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triangle.c
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1/*****************************************************************************/
2/* */
3/* 888888888 ,o, / 888 */
4/* 888 88o88o " o8888o 88o8888o o88888o 888 o88888o */
5/* 888 888 888 88b 888 888 888 888 888 d888 88b */
6/* 888 888 888 o88^o888 888 888 "88888" 888 8888oo888 */
7/* 888 888 888 C888 888 888 888 / 888 q888 */
8/* 888 888 888 "88o^888 888 888 Cb 888 "88oooo" */
9/* "8oo8D */
10/* */
11/* A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator. */
12/* (triangle.c) */
13/* */
14/* Version 1.6 */
15/* July 28, 2005 */
16/* */
17/* Copyright 1993, 1995, 1997, 1998, 2002, 2005 */
18/* Jonathan Richard Shewchuk */
19/* 2360 Woolsey #H */
20/* Berkeley, California 94705-1927 */
21/* jrs@cs.berkeley.edu */
22/* */
23/* This program may be freely redistributed under the condition that the */
24/* copyright notices (including this entire header and the copyright */
25/* notice printed when the `-h' switch is selected) are not removed, and */
26/* no compensation is received. Private, research, and institutional */
27/* use is free. You may distribute modified versions of this code UNDER */
28/* THE CONDITION THAT THIS CODE AND ANY MODIFICATIONS MADE TO IT IN THE */
29/* SAME FILE REMAIN UNDER COPYRIGHT OF THE ORIGINAL AUTHOR, BOTH SOURCE */
30/* AND OBJECT CODE ARE MADE FREELY AVAILABLE WITHOUT CHARGE, AND CLEAR */
31/* NOTICE IS GIVEN OF THE MODIFICATIONS. Distribution of this code as */
32/* part of a commercial system is permissible ONLY BY DIRECT ARRANGEMENT */
33/* WITH THE AUTHOR. (If you are not directly supplying this code to a */
34/* customer, and you are instead telling them how they can obtain it for */
35/* free, then you are not required to make any arrangement with me.) */
36/* */
37/* Hypertext instructions for Triangle are available on the Web at */
38/* */
39/* http://www.cs.cmu.edu/~quake/triangle.html */
40/* */
41/* Disclaimer: Neither I nor Carnegie Mellon warrant this code in any way */
42/* whatsoever. This code is provided "as-is". Use at your own risk. */
43/* */
44/* Some of the references listed below are marked with an asterisk. [*] */
45/* These references are available for downloading from the Web page */
46/* */
47/* http://www.cs.cmu.edu/~quake/triangle.research.html */
48/* */
49/* Three papers discussing aspects of Triangle are available. A short */
50/* overview appears in "Triangle: Engineering a 2D Quality Mesh */
51/* Generator and Delaunay Triangulator," in Applied Computational */
52/* Geometry: Towards Geometric Engineering, Ming C. Lin and Dinesh */
53/* Manocha, editors, Lecture Notes in Computer Science volume 1148, */
54/* pages 203-222, Springer-Verlag, Berlin, May 1996 (from the First ACM */
55/* Workshop on Applied Computational Geometry). [*] */
56/* */
57/* The algorithms are discussed in the greatest detail in "Delaunay */
58/* Refinement Algorithms for Triangular Mesh Generation," Computational */
59/* Geometry: Theory and Applications 22(1-3):21-74, May 2002. [*] */
60/* */
61/* More detail about the data structures may be found in my dissertation: */
62/* "Delaunay Refinement Mesh Generation," Ph.D. thesis, Technical Report */
63/* CMU-CS-97-137, School of Computer Science, Carnegie Mellon University, */
64/* Pittsburgh, Pennsylvania, 18 May 1997. [*] */
65/* */
66/* Triangle was created as part of the Quake Project in the School of */
67/* Computer Science at Carnegie Mellon University. For further */
68/* information, see Hesheng Bao, Jacobo Bielak, Omar Ghattas, Loukas F. */
69/* Kallivokas, David R. O'Hallaron, Jonathan R. Shewchuk, and Jifeng Xu, */
70/* "Large-scale Simulation of Elastic Wave Propagation in Heterogeneous */
71/* Media on Parallel Computers," Computer Methods in Applied Mechanics */
72/* and Engineering 152(1-2):85-102, 22 January 1998. */
73/* */
74/* Triangle's Delaunay refinement algorithm for quality mesh generation is */
75/* a hybrid of one due to Jim Ruppert, "A Delaunay Refinement Algorithm */
76/* for Quality 2-Dimensional Mesh Generation," Journal of Algorithms */
77/* 18(3):548-585, May 1995 [*], and one due to L. Paul Chew, "Guaranteed- */
78/* Quality Mesh Generation for Curved Surfaces," Proceedings of the Ninth */
79/* Annual Symposium on Computational Geometry (San Diego, California), */
80/* pages 274-280, Association for Computing Machinery, May 1993, */
81/* http://portal.acm.org/citation.cfm?id=161150 . */
82/* */
83/* The Delaunay refinement algorithm has been modified so that it meshes */
84/* domains with small input angles well, as described in Gary L. Miller, */
85/* Steven E. Pav, and Noel J. Walkington, "When and Why Ruppert's */
86/* Algorithm Works," Twelfth International Meshing Roundtable, pages */
87/* 91-102, Sandia National Laboratories, September 2003. [*] */
88/* */
89/* My implementation of the divide-and-conquer and incremental Delaunay */
90/* triangulation algorithms follows closely the presentation of Guibas */
91/* and Stolfi, even though I use a triangle-based data structure instead */
92/* of their quad-edge data structure. (In fact, I originally implemented */
93/* Triangle using the quad-edge data structure, but the switch to a */
94/* triangle-based data structure sped Triangle by a factor of two.) The */
95/* mesh manipulation primitives and the two aforementioned Delaunay */
96/* triangulation algorithms are described by Leonidas J. Guibas and Jorge */
97/* Stolfi, "Primitives for the Manipulation of General Subdivisions and */
98/* the Computation of Voronoi Diagrams," ACM Transactions on Graphics */
99/* 4(2):74-123, April 1985, http://portal.acm.org/citation.cfm?id=282923 .*/
100/* */
101/* Their O(n log n) divide-and-conquer algorithm is adapted from Der-Tsai */
102/* Lee and Bruce J. Schachter, "Two Algorithms for Constructing the */
103/* Delaunay Triangulation," International Journal of Computer and */
104/* Information Science 9(3):219-242, 1980. Triangle's improvement of the */
105/* divide-and-conquer algorithm by alternating between vertical and */
106/* horizontal cuts was introduced by Rex A. Dwyer, "A Faster Divide-and- */
107/* Conquer Algorithm for Constructing Delaunay Triangulations," */
108/* Algorithmica 2(2):137-151, 1987. */
109/* */
110/* The incremental insertion algorithm was first proposed by C. L. Lawson, */
111/* "Software for C1 Surface Interpolation," in Mathematical Software III, */
112/* John R. Rice, editor, Academic Press, New York, pp. 161-194, 1977. */
113/* For point location, I use the algorithm of Ernst P. Mucke, Isaac */
114/* Saias, and Binhai Zhu, "Fast Randomized Point Location Without */
115/* Preprocessing in Two- and Three-Dimensional Delaunay Triangulations," */
116/* Proceedings of the Twelfth Annual Symposium on Computational Geometry, */
117/* ACM, May 1996. [*] If I were to randomize the order of vertex */
118/* insertion (I currently don't bother), their result combined with the */
119/* result of Kenneth L. Clarkson and Peter W. Shor, "Applications of */
120/* Random Sampling in Computational Geometry II," Discrete & */
121/* Computational Geometry 4(1):387-421, 1989, would yield an expected */
122/* O(n^{4/3}) bound on running time. */
123/* */
124/* The O(n log n) sweepline Delaunay triangulation algorithm is taken from */
125/* Steven Fortune, "A Sweepline Algorithm for Voronoi Diagrams", */
126/* Algorithmica 2(2):153-174, 1987. A random sample of edges on the */
127/* boundary of the triangulation are maintained in a splay tree for the */
128/* purpose of point location. Splay trees are described by Daniel */
129/* Dominic Sleator and Robert Endre Tarjan, "Self-Adjusting Binary Search */
130/* Trees," Journal of the ACM 32(3):652-686, July 1985, */
131/* http://portal.acm.org/citation.cfm?id=3835 . */
132/* */
133/* The algorithms for exact computation of the signs of determinants are */
134/* described in Jonathan Richard Shewchuk, "Adaptive Precision Floating- */
135/* Point Arithmetic and Fast Robust Geometric Predicates," Discrete & */
136/* Computational Geometry 18(3):305-363, October 1997. (Also available */
137/* as Technical Report CMU-CS-96-140, School of Computer Science, */
138/* Carnegie Mellon University, Pittsburgh, Pennsylvania, May 1996.) [*] */
139/* An abbreviated version appears as Jonathan Richard Shewchuk, "Robust */
140/* Adaptive Floating-Point Geometric Predicates," Proceedings of the */
141/* Twelfth Annual Symposium on Computational Geometry, ACM, May 1996. [*] */
142/* Many of the ideas for my exact arithmetic routines originate with */
143/* Douglas M. Priest, "Algorithms for Arbitrary Precision Floating Point */
144/* Arithmetic," Tenth Symposium on Computer Arithmetic, pp. 132-143, IEEE */
145/* Computer Society Press, 1991. [*] Many of the ideas for the correct */
146/* evaluation of the signs of determinants are taken from Steven Fortune */
147/* and Christopher J. Van Wyk, "Efficient Exact Arithmetic for Computa- */
148/* tional Geometry," Proceedings of the Ninth Annual Symposium on */
149/* Computational Geometry, ACM, pp. 163-172, May 1993, and from Steven */
150/* Fortune, "Numerical Stability of Algorithms for 2D Delaunay Triangu- */
151/* lations," International Journal of Computational Geometry & Applica- */
152/* tions 5(1-2):193-213, March-June 1995. */
153/* */
154/* The method of inserting new vertices off-center (not precisely at the */
155/* circumcenter of every poor-quality triangle) is from Alper Ungor, */
156/* "Off-centers: A New Type of Steiner Points for Computing Size-Optimal */
157/* Quality-Guaranteed Delaunay Triangulations," Proceedings of LATIN */
158/* 2004 (Buenos Aires, Argentina), April 2004. */
159/* */
160/* For definitions of and results involving Delaunay triangulations, */
161/* constrained and conforming versions thereof, and other aspects of */
162/* triangular mesh generation, see the excellent survey by Marshall Bern */
163/* and David Eppstein, "Mesh Generation and Optimal Triangulation," in */
164/* Computing and Euclidean Geometry, Ding-Zhu Du and Frank Hwang, */
165/* editors, World Scientific, Singapore, pp. 23-90, 1992. [*] */
166/* */
167/* The time for incrementally adding PSLG (planar straight line graph) */
168/* segments to create a constrained Delaunay triangulation is probably */
169/* O(t^2) per segment in the worst case and O(t) per segment in the */
170/* common case, where t is the number of triangles that intersect the */
171/* segment before it is inserted. This doesn't count point location, */
172/* which can be much more expensive. I could improve this to O(d log d) */
173/* time, but d is usually quite small, so it's not worth the bother. */
174/* (This note does not apply when the -s switch is used, invoking a */
175/* different method is used to insert segments.) */
176/* */
177/* The time for deleting a vertex from a Delaunay triangulation is O(d^2) */
178/* in the worst case and O(d) in the common case, where d is the degree */
179/* of the vertex being deleted. I could improve this to O(d log d) time, */
180/* but d is usually quite small, so it's not worth the bother. */
181/* */
182/* Ruppert's Delaunay refinement algorithm typically generates triangles */
183/* at a linear rate (constant time per triangle) after the initial */
184/* triangulation is formed. There may be pathological cases where */
185/* quadratic time is required, but these never arise in practice. */
186/* */
187/* The geometric predicates (circumcenter calculations, segment */
188/* intersection formulae, etc.) appear in my "Lecture Notes on Geometric */
189/* Robustness" at http://www.cs.berkeley.edu/~jrs/mesh . */
190/* */
191/* If you make any improvements to this code, please please please let me */
192/* know, so that I may obtain the improvements. Even if you don't change */
193/* the code, I'd still love to hear what it's being used for. */
194/* */
195/*****************************************************************************/
196
197/* If yours is not a Unix system, define the NO_TIMER compiler switch to */
198/* remove the Unix-specific timing code. */
199
200#define NO_TIMER
201
202/* To insert lots of self-checks for internal errors, define the SELF_CHECK */
203/* symbol. This will slow down the program significantly. It is best to */
204/* define the symbol using the -DSELF_CHECK compiler switch, but you could */
205/* write "#define SELF_CHECK" below. If you are modifying this code, I */
206/* recommend you turn self-checks on until your work is debugged. */
207
208/* #define SELF_CHECK */
209
210/* To compile Triangle as a callable object library (triangle.o), define the */
211/* TRILIBRARY symbol. Read the file triangle.h for details on how to call */
212/* the procedure triangulate() that results. */
213
214#define TRILIBRARY
215
216/* It is possible to generate a smaller version of Triangle using one or */
217/* both of the following symbols. Define the REDUCED symbol to eliminate */
218/* all features that are primarily of research interest; specifically, the */
219/* -i, -F, -s, and -C switches. Define the CDT_ONLY symbol to eliminate */
220/* all meshing algorithms above and beyond constrained Delaunay */
221/* triangulation; specifically, the -r, -q, -a, -u, -D, -S, and -s */
222/* switches. These reductions are most likely to be useful when */
223/* generating an object library (triangle.o) by defining the TRILIBRARY */
224/* symbol. */
225
226#define REDUCED
227#define CDT_ONLY
228
229/* On some machines, my exact arithmetic routines might be defeated by the */
230/* use of internal extended precision floating-point registers. The best */
231/* way to solve this problem is to set the floating-point registers to use */
232/* single or double precision internally. On 80x86 processors, this may */
233/* be accomplished by setting the CPU86 symbol for the Microsoft C */
234/* compiler, or the LINUX symbol for the gcc compiler running on Linux. */
235/* */
236/* An inferior solution is to declare certain values as `volatile', thus */
237/* forcing them to be stored to memory and rounded off. Unfortunately, */
238/* this solution might slow Triangle down quite a bit. To use volatile */
239/* values, write "#define INEXACT volatile" below. Normally, however, */
240/* INEXACT should be defined to be nothing. ("#define INEXACT".) */
241/* */
242/* For more discussion, see http://www.cs.cmu.edu/~quake/robust.pc.html . */
243/* For yet more discussion, see Section 5 of my paper, "Adaptive Precision */
244/* Floating-Point Arithmetic and Fast Robust Geometric Predicates" (also */
245/* available as Section 6.6 of my dissertation). */
246
247/* #define CPU86 */
248/* #define LINUX */
249
250#define INEXACT /* Nothing */
251/* #define INEXACT volatile */
252
253/* Maximum number of characters in a file name (including the null). */
254
255#define FILENAMESIZE 2048
256
257/* Maximum number of characters in a line read from a file (including the */
258/* null). */
259
260#define INPUTLINESIZE 1024
261
262/* For efficiency, a variety of data structures are allocated in bulk. The */
263/* following constants determine how many of each structure is allocated */
264/* at once. */
265
266#define TRIPERBLOCK 4092 /* Number of triangles allocated at once. */
267#define SUBSEGPERBLOCK 508 /* Number of subsegments allocated at once. */
268#define VERTEXPERBLOCK 4092 /* Number of vertices allocated at once. */
269#define VIRUSPERBLOCK 1020 /* Number of virus triangles allocated at once. */
270/* Number of encroached subsegments allocated at once. */
271#define BADSUBSEGPERBLOCK 252
272/* Number of skinny triangles allocated at once. */
273#define BADTRIPERBLOCK 4092
274/* Number of flipped triangles allocated at once. */
275#define FLIPSTACKERPERBLOCK 252
276/* Number of splay tree nodes allocated at once. */
277#define SPLAYNODEPERBLOCK 508
278
279/* The vertex types. A DEADVERTEX has been deleted entirely. An */
280/* UNDEADVERTEX is not part of the mesh, but is written to the output */
281/* .node file and affects the node indexing in the other output files. */
282
283#define INPUTVERTEX 0
284#define SEGMENTVERTEX 1
285#define FREEVERTEX 2
286#define DEADVERTEX -32768
287#define UNDEADVERTEX -32767
288
289/* Two constants for algorithms based on random sampling. Both constants */
290/* have been chosen empirically to optimize their respective algorithms. */
291
292/* Used for the point location scheme of Mucke, Saias, and Zhu, to decide */
293/* how large a random sample of triangles to inspect. */
294
295#define SAMPLEFACTOR 11
296
297/* Used in Fortune's sweepline Delaunay algorithm to determine what fraction */
298/* of boundary edges should be maintained in the splay tree for point */
299/* location on the front. */
300
301#define SAMPLERATE 10
302
303/* A number that speaks for itself, every kissable digit. */
304
305#define PI 3.141592653589793238462643383279502884197169399375105820974944592308
306
307/* Another fave. */
308
309#define SQUAREROOTTWO 1.4142135623730950488016887242096980785696718753769480732
310
311/* And here's one for those of you who are intimidated by math. */
312
313#define ONETHIRD 0.333333333333333333333333333333333333333333333333333333333333
314
315#include <stdio.h>
316#include <stdlib.h>
317#include <string.h>
318#include <math.h>
319#ifndef NO_TIMER
320#include <sys/time.h>
321#endif /* not NO_TIMER */
322#ifdef CPU86
323#include <float.h>
324#endif /* CPU86 */
325#ifdef LINUX
326#include <fpu_control.h>
327#endif /* LINUX */
328#ifdef TRILIBRARY
329#include "triangle.h"
330#endif /* TRILIBRARY */
331
332/* A few forward declarations. */
333
334#ifndef TRILIBRARY
335char *readline();
336char *findfield();
337#endif /* not TRILIBRARY */
338
339/* Labels that signify the result of point location. The result of a */
340/* search indicates that the point falls in the interior of a triangle, on */
341/* an edge, on a vertex, or outside the mesh. */
342
343enum locateresult {INTRIANGLE, ONEDGE, ONVERTEX, OUTSIDE};
344
345/* Labels that signify the result of vertex insertion. The result indicates */
346/* that the vertex was inserted with complete success, was inserted but */
347/* encroaches upon a subsegment, was not inserted because it lies on a */
348/* segment, or was not inserted because another vertex occupies the same */
349/* location. */
350
351enum insertvertexresult {SUCCESSFULVERTEX, ENCROACHINGVERTEX, VIOLATINGVERTEX,
352 DUPLICATEVERTEX};
353
354/* Labels that signify the result of direction finding. The result */
355/* indicates that a segment connecting the two query points falls within */
356/* the direction triangle, along the left edge of the direction triangle, */
357/* or along the right edge of the direction triangle. */
358
359enum finddirectionresult {WITHIN, LEFTCOLLINEAR, RIGHTCOLLINEAR};
360
361/*****************************************************************************/
362/* */
363/* The basic mesh data structures */
364/* */
365/* There are three: vertices, triangles, and subsegments (abbreviated */
366/* `subseg'). These three data structures, linked by pointers, comprise */
367/* the mesh. A vertex simply represents a mesh vertex and its properties. */
368/* A triangle is a triangle. A subsegment is a special data structure used */
369/* to represent an impenetrable edge of the mesh (perhaps on the outer */
370/* boundary, on the boundary of a hole, or part of an internal boundary */
371/* separating two triangulated regions). Subsegments represent boundaries, */
372/* defined by the user, that triangles may not lie across. */
373/* */
374/* A triangle consists of a list of three vertices, a list of three */
375/* adjoining triangles, a list of three adjoining subsegments (when */
376/* segments exist), an arbitrary number of optional user-defined */
377/* floating-point attributes, and an optional area constraint. The latter */
378/* is an upper bound on the permissible area of each triangle in a region, */
379/* used for mesh refinement. */
380/* */
381/* For a triangle on a boundary of the mesh, some or all of the neighboring */
382/* triangles may not be present. For a triangle in the interior of the */
383/* mesh, often no neighboring subsegments are present. Such absent */
384/* triangles and subsegments are never represented by NULL pointers; they */
385/* are represented by two special records: `dummytri', the triangle that */
386/* fills "outer space", and `dummysub', the omnipresent subsegment. */
387/* `dummytri' and `dummysub' are used for several reasons; for instance, */
388/* they can be dereferenced and their contents examined without violating */
389/* protected memory. */
390/* */
391/* However, it is important to understand that a triangle includes other */
392/* information as well. The pointers to adjoining vertices, triangles, and */
393/* subsegments are ordered in a way that indicates their geometric relation */
394/* to each other. Furthermore, each of these pointers contains orientation */
395/* information. Each pointer to an adjoining triangle indicates which face */
396/* of that triangle is contacted. Similarly, each pointer to an adjoining */
397/* subsegment indicates which side of that subsegment is contacted, and how */
398/* the subsegment is oriented relative to the triangle. */
399/* */
400/* The data structure representing a subsegment may be thought to be */
401/* abutting the edge of one or two triangle data structures: either */
402/* sandwiched between two triangles, or resting against one triangle on an */
403/* exterior boundary or hole boundary. */
404/* */
405/* A subsegment consists of a list of four vertices--the vertices of the */
406/* subsegment, and the vertices of the segment it is a part of--a list of */
407/* two adjoining subsegments, and a list of two adjoining triangles. One */
408/* of the two adjoining triangles may not be present (though there should */
409/* always be one), and neighboring subsegments might not be present. */
410/* Subsegments also store a user-defined integer "boundary marker". */
411/* Typically, this integer is used to indicate what boundary conditions are */
412/* to be applied at that location in a finite element simulation. */
413/* */
414/* Like triangles, subsegments maintain information about the relative */
415/* orientation of neighboring objects. */
416/* */
417/* Vertices are relatively simple. A vertex is a list of floating-point */
418/* numbers, starting with the x, and y coordinates, followed by an */
419/* arbitrary number of optional user-defined floating-point attributes, */
420/* followed by an integer boundary marker. During the segment insertion */
421/* phase, there is also a pointer from each vertex to a triangle that may */
422/* contain it. Each pointer is not always correct, but when one is, it */
423/* speeds up segment insertion. These pointers are assigned values once */
424/* at the beginning of the segment insertion phase, and are not used or */
425/* updated except during this phase. Edge flipping during segment */
426/* insertion will render some of them incorrect. Hence, don't rely upon */
427/* them for anything. */
428/* */
429/* Other than the exception mentioned above, vertices have no information */
430/* about what triangles, subfacets, or subsegments they are linked to. */
431/* */
432/*****************************************************************************/
433
434/*****************************************************************************/
435/* */
436/* Handles */
437/* */
438/* The oriented triangle (`otri') and oriented subsegment (`osub') data */
439/* structures defined below do not themselves store any part of the mesh. */
440/* The mesh itself is made of `triangle's, `subseg's, and `vertex's. */
441/* */
442/* Oriented triangles and oriented subsegments will usually be referred to */
443/* as "handles." A handle is essentially a pointer into the mesh; it */
444/* allows you to "hold" one particular part of the mesh. Handles are used */
445/* to specify the regions in which one is traversing and modifying the mesh.*/
446/* A single `triangle' may be held by many handles, or none at all. (The */
447/* latter case is not a memory leak, because the triangle is still */
448/* connected to other triangles in the mesh.) */
449/* */
450/* An `otri' is a handle that holds a triangle. It holds a specific edge */
451/* of the triangle. An `osub' is a handle that holds a subsegment. It */
452/* holds either the left or right side of the subsegment. */
453/* */
454/* Navigation about the mesh is accomplished through a set of mesh */
455/* manipulation primitives, further below. Many of these primitives take */
456/* a handle and produce a new handle that holds the mesh near the first */
457/* handle. Other primitives take two handles and glue the corresponding */
458/* parts of the mesh together. The orientation of the handles is */
459/* important. For instance, when two triangles are glued together by the */
460/* bond() primitive, they are glued at the edges on which the handles lie. */
461/* */
462/* Because vertices have no information about which triangles they are */
463/* attached to, I commonly represent a vertex by use of a handle whose */
464/* origin is the vertex. A single handle can simultaneously represent a */
465/* triangle, an edge, and a vertex. */
466/* */
467/*****************************************************************************/
468
469/* The triangle data structure. Each triangle contains three pointers to */
470/* adjoining triangles, plus three pointers to vertices, plus three */
471/* pointers to subsegments (declared below; these pointers are usually */
472/* `dummysub'). It may or may not also contain user-defined attributes */
473/* and/or a floating-point "area constraint." It may also contain extra */
474/* pointers for nodes, when the user asks for high-order elements. */
475/* Because the size and structure of a `triangle' is not decided until */
476/* runtime, I haven't simply declared the type `triangle' as a struct. */
477
478typedef REAL **triangle; /* Really: typedef triangle *triangle */
479
480/* An oriented triangle: includes a pointer to a triangle and orientation. */
481/* The orientation denotes an edge of the triangle. Hence, there are */
482/* three possible orientations. By convention, each edge always points */
483/* counterclockwise about the corresponding triangle. */
484
485struct otri {
486 triangle *tri;
487 int orient; /* Ranges from 0 to 2. */
488};
489
490/* The subsegment data structure. Each subsegment contains two pointers to */
491/* adjoining subsegments, plus four pointers to vertices, plus two */
492/* pointers to adjoining triangles, plus one boundary marker, plus one */
493/* segment number. */
494
495typedef REAL **subseg; /* Really: typedef subseg *subseg */
496
497/* An oriented subsegment: includes a pointer to a subsegment and an */
498/* orientation. The orientation denotes a side of the edge. Hence, there */
499/* are two possible orientations. By convention, the edge is always */
500/* directed so that the "side" denoted is the right side of the edge. */
501
502struct osub {
503 subseg *ss;
504 int ssorient; /* Ranges from 0 to 1. */
505};
506
507/* The vertex data structure. Each vertex is actually an array of REALs. */
508/* The number of REALs is unknown until runtime. An integer boundary */
509/* marker, and sometimes a pointer to a triangle, is appended after the */
510/* REALs. */
511
512typedef REAL *vertex;
513
514/* A queue used to store encroached subsegments. Each subsegment's vertices */
515/* are stored so that we can check whether a subsegment is still the same. */
516
517struct badsubseg {
518 subseg encsubseg; /* An encroached subsegment. */
519 vertex subsegorg, subsegdest; /* Its two vertices. */
520};
521
522/* A queue used to store bad triangles. The key is the square of the cosine */
523/* of the smallest angle of the triangle. Each triangle's vertices are */
524/* stored so that one can check whether a triangle is still the same. */
525
526struct badtriang {
527 triangle poortri; /* A skinny or too-large triangle. */
528 REAL key; /* cos^2 of smallest (apical) angle. */
529 vertex triangorg, triangdest, triangapex; /* Its three vertices. */
530 struct badtriang *nexttriang; /* Pointer to next bad triangle. */
531};
532
533/* A stack of triangles flipped during the most recent vertex insertion. */
534/* The stack is used to undo the vertex insertion if the vertex encroaches */
535/* upon a subsegment. */
536
537struct flipstacker {
538 triangle flippedtri; /* A recently flipped triangle. */
539 struct flipstacker *prevflip; /* Previous flip in the stack. */
540};
541
542/* A node in a heap used to store events for the sweepline Delaunay */
543/* algorithm. Nodes do not point directly to their parents or children in */
544/* the heap. Instead, each node knows its position in the heap, and can */
545/* look up its parent and children in a separate array. The `eventptr' */
546/* points either to a `vertex' or to a triangle (in encoded format, so */
547/* that an orientation is included). In the latter case, the origin of */
548/* the oriented triangle is the apex of a "circle event" of the sweepline */
549/* algorithm. To distinguish site events from circle events, all circle */
550/* events are given an invalid (smaller than `xmin') x-coordinate `xkey'. */
551
552struct event {
553 REAL xkey, ykey; /* Coordinates of the event. */
554 VOID *eventptr; /* Can be a vertex or the location of a circle event. */
555 int heapposition; /* Marks this event's position in the heap. */
556};
557
558/* A node in the splay tree. Each node holds an oriented ghost triangle */
559/* that represents a boundary edge of the growing triangulation. When a */
560/* circle event covers two boundary edges with a triangle, so that they */
561/* are no longer boundary edges, those edges are not immediately deleted */
562/* from the tree; rather, they are lazily deleted when they are next */
563/* encountered. (Since only a random sample of boundary edges are kept */
564/* in the tree, lazy deletion is faster.) `keydest' is used to verify */
565/* that a triangle is still the same as when it entered the splay tree; if */
566/* it has been rotated (due to a circle event), it no longer represents a */
567/* boundary edge and should be deleted. */
568
569struct splaynode {
570 struct otri keyedge; /* Lprev of an edge on the front. */
571 vertex keydest; /* Used to verify that splay node is still live. */
572 struct splaynode *lchild, *rchild; /* Children in splay tree. */
573};
574
575/* A type used to allocate memory. firstblock is the first block of items. */
576/* nowblock is the block from which items are currently being allocated. */
577/* nextitem points to the next slab of free memory for an item. */
578/* deaditemstack is the head of a linked list (stack) of deallocated items */
579/* that can be recycled. unallocateditems is the number of items that */
580/* remain to be allocated from nowblock. */
581/* */
582/* Traversal is the process of walking through the entire list of items, and */
583/* is separate from allocation. Note that a traversal will visit items on */
584/* the "deaditemstack" stack as well as live items. pathblock points to */
585/* the block currently being traversed. pathitem points to the next item */
586/* to be traversed. pathitemsleft is the number of items that remain to */
587/* be traversed in pathblock. */
588/* */
589/* alignbytes determines how new records should be aligned in memory. */
590/* itembytes is the length of a record in bytes (after rounding up). */
591/* itemsperblock is the number of items allocated at once in a single */
592/* block. itemsfirstblock is the number of items in the first block, */
593/* which can vary from the others. items is the number of currently */
594/* allocated items. maxitems is the maximum number of items that have */
595/* been allocated at once; it is the current number of items plus the */
596/* number of records kept on deaditemstack. */
597
598struct memorypool {
599 VOID **firstblock, **nowblock;
600 VOID *nextitem;
601 VOID *deaditemstack;
602 VOID **pathblock;
603 VOID *pathitem;
604 int alignbytes;
605 int itembytes;
606 int itemsperblock;
607 int itemsfirstblock;
608 long items, maxitems;
609 int unallocateditems;
610 int pathitemsleft;
611};
612
613
614/* Global constants. */
615
616REAL splitter; /* Used to split REAL factors for exact multiplication. */
617REAL epsilon; /* Floating-point machine epsilon. */
618REAL resulterrbound;
619REAL ccwerrboundA, ccwerrboundB, ccwerrboundC;
620REAL iccerrboundA, iccerrboundB, iccerrboundC;
621REAL o3derrboundA, o3derrboundB, o3derrboundC;
622
623/* Random number seed is not constant, but I've made it global anyway. */
624
625unsigned long randomseed; /* Current random number seed. */
626
627
628/* Mesh data structure. Triangle operates on only one mesh, but the mesh */
629/* structure is used (instead of global variables) to allow reentrancy. */
630
631struct mesh {
632
633/* Variables used to allocate memory for triangles, subsegments, vertices, */
634/* viri (triangles being eaten), encroached segments, bad (skinny or too */
635/* large) triangles, and splay tree nodes. */
636
637 struct memorypool triangles;
638 struct memorypool subsegs;
639 struct memorypool vertices;
640 struct memorypool viri;
641 struct memorypool badsubsegs;
642 struct memorypool badtriangles;
643 struct memorypool flipstackers;
644 struct memorypool splaynodes;
645
646/* Variables that maintain the bad triangle queues. The queues are */
647/* ordered from 4095 (highest priority) to 0 (lowest priority). */
648
649 struct badtriang *queuefront[4096];
650 struct badtriang *queuetail[4096];
651 int nextnonemptyq[4096];
652 int firstnonemptyq;
653
654/* Variable that maintains the stack of recently flipped triangles. */
655
656 struct flipstacker *lastflip;
657
658/* Other variables. */
659
660 REAL xmin, xmax, ymin, ymax; /* x and y bounds. */
661 REAL xminextreme; /* Nonexistent x value used as a flag in sweepline. */
662 int invertices; /* Number of input vertices. */
663 int inelements; /* Number of input triangles. */
664 int insegments; /* Number of input segments. */
665 int holes; /* Number of input holes. */
666 int regions; /* Number of input regions. */
667 int undeads; /* Number of input vertices that don't appear in the mesh. */
668 long edges; /* Number of output edges. */
669 int mesh_dim; /* Dimension (ought to be 2). */
670 int nextras; /* Number of attributes per vertex. */
671 int eextras; /* Number of attributes per triangle. */
672 long hullsize; /* Number of edges in convex hull. */
673 int steinerleft; /* Number of Steiner points not yet used. */
674 int vertexmarkindex; /* Index to find boundary marker of a vertex. */
675 int vertex2triindex; /* Index to find a triangle adjacent to a vertex. */
676 int highorderindex; /* Index to find extra nodes for high-order elements. */
677 int elemattribindex; /* Index to find attributes of a triangle. */
678 int areaboundindex; /* Index to find area bound of a triangle. */
679 int checksegments; /* Are there segments in the triangulation yet? */
680 int checkquality; /* Has quality triangulation begun yet? */
681 int readnodefile; /* Has a .node file been read? */
682 long samples; /* Number of random samples for point location. */
683
684 long incirclecount; /* Number of incircle tests performed. */
685 long counterclockcount; /* Number of counterclockwise tests performed. */
686 long orient3dcount; /* Number of 3D orientation tests performed. */
687 long hyperbolacount; /* Number of right-of-hyperbola tests performed. */
688 long circumcentercount; /* Number of circumcenter calculations performed. */
689 long circletopcount; /* Number of circle top calculations performed. */
690
691/* Triangular bounding box vertices. */
692
693 vertex infvertex1, infvertex2, infvertex3;
694
695/* Pointer to the `triangle' that occupies all of "outer space." */
696
697 triangle *dummytri;
698 triangle *dummytribase; /* Keep base address so we can free() it later. */
699
700/* Pointer to the omnipresent subsegment. Referenced by any triangle or */
701/* subsegment that isn't really connected to a subsegment at that */
702/* location. */
703
704 subseg *dummysub;
705 subseg *dummysubbase; /* Keep base address so we can free() it later. */
706
707/* Pointer to a recently visited triangle. Improves point location if */
708/* proximate vertices are inserted sequentially. */
709
710 struct otri recenttri;
711
712}; /* End of `struct mesh'. */
713
714
715/* Data structure for command line switches and file names. This structure */
716/* is used (instead of global variables) to allow reentrancy. */
717
718struct behavior {
719
720/* Switches for the triangulator. */
721/* poly: -p switch. refine: -r switch. */
722/* quality: -q switch. */
723/* minangle: minimum angle bound, specified after -q switch. */
724/* goodangle: cosine squared of minangle. */
725/* offconstant: constant used to place off-center Steiner points. */
726/* vararea: -a switch without number. */
727/* fixedarea: -a switch with number. */
728/* maxarea: maximum area bound, specified after -a switch. */
729/* usertest: -u switch. */
730/* regionattrib: -A switch. convex: -c switch. */
731/* weighted: 1 for -w switch, 2 for -W switch. jettison: -j switch */
732/* firstnumber: inverse of -z switch. All items are numbered starting */
733/* from `firstnumber'. */
734/* edgesout: -e switch. voronoi: -v switch. */
735/* neighbors: -n switch. geomview: -g switch. */
736/* nobound: -B switch. nopolywritten: -P switch. */
737/* nonodewritten: -N switch. noelewritten: -E switch. */
738/* noiterationnum: -I switch. noholes: -O switch. */
739/* noexact: -X switch. */
740/* order: element order, specified after -o switch. */
741/* nobisect: count of how often -Y switch is selected. */
742/* steiner: maximum number of Steiner points, specified after -S switch. */
743/* incremental: -i switch. sweepline: -F switch. */
744/* dwyer: inverse of -l switch. */
745/* splitseg: -s switch. */
746/* conformdel: -D switch. docheck: -C switch. */
747/* quiet: -Q switch. verbose: count of how often -V switch is selected. */
748/* usesegments: -p, -r, -q, or -c switch; determines whether segments are */
749/* used at all. */
750/* */
751/* Read the instructions to find out the meaning of these switches. */
752
753 int poly, refine, quality, vararea, fixedarea, usertest;
754 int regionattrib, convex, weighted, jettison;
755 int firstnumber;
756 int edgesout, voronoi, neighbors, geomview;
757 int nobound, nopolywritten, nonodewritten, noelewritten, noiterationnum;
758 int noholes, noexact, conformdel;
759 int incremental, sweepline, dwyer;
760 int splitseg;
761 int docheck;
762 int quiet, verbose;
763 int usesegments;
764 int order;
765 int nobisect;
766 int steiner;
767 REAL minangle, goodangle, offconstant;
768 REAL maxarea;
769
770/* Variables for file names. */
771
772#ifndef TRILIBRARY
773 char innodefilename[FILENAMESIZE];
774 char inelefilename[FILENAMESIZE];
775 char inpolyfilename[FILENAMESIZE];
776 char areafilename[FILENAMESIZE];
777 char outnodefilename[FILENAMESIZE];
778 char outelefilename[FILENAMESIZE];
779 char outpolyfilename[FILENAMESIZE];
780 char edgefilename[FILENAMESIZE];
781 char vnodefilename[FILENAMESIZE];
782 char vedgefilename[FILENAMESIZE];
783 char neighborfilename[FILENAMESIZE];
784 char offfilename[FILENAMESIZE];
785#endif /* not TRILIBRARY */
786
787}; /* End of `struct behavior'. */
788
789
790/*****************************************************************************/
791/* */
792/* Mesh manipulation primitives. Each triangle contains three pointers to */
793/* other triangles, with orientations. Each pointer points not to the */
794/* first byte of a triangle, but to one of the first three bytes of a */
795/* triangle. It is necessary to extract both the triangle itself and the */
796/* orientation. To save memory, I keep both pieces of information in one */
797/* pointer. To make this possible, I assume that all triangles are aligned */
798/* to four-byte boundaries. The decode() routine below decodes a pointer, */
799/* extracting an orientation (in the range 0 to 2) and a pointer to the */
800/* beginning of a triangle. The encode() routine compresses a pointer to a */
801/* triangle and an orientation into a single pointer. My assumptions that */
802/* triangles are four-byte-aligned and that the `unsigned long' type is */
803/* long enough to hold a pointer are two of the few kludges in this program.*/
804/* */
805/* Subsegments are manipulated similarly. A pointer to a subsegment */
806/* carries both an address and an orientation in the range 0 to 1. */
807/* */
808/* The other primitives take an oriented triangle or oriented subsegment, */
809/* and return an oriented triangle or oriented subsegment or vertex; or */
810/* they change the connections in the data structure. */
811/* */
812/* Below, triangles and subsegments are denoted by their vertices. The */
813/* triangle abc has origin (org) a, destination (dest) b, and apex (apex) */
814/* c. These vertices occur in counterclockwise order about the triangle. */
815/* The handle abc may simultaneously denote vertex a, edge ab, and triangle */
816/* abc. */
817/* */
818/* Similarly, the subsegment ab has origin (sorg) a and destination (sdest) */
819/* b. If ab is thought to be directed upward (with b directly above a), */
820/* then the handle ab is thought to grasp the right side of ab, and may */
821/* simultaneously denote vertex a and edge ab. */
822/* */
823/* An asterisk (*) denotes a vertex whose identity is unknown. */
824/* */
825/* Given this notation, a partial list of mesh manipulation primitives */
826/* follows. */
827/* */
828/* */
829/* For triangles: */
830/* */
831/* sym: Find the abutting triangle; same edge. */
832/* sym(abc) -> ba* */
833/* */
834/* lnext: Find the next edge (counterclockwise) of a triangle. */
835/* lnext(abc) -> bca */
836/* */
837/* lprev: Find the previous edge (clockwise) of a triangle. */
838/* lprev(abc) -> cab */
839/* */
840/* onext: Find the next edge counterclockwise with the same origin. */
841/* onext(abc) -> ac* */
842/* */
843/* oprev: Find the next edge clockwise with the same origin. */
844/* oprev(abc) -> a*b */
845/* */
846/* dnext: Find the next edge counterclockwise with the same destination. */
847/* dnext(abc) -> *ba */
848/* */
849/* dprev: Find the next edge clockwise with the same destination. */
850/* dprev(abc) -> cb* */
851/* */
852/* rnext: Find the next edge (counterclockwise) of the adjacent triangle. */
853/* rnext(abc) -> *a* */
854/* */
855/* rprev: Find the previous edge (clockwise) of the adjacent triangle. */
856/* rprev(abc) -> b** */
857/* */
858/* org: Origin dest: Destination apex: Apex */
859/* org(abc) -> a dest(abc) -> b apex(abc) -> c */
860/* */
861/* bond: Bond two triangles together at the resepective handles. */
862/* bond(abc, bad) */
863/* */
864/* */
865/* For subsegments: */
866/* */
867/* ssym: Reverse the orientation of a subsegment. */
868/* ssym(ab) -> ba */
869/* */
870/* spivot: Find adjoining subsegment with the same origin. */
871/* spivot(ab) -> a* */
872/* */
873/* snext: Find next subsegment in sequence. */
874/* snext(ab) -> b* */
875/* */
876/* sorg: Origin sdest: Destination */
877/* sorg(ab) -> a sdest(ab) -> b */
878/* */
879/* sbond: Bond two subsegments together at the respective origins. */
880/* sbond(ab, ac) */
881/* */
882/* */
883/* For interacting tetrahedra and subfacets: */
884/* */
885/* tspivot: Find a subsegment abutting a triangle. */
886/* tspivot(abc) -> ba */
887/* */
888/* stpivot: Find a triangle abutting a subsegment. */
889/* stpivot(ab) -> ba* */
890/* */
891/* tsbond: Bond a triangle to a subsegment. */
892/* tsbond(abc, ba) */
893/* */
894/*****************************************************************************/
895
896/********* Mesh manipulation primitives begin here *********/
897/** **/
898/** **/
899
900/* Fast lookup arrays to speed some of the mesh manipulation primitives. */
901
902int plus1mod3[3] = {1, 2, 0};
903int minus1mod3[3] = {2, 0, 1};
904
905/********* Primitives for triangles *********/
906/* */
907/* */
908
909/* decode() converts a pointer to an oriented triangle. The orientation is */
910/* extracted from the two least significant bits of the pointer. */
911
912#define decode(ptr, otri) \
913 (otri).orient = (int) ((unsigned long) (ptr) & (unsigned long) 3l); \
914 (otri).tri = (triangle *) \
915 ((unsigned long) (ptr) ^ (unsigned long) (otri).orient)
916
917/* encode() compresses an oriented triangle into a single pointer. It */
918/* relies on the assumption that all triangles are aligned to four-byte */
919/* boundaries, so the two least significant bits of (otri).tri are zero. */
920
921#define encode(otri) \
922 (triangle) ((unsigned long) (otri).tri | (unsigned long) (otri).orient)
923
924/* The following handle manipulation primitives are all described by Guibas */
925/* and Stolfi. However, Guibas and Stolfi use an edge-based data */
926/* structure, whereas I use a triangle-based data structure. */
927
928/* sym() finds the abutting triangle, on the same edge. Note that the edge */
929/* direction is necessarily reversed, because the handle specified by an */
930/* oriented triangle is directed counterclockwise around the triangle. */
931
932#define sym(otri1, otri2) \
933 ptr = (otri1).tri[(otri1).orient]; \
934 decode(ptr, otri2);
935
936#define symself(otri) \
937 ptr = (otri).tri[(otri).orient]; \
938 decode(ptr, otri);
939
940/* lnext() finds the next edge (counterclockwise) of a triangle. */
941
942#define lnext(otri1, otri2) \
943 (otri2).tri = (otri1).tri; \
944 (otri2).orient = plus1mod3[(otri1).orient]
945
946#define lnextself(otri) \
947 (otri).orient = plus1mod3[(otri).orient]
948
949/* lprev() finds the previous edge (clockwise) of a triangle. */
950
951#define lprev(otri1, otri2) \
952 (otri2).tri = (otri1).tri; \
953 (otri2).orient = minus1mod3[(otri1).orient]
954
955#define lprevself(otri) \
956 (otri).orient = minus1mod3[(otri).orient]
957
958/* onext() spins counterclockwise around a vertex; that is, it finds the */
959/* next edge with the same origin in the counterclockwise direction. This */
960/* edge is part of a different triangle. */
961
962#define onext(otri1, otri2) \
963 lprev(otri1, otri2); \
964 symself(otri2);
965
966#define onextself(otri) \
967 lprevself(otri); \
968 symself(otri);
969
970/* oprev() spins clockwise around a vertex; that is, it finds the next edge */
971/* with the same origin in the clockwise direction. This edge is part of */
972/* a different triangle. */
973
974#define oprev(otri1, otri2) \
975 sym(otri1, otri2); \
976 lnextself(otri2);
977
978#define oprevself(otri) \
979 symself(otri); \
980 lnextself(otri);
981
982/* dnext() spins counterclockwise around a vertex; that is, it finds the */
983/* next edge with the same destination in the counterclockwise direction. */
984/* This edge is part of a different triangle. */
985
986#define dnext(otri1, otri2) \
987 sym(otri1, otri2); \
988 lprevself(otri2);
989
990#define dnextself(otri) \
991 symself(otri); \
992 lprevself(otri);
993
994/* dprev() spins clockwise around a vertex; that is, it finds the next edge */
995/* with the same destination in the clockwise direction. This edge is */
996/* part of a different triangle. */
997
998#define dprev(otri1, otri2) \
999 lnext(otri1, otri2); \
1000 symself(otri2);
1001
1002#define dprevself(otri) \
1003 lnextself(otri); \
1004 symself(otri);
1005
1006/* rnext() moves one edge counterclockwise about the adjacent triangle. */
1007/* (It's best understood by reading Guibas and Stolfi. It involves */
1008/* changing triangles twice.) */
1009
1010#define rnext(otri1, otri2) \
1011 sym(otri1, otri2); \
1012 lnextself(otri2); \
1013 symself(otri2);
1014
1015#define rnextself(otri) \
1016 symself(otri); \
1017 lnextself(otri); \
1018 symself(otri);
1019
1020/* rprev() moves one edge clockwise about the adjacent triangle. */
1021/* (It's best understood by reading Guibas and Stolfi. It involves */
1022/* changing triangles twice.) */
1023
1024#define rprev(otri1, otri2) \
1025 sym(otri1, otri2); \
1026 lprevself(otri2); \
1027 symself(otri2);
1028
1029#define rprevself(otri) \
1030 symself(otri); \
1031 lprevself(otri); \
1032 symself(otri);
1033
1034/* These primitives determine or set the origin, destination, or apex of a */
1035/* triangle. */
1036
1037#define org(otri, vertexptr) \
1038 vertexptr = (vertex) (otri).tri[plus1mod3[(otri).orient] + 3]
1039
1040#define dest(otri, vertexptr) \
1041 vertexptr = (vertex) (otri).tri[minus1mod3[(otri).orient] + 3]
1042
1043#define apex(otri, vertexptr) \
1044 vertexptr = (vertex) (otri).tri[(otri).orient + 3]
1045
1046#define setorg(otri, vertexptr) \
1047 (otri).tri[plus1mod3[(otri).orient] + 3] = (triangle) vertexptr
1048
1049#define setdest(otri, vertexptr) \
1050 (otri).tri[minus1mod3[(otri).orient] + 3] = (triangle) vertexptr
1051
1052#define setapex(otri, vertexptr) \
1053 (otri).tri[(otri).orient + 3] = (triangle) vertexptr
1054
1055/* Bond two triangles together. */
1056
1057#define bond(otri1, otri2) \
1058 (otri1).tri[(otri1).orient] = encode(otri2); \
1059 (otri2).tri[(otri2).orient] = encode(otri1)
1060
1061/* Dissolve a bond (from one side). Note that the other triangle will still */
1062/* think it's connected to this triangle. Usually, however, the other */
1063/* triangle is being deleted entirely, or bonded to another triangle, so */
1064/* it doesn't matter. */
1065
1066#define dissolve(otri) \
1067 (otri).tri[(otri).orient] = (triangle) m->dummytri
1068
1069/* Copy an oriented triangle. */
1070
1071#define otricopy(otri1, otri2) \
1072 (otri2).tri = (otri1).tri; \
1073 (otri2).orient = (otri1).orient
1074
1075/* Test for equality of oriented triangles. */
1076
1077#define otriequal(otri1, otri2) \
1078 (((otri1).tri == (otri2).tri) && \
1079 ((otri1).orient == (otri2).orient))
1080
1081/* Primitives to infect or cure a triangle with the virus. These rely on */
1082/* the assumption that all subsegments are aligned to four-byte boundaries.*/
1083
1084#define infect(otri) \
1085 (otri).tri[6] = (triangle) \
1086 ((unsigned long) (otri).tri[6] | (unsigned long) 2l)
1087
1088#define uninfect(otri) \
1089 (otri).tri[6] = (triangle) \
1090 ((unsigned long) (otri).tri[6] & ~ (unsigned long) 2l)
1091
1092/* Test a triangle for viral infection. */
1093
1094#define infected(otri) \
1095 (((unsigned long) (otri).tri[6] & (unsigned long) 2l) != 0l)
1096
1097/* Check or set a triangle's attributes. */
1098
1099#define elemattribute(otri, attnum) \
1100 ((REAL *) (otri).tri)[m->elemattribindex + (attnum)]
1101
1102#define setelemattribute(otri, attnum, value) \
1103 ((REAL *) (otri).tri)[m->elemattribindex + (attnum)] = value
1104
1105/* Check or set a triangle's maximum area bound. */
1106
1107#define areabound(otri) ((REAL *) (otri).tri)[m->areaboundindex]
1108
1109#define setareabound(otri, value) \
1110 ((REAL *) (otri).tri)[m->areaboundindex] = value
1111
1112/* Check or set a triangle's deallocation. Its second pointer is set to */
1113/* NULL to indicate that it is not allocated. (Its first pointer is used */
1114/* for the stack of dead items.) Its fourth pointer (its first vertex) */
1115/* is set to NULL in case a `badtriang' structure points to it. */
1116
1117#define deadtri(tria) ((tria)[1] == (triangle) NULL)
1118
1119#define killtri(tria) \
1120 (tria)[1] = (triangle) NULL; \
1121 (tria)[3] = (triangle) NULL
1122
1123/********* Primitives for subsegments *********/
1124/* */
1125/* */
1126
1127/* sdecode() converts a pointer to an oriented subsegment. The orientation */
1128/* is extracted from the least significant bit of the pointer. The two */
1129/* least significant bits (one for orientation, one for viral infection) */
1130/* are masked out to produce the real pointer. */
1131
1132#define sdecode(sptr, osub) \
1133 (osub).ssorient = (int) ((unsigned long) (sptr) & (unsigned long) 1l); \
1134 (osub).ss = (subseg *) \
1135 ((unsigned long) (sptr) & ~ (unsigned long) 3l)
1136
1137/* sencode() compresses an oriented subsegment into a single pointer. It */
1138/* relies on the assumption that all subsegments are aligned to two-byte */
1139/* boundaries, so the least significant bit of (osub).ss is zero. */
1140
1141#define sencode(osub) \
1142 (subseg) ((unsigned long) (osub).ss | (unsigned long) (osub).ssorient)
1143
1144/* ssym() toggles the orientation of a subsegment. */
1145
1146#define ssym(osub1, osub2) \
1147 (osub2).ss = (osub1).ss; \
1148 (osub2).ssorient = 1 - (osub1).ssorient
1149
1150#define ssymself(osub) \
1151 (osub).ssorient = 1 - (osub).ssorient
1152
1153/* spivot() finds the other subsegment (from the same segment) that shares */
1154/* the same origin. */
1155
1156#define spivot(osub1, osub2) \
1157 sptr = (osub1).ss[(osub1).ssorient]; \
1158 sdecode(sptr, osub2)
1159
1160#define spivotself(osub) \
1161 sptr = (osub).ss[(osub).ssorient]; \
1162 sdecode(sptr, osub)
1163
1164/* snext() finds the next subsegment (from the same segment) in sequence; */
1165/* one whose origin is the input subsegment's destination. */
1166
1167#define snext(osub1, osub2) \
1168 sptr = (osub1).ss[1 - (osub1).ssorient]; \
1169 sdecode(sptr, osub2)
1170
1171#define snextself(osub) \
1172 sptr = (osub).ss[1 - (osub).ssorient]; \
1173 sdecode(sptr, osub)
1174
1175/* These primitives determine or set the origin or destination of a */
1176/* subsegment or the segment that includes it. */
1177
1178#define sorg(osub, vertexptr) \
1179 vertexptr = (vertex) (osub).ss[2 + (osub).ssorient]
1180
1181#define sdest(osub, vertexptr) \
1182 vertexptr = (vertex) (osub).ss[3 - (osub).ssorient]
1183
1184#define setsorg(osub, vertexptr) \
1185 (osub).ss[2 + (osub).ssorient] = (subseg) vertexptr
1186
1187#define setsdest(osub, vertexptr) \
1188 (osub).ss[3 - (osub).ssorient] = (subseg) vertexptr
1189
1190#define segorg(osub, vertexptr) \
1191 vertexptr = (vertex) (osub).ss[4 + (osub).ssorient]
1192
1193#define segdest(osub, vertexptr) \
1194 vertexptr = (vertex) (osub).ss[5 - (osub).ssorient]
1195
1196#define setsegorg(osub, vertexptr) \
1197 (osub).ss[4 + (osub).ssorient] = (subseg) vertexptr
1198
1199#define setsegdest(osub, vertexptr) \
1200 (osub).ss[5 - (osub).ssorient] = (subseg) vertexptr
1201
1202/* These primitives read or set a boundary marker. Boundary markers are */
1203/* used to hold user-defined tags for setting boundary conditions in */
1204/* finite element solvers. */
1205
1206#define mark(osub) (* (int *) ((osub).ss + 8))
1207
1208#define setmark(osub, value) \
1209 * (int *) ((osub).ss + 8) = value
1210
1211/* Bond two subsegments together. */
1212
1213#define sbond(osub1, osub2) \
1214 (osub1).ss[(osub1).ssorient] = sencode(osub2); \
1215 (osub2).ss[(osub2).ssorient] = sencode(osub1)
1216
1217/* Dissolve a subsegment bond (from one side). Note that the other */
1218/* subsegment will still think it's connected to this subsegment. */
1219
1220#define sdissolve(osub) \
1221 (osub).ss[(osub).ssorient] = (subseg) m->dummysub
1222
1223/* Copy a subsegment. */
1224
1225#define subsegcopy(osub1, osub2) \
1226 (osub2).ss = (osub1).ss; \
1227 (osub2).ssorient = (osub1).ssorient
1228
1229/* Test for equality of subsegments. */
1230
1231#define subsegequal(osub1, osub2) \
1232 (((osub1).ss == (osub2).ss) && \
1233 ((osub1).ssorient == (osub2).ssorient))
1234
1235/* Check or set a subsegment's deallocation. Its second pointer is set to */
1236/* NULL to indicate that it is not allocated. (Its first pointer is used */
1237/* for the stack of dead items.) Its third pointer (its first vertex) */
1238/* is set to NULL in case a `badsubseg' structure points to it. */
1239
1240#define deadsubseg(sub) ((sub)[1] == (subseg) NULL)
1241
1242#define killsubseg(sub) \
1243 (sub)[1] = (subseg) NULL; \
1244 (sub)[2] = (subseg) NULL
1245
1246/********* Primitives for interacting triangles and subsegments *********/
1247/* */
1248/* */
1249
1250/* tspivot() finds a subsegment abutting a triangle. */
1251
1252#define tspivot(otri, osub) \
1253 sptr = (subseg) (otri).tri[6 + (otri).orient]; \
1254 sdecode(sptr, osub)
1255
1256/* stpivot() finds a triangle abutting a subsegment. It requires that the */
1257/* variable `ptr' of type `triangle' be defined. */
1258
1259#define stpivot(osub, otri) \
1260 ptr = (triangle) (osub).ss[6 + (osub).ssorient]; \
1261 decode(ptr, otri)
1262
1263/* Bond a triangle to a subsegment. */
1264
1265#define tsbond(otri, osub) \
1266 (otri).tri[6 + (otri).orient] = (triangle) sencode(osub); \
1267 (osub).ss[6 + (osub).ssorient] = (subseg) encode(otri)
1268
1269/* Dissolve a bond (from the triangle side). */
1270
1271#define tsdissolve(otri) \
1272 (otri).tri[6 + (otri).orient] = (triangle) m->dummysub
1273
1274/* Dissolve a bond (from the subsegment side). */
1275
1276#define stdissolve(osub) \
1277 (osub).ss[6 + (osub).ssorient] = (subseg) m->dummytri
1278
1279/********* Primitives for vertices *********/
1280/* */
1281/* */
1282
1283#define vertexmark(vx) ((int *) (vx))[m->vertexmarkindex]
1284
1285#define setvertexmark(vx, value) \
1286 ((int *) (vx))[m->vertexmarkindex] = value
1287
1288#define vertextype(vx) ((int *) (vx))[m->vertexmarkindex + 1]
1289
1290#define setvertextype(vx, value) \
1291 ((int *) (vx))[m->vertexmarkindex + 1] = value
1292
1293#define vertex2tri(vx) ((triangle *) (vx))[m->vertex2triindex]
1294
1295#define setvertex2tri(vx, value) \
1296 ((triangle *) (vx))[m->vertex2triindex] = value
1297
1298/** **/
1299/** **/
1300/********* Mesh manipulation primitives end here *********/
1301
1302/********* User-defined triangle evaluation routine begins here *********/
1303/** **/
1304/** **/
1305
1306/*****************************************************************************/
1307/* */
1308/* triunsuitable() Determine if a triangle is unsuitable, and thus must */
1309/* be further refined. */
1310/* */
1311/* You may write your own procedure that decides whether or not a selected */
1312/* triangle is too big (and needs to be refined). There are two ways to do */
1313/* this. */
1314/* */
1315/* (1) Modify the procedure `triunsuitable' below, then recompile */
1316/* Triangle. */
1317/* */
1318/* (2) Define the symbol EXTERNAL_TEST (either by adding the definition */
1319/* to this file, or by using the appropriate compiler switch). This way, */
1320/* you can compile triangle.c separately from your test. Write your own */
1321/* `triunsuitable' procedure in a separate C file (using the same prototype */
1322/* as below). Compile it and link the object code with triangle.o. */
1323/* */
1324/* This procedure returns 1 if the triangle is too large and should be */
1325/* refined; 0 otherwise. */
1326/* */
1327/*****************************************************************************/
1328
1329#ifdef EXTERNAL_TEST
1330
1331int triunsuitable();
1332
1333#else /* not EXTERNAL_TEST */
1334
1335#ifdef ANSI_DECLARATORS
1336int triunsuitable(vertex triorg, vertex tridest, vertex triapex, REAL area )
1337#else /* not ANSI_DECLARATORS */
1338int triunsuitable(triorg, tridest, triapex, area)
1339vertex triorg; /* The triangle's origin vertex. */
1340vertex tridest; /* The triangle's destination vertex. */
1341vertex triapex; /* The triangle's apex vertex. */
1342REAL area; /* The area of the triangle. */
1343#endif /* not ANSI_DECLARATORS */
1344
1345{
1346 REAL dxoa, dxda, dxod;
1347 REAL dyoa, dyda, dyod;
1348 REAL oalen, dalen, odlen;
1349 REAL maxlen;
1350
1351 (void)area; /*LM: added to suppress warning */
1352
1353 dxoa = triorg[0] - triapex[0];
1354 dyoa = triorg[1] - triapex[1];
1355 dxda = tridest[0] - triapex[0];
1356 dyda = tridest[1] - triapex[1];
1357 dxod = triorg[0] - tridest[0];
1358 dyod = triorg[1] - tridest[1];
1359 /* Find the squares of the lengths of the triangle's three edges. */
1360 oalen = dxoa * dxoa + dyoa * dyoa;
1361 dalen = dxda * dxda + dyda * dyda;
1362 odlen = dxod * dxod + dyod * dyod;
1363 /* Find the square of the length of the longest edge. */
1364 maxlen = (dalen > oalen) ? dalen : oalen;
1365 maxlen = (odlen > maxlen) ? odlen : maxlen;
1366
1367 if (maxlen > 0.05 * (triorg[0] * triorg[0] + triorg[1] * triorg[1]) + 0.02) {
1368 return 1;
1369 } else {
1370 return 0;
1371 }
1372}
1373
1374#endif /* not EXTERNAL_TEST */
1375
1376/** **/
1377/** **/
1378/********* User-defined triangle evaluation routine ends here *********/
1379
1380/********* Memory allocation and program exit wrappers begin here *********/
1381/** **/
1382/** **/
1383
1384#ifdef ANSI_DECLARATORS
1385void triexit(int status)
1386#else /* not ANSI_DECLARATORS */
1387void triexit(status)
1388int status;
1389#endif /* not ANSI_DECLARATORS */
1390
1391{
1392 exit(status);
1393}
1394
1395#ifdef ANSI_DECLARATORS
1396VOID *trimalloc(int size)
1397#else /* not ANSI_DECLARATORS */
1398VOID *trimalloc(size)
1399int size;
1400#endif /* not ANSI_DECLARATORS */
1401
1402{
1403 VOID *memptr;
1404
1405 memptr = (VOID *) malloc((unsigned int) size);
1406 if (memptr == (VOID *) NULL) {
1407 printf("Error: Out of memory.\n");
1408 triexit(1);
1409 }
1410 return(memptr);
1411}
1412
1413#ifdef ANSI_DECLARATORS
1414void trifree(VOID *memptr)
1415#else /* not ANSI_DECLARATORS */
1416void trifree(memptr)
1417VOID *memptr;
1418#endif /* not ANSI_DECLARATORS */
1419
1420{
1421 free(memptr);
1422}
1423
1424/** **/
1425/** **/
1426/********* Memory allocation and program exit wrappers end here *********/
1427
1428/********* User interaction routines begin here *********/
1429/** **/
1430/** **/
1431
1432/*****************************************************************************/
1433/* */
1434/* syntax() Print list of command line switches. */
1435/* */
1436/*****************************************************************************/
1437
1438#ifndef TRILIBRARY
1439
1440void syntax()
1441{
1442#ifdef CDT_ONLY
1443#ifdef REDUCED
1444 printf("triangle [-pAcjevngBPNEIOXzo_lQVh] input_file\n");
1445#else /* not REDUCED */
1446 printf("triangle [-pAcjevngBPNEIOXzo_iFlCQVh] input_file\n");
1447#endif /* not REDUCED */
1448#else /* not CDT_ONLY */
1449#ifdef REDUCED
1450 printf("triangle [-prq__a__uAcDjevngBPNEIOXzo_YS__lQVh] input_file\n");
1451#else /* not REDUCED */
1452 printf("triangle [-prq__a__uAcDjevngBPNEIOXzo_YS__iFlsCQVh] input_file\n");
1453#endif /* not REDUCED */
1454#endif /* not CDT_ONLY */
1455
1456 printf(" -p Triangulates a Planar Straight Line Graph (.poly file).\n");
1457#ifndef CDT_ONLY
1458 printf(" -r Refines a previously generated mesh.\n");
1459 printf(
1460 " -q Quality mesh generation. A minimum angle may be specified.\n");
1461 printf(" -a Applies a maximum triangle area constraint.\n");
1462 printf(" -u Applies a user-defined triangle constraint.\n");
1463#endif /* not CDT_ONLY */
1464 printf(
1465 " -A Applies attributes to identify triangles in certain regions.\n");
1466 printf(" -c Encloses the convex hull with segments.\n");
1467#ifndef CDT_ONLY
1468 printf(" -D Conforming Delaunay: all triangles are truly Delaunay.\n");
1469#endif /* not CDT_ONLY */
1470/*
1471 printf(" -w Weighted Delaunay triangulation.\n");
1472 printf(" -W Regular triangulation (lower hull of a height field).\n");
1473*/
1474 printf(" -j Jettison unused vertices from output .node file.\n");
1475 printf(" -e Generates an edge list.\n");
1476 printf(" -v Generates a Voronoi diagram.\n");
1477 printf(" -n Generates a list of triangle neighbors.\n");
1478 printf(" -g Generates an .off file for Geomview.\n");
1479 printf(" -B Suppresses output of boundary information.\n");
1480 printf(" -P Suppresses output of .poly file.\n");
1481 printf(" -N Suppresses output of .node file.\n");
1482 printf(" -E Suppresses output of .ele file.\n");
1483 printf(" -I Suppresses mesh iteration numbers.\n");
1484 printf(" -O Ignores holes in .poly file.\n");
1485 printf(" -X Suppresses use of exact arithmetic.\n");
1486 printf(" -z Numbers all items starting from zero (rather than one).\n");
1487 printf(" -o2 Generates second-order subparametric elements.\n");
1488#ifndef CDT_ONLY
1489 printf(" -Y Suppresses boundary segment splitting.\n");
1490 printf(" -S Specifies maximum number of added Steiner points.\n");
1491#endif /* not CDT_ONLY */
1492#ifndef REDUCED
1493 printf(" -i Uses incremental method, rather than divide-and-conquer.\n");
1494 printf(" -F Uses Fortune's sweepline algorithm, rather than d-and-c.\n");
1495#endif /* not REDUCED */
1496 printf(" -l Uses vertical cuts only, rather than alternating cuts.\n");
1497#ifndef REDUCED
1498#ifndef CDT_ONLY
1499 printf(
1500 " -s Force segments into mesh by splitting (instead of using CDT).\n");
1501#endif /* not CDT_ONLY */
1502 printf(" -C Check consistency of final mesh.\n");
1503#endif /* not REDUCED */
1504 printf(" -Q Quiet: No terminal output except errors.\n");
1505 printf(" -V Verbose: Detailed information on what I'm doing.\n");
1506 printf(" -h Help: Detailed instructions for Triangle.\n");
1507 triexit(0);
1508}
1509
1510#endif /* not TRILIBRARY */
1511
1512/*****************************************************************************/
1513/* */
1514/* info() Print out complete instructions. */
1515/* */
1516/*****************************************************************************/
1517
1518#ifndef TRILIBRARY
1519
1520void info()
1521{
1522 printf("Triangle\n");
1523 printf(
1524"A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator.\n");
1525 printf("Version 1.6\n\n");
1526 printf(
1527"Copyright 1993, 1995, 1997, 1998, 2002, 2005 Jonathan Richard Shewchuk\n");
1528 printf("2360 Woolsey #H / Berkeley, California 94705-1927\n");
1529 printf("Bugs/comments to jrs@cs.berkeley.edu\n");
1530 printf(
1531"Created as part of the Quake project (tools for earthquake simulation).\n");
1532 printf(
1533"Supported in part by NSF Grant CMS-9318163 and an NSERC 1967 Scholarship.\n");
1534 printf("There is no warranty whatsoever. Use at your own risk.\n");
1535#ifdef SINGLE
1536 printf("This executable is compiled for single precision arithmetic.\n\n\n");
1537#else /* not SINGLE */
1538 printf("This executable is compiled for double precision arithmetic.\n\n\n");
1539#endif /* not SINGLE */
1540 printf(
1541"Triangle generates exact Delaunay triangulations, constrained Delaunay\n");
1542 printf(
1543"triangulations, conforming Delaunay triangulations, Voronoi diagrams, and\n");
1544 printf(
1545"high-quality triangular meshes. The latter can be generated with no small\n"
1546);
1547 printf(
1548"or large angles, and are thus suitable for finite element analysis. If no\n"
1549);
1550 printf(
1551"command line switch is specified, your .node input file is read, and the\n");
1552 printf(
1553"Delaunay triangulation is returned in .node and .ele output files. The\n");
1554 printf("command syntax is:\n\n");
1555 printf("triangle [-prq__a__uAcDjevngBPNEIOXzo_YS__iFlsCQVh] input_file\n\n");
1556 printf(
1557"Underscores indicate that numbers may optionally follow certain switches.\n");
1558 printf(
1559"Do not leave any space between a switch and its numeric parameter.\n");
1560 printf(
1561"input_file must be a file with extension .node, or extension .poly if the\n");
1562 printf(
1563"-p switch is used. If -r is used, you must supply .node and .ele files,\n");
1564 printf(
1565"and possibly a .poly file and an .area file as well. The formats of these\n"
1566);
1567 printf("files are described below.\n\n");
1568 printf("Command Line Switches:\n\n");
1569 printf(
1570" -p Reads a Planar Straight Line Graph (.poly file), which can specify\n"
1571);
1572 printf(
1573" vertices, segments, holes, regional attributes, and regional area\n");
1574 printf(
1575" constraints. Generates a constrained Delaunay triangulation (CDT)\n"
1576);
1577 printf(
1578" fitting the input; or, if -s, -q, -a, or -u is used, a conforming\n");
1579 printf(
1580" constrained Delaunay triangulation (CCDT). If you want a truly\n");
1581 printf(
1582" Delaunay (not just constrained Delaunay) triangulation, use -D as\n");
1583 printf(
1584" well. When -p is not used, Triangle reads a .node file by default.\n"
1585);
1586 printf(
1587" -r Refines a previously generated mesh. The mesh is read from a .node\n"
1588);
1589 printf(
1590" file and an .ele file. If -p is also used, a .poly file is read\n");
1591 printf(
1592" and used to constrain segments in the mesh. If -a is also used\n");
1593 printf(
1594" (with no number following), an .area file is read and used to\n");
1595 printf(
1596" impose area constraints on the mesh. Further details on refinement\n"
1597);
1598 printf(" appear below.\n");
1599 printf(
1600" -q Quality mesh generation by Delaunay refinement (a hybrid of Paul\n");
1601 printf(
1602" Chew's and Jim Ruppert's algorithms). Adds vertices to the mesh to\n"
1603);
1604 printf(
1605" ensure that all angles are between 20 and 140 degrees. An\n");
1606 printf(
1607" alternative bound on the minimum angle, replacing 20 degrees, may\n");
1608 printf(
1609" be specified after the `q'. The specified angle may include a\n");
1610 printf(
1611" decimal point, but not exponential notation. Note that a bound of\n"
1612);
1613 printf(
1614" theta degrees on the smallest angle also implies a bound of\n");
1615 printf(
1616" (180 - 2 theta) on the largest angle. If the minimum angle is 28.6\n"
1617);
1618 printf(
1619" degrees or smaller, Triangle is mathematically guaranteed to\n");
1620 printf(
1621" terminate (assuming infinite precision arithmetic--Triangle may\n");
1622 printf(
1623" fail to terminate if you run out of precision). In practice,\n");
1624 printf(
1625" Triangle often succeeds for minimum angles up to 34 degrees. For\n");
1626 printf(
1627" some meshes, however, you might need to reduce the minimum angle to\n"
1628);
1629 printf(
1630" avoid problems associated with insufficient floating-point\n");
1631 printf(" precision.\n");
1632 printf(
1633" -a Imposes a maximum triangle area. If a number follows the `a', no\n");
1634 printf(
1635" triangle is generated whose area is larger than that number. If no\n"
1636);
1637 printf(
1638" number is specified, an .area file (if -r is used) or .poly file\n");
1639 printf(
1640" (if -r is not used) specifies a set of maximum area constraints.\n");
1641 printf(
1642" An .area file contains a separate area constraint for each\n");
1643 printf(
1644" triangle, and is useful for refining a finite element mesh based on\n"
1645);
1646 printf(
1647" a posteriori error estimates. A .poly file can optionally contain\n"
1648);
1649 printf(
1650" an area constraint for each segment-bounded region, thereby\n");
1651 printf(
1652" controlling triangle densities in a first triangulation of a PSLG.\n"
1653);
1654 printf(
1655" You can impose both a fixed area constraint and a varying area\n");
1656 printf(
1657" constraint by invoking the -a switch twice, once with and once\n");
1658 printf(
1659" without a number following. Each area specified may include a\n");
1660 printf(" decimal point.\n");
1661 printf(
1662" -u Imposes a user-defined constraint on triangle size. There are two\n"
1663);
1664 printf(
1665" ways to use this feature. One is to edit the triunsuitable()\n");
1666 printf(
1667" procedure in triangle.c to encode any constraint you like, then\n");
1668 printf(
1669" recompile Triangle. The other is to compile triangle.c with the\n");
1670 printf(
1671" EXTERNAL_TEST symbol set (compiler switch -DEXTERNAL_TEST), then\n");
1672 printf(
1673" link Triangle with a separate object file that implements\n");
1674 printf(
1675" triunsuitable(). In either case, the -u switch causes the user-\n");
1676 printf(" defined test to be applied to every triangle.\n");
1677 printf(
1678" -A Assigns an additional floating-point attribute to each triangle\n");
1679 printf(
1680" that identifies what segment-bounded region each triangle belongs\n");
1681 printf(
1682" to. Attributes are assigned to regions by the .poly file. If a\n");
1683 printf(
1684" region is not explicitly marked by the .poly file, triangles in\n");
1685 printf(
1686" that region are assigned an attribute of zero. The -A switch has\n");
1687 printf(
1688" an effect only when the -p switch is used and the -r switch is not.\n"
1689);
1690 printf(
1691" -c Creates segments on the convex hull of the triangulation. If you\n");
1692 printf(
1693" are triangulating a vertex set, this switch causes a .poly file to\n"
1694);
1695 printf(
1696" be written, containing all edges of the convex hull. If you are\n");
1697 printf(
1698" triangulating a PSLG, this switch specifies that the whole convex\n");
1699 printf(
1700" hull of the PSLG should be triangulated, regardless of what\n");
1701 printf(
1702" segments the PSLG has. If you do not use this switch when\n");
1703 printf(
1704" triangulating a PSLG, Triangle assumes that you have identified the\n"
1705);
1706 printf(
1707" region to be triangulated by surrounding it with segments of the\n");
1708 printf(
1709" input PSLG. Beware: if you are not careful, this switch can cause\n"
1710);
1711 printf(
1712" the introduction of an extremely thin angle between a PSLG segment\n"
1713);
1714 printf(
1715" and a convex hull segment, which can cause overrefinement (and\n");
1716 printf(
1717" possibly failure if Triangle runs out of precision). If you are\n");
1718 printf(
1719" refining a mesh, the -c switch works differently: it causes a\n");
1720 printf(
1721" .poly file to be written containing the boundary edges of the mesh\n"
1722);
1723 printf(" (useful if no .poly file was read).\n");
1724 printf(
1725" -D Conforming Delaunay triangulation: use this switch if you want to\n"
1726);
1727 printf(
1728" ensure that all the triangles in the mesh are Delaunay, and not\n");
1729 printf(
1730" merely constrained Delaunay; or if you want to ensure that all the\n"
1731);
1732 printf(
1733" Voronoi vertices lie within the triangulation. (Some finite volume\n"
1734);
1735 printf(
1736" methods have this requirement.) This switch invokes Ruppert's\n");
1737 printf(
1738" original algorithm, which splits every subsegment whose diametral\n");
1739 printf(
1740" circle is encroached. It usually increases the number of vertices\n"
1741);
1742 printf(" and triangles.\n");
1743 printf(
1744" -j Jettisons vertices that are not part of the final triangulation\n");
1745 printf(
1746" from the output .node file. By default, Triangle copies all\n");
1747 printf(
1748" vertices in the input .node file to the output .node file, in the\n");
1749 printf(
1750" same order, so their indices do not change. The -j switch prevents\n"
1751);
1752 printf(
1753" duplicated input vertices, or vertices `eaten' by holes, from\n");
1754 printf(
1755" appearing in the output .node file. Thus, if two input vertices\n");
1756 printf(
1757" have exactly the same coordinates, only the first appears in the\n");
1758 printf(
1759" output. If any vertices are jettisoned, the vertex numbering in\n");
1760 printf(
1761" the output .node file differs from that of the input .node file.\n");
1762 printf(
1763" -e Outputs (to an .edge file) a list of edges of the triangulation.\n");
1764 printf(
1765" -v Outputs the Voronoi diagram associated with the triangulation.\n");
1766 printf(
1767" Does not attempt to detect degeneracies, so some Voronoi vertices\n");
1768 printf(
1769" may be duplicated. See the discussion of Voronoi diagrams below.\n");
1770 printf(
1771" -n Outputs (to a .neigh file) a list of triangles neighboring each\n");
1772 printf(" triangle.\n");
1773 printf(
1774" -g Outputs the mesh to an Object File Format (.off) file, suitable for\n"
1775);
1776 printf(" viewing with the Geometry Center's Geomview package.\n");
1777 printf(
1778" -B No boundary markers in the output .node, .poly, and .edge output\n");
1779 printf(
1780" files. See the detailed discussion of boundary markers below.\n");
1781 printf(
1782" -P No output .poly file. Saves disk space, but you lose the ability\n");
1783 printf(
1784" to maintain constraining segments on later refinements of the mesh.\n"
1785);
1786 printf(" -N No output .node file.\n");
1787 printf(" -E No output .ele file.\n");
1788 printf(
1789" -I No iteration numbers. Suppresses the output of .node and .poly\n");
1790 printf(
1791" files, so your input files won't be overwritten. (If your input is\n"
1792);
1793 printf(
1794" a .poly file only, a .node file is written.) Cannot be used with\n");
1795 printf(
1796" the -r switch, because that would overwrite your input .ele file.\n");
1797 printf(
1798" Shouldn't be used with the -q, -a, -u, or -s switch if you are\n");
1799 printf(
1800" using a .node file for input, because no .node file is written, so\n"
1801);
1802 printf(" there is no record of any added Steiner points.\n");
1803 printf(" -O No holes. Ignores the holes in the .poly file.\n");
1804 printf(
1805" -X No exact arithmetic. Normally, Triangle uses exact floating-point\n"
1806);
1807 printf(
1808" arithmetic for certain tests if it thinks the inexact tests are not\n"
1809);
1810 printf(
1811" accurate enough. Exact arithmetic ensures the robustness of the\n");
1812 printf(
1813" triangulation algorithms, despite floating-point roundoff error.\n");
1814 printf(
1815" Disabling exact arithmetic with the -X switch causes a small\n");
1816 printf(
1817" improvement in speed and creates the possibility that Triangle will\n"
1818);
1819 printf(" fail to produce a valid mesh. Not recommended.\n");
1820 printf(
1821" -z Numbers all items starting from zero (rather than one). Note that\n"
1822);
1823 printf(
1824" this switch is normally overridden by the value used to number the\n"
1825);
1826 printf(
1827" first vertex of the input .node or .poly file. However, this\n");
1828 printf(
1829" switch is useful when calling Triangle from another program.\n");
1830 printf(
1831" -o2 Generates second-order subparametric elements with six nodes each.\n"
1832);
1833 printf(
1834" -Y No new vertices on the boundary. This switch is useful when the\n");
1835 printf(
1836" mesh boundary must be preserved so that it conforms to some\n");
1837 printf(
1838" adjacent mesh. Be forewarned that you will probably sacrifice much\n"
1839);
1840 printf(
1841" of the quality of the mesh; Triangle will try, but the resulting\n");
1842 printf(
1843" mesh may contain poorly shaped triangles. Works well if all the\n");
1844 printf(
1845" boundary vertices are closely spaced. Specify this switch twice\n");
1846 printf(
1847" (`-YY') to prevent all segment splitting, including internal\n");
1848 printf(" boundaries.\n");
1849 printf(
1850" -S Specifies the maximum number of Steiner points (vertices that are\n");
1851 printf(
1852" not in the input, but are added to meet the constraints on minimum\n"
1853);
1854 printf(
1855" angle and maximum area). The default is to allow an unlimited\n");
1856 printf(
1857" number. If you specify this switch with no number after it,\n");
1858 printf(
1859" the limit is set to zero. Triangle always adds vertices at segment\n"
1860);
1861 printf(
1862" intersections, even if it needs to use more vertices than the limit\n"
1863);
1864 printf(
1865" you set. When Triangle inserts segments by splitting (-s), it\n");
1866 printf(
1867" always adds enough vertices to ensure that all the segments of the\n"
1868);
1869 printf(" PLSG are recovered, ignoring the limit if necessary.\n");
1870 printf(
1871" -i Uses an incremental rather than a divide-and-conquer algorithm to\n");
1872 printf(
1873" construct a Delaunay triangulation. Try it if the divide-and-\n");
1874 printf(" conquer algorithm fails.\n");
1875 printf(
1876" -F Uses Steven Fortune's sweepline algorithm to construct a Delaunay\n");
1877 printf(
1878" triangulation. Warning: does not use exact arithmetic for all\n");
1879 printf(" calculations. An exact result is not guaranteed.\n");
1880 printf(
1881" -l Uses only vertical cuts in the divide-and-conquer algorithm. By\n");
1882 printf(
1883" default, Triangle alternates between vertical and horizontal cuts,\n"
1884);
1885 printf(
1886" which usually improve the speed except with vertex sets that are\n");
1887 printf(
1888" small or short and wide. This switch is primarily of theoretical\n");
1889 printf(" interest.\n");
1890 printf(
1891" -s Specifies that segments should be forced into the triangulation by\n"
1892);
1893 printf(
1894" recursively splitting them at their midpoints, rather than by\n");
1895 printf(
1896" generating a constrained Delaunay triangulation. Segment splitting\n"
1897);
1898 printf(
1899" is true to Ruppert's original algorithm, but can create needlessly\n"
1900);
1901 printf(
1902" small triangles. This switch is primarily of theoretical interest.\n"
1903);
1904 printf(
1905" -C Check the consistency of the final mesh. Uses exact arithmetic for\n"
1906);
1907 printf(
1908" checking, even if the -X switch is used. Useful if you suspect\n");
1909 printf(" Triangle is buggy.\n");
1910 printf(
1911" -Q Quiet: Suppresses all explanation of what Triangle is doing,\n");
1912 printf(" unless an error occurs.\n");
1913 printf(
1914" -V Verbose: Gives detailed information about what Triangle is doing.\n"
1915);
1916 printf(
1917" Add more `V's for increasing amount of detail. `-V' is most\n");
1918 printf(
1919" useful; itgives information on algorithmic progress and much more\n");
1920 printf(
1921" detailed statistics. `-VV' gives vertex-by-vertex details, and\n");
1922 printf(
1923" prints so much that Triangle runs much more slowly. `-VVVV' gives\n"
1924);
1925 printf(" information only a debugger could love.\n");
1926 printf(" -h Help: Displays these instructions.\n");
1927 printf("\n");
1928 printf("Definitions:\n");
1929 printf("\n");
1930 printf(
1931" A Delaunay triangulation of a vertex set is a triangulation whose\n");
1932 printf(
1933" vertices are the vertex set, that covers the convex hull of the vertex\n");
1934 printf(
1935" set. A Delaunay triangulation has the property that no vertex lies\n");
1936 printf(
1937" inside the circumscribing circle (circle that passes through all three\n");
1938 printf(" vertices) of any triangle in the triangulation.\n\n");
1939 printf(
1940" A Voronoi diagram of a vertex set is a subdivision of the plane into\n");
1941 printf(
1942" polygonal cells (some of which may be unbounded, meaning infinitely\n");
1943 printf(
1944" large), where each cell is the set of points in the plane that are closer\n"
1945);
1946 printf(
1947" to some input vertex than to any other input vertex. The Voronoi diagram\n"
1948);
1949 printf(" is a geometric dual of the Delaunay triangulation.\n\n");
1950 printf(
1951" A Planar Straight Line Graph (PSLG) is a set of vertices and segments.\n");
1952 printf(
1953" Segments are simply edges, whose endpoints are all vertices in the PSLG.\n"
1954);
1955 printf(
1956" Segments may intersect each other only at their endpoints. The file\n");
1957 printf(" format for PSLGs (.poly files) is described below.\n\n");
1958 printf(
1959" A constrained Delaunay triangulation (CDT) of a PSLG is similar to a\n");
1960 printf(
1961" Delaunay triangulation, but each PSLG segment is present as a single edge\n"
1962);
1963 printf(
1964" of the CDT. (A constrained Delaunay triangulation is not truly a\n");
1965 printf(
1966" Delaunay triangulation, because some of its triangles might not be\n");
1967 printf(
1968" Delaunay.) By definition, a CDT does not have any vertices other than\n");
1969 printf(
1970" those specified in the input PSLG. Depending on context, a CDT might\n");
1971 printf(
1972" cover the convex hull of the PSLG, or it might cover only a segment-\n");
1973 printf(" bounded region (e.g. a polygon).\n\n");
1974 printf(
1975" A conforming Delaunay triangulation of a PSLG is a triangulation in which\n"
1976);
1977 printf(
1978" each triangle is truly Delaunay, and each PSLG segment is represented by\n"
1979);
1980 printf(
1981" a linear contiguous sequence of edges of the triangulation. New vertices\n"
1982);
1983 printf(
1984" (not part of the PSLG) may appear, and each input segment may have been\n");
1985 printf(
1986" subdivided into shorter edges (subsegments) by these additional vertices.\n"
1987);
1988 printf(
1989" The new vertices are frequently necessary to maintain the Delaunay\n");
1990 printf(" property while ensuring that every segment is represented.\n\n");
1991 printf(
1992" A conforming constrained Delaunay triangulation (CCDT) of a PSLG is a\n");
1993 printf(
1994" triangulation of a PSLG whose triangles are constrained Delaunay. New\n");
1995 printf(" vertices may appear, and input segments may be subdivided into\n");
1996 printf(
1997" subsegments, but not to guarantee that segments are respected; rather, to\n"
1998);
1999 printf(
2000" improve the quality of the triangles. The high-quality meshes produced\n");
2001 printf(
2002" by the -q switch are usually CCDTs, but can be made conforming Delaunay\n");
2003 printf(" with the -D switch.\n\n");
2004 printf("File Formats:\n\n");
2005 printf(
2006" All files may contain comments prefixed by the character '#'. Vertices,\n"
2007);
2008 printf(
2009" triangles, edges, holes, and maximum area constraints must be numbered\n");
2010 printf(
2011" consecutively, starting from either 1 or 0. Whichever you choose, all\n");
2012 printf(
2013" input files must be consistent; if the vertices are numbered from 1, so\n");
2014 printf(
2015" must be all other objects. Triangle automatically detects your choice\n");
2016 printf(
2017" while reading the .node (or .poly) file. (When calling Triangle from\n");
2018 printf(
2019" another program, use the -z switch if you wish to number objects from\n");
2020 printf(" zero.) Examples of these file formats are given below.\n\n");
2021 printf(" .node files:\n");
2022 printf(
2023" First line: <# of vertices> <dimension (must be 2)> <# of attributes>\n"
2024);
2025 printf(
2026" <# of boundary markers (0 or 1)>\n"
2027);
2028 printf(
2029" Remaining lines: <vertex #> <x> <y> [attributes] [boundary marker]\n");
2030 printf("\n");
2031 printf(
2032" The attributes, which are typically floating-point values of physical\n");
2033 printf(
2034" quantities (such as mass or conductivity) associated with the nodes of\n"
2035);
2036 printf(
2037" a finite element mesh, are copied unchanged to the output mesh. If -q,\n"
2038);
2039 printf(
2040" -a, -u, -D, or -s is selected, each new Steiner point added to the mesh\n"
2041);
2042 printf(" has attributes assigned to it by linear interpolation.\n\n");
2043 printf(
2044" If the fourth entry of the first line is `1', the last column of the\n");
2045 printf(
2046" remainder of the file is assumed to contain boundary markers. Boundary\n"
2047);
2048 printf(
2049" markers are used to identify boundary vertices and vertices resting on\n"
2050);
2051 printf(
2052" PSLG segments; a complete description appears in a section below. The\n"
2053);
2054 printf(
2055" .node file produced by Triangle contains boundary markers in the last\n");
2056 printf(" column unless they are suppressed by the -B switch.\n\n");
2057 printf(" .ele files:\n");
2058 printf(
2059" First line: <# of triangles> <nodes per triangle> <# of attributes>\n");
2060 printf(
2061" Remaining lines: <triangle #> <node> <node> <node> ... [attributes]\n");
2062 printf("\n");
2063 printf(
2064" Nodes are indices into the corresponding .node file. The first three\n");
2065 printf(
2066" nodes are the corner vertices, and are listed in counterclockwise order\n"
2067);
2068 printf(
2069" around each triangle. (The remaining nodes, if any, depend on the type\n"
2070);
2071 printf(" of finite element used.)\n\n");
2072 printf(
2073" The attributes are just like those of .node files. Because there is no\n"
2074);
2075 printf(
2076" simple mapping from input to output triangles, Triangle attempts to\n");
2077 printf(
2078" interpolate attributes, and may cause a lot of diffusion of attributes\n"
2079);
2080 printf(
2081" among nearby triangles as the triangulation is refined. Attributes do\n"
2082);
2083 printf(" not diffuse across segments, so attributes used to identify\n");
2084 printf(" segment-bounded regions remain intact.\n\n");
2085 printf(
2086" In .ele files produced by Triangle, each triangular element has three\n");
2087 printf(
2088" nodes (vertices) unless the -o2 switch is used, in which case\n");
2089 printf(
2090" subparametric quadratic elements with six nodes each are generated.\n");
2091 printf(
2092" The first three nodes are the corners in counterclockwise order, and\n");
2093 printf(
2094" the fourth, fifth, and sixth nodes lie on the midpoints of the edges\n");
2095 printf(
2096" opposite the first, second, and third vertices, respectively.\n");
2097 printf("\n");
2098 printf(" .poly files:\n");
2099 printf(
2100" First line: <# of vertices> <dimension (must be 2)> <# of attributes>\n"
2101);
2102 printf(
2103" <# of boundary markers (0 or 1)>\n"
2104);
2105 printf(
2106" Following lines: <vertex #> <x> <y> [attributes] [boundary marker]\n");
2107 printf(" One line: <# of segments> <# of boundary markers (0 or 1)>\n");
2108 printf(
2109" Following lines: <segment #> <endpoint> <endpoint> [boundary marker]\n");
2110 printf(" One line: <# of holes>\n");
2111 printf(" Following lines: <hole #> <x> <y>\n");
2112 printf(
2113" Optional line: <# of regional attributes and/or area constraints>\n");
2114 printf(
2115" Optional following lines: <region #> <x> <y> <attribute> <max area>\n");
2116 printf("\n");
2117 printf(
2118" A .poly file represents a PSLG, as well as some additional information.\n"
2119);
2120 printf(
2121" The first section lists all the vertices, and is identical to the\n");
2122 printf(
2123" format of .node files. <# of vertices> may be set to zero to indicate\n"
2124);
2125 printf(
2126" that the vertices are listed in a separate .node file; .poly files\n");
2127 printf(
2128" produced by Triangle always have this format. A vertex set represented\n"
2129);
2130 printf(
2131" this way has the advantage that it may easily be triangulated with or\n");
2132 printf(
2133" without segments (depending on whether the -p switch is invoked).\n");
2134 printf("\n");
2135 printf(
2136" The second section lists the segments. Segments are edges whose\n");
2137 printf(
2138" presence in the triangulation is enforced. (Depending on the choice of\n"
2139);
2140 printf(
2141" switches, segment might be subdivided into smaller edges). Each\n");
2142 printf(
2143" segment is specified by listing the indices of its two endpoints. This\n"
2144);
2145 printf(
2146" means that you must include its endpoints in the vertex list. Each\n");
2147 printf(" segment, like each point, may have a boundary marker.\n\n");
2148 printf(
2149" If -q, -a, -u, and -s are not selected, Triangle produces a constrained\n"
2150);
2151 printf(
2152" Delaunay triangulation (CDT), in which each segment appears as a single\n"
2153);
2154 printf(
2155" edge in the triangulation. If -q, -a, -u, or -s is selected, Triangle\n"
2156);
2157 printf(
2158" produces a conforming constrained Delaunay triangulation (CCDT), in\n");
2159 printf(
2160" which segments may be subdivided into smaller edges. If -D is\n");
2161 printf(
2162" selected, Triangle produces a conforming Delaunay triangulation, so\n");
2163 printf(
2164" that every triangle is Delaunay, and not just constrained Delaunay.\n");
2165 printf("\n");
2166 printf(
2167" The third section lists holes (and concavities, if -c is selected) in\n");
2168 printf(
2169" the triangulation. Holes are specified by identifying a point inside\n");
2170 printf(
2171" each hole. After the triangulation is formed, Triangle creates holes\n");
2172 printf(
2173" by eating triangles, spreading out from each hole point until its\n");
2174 printf(
2175" progress is blocked by segments in the PSLG. You must be careful to\n");
2176 printf(
2177" enclose each hole in segments, or your whole triangulation might be\n");
2178 printf(
2179" eaten away. If the two triangles abutting a segment are eaten, the\n");
2180 printf(
2181" segment itself is also eaten. Do not place a hole directly on a\n");
2182 printf(" segment; if you do, Triangle chooses one side of the segment\n");
2183 printf(" arbitrarily.\n\n");
2184 printf(
2185" The optional fourth section lists regional attributes (to be assigned\n");
2186 printf(
2187" to all triangles in a region) and regional constraints on the maximum\n");
2188 printf(
2189" triangle area. Triangle reads this section only if the -A switch is\n");
2190 printf(
2191" used or the -a switch is used without a number following it, and the -r\n"
2192);
2193 printf(
2194" switch is not used. Regional attributes and area constraints are\n");
2195 printf(
2196" propagated in the same manner as holes: you specify a point for each\n");
2197 printf(
2198" attribute and/or constraint, and the attribute and/or constraint\n");
2199 printf(
2200" affects the whole region (bounded by segments) containing the point.\n");
2201 printf(
2202" If two values are written on a line after the x and y coordinate, the\n");
2203 printf(
2204" first such value is assumed to be a regional attribute (but is only\n");
2205 printf(
2206" applied if the -A switch is selected), and the second value is assumed\n"
2207);
2208 printf(
2209" to be a regional area constraint (but is only applied if the -a switch\n"
2210);
2211 printf(
2212" is selected). You may specify just one value after the coordinates,\n");
2213 printf(
2214" which can serve as both an attribute and an area constraint, depending\n"
2215);
2216 printf(
2217" on the choice of switches. If you are using the -A and -a switches\n");
2218 printf(
2219" simultaneously and wish to assign an attribute to some region without\n");
2220 printf(" imposing an area constraint, use a negative maximum area.\n\n");
2221 printf(
2222" When a triangulation is created from a .poly file, you must either\n");
2223 printf(
2224" enclose the entire region to be triangulated in PSLG segments, or\n");
2225 printf(
2226" use the -c switch, which automatically creates extra segments that\n");
2227 printf(
2228" enclose the convex hull of the PSLG. If you do not use the -c switch,\n"
2229);
2230 printf(
2231" Triangle eats all triangles that are not enclosed by segments; if you\n");
2232 printf(
2233" are not careful, your whole triangulation may be eaten away. If you do\n"
2234);
2235 printf(
2236" use the -c switch, you can still produce concavities by the appropriate\n"
2237);
2238 printf(
2239" placement of holes just inside the boundary of the convex hull.\n");
2240 printf("\n");
2241 printf(
2242" An ideal PSLG has no intersecting segments, nor any vertices that lie\n");
2243 printf(
2244" upon segments (except, of course, the endpoints of each segment). You\n"
2245);
2246 printf(
2247" aren't required to make your .poly files ideal, but you should be aware\n"
2248);
2249 printf(
2250" of what can go wrong. Segment intersections are relatively safe--\n");
2251 printf(
2252" Triangle calculates the intersection points for you and adds them to\n");
2253 printf(
2254" the triangulation--as long as your machine's floating-point precision\n");
2255 printf(
2256" doesn't become a problem. You are tempting the fates if you have three\n"
2257);
2258 printf(
2259" segments that cross at the same location, and expect Triangle to figure\n"
2260);
2261 printf(
2262" out where the intersection point is. Thanks to floating-point roundoff\n"
2263);
2264 printf(
2265" error, Triangle will probably decide that the three segments intersect\n"
2266);
2267 printf(
2268" at three different points, and you will find a minuscule triangle in\n");
2269 printf(
2270" your output--unless Triangle tries to refine the tiny triangle, uses\n");
2271 printf(
2272" up the last bit of machine precision, and fails to terminate at all.\n");
2273 printf(
2274" You're better off putting the intersection point in the input files,\n");
2275 printf(
2276" and manually breaking up each segment into two. Similarly, if you\n");
2277 printf(
2278" place a vertex at the middle of a segment, and hope that Triangle will\n"
2279);
2280 printf(
2281" break up the segment at that vertex, you might get lucky. On the other\n"
2282);
2283 printf(
2284" hand, Triangle might decide that the vertex doesn't lie precisely on\n");
2285 printf(
2286" the segment, and you'll have a needle-sharp triangle in your output--or\n"
2287);
2288 printf(" a lot of tiny triangles if you're generating a quality mesh.\n");
2289 printf("\n");
2290 printf(
2291" When Triangle reads a .poly file, it also writes a .poly file, which\n");
2292 printf(
2293" includes all the subsegments--the edges that are parts of input\n");
2294 printf(
2295" segments. If the -c switch is used, the output .poly file also\n");
2296 printf(
2297" includes all of the edges on the convex hull. Hence, the output .poly\n"
2298);
2299 printf(
2300" file is useful for finding edges associated with input segments and for\n"
2301);
2302 printf(
2303" setting boundary conditions in finite element simulations. Moreover,\n");
2304 printf(
2305" you will need the output .poly file if you plan to refine the output\n");
2306 printf(
2307" mesh, and don't want segments to be missing in later triangulations.\n");
2308 printf("\n");
2309 printf(" .area files:\n");
2310 printf(" First line: <# of triangles>\n");
2311 printf(" Following lines: <triangle #> <maximum area>\n");
2312 printf("\n");
2313 printf(
2314" An .area file associates with each triangle a maximum area that is used\n"
2315);
2316 printf(
2317" for mesh refinement. As with other file formats, every triangle must\n");
2318 printf(
2319" be represented, and the triangles must be numbered consecutively. A\n");
2320 printf(
2321" triangle may be left unconstrained by assigning it a negative maximum\n");
2322 printf(" area.\n\n");
2323 printf(" .edge files:\n");
2324 printf(" First line: <# of edges> <# of boundary markers (0 or 1)>\n");
2325 printf(
2326" Following lines: <edge #> <endpoint> <endpoint> [boundary marker]\n");
2327 printf("\n");
2328 printf(
2329" Endpoints are indices into the corresponding .node file. Triangle can\n"
2330);
2331 printf(
2332" produce .edge files (use the -e switch), but cannot read them. The\n");
2333 printf(
2334" optional column of boundary markers is suppressed by the -B switch.\n");
2335 printf("\n");
2336 printf(
2337" In Voronoi diagrams, one also finds a special kind of edge that is an\n");
2338 printf(
2339" infinite ray with only one endpoint. For these edges, a different\n");
2340 printf(" format is used:\n\n");
2341 printf(" <edge #> <endpoint> -1 <direction x> <direction y>\n\n");
2342 printf(
2343" The `direction' is a floating-point vector that indicates the direction\n"
2344);
2345 printf(" of the infinite ray.\n\n");
2346 printf(" .neigh files:\n");
2347 printf(
2348" First line: <# of triangles> <# of neighbors per triangle (always 3)>\n"
2349);
2350 printf(
2351" Following lines: <triangle #> <neighbor> <neighbor> <neighbor>\n");
2352 printf("\n");
2353 printf(
2354" Neighbors are indices into the corresponding .ele file. An index of -1\n"
2355);
2356 printf(
2357" indicates no neighbor (because the triangle is on an exterior\n");
2358 printf(
2359" boundary). The first neighbor of triangle i is opposite the first\n");
2360 printf(" corner of triangle i, and so on.\n\n");
2361 printf(
2362" Triangle can produce .neigh files (use the -n switch), but cannot read\n"
2363);
2364 printf(" them.\n\n");
2365 printf("Boundary Markers:\n\n");
2366 printf(
2367" Boundary markers are tags used mainly to identify which output vertices\n");
2368 printf(
2369" and edges are associated with which PSLG segment, and to identify which\n");
2370 printf(
2371" vertices and edges occur on a boundary of the triangulation. A common\n");
2372 printf(
2373" use is to determine where boundary conditions should be applied to a\n");
2374 printf(
2375" finite element mesh. You can prevent boundary markers from being written\n"
2376);
2377 printf(" into files produced by Triangle by using the -B switch.\n\n");
2378 printf(
2379" The boundary marker associated with each segment in an output .poly file\n"
2380);
2381 printf(" and each edge in an output .edge file is chosen as follows:\n");
2382 printf(
2383" - If an output edge is part or all of a PSLG segment with a nonzero\n");
2384 printf(
2385" boundary marker, then the edge is assigned the same marker.\n");
2386 printf(
2387" - Otherwise, if the edge lies on a boundary of the triangulation\n");
2388 printf(
2389" (even the boundary of a hole), then the edge is assigned the marker\n");
2390 printf(" one (1).\n");
2391 printf(" - Otherwise, the edge is assigned the marker zero (0).\n");
2392 printf(
2393" The boundary marker associated with each vertex in an output .node file\n");
2394 printf(" is chosen as follows:\n");
2395 printf(
2396" - If a vertex is assigned a nonzero boundary marker in the input file,\n"
2397);
2398 printf(
2399" then it is assigned the same marker in the output .node file.\n");
2400 printf(
2401" - Otherwise, if the vertex lies on a PSLG segment (even if it is an\n");
2402 printf(
2403" endpoint of the segment) with a nonzero boundary marker, then the\n");
2404 printf(
2405" vertex is assigned the same marker. If the vertex lies on several\n");
2406 printf(" such segments, one of the markers is chosen arbitrarily.\n");
2407 printf(
2408" - Otherwise, if the vertex occurs on a boundary of the triangulation,\n");
2409 printf(" then the vertex is assigned the marker one (1).\n");
2410 printf(" - Otherwise, the vertex is assigned the marker zero (0).\n");
2411 printf("\n");
2412 printf(
2413" If you want Triangle to determine for you which vertices and edges are on\n"
2414);
2415 printf(
2416" the boundary, assign them the boundary marker zero (or use no markers at\n"
2417);
2418 printf(
2419" all) in your input files. In the output files, all boundary vertices,\n");
2420 printf(" edges, and segments will be assigned the value one.\n\n");
2421 printf("Triangulation Iteration Numbers:\n\n");
2422 printf(
2423" Because Triangle can read and refine its own triangulations, input\n");
2424 printf(
2425" and output files have iteration numbers. For instance, Triangle might\n");
2426 printf(
2427" read the files mesh.3.node, mesh.3.ele, and mesh.3.poly, refine the\n");
2428 printf(
2429" triangulation, and output the files mesh.4.node, mesh.4.ele, and\n");
2430 printf(" mesh.4.poly. Files with no iteration number are treated as if\n");
2431 printf(
2432" their iteration number is zero; hence, Triangle might read the file\n");
2433 printf(
2434" points.node, triangulate it, and produce the files points.1.node and\n");
2435 printf(" points.1.ele.\n\n");
2436 printf(
2437" Iteration numbers allow you to create a sequence of successively finer\n");
2438 printf(
2439" meshes suitable for multigrid methods. They also allow you to produce a\n"
2440);
2441 printf(
2442" sequence of meshes using error estimate-driven mesh refinement.\n");
2443 printf("\n");
2444 printf(
2445" If you're not using refinement or quality meshing, and you don't like\n");
2446 printf(
2447" iteration numbers, use the -I switch to disable them. This switch also\n");
2448 printf(
2449" disables output of .node and .poly files to prevent your input files from\n"
2450);
2451 printf(
2452" being overwritten. (If the input is a .poly file that contains its own\n");
2453 printf(
2454" points, a .node file is written. This can be quite convenient for\n");
2455 printf(" computing CDTs or quality meshes.)\n\n");
2456 printf("Examples of How to Use Triangle:\n\n");
2457 printf(
2458" `triangle dots' reads vertices from dots.node, and writes their Delaunay\n"
2459);
2460 printf(
2461" triangulation to dots.1.node and dots.1.ele. (dots.1.node is identical\n");
2462 printf(
2463" to dots.node.) `triangle -I dots' writes the triangulation to dots.ele\n");
2464 printf(
2465" instead. (No additional .node file is needed, so none is written.)\n");
2466 printf("\n");
2467 printf(
2468" `triangle -pe object.1' reads a PSLG from object.1.poly (and possibly\n");
2469 printf(
2470" object.1.node, if the vertices are omitted from object.1.poly) and writes\n"
2471);
2472 printf(
2473" its constrained Delaunay triangulation to object.2.node and object.2.ele.\n"
2474);
2475 printf(
2476" The segments are copied to object.2.poly, and all edges are written to\n");
2477 printf(" object.2.edge.\n\n");
2478 printf(
2479" `triangle -pq31.5a.1 object' reads a PSLG from object.poly (and possibly\n"
2480);
2481 printf(
2482" object.node), generates a mesh whose angles are all between 31.5 and 117\n"
2483);
2484 printf(
2485" degrees and whose triangles all have areas of 0.1 or less, and writes the\n"
2486);
2487 printf(
2488" mesh to object.1.node and object.1.ele. Each segment may be broken up\n");
2489 printf(" into multiple subsegments; these are written to object.1.poly.\n");
2490 printf("\n");
2491 printf(
2492" Here is a sample file `box.poly' describing a square with a square hole:\n"
2493);
2494 printf("\n");
2495 printf(
2496" # A box with eight vertices in 2D, no attributes, one boundary marker.\n"
2497);
2498 printf(" 8 2 0 1\n");
2499 printf(" # Outer box has these vertices:\n");
2500 printf(" 1 0 0 0\n");
2501 printf(" 2 0 3 0\n");
2502 printf(" 3 3 0 0\n");
2503 printf(" 4 3 3 33 # A special marker for this vertex.\n");
2504 printf(" # Inner square has these vertices:\n");
2505 printf(" 5 1 1 0\n");
2506 printf(" 6 1 2 0\n");
2507 printf(" 7 2 1 0\n");
2508 printf(" 8 2 2 0\n");
2509 printf(" # Five segments with boundary markers.\n");
2510 printf(" 5 1\n");
2511 printf(" 1 1 2 5 # Left side of outer box.\n");
2512 printf(" # Square hole has these segments:\n");
2513 printf(" 2 5 7 0\n");
2514 printf(" 3 7 8 0\n");
2515 printf(" 4 8 6 10\n");
2516 printf(" 5 6 5 0\n");
2517 printf(" # One hole in the middle of the inner square.\n");
2518 printf(" 1\n");
2519 printf(" 1 1.5 1.5\n");
2520 printf("\n");
2521 printf(
2522" Note that some segments are missing from the outer square, so you must\n");
2523 printf(
2524" use the `-c' switch. After `triangle -pqc box.poly', here is the output\n"
2525);
2526 printf(
2527" file `box.1.node', with twelve vertices. The last four vertices were\n");
2528 printf(
2529" added to meet the angle constraint. Vertices 1, 2, and 9 have markers\n");
2530 printf(
2531" from segment 1. Vertices 6 and 8 have markers from segment 4. All the\n");
2532 printf(
2533" other vertices but 4 have been marked to indicate that they lie on a\n");
2534 printf(" boundary.\n\n");
2535 printf(" 12 2 0 1\n");
2536 printf(" 1 0 0 5\n");
2537 printf(" 2 0 3 5\n");
2538 printf(" 3 3 0 1\n");
2539 printf(" 4 3 3 33\n");
2540 printf(" 5 1 1 1\n");
2541 printf(" 6 1 2 10\n");
2542 printf(" 7 2 1 1\n");
2543 printf(" 8 2 2 10\n");
2544 printf(" 9 0 1.5 5\n");
2545 printf(" 10 1.5 0 1\n");
2546 printf(" 11 3 1.5 1\n");
2547 printf(" 12 1.5 3 1\n");
2548 printf(" # Generated by triangle -pqc box.poly\n");
2549 printf("\n");
2550 printf(" Here is the output file `box.1.ele', with twelve triangles.\n");
2551 printf("\n");
2552 printf(" 12 3 0\n");
2553 printf(" 1 5 6 9\n");
2554 printf(" 2 10 3 7\n");
2555 printf(" 3 6 8 12\n");
2556 printf(" 4 9 1 5\n");
2557 printf(" 5 6 2 9\n");
2558 printf(" 6 7 3 11\n");
2559 printf(" 7 11 4 8\n");
2560 printf(" 8 7 5 10\n");
2561 printf(" 9 12 2 6\n");
2562 printf(" 10 8 7 11\n");
2563 printf(" 11 5 1 10\n");
2564 printf(" 12 8 4 12\n");
2565 printf(" # Generated by triangle -pqc box.poly\n\n");
2566 printf(
2567" Here is the output file `box.1.poly'. Note that segments have been added\n"
2568);
2569 printf(
2570" to represent the convex hull, and some segments have been subdivided by\n");
2571 printf(
2572" newly added vertices. Note also that <# of vertices> is set to zero to\n");
2573 printf(" indicate that the vertices should be read from the .node file.\n");
2574 printf("\n");
2575 printf(" 0 2 0 1\n");
2576 printf(" 12 1\n");
2577 printf(" 1 1 9 5\n");
2578 printf(" 2 5 7 1\n");
2579 printf(" 3 8 7 1\n");
2580 printf(" 4 6 8 10\n");
2581 printf(" 5 5 6 1\n");
2582 printf(" 6 3 10 1\n");
2583 printf(" 7 4 11 1\n");
2584 printf(" 8 2 12 1\n");
2585 printf(" 9 9 2 5\n");
2586 printf(" 10 10 1 1\n");
2587 printf(" 11 11 3 1\n");
2588 printf(" 12 12 4 1\n");
2589 printf(" 1\n");
2590 printf(" 1 1.5 1.5\n");
2591 printf(" # Generated by triangle -pqc box.poly\n");
2592 printf("\n");
2593 printf("Refinement and Area Constraints:\n");
2594 printf("\n");
2595 printf(
2596" The -r switch causes a mesh (.node and .ele files) to be read and\n");
2597 printf(
2598" refined. If the -p switch is also used, a .poly file is read and used to\n"
2599);
2600 printf(
2601" specify edges that are constrained and cannot be eliminated (although\n");
2602 printf(
2603" they can be subdivided into smaller edges) by the refinement process.\n");
2604 printf("\n");
2605 printf(
2606" When you refine a mesh, you generally want to impose tighter constraints.\n"
2607);
2608 printf(
2609" One way to accomplish this is to use -q with a larger angle, or -a\n");
2610 printf(
2611" followed by a smaller area than you used to generate the mesh you are\n");
2612 printf(
2613" refining. Another way to do this is to create an .area file, which\n");
2614 printf(
2615" specifies a maximum area for each triangle, and use the -a switch\n");
2616 printf(
2617" (without a number following). Each triangle's area constraint is applied\n"
2618);
2619 printf(
2620" to that triangle. Area constraints tend to diffuse as the mesh is\n");
2621 printf(
2622" refined, so if there are large variations in area constraint between\n");
2623 printf(
2624" adjacent triangles, you may not get the results you want. In that case,\n"
2625);
2626 printf(
2627" consider instead using the -u switch and writing a C procedure that\n");
2628 printf(" determines which triangles are too large.\n\n");
2629 printf(
2630" If you are refining a mesh composed of linear (three-node) elements, the\n"
2631);
2632 printf(
2633" output mesh contains all the nodes present in the input mesh, in the same\n"
2634);
2635 printf(
2636" order, with new nodes added at the end of the .node file. However, the\n");
2637 printf(
2638" refinement is not hierarchical: there is no guarantee that each output\n");
2639 printf(
2640" element is contained in a single input element. Often, an output element\n"
2641);
2642 printf(
2643" can overlap two or three input elements, and some input edges are not\n");
2644 printf(
2645" present in the output mesh. Hence, a sequence of refined meshes forms a\n"
2646);
2647 printf(
2648" hierarchy of nodes, but not a hierarchy of elements. If you refine a\n");
2649 printf(
2650" mesh of higher-order elements, the hierarchical property applies only to\n"
2651);
2652 printf(
2653" the nodes at the corners of an element; the midpoint nodes on each edge\n");
2654 printf(" are discarded before the mesh is refined.\n\n");
2655 printf(
2656" Maximum area constraints in .poly files operate differently from those in\n"
2657);
2658 printf(
2659" .area files. A maximum area in a .poly file applies to the whole\n");
2660 printf(
2661" (segment-bounded) region in which a point falls, whereas a maximum area\n");
2662 printf(
2663" in an .area file applies to only one triangle. Area constraints in .poly\n"
2664);
2665 printf(
2666" files are used only when a mesh is first generated, whereas area\n");
2667 printf(
2668" constraints in .area files are used only to refine an existing mesh, and\n"
2669);
2670 printf(
2671" are typically based on a posteriori error estimates resulting from a\n");
2672 printf(" finite element simulation on that mesh.\n\n");
2673 printf(
2674" `triangle -rq25 object.1' reads object.1.node and object.1.ele, then\n");
2675 printf(
2676" refines the triangulation to enforce a 25 degree minimum angle, and then\n"
2677);
2678 printf(
2679" writes the refined triangulation to object.2.node and object.2.ele.\n");
2680 printf("\n");
2681 printf(
2682" `triangle -rpaa6.2 z.3' reads z.3.node, z.3.ele, z.3.poly, and z.3.area.\n"
2683);
2684 printf(
2685" After reconstructing the mesh and its subsegments, Triangle refines the\n");
2686 printf(
2687" mesh so that no triangle has area greater than 6.2, and furthermore the\n");
2688 printf(
2689" triangles satisfy the maximum area constraints in z.3.area. No angle\n");
2690 printf(
2691" bound is imposed at all. The output is written to z.4.node, z.4.ele, and\n"
2692);
2693 printf(" z.4.poly.\n\n");
2694 printf(
2695" The sequence `triangle -qa1 x', `triangle -rqa.3 x.1', `triangle -rqa.1\n");
2696 printf(
2697" x.2' creates a sequence of successively finer meshes x.1, x.2, and x.3,\n");
2698 printf(" suitable for multigrid.\n\n");
2699 printf("Convex Hulls and Mesh Boundaries:\n\n");
2700 printf(
2701" If the input is a vertex set (not a PSLG), Triangle produces its convex\n");
2702 printf(
2703" hull as a by-product in the output .poly file if you use the -c switch.\n");
2704 printf(
2705" There are faster algorithms for finding a two-dimensional convex hull\n");
2706 printf(" than triangulation, of course, but this one comes for free.\n\n");
2707 printf(
2708" If the input is an unconstrained mesh (you are using the -r switch but\n");
2709 printf(
2710" not the -p switch), Triangle produces a list of its boundary edges\n");
2711 printf(
2712" (including hole boundaries) as a by-product when you use the -c switch.\n");
2713 printf(
2714" If you also use the -p switch, the output .poly file contains all the\n");
2715 printf(" segments from the input .poly file as well.\n\n");
2716 printf("Voronoi Diagrams:\n\n");
2717 printf(
2718" The -v switch produces a Voronoi diagram, in files suffixed .v.node and\n");
2719 printf(
2720" .v.edge. For example, `triangle -v points' reads points.node, produces\n");
2721 printf(
2722" its Delaunay triangulation in points.1.node and points.1.ele, and\n");
2723 printf(
2724" produces its Voronoi diagram in points.1.v.node and points.1.v.edge. The\n"
2725);
2726 printf(
2727" .v.node file contains a list of all Voronoi vertices, and the .v.edge\n");
2728 printf(
2729" file contains a list of all Voronoi edges, some of which may be infinite\n"
2730);
2731 printf(
2732" rays. (The choice of filenames makes it easy to run the set of Voronoi\n");
2733 printf(" vertices through Triangle, if so desired.)\n\n");
2734 printf(
2735" This implementation does not use exact arithmetic to compute the Voronoi\n"
2736);
2737 printf(
2738" vertices, and does not check whether neighboring vertices are identical.\n"
2739);
2740 printf(
2741" Be forewarned that if the Delaunay triangulation is degenerate or\n");
2742 printf(
2743" near-degenerate, the Voronoi diagram may have duplicate vertices or\n");
2744 printf(" crossing edges.\n\n");
2745 printf(
2746" The result is a valid Voronoi diagram only if Triangle's output is a true\n"
2747);
2748 printf(
2749" Delaunay triangulation. The Voronoi output is usually meaningless (and\n");
2750 printf(
2751" may contain crossing edges and other pathology) if the output is a CDT or\n"
2752);
2753 printf(
2754" CCDT, or if it has holes or concavities. If the triangulated domain is\n");
2755 printf(
2756" convex and has no holes, you can use -D switch to force Triangle to\n");
2757 printf(
2758" construct a conforming Delaunay triangulation instead of a CCDT, so the\n");
2759 printf(" Voronoi diagram will be valid.\n\n");
2760 printf("Mesh Topology:\n\n");
2761 printf(
2762" You may wish to know which triangles are adjacent to a certain Delaunay\n");
2763 printf(
2764" edge in an .edge file, which Voronoi cells are adjacent to a certain\n");
2765 printf(
2766" Voronoi edge in a .v.edge file, or which Voronoi cells are adjacent to\n");
2767 printf(
2768" each other. All of this information can be found by cross-referencing\n");
2769 printf(
2770" output files with the recollection that the Delaunay triangulation and\n");
2771 printf(" the Voronoi diagram are planar duals.\n\n");
2772 printf(
2773" Specifically, edge i of an .edge file is the dual of Voronoi edge i of\n");
2774 printf(
2775" the corresponding .v.edge file, and is rotated 90 degrees counterclock-\n");
2776 printf(
2777" wise from the Voronoi edge. Triangle j of an .ele file is the dual of\n");
2778 printf(
2779" vertex j of the corresponding .v.node file. Voronoi cell k is the dual\n");
2780 printf(" of vertex k of the corresponding .node file.\n\n");
2781 printf(
2782" Hence, to find the triangles adjacent to a Delaunay edge, look at the\n");
2783 printf(
2784" vertices of the corresponding Voronoi edge. If the endpoints of a\n");
2785 printf(
2786" Voronoi edge are Voronoi vertices 2 and 6 respectively, then triangles 2\n"
2787);
2788 printf(
2789" and 6 adjoin the left and right sides of the corresponding Delaunay edge,\n"
2790);
2791 printf(
2792" respectively. To find the Voronoi cells adjacent to a Voronoi edge, look\n"
2793);
2794 printf(
2795" at the endpoints of the corresponding Delaunay edge. If the endpoints of\n"
2796);
2797 printf(
2798" a Delaunay edge are input vertices 7 and 12, then Voronoi cells 7 and 12\n"
2799);
2800 printf(
2801" adjoin the right and left sides of the corresponding Voronoi edge,\n");
2802 printf(
2803" respectively. To find which Voronoi cells are adjacent to each other,\n");
2804 printf(" just read the list of Delaunay edges.\n\n");
2805 printf(
2806" Triangle does not write a list of the edges adjoining each Voronoi cell,\n"
2807);
2808 printf(
2809" but you can reconstructed it straightforwardly. For instance, to find\n");
2810 printf(
2811" all the edges of Voronoi cell 1, search the output .edge file for every\n");
2812 printf(
2813" edge that has input vertex 1 as an endpoint. The corresponding dual\n");
2814 printf(
2815" edges in the output .v.edge file form the boundary of Voronoi cell 1.\n");
2816 printf("\n");
2817 printf(
2818" For each Voronoi vertex, the .neigh file gives a list of the three\n");
2819 printf(
2820" Voronoi vertices attached to it. You might find this more convenient\n");
2821 printf(" than the .v.edge file.\n\n");
2822 printf("Quadratic Elements:\n\n");
2823 printf(
2824" Triangle generates meshes with subparametric quadratic elements if the\n");
2825 printf(
2826" -o2 switch is specified. Quadratic elements have six nodes per element,\n"
2827);
2828 printf(
2829" rather than three. `Subparametric' means that the edges of the triangles\n"
2830);
2831 printf(
2832" are always straight, so that subparametric quadratic elements are\n");
2833 printf(
2834" geometrically identical to linear elements, even though they can be used\n"
2835);
2836 printf(
2837" with quadratic interpolating functions. The three extra nodes of an\n");
2838 printf(
2839" element fall at the midpoints of the three edges, with the fourth, fifth,\n"
2840);
2841 printf(
2842" and sixth nodes appearing opposite the first, second, and third corners\n");
2843 printf(" respectively.\n\n");
2844 printf("Domains with Small Angles:\n\n");
2845 printf(
2846" If two input segments adjoin each other at a small angle, clearly the -q\n"
2847);
2848 printf(
2849" switch cannot remove the small angle. Moreover, Triangle may have no\n");
2850 printf(
2851" choice but to generate additional triangles whose smallest angles are\n");
2852 printf(
2853" smaller than the specified bound. However, these triangles only appear\n");
2854 printf(
2855" between input segments separated by small angles. Moreover, if you\n");
2856 printf(
2857" request a minimum angle of theta degrees, Triangle will generally produce\n"
2858);
2859 printf(
2860" no angle larger than 180 - 2 theta, even if it is forced to compromise on\n"
2861);
2862 printf(" the minimum angle.\n\n");
2863 printf("Statistics:\n\n");
2864 printf(
2865" After generating a mesh, Triangle prints a count of entities in the\n");
2866 printf(
2867" output mesh, including the number of vertices, triangles, edges, exterior\n"
2868);
2869 printf(
2870" boundary edges (i.e. subsegments on the boundary of the triangulation,\n");
2871 printf(
2872" including hole boundaries), interior boundary edges (i.e. subsegments of\n"
2873);
2874 printf(
2875" input segments not on the boundary), and total subsegments. If you've\n");
2876 printf(
2877" forgotten the statistics for an existing mesh, run Triangle on that mesh\n"
2878);
2879 printf(
2880" with the -rNEP switches to read the mesh and print the statistics without\n"
2881);
2882 printf(
2883" writing any files. Use -rpNEP if you've got a .poly file for the mesh.\n");
2884 printf("\n");
2885 printf(
2886" The -V switch produces extended statistics, including a rough estimate\n");
2887 printf(
2888" of memory use, the number of calls to geometric predicates, and\n");
2889 printf(
2890" histograms of the angles and the aspect ratios of the triangles in the\n");
2891 printf(" mesh.\n\n");
2892 printf("Exact Arithmetic:\n\n");
2893 printf(
2894" Triangle uses adaptive exact arithmetic to perform what computational\n");
2895 printf(
2896" geometers call the `orientation' and `incircle' tests. If the floating-\n"
2897);
2898 printf(
2899" point arithmetic of your machine conforms to the IEEE 754 standard (as\n");
2900 printf(
2901" most workstations do), and does not use extended precision internal\n");
2902 printf(
2903" floating-point registers, then your output is guaranteed to be an\n");
2904 printf(
2905" absolutely true Delaunay or constrained Delaunay triangulation, roundoff\n"
2906);
2907 printf(
2908" error notwithstanding. The word `adaptive' implies that these arithmetic\n"
2909);
2910 printf(
2911" routines compute the result only to the precision necessary to guarantee\n"
2912);
2913 printf(
2914" correctness, so they are usually nearly as fast as their approximate\n");
2915 printf(" counterparts.\n\n");
2916 printf(
2917" May CPUs, including Intel x86 processors, have extended precision\n");
2918 printf(
2919" floating-point registers. These must be reconfigured so their precision\n"
2920);
2921 printf(
2922" is reduced to memory precision. Triangle does this if it is compiled\n");
2923 printf(" correctly. See the makefile for details.\n\n");
2924 printf(
2925" The exact tests can be disabled with the -X switch. On most inputs, this\n"
2926);
2927 printf(
2928" switch reduces the computation time by about eight percent--it's not\n");
2929 printf(
2930" worth the risk. There are rare difficult inputs (having many collinear\n");
2931 printf(
2932" and cocircular vertices), however, for which the difference in speed\n");
2933 printf(
2934" could be a factor of two. Be forewarned that these are precisely the\n");
2935 printf(
2936" inputs most likely to cause errors if you use the -X switch. Hence, the\n"
2937);
2938 printf(" -X switch is not recommended.\n\n");
2939 printf(
2940" Unfortunately, the exact tests don't solve every numerical problem.\n");
2941 printf(
2942" Exact arithmetic is not used to compute the positions of new vertices,\n");
2943 printf(
2944" because the bit complexity of vertex coordinates would grow without\n");
2945 printf(
2946" bound. Hence, segment intersections aren't computed exactly; in very\n");
2947 printf(
2948" unusual cases, roundoff error in computing an intersection point might\n");
2949 printf(
2950" actually lead to an inverted triangle and an invalid triangulation.\n");
2951 printf(
2952" (This is one reason to specify your own intersection points in your .poly\n"
2953);
2954 printf(
2955" files.) Similarly, exact arithmetic is not used to compute the vertices\n"
2956);
2957 printf(" of the Voronoi diagram.\n\n");
2958 printf(
2959" Another pair of problems not solved by the exact arithmetic routines is\n");
2960 printf(
2961" underflow and overflow. If Triangle is compiled for double precision\n");
2962 printf(
2963" arithmetic, I believe that Triangle's geometric predicates work correctly\n"
2964);
2965 printf(
2966" if the exponent of every input coordinate falls in the range [-148, 201].\n"
2967);
2968 printf(
2969" Underflow can silently prevent the orientation and incircle tests from\n");
2970 printf(
2971" being performed exactly, while overflow typically causes a floating\n");
2972 printf(" exception.\n\n");
2973 printf("Calling Triangle from Another Program:\n\n");
2974 printf(" Read the file triangle.h for details.\n\n");
2975 printf("Troubleshooting:\n\n");
2976 printf(" Please read this section before mailing me bugs.\n\n");
2977 printf(" `My output mesh has no triangles!'\n\n");
2978 printf(
2979" If you're using a PSLG, you've probably failed to specify a proper set\n"
2980);
2981 printf(
2982" of bounding segments, or forgotten to use the -c switch. Or you may\n");
2983 printf(
2984" have placed a hole badly, thereby eating all your triangles. To test\n");
2985 printf(" these possibilities, try again with the -c and -O switches.\n");
2986 printf(
2987" Alternatively, all your input vertices may be collinear, in which case\n"
2988);
2989 printf(" you can hardly expect to triangulate them.\n\n");
2990 printf(" `Triangle doesn't terminate, or just crashes.'\n\n");
2991 printf(
2992" Bad things can happen when triangles get so small that the distance\n");
2993 printf(
2994" between their vertices isn't much larger than the precision of your\n");
2995 printf(
2996" machine's arithmetic. If you've compiled Triangle for single-precision\n"
2997);
2998 printf(
2999" arithmetic, you might do better by recompiling it for double-precision.\n"
3000);
3001 printf(
3002" Then again, you might just have to settle for more lenient constraints\n"
3003);
3004 printf(
3005" on the minimum angle and the maximum area than you had planned.\n");
3006 printf("\n");
3007 printf(
3008" You can minimize precision problems by ensuring that the origin lies\n");
3009 printf(
3010" inside your vertex set, or even inside the densest part of your\n");
3011 printf(
3012" mesh. If you're triangulating an object whose x-coordinates all fall\n");
3013 printf(
3014" between 6247133 and 6247134, you're not leaving much floating-point\n");
3015 printf(" precision for Triangle to work with.\n\n");
3016 printf(
3017" Precision problems can occur covertly if the input PSLG contains two\n");
3018 printf(
3019" segments that meet (or intersect) at an extremely small angle, or if\n");
3020 printf(
3021" such an angle is introduced by the -c switch. If you don't realize\n");
3022 printf(
3023" that a tiny angle is being formed, you might never discover why\n");
3024 printf(
3025" Triangle is crashing. To check for this possibility, use the -S switch\n"
3026);
3027 printf(
3028" (with an appropriate limit on the number of Steiner points, found by\n");
3029 printf(
3030" trial-and-error) to stop Triangle early, and view the output .poly file\n"
3031);
3032 printf(
3033" with Show Me (described below). Look carefully for regions where dense\n"
3034);
3035 printf(
3036" clusters of vertices are forming and for small angles between segments.\n"
3037);
3038 printf(
3039" Zoom in closely, as such segments might look like a single segment from\n"
3040);
3041 printf(" a distance.\n\n");
3042 printf(
3043" If some of the input values are too large, Triangle may suffer a\n");
3044 printf(
3045" floating exception due to overflow when attempting to perform an\n");
3046 printf(
3047" orientation or incircle test. (Read the section on exact arithmetic\n");
3048 printf(
3049" above.) Again, I recommend compiling Triangle for double (rather\n");
3050 printf(" than single) precision arithmetic.\n\n");
3051 printf(
3052" Unexpected problems can arise if you use quality meshing (-q, -a, or\n");
3053 printf(
3054" -u) with an input that is not segment-bounded--that is, if your input\n");
3055 printf(
3056" is a vertex set, or you're using the -c switch. If the convex hull of\n"
3057);
3058 printf(
3059" your input vertices has collinear vertices on its boundary, an input\n");
3060 printf(
3061" vertex that you think lies on the convex hull might actually lie just\n");
3062 printf(
3063" inside the convex hull. If so, the vertex and the nearby convex hull\n");
3064 printf(
3065" edge form an extremely thin triangle. When Triangle tries to refine\n");
3066 printf(
3067" the mesh to enforce angle and area constraints, Triangle might generate\n"
3068);
3069 printf(
3070" extremely tiny triangles, or it might fail because of insufficient\n");
3071 printf(" floating-point precision.\n\n");
3072 printf(
3073" `The numbering of the output vertices doesn't match the input vertices.'\n"
3074);
3075 printf("\n");
3076 printf(
3077" You may have had duplicate input vertices, or you may have eaten some\n");
3078 printf(
3079" of your input vertices with a hole, or by placing them outside the area\n"
3080);
3081 printf(
3082" enclosed by segments. In any case, you can solve the problem by not\n");
3083 printf(" using the -j switch.\n\n");
3084 printf(
3085" `Triangle executes without incident, but when I look at the resulting\n");
3086 printf(
3087" mesh, it has overlapping triangles or other geometric inconsistencies.'\n");
3088 printf("\n");
3089 printf(
3090" If you select the -X switch, Triangle occasionally makes mistakes due\n");
3091 printf(
3092" to floating-point roundoff error. Although these errors are rare,\n");
3093 printf(
3094" don't use the -X switch. If you still have problems, please report the\n"
3095);
3096 printf(" bug.\n\n");
3097 printf(
3098" `Triangle executes without incident, but when I look at the resulting\n");
3099 printf(" Voronoi diagram, it has overlapping edges or other geometric\n");
3100 printf(" inconsistencies.'\n");
3101 printf("\n");
3102 printf(
3103" If your input is a PSLG (-p), you can only expect a meaningful Voronoi\n"
3104);
3105 printf(
3106" diagram if the domain you are triangulating is convex and free of\n");
3107 printf(
3108" holes, and you use the -D switch to construct a conforming Delaunay\n");
3109 printf(" triangulation (instead of a CDT or CCDT).\n\n");
3110 printf(
3111" Strange things can happen if you've taken liberties with your PSLG. Do\n");
3112 printf(
3113" you have a vertex lying in the middle of a segment? Triangle sometimes\n");
3114 printf(
3115" copes poorly with that sort of thing. Do you want to lay out a collinear\n"
3116);
3117 printf(
3118" row of evenly spaced, segment-connected vertices? Have you simply\n");
3119 printf(
3120" defined one long segment connecting the leftmost vertex to the rightmost\n"
3121);
3122 printf(
3123" vertex, and a bunch of vertices lying along it? This method occasionally\n"
3124);
3125 printf(
3126" works, especially with horizontal and vertical lines, but often it\n");
3127 printf(
3128" doesn't, and you'll have to connect each adjacent pair of vertices with a\n"
3129);
3130 printf(" separate segment. If you don't like it, tough.\n\n");
3131 printf(
3132" Furthermore, if you have segments that intersect other than at their\n");
3133 printf(
3134" endpoints, try not to let the intersections fall extremely close to PSLG\n"
3135);
3136 printf(" vertices or each other.\n\n");
3137 printf(
3138" If you have problems refining a triangulation not produced by Triangle:\n");
3139 printf(
3140" Are you sure the triangulation is geometrically valid? Is it formatted\n");
3141 printf(
3142" correctly for Triangle? Are the triangles all listed so the first three\n"
3143);
3144 printf(
3145" vertices are their corners in counterclockwise order? Are all of the\n");
3146 printf(
3147" triangles constrained Delaunay? Triangle's Delaunay refinement algorithm\n"
3148);
3149 printf(" assumes that it starts with a CDT.\n\n");
3150 printf("Show Me:\n\n");
3151 printf(
3152" Triangle comes with a separate program named `Show Me', whose primary\n");
3153 printf(
3154" purpose is to draw meshes on your screen or in PostScript. Its secondary\n"
3155);
3156 printf(
3157" purpose is to check the validity of your input files, and do so more\n");
3158 printf(
3159" thoroughly than Triangle does. Unlike Triangle, Show Me requires that\n");
3160 printf(
3161" you have the X Windows system. Sorry, Microsoft Windows users.\n");
3162 printf("\n");
3163 printf("Triangle on the Web:\n");
3164 printf("\n");
3165 printf(" To see an illustrated version of these instructions, check out\n");
3166 printf("\n");
3167 printf(" http://www.cs.cmu.edu/~quake/triangle.html\n");
3168 printf("\n");
3169 printf("A Brief Plea:\n");
3170 printf("\n");
3171 printf(
3172" If you use Triangle, and especially if you use it to accomplish real\n");
3173 printf(
3174" work, I would like very much to hear from you. A short letter or email\n");
3175 printf(
3176" (to jrs@cs.berkeley.edu) describing how you use Triangle will mean a lot\n"
3177);
3178 printf(
3179" to me. The more people I know are using this program, the more easily I\n"
3180);
3181 printf(
3182" can justify spending time on improvements, which in turn will benefit\n");
3183 printf(
3184" you. Also, I can put you on a list to receive email whenever a new\n");
3185 printf(" version of Triangle is available.\n\n");
3186 printf(
3187" If you use a mesh generated by Triangle in a publication, please include\n"
3188);
3189 printf(
3190" an acknowledgment as well. And please spell Triangle with a capital `T'!\n"
3191);
3192 printf(
3193" If you want to include a citation, use `Jonathan Richard Shewchuk,\n");
3194 printf(
3195" ``Triangle: Engineering a 2D Quality Mesh Generator and Delaunay\n");
3196 printf(
3197" Triangulator,'' in Applied Computational Geometry: Towards Geometric\n");
3198 printf(
3199" Engineering (Ming C. Lin and Dinesh Manocha, editors), volume 1148 of\n");
3200 printf(
3201" Lecture Notes in Computer Science, pages 203-222, Springer-Verlag,\n");
3202 printf(
3203" Berlin, May 1996. (From the First ACM Workshop on Applied Computational\n"
3204);
3205 printf(" Geometry.)'\n\n");
3206 printf("Research credit:\n\n");
3207 printf(
3208" Of course, I can take credit for only a fraction of the ideas that made\n");
3209 printf(
3210" this mesh generator possible. Triangle owes its existence to the efforts\n"
3211);
3212 printf(
3213" of many fine computational geometers and other researchers, including\n");
3214 printf(
3215" Marshall Bern, L. Paul Chew, Kenneth L. Clarkson, Boris Delaunay, Rex A.\n"
3216);
3217 printf(
3218" Dwyer, David Eppstein, Steven Fortune, Leonidas J. Guibas, Donald E.\n");
3219 printf(
3220" Knuth, Charles L. Lawson, Der-Tsai Lee, Gary L. Miller, Ernst P. Mucke,\n");
3221 printf(
3222" Steven E. Pav, Douglas M. Priest, Jim Ruppert, Isaac Saias, Bruce J.\n");
3223 printf(
3224" Schachter, Micha Sharir, Peter W. Shor, Daniel D. Sleator, Jorge Stolfi,\n"
3225);
3226 printf(" Robert E. Tarjan, Alper Ungor, Christopher J. Van Wyk, Noel J.\n");
3227 printf(
3228" Walkington, and Binhai Zhu. See the comments at the beginning of the\n");
3229 printf(" source code for references.\n\n");
3230 triexit(0);
3231}
3232
3233#endif /* not TRILIBRARY */
3234
3235/*****************************************************************************/
3236/* */
3237/* internalerror() Ask the user to send me the defective product. Exit. */
3238/* */
3239/*****************************************************************************/
3240
3241void internalerror()
3242{
3243 printf(" Please report this bug to jrs@cs.berkeley.edu\n");
3244 printf(" Include the message above, your input data set, and the exact\n");
3245 printf(" command line you used to run Triangle.\n");
3246 triexit(1);
3247}
3248
3249/*****************************************************************************/
3250/* */
3251/* parsecommandline() Read the command line, identify switches, and set */
3252/* up options and file names. */
3253/* */
3254/*****************************************************************************/
3255
3256#ifdef ANSI_DECLARATORS
3257void parsecommandline(int argc, char **argv, struct behavior *b)
3258#else /* not ANSI_DECLARATORS */
3259void parsecommandline(argc, argv, b)
3260int argc;
3261char **argv;
3262struct behavior *b;
3263#endif /* not ANSI_DECLARATORS */
3264
3265{
3266#ifdef TRILIBRARY
3267#define STARTINDEX 0
3268#else /* not TRILIBRARY */
3269#define STARTINDEX 1
3270 int increment;
3271 int meshnumber;
3272#endif /* not TRILIBRARY */
3273 /* int i, j, k; */
3274 int i, j;
3275 /* char workstring[FILENAMESIZE]; */
3276
3277 b->poly = b->refine = b->quality = 0;
3278 b->vararea = b->fixedarea = b->usertest = 0;
3279 b->regionattrib = b->convex = b->weighted = b->jettison = 0;
3280 b->firstnumber = 1;
3281 b->edgesout = b->voronoi = b->neighbors = b->geomview = 0;
3282 b->nobound = b->nopolywritten = b->nonodewritten = b->noelewritten = 0;
3283 b->noiterationnum = 0;
3284 b->noholes = b->noexact = 0;
3285 b->incremental = b->sweepline = 0;
3286 b->dwyer = 1;
3287 b->splitseg = 0;
3288 b->docheck = 0;
3289 b->nobisect = 0;
3290 b->conformdel = 0;
3291 b->steiner = -1;
3292 b->order = 1;
3293 b->minangle = 0.0;
3294 b->maxarea = -1.0;
3295 b->quiet = b->verbose = 0;
3296#ifndef TRILIBRARY
3297 b->innodefilename[0] = '\0';
3298#endif /* not TRILIBRARY */
3299
3300 for (i = STARTINDEX; i < argc; i++) {
3301#ifndef TRILIBRARY
3302 if (argv[i][0] == '-') {
3303#endif /* not TRILIBRARY */
3304 for (j = STARTINDEX; argv[i][j] != '\0'; j++) {
3305 if (argv[i][j] == 'p') {
3306 b->poly = 1;
3307 }
3308#ifndef CDT_ONLY
3309 if (argv[i][j] == 'r') {
3310 b->refine = 1;
3311 }
3312 if (argv[i][j] == 'q') {
3313 b->quality = 1;
3314 if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
3315 (argv[i][j + 1] == '.')) {
3316 k = 0;
3317 while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
3318 (argv[i][j + 1] == '.')) {
3319 j++;
3320 workstring[k] = argv[i][j];
3321 k++;
3322 }
3323 workstring[k] = '\0';
3324 b->minangle = (REAL) strtod(workstring, (char **) NULL);
3325 } else {
3326 b->minangle = 20.0;
3327 }
3328 }
3329 if (argv[i][j] == 'a') {
3330 b->quality = 1;
3331 if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
3332 (argv[i][j + 1] == '.')) {
3333 b->fixedarea = 1;
3334 k = 0;
3335 while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
3336 (argv[i][j + 1] == '.')) {
3337 j++;
3338 workstring[k] = argv[i][j];
3339 k++;
3340 }
3341 workstring[k] = '\0';
3342 b->maxarea = (REAL) strtod(workstring, (char **) NULL);
3343 if (b->maxarea <= 0.0) {
3344 printf("Error: Maximum area must be greater than zero.\n");
3345 triexit(1);
3346 }
3347 } else {
3348 b->vararea = 1;
3349 }
3350 }
3351 if (argv[i][j] == 'u') {
3352 b->quality = 1;
3353 b->usertest = 1;
3354 }
3355#endif /* not CDT_ONLY */
3356 if (argv[i][j] == 'A') {
3357 b->regionattrib = 1;
3358 }
3359 if (argv[i][j] == 'c') {
3360 b->convex = 1;
3361 }
3362 if (argv[i][j] == 'w') {
3363 b->weighted = 1;
3364 }
3365 if (argv[i][j] == 'W') {
3366 b->weighted = 2;
3367 }
3368 if (argv[i][j] == 'j') {
3369 b->jettison = 1;
3370 }
3371 if (argv[i][j] == 'z') {
3372 b->firstnumber = 0;
3373 }
3374 if (argv[i][j] == 'e') {
3375 b->edgesout = 1;
3376 }
3377 if (argv[i][j] == 'v') {
3378 b->voronoi = 1;
3379 }
3380 if (argv[i][j] == 'n') {
3381 b->neighbors = 1;
3382 }
3383 if (argv[i][j] == 'g') {
3384 b->geomview = 1;
3385 }
3386 if (argv[i][j] == 'B') {
3387 b->nobound = 1;
3388 }
3389 if (argv[i][j] == 'P') {
3390 b->nopolywritten = 1;
3391 }
3392 if (argv[i][j] == 'N') {
3393 b->nonodewritten = 1;
3394 }
3395 if (argv[i][j] == 'E') {
3396 b->noelewritten = 1;
3397 }
3398#ifndef TRILIBRARY
3399 if (argv[i][j] == 'I') {
3400 b->noiterationnum = 1;
3401 }
3402#endif /* not TRILIBRARY */
3403 if (argv[i][j] == 'O') {
3404 b->noholes = 1;
3405 }
3406 if (argv[i][j] == 'X') {
3407 b->noexact = 1;
3408 }
3409 if (argv[i][j] == 'o') {
3410 if (argv[i][j + 1] == '2') {
3411 j++;
3412 b->order = 2;
3413 }
3414 }
3415#ifndef CDT_ONLY
3416 if (argv[i][j] == 'Y') {
3417 b->nobisect++;
3418 }
3419 if (argv[i][j] == 'S') {
3420 b->steiner = 0;
3421 while ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) {
3422 j++;
3423 b->steiner = b->steiner * 10 + (int) (argv[i][j] - '0');
3424 }
3425 }
3426#endif /* not CDT_ONLY */
3427#ifndef REDUCED
3428 if (argv[i][j] == 'i') {
3429 b->incremental = 1;
3430 }
3431 if (argv[i][j] == 'F') {
3432 b->sweepline = 1;
3433 }
3434#endif /* not REDUCED */
3435 if (argv[i][j] == 'l') {
3436 b->dwyer = 0;
3437 }
3438#ifndef REDUCED
3439#ifndef CDT_ONLY
3440 if (argv[i][j] == 's') {
3441 b->splitseg = 1;
3442 }
3443 if ((argv[i][j] == 'D') || (argv[i][j] == 'L')) {
3444 b->quality = 1;
3445 b->conformdel = 1;
3446 }
3447#endif /* not CDT_ONLY */
3448 if (argv[i][j] == 'C') {
3449 b->docheck = 1;
3450 }
3451#endif /* not REDUCED */
3452 if (argv[i][j] == 'Q') {
3453 b->quiet = 1;
3454 }
3455 if (argv[i][j] == 'V') {
3456 b->verbose++;
3457 }
3458#ifndef TRILIBRARY
3459 if ((argv[i][j] == 'h') || (argv[i][j] == 'H') ||
3460 (argv[i][j] == '?')) {
3461 info();
3462 }
3463#endif /* not TRILIBRARY */
3464 }
3465#ifndef TRILIBRARY
3466 } else {
3467 strncpy(b->innodefilename, argv[i], FILENAMESIZE - 1);
3468 b->innodefilename[FILENAMESIZE - 1] = '\0';
3469 }
3470#endif /* not TRILIBRARY */
3471 }
3472#ifndef TRILIBRARY
3473 if (b->innodefilename[0] == '\0') {
3474 syntax();
3475 }
3476 if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 5], ".node")) {
3477 b->innodefilename[strlen(b->innodefilename) - 5] = '\0';
3478 }
3479 if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 5], ".poly")) {
3480 b->innodefilename[strlen(b->innodefilename) - 5] = '\0';
3481 b->poly = 1;
3482 }
3483#ifndef CDT_ONLY
3484 if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 4], ".ele")) {
3485 b->innodefilename[strlen(b->innodefilename) - 4] = '\0';
3486 b->refine = 1;
3487 }
3488 if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 5], ".area")) {
3489 b->innodefilename[strlen(b->innodefilename) - 5] = '\0';
3490 b->refine = 1;
3491 b->quality = 1;
3492 b->vararea = 1;
3493 }
3494#endif /* not CDT_ONLY */
3495#endif /* not TRILIBRARY */
3496 b->usesegments = b->poly || b->refine || b->quality || b->convex;
3497 b->goodangle = cos(b->minangle * PI / 180.0);
3498 if (b->goodangle == 1.0) {
3499 b->offconstant = 0.0;
3500 } else {
3501 b->offconstant = 0.475 * sqrt((1.0 + b->goodangle) / (1.0 - b->goodangle));
3502 }
3503 b->goodangle *= b->goodangle;
3504 if (b->refine && b->noiterationnum) {
3505 printf(
3506 "Error: You cannot use the -I switch when refining a triangulation.\n");
3507 triexit(1);
3508 }
3509 /* Be careful not to allocate space for element area constraints that */
3510 /* will never be assigned any value (other than the default -1.0). */
3511 if (!b->refine && !b->poly) {
3512 b->vararea = 0;
3513 }
3514 /* Be careful not to add an extra attribute to each element unless the */
3515 /* input supports it (PSLG in, but not refining a preexisting mesh). */
3516 if (b->refine || !b->poly) {
3517 b->regionattrib = 0;
3518 }
3519 /* Regular/weighted triangulations are incompatible with PSLGs */
3520 /* and meshing. */
3521 if (b->weighted && (b->poly || b->quality)) {
3522 b->weighted = 0;
3523 if (!b->quiet) {
3524 printf("Warning: weighted triangulations (-w, -W) are incompatible\n");
3525 printf(" with PSLGs (-p) and meshing (-q, -a, -u). Weights ignored.\n"
3526 );
3527 }
3528 }
3529 if (b->jettison && b->nonodewritten && !b->quiet) {
3530 printf("Warning: -j and -N switches are somewhat incompatible.\n");
3531 printf(" If any vertices are jettisoned, you will need the output\n");
3532 printf(" .node file to reconstruct the new node indices.");
3533 }
3534
3535#ifndef TRILIBRARY
3536 strcpy(b->inpolyfilename, b->innodefilename);
3537 strcpy(b->inelefilename, b->innodefilename);
3538 strcpy(b->areafilename, b->innodefilename);
3539 increment = 0;
3540 strcpy(workstring, b->innodefilename);
3541 j = 1;
3542 while (workstring[j] != '\0') {
3543 if ((workstring[j] == '.') && (workstring[j + 1] != '\0')) {
3544 increment = j + 1;
3545 }
3546 j++;
3547 }
3548 meshnumber = 0;
3549 if (increment > 0) {
3550 j = increment;
3551 do {
3552 if ((workstring[j] >= '0') && (workstring[j] <= '9')) {
3553 meshnumber = meshnumber * 10 + (int) (workstring[j] - '0');
3554 } else {
3555 increment = 0;
3556 }
3557 j++;
3558 } while (workstring[j] != '\0');
3559 }
3560 if (b->noiterationnum) {
3561 strcpy(b->outnodefilename, b->innodefilename);
3562 strcpy(b->outelefilename, b->innodefilename);
3563 strcpy(b->edgefilename, b->innodefilename);
3564 strcpy(b->vnodefilename, b->innodefilename);
3565 strcpy(b->vedgefilename, b->innodefilename);
3566 strcpy(b->neighborfilename, b->innodefilename);
3567 strcpy(b->offfilename, b->innodefilename);
3568 strcat(b->outnodefilename, ".node");
3569 strcat(b->outelefilename, ".ele");
3570 strcat(b->edgefilename, ".edge");
3571 strcat(b->vnodefilename, ".v.node");
3572 strcat(b->vedgefilename, ".v.edge");
3573 strcat(b->neighborfilename, ".neigh");
3574 strcat(b->offfilename, ".off");
3575 } else if (increment == 0) {
3576 strcpy(b->outnodefilename, b->innodefilename);
3577 strcpy(b->outpolyfilename, b->innodefilename);
3578 strcpy(b->outelefilename, b->innodefilename);
3579 strcpy(b->edgefilename, b->innodefilename);
3580 strcpy(b->vnodefilename, b->innodefilename);
3581 strcpy(b->vedgefilename, b->innodefilename);
3582 strcpy(b->neighborfilename, b->innodefilename);
3583 strcpy(b->offfilename, b->innodefilename);
3584 strcat(b->outnodefilename, ".1.node");
3585 strcat(b->outpolyfilename, ".1.poly");
3586 strcat(b->outelefilename, ".1.ele");
3587 strcat(b->edgefilename, ".1.edge");
3588 strcat(b->vnodefilename, ".1.v.node");
3589 strcat(b->vedgefilename, ".1.v.edge");
3590 strcat(b->neighborfilename, ".1.neigh");
3591 strcat(b->offfilename, ".1.off");
3592 } else {
3593 workstring[increment] = '%';
3594 workstring[increment + 1] = 'd';
3595 workstring[increment + 2] = '\0';
3596 sprintf(b->outnodefilename, workstring, meshnumber + 1);
3597 strcpy(b->outpolyfilename, b->outnodefilename);
3598 strcpy(b->outelefilename, b->outnodefilename);
3599 strcpy(b->edgefilename, b->outnodefilename);
3600 strcpy(b->vnodefilename, b->outnodefilename);
3601 strcpy(b->vedgefilename, b->outnodefilename);
3602 strcpy(b->neighborfilename, b->outnodefilename);
3603 strcpy(b->offfilename, b->outnodefilename);
3604 strcat(b->outnodefilename, ".node");
3605 strcat(b->outpolyfilename, ".poly");
3606 strcat(b->outelefilename, ".ele");
3607 strcat(b->edgefilename, ".edge");
3608 strcat(b->vnodefilename, ".v.node");
3609 strcat(b->vedgefilename, ".v.edge");
3610 strcat(b->neighborfilename, ".neigh");
3611 strcat(b->offfilename, ".off");
3612 }
3613 strcat(b->innodefilename, ".node");
3614 strcat(b->inpolyfilename, ".poly");
3615 strcat(b->inelefilename, ".ele");
3616 strcat(b->areafilename, ".area");
3617#endif /* not TRILIBRARY */
3618}
3619
3620/** **/
3621/** **/
3622/********* User interaction routines begin here *********/
3623
3624/********* Debugging routines begin here *********/
3625/** **/
3626/** **/
3627
3628/*****************************************************************************/
3629/* */
3630/* printtriangle() Print out the details of an oriented triangle. */
3631/* */
3632/* I originally wrote this procedure to simplify debugging; it can be */
3633/* called directly from the debugger, and presents information about an */
3634/* oriented triangle in digestible form. It's also used when the */
3635/* highest level of verbosity (`-VVV') is specified. */
3636/* */
3637/*****************************************************************************/
3638
3639#ifdef ANSI_DECLARATORS
3640void printtriangle(struct mesh *m, struct behavior *b, struct otri *t)
3641#else /* not ANSI_DECLARATORS */
3642void printtriangle(m, b, t)
3643struct mesh *m;
3644struct behavior *b;
3645struct otri *t;
3646#endif /* not ANSI_DECLARATORS */
3647
3648{
3649 struct otri printtri;
3650 struct osub printsh;
3651 vertex printvertex;
3652
3653 printf("triangle x%lx with orientation %d:\n", (unsigned long) t->tri,
3654 t->orient);
3655 decode(t->tri[0], printtri);
3656 if (printtri.tri == m->dummytri) {
3657 printf(" [0] = Outer space\n");
3658 } else {
3659 printf(" [0] = x%lx %d\n", (unsigned long) printtri.tri,
3660 printtri.orient);
3661 }
3662 decode(t->tri[1], printtri);
3663 if (printtri.tri == m->dummytri) {
3664 printf(" [1] = Outer space\n");
3665 } else {
3666 printf(" [1] = x%lx %d\n", (unsigned long) printtri.tri,
3667 printtri.orient);
3668 }
3669 decode(t->tri[2], printtri);
3670 if (printtri.tri == m->dummytri) {
3671 printf(" [2] = Outer space\n");
3672 } else {
3673 printf(" [2] = x%lx %d\n", (unsigned long) printtri.tri,
3674 printtri.orient);
3675 }
3676
3677 org(*t, printvertex);
3678 if (printvertex == (vertex) NULL)
3679 printf(" Origin[%d] = NULL\n", (t->orient + 1) % 3 + 3);
3680 else
3681 printf(" Origin[%d] = x%lx (%.12g, %.12g)\n",
3682 (t->orient + 1) % 3 + 3, (unsigned long) printvertex,
3683 printvertex[0], printvertex[1]);
3684 dest(*t, printvertex);
3685 if (printvertex == (vertex) NULL)
3686 printf(" Dest [%d] = NULL\n", (t->orient + 2) % 3 + 3);
3687 else
3688 printf(" Dest [%d] = x%lx (%.12g, %.12g)\n",
3689 (t->orient + 2) % 3 + 3, (unsigned long) printvertex,
3690 printvertex[0], printvertex[1]);
3691 apex(*t, printvertex);
3692 if (printvertex == (vertex) NULL)
3693 printf(" Apex [%d] = NULL\n", t->orient + 3);
3694 else
3695 printf(" Apex [%d] = x%lx (%.12g, %.12g)\n",
3696 t->orient + 3, (unsigned long) printvertex,
3697 printvertex[0], printvertex[1]);
3698
3699 if (b->usesegments) {
3700 sdecode(t->tri[6], printsh);
3701 if (printsh.ss != m->dummysub) {
3702 printf(" [6] = x%lx %d\n", (unsigned long) printsh.ss,
3703 printsh.ssorient);
3704 }
3705 sdecode(t->tri[7], printsh);
3706 if (printsh.ss != m->dummysub) {
3707 printf(" [7] = x%lx %d\n", (unsigned long) printsh.ss,
3708 printsh.ssorient);
3709 }
3710 sdecode(t->tri[8], printsh);
3711 if (printsh.ss != m->dummysub) {
3712 printf(" [8] = x%lx %d\n", (unsigned long) printsh.ss,
3713 printsh.ssorient);
3714 }
3715 }
3716
3717 if (b->vararea) {
3718 printf(" Area constraint: %.4g\n", areabound(*t));
3719 }
3720}
3721
3722/*****************************************************************************/
3723/* */
3724/* printsubseg() Print out the details of an oriented subsegment. */
3725/* */
3726/* I originally wrote this procedure to simplify debugging; it can be */
3727/* called directly from the debugger, and presents information about an */
3728/* oriented subsegment in digestible form. It's also used when the highest */
3729/* level of verbosity (`-VVV') is specified. */
3730/* */
3731/*****************************************************************************/
3732
3733#ifdef ANSI_DECLARATORS
3734void printsubseg(struct mesh *m, struct behavior *b, struct osub *s)
3735#else /* not ANSI_DECLARATORS */
3736void printsubseg(m, b, s)
3737struct mesh *m;
3738struct behavior *b;
3739struct osub *s;
3740#endif /* not ANSI_DECLARATORS */
3741
3742{
3743 struct osub printsh;
3744 struct otri printtri;
3745 vertex printvertex;
3746
3747 (void)b; /*LM: added to suppress warning */
3748
3749 printf("subsegment x%lx with orientation %d and mark %d:\n",
3750 (unsigned long) s->ss, s->ssorient, mark(*s));
3751 sdecode(s->ss[0], printsh);
3752 if (printsh.ss == m->dummysub) {
3753 printf(" [0] = No subsegment\n");
3754 } else {
3755 printf(" [0] = x%lx %d\n", (unsigned long) printsh.ss,
3756 printsh.ssorient);
3757 }
3758 sdecode(s->ss[1], printsh);
3759 if (printsh.ss == m->dummysub) {
3760 printf(" [1] = No subsegment\n");
3761 } else {
3762 printf(" [1] = x%lx %d\n", (unsigned long) printsh.ss,
3763 printsh.ssorient);
3764 }
3765
3766 sorg(*s, printvertex);
3767 if (printvertex == (vertex) NULL)
3768 printf(" Origin[%d] = NULL\n", 2 + s->ssorient);
3769 else
3770 printf(" Origin[%d] = x%lx (%.12g, %.12g)\n",
3771 2 + s->ssorient, (unsigned long) printvertex,
3772 printvertex[0], printvertex[1]);
3773 sdest(*s, printvertex);
3774 if (printvertex == (vertex) NULL)
3775 printf(" Dest [%d] = NULL\n", 3 - s->ssorient);
3776 else
3777 printf(" Dest [%d] = x%lx (%.12g, %.12g)\n",
3778 3 - s->ssorient, (unsigned long) printvertex,
3779 printvertex[0], printvertex[1]);
3780
3781 decode(s->ss[6], printtri);
3782 if (printtri.tri == m->dummytri) {
3783 printf(" [6] = Outer space\n");
3784 } else {
3785 printf(" [6] = x%lx %d\n", (unsigned long) printtri.tri,
3786 printtri.orient);
3787 }
3788 decode(s->ss[7], printtri);
3789 if (printtri.tri == m->dummytri) {
3790 printf(" [7] = Outer space\n");
3791 } else {
3792 printf(" [7] = x%lx %d\n", (unsigned long) printtri.tri,
3793 printtri.orient);
3794 }
3795
3796 segorg(*s, printvertex);
3797 if (printvertex == (vertex) NULL)
3798 printf(" Segment origin[%d] = NULL\n", 4 + s->ssorient);
3799 else
3800 printf(" Segment origin[%d] = x%lx (%.12g, %.12g)\n",
3801 4 + s->ssorient, (unsigned long) printvertex,
3802 printvertex[0], printvertex[1]);
3803 segdest(*s, printvertex);
3804 if (printvertex == (vertex) NULL)
3805 printf(" Segment dest [%d] = NULL\n", 5 - s->ssorient);
3806 else
3807 printf(" Segment dest [%d] = x%lx (%.12g, %.12g)\n",
3808 5 - s->ssorient, (unsigned long) printvertex,
3809 printvertex[0], printvertex[1]);
3810}
3811
3812/** **/
3813/** **/
3814/********* Debugging routines end here *********/
3815
3816/********* Memory management routines begin here *********/
3817/** **/
3818/** **/
3819
3820/*****************************************************************************/
3821/* */
3822/* poolzero() Set all of a pool's fields to zero. */
3823/* */
3824/* This procedure should never be called on a pool that has any memory */
3825/* allocated to it, as that memory would leak. */
3826/* */
3827/*****************************************************************************/
3828
3829#ifdef ANSI_DECLARATORS
3830void poolzero(struct memorypool *pool)
3831#else /* not ANSI_DECLARATORS */
3832void poolzero(pool)
3833struct memorypool *pool;
3834#endif /* not ANSI_DECLARATORS */
3835
3836{
3837 pool->firstblock = (VOID **) NULL;
3838 pool->nowblock = (VOID **) NULL;
3839 pool->nextitem = (VOID *) NULL;
3840 pool->deaditemstack = (VOID *) NULL;
3841 pool->pathblock = (VOID **) NULL;
3842 pool->pathitem = (VOID *) NULL;
3843 pool->alignbytes = 0;
3844 pool->itembytes = 0;
3845 pool->itemsperblock = 0;
3846 pool->itemsfirstblock = 0;
3847 pool->items = 0;
3848 pool->maxitems = 0;
3849 pool->unallocateditems = 0;
3850 pool->pathitemsleft = 0;
3851}
3852
3853/*****************************************************************************/
3854/* */
3855/* poolrestart() Deallocate all items in a pool. */
3856/* */
3857/* The pool is returned to its starting state, except that no memory is */
3858/* freed to the operating system. Rather, the previously allocated blocks */
3859/* are ready to be reused. */
3860/* */
3861/*****************************************************************************/
3862
3863#ifdef ANSI_DECLARATORS
3864void poolrestart(struct memorypool *pool)
3865#else /* not ANSI_DECLARATORS */
3866void poolrestart(pool)
3867struct memorypool *pool;
3868#endif /* not ANSI_DECLARATORS */
3869
3870{
3871 unsigned long alignptr;
3872
3873 pool->items = 0;
3874 pool->maxitems = 0;
3875
3876 /* Set the currently active block. */
3877 pool->nowblock = pool->firstblock;
3878 /* Find the first item in the pool. Increment by the size of (VOID *). */
3879 alignptr = (unsigned long) (pool->nowblock + 1);
3880 /* Align the item on an `alignbytes'-byte boundary. */
3881 pool->nextitem = (VOID *)
3882 (alignptr + (unsigned long) pool->alignbytes -
3883 (alignptr % (unsigned long) pool->alignbytes));
3884 /* There are lots of unallocated items left in this block. */
3885 pool->unallocateditems = pool->itemsfirstblock;
3886 /* The stack of deallocated items is empty. */
3887 pool->deaditemstack = (VOID *) NULL;
3888}
3889
3890/*****************************************************************************/
3891/* */
3892/* poolinit() Initialize a pool of memory for allocation of items. */
3893/* */
3894/* This routine initializes the machinery for allocating items. A `pool' */
3895/* is created whose records have size at least `bytecount'. Items will be */
3896/* allocated in `itemcount'-item blocks. Each item is assumed to be a */
3897/* collection of words, and either pointers or floating-point values are */
3898/* assumed to be the "primary" word type. (The "primary" word type is used */
3899/* to determine alignment of items.) If `alignment' isn't zero, all items */
3900/* will be `alignment'-byte aligned in memory. `alignment' must be either */
3901/* a multiple or a factor of the primary word size; powers of two are safe. */
3902/* `alignment' is normally used to create a few unused bits at the bottom */
3903/* of each item's pointer, in which information may be stored. */
3904/* */
3905/* Don't change this routine unless you understand it. */
3906/* */
3907/*****************************************************************************/
3908
3909#ifdef ANSI_DECLARATORS
3910void poolinit(struct memorypool *pool, int bytecount, int itemcount,
3911 int firstitemcount, int alignment)
3912#else /* not ANSI_DECLARATORS */
3913void poolinit(pool, bytecount, itemcount, firstitemcount, alignment)
3914struct memorypool *pool;
3915int bytecount;
3916int itemcount;
3917int firstitemcount;
3918int alignment;
3919#endif /* not ANSI_DECLARATORS */
3920
3921{
3922 /* Find the proper alignment, which must be at least as large as: */
3923 /* - The parameter `alignment'. */
3924 /* - sizeof(VOID *), so the stack of dead items can be maintained */
3925 /* without unaligned accesses. */
3926 if (alignment > (int) sizeof(VOID *)) {
3927 pool->alignbytes = alignment;
3928 } else {
3929 pool->alignbytes = sizeof(VOID *);
3930 }
3931 pool->itembytes = ((bytecount - 1) / pool->alignbytes + 1) *
3932 pool->alignbytes;
3933 pool->itemsperblock = itemcount;
3934 if (firstitemcount == 0) {
3935 pool->itemsfirstblock = itemcount;
3936 } else {
3937 pool->itemsfirstblock = firstitemcount;
3938 }
3939
3940 /* Allocate a block of items. Space for `itemsfirstblock' items and one */
3941 /* pointer (to point to the next block) are allocated, as well as space */
3942 /* to ensure alignment of the items. */
3943 pool->firstblock = (VOID **)
3944 trimalloc(pool->itemsfirstblock * pool->itembytes + (int) sizeof(VOID *) +
3945 pool->alignbytes);
3946 /* Set the next block pointer to NULL. */
3947 *(pool->firstblock) = (VOID *) NULL;
3948 poolrestart(pool);
3949}
3950
3951/*****************************************************************************/
3952/* */
3953/* pooldeinit() Free to the operating system all memory taken by a pool. */
3954/* */
3955/*****************************************************************************/
3956
3957#ifdef ANSI_DECLARATORS
3958void pooldeinit(struct memorypool *pool)
3959#else /* not ANSI_DECLARATORS */
3960void pooldeinit(pool)
3961struct memorypool *pool;
3962#endif /* not ANSI_DECLARATORS */
3963
3964{
3965 while (pool->firstblock != (VOID **) NULL) {
3966 pool->nowblock = (VOID **) *(pool->firstblock);
3967 trifree((VOID *) pool->firstblock);
3968 pool->firstblock = pool->nowblock;
3969 }
3970}
3971
3972/*****************************************************************************/
3973/* */
3974/* poolalloc() Allocate space for an item. */
3975/* */
3976/*****************************************************************************/
3977
3978#ifdef ANSI_DECLARATORS
3979VOID *poolalloc(struct memorypool *pool)
3980#else /* not ANSI_DECLARATORS */
3981VOID *poolalloc(pool)
3982struct memorypool *pool;
3983#endif /* not ANSI_DECLARATORS */
3984
3985{
3986 VOID *newitem;
3987 VOID **newblock;
3988 unsigned long alignptr;
3989
3990 /* First check the linked list of dead items. If the list is not */
3991 /* empty, allocate an item from the list rather than a fresh one. */
3992 if (pool->deaditemstack != (VOID *) NULL) {
3993 newitem = pool->deaditemstack; /* Take first item in list. */
3994 pool->deaditemstack = * (VOID **) pool->deaditemstack;
3995 } else {
3996 /* Check if there are any free items left in the current block. */
3997 if (pool->unallocateditems == 0) {
3998 /* Check if another block must be allocated. */
3999 if (*(pool->nowblock) == (VOID *) NULL) {
4000 /* Allocate a new block of items, pointed to by the previous block. */
4001 newblock = (VOID **) trimalloc(pool->itemsperblock * pool->itembytes +
4002 (int) sizeof(VOID *) +
4003 pool->alignbytes);
4004 *(pool->nowblock) = (VOID *) newblock;
4005 /* The next block pointer is NULL. */
4006 *newblock = (VOID *) NULL;
4007 }
4008
4009 /* Move to the new block. */
4010 pool->nowblock = (VOID **) *(pool->nowblock);
4011 /* Find the first item in the block. */
4012 /* Increment by the size of (VOID *). */
4013 alignptr = (unsigned long) (pool->nowblock + 1);
4014 /* Align the item on an `alignbytes'-byte boundary. */
4015 pool->nextitem = (VOID *)
4016 (alignptr + (unsigned long) pool->alignbytes -
4017 (alignptr % (unsigned long) pool->alignbytes));
4018 /* There are lots of unallocated items left in this block. */
4019 pool->unallocateditems = pool->itemsperblock;
4020 }
4021
4022 /* Allocate a new item. */
4023 newitem = pool->nextitem;
4024 /* Advance `nextitem' pointer to next free item in block. */
4025 pool->nextitem = (VOID *) ((char *) pool->nextitem + pool->itembytes);
4026 pool->unallocateditems--;
4027 pool->maxitems++;
4028 }
4029 pool->items++;
4030 return newitem;
4031}
4032
4033/*****************************************************************************/
4034/* */
4035/* pooldealloc() Deallocate space for an item. */
4036/* */
4037/* The deallocated space is stored in a queue for later reuse. */
4038/* */
4039/*****************************************************************************/
4040
4041#ifdef ANSI_DECLARATORS
4042void pooldealloc(struct memorypool *pool, VOID *dyingitem)
4043#else /* not ANSI_DECLARATORS */
4044void pooldealloc(pool, dyingitem)
4045struct memorypool *pool;
4046VOID *dyingitem;
4047#endif /* not ANSI_DECLARATORS */
4048
4049{
4050 /* Push freshly killed item onto stack. */
4051 *((VOID **) dyingitem) = pool->deaditemstack;
4052 pool->deaditemstack = dyingitem;
4053 pool->items--;
4054}
4055
4056/*****************************************************************************/
4057/* */
4058/* traversalinit() Prepare to traverse the entire list of items. */
4059/* */
4060/* This routine is used in conjunction with traverse(). */
4061/* */
4062/*****************************************************************************/
4063
4064#ifdef ANSI_DECLARATORS
4065void traversalinit(struct memorypool *pool)
4066#else /* not ANSI_DECLARATORS */
4067void traversalinit(pool)
4068struct memorypool *pool;
4069#endif /* not ANSI_DECLARATORS */
4070
4071{
4072 unsigned long alignptr;
4073
4074 /* Begin the traversal in the first block. */
4075 pool->pathblock = pool->firstblock;
4076 /* Find the first item in the block. Increment by the size of (VOID *). */
4077 alignptr = (unsigned long) (pool->pathblock + 1);
4078 /* Align with item on an `alignbytes'-byte boundary. */
4079 pool->pathitem = (VOID *)
4080 (alignptr + (unsigned long) pool->alignbytes -
4081 (alignptr % (unsigned long) pool->alignbytes));
4082 /* Set the number of items left in the current block. */
4083 pool->pathitemsleft = pool->itemsfirstblock;
4084}
4085
4086/*****************************************************************************/
4087/* */
4088/* traverse() Find the next item in the list. */
4089/* */
4090/* This routine is used in conjunction with traversalinit(). Be forewarned */
4091/* that this routine successively returns all items in the list, including */
4092/* deallocated ones on the deaditemqueue. It's up to you to figure out */
4093/* which ones are actually dead. Why? I don't want to allocate extra */
4094/* space just to demarcate dead items. It can usually be done more */
4095/* space-efficiently by a routine that knows something about the structure */
4096/* of the item. */
4097/* */
4098/*****************************************************************************/
4099
4100#ifdef ANSI_DECLARATORS
4101VOID *traverse(struct memorypool *pool)
4102#else /* not ANSI_DECLARATORS */
4103VOID *traverse(pool)
4104struct memorypool *pool;
4105#endif /* not ANSI_DECLARATORS */
4106
4107{
4108 VOID *newitem;
4109 unsigned long alignptr;
4110
4111 /* Stop upon exhausting the list of items. */
4112 if (pool->pathitem == pool->nextitem) {
4113 return (VOID *) NULL;
4114 }
4115
4116 /* Check whether any untraversed items remain in the current block. */
4117 if (pool->pathitemsleft == 0) {
4118 /* Find the next block. */
4119 pool->pathblock = (VOID **) *(pool->pathblock);
4120 /* Find the first item in the block. Increment by the size of (VOID *). */
4121 alignptr = (unsigned long) (pool->pathblock + 1);
4122 /* Align with item on an `alignbytes'-byte boundary. */
4123 pool->pathitem = (VOID *)
4124 (alignptr + (unsigned long) pool->alignbytes -
4125 (alignptr % (unsigned long) pool->alignbytes));
4126 /* Set the number of items left in the current block. */
4127 pool->pathitemsleft = pool->itemsperblock;
4128 }
4129
4130 newitem = pool->pathitem;
4131 /* Find the next item in the block. */
4132 pool->pathitem = (VOID *) ((char *) pool->pathitem + pool->itembytes);
4133 pool->pathitemsleft--;
4134 return newitem;
4135}
4136
4137/*****************************************************************************/
4138/* */
4139/* dummyinit() Initialize the triangle that fills "outer space" and the */
4140/* omnipresent subsegment. */
4141/* */
4142/* The triangle that fills "outer space," called `dummytri', is pointed to */
4143/* by every triangle and subsegment on a boundary (be it outer or inner) of */
4144/* the triangulation. Also, `dummytri' points to one of the triangles on */
4145/* the convex hull (until the holes and concavities are carved), making it */
4146/* possible to find a starting triangle for point location. */
4147/* */
4148/* The omnipresent subsegment, `dummysub', is pointed to by every triangle */
4149/* or subsegment that doesn't have a full complement of real subsegments */
4150/* to point to. */
4151/* */
4152/* `dummytri' and `dummysub' are generally required to fulfill only a few */
4153/* invariants: their vertices must remain NULL and `dummytri' must always */
4154/* be bonded (at offset zero) to some triangle on the convex hull of the */
4155/* mesh, via a boundary edge. Otherwise, the connections of `dummytri' and */
4156/* `dummysub' may change willy-nilly. This makes it possible to avoid */
4157/* writing a good deal of special-case code (in the edge flip, for example) */
4158/* for dealing with the boundary of the mesh, places where no subsegment is */
4159/* present, and so forth. Other entities are frequently bonded to */
4160/* `dummytri' and `dummysub' as if they were real mesh entities, with no */
4161/* harm done. */
4162/* */
4163/*****************************************************************************/
4164
4165#ifdef ANSI_DECLARATORS
4166void dummyinit(struct mesh *m, struct behavior *b, int trianglebytes,
4167 int subsegbytes)
4168#else /* not ANSI_DECLARATORS */
4169void dummyinit(m, b, trianglebytes, subsegbytes)
4170struct mesh *m;
4171struct behavior *b;
4172int trianglebytes;
4173int subsegbytes;
4174#endif /* not ANSI_DECLARATORS */
4175
4176{
4177 unsigned long alignptr;
4178
4179 /* Set up `dummytri', the `triangle' that occupies "outer space." */
4180 m->dummytribase = (triangle *) trimalloc(trianglebytes +
4181 m->triangles.alignbytes);
4182 /* Align `dummytri' on a `triangles.alignbytes'-byte boundary. */
4183 alignptr = (unsigned long) m->dummytribase;
4184 m->dummytri = (triangle *)
4185 (alignptr + (unsigned long) m->triangles.alignbytes -
4186 (alignptr % (unsigned long) m->triangles.alignbytes));
4187 /* Initialize the three adjoining triangles to be "outer space." These */
4188 /* will eventually be changed by various bonding operations, but their */
4189 /* values don't really matter, as long as they can legally be */
4190 /* dereferenced. */
4191 m->dummytri[0] = (triangle) m->dummytri;
4192 m->dummytri[1] = (triangle) m->dummytri;
4193 m->dummytri[2] = (triangle) m->dummytri;
4194 /* Three NULL vertices. */
4195 m->dummytri[3] = (triangle) NULL;
4196 m->dummytri[4] = (triangle) NULL;
4197 m->dummytri[5] = (triangle) NULL;
4198
4199 if (b->usesegments) {
4200 /* Set up `dummysub', the omnipresent subsegment pointed to by any */
4201 /* triangle side or subsegment end that isn't attached to a real */
4202 /* subsegment. */
4203 m->dummysubbase = (subseg *) trimalloc(subsegbytes +
4204 m->subsegs.alignbytes);
4205 /* Align `dummysub' on a `subsegs.alignbytes'-byte boundary. */
4206 alignptr = (unsigned long) m->dummysubbase;
4207 m->dummysub = (subseg *)
4208 (alignptr + (unsigned long) m->subsegs.alignbytes -
4209 (alignptr % (unsigned long) m->subsegs.alignbytes));
4210 /* Initialize the two adjoining subsegments to be the omnipresent */
4211 /* subsegment. These will eventually be changed by various bonding */
4212 /* operations, but their values don't really matter, as long as they */
4213 /* can legally be dereferenced. */
4214 m->dummysub[0] = (subseg) m->dummysub;
4215 m->dummysub[1] = (subseg) m->dummysub;
4216 /* Four NULL vertices. */
4217 m->dummysub[2] = (subseg) NULL;
4218 m->dummysub[3] = (subseg) NULL;
4219 m->dummysub[4] = (subseg) NULL;
4220 m->dummysub[5] = (subseg) NULL;
4221 /* Initialize the two adjoining triangles to be "outer space." */
4222 m->dummysub[6] = (subseg) m->dummytri;
4223 m->dummysub[7] = (subseg) m->dummytri;
4224 /* Set the boundary marker to zero. */
4225 * (int *) (m->dummysub + 8) = 0;
4226
4227 /* Initialize the three adjoining subsegments of `dummytri' to be */
4228 /* the omnipresent subsegment. */
4229 m->dummytri[6] = (triangle) m->dummysub;
4230 m->dummytri[7] = (triangle) m->dummysub;
4231 m->dummytri[8] = (triangle) m->dummysub;
4232 }
4233}
4234
4235/*****************************************************************************/
4236/* */
4237/* initializevertexpool() Calculate the size of the vertex data structure */
4238/* and initialize its memory pool. */
4239/* */
4240/* This routine also computes the `vertexmarkindex' and `vertex2triindex' */
4241/* indices used to find values within each vertex. */
4242/* */
4243/*****************************************************************************/
4244
4245#ifdef ANSI_DECLARATORS
4246void initializevertexpool(struct mesh *m, struct behavior *b)
4247#else /* not ANSI_DECLARATORS */
4248void initializevertexpool(m, b)
4249struct mesh *m;
4250struct behavior *b;
4251#endif /* not ANSI_DECLARATORS */
4252
4253{
4254 int vertexsize;
4255
4256 /* The index within each vertex at which the boundary marker is found, */
4257 /* followed by the vertex type. Ensure the vertex marker is aligned to */
4258 /* a sizeof(int)-byte address. */
4259 m->vertexmarkindex = ((m->mesh_dim + m->nextras) * sizeof(REAL) +
4260 sizeof(int) - 1) /
4261 sizeof(int);
4262 vertexsize = (m->vertexmarkindex + 2) * sizeof(int);
4263 if (b->poly) {
4264 /* The index within each vertex at which a triangle pointer is found. */
4265 /* Ensure the pointer is aligned to a sizeof(triangle)-byte address. */
4266 m->vertex2triindex = (vertexsize + sizeof(triangle) - 1) /
4267 sizeof(triangle);
4268 vertexsize = (m->vertex2triindex + 1) * sizeof(triangle);
4269 }
4270
4271 /* Initialize the pool of vertices. */
4272 poolinit(&m->vertices, vertexsize, VERTEXPERBLOCK,
4273 m->invertices > VERTEXPERBLOCK ? m->invertices : VERTEXPERBLOCK,
4274 sizeof(REAL));
4275}
4276
4277/*****************************************************************************/
4278/* */
4279/* initializetrisubpools() Calculate the sizes of the triangle and */
4280/* subsegment data structures and initialize */
4281/* their memory pools. */
4282/* */
4283/* This routine also computes the `highorderindex', `elemattribindex', and */
4284/* `areaboundindex' indices used to find values within each triangle. */
4285/* */
4286/*****************************************************************************/
4287
4288#ifdef ANSI_DECLARATORS
4289void initializetrisubpools(struct mesh *m, struct behavior *b)
4290#else /* not ANSI_DECLARATORS */
4291void initializetrisubpools(m, b)
4292struct mesh *m;
4293struct behavior *b;
4294#endif /* not ANSI_DECLARATORS */
4295
4296{
4297 int trisize;
4298
4299 /* The index within each triangle at which the extra nodes (above three) */
4300 /* associated with high order elements are found. There are three */
4301 /* pointers to other triangles, three pointers to corners, and possibly */
4302 /* three pointers to subsegments before the extra nodes. */
4303 m->highorderindex = 6 + (b->usesegments * 3);
4304 /* The number of bytes occupied by a triangle. */
4305 trisize = ((b->order + 1) * (b->order + 2) / 2 + (m->highorderindex - 3)) *
4306 sizeof(triangle);
4307 /* The index within each triangle at which its attributes are found, */
4308 /* where the index is measured in REALs. */
4309 m->elemattribindex = (trisize + sizeof(REAL) - 1) / sizeof(REAL);
4310 /* The index within each triangle at which the maximum area constraint */
4311 /* is found, where the index is measured in REALs. Note that if the */
4312 /* `regionattrib' flag is set, an additional attribute will be added. */
4313 m->areaboundindex = m->elemattribindex + m->eextras + b->regionattrib;
4314 /* If triangle attributes or an area bound are needed, increase the number */
4315 /* of bytes occupied by a triangle. */
4316 if (b->vararea) {
4317 trisize = (m->areaboundindex + 1) * sizeof(REAL);
4318 } else if (m->eextras + b->regionattrib > 0) {
4319 trisize = m->areaboundindex * sizeof(REAL);
4320 }
4321 /* If a Voronoi diagram or triangle neighbor graph is requested, make */
4322 /* sure there's room to store an integer index in each triangle. This */
4323 /* integer index can occupy the same space as the subsegment pointers */
4324 /* or attributes or area constraint or extra nodes. */
4325 if ((b->voronoi || b->neighbors) &&
4326 (trisize < (int) ( 6 * sizeof(triangle) + sizeof(int)))) {
4327 trisize = 6 * sizeof(triangle) + sizeof(int);
4328 }
4329
4330 /* Having determined the memory size of a triangle, initialize the pool. */
4331 poolinit(&m->triangles, trisize, TRIPERBLOCK,
4332 (2 * m->invertices - 2) > TRIPERBLOCK ? (2 * m->invertices - 2) :
4333 TRIPERBLOCK, 4);
4334
4335 if (b->usesegments) {
4336 /* Initialize the pool of subsegments. Take into account all eight */
4337 /* pointers and one boundary marker. */
4338 poolinit(&m->subsegs, 8 * sizeof(triangle) + sizeof(int),
4339 SUBSEGPERBLOCK, SUBSEGPERBLOCK, 4);
4340
4341 /* Initialize the "outer space" triangle and omnipresent subsegment. */
4342 dummyinit(m, b, m->triangles.itembytes, m->subsegs.itembytes);
4343 } else {
4344 /* Initialize the "outer space" triangle. */
4345 dummyinit(m, b, m->triangles.itembytes, 0);
4346 }
4347}
4348
4349/*****************************************************************************/
4350/* */
4351/* triangledealloc() Deallocate space for a triangle, marking it dead. */
4352/* */
4353/*****************************************************************************/
4354
4355#ifdef ANSI_DECLARATORS
4356void triangledealloc(struct mesh *m, triangle *dyingtriangle)
4357#else /* not ANSI_DECLARATORS */
4358void triangledealloc(m, dyingtriangle)
4359struct mesh *m;
4360triangle *dyingtriangle;
4361#endif /* not ANSI_DECLARATORS */
4362
4363{
4364 /* Mark the triangle as dead. This makes it possible to detect dead */
4365 /* triangles when traversing the list of all triangles. */
4366 killtri(dyingtriangle);
4367 pooldealloc(&m->triangles, (VOID *) dyingtriangle);
4368}
4369
4370/*****************************************************************************/
4371/* */
4372/* triangletraverse() Traverse the triangles, skipping dead ones. */
4373/* */
4374/*****************************************************************************/
4375
4376#ifdef ANSI_DECLARATORS
4377triangle *triangletraverse(struct mesh *m)
4378#else /* not ANSI_DECLARATORS */
4379triangle *triangletraverse(m)
4380struct mesh *m;
4381#endif /* not ANSI_DECLARATORS */
4382
4383{
4384 triangle *newtriangle;
4385
4386 do {
4387 newtriangle = (triangle *) traverse(&m->triangles);
4388 if (newtriangle == (triangle *) NULL) {
4389 return (triangle *) NULL;
4390 }
4391 } while (deadtri(newtriangle)); /* Skip dead ones. */
4392 return newtriangle;
4393}
4394
4395/*****************************************************************************/
4396/* */
4397/* subsegdealloc() Deallocate space for a subsegment, marking it dead. */
4398/* */
4399/*****************************************************************************/
4400
4401#ifdef ANSI_DECLARATORS
4402void subsegdealloc(struct mesh *m, subseg *dyingsubseg)
4403#else /* not ANSI_DECLARATORS */
4404void subsegdealloc(m, dyingsubseg)
4405struct mesh *m;
4406subseg *dyingsubseg;
4407#endif /* not ANSI_DECLARATORS */
4408
4409{
4410 /* Mark the subsegment as dead. This makes it possible to detect dead */
4411 /* subsegments when traversing the list of all subsegments. */
4412 killsubseg(dyingsubseg);
4413 pooldealloc(&m->subsegs, (VOID *) dyingsubseg);
4414}
4415
4416/*****************************************************************************/
4417/* */
4418/* subsegtraverse() Traverse the subsegments, skipping dead ones. */
4419/* */
4420/*****************************************************************************/
4421
4422#ifdef ANSI_DECLARATORS
4423subseg *subsegtraverse(struct mesh *m)
4424#else /* not ANSI_DECLARATORS */
4425subseg *subsegtraverse(m)
4426struct mesh *m;
4427#endif /* not ANSI_DECLARATORS */
4428
4429{
4430 subseg *newsubseg;
4431
4432 do {
4433 newsubseg = (subseg *) traverse(&m->subsegs);
4434 if (newsubseg == (subseg *) NULL) {
4435 return (subseg *) NULL;
4436 }
4437 } while (deadsubseg(newsubseg)); /* Skip dead ones. */
4438 return newsubseg;
4439}
4440
4441/*****************************************************************************/
4442/* */
4443/* vertexdealloc() Deallocate space for a vertex, marking it dead. */
4444/* */
4445/*****************************************************************************/
4446
4447#ifdef ANSI_DECLARATORS
4448void vertexdealloc(struct mesh *m, vertex dyingvertex)
4449#else /* not ANSI_DECLARATORS */
4450void vertexdealloc(m, dyingvertex)
4451struct mesh *m;
4452vertex dyingvertex;
4453#endif /* not ANSI_DECLARATORS */
4454
4455{
4456 /* Mark the vertex as dead. This makes it possible to detect dead */
4457 /* vertices when traversing the list of all vertices. */
4458 setvertextype(dyingvertex, DEADVERTEX);
4459 pooldealloc(&m->vertices, (VOID *) dyingvertex);
4460}
4461
4462/*****************************************************************************/
4463/* */
4464/* vertextraverse() Traverse the vertices, skipping dead ones. */
4465/* */
4466/*****************************************************************************/
4467
4468#ifdef ANSI_DECLARATORS
4469vertex vertextraverse(struct mesh *m)
4470#else /* not ANSI_DECLARATORS */
4471vertex vertextraverse(m)
4472struct mesh *m;
4473#endif /* not ANSI_DECLARATORS */
4474
4475{
4476 vertex newvertex;
4477
4478 do {
4479 newvertex = (vertex) traverse(&m->vertices);
4480 if (newvertex == (vertex) NULL) {
4481 return (vertex) NULL;
4482 }
4483 } while (vertextype(newvertex) == DEADVERTEX); /* Skip dead ones. */
4484 return newvertex;
4485}
4486
4487/*****************************************************************************/
4488/* */
4489/* badsubsegdealloc() Deallocate space for a bad subsegment, marking it */
4490/* dead. */
4491/* */
4492/*****************************************************************************/
4493
4494#ifndef CDT_ONLY
4495
4496#ifdef ANSI_DECLARATORS
4497void badsubsegdealloc(struct mesh *m, struct badsubseg *dyingseg)
4498#else /* not ANSI_DECLARATORS */
4499void badsubsegdealloc(m, dyingseg)
4500struct mesh *m;
4501struct badsubseg *dyingseg;
4502#endif /* not ANSI_DECLARATORS */
4503
4504{
4505 /* Set subsegment's origin to NULL. This makes it possible to detect dead */
4506 /* badsubsegs when traversing the list of all badsubsegs . */
4507 dyingseg->subsegorg = (vertex) NULL;
4508 pooldealloc(&m->badsubsegs, (VOID *) dyingseg);
4509}
4510
4511#endif /* not CDT_ONLY */
4512
4513/*****************************************************************************/
4514/* */
4515/* badsubsegtraverse() Traverse the bad subsegments, skipping dead ones. */
4516/* */
4517/*****************************************************************************/
4518
4519#ifndef CDT_ONLY
4520
4521#ifdef ANSI_DECLARATORS
4522struct badsubseg *badsubsegtraverse(struct mesh *m)
4523#else /* not ANSI_DECLARATORS */
4524struct badsubseg *badsubsegtraverse(m)
4525struct mesh *m;
4526#endif /* not ANSI_DECLARATORS */
4527
4528{
4529 struct badsubseg *newseg;
4530
4531 do {
4532 newseg = (struct badsubseg *) traverse(&m->badsubsegs);
4533 if (newseg == (struct badsubseg *) NULL) {
4534 return (struct badsubseg *) NULL;
4535 }
4536 } while (newseg->subsegorg == (vertex) NULL); /* Skip dead ones. */
4537 return newseg;
4538}
4539
4540#endif /* not CDT_ONLY */
4541
4542/*****************************************************************************/
4543/* */
4544/* getvertex() Get a specific vertex, by number, from the list. */
4545/* */
4546/* The first vertex is number 'firstnumber'. */
4547/* */
4548/* Note that this takes O(n) time (with a small constant, if VERTEXPERBLOCK */
4549/* is large). I don't care to take the trouble to make it work in constant */
4550/* time. */
4551/* */
4552/*****************************************************************************/
4553
4554#ifdef ANSI_DECLARATORS
4555vertex getvertex(struct mesh *m, struct behavior *b, int number)
4556#else /* not ANSI_DECLARATORS */
4557vertex getvertex(m, b, number)
4558struct mesh *m;
4559struct behavior *b;
4560int number;
4561#endif /* not ANSI_DECLARATORS */
4562
4563{
4564 VOID **getblock;
4565 char *foundvertex;
4566 unsigned long alignptr;
4567 int current;
4568
4569 getblock = m->vertices.firstblock;
4570 current = b->firstnumber;
4571
4572 /* Find the right block. */
4573 if (current + m->vertices.itemsfirstblock <= number) {
4574 getblock = (VOID **) *getblock;
4575 current += m->vertices.itemsfirstblock;
4576 while (current + m->vertices.itemsperblock <= number) {
4577 getblock = (VOID **) *getblock;
4578 current += m->vertices.itemsperblock;
4579 }
4580 }
4581
4582 /* Now find the right vertex. */
4583 alignptr = (unsigned long) (getblock + 1);
4584 foundvertex = (char *) (alignptr + (unsigned long) m->vertices.alignbytes -
4585 (alignptr % (unsigned long) m->vertices.alignbytes));
4586 return (vertex) (foundvertex + m->vertices.itembytes * (number - current));
4587}
4588
4589/*****************************************************************************/
4590/* */
4591/* triangledeinit() Free all remaining allocated memory. */
4592/* */
4593/*****************************************************************************/
4594
4595#ifdef ANSI_DECLARATORS
4596void triangledeinit(struct mesh *m, struct behavior *b)
4597#else /* not ANSI_DECLARATORS */
4598void triangledeinit(m, b)
4599struct mesh *m;
4600struct behavior *b;
4601#endif /* not ANSI_DECLARATORS */
4602
4603{
4604 pooldeinit(&m->triangles);
4605 trifree((VOID *) m->dummytribase);
4606 if (b->usesegments) {
4607 pooldeinit(&m->subsegs);
4608 trifree((VOID *) m->dummysubbase);
4609 }
4610 pooldeinit(&m->vertices);
4611#ifndef CDT_ONLY
4612 if (b->quality) {
4613 pooldeinit(&m->badsubsegs);
4614 if ((b->minangle > 0.0) || b->vararea || b->fixedarea || b->usertest) {
4615 pooldeinit(&m->badtriangles);
4616 pooldeinit(&m->flipstackers);
4617 }
4618 }
4619#endif /* not CDT_ONLY */
4620}
4621
4622/** **/
4623/** **/
4624/********* Memory management routines end here *********/
4625
4626/********* Constructors begin here *********/
4627/** **/
4628/** **/
4629
4630/*****************************************************************************/
4631/* */
4632/* maketriangle() Create a new triangle with orientation zero. */
4633/* */
4634/*****************************************************************************/
4635
4636#ifdef ANSI_DECLARATORS
4637void maketriangle(struct mesh *m, struct behavior *b, struct otri *newotri)
4638#else /* not ANSI_DECLARATORS */
4639void maketriangle(m, b, newotri)
4640struct mesh *m;
4641struct behavior *b;
4642struct otri *newotri;
4643#endif /* not ANSI_DECLARATORS */
4644
4645{
4646 int i;
4647
4648 newotri->tri = (triangle *) poolalloc(&m->triangles);
4649 /* Initialize the three adjoining triangles to be "outer space". */
4650 newotri->tri[0] = (triangle) m->dummytri;
4651 newotri->tri[1] = (triangle) m->dummytri;
4652 newotri->tri[2] = (triangle) m->dummytri;
4653 /* Three NULL vertices. */
4654 newotri->tri[3] = (triangle) NULL;
4655 newotri->tri[4] = (triangle) NULL;
4656 newotri->tri[5] = (triangle) NULL;
4657 if (b->usesegments) {
4658 /* Initialize the three adjoining subsegments to be the omnipresent */
4659 /* subsegment. */
4660 newotri->tri[6] = (triangle) m->dummysub;
4661 newotri->tri[7] = (triangle) m->dummysub;
4662 newotri->tri[8] = (triangle) m->dummysub;
4663 }
4664 for (i = 0; i < m->eextras; i++) {
4665 setelemattribute(*newotri, i, 0.0);
4666 }
4667 if (b->vararea) {
4668 setareabound(*newotri, -1.0);
4669 }
4670
4671 newotri->orient = 0;
4672}
4673
4674/*****************************************************************************/
4675/* */
4676/* makesubseg() Create a new subsegment with orientation zero. */
4677/* */
4678/*****************************************************************************/
4679
4680#ifdef ANSI_DECLARATORS
4681void makesubseg(struct mesh *m, struct osub *newsubseg)
4682#else /* not ANSI_DECLARATORS */
4683void makesubseg(m, newsubseg)
4684struct mesh *m;
4685struct osub *newsubseg;
4686#endif /* not ANSI_DECLARATORS */
4687
4688{
4689 newsubseg->ss = (subseg *) poolalloc(&m->subsegs);
4690 /* Initialize the two adjoining subsegments to be the omnipresent */
4691 /* subsegment. */
4692 newsubseg->ss[0] = (subseg) m->dummysub;
4693 newsubseg->ss[1] = (subseg) m->dummysub;
4694 /* Four NULL vertices. */
4695 newsubseg->ss[2] = (subseg) NULL;
4696 newsubseg->ss[3] = (subseg) NULL;
4697 newsubseg->ss[4] = (subseg) NULL;
4698 newsubseg->ss[5] = (subseg) NULL;
4699 /* Initialize the two adjoining triangles to be "outer space." */
4700 newsubseg->ss[6] = (subseg) m->dummytri;
4701 newsubseg->ss[7] = (subseg) m->dummytri;
4702 /* Set the boundary marker to zero. */
4703 setmark(*newsubseg, 0);
4704
4705 newsubseg->ssorient = 0;
4706}
4707
4708/** **/
4709/** **/
4710/********* Constructors end here *********/
4711
4712/********* Geometric primitives begin here *********/
4713/** **/
4714/** **/
4715
4716/* The adaptive exact arithmetic geometric predicates implemented herein are */
4717/* described in detail in my paper, "Adaptive Precision Floating-Point */
4718/* Arithmetic and Fast Robust Geometric Predicates." See the header for a */
4719/* full citation. */
4720
4721/* Which of the following two methods of finding the absolute values is */
4722/* fastest is compiler-dependent. A few compilers can inline and optimize */
4723/* the fabs() call; but most will incur the overhead of a function call, */
4724/* which is disastrously slow. A faster way on IEEE machines might be to */
4725/* mask the appropriate bit, but that's difficult to do in C without */
4726/* forcing the value to be stored to memory (rather than be kept in the */
4727/* register to which the optimizer assigned it). */
4728
4729#define Absolute(a) ((a) >= 0.0 ? (a) : -(a))
4730/* #define Absolute(a) fabs(a) */
4731
4732/* Many of the operations are broken up into two pieces, a main part that */
4733/* performs an approximate operation, and a "tail" that computes the */
4734/* roundoff error of that operation. */
4735/* */
4736/* The operations Fast_Two_Sum(), Fast_Two_Diff(), Two_Sum(), Two_Diff(), */
4737/* Split(), and Two_Product() are all implemented as described in the */
4738/* reference. Each of these macros requires certain variables to be */
4739/* defined in the calling routine. The variables `bvirt', `c', `abig', */
4740/* `_i', `_j', `_k', `_l', `_m', and `_n' are declared `INEXACT' because */
4741/* they store the result of an operation that may incur roundoff error. */
4742/* The input parameter `x' (or the highest numbered `x_' parameter) must */
4743/* also be declared `INEXACT'. */
4744
4745#define Fast_Two_Sum_Tail(a, b, x, y) \
4746 bvirt = x - a; \
4747 y = b - bvirt
4748
4749#define Fast_Two_Sum(a, b, x, y) \
4750 x = (REAL) (a + b); \
4751 Fast_Two_Sum_Tail(a, b, x, y)
4752
4753#define Two_Sum_Tail(a, b, x, y) \
4754 bvirt = (REAL) (x - a); \
4755 avirt = x - bvirt; \
4756 bround = b - bvirt; \
4757 around = a - avirt; \
4758 y = around + bround
4759
4760#define Two_Sum(a, b, x, y) \
4761 x = (REAL) (a + b); \
4762 Two_Sum_Tail(a, b, x, y)
4763
4764#define Two_Diff_Tail(a, b, x, y) \
4765 bvirt = (REAL) (a - x); \
4766 avirt = x + bvirt; \
4767 bround = bvirt - b; \
4768 around = a - avirt; \
4769 y = around + bround
4770
4771#define Two_Diff(a, b, x, y) \
4772 x = (REAL) (a - b); \
4773 Two_Diff_Tail(a, b, x, y)
4774
4775#define Split(a, ahi, alo) \
4776 c = (REAL) (splitter * a); \
4777 abig = (REAL) (c - a); \
4778 ahi = c - abig; \
4779 alo = a - ahi
4780
4781#define Two_Product_Tail(a, b, x, y) \
4782 Split(a, ahi, alo); \
4783 Split(b, bhi, blo); \
4784 err1 = x - (ahi * bhi); \
4785 err2 = err1 - (alo * bhi); \
4786 err3 = err2 - (ahi * blo); \
4787 y = (alo * blo) - err3
4788
4789#define Two_Product(a, b, x, y) \
4790 x = (REAL) (a * b); \
4791 Two_Product_Tail(a, b, x, y)
4792
4793/* Two_Product_Presplit() is Two_Product() where one of the inputs has */
4794/* already been split. Avoids redundant splitting. */
4795
4796#define Two_Product_Presplit(a, b, bhi, blo, x, y) \
4797 x = (REAL) (a * b); \
4798 Split(a, ahi, alo); \
4799 err1 = x - (ahi * bhi); \
4800 err2 = err1 - (alo * bhi); \
4801 err3 = err2 - (ahi * blo); \
4802 y = (alo * blo) - err3
4803
4804/* Square() can be done more quickly than Two_Product(). */
4805
4806#define Square_Tail(a, x, y) \
4807 Split(a, ahi, alo); \
4808 err1 = x - (ahi * ahi); \
4809 err3 = err1 - ((ahi + ahi) * alo); \
4810 y = (alo * alo) - err3
4811
4812#define Square(a, x, y) \
4813 x = (REAL) (a * a); \
4814 Square_Tail(a, x, y)
4815
4816/* Macros for summing expansions of various fixed lengths. These are all */
4817/* unrolled versions of Expansion_Sum(). */
4818
4819#define Two_One_Sum(a1, a0, b, x2, x1, x0) \
4820 Two_Sum(a0, b , _i, x0); \
4821 Two_Sum(a1, _i, x2, x1)
4822
4823#define Two_One_Diff(a1, a0, b, x2, x1, x0) \
4824 Two_Diff(a0, b , _i, x0); \
4825 Two_Sum( a1, _i, x2, x1)
4826
4827#define Two_Two_Sum(a1, a0, b1, b0, x3, x2, x1, x0) \
4828 Two_One_Sum(a1, a0, b0, _j, _0, x0); \
4829 Two_One_Sum(_j, _0, b1, x3, x2, x1)
4830
4831#define Two_Two_Diff(a1, a0, b1, b0, x3, x2, x1, x0) \
4832 Two_One_Diff(a1, a0, b0, _j, _0, x0); \
4833 Two_One_Diff(_j, _0, b1, x3, x2, x1)
4834
4835/* Macro for multiplying a two-component expansion by a single component. */
4836
4837#define Two_One_Product(a1, a0, b, x3, x2, x1, x0) \
4838 Split(b, bhi, blo); \
4839 Two_Product_Presplit(a0, b, bhi, blo, _i, x0); \
4840 Two_Product_Presplit(a1, b, bhi, blo, _j, _0); \
4841 Two_Sum(_i, _0, _k, x1); \
4842 Fast_Two_Sum(_j, _k, x3, x2)
4843
4844/*****************************************************************************/
4845/* */
4846/* exactinit() Initialize the variables used for exact arithmetic. */
4847/* */
4848/* `epsilon' is the largest power of two such that 1.0 + epsilon = 1.0 in */
4849/* floating-point arithmetic. `epsilon' bounds the relative roundoff */
4850/* error. It is used for floating-point error analysis. */
4851/* */
4852/* `splitter' is used to split floating-point numbers into two half- */
4853/* length significands for exact multiplication. */
4854/* */
4855/* I imagine that a highly optimizing compiler might be too smart for its */
4856/* own good, and somehow cause this routine to fail, if it pretends that */
4857/* floating-point arithmetic is too much like real arithmetic. */
4858/* */
4859/* Don't change this routine unless you fully understand it. */
4860/* */
4861/*****************************************************************************/
4862
4863void exactinit()
4864{
4865 REAL half;
4866 REAL check, lastcheck;
4867 int every_other;
4868#ifdef LINUX
4869 int cword;
4870#endif /* LINUX */
4871
4872#ifdef CPU86
4873#ifdef SINGLE
4874 _control87(_PC_24, _MCW_PC); /* Set FPU control word for single precision. */
4875#else /* not SINGLE */
4876 _control87(_PC_53, _MCW_PC); /* Set FPU control word for double precision. */
4877#endif /* not SINGLE */
4878#endif /* CPU86 */
4879#ifdef LINUX
4880#ifdef SINGLE
4881 /* cword = 4223; */
4882 cword = 4210; /* set FPU control word for single precision */
4883#else /* not SINGLE */
4884 /* cword = 4735; */
4885 cword = 4722; /* set FPU control word for double precision */
4886#endif /* not SINGLE */
4887 _FPU_SETCW(cword);
4888#endif /* LINUX */
4889
4890 every_other = 1;
4891 half = 0.5;
4892 epsilon = 1.0;
4893 splitter = 1.0;
4894 check = 1.0;
4895 /* Repeatedly divide `epsilon' by two until it is too small to add to */
4896 /* one without causing roundoff. (Also check if the sum is equal to */
4897 /* the previous sum, for machines that round up instead of using exact */
4898 /* rounding. Not that these routines will work on such machines.) */
4899 do {
4900 lastcheck = check;
4901 epsilon *= half;
4902 if (every_other) {
4903 splitter *= 2.0;
4904 }
4905 every_other = !every_other;
4906 check = 1.0 + epsilon;
4907 } while ((check != 1.0) && (check != lastcheck));
4908 splitter += 1.0;
4909 /* Error bounds for orientation and incircle tests. */
4910 resulterrbound = (3.0 + 8.0 * epsilon) * epsilon;
4911 ccwerrboundA = (3.0 + 16.0 * epsilon) * epsilon;
4912 ccwerrboundB = (2.0 + 12.0 * epsilon) * epsilon;
4913 ccwerrboundC = (9.0 + 64.0 * epsilon) * epsilon * epsilon;
4914 iccerrboundA = (10.0 + 96.0 * epsilon) * epsilon;
4915 iccerrboundB = (4.0 + 48.0 * epsilon) * epsilon;
4916 iccerrboundC = (44.0 + 576.0 * epsilon) * epsilon * epsilon;
4917 o3derrboundA = (7.0 + 56.0 * epsilon) * epsilon;
4918 o3derrboundB = (3.0 + 28.0 * epsilon) * epsilon;
4919 o3derrboundC = (26.0 + 288.0 * epsilon) * epsilon * epsilon;
4920}
4921
4922/*****************************************************************************/
4923/* */
4924/* fast_expansion_sum_zeroelim() Sum two expansions, eliminating zero */
4925/* components from the output expansion. */
4926/* */
4927/* Sets h = e + f. See my Robust Predicates paper for details. */
4928/* */
4929/* If round-to-even is used (as with IEEE 754), maintains the strongly */
4930/* nonoverlapping property. (That is, if e is strongly nonoverlapping, h */
4931/* will be also.) Does NOT maintain the nonoverlapping or nonadjacent */
4932/* properties. */
4933/* */
4934/*****************************************************************************/
4935
4936#ifdef ANSI_DECLARATORS
4937int fast_expansion_sum_zeroelim(int elen, REAL *e, int flen, REAL *f, REAL *h)
4938#else /* not ANSI_DECLARATORS */
4939int fast_expansion_sum_zeroelim(elen, e, flen, f, h) /* h cannot be e or f. */
4940int elen;
4941REAL *e;
4942int flen;
4943REAL *f;
4944REAL *h;
4945#endif /* not ANSI_DECLARATORS */
4946
4947{
4948 REAL Q;
4949 INEXACT REAL Qnew;
4950 INEXACT REAL hh;
4951 INEXACT REAL bvirt;
4952 REAL avirt, bround, around;
4953 int eindex, findex, hindex;
4954 REAL enow, fnow;
4955
4956 enow = e[0];
4957 fnow = f[0];
4958 eindex = findex = 0;
4959 if ((fnow > enow) == (fnow > -enow)) {
4960 Q = enow;
4961 enow = e[++eindex];
4962 } else {
4963 Q = fnow;
4964 fnow = f[++findex];
4965 }
4966 hindex = 0;
4967 if ((eindex < elen) && (findex < flen)) {
4968 if ((fnow > enow) == (fnow > -enow)) {
4969 Fast_Two_Sum(enow, Q, Qnew, hh);
4970 enow = e[++eindex];
4971 } else {
4972 Fast_Two_Sum(fnow, Q, Qnew, hh);
4973 fnow = f[++findex];
4974 }
4975 Q = Qnew;
4976 if (hh != 0.0) {
4977 h[hindex++] = hh;
4978 }
4979 while ((eindex < elen) && (findex < flen)) {
4980 if ((fnow > enow) == (fnow > -enow)) {
4981 Two_Sum(Q, enow, Qnew, hh);
4982 enow = e[++eindex];
4983 } else {
4984 Two_Sum(Q, fnow, Qnew, hh);
4985 fnow = f[++findex];
4986 }
4987 Q = Qnew;
4988 if (hh != 0.0) {
4989 h[hindex++] = hh;
4990 }
4991 }
4992 }
4993 while (eindex < elen) {
4994 Two_Sum(Q, enow, Qnew, hh);
4995 enow = e[++eindex];
4996 Q = Qnew;
4997 if (hh != 0.0) {
4998 h[hindex++] = hh;
4999 }
5000 }
5001 while (findex < flen) {
5002 Two_Sum(Q, fnow, Qnew, hh);
5003 fnow = f[++findex];
5004 Q = Qnew;
5005 if (hh != 0.0) {
5006 h[hindex++] = hh;
5007 }
5008 }
5009 if ((Q != 0.0) || (hindex == 0)) {
5010 h[hindex++] = Q;
5011 }
5012 return hindex;
5013}
5014
5015/*****************************************************************************/
5016/* */
5017/* scale_expansion_zeroelim() Multiply an expansion by a scalar, */
5018/* eliminating zero components from the */
5019/* output expansion. */
5020/* */
5021/* Sets h = be. See my Robust Predicates paper for details. */
5022/* */
5023/* Maintains the nonoverlapping property. If round-to-even is used (as */
5024/* with IEEE 754), maintains the strongly nonoverlapping and nonadjacent */
5025/* properties as well. (That is, if e has one of these properties, so */
5026/* will h.) */
5027/* */
5028/*****************************************************************************/
5029
5030#ifdef ANSI_DECLARATORS
5031int scale_expansion_zeroelim(int elen, REAL *e, REAL b, REAL *h)
5032#else /* not ANSI_DECLARATORS */
5033int scale_expansion_zeroelim(elen, e, b, h) /* e and h cannot be the same. */
5034int elen;
5035REAL *e;
5036REAL b;
5037REAL *h;
5038#endif /* not ANSI_DECLARATORS */
5039
5040{
5041 INEXACT REAL Q, sum;
5042 REAL hh;
5043 INEXACT REAL product1;
5044 REAL product0;
5045 int eindex, hindex;
5046 REAL enow;
5047 INEXACT REAL bvirt;
5048 REAL avirt, bround, around;
5049 INEXACT REAL c;
5050 INEXACT REAL abig;
5051 REAL ahi, alo, bhi, blo;
5052 REAL err1, err2, err3;
5053
5054 Split(b, bhi, blo);
5055 Two_Product_Presplit(e[0], b, bhi, blo, Q, hh);
5056 hindex = 0;
5057 if (hh != 0) {
5058 h[hindex++] = hh;
5059 }
5060 for (eindex = 1; eindex < elen; eindex++) {
5061 enow = e[eindex];
5062 Two_Product_Presplit(enow, b, bhi, blo, product1, product0);
5063 Two_Sum(Q, product0, sum, hh);
5064 if (hh != 0) {
5065 h[hindex++] = hh;
5066 }
5067 Fast_Two_Sum(product1, sum, Q, hh);
5068 if (hh != 0) {
5069 h[hindex++] = hh;
5070 }
5071 }
5072 if ((Q != 0.0) || (hindex == 0)) {
5073 h[hindex++] = Q;
5074 }
5075 return hindex;
5076}
5077
5078/*****************************************************************************/
5079/* */
5080/* estimate() Produce a one-word estimate of an expansion's value. */
5081/* */
5082/* See my Robust Predicates paper for details. */
5083/* */
5084/*****************************************************************************/
5085
5086#ifdef ANSI_DECLARATORS
5087REAL estimate(int elen, REAL *e)
5088#else /* not ANSI_DECLARATORS */
5089REAL estimate(elen, e)
5090int elen;
5091REAL *e;
5092#endif /* not ANSI_DECLARATORS */
5093
5094{
5095 REAL Q;
5096 int eindex;
5097
5098 Q = e[0];
5099 for (eindex = 1; eindex < elen; eindex++) {
5100 Q += e[eindex];
5101 }
5102 return Q;
5103}
5104
5105/*****************************************************************************/
5106/* */
5107/* counterclockwise() Return a positive value if the points pa, pb, and */
5108/* pc occur in counterclockwise order; a negative */
5109/* value if they occur in clockwise order; and zero */
5110/* if they are collinear. The result is also a rough */
5111/* approximation of twice the signed area of the */
5112/* triangle defined by the three points. */
5113/* */
5114/* Uses exact arithmetic if necessary to ensure a correct answer. The */
5115/* result returned is the determinant of a matrix. This determinant is */
5116/* computed adaptively, in the sense that exact arithmetic is used only to */
5117/* the degree it is needed to ensure that the returned value has the */
5118/* correct sign. Hence, this function is usually quite fast, but will run */
5119/* more slowly when the input points are collinear or nearly so. */
5120/* */
5121/* See my Robust Predicates paper for details. */
5122/* */
5123/*****************************************************************************/
5124
5125#ifdef ANSI_DECLARATORS
5126REAL counterclockwiseadapt(vertex pa, vertex pb, vertex pc, REAL detsum)
5127#else /* not ANSI_DECLARATORS */
5128REAL counterclockwiseadapt(pa, pb, pc, detsum)
5129vertex pa;
5130vertex pb;
5131vertex pc;
5132REAL detsum;
5133#endif /* not ANSI_DECLARATORS */
5134
5135{
5136 INEXACT REAL acx, acy, bcx, bcy;
5137 REAL acxtail, acytail, bcxtail, bcytail;
5138 INEXACT REAL detleft, detright;
5139 REAL detlefttail, detrighttail;
5140 REAL det, errbound;
5141 REAL B[4], C1[8], C2[12], D[16];
5142 INEXACT REAL B3;
5143 int C1length, C2length, Dlength;
5144 REAL u[4];
5145 INEXACT REAL u3;
5146 INEXACT REAL s1, t1;
5147 REAL s0, t0;
5148
5149 INEXACT REAL bvirt;
5150 REAL avirt, bround, around;
5151 INEXACT REAL c;
5152 INEXACT REAL abig;
5153 REAL ahi, alo, bhi, blo;
5154 REAL err1, err2, err3;
5155 INEXACT REAL _i, _j;
5156 REAL _0;
5157
5158 acx = (REAL) (pa[0] - pc[0]);
5159 bcx = (REAL) (pb[0] - pc[0]);
5160 acy = (REAL) (pa[1] - pc[1]);
5161 bcy = (REAL) (pb[1] - pc[1]);
5162
5163 Two_Product(acx, bcy, detleft, detlefttail);
5164 Two_Product(acy, bcx, detright, detrighttail);
5165
5166 Two_Two_Diff(detleft, detlefttail, detright, detrighttail,
5167 B3, B[2], B[1], B[0]);
5168 B[3] = B3;
5169
5170 det = estimate(4, B);
5171 errbound = ccwerrboundB * detsum;
5172 if ((det >= errbound) || (-det >= errbound)) {
5173 return det;
5174 }
5175
5176 Two_Diff_Tail(pa[0], pc[0], acx, acxtail);
5177 Two_Diff_Tail(pb[0], pc[0], bcx, bcxtail);
5178 Two_Diff_Tail(pa[1], pc[1], acy, acytail);
5179 Two_Diff_Tail(pb[1], pc[1], bcy, bcytail);
5180
5181 if ((acxtail == 0.0) && (acytail == 0.0)
5182 && (bcxtail == 0.0) && (bcytail == 0.0)) {
5183 return det;
5184 }
5185
5186 errbound = ccwerrboundC * detsum + resulterrbound * Absolute(det);
5187 det += (acx * bcytail + bcy * acxtail)
5188 - (acy * bcxtail + bcx * acytail);
5189 if ((det >= errbound) || (-det >= errbound)) {
5190 return det;
5191 }
5192
5193 Two_Product(acxtail, bcy, s1, s0);
5194 Two_Product(acytail, bcx, t1, t0);
5195 Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
5196 u[3] = u3;
5197 C1length = fast_expansion_sum_zeroelim(4, B, 4, u, C1);
5198
5199 Two_Product(acx, bcytail, s1, s0);
5200 Two_Product(acy, bcxtail, t1, t0);
5201 Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
5202 u[3] = u3;
5203 C2length = fast_expansion_sum_zeroelim(C1length, C1, 4, u, C2);
5204
5205 Two_Product(acxtail, bcytail, s1, s0);
5206 Two_Product(acytail, bcxtail, t1, t0);
5207 Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
5208 u[3] = u3;
5209 Dlength = fast_expansion_sum_zeroelim(C2length, C2, 4, u, D);
5210
5211 return(D[Dlength - 1]);
5212}
5213
5214#ifdef ANSI_DECLARATORS
5215REAL counterclockwise(struct mesh *m, struct behavior *b,
5216 vertex pa, vertex pb, vertex pc)
5217#else /* not ANSI_DECLARATORS */
5218REAL counterclockwise(m, b, pa, pb, pc)
5219struct mesh *m;
5220struct behavior *b;
5221vertex pa;
5222vertex pb;
5223vertex pc;
5224#endif /* not ANSI_DECLARATORS */
5225
5226{
5227 REAL detleft, detright, det;
5228 REAL detsum, errbound;
5229
5230 m->counterclockcount++;
5231
5232 detleft = (pa[0] - pc[0]) * (pb[1] - pc[1]);
5233 detright = (pa[1] - pc[1]) * (pb[0] - pc[0]);
5234 det = detleft - detright;
5235
5236 if (b->noexact) {
5237 return det;
5238 }
5239
5240 if (detleft > 0.0) {
5241 if (detright <= 0.0) {
5242 return det;
5243 } else {
5244 detsum = detleft + detright;
5245 }
5246 } else if (detleft < 0.0) {
5247 if (detright >= 0.0) {
5248 return det;
5249 } else {
5250 detsum = -detleft - detright;
5251 }
5252 } else {
5253 return det;
5254 }
5255
5256 errbound = ccwerrboundA * detsum;
5257 if ((det >= errbound) || (-det >= errbound)) {
5258 return det;
5259 }
5260
5261 return counterclockwiseadapt(pa, pb, pc, detsum);
5262}
5263
5264/*****************************************************************************/
5265/* */
5266/* incircle() Return a positive value if the point pd lies inside the */
5267/* circle passing through pa, pb, and pc; a negative value if */
5268/* it lies outside; and zero if the four points are cocircular.*/
5269/* The points pa, pb, and pc must be in counterclockwise */
5270/* order, or the sign of the result will be reversed. */
5271/* */
5272/* Uses exact arithmetic if necessary to ensure a correct answer. The */
5273/* result returned is the determinant of a matrix. This determinant is */
5274/* computed adaptively, in the sense that exact arithmetic is used only to */
5275/* the degree it is needed to ensure that the returned value has the */
5276/* correct sign. Hence, this function is usually quite fast, but will run */
5277/* more slowly when the input points are cocircular or nearly so. */
5278/* */
5279/* See my Robust Predicates paper for details. */
5280/* */
5281/*****************************************************************************/
5282
5283#ifdef ANSI_DECLARATORS
5284REAL incircleadapt(vertex pa, vertex pb, vertex pc, vertex pd, REAL permanent)
5285#else /* not ANSI_DECLARATORS */
5286REAL incircleadapt(pa, pb, pc, pd, permanent)
5287vertex pa;
5288vertex pb;
5289vertex pc;
5290vertex pd;
5291REAL permanent;
5292#endif /* not ANSI_DECLARATORS */
5293
5294{
5295 INEXACT REAL adx, bdx, cdx, ady, bdy, cdy;
5296 REAL det, errbound;
5297
5298 INEXACT REAL bdxcdy1, cdxbdy1, cdxady1, adxcdy1, adxbdy1, bdxady1;
5299 REAL bdxcdy0, cdxbdy0, cdxady0, adxcdy0, adxbdy0, bdxady0;
5300 REAL bc[4], ca[4], ab[4];
5301 INEXACT REAL bc3, ca3, ab3;
5302 REAL axbc[8], axxbc[16], aybc[8], ayybc[16], adet[32];
5303 int axbclen, axxbclen, aybclen, ayybclen, alen;
5304 REAL bxca[8], bxxca[16], byca[8], byyca[16], bdet[32];
5305 int bxcalen, bxxcalen, bycalen, byycalen, blen;
5306 REAL cxab[8], cxxab[16], cyab[8], cyyab[16], cdet[32];
5307 int cxablen, cxxablen, cyablen, cyyablen, clen;
5308 REAL abdet[64];
5309 int ablen;
5310 REAL fin1[1152], fin2[1152];
5311 REAL *finnow, *finother, *finswap;
5312 int finlength;
5313
5314 REAL adxtail, bdxtail, cdxtail, adytail, bdytail, cdytail;
5315 INEXACT REAL adxadx1, adyady1, bdxbdx1, bdybdy1, cdxcdx1, cdycdy1;
5316 REAL adxadx0, adyady0, bdxbdx0, bdybdy0, cdxcdx0, cdycdy0;
5317 REAL aa[4], bb[4], cc[4];
5318 INEXACT REAL aa3, bb3, cc3;
5319 INEXACT REAL ti1, tj1;
5320 REAL ti0, tj0;
5321 REAL u[4], v[4];
5322 INEXACT REAL u3, v3;
5323 REAL temp8[8], temp16a[16], temp16b[16], temp16c[16];
5324 REAL temp32a[32], temp32b[32], temp48[48], temp64[64];
5325 int temp8len, temp16alen, temp16blen, temp16clen;
5326 int temp32alen, temp32blen, temp48len, temp64len;
5327 REAL axtbb[8], axtcc[8], aytbb[8], aytcc[8];
5328 int axtbblen, axtcclen, aytbblen, aytcclen;
5329 REAL bxtaa[8], bxtcc[8], bytaa[8], bytcc[8];
5330 int bxtaalen, bxtcclen, bytaalen, bytcclen;
5331 REAL cxtaa[8], cxtbb[8], cytaa[8], cytbb[8];
5332 int cxtaalen, cxtbblen, cytaalen, cytbblen;
5333 REAL axtbc[8], aytbc[8], bxtca[8], bytca[8], cxtab[8], cytab[8];
5334 int axtbclen, aytbclen, bxtcalen, bytcalen, cxtablen, cytablen;
5335 REAL axtbct[16], aytbct[16], bxtcat[16], bytcat[16], cxtabt[16], cytabt[16];
5336 int axtbctlen, aytbctlen, bxtcatlen, bytcatlen, cxtabtlen, cytabtlen;
5337 REAL axtbctt[8], aytbctt[8], bxtcatt[8];
5338 REAL bytcatt[8], cxtabtt[8], cytabtt[8];
5339 int axtbcttlen, aytbcttlen, bxtcattlen, bytcattlen, cxtabttlen, cytabttlen;
5340 REAL abt[8], bct[8], cat[8];
5341 int abtlen, bctlen, catlen;
5342 REAL abtt[4], bctt[4], catt[4];
5343 int abttlen, bcttlen, cattlen;
5344 INEXACT REAL abtt3, bctt3, catt3;
5345 REAL negate;
5346
5347 INEXACT REAL bvirt;
5348 REAL avirt, bround, around;
5349 INEXACT REAL c;
5350 INEXACT REAL abig;
5351 REAL ahi, alo, bhi, blo;
5352 REAL err1, err2, err3;
5353 INEXACT REAL _i, _j;
5354 REAL _0;
5355
5356 adx = (REAL) (pa[0] - pd[0]);
5357 bdx = (REAL) (pb[0] - pd[0]);
5358 cdx = (REAL) (pc[0] - pd[0]);
5359 ady = (REAL) (pa[1] - pd[1]);
5360 bdy = (REAL) (pb[1] - pd[1]);
5361 cdy = (REAL) (pc[1] - pd[1]);
5362
5363 Two_Product(bdx, cdy, bdxcdy1, bdxcdy0);
5364 Two_Product(cdx, bdy, cdxbdy1, cdxbdy0);
5365 Two_Two_Diff(bdxcdy1, bdxcdy0, cdxbdy1, cdxbdy0, bc3, bc[2], bc[1], bc[0]);
5366 bc[3] = bc3;
5367 axbclen = scale_expansion_zeroelim(4, bc, adx, axbc);
5368 axxbclen = scale_expansion_zeroelim(axbclen, axbc, adx, axxbc);
5369 aybclen = scale_expansion_zeroelim(4, bc, ady, aybc);
5370 ayybclen = scale_expansion_zeroelim(aybclen, aybc, ady, ayybc);
5371 alen = fast_expansion_sum_zeroelim(axxbclen, axxbc, ayybclen, ayybc, adet);
5372
5373 Two_Product(cdx, ady, cdxady1, cdxady0);
5374 Two_Product(adx, cdy, adxcdy1, adxcdy0);
5375 Two_Two_Diff(cdxady1, cdxady0, adxcdy1, adxcdy0, ca3, ca[2], ca[1], ca[0]);
5376 ca[3] = ca3;
5377 bxcalen = scale_expansion_zeroelim(4, ca, bdx, bxca);
5378 bxxcalen = scale_expansion_zeroelim(bxcalen, bxca, bdx, bxxca);
5379 bycalen = scale_expansion_zeroelim(4, ca, bdy, byca);
5380 byycalen = scale_expansion_zeroelim(bycalen, byca, bdy, byyca);
5381 blen = fast_expansion_sum_zeroelim(bxxcalen, bxxca, byycalen, byyca, bdet);
5382
5383 Two_Product(adx, bdy, adxbdy1, adxbdy0);
5384 Two_Product(bdx, ady, bdxady1, bdxady0);
5385 Two_Two_Diff(adxbdy1, adxbdy0, bdxady1, bdxady0, ab3, ab[2], ab[1], ab[0]);
5386 ab[3] = ab3;
5387 cxablen = scale_expansion_zeroelim(4, ab, cdx, cxab);
5388 cxxablen = scale_expansion_zeroelim(cxablen, cxab, cdx, cxxab);
5389 cyablen = scale_expansion_zeroelim(4, ab, cdy, cyab);
5390 cyyablen = scale_expansion_zeroelim(cyablen, cyab, cdy, cyyab);
5391 clen = fast_expansion_sum_zeroelim(cxxablen, cxxab, cyyablen, cyyab, cdet);
5392
5393 ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
5394 finlength = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, fin1);
5395
5396 det = estimate(finlength, fin1);
5397 errbound = iccerrboundB * permanent;
5398 if ((det >= errbound) || (-det >= errbound)) {
5399 return det;
5400 }
5401
5402 Two_Diff_Tail(pa[0], pd[0], adx, adxtail);
5403 Two_Diff_Tail(pa[1], pd[1], ady, adytail);
5404 Two_Diff_Tail(pb[0], pd[0], bdx, bdxtail);
5405 Two_Diff_Tail(pb[1], pd[1], bdy, bdytail);
5406 Two_Diff_Tail(pc[0], pd[0], cdx, cdxtail);
5407 Two_Diff_Tail(pc[1], pd[1], cdy, cdytail);
5408 if ((adxtail == 0.0) && (bdxtail == 0.0) && (cdxtail == 0.0)
5409 && (adytail == 0.0) && (bdytail == 0.0) && (cdytail == 0.0)) {
5410 return det;
5411 }
5412
5413 errbound = iccerrboundC * permanent + resulterrbound * Absolute(det);
5414 det += ((adx * adx + ady * ady) * ((bdx * cdytail + cdy * bdxtail)
5415 - (bdy * cdxtail + cdx * bdytail))
5416 + 2.0 * (adx * adxtail + ady * adytail) * (bdx * cdy - bdy * cdx))
5417 + ((bdx * bdx + bdy * bdy) * ((cdx * adytail + ady * cdxtail)
5418 - (cdy * adxtail + adx * cdytail))
5419 + 2.0 * (bdx * bdxtail + bdy * bdytail) * (cdx * ady - cdy * adx))
5420 + ((cdx * cdx + cdy * cdy) * ((adx * bdytail + bdy * adxtail)
5421 - (ady * bdxtail + bdx * adytail))
5422 + 2.0 * (cdx * cdxtail + cdy * cdytail) * (adx * bdy - ady * bdx));
5423 if ((det >= errbound) || (-det >= errbound)) {
5424 return det;
5425 }
5426
5427 finnow = fin1;
5428 finother = fin2;
5429
5430 if ((bdxtail != 0.0) || (bdytail != 0.0)
5431 || (cdxtail != 0.0) || (cdytail != 0.0)) {
5432 Square(adx, adxadx1, adxadx0);
5433 Square(ady, adyady1, adyady0);
5434 Two_Two_Sum(adxadx1, adxadx0, adyady1, adyady0, aa3, aa[2], aa[1], aa[0]);
5435 aa[3] = aa3;
5436 }
5437 if ((cdxtail != 0.0) || (cdytail != 0.0)
5438 || (adxtail != 0.0) || (adytail != 0.0)) {
5439 Square(bdx, bdxbdx1, bdxbdx0);
5440 Square(bdy, bdybdy1, bdybdy0);
5441 Two_Two_Sum(bdxbdx1, bdxbdx0, bdybdy1, bdybdy0, bb3, bb[2], bb[1], bb[0]);
5442 bb[3] = bb3;
5443 }
5444 if ((adxtail != 0.0) || (adytail != 0.0)
5445 || (bdxtail != 0.0) || (bdytail != 0.0)) {
5446 Square(cdx, cdxcdx1, cdxcdx0);
5447 Square(cdy, cdycdy1, cdycdy0);
5448 Two_Two_Sum(cdxcdx1, cdxcdx0, cdycdy1, cdycdy0, cc3, cc[2], cc[1], cc[0]);
5449 cc[3] = cc3;
5450 }
5451
5452 if (adxtail != 0.0) {
5453 axtbclen = scale_expansion_zeroelim(4, bc, adxtail, axtbc);
5454 temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, 2.0 * adx,
5455 temp16a);
5456
5457 axtcclen = scale_expansion_zeroelim(4, cc, adxtail, axtcc);
5458 temp16blen = scale_expansion_zeroelim(axtcclen, axtcc, bdy, temp16b);
5459
5460 axtbblen = scale_expansion_zeroelim(4, bb, adxtail, axtbb);
5461 temp16clen = scale_expansion_zeroelim(axtbblen, axtbb, -cdy, temp16c);
5462
5463 temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5464 temp16blen, temp16b, temp32a);
5465 temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
5466 temp32alen, temp32a, temp48);
5467 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
5468 temp48, finother);
5469 finswap = finnow; finnow = finother; finother = finswap;
5470 }
5471 if (adytail != 0.0) {
5472 aytbclen = scale_expansion_zeroelim(4, bc, adytail, aytbc);
5473 temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, 2.0 * ady,
5474 temp16a);
5475
5476 aytbblen = scale_expansion_zeroelim(4, bb, adytail, aytbb);
5477 temp16blen = scale_expansion_zeroelim(aytbblen, aytbb, cdx, temp16b);
5478
5479 aytcclen = scale_expansion_zeroelim(4, cc, adytail, aytcc);
5480 temp16clen = scale_expansion_zeroelim(aytcclen, aytcc, -bdx, temp16c);
5481
5482 temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5483 temp16blen, temp16b, temp32a);
5484 temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
5485 temp32alen, temp32a, temp48);
5486 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
5487 temp48, finother);
5488 finswap = finnow; finnow = finother; finother = finswap;
5489 }
5490 if (bdxtail != 0.0) {
5491 bxtcalen = scale_expansion_zeroelim(4, ca, bdxtail, bxtca);
5492 temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, 2.0 * bdx,
5493 temp16a);
5494
5495 bxtaalen = scale_expansion_zeroelim(4, aa, bdxtail, bxtaa);
5496 temp16blen = scale_expansion_zeroelim(bxtaalen, bxtaa, cdy, temp16b);
5497
5498 bxtcclen = scale_expansion_zeroelim(4, cc, bdxtail, bxtcc);
5499 temp16clen = scale_expansion_zeroelim(bxtcclen, bxtcc, -ady, temp16c);
5500
5501 temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5502 temp16blen, temp16b, temp32a);
5503 temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
5504 temp32alen, temp32a, temp48);
5505 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
5506 temp48, finother);
5507 finswap = finnow; finnow = finother; finother = finswap;
5508 }
5509 if (bdytail != 0.0) {
5510 bytcalen = scale_expansion_zeroelim(4, ca, bdytail, bytca);
5511 temp16alen = scale_expansion_zeroelim(bytcalen, bytca, 2.0 * bdy,
5512 temp16a);
5513
5514 bytcclen = scale_expansion_zeroelim(4, cc, bdytail, bytcc);
5515 temp16blen = scale_expansion_zeroelim(bytcclen, bytcc, adx, temp16b);
5516
5517 bytaalen = scale_expansion_zeroelim(4, aa, bdytail, bytaa);
5518 temp16clen = scale_expansion_zeroelim(bytaalen, bytaa, -cdx, temp16c);
5519
5520 temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5521 temp16blen, temp16b, temp32a);
5522 temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
5523 temp32alen, temp32a, temp48);
5524 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
5525 temp48, finother);
5526 finswap = finnow; finnow = finother; finother = finswap;
5527 }
5528 if (cdxtail != 0.0) {
5529 cxtablen = scale_expansion_zeroelim(4, ab, cdxtail, cxtab);
5530 temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, 2.0 * cdx,
5531 temp16a);
5532
5533 cxtbblen = scale_expansion_zeroelim(4, bb, cdxtail, cxtbb);
5534 temp16blen = scale_expansion_zeroelim(cxtbblen, cxtbb, ady, temp16b);
5535
5536 cxtaalen = scale_expansion_zeroelim(4, aa, cdxtail, cxtaa);
5537 temp16clen = scale_expansion_zeroelim(cxtaalen, cxtaa, -bdy, temp16c);
5538
5539 temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5540 temp16blen, temp16b, temp32a);
5541 temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
5542 temp32alen, temp32a, temp48);
5543 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
5544 temp48, finother);
5545 finswap = finnow; finnow = finother; finother = finswap;
5546 }
5547 if (cdytail != 0.0) {
5548 cytablen = scale_expansion_zeroelim(4, ab, cdytail, cytab);
5549 temp16alen = scale_expansion_zeroelim(cytablen, cytab, 2.0 * cdy,
5550 temp16a);
5551
5552 cytaalen = scale_expansion_zeroelim(4, aa, cdytail, cytaa);
5553 temp16blen = scale_expansion_zeroelim(cytaalen, cytaa, bdx, temp16b);
5554
5555 cytbblen = scale_expansion_zeroelim(4, bb, cdytail, cytbb);
5556 temp16clen = scale_expansion_zeroelim(cytbblen, cytbb, -adx, temp16c);
5557
5558 temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5559 temp16blen, temp16b, temp32a);
5560 temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
5561 temp32alen, temp32a, temp48);
5562 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
5563 temp48, finother);
5564 finswap = finnow; finnow = finother; finother = finswap;
5565 }
5566
5567 if ((adxtail != 0.0) || (adytail != 0.0)) {
5568 if ((bdxtail != 0.0) || (bdytail != 0.0)
5569 || (cdxtail != 0.0) || (cdytail != 0.0)) {
5570 Two_Product(bdxtail, cdy, ti1, ti0);
5571 Two_Product(bdx, cdytail, tj1, tj0);
5572 Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
5573 u[3] = u3;
5574 negate = -bdy;
5575 Two_Product(cdxtail, negate, ti1, ti0);
5576 negate = -bdytail;
5577 Two_Product(cdx, negate, tj1, tj0);
5578 Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
5579 v[3] = v3;
5580 bctlen = fast_expansion_sum_zeroelim(4, u, 4, v, bct);
5581
5582 Two_Product(bdxtail, cdytail, ti1, ti0);
5583 Two_Product(cdxtail, bdytail, tj1, tj0);
5584 Two_Two_Diff(ti1, ti0, tj1, tj0, bctt3, bctt[2], bctt[1], bctt[0]);
5585 bctt[3] = bctt3;
5586 bcttlen = 4;
5587 } else {
5588 bct[0] = 0.0;
5589 bctlen = 1;
5590 bctt[0] = 0.0;
5591 bcttlen = 1;
5592 }
5593
5594 if (adxtail != 0.0) {
5595 temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, adxtail, temp16a);
5596 axtbctlen = scale_expansion_zeroelim(bctlen, bct, adxtail, axtbct);
5597 temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, 2.0 * adx,
5598 temp32a);
5599 temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5600 temp32alen, temp32a, temp48);
5601 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
5602 temp48, finother);
5603 finswap = finnow; finnow = finother; finother = finswap;
5604 if (bdytail != 0.0) {
5605 temp8len = scale_expansion_zeroelim(4, cc, adxtail, temp8);
5606 temp16alen = scale_expansion_zeroelim(temp8len, temp8, bdytail,
5607 temp16a);
5608 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
5609 temp16a, finother);
5610 finswap = finnow; finnow = finother; finother = finswap;
5611 }
5612 if (cdytail != 0.0) {
5613 temp8len = scale_expansion_zeroelim(4, bb, -adxtail, temp8);
5614 temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail,
5615 temp16a);
5616 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
5617 temp16a, finother);
5618 finswap = finnow; finnow = finother; finother = finswap;
5619 }
5620
5621 temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, adxtail,
5622 temp32a);
5623 axtbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adxtail, axtbctt);
5624 temp16alen = scale_expansion_zeroelim(axtbcttlen, axtbctt, 2.0 * adx,
5625 temp16a);
5626 temp16blen = scale_expansion_zeroelim(axtbcttlen, axtbctt, adxtail,
5627 temp16b);
5628 temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5629 temp16blen, temp16b, temp32b);
5630 temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
5631 temp32blen, temp32b, temp64);
5632 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
5633 temp64, finother);
5634 finswap = finnow; finnow = finother; finother = finswap;
5635 }
5636 if (adytail != 0.0) {
5637 temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, adytail, temp16a);
5638 aytbctlen = scale_expansion_zeroelim(bctlen, bct, adytail, aytbct);
5639 temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, 2.0 * ady,
5640 temp32a);
5641 temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5642 temp32alen, temp32a, temp48);
5643 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
5644 temp48, finother);
5645 finswap = finnow; finnow = finother; finother = finswap;
5646
5647
5648 temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, adytail,
5649 temp32a);
5650 aytbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adytail, aytbctt);
5651 temp16alen = scale_expansion_zeroelim(aytbcttlen, aytbctt, 2.0 * ady,
5652 temp16a);
5653 temp16blen = scale_expansion_zeroelim(aytbcttlen, aytbctt, adytail,
5654 temp16b);
5655 temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5656 temp16blen, temp16b, temp32b);
5657 temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
5658 temp32blen, temp32b, temp64);
5659 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
5660 temp64, finother);
5661 finswap = finnow; finnow = finother; finother = finswap;
5662 }
5663 }
5664 if ((bdxtail != 0.0) || (bdytail != 0.0)) {
5665 if ((cdxtail != 0.0) || (cdytail != 0.0)
5666 || (adxtail != 0.0) || (adytail != 0.0)) {
5667 Two_Product(cdxtail, ady, ti1, ti0);
5668 Two_Product(cdx, adytail, tj1, tj0);
5669 Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
5670 u[3] = u3;
5671 negate = -cdy;
5672 Two_Product(adxtail, negate, ti1, ti0);
5673 negate = -cdytail;
5674 Two_Product(adx, negate, tj1, tj0);
5675 Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
5676 v[3] = v3;
5677 catlen = fast_expansion_sum_zeroelim(4, u, 4, v, cat);
5678
5679 Two_Product(cdxtail, adytail, ti1, ti0);
5680 Two_Product(adxtail, cdytail, tj1, tj0);
5681 Two_Two_Diff(ti1, ti0, tj1, tj0, catt3, catt[2], catt[1], catt[0]);
5682 catt[3] = catt3;
5683 cattlen = 4;
5684 } else {
5685 cat[0] = 0.0;
5686 catlen = 1;
5687 catt[0] = 0.0;
5688 cattlen = 1;
5689 }
5690
5691 if (bdxtail != 0.0) {
5692 temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, bdxtail, temp16a);
5693 bxtcatlen = scale_expansion_zeroelim(catlen, cat, bdxtail, bxtcat);
5694 temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, 2.0 * bdx,
5695 temp32a);
5696 temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5697 temp32alen, temp32a, temp48);
5698 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
5699 temp48, finother);
5700 finswap = finnow; finnow = finother; finother = finswap;
5701 if (cdytail != 0.0) {
5702 temp8len = scale_expansion_zeroelim(4, aa, bdxtail, temp8);
5703 temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail,
5704 temp16a);
5705 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
5706 temp16a, finother);
5707 finswap = finnow; finnow = finother; finother = finswap;
5708 }
5709 if (adytail != 0.0) {
5710 temp8len = scale_expansion_zeroelim(4, cc, -bdxtail, temp8);
5711 temp16alen = scale_expansion_zeroelim(temp8len, temp8, adytail,
5712 temp16a);
5713 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
5714 temp16a, finother);
5715 finswap = finnow; finnow = finother; finother = finswap;
5716 }
5717
5718 temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, bdxtail,
5719 temp32a);
5720 bxtcattlen = scale_expansion_zeroelim(cattlen, catt, bdxtail, bxtcatt);
5721 temp16alen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, 2.0 * bdx,
5722 temp16a);
5723 temp16blen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, bdxtail,
5724 temp16b);
5725 temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5726 temp16blen, temp16b, temp32b);
5727 temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
5728 temp32blen, temp32b, temp64);
5729 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
5730 temp64, finother);
5731 finswap = finnow; finnow = finother; finother = finswap;
5732 }
5733 if (bdytail != 0.0) {
5734 temp16alen = scale_expansion_zeroelim(bytcalen, bytca, bdytail, temp16a);
5735 bytcatlen = scale_expansion_zeroelim(catlen, cat, bdytail, bytcat);
5736 temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, 2.0 * bdy,
5737 temp32a);
5738 temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5739 temp32alen, temp32a, temp48);
5740 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
5741 temp48, finother);
5742 finswap = finnow; finnow = finother; finother = finswap;
5743
5744
5745 temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, bdytail,
5746 temp32a);
5747 bytcattlen = scale_expansion_zeroelim(cattlen, catt, bdytail, bytcatt);
5748 temp16alen = scale_expansion_zeroelim(bytcattlen, bytcatt, 2.0 * bdy,
5749 temp16a);
5750 temp16blen = scale_expansion_zeroelim(bytcattlen, bytcatt, bdytail,
5751 temp16b);
5752 temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5753 temp16blen, temp16b, temp32b);
5754 temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
5755 temp32blen, temp32b, temp64);
5756 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
5757 temp64, finother);
5758 finswap = finnow; finnow = finother; finother = finswap;
5759 }
5760 }
5761 if ((cdxtail != 0.0) || (cdytail != 0.0)) {
5762 if ((adxtail != 0.0) || (adytail != 0.0)
5763 || (bdxtail != 0.0) || (bdytail != 0.0)) {
5764 Two_Product(adxtail, bdy, ti1, ti0);
5765 Two_Product(adx, bdytail, tj1, tj0);
5766 Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
5767 u[3] = u3;
5768 negate = -ady;
5769 Two_Product(bdxtail, negate, ti1, ti0);
5770 negate = -adytail;
5771 Two_Product(bdx, negate, tj1, tj0);
5772 Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
5773 v[3] = v3;
5774 abtlen = fast_expansion_sum_zeroelim(4, u, 4, v, abt);
5775
5776 Two_Product(adxtail, bdytail, ti1, ti0);
5777 Two_Product(bdxtail, adytail, tj1, tj0);
5778 Two_Two_Diff(ti1, ti0, tj1, tj0, abtt3, abtt[2], abtt[1], abtt[0]);
5779 abtt[3] = abtt3;
5780 abttlen = 4;
5781 } else {
5782 abt[0] = 0.0;
5783 abtlen = 1;
5784 abtt[0] = 0.0;
5785 abttlen = 1;
5786 }
5787
5788 if (cdxtail != 0.0) {
5789 temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, cdxtail, temp16a);
5790 cxtabtlen = scale_expansion_zeroelim(abtlen, abt, cdxtail, cxtabt);
5791 temp32alen = scale_expansion_zeroelim(cxtabtlen, cxtabt, 2.0 * cdx,
5792 temp32a);
5793 temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5794 temp32alen, temp32a, temp48);
5795 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
5796 temp48, finother);
5797 finswap = finnow; finnow = finother; finother = finswap;
5798 if (adytail != 0.0) {
5799 temp8len = scale_expansion_zeroelim(4, bb, cdxtail, temp8);
5800 temp16alen = scale_expansion_zeroelim(temp8len, temp8, adytail,
5801 temp16a);
5802 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
5803 temp16a, finother);
5804 finswap = finnow; finnow = finother; finother = finswap;
5805 }
5806 if (bdytail != 0.0) {
5807 temp8len = scale_expansion_zeroelim(4, aa, -cdxtail, temp8);
5808 temp16alen = scale_expansion_zeroelim(temp8len, temp8, bdytail,
5809 temp16a);
5810 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
5811 temp16a, finother);
5812 finswap = finnow; finnow = finother; finother = finswap;
5813 }
5814
5815 temp32alen = scale_expansion_zeroelim(cxtabtlen, cxtabt, cdxtail,
5816 temp32a);
5817 cxtabttlen = scale_expansion_zeroelim(abttlen, abtt, cdxtail, cxtabtt);
5818 temp16alen = scale_expansion_zeroelim(cxtabttlen, cxtabtt, 2.0 * cdx,
5819 temp16a);
5820 temp16blen = scale_expansion_zeroelim(cxtabttlen, cxtabtt, cdxtail,
5821 temp16b);
5822 temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5823 temp16blen, temp16b, temp32b);
5824 temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
5825 temp32blen, temp32b, temp64);
5826 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
5827 temp64, finother);
5828 finswap = finnow; finnow = finother; finother = finswap;
5829 }
5830 if (cdytail != 0.0) {
5831 temp16alen = scale_expansion_zeroelim(cytablen, cytab, cdytail, temp16a);
5832 cytabtlen = scale_expansion_zeroelim(abtlen, abt, cdytail, cytabt);
5833 temp32alen = scale_expansion_zeroelim(cytabtlen, cytabt, 2.0 * cdy,
5834 temp32a);
5835 temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5836 temp32alen, temp32a, temp48);
5837 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
5838 temp48, finother);
5839 finswap = finnow; finnow = finother; finother = finswap;
5840
5841
5842 temp32alen = scale_expansion_zeroelim(cytabtlen, cytabt, cdytail,
5843 temp32a);
5844 cytabttlen = scale_expansion_zeroelim(abttlen, abtt, cdytail, cytabtt);
5845 temp16alen = scale_expansion_zeroelim(cytabttlen, cytabtt, 2.0 * cdy,
5846 temp16a);
5847 temp16blen = scale_expansion_zeroelim(cytabttlen, cytabtt, cdytail,
5848 temp16b);
5849 temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5850 temp16blen, temp16b, temp32b);
5851 temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
5852 temp32blen, temp32b, temp64);
5853 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
5854 temp64, finother);
5855 finswap = finnow; finnow = finother; finother = finswap;
5856 }
5857 }
5858
5859 return finnow[finlength - 1];
5860}
5861
5862#ifdef ANSI_DECLARATORS
5863REAL incircle(struct mesh *m, struct behavior *b,
5864 vertex pa, vertex pb, vertex pc, vertex pd)
5865#else /* not ANSI_DECLARATORS */
5866REAL incircle(m, b, pa, pb, pc, pd)
5867struct mesh *m;
5868struct behavior *b;
5869vertex pa;
5870vertex pb;
5871vertex pc;
5872vertex pd;
5873#endif /* not ANSI_DECLARATORS */
5874
5875{
5876 REAL adx, bdx, cdx, ady, bdy, cdy;
5877 REAL bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady;
5878 REAL alift, blift, clift;
5879 REAL det;
5880 REAL permanent, errbound;
5881
5882 m->incirclecount++;
5883
5884 adx = pa[0] - pd[0];
5885 bdx = pb[0] - pd[0];
5886 cdx = pc[0] - pd[0];
5887 ady = pa[1] - pd[1];
5888 bdy = pb[1] - pd[1];
5889 cdy = pc[1] - pd[1];
5890
5891 bdxcdy = bdx * cdy;
5892 cdxbdy = cdx * bdy;
5893 alift = adx * adx + ady * ady;
5894
5895 cdxady = cdx * ady;
5896 adxcdy = adx * cdy;
5897 blift = bdx * bdx + bdy * bdy;
5898
5899 adxbdy = adx * bdy;
5900 bdxady = bdx * ady;
5901 clift = cdx * cdx + cdy * cdy;
5902
5903 det = alift * (bdxcdy - cdxbdy)
5904 + blift * (cdxady - adxcdy)
5905 + clift * (adxbdy - bdxady);
5906
5907 if (b->noexact) {
5908 return det;
5909 }
5910
5911 permanent = (Absolute(bdxcdy) + Absolute(cdxbdy)) * alift
5912 + (Absolute(cdxady) + Absolute(adxcdy)) * blift
5913 + (Absolute(adxbdy) + Absolute(bdxady)) * clift;
5914 errbound = iccerrboundA * permanent;
5915 if ((det > errbound) || (-det > errbound)) {
5916 return det;
5917 }
5918
5919 return incircleadapt(pa, pb, pc, pd, permanent);
5920}
5921
5922/*****************************************************************************/
5923/* */
5924/* orient3d() Return a positive value if the point pd lies below the */
5925/* plane passing through pa, pb, and pc; "below" is defined so */
5926/* that pa, pb, and pc appear in counterclockwise order when */
5927/* viewed from above the plane. Returns a negative value if */
5928/* pd lies above the plane. Returns zero if the points are */
5929/* coplanar. The result is also a rough approximation of six */
5930/* times the signed volume of the tetrahedron defined by the */
5931/* four points. */
5932/* */
5933/* Uses exact arithmetic if necessary to ensure a correct answer. The */
5934/* result returned is the determinant of a matrix. This determinant is */
5935/* computed adaptively, in the sense that exact arithmetic is used only to */
5936/* the degree it is needed to ensure that the returned value has the */
5937/* correct sign. Hence, this function is usually quite fast, but will run */
5938/* more slowly when the input points are coplanar or nearly so. */
5939/* */
5940/* See my Robust Predicates paper for details. */
5941/* */
5942/*****************************************************************************/
5943
5944#ifdef ANSI_DECLARATORS
5945REAL orient3dadapt(vertex pa, vertex pb, vertex pc, vertex pd,
5946 REAL aheight, REAL bheight, REAL cheight, REAL dheight,
5947 REAL permanent)
5948#else /* not ANSI_DECLARATORS */
5949REAL orient3dadapt(pa, pb, pc, pd,
5950 aheight, bheight, cheight, dheight, permanent)
5951vertex pa;
5952vertex pb;
5953vertex pc;
5954vertex pd;
5955REAL aheight;
5956REAL bheight;
5957REAL cheight;
5958REAL dheight;
5959REAL permanent;
5960#endif /* not ANSI_DECLARATORS */
5961
5962{
5963 INEXACT REAL adx, bdx, cdx, ady, bdy, cdy, adheight, bdheight, cdheight;
5964 REAL det, errbound;
5965
5966 INEXACT REAL bdxcdy1, cdxbdy1, cdxady1, adxcdy1, adxbdy1, bdxady1;
5967 REAL bdxcdy0, cdxbdy0, cdxady0, adxcdy0, adxbdy0, bdxady0;
5968 REAL bc[4], ca[4], ab[4];
5969 INEXACT REAL bc3, ca3, ab3;
5970 REAL adet[8], bdet[8], cdet[8];
5971 int alen, blen, clen;
5972 REAL abdet[16];
5973 int ablen;
5974 REAL *finnow, *finother, *finswap;
5975 REAL fin1[192], fin2[192];
5976 int finlength;
5977
5978 REAL adxtail, bdxtail, cdxtail;
5979 REAL adytail, bdytail, cdytail;
5980 REAL adheighttail, bdheighttail, cdheighttail;
5981 INEXACT REAL at_blarge, at_clarge;
5982 INEXACT REAL bt_clarge, bt_alarge;
5983 INEXACT REAL ct_alarge, ct_blarge;
5984 REAL at_b[4], at_c[4], bt_c[4], bt_a[4], ct_a[4], ct_b[4];
5985 int at_blen, at_clen, bt_clen, bt_alen, ct_alen, ct_blen;
5986 INEXACT REAL bdxt_cdy1, cdxt_bdy1, cdxt_ady1;
5987 INEXACT REAL adxt_cdy1, adxt_bdy1, bdxt_ady1;
5988 REAL bdxt_cdy0, cdxt_bdy0, cdxt_ady0;
5989 REAL adxt_cdy0, adxt_bdy0, bdxt_ady0;
5990 INEXACT REAL bdyt_cdx1, cdyt_bdx1, cdyt_adx1;
5991 INEXACT REAL adyt_cdx1, adyt_bdx1, bdyt_adx1;
5992 REAL bdyt_cdx0, cdyt_bdx0, cdyt_adx0;
5993 REAL adyt_cdx0, adyt_bdx0, bdyt_adx0;
5994 REAL bct[8], cat[8], abt[8];
5995 int bctlen, catlen, abtlen;
5996 INEXACT REAL bdxt_cdyt1, cdxt_bdyt1, cdxt_adyt1;
5997 INEXACT REAL adxt_cdyt1, adxt_bdyt1, bdxt_adyt1;
5998 REAL bdxt_cdyt0, cdxt_bdyt0, cdxt_adyt0;
5999 REAL adxt_cdyt0, adxt_bdyt0, bdxt_adyt0;
6000 REAL u[4], v[12], w[16];
6001 INEXACT REAL u3;
6002 int vlength, wlength;
6003 REAL negate;
6004
6005 INEXACT REAL bvirt;
6006 REAL avirt, bround, around;
6007 INEXACT REAL c;
6008 INEXACT REAL abig;
6009 REAL ahi, alo, bhi, blo;
6010 REAL err1, err2, err3;
6011 INEXACT REAL _i, _j, _k;
6012 REAL _0;
6013
6014 adx = (REAL) (pa[0] - pd[0]);
6015 bdx = (REAL) (pb[0] - pd[0]);
6016 cdx = (REAL) (pc[0] - pd[0]);
6017 ady = (REAL) (pa[1] - pd[1]);
6018 bdy = (REAL) (pb[1] - pd[1]);
6019 cdy = (REAL) (pc[1] - pd[1]);
6020 adheight = (REAL) (aheight - dheight);
6021 bdheight = (REAL) (bheight - dheight);
6022 cdheight = (REAL) (cheight - dheight);
6023
6024 Two_Product(bdx, cdy, bdxcdy1, bdxcdy0);
6025 Two_Product(cdx, bdy, cdxbdy1, cdxbdy0);
6026 Two_Two_Diff(bdxcdy1, bdxcdy0, cdxbdy1, cdxbdy0, bc3, bc[2], bc[1], bc[0]);
6027 bc[3] = bc3;
6028 alen = scale_expansion_zeroelim(4, bc, adheight, adet);
6029
6030 Two_Product(cdx, ady, cdxady1, cdxady0);
6031 Two_Product(adx, cdy, adxcdy1, adxcdy0);
6032 Two_Two_Diff(cdxady1, cdxady0, adxcdy1, adxcdy0, ca3, ca[2], ca[1], ca[0]);
6033 ca[3] = ca3;
6034 blen = scale_expansion_zeroelim(4, ca, bdheight, bdet);
6035
6036 Two_Product(adx, bdy, adxbdy1, adxbdy0);
6037 Two_Product(bdx, ady, bdxady1, bdxady0);
6038 Two_Two_Diff(adxbdy1, adxbdy0, bdxady1, bdxady0, ab3, ab[2], ab[1], ab[0]);
6039 ab[3] = ab3;
6040 clen = scale_expansion_zeroelim(4, ab, cdheight, cdet);
6041
6042 ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
6043 finlength = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, fin1);
6044
6045 det = estimate(finlength, fin1);
6046 errbound = o3derrboundB * permanent;
6047 if ((det >= errbound) || (-det >= errbound)) {
6048 return det;
6049 }
6050
6051 Two_Diff_Tail(pa[0], pd[0], adx, adxtail);
6052 Two_Diff_Tail(pb[0], pd[0], bdx, bdxtail);
6053 Two_Diff_Tail(pc[0], pd[0], cdx, cdxtail);
6054 Two_Diff_Tail(pa[1], pd[1], ady, adytail);
6055 Two_Diff_Tail(pb[1], pd[1], bdy, bdytail);
6056 Two_Diff_Tail(pc[1], pd[1], cdy, cdytail);
6057 Two_Diff_Tail(aheight, dheight, adheight, adheighttail);
6058 Two_Diff_Tail(bheight, dheight, bdheight, bdheighttail);
6059 Two_Diff_Tail(cheight, dheight, cdheight, cdheighttail);
6060
6061 if ((adxtail == 0.0) && (bdxtail == 0.0) && (cdxtail == 0.0) &&
6062 (adytail == 0.0) && (bdytail == 0.0) && (cdytail == 0.0) &&
6063 (adheighttail == 0.0) &&
6064 (bdheighttail == 0.0) &&
6065 (cdheighttail == 0.0)) {
6066 return det;
6067 }
6068
6069 errbound = o3derrboundC * permanent + resulterrbound * Absolute(det);
6070 det += (adheight * ((bdx * cdytail + cdy * bdxtail) -
6071 (bdy * cdxtail + cdx * bdytail)) +
6072 adheighttail * (bdx * cdy - bdy * cdx)) +
6073 (bdheight * ((cdx * adytail + ady * cdxtail) -
6074 (cdy * adxtail + adx * cdytail)) +
6075 bdheighttail * (cdx * ady - cdy * adx)) +
6076 (cdheight * ((adx * bdytail + bdy * adxtail) -
6077 (ady * bdxtail + bdx * adytail)) +
6078 cdheighttail * (adx * bdy - ady * bdx));
6079 if ((det >= errbound) || (-det >= errbound)) {
6080 return det;
6081 }
6082
6083 finnow = fin1;
6084 finother = fin2;
6085
6086 if (adxtail == 0.0) {
6087 if (adytail == 0.0) {
6088 at_b[0] = 0.0;
6089 at_blen = 1;
6090 at_c[0] = 0.0;
6091 at_clen = 1;
6092 } else {
6093 negate = -adytail;
6094 Two_Product(negate, bdx, at_blarge, at_b[0]);
6095 at_b[1] = at_blarge;
6096 at_blen = 2;
6097 Two_Product(adytail, cdx, at_clarge, at_c[0]);
6098 at_c[1] = at_clarge;
6099 at_clen = 2;
6100 }
6101 } else {
6102 if (adytail == 0.0) {
6103 Two_Product(adxtail, bdy, at_blarge, at_b[0]);
6104 at_b[1] = at_blarge;
6105 at_blen = 2;
6106 negate = -adxtail;
6107 Two_Product(negate, cdy, at_clarge, at_c[0]);
6108 at_c[1] = at_clarge;
6109 at_clen = 2;
6110 } else {
6111 Two_Product(adxtail, bdy, adxt_bdy1, adxt_bdy0);
6112 Two_Product(adytail, bdx, adyt_bdx1, adyt_bdx0);
6113 Two_Two_Diff(adxt_bdy1, adxt_bdy0, adyt_bdx1, adyt_bdx0,
6114 at_blarge, at_b[2], at_b[1], at_b[0]);
6115 at_b[3] = at_blarge;
6116 at_blen = 4;
6117 Two_Product(adytail, cdx, adyt_cdx1, adyt_cdx0);
6118 Two_Product(adxtail, cdy, adxt_cdy1, adxt_cdy0);
6119 Two_Two_Diff(adyt_cdx1, adyt_cdx0, adxt_cdy1, adxt_cdy0,
6120 at_clarge, at_c[2], at_c[1], at_c[0]);
6121 at_c[3] = at_clarge;
6122 at_clen = 4;
6123 }
6124 }
6125 if (bdxtail == 0.0) {
6126 if (bdytail == 0.0) {
6127 bt_c[0] = 0.0;
6128 bt_clen = 1;
6129 bt_a[0] = 0.0;
6130 bt_alen = 1;
6131 } else {
6132 negate = -bdytail;
6133 Two_Product(negate, cdx, bt_clarge, bt_c[0]);
6134 bt_c[1] = bt_clarge;
6135 bt_clen = 2;
6136 Two_Product(bdytail, adx, bt_alarge, bt_a[0]);
6137 bt_a[1] = bt_alarge;
6138 bt_alen = 2;
6139 }
6140 } else {
6141 if (bdytail == 0.0) {
6142 Two_Product(bdxtail, cdy, bt_clarge, bt_c[0]);
6143 bt_c[1] = bt_clarge;
6144 bt_clen = 2;
6145 negate = -bdxtail;
6146 Two_Product(negate, ady, bt_alarge, bt_a[0]);
6147 bt_a[1] = bt_alarge;
6148 bt_alen = 2;
6149 } else {
6150 Two_Product(bdxtail, cdy, bdxt_cdy1, bdxt_cdy0);
6151 Two_Product(bdytail, cdx, bdyt_cdx1, bdyt_cdx0);
6152 Two_Two_Diff(bdxt_cdy1, bdxt_cdy0, bdyt_cdx1, bdyt_cdx0,
6153 bt_clarge, bt_c[2], bt_c[1], bt_c[0]);
6154 bt_c[3] = bt_clarge;
6155 bt_clen = 4;
6156 Two_Product(bdytail, adx, bdyt_adx1, bdyt_adx0);
6157 Two_Product(bdxtail, ady, bdxt_ady1, bdxt_ady0);
6158 Two_Two_Diff(bdyt_adx1, bdyt_adx0, bdxt_ady1, bdxt_ady0,
6159 bt_alarge, bt_a[2], bt_a[1], bt_a[0]);
6160 bt_a[3] = bt_alarge;
6161 bt_alen = 4;
6162 }
6163 }
6164 if (cdxtail == 0.0) {
6165 if (cdytail == 0.0) {
6166 ct_a[0] = 0.0;
6167 ct_alen = 1;
6168 ct_b[0] = 0.0;
6169 ct_blen = 1;
6170 } else {
6171 negate = -cdytail;
6172 Two_Product(negate, adx, ct_alarge, ct_a[0]);
6173 ct_a[1] = ct_alarge;
6174 ct_alen = 2;
6175 Two_Product(cdytail, bdx, ct_blarge, ct_b[0]);
6176 ct_b[1] = ct_blarge;
6177 ct_blen = 2;
6178 }
6179 } else {
6180 if (cdytail == 0.0) {
6181 Two_Product(cdxtail, ady, ct_alarge, ct_a[0]);
6182 ct_a[1] = ct_alarge;
6183 ct_alen = 2;
6184 negate = -cdxtail;
6185 Two_Product(negate, bdy, ct_blarge, ct_b[0]);
6186 ct_b[1] = ct_blarge;
6187 ct_blen = 2;
6188 } else {
6189 Two_Product(cdxtail, ady, cdxt_ady1, cdxt_ady0);
6190 Two_Product(cdytail, adx, cdyt_adx1, cdyt_adx0);
6191 Two_Two_Diff(cdxt_ady1, cdxt_ady0, cdyt_adx1, cdyt_adx0,
6192 ct_alarge, ct_a[2], ct_a[1], ct_a[0]);
6193 ct_a[3] = ct_alarge;
6194 ct_alen = 4;
6195 Two_Product(cdytail, bdx, cdyt_bdx1, cdyt_bdx0);
6196 Two_Product(cdxtail, bdy, cdxt_bdy1, cdxt_bdy0);
6197 Two_Two_Diff(cdyt_bdx1, cdyt_bdx0, cdxt_bdy1, cdxt_bdy0,
6198 ct_blarge, ct_b[2], ct_b[1], ct_b[0]);
6199 ct_b[3] = ct_blarge;
6200 ct_blen = 4;
6201 }
6202 }
6203
6204 bctlen = fast_expansion_sum_zeroelim(bt_clen, bt_c, ct_blen, ct_b, bct);
6205 wlength = scale_expansion_zeroelim(bctlen, bct, adheight, w);
6206 finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
6207 finother);
6208 finswap = finnow; finnow = finother; finother = finswap;
6209
6210 catlen = fast_expansion_sum_zeroelim(ct_alen, ct_a, at_clen, at_c, cat);
6211 wlength = scale_expansion_zeroelim(catlen, cat, bdheight, w);
6212 finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
6213 finother);
6214 finswap = finnow; finnow = finother; finother = finswap;
6215
6216 abtlen = fast_expansion_sum_zeroelim(at_blen, at_b, bt_alen, bt_a, abt);
6217 wlength = scale_expansion_zeroelim(abtlen, abt, cdheight, w);
6218 finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
6219 finother);
6220 finswap = finnow; finnow = finother; finother = finswap;
6221
6222 if (adheighttail != 0.0) {
6223 vlength = scale_expansion_zeroelim(4, bc, adheighttail, v);
6224 finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v,
6225 finother);
6226 finswap = finnow; finnow = finother; finother = finswap;
6227 }
6228 if (bdheighttail != 0.0) {
6229 vlength = scale_expansion_zeroelim(4, ca, bdheighttail, v);
6230 finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v,
6231 finother);
6232 finswap = finnow; finnow = finother; finother = finswap;
6233 }
6234 if (cdheighttail != 0.0) {
6235 vlength = scale_expansion_zeroelim(4, ab, cdheighttail, v);
6236 finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v,
6237 finother);
6238 finswap = finnow; finnow = finother; finother = finswap;
6239 }
6240
6241 if (adxtail != 0.0) {
6242 if (bdytail != 0.0) {
6243 Two_Product(adxtail, bdytail, adxt_bdyt1, adxt_bdyt0);
6244 Two_One_Product(adxt_bdyt1, adxt_bdyt0, cdheight, u3, u[2], u[1], u[0]);
6245 u[3] = u3;
6246 finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
6247 finother);
6248 finswap = finnow; finnow = finother; finother = finswap;
6249 if (cdheighttail != 0.0) {
6250 Two_One_Product(adxt_bdyt1, adxt_bdyt0, cdheighttail,
6251 u3, u[2], u[1], u[0]);
6252 u[3] = u3;
6253 finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
6254 finother);
6255 finswap = finnow; finnow = finother; finother = finswap;
6256 }
6257 }
6258 if (cdytail != 0.0) {
6259 negate = -adxtail;
6260 Two_Product(negate, cdytail, adxt_cdyt1, adxt_cdyt0);
6261 Two_One_Product(adxt_cdyt1, adxt_cdyt0, bdheight, u3, u[2], u[1], u[0]);
6262 u[3] = u3;
6263 finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
6264 finother);
6265 finswap = finnow; finnow = finother; finother = finswap;
6266 if (bdheighttail != 0.0) {
6267 Two_One_Product(adxt_cdyt1, adxt_cdyt0, bdheighttail,
6268 u3, u[2], u[1], u[0]);
6269 u[3] = u3;
6270 finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
6271 finother);
6272 finswap = finnow; finnow = finother; finother = finswap;
6273 }
6274 }
6275 }
6276 if (bdxtail != 0.0) {
6277 if (cdytail != 0.0) {
6278 Two_Product(bdxtail, cdytail, bdxt_cdyt1, bdxt_cdyt0);
6279 Two_One_Product(bdxt_cdyt1, bdxt_cdyt0, adheight, u3, u[2], u[1], u[0]);
6280 u[3] = u3;
6281 finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
6282 finother);
6283 finswap = finnow; finnow = finother; finother = finswap;
6284 if (adheighttail != 0.0) {
6285 Two_One_Product(bdxt_cdyt1, bdxt_cdyt0, adheighttail,
6286 u3, u[2], u[1], u[0]);
6287 u[3] = u3;
6288 finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
6289 finother);
6290 finswap = finnow; finnow = finother; finother = finswap;
6291 }
6292 }
6293 if (adytail != 0.0) {
6294 negate = -bdxtail;
6295 Two_Product(negate, adytail, bdxt_adyt1, bdxt_adyt0);
6296 Two_One_Product(bdxt_adyt1, bdxt_adyt0, cdheight, u3, u[2], u[1], u[0]);
6297 u[3] = u3;
6298 finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
6299 finother);
6300 finswap = finnow; finnow = finother; finother = finswap;
6301 if (cdheighttail != 0.0) {
6302 Two_One_Product(bdxt_adyt1, bdxt_adyt0, cdheighttail,
6303 u3, u[2], u[1], u[0]);
6304 u[3] = u3;
6305 finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
6306 finother);
6307 finswap = finnow; finnow = finother; finother = finswap;
6308 }
6309 }
6310 }
6311 if (cdxtail != 0.0) {
6312 if (adytail != 0.0) {
6313 Two_Product(cdxtail, adytail, cdxt_adyt1, cdxt_adyt0);
6314 Two_One_Product(cdxt_adyt1, cdxt_adyt0, bdheight, u3, u[2], u[1], u[0]);
6315 u[3] = u3;
6316 finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
6317 finother);
6318 finswap = finnow; finnow = finother; finother = finswap;
6319 if (bdheighttail != 0.0) {
6320 Two_One_Product(cdxt_adyt1, cdxt_adyt0, bdheighttail,
6321 u3, u[2], u[1], u[0]);
6322 u[3] = u3;
6323 finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
6324 finother);
6325 finswap = finnow; finnow = finother; finother = finswap;
6326 }
6327 }
6328 if (bdytail != 0.0) {
6329 negate = -cdxtail;
6330 Two_Product(negate, bdytail, cdxt_bdyt1, cdxt_bdyt0);
6331 Two_One_Product(cdxt_bdyt1, cdxt_bdyt0, adheight, u3, u[2], u[1], u[0]);
6332 u[3] = u3;
6333 finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
6334 finother);
6335 finswap = finnow; finnow = finother; finother = finswap;
6336 if (adheighttail != 0.0) {
6337 Two_One_Product(cdxt_bdyt1, cdxt_bdyt0, adheighttail,
6338 u3, u[2], u[1], u[0]);
6339 u[3] = u3;
6340 finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
6341 finother);
6342 finswap = finnow; finnow = finother; finother = finswap;
6343 }
6344 }
6345 }
6346
6347 if (adheighttail != 0.0) {
6348 wlength = scale_expansion_zeroelim(bctlen, bct, adheighttail, w);
6349 finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
6350 finother);
6351 finswap = finnow; finnow = finother; finother = finswap;
6352 }
6353 if (bdheighttail != 0.0) {
6354 wlength = scale_expansion_zeroelim(catlen, cat, bdheighttail, w);
6355 finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
6356 finother);
6357 finswap = finnow; finnow = finother; finother = finswap;
6358 }
6359 if (cdheighttail != 0.0) {
6360 wlength = scale_expansion_zeroelim(abtlen, abt, cdheighttail, w);
6361 finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
6362 finother);
6363 finswap = finnow; finnow = finother; finother = finswap;
6364 }
6365
6366 return finnow[finlength - 1];
6367}
6368
6369#ifdef ANSI_DECLARATORS
6370REAL orient3d(struct mesh *m, struct behavior *b,
6371 vertex pa, vertex pb, vertex pc, vertex pd,
6372 REAL aheight, REAL bheight, REAL cheight, REAL dheight)
6373#else /* not ANSI_DECLARATORS */
6374REAL orient3d(m, b, pa, pb, pc, pd, aheight, bheight, cheight, dheight)
6375struct mesh *m;
6376struct behavior *b;
6377vertex pa;
6378vertex pb;
6379vertex pc;
6380vertex pd;
6381REAL aheight;
6382REAL bheight;
6383REAL cheight;
6384REAL dheight;
6385#endif /* not ANSI_DECLARATORS */
6386
6387{
6388 REAL adx, bdx, cdx, ady, bdy, cdy, adheight, bdheight, cdheight;
6389 REAL bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady;
6390 REAL det;
6391 REAL permanent, errbound;
6392
6393 m->orient3dcount++;
6394
6395 adx = pa[0] - pd[0];
6396 bdx = pb[0] - pd[0];
6397 cdx = pc[0] - pd[0];
6398 ady = pa[1] - pd[1];
6399 bdy = pb[1] - pd[1];
6400 cdy = pc[1] - pd[1];
6401 adheight = aheight - dheight;
6402 bdheight = bheight - dheight;
6403 cdheight = cheight - dheight;
6404
6405 bdxcdy = bdx * cdy;
6406 cdxbdy = cdx * bdy;
6407
6408 cdxady = cdx * ady;
6409 adxcdy = adx * cdy;
6410
6411 adxbdy = adx * bdy;
6412 bdxady = bdx * ady;
6413
6414 det = adheight * (bdxcdy - cdxbdy)
6415 + bdheight * (cdxady - adxcdy)
6416 + cdheight * (adxbdy - bdxady);
6417
6418 if (b->noexact) {
6419 return det;
6420 }
6421
6422 permanent = (Absolute(bdxcdy) + Absolute(cdxbdy)) * Absolute(adheight)
6423 + (Absolute(cdxady) + Absolute(adxcdy)) * Absolute(bdheight)
6424 + (Absolute(adxbdy) + Absolute(bdxady)) * Absolute(cdheight);
6425 errbound = o3derrboundA * permanent;
6426 if ((det > errbound) || (-det > errbound)) {
6427 return det;
6428 }
6429
6430 return orient3dadapt(pa, pb, pc, pd, aheight, bheight, cheight, dheight,
6431 permanent);
6432}
6433
6434/*****************************************************************************/
6435/* */
6436/* nonregular() Return a positive value if the point pd is incompatible */
6437/* with the circle or plane passing through pa, pb, and pc */
6438/* (meaning that pd is inside the circle or below the */
6439/* plane); a negative value if it is compatible; and zero if */
6440/* the four points are cocircular/coplanar. The points pa, */
6441/* pb, and pc must be in counterclockwise order, or the sign */
6442/* of the result will be reversed. */
6443/* */
6444/* If the -w switch is used, the points are lifted onto the parabolic */
6445/* lifting map, then they are dropped according to their weights, then the */
6446/* 3D orientation test is applied. If the -W switch is used, the points' */
6447/* heights are already provided, so the 3D orientation test is applied */
6448/* directly. If neither switch is used, the incircle test is applied. */
6449/* */
6450/*****************************************************************************/
6451
6452#ifdef ANSI_DECLARATORS
6453REAL nonregular(struct mesh *m, struct behavior *b,
6454 vertex pa, vertex pb, vertex pc, vertex pd)
6455#else /* not ANSI_DECLARATORS */
6456REAL nonregular(m, b, pa, pb, pc, pd)
6457struct mesh *m;
6458struct behavior *b;
6459vertex pa;
6460vertex pb;
6461vertex pc;
6462vertex pd;
6463#endif /* not ANSI_DECLARATORS */
6464
6465{
6466 if (b->weighted == 0) {
6467 return incircle(m, b, pa, pb, pc, pd);
6468 } else if (b->weighted == 1) {
6469 return orient3d(m, b, pa, pb, pc, pd,
6470 pa[0] * pa[0] + pa[1] * pa[1] - pa[2],
6471 pb[0] * pb[0] + pb[1] * pb[1] - pb[2],
6472 pc[0] * pc[0] + pc[1] * pc[1] - pc[2],
6473 pd[0] * pd[0] + pd[1] * pd[1] - pd[2]);
6474 } else {
6475 return orient3d(m, b, pa, pb, pc, pd, pa[2], pb[2], pc[2], pd[2]);
6476 }
6477}
6478
6479/*****************************************************************************/
6480/* */
6481/* findcircumcenter() Find the circumcenter of a triangle. */
6482/* */
6483/* The result is returned both in terms of x-y coordinates and xi-eta */
6484/* (barycentric) coordinates. The xi-eta coordinate system is defined in */
6485/* terms of the triangle: the origin of the triangle is the origin of the */
6486/* coordinate system; the destination of the triangle is one unit along the */
6487/* xi axis; and the apex of the triangle is one unit along the eta axis. */
6488/* This procedure also returns the square of the length of the triangle's */
6489/* shortest edge. */
6490/* */
6491/*****************************************************************************/
6492
6493#ifdef ANSI_DECLARATORS
6494void findcircumcenter(struct mesh *m, struct behavior *b,
6495 vertex torg, vertex tdest, vertex tapex,
6496 vertex circumcenter, REAL *xi, REAL *eta, int offcenter)
6497#else /* not ANSI_DECLARATORS */
6498void findcircumcenter(m, b, torg, tdest, tapex, circumcenter, xi, eta,
6499 offcenter)
6500struct mesh *m;
6501struct behavior *b;
6502vertex torg;
6503vertex tdest;
6504vertex tapex;
6505vertex circumcenter;
6506REAL *xi;
6507REAL *eta;
6508int offcenter;
6509#endif /* not ANSI_DECLARATORS */
6510
6511{
6512 REAL xdo, ydo, xao, yao;
6513 REAL dodist, aodist, dadist;
6514 REAL denominator;
6515 REAL dx, dy, dxoff, dyoff;
6516
6517 m->circumcentercount++;
6518
6519 /* Compute the circumcenter of the triangle. */
6520 xdo = tdest[0] - torg[0];
6521 ydo = tdest[1] - torg[1];
6522 xao = tapex[0] - torg[0];
6523 yao = tapex[1] - torg[1];
6524 dodist = xdo * xdo + ydo * ydo;
6525 aodist = xao * xao + yao * yao;
6526 dadist = (tdest[0] - tapex[0]) * (tdest[0] - tapex[0]) +
6527 (tdest[1] - tapex[1]) * (tdest[1] - tapex[1]);
6528 if (b->noexact) {
6529 denominator = 0.5 / (xdo * yao - xao * ydo);
6530 } else {
6531 /* Use the counterclockwise() routine to ensure a positive (and */
6532 /* reasonably accurate) result, avoiding any possibility of */
6533 /* division by zero. */
6534 denominator = 0.5 / counterclockwise(m, b, tdest, tapex, torg);
6535 /* Don't count the above as an orientation test. */
6536 m->counterclockcount--;
6537 }
6538 dx = (yao * dodist - ydo * aodist) * denominator;
6539 dy = (xdo * aodist - xao * dodist) * denominator;
6540
6541 /* Find the (squared) length of the triangle's shortest edge. This */
6542 /* serves as a conservative estimate of the insertion radius of the */
6543 /* circumcenter's parent. The estimate is used to ensure that */
6544 /* the algorithm terminates even if very small angles appear in */
6545 /* the input PSLG. */
6546 if ((dodist < aodist) && (dodist < dadist)) {
6547 if (offcenter && (b->offconstant > 0.0)) {
6548 /* Find the position of the off-center, as described by Alper Ungor. */
6549 dxoff = 0.5 * xdo - b->offconstant * ydo;
6550 dyoff = 0.5 * ydo + b->offconstant * xdo;
6551 /* If the off-center is closer to the origin than the */
6552 /* circumcenter, use the off-center instead. */
6553 if (dxoff * dxoff + dyoff * dyoff < dx * dx + dy * dy) {
6554 dx = dxoff;
6555 dy = dyoff;
6556 }
6557 }
6558 } else if (aodist < dadist) {
6559 if (offcenter && (b->offconstant > 0.0)) {
6560 dxoff = 0.5 * xao + b->offconstant * yao;
6561 dyoff = 0.5 * yao - b->offconstant * xao;
6562 /* If the off-center is closer to the origin than the */
6563 /* circumcenter, use the off-center instead. */
6564 if (dxoff * dxoff + dyoff * dyoff < dx * dx + dy * dy) {
6565 dx = dxoff;
6566 dy = dyoff;
6567 }
6568 }
6569 } else {
6570 if (offcenter && (b->offconstant > 0.0)) {
6571 dxoff = 0.5 * (tapex[0] - tdest[0]) -
6572 b->offconstant * (tapex[1] - tdest[1]);
6573 dyoff = 0.5 * (tapex[1] - tdest[1]) +
6574 b->offconstant * (tapex[0] - tdest[0]);
6575 /* If the off-center is closer to the destination than the */
6576 /* circumcenter, use the off-center instead. */
6577 if (dxoff * dxoff + dyoff * dyoff <
6578 (dx - xdo) * (dx - xdo) + (dy - ydo) * (dy - ydo)) {
6579 dx = xdo + dxoff;
6580 dy = ydo + dyoff;
6581 }
6582 }
6583 }
6584
6585 circumcenter[0] = torg[0] + dx;
6586 circumcenter[1] = torg[1] + dy;
6587
6588 /* To interpolate vertex attributes for the new vertex inserted at */
6589 /* the circumcenter, define a coordinate system with a xi-axis, */
6590 /* directed from the triangle's origin to its destination, and */
6591 /* an eta-axis, directed from its origin to its apex. */
6592 /* Calculate the xi and eta coordinates of the circumcenter. */
6593 *xi = (yao * dx - xao * dy) * (2.0 * denominator);
6594 *eta = (xdo * dy - ydo * dx) * (2.0 * denominator);
6595}
6596
6597/** **/
6598/** **/
6599/********* Geometric primitives end here *********/
6600
6601/*****************************************************************************/
6602/* */
6603/* triangleinit() Initialize some variables. */
6604/* */
6605/*****************************************************************************/
6606
6607#ifdef ANSI_DECLARATORS
6608void triangleinit(struct mesh *m)
6609#else /* not ANSI_DECLARATORS */
6610void triangleinit(m)
6611struct mesh *m;
6612#endif /* not ANSI_DECLARATORS */
6613
6614{
6615 poolzero(&m->vertices);
6616 poolzero(&m->triangles);
6617 poolzero(&m->subsegs);
6618 poolzero(&m->viri);
6619 poolzero(&m->badsubsegs);
6620 poolzero(&m->badtriangles);
6621 poolzero(&m->flipstackers);
6622 poolzero(&m->splaynodes);
6623
6624 m->recenttri.tri = (triangle *) NULL; /* No triangle has been visited yet. */
6625 m->undeads = 0; /* No eliminated input vertices yet. */
6626 m->samples = 1; /* Point location should take at least one sample. */
6627 m->checksegments = 0; /* There are no segments in the triangulation yet. */
6628 m->checkquality = 0; /* The quality triangulation stage has not begun. */
6629 m->incirclecount = m->counterclockcount = m->orient3dcount = 0;
6630 m->hyperbolacount = m->circletopcount = m->circumcentercount = 0;
6631 randomseed = 1;
6632
6633 exactinit(); /* Initialize exact arithmetic constants. */
6634}
6635
6636/*****************************************************************************/
6637/* */
6638/* randomnation() Generate a random number between 0 and `choices' - 1. */
6639/* */
6640/* This is a simple linear congruential random number generator. Hence, it */
6641/* is a bad random number generator, but good enough for most randomized */
6642/* geometric algorithms. */
6643/* */
6644/*****************************************************************************/
6645
6646#ifdef ANSI_DECLARATORS
6647unsigned long randomnation(unsigned int choices)
6648#else /* not ANSI_DECLARATORS */
6649unsigned long randomnation(choices)
6650unsigned int choices;
6651#endif /* not ANSI_DECLARATORS */
6652
6653{
6654 randomseed = (randomseed * 1366l + 150889l) % 714025l;
6655 return randomseed / (714025l / choices + 1);
6656}
6657
6658/********* Mesh quality testing routines begin here *********/
6659/** **/
6660/** **/
6661
6662/*****************************************************************************/
6663/* */
6664/* checkmesh() Test the mesh for topological consistency. */
6665/* */
6666/*****************************************************************************/
6667
6668#ifndef REDUCED
6669
6670#ifdef ANSI_DECLARATORS
6671void checkmesh(struct mesh *m, struct behavior *b)
6672#else /* not ANSI_DECLARATORS */
6673void checkmesh(m, b)
6674struct mesh *m;
6675struct behavior *b;
6676#endif /* not ANSI_DECLARATORS */
6677
6678{
6679 struct otri triangleloop;
6680 struct otri oppotri, oppooppotri;
6681 vertex triorg, tridest, triapex;
6682 vertex oppoorg, oppodest;
6683 int horrors;
6684 int saveexact;
6685 triangle ptr; /* Temporary variable used by sym(). */
6686
6687 /* Temporarily turn on exact arithmetic if it's off. */
6688 saveexact = b->noexact;
6689 b->noexact = 0;
6690 if (!b->quiet) {
6691 printf(" Checking consistency of mesh...\n");
6692 }
6693 horrors = 0;
6694 /* Run through the list of triangles, checking each one. */
6695 traversalinit(&m->triangles);
6696 triangleloop.tri = triangletraverse(m);
6697 while (triangleloop.tri != (triangle *) NULL) {
6698 /* Check all three edges of the triangle. */
6699 for (triangleloop.orient = 0; triangleloop.orient < 3;
6700 triangleloop.orient++) {
6701 org(triangleloop, triorg);
6702 dest(triangleloop, tridest);
6703 if (triangleloop.orient == 0) { /* Only test for inversion once. */
6704 /* Test if the triangle is flat or inverted. */
6705 apex(triangleloop, triapex);
6706 if (counterclockwise(m, b, triorg, tridest, triapex) <= 0.0) {
6707 printf(" !! !! Inverted ");
6708 printtriangle(m, b, &triangleloop);
6709 horrors++;
6710 }
6711 }
6712 /* Find the neighboring triangle on this edge. */
6713 sym(triangleloop, oppotri);
6714 if (oppotri.tri != m->dummytri) {
6715 /* Check that the triangle's neighbor knows it's a neighbor. */
6716 sym(oppotri, oppooppotri);
6717 if ((triangleloop.tri != oppooppotri.tri)
6718 || (triangleloop.orient != oppooppotri.orient)) {
6719 printf(" !! !! Asymmetric triangle-triangle bond:\n");
6720 if (triangleloop.tri == oppooppotri.tri) {
6721 printf(" (Right triangle, wrong orientation)\n");
6722 }
6723 printf(" First ");
6724 printtriangle(m, b, &triangleloop);
6725 printf(" Second (nonreciprocating) ");
6726 printtriangle(m, b, &oppotri);
6727 horrors++;
6728 }
6729 /* Check that both triangles agree on the identities */
6730 /* of their shared vertices. */
6731 org(oppotri, oppoorg);
6732 dest(oppotri, oppodest);
6733 if ((triorg != oppodest) || (tridest != oppoorg)) {
6734 printf(" !! !! Mismatched edge coordinates between two triangles:\n"
6735 );
6736 printf(" First mismatched ");
6737 printtriangle(m, b, &triangleloop);
6738 printf(" Second mismatched ");
6739 printtriangle(m, b, &oppotri);
6740 horrors++;
6741 }
6742 }
6743 }
6744 triangleloop.tri = triangletraverse(m);
6745 }
6746 if (horrors == 0) {
6747 if (!b->quiet) {
6748 printf(" In my studied opinion, the mesh appears to be consistent.\n");
6749 }
6750 } else if (horrors == 1) {
6751 printf(" !! !! !! !! Precisely one festering wound discovered.\n");
6752 } else {
6753 printf(" !! !! !! !! %d abominations witnessed.\n", horrors);
6754 }
6755 /* Restore the status of exact arithmetic. */
6756 b->noexact = saveexact;
6757}
6758
6759#endif /* not REDUCED */
6760
6761/*****************************************************************************/
6762/* */
6763/* checkdelaunay() Ensure that the mesh is (constrained) Delaunay. */
6764/* */
6765/*****************************************************************************/
6766
6767#ifndef REDUCED
6768
6769#ifdef ANSI_DECLARATORS
6770void checkdelaunay(struct mesh *m, struct behavior *b)
6771#else /* not ANSI_DECLARATORS */
6772void checkdelaunay(m, b)
6773struct mesh *m;
6774struct behavior *b;
6775#endif /* not ANSI_DECLARATORS */
6776
6777{
6778 struct otri triangleloop;
6779 struct otri oppotri;
6780 struct osub opposubseg;
6781 vertex triorg, tridest, triapex;
6782 vertex oppoapex;
6783 int shouldbedelaunay;
6784 int horrors;
6785 int saveexact;
6786 triangle ptr; /* Temporary variable used by sym(). */
6787 subseg sptr; /* Temporary variable used by tspivot(). */
6788
6789 /* Temporarily turn on exact arithmetic if it's off. */
6790 saveexact = b->noexact;
6791 b->noexact = 0;
6792 if (!b->quiet) {
6793 printf(" Checking Delaunay property of mesh...\n");
6794 }
6795 horrors = 0;
6796 /* Run through the list of triangles, checking each one. */
6797 traversalinit(&m->triangles);
6798 triangleloop.tri = triangletraverse(m);
6799 while (triangleloop.tri != (triangle *) NULL) {
6800 /* Check all three edges of the triangle. */
6801 for (triangleloop.orient = 0; triangleloop.orient < 3;
6802 triangleloop.orient++) {
6803 org(triangleloop, triorg);
6804 dest(triangleloop, tridest);
6805 apex(triangleloop, triapex);
6806 sym(triangleloop, oppotri);
6807 apex(oppotri, oppoapex);
6808 /* Only test that the edge is locally Delaunay if there is an */
6809 /* adjoining triangle whose pointer is larger (to ensure that */
6810 /* each pair isn't tested twice). */
6811 shouldbedelaunay = (oppotri.tri != m->dummytri) &&
6812 !deadtri(oppotri.tri) && (triangleloop.tri < oppotri.tri) &&
6813 (triorg != m->infvertex1) && (triorg != m->infvertex2) &&
6814 (triorg != m->infvertex3) &&
6815 (tridest != m->infvertex1) && (tridest != m->infvertex2) &&
6816 (tridest != m->infvertex3) &&
6817 (triapex != m->infvertex1) && (triapex != m->infvertex2) &&
6818 (triapex != m->infvertex3) &&
6819 (oppoapex != m->infvertex1) && (oppoapex != m->infvertex2) &&
6820 (oppoapex != m->infvertex3);
6821 if (m->checksegments && shouldbedelaunay) {
6822 /* If a subsegment separates the triangles, then the edge is */
6823 /* constrained, so no local Delaunay test should be done. */
6824 tspivot(triangleloop, opposubseg);
6825 if (opposubseg.ss != m->dummysub){
6826 shouldbedelaunay = 0;
6827 }
6828 }
6829 if (shouldbedelaunay) {
6830 if (nonregular(m, b, triorg, tridest, triapex, oppoapex) > 0.0) {
6831 if (!b->weighted) {
6832 printf(" !! !! Non-Delaunay pair of triangles:\n");
6833 printf(" First non-Delaunay ");
6834 printtriangle(m, b, &triangleloop);
6835 printf(" Second non-Delaunay ");
6836 } else {
6837 printf(" !! !! Non-regular pair of triangles:\n");
6838 printf(" First non-regular ");
6839 printtriangle(m, b, &triangleloop);
6840 printf(" Second non-regular ");
6841 }
6842 printtriangle(m, b, &oppotri);
6843 horrors++;
6844 }
6845 }
6846 }
6847 triangleloop.tri = triangletraverse(m);
6848 }
6849 if (horrors == 0) {
6850 if (!b->quiet) {
6851 printf(
6852 " By virtue of my perceptive intelligence, I declare the mesh Delaunay.\n");
6853 }
6854 } else if (horrors == 1) {
6855 printf(
6856 " !! !! !! !! Precisely one terrifying transgression identified.\n");
6857 } else {
6858 printf(" !! !! !! !! %d obscenities viewed with horror.\n", horrors);
6859 }
6860 /* Restore the status of exact arithmetic. */
6861 b->noexact = saveexact;
6862}
6863
6864#endif /* not REDUCED */
6865
6866/*****************************************************************************/
6867/* */
6868/* enqueuebadtriang() Add a bad triangle data structure to the end of a */
6869/* queue. */
6870/* */
6871/* The queue is actually a set of 4096 queues. I use multiple queues to */
6872/* give priority to smaller angles. I originally implemented a heap, but */
6873/* the queues are faster by a larger margin than I'd suspected. */
6874/* */
6875/*****************************************************************************/
6876
6877#ifndef CDT_ONLY
6878
6879#ifdef ANSI_DECLARATORS
6880void enqueuebadtriang(struct mesh *m, struct behavior *b,
6881 struct badtriang *badtri)
6882#else /* not ANSI_DECLARATORS */
6883void enqueuebadtriang(m, b, badtri)
6884struct mesh *m;
6885struct behavior *b;
6886struct badtriang *badtri;
6887#endif /* not ANSI_DECLARATORS */
6888
6889{
6890 REAL length, multiplier;
6891 int exponent, expincrement;
6892 int queuenumber;
6893 int posexponent;
6894 int i;
6895
6896 if (b->verbose > 2) {
6897 printf(" Queueing bad triangle:\n");
6898 printf(" (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
6899 badtri->triangorg[0], badtri->triangorg[1],
6900 badtri->triangdest[0], badtri->triangdest[1],
6901 badtri->triangapex[0], badtri->triangapex[1]);
6902 }
6903
6904 /* Determine the appropriate queue to put the bad triangle into. */
6905 /* Recall that the key is the square of its shortest edge length. */
6906 if (badtri->key >= 1.0) {
6907 length = badtri->key;
6908 posexponent = 1;
6909 } else {
6910 /* `badtri->key' is 2.0 to a negative exponent, so we'll record that */
6911 /* fact and use the reciprocal of `badtri->key', which is > 1.0. */
6912 length = 1.0 / badtri->key;
6913 posexponent = 0;
6914 }
6915 /* `length' is approximately 2.0 to what exponent? The following code */
6916 /* determines the answer in time logarithmic in the exponent. */
6917 exponent = 0;
6918 while (length > 2.0) {
6919 /* Find an approximation by repeated squaring of two. */
6920 expincrement = 1;
6921 multiplier = 0.5;
6922 while (length * multiplier * multiplier > 1.0) {
6923 expincrement *= 2;
6924 multiplier *= multiplier;
6925 }
6926 /* Reduce the value of `length', then iterate if necessary. */
6927 exponent += expincrement;
6928 length *= multiplier;
6929 }
6930 /* `length' is approximately squareroot(2.0) to what exponent? */
6931 exponent = 2.0 * exponent + (length > SQUAREROOTTWO);
6932 /* `exponent' is now in the range 0...2047 for IEEE double precision. */
6933 /* Choose a queue in the range 0...4095. The shortest edges have the */
6934 /* highest priority (queue 4095). */
6935 if (posexponent) {
6936 queuenumber = 2047 - exponent;
6937 } else {
6938 queuenumber = 2048 + exponent;
6939 }
6940
6941 /* Are we inserting into an empty queue? */
6942 if (m->queuefront[queuenumber] == (struct badtriang *) NULL) {
6943 /* Yes, we are inserting into an empty queue. */
6944 /* Will this become the highest-priority queue? */
6945 if (queuenumber > m->firstnonemptyq) {
6946 /* Yes, this is the highest-priority queue. */
6947 m->nextnonemptyq[queuenumber] = m->firstnonemptyq;
6948 m->firstnonemptyq = queuenumber;
6949 } else {
6950 /* No, this is not the highest-priority queue. */
6951 /* Find the queue with next higher priority. */
6952 i = queuenumber + 1;
6953 while (m->queuefront[i] == (struct badtriang *) NULL) {
6954 i++;
6955 }
6956 /* Mark the newly nonempty queue as following a higher-priority queue. */
6957 m->nextnonemptyq[queuenumber] = m->nextnonemptyq[i];
6958 m->nextnonemptyq[i] = queuenumber;
6959 }
6960 /* Put the bad triangle at the beginning of the (empty) queue. */
6961 m->queuefront[queuenumber] = badtri;
6962 } else {
6963 /* Add the bad triangle to the end of an already nonempty queue. */
6964 m->queuetail[queuenumber]->nexttriang = badtri;
6965 }
6966 /* Maintain a pointer to the last triangle of the queue. */
6967 m->queuetail[queuenumber] = badtri;
6968 /* Newly enqueued bad triangle has no successor in the queue. */
6969 badtri->nexttriang = (struct badtriang *) NULL;
6970}
6971
6972#endif /* not CDT_ONLY */
6973
6974/*****************************************************************************/
6975/* */
6976/* enqueuebadtri() Add a bad triangle to the end of a queue. */
6977/* */
6978/* Allocates a badtriang data structure for the triangle, then passes it to */
6979/* enqueuebadtriang(). */
6980/* */
6981/*****************************************************************************/
6982
6983#ifndef CDT_ONLY
6984
6985#ifdef ANSI_DECLARATORS
6986void enqueuebadtri(struct mesh *m, struct behavior *b, struct otri *enqtri,
6987 REAL minedge, vertex enqapex, vertex enqorg, vertex enqdest)
6988#else /* not ANSI_DECLARATORS */
6989void enqueuebadtri(m, b, enqtri, minedge, enqapex, enqorg, enqdest)
6990struct mesh *m;
6991struct behavior *b;
6992struct otri *enqtri;
6993REAL minedge;
6994vertex enqapex;
6995vertex enqorg;
6996vertex enqdest;
6997#endif /* not ANSI_DECLARATORS */
6998
6999{
7000 struct badtriang *newbad;
7001
7002 /* Allocate space for the bad triangle. */
7003 newbad = (struct badtriang *) poolalloc(&m->badtriangles);
7004 newbad->poortri = encode(*enqtri);
7005 newbad->key = minedge;
7006 newbad->triangapex = enqapex;
7007 newbad->triangorg = enqorg;
7008 newbad->triangdest = enqdest;
7009 enqueuebadtriang(m, b, newbad);
7010}
7011
7012#endif /* not CDT_ONLY */
7013
7014/*****************************************************************************/
7015/* */
7016/* dequeuebadtriang() Remove a triangle from the front of the queue. */
7017/* */
7018/*****************************************************************************/
7019
7020#ifndef CDT_ONLY
7021
7022#ifdef ANSI_DECLARATORS
7023struct badtriang *dequeuebadtriang(struct mesh *m)
7024#else /* not ANSI_DECLARATORS */
7025struct badtriang *dequeuebadtriang(m)
7026struct mesh *m;
7027#endif /* not ANSI_DECLARATORS */
7028
7029{
7030 struct badtriang *result;
7031
7032 /* If no queues are nonempty, return NULL. */
7033 if (m->firstnonemptyq < 0) {
7034 return (struct badtriang *) NULL;
7035 }
7036 /* Find the first triangle of the highest-priority queue. */
7037 result = m->queuefront[m->firstnonemptyq];
7038 /* Remove the triangle from the queue. */
7039 m->queuefront[m->firstnonemptyq] = result->nexttriang;
7040 /* If this queue is now empty, note the new highest-priority */
7041 /* nonempty queue. */
7042 if (result == m->queuetail[m->firstnonemptyq]) {
7043 m->firstnonemptyq = m->nextnonemptyq[m->firstnonemptyq];
7044 }
7045 return result;
7046}
7047
7048#endif /* not CDT_ONLY */
7049
7050/*****************************************************************************/
7051/* */
7052/* checkseg4encroach() Check a subsegment to see if it is encroached; add */
7053/* it to the list if it is. */
7054/* */
7055/* A subsegment is encroached if there is a vertex in its diametral lens. */
7056/* For Ruppert's algorithm (-D switch), the "diametral lens" is the */
7057/* diametral circle. For Chew's algorithm (default), the diametral lens is */
7058/* just big enough to enclose two isosceles triangles whose bases are the */
7059/* subsegment. Each of the two isosceles triangles has two angles equal */
7060/* to `b->minangle'. */
7061/* */
7062/* Chew's algorithm does not require diametral lenses at all--but they save */
7063/* time. Any vertex inside a subsegment's diametral lens implies that the */
7064/* triangle adjoining the subsegment will be too skinny, so it's only a */
7065/* matter of time before the encroaching vertex is deleted by Chew's */
7066/* algorithm. It's faster to simply not insert the doomed vertex in the */
7067/* first place, which is why I use diametral lenses with Chew's algorithm. */
7068/* */
7069/* Returns a nonzero value if the subsegment is encroached. */
7070/* */
7071/*****************************************************************************/
7072
7073#ifndef CDT_ONLY
7074
7075#ifdef ANSI_DECLARATORS
7076int checkseg4encroach(struct mesh *m, struct behavior *b,
7077 struct osub *testsubseg)
7078#else /* not ANSI_DECLARATORS */
7079int checkseg4encroach(m, b, testsubseg)
7080struct mesh *m;
7081struct behavior *b;
7082struct osub *testsubseg;
7083#endif /* not ANSI_DECLARATORS */
7084
7085{
7086 struct otri neighbortri;
7087 struct osub testsym;
7088 struct badsubseg *encroachedseg;
7089 REAL dotproduct;
7090 int encroached;
7091 int sides;
7092 vertex eorg, edest, eapex;
7093 triangle ptr; /* Temporary variable used by stpivot(). */
7094
7095 encroached = 0;
7096 sides = 0;
7097
7098 sorg(*testsubseg, eorg);
7099 sdest(*testsubseg, edest);
7100 /* Check one neighbor of the subsegment. */
7101 stpivot(*testsubseg, neighbortri);
7102 /* Does the neighbor exist, or is this a boundary edge? */
7103 if (neighbortri.tri != m->dummytri) {
7104 sides++;
7105 /* Find a vertex opposite this subsegment. */
7106 apex(neighbortri, eapex);
7107 /* Check whether the apex is in the diametral lens of the subsegment */
7108 /* (the diametral circle if `conformdel' is set). A dot product */
7109 /* of two sides of the triangle is used to check whether the angle */
7110 /* at the apex is greater than (180 - 2 `minangle') degrees (for */
7111 /* lenses; 90 degrees for diametral circles). */
7112 dotproduct = (eorg[0] - eapex[0]) * (edest[0] - eapex[0]) +
7113 (eorg[1] - eapex[1]) * (edest[1] - eapex[1]);
7114 if (dotproduct < 0.0) {
7115 if (b->conformdel ||
7116 (dotproduct * dotproduct >=
7117 (2.0 * b->goodangle - 1.0) * (2.0 * b->goodangle - 1.0) *
7118 ((eorg[0] - eapex[0]) * (eorg[0] - eapex[0]) +
7119 (eorg[1] - eapex[1]) * (eorg[1] - eapex[1])) *
7120 ((edest[0] - eapex[0]) * (edest[0] - eapex[0]) +
7121 (edest[1] - eapex[1]) * (edest[1] - eapex[1])))) {
7122 encroached = 1;
7123 }
7124 }
7125 }
7126 /* Check the other neighbor of the subsegment. */
7127 ssym(*testsubseg, testsym);
7128 stpivot(testsym, neighbortri);
7129 /* Does the neighbor exist, or is this a boundary edge? */
7130 if (neighbortri.tri != m->dummytri) {
7131 sides++;
7132 /* Find the other vertex opposite this subsegment. */
7133 apex(neighbortri, eapex);
7134 /* Check whether the apex is in the diametral lens of the subsegment */
7135 /* (or the diametral circle, if `conformdel' is set). */
7136 dotproduct = (eorg[0] - eapex[0]) * (edest[0] - eapex[0]) +
7137 (eorg[1] - eapex[1]) * (edest[1] - eapex[1]);
7138 if (dotproduct < 0.0) {
7139 if (b->conformdel ||
7140 (dotproduct * dotproduct >=
7141 (2.0 * b->goodangle - 1.0) * (2.0 * b->goodangle - 1.0) *
7142 ((eorg[0] - eapex[0]) * (eorg[0] - eapex[0]) +
7143 (eorg[1] - eapex[1]) * (eorg[1] - eapex[1])) *
7144 ((edest[0] - eapex[0]) * (edest[0] - eapex[0]) +
7145 (edest[1] - eapex[1]) * (edest[1] - eapex[1])))) {
7146 encroached += 2;
7147 }
7148 }
7149 }
7150
7151 if (encroached && (!b->nobisect || ((b->nobisect == 1) && (sides == 2)))) {
7152 if (b->verbose > 2) {
7153 printf(
7154 " Queueing encroached subsegment (%.12g, %.12g) (%.12g, %.12g).\n",
7155 eorg[0], eorg[1], edest[0], edest[1]);
7156 }
7157 /* Add the subsegment to the list of encroached subsegments. */
7158 /* Be sure to get the orientation right. */
7159 encroachedseg = (struct badsubseg *) poolalloc(&m->badsubsegs);
7160 if (encroached == 1) {
7161 encroachedseg->encsubseg = sencode(*testsubseg);
7162 encroachedseg->subsegorg = eorg;
7163 encroachedseg->subsegdest = edest;
7164 } else {
7165 encroachedseg->encsubseg = sencode(testsym);
7166 encroachedseg->subsegorg = edest;
7167 encroachedseg->subsegdest = eorg;
7168 }
7169 }
7170
7171 return encroached;
7172}
7173
7174#endif /* not CDT_ONLY */
7175
7176/*****************************************************************************/
7177/* */
7178/* testtriangle() Test a triangle for quality and size. */
7179/* */
7180/* Tests a triangle to see if it satisfies the minimum angle condition and */
7181/* the maximum area condition. Triangles that aren't up to spec are added */
7182/* to the bad triangle queue. */
7183/* */
7184/*****************************************************************************/
7185
7186#ifndef CDT_ONLY
7187
7188#ifdef ANSI_DECLARATORS
7189void testtriangle(struct mesh *m, struct behavior *b, struct otri *testtri)
7190#else /* not ANSI_DECLARATORS */
7191void testtriangle(m, b, testtri)
7192struct mesh *m;
7193struct behavior *b;
7194struct otri *testtri;
7195#endif /* not ANSI_DECLARATORS */
7196
7197{
7198 struct otri tri1, tri2;
7199 struct osub testsub;
7200 vertex torg, tdest, tapex;
7201 vertex base1, base2;
7202 vertex org1, dest1, org2, dest2;
7203 vertex joinvertex;
7204 REAL dxod, dyod, dxda, dyda, dxao, dyao;
7205 REAL dxod2, dyod2, dxda2, dyda2, dxao2, dyao2;
7206 REAL apexlen, orglen, destlen, minedge;
7207 REAL angle;
7208 REAL area;
7209 REAL dist1, dist2;
7210 subseg sptr; /* Temporary variable used by tspivot(). */
7211 triangle ptr; /* Temporary variable used by oprev() and dnext(). */
7212
7213 org(*testtri, torg);
7214 dest(*testtri, tdest);
7215 apex(*testtri, tapex);
7216 dxod = torg[0] - tdest[0];
7217 dyod = torg[1] - tdest[1];
7218 dxda = tdest[0] - tapex[0];
7219 dyda = tdest[1] - tapex[1];
7220 dxao = tapex[0] - torg[0];
7221 dyao = tapex[1] - torg[1];
7222 dxod2 = dxod * dxod;
7223 dyod2 = dyod * dyod;
7224 dxda2 = dxda * dxda;
7225 dyda2 = dyda * dyda;
7226 dxao2 = dxao * dxao;
7227 dyao2 = dyao * dyao;
7228 /* Find the lengths of the triangle's three edges. */
7229 apexlen = dxod2 + dyod2;
7230 orglen = dxda2 + dyda2;
7231 destlen = dxao2 + dyao2;
7232
7233 if ((apexlen < orglen) && (apexlen < destlen)) {
7234 /* The edge opposite the apex is shortest. */
7235 minedge = apexlen;
7236 /* Find the square of the cosine of the angle at the apex. */
7237 angle = dxda * dxao + dyda * dyao;
7238 angle = angle * angle / (orglen * destlen);
7239 base1 = torg;
7240 base2 = tdest;
7241 otricopy(*testtri, tri1);
7242 } else if (orglen < destlen) {
7243 /* The edge opposite the origin is shortest. */
7244 minedge = orglen;
7245 /* Find the square of the cosine of the angle at the origin. */
7246 angle = dxod * dxao + dyod * dyao;
7247 angle = angle * angle / (apexlen * destlen);
7248 base1 = tdest;
7249 base2 = tapex;
7250 lnext(*testtri, tri1);
7251 } else {
7252 /* The edge opposite the destination is shortest. */
7253 minedge = destlen;
7254 /* Find the square of the cosine of the angle at the destination. */
7255 angle = dxod * dxda + dyod * dyda;
7256 angle = angle * angle / (apexlen * orglen);
7257 base1 = tapex;
7258 base2 = torg;
7259 lprev(*testtri, tri1);
7260 }
7261
7262 if (b->vararea || b->fixedarea || b->usertest) {
7263 /* Check whether the area is larger than permitted. */
7264 area = 0.5 * (dxod * dyda - dyod * dxda);
7265 if (b->fixedarea && (area > b->maxarea)) {
7266 /* Add this triangle to the list of bad triangles. */
7267 enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest);
7268 return;
7269 }
7270
7271 /* Nonpositive area constraints are treated as unconstrained. */
7272 if ((b->vararea) && (area > areabound(*testtri)) &&
7273 (areabound(*testtri) > 0.0)) {
7274 /* Add this triangle to the list of bad triangles. */
7275 enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest);
7276 return;
7277 }
7278
7279 if (b->usertest) {
7280 /* Check whether the user thinks this triangle is too large. */
7281 if (triunsuitable(torg, tdest, tapex, area)) {
7282 enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest);
7283 return;
7284 }
7285 }
7286 }
7287
7288 /* Check whether the angle is smaller than permitted. */
7289 if (angle > b->goodangle) {
7290 /* Use the rules of Miller, Pav, and Walkington to decide that certain */
7291 /* triangles should not be split, even if they have bad angles. */
7292 /* A skinny triangle is not split if its shortest edge subtends a */
7293 /* small input angle, and both endpoints of the edge lie on a */
7294 /* concentric circular shell. For convenience, I make a small */
7295 /* adjustment to that rule: I check if the endpoints of the edge */
7296 /* both lie in segment interiors, equidistant from the apex where */
7297 /* the two segments meet. */
7298 /* First, check if both points lie in segment interiors. */
7299 if ((vertextype(base1) == SEGMENTVERTEX) &&
7300 (vertextype(base2) == SEGMENTVERTEX)) {
7301 /* Check if both points lie in a common segment. If they do, the */
7302 /* skinny triangle is enqueued to be split as usual. */
7303 tspivot(tri1, testsub);
7304 if (testsub.ss == m->dummysub) {
7305 /* No common segment. Find a subsegment that contains `torg'. */
7306 otricopy(tri1, tri2);
7307 do {
7308 oprevself(tri1);
7309 tspivot(tri1, testsub);
7310 } while (testsub.ss == m->dummysub);
7311 /* Find the endpoints of the containing segment. */
7312 segorg(testsub, org1);
7313 segdest(testsub, dest1);
7314 /* Find a subsegment that contains `tdest'. */
7315 do {
7316 dnextself(tri2);
7317 tspivot(tri2, testsub);
7318 } while (testsub.ss == m->dummysub);
7319 /* Find the endpoints of the containing segment. */
7320 segorg(testsub, org2);
7321 segdest(testsub, dest2);
7322 /* Check if the two containing segments have an endpoint in common. */
7323 joinvertex = (vertex) NULL;
7324 if ((dest1[0] == org2[0]) && (dest1[1] == org2[1])) {
7325 joinvertex = dest1;
7326 } else if ((org1[0] == dest2[0]) && (org1[1] == dest2[1])) {
7327 joinvertex = org1;
7328 }
7329 if (joinvertex != (vertex) NULL) {
7330 /* Compute the distance from the common endpoint (of the two */
7331 /* segments) to each of the endpoints of the shortest edge. */
7332 dist1 = ((base1[0] - joinvertex[0]) * (base1[0] - joinvertex[0]) +
7333 (base1[1] - joinvertex[1]) * (base1[1] - joinvertex[1]));
7334 dist2 = ((base2[0] - joinvertex[0]) * (base2[0] - joinvertex[0]) +
7335 (base2[1] - joinvertex[1]) * (base2[1] - joinvertex[1]));
7336 /* If the two distances are equal, don't split the triangle. */
7337 if ((dist1 < 1.001 * dist2) && (dist1 > 0.999 * dist2)) {
7338 /* Return now to avoid enqueueing the bad triangle. */
7339 return;
7340 }
7341 }
7342 }
7343 }
7344
7345 /* Add this triangle to the list of bad triangles. */
7346 enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest);
7347 }
7348}
7349
7350#endif /* not CDT_ONLY */
7351
7352/** **/
7353/** **/
7354/********* Mesh quality testing routines end here *********/
7355
7356/********* Point location routines begin here *********/
7357/** **/
7358/** **/
7359
7360/*****************************************************************************/
7361/* */
7362/* makevertexmap() Construct a mapping from vertices to triangles to */
7363/* improve the speed of point location for segment */
7364/* insertion. */
7365/* */
7366/* Traverses all the triangles, and provides each corner of each triangle */
7367/* with a pointer to that triangle. Of course, pointers will be */
7368/* overwritten by other pointers because (almost) each vertex is a corner */
7369/* of several triangles, but in the end every vertex will point to some */
7370/* triangle that contains it. */
7371/* */
7372/*****************************************************************************/
7373
7374#ifdef ANSI_DECLARATORS
7375void makevertexmap(struct mesh *m, struct behavior *b)
7376#else /* not ANSI_DECLARATORS */
7377void makevertexmap(m, b)
7378struct mesh *m;
7379struct behavior *b;
7380#endif /* not ANSI_DECLARATORS */
7381
7382{
7383 struct otri triangleloop;
7384 vertex triorg;
7385
7386 if (b->verbose) {
7387 printf(" Constructing mapping from vertices to triangles.\n");
7388 }
7389 traversalinit(&m->triangles);
7390 triangleloop.tri = triangletraverse(m);
7391 while (triangleloop.tri != (triangle *) NULL) {
7392 /* Check all three vertices of the triangle. */
7393 for (triangleloop.orient = 0; triangleloop.orient < 3;
7394 triangleloop.orient++) {
7395 org(triangleloop, triorg);
7396 setvertex2tri(triorg, encode(triangleloop));
7397 }
7398 triangleloop.tri = triangletraverse(m);
7399 }
7400}
7401
7402/*****************************************************************************/
7403/* */
7404/* preciselocate() Find a triangle or edge containing a given point. */
7405/* */
7406/* Begins its search from `searchtri'. It is important that `searchtri' */
7407/* be a handle with the property that `searchpoint' is strictly to the left */
7408/* of the edge denoted by `searchtri', or is collinear with that edge and */
7409/* does not intersect that edge. (In particular, `searchpoint' should not */
7410/* be the origin or destination of that edge.) */
7411/* */
7412/* These conditions are imposed because preciselocate() is normally used in */
7413/* one of two situations: */
7414/* */
7415/* (1) To try to find the location to insert a new point. Normally, we */
7416/* know an edge that the point is strictly to the left of. In the */
7417/* incremental Delaunay algorithm, that edge is a bounding box edge. */
7418/* In Ruppert's Delaunay refinement algorithm for quality meshing, */
7419/* that edge is the shortest edge of the triangle whose circumcenter */
7420/* is being inserted. */
7421/* */
7422/* (2) To try to find an existing point. In this case, any edge on the */
7423/* convex hull is a good starting edge. You must screen out the */
7424/* possibility that the vertex sought is an endpoint of the starting */
7425/* edge before you call preciselocate(). */
7426/* */
7427/* On completion, `searchtri' is a triangle that contains `searchpoint'. */
7428/* */
7429/* This implementation differs from that given by Guibas and Stolfi. It */
7430/* walks from triangle to triangle, crossing an edge only if `searchpoint' */
7431/* is on the other side of the line containing that edge. After entering */
7432/* a triangle, there are two edges by which one can leave that triangle. */
7433/* If both edges are valid (`searchpoint' is on the other side of both */
7434/* edges), one of the two is chosen by drawing a line perpendicular to */
7435/* the entry edge (whose endpoints are `forg' and `fdest') passing through */
7436/* `fapex'. Depending on which side of this perpendicular `searchpoint' */
7437/* falls on, an exit edge is chosen. */
7438/* */
7439/* This implementation is empirically faster than the Guibas and Stolfi */
7440/* point location routine (which I originally used), which tends to spiral */
7441/* in toward its target. */
7442/* */
7443/* Returns ONVERTEX if the point lies on an existing vertex. `searchtri' */
7444/* is a handle whose origin is the existing vertex. */
7445/* */
7446/* Returns ONEDGE if the point lies on a mesh edge. `searchtri' is a */
7447/* handle whose primary edge is the edge on which the point lies. */
7448/* */
7449/* Returns INTRIANGLE if the point lies strictly within a triangle. */
7450/* `searchtri' is a handle on the triangle that contains the point. */
7451/* */
7452/* Returns OUTSIDE if the point lies outside the mesh. `searchtri' is a */
7453/* handle whose primary edge the point is to the right of. This might */
7454/* occur when the circumcenter of a triangle falls just slightly outside */
7455/* the mesh due to floating-point roundoff error. It also occurs when */
7456/* seeking a hole or region point that a foolish user has placed outside */
7457/* the mesh. */
7458/* */
7459/* If `stopatsubsegment' is nonzero, the search will stop if it tries to */
7460/* walk through a subsegment, and will return OUTSIDE. */
7461/* */
7462/* WARNING: This routine is designed for convex triangulations, and will */
7463/* not generally work after the holes and concavities have been carved. */
7464/* However, it can still be used to find the circumcenter of a triangle, as */
7465/* long as the search is begun from the triangle in question. */
7466/* */
7467/*****************************************************************************/
7468
7469#ifdef ANSI_DECLARATORS
7470enum locateresult preciselocate(struct mesh *m, struct behavior *b,
7471 vertex searchpoint, struct otri *searchtri,
7472 int stopatsubsegment)
7473#else /* not ANSI_DECLARATORS */
7474enum locateresult preciselocate(m, b, searchpoint, searchtri, stopatsubsegment)
7475struct mesh *m;
7476struct behavior *b;
7477vertex searchpoint;
7478struct otri *searchtri;
7479int stopatsubsegment;
7480#endif /* not ANSI_DECLARATORS */
7481
7482{
7483 struct otri backtracktri;
7484 struct osub checkedge;
7485 vertex forg, fdest, fapex;
7486 REAL orgorient, destorient;
7487 int moveleft;
7488 triangle ptr; /* Temporary variable used by sym(). */
7489 subseg sptr; /* Temporary variable used by tspivot(). */
7490
7491 if (b->verbose > 2) {
7492 printf(" Searching for point (%.12g, %.12g).\n",
7493 searchpoint[0], searchpoint[1]);
7494 }
7495 /* Where are we? */
7496 org(*searchtri, forg);
7497 dest(*searchtri, fdest);
7498 apex(*searchtri, fapex);
7499 while (1) {
7500 if (b->verbose > 2) {
7501 printf(" At (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
7502 forg[0], forg[1], fdest[0], fdest[1], fapex[0], fapex[1]);
7503 }
7504 /* Check whether the apex is the point we seek. */
7505 if ((fapex[0] == searchpoint[0]) && (fapex[1] == searchpoint[1])) {
7506 lprevself(*searchtri);
7507 return ONVERTEX;
7508 }
7509 /* Does the point lie on the other side of the line defined by the */
7510 /* triangle edge opposite the triangle's destination? */
7511 destorient = counterclockwise(m, b, forg, fapex, searchpoint);
7512 /* Does the point lie on the other side of the line defined by the */
7513 /* triangle edge opposite the triangle's origin? */
7514 orgorient = counterclockwise(m, b, fapex, fdest, searchpoint);
7515 if (destorient > 0.0) {
7516 if (orgorient > 0.0) {
7517 /* Move left if the inner product of (fapex - searchpoint) and */
7518 /* (fdest - forg) is positive. This is equivalent to drawing */
7519 /* a line perpendicular to the line (forg, fdest) and passing */
7520 /* through `fapex', and determining which side of this line */
7521 /* `searchpoint' falls on. */
7522 moveleft = (fapex[0] - searchpoint[0]) * (fdest[0] - forg[0]) +
7523 (fapex[1] - searchpoint[1]) * (fdest[1] - forg[1]) > 0.0;
7524 } else {
7525 moveleft = 1;
7526 }
7527 } else {
7528 if (orgorient > 0.0) {
7529 moveleft = 0;
7530 } else {
7531 /* The point we seek must be on the boundary of or inside this */
7532 /* triangle. */
7533 if (destorient == 0.0) {
7534 lprevself(*searchtri);
7535 return ONEDGE;
7536 }
7537 if (orgorient == 0.0) {
7538 lnextself(*searchtri);
7539 return ONEDGE;
7540 }
7541 return INTRIANGLE;
7542 }
7543 }
7544
7545 /* Move to another triangle. Leave a trace `backtracktri' in case */
7546 /* floating-point roundoff or some such bogey causes us to walk */
7547 /* off a boundary of the triangulation. */
7548 if (moveleft) {
7549 lprev(*searchtri, backtracktri);
7550 fdest = fapex;
7551 } else {
7552 lnext(*searchtri, backtracktri);
7553 forg = fapex;
7554 }
7555 sym(backtracktri, *searchtri);
7556
7557 if (m->checksegments && stopatsubsegment) {
7558 /* Check for walking through a subsegment. */
7559 tspivot(backtracktri, checkedge);
7560 if (checkedge.ss != m->dummysub) {
7561 /* Go back to the last triangle. */
7562 otricopy(backtracktri, *searchtri);
7563 return OUTSIDE;
7564 }
7565 }
7566 /* Check for walking right out of the triangulation. */
7567 if (searchtri->tri == m->dummytri) {
7568 /* Go back to the last triangle. */
7569 otricopy(backtracktri, *searchtri);
7570 return OUTSIDE;
7571 }
7572
7573 apex(*searchtri, fapex);
7574 }
7575}
7576
7577/*****************************************************************************/
7578/* */
7579/* locate() Find a triangle or edge containing a given point. */
7580/* */
7581/* Searching begins from one of: the input `searchtri', a recently */
7582/* encountered triangle `recenttri', or from a triangle chosen from a */
7583/* random sample. The choice is made by determining which triangle's */
7584/* origin is closest to the point we are searching for. Normally, */
7585/* `searchtri' should be a handle on the convex hull of the triangulation. */
7586/* */
7587/* Details on the random sampling method can be found in the Mucke, Saias, */
7588/* and Zhu paper cited in the header of this code. */
7589/* */
7590/* On completion, `searchtri' is a triangle that contains `searchpoint'. */
7591/* */
7592/* Returns ONVERTEX if the point lies on an existing vertex. `searchtri' */
7593/* is a handle whose origin is the existing vertex. */
7594/* */
7595/* Returns ONEDGE if the point lies on a mesh edge. `searchtri' is a */
7596/* handle whose primary edge is the edge on which the point lies. */
7597/* */
7598/* Returns INTRIANGLE if the point lies strictly within a triangle. */
7599/* `searchtri' is a handle on the triangle that contains the point. */
7600/* */
7601/* Returns OUTSIDE if the point lies outside the mesh. `searchtri' is a */
7602/* handle whose primary edge the point is to the right of. This might */
7603/* occur when the circumcenter of a triangle falls just slightly outside */
7604/* the mesh due to floating-point roundoff error. It also occurs when */
7605/* seeking a hole or region point that a foolish user has placed outside */
7606/* the mesh. */
7607/* */
7608/* WARNING: This routine is designed for convex triangulations, and will */
7609/* not generally work after the holes and concavities have been carved. */
7610/* */
7611/*****************************************************************************/
7612
7613#ifdef ANSI_DECLARATORS
7614enum locateresult locate(struct mesh *m, struct behavior *b,
7615 vertex searchpoint, struct otri *searchtri)
7616#else /* not ANSI_DECLARATORS */
7617enum locateresult locate(m, b, searchpoint, searchtri)
7618struct mesh *m;
7619struct behavior *b;
7620vertex searchpoint;
7621struct otri *searchtri;
7622#endif /* not ANSI_DECLARATORS */
7623
7624{
7625 VOID **sampleblock;
7626 char *firsttri;
7627 struct otri sampletri;
7628 vertex torg, tdest;
7629 unsigned long alignptr;
7630 REAL searchdist, dist;
7631 REAL ahead;
7632 long samplesperblock, totalsamplesleft, samplesleft;
7633 long population, totalpopulation;
7634 triangle ptr; /* Temporary variable used by sym(). */
7635
7636 if (b->verbose > 2) {
7637 printf(" Randomly sampling for a triangle near point (%.12g, %.12g).\n",
7638 searchpoint[0], searchpoint[1]);
7639 }
7640 /* Record the distance from the suggested starting triangle to the */
7641 /* point we seek. */
7642 org(*searchtri, torg);
7643 searchdist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) +
7644 (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]);
7645 if (b->verbose > 2) {
7646 printf(" Boundary triangle has origin (%.12g, %.12g).\n",
7647 torg[0], torg[1]);
7648 }
7649
7650 /* If a recently encountered triangle has been recorded and has not been */
7651 /* deallocated, test it as a good starting point. */
7652 if (m->recenttri.tri != (triangle *) NULL) {
7653 if (!deadtri(m->recenttri.tri)) {
7654 org(m->recenttri, torg);
7655 if ((torg[0] == searchpoint[0]) && (torg[1] == searchpoint[1])) {
7656 otricopy(m->recenttri, *searchtri);
7657 return ONVERTEX;
7658 }
7659 dist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) +
7660 (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]);
7661 if (dist < searchdist) {
7662 otricopy(m->recenttri, *searchtri);
7663 searchdist = dist;
7664 if (b->verbose > 2) {
7665 printf(" Choosing recent triangle with origin (%.12g, %.12g).\n",
7666 torg[0], torg[1]);
7667 }
7668 }
7669 }
7670 }
7671
7672 /* The number of random samples taken is proportional to the cube root of */
7673 /* the number of triangles in the mesh. The next bit of code assumes */
7674 /* that the number of triangles increases monotonically (or at least */
7675 /* doesn't decrease enough to matter). */
7676 while (SAMPLEFACTOR * m->samples * m->samples * m->samples <
7677 m->triangles.items) {
7678 m->samples++;
7679 }
7680
7681 /* We'll draw ceiling(samples * TRIPERBLOCK / maxitems) random samples */
7682 /* from each block of triangles (except the first)--until we meet the */
7683 /* sample quota. The ceiling means that blocks at the end might be */
7684 /* neglected, but I don't care. */
7685 samplesperblock = (m->samples * TRIPERBLOCK - 1) / m->triangles.maxitems + 1;
7686 /* We'll draw ceiling(samples * itemsfirstblock / maxitems) random samples */
7687 /* from the first block of triangles. */
7688 samplesleft = (m->samples * m->triangles.itemsfirstblock - 1) /
7689 m->triangles.maxitems + 1;
7690 totalsamplesleft = m->samples;
7691 population = m->triangles.itemsfirstblock;
7692 totalpopulation = m->triangles.maxitems;
7693 sampleblock = m->triangles.firstblock;
7694 sampletri.orient = 0;
7695 while (totalsamplesleft > 0) {
7696 /* If we're in the last block, `population' needs to be corrected. */
7697 if (population > totalpopulation) {
7698 population = totalpopulation;
7699 }
7700 /* Find a pointer to the first triangle in the block. */
7701 alignptr = (unsigned long) (sampleblock + 1);
7702 firsttri = (char *) (alignptr +
7703 (unsigned long) m->triangles.alignbytes -
7704 (alignptr %
7705 (unsigned long) m->triangles.alignbytes));
7706
7707 /* Choose `samplesleft' randomly sampled triangles in this block. */
7708 do {
7709 sampletri.tri = (triangle *) (firsttri +
7710 (randomnation((unsigned int) population) *
7711 m->triangles.itembytes));
7712 if (!deadtri(sampletri.tri)) {
7713 org(sampletri, torg);
7714 dist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) +
7715 (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]);
7716 if (dist < searchdist) {
7717 otricopy(sampletri, *searchtri);
7718 searchdist = dist;
7719 if (b->verbose > 2) {
7720 printf(" Choosing triangle with origin (%.12g, %.12g).\n",
7721 torg[0], torg[1]);
7722 }
7723 }
7724 }
7725
7726 samplesleft--;
7727 totalsamplesleft--;
7728 } while ((samplesleft > 0) && (totalsamplesleft > 0));
7729
7730 if (totalsamplesleft > 0) {
7731 sampleblock = (VOID **) *sampleblock;
7732 samplesleft = samplesperblock;
7733 totalpopulation -= population;
7734 population = TRIPERBLOCK;
7735 }
7736 }
7737
7738 /* Where are we? */
7739 org(*searchtri, torg);
7740 dest(*searchtri, tdest);
7741 /* Check the starting triangle's vertices. */
7742 if ((torg[0] == searchpoint[0]) && (torg[1] == searchpoint[1])) {
7743 return ONVERTEX;
7744 }
7745 if ((tdest[0] == searchpoint[0]) && (tdest[1] == searchpoint[1])) {
7746 lnextself(*searchtri);
7747 return ONVERTEX;
7748 }
7749 /* Orient `searchtri' to fit the preconditions of calling preciselocate(). */
7750 ahead = counterclockwise(m, b, torg, tdest, searchpoint);
7751 if (ahead < 0.0) {
7752 /* Turn around so that `searchpoint' is to the left of the */
7753 /* edge specified by `searchtri'. */
7754 symself(*searchtri);
7755 } else if (ahead == 0.0) {
7756 /* Check if `searchpoint' is between `torg' and `tdest'. */
7757 if (((torg[0] < searchpoint[0]) == (searchpoint[0] < tdest[0])) &&
7758 ((torg[1] < searchpoint[1]) == (searchpoint[1] < tdest[1]))) {
7759 return ONEDGE;
7760 }
7761 }
7762 return preciselocate(m, b, searchpoint, searchtri, 0);
7763}
7764
7765/** **/
7766/** **/
7767/********* Point location routines end here *********/
7768
7769/********* Mesh transformation routines begin here *********/
7770/** **/
7771/** **/
7772
7773/*****************************************************************************/
7774/* */
7775/* insertsubseg() Create a new subsegment and insert it between two */
7776/* triangles. */
7777/* */
7778/* The new subsegment is inserted at the edge described by the handle */
7779/* `tri'. Its vertices are properly initialized. The marker `subsegmark' */
7780/* is applied to the subsegment and, if appropriate, its vertices. */
7781/* */
7782/*****************************************************************************/
7783
7784#ifdef ANSI_DECLARATORS
7785void insertsubseg(struct mesh *m, struct behavior *b, struct otri *tri,
7786 int subsegmark)
7787#else /* not ANSI_DECLARATORS */
7788void insertsubseg(m, b, tri, subsegmark)
7789struct mesh *m;
7790struct behavior *b;
7791struct otri *tri; /* Edge at which to insert the new subsegment. */
7792int subsegmark; /* Marker for the new subsegment. */
7793#endif /* not ANSI_DECLARATORS */
7794
7795{
7796 struct otri oppotri;
7797 struct osub newsubseg;
7798 vertex triorg, tridest;
7799 triangle ptr; /* Temporary variable used by sym(). */
7800 subseg sptr; /* Temporary variable used by tspivot(). */
7801
7802 org(*tri, triorg);
7803 dest(*tri, tridest);
7804 /* Mark vertices if possible. */
7805 if (vertexmark(triorg) == 0) {
7806 setvertexmark(triorg, subsegmark);
7807 }
7808 if (vertexmark(tridest) == 0) {
7809 setvertexmark(tridest, subsegmark);
7810 }
7811 /* Check if there's already a subsegment here. */
7812 tspivot(*tri, newsubseg);
7813 if (newsubseg.ss == m->dummysub) {
7814 /* Make new subsegment and initialize its vertices. */
7815 makesubseg(m, &newsubseg);
7816 setsorg(newsubseg, tridest);
7817 setsdest(newsubseg, triorg);
7818 setsegorg(newsubseg, tridest);
7819 setsegdest(newsubseg, triorg);
7820 /* Bond new subsegment to the two triangles it is sandwiched between. */
7821 /* Note that the facing triangle `oppotri' might be equal to */
7822 /* `dummytri' (outer space), but the new subsegment is bonded to it */
7823 /* all the same. */
7824 tsbond(*tri, newsubseg);
7825 sym(*tri, oppotri);
7826 ssymself(newsubseg);
7827 tsbond(oppotri, newsubseg);
7828 setmark(newsubseg, subsegmark);
7829 if (b->verbose > 2) {
7830 printf(" Inserting new ");
7831 printsubseg(m, b, &newsubseg);
7832 }
7833 } else {
7834 if (mark(newsubseg) == 0) {
7835 setmark(newsubseg, subsegmark);
7836 }
7837 }
7838}
7839
7840/*****************************************************************************/
7841/* */
7842/* Terminology */
7843/* */
7844/* A "local transformation" replaces a small set of triangles with another */
7845/* set of triangles. This may or may not involve inserting or deleting a */
7846/* vertex. */
7847/* */
7848/* The term "casing" is used to describe the set of triangles that are */
7849/* attached to the triangles being transformed, but are not transformed */
7850/* themselves. Think of the casing as a fixed hollow structure inside */
7851/* which all the action happens. A "casing" is only defined relative to */
7852/* a single transformation; each occurrence of a transformation will */
7853/* involve a different casing. */
7854/* */
7855/*****************************************************************************/
7856
7857/*****************************************************************************/
7858/* */
7859/* flip() Transform two triangles to two different triangles by flipping */
7860/* an edge counterclockwise within a quadrilateral. */
7861/* */
7862/* Imagine the original triangles, abc and bad, oriented so that the */
7863/* shared edge ab lies in a horizontal plane, with the vertex b on the left */
7864/* and the vertex a on the right. The vertex c lies below the edge, and */
7865/* the vertex d lies above the edge. The `flipedge' handle holds the edge */
7866/* ab of triangle abc, and is directed left, from vertex a to vertex b. */
7867/* */
7868/* The triangles abc and bad are deleted and replaced by the triangles cdb */
7869/* and dca. The triangles that represent abc and bad are NOT deallocated; */
7870/* they are reused for dca and cdb, respectively. Hence, any handles that */
7871/* may have held the original triangles are still valid, although not */
7872/* directed as they were before. */
7873/* */
7874/* Upon completion of this routine, the `flipedge' handle holds the edge */
7875/* dc of triangle dca, and is directed down, from vertex d to vertex c. */
7876/* (Hence, the two triangles have rotated counterclockwise.) */
7877/* */
7878/* WARNING: This transformation is geometrically valid only if the */
7879/* quadrilateral adbc is convex. Furthermore, this transformation is */
7880/* valid only if there is not a subsegment between the triangles abc and */
7881/* bad. This routine does not check either of these preconditions, and */
7882/* it is the responsibility of the calling routine to ensure that they are */
7883/* met. If they are not, the streets shall be filled with wailing and */
7884/* gnashing of teeth. */
7885/* */
7886/*****************************************************************************/
7887
7888#ifdef ANSI_DECLARATORS
7889void flip(struct mesh *m, struct behavior *b, struct otri *flipedge)
7890#else /* not ANSI_DECLARATORS */
7891void flip(m, b, flipedge)
7892struct mesh *m;
7893struct behavior *b;
7894struct otri *flipedge; /* Handle for the triangle abc. */
7895#endif /* not ANSI_DECLARATORS */
7896
7897{
7898 struct otri botleft, botright;
7899 struct otri topleft, topright;
7900 struct otri top;
7901 struct otri botlcasing, botrcasing;
7902 struct otri toplcasing, toprcasing;
7903 struct osub botlsubseg, botrsubseg;
7904 struct osub toplsubseg, toprsubseg;
7905 vertex leftvertex, rightvertex, botvertex;
7906 vertex farvertex;
7907 triangle ptr; /* Temporary variable used by sym(). */
7908 subseg sptr; /* Temporary variable used by tspivot(). */
7909
7910 /* Identify the vertices of the quadrilateral. */
7911 org(*flipedge, rightvertex);
7912 dest(*flipedge, leftvertex);
7913 apex(*flipedge, botvertex);
7914 sym(*flipedge, top);
7915#ifdef SELF_CHECK
7916 if (top.tri == m->dummytri) {
7917 printf("Internal error in flip(): Attempt to flip on boundary.\n");
7918 lnextself(*flipedge);
7919 return;
7920 }
7921 if (m->checksegments) {
7922 tspivot(*flipedge, toplsubseg);
7923 if (toplsubseg.ss != m->dummysub) {
7924 printf("Internal error in flip(): Attempt to flip a segment.\n");
7925 lnextself(*flipedge);
7926 return;
7927 }
7928 }
7929#endif /* SELF_CHECK */
7930 apex(top, farvertex);
7931
7932 /* Identify the casing of the quadrilateral. */
7933 lprev(top, topleft);
7934 sym(topleft, toplcasing);
7935 lnext(top, topright);
7936 sym(topright, toprcasing);
7937 lnext(*flipedge, botleft);
7938 sym(botleft, botlcasing);
7939 lprev(*flipedge, botright);
7940 sym(botright, botrcasing);
7941 /* Rotate the quadrilateral one-quarter turn counterclockwise. */
7942 bond(topleft, botlcasing);
7943 bond(botleft, botrcasing);
7944 bond(botright, toprcasing);
7945 bond(topright, toplcasing);
7946
7947 if (m->checksegments) {
7948 /* Check for subsegments and rebond them to the quadrilateral. */
7949 tspivot(topleft, toplsubseg);
7950 tspivot(botleft, botlsubseg);
7951 tspivot(botright, botrsubseg);
7952 tspivot(topright, toprsubseg);
7953 if (toplsubseg.ss == m->dummysub) {
7954 tsdissolve(topright);
7955 } else {
7956 tsbond(topright, toplsubseg);
7957 }
7958 if (botlsubseg.ss == m->dummysub) {
7959 tsdissolve(topleft);
7960 } else {
7961 tsbond(topleft, botlsubseg);
7962 }
7963 if (botrsubseg.ss == m->dummysub) {
7964 tsdissolve(botleft);
7965 } else {
7966 tsbond(botleft, botrsubseg);
7967 }
7968 if (toprsubseg.ss == m->dummysub) {
7969 tsdissolve(botright);
7970 } else {
7971 tsbond(botright, toprsubseg);
7972 }
7973 }
7974
7975 /* New vertex assignments for the rotated quadrilateral. */
7976 setorg(*flipedge, farvertex);
7977 setdest(*flipedge, botvertex);
7978 setapex(*flipedge, rightvertex);
7979 setorg(top, botvertex);
7980 setdest(top, farvertex);
7981 setapex(top, leftvertex);
7982 if (b->verbose > 2) {
7983 printf(" Edge flip results in left ");
7984 printtriangle(m, b, &top);
7985 printf(" and right ");
7986 printtriangle(m, b, flipedge);
7987 }
7988}
7989
7990/*****************************************************************************/
7991/* */
7992/* unflip() Transform two triangles to two different triangles by */
7993/* flipping an edge clockwise within a quadrilateral. Reverses */
7994/* the flip() operation so that the data structures representing */
7995/* the triangles are back where they were before the flip(). */
7996/* */
7997/* Imagine the original triangles, abc and bad, oriented so that the */
7998/* shared edge ab lies in a horizontal plane, with the vertex b on the left */
7999/* and the vertex a on the right. The vertex c lies below the edge, and */
8000/* the vertex d lies above the edge. The `flipedge' handle holds the edge */
8001/* ab of triangle abc, and is directed left, from vertex a to vertex b. */
8002/* */
8003/* The triangles abc and bad are deleted and replaced by the triangles cdb */
8004/* and dca. The triangles that represent abc and bad are NOT deallocated; */
8005/* they are reused for cdb and dca, respectively. Hence, any handles that */
8006/* may have held the original triangles are still valid, although not */
8007/* directed as they were before. */
8008/* */
8009/* Upon completion of this routine, the `flipedge' handle holds the edge */
8010/* cd of triangle cdb, and is directed up, from vertex c to vertex d. */
8011/* (Hence, the two triangles have rotated clockwise.) */
8012/* */
8013/* WARNING: This transformation is geometrically valid only if the */
8014/* quadrilateral adbc is convex. Furthermore, this transformation is */
8015/* valid only if there is not a subsegment between the triangles abc and */
8016/* bad. This routine does not check either of these preconditions, and */
8017/* it is the responsibility of the calling routine to ensure that they are */
8018/* met. If they are not, the streets shall be filled with wailing and */
8019/* gnashing of teeth. */
8020/* */
8021/*****************************************************************************/
8022
8023#ifdef ANSI_DECLARATORS
8024void unflip(struct mesh *m, struct behavior *b, struct otri *flipedge)
8025#else /* not ANSI_DECLARATORS */
8026void unflip(m, b, flipedge)
8027struct mesh *m;
8028struct behavior *b;
8029struct otri *flipedge; /* Handle for the triangle abc. */
8030#endif /* not ANSI_DECLARATORS */
8031
8032{
8033 struct otri botleft, botright;
8034 struct otri topleft, topright;
8035 struct otri top;
8036 struct otri botlcasing, botrcasing;
8037 struct otri toplcasing, toprcasing;
8038 struct osub botlsubseg, botrsubseg;
8039 struct osub toplsubseg, toprsubseg;
8040 vertex leftvertex, rightvertex, botvertex;
8041 vertex farvertex;
8042 triangle ptr; /* Temporary variable used by sym(). */
8043 subseg sptr; /* Temporary variable used by tspivot(). */
8044
8045 /* Identify the vertices of the quadrilateral. */
8046 org(*flipedge, rightvertex);
8047 dest(*flipedge, leftvertex);
8048 apex(*flipedge, botvertex);
8049 sym(*flipedge, top);
8050#ifdef SELF_CHECK
8051 if (top.tri == m->dummytri) {
8052 printf("Internal error in unflip(): Attempt to flip on boundary.\n");
8053 lnextself(*flipedge);
8054 return;
8055 }
8056 if (m->checksegments) {
8057 tspivot(*flipedge, toplsubseg);
8058 if (toplsubseg.ss != m->dummysub) {
8059 printf("Internal error in unflip(): Attempt to flip a subsegment.\n");
8060 lnextself(*flipedge);
8061 return;
8062 }
8063 }
8064#endif /* SELF_CHECK */
8065 apex(top, farvertex);
8066
8067 /* Identify the casing of the quadrilateral. */
8068 lprev(top, topleft);
8069 sym(topleft, toplcasing);
8070 lnext(top, topright);
8071 sym(topright, toprcasing);
8072 lnext(*flipedge, botleft);
8073 sym(botleft, botlcasing);
8074 lprev(*flipedge, botright);
8075 sym(botright, botrcasing);
8076 /* Rotate the quadrilateral one-quarter turn clockwise. */
8077 bond(topleft, toprcasing);
8078 bond(botleft, toplcasing);
8079 bond(botright, botlcasing);
8080 bond(topright, botrcasing);
8081
8082 if (m->checksegments) {
8083 /* Check for subsegments and rebond them to the quadrilateral. */
8084 tspivot(topleft, toplsubseg);
8085 tspivot(botleft, botlsubseg);
8086 tspivot(botright, botrsubseg);
8087 tspivot(topright, toprsubseg);
8088 if (toplsubseg.ss == m->dummysub) {
8089 tsdissolve(botleft);
8090 } else {
8091 tsbond(botleft, toplsubseg);
8092 }
8093 if (botlsubseg.ss == m->dummysub) {
8094 tsdissolve(botright);
8095 } else {
8096 tsbond(botright, botlsubseg);
8097 }
8098 if (botrsubseg.ss == m->dummysub) {
8099 tsdissolve(topright);
8100 } else {
8101 tsbond(topright, botrsubseg);
8102 }
8103 if (toprsubseg.ss == m->dummysub) {
8104 tsdissolve(topleft);
8105 } else {
8106 tsbond(topleft, toprsubseg);
8107 }
8108 }
8109
8110 /* New vertex assignments for the rotated quadrilateral. */
8111 setorg(*flipedge, botvertex);
8112 setdest(*flipedge, farvertex);
8113 setapex(*flipedge, leftvertex);
8114 setorg(top, farvertex);
8115 setdest(top, botvertex);
8116 setapex(top, rightvertex);
8117 if (b->verbose > 2) {
8118 printf(" Edge unflip results in left ");
8119 printtriangle(m, b, flipedge);
8120 printf(" and right ");
8121 printtriangle(m, b, &top);
8122 }
8123}
8124
8125/*****************************************************************************/
8126/* */
8127/* insertvertex() Insert a vertex into a Delaunay triangulation, */
8128/* performing flips as necessary to maintain the Delaunay */
8129/* property. */
8130/* */
8131/* The point `insertvertex' is located. If `searchtri.tri' is not NULL, */
8132/* the search for the containing triangle begins from `searchtri'. If */
8133/* `searchtri.tri' is NULL, a full point location procedure is called. */
8134/* If `insertvertex' is found inside a triangle, the triangle is split into */
8135/* three; if `insertvertex' lies on an edge, the edge is split in two, */
8136/* thereby splitting the two adjacent triangles into four. Edge flips are */
8137/* used to restore the Delaunay property. If `insertvertex' lies on an */
8138/* existing vertex, no action is taken, and the value DUPLICATEVERTEX is */
8139/* returned. On return, `searchtri' is set to a handle whose origin is the */
8140/* existing vertex. */
8141/* */
8142/* Normally, the parameter `splitseg' is set to NULL, implying that no */
8143/* subsegment should be split. In this case, if `insertvertex' is found to */
8144/* lie on a segment, no action is taken, and the value VIOLATINGVERTEX is */
8145/* returned. On return, `searchtri' is set to a handle whose primary edge */
8146/* is the violated subsegment. */
8147/* */
8148/* If the calling routine wishes to split a subsegment by inserting a */
8149/* vertex in it, the parameter `splitseg' should be that subsegment. In */
8150/* this case, `searchtri' MUST be the triangle handle reached by pivoting */
8151/* from that subsegment; no point location is done. */
8152/* */
8153/* `segmentflaws' and `triflaws' are flags that indicate whether or not */
8154/* there should be checks for the creation of encroached subsegments or bad */
8155/* quality triangles. If a newly inserted vertex encroaches upon */
8156/* subsegments, these subsegments are added to the list of subsegments to */
8157/* be split if `segmentflaws' is set. If bad triangles are created, these */
8158/* are added to the queue if `triflaws' is set. */
8159/* */
8160/* If a duplicate vertex or violated segment does not prevent the vertex */
8161/* from being inserted, the return value will be ENCROACHINGVERTEX if the */
8162/* vertex encroaches upon a subsegment (and checking is enabled), or */
8163/* SUCCESSFULVERTEX otherwise. In either case, `searchtri' is set to a */
8164/* handle whose origin is the newly inserted vertex. */
8165/* */
8166/* insertvertex() does not use flip() for reasons of speed; some */
8167/* information can be reused from edge flip to edge flip, like the */
8168/* locations of subsegments. */
8169/* */
8170/*****************************************************************************/
8171
8172#ifdef ANSI_DECLARATORS
8173enum insertvertexresult insertvertex(struct mesh *m, struct behavior *b,
8174 vertex newvertex, struct otri *searchtri,
8175 struct osub *splitseg,
8176 int segmentflaws, int triflaws )
8177#else /* not ANSI_DECLARATORS */
8178enum insertvertexresult insertvertex(m, b, newvertex, searchtri, splitseg,
8179 segmentflaws, triflaws)
8180struct mesh *m;
8181struct behavior *b;
8182vertex newvertex;
8183struct otri *searchtri;
8184struct osub *splitseg;
8185int segmentflaws;
8186int triflaws;
8187#endif /* not ANSI_DECLARATORS */
8188
8189{
8190
8191 struct otri horiz;
8192 struct otri top;
8193 struct otri botleft, botright;
8194 struct otri topleft, topright;
8195 struct otri newbotleft, newbotright;
8196 struct otri newtopright;
8197 struct otri botlcasing, botrcasing;
8198 struct otri toplcasing, toprcasing;
8199 struct otri testtri;
8200 struct osub botlsubseg, botrsubseg;
8201 struct osub toplsubseg, toprsubseg;
8202 struct osub brokensubseg;
8203 struct osub checksubseg;
8204 struct osub rightsubseg;
8205 struct osub newsubseg;
8206 struct badsubseg *encroached;
8207 struct flipstacker *newflip;
8208 vertex first;
8209 vertex leftvertex, rightvertex, botvertex, topvertex, farvertex;
8210 vertex segmentorg, segmentdest;
8211 REAL attrib;
8212 REAL area;
8213 enum insertvertexresult success;
8214 enum locateresult intersect;
8215 int doflip;
8216 int mirrorflag;
8217 int enq;
8218 int i;
8219 triangle ptr; /* Temporary variable used by sym(). */
8220 subseg sptr; /* Temporary variable used by spivot() and tspivot(). */
8221
8222
8223 (void)triflaws; /*LM: added to suppress warning */
8224
8225 if (b->verbose > 1) {
8226 printf(" Inserting (%.12g, %.12g).\n", newvertex[0], newvertex[1]);
8227 }
8228
8229 if (splitseg == (struct osub *) NULL) {
8230 /* Find the location of the vertex to be inserted. Check if a good */
8231 /* starting triangle has already been provided by the caller. */
8232 if (searchtri->tri == m->dummytri) {
8233 /* Find a boundary triangle. */
8234 horiz.tri = m->dummytri;
8235 horiz.orient = 0;
8236 symself(horiz);
8237 /* Search for a triangle containing `newvertex'. */
8238 intersect = locate(m, b, newvertex, &horiz);
8239 } else {
8240 /* Start searching from the triangle provided by the caller. */
8241 otricopy(*searchtri, horiz);
8242 intersect = preciselocate(m, b, newvertex, &horiz, 1);
8243 }
8244 } else {
8245 /* The calling routine provides the subsegment in which */
8246 /* the vertex is inserted. */
8247 otricopy(*searchtri, horiz);
8248 intersect = ONEDGE;
8249 }
8250
8251 if (intersect == ONVERTEX) {
8252 /* There's already a vertex there. Return in `searchtri' a triangle */
8253 /* whose origin is the existing vertex. */
8254 otricopy(horiz, *searchtri);
8255 otricopy(horiz, m->recenttri);
8256 return DUPLICATEVERTEX;
8257 }
8258 if ((intersect == ONEDGE) || (intersect == OUTSIDE)) {
8259 /* The vertex falls on an edge or boundary. */
8260 if (m->checksegments && (splitseg == (struct osub *) NULL)) {
8261 /* Check whether the vertex falls on a subsegment. */
8262 tspivot(horiz, brokensubseg);
8263 if (brokensubseg.ss != m->dummysub) {
8264 /* The vertex falls on a subsegment, and hence will not be inserted. */
8265 if (segmentflaws) {
8266 enq = b->nobisect != 2;
8267 if (enq && (b->nobisect == 1)) {
8268 /* This subsegment may be split only if it is an */
8269 /* internal boundary. */
8270 sym(horiz, testtri);
8271 enq = testtri.tri != m->dummytri;
8272 }
8273 if (enq) {
8274 /* Add the subsegment to the list of encroached subsegments. */
8275 encroached = (struct badsubseg *) poolalloc(&m->badsubsegs);
8276 encroached->encsubseg = sencode(brokensubseg);
8277 sorg(brokensubseg, encroached->subsegorg);
8278 sdest(brokensubseg, encroached->subsegdest);
8279 if (b->verbose > 2) {
8280 printf(
8281 " Queueing encroached subsegment (%.12g, %.12g) (%.12g, %.12g).\n",
8282 encroached->subsegorg[0], encroached->subsegorg[1],
8283 encroached->subsegdest[0], encroached->subsegdest[1]);
8284 }
8285 }
8286 }
8287 /* Return a handle whose primary edge contains the vertex, */
8288 /* which has not been inserted. */
8289 otricopy(horiz, *searchtri);
8290 otricopy(horiz, m->recenttri);
8291 return VIOLATINGVERTEX;
8292 }
8293 }
8294
8295 /* Insert the vertex on an edge, dividing one triangle into two (if */
8296 /* the edge lies on a boundary) or two triangles into four. */
8297 lprev(horiz, botright);
8298 sym(botright, botrcasing);
8299 sym(horiz, topright);
8300 /* Is there a second triangle? (Or does this edge lie on a boundary?) */
8301 mirrorflag = topright.tri != m->dummytri;
8302 if (mirrorflag) {
8303 lnextself(topright);
8304 sym(topright, toprcasing);
8305 maketriangle(m, b, &newtopright);
8306 } else {
8307 /* Splitting a boundary edge increases the number of boundary edges. */
8308 m->hullsize++;
8309 }
8310 maketriangle(m, b, &newbotright);
8311
8312 /* Set the vertices of changed and new triangles. */
8313 org(horiz, rightvertex);
8314 dest(horiz, leftvertex);
8315 apex(horiz, botvertex);
8316 setorg(newbotright, botvertex);
8317 setdest(newbotright, rightvertex);
8318 setapex(newbotright, newvertex);
8319 setorg(horiz, newvertex);
8320 for (i = 0; i < m->eextras; i++) {
8321 /* Set the element attributes of a new triangle. */
8322 setelemattribute(newbotright, i, elemattribute(botright, i));
8323 }
8324 if (b->vararea) {
8325 /* Set the area constraint of a new triangle. */
8326 setareabound(newbotright, areabound(botright));
8327 }
8328 if (mirrorflag) {
8329 dest(topright, topvertex);
8330 setorg(newtopright, rightvertex);
8331 setdest(newtopright, topvertex);
8332 setapex(newtopright, newvertex);
8333 setorg(topright, newvertex);
8334 for (i = 0; i < m->eextras; i++) {
8335 /* Set the element attributes of another new triangle. */
8336 setelemattribute(newtopright, i, elemattribute(topright, i));
8337 }
8338 if (b->vararea) {
8339 /* Set the area constraint of another new triangle. */
8340 setareabound(newtopright, areabound(topright));
8341 }
8342 }
8343
8344 /* There may be subsegments that need to be bonded */
8345 /* to the new triangle(s). */
8346 if (m->checksegments) {
8347 tspivot(botright, botrsubseg);
8348 if (botrsubseg.ss != m->dummysub) {
8349 tsdissolve(botright);
8350 tsbond(newbotright, botrsubseg);
8351 }
8352 if (mirrorflag) {
8353 tspivot(topright, toprsubseg);
8354 if (toprsubseg.ss != m->dummysub) {
8355 tsdissolve(topright);
8356 tsbond(newtopright, toprsubseg);
8357 }
8358 }
8359 }
8360
8361 /* Bond the new triangle(s) to the surrounding triangles. */
8362 bond(newbotright, botrcasing);
8363 lprevself(newbotright);
8364 bond(newbotright, botright);
8365 lprevself(newbotright);
8366 if (mirrorflag) {
8367 bond(newtopright, toprcasing);
8368 lnextself(newtopright);
8369 bond(newtopright, topright);
8370 lnextself(newtopright);
8371 bond(newtopright, newbotright);
8372 }
8373
8374 if (splitseg != (struct osub *) NULL) {
8375 /* Split the subsegment into two. */
8376 setsdest(*splitseg, newvertex);
8377 segorg(*splitseg, segmentorg);
8378 segdest(*splitseg, segmentdest);
8379 ssymself(*splitseg);
8380 spivot(*splitseg, rightsubseg);
8381 insertsubseg(m, b, &newbotright, mark(*splitseg));
8382 tspivot(newbotright, newsubseg);
8383 setsegorg(newsubseg, segmentorg);
8384 setsegdest(newsubseg, segmentdest);
8385 sbond(*splitseg, newsubseg);
8386 ssymself(newsubseg);
8387 sbond(newsubseg, rightsubseg);
8388 ssymself(*splitseg);
8389 /* Transfer the subsegment's boundary marker to the vertex */
8390 /* if required. */
8391 if (vertexmark(newvertex) == 0) {
8392 setvertexmark(newvertex, mark(*splitseg));
8393 }
8394 }
8395
8396 if (m->checkquality) {
8397 poolrestart(&m->flipstackers);
8398 m->lastflip = (struct flipstacker *) poolalloc(&m->flipstackers);
8399 m->lastflip->flippedtri = encode(horiz);
8400 m->lastflip->prevflip = (struct flipstacker *) &insertvertex;
8401 }
8402
8403#ifdef SELF_CHECK
8404 if (counterclockwise(m, b, rightvertex, leftvertex, botvertex) < 0.0) {
8405 printf("Internal error in insertvertex():\n");
8406 printf(
8407 " Clockwise triangle prior to edge vertex insertion (bottom).\n");
8408 }
8409 if (mirrorflag) {
8410 if (counterclockwise(m, b, leftvertex, rightvertex, topvertex) < 0.0) {
8411 printf("Internal error in insertvertex():\n");
8412 printf(" Clockwise triangle prior to edge vertex insertion (top).\n");
8413 }
8414 if (counterclockwise(m, b, rightvertex, topvertex, newvertex) < 0.0) {
8415 printf("Internal error in insertvertex():\n");
8416 printf(
8417 " Clockwise triangle after edge vertex insertion (top right).\n");
8418 }
8419 if (counterclockwise(m, b, topvertex, leftvertex, newvertex) < 0.0) {
8420 printf("Internal error in insertvertex():\n");
8421 printf(
8422 " Clockwise triangle after edge vertex insertion (top left).\n");
8423 }
8424 }
8425 if (counterclockwise(m, b, leftvertex, botvertex, newvertex) < 0.0) {
8426 printf("Internal error in insertvertex():\n");
8427 printf(
8428 " Clockwise triangle after edge vertex insertion (bottom left).\n");
8429 }
8430 if (counterclockwise(m, b, botvertex, rightvertex, newvertex) < 0.0) {
8431 printf("Internal error in insertvertex():\n");
8432 printf(
8433 " Clockwise triangle after edge vertex insertion (bottom right).\n");
8434 }
8435#endif /* SELF_CHECK */
8436 if (b->verbose > 2) {
8437 printf(" Updating bottom left ");
8438 printtriangle(m, b, &botright);
8439 if (mirrorflag) {
8440 printf(" Updating top left ");
8441 printtriangle(m, b, &topright);
8442 printf(" Creating top right ");
8443 printtriangle(m, b, &newtopright);
8444 }
8445 printf(" Creating bottom right ");
8446 printtriangle(m, b, &newbotright);
8447 }
8448
8449 /* Position `horiz' on the first edge to check for */
8450 /* the Delaunay property. */
8451 lnextself(horiz);
8452 } else {
8453 /* Insert the vertex in a triangle, splitting it into three. */
8454 lnext(horiz, botleft);
8455 lprev(horiz, botright);
8456 sym(botleft, botlcasing);
8457 sym(botright, botrcasing);
8458 maketriangle(m, b, &newbotleft);
8459 maketriangle(m, b, &newbotright);
8460
8461 /* Set the vertices of changed and new triangles. */
8462 org(horiz, rightvertex);
8463 dest(horiz, leftvertex);
8464 apex(horiz, botvertex);
8465 setorg(newbotleft, leftvertex);
8466 setdest(newbotleft, botvertex);
8467 setapex(newbotleft, newvertex);
8468 setorg(newbotright, botvertex);
8469 setdest(newbotright, rightvertex);
8470 setapex(newbotright, newvertex);
8471 setapex(horiz, newvertex);
8472 for (i = 0; i < m->eextras; i++) {
8473 /* Set the element attributes of the new triangles. */
8474 attrib = elemattribute(horiz, i);
8475 setelemattribute(newbotleft, i, attrib);
8476 setelemattribute(newbotright, i, attrib);
8477 }
8478 if (b->vararea) {
8479 /* Set the area constraint of the new triangles. */
8480 area = areabound(horiz);
8481 setareabound(newbotleft, area);
8482 setareabound(newbotright, area);
8483 }
8484
8485 /* There may be subsegments that need to be bonded */
8486 /* to the new triangles. */
8487 if (m->checksegments) {
8488 tspivot(botleft, botlsubseg);
8489 if (botlsubseg.ss != m->dummysub) {
8490 tsdissolve(botleft);
8491 tsbond(newbotleft, botlsubseg);
8492 }
8493 tspivot(botright, botrsubseg);
8494 if (botrsubseg.ss != m->dummysub) {
8495 tsdissolve(botright);
8496 tsbond(newbotright, botrsubseg);
8497 }
8498 }
8499
8500 /* Bond the new triangles to the surrounding triangles. */
8501 bond(newbotleft, botlcasing);
8502 bond(newbotright, botrcasing);
8503 lnextself(newbotleft);
8504 lprevself(newbotright);
8505 bond(newbotleft, newbotright);
8506 lnextself(newbotleft);
8507 bond(botleft, newbotleft);
8508 lprevself(newbotright);
8509 bond(botright, newbotright);
8510
8511 if (m->checkquality) {
8512 poolrestart(&m->flipstackers);
8513 m->lastflip = (struct flipstacker *) poolalloc(&m->flipstackers);
8514 m->lastflip->flippedtri = encode(horiz);
8515 m->lastflip->prevflip = (struct flipstacker *) NULL;
8516 }
8517
8518#ifdef SELF_CHECK
8519 if (counterclockwise(m, b, rightvertex, leftvertex, botvertex) < 0.0) {
8520 printf("Internal error in insertvertex():\n");
8521 printf(" Clockwise triangle prior to vertex insertion.\n");
8522 }
8523 if (counterclockwise(m, b, rightvertex, leftvertex, newvertex) < 0.0) {
8524 printf("Internal error in insertvertex():\n");
8525 printf(" Clockwise triangle after vertex insertion (top).\n");
8526 }
8527 if (counterclockwise(m, b, leftvertex, botvertex, newvertex) < 0.0) {
8528 printf("Internal error in insertvertex():\n");
8529 printf(" Clockwise triangle after vertex insertion (left).\n");
8530 }
8531 if (counterclockwise(m, b, botvertex, rightvertex, newvertex) < 0.0) {
8532 printf("Internal error in insertvertex():\n");
8533 printf(" Clockwise triangle after vertex insertion (right).\n");
8534 }
8535#endif /* SELF_CHECK */
8536 if (b->verbose > 2) {
8537 printf(" Updating top ");
8538 printtriangle(m, b, &horiz);
8539 printf(" Creating left ");
8540 printtriangle(m, b, &newbotleft);
8541 printf(" Creating right ");
8542 printtriangle(m, b, &newbotright);
8543 }
8544 }
8545
8546 /* The insertion is successful by default, unless an encroached */
8547 /* subsegment is found. */
8548 success = SUCCESSFULVERTEX;
8549 /* Circle around the newly inserted vertex, checking each edge opposite */
8550 /* it for the Delaunay property. Non-Delaunay edges are flipped. */
8551 /* `horiz' is always the edge being checked. `first' marks where to */
8552 /* stop circling. */
8553 org(horiz, first);
8554 rightvertex = first;
8555 dest(horiz, leftvertex);
8556 /* Circle until finished. */
8557 while (1) {
8558 /* By default, the edge will be flipped. */
8559 doflip = 1;
8560
8561 if (m->checksegments) {
8562 /* Check for a subsegment, which cannot be flipped. */
8563 tspivot(horiz, checksubseg);
8564 if (checksubseg.ss != m->dummysub) {
8565 /* The edge is a subsegment and cannot be flipped. */
8566 doflip = 0;
8567#ifndef CDT_ONLY
8568 if (segmentflaws) {
8569 /* Does the new vertex encroach upon this subsegment? */
8570 if (checkseg4encroach(m, b, &checksubseg)) {
8571 success = ENCROACHINGVERTEX;
8572 }
8573 }
8574#endif /* not CDT_ONLY */
8575 }
8576 }
8577
8578 if (doflip) {
8579 /* Check if the edge is a boundary edge. */
8580 sym(horiz, top);
8581 if (top.tri == m->dummytri) {
8582 /* The edge is a boundary edge and cannot be flipped. */
8583 doflip = 0;
8584 } else {
8585 /* Find the vertex on the other side of the edge. */
8586 apex(top, farvertex);
8587 /* In the incremental Delaunay triangulation algorithm, any of */
8588 /* `leftvertex', `rightvertex', and `farvertex' could be vertices */
8589 /* of the triangular bounding box. These vertices must be */
8590 /* treated as if they are infinitely distant, even though their */
8591 /* "coordinates" are not. */
8592 if ((leftvertex == m->infvertex1) || (leftvertex == m->infvertex2) ||
8593 (leftvertex == m->infvertex3)) {
8594 /* `leftvertex' is infinitely distant. Check the convexity of */
8595 /* the boundary of the triangulation. 'farvertex' might be */
8596 /* infinite as well, but trust me, this same condition should */
8597 /* be applied. */
8598 doflip = counterclockwise(m, b, newvertex, rightvertex, farvertex)
8599 > 0.0;
8600 } else if ((rightvertex == m->infvertex1) ||
8601 (rightvertex == m->infvertex2) ||
8602 (rightvertex == m->infvertex3)) {
8603 /* `rightvertex' is infinitely distant. Check the convexity of */
8604 /* the boundary of the triangulation. 'farvertex' might be */
8605 /* infinite as well, but trust me, this same condition should */
8606 /* be applied. */
8607 doflip = counterclockwise(m, b, farvertex, leftvertex, newvertex)
8608 > 0.0;
8609 } else if ((farvertex == m->infvertex1) ||
8610 (farvertex == m->infvertex2) ||
8611 (farvertex == m->infvertex3)) {
8612 /* `farvertex' is infinitely distant and cannot be inside */
8613 /* the circumcircle of the triangle `horiz'. */
8614 doflip = 0;
8615 } else {
8616 /* Test whether the edge is locally Delaunay. */
8617 doflip = incircle(m, b, leftvertex, newvertex, rightvertex,
8618 farvertex) > 0.0;
8619 }
8620 if (doflip) {
8621 /* We made it! Flip the edge `horiz' by rotating its containing */
8622 /* quadrilateral (the two triangles adjacent to `horiz'). */
8623 /* Identify the casing of the quadrilateral. */
8624 lprev(top, topleft);
8625 sym(topleft, toplcasing);
8626 lnext(top, topright);
8627 sym(topright, toprcasing);
8628 lnext(horiz, botleft);
8629 sym(botleft, botlcasing);
8630 lprev(horiz, botright);
8631 sym(botright, botrcasing);
8632 /* Rotate the quadrilateral one-quarter turn counterclockwise. */
8633 bond(topleft, botlcasing);
8634 bond(botleft, botrcasing);
8635 bond(botright, toprcasing);
8636 bond(topright, toplcasing);
8637 if (m->checksegments) {
8638 /* Check for subsegments and rebond them to the quadrilateral. */
8639 tspivot(topleft, toplsubseg);
8640 tspivot(botleft, botlsubseg);
8641 tspivot(botright, botrsubseg);
8642 tspivot(topright, toprsubseg);
8643 if (toplsubseg.ss == m->dummysub) {
8644 tsdissolve(topright);
8645 } else {
8646 tsbond(topright, toplsubseg);
8647 }
8648 if (botlsubseg.ss == m->dummysub) {
8649 tsdissolve(topleft);
8650 } else {
8651 tsbond(topleft, botlsubseg);
8652 }
8653 if (botrsubseg.ss == m->dummysub) {
8654 tsdissolve(botleft);
8655 } else {
8656 tsbond(botleft, botrsubseg);
8657 }
8658 if (toprsubseg.ss == m->dummysub) {
8659 tsdissolve(botright);
8660 } else {
8661 tsbond(botright, toprsubseg);
8662 }
8663 }
8664 /* New vertex assignments for the rotated quadrilateral. */
8665 setorg(horiz, farvertex);
8666 setdest(horiz, newvertex);
8667 setapex(horiz, rightvertex);
8668 setorg(top, newvertex);
8669 setdest(top, farvertex);
8670 setapex(top, leftvertex);
8671 for (i = 0; i < m->eextras; i++) {
8672 /* Take the average of the two triangles' attributes. */
8673 attrib = 0.5 * (elemattribute(top, i) + elemattribute(horiz, i));
8674 setelemattribute(top, i, attrib);
8675 setelemattribute(horiz, i, attrib);
8676 }
8677 if (b->vararea) {
8678 if ((areabound(top) <= 0.0) || (areabound(horiz) <= 0.0)) {
8679 area = -1.0;
8680 } else {
8681 /* Take the average of the two triangles' area constraints. */
8682 /* This prevents small area constraints from migrating a */
8683 /* long, long way from their original location due to flips. */
8684 area = 0.5 * (areabound(top) + areabound(horiz));
8685 }
8686 setareabound(top, area);
8687 setareabound(horiz, area);
8688 }
8689
8690 if (m->checkquality) {
8691 newflip = (struct flipstacker *) poolalloc(&m->flipstackers);
8692 newflip->flippedtri = encode(horiz);
8693 newflip->prevflip = m->lastflip;
8694 m->lastflip = newflip;
8695 }
8696
8697#ifdef SELF_CHECK
8698 if (newvertex != (vertex) NULL) {
8699 if (counterclockwise(m, b, leftvertex, newvertex, rightvertex) <
8700 0.0) {
8701 printf("Internal error in insertvertex():\n");
8702 printf(" Clockwise triangle prior to edge flip (bottom).\n");
8703 }
8704 /* The following test has been removed because constrainededge() */
8705 /* sometimes generates inverted triangles that insertvertex() */
8706 /* removes. */
8707/*
8708 if (counterclockwise(m, b, rightvertex, farvertex, leftvertex) <
8709 0.0) {
8710 printf("Internal error in insertvertex():\n");
8711 printf(" Clockwise triangle prior to edge flip (top).\n");
8712 }
8713*/
8714 if (counterclockwise(m, b, farvertex, leftvertex, newvertex) <
8715 0.0) {
8716 printf("Internal error in insertvertex():\n");
8717 printf(" Clockwise triangle after edge flip (left).\n");
8718 }
8719 if (counterclockwise(m, b, newvertex, rightvertex, farvertex) <
8720 0.0) {
8721 printf("Internal error in insertvertex():\n");
8722 printf(" Clockwise triangle after edge flip (right).\n");
8723 }
8724 }
8725#endif /* SELF_CHECK */
8726 if (b->verbose > 2) {
8727 printf(" Edge flip results in left ");
8728 lnextself(topleft);
8729 printtriangle(m, b, &topleft);
8730 printf(" and right ");
8731 printtriangle(m, b, &horiz);
8732 }
8733 /* On the next iterations, consider the two edges that were */
8734 /* exposed (this is, are now visible to the newly inserted */
8735 /* vertex) by the edge flip. */
8736 lprevself(horiz);
8737 leftvertex = farvertex;
8738 }
8739 }
8740 }
8741 if (!doflip) {
8742 /* The handle `horiz' is accepted as locally Delaunay. */
8743#ifndef CDT_ONLY
8744 if (triflaws) {
8745 /* Check the triangle `horiz' for quality. */
8746 testtriangle(m, b, &horiz);
8747 }
8748#endif /* not CDT_ONLY */
8749 /* Look for the next edge around the newly inserted vertex. */
8750 lnextself(horiz);
8751 sym(horiz, testtri);
8752 /* Check for finishing a complete revolution about the new vertex, or */
8753 /* falling outside of the triangulation. The latter will happen */
8754 /* when a vertex is inserted at a boundary. */
8755 if ((leftvertex == first) || (testtri.tri == m->dummytri)) {
8756 /* We're done. Return a triangle whose origin is the new vertex. */
8757 lnext(horiz, *searchtri);
8758 lnext(horiz, m->recenttri);
8759 return success;
8760 }
8761 /* Finish finding the next edge around the newly inserted vertex. */
8762 lnext(testtri, horiz);
8763 rightvertex = leftvertex;
8764 dest(horiz, leftvertex);
8765 }
8766 }
8767}
8768
8769/*****************************************************************************/
8770/* */
8771/* triangulatepolygon() Find the Delaunay triangulation of a polygon that */
8772/* has a certain "nice" shape. This includes the */
8773/* polygons that result from deletion of a vertex or */
8774/* insertion of a segment. */
8775/* */
8776/* This is a conceptually difficult routine. The starting assumption is */
8777/* that we have a polygon with n sides. n - 1 of these sides are currently */
8778/* represented as edges in the mesh. One side, called the "base", need not */
8779/* be. */
8780/* */
8781/* Inside the polygon is a structure I call a "fan", consisting of n - 1 */
8782/* triangles that share a common origin. For each of these triangles, the */
8783/* edge opposite the origin is one of the sides of the polygon. The */
8784/* primary edge of each triangle is the edge directed from the origin to */
8785/* the destination; note that this is not the same edge that is a side of */
8786/* the polygon. `firstedge' is the primary edge of the first triangle. */
8787/* From there, the triangles follow in counterclockwise order about the */
8788/* polygon, until `lastedge', the primary edge of the last triangle. */
8789/* `firstedge' and `lastedge' are probably connected to other triangles */
8790/* beyond the extremes of the fan, but their identity is not important, as */
8791/* long as the fan remains connected to them. */
8792/* */
8793/* Imagine the polygon oriented so that its base is at the bottom. This */
8794/* puts `firstedge' on the far right, and `lastedge' on the far left. */
8795/* The right vertex of the base is the destination of `firstedge', and the */
8796/* left vertex of the base is the apex of `lastedge'. */
8797/* */
8798/* The challenge now is to find the right sequence of edge flips to */
8799/* transform the fan into a Delaunay triangulation of the polygon. Each */
8800/* edge flip effectively removes one triangle from the fan, committing it */
8801/* to the polygon. The resulting polygon has one fewer edge. If `doflip' */
8802/* is set, the final flip will be performed, resulting in a fan of one */
8803/* (useless?) triangle. If `doflip' is not set, the final flip is not */
8804/* performed, resulting in a fan of two triangles, and an unfinished */
8805/* triangular polygon that is not yet filled out with a single triangle. */
8806/* On completion of the routine, `lastedge' is the last remaining triangle, */
8807/* or the leftmost of the last two. */
8808/* */
8809/* Although the flips are performed in the order described above, the */
8810/* decisions about what flips to perform are made in precisely the reverse */
8811/* order. The recursive triangulatepolygon() procedure makes a decision, */
8812/* uses up to two recursive calls to triangulate the "subproblems" */
8813/* (polygons with fewer edges), and then performs an edge flip. */
8814/* */
8815/* The "decision" it makes is which vertex of the polygon should be */
8816/* connected to the base. This decision is made by testing every possible */
8817/* vertex. Once the best vertex is found, the two edges that connect this */
8818/* vertex to the base become the bases for two smaller polygons. These */
8819/* are triangulated recursively. Unfortunately, this approach can take */
8820/* O(n^2) time not only in the worst case, but in many common cases. It's */
8821/* rarely a big deal for vertex deletion, where n is rarely larger than */
8822/* ten, but it could be a big deal for segment insertion, especially if */
8823/* there's a lot of long segments that each cut many triangles. I ought to */
8824/* code a faster algorithm some day. */
8825/* */
8826/* The `edgecount' parameter is the number of sides of the polygon, */
8827/* including its base. `triflaws' is a flag that determines whether the */
8828/* new triangles should be tested for quality, and enqueued if they are */
8829/* bad. */
8830/* */
8831/*****************************************************************************/
8832
8833#ifdef ANSI_DECLARATORS
8834void triangulatepolygon(struct mesh *m, struct behavior *b,
8835 struct otri *firstedge, struct otri *lastedge,
8836 int edgecount, int doflip, int triflaws)
8837#else /* not ANSI_DECLARATORS */
8838void triangulatepolygon(m, b, firstedge, lastedge, edgecount, doflip, triflaws)
8839struct mesh *m;
8840struct behavior *b;
8841struct otri *firstedge;
8842struct otri *lastedge;
8843int edgecount;
8844int doflip;
8845int triflaws;
8846#endif /* not ANSI_DECLARATORS */
8847
8848{
8849 struct otri testtri;
8850 struct otri besttri;
8851 struct otri tempedge;
8852 vertex leftbasevertex, rightbasevertex;
8853 vertex testvertex;
8854 vertex bestvertex;
8855 int bestnumber;
8856 int i;
8857 triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */
8858
8859 /* Identify the base vertices. */
8860 apex(*lastedge, leftbasevertex);
8861 dest(*firstedge, rightbasevertex);
8862 if (b->verbose > 2) {
8863 printf(" Triangulating interior polygon at edge\n");
8864 printf(" (%.12g, %.12g) (%.12g, %.12g)\n", leftbasevertex[0],
8865 leftbasevertex[1], rightbasevertex[0], rightbasevertex[1]);
8866 }
8867 /* Find the best vertex to connect the base to. */
8868 onext(*firstedge, besttri);
8869 dest(besttri, bestvertex);
8870 otricopy(besttri, testtri);
8871 bestnumber = 1;
8872 for (i = 2; i <= edgecount - 2; i++) {
8873 onextself(testtri);
8874 dest(testtri, testvertex);
8875 /* Is this a better vertex? */
8876 if (incircle(m, b, leftbasevertex, rightbasevertex, bestvertex,
8877 testvertex) > 0.0) {
8878 otricopy(testtri, besttri);
8879 bestvertex = testvertex;
8880 bestnumber = i;
8881 }
8882 }
8883 if (b->verbose > 2) {
8884 printf(" Connecting edge to (%.12g, %.12g)\n", bestvertex[0],
8885 bestvertex[1]);
8886 }
8887 if (bestnumber > 1) {
8888 /* Recursively triangulate the smaller polygon on the right. */
8889 oprev(besttri, tempedge);
8890 triangulatepolygon(m, b, firstedge, &tempedge, bestnumber + 1, 1,
8891 triflaws);
8892 }
8893 if (bestnumber < edgecount - 2) {
8894 /* Recursively triangulate the smaller polygon on the left. */
8895 sym(besttri, tempedge);
8896 triangulatepolygon(m, b, &besttri, lastedge, edgecount - bestnumber, 1,
8897 triflaws);
8898 /* Find `besttri' again; it may have been lost to edge flips. */
8899 sym(tempedge, besttri);
8900 }
8901 if (doflip) {
8902 /* Do one final edge flip. */
8903 flip(m, b, &besttri);
8904#ifndef CDT_ONLY
8905 if (triflaws) {
8906 /* Check the quality of the newly committed triangle. */
8907 sym(besttri, testtri);
8908 testtriangle(m, b, &testtri);
8909 }
8910#endif /* not CDT_ONLY */
8911 }
8912 /* Return the base triangle. */
8913 otricopy(besttri, *lastedge);
8914}
8915
8916/*****************************************************************************/
8917/* */
8918/* deletevertex() Delete a vertex from a Delaunay triangulation, ensuring */
8919/* that the triangulation remains Delaunay. */
8920/* */
8921/* The origin of `deltri' is deleted. The union of the triangles adjacent */
8922/* to this vertex is a polygon, for which the Delaunay triangulation is */
8923/* found. Two triangles are removed from the mesh. */
8924/* */
8925/* Only interior vertices that do not lie on segments or boundaries may be */
8926/* deleted. */
8927/* */
8928/*****************************************************************************/
8929
8930#ifndef CDT_ONLY
8931
8932#ifdef ANSI_DECLARATORS
8933void deletevertex(struct mesh *m, struct behavior *b, struct otri *deltri)
8934#else /* not ANSI_DECLARATORS */
8935void deletevertex(m, b, deltri)
8936struct mesh *m;
8937struct behavior *b;
8938struct otri *deltri;
8939#endif /* not ANSI_DECLARATORS */
8940
8941{
8942 struct otri countingtri;
8943 struct otri firstedge, lastedge;
8944 struct otri deltriright;
8945 struct otri lefttri, righttri;
8946 struct otri leftcasing, rightcasing;
8947 struct osub leftsubseg, rightsubseg;
8948 vertex delvertex;
8949 vertex neworg;
8950 int edgecount;
8951 triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */
8952 subseg sptr; /* Temporary variable used by tspivot(). */
8953
8954 org(*deltri, delvertex);
8955 if (b->verbose > 1) {
8956 printf(" Deleting (%.12g, %.12g).\n", delvertex[0], delvertex[1]);
8957 }
8958 vertexdealloc(m, delvertex);
8959
8960 /* Count the degree of the vertex being deleted. */
8961 onext(*deltri, countingtri);
8962 edgecount = 1;
8963 while (!otriequal(*deltri, countingtri)) {
8964#ifdef SELF_CHECK
8965 if (countingtri.tri == m->dummytri) {
8966 printf("Internal error in deletevertex():\n");
8967 printf(" Attempt to delete boundary vertex.\n");
8968 internalerror();
8969 }
8970#endif /* SELF_CHECK */
8971 edgecount++;
8972 onextself(countingtri);
8973 }
8974
8975#ifdef SELF_CHECK
8976 if (edgecount < 3) {
8977 printf("Internal error in deletevertex():\n Vertex has degree %d.\n",
8978 edgecount);
8979 internalerror();
8980 }
8981#endif /* SELF_CHECK */
8982 if (edgecount > 3) {
8983 /* Triangulate the polygon defined by the union of all triangles */
8984 /* adjacent to the vertex being deleted. Check the quality of */
8985 /* the resulting triangles. */
8986 onext(*deltri, firstedge);
8987 oprev(*deltri, lastedge);
8988 triangulatepolygon(m, b, &firstedge, &lastedge, edgecount, 0,
8989 !b->nobisect);
8990 }
8991 /* Splice out two triangles. */
8992 lprev(*deltri, deltriright);
8993 dnext(*deltri, lefttri);
8994 sym(lefttri, leftcasing);
8995 oprev(deltriright, righttri);
8996 sym(righttri, rightcasing);
8997 bond(*deltri, leftcasing);
8998 bond(deltriright, rightcasing);
8999 tspivot(lefttri, leftsubseg);
9000 if (leftsubseg.ss != m->dummysub) {
9001 tsbond(*deltri, leftsubseg);
9002 }
9003 tspivot(righttri, rightsubseg);
9004 if (rightsubseg.ss != m->dummysub) {
9005 tsbond(deltriright, rightsubseg);
9006 }
9007
9008 /* Set the new origin of `deltri' and check its quality. */
9009 org(lefttri, neworg);
9010 setorg(*deltri, neworg);
9011 if (!b->nobisect) {
9012 testtriangle(m, b, deltri);
9013 }
9014
9015 /* Delete the two spliced-out triangles. */
9016 triangledealloc(m, lefttri.tri);
9017 triangledealloc(m, righttri.tri);
9018}
9019
9020#endif /* not CDT_ONLY */
9021
9022/*****************************************************************************/
9023/* */
9024/* undovertex() Undo the most recent vertex insertion. */
9025/* */
9026/* Walks through the list of transformations (flips and a vertex insertion) */
9027/* in the reverse of the order in which they were done, and undoes them. */
9028/* The inserted vertex is removed from the triangulation and deallocated. */
9029/* Two triangles (possibly just one) are also deallocated. */
9030/* */
9031/*****************************************************************************/
9032
9033#ifndef CDT_ONLY
9034
9035#ifdef ANSI_DECLARATORS
9036void undovertex(struct mesh *m, struct behavior *b)
9037#else /* not ANSI_DECLARATORS */
9038void undovertex(m, b)
9039struct mesh *m;
9040struct behavior *b;
9041#endif /* not ANSI_DECLARATORS */
9042
9043{
9044 struct otri fliptri;
9045 struct otri botleft, botright, topright;
9046 struct otri botlcasing, botrcasing, toprcasing;
9047 struct otri gluetri;
9048 struct osub botlsubseg, botrsubseg, toprsubseg;
9049 vertex botvertex, rightvertex;
9050 triangle ptr; /* Temporary variable used by sym(). */
9051 subseg sptr; /* Temporary variable used by tspivot(). */
9052
9053 /* Walk through the list of transformations (flips and a vertex insertion) */
9054 /* in the reverse of the order in which they were done, and undo them. */
9055 while (m->lastflip != (struct flipstacker *) NULL) {
9056 /* Find a triangle involved in the last unreversed transformation. */
9057 decode(m->lastflip->flippedtri, fliptri);
9058
9059 /* We are reversing one of three transformations: a trisection of one */
9060 /* triangle into three (by inserting a vertex in the triangle), a */
9061 /* bisection of two triangles into four (by inserting a vertex in an */
9062 /* edge), or an edge flip. */
9063 if (m->lastflip->prevflip == (struct flipstacker *) NULL) {
9064 /* Restore a triangle that was split into three triangles, */
9065 /* so it is again one triangle. */
9066 dprev(fliptri, botleft);
9067 lnextself(botleft);
9068 onext(fliptri, botright);
9069 lprevself(botright);
9070 sym(botleft, botlcasing);
9071 sym(botright, botrcasing);
9072 dest(botleft, botvertex);
9073
9074 setapex(fliptri, botvertex);
9075 lnextself(fliptri);
9076 bond(fliptri, botlcasing);
9077 tspivot(botleft, botlsubseg);
9078 tsbond(fliptri, botlsubseg);
9079 lnextself(fliptri);
9080 bond(fliptri, botrcasing);
9081 tspivot(botright, botrsubseg);
9082 tsbond(fliptri, botrsubseg);
9083
9084 /* Delete the two spliced-out triangles. */
9085 triangledealloc(m, botleft.tri);
9086 triangledealloc(m, botright.tri);
9087 } else if (m->lastflip->prevflip == (struct flipstacker *) &insertvertex) {
9088 /* Restore two triangles that were split into four triangles, */
9089 /* so they are again two triangles. */
9090 lprev(fliptri, gluetri);
9091 sym(gluetri, botright);
9092 lnextself(botright);
9093 sym(botright, botrcasing);
9094 dest(botright, rightvertex);
9095
9096 setorg(fliptri, rightvertex);
9097 bond(gluetri, botrcasing);
9098 tspivot(botright, botrsubseg);
9099 tsbond(gluetri, botrsubseg);
9100
9101 /* Delete the spliced-out triangle. */
9102 triangledealloc(m, botright.tri);
9103
9104 sym(fliptri, gluetri);
9105 if (gluetri.tri != m->dummytri) {
9106 lnextself(gluetri);
9107 dnext(gluetri, topright);
9108 sym(topright, toprcasing);
9109
9110 setorg(gluetri, rightvertex);
9111 bond(gluetri, toprcasing);
9112 tspivot(topright, toprsubseg);
9113 tsbond(gluetri, toprsubseg);
9114
9115 /* Delete the spliced-out triangle. */
9116 triangledealloc(m, topright.tri);
9117 }
9118
9119 /* This is the end of the list, sneakily encoded. */
9120 m->lastflip->prevflip = (struct flipstacker *) NULL;
9121 } else {
9122 /* Undo an edge flip. */
9123 unflip(m, b, &fliptri);
9124 }
9125
9126 /* Go on and process the next transformation. */
9127 m->lastflip = m->lastflip->prevflip;
9128 }
9129}
9130
9131#endif /* not CDT_ONLY */
9132
9133/** **/
9134/** **/
9135/********* Mesh transformation routines end here *********/
9136
9137/********* Divide-and-conquer Delaunay triangulation begins here *********/
9138/** **/
9139/** **/
9140
9141/*****************************************************************************/
9142/* */
9143/* The divide-and-conquer bounding box */
9144/* */
9145/* I originally implemented the divide-and-conquer and incremental Delaunay */
9146/* triangulations using the edge-based data structure presented by Guibas */
9147/* and Stolfi. Switching to a triangle-based data structure doubled the */
9148/* speed. However, I had to think of a few extra tricks to maintain the */
9149/* elegance of the original algorithms. */
9150/* */
9151/* The "bounding box" used by my variant of the divide-and-conquer */
9152/* algorithm uses one triangle for each edge of the convex hull of the */
9153/* triangulation. These bounding triangles all share a common apical */
9154/* vertex, which is represented by NULL and which represents nothing. */
9155/* The bounding triangles are linked in a circular fan about this NULL */
9156/* vertex, and the edges on the convex hull of the triangulation appear */
9157/* opposite the NULL vertex. You might find it easiest to imagine that */
9158/* the NULL vertex is a point in 3D space behind the center of the */
9159/* triangulation, and that the bounding triangles form a sort of cone. */
9160/* */
9161/* This bounding box makes it easy to represent degenerate cases. For */
9162/* instance, the triangulation of two vertices is a single edge. This edge */
9163/* is represented by two bounding box triangles, one on each "side" of the */
9164/* edge. These triangles are also linked together in a fan about the NULL */
9165/* vertex. */
9166/* */
9167/* The bounding box also makes it easy to traverse the convex hull, as the */
9168/* divide-and-conquer algorithm needs to do. */
9169/* */
9170/*****************************************************************************/
9171
9172/*****************************************************************************/
9173/* */
9174/* vertexsort() Sort an array of vertices by x-coordinate, using the */
9175/* y-coordinate as a secondary key. */
9176/* */
9177/* Uses quicksort. Randomized O(n log n) time. No, I did not make any of */
9178/* the usual quicksort mistakes. */
9179/* */
9180/*****************************************************************************/
9181
9182#ifdef ANSI_DECLARATORS
9183void vertexsort(vertex *sortarray, int arraysize)
9184#else /* not ANSI_DECLARATORS */
9185void vertexsort(sortarray, arraysize)
9186vertex *sortarray;
9187int arraysize;
9188#endif /* not ANSI_DECLARATORS */
9189
9190{
9191 int left, right;
9192 int pivot;
9193 REAL pivotx, pivoty;
9194 vertex temp;
9195
9196 if (arraysize == 2) {
9197 /* Recursive base case. */
9198 if ((sortarray[0][0] > sortarray[1][0]) ||
9199 ((sortarray[0][0] == sortarray[1][0]) &&
9200 (sortarray[0][1] > sortarray[1][1]))) {
9201 temp = sortarray[1];
9202 sortarray[1] = sortarray[0];
9203 sortarray[0] = temp;
9204 }
9205 return;
9206 }
9207 /* Choose a random pivot to split the array. */
9208 pivot = (int) randomnation((unsigned int) arraysize);
9209 pivotx = sortarray[pivot][0];
9210 pivoty = sortarray[pivot][1];
9211 /* Split the array. */
9212 left = -1;
9213 right = arraysize;
9214 while (left < right) {
9215 /* Search for a vertex whose x-coordinate is too large for the left. */
9216 do {
9217 left++;
9218 } while ((left <= right) && ((sortarray[left][0] < pivotx) ||
9219 ((sortarray[left][0] == pivotx) &&
9220 (sortarray[left][1] < pivoty))));
9221 /* Search for a vertex whose x-coordinate is too small for the right. */
9222 do {
9223 right--;
9224 } while ((left <= right) && ((sortarray[right][0] > pivotx) ||
9225 ((sortarray[right][0] == pivotx) &&
9226 (sortarray[right][1] > pivoty))));
9227 if (left < right) {
9228 /* Swap the left and right vertices. */
9229 temp = sortarray[left];
9230 sortarray[left] = sortarray[right];
9231 sortarray[right] = temp;
9232 }
9233 }
9234 if (left > 1) {
9235 /* Recursively sort the left subset. */
9236 vertexsort(sortarray, left);
9237 }
9238 if (right < arraysize - 2) {
9239 /* Recursively sort the right subset. */
9240 vertexsort(&sortarray[right + 1], arraysize - right - 1);
9241 }
9242}
9243
9244/*****************************************************************************/
9245/* */
9246/* vertexmedian() An order statistic algorithm, almost. Shuffles an */
9247/* array of vertices so that the first `median' vertices */
9248/* occur lexicographically before the remaining vertices. */
9249/* */
9250/* Uses the x-coordinate as the primary key if axis == 0; the y-coordinate */
9251/* if axis == 1. Very similar to the vertexsort() procedure, but runs in */
9252/* randomized linear time. */
9253/* */
9254/*****************************************************************************/
9255
9256#ifdef ANSI_DECLARATORS
9257void vertexmedian(vertex *sortarray, int arraysize, int median, int axis)
9258#else /* not ANSI_DECLARATORS */
9259void vertexmedian(sortarray, arraysize, median, axis)
9260vertex *sortarray;
9261int arraysize;
9262int median;
9263int axis;
9264#endif /* not ANSI_DECLARATORS */
9265
9266{
9267 int left, right;
9268 int pivot;
9269 REAL pivot1, pivot2;
9270 vertex temp;
9271
9272 if (arraysize == 2) {
9273 /* Recursive base case. */
9274 if ((sortarray[0][axis] > sortarray[1][axis]) ||
9275 ((sortarray[0][axis] == sortarray[1][axis]) &&
9276 (sortarray[0][1 - axis] > sortarray[1][1 - axis]))) {
9277 temp = sortarray[1];
9278 sortarray[1] = sortarray[0];
9279 sortarray[0] = temp;
9280 }
9281 return;
9282 }
9283 /* Choose a random pivot to split the array. */
9284 pivot = (int) randomnation((unsigned int) arraysize);
9285 pivot1 = sortarray[pivot][axis];
9286 pivot2 = sortarray[pivot][1 - axis];
9287 /* Split the array. */
9288 left = -1;
9289 right = arraysize;
9290 while (left < right) {
9291 /* Search for a vertex whose x-coordinate is too large for the left. */
9292 do {
9293 left++;
9294 } while ((left <= right) && ((sortarray[left][axis] < pivot1) ||
9295 ((sortarray[left][axis] == pivot1) &&
9296 (sortarray[left][1 - axis] < pivot2))));
9297 /* Search for a vertex whose x-coordinate is too small for the right. */
9298 do {
9299 right--;
9300 } while ((left <= right) && ((sortarray[right][axis] > pivot1) ||
9301 ((sortarray[right][axis] == pivot1) &&
9302 (sortarray[right][1 - axis] > pivot2))));
9303 if (left < right) {
9304 /* Swap the left and right vertices. */
9305 temp = sortarray[left];
9306 sortarray[left] = sortarray[right];
9307 sortarray[right] = temp;
9308 }
9309 }
9310 /* Unlike in vertexsort(), at most one of the following */
9311 /* conditionals is true. */
9312 if (left > median) {
9313 /* Recursively shuffle the left subset. */
9314 vertexmedian(sortarray, left, median, axis);
9315 }
9316 if (right < median - 1) {
9317 /* Recursively shuffle the right subset. */
9318 vertexmedian(&sortarray[right + 1], arraysize - right - 1,
9319 median - right - 1, axis);
9320 }
9321}
9322
9323/*****************************************************************************/
9324/* */
9325/* alternateaxes() Sorts the vertices as appropriate for the divide-and- */
9326/* conquer algorithm with alternating cuts. */
9327/* */
9328/* Partitions by x-coordinate if axis == 0; by y-coordinate if axis == 1. */
9329/* For the base case, subsets containing only two or three vertices are */
9330/* always sorted by x-coordinate. */
9331/* */
9332/*****************************************************************************/
9333
9334#ifdef ANSI_DECLARATORS
9335void alternateaxes(vertex *sortarray, int arraysize, int axis)
9336#else /* not ANSI_DECLARATORS */
9337void alternateaxes(sortarray, arraysize, axis)
9338vertex *sortarray;
9339int arraysize;
9340int axis;
9341#endif /* not ANSI_DECLARATORS */
9342
9343{
9344 int divider;
9345
9346 divider = arraysize >> 1;
9347 if (arraysize <= 3) {
9348 /* Recursive base case: subsets of two or three vertices will be */
9349 /* handled specially, and should always be sorted by x-coordinate. */
9350 axis = 0;
9351 }
9352 /* Partition with a horizontal or vertical cut. */
9353 vertexmedian(sortarray, arraysize, divider, axis);
9354 /* Recursively partition the subsets with a cross cut. */
9355 if (arraysize - divider >= 2) {
9356 if (divider >= 2) {
9357 alternateaxes(sortarray, divider, 1 - axis);
9358 }
9359 alternateaxes(&sortarray[divider], arraysize - divider, 1 - axis);
9360 }
9361}
9362
9363/*****************************************************************************/
9364/* */
9365/* mergehulls() Merge two adjacent Delaunay triangulations into a */
9366/* single Delaunay triangulation. */
9367/* */
9368/* This is similar to the algorithm given by Guibas and Stolfi, but uses */
9369/* a triangle-based, rather than edge-based, data structure. */
9370/* */
9371/* The algorithm walks up the gap between the two triangulations, knitting */
9372/* them together. As they are merged, some of their bounding triangles */
9373/* are converted into real triangles of the triangulation. The procedure */
9374/* pulls each hull's bounding triangles apart, then knits them together */
9375/* like the teeth of two gears. The Delaunay property determines, at each */
9376/* step, whether the next "tooth" is a bounding triangle of the left hull */
9377/* or the right. When a bounding triangle becomes real, its apex is */
9378/* changed from NULL to a real vertex. */
9379/* */
9380/* Only two new triangles need to be allocated. These become new bounding */
9381/* triangles at the top and bottom of the seam. They are used to connect */
9382/* the remaining bounding triangles (those that have not been converted */
9383/* into real triangles) into a single fan. */
9384/* */
9385/* On entry, `farleft' and `innerleft' are bounding triangles of the left */
9386/* triangulation. The origin of `farleft' is the leftmost vertex, and */
9387/* the destination of `innerleft' is the rightmost vertex of the */
9388/* triangulation. Similarly, `innerright' and `farright' are bounding */
9389/* triangles of the right triangulation. The origin of `innerright' and */
9390/* destination of `farright' are the leftmost and rightmost vertices. */
9391/* */
9392/* On completion, the origin of `farleft' is the leftmost vertex of the */
9393/* merged triangulation, and the destination of `farright' is the rightmost */
9394/* vertex. */
9395/* */
9396/*****************************************************************************/
9397
9398#ifdef ANSI_DECLARATORS
9399void mergehulls(struct mesh *m, struct behavior *b, struct otri *farleft,
9400 struct otri *innerleft, struct otri *innerright,
9401 struct otri *farright, int axis)
9402#else /* not ANSI_DECLARATORS */
9403void mergehulls(m, b, farleft, innerleft, innerright, farright, axis)
9404struct mesh *m;
9405struct behavior *b;
9406struct otri *farleft;
9407struct otri *innerleft;
9408struct otri *innerright;
9409struct otri *farright;
9410int axis;
9411#endif /* not ANSI_DECLARATORS */
9412
9413{
9414 struct otri leftcand, rightcand;
9415 struct otri baseedge;
9416 struct otri nextedge;
9417 struct otri sidecasing, topcasing, outercasing;
9418 struct otri checkedge;
9419 vertex innerleftdest;
9420 vertex innerrightorg;
9421 vertex innerleftapex, innerrightapex;
9422 vertex farleftpt, farrightpt;
9423 vertex farleftapex, farrightapex;
9424 vertex lowerleft, lowerright;
9425 vertex upperleft, upperright;
9426 vertex nextapex;
9427 vertex checkvertex;
9428 int changemade;
9429 int badedge;
9430 int leftfinished, rightfinished;
9431 triangle ptr; /* Temporary variable used by sym(). */
9432
9433 dest(*innerleft, innerleftdest);
9434 apex(*innerleft, innerleftapex);
9435 org(*innerright, innerrightorg);
9436 apex(*innerright, innerrightapex);
9437 /* Special treatment for horizontal cuts. */
9438 if (b->dwyer && (axis == 1)) {
9439 org(*farleft, farleftpt);
9440 apex(*farleft, farleftapex);
9441 dest(*farright, farrightpt);
9442 apex(*farright, farrightapex);
9443 /* The pointers to the extremal vertices are shifted to point to the */
9444 /* topmost and bottommost vertex of each hull, rather than the */
9445 /* leftmost and rightmost vertices. */
9446 while (farleftapex[1] < farleftpt[1]) {
9447 lnextself(*farleft);
9448 symself(*farleft);
9449 farleftpt = farleftapex;
9450 apex(*farleft, farleftapex);
9451 }
9452 sym(*innerleft, checkedge);
9453 apex(checkedge, checkvertex);
9454 while (checkvertex[1] > innerleftdest[1]) {
9455 lnext(checkedge, *innerleft);
9456 innerleftapex = innerleftdest;
9457 innerleftdest = checkvertex;
9458 sym(*innerleft, checkedge);
9459 apex(checkedge, checkvertex);
9460 }
9461 while (innerrightapex[1] < innerrightorg[1]) {
9462 lnextself(*innerright);
9463 symself(*innerright);
9464 innerrightorg = innerrightapex;
9465 apex(*innerright, innerrightapex);
9466 }
9467 sym(*farright, checkedge);
9468 apex(checkedge, checkvertex);
9469 while (checkvertex[1] > farrightpt[1]) {
9470 lnext(checkedge, *farright);
9471 farrightapex = farrightpt;
9472 farrightpt = checkvertex;
9473 sym(*farright, checkedge);
9474 apex(checkedge, checkvertex);
9475 }
9476 }
9477 /* Find a line tangent to and below both hulls. */
9478 do {
9479 changemade = 0;
9480 /* Make innerleftdest the "bottommost" vertex of the left hull. */
9481 if (counterclockwise(m, b, innerleftdest, innerleftapex, innerrightorg) >
9482 0.0) {
9483 lprevself(*innerleft);
9484 symself(*innerleft);
9485 innerleftdest = innerleftapex;
9486 apex(*innerleft, innerleftapex);
9487 changemade = 1;
9488 }
9489 /* Make innerrightorg the "bottommost" vertex of the right hull. */
9490 if (counterclockwise(m, b, innerrightapex, innerrightorg, innerleftdest) >
9491 0.0) {
9492 lnextself(*innerright);
9493 symself(*innerright);
9494 innerrightorg = innerrightapex;
9495 apex(*innerright, innerrightapex);
9496 changemade = 1;
9497 }
9498 } while (changemade);
9499 /* Find the two candidates to be the next "gear tooth." */
9500 sym(*innerleft, leftcand);
9501 sym(*innerright, rightcand);
9502 /* Create the bottom new bounding triangle. */
9503 maketriangle(m, b, &baseedge);
9504 /* Connect it to the bounding boxes of the left and right triangulations. */
9505 bond(baseedge, *innerleft);
9506 lnextself(baseedge);
9507 bond(baseedge, *innerright);
9508 lnextself(baseedge);
9509 setorg(baseedge, innerrightorg);
9510 setdest(baseedge, innerleftdest);
9511 /* Apex is intentionally left NULL. */
9512 if (b->verbose > 2) {
9513 printf(" Creating base bounding ");
9514 printtriangle(m, b, &baseedge);
9515 }
9516 /* Fix the extreme triangles if necessary. */
9517 org(*farleft, farleftpt);
9518 if (innerleftdest == farleftpt) {
9519 lnext(baseedge, *farleft);
9520 }
9521 dest(*farright, farrightpt);
9522 if (innerrightorg == farrightpt) {
9523 lprev(baseedge, *farright);
9524 }
9525 /* The vertices of the current knitting edge. */
9526 lowerleft = innerleftdest;
9527 lowerright = innerrightorg;
9528 /* The candidate vertices for knitting. */
9529 apex(leftcand, upperleft);
9530 apex(rightcand, upperright);
9531 /* Walk up the gap between the two triangulations, knitting them together. */
9532 while (1) {
9533 /* Have we reached the top? (This isn't quite the right question, */
9534 /* because even though the left triangulation might seem finished now, */
9535 /* moving up on the right triangulation might reveal a new vertex of */
9536 /* the left triangulation. And vice-versa.) */
9537 leftfinished = counterclockwise(m, b, upperleft, lowerleft, lowerright) <=
9538 0.0;
9539 rightfinished = counterclockwise(m, b, upperright, lowerleft, lowerright)
9540 <= 0.0;
9541 if (leftfinished && rightfinished) {
9542 /* Create the top new bounding triangle. */
9543 maketriangle(m, b, &nextedge);
9544 setorg(nextedge, lowerleft);
9545 setdest(nextedge, lowerright);
9546 /* Apex is intentionally left NULL. */
9547 /* Connect it to the bounding boxes of the two triangulations. */
9548 bond(nextedge, baseedge);
9549 lnextself(nextedge);
9550 bond(nextedge, rightcand);
9551 lnextself(nextedge);
9552 bond(nextedge, leftcand);
9553 if (b->verbose > 2) {
9554 printf(" Creating top bounding ");
9555 printtriangle(m, b, &nextedge);
9556 }
9557 /* Special treatment for horizontal cuts. */
9558 if (b->dwyer && (axis == 1)) {
9559 org(*farleft, farleftpt);
9560 apex(*farleft, farleftapex);
9561 dest(*farright, farrightpt);
9562 apex(*farright, farrightapex);
9563 sym(*farleft, checkedge);
9564 apex(checkedge, checkvertex);
9565 /* The pointers to the extremal vertices are restored to the */
9566 /* leftmost and rightmost vertices (rather than topmost and */
9567 /* bottommost). */
9568 while (checkvertex[0] < farleftpt[0]) {
9569 lprev(checkedge, *farleft);
9570 farleftapex = farleftpt;
9571 farleftpt = checkvertex;
9572 sym(*farleft, checkedge);
9573 apex(checkedge, checkvertex);
9574 }
9575 while (farrightapex[0] > farrightpt[0]) {
9576 lprevself(*farright);
9577 symself(*farright);
9578 farrightpt = farrightapex;
9579 apex(*farright, farrightapex);
9580 }
9581 }
9582 return;
9583 }
9584 /* Consider eliminating edges from the left triangulation. */
9585 if (!leftfinished) {
9586 /* What vertex would be exposed if an edge were deleted? */
9587 lprev(leftcand, nextedge);
9588 symself(nextedge);
9589 apex(nextedge, nextapex);
9590 /* If nextapex is NULL, then no vertex would be exposed; the */
9591 /* triangulation would have been eaten right through. */
9592 if (nextapex != (vertex) NULL) {
9593 /* Check whether the edge is Delaunay. */
9594 badedge = incircle(m, b, lowerleft, lowerright, upperleft, nextapex) >
9595 0.0;
9596 while (badedge) {
9597 /* Eliminate the edge with an edge flip. As a result, the */
9598 /* left triangulation will have one more boundary triangle. */
9599 lnextself(nextedge);
9600 sym(nextedge, topcasing);
9601 lnextself(nextedge);
9602 sym(nextedge, sidecasing);
9603 bond(nextedge, topcasing);
9604 bond(leftcand, sidecasing);
9605 lnextself(leftcand);
9606 sym(leftcand, outercasing);
9607 lprevself(nextedge);
9608 bond(nextedge, outercasing);
9609 /* Correct the vertices to reflect the edge flip. */
9610 setorg(leftcand, lowerleft);
9611 setdest(leftcand, NULL);
9612 setapex(leftcand, nextapex);
9613 setorg(nextedge, NULL);
9614 setdest(nextedge, upperleft);
9615 setapex(nextedge, nextapex);
9616 /* Consider the newly exposed vertex. */
9617 upperleft = nextapex;
9618 /* What vertex would be exposed if another edge were deleted? */
9619 otricopy(sidecasing, nextedge);
9620 apex(nextedge, nextapex);
9621 if (nextapex != (vertex) NULL) {
9622 /* Check whether the edge is Delaunay. */
9623 badedge = incircle(m, b, lowerleft, lowerright, upperleft,
9624 nextapex) > 0.0;
9625 } else {
9626 /* Avoid eating right through the triangulation. */
9627 badedge = 0;
9628 }
9629 }
9630 }
9631 }
9632 /* Consider eliminating edges from the right triangulation. */
9633 if (!rightfinished) {
9634 /* What vertex would be exposed if an edge were deleted? */
9635 lnext(rightcand, nextedge);
9636 symself(nextedge);
9637 apex(nextedge, nextapex);
9638 /* If nextapex is NULL, then no vertex would be exposed; the */
9639 /* triangulation would have been eaten right through. */
9640 if (nextapex != (vertex) NULL) {
9641 /* Check whether the edge is Delaunay. */
9642 badedge = incircle(m, b, lowerleft, lowerright, upperright, nextapex) >
9643 0.0;
9644 while (badedge) {
9645 /* Eliminate the edge with an edge flip. As a result, the */
9646 /* right triangulation will have one more boundary triangle. */
9647 lprevself(nextedge);
9648 sym(nextedge, topcasing);
9649 lprevself(nextedge);
9650 sym(nextedge, sidecasing);
9651 bond(nextedge, topcasing);
9652 bond(rightcand, sidecasing);
9653 lprevself(rightcand);
9654 sym(rightcand, outercasing);
9655 lnextself(nextedge);
9656 bond(nextedge, outercasing);
9657 /* Correct the vertices to reflect the edge flip. */
9658 setorg(rightcand, NULL);
9659 setdest(rightcand, lowerright);
9660 setapex(rightcand, nextapex);
9661 setorg(nextedge, upperright);
9662 setdest(nextedge, NULL);
9663 setapex(nextedge, nextapex);
9664 /* Consider the newly exposed vertex. */
9665 upperright = nextapex;
9666 /* What vertex would be exposed if another edge were deleted? */
9667 otricopy(sidecasing, nextedge);
9668 apex(nextedge, nextapex);
9669 if (nextapex != (vertex) NULL) {
9670 /* Check whether the edge is Delaunay. */
9671 badedge = incircle(m, b, lowerleft, lowerright, upperright,
9672 nextapex) > 0.0;
9673 } else {
9674 /* Avoid eating right through the triangulation. */
9675 badedge = 0;
9676 }
9677 }
9678 }
9679 }
9680 if (leftfinished || (!rightfinished &&
9681 (incircle(m, b, upperleft, lowerleft, lowerright, upperright) >
9682 0.0))) {
9683 /* Knit the triangulations, adding an edge from `lowerleft' */
9684 /* to `upperright'. */
9685 bond(baseedge, rightcand);
9686 lprev(rightcand, baseedge);
9687 setdest(baseedge, lowerleft);
9688 lowerright = upperright;
9689 sym(baseedge, rightcand);
9690 apex(rightcand, upperright);
9691 } else {
9692 /* Knit the triangulations, adding an edge from `upperleft' */
9693 /* to `lowerright'. */
9694 bond(baseedge, leftcand);
9695 lnext(leftcand, baseedge);
9696 setorg(baseedge, lowerright);
9697 lowerleft = upperleft;
9698 sym(baseedge, leftcand);
9699 apex(leftcand, upperleft);
9700 }
9701 if (b->verbose > 2) {
9702 printf(" Connecting ");
9703 printtriangle(m, b, &baseedge);
9704 }
9705 }
9706}
9707
9708/*****************************************************************************/
9709/* */
9710/* divconqrecurse() Recursively form a Delaunay triangulation by the */
9711/* divide-and-conquer method. */
9712/* */
9713/* Recursively breaks down the problem into smaller pieces, which are */
9714/* knitted together by mergehulls(). The base cases (problems of two or */
9715/* three vertices) are handled specially here. */
9716/* */
9717/* On completion, `farleft' and `farright' are bounding triangles such that */
9718/* the origin of `farleft' is the leftmost vertex (breaking ties by */
9719/* choosing the highest leftmost vertex), and the destination of */
9720/* `farright' is the rightmost vertex (breaking ties by choosing the */
9721/* lowest rightmost vertex). */
9722/* */
9723/*****************************************************************************/
9724
9725#ifdef ANSI_DECLARATORS
9726void divconqrecurse(struct mesh *m, struct behavior *b, vertex *sortarray,
9727 int vertices, int axis,
9728 struct otri *farleft, struct otri *farright)
9729#else /* not ANSI_DECLARATORS */
9730void divconqrecurse(m, b, sortarray, vertices, axis, farleft, farright)
9731struct mesh *m;
9732struct behavior *b;
9733vertex *sortarray;
9734int vertices;
9735int axis;
9736struct otri *farleft;
9737struct otri *farright;
9738#endif /* not ANSI_DECLARATORS */
9739
9740{
9741 struct otri midtri, tri1, tri2, tri3;
9742 struct otri innerleft, innerright;
9743 REAL area;
9744 int divider;
9745
9746 if (b->verbose > 2) {
9747 printf(" Triangulating %d vertices.\n", vertices);
9748 }
9749 if (vertices == 2) {
9750 /* The triangulation of two vertices is an edge. An edge is */
9751 /* represented by two bounding triangles. */
9752 maketriangle(m, b, farleft);
9753 setorg(*farleft, sortarray[0]);
9754 setdest(*farleft, sortarray[1]);
9755 /* The apex is intentionally left NULL. */
9756 maketriangle(m, b, farright);
9757 setorg(*farright, sortarray[1]);
9758 setdest(*farright, sortarray[0]);
9759 /* The apex is intentionally left NULL. */
9760 bond(*farleft, *farright);
9761 lprevself(*farleft);
9762 lnextself(*farright);
9763 bond(*farleft, *farright);
9764 lprevself(*farleft);
9765 lnextself(*farright);
9766 bond(*farleft, *farright);
9767 if (b->verbose > 2) {
9768 printf(" Creating ");
9769 printtriangle(m, b, farleft);
9770 printf(" Creating ");
9771 printtriangle(m, b, farright);
9772 }
9773 /* Ensure that the origin of `farleft' is sortarray[0]. */
9774 lprev(*farright, *farleft);
9775 return;
9776 } else if (vertices == 3) {
9777 /* The triangulation of three vertices is either a triangle (with */
9778 /* three bounding triangles) or two edges (with four bounding */
9779 /* triangles). In either case, four triangles are created. */
9780 maketriangle(m, b, &midtri);
9781 maketriangle(m, b, &tri1);
9782 maketriangle(m, b, &tri2);
9783 maketriangle(m, b, &tri3);
9784 area = counterclockwise(m, b, sortarray[0], sortarray[1], sortarray[2]);
9785 if (area == 0.0) {
9786 /* Three collinear vertices; the triangulation is two edges. */
9787 setorg(midtri, sortarray[0]);
9788 setdest(midtri, sortarray[1]);
9789 setorg(tri1, sortarray[1]);
9790 setdest(tri1, sortarray[0]);
9791 setorg(tri2, sortarray[2]);
9792 setdest(tri2, sortarray[1]);
9793 setorg(tri3, sortarray[1]);
9794 setdest(tri3, sortarray[2]);
9795 /* All apices are intentionally left NULL. */
9796 bond(midtri, tri1);
9797 bond(tri2, tri3);
9798 lnextself(midtri);
9799 lprevself(tri1);
9800 lnextself(tri2);
9801 lprevself(tri3);
9802 bond(midtri, tri3);
9803 bond(tri1, tri2);
9804 lnextself(midtri);
9805 lprevself(tri1);
9806 lnextself(tri2);
9807 lprevself(tri3);
9808 bond(midtri, tri1);
9809 bond(tri2, tri3);
9810 /* Ensure that the origin of `farleft' is sortarray[0]. */
9811 otricopy(tri1, *farleft);
9812 /* Ensure that the destination of `farright' is sortarray[2]. */
9813 otricopy(tri2, *farright);
9814 } else {
9815 /* The three vertices are not collinear; the triangulation is one */
9816 /* triangle, namely `midtri'. */
9817 setorg(midtri, sortarray[0]);
9818 setdest(tri1, sortarray[0]);
9819 setorg(tri3, sortarray[0]);
9820 /* Apices of tri1, tri2, and tri3 are left NULL. */
9821 if (area > 0.0) {
9822 /* The vertices are in counterclockwise order. */
9823 setdest(midtri, sortarray[1]);
9824 setorg(tri1, sortarray[1]);
9825 setdest(tri2, sortarray[1]);
9826 setapex(midtri, sortarray[2]);
9827 setorg(tri2, sortarray[2]);
9828 setdest(tri3, sortarray[2]);
9829 } else {
9830 /* The vertices are in clockwise order. */
9831 setdest(midtri, sortarray[2]);
9832 setorg(tri1, sortarray[2]);
9833 setdest(tri2, sortarray[2]);
9834 setapex(midtri, sortarray[1]);
9835 setorg(tri2, sortarray[1]);
9836 setdest(tri3, sortarray[1]);
9837 }
9838 /* The topology does not depend on how the vertices are ordered. */
9839 bond(midtri, tri1);
9840 lnextself(midtri);
9841 bond(midtri, tri2);
9842 lnextself(midtri);
9843 bond(midtri, tri3);
9844 lprevself(tri1);
9845 lnextself(tri2);
9846 bond(tri1, tri2);
9847 lprevself(tri1);
9848 lprevself(tri3);
9849 bond(tri1, tri3);
9850 lnextself(tri2);
9851 lprevself(tri3);
9852 bond(tri2, tri3);
9853 /* Ensure that the origin of `farleft' is sortarray[0]. */
9854 otricopy(tri1, *farleft);
9855 /* Ensure that the destination of `farright' is sortarray[2]. */
9856 if (area > 0.0) {
9857 otricopy(tri2, *farright);
9858 } else {
9859 lnext(*farleft, *farright);
9860 }
9861 }
9862 if (b->verbose > 2) {
9863 printf(" Creating ");
9864 printtriangle(m, b, &midtri);
9865 printf(" Creating ");
9866 printtriangle(m, b, &tri1);
9867 printf(" Creating ");
9868 printtriangle(m, b, &tri2);
9869 printf(" Creating ");
9870 printtriangle(m, b, &tri3);
9871 }
9872 return;
9873 } else {
9874 /* Split the vertices in half. */
9875 divider = vertices >> 1;
9876 /* Recursively triangulate each half. */
9877 divconqrecurse(m, b, sortarray, divider, 1 - axis, farleft, &innerleft);
9878 divconqrecurse(m, b, &sortarray[divider], vertices - divider, 1 - axis,
9879 &innerright, farright);
9880 if (b->verbose > 1) {
9881 printf(" Joining triangulations with %d and %d vertices.\n", divider,
9882 vertices - divider);
9883 }
9884 /* Merge the two triangulations into one. */
9885 mergehulls(m, b, farleft, &innerleft, &innerright, farright, axis);
9886 }
9887}
9888
9889#ifdef ANSI_DECLARATORS
9890long removeghosts(struct mesh *m, struct behavior *b, struct otri *startghost)
9891#else /* not ANSI_DECLARATORS */
9892long removeghosts(m, b, startghost)
9893struct mesh *m;
9894struct behavior *b;
9895struct otri *startghost;
9896#endif /* not ANSI_DECLARATORS */
9897
9898{
9899 struct otri searchedge;
9900 struct otri dissolveedge;
9901 struct otri deadtriangle;
9902 vertex markorg;
9903 long hullsize;
9904 triangle ptr; /* Temporary variable used by sym(). */
9905
9906 if (b->verbose) {
9907 printf(" Removing ghost triangles.\n");
9908 }
9909 /* Find an edge on the convex hull to start point location from. */
9910 lprev(*startghost, searchedge);
9911 symself(searchedge);
9912 m->dummytri[0] = encode(searchedge);
9913 /* Remove the bounding box and count the convex hull edges. */
9914 otricopy(*startghost, dissolveedge);
9915 hullsize = 0;
9916 do {
9917 hullsize++;
9918 lnext(dissolveedge, deadtriangle);
9919 lprevself(dissolveedge);
9920 symself(dissolveedge);
9921 /* If no PSLG is involved, set the boundary markers of all the vertices */
9922 /* on the convex hull. If a PSLG is used, this step is done later. */
9923 if (!b->poly) {
9924 /* Watch out for the case where all the input vertices are collinear. */
9925 if (dissolveedge.tri != m->dummytri) {
9926 org(dissolveedge, markorg);
9927 if (vertexmark(markorg) == 0) {
9928 setvertexmark(markorg, 1);
9929 }
9930 }
9931 }
9932 /* Remove a bounding triangle from a convex hull triangle. */
9933 dissolve(dissolveedge);
9934 /* Find the next bounding triangle. */
9935 sym(deadtriangle, dissolveedge);
9936 /* Delete the bounding triangle. */
9937 triangledealloc(m, deadtriangle.tri);
9938 } while (!otriequal(dissolveedge, *startghost));
9939 return hullsize;
9940}
9941
9942/*****************************************************************************/
9943/* */
9944/* divconqdelaunay() Form a Delaunay triangulation by the divide-and- */
9945/* conquer method. */
9946/* */
9947/* Sorts the vertices, calls a recursive procedure to triangulate them, and */
9948/* removes the bounding box, setting boundary markers as appropriate. */
9949/* */
9950/*****************************************************************************/
9951
9952#ifdef ANSI_DECLARATORS
9953long divconqdelaunay(struct mesh *m, struct behavior *b)
9954#else /* not ANSI_DECLARATORS */
9955long divconqdelaunay(m, b)
9956struct mesh *m;
9957struct behavior *b;
9958#endif /* not ANSI_DECLARATORS */
9959
9960{
9961 vertex *sortarray;
9962 struct otri hullleft, hullright;
9963 int divider;
9964 int i, j;
9965
9966 if (b->verbose) {
9967 printf(" Sorting vertices.\n");
9968 }
9969
9970 /* Allocate an array of pointers to vertices for sorting. */
9971 sortarray = (vertex *) trimalloc(m->invertices * (int) sizeof(vertex));
9972 traversalinit(&m->vertices);
9973 for (i = 0; i < m->invertices; i++) {
9974 sortarray[i] = vertextraverse(m);
9975 }
9976 /* Sort the vertices. */
9977 vertexsort(sortarray, m->invertices);
9978 /* Discard duplicate vertices, which can really mess up the algorithm. */
9979 i = 0;
9980 for (j = 1; j < m->invertices; j++) {
9981 if ((sortarray[i][0] == sortarray[j][0])
9982 && (sortarray[i][1] == sortarray[j][1])) {
9983 if (!b->quiet) {
9984 printf(
9985"Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n",
9986 sortarray[j][0], sortarray[j][1]);
9987 }
9988 setvertextype(sortarray[j], UNDEADVERTEX);
9989 m->undeads++;
9990 } else {
9991 i++;
9992 sortarray[i] = sortarray[j];
9993 }
9994 }
9995 i++;
9996 if (b->dwyer) {
9997 /* Re-sort the array of vertices to accommodate alternating cuts. */
9998 divider = i >> 1;
9999 if (i - divider >= 2) {
10000 if (divider >= 2) {
10001 alternateaxes(sortarray, divider, 1);
10002 }
10003 alternateaxes(&sortarray[divider], i - divider, 1);
10004 }
10005 }
10006
10007 if (b->verbose) {
10008 printf(" Forming triangulation.\n");
10009 }
10010
10011 /* Form the Delaunay triangulation. */
10012 divconqrecurse(m, b, sortarray, i, 0, &hullleft, &hullright);
10013 trifree((VOID *) sortarray);
10014
10015 return removeghosts(m, b, &hullleft);
10016}
10017
10018/** **/
10019/** **/
10020/********* Divide-and-conquer Delaunay triangulation ends here *********/
10021
10022/********* Incremental Delaunay triangulation begins here *********/
10023/** **/
10024/** **/
10025
10026/*****************************************************************************/
10027/* */
10028/* boundingbox() Form an "infinite" bounding triangle to insert vertices */
10029/* into. */
10030/* */
10031/* The vertices at "infinity" are assigned finite coordinates, which are */
10032/* used by the point location routines, but (mostly) ignored by the */
10033/* Delaunay edge flip routines. */
10034/* */
10035/*****************************************************************************/
10036
10037#ifndef REDUCED
10038
10039#ifdef ANSI_DECLARATORS
10040void boundingbox(struct mesh *m, struct behavior *b)
10041#else /* not ANSI_DECLARATORS */
10042void boundingbox(m, b)
10043struct mesh *m;
10044struct behavior *b;
10045#endif /* not ANSI_DECLARATORS */
10046
10047{
10048 struct otri inftri; /* Handle for the triangular bounding box. */
10049 REAL width;
10050
10051 if (b->verbose) {
10052 printf(" Creating triangular bounding box.\n");
10053 }
10054 /* Find the width (or height, whichever is larger) of the triangulation. */
10055 width = m->xmax - m->xmin;
10056 if (m->ymax - m->ymin > width) {
10057 width = m->ymax - m->ymin;
10058 }
10059 if (width == 0.0) {
10060 width = 1.0;
10061 }
10062 /* Create the vertices of the bounding box. */
10063 m->infvertex1 = (vertex) trimalloc(m->vertices.itembytes);
10064 m->infvertex2 = (vertex) trimalloc(m->vertices.itembytes);
10065 m->infvertex3 = (vertex) trimalloc(m->vertices.itembytes);
10066 m->infvertex1[0] = m->xmin - 50.0 * width;
10067 m->infvertex1[1] = m->ymin - 40.0 * width;
10068 m->infvertex2[0] = m->xmax + 50.0 * width;
10069 m->infvertex2[1] = m->ymin - 40.0 * width;
10070 m->infvertex3[0] = 0.5 * (m->xmin + m->xmax);
10071 m->infvertex3[1] = m->ymax + 60.0 * width;
10072
10073 /* Create the bounding box. */
10074 maketriangle(m, b, &inftri);
10075 setorg(inftri, m->infvertex1);
10076 setdest(inftri, m->infvertex2);
10077 setapex(inftri, m->infvertex3);
10078 /* Link dummytri to the bounding box so we can always find an */
10079 /* edge to begin searching (point location) from. */
10080 m->dummytri[0] = (triangle) inftri.tri;
10081 if (b->verbose > 2) {
10082 printf(" Creating ");
10083 printtriangle(m, b, &inftri);
10084 }
10085}
10086
10087#endif /* not REDUCED */
10088
10089/*****************************************************************************/
10090/* */
10091/* removebox() Remove the "infinite" bounding triangle, setting boundary */
10092/* markers as appropriate. */
10093/* */
10094/* The triangular bounding box has three boundary triangles (one for each */
10095/* side of the bounding box), and a bunch of triangles fanning out from */
10096/* the three bounding box vertices (one triangle for each edge of the */
10097/* convex hull of the inner mesh). This routine removes these triangles. */
10098/* */
10099/* Returns the number of edges on the convex hull of the triangulation. */
10100/* */
10101/*****************************************************************************/
10102
10103#ifndef REDUCED
10104
10105#ifdef ANSI_DECLARATORS
10106long removebox(struct mesh *m, struct behavior *b)
10107#else /* not ANSI_DECLARATORS */
10108long removebox(m, b)
10109struct mesh *m;
10110struct behavior *b;
10111#endif /* not ANSI_DECLARATORS */
10112
10113{
10114 struct otri deadtriangle;
10115 struct otri searchedge;
10116 struct otri checkedge;
10117 struct otri nextedge, finaledge, dissolveedge;
10118 vertex markorg;
10119 long hullsize;
10120 triangle ptr; /* Temporary variable used by sym(). */
10121
10122 if (b->verbose) {
10123 printf(" Removing triangular bounding box.\n");
10124 }
10125 /* Find a boundary triangle. */
10126 nextedge.tri = m->dummytri;
10127 nextedge.orient = 0;
10128 symself(nextedge);
10129 /* Mark a place to stop. */
10130 lprev(nextedge, finaledge);
10131 lnextself(nextedge);
10132 symself(nextedge);
10133 /* Find a triangle (on the boundary of the vertex set) that isn't */
10134 /* a bounding box triangle. */
10135 lprev(nextedge, searchedge);
10136 symself(searchedge);
10137 /* Check whether nextedge is another boundary triangle */
10138 /* adjacent to the first one. */
10139 lnext(nextedge, checkedge);
10140 symself(checkedge);
10141 if (checkedge.tri == m->dummytri) {
10142 /* Go on to the next triangle. There are only three boundary */
10143 /* triangles, and this next triangle cannot be the third one, */
10144 /* so it's safe to stop here. */
10145 lprevself(searchedge);
10146 symself(searchedge);
10147 }
10148 /* Find a new boundary edge to search from, as the current search */
10149 /* edge lies on a bounding box triangle and will be deleted. */
10150 m->dummytri[0] = encode(searchedge);
10151 hullsize = -2l;
10152 while (!otriequal(nextedge, finaledge)) {
10153 hullsize++;
10154 lprev(nextedge, dissolveedge);
10155 symself(dissolveedge);
10156 /* If not using a PSLG, the vertices should be marked now. */
10157 /* (If using a PSLG, markhull() will do the job.) */
10158 if (!b->poly) {
10159 /* Be careful! One must check for the case where all the input */
10160 /* vertices are collinear, and thus all the triangles are part of */
10161 /* the bounding box. Otherwise, the setvertexmark() call below */
10162 /* will cause a bad pointer reference. */
10163 if (dissolveedge.tri != m->dummytri) {
10164 org(dissolveedge, markorg);
10165 if (vertexmark(markorg) == 0) {
10166 setvertexmark(markorg, 1);
10167 }
10168 }
10169 }
10170 /* Disconnect the bounding box triangle from the mesh triangle. */
10171 dissolve(dissolveedge);
10172 lnext(nextedge, deadtriangle);
10173 sym(deadtriangle, nextedge);
10174 /* Get rid of the bounding box triangle. */
10175 triangledealloc(m, deadtriangle.tri);
10176 /* Do we need to turn the corner? */
10177 if (nextedge.tri == m->dummytri) {
10178 /* Turn the corner. */
10179 otricopy(dissolveedge, nextedge);
10180 }
10181 }
10182 triangledealloc(m, finaledge.tri);
10183
10184 trifree((VOID *) m->infvertex1); /* Deallocate the bounding box vertices. */
10185 trifree((VOID *) m->infvertex2);
10186 trifree((VOID *) m->infvertex3);
10187
10188 return hullsize;
10189}
10190
10191#endif /* not REDUCED */
10192
10193/*****************************************************************************/
10194/* */
10195/* incrementaldelaunay() Form a Delaunay triangulation by incrementally */
10196/* inserting vertices. */
10197/* */
10198/* Returns the number of edges on the convex hull of the triangulation. */
10199/* */
10200/*****************************************************************************/
10201
10202#ifndef REDUCED
10203
10204#ifdef ANSI_DECLARATORS
10205long incrementaldelaunay(struct mesh *m, struct behavior *b)
10206#else /* not ANSI_DECLARATORS */
10207long incrementaldelaunay(m, b)
10208struct mesh *m;
10209struct behavior *b;
10210#endif /* not ANSI_DECLARATORS */
10211
10212{
10213 struct otri starttri;
10214 vertex vertexloop;
10215
10216 /* Create a triangular bounding box. */
10217 boundingbox(m, b);
10218 if (b->verbose) {
10219 printf(" Incrementally inserting vertices.\n");
10220 }
10221 traversalinit(&m->vertices);
10222 vertexloop = vertextraverse(m);
10223 while (vertexloop != (vertex) NULL) {
10224 starttri.tri = m->dummytri;
10225 if (insertvertex(m, b, vertexloop, &starttri, (struct osub *) NULL, 0, 0)
10226 == DUPLICATEVERTEX) {
10227 if (!b->quiet) {
10228 printf(
10229"Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n",
10230 vertexloop[0], vertexloop[1]);
10231 }
10232 setvertextype(vertexloop, UNDEADVERTEX);
10233 m->undeads++;
10234 }
10235 vertexloop = vertextraverse(m);
10236 }
10237 /* Remove the bounding box. */
10238 return removebox(m, b);
10239}
10240
10241#endif /* not REDUCED */
10242
10243/** **/
10244/** **/
10245/********* Incremental Delaunay triangulation ends here *********/
10246
10247/********* Sweepline Delaunay triangulation begins here *********/
10248/** **/
10249/** **/
10250
10251#ifndef REDUCED
10252
10253#ifdef ANSI_DECLARATORS
10254void eventheapinsert(struct event **heap, int heapsize, struct event *newevent)
10255#else /* not ANSI_DECLARATORS */
10256void eventheapinsert(heap, heapsize, newevent)
10257struct event **heap;
10258int heapsize;
10259struct event *newevent;
10260#endif /* not ANSI_DECLARATORS */
10261
10262{
10263 REAL eventx, eventy;
10264 int eventnum;
10265 int parent;
10266 int notdone;
10267
10268 eventx = newevent->xkey;
10269 eventy = newevent->ykey;
10270 eventnum = heapsize;
10271 notdone = eventnum > 0;
10272 while (notdone) {
10273 parent = (eventnum - 1) >> 1;
10274 if ((heap[parent]->ykey < eventy) ||
10275 ((heap[parent]->ykey == eventy)
10276 && (heap[parent]->xkey <= eventx))) {
10277 notdone = 0;
10278 } else {
10279 heap[eventnum] = heap[parent];
10280 heap[eventnum]->heapposition = eventnum;
10281
10282 eventnum = parent;
10283 notdone = eventnum > 0;
10284 }
10285 }
10286 heap[eventnum] = newevent;
10287 newevent->heapposition = eventnum;
10288}
10289
10290#endif /* not REDUCED */
10291
10292#ifndef REDUCED
10293
10294#ifdef ANSI_DECLARATORS
10295void eventheapify(struct event **heap, int heapsize, int eventnum)
10296#else /* not ANSI_DECLARATORS */
10297void eventheapify(heap, heapsize, eventnum)
10298struct event **heap;
10299int heapsize;
10300int eventnum;
10301#endif /* not ANSI_DECLARATORS */
10302
10303{
10304 struct event *thisevent;
10305 REAL eventx, eventy;
10306 int leftchild, rightchild;
10307 int smallest;
10308 int notdone;
10309
10310 thisevent = heap[eventnum];
10311 eventx = thisevent->xkey;
10312 eventy = thisevent->ykey;
10313 leftchild = 2 * eventnum + 1;
10314 notdone = leftchild < heapsize;
10315 while (notdone) {
10316 if ((heap[leftchild]->ykey < eventy) ||
10317 ((heap[leftchild]->ykey == eventy)
10318 && (heap[leftchild]->xkey < eventx))) {
10319 smallest = leftchild;
10320 } else {
10321 smallest = eventnum;
10322 }
10323 rightchild = leftchild + 1;
10324 if (rightchild < heapsize) {
10325 if ((heap[rightchild]->ykey < heap[smallest]->ykey) ||
10326 ((heap[rightchild]->ykey == heap[smallest]->ykey)
10327 && (heap[rightchild]->xkey < heap[smallest]->xkey))) {
10328 smallest = rightchild;
10329 }
10330 }
10331 if (smallest == eventnum) {
10332 notdone = 0;
10333 } else {
10334 heap[eventnum] = heap[smallest];
10335 heap[eventnum]->heapposition = eventnum;
10336 heap[smallest] = thisevent;
10337 thisevent->heapposition = smallest;
10338
10339 eventnum = smallest;
10340 leftchild = 2 * eventnum + 1;
10341 notdone = leftchild < heapsize;
10342 }
10343 }
10344}
10345
10346#endif /* not REDUCED */
10347
10348#ifndef REDUCED
10349
10350#ifdef ANSI_DECLARATORS
10351void eventheapdelete(struct event **heap, int heapsize, int eventnum)
10352#else /* not ANSI_DECLARATORS */
10353void eventheapdelete(heap, heapsize, eventnum)
10354struct event **heap;
10355int heapsize;
10356int eventnum;
10357#endif /* not ANSI_DECLARATORS */
10358
10359{
10360 struct event *moveevent;
10361 REAL eventx, eventy;
10362 int parent;
10363 int notdone;
10364
10365 moveevent = heap[heapsize - 1];
10366 if (eventnum > 0) {
10367 eventx = moveevent->xkey;
10368 eventy = moveevent->ykey;
10369 do {
10370 parent = (eventnum - 1) >> 1;
10371 if ((heap[parent]->ykey < eventy) ||
10372 ((heap[parent]->ykey == eventy)
10373 && (heap[parent]->xkey <= eventx))) {
10374 notdone = 0;
10375 } else {
10376 heap[eventnum] = heap[parent];
10377 heap[eventnum]->heapposition = eventnum;
10378
10379 eventnum = parent;
10380 notdone = eventnum > 0;
10381 }
10382 } while (notdone);
10383 }
10384 heap[eventnum] = moveevent;
10385 moveevent->heapposition = eventnum;
10386 eventheapify(heap, heapsize - 1, eventnum);
10387}
10388
10389#endif /* not REDUCED */
10390
10391#ifndef REDUCED
10392
10393#ifdef ANSI_DECLARATORS
10394void createeventheap(struct mesh *m, struct event ***eventheap,
10395 struct event **events, struct event **freeevents)
10396#else /* not ANSI_DECLARATORS */
10397void createeventheap(m, eventheap, events, freeevents)
10398struct mesh *m;
10399struct event ***eventheap;
10400struct event **events;
10401struct event **freeevents;
10402#endif /* not ANSI_DECLARATORS */
10403
10404{
10405 vertex thisvertex;
10406 int maxevents;
10407 int i;
10408
10409 maxevents = (3 * m->invertices) / 2;
10410 *eventheap = (struct event **) trimalloc(maxevents *
10411 (int) sizeof(struct event *));
10412 *events = (struct event *) trimalloc(maxevents * (int) sizeof(struct event));
10413 traversalinit(&m->vertices);
10414 for (i = 0; i < m->invertices; i++) {
10415 thisvertex = vertextraverse(m);
10416 (*events)[i].eventptr = (VOID *) thisvertex;
10417 (*events)[i].xkey = thisvertex[0];
10418 (*events)[i].ykey = thisvertex[1];
10419 eventheapinsert(*eventheap, i, *events + i);
10420 }
10421 *freeevents = (struct event *) NULL;
10422 for (i = maxevents - 1; i >= m->invertices; i--) {
10423 (*events)[i].eventptr = (VOID *) *freeevents;
10424 *freeevents = *events + i;
10425 }
10426}
10427
10428#endif /* not REDUCED */
10429
10430#ifndef REDUCED
10431
10432#ifdef ANSI_DECLARATORS
10433int rightofhyperbola(struct mesh *m, struct otri *fronttri, vertex newsite)
10434#else /* not ANSI_DECLARATORS */
10435int rightofhyperbola(m, fronttri, newsite)
10436struct mesh *m;
10437struct otri *fronttri;
10438vertex newsite;
10439#endif /* not ANSI_DECLARATORS */
10440
10441{
10442 vertex leftvertex, rightvertex;
10443 REAL dxa, dya, dxb, dyb;
10444
10445 m->hyperbolacount++;
10446
10447 dest(*fronttri, leftvertex);
10448 apex(*fronttri, rightvertex);
10449 if ((leftvertex[1] < rightvertex[1]) ||
10450 ((leftvertex[1] == rightvertex[1]) &&
10451 (leftvertex[0] < rightvertex[0]))) {
10452 if (newsite[0] >= rightvertex[0]) {
10453 return 1;
10454 }
10455 } else {
10456 if (newsite[0] <= leftvertex[0]) {
10457 return 0;
10458 }
10459 }
10460 dxa = leftvertex[0] - newsite[0];
10461 dya = leftvertex[1] - newsite[1];
10462 dxb = rightvertex[0] - newsite[0];
10463 dyb = rightvertex[1] - newsite[1];
10464 return dya * (dxb * dxb + dyb * dyb) > dyb * (dxa * dxa + dya * dya);
10465}
10466
10467#endif /* not REDUCED */
10468
10469#ifndef REDUCED
10470
10471#ifdef ANSI_DECLARATORS
10472REAL circletop(struct mesh *m, vertex pa, vertex pb, vertex pc, REAL ccwabc)
10473#else /* not ANSI_DECLARATORS */
10474REAL circletop(m, pa, pb, pc, ccwabc)
10475struct mesh *m;
10476vertex pa;
10477vertex pb;
10478vertex pc;
10479REAL ccwabc;
10480#endif /* not ANSI_DECLARATORS */
10481
10482{
10483 REAL xac, yac, xbc, ybc, xab, yab;
10484 REAL aclen2, bclen2, ablen2;
10485
10486 m->circletopcount++;
10487
10488 xac = pa[0] - pc[0];
10489 yac = pa[1] - pc[1];
10490 xbc = pb[0] - pc[0];
10491 ybc = pb[1] - pc[1];
10492 xab = pa[0] - pb[0];
10493 yab = pa[1] - pb[1];
10494 aclen2 = xac * xac + yac * yac;
10495 bclen2 = xbc * xbc + ybc * ybc;
10496 ablen2 = xab * xab + yab * yab;
10497 return pc[1] + (xac * bclen2 - xbc * aclen2 + sqrt(aclen2 * bclen2 * ablen2))
10498 / (2.0 * ccwabc);
10499}
10500
10501#endif /* not REDUCED */
10502
10503#ifndef REDUCED
10504
10505#ifdef ANSI_DECLARATORS
10506void check4deadevent(struct otri *checktri, struct event **freeevents,
10507 struct event **eventheap, int *heapsize)
10508#else /* not ANSI_DECLARATORS */
10509void check4deadevent(checktri, freeevents, eventheap, heapsize)
10510struct otri *checktri;
10511struct event **freeevents;
10512struct event **eventheap;
10513int *heapsize;
10514#endif /* not ANSI_DECLARATORS */
10515
10516{
10517 struct event *deadevent;
10518 vertex eventvertex;
10519 int eventnum;
10520
10521 org(*checktri, eventvertex);
10522 if (eventvertex != (vertex) NULL) {
10523 deadevent = (struct event *) eventvertex;
10524 eventnum = deadevent->heapposition;
10525 deadevent->eventptr = (VOID *) *freeevents;
10526 *freeevents = deadevent;
10527 eventheapdelete(eventheap, *heapsize, eventnum);
10528 (*heapsize)--;
10529 setorg(*checktri, NULL);
10530 }
10531}
10532
10533#endif /* not REDUCED */
10534
10535#ifndef REDUCED
10536
10537#ifdef ANSI_DECLARATORS
10538struct splaynode *splay(struct mesh *m, struct splaynode *splaytree,
10539 vertex searchpoint, struct otri *searchtri)
10540#else /* not ANSI_DECLARATORS */
10541struct splaynode *splay(m, splaytree, searchpoint, searchtri)
10542struct mesh *m;
10543struct splaynode *splaytree;
10544vertex searchpoint;
10545struct otri *searchtri;
10546#endif /* not ANSI_DECLARATORS */
10547
10548{
10549 struct splaynode *child, *grandchild;
10550 struct splaynode *lefttree, *righttree;
10551 struct splaynode *leftright;
10552 vertex checkvertex;
10553 int rightofroot, rightofchild;
10554
10555 if (splaytree == (struct splaynode *) NULL) {
10556 return (struct splaynode *) NULL;
10557 }
10558 dest(splaytree->keyedge, checkvertex);
10559 if (checkvertex == splaytree->keydest) {
10560 rightofroot = rightofhyperbola(m, &splaytree->keyedge, searchpoint);
10561 if (rightofroot) {
10562 otricopy(splaytree->keyedge, *searchtri);
10563 child = splaytree->rchild;
10564 } else {
10565 child = splaytree->lchild;
10566 }
10567 if (child == (struct splaynode *) NULL) {
10568 return splaytree;
10569 }
10570 dest(child->keyedge, checkvertex);
10571 if (checkvertex != child->keydest) {
10572 child = splay(m, child, searchpoint, searchtri);
10573 if (child == (struct splaynode *) NULL) {
10574 if (rightofroot) {
10575 splaytree->rchild = (struct splaynode *) NULL;
10576 } else {
10577 splaytree->lchild = (struct splaynode *) NULL;
10578 }
10579 return splaytree;
10580 }
10581 }
10582 rightofchild = rightofhyperbola(m, &child->keyedge, searchpoint);
10583 if (rightofchild) {
10584 otricopy(child->keyedge, *searchtri);
10585 grandchild = splay(m, child->rchild, searchpoint, searchtri);
10586 child->rchild = grandchild;
10587 } else {
10588 grandchild = splay(m, child->lchild, searchpoint, searchtri);
10589 child->lchild = grandchild;
10590 }
10591 if (grandchild == (struct splaynode *) NULL) {
10592 if (rightofroot) {
10593 splaytree->rchild = child->lchild;
10594 child->lchild = splaytree;
10595 } else {
10596 splaytree->lchild = child->rchild;
10597 child->rchild = splaytree;
10598 }
10599 return child;
10600 }
10601 if (rightofchild) {
10602 if (rightofroot) {
10603 splaytree->rchild = child->lchild;
10604 child->lchild = splaytree;
10605 } else {
10606 splaytree->lchild = grandchild->rchild;
10607 grandchild->rchild = splaytree;
10608 }
10609 child->rchild = grandchild->lchild;
10610 grandchild->lchild = child;
10611 } else {
10612 if (rightofroot) {
10613 splaytree->rchild = grandchild->lchild;
10614 grandchild->lchild = splaytree;
10615 } else {
10616 splaytree->lchild = child->rchild;
10617 child->rchild = splaytree;
10618 }
10619 child->lchild = grandchild->rchild;
10620 grandchild->rchild = child;
10621 }
10622 return grandchild;
10623 } else {
10624 lefttree = splay(m, splaytree->lchild, searchpoint, searchtri);
10625 righttree = splay(m, splaytree->rchild, searchpoint, searchtri);
10626
10627 pooldealloc(&m->splaynodes, (VOID *) splaytree);
10628 if (lefttree == (struct splaynode *) NULL) {
10629 return righttree;
10630 } else if (righttree == (struct splaynode *) NULL) {
10631 return lefttree;
10632 } else if (lefttree->rchild == (struct splaynode *) NULL) {
10633 lefttree->rchild = righttree->lchild;
10634 righttree->lchild = lefttree;
10635 return righttree;
10636 } else if (righttree->lchild == (struct splaynode *) NULL) {
10637 righttree->lchild = lefttree->rchild;
10638 lefttree->rchild = righttree;
10639 return lefttree;
10640 } else {
10641/* printf("Holy Toledo!!!\n"); */
10642 leftright = lefttree->rchild;
10643 while (leftright->rchild != (struct splaynode *) NULL) {
10644 leftright = leftright->rchild;
10645 }
10646 leftright->rchild = righttree;
10647 return lefttree;
10648 }
10649 }
10650}
10651
10652#endif /* not REDUCED */
10653
10654#ifndef REDUCED
10655
10656#ifdef ANSI_DECLARATORS
10657struct splaynode *splayinsert(struct mesh *m, struct splaynode *splayroot,
10658 struct otri *newkey, vertex searchpoint)
10659#else /* not ANSI_DECLARATORS */
10660struct splaynode *splayinsert(m, splayroot, newkey, searchpoint)
10661struct mesh *m;
10662struct splaynode *splayroot;
10663struct otri *newkey;
10664vertex searchpoint;
10665#endif /* not ANSI_DECLARATORS */
10666
10667{
10668 struct splaynode *newsplaynode;
10669
10670 newsplaynode = (struct splaynode *) poolalloc(&m->splaynodes);
10671 otricopy(*newkey, newsplaynode->keyedge);
10672 dest(*newkey, newsplaynode->keydest);
10673 if (splayroot == (struct splaynode *) NULL) {
10674 newsplaynode->lchild = (struct splaynode *) NULL;
10675 newsplaynode->rchild = (struct splaynode *) NULL;
10676 } else if (rightofhyperbola(m, &splayroot->keyedge, searchpoint)) {
10677 newsplaynode->lchild = splayroot;
10678 newsplaynode->rchild = splayroot->rchild;
10679 splayroot->rchild = (struct splaynode *) NULL;
10680 } else {
10681 newsplaynode->lchild = splayroot->lchild;
10682 newsplaynode->rchild = splayroot;
10683 splayroot->lchild = (struct splaynode *) NULL;
10684 }
10685 return newsplaynode;
10686}
10687
10688#endif /* not REDUCED */
10689
10690#ifndef REDUCED
10691
10692#ifdef ANSI_DECLARATORS
10693struct splaynode *circletopinsert(struct mesh *m, struct behavior *b,
10694 struct splaynode *splayroot,
10695 struct otri *newkey,
10696 vertex pa, vertex pb, vertex pc, REAL topy)
10697#else /* not ANSI_DECLARATORS */
10698struct splaynode *circletopinsert(m, b, splayroot, newkey, pa, pb, pc, topy)
10699struct mesh *m;
10700struct behavior *b;
10701struct splaynode *splayroot;
10702struct otri *newkey;
10703vertex pa;
10704vertex pb;
10705vertex pc;
10706REAL topy;
10707#endif /* not ANSI_DECLARATORS */
10708
10709{
10710 REAL ccwabc;
10711 REAL xac, yac, xbc, ybc;
10712 REAL aclen2, bclen2;
10713 REAL searchpoint[2];
10714 struct otri dummytri;
10715
10716 ccwabc = counterclockwise(m, b, pa, pb, pc);
10717 xac = pa[0] - pc[0];
10718 yac = pa[1] - pc[1];
10719 xbc = pb[0] - pc[0];
10720 ybc = pb[1] - pc[1];
10721 aclen2 = xac * xac + yac * yac;
10722 bclen2 = xbc * xbc + ybc * ybc;
10723 searchpoint[0] = pc[0] - (yac * bclen2 - ybc * aclen2) / (2.0 * ccwabc);
10724 searchpoint[1] = topy;
10725 return splayinsert(m, splay(m, splayroot, (vertex) searchpoint, &dummytri),
10726 newkey, (vertex) searchpoint);
10727}
10728
10729#endif /* not REDUCED */
10730
10731#ifndef REDUCED
10732
10733#ifdef ANSI_DECLARATORS
10734struct splaynode *frontlocate(struct mesh *m, struct splaynode *splayroot,
10735 struct otri *bottommost, vertex searchvertex,
10736 struct otri *searchtri, int *farright)
10737#else /* not ANSI_DECLARATORS */
10738struct splaynode *frontlocate(m, splayroot, bottommost, searchvertex,
10739 searchtri, farright)
10740struct mesh *m;
10741struct splaynode *splayroot;
10742struct otri *bottommost;
10743vertex searchvertex;
10744struct otri *searchtri;
10745int *farright;
10746#endif /* not ANSI_DECLARATORS */
10747
10748{
10749 int farrightflag;
10750 triangle ptr; /* Temporary variable used by onext(). */
10751
10752 otricopy(*bottommost, *searchtri);
10753 splayroot = splay(m, splayroot, searchvertex, searchtri);
10754
10755 farrightflag = 0;
10756 while (!farrightflag && rightofhyperbola(m, searchtri, searchvertex)) {
10757 onextself(*searchtri);
10758 farrightflag = otriequal(*searchtri, *bottommost);
10759 }
10760 *farright = farrightflag;
10761 return splayroot;
10762}
10763
10764#endif /* not REDUCED */
10765
10766#ifndef REDUCED
10767
10768#ifdef ANSI_DECLARATORS
10769long sweeplinedelaunay(struct mesh *m, struct behavior *b)
10770#else /* not ANSI_DECLARATORS */
10771long sweeplinedelaunay(m, b)
10772struct mesh *m;
10773struct behavior *b;
10774#endif /* not ANSI_DECLARATORS */
10775
10776{
10777 struct event **eventheap;
10778 struct event *events;
10779 struct event *freeevents;
10780 struct event *nextevent;
10781 struct event *newevent;
10782 struct splaynode *splayroot;
10783 struct otri bottommost;
10784 struct otri searchtri;
10785 struct otri fliptri;
10786 struct otri lefttri, righttri, farlefttri, farrighttri;
10787 struct otri inserttri;
10788 vertex firstvertex, secondvertex;
10789 vertex nextvertex, lastvertex;
10790 vertex connectvertex;
10791 vertex leftvertex, midvertex, rightvertex;
10792 REAL lefttest, righttest;
10793 int heapsize;
10794 int check4events, farrightflag;
10795 triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */
10796
10797 poolinit(&m->splaynodes, sizeof(struct splaynode), SPLAYNODEPERBLOCK,
10798 SPLAYNODEPERBLOCK, 0);
10799 splayroot = (struct splaynode *) NULL;
10800
10801 if (b->verbose) {
10802 printf(" Placing vertices in event heap.\n");
10803 }
10804 createeventheap(m, &eventheap, &events, &freeevents);
10805 heapsize = m->invertices;
10806
10807 if (b->verbose) {
10808 printf(" Forming triangulation.\n");
10809 }
10810 maketriangle(m, b, &lefttri);
10811 maketriangle(m, b, &righttri);
10812 bond(lefttri, righttri);
10813 lnextself(lefttri);
10814 lprevself(righttri);
10815 bond(lefttri, righttri);
10816 lnextself(lefttri);
10817 lprevself(righttri);
10818 bond(lefttri, righttri);
10819 firstvertex = (vertex) eventheap[0]->eventptr;
10820 eventheap[0]->eventptr = (VOID *) freeevents;
10821 freeevents = eventheap[0];
10822 eventheapdelete(eventheap, heapsize, 0);
10823 heapsize--;
10824 do {
10825 if (heapsize == 0) {
10826 printf("Error: Input vertices are all identical.\n");
10827 triexit(1);
10828 }
10829 secondvertex = (vertex) eventheap[0]->eventptr;
10830 eventheap[0]->eventptr = (VOID *) freeevents;
10831 freeevents = eventheap[0];
10832 eventheapdelete(eventheap, heapsize, 0);
10833 heapsize--;
10834 if ((firstvertex[0] == secondvertex[0]) &&
10835 (firstvertex[1] == secondvertex[1])) {
10836 if (!b->quiet) {
10837 printf(
10838"Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n",
10839 secondvertex[0], secondvertex[1]);
10840 }
10841 setvertextype(secondvertex, UNDEADVERTEX);
10842 m->undeads++;
10843 }
10844 } while ((firstvertex[0] == secondvertex[0]) &&
10845 (firstvertex[1] == secondvertex[1]));
10846 setorg(lefttri, firstvertex);
10847 setdest(lefttri, secondvertex);
10848 setorg(righttri, secondvertex);
10849 setdest(righttri, firstvertex);
10850 lprev(lefttri, bottommost);
10851 lastvertex = secondvertex;
10852 while (heapsize > 0) {
10853 nextevent = eventheap[0];
10854 eventheapdelete(eventheap, heapsize, 0);
10855 heapsize--;
10856 check4events = 1;
10857 if (nextevent->xkey < m->xmin) {
10858 decode(nextevent->eventptr, fliptri);
10859 oprev(fliptri, farlefttri);
10860 check4deadevent(&farlefttri, &freeevents, eventheap, &heapsize);
10861 onext(fliptri, farrighttri);
10862 check4deadevent(&farrighttri, &freeevents, eventheap, &heapsize);
10863
10864 if (otriequal(farlefttri, bottommost)) {
10865 lprev(fliptri, bottommost);
10866 }
10867 flip(m, b, &fliptri);
10868 setapex(fliptri, NULL);
10869 lprev(fliptri, lefttri);
10870 lnext(fliptri, righttri);
10871 sym(lefttri, farlefttri);
10872
10873 if (randomnation(SAMPLERATE) == 0) {
10874 symself(fliptri);
10875 dest(fliptri, leftvertex);
10876 apex(fliptri, midvertex);
10877 org(fliptri, rightvertex);
10878 splayroot = circletopinsert(m, b, splayroot, &lefttri, leftvertex,
10879 midvertex, rightvertex, nextevent->ykey);
10880 }
10881 } else {
10882 nextvertex = (vertex) nextevent->eventptr;
10883 if ((nextvertex[0] == lastvertex[0]) &&
10884 (nextvertex[1] == lastvertex[1])) {
10885 if (!b->quiet) {
10886 printf(
10887"Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n",
10888 nextvertex[0], nextvertex[1]);
10889 }
10890 setvertextype(nextvertex, UNDEADVERTEX);
10891 m->undeads++;
10892 check4events = 0;
10893 } else {
10894 lastvertex = nextvertex;
10895
10896 splayroot = frontlocate(m, splayroot, &bottommost, nextvertex,
10897 &searchtri, &farrightflag);
10898/*
10899 otricopy(bottommost, searchtri);
10900 farrightflag = 0;
10901 while (!farrightflag && rightofhyperbola(m, &searchtri, nextvertex)) {
10902 onextself(searchtri);
10903 farrightflag = otriequal(searchtri, bottommost);
10904 }
10905*/
10906
10907 check4deadevent(&searchtri, &freeevents, eventheap, &heapsize);
10908
10909 otricopy(searchtri, farrighttri);
10910 sym(searchtri, farlefttri);
10911 maketriangle(m, b, &lefttri);
10912 maketriangle(m, b, &righttri);
10913 dest(farrighttri, connectvertex);
10914 setorg(lefttri, connectvertex);
10915 setdest(lefttri, nextvertex);
10916 setorg(righttri, nextvertex);
10917 setdest(righttri, connectvertex);
10918 bond(lefttri, righttri);
10919 lnextself(lefttri);
10920 lprevself(righttri);
10921 bond(lefttri, righttri);
10922 lnextself(lefttri);
10923 lprevself(righttri);
10924 bond(lefttri, farlefttri);
10925 bond(righttri, farrighttri);
10926 if (!farrightflag && otriequal(farrighttri, bottommost)) {
10927 otricopy(lefttri, bottommost);
10928 }
10929
10930 if (randomnation(SAMPLERATE) == 0) {
10931 splayroot = splayinsert(m, splayroot, &lefttri, nextvertex);
10932 } else if (randomnation(SAMPLERATE) == 0) {
10933 lnext(righttri, inserttri);
10934 splayroot = splayinsert(m, splayroot, &inserttri, nextvertex);
10935 }
10936 }
10937 }
10938 nextevent->eventptr = (VOID *) freeevents;
10939 freeevents = nextevent;
10940
10941 if (check4events) {
10942 apex(farlefttri, leftvertex);
10943 dest(lefttri, midvertex);
10944 apex(lefttri, rightvertex);
10945 lefttest = counterclockwise(m, b, leftvertex, midvertex, rightvertex);
10946 if (lefttest > 0.0) {
10947 newevent = freeevents;
10948 freeevents = (struct event *) freeevents->eventptr;
10949 newevent->xkey = m->xminextreme;
10950 newevent->ykey = circletop(m, leftvertex, midvertex, rightvertex,
10951 lefttest);
10952 newevent->eventptr = (VOID *) encode(lefttri);
10953 eventheapinsert(eventheap, heapsize, newevent);
10954 heapsize++;
10955 setorg(lefttri, newevent);
10956 }
10957 apex(righttri, leftvertex);
10958 org(righttri, midvertex);
10959 apex(farrighttri, rightvertex);
10960 righttest = counterclockwise(m, b, leftvertex, midvertex, rightvertex);
10961 if (righttest > 0.0) {
10962 newevent = freeevents;
10963 freeevents = (struct event *) freeevents->eventptr;
10964 newevent->xkey = m->xminextreme;
10965 newevent->ykey = circletop(m, leftvertex, midvertex, rightvertex,
10966 righttest);
10967 newevent->eventptr = (VOID *) encode(farrighttri);
10968 eventheapinsert(eventheap, heapsize, newevent);
10969 heapsize++;
10970 setorg(farrighttri, newevent);
10971 }
10972 }
10973 }
10974
10975 pooldeinit(&m->splaynodes);
10976 lprevself(bottommost);
10977 return removeghosts(m, b, &bottommost);
10978}
10979
10980#endif /* not REDUCED */
10981
10982/** **/
10983/** **/
10984/********* Sweepline Delaunay triangulation ends here *********/
10985
10986/********* General mesh construction routines begin here *********/
10987/** **/
10988/** **/
10989
10990/*****************************************************************************/
10991/* */
10992/* delaunay() Form a Delaunay triangulation. */
10993/* */
10994/*****************************************************************************/
10995
10996#ifdef ANSI_DECLARATORS
10997long delaunay(struct mesh *m, struct behavior *b)
10998#else /* not ANSI_DECLARATORS */
10999long delaunay(m, b)
11000struct mesh *m;
11001struct behavior *b;
11002#endif /* not ANSI_DECLARATORS */
11003
11004{
11005 long hulledges;
11006
11007 m->eextras = 0;
11008 initializetrisubpools(m, b);
11009
11010#ifdef REDUCED
11011 if (!b->quiet) {
11012 printf(
11013 "Constructing Delaunay triangulation by divide-and-conquer method.\n");
11014 }
11015 hulledges = divconqdelaunay(m, b);
11016#else /* not REDUCED */
11017 if (!b->quiet) {
11018 printf("Constructing Delaunay triangulation ");
11019 if (b->incremental) {
11020 printf("by incremental method.\n");
11021 } else if (b->sweepline) {
11022 printf("by sweepline method.\n");
11023 } else {
11024 printf("by divide-and-conquer method.\n");
11025 }
11026 }
11027 if (b->incremental) {
11028 hulledges = incrementaldelaunay(m, b);
11029 } else if (b->sweepline) {
11030 hulledges = sweeplinedelaunay(m, b);
11031 } else {
11032 hulledges = divconqdelaunay(m, b);
11033 }
11034#endif /* not REDUCED */
11035
11036 if (m->triangles.items == 0) {
11037 /* The input vertices were all collinear, so there are no triangles. */
11038 return 0l;
11039 } else {
11040 return hulledges;
11041 }
11042}
11043
11044/*****************************************************************************/
11045/* */
11046/* reconstruct() Reconstruct a triangulation from its .ele (and possibly */
11047/* .poly) file. Used when the -r switch is used. */
11048/* */
11049/* Reads an .ele file and reconstructs the original mesh. If the -p switch */
11050/* is used, this procedure will also read a .poly file and reconstruct the */
11051/* subsegments of the original mesh. If the -a switch is used, this */
11052/* procedure will also read an .area file and set a maximum area constraint */
11053/* on each triangle. */
11054/* */
11055/* Vertices that are not corners of triangles, such as nodes on edges of */
11056/* subparametric elements, are discarded. */
11057/* */
11058/* This routine finds the adjacencies between triangles (and subsegments) */
11059/* by forming one stack of triangles for each vertex. Each triangle is on */
11060/* three different stacks simultaneously. Each triangle's subsegment */
11061/* pointers are used to link the items in each stack. This memory-saving */
11062/* feature makes the code harder to read. The most important thing to keep */
11063/* in mind is that each triangle is removed from a stack precisely when */
11064/* the corresponding pointer is adjusted to refer to a subsegment rather */
11065/* than the next triangle of the stack. */
11066/* */
11067/*****************************************************************************/
11068
11069#ifndef CDT_ONLY
11070
11071#ifdef TRILIBRARY
11072
11073#ifdef ANSI_DECLARATORS
11074int reconstruct(struct mesh *m, struct behavior *b, int *trianglelist,
11075 REAL *triangleattriblist, REAL *trianglearealist,
11076 int elements, int corners, int attribs,
11077 int *segmentlist,int *segmentmarkerlist, int numberofsegments)
11078#else /* not ANSI_DECLARATORS */
11079int reconstruct(m, b, trianglelist, triangleattriblist, trianglearealist,
11080 elements, corners, attribs, segmentlist, segmentmarkerlist,
11081 numberofsegments)
11082struct mesh *m;
11083struct behavior *b;
11084int *trianglelist;
11085REAL *triangleattriblist;
11086REAL *trianglearealist;
11087int elements;
11088int corners;
11089int attribs;
11090int *segmentlist;
11091int *segmentmarkerlist;
11092int numberofsegments;
11093#endif /* not ANSI_DECLARATORS */
11094
11095#else /* not TRILIBRARY */
11096
11097#ifdef ANSI_DECLARATORS
11098long reconstruct(struct mesh *m, struct behavior *b, char *elefilename,
11099 char *areafilename, char *polyfilename, FILE *polyfile)
11100#else /* not ANSI_DECLARATORS */
11101long reconstruct(m, b, elefilename, areafilename, polyfilename, polyfile)
11102struct mesh *m;
11103struct behavior *b;
11104char *elefilename;
11105char *areafilename;
11106char *polyfilename;
11107FILE *polyfile;
11108#endif /* not ANSI_DECLARATORS */
11109
11110#endif /* not TRILIBRARY */
11111
11112{
11113#ifdef TRILIBRARY
11114 int vertexindex;
11115 int attribindex;
11116#else /* not TRILIBRARY */
11117 FILE *elefile;
11118 FILE *areafile;
11119 char inputline[INPUTLINESIZE];
11120 char *stringptr;
11121 int areaelements;
11122#endif /* not TRILIBRARY */
11123 struct otri triangleloop;
11124 struct otri triangleleft;
11125 struct otri checktri;
11126 struct otri checkleft;
11127 struct otri checkneighbor;
11128 struct osub subsegloop;
11129 triangle *vertexarray;
11130 triangle *prevlink;
11131 triangle nexttri;
11132 vertex tdest, tapex;
11133 vertex checkdest, checkapex;
11134 vertex shorg;
11135 vertex killvertex;
11136 vertex segmentorg, segmentdest;
11137 REAL area;
11138 int corner[3];
11139 int end[2];
11140 int killvertexindex;
11141 int incorners;
11142 int segmentmarkers;
11143 int boundmarker;
11144 int aroundvertex;
11145 long hullsize;
11146 int notfound;
11147 long elementnumber, segmentnumber;
11148 int i, j;
11149 triangle ptr; /* Temporary variable used by sym(). */
11150
11151#ifdef TRILIBRARY
11152 m->inelements = elements;
11153 incorners = corners;
11154 if (incorners < 3) {
11155 printf("Error: Triangles must have at least 3 vertices.\n");
11156 triexit(1);
11157 }
11158 m->eextras = attribs;
11159#else /* not TRILIBRARY */
11160 /* Read the triangles from an .ele file. */
11161 if (!b->quiet) {
11162 printf("Opening %s.\n", elefilename);
11163 }
11164 elefile = fopen(elefilename, "r");
11165 if (elefile == (FILE *) NULL) {
11166 printf(" Error: Cannot access file %s.\n", elefilename);
11167 triexit(1);
11168 }
11169 /* Read number of triangles, number of vertices per triangle, and */
11170 /* number of triangle attributes from .ele file. */
11171 stringptr = readline(inputline, elefile, elefilename);
11172 m->inelements = (int) strtol(stringptr, &stringptr, 0);
11173 stringptr = findfield(stringptr);
11174 if (*stringptr == '\0') {
11175 incorners = 3;
11176 } else {
11177 incorners = (int) strtol(stringptr, &stringptr, 0);
11178 if (incorners < 3) {
11179 printf("Error: Triangles in %s must have at least 3 vertices.\n",
11180 elefilename);
11181 triexit(1);
11182 }
11183 }
11184 stringptr = findfield(stringptr);
11185 if (*stringptr == '\0') {
11186 m->eextras = 0;
11187 } else {
11188 m->eextras = (int) strtol(stringptr, &stringptr, 0);
11189 }
11190#endif /* not TRILIBRARY */
11191
11192 initializetrisubpools(m, b);
11193
11194 /* Create the triangles. */
11195 for (elementnumber = 1; elementnumber <= m->inelements; elementnumber++) {
11196 maketriangle(m, b, &triangleloop);
11197 /* Mark the triangle as living. */
11198 triangleloop.tri[3] = (triangle) triangleloop.tri;
11199 }
11200
11201 segmentmarkers = 0;
11202 if (b->poly) {
11203#ifdef TRILIBRARY
11204 m->insegments = numberofsegments;
11205 segmentmarkers = segmentmarkerlist != (int *) NULL;
11206#else /* not TRILIBRARY */
11207 /* Read number of segments and number of segment */
11208 /* boundary markers from .poly file. */
11209 stringptr = readline(inputline, polyfile, b->inpolyfilename);
11210 m->insegments = (int) strtol(stringptr, &stringptr, 0);
11211 stringptr = findfield(stringptr);
11212 if (*stringptr != '\0') {
11213 segmentmarkers = (int) strtol(stringptr, &stringptr, 0);
11214 }
11215#endif /* not TRILIBRARY */
11216
11217 /* Create the subsegments. */
11218 for (segmentnumber = 1; segmentnumber <= m->insegments; segmentnumber++) {
11219 makesubseg(m, &subsegloop);
11220 /* Mark the subsegment as living. */
11221 subsegloop.ss[2] = (subseg) subsegloop.ss;
11222 }
11223 }
11224
11225#ifdef TRILIBRARY
11226 vertexindex = 0;
11227 attribindex = 0;
11228#else /* not TRILIBRARY */
11229 if (b->vararea) {
11230 /* Open an .area file, check for consistency with the .ele file. */
11231 if (!b->quiet) {
11232 printf("Opening %s.\n", areafilename);
11233 }
11234 areafile = fopen(areafilename, "r");
11235 if (areafile == (FILE *) NULL) {
11236 printf(" Error: Cannot access file %s.\n", areafilename);
11237 triexit(1);
11238 }
11239 stringptr = readline(inputline, areafile, areafilename);
11240 areaelements = (int) strtol(stringptr, &stringptr, 0);
11241 if (areaelements != m->inelements) {
11242 printf("Error: %s and %s disagree on number of triangles.\n",
11243 elefilename, areafilename);
11244 triexit(1);
11245 }
11246 }
11247#endif /* not TRILIBRARY */
11248
11249 if (!b->quiet) {
11250 printf("Reconstructing mesh.\n");
11251 }
11252 /* Allocate a temporary array that maps each vertex to some adjacent */
11253 /* triangle. I took care to allocate all the permanent memory for */
11254 /* triangles and subsegments first. */
11255 vertexarray = (triangle *) trimalloc(m->vertices.items *
11256 (int) sizeof(triangle));
11257 /* Each vertex is initially unrepresented. */
11258 for (i = 0; i < m->vertices.items; i++) {
11259 vertexarray[i] = (triangle) m->dummytri;
11260 }
11261
11262 if (b->verbose) {
11263 printf(" Assembling triangles.\n");
11264 }
11265 /* Read the triangles from the .ele file, and link */
11266 /* together those that share an edge. */
11267 traversalinit(&m->triangles);
11268 triangleloop.tri = triangletraverse(m);
11269 elementnumber = b->firstnumber;
11270 while (triangleloop.tri != (triangle *) NULL) {
11271#ifdef TRILIBRARY
11272 /* Copy the triangle's three corners. */
11273 for (j = 0; j < 3; j++) {
11274 corner[j] = trianglelist[vertexindex++];
11275 if ((corner[j] < b->firstnumber) ||
11276 (corner[j] >= b->firstnumber + m->invertices)) {
11277 printf("Error: Triangle %ld has an invalid vertex index.\n",
11278 elementnumber);
11279 triexit(1);
11280 }
11281 }
11282#else /* not TRILIBRARY */
11283 /* Read triangle number and the triangle's three corners. */
11284 stringptr = readline(inputline, elefile, elefilename);
11285 for (j = 0; j < 3; j++) {
11286 stringptr = findfield(stringptr);
11287 if (*stringptr == '\0') {
11288 printf("Error: Triangle %ld is missing vertex %d in %s.\n",
11289 elementnumber, j + 1, elefilename);
11290 triexit(1);
11291 } else {
11292 corner[j] = (int) strtol(stringptr, &stringptr, 0);
11293 if ((corner[j] < b->firstnumber) ||
11294 (corner[j] >= b->firstnumber + m->invertices)) {
11295 printf("Error: Triangle %ld has an invalid vertex index.\n",
11296 elementnumber);
11297 triexit(1);
11298 }
11299 }
11300 }
11301#endif /* not TRILIBRARY */
11302
11303 /* Find out about (and throw away) extra nodes. */
11304 for (j = 3; j < incorners; j++) {
11305#ifdef TRILIBRARY
11306 killvertexindex = trianglelist[vertexindex++];
11307#else /* not TRILIBRARY */
11308 stringptr = findfield(stringptr);
11309 if (*stringptr != '\0') {
11310 killvertexindex = (int) strtol(stringptr, &stringptr, 0);
11311#endif /* not TRILIBRARY */
11312 if ((killvertexindex >= b->firstnumber) &&
11313 (killvertexindex < b->firstnumber + m->invertices)) {
11314 /* Delete the non-corner vertex if it's not already deleted. */
11315 killvertex = getvertex(m, b, killvertexindex);
11316 if (vertextype(killvertex) != DEADVERTEX) {
11317 vertexdealloc(m, killvertex);
11318 }
11319 }
11320#ifndef TRILIBRARY
11321 }
11322#endif /* not TRILIBRARY */
11323 }
11324
11325 /* Read the triangle's attributes. */
11326 for (j = 0; j < m->eextras; j++) {
11327#ifdef TRILIBRARY
11328 setelemattribute(triangleloop, j, triangleattriblist[attribindex++]);
11329#else /* not TRILIBRARY */
11330 stringptr = findfield(stringptr);
11331 if (*stringptr == '\0') {
11332 setelemattribute(triangleloop, j, 0);
11333 } else {
11334 setelemattribute(triangleloop, j,
11335 (REAL) strtod(stringptr, &stringptr));
11336 }
11337#endif /* not TRILIBRARY */
11338 }
11339
11340 if (b->vararea) {
11341#ifdef TRILIBRARY
11342 area = trianglearealist[elementnumber - b->firstnumber];
11343#else /* not TRILIBRARY */
11344 /* Read an area constraint from the .area file. */
11345 stringptr = readline(inputline, areafile, areafilename);
11346 stringptr = findfield(stringptr);
11347 if (*stringptr == '\0') {
11348 area = -1.0; /* No constraint on this triangle. */
11349 } else {
11350 area = (REAL) strtod(stringptr, &stringptr);
11351 }
11352#endif /* not TRILIBRARY */
11353 setareabound(triangleloop, area);
11354 }
11355
11356 /* Set the triangle's vertices. */
11357 triangleloop.orient = 0;
11358 setorg(triangleloop, getvertex(m, b, corner[0]));
11359 setdest(triangleloop, getvertex(m, b, corner[1]));
11360 setapex(triangleloop, getvertex(m, b, corner[2]));
11361 /* Try linking the triangle to others that share these vertices. */
11362 for (triangleloop.orient = 0; triangleloop.orient < 3;
11363 triangleloop.orient++) {
11364 /* Take the number for the origin of triangleloop. */
11365 aroundvertex = corner[triangleloop.orient];
11366 /* Look for other triangles having this vertex. */
11367 nexttri = vertexarray[aroundvertex - b->firstnumber];
11368 /* Link the current triangle to the next one in the stack. */
11369 triangleloop.tri[6 + triangleloop.orient] = nexttri;
11370 /* Push the current triangle onto the stack. */
11371 vertexarray[aroundvertex - b->firstnumber] = encode(triangleloop);
11372 decode(nexttri, checktri);
11373 if (checktri.tri != m->dummytri) {
11374 dest(triangleloop, tdest);
11375 apex(triangleloop, tapex);
11376 /* Look for other triangles that share an edge. */
11377 do {
11378 dest(checktri, checkdest);
11379 apex(checktri, checkapex);
11380 if (tapex == checkdest) {
11381 /* The two triangles share an edge; bond them together. */
11382 lprev(triangleloop, triangleleft);
11383 bond(triangleleft, checktri);
11384 }
11385 if (tdest == checkapex) {
11386 /* The two triangles share an edge; bond them together. */
11387 lprev(checktri, checkleft);
11388 bond(triangleloop, checkleft);
11389 }
11390 /* Find the next triangle in the stack. */
11391 nexttri = checktri.tri[6 + checktri.orient];
11392 decode(nexttri, checktri);
11393 } while (checktri.tri != m->dummytri);
11394 }
11395 }
11396 triangleloop.tri = triangletraverse(m);
11397 elementnumber++;
11398 }
11399
11400#ifdef TRILIBRARY
11401 vertexindex = 0;
11402#else /* not TRILIBRARY */
11403 fclose(elefile);
11404 if (b->vararea) {
11405 fclose(areafile);
11406 }
11407#endif /* not TRILIBRARY */
11408
11409 hullsize = 0; /* Prepare to count the boundary edges. */
11410 if (b->poly) {
11411 if (b->verbose) {
11412 printf(" Marking segments in triangulation.\n");
11413 }
11414 /* Read the segments from the .poly file, and link them */
11415 /* to their neighboring triangles. */
11416 boundmarker = 0;
11417 traversalinit(&m->subsegs);
11418 subsegloop.ss = subsegtraverse(m);
11419 segmentnumber = b->firstnumber;
11420 while (subsegloop.ss != (subseg *) NULL) {
11421#ifdef TRILIBRARY
11422 end[0] = segmentlist[vertexindex++];
11423 end[1] = segmentlist[vertexindex++];
11424 if (segmentmarkers) {
11425 boundmarker = segmentmarkerlist[segmentnumber - b->firstnumber];
11426 }
11427#else /* not TRILIBRARY */
11428 /* Read the endpoints of each segment, and possibly a boundary marker. */
11429 stringptr = readline(inputline, polyfile, b->inpolyfilename);
11430 /* Skip the first (segment number) field. */
11431 stringptr = findfield(stringptr);
11432 if (*stringptr == '\0') {
11433 printf("Error: Segment %ld has no endpoints in %s.\n", segmentnumber,
11434 polyfilename);
11435 triexit(1);
11436 } else {
11437 end[0] = (int) strtol(stringptr, &stringptr, 0);
11438 }
11439 stringptr = findfield(stringptr);
11440 if (*stringptr == '\0') {
11441 printf("Error: Segment %ld is missing its second endpoint in %s.\n",
11442 segmentnumber, polyfilename);
11443 triexit(1);
11444 } else {
11445 end[1] = (int) strtol(stringptr, &stringptr, 0);
11446 }
11447 if (segmentmarkers) {
11448 stringptr = findfield(stringptr);
11449 if (*stringptr == '\0') {
11450 boundmarker = 0;
11451 } else {
11452 boundmarker = (int) strtol(stringptr, &stringptr, 0);
11453 }
11454 }
11455#endif /* not TRILIBRARY */
11456 for (j = 0; j < 2; j++) {
11457 if ((end[j] < b->firstnumber) ||
11458 (end[j] >= b->firstnumber + m->invertices)) {
11459 printf("Error: Segment %ld has an invalid vertex index.\n",
11460 segmentnumber);
11461 triexit(1);
11462 }
11463 }
11464
11465 /* set the subsegment's vertices. */
11466 subsegloop.ssorient = 0;
11467 segmentorg = getvertex(m, b, end[0]);
11468 segmentdest = getvertex(m, b, end[1]);
11469 setsorg(subsegloop, segmentorg);
11470 setsdest(subsegloop, segmentdest);
11471 setsegorg(subsegloop, segmentorg);
11472 setsegdest(subsegloop, segmentdest);
11473 setmark(subsegloop, boundmarker);
11474 /* Try linking the subsegment to triangles that share these vertices. */
11475 for (subsegloop.ssorient = 0; subsegloop.ssorient < 2;
11476 subsegloop.ssorient++) {
11477 /* Take the number for the destination of subsegloop. */
11478 aroundvertex = end[1 - subsegloop.ssorient];
11479 /* Look for triangles having this vertex. */
11480 prevlink = &vertexarray[aroundvertex - b->firstnumber];
11481 nexttri = vertexarray[aroundvertex - b->firstnumber];
11482 decode(nexttri, checktri);
11483 sorg(subsegloop, shorg);
11484 notfound = 1;
11485 /* Look for triangles having this edge. Note that I'm only */
11486 /* comparing each triangle's destination with the subsegment; */
11487 /* each triangle's apex is handled through a different vertex. */
11488 /* Because each triangle appears on three vertices' lists, each */
11489 /* occurrence of a triangle on a list can (and does) represent */
11490 /* an edge. In this way, most edges are represented twice, and */
11491 /* every triangle-subsegment bond is represented once. */
11492 while (notfound && (checktri.tri != m->dummytri)) {
11493 dest(checktri, checkdest);
11494 if (shorg == checkdest) {
11495 /* We have a match. Remove this triangle from the list. */
11496 *prevlink = checktri.tri[6 + checktri.orient];
11497 /* Bond the subsegment to the triangle. */
11498 tsbond(checktri, subsegloop);
11499 /* Check if this is a boundary edge. */
11500 sym(checktri, checkneighbor);
11501 if (checkneighbor.tri == m->dummytri) {
11502 /* The next line doesn't insert a subsegment (because there's */
11503 /* already one there), but it sets the boundary markers of */
11504 /* the existing subsegment and its vertices. */
11505 insertsubseg(m, b, &checktri, 1);
11506 hullsize++;
11507 }
11508 notfound = 0;
11509 }
11510 /* Find the next triangle in the stack. */
11511 prevlink = &checktri.tri[6 + checktri.orient];
11512 nexttri = checktri.tri[6 + checktri.orient];
11513 decode(nexttri, checktri);
11514 }
11515 }
11516 subsegloop.ss = subsegtraverse(m);
11517 segmentnumber++;
11518 }
11519 }
11520
11521 /* Mark the remaining edges as not being attached to any subsegment. */
11522 /* Also, count the (yet uncounted) boundary edges. */
11523 for (i = 0; i < m->vertices.items; i++) {
11524 /* Search the stack of triangles adjacent to a vertex. */
11525 nexttri = vertexarray[i];
11526 decode(nexttri, checktri);
11527 while (checktri.tri != m->dummytri) {
11528 /* Find the next triangle in the stack before this */
11529 /* information gets overwritten. */
11530 nexttri = checktri.tri[6 + checktri.orient];
11531 /* No adjacent subsegment. (This overwrites the stack info.) */
11532 tsdissolve(checktri);
11533 sym(checktri, checkneighbor);
11534 if (checkneighbor.tri == m->dummytri) {
11535 insertsubseg(m, b, &checktri, 1);
11536 hullsize++;
11537 }
11538 decode(nexttri, checktri);
11539 }
11540 }
11541
11542 trifree((VOID *) vertexarray);
11543 return hullsize;
11544}
11545
11546#endif /* not CDT_ONLY */
11547
11548/** **/
11549/** **/
11550/********* General mesh construction routines end here *********/
11551
11552/********* Segment insertion begins here *********/
11553/** **/
11554/** **/
11555
11556/*****************************************************************************/
11557/* */
11558/* finddirection() Find the first triangle on the path from one point */
11559/* to another. */
11560/* */
11561/* Finds the triangle that intersects a line segment drawn from the */
11562/* origin of `searchtri' to the point `searchpoint', and returns the result */
11563/* in `searchtri'. The origin of `searchtri' does not change, even though */
11564/* the triangle returned may differ from the one passed in. This routine */
11565/* is used to find the direction to move in to get from one point to */
11566/* another. */
11567/* */
11568/* The return value notes whether the destination or apex of the found */
11569/* triangle is collinear with the two points in question. */
11570/* */
11571/*****************************************************************************/
11572
11573#ifdef ANSI_DECLARATORS
11574enum finddirectionresult finddirection(struct mesh *m, struct behavior *b,
11575 struct otri *searchtri,
11576 vertex searchpoint)
11577#else /* not ANSI_DECLARATORS */
11578enum finddirectionresult finddirection(m, b, searchtri, searchpoint)
11579struct mesh *m;
11580struct behavior *b;
11581struct otri *searchtri;
11582vertex searchpoint;
11583#endif /* not ANSI_DECLARATORS */
11584
11585{
11586 struct otri checktri;
11587 vertex startvertex;
11588 vertex leftvertex, rightvertex;
11589 REAL leftccw, rightccw;
11590 int leftflag, rightflag;
11591 triangle ptr; /* Temporary variable used by onext() and oprev(). */
11592
11593 org(*searchtri, startvertex);
11594 dest(*searchtri, rightvertex);
11595 apex(*searchtri, leftvertex);
11596 /* Is `searchpoint' to the left? */
11597 leftccw = counterclockwise(m, b, searchpoint, startvertex, leftvertex);
11598 leftflag = leftccw > 0.0;
11599 /* Is `searchpoint' to the right? */
11600 rightccw = counterclockwise(m, b, startvertex, searchpoint, rightvertex);
11601 rightflag = rightccw > 0.0;
11602 if (leftflag && rightflag) {
11603 /* `searchtri' faces directly away from `searchpoint'. We could go left */
11604 /* or right. Ask whether it's a triangle or a boundary on the left. */
11605 onext(*searchtri, checktri);
11606 if (checktri.tri == m->dummytri) {
11607 leftflag = 0;
11608 } else {
11609 rightflag = 0;
11610 }
11611 }
11612 while (leftflag) {
11613 /* Turn left until satisfied. */
11614 onextself(*searchtri);
11615 if (searchtri->tri == m->dummytri) {
11616 printf("Internal error in finddirection(): Unable to find a\n");
11617 printf(" triangle leading from (%.12g, %.12g) to", startvertex[0],
11618 startvertex[1]);
11619 printf(" (%.12g, %.12g).\n", searchpoint[0], searchpoint[1]);
11620 internalerror();
11621 }
11622 apex(*searchtri, leftvertex);
11623 rightccw = leftccw;
11624 leftccw = counterclockwise(m, b, searchpoint, startvertex, leftvertex);
11625 leftflag = leftccw > 0.0;
11626 }
11627 while (rightflag) {
11628 /* Turn right until satisfied. */
11629 oprevself(*searchtri);
11630 if (searchtri->tri == m->dummytri) {
11631 printf("Internal error in finddirection(): Unable to find a\n");
11632 printf(" triangle leading from (%.12g, %.12g) to", startvertex[0],
11633 startvertex[1]);
11634 printf(" (%.12g, %.12g).\n", searchpoint[0], searchpoint[1]);
11635 internalerror();
11636 }
11637 dest(*searchtri, rightvertex);
11638 leftccw = rightccw;
11639 rightccw = counterclockwise(m, b, startvertex, searchpoint, rightvertex);
11640 rightflag = rightccw > 0.0;
11641 }
11642 if (leftccw == 0.0) {
11643 return LEFTCOLLINEAR;
11644 } else if (rightccw == 0.0) {
11645 return RIGHTCOLLINEAR;
11646 } else {
11647 return WITHIN;
11648 }
11649}
11650
11651/*****************************************************************************/
11652/* */
11653/* segmentintersection() Find the intersection of an existing segment */
11654/* and a segment that is being inserted. Insert */
11655/* a vertex at the intersection, splitting an */
11656/* existing subsegment. */
11657/* */
11658/* The segment being inserted connects the apex of splittri to endpoint2. */
11659/* splitsubseg is the subsegment being split, and MUST adjoin splittri. */
11660/* Hence, endpoints of the subsegment being split are the origin and */
11661/* destination of splittri. */
11662/* */
11663/* On completion, splittri is a handle having the newly inserted */
11664/* intersection point as its origin, and endpoint1 as its destination. */
11665/* */
11666/*****************************************************************************/
11667
11668#ifdef ANSI_DECLARATORS
11669void segmentintersection(struct mesh *m, struct behavior *b,
11670 struct otri *splittri, struct osub *splitsubseg,
11671 vertex endpoint2)
11672#else /* not ANSI_DECLARATORS */
11673void segmentintersection(m, b, splittri, splitsubseg, endpoint2)
11674struct mesh *m;
11675struct behavior *b;
11676struct otri *splittri;
11677struct osub *splitsubseg;
11678vertex endpoint2;
11679#endif /* not ANSI_DECLARATORS */
11680
11681{
11682 struct osub opposubseg;
11683 vertex endpoint1;
11684 vertex torg, tdest;
11685 vertex leftvertex, rightvertex;
11686 vertex newvertex;
11687 enum insertvertexresult success;
11688 /* enum finddirectionresult collinear; LM: remove unsed variable warning */
11689 REAL ex, ey;
11690 REAL tx, ty;
11691 REAL etx, ety;
11692 REAL split, denom;
11693 int i;
11694 triangle ptr; /* Temporary variable used by onext(). */
11695 subseg sptr; /* Temporary variable used by snext(). */
11696
11697 /* Find the other three segment endpoints. */
11698 apex(*splittri, endpoint1);
11699 org(*splittri, torg);
11700 dest(*splittri, tdest);
11701 /* Segment intersection formulae; see the Antonio reference. */
11702 tx = tdest[0] - torg[0];
11703 ty = tdest[1] - torg[1];
11704 ex = endpoint2[0] - endpoint1[0];
11705 ey = endpoint2[1] - endpoint1[1];
11706 etx = torg[0] - endpoint2[0];
11707 ety = torg[1] - endpoint2[1];
11708 denom = ty * ex - tx * ey;
11709 if (denom == 0.0) {
11710 printf("Internal error in segmentintersection():");
11711 printf(" Attempt to find intersection of parallel segments.\n");
11712 internalerror();
11713 }
11714 split = (ey * etx - ex * ety) / denom;
11715 /* Create the new vertex. */
11716 newvertex = (vertex) poolalloc(&m->vertices);
11717 /* Interpolate its coordinate and attributes. */
11718 for (i = 0; i < 2 + m->nextras; i++) {
11719 newvertex[i] = torg[i] + split * (tdest[i] - torg[i]);
11720 }
11721 setvertexmark(newvertex, mark(*splitsubseg));
11722 setvertextype(newvertex, INPUTVERTEX);
11723 if (b->verbose > 1) {
11724 printf(
11725 " Splitting subsegment (%.12g, %.12g) (%.12g, %.12g) at (%.12g, %.12g).\n",
11726 torg[0], torg[1], tdest[0], tdest[1], newvertex[0], newvertex[1]);
11727 }
11728 /* Insert the intersection vertex. This should always succeed. */
11729 success = insertvertex(m, b, newvertex, splittri, splitsubseg, 0, 0);
11730 if (success != SUCCESSFULVERTEX) {
11731 printf("Internal error in segmentintersection():\n");
11732 printf(" Failure to split a segment.\n");
11733 internalerror();
11734 }
11735 /* Record a triangle whose origin is the new vertex. */
11736 setvertex2tri(newvertex, encode(*splittri));
11737 if (m->steinerleft > 0) {
11738 m->steinerleft--;
11739 }
11740
11741 /* Divide the segment into two, and correct the segment endpoints. */
11742 ssymself(*splitsubseg);
11743 spivot(*splitsubseg, opposubseg);
11744 sdissolve(*splitsubseg);
11745 sdissolve(opposubseg);
11746 do {
11747 setsegorg(*splitsubseg, newvertex);
11748 snextself(*splitsubseg);
11749 } while (splitsubseg->ss != m->dummysub);
11750 do {
11751 setsegorg(opposubseg, newvertex);
11752 snextself(opposubseg);
11753 } while (opposubseg.ss != m->dummysub);
11754
11755 /* Inserting the vertex may have caused edge flips. We wish to rediscover */
11756 /* the edge connecting endpoint1 to the new intersection vertex. */
11757 /* collinear = LN: remove unsed variable warning */
11758 finddirection(m, b, splittri, endpoint1);
11759 dest(*splittri, rightvertex);
11760 apex(*splittri, leftvertex);
11761 if ((leftvertex[0] == endpoint1[0]) && (leftvertex[1] == endpoint1[1])) {
11762 onextself(*splittri);
11763 } else if ((rightvertex[0] != endpoint1[0]) ||
11764 (rightvertex[1] != endpoint1[1])) {
11765 printf("Internal error in segmentintersection():\n");
11766 printf(" Topological inconsistency after splitting a segment.\n");
11767 internalerror();
11768 }
11769 /* `splittri' should have destination endpoint1. */
11770}
11771
11772/*****************************************************************************/
11773/* */
11774/* scoutsegment() Scout the first triangle on the path from one endpoint */
11775/* to another, and check for completion (reaching the */
11776/* second endpoint), a collinear vertex, or the */
11777/* intersection of two segments. */
11778/* */
11779/* Returns one if the entire segment is successfully inserted, and zero if */
11780/* the job must be finished by conformingedge() or constrainededge(). */
11781/* */
11782/* If the first triangle on the path has the second endpoint as its */
11783/* destination or apex, a subsegment is inserted and the job is done. */
11784/* */
11785/* If the first triangle on the path has a destination or apex that lies on */
11786/* the segment, a subsegment is inserted connecting the first endpoint to */
11787/* the collinear vertex, and the search is continued from the collinear */
11788/* vertex. */
11789/* */
11790/* If the first triangle on the path has a subsegment opposite its origin, */
11791/* then there is a segment that intersects the segment being inserted. */
11792/* Their intersection vertex is inserted, splitting the subsegment. */
11793/* */
11794/*****************************************************************************/
11795
11796#ifdef ANSI_DECLARATORS
11797int scoutsegment(struct mesh *m, struct behavior *b, struct otri *searchtri,
11798 vertex endpoint2, int newmark)
11799#else /* not ANSI_DECLARATORS */
11800int scoutsegment(m, b, searchtri, endpoint2, newmark)
11801struct mesh *m;
11802struct behavior *b;
11803struct otri *searchtri;
11804vertex endpoint2;
11805int newmark;
11806#endif /* not ANSI_DECLARATORS */
11807
11808{
11809 struct otri crosstri;
11810 struct osub crosssubseg;
11811 vertex leftvertex, rightvertex;
11812 enum finddirectionresult collinear;
11813 subseg sptr; /* Temporary variable used by tspivot(). */
11814
11815 collinear = finddirection(m, b, searchtri, endpoint2);
11816 dest(*searchtri, rightvertex);
11817 apex(*searchtri, leftvertex);
11818 if (((leftvertex[0] == endpoint2[0]) && (leftvertex[1] == endpoint2[1])) ||
11819 ((rightvertex[0] == endpoint2[0]) && (rightvertex[1] == endpoint2[1]))) {
11820 /* The segment is already an edge in the mesh. */
11821 if ((leftvertex[0] == endpoint2[0]) && (leftvertex[1] == endpoint2[1])) {
11822 lprevself(*searchtri);
11823 }
11824 /* Insert a subsegment, if there isn't already one there. */
11825 insertsubseg(m, b, searchtri, newmark);
11826 return 1;
11827 } else if (collinear == LEFTCOLLINEAR) {
11828 /* We've collided with a vertex between the segment's endpoints. */
11829 /* Make the collinear vertex be the triangle's origin. */
11830 lprevself(*searchtri);
11831 insertsubseg(m, b, searchtri, newmark);
11832 /* Insert the remainder of the segment. */
11833 return scoutsegment(m, b, searchtri, endpoint2, newmark);
11834 } else if (collinear == RIGHTCOLLINEAR) {
11835 /* We've collided with a vertex between the segment's endpoints. */
11836 insertsubseg(m, b, searchtri, newmark);
11837 /* Make the collinear vertex be the triangle's origin. */
11838 lnextself(*searchtri);
11839 /* Insert the remainder of the segment. */
11840 return scoutsegment(m, b, searchtri, endpoint2, newmark);
11841 } else {
11842 lnext(*searchtri, crosstri);
11843 tspivot(crosstri, crosssubseg);
11844 /* Check for a crossing segment. */
11845 if (crosssubseg.ss == m->dummysub) {
11846 return 0;
11847 } else {
11848 /* Insert a vertex at the intersection. */
11849 segmentintersection(m, b, &crosstri, &crosssubseg, endpoint2);
11850 otricopy(crosstri, *searchtri);
11851 insertsubseg(m, b, searchtri, newmark);
11852 /* Insert the remainder of the segment. */
11853 return scoutsegment(m, b, searchtri, endpoint2, newmark);
11854 }
11855 }
11856}
11857
11858/*****************************************************************************/
11859/* */
11860/* conformingedge() Force a segment into a conforming Delaunay */
11861/* triangulation by inserting a vertex at its midpoint, */
11862/* and recursively forcing in the two half-segments if */
11863/* necessary. */
11864/* */
11865/* Generates a sequence of subsegments connecting `endpoint1' to */
11866/* `endpoint2'. `newmark' is the boundary marker of the segment, assigned */
11867/* to each new splitting vertex and subsegment. */
11868/* */
11869/* Note that conformingedge() does not always maintain the conforming */
11870/* Delaunay property. Once inserted, segments are locked into place; */
11871/* vertices inserted later (to force other segments in) may render these */
11872/* fixed segments non-Delaunay. The conforming Delaunay property will be */
11873/* restored by enforcequality() by splitting encroached subsegments. */
11874/* */
11875/*****************************************************************************/
11876
11877#ifndef REDUCED
11878#ifndef CDT_ONLY
11879
11880#ifdef ANSI_DECLARATORS
11881void conformingedge(struct mesh *m, struct behavior *b,
11882 vertex endpoint1, vertex endpoint2, int newmark)
11883#else /* not ANSI_DECLARATORS */
11884void conformingedge(m, b, endpoint1, endpoint2, newmark)
11885struct mesh *m;
11886struct behavior *b;
11887vertex endpoint1;
11888vertex endpoint2;
11889int newmark;
11890#endif /* not ANSI_DECLARATORS */
11891
11892{
11893 struct otri searchtri1, searchtri2;
11894 struct osub brokensubseg;
11895 vertex newvertex;
11896 vertex midvertex1, midvertex2;
11897 enum insertvertexresult success;
11898 int i;
11899 subseg sptr; /* Temporary variable used by tspivot(). */
11900
11901 if (b->verbose > 2) {
11902 printf("Forcing segment into triangulation by recursive splitting:\n");
11903 printf(" (%.12g, %.12g) (%.12g, %.12g)\n", endpoint1[0], endpoint1[1],
11904 endpoint2[0], endpoint2[1]);
11905 }
11906 /* Create a new vertex to insert in the middle of the segment. */
11907 newvertex = (vertex) poolalloc(&m->vertices);
11908 /* Interpolate coordinates and attributes. */
11909 for (i = 0; i < 2 + m->nextras; i++) {
11910 newvertex[i] = 0.5 * (endpoint1[i] + endpoint2[i]);
11911 }
11912 setvertexmark(newvertex, newmark);
11913 setvertextype(newvertex, SEGMENTVERTEX);
11914 /* No known triangle to search from. */
11915 searchtri1.tri = m->dummytri;
11916 /* Attempt to insert the new vertex. */
11917 success = insertvertex(m, b, newvertex, &searchtri1, (struct osub *) NULL,
11918 0, 0);
11919 if (success == DUPLICATEVERTEX) {
11920 if (b->verbose > 2) {
11921 printf(" Segment intersects existing vertex (%.12g, %.12g).\n",
11922 newvertex[0], newvertex[1]);
11923 }
11924 /* Use the vertex that's already there. */
11925 vertexdealloc(m, newvertex);
11926 org(searchtri1, newvertex);
11927 } else {
11928 if (success == VIOLATINGVERTEX) {
11929 if (b->verbose > 2) {
11930 printf(" Two segments intersect at (%.12g, %.12g).\n",
11931 newvertex[0], newvertex[1]);
11932 }
11933 /* By fluke, we've landed right on another segment. Split it. */
11934 tspivot(searchtri1, brokensubseg);
11935 success = insertvertex(m, b, newvertex, &searchtri1, &brokensubseg,
11936 0, 0);
11937 if (success != SUCCESSFULVERTEX) {
11938 printf("Internal error in conformingedge():\n");
11939 printf(" Failure to split a segment.\n");
11940 internalerror();
11941 }
11942 }
11943 /* The vertex has been inserted successfully. */
11944 if (m->steinerleft > 0) {
11945 m->steinerleft--;
11946 }
11947 }
11948 otricopy(searchtri1, searchtri2);
11949 /* `searchtri1' and `searchtri2' are fastened at their origins to */
11950 /* `newvertex', and will be directed toward `endpoint1' and `endpoint2' */
11951 /* respectively. First, we must get `searchtri2' out of the way so it */
11952 /* won't be invalidated during the insertion of the first half of the */
11953 /* segment. */
11954 finddirection(m, b, &searchtri2, endpoint2);
11955 if (!scoutsegment(m, b, &searchtri1, endpoint1, newmark)) {
11956 /* The origin of searchtri1 may have changed if a collision with an */
11957 /* intervening vertex on the segment occurred. */
11958 org(searchtri1, midvertex1);
11959 conformingedge(m, b, midvertex1, endpoint1, newmark);
11960 }
11961 if (!scoutsegment(m, b, &searchtri2, endpoint2, newmark)) {
11962 /* The origin of searchtri2 may have changed if a collision with an */
11963 /* intervening vertex on the segment occurred. */
11964 org(searchtri2, midvertex2);
11965 conformingedge(m, b, midvertex2, endpoint2, newmark);
11966 }
11967}
11968
11969#endif /* not CDT_ONLY */
11970#endif /* not REDUCED */
11971
11972/*****************************************************************************/
11973/* */
11974/* delaunayfixup() Enforce the Delaunay condition at an edge, fanning out */
11975/* recursively from an existing vertex. Pay special */
11976/* attention to stacking inverted triangles. */
11977/* */
11978/* This is a support routine for inserting segments into a constrained */
11979/* Delaunay triangulation. */
11980/* */
11981/* The origin of fixuptri is treated as if it has just been inserted, and */
11982/* the local Delaunay condition needs to be enforced. It is only enforced */
11983/* in one sector, however, that being the angular range defined by */
11984/* fixuptri. */
11985/* */
11986/* This routine also needs to make decisions regarding the "stacking" of */
11987/* triangles. (Read the description of constrainededge() below before */
11988/* reading on here, so you understand the algorithm.) If the position of */
11989/* the new vertex (the origin of fixuptri) indicates that the vertex before */
11990/* it on the polygon is a reflex vertex, then "stack" the triangle by */
11991/* doing nothing. (fixuptri is an inverted triangle, which is how stacked */
11992/* triangles are identified.) */
11993/* */
11994/* Otherwise, check whether the vertex before that was a reflex vertex. */
11995/* If so, perform an edge flip, thereby eliminating an inverted triangle */
11996/* (popping it off the stack). The edge flip may result in the creation */
11997/* of a new inverted triangle, depending on whether or not the new vertex */
11998/* is visible to the vertex three edges behind on the polygon. */
11999/* */
12000/* If neither of the two vertices behind the new vertex are reflex */
12001/* vertices, fixuptri and fartri, the triangle opposite it, are not */
12002/* inverted; hence, ensure that the edge between them is locally Delaunay. */
12003/* */
12004/* `leftside' indicates whether or not fixuptri is to the left of the */
12005/* segment being inserted. (Imagine that the segment is pointing up from */
12006/* endpoint1 to endpoint2.) */
12007/* */
12008/*****************************************************************************/
12009
12010#ifdef ANSI_DECLARATORS
12011void delaunayfixup(struct mesh *m, struct behavior *b,
12012 struct otri *fixuptri, int leftside)
12013#else /* not ANSI_DECLARATORS */
12014void delaunayfixup(m, b, fixuptri, leftside)
12015struct mesh *m;
12016struct behavior *b;
12017struct otri *fixuptri;
12018int leftside;
12019#endif /* not ANSI_DECLARATORS */
12020
12021{
12022 struct otri neartri;
12023 struct otri fartri;
12024 struct osub faredge;
12025 vertex nearvertex, leftvertex, rightvertex, farvertex;
12026 triangle ptr; /* Temporary variable used by sym(). */
12027 subseg sptr; /* Temporary variable used by tspivot(). */
12028
12029 lnext(*fixuptri, neartri);
12030 sym(neartri, fartri);
12031 /* Check if the edge opposite the origin of fixuptri can be flipped. */
12032 if (fartri.tri == m->dummytri) {
12033 return;
12034 }
12035 tspivot(neartri, faredge);
12036 if (faredge.ss != m->dummysub) {
12037 return;
12038 }
12039 /* Find all the relevant vertices. */
12040 apex(neartri, nearvertex);
12041 org(neartri, leftvertex);
12042 dest(neartri, rightvertex);
12043 apex(fartri, farvertex);
12044 /* Check whether the previous polygon vertex is a reflex vertex. */
12045 if (leftside) {
12046 if (counterclockwise(m, b, nearvertex, leftvertex, farvertex) <= 0.0) {
12047 /* leftvertex is a reflex vertex too. Nothing can */
12048 /* be done until a convex section is found. */
12049 return;
12050 }
12051 } else {
12052 if (counterclockwise(m, b, farvertex, rightvertex, nearvertex) <= 0.0) {
12053 /* rightvertex is a reflex vertex too. Nothing can */
12054 /* be done until a convex section is found. */
12055 return;
12056 }
12057 }
12058 if (counterclockwise(m, b, rightvertex, leftvertex, farvertex) > 0.0) {
12059 /* fartri is not an inverted triangle, and farvertex is not a reflex */
12060 /* vertex. As there are no reflex vertices, fixuptri isn't an */
12061 /* inverted triangle, either. Hence, test the edge between the */
12062 /* triangles to ensure it is locally Delaunay. */
12063 if (incircle(m, b, leftvertex, farvertex, rightvertex, nearvertex) <=
12064 0.0) {
12065 return;
12066 }
12067 /* Not locally Delaunay; go on to an edge flip. */
12068 } /* else fartri is inverted; remove it from the stack by flipping. */
12069 flip(m, b, &neartri);
12070 lprevself(*fixuptri); /* Restore the origin of fixuptri after the flip. */
12071 /* Recursively process the two triangles that result from the flip. */
12072 delaunayfixup(m, b, fixuptri, leftside);
12073 delaunayfixup(m, b, &fartri, leftside);
12074}
12075
12076/*****************************************************************************/
12077/* */
12078/* constrainededge() Force a segment into a constrained Delaunay */
12079/* triangulation by deleting the triangles it */
12080/* intersects, and triangulating the polygons that */
12081/* form on each side of it. */
12082/* */
12083/* Generates a single subsegment connecting `endpoint1' to `endpoint2'. */
12084/* The triangle `starttri' has `endpoint1' as its origin. `newmark' is the */
12085/* boundary marker of the segment. */
12086/* */
12087/* To insert a segment, every triangle whose interior intersects the */
12088/* segment is deleted. The union of these deleted triangles is a polygon */
12089/* (which is not necessarily monotone, but is close enough), which is */
12090/* divided into two polygons by the new segment. This routine's task is */
12091/* to generate the Delaunay triangulation of these two polygons. */
12092/* */
12093/* You might think of this routine's behavior as a two-step process. The */
12094/* first step is to walk from endpoint1 to endpoint2, flipping each edge */
12095/* encountered. This step creates a fan of edges connected to endpoint1, */
12096/* including the desired edge to endpoint2. The second step enforces the */
12097/* Delaunay condition on each side of the segment in an incremental manner: */
12098/* proceeding along the polygon from endpoint1 to endpoint2 (this is done */
12099/* independently on each side of the segment), each vertex is "enforced" */
12100/* as if it had just been inserted, but affecting only the previous */
12101/* vertices. The result is the same as if the vertices had been inserted */
12102/* in the order they appear on the polygon, so the result is Delaunay. */
12103/* */
12104/* In truth, constrainededge() interleaves these two steps. The procedure */
12105/* walks from endpoint1 to endpoint2, and each time an edge is encountered */
12106/* and flipped, the newly exposed vertex (at the far end of the flipped */
12107/* edge) is "enforced" upon the previously flipped edges, usually affecting */
12108/* only one side of the polygon (depending upon which side of the segment */
12109/* the vertex falls on). */
12110/* */
12111/* The algorithm is complicated by the need to handle polygons that are not */
12112/* convex. Although the polygon is not necessarily monotone, it can be */
12113/* triangulated in a manner similar to the stack-based algorithms for */
12114/* monotone polygons. For each reflex vertex (local concavity) of the */
12115/* polygon, there will be an inverted triangle formed by one of the edge */
12116/* flips. (An inverted triangle is one with negative area - that is, its */
12117/* vertices are arranged in clockwise order - and is best thought of as a */
12118/* wrinkle in the fabric of the mesh.) Each inverted triangle can be */
12119/* thought of as a reflex vertex pushed on the stack, waiting to be fixed */
12120/* later. */
12121/* */
12122/* A reflex vertex is popped from the stack when a vertex is inserted that */
12123/* is visible to the reflex vertex. (However, if the vertex behind the */
12124/* reflex vertex is not visible to the reflex vertex, a new inverted */
12125/* triangle will take its place on the stack.) These details are handled */
12126/* by the delaunayfixup() routine above. */
12127/* */
12128/*****************************************************************************/
12129
12130#ifdef ANSI_DECLARATORS
12131void constrainededge(struct mesh *m, struct behavior *b,
12132 struct otri *starttri, vertex endpoint2, int newmark)
12133#else /* not ANSI_DECLARATORS */
12134void constrainededge(m, b, starttri, endpoint2, newmark)
12135struct mesh *m;
12136struct behavior *b;
12137struct otri *starttri;
12138vertex endpoint2;
12139int newmark;
12140#endif /* not ANSI_DECLARATORS */
12141
12142{
12143 struct otri fixuptri, fixuptri2;
12144 struct osub crosssubseg;
12145 vertex endpoint1;
12146 vertex farvertex;
12147 REAL area;
12148 int collision;
12149 int done;
12150 triangle ptr; /* Temporary variable used by sym() and oprev(). */
12151 subseg sptr; /* Temporary variable used by tspivot(). */
12152
12153 org(*starttri, endpoint1);
12154 lnext(*starttri, fixuptri);
12155 flip(m, b, &fixuptri);
12156 /* `collision' indicates whether we have found a vertex directly */
12157 /* between endpoint1 and endpoint2. */
12158 collision = 0;
12159 done = 0;
12160 do {
12161 org(fixuptri, farvertex);
12162 /* `farvertex' is the extreme point of the polygon we are "digging" */
12163 /* to get from endpoint1 to endpoint2. */
12164 if ((farvertex[0] == endpoint2[0]) && (farvertex[1] == endpoint2[1])) {
12165 oprev(fixuptri, fixuptri2);
12166 /* Enforce the Delaunay condition around endpoint2. */
12167 delaunayfixup(m, b, &fixuptri, 0);
12168 delaunayfixup(m, b, &fixuptri2, 1);
12169 done = 1;
12170 } else {
12171 /* Check whether farvertex is to the left or right of the segment */
12172 /* being inserted, to decide which edge of fixuptri to dig */
12173 /* through next. */
12174 area = counterclockwise(m, b, endpoint1, endpoint2, farvertex);
12175 if (area == 0.0) {
12176 /* We've collided with a vertex between endpoint1 and endpoint2. */
12177 collision = 1;
12178 oprev(fixuptri, fixuptri2);
12179 /* Enforce the Delaunay condition around farvertex. */
12180 delaunayfixup(m, b, &fixuptri, 0);
12181 delaunayfixup(m, b, &fixuptri2, 1);
12182 done = 1;
12183 } else {
12184 if (area > 0.0) { /* farvertex is to the left of the segment. */
12185 oprev(fixuptri, fixuptri2);
12186 /* Enforce the Delaunay condition around farvertex, on the */
12187 /* left side of the segment only. */
12188 delaunayfixup(m, b, &fixuptri2, 1);
12189 /* Flip the edge that crosses the segment. After the edge is */
12190 /* flipped, one of its endpoints is the fan vertex, and the */
12191 /* destination of fixuptri is the fan vertex. */
12192 lprevself(fixuptri);
12193 } else { /* farvertex is to the right of the segment. */
12194 delaunayfixup(m, b, &fixuptri, 0);
12195 /* Flip the edge that crosses the segment. After the edge is */
12196 /* flipped, one of its endpoints is the fan vertex, and the */
12197 /* destination of fixuptri is the fan vertex. */
12198 oprevself(fixuptri);
12199 }
12200 /* Check for two intersecting segments. */
12201 tspivot(fixuptri, crosssubseg);
12202 if (crosssubseg.ss == m->dummysub) {
12203 flip(m, b, &fixuptri); /* May create inverted triangle at left. */
12204 } else {
12205 /* We've collided with a segment between endpoint1 and endpoint2. */
12206 collision = 1;
12207 /* Insert a vertex at the intersection. */
12208 segmentintersection(m, b, &fixuptri, &crosssubseg, endpoint2);
12209 done = 1;
12210 }
12211 }
12212 }
12213 } while (!done);
12214 /* Insert a subsegment to make the segment permanent. */
12215 insertsubseg(m, b, &fixuptri, newmark);
12216 /* If there was a collision with an interceding vertex, install another */
12217 /* segment connecting that vertex with endpoint2. */
12218 if (collision) {
12219 /* Insert the remainder of the segment. */
12220 if (!scoutsegment(m, b, &fixuptri, endpoint2, newmark)) {
12221 constrainededge(m, b, &fixuptri, endpoint2, newmark);
12222 }
12223 }
12224}
12225
12226/*****************************************************************************/
12227/* */
12228/* insertsegment() Insert a PSLG segment into a triangulation. */
12229/* */
12230/*****************************************************************************/
12231
12232#ifdef ANSI_DECLARATORS
12233void insertsegment(struct mesh *m, struct behavior *b,
12234 vertex endpoint1, vertex endpoint2, int newmark)
12235#else /* not ANSI_DECLARATORS */
12236void insertsegment(m, b, endpoint1, endpoint2, newmark)
12237struct mesh *m;
12238struct behavior *b;
12239vertex endpoint1;
12240vertex endpoint2;
12241int newmark;
12242#endif /* not ANSI_DECLARATORS */
12243
12244{
12245 struct otri searchtri1, searchtri2;
12246 triangle encodedtri;
12247 vertex checkvertex;
12248 triangle ptr; /* Temporary variable used by sym(). */
12249
12250 if (b->verbose > 1) {
12251 printf(" Connecting (%.12g, %.12g) to (%.12g, %.12g).\n",
12252 endpoint1[0], endpoint1[1], endpoint2[0], endpoint2[1]);
12253 }
12254
12255 /* Find a triangle whose origin is the segment's first endpoint. */
12256 checkvertex = (vertex) NULL;
12257 encodedtri = vertex2tri(endpoint1);
12258 if (encodedtri != (triangle) NULL) {
12259 decode(encodedtri, searchtri1);
12260 org(searchtri1, checkvertex);
12261 }
12262 if (checkvertex != endpoint1) {
12263 /* Find a boundary triangle to search from. */
12264 searchtri1.tri = m->dummytri;
12265 searchtri1.orient = 0;
12266 symself(searchtri1);
12267 /* Search for the segment's first endpoint by point location. */
12268 if (locate(m, b, endpoint1, &searchtri1) != ONVERTEX) {
12269 printf(
12270 "Internal error in insertsegment(): Unable to locate PSLG vertex\n");
12271 printf(" (%.12g, %.12g) in triangulation.\n",
12272 endpoint1[0], endpoint1[1]);
12273 internalerror();
12274 }
12275 }
12276 /* Remember this triangle to improve subsequent point location. */
12277 otricopy(searchtri1, m->recenttri);
12278 /* Scout the beginnings of a path from the first endpoint */
12279 /* toward the second. */
12280 if (scoutsegment(m, b, &searchtri1, endpoint2, newmark)) {
12281 /* The segment was easily inserted. */
12282 return;
12283 }
12284 /* The first endpoint may have changed if a collision with an intervening */
12285 /* vertex on the segment occurred. */
12286 org(searchtri1, endpoint1);
12287
12288 /* Find a triangle whose origin is the segment's second endpoint. */
12289 checkvertex = (vertex) NULL;
12290 encodedtri = vertex2tri(endpoint2);
12291 if (encodedtri != (triangle) NULL) {
12292 decode(encodedtri, searchtri2);
12293 org(searchtri2, checkvertex);
12294 }
12295 if (checkvertex != endpoint2) {
12296 /* Find a boundary triangle to search from. */
12297 searchtri2.tri = m->dummytri;
12298 searchtri2.orient = 0;
12299 symself(searchtri2);
12300 /* Search for the segment's second endpoint by point location. */
12301 if (locate(m, b, endpoint2, &searchtri2) != ONVERTEX) {
12302 printf(
12303 "Internal error in insertsegment(): Unable to locate PSLG vertex\n");
12304 printf(" (%.12g, %.12g) in triangulation.\n",
12305 endpoint2[0], endpoint2[1]);
12306 internalerror();
12307 }
12308 }
12309 /* Remember this triangle to improve subsequent point location. */
12310 otricopy(searchtri2, m->recenttri);
12311 /* Scout the beginnings of a path from the second endpoint */
12312 /* toward the first. */
12313 if (scoutsegment(m, b, &searchtri2, endpoint1, newmark)) {
12314 /* The segment was easily inserted. */
12315 return;
12316 }
12317 /* The second endpoint may have changed if a collision with an intervening */
12318 /* vertex on the segment occurred. */
12319 org(searchtri2, endpoint2);
12320
12321#ifndef REDUCED
12322#ifndef CDT_ONLY
12323 if (b->splitseg) {
12324 /* Insert vertices to force the segment into the triangulation. */
12325 conformingedge(m, b, endpoint1, endpoint2, newmark);
12326 } else {
12327#endif /* not CDT_ONLY */
12328#endif /* not REDUCED */
12329 /* Insert the segment directly into the triangulation. */
12330 constrainededge(m, b, &searchtri1, endpoint2, newmark);
12331#ifndef REDUCED
12332#ifndef CDT_ONLY
12333 }
12334#endif /* not CDT_ONLY */
12335#endif /* not REDUCED */
12336}
12337
12338/*****************************************************************************/
12339/* */
12340/* markhull() Cover the convex hull of a triangulation with subsegments. */
12341/* */
12342/*****************************************************************************/
12343
12344#ifdef ANSI_DECLARATORS
12345void markhull(struct mesh *m, struct behavior *b)
12346#else /* not ANSI_DECLARATORS */
12347void markhull(m, b)
12348struct mesh *m;
12349struct behavior *b;
12350#endif /* not ANSI_DECLARATORS */
12351
12352{
12353 struct otri hulltri;
12354 struct otri nexttri;
12355 struct otri starttri;
12356 triangle ptr; /* Temporary variable used by sym() and oprev(). */
12357
12358 /* Find a triangle handle on the hull. */
12359 hulltri.tri = m->dummytri;
12360 hulltri.orient = 0;
12361 symself(hulltri);
12362 /* Remember where we started so we know when to stop. */
12363 otricopy(hulltri, starttri);
12364 /* Go once counterclockwise around the convex hull. */
12365 do {
12366 /* Create a subsegment if there isn't already one here. */
12367 insertsubseg(m, b, &hulltri, 1);
12368 /* To find the next hull edge, go clockwise around the next vertex. */
12369 lnextself(hulltri);
12370 oprev(hulltri, nexttri);
12371 while (nexttri.tri != m->dummytri) {
12372 otricopy(nexttri, hulltri);
12373 oprev(hulltri, nexttri);
12374 }
12375 } while (!otriequal(hulltri, starttri));
12376}
12377
12378/*****************************************************************************/
12379/* */
12380/* formskeleton() Create the segments of a triangulation, including PSLG */
12381/* segments and edges on the convex hull. */
12382/* */
12383/* The PSLG segments are read from a .poly file. The return value is the */
12384/* number of segments in the file. */
12385/* */
12386/*****************************************************************************/
12387
12388#ifdef TRILIBRARY
12389
12390#ifdef ANSI_DECLARATORS
12391void formskeleton(struct mesh *m, struct behavior *b, int *segmentlist,
12392 int *segmentmarkerlist, int numberofsegments)
12393#else /* not ANSI_DECLARATORS */
12394void formskeleton(m, b, segmentlist, segmentmarkerlist, numberofsegments)
12395struct mesh *m;
12396struct behavior *b;
12397int *segmentlist;
12398int *segmentmarkerlist;
12399int numberofsegments;
12400#endif /* not ANSI_DECLARATORS */
12401
12402#else /* not TRILIBRARY */
12403
12404#ifdef ANSI_DECLARATORS
12405void formskeleton(struct mesh *m, struct behavior *b,
12406 FILE *polyfile, char *polyfilename)
12407#else /* not ANSI_DECLARATORS */
12408void formskeleton(m, b, polyfile, polyfilename)
12409struct mesh *m;
12410struct behavior *b;
12411FILE *polyfile;
12412char *polyfilename;
12413#endif /* not ANSI_DECLARATORS */
12414
12415#endif /* not TRILIBRARY */
12416
12417{
12418#ifdef TRILIBRARY
12419 char polyfilename[6];
12420 int index;
12421#else /* not TRILIBRARY */
12422 char inputline[INPUTLINESIZE];
12423 char *stringptr;
12424#endif /* not TRILIBRARY */
12425 vertex endpoint1, endpoint2;
12426 int segmentmarkers;
12427 int end1, end2;
12428 int boundmarker;
12429 int i;
12430
12431 if (b->poly) {
12432 if (!b->quiet) {
12433 printf("Recovering segments in Delaunay triangulation.\n");
12434 }
12435#ifdef TRILIBRARY
12436 strcpy(polyfilename, "input");
12437 m->insegments = numberofsegments;
12438 segmentmarkers = segmentmarkerlist != (int *) NULL;
12439 index = 0;
12440#else /* not TRILIBRARY */
12441 /* Read the segments from a .poly file. */
12442 /* Read number of segments and number of boundary markers. */
12443 stringptr = readline(inputline, polyfile, polyfilename);
12444 m->insegments = (int) strtol(stringptr, &stringptr, 0);
12445 stringptr = findfield(stringptr);
12446 if (*stringptr == '\0') {
12447 segmentmarkers = 0;
12448 } else {
12449 segmentmarkers = (int) strtol(stringptr, &stringptr, 0);
12450 }
12451#endif /* not TRILIBRARY */
12452 /* If the input vertices are collinear, there is no triangulation, */
12453 /* so don't try to insert segments. */
12454 if (m->triangles.items == 0) {
12455 return;
12456 }
12457
12458 /* If segments are to be inserted, compute a mapping */
12459 /* from vertices to triangles. */
12460 if (m->insegments > 0) {
12461 makevertexmap(m, b);
12462 if (b->verbose) {
12463 printf(" Recovering PSLG segments.\n");
12464 }
12465 }
12466
12467 boundmarker = 0;
12468 /* Read and insert the segments. */
12469 for (i = 0; i < m->insegments; i++) {
12470#ifdef TRILIBRARY
12471 end1 = segmentlist[index++];
12472 end2 = segmentlist[index++];
12473 if (segmentmarkers) {
12474 boundmarker = segmentmarkerlist[i];
12475 }
12476#else /* not TRILIBRARY */
12477 stringptr = readline(inputline, polyfile, b->inpolyfilename);
12478 stringptr = findfield(stringptr);
12479 if (*stringptr == '\0') {
12480 printf("Error: Segment %d has no endpoints in %s.\n",
12481 b->firstnumber + i, polyfilename);
12482 triexit(1);
12483 } else {
12484 end1 = (int) strtol(stringptr, &stringptr, 0);
12485 }
12486 stringptr = findfield(stringptr);
12487 if (*stringptr == '\0') {
12488 printf("Error: Segment %d is missing its second endpoint in %s.\n",
12489 b->firstnumber + i, polyfilename);
12490 triexit(1);
12491 } else {
12492 end2 = (int) strtol(stringptr, &stringptr, 0);
12493 }
12494 if (segmentmarkers) {
12495 stringptr = findfield(stringptr);
12496 if (*stringptr == '\0') {
12497 boundmarker = 0;
12498 } else {
12499 boundmarker = (int) strtol(stringptr, &stringptr, 0);
12500 }
12501 }
12502#endif /* not TRILIBRARY */
12503 if ((end1 < b->firstnumber) ||
12504 (end1 >= b->firstnumber + m->invertices)) {
12505 if (!b->quiet) {
12506 printf("Warning: Invalid first endpoint of segment %d in %s.\n",
12507 b->firstnumber + i, polyfilename);
12508 }
12509 } else if ((end2 < b->firstnumber) ||
12510 (end2 >= b->firstnumber + m->invertices)) {
12511 if (!b->quiet) {
12512 printf("Warning: Invalid second endpoint of segment %d in %s.\n",
12513 b->firstnumber + i, polyfilename);
12514 }
12515 } else {
12516 /* Find the vertices numbered `end1' and `end2'. */
12517 endpoint1 = getvertex(m, b, end1);
12518 endpoint2 = getvertex(m, b, end2);
12519 if ((endpoint1[0] == endpoint2[0]) && (endpoint1[1] == endpoint2[1])) {
12520 if (!b->quiet) {
12521 printf("Warning: Endpoints of segment %d are coincident in %s.\n",
12522 b->firstnumber + i, polyfilename);
12523 }
12524 } else {
12525 insertsegment(m, b, endpoint1, endpoint2, boundmarker);
12526 }
12527 }
12528 }
12529 } else {
12530 m->insegments = 0;
12531 }
12532 if (b->convex || !b->poly) {
12533 /* Enclose the convex hull with subsegments. */
12534 if (b->verbose) {
12535 printf(" Enclosing convex hull with segments.\n");
12536 }
12537 markhull(m, b);
12538 }
12539}
12540
12541/** **/
12542/** **/
12543/********* Segment insertion ends here *********/
12544
12545/********* Carving out holes and concavities begins here *********/
12546/** **/
12547/** **/
12548
12549/*****************************************************************************/
12550/* */
12551/* infecthull() Virally infect all of the triangles of the convex hull */
12552/* that are not protected by subsegments. Where there are */
12553/* subsegments, set boundary markers as appropriate. */
12554/* */
12555/*****************************************************************************/
12556
12557#ifdef ANSI_DECLARATORS
12558void infecthull(struct mesh *m, struct behavior *b)
12559#else /* not ANSI_DECLARATORS */
12560void infecthull(m, b)
12561struct mesh *m;
12562struct behavior *b;
12563#endif /* not ANSI_DECLARATORS */
12564
12565{
12566 struct otri hulltri;
12567 struct otri nexttri;
12568 struct otri starttri;
12569 struct osub hullsubseg;
12570 triangle **deadtriangle;
12571 vertex horg, hdest;
12572 triangle ptr; /* Temporary variable used by sym(). */
12573 subseg sptr; /* Temporary variable used by tspivot(). */
12574
12575 if (b->verbose) {
12576 printf(" Marking concavities (external triangles) for elimination.\n");
12577 }
12578 /* Find a triangle handle on the hull. */
12579 hulltri.tri = m->dummytri;
12580 hulltri.orient = 0;
12581 symself(hulltri);
12582 /* Remember where we started so we know when to stop. */
12583 otricopy(hulltri, starttri);
12584 /* Go once counterclockwise around the convex hull. */
12585 do {
12586 /* Ignore triangles that are already infected. */
12587 if (!infected(hulltri)) {
12588 /* Is the triangle protected by a subsegment? */
12589 tspivot(hulltri, hullsubseg);
12590 if (hullsubseg.ss == m->dummysub) {
12591 /* The triangle is not protected; infect it. */
12592 if (!infected(hulltri)) {
12593 infect(hulltri);
12594 deadtriangle = (triangle **) poolalloc(&m->viri);
12595 *deadtriangle = hulltri.tri;
12596 }
12597 } else {
12598 /* The triangle is protected; set boundary markers if appropriate. */
12599 if (mark(hullsubseg) == 0) {
12600 setmark(hullsubseg, 1);
12601 org(hulltri, horg);
12602 dest(hulltri, hdest);
12603 if (vertexmark(horg) == 0) {
12604 setvertexmark(horg, 1);
12605 }
12606 if (vertexmark(hdest) == 0) {
12607 setvertexmark(hdest, 1);
12608 }
12609 }
12610 }
12611 }
12612 /* To find the next hull edge, go clockwise around the next vertex. */
12613 lnextself(hulltri);
12614 oprev(hulltri, nexttri);
12615 while (nexttri.tri != m->dummytri) {
12616 otricopy(nexttri, hulltri);
12617 oprev(hulltri, nexttri);
12618 }
12619 } while (!otriequal(hulltri, starttri));
12620}
12621
12622/*****************************************************************************/
12623/* */
12624/* plague() Spread the virus from all infected triangles to any neighbors */
12625/* not protected by subsegments. Delete all infected triangles. */
12626/* */
12627/* This is the procedure that actually creates holes and concavities. */
12628/* */
12629/* This procedure operates in two phases. The first phase identifies all */
12630/* the triangles that will die, and marks them as infected. They are */
12631/* marked to ensure that each triangle is added to the virus pool only */
12632/* once, so the procedure will terminate. */
12633/* */
12634/* The second phase actually eliminates the infected triangles. It also */
12635/* eliminates orphaned vertices. */
12636/* */
12637/*****************************************************************************/
12638
12639#ifdef ANSI_DECLARATORS
12640void plague(struct mesh *m, struct behavior *b)
12641#else /* not ANSI_DECLARATORS */
12642void plague(m, b)
12643struct mesh *m;
12644struct behavior *b;
12645#endif /* not ANSI_DECLARATORS */
12646
12647{
12648 struct otri testtri;
12649 struct otri neighbor;
12650 triangle **virusloop;
12651 triangle **deadtriangle;
12652 struct osub neighborsubseg;
12653 vertex testvertex;
12654 vertex norg, ndest;
12655 vertex deadorg, deaddest, deadapex;
12656 int killorg;
12657 triangle ptr; /* Temporary variable used by sym() and onext(). */
12658 subseg sptr; /* Temporary variable used by tspivot(). */
12659
12660 if (b->verbose) {
12661 printf(" Marking neighbors of marked triangles.\n");
12662 }
12663 /* Loop through all the infected triangles, spreading the virus to */
12664 /* their neighbors, then to their neighbors' neighbors. */
12665 traversalinit(&m->viri);
12666 virusloop = (triangle **) traverse(&m->viri);
12667 while (virusloop != (triangle **) NULL) {
12668 testtri.tri = *virusloop;
12669 /* A triangle is marked as infected by messing with one of its pointers */
12670 /* to subsegments, setting it to an illegal value. Hence, we have to */
12671 /* temporarily uninfect this triangle so that we can examine its */
12672 /* adjacent subsegments. */
12673 uninfect(testtri);
12674 if (b->verbose > 2) {
12675 /* Assign the triangle an orientation for convenience in */
12676 /* checking its vertices. */
12677 testtri.orient = 0;
12678 org(testtri, deadorg);
12679 dest(testtri, deaddest);
12680 apex(testtri, deadapex);
12681 printf(" Checking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
12682 deadorg[0], deadorg[1], deaddest[0], deaddest[1],
12683 deadapex[0], deadapex[1]);
12684 }
12685 /* Check each of the triangle's three neighbors. */
12686 for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
12687 /* Find the neighbor. */
12688 sym(testtri, neighbor);
12689 /* Check for a subsegment between the triangle and its neighbor. */
12690 tspivot(testtri, neighborsubseg);
12691 /* Check if the neighbor is nonexistent or already infected. */
12692 if ((neighbor.tri == m->dummytri) || infected(neighbor)) {
12693 if (neighborsubseg.ss != m->dummysub) {
12694 /* There is a subsegment separating the triangle from its */
12695 /* neighbor, but both triangles are dying, so the subsegment */
12696 /* dies too. */
12697 subsegdealloc(m, neighborsubseg.ss);
12698 if (neighbor.tri != m->dummytri) {
12699 /* Make sure the subsegment doesn't get deallocated again */
12700 /* later when the infected neighbor is visited. */
12701 uninfect(neighbor);
12702 tsdissolve(neighbor);
12703 infect(neighbor);
12704 }
12705 }
12706 } else { /* The neighbor exists and is not infected. */
12707 if (neighborsubseg.ss == m->dummysub) {
12708 /* There is no subsegment protecting the neighbor, so */
12709 /* the neighbor becomes infected. */
12710 if (b->verbose > 2) {
12711 org(neighbor, deadorg);
12712 dest(neighbor, deaddest);
12713 apex(neighbor, deadapex);
12714 printf(
12715 " Marking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
12716 deadorg[0], deadorg[1], deaddest[0], deaddest[1],
12717 deadapex[0], deadapex[1]);
12718 }
12719 infect(neighbor);
12720 /* Ensure that the neighbor's neighbors will be infected. */
12721 deadtriangle = (triangle **) poolalloc(&m->viri);
12722 *deadtriangle = neighbor.tri;
12723 } else { /* The neighbor is protected by a subsegment. */
12724 /* Remove this triangle from the subsegment. */
12725 stdissolve(neighborsubseg);
12726 /* The subsegment becomes a boundary. Set markers accordingly. */
12727 if (mark(neighborsubseg) == 0) {
12728 setmark(neighborsubseg, 1);
12729 }
12730 org(neighbor, norg);
12731 dest(neighbor, ndest);
12732 if (vertexmark(norg) == 0) {
12733 setvertexmark(norg, 1);
12734 }
12735 if (vertexmark(ndest) == 0) {
12736 setvertexmark(ndest, 1);
12737 }
12738 }
12739 }
12740 }
12741 /* Remark the triangle as infected, so it doesn't get added to the */
12742 /* virus pool again. */
12743 infect(testtri);
12744 virusloop = (triangle **) traverse(&m->viri);
12745 }
12746
12747 if (b->verbose) {
12748 printf(" Deleting marked triangles.\n");
12749 }
12750
12751 traversalinit(&m->viri);
12752 virusloop = (triangle **) traverse(&m->viri);
12753 while (virusloop != (triangle **) NULL) {
12754 testtri.tri = *virusloop;
12755
12756 /* Check each of the three corners of the triangle for elimination. */
12757 /* This is done by walking around each vertex, checking if it is */
12758 /* still connected to at least one live triangle. */
12759 for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
12760 org(testtri, testvertex);
12761 /* Check if the vertex has already been tested. */
12762 if (testvertex != (vertex) NULL) {
12763 killorg = 1;
12764 /* Mark the corner of the triangle as having been tested. */
12765 setorg(testtri, NULL);
12766 /* Walk counterclockwise about the vertex. */
12767 onext(testtri, neighbor);
12768 /* Stop upon reaching a boundary or the starting triangle. */
12769 while ((neighbor.tri != m->dummytri) &&
12770 (!otriequal(neighbor, testtri))) {
12771 if (infected(neighbor)) {
12772 /* Mark the corner of this triangle as having been tested. */
12773 setorg(neighbor, NULL);
12774 } else {
12775 /* A live triangle. The vertex survives. */
12776 killorg = 0;
12777 }
12778 /* Walk counterclockwise about the vertex. */
12779 onextself(neighbor);
12780 }
12781 /* If we reached a boundary, we must walk clockwise as well. */
12782 if (neighbor.tri == m->dummytri) {
12783 /* Walk clockwise about the vertex. */
12784 oprev(testtri, neighbor);
12785 /* Stop upon reaching a boundary. */
12786 while (neighbor.tri != m->dummytri) {
12787 if (infected(neighbor)) {
12788 /* Mark the corner of this triangle as having been tested. */
12789 setorg(neighbor, NULL);
12790 } else {
12791 /* A live triangle. The vertex survives. */
12792 killorg = 0;
12793 }
12794 /* Walk clockwise about the vertex. */
12795 oprevself(neighbor);
12796 }
12797 }
12798 if (killorg) {
12799 if (b->verbose > 1) {
12800 printf(" Deleting vertex (%.12g, %.12g)\n",
12801 testvertex[0], testvertex[1]);
12802 }
12803 setvertextype(testvertex, UNDEADVERTEX);
12804 m->undeads++;
12805 }
12806 }
12807 }
12808
12809 /* Record changes in the number of boundary edges, and disconnect */
12810 /* dead triangles from their neighbors. */
12811 for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
12812 sym(testtri, neighbor);
12813 if (neighbor.tri == m->dummytri) {
12814 /* There is no neighboring triangle on this edge, so this edge */
12815 /* is a boundary edge. This triangle is being deleted, so this */
12816 /* boundary edge is deleted. */
12817 m->hullsize--;
12818 } else {
12819 /* Disconnect the triangle from its neighbor. */
12820 dissolve(neighbor);
12821 /* There is a neighboring triangle on this edge, so this edge */
12822 /* becomes a boundary edge when this triangle is deleted. */
12823 m->hullsize++;
12824 }
12825 }
12826 /* Return the dead triangle to the pool of triangles. */
12827 triangledealloc(m, testtri.tri);
12828 virusloop = (triangle **) traverse(&m->viri);
12829 }
12830 /* Empty the virus pool. */
12831 poolrestart(&m->viri);
12832}
12833
12834/*****************************************************************************/
12835/* */
12836/* regionplague() Spread regional attributes and/or area constraints */
12837/* (from a .poly file) throughout the mesh. */
12838/* */
12839/* This procedure operates in two phases. The first phase spreads an */
12840/* attribute and/or an area constraint through a (segment-bounded) region. */
12841/* The triangles are marked to ensure that each triangle is added to the */
12842/* virus pool only once, so the procedure will terminate. */
12843/* */
12844/* The second phase uninfects all infected triangles, returning them to */
12845/* normal. */
12846/* */
12847/*****************************************************************************/
12848
12849#ifdef ANSI_DECLARATORS
12850void regionplague(struct mesh *m, struct behavior *b,
12851 REAL attribute, REAL area)
12852#else /* not ANSI_DECLARATORS */
12853void regionplague(m, b, attribute, area)
12854struct mesh *m;
12855struct behavior *b;
12856REAL attribute;
12857REAL area;
12858#endif /* not ANSI_DECLARATORS */
12859
12860{
12861 struct otri testtri;
12862 struct otri neighbor;
12863 triangle **virusloop;
12864 triangle **regiontri;
12865 struct osub neighborsubseg;
12866 vertex regionorg, regiondest, regionapex;
12867 triangle ptr; /* Temporary variable used by sym() and onext(). */
12868 subseg sptr; /* Temporary variable used by tspivot(). */
12869
12870 if (b->verbose > 1) {
12871 printf(" Marking neighbors of marked triangles.\n");
12872 }
12873 /* Loop through all the infected triangles, spreading the attribute */
12874 /* and/or area constraint to their neighbors, then to their neighbors' */
12875 /* neighbors. */
12876 traversalinit(&m->viri);
12877 virusloop = (triangle **) traverse(&m->viri);
12878 while (virusloop != (triangle **) NULL) {
12879 testtri.tri = *virusloop;
12880 /* A triangle is marked as infected by messing with one of its pointers */
12881 /* to subsegments, setting it to an illegal value. Hence, we have to */
12882 /* temporarily uninfect this triangle so that we can examine its */
12883 /* adjacent subsegments. */
12884 uninfect(testtri);
12885 if (b->regionattrib) {
12886 /* Set an attribute. */
12887 setelemattribute(testtri, m->eextras, attribute);
12888 }
12889 if (b->vararea) {
12890 /* Set an area constraint. */
12891 setareabound(testtri, area);
12892 }
12893 if (b->verbose > 2) {
12894 /* Assign the triangle an orientation for convenience in */
12895 /* checking its vertices. */
12896 testtri.orient = 0;
12897 org(testtri, regionorg);
12898 dest(testtri, regiondest);
12899 apex(testtri, regionapex);
12900 printf(" Checking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
12901 regionorg[0], regionorg[1], regiondest[0], regiondest[1],
12902 regionapex[0], regionapex[1]);
12903 }
12904 /* Check each of the triangle's three neighbors. */
12905 for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
12906 /* Find the neighbor. */
12907 sym(testtri, neighbor);
12908 /* Check for a subsegment between the triangle and its neighbor. */
12909 tspivot(testtri, neighborsubseg);
12910 /* Make sure the neighbor exists, is not already infected, and */
12911 /* isn't protected by a subsegment. */
12912 if ((neighbor.tri != m->dummytri) && !infected(neighbor)
12913 && (neighborsubseg.ss == m->dummysub)) {
12914 if (b->verbose > 2) {
12915 org(neighbor, regionorg);
12916 dest(neighbor, regiondest);
12917 apex(neighbor, regionapex);
12918 printf(" Marking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
12919 regionorg[0], regionorg[1], regiondest[0], regiondest[1],
12920 regionapex[0], regionapex[1]);
12921 }
12922 /* Infect the neighbor. */
12923 infect(neighbor);
12924 /* Ensure that the neighbor's neighbors will be infected. */
12925 regiontri = (triangle **) poolalloc(&m->viri);
12926 *regiontri = neighbor.tri;
12927 }
12928 }
12929 /* Remark the triangle as infected, so it doesn't get added to the */
12930 /* virus pool again. */
12931 infect(testtri);
12932 virusloop = (triangle **) traverse(&m->viri);
12933 }
12934
12935 /* Uninfect all triangles. */
12936 if (b->verbose > 1) {
12937 printf(" Unmarking marked triangles.\n");
12938 }
12939 traversalinit(&m->viri);
12940 virusloop = (triangle **) traverse(&m->viri);
12941 while (virusloop != (triangle **) NULL) {
12942 testtri.tri = *virusloop;
12943 uninfect(testtri);
12944 virusloop = (triangle **) traverse(&m->viri);
12945 }
12946 /* Empty the virus pool. */
12947 poolrestart(&m->viri);
12948}
12949
12950/*****************************************************************************/
12951/* */
12952/* carveholes() Find the holes and infect them. Find the area */
12953/* constraints and infect them. Infect the convex hull. */
12954/* Spread the infection and kill triangles. Spread the */
12955/* area constraints. */
12956/* */
12957/* This routine mainly calls other routines to carry out all these */
12958/* functions. */
12959/* */
12960/*****************************************************************************/
12961
12962#ifdef ANSI_DECLARATORS
12963void carveholes(struct mesh *m, struct behavior *b, REAL *holelist, int holes,
12964 REAL *regionlist, int regions)
12965#else /* not ANSI_DECLARATORS */
12966void carveholes(m, b, holelist, holes, regionlist, regions)
12967struct mesh *m;
12968struct behavior *b;
12969REAL *holelist;
12970int holes;
12971REAL *regionlist;
12972int regions;
12973#endif /* not ANSI_DECLARATORS */
12974
12975{
12976 struct otri searchtri;
12977 struct otri triangleloop;
12978 struct otri *regiontris;
12979 triangle **holetri;
12980 triangle **regiontri;
12981 vertex searchorg, searchdest;
12982 enum locateresult intersect;
12983 int i;
12984 triangle ptr; /* Temporary variable used by sym(). */
12985
12986 if (!(b->quiet || (b->noholes && b->convex))) {
12987 printf("Removing unwanted triangles.\n");
12988 if (b->verbose && (holes > 0)) {
12989 printf(" Marking holes for elimination.\n");
12990 }
12991 }
12992
12993 if (regions > 0) {
12994 /* Allocate storage for the triangles in which region points fall. */
12995 regiontris = (struct otri *) trimalloc(regions *
12996 (int) sizeof(struct otri));
12997 } else {
12998 regiontris = (struct otri *) NULL;
12999 }
13000
13001 if (((holes > 0) && !b->noholes) || !b->convex || (regions > 0)) {
13002 /* Initialize a pool of viri to be used for holes, concavities, */
13003 /* regional attributes, and/or regional area constraints. */
13004 poolinit(&m->viri, sizeof(triangle *), VIRUSPERBLOCK, VIRUSPERBLOCK, 0);
13005 }
13006
13007 if (!b->convex) {
13008 /* Mark as infected any unprotected triangles on the boundary. */
13009 /* This is one way by which concavities are created. */
13010 infecthull(m, b);
13011 }
13012
13013 if ((holes > 0) && !b->noholes) {
13014 /* Infect each triangle in which a hole lies. */
13015 for (i = 0; i < 2 * holes; i += 2) {
13016 /* Ignore holes that aren't within the bounds of the mesh. */
13017 if ((holelist[i] >= m->xmin) && (holelist[i] <= m->xmax)
13018 && (holelist[i + 1] >= m->ymin) && (holelist[i + 1] <= m->ymax)) {
13019 /* Start searching from some triangle on the outer boundary. */
13020 searchtri.tri = m->dummytri;
13021 searchtri.orient = 0;
13022 symself(searchtri);
13023 /* Ensure that the hole is to the left of this boundary edge; */
13024 /* otherwise, locate() will falsely report that the hole */
13025 /* falls within the starting triangle. */
13026 org(searchtri, searchorg);
13027 dest(searchtri, searchdest);
13028 if (counterclockwise(m, b, searchorg, searchdest, &holelist[i]) >
13029 0.0) {
13030 /* Find a triangle that contains the hole. */
13031 intersect = locate(m, b, &holelist[i], &searchtri);
13032 if ((intersect != OUTSIDE) && (!infected(searchtri))) {
13033 /* Infect the triangle. This is done by marking the triangle */
13034 /* as infected and including the triangle in the virus pool. */
13035 infect(searchtri);
13036 holetri = (triangle **) poolalloc(&m->viri);
13037 *holetri = searchtri.tri;
13038 }
13039 }
13040 }
13041 }
13042 }
13043
13044 /* Now, we have to find all the regions BEFORE we carve the holes, because */
13045 /* locate() won't work when the triangulation is no longer convex. */
13046 /* (Incidentally, this is the reason why regional attributes and area */
13047 /* constraints can't be used when refining a preexisting mesh, which */
13048 /* might not be convex; they can only be used with a freshly */
13049 /* triangulated PSLG.) */
13050 if (regions > 0) {
13051 /* Find the starting triangle for each region. */
13052 for (i = 0; i < regions; i++) {
13053 regiontris[i].tri = m->dummytri;
13054 /* Ignore region points that aren't within the bounds of the mesh. */
13055 if ((regionlist[4 * i] >= m->xmin) && (regionlist[4 * i] <= m->xmax) &&
13056 (regionlist[4 * i + 1] >= m->ymin) &&
13057 (regionlist[4 * i + 1] <= m->ymax)) {
13058 /* Start searching from some triangle on the outer boundary. */
13059 searchtri.tri = m->dummytri;
13060 searchtri.orient = 0;
13061 symself(searchtri);
13062 /* Ensure that the region point is to the left of this boundary */
13063 /* edge; otherwise, locate() will falsely report that the */
13064 /* region point falls within the starting triangle. */
13065 org(searchtri, searchorg);
13066 dest(searchtri, searchdest);
13067 if (counterclockwise(m, b, searchorg, searchdest, &regionlist[4 * i]) >
13068 0.0) {
13069 /* Find a triangle that contains the region point. */
13070 intersect = locate(m, b, &regionlist[4 * i], &searchtri);
13071 if ((intersect != OUTSIDE) && (!infected(searchtri))) {
13072 /* Record the triangle for processing after the */
13073 /* holes have been carved. */
13074 otricopy(searchtri, regiontris[i]);
13075 }
13076 }
13077 }
13078 }
13079 }
13080
13081 if (m->viri.items > 0) {
13082 /* Carve the holes and concavities. */
13083 plague(m, b);
13084 }
13085 /* The virus pool should be empty now. */
13086
13087 if (regions > 0) {
13088 if (!b->quiet) {
13089 if (b->regionattrib) {
13090 if (b->vararea) {
13091 printf("Spreading regional attributes and area constraints.\n");
13092 } else {
13093 printf("Spreading regional attributes.\n");
13094 }
13095 } else {
13096 printf("Spreading regional area constraints.\n");
13097 }
13098 }
13099 if (b->regionattrib && !b->refine) {
13100 /* Assign every triangle a regional attribute of zero. */
13101 traversalinit(&m->triangles);
13102 triangleloop.orient = 0;
13103 triangleloop.tri = triangletraverse(m);
13104 while (triangleloop.tri != (triangle *) NULL) {
13105 setelemattribute(triangleloop, m->eextras, 0.0);
13106 triangleloop.tri = triangletraverse(m);
13107 }
13108 }
13109 for (i = 0; i < regions; i++) {
13110 if (regiontris[i].tri != m->dummytri) {
13111 /* Make sure the triangle under consideration still exists. */
13112 /* It may have been eaten by the virus. */
13113 if (!deadtri(regiontris[i].tri)) {
13114 /* Put one triangle in the virus pool. */
13115 infect(regiontris[i]);
13116 regiontri = (triangle **) poolalloc(&m->viri);
13117 *regiontri = regiontris[i].tri;
13118 /* Apply one region's attribute and/or area constraint. */
13119 regionplague(m, b, regionlist[4 * i + 2], regionlist[4 * i + 3]);
13120 /* The virus pool should be empty now. */
13121 }
13122 }
13123 }
13124 if (b->regionattrib && !b->refine) {
13125 /* Note the fact that each triangle has an additional attribute. */
13126 m->eextras++;
13127 }
13128 }
13129
13130 /* Free up memory. */
13131 if (((holes > 0) && !b->noholes) || !b->convex || (regions > 0)) {
13132 pooldeinit(&m->viri);
13133 }
13134 if (regions > 0) {
13135 trifree((VOID *) regiontris);
13136 }
13137}
13138
13139/** **/
13140/** **/
13141/********* Carving out holes and concavities ends here *********/
13142
13143/********* Mesh quality maintenance begins here *********/
13144/** **/
13145/** **/
13146
13147/*****************************************************************************/
13148/* */
13149/* tallyencs() Traverse the entire list of subsegments, and check each */
13150/* to see if it is encroached. If so, add it to the list. */
13151/* */
13152/*****************************************************************************/
13153
13154#ifndef CDT_ONLY
13155
13156#ifdef ANSI_DECLARATORS
13157void tallyencs(struct mesh *m, struct behavior *b)
13158#else /* not ANSI_DECLARATORS */
13159void tallyencs(m, b)
13160struct mesh *m;
13161struct behavior *b;
13162#endif /* not ANSI_DECLARATORS */
13163
13164{
13165 struct osub subsegloop;
13166 int dummy;
13167
13168 traversalinit(&m->subsegs);
13169 subsegloop.ssorient = 0;
13170 subsegloop.ss = subsegtraverse(m);
13171 while (subsegloop.ss != (subseg *) NULL) {
13172 /* If the segment is encroached, add it to the list. */
13173 dummy = checkseg4encroach(m, b, &subsegloop);
13174 subsegloop.ss = subsegtraverse(m);
13175 }
13176}
13177
13178#endif /* not CDT_ONLY */
13179
13180/*****************************************************************************/
13181/* */
13182/* precisionerror() Print an error message for precision problems. */
13183/* */
13184/*****************************************************************************/
13185
13186#ifndef CDT_ONLY
13187
13188void precisionerror()
13189{
13190 printf("Try increasing the area criterion and/or reducing the minimum\n");
13191 printf(" allowable angle so that tiny triangles are not created.\n");
13192#ifdef SINGLE
13193 printf("Alternatively, try recompiling me with double precision\n");
13194 printf(" arithmetic (by removing \"#define SINGLE\" from the\n");
13195 printf(" source file or \"-DSINGLE\" from the makefile).\n");
13196#endif /* SINGLE */
13197}
13198
13199#endif /* not CDT_ONLY */
13200
13201/*****************************************************************************/
13202/* */
13203/* splitencsegs() Split all the encroached subsegments. */
13204/* */
13205/* Each encroached subsegment is repaired by splitting it - inserting a */
13206/* vertex at or near its midpoint. Newly inserted vertices may encroach */
13207/* upon other subsegments; these are also repaired. */
13208/* */
13209/* `triflaws' is a flag that specifies whether one should take note of new */
13210/* bad triangles that result from inserting vertices to repair encroached */
13211/* subsegments. */
13212/* */
13213/*****************************************************************************/
13214
13215#ifndef CDT_ONLY
13216
13217#ifdef ANSI_DECLARATORS
13218void splitencsegs(struct mesh *m, struct behavior *b, int triflaws)
13219#else /* not ANSI_DECLARATORS */
13220void splitencsegs(m, b, triflaws)
13221struct mesh *m;
13222struct behavior *b;
13223int triflaws;
13224#endif /* not ANSI_DECLARATORS */
13225
13226{
13227 struct otri enctri;
13228 struct otri testtri;
13229 struct osub testsh;
13230 struct osub currentenc;
13231 struct badsubseg *encloop;
13232 vertex eorg, edest, eapex;
13233 vertex newvertex;
13234 enum insertvertexresult success;
13235 REAL segmentlength, nearestpoweroftwo;
13236 REAL split;
13237 REAL multiplier, divisor;
13238 int acuteorg, acuteorg2, acutedest, acutedest2;
13239 int dummy;
13240 int i;
13241 triangle ptr; /* Temporary variable used by stpivot(). */
13242 subseg sptr; /* Temporary variable used by snext(). */
13243
13244 /* Note that steinerleft == -1 if an unlimited number */
13245 /* of Steiner points is allowed. */
13246 while ((m->badsubsegs.items > 0) && (m->steinerleft != 0)) {
13247 traversalinit(&m->badsubsegs);
13248 encloop = badsubsegtraverse(m);
13249 while ((encloop != (struct badsubseg *) NULL) && (m->steinerleft != 0)) {
13250 sdecode(encloop->encsubseg, currentenc);
13251 sorg(currentenc, eorg);
13252 sdest(currentenc, edest);
13253 /* Make sure that this segment is still the same segment it was */
13254 /* when it was determined to be encroached. If the segment was */
13255 /* enqueued multiple times (because several newly inserted */
13256 /* vertices encroached it), it may have already been split. */
13257 if (!deadsubseg(currentenc.ss) &&
13258 (eorg == encloop->subsegorg) && (edest == encloop->subsegdest)) {
13259 /* To decide where to split a segment, we need to know if the */
13260 /* segment shares an endpoint with an adjacent segment. */
13261 /* The concern is that, if we simply split every encroached */
13262 /* segment in its center, two adjacent segments with a small */
13263 /* angle between them might lead to an infinite loop; each */
13264 /* vertex added to split one segment will encroach upon the */
13265 /* other segment, which must then be split with a vertex that */
13266 /* will encroach upon the first segment, and so on forever. */
13267 /* To avoid this, imagine a set of concentric circles, whose */
13268 /* radii are powers of two, about each segment endpoint. */
13269 /* These concentric circles determine where the segment is */
13270 /* split. (If both endpoints are shared with adjacent */
13271 /* segments, split the segment in the middle, and apply the */
13272 /* concentric circles for later splittings.) */
13273
13274 /* Is the origin shared with another segment? */
13275 stpivot(currentenc, enctri);
13276 lnext(enctri, testtri);
13277 tspivot(testtri, testsh);
13278 acuteorg = testsh.ss != m->dummysub;
13279 /* Is the destination shared with another segment? */
13280 lnextself(testtri);
13281 tspivot(testtri, testsh);
13282 acutedest = testsh.ss != m->dummysub;
13283
13284 /* If we're using Chew's algorithm (rather than Ruppert's) */
13285 /* to define encroachment, delete free vertices from the */
13286 /* subsegment's diametral circle. */
13287 if (!b->conformdel && !acuteorg && !acutedest) {
13288 apex(enctri, eapex);
13289 while ((vertextype(eapex) == FREEVERTEX) &&
13290 ((eorg[0] - eapex[0]) * (edest[0] - eapex[0]) +
13291 (eorg[1] - eapex[1]) * (edest[1] - eapex[1]) < 0.0)) {
13292 deletevertex(m, b, &testtri);
13293 stpivot(currentenc, enctri);
13294 apex(enctri, eapex);
13295 lprev(enctri, testtri);
13296 }
13297 }
13298
13299 /* Now, check the other side of the segment, if there's a triangle */
13300 /* there. */
13301 sym(enctri, testtri);
13302 if (testtri.tri != m->dummytri) {
13303 /* Is the destination shared with another segment? */
13304 lnextself(testtri);
13305 tspivot(testtri, testsh);
13306 acutedest2 = testsh.ss != m->dummysub;
13307 acutedest = acutedest || acutedest2;
13308 /* Is the origin shared with another segment? */
13309 lnextself(testtri);
13310 tspivot(testtri, testsh);
13311 acuteorg2 = testsh.ss != m->dummysub;
13312 acuteorg = acuteorg || acuteorg2;
13313
13314 /* Delete free vertices from the subsegment's diametral circle. */
13315 if (!b->conformdel && !acuteorg2 && !acutedest2) {
13316 org(testtri, eapex);
13317 while ((vertextype(eapex) == FREEVERTEX) &&
13318 ((eorg[0] - eapex[0]) * (edest[0] - eapex[0]) +
13319 (eorg[1] - eapex[1]) * (edest[1] - eapex[1]) < 0.0)) {
13320 deletevertex(m, b, &testtri);
13321 sym(enctri, testtri);
13322 apex(testtri, eapex);
13323 lprevself(testtri);
13324 }
13325 }
13326 }
13327
13328 /* Use the concentric circles if exactly one endpoint is shared */
13329 /* with another adjacent segment. */
13330 if (acuteorg || acutedest) {
13331 segmentlength = sqrt((edest[0] - eorg[0]) * (edest[0] - eorg[0]) +
13332 (edest[1] - eorg[1]) * (edest[1] - eorg[1]));
13333 /* Find the power of two that most evenly splits the segment. */
13334 /* The worst case is a 2:1 ratio between subsegment lengths. */
13335 nearestpoweroftwo = 1.0;
13336 while (segmentlength > 3.0 * nearestpoweroftwo) {
13337 nearestpoweroftwo *= 2.0;
13338 }
13339 while (segmentlength < 1.5 * nearestpoweroftwo) {
13340 nearestpoweroftwo *= 0.5;
13341 }
13342 /* Where do we split the segment? */
13343 split = nearestpoweroftwo / segmentlength;
13344 if (acutedest) {
13345 split = 1.0 - split;
13346 }
13347 } else {
13348 /* If we're not worried about adjacent segments, split */
13349 /* this segment in the middle. */
13350 split = 0.5;
13351 }
13352
13353 /* Create the new vertex. */
13354 newvertex = (vertex) poolalloc(&m->vertices);
13355 /* Interpolate its coordinate and attributes. */
13356 for (i = 0; i < 2 + m->nextras; i++) {
13357 newvertex[i] = eorg[i] + split * (edest[i] - eorg[i]);
13358 }
13359
13360 if (!b->noexact) {
13361 /* Roundoff in the above calculation may yield a `newvertex' */
13362 /* that is not precisely collinear with `eorg' and `edest'. */
13363 /* Improve collinearity by one step of iterative refinement. */
13364 multiplier = counterclockwise(m, b, eorg, edest, newvertex);
13365 divisor = ((eorg[0] - edest[0]) * (eorg[0] - edest[0]) +
13366 (eorg[1] - edest[1]) * (eorg[1] - edest[1]));
13367 if ((multiplier != 0.0) && (divisor != 0.0)) {
13368 multiplier = multiplier / divisor;
13369 /* Watch out for NANs. */
13370 if (multiplier == multiplier) {
13371 newvertex[0] += multiplier * (edest[1] - eorg[1]);
13372 newvertex[1] += multiplier * (eorg[0] - edest[0]);
13373 }
13374 }
13375 }
13376
13377 setvertexmark(newvertex, mark(currentenc));
13378 setvertextype(newvertex, SEGMENTVERTEX);
13379 if (b->verbose > 1) {
13380 printf(
13381 " Splitting subsegment (%.12g, %.12g) (%.12g, %.12g) at (%.12g, %.12g).\n",
13382 eorg[0], eorg[1], edest[0], edest[1],
13383 newvertex[0], newvertex[1]);
13384 }
13385 /* Check whether the new vertex lies on an endpoint. */
13386 if (((newvertex[0] == eorg[0]) && (newvertex[1] == eorg[1])) ||
13387 ((newvertex[0] == edest[0]) && (newvertex[1] == edest[1]))) {
13388 printf("Error: Ran out of precision at (%.12g, %.12g).\n",
13389 newvertex[0], newvertex[1]);
13390 printf("I attempted to split a segment to a smaller size than\n");
13391 printf(" can be accommodated by the finite precision of\n");
13392 printf(" floating point arithmetic.\n");
13393 precisionerror();
13394 triexit(1);
13395 }
13396 /* Insert the splitting vertex. This should always succeed. */
13397 success = insertvertex(m, b, newvertex, &enctri, &currentenc,
13398 1, triflaws);
13399 if ((success != SUCCESSFULVERTEX) && (success != ENCROACHINGVERTEX)) {
13400 printf("Internal error in splitencsegs():\n");
13401 printf(" Failure to split a segment.\n");
13402 internalerror();
13403 }
13404 if (m->steinerleft > 0) {
13405 m->steinerleft--;
13406 }
13407 /* Check the two new subsegments to see if they're encroached. */
13408 dummy = checkseg4encroach(m, b, &currentenc);
13409 snextself(currentenc);
13410 dummy = checkseg4encroach(m, b, &currentenc);
13411 }
13412
13413 badsubsegdealloc(m, encloop);
13414 encloop = badsubsegtraverse(m);
13415 }
13416 }
13417}
13418
13419#endif /* not CDT_ONLY */
13420
13421/*****************************************************************************/
13422/* */
13423/* tallyfaces() Test every triangle in the mesh for quality measures. */
13424/* */
13425/*****************************************************************************/
13426
13427#ifndef CDT_ONLY
13428
13429#ifdef ANSI_DECLARATORS
13430void tallyfaces(struct mesh *m, struct behavior *b)
13431#else /* not ANSI_DECLARATORS */
13432void tallyfaces(m, b)
13433struct mesh *m;
13434struct behavior *b;
13435#endif /* not ANSI_DECLARATORS */
13436
13437{
13438 struct otri triangleloop;
13439
13440 if (b->verbose) {
13441 printf(" Making a list of bad triangles.\n");
13442 }
13443 traversalinit(&m->triangles);
13444 triangleloop.orient = 0;
13445 triangleloop.tri = triangletraverse(m);
13446 while (triangleloop.tri != (triangle *) NULL) {
13447 /* If the triangle is bad, enqueue it. */
13448 testtriangle(m, b, &triangleloop);
13449 triangleloop.tri = triangletraverse(m);
13450 }
13451}
13452
13453#endif /* not CDT_ONLY */
13454
13455/*****************************************************************************/
13456/* */
13457/* splittriangle() Inserts a vertex at the circumcenter of a triangle. */
13458/* Deletes the newly inserted vertex if it encroaches */
13459/* upon a segment. */
13460/* */
13461/*****************************************************************************/
13462
13463#ifndef CDT_ONLY
13464
13465#ifdef ANSI_DECLARATORS
13466void splittriangle(struct mesh *m, struct behavior *b,
13467 struct badtriang *badtri)
13468#else /* not ANSI_DECLARATORS */
13469void splittriangle(m, b, badtri)
13470struct mesh *m;
13471struct behavior *b;
13472struct badtriang *badtri;
13473#endif /* not ANSI_DECLARATORS */
13474
13475{
13476 struct otri badotri;
13477 vertex borg, bdest, bapex;
13478 vertex newvertex;
13479 REAL xi, eta;
13480 enum insertvertexresult success;
13481 int errorflag;
13482 int i;
13483
13484 decode(badtri->poortri, badotri);
13485 org(badotri, borg);
13486 dest(badotri, bdest);
13487 apex(badotri, bapex);
13488 /* Make sure that this triangle is still the same triangle it was */
13489 /* when it was tested and determined to be of bad quality. */
13490 /* Subsequent transformations may have made it a different triangle. */
13491 if (!deadtri(badotri.tri) && (borg == badtri->triangorg) &&
13492 (bdest == badtri->triangdest) && (bapex == badtri->triangapex)) {
13493 if (b->verbose > 1) {
13494 printf(" Splitting this triangle at its circumcenter:\n");
13495 printf(" (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", borg[0],
13496 borg[1], bdest[0], bdest[1], bapex[0], bapex[1]);
13497 }
13498
13499 errorflag = 0;
13500 /* Create a new vertex at the triangle's circumcenter. */
13501 newvertex = (vertex) poolalloc(&m->vertices);
13502 findcircumcenter(m, b, borg, bdest, bapex, newvertex, &xi, &eta, 1);
13503
13504 /* Check whether the new vertex lies on a triangle vertex. */
13505 if (((newvertex[0] == borg[0]) && (newvertex[1] == borg[1])) ||
13506 ((newvertex[0] == bdest[0]) && (newvertex[1] == bdest[1])) ||
13507 ((newvertex[0] == bapex[0]) && (newvertex[1] == bapex[1]))) {
13508 if (!b->quiet) {
13509 printf(
13510 "Warning: New vertex (%.12g, %.12g) falls on existing vertex.\n",
13511 newvertex[0], newvertex[1]);
13512 errorflag = 1;
13513 }
13514 vertexdealloc(m, newvertex);
13515 } else {
13516 for (i = 2; i < 2 + m->nextras; i++) {
13517 /* Interpolate the vertex attributes at the circumcenter. */
13518 newvertex[i] = borg[i] + xi * (bdest[i] - borg[i])
13519 + eta * (bapex[i] - borg[i]);
13520 }
13521 /* The new vertex must be in the interior, and therefore is a */
13522 /* free vertex with a marker of zero. */
13523 setvertexmark(newvertex, 0);
13524 setvertextype(newvertex, FREEVERTEX);
13525
13526 /* Ensure that the handle `badotri' does not represent the longest */
13527 /* edge of the triangle. This ensures that the circumcenter must */
13528 /* fall to the left of this edge, so point location will work. */
13529 /* (If the angle org-apex-dest exceeds 90 degrees, then the */
13530 /* circumcenter lies outside the org-dest edge, and eta is */
13531 /* negative. Roundoff error might prevent eta from being */
13532 /* negative when it should be, so I test eta against xi.) */
13533 if (eta < xi) {
13534 lprevself(badotri);
13535 }
13536
13537 /* Insert the circumcenter, searching from the edge of the triangle, */
13538 /* and maintain the Delaunay property of the triangulation. */
13539 success = insertvertex(m, b, newvertex, &badotri, (struct osub *) NULL,
13540 1, 1);
13541 if (success == SUCCESSFULVERTEX) {
13542 if (m->steinerleft > 0) {
13543 m->steinerleft--;
13544 }
13545 } else if (success == ENCROACHINGVERTEX) {
13546 /* If the newly inserted vertex encroaches upon a subsegment, */
13547 /* delete the new vertex. */
13548 undovertex(m, b);
13549 if (b->verbose > 1) {
13550 printf(" Rejecting (%.12g, %.12g).\n", newvertex[0], newvertex[1]);
13551 }
13552 vertexdealloc(m, newvertex);
13553 } else if (success == VIOLATINGVERTEX) {
13554 /* Failed to insert the new vertex, but some subsegment was */
13555 /* marked as being encroached. */
13556 vertexdealloc(m, newvertex);
13557 } else { /* success == DUPLICATEVERTEX */
13558 /* Couldn't insert the new vertex because a vertex is already there. */
13559 if (!b->quiet) {
13560 printf(
13561 "Warning: New vertex (%.12g, %.12g) falls on existing vertex.\n",
13562 newvertex[0], newvertex[1]);
13563 errorflag = 1;
13564 }
13565 vertexdealloc(m, newvertex);
13566 }
13567 }
13568 if (errorflag) {
13569 if (b->verbose) {
13570 printf(" The new vertex is at the circumcenter of triangle\n");
13571 printf(" (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
13572 borg[0], borg[1], bdest[0], bdest[1], bapex[0], bapex[1]);
13573 }
13574 printf("This probably means that I am trying to refine triangles\n");
13575 printf(" to a smaller size than can be accommodated by the finite\n");
13576 printf(" precision of floating point arithmetic. (You can be\n");
13577 printf(" sure of this if I fail to terminate.)\n");
13578 precisionerror();
13579 }
13580 }
13581}
13582
13583#endif /* not CDT_ONLY */
13584
13585/*****************************************************************************/
13586/* */
13587/* enforcequality() Remove all the encroached subsegments and bad */
13588/* triangles from the triangulation. */
13589/* */
13590/*****************************************************************************/
13591
13592#ifndef CDT_ONLY
13593
13594#ifdef ANSI_DECLARATORS
13595void enforcequality(struct mesh *m, struct behavior *b)
13596#else /* not ANSI_DECLARATORS */
13597void enforcequality(m, b)
13598struct mesh *m;
13599struct behavior *b;
13600#endif /* not ANSI_DECLARATORS */
13601
13602{
13603 struct badtriang *badtri;
13604 int i;
13605
13606 if (!b->quiet) {
13607 printf("Adding Steiner points to enforce quality.\n");
13608 }
13609 /* Initialize the pool of encroached subsegments. */
13610 poolinit(&m->badsubsegs, sizeof(struct badsubseg), BADSUBSEGPERBLOCK,
13611 BADSUBSEGPERBLOCK, 0);
13612 if (b->verbose) {
13613 printf(" Looking for encroached subsegments.\n");
13614 }
13615 /* Test all segments to see if they're encroached. */
13616 tallyencs(m, b);
13617 if (b->verbose && (m->badsubsegs.items > 0)) {
13618 printf(" Splitting encroached subsegments.\n");
13619 }
13620 /* Fix encroached subsegments without noting bad triangles. */
13621 splitencsegs(m, b, 0);
13622 /* At this point, if we haven't run out of Steiner points, the */
13623 /* triangulation should be (conforming) Delaunay. */
13624
13625 /* Next, we worry about enforcing triangle quality. */
13626 if ((b->minangle > 0.0) || b->vararea || b->fixedarea || b->usertest) {
13627 /* Initialize the pool of bad triangles. */
13628 poolinit(&m->badtriangles, sizeof(struct badtriang), BADTRIPERBLOCK,
13629 BADTRIPERBLOCK, 0);
13630 /* Initialize the queues of bad triangles. */
13631 for (i = 0; i < 4096; i++) {
13632 m->queuefront[i] = (struct badtriang *) NULL;
13633 }
13634 m->firstnonemptyq = -1;
13635 /* Test all triangles to see if they're bad. */
13636 tallyfaces(m, b);
13637 /* Initialize the pool of recently flipped triangles. */
13638 poolinit(&m->flipstackers, sizeof(struct flipstacker), FLIPSTACKERPERBLOCK,
13639 FLIPSTACKERPERBLOCK, 0);
13640 m->checkquality = 1;
13641 if (b->verbose) {
13642 printf(" Splitting bad triangles.\n");
13643 }
13644 while ((m->badtriangles.items > 0) && (m->steinerleft != 0)) {
13645 /* Fix one bad triangle by inserting a vertex at its circumcenter. */
13646 badtri = dequeuebadtriang(m);
13647 splittriangle(m, b, badtri);
13648 if (m->badsubsegs.items > 0) {
13649 /* Put bad triangle back in queue for another try later. */
13650 enqueuebadtriang(m, b, badtri);
13651 /* Fix any encroached subsegments that resulted. */
13652 /* Record any new bad triangles that result. */
13653 splitencsegs(m, b, 1);
13654 } else {
13655 /* Return the bad triangle to the pool. */
13656 pooldealloc(&m->badtriangles, (VOID *) badtri);
13657 }
13658 }
13659 }
13660 /* At this point, if the "-D" switch was selected and we haven't run out */
13661 /* of Steiner points, the triangulation should be (conforming) Delaunay */
13662 /* and have no low-quality triangles. */
13663
13664 /* Might we have run out of Steiner points too soon? */
13665 if (!b->quiet && b->conformdel && (m->badsubsegs.items > 0) &&
13666 (m->steinerleft == 0)) {
13667 printf("\nWarning: I ran out of Steiner points, but the mesh has\n");
13668 if (m->badsubsegs.items == 1) {
13669 printf(" one encroached subsegment, and therefore might not be truly\n"
13670 );
13671 } else {
13672 printf(" %ld encroached subsegments, and therefore might not be truly\n"
13673 , m->badsubsegs.items);
13674 }
13675 printf(" Delaunay. If the Delaunay property is important to you,\n");
13676 printf(" try increasing the number of Steiner points (controlled by\n");
13677 printf(" the -S switch) slightly and try again.\n\n");
13678 }
13679}
13680
13681#endif /* not CDT_ONLY */
13682
13683/** **/
13684/** **/
13685/********* Mesh quality maintenance ends here *********/
13686
13687/*****************************************************************************/
13688/* */
13689/* highorder() Create extra nodes for quadratic subparametric elements. */
13690/* */
13691/*****************************************************************************/
13692
13693#ifdef ANSI_DECLARATORS
13694void highorder(struct mesh *m, struct behavior *b)
13695#else /* not ANSI_DECLARATORS */
13696void highorder(m, b)
13697struct mesh *m;
13698struct behavior *b;
13699#endif /* not ANSI_DECLARATORS */
13700
13701{
13702 struct otri triangleloop, trisym;
13703 struct osub checkmark;
13704 vertex newvertex;
13705 vertex torg, tdest;
13706 int i;
13707 triangle ptr; /* Temporary variable used by sym(). */
13708 subseg sptr; /* Temporary variable used by tspivot(). */
13709
13710 if (!b->quiet) {
13711 printf("Adding vertices for second-order triangles.\n");
13712 }
13713 /* The following line ensures that dead items in the pool of nodes */
13714 /* cannot be allocated for the extra nodes associated with high */
13715 /* order elements. This ensures that the primary nodes (at the */
13716 /* corners of elements) will occur earlier in the output files, and */
13717 /* have lower indices, than the extra nodes. */
13718 m->vertices.deaditemstack = (VOID *) NULL;
13719
13720 traversalinit(&m->triangles);
13721 triangleloop.tri = triangletraverse(m);
13722 /* To loop over the set of edges, loop over all triangles, and look at */
13723 /* the three edges of each triangle. If there isn't another triangle */
13724 /* adjacent to the edge, operate on the edge. If there is another */
13725 /* adjacent triangle, operate on the edge only if the current triangle */
13726 /* has a smaller pointer than its neighbor. This way, each edge is */
13727 /* considered only once. */
13728 while (triangleloop.tri != (triangle *) NULL) {
13729 for (triangleloop.orient = 0; triangleloop.orient < 3;
13730 triangleloop.orient++) {
13731 sym(triangleloop, trisym);
13732 if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) {
13733 org(triangleloop, torg);
13734 dest(triangleloop, tdest);
13735 /* Create a new node in the middle of the edge. Interpolate */
13736 /* its attributes. */
13737 newvertex = (vertex) poolalloc(&m->vertices);
13738 for (i = 0; i < 2 + m->nextras; i++) {
13739 newvertex[i] = 0.5 * (torg[i] + tdest[i]);
13740 }
13741 /* Set the new node's marker to zero or one, depending on */
13742 /* whether it lies on a boundary. */
13743 setvertexmark(newvertex, trisym.tri == m->dummytri);
13744 setvertextype(newvertex,
13745 trisym.tri == m->dummytri ? FREEVERTEX : SEGMENTVERTEX);
13746 if (b->usesegments) {
13747 tspivot(triangleloop, checkmark);
13748 /* If this edge is a segment, transfer the marker to the new node. */
13749 if (checkmark.ss != m->dummysub) {
13750 setvertexmark(newvertex, mark(checkmark));
13751 setvertextype(newvertex, SEGMENTVERTEX);
13752 }
13753 }
13754 if (b->verbose > 1) {
13755 printf(" Creating (%.12g, %.12g).\n", newvertex[0], newvertex[1]);
13756 }
13757 /* Record the new node in the (one or two) adjacent elements. */
13758 triangleloop.tri[m->highorderindex + triangleloop.orient] =
13759 (triangle) newvertex;
13760 if (trisym.tri != m->dummytri) {
13761 trisym.tri[m->highorderindex + trisym.orient] = (triangle) newvertex;
13762 }
13763 }
13764 }
13765 triangleloop.tri = triangletraverse(m);
13766 }
13767}
13768
13769/********* File I/O routines begin here *********/
13770/** **/
13771/** **/
13772
13773/*****************************************************************************/
13774/* */
13775/* readline() Read a nonempty line from a file. */
13776/* */
13777/* A line is considered "nonempty" if it contains something that looks like */
13778/* a number. Comments (prefaced by `#') are ignored. */
13779/* */
13780/*****************************************************************************/
13781
13782#ifndef TRILIBRARY
13783
13784#ifdef ANSI_DECLARATORS
13785char *readline(char *string, FILE *infile, char *infilename)
13786#else /* not ANSI_DECLARATORS */
13787char *readline(string, infile, infilename)
13788char *string;
13789FILE *infile;
13790char *infilename;
13791#endif /* not ANSI_DECLARATORS */
13792
13793{
13794 char *result;
13795
13796 /* Search for something that looks like a number. */
13797 do {
13798 result = fgets(string, INPUTLINESIZE, infile);
13799 if (result == (char *) NULL) {
13800 printf(" Error: Unexpected end of file in %s.\n", infilename);
13801 triexit(1);
13802 }
13803 /* Skip anything that doesn't look like a number, a comment, */
13804 /* or the end of a line. */
13805 while ((*result != '\0') && (*result != '#')
13806 && (*result != '.') && (*result != '+') && (*result != '-')
13807 && ((*result < '0') || (*result > '9'))) {
13808 result++;
13809 }
13810 /* If it's a comment or end of line, read another line and try again. */
13811 } while ((*result == '#') || (*result == '\0'));
13812 return result;
13813}
13814
13815#endif /* not TRILIBRARY */
13816
13817/*****************************************************************************/
13818/* */
13819/* findfield() Find the next field of a string. */
13820/* */
13821/* Jumps past the current field by searching for whitespace, then jumps */
13822/* past the whitespace to find the next field. */
13823/* */
13824/*****************************************************************************/
13825
13826#ifndef TRILIBRARY
13827
13828#ifdef ANSI_DECLARATORS
13829char *findfield(char *string)
13830#else /* not ANSI_DECLARATORS */
13831char *findfield(string)
13832char *string;
13833#endif /* not ANSI_DECLARATORS */
13834
13835{
13836 char *result;
13837
13838 result = string;
13839 /* Skip the current field. Stop upon reaching whitespace. */
13840 while ((*result != '\0') && (*result != '#')
13841 && (*result != ' ') && (*result != '\t')) {
13842 result++;
13843 }
13844 /* Now skip the whitespace and anything else that doesn't look like a */
13845 /* number, a comment, or the end of a line. */
13846 while ((*result != '\0') && (*result != '#')
13847 && (*result != '.') && (*result != '+') && (*result != '-')
13848 && ((*result < '0') || (*result > '9'))) {
13849 result++;
13850 }
13851 /* Check for a comment (prefixed with `#'). */
13852 if (*result == '#') {
13853 *result = '\0';
13854 }
13855 return result;
13856}
13857
13858#endif /* not TRILIBRARY */
13859
13860/*****************************************************************************/
13861/* */
13862/* readnodes() Read the vertices from a file, which may be a .node or */
13863/* .poly file. */
13864/* */
13865/*****************************************************************************/
13866
13867#ifndef TRILIBRARY
13868
13869#ifdef ANSI_DECLARATORS
13870void readnodes(struct mesh *m, struct behavior *b, char *nodefilename,
13871 char *polyfilename, FILE **polyfile)
13872#else /* not ANSI_DECLARATORS */
13873void readnodes(m, b, nodefilename, polyfilename, polyfile)
13874struct mesh *m;
13875struct behavior *b;
13876char *nodefilename;
13877char *polyfilename;
13878FILE **polyfile;
13879#endif /* not ANSI_DECLARATORS */
13880
13881{
13882 FILE *infile;
13883 vertex vertexloop;
13884 char inputline[INPUTLINESIZE];
13885 char *stringptr;
13886 char *infilename;
13887 REAL x, y;
13888 int firstnode;
13889 int nodemarkers;
13890 int currentmarker;
13891 int i, j;
13892
13893 if (b->poly) {
13894 /* Read the vertices from a .poly file. */
13895 if (!b->quiet) {
13896 printf("Opening %s.\n", polyfilename);
13897 }
13898 *polyfile = fopen(polyfilename, "r");
13899 if (*polyfile == (FILE *) NULL) {
13900 printf(" Error: Cannot access file %s.\n", polyfilename);
13901 triexit(1);
13902 }
13903 /* Read number of vertices, number of dimensions, number of vertex */
13904 /* attributes, and number of boundary markers. */
13905 stringptr = readline(inputline, *polyfile, polyfilename);
13906 m->invertices = (int) strtol(stringptr, &stringptr, 0);
13907 stringptr = findfield(stringptr);
13908 if (*stringptr == '\0') {
13909 m->mesh_dim = 2;
13910 } else {
13911 m->mesh_dim = (int) strtol(stringptr, &stringptr, 0);
13912 }
13913 stringptr = findfield(stringptr);
13914 if (*stringptr == '\0') {
13915 m->nextras = 0;
13916 } else {
13917 m->nextras = (int) strtol(stringptr, &stringptr, 0);
13918 }
13919 stringptr = findfield(stringptr);
13920 if (*stringptr == '\0') {
13921 nodemarkers = 0;
13922 } else {
13923 nodemarkers = (int) strtol(stringptr, &stringptr, 0);
13924 }
13925 if (m->invertices > 0) {
13926 infile = *polyfile;
13927 infilename = polyfilename;
13928 m->readnodefile = 0;
13929 } else {
13930 /* If the .poly file claims there are zero vertices, that means that */
13931 /* the vertices should be read from a separate .node file. */
13932 m->readnodefile = 1;
13933 infilename = nodefilename;
13934 }
13935 } else {
13936 m->readnodefile = 1;
13937 infilename = nodefilename;
13938 *polyfile = (FILE *) NULL;
13939 }
13940
13941 if (m->readnodefile) {
13942 /* Read the vertices from a .node file. */
13943 if (!b->quiet) {
13944 printf("Opening %s.\n", nodefilename);
13945 }
13946 infile = fopen(nodefilename, "r");
13947 if (infile == (FILE *) NULL) {
13948 printf(" Error: Cannot access file %s.\n", nodefilename);
13949 triexit(1);
13950 }
13951 /* Read number of vertices, number of dimensions, number of vertex */
13952 /* attributes, and number of boundary markers. */
13953 stringptr = readline(inputline, infile, nodefilename);
13954 m->invertices = (int) strtol(stringptr, &stringptr, 0);
13955 stringptr = findfield(stringptr);
13956 if (*stringptr == '\0') {
13957 m->mesh_dim = 2;
13958 } else {
13959 m->mesh_dim = (int) strtol(stringptr, &stringptr, 0);
13960 }
13961 stringptr = findfield(stringptr);
13962 if (*stringptr == '\0') {
13963 m->nextras = 0;
13964 } else {
13965 m->nextras = (int) strtol(stringptr, &stringptr, 0);
13966 }
13967 stringptr = findfield(stringptr);
13968 if (*stringptr == '\0') {
13969 nodemarkers = 0;
13970 } else {
13971 nodemarkers = (int) strtol(stringptr, &stringptr, 0);
13972 }
13973 }
13974
13975 if (m->invertices < 3) {
13976 printf("Error: Input must have at least three input vertices.\n");
13977 triexit(1);
13978 }
13979 if (m->mesh_dim != 2) {
13980 printf("Error: Triangle only works with two-dimensional meshes.\n");
13981 triexit(1);
13982 }
13983 if (m->nextras == 0) {
13984 b->weighted = 0;
13985 }
13986
13987 initializevertexpool(m, b);
13988
13989 /* Read the vertices. */
13990 for (i = 0; i < m->invertices; i++) {
13991 vertexloop = (vertex) poolalloc(&m->vertices);
13992 stringptr = readline(inputline, infile, infilename);
13993 if (i == 0) {
13994 firstnode = (int) strtol(stringptr, &stringptr, 0);
13995 if ((firstnode == 0) || (firstnode == 1)) {
13996 b->firstnumber = firstnode;
13997 }
13998 }
13999 stringptr = findfield(stringptr);
14000 if (*stringptr == '\0') {
14001 printf("Error: Vertex %d has no x coordinate.\n", b->firstnumber + i);
14002 triexit(1);
14003 }
14004 x = (REAL) strtod(stringptr, &stringptr);
14005 stringptr = findfield(stringptr);
14006 if (*stringptr == '\0') {
14007 printf("Error: Vertex %d has no y coordinate.\n", b->firstnumber + i);
14008 triexit(1);
14009 }
14010 y = (REAL) strtod(stringptr, &stringptr);
14011 vertexloop[0] = x;
14012 vertexloop[1] = y;
14013 /* Read the vertex attributes. */
14014 for (j = 2; j < 2 + m->nextras; j++) {
14015 stringptr = findfield(stringptr);
14016 if (*stringptr == '\0') {
14017 vertexloop[j] = 0.0;
14018 } else {
14019 vertexloop[j] = (REAL) strtod(stringptr, &stringptr);
14020 }
14021 }
14022 if (nodemarkers) {
14023 /* Read a vertex marker. */
14024 stringptr = findfield(stringptr);
14025 if (*stringptr == '\0') {
14026 setvertexmark(vertexloop, 0);
14027 } else {
14028 currentmarker = (int) strtol(stringptr, &stringptr, 0);
14029 setvertexmark(vertexloop, currentmarker);
14030 }
14031 } else {
14032 /* If no markers are specified in the file, they default to zero. */
14033 setvertexmark(vertexloop, 0);
14034 }
14035 setvertextype(vertexloop, INPUTVERTEX);
14036 /* Determine the smallest and largest x and y coordinates. */
14037 if (i == 0) {
14038 m->xmin = m->xmax = x;
14039 m->ymin = m->ymax = y;
14040 } else {
14041 m->xmin = (x < m->xmin) ? x : m->xmin;
14042 m->xmax = (x > m->xmax) ? x : m->xmax;
14043 m->ymin = (y < m->ymin) ? y : m->ymin;
14044 m->ymax = (y > m->ymax) ? y : m->ymax;
14045 }
14046 }
14047 if (m->readnodefile) {
14048 fclose(infile);
14049 }
14050
14051 /* Nonexistent x value used as a flag to mark circle events in sweepline */
14052 /* Delaunay algorithm. */
14053 m->xminextreme = 10 * m->xmin - 9 * m->xmax;
14054}
14055
14056#endif /* not TRILIBRARY */
14057
14058/*****************************************************************************/
14059/* */
14060/* transfernodes() Read the vertices from memory. */
14061/* */
14062/*****************************************************************************/
14063
14064#ifdef TRILIBRARY
14065
14066#ifdef ANSI_DECLARATORS
14067void transfernodes(struct mesh *m, struct behavior *b, REAL *pointlist,
14068 REAL *pointattriblist, int *pointmarkerlist,
14069 int numberofpoints, int numberofpointattribs)
14070#else /* not ANSI_DECLARATORS */
14071void transfernodes(m, b, pointlist, pointattriblist, pointmarkerlist,
14072 numberofpoints, numberofpointattribs)
14073struct mesh *m;
14074struct behavior *b;
14075REAL *pointlist;
14076REAL *pointattriblist;
14077int *pointmarkerlist;
14078int numberofpoints;
14079int numberofpointattribs;
14080#endif /* not ANSI_DECLARATORS */
14081
14082{
14083 vertex vertexloop;
14084 REAL x, y;
14085 int i, j;
14086 int coordindex;
14087 int attribindex;
14088
14089 m->invertices = numberofpoints;
14090 m->mesh_dim = 2;
14091 m->nextras = numberofpointattribs;
14092 m->readnodefile = 0;
14093 if (m->invertices < 3) {
14094 printf("Error: Input must have at least three input vertices.\n");
14095 triexit(1);
14096 }
14097 if (m->nextras == 0) {
14098 b->weighted = 0;
14099 }
14100
14101 initializevertexpool(m, b);
14102
14103 /* Read the vertices. */
14104 coordindex = 0;
14105 attribindex = 0;
14106 for (i = 0; i < m->invertices; i++) {
14107 vertexloop = (vertex) poolalloc(&m->vertices);
14108 /* Read the vertex coordinates. */
14109 x = vertexloop[0] = pointlist[coordindex++];
14110 y = vertexloop[1] = pointlist[coordindex++];
14111 /* Read the vertex attributes. */
14112 for (j = 0; j < numberofpointattribs; j++) {
14113 vertexloop[2 + j] = pointattriblist[attribindex++];
14114 }
14115 if (pointmarkerlist != (int *) NULL) {
14116 /* Read a vertex marker. */
14117 setvertexmark(vertexloop, pointmarkerlist[i]);
14118 } else {
14119 /* If no markers are specified, they default to zero. */
14120 setvertexmark(vertexloop, 0);
14121 }
14122 setvertextype(vertexloop, INPUTVERTEX);
14123 /* Determine the smallest and largest x and y coordinates. */
14124 if (i == 0) {
14125 m->xmin = m->xmax = x;
14126 m->ymin = m->ymax = y;
14127 } else {
14128 m->xmin = (x < m->xmin) ? x : m->xmin;
14129 m->xmax = (x > m->xmax) ? x : m->xmax;
14130 m->ymin = (y < m->ymin) ? y : m->ymin;
14131 m->ymax = (y > m->ymax) ? y : m->ymax;
14132 }
14133 }
14134
14135 /* Nonexistent x value used as a flag to mark circle events in sweepline */
14136 /* Delaunay algorithm. */
14137 m->xminextreme = 10 * m->xmin - 9 * m->xmax;
14138}
14139
14140#endif /* TRILIBRARY */
14141
14142/*****************************************************************************/
14143/* */
14144/* readholes() Read the holes, and possibly regional attributes and area */
14145/* constraints, from a .poly file. */
14146/* */
14147/*****************************************************************************/
14148
14149#ifndef TRILIBRARY
14150
14151#ifdef ANSI_DECLARATORS
14152void readholes(struct mesh *m, struct behavior *b,
14153 FILE *polyfile, char *polyfilename, REAL **hlist, int *holes,
14154 REAL **rlist, int *regions)
14155#else /* not ANSI_DECLARATORS */
14156void readholes(m, b, polyfile, polyfilename, hlist, holes, rlist, regions)
14157struct mesh *m;
14158struct behavior *b;
14159FILE *polyfile;
14160char *polyfilename;
14161REAL **hlist;
14162int *holes;
14163REAL **rlist;
14164int *regions;
14165#endif /* not ANSI_DECLARATORS */
14166
14167{
14168 REAL *holelist;
14169 REAL *regionlist;
14170 char inputline[INPUTLINESIZE];
14171 char *stringptr;
14172 int index;
14173 int i;
14174
14175 /* Read the holes. */
14176 stringptr = readline(inputline, polyfile, polyfilename);
14177 *holes = (int) strtol(stringptr, &stringptr, 0);
14178 if (*holes > 0) {
14179 holelist = (REAL *) trimalloc(2 * *holes * (int) sizeof(REAL));
14180 *hlist = holelist;
14181 for (i = 0; i < 2 * *holes; i += 2) {
14182 stringptr = readline(inputline, polyfile, polyfilename);
14183 stringptr = findfield(stringptr);
14184 if (*stringptr == '\0') {
14185 printf("Error: Hole %d has no x coordinate.\n",
14186 b->firstnumber + (i >> 1));
14187 triexit(1);
14188 } else {
14189 holelist[i] = (REAL) strtod(stringptr, &stringptr);
14190 }
14191 stringptr = findfield(stringptr);
14192 if (*stringptr == '\0') {
14193 printf("Error: Hole %d has no y coordinate.\n",
14194 b->firstnumber + (i >> 1));
14195 triexit(1);
14196 } else {
14197 holelist[i + 1] = (REAL) strtod(stringptr, &stringptr);
14198 }
14199 }
14200 } else {
14201 *hlist = (REAL *) NULL;
14202 }
14203
14204#ifndef CDT_ONLY
14205 if ((b->regionattrib || b->vararea) && !b->refine) {
14206 /* Read the area constraints. */
14207 stringptr = readline(inputline, polyfile, polyfilename);
14208 *regions = (int) strtol(stringptr, &stringptr, 0);
14209 if (*regions > 0) {
14210 regionlist = (REAL *) trimalloc(4 * *regions * (int) sizeof(REAL));
14211 *rlist = regionlist;
14212 index = 0;
14213 for (i = 0; i < *regions; i++) {
14214 stringptr = readline(inputline, polyfile, polyfilename);
14215 stringptr = findfield(stringptr);
14216 if (*stringptr == '\0') {
14217 printf("Error: Region %d has no x coordinate.\n",
14218 b->firstnumber + i);
14219 triexit(1);
14220 } else {
14221 regionlist[index++] = (REAL) strtod(stringptr, &stringptr);
14222 }
14223 stringptr = findfield(stringptr);
14224 if (*stringptr == '\0') {
14225 printf("Error: Region %d has no y coordinate.\n",
14226 b->firstnumber + i);
14227 triexit(1);
14228 } else {
14229 regionlist[index++] = (REAL) strtod(stringptr, &stringptr);
14230 }
14231 stringptr = findfield(stringptr);
14232 if (*stringptr == '\0') {
14233 printf(
14234 "Error: Region %d has no region attribute or area constraint.\n",
14235 b->firstnumber + i);
14236 triexit(1);
14237 } else {
14238 regionlist[index++] = (REAL) strtod(stringptr, &stringptr);
14239 }
14240 stringptr = findfield(stringptr);
14241 if (*stringptr == '\0') {
14242 regionlist[index] = regionlist[index - 1];
14243 } else {
14244 regionlist[index] = (REAL) strtod(stringptr, &stringptr);
14245 }
14246 index++;
14247 }
14248 }
14249 } else {
14250 /* Set `*regions' to zero to avoid an accidental free() later. */
14251 *regions = 0;
14252 *rlist = (REAL *) NULL;
14253 }
14254#endif /* not CDT_ONLY */
14255
14256 fclose(polyfile);
14257}
14258
14259#endif /* not TRILIBRARY */
14260
14261/*****************************************************************************/
14262/* */
14263/* finishfile() Write the command line to the output file so the user */
14264/* can remember how the file was generated. Close the file. */
14265/* */
14266/*****************************************************************************/
14267
14268#ifndef TRILIBRARY
14269
14270#ifdef ANSI_DECLARATORS
14271void finishfile(FILE *outfile, int argc, char **argv)
14272#else /* not ANSI_DECLARATORS */
14273void finishfile(outfile, argc, argv)
14274FILE *outfile;
14275int argc;
14276char **argv;
14277#endif /* not ANSI_DECLARATORS */
14278
14279{
14280 int i;
14281
14282 fprintf(outfile, "# Generated by");
14283 for (i = 0; i < argc; i++) {
14284 fprintf(outfile, " ");
14285 fputs(argv[i], outfile);
14286 }
14287 fprintf(outfile, "\n");
14288 fclose(outfile);
14289}
14290
14291#endif /* not TRILIBRARY */
14292
14293/*****************************************************************************/
14294/* */
14295/* writenodes() Number the vertices and write them to a .node file. */
14296/* */
14297/* To save memory, the vertex numbers are written over the boundary markers */
14298/* after the vertices are written to a file. */
14299/* */
14300/*****************************************************************************/
14301
14302#ifdef TRILIBRARY
14303
14304#ifdef ANSI_DECLARATORS
14305void writenodes(struct mesh *m, struct behavior *b, REAL **pointlist,
14306 REAL **pointattriblist, int **pointmarkerlist)
14307#else /* not ANSI_DECLARATORS */
14308void writenodes(m, b, pointlist, pointattriblist, pointmarkerlist)
14309struct mesh *m;
14310struct behavior *b;
14311REAL **pointlist;
14312REAL **pointattriblist;
14313int **pointmarkerlist;
14314#endif /* not ANSI_DECLARATORS */
14315
14316#else /* not TRILIBRARY */
14317
14318#ifdef ANSI_DECLARATORS
14319void writenodes(struct mesh *m, struct behavior *b, char *nodefilename,
14320 int argc, char **argv)
14321#else /* not ANSI_DECLARATORS */
14322void writenodes(m, b, nodefilename, argc, argv)
14323struct mesh *m;
14324struct behavior *b;
14325char *nodefilename;
14326int argc;
14327char **argv;
14328#endif /* not ANSI_DECLARATORS */
14329
14330#endif /* not TRILIBRARY */
14331
14332{
14333#ifdef TRILIBRARY
14334 REAL *plist;
14335 REAL *palist;
14336 int *pmlist;
14337 int coordindex;
14338 int attribindex;
14339#else /* not TRILIBRARY */
14340 FILE *outfile;
14341#endif /* not TRILIBRARY */
14342 vertex vertexloop;
14343 long outvertices;
14344 int vertexnumber;
14345 int i;
14346
14347 if (b->jettison) {
14348 outvertices = m->vertices.items - m->undeads;
14349 } else {
14350 outvertices = m->vertices.items;
14351 }
14352
14353#ifdef TRILIBRARY
14354 if (!b->quiet) {
14355 printf("Writing vertices.\n");
14356 }
14357 /* Allocate memory for output vertices if necessary. */
14358 if (*pointlist == (REAL *) NULL) {
14359 *pointlist = (REAL *) trimalloc((int) (outvertices * 2 * sizeof(REAL)));
14360 }
14361 /* Allocate memory for output vertex attributes if necessary. */
14362 if ((m->nextras > 0) && (*pointattriblist == (REAL *) NULL)) {
14363 *pointattriblist = (REAL *) trimalloc((int) (outvertices * m->nextras *
14364 sizeof(REAL)));
14365 }
14366 /* Allocate memory for output vertex markers if necessary. */
14367 if (!b->nobound && (*pointmarkerlist == (int *) NULL)) {
14368 *pointmarkerlist = (int *) trimalloc((int) (outvertices * sizeof(int)));
14369 }
14370 plist = *pointlist;
14371 palist = *pointattriblist;
14372 pmlist = *pointmarkerlist;
14373 coordindex = 0;
14374 attribindex = 0;
14375#else /* not TRILIBRARY */
14376 if (!b->quiet) {
14377 printf("Writing %s.\n", nodefilename);
14378 }
14379 outfile = fopen(nodefilename, "w");
14380 if (outfile == (FILE *) NULL) {
14381 printf(" Error: Cannot create file %s.\n", nodefilename);
14382 triexit(1);
14383 }
14384 /* Number of vertices, number of dimensions, number of vertex attributes, */
14385 /* and number of boundary markers (zero or one). */
14386 fprintf(outfile, "%ld %d %d %d\n", outvertices, m->mesh_dim,
14387 m->nextras, 1 - b->nobound);
14388#endif /* not TRILIBRARY */
14389
14390 traversalinit(&m->vertices);
14391 vertexnumber = b->firstnumber;
14392 vertexloop = vertextraverse(m);
14393 while (vertexloop != (vertex) NULL) {
14394 if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) {
14395#ifdef TRILIBRARY
14396 /* X and y coordinates. */
14397 plist[coordindex++] = vertexloop[0];
14398 plist[coordindex++] = vertexloop[1];
14399 /* Vertex attributes. */
14400 for (i = 0; i < m->nextras; i++) {
14401 palist[attribindex++] = vertexloop[2 + i];
14402 }
14403 if (!b->nobound) {
14404 /* Copy the boundary marker. */
14405 pmlist[vertexnumber - b->firstnumber] = vertexmark(vertexloop);
14406 }
14407#else /* not TRILIBRARY */
14408 /* Vertex number, x and y coordinates. */
14409 fprintf(outfile, "%4d %.17g %.17g", vertexnumber, vertexloop[0],
14410 vertexloop[1]);
14411 for (i = 0; i < m->nextras; i++) {
14412 /* Write an attribute. */
14413 fprintf(outfile, " %.17g", vertexloop[i + 2]);
14414 }
14415 if (b->nobound) {
14416 fprintf(outfile, "\n");
14417 } else {
14418 /* Write the boundary marker. */
14419 fprintf(outfile, " %d\n", vertexmark(vertexloop));
14420 }
14421#endif /* not TRILIBRARY */
14422
14423 setvertexmark(vertexloop, vertexnumber);
14424 vertexnumber++;
14425 }
14426 vertexloop = vertextraverse(m);
14427 }
14428
14429#ifndef TRILIBRARY
14430 finishfile(outfile, argc, argv);
14431#endif /* not TRILIBRARY */
14432}
14433
14434/*****************************************************************************/
14435/* */
14436/* numbernodes() Number the vertices. */
14437/* */
14438/* Each vertex is assigned a marker equal to its number. */
14439/* */
14440/* Used when writenodes() is not called because no .node file is written. */
14441/* */
14442/*****************************************************************************/
14443
14444#ifdef ANSI_DECLARATORS
14445void numbernodes(struct mesh *m, struct behavior *b)
14446#else /* not ANSI_DECLARATORS */
14447void numbernodes(m, b)
14448struct mesh *m;
14449struct behavior *b;
14450#endif /* not ANSI_DECLARATORS */
14451
14452{
14453 vertex vertexloop;
14454 int vertexnumber;
14455
14456 traversalinit(&m->vertices);
14457 vertexnumber = b->firstnumber;
14458 vertexloop = vertextraverse(m);
14459 while (vertexloop != (vertex) NULL) {
14460 setvertexmark(vertexloop, vertexnumber);
14461 if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) {
14462 vertexnumber++;
14463 }
14464 vertexloop = vertextraverse(m);
14465 }
14466}
14467
14468/*****************************************************************************/
14469/* */
14470/* writeelements() Write the triangles to an .ele file. */
14471/* */
14472/*****************************************************************************/
14473
14474#ifdef TRILIBRARY
14475
14476#ifdef ANSI_DECLARATORS
14477void writeelements(struct mesh *m, struct behavior *b,
14478 int **trianglelist, REAL **triangleattriblist)
14479#else /* not ANSI_DECLARATORS */
14480void writeelements(m, b, trianglelist, triangleattriblist)
14481struct mesh *m;
14482struct behavior *b;
14483int **trianglelist;
14484REAL **triangleattriblist;
14485#endif /* not ANSI_DECLARATORS */
14486
14487#else /* not TRILIBRARY */
14488
14489#ifdef ANSI_DECLARATORS
14490void writeelements(struct mesh *m, struct behavior *b, char *elefilename,
14491 int argc, char **argv)
14492#else /* not ANSI_DECLARATORS */
14493void writeelements(m, b, elefilename, argc, argv)
14494struct mesh *m;
14495struct behavior *b;
14496char *elefilename;
14497int argc;
14498char **argv;
14499#endif /* not ANSI_DECLARATORS */
14500
14501#endif /* not TRILIBRARY */
14502
14503{
14504#ifdef TRILIBRARY
14505 int *tlist;
14506 REAL *talist;
14507 int vertexindex;
14508 int attribindex;
14509#else /* not TRILIBRARY */
14510 FILE *outfile;
14511#endif /* not TRILIBRARY */
14512 struct otri triangleloop;
14513 vertex p1, p2, p3;
14514 vertex mid1, mid2, mid3;
14515 long elementnumber;
14516 int i;
14517
14518#ifdef TRILIBRARY
14519 if (!b->quiet) {
14520 printf("Writing triangles.\n");
14521 }
14522 /* Allocate memory for output triangles if necessary. */
14523 if (*trianglelist == (int *) NULL) {
14524 *trianglelist = (int *) trimalloc((int) (m->triangles.items *
14525 ((b->order + 1) * (b->order + 2) /
14526 2) * sizeof(int)));
14527 }
14528 /* Allocate memory for output triangle attributes if necessary. */
14529 if ((m->eextras > 0) && (*triangleattriblist == (REAL *) NULL)) {
14530 *triangleattriblist = (REAL *) trimalloc((int) (m->triangles.items *
14531 m->eextras *
14532 sizeof(REAL)));
14533 }
14534 tlist = *trianglelist;
14535 talist = *triangleattriblist;
14536 vertexindex = 0;
14537 attribindex = 0;
14538#else /* not TRILIBRARY */
14539 if (!b->quiet) {
14540 printf("Writing %s.\n", elefilename);
14541 }
14542 outfile = fopen(elefilename, "w");
14543 if (outfile == (FILE *) NULL) {
14544 printf(" Error: Cannot create file %s.\n", elefilename);
14545 triexit(1);
14546 }
14547 /* Number of triangles, vertices per triangle, attributes per triangle. */
14548 fprintf(outfile, "%ld %d %d\n", m->triangles.items,
14549 (b->order + 1) * (b->order + 2) / 2, m->eextras);
14550#endif /* not TRILIBRARY */
14551
14552 traversalinit(&m->triangles);
14553 triangleloop.tri = triangletraverse(m);
14554 triangleloop.orient = 0;
14555 elementnumber = b->firstnumber;
14556 while (triangleloop.tri != (triangle *) NULL) {
14557 org(triangleloop, p1);
14558 dest(triangleloop, p2);
14559 apex(triangleloop, p3);
14560 if (b->order == 1) {
14561#ifdef TRILIBRARY
14562 tlist[vertexindex++] = vertexmark(p1);
14563 tlist[vertexindex++] = vertexmark(p2);
14564 tlist[vertexindex++] = vertexmark(p3);
14565#else /* not TRILIBRARY */
14566 /* Triangle number, indices for three vertices. */
14567 fprintf(outfile, "%4ld %4d %4d %4d", elementnumber,
14568 vertexmark(p1), vertexmark(p2), vertexmark(p3));
14569#endif /* not TRILIBRARY */
14570 } else {
14571 mid1 = (vertex) triangleloop.tri[m->highorderindex + 1];
14572 mid2 = (vertex) triangleloop.tri[m->highorderindex + 2];
14573 mid3 = (vertex) triangleloop.tri[m->highorderindex];
14574#ifdef TRILIBRARY
14575 tlist[vertexindex++] = vertexmark(p1);
14576 tlist[vertexindex++] = vertexmark(p2);
14577 tlist[vertexindex++] = vertexmark(p3);
14578 tlist[vertexindex++] = vertexmark(mid1);
14579 tlist[vertexindex++] = vertexmark(mid2);
14580 tlist[vertexindex++] = vertexmark(mid3);
14581#else /* not TRILIBRARY */
14582 /* Triangle number, indices for six vertices. */
14583 fprintf(outfile, "%4ld %4d %4d %4d %4d %4d %4d", elementnumber,
14584 vertexmark(p1), vertexmark(p2), vertexmark(p3), vertexmark(mid1),
14585 vertexmark(mid2), vertexmark(mid3));
14586#endif /* not TRILIBRARY */
14587 }
14588
14589#ifdef TRILIBRARY
14590 for (i = 0; i < m->eextras; i++) {
14591 talist[attribindex++] = elemattribute(triangleloop, i);
14592 }
14593#else /* not TRILIBRARY */
14594 for (i = 0; i < m->eextras; i++) {
14595 fprintf(outfile, " %.17g", elemattribute(triangleloop, i));
14596 }
14597 fprintf(outfile, "\n");
14598#endif /* not TRILIBRARY */
14599
14600 triangleloop.tri = triangletraverse(m);
14601 elementnumber++;
14602 }
14603
14604#ifndef TRILIBRARY
14605 finishfile(outfile, argc, argv);
14606#endif /* not TRILIBRARY */
14607}
14608
14609/*****************************************************************************/
14610/* */
14611/* writepoly() Write the segments and holes to a .poly file. */
14612/* */
14613/*****************************************************************************/
14614
14615#ifdef TRILIBRARY
14616
14617#ifdef ANSI_DECLARATORS
14618void writepoly(struct mesh *m, struct behavior *b,
14619 int **segmentlist, int **segmentmarkerlist)
14620#else /* not ANSI_DECLARATORS */
14621void writepoly(m, b, segmentlist, segmentmarkerlist)
14622struct mesh *m;
14623struct behavior *b;
14624int **segmentlist;
14625int **segmentmarkerlist;
14626#endif /* not ANSI_DECLARATORS */
14627
14628#else /* not TRILIBRARY */
14629
14630#ifdef ANSI_DECLARATORS
14631void writepoly(struct mesh *m, struct behavior *b, char *polyfilename,
14632 REAL *holelist, int holes, REAL *regionlist, int regions,
14633 int argc, char **argv)
14634#else /* not ANSI_DECLARATORS */
14635void writepoly(m, b, polyfilename, holelist, holes, regionlist, regions,
14636 argc, argv)
14637struct mesh *m;
14638struct behavior *b;
14639char *polyfilename;
14640REAL *holelist;
14641int holes;
14642REAL *regionlist;
14643int regions;
14644int argc;
14645char **argv;
14646#endif /* not ANSI_DECLARATORS */
14647
14648#endif /* not TRILIBRARY */
14649
14650{
14651#ifdef TRILIBRARY
14652 int *slist;
14653 int *smlist;
14654 int index;
14655#else /* not TRILIBRARY */
14656 FILE *outfile;
14657 long holenumber, regionnumber;
14658#endif /* not TRILIBRARY */
14659 struct osub subsegloop;
14660 vertex endpoint1, endpoint2;
14661 long subsegnumber;
14662
14663#ifdef TRILIBRARY
14664 if (!b->quiet) {
14665 printf("Writing segments.\n");
14666 }
14667 /* Allocate memory for output segments if necessary. */
14668 if (*segmentlist == (int *) NULL) {
14669 *segmentlist = (int *) trimalloc((int) (m->subsegs.items * 2 *
14670 sizeof(int)));
14671 }
14672 /* Allocate memory for output segment markers if necessary. */
14673 if (!b->nobound && (*segmentmarkerlist == (int *) NULL)) {
14674 *segmentmarkerlist = (int *) trimalloc((int) (m->subsegs.items *
14675 sizeof(int)));
14676 }
14677 slist = *segmentlist;
14678 smlist = *segmentmarkerlist;
14679 index = 0;
14680#else /* not TRILIBRARY */
14681 if (!b->quiet) {
14682 printf("Writing %s.\n", polyfilename);
14683 }
14684 outfile = fopen(polyfilename, "w");
14685 if (outfile == (FILE *) NULL) {
14686 printf(" Error: Cannot create file %s.\n", polyfilename);
14687 triexit(1);
14688 }
14689 /* The zero indicates that the vertices are in a separate .node file. */
14690 /* Followed by number of dimensions, number of vertex attributes, */
14691 /* and number of boundary markers (zero or one). */
14692 fprintf(outfile, "%d %d %d %d\n", 0, m->mesh_dim, m->nextras,
14693 1 - b->nobound);
14694 /* Number of segments, number of boundary markers (zero or one). */
14695 fprintf(outfile, "%ld %d\n", m->subsegs.items, 1 - b->nobound);
14696#endif /* not TRILIBRARY */
14697
14698 traversalinit(&m->subsegs);
14699 subsegloop.ss = subsegtraverse(m);
14700 subsegloop.ssorient = 0;
14701 subsegnumber = b->firstnumber;
14702 while (subsegloop.ss != (subseg *) NULL) {
14703 sorg(subsegloop, endpoint1);
14704 sdest(subsegloop, endpoint2);
14705#ifdef TRILIBRARY
14706 /* Copy indices of the segment's two endpoints. */
14707 slist[index++] = vertexmark(endpoint1);
14708 slist[index++] = vertexmark(endpoint2);
14709 if (!b->nobound) {
14710 /* Copy the boundary marker. */
14711 smlist[subsegnumber - b->firstnumber] = mark(subsegloop);
14712 }
14713#else /* not TRILIBRARY */
14714 /* Segment number, indices of its two endpoints, and possibly a marker. */
14715 if (b->nobound) {
14716 fprintf(outfile, "%4ld %4d %4d\n", subsegnumber,
14717 vertexmark(endpoint1), vertexmark(endpoint2));
14718 } else {
14719 fprintf(outfile, "%4ld %4d %4d %4d\n", subsegnumber,
14720 vertexmark(endpoint1), vertexmark(endpoint2), mark(subsegloop));
14721 }
14722#endif /* not TRILIBRARY */
14723
14724 subsegloop.ss = subsegtraverse(m);
14725 subsegnumber++;
14726 }
14727
14728#ifndef TRILIBRARY
14729#ifndef CDT_ONLY
14730 fprintf(outfile, "%d\n", holes);
14731 if (holes > 0) {
14732 for (holenumber = 0; holenumber < holes; holenumber++) {
14733 /* Hole number, x and y coordinates. */
14734 fprintf(outfile, "%4ld %.17g %.17g\n", b->firstnumber + holenumber,
14735 holelist[2 * holenumber], holelist[2 * holenumber + 1]);
14736 }
14737 }
14738 if (regions > 0) {
14739 fprintf(outfile, "%d\n", regions);
14740 for (regionnumber = 0; regionnumber < regions; regionnumber++) {
14741 /* Region number, x and y coordinates, attribute, maximum area. */
14742 fprintf(outfile, "%4ld %.17g %.17g %.17g %.17g\n",
14743 b->firstnumber + regionnumber,
14744 regionlist[4 * regionnumber], regionlist[4 * regionnumber + 1],
14745 regionlist[4 * regionnumber + 2],
14746 regionlist[4 * regionnumber + 3]);
14747 }
14748 }
14749#endif /* not CDT_ONLY */
14750
14751 finishfile(outfile, argc, argv);
14752#endif /* not TRILIBRARY */
14753}
14754
14755/*****************************************************************************/
14756/* */
14757/* writeedges() Write the edges to an .edge file. */
14758/* */
14759/*****************************************************************************/
14760
14761#ifdef TRILIBRARY
14762
14763#ifdef ANSI_DECLARATORS
14764void writeedges(struct mesh *m, struct behavior *b,
14765 int **edgelist, int **edgemarkerlist)
14766#else /* not ANSI_DECLARATORS */
14767void writeedges(m, b, edgelist, edgemarkerlist)
14768struct mesh *m;
14769struct behavior *b;
14770int **edgelist;
14771int **edgemarkerlist;
14772#endif /* not ANSI_DECLARATORS */
14773
14774#else /* not TRILIBRARY */
14775
14776#ifdef ANSI_DECLARATORS
14777void writeedges(struct mesh *m, struct behavior *b, char *edgefilename,
14778 int argc, char **argv)
14779#else /* not ANSI_DECLARATORS */
14780void writeedges(m, b, edgefilename, argc, argv)
14781struct mesh *m;
14782struct behavior *b;
14783char *edgefilename;
14784int argc;
14785char **argv;
14786#endif /* not ANSI_DECLARATORS */
14787
14788#endif /* not TRILIBRARY */
14789
14790{
14791#ifdef TRILIBRARY
14792 int *elist;
14793 int *emlist;
14794 int index;
14795#else /* not TRILIBRARY */
14796 FILE *outfile;
14797#endif /* not TRILIBRARY */
14798 struct otri triangleloop, trisym;
14799 struct osub checkmark;
14800 vertex p1, p2;
14801 long edgenumber;
14802 triangle ptr; /* Temporary variable used by sym(). */
14803 subseg sptr; /* Temporary variable used by tspivot(). */
14804
14805#ifdef TRILIBRARY
14806 if (!b->quiet) {
14807 printf("Writing edges.\n");
14808 }
14809 /* Allocate memory for edges if necessary. */
14810 if (*edgelist == (int *) NULL) {
14811 *edgelist = (int *) trimalloc((int) (m->edges * 2 * sizeof(int)));
14812 }
14813 /* Allocate memory for edge markers if necessary. */
14814 if (!b->nobound && (*edgemarkerlist == (int *) NULL)) {
14815 *edgemarkerlist = (int *) trimalloc((int) (m->edges * sizeof(int)));
14816 }
14817 elist = *edgelist;
14818 emlist = *edgemarkerlist;
14819 index = 0;
14820#else /* not TRILIBRARY */
14821 if (!b->quiet) {
14822 printf("Writing %s.\n", edgefilename);
14823 }
14824 outfile = fopen(edgefilename, "w");
14825 if (outfile == (FILE *) NULL) {
14826 printf(" Error: Cannot create file %s.\n", edgefilename);
14827 triexit(1);
14828 }
14829 /* Number of edges, number of boundary markers (zero or one). */
14830 fprintf(outfile, "%ld %d\n", m->edges, 1 - b->nobound);
14831#endif /* not TRILIBRARY */
14832
14833 traversalinit(&m->triangles);
14834 triangleloop.tri = triangletraverse(m);
14835 edgenumber = b->firstnumber;
14836 /* To loop over the set of edges, loop over all triangles, and look at */
14837 /* the three edges of each triangle. If there isn't another triangle */
14838 /* adjacent to the edge, operate on the edge. If there is another */
14839 /* adjacent triangle, operate on the edge only if the current triangle */
14840 /* has a smaller pointer than its neighbor. This way, each edge is */
14841 /* considered only once. */
14842 while (triangleloop.tri != (triangle *) NULL) {
14843 for (triangleloop.orient = 0; triangleloop.orient < 3;
14844 triangleloop.orient++) {
14845 sym(triangleloop, trisym);
14846 if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) {
14847 org(triangleloop, p1);
14848 dest(triangleloop, p2);
14849#ifdef TRILIBRARY
14850 elist[index++] = vertexmark(p1);
14851 elist[index++] = vertexmark(p2);
14852#endif /* TRILIBRARY */
14853 if (b->nobound) {
14854#ifndef TRILIBRARY
14855 /* Edge number, indices of two endpoints. */
14856 fprintf(outfile, "%4ld %d %d\n", edgenumber,
14857 vertexmark(p1), vertexmark(p2));
14858#endif /* not TRILIBRARY */
14859 } else {
14860 /* Edge number, indices of two endpoints, and a boundary marker. */
14861 /* If there's no subsegment, the boundary marker is zero. */
14862 if (b->usesegments) {
14863 tspivot(triangleloop, checkmark);
14864 if (checkmark.ss == m->dummysub) {
14865#ifdef TRILIBRARY
14866 emlist[edgenumber - b->firstnumber] = 0;
14867#else /* not TRILIBRARY */
14868 fprintf(outfile, "%4ld %d %d %d\n", edgenumber,
14869 vertexmark(p1), vertexmark(p2), 0);
14870#endif /* not TRILIBRARY */
14871 } else {
14872#ifdef TRILIBRARY
14873 emlist[edgenumber - b->firstnumber] = mark(checkmark);
14874#else /* not TRILIBRARY */
14875 fprintf(outfile, "%4ld %d %d %d\n", edgenumber,
14876 vertexmark(p1), vertexmark(p2), mark(checkmark));
14877#endif /* not TRILIBRARY */
14878 }
14879 } else {
14880#ifdef TRILIBRARY
14881 emlist[edgenumber - b->firstnumber] = trisym.tri == m->dummytri;
14882#else /* not TRILIBRARY */
14883 fprintf(outfile, "%4ld %d %d %d\n", edgenumber,
14884 vertexmark(p1), vertexmark(p2), trisym.tri == m->dummytri);
14885#endif /* not TRILIBRARY */
14886 }
14887 }
14888 edgenumber++;
14889 }
14890 }
14891 triangleloop.tri = triangletraverse(m);
14892 }
14893
14894#ifndef TRILIBRARY
14895 finishfile(outfile, argc, argv);
14896#endif /* not TRILIBRARY */
14897}
14898
14899/*****************************************************************************/
14900/* */
14901/* writevoronoi() Write the Voronoi diagram to a .v.node and .v.edge */
14902/* file. */
14903/* */
14904/* The Voronoi diagram is the geometric dual of the Delaunay triangulation. */
14905/* Hence, the Voronoi vertices are listed by traversing the Delaunay */
14906/* triangles, and the Voronoi edges are listed by traversing the Delaunay */
14907/* edges. */
14908/* */
14909/* WARNING: In order to assign numbers to the Voronoi vertices, this */
14910/* procedure messes up the subsegments or the extra nodes of every */
14911/* element. Hence, you should call this procedure last. */
14912/* */
14913/*****************************************************************************/
14914
14915#ifdef TRILIBRARY
14916
14917#ifdef ANSI_DECLARATORS
14918void writevoronoi(struct mesh *m, struct behavior *b, REAL **vpointlist,
14919 REAL **vpointattriblist, int **vpointmarkerlist,
14920 int **vedgelist, int **vedgemarkerlist, REAL **vnormlist)
14921#else /* not ANSI_DECLARATORS */
14922void writevoronoi(m, b, vpointlist, vpointattriblist, vpointmarkerlist,
14923 vedgelist, vedgemarkerlist, vnormlist)
14924struct mesh *m;
14925struct behavior *b;
14926REAL **vpointlist;
14927REAL **vpointattriblist;
14928int **vpointmarkerlist;
14929int **vedgelist;
14930int **vedgemarkerlist;
14931REAL **vnormlist;
14932#endif /* not ANSI_DECLARATORS */
14933
14934#else /* not TRILIBRARY */
14935
14936#ifdef ANSI_DECLARATORS
14937void writevoronoi(struct mesh *m, struct behavior *b, char *vnodefilename,
14938 char *vedgefilename, int argc, char **argv)
14939#else /* not ANSI_DECLARATORS */
14940void writevoronoi(m, b, vnodefilename, vedgefilename, argc, argv)
14941struct mesh *m;
14942struct behavior *b;
14943char *vnodefilename;
14944char *vedgefilename;
14945int argc;
14946char **argv;
14947#endif /* not ANSI_DECLARATORS */
14948
14949#endif /* not TRILIBRARY */
14950
14951{
14952#ifdef TRILIBRARY
14953 REAL *plist;
14954 REAL *palist;
14955 int *elist;
14956 REAL *normlist;
14957 int coordindex;
14958 int attribindex;
14959#else /* not TRILIBRARY */
14960 FILE *outfile;
14961#endif /* not TRILIBRARY */
14962 struct otri triangleloop, trisym;
14963 vertex torg, tdest, tapex;
14964 REAL circumcenter[2];
14965 REAL xi, eta;
14966 long vnodenumber, vedgenumber;
14967 int p1, p2;
14968 int i;
14969 triangle ptr; /* Temporary variable used by sym(). */
14970
14971#ifdef TRILIBRARY
14972 if (!b->quiet) {
14973 printf("Writing Voronoi vertices.\n");
14974 }
14975 /* Allocate memory for Voronoi vertices if necessary. */
14976 if (*vpointlist == (REAL *) NULL) {
14977 *vpointlist = (REAL *) trimalloc((int) (m->triangles.items * 2 *
14978 sizeof(REAL)));
14979 }
14980 /* Allocate memory for Voronoi vertex attributes if necessary. */
14981 if (*vpointattriblist == (REAL *) NULL) {
14982 *vpointattriblist = (REAL *) trimalloc((int) (m->triangles.items *
14983 m->nextras * sizeof(REAL)));
14984 }
14985 *vpointmarkerlist = (int *) NULL;
14986 plist = *vpointlist;
14987 palist = *vpointattriblist;
14988 coordindex = 0;
14989 attribindex = 0;
14990#else /* not TRILIBRARY */
14991 if (!b->quiet) {
14992 printf("Writing %s.\n", vnodefilename);
14993 }
14994 outfile = fopen(vnodefilename, "w");
14995 if (outfile == (FILE *) NULL) {
14996 printf(" Error: Cannot create file %s.\n", vnodefilename);
14997 triexit(1);
14998 }
14999 /* Number of triangles, two dimensions, number of vertex attributes, */
15000 /* no markers. */
15001 fprintf(outfile, "%ld %d %d %d\n", m->triangles.items, 2, m->nextras, 0);
15002#endif /* not TRILIBRARY */
15003
15004 traversalinit(&m->triangles);
15005 triangleloop.tri = triangletraverse(m);
15006 triangleloop.orient = 0;
15007 vnodenumber = b->firstnumber;
15008 while (triangleloop.tri != (triangle *) NULL) {
15009 org(triangleloop, torg);
15010 dest(triangleloop, tdest);
15011 apex(triangleloop, tapex);
15012 findcircumcenter(m, b, torg, tdest, tapex, circumcenter, &xi, &eta, 0);
15013#ifdef TRILIBRARY
15014 /* X and y coordinates. */
15015 plist[coordindex++] = circumcenter[0];
15016 plist[coordindex++] = circumcenter[1];
15017 for (i = 2; i < 2 + m->nextras; i++) {
15018 /* Interpolate the vertex attributes at the circumcenter. */
15019 palist[attribindex++] = torg[i] + xi * (tdest[i] - torg[i])
15020 + eta * (tapex[i] - torg[i]);
15021 }
15022#else /* not TRILIBRARY */
15023 /* Voronoi vertex number, x and y coordinates. */
15024 fprintf(outfile, "%4ld %.17g %.17g", vnodenumber, circumcenter[0],
15025 circumcenter[1]);
15026 for (i = 2; i < 2 + m->nextras; i++) {
15027 /* Interpolate the vertex attributes at the circumcenter. */
15028 fprintf(outfile, " %.17g", torg[i] + xi * (tdest[i] - torg[i])
15029 + eta * (tapex[i] - torg[i]));
15030 }
15031 fprintf(outfile, "\n");
15032#endif /* not TRILIBRARY */
15033
15034 * (int *) (triangleloop.tri + 6) = (int) vnodenumber;
15035 triangleloop.tri = triangletraverse(m);
15036 vnodenumber++;
15037 }
15038
15039#ifndef TRILIBRARY
15040 finishfile(outfile, argc, argv);
15041#endif /* not TRILIBRARY */
15042
15043#ifdef TRILIBRARY
15044 if (!b->quiet) {
15045 printf("Writing Voronoi edges.\n");
15046 }
15047 /* Allocate memory for output Voronoi edges if necessary. */
15048 if (*vedgelist == (int *) NULL) {
15049 *vedgelist = (int *) trimalloc((int) (m->edges * 2 * sizeof(int)));
15050 }
15051 *vedgemarkerlist = (int *) NULL;
15052 /* Allocate memory for output Voronoi norms if necessary. */
15053 if (*vnormlist == (REAL *) NULL) {
15054 *vnormlist = (REAL *) trimalloc((int) (m->edges * 2 * sizeof(REAL)));
15055 }
15056 elist = *vedgelist;
15057 normlist = *vnormlist;
15058 coordindex = 0;
15059#else /* not TRILIBRARY */
15060 if (!b->quiet) {
15061 printf("Writing %s.\n", vedgefilename);
15062 }
15063 outfile = fopen(vedgefilename, "w");
15064 if (outfile == (FILE *) NULL) {
15065 printf(" Error: Cannot create file %s.\n", vedgefilename);
15066 triexit(1);
15067 }
15068 /* Number of edges, zero boundary markers. */
15069 fprintf(outfile, "%ld %d\n", m->edges, 0);
15070#endif /* not TRILIBRARY */
15071
15072 traversalinit(&m->triangles);
15073 triangleloop.tri = triangletraverse(m);
15074 vedgenumber = b->firstnumber;
15075 /* To loop over the set of edges, loop over all triangles, and look at */
15076 /* the three edges of each triangle. If there isn't another triangle */
15077 /* adjacent to the edge, operate on the edge. If there is another */
15078 /* adjacent triangle, operate on the edge only if the current triangle */
15079 /* has a smaller pointer than its neighbor. This way, each edge is */
15080 /* considered only once. */
15081 while (triangleloop.tri != (triangle *) NULL) {
15082 for (triangleloop.orient = 0; triangleloop.orient < 3;
15083 triangleloop.orient++) {
15084 sym(triangleloop, trisym);
15085 if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) {
15086 /* Find the number of this triangle (and Voronoi vertex). */
15087 p1 = * (int *) (triangleloop.tri + 6);
15088 if (trisym.tri == m->dummytri) {
15089 org(triangleloop, torg);
15090 dest(triangleloop, tdest);
15091#ifdef TRILIBRARY
15092 /* Copy an infinite ray. Index of one endpoint, and -1. */
15093 elist[coordindex] = p1;
15094 normlist[coordindex++] = tdest[1] - torg[1];
15095 elist[coordindex] = -1;
15096 normlist[coordindex++] = torg[0] - tdest[0];
15097#else /* not TRILIBRARY */
15098 /* Write an infinite ray. Edge number, index of one endpoint, -1, */
15099 /* and x and y coordinates of a vector representing the */
15100 /* direction of the ray. */
15101 fprintf(outfile, "%4ld %d %d %.17g %.17g\n", vedgenumber,
15102 p1, -1, tdest[1] - torg[1], torg[0] - tdest[0]);
15103#endif /* not TRILIBRARY */
15104 } else {
15105 /* Find the number of the adjacent triangle (and Voronoi vertex). */
15106 p2 = * (int *) (trisym.tri + 6);
15107 /* Finite edge. Write indices of two endpoints. */
15108#ifdef TRILIBRARY
15109 elist[coordindex] = p1;
15110 normlist[coordindex++] = 0.0;
15111 elist[coordindex] = p2;
15112 normlist[coordindex++] = 0.0;
15113#else /* not TRILIBRARY */
15114 fprintf(outfile, "%4ld %d %d\n", vedgenumber, p1, p2);
15115#endif /* not TRILIBRARY */
15116 }
15117 vedgenumber++;
15118 }
15119 }
15120 triangleloop.tri = triangletraverse(m);
15121 }
15122
15123#ifndef TRILIBRARY
15124 finishfile(outfile, argc, argv);
15125#endif /* not TRILIBRARY */
15126}
15127
15128#ifdef TRILIBRARY
15129
15130#ifdef ANSI_DECLARATORS
15131void writeneighbors(struct mesh *m, struct behavior *b, int **neighborlist)
15132#else /* not ANSI_DECLARATORS */
15133void writeneighbors(m, b, neighborlist)
15134struct mesh *m;
15135struct behavior *b;
15136int **neighborlist;
15137#endif /* not ANSI_DECLARATORS */
15138
15139#else /* not TRILIBRARY */
15140
15141#ifdef ANSI_DECLARATORS
15142void writeneighbors(struct mesh *m, struct behavior *b, char *neighborfilename,
15143 int argc, char **argv)
15144#else /* not ANSI_DECLARATORS */
15145void writeneighbors(m, b, neighborfilename, argc, argv)
15146struct mesh *m;
15147struct behavior *b;
15148char *neighborfilename;
15149int argc;
15150char **argv;
15151#endif /* not ANSI_DECLARATORS */
15152
15153#endif /* not TRILIBRARY */
15154
15155{
15156#ifdef TRILIBRARY
15157 int *nlist;
15158 int index;
15159#else /* not TRILIBRARY */
15160 FILE *outfile;
15161#endif /* not TRILIBRARY */
15162 struct otri triangleloop, trisym;
15163 long elementnumber;
15164 int neighbor1, neighbor2, neighbor3;
15165 triangle ptr; /* Temporary variable used by sym(). */
15166
15167#ifdef TRILIBRARY
15168 if (!b->quiet) {
15169 printf("Writing neighbors.\n");
15170 }
15171 /* Allocate memory for neighbors if necessary. */
15172 if (*neighborlist == (int *) NULL) {
15173 *neighborlist = (int *) trimalloc((int) (m->triangles.items * 3 *
15174 sizeof(int)));
15175 }
15176 nlist = *neighborlist;
15177 index = 0;
15178#else /* not TRILIBRARY */
15179 if (!b->quiet) {
15180 printf("Writing %s.\n", neighborfilename);
15181 }
15182 outfile = fopen(neighborfilename, "w");
15183 if (outfile == (FILE *) NULL) {
15184 printf(" Error: Cannot create file %s.\n", neighborfilename);
15185 triexit(1);
15186 }
15187 /* Number of triangles, three neighbors per triangle. */
15188 fprintf(outfile, "%ld %d\n", m->triangles.items, 3);
15189#endif /* not TRILIBRARY */
15190
15191 traversalinit(&m->triangles);
15192 triangleloop.tri = triangletraverse(m);
15193 triangleloop.orient = 0;
15194 elementnumber = b->firstnumber;
15195 while (triangleloop.tri != (triangle *) NULL) {
15196 * (int *) (triangleloop.tri + 6) = (int) elementnumber;
15197 triangleloop.tri = triangletraverse(m);
15198 elementnumber++;
15199 }
15200 * (int *) (m->dummytri + 6) = -1;
15201
15202 traversalinit(&m->triangles);
15203 triangleloop.tri = triangletraverse(m);
15204 elementnumber = b->firstnumber;
15205 while (triangleloop.tri != (triangle *) NULL) {
15206 triangleloop.orient = 1;
15207 sym(triangleloop, trisym);
15208 neighbor1 = * (int *) (trisym.tri + 6);
15209 triangleloop.orient = 2;
15210 sym(triangleloop, trisym);
15211 neighbor2 = * (int *) (trisym.tri + 6);
15212 triangleloop.orient = 0;
15213 sym(triangleloop, trisym);
15214 neighbor3 = * (int *) (trisym.tri + 6);
15215#ifdef TRILIBRARY
15216 nlist[index++] = neighbor1;
15217 nlist[index++] = neighbor2;
15218 nlist[index++] = neighbor3;
15219#else /* not TRILIBRARY */
15220 /* Triangle number, neighboring triangle numbers. */
15221 fprintf(outfile, "%4ld %d %d %d\n", elementnumber,
15222 neighbor1, neighbor2, neighbor3);
15223#endif /* not TRILIBRARY */
15224
15225 triangleloop.tri = triangletraverse(m);
15226 elementnumber++;
15227 }
15228
15229#ifndef TRILIBRARY
15230 finishfile(outfile, argc, argv);
15231#endif /* not TRILIBRARY */
15232}
15233
15234/*****************************************************************************/
15235/* */
15236/* writeoff() Write the triangulation to an .off file. */
15237/* */
15238/* OFF stands for the Object File Format, a format used by the Geometry */
15239/* Center's Geomview package. */
15240/* */
15241/*****************************************************************************/
15242
15243#ifndef TRILIBRARY
15244
15245#ifdef ANSI_DECLARATORS
15246void writeoff(struct mesh *m, struct behavior *b, char *offfilename,
15247 int argc, char **argv)
15248#else /* not ANSI_DECLARATORS */
15249void writeoff(m, b, offfilename, argc, argv)
15250struct mesh *m;
15251struct behavior *b;
15252char *offfilename;
15253int argc;
15254char **argv;
15255#endif /* not ANSI_DECLARATORS */
15256
15257{
15258 FILE *outfile;
15259 struct otri triangleloop;
15260 vertex vertexloop;
15261 vertex p1, p2, p3;
15262 long outvertices;
15263
15264 if (!b->quiet) {
15265 printf("Writing %s.\n", offfilename);
15266 }
15267
15268 if (b->jettison) {
15269 outvertices = m->vertices.items - m->undeads;
15270 } else {
15271 outvertices = m->vertices.items;
15272 }
15273
15274 outfile = fopen(offfilename, "w");
15275 if (outfile == (FILE *) NULL) {
15276 printf(" Error: Cannot create file %s.\n", offfilename);
15277 triexit(1);
15278 }
15279 /* Number of vertices, triangles, and edges. */
15280 fprintf(outfile, "OFF\n%ld %ld %ld\n", outvertices, m->triangles.items,
15281 m->edges);
15282
15283 /* Write the vertices. */
15284 traversalinit(&m->vertices);
15285 vertexloop = vertextraverse(m);
15286 while (vertexloop != (vertex) NULL) {
15287 if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) {
15288 /* The "0.0" is here because the OFF format uses 3D coordinates. */
15289 fprintf(outfile, " %.17g %.17g %.17g\n", vertexloop[0], vertexloop[1],
15290 0.0);
15291 }
15292 vertexloop = vertextraverse(m);
15293 }
15294
15295 /* Write the triangles. */
15296 traversalinit(&m->triangles);
15297 triangleloop.tri = triangletraverse(m);
15298 triangleloop.orient = 0;
15299 while (triangleloop.tri != (triangle *) NULL) {
15300 org(triangleloop, p1);
15301 dest(triangleloop, p2);
15302 apex(triangleloop, p3);
15303 /* The "3" means a three-vertex polygon. */
15304 fprintf(outfile, " 3 %4d %4d %4d\n", vertexmark(p1) - b->firstnumber,
15305 vertexmark(p2) - b->firstnumber, vertexmark(p3) - b->firstnumber);
15306 triangleloop.tri = triangletraverse(m);
15307 }
15308 finishfile(outfile, argc, argv);
15309}
15310
15311#endif /* not TRILIBRARY */
15312
15313/** **/
15314/** **/
15315/********* File I/O routines end here *********/
15316
15317/*****************************************************************************/
15318/* */
15319/* quality_statistics() Print statistics about the quality of the mesh. */
15320/* */
15321/*****************************************************************************/
15322
15323#ifdef ANSI_DECLARATORS
15324void quality_statistics(struct mesh *m, struct behavior *b)
15325#else /* not ANSI_DECLARATORS */
15326void quality_statistics(m, b)
15327struct mesh *m;
15328struct behavior *b;
15329#endif /* not ANSI_DECLARATORS */
15330
15331{
15332 struct otri triangleloop;
15333 vertex p[3];
15334 REAL cossquaretable[8];
15335 REAL ratiotable[16];
15336 REAL dx[3], dy[3];
15337 REAL edgelength[3];
15338 REAL dotproduct;
15339 REAL cossquare;
15340 REAL triarea;
15341 REAL shortest, longest;
15342 REAL trilongest2;
15343 REAL smallestarea, biggestarea;
15344 REAL triminaltitude2;
15345 REAL minaltitude;
15346 REAL triaspect2;
15347 REAL worstaspect;
15348 REAL smallestangle, biggestangle;
15349 REAL radconst, degconst;
15350 int angletable[18];
15351 int aspecttable[16];
15352 int aspectindex;
15353 int tendegree;
15354 int acutebiggest;
15355 int i, ii, j, k;
15356
15357 printf("Mesh quality statistics:\n\n");
15358 radconst = PI / 18.0;
15359 degconst = 180.0 / PI;
15360 for (i = 0; i < 8; i++) {
15361 cossquaretable[i] = cos(radconst * (REAL) (i + 1));
15362 cossquaretable[i] = cossquaretable[i] * cossquaretable[i];
15363 }
15364 for (i = 0; i < 18; i++) {
15365 angletable[i] = 0;
15366 }
15367
15368 ratiotable[0] = 1.5; ratiotable[1] = 2.0;
15369 ratiotable[2] = 2.5; ratiotable[3] = 3.0;
15370 ratiotable[4] = 4.0; ratiotable[5] = 6.0;
15371 ratiotable[6] = 10.0; ratiotable[7] = 15.0;
15372 ratiotable[8] = 25.0; ratiotable[9] = 50.0;
15373 ratiotable[10] = 100.0; ratiotable[11] = 300.0;
15374 ratiotable[12] = 1000.0; ratiotable[13] = 10000.0;
15375 ratiotable[14] = 100000.0; ratiotable[15] = 0.0;
15376 for (i = 0; i < 16; i++) {
15377 aspecttable[i] = 0;
15378 }
15379
15380 worstaspect = 0.0;
15381 minaltitude = m->xmax - m->xmin + m->ymax - m->ymin;
15382 minaltitude = minaltitude * minaltitude;
15383 shortest = minaltitude;
15384 longest = 0.0;
15385 smallestarea = minaltitude;
15386 biggestarea = 0.0;
15387 worstaspect = 0.0;
15388 smallestangle = 0.0;
15389 biggestangle = 2.0;
15390 acutebiggest = 1;
15391
15392 traversalinit(&m->triangles);
15393 triangleloop.tri = triangletraverse(m);
15394 triangleloop.orient = 0;
15395 while (triangleloop.tri != (triangle *) NULL) {
15396 org(triangleloop, p[0]);
15397 dest(triangleloop, p[1]);
15398 apex(triangleloop, p[2]);
15399 trilongest2 = 0.0;
15400
15401 for (i = 0; i < 3; i++) {
15402 j = plus1mod3[i];
15403 k = minus1mod3[i];
15404 dx[i] = p[j][0] - p[k][0];
15405 dy[i] = p[j][1] - p[k][1];
15406 edgelength[i] = dx[i] * dx[i] + dy[i] * dy[i];
15407 if (edgelength[i] > trilongest2) {
15408 trilongest2 = edgelength[i];
15409 }
15410 if (edgelength[i] > longest) {
15411 longest = edgelength[i];
15412 }
15413 if (edgelength[i] < shortest) {
15414 shortest = edgelength[i];
15415 }
15416 }
15417
15418 triarea = counterclockwise(m, b, p[0], p[1], p[2]);
15419 if (triarea < smallestarea) {
15420 smallestarea = triarea;
15421 }
15422 if (triarea > biggestarea) {
15423 biggestarea = triarea;
15424 }
15425 triminaltitude2 = triarea * triarea / trilongest2;
15426 if (triminaltitude2 < minaltitude) {
15427 minaltitude = triminaltitude2;
15428 }
15429 triaspect2 = trilongest2 / triminaltitude2;
15430 if (triaspect2 > worstaspect) {
15431 worstaspect = triaspect2;
15432 }
15433 aspectindex = 0;
15434 while ((aspectindex < 15) &&
15435 (triaspect2 > ratiotable[aspectindex] * ratiotable[aspectindex])
15436 ) {
15437 aspectindex++;
15438 }
15439 aspecttable[aspectindex]++;
15440
15441 for (i = 0; i < 3; i++) {
15442 j = plus1mod3[i];
15443 k = minus1mod3[i];
15444 dotproduct = dx[j] * dx[k] + dy[j] * dy[k];
15445 cossquare = dotproduct * dotproduct / (edgelength[j] * edgelength[k]);
15446 tendegree = 8;
15447 for (ii = 7; ii >= 0; ii--) {
15448 if (cossquare > cossquaretable[ii]) {
15449 tendegree = ii;
15450 }
15451 }
15452 if (dotproduct <= 0.0) {
15453 angletable[tendegree]++;
15454 if (cossquare > smallestangle) {
15455 smallestangle = cossquare;
15456 }
15457 if (acutebiggest && (cossquare < biggestangle)) {
15458 biggestangle = cossquare;
15459 }
15460 } else {
15461 angletable[17 - tendegree]++;
15462 if (acutebiggest || (cossquare > biggestangle)) {
15463 biggestangle = cossquare;
15464 acutebiggest = 0;
15465 }
15466 }
15467 }
15468 triangleloop.tri = triangletraverse(m);
15469 }
15470
15471 shortest = sqrt(shortest);
15472 longest = sqrt(longest);
15473 minaltitude = sqrt(minaltitude);
15474 worstaspect = sqrt(worstaspect);
15475 smallestarea *= 0.5;
15476 biggestarea *= 0.5;
15477 if (smallestangle >= 1.0) {
15478 smallestangle = 0.0;
15479 } else {
15480 smallestangle = degconst * acos(sqrt(smallestangle));
15481 }
15482 if (biggestangle >= 1.0) {
15483 biggestangle = 180.0;
15484 } else {
15485 if (acutebiggest) {
15486 biggestangle = degconst * acos(sqrt(biggestangle));
15487 } else {
15488 biggestangle = 180.0 - degconst * acos(sqrt(biggestangle));
15489 }
15490 }
15491
15492 printf(" Smallest area: %16.5g | Largest area: %16.5g\n",
15493 smallestarea, biggestarea);
15494 printf(" Shortest edge: %16.5g | Longest edge: %16.5g\n",
15495 shortest, longest);
15496 printf(" Shortest altitude: %12.5g | Largest aspect ratio: %8.5g\n\n",
15497 minaltitude, worstaspect);
15498
15499 printf(" Triangle aspect ratio histogram:\n");
15500 printf(" 1.1547 - %-6.6g : %8d | %6.6g - %-6.6g : %8d\n",
15501 ratiotable[0], aspecttable[0], ratiotable[7], ratiotable[8],
15502 aspecttable[8]);
15503 for (i = 1; i < 7; i++) {
15504 printf(" %6.6g - %-6.6g : %8d | %6.6g - %-6.6g : %8d\n",
15505 ratiotable[i - 1], ratiotable[i], aspecttable[i],
15506 ratiotable[i + 7], ratiotable[i + 8], aspecttable[i + 8]);
15507 }
15508 printf(" %6.6g - %-6.6g : %8d | %6.6g - : %8d\n",
15509 ratiotable[6], ratiotable[7], aspecttable[7], ratiotable[14],
15510 aspecttable[15]);
15511 printf(" (Aspect ratio is longest edge divided by shortest altitude)\n\n");
15512
15513 printf(" Smallest angle: %15.5g | Largest angle: %15.5g\n\n",
15514 smallestangle, biggestangle);
15515
15516 printf(" Angle histogram:\n");
15517 for (i = 0; i < 9; i++) {
15518 printf(" %3d - %3d degrees: %8d | %3d - %3d degrees: %8d\n",
15519 i * 10, i * 10 + 10, angletable[i],
15520 i * 10 + 90, i * 10 + 100, angletable[i + 9]);
15521 }
15522 printf("\n");
15523}
15524
15525/*****************************************************************************/
15526/* */
15527/* statistics() Print all sorts of cool facts. */
15528/* */
15529/*****************************************************************************/
15530
15531#ifdef ANSI_DECLARATORS
15532void statistics(struct mesh *m, struct behavior *b)
15533#else /* not ANSI_DECLARATORS */
15534void statistics(m, b)
15535struct mesh *m;
15536struct behavior *b;
15537#endif /* not ANSI_DECLARATORS */
15538
15539{
15540 printf("\nStatistics:\n\n");
15541 printf(" Input vertices: %d\n", m->invertices);
15542 if (b->refine) {
15543 printf(" Input triangles: %d\n", m->inelements);
15544 }
15545 if (b->poly) {
15546 printf(" Input segments: %d\n", m->insegments);
15547 if (!b->refine) {
15548 printf(" Input holes: %d\n", m->holes);
15549 }
15550 }
15551
15552 printf("\n Mesh vertices: %ld\n", m->vertices.items - m->undeads);
15553 printf(" Mesh triangles: %ld\n", m->triangles.items);
15554 printf(" Mesh edges: %ld\n", m->edges);
15555 printf(" Mesh exterior boundary edges: %ld\n", m->hullsize);
15556 if (b->poly || b->refine) {
15557 printf(" Mesh interior boundary edges: %ld\n",
15558 m->subsegs.items - m->hullsize);
15559 printf(" Mesh subsegments (constrained edges): %ld\n",
15560 m->subsegs.items);
15561 }
15562 printf("\n");
15563
15564 if (b->verbose) {
15565 quality_statistics(m, b);
15566 printf("Memory allocation statistics:\n\n");
15567 printf(" Maximum number of vertices: %ld\n", m->vertices.maxitems);
15568 printf(" Maximum number of triangles: %ld\n", m->triangles.maxitems);
15569 if (m->subsegs.maxitems > 0) {
15570 printf(" Maximum number of subsegments: %ld\n", m->subsegs.maxitems);
15571 }
15572 if (m->viri.maxitems > 0) {
15573 printf(" Maximum number of viri: %ld\n", m->viri.maxitems);
15574 }
15575 if (m->badsubsegs.maxitems > 0) {
15576 printf(" Maximum number of encroached subsegments: %ld\n",
15577 m->badsubsegs.maxitems);
15578 }
15579 if (m->badtriangles.maxitems > 0) {
15580 printf(" Maximum number of bad triangles: %ld\n",
15581 m->badtriangles.maxitems);
15582 }
15583 if (m->flipstackers.maxitems > 0) {
15584 printf(" Maximum number of stacked triangle flips: %ld\n",
15585 m->flipstackers.maxitems);
15586 }
15587 if (m->splaynodes.maxitems > 0) {
15588 printf(" Maximum number of splay tree nodes: %ld\n",
15589 m->splaynodes.maxitems);
15590 }
15591 printf(" Approximate heap memory use (bytes): %ld\n\n",
15592 m->vertices.maxitems * m->vertices.itembytes +
15593 m->triangles.maxitems * m->triangles.itembytes +
15594 m->subsegs.maxitems * m->subsegs.itembytes +
15595 m->viri.maxitems * m->viri.itembytes +
15596 m->badsubsegs.maxitems * m->badsubsegs.itembytes +
15597 m->badtriangles.maxitems * m->badtriangles.itembytes +
15598 m->flipstackers.maxitems * m->flipstackers.itembytes +
15599 m->splaynodes.maxitems * m->splaynodes.itembytes);
15600
15601 printf("Algorithmic statistics:\n\n");
15602 if (!b->weighted) {
15603 printf(" Number of incircle tests: %ld\n", m->incirclecount);
15604 } else {
15605 printf(" Number of 3D orientation tests: %ld\n", m->orient3dcount);
15606 }
15607 printf(" Number of 2D orientation tests: %ld\n", m->counterclockcount);
15608 if (m->hyperbolacount > 0) {
15609 printf(" Number of right-of-hyperbola tests: %ld\n",
15610 m->hyperbolacount);
15611 }
15612 if (m->circletopcount > 0) {
15613 printf(" Number of circle top computations: %ld\n",
15614 m->circletopcount);
15615 }
15616 if (m->circumcentercount > 0) {
15617 printf(" Number of triangle circumcenter computations: %ld\n",
15618 m->circumcentercount);
15619 }
15620 printf("\n");
15621 }
15622}
15623
15624/*****************************************************************************/
15625/* */
15626/* main() or triangulate() Gosh, do everything. */
15627/* */
15628/* The sequence is roughly as follows. Many of these steps can be skipped, */
15629/* depending on the command line switches. */
15630/* */
15631/* - Initialize constants and parse the command line. */
15632/* - Read the vertices from a file and either */
15633/* - triangulate them (no -r), or */
15634/* - read an old mesh from files and reconstruct it (-r). */
15635/* - Insert the PSLG segments (-p), and possibly segments on the convex */
15636/* hull (-c). */
15637/* - Read the holes (-p), regional attributes (-pA), and regional area */
15638/* constraints (-pa). Carve the holes and concavities, and spread the */
15639/* regional attributes and area constraints. */
15640/* - Enforce the constraints on minimum angle (-q) and maximum area (-a). */
15641/* Also enforce the conforming Delaunay property (-q and -a). */
15642/* - Compute the number of edges in the resulting mesh. */
15643/* - Promote the mesh's linear triangles to higher order elements (-o). */
15644/* - Write the output files and print the statistics. */
15645/* - Check the consistency and Delaunay property of the mesh (-C). */
15646/* */
15647/*****************************************************************************/
15648
15649#ifdef TRILIBRARY
15650
15651#ifdef ANSI_DECLARATORS
15652void triangulate(char *triswitches, struct triangulateio *in,
15653 struct triangulateio *out, struct triangulateio *vorout)
15654#else /* not ANSI_DECLARATORS */
15655void triangulate(triswitches, in, out, vorout)
15656char *triswitches;
15657struct triangulateio *in;
15658struct triangulateio *out;
15659struct triangulateio *vorout;
15660#endif /* not ANSI_DECLARATORS */
15661
15662#else /* not TRILIBRARY */
15663
15664#ifdef ANSI_DECLARATORS
15665int main(int argc, char **argv)
15666#else /* not ANSI_DECLARATORS */
15667int main(argc, argv)
15668int argc;
15669char **argv;
15670#endif /* not ANSI_DECLARATORS */
15671
15672#endif /* not TRILIBRARY */
15673
15674{
15675 struct mesh m;
15676 struct behavior b;
15677 REAL *holearray; /* Array of holes. */
15678 REAL *regionarray; /* Array of regional attributes and area constraints. */
15679#ifndef TRILIBRARY
15680 FILE *polyfile;
15681#endif /* not TRILIBRARY */
15682#ifndef NO_TIMER
15683 /* Variables for timing the performance of Triangle. The types are */
15684 /* defined in sys/time.h. */
15685 struct timeval tv0, tv1, tv2, tv3, tv4, tv5, tv6;
15686 struct timezone tz;
15687#endif /* not NO_TIMER */
15688
15689#ifndef NO_TIMER
15690 gettimeofday(&tv0, &tz);
15691#endif /* not NO_TIMER */
15692
15693 triangleinit(&m);
15694#ifdef TRILIBRARY
15695 parsecommandline(1, &triswitches, &b);
15696#else /* not TRILIBRARY */
15697 parsecommandline(argc, argv, &b);
15698#endif /* not TRILIBRARY */
15699 m.steinerleft = b.steiner;
15700
15701#ifdef TRILIBRARY
15702 transfernodes(&m, &b, in->pointlist, in->pointattributelist,
15703 in->pointmarkerlist, in->numberofpoints,
15704 in->numberofpointattributes);
15705#else /* not TRILIBRARY */
15706 readnodes(&m, &b, b.innodefilename, b.inpolyfilename, &polyfile);
15707#endif /* not TRILIBRARY */
15708
15709#ifndef NO_TIMER
15710 if (!b.quiet) {
15711 gettimeofday(&tv1, &tz);
15712 }
15713#endif /* not NO_TIMER */
15714
15715#ifdef CDT_ONLY
15716 m.hullsize = delaunay(&m, &b); /* Triangulate the vertices. */
15717#else /* not CDT_ONLY */
15718 if (b.refine) {
15719 /* Read and reconstruct a mesh. */
15720#ifdef TRILIBRARY
15721 m.hullsize = reconstruct(&m, &b, in->trianglelist,
15722 in->triangleattributelist, in->trianglearealist,
15723 in->numberoftriangles, in->numberofcorners,
15724 in->numberoftriangleattributes,
15725 in->segmentlist, in->segmentmarkerlist,
15726 in->numberofsegments);
15727#else /* not TRILIBRARY */
15728 m.hullsize = reconstruct(&m, &b, b.inelefilename, b.areafilename,
15729 b.inpolyfilename, polyfile);
15730#endif /* not TRILIBRARY */
15731 } else {
15732 m.hullsize = delaunay(&m, &b); /* Triangulate the vertices. */
15733 }
15734#endif /* not CDT_ONLY */
15735
15736#ifndef NO_TIMER
15737 if (!b.quiet) {
15738 gettimeofday(&tv2, &tz);
15739 if (b.refine) {
15740 printf("Mesh reconstruction");
15741 } else {
15742 printf("Delaunay");
15743 }
15744 printf(" milliseconds: %ld\n", 1000l * (tv2.tv_sec - tv1.tv_sec) +
15745 (tv2.tv_usec - tv1.tv_usec) / 1000l);
15746 }
15747#endif /* not NO_TIMER */
15748
15749 /* Ensure that no vertex can be mistaken for a triangular bounding */
15750 /* box vertex in insertvertex(). */
15751 m.infvertex1 = (vertex) NULL;
15752 m.infvertex2 = (vertex) NULL;
15753 m.infvertex3 = (vertex) NULL;
15754
15755 if (b.usesegments) {
15756 m.checksegments = 1; /* Segments will be introduced next. */
15757 if (!b.refine) {
15758 /* Insert PSLG segments and/or convex hull segments. */
15759#ifdef TRILIBRARY
15760 formskeleton(&m, &b, in->segmentlist,
15761 in->segmentmarkerlist, in->numberofsegments);
15762#else /* not TRILIBRARY */
15763 formskeleton(&m, &b, polyfile, b.inpolyfilename);
15764#endif /* not TRILIBRARY */
15765 }
15766 }
15767
15768#ifndef NO_TIMER
15769 if (!b.quiet) {
15770 gettimeofday(&tv3, &tz);
15771 if (b.usesegments && !b.refine) {
15772 printf("Segment milliseconds: %ld\n",
15773 1000l * (tv3.tv_sec - tv2.tv_sec) +
15774 (tv3.tv_usec - tv2.tv_usec) / 1000l);
15775 }
15776 }
15777#endif /* not NO_TIMER */
15778
15779 if (b.poly && (m.triangles.items > 0)) {
15780#ifdef TRILIBRARY
15781 holearray = in->holelist;
15782 m.holes = in->numberofholes;
15783 regionarray = in->regionlist;
15784 m.regions = in->numberofregions;
15785#else /* not TRILIBRARY */
15786 readholes(&m, &b, polyfile, b.inpolyfilename, &holearray, &m.holes,
15787 &regionarray, &m.regions);
15788#endif /* not TRILIBRARY */
15789 if (!b.refine) {
15790 /* Carve out holes and concavities. */
15791 carveholes(&m, &b, holearray, m.holes, regionarray, m.regions);
15792 }
15793 } else {
15794 /* Without a PSLG, there can be no holes or regional attributes */
15795 /* or area constraints. The following are set to zero to avoid */
15796 /* an accidental free() later. */
15797 m.holes = 0;
15798 m.regions = 0;
15799 }
15800
15801#ifndef NO_TIMER
15802 if (!b.quiet) {
15803 gettimeofday(&tv4, &tz);
15804 if (b.poly && !b.refine) {
15805 printf("Hole milliseconds: %ld\n", 1000l * (tv4.tv_sec - tv3.tv_sec) +
15806 (tv4.tv_usec - tv3.tv_usec) / 1000l);
15807 }
15808 }
15809#endif /* not NO_TIMER */
15810
15811#ifndef CDT_ONLY
15812 if (b.quality && (m.triangles.items > 0)) {
15813 enforcequality(&m, &b); /* Enforce angle and area constraints. */
15814 }
15815#endif /* not CDT_ONLY */
15816
15817#ifndef NO_TIMER
15818 if (!b.quiet) {
15819 gettimeofday(&tv5, &tz);
15820#ifndef CDT_ONLY
15821 if (b.quality) {
15822 printf("Quality milliseconds: %ld\n",
15823 1000l * (tv5.tv_sec - tv4.tv_sec) +
15824 (tv5.tv_usec - tv4.tv_usec) / 1000l);
15825 }
15826#endif /* not CDT_ONLY */
15827 }
15828#endif /* not NO_TIMER */
15829
15830 /* Calculate the number of edges. */
15831 m.edges = (3l * m.triangles.items + m.hullsize) / 2l;
15832
15833 if (b.order > 1) {
15834 highorder(&m, &b); /* Promote elements to higher polynomial order. */
15835 }
15836 if (!b.quiet) {
15837 printf("\n");
15838 }
15839
15840#ifdef TRILIBRARY
15841 if (b.jettison) {
15842 out->numberofpoints = m.vertices.items - m.undeads;
15843 } else {
15844 out->numberofpoints = m.vertices.items;
15845 }
15846 out->numberofpointattributes = m.nextras;
15847 out->numberoftriangles = m.triangles.items;
15848 out->numberofcorners = (b.order + 1) * (b.order + 2) / 2;
15849 out->numberoftriangleattributes = m.eextras;
15850 out->numberofedges = m.edges;
15851 if (b.usesegments) {
15852 out->numberofsegments = m.subsegs.items;
15853 } else {
15854 out->numberofsegments = m.hullsize;
15855 }
15856 if (vorout != (struct triangulateio *) NULL) {
15857 vorout->numberofpoints = m.triangles.items;
15858 vorout->numberofpointattributes = m.nextras;
15859 vorout->numberofedges = m.edges;
15860 }
15861#endif /* TRILIBRARY */
15862 /* If not using iteration numbers, don't write a .node file if one was */
15863 /* read, because the original one would be overwritten! */
15864 if (b.nonodewritten || (b.noiterationnum && m.readnodefile)) {
15865 if (!b.quiet) {
15866#ifdef TRILIBRARY
15867 printf("NOT writing vertices.\n");
15868#else /* not TRILIBRARY */
15869 printf("NOT writing a .node file.\n");
15870#endif /* not TRILIBRARY */
15871 }
15872 numbernodes(&m, &b); /* We must remember to number the vertices. */
15873 } else {
15874 /* writenodes() numbers the vertices too. */
15875#ifdef TRILIBRARY
15876 writenodes(&m, &b, &out->pointlist, &out->pointattributelist,
15877 &out->pointmarkerlist);
15878#else /* not TRILIBRARY */
15879 writenodes(&m, &b, b.outnodefilename, argc, argv);
15880#endif /* TRILIBRARY */
15881 }
15882 if (b.noelewritten) {
15883 if (!b.quiet) {
15884#ifdef TRILIBRARY
15885 printf("NOT writing triangles.\n");
15886#else /* not TRILIBRARY */
15887 printf("NOT writing an .ele file.\n");
15888#endif /* not TRILIBRARY */
15889 }
15890 } else {
15891#ifdef TRILIBRARY
15892 writeelements(&m, &b, &out->trianglelist, &out->triangleattributelist);
15893#else /* not TRILIBRARY */
15894 writeelements(&m, &b, b.outelefilename, argc, argv);
15895#endif /* not TRILIBRARY */
15896 }
15897 /* The -c switch (convex switch) causes a PSLG to be written */
15898 /* even if none was read. */
15899 if (b.poly || b.convex) {
15900 /* If not using iteration numbers, don't overwrite the .poly file. */
15901 if (b.nopolywritten || b.noiterationnum) {
15902 if (!b.quiet) {
15903#ifdef TRILIBRARY
15904 printf("NOT writing segments.\n");
15905#else /* not TRILIBRARY */
15906 printf("NOT writing a .poly file.\n");
15907#endif /* not TRILIBRARY */
15908 }
15909 } else {
15910#ifdef TRILIBRARY
15911 writepoly(&m, &b, &out->segmentlist, &out->segmentmarkerlist);
15912 out->numberofholes = m.holes;
15913 out->numberofregions = m.regions;
15914 if (b.poly) {
15915 out->holelist = in->holelist;
15916 out->regionlist = in->regionlist;
15917 } else {
15918 out->holelist = (REAL *) NULL;
15919 out->regionlist = (REAL *) NULL;
15920 }
15921#else /* not TRILIBRARY */
15922 writepoly(&m, &b, b.outpolyfilename, holearray, m.holes, regionarray,
15923 m.regions, argc, argv);
15924#endif /* not TRILIBRARY */
15925 }
15926 }
15927#ifndef TRILIBRARY
15928#ifndef CDT_ONLY
15929 if (m.regions > 0) {
15930 trifree((VOID *) regionarray);
15931 }
15932#endif /* not CDT_ONLY */
15933 if (m.holes > 0) {
15934 trifree((VOID *) holearray);
15935 }
15936 if (b.geomview) {
15937 writeoff(&m, &b, b.offfilename, argc, argv);
15938 }
15939#endif /* not TRILIBRARY */
15940 if (b.edgesout) {
15941#ifdef TRILIBRARY
15942 writeedges(&m, &b, &out->edgelist, &out->edgemarkerlist);
15943#else /* not TRILIBRARY */
15944 writeedges(&m, &b, b.edgefilename, argc, argv);
15945#endif /* not TRILIBRARY */
15946 }
15947 if (b.voronoi) {
15948#ifdef TRILIBRARY
15949 writevoronoi(&m, &b, &vorout->pointlist, &vorout->pointattributelist,
15950 &vorout->pointmarkerlist, &vorout->edgelist,
15951 &vorout->edgemarkerlist, &vorout->normlist);
15952#else /* not TRILIBRARY */
15953 writevoronoi(&m, &b, b.vnodefilename, b.vedgefilename, argc, argv);
15954#endif /* not TRILIBRARY */
15955 }
15956 if (b.neighbors) {
15957#ifdef TRILIBRARY
15958 writeneighbors(&m, &b, &out->neighborlist);
15959#else /* not TRILIBRARY */
15960 writeneighbors(&m, &b, b.neighborfilename, argc, argv);
15961#endif /* not TRILIBRARY */
15962 }
15963
15964 if (!b.quiet) {
15965#ifndef NO_TIMER
15966 gettimeofday(&tv6, &tz);
15967 printf("\nOutput milliseconds: %ld\n",
15968 1000l * (tv6.tv_sec - tv5.tv_sec) +
15969 (tv6.tv_usec - tv5.tv_usec) / 1000l);
15970 printf("Total running milliseconds: %ld\n",
15971 1000l * (tv6.tv_sec - tv0.tv_sec) +
15972 (tv6.tv_usec - tv0.tv_usec) / 1000l);
15973#endif /* not NO_TIMER */
15974
15975 statistics(&m, &b);
15976 }
15977
15978#ifndef REDUCED
15979 if (b.docheck) {
15980 checkmesh(&m, &b);
15981 checkdelaunay(&m, &b);
15982 }
15983#endif /* not REDUCED */
15984
15985 triangledeinit(&m, &b);
15986#ifndef TRILIBRARY
15987 return 0;
15988#endif /* not TRILIBRARY */
15989}
b
#define b(i)
Definition: RSha256.hxx:100
f
#define f(i)
Definition: RSha256.hxx:104
c
#define c(i)
Definition: RSha256.hxx:101
s0
#define s0(x)
Definition: RSha256.hxx:90
s1
#define s1(x)
Definition: RSha256.hxx:91
h
#define h(i)
Definition: RSha256.hxx:106
e
#define e(i)
Definition: RSha256.hxx:103
dummy
static RooMathCoreReg dummy
Definition: RooMathCoreReg.cxx:27
width
include TDocParser_001 C image html pict1_TDocParser_001 png width
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xmin
float xmin
Definition: THbookFile.cxx:93
ymin
float ymin
Definition: THbookFile.cxx:93
xmax
float xmax
Definition: THbookFile.cxx:93
ymax
float ymax
Definition: THbookFile.cxx:93
acos
double acos(double)
cos
double cos(double)
sqrt
double sqrt(double)
void
typedef void((*Func_t)())
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TCanvas * alignment()
Definition: alignment.C:1
free
#define free
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malloc
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main
int main(int argc, char **argv)
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y
Double_t y[n]
Definition: legend1.C:17
x
Double_t x[n]
Definition: legend1.C:17
ey
Double_t ey[n]
Definition: legend1.C:17
ex
Double_t ex[n]
Definition: legend1.C:17
ROOT::Math::Cephes::B
static double B[]
Definition: SpecFuncCephes.cxx:178
ROOT::Math::Cephes::Q
static double Q[]
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ROOT::Math::gv_detail::dist
double dist(Rotation3D const &r1, Rotation3D const &r2)
Definition: 3DDistances.cxx:48
TGeant4Unit::s
static constexpr double s
Definition: TGeant4SystemOfUnits.h:162
TGeant4Unit::pc
static constexpr double pc
Definition: TGeant4SystemOfUnits.h:130
first
Definition: first.py:1
v
@ v
Definition: rootcling_impl.cxx:3622
v3
@ v3
Definition: rootcling_impl.cxx:3626
triangulateio::pointattributelist
REAL * pointattributelist
Definition: triangle.h:290
triangulateio::neighborlist
int * neighborlist
Definition: triangle.h:298
triangulateio::numberoftriangleattributes
int numberoftriangleattributes
Definition: triangle.h:301
triangulateio::numberofpoints
int numberofpoints
Definition: triangle.h:292
triangulateio::edgemarkerlist
int * edgemarkerlist
Definition: triangle.h:314
triangulateio::numberofsegments
int numberofsegments
Definition: triangle.h:305
triangulateio::normlist
REAL * normlist
Definition: triangle.h:315
triangulateio::numberoftriangles
int numberoftriangles
Definition: triangle.h:299
triangulateio::trianglearealist
REAL * trianglearealist
Definition: triangle.h:297
triangulateio::trianglelist
int * trianglelist
Definition: triangle.h:295
triangulateio::pointlist
REAL * pointlist
Definition: triangle.h:289
triangulateio::segmentmarkerlist
int * segmentmarkerlist
Definition: triangle.h:304
triangulateio::numberofholes
int numberofholes
Definition: triangle.h:308
triangulateio::regionlist
REAL * regionlist
Definition: triangle.h:310
triangulateio::numberofpointattributes
int numberofpointattributes
Definition: triangle.h:293
triangulateio::numberofcorners
int numberofcorners
Definition: triangle.h:300
triangulateio::numberofregions
int numberofregions
Definition: triangle.h:311
triangulateio::numberofedges
int numberofedges
Definition: triangle.h:316
triangulateio::pointmarkerlist
int * pointmarkerlist
Definition: triangle.h:291
triangulateio::segmentlist
int * segmentlist
Definition: triangle.h:303
triangulateio::triangleattributelist
REAL * triangleattributelist
Definition: triangle.h:296
triangulateio::holelist
REAL * holelist
Definition: triangle.h:307
triangulateio::edgelist
int * edgelist
Definition: triangle.h:313
tv3
auto * tv3
Definition: textalign.C:34
tv1
auto * tv1
Definition: textalign.C:26
tv2
auto * tv2
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m
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Definition: textangle.C:8
l
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Definition: textangle.C:4
t1
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Definition: textangle.C:20
sum
static long int sum(long int i)
Definition: Factory.cxx:2276
SEGMENTVERTEX
#define SEGMENTVERTEX
Definition: triangle.c:284
sdest
#define sdest(osub, vertexptr)
Definition: triangle.c:1181
sorg
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Definition: triangle.c:1178
VIRUSPERBLOCK
#define VIRUSPERBLOCK
Definition: triangle.c:269
splitter
REAL splitter
Definition: triangle.c:616
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Definition: triangle.c:4101
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void highorder(struct mesh *m, struct behavior *b)
Definition: triangle.c:13694
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#define apex(otri, vertexptr)
Definition: triangle.c:1043
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void makevertexmap(struct mesh *m, struct behavior *b)
Definition: triangle.c:7375
Square
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Definition: triangle.c:4812
dnext
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Definition: triangle.c:986
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void writenodes(struct mesh *m, struct behavior *b, REAL **pointlist, REAL **pointattriblist, int **pointmarkerlist)
Definition: triangle.c:14305
finddirectionresult
finddirectionresult
Definition: triangle.c:359
LEFTCOLLINEAR
@ LEFTCOLLINEAR
Definition: triangle.c:359
RIGHTCOLLINEAR
@ RIGHTCOLLINEAR
Definition: triangle.c:359
WITHIN
@ WITHIN
Definition: triangle.c:359
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void numbernodes(struct mesh *m, struct behavior *b)
Definition: triangle.c:14445
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Definition: triangle.c:1288
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void writepoly(struct mesh *m, struct behavior *b, int **segmentlist, int **segmentmarkerlist)
Definition: triangle.c:14618
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vertex getvertex(struct mesh *m, struct behavior *b, int number)
Definition: triangle.c:4555
setelemattribute
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Definition: triangle.c:1102
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Definition: triangle.c:1184
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Definition: triangle.c:1193
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Definition: triangle.c:3864
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Definition: triangle.c:1190
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Definition: triangle.c:4789
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Definition: triangle.c:9257
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Definition: triangle.c:1132
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enum insertvertexresult insertvertex(struct mesh *m, struct behavior *b, vertex newvertex, struct otri *searchtri, struct osub *splitseg, int segmentflaws, int triflaws)
Definition: triangle.c:8173
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Definition: triangle.c:1046
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Definition: triangle.c:4863
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Definition: triangle.c:5087
SUBSEGPERBLOCK
#define SUBSEGPERBLOCK
Definition: triangle.c:267
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enum locateresult preciselocate(struct mesh *m, struct behavior *b, vertex searchpoint, struct otri *searchtri, int stopatsubsegment)
Definition: triangle.c:7470
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Definition: triangle.c:1099
FILENAMESIZE
#define FILENAMESIZE
Definition: triangle.c:255
fast_expansion_sum_zeroelim
int fast_expansion_sum_zeroelim(int elen, REAL *e, int flen, REAL *f, REAL *h)
Definition: triangle.c:4937
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void makesubseg(struct mesh *m, struct osub *newsubseg)
Definition: triangle.c:4681
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Definition: triangle.c:1283
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Definition: triangle.c:1057
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Definition: triangle.c:1171
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Definition: triangle.c:966
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Definition: triangle.c:921
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Definition: triangle.c:1414
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void triangledealloc(struct mesh *m, triangle *dyingtriangle)
Definition: triangle.c:4356
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unsigned long randomseed
Definition: triangle.c:625
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void pooldealloc(struct memorypool *pool, VOID *dyingitem)
Definition: triangle.c:4042
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#define infect(otri)
Definition: triangle.c:1084
INPUTLINESIZE
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Definition: triangle.c:260
tsdissolve
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Definition: triangle.c:1271
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Definition: triangle.c:1196
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void alternateaxes(vertex *sortarray, int arraysize, int axis)
Definition: triangle.c:9335
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Definition: triangle.c:942
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int triunsuitable(vertex triorg, vertex tridest, vertex triapex, REAL area)
Definition: triangle.c:1336
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void writeneighbors(struct mesh *m, struct behavior *b, int **neighborlist)
Definition: triangle.c:15131
triangle
REAL ** triangle
Definition: triangle.c:478
iccerrboundB
REAL iccerrboundB
Definition: triangle.c:620
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Definition: triangle.c:1066
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Definition: triangle.c:1206
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Definition: triangle.c:5945
segmentintersection
void segmentintersection(struct mesh *m, struct behavior *b, struct otri *splittri, struct osub *splitsubseg, vertex endpoint2)
Definition: triangle.c:11669
divconqdelaunay
long divconqdelaunay(struct mesh *m, struct behavior *b)
Definition: triangle.c:9953
Two_Product_Presplit
#define Two_Product_Presplit(a, b, bhi, blo, x, y)
Definition: triangle.c:4796
regionplague
void regionplague(struct mesh *m, struct behavior *b, REAL attribute, REAL area)
Definition: triangle.c:12850
ccwerrboundB
REAL ccwerrboundB
Definition: triangle.c:619
onext
#define onext(otri1, otri2)
Definition: triangle.c:962
TRIPERBLOCK
#define TRIPERBLOCK
Definition: triangle.c:266
delaunayfixup
void delaunayfixup(struct mesh *m, struct behavior *b, struct otri *fixuptri, int leftside)
Definition: triangle.c:12011
triangledeinit
void triangledeinit(struct mesh *m, struct behavior *b)
Definition: triangle.c:4596
poolinit
void poolinit(struct memorypool *pool, int bytecount, int itemcount, int firstitemcount, int alignment)
Definition: triangle.c:3910
locate
enum locateresult locate(struct mesh *m, struct behavior *b, vertex searchpoint, struct otri *searchtri)
Definition: triangle.c:7614
vertextraverse
vertex vertextraverse(struct mesh *m)
Definition: triangle.c:4469
oprevself
#define oprevself(otri)
Definition: triangle.c:978
SAMPLERATE
#define SAMPLERATE
Definition: triangle.c:301
lprev
#define lprev(otri1, otri2)
Definition: triangle.c:951
killsubseg
#define killsubseg(sub)
Definition: triangle.c:1242
FREEVERTEX
#define FREEVERTEX
Definition: triangle.c:285
triangletraverse
triangle * triangletraverse(struct mesh *m)
Definition: triangle.c:4377
tspivot
#define tspivot(otri, osub)
Definition: triangle.c:1252
STARTINDEX
#define STARTINDEX
ssymself
#define ssymself(osub)
Definition: triangle.c:1150
PI
#define PI
Definition: triangle.c:305
poolalloc
VOID * poolalloc(struct memorypool *pool)
Definition: triangle.c:3979
o3derrboundC
REAL o3derrboundC
Definition: triangle.c:621
plus1mod3
int plus1mod3[3]
Definition: triangle.c:902
maketriangle
void maketriangle(struct mesh *m, struct behavior *b, struct otri *newotri)
Definition: triangle.c:4637
printtriangle
void printtriangle(struct mesh *m, struct behavior *b, struct otri *t)
Definition: triangle.c:3640
Two_Diff_Tail
#define Two_Diff_Tail(a, b, x, y)
Definition: triangle.c:4764
writevoronoi
void writevoronoi(struct mesh *m, struct behavior *b, REAL **vpointlist, REAL **vpointattriblist, int **vpointmarkerlist, int **vedgelist, int **vedgemarkerlist, REAL **vnormlist)
Definition: triangle.c:14918
insertvertexresult
insertvertexresult
Definition: triangle.c:351
SUCCESSFULVERTEX
@ SUCCESSFULVERTEX
Definition: triangle.c:351
ENCROACHINGVERTEX
@ ENCROACHINGVERTEX
Definition: triangle.c:351
VIOLATINGVERTEX
@ VIOLATINGVERTEX
Definition: triangle.c:351
DUPLICATEVERTEX
@ DUPLICATEVERTEX
Definition: triangle.c:352
triexit
void triexit(int status)
Definition: triangle.c:1385
poolzero
void poolzero(struct memorypool *pool)
Definition: triangle.c:3830
insertsubseg
void insertsubseg(struct mesh *m, struct behavior *b, struct otri *tri, int subsegmark)
Definition: triangle.c:7785
dprev
#define dprev(otri1, otri2)
Definition: triangle.c:998
vertex2tri
#define vertex2tri(vx)
Definition: triangle.c:1293
ccwerrboundC
REAL ccwerrboundC
Definition: triangle.c:619
lnextself
#define lnextself(otri)
Definition: triangle.c:946
areabound
#define areabound(otri)
Definition: triangle.c:1107
DEADVERTEX
#define DEADVERTEX
Definition: triangle.c:286
formskeleton
void formskeleton(struct mesh *m, struct behavior *b, int *segmentlist, int *segmentmarkerlist, int numberofsegments)
Definition: triangle.c:12391
locateresult
locateresult
Definition: triangle.c:343
OUTSIDE
@ OUTSIDE
Definition: triangle.c:343
INTRIANGLE
@ INTRIANGLE
Definition: triangle.c:343
ONVERTEX
@ ONVERTEX
Definition: triangle.c:343
ONEDGE
@ ONEDGE
Definition: triangle.c:343
TRILIBRARY
#define TRILIBRARY
Definition: triangle.c:214
deadtri
#define deadtri(tria)
Definition: triangle.c:1117
setvertexmark
#define setvertexmark(vx, value)
Definition: triangle.c:1285
o3derrboundB
REAL o3derrboundB
Definition: triangle.c:621
SPLAYNODEPERBLOCK
#define SPLAYNODEPERBLOCK
Definition: triangle.c:277
triangulate
void triangulate(char *triswitches, struct triangulateio *in, struct triangulateio *out, struct triangulateio *vorout)
Definition: triangle.c:15652
setvertex2tri
#define setvertex2tri(vx, value)
Definition: triangle.c:1295
deadsubseg
#define deadsubseg(sub)
Definition: triangle.c:1240
initializevertexpool
void initializevertexpool(struct mesh *m, struct behavior *b)
Definition: triangle.c:4246
triangulatepolygon
void triangulatepolygon(struct mesh *m, struct behavior *b, struct otri *firstedge, struct otri *lastedge, int edgecount, int doflip, int triflaws)
Definition: triangle.c:8834
SQUAREROOTTWO
#define SQUAREROOTTWO
Definition: triangle.c:309
mergehulls
void mergehulls(struct mesh *m, struct behavior *b, struct otri *farleft, struct otri *innerleft, struct otri *innerright, struct otri *farright, int axis)
Definition: triangle.c:9399
parsecommandline
void parsecommandline(int argc, char **argv, struct behavior *b)
Definition: triangle.c:3257
trimalloc
VOID * trimalloc(int size)
Definition: triangle.c:1396
oprev
#define oprev(otri1, otri2)
Definition: triangle.c:974
killtri
#define killtri(tria)
Definition: triangle.c:1119
epsilon
REAL epsilon
Definition: triangle.c:617
BADSUBSEGPERBLOCK
#define BADSUBSEGPERBLOCK
Definition: triangle.c:271
subsegdealloc
void subsegdealloc(struct mesh *m, subseg *dyingsubseg)
Definition: triangle.c:4402
INPUTVERTEX
#define INPUTVERTEX
Definition: triangle.c:283
removeghosts
long removeghosts(struct mesh *m, struct behavior *b, struct otri *startghost)
Definition: triangle.c:9890
vertexdealloc
void vertexdealloc(struct mesh *m, vertex dyingvertex)
Definition: triangle.c:4448
infecthull
void infecthull(struct mesh *m, struct behavior *b)
Definition: triangle.c:12558
carveholes
void carveholes(struct mesh *m, struct behavior *b, REAL *holelist, int holes, REAL *regionlist, int regions)
Definition: triangle.c:12963
setapex
#define setapex(otri, vertexptr)
Definition: triangle.c:1052
UNDEADVERTEX
#define UNDEADVERTEX
Definition: triangle.c:287
dest
#define dest(otri, vertexptr)
Definition: triangle.c:1040
transfernodes
void transfernodes(struct mesh *m, struct behavior *b, REAL *pointlist, REAL *pointattriblist, int *pointmarkerlist, int numberofpoints, int numberofpointattribs)
Definition: triangle.c:14067
otricopy
#define otricopy(otri1, otri2)
Definition: triangle.c:1071
Two_Sum
#define Two_Sum(a, b, x, y)
Definition: triangle.c:4760
tsbond
#define tsbond(otri, osub)
Definition: triangle.c:1265
setmark
#define setmark(osub, value)
Definition: triangle.c:1208
stdissolve
#define stdissolve(osub)
Definition: triangle.c:1276
initializetrisubpools
void initializetrisubpools(struct mesh *m, struct behavior *b)
Definition: triangle.c:4289
BADTRIPERBLOCK
#define BADTRIPERBLOCK
Definition: triangle.c:273
minus1mod3
int minus1mod3[3]
Definition: triangle.c:903
writeedges
void writeedges(struct mesh *m, struct behavior *b, int **edgelist, int **edgemarkerlist)
Definition: triangle.c:14764
subseg
REAL ** subseg
Definition: triangle.c:495
Two_One_Product
#define Two_One_Product(a1, a0, b, x3, x2, x1, x0)
Definition: triangle.c:4837
Two_Two_Diff
#define Two_Two_Diff(a1, a0, b1, b0, x3, x2, x1, x0)
Definition: triangle.c:4831
delaunay
long delaunay(struct mesh *m, struct behavior *b)
Definition: triangle.c:10997
setdest
#define setdest(otri, vertexptr)
Definition: triangle.c:1049
markhull
void markhull(struct mesh *m, struct behavior *b)
Definition: triangle.c:12345
vertexsort
void vertexsort(vertex *sortarray, int arraysize)
Definition: triangle.c:9183
randomnation
unsigned long randomnation(unsigned int choices)
Definition: triangle.c:6647
o3derrboundA
REAL o3derrboundA
Definition: triangle.c:621
incircle
REAL incircle(struct mesh *m, struct behavior *b, vertex pa, vertex pb, vertex pc, vertex pd)
Definition: triangle.c:5863
dnextself
#define dnextself(otri)
Definition: triangle.c:990
stpivot
#define stpivot(osub, otri)
Definition: triangle.c:1259
VERTEXPERBLOCK
#define VERTEXPERBLOCK
Definition: triangle.c:268
counterclockwiseadapt
REAL counterclockwiseadapt(vertex pa, vertex pb, vertex pc, REAL detsum)
Definition: triangle.c:5126
scale_expansion_zeroelim
int scale_expansion_zeroelim(int elen, REAL *e, REAL b, REAL *h)
Definition: triangle.c:5031
decode
#define decode(ptr, otri)
Definition: triangle.c:912
otriequal
#define otriequal(otri1, otri2)
Definition: triangle.c:1077
org
#define org(otri, vertexptr)
Definition: triangle.c:1037
sdissolve
#define sdissolve(osub)
Definition: triangle.c:1220
traversalinit
void traversalinit(struct memorypool *pool)
Definition: triangle.c:4065
symself
#define symself(otri)
Definition: triangle.c:936
SAMPLEFACTOR
#define SAMPLEFACTOR
Definition: triangle.c:295
nonregular
REAL nonregular(struct mesh *m, struct behavior *b, vertex pa, vertex pb, vertex pc, vertex pd)
Definition: triangle.c:6453
plague
void plague(struct mesh *m, struct behavior *b)
Definition: triangle.c:12640
setsegdest
#define setsegdest(osub, vertexptr)
Definition: triangle.c:1199
uninfect
#define uninfect(otri)
Definition: triangle.c:1088
lprevself
#define lprevself(otri)
Definition: triangle.c:955
resulterrbound
REAL resulterrbound
Definition: triangle.c:618
internalerror
void internalerror()
Definition: triangle.c:3241
FLIPSTACKERPERBLOCK
#define FLIPSTACKERPERBLOCK
Definition: triangle.c:275
vertex
REAL * vertex
Definition: triangle.c:512
unflip
void unflip(struct mesh *m, struct behavior *b, struct otri *flipedge)
Definition: triangle.c:8024
setvertextype
#define setvertextype(vx, value)
Definition: triangle.c:1290
INEXACT
#define INEXACT
Definition: triangle.c:250
dummyinit
void dummyinit(struct mesh *m, struct behavior *b, int trianglebytes, int subsegbytes)
Definition: triangle.c:4166
sym
#define sym(otri1, otri2)
Definition: triangle.c:932
quality_statistics
void quality_statistics(struct mesh *m, struct behavior *b)
Definition: triangle.c:15324
flip
void flip(struct mesh *m, struct behavior *b, struct otri *flipedge)
Definition: triangle.c:7889
sencode
#define sencode(osub)
Definition: triangle.c:1141
counterclockwise
REAL counterclockwise(struct mesh *m, struct behavior *b, vertex pa, vertex pb, vertex pc)
Definition: triangle.c:5215
pooldeinit
void pooldeinit(struct memorypool *pool)
Definition: triangle.c:3958
finddirection
enum finddirectionresult finddirection(struct mesh *m, struct behavior *b, struct otri *searchtri, vertex searchpoint)
Definition: triangle.c:11574
ccwerrboundA
REAL ccwerrboundA
Definition: triangle.c:619
incircleadapt
REAL incircleadapt(vertex pa, vertex pb, vertex pc, vertex pd, REAL permanent)
Definition: triangle.c:5284
constrainededge
void constrainededge(struct mesh *m, struct behavior *b, struct otri *starttri, vertex endpoint2, int newmark)
Definition: triangle.c:12131
setsdest
#define setsdest(osub, vertexptr)
Definition: triangle.c:1187
iccerrboundA
REAL iccerrboundA
Definition: triangle.c:620
spivot
#define spivot(osub1, osub2)
Definition: triangle.c:1156
infected
#define infected(otri)
Definition: triangle.c:1094
ssym
#define ssym(osub1, osub2)
Definition: triangle.c:1146
writeelements
void writeelements(struct mesh *m, struct behavior *b, int **trianglelist, REAL **triangleattriblist)
Definition: triangle.c:14477
insertsegment
void insertsegment(struct mesh *m, struct behavior *b, vertex endpoint1, vertex endpoint2, int newmark)
Definition: triangle.c:12233
Two_Two_Sum
#define Two_Two_Sum(a1, a0, b1, b0, x3, x2, x1, x0)
Definition: triangle.c:4827
printsubseg
void printsubseg(struct mesh *m, struct behavior *b, struct osub *s)
Definition: triangle.c:3734
divconqrecurse
void divconqrecurse(struct mesh *m, struct behavior *b, vertex *sortarray, int vertices, int axis, struct otri *farleft, struct otri *farright)
Definition: triangle.c:9726
Fast_Two_Sum
#define Fast_Two_Sum(a, b, x, y)
Definition: triangle.c:4749
scoutsegment
int scoutsegment(struct mesh *m, struct behavior *b, struct otri *searchtri, vertex endpoint2, int newmark)
Definition: triangle.c:11797
findcircumcenter
void findcircumcenter(struct mesh *m, struct behavior *b, vertex torg, vertex tdest, vertex tapex, vertex circumcenter, REAL *xi, REAL *eta, int offcenter)
Definition: triangle.c:6494
Split
#define Split(a, ahi, alo)
Definition: triangle.c:4775
Absolute
#define Absolute(a)
Definition: triangle.c:4729
subsegtraverse
subseg * subsegtraverse(struct mesh *m)
Definition: triangle.c:4423
orient3d
REAL orient3d(struct mesh *m, struct behavior *b, vertex pa, vertex pb, vertex pc, vertex pd, REAL aheight, REAL bheight, REAL cheight, REAL dheight)
Definition: triangle.c:6370
statistics
void statistics(struct mesh *m, struct behavior *b)
Definition: triangle.c:15532
iccerrboundC
REAL iccerrboundC
Definition: triangle.c:620
sbond
#define sbond(osub1, osub2)
Definition: triangle.c:1213
setareabound
#define setareabound(otri, value)
Definition: triangle.c:1109
triangleinit
void triangleinit(struct mesh *m)
Definition: triangle.c:6608
REAL
#define REAL
Definition: triangle.h:277
VOID
#define VOID
Definition: triangle.h:286