.0)
|| (bdxtail != 0.0) || (bdytail != 0.0)) {
Two_Product(adxtail, bdy, ti1, ti0);
Two_Product(adx, bdytail, tj1, tj0);
Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
u[3] = u3;
negate = -ady;
Two_Product(bdxtail, negate, ti1, ti0);
negate = -adytail;
Two_Product(bdx, negate, tj1, tj0);
Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
v[3] = v3;
abtlen = fast_expansion_sum_zeroelim(4, u, 4, v, abt);
Two_Product(adxtail, bdytail, ti1, ti0);
Two_Product(bdxtail, adytail, tj1, tj0);
Two_Two_Diff(ti1, ti0, tj1, tj0, abtt3, abtt[2], abtt[1], abtt[0]);
abtt[3] = abtt3;
abttlen = 4;
} else {
abt[0] = 0.0;
abtlen = 1;
abtt[0] = 0.0;
abttlen = 1;
}
if (cdxtail != 0.0) {
temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, cdxtail, temp16a);
cxtabtlen = scale_expansion_zeroelim(abtlen, abt, cdxtail, cxtabt);
temp32alen = scale_expansion_zeroelim(cxtabtlen, cxtabt, 2.0 * cdx,
temp32a); temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
temp32alen, temp32a, temp48);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
temp48, finother);
finswap = finnow; finnow = finother; finother = finswap;
if (adytail != 0.0) {
temp8len = scale_expansion_zeroelim(4, bb, cdxtail, temp8);
temp16alen = scale_expansion_zeroelim(temp8len, temp8, adytail,
temp16a);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
temp16a, finother);
finswap = finnow; finnow = finother; finother = finswap;
}
if (bdytail != 0.0) {
temp8len = scale_expansion_zeroelim(4, aa, -cdxtail, temp8);
temp16alen = scale_expansion_zeroelim(temp8len, temp8, bdytail,
temp16a);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
temp16a, finother);
finswap = finnow; finnow = finother; finother = finswap;
}
temp32alen = scale_expansion_zeroelim(cxtabtlen, cxtabt, cdxtail,
temp32a);
cxtabttlen = scale_expansion_zeroelim(abttlen, abtt, cdxtail, cxtabtt);
temp16alen = scale_expansion_zeroelim(cxtabttlen, cxtabtt, 2.0 * cdx,
temp16a);
temp16blen = scale_expansion_zeroelim(cxtabttlen, cxtabtt, cdxtail,
temp16b);
temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
temp16blen, temp16b, temp32b);
temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
temp32blen, temp32b, temp64);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
temp64, finother);
finswap = finnow; finnow = finother; finother = finswap;
}
if (cdytail != 0.0) {
temp16alen = scale_expansion_zeroelim(cytablen, cytab, cdytail, temp16a);
cytabtlen = scale_expansion_zeroelim(abtlen, abt, cdytail, cytabt);
temp32alen = scale_expansion_zeroelim(cytabtlen, cytabt, 2.0 * cdy,
temp32a);
temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
temp32alen, temp32a, temp48);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
temp48, finother);
finswap = finnow; finnow = finother; finother = finswap;
temp32alen = scale_expansion_zeroelim(cytabtlen, cytabt, cdytail,
temp32a);
cytabttlen = scale_expansion_zeroelim(abttlen, abtt, cdytail, cytabtt);
temp16alen = scale_expansion_zeroelim(cytabttlen, cytabtt, 2.0 * cdy,
temp16a);
temp16blen = scale_expansion_zeroelim(cytabttlen, cytabtt, cdytail,
temp16b);
temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
temp16blen, temp16b, temp32b);
temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
temp32blen, temp32b, temp64);
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
temp64, finother);
finswap = finnow; finnow = finother; finother = finswap;
}
}
return finnow[finlength - 1];
}
REAL incircle(pa, pb, pc, pd)point pa;
point pb;
point pc;
point pd;
{
REAL adx, bdx, cdx, ady, bdy, cdy;
REAL bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady;
REAL alift, blift, clift;
REAL det;
REAL permanent, errbound;
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 (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);
}
/** **/
/** **/
/********* Determinant evaluation routines end here *********/
/*****************************************************************************/
/* */
/* triangleinit() Initialize some variables. */
/* */
/*****************************************************************************/
void triangleinit()
{
points.maxitems = triangles.maxitems = shelles.maxitems = viri.maxitems =
badsegments.maxitems = badtriangles.maxitems = splaynodes.maxitems = 0l;
points.itembytes = triangles.itembytes = shelles.itembytes = viri.itembytes =
badsegments.itembytes = badtriangles.itembytes = splaynodes.itembytes = 0;
recenttri.tri = (triangle *) NULL; /* No triangle has been visited yet. */
samples = 1; /* Point location should take at least one sample. */
checksegments = 0; /* There are no segments in the triangulation yet. */ incirclecount = counterclockcount = hyperbolacount = 0;
circumcentercount = circletopcount = 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. */
/* */
/*****************************************************************************/
unsigned long randomnation(choices)
unsigned int choices;
{
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
void checkmesh()
{
struct triedge triangleloop;
struct triedge oppotri, oppooppotri;
point triorg, tridest, triapex;
point oppoorg, oppodest;
int horrors;
int saveexact;
triangle ptr; /* Temporary variable used by sym(). */
/* Temporarily turn on exact arithmetic if it's off. */
saveexact = noexact;
noexact = 0;
if (!quiet) {
printf(" Checking consistency of mesh...\n");
}
horrors = 0;
/* Run through the list of triangles, checking each one. */
traversalinit(&triangles);
triangleloop.tri = triangletraverse();
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(triorg, tridest, triapex) <= 0.0) {
printf(" !! !! Inverted ");
printtriangle(&triangleloop);
horrors++;
} }
/* Find the neighboring triangle on this edge. */
sym(triangleloop, oppotri);
if (oppotri.tri != 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(&triangleloop);
printf(" Second (nonreciprocating) ");
printtriangle(&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(&triangleloop);
printf(" Second mismatched ");
printtriangle(&oppotri);
horrors++;
}
}
}
triangleloop.tri = triangletraverse();
}
if (horrors == 0) {
if (!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. */
noexact = saveexact;
}
#endif /* not REDUCED */
/*****************************************************************************/
/* */
/* checkdelaunay() Ensure that the mesh is (constrained) Delaunay. */
/* */
/*****************************************************************************/
#ifndef REDUCED
void checkdelaunay()
{
struct triedge triangleloop;
struct triedge oppotri;
struct edge opposhelle;
point triorg, tridest, triapex;
point oppoapex;
int shouldbedelaunay;
int horrors;
int saveexact;
triangle ptr; /* Temporary variable used by sym(). */
shelle sptr; /* Temporary variable used by tspivot(). */
/* Temporarily turn on exact arithmetic if it's off. */
saveexact = noexact;
noexact = 0;
if (!quiet) {
printf(" Checking Delaunay property of mesh...\n");
}
horrors = 0;
/* Run through the list of triangles, checking each one. */
traversalinit(&triangles);
triangleloop.tri = triangletraverse();
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 != dummytri)
&& (triapex != (point) NULL) && (oppoapex != (point) NULL)
&& (triangleloop.tri < oppotri.tri);
if (checksegments && shouldbedelaunay) {
/* If a shell edge separates the triangles, then the edge is */
/* constrained, so no local Delaunay test should be done. */
tspivot(triangleloop, opposhelle);
if (opposhelle.sh != dummysh){
shouldbedelaunay = 0;
}
}
if (shouldbedelaunay) {
if (incircle(triorg, tridest, triapex, oppoapex) > 0.0) {
printf(" !! !! Non-Delaunay pair of triangles:\n");
printf(" First non-Delaunay ");
printtriangle(&triangleloop);
printf(" Second non-Delaunay ");
printtriangle(&oppotri);
horrors++;
}
}
}
triangleloop.tri = triangletraverse();
}
if (horrors == 0) {
if (!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. */
noexact = saveexact;
}
#endif /* not REDUCED */
/*****************************************************************************/
/* */
/* enqueuebadtri() Add a bad triangle to the end of a queue. */
/* */
/* The queue is actually a set of 64 queues. I use multiple queues to give */
/* priority to smaller angles. I originally implemented a heap, but the *//* queues are (to my surprise) much faster. */
/* */
/*****************************************************************************/
#ifndef CDT_ONLY
void enqueuebadtri(instri, angle, insapex, insorg, insdest)
struct triedge *instri;
REAL angle;
point insapex;
point insorg;
point insdest;
{
struct badface *newface;
int queuenumber;
if (verbose > 2) {
printf(" Queueing bad triangle:\n");
printf(" (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", insorg[0],
insorg[1], insdest[0], insdest[1], insapex[0], insapex[1]);
}
/* Allocate space for the bad triangle. */
newface = (struct badface *) poolalloc(&badtriangles);
triedgecopy(*instri, newface->badfacetri);
newface->key = angle;
newface->faceapex = insapex;
newface->faceorg = insorg;
newface->facedest = insdest;
newface->nextface = (struct badface *) NULL;
/* Determine the appropriate queue to put the bad triangle into. */
if (angle > 0.6) {
queuenumber = (int) (160.0 * (angle - 0.6));
if (queuenumber > 63) {
queuenumber = 63;
}
} else {
/* It's not a bad angle; put the triangle in the lowest-priority queue. */
queuenumber = 0;
}
/* Add the triangle to the end of a queue. */
*queuetail[queuenumber] = newface;
/* Maintain a pointer to the NULL pointer at the end of the queue. */
queuetail[queuenumber] = &newface->nextface;
}
#endif /* not CDT_ONLY */
/*****************************************************************************/
/* */
/* dequeuebadtri() Remove a triangle from the front of the queue. */
/* */
/*****************************************************************************/
#ifndef CDT_ONLY
struct badface *dequeuebadtri()
{
struct badface *result;
int queuenumber;
/* Look for a nonempty queue. */
for (queuenumber = 63; queuenumber >= 0; queuenumber--) {
result = queuefront[queuenumber];
if (result != (struct badface *) NULL) {
/* Remove the triangle from the queue. */
queuefront[queuenumber] = result->nextface;
/* Maintain a pointer to the NULL pointer at the end of the queue. */
if (queuefront[queuenumber] == (struct badface *) NULL) {
queuetail[queuenumber] = &queuefront[queuenumber];
} return result;
}
}
return (struct badface *) NULL;
}
#endif /* not CDT_ONLY */
/*****************************************************************************/
/* */
/* checkedge4encroach() Check a segment to see if it is encroached; add */
/* it to the list if it is. */
/* */
/* An encroached segment is an unflippable edge that has a point in its */
/* diametral circle (that is, it faces an angle greater than 90 degrees). */
/* This definition is due to Ruppert. */
/* */
/* Returns a nonzero value if the edge is encroached. */
/* */
/*****************************************************************************/
#ifndef CDT_ONLY
int checkedge4encroach(testedge)
struct edge *testedge;
{
struct triedge neighbortri;
struct edge testsym;
struct edge *badedge;
int addtolist;
int sides;
point eorg, edest, eapex;
triangle ptr; /* Temporary variable used by stpivot(). */
addtolist = 0;
sides = 0;
sorg(*testedge, eorg);
sdest(*testedge, edest);
/* Check one neighbor of the shell edge. */
stpivot(*testedge, neighbortri);
/* Does the neighbor exist, or is this a boundary edge? */
if (neighbortri.tri != dummytri) {
sides++;
/* Find a vertex opposite this edge. */
apex(neighbortri, eapex);
/* Check whether the vertex is inside the diametral circle of the */
/* shell edge. Pythagoras' Theorem is used to check whether the */
/* angle at the vertex is greater than 90 degrees. */
if (eapex[0] * (eorg[0] + edest[0]) + eapex[1] * (eorg[1] + edest[1]) >
eapex[0] * eapex[0] + eorg[0] * edest[0] +
eapex[1] * eapex[1] + eorg[1] * edest[1]) {
addtolist = 1;
}
}
/* Check the other neighbor of the shell edge. */
ssym(*testedge, testsym);
stpivot(testsym, neighbortri);
/* Does the neighbor exist, or is this a boundary edge? */
if (neighbortri.tri != dummytri) {
sides++;
/* Find the other vertex opposite this edge. */
apex(neighbortri, eapex);
/* Check whether the vertex is inside the diametral circle of the */
/* shell edge. Pythagoras' Theorem is used to check whether the */
/* angle at the vertex is greater than 90 degrees. */
if (eapex[0] * (eorg[0] + edest[0]) +
eapex[1] * (eorg[1] + edest[1]) >
eapex[0] * eapex[0] + eorg[0] * edest[0] +
eapex[1] * eapex[1] + eorg[1] * edest[1]) { addtolist += 2;
}
}
if (addtolist && (!nobisect || ((nobisect == 1) && (sides == 2)))) {
if (verbose > 2) {
printf(" Queueing encroached segment (%.12g, %.12g) (%.12g, %.12g).\n",
eorg[0], eorg[1], edest[0], edest[1]);
}
/* Add the shell edge to the list of encroached segments. */
/* Be sure to get the orientation right. */
badedge = (struct edge *) poolalloc(&badsegments);
if (addtolist == 1) {
shellecopy(*testedge, *badedge);
} else {
shellecopy(testsym, *badedge);
}
}
return addtolist;
}
#endif /* not CDT_ONLY */
/*****************************************************************************/
/* */
/* testtriangle() Test a face for quality measures. */
/* */
/* 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
void testtriangle(testtri)
struct triedge *testtri;
{
struct triedge sametesttri;
struct edge edge1, edge2;
point torg, tdest, tapex;
point anglevertex;
REAL dxod, dyod, dxda, dyda, dxao, dyao;
REAL dxod2, dyod2, dxda2, dyda2, dxao2, dyao2;
REAL apexlen, orglen, destlen;
REAL angle;
REAL area;
shelle sptr; /* Temporary variable used by tspivot(). */
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. */ /* Find the square of the cosine of the angle at the apex. */
angle = dxda * dxao + dyda * dyao;
angle = angle * angle / (orglen * destlen);
anglevertex = tapex;
lnext(*testtri, sametesttri);
tspivot(sametesttri, edge1);
lnextself(sametesttri);
tspivot(sametesttri, edge2);
} else if (orglen < destlen) {
/* The edge opposite the origin is shortest. */
/* Find the square of the cosine of the angle at the origin. */
angle = dxod * dxao + dyod * dyao;
angle = angle * angle / (apexlen * destlen);
anglevertex = torg;
tspivot(*testtri, edge1);
lprev(*testtri, sametesttri);
tspivot(sametesttri, edge2);
} else {
/* The edge opposite the destination is shortest. */
/* Find the square of the cosine of the angle at the destination. */
angle = dxod * dxda + dyod * dyda;
angle = angle * angle / (apexlen * orglen);
anglevertex = tdest;
tspivot(*testtri, edge1);
lnext(*testtri, sametesttri);
tspivot(sametesttri, edge2);
}
/* Check if both edges that form the angle are segments. */
if ((edge1.sh != dummysh) && (edge2.sh != dummysh)) {
/* The angle is a segment intersection. */
if ((angle > 0.9924) && !quiet) { /* Roughly 5 degrees. */
if (angle > 1.0) {
/* Beware of a floating exception in acos(). */
angle = 1.0;
}
/* Find the actual angle in degrees, for printing. */
angle = acos(sqrt(angle)) * (180.0 / PI);
printf(
"Warning: Small angle (%.4g degrees) between segments at point\n",
angle);
printf(" (%.12g, %.12g)\n", anglevertex[0], anglevertex[1]);
}
/* Don't add this bad triangle to the list; there's nothing that */
/* can be done about a small angle between two segments. */
angle = 0.0;
}
/* Check whether the angle is smaller than permitted. */
if (angle > goodangle) {
/* Add this triangle to the list of bad triangles. */
enqueuebadtri(testtri, angle, tapex, torg, tdest);
return;
}
if (vararea || fixedarea) {
/* Check whether the area is larger than permitted. */
area = 0.5 * (dxod * dyda - dyod * dxda);
if (fixedarea && (area > maxarea)) {
/* Add this triangle to the list of bad triangles. */
enqueuebadtri(testtri, angle, tapex, torg, tdest);
} else if (vararea) {
/* Nonpositive area constraints are treated as unconstrained. */
if ((area > areabound(*testtri)) && (areabound(*testtri) > 0.0)) {
/* Add this triangle to the list of bad triangles. */
enqueuebadtri(testtri, angle, tapex, torg, tdest);
}
}
}
}
#endif /* not CDT_ONLY */
/** **/
/** **/
/********* Mesh quality testing routines end here *********/
/********* Point location routines begin here *********/
/** **/
/** **/
/*****************************************************************************/
/* */
/* makepointmap() Construct a mapping from points 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 point is a corner */
/* of several triangles, but in the end every point will point to some */
/* triangle that contains it. */
/* */
/*****************************************************************************/
void makepointmap()
{
struct triedge triangleloop;
point triorg;
if (verbose) {
printf(" Constructing mapping from points to triangles.\n");
}
traversalinit(&triangles);
triangleloop.tri = triangletraverse();
while (triangleloop.tri != (triangle *) NULL) {
/* Check all three points of the triangle. */
for (triangleloop.orient = 0; triangleloop.orient < 3;
triangleloop.orient++) {
org(triangleloop, triorg);
setpoint2tri(triorg, encode(triangleloop));
}
triangleloop.tri = triangletraverse();
}
}
/*****************************************************************************/
/* */
/* 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. The possibility that the */
/* vertex one seeks is an endpoint of the starting edge must be */
/* screened out before preciselocate() is called. */
/* */
/* 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. */
/* */
/* 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. */
/* */
/*****************************************************************************/
enum locateresult preciselocate(searchpoint, searchtri)
point searchpoint;
struct triedge *searchtri;
{
struct triedge backtracktri;
point forg, fdest, fapex;
point swappoint;
REAL orgorient, destorient;
int moveleft;
triangle ptr; /* Temporary variable used by sym(). */
if (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 (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(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(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) 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. We can just bounce off */
/* the boundary as if it were an elastic band. */
if (moveleft) {
lprev(*searchtri, backtracktri);
fdest = fapex;
} else {
lnext(*searchtri, backtracktri);
forg = fapex;
}
sym(backtracktri, *searchtri);
/* Check for walking off the edge. */
if (searchtri->tri == dummytri) {
/* Turn around. */
triedgecopy(backtracktri, *searchtri);
swappoint = forg;
forg = fdest;
fdest = swappoint;
apex(*searchtri, fapex);
/* Check if the point really is beyond the triangulation boundary. */
destorient = counterclockwise(forg, fapex, searchpoint);
orgorient = counterclockwise(fapex, fdest, searchpoint);
if ((orgorient < 0.0) && (destorient < 0.0)) {
return OUTSIDE;
}
} else {
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 searcing 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. */
/* */
/*****************************************************************************/
enum locateresult locate(searchpoint, searchtri)
point searchpoint;
struct triedge *searchtri;
{
VOID **sampleblock;
triangle *firsttri;
struct triedge sampletri;
point torg, tdest;
unsigned long alignptr;
REAL searchdist, dist;
REAL ahead;
long sampleblocks, samplesperblock, samplenum;
long triblocks;
long i, j;
triangle ptr; /* Temporary variable used by sym(). */
if (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 (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 (recenttri.tri != (triangle *) NULL) {
if (recenttri.tri[3] != (triangle) NULL) {
org(recenttri, torg);
if ((torg[0] == searchpoint[0]) && (torg[1] == searchpoint[1])) {
triedgecopy(recenttri, *searchtri);
return ONVERTEX;
}
dist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) + (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]);
if (dist < searchdist) {
triedgecopy(recenttri, *searchtri);
searchdist = dist;
if (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. */
while (SAMPLEFACTOR * samples * samples * samples < triangles.items) {
samples++;
}
triblocks = (triangles.maxitems + TRIPERBLOCK - 1) / TRIPERBLOCK;
samplesperblock = 1 + (samples / triblocks);
sampleblocks = samples / samplesperblock;
sampleblock = triangles.firstblock;
sampletri.orient = 0;
for (i = 0; i < sampleblocks; i++) {
alignptr = (unsigned long) (sampleblock + 1);
firsttri = (triangle *) (alignptr + (unsigned long) triangles.alignbytes
- (alignptr % (unsigned long) triangles.alignbytes));
for (j = 0; j < samplesperblock; j++) {
if (i == triblocks - 1) {
samplenum = randomnation((int)
(triangles.maxitems - (i * TRIPERBLOCK)));
} else {
samplenum = randomnation(TRIPERBLOCK);
}
sampletri.tri = (triangle *)
(firsttri + (samplenum * triangles.itemwords));
if (sampletri.tri[3] != (triangle) NULL) {
org(sampletri, torg);
dist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0])
+ (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]);
if (dist < searchdist) {
triedgecopy(sampletri, *searchtri);
searchdist = dist;
if (verbose > 2) {
printf(" Choosing triangle with origin (%.12g, %.12g).\n",
torg[0], torg[1]);
}
}
}
}
sampleblock = (VOID **) *sampleblock;
}
/* 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(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(searchpoint, searchtri);
}
/** **/
/** **/
/********* Point location routines end here *********/
/********* Mesh transformation routines begin here *********/
/** **/
/** **/
/*****************************************************************************/
/* */
/* insertshelle() Create a new shell edge and insert it between two */
/* triangles. */
/* */
/* The new shell edge is inserted at the edge described by the handle */
/* `tri'. Its vertices are properly initialized. The marker `shellemark' */
/* is applied to the shell edge and, if appropriate, its vertices. */
/* */
/*****************************************************************************/
void insertshelle(tri, shellemark)
struct triedge *tri; /* Edge at which to insert the new shell edge. */
int shellemark; /* Marker for the new shell edge. */
{
struct triedge oppotri;
struct edge newshelle;
point triorg, tridest;
triangle ptr; /* Temporary variable used by sym(). */
shelle sptr; /* Temporary variable used by tspivot(). */
/* Mark points if possible. */
org(*tri, triorg);
dest(*tri, tridest);
if (pointmark(triorg) == 0) {
setpointmark(triorg, shellemark);
}
if (pointmark(tridest) == 0) {
setpointmark(tridest, shellemark);
}
/* Check if there's already a shell edge here. */
tspivot(*tri, newshelle);
if (newshelle.sh == dummysh) {
/* Make new shell edge and initialize its vertices. */
makeshelle(&newshelle);
setsorg(newshelle, tridest);
setsdest(newshelle, triorg);
/* Bond new shell edge to the two triangles it is sandwiched between. */
/* Note that the facing triangle `oppotri' might be equal to */
/* `dummytri' (outer space), but the new shell edge is bonded to it */
/* all the same. */
tsbond(*tri, newshelle);
sym(*tri, oppotri);
ssymself(newshelle);
tsbond(oppotri, newshelle);
setmark(newshelle, shellemark);
if (verbose > 2) {
printf(" Inserting new ");
printshelle(&newshelle);
}
} else {
if (mark(newshelle) == 0) {
setmark(newshelle, shellemark); }
}
}
/*****************************************************************************/
/* */
/* 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 */
/* point. */
/* */
/* 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. */
/* */
/* A "shell" is similar to a "casing". The term "shell" describes the set */
/* of shell edges (if any) that are attached to the triangles being */
/* transformed. However, I sometimes use "shell" to refer to a single */
/* shell edge, so don't get confused. */
/* */
/*****************************************************************************/
/*****************************************************************************/
/* */
/* flip() Transform two triangles to two different triangles by flipping */
/* an edge within a quadrilateral. */
/* */
/* Imagine the original triangles, abc and bad, oriented so that the */
/* shared edge ab lies in a horizontal plane, with the point b on the left */
/* and the point a on the right. The point c lies below the edge, and the */
/* point 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 shell edge 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. */
/* */
/*****************************************************************************/
void flip(flipedge)
struct triedge *flipedge; /* Handle for the triangle abc. */
{
struct triedge botleft, botright;
struct triedge topleft, topright;
struct triedge top;
struct triedge botlcasing, botrcasing;
struct triedge toplcasing, toprcasing;
struct edge botlshelle, botrshelle;
struct edge toplshelle, toprshelle;
point leftpoint, rightpoint, botpoint;
point farpoint;
triangle ptr; /* Temporary variable used by sym(). */ shelle sptr; /* Temporary variable used by tspivot(). */
/* Identify the vertices of the quadrilateral. */
org(*flipedge, rightpoint);
dest(*flipedge, leftpoint);
apex(*flipedge, botpoint);
sym(*flipedge, top);
#ifdef SELF_CHECK
if (top.tri == dummytri) {
printf("Internal error in flip(): Attempt to flip on boundary.\n");
lnextself(*flipedge);
return;
}
if (checksegments) {
tspivot(*flipedge, toplshelle);
if (toplshelle.sh != dummysh) {
printf("Internal error in flip(): Attempt to flip a segment.\n");
lnextself(*flipedge);
return;
}
}
#endif /* SELF_CHECK */
apex(top, farpoint);
/* 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 (checksegments) {
/* Check for shell edges and rebond them to the quadrilateral. */
tspivot(topleft, toplshelle);
tspivot(botleft, botlshelle);
tspivot(botright, botrshelle);
tspivot(topright, toprshelle);
if (toplshelle.sh == dummysh) {
tsdissolve(topright);
} else {
tsbond(topright, toplshelle);
}
if (botlshelle.sh == dummysh) {
tsdissolve(topleft);
} else {
tsbond(topleft, botlshelle);
}
if (botrshelle.sh == dummysh) {
tsdissolve(botleft);
} else {
tsbond(botleft, botrshelle);
}
if (toprshelle.sh == dummysh) {
tsdissolve(botright);
} else {
tsbond(botright, toprshelle);
}
}
/* New point assignments for the rotated quadrilateral. */
setorg(*flipedge, farpoint);
setdest(*flipedge, botpoint); setapex(*flipedge, rightpoint);
setorg(top, botpoint);
setdest(top, farpoint);
setapex(top, leftpoint);
if (verbose > 2) {
printf(" Edge flip results in left ");
lnextself(topleft);
printtriangle(&topleft);
printf(" and right ");
printtriangle(flipedge);
}
}
/*****************************************************************************/
/* */
/* insertsite() Insert a vertex into a Delaunay triangulation, */
/* performing flips as necessary to maintain the Delaunay */
/* property. */
/* */
/* The point `insertpoint' 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 `insertpoint' is found inside a triangle, the triangle is split into */
/* three; if `insertpoint' 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 `insertpoint' lies on an */
/* existing vertex, no action is taken, and the value DUPLICATEPOINT is */
/* returned. On return, `searchtri' is set to a handle whose origin is the */
/* existing vertex. */
/* */
/* Normally, the parameter `splitedge' is set to NULL, implying that no */
/* segment should be split. In this case, if `insertpoint' is found to */
/* lie on a segment, no action is taken, and the value VIOLATINGPOINT is */
/* returned. On return, `searchtri' is set to a handle whose primary edge */
/* is the violated segment. */
/* */
/* If the calling routine wishes to split a segment by inserting a point in */
/* it, the parameter `splitedge' should be that segment. In this case, */
/* `searchtri' MUST be the triangle handle reached by pivoting from that */
/* segment; no point location is done. */
/* */
/* `segmentflaws' and `triflaws' are flags that indicate whether or not */
/* there should be checks for the creation of encroached segments or bad */
/* quality faces. If a newly inserted point encroaches upon segments, */
/* these segments are added to the list of segments 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 point or violated segment does not prevent the point */
/* from being inserted, the return value will be ENCROACHINGPOINT if the */
/* point encroaches upon a segment (and checking is enabled), or */
/* SUCCESSFULPOINT otherwise. In either case, `searchtri' is set to a */
/* handle whose origin is the newly inserted vertex. */
/* */
/* insertsite() does not use flip() for reasons of speed; some */
/* information can be reused from edge flip to edge flip, like the */
/* locations of shell edges. */
/* */
/*****************************************************************************/
enum insertsiteresult insertsite(insertpoint, searchtri, splitedge,
segmentflaws, triflaws)
point insertpoint;
struct triedge *searchtri;
struct edge *splitedge;
int segmentflaws;
int triflaws;
{
struct triedge horiz;
struct triedge top; struct triedge botleft, botright;
struct triedge topleft, topright;
struct triedge newbotleft, newbotright;
struct triedge newtopright;
struct triedge botlcasing, botrcasing;
struct triedge toplcasing, toprcasing;
struct triedge testtri;
struct edge botlshelle, botrshelle;
struct edge toplshelle, toprshelle;
struct edge brokenshelle;
struct edge checkshelle;
struct edge rightedge;
struct edge newedge;
struct edge *encroached;
point first;
point leftpoint, rightpoint, botpoint, toppoint, farpoint;
REAL attrib;
REAL area;
enum insertsiteresult success;
enum locateresult intersect;
int doflip;
int mirrorflag;
int i;
triangle ptr; /* Temporary variable used by sym(). */
shelle sptr; /* Temporary variable used by spivot() and tspivot(). */
if (verbose > 1) {
printf(" Inserting (%.12g, %.12g).\n", insertpoint[0], insertpoint[1]);
}
if (splitedge == (struct edge *) NULL) {
/* Find the location of the point to be inserted. Check if a good */
/* starting triangle has already been provided by the caller. */
if (searchtri->tri == (triangle *) NULL) {
/* Find a boundary triangle. */
horiz.tri = dummytri;
horiz.orient = 0;
symself(horiz);
/* Search for a triangle containing `insertpoint'. */
intersect = locate(insertpoint, &horiz);
} else {
/* Start searching from the triangle provided by the caller. */
triedgecopy(*searchtri, horiz);
intersect = preciselocate(insertpoint, &horiz);
}
} else {
/* The calling routine provides the edge in which the point is inserted. */
triedgecopy(*searchtri, horiz);
intersect = ONEDGE;
}
if (intersect == ONVERTEX) {
/* There's already a vertex there. Return in `searchtri' a triangle */
/* whose origin is the existing vertex. */
triedgecopy(horiz, *searchtri);
triedgecopy(horiz, recenttri);
return DUPLICATEPOINT;
}
if ((intersect == ONEDGE) || (intersect == OUTSIDE)) {
/* The vertex falls on an edge or boundary. */
if (checksegments && (splitedge == (struct edge *) NULL)) {
/* Check whether the vertex falls on a shell edge. */
tspivot(horiz, brokenshelle);
if (brokenshelle.sh != dummysh) {
/* The vertex falls on a shell edge. */
if (segmentflaws) {
if (nobisect == 0) {
/* Add the shell edge to the list of encroached segments. */
encroached = (struct edge *) poolalloc(&badsegments);
shellecopy(brokenshelle, *encroached);
} else if ((nobisect == 1) && (intersect == ONEDGE)) {
/* This segment may be split only if it is an internal boundary. */ sym(horiz, testtri);
if (testtri.tri != dummytri) {
/* Add the shell edge to the list of encroached segments. */
encroached = (struct edge *) poolalloc(&badsegments);
shellecopy(brokenshelle, *encroached);
}
}
}
/* Return a handle whose primary edge contains the point, */
/* which has not been inserted. */
triedgecopy(horiz, *searchtri);
triedgecopy(horiz, recenttri);
return VIOLATINGPOINT;
}
}
/* Insert the point 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 != dummytri;
if (mirrorflag) {
lnextself(topright);
sym(topright, toprcasing);
maketriangle(&newtopright);
} else {
/* Splitting the boundary edge increases the number of boundary edges. */
hullsize++;
}
maketriangle(&newbotright);
/* Set the vertices of changed and new triangles. */
org(horiz, rightpoint);
dest(horiz, leftpoint);
apex(horiz, botpoint);
setorg(newbotright, botpoint);
setdest(newbotright, rightpoint);
setapex(newbotright, insertpoint);
setorg(horiz, insertpoint);
for (i = 0; i < eextras; i++) {
/* Set the element attributes of a new triangle. */
setelemattribute(newbotright, i, elemattribute(botright, i));
}
if (vararea) {
/* Set the area constraint of a new triangle. */
setareabound(newbotright, areabound(botright));
}
if (mirrorflag) {
dest(topright, toppoint);
setorg(newtopright, rightpoint);
setdest(newtopright, toppoint);
setapex(newtopright, insertpoint);
setorg(topright, insertpoint);
for (i = 0; i < eextras; i++) {
/* Set the element attributes of another new triangle. */
setelemattribute(newtopright, i, elemattribute(topright, i));
}
if (vararea) {
/* Set the area constraint of another new triangle. */
setareabound(newtopright, areabound(topright));
}
}
/* There may be shell edges that need to be bonded */
/* to the new triangle(s). */
if (checksegments) {
tspivot(botright, botrshelle);
if (botrshelle.sh != dummysh) {
tsdissolve(botright); tsbond(newbotright, botrshelle);
}
if (mirrorflag) {
tspivot(topright, toprshelle);
if (toprshelle.sh != dummysh) {
tsdissolve(topright);
tsbond(newtopright, toprshelle);
}
}
}
/* 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 (splitedge != (struct edge *) NULL) {
/* Split the shell edge into two. */
setsdest(*splitedge, insertpoint);
ssymself(*splitedge);
spivot(*splitedge, rightedge);
insertshelle(&newbotright, mark(*splitedge));
tspivot(newbotright, newedge);
sbond(*splitedge, newedge);
ssymself(newedge);
sbond(newedge, rightedge);
ssymself(*splitedge);
}
#ifdef SELF_CHECK
if (counterclockwise(rightpoint, leftpoint, botpoint) < 0.0) {
printf("Internal error in insertsite():\n");
printf(" Clockwise triangle prior to edge point insertion (bottom).\n");
}
if (mirrorflag) {
if (counterclockwise(leftpoint, rightpoint, toppoint) < 0.0) {
printf("Internal error in insertsite():\n");
printf(" Clockwise triangle prior to edge point insertion (top).\n");
}
if (counterclockwise(rightpoint, toppoint, insertpoint) < 0.0) {
printf("Internal error in insertsite():\n");
printf(" Clockwise triangle after edge point insertion (top right).\n"
);
}
if (counterclockwise(toppoint, leftpoint, insertpoint) < 0.0) {
printf("Internal error in insertsite():\n");
printf(" Clockwise triangle after edge point insertion (top left).\n"
);
}
}
if (counterclockwise(leftpoint, botpoint, insertpoint) < 0.0) {
printf("Internal error in insertsite():\n");
printf(" Clockwise triangle after edge point insertion (bottom left).\n"
);
}
if (counterclockwise(botpoint, rightpoint, insertpoint) < 0.0) {
printf("Internal error in insertsite():\n");
printf(
" Clockwise triangle after edge point insertion (bottom right).\n");
}
#endif /* SELF_CHECK */
if (verbose > 2) { printf(" Updating bottom left ");
printtriangle(&botright);
if (mirrorflag) {
printf(" Updating top left ");
printtriangle(&topright);
printf(" Creating top right ");
printtriangle(&newtopright);
}
printf(" Creating bottom right ");
printtriangle(&newbotright);
}
/* Position `horiz' on the first edge to check for */
/* the Delaunay property. */
lnextself(horiz);
} else {
/* Insert the point in a triangle, splitting it into three. */
lnext(horiz, botleft);
lprev(horiz, botright);
sym(botleft, botlcasing);
sym(botright, botrcasing);
maketriangle(&newbotleft);
maketriangle(&newbotright);
/* Set the vertices of changed and new triangles. */
org(horiz, rightpoint);
dest(horiz, leftpoint);
apex(horiz, botpoint);
setorg(newbotleft, leftpoint);
setdest(newbotleft, botpoint);
setapex(newbotleft, insertpoint);
setorg(newbotright, botpoint);
setdest(newbotright, rightpoint);
setapex(newbotright, insertpoint);
setapex(horiz, insertpoint);
for (i = 0; i < eextras; i++) {
/* Set the element attributes of the new triangles. */
attrib = elemattribute(horiz, i);
setelemattribute(newbotleft, i, attrib);
setelemattribute(newbotright, i, attrib);
}
if (vararea) {
/* Set the area constraint of the new triangles. */
area = areabound(horiz);
setareabound(newbotleft, area);
setareabound(newbotright, area);
}
/* There may be shell edges that need to be bonded */
/* to the new triangles. */
if (checksegments) {
tspivot(botleft, botlshelle);
if (botlshelle.sh != dummysh) {
tsdissolve(botleft);
tsbond(newbotleft, botlshelle);
}
tspivot(botright, botrshelle);
if (botrshelle.sh != dummysh) {
tsdissolve(botright);
tsbond(newbotright, botrshelle);
}
}
/* 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);
#ifdef SELF_CHECK
if (counterclockwise(rightpoint, leftpoint, botpoint) < 0.0) {
printf("Internal error in insertsite():\n");
printf(" Clockwise triangle prior to point insertion.\n");
}
if (counterclockwise(rightpoint, leftpoint, insertpoint) < 0.0) {
printf("Internal error in insertsite():\n");
printf(" Clockwise triangle after point insertion (top).\n");
}
if (counterclockwise(leftpoint, botpoint, insertpoint) < 0.0) {
printf("Internal error in insertsite():\n");
printf(" Clockwise triangle after point insertion (left).\n");
}
if (counterclockwise(botpoint, rightpoint, insertpoint) < 0.0) {
printf("Internal error in insertsite():\n");
printf(" Clockwise triangle after point insertion (right).\n");
}
#endif /* SELF_CHECK */
if (verbose > 2) {
printf(" Updating top ");
printtriangle(&horiz);
printf(" Creating left ");
printtriangle(&newbotleft);
printf(" Creating right ");
printtriangle(&newbotright);
}
}
/* The insertion is successful by default, unless an encroached */
/* edge is found. */
success = SUCCESSFULPOINT;
/* 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);
rightpoint = first;
dest(horiz, leftpoint);
/* Circle until finished. */
while (1) {
/* By default, the edge will be flipped. */
doflip = 1;
if (checksegments) {
/* Check for a segment, which cannot be flipped. */
tspivot(horiz, checkshelle);
if (checkshelle.sh != dummysh) {
/* The edge is a segment and cannot be flipped. */
doflip = 0;
#ifndef CDT_ONLY
if (segmentflaws) {
/* Does the new point encroach upon this segment? */
if (checkedge4encroach(&checkshelle)) {
success = ENCROACHINGPOINT;
}
}
#endif /* not CDT_ONLY */
}
}
if (doflip) {
/* Check if the edge is a boundary edge. */
sym(horiz, top);
if (top.tri == dummytri) {
/* The edge is a boundary edge and cannot be flipped. */
doflip = 0;
} else {
/* Find the point on the other side of the edge. */ apex(top, farpoint);
/* In the incremental Delaunay triangulation algorithm, any of */
/* `leftpoint', `rightpoint', and `farpoint' 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 ((leftpoint == infpoint1) || (leftpoint == infpoint2)
|| (leftpoint == infpoint3)) {
/* `leftpoint' is infinitely distant. Check the convexity of */
/* the boundary of the triangulation. 'farpoint' might be */
/* infinite as well, but trust me, this same condition */
/* should be applied. */
doflip = counterclockwise(insertpoint, rightpoint, farpoint) > 0.0;
} else if ((rightpoint == infpoint1) || (rightpoint == infpoint2)
|| (rightpoint == infpoint3)) {
/* `rightpoint' is infinitely distant. Check the convexity of */
/* the boundary of the triangulation. 'farpoint' might be */
/* infinite as well, but trust me, this same condition */
/* should be applied. */
doflip = counterclockwise(farpoint, leftpoint, insertpoint) > 0.0;
} else if ((farpoint == infpoint1) || (farpoint == infpoint2)
|| (farpoint == infpoint3)) {
/* `farpoint' 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(leftpoint, insertpoint, rightpoint, farpoint)
> 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 (checksegments) {
/* Check for shell edges and rebond them to the quadrilateral. */
tspivot(topleft, toplshelle);
tspivot(botleft, botlshelle);
tspivot(botright, botrshelle);
tspivot(topright, toprshelle);
if (toplshelle.sh == dummysh) {
tsdissolve(topright);
} else {
tsbond(topright, toplshelle);
}
if (botlshelle.sh == dummysh) {
tsdissolve(topleft);
} else {
tsbond(topleft, botlshelle);
}
if (botrshelle.sh == dummysh) {
tsdissolve(botleft);
} else {
tsbond(botleft, botrshelle);
}
if (toprshelle.sh == dummysh) {
tsdissolve(botright); } else {
tsbond(botright, toprshelle);
}
}
/* New point assignments for the rotated quadrilateral. */
setorg(horiz, farpoint);
setdest(horiz, insertpoint);
setapex(horiz, rightpoint);
setorg(top, insertpoint);
setdest(top, farpoint);
setapex(top, leftpoint);
for (i = 0; i < 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 (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);
}
#ifdef SELF_CHECK
if (insertpoint != (point) NULL) {
if (counterclockwise(leftpoint, insertpoint, rightpoint) < 0.0) {
printf("Internal error in insertsite():\n");
printf(" Clockwise triangle prior to edge flip (bottom).\n");
}
/* The following test has been removed because constrainededge() */
/* sometimes generates inverted triangles that insertsite() */
/* removes. */
/*
if (counterclockwise(rightpoint, farpoint, leftpoint) < 0.0) {
printf("Internal error in insertsite():\n");
printf(" Clockwise triangle prior to edge flip (top).\n");
}
*/
if (counterclockwise(farpoint, leftpoint, insertpoint) < 0.0) {
printf("Internal error in insertsite():\n");
printf(" Clockwise triangle after edge flip (left).\n");
}
if (counterclockwise(insertpoint, rightpoint, farpoint) < 0.0) {
printf("Internal error in insertsite():\n");
printf(" Clockwise triangle after edge flip (right).\n");
}
}
#endif /* SELF_CHECK */
if (verbose > 2) {
printf(" Edge flip results in left ");
lnextself(topleft);
printtriangle(&topleft);
printf(" and right ");
printtriangle(&horiz);
}
/* On the next iterations, consider the two edges that were */
/* exposed (this is, are now visible to the newly inserted */
/* point) by the edge flip. */
lprevself(horiz);
leftpoint = farpoint;
}
}
}
if (!doflip) { /* The handle `horiz' is accepted as locally Delaunay. */
#ifndef CDT_ONLY
if (triflaws) {
/* Check the triangle `horiz' for quality. */
testtriangle(&horiz);
}
#endif /* not CDT_ONLY */
/* Look for the next edge around the newly inserted point. */
lnextself(horiz);
sym(horiz, testtri);
/* Check for finishing a complete revolution about the new point, or */
/* falling off the edge of the triangulation. The latter will */
/* happen when a point is inserted at a boundary. */
if ((leftpoint == first) || (testtri.tri == dummytri)) {
/* We're done. Return a triangle whose origin is the new point. */
lnext(horiz, *searchtri);
lnext(horiz, recenttri);
return success;
}
/* Finish finding the next edge around the newly inserted point. */
lnext(testtri, horiz);
rightpoint = leftpoint;
dest(horiz, leftpoint);
}
}
}
/*****************************************************************************/
/* */
/* triangulatepolygon() Find the Delaunay triangulation of a polygon that */
/* has a certain "nice" shape. This includes the */
/* polygons that result from deletion of a point 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 point 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 time. */
/* */
/* 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. */
/* */
/*****************************************************************************/
void triangulatepolygon(firstedge, lastedge, edgecount, doflip, triflaws)
struct triedge *firstedge;
struct triedge *lastedge;
int edgecount;
int doflip;
int triflaws;
{
struct triedge testtri;
struct triedge besttri;
struct triedge tempedge;
point leftbasepoint, rightbasepoint;
point testpoint;
point bestpoint;
int bestnumber;
int i;
triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */
/* Identify the base vertices. */
apex(*lastedge, leftbasepoint);
dest(*firstedge, rightbasepoint);
if (verbose > 2) {
printf(" Triangulating interior polygon at edge\n");
printf(" (%.12g, %.12g) (%.12g, %.12g)\n", leftbasepoint[0],
leftbasepoint[1], rightbasepoint[0], rightbasepoint[1]);
}
/* Find the best vertex to connect the base to. */
onext(*firstedge, besttri);
dest(besttri, bestpoint);
triedgecopy(besttri, testtri);
bestnumber = 1;
for (i = 2; i <= edgecount - 2; i++) {
onextself(testtri);
dest(testtri, testpoint);
/* Is this a better vertex? */
if (incircle(leftbasepoint, rightbasepoint, bestpoint, testpoint) > 0.0) {
triedgecopy(testtri, besttri);
bestpoint = testpoint;
bestnumber = i;
}
}
if (verbose > 2) {
printf(" Connecting edge to (%.12g, %.12g)\n", bestpoint[0],
bestpoint[1]);
}
if (bestnumber > 1) {
/* Recursively triangulate the smaller polygon on the right. */
oprev(besttri, tempedge);
triangulatepolygon(firstedge, &tempedge, bestnumber + 1, 1, triflaws);
} if (bestnumber < edgecount - 2) {
/* Recursively triangulate the smaller polygon on the left. */
sym(besttri, tempedge);
triangulatepolygon(&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(&besttri);
#ifndef CDT_ONLY
if (triflaws) {
/* Check the quality of the newly committed triangle. */
sym(besttri, testtri);
testtriangle(&testtri);
}
#endif /* not CDT_ONLY */
}
/* Return the base triangle. */
triedgecopy(besttri, *lastedge);
}
/*****************************************************************************/
/* */
/* deletesite() 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 point is a polygon, for which the Delaunay triangulation is */
/* found. Two triangles are removed from the mesh. */
/* */
/* Only interior points that do not lie on segments (shell edges) or */
/* boundaries may be deleted. */
/* */
/*****************************************************************************/
#ifndef CDT_ONLY
void deletesite(deltri)
struct triedge *deltri;
{
struct triedge countingtri;
struct triedge firstedge, lastedge;
struct triedge deltriright;
struct triedge lefttri, righttri;
struct triedge leftcasing, rightcasing;
struct edge leftshelle, rightshelle;
point delpoint;
point neworg;
int edgecount;
triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */
shelle sptr; /* Temporary variable used by tspivot(). */
org(*deltri, delpoint);
if (verbose > 1) {
printf(" Deleting (%.12g, %.12g).\n", delpoint[0], delpoint[1]);
}
pointdealloc(delpoint);
/* Count the degree of the point being deleted. */
onext(*deltri, countingtri);
edgecount = 1;
while (!triedgeequal(*deltri, countingtri)) {
#ifdef SELF_CHECK
if (countingtri.tri == dummytri) {
printf("Internal error in deletesite():\n");
printf(" Attempt to delete boundary point.\n");
internalerror();
}#endif /* SELF_CHECK */
edgecount++;
onextself(countingtri);
}
#ifdef SELF_CHECK
if (edgecount < 3) {
printf("Internal error in deletesite():\n Point 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 point being deleted. Check the quality of */
/* the resulting triangles. */
onext(*deltri, firstedge);
oprev(*deltri, lastedge);
triangulatepolygon(&firstedge, &lastedge, edgecount, 0, !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, leftshelle);
if (leftshelle.sh != dummysh) {
tsbond(*deltri, leftshelle);
}
tspivot(righttri, rightshelle);
if (rightshelle.sh != dummysh) {
tsbond(deltriright, rightshelle);
}
/* Set the new origin of `deltri' and check its quality. */
org(lefttri, neworg);
setorg(*deltri, neworg);
if (!nobisect) {
testtriangle(deltri);
}
/* Delete the two spliced-out triangles. */
triangledealloc(lefttri.tri);
triangledealloc(righttri.tri);
}
#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. */
/* */
/*****************************************************************************/
/*****************************************************************************/
/* */
/* pointsort() Sort an array of points 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. */
/* */
/*****************************************************************************/
void pointsort(sortarray, arraysize)
point *sortarray;
int arraysize;
{
int left, right;
int pivot;
REAL pivotx, pivoty;
point 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(arraysize);
pivotx = sortarray[pivot][0];
pivoty = sortarray[pivot][1];
/* Split the array. */
left = -1;
right = arraysize;
while (left < right) {
/* Search for a point 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 point 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 points. */
temp = sortarray[left];
sortarray[left] = sortarray[right];
sortarray[right] = temp;
}
}
if (left > 1) {
/* Recursively sort the left subset. */
pointsort(sortarray, left);
}
if (right < arraysize - 2) {
/* Recursively sort the right subset. */
pointsort(&sortarray[right + 1], arraysize - right - 1);
}
}
/*****************************************************************************/
/* */
/* pointmedian() An order statistic algorithm, almost. Shuffles an array */
/* of points so that the first `median' points occur */
/* lexicographically before the remaining points. */
/* */
/* Uses the x-coordinate as the primary key if axis == 0; the y-coordinate */
/* if axis == 1. Very similar to the pointsort() procedure, but runs in */
/* randomized linear time. */
/* */
/*****************************************************************************/
void pointmedian(sortarray, arraysize, median, axis)
point *sortarray;
int arraysize;
int median;
int axis;
{
int left, right;
int pivot;
REAL pivot1, pivot2;
point 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(arraysize);
pivot1 = sortarray[pivot][axis];
pivot2 = sortarray[pivot][1 - axis];
/* Split the array. */
left = -1;
right = arraysize;
while (left < right) {
/* Search for a point 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 point 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 points. */
temp = sortarray[left];
sortarray[left] = sortarray[right];
sortarray[right] = temp;
}
}
/* Unlike in pointsort(), at most one of the following */
/* conditionals is true. */
if (left > median) {
/* Recursively shuffle the left subset. */
pointmedian(sortarray, left, median, axis);
}
if (right < median - 1) {
/* Recursively shuffle the right subset. */
pointmedian(&sortarray[right + 1], arraysize - right - 1,
median - right - 1, axis);
}
}
/*****************************************************************************/
/* */
/* alternateaxes() Sorts the points 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 points are */
/* always sorted by x-coordinate. */
/* */
/*****************************************************************************/
void alternateaxes(sortarray, arraysize, axis)
point *sortarray;
int arraysize;
int axis;
{
int divider;
divider = arraysize >> 1;
if (arraysize <= 3) {
/* Recursive base case: subsets of two or three points will be */
/* handled specially, and should always be sorted by x-coordinate. */
axis = 0;
}
/* Partition with a horizontal or vertical cut. */
pointmedian(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 point. */
/* */
/* 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. */
/* */
/*****************************************************************************/
void mergehulls(farleft, innerleft, innerright, farright, axis)
struct triedge *farleft;
struct triedge *innerleft;
struct triedge *innerright;
struct triedge *farright;
int axis;
{
struct triedge leftcand, rightcand;
struct triedge baseedge;
struct triedge nextedge;
struct triedge sidecasing, topcasing, outercasing;
struct triedge checkedge;
point innerleftdest;
point innerrightorg;
point innerleftapex, innerrightapex;
point farleftpt, farrightpt;
point farleftapex, farrightapex;
point lowerleft, lowerright;
point upperleft, upperright;
point nextapex;
point 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 (dwyer && (axis == 1)) {
org(*farleft, farleftpt);
apex(*farleft, farleftapex);
dest(*farright, farrightpt);
apex(*farright, farrightapex);
/* The pointers to the extremal points are shifted to point to the */
/* topmost and bottommost point of each hull, rather than the */
/* leftmost and rightmost points. */
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" point of the left hull. */
if (counterclockwise(innerleftdest, innerleftapex, innerrightorg) > 0.0) {
lprevself(*innerleft);
symself(*innerleft);
innerleftdest = innerleftapex;
apex(*innerleft, innerleftapex);
changemade = 1;
}
/* Make innerrightorg the "bottommost" point of the right hull. */
if (counterclockwise(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(&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 (verbose > 2) {
printf(" Creating base bounding ");
printtriangle(&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 point of */
/* the left triangulation. And vice-versa.) */
leftfinished = counterclockwise(upperleft, lowerleft, lowerright) <= 0.0;
rightfinished = counterclockwise(upperright, lowerleft, lowerright) <= 0.0;
if (leftfinished && rightfinished) {
/* Create the top new bounding triangle. */
maketriangle(&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 (verbose > 2) {
printf(" Creating top bounding ");
printtriangle(&baseedge);
}
/* Special treatment for horizontal cuts. */
if (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 points are restored to the leftmost */
/* and rightmost points (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 != (point) NULL) {
/* Check whether the edge is Delaunay. */
badedge = incircle(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? */
triedgecopy(sidecasing, nextedge);
apex(nextedge, nextapex);
if (nextapex != (point) NULL) {
/* Check whether the edge is Delaunay. */
badedge = incircle(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 != (point) NULL) {
/* Check whether the edge is Delaunay. */
badedge = incircle(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? */
triedgecopy(sidecasing, nextedge);
apex(nextedge, nextapex);
if (nextapex != (point) NULL) {
/* Check whether the edge is Delaunay. */
badedge = incircle(lowerleft, lowerright, upperright, nextapex)
> 0.0; } else {
/* Avoid eating right through the triangulation. */
badedge = 0;
}
}
}
}
if (leftfinished || (!rightfinished &&
(incircle(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 (verbose > 2) {
printf(" Connecting ");
printtriangle(&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 points) 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). */
/* */
/*****************************************************************************/
void divconqrecurse(sortarray, vertices, axis, farleft, farright)
point *sortarray;
int vertices;
int axis;
struct triedge *farleft;
struct triedge *farright;
{
struct triedge midtri, tri1, tri2, tri3;
struct triedge innerleft, innerright;
REAL area;
int divider;
if (verbose > 2) {
printf(" Triangulating %d points.\n", vertices);
}
if (vertices == 2) {
/* The triangulation of two vertices is an edge. An edge is */
/* represented by two bounding triangles. */
maketriangle(farleft); setorg(*farleft, sortarray[0]);
setdest(*farleft, sortarray[1]);
/* The apex is intentionally left NULL. */
maketriangle(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 (verbose > 2) {
printf(" Creating ");
printtriangle(farleft);
printf(" Creating ");
printtriangle(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(&midtri);
maketriangle(&tri1);
maketriangle(&tri2);
maketriangle(&tri3);
area = counterclockwise(sortarray[0], sortarray[1], sortarray[2]);
if (area == 0.0) {
/* Three collinear points; 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]. */
triedgecopy(tri1, *farleft);
/* Ensure that the destination of `farright' is sortarray[2]. */
triedgecopy(tri2, *farright);
} else {
/* The three points 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]. */
triedgecopy(tri1, *farleft);
/* Ensure that the destination of `farright' is sortarray[2]. */
if (area > 0.0) {
triedgecopy(tri2, *farright);
} else {
lnext(*farleft, *farright);
}
}
if (verbose > 2) {
printf(" Creating ");
printtriangle(&midtri);
printf(" Creating ");
printtriangle(&tri1);
printf(" Creating ");
printtriangle(&tri2);
printf(" Creating ");
printtriangle(&tri3);
}
return;
} else {
/* Split the vertices in half. */
divider = vertices >> 1;
/* Recursively triangulate each half. */
divconqrecurse(sortarray, divider, 1 - axis, farleft, &innerleft);
divconqrecurse(&sortarray[divider], vertices - divider, 1 - axis,
&innerright, farright);
if (verbose > 1) {
printf(" Joining triangulations with %d and %d vertices.\n", divider,
vertices - divider);
}
/* Merge the two triangulations into one. */
mergehulls(farleft, &innerleft, &innerright, farright, axis);
}
}
long removeghosts(startghost)
struct triedge *startghost;
{
struct triedge searchedge; struct triedge dissolveedge;
struct triedge deadtri;
point markorg;
long hullsize;
triangle ptr; /* Temporary variable used by sym(). */
if (verbose) {
printf(" Removing ghost triangles.\n");
}
/* Find an edge on the convex hull to start point location from. */
lprev(*startghost, searchedge);
symself(searchedge);
dummytri[0] = encode(searchedge);
/* Remove the bounding box and count the convex hull edges. */
triedgecopy(*startghost, dissolveedge);
hullsize = 0;
do {
hullsize++;
lnext(dissolveedge, deadtri);
lprevself(dissolveedge);
symself(dissolveedge);
/* If no PSLG is involved, set the boundary markers of all the points */
/* on the convex hull. If a PSLG is used, this step is done later. */
if (!poly) {
/* Watch out for the case where all the input points are collinear. */
if (dissolveedge.tri != dummytri) {
org(dissolveedge, markorg);
if (pointmark(markorg) == 0) {
setpointmark(markorg, 1);
}
}
}
/* Remove a bounding triangle from a convex hull triangle. */
dissolve(dissolveedge);
/* Find the next bounding triangle. */
sym(deadtri, dissolveedge);
/* Delete the bounding triangle. */
triangledealloc(deadtri.tri);
} while (!triedgeequal(dissolveedge, *startghost));
return hullsize;
}
/*****************************************************************************/
/* */
/* divconqdelaunay() Form a Delaunay triangulation by the divide-and- */
/* conquer method. */
/* */
/* Sorts the points, calls a recursive procedure to triangulate them, and */
/* removes the bounding box, setting boundary markers as appropriate. */
/* */
/*****************************************************************************/
long divconqdelaunay()
{
point *sortarray;
struct triedge hullleft, hullright;
int divider;
int i, j;
/* Allocate an array of pointers to points for sorting. */
sortarray = (point *) malloc(inpoints * sizeof(point));
if (sortarray == (point *) NULL) {
printf("Error: Out of memory.\n");
exit(1);
}
traversalinit(&points);
for (i = 0; i < inpoints; i++) {
sortarray[i] = pointtraverse();
}
if (verbose) { printf(" Sorting points.\n");
}
/* Sort the points. */
pointsort(sortarray, inpoints);
/* Discard duplicate points, which can really mess up the algorithm. */
i = 0;
for (j = 1; j < inpoints; j++) {
if ((sortarray[i][0] == sortarray[j][0])
&& (sortarray[i][1] == sortarray[j][1])) {
if (!quiet) {
printf(
"Warning: A duplicate point at (%.12g, %.12g) appeared and was ignored.\n",
sortarray[j][0], sortarray[j][1]);
}
/* Commented out - would eliminate point from output .node file, but causes
a failure if some segment has this point as an endpoint.
setpointmark(sortarray[j], DEADPOINT);
*/
} else {
i++;
sortarray[i] = sortarray[j];
}
}
i++;
if (dwyer) {
/* Re-sort the array of points 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 (verbose) {
printf(" Forming triangulation.\n");
}
/* Form the Delaunay triangulation. */
divconqrecurse(sortarray, i, 0, &hullleft, &hullright);
free(sortarray);
return removeghosts(&hullleft);
}
/** **/
/** **/
/********* Divide-and-conquer Delaunay triangulation ends here *********/
/********* Incremental Delaunay triangulation begins here *********/
/** **/
/** **/
/*****************************************************************************/
/* */
/* boundingbox() Form an "infinite" bounding triangle to insert points */
/* into. */
/* */
/* The points 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
void boundingbox()
{
struct triedge inftri; /* Handle for the triangular bounding box. */
REAL width;
if (verbose) {
printf(" Creating triangular bounding box.\n");
}
/* Find the width (or height, whichever is larger) of the triangulation. */
width = xmax - xmin;
if (ymax - ymin > width) {
width = ymax - ymin;
}
if (width == 0.0) {
width = 1.0;
}
/* Create the vertices of the bounding box. */
infpoint1 = (point) malloc(points.itembytes);
infpoint2 = (point) malloc(points.itembytes);
infpoint3 = (point) malloc(points.itembytes);
if ((infpoint1 == (point) NULL) || (infpoint2 == (point) NULL)
|| (infpoint3 == (point) NULL)) {
printf("Error: Out of memory.\n");
exit(1);
}
infpoint1[0] = xmin - 50.0 * width;
infpoint1[1] = ymin - 40.0 * width;
infpoint2[0] = xmax + 50.0 * width;
infpoint2[1] = ymin - 40.0 * width;
infpoint3[0] = 0.5 * (xmin + xmax);
infpoint3[1] = ymax + 60.0 * width;
/* Create the bounding box. */
maketriangle(&inftri);
setorg(inftri, infpoint1);
setdest(inftri, infpoint2);
setapex(inftri, infpoint3);
/* Link dummytri to the bounding box so we can always find an */
/* edge to begin searching (point location) from. */
dummytri[0] = (triangle) inftri.tri;
if (verbose > 2) {
printf(" Creating ");
printtriangle(&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. */
/* */
/*****************************************************************************/
#ifndef REDUCED
long removebox()
{
struct triedge deadtri;
struct triedge searchedge;
struct triedge checkedge;
struct triedge nextedge, finaledge, dissolveedge;
point markorg;
long hullsize;
triangle ptr; /* Temporary variable used by sym(). */
if (verbose) {
printf(" Removing triangular bounding box.\n");
} /* Find a boundary triangle. */
nextedge.tri = 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 point 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 == 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. */
dummytri[0] = encode(searchedge);
hullsize = -2l;
while (!triedgeequal(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 (!poly) {
/* Be careful! One must check for the case where all the input */
/* points are collinear, and thus all the triangles are part of */
/* the bounding box. Otherwise, the setpointmark() call below */
/* will cause a bad pointer reference. */
if (dissolveedge.tri != dummytri) {
org(dissolveedge, markorg);
if (pointmark(markorg) == 0) {
setpointmark(markorg, 1);
}
}
}
/* Disconnect the bounding box triangle from the mesh triangle. */
dissolve(dissolveedge);
lnext(nextedge, deadtri);
sym(deadtri, nextedge);
/* Get rid of the bounding box triangle. */
triangledealloc(deadtri.tri);
/* Do we need to turn the corner? */
if (nextedge.tri == dummytri) {
/* Turn the corner. */
triedgecopy(dissolveedge, nextedge);
}
}
triangledealloc(finaledge.tri);
free(infpoint1); /* Deallocate the bounding box vertices. */
free(infpoint2);
free(infpoint3);
return hullsize;
}
#endif /* not REDUCED */
/*****************************************************************************/
/* *//* incrementaldelaunay() Form a Delaunay triangulation by incrementally */
/* adding vertices. */
/* */
/*****************************************************************************/
#ifndef REDUCED
long incrementaldelaunay()
{
struct triedge starttri;
point pointloop;
int i;
/* Create a triangular bounding box. */
boundingbox();
if (verbose) {
printf(" Incrementally inserting points.\n");
}
traversalinit(&points);
pointloop = pointtraverse();
i = 1;
while (pointloop != (point) NULL) {
/* Find a boundary triangle to search from. */
starttri.tri = (triangle *) NULL;
if (insertsite(pointloop, &starttri, (struct edge *) NULL, 0, 0) ==
DUPLICATEPOINT) {
if (!quiet) {
printf(
"Warning: A duplicate point at (%.12g, %.12g) appeared and was ignored.\n",
pointloop[0], pointloop[1]);
}
/* Commented out - would eliminate point from output .node file.
setpointmark(pointloop, DEADPOINT);
*/
}
pointloop = pointtraverse();
i++;
}
/* Remove the bounding box. */
return removebox();
}
#endif /* not REDUCED */
/** **/
/** **/
/********* Incremental Delaunay triangulation ends here *********/
/********* Sweepline Delaunay triangulation begins here *********/
/** **/
/** **/
#ifndef REDUCED
void eventheapinsert(heap, heapsize, newevent)
struct event **heap;
int heapsize;
struct event *newevent;
{
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
void eventheapify(heap, heapsize, eventnum)
struct event **heap;
int heapsize;
int eventnum;
{
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
void eventheapdelete(heap, heapsize, eventnum)
struct event **heap;
int heapsize;
int eventnum;
{
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
void createeventheap(eventheap, events, freeevents)
struct event ***eventheap;
struct event **events;
struct event **freeevents;
{
point thispoint;
int maxevents;
int i;
maxevents = (3 * inpoints) / 2;
*eventheap = (struct event **) malloc(maxevents * sizeof(struct event *));
if (*eventheap == (struct event **) NULL) {
printf("Error: Out of memory.\n");
exit(1);
}
*events = (struct event *) malloc(maxevents * sizeof(struct event));
if (*events == (struct event *) NULL) {
printf("Error: Out of memory.\n");
exit(1);
}
traversalinit(&points);
for (i = 0; i < inpoints; i++) {
thispoint = pointtraverse();
(*events)[i].eventptr = (VOID *) thispoint;
(*events)[i].xkey = thispoint[0];
(*events)[i].ykey = thispoint[1];
eventheapinsert(*eventheap, i, *events + i);
}
*freeevents = (struct event *) NULL;
for (i = maxevents - 1; i >= inpoints; i--) {
(*events)[i].eventptr = (VOID *) *freeevents; *freeevents = *events + i;
}
}
#endif /* not REDUCED */
#ifndef REDUCED
int rightofhyperbola(fronttri, newsite)
struct triedge *fronttri;
point newsite;
{
point leftpoint, rightpoint;
REAL dxa, dya, dxb, dyb;
hyperbolacount++;
dest(*fronttri, leftpoint);
apex(*fronttri, rightpoint);
if ((leftpoint[1] < rightpoint[1])
|| ((leftpoint[1] == rightpoint[1]) && (leftpoint[0] < rightpoint[0]))) {
if (newsite[0] >= rightpoint[0]) {
return 1;
}
} else {
if (newsite[0] <= leftpoint[0]) {
return 0;
}
}
dxa = leftpoint[0] - newsite[0];
dya = leftpoint[1] - newsite[1];
dxb = rightpoint[0] - newsite[0];
dyb = rightpoint[1] - newsite[1];
return dya * (dxb * dxb + dyb * dyb) > dyb * (dxa * dxa + dya * dya);
}
#endif /* not REDUCED */
#ifndef REDUCED
REAL circletop(pa, pb, pc, ccwabc)
point pa;
point pb;
point pc;
REAL ccwabc;
{
REAL xac, yac, xbc, ybc, xab, yab;
REAL aclen2, bclen2, ablen2;
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
void check4deadevent(checktri, freeevents, eventheap, heapsize)
struct triedge *checktri;struct event **freeevents;
struct event **eventheap;
int *heapsize;
{
struct event *deadevent;
point eventpoint;
int eventnum;
org(*checktri, eventpoint);
if (eventpoint != (point) NULL) {
deadevent = (struct event *) eventpoint;
eventnum = deadevent->heapposition;
deadevent->eventptr = (VOID *) *freeevents;
*freeevents = deadevent;
eventheapdelete(eventheap, *heapsize, eventnum);
(*heapsize)--;
setorg(*checktri, NULL);
}
}
#endif /* not REDUCED */
#ifndef REDUCED
struct splaynode *splay(splaytree, searchpoint, searchtri)
struct splaynode *splaytree;
point searchpoint;
struct triedge *searchtri;
{
struct splaynode *child, *grandchild;
struct splaynode *lefttree, *righttree;
struct splaynode *leftright;
point checkpoint;
int rightofroot, rightofchild;
if (splaytree == (struct splaynode *) NULL) {
return (struct splaynode *) NULL;
}
dest(splaytree->keyedge, checkpoint);
if (checkpoint == splaytree->keydest) {
rightofroot = rightofhyperbola(&splaytree->keyedge, searchpoint);
if (rightofroot) {
triedgecopy(splaytree->keyedge, *searchtri);
child = splaytree->rchild;
} else {
child = splaytree->lchild;
}
if (child == (struct splaynode *) NULL) {
return splaytree;
}
dest(child->keyedge, checkpoint);
if (checkpoint != child->keydest) {
child = splay(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(&child->keyedge, searchpoint);
if (rightofchild) {
triedgecopy(child->keyedge, *searchtri);
grandchild = splay(child->rchild, searchpoint, searchtri);
child->rchild = grandchild;
} else {
grandchild = splay(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(splaytree->lchild, searchpoint, searchtri);
righttree = splay(splaytree->rchild, searchpoint, searchtri);
pooldealloc(&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
struct splaynode *splayinsert(splayroot, newkey, searchpoint)
struct splaynode *splayroot;
struct triedge *newkey;
point searchpoint;{
struct splaynode *newsplaynode;
newsplaynode = (struct splaynode *) poolalloc(&splaynodes);
triedgecopy(*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(&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
struct splaynode *circletopinsert(splayroot, newkey, pa, pb, pc, topy)
struct splaynode *splayroot;
struct triedge *newkey;
point pa;
point pb;
point pc;
REAL topy;
{
REAL ccwabc;
REAL xac, yac, xbc, ybc;
REAL aclen2, bclen2;
REAL searchpoint[2];
struct triedge dummytri;
ccwabc = counterclockwise(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(splay(splayroot, (point) searchpoint, &dummytri), newkey,
(point) searchpoint);
}
#endif /* not REDUCED */
#ifndef REDUCED
struct splaynode *frontlocate(splayroot, bottommost, searchpoint, searchtri,
farright)
struct splaynode *splayroot;
struct triedge *bottommost;
point searchpoint;
struct triedge *searchtri;
int *farright;
{
int farrightflag;
triangle ptr; /* Temporary variable used by onext(). */
triedgecopy(*bottommost, *searchtri);
splayroot = splay(splayroot, searchpoint, searchtri);
farrightflag = 0;
while (!farrightflag && rightofhyperbola(searchtri, searchpoint)) {
onextself(*searchtri);
farrightflag = triedgeequal(*searchtri, *bottommost);
}
*farright = farrightflag;
return splayroot;
}
#endif /* not REDUCED */
#ifndef REDUCED
long sweeplinedelaunay()
{
struct event **eventheap;
struct event *events;
struct event *freeevents;
struct event *nextevent;
struct event *newevent;
struct splaynode *splayroot;
struct triedge bottommost;
struct triedge searchtri;
struct triedge fliptri;
struct triedge lefttri, righttri, farlefttri, farrighttri;
struct triedge inserttri;
point firstpoint, secondpoint;
point nextpoint, lastpoint;
point connectpoint;
point leftpoint, midpoint, rightpoint;
REAL lefttest, righttest;
int heapsize;
int check4events, farrightflag;
triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */
poolinit(&splaynodes, sizeof(struct splaynode), SPLAYNODEPERBLOCK, POINTER,
0);
splayroot = (struct splaynode *) NULL;
if (verbose) {
printf(" Placing points in event heap.\n");
}
createeventheap(&eventheap, &events, &freeevents);
heapsize = inpoints;
if (verbose) {
printf(" Forming triangulation.\n");
}
maketriangle(&lefttri);
maketriangle(&righttri);
bond(lefttri, righttri);
lnextself(lefttri);
lprevself(righttri);
bond(lefttri, righttri);
lnextself(lefttri);
lprevself(righttri);
bond(lefttri, righttri);
firstpoint = (point) eventheap[0]->eventptr;
eventheap[0]->eventptr = (VOID *) freeevents;
freeevents = eventheap[0];
eventheapdelete(eventheap, heapsize, 0);
heapsize--;
do {
if (heapsize == 0) {
printf("Error: Input points are all identical.\n");
exit(1);
}
secondpoint = (point) eventheap[0]->eventptr;
eventheap[0]->eventptr = (VOID *) freeevents;
freeevents = eventheap[0]; eventheapdelete(eventheap, heapsize, 0);
heapsize--;
if ((firstpoint[0] == secondpoint[0])
&& (firstpoint[1] == secondpoint[1])) {
printf(
"Warning: A duplicate point at (%.12g, %.12g) appeared and was ignored.\n",
secondpoint[0], secondpoint[1]);
/* Commented out - would eliminate point from output .node file.
setpointmark(secondpoint, DEADPOINT);
*/
}
} while ((firstpoint[0] == secondpoint[0])
&& (firstpoint[1] == secondpoint[1]));
setorg(lefttri, firstpoint);
setdest(lefttri, secondpoint);
setorg(righttri, secondpoint);
setdest(righttri, firstpoint);
lprev(lefttri, bottommost);
lastpoint = secondpoint;
while (heapsize > 0) {
nextevent = eventheap[0];
eventheapdelete(eventheap, heapsize, 0);
heapsize--;
check4events = 1;
if (nextevent->xkey < xmin) {
decode(nextevent->eventptr, fliptri);
oprev(fliptri, farlefttri);
check4deadevent(&farlefttri, &freeevents, eventheap, &heapsize);
onext(fliptri, farrighttri);
check4deadevent(&farrighttri, &freeevents, eventheap, &heapsize);
if (triedgeequal(farlefttri, bottommost)) {
lprev(fliptri, bottommost);
}
flip(&fliptri);
setapex(fliptri, NULL);
lprev(fliptri, lefttri);
lnext(fliptri, righttri);
sym(lefttri, farlefttri);
if (randomnation(SAMPLERATE) == 0) {
symself(fliptri);
dest(fliptri, leftpoint);
apex(fliptri, midpoint);
org(fliptri, rightpoint);
splayroot = circletopinsert(splayroot, &lefttri, leftpoint, midpoint,
rightpoint, nextevent->ykey);
}
} else {
nextpoint = (point) nextevent->eventptr;
if ((nextpoint[0] == lastpoint[0]) && (nextpoint[1] == lastpoint[1])) {
printf(
"Warning: A duplicate point at (%.12g, %.12g) appeared and was ignored.\n",
nextpoint[0], nextpoint[1]);
/* Commented out - would eliminate point from output .node file.
setpointmark(nextpoint, DEADPOINT);
*/
check4events = 0;
} else {
lastpoint = nextpoint;
splayroot = frontlocate(splayroot, &bottommost, nextpoint, &searchtri,
&farrightflag);
/*
triedgecopy(bottommost, searchtri);
farrightflag = 0;
while (!farrightflag && rightofhyperbola(&searchtri, nextpoint)) {
onextself(searchtri);
farrightflag = triedgeequal(searchtri, bottommost);
}*/
check4deadevent(&searchtri, &freeevents, eventheap, &heapsize);
triedgecopy(searchtri, farrighttri);
sym(searchtri, farlefttri);
maketriangle(&lefttri);
maketriangle(&righttri);
dest(farrighttri, connectpoint);
setorg(lefttri, connectpoint);
setdest(lefttri, nextpoint);
setorg(righttri, nextpoint);
setdest(righttri, connectpoint);
bond(lefttri, righttri);
lnextself(lefttri);
lprevself(righttri);
bond(lefttri, righttri);
lnextself(lefttri);
lprevself(righttri);
bond(lefttri, farlefttri);
bond(righttri, farrighttri);
if (!farrightflag && triedgeequal(farrighttri, bottommost)) {
triedgecopy(lefttri, bottommost);
}
if (randomnation(SAMPLERATE) == 0) {
splayroot = splayinsert(splayroot, &lefttri, nextpoint);
} else if (randomnation(SAMPLERATE) == 0) {
lnext(righttri, inserttri);
splayroot = splayinsert(splayroot, &inserttri, nextpoint);
}
}
}
nextevent->eventptr = (VOID *) freeevents;
freeevents = nextevent;
if (check4events) {
apex(farlefttri, leftpoint);
dest(lefttri, midpoint);
apex(lefttri, rightpoint);
lefttest = counterclockwise(leftpoint, midpoint, rightpoint);
if (lefttest > 0.0) {
newevent = freeevents;
freeevents = (struct event *) freeevents->eventptr;
newevent->xkey = xminextreme;
newevent->ykey = circletop(leftpoint, midpoint, rightpoint,
lefttest);
newevent->eventptr = (VOID *) encode(lefttri);
eventheapinsert(eventheap, heapsize, newevent);
heapsize++;
setorg(lefttri, newevent);
}
apex(righttri, leftpoint);
org(righttri, midpoint);
apex(farrighttri, rightpoint);
righttest = counterclockwise(leftpoint, midpoint, rightpoint);
if (righttest > 0.0) {
newevent = freeevents;
freeevents = (struct event *) freeevents->eventptr;
newevent->xkey = xminextreme;
newevent->ykey = circletop(leftpoint, midpoint, rightpoint,
righttest);
newevent->eventptr = (VOID *) encode(farrighttri);
eventheapinsert(eventheap, heapsize, newevent);
heapsize++;
setorg(farrighttri, newevent);
}
}
}
pooldeinit(&splaynodes);
lprevself(bottommost);
return removeghosts(&bottommost);
}
#endif /* not REDUCED */
/** **/
/** **/
/********* Sweepline Delaunay triangulation ends here *********/
/********* General mesh construction routines begin here *********/
/** **/
/** **/
/*****************************************************************************/
/* */
/* delaunay() Form a Delaunay triangulation. */
/* */
/*****************************************************************************/
long delaunay()
{
eextras = 0;
initializetrisegpools();
#ifdef REDUCED
if (!quiet) {
printf(
"Constructing Delaunay triangulation by divide-and-conquer method.\n");
}
return divconqdelaunay();
#else /* not REDUCED */
if (!quiet) {
printf("Constructing Delaunay triangulation ");
if (incremental) {
printf("by incremental method.\n");
} else if (sweepline) {
printf("by sweepline method.\n");
} else {
printf("by divide-and-conquer method.\n");
}
}
if (incremental) {
return incrementaldelaunay();
} else if (sweepline) {
return sweeplinedelaunay();
} else {
return divconqdelaunay();
}
#endif /* not REDUCED */
}
/*****************************************************************************/
/* */
/* 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 */
/* shell edges 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. */
/* */
/* Points that are not corners of triangles, such as nodes on edges of */
/* subparametric elements, are discarded. */
/* */
/* This routine finds the adjacencies between triangles (and shell edges) */
/* by forming one stack of triangles for each vertex. Each triangle is on */
/* three different stacks simultaneously. Each triangle's shell edge *//* 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 shell edge rather */
/* than the next triangle of the stack. */
/* */
/*****************************************************************************/
#ifndef CDT_ONLY
#ifdef TRILIBRARY
int reconstruct(trianglelist, triangleattriblist, trianglearealist, elements,
corners, attribs, segmentlist, segmentmarkerlist,
numberofsegments)
int *trianglelist;
REAL *triangleattriblist;
REAL *trianglearealist;
int elements;
int corners;
int attribs;
int *segmentlist;
int *segmentmarkerlist;
int numberofsegments;
#else /* not TRILIBRARY */
long reconstruct(elefilename, areafilename, polyfilename, polyfile)
char *elefilename;
char *areafilename;
char *polyfilename;
FILE *polyfile;
#endif /* not TRILIBRARY */
{
#ifdef TRILIBRARY
int pointindex;
int attribindex;
#else /* not TRILIBRARY */
FILE *elefile;
FILE *areafile;
char inputline[INPUTLINESIZE];
char *stringptr;
int areaelements;
#endif /* not TRILIBRARY */
struct triedge triangleloop;
struct triedge triangleleft;
struct triedge checktri;
struct triedge checkleft;
struct triedge checkneighbor;
struct edge shelleloop;
triangle *vertexarray;
triangle *prevlink;
triangle nexttri;
point tdest, tapex;
point checkdest, checkapex;
point shorg;
point killpoint;
REAL area;
int corner[3];
int end[2];
int killpointindex;
int incorners;
int segmentmarkers;
int boundmarker;
int aroundpoint;
long hullsize;
int notfound;
int elementnumber, segmentnumber; int i, j;
triangle ptr; /* Temporary variable used by sym(). */
#ifdef TRILIBRARY
inelements = elements;
incorners = corners;
if (incorners < 3) {
printf("Error: Triangles must have at least 3 points.\n");
exit(1);
}
eextras = attribs;
#else /* not TRILIBRARY */
/* Read the triangles from an .ele file. */
if (!quiet) {
printf("Opening %s.\n", elefilename);
}
elefile = fopen(elefilename, "r");
if (elefile == (FILE *) NULL) {
printf(" Error: Cannot access file %s.\n", elefilename);
exit(1);
}
/* Read number of triangles, number of points per triangle, and */
/* number of triangle attributes from .ele file. */
stringptr = readline(inputline, elefile, elefilename);
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 points.\n",
elefilename);
exit(1);
}
}
stringptr = findfield(stringptr);
if (*stringptr == '\0') {
eextras = 0;
} else {
eextras = (int) strtol (stringptr, &stringptr, 0);
}
#endif /* not TRILIBRARY */
initializetrisegpools();
/* Create the triangles. */
for (elementnumber = 1; elementnumber <= inelements; elementnumber++) {
maketriangle(&triangleloop);
/* Mark the triangle as living. */
triangleloop.tri[3] = (triangle) triangleloop.tri;
}
if (poly) {
#ifdef TRILIBRARY
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, inpolyfilename);
insegments = (int) strtol (stringptr, &stringptr, 0);
stringptr = findfield(stringptr);
if (*stringptr == '\0') {
segmentmarkers = 0;
} else {
segmentmarkers = (int) strtol (stringptr, &stringptr, 0);
}
#endif /* not TRILIBRARY */
/* Create the shell edges. */
for (segmentnumber = 1; segmentnumber <= insegments; segmentnumber++) {
makeshelle(&shelleloop);
/* Mark the shell edge as living. */
shelleloop.sh[2] = (shelle) shelleloop.sh;
}
}
#ifdef TRILIBRARY
pointindex = 0;
attribindex = 0;
#else /* not TRILIBRARY */
if (vararea) {
/* Open an .area file, check for consistency with the .ele file. */
if (!quiet) {
printf("Opening %s.\n", areafilename);
}
areafile = fopen(areafilename, "r");
if (areafile == (FILE *) NULL) {
printf(" Error: Cannot access file %s.\n", areafilename);
exit(1);
}
stringptr = readline(inputline, areafile, areafilename);
areaelements = (int) strtol (stringptr, &stringptr, 0);
if (areaelements != inelements) {
printf("Error: %s and %s disagree on number of triangles.\n",
elefilename, areafilename);
exit(1);
}
}
#endif /* not TRILIBRARY */
if (!quiet) {
printf("Reconstructing mesh.\n");
}
/* Allocate a temporary array that maps each point to some adjacent */
/* triangle. I took care to allocate all the permanent memory for */
/* triangles and shell edges first. */
vertexarray = (triangle *) malloc(points.items * sizeof(triangle));
if (vertexarray == (triangle *) NULL) {
printf("Error: Out of memory.\n");
exit(1);
}
/* Each point is initially unrepresented. */
for (i = 0; i < points.items; i++) {
vertexarray[i] = (triangle) dummytri;
}
if (verbose) {
printf(" Assembling triangles.\n");
}
/* Read the triangles from the .ele file, and link */
/* together those that share an edge. */
traversalinit(&triangles);
triangleloop.tri = triangletraverse();
elementnumber = firstnumber;
while (triangleloop.tri != (triangle *) NULL) {
#ifdef TRILIBRARY
/* Copy the triangle's three corners. */
for (j = 0; j < 3; j++) {
corner[j] = trianglelist[pointindex++];
if ((corner[j] < firstnumber) || (corner[j] >= firstnumber + inpoints)) {
printf("Error: Triangle %d has an invalid vertex index.\n",
elementnumber);
exit(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 %d is missing point %d in %s.\n",
elementnumber, j + 1, elefilename);
exit(1);
} else {
corner[j] = (int) strtol (stringptr, &stringptr, 0);
if ((corner[j] < firstnumber) ||
(corner[j] >= firstnumber + inpoints)) {
printf("Error: Triangle %d has an invalid vertex index.\n",
elementnumber);
exit(1);
}
}
}
#endif /* not TRILIBRARY */
/* Find out about (and throw away) extra nodes. */
for (j = 3; j < incorners; j++) {
#ifdef TRILIBRARY
killpointindex = trianglelist[pointindex++];
#else /* not TRILIBRARY */
stringptr = findfield(stringptr);
if (*stringptr != '\0') {
killpointindex = (int) strtol (stringptr, &stringptr, 0);
#endif /* not TRILIBRARY */
if ((killpointindex >= firstnumber) &&
(killpointindex < firstnumber + inpoints)) {
/* Delete the non-corner point if it's not already deleted. */
killpoint = getpoint(killpointindex);
if (pointmark(killpoint) != DEADPOINT) {
pointdealloc(killpoint);
}
}
#ifndef TRILIBRARY
}
#endif /* not TRILIBRARY */
}
/* Read the triangle's attributes. */
for (j = 0; j < 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 (vararea) {
#ifdef TRILIBRARY
area = trianglearealist[elementnumber - 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, getpoint(corner[0]));
setdest(triangleloop, getpoint(corner[1]));
setapex(triangleloop, getpoint(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. */
aroundpoint = corner[triangleloop.orient];
/* Look for other triangles having this vertex. */
nexttri = vertexarray[aroundpoint - 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[aroundpoint - firstnumber] = encode(triangleloop);
decode(nexttri, checktri);
if (checktri.tri != 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 != dummytri);
}
}
triangleloop.tri = triangletraverse();
elementnumber++;
}
#ifdef TRILIBRARY
pointindex = 0;
#else /* not TRILIBRARY */
fclose(elefile);
if (vararea) {
fclose(areafile);
}
#endif /* not TRILIBRARY */
hullsize = 0; /* Prepare to count the boundary edges. */
if (poly) {
if (verbose) {
printf(" Marking segments in triangulation.\n");
}
/* Read the segments from the .poly file, and link them */
/* to their neighboring triangles. */
boundmarker = 0;
traversalinit(&shelles);
shelleloop.sh = shelletraverse();
segmentnumber = firstnumber;
while (shelleloop.sh != (shelle *) NULL) {
#ifdef TRILIBRARY
end[0] = segmentlist[pointindex++];
end[1] = segmentlist[pointindex++];
if (segmentmarkers) { boundmarker = segmentmarkerlist[segmentnumber - firstnumber];
}
#else /* not TRILIBRARY */
/* Read the endpoints of each segment, and possibly a boundary marker. */
stringptr = readline(inputline, polyfile, inpolyfilename);
/* Skip the first (segment number) field. */
stringptr = findfield(stringptr);
if (*stringptr == '\0') {
printf("Error: Segment %d has no endpoints in %s.\n", segmentnumber,
polyfilename);
exit(1);
} else {
end[0] = (int) strtol (stringptr, &stringptr, 0);
}
stringptr = findfield(stringptr);
if (*stringptr == '\0') {
printf("Error: Segment %d is missing its second endpoint in %s.\n",
segmentnumber, polyfilename);
exit(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] < firstnumber) || (end[j] >= firstnumber + inpoints)) {
printf("Error: Segment %d has an invalid vertex index.\n",
segmentnumber);
exit(1);
}
}
/* set the shell edge's vertices. */
shelleloop.shorient = 0;
setsorg(shelleloop, getpoint(end[0]));
setsdest(shelleloop, getpoint(end[1]));
setmark(shelleloop, boundmarker);
/* Try linking the shell edge to triangles that share these vertices. */
for (shelleloop.shorient = 0; shelleloop.shorient < 2;
shelleloop.shorient++) {
/* Take the number for the destination of shelleloop. */
aroundpoint = end[1 - shelleloop.shorient];
/* Look for triangles having this vertex. */
prevlink = &vertexarray[aroundpoint - firstnumber];
nexttri = vertexarray[aroundpoint - firstnumber];
decode(nexttri, checktri);
sorg(shelleloop, shorg);
notfound = 1;
/* Look for triangles having this edge. Note that I'm only */
/* comparing each triangle's destination with the shell edge; */
/* 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-segment bond is represented once. */
while (notfound && (checktri.tri != 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 shell edge to the triangle. */
tsbond(checktri, shelleloop);
/* Check if this is a boundary edge. */ sym(checktri, checkneighbor);
if (checkneighbor.tri == dummytri) {
/* The next line doesn't insert a shell edge (because there's */
/* already one there), but it sets the boundary markers of */
/* the existing shell edge and its vertices. */
insertshelle(&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);
}
}
shelleloop.sh = shelletraverse();
segmentnumber++;
}
}
/* Mark the remaining edges as not being attached to any shell edge. */
/* Also, count the (yet uncounted) boundary edges. */
for (i = 0; i < points.items; i++) {
/* Search the stack of triangles adjacent to a point. */
nexttri = vertexarray[i];
decode(nexttri, checktri);
while (checktri.tri != dummytri) {
/* Find the next triangle in the stack before this */
/* information gets overwritten. */
nexttri = checktri.tri[6 + checktri.orient];
/* No adjacent shell edge. (This overwrites the stack info.) */
tsdissolve(checktri);
sym(checktri, checkneighbor);
if (checkneighbor.tri == dummytri) {
insertshelle(&checktri, 1);
hullsize++;
}
decode(nexttri, checktri);
}
}
free(vertexarray);
return hullsize;
}
#endif /* not CDT_ONLY */
/** **/
/** **/
/********* General mesh construction routines end here *********/
/********* Segment (shell edge) 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 `endpoint', 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. *//* */
/*****************************************************************************/
enum finddirectionresult finddirection(searchtri, endpoint)
struct triedge *searchtri;
point endpoint;
{
struct triedge checktri;
point startpoint;
point leftpoint, rightpoint;
REAL leftccw, rightccw;
int leftflag, rightflag;
triangle ptr; /* Temporary variable used by onext() and oprev(). */
org(*searchtri, startpoint);
dest(*searchtri, rightpoint);
apex(*searchtri, leftpoint);
/* Is `endpoint' to the left? */
leftccw = counterclockwise(endpoint, startpoint, leftpoint);
leftflag = leftccw > 0.0;
/* Is `endpoint' to the right? */
rightccw = counterclockwise(startpoint, endpoint, rightpoint);
rightflag = rightccw > 0.0;
if (leftflag && rightflag) {
/* `searchtri' faces directly away from `endpoint'. We could go */
/* left or right. Ask whether it's a triangle or a boundary */
/* on the left. */
onext(*searchtri, checktri);
if (checktri.tri == dummytri) {
leftflag = 0;
} else {
rightflag = 0;
}
}
while (leftflag) {
/* Turn left until satisfied. */
onextself(*searchtri);
if (searchtri->tri == dummytri) {
printf("Internal error in finddirection(): Unable to find a\n");
printf(" triangle leading from (%.12g, %.12g) to", startpoint[0],
startpoint[1]);
printf(" (%.12g, %.12g).\n", endpoint[0], endpoint[1]);
internalerror();
}
apex(*searchtri, leftpoint);
rightccw = leftccw;
leftccw = counterclockwise(endpoint, startpoint, leftpoint);
leftflag = leftccw > 0.0;
}
while (rightflag) {
/* Turn right until satisfied. */
oprevself(*searchtri);
if (searchtri->tri == dummytri) {
printf("Internal error in finddirection(): Unable to find a\n");
printf(" triangle leading from (%.12g, %.12g) to", startpoint[0],
startpoint[1]);
printf(" (%.12g, %.12g).\n", endpoint[0], endpoint[1]);
internalerror();
}
dest(*searchtri, rightpoint);
leftccw = rightccw;
rightccw = counterclockwise(startpoint, endpoint, rightpoint);
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 point at the intersection, splitting an */
/* existing shell edge. */
/* */
/* The segment being inserted connects the apex of splittri to endpoint2. */
/* splitshelle is the shell edge being split, and MUST be opposite */
/* splittri. Hence, the edge being split connects 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. */
/* */
/*****************************************************************************/
void segmentintersection(splittri, splitshelle, endpoint2)
struct triedge *splittri;
struct edge *splitshelle;
point endpoint2;
{
point endpoint1;
point torg, tdest;
point leftpoint, rightpoint;
point newpoint;
enum insertsiteresult 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(). */
/* 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 point. */
newpoint = (point) poolalloc(&points);
/* Interpolate its coordinate and attributes. */
for (i = 0; i < 2 + nextras; i++) {
newpoint[i] = torg[i] + split * (tdest[i] - torg[i]);
}
setpointmark(newpoint, mark(*splitshelle));
if (verbose > 1) {
printf(
" Splitting edge (%.12g, %.12g) (%.12g, %.12g) at (%.12g, %.12g).\n",
torg[0], torg[1], tdest[0], tdest[1], newpoint[0], newpoint[1]);
}
/* Insert the intersection point. This should always succeed. */
success = insertsite(newpoint, splittri, splitshelle, 0, 0); if (success != SUCCESSFULPOINT) {
printf("Internal error in segmentintersection():\n");
printf(" Failure to split a segment.\n");
internalerror();
}
if (steinerleft > 0) {
steinerleft--;
}
/* Inserting the point may have caused edge flips. We wish to rediscover */
/* the edge connecting endpoint1 to the new intersection point. */
collinear = finddirection(splittri, endpoint1);
dest(*splittri, rightpoint);
apex(*splittri, leftpoint);
if ((leftpoint[0] == endpoint1[0]) && (leftpoint[1] == endpoint1[1])) {
onextself(*splittri);
} else if ((rightpoint[0] != endpoint1[0]) ||
(rightpoint[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 point, and 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 shell edge 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 shell edge is inserted connecting the first endpoint to */
/* the collinear point, and the search is continued from the collinear */
/* point. */
/* */
/* If the first triangle on the path has a shell edge opposite its origin, */
/* then there is a segment that intersects the segment being inserted. */
/* Their intersection point is inserted, splitting the shell edge. */
/* */
/* Otherwise, return zero. */
/* */
/*****************************************************************************/
int scoutsegment(searchtri, endpoint2, newmark)
struct triedge *searchtri;
point endpoint2;
int newmark;
{
struct triedge crosstri;
struct edge crossedge;
point leftpoint, rightpoint;
point endpoint1;
enum finddirectionresult collinear;
shelle sptr; /* Temporary variable used by tspivot(). */
collinear = finddirection(searchtri, endpoint2);
dest(*searchtri, rightpoint);
apex(*searchtri, leftpoint);
if (((leftpoint[0] == endpoint2[0]) && (leftpoint[1] == endpoint2[1])) ||
((rightpoint[0] == endpoint2[0]) && (rightpoint[1] == endpoint2[1]))) {
/* The segment is already an edge in the mesh. */
if ((leftpoint[0] == endpoint2[0]) && (leftpoint[1] == endpoint2[1])) {
lprevself(*searchtri); }
/* Insert a shell edge, if there isn't already one there. */
insertshelle(searchtri, newmark);
return 1;
} else if (collinear == LEFTCOLLINEAR) {
/* We've collided with a point between the segment's endpoints. */
/* Make the collinear point be the triangle's origin. */
lprevself(*searchtri);
insertshelle(searchtri, newmark);
/* Insert the remainder of the segment. */
return scoutsegment(searchtri, endpoint2, newmark);
} else if (collinear == RIGHTCOLLINEAR) {
/* We've collided with a point between the segment's endpoints. */
insertshelle(searchtri, newmark);
/* Make the collinear point be the triangle's origin. */
lnextself(*searchtri);
/* Insert the remainder of the segment. */
return scoutsegment(searchtri, endpoint2, newmark);
} else {
lnext(*searchtri, crosstri);
tspivot(crosstri, crossedge);
/* Check for a crossing segment. */
if (crossedge.sh == dummysh) {
return 0;
} else {
org(*searchtri, endpoint1);
/* Insert a point at the intersection. */
segmentintersection(&crosstri, &crossedge, endpoint2);
triedgecopy(crosstri, *searchtri);
insertshelle(searchtri, newmark);
/* Insert the remainder of the segment. */
return scoutsegment(searchtri, endpoint2, newmark);
}
}
}
/*****************************************************************************/
/* */
/* conformingedge() Force a segment into a conforming Delaunay */
/* triangulation by inserting a point at its midpoint, */
/* and recursively forcing in the two half-segments if */
/* necessary. */
/* */
/* Generates a sequence of edges connecting `endpoint1' to `endpoint2'. */
/* `newmark' is the boundary marker of the segment, assigned to each new */
/* splitting point and shell edge. */
/* */
/* Note that conformingedge() does not always maintain the conforming */
/* Delaunay property. Once inserted, segments are locked into place; */
/* points 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 segments. */
/* */
/*****************************************************************************/
#ifndef REDUCED
#ifndef CDT_ONLY
void conformingedge(endpoint1, endpoint2, newmark)
point endpoint1;
point endpoint2;
int newmark;
{
struct triedge searchtri1, searchtri2;
struct edge brokenshelle;
point newpoint;
point midpoint1, midpoint2;
enum insertsiteresult success;
int result1, result2;
int i; shelle sptr; /* Temporary variable used by tspivot(). */
if (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 point to insert in the middle of the segment. */
newpoint = (point) poolalloc(&points);
/* Interpolate coordinates and attributes. */
for (i = 0; i < 2 + nextras; i++) {
newpoint[i] = 0.5 * (endpoint1[i] + endpoint2[i]);
}
setpointmark(newpoint, newmark);
/* Find a boundary triangle to search from. */
searchtri1.tri = (triangle *) NULL;
/* Attempt to insert the new point. */
success = insertsite(newpoint, &searchtri1, (struct edge *) NULL, 0, 0);
if (success == DUPLICATEPOINT) {
if (verbose > 2) {
printf(" Segment intersects existing point (%.12g, %.12g).\n",
newpoint[0], newpoint[1]);
}
/* Use the point that's already there. */
pointdealloc(newpoint);
org(searchtri1, newpoint);
} else {
if (success == VIOLATINGPOINT) {
if (verbose > 2) {
printf(" Two segments intersect at (%.12g, %.12g).\n",
newpoint[0], newpoint[1]);
}
/* By fluke, we've landed right on another segment. Split it. */
tspivot(searchtri1, brokenshelle);
success = insertsite(newpoint, &searchtri1, &brokenshelle, 0, 0);
if (success != SUCCESSFULPOINT) {
printf("Internal error in conformingedge():\n");
printf(" Failure to split a segment.\n");
internalerror();
}
}
/* The point has been inserted successfully. */
if (steinerleft > 0) {
steinerleft--;
}
}
triedgecopy(searchtri1, searchtri2);
result1 = scoutsegment(&searchtri1, endpoint1, newmark);
result2 = scoutsegment(&searchtri2, endpoint2, newmark);
if (!result1) {
/* The origin of searchtri1 may have changed if a collision with an */
/* intervening vertex on the segment occurred. */
org(searchtri1, midpoint1);
conformingedge(midpoint1, endpoint1, newmark);
}
if (!result2) {
/* The origin of searchtri2 may have changed if a collision with an */
/* intervening vertex on the segment occurred. */
org(searchtri2, midpoint2);
conformingedge(midpoint2, endpoint2, newmark);
}
}
#endif /* not CDT_ONLY */
#endif /* not REDUCED */
/*****************************************************************************/
/* */
/* delaunayfixup() Enforce the Delaunay condition at an edge, fanning out */
/* recursively from an existing point. 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 point (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.) */
/* */
/*****************************************************************************/
void delaunayfixup(fixuptri, leftside)
struct triedge *fixuptri;
int leftside;
{
struct triedge neartri;
struct triedge fartri;
struct edge faredge;
point nearpoint, leftpoint, rightpoint, farpoint;
triangle ptr; /* Temporary variable used by sym(). */
shelle 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 == dummytri) {
return;
}
tspivot(neartri, faredge);
if (faredge.sh != dummysh) {
return;
}
/* Find all the relevant vertices. */
apex(neartri, nearpoint);
org(neartri, leftpoint);
dest(neartri, rightpoint);
apex(fartri, farpoint);
/* Check whether the previous polygon vertex is a reflex vertex. */
if (leftside) {
if (counterclockwise(nearpoint, leftpoint, farpoint) <= 0.0) {
/* leftpoint is a reflex vertex too. Nothing can */
/* be done until a convex section is found. */
return;
}
} else {
if (counterclockwise(farpoint, rightpoint, nearpoint) <= 0.0) {
/* rightpoint is a reflex vertex too. Nothing can */ /* be done until a convex section is found. */
return;
}
}
if (counterclockwise(rightpoint, leftpoint, farpoint) > 0.0) {
/* fartri is not an inverted triangle, and farpoint 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(leftpoint, farpoint, rightpoint, nearpoint) <= 0.0) {
return;
}
/* Not locally Delaunay; go on to an edge flip. */
} /* else fartri is inverted; remove it from the stack by flipping. */
flip(&neartri);
lprevself(*fixuptri); /* Restore the origin of fixuptri after the flip. */
/* Recursively process the two triangles that result from the flip. */
delaunayfixup(fixuptri, leftside);
delaunayfixup(&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 edge 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. */
/* */
/*****************************************************************************/
void constrainededge(starttri, endpoint2, newmark)
struct triedge *starttri;
point endpoint2;
int newmark;
{
struct triedge fixuptri, fixuptri2;
struct edge fixupedge;
point endpoint1;
point farpoint;
REAL area;
int collision;
int done;
triangle ptr; /* Temporary variable used by sym() and oprev(). */
shelle sptr; /* Temporary variable used by tspivot(). */
org(*starttri, endpoint1);
lnext(*starttri, fixuptri);
flip(&fixuptri);
/* `collision' indicates whether we have found a point directly */
/* between endpoint1 and endpoint2. */
collision = 0;
done = 0;
do {
org(fixuptri, farpoint);
/* `farpoint' is the extreme point of the polygon we are "digging" */
/* to get from endpoint1 to endpoint2. */
if ((farpoint[0] == endpoint2[0]) && (farpoint[1] == endpoint2[1])) {
oprev(fixuptri, fixuptri2);
/* Enforce the Delaunay condition around endpoint2. */
delaunayfixup(&fixuptri, 0);
delaunayfixup(&fixuptri2, 1);
done = 1;
} else {
/* Check whether farpoint is to the left or right of the segment */
/* being inserted, to decide which edge of fixuptri to dig */
/* through next. */
area = counterclockwise(endpoint1, endpoint2, farpoint);
if (area == 0.0) {
/* We've collided with a point between endpoint1 and endpoint2. */
collision = 1;
oprev(fixuptri, fixuptri2);
/* Enforce the Delaunay condition around farpoint. */
delaunayfixup(&fixuptri, 0);
delaunayfixup(&fixuptri2, 1);
done = 1;
} else {
if (area > 0.0) { /* farpoint is to the left of the segment. */
oprev(fixuptri, fixuptri2);
/* Enforce the Delaunay condition around farpoint, on the */
/* left side of the segment only. */
delaunayfixup(&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 { /* farpoint is to the right of the segment. */
delaunayfixup(&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, fixupedge);
if (fixupedge.sh == dummysh) { flip(&fixuptri); /* May create an inverted triangle on the left. */
} else {
/* We've collided with a segment between endpoint1 and endpoint2. */
collision = 1;
/* Insert a point at the intersection. */
segmentintersection(&fixuptri, &fixupedge, endpoint2);
done = 1;
}
}
}
} while (!done);
/* Insert a shell edge to make the segment permanent. */
insertshelle(&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(&fixuptri, endpoint2, newmark)) {
constrainededge(&fixuptri, endpoint2, newmark);
}
}
}
/*****************************************************************************/
/* */
/* insertsegment() Insert a PSLG segment into a triangulation. */
/* */
/*****************************************************************************/
void insertsegment(endpoint1, endpoint2, newmark)
point endpoint1;
point endpoint2;
int newmark;
{
struct triedge searchtri1, searchtri2;
triangle encodedtri;
point checkpoint;
triangle ptr; /* Temporary variable used by sym(). */
if (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. */
checkpoint = (point) NULL;
encodedtri = point2tri(endpoint1);
if (encodedtri != (triangle) NULL) {
decode(encodedtri, searchtri1);
org(searchtri1, checkpoint);
}
if (checkpoint != endpoint1) {
/* Find a boundary triangle to search from. */
searchtri1.tri = dummytri;
searchtri1.orient = 0;
symself(searchtri1);
/* Search for the segment's first endpoint by point location. */
if (locate(endpoint1, &searchtri1) != ONVERTEX) {
printf(
"Internal error in insertsegment(): Unable to locate PSLG point\n");
printf(" (%.12g, %.12g) in triangulation.\n",
endpoint1[0], endpoint1[1]);
internalerror();
}
}
/* Remember this triangle to improve subsequent point location. */
triedgecopy(searchtri1, recenttri);
/* Scout the beginnings of a path from the first endpoint */
/* toward the second. */
if (scoutsegment(&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. */
checkpoint = (point) NULL;
encodedtri = point2tri(endpoint2);
if (encodedtri != (triangle) NULL) {
decode(encodedtri, searchtri2);
org(searchtri2, checkpoint);
}
if (checkpoint != endpoint2) {
/* Find a boundary triangle to search from. */
searchtri2.tri = dummytri;
searchtri2.orient = 0;
symself(searchtri2);
/* Search for the segment's second endpoint by point location. */
if (locate(endpoint2, &searchtri2) != ONVERTEX) {
printf(
"Internal error in insertsegment(): Unable to locate PSLG point\n");
printf(" (%.12g, %.12g) in triangulation.\n",
endpoint2[0], endpoint2[1]);
internalerror();
}
}
/* Remember this triangle to improve subsequent point location. */
triedgecopy(searchtri2, recenttri);
/* Scout the beginnings of a path from the second endpoint */
/* toward the first. */
if (scoutsegment(&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 (splitseg) {
/* Insert vertices to force the segment into the triangulation. */
conformingedge(endpoint1, endpoint2, newmark);
} else {
#endif /* not CDT_ONLY */
#endif /* not REDUCED */
/* Insert the segment directly into the triangulation. */
constrainededge(&searchtri1, endpoint2, newmark);
#ifndef REDUCED
#ifndef CDT_ONLY
}
#endif /* not CDT_ONLY */
#endif /* not REDUCED */
}
/*****************************************************************************/
/* */
/* markhull() Cover the convex hull of a triangulation with shell edges. */
/* */
/*****************************************************************************/
void markhull()
{
struct triedge hulltri;
struct triedge nexttri;
struct triedge starttri;
triangle ptr; /* Temporary variable used by sym() and oprev(). */
/* Find a triangle handle on the hull. */
hulltri.tri = dummytri;
hulltri.orient = 0;
symself(hulltri);
/* Remember where we started so we know when to stop. */
triedgecopy(hulltri, starttri);
/* Go once counterclockwise around the convex hull. */
do {
/* Create a shell edge if there isn't already one here. */
insertshelle(&hulltri, 1);
/* To find the next hull edge, go clockwise around the next vertex. */
lnextself(hulltri);
oprev(hulltri, nexttri);
while (nexttri.tri != dummytri) {
triedgecopy(nexttri, hulltri);
oprev(hulltri, nexttri);
}
} while (!triedgeequal(hulltri, starttri));
}
/*****************************************************************************/
/* */
/* formskeleton() Create the shell edges of a triangulation, including */
/* PSLG edges and edges on the convex hull. */
/* */
/* The PSLG edges are read from a .poly file. The return value is the */
/* number of segments in the file. */
/* */
/*****************************************************************************/
#ifdef TRILIBRARY
int formskeleton(segmentlist, segmentmarkerlist, numberofsegments)
int *segmentlist;
int *segmentmarkerlist;
int numberofsegments;
#else /* not TRILIBRARY */
int formskeleton(polyfile, polyfilename)
FILE *polyfile;
char *polyfilename;
#endif /* not TRILIBRARY */
{
#ifdef TRILIBRARY
char polyfilename[6];
int index;
#else /* not TRILIBRARY */
char inputline[INPUTLINESIZE];
char *stringptr;
#endif /* not TRILIBRARY */
point endpoint1, endpoint2;
int segments;
int segmentmarkers;
int end1, end2;
int boundmarker;
int i;
if (poly) {
if (!quiet) {
printf("Inserting segments into Delaunay triangulation.\n");
}
#ifdef TRILIBRARY
strcpy(polyfilename, "input");
segments = 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);
segments = (int) strtol (stringptr, &stringptr, 0);
stringptr = findfield(stringptr);
if (*stringptr == '\0') {
segmentmarkers = 0;
} else {
segmentmarkers = (int) strtol (stringptr, &stringptr, 0);
}
#endif /* not TRILIBRARY */
/* If segments are to be inserted, compute a mapping */
/* from points to triangles. */
if (segments > 0) {
if (verbose) {
printf(" Inserting PSLG segments.\n");
}
makepointmap();
}
boundmarker = 0;
/* Read and insert the segments. */
for (i = 1; i <= segments; i++) {
#ifdef TRILIBRARY
end1 = segmentlist[index++];
end2 = segmentlist[index++];
if (segmentmarkers) {
boundmarker = segmentmarkerlist[i - 1];
}
#else /* not TRILIBRARY */
stringptr = readline(inputline, polyfile, inpolyfilename);
stringptr = findfield(stringptr);
if (*stringptr == '\0') {
printf("Error: Segment %d has no endpoints in %s.\n", i,
polyfilename);
exit(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", i,
polyfilename);
exit(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 < firstnumber) || (end1 >= firstnumber + inpoints)) {
if (!quiet) {
printf("Warning: Invalid first endpoint of segment %d in %s.\n", i,
polyfilename);
}
} else if ((end2 < firstnumber) || (end2 >= firstnumber + inpoints)) {
if (!quiet) {
printf("Warning: Invalid second endpoint of segment %d in %s.\n", i,
polyfilename);
}
} else {
endpoint1 = getpoint(end1);
endpoint2 = getpoint(end2);
if ((endpoint1[0] == endpoint2[0]) && (endpoint1[1] == endpoint2[1])) { if (!quiet) {
printf("Warning: Endpoints of segment %d are coincident in %s.\n",
i, polyfilename);
}
} else {
insertsegment(endpoint1, endpoint2, boundmarker);
}
}
}
} else {
segments = 0;
}
if (convex || !poly) {
/* Enclose the convex hull with shell edges. */
if (verbose) {
printf(" Enclosing convex hull with segments.\n");
}
markhull();
}
return segments;
}
/** **/
/** **/
/********* Segment (shell edge) 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 shell edges. Where there are */
/* shell edges, set boundary markers as appropriate. */
/* */
/*****************************************************************************/
void infecthull()
{
struct triedge hulltri;
struct triedge nexttri;
struct triedge starttri;
struct edge hulledge;
triangle **deadtri;
point horg, hdest;
triangle ptr; /* Temporary variable used by sym(). */
shelle sptr; /* Temporary variable used by tspivot(). */
if (verbose) {
printf(" Marking concavities (external triangles) for elimination.\n");
}
/* Find a triangle handle on the hull. */
hulltri.tri = dummytri;
hulltri.orient = 0;
symself(hulltri);
/* Remember where we started so we know when to stop. */
triedgecopy(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 shell edge? */
tspivot(hulltri, hulledge);
if (hulledge.sh == dummysh) {
/* The triangle is not protected; infect it. */
infect(hulltri);
deadtri = (triangle **) poolalloc(&viri);
*deadtri = hulltri.tri;
} else { /* The triangle is protected; set boundary markers if appropriate. */
if (mark(hulledge) == 0) {
setmark(hulledge, 1);
org(hulltri, horg);
dest(hulltri, hdest);
if (pointmark(horg) == 0) {
setpointmark(horg, 1);
}
if (pointmark(hdest) == 0) {
setpointmark(hdest, 1);
}
}
}
}
/* To find the next hull edge, go clockwise around the next vertex. */
lnextself(hulltri);
oprev(hulltri, nexttri);
while (nexttri.tri != dummytri) {
triedgecopy(nexttri, hulltri);
oprev(hulltri, nexttri);
}
} while (!triedgeequal(hulltri, starttri));
}
/*****************************************************************************/
/* */
/* plague() Spread the virus from all infected triangles to any neighbors */
/* not protected by shell edges. 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 points. */
/* */
/*****************************************************************************/
void plague()
{
struct triedge testtri;
struct triedge neighbor;
triangle **virusloop;
triangle **deadtri;
struct edge neighborshelle;
point testpoint;
point norg, ndest;
point deadorg, deaddest, deadapex;
int killorg;
triangle ptr; /* Temporary variable used by sym() and onext(). */
shelle sptr; /* Temporary variable used by tspivot(). */
if (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(&viri);
virusloop = (triangle **) traverse(&viri);
while (virusloop != (triangle **) NULL) {
testtri.tri = *virusloop;
/* A triangle is marked as infected by messing with one of its shell */
/* edges, setting it to an illegal value. Hence, we have to */
/* temporarily uninfect this triangle so that we can examine its */
/* adjacent shell edges. */
uninfect(testtri);
if (verbose > 2) { /* Assign the triangle an orientation for convenience in */
/* checking its points. */
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 shell between the triangle and its neighbor. */
tspivot(testtri, neighborshelle);
/* Check if the neighbor is nonexistent or already infected. */
if ((neighbor.tri == dummytri) || infected(neighbor)) {
if (neighborshelle.sh != dummysh) {
/* There is a shell edge separating the triangle from its */
/* neighbor, but both triangles are dying, so the shell */
/* edge dies too. */
shelledealloc(neighborshelle.sh);
if (neighbor.tri != dummytri) {
/* Make sure the shell edge 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 (neighborshelle.sh == dummysh) {
/* There is no shell edge protecting the neighbor, so */
/* the neighbor becomes infected. */
if (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. */
deadtri = (triangle **) poolalloc(&viri);
*deadtri = neighbor.tri;
} else { /* The neighbor is protected by a shell edge. */
/* Remove this triangle from the shell edge. */
stdissolve(neighborshelle);
/* The shell edge becomes a boundary. Set markers accordingly. */
if (mark(neighborshelle) == 0) {
setmark(neighborshelle, 1);
}
org(neighbor, norg);
dest(neighbor, ndest);
if (pointmark(norg) == 0) {
setpointmark(norg, 1);
}
if (pointmark(ndest) == 0) {
setpointmark(ndest, 1);
}
}
}
}
/* Remark the triangle as infected, so it doesn't get added to the */
/* virus pool again. */
infect(testtri);
virusloop = (triangle **) traverse(&viri); }
if (verbose) {
printf(" Deleting marked triangles.\n");
}
traversalinit(&viri);
virusloop = (triangle **) traverse(&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 point, checking if it is */
/* still connected to at least one live triangle. */
for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
org(testtri, testpoint);
/* Check if the point has already been tested. */
if (testpoint != (point) NULL) {
killorg = 1;
/* Mark the corner of the triangle as having been tested. */
setorg(testtri, NULL);
/* Walk counterclockwise about the point. */
onext(testtri, neighbor);
/* Stop upon reaching a boundary or the starting triangle. */
while ((neighbor.tri != dummytri)
&& (!triedgeequal(neighbor, testtri))) {
if (infected(neighbor)) {
/* Mark the corner of this triangle as having been tested. */
setorg(neighbor, NULL);
} else {
/* A live triangle. The point survives. */
killorg = 0;
}
/* Walk counterclockwise about the point. */
onextself(neighbor);
}
/* If we reached a boundary, we must walk clockwise as well. */
if (neighbor.tri == dummytri) {
/* Walk clockwise about the point. */
oprev(testtri, neighbor);
/* Stop upon reaching a boundary. */
while (neighbor.tri != dummytri) {
if (infected(neighbor)) {
/* Mark the corner of this triangle as having been tested. */
setorg(neighbor, NULL);
} else {
/* A live triangle. The point survives. */
killorg = 0;
}
/* Walk clockwise about the point. */
oprevself(neighbor);
}
}
if (killorg) {
if (verbose > 1) {
printf(" Deleting point (%.12g, %.12g)\n",
testpoint[0], testpoint[1]);
}
pointdealloc(testpoint);
}
}
}
/* 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 == 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. */ 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. */
hullsize++;
}
}
/* Return the dead triangle to the pool of triangles. */
triangledealloc(testtri.tri);
virusloop = (triangle **) traverse(&viri);
}
/* Empty the virus pool. */
poolrestart(&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. */
/* */
/*****************************************************************************/
void regionplague(attribute, area)
REAL attribute;
REAL area;
{
struct triedge testtri;
struct triedge neighbor;
triangle **virusloop;
triangle **regiontri;
struct edge neighborshelle;
point regionorg, regiondest, regionapex;
triangle ptr; /* Temporary variable used by sym() and onext(). */
shelle sptr; /* Temporary variable used by tspivot(). */
if (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(&viri);
virusloop = (triangle **) traverse(&viri);
while (virusloop != (triangle **) NULL) {
testtri.tri = *virusloop;
/* A triangle is marked as infected by messing with one of its shell */
/* edges, setting it to an illegal value. Hence, we have to */
/* temporarily uninfect this triangle so that we can examine its */
/* adjacent shell edges. */
uninfect(testtri);
if (regionattrib) {
/* Set an attribute. */
setelemattribute(testtri, eextras, attribute);
}
if (vararea) {
/* Set an area constraint. */
setareabound(testtri, area);
}
if (verbose > 2) {
/* Assign the triangle an orientation for convenience in */ /* checking its points. */
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 shell between the triangle and its neighbor. */
tspivot(testtri, neighborshelle);
/* Make sure the neighbor exists, is not already infected, and */
/* isn't protected by a shell edge. */
if ((neighbor.tri != dummytri) && !infected(neighbor)
&& (neighborshelle.sh == dummysh)) {
if (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(&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(&viri);
}
/* Uninfect all triangles. */
if (verbose > 1) {
printf(" Unmarking marked triangles.\n");
}
traversalinit(&viri);
virusloop = (triangle **) traverse(&viri);
while (virusloop != (triangle **) NULL) {
testtri.tri = *virusloop;
uninfect(testtri);
virusloop = (triangle **) traverse(&viri);
}
/* Empty the virus pool. */
poolrestart(&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. */
/* */
/*****************************************************************************/
void carveholes(holelist, holes, regionlist, regions)
REAL *holelist;
int holes;REAL *regionlist;
int regions;
{
struct triedge searchtri;
struct triedge triangleloop;
struct triedge *regiontris;
triangle **holetri;
triangle **regiontri;
point searchorg, searchdest;
enum locateresult intersect;
int i;
triangle ptr; /* Temporary variable used by sym(). */
if (!(quiet || (noholes && convex))) {
printf("Removing unwanted triangles.\n");
if (verbose && (holes > 0)) {
printf(" Marking holes for elimination.\n");
}
}
if (regions > 0) {
/* Allocate storage for the triangles in which region points fall. */
regiontris = (struct triedge *) malloc(regions * sizeof(struct triedge));
if (regiontris == (struct triedge *) NULL) {
printf("Error: Out of memory.\n");
exit(1);
}
}
if (((holes > 0) && !noholes) || !convex || (regions > 0)) {
/* Initialize a pool of viri to be used for holes, concavities, */
/* regional attributes, and/or regional area constraints. */
poolinit(&viri, sizeof(triangle *), VIRUSPERBLOCK, POINTER, 0);
}
if (!convex) {
/* Mark as infected any unprotected triangles on the boundary. */
/* This is one way by which concavities are created. */
infecthull();
}
if ((holes > 0) && !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] >= xmin) && (holelist[i] <= xmax)
&& (holelist[i + 1] >= ymin) && (holelist[i + 1] <= ymax)) {
/* Start searching from some triangle on the outer boundary. */
searchtri.tri = 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(searchorg, searchdest, &holelist[i]) > 0.0) {
/* Find a triangle that contains the hole. */
intersect = locate(&holelist[i], &searchtri);
if ((intersect != OUTSIDE) && (!infected(searchtri))) {
/* Infect the triangle. This is done by marking the triangle */
/* as infect and including the triangle in the virus pool. */
infect(searchtri);
holetri = (triangle **) poolalloc(&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 = dummytri;
/* Ignore region points that aren't within the bounds of the mesh. */
if ((regionlist[4 * i] >= xmin) && (regionlist[4 * i] <= xmax) &&
(regionlist[4 * i + 1] >= ymin) && (regionlist[4 * i + 1] <= ymax)) {
/* Start searching from some triangle on the outer boundary. */
searchtri.tri = 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(searchorg, searchdest, ®ionlist[4 * i]) >
0.0) {
/* Find a triangle that contains the region point. */
intersect = locate(®ionlist[4 * i], &searchtri);
if ((intersect != OUTSIDE) && (!infected(searchtri))) {
/* Record the triangle for processing after the */
/* holes have been carved. */
triedgecopy(searchtri, regiontris[i]);
}
}
}
}
}
if (viri.items > 0) {
/* Carve the holes and concavities. */
plague();
}
/* The virus pool should be empty now. */
if (regions > 0) {
if (!quiet) {
if (regionattrib) {
if (vararea) {
printf("Spreading regional attributes and area constraints.\n");
} else {
printf("Spreading regional attributes.\n");
}
} else {
printf("Spreading regional area constraints.\n");
}
}
if (regionattrib && !refine) {
/* Assign every triangle a regional attribute of zero. */
traversalinit(&triangles);
triangleloop.orient = 0;
triangleloop.tri = triangletraverse();
while (triangleloop.tri != (triangle *) NULL) {
setelemattribute(triangleloop, eextras, 0.0);
triangleloop.tri = triangletraverse();
}
}
for (i = 0; i < regions; i++) {
if (regiontris[i].tri != dummytri) {
/* Make sure the triangle under consideration still exists. */
/* It may have been eaten by the virus. */
if (regiontris[i].tri[3] != (triangle) NULL) { /* Put one triangle in the virus pool. */
infect(regiontris[i]);
regiontri = (triangle **) poolalloc(&viri);
*regiontri = regiontris[i].tri;
/* Apply one region's attribute and/or area constraint. */
regionplague(regionlist[4 * i + 2], regionlist[4 * i + 3]);
/* The virus pool should be empty now. */
}
}
}
if (regionattrib && !refine) {
/* Note the fact that each triangle has an additional attribute. */
eextras++;
}
}
/* Free up memory. */
if (((holes > 0) && !noholes) || !convex || (regions > 0)) {
pooldeinit(&viri);
}
if (regions > 0) {
free(regiontris);
}
}
/** **/
/** **/
/********* Carving out holes and concavities ends here *********/
/********* Mesh quality maintenance begins here *********/
/** **/
/** **/
/*****************************************************************************/
/* */
/* tallyencs() Traverse the entire list of shell edges, check each edge */
/* to see if it is encroached. If so, add it to the list. */
/* */
/*****************************************************************************/
#ifndef CDT_ONLY
void tallyencs()
{
struct edge edgeloop;
int dummy;
traversalinit(&shelles);
edgeloop.shorient = 0;
edgeloop.sh = shelletraverse();
while (edgeloop.sh != (shelle *) NULL) {
/* If the segment is encroached, add it to the list. */
dummy = checkedge4encroach(&edgeloop);
edgeloop.sh = shelletraverse();
}
}
#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 */
/*****************************************************************************/
/* */
/* repairencs() Find and repair all the encroached segments. */
/* */
/* Encroached segments are repaired by splitting them by inserting a point */
/* at or near their centers. */
/* */
/* `flaws' is a flag that specifies whether one should take note of new */
/* encroached segments and bad triangles that result from inserting points */
/* to repair existing encroached segments. */
/* */
/* When a segment is split, the two resulting subsegments are always */
/* tested to see if they are encroached upon, regardless of the value */
/* of `flaws'. */
/* */
/*****************************************************************************/
#ifndef CDT_ONLY
void repairencs(flaws)
int flaws;
{
struct triedge enctri;
struct triedge testtri;
struct edge *encloop;
struct edge testsh;
point eorg, edest;
point newpoint;
enum insertsiteresult success;
REAL segmentlength, nearestpoweroftwo;
REAL split;
int acuteorg, acutedest;
int dummy;
int i;
triangle ptr; /* Temporary variable used by stpivot(). */
shelle sptr; /* Temporary variable used by snext(). */
while ((badsegments.items > 0) && (steinerleft != 0)) {
traversalinit(&badsegments);
encloop = badsegmenttraverse();
while ((encloop != (struct edge *) NULL) && (steinerleft != 0)) {
/* 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 */
/* point added to split one segment will encroach upon the */
/* other segment, which must then be split with a point 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 shells for later splittings.) */
/* Is the origin shared with another segment? */
stpivot(*encloop, enctri);
lnext(enctri, testtri);
tspivot(testtri, testsh); acuteorg = testsh.sh != dummysh;
/* Is the destination shared with another segment? */
lnextself(testtri);
tspivot(testtri, testsh);
acutedest = testsh.sh != dummysh;
/* Now, check the other side of the segment, if there's a triangle */
/* there. */
sym(enctri, testtri);
if (testtri.tri != dummytri) {
/* Is the destination shared with another segment? */
lnextself(testtri);
tspivot(testtri, testsh);
acutedest = acutedest || (testsh.sh != dummysh);
/* Is the origin shared with another segment? */
lnextself(testtri);
tspivot(testtri, testsh);
acuteorg = acuteorg || (testsh.sh != dummysh);
}
sorg(*encloop, eorg);
sdest(*encloop, edest);
/* 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 nearest the segment's length. */
nearestpoweroftwo = 1.0;
while (segmentlength > SQUAREROOTTWO * nearestpoweroftwo) {
nearestpoweroftwo *= 2.0;
}
while (segmentlength < (0.5 * SQUAREROOTTWO) * nearestpoweroftwo) {
nearestpoweroftwo *= 0.5;
}
/* Where do we split the segment? */
split = 0.5 * 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 point. */
newpoint = (point) poolalloc(&points);
/* Interpolate its coordinate and attributes. */
for (i = 0; i < 2 + nextras; i++) {
newpoint[i] = (1.0 - split) * eorg[i] + split * edest[i];
}
setpointmark(newpoint, mark(*encloop));
if (verbose > 1) {
printf(
" Splitting edge (%.12g, %.12g) (%.12g, %.12g) at (%.12g, %.12g).\n",
eorg[0], eorg[1], edest[0], edest[1], newpoint[0], newpoint[1]);
}
/* Check whether the new point lies on an endpoint. */
if (((newpoint[0] == eorg[0]) && (newpoint[1] == eorg[1]))
|| ((newpoint[0] == edest[0]) && (newpoint[1] == edest[1]))) {
printf("Error: Ran out of precision at (%.12g, %.12g).\n",
newpoint[0], newpoint[1]);
printf("I attempted to split a segment to a smaller size than can\n");
printf(" be accommodated by the finite precision of floating point\n"
);
printf(" arithmetic.\n");
precisionerror();
exit(1);
}
/* Insert the splitting point. This should always succeed. */ success = insertsite(newpoint, &enctri, encloop, flaws, flaws);
if ((success != SUCCESSFULPOINT) && (success != ENCROACHINGPOINT)) {
printf("Internal error in repairencs():\n");
printf(" Failure to split a segment.\n");
internalerror();
}
if (steinerleft > 0) {
steinerleft--;
}
/* Check the two new subsegments to see if they're encroached. */
dummy = checkedge4encroach(encloop);
snextself(*encloop);
dummy = checkedge4encroach(encloop);
badsegmentdealloc(encloop);
encloop = badsegmenttraverse();
}
}
}
#endif /* not CDT_ONLY */
/*****************************************************************************/
/* */
/* tallyfaces() Test every triangle in the mesh for quality measures. */
/* */
/*****************************************************************************/
#ifndef CDT_ONLY
void tallyfaces()
{
struct triedge triangleloop;
if (verbose) {
printf(" Making a list of bad triangles.\n");
}
traversalinit(&triangles);
triangleloop.orient = 0;
triangleloop.tri = triangletraverse();
while (triangleloop.tri != (triangle *) NULL) {
/* If the triangle is bad, enqueue it. */
testtriangle(&triangleloop);
triangleloop.tri = triangletraverse();
}
}
#endif /* not CDT_ONLY */
/*****************************************************************************/
/* */
/* findcircumcenter() Find the circumcenter of a triangle. */
/* */
/* The result is returned both in terms of x-y coordinates and xi-eta */
/* 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. */
/* */
/* The return value indicates which edge of the triangle is shortest. */
/* */
/*****************************************************************************/
enum circumcenterresult findcircumcenter(torg, tdest, tapex, circumcenter,
xi, eta)
point torg;
point tdest;
point tapex;
point circumcenter;
REAL *xi;REAL *eta;
{
REAL xdo, ydo, xao, yao, xad, yad;
REAL dodist, aodist, addist;
REAL denominator;
REAL dx, dy;
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;
if (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(tdest, tapex, torg);
/* Don't count the above as an orientation test. */
counterclockcount--;
}
circumcenter[0] = torg[0] - (ydo * aodist - yao * dodist) * denominator;
circumcenter[1] = torg[1] + (xdo * aodist - xao * dodist) * denominator;
/* To interpolate point attributes for the new point 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. */
dx = circumcenter[0] - torg[0];
dy = circumcenter[1] - torg[1];
*xi = (dx * yao - xao * dy) * (2.0 * denominator);
*eta = (xdo * dy - dx * ydo) * (2.0 * denominator);
xad = tapex[0] - tdest[0];
yad = tapex[1] - tdest[1];
addist = xad * xad + yad * yad;
if ((addist < dodist) && (addist < aodist)) {
return OPPOSITEORG;
} else if (dodist < aodist) {
return OPPOSITEAPEX;
} else {
return OPPOSITEDEST;
}
}
/*****************************************************************************/
/* */
/* splittriangle() Inserts a point at the circumcenter of a triangle. */
/* Deletes the newly inserted point if it encroaches upon */
/* a segment. */
/* */
/*****************************************************************************/
#ifndef CDT_ONLY
void splittriangle(badtri)
struct badface *badtri;
{
point borg, bdest, bapex;
point newpoint;
REAL xi, eta;
enum insertsiteresult success;
enum circumcenterresult shortedge;
int errorflag; int i;
org(badtri->badfacetri, borg);
dest(badtri->badfacetri, bdest);
apex(badtri->badfacetri, 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 ((borg == badtri->faceorg) && (bdest == badtri->facedest) &&
(bapex == badtri->faceapex)) {
if (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 point at the triangle's circumcenter. */
newpoint = (point) poolalloc(&points);
shortedge = findcircumcenter(borg, bdest, bapex, newpoint, &xi, &eta);
/* Check whether the new point lies on a triangle vertex. */
if (((newpoint[0] == borg[0]) && (newpoint[1] == borg[1]))
|| ((newpoint[0] == bdest[0]) && (newpoint[1] == bdest[1]))
|| ((newpoint[0] == bapex[0]) && (newpoint[1] == bapex[1]))) {
if (!quiet) {
printf("Warning: New point (%.12g, %.12g) falls on existing vertex.\n"
, newpoint[0], newpoint[1]);
errorflag = 1;
}
pointdealloc(newpoint);
} else {
for (i = 2; i < 2 + nextras; i++) {
/* Interpolate the point attributes at the circumcenter. */
newpoint[i] = borg[i] + xi * (bdest[i] - borg[i])
+ eta * (bapex[i] - borg[i]);
}
/* The new point must be in the interior, and have a marker of zero. */
setpointmark(newpoint, 0);
/* Ensure that the handle `badtri->badfacetri' represents the shortest */
/* edge of the triangle. This ensures that the circumcenter must */
/* fall to the left of this edge, so point location will work. */
if (shortedge == OPPOSITEORG) {
lnextself(badtri->badfacetri);
} else if (shortedge == OPPOSITEDEST) {
lprevself(badtri->badfacetri);
}
/* Insert the circumcenter, searching from the edge of the triangle, */
/* and maintain the Delaunay property of the triangulation. */
success = insertsite(newpoint, &(badtri->badfacetri),
(struct edge *) NULL, 1, 1);
if (success == SUCCESSFULPOINT) {
if (steinerleft > 0) {
steinerleft--;
}
} else if (success == ENCROACHINGPOINT) {
/* If the newly inserted point encroaches upon a segment, delete it. */
deletesite(&(badtri->badfacetri));
} else if (success == VIOLATINGPOINT) {
/* Failed to insert the new point, but some segment was */
/* marked as being encroached. */
pointdealloc(newpoint);
} else { /* success == DUPLICATEPOINT */
/* Failed to insert the new point because a vertex is already there. */
if (!quiet) {
printf(
"Warning: New point (%.12g, %.12g) falls on existing vertex.\n"
, newpoint[0], newpoint[1]);
errorflag = 1;
}
pointdealloc(newpoint);
} }
if (errorflag) {
if (verbose) {
printf(" The new point 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();
}
}
/* Return the bad triangle to the pool. */
pooldealloc(&badtriangles, (VOID *) badtri);
}
#endif /* not CDT_ONLY */
/*****************************************************************************/
/* */
/* enforcequality() Remove all the encroached edges and bad triangles */
/* from the triangulation. */
/* */
/*****************************************************************************/
#ifndef CDT_ONLY
void enforcequality()
{
int i;
if (!quiet) {
printf("Adding Steiner points to enforce quality.\n");
}
/* Initialize the pool of encroached segments. */
poolinit(&badsegments, sizeof(struct edge), BADSEGMENTPERBLOCK, POINTER, 0);
if (verbose) {
printf(" Looking for encroached segments.\n");
}
/* Test all segments to see if they're encroached. */
tallyencs();
if (verbose && (badsegments.items > 0)) {
printf(" Splitting encroached segments.\n");
}
/* Note that steinerleft == -1 if an unlimited number */
/* of Steiner points is allowed. */
while ((badsegments.items > 0) && (steinerleft != 0)) {
/* Fix the segments without noting newly encroached segments or */
/* bad triangles. The reason we don't want to note newly */
/* encroached segments is because some encroached segments are */
/* likely to be noted multiple times, and would then be blindly */
/* split multiple times. I should fix that some time. */
repairencs(0);
/* Now, find all the segments that became encroached while adding */
/* points to split encroached segments. */
tallyencs();
}
/* 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 ((minangle > 0.0) || vararea || fixedarea) {
/* Initialize the pool of bad triangles. */
poolinit(&badtriangles, sizeof(struct badface), BADTRIPERBLOCK, POINTER,
0);
/* Initialize the queues of bad triangles. */
for (i = 0; i < 64; i++) {
queuefront[i] = (struct badface *) NULL; queuetail[i] = &queuefront[i];
}
/* Test all triangles to see if they're bad. */
tallyfaces();
if (verbose) {
printf(" Splitting bad triangles.\n");
}
while ((badtriangles.items > 0) && (steinerleft != 0)) {
/* Fix one bad triangle by inserting a point at its circumcenter. */
splittriangle(dequeuebadtri());
/* Fix any encroached segments that may have resulted. Record */
/* any new bad triangles or encroached segments that result. */
if (badsegments.items > 0) {
repairencs(1);
}
}
}
/* At this point, if 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 (!quiet && (badsegments.items > 0) && (steinerleft == 0)) {
printf("\nWarning: I ran out of Steiner points, but the mesh has\n");
if (badsegments.items == 1) {
printf(" an encroached segment, and therefore might not be truly\n");
} else {
printf(" %ld encroached segments, and therefore might not be truly\n",
badsegments.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. */
/* */
/*****************************************************************************/
void highorder()
{
struct triedge triangleloop, trisym;
struct edge checkmark;
point newpoint;
point torg, tdest;
int i;
triangle ptr; /* Temporary variable used by sym(). */
shelle sptr; /* Temporary variable used by tspivot(). */
if (!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. */
points.deaditemstack = (VOID *) NULL;
traversalinit(&triangles);
triangleloop.tri = triangletraverse(); /* 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 == dummytri)) {
org(triangleloop, torg);
dest(triangleloop, tdest);
/* Create a new node in the middle of the edge. Interpolate */
/* its attributes. */
newpoint = (point) poolalloc(&points);
for (i = 0; i < 2 + nextras; i++) {
newpoint[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. */
setpointmark(newpoint, trisym.tri == dummytri);
if (useshelles) {
tspivot(triangleloop, checkmark);
/* If this edge is a segment, transfer the marker to the new node. */
if (checkmark.sh != dummysh) {
setpointmark(newpoint, mark(checkmark));
}
}
if (verbose > 1) {
printf(" Creating (%.12g, %.12g).\n", newpoint[0], newpoint[1]);
}
/* Record the new node in the (one or two) adjacent elements. */
triangleloop.tri[highorderindex + triangleloop.orient] =
(triangle) newpoint;
if (trisym.tri != dummytri) {
trisym.tri[highorderindex + trisym.orient] = (triangle) newpoint;
}
}
}
triangleloop.tri = triangletraverse();
}
}
/********* 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. */
/* */
/*****************************************************************************/
#ifndef TRILIBRARY
char *readline(string, infile, infilename)
char *string;
FILE *infile;
char *infilename;
{
char *result;
/* Search for something that looks like a number. */
do {
result = fgets(string, INPUTLINESIZE, infile);
if (result == (char *) NULL) { printf(" Error: Unexpected end of file in %s.\n", infilename);
exit(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
char *findfield(string)
char *string;
{
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 points from a file, which may be a .node or .poly */
/* file. */
/* */
/*****************************************************************************/
#ifndef TRILIBRARY
void readnodes(nodefilename, polyfilename, polyfile)
char *nodefilename;
char *polyfilename;
FILE **polyfile;
{
FILE *infile; point pointloop;
char inputline[INPUTLINESIZE];
char *stringptr;
char *infilename;
REAL x, y;
int firstnode;
int nodemarkers;
int currentmarker;
int i, j;
if (poly) {
/* Read the points from a .poly file. */
if (!quiet) {
printf("Opening %s.\n", polyfilename);
}
*polyfile = fopen(polyfilename, "r");
if (*polyfile == (FILE *) NULL) {
printf(" Error: Cannot access file %s.\n", polyfilename);
exit(1);
}
/* Read number of points, number of dimensions, number of point */
/* attributes, and number of boundary markers. */
stringptr = readline(inputline, *polyfile, polyfilename);
inpoints = (int) strtol (stringptr, &stringptr, 0);
stringptr = findfield(stringptr);
if (*stringptr == '\0') {
mesh_dim = 2;
} else {
mesh_dim = (int) strtol (stringptr, &stringptr, 0);
}
stringptr = findfield(stringptr);
if (*stringptr == '\0') {
nextras = 0;
} else {
nextras = (int) strtol (stringptr, &stringptr, 0);
}
stringptr = findfield(stringptr);
if (*stringptr == '\0') {
nodemarkers = 0;
} else {
nodemarkers = (int) strtol (stringptr, &stringptr, 0);
}
if (inpoints > 0) {
infile = *polyfile;
infilename = polyfilename;
readnodefile = 0;
} else {
/* If the .poly file claims there are zero points, that means that */
/* the points should be read from a separate .node file. */
readnodefile = 1;
infilename = innodefilename;
}
} else {
readnodefile = 1;
infilename = innodefilename;
*polyfile = (FILE *) NULL;
}
if (readnodefile) {
/* Read the points from a .node file. */
if (!quiet) {
printf("Opening %s.\n", innodefilename);
}
infile = fopen(innodefilename, "r");
if (infile == (FILE *) NULL) {
printf(" Error: Cannot access file %s.\n", innodefilename);
exit(1);
}
/* Read number of points, number of dimensions, number of point */
/* attributes, and number of boundary markers. */ stringptr = readline(inputline, infile, innodefilename);
inpoints = (int) strtol (stringptr, &stringptr, 0);
stringptr = findfield(stringptr);
if (*stringptr == '\0') {
mesh_dim = 2;
} else {
mesh_dim = (int) strtol (stringptr, &stringptr, 0);
}
stringptr = findfield(stringptr);
if (*stringptr == '\0') {
nextras = 0;
} else {
nextras = (int) strtol (stringptr, &stringptr, 0);
}
stringptr = findfield(stringptr);
if (*stringptr == '\0') {
nodemarkers = 0;
} else {
nodemarkers = (int) strtol (stringptr, &stringptr, 0);
}
}
if (inpoints < 3) {
printf("Error: Input must have at least three input points.\n");
exit(1);
}
if (mesh_dim != 2) {
printf("Error: Triangle only works with two-dimensional meshes.\n");
exit(1);
}
initializepointpool();
/* Read the points. */
for (i = 0; i < inpoints; i++) {
pointloop = (point) poolalloc(&points);
stringptr = readline(inputline, infile, infilename);
if (i == 0) {
firstnode = (int) strtol (stringptr, &stringptr, 0);
if ((firstnode == 0) || (firstnode == 1)) {
firstnumber = firstnode;
}
}
stringptr = findfield(stringptr);
if (*stringptr == '\0') {
printf("Error: Point %d has no x coordinate.\n", firstnumber + i);
exit(1);
}
x = (REAL) strtod(stringptr, &stringptr);
stringptr = findfield(stringptr);
if (*stringptr == '\0') {
printf("Error: Point %d has no y coordinate.\n", firstnumber + i);
exit(1);
}
y = (REAL) strtod(stringptr, &stringptr);
pointloop[0] = x;
pointloop[1] = y;
/* Read the point attributes. */
for (j = 2; j < 2 + nextras; j++) {
stringptr = findfield(stringptr);
if (*stringptr == '\0') {
pointloop[j] = 0.0;
} else {
pointloop[j] = (REAL) strtod(stringptr, &stringptr);
}
}
if (nodemarkers) {
/* Read a point marker. */
stringptr = findfield(stringptr);
if (*stringptr == '\0') { setpointmark(pointloop, 0);
} else {
currentmarker = (int) strtol (stringptr, &stringptr, 0);
setpointmark(pointloop, currentmarker);
}
} else {
/* If no markers are specified in the file, they default to zero. */
setpointmark(pointloop, 0);
}
/* Determine the smallest and largest x and y coordinates. */
if (i == 0) {
xmin = xmax = x;
ymin = ymax = y;
} else {
xmin = (x < xmin) ? x : xmin;
xmax = (x > xmax) ? x : xmax;
ymin = (y < ymin) ? y : ymin;
ymax = (y > ymax) ? y : ymax;
}
}
if (readnodefile) {
fclose(infile);
}
/* Nonexistent x value used as a flag to mark circle events in sweepline */
/* Delaunay algorithm. */
xminextreme = 10 * xmin - 9 * xmax;
}
#endif /* not TRILIBRARY */
/*****************************************************************************/
/* */
/* transfernodes() Read the points from memory. */
/* */
/*****************************************************************************/
#ifdef TRILIBRARY
void transfernodes(pointlist, pointattriblist, pointmarkerlist, numberofpoints,
numberofpointattribs)
REAL *pointlist;
REAL *pointattriblist;
int *pointmarkerlist;
int numberofpoints;
int numberofpointattribs;
{
point pointloop;
REAL x, y;
int i, j;
int coordindex;
int attribindex;
inpoints = numberofpoints;
mesh_dim = 2;
nextras = numberofpointattribs;
readnodefile = 0;
if (inpoints < 3) {
printf("Error: Input must have at least three input points.\n");
exit(1);
}
initializepointpool();
/* Read the points. */
coordindex = 0;
attribindex = 0;
for (i = 0; i < inpoints; i++) {
pointloop = (point) poolalloc(&points);
/* Read the point coordinates. */ x = pointloop[0] = pointlist[coordindex++];
y = pointloop[1] = pointlist[coordindex++];
/* Read the point attributes. */
for (j = 0; j < numberofpointattribs; j++) {
pointloop[2 + j] = pointattriblist[attribindex++];
}
if (pointmarkerlist != (int *) NULL) {
/* Read a point marker. */
setpointmark(pointloop, pointmarkerlist[i]);
} else {
/* If no markers are specified, they default to zero. */
setpointmark(pointloop, 0);
}
x = pointloop[0];
y = pointloop[1];
/* Determine the smallest and largest x and y coordinates. */
if (i == 0) {
xmin = xmax = x;
ymin = ymax = y;
} else {
xmin = (x < xmin) ? x : xmin;
xmax = (x > xmax) ? x : xmax;
ymin = (y < ymin) ? y : ymin;
ymax = (y > ymax) ? y : ymax;
}
}
/* Nonexistent x value used as a flag to mark circle events in sweepline */
/* Delaunay algorithm. */
xminextreme = 10 * xmin - 9 * xmax;
}
#endif /* TRILIBRARY */
/*****************************************************************************/
/* */
/* readholes() Read the holes, and possibly regional attributes and area */
/* constraints, from a .poly file. */
/* */
/*****************************************************************************/
#ifndef TRILIBRARY
void readholes(polyfile, polyfilename, hlist, holes, rlist, regions)
FILE *polyfile;
char *polyfilename;
REAL **hlist;
int *holes;
REAL **rlist;
int *regions;
{
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 *) malloc(2 * *holes * sizeof(REAL));
*hlist = holelist;
if (holelist == (REAL *) NULL) {
printf("Error: Out of memory.\n");
exit(1);
}
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",
firstnumber + (i >> 1));
exit(1);
} else {
holelist[i] = (REAL) strtod(stringptr, &stringptr);
}
stringptr = findfield(stringptr);
if (*stringptr == '\0') {
printf("Error: Hole %d has no y coordinate.\n",
firstnumber + (i >> 1));
exit(1);
} else {
holelist[i + 1] = (REAL) strtod(stringptr, &stringptr);
}
}
} else {
*hlist = (REAL *) NULL;
}
#ifndef CDT_ONLY
if ((regionattrib || vararea) && !refine) {
/* Read the area constraints. */
stringptr = readline(inputline, polyfile, polyfilename);
*regions = (int) strtol (stringptr, &stringptr, 0);
if (*regions > 0) {
regionlist = (REAL *) malloc(4 * *regions * sizeof(REAL));
*rlist = regionlist;
if (regionlist == (REAL *) NULL) {
printf("Error: Out of memory.\n");
exit(1);
}
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",
firstnumber + i);
exit(1);
} else {
regionlist[index++] = (REAL) strtod(stringptr, &stringptr);
}
stringptr = findfield(stringptr);
if (*stringptr == '\0') {
printf("Error: Region %d has no y coordinate.\n",
firstnumber + i);
exit(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",
firstnumber + i);
exit(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
void finishfile(outfile, argc, argv)
FILE *outfile;
int argc;
char **argv;
{
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 points and write them to a .node file. */
/* */
/* To save memory, the point numbers are written over the shell markers */
/* after the points are written to a file. */
/* */
/*****************************************************************************/
#ifdef TRILIBRARY
void writenodes(pointlist, pointattriblist, pointmarkerlist)
REAL **pointlist;
REAL **pointattriblist;
int **pointmarkerlist;
#else /* not TRILIBRARY */
void writenodes(nodefilename, argc, argv)
char *nodefilename;
int argc;
char **argv;
#endif /* not TRILIBRARY */
{
#ifdef TRILIBRARY
REAL *plist;
REAL *palist;
int *pmlist;
int coordindex; int attribindex;
#else /* not TRILIBRARY */
FILE *outfile;
#endif /* not TRILIBRARY */
point pointloop;
int pointnumber;
int i;
#ifdef TRILIBRARY
if (!quiet) {
printf("Writing points.\n");
}
/* Allocate memory for output points if necessary. */
if (*pointlist == (REAL *) NULL) {
*pointlist = (REAL *) malloc(points.items * 2 * sizeof(REAL));
if (*pointlist == (REAL *) NULL) {
printf("Error: Out of memory.\n");
exit(1);
}
}
/* Allocate memory for output point attributes if necessary. */
if ((nextras > 0) && (*pointattriblist == (REAL *) NULL)) {
*pointattriblist = (REAL *) malloc(points.items * nextras * sizeof(REAL));
if (*pointattriblist == (REAL *) NULL) {
printf("Error: Out of memory.\n");
exit(1);
}
}
/* Allocate memory for output point markers if necessary. */
if (!nobound && (*pointmarkerlist == (int *) NULL)) {
*pointmarkerlist = (int *) malloc(points.items * sizeof(int));
if (*pointmarkerlist == (int *) NULL) {
printf("Error: Out of memory.\n");
exit(1);
}
}
plist = *pointlist;
palist = *pointattriblist;
pmlist = *pointmarkerlist;
coordindex = 0;
attribindex = 0;
#else /* not TRILIBRARY */
if (!quiet) {
printf("Writing %s.\n", nodefilename);
}
outfile = fopen(nodefilename, "w");
if (outfile == (FILE *) NULL) {
printf(" Error: Cannot create file %s.\n", nodefilename);
exit(1);
}
/* Number of points, number of dimensions, number of point attributes, */
/* and number of boundary markers (zero or one). */
fprintf(outfile, "%ld %d %d %d\n", points.items, mesh_dim, nextras,
1 - nobound);
#endif /* not TRILIBRARY */
traversalinit(&points);
pointloop = pointtraverse();
pointnumber = firstnumber;
while (pointloop != (point) NULL) {
#ifdef TRILIBRARY
/* X and y coordinates. */
plist[coordindex++] = pointloop[0];
plist[coordindex++] = pointloop[1];
/* Point attributes. */
for (i = 0; i < nextras; i++) {
palist[attribindex++] = pointloop[2 + i];
}
if (!nobound) {
/* Copy the boundary marker. */ pmlist[pointnumber - firstnumber] = pointmark(pointloop);
}
#else /* not TRILIBRARY */
/* Point number, x and y coordinates. */
fprintf(outfile, "%4d %.17g %.17g", pointnumber, pointloop[0],
pointloop[1]);
for (i = 0; i < nextras; i++) {
/* Write an attribute. */
fprintf(outfile, " %.17g", pointloop[i + 2]);
}
if (nobound) {
fprintf(outfile, "\n");
} else {
/* Write the boundary marker. */
fprintf(outfile, " %d\n", pointmark(pointloop));
}
#endif /* not TRILIBRARY */
setpointmark(pointloop, pointnumber);
pointloop = pointtraverse();
pointnumber++;
}
#ifndef TRILIBRARY
finishfile(outfile, argc, argv);
#endif /* not TRILIBRARY */
}
/*****************************************************************************/
/* */
/* numbernodes() Number the points. */
/* */
/* Each point is assigned a marker equal to its number. */
/* */
/* Used when writenodes() is not called because no .node file is written. */
/* */
/*****************************************************************************/
void numbernodes()
{
point pointloop;
int pointnumber;
traversalinit(&points);
pointloop = pointtraverse();
pointnumber = firstnumber;
while (pointloop != (point) NULL) {
setpointmark(pointloop, pointnumber);
pointloop = pointtraverse();
pointnumber++;
}
}
/*****************************************************************************/
/* */
/* writeelements() Write the triangles to an .ele file. */
/* */
/*****************************************************************************/
#ifdef TRILIBRARY
void writeelements(trianglelist, triangleattriblist)
int **trianglelist;
REAL **triangleattriblist;
#else /* not TRILIBRARY */
void writeelements(elefilename, argc, argv)
char *elefilename;
int argc;char **argv;
#endif /* not TRILIBRARY */
{
#ifdef TRILIBRARY
int *tlist;
REAL *talist;
int pointindex;
int attribindex;
#else /* not TRILIBRARY */
FILE *outfile;
#endif /* not TRILIBRARY */
struct triedge triangleloop;
point p1, p2, p3;
point mid1, mid2, mid3;
int elementnumber;
int i;
#ifdef TRILIBRARY
if (!quiet) {
printf("Writing triangles.\n");
}
/* Allocate memory for output triangles if necessary. */
if (*trianglelist == (int *) NULL) {
*trianglelist = (int *) malloc(triangles.items *
((order + 1) * (order + 2) / 2) * sizeof(int));
if (*trianglelist == (int *) NULL) {
printf("Error: Out of memory.\n");
exit(1);
}
}
/* Allocate memory for output triangle attributes if necessary. */
if ((eextras > 0) && (*triangleattriblist == (REAL *) NULL)) {
*triangleattriblist = (REAL *) malloc(triangles.items * eextras *
sizeof(REAL));
if (*triangleattriblist == (REAL *) NULL) {
printf("Error: Out of memory.\n");
exit(1);
}
}
tlist = *trianglelist;
talist = *triangleattriblist;
pointindex = 0;
attribindex = 0;
#else /* not TRILIBRARY */
if (!quiet) {
printf("Writing %s.\n", elefilename);
}
outfile = fopen(elefilename, "w");
if (outfile == (FILE *) NULL) {
printf(" Error: Cannot create file %s.\n", elefilename);
exit(1);
}
/* Number of triangles, points per triangle, attributes per triangle. */
fprintf(outfile, "%ld %d %d\n", triangles.items,
(order + 1) * (order + 2) / 2, eextras);
#endif /* not TRILIBRARY */
traversalinit(&triangles);
triangleloop.tri = triangletraverse();
triangleloop.orient = 0;
elementnumber = firstnumber;
while (triangleloop.tri != (triangle *) NULL) {
org(triangleloop, p1);
dest(triangleloop, p2);
apex(triangleloop, p3);
if (order == 1) {
#ifdef TRILIBRARY
tlist[pointindex++] = pointmark(p1); tlist[pointindex++] = pointmark(p2);
tlist[pointindex++] = pointmark(p3);
#else /* not TRILIBRARY */
/* Triangle number, indices for three points. */
fprintf(outfile, "%4d %4d %4d %4d", elementnumber,
pointmark(p1), pointmark(p2), pointmark(p3));
#endif /* not TRILIBRARY */
} else {
mid1 = (point) triangleloop.tri[highorderindex + 1];
mid2 = (point) triangleloop.tri[highorderindex + 2];
mid3 = (point) triangleloop.tri[highorderindex];
#ifdef TRILIBRARY
tlist[pointindex++] = pointmark(p1);
tlist[pointindex++] = pointmark(p2);
tlist[pointindex++] = pointmark(p3);
tlist[pointindex++] = pointmark(mid1);
tlist[pointindex++] = pointmark(mid2);
tlist[pointindex++] = pointmark(mid3);
#else /* not TRILIBRARY */
/* Triangle number, indices for six points. */
fprintf(outfile, "%4d %4d %4d %4d %4d %4d %4d", elementnumber,
pointmark(p1), pointmark(p2), pointmark(p3), pointmark(mid1),
pointmark(mid2), pointmark(mid3));
#endif /* not TRILIBRARY */
}
#ifdef TRILIBRARY
for (i = 0; i < eextras; i++) {
talist[attribindex++] = elemattribute(triangleloop, i);
}
#else /* not TRILIBRARY */
for (i = 0; i < eextras; i++) {
fprintf(outfile, " %.17g", elemattribute(triangleloop, i));
}
fprintf(outfile, "\n");
#endif /* not TRILIBRARY */
triangleloop.tri = triangletraverse();
elementnumber++;
}
#ifndef TRILIBRARY
finishfile(outfile, argc, argv);
#endif /* not TRILIBRARY */
}
/*****************************************************************************/
/* */
/* writepoly() Write the segments and holes to a .poly file. */
/* */
/*****************************************************************************/
#ifdef TRILIBRARY
void writepoly(segmentlist, segmentmarkerlist)
int **segmentlist;
int **segmentmarkerlist;
#else /* not TRILIBRARY */
void writepoly(polyfilename, holelist, holes, regionlist, regions, argc, argv)
char *polyfilename;
REAL *holelist;
int holes;
REAL *regionlist;
int regions;
int argc;
char **argv;
#endif /* not TRILIBRARY */
{
#ifdef TRILIBRARY
int *slist;
int *smlist;
int index;
#else /* not TRILIBRARY */
FILE *outfile;
int i;
#endif /* not TRILIBRARY */
struct edge shelleloop;
point endpoint1, endpoint2;
int shellenumber;
#ifdef TRILIBRARY
if (!quiet) {
printf("Writing segments.\n");
}
/* Allocate memory for output segments if necessary. */
if (*segmentlist == (int *) NULL) {
*segmentlist = (int *) malloc(shelles.items * 2 * sizeof(int));
if (*segmentlist == (int *) NULL) {
printf("Error: Out of memory.\n");
exit(1);
}
}
/* Allocate memory for output segment markers if necessary. */
if (!nobound && (*segmentmarkerlist == (int *) NULL)) {
*segmentmarkerlist = (int *) malloc(shelles.items * sizeof(int));
if (*segmentmarkerlist == (int *) NULL) {
printf("Error: Out of memory.\n");
exit(1);
}
}
slist = *segmentlist;
smlist = *segmentmarkerlist;
index = 0;
#else /* not TRILIBRARY */
if (!quiet) {
printf("Writing %s.\n", polyfilename);
}
outfile = fopen(polyfilename, "w");
if (outfile == (FILE *) NULL) {
printf(" Error: Cannot create file %s.\n", polyfilename);
exit(1);
}
/* The zero indicates that the points are in a separate .node file. */
/* Followed by number of dimensions, number of point attributes, */
/* and number of boundary markers (zero or one). */
fprintf(outfile, "%d %d %d %d\n", 0, mesh_dim, nextras, 1 - nobound);
/* Number of segments, number of boundary markers (zero or one). */
fprintf(outfile, "%ld %d\n", shelles.items, 1 - nobound);
#endif /* not TRILIBRARY */
traversalinit(&shelles);
shelleloop.sh = shelletraverse();
shelleloop.shorient = 0;
shellenumber = firstnumber;
while (shelleloop.sh != (shelle *) NULL) {
sorg(shelleloop, endpoint1);
sdest(shelleloop, endpoint2);
#ifdef TRILIBRARY
/* Copy indices of the segment's two endpoints. */
slist[index++] = pointmark(endpoint1);
slist[index++] = pointmark(endpoint2);
if (!nobound) {
/* Copy the boundary marker. */
smlist[shellenumber - firstnumber] = mark(shelleloop);
}
#else /* not TRILIBRARY */ /* Segment number, indices of its two endpoints, and possibly a marker. */
if (nobound) {
fprintf(outfile, "%4d %4d %4d\n", shellenumber,
pointmark(endpoint1), pointmark(endpoint2));
} else {
fprintf(outfile, "%4d %4d %4d %4d\n", shellenumber,
pointmark(endpoint1), pointmark(endpoint2), mark(shelleloop));
}
#endif /* not TRILIBRARY */
shelleloop.sh = shelletraverse();
shellenumber++;
}
#ifndef TRILIBRARY
#ifndef CDT_ONLY
fprintf(outfile, "%d\n", holes);
if (holes > 0) {
for (i = 0; i < holes; i++) {
/* Hole number, x and y coordinates. */
fprintf(outfile, "%4d %.17g %.17g\n", firstnumber + i,
holelist[2 * i], holelist[2 * i + 1]);
}
}
if (regions > 0) {
fprintf(outfile, "%d\n", regions);
for (i = 0; i < regions; i++) {
/* Region number, x and y coordinates, attribute, maximum area. */
fprintf(outfile, "%4d %.17g %.17g %.17g %.17g\n", firstnumber + i,
regionlist[4 * i], regionlist[4 * i + 1],
regionlist[4 * i + 2], regionlist[4 * i + 3]);
}
}
#endif /* not CDT_ONLY */
finishfile(outfile, argc, argv);
#endif /* not TRILIBRARY */
}
/*****************************************************************************/
/* */
/* writeedges() Write the edges to a .edge file. */
/* */
/*****************************************************************************/
#ifdef TRILIBRARY
void writeedges(edgelist, edgemarkerlist)
int **edgelist;
int **edgemarkerlist;
#else /* not TRILIBRARY */
void writeedges(edgefilename, argc, argv)
char *edgefilename;
int argc;
char **argv;
#endif /* not TRILIBRARY */
{
#ifdef TRILIBRARY
int *elist;
int *emlist;
int index;
#else /* not TRILIBRARY */
FILE *outfile;
#endif /* not TRILIBRARY */
struct triedge triangleloop, trisym;
struct edge checkmark; point p1, p2;
int edgenumber;
triangle ptr; /* Temporary variable used by sym(). */
shelle sptr; /* Temporary variable used by tspivot(). */
#ifdef TRILIBRARY
if (!quiet) {
printf("Writing edges.\n");
}
/* Allocate memory for edges if necessary. */
if (*edgelist == (int *) NULL) {
*edgelist = (int *) malloc(edges * 2 * sizeof(int));
if (*edgelist == (int *) NULL) {
printf("Error: Out of memory.\n");
exit(1);
}
}
/* Allocate memory for edge markers if necessary. */
if (!nobound && (*edgemarkerlist == (int *) NULL)) {
*edgemarkerlist = (int *) malloc(edges * sizeof(int));
if (*edgemarkerlist == (int *) NULL) {
printf("Error: Out of memory.\n");
exit(1);
}
}
elist = *edgelist;
emlist = *edgemarkerlist;
index = 0;
#else /* not TRILIBRARY */
if (!quiet) {
printf("Writing %s.\n", edgefilename);
}
outfile = fopen(edgefilename, "w");
if (outfile == (FILE *) NULL) {
printf(" Error: Cannot create file %s.\n", edgefilename);
exit(1);
}
/* Number of edges, number of boundary markers (zero or one). */
fprintf(outfile, "%ld %d\n", edges, 1 - nobound);
#endif /* not TRILIBRARY */
traversalinit(&triangles);
triangleloop.tri = triangletraverse();
edgenumber = 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 == dummytri)) {
org(triangleloop, p1);
dest(triangleloop, p2);
#ifdef TRILIBRARY
elist[index++] = pointmark(p1);
elist[index++] = pointmark(p2);
#endif /* TRILIBRARY */
if (nobound) {
#ifndef TRILIBRARY
/* Edge number, indices of two endpoints. */
fprintf(outfile, "%4d %d %d\n", edgenumber,
pointmark(p1), pointmark(p2));
#endif /* not TRILIBRARY */
} else {
/* Edge number, indices of two endpoints, and a boundary marker. */
/* If there's no shell edge, the boundary marker is zero. */ if (useshelles) {
tspivot(triangleloop, checkmark);
if (checkmark.sh == dummysh) {
#ifdef TRILIBRARY
emlist[edgenumber - firstnumber] = 0;
#else /* not TRILIBRARY */
fprintf(outfile, "%4d %d %d %d\n", edgenumber,
pointmark(p1), pointmark(p2), 0);
#endif /* not TRILIBRARY */
} else {
#ifdef TRILIBRARY
emlist[edgenumber - firstnumber] = mark(checkmark);
#else /* not TRILIBRARY */
fprintf(outfile, "%4d %d %d %d\n", edgenumber,
pointmark(p1), pointmark(p2), mark(checkmark));
#endif /* not TRILIBRARY */
}
} else {
#ifdef TRILIBRARY
emlist[edgenumber - firstnumber] = trisym.tri == dummytri;
#else /* not TRILIBRARY */
fprintf(outfile, "%4d %d %d %d\n", edgenumber,
pointmark(p1), pointmark(p2), trisym.tri == dummytri);
#endif /* not TRILIBRARY */
}
}
edgenumber++;
}
}
triangleloop.tri = triangletraverse();
}
#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 shell edges or the extra nodes of every */
/* element. Hence, you should call this procedure last. */
/* */
/*****************************************************************************/
#ifdef TRILIBRARY
void writevoronoi(vpointlist, vpointattriblist, vpointmarkerlist, vedgelist,
vedgemarkerlist, vnormlist)
REAL **vpointlist;
REAL **vpointattriblist;
int **vpointmarkerlist;
int **vedgelist;
int **vedgemarkerlist;
REAL **vnormlist;
#else /* not TRILIBRARY */
void writevoronoi(vnodefilename, vedgefilename, argc, argv)
char *vnodefilename;
char *vedgefilename;
int argc;char **argv;
#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 triedge triangleloop, trisym;
point torg, tdest, tapex;
REAL circumcenter[2];
REAL xi, eta;
int vnodenumber, vedgenumber;
int p1, p2;
int i;
triangle ptr; /* Temporary variable used by sym(). */
#ifdef TRILIBRARY
if (!quiet) {
printf("Writing Voronoi vertices.\n");
}
/* Allocate memory for Voronoi vertices if necessary. */
if (*vpointlist == (REAL *) NULL) {
*vpointlist = (REAL *) malloc(triangles.items * 2 * sizeof(REAL));
if (*vpointlist == (REAL *) NULL) {
printf("Error: Out of memory.\n");
exit(1);
}
}
/* Allocate memory for Voronoi vertex attributes if necessary. */
if (*vpointattriblist == (REAL *) NULL) {
*vpointattriblist = (REAL *) malloc(triangles.items * nextras *
sizeof(REAL));
if (*vpointattriblist == (REAL *) NULL) {
printf("Error: Out of memory.\n");
exit(1);
}
}
*vpointmarkerlist = (int *) NULL;
plist = *vpointlist;
palist = *vpointattriblist;
coordindex = 0;
attribindex = 0;
#else /* not TRILIBRARY */
if (!quiet) {
printf("Writing %s.\n", vnodefilename);
}
outfile = fopen(vnodefilename, "w");
if (outfile == (FILE *) NULL) {
printf(" Error: Cannot create file %s.\n", vnodefilename);
exit(1);
}
/* Number of triangles, two dimensions, number of point attributes, */
/* zero markers. */
fprintf(outfile, "%ld %d %d %d\n", triangles.items, 2, nextras, 0);
#endif /* not TRILIBRARY */
traversalinit(&triangles);
triangleloop.tri = triangletraverse();
triangleloop.orient = 0;
vnodenumber = firstnumber;
while (triangleloop.tri != (triangle *) NULL) {
org(triangleloop, torg); dest(triangleloop, tdest);
apex(triangleloop, tapex);
findcircumcenter(torg, tdest, tapex, circumcenter, &xi, &eta);
#ifdef TRILIBRARY
/* X and y coordinates. */
plist[coordindex++] = circumcenter[0];
plist[coordindex++] = circumcenter[1];
for (i = 2; i < 2 + nextras; i++) {
/* Interpolate the point 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, "%4d %.17g %.17g", vnodenumber, circumcenter[0],
circumcenter[1]);
for (i = 2; i < 2 + nextras; i++) {
/* Interpolate the point 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) = vnodenumber;
triangleloop.tri = triangletraverse();
vnodenumber++;
}
#ifndef TRILIBRARY
finishfile(outfile, argc, argv);
#endif /* not TRILIBRARY */
#ifdef TRILIBRARY
if (!quiet) {
printf("Writing Voronoi edges.\n");
}
/* Allocate memory for output Voronoi edges if necessary. */
if (*vedgelist == (int *) NULL) {
*vedgelist = (int *) malloc(edges * 2 * sizeof(int));
if (*vedgelist == (int *) NULL) {
printf("Error: Out of memory.\n");
exit(1);
}
}
*vedgemarkerlist = (int *) NULL;
/* Allocate memory for output Voronoi norms if necessary. */
if (*vnormlist == (REAL *) NULL) {
*vnormlist = (REAL *) malloc(edges * 2 * sizeof(REAL));
if (*vnormlist == (REAL *) NULL) {
printf("Error: Out of memory.\n");
exit(1);
}
}
elist = *vedgelist;
normlist = *vnormlist;
coordindex = 0;
#else /* not TRILIBRARY */
if (!quiet) {
printf("Writing %s.\n", vedgefilename);
}
outfile = fopen(vedgefilename, "w");
if (outfile == (FILE *) NULL) {
printf(" Error: Cannot create file %s.\n", vedgefilename);
exit(1);
}
/* Number of edges, zero boundary markers. */
fprintf(outfile, "%ld %d\n", edges, 0);
#endif /* not TRILIBRARY */
traversalinit(&triangles);
triangleloop.tri = triangletraverse();
vedgenumber = 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 == dummytri)) {
/* Find the number of this triangle (and Voronoi vertex). */
p1 = * (int *) (triangleloop.tri + 6);
if (trisym.tri == 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, "%4d %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, "%4d %d %d\n", vedgenumber, p1, p2);
#endif /* not TRILIBRARY */
}
vedgenumber++;
}
}
triangleloop.tri = triangletraverse();
}
#ifndef TRILIBRARY
finishfile(outfile, argc, argv);
#endif /* not TRILIBRARY */
}
#ifdef TRILIBRARY
void writeneighbors(neighborlist)
int **neighborlist;
#else /* not TRILIBRARY */
void writeneighbors(neighborfilename, argc, argv)
char *neighborfilename;
int argc;
char **argv;
#endif /* not TRILIBRARY */
{
#ifdef TRILIBRARY
int *nlist;
int index;
#else /* not TRILIBRARY */
FILE *outfile;
#endif /* not TRILIBRARY */
struct triedge triangleloop, trisym;
int elementnumber;
int neighbor1, neighbor2, neighbor3;
triangle ptr; /* Temporary variable used by sym(). */
#ifdef TRILIBRARY
if (!quiet) {
printf("Writing neighbors.\n");
}
/* Allocate memory for neighbors if necessary. */
if (*neighborlist == (int *) NULL) {
*neighborlist = (int *) malloc(triangles.items * 3 * sizeof(int));
if (*neighborlist == (int *) NULL) {
printf("Error: Out of memory.\n");
exit(1);
}
}
nlist = *neighborlist;
index = 0;
#else /* not TRILIBRARY */
if (!quiet) {
printf("Writing %s.\n", neighborfilename);
}
outfile = fopen(neighborfilename, "w");
if (outfile == (FILE *) NULL) {
printf(" Error: Cannot create file %s.\n", neighborfilename);
exit(1);
}
/* Number of triangles, three edges per triangle. */
fprintf(outfile, "%ld %d\n", triangles.items, 3);
#endif /* not TRILIBRARY */
traversalinit(&triangles);
triangleloop.tri = triangletraverse();
triangleloop.orient = 0;
elementnumber = firstnumber;
while (triangleloop.tri != (triangle *) NULL) {
* (int *) (triangleloop.tri + 6) = elementnumber;
triangleloop.tri = triangletraverse();
elementnumber++;
}
* (int *) (dummytri + 6) = -1;
traversalinit(&triangles);
triangleloop.tri = triangletraverse();
elementnumber = 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, "%4d %d %d %d\n", elementnumber, neighbor1, neighbor2, neighbor3);
#endif /* not TRILIBRARY */
triangleloop.tri = triangletraverse();
elementnumber++;
}
#ifndef TRILIBRARY
finishfile(outfile, argc, argv);
#endif /* 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
void writeoff(offfilename, argc, argv)
char *offfilename;
int argc;
char **argv;
{
FILE *outfile;
struct triedge triangleloop;
point pointloop;
point p1, p2, p3;
if (!quiet) {
printf("Writing %s.\n", offfilename);
}
outfile = fopen(offfilename, "w");
if (outfile == (FILE *) NULL) {
printf(" Error: Cannot create file %s.\n", offfilename);
exit(1);
}
/* Number of points, triangles, and edges. */
fprintf(outfile, "OFF\n%ld %ld %ld\n", points.items, triangles.items,
edges);
/* Write the points. */
traversalinit(&points);
pointloop = pointtraverse();
while (pointloop != (point) NULL) {
/* The "0.0" is here because the OFF format uses 3D coordinates. */
fprintf(outfile, " %.17g %.17g %.17g\n", pointloop[0],
pointloop[1], 0.0);
pointloop = pointtraverse();
}
/* Write the triangles. */
traversalinit(&triangles);
triangleloop.tri = triangletraverse();
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", pointmark(p1) - 1,
pointmark(p2) - 1, pointmark(p3) - 1);
triangleloop.tri = triangletraverse();
}
finishfile(outfile, argc, argv);
}
#endif /* not TRILIBRARY */
/** **/
/** **/
/********* File I/O routines end here *********/
/*****************************************************************************/
/* */
/* quality_statistics() Print statistics about the quality of the mesh. */
/* */
/*****************************************************************************/
void quality_statistics()
{
struct triedge triangleloop;
point 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 = xmax - xmin + ymax - 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(&triangles);
triangleloop.tri = triangletraverse();
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(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();
}
shortest = sqrt(shortest);
longest = sqrt(longest);
minaltitude = sqrt(minaltitude);
worstaspect = sqrt(worstaspect);
smallestarea *= 2.0;
biggestarea *= 2.0;
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(" 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(
" (Triangle 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. */
/* */
/*****************************************************************************/
void statistics()
{
printf("\nStatistics:\n\n");
printf(" Input points: %d\n", inpoints);
if (refine) {
printf(" Input triangles: %d\n", inelements);
}
if (poly) {
printf(" Input segments: %d\n", insegments);
if (!refine) {
printf(" Input holes: %d\n", holes);
}
}
printf("\n Mesh points: %ld\n", points.items);
printf(" Mesh triangles: %ld\n", triangles.items);
printf(" Mesh edges: %ld\n", edges);
if (poly || refine) {
printf(" Mesh boundary edges: %ld\n", hullsize);
printf(" Mesh segments: %ld\n\n", shelles.items);
} else {
printf(" Mesh convex hull edges: %ld\n\n", hullsize);
}
if (verbose) {
quality_statistics();
printf("Memory allocation statistics:\n\n");
printf(" Maximum number of points: %ld\n", points.maxitems);
printf(" Maximum number of triangles: %ld\n", triangles.maxitems);
if (shelles.maxitems > 0) {
printf(" Maximum number of segments: %ld\n", shelles.maxitems);
}
if (viri.maxitems > 0) {
printf(" Maximum number of viri: %ld\n", viri.maxitems);
}
if (badsegments.maxitems > 0) {
printf(" Maximum number of encroached segments: %ld\n",
badsegments.maxitems);
}
if (badtriangles.maxitems > 0) {
printf(" Maximum number of bad triangles: %ld\n",
badtriangles.maxitems);
}
if (splaynodes.maxitems > 0) {
printf(" Maximum number of splay tree nodes: %ld\n",
splaynodes.maxitems);
}
printf(" Approximate heap memory use (bytes): %ld\n\n",
points.maxitems * points.itembytes
+ triangles.maxitems * triangles.itembytes
+ shelles.maxitems * shelles.itembytes
+ viri.maxitems * viri.itembytes
+ badsegments.maxitems * badsegments.itembytes
+ badtriangles.maxitems * badtriangles.itembytes
+ splaynodes.maxitems * splaynodes.itembytes);
printf("Algorithmic statistics:\n\n");
printf(" Number of incircle tests: %ld\n", incirclecount);
printf(" Number of orientation tests: %ld\n", counterclockcount);
if (hyperbolacount > 0) {
printf(" Number of right-of-hyperbola tests: %ld\n",
hyperbolacount);
}
if (circumcentercount > 0) {
printf(" Number of circumcenter computations: %ld\n",
circumcentercount);
}
if (circletopcount > 0) {
printf(" Number of circle top computations: %ld\n",
circletopcount); }
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 points 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
void triangulate(triswitches, in, out, vorout)
char *triswitches;
struct triangulateio *in;
struct triangulateio *out;
struct triangulateio *vorout;
#else /* not TRILIBRARY */
int main(argc, argv)
int argc;
char **argv;
#endif /* not TRILIBRARY */
{
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 /* NO_TIMER */
#ifndef NO_TIMER
gettimeofday(&tv0, &tz);
#endif /* NO_TIMER */
triangleinit();
#ifdef TRILIBRARY
parsecommandline(1, &triswitches);
#else /* not TRILIBRARY */
parsecommandline(argc, argv);
#endif /* not TRILIBRARY */
#ifdef TRILIBRARY
transfernodes(in->pointlist, in->pointattributelist, in->pointmarkerlist,
in->numberofpoints, in->numberofpointattributes);
#else /* not TRILIBRARY */
readnodes(innodefilename, inpolyfilename, &polyfile);
#endif /* not TRILIBRARY */
#ifndef NO_TIMER
if (!quiet) {
gettimeofday(&tv1, &tz);
}
#endif /* NO_TIMER */
#ifdef CDT_ONLY
hullsize = delaunay(); /* Triangulate the points. */
#else /* not CDT_ONLY */
if (refine) {
/* Read and reconstruct a mesh. */
#ifdef TRILIBRARY
hullsize = reconstruct(in->trianglelist, in->triangleattributelist,
in->trianglearealist, in->numberoftriangles,
in->numberofcorners, in->numberoftriangleattributes,
in->segmentlist, in->segmentmarkerlist,
in->numberofsegments);
#else /* not TRILIBRARY */
hullsize = reconstruct(inelefilename, areafilename, inpolyfilename,
polyfile);
#endif /* not TRILIBRARY */
} else {
hullsize = delaunay(); /* Triangulate the points. */
}
#endif /* not CDT_ONLY */
#ifndef NO_TIMER
if (!quiet) {
gettimeofday(&tv2, &tz);
if (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 /* NO_TIMER */
/* Ensure that no point can be mistaken for a triangular bounding */
/* box point in insertsite(). */
infpoint1 = (point) NULL;
infpoint2 = (point) NULL;
infpoint3 = (point) NULL;
if (useshelles) {
checksegments = 1; /* Segments will be introduced next. */
if (!refine) {
/* Insert PSLG segments and/or convex hull segments. */
#ifdef TRILIBRARY
insegments = formskeleton(in->segmentlist, in->segmentmarkerlist,
in->numberofsegments);
#else /* not TRILIBRARY */
insegments = formskeleton(polyfile, inpolyfilename);
#endif /* not TRILIBRARY */
}
}
#ifndef NO_TIMER
if (!quiet) {
gettimeofday(&tv3, &tz);
if (useshelles && !refine) {
printf("Segment milliseconds: %ld\n", 1000l * (tv3.tv_sec - tv2.tv_sec)
+ (tv3.tv_usec - tv2.tv_usec) / 1000l);
}
}
#endif /* NO_TIMER */
if (poly) {
#ifdef TRILIBRARY
holearray = in->holelist;
holes = in->numberofholes;
regionarray = in->regionlist;
regions = in->numberofregions;
#else /* not TRILIBRARY */
readholes(polyfile, inpolyfilename, &holearray, &holes,
®ionarray, ®ions);
#endif /* not TRILIBRARY */
if (!refine) {
/* Carve out holes and concavities. */
carveholes(holearray, holes, regionarray, 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. */
holes = 0;
regions = 0;
}
#ifndef NO_TIMER
if (!quiet) {
gettimeofday(&tv4, &tz);
if (poly && !refine) {
printf("Hole milliseconds: %ld\n", 1000l * (tv4.tv_sec - tv3.tv_sec)
+ (tv4.tv_usec - tv3.tv_usec) / 1000l);
}
}
#endif /* NO_TIMER */
#ifndef CDT_ONLY
if (quality) {
enforcequality(); /* Enforce angle and area constraints. */
}
#endif /* not CDT_ONLY */
#ifndef NO_TIMER
if (!quiet) {
gettimeofday(&tv5, &tz);
#ifndef CDT_ONLY
if (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 /* NO_TIMER */
/* Compute the number of edges. */
edges = (3l * triangles.items + hullsize) / 2l;
if (order > 1) {
highorder(); /* Promote elements to higher polynomial order. */
}
if (!quiet) {
printf("\n");
}
#ifdef TRILIBRARY
out->numberofpoints = points.items;
out->numberofpointattributes = nextras; out->numberoftriangles = triangles.items;
out->numberofcorners = (order + 1) * (order + 2) / 2;
out->numberoftriangleattributes = eextras;
out->numberofedges = edges;
if (useshelles) {
out->numberofsegments = shelles.items;
} else {
out->numberofsegments = hullsize;
}
if (vorout != (struct triangulateio *) NULL) {
vorout->numberofpoints = triangles.items;
vorout->numberofpointattributes = nextras;
vorout->numberofedges = 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 (nonodewritten || (noiterationnum && readnodefile)) {
if (!quiet) {
#ifdef TRILIBRARY
printf("NOT writing points.\n");
#else /* not TRILIBRARY */
printf("NOT writing a .node file.\n");
#endif /* not TRILIBRARY */
}
numbernodes(); /* We must remember to number the points. */
} else {
#ifdef TRILIBRARY
writenodes(&out->pointlist, &out->pointattributelist,
&out->pointmarkerlist);
#else /* not TRILIBRARY */
writenodes(outnodefilename, argc, argv); /* Numbers the points too. */
#endif /* TRILIBRARY */
}
if (noelewritten) {
if (!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(&out->trianglelist, &out->triangleattributelist);
#else /* not TRILIBRARY */
writeelements(outelefilename, argc, argv);
#endif /* not TRILIBRARY */
}
/* The -c switch (convex switch) causes a PSLG to be written */
/* even if none was read. */
if (poly || convex) {
/* If not using iteration numbers, don't overwrite the .poly file. */
if (nopolywritten || noiterationnum) {
if (!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(&out->segmentlist, &out->segmentmarkerlist);
out->numberofholes = holes;
out->numberofregions = regions;
if (poly) {
out->holelist = in->holelist;
out->regionlist = in->regionlist;
} else { out->holelist = (REAL *) NULL;
out->regionlist = (REAL *) NULL;
}
#else /* not TRILIBRARY */
writepoly(outpolyfilename, holearray, holes, regionarray, regions,
argc, argv);
#endif /* not TRILIBRARY */
}
}
#ifndef TRILIBRARY
#ifndef CDT_ONLY
if (regions > 0) {
free(regionarray);
}
#endif /* not CDT_ONLY */
if (holes > 0) {
free(holearray);
}
if (geomview) {
writeoff(offfilename, argc, argv);
}
#endif /* not TRILIBRARY */
if (edgesout) {
#ifdef TRILIBRARY
writeedges(&out->edgelist, &out->edgemarkerlist);
#else /* not TRILIBRARY */
writeedges(edgefilename, argc, argv);
#endif /* not TRILIBRARY */
}
if (voronoi) {
#ifdef TRILIBRARY
writevoronoi(&vorout->pointlist, &vorout->pointattributelist,
&vorout->pointmarkerlist, &vorout->edgelist,
&vorout->edgemarkerlist, &vorout->normlist);
#else /* not TRILIBRARY */
writevoronoi(vnodefilename, vedgefilename, argc, argv);
#endif /* not TRILIBRARY */
}
if (neighbors) {
#ifdef TRILIBRARY
writeneighbors(&out->neighborlist);
#else /* not TRILIBRARY */
writeneighbors(neighborfilename, argc, argv);
#endif /* not TRILIBRARY */
}
if (!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 /* NO_TIMER */
statistics();
}
#ifndef REDUCED
if (docheck) {
checkmesh();
checkdelaunay();
}
#endif /* not REDUCED */
triangledeinit();
#ifndef TRILIBRARY
return 0;#endif /* not TRILIBRARY */
}