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 /* For single precision (which will save some memory and reduce paging), */
198 /* define the symbol SINGLE by using the -DSINGLE compiler switch or by */
199 /* writing "#define SINGLE" below. */
200 /* */
201 /* For double precision (which will allow you to refine meshes to a smaller */
202 /* edge length), leave SINGLE undefined. */
203 /* */
204 /* Double precision uses more memory, but improves the resolution of the */
205 /* meshes you can generate with Triangle. It also reduces the likelihood */
206 /* of a floating exception due to overflow. Finally, it is much faster */
207 /* than single precision on 64-bit architectures like the DEC Alpha. I */
208 /* recommend double precision unless you want to generate a mesh for which */
209 /* you do not have enough memory. */
210
211 /* #define SINGLE */
212
213 #ifdef SINGLE
214 #define REAL float
215 #else /* not SINGLE */
216 #define REAL double
217 #endif /* not SINGLE */
218
219 /* If yours is not a Unix system, define the NO_TIMER compiler switch to */
220 /* remove the Unix-specific timing code. */
221
222 /* #define NO_TIMER */
223
224 /* To insert lots of self-checks for internal errors, define the SELF_CHECK */
225 /* symbol. This will slow down the program significantly. It is best to */
226 /* define the symbol using the -DSELF_CHECK compiler switch, but you could */
227 /* write "#define SELF_CHECK" below. If you are modifying this code, I */
228 /* recommend you turn self-checks on until your work is debugged. */
229
230 /* #define SELF_CHECK */
231
232 /* To compile Triangle as a callable object library (triangle.o), define the */
233 /* TRILIBRARY symbol. Read the file triangle.h for details on how to call */
234 /* the procedure triangulate() that results. */
235
236 /* #define TRILIBRARY */
237
238 /* It is possible to generate a smaller version of Triangle using one or */
239 /* both of the following symbols. Define the REDUCED symbol to eliminate */
240 /* all features that are primarily of research interest; specifically, the */
241 /* -i, -F, -s, and -C switches. Define the CDT_ONLY symbol to eliminate */
242 /* all meshing algorithms above and beyond constrained Delaunay */
243 /* triangulation; specifically, the -r, -q, -a, -u, -D, -S, and -s */
244 /* switches. These reductions are most likely to be useful when */
245 /* generating an object library (triangle.o) by defining the TRILIBRARY */
246 /* symbol. */
247
248 /* #define REDUCED */
249 /* #define CDT_ONLY */
250
251 /* On some machines, my exact arithmetic routines might be defeated by the */
252 /* use of internal extended precision floating-point registers. The best */
253 /* way to solve this problem is to set the floating-point registers to use */
254 /* single or double precision internally. On 80x86 processors, this may */
255 /* be accomplished by setting the CPU86 symbol for the Microsoft C */
256 /* compiler, or the LINUX symbol for the gcc compiler running on Linux. */
257 /* */
258 /* An inferior solution is to declare certain values as `volatile', thus */
259 /* forcing them to be stored to memory and rounded off. Unfortunately, */
260 /* this solution might slow Triangle down quite a bit. To use volatile */
261 /* values, write "#define INEXACT volatile" below. Normally, however, */
262 /* INEXACT should be defined to be nothing. ("#define INEXACT".) */
263 /* */
264 /* For more discussion, see http://www.cs.cmu.edu/~quake/robust.pc.html . */
265 /* For yet more discussion, see Section 5 of my paper, "Adaptive Precision */
266 /* Floating-Point Arithmetic and Fast Robust Geometric Predicates" (also */
267 /* available as Section 6.6 of my dissertation). */
268
269 /* #define CPU86 */
270 /* #define LINUX */
271
272 #define INEXACT /* Nothing */
273 /* #define INEXACT volatile */
274
275 /* Maximum number of characters in a file name (including the null). */
276
277 #define FILENAMESIZE 2048
278
279 /* Maximum number of characters in a line read from a file (including the */
280 /* null). */
281
282 #define INPUTLINESIZE 1024
283
284 /* For efficiency, a variety of data structures are allocated in bulk. The */
285 /* following constants determine how many of each structure is allocated */
286 /* at once. */
287
288 #define TRIPERBLOCK 4092 /* Number of triangles allocated at once. */
289 #define SUBSEGPERBLOCK 508 /* Number of subsegments allocated at once. */
290 #define VERTEXPERBLOCK 4092 /* Number of vertices allocated at once. */
291 #define VIRUSPERBLOCK 1020 /* Number of virus triangles allocated at once. */
292 /* Number of encroached subsegments allocated at once. */
293 #define BADSUBSEGPERBLOCK 252
294 /* Number of skinny triangles allocated at once. */
295 #define BADTRIPERBLOCK 4092
296 /* Number of flipped triangles allocated at once. */
297 #define FLIPSTACKERPERBLOCK 252
298 /* Number of splay tree nodes allocated at once. */
299 #define SPLAYNODEPERBLOCK 508
300
301 /* The vertex types. A DEADVERTEX has been deleted entirely. An */
302 /* UNDEADVERTEX is not part of the mesh, but is written to the output */
303 /* .node file and affects the node indexing in the other output files. */
304
305 #define INPUTVERTEX 0
306 #define SEGMENTVERTEX 1
307 #define FREEVERTEX 2
308 #define DEADVERTEX -32768
309 #define UNDEADVERTEX -32767
310
311 /* The next line is used to outsmart some very stupid compilers. If your */
312 /* compiler is smarter, feel free to replace the "int" with "void". */
313 /* Not that it matters. */
314
315 #define VOID int
316
317 /* Two constants for algorithms based on random sampling. Both constants */
318 /* have been chosen empirically to optimize their respective algorithms. */
319
320 /* Used for the point location scheme of Mucke, Saias, and Zhu, to decide */
321 /* how large a random sample of triangles to inspect. */
322
323 #define SAMPLEFACTOR 11
324
325 /* Used in Fortune's sweepline Delaunay algorithm to determine what fraction */
326 /* of boundary edges should be maintained in the splay tree for point */
327 /* location on the front. */
328
329 #define SAMPLERATE 10
330
331 /* A number that speaks for itself, every kissable digit. */
332
333 #define PI 3.141592653589793238462643383279502884197169399375105820974944592308
334
335 /* Another fave. */
336
337 #define SQUAREROOTTWO 1.4142135623730950488016887242096980785696718753769480732
338
339 /* And here's one for those of you who are intimidated by math. */
340
341 #define ONETHIRD 0.333333333333333333333333333333333333333333333333333333333333
342
343 #include <stdio.h>
344 #include <stdlib.h>
345 #include <string.h>
346 #include <math.h>
347 #ifndef NO_TIMER
348 #include <sys/time.h>
349 #endif /* not NO_TIMER */
350 #ifdef CPU86
351 #include <float.h>
352 #endif /* CPU86 */
353 #ifdef LINUX
354 #include <fpu_control.h>
355 #endif /* LINUX */
356 #ifdef TRILIBRARY
357 #include "triangle.h"
358 #endif /* TRILIBRARY */
359
360 /* A few forward declarations. */
361
362 #ifndef TRILIBRARY
363 char *readline();
364 char *findfield();
365 #endif /* not TRILIBRARY */
366
367 /* Labels that signify the result of point location. The result of a */
368 /* search indicates that the point falls in the interior of a triangle, on */
369 /* an edge, on a vertex, or outside the mesh. */
370
371 enum locateresult {INTRIANGLE, ONEDGE, ONVERTEX, OUTSIDE};
372
373 /* Labels that signify the result of vertex insertion. The result indicates */
374 /* that the vertex was inserted with complete success, was inserted but */
375 /* encroaches upon a subsegment, was not inserted because it lies on a */
376 /* segment, or was not inserted because another vertex occupies the same */
377 /* location. */
378
379 enum insertvertexresult {SUCCESSFULVERTEX, ENCROACHINGVERTEX, VIOLATINGVERTEX,
380 DUPLICATEVERTEX};
381
382 /* Labels that signify the result of direction finding. The result */
383 /* indicates that a segment connecting the two query points falls within */
384 /* the direction triangle, along the left edge of the direction triangle, */
385 /* or along the right edge of the direction triangle. */
386
387 enum finddirectionresult {WITHIN, LEFTCOLLINEAR, RIGHTCOLLINEAR};
388
389 /*****************************************************************************/
390 /* */
391 /* The basic mesh data structures */
392 /* */
393 /* There are three: vertices, triangles, and subsegments (abbreviated */
394 /* `subseg'). These three data structures, linked by pointers, comprise */
395 /* the mesh. A vertex simply represents a mesh vertex and its properties. */
396 /* A triangle is a triangle. A subsegment is a special data structure used */
397 /* to represent an impenetrable edge of the mesh (perhaps on the outer */
398 /* boundary, on the boundary of a hole, or part of an internal boundary */
399 /* separating two triangulated regions). Subsegments represent boundaries, */
400 /* defined by the user, that triangles may not lie across. */
401 /* */
402 /* A triangle consists of a list of three vertices, a list of three */
403 /* adjoining triangles, a list of three adjoining subsegments (when */
404 /* segments exist), an arbitrary number of optional user-defined */
405 /* floating-point attributes, and an optional area constraint. The latter */
406 /* is an upper bound on the permissible area of each triangle in a region, */
407 /* used for mesh refinement. */
408 /* */
409 /* For a triangle on a boundary of the mesh, some or all of the neighboring */
410 /* triangles may not be present. For a triangle in the interior of the */
411 /* mesh, often no neighboring subsegments are present. Such absent */
412 /* triangles and subsegments are never represented by NULL pointers; they */
413 /* are represented by two special records: `dummytri', the triangle that */
414 /* fills "outer space", and `dummysub', the omnipresent subsegment. */
415 /* `dummytri' and `dummysub' are used for several reasons; for instance, */
416 /* they can be dereferenced and their contents examined without violating */
417 /* protected memory. */
418 /* */
419 /* However, it is important to understand that a triangle includes other */
420 /* information as well. The pointers to adjoining vertices, triangles, and */
421 /* subsegments are ordered in a way that indicates their geometric relation */
422 /* to each other. Furthermore, each of these pointers contains orientation */
423 /* information. Each pointer to an adjoining triangle indicates which face */
424 /* of that triangle is contacted. Similarly, each pointer to an adjoining */
425 /* subsegment indicates which side of that subsegment is contacted, and how */
426 /* the subsegment is oriented relative to the triangle. */
427 /* */
428 /* The data structure representing a subsegment may be thought to be */
429 /* abutting the edge of one or two triangle data structures: either */
430 /* sandwiched between two triangles, or resting against one triangle on an */
431 /* exterior boundary or hole boundary. */
432 /* */
433 /* A subsegment consists of a list of four vertices--the vertices of the */
434 /* subsegment, and the vertices of the segment it is a part of--a list of */
435 /* two adjoining subsegments, and a list of two adjoining triangles. One */
436 /* of the two adjoining triangles may not be present (though there should */
437 /* always be one), and neighboring subsegments might not be present. */
438 /* Subsegments also store a user-defined integer "boundary marker". */
439 /* Typically, this integer is used to indicate what boundary conditions are */
440 /* to be applied at that location in a finite element simulation. */
441 /* */
442 /* Like triangles, subsegments maintain information about the relative */
443 /* orientation of neighboring objects. */
444 /* */
445 /* Vertices are relatively simple. A vertex is a list of floating-point */
446 /* numbers, starting with the x, and y coordinates, followed by an */
447 /* arbitrary number of optional user-defined floating-point attributes, */
448 /* followed by an integer boundary marker. During the segment insertion */
449 /* phase, there is also a pointer from each vertex to a triangle that may */
450 /* contain it. Each pointer is not always correct, but when one is, it */
451 /* speeds up segment insertion. These pointers are assigned values once */
452 /* at the beginning of the segment insertion phase, and are not used or */
453 /* updated except during this phase. Edge flipping during segment */
454 /* insertion will render some of them incorrect. Hence, don't rely upon */
455 /* them for anything. */
456 /* */
457 /* Other than the exception mentioned above, vertices have no information */
458 /* about what triangles, subfacets, or subsegments they are linked to. */
459 /* */
460 /*****************************************************************************/
461
462 /*****************************************************************************/
463 /* */
464 /* Handles */
465 /* */
466 /* The oriented triangle (`otri') and oriented subsegment (`osub') data */
467 /* structures defined below do not themselves store any part of the mesh. */
468 /* The mesh itself is made of `triangle's, `subseg's, and `vertex's. */
469 /* */
470 /* Oriented triangles and oriented subsegments will usually be referred to */
471 /* as "handles." A handle is essentially a pointer into the mesh; it */
472 /* allows you to "hold" one particular part of the mesh. Handles are used */
473 /* to specify the regions in which one is traversing and modifying the mesh.*/
474 /* A single `triangle' may be held by many handles, or none at all. (The */
475 /* latter case is not a memory leak, because the triangle is still */
476 /* connected to other triangles in the mesh.) */
477 /* */
478 /* An `otri' is a handle that holds a triangle. It holds a specific edge */
479 /* of the triangle. An `osub' is a handle that holds a subsegment. It */
480 /* holds either the left or right side of the subsegment. */
481 /* */
482 /* Navigation about the mesh is accomplished through a set of mesh */
483 /* manipulation primitives, further below. Many of these primitives take */
484 /* a handle and produce a new handle that holds the mesh near the first */
485 /* handle. Other primitives take two handles and glue the corresponding */
486 /* parts of the mesh together. The orientation of the handles is */
487 /* important. For instance, when two triangles are glued together by the */
488 /* bond() primitive, they are glued at the edges on which the handles lie. */
489 /* */
490 /* Because vertices have no information about which triangles they are */
491 /* attached to, I commonly represent a vertex by use of a handle whose */
492 /* origin is the vertex. A single handle can simultaneously represent a */
493 /* triangle, an edge, and a vertex. */
494 /* */
495 /*****************************************************************************/
496
497 /* The triangle data structure. Each triangle contains three pointers to */
498 /* adjoining triangles, plus three pointers to vertices, plus three */
499 /* pointers to subsegments (declared below; these pointers are usually */
500 /* `dummysub'). It may or may not also contain user-defined attributes */
501 /* and/or a floating-point "area constraint." It may also contain extra */
502 /* pointers for nodes, when the user asks for high-order elements. */
503 /* Because the size and structure of a `triangle' is not decided until */
504 /* runtime, I haven't simply declared the type `triangle' as a struct. */
505
506 typedef REAL **triangle; /* Really: typedef triangle *triangle */
507
508 /* An oriented triangle: includes a pointer to a triangle and orientation. */
509 /* The orientation denotes an edge of the triangle. Hence, there are */
510 /* three possible orientations. By convention, each edge always points */
511 /* counterclockwise about the corresponding triangle. */
512
513 struct otri {
514 triangle *tri;
515 int orient; /* Ranges from 0 to 2. */
516 };
517
518 /* The subsegment data structure. Each subsegment contains two pointers to */
519 /* adjoining subsegments, plus four pointers to vertices, plus two */
520 /* pointers to adjoining triangles, plus one boundary marker, plus one */
521 /* segment number. */
522
523 typedef REAL **subseg; /* Really: typedef subseg *subseg */
524
525 /* An oriented subsegment: includes a pointer to a subsegment and an */
526 /* orientation. The orientation denotes a side of the edge. Hence, there */
527 /* are two possible orientations. By convention, the edge is always */
528 /* directed so that the "side" denoted is the right side of the edge. */
529
530 struct osub {
531 subseg *ss;
532 int ssorient; /* Ranges from 0 to 1. */
533 };
534
535 /* The vertex data structure. Each vertex is actually an array of REALs. */
536 /* The number of REALs is unknown until runtime. An integer boundary */
537 /* marker, and sometimes a pointer to a triangle, is appended after the */
538 /* REALs. */
539
540 typedef REAL *vertex;
541
542 /* A queue used to store encroached subsegments. Each subsegment's vertices */
543 /* are stored so that we can check whether a subsegment is still the same. */
544
545 struct badsubseg {
546 subseg encsubseg; /* An encroached subsegment. */
547 vertex subsegorg, subsegdest; /* Its two vertices. */
548 };
549
550 /* A queue used to store bad triangles. The key is the square of the cosine */
551 /* of the smallest angle of the triangle. Each triangle's vertices are */
552 /* stored so that one can check whether a triangle is still the same. */
553
554 struct badtriang {
555 triangle poortri; /* A skinny or too-large triangle. */
556 REAL key; /* cos^2 of smallest (apical) angle. */
557 vertex triangorg, triangdest, triangapex; /* Its three vertices. */
558 struct badtriang *nexttriang; /* Pointer to next bad triangle. */
559 };
560
561 /* A stack of triangles flipped during the most recent vertex insertion. */
562 /* The stack is used to undo the vertex insertion if the vertex encroaches */
563 /* upon a subsegment. */
564
565 struct flipstacker {
566 triangle flippedtri; /* A recently flipped triangle. */
567 struct flipstacker *prevflip; /* Previous flip in the stack. */
568 };
569
570 /* A node in a heap used to store events for the sweepline Delaunay */
571 /* algorithm. Nodes do not point directly to their parents or children in */
572 /* the heap. Instead, each node knows its position in the heap, and can */
573 /* look up its parent and children in a separate array. The `eventptr' */
574 /* points either to a `vertex' or to a triangle (in encoded format, so */
575 /* that an orientation is included). In the latter case, the origin of */
576 /* the oriented triangle is the apex of a "circle event" of the sweepline */
577 /* algorithm. To distinguish site events from circle events, all circle */
578 /* events are given an invalid (smaller than `xmin') x-coordinate `xkey'. */
579
580 struct event {
581 REAL xkey, ykey; /* Coordinates of the event. */
582 VOID *eventptr; /* Can be a vertex or the location of a circle event. */
583 int heapposition; /* Marks this event's position in the heap. */
584 };
585
586 /* A node in the splay tree. Each node holds an oriented ghost triangle */
587 /* that represents a boundary edge of the growing triangulation. When a */
588 /* circle event covers two boundary edges with a triangle, so that they */
589 /* are no longer boundary edges, those edges are not immediately deleted */
590 /* from the tree; rather, they are lazily deleted when they are next */
591 /* encountered. (Since only a random sample of boundary edges are kept */
592 /* in the tree, lazy deletion is faster.) `keydest' is used to verify */
593 /* that a triangle is still the same as when it entered the splay tree; if */
594 /* it has been rotated (due to a circle event), it no longer represents a */
595 /* boundary edge and should be deleted. */
596
597 struct splaynode {
598 struct otri keyedge; /* Lprev of an edge on the front. */
599 vertex keydest; /* Used to verify that splay node is still live. */
600 struct splaynode *lchild, *rchild; /* Children in splay tree. */
601 };
602
603 /* A type used to allocate memory. firstblock is the first block of items. */
604 /* nowblock is the block from which items are currently being allocated. */
605 /* nextitem points to the next slab of free memory for an item. */
606 /* deaditemstack is the head of a linked list (stack) of deallocated items */
607 /* that can be recycled. unallocateditems is the number of items that */
608 /* remain to be allocated from nowblock. */
609 /* */
610 /* Traversal is the process of walking through the entire list of items, and */
611 /* is separate from allocation. Note that a traversal will visit items on */
612 /* the "deaditemstack" stack as well as live items. pathblock points to */
613 /* the block currently being traversed. pathitem points to the next item */
614 /* to be traversed. pathitemsleft is the number of items that remain to */
615 /* be traversed in pathblock. */
616 /* */
617 /* alignbytes determines how new records should be aligned in memory. */
618 /* itembytes is the length of a record in bytes (after rounding up). */
619 /* itemsperblock is the number of items allocated at once in a single */
620 /* block. itemsfirstblock is the number of items in the first block, */
621 /* which can vary from the others. items is the number of currently */
622 /* allocated items. maxitems is the maximum number of items that have */
623 /* been allocated at once; it is the current number of items plus the */
624 /* number of records kept on deaditemstack. */
625
626 struct memorypool {
627 VOID **firstblock, **nowblock;
628 VOID *nextitem;
629 VOID *deaditemstack;
630 VOID **pathblock;
631 VOID *pathitem;
632 int alignbytes;
633 int itembytes;
634 int itemsperblock;
635 int itemsfirstblock;
636 long items, maxitems;
637 int unallocateditems;
638 int pathitemsleft;
639 };
640
641
642 /* Global constants. */
643
644 REAL splitter; /* Used to split REAL factors for exact multiplication. */
645 REAL epsilon; /* Floating-point machine epsilon. */
646 REAL resulterrbound;
647 REAL ccwerrboundA, ccwerrboundB, ccwerrboundC;
648 REAL iccerrboundA, iccerrboundB, iccerrboundC;
649 REAL o3derrboundA, o3derrboundB, o3derrboundC;
650
651 /* Random number seed is not constant, but I've made it global anyway. */
652
653 unsigned long randomseed; /* Current random number seed. */
654
655
656 /* Mesh data structure. Triangle operates on only one mesh, but the mesh */
657 /* structure is used (instead of global variables) to allow reentrancy. */
658
659 struct mesh {
660
661 /* Variables used to allocate memory for triangles, subsegments, vertices, */
662 /* viri (triangles being eaten), encroached segments, bad (skinny or too */
663 /* large) triangles, and splay tree nodes. */
664
665 struct memorypool triangles;
666 struct memorypool subsegs;
667 struct memorypool vertices;
668 struct memorypool viri;
669 struct memorypool badsubsegs;
670 struct memorypool badtriangles;
671 struct memorypool flipstackers;
672 struct memorypool splaynodes;
673
674 /* Variables that maintain the bad triangle queues. The queues are */
675 /* ordered from 4095 (highest priority) to 0 (lowest priority). */
676
677 struct badtriang *queuefront[4096];
678 struct badtriang *queuetail[4096];
679 int nextnonemptyq[4096];
680 int firstnonemptyq;
681
682 /* Variable that maintains the stack of recently flipped triangles. */
683
684 struct flipstacker *lastflip;
685
686 /* Other variables. */
687
688 REAL xmin, xmax, ymin, ymax; /* x and y bounds. */
689 REAL xminextreme; /* Nonexistent x value used as a flag in sweepline. */
690 int invertices; /* Number of input vertices. */
691 int inelements; /* Number of input triangles. */
692 int insegments; /* Number of input segments. */
693 int holes; /* Number of input holes. */
694 int regions; /* Number of input regions. */
695 int undeads; /* Number of input vertices that don't appear in the mesh. */
696 long edges; /* Number of output edges. */
697 int mesh_dim; /* Dimension (ought to be 2). */
698 int nextras; /* Number of attributes per vertex. */
699 int eextras; /* Number of attributes per triangle. */
700 long hullsize; /* Number of edges in convex hull. */
701 int steinerleft; /* Number of Steiner points not yet used. */
702 int vertexmarkindex; /* Index to find boundary marker of a vertex. */
703 int vertex2triindex; /* Index to find a triangle adjacent to a vertex. */
704 int highorderindex; /* Index to find extra nodes for high-order elements. */
705 int elemattribindex; /* Index to find attributes of a triangle. */
706 int areaboundindex; /* Index to find area bound of a triangle. */
707 int checksegments; /* Are there segments in the triangulation yet? */
708 int checkquality; /* Has quality triangulation begun yet? */
709 int readnodefile; /* Has a .node file been read? */
710 long samples; /* Number of random samples for point location. */
711
712 long incirclecount; /* Number of incircle tests performed. */
713 long counterclockcount; /* Number of counterclockwise tests performed. */
714 long orient3dcount; /* Number of 3D orientation tests performed. */
715 long hyperbolacount; /* Number of right-of-hyperbola tests performed. */
716 long circumcentercount; /* Number of circumcenter calculations performed. */
717 long circletopcount; /* Number of circle top calculations performed. */
718
719 /* Triangular bounding box vertices. */
720
721 vertex infvertex1, infvertex2, infvertex3;
722
723 /* Pointer to the `triangle' that occupies all of "outer space." */
724
725 triangle *dummytri;
726 triangle *dummytribase; /* Keep base address so we can free() it later. */
727
728 /* Pointer to the omnipresent subsegment. Referenced by any triangle or */
729 /* subsegment that isn't really connected to a subsegment at that */
730 /* location. */
731
732 subseg *dummysub;
733 subseg *dummysubbase; /* Keep base address so we can free() it later. */
734
735 /* Pointer to a recently visited triangle. Improves point location if */
736 /* proximate vertices are inserted sequentially. */
737
738 struct otri recenttri;
739
740 }; /* End of `struct mesh'. */
741
742
743 /* Data structure for command line switches and file names. This structure */
744 /* is used (instead of global variables) to allow reentrancy. */
745
746 struct behavior {
747
748 /* Switches for the triangulator. */
749 /* poly: -p switch. refine: -r switch. */
750 /* quality: -q switch. */
751 /* minangle: minimum angle bound, specified after -q switch. */
752 /* goodangle: cosine squared of minangle. */
753 /* offconstant: constant used to place off-center Steiner points. */
754 /* vararea: -a switch without number. */
755 /* fixedarea: -a switch with number. */
756 /* maxarea: maximum area bound, specified after -a switch. */
757 /* usertest: -u switch. */
758 /* regionattrib: -A switch. convex: -c switch. */
759 /* weighted: 1 for -w switch, 2 for -W switch. jettison: -j switch */
760 /* firstnumber: inverse of -z switch. All items are numbered starting */
761 /* from `firstnumber'. */
762 /* edgesout: -e switch. voronoi: -v switch. */
763 /* neighbors: -n switch. geomview: -g switch. */
764 /* nobound: -B switch. nopolywritten: -P switch. */
765 /* nonodewritten: -N switch. noelewritten: -E switch. */
766 /* noiterationnum: -I switch. noholes: -O switch. */
767 /* noexact: -X switch. */
768 /* order: element order, specified after -o switch. */
769 /* nobisect: count of how often -Y switch is selected. */
770 /* steiner: maximum number of Steiner points, specified after -S switch. */
771 /* incremental: -i switch. sweepline: -F switch. */
772 /* dwyer: inverse of -l switch. */
773 /* splitseg: -s switch. */
774 /* conformdel: -D switch. docheck: -C switch. */
775 /* quiet: -Q switch. verbose: count of how often -V switch is selected. */
776 /* usesegments: -p, -r, -q, or -c switch; determines whether segments are */
777 /* used at all. */
778 /* */
779 /* Read the instructions to find out the meaning of these switches. */
780
781 int poly, refine, quality, vararea, fixedarea, usertest;
782 int regionattrib, convex, weighted, jettison;
783 int firstnumber;
784 int edgesout, voronoi, neighbors, geomview;
785 int nobound, nopolywritten, nonodewritten, noelewritten, noiterationnum;
786 int noholes, noexact, conformdel;
787 int incremental, sweepline, dwyer;
788 int splitseg;
789 int docheck;
790 int quiet, verbose;
791 int usesegments;
792 int order;
793 int nobisect;
794 int steiner;
795 REAL minangle, goodangle, offconstant;
796 REAL maxarea;
797
798 /* Variables for file names. */
799
800 #ifndef TRILIBRARY
801 char innodefilename[FILENAMESIZE];
802 char inelefilename[FILENAMESIZE];
803 char inpolyfilename[FILENAMESIZE];
804 char areafilename[FILENAMESIZE];
805 char outnodefilename[FILENAMESIZE];
806 char outelefilename[FILENAMESIZE];
807 char outpolyfilename[FILENAMESIZE];
808 char edgefilename[FILENAMESIZE];
809 char vnodefilename[FILENAMESIZE];
810 char vedgefilename[FILENAMESIZE];
811 char neighborfilename[FILENAMESIZE];
812 char offfilename[FILENAMESIZE];
813 #endif /* not TRILIBRARY */
814
815 }; /* End of `struct behavior'. */
816
817
818 /*****************************************************************************/
819 /* */
820 /* Mesh manipulation primitives. Each triangle contains three pointers to */
821 /* other triangles, with orientations. Each pointer points not to the */
822 /* first byte of a triangle, but to one of the first three bytes of a */
823 /* triangle. It is necessary to extract both the triangle itself and the */
824 /* orientation. To save memory, I keep both pieces of information in one */
825 /* pointer. To make this possible, I assume that all triangles are aligned */
826 /* to four-byte boundaries. The decode() routine below decodes a pointer, */
827 /* extracting an orientation (in the range 0 to 2) and a pointer to the */
828 /* beginning of a triangle. The encode() routine compresses a pointer to a */
829 /* triangle and an orientation into a single pointer. My assumptions that */
830 /* triangles are four-byte-aligned and that the `unsigned long' type is */
831 /* long enough to hold a pointer are two of the few kludges in this program.*/
832 /* */
833 /* Subsegments are manipulated similarly. A pointer to a subsegment */
834 /* carries both an address and an orientation in the range 0 to 1. */
835 /* */
836 /* The other primitives take an oriented triangle or oriented subsegment, */
837 /* and return an oriented triangle or oriented subsegment or vertex; or */
838 /* they change the connections in the data structure. */
839 /* */
840 /* Below, triangles and subsegments are denoted by their vertices. The */
841 /* triangle abc has origin (org) a, destination (dest) b, and apex (apex) */
842 /* c. These vertices occur in counterclockwise order about the triangle. */
843 /* The handle abc may simultaneously denote vertex a, edge ab, and triangle */
844 /* abc. */
845 /* */
846 /* Similarly, the subsegment ab has origin (sorg) a and destination (sdest) */
847 /* b. If ab is thought to be directed upward (with b directly above a), */
848 /* then the handle ab is thought to grasp the right side of ab, and may */
849 /* simultaneously denote vertex a and edge ab. */
850 /* */
851 /* An asterisk (*) denotes a vertex whose identity is unknown. */
852 /* */
853 /* Given this notation, a partial list of mesh manipulation primitives */
854 /* follows. */
855 /* */
856 /* */
857 /* For triangles: */
858 /* */
859 /* sym: Find the abutting triangle; same edge. */
860 /* sym(abc) -> ba* */
861 /* */
862 /* lnext: Find the next edge (counterclockwise) of a triangle. */
863 /* lnext(abc) -> bca */
864 /* */
865 /* lprev: Find the previous edge (clockwise) of a triangle. */
866 /* lprev(abc) -> cab */
867 /* */
868 /* onext: Find the next edge counterclockwise with the same origin. */
869 /* onext(abc) -> ac* */
870 /* */
871 /* oprev: Find the next edge clockwise with the same origin. */
872 /* oprev(abc) -> a*b */
873 /* */
874 /* dnext: Find the next edge counterclockwise with the same destination. */
875 /* dnext(abc) -> *ba */
876 /* */
877 /* dprev: Find the next edge clockwise with the same destination. */
878 /* dprev(abc) -> cb* */
879 /* */
880 /* rnext: Find the next edge (counterclockwise) of the adjacent triangle. */
881 /* rnext(abc) -> *a* */
882 /* */
883 /* rprev: Find the previous edge (clockwise) of the adjacent triangle. */
884 /* rprev(abc) -> b** */
885 /* */
886 /* org: Origin dest: Destination apex: Apex */
887 /* org(abc) -> a dest(abc) -> b apex(abc) -> c */
888 /* */
889 /* bond: Bond two triangles together at the resepective handles. */
890 /* bond(abc, bad) */
891 /* */
892 /* */
893 /* For subsegments: */
894 /* */
895 /* ssym: Reverse the orientation of a subsegment. */
896 /* ssym(ab) -> ba */
897 /* */
898 /* spivot: Find adjoining subsegment with the same origin. */
899 /* spivot(ab) -> a* */
900 /* */
901 /* snext: Find next subsegment in sequence. */
902 /* snext(ab) -> b* */
903 /* */
904 /* sorg: Origin sdest: Destination */
905 /* sorg(ab) -> a sdest(ab) -> b */
906 /* */
907 /* sbond: Bond two subsegments together at the respective origins. */
908 /* sbond(ab, ac) */
909 /* */
910 /* */
911 /* For interacting tetrahedra and subfacets: */
912 /* */
913 /* tspivot: Find a subsegment abutting a triangle. */
914 /* tspivot(abc) -> ba */
915 /* */
916 /* stpivot: Find a triangle abutting a subsegment. */
917 /* stpivot(ab) -> ba* */
918 /* */
919 /* tsbond: Bond a triangle to a subsegment. */
920 /* tsbond(abc, ba) */
921 /* */
922 /*****************************************************************************/
923
924 /********* Mesh manipulation primitives begin here *********/
925 /** **/
926 /** **/
927
928 /* Fast lookup arrays to speed some of the mesh manipulation primitives. */
929
930 int plus1mod3[3] = {1, 2, 0};
931 int minus1mod3[3] = {2, 0, 1};
932
933 /********* Primitives for triangles *********/
934 /* */
935 /* */
936
937 /* decode() converts a pointer to an oriented triangle. The orientation is */
938 /* extracted from the two least significant bits of the pointer. */
939
940 #define decode(ptr, otri) \
941 (otri).orient = (int) ((unsigned long) (ptr) & (unsigned long) 3l); \
942 (otri).tri = (triangle *) \
943 ((unsigned long) (ptr) ^ (unsigned long) (otri).orient)
944
945 /* encode() compresses an oriented triangle into a single pointer. It */
946 /* relies on the assumption that all triangles are aligned to four-byte */
947 /* boundaries, so the two least significant bits of (otri).tri are zero. */
948
949 #define encode(otri) \
950 (triangle) ((unsigned long) (otri).tri | (unsigned long) (otri).orient)
951
952 /* The following handle manipulation primitives are all described by Guibas */
953 /* and Stolfi. However, Guibas and Stolfi use an edge-based data */
954 /* structure, whereas I use a triangle-based data structure. */
955
956 /* sym() finds the abutting triangle, on the same edge. Note that the edge */
957 /* direction is necessarily reversed, because the handle specified by an */
958 /* oriented triangle is directed counterclockwise around the triangle. */
959
960 #define sym(otri1, otri2) \
961 ptr = (otri1).tri[(otri1).orient]; \
962 decode(ptr, otri2);
963
964 #define symself(otri) \
965 ptr = (otri).tri[(otri).orient]; \
966 decode(ptr, otri);
967
968 /* lnext() finds the next edge (counterclockwise) of a triangle. */
969
970 #define lnext(otri1, otri2) \
971 (otri2).tri = (otri1).tri; \
972 (otri2).orient = plus1mod3[(otri1).orient]
973
974 #define lnextself(otri) \
975 (otri).orient = plus1mod3[(otri).orient]
976
977 /* lprev() finds the previous edge (clockwise) of a triangle. */
978
979 #define lprev(otri1, otri2) \
980 (otri2).tri = (otri1).tri; \
981 (otri2).orient = minus1mod3[(otri1).orient]
982
983 #define lprevself(otri) \
984 (otri).orient = minus1mod3[(otri).orient]
985
986 /* onext() spins counterclockwise around a vertex; that is, it finds the */
987 /* next edge with the same origin in the counterclockwise direction. This */
988 /* edge is part of a different triangle. */
989
990 #define onext(otri1, otri2) \
991 lprev(otri1, otri2); \
992 symself(otri2);
993
994 #define onextself(otri) \
995 lprevself(otri); \
996 symself(otri);
997
998 /* oprev() spins clockwise around a vertex; that is, it finds the next edge */
999 /* with the same origin in the clockwise direction. This edge is part of */
1000 /* a different triangle. */
1001
1002 #define oprev(otri1, otri2) \
1003 sym(otri1, otri2); \
1004 lnextself(otri2);
1005
1006 #define oprevself(otri) \
1007 symself(otri); \
1008 lnextself(otri);
1009
1010 /* dnext() spins counterclockwise around a vertex; that is, it finds the */
1011 /* next edge with the same destination in the counterclockwise direction. */
1012 /* This edge is part of a different triangle. */
1013
1014 #define dnext(otri1, otri2) \
1015 sym(otri1, otri2); \
1016 lprevself(otri2);
1017
1018 #define dnextself(otri) \
1019 symself(otri); \
1020 lprevself(otri);
1021
1022 /* dprev() spins clockwise around a vertex; that is, it finds the next edge */
1023 /* with the same destination in the clockwise direction. This edge is */
1024 /* part of a different triangle. */
1025
1026 #define dprev(otri1, otri2) \
1027 lnext(otri1, otri2); \
1028 symself(otri2);
1029
1030 #define dprevself(otri) \
1031 lnextself(otri); \
1032 symself(otri);
1033
1034 /* rnext() moves one edge counterclockwise about the adjacent triangle. */
1035 /* (It's best understood by reading Guibas and Stolfi. It involves */
1036 /* changing triangles twice.) */
1037
1038 #define rnext(otri1, otri2) \
1039 sym(otri1, otri2); \
1040 lnextself(otri2); \
1041 symself(otri2);
1042
1043 #define rnextself(otri) \
1044 symself(otri); \
1045 lnextself(otri); \
1046 symself(otri);
1047
1048 /* rprev() moves one edge clockwise about the adjacent triangle. */
1049 /* (It's best understood by reading Guibas and Stolfi. It involves */
1050 /* changing triangles twice.) */
1051
1052 #define rprev(otri1, otri2) \
1053 sym(otri1, otri2); \
1054 lprevself(otri2); \
1055 symself(otri2);
1056
1057 #define rprevself(otri) \
1058 symself(otri); \
1059 lprevself(otri); \
1060 symself(otri);
1061
1062 /* These primitives determine or set the origin, destination, or apex of a */
1063 /* triangle. */
1064
1065 #define org(otri, vertexptr) \
1066 vertexptr = (vertex) (otri).tri[plus1mod3[(otri).orient] + 3]
1067
1068 #define dest(otri, vertexptr) \
1069 vertexptr = (vertex) (otri).tri[minus1mod3[(otri).orient] + 3]
1070
1071 #define apex(otri, vertexptr) \
1072 vertexptr = (vertex) (otri).tri[(otri).orient + 3]
1073
1074 #define setorg(otri, vertexptr) \
1075 (otri).tri[plus1mod3[(otri).orient] + 3] = (triangle) vertexptr
1076
1077 #define setdest(otri, vertexptr) \
1078 (otri).tri[minus1mod3[(otri).orient] + 3] = (triangle) vertexptr
1079
1080 #define setapex(otri, vertexptr) \
1081 (otri).tri[(otri).orient + 3] = (triangle) vertexptr
1082
1083 /* Bond two triangles together. */
1084
1085 #define bond(otri1, otri2) \
1086 (otri1).tri[(otri1).orient] = encode(otri2); \
1087 (otri2).tri[(otri2).orient] = encode(otri1)
1088
1089 /* Dissolve a bond (from one side). Note that the other triangle will still */
1090 /* think it's connected to this triangle. Usually, however, the other */
1091 /* triangle is being deleted entirely, or bonded to another triangle, so */
1092 /* it doesn't matter. */
1093
1094 #define dissolve(otri) \
1095 (otri).tri[(otri).orient] = (triangle) m->dummytri
1096
1097 /* Copy an oriented triangle. */
1098
1099 #define otricopy(otri1, otri2) \
1100 (otri2).tri = (otri1).tri; \
1101 (otri2).orient = (otri1).orient
1102
1103 /* Test for equality of oriented triangles. */
1104
1105 #define otriequal(otri1, otri2) \
1106 (((otri1).tri == (otri2).tri) && \
1107 ((otri1).orient == (otri2).orient))
1108
1109 /* Primitives to infect or cure a triangle with the virus. These rely on */
1110 /* the assumption that all subsegments are aligned to four-byte boundaries.*/
1111
1112 #define infect(otri) \
1113 (otri).tri[6] = (triangle) \
1114 ((unsigned long) (otri).tri[6] | (unsigned long) 2l)
1115
1116 #define uninfect(otri) \
1117 (otri).tri[6] = (triangle) \
1118 ((unsigned long) (otri).tri[6] & ~ (unsigned long) 2l)
1119
1120 /* Test a triangle for viral infection. */
1121
1122 #define infected(otri) \
1123 (((unsigned long) (otri).tri[6] & (unsigned long) 2l) != 0l)
1124
1125 /* Check or set a triangle's attributes. */
1126
1127 #define elemattribute(otri, attnum) \
1128 ((REAL *) (otri).tri)[m->elemattribindex + (attnum)]
1129
1130 #define setelemattribute(otri, attnum, value) \
1131 ((REAL *) (otri).tri)[m->elemattribindex + (attnum)] = value
1132
1133 /* Check or set a triangle's maximum area bound. */
1134
1135 #define areabound(otri) ((REAL *) (otri).tri)[m->areaboundindex]
1136
1137 #define setareabound(otri, value) \
1138 ((REAL *) (otri).tri)[m->areaboundindex] = value
1139
1140 /* Check or set a triangle's deallocation. Its second pointer is set to */
1141 /* NULL to indicate that it is not allocated. (Its first pointer is used */
1142 /* for the stack of dead items.) Its fourth pointer (its first vertex) */
1143 /* is set to NULL in case a `badtriang' structure points to it. */
1144
1145 #define deadtri(tria) ((tria)[1] == (triangle) NULL)
1146
1147 #define killtri(tria) \
1148 (tria)[1] = (triangle) NULL; \
1149 (tria)[3] = (triangle) NULL
1150
1151 /********* Primitives for subsegments *********/
1152 /* */
1153 /* */
1154
1155 /* sdecode() converts a pointer to an oriented subsegment. The orientation */
1156 /* is extracted from the least significant bit of the pointer. The two */
1157 /* least significant bits (one for orientation, one for viral infection) */
1158 /* are masked out to produce the real pointer. */
1159
1160 #define sdecode(sptr, osub) \
1161 (osub).ssorient = (int) ((unsigned long) (sptr) & (unsigned long) 1l); \
1162 (osub).ss = (subseg *) \
1163 ((unsigned long) (sptr) & ~ (unsigned long) 3l)
1164
1165 /* sencode() compresses an oriented subsegment into a single pointer. It */
1166 /* relies on the assumption that all subsegments are aligned to two-byte */
1167 /* boundaries, so the least significant bit of (osub).ss is zero. */
1168
1169 #define sencode(osub) \
1170 (subseg) ((unsigned long) (osub).ss | (unsigned long) (osub).ssorient)
1171
1172 /* ssym() toggles the orientation of a subsegment. */
1173
1174 #define ssym(osub1, osub2) \
1175 (osub2).ss = (osub1).ss; \
1176 (osub2).ssorient = 1 - (osub1).ssorient
1177
1178 #define ssymself(osub) \
1179 (osub).ssorient = 1 - (osub).ssorient
1180
1181 /* spivot() finds the other subsegment (from the same segment) that shares */
1182 /* the same origin. */
1183
1184 #define spivot(osub1, osub2) \
1185 sptr = (osub1).ss[(osub1).ssorient]; \
1186 sdecode(sptr, osub2)
1187
1188 #define spivotself(osub) \
1189 sptr = (osub).ss[(osub).ssorient]; \
1190 sdecode(sptr, osub)
1191
1192 /* snext() finds the next subsegment (from the same segment) in sequence; */
1193 /* one whose origin is the input subsegment's destination. */
1194
1195 #define snext(osub1, osub2) \
1196 sptr = (osub1).ss[1 - (osub1).ssorient]; \
1197 sdecode(sptr, osub2)
1198
1199 #define snextself(osub) \
1200 sptr = (osub).ss[1 - (osub).ssorient]; \
1201 sdecode(sptr, osub)
1202
1203 /* These primitives determine or set the origin or destination of a */
1204 /* subsegment or the segment that includes it. */
1205
1206 #define sorg(osub, vertexptr) \
1207 vertexptr = (vertex) (osub).ss[2 + (osub).ssorient]
1208
1209 #define sdest(osub, vertexptr) \
1210 vertexptr = (vertex) (osub).ss[3 - (osub).ssorient]
1211
1212 #define setsorg(osub, vertexptr) \
1213 (osub).ss[2 + (osub).ssorient] = (subseg) vertexptr
1214
1215 #define setsdest(osub, vertexptr) \
1216 (osub).ss[3 - (osub).ssorient] = (subseg) vertexptr
1217
1218 #define segorg(osub, vertexptr) \
1219 vertexptr = (vertex) (osub).ss[4 + (osub).ssorient]
1220
1221 #define segdest(osub, vertexptr) \
1222 vertexptr = (vertex) (osub).ss[5 - (osub).ssorient]
1223
1224 #define setsegorg(osub, vertexptr) \
1225 (osub).ss[4 + (osub).ssorient] = (subseg) vertexptr
1226
1227 #define setsegdest(osub, vertexptr) \
1228 (osub).ss[5 - (osub).ssorient] = (subseg) vertexptr
1229
1230 /* These primitives read or set a boundary marker. Boundary markers are */
1231 /* used to hold user-defined tags for setting boundary conditions in */
1232 /* finite element solvers. */
1233
1234 #define mark(osub) (* (int *) ((osub).ss + 8))
1235
1236 #define setmark(osub, value) \
1237 * (int *) ((osub).ss + 8) = value
1238
1239 /* Bond two subsegments together. */
1240
1241 #define sbond(osub1, osub2) \
1242 (osub1).ss[(osub1).ssorient] = sencode(osub2); \
1243 (osub2).ss[(osub2).ssorient] = sencode(osub1)
1244
1245 /* Dissolve a subsegment bond (from one side). Note that the other */
1246 /* subsegment will still think it's connected to this subsegment. */
1247
1248 #define sdissolve(osub) \
1249 (osub).ss[(osub).ssorient] = (subseg) m->dummysub
1250
1251 /* Copy a subsegment. */
1252
1253 #define subsegcopy(osub1, osub2) \
1254 (osub2).ss = (osub1).ss; \
1255 (osub2).ssorient = (osub1).ssorient
1256
1257 /* Test for equality of subsegments. */
1258
1259 #define subsegequal(osub1, osub2) \
1260 (((osub1).ss == (osub2).ss) && \
1261 ((osub1).ssorient == (osub2).ssorient))
1262
1263 /* Check or set a subsegment's deallocation. Its second pointer is set to */
1264 /* NULL to indicate that it is not allocated. (Its first pointer is used */
1265 /* for the stack of dead items.) Its third pointer (its first vertex) */
1266 /* is set to NULL in case a `badsubseg' structure points to it. */
1267
1268 #define deadsubseg(sub) ((sub)[1] == (subseg) NULL)
1269
1270 #define killsubseg(sub) \
1271 (sub)[1] = (subseg) NULL; \
1272 (sub)[2] = (subseg) NULL
1273
1274 /********* Primitives for interacting triangles and subsegments *********/
1275 /* */
1276 /* */
1277
1278 /* tspivot() finds a subsegment abutting a triangle. */
1279
1280 #define tspivot(otri, osub) \
1281 sptr = (subseg) (otri).tri[6 + (otri).orient]; \
1282 sdecode(sptr, osub)
1283
1284 /* stpivot() finds a triangle abutting a subsegment. It requires that the */
1285 /* variable `ptr' of type `triangle' be defined. */
1286
1287 #define stpivot(osub, otri) \
1288 ptr = (triangle) (osub).ss[6 + (osub).ssorient]; \
1289 decode(ptr, otri)
1290
1291 /* Bond a triangle to a subsegment. */
1292
1293 #define tsbond(otri, osub) \
1294 (otri).tri[6 + (otri).orient] = (triangle) sencode(osub); \
1295 (osub).ss[6 + (osub).ssorient] = (subseg) encode(otri)
1296
1297 /* Dissolve a bond (from the triangle side). */
1298
1299 #define tsdissolve(otri) \
1300 (otri).tri[6 + (otri).orient] = (triangle) m->dummysub
1301
1302 /* Dissolve a bond (from the subsegment side). */
1303
1304 #define stdissolve(osub) \
1305 (osub).ss[6 + (osub).ssorient] = (subseg) m->dummytri
1306
1307 /********* Primitives for vertices *********/
1308 /* */
1309 /* */
1310
1311 #define vertexmark(vx) ((int *) (vx))[m->vertexmarkindex]
1312
1313 #define setvertexmark(vx, value) \
1314 ((int *) (vx))[m->vertexmarkindex] = value
1315
1316 #define vertextype(vx) ((int *) (vx))[m->vertexmarkindex + 1]
1317
1318 #define setvertextype(vx, value) \
1319 ((int *) (vx))[m->vertexmarkindex + 1] = value
1320
1321 #define vertex2tri(vx) ((triangle *) (vx))[m->vertex2triindex]
1322
1323 #define setvertex2tri(vx, value) \
1324 ((triangle *) (vx))[m->vertex2triindex] = value
1325
1326 /** **/
1327 /** **/
1328 /********* Mesh manipulation primitives end here *********/
1329
1330 /********* User-defined triangle evaluation routine begins here *********/
1331 /** **/
1332 /** **/
1333
1334 /*****************************************************************************/
1335 /* */
1336 /* triunsuitable() Determine if a triangle is unsuitable, and thus must */
1337 /* be further refined. */
1338 /* */
1339 /* You may write your own procedure that decides whether or not a selected */
1340 /* triangle is too big (and needs to be refined). There are two ways to do */
1341 /* this. */
1342 /* */
1343 /* (1) Modify the procedure `triunsuitable' below, then recompile */
1344 /* Triangle. */
1345 /* */
1346 /* (2) Define the symbol EXTERNAL_TEST (either by adding the definition */
1347 /* to this file, or by using the appropriate compiler switch). This way, */
1348 /* you can compile triangle.c separately from your test. Write your own */
1349 /* `triunsuitable' procedure in a separate C file (using the same prototype */
1350 /* as below). Compile it and link the object code with triangle.o. */
1351 /* */
1352 /* This procedure returns 1 if the triangle is too large and should be */
1353 /* refined; 0 otherwise. */
1354 /* */
1355 /*****************************************************************************/
1356
1357 #ifdef EXTERNAL_TEST
1358
1359 int triunsuitable();
1360
1361 #else /* not EXTERNAL_TEST */
1362
1363 #ifdef ANSI_DECLARATORS
1364 int triunsuitable(vertex triorg, vertex tridest, vertex triapex, REAL area)
1365 #else /* not ANSI_DECLARATORS */
1366 int triunsuitable(triorg, tridest, triapex, area)
1367 vertex triorg; /* The triangle's origin vertex. */
1368 vertex tridest; /* The triangle's destination vertex. */
1369 vertex triapex; /* The triangle's apex vertex. */
1370 REAL area; /* The area of the triangle. */
1371 #endif /* not ANSI_DECLARATORS */
1372
1373 {
1374 REAL dxoa, dxda, dxod;
1375 REAL dyoa, dyda, dyod;
1376 REAL oalen, dalen, odlen;
1377 REAL maxlen;
1378
1379 dxoa = triorg[0] - triapex[0];
1380 dyoa = triorg[1] - triapex[1];
1381 dxda = tridest[0] - triapex[0];
1382 dyda = tridest[1] - triapex[1];
1383 dxod = triorg[0] - tridest[0];
1384 dyod = triorg[1] - tridest[1];
1385 /* Find the squares of the lengths of the triangle's three edges. */
1386 oalen = dxoa * dxoa + dyoa * dyoa;
1387 dalen = dxda * dxda + dyda * dyda;
1388 odlen = dxod * dxod + dyod * dyod;
1389 /* Find the square of the length of the longest edge. */
1390 maxlen = (dalen > oalen) ? dalen : oalen;
1391 maxlen = (odlen > maxlen) ? odlen : maxlen;
1392
1393 if (maxlen > 0.05 * (triorg[0] * triorg[0] + triorg[1] * triorg[1]) + 0.02) {
1394 return 1;
1395 } else {
1396 return 0;
1397 }
1398 }
1399
1400 #endif /* not EXTERNAL_TEST */
1401
1402 /** **/
1403 /** **/
1404 /********* User-defined triangle evaluation routine ends here *********/
1405
1406 /********* Memory allocation and program exit wrappers begin here *********/
1407 /** **/
1408 /** **/
1409
1410 #ifdef ANSI_DECLARATORS
1411 void triexit(int status)
1412 #else /* not ANSI_DECLARATORS */
1413 void triexit(status)
1414 int status;
1415 #endif /* not ANSI_DECLARATORS */
1416
1417 {
1418 exit(status);
1419 }
1420
1421 #ifdef ANSI_DECLARATORS
1422 VOID *trimalloc(int size)
1423 #else /* not ANSI_DECLARATORS */
1424 VOID *trimalloc(size)
1425 int size;
1426 #endif /* not ANSI_DECLARATORS */
1427
1428 {
1429 VOID *memptr;
1430
1431 memptr = (VOID *) malloc((unsigned int) size);
1432 if (memptr == (VOID *) NULL) {
1433 printf("Error: Out of memory.\n");
1434 triexit(1);
1435 }
1436 return(memptr);
1437 }
1438
1439 #ifdef ANSI_DECLARATORS
1440 void trifree(VOID *memptr)
1441 #else /* not ANSI_DECLARATORS */
1442 void trifree(memptr)
1443 VOID *memptr;
1444 #endif /* not ANSI_DECLARATORS */
1445
1446 {
1447 free(memptr);
1448 }
1449
1450 /** **/
1451 /** **/
1452 /********* Memory allocation and program exit wrappers end here *********/
1453
1454 /********* User interaction routines begin here *********/
1455 /** **/
1456 /** **/
1457
1458 /*****************************************************************************/
1459 /* */
1460 /* syntax() Print list of command line switches. */
1461 /* */
1462 /*****************************************************************************/
1463
1464 #ifndef TRILIBRARY
1465
syntax()1466 void syntax()
1467 {
1468 #ifdef CDT_ONLY
1469 #ifdef REDUCED
1470 printf("triangle [-pAcjevngBPNEIOXzo_lQVh] input_file\n");
1471 #else /* not REDUCED */
1472 printf("triangle [-pAcjevngBPNEIOXzo_iFlCQVh] input_file\n");
1473 #endif /* not REDUCED */
1474 #else /* not CDT_ONLY */
1475 #ifdef REDUCED
1476 printf("triangle [-prq__a__uAcDjevngBPNEIOXzo_YS__lQVh] input_file\n");
1477 #else /* not REDUCED */
1478 printf("triangle [-prq__a__uAcDjevngBPNEIOXzo_YS__iFlsCQVh] input_file\n");
1479 #endif /* not REDUCED */
1480 #endif /* not CDT_ONLY */
1481
1482 printf(" -p Triangulates a Planar Straight Line Graph (.poly file).\n");
1483 #ifndef CDT_ONLY
1484 printf(" -r Refines a previously generated mesh.\n");
1485 printf(
1486 " -q Quality mesh generation. A minimum angle may be specified.\n");
1487 printf(" -a Applies a maximum triangle area constraint.\n");
1488 printf(" -u Applies a user-defined triangle constraint.\n");
1489 #endif /* not CDT_ONLY */
1490 printf(
1491 " -A Applies attributes to identify triangles in certain regions.\n");
1492 printf(" -c Encloses the convex hull with segments.\n");
1493 #ifndef CDT_ONLY
1494 printf(" -D Conforming Delaunay: all triangles are truly Delaunay.\n");
1495 #endif /* not CDT_ONLY */
1496 /*
1497 printf(" -w Weighted Delaunay triangulation.\n");
1498 printf(" -W Regular triangulation (lower hull of a height field).\n");
1499 */
1500 printf(" -j Jettison unused vertices from output .node file.\n");
1501 printf(" -e Generates an edge list.\n");
1502 printf(" -v Generates a Voronoi diagram.\n");
1503 printf(" -n Generates a list of triangle neighbors.\n");
1504 printf(" -g Generates an .off file for Geomview.\n");
1505 printf(" -B Suppresses output of boundary information.\n");
1506 printf(" -P Suppresses output of .poly file.\n");
1507 printf(" -N Suppresses output of .node file.\n");
1508 printf(" -E Suppresses output of .ele file.\n");
1509 printf(" -I Suppresses mesh iteration numbers.\n");
1510 printf(" -O Ignores holes in .poly file.\n");
1511 printf(" -X Suppresses use of exact arithmetic.\n");
1512 printf(" -z Numbers all items starting from zero (rather than one).\n");
1513 printf(" -o2 Generates second-order subparametric elements.\n");
1514 #ifndef CDT_ONLY
1515 printf(" -Y Suppresses boundary segment splitting.\n");
1516 printf(" -S Specifies maximum number of added Steiner points.\n");
1517 #endif /* not CDT_ONLY */
1518 #ifndef REDUCED
1519 printf(" -i Uses incremental method, rather than divide-and-conquer.\n");
1520 printf(" -F Uses Fortune's sweepline algorithm, rather than d-and-c.\n");
1521 #endif /* not REDUCED */
1522 printf(" -l Uses vertical cuts only, rather than alternating cuts.\n");
1523 #ifndef REDUCED
1524 #ifndef CDT_ONLY
1525 printf(
1526 " -s Force segments into mesh by splitting (instead of using CDT).\n");
1527 #endif /* not CDT_ONLY */
1528 printf(" -C Check consistency of final mesh.\n");
1529 #endif /* not REDUCED */
1530 printf(" -Q Quiet: No terminal output except errors.\n");
1531 printf(" -V Verbose: Detailed information on what I'm doing.\n");
1532 printf(" -h Help: Detailed instructions for Triangle.\n");
1533 triexit(0);
1534 }
1535
1536 #endif /* not TRILIBRARY */
1537
1538 /*****************************************************************************/
1539 /* */
1540 /* info() Print out complete instructions. */
1541 /* */
1542 /*****************************************************************************/
1543
1544 #ifndef TRILIBRARY
1545
info()1546 void info()
1547 {
1548 printf("Triangle\n");
1549 printf(
1550 "A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator.\n");
1551 printf("Version 1.6\n\n");
1552 printf(
1553 "Copyright 1993, 1995, 1997, 1998, 2002, 2005 Jonathan Richard Shewchuk\n");
1554 printf("2360 Woolsey #H / Berkeley, California 94705-1927\n");
1555 printf("Bugs/comments to jrs@cs.berkeley.edu\n");
1556 printf(
1557 "Created as part of the Quake project (tools for earthquake simulation).\n");
1558 printf(
1559 "Supported in part by NSF Grant CMS-9318163 and an NSERC 1967 Scholarship.\n");
1560 printf("There is no warranty whatsoever. Use at your own risk.\n");
1561 #ifdef SINGLE
1562 printf("This executable is compiled for single precision arithmetic.\n\n\n");
1563 #else /* not SINGLE */
1564 printf("This executable is compiled for double precision arithmetic.\n\n\n");
1565 #endif /* not SINGLE */
1566 printf(
1567 "Triangle generates exact Delaunay triangulations, constrained Delaunay\n");
1568 printf(
1569 "triangulations, conforming Delaunay triangulations, Voronoi diagrams, and\n");
1570 printf(
1571 "high-quality triangular meshes. The latter can be generated with no small\n"
1572 );
1573 printf(
1574 "or large angles, and are thus suitable for finite element analysis. If no\n"
1575 );
1576 printf(
1577 "command line switch is specified, your .node input file is read, and the\n");
1578 printf(
1579 "Delaunay triangulation is returned in .node and .ele output files. The\n");
1580 printf("command syntax is:\n\n");
1581 printf("triangle [-prq__a__uAcDjevngBPNEIOXzo_YS__iFlsCQVh] input_file\n\n");
1582 printf(
1583 "Underscores indicate that numbers may optionally follow certain switches.\n");
1584 printf(
1585 "Do not leave any space between a switch and its numeric parameter.\n");
1586 printf(
1587 "input_file must be a file with extension .node, or extension .poly if the\n");
1588 printf(
1589 "-p switch is used. If -r is used, you must supply .node and .ele files,\n");
1590 printf(
1591 "and possibly a .poly file and an .area file as well. The formats of these\n"
1592 );
1593 printf("files are described below.\n\n");
1594 printf("Command Line Switches:\n\n");
1595 printf(
1596 " -p Reads a Planar Straight Line Graph (.poly file), which can specify\n"
1597 );
1598 printf(
1599 " vertices, segments, holes, regional attributes, and regional area\n");
1600 printf(
1601 " constraints. Generates a constrained Delaunay triangulation (CDT)\n"
1602 );
1603 printf(
1604 " fitting the input; or, if -s, -q, -a, or -u is used, a conforming\n");
1605 printf(
1606 " constrained Delaunay triangulation (CCDT). If you want a truly\n");
1607 printf(
1608 " Delaunay (not just constrained Delaunay) triangulation, use -D as\n");
1609 printf(
1610 " well. When -p is not used, Triangle reads a .node file by default.\n"
1611 );
1612 printf(
1613 " -r Refines a previously generated mesh. The mesh is read from a .node\n"
1614 );
1615 printf(
1616 " file and an .ele file. If -p is also used, a .poly file is read\n");
1617 printf(
1618 " and used to constrain segments in the mesh. If -a is also used\n");
1619 printf(
1620 " (with no number following), an .area file is read and used to\n");
1621 printf(
1622 " impose area constraints on the mesh. Further details on refinement\n"
1623 );
1624 printf(" appear below.\n");
1625 printf(
1626 " -q Quality mesh generation by Delaunay refinement (a hybrid of Paul\n");
1627 printf(
1628 " Chew's and Jim Ruppert's algorithms). Adds vertices to the mesh to\n"
1629 );
1630 printf(
1631 " ensure that all angles are between 20 and 140 degrees. An\n");
1632 printf(
1633 " alternative bound on the minimum angle, replacing 20 degrees, may\n");
1634 printf(
1635 " be specified after the `q'. The specified angle may include a\n");
1636 printf(
1637 " decimal point, but not exponential notation. Note that a bound of\n"
1638 );
1639 printf(
1640 " theta degrees on the smallest angle also implies a bound of\n");
1641 printf(
1642 " (180 - 2 theta) on the largest angle. If the minimum angle is 28.6\n"
1643 );
1644 printf(
1645 " degrees or smaller, Triangle is mathematically guaranteed to\n");
1646 printf(
1647 " terminate (assuming infinite precision arithmetic--Triangle may\n");
1648 printf(
1649 " fail to terminate if you run out of precision). In practice,\n");
1650 printf(
1651 " Triangle often succeeds for minimum angles up to 34 degrees. For\n");
1652 printf(
1653 " some meshes, however, you might need to reduce the minimum angle to\n"
1654 );
1655 printf(
1656 " avoid problems associated with insufficient floating-point\n");
1657 printf(" precision.\n");
1658 printf(
1659 " -a Imposes a maximum triangle area. If a number follows the `a', no\n");
1660 printf(
1661 " triangle is generated whose area is larger than that number. If no\n"
1662 );
1663 printf(
1664 " number is specified, an .area file (if -r is used) or .poly file\n");
1665 printf(
1666 " (if -r is not used) specifies a set of maximum area constraints.\n");
1667 printf(
1668 " An .area file contains a separate area constraint for each\n");
1669 printf(
1670 " triangle, and is useful for refining a finite element mesh based on\n"
1671 );
1672 printf(
1673 " a posteriori error estimates. A .poly file can optionally contain\n"
1674 );
1675 printf(
1676 " an area constraint for each segment-bounded region, thereby\n");
1677 printf(
1678 " controlling triangle densities in a first triangulation of a PSLG.\n"
1679 );
1680 printf(
1681 " You can impose both a fixed area constraint and a varying area\n");
1682 printf(
1683 " constraint by invoking the -a switch twice, once with and once\n");
1684 printf(
1685 " without a number following. Each area specified may include a\n");
1686 printf(" decimal point.\n");
1687 printf(
1688 " -u Imposes a user-defined constraint on triangle size. There are two\n"
1689 );
1690 printf(
1691 " ways to use this feature. One is to edit the triunsuitable()\n");
1692 printf(
1693 " procedure in triangle.c to encode any constraint you like, then\n");
1694 printf(
1695 " recompile Triangle. The other is to compile triangle.c with the\n");
1696 printf(
1697 " EXTERNAL_TEST symbol set (compiler switch -DEXTERNAL_TEST), then\n");
1698 printf(
1699 " link Triangle with a separate object file that implements\n");
1700 printf(
1701 " triunsuitable(). In either case, the -u switch causes the user-\n");
1702 printf(" defined test to be applied to every triangle.\n");
1703 printf(
1704 " -A Assigns an additional floating-point attribute to each triangle\n");
1705 printf(
1706 " that identifies what segment-bounded region each triangle belongs\n");
1707 printf(
1708 " to. Attributes are assigned to regions by the .poly file. If a\n");
1709 printf(
1710 " region is not explicitly marked by the .poly file, triangles in\n");
1711 printf(
1712 " that region are assigned an attribute of zero. The -A switch has\n");
1713 printf(
1714 " an effect only when the -p switch is used and the -r switch is not.\n"
1715 );
1716 printf(
1717 " -c Creates segments on the convex hull of the triangulation. If you\n");
1718 printf(
1719 " are triangulating a vertex set, this switch causes a .poly file to\n"
1720 );
1721 printf(
1722 " be written, containing all edges of the convex hull. If you are\n");
1723 printf(
1724 " triangulating a PSLG, this switch specifies that the whole convex\n");
1725 printf(
1726 " hull of the PSLG should be triangulated, regardless of what\n");
1727 printf(
1728 " segments the PSLG has. If you do not use this switch when\n");
1729 printf(
1730 " triangulating a PSLG, Triangle assumes that you have identified the\n"
1731 );
1732 printf(
1733 " region to be triangulated by surrounding it with segments of the\n");
1734 printf(
1735 " input PSLG. Beware: if you are not careful, this switch can cause\n"
1736 );
1737 printf(
1738 " the introduction of an extremely thin angle between a PSLG segment\n"
1739 );
1740 printf(
1741 " and a convex hull segment, which can cause overrefinement (and\n");
1742 printf(
1743 " possibly failure if Triangle runs out of precision). If you are\n");
1744 printf(
1745 " refining a mesh, the -c switch works differently: it causes a\n");
1746 printf(
1747 " .poly file to be written containing the boundary edges of the mesh\n"
1748 );
1749 printf(" (useful if no .poly file was read).\n");
1750 printf(
1751 " -D Conforming Delaunay triangulation: use this switch if you want to\n"
1752 );
1753 printf(
1754 " ensure that all the triangles in the mesh are Delaunay, and not\n");
1755 printf(
1756 " merely constrained Delaunay; or if you want to ensure that all the\n"
1757 );
1758 printf(
1759 " Voronoi vertices lie within the triangulation. (Some finite volume\n"
1760 );
1761 printf(
1762 " methods have this requirement.) This switch invokes Ruppert's\n");
1763 printf(
1764 " original algorithm, which splits every subsegment whose diametral\n");
1765 printf(
1766 " circle is encroached. It usually increases the number of vertices\n"
1767 );
1768 printf(" and triangles.\n");
1769 printf(
1770 " -j Jettisons vertices that are not part of the final triangulation\n");
1771 printf(
1772 " from the output .node file. By default, Triangle copies all\n");
1773 printf(
1774 " vertices in the input .node file to the output .node file, in the\n");
1775 printf(
1776 " same order, so their indices do not change. The -j switch prevents\n"
1777 );
1778 printf(
1779 " duplicated input vertices, or vertices `eaten' by holes, from\n");
1780 printf(
1781 " appearing in the output .node file. Thus, if two input vertices\n");
1782 printf(
1783 " have exactly the same coordinates, only the first appears in the\n");
1784 printf(
1785 " output. If any vertices are jettisoned, the vertex numbering in\n");
1786 printf(
1787 " the output .node file differs from that of the input .node file.\n");
1788 printf(
1789 " -e Outputs (to an .edge file) a list of edges of the triangulation.\n");
1790 printf(
1791 " -v Outputs the Voronoi diagram associated with the triangulation.\n");
1792 printf(
1793 " Does not attempt to detect degeneracies, so some Voronoi vertices\n");
1794 printf(
1795 " may be duplicated. See the discussion of Voronoi diagrams below.\n");
1796 printf(
1797 " -n Outputs (to a .neigh file) a list of triangles neighboring each\n");
1798 printf(" triangle.\n");
1799 printf(
1800 " -g Outputs the mesh to an Object File Format (.off) file, suitable for\n"
1801 );
1802 printf(" viewing with the Geometry Center's Geomview package.\n");
1803 printf(
1804 " -B No boundary markers in the output .node, .poly, and .edge output\n");
1805 printf(
1806 " files. See the detailed discussion of boundary markers below.\n");
1807 printf(
1808 " -P No output .poly file. Saves disk space, but you lose the ability\n");
1809 printf(
1810 " to maintain constraining segments on later refinements of the mesh.\n"
1811 );
1812 printf(" -N No output .node file.\n");
1813 printf(" -E No output .ele file.\n");
1814 printf(
1815 " -I No iteration numbers. Suppresses the output of .node and .poly\n");
1816 printf(
1817 " files, so your input files won't be overwritten. (If your input is\n"
1818 );
1819 printf(
1820 " a .poly file only, a .node file is written.) Cannot be used with\n");
1821 printf(
1822 " the -r switch, because that would overwrite your input .ele file.\n");
1823 printf(
1824 " Shouldn't be used with the -q, -a, -u, or -s switch if you are\n");
1825 printf(
1826 " using a .node file for input, because no .node file is written, so\n"
1827 );
1828 printf(" there is no record of any added Steiner points.\n");
1829 printf(" -O No holes. Ignores the holes in the .poly file.\n");
1830 printf(
1831 " -X No exact arithmetic. Normally, Triangle uses exact floating-point\n"
1832 );
1833 printf(
1834 " arithmetic for certain tests if it thinks the inexact tests are not\n"
1835 );
1836 printf(
1837 " accurate enough. Exact arithmetic ensures the robustness of the\n");
1838 printf(
1839 " triangulation algorithms, despite floating-point roundoff error.\n");
1840 printf(
1841 " Disabling exact arithmetic with the -X switch causes a small\n");
1842 printf(
1843 " improvement in speed and creates the possibility that Triangle will\n"
1844 );
1845 printf(" fail to produce a valid mesh. Not recommended.\n");
1846 printf(
1847 " -z Numbers all items starting from zero (rather than one). Note that\n"
1848 );
1849 printf(
1850 " this switch is normally overridden by the value used to number the\n"
1851 );
1852 printf(
1853 " first vertex of the input .node or .poly file. However, this\n");
1854 printf(
1855 " switch is useful when calling Triangle from another program.\n");
1856 printf(
1857 " -o2 Generates second-order subparametric elements with six nodes each.\n"
1858 );
1859 printf(
1860 " -Y No new vertices on the boundary. This switch is useful when the\n");
1861 printf(
1862 " mesh boundary must be preserved so that it conforms to some\n");
1863 printf(
1864 " adjacent mesh. Be forewarned that you will probably sacrifice much\n"
1865 );
1866 printf(
1867 " of the quality of the mesh; Triangle will try, but the resulting\n");
1868 printf(
1869 " mesh may contain poorly shaped triangles. Works well if all the\n");
1870 printf(
1871 " boundary vertices are closely spaced. Specify this switch twice\n");
1872 printf(
1873 " (`-YY') to prevent all segment splitting, including internal\n");
1874 printf(" boundaries.\n");
1875 printf(
1876 " -S Specifies the maximum number of Steiner points (vertices that are\n");
1877 printf(
1878 " not in the input, but are added to meet the constraints on minimum\n"
1879 );
1880 printf(
1881 " angle and maximum area). The default is to allow an unlimited\n");
1882 printf(
1883 " number. If you specify this switch with no number after it,\n");
1884 printf(
1885 " the limit is set to zero. Triangle always adds vertices at segment\n"
1886 );
1887 printf(
1888 " intersections, even if it needs to use more vertices than the limit\n"
1889 );
1890 printf(
1891 " you set. When Triangle inserts segments by splitting (-s), it\n");
1892 printf(
1893 " always adds enough vertices to ensure that all the segments of the\n"
1894 );
1895 printf(" PLSG are recovered, ignoring the limit if necessary.\n");
1896 printf(
1897 " -i Uses an incremental rather than a divide-and-conquer algorithm to\n");
1898 printf(
1899 " construct a Delaunay triangulation. Try it if the divide-and-\n");
1900 printf(" conquer algorithm fails.\n");
1901 printf(
1902 " -F Uses Steven Fortune's sweepline algorithm to construct a Delaunay\n");
1903 printf(
1904 " triangulation. Warning: does not use exact arithmetic for all\n");
1905 printf(" calculations. An exact result is not guaranteed.\n");
1906 printf(
1907 " -l Uses only vertical cuts in the divide-and-conquer algorithm. By\n");
1908 printf(
1909 " default, Triangle alternates between vertical and horizontal cuts,\n"
1910 );
1911 printf(
1912 " which usually improve the speed except with vertex sets that are\n");
1913 printf(
1914 " small or short and wide. This switch is primarily of theoretical\n");
1915 printf(" interest.\n");
1916 printf(
1917 " -s Specifies that segments should be forced into the triangulation by\n"
1918 );
1919 printf(
1920 " recursively splitting them at their midpoints, rather than by\n");
1921 printf(
1922 " generating a constrained Delaunay triangulation. Segment splitting\n"
1923 );
1924 printf(
1925 " is true to Ruppert's original algorithm, but can create needlessly\n"
1926 );
1927 printf(
1928 " small triangles. This switch is primarily of theoretical interest.\n"
1929 );
1930 printf(
1931 " -C Check the consistency of the final mesh. Uses exact arithmetic for\n"
1932 );
1933 printf(
1934 " checking, even if the -X switch is used. Useful if you suspect\n");
1935 printf(" Triangle is buggy.\n");
1936 printf(
1937 " -Q Quiet: Suppresses all explanation of what Triangle is doing,\n");
1938 printf(" unless an error occurs.\n");
1939 printf(
1940 " -V Verbose: Gives detailed information about what Triangle is doing.\n"
1941 );
1942 printf(
1943 " Add more `V's for increasing amount of detail. `-V' is most\n");
1944 printf(
1945 " useful; itgives information on algorithmic progress and much more\n");
1946 printf(
1947 " detailed statistics. `-VV' gives vertex-by-vertex details, and\n");
1948 printf(
1949 " prints so much that Triangle runs much more slowly. `-VVVV' gives\n"
1950 );
1951 printf(" information only a debugger could love.\n");
1952 printf(" -h Help: Displays these instructions.\n");
1953 printf("\n");
1954 printf("Definitions:\n");
1955 printf("\n");
1956 printf(
1957 " A Delaunay triangulation of a vertex set is a triangulation whose\n");
1958 printf(
1959 " vertices are the vertex set, that covers the convex hull of the vertex\n");
1960 printf(
1961 " set. A Delaunay triangulation has the property that no vertex lies\n");
1962 printf(
1963 " inside the circumscribing circle (circle that passes through all three\n");
1964 printf(" vertices) of any triangle in the triangulation.\n\n");
1965 printf(
1966 " A Voronoi diagram of a vertex set is a subdivision of the plane into\n");
1967 printf(
1968 " polygonal cells (some of which may be unbounded, meaning infinitely\n");
1969 printf(
1970 " large), where each cell is the set of points in the plane that are closer\n"
1971 );
1972 printf(
1973 " to some input vertex than to any other input vertex. The Voronoi diagram\n"
1974 );
1975 printf(" is a geometric dual of the Delaunay triangulation.\n\n");
1976 printf(
1977 " A Planar Straight Line Graph (PSLG) is a set of vertices and segments.\n");
1978 printf(
1979 " Segments are simply edges, whose endpoints are all vertices in the PSLG.\n"
1980 );
1981 printf(
1982 " Segments may intersect each other only at their endpoints. The file\n");
1983 printf(" format for PSLGs (.poly files) is described below.\n\n");
1984 printf(
1985 " A constrained Delaunay triangulation (CDT) of a PSLG is similar to a\n");
1986 printf(
1987 " Delaunay triangulation, but each PSLG segment is present as a single edge\n"
1988 );
1989 printf(
1990 " of the CDT. (A constrained Delaunay triangulation is not truly a\n");
1991 printf(
1992 " Delaunay triangulation, because some of its triangles might not be\n");
1993 printf(
1994 " Delaunay.) By definition, a CDT does not have any vertices other than\n");
1995 printf(
1996 " those specified in the input PSLG. Depending on context, a CDT might\n");
1997 printf(
1998 " cover the convex hull of the PSLG, or it might cover only a segment-\n");
1999 printf(" bounded region (e.g. a polygon).\n\n");
2000 printf(
2001 " A conforming Delaunay triangulation of a PSLG is a triangulation in which\n"
2002 );
2003 printf(
2004 " each triangle is truly Delaunay, and each PSLG segment is represented by\n"
2005 );
2006 printf(
2007 " a linear contiguous sequence of edges of the triangulation. New vertices\n"
2008 );
2009 printf(
2010 " (not part of the PSLG) may appear, and each input segment may have been\n");
2011 printf(
2012 " subdivided into shorter edges (subsegments) by these additional vertices.\n"
2013 );
2014 printf(
2015 " The new vertices are frequently necessary to maintain the Delaunay\n");
2016 printf(" property while ensuring that every segment is represented.\n\n");
2017 printf(
2018 " A conforming constrained Delaunay triangulation (CCDT) of a PSLG is a\n");
2019 printf(
2020 " triangulation of a PSLG whose triangles are constrained Delaunay. New\n");
2021 printf(" vertices may appear, and input segments may be subdivided into\n");
2022 printf(
2023 " subsegments, but not to guarantee that segments are respected; rather, to\n"
2024 );
2025 printf(
2026 " improve the quality of the triangles. The high-quality meshes produced\n");
2027 printf(
2028 " by the -q switch are usually CCDTs, but can be made conforming Delaunay\n");
2029 printf(" with the -D switch.\n\n");
2030 printf("File Formats:\n\n");
2031 printf(
2032 " All files may contain comments prefixed by the character '#'. Vertices,\n"
2033 );
2034 printf(
2035 " triangles, edges, holes, and maximum area constraints must be numbered\n");
2036 printf(
2037 " consecutively, starting from either 1 or 0. Whichever you choose, all\n");
2038 printf(
2039 " input files must be consistent; if the vertices are numbered from 1, so\n");
2040 printf(
2041 " must be all other objects. Triangle automatically detects your choice\n");
2042 printf(
2043 " while reading the .node (or .poly) file. (When calling Triangle from\n");
2044 printf(
2045 " another program, use the -z switch if you wish to number objects from\n");
2046 printf(" zero.) Examples of these file formats are given below.\n\n");
2047 printf(" .node files:\n");
2048 printf(
2049 " First line: <# of vertices> <dimension (must be 2)> <# of attributes>\n"
2050 );
2051 printf(
2052 " <# of boundary markers (0 or 1)>\n"
2053 );
2054 printf(
2055 " Remaining lines: <vertex #> <x> <y> [attributes] [boundary marker]\n");
2056 printf("\n");
2057 printf(
2058 " The attributes, which are typically floating-point values of physical\n");
2059 printf(
2060 " quantities (such as mass or conductivity) associated with the nodes of\n"
2061 );
2062 printf(
2063 " a finite element mesh, are copied unchanged to the output mesh. If -q,\n"
2064 );
2065 printf(
2066 " -a, -u, -D, or -s is selected, each new Steiner point added to the mesh\n"
2067 );
2068 printf(" has attributes assigned to it by linear interpolation.\n\n");
2069 printf(
2070 " If the fourth entry of the first line is `1', the last column of the\n");
2071 printf(
2072 " remainder of the file is assumed to contain boundary markers. Boundary\n"
2073 );
2074 printf(
2075 " markers are used to identify boundary vertices and vertices resting on\n"
2076 );
2077 printf(
2078 " PSLG segments; a complete description appears in a section below. The\n"
2079 );
2080 printf(
2081 " .node file produced by Triangle contains boundary markers in the last\n");
2082 printf(" column unless they are suppressed by the -B switch.\n\n");
2083 printf(" .ele files:\n");
2084 printf(
2085 " First line: <# of triangles> <nodes per triangle> <# of attributes>\n");
2086 printf(
2087 " Remaining lines: <triangle #> <node> <node> <node> ... [attributes]\n");
2088 printf("\n");
2089 printf(
2090 " Nodes are indices into the corresponding .node file. The first three\n");
2091 printf(
2092 " nodes are the corner vertices, and are listed in counterclockwise order\n"
2093 );
2094 printf(
2095 " around each triangle. (The remaining nodes, if any, depend on the type\n"
2096 );
2097 printf(" of finite element used.)\n\n");
2098 printf(
2099 " The attributes are just like those of .node files. Because there is no\n"
2100 );
2101 printf(
2102 " simple mapping from input to output triangles, Triangle attempts to\n");
2103 printf(
2104 " interpolate attributes, and may cause a lot of diffusion of attributes\n"
2105 );
2106 printf(
2107 " among nearby triangles as the triangulation is refined. Attributes do\n"
2108 );
2109 printf(" not diffuse across segments, so attributes used to identify\n");
2110 printf(" segment-bounded regions remain intact.\n\n");
2111 printf(
2112 " In .ele files produced by Triangle, each triangular element has three\n");
2113 printf(
2114 " nodes (vertices) unless the -o2 switch is used, in which case\n");
2115 printf(
2116 " subparametric quadratic elements with six nodes each are generated.\n");
2117 printf(
2118 " The first three nodes are the corners in counterclockwise order, and\n");
2119 printf(
2120 " the fourth, fifth, and sixth nodes lie on the midpoints of the edges\n");
2121 printf(
2122 " opposite the first, second, and third vertices, respectively.\n");
2123 printf("\n");
2124 printf(" .poly files:\n");
2125 printf(
2126 " First line: <# of vertices> <dimension (must be 2)> <# of attributes>\n"
2127 );
2128 printf(
2129 " <# of boundary markers (0 or 1)>\n"
2130 );
2131 printf(
2132 " Following lines: <vertex #> <x> <y> [attributes] [boundary marker]\n");
2133 printf(" One line: <# of segments> <# of boundary markers (0 or 1)>\n");
2134 printf(
2135 " Following lines: <segment #> <endpoint> <endpoint> [boundary marker]\n");
2136 printf(" One line: <# of holes>\n");
2137 printf(" Following lines: <hole #> <x> <y>\n");
2138 printf(
2139 " Optional line: <# of regional attributes and/or area constraints>\n");
2140 printf(
2141 " Optional following lines: <region #> <x> <y> <attribute> <max area>\n");
2142 printf("\n");
2143 printf(
2144 " A .poly file represents a PSLG, as well as some additional information.\n"
2145 );
2146 printf(
2147 " The first section lists all the vertices, and is identical to the\n");
2148 printf(
2149 " format of .node files. <# of vertices> may be set to zero to indicate\n"
2150 );
2151 printf(
2152 " that the vertices are listed in a separate .node file; .poly files\n");
2153 printf(
2154 " produced by Triangle always have this format. A vertex set represented\n"
2155 );
2156 printf(
2157 " this way has the advantage that it may easily be triangulated with or\n");
2158 printf(
2159 " without segments (depending on whether the -p switch is invoked).\n");
2160 printf("\n");
2161 printf(
2162 " The second section lists the segments. Segments are edges whose\n");
2163 printf(
2164 " presence in the triangulation is enforced. (Depending on the choice of\n"
2165 );
2166 printf(
2167 " switches, segment might be subdivided into smaller edges). Each\n");
2168 printf(
2169 " segment is specified by listing the indices of its two endpoints. This\n"
2170 );
2171 printf(
2172 " means that you must include its endpoints in the vertex list. Each\n");
2173 printf(" segment, like each point, may have a boundary marker.\n\n");
2174 printf(
2175 " If -q, -a, -u, and -s are not selected, Triangle produces a constrained\n"
2176 );
2177 printf(
2178 " Delaunay triangulation (CDT), in which each segment appears as a single\n"
2179 );
2180 printf(
2181 " edge in the triangulation. If -q, -a, -u, or -s is selected, Triangle\n"
2182 );
2183 printf(
2184 " produces a conforming constrained Delaunay triangulation (CCDT), in\n");
2185 printf(
2186 " which segments may be subdivided into smaller edges. If -D is\n");
2187 printf(
2188 " selected, Triangle produces a conforming Delaunay triangulation, so\n");
2189 printf(
2190 " that every triangle is Delaunay, and not just constrained Delaunay.\n");
2191 printf("\n");
2192 printf(
2193 " The third section lists holes (and concavities, if -c is selected) in\n");
2194 printf(
2195 " the triangulation. Holes are specified by identifying a point inside\n");
2196 printf(
2197 " each hole. After the triangulation is formed, Triangle creates holes\n");
2198 printf(
2199 " by eating triangles, spreading out from each hole point until its\n");
2200 printf(
2201 " progress is blocked by segments in the PSLG. You must be careful to\n");
2202 printf(
2203 " enclose each hole in segments, or your whole triangulation might be\n");
2204 printf(
2205 " eaten away. If the two triangles abutting a segment are eaten, the\n");
2206 printf(
2207 " segment itself is also eaten. Do not place a hole directly on a\n");
2208 printf(" segment; if you do, Triangle chooses one side of the segment\n");
2209 printf(" arbitrarily.\n\n");
2210 printf(
2211 " The optional fourth section lists regional attributes (to be assigned\n");
2212 printf(
2213 " to all triangles in a region) and regional constraints on the maximum\n");
2214 printf(
2215 " triangle area. Triangle reads this section only if the -A switch is\n");
2216 printf(
2217 " used or the -a switch is used without a number following it, and the -r\n"
2218 );
2219 printf(
2220 " switch is not used. Regional attributes and area constraints are\n");
2221 printf(
2222 " propagated in the same manner as holes: you specify a point for each\n");
2223 printf(
2224 " attribute and/or constraint, and the attribute and/or constraint\n");
2225 printf(
2226 " affects the whole region (bounded by segments) containing the point.\n");
2227 printf(
2228 " If two values are written on a line after the x and y coordinate, the\n");
2229 printf(
2230 " first such value is assumed to be a regional attribute (but is only\n");
2231 printf(
2232 " applied if the -A switch is selected), and the second value is assumed\n"
2233 );
2234 printf(
2235 " to be a regional area constraint (but is only applied if the -a switch\n"
2236 );
2237 printf(
2238 " is selected). You may specify just one value after the coordinates,\n");
2239 printf(
2240 " which can serve as both an attribute and an area constraint, depending\n"
2241 );
2242 printf(
2243 " on the choice of switches. If you are using the -A and -a switches\n");
2244 printf(
2245 " simultaneously and wish to assign an attribute to some region without\n");
2246 printf(" imposing an area constraint, use a negative maximum area.\n\n");
2247 printf(
2248 " When a triangulation is created from a .poly file, you must either\n");
2249 printf(
2250 " enclose the entire region to be triangulated in PSLG segments, or\n");
2251 printf(
2252 " use the -c switch, which automatically creates extra segments that\n");
2253 printf(
2254 " enclose the convex hull of the PSLG. If you do not use the -c switch,\n"
2255 );
2256 printf(
2257 " Triangle eats all triangles that are not enclosed by segments; if you\n");
2258 printf(
2259 " are not careful, your whole triangulation may be eaten away. If you do\n"
2260 );
2261 printf(
2262 " use the -c switch, you can still produce concavities by the appropriate\n"
2263 );
2264 printf(
2265 " placement of holes just inside the boundary of the convex hull.\n");
2266 printf("\n");
2267 printf(
2268 " An ideal PSLG has no intersecting segments, nor any vertices that lie\n");
2269 printf(
2270 " upon segments (except, of course, the endpoints of each segment). You\n"
2271 );
2272 printf(
2273 " aren't required to make your .poly files ideal, but you should be aware\n"
2274 );
2275 printf(
2276 " of what can go wrong. Segment intersections are relatively safe--\n");
2277 printf(
2278 " Triangle calculates the intersection points for you and adds them to\n");
2279 printf(
2280 " the triangulation--as long as your machine's floating-point precision\n");
2281 printf(
2282 " doesn't become a problem. You are tempting the fates if you have three\n"
2283 );
2284 printf(
2285 " segments that cross at the same location, and expect Triangle to figure\n"
2286 );
2287 printf(
2288 " out where the intersection point is. Thanks to floating-point roundoff\n"
2289 );
2290 printf(
2291 " error, Triangle will probably decide that the three segments intersect\n"
2292 );
2293 printf(
2294 " at three different points, and you will find a minuscule triangle in\n");
2295 printf(
2296 " your output--unless Triangle tries to refine the tiny triangle, uses\n");
2297 printf(
2298 " up the last bit of machine precision, and fails to terminate at all.\n");
2299 printf(
2300 " You're better off putting the intersection point in the input files,\n");
2301 printf(
2302 " and manually breaking up each segment into two. Similarly, if you\n");
2303 printf(
2304 " place a vertex at the middle of a segment, and hope that Triangle will\n"
2305 );
2306 printf(
2307 " break up the segment at that vertex, you might get lucky. On the other\n"
2308 );
2309 printf(
2310 " hand, Triangle might decide that the vertex doesn't lie precisely on\n");
2311 printf(
2312 " the segment, and you'll have a needle-sharp triangle in your output--or\n"
2313 );
2314 printf(" a lot of tiny triangles if you're generating a quality mesh.\n");
2315 printf("\n");
2316 printf(
2317 " When Triangle reads a .poly file, it also writes a .poly file, which\n");
2318 printf(
2319 " includes all the subsegments--the edges that are parts of input\n");
2320 printf(
2321 " segments. If the -c switch is used, the output .poly file also\n");
2322 printf(
2323 " includes all of the edges on the convex hull. Hence, the output .poly\n"
2324 );
2325 printf(
2326 " file is useful for finding edges associated with input segments and for\n"
2327 );
2328 printf(
2329 " setting boundary conditions in finite element simulations. Moreover,\n");
2330 printf(
2331 " you will need the output .poly file if you plan to refine the output\n");
2332 printf(
2333 " mesh, and don't want segments to be missing in later triangulations.\n");
2334 printf("\n");
2335 printf(" .area files:\n");
2336 printf(" First line: <# of triangles>\n");
2337 printf(" Following lines: <triangle #> <maximum area>\n");
2338 printf("\n");
2339 printf(
2340 " An .area file associates with each triangle a maximum area that is used\n"
2341 );
2342 printf(
2343 " for mesh refinement. As with other file formats, every triangle must\n");
2344 printf(
2345 " be represented, and the triangles must be numbered consecutively. A\n");
2346 printf(
2347 " triangle may be left unconstrained by assigning it a negative maximum\n");
2348 printf(" area.\n\n");
2349 printf(" .edge files:\n");
2350 printf(" First line: <# of edges> <# of boundary markers (0 or 1)>\n");
2351 printf(
2352 " Following lines: <edge #> <endpoint> <endpoint> [boundary marker]\n");
2353 printf("\n");
2354 printf(
2355 " Endpoints are indices into the corresponding .node file. Triangle can\n"
2356 );
2357 printf(
2358 " produce .edge files (use the -e switch), but cannot read them. The\n");
2359 printf(
2360 " optional column of boundary markers is suppressed by the -B switch.\n");
2361 printf("\n");
2362 printf(
2363 " In Voronoi diagrams, one also finds a special kind of edge that is an\n");
2364 printf(
2365 " infinite ray with only one endpoint. For these edges, a different\n");
2366 printf(" format is used:\n\n");
2367 printf(" <edge #> <endpoint> -1 <direction x> <direction y>\n\n");
2368 printf(
2369 " The `direction' is a floating-point vector that indicates the direction\n"
2370 );
2371 printf(" of the infinite ray.\n\n");
2372 printf(" .neigh files:\n");
2373 printf(
2374 " First line: <# of triangles> <# of neighbors per triangle (always 3)>\n"
2375 );
2376 printf(
2377 " Following lines: <triangle #> <neighbor> <neighbor> <neighbor>\n");
2378 printf("\n");
2379 printf(
2380 " Neighbors are indices into the corresponding .ele file. An index of -1\n"
2381 );
2382 printf(
2383 " indicates no neighbor (because the triangle is on an exterior\n");
2384 printf(
2385 " boundary). The first neighbor of triangle i is opposite the first\n");
2386 printf(" corner of triangle i, and so on.\n\n");
2387 printf(
2388 " Triangle can produce .neigh files (use the -n switch), but cannot read\n"
2389 );
2390 printf(" them.\n\n");
2391 printf("Boundary Markers:\n\n");
2392 printf(
2393 " Boundary markers are tags used mainly to identify which output vertices\n");
2394 printf(
2395 " and edges are associated with which PSLG segment, and to identify which\n");
2396 printf(
2397 " vertices and edges occur on a boundary of the triangulation. A common\n");
2398 printf(
2399 " use is to determine where boundary conditions should be applied to a\n");
2400 printf(
2401 " finite element mesh. You can prevent boundary markers from being written\n"
2402 );
2403 printf(" into files produced by Triangle by using the -B switch.\n\n");
2404 printf(
2405 " The boundary marker associated with each segment in an output .poly file\n"
2406 );
2407 printf(" and each edge in an output .edge file is chosen as follows:\n");
2408 printf(
2409 " - If an output edge is part or all of a PSLG segment with a nonzero\n");
2410 printf(
2411 " boundary marker, then the edge is assigned the same marker.\n");
2412 printf(
2413 " - Otherwise, if the edge lies on a boundary of the triangulation\n");
2414 printf(
2415 " (even the boundary of a hole), then the edge is assigned the marker\n");
2416 printf(" one (1).\n");
2417 printf(" - Otherwise, the edge is assigned the marker zero (0).\n");
2418 printf(
2419 " The boundary marker associated with each vertex in an output .node file\n");
2420 printf(" is chosen as follows:\n");
2421 printf(
2422 " - If a vertex is assigned a nonzero boundary marker in the input file,\n"
2423 );
2424 printf(
2425 " then it is assigned the same marker in the output .node file.\n");
2426 printf(
2427 " - Otherwise, if the vertex lies on a PSLG segment (even if it is an\n");
2428 printf(
2429 " endpoint of the segment) with a nonzero boundary marker, then the\n");
2430 printf(
2431 " vertex is assigned the same marker. If the vertex lies on several\n");
2432 printf(" such segments, one of the markers is chosen arbitrarily.\n");
2433 printf(
2434 " - Otherwise, if the vertex occurs on a boundary of the triangulation,\n");
2435 printf(" then the vertex is assigned the marker one (1).\n");
2436 printf(" - Otherwise, the vertex is assigned the marker zero (0).\n");
2437 printf("\n");
2438 printf(
2439 " If you want Triangle to determine for you which vertices and edges are on\n"
2440 );
2441 printf(
2442 " the boundary, assign them the boundary marker zero (or use no markers at\n"
2443 );
2444 printf(
2445 " all) in your input files. In the output files, all boundary vertices,\n");
2446 printf(" edges, and segments will be assigned the value one.\n\n");
2447 printf("Triangulation Iteration Numbers:\n\n");
2448 printf(
2449 " Because Triangle can read and refine its own triangulations, input\n");
2450 printf(
2451 " and output files have iteration numbers. For instance, Triangle might\n");
2452 printf(
2453 " read the files mesh.3.node, mesh.3.ele, and mesh.3.poly, refine the\n");
2454 printf(
2455 " triangulation, and output the files mesh.4.node, mesh.4.ele, and\n");
2456 printf(" mesh.4.poly. Files with no iteration number are treated as if\n");
2457 printf(
2458 " their iteration number is zero; hence, Triangle might read the file\n");
2459 printf(
2460 " points.node, triangulate it, and produce the files points.1.node and\n");
2461 printf(" points.1.ele.\n\n");
2462 printf(
2463 " Iteration numbers allow you to create a sequence of successively finer\n");
2464 printf(
2465 " meshes suitable for multigrid methods. They also allow you to produce a\n"
2466 );
2467 printf(
2468 " sequence of meshes using error estimate-driven mesh refinement.\n");
2469 printf("\n");
2470 printf(
2471 " If you're not using refinement or quality meshing, and you don't like\n");
2472 printf(
2473 " iteration numbers, use the -I switch to disable them. This switch also\n");
2474 printf(
2475 " disables output of .node and .poly files to prevent your input files from\n"
2476 );
2477 printf(
2478 " being overwritten. (If the input is a .poly file that contains its own\n");
2479 printf(
2480 " points, a .node file is written. This can be quite convenient for\n");
2481 printf(" computing CDTs or quality meshes.)\n\n");
2482 printf("Examples of How to Use Triangle:\n\n");
2483 printf(
2484 " `triangle dots' reads vertices from dots.node, and writes their Delaunay\n"
2485 );
2486 printf(
2487 " triangulation to dots.1.node and dots.1.ele. (dots.1.node is identical\n");
2488 printf(
2489 " to dots.node.) `triangle -I dots' writes the triangulation to dots.ele\n");
2490 printf(
2491 " instead. (No additional .node file is needed, so none is written.)\n");
2492 printf("\n");
2493 printf(
2494 " `triangle -pe object.1' reads a PSLG from object.1.poly (and possibly\n");
2495 printf(
2496 " object.1.node, if the vertices are omitted from object.1.poly) and writes\n"
2497 );
2498 printf(
2499 " its constrained Delaunay triangulation to object.2.node and object.2.ele.\n"
2500 );
2501 printf(
2502 " The segments are copied to object.2.poly, and all edges are written to\n");
2503 printf(" object.2.edge.\n\n");
2504 printf(
2505 " `triangle -pq31.5a.1 object' reads a PSLG from object.poly (and possibly\n"
2506 );
2507 printf(
2508 " object.node), generates a mesh whose angles are all between 31.5 and 117\n"
2509 );
2510 printf(
2511 " degrees and whose triangles all have areas of 0.1 or less, and writes the\n"
2512 );
2513 printf(
2514 " mesh to object.1.node and object.1.ele. Each segment may be broken up\n");
2515 printf(" into multiple subsegments; these are written to object.1.poly.\n");
2516 printf("\n");
2517 printf(
2518 " Here is a sample file `box.poly' describing a square with a square hole:\n"
2519 );
2520 printf("\n");
2521 printf(
2522 " # A box with eight vertices in 2D, no attributes, one boundary marker.\n"
2523 );
2524 printf(" 8 2 0 1\n");
2525 printf(" # Outer box has these vertices:\n");
2526 printf(" 1 0 0 0\n");
2527 printf(" 2 0 3 0\n");
2528 printf(" 3 3 0 0\n");
2529 printf(" 4 3 3 33 # A special marker for this vertex.\n");
2530 printf(" # Inner square has these vertices:\n");
2531 printf(" 5 1 1 0\n");
2532 printf(" 6 1 2 0\n");
2533 printf(" 7 2 1 0\n");
2534 printf(" 8 2 2 0\n");
2535 printf(" # Five segments with boundary markers.\n");
2536 printf(" 5 1\n");
2537 printf(" 1 1 2 5 # Left side of outer box.\n");
2538 printf(" # Square hole has these segments:\n");
2539 printf(" 2 5 7 0\n");
2540 printf(" 3 7 8 0\n");
2541 printf(" 4 8 6 10\n");
2542 printf(" 5 6 5 0\n");
2543 printf(" # One hole in the middle of the inner square.\n");
2544 printf(" 1\n");
2545 printf(" 1 1.5 1.5\n");
2546 printf("\n");
2547 printf(
2548 " Note that some segments are missing from the outer square, so you must\n");
2549 printf(
2550 " use the `-c' switch. After `triangle -pqc box.poly', here is the output\n"
2551 );
2552 printf(
2553 " file `box.1.node', with twelve vertices. The last four vertices were\n");
2554 printf(
2555 " added to meet the angle constraint. Vertices 1, 2, and 9 have markers\n");
2556 printf(
2557 " from segment 1. Vertices 6 and 8 have markers from segment 4. All the\n");
2558 printf(
2559 " other vertices but 4 have been marked to indicate that they lie on a\n");
2560 printf(" boundary.\n\n");
2561 printf(" 12 2 0 1\n");
2562 printf(" 1 0 0 5\n");
2563 printf(" 2 0 3 5\n");
2564 printf(" 3 3 0 1\n");
2565 printf(" 4 3 3 33\n");
2566 printf(" 5 1 1 1\n");
2567 printf(" 6 1 2 10\n");
2568 printf(" 7 2 1 1\n");
2569 printf(" 8 2 2 10\n");
2570 printf(" 9 0 1.5 5\n");
2571 printf(" 10 1.5 0 1\n");
2572 printf(" 11 3 1.5 1\n");
2573 printf(" 12 1.5 3 1\n");
2574 printf(" # Generated by triangle -pqc box.poly\n");
2575 printf("\n");
2576 printf(" Here is the output file `box.1.ele', with twelve triangles.\n");
2577 printf("\n");
2578 printf(" 12 3 0\n");
2579 printf(" 1 5 6 9\n");
2580 printf(" 2 10 3 7\n");
2581 printf(" 3 6 8 12\n");
2582 printf(" 4 9 1 5\n");
2583 printf(" 5 6 2 9\n");
2584 printf(" 6 7 3 11\n");
2585 printf(" 7 11 4 8\n");
2586 printf(" 8 7 5 10\n");
2587 printf(" 9 12 2 6\n");
2588 printf(" 10 8 7 11\n");
2589 printf(" 11 5 1 10\n");
2590 printf(" 12 8 4 12\n");
2591 printf(" # Generated by triangle -pqc box.poly\n\n");
2592 printf(
2593 " Here is the output file `box.1.poly'. Note that segments have been added\n"
2594 );
2595 printf(
2596 " to represent the convex hull, and some segments have been subdivided by\n");
2597 printf(
2598 " newly added vertices. Note also that <# of vertices> is set to zero to\n");
2599 printf(" indicate that the vertices should be read from the .node file.\n");
2600 printf("\n");
2601 printf(" 0 2 0 1\n");
2602 printf(" 12 1\n");
2603 printf(" 1 1 9 5\n");
2604 printf(" 2 5 7 1\n");
2605 printf(" 3 8 7 1\n");
2606 printf(" 4 6 8 10\n");
2607 printf(" 5 5 6 1\n");
2608 printf(" 6 3 10 1\n");
2609 printf(" 7 4 11 1\n");
2610 printf(" 8 2 12 1\n");
2611 printf(" 9 9 2 5\n");
2612 printf(" 10 10 1 1\n");
2613 printf(" 11 11 3 1\n");
2614 printf(" 12 12 4 1\n");
2615 printf(" 1\n");
2616 printf(" 1 1.5 1.5\n");
2617 printf(" # Generated by triangle -pqc box.poly\n");
2618 printf("\n");
2619 printf("Refinement and Area Constraints:\n");
2620 printf("\n");
2621 printf(
2622 " The -r switch causes a mesh (.node and .ele files) to be read and\n");
2623 printf(
2624 " refined. If the -p switch is also used, a .poly file is read and used to\n"
2625 );
2626 printf(
2627 " specify edges that are constrained and cannot be eliminated (although\n");
2628 printf(
2629 " they can be subdivided into smaller edges) by the refinement process.\n");
2630 printf("\n");
2631 printf(
2632 " When you refine a mesh, you generally want to impose tighter constraints.\n"
2633 );
2634 printf(
2635 " One way to accomplish this is to use -q with a larger angle, or -a\n");
2636 printf(
2637 " followed by a smaller area than you used to generate the mesh you are\n");
2638 printf(
2639 " refining. Another way to do this is to create an .area file, which\n");
2640 printf(
2641 " specifies a maximum area for each triangle, and use the -a switch\n");
2642 printf(
2643 " (without a number following). Each triangle's area constraint is applied\n"
2644 );
2645 printf(
2646 " to that triangle. Area constraints tend to diffuse as the mesh is\n");
2647 printf(
2648 " refined, so if there are large variations in area constraint between\n");
2649 printf(
2650 " adjacent triangles, you may not get the results you want. In that case,\n"
2651 );
2652 printf(
2653 " consider instead using the -u switch and writing a C procedure that\n");
2654 printf(" determines which triangles are too large.\n\n");
2655 printf(
2656 " If you are refining a mesh composed of linear (three-node) elements, the\n"
2657 );
2658 printf(
2659 " output mesh contains all the nodes present in the input mesh, in the same\n"
2660 );
2661 printf(
2662 " order, with new nodes added at the end of the .node file. However, the\n");
2663 printf(
2664 " refinement is not hierarchical: there is no guarantee that each output\n");
2665 printf(
2666 " element is contained in a single input element. Often, an output element\n"
2667 );
2668 printf(
2669 " can overlap two or three input elements, and some input edges are not\n");
2670 printf(
2671 " present in the output mesh. Hence, a sequence of refined meshes forms a\n"
2672 );
2673 printf(
2674 " hierarchy of nodes, but not a hierarchy of elements. If you refine a\n");
2675 printf(
2676 " mesh of higher-order elements, the hierarchical property applies only to\n"
2677 );
2678 printf(
2679 " the nodes at the corners of an element; the midpoint nodes on each edge\n");
2680 printf(" are discarded before the mesh is refined.\n\n");
2681 printf(
2682 " Maximum area constraints in .poly files operate differently from those in\n"
2683 );
2684 printf(
2685 " .area files. A maximum area in a .poly file applies to the whole\n");
2686 printf(
2687 " (segment-bounded) region in which a point falls, whereas a maximum area\n");
2688 printf(
2689 " in an .area file applies to only one triangle. Area constraints in .poly\n"
2690 );
2691 printf(
2692 " files are used only when a mesh is first generated, whereas area\n");
2693 printf(
2694 " constraints in .area files are used only to refine an existing mesh, and\n"
2695 );
2696 printf(
2697 " are typically based on a posteriori error estimates resulting from a\n");
2698 printf(" finite element simulation on that mesh.\n\n");
2699 printf(
2700 " `triangle -rq25 object.1' reads object.1.node and object.1.ele, then\n");
2701 printf(
2702 " refines the triangulation to enforce a 25 degree minimum angle, and then\n"
2703 );
2704 printf(
2705 " writes the refined triangulation to object.2.node and object.2.ele.\n");
2706 printf("\n");
2707 printf(
2708 " `triangle -rpaa6.2 z.3' reads z.3.node, z.3.ele, z.3.poly, and z.3.area.\n"
2709 );
2710 printf(
2711 " After reconstructing the mesh and its subsegments, Triangle refines the\n");
2712 printf(
2713 " mesh so that no triangle has area greater than 6.2, and furthermore the\n");
2714 printf(
2715 " triangles satisfy the maximum area constraints in z.3.area. No angle\n");
2716 printf(
2717 " bound is imposed at all. The output is written to z.4.node, z.4.ele, and\n"
2718 );
2719 printf(" z.4.poly.\n\n");
2720 printf(
2721 " The sequence `triangle -qa1 x', `triangle -rqa.3 x.1', `triangle -rqa.1\n");
2722 printf(
2723 " x.2' creates a sequence of successively finer meshes x.1, x.2, and x.3,\n");
2724 printf(" suitable for multigrid.\n\n");
2725 printf("Convex Hulls and Mesh Boundaries:\n\n");
2726 printf(
2727 " If the input is a vertex set (not a PSLG), Triangle produces its convex\n");
2728 printf(
2729 " hull as a by-product in the output .poly file if you use the -c switch.\n");
2730 printf(
2731 " There are faster algorithms for finding a two-dimensional convex hull\n");
2732 printf(" than triangulation, of course, but this one comes for free.\n\n");
2733 printf(
2734 " If the input is an unconstrained mesh (you are using the -r switch but\n");
2735 printf(
2736 " not the -p switch), Triangle produces a list of its boundary edges\n");
2737 printf(
2738 " (including hole boundaries) as a by-product when you use the -c switch.\n");
2739 printf(
2740 " If you also use the -p switch, the output .poly file contains all the\n");
2741 printf(" segments from the input .poly file as well.\n\n");
2742 printf("Voronoi Diagrams:\n\n");
2743 printf(
2744 " The -v switch produces a Voronoi diagram, in files suffixed .v.node and\n");
2745 printf(
2746 " .v.edge. For example, `triangle -v points' reads points.node, produces\n");
2747 printf(
2748 " its Delaunay triangulation in points.1.node and points.1.ele, and\n");
2749 printf(
2750 " produces its Voronoi diagram in points.1.v.node and points.1.v.edge. The\n"
2751 );
2752 printf(
2753 " .v.node file contains a list of all Voronoi vertices, and the .v.edge\n");
2754 printf(
2755 " file contains a list of all Voronoi edges, some of which may be infinite\n"
2756 );
2757 printf(
2758 " rays. (The choice of filenames makes it easy to run the set of Voronoi\n");
2759 printf(" vertices through Triangle, if so desired.)\n\n");
2760 printf(
2761 " This implementation does not use exact arithmetic to compute the Voronoi\n"
2762 );
2763 printf(
2764 " vertices, and does not check whether neighboring vertices are identical.\n"
2765 );
2766 printf(
2767 " Be forewarned that if the Delaunay triangulation is degenerate or\n");
2768 printf(
2769 " near-degenerate, the Voronoi diagram may have duplicate vertices or\n");
2770 printf(" crossing edges.\n\n");
2771 printf(
2772 " The result is a valid Voronoi diagram only if Triangle's output is a true\n"
2773 );
2774 printf(
2775 " Delaunay triangulation. The Voronoi output is usually meaningless (and\n");
2776 printf(
2777 " may contain crossing edges and other pathology) if the output is a CDT or\n"
2778 );
2779 printf(
2780 " CCDT, or if it has holes or concavities. If the triangulated domain is\n");
2781 printf(
2782 " convex and has no holes, you can use -D switch to force Triangle to\n");
2783 printf(
2784 " construct a conforming Delaunay triangulation instead of a CCDT, so the\n");
2785 printf(" Voronoi diagram will be valid.\n\n");
2786 printf("Mesh Topology:\n\n");
2787 printf(
2788 " You may wish to know which triangles are adjacent to a certain Delaunay\n");
2789 printf(
2790 " edge in an .edge file, which Voronoi cells are adjacent to a certain\n");
2791 printf(
2792 " Voronoi edge in a .v.edge file, or which Voronoi cells are adjacent to\n");
2793 printf(
2794 " each other. All of this information can be found by cross-referencing\n");
2795 printf(
2796 " output files with the recollection that the Delaunay triangulation and\n");
2797 printf(" the Voronoi diagram are planar duals.\n\n");
2798 printf(
2799 " Specifically, edge i of an .edge file is the dual of Voronoi edge i of\n");
2800 printf(
2801 " the corresponding .v.edge file, and is rotated 90 degrees counterclock-\n");
2802 printf(
2803 " wise from the Voronoi edge. Triangle j of an .ele file is the dual of\n");
2804 printf(
2805 " vertex j of the corresponding .v.node file. Voronoi cell k is the dual\n");
2806 printf(" of vertex k of the corresponding .node file.\n\n");
2807 printf(
2808 " Hence, to find the triangles adjacent to a Delaunay edge, look at the\n");
2809 printf(
2810 " vertices of the corresponding Voronoi edge. If the endpoints of a\n");
2811 printf(
2812 " Voronoi edge are Voronoi vertices 2 and 6 respectively, then triangles 2\n"
2813 );
2814 printf(
2815 " and 6 adjoin the left and right sides of the corresponding Delaunay edge,\n"
2816 );
2817 printf(
2818 " respectively. To find the Voronoi cells adjacent to a Voronoi edge, look\n"
2819 );
2820 printf(
2821 " at the endpoints of the corresponding Delaunay edge. If the endpoints of\n"
2822 );
2823 printf(
2824 " a Delaunay edge are input vertices 7 and 12, then Voronoi cells 7 and 12\n"
2825 );
2826 printf(
2827 " adjoin the right and left sides of the corresponding Voronoi edge,\n");
2828 printf(
2829 " respectively. To find which Voronoi cells are adjacent to each other,\n");
2830 printf(" just read the list of Delaunay edges.\n\n");
2831 printf(
2832 " Triangle does not write a list of the edges adjoining each Voronoi cell,\n"
2833 );
2834 printf(
2835 " but you can reconstructed it straightforwardly. For instance, to find\n");
2836 printf(
2837 " all the edges of Voronoi cell 1, search the output .edge file for every\n");
2838 printf(
2839 " edge that has input vertex 1 as an endpoint. The corresponding dual\n");
2840 printf(
2841 " edges in the output .v.edge file form the boundary of Voronoi cell 1.\n");
2842 printf("\n");
2843 printf(
2844 " For each Voronoi vertex, the .neigh file gives a list of the three\n");
2845 printf(
2846 " Voronoi vertices attached to it. You might find this more convenient\n");
2847 printf(" than the .v.edge file.\n\n");
2848 printf("Quadratic Elements:\n\n");
2849 printf(
2850 " Triangle generates meshes with subparametric quadratic elements if the\n");
2851 printf(
2852 " -o2 switch is specified. Quadratic elements have six nodes per element,\n"
2853 );
2854 printf(
2855 " rather than three. `Subparametric' means that the edges of the triangles\n"
2856 );
2857 printf(
2858 " are always straight, so that subparametric quadratic elements are\n");
2859 printf(
2860 " geometrically identical to linear elements, even though they can be used\n"
2861 );
2862 printf(
2863 " with quadratic interpolating functions. The three extra nodes of an\n");
2864 printf(
2865 " element fall at the midpoints of the three edges, with the fourth, fifth,\n"
2866 );
2867 printf(
2868 " and sixth nodes appearing opposite the first, second, and third corners\n");
2869 printf(" respectively.\n\n");
2870 printf("Domains with Small Angles:\n\n");
2871 printf(
2872 " If two input segments adjoin each other at a small angle, clearly the -q\n"
2873 );
2874 printf(
2875 " switch cannot remove the small angle. Moreover, Triangle may have no\n");
2876 printf(
2877 " choice but to generate additional triangles whose smallest angles are\n");
2878 printf(
2879 " smaller than the specified bound. However, these triangles only appear\n");
2880 printf(
2881 " between input segments separated by small angles. Moreover, if you\n");
2882 printf(
2883 " request a minimum angle of theta degrees, Triangle will generally produce\n"
2884 );
2885 printf(
2886 " no angle larger than 180 - 2 theta, even if it is forced to compromise on\n"
2887 );
2888 printf(" the minimum angle.\n\n");
2889 printf("Statistics:\n\n");
2890 printf(
2891 " After generating a mesh, Triangle prints a count of entities in the\n");
2892 printf(
2893 " output mesh, including the number of vertices, triangles, edges, exterior\n"
2894 );
2895 printf(
2896 " boundary edges (i.e. subsegments on the boundary of the triangulation,\n");
2897 printf(
2898 " including hole boundaries), interior boundary edges (i.e. subsegments of\n"
2899 );
2900 printf(
2901 " input segments not on the boundary), and total subsegments. If you've\n");
2902 printf(
2903 " forgotten the statistics for an existing mesh, run Triangle on that mesh\n"
2904 );
2905 printf(
2906 " with the -rNEP switches to read the mesh and print the statistics without\n"
2907 );
2908 printf(
2909 " writing any files. Use -rpNEP if you've got a .poly file for the mesh.\n");
2910 printf("\n");
2911 printf(
2912 " The -V switch produces extended statistics, including a rough estimate\n");
2913 printf(
2914 " of memory use, the number of calls to geometric predicates, and\n");
2915 printf(
2916 " histograms of the angles and the aspect ratios of the triangles in the\n");
2917 printf(" mesh.\n\n");
2918 printf("Exact Arithmetic:\n\n");
2919 printf(
2920 " Triangle uses adaptive exact arithmetic to perform what computational\n");
2921 printf(
2922 " geometers call the `orientation' and `incircle' tests. If the floating-\n"
2923 );
2924 printf(
2925 " point arithmetic of your machine conforms to the IEEE 754 standard (as\n");
2926 printf(
2927 " most workstations do), and does not use extended precision internal\n");
2928 printf(
2929 " floating-point registers, then your output is guaranteed to be an\n");
2930 printf(
2931 " absolutely true Delaunay or constrained Delaunay triangulation, roundoff\n"
2932 );
2933 printf(
2934 " error notwithstanding. The word `adaptive' implies that these arithmetic\n"
2935 );
2936 printf(
2937 " routines compute the result only to the precision necessary to guarantee\n"
2938 );
2939 printf(
2940 " correctness, so they are usually nearly as fast as their approximate\n");
2941 printf(" counterparts.\n\n");
2942 printf(
2943 " May CPUs, including Intel x86 processors, have extended precision\n");
2944 printf(
2945 " floating-point registers. These must be reconfigured so their precision\n"
2946 );
2947 printf(
2948 " is reduced to memory precision. Triangle does this if it is compiled\n");
2949 printf(" correctly. See the makefile for details.\n\n");
2950 printf(
2951 " The exact tests can be disabled with the -X switch. On most inputs, this\n"
2952 );
2953 printf(
2954 " switch reduces the computation time by about eight percent--it's not\n");
2955 printf(
2956 " worth the risk. There are rare difficult inputs (having many collinear\n");
2957 printf(
2958 " and cocircular vertices), however, for which the difference in speed\n");
2959 printf(
2960 " could be a factor of two. Be forewarned that these are precisely the\n");
2961 printf(
2962 " inputs most likely to cause errors if you use the -X switch. Hence, the\n"
2963 );
2964 printf(" -X switch is not recommended.\n\n");
2965 printf(
2966 " Unfortunately, the exact tests don't solve every numerical problem.\n");
2967 printf(
2968 " Exact arithmetic is not used to compute the positions of new vertices,\n");
2969 printf(
2970 " because the bit complexity of vertex coordinates would grow without\n");
2971 printf(
2972 " bound. Hence, segment intersections aren't computed exactly; in very\n");
2973 printf(
2974 " unusual cases, roundoff error in computing an intersection point might\n");
2975 printf(
2976 " actually lead to an inverted triangle and an invalid triangulation.\n");
2977 printf(
2978 " (This is one reason to specify your own intersection points in your .poly\n"
2979 );
2980 printf(
2981 " files.) Similarly, exact arithmetic is not used to compute the vertices\n"
2982 );
2983 printf(" of the Voronoi diagram.\n\n");
2984 printf(
2985 " Another pair of problems not solved by the exact arithmetic routines is\n");
2986 printf(
2987 " underflow and overflow. If Triangle is compiled for double precision\n");
2988 printf(
2989 " arithmetic, I believe that Triangle's geometric predicates work correctly\n"
2990 );
2991 printf(
2992 " if the exponent of every input coordinate falls in the range [-148, 201].\n"
2993 );
2994 printf(
2995 " Underflow can silently prevent the orientation and incircle tests from\n");
2996 printf(
2997 " being performed exactly, while overflow typically causes a floating\n");
2998 printf(" exception.\n\n");
2999 printf("Calling Triangle from Another Program:\n\n");
3000 printf(" Read the file triangle.h for details.\n\n");
3001 printf("Troubleshooting:\n\n");
3002 printf(" Please read this section before mailing me bugs.\n\n");
3003 printf(" `My output mesh has no triangles!'\n\n");
3004 printf(
3005 " If you're using a PSLG, you've probably failed to specify a proper set\n"
3006 );
3007 printf(
3008 " of bounding segments, or forgotten to use the -c switch. Or you may\n");
3009 printf(
3010 " have placed a hole badly, thereby eating all your triangles. To test\n");
3011 printf(" these possibilities, try again with the -c and -O switches.\n");
3012 printf(
3013 " Alternatively, all your input vertices may be collinear, in which case\n"
3014 );
3015 printf(" you can hardly expect to triangulate them.\n\n");
3016 printf(" `Triangle doesn't terminate, or just crashes.'\n\n");
3017 printf(
3018 " Bad things can happen when triangles get so small that the distance\n");
3019 printf(
3020 " between their vertices isn't much larger than the precision of your\n");
3021 printf(
3022 " machine's arithmetic. If you've compiled Triangle for single-precision\n"
3023 );
3024 printf(
3025 " arithmetic, you might do better by recompiling it for double-precision.\n"
3026 );
3027 printf(
3028 " Then again, you might just have to settle for more lenient constraints\n"
3029 );
3030 printf(
3031 " on the minimum angle and the maximum area than you had planned.\n");
3032 printf("\n");
3033 printf(
3034 " You can minimize precision problems by ensuring that the origin lies\n");
3035 printf(
3036 " inside your vertex set, or even inside the densest part of your\n");
3037 printf(
3038 " mesh. If you're triangulating an object whose x-coordinates all fall\n");
3039 printf(
3040 " between 6247133 and 6247134, you're not leaving much floating-point\n");
3041 printf(" precision for Triangle to work with.\n\n");
3042 printf(
3043 " Precision problems can occur covertly if the input PSLG contains two\n");
3044 printf(
3045 " segments that meet (or intersect) at an extremely small angle, or if\n");
3046 printf(
3047 " such an angle is introduced by the -c switch. If you don't realize\n");
3048 printf(
3049 " that a tiny angle is being formed, you might never discover why\n");
3050 printf(
3051 " Triangle is crashing. To check for this possibility, use the -S switch\n"
3052 );
3053 printf(
3054 " (with an appropriate limit on the number of Steiner points, found by\n");
3055 printf(
3056 " trial-and-error) to stop Triangle early, and view the output .poly file\n"
3057 );
3058 printf(
3059 " with Show Me (described below). Look carefully for regions where dense\n"
3060 );
3061 printf(
3062 " clusters of vertices are forming and for small angles between segments.\n"
3063 );
3064 printf(
3065 " Zoom in closely, as such segments might look like a single segment from\n"
3066 );
3067 printf(" a distance.\n\n");
3068 printf(
3069 " If some of the input values are too large, Triangle may suffer a\n");
3070 printf(
3071 " floating exception due to overflow when attempting to perform an\n");
3072 printf(
3073 " orientation or incircle test. (Read the section on exact arithmetic\n");
3074 printf(
3075 " above.) Again, I recommend compiling Triangle for double (rather\n");
3076 printf(" than single) precision arithmetic.\n\n");
3077 printf(
3078 " Unexpected problems can arise if you use quality meshing (-q, -a, or\n");
3079 printf(
3080 " -u) with an input that is not segment-bounded--that is, if your input\n");
3081 printf(
3082 " is a vertex set, or you're using the -c switch. If the convex hull of\n"
3083 );
3084 printf(
3085 " your input vertices has collinear vertices on its boundary, an input\n");
3086 printf(
3087 " vertex that you think lies on the convex hull might actually lie just\n");
3088 printf(
3089 " inside the convex hull. If so, the vertex and the nearby convex hull\n");
3090 printf(
3091 " edge form an extremely thin triangle. When Triangle tries to refine\n");
3092 printf(
3093 " the mesh to enforce angle and area constraints, Triangle might generate\n"
3094 );
3095 printf(
3096 " extremely tiny triangles, or it might fail because of insufficient\n");
3097 printf(" floating-point precision.\n\n");
3098 printf(
3099 " `The numbering of the output vertices doesn't match the input vertices.'\n"
3100 );
3101 printf("\n");
3102 printf(
3103 " You may have had duplicate input vertices, or you may have eaten some\n");
3104 printf(
3105 " of your input vertices with a hole, or by placing them outside the area\n"
3106 );
3107 printf(
3108 " enclosed by segments. In any case, you can solve the problem by not\n");
3109 printf(" using the -j switch.\n\n");
3110 printf(
3111 " `Triangle executes without incident, but when I look at the resulting\n");
3112 printf(
3113 " mesh, it has overlapping triangles or other geometric inconsistencies.'\n");
3114 printf("\n");
3115 printf(
3116 " If you select the -X switch, Triangle occasionally makes mistakes due\n");
3117 printf(
3118 " to floating-point roundoff error. Although these errors are rare,\n");
3119 printf(
3120 " don't use the -X switch. If you still have problems, please report the\n"
3121 );
3122 printf(" bug.\n\n");
3123 printf(
3124 " `Triangle executes without incident, but when I look at the resulting\n");
3125 printf(" Voronoi diagram, it has overlapping edges or other geometric\n");
3126 printf(" inconsistencies.'\n");
3127 printf("\n");
3128 printf(
3129 " If your input is a PSLG (-p), you can only expect a meaningful Voronoi\n"
3130 );
3131 printf(
3132 " diagram if the domain you are triangulating is convex and free of\n");
3133 printf(
3134 " holes, and you use the -D switch to construct a conforming Delaunay\n");
3135 printf(" triangulation (instead of a CDT or CCDT).\n\n");
3136 printf(
3137 " Strange things can happen if you've taken liberties with your PSLG. Do\n");
3138 printf(
3139 " you have a vertex lying in the middle of a segment? Triangle sometimes\n");
3140 printf(
3141 " copes poorly with that sort of thing. Do you want to lay out a collinear\n"
3142 );
3143 printf(
3144 " row of evenly spaced, segment-connected vertices? Have you simply\n");
3145 printf(
3146 " defined one long segment connecting the leftmost vertex to the rightmost\n"
3147 );
3148 printf(
3149 " vertex, and a bunch of vertices lying along it? This method occasionally\n"
3150 );
3151 printf(
3152 " works, especially with horizontal and vertical lines, but often it\n");
3153 printf(
3154 " doesn't, and you'll have to connect each adjacent pair of vertices with a\n"
3155 );
3156 printf(" separate segment. If you don't like it, tough.\n\n");
3157 printf(
3158 " Furthermore, if you have segments that intersect other than at their\n");
3159 printf(
3160 " endpoints, try not to let the intersections fall extremely close to PSLG\n"
3161 );
3162 printf(" vertices or each other.\n\n");
3163 printf(
3164 " If you have problems refining a triangulation not produced by Triangle:\n");
3165 printf(
3166 " Are you sure the triangulation is geometrically valid? Is it formatted\n");
3167 printf(
3168 " correctly for Triangle? Are the triangles all listed so the first three\n"
3169 );
3170 printf(
3171 " vertices are their corners in counterclockwise order? Are all of the\n");
3172 printf(
3173 " triangles constrained Delaunay? Triangle's Delaunay refinement algorithm\n"
3174 );
3175 printf(" assumes that it starts with a CDT.\n\n");
3176 printf("Show Me:\n\n");
3177 printf(
3178 " Triangle comes with a separate program named `Show Me', whose primary\n");
3179 printf(
3180 " purpose is to draw meshes on your screen or in PostScript. Its secondary\n"
3181 );
3182 printf(
3183 " purpose is to check the validity of your input files, and do so more\n");
3184 printf(
3185 " thoroughly than Triangle does. Unlike Triangle, Show Me requires that\n");
3186 printf(
3187 " you have the X Windows system. Sorry, Microsoft Windows users.\n");
3188 printf("\n");
3189 printf("Triangle on the Web:\n");
3190 printf("\n");
3191 printf(" To see an illustrated version of these instructions, check out\n");
3192 printf("\n");
3193 printf(" http://www.cs.cmu.edu/~quake/triangle.html\n");
3194 printf("\n");
3195 printf("A Brief Plea:\n");
3196 printf("\n");
3197 printf(
3198 " If you use Triangle, and especially if you use it to accomplish real\n");
3199 printf(
3200 " work, I would like very much to hear from you. A short letter or email\n");
3201 printf(
3202 " (to jrs@cs.berkeley.edu) describing how you use Triangle will mean a lot\n"
3203 );
3204 printf(
3205 " to me. The more people I know are using this program, the more easily I\n"
3206 );
3207 printf(
3208 " can justify spending time on improvements, which in turn will benefit\n");
3209 printf(
3210 " you. Also, I can put you on a list to receive email whenever a new\n");
3211 printf(" version of Triangle is available.\n\n");
3212 printf(
3213 " If you use a mesh generated by Triangle in a publication, please include\n"
3214 );
3215 printf(
3216 " an acknowledgment as well. And please spell Triangle with a capital `T'!\n"
3217 );
3218 printf(
3219 " If you want to include a citation, use `Jonathan Richard Shewchuk,\n");
3220 printf(
3221 " ``Triangle: Engineering a 2D Quality Mesh Generator and Delaunay\n");
3222 printf(
3223 " Triangulator,'' in Applied Computational Geometry: Towards Geometric\n");
3224 printf(
3225 " Engineering (Ming C. Lin and Dinesh Manocha, editors), volume 1148 of\n");
3226 printf(
3227 " Lecture Notes in Computer Science, pages 203-222, Springer-Verlag,\n");
3228 printf(
3229 " Berlin, May 1996. (From the First ACM Workshop on Applied Computational\n"
3230 );
3231 printf(" Geometry.)'\n\n");
3232 printf("Research credit:\n\n");
3233 printf(
3234 " Of course, I can take credit for only a fraction of the ideas that made\n");
3235 printf(
3236 " this mesh generator possible. Triangle owes its existence to the efforts\n"
3237 );
3238 printf(
3239 " of many fine computational geometers and other researchers, including\n");
3240 printf(
3241 " Marshall Bern, L. Paul Chew, Kenneth L. Clarkson, Boris Delaunay, Rex A.\n"
3242 );
3243 printf(
3244 " Dwyer, David Eppstein, Steven Fortune, Leonidas J. Guibas, Donald E.\n");
3245 printf(
3246 " Knuth, Charles L. Lawson, Der-Tsai Lee, Gary L. Miller, Ernst P. Mucke,\n");
3247 printf(
3248 " Steven E. Pav, Douglas M. Priest, Jim Ruppert, Isaac Saias, Bruce J.\n");
3249 printf(
3250 " Schachter, Micha Sharir, Peter W. Shor, Daniel D. Sleator, Jorge Stolfi,\n"
3251 );
3252 printf(" Robert E. Tarjan, Alper Ungor, Christopher J. Van Wyk, Noel J.\n");
3253 printf(
3254 " Walkington, and Binhai Zhu. See the comments at the beginning of the\n");
3255 printf(" source code for references.\n\n");
3256 triexit(0);
3257 }
3258
3259 #endif /* not TRILIBRARY */
3260
3261 /*****************************************************************************/
3262 /* */
3263 /* internalerror() Ask the user to send me the defective product. Exit. */
3264 /* */
3265 /*****************************************************************************/
3266
internalerror()3267 void internalerror()
3268 {
3269 printf(" Please report this bug to jrs@cs.berkeley.edu\n");
3270 printf(" Include the message above, your input data set, and the exact\n");
3271 printf(" command line you used to run Triangle.\n");
3272 triexit(1);
3273 }
3274
3275 /*****************************************************************************/
3276 /* */
3277 /* parsecommandline() Read the command line, identify switches, and set */
3278 /* up options and file names. */
3279 /* */
3280 /*****************************************************************************/
3281
3282 #ifdef ANSI_DECLARATORS
3283 void parsecommandline(int argc, char **argv, struct behavior *b)
3284 #else /* not ANSI_DECLARATORS */
3285 void parsecommandline(argc, argv, b)
3286 int argc;
3287 char **argv;
3288 struct behavior *b;
3289 #endif /* not ANSI_DECLARATORS */
3290
3291 {
3292 #ifdef TRILIBRARY
3293 #define STARTINDEX 0
3294 #else /* not TRILIBRARY */
3295 #define STARTINDEX 1
3296 int increment;
3297 int meshnumber;
3298 #endif /* not TRILIBRARY */
3299 int i, j, k;
3300 char workstring[FILENAMESIZE];
3301
3302 b->poly = b->refine = b->quality = 0;
3303 b->vararea = b->fixedarea = b->usertest = 0;
3304 b->regionattrib = b->convex = b->weighted = b->jettison = 0;
3305 b->firstnumber = 1;
3306 b->edgesout = b->voronoi = b->neighbors = b->geomview = 0;
3307 b->nobound = b->nopolywritten = b->nonodewritten = b->noelewritten = 0;
3308 b->noiterationnum = 0;
3309 b->noholes = b->noexact = 0;
3310 b->incremental = b->sweepline = 0;
3311 b->dwyer = 1;
3312 b->splitseg = 0;
3313 b->docheck = 0;
3314 b->nobisect = 0;
3315 b->conformdel = 0;
3316 b->steiner = -1;
3317 b->order = 1;
3318 b->minangle = 0.0;
3319 b->maxarea = -1.0;
3320 b->quiet = b->verbose = 0;
3321 #ifndef TRILIBRARY
3322 b->innodefilename[0] = '\0';
3323 #endif /* not TRILIBRARY */
3324
3325 for (i = STARTINDEX; i < argc; i++) {
3326 #ifndef TRILIBRARY
3327 if (argv[i][0] == '-') {
3328 #endif /* not TRILIBRARY */
3329 for (j = STARTINDEX; argv[i][j] != '\0'; j++) {
3330 if (argv[i][j] == 'p') {
3331 b->poly = 1;
3332 }
3333 #ifndef CDT_ONLY
3334 if (argv[i][j] == 'r') {
3335 b->refine = 1;
3336 }
3337 if (argv[i][j] == 'q') {
3338 b->quality = 1;
3339 if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
3340 (argv[i][j + 1] == '.')) {
3341 k = 0;
3342 while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
3343 (argv[i][j + 1] == '.')) {
3344 j++;
3345 workstring[k] = argv[i][j];
3346 k++;
3347 }
3348 workstring[k] = '\0';
3349 b->minangle = (REAL) strtod(workstring, (char **) NULL);
3350 } else {
3351 b->minangle = 20.0;
3352 }
3353 }
3354 if (argv[i][j] == 'a') {
3355 b->quality = 1;
3356 if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
3357 (argv[i][j + 1] == '.')) {
3358 b->fixedarea = 1;
3359 k = 0;
3360 while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
3361 (argv[i][j + 1] == '.')) {
3362 j++;
3363 workstring[k] = argv[i][j];
3364 k++;
3365 }
3366 workstring[k] = '\0';
3367 b->maxarea = (REAL) strtod(workstring, (char **) NULL);
3368 if (b->maxarea <= 0.0) {
3369 printf("Error: Maximum area must be greater than zero.\n");
3370 triexit(1);
3371 }
3372 } else {
3373 b->vararea = 1;
3374 }
3375 }
3376 if (argv[i][j] == 'u') {
3377 b->quality = 1;
3378 b->usertest = 1;
3379 }
3380 #endif /* not CDT_ONLY */
3381 if (argv[i][j] == 'A') {
3382 b->regionattrib = 1;
3383 }
3384 if (argv[i][j] == 'c') {
3385 b->convex = 1;
3386 }
3387 if (argv[i][j] == 'w') {
3388 b->weighted = 1;
3389 }
3390 if (argv[i][j] == 'W') {
3391 b->weighted = 2;
3392 }
3393 if (argv[i][j] == 'j') {
3394 b->jettison = 1;
3395 }
3396 if (argv[i][j] == 'z') {
3397 b->firstnumber = 0;
3398 }
3399 if (argv[i][j] == 'e') {
3400 b->edgesout = 1;
3401 }
3402 if (argv[i][j] == 'v') {
3403 b->voronoi = 1;
3404 }
3405 if (argv[i][j] == 'n') {
3406 b->neighbors = 1;
3407 }
3408 if (argv[i][j] == 'g') {
3409 b->geomview = 1;
3410 }
3411 if (argv[i][j] == 'B') {
3412 b->nobound = 1;
3413 }
3414 if (argv[i][j] == 'P') {
3415 b->nopolywritten = 1;
3416 }
3417 if (argv[i][j] == 'N') {
3418 b->nonodewritten = 1;
3419 }
3420 if (argv[i][j] == 'E') {
3421 b->noelewritten = 1;
3422 }
3423 #ifndef TRILIBRARY
3424 if (argv[i][j] == 'I') {
3425 b->noiterationnum = 1;
3426 }
3427 #endif /* not TRILIBRARY */
3428 if (argv[i][j] == 'O') {
3429 b->noholes = 1;
3430 }
3431 if (argv[i][j] == 'X') {
3432 b->noexact = 1;
3433 }
3434 if (argv[i][j] == 'o') {
3435 if (argv[i][j + 1] == '2') {
3436 j++;
3437 b->order = 2;
3438 }
3439 }
3440 #ifndef CDT_ONLY
3441 if (argv[i][j] == 'Y') {
3442 b->nobisect++;
3443 }
3444 if (argv[i][j] == 'S') {
3445 b->steiner = 0;
3446 while ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) {
3447 j++;
3448 b->steiner = b->steiner * 10 + (int) (argv[i][j] - '0');
3449 }
3450 }
3451 #endif /* not CDT_ONLY */
3452 #ifndef REDUCED
3453 if (argv[i][j] == 'i') {
3454 b->incremental = 1;
3455 }
3456 if (argv[i][j] == 'F') {
3457 b->sweepline = 1;
3458 }
3459 #endif /* not REDUCED */
3460 if (argv[i][j] == 'l') {
3461 b->dwyer = 0;
3462 }
3463 #ifndef REDUCED
3464 #ifndef CDT_ONLY
3465 if (argv[i][j] == 's') {
3466 b->splitseg = 1;
3467 }
3468 if ((argv[i][j] == 'D') || (argv[i][j] == 'L')) {
3469 b->quality = 1;
3470 b->conformdel = 1;
3471 }
3472 #endif /* not CDT_ONLY */
3473 if (argv[i][j] == 'C') {
3474 b->docheck = 1;
3475 }
3476 #endif /* not REDUCED */
3477 if (argv[i][j] == 'Q') {
3478 b->quiet = 1;
3479 }
3480 if (argv[i][j] == 'V') {
3481 b->verbose++;
3482 }
3483 #ifndef TRILIBRARY
3484 if ((argv[i][j] == 'h') || (argv[i][j] == 'H') ||
3485 (argv[i][j] == '?')) {
3486 info();
3487 }
3488 #endif /* not TRILIBRARY */
3489 }
3490 #ifndef TRILIBRARY
3491 } else {
3492 strncpy(b->innodefilename, argv[i], FILENAMESIZE - 1);
3493 b->innodefilename[FILENAMESIZE - 1] = '\0';
3494 }
3495 #endif /* not TRILIBRARY */
3496 }
3497 #ifndef TRILIBRARY
3498 if (b->innodefilename[0] == '\0') {
3499 syntax();
3500 }
3501 if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 5], ".node")) {
3502 b->innodefilename[strlen(b->innodefilename) - 5] = '\0';
3503 }
3504 if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 5], ".poly")) {
3505 b->innodefilename[strlen(b->innodefilename) - 5] = '\0';
3506 b->poly = 1;
3507 }
3508 #ifndef CDT_ONLY
3509 if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 4], ".ele")) {
3510 b->innodefilename[strlen(b->innodefilename) - 4] = '\0';
3511 b->refine = 1;
3512 }
3513 if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 5], ".area")) {
3514 b->innodefilename[strlen(b->innodefilename) - 5] = '\0';
3515 b->refine = 1;
3516 b->quality = 1;
3517 b->vararea = 1;
3518 }
3519 #endif /* not CDT_ONLY */
3520 #endif /* not TRILIBRARY */
3521 b->usesegments = b->poly || b->refine || b->quality || b->convex;
3522 b->goodangle = cos(b->minangle * PI / 180.0);
3523 if (b->goodangle == 1.0) {
3524 b->offconstant = 0.0;
3525 } else {
3526 b->offconstant = 0.475 * sqrt((1.0 + b->goodangle) / (1.0 - b->goodangle));
3527 }
3528 b->goodangle *= b->goodangle;
3529 if (b->refine && b->noiterationnum) {
3530 printf(
3531 "Error: You cannot use the -I switch when refining a triangulation.\n");
3532 triexit(1);
3533 }
3534 /* Be careful not to allocate space for element area constraints that */
3535 /* will never be assigned any value (other than the default -1.0). */
3536 if (!b->refine && !b->poly) {
3537 b->vararea = 0;
3538 }
3539 /* Be careful not to add an extra attribute to each element unless the */
3540 /* input supports it (PSLG in, but not refining a preexisting mesh). */
3541 if (b->refine || !b->poly) {
3542 b->regionattrib = 0;
3543 }
3544 /* Regular/weighted triangulations are incompatible with PSLGs */
3545 /* and meshing. */
3546 if (b->weighted && (b->poly || b->quality)) {
3547 b->weighted = 0;
3548 if (!b->quiet) {
3549 printf("Warning: weighted triangulations (-w, -W) are incompatible\n");
3550 printf(" with PSLGs (-p) and meshing (-q, -a, -u). Weights ignored.\n"
3551 );
3552 }
3553 }
3554 if (b->jettison && b->nonodewritten && !b->quiet) {
3555 printf("Warning: -j and -N switches are somewhat incompatible.\n");
3556 printf(" If any vertices are jettisoned, you will need the output\n");
3557 printf(" .node file to reconstruct the new node indices.");
3558 }
3559
3560 #ifndef TRILIBRARY
3561 strcpy(b->inpolyfilename, b->innodefilename);
3562 strcpy(b->inelefilename, b->innodefilename);
3563 strcpy(b->areafilename, b->innodefilename);
3564 increment = 0;
3565 strcpy(workstring, b->innodefilename);
3566 j = 1;
3567 while (workstring[j] != '\0') {
3568 if ((workstring[j] == '.') && (workstring[j + 1] != '\0')) {
3569 increment = j + 1;
3570 }
3571 j++;
3572 }
3573 meshnumber = 0;
3574 if (increment > 0) {
3575 j = increment;
3576 do {
3577 if ((workstring[j] >= '0') && (workstring[j] <= '9')) {
3578 meshnumber = meshnumber * 10 + (int) (workstring[j] - '0');
3579 } else {
3580 increment = 0;
3581 }
3582 j++;
3583 } while (workstring[j] != '\0');
3584 }
3585 if (b->noiterationnum) {
3586 strcpy(b->outnodefilename, b->innodefilename);
3587 strcpy(b->outelefilename, b->innodefilename);
3588 strcpy(b->edgefilename, b->innodefilename);
3589 strcpy(b->vnodefilename, b->innodefilename);
3590 strcpy(b->vedgefilename, b->innodefilename);
3591 strcpy(b->neighborfilename, b->innodefilename);
3592 strcpy(b->offfilename, b->innodefilename);
3593 strcat(b->outnodefilename, ".node");
3594 strcat(b->outelefilename, ".ele");
3595 strcat(b->edgefilename, ".edge");
3596 strcat(b->vnodefilename, ".v.node");
3597 strcat(b->vedgefilename, ".v.edge");
3598 strcat(b->neighborfilename, ".neigh");
3599 strcat(b->offfilename, ".off");
3600 } else if (increment == 0) {
3601 strcpy(b->outnodefilename, b->innodefilename);
3602 strcpy(b->outpolyfilename, b->innodefilename);
3603 strcpy(b->outelefilename, b->innodefilename);
3604 strcpy(b->edgefilename, b->innodefilename);
3605 strcpy(b->vnodefilename, b->innodefilename);
3606 strcpy(b->vedgefilename, b->innodefilename);
3607 strcpy(b->neighborfilename, b->innodefilename);
3608 strcpy(b->offfilename, b->innodefilename);
3609 strcat(b->outnodefilename, ".1.node");
3610 strcat(b->outpolyfilename, ".1.poly");
3611 strcat(b->outelefilename, ".1.ele");
3612 strcat(b->edgefilename, ".1.edge");
3613 strcat(b->vnodefilename, ".1.v.node");
3614 strcat(b->vedgefilename, ".1.v.edge");
3615 strcat(b->neighborfilename, ".1.neigh");
3616 strcat(b->offfilename, ".1.off");
3617 } else {
3618 workstring[increment] = '%';
3619 workstring[increment + 1] = 'd';
3620 workstring[increment + 2] = '\0';
3621 sprintf(b->outnodefilename, workstring, meshnumber + 1);
3622 strcpy(b->outpolyfilename, b->outnodefilename);
3623 strcpy(b->outelefilename, b->outnodefilename);
3624 strcpy(b->edgefilename, b->outnodefilename);
3625 strcpy(b->vnodefilename, b->outnodefilename);
3626 strcpy(b->vedgefilename, b->outnodefilename);
3627 strcpy(b->neighborfilename, b->outnodefilename);
3628 strcpy(b->offfilename, b->outnodefilename);
3629 strcat(b->outnodefilename, ".node");
3630 strcat(b->outpolyfilename, ".poly");
3631 strcat(b->outelefilename, ".ele");
3632 strcat(b->edgefilename, ".edge");
3633 strcat(b->vnodefilename, ".v.node");
3634 strcat(b->vedgefilename, ".v.edge");
3635 strcat(b->neighborfilename, ".neigh");
3636 strcat(b->offfilename, ".off");
3637 }
3638 strcat(b->innodefilename, ".node");
3639 strcat(b->inpolyfilename, ".poly");
3640 strcat(b->inelefilename, ".ele");
3641 strcat(b->areafilename, ".area");
3642 #endif /* not TRILIBRARY */
3643 }
3644
3645 /** **/
3646 /** **/
3647 /********* User interaction routines begin here *********/
3648
3649 /********* Debugging routines begin here *********/
3650 /** **/
3651 /** **/
3652
3653 /*****************************************************************************/
3654 /* */
3655 /* printtriangle() Print out the details of an oriented triangle. */
3656 /* */
3657 /* I originally wrote this procedure to simplify debugging; it can be */
3658 /* called directly from the debugger, and presents information about an */
3659 /* oriented triangle in digestible form. It's also used when the */
3660 /* highest level of verbosity (`-VVV') is specified. */
3661 /* */
3662 /*****************************************************************************/
3663
3664 #ifdef ANSI_DECLARATORS
3665 void printtriangle(struct mesh *m, struct behavior *b, struct otri *t)
3666 #else /* not ANSI_DECLARATORS */
3667 void printtriangle(m, b, t)
3668 struct mesh *m;
3669 struct behavior *b;
3670 struct otri *t;
3671 #endif /* not ANSI_DECLARATORS */
3672
3673 {
3674 struct otri printtri;
3675 struct osub printsh;
3676 vertex printvertex;
3677
3678 printf("triangle x%lx with orientation %d:\n", (unsigned long) t->tri,
3679 t->orient);
3680 decode(t->tri[0], printtri);
3681 if (printtri.tri == m->dummytri) {
3682 printf(" [0] = Outer space\n");
3683 } else {
3684 printf(" [0] = x%lx %d\n", (unsigned long) printtri.tri,
3685 printtri.orient);
3686 }
3687 decode(t->tri[1], printtri);
3688 if (printtri.tri == m->dummytri) {
3689 printf(" [1] = Outer space\n");
3690 } else {
3691 printf(" [1] = x%lx %d\n", (unsigned long) printtri.tri,
3692 printtri.orient);
3693 }
3694 decode(t->tri[2], printtri);
3695 if (printtri.tri == m->dummytri) {
3696 printf(" [2] = Outer space\n");
3697 } else {
3698 printf(" [2] = x%lx %d\n", (unsigned long) printtri.tri,
3699 printtri.orient);
3700 }
3701
3702 org(*t, printvertex);
3703 if (printvertex == (vertex) NULL)
3704 printf(" Origin[%d] = NULL\n", (t->orient + 1) % 3 + 3);
3705 else
3706 printf(" Origin[%d] = x%lx (%.12g, %.12g)\n",
3707 (t->orient + 1) % 3 + 3, (unsigned long) printvertex,
3708 printvertex[0], printvertex[1]);
3709 dest(*t, printvertex);
3710 if (printvertex == (vertex) NULL)
3711 printf(" Dest [%d] = NULL\n", (t->orient + 2) % 3 + 3);
3712 else
3713 printf(" Dest [%d] = x%lx (%.12g, %.12g)\n",
3714 (t->orient + 2) % 3 + 3, (unsigned long) printvertex,
3715 printvertex[0], printvertex[1]);
3716 apex(*t, printvertex);
3717 if (printvertex == (vertex) NULL)
3718 printf(" Apex [%d] = NULL\n", t->orient + 3);
3719 else
3720 printf(" Apex [%d] = x%lx (%.12g, %.12g)\n",
3721 t->orient + 3, (unsigned long) printvertex,
3722 printvertex[0], printvertex[1]);
3723
3724 if (b->usesegments) {
3725 sdecode(t->tri[6], printsh);
3726 if (printsh.ss != m->dummysub) {
3727 printf(" [6] = x%lx %d\n", (unsigned long) printsh.ss,
3728 printsh.ssorient);
3729 }
3730 sdecode(t->tri[7], printsh);
3731 if (printsh.ss != m->dummysub) {
3732 printf(" [7] = x%lx %d\n", (unsigned long) printsh.ss,
3733 printsh.ssorient);
3734 }
3735 sdecode(t->tri[8], printsh);
3736 if (printsh.ss != m->dummysub) {
3737 printf(" [8] = x%lx %d\n", (unsigned long) printsh.ss,
3738 printsh.ssorient);
3739 }
3740 }
3741
3742 if (b->vararea) {
3743 printf(" Area constraint: %.4g\n", areabound(*t));
3744 }
3745 }
3746
3747 /*****************************************************************************/
3748 /* */
3749 /* printsubseg() Print out the details of an oriented subsegment. */
3750 /* */
3751 /* I originally wrote this procedure to simplify debugging; it can be */
3752 /* called directly from the debugger, and presents information about an */
3753 /* oriented subsegment in digestible form. It's also used when the highest */
3754 /* level of verbosity (`-VVV') is specified. */
3755 /* */
3756 /*****************************************************************************/
3757
3758 #ifdef ANSI_DECLARATORS
3759 void printsubseg(struct mesh *m, struct behavior *b, struct osub *s)
3760 #else /* not ANSI_DECLARATORS */
3761 void printsubseg(m, b, s)
3762 struct mesh *m;
3763 struct behavior *b;
3764 struct osub *s;
3765 #endif /* not ANSI_DECLARATORS */
3766
3767 {
3768 struct osub printsh;
3769 struct otri printtri;
3770 vertex printvertex;
3771
3772 printf("subsegment x%lx with orientation %d and mark %d:\n",
3773 (unsigned long) s->ss, s->ssorient, mark(*s));
3774 sdecode(s->ss[0], printsh);
3775 if (printsh.ss == m->dummysub) {
3776 printf(" [0] = No subsegment\n");
3777 } else {
3778 printf(" [0] = x%lx %d\n", (unsigned long) printsh.ss,
3779 printsh.ssorient);
3780 }
3781 sdecode(s->ss[1], printsh);
3782 if (printsh.ss == m->dummysub) {
3783 printf(" [1] = No subsegment\n");
3784 } else {
3785 printf(" [1] = x%lx %d\n", (unsigned long) printsh.ss,
3786 printsh.ssorient);
3787 }
3788
3789 sorg(*s, printvertex);
3790 if (printvertex == (vertex) NULL)
3791 printf(" Origin[%d] = NULL\n", 2 + s->ssorient);
3792 else
3793 printf(" Origin[%d] = x%lx (%.12g, %.12g)\n",
3794 2 + s->ssorient, (unsigned long) printvertex,
3795 printvertex[0], printvertex[1]);
3796 sdest(*s, printvertex);
3797 if (printvertex == (vertex) NULL)
3798 printf(" Dest [%d] = NULL\n", 3 - s->ssorient);
3799 else
3800 printf(" Dest [%d] = x%lx (%.12g, %.12g)\n",
3801 3 - s->ssorient, (unsigned long) printvertex,
3802 printvertex[0], printvertex[1]);
3803
3804 decode(s->ss[6], printtri);
3805 if (printtri.tri == m->dummytri) {
3806 printf(" [6] = Outer space\n");
3807 } else {
3808 printf(" [6] = x%lx %d\n", (unsigned long) printtri.tri,
3809 printtri.orient);
3810 }
3811 decode(s->ss[7], printtri);
3812 if (printtri.tri == m->dummytri) {
3813 printf(" [7] = Outer space\n");
3814 } else {
3815 printf(" [7] = x%lx %d\n", (unsigned long) printtri.tri,
3816 printtri.orient);
3817 }
3818
3819 segorg(*s, printvertex);
3820 if (printvertex == (vertex) NULL)
3821 printf(" Segment origin[%d] = NULL\n", 4 + s->ssorient);
3822 else
3823 printf(" Segment origin[%d] = x%lx (%.12g, %.12g)\n",
3824 4 + s->ssorient, (unsigned long) printvertex,
3825 printvertex[0], printvertex[1]);
3826 segdest(*s, printvertex);
3827 if (printvertex == (vertex) NULL)
3828 printf(" Segment dest [%d] = NULL\n", 5 - s->ssorient);
3829 else
3830 printf(" Segment dest [%d] = x%lx (%.12g, %.12g)\n",
3831 5 - s->ssorient, (unsigned long) printvertex,
3832 printvertex[0], printvertex[1]);
3833 }
3834
3835 /** **/
3836 /** **/
3837 /********* Debugging routines end here *********/
3838
3839 /********* Memory management routines begin here *********/
3840 /** **/
3841 /** **/
3842
3843 /*****************************************************************************/
3844 /* */
3845 /* poolzero() Set all of a pool's fields to zero. */
3846 /* */
3847 /* This procedure should never be called on a pool that has any memory */
3848 /* allocated to it, as that memory would leak. */
3849 /* */
3850 /*****************************************************************************/
3851
3852 #ifdef ANSI_DECLARATORS
3853 void poolzero(struct memorypool *pool)
3854 #else /* not ANSI_DECLARATORS */
3855 void poolzero(pool)
3856 struct memorypool *pool;
3857 #endif /* not ANSI_DECLARATORS */
3858
3859 {
3860 pool->firstblock = (VOID **) NULL;
3861 pool->nowblock = (VOID **) NULL;
3862 pool->nextitem = (VOID *) NULL;
3863 pool->deaditemstack = (VOID *) NULL;
3864 pool->pathblock = (VOID **) NULL;
3865 pool->pathitem = (VOID *) NULL;
3866 pool->alignbytes = 0;
3867 pool->itembytes = 0;
3868 pool->itemsperblock = 0;
3869 pool->itemsfirstblock = 0;
3870 pool->items = 0;
3871 pool->maxitems = 0;
3872 pool->unallocateditems = 0;
3873 pool->pathitemsleft = 0;
3874 }
3875
3876 /*****************************************************************************/
3877 /* */
3878 /* poolrestart() Deallocate all items in a pool. */
3879 /* */
3880 /* The pool is returned to its starting state, except that no memory is */
3881 /* freed to the operating system. Rather, the previously allocated blocks */
3882 /* are ready to be reused. */
3883 /* */
3884 /*****************************************************************************/
3885
3886 #ifdef ANSI_DECLARATORS
3887 void poolrestart(struct memorypool *pool)
3888 #else /* not ANSI_DECLARATORS */
3889 void poolrestart(pool)
3890 struct memorypool *pool;
3891 #endif /* not ANSI_DECLARATORS */
3892
3893 {
3894 unsigned long alignptr;
3895
3896 pool->items = 0;
3897 pool->maxitems = 0;
3898
3899 /* Set the currently active block. */
3900 pool->nowblock = pool->firstblock;
3901 /* Find the first item in the pool. Increment by the size of (VOID *). */
3902 alignptr = (unsigned long) (pool->nowblock + 1);
3903 /* Align the item on an `alignbytes'-byte boundary. */
3904 pool->nextitem = (VOID *)
3905 (alignptr + (unsigned long) pool->alignbytes -
3906 (alignptr % (unsigned long) pool->alignbytes));
3907 /* There are lots of unallocated items left in this block. */
3908 pool->unallocateditems = pool->itemsfirstblock;
3909 /* The stack of deallocated items is empty. */
3910 pool->deaditemstack = (VOID *) NULL;
3911 }
3912
3913 /*****************************************************************************/
3914 /* */
3915 /* poolinit() Initialize a pool of memory for allocation of items. */
3916 /* */
3917 /* This routine initializes the machinery for allocating items. A `pool' */
3918 /* is created whose records have size at least `bytecount'. Items will be */
3919 /* allocated in `itemcount'-item blocks. Each item is assumed to be a */
3920 /* collection of words, and either pointers or floating-point values are */
3921 /* assumed to be the "primary" word type. (The "primary" word type is used */
3922 /* to determine alignment of items.) If `alignment' isn't zero, all items */
3923 /* will be `alignment'-byte aligned in memory. `alignment' must be either */
3924 /* a multiple or a factor of the primary word size; powers of two are safe. */
3925 /* `alignment' is normally used to create a few unused bits at the bottom */
3926 /* of each item's pointer, in which information may be stored. */
3927 /* */
3928 /* Don't change this routine unless you understand it. */
3929 /* */
3930 /*****************************************************************************/
3931
3932 #ifdef ANSI_DECLARATORS
3933 void poolinit(struct memorypool *pool, int bytecount, int itemcount,
3934 int firstitemcount, int alignment)
3935 #else /* not ANSI_DECLARATORS */
3936 void poolinit(pool, bytecount, itemcount, firstitemcount, alignment)
3937 struct memorypool *pool;
3938 int bytecount;
3939 int itemcount;
3940 int firstitemcount;
3941 int alignment;
3942 #endif /* not ANSI_DECLARATORS */
3943
3944 {
3945 /* Find the proper alignment, which must be at least as large as: */
3946 /* - The parameter `alignment'. */
3947 /* - sizeof(VOID *), so the stack of dead items can be maintained */
3948 /* without unaligned accesses. */
3949 if (alignment > sizeof(VOID *)) {
3950 pool->alignbytes = alignment;
3951 } else {
3952 pool->alignbytes = sizeof(VOID *);
3953 }
3954 pool->itembytes = ((bytecount - 1) / pool->alignbytes + 1) *
3955 pool->alignbytes;
3956 pool->itemsperblock = itemcount;
3957 if (firstitemcount == 0) {
3958 pool->itemsfirstblock = itemcount;
3959 } else {
3960 pool->itemsfirstblock = firstitemcount;
3961 }
3962
3963 /* Allocate a block of items. Space for `itemsfirstblock' items and one */
3964 /* pointer (to point to the next block) are allocated, as well as space */
3965 /* to ensure alignment of the items. */
3966 pool->firstblock = (VOID **)
3967 trimalloc(pool->itemsfirstblock * pool->itembytes + (int) sizeof(VOID *) +
3968 pool->alignbytes);
3969 /* Set the next block pointer to NULL. */
3970 *(pool->firstblock) = (VOID *) NULL;
3971 poolrestart(pool);
3972 }
3973
3974 /*****************************************************************************/
3975 /* */
3976 /* pooldeinit() Free to the operating system all memory taken by a pool. */
3977 /* */
3978 /*****************************************************************************/
3979
3980 #ifdef ANSI_DECLARATORS
3981 void pooldeinit(struct memorypool *pool)
3982 #else /* not ANSI_DECLARATORS */
3983 void pooldeinit(pool)
3984 struct memorypool *pool;
3985 #endif /* not ANSI_DECLARATORS */
3986
3987 {
3988 while (pool->firstblock != (VOID **) NULL) {
3989 pool->nowblock = (VOID **) *(pool->firstblock);
3990 trifree((VOID *) pool->firstblock);
3991 pool->firstblock = pool->nowblock;
3992 }
3993 }
3994
3995 /*****************************************************************************/
3996 /* */
3997 /* poolalloc() Allocate space for an item. */
3998 /* */
3999 /*****************************************************************************/
4000
4001 #ifdef ANSI_DECLARATORS
4002 VOID *poolalloc(struct memorypool *pool)
4003 #else /* not ANSI_DECLARATORS */
4004 VOID *poolalloc(pool)
4005 struct memorypool *pool;
4006 #endif /* not ANSI_DECLARATORS */
4007
4008 {
4009 VOID *newitem;
4010 VOID **newblock;
4011 unsigned long alignptr;
4012
4013 /* First check the linked list of dead items. If the list is not */
4014 /* empty, allocate an item from the list rather than a fresh one. */
4015 if (pool->deaditemstack != (VOID *) NULL) {
4016 newitem = pool->deaditemstack; /* Take first item in list. */
4017 pool->deaditemstack = * (VOID **) pool->deaditemstack;
4018 } else {
4019 /* Check if there are any free items left in the current block. */
4020 if (pool->unallocateditems == 0) {
4021 /* Check if another block must be allocated. */
4022 if (*(pool->nowblock) == (VOID *) NULL) {
4023 /* Allocate a new block of items, pointed to by the previous block. */
4024 newblock = (VOID **) trimalloc(pool->itemsperblock * pool->itembytes +
4025 (int) sizeof(VOID *) +
4026 pool->alignbytes);
4027 *(pool->nowblock) = (VOID *) newblock;
4028 /* The next block pointer is NULL. */
4029 *newblock = (VOID *) NULL;
4030 }
4031
4032 /* Move to the new block. */
4033 pool->nowblock = (VOID **) *(pool->nowblock);
4034 /* Find the first item in the block. */
4035 /* Increment by the size of (VOID *). */
4036 alignptr = (unsigned long) (pool->nowblock + 1);
4037 /* Align the item on an `alignbytes'-byte boundary. */
4038 pool->nextitem = (VOID *)
4039 (alignptr + (unsigned long) pool->alignbytes -
4040 (alignptr % (unsigned long) pool->alignbytes));
4041 /* There are lots of unallocated items left in this block. */
4042 pool->unallocateditems = pool->itemsperblock;
4043 }
4044
4045 /* Allocate a new item. */
4046 newitem = pool->nextitem;
4047 /* Advance `nextitem' pointer to next free item in block. */
4048 pool->nextitem = (VOID *) ((char *) pool->nextitem + pool->itembytes);
4049 pool->unallocateditems--;
4050 pool->maxitems++;
4051 }
4052 pool->items++;
4053 return newitem;
4054 }
4055
4056 /*****************************************************************************/
4057 /* */
4058 /* pooldealloc() Deallocate space for an item. */
4059 /* */
4060 /* The deallocated space is stored in a queue for later reuse. */
4061 /* */
4062 /*****************************************************************************/
4063
4064 #ifdef ANSI_DECLARATORS
4065 void pooldealloc(struct memorypool *pool, VOID *dyingitem)
4066 #else /* not ANSI_DECLARATORS */
4067 void pooldealloc(pool, dyingitem)
4068 struct memorypool *pool;
4069 VOID *dyingitem;
4070 #endif /* not ANSI_DECLARATORS */
4071
4072 {
4073 /* Push freshly killed item onto stack. */
4074 *((VOID **) dyingitem) = pool->deaditemstack;
4075 pool->deaditemstack = dyingitem;
4076 pool->items--;
4077 }
4078
4079 /*****************************************************************************/
4080 /* */
4081 /* traversalinit() Prepare to traverse the entire list of items. */
4082 /* */
4083 /* This routine is used in conjunction with traverse(). */
4084 /* */
4085 /*****************************************************************************/
4086
4087 #ifdef ANSI_DECLARATORS
4088 void traversalinit(struct memorypool *pool)
4089 #else /* not ANSI_DECLARATORS */
4090 void traversalinit(pool)
4091 struct memorypool *pool;
4092 #endif /* not ANSI_DECLARATORS */
4093
4094 {
4095 unsigned long alignptr;
4096
4097 /* Begin the traversal in the first block. */
4098 pool->pathblock = pool->firstblock;
4099 /* Find the first item in the block. Increment by the size of (VOID *). */
4100 alignptr = (unsigned long) (pool->pathblock + 1);
4101 /* Align with item on an `alignbytes'-byte boundary. */
4102 pool->pathitem = (VOID *)
4103 (alignptr + (unsigned long) pool->alignbytes -
4104 (alignptr % (unsigned long) pool->alignbytes));
4105 /* Set the number of items left in the current block. */
4106 pool->pathitemsleft = pool->itemsfirstblock;
4107 }
4108
4109 /*****************************************************************************/
4110 /* */
4111 /* traverse() Find the next item in the list. */
4112 /* */
4113 /* This routine is used in conjunction with traversalinit(). Be forewarned */
4114 /* that this routine successively returns all items in the list, including */
4115 /* deallocated ones on the deaditemqueue. It's up to you to figure out */
4116 /* which ones are actually dead. Why? I don't want to allocate extra */
4117 /* space just to demarcate dead items. It can usually be done more */
4118 /* space-efficiently by a routine that knows something about the structure */
4119 /* of the item. */
4120 /* */
4121 /*****************************************************************************/
4122
4123 #ifdef ANSI_DECLARATORS
4124 VOID *traverse(struct memorypool *pool)
4125 #else /* not ANSI_DECLARATORS */
4126 VOID *traverse(pool)
4127 struct memorypool *pool;
4128 #endif /* not ANSI_DECLARATORS */
4129
4130 {
4131 VOID *newitem;
4132 unsigned long alignptr;
4133
4134 /* Stop upon exhausting the list of items. */
4135 if (pool->pathitem == pool->nextitem) {
4136 return (VOID *) NULL;
4137 }
4138
4139 /* Check whether any untraversed items remain in the current block. */
4140 if (pool->pathitemsleft == 0) {
4141 /* Find the next block. */
4142 pool->pathblock = (VOID **) *(pool->pathblock);
4143 /* Find the first item in the block. Increment by the size of (VOID *). */
4144 alignptr = (unsigned long) (pool->pathblock + 1);
4145 /* Align with item on an `alignbytes'-byte boundary. */
4146 pool->pathitem = (VOID *)
4147 (alignptr + (unsigned long) pool->alignbytes -
4148 (alignptr % (unsigned long) pool->alignbytes));
4149 /* Set the number of items left in the current block. */
4150 pool->pathitemsleft = pool->itemsperblock;
4151 }
4152
4153 newitem = pool->pathitem;
4154 /* Find the next item in the block. */
4155 pool->pathitem = (VOID *) ((char *) pool->pathitem + pool->itembytes);
4156 pool->pathitemsleft--;
4157 return newitem;
4158 }
4159
4160 /*****************************************************************************/
4161 /* */
4162 /* dummyinit() Initialize the triangle that fills "outer space" and the */
4163 /* omnipresent subsegment. */
4164 /* */
4165 /* The triangle that fills "outer space," called `dummytri', is pointed to */
4166 /* by every triangle and subsegment on a boundary (be it outer or inner) of */
4167 /* the triangulation. Also, `dummytri' points to one of the triangles on */
4168 /* the convex hull (until the holes and concavities are carved), making it */
4169 /* possible to find a starting triangle for point location. */
4170 /* */
4171 /* The omnipresent subsegment, `dummysub', is pointed to by every triangle */
4172 /* or subsegment that doesn't have a full complement of real subsegments */
4173 /* to point to. */
4174 /* */
4175 /* `dummytri' and `dummysub' are generally required to fulfill only a few */
4176 /* invariants: their vertices must remain NULL and `dummytri' must always */
4177 /* be bonded (at offset zero) to some triangle on the convex hull of the */
4178 /* mesh, via a boundary edge. Otherwise, the connections of `dummytri' and */
4179 /* `dummysub' may change willy-nilly. This makes it possible to avoid */
4180 /* writing a good deal of special-case code (in the edge flip, for example) */
4181 /* for dealing with the boundary of the mesh, places where no subsegment is */
4182 /* present, and so forth. Other entities are frequently bonded to */
4183 /* `dummytri' and `dummysub' as if they were real mesh entities, with no */
4184 /* harm done. */
4185 /* */
4186 /*****************************************************************************/
4187
4188 #ifdef ANSI_DECLARATORS
4189 void dummyinit(struct mesh *m, struct behavior *b, int trianglebytes,
4190 int subsegbytes)
4191 #else /* not ANSI_DECLARATORS */
4192 void dummyinit(m, b, trianglebytes, subsegbytes)
4193 struct mesh *m;
4194 struct behavior *b;
4195 int trianglebytes;
4196 int subsegbytes;
4197 #endif /* not ANSI_DECLARATORS */
4198
4199 {
4200 unsigned long alignptr;
4201
4202 /* Set up `dummytri', the `triangle' that occupies "outer space." */
4203 m->dummytribase = (triangle *) trimalloc(trianglebytes +
4204 m->triangles.alignbytes);
4205 /* Align `dummytri' on a `triangles.alignbytes'-byte boundary. */
4206 alignptr = (unsigned long) m->dummytribase;
4207 m->dummytri = (triangle *)
4208 (alignptr + (unsigned long) m->triangles.alignbytes -
4209 (alignptr % (unsigned long) m->triangles.alignbytes));
4210 /* Initialize the three adjoining triangles to be "outer space." These */
4211 /* will eventually be changed by various bonding operations, but their */
4212 /* values don't really matter, as long as they can legally be */
4213 /* dereferenced. */
4214 m->dummytri[0] = (triangle) m->dummytri;
4215 m->dummytri[1] = (triangle) m->dummytri;
4216 m->dummytri[2] = (triangle) m->dummytri;
4217 /* Three NULL vertices. */
4218 m->dummytri[3] = (triangle) NULL;
4219 m->dummytri[4] = (triangle) NULL;
4220 m->dummytri[5] = (triangle) NULL;
4221
4222 if (b->usesegments) {
4223 /* Set up `dummysub', the omnipresent subsegment pointed to by any */
4224 /* triangle side or subsegment end that isn't attached to a real */
4225 /* subsegment. */
4226 m->dummysubbase = (subseg *) trimalloc(subsegbytes +
4227 m->subsegs.alignbytes);
4228 /* Align `dummysub' on a `subsegs.alignbytes'-byte boundary. */
4229 alignptr = (unsigned long) m->dummysubbase;
4230 m->dummysub = (subseg *)
4231 (alignptr + (unsigned long) m->subsegs.alignbytes -
4232 (alignptr % (unsigned long) m->subsegs.alignbytes));
4233 /* Initialize the two adjoining subsegments to be the omnipresent */
4234 /* subsegment. These will eventually be changed by various bonding */
4235 /* operations, but their values don't really matter, as long as they */
4236 /* can legally be dereferenced. */
4237 m->dummysub[0] = (subseg) m->dummysub;
4238 m->dummysub[1] = (subseg) m->dummysub;
4239 /* Four NULL vertices. */
4240 m->dummysub[2] = (subseg) NULL;
4241 m->dummysub[3] = (subseg) NULL;
4242 m->dummysub[4] = (subseg) NULL;
4243 m->dummysub[5] = (subseg) NULL;
4244 /* Initialize the two adjoining triangles to be "outer space." */
4245 m->dummysub[6] = (subseg) m->dummytri;
4246 m->dummysub[7] = (subseg) m->dummytri;
4247 /* Set the boundary marker to zero. */
4248 * (int *) (m->dummysub + 8) = 0;
4249
4250 /* Initialize the three adjoining subsegments of `dummytri' to be */
4251 /* the omnipresent subsegment. */
4252 m->dummytri[6] = (triangle) m->dummysub;
4253 m->dummytri[7] = (triangle) m->dummysub;
4254 m->dummytri[8] = (triangle) m->dummysub;
4255 }
4256 }
4257
4258 /*****************************************************************************/
4259 /* */
4260 /* initializevertexpool() Calculate the size of the vertex data structure */
4261 /* and initialize its memory pool. */
4262 /* */
4263 /* This routine also computes the `vertexmarkindex' and `vertex2triindex' */
4264 /* indices used to find values within each vertex. */
4265 /* */
4266 /*****************************************************************************/
4267
4268 #ifdef ANSI_DECLARATORS
4269 void initializevertexpool(struct mesh *m, struct behavior *b)
4270 #else /* not ANSI_DECLARATORS */
4271 void initializevertexpool(m, b)
4272 struct mesh *m;
4273 struct behavior *b;
4274 #endif /* not ANSI_DECLARATORS */
4275
4276 {
4277 int vertexsize;
4278
4279 /* The index within each vertex at which the boundary marker is found, */
4280 /* followed by the vertex type. Ensure the vertex marker is aligned to */
4281 /* a sizeof(int)-byte address. */
4282 m->vertexmarkindex = ((m->mesh_dim + m->nextras) * sizeof(REAL) +
4283 sizeof(int) - 1) /
4284 sizeof(int);
4285 vertexsize = (m->vertexmarkindex + 2) * sizeof(int);
4286 if (b->poly) {
4287 /* The index within each vertex at which a triangle pointer is found. */
4288 /* Ensure the pointer is aligned to a sizeof(triangle)-byte address. */
4289 m->vertex2triindex = (vertexsize + sizeof(triangle) - 1) /
4290 sizeof(triangle);
4291 vertexsize = (m->vertex2triindex + 1) * sizeof(triangle);
4292 }
4293
4294 /* Initialize the pool of vertices. */
4295 poolinit(&m->vertices, vertexsize, VERTEXPERBLOCK,
4296 m->invertices > VERTEXPERBLOCK ? m->invertices : VERTEXPERBLOCK,
4297 sizeof(REAL));
4298 }
4299
4300 /*****************************************************************************/
4301 /* */
4302 /* initializetrisubpools() Calculate the sizes of the triangle and */
4303 /* subsegment data structures and initialize */
4304 /* their memory pools. */
4305 /* */
4306 /* This routine also computes the `highorderindex', `elemattribindex', and */
4307 /* `areaboundindex' indices used to find values within each triangle. */
4308 /* */
4309 /*****************************************************************************/
4310
4311 #ifdef ANSI_DECLARATORS
4312 void initializetrisubpools(struct mesh *m, struct behavior *b)
4313 #else /* not ANSI_DECLARATORS */
4314 void initializetrisubpools(m, b)
4315 struct mesh *m;
4316 struct behavior *b;
4317 #endif /* not ANSI_DECLARATORS */
4318
4319 {
4320 int trisize;
4321
4322 /* The index within each triangle at which the extra nodes (above three) */
4323 /* associated with high order elements are found. There are three */
4324 /* pointers to other triangles, three pointers to corners, and possibly */
4325 /* three pointers to subsegments before the extra nodes. */
4326 m->highorderindex = 6 + (b->usesegments * 3);
4327 /* The number of bytes occupied by a triangle. */
4328 trisize = ((b->order + 1) * (b->order + 2) / 2 + (m->highorderindex - 3)) *
4329 sizeof(triangle);
4330 /* The index within each triangle at which its attributes are found, */
4331 /* where the index is measured in REALs. */
4332 m->elemattribindex = (trisize + sizeof(REAL) - 1) / sizeof(REAL);
4333 /* The index within each triangle at which the maximum area constraint */
4334 /* is found, where the index is measured in REALs. Note that if the */
4335 /* `regionattrib' flag is set, an additional attribute will be added. */
4336 m->areaboundindex = m->elemattribindex + m->eextras + b->regionattrib;
4337 /* If triangle attributes or an area bound are needed, increase the number */
4338 /* of bytes occupied by a triangle. */
4339 if (b->vararea) {
4340 trisize = (m->areaboundindex + 1) * sizeof(REAL);
4341 } else if (m->eextras + b->regionattrib > 0) {
4342 trisize = m->areaboundindex * sizeof(REAL);
4343 }
4344 /* If a Voronoi diagram or triangle neighbor graph is requested, make */
4345 /* sure there's room to store an integer index in each triangle. This */
4346 /* integer index can occupy the same space as the subsegment pointers */
4347 /* or attributes or area constraint or extra nodes. */
4348 if ((b->voronoi || b->neighbors) &&
4349 (trisize < 6 * sizeof(triangle) + sizeof(int))) {
4350 trisize = 6 * sizeof(triangle) + sizeof(int);
4351 }
4352
4353 /* Having determined the memory size of a triangle, initialize the pool. */
4354 poolinit(&m->triangles, trisize, TRIPERBLOCK,
4355 (2 * m->invertices - 2) > TRIPERBLOCK ? (2 * m->invertices - 2) :
4356 TRIPERBLOCK, 4);
4357
4358 if (b->usesegments) {
4359 /* Initialize the pool of subsegments. Take into account all eight */
4360 /* pointers and one boundary marker. */
4361 poolinit(&m->subsegs, 8 * sizeof(triangle) + sizeof(int),
4362 SUBSEGPERBLOCK, SUBSEGPERBLOCK, 4);
4363
4364 /* Initialize the "outer space" triangle and omnipresent subsegment. */
4365 dummyinit(m, b, m->triangles.itembytes, m->subsegs.itembytes);
4366 } else {
4367 /* Initialize the "outer space" triangle. */
4368 dummyinit(m, b, m->triangles.itembytes, 0);
4369 }
4370 }
4371
4372 /*****************************************************************************/
4373 /* */
4374 /* triangledealloc() Deallocate space for a triangle, marking it dead. */
4375 /* */
4376 /*****************************************************************************/
4377
4378 #ifdef ANSI_DECLARATORS
4379 void triangledealloc(struct mesh *m, triangle *dyingtriangle)
4380 #else /* not ANSI_DECLARATORS */
4381 void triangledealloc(m, dyingtriangle)
4382 struct mesh *m;
4383 triangle *dyingtriangle;
4384 #endif /* not ANSI_DECLARATORS */
4385
4386 {
4387 /* Mark the triangle as dead. This makes it possible to detect dead */
4388 /* triangles when traversing the list of all triangles. */
4389 killtri(dyingtriangle);
4390 pooldealloc(&m->triangles, (VOID *) dyingtriangle);
4391 }
4392
4393 /*****************************************************************************/
4394 /* */
4395 /* triangletraverse() Traverse the triangles, skipping dead ones. */
4396 /* */
4397 /*****************************************************************************/
4398
4399 #ifdef ANSI_DECLARATORS
4400 triangle *triangletraverse(struct mesh *m)
4401 #else /* not ANSI_DECLARATORS */
4402 triangle *triangletraverse(m)
4403 struct mesh *m;
4404 #endif /* not ANSI_DECLARATORS */
4405
4406 {
4407 triangle *newtriangle;
4408
4409 do {
4410 newtriangle = (triangle *) traverse(&m->triangles);
4411 if (newtriangle == (triangle *) NULL) {
4412 return (triangle *) NULL;
4413 }
4414 } while (deadtri(newtriangle)); /* Skip dead ones. */
4415 return newtriangle;
4416 }
4417
4418 /*****************************************************************************/
4419 /* */
4420 /* subsegdealloc() Deallocate space for a subsegment, marking it dead. */
4421 /* */
4422 /*****************************************************************************/
4423
4424 #ifdef ANSI_DECLARATORS
4425 void subsegdealloc(struct mesh *m, subseg *dyingsubseg)
4426 #else /* not ANSI_DECLARATORS */
4427 void subsegdealloc(m, dyingsubseg)
4428 struct mesh *m;
4429 subseg *dyingsubseg;
4430 #endif /* not ANSI_DECLARATORS */
4431
4432 {
4433 /* Mark the subsegment as dead. This makes it possible to detect dead */
4434 /* subsegments when traversing the list of all subsegments. */
4435 killsubseg(dyingsubseg);
4436 pooldealloc(&m->subsegs, (VOID *) dyingsubseg);
4437 }
4438
4439 /*****************************************************************************/
4440 /* */
4441 /* subsegtraverse() Traverse the subsegments, skipping dead ones. */
4442 /* */
4443 /*****************************************************************************/
4444
4445 #ifdef ANSI_DECLARATORS
4446 subseg *subsegtraverse(struct mesh *m)
4447 #else /* not ANSI_DECLARATORS */
4448 subseg *subsegtraverse(m)
4449 struct mesh *m;
4450 #endif /* not ANSI_DECLARATORS */
4451
4452 {
4453 subseg *newsubseg;
4454
4455 do {
4456 newsubseg = (subseg *) traverse(&m->subsegs);
4457 if (newsubseg == (subseg *) NULL) {
4458 return (subseg *) NULL;
4459 }
4460 } while (deadsubseg(newsubseg)); /* Skip dead ones. */
4461 return newsubseg;
4462 }
4463
4464 /*****************************************************************************/
4465 /* */
4466 /* vertexdealloc() Deallocate space for a vertex, marking it dead. */
4467 /* */
4468 /*****************************************************************************/
4469
4470 #ifdef ANSI_DECLARATORS
4471 void vertexdealloc(struct mesh *m, vertex dyingvertex)
4472 #else /* not ANSI_DECLARATORS */
4473 void vertexdealloc(m, dyingvertex)
4474 struct mesh *m;
4475 vertex dyingvertex;
4476 #endif /* not ANSI_DECLARATORS */
4477
4478 {
4479 /* Mark the vertex as dead. This makes it possible to detect dead */
4480 /* vertices when traversing the list of all vertices. */
4481 setvertextype(dyingvertex, DEADVERTEX);
4482 pooldealloc(&m->vertices, (VOID *) dyingvertex);
4483 }
4484
4485 /*****************************************************************************/
4486 /* */
4487 /* vertextraverse() Traverse the vertices, skipping dead ones. */
4488 /* */
4489 /*****************************************************************************/
4490
4491 #ifdef ANSI_DECLARATORS
4492 vertex vertextraverse(struct mesh *m)
4493 #else /* not ANSI_DECLARATORS */
4494 vertex vertextraverse(m)
4495 struct mesh *m;
4496 #endif /* not ANSI_DECLARATORS */
4497
4498 {
4499 vertex newvertex;
4500
4501 do {
4502 newvertex = (vertex) traverse(&m->vertices);
4503 if (newvertex == (vertex) NULL) {
4504 return (vertex) NULL;
4505 }
4506 } while (vertextype(newvertex) == DEADVERTEX); /* Skip dead ones. */
4507 return newvertex;
4508 }
4509
4510 /*****************************************************************************/
4511 /* */
4512 /* badsubsegdealloc() Deallocate space for a bad subsegment, marking it */
4513 /* dead. */
4514 /* */
4515 /*****************************************************************************/
4516
4517 #ifndef CDT_ONLY
4518
4519 #ifdef ANSI_DECLARATORS
4520 void badsubsegdealloc(struct mesh *m, struct badsubseg *dyingseg)
4521 #else /* not ANSI_DECLARATORS */
4522 void badsubsegdealloc(m, dyingseg)
4523 struct mesh *m;
4524 struct badsubseg *dyingseg;
4525 #endif /* not ANSI_DECLARATORS */
4526
4527 {
4528 /* Set subsegment's origin to NULL. This makes it possible to detect dead */
4529 /* badsubsegs when traversing the list of all badsubsegs . */
4530 dyingseg->subsegorg = (vertex) NULL;
4531 pooldealloc(&m->badsubsegs, (VOID *) dyingseg);
4532 }
4533
4534 #endif /* not CDT_ONLY */
4535
4536 /*****************************************************************************/
4537 /* */
4538 /* badsubsegtraverse() Traverse the bad subsegments, skipping dead ones. */
4539 /* */
4540 /*****************************************************************************/
4541
4542 #ifndef CDT_ONLY
4543
4544 #ifdef ANSI_DECLARATORS
4545 struct badsubseg *badsubsegtraverse(struct mesh *m)
4546 #else /* not ANSI_DECLARATORS */
4547 struct badsubseg *badsubsegtraverse(m)
4548 struct mesh *m;
4549 #endif /* not ANSI_DECLARATORS */
4550
4551 {
4552 struct badsubseg *newseg;
4553
4554 do {
4555 newseg = (struct badsubseg *) traverse(&m->badsubsegs);
4556 if (newseg == (struct badsubseg *) NULL) {
4557 return (struct badsubseg *) NULL;
4558 }
4559 } while (newseg->subsegorg == (vertex) NULL); /* Skip dead ones. */
4560 return newseg;
4561 }
4562
4563 #endif /* not CDT_ONLY */
4564
4565 /*****************************************************************************/
4566 /* */
4567 /* getvertex() Get a specific vertex, by number, from the list. */
4568 /* */
4569 /* The first vertex is number 'firstnumber'. */
4570 /* */
4571 /* Note that this takes O(n) time (with a small constant, if VERTEXPERBLOCK */
4572 /* is large). I don't care to take the trouble to make it work in constant */
4573 /* time. */
4574 /* */
4575 /*****************************************************************************/
4576
4577 #ifdef ANSI_DECLARATORS
4578 vertex getvertex(struct mesh *m, struct behavior *b, int number)
4579 #else /* not ANSI_DECLARATORS */
4580 vertex getvertex(m, b, number)
4581 struct mesh *m;
4582 struct behavior *b;
4583 int number;
4584 #endif /* not ANSI_DECLARATORS */
4585
4586 {
4587 VOID **getblock;
4588 char *foundvertex;
4589 unsigned long alignptr;
4590 int current;
4591
4592 getblock = m->vertices.firstblock;
4593 current = b->firstnumber;
4594
4595 /* Find the right block. */
4596 if (current + m->vertices.itemsfirstblock <= number) {
4597 getblock = (VOID **) *getblock;
4598 current += m->vertices.itemsfirstblock;
4599 while (current + m->vertices.itemsperblock <= number) {
4600 getblock = (VOID **) *getblock;
4601 current += m->vertices.itemsperblock;
4602 }
4603 }
4604
4605 /* Now find the right vertex. */
4606 alignptr = (unsigned long) (getblock + 1);
4607 foundvertex = (char *) (alignptr + (unsigned long) m->vertices.alignbytes -
4608 (alignptr % (unsigned long) m->vertices.alignbytes));
4609 return (vertex) (foundvertex + m->vertices.itembytes * (number - current));
4610 }
4611
4612 /*****************************************************************************/
4613 /* */
4614 /* triangledeinit() Free all remaining allocated memory. */
4615 /* */
4616 /*****************************************************************************/
4617
4618 #ifdef ANSI_DECLARATORS
4619 void triangledeinit(struct mesh *m, struct behavior *b)
4620 #else /* not ANSI_DECLARATORS */
4621 void triangledeinit(m, b)
4622 struct mesh *m;
4623 struct behavior *b;
4624 #endif /* not ANSI_DECLARATORS */
4625
4626 {
4627 pooldeinit(&m->triangles);
4628 trifree((VOID *) m->dummytribase);
4629 if (b->usesegments) {
4630 pooldeinit(&m->subsegs);
4631 trifree((VOID *) m->dummysubbase);
4632 }
4633 pooldeinit(&m->vertices);
4634 #ifndef CDT_ONLY
4635 if (b->quality) {
4636 pooldeinit(&m->badsubsegs);
4637 if ((b->minangle > 0.0) || b->vararea || b->fixedarea || b->usertest) {
4638 pooldeinit(&m->badtriangles);
4639 pooldeinit(&m->flipstackers);
4640 }
4641 }
4642 #endif /* not CDT_ONLY */
4643 }
4644
4645 /** **/
4646 /** **/
4647 /********* Memory management routines end here *********/
4648
4649 /********* Constructors begin here *********/
4650 /** **/
4651 /** **/
4652
4653 /*****************************************************************************/
4654 /* */
4655 /* maketriangle() Create a new triangle with orientation zero. */
4656 /* */
4657 /*****************************************************************************/
4658
4659 #ifdef ANSI_DECLARATORS
4660 void maketriangle(struct mesh *m, struct behavior *b, struct otri *newotri)
4661 #else /* not ANSI_DECLARATORS */
4662 void maketriangle(m, b, newotri)
4663 struct mesh *m;
4664 struct behavior *b;
4665 struct otri *newotri;
4666 #endif /* not ANSI_DECLARATORS */
4667
4668 {
4669 int i;
4670
4671 newotri->tri = (triangle *) poolalloc(&m->triangles);
4672 /* Initialize the three adjoining triangles to be "outer space". */
4673 newotri->tri[0] = (triangle) m->dummytri;
4674 newotri->tri[1] = (triangle) m->dummytri;
4675 newotri->tri[2] = (triangle) m->dummytri;
4676 /* Three NULL vertices. */
4677 newotri->tri[3] = (triangle) NULL;
4678 newotri->tri[4] = (triangle) NULL;
4679 newotri->tri[5] = (triangle) NULL;
4680 if (b->usesegments) {
4681 /* Initialize the three adjoining subsegments to be the omnipresent */
4682 /* subsegment. */
4683 newotri->tri[6] = (triangle) m->dummysub;
4684 newotri->tri[7] = (triangle) m->dummysub;
4685 newotri->tri[8] = (triangle) m->dummysub;
4686 }
4687 for (i = 0; i < m->eextras; i++) {
4688 setelemattribute(*newotri, i, 0.0);
4689 }
4690 if (b->vararea) {
4691 setareabound(*newotri, -1.0);
4692 }
4693
4694 newotri->orient = 0;
4695 }
4696
4697 /*****************************************************************************/
4698 /* */
4699 /* makesubseg() Create a new subsegment with orientation zero. */
4700 /* */
4701 /*****************************************************************************/
4702
4703 #ifdef ANSI_DECLARATORS
4704 void makesubseg(struct mesh *m, struct osub *newsubseg)
4705 #else /* not ANSI_DECLARATORS */
4706 void makesubseg(m, newsubseg)
4707 struct mesh *m;
4708 struct osub *newsubseg;
4709 #endif /* not ANSI_DECLARATORS */
4710
4711 {
4712 newsubseg->ss = (subseg *) poolalloc(&m->subsegs);
4713 /* Initialize the two adjoining subsegments to be the omnipresent */
4714 /* subsegment. */
4715 newsubseg->ss[0] = (subseg) m->dummysub;
4716 newsubseg->ss[1] = (subseg) m->dummysub;
4717 /* Four NULL vertices. */
4718 newsubseg->ss[2] = (subseg) NULL;
4719 newsubseg->ss[3] = (subseg) NULL;
4720 newsubseg->ss[4] = (subseg) NULL;
4721 newsubseg->ss[5] = (subseg) NULL;
4722 /* Initialize the two adjoining triangles to be "outer space." */
4723 newsubseg->ss[6] = (subseg) m->dummytri;
4724 newsubseg->ss[7] = (subseg) m->dummytri;
4725 /* Set the boundary marker to zero. */
4726 setmark(*newsubseg, 0);
4727
4728 newsubseg->ssorient = 0;
4729 }
4730
4731 /** **/
4732 /** **/
4733 /********* Constructors end here *********/
4734
4735 /********* Geometric primitives begin here *********/
4736 /** **/
4737 /** **/
4738
4739 /* The adaptive exact arithmetic geometric predicates implemented herein are */
4740 /* described in detail in my paper, "Adaptive Precision Floating-Point */
4741 /* Arithmetic and Fast Robust Geometric Predicates." See the header for a */
4742 /* full citation. */
4743
4744 /* Which of the following two methods of finding the absolute values is */
4745 /* fastest is compiler-dependent. A few compilers can inline and optimize */
4746 /* the fabs() call; but most will incur the overhead of a function call, */
4747 /* which is disastrously slow. A faster way on IEEE machines might be to */
4748 /* mask the appropriate bit, but that's difficult to do in C without */
4749 /* forcing the value to be stored to memory (rather than be kept in the */
4750 /* register to which the optimizer assigned it). */
4751
4752 #define Absolute(a) ((a) >= 0.0 ? (a) : -(a))
4753 /* #define Absolute(a) fabs(a) */
4754
4755 /* Many of the operations are broken up into two pieces, a main part that */
4756 /* performs an approximate operation, and a "tail" that computes the */
4757 /* roundoff error of that operation. */
4758 /* */
4759 /* The operations Fast_Two_Sum(), Fast_Two_Diff(), Two_Sum(), Two_Diff(), */
4760 /* Split(), and Two_Product() are all implemented as described in the */
4761 /* reference. Each of these macros requires certain variables to be */
4762 /* defined in the calling routine. The variables `bvirt', `c', `abig', */
4763 /* `_i', `_j', `_k', `_l', `_m', and `_n' are declared `INEXACT' because */
4764 /* they store the result of an operation that may incur roundoff error. */
4765 /* The input parameter `x' (or the highest numbered `x_' parameter) must */
4766 /* also be declared `INEXACT'. */
4767
4768 #define Fast_Two_Sum_Tail(a, b, x, y) \
4769 bvirt = x - a; \
4770 y = b - bvirt
4771
4772 #define Fast_Two_Sum(a, b, x, y) \
4773 x = (REAL) (a + b); \
4774 Fast_Two_Sum_Tail(a, b, x, y)
4775
4776 #define Two_Sum_Tail(a, b, x, y) \
4777 bvirt = (REAL) (x - a); \
4778 avirt = x - bvirt; \
4779 bround = b - bvirt; \
4780 around = a - avirt; \
4781 y = around + bround
4782
4783 #define Two_Sum(a, b, x, y) \
4784 x = (REAL) (a + b); \
4785 Two_Sum_Tail(a, b, x, y)
4786
4787 #define Two_Diff_Tail(a, b, x, y) \
4788 bvirt = (REAL) (a - x); \
4789 avirt = x + bvirt; \
4790 bround = bvirt - b; \
4791 around = a - avirt; \
4792 y = around + bround
4793
4794 #define Two_Diff(a, b, x, y) \
4795 x = (REAL) (a - b); \
4796 Two_Diff_Tail(a, b, x, y)
4797
4798 #define Split(a, ahi, alo) \
4799 c = (REAL) (splitter * a); \
4800 abig = (REAL) (c - a); \
4801 ahi = c - abig; \
4802 alo = a - ahi
4803
4804 #define Two_Product_Tail(a, b, x, y) \
4805 Split(a, ahi, alo); \
4806 Split(b, bhi, blo); \
4807 err1 = x - (ahi * bhi); \
4808 err2 = err1 - (alo * bhi); \
4809 err3 = err2 - (ahi * blo); \
4810 y = (alo * blo) - err3
4811
4812 #define Two_Product(a, b, x, y) \
4813 x = (REAL) (a * b); \
4814 Two_Product_Tail(a, b, x, y)
4815
4816 /* Two_Product_Presplit() is Two_Product() where one of the inputs has */
4817 /* already been split. Avoids redundant splitting. */
4818
4819 #define Two_Product_Presplit(a, b, bhi, blo, x, y) \
4820 x = (REAL) (a * b); \
4821 Split(a, ahi, alo); \
4822 err1 = x - (ahi * bhi); \
4823 err2 = err1 - (alo * bhi); \
4824 err3 = err2 - (ahi * blo); \
4825 y = (alo * blo) - err3
4826
4827 /* Square() can be done more quickly than Two_Product(). */
4828
4829 #define Square_Tail(a, x, y) \
4830 Split(a, ahi, alo); \
4831 err1 = x - (ahi * ahi); \
4832 err3 = err1 - ((ahi + ahi) * alo); \
4833 y = (alo * alo) - err3
4834
4835 #define Square(a, x, y) \
4836 x = (REAL) (a * a); \
4837 Square_Tail(a, x, y)
4838
4839 /* Macros for summing expansions of various fixed lengths. These are all */
4840 /* unrolled versions of Expansion_Sum(). */
4841
4842 #define Two_One_Sum(a1, a0, b, x2, x1, x0) \
4843 Two_Sum(a0, b , _i, x0); \
4844 Two_Sum(a1, _i, x2, x1)
4845
4846 #define Two_One_Diff(a1, a0, b, x2, x1, x0) \
4847 Two_Diff(a0, b , _i, x0); \
4848 Two_Sum( a1, _i, x2, x1)
4849
4850 #define Two_Two_Sum(a1, a0, b1, b0, x3, x2, x1, x0) \
4851 Two_One_Sum(a1, a0, b0, _j, _0, x0); \
4852 Two_One_Sum(_j, _0, b1, x3, x2, x1)
4853
4854 #define Two_Two_Diff(a1, a0, b1, b0, x3, x2, x1, x0) \
4855 Two_One_Diff(a1, a0, b0, _j, _0, x0); \
4856 Two_One_Diff(_j, _0, b1, x3, x2, x1)
4857
4858 /* Macro for multiplying a two-component expansion by a single component. */
4859
4860 #define Two_One_Product(a1, a0, b, x3, x2, x1, x0) \
4861 Split(b, bhi, blo); \
4862 Two_Product_Presplit(a0, b, bhi, blo, _i, x0); \
4863 Two_Product_Presplit(a1, b, bhi, blo, _j, _0); \
4864 Two_Sum(_i, _0, _k, x1); \
4865 Fast_Two_Sum(_j, _k, x3, x2)
4866
4867 /*****************************************************************************/
4868 /* */
4869 /* exactinit() Initialize the variables used for exact arithmetic. */
4870 /* */
4871 /* `epsilon' is the largest power of two such that 1.0 + epsilon = 1.0 in */
4872 /* floating-point arithmetic. `epsilon' bounds the relative roundoff */
4873 /* error. It is used for floating-point error analysis. */
4874 /* */
4875 /* `splitter' is used to split floating-point numbers into two half- */
4876 /* length significands for exact multiplication. */
4877 /* */
4878 /* I imagine that a highly optimizing compiler might be too smart for its */
4879 /* own good, and somehow cause this routine to fail, if it pretends that */
4880 /* floating-point arithmetic is too much like real arithmetic. */
4881 /* */
4882 /* Don't change this routine unless you fully understand it. */
4883 /* */
4884 /*****************************************************************************/
4885
exactinit()4886 void exactinit()
4887 {
4888 REAL half;
4889 REAL check, lastcheck;
4890 int every_other;
4891 #ifdef LINUX
4892 int cword;
4893 #endif /* LINUX */
4894
4895 #ifdef CPU86
4896 #ifdef SINGLE
4897 _control87(_PC_24, _MCW_PC); /* Set FPU control word for single precision. */
4898 #else /* not SINGLE */
4899 _control87(_PC_53, _MCW_PC); /* Set FPU control word for double precision. */
4900 #endif /* not SINGLE */
4901 #endif /* CPU86 */
4902 #ifdef LINUX
4903 #ifdef SINGLE
4904 /* cword = 4223; */
4905 cword = 4210; /* set FPU control word for single precision */
4906 #else /* not SINGLE */
4907 /* cword = 4735; */
4908 cword = 4722; /* set FPU control word for double precision */
4909 #endif /* not SINGLE */
4910 _FPU_SETCW(cword);
4911 #endif /* LINUX */
4912
4913 every_other = 1;
4914 half = 0.5;
4915 epsilon = 1.0;
4916 splitter = 1.0;
4917 check = 1.0;
4918 /* Repeatedly divide `epsilon' by two until it is too small to add to */
4919 /* one without causing roundoff. (Also check if the sum is equal to */
4920 /* the previous sum, for machines that round up instead of using exact */
4921 /* rounding. Not that these routines will work on such machines.) */
4922 do {
4923 lastcheck = check;
4924 epsilon *= half;
4925 if (every_other) {
4926 splitter *= 2.0;
4927 }
4928 every_other = !every_other;
4929 check = 1.0 + epsilon;
4930 } while ((check != 1.0) && (check != lastcheck));
4931 splitter += 1.0;
4932 /* Error bounds for orientation and incircle tests. */
4933 resulterrbound = (3.0 + 8.0 * epsilon) * epsilon;
4934 ccwerrboundA = (3.0 + 16.0 * epsilon) * epsilon;
4935 ccwerrboundB = (2.0 + 12.0 * epsilon) * epsilon;
4936 ccwerrboundC = (9.0 + 64.0 * epsilon) * epsilon * epsilon;
4937 iccerrboundA = (10.0 + 96.0 * epsilon) * epsilon;
4938 iccerrboundB = (4.0 + 48.0 * epsilon) * epsilon;
4939 iccerrboundC = (44.0 + 576.0 * epsilon) * epsilon * epsilon;
4940 o3derrboundA = (7.0 + 56.0 * epsilon) * epsilon;
4941 o3derrboundB = (3.0 + 28.0 * epsilon) * epsilon;
4942 o3derrboundC = (26.0 + 288.0 * epsilon) * epsilon * epsilon;
4943 }
4944
4945 /*****************************************************************************/
4946 /* */
4947 /* fast_expansion_sum_zeroelim() Sum two expansions, eliminating zero */
4948 /* components from the output expansion. */
4949 /* */
4950 /* Sets h = e + f. See my Robust Predicates paper for details. */
4951 /* */
4952 /* If round-to-even is used (as with IEEE 754), maintains the strongly */
4953 /* nonoverlapping property. (That is, if e is strongly nonoverlapping, h */
4954 /* will be also.) Does NOT maintain the nonoverlapping or nonadjacent */
4955 /* properties. */
4956 /* */
4957 /*****************************************************************************/
4958
4959 #ifdef ANSI_DECLARATORS
4960 int fast_expansion_sum_zeroelim(int elen, REAL *e, int flen, REAL *f, REAL *h)
4961 #else /* not ANSI_DECLARATORS */
4962 int fast_expansion_sum_zeroelim(elen, e, flen, f, h) /* h cannot be e or f. */
4963 int elen;
4964 REAL *e;
4965 int flen;
4966 REAL *f;
4967 REAL *h;
4968 #endif /* not ANSI_DECLARATORS */
4969
4970 {
4971 REAL Q;
4972 INEXACT REAL Qnew;
4973 INEXACT REAL hh;
4974 INEXACT REAL bvirt;
4975 REAL avirt, bround, around;
4976 int eindex, findex, hindex;
4977 REAL enow, fnow;
4978
4979 enow = e[0];
4980 fnow = f[0];
4981 eindex = findex = 0;
4982 if ((fnow > enow) == (fnow > -enow)) {
4983 Q = enow;
4984 enow = e[++eindex];
4985 } else {
4986 Q = fnow;
4987 fnow = f[++findex];
4988 }
4989 hindex = 0;
4990 if ((eindex < elen) && (findex < flen)) {
4991 if ((fnow > enow) == (fnow > -enow)) {
4992 Fast_Two_Sum(enow, Q, Qnew, hh);
4993 enow = e[++eindex];
4994 } else {
4995 Fast_Two_Sum(fnow, Q, Qnew, hh);
4996 fnow = f[++findex];
4997 }
4998 Q = Qnew;
4999 if (hh != 0.0) {
5000 h[hindex++] = hh;
5001 }
5002 while ((eindex < elen) && (findex < flen)) {
5003 if ((fnow > enow) == (fnow > -enow)) {
5004 Two_Sum(Q, enow, Qnew, hh);
5005 enow = e[++eindex];
5006 } else {
5007 Two_Sum(Q, fnow, Qnew, hh);
5008 fnow = f[++findex];
5009 }
5010 Q = Qnew;
5011 if (hh != 0.0) {
5012 h[hindex++] = hh;
5013 }
5014 }
5015 }
5016 while (eindex < elen) {
5017 Two_Sum(Q, enow, Qnew, hh);
5018 enow = e[++eindex];
5019 Q = Qnew;
5020 if (hh != 0.0) {
5021 h[hindex++] = hh;
5022 }
5023 }
5024 while (findex < flen) {
5025 Two_Sum(Q, fnow, Qnew, hh);
5026 fnow = f[++findex];
5027 Q = Qnew;
5028 if (hh != 0.0) {
5029 h[hindex++] = hh;
5030 }
5031 }
5032 if ((Q != 0.0) || (hindex == 0)) {
5033 h[hindex++] = Q;
5034 }
5035 return hindex;
5036 }
5037
5038 /*****************************************************************************/
5039 /* */
5040 /* scale_expansion_zeroelim() Multiply an expansion by a scalar, */
5041 /* eliminating zero components from the */
5042 /* output expansion. */
5043 /* */
5044 /* Sets h = be. See my Robust Predicates paper for details. */
5045 /* */
5046 /* Maintains the nonoverlapping property. If round-to-even is used (as */
5047 /* with IEEE 754), maintains the strongly nonoverlapping and nonadjacent */
5048 /* properties as well. (That is, if e has one of these properties, so */
5049 /* will h.) */
5050 /* */
5051 /*****************************************************************************/
5052
5053 #ifdef ANSI_DECLARATORS
5054 int scale_expansion_zeroelim(int elen, REAL *e, REAL b, REAL *h)
5055 #else /* not ANSI_DECLARATORS */
5056 int scale_expansion_zeroelim(elen, e, b, h) /* e and h cannot be the same. */
5057 int elen;
5058 REAL *e;
5059 REAL b;
5060 REAL *h;
5061 #endif /* not ANSI_DECLARATORS */
5062
5063 {
5064 INEXACT REAL Q, sum;
5065 REAL hh;
5066 INEXACT REAL product1;
5067 REAL product0;
5068 int eindex, hindex;
5069 REAL enow;
5070 INEXACT REAL bvirt;
5071 REAL avirt, bround, around;
5072 INEXACT REAL c;
5073 INEXACT REAL abig;
5074 REAL ahi, alo, bhi, blo;
5075 REAL err1, err2, err3;
5076
5077 Split(b, bhi, blo);
5078 Two_Product_Presplit(e[0], b, bhi, blo, Q, hh);
5079 hindex = 0;
5080 if (hh != 0) {
5081 h[hindex++] = hh;
5082 }
5083 for (eindex = 1; eindex < elen; eindex++) {
5084 enow = e[eindex];
5085 Two_Product_Presplit(enow, b, bhi, blo, product1, product0);
5086 Two_Sum(Q, product0, sum, hh);
5087 if (hh != 0) {
5088 h[hindex++] = hh;
5089 }
5090 Fast_Two_Sum(product1, sum, Q, hh);
5091 if (hh != 0) {
5092 h[hindex++] = hh;
5093 }
5094 }
5095 if ((Q != 0.0) || (hindex == 0)) {
5096 h[hindex++] = Q;
5097 }
5098 return hindex;
5099 }
5100
5101 /*****************************************************************************/
5102 /* */
5103 /* estimate() Produce a one-word estimate of an expansion's value. */
5104 /* */
5105 /* See my Robust Predicates paper for details. */
5106 /* */
5107 /*****************************************************************************/
5108
5109 #ifdef ANSI_DECLARATORS
5110 REAL estimate(int elen, REAL *e)
5111 #else /* not ANSI_DECLARATORS */
5112 REAL estimate(elen, e)
5113 int elen;
5114 REAL *e;
5115 #endif /* not ANSI_DECLARATORS */
5116
5117 {
5118 REAL Q;
5119 int eindex;
5120
5121 Q = e[0];
5122 for (eindex = 1; eindex < elen; eindex++) {
5123 Q += e[eindex];
5124 }
5125 return Q;
5126 }
5127
5128 /*****************************************************************************/
5129 /* */
5130 /* counterclockwise() Return a positive value if the points pa, pb, and */
5131 /* pc occur in counterclockwise order; a negative */
5132 /* value if they occur in clockwise order; and zero */
5133 /* if they are collinear. The result is also a rough */
5134 /* approximation of twice the signed area of the */
5135 /* triangle defined by the three points. */
5136 /* */
5137 /* Uses exact arithmetic if necessary to ensure a correct answer. The */
5138 /* result returned is the determinant of a matrix. This determinant is */
5139 /* computed adaptively, in the sense that exact arithmetic is used only to */
5140 /* the degree it is needed to ensure that the returned value has the */
5141 /* correct sign. Hence, this function is usually quite fast, but will run */
5142 /* more slowly when the input points are collinear or nearly so. */
5143 /* */
5144 /* See my Robust Predicates paper for details. */
5145 /* */
5146 /*****************************************************************************/
5147
5148 #ifdef ANSI_DECLARATORS
5149 REAL counterclockwiseadapt(vertex pa, vertex pb, vertex pc, REAL detsum)
5150 #else /* not ANSI_DECLARATORS */
5151 REAL counterclockwiseadapt(pa, pb, pc, detsum)
5152 vertex pa;
5153 vertex pb;
5154 vertex pc;
5155 REAL detsum;
5156 #endif /* not ANSI_DECLARATORS */
5157
5158 {
5159 INEXACT REAL acx, acy, bcx, bcy;
5160 REAL acxtail, acytail, bcxtail, bcytail;
5161 INEXACT REAL detleft, detright;
5162 REAL detlefttail, detrighttail;
5163 REAL det, errbound;
5164 REAL B[4], C1[8], C2[12], D[16];
5165 INEXACT REAL B3;
5166 int C1length, C2length, Dlength;
5167 REAL u[4];
5168 INEXACT REAL u3;
5169 INEXACT REAL s1, t1;
5170 REAL s0, t0;
5171
5172 INEXACT REAL bvirt;
5173 REAL avirt, bround, around;
5174 INEXACT REAL c;
5175 INEXACT REAL abig;
5176 REAL ahi, alo, bhi, blo;
5177 REAL err1, err2, err3;
5178 INEXACT REAL _i, _j;
5179 REAL _0;
5180
5181 acx = (REAL) (pa[0] - pc[0]);
5182 bcx = (REAL) (pb[0] - pc[0]);
5183 acy = (REAL) (pa[1] - pc[1]);
5184 bcy = (REAL) (pb[1] - pc[1]);
5185
5186 Two_Product(acx, bcy, detleft, detlefttail);
5187 Two_Product(acy, bcx, detright, detrighttail);
5188
5189 Two_Two_Diff(detleft, detlefttail, detright, detrighttail,
5190 B3, B[2], B[1], B[0]);
5191 B[3] = B3;
5192
5193 det = estimate(4, B);
5194 errbound = ccwerrboundB * detsum;
5195 if ((det >= errbound) || (-det >= errbound)) {
5196 return det;
5197 }
5198
5199 Two_Diff_Tail(pa[0], pc[0], acx, acxtail);
5200 Two_Diff_Tail(pb[0], pc[0], bcx, bcxtail);
5201 Two_Diff_Tail(pa[1], pc[1], acy, acytail);
5202 Two_Diff_Tail(pb[1], pc[1], bcy, bcytail);
5203
5204 if ((acxtail == 0.0) && (acytail == 0.0)
5205 && (bcxtail == 0.0) && (bcytail == 0.0)) {
5206 return det;
5207 }
5208
5209 errbound = ccwerrboundC * detsum + resulterrbound * Absolute(det);
5210 det += (acx * bcytail + bcy * acxtail)
5211 - (acy * bcxtail + bcx * acytail);
5212 if ((det >= errbound) || (-det >= errbound)) {
5213 return det;
5214 }
5215
5216 Two_Product(acxtail, bcy, s1, s0);
5217 Two_Product(acytail, bcx, t1, t0);
5218 Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
5219 u[3] = u3;
5220 C1length = fast_expansion_sum_zeroelim(4, B, 4, u, C1);
5221
5222 Two_Product(acx, bcytail, s1, s0);
5223 Two_Product(acy, bcxtail, t1, t0);
5224 Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
5225 u[3] = u3;
5226 C2length = fast_expansion_sum_zeroelim(C1length, C1, 4, u, C2);
5227
5228 Two_Product(acxtail, bcytail, s1, s0);
5229 Two_Product(acytail, bcxtail, t1, t0);
5230 Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
5231 u[3] = u3;
5232 Dlength = fast_expansion_sum_zeroelim(C2length, C2, 4, u, D);
5233
5234 return(D[Dlength - 1]);
5235 }
5236
5237 #ifdef ANSI_DECLARATORS
5238 REAL counterclockwise(struct mesh *m, struct behavior *b,
5239 vertex pa, vertex pb, vertex pc)
5240 #else /* not ANSI_DECLARATORS */
5241 REAL counterclockwise(m, b, pa, pb, pc)
5242 struct mesh *m;
5243 struct behavior *b;
5244 vertex pa;
5245 vertex pb;
5246 vertex pc;
5247 #endif /* not ANSI_DECLARATORS */
5248
5249 {
5250 REAL detleft, detright, det;
5251 REAL detsum, errbound;
5252
5253 m->counterclockcount++;
5254
5255 detleft = (pa[0] - pc[0]) * (pb[1] - pc[1]);
5256 detright = (pa[1] - pc[1]) * (pb[0] - pc[0]);
5257 det = detleft - detright;
5258
5259 if (b->noexact) {
5260 return det;
5261 }
5262
5263 if (detleft > 0.0) {
5264 if (detright <= 0.0) {
5265 return det;
5266 } else {
5267 detsum = detleft + detright;
5268 }
5269 } else if (detleft < 0.0) {
5270 if (detright >= 0.0) {
5271 return det;
5272 } else {
5273 detsum = -detleft - detright;
5274 }
5275 } else {
5276 return det;
5277 }
5278
5279 errbound = ccwerrboundA * detsum;
5280 if ((det >= errbound) || (-det >= errbound)) {
5281 return det;
5282 }
5283
5284 return counterclockwiseadapt(pa, pb, pc, detsum);
5285 }
5286
5287 /*****************************************************************************/
5288 /* */
5289 /* incircle() Return a positive value if the point pd lies inside the */
5290 /* circle passing through pa, pb, and pc; a negative value if */
5291 /* it lies outside; and zero if the four points are cocircular.*/
5292 /* The points pa, pb, and pc must be in counterclockwise */
5293 /* order, or the sign of the result will be reversed. */
5294 /* */
5295 /* Uses exact arithmetic if necessary to ensure a correct answer. The */
5296 /* result returned is the determinant of a matrix. This determinant is */
5297 /* computed adaptively, in the sense that exact arithmetic is used only to */
5298 /* the degree it is needed to ensure that the returned value has the */
5299 /* correct sign. Hence, this function is usually quite fast, but will run */
5300 /* more slowly when the input points are cocircular or nearly so. */
5301 /* */
5302 /* See my Robust Predicates paper for details. */
5303 /* */
5304 /*****************************************************************************/
5305
5306 #ifdef ANSI_DECLARATORS
5307 REAL incircleadapt(vertex pa, vertex pb, vertex pc, vertex pd, REAL permanent)
5308 #else /* not ANSI_DECLARATORS */
5309 REAL incircleadapt(pa, pb, pc, pd, permanent)
5310 vertex pa;
5311 vertex pb;
5312 vertex pc;
5313 vertex pd;
5314 REAL permanent;
5315 #endif /* not ANSI_DECLARATORS */
5316
5317 {
5318 INEXACT REAL adx, bdx, cdx, ady, bdy, cdy;
5319 REAL det, errbound;
5320
5321 INEXACT REAL bdxcdy1, cdxbdy1, cdxady1, adxcdy1, adxbdy1, bdxady1;
5322 REAL bdxcdy0, cdxbdy0, cdxady0, adxcdy0, adxbdy0, bdxady0;
5323 REAL bc[4], ca[4], ab[4];
5324 INEXACT REAL bc3, ca3, ab3;
5325 REAL axbc[8], axxbc[16], aybc[8], ayybc[16], adet[32];
5326 int axbclen, axxbclen, aybclen, ayybclen, alen;
5327 REAL bxca[8], bxxca[16], byca[8], byyca[16], bdet[32];
5328 int bxcalen, bxxcalen, bycalen, byycalen, blen;
5329 REAL cxab[8], cxxab[16], cyab[8], cyyab[16], cdet[32];
5330 int cxablen, cxxablen, cyablen, cyyablen, clen;
5331 REAL abdet[64];
5332 int ablen;
5333 REAL fin1[1152], fin2[1152];
5334 REAL *finnow, *finother, *finswap;
5335 int finlength;
5336
5337 REAL adxtail, bdxtail, cdxtail, adytail, bdytail, cdytail;
5338 INEXACT REAL adxadx1, adyady1, bdxbdx1, bdybdy1, cdxcdx1, cdycdy1;
5339 REAL adxadx0, adyady0, bdxbdx0, bdybdy0, cdxcdx0, cdycdy0;
5340 REAL aa[4], bb[4], cc[4];
5341 INEXACT REAL aa3, bb3, cc3;
5342 INEXACT REAL ti1, tj1;
5343 REAL ti0, tj0;
5344 REAL u[4], v[4];
5345 INEXACT REAL u3, v3;
5346 REAL temp8[8], temp16a[16], temp16b[16], temp16c[16];
5347 REAL temp32a[32], temp32b[32], temp48[48], temp64[64];
5348 int temp8len, temp16alen, temp16blen, temp16clen;
5349 int temp32alen, temp32blen, temp48len, temp64len;
5350 REAL axtbb[8], axtcc[8], aytbb[8], aytcc[8];
5351 int axtbblen, axtcclen, aytbblen, aytcclen;
5352 REAL bxtaa[8], bxtcc[8], bytaa[8], bytcc[8];
5353 int bxtaalen, bxtcclen, bytaalen, bytcclen;
5354 REAL cxtaa[8], cxtbb[8], cytaa[8], cytbb[8];
5355 int cxtaalen, cxtbblen, cytaalen, cytbblen;
5356 REAL axtbc[8], aytbc[8], bxtca[8], bytca[8], cxtab[8], cytab[8];
5357 int axtbclen, aytbclen, bxtcalen, bytcalen, cxtablen, cytablen;
5358 REAL axtbct[16], aytbct[16], bxtcat[16], bytcat[16], cxtabt[16], cytabt[16];
5359 int axtbctlen, aytbctlen, bxtcatlen, bytcatlen, cxtabtlen, cytabtlen;
5360 REAL axtbctt[8], aytbctt[8], bxtcatt[8];
5361 REAL bytcatt[8], cxtabtt[8], cytabtt[8];
5362 int axtbcttlen, aytbcttlen, bxtcattlen, bytcattlen, cxtabttlen, cytabttlen;
5363 REAL abt[8], bct[8], cat[8];
5364 int abtlen, bctlen, catlen;
5365 REAL abtt[4], bctt[4], catt[4];
5366 int abttlen, bcttlen, cattlen;
5367 INEXACT REAL abtt3, bctt3, catt3;
5368 REAL negate;
5369
5370 INEXACT REAL bvirt;
5371 REAL avirt, bround, around;
5372 INEXACT REAL c;
5373 INEXACT REAL abig;
5374 REAL ahi, alo, bhi, blo;
5375 REAL err1, err2, err3;
5376 INEXACT REAL _i, _j;
5377 REAL _0;
5378
5379 adx = (REAL) (pa[0] - pd[0]);
5380 bdx = (REAL) (pb[0] - pd[0]);
5381 cdx = (REAL) (pc[0] - pd[0]);
5382 ady = (REAL) (pa[1] - pd[1]);
5383 bdy = (REAL) (pb[1] - pd[1]);
5384 cdy = (REAL) (pc[1] - pd[1]);
5385
5386 Two_Product(bdx, cdy, bdxcdy1, bdxcdy0);
5387 Two_Product(cdx, bdy, cdxbdy1, cdxbdy0);
5388 Two_Two_Diff(bdxcdy1, bdxcdy0, cdxbdy1, cdxbdy0, bc3, bc[2], bc[1], bc[0]);
5389 bc[3] = bc3;
5390 axbclen = scale_expansion_zeroelim(4, bc, adx, axbc);
5391 axxbclen = scale_expansion_zeroelim(axbclen, axbc, adx, axxbc);
5392 aybclen = scale_expansion_zeroelim(4, bc, ady, aybc);
5393 ayybclen = scale_expansion_zeroelim(aybclen, aybc, ady, ayybc);
5394 alen = fast_expansion_sum_zeroelim(axxbclen, axxbc, ayybclen, ayybc, adet);
5395
5396 Two_Product(cdx, ady, cdxady1, cdxady0);
5397 Two_Product(adx, cdy, adxcdy1, adxcdy0);
5398 Two_Two_Diff(cdxady1, cdxady0, adxcdy1, adxcdy0, ca3, ca[2], ca[1], ca[0]);
5399 ca[3] = ca3;
5400 bxcalen = scale_expansion_zeroelim(4, ca, bdx, bxca);
5401 bxxcalen = scale_expansion_zeroelim(bxcalen, bxca, bdx, bxxca);
5402 bycalen = scale_expansion_zeroelim(4, ca, bdy, byca);
5403 byycalen = scale_expansion_zeroelim(bycalen, byca, bdy, byyca);
5404 blen = fast_expansion_sum_zeroelim(bxxcalen, bxxca, byycalen, byyca, bdet);
5405
5406 Two_Product(adx, bdy, adxbdy1, adxbdy0);
5407 Two_Product(bdx, ady, bdxady1, bdxady0);
5408 Two_Two_Diff(adxbdy1, adxbdy0, bdxady1, bdxady0, ab3, ab[2], ab[1], ab[0]);
5409 ab[3] = ab3;
5410 cxablen = scale_expansion_zeroelim(4, ab, cdx, cxab);
5411 cxxablen = scale_expansion_zeroelim(cxablen, cxab, cdx, cxxab);
5412 cyablen = scale_expansion_zeroelim(4, ab, cdy, cyab);
5413 cyyablen = scale_expansion_zeroelim(cyablen, cyab, cdy, cyyab);
5414 clen = fast_expansion_sum_zeroelim(cxxablen, cxxab, cyyablen, cyyab, cdet);
5415
5416 ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
5417 finlength = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, fin1);
5418
5419 det = estimate(finlength, fin1);
5420 errbound = iccerrboundB * permanent;
5421 if ((det >= errbound) || (-det >= errbound)) {
5422 return det;
5423 }
5424
5425 Two_Diff_Tail(pa[0], pd[0], adx, adxtail);
5426 Two_Diff_Tail(pa[1], pd[1], ady, adytail);
5427 Two_Diff_Tail(pb[0], pd[0], bdx, bdxtail);
5428 Two_Diff_Tail(pb[1], pd[1], bdy, bdytail);
5429 Two_Diff_Tail(pc[0], pd[0], cdx, cdxtail);
5430 Two_Diff_Tail(pc[1], pd[1], cdy, cdytail);
5431 if ((adxtail == 0.0) && (bdxtail == 0.0) && (cdxtail == 0.0)
5432 && (adytail == 0.0) && (bdytail == 0.0) && (cdytail == 0.0)) {
5433 return det;
5434 }
5435
5436 errbound = iccerrboundC * permanent + resulterrbound * Absolute(det);
5437 det += ((adx * adx + ady * ady) * ((bdx * cdytail + cdy * bdxtail)
5438 - (bdy * cdxtail + cdx * bdytail))
5439 + 2.0 * (adx * adxtail + ady * adytail) * (bdx * cdy - bdy * cdx))
5440 + ((bdx * bdx + bdy * bdy) * ((cdx * adytail + ady * cdxtail)
5441 - (cdy * adxtail + adx * cdytail))
5442 + 2.0 * (bdx * bdxtail + bdy * bdytail) * (cdx * ady - cdy * adx))
5443 + ((cdx * cdx + cdy * cdy) * ((adx * bdytail + bdy * adxtail)
5444 - (ady * bdxtail + bdx * adytail))
5445 + 2.0 * (cdx * cdxtail + cdy * cdytail) * (adx * bdy - ady * bdx));
5446 if ((det >= errbound) || (-det >= errbound)) {
5447 return det;
5448 }
5449
5450 finnow = fin1;
5451 finother = fin2;
5452
5453 if ((bdxtail != 0.0) || (bdytail != 0.0)
5454 || (cdxtail != 0.0) || (cdytail != 0.0)) {
5455 Square(adx, adxadx1, adxadx0);
5456 Square(ady, adyady1, adyady0);
5457 Two_Two_Sum(adxadx1, adxadx0, adyady1, adyady0, aa3, aa[2], aa[1], aa[0]);
5458 aa[3] = aa3;
5459 }
5460 if ((cdxtail != 0.0) || (cdytail != 0.0)
5461 || (adxtail != 0.0) || (adytail != 0.0)) {
5462 Square(bdx, bdxbdx1, bdxbdx0);
5463 Square(bdy, bdybdy1, bdybdy0);
5464 Two_Two_Sum(bdxbdx1, bdxbdx0, bdybdy1, bdybdy0, bb3, bb[2], bb[1], bb[0]);
5465 bb[3] = bb3;
5466 }
5467 if ((adxtail != 0.0) || (adytail != 0.0)
5468 || (bdxtail != 0.0) || (bdytail != 0.0)) {
5469 Square(cdx, cdxcdx1, cdxcdx0);
5470 Square(cdy, cdycdy1, cdycdy0);
5471 Two_Two_Sum(cdxcdx1, cdxcdx0, cdycdy1, cdycdy0, cc3, cc[2], cc[1], cc[0]);
5472 cc[3] = cc3;
5473 }
5474
5475 if (adxtail != 0.0) {
5476 axtbclen = scale_expansion_zeroelim(4, bc, adxtail, axtbc);
5477 temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, 2.0 * adx,
5478 temp16a);
5479
5480 axtcclen = scale_expansion_zeroelim(4, cc, adxtail, axtcc);
5481 temp16blen = scale_expansion_zeroelim(axtcclen, axtcc, bdy, temp16b);
5482
5483 axtbblen = scale_expansion_zeroelim(4, bb, adxtail, axtbb);
5484 temp16clen = scale_expansion_zeroelim(axtbblen, axtbb, -cdy, temp16c);
5485
5486 temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5487 temp16blen, temp16b, temp32a);
5488 temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
5489 temp32alen, temp32a, temp48);
5490 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
5491 temp48, finother);
5492 finswap = finnow; finnow = finother; finother = finswap;
5493 }
5494 if (adytail != 0.0) {
5495 aytbclen = scale_expansion_zeroelim(4, bc, adytail, aytbc);
5496 temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, 2.0 * ady,
5497 temp16a);
5498
5499 aytbblen = scale_expansion_zeroelim(4, bb, adytail, aytbb);
5500 temp16blen = scale_expansion_zeroelim(aytbblen, aytbb, cdx, temp16b);
5501
5502 aytcclen = scale_expansion_zeroelim(4, cc, adytail, aytcc);
5503 temp16clen = scale_expansion_zeroelim(aytcclen, aytcc, -bdx, temp16c);
5504
5505 temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5506 temp16blen, temp16b, temp32a);
5507 temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
5508 temp32alen, temp32a, temp48);
5509 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
5510 temp48, finother);
5511 finswap = finnow; finnow = finother; finother = finswap;
5512 }
5513 if (bdxtail != 0.0) {
5514 bxtcalen = scale_expansion_zeroelim(4, ca, bdxtail, bxtca);
5515 temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, 2.0 * bdx,
5516 temp16a);
5517
5518 bxtaalen = scale_expansion_zeroelim(4, aa, bdxtail, bxtaa);
5519 temp16blen = scale_expansion_zeroelim(bxtaalen, bxtaa, cdy, temp16b);
5520
5521 bxtcclen = scale_expansion_zeroelim(4, cc, bdxtail, bxtcc);
5522 temp16clen = scale_expansion_zeroelim(bxtcclen, bxtcc, -ady, temp16c);
5523
5524 temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5525 temp16blen, temp16b, temp32a);
5526 temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
5527 temp32alen, temp32a, temp48);
5528 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
5529 temp48, finother);
5530 finswap = finnow; finnow = finother; finother = finswap;
5531 }
5532 if (bdytail != 0.0) {
5533 bytcalen = scale_expansion_zeroelim(4, ca, bdytail, bytca);
5534 temp16alen = scale_expansion_zeroelim(bytcalen, bytca, 2.0 * bdy,
5535 temp16a);
5536
5537 bytcclen = scale_expansion_zeroelim(4, cc, bdytail, bytcc);
5538 temp16blen = scale_expansion_zeroelim(bytcclen, bytcc, adx, temp16b);
5539
5540 bytaalen = scale_expansion_zeroelim(4, aa, bdytail, bytaa);
5541 temp16clen = scale_expansion_zeroelim(bytaalen, bytaa, -cdx, temp16c);
5542
5543 temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5544 temp16blen, temp16b, temp32a);
5545 temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
5546 temp32alen, temp32a, temp48);
5547 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
5548 temp48, finother);
5549 finswap = finnow; finnow = finother; finother = finswap;
5550 }
5551 if (cdxtail != 0.0) {
5552 cxtablen = scale_expansion_zeroelim(4, ab, cdxtail, cxtab);
5553 temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, 2.0 * cdx,
5554 temp16a);
5555
5556 cxtbblen = scale_expansion_zeroelim(4, bb, cdxtail, cxtbb);
5557 temp16blen = scale_expansion_zeroelim(cxtbblen, cxtbb, ady, temp16b);
5558
5559 cxtaalen = scale_expansion_zeroelim(4, aa, cdxtail, cxtaa);
5560 temp16clen = scale_expansion_zeroelim(cxtaalen, cxtaa, -bdy, temp16c);
5561
5562 temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5563 temp16blen, temp16b, temp32a);
5564 temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
5565 temp32alen, temp32a, temp48);
5566 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
5567 temp48, finother);
5568 finswap = finnow; finnow = finother; finother = finswap;
5569 }
5570 if (cdytail != 0.0) {
5571 cytablen = scale_expansion_zeroelim(4, ab, cdytail, cytab);
5572 temp16alen = scale_expansion_zeroelim(cytablen, cytab, 2.0 * cdy,
5573 temp16a);
5574
5575 cytaalen = scale_expansion_zeroelim(4, aa, cdytail, cytaa);
5576 temp16blen = scale_expansion_zeroelim(cytaalen, cytaa, bdx, temp16b);
5577
5578 cytbblen = scale_expansion_zeroelim(4, bb, cdytail, cytbb);
5579 temp16clen = scale_expansion_zeroelim(cytbblen, cytbb, -adx, temp16c);
5580
5581 temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5582 temp16blen, temp16b, temp32a);
5583 temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
5584 temp32alen, temp32a, temp48);
5585 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
5586 temp48, finother);
5587 finswap = finnow; finnow = finother; finother = finswap;
5588 }
5589
5590 if ((adxtail != 0.0) || (adytail != 0.0)) {
5591 if ((bdxtail != 0.0) || (bdytail != 0.0)
5592 || (cdxtail != 0.0) || (cdytail != 0.0)) {
5593 Two_Product(bdxtail, cdy, ti1, ti0);
5594 Two_Product(bdx, cdytail, tj1, tj0);
5595 Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
5596 u[3] = u3;
5597 negate = -bdy;
5598 Two_Product(cdxtail, negate, ti1, ti0);
5599 negate = -bdytail;
5600 Two_Product(cdx, negate, tj1, tj0);
5601 Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
5602 v[3] = v3;
5603 bctlen = fast_expansion_sum_zeroelim(4, u, 4, v, bct);
5604
5605 Two_Product(bdxtail, cdytail, ti1, ti0);
5606 Two_Product(cdxtail, bdytail, tj1, tj0);
5607 Two_Two_Diff(ti1, ti0, tj1, tj0, bctt3, bctt[2], bctt[1], bctt[0]);
5608 bctt[3] = bctt3;
5609 bcttlen = 4;
5610 } else {
5611 bct[0] = 0.0;
5612 bctlen = 1;
5613 bctt[0] = 0.0;
5614 bcttlen = 1;
5615 }
5616
5617 if (adxtail != 0.0) {
5618 temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, adxtail, temp16a);
5619 axtbctlen = scale_expansion_zeroelim(bctlen, bct, adxtail, axtbct);
5620 temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, 2.0 * adx,
5621 temp32a);
5622 temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5623 temp32alen, temp32a, temp48);
5624 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
5625 temp48, finother);
5626 finswap = finnow; finnow = finother; finother = finswap;
5627 if (bdytail != 0.0) {
5628 temp8len = scale_expansion_zeroelim(4, cc, adxtail, temp8);
5629 temp16alen = scale_expansion_zeroelim(temp8len, temp8, bdytail,
5630 temp16a);
5631 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
5632 temp16a, finother);
5633 finswap = finnow; finnow = finother; finother = finswap;
5634 }
5635 if (cdytail != 0.0) {
5636 temp8len = scale_expansion_zeroelim(4, bb, -adxtail, temp8);
5637 temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail,
5638 temp16a);
5639 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
5640 temp16a, finother);
5641 finswap = finnow; finnow = finother; finother = finswap;
5642 }
5643
5644 temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, adxtail,
5645 temp32a);
5646 axtbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adxtail, axtbctt);
5647 temp16alen = scale_expansion_zeroelim(axtbcttlen, axtbctt, 2.0 * adx,
5648 temp16a);
5649 temp16blen = scale_expansion_zeroelim(axtbcttlen, axtbctt, adxtail,
5650 temp16b);
5651 temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5652 temp16blen, temp16b, temp32b);
5653 temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
5654 temp32blen, temp32b, temp64);
5655 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
5656 temp64, finother);
5657 finswap = finnow; finnow = finother; finother = finswap;
5658 }
5659 if (adytail != 0.0) {
5660 temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, adytail, temp16a);
5661 aytbctlen = scale_expansion_zeroelim(bctlen, bct, adytail, aytbct);
5662 temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, 2.0 * ady,
5663 temp32a);
5664 temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5665 temp32alen, temp32a, temp48);
5666 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
5667 temp48, finother);
5668 finswap = finnow; finnow = finother; finother = finswap;
5669
5670
5671 temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, adytail,
5672 temp32a);
5673 aytbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adytail, aytbctt);
5674 temp16alen = scale_expansion_zeroelim(aytbcttlen, aytbctt, 2.0 * ady,
5675 temp16a);
5676 temp16blen = scale_expansion_zeroelim(aytbcttlen, aytbctt, adytail,
5677 temp16b);
5678 temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5679 temp16blen, temp16b, temp32b);
5680 temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
5681 temp32blen, temp32b, temp64);
5682 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
5683 temp64, finother);
5684 finswap = finnow; finnow = finother; finother = finswap;
5685 }
5686 }
5687 if ((bdxtail != 0.0) || (bdytail != 0.0)) {
5688 if ((cdxtail != 0.0) || (cdytail != 0.0)
5689 || (adxtail != 0.0) || (adytail != 0.0)) {
5690 Two_Product(cdxtail, ady, ti1, ti0);
5691 Two_Product(cdx, adytail, tj1, tj0);
5692 Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
5693 u[3] = u3;
5694 negate = -cdy;
5695 Two_Product(adxtail, negate, ti1, ti0);
5696 negate = -cdytail;
5697 Two_Product(adx, negate, tj1, tj0);
5698 Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
5699 v[3] = v3;
5700 catlen = fast_expansion_sum_zeroelim(4, u, 4, v, cat);
5701
5702 Two_Product(cdxtail, adytail, ti1, ti0);
5703 Two_Product(adxtail, cdytail, tj1, tj0);
5704 Two_Two_Diff(ti1, ti0, tj1, tj0, catt3, catt[2], catt[1], catt[0]);
5705 catt[3] = catt3;
5706 cattlen = 4;
5707 } else {
5708 cat[0] = 0.0;
5709 catlen = 1;
5710 catt[0] = 0.0;
5711 cattlen = 1;
5712 }
5713
5714 if (bdxtail != 0.0) {
5715 temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, bdxtail, temp16a);
5716 bxtcatlen = scale_expansion_zeroelim(catlen, cat, bdxtail, bxtcat);
5717 temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, 2.0 * bdx,
5718 temp32a);
5719 temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5720 temp32alen, temp32a, temp48);
5721 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
5722 temp48, finother);
5723 finswap = finnow; finnow = finother; finother = finswap;
5724 if (cdytail != 0.0) {
5725 temp8len = scale_expansion_zeroelim(4, aa, bdxtail, temp8);
5726 temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail,
5727 temp16a);
5728 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
5729 temp16a, finother);
5730 finswap = finnow; finnow = finother; finother = finswap;
5731 }
5732 if (adytail != 0.0) {
5733 temp8len = scale_expansion_zeroelim(4, cc, -bdxtail, temp8);
5734 temp16alen = scale_expansion_zeroelim(temp8len, temp8, adytail,
5735 temp16a);
5736 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
5737 temp16a, finother);
5738 finswap = finnow; finnow = finother; finother = finswap;
5739 }
5740
5741 temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, bdxtail,
5742 temp32a);
5743 bxtcattlen = scale_expansion_zeroelim(cattlen, catt, bdxtail, bxtcatt);
5744 temp16alen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, 2.0 * bdx,
5745 temp16a);
5746 temp16blen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, bdxtail,
5747 temp16b);
5748 temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5749 temp16blen, temp16b, temp32b);
5750 temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
5751 temp32blen, temp32b, temp64);
5752 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
5753 temp64, finother);
5754 finswap = finnow; finnow = finother; finother = finswap;
5755 }
5756 if (bdytail != 0.0) {
5757 temp16alen = scale_expansion_zeroelim(bytcalen, bytca, bdytail, temp16a);
5758 bytcatlen = scale_expansion_zeroelim(catlen, cat, bdytail, bytcat);
5759 temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, 2.0 * bdy,
5760 temp32a);
5761 temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5762 temp32alen, temp32a, temp48);
5763 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
5764 temp48, finother);
5765 finswap = finnow; finnow = finother; finother = finswap;
5766
5767
5768 temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, bdytail,
5769 temp32a);
5770 bytcattlen = scale_expansion_zeroelim(cattlen, catt, bdytail, bytcatt);
5771 temp16alen = scale_expansion_zeroelim(bytcattlen, bytcatt, 2.0 * bdy,
5772 temp16a);
5773 temp16blen = scale_expansion_zeroelim(bytcattlen, bytcatt, bdytail,
5774 temp16b);
5775 temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5776 temp16blen, temp16b, temp32b);
5777 temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
5778 temp32blen, temp32b, temp64);
5779 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
5780 temp64, finother);
5781 finswap = finnow; finnow = finother; finother = finswap;
5782 }
5783 }
5784 if ((cdxtail != 0.0) || (cdytail != 0.0)) {
5785 if ((adxtail != 0.0) || (adytail != 0.0)
5786 || (bdxtail != 0.0) || (bdytail != 0.0)) {
5787 Two_Product(adxtail, bdy, ti1, ti0);
5788 Two_Product(adx, bdytail, tj1, tj0);
5789 Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
5790 u[3] = u3;
5791 negate = -ady;
5792 Two_Product(bdxtail, negate, ti1, ti0);
5793 negate = -adytail;
5794 Two_Product(bdx, negate, tj1, tj0);
5795 Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
5796 v[3] = v3;
5797 abtlen = fast_expansion_sum_zeroelim(4, u, 4, v, abt);
5798
5799 Two_Product(adxtail, bdytail, ti1, ti0);
5800 Two_Product(bdxtail, adytail, tj1, tj0);
5801 Two_Two_Diff(ti1, ti0, tj1, tj0, abtt3, abtt[2], abtt[1], abtt[0]);
5802 abtt[3] = abtt3;
5803 abttlen = 4;
5804 } else {
5805 abt[0] = 0.0;
5806 abtlen = 1;
5807 abtt[0] = 0.0;
5808 abttlen = 1;
5809 }
5810
5811 if (cdxtail != 0.0) {
5812 temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, cdxtail, temp16a);
5813 cxtabtlen = scale_expansion_zeroelim(abtlen, abt, cdxtail, cxtabt);
5814 temp32alen = scale_expansion_zeroelim(cxtabtlen, cxtabt, 2.0 * cdx,
5815 temp32a);
5816 temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5817 temp32alen, temp32a, temp48);
5818 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
5819 temp48, finother);
5820 finswap = finnow; finnow = finother; finother = finswap;
5821 if (adytail != 0.0) {
5822 temp8len = scale_expansion_zeroelim(4, bb, cdxtail, temp8);
5823 temp16alen = scale_expansion_zeroelim(temp8len, temp8, adytail,
5824 temp16a);
5825 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
5826 temp16a, finother);
5827 finswap = finnow; finnow = finother; finother = finswap;
5828 }
5829 if (bdytail != 0.0) {
5830 temp8len = scale_expansion_zeroelim(4, aa, -cdxtail, temp8);
5831 temp16alen = scale_expansion_zeroelim(temp8len, temp8, bdytail,
5832 temp16a);
5833 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
5834 temp16a, finother);
5835 finswap = finnow; finnow = finother; finother = finswap;
5836 }
5837
5838 temp32alen = scale_expansion_zeroelim(cxtabtlen, cxtabt, cdxtail,
5839 temp32a);
5840 cxtabttlen = scale_expansion_zeroelim(abttlen, abtt, cdxtail, cxtabtt);
5841 temp16alen = scale_expansion_zeroelim(cxtabttlen, cxtabtt, 2.0 * cdx,
5842 temp16a);
5843 temp16blen = scale_expansion_zeroelim(cxtabttlen, cxtabtt, cdxtail,
5844 temp16b);
5845 temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5846 temp16blen, temp16b, temp32b);
5847 temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
5848 temp32blen, temp32b, temp64);
5849 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
5850 temp64, finother);
5851 finswap = finnow; finnow = finother; finother = finswap;
5852 }
5853 if (cdytail != 0.0) {
5854 temp16alen = scale_expansion_zeroelim(cytablen, cytab, cdytail, temp16a);
5855 cytabtlen = scale_expansion_zeroelim(abtlen, abt, cdytail, cytabt);
5856 temp32alen = scale_expansion_zeroelim(cytabtlen, cytabt, 2.0 * cdy,
5857 temp32a);
5858 temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5859 temp32alen, temp32a, temp48);
5860 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
5861 temp48, finother);
5862 finswap = finnow; finnow = finother; finother = finswap;
5863
5864
5865 temp32alen = scale_expansion_zeroelim(cytabtlen, cytabt, cdytail,
5866 temp32a);
5867 cytabttlen = scale_expansion_zeroelim(abttlen, abtt, cdytail, cytabtt);
5868 temp16alen = scale_expansion_zeroelim(cytabttlen, cytabtt, 2.0 * cdy,
5869 temp16a);
5870 temp16blen = scale_expansion_zeroelim(cytabttlen, cytabtt, cdytail,
5871 temp16b);
5872 temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5873 temp16blen, temp16b, temp32b);
5874 temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
5875 temp32blen, temp32b, temp64);
5876 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
5877 temp64, finother);
5878 finswap = finnow; finnow = finother; finother = finswap;
5879 }
5880 }
5881
5882 return finnow[finlength - 1];
5883 }
5884
5885 #ifdef ANSI_DECLARATORS
5886 REAL incircle(struct mesh *m, struct behavior *b,
5887 vertex pa, vertex pb, vertex pc, vertex pd)
5888 #else /* not ANSI_DECLARATORS */
5889 REAL incircle(m, b, pa, pb, pc, pd)
5890 struct mesh *m;
5891 struct behavior *b;
5892 vertex pa;
5893 vertex pb;
5894 vertex pc;
5895 vertex pd;
5896 #endif /* not ANSI_DECLARATORS */
5897
5898 {
5899 REAL adx, bdx, cdx, ady, bdy, cdy;
5900 REAL bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady;
5901 REAL alift, blift, clift;
5902 REAL det;
5903 REAL permanent, errbound;
5904
5905 m->incirclecount++;
5906
5907 adx = pa[0] - pd[0];
5908 bdx = pb[0] - pd[0];
5909 cdx = pc[0] - pd[0];
5910 ady = pa[1] - pd[1];
5911 bdy = pb[1] - pd[1];
5912 cdy = pc[1] - pd[1];
5913
5914 bdxcdy = bdx * cdy;
5915 cdxbdy = cdx * bdy;
5916 alift = adx * adx + ady * ady;
5917
5918 cdxady = cdx * ady;
5919 adxcdy = adx * cdy;
5920 blift = bdx * bdx + bdy * bdy;
5921
5922 adxbdy = adx * bdy;
5923 bdxady = bdx * ady;
5924 clift = cdx * cdx + cdy * cdy;
5925
5926 det = alift * (bdxcdy - cdxbdy)
5927 + blift * (cdxady - adxcdy)
5928 + clift * (adxbdy - bdxady);
5929
5930 if (b->noexact) {
5931 return det;
5932 }
5933
5934 permanent = (Absolute(bdxcdy) + Absolute(cdxbdy)) * alift
5935 + (Absolute(cdxady) + Absolute(adxcdy)) * blift
5936 + (Absolute(adxbdy) + Absolute(bdxady)) * clift;
5937 errbound = iccerrboundA * permanent;
5938 if ((det > errbound) || (-det > errbound)) {
5939 return det;
5940 }
5941
5942 return incircleadapt(pa, pb, pc, pd, permanent);
5943 }
5944
5945 /*****************************************************************************/
5946 /* */
5947 /* orient3d() Return a positive value if the point pd lies below the */
5948 /* plane passing through pa, pb, and pc; "below" is defined so */
5949 /* that pa, pb, and pc appear in counterclockwise order when */
5950 /* viewed from above the plane. Returns a negative value if */
5951 /* pd lies above the plane. Returns zero if the points are */
5952 /* coplanar. The result is also a rough approximation of six */
5953 /* times the signed volume of the tetrahedron defined by the */
5954 /* four points. */
5955 /* */
5956 /* Uses exact arithmetic if necessary to ensure a correct answer. The */
5957 /* result returned is the determinant of a matrix. This determinant is */
5958 /* computed adaptively, in the sense that exact arithmetic is used only to */
5959 /* the degree it is needed to ensure that the returned value has the */
5960 /* correct sign. Hence, this function is usually quite fast, but will run */
5961 /* more slowly when the input points are coplanar or nearly so. */
5962 /* */
5963 /* See my Robust Predicates paper for details. */
5964 /* */
5965 /*****************************************************************************/
5966
5967 #ifdef ANSI_DECLARATORS
5968 REAL orient3dadapt(vertex pa, vertex pb, vertex pc, vertex pd,
5969 REAL aheight, REAL bheight, REAL cheight, REAL dheight,
5970 REAL permanent)
5971 #else /* not ANSI_DECLARATORS */
5972 REAL orient3dadapt(pa, pb, pc, pd,
5973 aheight, bheight, cheight, dheight, permanent)
5974 vertex pa;
5975 vertex pb;
5976 vertex pc;
5977 vertex pd;
5978 REAL aheight;
5979 REAL bheight;
5980 REAL cheight;
5981 REAL dheight;
5982 REAL permanent;
5983 #endif /* not ANSI_DECLARATORS */
5984
5985 {
5986 INEXACT REAL adx, bdx, cdx, ady, bdy, cdy, adheight, bdheight, cdheight;
5987 REAL det, errbound;
5988
5989 INEXACT REAL bdxcdy1, cdxbdy1, cdxady1, adxcdy1, adxbdy1, bdxady1;
5990 REAL bdxcdy0, cdxbdy0, cdxady0, adxcdy0, adxbdy0, bdxady0;
5991 REAL bc[4], ca[4], ab[4];
5992 INEXACT REAL bc3, ca3, ab3;
5993 REAL adet[8], bdet[8], cdet[8];
5994 int alen, blen, clen;
5995 REAL abdet[16];
5996 int ablen;
5997 REAL *finnow, *finother, *finswap;
5998 REAL fin1[192], fin2[192];
5999 int finlength;
6000
6001 REAL adxtail, bdxtail, cdxtail;
6002 REAL adytail, bdytail, cdytail;
6003 REAL adheighttail, bdheighttail, cdheighttail;
6004 INEXACT REAL at_blarge, at_clarge;
6005 INEXACT REAL bt_clarge, bt_alarge;
6006 INEXACT REAL ct_alarge, ct_blarge;
6007 REAL at_b[4], at_c[4], bt_c[4], bt_a[4], ct_a[4], ct_b[4];
6008 int at_blen, at_clen, bt_clen, bt_alen, ct_alen, ct_blen;
6009 INEXACT REAL bdxt_cdy1, cdxt_bdy1, cdxt_ady1;
6010 INEXACT REAL adxt_cdy1, adxt_bdy1, bdxt_ady1;
6011 REAL bdxt_cdy0, cdxt_bdy0, cdxt_ady0;
6012 REAL adxt_cdy0, adxt_bdy0, bdxt_ady0;
6013 INEXACT REAL bdyt_cdx1, cdyt_bdx1, cdyt_adx1;
6014 INEXACT REAL adyt_cdx1, adyt_bdx1, bdyt_adx1;
6015 REAL bdyt_cdx0, cdyt_bdx0, cdyt_adx0;
6016 REAL adyt_cdx0, adyt_bdx0, bdyt_adx0;
6017 REAL bct[8], cat[8], abt[8];
6018 int bctlen, catlen, abtlen;
6019 INEXACT REAL bdxt_cdyt1, cdxt_bdyt1, cdxt_adyt1;
6020 INEXACT REAL adxt_cdyt1, adxt_bdyt1, bdxt_adyt1;
6021 REAL bdxt_cdyt0, cdxt_bdyt0, cdxt_adyt0;
6022 REAL adxt_cdyt0, adxt_bdyt0, bdxt_adyt0;
6023 REAL u[4], v[12], w[16];
6024 INEXACT REAL u3;
6025 int vlength, wlength;
6026 REAL negate;
6027
6028 INEXACT REAL bvirt;
6029 REAL avirt, bround, around;
6030 INEXACT REAL c;
6031 INEXACT REAL abig;
6032 REAL ahi, alo, bhi, blo;
6033 REAL err1, err2, err3;
6034 INEXACT REAL _i, _j, _k;
6035 REAL _0;
6036
6037 adx = (REAL) (pa[0] - pd[0]);
6038 bdx = (REAL) (pb[0] - pd[0]);
6039 cdx = (REAL) (pc[0] - pd[0]);
6040 ady = (REAL) (pa[1] - pd[1]);
6041 bdy = (REAL) (pb[1] - pd[1]);
6042 cdy = (REAL) (pc[1] - pd[1]);
6043 adheight = (REAL) (aheight - dheight);
6044 bdheight = (REAL) (bheight - dheight);
6045 cdheight = (REAL) (cheight - dheight);
6046
6047 Two_Product(bdx, cdy, bdxcdy1, bdxcdy0);
6048 Two_Product(cdx, bdy, cdxbdy1, cdxbdy0);
6049 Two_Two_Diff(bdxcdy1, bdxcdy0, cdxbdy1, cdxbdy0, bc3, bc[2], bc[1], bc[0]);
6050 bc[3] = bc3;
6051 alen = scale_expansion_zeroelim(4, bc, adheight, adet);
6052
6053 Two_Product(cdx, ady, cdxady1, cdxady0);
6054 Two_Product(adx, cdy, adxcdy1, adxcdy0);
6055 Two_Two_Diff(cdxady1, cdxady0, adxcdy1, adxcdy0, ca3, ca[2], ca[1], ca[0]);
6056 ca[3] = ca3;
6057 blen = scale_expansion_zeroelim(4, ca, bdheight, bdet);
6058
6059 Two_Product(adx, bdy, adxbdy1, adxbdy0);
6060 Two_Product(bdx, ady, bdxady1, bdxady0);
6061 Two_Two_Diff(adxbdy1, adxbdy0, bdxady1, bdxady0, ab3, ab[2], ab[1], ab[0]);
6062 ab[3] = ab3;
6063 clen = scale_expansion_zeroelim(4, ab, cdheight, cdet);
6064
6065 ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
6066 finlength = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, fin1);
6067
6068 det = estimate(finlength, fin1);
6069 errbound = o3derrboundB * permanent;
6070 if ((det >= errbound) || (-det >= errbound)) {
6071 return det;
6072 }
6073
6074 Two_Diff_Tail(pa[0], pd[0], adx, adxtail);
6075 Two_Diff_Tail(pb[0], pd[0], bdx, bdxtail);
6076 Two_Diff_Tail(pc[0], pd[0], cdx, cdxtail);
6077 Two_Diff_Tail(pa[1], pd[1], ady, adytail);
6078 Two_Diff_Tail(pb[1], pd[1], bdy, bdytail);
6079 Two_Diff_Tail(pc[1], pd[1], cdy, cdytail);
6080 Two_Diff_Tail(aheight, dheight, adheight, adheighttail);
6081 Two_Diff_Tail(bheight, dheight, bdheight, bdheighttail);
6082 Two_Diff_Tail(cheight, dheight, cdheight, cdheighttail);
6083
6084 if ((adxtail == 0.0) && (bdxtail == 0.0) && (cdxtail == 0.0) &&
6085 (adytail == 0.0) && (bdytail == 0.0) && (cdytail == 0.0) &&
6086 (adheighttail == 0.0) &&
6087 (bdheighttail == 0.0) &&
6088 (cdheighttail == 0.0)) {
6089 return det;
6090 }
6091
6092 errbound = o3derrboundC * permanent + resulterrbound * Absolute(det);
6093 det += (adheight * ((bdx * cdytail + cdy * bdxtail) -
6094 (bdy * cdxtail + cdx * bdytail)) +
6095 adheighttail * (bdx * cdy - bdy * cdx)) +
6096 (bdheight * ((cdx * adytail + ady * cdxtail) -
6097 (cdy * adxtail + adx * cdytail)) +
6098 bdheighttail * (cdx * ady - cdy * adx)) +
6099 (cdheight * ((adx * bdytail + bdy * adxtail) -
6100 (ady * bdxtail + bdx * adytail)) +
6101 cdheighttail * (adx * bdy - ady * bdx));
6102 if ((det >= errbound) || (-det >= errbound)) {
6103 return det;
6104 }
6105
6106 finnow = fin1;
6107 finother = fin2;
6108
6109 if (adxtail == 0.0) {
6110 if (adytail == 0.0) {
6111 at_b[0] = 0.0;
6112 at_blen = 1;
6113 at_c[0] = 0.0;
6114 at_clen = 1;
6115 } else {
6116 negate = -adytail;
6117 Two_Product(negate, bdx, at_blarge, at_b[0]);
6118 at_b[1] = at_blarge;
6119 at_blen = 2;
6120 Two_Product(adytail, cdx, at_clarge, at_c[0]);
6121 at_c[1] = at_clarge;
6122 at_clen = 2;
6123 }
6124 } else {
6125 if (adytail == 0.0) {
6126 Two_Product(adxtail, bdy, at_blarge, at_b[0]);
6127 at_b[1] = at_blarge;
6128 at_blen = 2;
6129 negate = -adxtail;
6130 Two_Product(negate, cdy, at_clarge, at_c[0]);
6131 at_c[1] = at_clarge;
6132 at_clen = 2;
6133 } else {
6134 Two_Product(adxtail, bdy, adxt_bdy1, adxt_bdy0);
6135 Two_Product(adytail, bdx, adyt_bdx1, adyt_bdx0);
6136 Two_Two_Diff(adxt_bdy1, adxt_bdy0, adyt_bdx1, adyt_bdx0,
6137 at_blarge, at_b[2], at_b[1], at_b[0]);
6138 at_b[3] = at_blarge;
6139 at_blen = 4;
6140 Two_Product(adytail, cdx, adyt_cdx1, adyt_cdx0);
6141 Two_Product(adxtail, cdy, adxt_cdy1, adxt_cdy0);
6142 Two_Two_Diff(adyt_cdx1, adyt_cdx0, adxt_cdy1, adxt_cdy0,
6143 at_clarge, at_c[2], at_c[1], at_c[0]);
6144 at_c[3] = at_clarge;
6145 at_clen = 4;
6146 }
6147 }
6148 if (bdxtail == 0.0) {
6149 if (bdytail == 0.0) {
6150 bt_c[0] = 0.0;
6151 bt_clen = 1;
6152 bt_a[0] = 0.0;
6153 bt_alen = 1;
6154 } else {
6155 negate = -bdytail;
6156 Two_Product(negate, cdx, bt_clarge, bt_c[0]);
6157 bt_c[1] = bt_clarge;
6158 bt_clen = 2;
6159 Two_Product(bdytail, adx, bt_alarge, bt_a[0]);
6160 bt_a[1] = bt_alarge;
6161 bt_alen = 2;
6162 }
6163 } else {
6164 if (bdytail == 0.0) {
6165 Two_Product(bdxtail, cdy, bt_clarge, bt_c[0]);
6166 bt_c[1] = bt_clarge;
6167 bt_clen = 2;
6168 negate = -bdxtail;
6169 Two_Product(negate, ady, bt_alarge, bt_a[0]);
6170 bt_a[1] = bt_alarge;
6171 bt_alen = 2;
6172 } else {
6173 Two_Product(bdxtail, cdy, bdxt_cdy1, bdxt_cdy0);
6174 Two_Product(bdytail, cdx, bdyt_cdx1, bdyt_cdx0);
6175 Two_Two_Diff(bdxt_cdy1, bdxt_cdy0, bdyt_cdx1, bdyt_cdx0,
6176 bt_clarge, bt_c[2], bt_c[1], bt_c[0]);
6177 bt_c[3] = bt_clarge;
6178 bt_clen = 4;
6179 Two_Product(bdytail, adx, bdyt_adx1, bdyt_adx0);
6180 Two_Product(bdxtail, ady, bdxt_ady1, bdxt_ady0);
6181 Two_Two_Diff(bdyt_adx1, bdyt_adx0, bdxt_ady1, bdxt_ady0,
6182 bt_alarge, bt_a[2], bt_a[1], bt_a[0]);
6183 bt_a[3] = bt_alarge;
6184 bt_alen = 4;
6185 }
6186 }
6187 if (cdxtail == 0.0) {
6188 if (cdytail == 0.0) {
6189 ct_a[0] = 0.0;
6190 ct_alen = 1;
6191 ct_b[0] = 0.0;
6192 ct_blen = 1;
6193 } else {
6194 negate = -cdytail;
6195 Two_Product(negate, adx, ct_alarge, ct_a[0]);
6196 ct_a[1] = ct_alarge;
6197 ct_alen = 2;
6198 Two_Product(cdytail, bdx, ct_blarge, ct_b[0]);
6199 ct_b[1] = ct_blarge;
6200 ct_blen = 2;
6201 }
6202 } else {
6203 if (cdytail == 0.0) {
6204 Two_Product(cdxtail, ady, ct_alarge, ct_a[0]);
6205 ct_a[1] = ct_alarge;
6206 ct_alen = 2;
6207 negate = -cdxtail;
6208 Two_Product(negate, bdy, ct_blarge, ct_b[0]);
6209 ct_b[1] = ct_blarge;
6210 ct_blen = 2;
6211 } else {
6212 Two_Product(cdxtail, ady, cdxt_ady1, cdxt_ady0);
6213 Two_Product(cdytail, adx, cdyt_adx1, cdyt_adx0);
6214 Two_Two_Diff(cdxt_ady1, cdxt_ady0, cdyt_adx1, cdyt_adx0,
6215 ct_alarge, ct_a[2], ct_a[1], ct_a[0]);
6216 ct_a[3] = ct_alarge;
6217 ct_alen = 4;
6218 Two_Product(cdytail, bdx, cdyt_bdx1, cdyt_bdx0);
6219 Two_Product(cdxtail, bdy, cdxt_bdy1, cdxt_bdy0);
6220 Two_Two_Diff(cdyt_bdx1, cdyt_bdx0, cdxt_bdy1, cdxt_bdy0,
6221 ct_blarge, ct_b[2], ct_b[1], ct_b[0]);
6222 ct_b[3] = ct_blarge;
6223 ct_blen = 4;
6224 }
6225 }
6226
6227 bctlen = fast_expansion_sum_zeroelim(bt_clen, bt_c, ct_blen, ct_b, bct);
6228 wlength = scale_expansion_zeroelim(bctlen, bct, adheight, w);
6229 finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
6230 finother);
6231 finswap = finnow; finnow = finother; finother = finswap;
6232
6233 catlen = fast_expansion_sum_zeroelim(ct_alen, ct_a, at_clen, at_c, cat);
6234 wlength = scale_expansion_zeroelim(catlen, cat, bdheight, w);
6235 finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
6236 finother);
6237 finswap = finnow; finnow = finother; finother = finswap;
6238
6239 abtlen = fast_expansion_sum_zeroelim(at_blen, at_b, bt_alen, bt_a, abt);
6240 wlength = scale_expansion_zeroelim(abtlen, abt, cdheight, w);
6241 finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
6242 finother);
6243 finswap = finnow; finnow = finother; finother = finswap;
6244
6245 if (adheighttail != 0.0) {
6246 vlength = scale_expansion_zeroelim(4, bc, adheighttail, v);
6247 finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v,
6248 finother);
6249 finswap = finnow; finnow = finother; finother = finswap;
6250 }
6251 if (bdheighttail != 0.0) {
6252 vlength = scale_expansion_zeroelim(4, ca, bdheighttail, v);
6253 finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v,
6254 finother);
6255 finswap = finnow; finnow = finother; finother = finswap;
6256 }
6257 if (cdheighttail != 0.0) {
6258 vlength = scale_expansion_zeroelim(4, ab, cdheighttail, v);
6259 finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v,
6260 finother);
6261 finswap = finnow; finnow = finother; finother = finswap;
6262 }
6263
6264 if (adxtail != 0.0) {
6265 if (bdytail != 0.0) {
6266 Two_Product(adxtail, bdytail, adxt_bdyt1, adxt_bdyt0);
6267 Two_One_Product(adxt_bdyt1, adxt_bdyt0, cdheight, u3, u[2], u[1], u[0]);
6268 u[3] = u3;
6269 finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
6270 finother);
6271 finswap = finnow; finnow = finother; finother = finswap;
6272 if (cdheighttail != 0.0) {
6273 Two_One_Product(adxt_bdyt1, adxt_bdyt0, cdheighttail,
6274 u3, u[2], u[1], u[0]);
6275 u[3] = u3;
6276 finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
6277 finother);
6278 finswap = finnow; finnow = finother; finother = finswap;
6279 }
6280 }
6281 if (cdytail != 0.0) {
6282 negate = -adxtail;
6283 Two_Product(negate, cdytail, adxt_cdyt1, adxt_cdyt0);
6284 Two_One_Product(adxt_cdyt1, adxt_cdyt0, bdheight, u3, u[2], u[1], u[0]);
6285 u[3] = u3;
6286 finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
6287 finother);
6288 finswap = finnow; finnow = finother; finother = finswap;
6289 if (bdheighttail != 0.0) {
6290 Two_One_Product(adxt_cdyt1, adxt_cdyt0, bdheighttail,
6291 u3, u[2], u[1], u[0]);
6292 u[3] = u3;
6293 finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
6294 finother);
6295 finswap = finnow; finnow = finother; finother = finswap;
6296 }
6297 }
6298 }
6299 if (bdxtail != 0.0) {
6300 if (cdytail != 0.0) {
6301 Two_Product(bdxtail, cdytail, bdxt_cdyt1, bdxt_cdyt0);
6302 Two_One_Product(bdxt_cdyt1, bdxt_cdyt0, adheight, u3, u[2], u[1], u[0]);
6303 u[3] = u3;
6304 finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
6305 finother);
6306 finswap = finnow; finnow = finother; finother = finswap;
6307 if (adheighttail != 0.0) {
6308 Two_One_Product(bdxt_cdyt1, bdxt_cdyt0, adheighttail,
6309 u3, u[2], u[1], u[0]);
6310 u[3] = u3;
6311 finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
6312 finother);
6313 finswap = finnow; finnow = finother; finother = finswap;
6314 }
6315 }
6316 if (adytail != 0.0) {
6317 negate = -bdxtail;
6318 Two_Product(negate, adytail, bdxt_adyt1, bdxt_adyt0);
6319 Two_One_Product(bdxt_adyt1, bdxt_adyt0, cdheight, u3, u[2], u[1], u[0]);
6320 u[3] = u3;
6321 finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
6322 finother);
6323 finswap = finnow; finnow = finother; finother = finswap;
6324 if (cdheighttail != 0.0) {
6325 Two_One_Product(bdxt_adyt1, bdxt_adyt0, cdheighttail,
6326 u3, u[2], u[1], u[0]);
6327 u[3] = u3;
6328 finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
6329 finother);
6330 finswap = finnow; finnow = finother; finother = finswap;
6331 }
6332 }
6333 }
6334 if (cdxtail != 0.0) {
6335 if (adytail != 0.0) {
6336 Two_Product(cdxtail, adytail, cdxt_adyt1, cdxt_adyt0);
6337 Two_One_Product(cdxt_adyt1, cdxt_adyt0, bdheight, u3, u[2], u[1], u[0]);
6338 u[3] = u3;
6339 finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
6340 finother);
6341 finswap = finnow; finnow = finother; finother = finswap;
6342 if (bdheighttail != 0.0) {
6343 Two_One_Product(cdxt_adyt1, cdxt_adyt0, bdheighttail,
6344 u3, u[2], u[1], u[0]);
6345 u[3] = u3;
6346 finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
6347 finother);
6348 finswap = finnow; finnow = finother; finother = finswap;
6349 }
6350 }
6351 if (bdytail != 0.0) {
6352 negate = -cdxtail;
6353 Two_Product(negate, bdytail, cdxt_bdyt1, cdxt_bdyt0);
6354 Two_One_Product(cdxt_bdyt1, cdxt_bdyt0, adheight, u3, u[2], u[1], u[0]);
6355 u[3] = u3;
6356 finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
6357 finother);
6358 finswap = finnow; finnow = finother; finother = finswap;
6359 if (adheighttail != 0.0) {
6360 Two_One_Product(cdxt_bdyt1, cdxt_bdyt0, adheighttail,
6361 u3, u[2], u[1], u[0]);
6362 u[3] = u3;
6363 finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
6364 finother);
6365 finswap = finnow; finnow = finother; finother = finswap;
6366 }
6367 }
6368 }
6369
6370 if (adheighttail != 0.0) {
6371 wlength = scale_expansion_zeroelim(bctlen, bct, adheighttail, w);
6372 finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
6373 finother);
6374 finswap = finnow; finnow = finother; finother = finswap;
6375 }
6376 if (bdheighttail != 0.0) {
6377 wlength = scale_expansion_zeroelim(catlen, cat, bdheighttail, w);
6378 finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
6379 finother);
6380 finswap = finnow; finnow = finother; finother = finswap;
6381 }
6382 if (cdheighttail != 0.0) {
6383 wlength = scale_expansion_zeroelim(abtlen, abt, cdheighttail, w);
6384 finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
6385 finother);
6386 finswap = finnow; finnow = finother; finother = finswap;
6387 }
6388
6389 return finnow[finlength - 1];
6390 }
6391
6392 #ifdef ANSI_DECLARATORS
6393 REAL orient3d(struct mesh *m, struct behavior *b,
6394 vertex pa, vertex pb, vertex pc, vertex pd,
6395 REAL aheight, REAL bheight, REAL cheight, REAL dheight)
6396 #else /* not ANSI_DECLARATORS */
6397 REAL orient3d(m, b, pa, pb, pc, pd, aheight, bheight, cheight, dheight)
6398 struct mesh *m;
6399 struct behavior *b;
6400 vertex pa;
6401 vertex pb;
6402 vertex pc;
6403 vertex pd;
6404 REAL aheight;
6405 REAL bheight;
6406 REAL cheight;
6407 REAL dheight;
6408 #endif /* not ANSI_DECLARATORS */
6409
6410 {
6411 REAL adx, bdx, cdx, ady, bdy, cdy, adheight, bdheight, cdheight;
6412 REAL bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady;
6413 REAL det;
6414 REAL permanent, errbound;
6415
6416 m->orient3dcount++;
6417
6418 adx = pa[0] - pd[0];
6419 bdx = pb[0] - pd[0];
6420 cdx = pc[0] - pd[0];
6421 ady = pa[1] - pd[1];
6422 bdy = pb[1] - pd[1];
6423 cdy = pc[1] - pd[1];
6424 adheight = aheight - dheight;
6425 bdheight = bheight - dheight;
6426 cdheight = cheight - dheight;
6427
6428 bdxcdy = bdx * cdy;
6429 cdxbdy = cdx * bdy;
6430
6431 cdxady = cdx * ady;
6432 adxcdy = adx * cdy;
6433
6434 adxbdy = adx * bdy;
6435 bdxady = bdx * ady;
6436
6437 det = adheight * (bdxcdy - cdxbdy)
6438 + bdheight * (cdxady - adxcdy)
6439 + cdheight * (adxbdy - bdxady);
6440
6441 if (b->noexact) {
6442 return det;
6443 }
6444
6445 permanent = (Absolute(bdxcdy) + Absolute(cdxbdy)) * Absolute(adheight)
6446 + (Absolute(cdxady) + Absolute(adxcdy)) * Absolute(bdheight)
6447 + (Absolute(adxbdy) + Absolute(bdxady)) * Absolute(cdheight);
6448 errbound = o3derrboundA * permanent;
6449 if ((det > errbound) || (-det > errbound)) {
6450 return det;
6451 }
6452
6453 return orient3dadapt(pa, pb, pc, pd, aheight, bheight, cheight, dheight,
6454 permanent);
6455 }
6456
6457 /*****************************************************************************/
6458 /* */
6459 /* nonregular() Return a positive value if the point pd is incompatible */
6460 /* with the circle or plane passing through pa, pb, and pc */
6461 /* (meaning that pd is inside the circle or below the */
6462 /* plane); a negative value if it is compatible; and zero if */
6463 /* the four points are cocircular/coplanar. The points pa, */
6464 /* pb, and pc must be in counterclockwise order, or the sign */
6465 /* of the result will be reversed. */
6466 /* */
6467 /* If the -w switch is used, the points are lifted onto the parabolic */
6468 /* lifting map, then they are dropped according to their weights, then the */
6469 /* 3D orientation test is applied. If the -W switch is used, the points' */
6470 /* heights are already provided, so the 3D orientation test is applied */
6471 /* directly. If neither switch is used, the incircle test is applied. */
6472 /* */
6473 /*****************************************************************************/
6474
6475 #ifdef ANSI_DECLARATORS
6476 REAL nonregular(struct mesh *m, struct behavior *b,
6477 vertex pa, vertex pb, vertex pc, vertex pd)
6478 #else /* not ANSI_DECLARATORS */
6479 REAL nonregular(m, b, pa, pb, pc, pd)
6480 struct mesh *m;
6481 struct behavior *b;
6482 vertex pa;
6483 vertex pb;
6484 vertex pc;
6485 vertex pd;
6486 #endif /* not ANSI_DECLARATORS */
6487
6488 {
6489 if (b->weighted == 0) {
6490 return incircle(m, b, pa, pb, pc, pd);
6491 } else if (b->weighted == 1) {
6492 return orient3d(m, b, pa, pb, pc, pd,
6493 pa[0] * pa[0] + pa[1] * pa[1] - pa[2],
6494 pb[0] * pb[0] + pb[1] * pb[1] - pb[2],
6495 pc[0] * pc[0] + pc[1] * pc[1] - pc[2],
6496 pd[0] * pd[0] + pd[1] * pd[1] - pd[2]);
6497 } else {
6498 return orient3d(m, b, pa, pb, pc, pd, pa[2], pb[2], pc[2], pd[2]);
6499 }
6500 }
6501
6502 /*****************************************************************************/
6503 /* */
6504 /* findcircumcenter() Find the circumcenter of a triangle. */
6505 /* */
6506 /* The result is returned both in terms of x-y coordinates and xi-eta */
6507 /* (barycentric) coordinates. The xi-eta coordinate system is defined in */
6508 /* terms of the triangle: the origin of the triangle is the origin of the */
6509 /* coordinate system; the destination of the triangle is one unit along the */
6510 /* xi axis; and the apex of the triangle is one unit along the eta axis. */
6511 /* This procedure also returns the square of the length of the triangle's */
6512 /* shortest edge. */
6513 /* */
6514 /*****************************************************************************/
6515
6516 #ifdef ANSI_DECLARATORS
6517 void findcircumcenter(struct mesh *m, struct behavior *b,
6518 vertex torg, vertex tdest, vertex tapex,
6519 vertex circumcenter, REAL *xi, REAL *eta, int offcenter)
6520 #else /* not ANSI_DECLARATORS */
6521 void findcircumcenter(m, b, torg, tdest, tapex, circumcenter, xi, eta,
6522 offcenter)
6523 struct mesh *m;
6524 struct behavior *b;
6525 vertex torg;
6526 vertex tdest;
6527 vertex tapex;
6528 vertex circumcenter;
6529 REAL *xi;
6530 REAL *eta;
6531 int offcenter;
6532 #endif /* not ANSI_DECLARATORS */
6533
6534 {
6535 REAL xdo, ydo, xao, yao;
6536 REAL dodist, aodist, dadist;
6537 REAL denominator;
6538 REAL dx, dy, dxoff, dyoff;
6539
6540 m->circumcentercount++;
6541
6542 /* Compute the circumcenter of the triangle. */
6543 xdo = tdest[0] - torg[0];
6544 ydo = tdest[1] - torg[1];
6545 xao = tapex[0] - torg[0];
6546 yao = tapex[1] - torg[1];
6547 dodist = xdo * xdo + ydo * ydo;
6548 aodist = xao * xao + yao * yao;
6549 dadist = (tdest[0] - tapex[0]) * (tdest[0] - tapex[0]) +
6550 (tdest[1] - tapex[1]) * (tdest[1] - tapex[1]);
6551 if (b->noexact) {
6552 denominator = 0.5 / (xdo * yao - xao * ydo);
6553 } else {
6554 /* Use the counterclockwise() routine to ensure a positive (and */
6555 /* reasonably accurate) result, avoiding any possibility of */
6556 /* division by zero. */
6557 denominator = 0.5 / counterclockwise(m, b, tdest, tapex, torg);
6558 /* Don't count the above as an orientation test. */
6559 m->counterclockcount--;
6560 }
6561 dx = (yao * dodist - ydo * aodist) * denominator;
6562 dy = (xdo * aodist - xao * dodist) * denominator;
6563
6564 /* Find the (squared) length of the triangle's shortest edge. This */
6565 /* serves as a conservative estimate of the insertion radius of the */
6566 /* circumcenter's parent. The estimate is used to ensure that */
6567 /* the algorithm terminates even if very small angles appear in */
6568 /* the input PSLG. */
6569 if ((dodist < aodist) && (dodist < dadist)) {
6570 if (offcenter && (b->offconstant > 0.0)) {
6571 /* Find the position of the off-center, as described by Alper Ungor. */
6572 dxoff = 0.5 * xdo - b->offconstant * ydo;
6573 dyoff = 0.5 * ydo + b->offconstant * xdo;
6574 /* If the off-center is closer to the origin than the */
6575 /* circumcenter, use the off-center instead. */
6576 if (dxoff * dxoff + dyoff * dyoff < dx * dx + dy * dy) {
6577 dx = dxoff;
6578 dy = dyoff;
6579 }
6580 }
6581 } else if (aodist < dadist) {
6582 if (offcenter && (b->offconstant > 0.0)) {
6583 dxoff = 0.5 * xao + b->offconstant * yao;
6584 dyoff = 0.5 * yao - b->offconstant * xao;
6585 /* If the off-center is closer to the origin than the */
6586 /* circumcenter, use the off-center instead. */
6587 if (dxoff * dxoff + dyoff * dyoff < dx * dx + dy * dy) {
6588 dx = dxoff;
6589 dy = dyoff;
6590 }
6591 }
6592 } else {
6593 if (offcenter && (b->offconstant > 0.0)) {
6594 dxoff = 0.5 * (tapex[0] - tdest[0]) -
6595 b->offconstant * (tapex[1] - tdest[1]);
6596 dyoff = 0.5 * (tapex[1] - tdest[1]) +
6597 b->offconstant * (tapex[0] - tdest[0]);
6598 /* If the off-center is closer to the destination than the */
6599 /* circumcenter, use the off-center instead. */
6600 if (dxoff * dxoff + dyoff * dyoff <
6601 (dx - xdo) * (dx - xdo) + (dy - ydo) * (dy - ydo)) {
6602 dx = xdo + dxoff;
6603 dy = ydo + dyoff;
6604 }
6605 }
6606 }
6607
6608 circumcenter[0] = torg[0] + dx;
6609 circumcenter[1] = torg[1] + dy;
6610
6611 /* To interpolate vertex attributes for the new vertex inserted at */
6612 /* the circumcenter, define a coordinate system with a xi-axis, */
6613 /* directed from the triangle's origin to its destination, and */
6614 /* an eta-axis, directed from its origin to its apex. */
6615 /* Calculate the xi and eta coordinates of the circumcenter. */
6616 *xi = (yao * dx - xao * dy) * (2.0 * denominator);
6617 *eta = (xdo * dy - ydo * dx) * (2.0 * denominator);
6618 }
6619
6620 /** **/
6621 /** **/
6622 /********* Geometric primitives end here *********/
6623
6624 /*****************************************************************************/
6625 /* */
6626 /* triangleinit() Initialize some variables. */
6627 /* */
6628 /*****************************************************************************/
6629
6630 #ifdef ANSI_DECLARATORS
6631 void triangleinit(struct mesh *m)
6632 #else /* not ANSI_DECLARATORS */
6633 void triangleinit(m)
6634 struct mesh *m;
6635 #endif /* not ANSI_DECLARATORS */
6636
6637 {
6638 poolzero(&m->vertices);
6639 poolzero(&m->triangles);
6640 poolzero(&m->subsegs);
6641 poolzero(&m->viri);
6642 poolzero(&m->badsubsegs);
6643 poolzero(&m->badtriangles);
6644 poolzero(&m->flipstackers);
6645 poolzero(&m->splaynodes);
6646
6647 m->recenttri.tri = (triangle *) NULL; /* No triangle has been visited yet. */
6648 m->undeads = 0; /* No eliminated input vertices yet. */
6649 m->samples = 1; /* Point location should take at least one sample. */
6650 m->checksegments = 0; /* There are no segments in the triangulation yet. */
6651 m->checkquality = 0; /* The quality triangulation stage has not begun. */
6652 m->incirclecount = m->counterclockcount = m->orient3dcount = 0;
6653 m->hyperbolacount = m->circletopcount = m->circumcentercount = 0;
6654 randomseed = 1;
6655
6656 exactinit(); /* Initialize exact arithmetic constants. */
6657 }
6658
6659 /*****************************************************************************/
6660 /* */
6661 /* randomnation() Generate a random number between 0 and `choices' - 1. */
6662 /* */
6663 /* This is a simple linear congruential random number generator. Hence, it */
6664 /* is a bad random number generator, but good enough for most randomized */
6665 /* geometric algorithms. */
6666 /* */
6667 /*****************************************************************************/
6668
6669 #ifdef ANSI_DECLARATORS
6670 unsigned long randomnation(unsigned int choices)
6671 #else /* not ANSI_DECLARATORS */
6672 unsigned long randomnation(choices)
6673 unsigned int choices;
6674 #endif /* not ANSI_DECLARATORS */
6675
6676 {
6677 randomseed = (randomseed * 1366l + 150889l) % 714025l;
6678 return randomseed / (714025l / choices + 1);
6679 }
6680
6681 /********* Mesh quality testing routines begin here *********/
6682 /** **/
6683 /** **/
6684
6685 /*****************************************************************************/
6686 /* */
6687 /* checkmesh() Test the mesh for topological consistency. */
6688 /* */
6689 /*****************************************************************************/
6690
6691 #ifndef REDUCED
6692
6693 #ifdef ANSI_DECLARATORS
6694 void checkmesh(struct mesh *m, struct behavior *b)
6695 #else /* not ANSI_DECLARATORS */
6696 void checkmesh(m, b)
6697 struct mesh *m;
6698 struct behavior *b;
6699 #endif /* not ANSI_DECLARATORS */
6700
6701 {
6702 struct otri triangleloop;
6703 struct otri oppotri, oppooppotri;
6704 vertex triorg, tridest, triapex;
6705 vertex oppoorg, oppodest;
6706 int horrors;
6707 int saveexact;
6708 triangle ptr; /* Temporary variable used by sym(). */
6709
6710 /* Temporarily turn on exact arithmetic if it's off. */
6711 saveexact = b->noexact;
6712 b->noexact = 0;
6713 if (!b->quiet) {
6714 printf(" Checking consistency of mesh...\n");
6715 }
6716 horrors = 0;
6717 /* Run through the list of triangles, checking each one. */
6718 traversalinit(&m->triangles);
6719 triangleloop.tri = triangletraverse(m);
6720 while (triangleloop.tri != (triangle *) NULL) {
6721 /* Check all three edges of the triangle. */
6722 for (triangleloop.orient = 0; triangleloop.orient < 3;
6723 triangleloop.orient++) {
6724 org(triangleloop, triorg);
6725 dest(triangleloop, tridest);
6726 if (triangleloop.orient == 0) { /* Only test for inversion once. */
6727 /* Test if the triangle is flat or inverted. */
6728 apex(triangleloop, triapex);
6729 if (counterclockwise(m, b, triorg, tridest, triapex) <= 0.0) {
6730 printf(" !! !! Inverted ");
6731 printtriangle(m, b, &triangleloop);
6732 horrors++;
6733 }
6734 }
6735 /* Find the neighboring triangle on this edge. */
6736 sym(triangleloop, oppotri);
6737 if (oppotri.tri != m->dummytri) {
6738 /* Check that the triangle's neighbor knows it's a neighbor. */
6739 sym(oppotri, oppooppotri);
6740 if ((triangleloop.tri != oppooppotri.tri)
6741 || (triangleloop.orient != oppooppotri.orient)) {
6742 printf(" !! !! Asymmetric triangle-triangle bond:\n");
6743 if (triangleloop.tri == oppooppotri.tri) {
6744 printf(" (Right triangle, wrong orientation)\n");
6745 }
6746 printf(" First ");
6747 printtriangle(m, b, &triangleloop);
6748 printf(" Second (nonreciprocating) ");
6749 printtriangle(m, b, &oppotri);
6750 horrors++;
6751 }
6752 /* Check that both triangles agree on the identities */
6753 /* of their shared vertices. */
6754 org(oppotri, oppoorg);
6755 dest(oppotri, oppodest);
6756 if ((triorg != oppodest) || (tridest != oppoorg)) {
6757 printf(" !! !! Mismatched edge coordinates between two triangles:\n"
6758 );
6759 printf(" First mismatched ");
6760 printtriangle(m, b, &triangleloop);
6761 printf(" Second mismatched ");
6762 printtriangle(m, b, &oppotri);
6763 horrors++;
6764 }
6765 }
6766 }
6767 triangleloop.tri = triangletraverse(m);
6768 }
6769 if (horrors == 0) {
6770 if (!b->quiet) {
6771 printf(" In my studied opinion, the mesh appears to be consistent.\n");
6772 }
6773 } else if (horrors == 1) {
6774 printf(" !! !! !! !! Precisely one festering wound discovered.\n");
6775 } else {
6776 printf(" !! !! !! !! %d abominations witnessed.\n", horrors);
6777 }
6778 /* Restore the status of exact arithmetic. */
6779 b->noexact = saveexact;
6780 }
6781
6782 #endif /* not REDUCED */
6783
6784 /*****************************************************************************/
6785 /* */
6786 /* checkdelaunay() Ensure that the mesh is (constrained) Delaunay. */
6787 /* */
6788 /*****************************************************************************/
6789
6790 #ifndef REDUCED
6791
6792 #ifdef ANSI_DECLARATORS
6793 void checkdelaunay(struct mesh *m, struct behavior *b)
6794 #else /* not ANSI_DECLARATORS */
6795 void checkdelaunay(m, b)
6796 struct mesh *m;
6797 struct behavior *b;
6798 #endif /* not ANSI_DECLARATORS */
6799
6800 {
6801 struct otri triangleloop;
6802 struct otri oppotri;
6803 struct osub opposubseg;
6804 vertex triorg, tridest, triapex;
6805 vertex oppoapex;
6806 int shouldbedelaunay;
6807 int horrors;
6808 int saveexact;
6809 triangle ptr; /* Temporary variable used by sym(). */
6810 subseg sptr; /* Temporary variable used by tspivot(). */
6811
6812 /* Temporarily turn on exact arithmetic if it's off. */
6813 saveexact = b->noexact;
6814 b->noexact = 0;
6815 if (!b->quiet) {
6816 printf(" Checking Delaunay property of mesh...\n");
6817 }
6818 horrors = 0;
6819 /* Run through the list of triangles, checking each one. */
6820 traversalinit(&m->triangles);
6821 triangleloop.tri = triangletraverse(m);
6822 while (triangleloop.tri != (triangle *) NULL) {
6823 /* Check all three edges of the triangle. */
6824 for (triangleloop.orient = 0; triangleloop.orient < 3;
6825 triangleloop.orient++) {
6826 org(triangleloop, triorg);
6827 dest(triangleloop, tridest);
6828 apex(triangleloop, triapex);
6829 sym(triangleloop, oppotri);
6830 apex(oppotri, oppoapex);
6831 /* Only test that the edge is locally Delaunay if there is an */
6832 /* adjoining triangle whose pointer is larger (to ensure that */
6833 /* each pair isn't tested twice). */
6834 shouldbedelaunay = (oppotri.tri != m->dummytri) &&
6835 !deadtri(oppotri.tri) && (triangleloop.tri < oppotri.tri) &&
6836 (triorg != m->infvertex1) && (triorg != m->infvertex2) &&
6837 (triorg != m->infvertex3) &&
6838 (tridest != m->infvertex1) && (tridest != m->infvertex2) &&
6839 (tridest != m->infvertex3) &&
6840 (triapex != m->infvertex1) && (triapex != m->infvertex2) &&
6841 (triapex != m->infvertex3) &&
6842 (oppoapex != m->infvertex1) && (oppoapex != m->infvertex2) &&
6843 (oppoapex != m->infvertex3);
6844 if (m->checksegments && shouldbedelaunay) {
6845 /* If a subsegment separates the triangles, then the edge is */
6846 /* constrained, so no local Delaunay test should be done. */
6847 tspivot(triangleloop, opposubseg);
6848 if (opposubseg.ss != m->dummysub){
6849 shouldbedelaunay = 0;
6850 }
6851 }
6852 if (shouldbedelaunay) {
6853 if (nonregular(m, b, triorg, tridest, triapex, oppoapex) > 0.0) {
6854 if (!b->weighted) {
6855 printf(" !! !! Non-Delaunay pair of triangles:\n");
6856 printf(" First non-Delaunay ");
6857 printtriangle(m, b, &triangleloop);
6858 printf(" Second non-Delaunay ");
6859 } else {
6860 printf(" !! !! Non-regular pair of triangles:\n");
6861 printf(" First non-regular ");
6862 printtriangle(m, b, &triangleloop);
6863 printf(" Second non-regular ");
6864 }
6865 printtriangle(m, b, &oppotri);
6866 horrors++;
6867 }
6868 }
6869 }
6870 triangleloop.tri = triangletraverse(m);
6871 }
6872 if (horrors == 0) {
6873 if (!b->quiet) {
6874 printf(
6875 " By virtue of my perceptive intelligence, I declare the mesh Delaunay.\n");
6876 }
6877 } else if (horrors == 1) {
6878 printf(
6879 " !! !! !! !! Precisely one terrifying transgression identified.\n");
6880 } else {
6881 printf(" !! !! !! !! %d obscenities viewed with horror.\n", horrors);
6882 }
6883 /* Restore the status of exact arithmetic. */
6884 b->noexact = saveexact;
6885 }
6886
6887 #endif /* not REDUCED */
6888
6889 /*****************************************************************************/
6890 /* */
6891 /* enqueuebadtriang() Add a bad triangle data structure to the end of a */
6892 /* queue. */
6893 /* */
6894 /* The queue is actually a set of 4096 queues. I use multiple queues to */
6895 /* give priority to smaller angles. I originally implemented a heap, but */
6896 /* the queues are faster by a larger margin than I'd suspected. */
6897 /* */
6898 /*****************************************************************************/
6899
6900 #ifndef CDT_ONLY
6901
6902 #ifdef ANSI_DECLARATORS
6903 void enqueuebadtriang(struct mesh *m, struct behavior *b,
6904 struct badtriang *badtri)
6905 #else /* not ANSI_DECLARATORS */
6906 void enqueuebadtriang(m, b, badtri)
6907 struct mesh *m;
6908 struct behavior *b;
6909 struct badtriang *badtri;
6910 #endif /* not ANSI_DECLARATORS */
6911
6912 {
6913 REAL length, multiplier;
6914 int exponent, expincrement;
6915 int queuenumber;
6916 int posexponent;
6917 int i;
6918
6919 if (b->verbose > 2) {
6920 printf(" Queueing bad triangle:\n");
6921 printf(" (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
6922 badtri->triangorg[0], badtri->triangorg[1],
6923 badtri->triangdest[0], badtri->triangdest[1],
6924 badtri->triangapex[0], badtri->triangapex[1]);
6925 }
6926
6927 /* Determine the appropriate queue to put the bad triangle into. */
6928 /* Recall that the key is the square of its shortest edge length. */
6929 if (badtri->key >= 1.0) {
6930 length = badtri->key;
6931 posexponent = 1;
6932 } else {
6933 /* `badtri->key' is 2.0 to a negative exponent, so we'll record that */
6934 /* fact and use the reciprocal of `badtri->key', which is > 1.0. */
6935 length = 1.0 / badtri->key;
6936 posexponent = 0;
6937 }
6938 /* `length' is approximately 2.0 to what exponent? The following code */
6939 /* determines the answer in time logarithmic in the exponent. */
6940 exponent = 0;
6941 while (length > 2.0) {
6942 /* Find an approximation by repeated squaring of two. */
6943 expincrement = 1;
6944 multiplier = 0.5;
6945 while (length * multiplier * multiplier > 1.0) {
6946 expincrement *= 2;
6947 multiplier *= multiplier;
6948 }
6949 /* Reduce the value of `length', then iterate if necessary. */
6950 exponent += expincrement;
6951 length *= multiplier;
6952 }
6953 /* `length' is approximately squareroot(2.0) to what exponent? */
6954 exponent = 2.0 * exponent + (length > SQUAREROOTTWO);
6955 /* `exponent' is now in the range 0...2047 for IEEE double precision. */
6956 /* Choose a queue in the range 0...4095. The shortest edges have the */
6957 /* highest priority (queue 4095). */
6958 if (posexponent) {
6959 queuenumber = 2047 - exponent;
6960 } else {
6961 queuenumber = 2048 + exponent;
6962 }
6963
6964 /* Are we inserting into an empty queue? */
6965 if (m->queuefront[queuenumber] == (struct badtriang *) NULL) {
6966 /* Yes, we are inserting into an empty queue. */
6967 /* Will this become the highest-priority queue? */
6968 if (queuenumber > m->firstnonemptyq) {
6969 /* Yes, this is the highest-priority queue. */
6970 m->nextnonemptyq[queuenumber] = m->firstnonemptyq;
6971 m->firstnonemptyq = queuenumber;
6972 } else {
6973 /* No, this is not the highest-priority queue. */
6974 /* Find the queue with next higher priority. */
6975 i = queuenumber + 1;
6976 while (m->queuefront[i] == (struct badtriang *) NULL) {
6977 i++;
6978 }
6979 /* Mark the newly nonempty queue as following a higher-priority queue. */
6980 m->nextnonemptyq[queuenumber] = m->nextnonemptyq[i];
6981 m->nextnonemptyq[i] = queuenumber;
6982 }
6983 /* Put the bad triangle at the beginning of the (empty) queue. */
6984 m->queuefront[queuenumber] = badtri;
6985 } else {
6986 /* Add the bad triangle to the end of an already nonempty queue. */
6987 m->queuetail[queuenumber]->nexttriang = badtri;
6988 }
6989 /* Maintain a pointer to the last triangle of the queue. */
6990 m->queuetail[queuenumber] = badtri;
6991 /* Newly enqueued bad triangle has no successor in the queue. */
6992 badtri->nexttriang = (struct badtriang *) NULL;
6993 }
6994
6995 #endif /* not CDT_ONLY */
6996
6997 /*****************************************************************************/
6998 /* */
6999 /* enqueuebadtri() Add a bad triangle to the end of a queue. */
7000 /* */
7001 /* Allocates a badtriang data structure for the triangle, then passes it to */
7002 /* enqueuebadtriang(). */
7003 /* */
7004 /*****************************************************************************/
7005
7006 #ifndef CDT_ONLY
7007
7008 #ifdef ANSI_DECLARATORS
7009 void enqueuebadtri(struct mesh *m, struct behavior *b, struct otri *enqtri,
7010 REAL minedge, vertex enqapex, vertex enqorg, vertex enqdest)
7011 #else /* not ANSI_DECLARATORS */
7012 void enqueuebadtri(m, b, enqtri, minedge, enqapex, enqorg, enqdest)
7013 struct mesh *m;
7014 struct behavior *b;
7015 struct otri *enqtri;
7016 REAL minedge;
7017 vertex enqapex;
7018 vertex enqorg;
7019 vertex enqdest;
7020 #endif /* not ANSI_DECLARATORS */
7021
7022 {
7023 struct badtriang *newbad;
7024
7025 /* Allocate space for the bad triangle. */
7026 newbad = (struct badtriang *) poolalloc(&m->badtriangles);
7027 newbad->poortri = encode(*enqtri);
7028 newbad->key = minedge;
7029 newbad->triangapex = enqapex;
7030 newbad->triangorg = enqorg;
7031 newbad->triangdest = enqdest;
7032 enqueuebadtriang(m, b, newbad);
7033 }
7034
7035 #endif /* not CDT_ONLY */
7036
7037 /*****************************************************************************/
7038 /* */
7039 /* dequeuebadtriang() Remove a triangle from the front of the queue. */
7040 /* */
7041 /*****************************************************************************/
7042
7043 #ifndef CDT_ONLY
7044
7045 #ifdef ANSI_DECLARATORS
7046 struct badtriang *dequeuebadtriang(struct mesh *m)
7047 #else /* not ANSI_DECLARATORS */
7048 struct badtriang *dequeuebadtriang(m)
7049 struct mesh *m;
7050 #endif /* not ANSI_DECLARATORS */
7051
7052 {
7053 struct badtriang *result;
7054
7055 /* If no queues are nonempty, return NULL. */
7056 if (m->firstnonemptyq < 0) {
7057 return (struct badtriang *) NULL;
7058 }
7059 /* Find the first triangle of the highest-priority queue. */
7060 result = m->queuefront[m->firstnonemptyq];
7061 /* Remove the triangle from the queue. */
7062 m->queuefront[m->firstnonemptyq] = result->nexttriang;
7063 /* If this queue is now empty, note the new highest-priority */
7064 /* nonempty queue. */
7065 if (result == m->queuetail[m->firstnonemptyq]) {
7066 m->firstnonemptyq = m->nextnonemptyq[m->firstnonemptyq];
7067 }
7068 return result;
7069 }
7070
7071 #endif /* not CDT_ONLY */
7072
7073 /*****************************************************************************/
7074 /* */
7075 /* checkseg4encroach() Check a subsegment to see if it is encroached; add */
7076 /* it to the list if it is. */
7077 /* */
7078 /* A subsegment is encroached if there is a vertex in its diametral lens. */
7079 /* For Ruppert's algorithm (-D switch), the "diametral lens" is the */
7080 /* diametral circle. For Chew's algorithm (default), the diametral lens is */
7081 /* just big enough to enclose two isosceles triangles whose bases are the */
7082 /* subsegment. Each of the two isosceles triangles has two angles equal */
7083 /* to `b->minangle'. */
7084 /* */
7085 /* Chew's algorithm does not require diametral lenses at all--but they save */
7086 /* time. Any vertex inside a subsegment's diametral lens implies that the */
7087 /* triangle adjoining the subsegment will be too skinny, so it's only a */
7088 /* matter of time before the encroaching vertex is deleted by Chew's */
7089 /* algorithm. It's faster to simply not insert the doomed vertex in the */
7090 /* first place, which is why I use diametral lenses with Chew's algorithm. */
7091 /* */
7092 /* Returns a nonzero value if the subsegment is encroached. */
7093 /* */
7094 /*****************************************************************************/
7095
7096 #ifndef CDT_ONLY
7097
7098 #ifdef ANSI_DECLARATORS
7099 int checkseg4encroach(struct mesh *m, struct behavior *b,
7100 struct osub *testsubseg)
7101 #else /* not ANSI_DECLARATORS */
7102 int checkseg4encroach(m, b, testsubseg)
7103 struct mesh *m;
7104 struct behavior *b;
7105 struct osub *testsubseg;
7106 #endif /* not ANSI_DECLARATORS */
7107
7108 {
7109 struct otri neighbortri;
7110 struct osub testsym;
7111 struct badsubseg *encroachedseg;
7112 REAL dotproduct;
7113 int encroached;
7114 int sides;
7115 vertex eorg, edest, eapex;
7116 triangle ptr; /* Temporary variable used by stpivot(). */
7117
7118 encroached = 0;
7119 sides = 0;
7120
7121 sorg(*testsubseg, eorg);
7122 sdest(*testsubseg, edest);
7123 /* Check one neighbor of the subsegment. */
7124 stpivot(*testsubseg, neighbortri);
7125 /* Does the neighbor exist, or is this a boundary edge? */
7126 if (neighbortri.tri != m->dummytri) {
7127 sides++;
7128 /* Find a vertex opposite this subsegment. */
7129 apex(neighbortri, eapex);
7130 /* Check whether the apex is in the diametral lens of the subsegment */
7131 /* (the diametral circle if `conformdel' is set). A dot product */
7132 /* of two sides of the triangle is used to check whether the angle */
7133 /* at the apex is greater than (180 - 2 `minangle') degrees (for */
7134 /* lenses; 90 degrees for diametral circles). */
7135 dotproduct = (eorg[0] - eapex[0]) * (edest[0] - eapex[0]) +
7136 (eorg[1] - eapex[1]) * (edest[1] - eapex[1]);
7137 if (dotproduct < 0.0) {
7138 if (b->conformdel ||
7139 (dotproduct * dotproduct >=
7140 (2.0 * b->goodangle - 1.0) * (2.0 * b->goodangle - 1.0) *
7141 ((eorg[0] - eapex[0]) * (eorg[0] - eapex[0]) +
7142 (eorg[1] - eapex[1]) * (eorg[1] - eapex[1])) *
7143 ((edest[0] - eapex[0]) * (edest[0] - eapex[0]) +
7144 (edest[1] - eapex[1]) * (edest[1] - eapex[1])))) {
7145 encroached = 1;
7146 }
7147 }
7148 }
7149 /* Check the other neighbor of the subsegment. */
7150 ssym(*testsubseg, testsym);
7151 stpivot(testsym, neighbortri);
7152 /* Does the neighbor exist, or is this a boundary edge? */
7153 if (neighbortri.tri != m->dummytri) {
7154 sides++;
7155 /* Find the other vertex opposite this subsegment. */
7156 apex(neighbortri, eapex);
7157 /* Check whether the apex is in the diametral lens of the subsegment */
7158 /* (or the diametral circle, if `conformdel' is set). */
7159 dotproduct = (eorg[0] - eapex[0]) * (edest[0] - eapex[0]) +
7160 (eorg[1] - eapex[1]) * (edest[1] - eapex[1]);
7161 if (dotproduct < 0.0) {
7162 if (b->conformdel ||
7163 (dotproduct * dotproduct >=
7164 (2.0 * b->goodangle - 1.0) * (2.0 * b->goodangle - 1.0) *
7165 ((eorg[0] - eapex[0]) * (eorg[0] - eapex[0]) +
7166 (eorg[1] - eapex[1]) * (eorg[1] - eapex[1])) *
7167 ((edest[0] - eapex[0]) * (edest[0] - eapex[0]) +
7168 (edest[1] - eapex[1]) * (edest[1] - eapex[1])))) {
7169 encroached += 2;
7170 }
7171 }
7172 }
7173
7174 if (encroached && (!b->nobisect || ((b->nobisect == 1) && (sides == 2)))) {
7175 if (b->verbose > 2) {
7176 printf(
7177 " Queueing encroached subsegment (%.12g, %.12g) (%.12g, %.12g).\n",
7178 eorg[0], eorg[1], edest[0], edest[1]);
7179 }
7180 /* Add the subsegment to the list of encroached subsegments. */
7181 /* Be sure to get the orientation right. */
7182 encroachedseg = (struct badsubseg *) poolalloc(&m->badsubsegs);
7183 if (encroached == 1) {
7184 encroachedseg->encsubseg = sencode(*testsubseg);
7185 encroachedseg->subsegorg = eorg;
7186 encroachedseg->subsegdest = edest;
7187 } else {
7188 encroachedseg->encsubseg = sencode(testsym);
7189 encroachedseg->subsegorg = edest;
7190 encroachedseg->subsegdest = eorg;
7191 }
7192 }
7193
7194 return encroached;
7195 }
7196
7197 #endif /* not CDT_ONLY */
7198
7199 /*****************************************************************************/
7200 /* */
7201 /* testtriangle() Test a triangle for quality and size. */
7202 /* */
7203 /* Tests a triangle to see if it satisfies the minimum angle condition and */
7204 /* the maximum area condition. Triangles that aren't up to spec are added */
7205 /* to the bad triangle queue. */
7206 /* */
7207 /*****************************************************************************/
7208
7209 #ifndef CDT_ONLY
7210
7211 #ifdef ANSI_DECLARATORS
7212 void testtriangle(struct mesh *m, struct behavior *b, struct otri *testtri)
7213 #else /* not ANSI_DECLARATORS */
7214 void testtriangle(m, b, testtri)
7215 struct mesh *m;
7216 struct behavior *b;
7217 struct otri *testtri;
7218 #endif /* not ANSI_DECLARATORS */
7219
7220 {
7221 struct otri tri1, tri2;
7222 struct osub testsub;
7223 vertex torg, tdest, tapex;
7224 vertex base1, base2;
7225 vertex org1, dest1, org2, dest2;
7226 vertex joinvertex;
7227 REAL dxod, dyod, dxda, dyda, dxao, dyao;
7228 REAL dxod2, dyod2, dxda2, dyda2, dxao2, dyao2;
7229 REAL apexlen, orglen, destlen, minedge;
7230 REAL angle;
7231 REAL area;
7232 REAL dist1, dist2;
7233 subseg sptr; /* Temporary variable used by tspivot(). */
7234 triangle ptr; /* Temporary variable used by oprev() and dnext(). */
7235
7236 org(*testtri, torg);
7237 dest(*testtri, tdest);
7238 apex(*testtri, tapex);
7239 dxod = torg[0] - tdest[0];
7240 dyod = torg[1] - tdest[1];
7241 dxda = tdest[0] - tapex[0];
7242 dyda = tdest[1] - tapex[1];
7243 dxao = tapex[0] - torg[0];
7244 dyao = tapex[1] - torg[1];
7245 dxod2 = dxod * dxod;
7246 dyod2 = dyod * dyod;
7247 dxda2 = dxda * dxda;
7248 dyda2 = dyda * dyda;
7249 dxao2 = dxao * dxao;
7250 dyao2 = dyao * dyao;
7251 /* Find the lengths of the triangle's three edges. */
7252 apexlen = dxod2 + dyod2;
7253 orglen = dxda2 + dyda2;
7254 destlen = dxao2 + dyao2;
7255
7256 if ((apexlen < orglen) && (apexlen < destlen)) {
7257 /* The edge opposite the apex is shortest. */
7258 minedge = apexlen;
7259 /* Find the square of the cosine of the angle at the apex. */
7260 angle = dxda * dxao + dyda * dyao;
7261 angle = angle * angle / (orglen * destlen);
7262 base1 = torg;
7263 base2 = tdest;
7264 otricopy(*testtri, tri1);
7265 } else if (orglen < destlen) {
7266 /* The edge opposite the origin is shortest. */
7267 minedge = orglen;
7268 /* Find the square of the cosine of the angle at the origin. */
7269 angle = dxod * dxao + dyod * dyao;
7270 angle = angle * angle / (apexlen * destlen);
7271 base1 = tdest;
7272 base2 = tapex;
7273 lnext(*testtri, tri1);
7274 } else {
7275 /* The edge opposite the destination is shortest. */
7276 minedge = destlen;
7277 /* Find the square of the cosine of the angle at the destination. */
7278 angle = dxod * dxda + dyod * dyda;
7279 angle = angle * angle / (apexlen * orglen);
7280 base1 = tapex;
7281 base2 = torg;
7282 lprev(*testtri, tri1);
7283 }
7284
7285 if (b->vararea || b->fixedarea || b->usertest) {
7286 /* Check whether the area is larger than permitted. */
7287 area = 0.5 * (dxod * dyda - dyod * dxda);
7288 if (b->fixedarea && (area > b->maxarea)) {
7289 /* Add this triangle to the list of bad triangles. */
7290 enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest);
7291 return;
7292 }
7293
7294 /* Nonpositive area constraints are treated as unconstrained. */
7295 if ((b->vararea) && (area > areabound(*testtri)) &&
7296 (areabound(*testtri) > 0.0)) {
7297 /* Add this triangle to the list of bad triangles. */
7298 enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest);
7299 return;
7300 }
7301
7302 if (b->usertest) {
7303 /* Check whether the user thinks this triangle is too large. */
7304 if (triunsuitable(torg, tdest, tapex, area)) {
7305 enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest);
7306 return;
7307 }
7308 }
7309 }
7310
7311 /* Check whether the angle is smaller than permitted. */
7312 if (angle > b->goodangle) {
7313 /* Use the rules of Miller, Pav, and Walkington to decide that certain */
7314 /* triangles should not be split, even if they have bad angles. */
7315 /* A skinny triangle is not split if its shortest edge subtends a */
7316 /* small input angle, and both endpoints of the edge lie on a */
7317 /* concentric circular shell. For convenience, I make a small */
7318 /* adjustment to that rule: I check if the endpoints of the edge */
7319 /* both lie in segment interiors, equidistant from the apex where */
7320 /* the two segments meet. */
7321 /* First, check if both points lie in segment interiors. */
7322 if ((vertextype(base1) == SEGMENTVERTEX) &&
7323 (vertextype(base2) == SEGMENTVERTEX)) {
7324 /* Check if both points lie in a common segment. If they do, the */
7325 /* skinny triangle is enqueued to be split as usual. */
7326 tspivot(tri1, testsub);
7327 if (testsub.ss == m->dummysub) {
7328 /* No common segment. Find a subsegment that contains `torg'. */
7329 otricopy(tri1, tri2);
7330 do {
7331 oprevself(tri1);
7332 tspivot(tri1, testsub);
7333 } while (testsub.ss == m->dummysub);
7334 /* Find the endpoints of the containing segment. */
7335 segorg(testsub, org1);
7336 segdest(testsub, dest1);
7337 /* Find a subsegment that contains `tdest'. */
7338 do {
7339 dnextself(tri2);
7340 tspivot(tri2, testsub);
7341 } while (testsub.ss == m->dummysub);
7342 /* Find the endpoints of the containing segment. */
7343 segorg(testsub, org2);
7344 segdest(testsub, dest2);
7345 /* Check if the two containing segments have an endpoint in common. */
7346 joinvertex = (vertex) NULL;
7347 if ((dest1[0] == org2[0]) && (dest1[1] == org2[1])) {
7348 joinvertex = dest1;
7349 } else if ((org1[0] == dest2[0]) && (org1[1] == dest2[1])) {
7350 joinvertex = org1;
7351 }
7352 if (joinvertex != (vertex) NULL) {
7353 /* Compute the distance from the common endpoint (of the two */
7354 /* segments) to each of the endpoints of the shortest edge. */
7355 dist1 = ((base1[0] - joinvertex[0]) * (base1[0] - joinvertex[0]) +
7356 (base1[1] - joinvertex[1]) * (base1[1] - joinvertex[1]));
7357 dist2 = ((base2[0] - joinvertex[0]) * (base2[0] - joinvertex[0]) +
7358 (base2[1] - joinvertex[1]) * (base2[1] - joinvertex[1]));
7359 /* If the two distances are equal, don't split the triangle. */
7360 if ((dist1 < 1.001 * dist2) && (dist1 > 0.999 * dist2)) {
7361 /* Return now to avoid enqueueing the bad triangle. */
7362 return;
7363 }
7364 }
7365 }
7366 }
7367
7368 /* Add this triangle to the list of bad triangles. */
7369 enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest);
7370 }
7371 }
7372
7373 #endif /* not CDT_ONLY */
7374
7375 /** **/
7376 /** **/
7377 /********* Mesh quality testing routines end here *********/
7378
7379 /********* Point location routines begin here *********/
7380 /** **/
7381 /** **/
7382
7383 /*****************************************************************************/
7384 /* */
7385 /* makevertexmap() Construct a mapping from vertices to triangles to */
7386 /* improve the speed of point location for segment */
7387 /* insertion. */
7388 /* */
7389 /* Traverses all the triangles, and provides each corner of each triangle */
7390 /* with a pointer to that triangle. Of course, pointers will be */
7391 /* overwritten by other pointers because (almost) each vertex is a corner */
7392 /* of several triangles, but in the end every vertex will point to some */
7393 /* triangle that contains it. */
7394 /* */
7395 /*****************************************************************************/
7396
7397 #ifdef ANSI_DECLARATORS
7398 void makevertexmap(struct mesh *m, struct behavior *b)
7399 #else /* not ANSI_DECLARATORS */
7400 void makevertexmap(m, b)
7401 struct mesh *m;
7402 struct behavior *b;
7403 #endif /* not ANSI_DECLARATORS */
7404
7405 {
7406 struct otri triangleloop;
7407 vertex triorg;
7408
7409 if (b->verbose) {
7410 printf(" Constructing mapping from vertices to triangles.\n");
7411 }
7412 traversalinit(&m->triangles);
7413 triangleloop.tri = triangletraverse(m);
7414 while (triangleloop.tri != (triangle *) NULL) {
7415 /* Check all three vertices of the triangle. */
7416 for (triangleloop.orient = 0; triangleloop.orient < 3;
7417 triangleloop.orient++) {
7418 org(triangleloop, triorg);
7419 setvertex2tri(triorg, encode(triangleloop));
7420 }
7421 triangleloop.tri = triangletraverse(m);
7422 }
7423 }
7424
7425 /*****************************************************************************/
7426 /* */
7427 /* preciselocate() Find a triangle or edge containing a given point. */
7428 /* */
7429 /* Begins its search from `searchtri'. It is important that `searchtri' */
7430 /* be a handle with the property that `searchpoint' is strictly to the left */
7431 /* of the edge denoted by `searchtri', or is collinear with that edge and */
7432 /* does not intersect that edge. (In particular, `searchpoint' should not */
7433 /* be the origin or destination of that edge.) */
7434 /* */
7435 /* These conditions are imposed because preciselocate() is normally used in */
7436 /* one of two situations: */
7437 /* */
7438 /* (1) To try to find the location to insert a new point. Normally, we */
7439 /* know an edge that the point is strictly to the left of. In the */
7440 /* incremental Delaunay algorithm, that edge is a bounding box edge. */
7441 /* In Ruppert's Delaunay refinement algorithm for quality meshing, */
7442 /* that edge is the shortest edge of the triangle whose circumcenter */
7443 /* is being inserted. */
7444 /* */
7445 /* (2) To try to find an existing point. In this case, any edge on the */
7446 /* convex hull is a good starting edge. You must screen out the */
7447 /* possibility that the vertex sought is an endpoint of the starting */
7448 /* edge before you call preciselocate(). */
7449 /* */
7450 /* On completion, `searchtri' is a triangle that contains `searchpoint'. */
7451 /* */
7452 /* This implementation differs from that given by Guibas and Stolfi. It */
7453 /* walks from triangle to triangle, crossing an edge only if `searchpoint' */
7454 /* is on the other side of the line containing that edge. After entering */
7455 /* a triangle, there are two edges by which one can leave that triangle. */
7456 /* If both edges are valid (`searchpoint' is on the other side of both */
7457 /* edges), one of the two is chosen by drawing a line perpendicular to */
7458 /* the entry edge (whose endpoints are `forg' and `fdest') passing through */
7459 /* `fapex'. Depending on which side of this perpendicular `searchpoint' */
7460 /* falls on, an exit edge is chosen. */
7461 /* */
7462 /* This implementation is empirically faster than the Guibas and Stolfi */
7463 /* point location routine (which I originally used), which tends to spiral */
7464 /* in toward its target. */
7465 /* */
7466 /* Returns ONVERTEX if the point lies on an existing vertex. `searchtri' */
7467 /* is a handle whose origin is the existing vertex. */
7468 /* */
7469 /* Returns ONEDGE if the point lies on a mesh edge. `searchtri' is a */
7470 /* handle whose primary edge is the edge on which the point lies. */
7471 /* */
7472 /* Returns INTRIANGLE if the point lies strictly within a triangle. */
7473 /* `searchtri' is a handle on the triangle that contains the point. */
7474 /* */
7475 /* Returns OUTSIDE if the point lies outside the mesh. `searchtri' is a */
7476 /* handle whose primary edge the point is to the right of. This might */
7477 /* occur when the circumcenter of a triangle falls just slightly outside */
7478 /* the mesh due to floating-point roundoff error. It also occurs when */
7479 /* seeking a hole or region point that a foolish user has placed outside */
7480 /* the mesh. */
7481 /* */
7482 /* If `stopatsubsegment' is nonzero, the search will stop if it tries to */
7483 /* walk through a subsegment, and will return OUTSIDE. */
7484 /* */
7485 /* WARNING: This routine is designed for convex triangulations, and will */
7486 /* not generally work after the holes and concavities have been carved. */
7487 /* However, it can still be used to find the circumcenter of a triangle, as */
7488 /* long as the search is begun from the triangle in question. */
7489 /* */
7490 /*****************************************************************************/
7491
7492 #ifdef ANSI_DECLARATORS
7493 enum locateresult preciselocate(struct mesh *m, struct behavior *b,
7494 vertex searchpoint, struct otri *searchtri,
7495 int stopatsubsegment)
7496 #else /* not ANSI_DECLARATORS */
7497 enum locateresult preciselocate(m, b, searchpoint, searchtri, stopatsubsegment)
7498 struct mesh *m;
7499 struct behavior *b;
7500 vertex searchpoint;
7501 struct otri *searchtri;
7502 int stopatsubsegment;
7503 #endif /* not ANSI_DECLARATORS */
7504
7505 {
7506 struct otri backtracktri;
7507 struct osub checkedge;
7508 vertex forg, fdest, fapex;
7509 REAL orgorient, destorient;
7510 int moveleft;
7511 triangle ptr; /* Temporary variable used by sym(). */
7512 subseg sptr; /* Temporary variable used by tspivot(). */
7513
7514 if (b->verbose > 2) {
7515 printf(" Searching for point (%.12g, %.12g).\n",
7516 searchpoint[0], searchpoint[1]);
7517 }
7518 /* Where are we? */
7519 org(*searchtri, forg);
7520 dest(*searchtri, fdest);
7521 apex(*searchtri, fapex);
7522 while (1) {
7523 if (b->verbose > 2) {
7524 printf(" At (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
7525 forg[0], forg[1], fdest[0], fdest[1], fapex[0], fapex[1]);
7526 }
7527 /* Check whether the apex is the point we seek. */
7528 if ((fapex[0] == searchpoint[0]) && (fapex[1] == searchpoint[1])) {
7529 lprevself(*searchtri);
7530 return ONVERTEX;
7531 }
7532 /* Does the point lie on the other side of the line defined by the */
7533 /* triangle edge opposite the triangle's destination? */
7534 destorient = counterclockwise(m, b, forg, fapex, searchpoint);
7535 /* Does the point lie on the other side of the line defined by the */
7536 /* triangle edge opposite the triangle's origin? */
7537 orgorient = counterclockwise(m, b, fapex, fdest, searchpoint);
7538 if (destorient > 0.0) {
7539 if (orgorient > 0.0) {
7540 /* Move left if the inner product of (fapex - searchpoint) and */
7541 /* (fdest - forg) is positive. This is equivalent to drawing */
7542 /* a line perpendicular to the line (forg, fdest) and passing */
7543 /* through `fapex', and determining which side of this line */
7544 /* `searchpoint' falls on. */
7545 moveleft = (fapex[0] - searchpoint[0]) * (fdest[0] - forg[0]) +
7546 (fapex[1] - searchpoint[1]) * (fdest[1] - forg[1]) > 0.0;
7547 } else {
7548 moveleft = 1;
7549 }
7550 } else {
7551 if (orgorient > 0.0) {
7552 moveleft = 0;
7553 } else {
7554 /* The point we seek must be on the boundary of or inside this */
7555 /* triangle. */
7556 if (destorient == 0.0) {
7557 lprevself(*searchtri);
7558 return ONEDGE;
7559 }
7560 if (orgorient == 0.0) {
7561 lnextself(*searchtri);
7562 return ONEDGE;
7563 }
7564 return INTRIANGLE;
7565 }
7566 }
7567
7568 /* Move to another triangle. Leave a trace `backtracktri' in case */
7569 /* floating-point roundoff or some such bogey causes us to walk */
7570 /* off a boundary of the triangulation. */
7571 if (moveleft) {
7572 lprev(*searchtri, backtracktri);
7573 fdest = fapex;
7574 } else {
7575 lnext(*searchtri, backtracktri);
7576 forg = fapex;
7577 }
7578 sym(backtracktri, *searchtri);
7579
7580 if (m->checksegments && stopatsubsegment) {
7581 /* Check for walking through a subsegment. */
7582 tspivot(backtracktri, checkedge);
7583 if (checkedge.ss != m->dummysub) {
7584 /* Go back to the last triangle. */
7585 otricopy(backtracktri, *searchtri);
7586 return OUTSIDE;
7587 }
7588 }
7589 /* Check for walking right out of the triangulation. */
7590 if (searchtri->tri == m->dummytri) {
7591 /* Go back to the last triangle. */
7592 otricopy(backtracktri, *searchtri);
7593 return OUTSIDE;
7594 }
7595
7596 apex(*searchtri, fapex);
7597 }
7598 }
7599
7600 /*****************************************************************************/
7601 /* */
7602 /* locate() Find a triangle or edge containing a given point. */
7603 /* */
7604 /* Searching begins from one of: the input `searchtri', a recently */
7605 /* encountered triangle `recenttri', or from a triangle chosen from a */
7606 /* random sample. The choice is made by determining which triangle's */
7607 /* origin is closest to the point we are searching for. Normally, */
7608 /* `searchtri' should be a handle on the convex hull of the triangulation. */
7609 /* */
7610 /* Details on the random sampling method can be found in the Mucke, Saias, */
7611 /* and Zhu paper cited in the header of this code. */
7612 /* */
7613 /* On completion, `searchtri' is a triangle that contains `searchpoint'. */
7614 /* */
7615 /* Returns ONVERTEX if the point lies on an existing vertex. `searchtri' */
7616 /* is a handle whose origin is the existing vertex. */
7617 /* */
7618 /* Returns ONEDGE if the point lies on a mesh edge. `searchtri' is a */
7619 /* handle whose primary edge is the edge on which the point lies. */
7620 /* */
7621 /* Returns INTRIANGLE if the point lies strictly within a triangle. */
7622 /* `searchtri' is a handle on the triangle that contains the point. */
7623 /* */
7624 /* Returns OUTSIDE if the point lies outside the mesh. `searchtri' is a */
7625 /* handle whose primary edge the point is to the right of. This might */
7626 /* occur when the circumcenter of a triangle falls just slightly outside */
7627 /* the mesh due to floating-point roundoff error. It also occurs when */
7628 /* seeking a hole or region point that a foolish user has placed outside */
7629 /* the mesh. */
7630 /* */
7631 /* WARNING: This routine is designed for convex triangulations, and will */
7632 /* not generally work after the holes and concavities have been carved. */
7633 /* */
7634 /*****************************************************************************/
7635
7636 #ifdef ANSI_DECLARATORS
7637 enum locateresult locate(struct mesh *m, struct behavior *b,
7638 vertex searchpoint, struct otri *searchtri)
7639 #else /* not ANSI_DECLARATORS */
7640 enum locateresult locate(m, b, searchpoint, searchtri)
7641 struct mesh *m;
7642 struct behavior *b;
7643 vertex searchpoint;
7644 struct otri *searchtri;
7645 #endif /* not ANSI_DECLARATORS */
7646
7647 {
7648 VOID **sampleblock;
7649 char *firsttri;
7650 struct otri sampletri;
7651 vertex torg, tdest;
7652 unsigned long alignptr;
7653 REAL searchdist, dist;
7654 REAL ahead;
7655 long samplesperblock, totalsamplesleft, samplesleft;
7656 long population, totalpopulation;
7657 triangle ptr; /* Temporary variable used by sym(). */
7658
7659 if (b->verbose > 2) {
7660 printf(" Randomly sampling for a triangle near point (%.12g, %.12g).\n",
7661 searchpoint[0], searchpoint[1]);
7662 }
7663 /* Record the distance from the suggested starting triangle to the */
7664 /* point we seek. */
7665 org(*searchtri, torg);
7666 searchdist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) +
7667 (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]);
7668 if (b->verbose > 2) {
7669 printf(" Boundary triangle has origin (%.12g, %.12g).\n",
7670 torg[0], torg[1]);
7671 }
7672
7673 /* If a recently encountered triangle has been recorded and has not been */
7674 /* deallocated, test it as a good starting point. */
7675 if (m->recenttri.tri != (triangle *) NULL) {
7676 if (!deadtri(m->recenttri.tri)) {
7677 org(m->recenttri, torg);
7678 if ((torg[0] == searchpoint[0]) && (torg[1] == searchpoint[1])) {
7679 otricopy(m->recenttri, *searchtri);
7680 return ONVERTEX;
7681 }
7682 dist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) +
7683 (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]);
7684 if (dist < searchdist) {
7685 otricopy(m->recenttri, *searchtri);
7686 searchdist = dist;
7687 if (b->verbose > 2) {
7688 printf(" Choosing recent triangle with origin (%.12g, %.12g).\n",
7689 torg[0], torg[1]);
7690 }
7691 }
7692 }
7693 }
7694
7695 /* The number of random samples taken is proportional to the cube root of */
7696 /* the number of triangles in the mesh. The next bit of code assumes */
7697 /* that the number of triangles increases monotonically (or at least */
7698 /* doesn't decrease enough to matter). */
7699 while (SAMPLEFACTOR * m->samples * m->samples * m->samples <
7700 m->triangles.items) {
7701 m->samples++;
7702 }
7703
7704 /* We'll draw ceiling(samples * TRIPERBLOCK / maxitems) random samples */
7705 /* from each block of triangles (except the first)--until we meet the */
7706 /* sample quota. The ceiling means that blocks at the end might be */
7707 /* neglected, but I don't care. */
7708 samplesperblock = (m->samples * TRIPERBLOCK - 1) / m->triangles.maxitems + 1;
7709 /* We'll draw ceiling(samples * itemsfirstblock / maxitems) random samples */
7710 /* from the first block of triangles. */
7711 samplesleft = (m->samples * m->triangles.itemsfirstblock - 1) /
7712 m->triangles.maxitems + 1;
7713 totalsamplesleft = m->samples;
7714 population = m->triangles.itemsfirstblock;
7715 totalpopulation = m->triangles.maxitems;
7716 sampleblock = m->triangles.firstblock;
7717 sampletri.orient = 0;
7718 while (totalsamplesleft > 0) {
7719 /* If we're in the last block, `population' needs to be corrected. */
7720 if (population > totalpopulation) {
7721 population = totalpopulation;
7722 }
7723 /* Find a pointer to the first triangle in the block. */
7724 alignptr = (unsigned long) (sampleblock + 1);
7725 firsttri = (char *) (alignptr +
7726 (unsigned long) m->triangles.alignbytes -
7727 (alignptr %
7728 (unsigned long) m->triangles.alignbytes));
7729
7730 /* Choose `samplesleft' randomly sampled triangles in this block. */
7731 do {
7732 sampletri.tri = (triangle *) (firsttri +
7733 (randomnation((unsigned int) population) *
7734 m->triangles.itembytes));
7735 if (!deadtri(sampletri.tri)) {
7736 org(sampletri, torg);
7737 dist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) +
7738 (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]);
7739 if (dist < searchdist) {
7740 otricopy(sampletri, *searchtri);
7741 searchdist = dist;
7742 if (b->verbose > 2) {
7743 printf(" Choosing triangle with origin (%.12g, %.12g).\n",
7744 torg[0], torg[1]);
7745 }
7746 }
7747 }
7748
7749 samplesleft--;
7750 totalsamplesleft--;
7751 } while ((samplesleft > 0) && (totalsamplesleft > 0));
7752
7753 if (totalsamplesleft > 0) {
7754 sampleblock = (VOID **) *sampleblock;
7755 samplesleft = samplesperblock;
7756 totalpopulation -= population;
7757 population = TRIPERBLOCK;
7758 }
7759 }
7760
7761 /* Where are we? */
7762 org(*searchtri, torg);
7763 dest(*searchtri, tdest);
7764 /* Check the starting triangle's vertices. */
7765 if ((torg[0] == searchpoint[0]) && (torg[1] == searchpoint[1])) {
7766 return ONVERTEX;
7767 }
7768 if ((tdest[0] == searchpoint[0]) && (tdest[1] == searchpoint[1])) {
7769 lnextself(*searchtri);
7770 return ONVERTEX;
7771 }
7772 /* Orient `searchtri' to fit the preconditions of calling preciselocate(). */
7773 ahead = counterclockwise(m, b, torg, tdest, searchpoint);
7774 if (ahead < 0.0) {
7775 /* Turn around so that `searchpoint' is to the left of the */
7776 /* edge specified by `searchtri'. */
7777 symself(*searchtri);
7778 } else if (ahead == 0.0) {
7779 /* Check if `searchpoint' is between `torg' and `tdest'. */
7780 if (((torg[0] < searchpoint[0]) == (searchpoint[0] < tdest[0])) &&
7781 ((torg[1] < searchpoint[1]) == (searchpoint[1] < tdest[1]))) {
7782 return ONEDGE;
7783 }
7784 }
7785 return preciselocate(m, b, searchpoint, searchtri, 0);
7786 }
7787
7788 /** **/
7789 /** **/
7790 /********* Point location routines end here *********/
7791
7792 /********* Mesh transformation routines begin here *********/
7793 /** **/
7794 /** **/
7795
7796 /*****************************************************************************/
7797 /* */
7798 /* insertsubseg() Create a new subsegment and insert it between two */
7799 /* triangles. */
7800 /* */
7801 /* The new subsegment is inserted at the edge described by the handle */
7802 /* `tri'. Its vertices are properly initialized. The marker `subsegmark' */
7803 /* is applied to the subsegment and, if appropriate, its vertices. */
7804 /* */
7805 /*****************************************************************************/
7806
7807 #ifdef ANSI_DECLARATORS
7808 void insertsubseg(struct mesh *m, struct behavior *b, struct otri *tri,
7809 int subsegmark)
7810 #else /* not ANSI_DECLARATORS */
7811 void insertsubseg(m, b, tri, subsegmark)
7812 struct mesh *m;
7813 struct behavior *b;
7814 struct otri *tri; /* Edge at which to insert the new subsegment. */
7815 int subsegmark; /* Marker for the new subsegment. */
7816 #endif /* not ANSI_DECLARATORS */
7817
7818 {
7819 struct otri oppotri;
7820 struct osub newsubseg;
7821 vertex triorg, tridest;
7822 triangle ptr; /* Temporary variable used by sym(). */
7823 subseg sptr; /* Temporary variable used by tspivot(). */
7824
7825 org(*tri, triorg);
7826 dest(*tri, tridest);
7827 /* Mark vertices if possible. */
7828 if (vertexmark(triorg) == 0) {
7829 setvertexmark(triorg, subsegmark);
7830 }
7831 if (vertexmark(tridest) == 0) {
7832 setvertexmark(tridest, subsegmark);
7833 }
7834 /* Check if there's already a subsegment here. */
7835 tspivot(*tri, newsubseg);
7836 if (newsubseg.ss == m->dummysub) {
7837 /* Make new subsegment and initialize its vertices. */
7838 makesubseg(m, &newsubseg);
7839 setsorg(newsubseg, tridest);
7840 setsdest(newsubseg, triorg);
7841 setsegorg(newsubseg, tridest);
7842 setsegdest(newsubseg, triorg);
7843 /* Bond new subsegment to the two triangles it is sandwiched between. */
7844 /* Note that the facing triangle `oppotri' might be equal to */
7845 /* `dummytri' (outer space), but the new subsegment is bonded to it */
7846 /* all the same. */
7847 tsbond(*tri, newsubseg);
7848 sym(*tri, oppotri);
7849 ssymself(newsubseg);
7850 tsbond(oppotri, newsubseg);
7851 setmark(newsubseg, subsegmark);
7852 if (b->verbose > 2) {
7853 printf(" Inserting new ");
7854 printsubseg(m, b, &newsubseg);
7855 }
7856 } else {
7857 if (mark(newsubseg) == 0) {
7858 setmark(newsubseg, subsegmark);
7859 }
7860 }
7861 }
7862
7863 /*****************************************************************************/
7864 /* */
7865 /* Terminology */
7866 /* */
7867 /* A "local transformation" replaces a small set of triangles with another */
7868 /* set of triangles. This may or may not involve inserting or deleting a */
7869 /* vertex. */
7870 /* */
7871 /* The term "casing" is used to describe the set of triangles that are */
7872 /* attached to the triangles being transformed, but are not transformed */
7873 /* themselves. Think of the casing as a fixed hollow structure inside */
7874 /* which all the action happens. A "casing" is only defined relative to */
7875 /* a single transformation; each occurrence of a transformation will */
7876 /* involve a different casing. */
7877 /* */
7878 /*****************************************************************************/
7879
7880 /*****************************************************************************/
7881 /* */
7882 /* flip() Transform two triangles to two different triangles by flipping */
7883 /* an edge counterclockwise within a quadrilateral. */
7884 /* */
7885 /* Imagine the original triangles, abc and bad, oriented so that the */
7886 /* shared edge ab lies in a horizontal plane, with the vertex b on the left */
7887 /* and the vertex a on the right. The vertex c lies below the edge, and */
7888 /* the vertex d lies above the edge. The `flipedge' handle holds the edge */
7889 /* ab of triangle abc, and is directed left, from vertex a to vertex b. */
7890 /* */
7891 /* The triangles abc and bad are deleted and replaced by the triangles cdb */
7892 /* and dca. The triangles that represent abc and bad are NOT deallocated; */
7893 /* they are reused for dca and cdb, respectively. Hence, any handles that */
7894 /* may have held the original triangles are still valid, although not */
7895 /* directed as they were before. */
7896 /* */
7897 /* Upon completion of this routine, the `flipedge' handle holds the edge */
7898 /* dc of triangle dca, and is directed down, from vertex d to vertex c. */
7899 /* (Hence, the two triangles have rotated counterclockwise.) */
7900 /* */
7901 /* WARNING: This transformation is geometrically valid only if the */
7902 /* quadrilateral adbc is convex. Furthermore, this transformation is */
7903 /* valid only if there is not a subsegment between the triangles abc and */
7904 /* bad. This routine does not check either of these preconditions, and */
7905 /* it is the responsibility of the calling routine to ensure that they are */
7906 /* met. If they are not, the streets shall be filled with wailing and */
7907 /* gnashing of teeth. */
7908 /* */
7909 /*****************************************************************************/
7910
7911 #ifdef ANSI_DECLARATORS
7912 void flip(struct mesh *m, struct behavior *b, struct otri *flipedge)
7913 #else /* not ANSI_DECLARATORS */
7914 void flip(m, b, flipedge)
7915 struct mesh *m;
7916 struct behavior *b;
7917 struct otri *flipedge; /* Handle for the triangle abc. */
7918 #endif /* not ANSI_DECLARATORS */
7919
7920 {
7921 struct otri botleft, botright;
7922 struct otri topleft, topright;
7923 struct otri top;
7924 struct otri botlcasing, botrcasing;
7925 struct otri toplcasing, toprcasing;
7926 struct osub botlsubseg, botrsubseg;
7927 struct osub toplsubseg, toprsubseg;
7928 vertex leftvertex, rightvertex, botvertex;
7929 vertex farvertex;
7930 triangle ptr; /* Temporary variable used by sym(). */
7931 subseg sptr; /* Temporary variable used by tspivot(). */
7932
7933 /* Identify the vertices of the quadrilateral. */
7934 org(*flipedge, rightvertex);
7935 dest(*flipedge, leftvertex);
7936 apex(*flipedge, botvertex);
7937 sym(*flipedge, top);
7938 #ifdef SELF_CHECK
7939 if (top.tri == m->dummytri) {
7940 printf("Internal error in flip(): Attempt to flip on boundary.\n");
7941 lnextself(*flipedge);
7942 return;
7943 }
7944 if (m->checksegments) {
7945 tspivot(*flipedge, toplsubseg);
7946 if (toplsubseg.ss != m->dummysub) {
7947 printf("Internal error in flip(): Attempt to flip a segment.\n");
7948 lnextself(*flipedge);
7949 return;
7950 }
7951 }
7952 #endif /* SELF_CHECK */
7953 apex(top, farvertex);
7954
7955 /* Identify the casing of the quadrilateral. */
7956 lprev(top, topleft);
7957 sym(topleft, toplcasing);
7958 lnext(top, topright);
7959 sym(topright, toprcasing);
7960 lnext(*flipedge, botleft);
7961 sym(botleft, botlcasing);
7962 lprev(*flipedge, botright);
7963 sym(botright, botrcasing);
7964 /* Rotate the quadrilateral one-quarter turn counterclockwise. */
7965 bond(topleft, botlcasing);
7966 bond(botleft, botrcasing);
7967 bond(botright, toprcasing);
7968 bond(topright, toplcasing);
7969
7970 if (m->checksegments) {
7971 /* Check for subsegments and rebond them to the quadrilateral. */
7972 tspivot(topleft, toplsubseg);
7973 tspivot(botleft, botlsubseg);
7974 tspivot(botright, botrsubseg);
7975 tspivot(topright, toprsubseg);
7976 if (toplsubseg.ss == m->dummysub) {
7977 tsdissolve(topright);
7978 } else {
7979 tsbond(topright, toplsubseg);
7980 }
7981 if (botlsubseg.ss == m->dummysub) {
7982 tsdissolve(topleft);
7983 } else {
7984 tsbond(topleft, botlsubseg);
7985 }
7986 if (botrsubseg.ss == m->dummysub) {
7987 tsdissolve(botleft);
7988 } else {
7989 tsbond(botleft, botrsubseg);
7990 }
7991 if (toprsubseg.ss == m->dummysub) {
7992 tsdissolve(botright);
7993 } else {
7994 tsbond(botright, toprsubseg);
7995 }
7996 }
7997
7998 /* New vertex assignments for the rotated quadrilateral. */
7999 setorg(*flipedge, farvertex);
8000 setdest(*flipedge, botvertex);
8001 setapex(*flipedge, rightvertex);
8002 setorg(top, botvertex);
8003 setdest(top, farvertex);
8004 setapex(top, leftvertex);
8005 if (b->verbose > 2) {
8006 printf(" Edge flip results in left ");
8007 printtriangle(m, b, &top);
8008 printf(" and right ");
8009 printtriangle(m, b, flipedge);
8010 }
8011 }
8012
8013 /*****************************************************************************/
8014 /* */
8015 /* unflip() Transform two triangles to two different triangles by */
8016 /* flipping an edge clockwise within a quadrilateral. Reverses */
8017 /* the flip() operation so that the data structures representing */
8018 /* the triangles are back where they were before the flip(). */
8019 /* */
8020 /* Imagine the original triangles, abc and bad, oriented so that the */
8021 /* shared edge ab lies in a horizontal plane, with the vertex b on the left */
8022 /* and the vertex a on the right. The vertex c lies below the edge, and */
8023 /* the vertex d lies above the edge. The `flipedge' handle holds the edge */
8024 /* ab of triangle abc, and is directed left, from vertex a to vertex b. */
8025 /* */
8026 /* The triangles abc and bad are deleted and replaced by the triangles cdb */
8027 /* and dca. The triangles that represent abc and bad are NOT deallocated; */
8028 /* they are reused for cdb and dca, respectively. Hence, any handles that */
8029 /* may have held the original triangles are still valid, although not */
8030 /* directed as they were before. */
8031 /* */
8032 /* Upon completion of this routine, the `flipedge' handle holds the edge */
8033 /* cd of triangle cdb, and is directed up, from vertex c to vertex d. */
8034 /* (Hence, the two triangles have rotated clockwise.) */
8035 /* */
8036 /* WARNING: This transformation is geometrically valid only if the */
8037 /* quadrilateral adbc is convex. Furthermore, this transformation is */
8038 /* valid only if there is not a subsegment between the triangles abc and */
8039 /* bad. This routine does not check either of these preconditions, and */
8040 /* it is the responsibility of the calling routine to ensure that they are */
8041 /* met. If they are not, the streets shall be filled with wailing and */
8042 /* gnashing of teeth. */
8043 /* */
8044 /*****************************************************************************/
8045
8046 #ifdef ANSI_DECLARATORS
8047 void unflip(struct mesh *m, struct behavior *b, struct otri *flipedge)
8048 #else /* not ANSI_DECLARATORS */
8049 void unflip(m, b, flipedge)
8050 struct mesh *m;
8051 struct behavior *b;
8052 struct otri *flipedge; /* Handle for the triangle abc. */
8053 #endif /* not ANSI_DECLARATORS */
8054
8055 {
8056 struct otri botleft, botright;
8057 struct otri topleft, topright;
8058 struct otri top;
8059 struct otri botlcasing, botrcasing;
8060 struct otri toplcasing, toprcasing;
8061 struct osub botlsubseg, botrsubseg;
8062 struct osub toplsubseg, toprsubseg;
8063 vertex leftvertex, rightvertex, botvertex;
8064 vertex farvertex;
8065 triangle ptr; /* Temporary variable used by sym(). */
8066 subseg sptr; /* Temporary variable used by tspivot(). */
8067
8068 /* Identify the vertices of the quadrilateral. */
8069 org(*flipedge, rightvertex);
8070 dest(*flipedge, leftvertex);
8071 apex(*flipedge, botvertex);
8072 sym(*flipedge, top);
8073 #ifdef SELF_CHECK
8074 if (top.tri == m->dummytri) {
8075 printf("Internal error in unflip(): Attempt to flip on boundary.\n");
8076 lnextself(*flipedge);
8077 return;
8078 }
8079 if (m->checksegments) {
8080 tspivot(*flipedge, toplsubseg);
8081 if (toplsubseg.ss != m->dummysub) {
8082 printf("Internal error in unflip(): Attempt to flip a subsegment.\n");
8083 lnextself(*flipedge);
8084 return;
8085 }
8086 }
8087 #endif /* SELF_CHECK */
8088 apex(top, farvertex);
8089
8090 /* Identify the casing of the quadrilateral. */
8091 lprev(top, topleft);
8092 sym(topleft, toplcasing);
8093 lnext(top, topright);
8094 sym(topright, toprcasing);
8095 lnext(*flipedge, botleft);
8096 sym(botleft, botlcasing);
8097 lprev(*flipedge, botright);
8098 sym(botright, botrcasing);
8099 /* Rotate the quadrilateral one-quarter turn clockwise. */
8100 bond(topleft, toprcasing);
8101 bond(botleft, toplcasing);
8102 bond(botright, botlcasing);
8103 bond(topright, botrcasing);
8104
8105 if (m->checksegments) {
8106 /* Check for subsegments and rebond them to the quadrilateral. */
8107 tspivot(topleft, toplsubseg);
8108 tspivot(botleft, botlsubseg);
8109 tspivot(botright, botrsubseg);
8110 tspivot(topright, toprsubseg);
8111 if (toplsubseg.ss == m->dummysub) {
8112 tsdissolve(botleft);
8113 } else {
8114 tsbond(botleft, toplsubseg);
8115 }
8116 if (botlsubseg.ss == m->dummysub) {
8117 tsdissolve(botright);
8118 } else {
8119 tsbond(botright, botlsubseg);
8120 }
8121 if (botrsubseg.ss == m->dummysub) {
8122 tsdissolve(topright);
8123 } else {
8124 tsbond(topright, botrsubseg);
8125 }
8126 if (toprsubseg.ss == m->dummysub) {
8127 tsdissolve(topleft);
8128 } else {
8129 tsbond(topleft, toprsubseg);
8130 }
8131 }
8132
8133 /* New vertex assignments for the rotated quadrilateral. */
8134 setorg(*flipedge, botvertex);
8135 setdest(*flipedge, farvertex);
8136 setapex(*flipedge, leftvertex);
8137 setorg(top, farvertex);
8138 setdest(top, botvertex);
8139 setapex(top, rightvertex);
8140 if (b->verbose > 2) {
8141 printf(" Edge unflip results in left ");
8142 printtriangle(m, b, flipedge);
8143 printf(" and right ");
8144 printtriangle(m, b, &top);
8145 }
8146 }
8147
8148 /*****************************************************************************/
8149 /* */
8150 /* insertvertex() Insert a vertex into a Delaunay triangulation, */
8151 /* performing flips as necessary to maintain the Delaunay */
8152 /* property. */
8153 /* */
8154 /* The point `insertvertex' is located. If `searchtri.tri' is not NULL, */
8155 /* the search for the containing triangle begins from `searchtri'. If */
8156 /* `searchtri.tri' is NULL, a full point location procedure is called. */
8157 /* If `insertvertex' is found inside a triangle, the triangle is split into */
8158 /* three; if `insertvertex' lies on an edge, the edge is split in two, */
8159 /* thereby splitting the two adjacent triangles into four. Edge flips are */
8160 /* used to restore the Delaunay property. If `insertvertex' lies on an */
8161 /* existing vertex, no action is taken, and the value DUPLICATEVERTEX is */
8162 /* returned. On return, `searchtri' is set to a handle whose origin is the */
8163 /* existing vertex. */
8164 /* */
8165 /* Normally, the parameter `splitseg' is set to NULL, implying that no */
8166 /* subsegment should be split. In this case, if `insertvertex' is found to */
8167 /* lie on a segment, no action is taken, and the value VIOLATINGVERTEX is */
8168 /* returned. On return, `searchtri' is set to a handle whose primary edge */
8169 /* is the violated subsegment. */
8170 /* */
8171 /* If the calling routine wishes to split a subsegment by inserting a */
8172 /* vertex in it, the parameter `splitseg' should be that subsegment. In */
8173 /* this case, `searchtri' MUST be the triangle handle reached by pivoting */
8174 /* from that subsegment; no point location is done. */
8175 /* */
8176 /* `segmentflaws' and `triflaws' are flags that indicate whether or not */
8177 /* there should be checks for the creation of encroached subsegments or bad */
8178 /* quality triangles. If a newly inserted vertex encroaches upon */
8179 /* subsegments, these subsegments are added to the list of subsegments to */
8180 /* be split if `segmentflaws' is set. If bad triangles are created, these */
8181 /* are added to the queue if `triflaws' is set. */
8182 /* */
8183 /* If a duplicate vertex or violated segment does not prevent the vertex */
8184 /* from being inserted, the return value will be ENCROACHINGVERTEX if the */
8185 /* vertex encroaches upon a subsegment (and checking is enabled), or */
8186 /* SUCCESSFULVERTEX otherwise. In either case, `searchtri' is set to a */
8187 /* handle whose origin is the newly inserted vertex. */
8188 /* */
8189 /* insertvertex() does not use flip() for reasons of speed; some */
8190 /* information can be reused from edge flip to edge flip, like the */
8191 /* locations of subsegments. */
8192 /* */
8193 /*****************************************************************************/
8194
8195 #ifdef ANSI_DECLARATORS
8196 enum insertvertexresult insertvertex(struct mesh *m, struct behavior *b,
8197 vertex newvertex, struct otri *searchtri,
8198 struct osub *splitseg,
8199 int segmentflaws, int triflaws)
8200 #else /* not ANSI_DECLARATORS */
8201 enum insertvertexresult insertvertex(m, b, newvertex, searchtri, splitseg,
8202 segmentflaws, triflaws)
8203 struct mesh *m;
8204 struct behavior *b;
8205 vertex newvertex;
8206 struct otri *searchtri;
8207 struct osub *splitseg;
8208 int segmentflaws;
8209 int triflaws;
8210 #endif /* not ANSI_DECLARATORS */
8211
8212 {
8213 struct otri horiz;
8214 struct otri top;
8215 struct otri botleft, botright;
8216 struct otri topleft, topright;
8217 struct otri newbotleft, newbotright;
8218 struct otri newtopright;
8219 struct otri botlcasing, botrcasing;
8220 struct otri toplcasing, toprcasing;
8221 struct otri testtri;
8222 struct osub botlsubseg, botrsubseg;
8223 struct osub toplsubseg, toprsubseg;
8224 struct osub brokensubseg;
8225 struct osub checksubseg;
8226 struct osub rightsubseg;
8227 struct osub newsubseg;
8228 struct badsubseg *encroached;
8229 struct flipstacker *newflip;
8230 vertex first;
8231 vertex leftvertex, rightvertex, botvertex, topvertex, farvertex;
8232 vertex segmentorg, segmentdest;
8233 REAL attrib;
8234 REAL area;
8235 enum insertvertexresult success;
8236 enum locateresult intersect;
8237 int doflip;
8238 int mirrorflag;
8239 int enq;
8240 int i;
8241 triangle ptr; /* Temporary variable used by sym(). */
8242 subseg sptr; /* Temporary variable used by spivot() and tspivot(). */
8243
8244 if (b->verbose > 1) {
8245 printf(" Inserting (%.12g, %.12g).\n", newvertex[0], newvertex[1]);
8246 }
8247
8248 if (splitseg == (struct osub *) NULL) {
8249 /* Find the location of the vertex to be inserted. Check if a good */
8250 /* starting triangle has already been provided by the caller. */
8251 if (searchtri->tri == m->dummytri) {
8252 /* Find a boundary triangle. */
8253 horiz.tri = m->dummytri;
8254 horiz.orient = 0;
8255 symself(horiz);
8256 /* Search for a triangle containing `newvertex'. */
8257 intersect = locate(m, b, newvertex, &horiz);
8258 } else {
8259 /* Start searching from the triangle provided by the caller. */
8260 otricopy(*searchtri, horiz);
8261 intersect = preciselocate(m, b, newvertex, &horiz, 1);
8262 }
8263 } else {
8264 /* The calling routine provides the subsegment in which */
8265 /* the vertex is inserted. */
8266 otricopy(*searchtri, horiz);
8267 intersect = ONEDGE;
8268 }
8269
8270 if (intersect == ONVERTEX) {
8271 /* There's already a vertex there. Return in `searchtri' a triangle */
8272 /* whose origin is the existing vertex. */
8273 otricopy(horiz, *searchtri);
8274 otricopy(horiz, m->recenttri);
8275 return DUPLICATEVERTEX;
8276 }
8277 if ((intersect == ONEDGE) || (intersect == OUTSIDE)) {
8278 /* The vertex falls on an edge or boundary. */
8279 if (m->checksegments && (splitseg == (struct osub *) NULL)) {
8280 /* Check whether the vertex falls on a subsegment. */
8281 tspivot(horiz, brokensubseg);
8282 if (brokensubseg.ss != m->dummysub) {
8283 /* The vertex falls on a subsegment, and hence will not be inserted. */
8284 if (segmentflaws) {
8285 enq = b->nobisect != 2;
8286 if (enq && (b->nobisect == 1)) {
8287 /* This subsegment may be split only if it is an */
8288 /* internal boundary. */
8289 sym(horiz, testtri);
8290 enq = testtri.tri != m->dummytri;
8291 }
8292 if (enq) {
8293 /* Add the subsegment to the list of encroached subsegments. */
8294 encroached = (struct badsubseg *) poolalloc(&m->badsubsegs);
8295 encroached->encsubseg = sencode(brokensubseg);
8296 sorg(brokensubseg, encroached->subsegorg);
8297 sdest(brokensubseg, encroached->subsegdest);
8298 if (b->verbose > 2) {
8299 printf(
8300 " Queueing encroached subsegment (%.12g, %.12g) (%.12g, %.12g).\n",
8301 encroached->subsegorg[0], encroached->subsegorg[1],
8302 encroached->subsegdest[0], encroached->subsegdest[1]);
8303 }
8304 }
8305 }
8306 /* Return a handle whose primary edge contains the vertex, */
8307 /* which has not been inserted. */
8308 otricopy(horiz, *searchtri);
8309 otricopy(horiz, m->recenttri);
8310 return VIOLATINGVERTEX;
8311 }
8312 }
8313
8314 /* Insert the vertex on an edge, dividing one triangle into two (if */
8315 /* the edge lies on a boundary) or two triangles into four. */
8316 lprev(horiz, botright);
8317 sym(botright, botrcasing);
8318 sym(horiz, topright);
8319 /* Is there a second triangle? (Or does this edge lie on a boundary?) */
8320 mirrorflag = topright.tri != m->dummytri;
8321 if (mirrorflag) {
8322 lnextself(topright);
8323 sym(topright, toprcasing);
8324 maketriangle(m, b, &newtopright);
8325 } else {
8326 /* Splitting a boundary edge increases the number of boundary edges. */
8327 m->hullsize++;
8328 }
8329 maketriangle(m, b, &newbotright);
8330
8331 /* Set the vertices of changed and new triangles. */
8332 org(horiz, rightvertex);
8333 dest(horiz, leftvertex);
8334 apex(horiz, botvertex);
8335 setorg(newbotright, botvertex);
8336 setdest(newbotright, rightvertex);
8337 setapex(newbotright, newvertex);
8338 setorg(horiz, newvertex);
8339 for (i = 0; i < m->eextras; i++) {
8340 /* Set the element attributes of a new triangle. */
8341 setelemattribute(newbotright, i, elemattribute(botright, i));
8342 }
8343 if (b->vararea) {
8344 /* Set the area constraint of a new triangle. */
8345 setareabound(newbotright, areabound(botright));
8346 }
8347 if (mirrorflag) {
8348 dest(topright, topvertex);
8349 setorg(newtopright, rightvertex);
8350 setdest(newtopright, topvertex);
8351 setapex(newtopright, newvertex);
8352 setorg(topright, newvertex);
8353 for (i = 0; i < m->eextras; i++) {
8354 /* Set the element attributes of another new triangle. */
8355 setelemattribute(newtopright, i, elemattribute(topright, i));
8356 }
8357 if (b->vararea) {
8358 /* Set the area constraint of another new triangle. */
8359 setareabound(newtopright, areabound(topright));
8360 }
8361 }
8362
8363 /* There may be subsegments that need to be bonded */
8364 /* to the new triangle(s). */
8365 if (m->checksegments) {
8366 tspivot(botright, botrsubseg);
8367 if (botrsubseg.ss != m->dummysub) {
8368 tsdissolve(botright);
8369 tsbond(newbotright, botrsubseg);
8370 }
8371 if (mirrorflag) {
8372 tspivot(topright, toprsubseg);
8373 if (toprsubseg.ss != m->dummysub) {
8374 tsdissolve(topright);
8375 tsbond(newtopright, toprsubseg);
8376 }
8377 }
8378 }
8379
8380 /* Bond the new triangle(s) to the surrounding triangles. */
8381 bond(newbotright, botrcasing);
8382 lprevself(newbotright);
8383 bond(newbotright, botright);
8384 lprevself(newbotright);
8385 if (mirrorflag) {
8386 bond(newtopright, toprcasing);
8387 lnextself(newtopright);
8388 bond(newtopright, topright);
8389 lnextself(newtopright);
8390 bond(newtopright, newbotright);
8391 }
8392
8393 if (splitseg != (struct osub *) NULL) {
8394 /* Split the subsegment into two. */
8395 setsdest(*splitseg, newvertex);
8396 segorg(*splitseg, segmentorg);
8397 segdest(*splitseg, segmentdest);
8398 ssymself(*splitseg);
8399 spivot(*splitseg, rightsubseg);
8400 insertsubseg(m, b, &newbotright, mark(*splitseg));
8401 tspivot(newbotright, newsubseg);
8402 setsegorg(newsubseg, segmentorg);
8403 setsegdest(newsubseg, segmentdest);
8404 sbond(*splitseg, newsubseg);
8405 ssymself(newsubseg);
8406 sbond(newsubseg, rightsubseg);
8407 ssymself(*splitseg);
8408 /* Transfer the subsegment's boundary marker to the vertex */
8409 /* if required. */
8410 if (vertexmark(newvertex) == 0) {
8411 setvertexmark(newvertex, mark(*splitseg));
8412 }
8413 }
8414
8415 if (m->checkquality) {
8416 poolrestart(&m->flipstackers);
8417 m->lastflip = (struct flipstacker *) poolalloc(&m->flipstackers);
8418 m->lastflip->flippedtri = encode(horiz);
8419 m->lastflip->prevflip = (struct flipstacker *) &insertvertex;
8420 }
8421
8422 #ifdef SELF_CHECK
8423 if (counterclockwise(m, b, rightvertex, leftvertex, botvertex) < 0.0) {
8424 printf("Internal error in insertvertex():\n");
8425 printf(
8426 " Clockwise triangle prior to edge vertex insertion (bottom).\n");
8427 }
8428 if (mirrorflag) {
8429 if (counterclockwise(m, b, leftvertex, rightvertex, topvertex) < 0.0) {
8430 printf("Internal error in insertvertex():\n");
8431 printf(" Clockwise triangle prior to edge vertex insertion (top).\n");
8432 }
8433 if (counterclockwise(m, b, rightvertex, topvertex, newvertex) < 0.0) {
8434 printf("Internal error in insertvertex():\n");
8435 printf(
8436 " Clockwise triangle after edge vertex insertion (top right).\n");
8437 }
8438 if (counterclockwise(m, b, topvertex, leftvertex, newvertex) < 0.0) {
8439 printf("Internal error in insertvertex():\n");
8440 printf(
8441 " Clockwise triangle after edge vertex insertion (top left).\n");
8442 }
8443 }
8444 if (counterclockwise(m, b, leftvertex, botvertex, newvertex) < 0.0) {
8445 printf("Internal error in insertvertex():\n");
8446 printf(
8447 " Clockwise triangle after edge vertex insertion (bottom left).\n");
8448 }
8449 if (counterclockwise(m, b, botvertex, rightvertex, newvertex) < 0.0) {
8450 printf("Internal error in insertvertex():\n");
8451 printf(
8452 " Clockwise triangle after edge vertex insertion (bottom right).\n");
8453 }
8454 #endif /* SELF_CHECK */
8455 if (b->verbose > 2) {
8456 printf(" Updating bottom left ");
8457 printtriangle(m, b, &botright);
8458 if (mirrorflag) {
8459 printf(" Updating top left ");
8460 printtriangle(m, b, &topright);
8461 printf(" Creating top right ");
8462 printtriangle(m, b, &newtopright);
8463 }
8464 printf(" Creating bottom right ");
8465 printtriangle(m, b, &newbotright);
8466 }
8467
8468 /* Position `horiz' on the first edge to check for */
8469 /* the Delaunay property. */
8470 lnextself(horiz);
8471 } else {
8472 /* Insert the vertex in a triangle, splitting it into three. */
8473 lnext(horiz, botleft);
8474 lprev(horiz, botright);
8475 sym(botleft, botlcasing);
8476 sym(botright, botrcasing);
8477 maketriangle(m, b, &newbotleft);
8478 maketriangle(m, b, &newbotright);
8479
8480 /* Set the vertices of changed and new triangles. */
8481 org(horiz, rightvertex);
8482 dest(horiz, leftvertex);
8483 apex(horiz, botvertex);
8484 setorg(newbotleft, leftvertex);
8485 setdest(newbotleft, botvertex);
8486 setapex(newbotleft, newvertex);
8487 setorg(newbotright, botvertex);
8488 setdest(newbotright, rightvertex);
8489 setapex(newbotright, newvertex);
8490 setapex(horiz, newvertex);
8491 for (i = 0; i < m->eextras; i++) {
8492 /* Set the element attributes of the new triangles. */
8493 attrib = elemattribute(horiz, i);
8494 setelemattribute(newbotleft, i, attrib);
8495 setelemattribute(newbotright, i, attrib);
8496 }
8497 if (b->vararea) {
8498 /* Set the area constraint of the new triangles. */
8499 area = areabound(horiz);
8500 setareabound(newbotleft, area);
8501 setareabound(newbotright, area);
8502 }
8503
8504 /* There may be subsegments that need to be bonded */
8505 /* to the new triangles. */
8506 if (m->checksegments) {
8507 tspivot(botleft, botlsubseg);
8508 if (botlsubseg.ss != m->dummysub) {
8509 tsdissolve(botleft);
8510 tsbond(newbotleft, botlsubseg);
8511 }
8512 tspivot(botright, botrsubseg);
8513 if (botrsubseg.ss != m->dummysub) {
8514 tsdissolve(botright);
8515 tsbond(newbotright, botrsubseg);
8516 }
8517 }
8518
8519 /* Bond the new triangles to the surrounding triangles. */
8520 bond(newbotleft, botlcasing);
8521 bond(newbotright, botrcasing);
8522 lnextself(newbotleft);
8523 lprevself(newbotright);
8524 bond(newbotleft, newbotright);
8525 lnextself(newbotleft);
8526 bond(botleft, newbotleft);
8527 lprevself(newbotright);
8528 bond(botright, newbotright);
8529
8530 if (m->checkquality) {
8531 poolrestart(&m->flipstackers);
8532 m->lastflip = (struct flipstacker *) poolalloc(&m->flipstackers);
8533 m->lastflip->flippedtri = encode(horiz);
8534 m->lastflip->prevflip = (struct flipstacker *) NULL;
8535 }
8536
8537 #ifdef SELF_CHECK
8538 if (counterclockwise(m, b, rightvertex, leftvertex, botvertex) < 0.0) {
8539 printf("Internal error in insertvertex():\n");
8540 printf(" Clockwise triangle prior to vertex insertion.\n");
8541 }
8542 if (counterclockwise(m, b, rightvertex, leftvertex, newvertex) < 0.0) {
8543 printf("Internal error in insertvertex():\n");
8544 printf(" Clockwise triangle after vertex insertion (top).\n");
8545 }
8546 if (counterclockwise(m, b, leftvertex, botvertex, newvertex) < 0.0) {
8547 printf("Internal error in insertvertex():\n");
8548 printf(" Clockwise triangle after vertex insertion (left).\n");
8549 }
8550 if (counterclockwise(m, b, botvertex, rightvertex, newvertex) < 0.0) {
8551 printf("Internal error in insertvertex():\n");
8552 printf(" Clockwise triangle after vertex insertion (right).\n");
8553 }
8554 #endif /* SELF_CHECK */
8555 if (b->verbose > 2) {
8556 printf(" Updating top ");
8557 printtriangle(m, b, &horiz);
8558 printf(" Creating left ");
8559 printtriangle(m, b, &newbotleft);
8560 printf(" Creating right ");
8561 printtriangle(m, b, &newbotright);
8562 }
8563 }
8564
8565 /* The insertion is successful by default, unless an encroached */
8566 /* subsegment is found. */
8567 success = SUCCESSFULVERTEX;
8568 /* Circle around the newly inserted vertex, checking each edge opposite */
8569 /* it for the Delaunay property. Non-Delaunay edges are flipped. */
8570 /* `horiz' is always the edge being checked. `first' marks where to */
8571 /* stop circling. */
8572 org(horiz, first);
8573 rightvertex = first;
8574 dest(horiz, leftvertex);
8575 /* Circle until finished. */
8576 while (1) {
8577 /* By default, the edge will be flipped. */
8578 doflip = 1;
8579
8580 if (m->checksegments) {
8581 /* Check for a subsegment, which cannot be flipped. */
8582 tspivot(horiz, checksubseg);
8583 if (checksubseg.ss != m->dummysub) {
8584 /* The edge is a subsegment and cannot be flipped. */
8585 doflip = 0;
8586 #ifndef CDT_ONLY
8587 if (segmentflaws) {
8588 /* Does the new vertex encroach upon this subsegment? */
8589 if (checkseg4encroach(m, b, &checksubseg)) {
8590 success = ENCROACHINGVERTEX;
8591 }
8592 }
8593 #endif /* not CDT_ONLY */
8594 }
8595 }
8596
8597 if (doflip) {
8598 /* Check if the edge is a boundary edge. */
8599 sym(horiz, top);
8600 if (top.tri == m->dummytri) {
8601 /* The edge is a boundary edge and cannot be flipped. */
8602 doflip = 0;
8603 } else {
8604 /* Find the vertex on the other side of the edge. */
8605 apex(top, farvertex);
8606 /* In the incremental Delaunay triangulation algorithm, any of */
8607 /* `leftvertex', `rightvertex', and `farvertex' could be vertices */
8608 /* of the triangular bounding box. These vertices must be */
8609 /* treated as if they are infinitely distant, even though their */
8610 /* "coordinates" are not. */
8611 if ((leftvertex == m->infvertex1) || (leftvertex == m->infvertex2) ||
8612 (leftvertex == m->infvertex3)) {
8613 /* `leftvertex' is infinitely distant. Check the convexity of */
8614 /* the boundary of the triangulation. 'farvertex' might be */
8615 /* infinite as well, but trust me, this same condition should */
8616 /* be applied. */
8617 doflip = counterclockwise(m, b, newvertex, rightvertex, farvertex)
8618 > 0.0;
8619 } else if ((rightvertex == m->infvertex1) ||
8620 (rightvertex == m->infvertex2) ||
8621 (rightvertex == m->infvertex3)) {
8622 /* `rightvertex' is infinitely distant. Check the convexity of */
8623 /* the boundary of the triangulation. 'farvertex' might be */
8624 /* infinite as well, but trust me, this same condition should */
8625 /* be applied. */
8626 doflip = counterclockwise(m, b, farvertex, leftvertex, newvertex)
8627 > 0.0;
8628 } else if ((farvertex == m->infvertex1) ||
8629 (farvertex == m->infvertex2) ||
8630 (farvertex == m->infvertex3)) {
8631 /* `farvertex' is infinitely distant and cannot be inside */
8632 /* the circumcircle of the triangle `horiz'. */
8633 doflip = 0;
8634 } else {
8635 /* Test whether the edge is locally Delaunay. */
8636 doflip = incircle(m, b, leftvertex, newvertex, rightvertex,
8637 farvertex) > 0.0;
8638 }
8639 if (doflip) {
8640 /* We made it! Flip the edge `horiz' by rotating its containing */
8641 /* quadrilateral (the two triangles adjacent to `horiz'). */
8642 /* Identify the casing of the quadrilateral. */
8643 lprev(top, topleft);
8644 sym(topleft, toplcasing);
8645 lnext(top, topright);
8646 sym(topright, toprcasing);
8647 lnext(horiz, botleft);
8648 sym(botleft, botlcasing);
8649 lprev(horiz, botright);
8650 sym(botright, botrcasing);
8651 /* Rotate the quadrilateral one-quarter turn counterclockwise. */
8652 bond(topleft, botlcasing);
8653 bond(botleft, botrcasing);
8654 bond(botright, toprcasing);
8655 bond(topright, toplcasing);
8656 if (m->checksegments) {
8657 /* Check for subsegments and rebond them to the quadrilateral. */
8658 tspivot(topleft, toplsubseg);
8659 tspivot(botleft, botlsubseg);
8660 tspivot(botright, botrsubseg);
8661 tspivot(topright, toprsubseg);
8662 if (toplsubseg.ss == m->dummysub) {
8663 tsdissolve(topright);
8664 } else {
8665 tsbond(topright, toplsubseg);
8666 }
8667 if (botlsubseg.ss == m->dummysub) {
8668 tsdissolve(topleft);
8669 } else {
8670 tsbond(topleft, botlsubseg);
8671 }
8672 if (botrsubseg.ss == m->dummysub) {
8673 tsdissolve(botleft);
8674 } else {
8675 tsbond(botleft, botrsubseg);
8676 }
8677 if (toprsubseg.ss == m->dummysub) {
8678 tsdissolve(botright);
8679 } else {
8680 tsbond(botright, toprsubseg);
8681 }
8682 }
8683 /* New vertex assignments for the rotated quadrilateral. */
8684 setorg(horiz, farvertex);
8685 setdest(horiz, newvertex);
8686 setapex(horiz, rightvertex);
8687 setorg(top, newvertex);
8688 setdest(top, farvertex);
8689 setapex(top, leftvertex);
8690 for (i = 0; i < m->eextras; i++) {
8691 /* Take the average of the two triangles' attributes. */
8692 attrib = 0.5 * (elemattribute(top, i) + elemattribute(horiz, i));
8693 setelemattribute(top, i, attrib);
8694 setelemattribute(horiz, i, attrib);
8695 }
8696 if (b->vararea) {
8697 if ((areabound(top) <= 0.0) || (areabound(horiz) <= 0.0)) {
8698 area = -1.0;
8699 } else {
8700 /* Take the average of the two triangles' area constraints. */
8701 /* This prevents small area constraints from migrating a */
8702 /* long, long way from their original location due to flips. */
8703 area = 0.5 * (areabound(top) + areabound(horiz));
8704 }
8705 setareabound(top, area);
8706 setareabound(horiz, area);
8707 }
8708
8709 if (m->checkquality) {
8710 newflip = (struct flipstacker *) poolalloc(&m->flipstackers);
8711 newflip->flippedtri = encode(horiz);
8712 newflip->prevflip = m->lastflip;
8713 m->lastflip = newflip;
8714 }
8715
8716 #ifdef SELF_CHECK
8717 if (newvertex != (vertex) NULL) {
8718 if (counterclockwise(m, b, leftvertex, newvertex, rightvertex) <
8719 0.0) {
8720 printf("Internal error in insertvertex():\n");
8721 printf(" Clockwise triangle prior to edge flip (bottom).\n");
8722 }
8723 /* The following test has been removed because constrainededge() */
8724 /* sometimes generates inverted triangles that insertvertex() */
8725 /* removes. */
8726 /*
8727 if (counterclockwise(m, b, rightvertex, farvertex, leftvertex) <
8728 0.0) {
8729 printf("Internal error in insertvertex():\n");
8730 printf(" Clockwise triangle prior to edge flip (top).\n");
8731 }
8732 */
8733 if (counterclockwise(m, b, farvertex, leftvertex, newvertex) <
8734 0.0) {
8735 printf("Internal error in insertvertex():\n");
8736 printf(" Clockwise triangle after edge flip (left).\n");
8737 }
8738 if (counterclockwise(m, b, newvertex, rightvertex, farvertex) <
8739 0.0) {
8740 printf("Internal error in insertvertex():\n");
8741 printf(" Clockwise triangle after edge flip (right).\n");
8742 }
8743 }
8744 #endif /* SELF_CHECK */
8745 if (b->verbose > 2) {
8746 printf(" Edge flip results in left ");
8747 lnextself(topleft);
8748 printtriangle(m, b, &topleft);
8749 printf(" and right ");
8750 printtriangle(m, b, &horiz);
8751 }
8752 /* On the next iterations, consider the two edges that were */
8753 /* exposed (this is, are now visible to the newly inserted */
8754 /* vertex) by the edge flip. */
8755 lprevself(horiz);
8756 leftvertex = farvertex;
8757 }
8758 }
8759 }
8760 if (!doflip) {
8761 /* The handle `horiz' is accepted as locally Delaunay. */
8762 #ifndef CDT_ONLY
8763 if (triflaws) {
8764 /* Check the triangle `horiz' for quality. */
8765 testtriangle(m, b, &horiz);
8766 }
8767 #endif /* not CDT_ONLY */
8768 /* Look for the next edge around the newly inserted vertex. */
8769 lnextself(horiz);
8770 sym(horiz, testtri);
8771 /* Check for finishing a complete revolution about the new vertex, or */
8772 /* falling outside of the triangulation. The latter will happen */
8773 /* when a vertex is inserted at a boundary. */
8774 if ((leftvertex == first) || (testtri.tri == m->dummytri)) {
8775 /* We're done. Return a triangle whose origin is the new vertex. */
8776 lnext(horiz, *searchtri);
8777 lnext(horiz, m->recenttri);
8778 return success;
8779 }
8780 /* Finish finding the next edge around the newly inserted vertex. */
8781 lnext(testtri, horiz);
8782 rightvertex = leftvertex;
8783 dest(horiz, leftvertex);
8784 }
8785 }
8786 }
8787
8788 /*****************************************************************************/
8789 /* */
8790 /* triangulatepolygon() Find the Delaunay triangulation of a polygon that */
8791 /* has a certain "nice" shape. This includes the */
8792 /* polygons that result from deletion of a vertex or */
8793 /* insertion of a segment. */
8794 /* */
8795 /* This is a conceptually difficult routine. The starting assumption is */
8796 /* that we have a polygon with n sides. n - 1 of these sides are currently */
8797 /* represented as edges in the mesh. One side, called the "base", need not */
8798 /* be. */
8799 /* */
8800 /* Inside the polygon is a structure I call a "fan", consisting of n - 1 */
8801 /* triangles that share a common origin. For each of these triangles, the */
8802 /* edge opposite the origin is one of the sides of the polygon. The */
8803 /* primary edge of each triangle is the edge directed from the origin to */
8804 /* the destination; note that this is not the same edge that is a side of */
8805 /* the polygon. `firstedge' is the primary edge of the first triangle. */
8806 /* From there, the triangles follow in counterclockwise order about the */
8807 /* polygon, until `lastedge', the primary edge of the last triangle. */
8808 /* `firstedge' and `lastedge' are probably connected to other triangles */
8809 /* beyond the extremes of the fan, but their identity is not important, as */
8810 /* long as the fan remains connected to them. */
8811 /* */
8812 /* Imagine the polygon oriented so that its base is at the bottom. This */
8813 /* puts `firstedge' on the far right, and `lastedge' on the far left. */
8814 /* The right vertex of the base is the destination of `firstedge', and the */
8815 /* left vertex of the base is the apex of `lastedge'. */
8816 /* */
8817 /* The challenge now is to find the right sequence of edge flips to */
8818 /* transform the fan into a Delaunay triangulation of the polygon. Each */
8819 /* edge flip effectively removes one triangle from the fan, committing it */
8820 /* to the polygon. The resulting polygon has one fewer edge. If `doflip' */
8821 /* is set, the final flip will be performed, resulting in a fan of one */
8822 /* (useless?) triangle. If `doflip' is not set, the final flip is not */
8823 /* performed, resulting in a fan of two triangles, and an unfinished */
8824 /* triangular polygon that is not yet filled out with a single triangle. */
8825 /* On completion of the routine, `lastedge' is the last remaining triangle, */
8826 /* or the leftmost of the last two. */
8827 /* */
8828 /* Although the flips are performed in the order described above, the */
8829 /* decisions about what flips to perform are made in precisely the reverse */
8830 /* order. The recursive triangulatepolygon() procedure makes a decision, */
8831 /* uses up to two recursive calls to triangulate the "subproblems" */
8832 /* (polygons with fewer edges), and then performs an edge flip. */
8833 /* */
8834 /* The "decision" it makes is which vertex of the polygon should be */
8835 /* connected to the base. This decision is made by testing every possible */
8836 /* vertex. Once the best vertex is found, the two edges that connect this */
8837 /* vertex to the base become the bases for two smaller polygons. These */
8838 /* are triangulated recursively. Unfortunately, this approach can take */
8839 /* O(n^2) time not only in the worst case, but in many common cases. It's */
8840 /* rarely a big deal for vertex deletion, where n is rarely larger than */
8841 /* ten, but it could be a big deal for segment insertion, especially if */
8842 /* there's a lot of long segments that each cut many triangles. I ought to */
8843 /* code a faster algorithm some day. */
8844 /* */
8845 /* The `edgecount' parameter is the number of sides of the polygon, */
8846 /* including its base. `triflaws' is a flag that determines whether the */
8847 /* new triangles should be tested for quality, and enqueued if they are */
8848 /* bad. */
8849 /* */
8850 /*****************************************************************************/
8851
8852 #ifdef ANSI_DECLARATORS
8853 void triangulatepolygon(struct mesh *m, struct behavior *b,
8854 struct otri *firstedge, struct otri *lastedge,
8855 int edgecount, int doflip, int triflaws)
8856 #else /* not ANSI_DECLARATORS */
8857 void triangulatepolygon(m, b, firstedge, lastedge, edgecount, doflip, triflaws)
8858 struct mesh *m;
8859 struct behavior *b;
8860 struct otri *firstedge;
8861 struct otri *lastedge;
8862 int edgecount;
8863 int doflip;
8864 int triflaws;
8865 #endif /* not ANSI_DECLARATORS */
8866
8867 {
8868 struct otri testtri;
8869 struct otri besttri;
8870 struct otri tempedge;
8871 vertex leftbasevertex, rightbasevertex;
8872 vertex testvertex;
8873 vertex bestvertex;
8874 int bestnumber;
8875 int i;
8876 triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */
8877
8878 /* Identify the base vertices. */
8879 apex(*lastedge, leftbasevertex);
8880 dest(*firstedge, rightbasevertex);
8881 if (b->verbose > 2) {
8882 printf(" Triangulating interior polygon at edge\n");
8883 printf(" (%.12g, %.12g) (%.12g, %.12g)\n", leftbasevertex[0],
8884 leftbasevertex[1], rightbasevertex[0], rightbasevertex[1]);
8885 }
8886 /* Find the best vertex to connect the base to. */
8887 onext(*firstedge, besttri);
8888 dest(besttri, bestvertex);
8889 otricopy(besttri, testtri);
8890 bestnumber = 1;
8891 for (i = 2; i <= edgecount - 2; i++) {
8892 onextself(testtri);
8893 dest(testtri, testvertex);
8894 /* Is this a better vertex? */
8895 if (incircle(m, b, leftbasevertex, rightbasevertex, bestvertex,
8896 testvertex) > 0.0) {
8897 otricopy(testtri, besttri);
8898 bestvertex = testvertex;
8899 bestnumber = i;
8900 }
8901 }
8902 if (b->verbose > 2) {
8903 printf(" Connecting edge to (%.12g, %.12g)\n", bestvertex[0],
8904 bestvertex[1]);
8905 }
8906 if (bestnumber > 1) {
8907 /* Recursively triangulate the smaller polygon on the right. */
8908 oprev(besttri, tempedge);
8909 triangulatepolygon(m, b, firstedge, &tempedge, bestnumber + 1, 1,
8910 triflaws);
8911 }
8912 if (bestnumber < edgecount - 2) {
8913 /* Recursively triangulate the smaller polygon on the left. */
8914 sym(besttri, tempedge);
8915 triangulatepolygon(m, b, &besttri, lastedge, edgecount - bestnumber, 1,
8916 triflaws);
8917 /* Find `besttri' again; it may have been lost to edge flips. */
8918 sym(tempedge, besttri);
8919 }
8920 if (doflip) {
8921 /* Do one final edge flip. */
8922 flip(m, b, &besttri);
8923 #ifndef CDT_ONLY
8924 if (triflaws) {
8925 /* Check the quality of the newly committed triangle. */
8926 sym(besttri, testtri);
8927 testtriangle(m, b, &testtri);
8928 }
8929 #endif /* not CDT_ONLY */
8930 }
8931 /* Return the base triangle. */
8932 otricopy(besttri, *lastedge);
8933 }
8934
8935 /*****************************************************************************/
8936 /* */
8937 /* deletevertex() Delete a vertex from a Delaunay triangulation, ensuring */
8938 /* that the triangulation remains Delaunay. */
8939 /* */
8940 /* The origin of `deltri' is deleted. The union of the triangles adjacent */
8941 /* to this vertex is a polygon, for which the Delaunay triangulation is */
8942 /* found. Two triangles are removed from the mesh. */
8943 /* */
8944 /* Only interior vertices that do not lie on segments or boundaries may be */
8945 /* deleted. */
8946 /* */
8947 /*****************************************************************************/
8948
8949 #ifndef CDT_ONLY
8950
8951 #ifdef ANSI_DECLARATORS
8952 void deletevertex(struct mesh *m, struct behavior *b, struct otri *deltri)
8953 #else /* not ANSI_DECLARATORS */
8954 void deletevertex(m, b, deltri)
8955 struct mesh *m;
8956 struct behavior *b;
8957 struct otri *deltri;
8958 #endif /* not ANSI_DECLARATORS */
8959
8960 {
8961 struct otri countingtri;
8962 struct otri firstedge, lastedge;
8963 struct otri deltriright;
8964 struct otri lefttri, righttri;
8965 struct otri leftcasing, rightcasing;
8966 struct osub leftsubseg, rightsubseg;
8967 vertex delvertex;
8968 vertex neworg;
8969 int edgecount;
8970 triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */
8971 subseg sptr; /* Temporary variable used by tspivot(). */
8972
8973 org(*deltri, delvertex);
8974 if (b->verbose > 1) {
8975 printf(" Deleting (%.12g, %.12g).\n", delvertex[0], delvertex[1]);
8976 }
8977 vertexdealloc(m, delvertex);
8978
8979 /* Count the degree of the vertex being deleted. */
8980 onext(*deltri, countingtri);
8981 edgecount = 1;
8982 while (!otriequal(*deltri, countingtri)) {
8983 #ifdef SELF_CHECK
8984 if (countingtri.tri == m->dummytri) {
8985 printf("Internal error in deletevertex():\n");
8986 printf(" Attempt to delete boundary vertex.\n");
8987 internalerror();
8988 }
8989 #endif /* SELF_CHECK */
8990 edgecount++;
8991 onextself(countingtri);
8992 }
8993
8994 #ifdef SELF_CHECK
8995 if (edgecount < 3) {
8996 printf("Internal error in deletevertex():\n Vertex has degree %d.\n",
8997 edgecount);
8998 internalerror();
8999 }
9000 #endif /* SELF_CHECK */
9001 if (edgecount > 3) {
9002 /* Triangulate the polygon defined by the union of all triangles */
9003 /* adjacent to the vertex being deleted. Check the quality of */
9004 /* the resulting triangles. */
9005 onext(*deltri, firstedge);
9006 oprev(*deltri, lastedge);
9007 triangulatepolygon(m, b, &firstedge, &lastedge, edgecount, 0,
9008 !b->nobisect);
9009 }
9010 /* Splice out two triangles. */
9011 lprev(*deltri, deltriright);
9012 dnext(*deltri, lefttri);
9013 sym(lefttri, leftcasing);
9014 oprev(deltriright, righttri);
9015 sym(righttri, rightcasing);
9016 bond(*deltri, leftcasing);
9017 bond(deltriright, rightcasing);
9018 tspivot(lefttri, leftsubseg);
9019 if (leftsubseg.ss != m->dummysub) {
9020 tsbond(*deltri, leftsubseg);
9021 }
9022 tspivot(righttri, rightsubseg);
9023 if (rightsubseg.ss != m->dummysub) {
9024 tsbond(deltriright, rightsubseg);
9025 }
9026
9027 /* Set the new origin of `deltri' and check its quality. */
9028 org(lefttri, neworg);
9029 setorg(*deltri, neworg);
9030 if (!b->nobisect) {
9031 testtriangle(m, b, deltri);
9032 }
9033
9034 /* Delete the two spliced-out triangles. */
9035 triangledealloc(m, lefttri.tri);
9036 triangledealloc(m, righttri.tri);
9037 }
9038
9039 #endif /* not CDT_ONLY */
9040
9041 /*****************************************************************************/
9042 /* */
9043 /* undovertex() Undo the most recent vertex insertion. */
9044 /* */
9045 /* Walks through the list of transformations (flips and a vertex insertion) */
9046 /* in the reverse of the order in which they were done, and undoes them. */
9047 /* The inserted vertex is removed from the triangulation and deallocated. */
9048 /* Two triangles (possibly just one) are also deallocated. */
9049 /* */
9050 /*****************************************************************************/
9051
9052 #ifndef CDT_ONLY
9053
9054 #ifdef ANSI_DECLARATORS
9055 void undovertex(struct mesh *m, struct behavior *b)
9056 #else /* not ANSI_DECLARATORS */
9057 void undovertex(m, b)
9058 struct mesh *m;
9059 struct behavior *b;
9060 #endif /* not ANSI_DECLARATORS */
9061
9062 {
9063 struct otri fliptri;
9064 struct otri botleft, botright, topright;
9065 struct otri botlcasing, botrcasing, toprcasing;
9066 struct otri gluetri;
9067 struct osub botlsubseg, botrsubseg, toprsubseg;
9068 vertex botvertex, rightvertex;
9069 triangle ptr; /* Temporary variable used by sym(). */
9070 subseg sptr; /* Temporary variable used by tspivot(). */
9071
9072 /* Walk through the list of transformations (flips and a vertex insertion) */
9073 /* in the reverse of the order in which they were done, and undo them. */
9074 while (m->lastflip != (struct flipstacker *) NULL) {
9075 /* Find a triangle involved in the last unreversed transformation. */
9076 decode(m->lastflip->flippedtri, fliptri);
9077
9078 /* We are reversing one of three transformations: a trisection of one */
9079 /* triangle into three (by inserting a vertex in the triangle), a */
9080 /* bisection of two triangles into four (by inserting a vertex in an */
9081 /* edge), or an edge flip. */
9082 if (m->lastflip->prevflip == (struct flipstacker *) NULL) {
9083 /* Restore a triangle that was split into three triangles, */
9084 /* so it is again one triangle. */
9085 dprev(fliptri, botleft);
9086 lnextself(botleft);
9087 onext(fliptri, botright);
9088 lprevself(botright);
9089 sym(botleft, botlcasing);
9090 sym(botright, botrcasing);
9091 dest(botleft, botvertex);
9092
9093 setapex(fliptri, botvertex);
9094 lnextself(fliptri);
9095 bond(fliptri, botlcasing);
9096 tspivot(botleft, botlsubseg);
9097 tsbond(fliptri, botlsubseg);
9098 lnextself(fliptri);
9099 bond(fliptri, botrcasing);
9100 tspivot(botright, botrsubseg);
9101 tsbond(fliptri, botrsubseg);
9102
9103 /* Delete the two spliced-out triangles. */
9104 triangledealloc(m, botleft.tri);
9105 triangledealloc(m, botright.tri);
9106 } else if (m->lastflip->prevflip == (struct flipstacker *) &insertvertex) {
9107 /* Restore two triangles that were split into four triangles, */
9108 /* so they are again two triangles. */
9109 lprev(fliptri, gluetri);
9110 sym(gluetri, botright);
9111 lnextself(botright);
9112 sym(botright, botrcasing);
9113 dest(botright, rightvertex);
9114
9115 setorg(fliptri, rightvertex);
9116 bond(gluetri, botrcasing);
9117 tspivot(botright, botrsubseg);
9118 tsbond(gluetri, botrsubseg);
9119
9120 /* Delete the spliced-out triangle. */
9121 triangledealloc(m, botright.tri);
9122
9123 sym(fliptri, gluetri);
9124 if (gluetri.tri != m->dummytri) {
9125 lnextself(gluetri);
9126 dnext(gluetri, topright);
9127 sym(topright, toprcasing);
9128
9129 setorg(gluetri, rightvertex);
9130 bond(gluetri, toprcasing);
9131 tspivot(topright, toprsubseg);
9132 tsbond(gluetri, toprsubseg);
9133
9134 /* Delete the spliced-out triangle. */
9135 triangledealloc(m, topright.tri);
9136 }
9137
9138 /* This is the end of the list, sneakily encoded. */
9139 m->lastflip->prevflip = (struct flipstacker *) NULL;
9140 } else {
9141 /* Undo an edge flip. */
9142 unflip(m, b, &fliptri);
9143 }
9144
9145 /* Go on and process the next transformation. */
9146 m->lastflip = m->lastflip->prevflip;
9147 }
9148 }
9149
9150 #endif /* not CDT_ONLY */
9151
9152 /** **/
9153 /** **/
9154 /********* Mesh transformation routines end here *********/
9155
9156 /********* Divide-and-conquer Delaunay triangulation begins here *********/
9157 /** **/
9158 /** **/
9159
9160 /*****************************************************************************/
9161 /* */
9162 /* The divide-and-conquer bounding box */
9163 /* */
9164 /* I originally implemented the divide-and-conquer and incremental Delaunay */
9165 /* triangulations using the edge-based data structure presented by Guibas */
9166 /* and Stolfi. Switching to a triangle-based data structure doubled the */
9167 /* speed. However, I had to think of a few extra tricks to maintain the */
9168 /* elegance of the original algorithms. */
9169 /* */
9170 /* The "bounding box" used by my variant of the divide-and-conquer */
9171 /* algorithm uses one triangle for each edge of the convex hull of the */
9172 /* triangulation. These bounding triangles all share a common apical */
9173 /* vertex, which is represented by NULL and which represents nothing. */
9174 /* The bounding triangles are linked in a circular fan about this NULL */
9175 /* vertex, and the edges on the convex hull of the triangulation appear */
9176 /* opposite the NULL vertex. You might find it easiest to imagine that */
9177 /* the NULL vertex is a point in 3D space behind the center of the */
9178 /* triangulation, and that the bounding triangles form a sort of cone. */
9179 /* */
9180 /* This bounding box makes it easy to represent degenerate cases. For */
9181 /* instance, the triangulation of two vertices is a single edge. This edge */
9182 /* is represented by two bounding box triangles, one on each "side" of the */
9183 /* edge. These triangles are also linked together in a fan about the NULL */
9184 /* vertex. */
9185 /* */
9186 /* The bounding box also makes it easy to traverse the convex hull, as the */
9187 /* divide-and-conquer algorithm needs to do. */
9188 /* */
9189 /*****************************************************************************/
9190
9191 /*****************************************************************************/
9192 /* */
9193 /* vertexsort() Sort an array of vertices by x-coordinate, using the */
9194 /* y-coordinate as a secondary key. */
9195 /* */
9196 /* Uses quicksort. Randomized O(n log n) time. No, I did not make any of */
9197 /* the usual quicksort mistakes. */
9198 /* */
9199 /*****************************************************************************/
9200
9201 #ifdef ANSI_DECLARATORS
9202 void vertexsort(vertex *sortarray, int arraysize)
9203 #else /* not ANSI_DECLARATORS */
9204 void vertexsort(sortarray, arraysize)
9205 vertex *sortarray;
9206 int arraysize;
9207 #endif /* not ANSI_DECLARATORS */
9208
9209 {
9210 int left, right;
9211 int pivot;
9212 REAL pivotx, pivoty;
9213 vertex temp;
9214
9215 if (arraysize == 2) {
9216 /* Recursive base case. */
9217 if ((sortarray[0][0] > sortarray[1][0]) ||
9218 ((sortarray[0][0] == sortarray[1][0]) &&
9219 (sortarray[0][1] > sortarray[1][1]))) {
9220 temp = sortarray[1];
9221 sortarray[1] = sortarray[0];
9222 sortarray[0] = temp;
9223 }
9224 return;
9225 }
9226 /* Choose a random pivot to split the array. */
9227 pivot = (int) randomnation((unsigned int) arraysize);
9228 pivotx = sortarray[pivot][0];
9229 pivoty = sortarray[pivot][1];
9230 /* Split the array. */
9231 left = -1;
9232 right = arraysize;
9233 while (left < right) {
9234 /* Search for a vertex whose x-coordinate is too large for the left. */
9235 do {
9236 left++;
9237 } while ((left <= right) && ((sortarray[left][0] < pivotx) ||
9238 ((sortarray[left][0] == pivotx) &&
9239 (sortarray[left][1] < pivoty))));
9240 /* Search for a vertex whose x-coordinate is too small for the right. */
9241 do {
9242 right--;
9243 } while ((left <= right) && ((sortarray[right][0] > pivotx) ||
9244 ((sortarray[right][0] == pivotx) &&
9245 (sortarray[right][1] > pivoty))));
9246 if (left < right) {
9247 /* Swap the left and right vertices. */
9248 temp = sortarray[left];
9249 sortarray[left] = sortarray[right];
9250 sortarray[right] = temp;
9251 }
9252 }
9253 if (left > 1) {
9254 /* Recursively sort the left subset. */
9255 vertexsort(sortarray, left);
9256 }
9257 if (right < arraysize - 2) {
9258 /* Recursively sort the right subset. */
9259 vertexsort(&sortarray[right + 1], arraysize - right - 1);
9260 }
9261 }
9262
9263 /*****************************************************************************/
9264 /* */
9265 /* vertexmedian() An order statistic algorithm, almost. Shuffles an */
9266 /* array of vertices so that the first `median' vertices */
9267 /* occur lexicographically before the remaining vertices. */
9268 /* */
9269 /* Uses the x-coordinate as the primary key if axis == 0; the y-coordinate */
9270 /* if axis == 1. Very similar to the vertexsort() procedure, but runs in */
9271 /* randomized linear time. */
9272 /* */
9273 /*****************************************************************************/
9274
9275 #ifdef ANSI_DECLARATORS
9276 void vertexmedian(vertex *sortarray, int arraysize, int median, int axis)
9277 #else /* not ANSI_DECLARATORS */
9278 void vertexmedian(sortarray, arraysize, median, axis)
9279 vertex *sortarray;
9280 int arraysize;
9281 int median;
9282 int axis;
9283 #endif /* not ANSI_DECLARATORS */
9284
9285 {
9286 int left, right;
9287 int pivot;
9288 REAL pivot1, pivot2;
9289 vertex temp;
9290
9291 if (arraysize == 2) {
9292 /* Recursive base case. */
9293 if ((sortarray[0][axis] > sortarray[1][axis]) ||
9294 ((sortarray[0][axis] == sortarray[1][axis]) &&
9295 (sortarray[0][1 - axis] > sortarray[1][1 - axis]))) {
9296 temp = sortarray[1];
9297 sortarray[1] = sortarray[0];
9298 sortarray[0] = temp;
9299 }
9300 return;
9301 }
9302 /* Choose a random pivot to split the array. */
9303 pivot = (int) randomnation((unsigned int) arraysize);
9304 pivot1 = sortarray[pivot][axis];
9305 pivot2 = sortarray[pivot][1 - axis];
9306 /* Split the array. */
9307 left = -1;
9308 right = arraysize;
9309 while (left < right) {
9310 /* Search for a vertex whose x-coordinate is too large for the left. */
9311 do {
9312 left++;
9313 } while ((left <= right) && ((sortarray[left][axis] < pivot1) ||
9314 ((sortarray[left][axis] == pivot1) &&
9315 (sortarray[left][1 - axis] < pivot2))));
9316 /* Search for a vertex whose x-coordinate is too small for the right. */
9317 do {
9318 right--;
9319 } while ((left <= right) && ((sortarray[right][axis] > pivot1) ||
9320 ((sortarray[right][axis] == pivot1) &&
9321 (sortarray[right][1 - axis] > pivot2))));
9322 if (left < right) {
9323 /* Swap the left and right vertices. */
9324 temp = sortarray[left];
9325 sortarray[left] = sortarray[right];
9326 sortarray[right] = temp;
9327 }
9328 }
9329 /* Unlike in vertexsort(), at most one of the following */
9330 /* conditionals is true. */
9331 if (left > median) {
9332 /* Recursively shuffle the left subset. */
9333 vertexmedian(sortarray, left, median, axis);
9334 }
9335 if (right < median - 1) {
9336 /* Recursively shuffle the right subset. */
9337 vertexmedian(&sortarray[right + 1], arraysize - right - 1,
9338 median - right - 1, axis);
9339 }
9340 }
9341
9342 /*****************************************************************************/
9343 /* */
9344 /* alternateaxes() Sorts the vertices as appropriate for the divide-and- */
9345 /* conquer algorithm with alternating cuts. */
9346 /* */
9347 /* Partitions by x-coordinate if axis == 0; by y-coordinate if axis == 1. */
9348 /* For the base case, subsets containing only two or three vertices are */
9349 /* always sorted by x-coordinate. */
9350 /* */
9351 /*****************************************************************************/
9352
9353 #ifdef ANSI_DECLARATORS
9354 void alternateaxes(vertex *sortarray, int arraysize, int axis)
9355 #else /* not ANSI_DECLARATORS */
9356 void alternateaxes(sortarray, arraysize, axis)
9357 vertex *sortarray;
9358 int arraysize;
9359 int axis;
9360 #endif /* not ANSI_DECLARATORS */
9361
9362 {
9363 int divider;
9364
9365 divider = arraysize >> 1;
9366 if (arraysize <= 3) {
9367 /* Recursive base case: subsets of two or three vertices will be */
9368 /* handled specially, and should always be sorted by x-coordinate. */
9369 axis = 0;
9370 }
9371 /* Partition with a horizontal or vertical cut. */
9372 vertexmedian(sortarray, arraysize, divider, axis);
9373 /* Recursively partition the subsets with a cross cut. */
9374 if (arraysize - divider >= 2) {
9375 if (divider >= 2) {
9376 alternateaxes(sortarray, divider, 1 - axis);
9377 }
9378 alternateaxes(&sortarray[divider], arraysize - divider, 1 - axis);
9379 }
9380 }
9381
9382 /*****************************************************************************/
9383 /* */
9384 /* mergehulls() Merge two adjacent Delaunay triangulations into a */
9385 /* single Delaunay triangulation. */
9386 /* */
9387 /* This is similar to the algorithm given by Guibas and Stolfi, but uses */
9388 /* a triangle-based, rather than edge-based, data structure. */
9389 /* */
9390 /* The algorithm walks up the gap between the two triangulations, knitting */
9391 /* them together. As they are merged, some of their bounding triangles */
9392 /* are converted into real triangles of the triangulation. The procedure */
9393 /* pulls each hull's bounding triangles apart, then knits them together */
9394 /* like the teeth of two gears. The Delaunay property determines, at each */
9395 /* step, whether the next "tooth" is a bounding triangle of the left hull */
9396 /* or the right. When a bounding triangle becomes real, its apex is */
9397 /* changed from NULL to a real vertex. */
9398 /* */
9399 /* Only two new triangles need to be allocated. These become new bounding */
9400 /* triangles at the top and bottom of the seam. They are used to connect */
9401 /* the remaining bounding triangles (those that have not been converted */
9402 /* into real triangles) into a single fan. */
9403 /* */
9404 /* On entry, `farleft' and `innerleft' are bounding triangles of the left */
9405 /* triangulation. The origin of `farleft' is the leftmost vertex, and */
9406 /* the destination of `innerleft' is the rightmost vertex of the */
9407 /* triangulation. Similarly, `innerright' and `farright' are bounding */
9408 /* triangles of the right triangulation. The origin of `innerright' and */
9409 /* destination of `farright' are the leftmost and rightmost vertices. */
9410 /* */
9411 /* On completion, the origin of `farleft' is the leftmost vertex of the */
9412 /* merged triangulation, and the destination of `farright' is the rightmost */
9413 /* vertex. */
9414 /* */
9415 /*****************************************************************************/
9416
9417 #ifdef ANSI_DECLARATORS
9418 void mergehulls(struct mesh *m, struct behavior *b, struct otri *farleft,
9419 struct otri *innerleft, struct otri *innerright,
9420 struct otri *farright, int axis)
9421 #else /* not ANSI_DECLARATORS */
9422 void mergehulls(m, b, farleft, innerleft, innerright, farright, axis)
9423 struct mesh *m;
9424 struct behavior *b;
9425 struct otri *farleft;
9426 struct otri *innerleft;
9427 struct otri *innerright;
9428 struct otri *farright;
9429 int axis;
9430 #endif /* not ANSI_DECLARATORS */
9431
9432 {
9433 struct otri leftcand, rightcand;
9434 struct otri baseedge;
9435 struct otri nextedge;
9436 struct otri sidecasing, topcasing, outercasing;
9437 struct otri checkedge;
9438 vertex innerleftdest;
9439 vertex innerrightorg;
9440 vertex innerleftapex, innerrightapex;
9441 vertex farleftpt, farrightpt;
9442 vertex farleftapex, farrightapex;
9443 vertex lowerleft, lowerright;
9444 vertex upperleft, upperright;
9445 vertex nextapex;
9446 vertex checkvertex;
9447 int changemade;
9448 int badedge;
9449 int leftfinished, rightfinished;
9450 triangle ptr; /* Temporary variable used by sym(). */
9451
9452 dest(*innerleft, innerleftdest);
9453 apex(*innerleft, innerleftapex);
9454 org(*innerright, innerrightorg);
9455 apex(*innerright, innerrightapex);
9456 /* Special treatment for horizontal cuts. */
9457 if (b->dwyer && (axis == 1)) {
9458 org(*farleft, farleftpt);
9459 apex(*farleft, farleftapex);
9460 dest(*farright, farrightpt);
9461 apex(*farright, farrightapex);
9462 /* The pointers to the extremal vertices are shifted to point to the */
9463 /* topmost and bottommost vertex of each hull, rather than the */
9464 /* leftmost and rightmost vertices. */
9465 while (farleftapex[1] < farleftpt[1]) {
9466 lnextself(*farleft);
9467 symself(*farleft);
9468 farleftpt = farleftapex;
9469 apex(*farleft, farleftapex);
9470 }
9471 sym(*innerleft, checkedge);
9472 apex(checkedge, checkvertex);
9473 while (checkvertex[1] > innerleftdest[1]) {
9474 lnext(checkedge, *innerleft);
9475 innerleftapex = innerleftdest;
9476 innerleftdest = checkvertex;
9477 sym(*innerleft, checkedge);
9478 apex(checkedge, checkvertex);
9479 }
9480 while (innerrightapex[1] < innerrightorg[1]) {
9481 lnextself(*innerright);
9482 symself(*innerright);
9483 innerrightorg = innerrightapex;
9484 apex(*innerright, innerrightapex);
9485 }
9486 sym(*farright, checkedge);
9487 apex(checkedge, checkvertex);
9488 while (checkvertex[1] > farrightpt[1]) {
9489 lnext(checkedge, *farright);
9490 farrightapex = farrightpt;
9491 farrightpt = checkvertex;
9492 sym(*farright, checkedge);
9493 apex(checkedge, checkvertex);
9494 }
9495 }
9496 /* Find a line tangent to and below both hulls. */
9497 do {
9498 changemade = 0;
9499 /* Make innerleftdest the "bottommost" vertex of the left hull. */
9500 if (counterclockwise(m, b, innerleftdest, innerleftapex, innerrightorg) >
9501 0.0) {
9502 lprevself(*innerleft);
9503 symself(*innerleft);
9504 innerleftdest = innerleftapex;
9505 apex(*innerleft, innerleftapex);
9506 changemade = 1;
9507 }
9508 /* Make innerrightorg the "bottommost" vertex of the right hull. */
9509 if (counterclockwise(m, b, innerrightapex, innerrightorg, innerleftdest) >
9510 0.0) {
9511 lnextself(*innerright);
9512 symself(*innerright);
9513 innerrightorg = innerrightapex;
9514 apex(*innerright, innerrightapex);
9515 changemade = 1;
9516 }
9517 } while (changemade);
9518 /* Find the two candidates to be the next "gear tooth." */
9519 sym(*innerleft, leftcand);
9520 sym(*innerright, rightcand);
9521 /* Create the bottom new bounding triangle. */
9522 maketriangle(m, b, &baseedge);
9523 /* Connect it to the bounding boxes of the left and right triangulations. */
9524 bond(baseedge, *innerleft);
9525 lnextself(baseedge);
9526 bond(baseedge, *innerright);
9527 lnextself(baseedge);
9528 setorg(baseedge, innerrightorg);
9529 setdest(baseedge, innerleftdest);
9530 /* Apex is intentionally left NULL. */
9531 if (b->verbose > 2) {
9532 printf(" Creating base bounding ");
9533 printtriangle(m, b, &baseedge);
9534 }
9535 /* Fix the extreme triangles if necessary. */
9536 org(*farleft, farleftpt);
9537 if (innerleftdest == farleftpt) {
9538 lnext(baseedge, *farleft);
9539 }
9540 dest(*farright, farrightpt);
9541 if (innerrightorg == farrightpt) {
9542 lprev(baseedge, *farright);
9543 }
9544 /* The vertices of the current knitting edge. */
9545 lowerleft = innerleftdest;
9546 lowerright = innerrightorg;
9547 /* The candidate vertices for knitting. */
9548 apex(leftcand, upperleft);
9549 apex(rightcand, upperright);
9550 /* Walk up the gap between the two triangulations, knitting them together. */
9551 while (1) {
9552 /* Have we reached the top? (This isn't quite the right question, */
9553 /* because even though the left triangulation might seem finished now, */
9554 /* moving up on the right triangulation might reveal a new vertex of */
9555 /* the left triangulation. And vice-versa.) */
9556 leftfinished = counterclockwise(m, b, upperleft, lowerleft, lowerright) <=
9557 0.0;
9558 rightfinished = counterclockwise(m, b, upperright, lowerleft, lowerright)
9559 <= 0.0;
9560 if (leftfinished && rightfinished) {
9561 /* Create the top new bounding triangle. */
9562 maketriangle(m, b, &nextedge);
9563 setorg(nextedge, lowerleft);
9564 setdest(nextedge, lowerright);
9565 /* Apex is intentionally left NULL. */
9566 /* Connect it to the bounding boxes of the two triangulations. */
9567 bond(nextedge, baseedge);
9568 lnextself(nextedge);
9569 bond(nextedge, rightcand);
9570 lnextself(nextedge);
9571 bond(nextedge, leftcand);
9572 if (b->verbose > 2) {
9573 printf(" Creating top bounding ");
9574 printtriangle(m, b, &nextedge);
9575 }
9576 /* Special treatment for horizontal cuts. */
9577 if (b->dwyer && (axis == 1)) {
9578 org(*farleft, farleftpt);
9579 apex(*farleft, farleftapex);
9580 dest(*farright, farrightpt);
9581 apex(*farright, farrightapex);
9582 sym(*farleft, checkedge);
9583 apex(checkedge, checkvertex);
9584 /* The pointers to the extremal vertices are restored to the */
9585 /* leftmost and rightmost vertices (rather than topmost and */
9586 /* bottommost). */
9587 while (checkvertex[0] < farleftpt[0]) {
9588 lprev(checkedge, *farleft);
9589 farleftapex = farleftpt;
9590 farleftpt = checkvertex;
9591 sym(*farleft, checkedge);
9592 apex(checkedge, checkvertex);
9593 }
9594 while (farrightapex[0] > farrightpt[0]) {
9595 lprevself(*farright);
9596 symself(*farright);
9597 farrightpt = farrightapex;
9598 apex(*farright, farrightapex);
9599 }
9600 }
9601 return;
9602 }
9603 /* Consider eliminating edges from the left triangulation. */
9604 if (!leftfinished) {
9605 /* What vertex would be exposed if an edge were deleted? */
9606 lprev(leftcand, nextedge);
9607 symself(nextedge);
9608 apex(nextedge, nextapex);
9609 /* If nextapex is NULL, then no vertex would be exposed; the */
9610 /* triangulation would have been eaten right through. */
9611 if (nextapex != (vertex) NULL) {
9612 /* Check whether the edge is Delaunay. */
9613 badedge = incircle(m, b, lowerleft, lowerright, upperleft, nextapex) >
9614 0.0;
9615 while (badedge) {
9616 /* Eliminate the edge with an edge flip. As a result, the */
9617 /* left triangulation will have one more boundary triangle. */
9618 lnextself(nextedge);
9619 sym(nextedge, topcasing);
9620 lnextself(nextedge);
9621 sym(nextedge, sidecasing);
9622 bond(nextedge, topcasing);
9623 bond(leftcand, sidecasing);
9624 lnextself(leftcand);
9625 sym(leftcand, outercasing);
9626 lprevself(nextedge);
9627 bond(nextedge, outercasing);
9628 /* Correct the vertices to reflect the edge flip. */
9629 setorg(leftcand, lowerleft);
9630 setdest(leftcand, NULL);
9631 setapex(leftcand, nextapex);
9632 setorg(nextedge, NULL);
9633 setdest(nextedge, upperleft);
9634 setapex(nextedge, nextapex);
9635 /* Consider the newly exposed vertex. */
9636 upperleft = nextapex;
9637 /* What vertex would be exposed if another edge were deleted? */
9638 otricopy(sidecasing, nextedge);
9639 apex(nextedge, nextapex);
9640 if (nextapex != (vertex) NULL) {
9641 /* Check whether the edge is Delaunay. */
9642 badedge = incircle(m, b, lowerleft, lowerright, upperleft,
9643 nextapex) > 0.0;
9644 } else {
9645 /* Avoid eating right through the triangulation. */
9646 badedge = 0;
9647 }
9648 }
9649 }
9650 }
9651 /* Consider eliminating edges from the right triangulation. */
9652 if (!rightfinished) {
9653 /* What vertex would be exposed if an edge were deleted? */
9654 lnext(rightcand, nextedge);
9655 symself(nextedge);
9656 apex(nextedge, nextapex);
9657 /* If nextapex is NULL, then no vertex would be exposed; the */
9658 /* triangulation would have been eaten right through. */
9659 if (nextapex != (vertex) NULL) {
9660 /* Check whether the edge is Delaunay. */
9661 badedge = incircle(m, b, lowerleft, lowerright, upperright, nextapex) >
9662 0.0;
9663 while (badedge) {
9664 /* Eliminate the edge with an edge flip. As a result, the */
9665 /* right triangulation will have one more boundary triangle. */
9666 lprevself(nextedge);
9667 sym(nextedge, topcasing);
9668 lprevself(nextedge);
9669 sym(nextedge, sidecasing);
9670 bond(nextedge, topcasing);
9671 bond(rightcand, sidecasing);
9672 lprevself(rightcand);
9673 sym(rightcand, outercasing);
9674 lnextself(nextedge);
9675 bond(nextedge, outercasing);
9676 /* Correct the vertices to reflect the edge flip. */
9677 setorg(rightcand, NULL);
9678 setdest(rightcand, lowerright);
9679 setapex(rightcand, nextapex);
9680 setorg(nextedge, upperright);
9681 setdest(nextedge, NULL);
9682 setapex(nextedge, nextapex);
9683 /* Consider the newly exposed vertex. */
9684 upperright = nextapex;
9685 /* What vertex would be exposed if another edge were deleted? */
9686 otricopy(sidecasing, nextedge);
9687 apex(nextedge, nextapex);
9688 if (nextapex != (vertex) NULL) {
9689 /* Check whether the edge is Delaunay. */
9690 badedge = incircle(m, b, lowerleft, lowerright, upperright,
9691 nextapex) > 0.0;
9692 } else {
9693 /* Avoid eating right through the triangulation. */
9694 badedge = 0;
9695 }
9696 }
9697 }
9698 }
9699 if (leftfinished || (!rightfinished &&
9700 (incircle(m, b, upperleft, lowerleft, lowerright, upperright) >
9701 0.0))) {
9702 /* Knit the triangulations, adding an edge from `lowerleft' */
9703 /* to `upperright'. */
9704 bond(baseedge, rightcand);
9705 lprev(rightcand, baseedge);
9706 setdest(baseedge, lowerleft);
9707 lowerright = upperright;
9708 sym(baseedge, rightcand);
9709 apex(rightcand, upperright);
9710 } else {
9711 /* Knit the triangulations, adding an edge from `upperleft' */
9712 /* to `lowerright'. */
9713 bond(baseedge, leftcand);
9714 lnext(leftcand, baseedge);
9715 setorg(baseedge, lowerright);
9716 lowerleft = upperleft;
9717 sym(baseedge, leftcand);
9718 apex(leftcand, upperleft);
9719 }
9720 if (b->verbose > 2) {
9721 printf(" Connecting ");
9722 printtriangle(m, b, &baseedge);
9723 }
9724 }
9725 }
9726
9727 /*****************************************************************************/
9728 /* */
9729 /* divconqrecurse() Recursively form a Delaunay triangulation by the */
9730 /* divide-and-conquer method. */
9731 /* */
9732 /* Recursively breaks down the problem into smaller pieces, which are */
9733 /* knitted together by mergehulls(). The base cases (problems of two or */
9734 /* three vertices) are handled specially here. */
9735 /* */
9736 /* On completion, `farleft' and `farright' are bounding triangles such that */
9737 /* the origin of `farleft' is the leftmost vertex (breaking ties by */
9738 /* choosing the highest leftmost vertex), and the destination of */
9739 /* `farright' is the rightmost vertex (breaking ties by choosing the */
9740 /* lowest rightmost vertex). */
9741 /* */
9742 /*****************************************************************************/
9743
9744 #ifdef ANSI_DECLARATORS
9745 void divconqrecurse(struct mesh *m, struct behavior *b, vertex *sortarray,
9746 int vertices, int axis,
9747 struct otri *farleft, struct otri *farright)
9748 #else /* not ANSI_DECLARATORS */
9749 void divconqrecurse(m, b, sortarray, vertices, axis, farleft, farright)
9750 struct mesh *m;
9751 struct behavior *b;
9752 vertex *sortarray;
9753 int vertices;
9754 int axis;
9755 struct otri *farleft;
9756 struct otri *farright;
9757 #endif /* not ANSI_DECLARATORS */
9758
9759 {
9760 struct otri midtri, tri1, tri2, tri3;
9761 struct otri innerleft, innerright;
9762 REAL area;
9763 int divider;
9764
9765 if (b->verbose > 2) {
9766 printf(" Triangulating %d vertices.\n", vertices);
9767 }
9768 if (vertices == 2) {
9769 /* The triangulation of two vertices is an edge. An edge is */
9770 /* represented by two bounding triangles. */
9771 maketriangle(m, b, farleft);
9772 setorg(*farleft, sortarray[0]);
9773 setdest(*farleft, sortarray[1]);
9774 /* The apex is intentionally left NULL. */
9775 maketriangle(m, b, farright);
9776 setorg(*farright, sortarray[1]);
9777 setdest(*farright, sortarray[0]);
9778 /* The apex is intentionally left NULL. */
9779 bond(*farleft, *farright);
9780 lprevself(*farleft);
9781 lnextself(*farright);
9782 bond(*farleft, *farright);
9783 lprevself(*farleft);
9784 lnextself(*farright);
9785 bond(*farleft, *farright);
9786 if (b->verbose > 2) {
9787 printf(" Creating ");
9788 printtriangle(m, b, farleft);
9789 printf(" Creating ");
9790 printtriangle(m, b, farright);
9791 }
9792 /* Ensure that the origin of `farleft' is sortarray[0]. */
9793 lprev(*farright, *farleft);
9794 return;
9795 } else if (vertices == 3) {
9796 /* The triangulation of three vertices is either a triangle (with */
9797 /* three bounding triangles) or two edges (with four bounding */
9798 /* triangles). In either case, four triangles are created. */
9799 maketriangle(m, b, &midtri);
9800 maketriangle(m, b, &tri1);
9801 maketriangle(m, b, &tri2);
9802 maketriangle(m, b, &tri3);
9803 area = counterclockwise(m, b, sortarray[0], sortarray[1], sortarray[2]);
9804 if (area == 0.0) {
9805 /* Three collinear vertices; the triangulation is two edges. */
9806 setorg(midtri, sortarray[0]);
9807 setdest(midtri, sortarray[1]);
9808 setorg(tri1, sortarray[1]);
9809 setdest(tri1, sortarray[0]);
9810 setorg(tri2, sortarray[2]);
9811 setdest(tri2, sortarray[1]);
9812 setorg(tri3, sortarray[1]);
9813 setdest(tri3, sortarray[2]);
9814 /* All apices are intentionally left NULL. */
9815 bond(midtri, tri1);
9816 bond(tri2, tri3);
9817 lnextself(midtri);
9818 lprevself(tri1);
9819 lnextself(tri2);
9820 lprevself(tri3);
9821 bond(midtri, tri3);
9822 bond(tri1, tri2);
9823 lnextself(midtri);
9824 lprevself(tri1);
9825 lnextself(tri2);
9826 lprevself(tri3);
9827 bond(midtri, tri1);
9828 bond(tri2, tri3);
9829 /* Ensure that the origin of `farleft' is sortarray[0]. */
9830 otricopy(tri1, *farleft);
9831 /* Ensure that the destination of `farright' is sortarray[2]. */
9832 otricopy(tri2, *farright);
9833 } else {
9834 /* The three vertices are not collinear; the triangulation is one */
9835 /* triangle, namely `midtri'. */
9836 setorg(midtri, sortarray[0]);
9837 setdest(tri1, sortarray[0]);
9838 setorg(tri3, sortarray[0]);
9839 /* Apices of tri1, tri2, and tri3 are left NULL. */
9840 if (area > 0.0) {
9841 /* The vertices are in counterclockwise order. */
9842 setdest(midtri, sortarray[1]);
9843 setorg(tri1, sortarray[1]);
9844 setdest(tri2, sortarray[1]);
9845 setapex(midtri, sortarray[2]);
9846 setorg(tri2, sortarray[2]);
9847 setdest(tri3, sortarray[2]);
9848 } else {
9849 /* The vertices are in clockwise order. */
9850 setdest(midtri, sortarray[2]);
9851 setorg(tri1, sortarray[2]);
9852 setdest(tri2, sortarray[2]);
9853 setapex(midtri, sortarray[1]);
9854 setorg(tri2, sortarray[1]);
9855 setdest(tri3, sortarray[1]);
9856 }
9857 /* The topology does not depend on how the vertices are ordered. */
9858 bond(midtri, tri1);
9859 lnextself(midtri);
9860 bond(midtri, tri2);
9861 lnextself(midtri);
9862 bond(midtri, tri3);
9863 lprevself(tri1);
9864 lnextself(tri2);
9865 bond(tri1, tri2);
9866 lprevself(tri1);
9867 lprevself(tri3);
9868 bond(tri1, tri3);
9869 lnextself(tri2);
9870 lprevself(tri3);
9871 bond(tri2, tri3);
9872 /* Ensure that the origin of `farleft' is sortarray[0]. */
9873 otricopy(tri1, *farleft);
9874 /* Ensure that the destination of `farright' is sortarray[2]. */
9875 if (area > 0.0) {
9876 otricopy(tri2, *farright);
9877 } else {
9878 lnext(*farleft, *farright);
9879 }
9880 }
9881 if (b->verbose > 2) {
9882 printf(" Creating ");
9883 printtriangle(m, b, &midtri);
9884 printf(" Creating ");
9885 printtriangle(m, b, &tri1);
9886 printf(" Creating ");
9887 printtriangle(m, b, &tri2);
9888 printf(" Creating ");
9889 printtriangle(m, b, &tri3);
9890 }
9891 return;
9892 } else {
9893 /* Split the vertices in half. */
9894 divider = vertices >> 1;
9895 /* Recursively triangulate each half. */
9896 divconqrecurse(m, b, sortarray, divider, 1 - axis, farleft, &innerleft);
9897 divconqrecurse(m, b, &sortarray[divider], vertices - divider, 1 - axis,
9898 &innerright, farright);
9899 if (b->verbose > 1) {
9900 printf(" Joining triangulations with %d and %d vertices.\n", divider,
9901 vertices - divider);
9902 }
9903 /* Merge the two triangulations into one. */
9904 mergehulls(m, b, farleft, &innerleft, &innerright, farright, axis);
9905 }
9906 }
9907
9908 #ifdef ANSI_DECLARATORS
9909 long removeghosts(struct mesh *m, struct behavior *b, struct otri *startghost)
9910 #else /* not ANSI_DECLARATORS */
9911 long removeghosts(m, b, startghost)
9912 struct mesh *m;
9913 struct behavior *b;
9914 struct otri *startghost;
9915 #endif /* not ANSI_DECLARATORS */
9916
9917 {
9918 struct otri searchedge;
9919 struct otri dissolveedge;
9920 struct otri deadtriangle;
9921 vertex markorg;
9922 long hullsize;
9923 triangle ptr; /* Temporary variable used by sym(). */
9924
9925 if (b->verbose) {
9926 printf(" Removing ghost triangles.\n");
9927 }
9928 /* Find an edge on the convex hull to start point location from. */
9929 lprev(*startghost, searchedge);
9930 symself(searchedge);
9931 m->dummytri[0] = encode(searchedge);
9932 /* Remove the bounding box and count the convex hull edges. */
9933 otricopy(*startghost, dissolveedge);
9934 hullsize = 0;
9935 do {
9936 hullsize++;
9937 lnext(dissolveedge, deadtriangle);
9938 lprevself(dissolveedge);
9939 symself(dissolveedge);
9940 /* If no PSLG is involved, set the boundary markers of all the vertices */
9941 /* on the convex hull. If a PSLG is used, this step is done later. */
9942 if (!b->poly) {
9943 /* Watch out for the case where all the input vertices are collinear. */
9944 if (dissolveedge.tri != m->dummytri) {
9945 org(dissolveedge, markorg);
9946 if (vertexmark(markorg) == 0) {
9947 setvertexmark(markorg, 1);
9948 }
9949 }
9950 }
9951 /* Remove a bounding triangle from a convex hull triangle. */
9952 dissolve(dissolveedge);
9953 /* Find the next bounding triangle. */
9954 sym(deadtriangle, dissolveedge);
9955 /* Delete the bounding triangle. */
9956 triangledealloc(m, deadtriangle.tri);
9957 } while (!otriequal(dissolveedge, *startghost));
9958 return hullsize;
9959 }
9960
9961 /*****************************************************************************/
9962 /* */
9963 /* divconqdelaunay() Form a Delaunay triangulation by the divide-and- */
9964 /* conquer method. */
9965 /* */
9966 /* Sorts the vertices, calls a recursive procedure to triangulate them, and */
9967 /* removes the bounding box, setting boundary markers as appropriate. */
9968 /* */
9969 /*****************************************************************************/
9970
9971 #ifdef ANSI_DECLARATORS
9972 long divconqdelaunay(struct mesh *m, struct behavior *b)
9973 #else /* not ANSI_DECLARATORS */
9974 long divconqdelaunay(m, b)
9975 struct mesh *m;
9976 struct behavior *b;
9977 #endif /* not ANSI_DECLARATORS */
9978
9979 {
9980 vertex *sortarray;
9981 struct otri hullleft, hullright;
9982 int divider;
9983 int i, j;
9984
9985 if (b->verbose) {
9986 printf(" Sorting vertices.\n");
9987 }
9988
9989 /* Allocate an array of pointers to vertices for sorting. */
9990 sortarray = (vertex *) trimalloc(m->invertices * (int) sizeof(vertex));
9991 traversalinit(&m->vertices);
9992 for (i = 0; i < m->invertices; i++) {
9993 sortarray[i] = vertextraverse(m);
9994 }
9995 /* Sort the vertices. */
9996 vertexsort(sortarray, m->invertices);
9997 /* Discard duplicate vertices, which can really mess up the algorithm. */
9998 i = 0;
9999 for (j = 1; j < m->invertices; j++) {
10000 if ((sortarray[i][0] == sortarray[j][0])
10001 && (sortarray[i][1] == sortarray[j][1])) {
10002 if (!b->quiet) {
10003 printf(
10004 "Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n",
10005 sortarray[j][0], sortarray[j][1]);
10006 }
10007 setvertextype(sortarray[j], UNDEADVERTEX);
10008 m->undeads++;
10009 } else {
10010 i++;
10011 sortarray[i] = sortarray[j];
10012 }
10013 }
10014 i++;
10015 if (b->dwyer) {
10016 /* Re-sort the array of vertices to accommodate alternating cuts. */
10017 divider = i >> 1;
10018 if (i - divider >= 2) {
10019 if (divider >= 2) {
10020 alternateaxes(sortarray, divider, 1);
10021 }
10022 alternateaxes(&sortarray[divider], i - divider, 1);
10023 }
10024 }
10025
10026 if (b->verbose) {
10027 printf(" Forming triangulation.\n");
10028 }
10029
10030 /* Form the Delaunay triangulation. */
10031 divconqrecurse(m, b, sortarray, i, 0, &hullleft, &hullright);
10032 trifree((VOID *) sortarray);
10033
10034 return removeghosts(m, b, &hullleft);
10035 }
10036
10037 /** **/
10038 /** **/
10039 /********* Divide-and-conquer Delaunay triangulation ends here *********/
10040
10041 /********* Incremental Delaunay triangulation begins here *********/
10042 /** **/
10043 /** **/
10044
10045 /*****************************************************************************/
10046 /* */
10047 /* boundingbox() Form an "infinite" bounding triangle to insert vertices */
10048 /* into. */
10049 /* */
10050 /* The vertices at "infinity" are assigned finite coordinates, which are */
10051 /* used by the point location routines, but (mostly) ignored by the */
10052 /* Delaunay edge flip routines. */
10053 /* */
10054 /*****************************************************************************/
10055
10056 #ifndef REDUCED
10057
10058 #ifdef ANSI_DECLARATORS
10059 void boundingbox(struct mesh *m, struct behavior *b)
10060 #else /* not ANSI_DECLARATORS */
10061 void boundingbox(m, b)
10062 struct mesh *m;
10063 struct behavior *b;
10064 #endif /* not ANSI_DECLARATORS */
10065
10066 {
10067 struct otri inftri; /* Handle for the triangular bounding box. */
10068 REAL width;
10069
10070 if (b->verbose) {
10071 printf(" Creating triangular bounding box.\n");
10072 }
10073 /* Find the width (or height, whichever is larger) of the triangulation. */
10074 width = m->xmax - m->xmin;
10075 if (m->ymax - m->ymin > width) {
10076 width = m->ymax - m->ymin;
10077 }
10078 if (width == 0.0) {
10079 width = 1.0;
10080 }
10081 /* Create the vertices of the bounding box. */
10082 m->infvertex1 = (vertex) trimalloc(m->vertices.itembytes);
10083 m->infvertex2 = (vertex) trimalloc(m->vertices.itembytes);
10084 m->infvertex3 = (vertex) trimalloc(m->vertices.itembytes);
10085 m->infvertex1[0] = m->xmin - 50.0 * width;
10086 m->infvertex1[1] = m->ymin - 40.0 * width;
10087 m->infvertex2[0] = m->xmax + 50.0 * width;
10088 m->infvertex2[1] = m->ymin - 40.0 * width;
10089 m->infvertex3[0] = 0.5 * (m->xmin + m->xmax);
10090 m->infvertex3[1] = m->ymax + 60.0 * width;
10091
10092 /* Create the bounding box. */
10093 maketriangle(m, b, &inftri);
10094 setorg(inftri, m->infvertex1);
10095 setdest(inftri, m->infvertex2);
10096 setapex(inftri, m->infvertex3);
10097 /* Link dummytri to the bounding box so we can always find an */
10098 /* edge to begin searching (point location) from. */
10099 m->dummytri[0] = (triangle) inftri.tri;
10100 if (b->verbose > 2) {
10101 printf(" Creating ");
10102 printtriangle(m, b, &inftri);
10103 }
10104 }
10105
10106 #endif /* not REDUCED */
10107
10108 /*****************************************************************************/
10109 /* */
10110 /* removebox() Remove the "infinite" bounding triangle, setting boundary */
10111 /* markers as appropriate. */
10112 /* */
10113 /* The triangular bounding box has three boundary triangles (one for each */
10114 /* side of the bounding box), and a bunch of triangles fanning out from */
10115 /* the three bounding box vertices (one triangle for each edge of the */
10116 /* convex hull of the inner mesh). This routine removes these triangles. */
10117 /* */
10118 /* Returns the number of edges on the convex hull of the triangulation. */
10119 /* */
10120 /*****************************************************************************/
10121
10122 #ifndef REDUCED
10123
10124 #ifdef ANSI_DECLARATORS
10125 long removebox(struct mesh *m, struct behavior *b)
10126 #else /* not ANSI_DECLARATORS */
10127 long removebox(m, b)
10128 struct mesh *m;
10129 struct behavior *b;
10130 #endif /* not ANSI_DECLARATORS */
10131
10132 {
10133 struct otri deadtriangle;
10134 struct otri searchedge;
10135 struct otri checkedge;
10136 struct otri nextedge, finaledge, dissolveedge;
10137 vertex markorg;
10138 long hullsize;
10139 triangle ptr; /* Temporary variable used by sym(). */
10140
10141 if (b->verbose) {
10142 printf(" Removing triangular bounding box.\n");
10143 }
10144 /* Find a boundary triangle. */
10145 nextedge.tri = m->dummytri;
10146 nextedge.orient = 0;
10147 symself(nextedge);
10148 /* Mark a place to stop. */
10149 lprev(nextedge, finaledge);
10150 lnextself(nextedge);
10151 symself(nextedge);
10152 /* Find a triangle (on the boundary of the vertex set) that isn't */
10153 /* a bounding box triangle. */
10154 lprev(nextedge, searchedge);
10155 symself(searchedge);
10156 /* Check whether nextedge is another boundary triangle */
10157 /* adjacent to the first one. */
10158 lnext(nextedge, checkedge);
10159 symself(checkedge);
10160 if (checkedge.tri == m->dummytri) {
10161 /* Go on to the next triangle. There are only three boundary */
10162 /* triangles, and this next triangle cannot be the third one, */
10163 /* so it's safe to stop here. */
10164 lprevself(searchedge);
10165 symself(searchedge);
10166 }
10167 /* Find a new boundary edge to search from, as the current search */
10168 /* edge lies on a bounding box triangle and will be deleted. */
10169 m->dummytri[0] = encode(searchedge);
10170 hullsize = -2l;
10171 while (!otriequal(nextedge, finaledge)) {
10172 hullsize++;
10173 lprev(nextedge, dissolveedge);
10174 symself(dissolveedge);
10175 /* If not using a PSLG, the vertices should be marked now. */
10176 /* (If using a PSLG, markhull() will do the job.) */
10177 if (!b->poly) {
10178 /* Be careful! One must check for the case where all the input */
10179 /* vertices are collinear, and thus all the triangles are part of */
10180 /* the bounding box. Otherwise, the setvertexmark() call below */
10181 /* will cause a bad pointer reference. */
10182 if (dissolveedge.tri != m->dummytri) {
10183 org(dissolveedge, markorg);
10184 if (vertexmark(markorg) == 0) {
10185 setvertexmark(markorg, 1);
10186 }
10187 }
10188 }
10189 /* Disconnect the bounding box triangle from the mesh triangle. */
10190 dissolve(dissolveedge);
10191 lnext(nextedge, deadtriangle);
10192 sym(deadtriangle, nextedge);
10193 /* Get rid of the bounding box triangle. */
10194 triangledealloc(m, deadtriangle.tri);
10195 /* Do we need to turn the corner? */
10196 if (nextedge.tri == m->dummytri) {
10197 /* Turn the corner. */
10198 otricopy(dissolveedge, nextedge);
10199 }
10200 }
10201 triangledealloc(m, finaledge.tri);
10202
10203 trifree((VOID *) m->infvertex1); /* Deallocate the bounding box vertices. */
10204 trifree((VOID *) m->infvertex2);
10205 trifree((VOID *) m->infvertex3);
10206
10207 return hullsize;
10208 }
10209
10210 #endif /* not REDUCED */
10211
10212 /*****************************************************************************/
10213 /* */
10214 /* incrementaldelaunay() Form a Delaunay triangulation by incrementally */
10215 /* inserting vertices. */
10216 /* */
10217 /* Returns the number of edges on the convex hull of the triangulation. */
10218 /* */
10219 /*****************************************************************************/
10220
10221 #ifndef REDUCED
10222
10223 #ifdef ANSI_DECLARATORS
10224 long incrementaldelaunay(struct mesh *m, struct behavior *b)
10225 #else /* not ANSI_DECLARATORS */
10226 long incrementaldelaunay(m, b)
10227 struct mesh *m;
10228 struct behavior *b;
10229 #endif /* not ANSI_DECLARATORS */
10230
10231 {
10232 struct otri starttri;
10233 vertex vertexloop;
10234
10235 /* Create a triangular bounding box. */
10236 boundingbox(m, b);
10237 if (b->verbose) {
10238 printf(" Incrementally inserting vertices.\n");
10239 }
10240 traversalinit(&m->vertices);
10241 vertexloop = vertextraverse(m);
10242 while (vertexloop != (vertex) NULL) {
10243 starttri.tri = m->dummytri;
10244 if (insertvertex(m, b, vertexloop, &starttri, (struct osub *) NULL, 0, 0)
10245 == DUPLICATEVERTEX) {
10246 if (!b->quiet) {
10247 printf(
10248 "Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n",
10249 vertexloop[0], vertexloop[1]);
10250 }
10251 setvertextype(vertexloop, UNDEADVERTEX);
10252 m->undeads++;
10253 }
10254 vertexloop = vertextraverse(m);
10255 }
10256 /* Remove the bounding box. */
10257 return removebox(m, b);
10258 }
10259
10260 #endif /* not REDUCED */
10261
10262 /** **/
10263 /** **/
10264 /********* Incremental Delaunay triangulation ends here *********/
10265
10266 /********* Sweepline Delaunay triangulation begins here *********/
10267 /** **/
10268 /** **/
10269
10270 #ifndef REDUCED
10271
10272 #ifdef ANSI_DECLARATORS
10273 void eventheapinsert(struct event **heap, int heapsize, struct event *newevent)
10274 #else /* not ANSI_DECLARATORS */
10275 void eventheapinsert(heap, heapsize, newevent)
10276 struct event **heap;
10277 int heapsize;
10278 struct event *newevent;
10279 #endif /* not ANSI_DECLARATORS */
10280
10281 {
10282 REAL eventx, eventy;
10283 int eventnum;
10284 int parent;
10285 int notdone;
10286
10287 eventx = newevent->xkey;
10288 eventy = newevent->ykey;
10289 eventnum = heapsize;
10290 notdone = eventnum > 0;
10291 while (notdone) {
10292 parent = (eventnum - 1) >> 1;
10293 if ((heap[parent]->ykey < eventy) ||
10294 ((heap[parent]->ykey == eventy)
10295 && (heap[parent]->xkey <= eventx))) {
10296 notdone = 0;
10297 } else {
10298 heap[eventnum] = heap[parent];
10299 heap[eventnum]->heapposition = eventnum;
10300
10301 eventnum = parent;
10302 notdone = eventnum > 0;
10303 }
10304 }
10305 heap[eventnum] = newevent;
10306 newevent->heapposition = eventnum;
10307 }
10308
10309 #endif /* not REDUCED */
10310
10311 #ifndef REDUCED
10312
10313 #ifdef ANSI_DECLARATORS
10314 void eventheapify(struct event **heap, int heapsize, int eventnum)
10315 #else /* not ANSI_DECLARATORS */
10316 void eventheapify(heap, heapsize, eventnum)
10317 struct event **heap;
10318 int heapsize;
10319 int eventnum;
10320 #endif /* not ANSI_DECLARATORS */
10321
10322 {
10323 struct event *thisevent;
10324 REAL eventx, eventy;
10325 int leftchild, rightchild;
10326 int smallest;
10327 int notdone;
10328
10329 thisevent = heap[eventnum];
10330 eventx = thisevent->xkey;
10331 eventy = thisevent->ykey;
10332 leftchild = 2 * eventnum + 1;
10333 notdone = leftchild < heapsize;
10334 while (notdone) {
10335 if ((heap[leftchild]->ykey < eventy) ||
10336 ((heap[leftchild]->ykey == eventy)
10337 && (heap[leftchild]->xkey < eventx))) {
10338 smallest = leftchild;
10339 } else {
10340 smallest = eventnum;
10341 }
10342 rightchild = leftchild + 1;
10343 if (rightchild < heapsize) {
10344 if ((heap[rightchild]->ykey < heap[smallest]->ykey) ||
10345 ((heap[rightchild]->ykey == heap[smallest]->ykey)
10346 && (heap[rightchild]->xkey < heap[smallest]->xkey))) {
10347 smallest = rightchild;
10348 }
10349 }
10350 if (smallest == eventnum) {
10351 notdone = 0;
10352 } else {
10353 heap[eventnum] = heap[smallest];
10354 heap[eventnum]->heapposition = eventnum;
10355 heap[smallest] = thisevent;
10356 thisevent->heapposition = smallest;
10357
10358 eventnum = smallest;
10359 leftchild = 2 * eventnum + 1;
10360 notdone = leftchild < heapsize;
10361 }
10362 }
10363 }
10364
10365 #endif /* not REDUCED */
10366
10367 #ifndef REDUCED
10368
10369 #ifdef ANSI_DECLARATORS
10370 void eventheapdelete(struct event **heap, int heapsize, int eventnum)
10371 #else /* not ANSI_DECLARATORS */
10372 void eventheapdelete(heap, heapsize, eventnum)
10373 struct event **heap;
10374 int heapsize;
10375 int eventnum;
10376 #endif /* not ANSI_DECLARATORS */
10377
10378 {
10379 struct event *moveevent;
10380 REAL eventx, eventy;
10381 int parent;
10382 int notdone;
10383
10384 moveevent = heap[heapsize - 1];
10385 if (eventnum > 0) {
10386 eventx = moveevent->xkey;
10387 eventy = moveevent->ykey;
10388 do {
10389 parent = (eventnum - 1) >> 1;
10390 if ((heap[parent]->ykey < eventy) ||
10391 ((heap[parent]->ykey == eventy)
10392 && (heap[parent]->xkey <= eventx))) {
10393 notdone = 0;
10394 } else {
10395 heap[eventnum] = heap[parent];
10396 heap[eventnum]->heapposition = eventnum;
10397
10398 eventnum = parent;
10399 notdone = eventnum > 0;
10400 }
10401 } while (notdone);
10402 }
10403 heap[eventnum] = moveevent;
10404 moveevent->heapposition = eventnum;
10405 eventheapify(heap, heapsize - 1, eventnum);
10406 }
10407
10408 #endif /* not REDUCED */
10409
10410 #ifndef REDUCED
10411
10412 #ifdef ANSI_DECLARATORS
10413 void createeventheap(struct mesh *m, struct event ***eventheap,
10414 struct event **events, struct event **freeevents)
10415 #else /* not ANSI_DECLARATORS */
10416 void createeventheap(m, eventheap, events, freeevents)
10417 struct mesh *m;
10418 struct event ***eventheap;
10419 struct event **events;
10420 struct event **freeevents;
10421 #endif /* not ANSI_DECLARATORS */
10422
10423 {
10424 vertex thisvertex;
10425 int maxevents;
10426 int i;
10427
10428 maxevents = (3 * m->invertices) / 2;
10429 *eventheap = (struct event **) trimalloc(maxevents *
10430 (int) sizeof(struct event *));
10431 *events = (struct event *) trimalloc(maxevents * (int) sizeof(struct event));
10432 traversalinit(&m->vertices);
10433 for (i = 0; i < m->invertices; i++) {
10434 thisvertex = vertextraverse(m);
10435 (*events)[i].eventptr = (VOID *) thisvertex;
10436 (*events)[i].xkey = thisvertex[0];
10437 (*events)[i].ykey = thisvertex[1];
10438 eventheapinsert(*eventheap, i, *events + i);
10439 }
10440 *freeevents = (struct event *) NULL;
10441 for (i = maxevents - 1; i >= m->invertices; i--) {
10442 (*events)[i].eventptr = (VOID *) *freeevents;
10443 *freeevents = *events + i;
10444 }
10445 }
10446
10447 #endif /* not REDUCED */
10448
10449 #ifndef REDUCED
10450
10451 #ifdef ANSI_DECLARATORS
10452 int rightofhyperbola(struct mesh *m, struct otri *fronttri, vertex newsite)
10453 #else /* not ANSI_DECLARATORS */
10454 int rightofhyperbola(m, fronttri, newsite)
10455 struct mesh *m;
10456 struct otri *fronttri;
10457 vertex newsite;
10458 #endif /* not ANSI_DECLARATORS */
10459
10460 {
10461 vertex leftvertex, rightvertex;
10462 REAL dxa, dya, dxb, dyb;
10463
10464 m->hyperbolacount++;
10465
10466 dest(*fronttri, leftvertex);
10467 apex(*fronttri, rightvertex);
10468 if ((leftvertex[1] < rightvertex[1]) ||
10469 ((leftvertex[1] == rightvertex[1]) &&
10470 (leftvertex[0] < rightvertex[0]))) {
10471 if (newsite[0] >= rightvertex[0]) {
10472 return 1;
10473 }
10474 } else {
10475 if (newsite[0] <= leftvertex[0]) {
10476 return 0;
10477 }
10478 }
10479 dxa = leftvertex[0] - newsite[0];
10480 dya = leftvertex[1] - newsite[1];
10481 dxb = rightvertex[0] - newsite[0];
10482 dyb = rightvertex[1] - newsite[1];
10483 return dya * (dxb * dxb + dyb * dyb) > dyb * (dxa * dxa + dya * dya);
10484 }
10485
10486 #endif /* not REDUCED */
10487
10488 #ifndef REDUCED
10489
10490 #ifdef ANSI_DECLARATORS
10491 REAL circletop(struct mesh *m, vertex pa, vertex pb, vertex pc, REAL ccwabc)
10492 #else /* not ANSI_DECLARATORS */
10493 REAL circletop(m, pa, pb, pc, ccwabc)
10494 struct mesh *m;
10495 vertex pa;
10496 vertex pb;
10497 vertex pc;
10498 REAL ccwabc;
10499 #endif /* not ANSI_DECLARATORS */
10500
10501 {
10502 REAL xac, yac, xbc, ybc, xab, yab;
10503 REAL aclen2, bclen2, ablen2;
10504
10505 m->circletopcount++;
10506
10507 xac = pa[0] - pc[0];
10508 yac = pa[1] - pc[1];
10509 xbc = pb[0] - pc[0];
10510 ybc = pb[1] - pc[1];
10511 xab = pa[0] - pb[0];
10512 yab = pa[1] - pb[1];
10513 aclen2 = xac * xac + yac * yac;
10514 bclen2 = xbc * xbc + ybc * ybc;
10515 ablen2 = xab * xab + yab * yab;
10516 return pc[1] + (xac * bclen2 - xbc * aclen2 + sqrt(aclen2 * bclen2 * ablen2))
10517 / (2.0 * ccwabc);
10518 }
10519
10520 #endif /* not REDUCED */
10521
10522 #ifndef REDUCED
10523
10524 #ifdef ANSI_DECLARATORS
10525 void check4deadevent(struct otri *checktri, struct event **freeevents,
10526 struct event **eventheap, int *heapsize)
10527 #else /* not ANSI_DECLARATORS */
10528 void check4deadevent(checktri, freeevents, eventheap, heapsize)
10529 struct otri *checktri;
10530 struct event **freeevents;
10531 struct event **eventheap;
10532 int *heapsize;
10533 #endif /* not ANSI_DECLARATORS */
10534
10535 {
10536 struct event *deadevent;
10537 vertex eventvertex;
10538 int eventnum;
10539
10540 org(*checktri, eventvertex);
10541 if (eventvertex != (vertex) NULL) {
10542 deadevent = (struct event *) eventvertex;
10543 eventnum = deadevent->heapposition;
10544 deadevent->eventptr = (VOID *) *freeevents;
10545 *freeevents = deadevent;
10546 eventheapdelete(eventheap, *heapsize, eventnum);
10547 (*heapsize)--;
10548 setorg(*checktri, NULL);
10549 }
10550 }
10551
10552 #endif /* not REDUCED */
10553
10554 #ifndef REDUCED
10555
10556 #ifdef ANSI_DECLARATORS
10557 struct splaynode *splay(struct mesh *m, struct splaynode *splaytree,
10558 vertex searchpoint, struct otri *searchtri)
10559 #else /* not ANSI_DECLARATORS */
10560 struct splaynode *splay(m, splaytree, searchpoint, searchtri)
10561 struct mesh *m;
10562 struct splaynode *splaytree;
10563 vertex searchpoint;
10564 struct otri *searchtri;
10565 #endif /* not ANSI_DECLARATORS */
10566
10567 {
10568 struct splaynode *child, *grandchild;
10569 struct splaynode *lefttree, *righttree;
10570 struct splaynode *leftright;
10571 vertex checkvertex;
10572 int rightofroot, rightofchild;
10573
10574 if (splaytree == (struct splaynode *) NULL) {
10575 return (struct splaynode *) NULL;
10576 }
10577 dest(splaytree->keyedge, checkvertex);
10578 if (checkvertex == splaytree->keydest) {
10579 rightofroot = rightofhyperbola(m, &splaytree->keyedge, searchpoint);
10580 if (rightofroot) {
10581 otricopy(splaytree->keyedge, *searchtri);
10582 child = splaytree->rchild;
10583 } else {
10584 child = splaytree->lchild;
10585 }
10586 if (child == (struct splaynode *) NULL) {
10587 return splaytree;
10588 }
10589 dest(child->keyedge, checkvertex);
10590 if (checkvertex != child->keydest) {
10591 child = splay(m, child, searchpoint, searchtri);
10592 if (child == (struct splaynode *) NULL) {
10593 if (rightofroot) {
10594 splaytree->rchild = (struct splaynode *) NULL;
10595 } else {
10596 splaytree->lchild = (struct splaynode *) NULL;
10597 }
10598 return splaytree;
10599 }
10600 }
10601 rightofchild = rightofhyperbola(m, &child->keyedge, searchpoint);
10602 if (rightofchild) {
10603 otricopy(child->keyedge, *searchtri);
10604 grandchild = splay(m, child->rchild, searchpoint, searchtri);
10605 child->rchild = grandchild;
10606 } else {
10607 grandchild = splay(m, child->lchild, searchpoint, searchtri);
10608 child->lchild = grandchild;
10609 }
10610 if (grandchild == (struct splaynode *) NULL) {
10611 if (rightofroot) {
10612 splaytree->rchild = child->lchild;
10613 child->lchild = splaytree;
10614 } else {
10615 splaytree->lchild = child->rchild;
10616 child->rchild = splaytree;
10617 }
10618 return child;
10619 }
10620 if (rightofchild) {
10621 if (rightofroot) {
10622 splaytree->rchild = child->lchild;
10623 child->lchild = splaytree;
10624 } else {
10625 splaytree->lchild = grandchild->rchild;
10626 grandchild->rchild = splaytree;
10627 }
10628 child->rchild = grandchild->lchild;
10629 grandchild->lchild = child;
10630 } else {
10631 if (rightofroot) {
10632 splaytree->rchild = grandchild->lchild;
10633 grandchild->lchild = splaytree;
10634 } else {
10635 splaytree->lchild = child->rchild;
10636 child->rchild = splaytree;
10637 }
10638 child->lchild = grandchild->rchild;
10639 grandchild->rchild = child;
10640 }
10641 return grandchild;
10642 } else {
10643 lefttree = splay(m, splaytree->lchild, searchpoint, searchtri);
10644 righttree = splay(m, splaytree->rchild, searchpoint, searchtri);
10645
10646 pooldealloc(&m->splaynodes, (VOID *) splaytree);
10647 if (lefttree == (struct splaynode *) NULL) {
10648 return righttree;
10649 } else if (righttree == (struct splaynode *) NULL) {
10650 return lefttree;
10651 } else if (lefttree->rchild == (struct splaynode *) NULL) {
10652 lefttree->rchild = righttree->lchild;
10653 righttree->lchild = lefttree;
10654 return righttree;
10655 } else if (righttree->lchild == (struct splaynode *) NULL) {
10656 righttree->lchild = lefttree->rchild;
10657 lefttree->rchild = righttree;
10658 return lefttree;
10659 } else {
10660 /* printf("Holy Toledo!!!\n"); */
10661 leftright = lefttree->rchild;
10662 while (leftright->rchild != (struct splaynode *) NULL) {
10663 leftright = leftright->rchild;
10664 }
10665 leftright->rchild = righttree;
10666 return lefttree;
10667 }
10668 }
10669 }
10670
10671 #endif /* not REDUCED */
10672
10673 #ifndef REDUCED
10674
10675 #ifdef ANSI_DECLARATORS
10676 struct splaynode *splayinsert(struct mesh *m, struct splaynode *splayroot,
10677 struct otri *newkey, vertex searchpoint)
10678 #else /* not ANSI_DECLARATORS */
10679 struct splaynode *splayinsert(m, splayroot, newkey, searchpoint)
10680 struct mesh *m;
10681 struct splaynode *splayroot;
10682 struct otri *newkey;
10683 vertex searchpoint;
10684 #endif /* not ANSI_DECLARATORS */
10685
10686 {
10687 struct splaynode *newsplaynode;
10688
10689 newsplaynode = (struct splaynode *) poolalloc(&m->splaynodes);
10690 otricopy(*newkey, newsplaynode->keyedge);
10691 dest(*newkey, newsplaynode->keydest);
10692 if (splayroot == (struct splaynode *) NULL) {
10693 newsplaynode->lchild = (struct splaynode *) NULL;
10694 newsplaynode->rchild = (struct splaynode *) NULL;
10695 } else if (rightofhyperbola(m, &splayroot->keyedge, searchpoint)) {
10696 newsplaynode->lchild = splayroot;
10697 newsplaynode->rchild = splayroot->rchild;
10698 splayroot->rchild = (struct splaynode *) NULL;
10699 } else {
10700 newsplaynode->lchild = splayroot->lchild;
10701 newsplaynode->rchild = splayroot;
10702 splayroot->lchild = (struct splaynode *) NULL;
10703 }
10704 return newsplaynode;
10705 }
10706
10707 #endif /* not REDUCED */
10708
10709 #ifndef REDUCED
10710
10711 #ifdef ANSI_DECLARATORS
10712 struct splaynode *circletopinsert(struct mesh *m, struct behavior *b,
10713 struct splaynode *splayroot,
10714 struct otri *newkey,
10715 vertex pa, vertex pb, vertex pc, REAL topy)
10716 #else /* not ANSI_DECLARATORS */
10717 struct splaynode *circletopinsert(m, b, splayroot, newkey, pa, pb, pc, topy)
10718 struct mesh *m;
10719 struct behavior *b;
10720 struct splaynode *splayroot;
10721 struct otri *newkey;
10722 vertex pa;
10723 vertex pb;
10724 vertex pc;
10725 REAL topy;
10726 #endif /* not ANSI_DECLARATORS */
10727
10728 {
10729 REAL ccwabc;
10730 REAL xac, yac, xbc, ybc;
10731 REAL aclen2, bclen2;
10732 REAL searchpoint[2];
10733 struct otri dummytri;
10734
10735 ccwabc = counterclockwise(m, b, pa, pb, pc);
10736 xac = pa[0] - pc[0];
10737 yac = pa[1] - pc[1];
10738 xbc = pb[0] - pc[0];
10739 ybc = pb[1] - pc[1];
10740 aclen2 = xac * xac + yac * yac;
10741 bclen2 = xbc * xbc + ybc * ybc;
10742 searchpoint[0] = pc[0] - (yac * bclen2 - ybc * aclen2) / (2.0 * ccwabc);
10743 searchpoint[1] = topy;
10744 return splayinsert(m, splay(m, splayroot, (vertex) searchpoint, &dummytri),
10745 newkey, (vertex) searchpoint);
10746 }
10747
10748 #endif /* not REDUCED */
10749
10750 #ifndef REDUCED
10751
10752 #ifdef ANSI_DECLARATORS
10753 struct splaynode *frontlocate(struct mesh *m, struct splaynode *splayroot,
10754 struct otri *bottommost, vertex searchvertex,
10755 struct otri *searchtri, int *farright)
10756 #else /* not ANSI_DECLARATORS */
10757 struct splaynode *frontlocate(m, splayroot, bottommost, searchvertex,
10758 searchtri, farright)
10759 struct mesh *m;
10760 struct splaynode *splayroot;
10761 struct otri *bottommost;
10762 vertex searchvertex;
10763 struct otri *searchtri;
10764 int *farright;
10765 #endif /* not ANSI_DECLARATORS */
10766
10767 {
10768 int farrightflag;
10769 triangle ptr; /* Temporary variable used by onext(). */
10770
10771 otricopy(*bottommost, *searchtri);
10772 splayroot = splay(m, splayroot, searchvertex, searchtri);
10773
10774 farrightflag = 0;
10775 while (!farrightflag && rightofhyperbola(m, searchtri, searchvertex)) {
10776 onextself(*searchtri);
10777 farrightflag = otriequal(*searchtri, *bottommost);
10778 }
10779 *farright = farrightflag;
10780 return splayroot;
10781 }
10782
10783 #endif /* not REDUCED */
10784
10785 #ifndef REDUCED
10786
10787 #ifdef ANSI_DECLARATORS
10788 long sweeplinedelaunay(struct mesh *m, struct behavior *b)
10789 #else /* not ANSI_DECLARATORS */
10790 long sweeplinedelaunay(m, b)
10791 struct mesh *m;
10792 struct behavior *b;
10793 #endif /* not ANSI_DECLARATORS */
10794
10795 {
10796 struct event **eventheap;
10797 struct event *events;
10798 struct event *freeevents;
10799 struct event *nextevent;
10800 struct event *newevent;
10801 struct splaynode *splayroot;
10802 struct otri bottommost;
10803 struct otri searchtri;
10804 struct otri fliptri;
10805 struct otri lefttri, righttri, farlefttri, farrighttri;
10806 struct otri inserttri;
10807 vertex firstvertex, secondvertex;
10808 vertex nextvertex, lastvertex;
10809 vertex connectvertex;
10810 vertex leftvertex, midvertex, rightvertex;
10811 REAL lefttest, righttest;
10812 int heapsize;
10813 int check4events, farrightflag;
10814 triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */
10815
10816 poolinit(&m->splaynodes, sizeof(struct splaynode), SPLAYNODEPERBLOCK,
10817 SPLAYNODEPERBLOCK, 0);
10818 splayroot = (struct splaynode *) NULL;
10819
10820 if (b->verbose) {
10821 printf(" Placing vertices in event heap.\n");
10822 }
10823 createeventheap(m, &eventheap, &events, &freeevents);
10824 heapsize = m->invertices;
10825
10826 if (b->verbose) {
10827 printf(" Forming triangulation.\n");
10828 }
10829 maketriangle(m, b, &lefttri);
10830 maketriangle(m, b, &righttri);
10831 bond(lefttri, righttri);
10832 lnextself(lefttri);
10833 lprevself(righttri);
10834 bond(lefttri, righttri);
10835 lnextself(lefttri);
10836 lprevself(righttri);
10837 bond(lefttri, righttri);
10838 firstvertex = (vertex) eventheap[0]->eventptr;
10839 eventheap[0]->eventptr = (VOID *) freeevents;
10840 freeevents = eventheap[0];
10841 eventheapdelete(eventheap, heapsize, 0);
10842 heapsize--;
10843 do {
10844 if (heapsize == 0) {
10845 printf("Error: Input vertices are all identical.\n");
10846 triexit(1);
10847 }
10848 secondvertex = (vertex) eventheap[0]->eventptr;
10849 eventheap[0]->eventptr = (VOID *) freeevents;
10850 freeevents = eventheap[0];
10851 eventheapdelete(eventheap, heapsize, 0);
10852 heapsize--;
10853 if ((firstvertex[0] == secondvertex[0]) &&
10854 (firstvertex[1] == secondvertex[1])) {
10855 if (!b->quiet) {
10856 printf(
10857 "Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n",
10858 secondvertex[0], secondvertex[1]);
10859 }
10860 setvertextype(secondvertex, UNDEADVERTEX);
10861 m->undeads++;
10862 }
10863 } while ((firstvertex[0] == secondvertex[0]) &&
10864 (firstvertex[1] == secondvertex[1]));
10865 setorg(lefttri, firstvertex);
10866 setdest(lefttri, secondvertex);
10867 setorg(righttri, secondvertex);
10868 setdest(righttri, firstvertex);
10869 lprev(lefttri, bottommost);
10870 lastvertex = secondvertex;
10871 while (heapsize > 0) {
10872 nextevent = eventheap[0];
10873 eventheapdelete(eventheap, heapsize, 0);
10874 heapsize--;
10875 check4events = 1;
10876 if (nextevent->xkey < m->xmin) {
10877 decode(nextevent->eventptr, fliptri);
10878 oprev(fliptri, farlefttri);
10879 check4deadevent(&farlefttri, &freeevents, eventheap, &heapsize);
10880 onext(fliptri, farrighttri);
10881 check4deadevent(&farrighttri, &freeevents, eventheap, &heapsize);
10882
10883 if (otriequal(farlefttri, bottommost)) {
10884 lprev(fliptri, bottommost);
10885 }
10886 flip(m, b, &fliptri);
10887 setapex(fliptri, NULL);
10888 lprev(fliptri, lefttri);
10889 lnext(fliptri, righttri);
10890 sym(lefttri, farlefttri);
10891
10892 if (randomnation(SAMPLERATE) == 0) {
10893 symself(fliptri);
10894 dest(fliptri, leftvertex);
10895 apex(fliptri, midvertex);
10896 org(fliptri, rightvertex);
10897 splayroot = circletopinsert(m, b, splayroot, &lefttri, leftvertex,
10898 midvertex, rightvertex, nextevent->ykey);
10899 }
10900 } else {
10901 nextvertex = (vertex) nextevent->eventptr;
10902 if ((nextvertex[0] == lastvertex[0]) &&
10903 (nextvertex[1] == lastvertex[1])) {
10904 if (!b->quiet) {
10905 printf(
10906 "Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n",
10907 nextvertex[0], nextvertex[1]);
10908 }
10909 setvertextype(nextvertex, UNDEADVERTEX);
10910 m->undeads++;
10911 check4events = 0;
10912 } else {
10913 lastvertex = nextvertex;
10914
10915 splayroot = frontlocate(m, splayroot, &bottommost, nextvertex,
10916 &searchtri, &farrightflag);
10917 /*
10918 otricopy(bottommost, searchtri);
10919 farrightflag = 0;
10920 while (!farrightflag && rightofhyperbola(m, &searchtri, nextvertex)) {
10921 onextself(searchtri);
10922 farrightflag = otriequal(searchtri, bottommost);
10923 }
10924 */
10925
10926 check4deadevent(&searchtri, &freeevents, eventheap, &heapsize);
10927
10928 otricopy(searchtri, farrighttri);
10929 sym(searchtri, farlefttri);
10930 maketriangle(m, b, &lefttri);
10931 maketriangle(m, b, &righttri);
10932 dest(farrighttri, connectvertex);
10933 setorg(lefttri, connectvertex);
10934 setdest(lefttri, nextvertex);
10935 setorg(righttri, nextvertex);
10936 setdest(righttri, connectvertex);
10937 bond(lefttri, righttri);
10938 lnextself(lefttri);
10939 lprevself(righttri);
10940 bond(lefttri, righttri);
10941 lnextself(lefttri);
10942 lprevself(righttri);
10943 bond(lefttri, farlefttri);
10944 bond(righttri, farrighttri);
10945 if (!farrightflag && otriequal(farrighttri, bottommost)) {
10946 otricopy(lefttri, bottommost);
10947 }
10948
10949 if (randomnation(SAMPLERATE) == 0) {
10950 splayroot = splayinsert(m, splayroot, &lefttri, nextvertex);
10951 } else if (randomnation(SAMPLERATE) == 0) {
10952 lnext(righttri, inserttri);
10953 splayroot = splayinsert(m, splayroot, &inserttri, nextvertex);
10954 }
10955 }
10956 }
10957 nextevent->eventptr = (VOID *) freeevents;
10958 freeevents = nextevent;
10959
10960 if (check4events) {
10961 apex(farlefttri, leftvertex);
10962 dest(lefttri, midvertex);
10963 apex(lefttri, rightvertex);
10964 lefttest = counterclockwise(m, b, leftvertex, midvertex, rightvertex);
10965 if (lefttest > 0.0) {
10966 newevent = freeevents;
10967 freeevents = (struct event *) freeevents->eventptr;
10968 newevent->xkey = m->xminextreme;
10969 newevent->ykey = circletop(m, leftvertex, midvertex, rightvertex,
10970 lefttest);
10971 newevent->eventptr = (VOID *) encode(lefttri);
10972 eventheapinsert(eventheap, heapsize, newevent);
10973 heapsize++;
10974 setorg(lefttri, newevent);
10975 }
10976 apex(righttri, leftvertex);
10977 org(righttri, midvertex);
10978 apex(farrighttri, rightvertex);
10979 righttest = counterclockwise(m, b, leftvertex, midvertex, rightvertex);
10980 if (righttest > 0.0) {
10981 newevent = freeevents;
10982 freeevents = (struct event *) freeevents->eventptr;
10983 newevent->xkey = m->xminextreme;
10984 newevent->ykey = circletop(m, leftvertex, midvertex, rightvertex,
10985 righttest);
10986 newevent->eventptr = (VOID *) encode(farrighttri);
10987 eventheapinsert(eventheap, heapsize, newevent);
10988 heapsize++;
10989 setorg(farrighttri, newevent);
10990 }
10991 }
10992 }
10993
10994 pooldeinit(&m->splaynodes);
10995 lprevself(bottommost);
10996 return removeghosts(m, b, &bottommost);
10997 }
10998
10999 #endif /* not REDUCED */
11000
11001 /** **/
11002 /** **/
11003 /********* Sweepline Delaunay triangulation ends here *********/
11004
11005 /********* General mesh construction routines begin here *********/
11006 /** **/
11007 /** **/
11008
11009 /*****************************************************************************/
11010 /* */
11011 /* delaunay() Form a Delaunay triangulation. */
11012 /* */
11013 /*****************************************************************************/
11014
11015 #ifdef ANSI_DECLARATORS
11016 long delaunay(struct mesh *m, struct behavior *b)
11017 #else /* not ANSI_DECLARATORS */
11018 long delaunay(m, b)
11019 struct mesh *m;
11020 struct behavior *b;
11021 #endif /* not ANSI_DECLARATORS */
11022
11023 {
11024 long hulledges;
11025
11026 m->eextras = 0;
11027 initializetrisubpools(m, b);
11028
11029 #ifdef REDUCED
11030 if (!b->quiet) {
11031 printf(
11032 "Constructing Delaunay triangulation by divide-and-conquer method.\n");
11033 }
11034 hulledges = divconqdelaunay(m, b);
11035 #else /* not REDUCED */
11036 if (!b->quiet) {
11037 printf("Constructing Delaunay triangulation ");
11038 if (b->incremental) {
11039 printf("by incremental method.\n");
11040 } else if (b->sweepline) {
11041 printf("by sweepline method.\n");
11042 } else {
11043 printf("by divide-and-conquer method.\n");
11044 }
11045 }
11046 if (b->incremental) {
11047 hulledges = incrementaldelaunay(m, b);
11048 } else if (b->sweepline) {
11049 hulledges = sweeplinedelaunay(m, b);
11050 } else {
11051 hulledges = divconqdelaunay(m, b);
11052 }
11053 #endif /* not REDUCED */
11054
11055 if (m->triangles.items == 0) {
11056 /* The input vertices were all collinear, so there are no triangles. */
11057 return 0l;
11058 } else {
11059 return hulledges;
11060 }
11061 }
11062
11063 /*****************************************************************************/
11064 /* */
11065 /* reconstruct() Reconstruct a triangulation from its .ele (and possibly */
11066 /* .poly) file. Used when the -r switch is used. */
11067 /* */
11068 /* Reads an .ele file and reconstructs the original mesh. If the -p switch */
11069 /* is used, this procedure will also read a .poly file and reconstruct the */
11070 /* subsegments of the original mesh. If the -a switch is used, this */
11071 /* procedure will also read an .area file and set a maximum area constraint */
11072 /* on each triangle. */
11073 /* */
11074 /* Vertices that are not corners of triangles, such as nodes on edges of */
11075 /* subparametric elements, are discarded. */
11076 /* */
11077 /* This routine finds the adjacencies between triangles (and subsegments) */
11078 /* by forming one stack of triangles for each vertex. Each triangle is on */
11079 /* three different stacks simultaneously. Each triangle's subsegment */
11080 /* pointers are used to link the items in each stack. This memory-saving */
11081 /* feature makes the code harder to read. The most important thing to keep */
11082 /* in mind is that each triangle is removed from a stack precisely when */
11083 /* the corresponding pointer is adjusted to refer to a subsegment rather */
11084 /* than the next triangle of the stack. */
11085 /* */
11086 /*****************************************************************************/
11087
11088 #ifndef CDT_ONLY
11089
11090 #ifdef TRILIBRARY
11091
11092 #ifdef ANSI_DECLARATORS
11093 int reconstruct(struct mesh *m, struct behavior *b, int *trianglelist,
11094 REAL *triangleattriblist, REAL *trianglearealist,
11095 int elements, int corners, int attribs,
11096 int *segmentlist,int *segmentmarkerlist, int numberofsegments)
11097 #else /* not ANSI_DECLARATORS */
11098 int reconstruct(m, b, trianglelist, triangleattriblist, trianglearealist,
11099 elements, corners, attribs, segmentlist, segmentmarkerlist,
11100 numberofsegments)
11101 struct mesh *m;
11102 struct behavior *b;
11103 int *trianglelist;
11104 REAL *triangleattriblist;
11105 REAL *trianglearealist;
11106 int elements;
11107 int corners;
11108 int attribs;
11109 int *segmentlist;
11110 int *segmentmarkerlist;
11111 int numberofsegments;
11112 #endif /* not ANSI_DECLARATORS */
11113
11114 #else /* not TRILIBRARY */
11115
11116 #ifdef ANSI_DECLARATORS
11117 long reconstruct(struct mesh *m, struct behavior *b, char *elefilename,
11118 char *areafilename, char *polyfilename, FILE *polyfile)
11119 #else /* not ANSI_DECLARATORS */
11120 long reconstruct(m, b, elefilename, areafilename, polyfilename, polyfile)
11121 struct mesh *m;
11122 struct behavior *b;
11123 char *elefilename;
11124 char *areafilename;
11125 char *polyfilename;
11126 FILE *polyfile;
11127 #endif /* not ANSI_DECLARATORS */
11128
11129 #endif /* not TRILIBRARY */
11130
11131 {
11132 #ifdef TRILIBRARY
11133 int vertexindex;
11134 int attribindex;
11135 #else /* not TRILIBRARY */
11136 FILE *elefile;
11137 FILE *areafile;
11138 char inputline[INPUTLINESIZE];
11139 char *stringptr;
11140 int areaelements;
11141 #endif /* not TRILIBRARY */
11142 struct otri triangleloop;
11143 struct otri triangleleft;
11144 struct otri checktri;
11145 struct otri checkleft;
11146 struct otri checkneighbor;
11147 struct osub subsegloop;
11148 triangle *vertexarray;
11149 triangle *prevlink;
11150 triangle nexttri;
11151 vertex tdest, tapex;
11152 vertex checkdest, checkapex;
11153 vertex shorg;
11154 vertex killvertex;
11155 vertex segmentorg, segmentdest;
11156 REAL area;
11157 int corner[3];
11158 int end[2];
11159 int killvertexindex;
11160 int incorners;
11161 int segmentmarkers;
11162 int boundmarker;
11163 int aroundvertex;
11164 long hullsize;
11165 int notfound;
11166 long elementnumber, segmentnumber;
11167 int i, j;
11168 triangle ptr; /* Temporary variable used by sym(). */
11169
11170 #ifdef TRILIBRARY
11171 m->inelements = elements;
11172 incorners = corners;
11173 if (incorners < 3) {
11174 printf("Error: Triangles must have at least 3 vertices.\n");
11175 triexit(1);
11176 }
11177 m->eextras = attribs;
11178 #else /* not TRILIBRARY */
11179 /* Read the triangles from an .ele file. */
11180 if (!b->quiet) {
11181 printf("Opening %s.\n", elefilename);
11182 }
11183 elefile = fopen(elefilename, "r");
11184 if (elefile == (FILE *) NULL) {
11185 printf(" Error: Cannot access file %s.\n", elefilename);
11186 triexit(1);
11187 }
11188 /* Read number of triangles, number of vertices per triangle, and */
11189 /* number of triangle attributes from .ele file. */
11190 stringptr = readline(inputline, elefile, elefilename);
11191 m->inelements = (int) strtol(stringptr, &stringptr, 0);
11192 stringptr = findfield(stringptr);
11193 if (*stringptr == '\0') {
11194 incorners = 3;
11195 } else {
11196 incorners = (int) strtol(stringptr, &stringptr, 0);
11197 if (incorners < 3) {
11198 printf("Error: Triangles in %s must have at least 3 vertices.\n",
11199 elefilename);
11200 triexit(1);
11201 }
11202 }
11203 stringptr = findfield(stringptr);
11204 if (*stringptr == '\0') {
11205 m->eextras = 0;
11206 } else {
11207 m->eextras = (int) strtol(stringptr, &stringptr, 0);
11208 }
11209 #endif /* not TRILIBRARY */
11210
11211 initializetrisubpools(m, b);
11212
11213 /* Create the triangles. */
11214 for (elementnumber = 1; elementnumber <= m->inelements; elementnumber++) {
11215 maketriangle(m, b, &triangleloop);
11216 /* Mark the triangle as living. */
11217 triangleloop.tri[3] = (triangle) triangleloop.tri;
11218 }
11219
11220 segmentmarkers = 0;
11221 if (b->poly) {
11222 #ifdef TRILIBRARY
11223 m->insegments = numberofsegments;
11224 segmentmarkers = segmentmarkerlist != (int *) NULL;
11225 #else /* not TRILIBRARY */
11226 /* Read number of segments and number of segment */
11227 /* boundary markers from .poly file. */
11228 stringptr = readline(inputline, polyfile, b->inpolyfilename);
11229 m->insegments = (int) strtol(stringptr, &stringptr, 0);
11230 stringptr = findfield(stringptr);
11231 if (*stringptr != '\0') {
11232 segmentmarkers = (int) strtol(stringptr, &stringptr, 0);
11233 }
11234 #endif /* not TRILIBRARY */
11235
11236 /* Create the subsegments. */
11237 for (segmentnumber = 1; segmentnumber <= m->insegments; segmentnumber++) {
11238 makesubseg(m, &subsegloop);
11239 /* Mark the subsegment as living. */
11240 subsegloop.ss[2] = (subseg) subsegloop.ss;
11241 }
11242 }
11243
11244 #ifdef TRILIBRARY
11245 vertexindex = 0;
11246 attribindex = 0;
11247 #else /* not TRILIBRARY */
11248 if (b->vararea) {
11249 /* Open an .area file, check for consistency with the .ele file. */
11250 if (!b->quiet) {
11251 printf("Opening %s.\n", areafilename);
11252 }
11253 areafile = fopen(areafilename, "r");
11254 if (areafile == (FILE *) NULL) {
11255 printf(" Error: Cannot access file %s.\n", areafilename);
11256 triexit(1);
11257 }
11258 stringptr = readline(inputline, areafile, areafilename);
11259 areaelements = (int) strtol(stringptr, &stringptr, 0);
11260 if (areaelements != m->inelements) {
11261 printf("Error: %s and %s disagree on number of triangles.\n",
11262 elefilename, areafilename);
11263 triexit(1);
11264 }
11265 }
11266 #endif /* not TRILIBRARY */
11267
11268 if (!b->quiet) {
11269 printf("Reconstructing mesh.\n");
11270 }
11271 /* Allocate a temporary array that maps each vertex to some adjacent */
11272 /* triangle. I took care to allocate all the permanent memory for */
11273 /* triangles and subsegments first. */
11274 vertexarray = (triangle *) trimalloc(m->vertices.items *
11275 (int) sizeof(triangle));
11276 /* Each vertex is initially unrepresented. */
11277 for (i = 0; i < m->vertices.items; i++) {
11278 vertexarray[i] = (triangle) m->dummytri;
11279 }
11280
11281 if (b->verbose) {
11282 printf(" Assembling triangles.\n");
11283 }
11284 /* Read the triangles from the .ele file, and link */
11285 /* together those that share an edge. */
11286 traversalinit(&m->triangles);
11287 triangleloop.tri = triangletraverse(m);
11288 elementnumber = b->firstnumber;
11289 while (triangleloop.tri != (triangle *) NULL) {
11290 #ifdef TRILIBRARY
11291 /* Copy the triangle's three corners. */
11292 for (j = 0; j < 3; j++) {
11293 corner[j] = trianglelist[vertexindex++];
11294 if ((corner[j] < b->firstnumber) ||
11295 (corner[j] >= b->firstnumber + m->invertices)) {
11296 printf("Error: Triangle %ld has an invalid vertex index.\n",
11297 elementnumber);
11298 triexit(1);
11299 }
11300 }
11301 #else /* not TRILIBRARY */
11302 /* Read triangle number and the triangle's three corners. */
11303 stringptr = readline(inputline, elefile, elefilename);
11304 for (j = 0; j < 3; j++) {
11305 stringptr = findfield(stringptr);
11306 if (*stringptr == '\0') {
11307 printf("Error: Triangle %ld is missing vertex %d in %s.\n",
11308 elementnumber, j + 1, elefilename);
11309 triexit(1);
11310 } else {
11311 corner[j] = (int) strtol(stringptr, &stringptr, 0);
11312 if ((corner[j] < b->firstnumber) ||
11313 (corner[j] >= b->firstnumber + m->invertices)) {
11314 printf("Error: Triangle %ld has an invalid vertex index.\n",
11315 elementnumber);
11316 triexit(1);
11317 }
11318 }
11319 }
11320 #endif /* not TRILIBRARY */
11321
11322 /* Find out about (and throw away) extra nodes. */
11323 for (j = 3; j < incorners; j++) {
11324 #ifdef TRILIBRARY
11325 killvertexindex = trianglelist[vertexindex++];
11326 #else /* not TRILIBRARY */
11327 stringptr = findfield(stringptr);
11328 if (*stringptr != '\0') {
11329 killvertexindex = (int) strtol(stringptr, &stringptr, 0);
11330 #endif /* not TRILIBRARY */
11331 if ((killvertexindex >= b->firstnumber) &&
11332 (killvertexindex < b->firstnumber + m->invertices)) {
11333 /* Delete the non-corner vertex if it's not already deleted. */
11334 killvertex = getvertex(m, b, killvertexindex);
11335 if (vertextype(killvertex) != DEADVERTEX) {
11336 vertexdealloc(m, killvertex);
11337 }
11338 }
11339 #ifndef TRILIBRARY
11340 }
11341 #endif /* not TRILIBRARY */
11342 }
11343
11344 /* Read the triangle's attributes. */
11345 for (j = 0; j < m->eextras; j++) {
11346 #ifdef TRILIBRARY
11347 setelemattribute(triangleloop, j, triangleattriblist[attribindex++]);
11348 #else /* not TRILIBRARY */
11349 stringptr = findfield(stringptr);
11350 if (*stringptr == '\0') {
11351 setelemattribute(triangleloop, j, 0);
11352 } else {
11353 setelemattribute(triangleloop, j,
11354 (REAL) strtod(stringptr, &stringptr));
11355 }
11356 #endif /* not TRILIBRARY */
11357 }
11358
11359 if (b->vararea) {
11360 #ifdef TRILIBRARY
11361 area = trianglearealist[elementnumber - b->firstnumber];
11362 #else /* not TRILIBRARY */
11363 /* Read an area constraint from the .area file. */
11364 stringptr = readline(inputline, areafile, areafilename);
11365 stringptr = findfield(stringptr);
11366 if (*stringptr == '\0') {
11367 area = -1.0; /* No constraint on this triangle. */
11368 } else {
11369 area = (REAL) strtod(stringptr, &stringptr);
11370 }
11371 #endif /* not TRILIBRARY */
11372 setareabound(triangleloop, area);
11373 }
11374
11375 /* Set the triangle's vertices. */
11376 triangleloop.orient = 0;
11377 setorg(triangleloop, getvertex(m, b, corner[0]));
11378 setdest(triangleloop, getvertex(m, b, corner[1]));
11379 setapex(triangleloop, getvertex(m, b, corner[2]));
11380 /* Try linking the triangle to others that share these vertices. */
11381 for (triangleloop.orient = 0; triangleloop.orient < 3;
11382 triangleloop.orient++) {
11383 /* Take the number for the origin of triangleloop. */
11384 aroundvertex = corner[triangleloop.orient];
11385 /* Look for other triangles having this vertex. */
11386 nexttri = vertexarray[aroundvertex - b->firstnumber];
11387 /* Link the current triangle to the next one in the stack. */
11388 triangleloop.tri[6 + triangleloop.orient] = nexttri;
11389 /* Push the current triangle onto the stack. */
11390 vertexarray[aroundvertex - b->firstnumber] = encode(triangleloop);
11391 decode(nexttri, checktri);
11392 if (checktri.tri != m->dummytri) {
11393 dest(triangleloop, tdest);
11394 apex(triangleloop, tapex);
11395 /* Look for other triangles that share an edge. */
11396 do {
11397 dest(checktri, checkdest);
11398 apex(checktri, checkapex);
11399 if (tapex == checkdest) {
11400 /* The two triangles share an edge; bond them together. */
11401 lprev(triangleloop, triangleleft);
11402 bond(triangleleft, checktri);
11403 }
11404 if (tdest == checkapex) {
11405 /* The two triangles share an edge; bond them together. */
11406 lprev(checktri, checkleft);
11407 bond(triangleloop, checkleft);
11408 }
11409 /* Find the next triangle in the stack. */
11410 nexttri = checktri.tri[6 + checktri.orient];
11411 decode(nexttri, checktri);
11412 } while (checktri.tri != m->dummytri);
11413 }
11414 }
11415 triangleloop.tri = triangletraverse(m);
11416 elementnumber++;
11417 }
11418
11419 #ifdef TRILIBRARY
11420 vertexindex = 0;
11421 #else /* not TRILIBRARY */
11422 fclose(elefile);
11423 if (b->vararea) {
11424 fclose(areafile);
11425 }
11426 #endif /* not TRILIBRARY */
11427
11428 hullsize = 0; /* Prepare to count the boundary edges. */
11429 if (b->poly) {
11430 if (b->verbose) {
11431 printf(" Marking segments in triangulation.\n");
11432 }
11433 /* Read the segments from the .poly file, and link them */
11434 /* to their neighboring triangles. */
11435 boundmarker = 0;
11436 traversalinit(&m->subsegs);
11437 subsegloop.ss = subsegtraverse(m);
11438 segmentnumber = b->firstnumber;
11439 while (subsegloop.ss != (subseg *) NULL) {
11440 #ifdef TRILIBRARY
11441 end[0] = segmentlist[vertexindex++];
11442 end[1] = segmentlist[vertexindex++];
11443 if (segmentmarkers) {
11444 boundmarker = segmentmarkerlist[segmentnumber - b->firstnumber];
11445 }
11446 #else /* not TRILIBRARY */
11447 /* Read the endpoints of each segment, and possibly a boundary marker. */
11448 stringptr = readline(inputline, polyfile, b->inpolyfilename);
11449 /* Skip the first (segment number) field. */
11450 stringptr = findfield(stringptr);
11451 if (*stringptr == '\0') {
11452 printf("Error: Segment %ld has no endpoints in %s.\n", segmentnumber,
11453 polyfilename);
11454 triexit(1);
11455 } else {
11456 end[0] = (int) strtol(stringptr, &stringptr, 0);
11457 }
11458 stringptr = findfield(stringptr);
11459 if (*stringptr == '\0') {
11460 printf("Error: Segment %ld is missing its second endpoint in %s.\n",
11461 segmentnumber, polyfilename);
11462 triexit(1);
11463 } else {
11464 end[1] = (int) strtol(stringptr, &stringptr, 0);
11465 }
11466 if (segmentmarkers) {
11467 stringptr = findfield(stringptr);
11468 if (*stringptr == '\0') {
11469 boundmarker = 0;
11470 } else {
11471 boundmarker = (int) strtol(stringptr, &stringptr, 0);
11472 }
11473 }
11474 #endif /* not TRILIBRARY */
11475 for (j = 0; j < 2; j++) {
11476 if ((end[j] < b->firstnumber) ||
11477 (end[j] >= b->firstnumber + m->invertices)) {
11478 printf("Error: Segment %ld has an invalid vertex index.\n",
11479 segmentnumber);
11480 triexit(1);
11481 }
11482 }
11483
11484 /* set the subsegment's vertices. */
11485 subsegloop.ssorient = 0;
11486 segmentorg = getvertex(m, b, end[0]);
11487 segmentdest = getvertex(m, b, end[1]);
11488 setsorg(subsegloop, segmentorg);
11489 setsdest(subsegloop, segmentdest);
11490 setsegorg(subsegloop, segmentorg);
11491 setsegdest(subsegloop, segmentdest);
11492 setmark(subsegloop, boundmarker);
11493 /* Try linking the subsegment to triangles that share these vertices. */
11494 for (subsegloop.ssorient = 0; subsegloop.ssorient < 2;
11495 subsegloop.ssorient++) {
11496 /* Take the number for the destination of subsegloop. */
11497 aroundvertex = end[1 - subsegloop.ssorient];
11498 /* Look for triangles having this vertex. */
11499 prevlink = &vertexarray[aroundvertex - b->firstnumber];
11500 nexttri = vertexarray[aroundvertex - b->firstnumber];
11501 decode(nexttri, checktri);
11502 sorg(subsegloop, shorg);
11503 notfound = 1;
11504 /* Look for triangles having this edge. Note that I'm only */
11505 /* comparing each triangle's destination with the subsegment; */
11506 /* each triangle's apex is handled through a different vertex. */
11507 /* Because each triangle appears on three vertices' lists, each */
11508 /* occurrence of a triangle on a list can (and does) represent */
11509 /* an edge. In this way, most edges are represented twice, and */
11510 /* every triangle-subsegment bond is represented once. */
11511 while (notfound && (checktri.tri != m->dummytri)) {
11512 dest(checktri, checkdest);
11513 if (shorg == checkdest) {
11514 /* We have a match. Remove this triangle from the list. */
11515 *prevlink = checktri.tri[6 + checktri.orient];
11516 /* Bond the subsegment to the triangle. */
11517 tsbond(checktri, subsegloop);
11518 /* Check if this is a boundary edge. */
11519 sym(checktri, checkneighbor);
11520 if (checkneighbor.tri == m->dummytri) {
11521 /* The next line doesn't insert a subsegment (because there's */
11522 /* already one there), but it sets the boundary markers of */
11523 /* the existing subsegment and its vertices. */
11524 insertsubseg(m, b, &checktri, 1);
11525 hullsize++;
11526 }
11527 notfound = 0;
11528 }
11529 /* Find the next triangle in the stack. */
11530 prevlink = &checktri.tri[6 + checktri.orient];
11531 nexttri = checktri.tri[6 + checktri.orient];
11532 decode(nexttri, checktri);
11533 }
11534 }
11535 subsegloop.ss = subsegtraverse(m);
11536 segmentnumber++;
11537 }
11538 }
11539
11540 /* Mark the remaining edges as not being attached to any subsegment. */
11541 /* Also, count the (yet uncounted) boundary edges. */
11542 for (i = 0; i < m->vertices.items; i++) {
11543 /* Search the stack of triangles adjacent to a vertex. */
11544 nexttri = vertexarray[i];
11545 decode(nexttri, checktri);
11546 while (checktri.tri != m->dummytri) {
11547 /* Find the next triangle in the stack before this */
11548 /* information gets overwritten. */
11549 nexttri = checktri.tri[6 + checktri.orient];
11550 /* No adjacent subsegment. (This overwrites the stack info.) */
11551 tsdissolve(checktri);
11552 sym(checktri, checkneighbor);
11553 if (checkneighbor.tri == m->dummytri) {
11554 insertsubseg(m, b, &checktri, 1);
11555 hullsize++;
11556 }
11557 decode(nexttri, checktri);
11558 }
11559 }
11560
11561 trifree((VOID *) vertexarray);
11562 return hullsize;
11563 }
11564
11565 #endif /* not CDT_ONLY */
11566
11567 /** **/
11568 /** **/
11569 /********* General mesh construction routines end here *********/
11570
11571 /********* Segment insertion begins here *********/
11572 /** **/
11573 /** **/
11574
11575 /*****************************************************************************/
11576 /* */
11577 /* finddirection() Find the first triangle on the path from one point */
11578 /* to another. */
11579 /* */
11580 /* Finds the triangle that intersects a line segment drawn from the */
11581 /* origin of `searchtri' to the point `searchpoint', and returns the result */
11582 /* in `searchtri'. The origin of `searchtri' does not change, even though */
11583 /* the triangle returned may differ from the one passed in. This routine */
11584 /* is used to find the direction to move in to get from one point to */
11585 /* another. */
11586 /* */
11587 /* The return value notes whether the destination or apex of the found */
11588 /* triangle is collinear with the two points in question. */
11589 /* */
11590 /*****************************************************************************/
11591
11592 #ifdef ANSI_DECLARATORS
11593 enum finddirectionresult finddirection(struct mesh *m, struct behavior *b,
11594 struct otri *searchtri,
11595 vertex searchpoint)
11596 #else /* not ANSI_DECLARATORS */
11597 enum finddirectionresult finddirection(m, b, searchtri, searchpoint)
11598 struct mesh *m;
11599 struct behavior *b;
11600 struct otri *searchtri;
11601 vertex searchpoint;
11602 #endif /* not ANSI_DECLARATORS */
11603
11604 {
11605 struct otri checktri;
11606 vertex startvertex;
11607 vertex leftvertex, rightvertex;
11608 REAL leftccw, rightccw;
11609 int leftflag, rightflag;
11610 triangle ptr; /* Temporary variable used by onext() and oprev(). */
11611
11612 org(*searchtri, startvertex);
11613 dest(*searchtri, rightvertex);
11614 apex(*searchtri, leftvertex);
11615 /* Is `searchpoint' to the left? */
11616 leftccw = counterclockwise(m, b, searchpoint, startvertex, leftvertex);
11617 leftflag = leftccw > 0.0;
11618 /* Is `searchpoint' to the right? */
11619 rightccw = counterclockwise(m, b, startvertex, searchpoint, rightvertex);
11620 rightflag = rightccw > 0.0;
11621 if (leftflag && rightflag) {
11622 /* `searchtri' faces directly away from `searchpoint'. We could go left */
11623 /* or right. Ask whether it's a triangle or a boundary on the left. */
11624 onext(*searchtri, checktri);
11625 if (checktri.tri == m->dummytri) {
11626 leftflag = 0;
11627 } else {
11628 rightflag = 0;
11629 }
11630 }
11631 while (leftflag) {
11632 /* Turn left until satisfied. */
11633 onextself(*searchtri);
11634 if (searchtri->tri == m->dummytri) {
11635 printf("Internal error in finddirection(): Unable to find a\n");
11636 printf(" triangle leading from (%.12g, %.12g) to", startvertex[0],
11637 startvertex[1]);
11638 printf(" (%.12g, %.12g).\n", searchpoint[0], searchpoint[1]);
11639 internalerror();
11640 }
11641 apex(*searchtri, leftvertex);
11642 rightccw = leftccw;
11643 leftccw = counterclockwise(m, b, searchpoint, startvertex, leftvertex);
11644 leftflag = leftccw > 0.0;
11645 }
11646 while (rightflag) {
11647 /* Turn right until satisfied. */
11648 oprevself(*searchtri);
11649 if (searchtri->tri == m->dummytri) {
11650 printf("Internal error in finddirection(): Unable to find a\n");
11651 printf(" triangle leading from (%.12g, %.12g) to", startvertex[0],
11652 startvertex[1]);
11653 printf(" (%.12g, %.12g).\n", searchpoint[0], searchpoint[1]);
11654 internalerror();
11655 }
11656 dest(*searchtri, rightvertex);
11657 leftccw = rightccw;
11658 rightccw = counterclockwise(m, b, startvertex, searchpoint, rightvertex);
11659 rightflag = rightccw > 0.0;
11660 }
11661 if (leftccw == 0.0) {
11662 return LEFTCOLLINEAR;
11663 } else if (rightccw == 0.0) {
11664 return RIGHTCOLLINEAR;
11665 } else {
11666 return WITHIN;
11667 }
11668 }
11669
11670 /*****************************************************************************/
11671 /* */
11672 /* segmentintersection() Find the intersection of an existing segment */
11673 /* and a segment that is being inserted. Insert */
11674 /* a vertex at the intersection, splitting an */
11675 /* existing subsegment. */
11676 /* */
11677 /* The segment being inserted connects the apex of splittri to endpoint2. */
11678 /* splitsubseg is the subsegment being split, and MUST adjoin splittri. */
11679 /* Hence, endpoints of the subsegment being split are the origin and */
11680 /* destination of splittri. */
11681 /* */
11682 /* On completion, splittri is a handle having the newly inserted */
11683 /* intersection point as its origin, and endpoint1 as its destination. */
11684 /* */
11685 /*****************************************************************************/
11686
11687 #ifdef ANSI_DECLARATORS
11688 void segmentintersection(struct mesh *m, struct behavior *b,
11689 struct otri *splittri, struct osub *splitsubseg,
11690 vertex endpoint2)
11691 #else /* not ANSI_DECLARATORS */
11692 void segmentintersection(m, b, splittri, splitsubseg, endpoint2)
11693 struct mesh *m;
11694 struct behavior *b;
11695 struct otri *splittri;
11696 struct osub *splitsubseg;
11697 vertex endpoint2;
11698 #endif /* not ANSI_DECLARATORS */
11699
11700 {
11701 struct osub opposubseg;
11702 vertex endpoint1;
11703 vertex torg, tdest;
11704 vertex leftvertex, rightvertex;
11705 vertex newvertex;
11706 enum insertvertexresult success;
11707 enum finddirectionresult collinear;
11708 REAL ex, ey;
11709 REAL tx, ty;
11710 REAL etx, ety;
11711 REAL split, denom;
11712 int i;
11713 triangle ptr; /* Temporary variable used by onext(). */
11714 subseg sptr; /* Temporary variable used by snext(). */
11715
11716 /* Find the other three segment endpoints. */
11717 apex(*splittri, endpoint1);
11718 org(*splittri, torg);
11719 dest(*splittri, tdest);
11720 /* Segment intersection formulae; see the Antonio reference. */
11721 tx = tdest[0] - torg[0];
11722 ty = tdest[1] - torg[1];
11723 ex = endpoint2[0] - endpoint1[0];
11724 ey = endpoint2[1] - endpoint1[1];
11725 etx = torg[0] - endpoint2[0];
11726 ety = torg[1] - endpoint2[1];
11727 denom = ty * ex - tx * ey;
11728 if (denom == 0.0) {
11729 printf("Internal error in segmentintersection():");
11730 printf(" Attempt to find intersection of parallel segments.\n");
11731 internalerror();
11732 }
11733 split = (ey * etx - ex * ety) / denom;
11734 /* Create the new vertex. */
11735 newvertex = (vertex) poolalloc(&m->vertices);
11736 /* Interpolate its coordinate and attributes. */
11737 for (i = 0; i < 2 + m->nextras; i++) {
11738 newvertex[i] = torg[i] + split * (tdest[i] - torg[i]);
11739 }
11740 setvertexmark(newvertex, mark(*splitsubseg));
11741 setvertextype(newvertex, INPUTVERTEX);
11742 if (b->verbose > 1) {
11743 printf(
11744 " Splitting subsegment (%.12g, %.12g) (%.12g, %.12g) at (%.12g, %.12g).\n",
11745 torg[0], torg[1], tdest[0], tdest[1], newvertex[0], newvertex[1]);
11746 }
11747 /* Insert the intersection vertex. This should always succeed. */
11748 success = insertvertex(m, b, newvertex, splittri, splitsubseg, 0, 0);
11749 if (success != SUCCESSFULVERTEX) {
11750 printf("Internal error in segmentintersection():\n");
11751 printf(" Failure to split a segment.\n");
11752 internalerror();
11753 }
11754 /* Record a triangle whose origin is the new vertex. */
11755 setvertex2tri(newvertex, encode(*splittri));
11756 if (m->steinerleft > 0) {
11757 m->steinerleft--;
11758 }
11759
11760 /* Divide the segment into two, and correct the segment endpoints. */
11761 ssymself(*splitsubseg);
11762 spivot(*splitsubseg, opposubseg);
11763 sdissolve(*splitsubseg);
11764 sdissolve(opposubseg);
11765 do {
11766 setsegorg(*splitsubseg, newvertex);
11767 snextself(*splitsubseg);
11768 } while (splitsubseg->ss != m->dummysub);
11769 do {
11770 setsegorg(opposubseg, newvertex);
11771 snextself(opposubseg);
11772 } while (opposubseg.ss != m->dummysub);
11773
11774 /* Inserting the vertex may have caused edge flips. We wish to rediscover */
11775 /* the edge connecting endpoint1 to the new intersection vertex. */
11776 collinear = finddirection(m, b, splittri, endpoint1);
11777 dest(*splittri, rightvertex);
11778 apex(*splittri, leftvertex);
11779 if ((leftvertex[0] == endpoint1[0]) && (leftvertex[1] == endpoint1[1])) {
11780 onextself(*splittri);
11781 } else if ((rightvertex[0] != endpoint1[0]) ||
11782 (rightvertex[1] != endpoint1[1])) {
11783 printf("Internal error in segmentintersection():\n");
11784 printf(" Topological inconsistency after splitting a segment.\n");
11785 internalerror();
11786 }
11787 /* `splittri' should have destination endpoint1. */
11788 }
11789
11790 /*****************************************************************************/
11791 /* */
11792 /* scoutsegment() Scout the first triangle on the path from one endpoint */
11793 /* to another, and check for completion (reaching the */
11794 /* second endpoint), a collinear vertex, or the */
11795 /* intersection of two segments. */
11796 /* */
11797 /* Returns one if the entire segment is successfully inserted, and zero if */
11798 /* the job must be finished by conformingedge() or constrainededge(). */
11799 /* */
11800 /* If the first triangle on the path has the second endpoint as its */
11801 /* destination or apex, a subsegment is inserted and the job is done. */
11802 /* */
11803 /* If the first triangle on the path has a destination or apex that lies on */
11804 /* the segment, a subsegment is inserted connecting the first endpoint to */
11805 /* the collinear vertex, and the search is continued from the collinear */
11806 /* vertex. */
11807 /* */
11808 /* If the first triangle on the path has a subsegment opposite its origin, */
11809 /* then there is a segment that intersects the segment being inserted. */
11810 /* Their intersection vertex is inserted, splitting the subsegment. */
11811 /* */
11812 /*****************************************************************************/
11813
11814 #ifdef ANSI_DECLARATORS
11815 int scoutsegment(struct mesh *m, struct behavior *b, struct otri *searchtri,
11816 vertex endpoint2, int newmark)
11817 #else /* not ANSI_DECLARATORS */
11818 int scoutsegment(m, b, searchtri, endpoint2, newmark)
11819 struct mesh *m;
11820 struct behavior *b;
11821 struct otri *searchtri;
11822 vertex endpoint2;
11823 int newmark;
11824 #endif /* not ANSI_DECLARATORS */
11825
11826 {
11827 struct otri crosstri;
11828 struct osub crosssubseg;
11829 vertex leftvertex, rightvertex;
11830 enum finddirectionresult collinear;
11831 subseg sptr; /* Temporary variable used by tspivot(). */
11832
11833 collinear = finddirection(m, b, searchtri, endpoint2);
11834 dest(*searchtri, rightvertex);
11835 apex(*searchtri, leftvertex);
11836 if (((leftvertex[0] == endpoint2[0]) && (leftvertex[1] == endpoint2[1])) ||
11837 ((rightvertex[0] == endpoint2[0]) && (rightvertex[1] == endpoint2[1]))) {
11838 /* The segment is already an edge in the mesh. */
11839 if ((leftvertex[0] == endpoint2[0]) && (leftvertex[1] == endpoint2[1])) {
11840 lprevself(*searchtri);
11841 }
11842 /* Insert a subsegment, if there isn't already one there. */
11843 insertsubseg(m, b, searchtri, newmark);
11844 return 1;
11845 } else if (collinear == LEFTCOLLINEAR) {
11846 /* We've collided with a vertex between the segment's endpoints. */
11847 /* Make the collinear vertex be the triangle's origin. */
11848 lprevself(*searchtri);
11849 insertsubseg(m, b, searchtri, newmark);
11850 /* Insert the remainder of the segment. */
11851 return scoutsegment(m, b, searchtri, endpoint2, newmark);
11852 } else if (collinear == RIGHTCOLLINEAR) {
11853 /* We've collided with a vertex between the segment's endpoints. */
11854 insertsubseg(m, b, searchtri, newmark);
11855 /* Make the collinear vertex be the triangle's origin. */
11856 lnextself(*searchtri);
11857 /* Insert the remainder of the segment. */
11858 return scoutsegment(m, b, searchtri, endpoint2, newmark);
11859 } else {
11860 lnext(*searchtri, crosstri);
11861 tspivot(crosstri, crosssubseg);
11862 /* Check for a crossing segment. */
11863 if (crosssubseg.ss == m->dummysub) {
11864 return 0;
11865 } else {
11866 /* Insert a vertex at the intersection. */
11867 segmentintersection(m, b, &crosstri, &crosssubseg, endpoint2);
11868 otricopy(crosstri, *searchtri);
11869 insertsubseg(m, b, searchtri, newmark);
11870 /* Insert the remainder of the segment. */
11871 return scoutsegment(m, b, searchtri, endpoint2, newmark);
11872 }
11873 }
11874 }
11875
11876 /*****************************************************************************/
11877 /* */
11878 /* conformingedge() Force a segment into a conforming Delaunay */
11879 /* triangulation by inserting a vertex at its midpoint, */
11880 /* and recursively forcing in the two half-segments if */
11881 /* necessary. */
11882 /* */
11883 /* Generates a sequence of subsegments connecting `endpoint1' to */
11884 /* `endpoint2'. `newmark' is the boundary marker of the segment, assigned */
11885 /* to each new splitting vertex and subsegment. */
11886 /* */
11887 /* Note that conformingedge() does not always maintain the conforming */
11888 /* Delaunay property. Once inserted, segments are locked into place; */
11889 /* vertices inserted later (to force other segments in) may render these */
11890 /* fixed segments non-Delaunay. The conforming Delaunay property will be */
11891 /* restored by enforcequality() by splitting encroached subsegments. */
11892 /* */
11893 /*****************************************************************************/
11894
11895 #ifndef REDUCED
11896 #ifndef CDT_ONLY
11897
11898 #ifdef ANSI_DECLARATORS
11899 void conformingedge(struct mesh *m, struct behavior *b,
11900 vertex endpoint1, vertex endpoint2, int newmark)
11901 #else /* not ANSI_DECLARATORS */
11902 void conformingedge(m, b, endpoint1, endpoint2, newmark)
11903 struct mesh *m;
11904 struct behavior *b;
11905 vertex endpoint1;
11906 vertex endpoint2;
11907 int newmark;
11908 #endif /* not ANSI_DECLARATORS */
11909
11910 {
11911 struct otri searchtri1, searchtri2;
11912 struct osub brokensubseg;
11913 vertex newvertex;
11914 vertex midvertex1, midvertex2;
11915 enum insertvertexresult success;
11916 int i;
11917 subseg sptr; /* Temporary variable used by tspivot(). */
11918
11919 if (b->verbose > 2) {
11920 printf("Forcing segment into triangulation by recursive splitting:\n");
11921 printf(" (%.12g, %.12g) (%.12g, %.12g)\n", endpoint1[0], endpoint1[1],
11922 endpoint2[0], endpoint2[1]);
11923 }
11924 /* Create a new vertex to insert in the middle of the segment. */
11925 newvertex = (vertex) poolalloc(&m->vertices);
11926 /* Interpolate coordinates and attributes. */
11927 for (i = 0; i < 2 + m->nextras; i++) {
11928 newvertex[i] = 0.5 * (endpoint1[i] + endpoint2[i]);
11929 }
11930 setvertexmark(newvertex, newmark);
11931 setvertextype(newvertex, SEGMENTVERTEX);
11932 /* No known triangle to search from. */
11933 searchtri1.tri = m->dummytri;
11934 /* Attempt to insert the new vertex. */
11935 success = insertvertex(m, b, newvertex, &searchtri1, (struct osub *) NULL,
11936 0, 0);
11937 if (success == DUPLICATEVERTEX) {
11938 if (b->verbose > 2) {
11939 printf(" Segment intersects existing vertex (%.12g, %.12g).\n",
11940 newvertex[0], newvertex[1]);
11941 }
11942 /* Use the vertex that's already there. */
11943 vertexdealloc(m, newvertex);
11944 org(searchtri1, newvertex);
11945 } else {
11946 if (success == VIOLATINGVERTEX) {
11947 if (b->verbose > 2) {
11948 printf(" Two segments intersect at (%.12g, %.12g).\n",
11949 newvertex[0], newvertex[1]);
11950 }
11951 /* By fluke, we've landed right on another segment. Split it. */
11952 tspivot(searchtri1, brokensubseg);
11953 success = insertvertex(m, b, newvertex, &searchtri1, &brokensubseg,
11954 0, 0);
11955 if (success != SUCCESSFULVERTEX) {
11956 printf("Internal error in conformingedge():\n");
11957 printf(" Failure to split a segment.\n");
11958 internalerror();
11959 }
11960 }
11961 /* The vertex has been inserted successfully. */
11962 if (m->steinerleft > 0) {
11963 m->steinerleft--;
11964 }
11965 }
11966 otricopy(searchtri1, searchtri2);
11967 /* `searchtri1' and `searchtri2' are fastened at their origins to */
11968 /* `newvertex', and will be directed toward `endpoint1' and `endpoint2' */
11969 /* respectively. First, we must get `searchtri2' out of the way so it */
11970 /* won't be invalidated during the insertion of the first half of the */
11971 /* segment. */
11972 finddirection(m, b, &searchtri2, endpoint2);
11973 if (!scoutsegment(m, b, &searchtri1, endpoint1, newmark)) {
11974 /* The origin of searchtri1 may have changed if a collision with an */
11975 /* intervening vertex on the segment occurred. */
11976 org(searchtri1, midvertex1);
11977 conformingedge(m, b, midvertex1, endpoint1, newmark);
11978 }
11979 if (!scoutsegment(m, b, &searchtri2, endpoint2, newmark)) {
11980 /* The origin of searchtri2 may have changed if a collision with an */
11981 /* intervening vertex on the segment occurred. */
11982 org(searchtri2, midvertex2);
11983 conformingedge(m, b, midvertex2, endpoint2, newmark);
11984 }
11985 }
11986
11987 #endif /* not CDT_ONLY */
11988 #endif /* not REDUCED */
11989
11990 /*****************************************************************************/
11991 /* */
11992 /* delaunayfixup() Enforce the Delaunay condition at an edge, fanning out */
11993 /* recursively from an existing vertex. Pay special */
11994 /* attention to stacking inverted triangles. */
11995 /* */
11996 /* This is a support routine for inserting segments into a constrained */
11997 /* Delaunay triangulation. */
11998 /* */
11999 /* The origin of fixuptri is treated as if it has just been inserted, and */
12000 /* the local Delaunay condition needs to be enforced. It is only enforced */
12001 /* in one sector, however, that being the angular range defined by */
12002 /* fixuptri. */
12003 /* */
12004 /* This routine also needs to make decisions regarding the "stacking" of */
12005 /* triangles. (Read the description of constrainededge() below before */
12006 /* reading on here, so you understand the algorithm.) If the position of */
12007 /* the new vertex (the origin of fixuptri) indicates that the vertex before */
12008 /* it on the polygon is a reflex vertex, then "stack" the triangle by */
12009 /* doing nothing. (fixuptri is an inverted triangle, which is how stacked */
12010 /* triangles are identified.) */
12011 /* */
12012 /* Otherwise, check whether the vertex before that was a reflex vertex. */
12013 /* If so, perform an edge flip, thereby eliminating an inverted triangle */
12014 /* (popping it off the stack). The edge flip may result in the creation */
12015 /* of a new inverted triangle, depending on whether or not the new vertex */
12016 /* is visible to the vertex three edges behind on the polygon. */
12017 /* */
12018 /* If neither of the two vertices behind the new vertex are reflex */
12019 /* vertices, fixuptri and fartri, the triangle opposite it, are not */
12020 /* inverted; hence, ensure that the edge between them is locally Delaunay. */
12021 /* */
12022 /* `leftside' indicates whether or not fixuptri is to the left of the */
12023 /* segment being inserted. (Imagine that the segment is pointing up from */
12024 /* endpoint1 to endpoint2.) */
12025 /* */
12026 /*****************************************************************************/
12027
12028 #ifdef ANSI_DECLARATORS
12029 void delaunayfixup(struct mesh *m, struct behavior *b,
12030 struct otri *fixuptri, int leftside)
12031 #else /* not ANSI_DECLARATORS */
12032 void delaunayfixup(m, b, fixuptri, leftside)
12033 struct mesh *m;
12034 struct behavior *b;
12035 struct otri *fixuptri;
12036 int leftside;
12037 #endif /* not ANSI_DECLARATORS */
12038
12039 {
12040 struct otri neartri;
12041 struct otri fartri;
12042 struct osub faredge;
12043 vertex nearvertex, leftvertex, rightvertex, farvertex;
12044 triangle ptr; /* Temporary variable used by sym(). */
12045 subseg sptr; /* Temporary variable used by tspivot(). */
12046
12047 lnext(*fixuptri, neartri);
12048 sym(neartri, fartri);
12049 /* Check if the edge opposite the origin of fixuptri can be flipped. */
12050 if (fartri.tri == m->dummytri) {
12051 return;
12052 }
12053 tspivot(neartri, faredge);
12054 if (faredge.ss != m->dummysub) {
12055 return;
12056 }
12057 /* Find all the relevant vertices. */
12058 apex(neartri, nearvertex);
12059 org(neartri, leftvertex);
12060 dest(neartri, rightvertex);
12061 apex(fartri, farvertex);
12062 /* Check whether the previous polygon vertex is a reflex vertex. */
12063 if (leftside) {
12064 if (counterclockwise(m, b, nearvertex, leftvertex, farvertex) <= 0.0) {
12065 /* leftvertex is a reflex vertex too. Nothing can */
12066 /* be done until a convex section is found. */
12067 return;
12068 }
12069 } else {
12070 if (counterclockwise(m, b, farvertex, rightvertex, nearvertex) <= 0.0) {
12071 /* rightvertex is a reflex vertex too. Nothing can */
12072 /* be done until a convex section is found. */
12073 return;
12074 }
12075 }
12076 if (counterclockwise(m, b, rightvertex, leftvertex, farvertex) > 0.0) {
12077 /* fartri is not an inverted triangle, and farvertex is not a reflex */
12078 /* vertex. As there are no reflex vertices, fixuptri isn't an */
12079 /* inverted triangle, either. Hence, test the edge between the */
12080 /* triangles to ensure it is locally Delaunay. */
12081 if (incircle(m, b, leftvertex, farvertex, rightvertex, nearvertex) <=
12082 0.0) {
12083 return;
12084 }
12085 /* Not locally Delaunay; go on to an edge flip. */
12086 } /* else fartri is inverted; remove it from the stack by flipping. */
12087 flip(m, b, &neartri);
12088 lprevself(*fixuptri); /* Restore the origin of fixuptri after the flip. */
12089 /* Recursively process the two triangles that result from the flip. */
12090 delaunayfixup(m, b, fixuptri, leftside);
12091 delaunayfixup(m, b, &fartri, leftside);
12092 }
12093
12094 /*****************************************************************************/
12095 /* */
12096 /* constrainededge() Force a segment into a constrained Delaunay */
12097 /* triangulation by deleting the triangles it */
12098 /* intersects, and triangulating the polygons that */
12099 /* form on each side of it. */
12100 /* */
12101 /* Generates a single subsegment connecting `endpoint1' to `endpoint2'. */
12102 /* The triangle `starttri' has `endpoint1' as its origin. `newmark' is the */
12103 /* boundary marker of the segment. */
12104 /* */
12105 /* To insert a segment, every triangle whose interior intersects the */
12106 /* segment is deleted. The union of these deleted triangles is a polygon */
12107 /* (which is not necessarily monotone, but is close enough), which is */
12108 /* divided into two polygons by the new segment. This routine's task is */
12109 /* to generate the Delaunay triangulation of these two polygons. */
12110 /* */
12111 /* You might think of this routine's behavior as a two-step process. The */
12112 /* first step is to walk from endpoint1 to endpoint2, flipping each edge */
12113 /* encountered. This step creates a fan of edges connected to endpoint1, */
12114 /* including the desired edge to endpoint2. The second step enforces the */
12115 /* Delaunay condition on each side of the segment in an incremental manner: */
12116 /* proceeding along the polygon from endpoint1 to endpoint2 (this is done */
12117 /* independently on each side of the segment), each vertex is "enforced" */
12118 /* as if it had just been inserted, but affecting only the previous */
12119 /* vertices. The result is the same as if the vertices had been inserted */
12120 /* in the order they appear on the polygon, so the result is Delaunay. */
12121 /* */
12122 /* In truth, constrainededge() interleaves these two steps. The procedure */
12123 /* walks from endpoint1 to endpoint2, and each time an edge is encountered */
12124 /* and flipped, the newly exposed vertex (at the far end of the flipped */
12125 /* edge) is "enforced" upon the previously flipped edges, usually affecting */
12126 /* only one side of the polygon (depending upon which side of the segment */
12127 /* the vertex falls on). */
12128 /* */
12129 /* The algorithm is complicated by the need to handle polygons that are not */
12130 /* convex. Although the polygon is not necessarily monotone, it can be */
12131 /* triangulated in a manner similar to the stack-based algorithms for */
12132 /* monotone polygons. For each reflex vertex (local concavity) of the */
12133 /* polygon, there will be an inverted triangle formed by one of the edge */
12134 /* flips. (An inverted triangle is one with negative area - that is, its */
12135 /* vertices are arranged in clockwise order - and is best thought of as a */
12136 /* wrinkle in the fabric of the mesh.) Each inverted triangle can be */
12137 /* thought of as a reflex vertex pushed on the stack, waiting to be fixed */
12138 /* later. */
12139 /* */
12140 /* A reflex vertex is popped from the stack when a vertex is inserted that */
12141 /* is visible to the reflex vertex. (However, if the vertex behind the */
12142 /* reflex vertex is not visible to the reflex vertex, a new inverted */
12143 /* triangle will take its place on the stack.) These details are handled */
12144 /* by the delaunayfixup() routine above. */
12145 /* */
12146 /*****************************************************************************/
12147
12148 #ifdef ANSI_DECLARATORS
12149 void constrainededge(struct mesh *m, struct behavior *b,
12150 struct otri *starttri, vertex endpoint2, int newmark)
12151 #else /* not ANSI_DECLARATORS */
12152 void constrainededge(m, b, starttri, endpoint2, newmark)
12153 struct mesh *m;
12154 struct behavior *b;
12155 struct otri *starttri;
12156 vertex endpoint2;
12157 int newmark;
12158 #endif /* not ANSI_DECLARATORS */
12159
12160 {
12161 struct otri fixuptri, fixuptri2;
12162 struct osub crosssubseg;
12163 vertex endpoint1;
12164 vertex farvertex;
12165 REAL area;
12166 int collision;
12167 int done;
12168 triangle ptr; /* Temporary variable used by sym() and oprev(). */
12169 subseg sptr; /* Temporary variable used by tspivot(). */
12170
12171 org(*starttri, endpoint1);
12172 lnext(*starttri, fixuptri);
12173 flip(m, b, &fixuptri);
12174 /* `collision' indicates whether we have found a vertex directly */
12175 /* between endpoint1 and endpoint2. */
12176 collision = 0;
12177 done = 0;
12178 do {
12179 org(fixuptri, farvertex);
12180 /* `farvertex' is the extreme point of the polygon we are "digging" */
12181 /* to get from endpoint1 to endpoint2. */
12182 if ((farvertex[0] == endpoint2[0]) && (farvertex[1] == endpoint2[1])) {
12183 oprev(fixuptri, fixuptri2);
12184 /* Enforce the Delaunay condition around endpoint2. */
12185 delaunayfixup(m, b, &fixuptri, 0);
12186 delaunayfixup(m, b, &fixuptri2, 1);
12187 done = 1;
12188 } else {
12189 /* Check whether farvertex is to the left or right of the segment */
12190 /* being inserted, to decide which edge of fixuptri to dig */
12191 /* through next. */
12192 area = counterclockwise(m, b, endpoint1, endpoint2, farvertex);
12193 if (area == 0.0) {
12194 /* We've collided with a vertex between endpoint1 and endpoint2. */
12195 collision = 1;
12196 oprev(fixuptri, fixuptri2);
12197 /* Enforce the Delaunay condition around farvertex. */
12198 delaunayfixup(m, b, &fixuptri, 0);
12199 delaunayfixup(m, b, &fixuptri2, 1);
12200 done = 1;
12201 } else {
12202 if (area > 0.0) { /* farvertex is to the left of the segment. */
12203 oprev(fixuptri, fixuptri2);
12204 /* Enforce the Delaunay condition around farvertex, on the */
12205 /* left side of the segment only. */
12206 delaunayfixup(m, b, &fixuptri2, 1);
12207 /* Flip the edge that crosses the segment. After the edge is */
12208 /* flipped, one of its endpoints is the fan vertex, and the */
12209 /* destination of fixuptri is the fan vertex. */
12210 lprevself(fixuptri);
12211 } else { /* farvertex is to the right of the segment. */
12212 delaunayfixup(m, b, &fixuptri, 0);
12213 /* Flip the edge that crosses the segment. After the edge is */
12214 /* flipped, one of its endpoints is the fan vertex, and the */
12215 /* destination of fixuptri is the fan vertex. */
12216 oprevself(fixuptri);
12217 }
12218 /* Check for two intersecting segments. */
12219 tspivot(fixuptri, crosssubseg);
12220 if (crosssubseg.ss == m->dummysub) {
12221 flip(m, b, &fixuptri); /* May create inverted triangle at left. */
12222 } else {
12223 /* We've collided with a segment between endpoint1 and endpoint2. */
12224 collision = 1;
12225 /* Insert a vertex at the intersection. */
12226 segmentintersection(m, b, &fixuptri, &crosssubseg, endpoint2);
12227 done = 1;
12228 }
12229 }
12230 }
12231 } while (!done);
12232 /* Insert a subsegment to make the segment permanent. */
12233 insertsubseg(m, b, &fixuptri, newmark);
12234 /* If there was a collision with an interceding vertex, install another */
12235 /* segment connecting that vertex with endpoint2. */
12236 if (collision) {
12237 /* Insert the remainder of the segment. */
12238 if (!scoutsegment(m, b, &fixuptri, endpoint2, newmark)) {
12239 constrainededge(m, b, &fixuptri, endpoint2, newmark);
12240 }
12241 }
12242 }
12243
12244 /*****************************************************************************/
12245 /* */
12246 /* insertsegment() Insert a PSLG segment into a triangulation. */
12247 /* */
12248 /*****************************************************************************/
12249
12250 #ifdef ANSI_DECLARATORS
12251 void insertsegment(struct mesh *m, struct behavior *b,
12252 vertex endpoint1, vertex endpoint2, int newmark)
12253 #else /* not ANSI_DECLARATORS */
12254 void insertsegment(m, b, endpoint1, endpoint2, newmark)
12255 struct mesh *m;
12256 struct behavior *b;
12257 vertex endpoint1;
12258 vertex endpoint2;
12259 int newmark;
12260 #endif /* not ANSI_DECLARATORS */
12261
12262 {
12263 struct otri searchtri1, searchtri2;
12264 triangle encodedtri;
12265 vertex checkvertex;
12266 triangle ptr; /* Temporary variable used by sym(). */
12267
12268 if (b->verbose > 1) {
12269 printf(" Connecting (%.12g, %.12g) to (%.12g, %.12g).\n",
12270 endpoint1[0], endpoint1[1], endpoint2[0], endpoint2[1]);
12271 }
12272
12273 /* Find a triangle whose origin is the segment's first endpoint. */
12274 checkvertex = (vertex) NULL;
12275 encodedtri = vertex2tri(endpoint1);
12276 if (encodedtri != (triangle) NULL) {
12277 decode(encodedtri, searchtri1);
12278 org(searchtri1, checkvertex);
12279 }
12280 if (checkvertex != endpoint1) {
12281 /* Find a boundary triangle to search from. */
12282 searchtri1.tri = m->dummytri;
12283 searchtri1.orient = 0;
12284 symself(searchtri1);
12285 /* Search for the segment's first endpoint by point location. */
12286 if (locate(m, b, endpoint1, &searchtri1) != ONVERTEX) {
12287 printf(
12288 "Internal error in insertsegment(): Unable to locate PSLG vertex\n");
12289 printf(" (%.12g, %.12g) in triangulation.\n",
12290 endpoint1[0], endpoint1[1]);
12291 internalerror();
12292 }
12293 }
12294 /* Remember this triangle to improve subsequent point location. */
12295 otricopy(searchtri1, m->recenttri);
12296 /* Scout the beginnings of a path from the first endpoint */
12297 /* toward the second. */
12298 if (scoutsegment(m, b, &searchtri1, endpoint2, newmark)) {
12299 /* The segment was easily inserted. */
12300 return;
12301 }
12302 /* The first endpoint may have changed if a collision with an intervening */
12303 /* vertex on the segment occurred. */
12304 org(searchtri1, endpoint1);
12305
12306 /* Find a triangle whose origin is the segment's second endpoint. */
12307 checkvertex = (vertex) NULL;
12308 encodedtri = vertex2tri(endpoint2);
12309 if (encodedtri != (triangle) NULL) {
12310 decode(encodedtri, searchtri2);
12311 org(searchtri2, checkvertex);
12312 }
12313 if (checkvertex != endpoint2) {
12314 /* Find a boundary triangle to search from. */
12315 searchtri2.tri = m->dummytri;
12316 searchtri2.orient = 0;
12317 symself(searchtri2);
12318 /* Search for the segment's second endpoint by point location. */
12319 if (locate(m, b, endpoint2, &searchtri2) != ONVERTEX) {
12320 printf(
12321 "Internal error in insertsegment(): Unable to locate PSLG vertex\n");
12322 printf(" (%.12g, %.12g) in triangulation.\n",
12323 endpoint2[0], endpoint2[1]);
12324 internalerror();
12325 }
12326 }
12327 /* Remember this triangle to improve subsequent point location. */
12328 otricopy(searchtri2, m->recenttri);
12329 /* Scout the beginnings of a path from the second endpoint */
12330 /* toward the first. */
12331 if (scoutsegment(m, b, &searchtri2, endpoint1, newmark)) {
12332 /* The segment was easily inserted. */
12333 return;
12334 }
12335 /* The second endpoint may have changed if a collision with an intervening */
12336 /* vertex on the segment occurred. */
12337 org(searchtri2, endpoint2);
12338
12339 #ifndef REDUCED
12340 #ifndef CDT_ONLY
12341 if (b->splitseg) {
12342 /* Insert vertices to force the segment into the triangulation. */
12343 conformingedge(m, b, endpoint1, endpoint2, newmark);
12344 } else {
12345 #endif /* not CDT_ONLY */
12346 #endif /* not REDUCED */
12347 /* Insert the segment directly into the triangulation. */
12348 constrainededge(m, b, &searchtri1, endpoint2, newmark);
12349 #ifndef REDUCED
12350 #ifndef CDT_ONLY
12351 }
12352 #endif /* not CDT_ONLY */
12353 #endif /* not REDUCED */
12354 }
12355
12356 /*****************************************************************************/
12357 /* */
12358 /* markhull() Cover the convex hull of a triangulation with subsegments. */
12359 /* */
12360 /*****************************************************************************/
12361
12362 #ifdef ANSI_DECLARATORS
12363 void markhull(struct mesh *m, struct behavior *b)
12364 #else /* not ANSI_DECLARATORS */
12365 void markhull(m, b)
12366 struct mesh *m;
12367 struct behavior *b;
12368 #endif /* not ANSI_DECLARATORS */
12369
12370 {
12371 struct otri hulltri;
12372 struct otri nexttri;
12373 struct otri starttri;
12374 triangle ptr; /* Temporary variable used by sym() and oprev(). */
12375
12376 /* Find a triangle handle on the hull. */
12377 hulltri.tri = m->dummytri;
12378 hulltri.orient = 0;
12379 symself(hulltri);
12380 /* Remember where we started so we know when to stop. */
12381 otricopy(hulltri, starttri);
12382 /* Go once counterclockwise around the convex hull. */
12383 do {
12384 /* Create a subsegment if there isn't already one here. */
12385 insertsubseg(m, b, &hulltri, 1);
12386 /* To find the next hull edge, go clockwise around the next vertex. */
12387 lnextself(hulltri);
12388 oprev(hulltri, nexttri);
12389 while (nexttri.tri != m->dummytri) {
12390 otricopy(nexttri, hulltri);
12391 oprev(hulltri, nexttri);
12392 }
12393 } while (!otriequal(hulltri, starttri));
12394 }
12395
12396 /*****************************************************************************/
12397 /* */
12398 /* formskeleton() Create the segments of a triangulation, including PSLG */
12399 /* segments and edges on the convex hull. */
12400 /* */
12401 /* The PSLG segments are read from a .poly file. The return value is the */
12402 /* number of segments in the file. */
12403 /* */
12404 /*****************************************************************************/
12405
12406 #ifdef TRILIBRARY
12407
12408 #ifdef ANSI_DECLARATORS
12409 void formskeleton(struct mesh *m, struct behavior *b, int *segmentlist,
12410 int *segmentmarkerlist, int numberofsegments)
12411 #else /* not ANSI_DECLARATORS */
12412 void formskeleton(m, b, segmentlist, segmentmarkerlist, numberofsegments)
12413 struct mesh *m;
12414 struct behavior *b;
12415 int *segmentlist;
12416 int *segmentmarkerlist;
12417 int numberofsegments;
12418 #endif /* not ANSI_DECLARATORS */
12419
12420 #else /* not TRILIBRARY */
12421
12422 #ifdef ANSI_DECLARATORS
12423 void formskeleton(struct mesh *m, struct behavior *b,
12424 FILE *polyfile, char *polyfilename)
12425 #else /* not ANSI_DECLARATORS */
12426 void formskeleton(m, b, polyfile, polyfilename)
12427 struct mesh *m;
12428 struct behavior *b;
12429 FILE *polyfile;
12430 char *polyfilename;
12431 #endif /* not ANSI_DECLARATORS */
12432
12433 #endif /* not TRILIBRARY */
12434
12435 {
12436 #ifdef TRILIBRARY
12437 char polyfilename[6];
12438 int index;
12439 #else /* not TRILIBRARY */
12440 char inputline[INPUTLINESIZE];
12441 char *stringptr;
12442 #endif /* not TRILIBRARY */
12443 vertex endpoint1, endpoint2;
12444 int segmentmarkers;
12445 int end1, end2;
12446 int boundmarker;
12447 int i;
12448
12449 if (b->poly) {
12450 if (!b->quiet) {
12451 printf("Recovering segments in Delaunay triangulation.\n");
12452 }
12453 #ifdef TRILIBRARY
12454 strcpy(polyfilename, "input");
12455 m->insegments = numberofsegments;
12456 segmentmarkers = segmentmarkerlist != (int *) NULL;
12457 index = 0;
12458 #else /* not TRILIBRARY */
12459 /* Read the segments from a .poly file. */
12460 /* Read number of segments and number of boundary markers. */
12461 stringptr = readline(inputline, polyfile, polyfilename);
12462 m->insegments = (int) strtol(stringptr, &stringptr, 0);
12463 stringptr = findfield(stringptr);
12464 if (*stringptr == '\0') {
12465 segmentmarkers = 0;
12466 } else {
12467 segmentmarkers = (int) strtol(stringptr, &stringptr, 0);
12468 }
12469 #endif /* not TRILIBRARY */
12470 /* If the input vertices are collinear, there is no triangulation, */
12471 /* so don't try to insert segments. */
12472 if (m->triangles.items == 0) {
12473 return;
12474 }
12475
12476 /* If segments are to be inserted, compute a mapping */
12477 /* from vertices to triangles. */
12478 if (m->insegments > 0) {
12479 makevertexmap(m, b);
12480 if (b->verbose) {
12481 printf(" Recovering PSLG segments.\n");
12482 }
12483 }
12484
12485 boundmarker = 0;
12486 /* Read and insert the segments. */
12487 for (i = 0; i < m->insegments; i++) {
12488 #ifdef TRILIBRARY
12489 end1 = segmentlist[index++];
12490 end2 = segmentlist[index++];
12491 if (segmentmarkers) {
12492 boundmarker = segmentmarkerlist[i];
12493 }
12494 #else /* not TRILIBRARY */
12495 stringptr = readline(inputline, polyfile, b->inpolyfilename);
12496 stringptr = findfield(stringptr);
12497 if (*stringptr == '\0') {
12498 printf("Error: Segment %d has no endpoints in %s.\n",
12499 b->firstnumber + i, polyfilename);
12500 triexit(1);
12501 } else {
12502 end1 = (int) strtol(stringptr, &stringptr, 0);
12503 }
12504 stringptr = findfield(stringptr);
12505 if (*stringptr == '\0') {
12506 printf("Error: Segment %d is missing its second endpoint in %s.\n",
12507 b->firstnumber + i, polyfilename);
12508 triexit(1);
12509 } else {
12510 end2 = (int) strtol(stringptr, &stringptr, 0);
12511 }
12512 if (segmentmarkers) {
12513 stringptr = findfield(stringptr);
12514 if (*stringptr == '\0') {
12515 boundmarker = 0;
12516 } else {
12517 boundmarker = (int) strtol(stringptr, &stringptr, 0);
12518 }
12519 }
12520 #endif /* not TRILIBRARY */
12521 if ((end1 < b->firstnumber) ||
12522 (end1 >= b->firstnumber + m->invertices)) {
12523 if (!b->quiet) {
12524 printf("Warning: Invalid first endpoint of segment %d in %s.\n",
12525 b->firstnumber + i, polyfilename);
12526 }
12527 } else if ((end2 < b->firstnumber) ||
12528 (end2 >= b->firstnumber + m->invertices)) {
12529 if (!b->quiet) {
12530 printf("Warning: Invalid second endpoint of segment %d in %s.\n",
12531 b->firstnumber + i, polyfilename);
12532 }
12533 } else {
12534 /* Find the vertices numbered `end1' and `end2'. */
12535 endpoint1 = getvertex(m, b, end1);
12536 endpoint2 = getvertex(m, b, end2);
12537 if ((endpoint1[0] == endpoint2[0]) && (endpoint1[1] == endpoint2[1])) {
12538 if (!b->quiet) {
12539 printf("Warning: Endpoints of segment %d are coincident in %s.\n",
12540 b->firstnumber + i, polyfilename);
12541 }
12542 } else {
12543 insertsegment(m, b, endpoint1, endpoint2, boundmarker);
12544 }
12545 }
12546 }
12547 } else {
12548 m->insegments = 0;
12549 }
12550 if (b->convex || !b->poly) {
12551 /* Enclose the convex hull with subsegments. */
12552 if (b->verbose) {
12553 printf(" Enclosing convex hull with segments.\n");
12554 }
12555 markhull(m, b);
12556 }
12557 }
12558
12559 /** **/
12560 /** **/
12561 /********* Segment insertion ends here *********/
12562
12563 /********* Carving out holes and concavities begins here *********/
12564 /** **/
12565 /** **/
12566
12567 /*****************************************************************************/
12568 /* */
12569 /* infecthull() Virally infect all of the triangles of the convex hull */
12570 /* that are not protected by subsegments. Where there are */
12571 /* subsegments, set boundary markers as appropriate. */
12572 /* */
12573 /*****************************************************************************/
12574
12575 #ifdef ANSI_DECLARATORS
12576 void infecthull(struct mesh *m, struct behavior *b)
12577 #else /* not ANSI_DECLARATORS */
12578 void infecthull(m, b)
12579 struct mesh *m;
12580 struct behavior *b;
12581 #endif /* not ANSI_DECLARATORS */
12582
12583 {
12584 struct otri hulltri;
12585 struct otri nexttri;
12586 struct otri starttri;
12587 struct osub hullsubseg;
12588 triangle **deadtriangle;
12589 vertex horg, hdest;
12590 triangle ptr; /* Temporary variable used by sym(). */
12591 subseg sptr; /* Temporary variable used by tspivot(). */
12592
12593 if (b->verbose) {
12594 printf(" Marking concavities (external triangles) for elimination.\n");
12595 }
12596 /* Find a triangle handle on the hull. */
12597 hulltri.tri = m->dummytri;
12598 hulltri.orient = 0;
12599 symself(hulltri);
12600 /* Remember where we started so we know when to stop. */
12601 otricopy(hulltri, starttri);
12602 /* Go once counterclockwise around the convex hull. */
12603 do {
12604 /* Ignore triangles that are already infected. */
12605 if (!infected(hulltri)) {
12606 /* Is the triangle protected by a subsegment? */
12607 tspivot(hulltri, hullsubseg);
12608 if (hullsubseg.ss == m->dummysub) {
12609 /* The triangle is not protected; infect it. */
12610 if (!infected(hulltri)) {
12611 infect(hulltri);
12612 deadtriangle = (triangle **) poolalloc(&m->viri);
12613 *deadtriangle = hulltri.tri;
12614 }
12615 } else {
12616 /* The triangle is protected; set boundary markers if appropriate. */
12617 if (mark(hullsubseg) == 0) {
12618 setmark(hullsubseg, 1);
12619 org(hulltri, horg);
12620 dest(hulltri, hdest);
12621 if (vertexmark(horg) == 0) {
12622 setvertexmark(horg, 1);
12623 }
12624 if (vertexmark(hdest) == 0) {
12625 setvertexmark(hdest, 1);
12626 }
12627 }
12628 }
12629 }
12630 /* To find the next hull edge, go clockwise around the next vertex. */
12631 lnextself(hulltri);
12632 oprev(hulltri, nexttri);
12633 while (nexttri.tri != m->dummytri) {
12634 otricopy(nexttri, hulltri);
12635 oprev(hulltri, nexttri);
12636 }
12637 } while (!otriequal(hulltri, starttri));
12638 }
12639
12640 /*****************************************************************************/
12641 /* */
12642 /* plague() Spread the virus from all infected triangles to any neighbors */
12643 /* not protected by subsegments. Delete all infected triangles. */
12644 /* */
12645 /* This is the procedure that actually creates holes and concavities. */
12646 /* */
12647 /* This procedure operates in two phases. The first phase identifies all */
12648 /* the triangles that will die, and marks them as infected. They are */
12649 /* marked to ensure that each triangle is added to the virus pool only */
12650 /* once, so the procedure will terminate. */
12651 /* */
12652 /* The second phase actually eliminates the infected triangles. It also */
12653 /* eliminates orphaned vertices. */
12654 /* */
12655 /*****************************************************************************/
12656
12657 #ifdef ANSI_DECLARATORS
12658 void plague(struct mesh *m, struct behavior *b)
12659 #else /* not ANSI_DECLARATORS */
12660 void plague(m, b)
12661 struct mesh *m;
12662 struct behavior *b;
12663 #endif /* not ANSI_DECLARATORS */
12664
12665 {
12666 struct otri testtri;
12667 struct otri neighbor;
12668 triangle **virusloop;
12669 triangle **deadtriangle;
12670 struct osub neighborsubseg;
12671 vertex testvertex;
12672 vertex norg, ndest;
12673 vertex deadorg, deaddest, deadapex;
12674 int killorg;
12675 triangle ptr; /* Temporary variable used by sym() and onext(). */
12676 subseg sptr; /* Temporary variable used by tspivot(). */
12677
12678 if (b->verbose) {
12679 printf(" Marking neighbors of marked triangles.\n");
12680 }
12681 /* Loop through all the infected triangles, spreading the virus to */
12682 /* their neighbors, then to their neighbors' neighbors. */
12683 traversalinit(&m->viri);
12684 virusloop = (triangle **) traverse(&m->viri);
12685 while (virusloop != (triangle **) NULL) {
12686 testtri.tri = *virusloop;
12687 /* A triangle is marked as infected by messing with one of its pointers */
12688 /* to subsegments, setting it to an illegal value. Hence, we have to */
12689 /* temporarily uninfect this triangle so that we can examine its */
12690 /* adjacent subsegments. */
12691 uninfect(testtri);
12692 if (b->verbose > 2) {
12693 /* Assign the triangle an orientation for convenience in */
12694 /* checking its vertices. */
12695 testtri.orient = 0;
12696 org(testtri, deadorg);
12697 dest(testtri, deaddest);
12698 apex(testtri, deadapex);
12699 printf(" Checking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
12700 deadorg[0], deadorg[1], deaddest[0], deaddest[1],
12701 deadapex[0], deadapex[1]);
12702 }
12703 /* Check each of the triangle's three neighbors. */
12704 for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
12705 /* Find the neighbor. */
12706 sym(testtri, neighbor);
12707 /* Check for a subsegment between the triangle and its neighbor. */
12708 tspivot(testtri, neighborsubseg);
12709 /* Check if the neighbor is nonexistent or already infected. */
12710 if ((neighbor.tri == m->dummytri) || infected(neighbor)) {
12711 if (neighborsubseg.ss != m->dummysub) {
12712 /* There is a subsegment separating the triangle from its */
12713 /* neighbor, but both triangles are dying, so the subsegment */
12714 /* dies too. */
12715 subsegdealloc(m, neighborsubseg.ss);
12716 if (neighbor.tri != m->dummytri) {
12717 /* Make sure the subsegment doesn't get deallocated again */
12718 /* later when the infected neighbor is visited. */
12719 uninfect(neighbor);
12720 tsdissolve(neighbor);
12721 infect(neighbor);
12722 }
12723 }
12724 } else { /* The neighbor exists and is not infected. */
12725 if (neighborsubseg.ss == m->dummysub) {
12726 /* There is no subsegment protecting the neighbor, so */
12727 /* the neighbor becomes infected. */
12728 if (b->verbose > 2) {
12729 org(neighbor, deadorg);
12730 dest(neighbor, deaddest);
12731 apex(neighbor, deadapex);
12732 printf(
12733 " Marking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
12734 deadorg[0], deadorg[1], deaddest[0], deaddest[1],
12735 deadapex[0], deadapex[1]);
12736 }
12737 infect(neighbor);
12738 /* Ensure that the neighbor's neighbors will be infected. */
12739 deadtriangle = (triangle **) poolalloc(&m->viri);
12740 *deadtriangle = neighbor.tri;
12741 } else { /* The neighbor is protected by a subsegment. */
12742 /* Remove this triangle from the subsegment. */
12743 stdissolve(neighborsubseg);
12744 /* The subsegment becomes a boundary. Set markers accordingly. */
12745 if (mark(neighborsubseg) == 0) {
12746 setmark(neighborsubseg, 1);
12747 }
12748 org(neighbor, norg);
12749 dest(neighbor, ndest);
12750 if (vertexmark(norg) == 0) {
12751 setvertexmark(norg, 1);
12752 }
12753 if (vertexmark(ndest) == 0) {
12754 setvertexmark(ndest, 1);
12755 }
12756 }
12757 }
12758 }
12759 /* Remark the triangle as infected, so it doesn't get added to the */
12760 /* virus pool again. */
12761 infect(testtri);
12762 virusloop = (triangle **) traverse(&m->viri);
12763 }
12764
12765 if (b->verbose) {
12766 printf(" Deleting marked triangles.\n");
12767 }
12768
12769 traversalinit(&m->viri);
12770 virusloop = (triangle **) traverse(&m->viri);
12771 while (virusloop != (triangle **) NULL) {
12772 testtri.tri = *virusloop;
12773
12774 /* Check each of the three corners of the triangle for elimination. */
12775 /* This is done by walking around each vertex, checking if it is */
12776 /* still connected to at least one live triangle. */
12777 for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
12778 org(testtri, testvertex);
12779 /* Check if the vertex has already been tested. */
12780 if (testvertex != (vertex) NULL) {
12781 killorg = 1;
12782 /* Mark the corner of the triangle as having been tested. */
12783 setorg(testtri, NULL);
12784 /* Walk counterclockwise about the vertex. */
12785 onext(testtri, neighbor);
12786 /* Stop upon reaching a boundary or the starting triangle. */
12787 while ((neighbor.tri != m->dummytri) &&
12788 (!otriequal(neighbor, testtri))) {
12789 if (infected(neighbor)) {
12790 /* Mark the corner of this triangle as having been tested. */
12791 setorg(neighbor, NULL);
12792 } else {
12793 /* A live triangle. The vertex survives. */
12794 killorg = 0;
12795 }
12796 /* Walk counterclockwise about the vertex. */
12797 onextself(neighbor);
12798 }
12799 /* If we reached a boundary, we must walk clockwise as well. */
12800 if (neighbor.tri == m->dummytri) {
12801 /* Walk clockwise about the vertex. */
12802 oprev(testtri, neighbor);
12803 /* Stop upon reaching a boundary. */
12804 while (neighbor.tri != m->dummytri) {
12805 if (infected(neighbor)) {
12806 /* Mark the corner of this triangle as having been tested. */
12807 setorg(neighbor, NULL);
12808 } else {
12809 /* A live triangle. The vertex survives. */
12810 killorg = 0;
12811 }
12812 /* Walk clockwise about the vertex. */
12813 oprevself(neighbor);
12814 }
12815 }
12816 if (killorg) {
12817 if (b->verbose > 1) {
12818 printf(" Deleting vertex (%.12g, %.12g)\n",
12819 testvertex[0], testvertex[1]);
12820 }
12821 setvertextype(testvertex, UNDEADVERTEX);
12822 m->undeads++;
12823 }
12824 }
12825 }
12826
12827 /* Record changes in the number of boundary edges, and disconnect */
12828 /* dead triangles from their neighbors. */
12829 for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
12830 sym(testtri, neighbor);
12831 if (neighbor.tri == m->dummytri) {
12832 /* There is no neighboring triangle on this edge, so this edge */
12833 /* is a boundary edge. This triangle is being deleted, so this */
12834 /* boundary edge is deleted. */
12835 m->hullsize--;
12836 } else {
12837 /* Disconnect the triangle from its neighbor. */
12838 dissolve(neighbor);
12839 /* There is a neighboring triangle on this edge, so this edge */
12840 /* becomes a boundary edge when this triangle is deleted. */
12841 m->hullsize++;
12842 }
12843 }
12844 /* Return the dead triangle to the pool of triangles. */
12845 triangledealloc(m, testtri.tri);
12846 virusloop = (triangle **) traverse(&m->viri);
12847 }
12848 /* Empty the virus pool. */
12849 poolrestart(&m->viri);
12850 }
12851
12852 /*****************************************************************************/
12853 /* */
12854 /* regionplague() Spread regional attributes and/or area constraints */
12855 /* (from a .poly file) throughout the mesh. */
12856 /* */
12857 /* This procedure operates in two phases. The first phase spreads an */
12858 /* attribute and/or an area constraint through a (segment-bounded) region. */
12859 /* The triangles are marked to ensure that each triangle is added to the */
12860 /* virus pool only once, so the procedure will terminate. */
12861 /* */
12862 /* The second phase uninfects all infected triangles, returning them to */
12863 /* normal. */
12864 /* */
12865 /*****************************************************************************/
12866
12867 #ifdef ANSI_DECLARATORS
12868 void regionplague(struct mesh *m, struct behavior *b,
12869 REAL attribute, REAL area)
12870 #else /* not ANSI_DECLARATORS */
12871 void regionplague(m, b, attribute, area)
12872 struct mesh *m;
12873 struct behavior *b;
12874 REAL attribute;
12875 REAL area;
12876 #endif /* not ANSI_DECLARATORS */
12877
12878 {
12879 struct otri testtri;
12880 struct otri neighbor;
12881 triangle **virusloop;
12882 triangle **regiontri;
12883 struct osub neighborsubseg;
12884 vertex regionorg, regiondest, regionapex;
12885 triangle ptr; /* Temporary variable used by sym() and onext(). */
12886 subseg sptr; /* Temporary variable used by tspivot(). */
12887
12888 if (b->verbose > 1) {
12889 printf(" Marking neighbors of marked triangles.\n");
12890 }
12891 /* Loop through all the infected triangles, spreading the attribute */
12892 /* and/or area constraint to their neighbors, then to their neighbors' */
12893 /* neighbors. */
12894 traversalinit(&m->viri);
12895 virusloop = (triangle **) traverse(&m->viri);
12896 while (virusloop != (triangle **) NULL) {
12897 testtri.tri = *virusloop;
12898 /* A triangle is marked as infected by messing with one of its pointers */
12899 /* to subsegments, setting it to an illegal value. Hence, we have to */
12900 /* temporarily uninfect this triangle so that we can examine its */
12901 /* adjacent subsegments. */
12902 uninfect(testtri);
12903 if (b->regionattrib) {
12904 /* Set an attribute. */
12905 setelemattribute(testtri, m->eextras, attribute);
12906 }
12907 if (b->vararea) {
12908 /* Set an area constraint. */
12909 setareabound(testtri, area);
12910 }
12911 if (b->verbose > 2) {
12912 /* Assign the triangle an orientation for convenience in */
12913 /* checking its vertices. */
12914 testtri.orient = 0;
12915 org(testtri, regionorg);
12916 dest(testtri, regiondest);
12917 apex(testtri, regionapex);
12918 printf(" Checking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
12919 regionorg[0], regionorg[1], regiondest[0], regiondest[1],
12920 regionapex[0], regionapex[1]);
12921 }
12922 /* Check each of the triangle's three neighbors. */
12923 for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
12924 /* Find the neighbor. */
12925 sym(testtri, neighbor);
12926 /* Check for a subsegment between the triangle and its neighbor. */
12927 tspivot(testtri, neighborsubseg);
12928 /* Make sure the neighbor exists, is not already infected, and */
12929 /* isn't protected by a subsegment. */
12930 if ((neighbor.tri != m->dummytri) && !infected(neighbor)
12931 && (neighborsubseg.ss == m->dummysub)) {
12932 if (b->verbose > 2) {
12933 org(neighbor, regionorg);
12934 dest(neighbor, regiondest);
12935 apex(neighbor, regionapex);
12936 printf(" Marking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
12937 regionorg[0], regionorg[1], regiondest[0], regiondest[1],
12938 regionapex[0], regionapex[1]);
12939 }
12940 /* Infect the neighbor. */
12941 infect(neighbor);
12942 /* Ensure that the neighbor's neighbors will be infected. */
12943 regiontri = (triangle **) poolalloc(&m->viri);
12944 *regiontri = neighbor.tri;
12945 }
12946 }
12947 /* Remark the triangle as infected, so it doesn't get added to the */
12948 /* virus pool again. */
12949 infect(testtri);
12950 virusloop = (triangle **) traverse(&m->viri);
12951 }
12952
12953 /* Uninfect all triangles. */
12954 if (b->verbose > 1) {
12955 printf(" Unmarking marked triangles.\n");
12956 }
12957 traversalinit(&m->viri);
12958 virusloop = (triangle **) traverse(&m->viri);
12959 while (virusloop != (triangle **) NULL) {
12960 testtri.tri = *virusloop;
12961 uninfect(testtri);
12962 virusloop = (triangle **) traverse(&m->viri);
12963 }
12964 /* Empty the virus pool. */
12965 poolrestart(&m->viri);
12966 }
12967
12968 /*****************************************************************************/
12969 /* */
12970 /* carveholes() Find the holes and infect them. Find the area */
12971 /* constraints and infect them. Infect the convex hull. */
12972 /* Spread the infection and kill triangles. Spread the */
12973 /* area constraints. */
12974 /* */
12975 /* This routine mainly calls other routines to carry out all these */
12976 /* functions. */
12977 /* */
12978 /*****************************************************************************/
12979
12980 #ifdef ANSI_DECLARATORS
12981 void carveholes(struct mesh *m, struct behavior *b, REAL *holelist, int holes,
12982 REAL *regionlist, int regions)
12983 #else /* not ANSI_DECLARATORS */
12984 void carveholes(m, b, holelist, holes, regionlist, regions)
12985 struct mesh *m;
12986 struct behavior *b;
12987 REAL *holelist;
12988 int holes;
12989 REAL *regionlist;
12990 int regions;
12991 #endif /* not ANSI_DECLARATORS */
12992
12993 {
12994 struct otri searchtri;
12995 struct otri triangleloop;
12996 struct otri *regiontris;
12997 triangle **holetri;
12998 triangle **regiontri;
12999 vertex searchorg, searchdest;
13000 enum locateresult intersect;
13001 int i;
13002 triangle ptr; /* Temporary variable used by sym(). */
13003
13004 if (!(b->quiet || (b->noholes && b->convex))) {
13005 printf("Removing unwanted triangles.\n");
13006 if (b->verbose && (holes > 0)) {
13007 printf(" Marking holes for elimination.\n");
13008 }
13009 }
13010
13011 if (regions > 0) {
13012 /* Allocate storage for the triangles in which region points fall. */
13013 regiontris = (struct otri *) trimalloc(regions *
13014 (int) sizeof(struct otri));
13015 } else {
13016 regiontris = (struct otri *) NULL;
13017 }
13018
13019 if (((holes > 0) && !b->noholes) || !b->convex || (regions > 0)) {
13020 /* Initialize a pool of viri to be used for holes, concavities, */
13021 /* regional attributes, and/or regional area constraints. */
13022 poolinit(&m->viri, sizeof(triangle *), VIRUSPERBLOCK, VIRUSPERBLOCK, 0);
13023 }
13024
13025 if (!b->convex) {
13026 /* Mark as infected any unprotected triangles on the boundary. */
13027 /* This is one way by which concavities are created. */
13028 infecthull(m, b);
13029 }
13030
13031 if ((holes > 0) && !b->noholes) {
13032 /* Infect each triangle in which a hole lies. */
13033 for (i = 0; i < 2 * holes; i += 2) {
13034 /* Ignore holes that aren't within the bounds of the mesh. */
13035 if ((holelist[i] >= m->xmin) && (holelist[i] <= m->xmax)
13036 && (holelist[i + 1] >= m->ymin) && (holelist[i + 1] <= m->ymax)) {
13037 /* Start searching from some triangle on the outer boundary. */
13038 searchtri.tri = m->dummytri;
13039 searchtri.orient = 0;
13040 symself(searchtri);
13041 /* Ensure that the hole is to the left of this boundary edge; */
13042 /* otherwise, locate() will falsely report that the hole */
13043 /* falls within the starting triangle. */
13044 org(searchtri, searchorg);
13045 dest(searchtri, searchdest);
13046 if (counterclockwise(m, b, searchorg, searchdest, &holelist[i]) >
13047 0.0) {
13048 /* Find a triangle that contains the hole. */
13049 intersect = locate(m, b, &holelist[i], &searchtri);
13050 if ((intersect != OUTSIDE) && (!infected(searchtri))) {
13051 /* Infect the triangle. This is done by marking the triangle */
13052 /* as infected and including the triangle in the virus pool. */
13053 infect(searchtri);
13054 holetri = (triangle **) poolalloc(&m->viri);
13055 *holetri = searchtri.tri;
13056 }
13057 }
13058 }
13059 }
13060 }
13061
13062 /* Now, we have to find all the regions BEFORE we carve the holes, because */
13063 /* locate() won't work when the triangulation is no longer convex. */
13064 /* (Incidentally, this is the reason why regional attributes and area */
13065 /* constraints can't be used when refining a preexisting mesh, which */
13066 /* might not be convex; they can only be used with a freshly */
13067 /* triangulated PSLG.) */
13068 if (regions > 0) {
13069 /* Find the starting triangle for each region. */
13070 for (i = 0; i < regions; i++) {
13071 regiontris[i].tri = m->dummytri;
13072 /* Ignore region points that aren't within the bounds of the mesh. */
13073 if ((regionlist[4 * i] >= m->xmin) && (regionlist[4 * i] <= m->xmax) &&
13074 (regionlist[4 * i + 1] >= m->ymin) &&
13075 (regionlist[4 * i + 1] <= m->ymax)) {
13076 /* Start searching from some triangle on the outer boundary. */
13077 searchtri.tri = m->dummytri;
13078 searchtri.orient = 0;
13079 symself(searchtri);
13080 /* Ensure that the region point is to the left of this boundary */
13081 /* edge; otherwise, locate() will falsely report that the */
13082 /* region point falls within the starting triangle. */
13083 org(searchtri, searchorg);
13084 dest(searchtri, searchdest);
13085 if (counterclockwise(m, b, searchorg, searchdest, ®ionlist[4 * i]) >
13086 0.0) {
13087 /* Find a triangle that contains the region point. */
13088 intersect = locate(m, b, ®ionlist[4 * i], &searchtri);
13089 if ((intersect != OUTSIDE) && (!infected(searchtri))) {
13090 /* Record the triangle for processing after the */
13091 /* holes have been carved. */
13092 otricopy(searchtri, regiontris[i]);
13093 }
13094 }
13095 }
13096 }
13097 }
13098
13099 if (m->viri.items > 0) {
13100 /* Carve the holes and concavities. */
13101 plague(m, b);
13102 }
13103 /* The virus pool should be empty now. */
13104
13105 if (regions > 0) {
13106 if (!b->quiet) {
13107 if (b->regionattrib) {
13108 if (b->vararea) {
13109 printf("Spreading regional attributes and area constraints.\n");
13110 } else {
13111 printf("Spreading regional attributes.\n");
13112 }
13113 } else {
13114 printf("Spreading regional area constraints.\n");
13115 }
13116 }
13117 if (b->regionattrib && !b->refine) {
13118 /* Assign every triangle a regional attribute of zero. */
13119 traversalinit(&m->triangles);
13120 triangleloop.orient = 0;
13121 triangleloop.tri = triangletraverse(m);
13122 while (triangleloop.tri != (triangle *) NULL) {
13123 setelemattribute(triangleloop, m->eextras, 0.0);
13124 triangleloop.tri = triangletraverse(m);
13125 }
13126 }
13127 for (i = 0; i < regions; i++) {
13128 if (regiontris[i].tri != m->dummytri) {
13129 /* Make sure the triangle under consideration still exists. */
13130 /* It may have been eaten by the virus. */
13131 if (!deadtri(regiontris[i].tri)) {
13132 /* Put one triangle in the virus pool. */
13133 infect(regiontris[i]);
13134 regiontri = (triangle **) poolalloc(&m->viri);
13135 *regiontri = regiontris[i].tri;
13136 /* Apply one region's attribute and/or area constraint. */
13137 regionplague(m, b, regionlist[4 * i + 2], regionlist[4 * i + 3]);
13138 /* The virus pool should be empty now. */
13139 }
13140 }
13141 }
13142 if (b->regionattrib && !b->refine) {
13143 /* Note the fact that each triangle has an additional attribute. */
13144 m->eextras++;
13145 }
13146 }
13147
13148 /* Free up memory. */
13149 if (((holes > 0) && !b->noholes) || !b->convex || (regions > 0)) {
13150 pooldeinit(&m->viri);
13151 }
13152 if (regions > 0) {
13153 trifree((VOID *) regiontris);
13154 }
13155 }
13156
13157 /** **/
13158 /** **/
13159 /********* Carving out holes and concavities ends here *********/
13160
13161 /********* Mesh quality maintenance begins here *********/
13162 /** **/
13163 /** **/
13164
13165 /*****************************************************************************/
13166 /* */
13167 /* tallyencs() Traverse the entire list of subsegments, and check each */
13168 /* to see if it is encroached. If so, add it to the list. */
13169 /* */
13170 /*****************************************************************************/
13171
13172 #ifndef CDT_ONLY
13173
13174 #ifdef ANSI_DECLARATORS
13175 void tallyencs(struct mesh *m, struct behavior *b)
13176 #else /* not ANSI_DECLARATORS */
13177 void tallyencs(m, b)
13178 struct mesh *m;
13179 struct behavior *b;
13180 #endif /* not ANSI_DECLARATORS */
13181
13182 {
13183 struct osub subsegloop;
13184 int dummy;
13185
13186 traversalinit(&m->subsegs);
13187 subsegloop.ssorient = 0;
13188 subsegloop.ss = subsegtraverse(m);
13189 while (subsegloop.ss != (subseg *) NULL) {
13190 /* If the segment is encroached, add it to the list. */
13191 dummy = checkseg4encroach(m, b, &subsegloop);
13192 subsegloop.ss = subsegtraverse(m);
13193 }
13194 }
13195
13196 #endif /* not CDT_ONLY */
13197
13198 /*****************************************************************************/
13199 /* */
13200 /* precisionerror() Print an error message for precision problems. */
13201 /* */
13202 /*****************************************************************************/
13203
13204 #ifndef CDT_ONLY
13205
13206 void precisionerror()
13207 {
13208 printf("Try increasing the area criterion and/or reducing the minimum\n");
13209 printf(" allowable angle so that tiny triangles are not created.\n");
13210 #ifdef SINGLE
13211 printf("Alternatively, try recompiling me with double precision\n");
13212 printf(" arithmetic (by removing \"#define SINGLE\" from the\n");
13213 printf(" source file or \"-DSINGLE\" from the makefile).\n");
13214 #endif /* SINGLE */
13215 }
13216
13217 #endif /* not CDT_ONLY */
13218
13219 /*****************************************************************************/
13220 /* */
13221 /* splitencsegs() Split all the encroached subsegments. */
13222 /* */
13223 /* Each encroached subsegment is repaired by splitting it - inserting a */
13224 /* vertex at or near its midpoint. Newly inserted vertices may encroach */
13225 /* upon other subsegments; these are also repaired. */
13226 /* */
13227 /* `triflaws' is a flag that specifies whether one should take note of new */
13228 /* bad triangles that result from inserting vertices to repair encroached */
13229 /* subsegments. */
13230 /* */
13231 /*****************************************************************************/
13232
13233 #ifndef CDT_ONLY
13234
13235 #ifdef ANSI_DECLARATORS
13236 void splitencsegs(struct mesh *m, struct behavior *b, int triflaws)
13237 #else /* not ANSI_DECLARATORS */
13238 void splitencsegs(m, b, triflaws)
13239 struct mesh *m;
13240 struct behavior *b;
13241 int triflaws;
13242 #endif /* not ANSI_DECLARATORS */
13243
13244 {
13245 struct otri enctri;
13246 struct otri testtri;
13247 struct osub testsh;
13248 struct osub currentenc;
13249 struct badsubseg *encloop;
13250 vertex eorg, edest, eapex;
13251 vertex newvertex;
13252 enum insertvertexresult success;
13253 REAL segmentlength, nearestpoweroftwo;
13254 REAL split;
13255 REAL multiplier, divisor;
13256 int acuteorg, acuteorg2, acutedest, acutedest2;
13257 int dummy;
13258 int i;
13259 triangle ptr; /* Temporary variable used by stpivot(). */
13260 subseg sptr; /* Temporary variable used by snext(). */
13261
13262 /* Note that steinerleft == -1 if an unlimited number */
13263 /* of Steiner points is allowed. */
13264 while ((m->badsubsegs.items > 0) && (m->steinerleft != 0)) {
13265 traversalinit(&m->badsubsegs);
13266 encloop = badsubsegtraverse(m);
13267 while ((encloop != (struct badsubseg *) NULL) && (m->steinerleft != 0)) {
13268 sdecode(encloop->encsubseg, currentenc);
13269 sorg(currentenc, eorg);
13270 sdest(currentenc, edest);
13271 /* Make sure that this segment is still the same segment it was */
13272 /* when it was determined to be encroached. If the segment was */
13273 /* enqueued multiple times (because several newly inserted */
13274 /* vertices encroached it), it may have already been split. */
13275 if (!deadsubseg(currentenc.ss) &&
13276 (eorg == encloop->subsegorg) && (edest == encloop->subsegdest)) {
13277 /* To decide where to split a segment, we need to know if the */
13278 /* segment shares an endpoint with an adjacent segment. */
13279 /* The concern is that, if we simply split every encroached */
13280 /* segment in its center, two adjacent segments with a small */
13281 /* angle between them might lead to an infinite loop; each */
13282 /* vertex added to split one segment will encroach upon the */
13283 /* other segment, which must then be split with a vertex that */
13284 /* will encroach upon the first segment, and so on forever. */
13285 /* To avoid this, imagine a set of concentric circles, whose */
13286 /* radii are powers of two, about each segment endpoint. */
13287 /* These concentric circles determine where the segment is */
13288 /* split. (If both endpoints are shared with adjacent */
13289 /* segments, split the segment in the middle, and apply the */
13290 /* concentric circles for later splittings.) */
13291
13292 /* Is the origin shared with another segment? */
13293 stpivot(currentenc, enctri);
13294 lnext(enctri, testtri);
13295 tspivot(testtri, testsh);
13296 acuteorg = testsh.ss != m->dummysub;
13297 /* Is the destination shared with another segment? */
13298 lnextself(testtri);
13299 tspivot(testtri, testsh);
13300 acutedest = testsh.ss != m->dummysub;
13301
13302 /* If we're using Chew's algorithm (rather than Ruppert's) */
13303 /* to define encroachment, delete free vertices from the */
13304 /* subsegment's diametral circle. */
13305 if (!b->conformdel && !acuteorg && !acutedest) {
13306 apex(enctri, eapex);
13307 while ((vertextype(eapex) == FREEVERTEX) &&
13308 ((eorg[0] - eapex[0]) * (edest[0] - eapex[0]) +
13309 (eorg[1] - eapex[1]) * (edest[1] - eapex[1]) < 0.0)) {
13310 deletevertex(m, b, &testtri);
13311 stpivot(currentenc, enctri);
13312 apex(enctri, eapex);
13313 lprev(enctri, testtri);
13314 }
13315 }
13316
13317 /* Now, check the other side of the segment, if there's a triangle */
13318 /* there. */
13319 sym(enctri, testtri);
13320 if (testtri.tri != m->dummytri) {
13321 /* Is the destination shared with another segment? */
13322 lnextself(testtri);
13323 tspivot(testtri, testsh);
13324 acutedest2 = testsh.ss != m->dummysub;
13325 acutedest = acutedest || acutedest2;
13326 /* Is the origin shared with another segment? */
13327 lnextself(testtri);
13328 tspivot(testtri, testsh);
13329 acuteorg2 = testsh.ss != m->dummysub;
13330 acuteorg = acuteorg || acuteorg2;
13331
13332 /* Delete free vertices from the subsegment's diametral circle. */
13333 if (!b->conformdel && !acuteorg2 && !acutedest2) {
13334 org(testtri, eapex);
13335 while ((vertextype(eapex) == FREEVERTEX) &&
13336 ((eorg[0] - eapex[0]) * (edest[0] - eapex[0]) +
13337 (eorg[1] - eapex[1]) * (edest[1] - eapex[1]) < 0.0)) {
13338 deletevertex(m, b, &testtri);
13339 sym(enctri, testtri);
13340 apex(testtri, eapex);
13341 lprevself(testtri);
13342 }
13343 }
13344 }
13345
13346 /* Use the concentric circles if exactly one endpoint is shared */
13347 /* with another adjacent segment. */
13348 if (acuteorg || acutedest) {
13349 segmentlength = sqrt((edest[0] - eorg[0]) * (edest[0] - eorg[0]) +
13350 (edest[1] - eorg[1]) * (edest[1] - eorg[1]));
13351 /* Find the power of two that most evenly splits the segment. */
13352 /* The worst case is a 2:1 ratio between subsegment lengths. */
13353 nearestpoweroftwo = 1.0;
13354 while (segmentlength > 3.0 * nearestpoweroftwo) {
13355 nearestpoweroftwo *= 2.0;
13356 }
13357 while (segmentlength < 1.5 * nearestpoweroftwo) {
13358 nearestpoweroftwo *= 0.5;
13359 }
13360 /* Where do we split the segment? */
13361 split = nearestpoweroftwo / segmentlength;
13362 if (acutedest) {
13363 split = 1.0 - split;
13364 }
13365 } else {
13366 /* If we're not worried about adjacent segments, split */
13367 /* this segment in the middle. */
13368 split = 0.5;
13369 }
13370
13371 /* Create the new vertex. */
13372 newvertex = (vertex) poolalloc(&m->vertices);
13373 /* Interpolate its coordinate and attributes. */
13374 for (i = 0; i < 2 + m->nextras; i++) {
13375 newvertex[i] = eorg[i] + split * (edest[i] - eorg[i]);
13376 }
13377
13378 if (!b->noexact) {
13379 /* Roundoff in the above calculation may yield a `newvertex' */
13380 /* that is not precisely collinear with `eorg' and `edest'. */
13381 /* Improve collinearity by one step of iterative refinement. */
13382 multiplier = counterclockwise(m, b, eorg, edest, newvertex);
13383 divisor = ((eorg[0] - edest[0]) * (eorg[0] - edest[0]) +
13384 (eorg[1] - edest[1]) * (eorg[1] - edest[1]));
13385 if ((multiplier != 0.0) && (divisor != 0.0)) {
13386 multiplier = multiplier / divisor;
13387 /* Watch out for NANs. */
13388 if (multiplier == multiplier) {
13389 newvertex[0] += multiplier * (edest[1] - eorg[1]);
13390 newvertex[1] += multiplier * (eorg[0] - edest[0]);
13391 }
13392 }
13393 }
13394
13395 setvertexmark(newvertex, mark(currentenc));
13396 setvertextype(newvertex, SEGMENTVERTEX);
13397 if (b->verbose > 1) {
13398 printf(
13399 " Splitting subsegment (%.12g, %.12g) (%.12g, %.12g) at (%.12g, %.12g).\n",
13400 eorg[0], eorg[1], edest[0], edest[1],
13401 newvertex[0], newvertex[1]);
13402 }
13403 /* Check whether the new vertex lies on an endpoint. */
13404 if (((newvertex[0] == eorg[0]) && (newvertex[1] == eorg[1])) ||
13405 ((newvertex[0] == edest[0]) && (newvertex[1] == edest[1]))) {
13406 printf("Error: Ran out of precision at (%.12g, %.12g).\n",
13407 newvertex[0], newvertex[1]);
13408 printf("I attempted to split a segment to a smaller size than\n");
13409 printf(" can be accommodated by the finite precision of\n");
13410 printf(" floating point arithmetic.\n");
13411 precisionerror();
13412 triexit(1);
13413 }
13414 /* Insert the splitting vertex. This should always succeed. */
13415 success = insertvertex(m, b, newvertex, &enctri, ¤tenc,
13416 1, triflaws);
13417 if ((success != SUCCESSFULVERTEX) && (success != ENCROACHINGVERTEX)) {
13418 printf("Internal error in splitencsegs():\n");
13419 printf(" Failure to split a segment.\n");
13420 internalerror();
13421 }
13422 if (m->steinerleft > 0) {
13423 m->steinerleft--;
13424 }
13425 /* Check the two new subsegments to see if they're encroached. */
13426 dummy = checkseg4encroach(m, b, ¤tenc);
13427 snextself(currentenc);
13428 dummy = checkseg4encroach(m, b, ¤tenc);
13429 }
13430
13431 badsubsegdealloc(m, encloop);
13432 encloop = badsubsegtraverse(m);
13433 }
13434 }
13435 }
13436
13437 #endif /* not CDT_ONLY */
13438
13439 /*****************************************************************************/
13440 /* */
13441 /* tallyfaces() Test every triangle in the mesh for quality measures. */
13442 /* */
13443 /*****************************************************************************/
13444
13445 #ifndef CDT_ONLY
13446
13447 #ifdef ANSI_DECLARATORS
13448 void tallyfaces(struct mesh *m, struct behavior *b)
13449 #else /* not ANSI_DECLARATORS */
13450 void tallyfaces(m, b)
13451 struct mesh *m;
13452 struct behavior *b;
13453 #endif /* not ANSI_DECLARATORS */
13454
13455 {
13456 struct otri triangleloop;
13457
13458 if (b->verbose) {
13459 printf(" Making a list of bad triangles.\n");
13460 }
13461 traversalinit(&m->triangles);
13462 triangleloop.orient = 0;
13463 triangleloop.tri = triangletraverse(m);
13464 while (triangleloop.tri != (triangle *) NULL) {
13465 /* If the triangle is bad, enqueue it. */
13466 testtriangle(m, b, &triangleloop);
13467 triangleloop.tri = triangletraverse(m);
13468 }
13469 }
13470
13471 #endif /* not CDT_ONLY */
13472
13473 /*****************************************************************************/
13474 /* */
13475 /* splittriangle() Inserts a vertex at the circumcenter of a triangle. */
13476 /* Deletes the newly inserted vertex if it encroaches */
13477 /* upon a segment. */
13478 /* */
13479 /*****************************************************************************/
13480
13481 #ifndef CDT_ONLY
13482
13483 #ifdef ANSI_DECLARATORS
13484 void splittriangle(struct mesh *m, struct behavior *b,
13485 struct badtriang *badtri)
13486 #else /* not ANSI_DECLARATORS */
13487 void splittriangle(m, b, badtri)
13488 struct mesh *m;
13489 struct behavior *b;
13490 struct badtriang *badtri;
13491 #endif /* not ANSI_DECLARATORS */
13492
13493 {
13494 struct otri badotri;
13495 vertex borg, bdest, bapex;
13496 vertex newvertex;
13497 REAL xi, eta;
13498 enum insertvertexresult success;
13499 int errorflag;
13500 int i;
13501
13502 decode(badtri->poortri, badotri);
13503 org(badotri, borg);
13504 dest(badotri, bdest);
13505 apex(badotri, bapex);
13506 /* Make sure that this triangle is still the same triangle it was */
13507 /* when it was tested and determined to be of bad quality. */
13508 /* Subsequent transformations may have made it a different triangle. */
13509 if (!deadtri(badotri.tri) && (borg == badtri->triangorg) &&
13510 (bdest == badtri->triangdest) && (bapex == badtri->triangapex)) {
13511 if (b->verbose > 1) {
13512 printf(" Splitting this triangle at its circumcenter:\n");
13513 printf(" (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", borg[0],
13514 borg[1], bdest[0], bdest[1], bapex[0], bapex[1]);
13515 }
13516
13517 errorflag = 0;
13518 /* Create a new vertex at the triangle's circumcenter. */
13519 newvertex = (vertex) poolalloc(&m->vertices);
13520 findcircumcenter(m, b, borg, bdest, bapex, newvertex, &xi, &eta, 1);
13521
13522 /* Check whether the new vertex lies on a triangle vertex. */
13523 if (((newvertex[0] == borg[0]) && (newvertex[1] == borg[1])) ||
13524 ((newvertex[0] == bdest[0]) && (newvertex[1] == bdest[1])) ||
13525 ((newvertex[0] == bapex[0]) && (newvertex[1] == bapex[1]))) {
13526 if (!b->quiet) {
13527 printf(
13528 "Warning: New vertex (%.12g, %.12g) falls on existing vertex.\n",
13529 newvertex[0], newvertex[1]);
13530 errorflag = 1;
13531 }
13532 vertexdealloc(m, newvertex);
13533 } else {
13534 for (i = 2; i < 2 + m->nextras; i++) {
13535 /* Interpolate the vertex attributes at the circumcenter. */
13536 newvertex[i] = borg[i] + xi * (bdest[i] - borg[i])
13537 + eta * (bapex[i] - borg[i]);
13538 }
13539 /* The new vertex must be in the interior, and therefore is a */
13540 /* free vertex with a marker of zero. */
13541 setvertexmark(newvertex, 0);
13542 setvertextype(newvertex, FREEVERTEX);
13543
13544 /* Ensure that the handle `badotri' does not represent the longest */
13545 /* edge of the triangle. This ensures that the circumcenter must */
13546 /* fall to the left of this edge, so point location will work. */
13547 /* (If the angle org-apex-dest exceeds 90 degrees, then the */
13548 /* circumcenter lies outside the org-dest edge, and eta is */
13549 /* negative. Roundoff error might prevent eta from being */
13550 /* negative when it should be, so I test eta against xi.) */
13551 if (eta < xi) {
13552 lprevself(badotri);
13553 }
13554
13555 /* Insert the circumcenter, searching from the edge of the triangle, */
13556 /* and maintain the Delaunay property of the triangulation. */
13557 success = insertvertex(m, b, newvertex, &badotri, (struct osub *) NULL,
13558 1, 1);
13559 if (success == SUCCESSFULVERTEX) {
13560 if (m->steinerleft > 0) {
13561 m->steinerleft--;
13562 }
13563 } else if (success == ENCROACHINGVERTEX) {
13564 /* If the newly inserted vertex encroaches upon a subsegment, */
13565 /* delete the new vertex. */
13566 undovertex(m, b);
13567 if (b->verbose > 1) {
13568 printf(" Rejecting (%.12g, %.12g).\n", newvertex[0], newvertex[1]);
13569 }
13570 vertexdealloc(m, newvertex);
13571 } else if (success == VIOLATINGVERTEX) {
13572 /* Failed to insert the new vertex, but some subsegment was */
13573 /* marked as being encroached. */
13574 vertexdealloc(m, newvertex);
13575 } else { /* success == DUPLICATEVERTEX */
13576 /* Couldn't insert the new vertex because a vertex is already there. */
13577 if (!b->quiet) {
13578 printf(
13579 "Warning: New vertex (%.12g, %.12g) falls on existing vertex.\n",
13580 newvertex[0], newvertex[1]);
13581 errorflag = 1;
13582 }
13583 vertexdealloc(m, newvertex);
13584 }
13585 }
13586 if (errorflag) {
13587 if (b->verbose) {
13588 printf(" The new vertex is at the circumcenter of triangle\n");
13589 printf(" (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
13590 borg[0], borg[1], bdest[0], bdest[1], bapex[0], bapex[1]);
13591 }
13592 printf("This probably means that I am trying to refine triangles\n");
13593 printf(" to a smaller size than can be accommodated by the finite\n");
13594 printf(" precision of floating point arithmetic. (You can be\n");
13595 printf(" sure of this if I fail to terminate.)\n");
13596 precisionerror();
13597 }
13598 }
13599 }
13600
13601 #endif /* not CDT_ONLY */
13602
13603 /*****************************************************************************/
13604 /* */
13605 /* enforcequality() Remove all the encroached subsegments and bad */
13606 /* triangles from the triangulation. */
13607 /* */
13608 /*****************************************************************************/
13609
13610 #ifndef CDT_ONLY
13611
13612 #ifdef ANSI_DECLARATORS
13613 void enforcequality(struct mesh *m, struct behavior *b)
13614 #else /* not ANSI_DECLARATORS */
13615 void enforcequality(m, b)
13616 struct mesh *m;
13617 struct behavior *b;
13618 #endif /* not ANSI_DECLARATORS */
13619
13620 {
13621 struct badtriang *badtri;
13622 int i;
13623
13624 if (!b->quiet) {
13625 printf("Adding Steiner points to enforce quality.\n");
13626 }
13627 /* Initialize the pool of encroached subsegments. */
13628 poolinit(&m->badsubsegs, sizeof(struct badsubseg), BADSUBSEGPERBLOCK,
13629 BADSUBSEGPERBLOCK, 0);
13630 if (b->verbose) {
13631 printf(" Looking for encroached subsegments.\n");
13632 }
13633 /* Test all segments to see if they're encroached. */
13634 tallyencs(m, b);
13635 if (b->verbose && (m->badsubsegs.items > 0)) {
13636 printf(" Splitting encroached subsegments.\n");
13637 }
13638 /* Fix encroached subsegments without noting bad triangles. */
13639 splitencsegs(m, b, 0);
13640 /* At this point, if we haven't run out of Steiner points, the */
13641 /* triangulation should be (conforming) Delaunay. */
13642
13643 /* Next, we worry about enforcing triangle quality. */
13644 if ((b->minangle > 0.0) || b->vararea || b->fixedarea || b->usertest) {
13645 /* Initialize the pool of bad triangles. */
13646 poolinit(&m->badtriangles, sizeof(struct badtriang), BADTRIPERBLOCK,
13647 BADTRIPERBLOCK, 0);
13648 /* Initialize the queues of bad triangles. */
13649 for (i = 0; i < 4096; i++) {
13650 m->queuefront[i] = (struct badtriang *) NULL;
13651 }
13652 m->firstnonemptyq = -1;
13653 /* Test all triangles to see if they're bad. */
13654 tallyfaces(m, b);
13655 /* Initialize the pool of recently flipped triangles. */
13656 poolinit(&m->flipstackers, sizeof(struct flipstacker), FLIPSTACKERPERBLOCK,
13657 FLIPSTACKERPERBLOCK, 0);
13658 m->checkquality = 1;
13659 if (b->verbose) {
13660 printf(" Splitting bad triangles.\n");
13661 }
13662 while ((m->badtriangles.items > 0) && (m->steinerleft != 0)) {
13663 /* Fix one bad triangle by inserting a vertex at its circumcenter. */
13664 badtri = dequeuebadtriang(m);
13665 splittriangle(m, b, badtri);
13666 if (m->badsubsegs.items > 0) {
13667 /* Put bad triangle back in queue for another try later. */
13668 enqueuebadtriang(m, b, badtri);
13669 /* Fix any encroached subsegments that resulted. */
13670 /* Record any new bad triangles that result. */
13671 splitencsegs(m, b, 1);
13672 } else {
13673 /* Return the bad triangle to the pool. */
13674 pooldealloc(&m->badtriangles, (VOID *) badtri);
13675 }
13676 }
13677 }
13678 /* At this point, if the "-D" switch was selected and we haven't run out */
13679 /* of Steiner points, the triangulation should be (conforming) Delaunay */
13680 /* and have no low-quality triangles. */
13681
13682 /* Might we have run out of Steiner points too soon? */
13683 if (!b->quiet && b->conformdel && (m->badsubsegs.items > 0) &&
13684 (m->steinerleft == 0)) {
13685 printf("\nWarning: I ran out of Steiner points, but the mesh has\n");
13686 if (m->badsubsegs.items == 1) {
13687 printf(" one encroached subsegment, and therefore might not be truly\n"
13688 );
13689 } else {
13690 printf(" %ld encroached subsegments, and therefore might not be truly\n"
13691 , m->badsubsegs.items);
13692 }
13693 printf(" Delaunay. If the Delaunay property is important to you,\n");
13694 printf(" try increasing the number of Steiner points (controlled by\n");
13695 printf(" the -S switch) slightly and try again.\n\n");
13696 }
13697 }
13698
13699 #endif /* not CDT_ONLY */
13700
13701 /** **/
13702 /** **/
13703 /********* Mesh quality maintenance ends here *********/
13704
13705 /*****************************************************************************/
13706 /* */
13707 /* highorder() Create extra nodes for quadratic subparametric elements. */
13708 /* */
13709 /*****************************************************************************/
13710
13711 #ifdef ANSI_DECLARATORS
13712 void highorder(struct mesh *m, struct behavior *b)
13713 #else /* not ANSI_DECLARATORS */
13714 void highorder(m, b)
13715 struct mesh *m;
13716 struct behavior *b;
13717 #endif /* not ANSI_DECLARATORS */
13718
13719 {
13720 struct otri triangleloop, trisym;
13721 struct osub checkmark;
13722 vertex newvertex;
13723 vertex torg, tdest;
13724 int i;
13725 triangle ptr; /* Temporary variable used by sym(). */
13726 subseg sptr; /* Temporary variable used by tspivot(). */
13727
13728 if (!b->quiet) {
13729 printf("Adding vertices for second-order triangles.\n");
13730 }
13731 /* The following line ensures that dead items in the pool of nodes */
13732 /* cannot be allocated for the extra nodes associated with high */
13733 /* order elements. This ensures that the primary nodes (at the */
13734 /* corners of elements) will occur earlier in the output files, and */
13735 /* have lower indices, than the extra nodes. */
13736 m->vertices.deaditemstack = (VOID *) NULL;
13737
13738 traversalinit(&m->triangles);
13739 triangleloop.tri = triangletraverse(m);
13740 /* To loop over the set of edges, loop over all triangles, and look at */
13741 /* the three edges of each triangle. If there isn't another triangle */
13742 /* adjacent to the edge, operate on the edge. If there is another */
13743 /* adjacent triangle, operate on the edge only if the current triangle */
13744 /* has a smaller pointer than its neighbor. This way, each edge is */
13745 /* considered only once. */
13746 while (triangleloop.tri != (triangle *) NULL) {
13747 for (triangleloop.orient = 0; triangleloop.orient < 3;
13748 triangleloop.orient++) {
13749 sym(triangleloop, trisym);
13750 if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) {
13751 org(triangleloop, torg);
13752 dest(triangleloop, tdest);
13753 /* Create a new node in the middle of the edge. Interpolate */
13754 /* its attributes. */
13755 newvertex = (vertex) poolalloc(&m->vertices);
13756 for (i = 0; i < 2 + m->nextras; i++) {
13757 newvertex[i] = 0.5 * (torg[i] + tdest[i]);
13758 }
13759 /* Set the new node's marker to zero or one, depending on */
13760 /* whether it lies on a boundary. */
13761 setvertexmark(newvertex, trisym.tri == m->dummytri);
13762 setvertextype(newvertex,
13763 trisym.tri == m->dummytri ? FREEVERTEX : SEGMENTVERTEX);
13764 if (b->usesegments) {
13765 tspivot(triangleloop, checkmark);
13766 /* If this edge is a segment, transfer the marker to the new node. */
13767 if (checkmark.ss != m->dummysub) {
13768 setvertexmark(newvertex, mark(checkmark));
13769 setvertextype(newvertex, SEGMENTVERTEX);
13770 }
13771 }
13772 if (b->verbose > 1) {
13773 printf(" Creating (%.12g, %.12g).\n", newvertex[0], newvertex[1]);
13774 }
13775 /* Record the new node in the (one or two) adjacent elements. */
13776 triangleloop.tri[m->highorderindex + triangleloop.orient] =
13777 (triangle) newvertex;
13778 if (trisym.tri != m->dummytri) {
13779 trisym.tri[m->highorderindex + trisym.orient] = (triangle) newvertex;
13780 }
13781 }
13782 }
13783 triangleloop.tri = triangletraverse(m);
13784 }
13785 }
13786
13787 /********* File I/O routines begin here *********/
13788 /** **/
13789 /** **/
13790
13791 /*****************************************************************************/
13792 /* */
13793 /* readline() Read a nonempty line from a file. */
13794 /* */
13795 /* A line is considered "nonempty" if it contains something that looks like */
13796 /* a number. Comments (prefaced by `#') are ignored. */
13797 /* */
13798 /*****************************************************************************/
13799
13800 #ifndef TRILIBRARY
13801
13802 #ifdef ANSI_DECLARATORS
13803 char *readline(char *string, FILE *infile, char *infilename)
13804 #else /* not ANSI_DECLARATORS */
13805 char *readline(string, infile, infilename)
13806 char *string;
13807 FILE *infile;
13808 char *infilename;
13809 #endif /* not ANSI_DECLARATORS */
13810
13811 {
13812 char *result;
13813
13814 /* Search for something that looks like a number. */
13815 do {
13816 result = fgets(string, INPUTLINESIZE, infile);
13817 if (result == (char *) NULL) {
13818 printf(" Error: Unexpected end of file in %s.\n", infilename);
13819 triexit(1);
13820 }
13821 /* Skip anything that doesn't look like a number, a comment, */
13822 /* or the end of a line. */
13823 while ((*result != '\0') && (*result != '#')
13824 && (*result != '.') && (*result != '+') && (*result != '-')
13825 && ((*result < '0') || (*result > '9'))) {
13826 result++;
13827 }
13828 /* If it's a comment or end of line, read another line and try again. */
13829 } while ((*result == '#') || (*result == '\0'));
13830 return result;
13831 }
13832
13833 #endif /* not TRILIBRARY */
13834
13835 /*****************************************************************************/
13836 /* */
13837 /* findfield() Find the next field of a string. */
13838 /* */
13839 /* Jumps past the current field by searching for whitespace, then jumps */
13840 /* past the whitespace to find the next field. */
13841 /* */
13842 /*****************************************************************************/
13843
13844 #ifndef TRILIBRARY
13845
13846 #ifdef ANSI_DECLARATORS
13847 char *findfield(char *string)
13848 #else /* not ANSI_DECLARATORS */
13849 char *findfield(string)
13850 char *string;
13851 #endif /* not ANSI_DECLARATORS */
13852
13853 {
13854 char *result;
13855
13856 result = string;
13857 /* Skip the current field. Stop upon reaching whitespace. */
13858 while ((*result != '\0') && (*result != '#')
13859 && (*result != ' ') && (*result != '\t')) {
13860 result++;
13861 }
13862 /* Now skip the whitespace and anything else that doesn't look like a */
13863 /* number, a comment, or the end of a line. */
13864 while ((*result != '\0') && (*result != '#')
13865 && (*result != '.') && (*result != '+') && (*result != '-')
13866 && ((*result < '0') || (*result > '9'))) {
13867 result++;
13868 }
13869 /* Check for a comment (prefixed with `#'). */
13870 if (*result == '#') {
13871 *result = '\0';
13872 }
13873 return result;
13874 }
13875
13876 #endif /* not TRILIBRARY */
13877
13878 /*****************************************************************************/
13879 /* */
13880 /* readnodes() Read the vertices from a file, which may be a .node or */
13881 /* .poly file. */
13882 /* */
13883 /*****************************************************************************/
13884
13885 #ifndef TRILIBRARY
13886
13887 #ifdef ANSI_DECLARATORS
13888 void readnodes(struct mesh *m, struct behavior *b, char *nodefilename,
13889 char *polyfilename, FILE **polyfile)
13890 #else /* not ANSI_DECLARATORS */
13891 void readnodes(m, b, nodefilename, polyfilename, polyfile)
13892 struct mesh *m;
13893 struct behavior *b;
13894 char *nodefilename;
13895 char *polyfilename;
13896 FILE **polyfile;
13897 #endif /* not ANSI_DECLARATORS */
13898
13899 {
13900 FILE *infile;
13901 vertex vertexloop;
13902 char inputline[INPUTLINESIZE];
13903 char *stringptr;
13904 char *infilename;
13905 REAL x, y;
13906 int firstnode;
13907 int nodemarkers;
13908 int currentmarker;
13909 int i, j;
13910
13911 if (b->poly) {
13912 /* Read the vertices from a .poly file. */
13913 if (!b->quiet) {
13914 printf("Opening %s.\n", polyfilename);
13915 }
13916 *polyfile = fopen(polyfilename, "r");
13917 if (*polyfile == (FILE *) NULL) {
13918 printf(" Error: Cannot access file %s.\n", polyfilename);
13919 triexit(1);
13920 }
13921 /* Read number of vertices, number of dimensions, number of vertex */
13922 /* attributes, and number of boundary markers. */
13923 stringptr = readline(inputline, *polyfile, polyfilename);
13924 m->invertices = (int) strtol(stringptr, &stringptr, 0);
13925 stringptr = findfield(stringptr);
13926 if (*stringptr == '\0') {
13927 m->mesh_dim = 2;
13928 } else {
13929 m->mesh_dim = (int) strtol(stringptr, &stringptr, 0);
13930 }
13931 stringptr = findfield(stringptr);
13932 if (*stringptr == '\0') {
13933 m->nextras = 0;
13934 } else {
13935 m->nextras = (int) strtol(stringptr, &stringptr, 0);
13936 }
13937 stringptr = findfield(stringptr);
13938 if (*stringptr == '\0') {
13939 nodemarkers = 0;
13940 } else {
13941 nodemarkers = (int) strtol(stringptr, &stringptr, 0);
13942 }
13943 if (m->invertices > 0) {
13944 infile = *polyfile;
13945 infilename = polyfilename;
13946 m->readnodefile = 0;
13947 } else {
13948 /* If the .poly file claims there are zero vertices, that means that */
13949 /* the vertices should be read from a separate .node file. */
13950 m->readnodefile = 1;
13951 infilename = nodefilename;
13952 }
13953 } else {
13954 m->readnodefile = 1;
13955 infilename = nodefilename;
13956 *polyfile = (FILE *) NULL;
13957 }
13958
13959 if (m->readnodefile) {
13960 /* Read the vertices from a .node file. */
13961 if (!b->quiet) {
13962 printf("Opening %s.\n", nodefilename);
13963 }
13964 infile = fopen(nodefilename, "r");
13965 if (infile == (FILE *) NULL) {
13966 printf(" Error: Cannot access file %s.\n", nodefilename);
13967 triexit(1);
13968 }
13969 /* Read number of vertices, number of dimensions, number of vertex */
13970 /* attributes, and number of boundary markers. */
13971 stringptr = readline(inputline, infile, nodefilename);
13972 m->invertices = (int) strtol(stringptr, &stringptr, 0);
13973 stringptr = findfield(stringptr);
13974 if (*stringptr == '\0') {
13975 m->mesh_dim = 2;
13976 } else {
13977 m->mesh_dim = (int) strtol(stringptr, &stringptr, 0);
13978 }
13979 stringptr = findfield(stringptr);
13980 if (*stringptr == '\0') {
13981 m->nextras = 0;
13982 } else {
13983 m->nextras = (int) strtol(stringptr, &stringptr, 0);
13984 }
13985 stringptr = findfield(stringptr);
13986 if (*stringptr == '\0') {
13987 nodemarkers = 0;
13988 } else {
13989 nodemarkers = (int) strtol(stringptr, &stringptr, 0);
13990 }
13991 }
13992
13993 if (m->invertices < 3) {
13994 printf("Error: Input must have at least three input vertices.\n");
13995 triexit(1);
13996 }
13997 if (m->mesh_dim != 2) {
13998 printf("Error: Triangle only works with two-dimensional meshes.\n");
13999 triexit(1);
14000 }
14001 if (m->nextras == 0) {
14002 b->weighted = 0;
14003 }
14004
14005 initializevertexpool(m, b);
14006
14007 /* Read the vertices. */
14008 for (i = 0; i < m->invertices; i++) {
14009 vertexloop = (vertex) poolalloc(&m->vertices);
14010 stringptr = readline(inputline, infile, infilename);
14011 if (i == 0) {
14012 firstnode = (int) strtol(stringptr, &stringptr, 0);
14013 if ((firstnode == 0) || (firstnode == 1)) {
14014 b->firstnumber = firstnode;
14015 }
14016 }
14017 stringptr = findfield(stringptr);
14018 if (*stringptr == '\0') {
14019 printf("Error: Vertex %d has no x coordinate.\n", b->firstnumber + i);
14020 triexit(1);
14021 }
14022 x = (REAL) strtod(stringptr, &stringptr);
14023 stringptr = findfield(stringptr);
14024 if (*stringptr == '\0') {
14025 printf("Error: Vertex %d has no y coordinate.\n", b->firstnumber + i);
14026 triexit(1);
14027 }
14028 y = (REAL) strtod(stringptr, &stringptr);
14029 vertexloop[0] = x;
14030 vertexloop[1] = y;
14031 /* Read the vertex attributes. */
14032 for (j = 2; j < 2 + m->nextras; j++) {
14033 stringptr = findfield(stringptr);
14034 if (*stringptr == '\0') {
14035 vertexloop[j] = 0.0;
14036 } else {
14037 vertexloop[j] = (REAL) strtod(stringptr, &stringptr);
14038 }
14039 }
14040 if (nodemarkers) {
14041 /* Read a vertex marker. */
14042 stringptr = findfield(stringptr);
14043 if (*stringptr == '\0') {
14044 setvertexmark(vertexloop, 0);
14045 } else {
14046 currentmarker = (int) strtol(stringptr, &stringptr, 0);
14047 setvertexmark(vertexloop, currentmarker);
14048 }
14049 } else {
14050 /* If no markers are specified in the file, they default to zero. */
14051 setvertexmark(vertexloop, 0);
14052 }
14053 setvertextype(vertexloop, INPUTVERTEX);
14054 /* Determine the smallest and largest x and y coordinates. */
14055 if (i == 0) {
14056 m->xmin = m->xmax = x;
14057 m->ymin = m->ymax = y;
14058 } else {
14059 m->xmin = (x < m->xmin) ? x : m->xmin;
14060 m->xmax = (x > m->xmax) ? x : m->xmax;
14061 m->ymin = (y < m->ymin) ? y : m->ymin;
14062 m->ymax = (y > m->ymax) ? y : m->ymax;
14063 }
14064 }
14065 if (m->readnodefile) {
14066 fclose(infile);
14067 }
14068
14069 /* Nonexistent x value used as a flag to mark circle events in sweepline */
14070 /* Delaunay algorithm. */
14071 m->xminextreme = 10 * m->xmin - 9 * m->xmax;
14072 }
14073
14074 #endif /* not TRILIBRARY */
14075
14076 /*****************************************************************************/
14077 /* */
14078 /* transfernodes() Read the vertices from memory. */
14079 /* */
14080 /*****************************************************************************/
14081
14082 #ifdef TRILIBRARY
14083
14084 #ifdef ANSI_DECLARATORS
14085 void transfernodes(struct mesh *m, struct behavior *b, REAL *pointlist,
14086 REAL *pointattriblist, int *pointmarkerlist,
14087 int numberofpoints, int numberofpointattribs)
14088 #else /* not ANSI_DECLARATORS */
14089 void transfernodes(m, b, pointlist, pointattriblist, pointmarkerlist,
14090 numberofpoints, numberofpointattribs)
14091 struct mesh *m;
14092 struct behavior *b;
14093 REAL *pointlist;
14094 REAL *pointattriblist;
14095 int *pointmarkerlist;
14096 int numberofpoints;
14097 int numberofpointattribs;
14098 #endif /* not ANSI_DECLARATORS */
14099
14100 {
14101 vertex vertexloop;
14102 REAL x, y;
14103 int i, j;
14104 int coordindex;
14105 int attribindex;
14106
14107 m->invertices = numberofpoints;
14108 m->mesh_dim = 2;
14109 m->nextras = numberofpointattribs;
14110 m->readnodefile = 0;
14111 if (m->invertices < 3) {
14112 printf("Error: Input must have at least three input vertices.\n");
14113 triexit(1);
14114 }
14115 if (m->nextras == 0) {
14116 b->weighted = 0;
14117 }
14118
14119 initializevertexpool(m, b);
14120
14121 /* Read the vertices. */
14122 coordindex = 0;
14123 attribindex = 0;
14124 for (i = 0; i < m->invertices; i++) {
14125 vertexloop = (vertex) poolalloc(&m->vertices);
14126 /* Read the vertex coordinates. */
14127 x = vertexloop[0] = pointlist[coordindex++];
14128 y = vertexloop[1] = pointlist[coordindex++];
14129 /* Read the vertex attributes. */
14130 for (j = 0; j < numberofpointattribs; j++) {
14131 vertexloop[2 + j] = pointattriblist[attribindex++];
14132 }
14133 if (pointmarkerlist != (int *) NULL) {
14134 /* Read a vertex marker. */
14135 setvertexmark(vertexloop, pointmarkerlist[i]);
14136 } else {
14137 /* If no markers are specified, they default to zero. */
14138 setvertexmark(vertexloop, 0);
14139 }
14140 setvertextype(vertexloop, INPUTVERTEX);
14141 /* Determine the smallest and largest x and y coordinates. */
14142 if (i == 0) {
14143 m->xmin = m->xmax = x;
14144 m->ymin = m->ymax = y;
14145 } else {
14146 m->xmin = (x < m->xmin) ? x : m->xmin;
14147 m->xmax = (x > m->xmax) ? x : m->xmax;
14148 m->ymin = (y < m->ymin) ? y : m->ymin;
14149 m->ymax = (y > m->ymax) ? y : m->ymax;
14150 }
14151 }
14152
14153 /* Nonexistent x value used as a flag to mark circle events in sweepline */
14154 /* Delaunay algorithm. */
14155 m->xminextreme = 10 * m->xmin - 9 * m->xmax;
14156 }
14157
14158 #endif /* TRILIBRARY */
14159
14160 /*****************************************************************************/
14161 /* */
14162 /* readholes() Read the holes, and possibly regional attributes and area */
14163 /* constraints, from a .poly file. */
14164 /* */
14165 /*****************************************************************************/
14166
14167 #ifndef TRILIBRARY
14168
14169 #ifdef ANSI_DECLARATORS
14170 void readholes(struct mesh *m, struct behavior *b,
14171 FILE *polyfile, char *polyfilename, REAL **hlist, int *holes,
14172 REAL **rlist, int *regions)
14173 #else /* not ANSI_DECLARATORS */
14174 void readholes(m, b, polyfile, polyfilename, hlist, holes, rlist, regions)
14175 struct mesh *m;
14176 struct behavior *b;
14177 FILE *polyfile;
14178 char *polyfilename;
14179 REAL **hlist;
14180 int *holes;
14181 REAL **rlist;
14182 int *regions;
14183 #endif /* not ANSI_DECLARATORS */
14184
14185 {
14186 REAL *holelist;
14187 REAL *regionlist;
14188 char inputline[INPUTLINESIZE];
14189 char *stringptr;
14190 int index;
14191 int i;
14192
14193 /* Read the holes. */
14194 stringptr = readline(inputline, polyfile, polyfilename);
14195 *holes = (int) strtol(stringptr, &stringptr, 0);
14196 if (*holes > 0) {
14197 holelist = (REAL *) trimalloc(2 * *holes * (int) sizeof(REAL));
14198 *hlist = holelist;
14199 for (i = 0; i < 2 * *holes; i += 2) {
14200 stringptr = readline(inputline, polyfile, polyfilename);
14201 stringptr = findfield(stringptr);
14202 if (*stringptr == '\0') {
14203 printf("Error: Hole %d has no x coordinate.\n",
14204 b->firstnumber + (i >> 1));
14205 triexit(1);
14206 } else {
14207 holelist[i] = (REAL) strtod(stringptr, &stringptr);
14208 }
14209 stringptr = findfield(stringptr);
14210 if (*stringptr == '\0') {
14211 printf("Error: Hole %d has no y coordinate.\n",
14212 b->firstnumber + (i >> 1));
14213 triexit(1);
14214 } else {
14215 holelist[i + 1] = (REAL) strtod(stringptr, &stringptr);
14216 }
14217 }
14218 } else {
14219 *hlist = (REAL *) NULL;
14220 }
14221
14222 #ifndef CDT_ONLY
14223 if ((b->regionattrib || b->vararea) && !b->refine) {
14224 /* Read the area constraints. */
14225 stringptr = readline(inputline, polyfile, polyfilename);
14226 *regions = (int) strtol(stringptr, &stringptr, 0);
14227 if (*regions > 0) {
14228 regionlist = (REAL *) trimalloc(4 * *regions * (int) sizeof(REAL));
14229 *rlist = regionlist;
14230 index = 0;
14231 for (i = 0; i < *regions; i++) {
14232 stringptr = readline(inputline, polyfile, polyfilename);
14233 stringptr = findfield(stringptr);
14234 if (*stringptr == '\0') {
14235 printf("Error: Region %d has no x coordinate.\n",
14236 b->firstnumber + i);
14237 triexit(1);
14238 } else {
14239 regionlist[index++] = (REAL) strtod(stringptr, &stringptr);
14240 }
14241 stringptr = findfield(stringptr);
14242 if (*stringptr == '\0') {
14243 printf("Error: Region %d has no y coordinate.\n",
14244 b->firstnumber + i);
14245 triexit(1);
14246 } else {
14247 regionlist[index++] = (REAL) strtod(stringptr, &stringptr);
14248 }
14249 stringptr = findfield(stringptr);
14250 if (*stringptr == '\0') {
14251 printf(
14252 "Error: Region %d has no region attribute or area constraint.\n",
14253 b->firstnumber + i);
14254 triexit(1);
14255 } else {
14256 regionlist[index++] = (REAL) strtod(stringptr, &stringptr);
14257 }
14258 stringptr = findfield(stringptr);
14259 if (*stringptr == '\0') {
14260 regionlist[index] = regionlist[index - 1];
14261 } else {
14262 regionlist[index] = (REAL) strtod(stringptr, &stringptr);
14263 }
14264 index++;
14265 }
14266 }
14267 } else {
14268 /* Set `*regions' to zero to avoid an accidental free() later. */
14269 *regions = 0;
14270 *rlist = (REAL *) NULL;
14271 }
14272 #endif /* not CDT_ONLY */
14273
14274 fclose(polyfile);
14275 }
14276
14277 #endif /* not TRILIBRARY */
14278
14279 /*****************************************************************************/
14280 /* */
14281 /* finishfile() Write the command line to the output file so the user */
14282 /* can remember how the file was generated. Close the file. */
14283 /* */
14284 /*****************************************************************************/
14285
14286 #ifndef TRILIBRARY
14287
14288 #ifdef ANSI_DECLARATORS
14289 void finishfile(FILE *outfile, int argc, char **argv)
14290 #else /* not ANSI_DECLARATORS */
14291 void finishfile(outfile, argc, argv)
14292 FILE *outfile;
14293 int argc;
14294 char **argv;
14295 #endif /* not ANSI_DECLARATORS */
14296
14297 {
14298 int i;
14299
14300 fprintf(outfile, "# Generated by");
14301 for (i = 0; i < argc; i++) {
14302 fprintf(outfile, " ");
14303 fputs(argv[i], outfile);
14304 }
14305 fprintf(outfile, "\n");
14306 fclose(outfile);
14307 }
14308
14309 #endif /* not TRILIBRARY */
14310
14311 /*****************************************************************************/
14312 /* */
14313 /* writenodes() Number the vertices and write them to a .node file. */
14314 /* */
14315 /* To save memory, the vertex numbers are written over the boundary markers */
14316 /* after the vertices are written to a file. */
14317 /* */
14318 /*****************************************************************************/
14319
14320 #ifdef TRILIBRARY
14321
14322 #ifdef ANSI_DECLARATORS
14323 void writenodes(struct mesh *m, struct behavior *b, REAL **pointlist,
14324 REAL **pointattriblist, int **pointmarkerlist)
14325 #else /* not ANSI_DECLARATORS */
14326 void writenodes(m, b, pointlist, pointattriblist, pointmarkerlist)
14327 struct mesh *m;
14328 struct behavior *b;
14329 REAL **pointlist;
14330 REAL **pointattriblist;
14331 int **pointmarkerlist;
14332 #endif /* not ANSI_DECLARATORS */
14333
14334 #else /* not TRILIBRARY */
14335
14336 #ifdef ANSI_DECLARATORS
14337 void writenodes(struct mesh *m, struct behavior *b, char *nodefilename,
14338 int argc, char **argv)
14339 #else /* not ANSI_DECLARATORS */
14340 void writenodes(m, b, nodefilename, argc, argv)
14341 struct mesh *m;
14342 struct behavior *b;
14343 char *nodefilename;
14344 int argc;
14345 char **argv;
14346 #endif /* not ANSI_DECLARATORS */
14347
14348 #endif /* not TRILIBRARY */
14349
14350 {
14351 #ifdef TRILIBRARY
14352 REAL *plist;
14353 REAL *palist;
14354 int *pmlist;
14355 int coordindex;
14356 int attribindex;
14357 #else /* not TRILIBRARY */
14358 FILE *outfile;
14359 #endif /* not TRILIBRARY */
14360 vertex vertexloop;
14361 long outvertices;
14362 int vertexnumber;
14363 int i;
14364
14365 if (b->jettison) {
14366 outvertices = m->vertices.items - m->undeads;
14367 } else {
14368 outvertices = m->vertices.items;
14369 }
14370
14371 #ifdef TRILIBRARY
14372 if (!b->quiet) {
14373 printf("Writing vertices.\n");
14374 }
14375 /* Allocate memory for output vertices if necessary. */
14376 if (*pointlist == (REAL *) NULL) {
14377 *pointlist = (REAL *) trimalloc((int) (outvertices * 2 * sizeof(REAL)));
14378 }
14379 /* Allocate memory for output vertex attributes if necessary. */
14380 if ((m->nextras > 0) && (*pointattriblist == (REAL *) NULL)) {
14381 *pointattriblist = (REAL *) trimalloc((int) (outvertices * m->nextras *
14382 sizeof(REAL)));
14383 }
14384 /* Allocate memory for output vertex markers if necessary. */
14385 if (!b->nobound && (*pointmarkerlist == (int *) NULL)) {
14386 *pointmarkerlist = (int *) trimalloc((int) (outvertices * sizeof(int)));
14387 }
14388 plist = *pointlist;
14389 palist = *pointattriblist;
14390 pmlist = *pointmarkerlist;
14391 coordindex = 0;
14392 attribindex = 0;
14393 #else /* not TRILIBRARY */
14394 if (!b->quiet) {
14395 printf("Writing %s.\n", nodefilename);
14396 }
14397 outfile = fopen(nodefilename, "w");
14398 if (outfile == (FILE *) NULL) {
14399 printf(" Error: Cannot create file %s.\n", nodefilename);
14400 triexit(1);
14401 }
14402 /* Number of vertices, number of dimensions, number of vertex attributes, */
14403 /* and number of boundary markers (zero or one). */
14404 fprintf(outfile, "%ld %d %d %d\n", outvertices, m->mesh_dim,
14405 m->nextras, 1 - b->nobound);
14406 #endif /* not TRILIBRARY */
14407
14408 traversalinit(&m->vertices);
14409 vertexnumber = b->firstnumber;
14410 vertexloop = vertextraverse(m);
14411 while (vertexloop != (vertex) NULL) {
14412 if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) {
14413 #ifdef TRILIBRARY
14414 /* X and y coordinates. */
14415 plist[coordindex++] = vertexloop[0];
14416 plist[coordindex++] = vertexloop[1];
14417 /* Vertex attributes. */
14418 for (i = 0; i < m->nextras; i++) {
14419 palist[attribindex++] = vertexloop[2 + i];
14420 }
14421 if (!b->nobound) {
14422 /* Copy the boundary marker. */
14423 pmlist[vertexnumber - b->firstnumber] = vertexmark(vertexloop);
14424 }
14425 #else /* not TRILIBRARY */
14426 /* Vertex number, x and y coordinates. */
14427 fprintf(outfile, "%4d %.17g %.17g", vertexnumber, vertexloop[0],
14428 vertexloop[1]);
14429 for (i = 0; i < m->nextras; i++) {
14430 /* Write an attribute. */
14431 fprintf(outfile, " %.17g", vertexloop[i + 2]);
14432 }
14433 if (b->nobound) {
14434 fprintf(outfile, "\n");
14435 } else {
14436 /* Write the boundary marker. */
14437 fprintf(outfile, " %d\n", vertexmark(vertexloop));
14438 }
14439 #endif /* not TRILIBRARY */
14440
14441 setvertexmark(vertexloop, vertexnumber);
14442 vertexnumber++;
14443 }
14444 vertexloop = vertextraverse(m);
14445 }
14446
14447 #ifndef TRILIBRARY
14448 finishfile(outfile, argc, argv);
14449 #endif /* not TRILIBRARY */
14450 }
14451
14452 /*****************************************************************************/
14453 /* */
14454 /* numbernodes() Number the vertices. */
14455 /* */
14456 /* Each vertex is assigned a marker equal to its number. */
14457 /* */
14458 /* Used when writenodes() is not called because no .node file is written. */
14459 /* */
14460 /*****************************************************************************/
14461
14462 #ifdef ANSI_DECLARATORS
14463 void numbernodes(struct mesh *m, struct behavior *b)
14464 #else /* not ANSI_DECLARATORS */
14465 void numbernodes(m, b)
14466 struct mesh *m;
14467 struct behavior *b;
14468 #endif /* not ANSI_DECLARATORS */
14469
14470 {
14471 vertex vertexloop;
14472 int vertexnumber;
14473
14474 traversalinit(&m->vertices);
14475 vertexnumber = b->firstnumber;
14476 vertexloop = vertextraverse(m);
14477 while (vertexloop != (vertex) NULL) {
14478 setvertexmark(vertexloop, vertexnumber);
14479 if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) {
14480 vertexnumber++;
14481 }
14482 vertexloop = vertextraverse(m);
14483 }
14484 }
14485
14486 /*****************************************************************************/
14487 /* */
14488 /* writeelements() Write the triangles to an .ele file. */
14489 /* */
14490 /*****************************************************************************/
14491
14492 #ifdef TRILIBRARY
14493
14494 #ifdef ANSI_DECLARATORS
14495 void writeelements(struct mesh *m, struct behavior *b,
14496 int **trianglelist, REAL **triangleattriblist)
14497 #else /* not ANSI_DECLARATORS */
14498 void writeelements(m, b, trianglelist, triangleattriblist)
14499 struct mesh *m;
14500 struct behavior *b;
14501 int **trianglelist;
14502 REAL **triangleattriblist;
14503 #endif /* not ANSI_DECLARATORS */
14504
14505 #else /* not TRILIBRARY */
14506
14507 #ifdef ANSI_DECLARATORS
14508 void writeelements(struct mesh *m, struct behavior *b, char *elefilename,
14509 int argc, char **argv)
14510 #else /* not ANSI_DECLARATORS */
14511 void writeelements(m, b, elefilename, argc, argv)
14512 struct mesh *m;
14513 struct behavior *b;
14514 char *elefilename;
14515 int argc;
14516 char **argv;
14517 #endif /* not ANSI_DECLARATORS */
14518
14519 #endif /* not TRILIBRARY */
14520
14521 {
14522 #ifdef TRILIBRARY
14523 int *tlist;
14524 REAL *talist;
14525 int vertexindex;
14526 int attribindex;
14527 #else /* not TRILIBRARY */
14528 FILE *outfile;
14529 #endif /* not TRILIBRARY */
14530 struct otri triangleloop;
14531 vertex p1, p2, p3;
14532 vertex mid1, mid2, mid3;
14533 long elementnumber;
14534 int i;
14535
14536 #ifdef TRILIBRARY
14537 if (!b->quiet) {
14538 printf("Writing triangles.\n");
14539 }
14540 /* Allocate memory for output triangles if necessary. */
14541 if (*trianglelist == (int *) NULL) {
14542 *trianglelist = (int *) trimalloc((int) (m->triangles.items *
14543 ((b->order + 1) * (b->order + 2) /
14544 2) * sizeof(int)));
14545 }
14546 /* Allocate memory for output triangle attributes if necessary. */
14547 if ((m->eextras > 0) && (*triangleattriblist == (REAL *) NULL)) {
14548 *triangleattriblist = (REAL *) trimalloc((int) (m->triangles.items *
14549 m->eextras *
14550 sizeof(REAL)));
14551 }
14552 tlist = *trianglelist;
14553 talist = *triangleattriblist;
14554 vertexindex = 0;
14555 attribindex = 0;
14556 #else /* not TRILIBRARY */
14557 if (!b->quiet) {
14558 printf("Writing %s.\n", elefilename);
14559 }
14560 outfile = fopen(elefilename, "w");
14561 if (outfile == (FILE *) NULL) {
14562 printf(" Error: Cannot create file %s.\n", elefilename);
14563 triexit(1);
14564 }
14565 /* Number of triangles, vertices per triangle, attributes per triangle. */
14566 fprintf(outfile, "%ld %d %d\n", m->triangles.items,
14567 (b->order + 1) * (b->order + 2) / 2, m->eextras);
14568 #endif /* not TRILIBRARY */
14569
14570 traversalinit(&m->triangles);
14571 triangleloop.tri = triangletraverse(m);
14572 triangleloop.orient = 0;
14573 elementnumber = b->firstnumber;
14574 while (triangleloop.tri != (triangle *) NULL) {
14575 org(triangleloop, p1);
14576 dest(triangleloop, p2);
14577 apex(triangleloop, p3);
14578 if (b->order == 1) {
14579 #ifdef TRILIBRARY
14580 tlist[vertexindex++] = vertexmark(p1);
14581 tlist[vertexindex++] = vertexmark(p2);
14582 tlist[vertexindex++] = vertexmark(p3);
14583 #else /* not TRILIBRARY */
14584 /* Triangle number, indices for three vertices. */
14585 fprintf(outfile, "%4ld %4d %4d %4d", elementnumber,
14586 vertexmark(p1), vertexmark(p2), vertexmark(p3));
14587 #endif /* not TRILIBRARY */
14588 } else {
14589 mid1 = (vertex) triangleloop.tri[m->highorderindex + 1];
14590 mid2 = (vertex) triangleloop.tri[m->highorderindex + 2];
14591 mid3 = (vertex) triangleloop.tri[m->highorderindex];
14592 #ifdef TRILIBRARY
14593 tlist[vertexindex++] = vertexmark(p1);
14594 tlist[vertexindex++] = vertexmark(p2);
14595 tlist[vertexindex++] = vertexmark(p3);
14596 tlist[vertexindex++] = vertexmark(mid1);
14597 tlist[vertexindex++] = vertexmark(mid2);
14598 tlist[vertexindex++] = vertexmark(mid3);
14599 #else /* not TRILIBRARY */
14600 /* Triangle number, indices for six vertices. */
14601 fprintf(outfile, "%4ld %4d %4d %4d %4d %4d %4d", elementnumber,
14602 vertexmark(p1), vertexmark(p2), vertexmark(p3), vertexmark(mid1),
14603 vertexmark(mid2), vertexmark(mid3));
14604 #endif /* not TRILIBRARY */
14605 }
14606
14607 #ifdef TRILIBRARY
14608 for (i = 0; i < m->eextras; i++) {
14609 talist[attribindex++] = elemattribute(triangleloop, i);
14610 }
14611 #else /* not TRILIBRARY */
14612 for (i = 0; i < m->eextras; i++) {
14613 fprintf(outfile, " %.17g", elemattribute(triangleloop, i));
14614 }
14615 fprintf(outfile, "\n");
14616 #endif /* not TRILIBRARY */
14617
14618 triangleloop.tri = triangletraverse(m);
14619 elementnumber++;
14620 }
14621
14622 #ifndef TRILIBRARY
14623 finishfile(outfile, argc, argv);
14624 #endif /* not TRILIBRARY */
14625 }
14626
14627 /*****************************************************************************/
14628 /* */
14629 /* writepoly() Write the segments and holes to a .poly file. */
14630 /* */
14631 /*****************************************************************************/
14632
14633 #ifdef TRILIBRARY
14634
14635 #ifdef ANSI_DECLARATORS
14636 void writepoly(struct mesh *m, struct behavior *b,
14637 int **segmentlist, int **segmentmarkerlist)
14638 #else /* not ANSI_DECLARATORS */
14639 void writepoly(m, b, segmentlist, segmentmarkerlist)
14640 struct mesh *m;
14641 struct behavior *b;
14642 int **segmentlist;
14643 int **segmentmarkerlist;
14644 #endif /* not ANSI_DECLARATORS */
14645
14646 #else /* not TRILIBRARY */
14647
14648 #ifdef ANSI_DECLARATORS
14649 void writepoly(struct mesh *m, struct behavior *b, char *polyfilename,
14650 REAL *holelist, int holes, REAL *regionlist, int regions,
14651 int argc, char **argv)
14652 #else /* not ANSI_DECLARATORS */
14653 void writepoly(m, b, polyfilename, holelist, holes, regionlist, regions,
14654 argc, argv)
14655 struct mesh *m;
14656 struct behavior *b;
14657 char *polyfilename;
14658 REAL *holelist;
14659 int holes;
14660 REAL *regionlist;
14661 int regions;
14662 int argc;
14663 char **argv;
14664 #endif /* not ANSI_DECLARATORS */
14665
14666 #endif /* not TRILIBRARY */
14667
14668 {
14669 #ifdef TRILIBRARY
14670 int *slist;
14671 int *smlist;
14672 int index;
14673 #else /* not TRILIBRARY */
14674 FILE *outfile;
14675 long holenumber, regionnumber;
14676 #endif /* not TRILIBRARY */
14677 struct osub subsegloop;
14678 vertex endpoint1, endpoint2;
14679 long subsegnumber;
14680
14681 #ifdef TRILIBRARY
14682 if (!b->quiet) {
14683 printf("Writing segments.\n");
14684 }
14685 /* Allocate memory for output segments if necessary. */
14686 if (*segmentlist == (int *) NULL) {
14687 *segmentlist = (int *) trimalloc((int) (m->subsegs.items * 2 *
14688 sizeof(int)));
14689 }
14690 /* Allocate memory for output segment markers if necessary. */
14691 if (!b->nobound && (*segmentmarkerlist == (int *) NULL)) {
14692 *segmentmarkerlist = (int *) trimalloc((int) (m->subsegs.items *
14693 sizeof(int)));
14694 }
14695 slist = *segmentlist;
14696 smlist = *segmentmarkerlist;
14697 index = 0;
14698 #else /* not TRILIBRARY */
14699 if (!b->quiet) {
14700 printf("Writing %s.\n", polyfilename);
14701 }
14702 outfile = fopen(polyfilename, "w");
14703 if (outfile == (FILE *) NULL) {
14704 printf(" Error: Cannot create file %s.\n", polyfilename);
14705 triexit(1);
14706 }
14707 /* The zero indicates that the vertices are in a separate .node file. */
14708 /* Followed by number of dimensions, number of vertex attributes, */
14709 /* and number of boundary markers (zero or one). */
14710 fprintf(outfile, "%d %d %d %d\n", 0, m->mesh_dim, m->nextras,
14711 1 - b->nobound);
14712 /* Number of segments, number of boundary markers (zero or one). */
14713 fprintf(outfile, "%ld %d\n", m->subsegs.items, 1 - b->nobound);
14714 #endif /* not TRILIBRARY */
14715
14716 traversalinit(&m->subsegs);
14717 subsegloop.ss = subsegtraverse(m);
14718 subsegloop.ssorient = 0;
14719 subsegnumber = b->firstnumber;
14720 while (subsegloop.ss != (subseg *) NULL) {
14721 sorg(subsegloop, endpoint1);
14722 sdest(subsegloop, endpoint2);
14723 #ifdef TRILIBRARY
14724 /* Copy indices of the segment's two endpoints. */
14725 slist[index++] = vertexmark(endpoint1);
14726 slist[index++] = vertexmark(endpoint2);
14727 if (!b->nobound) {
14728 /* Copy the boundary marker. */
14729 smlist[subsegnumber - b->firstnumber] = mark(subsegloop);
14730 }
14731 #else /* not TRILIBRARY */
14732 /* Segment number, indices of its two endpoints, and possibly a marker. */
14733 if (b->nobound) {
14734 fprintf(outfile, "%4ld %4d %4d\n", subsegnumber,
14735 vertexmark(endpoint1), vertexmark(endpoint2));
14736 } else {
14737 fprintf(outfile, "%4ld %4d %4d %4d\n", subsegnumber,
14738 vertexmark(endpoint1), vertexmark(endpoint2), mark(subsegloop));
14739 }
14740 #endif /* not TRILIBRARY */
14741
14742 subsegloop.ss = subsegtraverse(m);
14743 subsegnumber++;
14744 }
14745
14746 #ifndef TRILIBRARY
14747 #ifndef CDT_ONLY
14748 fprintf(outfile, "%d\n", holes);
14749 if (holes > 0) {
14750 for (holenumber = 0; holenumber < holes; holenumber++) {
14751 /* Hole number, x and y coordinates. */
14752 fprintf(outfile, "%4ld %.17g %.17g\n", b->firstnumber + holenumber,
14753 holelist[2 * holenumber], holelist[2 * holenumber + 1]);
14754 }
14755 }
14756 if (regions > 0) {
14757 fprintf(outfile, "%d\n", regions);
14758 for (regionnumber = 0; regionnumber < regions; regionnumber++) {
14759 /* Region number, x and y coordinates, attribute, maximum area. */
14760 fprintf(outfile, "%4ld %.17g %.17g %.17g %.17g\n",
14761 b->firstnumber + regionnumber,
14762 regionlist[4 * regionnumber], regionlist[4 * regionnumber + 1],
14763 regionlist[4 * regionnumber + 2],
14764 regionlist[4 * regionnumber + 3]);
14765 }
14766 }
14767 #endif /* not CDT_ONLY */
14768
14769 finishfile(outfile, argc, argv);
14770 #endif /* not TRILIBRARY */
14771 }
14772
14773 /*****************************************************************************/
14774 /* */
14775 /* writeedges() Write the edges to an .edge file. */
14776 /* */
14777 /*****************************************************************************/
14778
14779 #ifdef TRILIBRARY
14780
14781 #ifdef ANSI_DECLARATORS
14782 void writeedges(struct mesh *m, struct behavior *b,
14783 int **edgelist, int **edgemarkerlist)
14784 #else /* not ANSI_DECLARATORS */
14785 void writeedges(m, b, edgelist, edgemarkerlist)
14786 struct mesh *m;
14787 struct behavior *b;
14788 int **edgelist;
14789 int **edgemarkerlist;
14790 #endif /* not ANSI_DECLARATORS */
14791
14792 #else /* not TRILIBRARY */
14793
14794 #ifdef ANSI_DECLARATORS
14795 void writeedges(struct mesh *m, struct behavior *b, char *edgefilename,
14796 int argc, char **argv)
14797 #else /* not ANSI_DECLARATORS */
14798 void writeedges(m, b, edgefilename, argc, argv)
14799 struct mesh *m;
14800 struct behavior *b;
14801 char *edgefilename;
14802 int argc;
14803 char **argv;
14804 #endif /* not ANSI_DECLARATORS */
14805
14806 #endif /* not TRILIBRARY */
14807
14808 {
14809 #ifdef TRILIBRARY
14810 int *elist;
14811 int *emlist;
14812 int index;
14813 #else /* not TRILIBRARY */
14814 FILE *outfile;
14815 #endif /* not TRILIBRARY */
14816 struct otri triangleloop, trisym;
14817 struct osub checkmark;
14818 vertex p1, p2;
14819 long edgenumber;
14820 triangle ptr; /* Temporary variable used by sym(). */
14821 subseg sptr; /* Temporary variable used by tspivot(). */
14822
14823 #ifdef TRILIBRARY
14824 if (!b->quiet) {
14825 printf("Writing edges.\n");
14826 }
14827 /* Allocate memory for edges if necessary. */
14828 if (*edgelist == (int *) NULL) {
14829 *edgelist = (int *) trimalloc((int) (m->edges * 2 * sizeof(int)));
14830 }
14831 /* Allocate memory for edge markers if necessary. */
14832 if (!b->nobound && (*edgemarkerlist == (int *) NULL)) {
14833 *edgemarkerlist = (int *) trimalloc((int) (m->edges * sizeof(int)));
14834 }
14835 elist = *edgelist;
14836 emlist = *edgemarkerlist;
14837 index = 0;
14838 #else /* not TRILIBRARY */
14839 if (!b->quiet) {
14840 printf("Writing %s.\n", edgefilename);
14841 }
14842 outfile = fopen(edgefilename, "w");
14843 if (outfile == (FILE *) NULL) {
14844 printf(" Error: Cannot create file %s.\n", edgefilename);
14845 triexit(1);
14846 }
14847 /* Number of edges, number of boundary markers (zero or one). */
14848 fprintf(outfile, "%ld %d\n", m->edges, 1 - b->nobound);
14849 #endif /* not TRILIBRARY */
14850
14851 traversalinit(&m->triangles);
14852 triangleloop.tri = triangletraverse(m);
14853 edgenumber = b->firstnumber;
14854 /* To loop over the set of edges, loop over all triangles, and look at */
14855 /* the three edges of each triangle. If there isn't another triangle */
14856 /* adjacent to the edge, operate on the edge. If there is another */
14857 /* adjacent triangle, operate on the edge only if the current triangle */
14858 /* has a smaller pointer than its neighbor. This way, each edge is */
14859 /* considered only once. */
14860 while (triangleloop.tri != (triangle *) NULL) {
14861 for (triangleloop.orient = 0; triangleloop.orient < 3;
14862 triangleloop.orient++) {
14863 sym(triangleloop, trisym);
14864 if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) {
14865 org(triangleloop, p1);
14866 dest(triangleloop, p2);
14867 #ifdef TRILIBRARY
14868 elist[index++] = vertexmark(p1);
14869 elist[index++] = vertexmark(p2);
14870 #endif /* TRILIBRARY */
14871 if (b->nobound) {
14872 #ifndef TRILIBRARY
14873 /* Edge number, indices of two endpoints. */
14874 fprintf(outfile, "%4ld %d %d\n", edgenumber,
14875 vertexmark(p1), vertexmark(p2));
14876 #endif /* not TRILIBRARY */
14877 } else {
14878 /* Edge number, indices of two endpoints, and a boundary marker. */
14879 /* If there's no subsegment, the boundary marker is zero. */
14880 if (b->usesegments) {
14881 tspivot(triangleloop, checkmark);
14882 if (checkmark.ss == m->dummysub) {
14883 #ifdef TRILIBRARY
14884 emlist[edgenumber - b->firstnumber] = 0;
14885 #else /* not TRILIBRARY */
14886 fprintf(outfile, "%4ld %d %d %d\n", edgenumber,
14887 vertexmark(p1), vertexmark(p2), 0);
14888 #endif /* not TRILIBRARY */
14889 } else {
14890 #ifdef TRILIBRARY
14891 emlist[edgenumber - b->firstnumber] = mark(checkmark);
14892 #else /* not TRILIBRARY */
14893 fprintf(outfile, "%4ld %d %d %d\n", edgenumber,
14894 vertexmark(p1), vertexmark(p2), mark(checkmark));
14895 #endif /* not TRILIBRARY */
14896 }
14897 } else {
14898 #ifdef TRILIBRARY
14899 emlist[edgenumber - b->firstnumber] = trisym.tri == m->dummytri;
14900 #else /* not TRILIBRARY */
14901 fprintf(outfile, "%4ld %d %d %d\n", edgenumber,
14902 vertexmark(p1), vertexmark(p2), trisym.tri == m->dummytri);
14903 #endif /* not TRILIBRARY */
14904 }
14905 }
14906 edgenumber++;
14907 }
14908 }
14909 triangleloop.tri = triangletraverse(m);
14910 }
14911
14912 #ifndef TRILIBRARY
14913 finishfile(outfile, argc, argv);
14914 #endif /* not TRILIBRARY */
14915 }
14916
14917 /*****************************************************************************/
14918 /* */
14919 /* writevoronoi() Write the Voronoi diagram to a .v.node and .v.edge */
14920 /* file. */
14921 /* */
14922 /* The Voronoi diagram is the geometric dual of the Delaunay triangulation. */
14923 /* Hence, the Voronoi vertices are listed by traversing the Delaunay */
14924 /* triangles, and the Voronoi edges are listed by traversing the Delaunay */
14925 /* edges. */
14926 /* */
14927 /* WARNING: In order to assign numbers to the Voronoi vertices, this */
14928 /* procedure messes up the subsegments or the extra nodes of every */
14929 /* element. Hence, you should call this procedure last. */
14930 /* */
14931 /*****************************************************************************/
14932
14933 #ifdef TRILIBRARY
14934
14935 #ifdef ANSI_DECLARATORS
14936 void writevoronoi(struct mesh *m, struct behavior *b, REAL **vpointlist,
14937 REAL **vpointattriblist, int **vpointmarkerlist,
14938 int **vedgelist, int **vedgemarkerlist, REAL **vnormlist)
14939 #else /* not ANSI_DECLARATORS */
14940 void writevoronoi(m, b, vpointlist, vpointattriblist, vpointmarkerlist,
14941 vedgelist, vedgemarkerlist, vnormlist)
14942 struct mesh *m;
14943 struct behavior *b;
14944 REAL **vpointlist;
14945 REAL **vpointattriblist;
14946 int **vpointmarkerlist;
14947 int **vedgelist;
14948 int **vedgemarkerlist;
14949 REAL **vnormlist;
14950 #endif /* not ANSI_DECLARATORS */
14951
14952 #else /* not TRILIBRARY */
14953
14954 #ifdef ANSI_DECLARATORS
14955 void writevoronoi(struct mesh *m, struct behavior *b, char *vnodefilename,
14956 char *vedgefilename, int argc, char **argv)
14957 #else /* not ANSI_DECLARATORS */
14958 void writevoronoi(m, b, vnodefilename, vedgefilename, argc, argv)
14959 struct mesh *m;
14960 struct behavior *b;
14961 char *vnodefilename;
14962 char *vedgefilename;
14963 int argc;
14964 char **argv;
14965 #endif /* not ANSI_DECLARATORS */
14966
14967 #endif /* not TRILIBRARY */
14968
14969 {
14970 #ifdef TRILIBRARY
14971 REAL *plist;
14972 REAL *palist;
14973 int *elist;
14974 REAL *normlist;
14975 int coordindex;
14976 int attribindex;
14977 #else /* not TRILIBRARY */
14978 FILE *outfile;
14979 #endif /* not TRILIBRARY */
14980 struct otri triangleloop, trisym;
14981 vertex torg, tdest, tapex;
14982 REAL circumcenter[2];
14983 REAL xi, eta;
14984 long vnodenumber, vedgenumber;
14985 int p1, p2;
14986 int i;
14987 triangle ptr; /* Temporary variable used by sym(). */
14988
14989 #ifdef TRILIBRARY
14990 if (!b->quiet) {
14991 printf("Writing Voronoi vertices.\n");
14992 }
14993 /* Allocate memory for Voronoi vertices if necessary. */
14994 if (*vpointlist == (REAL *) NULL) {
14995 *vpointlist = (REAL *) trimalloc((int) (m->triangles.items * 2 *
14996 sizeof(REAL)));
14997 }
14998 /* Allocate memory for Voronoi vertex attributes if necessary. */
14999 if (*vpointattriblist == (REAL *) NULL) {
15000 *vpointattriblist = (REAL *) trimalloc((int) (m->triangles.items *
15001 m->nextras * sizeof(REAL)));
15002 }
15003 *vpointmarkerlist = (int *) NULL;
15004 plist = *vpointlist;
15005 palist = *vpointattriblist;
15006 coordindex = 0;
15007 attribindex = 0;
15008 #else /* not TRILIBRARY */
15009 if (!b->quiet) {
15010 printf("Writing %s.\n", vnodefilename);
15011 }
15012 outfile = fopen(vnodefilename, "w");
15013 if (outfile == (FILE *) NULL) {
15014 printf(" Error: Cannot create file %s.\n", vnodefilename);
15015 triexit(1);
15016 }
15017 /* Number of triangles, two dimensions, number of vertex attributes, */
15018 /* no markers. */
15019 fprintf(outfile, "%ld %d %d %d\n", m->triangles.items, 2, m->nextras, 0);
15020 #endif /* not TRILIBRARY */
15021
15022 traversalinit(&m->triangles);
15023 triangleloop.tri = triangletraverse(m);
15024 triangleloop.orient = 0;
15025 vnodenumber = b->firstnumber;
15026 while (triangleloop.tri != (triangle *) NULL) {
15027 org(triangleloop, torg);
15028 dest(triangleloop, tdest);
15029 apex(triangleloop, tapex);
15030 findcircumcenter(m, b, torg, tdest, tapex, circumcenter, &xi, &eta, 0);
15031 #ifdef TRILIBRARY
15032 /* X and y coordinates. */
15033 plist[coordindex++] = circumcenter[0];
15034 plist[coordindex++] = circumcenter[1];
15035 for (i = 2; i < 2 + m->nextras; i++) {
15036 /* Interpolate the vertex attributes at the circumcenter. */
15037 palist[attribindex++] = torg[i] + xi * (tdest[i] - torg[i])
15038 + eta * (tapex[i] - torg[i]);
15039 }
15040 #else /* not TRILIBRARY */
15041 /* Voronoi vertex number, x and y coordinates. */
15042 fprintf(outfile, "%4ld %.17g %.17g", vnodenumber, circumcenter[0],
15043 circumcenter[1]);
15044 for (i = 2; i < 2 + m->nextras; i++) {
15045 /* Interpolate the vertex attributes at the circumcenter. */
15046 fprintf(outfile, " %.17g", torg[i] + xi * (tdest[i] - torg[i])
15047 + eta * (tapex[i] - torg[i]));
15048 }
15049 fprintf(outfile, "\n");
15050 #endif /* not TRILIBRARY */
15051
15052 * (int *) (triangleloop.tri + 6) = (int) vnodenumber;
15053 triangleloop.tri = triangletraverse(m);
15054 vnodenumber++;
15055 }
15056
15057 #ifndef TRILIBRARY
15058 finishfile(outfile, argc, argv);
15059 #endif /* not TRILIBRARY */
15060
15061 #ifdef TRILIBRARY
15062 if (!b->quiet) {
15063 printf("Writing Voronoi edges.\n");
15064 }
15065 /* Allocate memory for output Voronoi edges if necessary. */
15066 if (*vedgelist == (int *) NULL) {
15067 *vedgelist = (int *) trimalloc((int) (m->edges * 2 * sizeof(int)));
15068 }
15069 *vedgemarkerlist = (int *) NULL;
15070 /* Allocate memory for output Voronoi norms if necessary. */
15071 if (*vnormlist == (REAL *) NULL) {
15072 *vnormlist = (REAL *) trimalloc((int) (m->edges * 2 * sizeof(REAL)));
15073 }
15074 elist = *vedgelist;
15075 normlist = *vnormlist;
15076 coordindex = 0;
15077 #else /* not TRILIBRARY */
15078 if (!b->quiet) {
15079 printf("Writing %s.\n", vedgefilename);
15080 }
15081 outfile = fopen(vedgefilename, "w");
15082 if (outfile == (FILE *) NULL) {
15083 printf(" Error: Cannot create file %s.\n", vedgefilename);
15084 triexit(1);
15085 }
15086 /* Number of edges, zero boundary markers. */
15087 fprintf(outfile, "%ld %d\n", m->edges, 0);
15088 #endif /* not TRILIBRARY */
15089
15090 traversalinit(&m->triangles);
15091 triangleloop.tri = triangletraverse(m);
15092 vedgenumber = b->firstnumber;
15093 /* To loop over the set of edges, loop over all triangles, and look at */
15094 /* the three edges of each triangle. If there isn't another triangle */
15095 /* adjacent to the edge, operate on the edge. If there is another */
15096 /* adjacent triangle, operate on the edge only if the current triangle */
15097 /* has a smaller pointer than its neighbor. This way, each edge is */
15098 /* considered only once. */
15099 while (triangleloop.tri != (triangle *) NULL) {
15100 for (triangleloop.orient = 0; triangleloop.orient < 3;
15101 triangleloop.orient++) {
15102 sym(triangleloop, trisym);
15103 if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) {
15104 /* Find the number of this triangle (and Voronoi vertex). */
15105 p1 = * (int *) (triangleloop.tri + 6);
15106 if (trisym.tri == m->dummytri) {
15107 org(triangleloop, torg);
15108 dest(triangleloop, tdest);
15109 #ifdef TRILIBRARY
15110 /* Copy an infinite ray. Index of one endpoint, and -1. */
15111 elist[coordindex] = p1;
15112 normlist[coordindex++] = tdest[1] - torg[1];
15113 elist[coordindex] = -1;
15114 normlist[coordindex++] = torg[0] - tdest[0];
15115 #else /* not TRILIBRARY */
15116 /* Write an infinite ray. Edge number, index of one endpoint, -1, */
15117 /* and x and y coordinates of a vector representing the */
15118 /* direction of the ray. */
15119 fprintf(outfile, "%4ld %d %d %.17g %.17g\n", vedgenumber,
15120 p1, -1, tdest[1] - torg[1], torg[0] - tdest[0]);
15121 #endif /* not TRILIBRARY */
15122 } else {
15123 /* Find the number of the adjacent triangle (and Voronoi vertex). */
15124 p2 = * (int *) (trisym.tri + 6);
15125 /* Finite edge. Write indices of two endpoints. */
15126 #ifdef TRILIBRARY
15127 elist[coordindex] = p1;
15128 normlist[coordindex++] = 0.0;
15129 elist[coordindex] = p2;
15130 normlist[coordindex++] = 0.0;
15131 #else /* not TRILIBRARY */
15132 fprintf(outfile, "%4ld %d %d\n", vedgenumber, p1, p2);
15133 #endif /* not TRILIBRARY */
15134 }
15135 vedgenumber++;
15136 }
15137 }
15138 triangleloop.tri = triangletraverse(m);
15139 }
15140
15141 #ifndef TRILIBRARY
15142 finishfile(outfile, argc, argv);
15143 #endif /* not TRILIBRARY */
15144 }
15145
15146 #ifdef TRILIBRARY
15147
15148 #ifdef ANSI_DECLARATORS
15149 void writeneighbors(struct mesh *m, struct behavior *b, int **neighborlist)
15150 #else /* not ANSI_DECLARATORS */
15151 void writeneighbors(m, b, neighborlist)
15152 struct mesh *m;
15153 struct behavior *b;
15154 int **neighborlist;
15155 #endif /* not ANSI_DECLARATORS */
15156
15157 #else /* not TRILIBRARY */
15158
15159 #ifdef ANSI_DECLARATORS
15160 void writeneighbors(struct mesh *m, struct behavior *b, char *neighborfilename,
15161 int argc, char **argv)
15162 #else /* not ANSI_DECLARATORS */
15163 void writeneighbors(m, b, neighborfilename, argc, argv)
15164 struct mesh *m;
15165 struct behavior *b;
15166 char *neighborfilename;
15167 int argc;
15168 char **argv;
15169 #endif /* not ANSI_DECLARATORS */
15170
15171 #endif /* not TRILIBRARY */
15172
15173 {
15174 #ifdef TRILIBRARY
15175 int *nlist;
15176 int index;
15177 #else /* not TRILIBRARY */
15178 FILE *outfile;
15179 #endif /* not TRILIBRARY */
15180 struct otri triangleloop, trisym;
15181 long elementnumber;
15182 int neighbor1, neighbor2, neighbor3;
15183 triangle ptr; /* Temporary variable used by sym(). */
15184
15185 #ifdef TRILIBRARY
15186 if (!b->quiet) {
15187 printf("Writing neighbors.\n");
15188 }
15189 /* Allocate memory for neighbors if necessary. */
15190 if (*neighborlist == (int *) NULL) {
15191 *neighborlist = (int *) trimalloc((int) (m->triangles.items * 3 *
15192 sizeof(int)));
15193 }
15194 nlist = *neighborlist;
15195 index = 0;
15196 #else /* not TRILIBRARY */
15197 if (!b->quiet) {
15198 printf("Writing %s.\n", neighborfilename);
15199 }
15200 outfile = fopen(neighborfilename, "w");
15201 if (outfile == (FILE *) NULL) {
15202 printf(" Error: Cannot create file %s.\n", neighborfilename);
15203 triexit(1);
15204 }
15205 /* Number of triangles, three neighbors per triangle. */
15206 fprintf(outfile, "%ld %d\n", m->triangles.items, 3);
15207 #endif /* not TRILIBRARY */
15208
15209 traversalinit(&m->triangles);
15210 triangleloop.tri = triangletraverse(m);
15211 triangleloop.orient = 0;
15212 elementnumber = b->firstnumber;
15213 while (triangleloop.tri != (triangle *) NULL) {
15214 * (int *) (triangleloop.tri + 6) = (int) elementnumber;
15215 triangleloop.tri = triangletraverse(m);
15216 elementnumber++;
15217 }
15218 * (int *) (m->dummytri + 6) = -1;
15219
15220 traversalinit(&m->triangles);
15221 triangleloop.tri = triangletraverse(m);
15222 elementnumber = b->firstnumber;
15223 while (triangleloop.tri != (triangle *) NULL) {
15224 triangleloop.orient = 1;
15225 sym(triangleloop, trisym);
15226 neighbor1 = * (int *) (trisym.tri + 6);
15227 triangleloop.orient = 2;
15228 sym(triangleloop, trisym);
15229 neighbor2 = * (int *) (trisym.tri + 6);
15230 triangleloop.orient = 0;
15231 sym(triangleloop, trisym);
15232 neighbor3 = * (int *) (trisym.tri + 6);
15233 #ifdef TRILIBRARY
15234 nlist[index++] = neighbor1;
15235 nlist[index++] = neighbor2;
15236 nlist[index++] = neighbor3;
15237 #else /* not TRILIBRARY */
15238 /* Triangle number, neighboring triangle numbers. */
15239 fprintf(outfile, "%4ld %d %d %d\n", elementnumber,
15240 neighbor1, neighbor2, neighbor3);
15241 #endif /* not TRILIBRARY */
15242
15243 triangleloop.tri = triangletraverse(m);
15244 elementnumber++;
15245 }
15246
15247 #ifndef TRILIBRARY
15248 finishfile(outfile, argc, argv);
15249 #endif /* not TRILIBRARY */
15250 }
15251
15252 /*****************************************************************************/
15253 /* */
15254 /* writeoff() Write the triangulation to an .off file. */
15255 /* */
15256 /* OFF stands for the Object File Format, a format used by the Geometry */
15257 /* Center's Geomview package. */
15258 /* */
15259 /*****************************************************************************/
15260
15261 #ifndef TRILIBRARY
15262
15263 #ifdef ANSI_DECLARATORS
15264 void writeoff(struct mesh *m, struct behavior *b, char *offfilename,
15265 int argc, char **argv)
15266 #else /* not ANSI_DECLARATORS */
15267 void writeoff(m, b, offfilename, argc, argv)
15268 struct mesh *m;
15269 struct behavior *b;
15270 char *offfilename;
15271 int argc;
15272 char **argv;
15273 #endif /* not ANSI_DECLARATORS */
15274
15275 {
15276 FILE *outfile;
15277 struct otri triangleloop;
15278 vertex vertexloop;
15279 vertex p1, p2, p3;
15280 long outvertices;
15281
15282 if (!b->quiet) {
15283 printf("Writing %s.\n", offfilename);
15284 }
15285
15286 if (b->jettison) {
15287 outvertices = m->vertices.items - m->undeads;
15288 } else {
15289 outvertices = m->vertices.items;
15290 }
15291
15292 outfile = fopen(offfilename, "w");
15293 if (outfile == (FILE *) NULL) {
15294 printf(" Error: Cannot create file %s.\n", offfilename);
15295 triexit(1);
15296 }
15297 /* Number of vertices, triangles, and edges. */
15298 fprintf(outfile, "OFF\n%ld %ld %ld\n", outvertices, m->triangles.items,
15299 m->edges);
15300
15301 /* Write the vertices. */
15302 traversalinit(&m->vertices);
15303 vertexloop = vertextraverse(m);
15304 while (vertexloop != (vertex) NULL) {
15305 if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) {
15306 /* The "0.0" is here because the OFF format uses 3D coordinates. */
15307 fprintf(outfile, " %.17g %.17g %.17g\n", vertexloop[0], vertexloop[1],
15308 0.0);
15309 }
15310 vertexloop = vertextraverse(m);
15311 }
15312
15313 /* Write the triangles. */
15314 traversalinit(&m->triangles);
15315 triangleloop.tri = triangletraverse(m);
15316 triangleloop.orient = 0;
15317 while (triangleloop.tri != (triangle *) NULL) {
15318 org(triangleloop, p1);
15319 dest(triangleloop, p2);
15320 apex(triangleloop, p3);
15321 /* The "3" means a three-vertex polygon. */
15322 fprintf(outfile, " 3 %4d %4d %4d\n", vertexmark(p1) - b->firstnumber,
15323 vertexmark(p2) - b->firstnumber, vertexmark(p3) - b->firstnumber);
15324 triangleloop.tri = triangletraverse(m);
15325 }
15326 finishfile(outfile, argc, argv);
15327 }
15328
15329 #endif /* not TRILIBRARY */
15330
15331 /** **/
15332 /** **/
15333 /********* File I/O routines end here *********/
15334
15335 /*****************************************************************************/
15336 /* */
15337 /* quality_statistics() Print statistics about the quality of the mesh. */
15338 /* */
15339 /*****************************************************************************/
15340
15341 #ifdef ANSI_DECLARATORS
15342 void quality_statistics(struct mesh *m, struct behavior *b)
15343 #else /* not ANSI_DECLARATORS */
15344 void quality_statistics(m, b)
15345 struct mesh *m;
15346 struct behavior *b;
15347 #endif /* not ANSI_DECLARATORS */
15348
15349 {
15350 struct otri triangleloop;
15351 vertex p[3];
15352 REAL cossquaretable[8];
15353 REAL ratiotable[16];
15354 REAL dx[3], dy[3];
15355 REAL edgelength[3];
15356 REAL dotproduct;
15357 REAL cossquare;
15358 REAL triarea;
15359 REAL shortest, longest;
15360 REAL trilongest2;
15361 REAL smallestarea, biggestarea;
15362 REAL triminaltitude2;
15363 REAL minaltitude;
15364 REAL triaspect2;
15365 REAL worstaspect;
15366 REAL smallestangle, biggestangle;
15367 REAL radconst, degconst;
15368 int angletable[18];
15369 int aspecttable[16];
15370 int aspectindex;
15371 int tendegree;
15372 int acutebiggest;
15373 int i, ii, j, k;
15374
15375 printf("Mesh quality statistics:\n\n");
15376 radconst = PI / 18.0;
15377 degconst = 180.0 / PI;
15378 for (i = 0; i < 8; i++) {
15379 cossquaretable[i] = cos(radconst * (REAL) (i + 1));
15380 cossquaretable[i] = cossquaretable[i] * cossquaretable[i];
15381 }
15382 for (i = 0; i < 18; i++) {
15383 angletable[i] = 0;
15384 }
15385
15386 ratiotable[0] = 1.5; ratiotable[1] = 2.0;
15387 ratiotable[2] = 2.5; ratiotable[3] = 3.0;
15388 ratiotable[4] = 4.0; ratiotable[5] = 6.0;
15389 ratiotable[6] = 10.0; ratiotable[7] = 15.0;
15390 ratiotable[8] = 25.0; ratiotable[9] = 50.0;
15391 ratiotable[10] = 100.0; ratiotable[11] = 300.0;
15392 ratiotable[12] = 1000.0; ratiotable[13] = 10000.0;
15393 ratiotable[14] = 100000.0; ratiotable[15] = 0.0;
15394 for (i = 0; i < 16; i++) {
15395 aspecttable[i] = 0;
15396 }
15397
15398 worstaspect = 0.0;
15399 minaltitude = m->xmax - m->xmin + m->ymax - m->ymin;
15400 minaltitude = minaltitude * minaltitude;
15401 shortest = minaltitude;
15402 longest = 0.0;
15403 smallestarea = minaltitude;
15404 biggestarea = 0.0;
15405 worstaspect = 0.0;
15406 smallestangle = 0.0;
15407 biggestangle = 2.0;
15408 acutebiggest = 1;
15409
15410 traversalinit(&m->triangles);
15411 triangleloop.tri = triangletraverse(m);
15412 triangleloop.orient = 0;
15413 while (triangleloop.tri != (triangle *) NULL) {
15414 org(triangleloop, p[0]);
15415 dest(triangleloop, p[1]);
15416 apex(triangleloop, p[2]);
15417 trilongest2 = 0.0;
15418
15419 for (i = 0; i < 3; i++) {
15420 j = plus1mod3[i];
15421 k = minus1mod3[i];
15422 dx[i] = p[j][0] - p[k][0];
15423 dy[i] = p[j][1] - p[k][1];
15424 edgelength[i] = dx[i] * dx[i] + dy[i] * dy[i];
15425 if (edgelength[i] > trilongest2) {
15426 trilongest2 = edgelength[i];
15427 }
15428 if (edgelength[i] > longest) {
15429 longest = edgelength[i];
15430 }
15431 if (edgelength[i] < shortest) {
15432 shortest = edgelength[i];
15433 }
15434 }
15435
15436 triarea = counterclockwise(m, b, p[0], p[1], p[2]);
15437 if (triarea < smallestarea) {
15438 smallestarea = triarea;
15439 }
15440 if (triarea > biggestarea) {
15441 biggestarea = triarea;
15442 }
15443 triminaltitude2 = triarea * triarea / trilongest2;
15444 if (triminaltitude2 < minaltitude) {
15445 minaltitude = triminaltitude2;
15446 }
15447 triaspect2 = trilongest2 / triminaltitude2;
15448 if (triaspect2 > worstaspect) {
15449 worstaspect = triaspect2;
15450 }
15451 aspectindex = 0;
15452 while ((triaspect2 > ratiotable[aspectindex] * ratiotable[aspectindex])
15453 && (aspectindex < 15)) {
15454 aspectindex++;
15455 }
15456 aspecttable[aspectindex]++;
15457
15458 for (i = 0; i < 3; i++) {
15459 j = plus1mod3[i];
15460 k = minus1mod3[i];
15461 dotproduct = dx[j] * dx[k] + dy[j] * dy[k];
15462 cossquare = dotproduct * dotproduct / (edgelength[j] * edgelength[k]);
15463 tendegree = 8;
15464 for (ii = 7; ii >= 0; ii--) {
15465 if (cossquare > cossquaretable[ii]) {
15466 tendegree = ii;
15467 }
15468 }
15469 if (dotproduct <= 0.0) {
15470 angletable[tendegree]++;
15471 if (cossquare > smallestangle) {
15472 smallestangle = cossquare;
15473 }
15474 if (acutebiggest && (cossquare < biggestangle)) {
15475 biggestangle = cossquare;
15476 }
15477 } else {
15478 angletable[17 - tendegree]++;
15479 if (acutebiggest || (cossquare > biggestangle)) {
15480 biggestangle = cossquare;
15481 acutebiggest = 0;
15482 }
15483 }
15484 }
15485 triangleloop.tri = triangletraverse(m);
15486 }
15487
15488 shortest = sqrt(shortest);
15489 longest = sqrt(longest);
15490 minaltitude = sqrt(minaltitude);
15491 worstaspect = sqrt(worstaspect);
15492 smallestarea *= 0.5;
15493 biggestarea *= 0.5;
15494 if (smallestangle >= 1.0) {
15495 smallestangle = 0.0;
15496 } else {
15497 smallestangle = degconst * acos(sqrt(smallestangle));
15498 }
15499 if (biggestangle >= 1.0) {
15500 biggestangle = 180.0;
15501 } else {
15502 if (acutebiggest) {
15503 biggestangle = degconst * acos(sqrt(biggestangle));
15504 } else {
15505 biggestangle = 180.0 - degconst * acos(sqrt(biggestangle));
15506 }
15507 }
15508
15509 printf(" Smallest area: %16.5g | Largest area: %16.5g\n",
15510 smallestarea, biggestarea);
15511 printf(" Shortest edge: %16.5g | Longest edge: %16.5g\n",
15512 shortest, longest);
15513 printf(" Shortest altitude: %12.5g | Largest aspect ratio: %8.5g\n\n",
15514 minaltitude, worstaspect);
15515
15516 printf(" Triangle aspect ratio histogram:\n");
15517 printf(" 1.1547 - %-6.6g : %8d | %6.6g - %-6.6g : %8d\n",
15518 ratiotable[0], aspecttable[0], ratiotable[7], ratiotable[8],
15519 aspecttable[8]);
15520 for (i = 1; i < 7; i++) {
15521 printf(" %6.6g - %-6.6g : %8d | %6.6g - %-6.6g : %8d\n",
15522 ratiotable[i - 1], ratiotable[i], aspecttable[i],
15523 ratiotable[i + 7], ratiotable[i + 8], aspecttable[i + 8]);
15524 }
15525 printf(" %6.6g - %-6.6g : %8d | %6.6g - : %8d\n",
15526 ratiotable[6], ratiotable[7], aspecttable[7], ratiotable[14],
15527 aspecttable[15]);
15528 printf(" (Aspect ratio is longest edge divided by shortest altitude)\n\n");
15529
15530 printf(" Smallest angle: %15.5g | Largest angle: %15.5g\n\n",
15531 smallestangle, biggestangle);
15532
15533 printf(" Angle histogram:\n");
15534 for (i = 0; i < 9; i++) {
15535 printf(" %3d - %3d degrees: %8d | %3d - %3d degrees: %8d\n",
15536 i * 10, i * 10 + 10, angletable[i],
15537 i * 10 + 90, i * 10 + 100, angletable[i + 9]);
15538 }
15539 printf("\n");
15540 }
15541
15542 /*****************************************************************************/
15543 /* */
15544 /* statistics() Print all sorts of cool facts. */
15545 /* */
15546 /*****************************************************************************/
15547
15548 #ifdef ANSI_DECLARATORS
15549 void statistics(struct mesh *m, struct behavior *b)
15550 #else /* not ANSI_DECLARATORS */
15551 void statistics(m, b)
15552 struct mesh *m;
15553 struct behavior *b;
15554 #endif /* not ANSI_DECLARATORS */
15555
15556 {
15557 printf("\nStatistics:\n\n");
15558 printf(" Input vertices: %d\n", m->invertices);
15559 if (b->refine) {
15560 printf(" Input triangles: %d\n", m->inelements);
15561 }
15562 if (b->poly) {
15563 printf(" Input segments: %d\n", m->insegments);
15564 if (!b->refine) {
15565 printf(" Input holes: %d\n", m->holes);
15566 }
15567 }
15568
15569 printf("\n Mesh vertices: %ld\n", m->vertices.items - m->undeads);
15570 printf(" Mesh triangles: %ld\n", m->triangles.items);
15571 printf(" Mesh edges: %ld\n", m->edges);
15572 printf(" Mesh exterior boundary edges: %ld\n", m->hullsize);
15573 if (b->poly || b->refine) {
15574 printf(" Mesh interior boundary edges: %ld\n",
15575 m->subsegs.items - m->hullsize);
15576 printf(" Mesh subsegments (constrained edges): %ld\n",
15577 m->subsegs.items);
15578 }
15579 printf("\n");
15580
15581 if (b->verbose) {
15582 quality_statistics(m, b);
15583 printf("Memory allocation statistics:\n\n");
15584 printf(" Maximum number of vertices: %ld\n", m->vertices.maxitems);
15585 printf(" Maximum number of triangles: %ld\n", m->triangles.maxitems);
15586 if (m->subsegs.maxitems > 0) {
15587 printf(" Maximum number of subsegments: %ld\n", m->subsegs.maxitems);
15588 }
15589 if (m->viri.maxitems > 0) {
15590 printf(" Maximum number of viri: %ld\n", m->viri.maxitems);
15591 }
15592 if (m->badsubsegs.maxitems > 0) {
15593 printf(" Maximum number of encroached subsegments: %ld\n",
15594 m->badsubsegs.maxitems);
15595 }
15596 if (m->badtriangles.maxitems > 0) {
15597 printf(" Maximum number of bad triangles: %ld\n",
15598 m->badtriangles.maxitems);
15599 }
15600 if (m->flipstackers.maxitems > 0) {
15601 printf(" Maximum number of stacked triangle flips: %ld\n",
15602 m->flipstackers.maxitems);
15603 }
15604 if (m->splaynodes.maxitems > 0) {
15605 printf(" Maximum number of splay tree nodes: %ld\n",
15606 m->splaynodes.maxitems);
15607 }
15608 printf(" Approximate heap memory use (bytes): %ld\n\n",
15609 m->vertices.maxitems * m->vertices.itembytes +
15610 m->triangles.maxitems * m->triangles.itembytes +
15611 m->subsegs.maxitems * m->subsegs.itembytes +
15612 m->viri.maxitems * m->viri.itembytes +
15613 m->badsubsegs.maxitems * m->badsubsegs.itembytes +
15614 m->badtriangles.maxitems * m->badtriangles.itembytes +
15615 m->flipstackers.maxitems * m->flipstackers.itembytes +
15616 m->splaynodes.maxitems * m->splaynodes.itembytes);
15617
15618 printf("Algorithmic statistics:\n\n");
15619 if (!b->weighted) {
15620 printf(" Number of incircle tests: %ld\n", m->incirclecount);
15621 } else {
15622 printf(" Number of 3D orientation tests: %ld\n", m->orient3dcount);
15623 }
15624 printf(" Number of 2D orientation tests: %ld\n", m->counterclockcount);
15625 if (m->hyperbolacount > 0) {
15626 printf(" Number of right-of-hyperbola tests: %ld\n",
15627 m->hyperbolacount);
15628 }
15629 if (m->circletopcount > 0) {
15630 printf(" Number of circle top computations: %ld\n",
15631 m->circletopcount);
15632 }
15633 if (m->circumcentercount > 0) {
15634 printf(" Number of triangle circumcenter computations: %ld\n",
15635 m->circumcentercount);
15636 }
15637 printf("\n");
15638 }
15639 }
15640
15641 /*****************************************************************************/
15642 /* */
15643 /* main() or triangulate() Gosh, do everything. */
15644 /* */
15645 /* The sequence is roughly as follows. Many of these steps can be skipped, */
15646 /* depending on the command line switches. */
15647 /* */
15648 /* - Initialize constants and parse the command line. */
15649 /* - Read the vertices from a file and either */
15650 /* - triangulate them (no -r), or */
15651 /* - read an old mesh from files and reconstruct it (-r). */
15652 /* - Insert the PSLG segments (-p), and possibly segments on the convex */
15653 /* hull (-c). */
15654 /* - Read the holes (-p), regional attributes (-pA), and regional area */
15655 /* constraints (-pa). Carve the holes and concavities, and spread the */
15656 /* regional attributes and area constraints. */
15657 /* - Enforce the constraints on minimum angle (-q) and maximum area (-a). */
15658 /* Also enforce the conforming Delaunay property (-q and -a). */
15659 /* - Compute the number of edges in the resulting mesh. */
15660 /* - Promote the mesh's linear triangles to higher order elements (-o). */
15661 /* - Write the output files and print the statistics. */
15662 /* - Check the consistency and Delaunay property of the mesh (-C). */
15663 /* */
15664 /*****************************************************************************/
15665
15666 #ifdef TRILIBRARY
15667
15668 #ifdef ANSI_DECLARATORS
15669 void triangulate(char *triswitches, struct triangulateio *in,
15670 struct triangulateio *out, struct triangulateio *vorout)
15671 #else /* not ANSI_DECLARATORS */
15672 void triangulate(triswitches, in, out, vorout)
15673 char *triswitches;
15674 struct triangulateio *in;
15675 struct triangulateio *out;
15676 struct triangulateio *vorout;
15677 #endif /* not ANSI_DECLARATORS */
15678
15679 #else /* not TRILIBRARY */
15680
15681 #ifdef ANSI_DECLARATORS
15682 int main(int argc, char **argv)
15683 #else /* not ANSI_DECLARATORS */
15684 int main(argc, argv)
15685 int argc;
15686 char **argv;
15687 #endif /* not ANSI_DECLARATORS */
15688
15689 #endif /* not TRILIBRARY */
15690
15691 {
15692 struct mesh m;
15693 struct behavior b;
15694 REAL *holearray; /* Array of holes. */
15695 REAL *regionarray; /* Array of regional attributes and area constraints. */
15696 #ifndef TRILIBRARY
15697 FILE *polyfile;
15698 #endif /* not TRILIBRARY */
15699 #ifndef NO_TIMER
15700 /* Variables for timing the performance of Triangle. The types are */
15701 /* defined in sys/time.h. */
15702 struct timeval tv0, tv1, tv2, tv3, tv4, tv5, tv6;
15703 struct timezone tz;
15704 #endif /* not NO_TIMER */
15705
15706 #ifndef NO_TIMER
15707 gettimeofday(&tv0, &tz);
15708 #endif /* not NO_TIMER */
15709
15710 triangleinit(&m);
15711 #ifdef TRILIBRARY
15712 parsecommandline(1, &triswitches, &b);
15713 #else /* not TRILIBRARY */
15714 parsecommandline(argc, argv, &b);
15715 #endif /* not TRILIBRARY */
15716 m.steinerleft = b.steiner;
15717
15718 #ifdef TRILIBRARY
15719 transfernodes(&m, &b, in->pointlist, in->pointattributelist,
15720 in->pointmarkerlist, in->numberofpoints,
15721 in->numberofpointattributes);
15722 #else /* not TRILIBRARY */
15723 readnodes(&m, &b, b.innodefilename, b.inpolyfilename, &polyfile);
15724 #endif /* not TRILIBRARY */
15725
15726 #ifndef NO_TIMER
15727 if (!b.quiet) {
15728 gettimeofday(&tv1, &tz);
15729 }
15730 #endif /* not NO_TIMER */
15731
15732 #ifdef CDT_ONLY
15733 m.hullsize = delaunay(&m, &b); /* Triangulate the vertices. */
15734 #else /* not CDT_ONLY */
15735 if (b.refine) {
15736 /* Read and reconstruct a mesh. */
15737 #ifdef TRILIBRARY
15738 m.hullsize = reconstruct(&m, &b, in->trianglelist,
15739 in->triangleattributelist, in->trianglearealist,
15740 in->numberoftriangles, in->numberofcorners,
15741 in->numberoftriangleattributes,
15742 in->segmentlist, in->segmentmarkerlist,
15743 in->numberofsegments);
15744 #else /* not TRILIBRARY */
15745 m.hullsize = reconstruct(&m, &b, b.inelefilename, b.areafilename,
15746 b.inpolyfilename, polyfile);
15747 #endif /* not TRILIBRARY */
15748 } else {
15749 m.hullsize = delaunay(&m, &b); /* Triangulate the vertices. */
15750 }
15751 #endif /* not CDT_ONLY */
15752
15753 #ifndef NO_TIMER
15754 if (!b.quiet) {
15755 gettimeofday(&tv2, &tz);
15756 if (b.refine) {
15757 printf("Mesh reconstruction");
15758 } else {
15759 printf("Delaunay");
15760 }
15761 printf(" milliseconds: %ld\n", 1000l * (tv2.tv_sec - tv1.tv_sec) +
15762 (tv2.tv_usec - tv1.tv_usec) / 1000l);
15763 }
15764 #endif /* not NO_TIMER */
15765
15766 /* Ensure that no vertex can be mistaken for a triangular bounding */
15767 /* box vertex in insertvertex(). */
15768 m.infvertex1 = (vertex) NULL;
15769 m.infvertex2 = (vertex) NULL;
15770 m.infvertex3 = (vertex) NULL;
15771
15772 if (b.usesegments) {
15773 m.checksegments = 1; /* Segments will be introduced next. */
15774 if (!b.refine) {
15775 /* Insert PSLG segments and/or convex hull segments. */
15776 #ifdef TRILIBRARY
15777 formskeleton(&m, &b, in->segmentlist,
15778 in->segmentmarkerlist, in->numberofsegments);
15779 #else /* not TRILIBRARY */
15780 formskeleton(&m, &b, polyfile, b.inpolyfilename);
15781 #endif /* not TRILIBRARY */
15782 }
15783 }
15784
15785 #ifndef NO_TIMER
15786 if (!b.quiet) {
15787 gettimeofday(&tv3, &tz);
15788 if (b.usesegments && !b.refine) {
15789 printf("Segment milliseconds: %ld\n",
15790 1000l * (tv3.tv_sec - tv2.tv_sec) +
15791 (tv3.tv_usec - tv2.tv_usec) / 1000l);
15792 }
15793 }
15794 #endif /* not NO_TIMER */
15795
15796 if (b.poly && (m.triangles.items > 0)) {
15797 #ifdef TRILIBRARY
15798 holearray = in->holelist;
15799 m.holes = in->numberofholes;
15800 regionarray = in->regionlist;
15801 m.regions = in->numberofregions;
15802 #else /* not TRILIBRARY */
15803 readholes(&m, &b, polyfile, b.inpolyfilename, &holearray, &m.holes,
15804 ®ionarray, &m.regions);
15805 #endif /* not TRILIBRARY */
15806 if (!b.refine) {
15807 /* Carve out holes and concavities. */
15808 carveholes(&m, &b, holearray, m.holes, regionarray, m.regions);
15809 }
15810 } else {
15811 /* Without a PSLG, there can be no holes or regional attributes */
15812 /* or area constraints. The following are set to zero to avoid */
15813 /* an accidental free() later. */
15814 m.holes = 0;
15815 m.regions = 0;
15816 }
15817
15818 #ifndef NO_TIMER
15819 if (!b.quiet) {
15820 gettimeofday(&tv4, &tz);
15821 if (b.poly && !b.refine) {
15822 printf("Hole milliseconds: %ld\n", 1000l * (tv4.tv_sec - tv3.tv_sec) +
15823 (tv4.tv_usec - tv3.tv_usec) / 1000l);
15824 }
15825 }
15826 #endif /* not NO_TIMER */
15827
15828 #ifndef CDT_ONLY
15829 if (b.quality && (m.triangles.items > 0)) {
15830 enforcequality(&m, &b); /* Enforce angle and area constraints. */
15831 }
15832 #endif /* not CDT_ONLY */
15833
15834 #ifndef NO_TIMER
15835 if (!b.quiet) {
15836 gettimeofday(&tv5, &tz);
15837 #ifndef CDT_ONLY
15838 if (b.quality) {
15839 printf("Quality milliseconds: %ld\n",
15840 1000l * (tv5.tv_sec - tv4.tv_sec) +
15841 (tv5.tv_usec - tv4.tv_usec) / 1000l);
15842 }
15843 #endif /* not CDT_ONLY */
15844 }
15845 #endif /* not NO_TIMER */
15846
15847 /* Calculate the number of edges. */
15848 m.edges = (3l * m.triangles.items + m.hullsize) / 2l;
15849
15850 if (b.order > 1) {
15851 highorder(&m, &b); /* Promote elements to higher polynomial order. */
15852 }
15853 if (!b.quiet) {
15854 printf("\n");
15855 }
15856
15857 #ifdef TRILIBRARY
15858 if (b.jettison) {
15859 out->numberofpoints = m.vertices.items - m.undeads;
15860 } else {
15861 out->numberofpoints = m.vertices.items;
15862 }
15863 out->numberofpointattributes = m.nextras;
15864 out->numberoftriangles = m.triangles.items;
15865 out->numberofcorners = (b.order + 1) * (b.order + 2) / 2;
15866 out->numberoftriangleattributes = m.eextras;
15867 out->numberofedges = m.edges;
15868 if (b.usesegments) {
15869 out->numberofsegments = m.subsegs.items;
15870 } else {
15871 out->numberofsegments = m.hullsize;
15872 }
15873 if (vorout != (struct triangulateio *) NULL) {
15874 vorout->numberofpoints = m.triangles.items;
15875 vorout->numberofpointattributes = m.nextras;
15876 vorout->numberofedges = m.edges;
15877 }
15878 #endif /* TRILIBRARY */
15879 /* If not using iteration numbers, don't write a .node file if one was */
15880 /* read, because the original one would be overwritten! */
15881 if (b.nonodewritten || (b.noiterationnum && m.readnodefile)) {
15882 if (!b.quiet) {
15883 #ifdef TRILIBRARY
15884 printf("NOT writing vertices.\n");
15885 #else /* not TRILIBRARY */
15886 printf("NOT writing a .node file.\n");
15887 #endif /* not TRILIBRARY */
15888 }
15889 numbernodes(&m, &b); /* We must remember to number the vertices. */
15890 } else {
15891 /* writenodes() numbers the vertices too. */
15892 #ifdef TRILIBRARY
15893 writenodes(&m, &b, &out->pointlist, &out->pointattributelist,
15894 &out->pointmarkerlist);
15895 #else /* not TRILIBRARY */
15896 writenodes(&m, &b, b.outnodefilename, argc, argv);
15897 #endif /* TRILIBRARY */
15898 }
15899 if (b.noelewritten) {
15900 if (!b.quiet) {
15901 #ifdef TRILIBRARY
15902 printf("NOT writing triangles.\n");
15903 #else /* not TRILIBRARY */
15904 printf("NOT writing an .ele file.\n");
15905 #endif /* not TRILIBRARY */
15906 }
15907 } else {
15908 #ifdef TRILIBRARY
15909 writeelements(&m, &b, &out->trianglelist, &out->triangleattributelist);
15910 #else /* not TRILIBRARY */
15911 writeelements(&m, &b, b.outelefilename, argc, argv);
15912 #endif /* not TRILIBRARY */
15913 }
15914 /* The -c switch (convex switch) causes a PSLG to be written */
15915 /* even if none was read. */
15916 if (b.poly || b.convex) {
15917 /* If not using iteration numbers, don't overwrite the .poly file. */
15918 if (b.nopolywritten || b.noiterationnum) {
15919 if (!b.quiet) {
15920 #ifdef TRILIBRARY
15921 printf("NOT writing segments.\n");
15922 #else /* not TRILIBRARY */
15923 printf("NOT writing a .poly file.\n");
15924 #endif /* not TRILIBRARY */
15925 }
15926 } else {
15927 #ifdef TRILIBRARY
15928 writepoly(&m, &b, &out->segmentlist, &out->segmentmarkerlist);
15929 out->numberofholes = m.holes;
15930 out->numberofregions = m.regions;
15931 if (b.poly) {
15932 out->holelist = in->holelist;
15933 out->regionlist = in->regionlist;
15934 } else {
15935 out->holelist = (REAL *) NULL;
15936 out->regionlist = (REAL *) NULL;
15937 }
15938 #else /* not TRILIBRARY */
15939 writepoly(&m, &b, b.outpolyfilename, holearray, m.holes, regionarray,
15940 m.regions, argc, argv);
15941 #endif /* not TRILIBRARY */
15942 }
15943 }
15944 #ifndef TRILIBRARY
15945 #ifndef CDT_ONLY
15946 if (m.regions > 0) {
15947 trifree((VOID *) regionarray);
15948 }
15949 #endif /* not CDT_ONLY */
15950 if (m.holes > 0) {
15951 trifree((VOID *) holearray);
15952 }
15953 if (b.geomview) {
15954 writeoff(&m, &b, b.offfilename, argc, argv);
15955 }
15956 #endif /* not TRILIBRARY */
15957 if (b.edgesout) {
15958 #ifdef TRILIBRARY
15959 writeedges(&m, &b, &out->edgelist, &out->edgemarkerlist);
15960 #else /* not TRILIBRARY */
15961 writeedges(&m, &b, b.edgefilename, argc, argv);
15962 #endif /* not TRILIBRARY */
15963 }
15964 if (b.voronoi) {
15965 #ifdef TRILIBRARY
15966 writevoronoi(&m, &b, &vorout->pointlist, &vorout->pointattributelist,
15967 &vorout->pointmarkerlist, &vorout->edgelist,
15968 &vorout->edgemarkerlist, &vorout->normlist);
15969 #else /* not TRILIBRARY */
15970 writevoronoi(&m, &b, b.vnodefilename, b.vedgefilename, argc, argv);
15971 #endif /* not TRILIBRARY */
15972 }
15973 if (b.neighbors) {
15974 #ifdef TRILIBRARY
15975 writeneighbors(&m, &b, &out->neighborlist);
15976 #else /* not TRILIBRARY */
15977 writeneighbors(&m, &b, b.neighborfilename, argc, argv);
15978 #endif /* not TRILIBRARY */
15979 }
15980
15981 if (!b.quiet) {
15982 #ifndef NO_TIMER
15983 gettimeofday(&tv6, &tz);
15984 printf("\nOutput milliseconds: %ld\n",
15985 1000l * (tv6.tv_sec - tv5.tv_sec) +
15986 (tv6.tv_usec - tv5.tv_usec) / 1000l);
15987 printf("Total running milliseconds: %ld\n",
15988 1000l * (tv6.tv_sec - tv0.tv_sec) +
15989 (tv6.tv_usec - tv0.tv_usec) / 1000l);
15990 #endif /* not NO_TIMER */
15991
15992 statistics(&m, &b);
15993 }
15994
15995 #ifndef REDUCED
15996 if (b.docheck) {
15997 checkmesh(&m, &b);
15998 checkdelaunay(&m, &b);
15999 }
16000 #endif /* not REDUCED */
16001
16002 triangledeinit(&m, &b);
16003 #ifndef TRILIBRARY
16004 return 0;
16005 #endif /* not TRILIBRARY */
16006 }
16007