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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
335 char *readline();
336 char *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 
343 enum 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 
351 enum 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 
359 enum 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 
478 typedef 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 
485 struct 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 
495 typedef 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 
502 struct 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 
512 typedef 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 
517 struct 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 
526 struct 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 
537 struct 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 
552 struct 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 
569 struct 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 
598 struct 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 
616 REAL splitter; /* Used to split REAL factors for exact multiplication. */
617 REAL epsilon; /* Floating-point machine epsilon. */
618 REAL resulterrbound;
619 REAL ccwerrboundA, ccwerrboundB, ccwerrboundC;
620 REAL iccerrboundA, iccerrboundB, iccerrboundC;
621 REAL o3derrboundA, o3derrboundB, o3derrboundC;
622 
623 /* Random number seed is not constant, but I've made it global anyway. */
624 
625 unsigned 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 
631 struct 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 
718 struct 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 
902 int plus1mod3[3] = {1, 2, 0};
903 int 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 
1331 int triunsuitable();
1332 
1333 #else /* not EXTERNAL_TEST */
1334 
1335 #ifdef ANSI_DECLARATORS
1336 int triunsuitable(vertex triorg, vertex tridest, vertex triapex, REAL area )
1337 #else /* not ANSI_DECLARATORS */
1338 int triunsuitable(triorg, tridest, triapex, area)
1339 vertex triorg; /* The triangle's origin vertex. */
1340 vertex tridest; /* The triangle's destination vertex. */
1341 vertex triapex; /* The triangle's apex vertex. */
1342 REAL 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
1385 void triexit(int status)
1386 #else /* not ANSI_DECLARATORS */
1387 void triexit(status)
1388 int status;
1389 #endif /* not ANSI_DECLARATORS */
1390 
1391 {
1392  exit(status);
1393 }
1394 
1395 #ifdef ANSI_DECLARATORS
1396 VOID *trimalloc(int size)
1397 #else /* not ANSI_DECLARATORS */
1398 VOID *trimalloc(size)
1399 int 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
1414 void trifree(VOID *memptr)
1415 #else /* not ANSI_DECLARATORS */
1416 void trifree(memptr)
1417 VOID *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 
1440 void 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 
1520 void 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 
3241 void 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
3257 void parsecommandline(int argc, char **argv, struct behavior *b)
3258 #else /* not ANSI_DECLARATORS */
3259 void parsecommandline(argc, argv, b)
3260 int argc;
3261 char **argv;
3262 struct 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
3640 void printtriangle(struct mesh *m, struct behavior *b, struct otri *t)
3641 #else /* not ANSI_DECLARATORS */
3642 void printtriangle(m, b, t)
3643 struct mesh *m;
3644 struct behavior *b;
3645 struct 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
3734 void printsubseg(struct mesh *m, struct behavior *b, struct osub *s)
3735 #else /* not ANSI_DECLARATORS */
3736 void printsubseg(m, b, s)
3737 struct mesh *m;
3738 struct behavior *b;
3739 struct 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
3830 void poolzero(struct memorypool *pool)
3831 #else /* not ANSI_DECLARATORS */
3832 void poolzero(pool)
3833 struct 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
3864 void poolrestart(struct memorypool *pool)
3865 #else /* not ANSI_DECLARATORS */
3866 void poolrestart(pool)
3867 struct 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
3910 void poolinit(struct memorypool *pool, int bytecount, int itemcount,
3911  int firstitemcount, int alignment)
3912 #else /* not ANSI_DECLARATORS */
3913 void poolinit(pool, bytecount, itemcount, firstitemcount, alignment)
3914 struct memorypool *pool;
3915 int bytecount;
3916 int itemcount;
3917 int firstitemcount;
3918 int 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
3958 void pooldeinit(struct memorypool *pool)
3959 #else /* not ANSI_DECLARATORS */
3960 void pooldeinit(pool)
3961 struct 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
3979 VOID *poolalloc(struct memorypool *pool)
3980 #else /* not ANSI_DECLARATORS */
3981 VOID *poolalloc(pool)
3982 struct 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
4042 void pooldealloc(struct memorypool *pool, VOID *dyingitem)
4043 #else /* not ANSI_DECLARATORS */
4044 void pooldealloc(pool, dyingitem)
4045 struct memorypool *pool;
4046 VOID *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
4065 void traversalinit(struct memorypool *pool)
4066 #else /* not ANSI_DECLARATORS */
4067 void traversalinit(pool)
4068 struct 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
4101 VOID *traverse(struct memorypool *pool)
4102 #else /* not ANSI_DECLARATORS */
4103 VOID *traverse(pool)
4104 struct 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
4166 void dummyinit(struct mesh *m, struct behavior *b, int trianglebytes,
4167  int subsegbytes)
4168 #else /* not ANSI_DECLARATORS */
4169 void dummyinit(m, b, trianglebytes, subsegbytes)
4170 struct mesh *m;
4171 struct behavior *b;
4172 int trianglebytes;
4173 int 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
4246 void initializevertexpool(struct mesh *m, struct behavior *b)
4247 #else /* not ANSI_DECLARATORS */
4248 void initializevertexpool(m, b)
4249 struct mesh *m;
4250 struct 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
4289 void initializetrisubpools(struct mesh *m, struct behavior *b)
4290 #else /* not ANSI_DECLARATORS */
4291 void initializetrisubpools(m, b)
4292 struct mesh *m;
4293 struct 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
4356 void triangledealloc(struct mesh *m, triangle *dyingtriangle)
4357 #else /* not ANSI_DECLARATORS */
4358 void triangledealloc(m, dyingtriangle)
4359 struct mesh *m;
4360 triangle *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
4377 triangle *triangletraverse(struct mesh *m)
4378 #else /* not ANSI_DECLARATORS */
4379 triangle *triangletraverse(m)
4380 struct 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
4402 void subsegdealloc(struct mesh *m, subseg *dyingsubseg)
4403 #else /* not ANSI_DECLARATORS */
4404 void subsegdealloc(m, dyingsubseg)
4405 struct mesh *m;
4406 subseg *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
4423 subseg *subsegtraverse(struct mesh *m)
4424 #else /* not ANSI_DECLARATORS */
4425 subseg *subsegtraverse(m)
4426 struct 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
4448 void vertexdealloc(struct mesh *m, vertex dyingvertex)
4449 #else /* not ANSI_DECLARATORS */
4450 void vertexdealloc(m, dyingvertex)
4451 struct mesh *m;
4452 vertex 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
4469 vertex vertextraverse(struct mesh *m)
4470 #else /* not ANSI_DECLARATORS */
4471 vertex vertextraverse(m)
4472 struct 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
4497 void badsubsegdealloc(struct mesh *m, struct badsubseg *dyingseg)
4498 #else /* not ANSI_DECLARATORS */
4499 void badsubsegdealloc(m, dyingseg)
4500 struct mesh *m;
4501 struct 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
4522 struct badsubseg *badsubsegtraverse(struct mesh *m)
4523 #else /* not ANSI_DECLARATORS */
4524 struct badsubseg *badsubsegtraverse(m)
4525 struct 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
4555 vertex getvertex(struct mesh *m, struct behavior *b, int number)
4556 #else /* not ANSI_DECLARATORS */
4557 vertex getvertex(m, b, number)
4558 struct mesh *m;
4559 struct behavior *b;
4560 int 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
4596 void triangledeinit(struct mesh *m, struct behavior *b)
4597 #else /* not ANSI_DECLARATORS */
4598 void triangledeinit(m, b)
4599 struct mesh *m;
4600 struct 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
4637 void maketriangle(struct mesh *m, struct behavior *b, struct otri *newotri)
4638 #else /* not ANSI_DECLARATORS */
4639 void maketriangle(m, b, newotri)
4640 struct mesh *m;
4641 struct behavior *b;
4642 struct 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
4681 void makesubseg(struct mesh *m, struct osub *newsubseg)
4682 #else /* not ANSI_DECLARATORS */
4683 void makesubseg(m, newsubseg)
4684 struct mesh *m;
4685 struct 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 
4863 void 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
4937 int fast_expansion_sum_zeroelim(int elen, REAL *e, int flen, REAL *f, REAL *h)
4938 #else /* not ANSI_DECLARATORS */
4939 int fast_expansion_sum_zeroelim(elen, e, flen, f, h) /* h cannot be e or f. */
4940 int elen;
4941 REAL *e;
4942 int flen;
4943 REAL *f;
4944 REAL *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
5031 int scale_expansion_zeroelim(int elen, REAL *e, REAL b, REAL *h)
5032 #else /* not ANSI_DECLARATORS */
5033 int scale_expansion_zeroelim(elen, e, b, h) /* e and h cannot be the same. */
5034 int elen;
5035 REAL *e;
5036 REAL b;
5037 REAL *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
5087 REAL estimate(int elen, REAL *e)
5088 #else /* not ANSI_DECLARATORS */
5089 REAL estimate(elen, e)
5090 int elen;
5091 REAL *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
5126 REAL counterclockwiseadapt(vertex pa, vertex pb, vertex pc, REAL detsum)
5127 #else /* not ANSI_DECLARATORS */
5128 REAL counterclockwiseadapt(pa, pb, pc, detsum)
5129 vertex pa;
5130 vertex pb;
5131 vertex pc;
5132 REAL 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
5215 REAL counterclockwise(struct mesh *m, struct behavior *b,
5216  vertex pa, vertex pb, vertex pc)
5217 #else /* not ANSI_DECLARATORS */
5218 REAL counterclockwise(m, b, pa, pb, pc)
5219 struct mesh *m;
5220 struct behavior *b;
5221 vertex pa;
5222 vertex pb;
5223 vertex 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
5284 REAL incircleadapt(vertex pa, vertex pb, vertex pc, vertex pd, REAL permanent)
5285 #else /* not ANSI_DECLARATORS */
5286 REAL incircleadapt(pa, pb, pc, pd, permanent)
5287 vertex pa;
5288 vertex pb;
5289 vertex pc;
5290 vertex pd;
5291 REAL 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
5863 REAL incircle(struct mesh *m, struct behavior *b,
5864  vertex pa, vertex pb, vertex pc, vertex pd)
5865 #else /* not ANSI_DECLARATORS */
5866 REAL incircle(m, b, pa, pb, pc, pd)
5867 struct mesh *m;
5868 struct behavior *b;
5869 vertex pa;
5870 vertex pb;
5871 vertex pc;
5872 vertex 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
5945 REAL 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 */
5949 REAL orient3dadapt(pa, pb, pc, pd,
5950  aheight, bheight, cheight, dheight, permanent)
5951 vertex pa;
5952 vertex pb;
5953 vertex pc;
5954 vertex pd;
5955 REAL aheight;
5956 REAL bheight;
5957 REAL cheight;
5958 REAL dheight;
5959 REAL 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
6370 REAL 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 */
6374 REAL orient3d(m, b, pa, pb, pc, pd, aheight, bheight, cheight, dheight)
6375 struct mesh *m;
6376 struct behavior *b;
6377 vertex pa;
6378 vertex pb;
6379 vertex pc;
6380 vertex pd;
6381 REAL aheight;
6382 REAL bheight;
6383 REAL cheight;
6384 REAL 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
6453 REAL nonregular(struct mesh *m, struct behavior *b,
6454  vertex pa, vertex pb, vertex pc, vertex pd)
6455 #else /* not ANSI_DECLARATORS */
6456 REAL nonregular(m, b, pa, pb, pc, pd)
6457 struct mesh *m;
6458 struct behavior *b;
6459 vertex pa;
6460 vertex pb;
6461 vertex pc;
6462 vertex 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
6494 void 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 */
6498 void findcircumcenter(m, b, torg, tdest, tapex, circumcenter, xi, eta,
6499  offcenter)
6500 struct mesh *m;
6501 struct behavior *b;
6502 vertex torg;
6503 vertex tdest;
6504 vertex tapex;
6505 vertex circumcenter;
6506 REAL *xi;
6507 REAL *eta;
6508 int 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
6608 void triangleinit(struct mesh *m)
6609 #else /* not ANSI_DECLARATORS */
6610 void triangleinit(m)
6611 struct 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
6647 unsigned long randomnation(unsigned int choices)
6648 #else /* not ANSI_DECLARATORS */
6649 unsigned long randomnation(choices)
6650 unsigned 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
6671 void checkmesh(struct mesh *m, struct behavior *b)
6672 #else /* not ANSI_DECLARATORS */
6673 void checkmesh(m, b)
6674 struct mesh *m;
6675 struct 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
6770 void checkdelaunay(struct mesh *m, struct behavior *b)
6771 #else /* not ANSI_DECLARATORS */
6772 void checkdelaunay(m, b)
6773 struct mesh *m;
6774 struct 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
6880 void enqueuebadtriang(struct mesh *m, struct behavior *b,
6881  struct badtriang *badtri)
6882 #else /* not ANSI_DECLARATORS */
6883 void enqueuebadtriang(m, b, badtri)
6884 struct mesh *m;
6885 struct behavior *b;
6886 struct 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
6986 void enqueuebadtri(struct mesh *m, struct behavior *b, struct otri *enqtri,
6987  REAL minedge, vertex enqapex, vertex enqorg, vertex enqdest)
6988 #else /* not ANSI_DECLARATORS */
6989 void enqueuebadtri(m, b, enqtri, minedge, enqapex, enqorg, enqdest)
6990 struct mesh *m;
6991 struct behavior *b;
6992 struct otri *enqtri;
6993 REAL minedge;
6994 vertex enqapex;
6995 vertex enqorg;
6996 vertex 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
7023 struct badtriang *dequeuebadtriang(struct mesh *m)
7024 #else /* not ANSI_DECLARATORS */
7025 struct badtriang *dequeuebadtriang(m)
7026 struct 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
7076 int checkseg4encroach(struct mesh *m, struct behavior *b,
7077  struct osub *testsubseg)
7078 #else /* not ANSI_DECLARATORS */
7079 int checkseg4encroach(m, b, testsubseg)
7080 struct mesh *m;
7081 struct behavior *b;
7082 struct 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
7189 void testtriangle(struct mesh *m, struct behavior *b, struct otri *testtri)
7190 #else /* not ANSI_DECLARATORS */
7191 void testtriangle(m, b, testtri)
7192 struct mesh *m;
7193 struct behavior *b;
7194 struct 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
7375 void makevertexmap(struct mesh *m, struct behavior *b)
7376 #else /* not ANSI_DECLARATORS */
7377 void makevertexmap(m, b)
7378 struct mesh *m;
7379 struct 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
7470 enum locateresult preciselocate(struct mesh *m, struct behavior *b,
7471  vertex searchpoint, struct otri *searchtri,
7472  int stopatsubsegment)
7473 #else /* not ANSI_DECLARATORS */
7474 enum locateresult preciselocate(m, b, searchpoint, searchtri, stopatsubsegment)
7475 struct mesh *m;
7476 struct behavior *b;
7477 vertex searchpoint;
7478 struct otri *searchtri;
7479 int 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
7614 enum locateresult locate(struct mesh *m, struct behavior *b,
7615  vertex searchpoint, struct otri *searchtri)
7616 #else /* not ANSI_DECLARATORS */
7617 enum locateresult locate(m, b, searchpoint, searchtri)
7618 struct mesh *m;
7619 struct behavior *b;
7620 vertex searchpoint;
7621 struct 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
7785 void insertsubseg(struct mesh *m, struct behavior *b, struct otri *tri,
7786  int subsegmark)
7787 #else /* not ANSI_DECLARATORS */
7788 void insertsubseg(m, b, tri, subsegmark)
7789 struct mesh *m;
7790 struct behavior *b;
7791 struct otri *tri; /* Edge at which to insert the new subsegment. */
7792 int 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
7889 void flip(struct mesh *m, struct behavior *b, struct otri *flipedge)
7890 #else /* not ANSI_DECLARATORS */
7891 void flip(m, b, flipedge)
7892 struct mesh *m;
7893 struct behavior *b;
7894 struct 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
8024 void unflip(struct mesh *m, struct behavior *b, struct otri *flipedge)
8025 #else /* not ANSI_DECLARATORS */
8026 void unflip(m, b, flipedge)
8027 struct mesh *m;
8028 struct behavior *b;
8029 struct 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
8173 enum 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 */
8178 enum insertvertexresult insertvertex(m, b, newvertex, searchtri, splitseg,
8179  segmentflaws, triflaws)
8180 struct mesh *m;
8181 struct behavior *b;
8182 vertex newvertex;
8183 struct otri *searchtri;
8184 struct osub *splitseg;
8185 int segmentflaws;
8186 int 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
8834 void 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 */
8838 void triangulatepolygon(m, b, firstedge, lastedge, edgecount, doflip, triflaws)
8839 struct mesh *m;
8840 struct behavior *b;
8841 struct otri *firstedge;
8842 struct otri *lastedge;
8843 int edgecount;
8844 int doflip;
8845 int 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
8933 void deletevertex(struct mesh *m, struct behavior *b, struct otri *deltri)
8934 #else /* not ANSI_DECLARATORS */
8935 void deletevertex(m, b, deltri)
8936 struct mesh *m;
8937 struct behavior *b;
8938 struct 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
9036 void undovertex(struct mesh *m, struct behavior *b)
9037 #else /* not ANSI_DECLARATORS */
9038 void undovertex(m, b)
9039 struct mesh *m;
9040 struct 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
9183 void vertexsort(vertex *sortarray, int arraysize)
9184 #else /* not ANSI_DECLARATORS */
9185 void vertexsort(sortarray, arraysize)
9186 vertex *sortarray;
9187 int 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
9257 void vertexmedian(vertex *sortarray, int arraysize, int median, int axis)
9258 #else /* not ANSI_DECLARATORS */
9259 void vertexmedian(sortarray, arraysize, median, axis)
9260 vertex *sortarray;
9261 int arraysize;
9262 int median;
9263 int 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
9335 void alternateaxes(vertex *sortarray, int arraysize, int axis)
9336 #else /* not ANSI_DECLARATORS */
9337 void alternateaxes(sortarray, arraysize, axis)
9338 vertex *sortarray;
9339 int arraysize;
9340 int 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
9399 void 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 */
9403 void mergehulls(m, b, farleft, innerleft, innerright, farright, axis)
9404 struct mesh *m;
9405 struct behavior *b;
9406 struct otri *farleft;
9407 struct otri *innerleft;
9408 struct otri *innerright;
9409 struct otri *farright;
9410 int 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
9726 void 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 */
9730 void divconqrecurse(m, b, sortarray, vertices, axis, farleft, farright)
9731 struct mesh *m;
9732 struct behavior *b;
9733 vertex *sortarray;
9734 int vertices;
9735 int axis;
9736 struct otri *farleft;
9737 struct 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
9890 long removeghosts(struct mesh *m, struct behavior *b, struct otri *startghost)
9891 #else /* not ANSI_DECLARATORS */
9892 long removeghosts(m, b, startghost)
9893 struct mesh *m;
9894 struct behavior *b;
9895 struct 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
9953 long divconqdelaunay(struct mesh *m, struct behavior *b)
9954 #else /* not ANSI_DECLARATORS */
9955 long divconqdelaunay(m, b)
9956 struct mesh *m;
9957 struct 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
10040 void boundingbox(struct mesh *m, struct behavior *b)
10041 #else /* not ANSI_DECLARATORS */
10042 void boundingbox(m, b)
10043 struct mesh *m;
10044 struct 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
10106 long removebox(struct mesh *m, struct behavior *b)
10107 #else /* not ANSI_DECLARATORS */
10108 long removebox(m, b)
10109 struct mesh *m;
10110 struct 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
10205 long incrementaldelaunay(struct mesh *m, struct behavior *b)
10206 #else /* not ANSI_DECLARATORS */
10207 long incrementaldelaunay(m, b)
10208 struct mesh *m;
10209 struct 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
10254 void eventheapinsert(struct event **heap, int heapsize, struct event *newevent)
10255 #else /* not ANSI_DECLARATORS */
10256 void eventheapinsert(heap, heapsize, newevent)
10257 struct event **heap;
10258 int heapsize;
10259 struct 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
10295 void eventheapify(struct event **heap, int heapsize, int eventnum)
10296 #else /* not ANSI_DECLARATORS */
10297 void eventheapify(heap, heapsize, eventnum)
10298 struct event **heap;
10299 int heapsize;
10300 int 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
10351 void eventheapdelete(struct event **heap, int heapsize, int eventnum)
10352 #else /* not ANSI_DECLARATORS */
10353 void eventheapdelete(heap, heapsize, eventnum)
10354 struct event **heap;
10355 int heapsize;
10356 int 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
10394 void createeventheap(struct mesh *m, struct event ***eventheap,
10395  struct event **events, struct event **freeevents)
10396 #else /* not ANSI_DECLARATORS */
10397 void createeventheap(m, eventheap, events, freeevents)
10398 struct mesh *m;
10399 struct event ***eventheap;
10400 struct event **events;
10401 struct 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
10433 int rightofhyperbola(struct mesh *m, struct otri *fronttri, vertex newsite)
10434 #else /* not ANSI_DECLARATORS */
10435 int rightofhyperbola(m, fronttri, newsite)
10436 struct mesh *m;
10437 struct otri *fronttri;
10438 vertex 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
10472 REAL circletop(struct mesh *m, vertex pa, vertex pb, vertex pc, REAL ccwabc)
10473 #else /* not ANSI_DECLARATORS */
10474 REAL circletop(m, pa, pb, pc, ccwabc)
10475 struct mesh *m;
10476 vertex pa;
10477 vertex pb;
10478 vertex pc;
10479 REAL 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
10506 void check4deadevent(struct otri *checktri, struct event **freeevents,
10507  struct event **eventheap, int *heapsize)
10508 #else /* not ANSI_DECLARATORS */
10509 void check4deadevent(checktri, freeevents, eventheap, heapsize)
10510 struct otri *checktri;
10511 struct event **freeevents;
10512 struct event **eventheap;
10513 int *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
10538 struct splaynode *splay(struct mesh *m, struct splaynode *splaytree,
10539  vertex searchpoint, struct otri *searchtri)
10540 #else /* not ANSI_DECLARATORS */
10541 struct splaynode *splay(m, splaytree, searchpoint, searchtri)
10542 struct mesh *m;
10543 struct splaynode *splaytree;
10544 vertex searchpoint;
10545 struct 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
10657 struct splaynode *splayinsert(struct mesh *m, struct splaynode *splayroot,
10658  struct otri *newkey, vertex searchpoint)
10659 #else /* not ANSI_DECLARATORS */
10660 struct splaynode *splayinsert(m, splayroot, newkey, searchpoint)
10661 struct mesh *m;
10662 struct splaynode *splayroot;
10663 struct otri *newkey;
10664 vertex 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
10693 struct 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 */
10698 struct splaynode *circletopinsert(m, b, splayroot, newkey, pa, pb, pc, topy)
10699 struct mesh *m;
10700 struct behavior *b;
10701 struct splaynode *splayroot;
10702 struct otri *newkey;
10703 vertex pa;
10704 vertex pb;
10705 vertex pc;
10706 REAL 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
10734 struct 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 */
10738 struct splaynode *frontlocate(m, splayroot, bottommost, searchvertex,
10739  searchtri, farright)
10740 struct mesh *m;
10741 struct splaynode *splayroot;
10742 struct otri *bottommost;
10743 vertex searchvertex;
10744 struct otri *searchtri;
10745 int *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
10769 long sweeplinedelaunay(struct mesh *m, struct behavior *b)
10770 #else /* not ANSI_DECLARATORS */
10771 long sweeplinedelaunay(m, b)
10772 struct mesh *m;
10773 struct 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
10997 long delaunay(struct mesh *m, struct behavior *b)
10998 #else /* not ANSI_DECLARATORS */
10999 long delaunay(m, b)
11000 struct mesh *m;
11001 struct 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
11074 int 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 */
11079 int reconstruct(m, b, trianglelist, triangleattriblist, trianglearealist,
11080  elements, corners, attribs, segmentlist, segmentmarkerlist,
11081  numberofsegments)
11082 struct mesh *m;
11083 struct behavior *b;
11084 int *trianglelist;
11085 REAL *triangleattriblist;
11086 REAL *trianglearealist;
11087 int elements;
11088 int corners;
11089 int attribs;
11090 int *segmentlist;
11091 int *segmentmarkerlist;
11092 int numberofsegments;
11093 #endif /* not ANSI_DECLARATORS */
11094 
11095 #else /* not TRILIBRARY */
11096 
11097 #ifdef ANSI_DECLARATORS
11098 long reconstruct(struct mesh *m, struct behavior *b, char *elefilename,
11099  char *areafilename, char *polyfilename, FILE *polyfile)
11100 #else /* not ANSI_DECLARATORS */
11101 long reconstruct(m, b, elefilename, areafilename, polyfilename, polyfile)
11102 struct mesh *m;
11103 struct behavior *b;
11104 char *elefilename;
11105 char *areafilename;
11106 char *polyfilename;
11107 FILE *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
11574 enum finddirectionresult finddirection(struct mesh *m, struct behavior *b,
11575  struct otri *searchtri,
11576  vertex searchpoint)
11577 #else /* not ANSI_DECLARATORS */
11578 enum finddirectionresult finddirection(m, b, searchtri, searchpoint)
11579 struct mesh *m;
11580 struct behavior *b;
11581 struct otri *searchtri;
11582 vertex 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
11669 void segmentintersection(struct mesh *m, struct behavior *b,
11670  struct otri *splittri, struct osub *splitsubseg,
11671  vertex endpoint2)
11672 #else /* not ANSI_DECLARATORS */
11673 void segmentintersection(m, b, splittri, splitsubseg, endpoint2)
11674 struct mesh *m;
11675 struct behavior *b;
11676 struct otri *splittri;
11677 struct osub *splitsubseg;
11678 vertex 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
11797 int scoutsegment(struct mesh *m, struct behavior *b, struct otri *searchtri,
11798  vertex endpoint2, int newmark)
11799 #else /* not ANSI_DECLARATORS */
11800 int scoutsegment(m, b, searchtri, endpoint2, newmark)
11801 struct mesh *m;
11802 struct behavior *b;
11803 struct otri *searchtri;
11804 vertex endpoint2;
11805 int 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
11881 void conformingedge(struct mesh *m, struct behavior *b,
11882  vertex endpoint1, vertex endpoint2, int newmark)
11883 #else /* not ANSI_DECLARATORS */
11884 void conformingedge(m, b, endpoint1, endpoint2, newmark)
11885 struct mesh *m;
11886 struct behavior *b;
11887 vertex endpoint1;
11888 vertex endpoint2;
11889 int 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
12011 void delaunayfixup(struct mesh *m, struct behavior *b,
12012  struct otri *fixuptri, int leftside)
12013 #else /* not ANSI_DECLARATORS */
12014 void delaunayfixup(m, b, fixuptri, leftside)
12015 struct mesh *m;
12016 struct behavior *b;
12017 struct otri *fixuptri;
12018 int 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
12131 void constrainededge(struct mesh *m, struct behavior *b,
12132  struct otri *starttri, vertex endpoint2, int newmark)
12133 #else /* not ANSI_DECLARATORS */
12134 void constrainededge(m, b, starttri, endpoint2, newmark)
12135 struct mesh *m;
12136 struct behavior *b;
12137 struct otri *starttri;
12138 vertex endpoint2;
12139 int 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
12233 void insertsegment(struct mesh *m, struct behavior *b,
12234  vertex endpoint1, vertex endpoint2, int newmark)
12235 #else /* not ANSI_DECLARATORS */
12236 void insertsegment(m, b, endpoint1, endpoint2, newmark)
12237 struct mesh *m;
12238 struct behavior *b;
12239 vertex endpoint1;
12240 vertex endpoint2;
12241 int 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
12345 void markhull(struct mesh *m, struct behavior *b)
12346 #else /* not ANSI_DECLARATORS */
12347 void markhull(m, b)
12348 struct mesh *m;
12349 struct 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
12391 void formskeleton(struct mesh *m, struct behavior *b, int *segmentlist,
12392  int *segmentmarkerlist, int numberofsegments)
12393 #else /* not ANSI_DECLARATORS */
12394 void formskeleton(m, b, segmentlist, segmentmarkerlist, numberofsegments)
12395 struct mesh *m;
12396 struct behavior *b;
12397 int *segmentlist;
12398 int *segmentmarkerlist;
12399 int numberofsegments;
12400 #endif /* not ANSI_DECLARATORS */
12401 
12402 #else /* not TRILIBRARY */
12403 
12404 #ifdef ANSI_DECLARATORS
12405 void formskeleton(struct mesh *m, struct behavior *b,
12406  FILE *polyfile, char *polyfilename)
12407 #else /* not ANSI_DECLARATORS */
12408 void formskeleton(m, b, polyfile, polyfilename)
12409 struct mesh *m;
12410 struct behavior *b;
12411 FILE *polyfile;
12412 char *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
12558 void infecthull(struct mesh *m, struct behavior *b)
12559 #else /* not ANSI_DECLARATORS */
12560 void infecthull(m, b)
12561 struct mesh *m;
12562 struct 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
12640 void plague(struct mesh *m, struct behavior *b)
12641 #else /* not ANSI_DECLARATORS */
12642 void plague(m, b)
12643 struct mesh *m;
12644 struct 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
12850 void regionplague(struct mesh *m, struct behavior *b,
12851  REAL attribute, REAL area)
12852 #else /* not ANSI_DECLARATORS */
12853 void regionplague(m, b, attribute, area)
12854 struct mesh *m;
12855 struct behavior *b;
12856 REAL attribute;
12857 REAL 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
12963 void carveholes(struct mesh *m, struct behavior *b, REAL *holelist, int holes,
12964  REAL *regionlist, int regions)
12965 #else /* not ANSI_DECLARATORS */
12966 void carveholes(m, b, holelist, holes, regionlist, regions)
12967 struct mesh *m;
12968 struct behavior *b;
12969 REAL *holelist;
12970 int holes;
12971 REAL *regionlist;
12972 int 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
13157 void tallyencs(struct mesh *m, struct behavior *b)
13158 #else /* not ANSI_DECLARATORS */
13159 void tallyencs(m, b)
13160 struct mesh *m;
13161 struct 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 
13188 void 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
13218 void splitencsegs(struct mesh *m, struct behavior *b, int triflaws)
13219 #else /* not ANSI_DECLARATORS */
13220 void splitencsegs(m, b, triflaws)
13221 struct mesh *m;
13222 struct behavior *b;
13223 int 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
13430 void tallyfaces(struct mesh *m, struct behavior *b)
13431 #else /* not ANSI_DECLARATORS */
13432 void tallyfaces(m, b)
13433 struct mesh *m;
13434 struct 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
13466 void splittriangle(struct mesh *m, struct behavior *b,
13467  struct badtriang *badtri)
13468 #else /* not ANSI_DECLARATORS */
13469 void splittriangle(m, b, badtri)
13470 struct mesh *m;
13471 struct behavior *b;
13472 struct 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
13595 void enforcequality(struct mesh *m, struct behavior *b)
13596 #else /* not ANSI_DECLARATORS */
13597 void enforcequality(m, b)
13598 struct mesh *m;
13599 struct 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
13694 void highorder(struct mesh *m, struct behavior *b)
13695 #else /* not ANSI_DECLARATORS */
13696 void highorder(m, b)
13697 struct mesh *m;
13698 struct 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
13785 char *readline(char *string, FILE *infile, char *infilename)
13786 #else /* not ANSI_DECLARATORS */
13787 char *readline(string, infile, infilename)
13788 char *string;
13789 FILE *infile;
13790 char *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
13829 char *findfield(char *string)
13830 #else /* not ANSI_DECLARATORS */
13831 char *findfield(string)
13832 char *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
13870 void readnodes(struct mesh *m, struct behavior *b, char *nodefilename,
13871  char *polyfilename, FILE **polyfile)
13872 #else /* not ANSI_DECLARATORS */
13873 void readnodes(m, b, nodefilename, polyfilename, polyfile)
13874 struct mesh *m;
13875 struct behavior *b;
13876 char *nodefilename;
13877 char *polyfilename;
13878 FILE **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
14067 void transfernodes(struct mesh *m, struct behavior *b, REAL *pointlist,
14068  REAL *pointattriblist, int *pointmarkerlist,
14069  int numberofpoints, int numberofpointattribs)
14070 #else /* not ANSI_DECLARATORS */
14071 void transfernodes(m, b, pointlist, pointattriblist, pointmarkerlist,
14072  numberofpoints, numberofpointattribs)
14073 struct mesh *m;
14074 struct behavior *b;
14075 REAL *pointlist;
14076 REAL *pointattriblist;
14077 int *pointmarkerlist;
14078 int numberofpoints;
14079 int 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
14152 void 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 */
14156 void readholes(m, b, polyfile, polyfilename, hlist, holes, rlist, regions)
14157 struct mesh *m;
14158 struct behavior *b;
14159 FILE *polyfile;
14160 char *polyfilename;
14161 REAL **hlist;
14162 int *holes;
14163 REAL **rlist;
14164 int *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
14271 void finishfile(FILE *outfile, int argc, char **argv)
14272 #else /* not ANSI_DECLARATORS */
14273 void finishfile(outfile, argc, argv)
14274 FILE *outfile;
14275 int argc;
14276 char **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
14305 void writenodes(struct mesh *m, struct behavior *b, REAL **pointlist,
14306  REAL **pointattriblist, int **pointmarkerlist)
14307 #else /* not ANSI_DECLARATORS */
14308 void writenodes(m, b, pointlist, pointattriblist, pointmarkerlist)
14309 struct mesh *m;
14310 struct behavior *b;
14311 REAL **pointlist;
14312 REAL **pointattriblist;
14313 int **pointmarkerlist;
14314 #endif /* not ANSI_DECLARATORS */
14315 
14316 #else /* not TRILIBRARY */
14317 
14318 #ifdef ANSI_DECLARATORS
14319 void writenodes(struct mesh *m, struct behavior *b, char *nodefilename,
14320  int argc, char **argv)
14321 #else /* not ANSI_DECLARATORS */
14322 void writenodes(m, b, nodefilename, argc, argv)
14323 struct mesh *m;
14324 struct behavior *b;
14325 char *nodefilename;
14326 int argc;
14327 char **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
14445 void numbernodes(struct mesh *m, struct behavior *b)
14446 #else /* not ANSI_DECLARATORS */
14447 void numbernodes(m, b)
14448 struct mesh *m;
14449 struct 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
14477 void writeelements(struct mesh *m, struct behavior *b,
14478  int **trianglelist, REAL **triangleattriblist)
14479 #else /* not ANSI_DECLARATORS */
14480 void writeelements(m, b, trianglelist, triangleattriblist)
14481 struct mesh *m;
14482 struct behavior *b;
14483 int **trianglelist;
14484 REAL **triangleattriblist;
14485 #endif /* not ANSI_DECLARATORS */
14486 
14487 #else /* not TRILIBRARY */
14488 
14489 #ifdef ANSI_DECLARATORS
14490 void writeelements(struct mesh *m, struct behavior *b, char *elefilename,
14491  int argc, char **argv)
14492 #else /* not ANSI_DECLARATORS */
14493 void writeelements(m, b, elefilename, argc, argv)
14494 struct mesh *m;
14495 struct behavior *b;
14496 char *elefilename;
14497 int argc;
14498 char **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
14618 void writepoly(struct mesh *m, struct behavior *b,
14619  int **segmentlist, int **segmentmarkerlist)
14620 #else /* not ANSI_DECLARATORS */
14621 void writepoly(m, b, segmentlist, segmentmarkerlist)
14622 struct mesh *m;
14623 struct behavior *b;
14624 int **segmentlist;
14625 int **segmentmarkerlist;
14626 #endif /* not ANSI_DECLARATORS */
14627 
14628 #else /* not TRILIBRARY */
14629 
14630 #ifdef ANSI_DECLARATORS
14631 void 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 */
14635 void writepoly(m, b, polyfilename, holelist, holes, regionlist, regions,
14636  argc, argv)
14637 struct mesh *m;
14638 struct behavior *b;
14639 char *polyfilename;
14640 REAL *holelist;
14641 int holes;
14642 REAL *regionlist;
14643 int regions;
14644 int argc;
14645 char **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
14764 void writeedges(struct mesh *m, struct behavior *b,
14765  int **edgelist, int **edgemarkerlist)
14766 #else /* not ANSI_DECLARATORS */
14767 void writeedges(m, b, edgelist, edgemarkerlist)
14768 struct mesh *m;
14769 struct behavior *b;
14770 int **edgelist;
14771 int **edgemarkerlist;
14772 #endif /* not ANSI_DECLARATORS */
14773 
14774 #else /* not TRILIBRARY */
14775 
14776 #ifdef ANSI_DECLARATORS
14777 void writeedges(struct mesh *m, struct behavior *b, char *edgefilename,
14778  int argc, char **argv)
14779 #else /* not ANSI_DECLARATORS */
14780 void writeedges(m, b, edgefilename, argc, argv)
14781 struct mesh *m;
14782 struct behavior *b;
14783 char *edgefilename;
14784 int argc;
14785 char **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
14918 void 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 */
14922 void writevoronoi(m, b, vpointlist, vpointattriblist, vpointmarkerlist,
14923  vedgelist, vedgemarkerlist, vnormlist)
14924 struct mesh *m;
14925 struct behavior *b;
14926 REAL **vpointlist;
14927 REAL **vpointattriblist;
14928 int **vpointmarkerlist;
14929 int **vedgelist;
14930 int **vedgemarkerlist;
14931 REAL **vnormlist;
14932 #endif /* not ANSI_DECLARATORS */
14933 
14934 #else /* not TRILIBRARY */
14935 
14936 #ifdef ANSI_DECLARATORS
14937 void writevoronoi(struct mesh *m, struct behavior *b, char *vnodefilename,
14938  char *vedgefilename, int argc, char **argv)
14939 #else /* not ANSI_DECLARATORS */
14940 void writevoronoi(m, b, vnodefilename, vedgefilename, argc, argv)
14941 struct mesh *m;
14942 struct behavior *b;
14943 char *vnodefilename;
14944 char *vedgefilename;
14945 int argc;
14946 char **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
15131 void writeneighbors(struct mesh *m, struct behavior *b, int **neighborlist)
15132 #else /* not ANSI_DECLARATORS */
15133 void writeneighbors(m, b, neighborlist)
15134 struct mesh *m;
15135 struct behavior *b;
15136 int **neighborlist;
15137 #endif /* not ANSI_DECLARATORS */
15138 
15139 #else /* not TRILIBRARY */
15140 
15141 #ifdef ANSI_DECLARATORS
15142 void writeneighbors(struct mesh *m, struct behavior *b, char *neighborfilename,
15143  int argc, char **argv)
15144 #else /* not ANSI_DECLARATORS */
15145 void writeneighbors(m, b, neighborfilename, argc, argv)
15146 struct mesh *m;
15147 struct behavior *b;
15148 char *neighborfilename;
15149 int argc;
15150 char **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
15246 void writeoff(struct mesh *m, struct behavior *b, char *offfilename,
15247  int argc, char **argv)
15248 #else /* not ANSI_DECLARATORS */
15249 void writeoff(m, b, offfilename, argc, argv)
15250 struct mesh *m;
15251 struct behavior *b;
15252 char *offfilename;
15253 int argc;
15254 char **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
15324 void quality_statistics(struct mesh *m, struct behavior *b)
15325 #else /* not ANSI_DECLARATORS */
15326 void quality_statistics(m, b)
15327 struct mesh *m;
15328 struct 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
15532 void statistics(struct mesh *m, struct behavior *b)
15533 #else /* not ANSI_DECLARATORS */
15534 void statistics(m, b)
15535 struct mesh *m;
15536 struct 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
15652 void triangulate(char *triswitches, struct triangulateio *in,
15653  struct triangulateio *out, struct triangulateio *vorout)
15654 #else /* not ANSI_DECLARATORS */
15655 void triangulate(triswitches, in, out, vorout)
15656 char *triswitches;
15657 struct triangulateio *in;
15658 struct triangulateio *out;
15659 struct triangulateio *vorout;
15660 #endif /* not ANSI_DECLARATORS */
15661 
15662 #else /* not TRILIBRARY */
15663 
15664 #ifdef ANSI_DECLARATORS
15665 int main(int argc, char **argv)
15666 #else /* not ANSI_DECLARATORS */
15667 int main(argc, argv)
15668 int argc;
15669 char **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 }
resulterrbound
REAL resulterrbound
Definition: triangle.c:618
sorg
#define sorg(osub, vertexptr)
Definition: triangle.c:1178
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void initializetrisubpools(struct mesh *m, struct behavior *b)
Definition: triangle.c:4289
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Definition: triangle.c:6608
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Definition: triangle.c:8173
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static double B[]
Definition: SpecFuncCephes.cxx:178
triangulateio::holelist
REAL * holelist
Definition: triangle.h:307
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double dist(Rotation3D const &r1, Rotation3D const &r2)
Definition: 3DDistances.cxx:48
Split
#define Split(a, ahi, alo)
Definition: triangle.c:4775
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int * edgelist
Definition: triangle.h:313
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static long int sum(long int i)
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int minus1mod3[3]
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Definition: triangle.c:1046
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Definition: triangle.c:1094
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int * edgemarkerlist
Definition: triangle.h:314
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Definition: triangle.c:1119
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Definition: triangle.c:287
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float xmin
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#define INPUTVERTEX
Definition: triangle.c:283
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#define bond(otri1, otri2)
Definition: triangle.c:1057
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void alternateaxes(vertex *sortarray, int arraysize, int axis)
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Definition: triangle.c:495
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#define oprev(otri1, otri2)
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static double p3(double t, double a, double b, double c, double d)
Definition: RooChebychev.cxx:92
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void highorder(struct mesh *m, struct behavior *b)
Definition: triangle.c:13694
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void writenodes(struct mesh *m, struct behavior *b, REAL **pointlist, REAL **pointattriblist, int **pointmarkerlist)
Definition: triangle.c:14305
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int * trianglelist
Definition: triangle.h:295
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#define segorg(osub, vertexptr)
Definition: triangle.c:1190
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Definition: triangle.h:305
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Definition: triangle.h:291
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#define s0(x)
Definition: RSha256.hxx:90
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long divconqdelaunay(struct mesh *m, struct behavior *b)
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Definition: THbookFile.cxx:93
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image html pict1_TGaxis_012 png width
Define new text attributes for the label number "labNum".
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#define mark(osub)
Definition: triangle.c:1206
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REAL splitter
Definition: triangle.c:616
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int numberofregions
Definition: triangle.h:311
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#define lnext(otri1, otri2)
Definition: triangle.c:942
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#define sdissolve(osub)
Definition: triangle.c:1220
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void pooldealloc(struct memorypool *pool, VOID *dyingitem)
Definition: triangle.c:4042
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REAL ccwerrboundB
Definition: triangle.c:619
Two_Two_Sum
#define Two_Two_Sum(a1, a0, b1, b0, x3, x2, x1, x0)
Definition: triangle.c:4827
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void makevertexmap(struct mesh *m, struct behavior *b)
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#define SPLAYNODEPERBLOCK
Definition: triangle.c:277
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long delaunay(struct mesh *m, struct behavior *b)
Definition: triangle.c:10997
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#define lprevself(otri)
Definition: triangle.c:955
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int triunsuitable(vertex triorg, vertex tridest, vertex triapex, REAL area)
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Definition: triangle.c:359
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void carveholes(struct mesh *m, struct behavior *b, REAL *holelist, int holes, REAL *regionlist, int regions)
Definition: triangle.c:12963
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Definition: triangle.c:1084
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void findcircumcenter(struct mesh *m, struct behavior *b, vertex torg, vertex tdest, vertex tapex, vertex circumcenter, REAL *xi, REAL *eta, int offcenter)
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Definition: triangle.c:4423
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Definition: triangle.c:620
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Definition: triangle.c:1109
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Definition: triangle.c:1043
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void subsegdealloc(struct mesh *m, subseg *dyingsubseg)
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Definition: triangle.h:298
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Definition: triangle.c:621
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Definition: triangle.c:1213
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Definition: triangle.c:512
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Definition: triangle.c:1271
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Definition: triangle.c:7614
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Definition: triangle.c:962
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Definition: triangle.c:998
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Definition: triangle.c:255
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Definition: triangle.c:4812
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Definition: THbookFile.cxx:93
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Definition: triangle.c:7785
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Definition: triangle.c:4637
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Definition: triangle.c:273
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Definition: Dict.h:5
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Definition: triangle.c:1283
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Definition: triangle.h:300
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Definition: triangle.c:1066
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Definition: triangle.c:1184
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Definition: triangle.h:315
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Definition: triangle.c:620
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void delaunayfixup(struct mesh *m, struct behavior *b, struct otri *fixuptri, int leftside)
Definition: triangle.c:12011
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Definition: triangle.c:6370
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Definition: RSha256.hxx:91
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Definition: triangle.c:4681
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Definition: triangle.c:621
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void formskeleton(struct mesh *m, struct behavior *b, int *segmentlist, int *segmentmarkerlist, int numberofsegments)
Definition: triangle.c:12391
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Definition: RooChebychev.cxx:90
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Definition: THbookFile.cxx:93
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void infecthull(struct mesh *m, struct behavior *b)
Definition: triangle.c:12558
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Definition: triangle.c:912
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Definition: triangle.c:309
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Definition: triangle.c:295
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Definition: triangle.h:286
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Definition: triangle.c:1288
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Definition: triangle.c:4377
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Definition: triangle.c:617
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Definition: triangle.c:11574
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Definition: RSha256.hxx:106
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void regionplague(struct mesh *m, struct behavior *b, REAL attribute, REAL area)
Definition: triangle.c:12850
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Definition: triangle.h:296
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Definition: triangle.c:286
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Definition: triangle.h:292
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Definition: triangle.c:267
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Definition: triangle.c:921
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Definition: triangle.c:5031
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void unflip(struct mesh *m, struct behavior *b, struct otri *flipedge)
Definition: triangle.c:8024
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void triangledealloc(struct mesh *m, triangle *dyingtriangle)
Definition: triangle.c:4356
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Definition: triangle.h:303
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Definition: triangle.c:3830
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Definition: triangle.c:990
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Definition: triangle.c:6453
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#define Absolute(a)
Definition: triangle.c:4729
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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
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Definition: triangle.c:1187
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#define tsbond(otri, osub)
Definition: triangle.c:1265
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void insertsegment(struct mesh *m, struct behavior *b, vertex endpoint1, vertex endpoint2, int newmark)
Definition: triangle.c:12233
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Definition: triangle.c:620
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Definition: triangle.c:14918
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Definition: textangle.C:20
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Definition: triangle.c:4831
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Definition: triangle.c:1208
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Definition: triangle.c:266
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Definition: triangle.c:1290
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Definition: triangle.h:316
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Definition: legend1.C:17
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Definition: triangle.c:268
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Definition: TGeoSystemOfUnits.h:162
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Definition: triangle.c:343
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Definition: triangle.c:260
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Definition: triangle.c:14445
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Definition: triangle.c:1037
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Definition: triangle.c:1196
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Definition: triangle.c:4469
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Definition: triangle.c:11669
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Definition: triangle.c:619
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Definition: alignment.C:1
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Definition: triangle.c:250
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Definition: triangle.h:310
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Definition: triangle.c:1193
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Definition: triangle.c:1240
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Definition: triangle.c:214
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Definition: TRolke.cxx:630
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Definition: triangle.c:12131
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Definition: triangle.c:15532
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Definition: triangle.c:4764
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Definition: triangle.c:9183
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Definition: RSha256.hxx:101
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Definition: TGeoSystemOfUnits.h:130
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Definition: triangle.c:8834
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Definition: triangle.c:285
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Definition: triangle.c:15324
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Definition: triangle.c:14618
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Definition: triangle.h:297
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Definition: triangle.c:1199
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Definition: triangle.c:7889
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Definition: first.py:1
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Definition: triangle.c:4065
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Definition: triangle.c:1285
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Definition: triangle.c:4246
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Definition: triangle.h:289
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Definition: triangle.c:1107
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Definition: triangle.c:932
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Definition: legend1.C:17
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Definition: triangle.c:478
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Definition: triangle.c:351
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Definition: triangle.c:1071
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static double Q[]
Definition: SpecFuncCephes.cxx:294
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Definition: triangle.h:293
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Definition: triangle.c:1102
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Definition: triangle.c:5945
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Definition: triangle.c:619
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Definition: triangle.c:4101
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Definition: triangle.c:14477
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Definition: triangle.c:1077
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Definition: triangle.c:4448
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Definition: triangle.h:308
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Definition: triangle.c:4555
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Definition: triangle.h:299