1 /*
2 * Modifed Triangle - this version has been altered for compatibility
3 * with libMesh non-double precision options.
4 */
5
6
7 /*****************************************************************************/
8 /* */
9 /* 888888888 ,o, / 888 */
10 /* 888 88o88o " o8888o 88o8888o o88888o 888 o88888o */
11 /* 888 888 888 88b 888 888 888 888 888 d888 88b */
12 /* 888 888 888 o88^o888 888 888 "88888" 888 8888oo888 */
13 /* 888 888 888 C888 888 888 888 / 888 q888 */
14 /* 888 888 888 "88o^888 888 888 Cb 888 "88oooo" */
15 /* "8oo8D */
16 /* */
17 /* A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator. */
18 /* (triangle.c) */
19 /* */
20 /* Version 1.6 */
21 /* July 28, 2005 */
22 /* */
23 /* Copyright 1993, 1995, 1997, 1998, 2002, 2005 */
24 /* Jonathan Richard Shewchuk */
25 /* 2360 Woolsey #H */
26 /* Berkeley, California 94705-1927 */
27 /* jrs@cs.berkeley.edu */
28 /* */
29 /* This program may be freely redistributed under the condition that the */
30 /* copyright notices (including this entire header and the copyright */
31 /* notice printed when the `-h' switch is selected) are not removed, and */
32 /* no compensation is received. Private, research, and institutional */
33 /* use is free. You may distribute modified versions of this code UNDER */
34 /* THE CONDITION THAT THIS CODE AND ANY MODIFICATIONS MADE TO IT IN THE */
35 /* SAME FILE REMAIN UNDER COPYRIGHT OF THE ORIGINAL AUTHOR, BOTH SOURCE */
36 /* AND OBJECT CODE ARE MADE FREELY AVAILABLE WITHOUT CHARGE, AND CLEAR */
37 /* NOTICE IS GIVEN OF THE MODIFICATIONS. Distribution of this code as */
38 /* part of a commercial system is permissible ONLY BY DIRECT ARRANGEMENT */
39 /* WITH THE AUTHOR. (If you are not directly supplying this code to a */
40 /* customer, and you are instead telling them how they can obtain it for */
41 /* free, then you are not required to make any arrangement with me.) */
42 /* */
43 /* Hypertext instructions for Triangle are available on the Web at */
44 /* */
45 /* http://www.cs.cmu.edu/~quake/triangle.html */
46 /* */
47 /* Disclaimer: Neither I nor Carnegie Mellon warrant this code in any way */
48 /* whatsoever. This code is provided "as-is". Use at your own risk. */
49 /* */
50 /* Some of the references listed below are marked with an asterisk. [*] */
51 /* These references are available for downloading from the Web page */
52 /* */
53 /* http://www.cs.cmu.edu/~quake/triangle.research.html */
54 /* */
55 /* Three papers discussing aspects of Triangle are available. A short */
56 /* overview appears in "Triangle: Engineering a 2D Quality Mesh */
57 /* Generator and Delaunay Triangulator," in Applied Computational */
58 /* Geometry: Towards Geometric Engineering, Ming C. Lin and Dinesh */
59 /* Manocha, editors, Lecture Notes in Computer Science volume 1148, */
60 /* pages 203-222, Springer-Verlag, Berlin, May 1996 (from the First ACM */
61 /* Workshop on Applied Computational Geometry). [*] */
62 /* */
63 /* The algorithms are discussed in the greatest detail in "Delaunay */
64 /* Refinement Algorithms for Triangular Mesh Generation," Computational */
65 /* Geometry: Theory and Applications 22(1-3):21-74, May 2002. [*] */
66 /* */
67 /* More detail about the data structures may be found in my dissertation: */
68 /* "Delaunay Refinement Mesh Generation," Ph.D. thesis, Technical Report */
69 /* CMU-CS-97-137, School of Computer Science, Carnegie Mellon University, */
70 /* Pittsburgh, Pennsylvania, 18 May 1997. [*] */
71 /* */
72 /* Triangle was created as part of the Quake Project in the School of */
73 /* Computer Science at Carnegie Mellon University. For further */
74 /* information, see Hesheng Bao, Jacobo Bielak, Omar Ghattas, Loukas F. */
75 /* Kallivokas, David R. O'Hallaron, Jonathan R. Shewchuk, and Jifeng Xu, */
76 /* "Large-scale Simulation of Elastic Wave Propagation in Heterogeneous */
77 /* Media on Parallel Computers," Computer Methods in Applied Mechanics */
78 /* and Engineering 152(1-2):85-102, 22 January 1998. */
79 /* */
80 /* Triangle's Delaunay refinement algorithm for quality mesh generation is */
81 /* a hybrid of one due to Jim Ruppert, "A Delaunay Refinement Algorithm */
82 /* for Quality 2-Dimensional Mesh Generation," Journal of Algorithms */
83 /* 18(3):548-585, May 1995 [*], and one due to L. Paul Chew, "Guaranteed- */
84 /* Quality Mesh Generation for Curved Surfaces," Proceedings of the Ninth */
85 /* Annual Symposium on Computational Geometry (San Diego, California), */
86 /* pages 274-280, Association for Computing Machinery, May 1993, */
87 /* http://portal.acm.org/citation.cfm?id=161150 . */
88 /* */
89 /* The Delaunay refinement algorithm has been modified so that it meshes */
90 /* domains with small input angles well, as described in Gary L. Miller, */
91 /* Steven E. Pav, and Noel J. Walkington, "When and Why Ruppert's */
92 /* Algorithm Works," Twelfth International Meshing Roundtable, pages */
93 /* 91-102, Sandia National Laboratories, September 2003. [*] */
94 /* */
95 /* My implementation of the divide-and-conquer and incremental Delaunay */
96 /* triangulation algorithms follows closely the presentation of Guibas */
97 /* and Stolfi, even though I use a triangle-based data structure instead */
98 /* of their quad-edge data structure. (In fact, I originally implemented */
99 /* Triangle using the quad-edge data structure, but the switch to a */
100 /* triangle-based data structure sped Triangle by a factor of two.) The */
101 /* mesh manipulation primitives and the two aforementioned Delaunay */
102 /* triangulation algorithms are described by Leonidas J. Guibas and Jorge */
103 /* Stolfi, "Primitives for the Manipulation of General Subdivisions and */
104 /* the Computation of Voronoi Diagrams," ACM Transactions on Graphics */
105 /* 4(2):74-123, April 1985, http://portal.acm.org/citation.cfm?id=282923 .*/
106 /* */
107 /* Their O(n log n) divide-and-conquer algorithm is adapted from Der-Tsai */
108 /* Lee and Bruce J. Schachter, "Two Algorithms for Constructing the */
109 /* Delaunay Triangulation," International Journal of Computer and */
110 /* Information Science 9(3):219-242, 1980. Triangle's improvement of the */
111 /* divide-and-conquer algorithm by alternating between vertical and */
112 /* horizontal cuts was introduced by Rex A. Dwyer, "A Faster Divide-and- */
113 /* Conquer Algorithm for Constructing Delaunay Triangulations," */
114 /* Algorithmica 2(2):137-151, 1987. */
115 /* */
116 /* The incremental insertion algorithm was first proposed by C. L. Lawson, */
117 /* "Software for C1 Surface Interpolation," in Mathematical Software III, */
118 /* John R. Rice, editor, Academic Press, New York, pp. 161-194, 1977. */
119 /* For point location, I use the algorithm of Ernst P. Mucke, Isaac */
120 /* Saias, and Binhai Zhu, "Fast Randomized Point Location Without */
121 /* Preprocessing in Two- and Three-Dimensional Delaunay Triangulations," */
122 /* Proceedings of the Twelfth Annual Symposium on Computational Geometry, */
123 /* ACM, May 1996. [*] If I were to randomize the order of vertex */
124 /* insertion (I currently don't bother), their result combined with the */
125 /* result of Kenneth L. Clarkson and Peter W. Shor, "Applications of */
126 /* Random Sampling in Computational Geometry II," Discrete & */
127 /* Computational Geometry 4(1):387-421, 1989, would yield an expected */
128 /* O(n^{4/3}) bound on running time. */
129 /* */
130 /* The O(n log n) sweepline Delaunay triangulation algorithm is taken from */
131 /* Steven Fortune, "A Sweepline Algorithm for Voronoi Diagrams", */
132 /* Algorithmica 2(2):153-174, 1987. A random sample of edges on the */
133 /* boundary of the triangulation are maintained in a splay tree for the */
134 /* purpose of point location. Splay trees are described by Daniel */
135 /* Dominic Sleator and Robert Endre Tarjan, "Self-Adjusting Binary Search */
136 /* Trees," Journal of the ACM 32(3):652-686, July 1985, */
137 /* http://portal.acm.org/citation.cfm?id=3835 . */
138 /* */
139 /* The algorithms for exact computation of the signs of determinants are */
140 /* described in Jonathan Richard Shewchuk, "Adaptive Precision Floating- */
141 /* Point Arithmetic and Fast Robust Geometric Predicates," Discrete & */
142 /* Computational Geometry 18(3):305-363, October 1997. (Also available */
143 /* as Technical Report CMU-CS-96-140, School of Computer Science, */
144 /* Carnegie Mellon University, Pittsburgh, Pennsylvania, May 1996.) [*] */
145 /* An abbreviated version appears as Jonathan Richard Shewchuk, "Robust */
146 /* Adaptive Floating-Point Geometric Predicates," Proceedings of the */
147 /* Twelfth Annual Symposium on Computational Geometry, ACM, May 1996. [*] */
148 /* Many of the ideas for my exact arithmetic routines originate with */
149 /* Douglas M. Priest, "Algorithms for Arbitrary Precision Floating Point */
150 /* Arithmetic," Tenth Symposium on Computer Arithmetic, pp. 132-143, IEEE */
151 /* Computer Society Press, 1991. [*] Many of the ideas for the correct */
152 /* evaluation of the signs of determinants are taken from Steven Fortune */
153 /* and Christopher J. Van Wyk, "Efficient Exact Arithmetic for Computa- */
154 /* tional Geometry," Proceedings of the Ninth Annual Symposium on */
155 /* Computational Geometry, ACM, pp. 163-172, May 1993, and from Steven */
156 /* Fortune, "Numerical Stability of Algorithms for 2D Delaunay Triangu- */
157 /* lations," International Journal of Computational Geometry & Applica- */
158 /* tions 5(1-2):193-213, March-June 1995. */
159 /* */
160 /* The method of inserting new vertices off-center (not precisely at the */
161 /* circumcenter of every poor-quality triangle) is from Alper Ungor, */
162 /* "Off-centers: A New Type of Steiner Points for Computing Size-Optimal */
163 /* Quality-Guaranteed Delaunay Triangulations," Proceedings of LATIN */
164 /* 2004 (Buenos Aires, Argentina), April 2004. */
165 /* */
166 /* For definitions of and results involving Delaunay triangulations, */
167 /* constrained and conforming versions thereof, and other aspects of */
168 /* triangular mesh generation, see the excellent survey by Marshall Bern */
169 /* and David Eppstein, "Mesh Generation and Optimal Triangulation," in */
170 /* Computing and Euclidean Geometry, Ding-Zhu Du and Frank Hwang, */
171 /* editors, World Scientific, Singapore, pp. 23-90, 1992. [*] */
172 /* */
173 /* The time for incrementally adding PSLG (planar straight line graph) */
174 /* segments to create a constrained Delaunay triangulation is probably */
175 /* O(t^2) per segment in the worst case and O(t) per segment in the */
176 /* common case, where t is the number of triangles that intersect the */
177 /* segment before it is inserted. This doesn't count point location, */
178 /* which can be much more expensive. I could improve this to O(d log d) */
179 /* time, but d is usually quite small, so it's not worth the bother. */
180 /* (This note does not apply when the -s switch is used, invoking a */
181 /* different method is used to insert segments.) */
182 /* */
183 /* The time for deleting a vertex from a Delaunay triangulation is O(d^2) */
184 /* in the worst case and O(d) in the common case, where d is the degree */
185 /* of the vertex being deleted. I could improve this to O(d log d) time, */
186 /* but d is usually quite small, so it's not worth the bother. */
187 /* */
188 /* Ruppert's Delaunay refinement algorithm typically generates triangles */
189 /* at a linear rate (constant time per triangle) after the initial */
190 /* triangulation is formed. There may be pathological cases where */
191 /* quadratic time is required, but these never arise in practice. */
192 /* */
193 /* The geometric predicates (circumcenter calculations, segment */
194 /* intersection formulae, etc.) appear in my "Lecture Notes on Geometric */
195 /* Robustness" at http://www.cs.berkeley.edu/~jrs/mesh . */
196 /* */
197 /* If you make any improvements to this code, please please please let me */
198 /* know, so that I may obtain the improvements. Even if you don't change */
199 /* the code, I'd still love to hear what it's being used for. */
200 /* */
201 /*****************************************************************************/
202
203 /* For single precision (which will save some memory and reduce paging), */
204 /* define the symbol SINGLE by using the -DSINGLE compiler switch or by */
205 /* writing "#define SINGLE" below. */
206 /* */
207 /* For double precision (which will allow you to refine meshes to a smaller */
208 /* edge length), leave SINGLE undefined. */
209 /* */
210 /* Double precision uses more memory, but improves the resolution of the */
211 /* meshes you can generate with Triangle. It also reduces the likelihood */
212 /* of a floating exception due to overflow. Finally, it is much faster */
213 /* than single precision on 64-bit architectures like the DEC Alpha. I */
214 /* recommend double precision unless you want to generate a mesh for which */
215 /* you do not have enough memory. */
216
217 /* #define SINGLE */
218
219 /* #ifdef SINGLE */
220 /* #define REAL float */
221 /* #else */ /* not SINGLE */
222 /* #define REAL double */
223 /* #endif */ /* not SINGLE */
224
225 /* Use libMesh-defined precision */
226 #include "libmesh/libmesh_config.h"
227 typedef LIBMESH_DEFAULT_SCALAR_TYPE REAL;
228
229 /* If yours is not a Unix system, define the NO_TIMER compiler switch to */
230 /* remove the Unix-specific timing code. */
231
232 /* #define NO_TIMER */
233
234 /* To insert lots of self-checks for internal errors, define the SELF_CHECK */
235 /* symbol. This will slow down the program significantly. It is best to */
236 /* define the symbol using the -DSELF_CHECK compiler switch, but you could */
237 /* write "#define SELF_CHECK" below. If you are modifying this code, I */
238 /* recommend you turn self-checks on until your work is debugged. */
239
240 /* #define SELF_CHECK */
241
242 /* To compile Triangle as a callable object library (triangle.o), define the */
243 /* TRILIBRARY symbol. Read the file triangle.h for details on how to call */
244 /* the procedure triangulate() that results. */
245
246 /* #define TRILIBRARY */
247
248 /* It is possible to generate a smaller version of Triangle using one or */
249 /* both of the following symbols. Define the REDUCED symbol to eliminate */
250 /* all features that are primarily of research interest; specifically, the */
251 /* -i, -F, -s, and -C switches. Define the CDT_ONLY symbol to eliminate */
252 /* all meshing algorithms above and beyond constrained Delaunay */
253 /* triangulation; specifically, the -r, -q, -a, -u, -D, -S, and -s */
254 /* switches. These reductions are most likely to be useful when */
255 /* generating an object library (triangle.o) by defining the TRILIBRARY */
256 /* symbol. */
257
258 /* #define REDUCED */
259 /* #define CDT_ONLY */
260
261 /* On some machines, my exact arithmetic routines might be defeated by the */
262 /* use of internal extended precision floating-point registers. The best */
263 /* way to solve this problem is to set the floating-point registers to use */
264 /* single or double precision internally. On 80x86 processors, this may */
265 /* be accomplished by setting the CPU86 symbol for the Microsoft C */
266 /* compiler, or the LINUX symbol for the gcc compiler running on Linux. */
267 /* */
268 /* An inferior solution is to declare certain values as `volatile', thus */
269 /* forcing them to be stored to memory and rounded off. Unfortunately, */
270 /* this solution might slow Triangle down quite a bit. To use volatile */
271 /* values, write "#define INEXACT volatile" below. Normally, however, */
272 /* INEXACT should be defined to be nothing. ("#define INEXACT".) */
273 /* */
274 /* For more discussion, see http://www.cs.cmu.edu/~quake/robust.pc.html . */
275 /* For yet more discussion, see Section 5 of my paper, "Adaptive Precision */
276 /* Floating-Point Arithmetic and Fast Robust Geometric Predicates" (also */
277 /* available as Section 6.6 of my dissertation). */
278
279 /* #define CPU86 */
280 /* #define LINUX */
281
282 #define INEXACT /* Nothing */
283 /* #define INEXACT volatile */
284
285 /* Maximum number of characters in a file name (including the null). */
286
287 #define FILENAMESIZE 2048
288
289 /* Maximum number of characters in a line read from a file (including the */
290 /* null). */
291
292 #define INPUTLINESIZE 1024
293
294 /* For efficiency, a variety of data structures are allocated in bulk. The */
295 /* following constants determine how many of each structure is allocated */
296 /* at once. */
297
298 #define TRIPERBLOCK 4092 /* Number of triangles allocated at once. */
299 #define SUBSEGPERBLOCK 508 /* Number of subsegments allocated at once. */
300 #define VERTEXPERBLOCK 4092 /* Number of vertices allocated at once. */
301 #define VIRUSPERBLOCK 1020 /* Number of virus triangles allocated at once. */
302 /* Number of encroached subsegments allocated at once. */
303 #define BADSUBSEGPERBLOCK 252
304 /* Number of skinny triangles allocated at once. */
305 #define BADTRIPERBLOCK 4092
306 /* Number of flipped triangles allocated at once. */
307 #define FLIPSTACKERPERBLOCK 252
308 /* Number of splay tree nodes allocated at once. */
309 #define SPLAYNODEPERBLOCK 508
310
311 /* The vertex types. A DEADVERTEX has been deleted entirely. An */
312 /* UNDEADVERTEX is not part of the mesh, but is written to the output */
313 /* .node file and affects the node indexing in the other output files. */
314
315 #define INPUTVERTEX 0
316 #define SEGMENTVERTEX 1
317 #define FREEVERTEX 2
318 #define DEADVERTEX -32768
319 #define UNDEADVERTEX -32767
320
321 /* The next line is used to outsmart some very stupid compilers. If your */
322 /* compiler is smarter, feel free to replace the "int" with "void". */
323 /* Not that it matters. */
324
325 #define VOID int
326
327 /* Two constants for algorithms based on random sampling. Both constants */
328 /* have been chosen empirically to optimize their respective algorithms. */
329
330 /* Used for the point location scheme of Mucke, Saias, and Zhu, to decide */
331 /* how large a random sample of triangles to inspect. */
332
333 #define SAMPLEFACTOR 11
334
335 /* Used in Fortune's sweepline Delaunay algorithm to determine what fraction */
336 /* of boundary edges should be maintained in the splay tree for point */
337 /* location on the front. */
338
339 #define SAMPLERATE 10
340
341 /* A number that speaks for itself, every kissable digit. */
342
343 #define PI 3.141592653589793238462643383279502884197169399375105820974944592308
344
345 /* Another fave. */
346
347 #define SQUAREROOTTWO 1.4142135623730950488016887242096980785696718753769480732
348
349 /* And here's one for those of you who are intimidated by math. */
350
351 #define ONETHIRD 0.333333333333333333333333333333333333333333333333333333333333
352
353 #include <stdio.h>
354 #include <stdlib.h>
355 #include <string.h>
356 #include <math.h>
357 #ifndef NO_TIMER
358 #include <sys/time.h>
359 #endif /* not NO_TIMER */
360 #ifdef CPU86
361 #include <float.h>
362 #endif /* CPU86 */
363 #ifdef LINUX
364 #include <fpu_control.h>
365 #endif /* LINUX */
366 #ifdef TRILIBRARY
367 #include "triangle.h"
368 #endif /* TRILIBRARY */
369
370 /* A few forward declarations. */
371
372 #ifndef TRILIBRARY
373 char *readline();
374 char *findfield();
375 #endif /* not TRILIBRARY */
376
377 /* Labels that signify the result of point location. The result of a */
378 /* search indicates that the point falls in the interior of a triangle, on */
379 /* an edge, on a vertex, or outside the mesh. */
380
381 enum locateresult {INTRIANGLE, ONEDGE, ONVERTEX, OUTSIDE};
382
383 /* Labels that signify the result of vertex insertion. The result indicates */
384 /* that the vertex was inserted with complete success, was inserted but */
385 /* encroaches upon a subsegment, was not inserted because it lies on a */
386 /* segment, or was not inserted because another vertex occupies the same */
387 /* location. */
388
389 enum insertvertexresult {SUCCESSFULVERTEX, ENCROACHINGVERTEX, VIOLATINGVERTEX,
390 DUPLICATEVERTEX};
391
392 /* Labels that signify the result of direction finding. The result */
393 /* indicates that a segment connecting the two query points falls within */
394 /* the direction triangle, along the left edge of the direction triangle, */
395 /* or along the right edge of the direction triangle. */
396
397 enum finddirectionresult {WITHIN, LEFTCOLLINEAR, RIGHTCOLLINEAR};
398
399 /*****************************************************************************/
400 /* */
401 /* The basic mesh data structures */
402 /* */
403 /* There are three: vertices, triangles, and subsegments (abbreviated */
404 /* `subseg'). These three data structures, linked by pointers, comprise */
405 /* the mesh. A vertex simply represents a mesh vertex and its properties. */
406 /* A triangle is a triangle. A subsegment is a special data structure used */
407 /* to represent an impenetrable edge of the mesh (perhaps on the outer */
408 /* boundary, on the boundary of a hole, or part of an internal boundary */
409 /* separating two triangulated regions). Subsegments represent boundaries, */
410 /* defined by the user, that triangles may not lie across. */
411 /* */
412 /* A triangle consists of a list of three vertices, a list of three */
413 /* adjoining triangles, a list of three adjoining subsegments (when */
414 /* segments exist), an arbitrary number of optional user-defined */
415 /* floating-point attributes, and an optional area constraint. The latter */
416 /* is an upper bound on the permissible area of each triangle in a region, */
417 /* used for mesh refinement. */
418 /* */
419 /* For a triangle on a boundary of the mesh, some or all of the neighboring */
420 /* triangles may not be present. For a triangle in the interior of the */
421 /* mesh, often no neighboring subsegments are present. Such absent */
422 /* triangles and subsegments are never represented by NULL pointers; they */
423 /* are represented by two special records: `dummytri', the triangle that */
424 /* fills "outer space", and `dummysub', the omnipresent subsegment. */
425 /* `dummytri' and `dummysub' are used for several reasons; for instance, */
426 /* they can be dereferenced and their contents examined without violating */
427 /* protected memory. */
428 /* */
429 /* However, it is important to understand that a triangle includes other */
430 /* information as well. The pointers to adjoining vertices, triangles, and */
431 /* subsegments are ordered in a way that indicates their geometric relation */
432 /* to each other. Furthermore, each of these pointers contains orientation */
433 /* information. Each pointer to an adjoining triangle indicates which face */
434 /* of that triangle is contacted. Similarly, each pointer to an adjoining */
435 /* subsegment indicates which side of that subsegment is contacted, and how */
436 /* the subsegment is oriented relative to the triangle. */
437 /* */
438 /* The data structure representing a subsegment may be thought to be */
439 /* abutting the edge of one or two triangle data structures: either */
440 /* sandwiched between two triangles, or resting against one triangle on an */
441 /* exterior boundary or hole boundary. */
442 /* */
443 /* A subsegment consists of a list of four vertices--the vertices of the */
444 /* subsegment, and the vertices of the segment it is a part of--a list of */
445 /* two adjoining subsegments, and a list of two adjoining triangles. One */
446 /* of the two adjoining triangles may not be present (though there should */
447 /* always be one), and neighboring subsegments might not be present. */
448 /* Subsegments also store a user-defined integer "boundary marker". */
449 /* Typically, this integer is used to indicate what boundary conditions are */
450 /* to be applied at that location in a finite element simulation. */
451 /* */
452 /* Like triangles, subsegments maintain information about the relative */
453 /* orientation of neighboring objects. */
454 /* */
455 /* Vertices are relatively simple. A vertex is a list of floating-point */
456 /* numbers, starting with the x, and y coordinates, followed by an */
457 /* arbitrary number of optional user-defined floating-point attributes, */
458 /* followed by an integer boundary marker. During the segment insertion */
459 /* phase, there is also a pointer from each vertex to a triangle that may */
460 /* contain it. Each pointer is not always correct, but when one is, it */
461 /* speeds up segment insertion. These pointers are assigned values once */
462 /* at the beginning of the segment insertion phase, and are not used or */
463 /* updated except during this phase. Edge flipping during segment */
464 /* insertion will render some of them incorrect. Hence, don't rely upon */
465 /* them for anything. */
466 /* */
467 /* Other than the exception mentioned above, vertices have no information */
468 /* about what triangles, subfacets, or subsegments they are linked to. */
469 /* */
470 /*****************************************************************************/
471
472 /*****************************************************************************/
473 /* */
474 /* Handles */
475 /* */
476 /* The oriented triangle (`otri') and oriented subsegment (`osub') data */
477 /* structures defined below do not themselves store any part of the mesh. */
478 /* The mesh itself is made of `triangle's, `subseg's, and `vertex's. */
479 /* */
480 /* Oriented triangles and oriented subsegments will usually be referred to */
481 /* as "handles." A handle is essentially a pointer into the mesh; it */
482 /* allows you to "hold" one particular part of the mesh. Handles are used */
483 /* to specify the regions in which one is traversing and modifying the mesh.*/
484 /* A single `triangle' may be held by many handles, or none at all. (The */
485 /* latter case is not a memory leak, because the triangle is still */
486 /* connected to other triangles in the mesh.) */
487 /* */
488 /* An `otri' is a handle that holds a triangle. It holds a specific edge */
489 /* of the triangle. An `osub' is a handle that holds a subsegment. It */
490 /* holds either the left or right side of the subsegment. */
491 /* */
492 /* Navigation about the mesh is accomplished through a set of mesh */
493 /* manipulation primitives, further below. Many of these primitives take */
494 /* a handle and produce a new handle that holds the mesh near the first */
495 /* handle. Other primitives take two handles and glue the corresponding */
496 /* parts of the mesh together. The orientation of the handles is */
497 /* important. For instance, when two triangles are glued together by the */
498 /* bond() primitive, they are glued at the edges on which the handles lie. */
499 /* */
500 /* Because vertices have no information about which triangles they are */
501 /* attached to, I commonly represent a vertex by use of a handle whose */
502 /* origin is the vertex. A single handle can simultaneously represent a */
503 /* triangle, an edge, and a vertex. */
504 /* */
505 /*****************************************************************************/
506
507 /* The triangle data structure. Each triangle contains three pointers to */
508 /* adjoining triangles, plus three pointers to vertices, plus three */
509 /* pointers to subsegments (declared below; these pointers are usually */
510 /* `dummysub'). It may or may not also contain user-defined attributes */
511 /* and/or a floating-point "area constraint." It may also contain extra */
512 /* pointers for nodes, when the user asks for high-order elements. */
513 /* Because the size and structure of a `triangle' is not decided until */
514 /* runtime, I haven't simply declared the type `triangle' as a struct. */
515
516 typedef REAL **triangle; /* Really: typedef triangle *triangle */
517
518 /* An oriented triangle: includes a pointer to a triangle and orientation. */
519 /* The orientation denotes an edge of the triangle. Hence, there are */
520 /* three possible orientations. By convention, each edge always points */
521 /* counterclockwise about the corresponding triangle. */
522
523 struct otri {
524 triangle *tri;
525 int orient; /* Ranges from 0 to 2. */
526 };
527
528 /* The subsegment data structure. Each subsegment contains two pointers to */
529 /* adjoining subsegments, plus four pointers to vertices, plus two */
530 /* pointers to adjoining triangles, plus one boundary marker, plus one */
531 /* segment number. */
532
533 typedef REAL **subseg; /* Really: typedef subseg *subseg */
534
535 /* An oriented subsegment: includes a pointer to a subsegment and an */
536 /* orientation. The orientation denotes a side of the edge. Hence, there */
537 /* are two possible orientations. By convention, the edge is always */
538 /* directed so that the "side" denoted is the right side of the edge. */
539
540 struct osub {
541 subseg *ss;
542 int ssorient; /* Ranges from 0 to 1. */
543 };
544
545 /* The vertex data structure. Each vertex is actually an array of REALs. */
546 /* The number of REALs is unknown until runtime. An integer boundary */
547 /* marker, and sometimes a pointer to a triangle, is appended after the */
548 /* REALs. */
549
550 typedef REAL *vertex;
551
552 /* A queue used to store encroached subsegments. Each subsegment's vertices */
553 /* are stored so that we can check whether a subsegment is still the same. */
554
555 struct badsubseg {
556 subseg encsubseg; /* An encroached subsegment. */
557 vertex subsegorg, subsegdest; /* Its two vertices. */
558 };
559
560 /* A queue used to store bad triangles. The key is the square of the cosine */
561 /* of the smallest angle of the triangle. Each triangle's vertices are */
562 /* stored so that one can check whether a triangle is still the same. */
563
564 struct badtriang {
565 triangle poortri; /* A skinny or too-large triangle. */
566 REAL key; /* cos^2 of smallest (apical) angle. */
567 vertex triangorg, triangdest, triangapex; /* Its three vertices. */
568 struct badtriang *nexttriang; /* Pointer to next bad triangle. */
569 };
570
571 /* A stack of triangles flipped during the most recent vertex insertion. */
572 /* The stack is used to undo the vertex insertion if the vertex encroaches */
573 /* upon a subsegment. */
574
575 struct flipstacker {
576 triangle flippedtri; /* A recently flipped triangle. */
577 struct flipstacker *prevflip; /* Previous flip in the stack. */
578 };
579
580 /* A node in a heap used to store events for the sweepline Delaunay */
581 /* algorithm. Nodes do not point directly to their parents or children in */
582 /* the heap. Instead, each node knows its position in the heap, and can */
583 /* look up its parent and children in a separate array. The `eventptr' */
584 /* points either to a `vertex' or to a triangle (in encoded format, so */
585 /* that an orientation is included). In the latter case, the origin of */
586 /* the oriented triangle is the apex of a "circle event" of the sweepline */
587 /* algorithm. To distinguish site events from circle events, all circle */
588 /* events are given an invalid (smaller than `xmin') x-coordinate `xkey'. */
589
590 struct event {
591 REAL xkey, ykey; /* Coordinates of the event. */
592 VOID *eventptr; /* Can be a vertex or the location of a circle event. */
593 int heapposition; /* Marks this event's position in the heap. */
594 };
595
596 /* A node in the splay tree. Each node holds an oriented ghost triangle */
597 /* that represents a boundary edge of the growing triangulation. When a */
598 /* circle event covers two boundary edges with a triangle, so that they */
599 /* are no longer boundary edges, those edges are not immediately deleted */
600 /* from the tree; rather, they are lazily deleted when they are next */
601 /* encountered. (Since only a random sample of boundary edges are kept */
602 /* in the tree, lazy deletion is faster.) `keydest' is used to verify */
603 /* that a triangle is still the same as when it entered the splay tree; if */
604 /* it has been rotated (due to a circle event), it no longer represents a */
605 /* boundary edge and should be deleted. */
606
607 struct splaynode {
608 struct otri keyedge; /* Lprev of an edge on the front. */
609 vertex keydest; /* Used to verify that splay node is still live. */
610 struct splaynode *lchild, *rchild; /* Children in splay tree. */
611 };
612
613 /* A type used to allocate memory. firstblock is the first block of items. */
614 /* nowblock is the block from which items are currently being allocated. */
615 /* nextitem points to the next slab of free memory for an item. */
616 /* deaditemstack is the head of a linked list (stack) of deallocated items */
617 /* that can be recycled. unallocateditems is the number of items that */
618 /* remain to be allocated from nowblock. */
619 /* */
620 /* Traversal is the process of walking through the entire list of items, and */
621 /* is separate from allocation. Note that a traversal will visit items on */
622 /* the "deaditemstack" stack as well as live items. pathblock points to */
623 /* the block currently being traversed. pathitem points to the next item */
624 /* to be traversed. pathitemsleft is the number of items that remain to */
625 /* be traversed in pathblock. */
626 /* */
627 /* alignbytes determines how new records should be aligned in memory. */
628 /* itembytes is the length of a record in bytes (after rounding up). */
629 /* itemsperblock is the number of items allocated at once in a single */
630 /* block. itemsfirstblock is the number of items in the first block, */
631 /* which can vary from the others. items is the number of currently */
632 /* allocated items. maxitems is the maximum number of items that have */
633 /* been allocated at once; it is the current number of items plus the */
634 /* number of records kept on deaditemstack. */
635
636 struct memorypool {
637 VOID **firstblock, **nowblock;
638 VOID *nextitem;
639 VOID *deaditemstack;
640 VOID **pathblock;
641 VOID *pathitem;
642 int alignbytes;
643 int itembytes;
644 int itemsperblock;
645 int itemsfirstblock;
646 long items, maxitems;
647 int unallocateditems;
648 int pathitemsleft;
649 };
650
651
652 /* Global constants. */
653
654 REAL splitter=0.; /* Used to split REAL factors for exact multiplication. */
655 REAL epsilon=0.; /* Floating-point machine epsilon. */
656 REAL resulterrbound=0.;
657 REAL ccwerrboundA=0., ccwerrboundB=0., ccwerrboundC=0.;
658 REAL iccerrboundA=0., iccerrboundB=0., iccerrboundC=0.;
659 REAL o3derrboundA=0., o3derrboundB=0., o3derrboundC=0.;
660
661 /* Random number seed is not constant, but I've made it global anyway. */
662
663 unsigned long randomseed; /* Current random number seed. */
664
665
666 /* Mesh data structure. Triangle operates on only one mesh, but the mesh */
667 /* structure is used (instead of global variables) to allow reentrancy. */
668
669 struct mesh {
670
671 /* Variables used to allocate memory for triangles, subsegments, vertices, */
672 /* viri (triangles being eaten), encroached segments, bad (skinny or too */
673 /* large) triangles, and splay tree nodes. */
674
675 struct memorypool triangles;
676 struct memorypool subsegs;
677 struct memorypool vertices;
678 struct memorypool viri;
679 struct memorypool badsubsegs;
680 struct memorypool badtriangles;
681 struct memorypool flipstackers;
682 struct memorypool splaynodes;
683
684 /* Variables that maintain the bad triangle queues. The queues are */
685 /* ordered from 4095 (highest priority) to 0 (lowest priority). */
686
687 struct badtriang *queuefront[4096];
688 struct badtriang *queuetail[4096];
689 int nextnonemptyq[4096];
690 int firstnonemptyq;
691
692 /* Variable that maintains the stack of recently flipped triangles. */
693
694 struct flipstacker *lastflip;
695
696 /* Other variables. */
697
698 REAL xmin, xmax, ymin, ymax; /* x and y bounds. */
699 REAL xminextreme; /* Nonexistent x value used as a flag in sweepline. */
700 int invertices; /* Number of input vertices. */
701 int inelements; /* Number of input triangles. */
702 int insegments; /* Number of input segments. */
703 int holes; /* Number of input holes. */
704 int regions; /* Number of input regions. */
705 int undeads; /* Number of input vertices that don't appear in the mesh. */
706 long edges; /* Number of output edges. */
707 int mesh_dim; /* Dimension (ought to be 2). */
708 int nextras; /* Number of attributes per vertex. */
709 int eextras; /* Number of attributes per triangle. */
710 long hullsize; /* Number of edges in convex hull. */
711 int steinerleft; /* Number of Steiner points not yet used. */
712 int vertexmarkindex; /* Index to find boundary marker of a vertex. */
713 int vertex2triindex; /* Index to find a triangle adjacent to a vertex. */
714 int highorderindex; /* Index to find extra nodes for high-order elements. */
715 int elemattribindex; /* Index to find attributes of a triangle. */
716 int areaboundindex; /* Index to find area bound of a triangle. */
717 int checksegments; /* Are there segments in the triangulation yet? */
718 int checkquality; /* Has quality triangulation begun yet? */
719 int readnodefile; /* Has a .node file been read? */
720 long samples; /* Number of random samples for point location. */
721
722 long incirclecount; /* Number of incircle tests performed. */
723 long counterclockcount; /* Number of counterclockwise tests performed. */
724 long orient3dcount; /* Number of 3D orientation tests performed. */
725 long hyperbolacount; /* Number of right-of-hyperbola tests performed. */
726 long circumcentercount; /* Number of circumcenter calculations performed. */
727 long circletopcount; /* Number of circle top calculations performed. */
728
729 /* Triangular bounding box vertices. */
730
731 vertex infvertex1, infvertex2, infvertex3;
732
733 /* Pointer to the `triangle' that occupies all of "outer space." */
734
735 triangle *dummytri;
736 triangle *dummytribase; /* Keep base address so we can free() it later. */
737
738 /* Pointer to the omnipresent subsegment. Referenced by any triangle or */
739 /* subsegment that isn't really connected to a subsegment at that */
740 /* location. */
741
742 subseg *dummysub;
743 subseg *dummysubbase; /* Keep base address so we can free() it later. */
744
745 /* Pointer to a recently visited triangle. Improves point location if */
746 /* proximate vertices are inserted sequentially. */
747
748 struct otri recenttri;
749
750 }; /* End of `struct mesh'. */
751
752
753 /* Data structure for command line switches and file names. This structure */
754 /* is used (instead of global variables) to allow reentrancy. */
755
756 struct behavior {
757
758 /* Switches for the triangulator. */
759 /* poly: -p switch. refine: -r switch. */
760 /* quality: -q switch. */
761 /* minangle: minimum angle bound, specified after -q switch. */
762 /* goodangle: cosine squared of minangle. */
763 /* offconstant: constant used to place off-center Steiner points. */
764 /* vararea: -a switch without number. */
765 /* fixedarea: -a switch with number. */
766 /* maxarea: maximum area bound, specified after -a switch. */
767 /* usertest: -u switch. */
768 /* regionattrib: -A switch. convex: -c switch. */
769 /* weighted: 1 for -w switch, 2 for -W switch. jettison: -j switch */
770 /* firstnumber: inverse of -z switch. All items are numbered starting */
771 /* from `firstnumber'. */
772 /* edgesout: -e switch. voronoi: -v switch. */
773 /* neighbors: -n switch. geomview: -g switch. */
774 /* nobound: -B switch. nopolywritten: -P switch. */
775 /* nonodewritten: -N switch. noelewritten: -E switch. */
776 /* noiterationnum: -I switch. noholes: -O switch. */
777 /* noexact: -X switch. */
778 /* order: element order, specified after -o switch. */
779 /* nobisect: count of how often -Y switch is selected. */
780 /* steiner: maximum number of Steiner points, specified after -S switch. */
781 /* incremental: -i switch. sweepline: -F switch. */
782 /* dwyer: inverse of -l switch. */
783 /* splitseg: -s switch. */
784 /* conformdel: -D switch. docheck: -C switch. */
785 /* quiet: -Q switch. verbose: count of how often -V switch is selected. */
786 /* usesegments: -p, -r, -q, or -c switch; determines whether segments are */
787 /* used at all. */
788 /* */
789 /* Read the instructions to find out the meaning of these switches. */
790
791 int poly, refine, quality, vararea, fixedarea, usertest;
792 int regionattrib, convex, weighted, jettison;
793 int firstnumber;
794 int edgesout, voronoi, neighbors, geomview;
795 int nobound, nopolywritten, nonodewritten, noelewritten, noiterationnum;
796 int noholes, noexact, conformdel;
797 int incremental, sweepline, dwyer;
798 int splitseg;
799 int docheck;
800 int quiet, verbose;
801 int usesegments;
802 int order;
803 int nobisect;
804 int steiner;
805 REAL minangle, goodangle, offconstant;
806 REAL maxarea;
807
808 /* Variables for file names. */
809
810 #ifndef TRILIBRARY
811 char innodefilename[FILENAMESIZE];
812 char inelefilename[FILENAMESIZE];
813 char inpolyfilename[FILENAMESIZE];
814 char areafilename[FILENAMESIZE];
815 char outnodefilename[FILENAMESIZE];
816 char outelefilename[FILENAMESIZE];
817 char outpolyfilename[FILENAMESIZE];
818 char edgefilename[FILENAMESIZE];
819 char vnodefilename[FILENAMESIZE];
820 char vedgefilename[FILENAMESIZE];
821 char neighborfilename[FILENAMESIZE];
822 char offfilename[FILENAMESIZE];
823 #endif /* not TRILIBRARY */
824
825 }; /* End of `struct behavior'. */
826
827
828 /*****************************************************************************/
829 /* */
830 /* Mesh manipulation primitives. Each triangle contains three pointers to */
831 /* other triangles, with orientations. Each pointer points not to the */
832 /* first byte of a triangle, but to one of the first three bytes of a */
833 /* triangle. It is necessary to extract both the triangle itself and the */
834 /* orientation. To save memory, I keep both pieces of information in one */
835 /* pointer. To make this possible, I assume that all triangles are aligned */
836 /* to four-byte boundaries. The decode() routine below decodes a pointer, */
837 /* extracting an orientation (in the range 0 to 2) and a pointer to the */
838 /* beginning of a triangle. The encode() routine compresses a pointer to a */
839 /* triangle and an orientation into a single pointer. My assumptions that */
840 /* triangles are four-byte-aligned and that the `unsigned long' type is */
841 /* long enough to hold a pointer are two of the few kludges in this program.*/
842 /* */
843 /* Subsegments are manipulated similarly. A pointer to a subsegment */
844 /* carries both an address and an orientation in the range 0 to 1. */
845 /* */
846 /* The other primitives take an oriented triangle or oriented subsegment, */
847 /* and return an oriented triangle or oriented subsegment or vertex; or */
848 /* they change the connections in the data structure. */
849 /* */
850 /* Below, triangles and subsegments are denoted by their vertices. The */
851 /* triangle abc has origin (org) a, destination (dest) b, and apex (apex) */
852 /* c. These vertices occur in counterclockwise order about the triangle. */
853 /* The handle abc may simultaneously denote vertex a, edge ab, and triangle */
854 /* abc. */
855 /* */
856 /* Similarly, the subsegment ab has origin (sorg) a and destination (sdest) */
857 /* b. If ab is thought to be directed upward (with b directly above a), */
858 /* then the handle ab is thought to grasp the right side of ab, and may */
859 /* simultaneously denote vertex a and edge ab. */
860 /* */
861 /* An asterisk (*) denotes a vertex whose identity is unknown. */
862 /* */
863 /* Given this notation, a partial list of mesh manipulation primitives */
864 /* follows. */
865 /* */
866 /* */
867 /* For triangles: */
868 /* */
869 /* sym: Find the abutting triangle; same edge. */
870 /* sym(abc) -> ba* */
871 /* */
872 /* lnext: Find the next edge (counterclockwise) of a triangle. */
873 /* lnext(abc) -> bca */
874 /* */
875 /* lprev: Find the previous edge (clockwise) of a triangle. */
876 /* lprev(abc) -> cab */
877 /* */
878 /* onext: Find the next edge counterclockwise with the same origin. */
879 /* onext(abc) -> ac* */
880 /* */
881 /* oprev: Find the next edge clockwise with the same origin. */
882 /* oprev(abc) -> a*b */
883 /* */
884 /* dnext: Find the next edge counterclockwise with the same destination. */
885 /* dnext(abc) -> *ba */
886 /* */
887 /* dprev: Find the next edge clockwise with the same destination. */
888 /* dprev(abc) -> cb* */
889 /* */
890 /* rnext: Find the next edge (counterclockwise) of the adjacent triangle. */
891 /* rnext(abc) -> *a* */
892 /* */
893 /* rprev: Find the previous edge (clockwise) of the adjacent triangle. */
894 /* rprev(abc) -> b** */
895 /* */
896 /* org: Origin dest: Destination apex: Apex */
897 /* org(abc) -> a dest(abc) -> b apex(abc) -> c */
898 /* */
899 /* bond: Bond two triangles together at the resepective handles. */
900 /* bond(abc, bad) */
901 /* */
902 /* */
903 /* For subsegments: */
904 /* */
905 /* ssym: Reverse the orientation of a subsegment. */
906 /* ssym(ab) -> ba */
907 /* */
908 /* spivot: Find adjoining subsegment with the same origin. */
909 /* spivot(ab) -> a* */
910 /* */
911 /* snext: Find next subsegment in sequence. */
912 /* snext(ab) -> b* */
913 /* */
914 /* sorg: Origin sdest: Destination */
915 /* sorg(ab) -> a sdest(ab) -> b */
916 /* */
917 /* sbond: Bond two subsegments together at the respective origins. */
918 /* sbond(ab, ac) */
919 /* */
920 /* */
921 /* For interacting tetrahedra and subfacets: */
922 /* */
923 /* tspivot: Find a subsegment abutting a triangle. */
924 /* tspivot(abc) -> ba */
925 /* */
926 /* stpivot: Find a triangle abutting a subsegment. */
927 /* stpivot(ab) -> ba* */
928 /* */
929 /* tsbond: Bond a triangle to a subsegment. */
930 /* tsbond(abc, ba) */
931 /* */
932 /*****************************************************************************/
933
934 /********* Mesh manipulation primitives begin here *********/
935 /** **/
936 /** **/
937
938 /* Fast lookup arrays to speed some of the mesh manipulation primitives. */
939
940 int plus1mod3[3] = {1, 2, 0};
941 int minus1mod3[3] = {2, 0, 1};
942
943 /********* Primitives for triangles *********/
944 /* */
945 /* */
946
947 /* decode() converts a pointer to an oriented triangle. The orientation is */
948 /* extracted from the two least significant bits of the pointer. */
949
950 #define decode(ptr, otri) \
951 (otri).orient = (int) ((unsigned long) (ptr) & (unsigned long) 3l); \
952 (otri).tri = (triangle *) \
953 ((unsigned long) (ptr) ^ (unsigned long) (otri).orient)
954
955 /* encode() compresses an oriented triangle into a single pointer. It */
956 /* relies on the assumption that all triangles are aligned to four-byte */
957 /* boundaries, so the two least significant bits of (otri).tri are zero. */
958
959 #define encode(otri) \
960 (triangle) ((unsigned long) (otri).tri | (unsigned long) (otri).orient)
961
962 /* The following handle manipulation primitives are all described by Guibas */
963 /* and Stolfi. However, Guibas and Stolfi use an edge-based data */
964 /* structure, whereas I use a triangle-based data structure. */
965
966 /* sym() finds the abutting triangle, on the same edge. Note that the edge */
967 /* direction is necessarily reversed, because the handle specified by an */
968 /* oriented triangle is directed counterclockwise around the triangle. */
969
970 #define sym(otri1, otri2) \
971 ptr = (otri1).tri[(otri1).orient]; \
972 decode(ptr, otri2);
973
974 #define symself(otri) \
975 ptr = (otri).tri[(otri).orient]; \
976 decode(ptr, otri);
977
978 /* lnext() finds the next edge (counterclockwise) of a triangle. */
979
980 #define lnext(otri1, otri2) \
981 (otri2).tri = (otri1).tri; \
982 (otri2).orient = plus1mod3[(otri1).orient]
983
984 #define lnextself(otri) \
985 (otri).orient = plus1mod3[(otri).orient]
986
987 /* lprev() finds the previous edge (clockwise) of a triangle. */
988
989 #define lprev(otri1, otri2) \
990 (otri2).tri = (otri1).tri; \
991 (otri2).orient = minus1mod3[(otri1).orient]
992
993 #define lprevself(otri) \
994 (otri).orient = minus1mod3[(otri).orient]
995
996 /* onext() spins counterclockwise around a vertex; that is, it finds the */
997 /* next edge with the same origin in the counterclockwise direction. This */
998 /* edge is part of a different triangle. */
999
1000 #define onext(otri1, otri2) \
1001 lprev(otri1, otri2); \
1002 symself(otri2);
1003
1004 #define onextself(otri) \
1005 lprevself(otri); \
1006 symself(otri);
1007
1008 /* oprev() spins clockwise around a vertex; that is, it finds the next edge */
1009 /* with the same origin in the clockwise direction. This edge is part of */
1010 /* a different triangle. */
1011
1012 #define oprev(otri1, otri2) \
1013 sym(otri1, otri2); \
1014 lnextself(otri2);
1015
1016 #define oprevself(otri) \
1017 symself(otri); \
1018 lnextself(otri);
1019
1020 /* dnext() spins counterclockwise around a vertex; that is, it finds the */
1021 /* next edge with the same destination in the counterclockwise direction. */
1022 /* This edge is part of a different triangle. */
1023
1024 #define dnext(otri1, otri2) \
1025 sym(otri1, otri2); \
1026 lprevself(otri2);
1027
1028 #define dnextself(otri) \
1029 symself(otri); \
1030 lprevself(otri);
1031
1032 /* dprev() spins clockwise around a vertex; that is, it finds the next edge */
1033 /* with the same destination in the clockwise direction. This edge is */
1034 /* part of a different triangle. */
1035
1036 #define dprev(otri1, otri2) \
1037 lnext(otri1, otri2); \
1038 symself(otri2);
1039
1040 #define dprevself(otri) \
1041 lnextself(otri); \
1042 symself(otri);
1043
1044 /* rnext() moves one edge counterclockwise about the adjacent triangle. */
1045 /* (It's best understood by reading Guibas and Stolfi. It involves */
1046 /* changing triangles twice.) */
1047
1048 #define rnext(otri1, otri2) \
1049 sym(otri1, otri2); \
1050 lnextself(otri2); \
1051 symself(otri2);
1052
1053 #define rnextself(otri) \
1054 symself(otri); \
1055 lnextself(otri); \
1056 symself(otri);
1057
1058 /* rprev() moves one edge clockwise about the adjacent triangle. */
1059 /* (It's best understood by reading Guibas and Stolfi. It involves */
1060 /* changing triangles twice.) */
1061
1062 #define rprev(otri1, otri2) \
1063 sym(otri1, otri2); \
1064 lprevself(otri2); \
1065 symself(otri2);
1066
1067 #define rprevself(otri) \
1068 symself(otri); \
1069 lprevself(otri); \
1070 symself(otri);
1071
1072 /* These primitives determine or set the origin, destination, or apex of a */
1073 /* triangle. */
1074
1075 #define org(otri, vertexptr) \
1076 vertexptr = (vertex) (otri).tri[plus1mod3[(otri).orient] + 3]
1077
1078 #define dest(otri, vertexptr) \
1079 vertexptr = (vertex) (otri).tri[minus1mod3[(otri).orient] + 3]
1080
1081 #define apex(otri, vertexptr) \
1082 vertexptr = (vertex) (otri).tri[(otri).orient + 3]
1083
1084 #define setorg(otri, vertexptr) \
1085 (otri).tri[plus1mod3[(otri).orient] + 3] = (triangle) vertexptr
1086
1087 #define setdest(otri, vertexptr) \
1088 (otri).tri[minus1mod3[(otri).orient] + 3] = (triangle) vertexptr
1089
1090 #define setapex(otri, vertexptr) \
1091 (otri).tri[(otri).orient + 3] = (triangle) vertexptr
1092
1093 /* Bond two triangles together. */
1094
1095 #define bond(otri1, otri2) \
1096 (otri1).tri[(otri1).orient] = encode(otri2); \
1097 (otri2).tri[(otri2).orient] = encode(otri1)
1098
1099 /* Dissolve a bond (from one side). Note that the other triangle will still */
1100 /* think it's connected to this triangle. Usually, however, the other */
1101 /* triangle is being deleted entirely, or bonded to another triangle, so */
1102 /* it doesn't matter. */
1103
1104 #define dissolve(otri) \
1105 (otri).tri[(otri).orient] = (triangle) m->dummytri
1106
1107 /* Copy an oriented triangle. */
1108
1109 #define otricopy(otri1, otri2) \
1110 (otri2).tri = (otri1).tri; \
1111 (otri2).orient = (otri1).orient
1112
1113 /* Test for equality of oriented triangles. */
1114
1115 #define otriequal(otri1, otri2) \
1116 (((otri1).tri == (otri2).tri) && \
1117 ((otri1).orient == (otri2).orient))
1118
1119 /* Primitives to infect or cure a triangle with the virus. These rely on */
1120 /* the assumption that all subsegments are aligned to four-byte boundaries.*/
1121
1122 #define infect(otri) \
1123 (otri).tri[6] = (triangle) \
1124 ((unsigned long) (otri).tri[6] | (unsigned long) 2l)
1125
1126 #define uninfect(otri) \
1127 (otri).tri[6] = (triangle) \
1128 ((unsigned long) (otri).tri[6] & ~ (unsigned long) 2l)
1129
1130 /* Test a triangle for viral infection. */
1131
1132 #define infected(otri) \
1133 (((unsigned long) (otri).tri[6] & (unsigned long) 2l) != 0l)
1134
1135 /* Check or set a triangle's attributes. */
1136
1137 #define elemattribute(otri, attnum) \
1138 ((REAL *) (otri).tri)[m->elemattribindex + (attnum)]
1139
1140 #define setelemattribute(otri, attnum, value) \
1141 ((REAL *) (otri).tri)[m->elemattribindex + (attnum)] = value
1142
1143 /* Check or set a triangle's maximum area bound. */
1144
1145 #define areabound(otri) ((REAL *) (otri).tri)[m->areaboundindex]
1146
1147 #define setareabound(otri, value) \
1148 ((REAL *) (otri).tri)[m->areaboundindex] = value
1149
1150 /* Check or set a triangle's deallocation. Its second pointer is set to */
1151 /* NULL to indicate that it is not allocated. (Its first pointer is used */
1152 /* for the stack of dead items.) Its fourth pointer (its first vertex) */
1153 /* is set to NULL in case a `badtriang' structure points to it. */
1154
1155 #define deadtri(tria) ((tria)[1] == (triangle) NULL)
1156
1157 #define killtri(tria) \
1158 (tria)[1] = (triangle) NULL; \
1159 (tria)[3] = (triangle) NULL
1160
1161 /********* Primitives for subsegments *********/
1162 /* */
1163 /* */
1164
1165 /* sdecode() converts a pointer to an oriented subsegment. The orientation */
1166 /* is extracted from the least significant bit of the pointer. The two */
1167 /* least significant bits (one for orientation, one for viral infection) */
1168 /* are masked out to produce the real pointer. */
1169
1170 #define sdecode(sptr, osub) \
1171 (osub).ssorient = (int) ((unsigned long) (sptr) & (unsigned long) 1l); \
1172 (osub).ss = (subseg *) \
1173 ((unsigned long) (sptr) & ~ (unsigned long) 3l)
1174
1175 /* sencode() compresses an oriented subsegment into a single pointer. It */
1176 /* relies on the assumption that all subsegments are aligned to two-byte */
1177 /* boundaries, so the least significant bit of (osub).ss is zero. */
1178
1179 #define sencode(osub) \
1180 (subseg) ((unsigned long) (osub).ss | (unsigned long) (osub).ssorient)
1181
1182 /* ssym() toggles the orientation of a subsegment. */
1183
1184 #define ssym(osub1, osub2) \
1185 (osub2).ss = (osub1).ss; \
1186 (osub2).ssorient = 1 - (osub1).ssorient
1187
1188 #define ssymself(osub) \
1189 (osub).ssorient = 1 - (osub).ssorient
1190
1191 /* spivot() finds the other subsegment (from the same segment) that shares */
1192 /* the same origin. */
1193
1194 #define spivot(osub1, osub2) \
1195 sptr = (osub1).ss[(osub1).ssorient]; \
1196 sdecode(sptr, osub2)
1197
1198 #define spivotself(osub) \
1199 sptr = (osub).ss[(osub).ssorient]; \
1200 sdecode(sptr, osub)
1201
1202 /* snext() finds the next subsegment (from the same segment) in sequence; */
1203 /* one whose origin is the input subsegment's destination. */
1204
1205 #define snext(osub1, osub2) \
1206 sptr = (osub1).ss[1 - (osub1).ssorient]; \
1207 sdecode(sptr, osub2)
1208
1209 #define snextself(osub) \
1210 sptr = (osub).ss[1 - (osub).ssorient]; \
1211 sdecode(sptr, osub)
1212
1213 /* These primitives determine or set the origin or destination of a */
1214 /* subsegment or the segment that includes it. */
1215
1216 #define sorg(osub, vertexptr) \
1217 vertexptr = (vertex) (osub).ss[2 + (osub).ssorient]
1218
1219 #define sdest(osub, vertexptr) \
1220 vertexptr = (vertex) (osub).ss[3 - (osub).ssorient]
1221
1222 #define setsorg(osub, vertexptr) \
1223 (osub).ss[2 + (osub).ssorient] = (subseg) vertexptr
1224
1225 #define setsdest(osub, vertexptr) \
1226 (osub).ss[3 - (osub).ssorient] = (subseg) vertexptr
1227
1228 #define segorg(osub, vertexptr) \
1229 vertexptr = (vertex) (osub).ss[4 + (osub).ssorient]
1230
1231 #define segdest(osub, vertexptr) \
1232 vertexptr = (vertex) (osub).ss[5 - (osub).ssorient]
1233
1234 #define setsegorg(osub, vertexptr) \
1235 (osub).ss[4 + (osub).ssorient] = (subseg) vertexptr
1236
1237 #define setsegdest(osub, vertexptr) \
1238 (osub).ss[5 - (osub).ssorient] = (subseg) vertexptr
1239
1240 /* These primitives read or set a boundary marker. Boundary markers are */
1241 /* used to hold user-defined tags for setting boundary conditions in */
1242 /* finite element solvers. */
1243
1244 #define mark(osub) (* (int *) ((osub).ss + 8))
1245
1246 #define setmark(osub, value) \
1247 * (int *) ((osub).ss + 8) = value
1248
1249 /* Bond two subsegments together. */
1250
1251 #define sbond(osub1, osub2) \
1252 (osub1).ss[(osub1).ssorient] = sencode(osub2); \
1253 (osub2).ss[(osub2).ssorient] = sencode(osub1)
1254
1255 /* Dissolve a subsegment bond (from one side). Note that the other */
1256 /* subsegment will still think it's connected to this subsegment. */
1257
1258 #define sdissolve(osub) \
1259 (osub).ss[(osub).ssorient] = (subseg) m->dummysub
1260
1261 /* Copy a subsegment. */
1262
1263 #define subsegcopy(osub1, osub2) \
1264 (osub2).ss = (osub1).ss; \
1265 (osub2).ssorient = (osub1).ssorient
1266
1267 /* Test for equality of subsegments. */
1268
1269 #define subsegequal(osub1, osub2) \
1270 (((osub1).ss == (osub2).ss) && \
1271 ((osub1).ssorient == (osub2).ssorient))
1272
1273 /* Check or set a subsegment's deallocation. Its second pointer is set to */
1274 /* NULL to indicate that it is not allocated. (Its first pointer is used */
1275 /* for the stack of dead items.) Its third pointer (its first vertex) */
1276 /* is set to NULL in case a `badsubseg' structure points to it. */
1277
1278 #define deadsubseg(sub) ((sub)[1] == (subseg) NULL)
1279
1280 #define killsubseg(sub) \
1281 (sub)[1] = (subseg) NULL; \
1282 (sub)[2] = (subseg) NULL
1283
1284 /********* Primitives for interacting triangles and subsegments *********/
1285 /* */
1286 /* */
1287
1288 /* tspivot() finds a subsegment abutting a triangle. */
1289
1290 #define tspivot(otri, osub) \
1291 sptr = (subseg) (otri).tri[6 + (otri).orient]; \
1292 sdecode(sptr, osub)
1293
1294 /* stpivot() finds a triangle abutting a subsegment. It requires that the */
1295 /* variable `ptr' of type `triangle' be defined. */
1296
1297 #define stpivot(osub, otri) \
1298 ptr = (triangle) (osub).ss[6 + (osub).ssorient]; \
1299 decode(ptr, otri)
1300
1301 /* Bond a triangle to a subsegment. */
1302
1303 #define tsbond(otri, osub) \
1304 (otri).tri[6 + (otri).orient] = (triangle) sencode(osub); \
1305 (osub).ss[6 + (osub).ssorient] = (subseg) encode(otri)
1306
1307 /* Dissolve a bond (from the triangle side). */
1308
1309 #define tsdissolve(otri) \
1310 (otri).tri[6 + (otri).orient] = (triangle) m->dummysub
1311
1312 /* Dissolve a bond (from the subsegment side). */
1313
1314 #define stdissolve(osub) \
1315 (osub).ss[6 + (osub).ssorient] = (subseg) m->dummytri
1316
1317 /********* Primitives for vertices *********/
1318 /* */
1319 /* */
1320
1321 #define vertexmark(vx) ((int *) (vx))[m->vertexmarkindex]
1322
1323 #define setvertexmark(vx, value) \
1324 ((int *) (vx))[m->vertexmarkindex] = value
1325
1326 #define vertextype(vx) ((int *) (vx))[m->vertexmarkindex + 1]
1327
1328 #define setvertextype(vx, value) \
1329 ((int *) (vx))[m->vertexmarkindex + 1] = value
1330
1331 #define vertex2tri(vx) ((triangle *) (vx))[m->vertex2triindex]
1332
1333 #define setvertex2tri(vx, value) \
1334 ((triangle *) (vx))[m->vertex2triindex] = value
1335
1336 /** **/
1337 /** **/
1338 /********* Mesh manipulation primitives end here *********/
1339
1340 /********* User-defined triangle evaluation routine begins here *********/
1341 /** **/
1342 /** **/
1343
1344 /*****************************************************************************/
1345 /* */
1346 /* triunsuitable() Determine if a triangle is unsuitable, and thus must */
1347 /* be further refined. */
1348 /* */
1349 /* You may write your own procedure that decides whether or not a selected */
1350 /* triangle is too big (and needs to be refined). There are two ways to do */
1351 /* this. */
1352 /* */
1353 /* (1) Modify the procedure `triunsuitable' below, then recompile */
1354 /* Triangle. */
1355 /* */
1356 /* (2) Define the symbol EXTERNAL_TEST (either by adding the definition */
1357 /* to this file, or by using the appropriate compiler switch). This way, */
1358 /* you can compile triangle.c separately from your test. Write your own */
1359 /* `triunsuitable' procedure in a separate C file (using the same prototype */
1360 /* as below). Compile it and link the object code with triangle.o. */
1361 /* */
1362 /* This procedure returns 1 if the triangle is too large and should be */
1363 /* refined; 0 otherwise. */
1364 /* */
1365 /*****************************************************************************/
1366
1367 #ifdef EXTERNAL_TEST
1368
1369 int triunsuitable();
1370
1371 #else /* not EXTERNAL_TEST */
1372
1373 #ifdef ANSI_DECLARATORS
1374 int triunsuitable(vertex triorg, vertex tridest, vertex triapex, REAL area)
1375 #else /* not ANSI_DECLARATORS */
1376 int triunsuitable(triorg, tridest, triapex, area)
1377 vertex triorg; /* The triangle's origin vertex. */
1378 vertex tridest; /* The triangle's destination vertex. */
1379 vertex triapex; /* The triangle's apex vertex. */
1380 REAL area; /* The area of the triangle. */
1381 #endif /* not ANSI_DECLARATORS */
1382
1383 {
1384 REAL dxoa, dxda, dxod;
1385 REAL dyoa, dyda, dyod;
1386 REAL oalen, dalen, odlen;
1387 REAL maxlen;
1388
1389 dxoa = triorg[0] - triapex[0];
1390 dyoa = triorg[1] - triapex[1];
1391 dxda = tridest[0] - triapex[0];
1392 dyda = tridest[1] - triapex[1];
1393 dxod = triorg[0] - tridest[0];
1394 dyod = triorg[1] - tridest[1];
1395 /* Find the squares of the lengths of the triangle's three edges. */
1396 oalen = dxoa * dxoa + dyoa * dyoa;
1397 dalen = dxda * dxda + dyda * dyda;
1398 odlen = dxod * dxod + dyod * dyod;
1399 /* Find the square of the length of the longest edge. */
1400 maxlen = (dalen > oalen) ? dalen : oalen;
1401 maxlen = (odlen > maxlen) ? odlen : maxlen;
1402
1403 if (maxlen > 0.05 * (triorg[0] * triorg[0] + triorg[1] * triorg[1]) + 0.02) {
1404 return 1;
1405 } else {
1406 return 0;
1407 }
1408 }
1409
1410 #endif /* not EXTERNAL_TEST */
1411
1412 /** **/
1413 /** **/
1414 /********* User-defined triangle evaluation routine ends here *********/
1415
1416 /********* Memory allocation and program exit wrappers begin here *********/
1417 /** **/
1418 /** **/
1419
1420 #ifdef ANSI_DECLARATORS
1421 void triexit(int status)
1422 #else /* not ANSI_DECLARATORS */
1423 void triexit(status)
1424 int status;
1425 #endif /* not ANSI_DECLARATORS */
1426
1427 {
1428 exit(status);
1429 }
1430
1431 #ifdef ANSI_DECLARATORS
1432 VOID *trimalloc(int size)
1433 #else /* not ANSI_DECLARATORS */
1434 VOID *trimalloc(size)
1435 int size;
1436 #endif /* not ANSI_DECLARATORS */
1437
1438 {
1439 VOID *memptr;
1440
1441 memptr = (VOID *) malloc((unsigned int) size);
1442 if (memptr == (VOID *) NULL) {
1443 printf("Error: Out of memory.\n");
1444 triexit(1);
1445 }
1446 return(memptr);
1447 }
1448
1449 #ifdef ANSI_DECLARATORS
1450 void trifree(VOID *memptr)
1451 #else /* not ANSI_DECLARATORS */
1452 void trifree(memptr)
1453 VOID *memptr;
1454 #endif /* not ANSI_DECLARATORS */
1455
1456 {
1457 free(memptr);
1458 }
1459
1460 /** **/
1461 /** **/
1462 /********* Memory allocation and program exit wrappers end here *********/
1463
1464 /********* User interaction routines begin here *********/
1465 /** **/
1466 /** **/
1467
1468 /*****************************************************************************/
1469 /* */
1470 /* syntax() Print list of command line switches. */
1471 /* */
1472 /*****************************************************************************/
1473
1474 #ifndef TRILIBRARY
1475
syntax()1476 void syntax()
1477 {
1478 #ifdef CDT_ONLY
1479 #ifdef REDUCED
1480 printf("triangle [-pAcjevngBPNEIOXzo_lQVh] input_file\n");
1481 #else /* not REDUCED */
1482 printf("triangle [-pAcjevngBPNEIOXzo_iFlCQVh] input_file\n");
1483 #endif /* not REDUCED */
1484 #else /* not CDT_ONLY */
1485 #ifdef REDUCED
1486 printf("triangle [-prq__a__uAcDjevngBPNEIOXzo_YS__lQVh] input_file\n");
1487 #else /* not REDUCED */
1488 printf("triangle [-prq__a__uAcDjevngBPNEIOXzo_YS__iFlsCQVh] input_file\n");
1489 #endif /* not REDUCED */
1490 #endif /* not CDT_ONLY */
1491
1492 printf(" -p Triangulates a Planar Straight Line Graph (.poly file).\n");
1493 #ifndef CDT_ONLY
1494 printf(" -r Refines a previously generated mesh.\n");
1495 printf(
1496 " -q Quality mesh generation. A minimum angle may be specified.\n");
1497 printf(" -a Applies a maximum triangle area constraint.\n");
1498 printf(" -u Applies a user-defined triangle constraint.\n");
1499 #endif /* not CDT_ONLY */
1500 printf(
1501 " -A Applies attributes to identify triangles in certain regions.\n");
1502 printf(" -c Encloses the convex hull with segments.\n");
1503 #ifndef CDT_ONLY
1504 printf(" -D Conforming Delaunay: all triangles are truly Delaunay.\n");
1505 #endif /* not CDT_ONLY */
1506 /*
1507 printf(" -w Weighted Delaunay triangulation.\n");
1508 printf(" -W Regular triangulation (lower hull of a height field).\n");
1509 */
1510 printf(" -j Jettison unused vertices from output .node file.\n");
1511 printf(" -e Generates an edge list.\n");
1512 printf(" -v Generates a Voronoi diagram.\n");
1513 printf(" -n Generates a list of triangle neighbors.\n");
1514 printf(" -g Generates an .off file for Geomview.\n");
1515 printf(" -B Suppresses output of boundary information.\n");
1516 printf(" -P Suppresses output of .poly file.\n");
1517 printf(" -N Suppresses output of .node file.\n");
1518 printf(" -E Suppresses output of .ele file.\n");
1519 printf(" -I Suppresses mesh iteration numbers.\n");
1520 printf(" -O Ignores holes in .poly file.\n");
1521 printf(" -X Suppresses use of exact arithmetic.\n");
1522 printf(" -z Numbers all items starting from zero (rather than one).\n");
1523 printf(" -o2 Generates second-order subparametric elements.\n");
1524 #ifndef CDT_ONLY
1525 printf(" -Y Suppresses boundary segment splitting.\n");
1526 printf(" -S Specifies maximum number of added Steiner points.\n");
1527 #endif /* not CDT_ONLY */
1528 #ifndef REDUCED
1529 printf(" -i Uses incremental method, rather than divide-and-conquer.\n");
1530 printf(" -F Uses Fortune's sweepline algorithm, rather than d-and-c.\n");
1531 #endif /* not REDUCED */
1532 printf(" -l Uses vertical cuts only, rather than alternating cuts.\n");
1533 #ifndef REDUCED
1534 #ifndef CDT_ONLY
1535 printf(
1536 " -s Force segments into mesh by splitting (instead of using CDT).\n");
1537 #endif /* not CDT_ONLY */
1538 printf(" -C Check consistency of final mesh.\n");
1539 #endif /* not REDUCED */
1540 printf(" -Q Quiet: No terminal output except errors.\n");
1541 printf(" -V Verbose: Detailed information on what I'm doing.\n");
1542 printf(" -h Help: Detailed instructions for Triangle.\n");
1543 triexit(0);
1544 }
1545
1546 #endif /* not TRILIBRARY */
1547
1548 /*****************************************************************************/
1549 /* */
1550 /* info() Print out complete instructions. */
1551 /* */
1552 /*****************************************************************************/
1553
1554 #ifndef TRILIBRARY
1555
info()1556 void info()
1557 {
1558 printf("Triangle\n");
1559 printf(
1560 "A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator.\n");
1561 printf("Version 1.6\n\n");
1562 printf(
1563 "Copyright 1993, 1995, 1997, 1998, 2002, 2005 Jonathan Richard Shewchuk\n");
1564 printf("2360 Woolsey #H / Berkeley, California 94705-1927\n");
1565 printf("Bugs/comments to jrs@cs.berkeley.edu\n");
1566 printf(
1567 "Created as part of the Quake project (tools for earthquake simulation).\n");
1568 printf(
1569 "Supported in part by NSF Grant CMS-9318163 and an NSERC 1967 Scholarship.\n");
1570 printf("There is no warranty whatsoever. Use at your own risk.\n");
1571 #ifdef SINGLE
1572 printf("This executable is compiled for single precision arithmetic.\n\n\n");
1573 #else /* not SINGLE */
1574 printf("This executable is compiled for double precision arithmetic.\n\n\n");
1575 #endif /* not SINGLE */
1576 printf(
1577 "Triangle generates exact Delaunay triangulations, constrained Delaunay\n");
1578 printf(
1579 "triangulations, conforming Delaunay triangulations, Voronoi diagrams, and\n");
1580 printf(
1581 "high-quality triangular meshes. The latter can be generated with no small\n"
1582 );
1583 printf(
1584 "or large angles, and are thus suitable for finite element analysis. If no\n"
1585 );
1586 printf(
1587 "command line switch is specified, your .node input file is read, and the\n");
1588 printf(
1589 "Delaunay triangulation is returned in .node and .ele output files. The\n");
1590 printf("command syntax is:\n\n");
1591 printf("triangle [-prq__a__uAcDjevngBPNEIOXzo_YS__iFlsCQVh] input_file\n\n");
1592 printf(
1593 "Underscores indicate that numbers may optionally follow certain switches.\n");
1594 printf(
1595 "Do not leave any space between a switch and its numeric parameter.\n");
1596 printf(
1597 "input_file must be a file with extension .node, or extension .poly if the\n");
1598 printf(
1599 "-p switch is used. If -r is used, you must supply .node and .ele files,\n");
1600 printf(
1601 "and possibly a .poly file and an .area file as well. The formats of these\n"
1602 );
1603 printf("files are described below.\n\n");
1604 printf("Command Line Switches:\n\n");
1605 printf(
1606 " -p Reads a Planar Straight Line Graph (.poly file), which can specify\n"
1607 );
1608 printf(
1609 " vertices, segments, holes, regional attributes, and regional area\n");
1610 printf(
1611 " constraints. Generates a constrained Delaunay triangulation (CDT)\n"
1612 );
1613 printf(
1614 " fitting the input; or, if -s, -q, -a, or -u is used, a conforming\n");
1615 printf(
1616 " constrained Delaunay triangulation (CCDT). If you want a truly\n");
1617 printf(
1618 " Delaunay (not just constrained Delaunay) triangulation, use -D as\n");
1619 printf(
1620 " well. When -p is not used, Triangle reads a .node file by default.\n"
1621 );
1622 printf(
1623 " -r Refines a previously generated mesh. The mesh is read from a .node\n"
1624 );
1625 printf(
1626 " file and an .ele file. If -p is also used, a .poly file is read\n");
1627 printf(
1628 " and used to constrain segments in the mesh. If -a is also used\n");
1629 printf(
1630 " (with no number following), an .area file is read and used to\n");
1631 printf(
1632 " impose area constraints on the mesh. Further details on refinement\n"
1633 );
1634 printf(" appear below.\n");
1635 printf(
1636 " -q Quality mesh generation by Delaunay refinement (a hybrid of Paul\n");
1637 printf(
1638 " Chew's and Jim Ruppert's algorithms). Adds vertices to the mesh to\n"
1639 );
1640 printf(
1641 " ensure that all angles are between 20 and 140 degrees. An\n");
1642 printf(
1643 " alternative bound on the minimum angle, replacing 20 degrees, may\n");
1644 printf(
1645 " be specified after the `q'. The specified angle may include a\n");
1646 printf(
1647 " decimal point, but not exponential notation. Note that a bound of\n"
1648 );
1649 printf(
1650 " theta degrees on the smallest angle also implies a bound of\n");
1651 printf(
1652 " (180 - 2 theta) on the largest angle. If the minimum angle is 28.6\n"
1653 );
1654 printf(
1655 " degrees or smaller, Triangle is mathematically guaranteed to\n");
1656 printf(
1657 " terminate (assuming infinite precision arithmetic--Triangle may\n");
1658 printf(
1659 " fail to terminate if you run out of precision). In practice,\n");
1660 printf(
1661 " Triangle often succeeds for minimum angles up to 34 degrees. For\n");
1662 printf(
1663 " some meshes, however, you might need to reduce the minimum angle to\n"
1664 );
1665 printf(
1666 " avoid problems associated with insufficient floating-point\n");
1667 printf(" precision.\n");
1668 printf(
1669 " -a Imposes a maximum triangle area. If a number follows the `a', no\n");
1670 printf(
1671 " triangle is generated whose area is larger than that number. If no\n"
1672 );
1673 printf(
1674 " number is specified, an .area file (if -r is used) or .poly file\n");
1675 printf(
1676 " (if -r is not used) specifies a set of maximum area constraints.\n");
1677 printf(
1678 " An .area file contains a separate area constraint for each\n");
1679 printf(
1680 " triangle, and is useful for refining a finite element mesh based on\n"
1681 );
1682 printf(
1683 " a posteriori error estimates. A .poly file can optionally contain\n"
1684 );
1685 printf(
1686 " an area constraint for each segment-bounded region, thereby\n");
1687 printf(
1688 " controlling triangle densities in a first triangulation of a PSLG.\n"
1689 );
1690 printf(
1691 " You can impose both a fixed area constraint and a varying area\n");
1692 printf(
1693 " constraint by invoking the -a switch twice, once with and once\n");
1694 printf(
1695 " without a number following. Each area specified may include a\n");
1696 printf(" decimal point.\n");
1697 printf(
1698 " -u Imposes a user-defined constraint on triangle size. There are two\n"
1699 );
1700 printf(
1701 " ways to use this feature. One is to edit the triunsuitable()\n");
1702 printf(
1703 " procedure in triangle.c to encode any constraint you like, then\n");
1704 printf(
1705 " recompile Triangle. The other is to compile triangle.c with the\n");
1706 printf(
1707 " EXTERNAL_TEST symbol set (compiler switch -DEXTERNAL_TEST), then\n");
1708 printf(
1709 " link Triangle with a separate object file that implements\n");
1710 printf(
1711 " triunsuitable(). In either case, the -u switch causes the user-\n");
1712 printf(" defined test to be applied to every triangle.\n");
1713 printf(
1714 " -A Assigns an additional floating-point attribute to each triangle\n");
1715 printf(
1716 " that identifies what segment-bounded region each triangle belongs\n");
1717 printf(
1718 " to. Attributes are assigned to regions by the .poly file. If a\n");
1719 printf(
1720 " region is not explicitly marked by the .poly file, triangles in\n");
1721 printf(
1722 " that region are assigned an attribute of zero. The -A switch has\n");
1723 printf(
1724 " an effect only when the -p switch is used and the -r switch is not.\n"
1725 );
1726 printf(
1727 " -c Creates segments on the convex hull of the triangulation. If you\n");
1728 printf(
1729 " are triangulating a vertex set, this switch causes a .poly file to\n"
1730 );
1731 printf(
1732 " be written, containing all edges of the convex hull. If you are\n");
1733 printf(
1734 " triangulating a PSLG, this switch specifies that the whole convex\n");
1735 printf(
1736 " hull of the PSLG should be triangulated, regardless of what\n");
1737 printf(
1738 " segments the PSLG has. If you do not use this switch when\n");
1739 printf(
1740 " triangulating a PSLG, Triangle assumes that you have identified the\n"
1741 );
1742 printf(
1743 " region to be triangulated by surrounding it with segments of the\n");
1744 printf(
1745 " input PSLG. Beware: if you are not careful, this switch can cause\n"
1746 );
1747 printf(
1748 " the introduction of an extremely thin angle between a PSLG segment\n"
1749 );
1750 printf(
1751 " and a convex hull segment, which can cause overrefinement (and\n");
1752 printf(
1753 " possibly failure if Triangle runs out of precision). If you are\n");
1754 printf(
1755 " refining a mesh, the -c switch works differently: it causes a\n");
1756 printf(
1757 " .poly file to be written containing the boundary edges of the mesh\n"
1758 );
1759 printf(" (useful if no .poly file was read).\n");
1760 printf(
1761 " -D Conforming Delaunay triangulation: use this switch if you want to\n"
1762 );
1763 printf(
1764 " ensure that all the triangles in the mesh are Delaunay, and not\n");
1765 printf(
1766 " merely constrained Delaunay; or if you want to ensure that all the\n"
1767 );
1768 printf(
1769 " Voronoi vertices lie within the triangulation. (Some finite volume\n"
1770 );
1771 printf(
1772 " methods have this requirement.) This switch invokes Ruppert's\n");
1773 printf(
1774 " original algorithm, which splits every subsegment whose diametral\n");
1775 printf(
1776 " circle is encroached. It usually increases the number of vertices\n"
1777 );
1778 printf(" and triangles.\n");
1779 printf(
1780 " -j Jettisons vertices that are not part of the final triangulation\n");
1781 printf(
1782 " from the output .node file. By default, Triangle copies all\n");
1783 printf(
1784 " vertices in the input .node file to the output .node file, in the\n");
1785 printf(
1786 " same order, so their indices do not change. The -j switch prevents\n"
1787 );
1788 printf(
1789 " duplicated input vertices, or vertices `eaten' by holes, from\n");
1790 printf(
1791 " appearing in the output .node file. Thus, if two input vertices\n");
1792 printf(
1793 " have exactly the same coordinates, only the first appears in the\n");
1794 printf(
1795 " output. If any vertices are jettisoned, the vertex numbering in\n");
1796 printf(
1797 " the output .node file differs from that of the input .node file.\n");
1798 printf(
1799 " -e Outputs (to an .edge file) a list of edges of the triangulation.\n");
1800 printf(
1801 " -v Outputs the Voronoi diagram associated with the triangulation.\n");
1802 printf(
1803 " Does not attempt to detect degeneracies, so some Voronoi vertices\n");
1804 printf(
1805 " may be duplicated. See the discussion of Voronoi diagrams below.\n");
1806 printf(
1807 " -n Outputs (to a .neigh file) a list of triangles neighboring each\n");
1808 printf(" triangle.\n");
1809 printf(
1810 " -g Outputs the mesh to an Object File Format (.off) file, suitable for\n"
1811 );
1812 printf(" viewing with the Geometry Center's Geomview package.\n");
1813 printf(
1814 " -B No boundary markers in the output .node, .poly, and .edge output\n");
1815 printf(
1816 " files. See the detailed discussion of boundary markers below.\n");
1817 printf(
1818 " -P No output .poly file. Saves disk space, but you lose the ability\n");
1819 printf(
1820 " to maintain constraining segments on later refinements of the mesh.\n"
1821 );
1822 printf(" -N No output .node file.\n");
1823 printf(" -E No output .ele file.\n");
1824 printf(
1825 " -I No iteration numbers. Suppresses the output of .node and .poly\n");
1826 printf(
1827 " files, so your input files won't be overwritten. (If your input is\n"
1828 );
1829 printf(
1830 " a .poly file only, a .node file is written.) Cannot be used with\n");
1831 printf(
1832 " the -r switch, because that would overwrite your input .ele file.\n");
1833 printf(
1834 " Shouldn't be used with the -q, -a, -u, or -s switch if you are\n");
1835 printf(
1836 " using a .node file for input, because no .node file is written, so\n"
1837 );
1838 printf(" there is no record of any added Steiner points.\n");
1839 printf(" -O No holes. Ignores the holes in the .poly file.\n");
1840 printf(
1841 " -X No exact arithmetic. Normally, Triangle uses exact floating-point\n"
1842 );
1843 printf(
1844 " arithmetic for certain tests if it thinks the inexact tests are not\n"
1845 );
1846 printf(
1847 " accurate enough. Exact arithmetic ensures the robustness of the\n");
1848 printf(
1849 " triangulation algorithms, despite floating-point roundoff error.\n");
1850 printf(
1851 " Disabling exact arithmetic with the -X switch causes a small\n");
1852 printf(
1853 " improvement in speed and creates the possibility that Triangle will\n"
1854 );
1855 printf(" fail to produce a valid mesh. Not recommended.\n");
1856 printf(
1857 " -z Numbers all items starting from zero (rather than one). Note that\n"
1858 );
1859 printf(
1860 " this switch is normally overridden by the value used to number the\n"
1861 );
1862 printf(
1863 " first vertex of the input .node or .poly file. However, this\n");
1864 printf(
1865 " switch is useful when calling Triangle from another program.\n");
1866 printf(
1867 " -o2 Generates second-order subparametric elements with six nodes each.\n"
1868 );
1869 printf(
1870 " -Y No new vertices on the boundary. This switch is useful when the\n");
1871 printf(
1872 " mesh boundary must be preserved so that it conforms to some\n");
1873 printf(
1874 " adjacent mesh. Be forewarned that you will probably sacrifice much\n"
1875 );
1876 printf(
1877 " of the quality of the mesh; Triangle will try, but the resulting\n");
1878 printf(
1879 " mesh may contain poorly shaped triangles. Works well if all the\n");
1880 printf(
1881 " boundary vertices are closely spaced. Specify this switch twice\n");
1882 printf(
1883 " (`-YY') to prevent all segment splitting, including internal\n");
1884 printf(" boundaries.\n");
1885 printf(
1886 " -S Specifies the maximum number of Steiner points (vertices that are\n");
1887 printf(
1888 " not in the input, but are added to meet the constraints on minimum\n"
1889 );
1890 printf(
1891 " angle and maximum area). The default is to allow an unlimited\n");
1892 printf(
1893 " number. If you specify this switch with no number after it,\n");
1894 printf(
1895 " the limit is set to zero. Triangle always adds vertices at segment\n"
1896 );
1897 printf(
1898 " intersections, even if it needs to use more vertices than the limit\n"
1899 );
1900 printf(
1901 " you set. When Triangle inserts segments by splitting (-s), it\n");
1902 printf(
1903 " always adds enough vertices to ensure that all the segments of the\n"
1904 );
1905 printf(" PLSG are recovered, ignoring the limit if necessary.\n");
1906 printf(
1907 " -i Uses an incremental rather than a divide-and-conquer algorithm to\n");
1908 printf(
1909 " construct a Delaunay triangulation. Try it if the divide-and-\n");
1910 printf(" conquer algorithm fails.\n");
1911 printf(
1912 " -F Uses Steven Fortune's sweepline algorithm to construct a Delaunay\n");
1913 printf(
1914 " triangulation. Warning: does not use exact arithmetic for all\n");
1915 printf(" calculations. An exact result is not guaranteed.\n");
1916 printf(
1917 " -l Uses only vertical cuts in the divide-and-conquer algorithm. By\n");
1918 printf(
1919 " default, Triangle alternates between vertical and horizontal cuts,\n"
1920 );
1921 printf(
1922 " which usually improve the speed except with vertex sets that are\n");
1923 printf(
1924 " small or short and wide. This switch is primarily of theoretical\n");
1925 printf(" interest.\n");
1926 printf(
1927 " -s Specifies that segments should be forced into the triangulation by\n"
1928 );
1929 printf(
1930 " recursively splitting them at their midpoints, rather than by\n");
1931 printf(
1932 " generating a constrained Delaunay triangulation. Segment splitting\n"
1933 );
1934 printf(
1935 " is true to Ruppert's original algorithm, but can create needlessly\n"
1936 );
1937 printf(
1938 " small triangles. This switch is primarily of theoretical interest.\n"
1939 );
1940 printf(
1941 " -C Check the consistency of the final mesh. Uses exact arithmetic for\n"
1942 );
1943 printf(
1944 " checking, even if the -X switch is used. Useful if you suspect\n");
1945 printf(" Triangle is buggy.\n");
1946 printf(
1947 " -Q Quiet: Suppresses all explanation of what Triangle is doing,\n");
1948 printf(" unless an error occurs.\n");
1949 printf(
1950 " -V Verbose: Gives detailed information about what Triangle is doing.\n"
1951 );
1952 printf(
1953 " Add more `V's for increasing amount of detail. `-V' is most\n");
1954 printf(
1955 " useful; itgives information on algorithmic progress and much more\n");
1956 printf(
1957 " detailed statistics. `-VV' gives vertex-by-vertex details, and\n");
1958 printf(
1959 " prints so much that Triangle runs much more slowly. `-VVVV' gives\n"
1960 );
1961 printf(" information only a debugger could love.\n");
1962 printf(" -h Help: Displays these instructions.\n");
1963 printf("\n");
1964 printf("Definitions:\n");
1965 printf("\n");
1966 printf(
1967 " A Delaunay triangulation of a vertex set is a triangulation whose\n");
1968 printf(
1969 " vertices are the vertex set, that covers the convex hull of the vertex\n");
1970 printf(
1971 " set. A Delaunay triangulation has the property that no vertex lies\n");
1972 printf(
1973 " inside the circumscribing circle (circle that passes through all three\n");
1974 printf(" vertices) of any triangle in the triangulation.\n\n");
1975 printf(
1976 " A Voronoi diagram of a vertex set is a subdivision of the plane into\n");
1977 printf(
1978 " polygonal cells (some of which may be unbounded, meaning infinitely\n");
1979 printf(
1980 " large), where each cell is the set of points in the plane that are closer\n"
1981 );
1982 printf(
1983 " to some input vertex than to any other input vertex. The Voronoi diagram\n"
1984 );
1985 printf(" is a geometric dual of the Delaunay triangulation.\n\n");
1986 printf(
1987 " A Planar Straight Line Graph (PSLG) is a set of vertices and segments.\n");
1988 printf(
1989 " Segments are simply edges, whose endpoints are all vertices in the PSLG.\n"
1990 );
1991 printf(
1992 " Segments may intersect each other only at their endpoints. The file\n");
1993 printf(" format for PSLGs (.poly files) is described below.\n\n");
1994 printf(
1995 " A constrained Delaunay triangulation (CDT) of a PSLG is similar to a\n");
1996 printf(
1997 " Delaunay triangulation, but each PSLG segment is present as a single edge\n"
1998 );
1999 printf(
2000 " of the CDT. (A constrained Delaunay triangulation is not truly a\n");
2001 printf(
2002 " Delaunay triangulation, because some of its triangles might not be\n");
2003 printf(
2004 " Delaunay.) By definition, a CDT does not have any vertices other than\n");
2005 printf(
2006 " those specified in the input PSLG. Depending on context, a CDT might\n");
2007 printf(
2008 " cover the convex hull of the PSLG, or it might cover only a segment-\n");
2009 printf(" bounded region (e.g. a polygon).\n\n");
2010 printf(
2011 " A conforming Delaunay triangulation of a PSLG is a triangulation in which\n"
2012 );
2013 printf(
2014 " each triangle is truly Delaunay, and each PSLG segment is represented by\n"
2015 );
2016 printf(
2017 " a linear contiguous sequence of edges of the triangulation. New vertices\n"
2018 );
2019 printf(
2020 " (not part of the PSLG) may appear, and each input segment may have been\n");
2021 printf(
2022 " subdivided into shorter edges (subsegments) by these additional vertices.\n"
2023 );
2024 printf(
2025 " The new vertices are frequently necessary to maintain the Delaunay\n");
2026 printf(" property while ensuring that every segment is represented.\n\n");
2027 printf(
2028 " A conforming constrained Delaunay triangulation (CCDT) of a PSLG is a\n");
2029 printf(
2030 " triangulation of a PSLG whose triangles are constrained Delaunay. New\n");
2031 printf(" vertices may appear, and input segments may be subdivided into\n");
2032 printf(
2033 " subsegments, but not to guarantee that segments are respected; rather, to\n"
2034 );
2035 printf(
2036 " improve the quality of the triangles. The high-quality meshes produced\n");
2037 printf(
2038 " by the -q switch are usually CCDTs, but can be made conforming Delaunay\n");
2039 printf(" with the -D switch.\n\n");
2040 printf("File Formats:\n\n");
2041 printf(
2042 " All files may contain comments prefixed by the character '#'. Vertices,\n"
2043 );
2044 printf(
2045 " triangles, edges, holes, and maximum area constraints must be numbered\n");
2046 printf(
2047 " consecutively, starting from either 1 or 0. Whichever you choose, all\n");
2048 printf(
2049 " input files must be consistent; if the vertices are numbered from 1, so\n");
2050 printf(
2051 " must be all other objects. Triangle automatically detects your choice\n");
2052 printf(
2053 " while reading the .node (or .poly) file. (When calling Triangle from\n");
2054 printf(
2055 " another program, use the -z switch if you wish to number objects from\n");
2056 printf(" zero.) Examples of these file formats are given below.\n\n");
2057 printf(" .node files:\n");
2058 printf(
2059 " First line: <# of vertices> <dimension (must be 2)> <# of attributes>\n"
2060 );
2061 printf(
2062 " <# of boundary markers (0 or 1)>\n"
2063 );
2064 printf(
2065 " Remaining lines: <vertex #> <x> <y> [attributes] [boundary marker]\n");
2066 printf("\n");
2067 printf(
2068 " The attributes, which are typically floating-point values of physical\n");
2069 printf(
2070 " quantities (such as mass or conductivity) associated with the nodes of\n"
2071 );
2072 printf(
2073 " a finite element mesh, are copied unchanged to the output mesh. If -q,\n"
2074 );
2075 printf(
2076 " -a, -u, -D, or -s is selected, each new Steiner point added to the mesh\n"
2077 );
2078 printf(" has attributes assigned to it by linear interpolation.\n\n");
2079 printf(
2080 " If the fourth entry of the first line is `1', the last column of the\n");
2081 printf(
2082 " remainder of the file is assumed to contain boundary markers. Boundary\n"
2083 );
2084 printf(
2085 " markers are used to identify boundary vertices and vertices resting on\n"
2086 );
2087 printf(
2088 " PSLG segments; a complete description appears in a section below. The\n"
2089 );
2090 printf(
2091 " .node file produced by Triangle contains boundary markers in the last\n");
2092 printf(" column unless they are suppressed by the -B switch.\n\n");
2093 printf(" .ele files:\n");
2094 printf(
2095 " First line: <# of triangles> <nodes per triangle> <# of attributes>\n");
2096 printf(
2097 " Remaining lines: <triangle #> <node> <node> <node> ... [attributes]\n");
2098 printf("\n");
2099 printf(
2100 " Nodes are indices into the corresponding .node file. The first three\n");
2101 printf(
2102 " nodes are the corner vertices, and are listed in counterclockwise order\n"
2103 );
2104 printf(
2105 " around each triangle. (The remaining nodes, if any, depend on the type\n"
2106 );
2107 printf(" of finite element used.)\n\n");
2108 printf(
2109 " The attributes are just like those of .node files. Because there is no\n"
2110 );
2111 printf(
2112 " simple mapping from input to output triangles, Triangle attempts to\n");
2113 printf(
2114 " interpolate attributes, and may cause a lot of diffusion of attributes\n"
2115 );
2116 printf(
2117 " among nearby triangles as the triangulation is refined. Attributes do\n"
2118 );
2119 printf(" not diffuse across segments, so attributes used to identify\n");
2120 printf(" segment-bounded regions remain intact.\n\n");
2121 printf(
2122 " In .ele files produced by Triangle, each triangular element has three\n");
2123 printf(
2124 " nodes (vertices) unless the -o2 switch is used, in which case\n");
2125 printf(
2126 " subparametric quadratic elements with six nodes each are generated.\n");
2127 printf(
2128 " The first three nodes are the corners in counterclockwise order, and\n");
2129 printf(
2130 " the fourth, fifth, and sixth nodes lie on the midpoints of the edges\n");
2131 printf(
2132 " opposite the first, second, and third vertices, respectively.\n");
2133 printf("\n");
2134 printf(" .poly files:\n");
2135 printf(
2136 " First line: <# of vertices> <dimension (must be 2)> <# of attributes>\n"
2137 );
2138 printf(
2139 " <# of boundary markers (0 or 1)>\n"
2140 );
2141 printf(
2142 " Following lines: <vertex #> <x> <y> [attributes] [boundary marker]\n");
2143 printf(" One line: <# of segments> <# of boundary markers (0 or 1)>\n");
2144 printf(
2145 " Following lines: <segment #> <endpoint> <endpoint> [boundary marker]\n");
2146 printf(" One line: <# of holes>\n");
2147 printf(" Following lines: <hole #> <x> <y>\n");
2148 printf(
2149 " Optional line: <# of regional attributes and/or area constraints>\n");
2150 printf(
2151 " Optional following lines: <region #> <x> <y> <attribute> <max area>\n");
2152 printf("\n");
2153 printf(
2154 " A .poly file represents a PSLG, as well as some additional information.\n"
2155 );
2156 printf(
2157 " The first section lists all the vertices, and is identical to the\n");
2158 printf(
2159 " format of .node files. <# of vertices> may be set to zero to indicate\n"
2160 );
2161 printf(
2162 " that the vertices are listed in a separate .node file; .poly files\n");
2163 printf(
2164 " produced by Triangle always have this format. A vertex set represented\n"
2165 );
2166 printf(
2167 " this way has the advantage that it may easily be triangulated with or\n");
2168 printf(
2169 " without segments (depending on whether the -p switch is invoked).\n");
2170 printf("\n");
2171 printf(
2172 " The second section lists the segments. Segments are edges whose\n");
2173 printf(
2174 " presence in the triangulation is enforced. (Depending on the choice of\n"
2175 );
2176 printf(
2177 " switches, segment might be subdivided into smaller edges). Each\n");
2178 printf(
2179 " segment is specified by listing the indices of its two endpoints. This\n"
2180 );
2181 printf(
2182 " means that you must include its endpoints in the vertex list. Each\n");
2183 printf(" segment, like each point, may have a boundary marker.\n\n");
2184 printf(
2185 " If -q, -a, -u, and -s are not selected, Triangle produces a constrained\n"
2186 );
2187 printf(
2188 " Delaunay triangulation (CDT), in which each segment appears as a single\n"
2189 );
2190 printf(
2191 " edge in the triangulation. If -q, -a, -u, or -s is selected, Triangle\n"
2192 );
2193 printf(
2194 " produces a conforming constrained Delaunay triangulation (CCDT), in\n");
2195 printf(
2196 " which segments may be subdivided into smaller edges. If -D is\n");
2197 printf(
2198 " selected, Triangle produces a conforming Delaunay triangulation, so\n");
2199 printf(
2200 " that every triangle is Delaunay, and not just constrained Delaunay.\n");
2201 printf("\n");
2202 printf(
2203 " The third section lists holes (and concavities, if -c is selected) in\n");
2204 printf(
2205 " the triangulation. Holes are specified by identifying a point inside\n");
2206 printf(
2207 " each hole. After the triangulation is formed, Triangle creates holes\n");
2208 printf(
2209 " by eating triangles, spreading out from each hole point until its\n");
2210 printf(
2211 " progress is blocked by segments in the PSLG. You must be careful to\n");
2212 printf(
2213 " enclose each hole in segments, or your whole triangulation might be\n");
2214 printf(
2215 " eaten away. If the two triangles abutting a segment are eaten, the\n");
2216 printf(
2217 " segment itself is also eaten. Do not place a hole directly on a\n");
2218 printf(" segment; if you do, Triangle chooses one side of the segment\n");
2219 printf(" arbitrarily.\n\n");
2220 printf(
2221 " The optional fourth section lists regional attributes (to be assigned\n");
2222 printf(
2223 " to all triangles in a region) and regional constraints on the maximum\n");
2224 printf(
2225 " triangle area. Triangle reads this section only if the -A switch is\n");
2226 printf(
2227 " used or the -a switch is used without a number following it, and the -r\n"
2228 );
2229 printf(
2230 " switch is not used. Regional attributes and area constraints are\n");
2231 printf(
2232 " propagated in the same manner as holes: you specify a point for each\n");
2233 printf(
2234 " attribute and/or constraint, and the attribute and/or constraint\n");
2235 printf(
2236 " affects the whole region (bounded by segments) containing the point.\n");
2237 printf(
2238 " If two values are written on a line after the x and y coordinate, the\n");
2239 printf(
2240 " first such value is assumed to be a regional attribute (but is only\n");
2241 printf(
2242 " applied if the -A switch is selected), and the second value is assumed\n"
2243 );
2244 printf(
2245 " to be a regional area constraint (but is only applied if the -a switch\n"
2246 );
2247 printf(
2248 " is selected). You may specify just one value after the coordinates,\n");
2249 printf(
2250 " which can serve as both an attribute and an area constraint, depending\n"
2251 );
2252 printf(
2253 " on the choice of switches. If you are using the -A and -a switches\n");
2254 printf(
2255 " simultaneously and wish to assign an attribute to some region without\n");
2256 printf(" imposing an area constraint, use a negative maximum area.\n\n");
2257 printf(
2258 " When a triangulation is created from a .poly file, you must either\n");
2259 printf(
2260 " enclose the entire region to be triangulated in PSLG segments, or\n");
2261 printf(
2262 " use the -c switch, which automatically creates extra segments that\n");
2263 printf(
2264 " enclose the convex hull of the PSLG. If you do not use the -c switch,\n"
2265 );
2266 printf(
2267 " Triangle eats all triangles that are not enclosed by segments; if you\n");
2268 printf(
2269 " are not careful, your whole triangulation may be eaten away. If you do\n"
2270 );
2271 printf(
2272 " use the -c switch, you can still produce concavities by the appropriate\n"
2273 );
2274 printf(
2275 " placement of holes just inside the boundary of the convex hull.\n");
2276 printf("\n");
2277 printf(
2278 " An ideal PSLG has no intersecting segments, nor any vertices that lie\n");
2279 printf(
2280 " upon segments (except, of course, the endpoints of each segment). You\n"
2281 );
2282 printf(
2283 " aren't required to make your .poly files ideal, but you should be aware\n"
2284 );
2285 printf(
2286 " of what can go wrong. Segment intersections are relatively safe--\n");
2287 printf(
2288 " Triangle calculates the intersection points for you and adds them to\n");
2289 printf(
2290 " the triangulation--as long as your machine's floating-point precision\n");
2291 printf(
2292 " doesn't become a problem. You are tempting the fates if you have three\n"
2293 );
2294 printf(
2295 " segments that cross at the same location, and expect Triangle to figure\n"
2296 );
2297 printf(
2298 " out where the intersection point is. Thanks to floating-point roundoff\n"
2299 );
2300 printf(
2301 " error, Triangle will probably decide that the three segments intersect\n"
2302 );
2303 printf(
2304 " at three different points, and you will find a minuscule triangle in\n");
2305 printf(
2306 " your output--unless Triangle tries to refine the tiny triangle, uses\n");
2307 printf(
2308 " up the last bit of machine precision, and fails to terminate at all.\n");
2309 printf(
2310 " You're better off putting the intersection point in the input files,\n");
2311 printf(
2312 " and manually breaking up each segment into two. Similarly, if you\n");
2313 printf(
2314 " place a vertex at the middle of a segment, and hope that Triangle will\n"
2315 );
2316 printf(
2317 " break up the segment at that vertex, you might get lucky. On the other\n"
2318 );
2319 printf(
2320 " hand, Triangle might decide that the vertex doesn't lie precisely on\n");
2321 printf(
2322 " the segment, and you'll have a needle-sharp triangle in your output--or\n"
2323 );
2324 printf(" a lot of tiny triangles if you're generating a quality mesh.\n");
2325 printf("\n");
2326 printf(
2327 " When Triangle reads a .poly file, it also writes a .poly file, which\n");
2328 printf(
2329 " includes all the subsegments--the edges that are parts of input\n");
2330 printf(
2331 " segments. If the -c switch is used, the output .poly file also\n");
2332 printf(
2333 " includes all of the edges on the convex hull. Hence, the output .poly\n"
2334 );
2335 printf(
2336 " file is useful for finding edges associated with input segments and for\n"
2337 );
2338 printf(
2339 " setting boundary conditions in finite element simulations. Moreover,\n");
2340 printf(
2341 " you will need the output .poly file if you plan to refine the output\n");
2342 printf(
2343 " mesh, and don't want segments to be missing in later triangulations.\n");
2344 printf("\n");
2345 printf(" .area files:\n");
2346 printf(" First line: <# of triangles>\n");
2347 printf(" Following lines: <triangle #> <maximum area>\n");
2348 printf("\n");
2349 printf(
2350 " An .area file associates with each triangle a maximum area that is used\n"
2351 );
2352 printf(
2353 " for mesh refinement. As with other file formats, every triangle must\n");
2354 printf(
2355 " be represented, and the triangles must be numbered consecutively. A\n");
2356 printf(
2357 " triangle may be left unconstrained by assigning it a negative maximum\n");
2358 printf(" area.\n\n");
2359 printf(" .edge files:\n");
2360 printf(" First line: <# of edges> <# of boundary markers (0 or 1)>\n");
2361 printf(
2362 " Following lines: <edge #> <endpoint> <endpoint> [boundary marker]\n");
2363 printf("\n");
2364 printf(
2365 " Endpoints are indices into the corresponding .node file. Triangle can\n"
2366 );
2367 printf(
2368 " produce .edge files (use the -e switch), but cannot read them. The\n");
2369 printf(
2370 " optional column of boundary markers is suppressed by the -B switch.\n");
2371 printf("\n");
2372 printf(
2373 " In Voronoi diagrams, one also finds a special kind of edge that is an\n");
2374 printf(
2375 " infinite ray with only one endpoint. For these edges, a different\n");
2376 printf(" format is used:\n\n");
2377 printf(" <edge #> <endpoint> -1 <direction x> <direction y>\n\n");
2378 printf(
2379 " The `direction' is a floating-point vector that indicates the direction\n"
2380 );
2381 printf(" of the infinite ray.\n\n");
2382 printf(" .neigh files:\n");
2383 printf(
2384 " First line: <# of triangles> <# of neighbors per triangle (always 3)>\n"
2385 );
2386 printf(
2387 " Following lines: <triangle #> <neighbor> <neighbor> <neighbor>\n");
2388 printf("\n");
2389 printf(
2390 " Neighbors are indices into the corresponding .ele file. An index of -1\n"
2391 );
2392 printf(
2393 " indicates no neighbor (because the triangle is on an exterior\n");
2394 printf(
2395 " boundary). The first neighbor of triangle i is opposite the first\n");
2396 printf(" corner of triangle i, and so on.\n\n");
2397 printf(
2398 " Triangle can produce .neigh files (use the -n switch), but cannot read\n"
2399 );
2400 printf(" them.\n\n");
2401 printf("Boundary Markers:\n\n");
2402 printf(
2403 " Boundary markers are tags used mainly to identify which output vertices\n");
2404 printf(
2405 " and edges are associated with which PSLG segment, and to identify which\n");
2406 printf(
2407 " vertices and edges occur on a boundary of the triangulation. A common\n");
2408 printf(
2409 " use is to determine where boundary conditions should be applied to a\n");
2410 printf(
2411 " finite element mesh. You can prevent boundary markers from being written\n"
2412 );
2413 printf(" into files produced by Triangle by using the -B switch.\n\n");
2414 printf(
2415 " The boundary marker associated with each segment in an output .poly file\n"
2416 );
2417 printf(" and each edge in an output .edge file is chosen as follows:\n");
2418 printf(
2419 " - If an output edge is part or all of a PSLG segment with a nonzero\n");
2420 printf(
2421 " boundary marker, then the edge is assigned the same marker.\n");
2422 printf(
2423 " - Otherwise, if the edge lies on a boundary of the triangulation\n");
2424 printf(
2425 " (even the boundary of a hole), then the edge is assigned the marker\n");
2426 printf(" one (1).\n");
2427 printf(" - Otherwise, the edge is assigned the marker zero (0).\n");
2428 printf(
2429 " The boundary marker associated with each vertex in an output .node file\n");
2430 printf(" is chosen as follows:\n");
2431 printf(
2432 " - If a vertex is assigned a nonzero boundary marker in the input file,\n"
2433 );
2434 printf(
2435 " then it is assigned the same marker in the output .node file.\n");
2436 printf(
2437 " - Otherwise, if the vertex lies on a PSLG segment (even if it is an\n");
2438 printf(
2439 " endpoint of the segment) with a nonzero boundary marker, then the\n");
2440 printf(
2441 " vertex is assigned the same marker. If the vertex lies on several\n");
2442 printf(" such segments, one of the markers is chosen arbitrarily.\n");
2443 printf(
2444 " - Otherwise, if the vertex occurs on a boundary of the triangulation,\n");
2445 printf(" then the vertex is assigned the marker one (1).\n");
2446 printf(" - Otherwise, the vertex is assigned the marker zero (0).\n");
2447 printf("\n");
2448 printf(
2449 " If you want Triangle to determine for you which vertices and edges are on\n"
2450 );
2451 printf(
2452 " the boundary, assign them the boundary marker zero (or use no markers at\n"
2453 );
2454 printf(
2455 " all) in your input files. In the output files, all boundary vertices,\n");
2456 printf(" edges, and segments will be assigned the value one.\n\n");
2457 printf("Triangulation Iteration Numbers:\n\n");
2458 printf(
2459 " Because Triangle can read and refine its own triangulations, input\n");
2460 printf(
2461 " and output files have iteration numbers. For instance, Triangle might\n");
2462 printf(
2463 " read the files mesh.3.node, mesh.3.ele, and mesh.3.poly, refine the\n");
2464 printf(
2465 " triangulation, and output the files mesh.4.node, mesh.4.ele, and\n");
2466 printf(" mesh.4.poly. Files with no iteration number are treated as if\n");
2467 printf(
2468 " their iteration number is zero; hence, Triangle might read the file\n");
2469 printf(
2470 " points.node, triangulate it, and produce the files points.1.node and\n");
2471 printf(" points.1.ele.\n\n");
2472 printf(
2473 " Iteration numbers allow you to create a sequence of successively finer\n");
2474 printf(
2475 " meshes suitable for multigrid methods. They also allow you to produce a\n"
2476 );
2477 printf(
2478 " sequence of meshes using error estimate-driven mesh refinement.\n");
2479 printf("\n");
2480 printf(
2481 " If you're not using refinement or quality meshing, and you don't like\n");
2482 printf(
2483 " iteration numbers, use the -I switch to disable them. This switch also\n");
2484 printf(
2485 " disables output of .node and .poly files to prevent your input files from\n"
2486 );
2487 printf(
2488 " being overwritten. (If the input is a .poly file that contains its own\n");
2489 printf(
2490 " points, a .node file is written. This can be quite convenient for\n");
2491 printf(" computing CDTs or quality meshes.)\n\n");
2492 printf("Examples of How to Use Triangle:\n\n");
2493 printf(
2494 " `triangle dots' reads vertices from dots.node, and writes their Delaunay\n"
2495 );
2496 printf(
2497 " triangulation to dots.1.node and dots.1.ele. (dots.1.node is identical\n");
2498 printf(
2499 " to dots.node.) `triangle -I dots' writes the triangulation to dots.ele\n");
2500 printf(
2501 " instead. (No additional .node file is needed, so none is written.)\n");
2502 printf("\n");
2503 printf(
2504 " `triangle -pe object.1' reads a PSLG from object.1.poly (and possibly\n");
2505 printf(
2506 " object.1.node, if the vertices are omitted from object.1.poly) and writes\n"
2507 );
2508 printf(
2509 " its constrained Delaunay triangulation to object.2.node and object.2.ele.\n"
2510 );
2511 printf(
2512 " The segments are copied to object.2.poly, and all edges are written to\n");
2513 printf(" object.2.edge.\n\n");
2514 printf(
2515 " `triangle -pq31.5a.1 object' reads a PSLG from object.poly (and possibly\n"
2516 );
2517 printf(
2518 " object.node), generates a mesh whose angles are all between 31.5 and 117\n"
2519 );
2520 printf(
2521 " degrees and whose triangles all have areas of 0.1 or less, and writes the\n"
2522 );
2523 printf(
2524 " mesh to object.1.node and object.1.ele. Each segment may be broken up\n");
2525 printf(" into multiple subsegments; these are written to object.1.poly.\n");
2526 printf("\n");
2527 printf(
2528 " Here is a sample file `box.poly' describing a square with a square hole:\n"
2529 );
2530 printf("\n");
2531 printf(
2532 " # A box with eight vertices in 2D, no attributes, one boundary marker.\n"
2533 );
2534 printf(" 8 2 0 1\n");
2535 printf(" # Outer box has these vertices:\n");
2536 printf(" 1 0 0 0\n");
2537 printf(" 2 0 3 0\n");
2538 printf(" 3 3 0 0\n");
2539 printf(" 4 3 3 33 # A special marker for this vertex.\n");
2540 printf(" # Inner square has these vertices:\n");
2541 printf(" 5 1 1 0\n");
2542 printf(" 6 1 2 0\n");
2543 printf(" 7 2 1 0\n");
2544 printf(" 8 2 2 0\n");
2545 printf(" # Five segments with boundary markers.\n");
2546 printf(" 5 1\n");
2547 printf(" 1 1 2 5 # Left side of outer box.\n");
2548 printf(" # Square hole has these segments:\n");
2549 printf(" 2 5 7 0\n");
2550 printf(" 3 7 8 0\n");
2551 printf(" 4 8 6 10\n");
2552 printf(" 5 6 5 0\n");
2553 printf(" # One hole in the middle of the inner square.\n");
2554 printf(" 1\n");
2555 printf(" 1 1.5 1.5\n");
2556 printf("\n");
2557 printf(
2558 " Note that some segments are missing from the outer square, so you must\n");
2559 printf(
2560 " use the `-c' switch. After `triangle -pqc box.poly', here is the output\n"
2561 );
2562 printf(
2563 " file `box.1.node', with twelve vertices. The last four vertices were\n");
2564 printf(
2565 " added to meet the angle constraint. Vertices 1, 2, and 9 have markers\n");
2566 printf(
2567 " from segment 1. Vertices 6 and 8 have markers from segment 4. All the\n");
2568 printf(
2569 " other vertices but 4 have been marked to indicate that they lie on a\n");
2570 printf(" boundary.\n\n");
2571 printf(" 12 2 0 1\n");
2572 printf(" 1 0 0 5\n");
2573 printf(" 2 0 3 5\n");
2574 printf(" 3 3 0 1\n");
2575 printf(" 4 3 3 33\n");
2576 printf(" 5 1 1 1\n");
2577 printf(" 6 1 2 10\n");
2578 printf(" 7 2 1 1\n");
2579 printf(" 8 2 2 10\n");
2580 printf(" 9 0 1.5 5\n");
2581 printf(" 10 1.5 0 1\n");
2582 printf(" 11 3 1.5 1\n");
2583 printf(" 12 1.5 3 1\n");
2584 printf(" # Generated by triangle -pqc box.poly\n");
2585 printf("\n");
2586 printf(" Here is the output file `box.1.ele', with twelve triangles.\n");
2587 printf("\n");
2588 printf(" 12 3 0\n");
2589 printf(" 1 5 6 9\n");
2590 printf(" 2 10 3 7\n");
2591 printf(" 3 6 8 12\n");
2592 printf(" 4 9 1 5\n");
2593 printf(" 5 6 2 9\n");
2594 printf(" 6 7 3 11\n");
2595 printf(" 7 11 4 8\n");
2596 printf(" 8 7 5 10\n");
2597 printf(" 9 12 2 6\n");
2598 printf(" 10 8 7 11\n");
2599 printf(" 11 5 1 10\n");
2600 printf(" 12 8 4 12\n");
2601 printf(" # Generated by triangle -pqc box.poly\n\n");
2602 printf(
2603 " Here is the output file `box.1.poly'. Note that segments have been added\n"
2604 );
2605 printf(
2606 " to represent the convex hull, and some segments have been subdivided by\n");
2607 printf(
2608 " newly added vertices. Note also that <# of vertices> is set to zero to\n");
2609 printf(" indicate that the vertices should be read from the .node file.\n");
2610 printf("\n");
2611 printf(" 0 2 0 1\n");
2612 printf(" 12 1\n");
2613 printf(" 1 1 9 5\n");
2614 printf(" 2 5 7 1\n");
2615 printf(" 3 8 7 1\n");
2616 printf(" 4 6 8 10\n");
2617 printf(" 5 5 6 1\n");
2618 printf(" 6 3 10 1\n");
2619 printf(" 7 4 11 1\n");
2620 printf(" 8 2 12 1\n");
2621 printf(" 9 9 2 5\n");
2622 printf(" 10 10 1 1\n");
2623 printf(" 11 11 3 1\n");
2624 printf(" 12 12 4 1\n");
2625 printf(" 1\n");
2626 printf(" 1 1.5 1.5\n");
2627 printf(" # Generated by triangle -pqc box.poly\n");
2628 printf("\n");
2629 printf("Refinement and Area Constraints:\n");
2630 printf("\n");
2631 printf(
2632 " The -r switch causes a mesh (.node and .ele files) to be read and\n");
2633 printf(
2634 " refined. If the -p switch is also used, a .poly file is read and used to\n"
2635 );
2636 printf(
2637 " specify edges that are constrained and cannot be eliminated (although\n");
2638 printf(
2639 " they can be subdivided into smaller edges) by the refinement process.\n");
2640 printf("\n");
2641 printf(
2642 " When you refine a mesh, you generally want to impose tighter constraints.\n"
2643 );
2644 printf(
2645 " One way to accomplish this is to use -q with a larger angle, or -a\n");
2646 printf(
2647 " followed by a smaller area than you used to generate the mesh you are\n");
2648 printf(
2649 " refining. Another way to do this is to create an .area file, which\n");
2650 printf(
2651 " specifies a maximum area for each triangle, and use the -a switch\n");
2652 printf(
2653 " (without a number following). Each triangle's area constraint is applied\n"
2654 );
2655 printf(
2656 " to that triangle. Area constraints tend to diffuse as the mesh is\n");
2657 printf(
2658 " refined, so if there are large variations in area constraint between\n");
2659 printf(
2660 " adjacent triangles, you may not get the results you want. In that case,\n"
2661 );
2662 printf(
2663 " consider instead using the -u switch and writing a C procedure that\n");
2664 printf(" determines which triangles are too large.\n\n");
2665 printf(
2666 " If you are refining a mesh composed of linear (three-node) elements, the\n"
2667 );
2668 printf(
2669 " output mesh contains all the nodes present in the input mesh, in the same\n"
2670 );
2671 printf(
2672 " order, with new nodes added at the end of the .node file. However, the\n");
2673 printf(
2674 " refinement is not hierarchical: there is no guarantee that each output\n");
2675 printf(
2676 " element is contained in a single input element. Often, an output element\n"
2677 );
2678 printf(
2679 " can overlap two or three input elements, and some input edges are not\n");
2680 printf(
2681 " present in the output mesh. Hence, a sequence of refined meshes forms a\n"
2682 );
2683 printf(
2684 " hierarchy of nodes, but not a hierarchy of elements. If you refine a\n");
2685 printf(
2686 " mesh of higher-order elements, the hierarchical property applies only to\n"
2687 );
2688 printf(
2689 " the nodes at the corners of an element; the midpoint nodes on each edge\n");
2690 printf(" are discarded before the mesh is refined.\n\n");
2691 printf(
2692 " Maximum area constraints in .poly files operate differently from those in\n"
2693 );
2694 printf(
2695 " .area files. A maximum area in a .poly file applies to the whole\n");
2696 printf(
2697 " (segment-bounded) region in which a point falls, whereas a maximum area\n");
2698 printf(
2699 " in an .area file applies to only one triangle. Area constraints in .poly\n"
2700 );
2701 printf(
2702 " files are used only when a mesh is first generated, whereas area\n");
2703 printf(
2704 " constraints in .area files are used only to refine an existing mesh, and\n"
2705 );
2706 printf(
2707 " are typically based on a posteriori error estimates resulting from a\n");
2708 printf(" finite element simulation on that mesh.\n\n");
2709 printf(
2710 " `triangle -rq25 object.1' reads object.1.node and object.1.ele, then\n");
2711 printf(
2712 " refines the triangulation to enforce a 25 degree minimum angle, and then\n"
2713 );
2714 printf(
2715 " writes the refined triangulation to object.2.node and object.2.ele.\n");
2716 printf("\n");
2717 printf(
2718 " `triangle -rpaa6.2 z.3' reads z.3.node, z.3.ele, z.3.poly, and z.3.area.\n"
2719 );
2720 printf(
2721 " After reconstructing the mesh and its subsegments, Triangle refines the\n");
2722 printf(
2723 " mesh so that no triangle has area greater than 6.2, and furthermore the\n");
2724 printf(
2725 " triangles satisfy the maximum area constraints in z.3.area. No angle\n");
2726 printf(
2727 " bound is imposed at all. The output is written to z.4.node, z.4.ele, and\n"
2728 );
2729 printf(" z.4.poly.\n\n");
2730 printf(
2731 " The sequence `triangle -qa1 x', `triangle -rqa.3 x.1', `triangle -rqa.1\n");
2732 printf(
2733 " x.2' creates a sequence of successively finer meshes x.1, x.2, and x.3,\n");
2734 printf(" suitable for multigrid.\n\n");
2735 printf("Convex Hulls and Mesh Boundaries:\n\n");
2736 printf(
2737 " If the input is a vertex set (not a PSLG), Triangle produces its convex\n");
2738 printf(
2739 " hull as a by-product in the output .poly file if you use the -c switch.\n");
2740 printf(
2741 " There are faster algorithms for finding a two-dimensional convex hull\n");
2742 printf(" than triangulation, of course, but this one comes for free.\n\n");
2743 printf(
2744 " If the input is an unconstrained mesh (you are using the -r switch but\n");
2745 printf(
2746 " not the -p switch), Triangle produces a list of its boundary edges\n");
2747 printf(
2748 " (including hole boundaries) as a by-product when you use the -c switch.\n");
2749 printf(
2750 " If you also use the -p switch, the output .poly file contains all the\n");
2751 printf(" segments from the input .poly file as well.\n\n");
2752 printf("Voronoi Diagrams:\n\n");
2753 printf(
2754 " The -v switch produces a Voronoi diagram, in files suffixed .v.node and\n");
2755 printf(
2756 " .v.edge. For example, `triangle -v points' reads points.node, produces\n");
2757 printf(
2758 " its Delaunay triangulation in points.1.node and points.1.ele, and\n");
2759 printf(
2760 " produces its Voronoi diagram in points.1.v.node and points.1.v.edge. The\n"
2761 );
2762 printf(
2763 " .v.node file contains a list of all Voronoi vertices, and the .v.edge\n");
2764 printf(
2765 " file contains a list of all Voronoi edges, some of which may be infinite\n"
2766 );
2767 printf(
2768 " rays. (The choice of filenames makes it easy to run the set of Voronoi\n");
2769 printf(" vertices through Triangle, if so desired.)\n\n");
2770 printf(
2771 " This implementation does not use exact arithmetic to compute the Voronoi\n"
2772 );
2773 printf(
2774 " vertices, and does not check whether neighboring vertices are identical.\n"
2775 );
2776 printf(
2777 " Be forewarned that if the Delaunay triangulation is degenerate or\n");
2778 printf(
2779 " near-degenerate, the Voronoi diagram may have duplicate vertices or\n");
2780 printf(" crossing edges.\n\n");
2781 printf(
2782 " The result is a valid Voronoi diagram only if Triangle's output is a true\n"
2783 );
2784 printf(
2785 " Delaunay triangulation. The Voronoi output is usually meaningless (and\n");
2786 printf(
2787 " may contain crossing edges and other pathology) if the output is a CDT or\n"
2788 );
2789 printf(
2790 " CCDT, or if it has holes or concavities. If the triangulated domain is\n");
2791 printf(
2792 " convex and has no holes, you can use -D switch to force Triangle to\n");
2793 printf(
2794 " construct a conforming Delaunay triangulation instead of a CCDT, so the\n");
2795 printf(" Voronoi diagram will be valid.\n\n");
2796 printf("Mesh Topology:\n\n");
2797 printf(
2798 " You may wish to know which triangles are adjacent to a certain Delaunay\n");
2799 printf(
2800 " edge in an .edge file, which Voronoi cells are adjacent to a certain\n");
2801 printf(
2802 " Voronoi edge in a .v.edge file, or which Voronoi cells are adjacent to\n");
2803 printf(
2804 " each other. All of this information can be found by cross-referencing\n");
2805 printf(
2806 " output files with the recollection that the Delaunay triangulation and\n");
2807 printf(" the Voronoi diagram are planar duals.\n\n");
2808 printf(
2809 " Specifically, edge i of an .edge file is the dual of Voronoi edge i of\n");
2810 printf(
2811 " the corresponding .v.edge file, and is rotated 90 degrees counterclock-\n");
2812 printf(
2813 " wise from the Voronoi edge. Triangle j of an .ele file is the dual of\n");
2814 printf(
2815 " vertex j of the corresponding .v.node file. Voronoi cell k is the dual\n");
2816 printf(" of vertex k of the corresponding .node file.\n\n");
2817 printf(
2818 " Hence, to find the triangles adjacent to a Delaunay edge, look at the\n");
2819 printf(
2820 " vertices of the corresponding Voronoi edge. If the endpoints of a\n");
2821 printf(
2822 " Voronoi edge are Voronoi vertices 2 and 6 respectively, then triangles 2\n"
2823 );
2824 printf(
2825 " and 6 adjoin the left and right sides of the corresponding Delaunay edge,\n"
2826 );
2827 printf(
2828 " respectively. To find the Voronoi cells adjacent to a Voronoi edge, look\n"
2829 );
2830 printf(
2831 " at the endpoints of the corresponding Delaunay edge. If the endpoints of\n"
2832 );
2833 printf(
2834 " a Delaunay edge are input vertices 7 and 12, then Voronoi cells 7 and 12\n"
2835 );
2836 printf(
2837 " adjoin the right and left sides of the corresponding Voronoi edge,\n");
2838 printf(
2839 " respectively. To find which Voronoi cells are adjacent to each other,\n");
2840 printf(" just read the list of Delaunay edges.\n\n");
2841 printf(
2842 " Triangle does not write a list of the edges adjoining each Voronoi cell,\n"
2843 );
2844 printf(
2845 " but you can reconstructed it straightforwardly. For instance, to find\n");
2846 printf(
2847 " all the edges of Voronoi cell 1, search the output .edge file for every\n");
2848 printf(
2849 " edge that has input vertex 1 as an endpoint. The corresponding dual\n");
2850 printf(
2851 " edges in the output .v.edge file form the boundary of Voronoi cell 1.\n");
2852 printf("\n");
2853 printf(
2854 " For each Voronoi vertex, the .neigh file gives a list of the three\n");
2855 printf(
2856 " Voronoi vertices attached to it. You might find this more convenient\n");
2857 printf(" than the .v.edge file.\n\n");
2858 printf("Quadratic Elements:\n\n");
2859 printf(
2860 " Triangle generates meshes with subparametric quadratic elements if the\n");
2861 printf(
2862 " -o2 switch is specified. Quadratic elements have six nodes per element,\n"
2863 );
2864 printf(
2865 " rather than three. `Subparametric' means that the edges of the triangles\n"
2866 );
2867 printf(
2868 " are always straight, so that subparametric quadratic elements are\n");
2869 printf(
2870 " geometrically identical to linear elements, even though they can be used\n"
2871 );
2872 printf(
2873 " with quadratic interpolating functions. The three extra nodes of an\n");
2874 printf(
2875 " element fall at the midpoints of the three edges, with the fourth, fifth,\n"
2876 );
2877 printf(
2878 " and sixth nodes appearing opposite the first, second, and third corners\n");
2879 printf(" respectively.\n\n");
2880 printf("Domains with Small Angles:\n\n");
2881 printf(
2882 " If two input segments adjoin each other at a small angle, clearly the -q\n"
2883 );
2884 printf(
2885 " switch cannot remove the small angle. Moreover, Triangle may have no\n");
2886 printf(
2887 " choice but to generate additional triangles whose smallest angles are\n");
2888 printf(
2889 " smaller than the specified bound. However, these triangles only appear\n");
2890 printf(
2891 " between input segments separated by small angles. Moreover, if you\n");
2892 printf(
2893 " request a minimum angle of theta degrees, Triangle will generally produce\n"
2894 );
2895 printf(
2896 " no angle larger than 180 - 2 theta, even if it is forced to compromise on\n"
2897 );
2898 printf(" the minimum angle.\n\n");
2899 printf("Statistics:\n\n");
2900 printf(
2901 " After generating a mesh, Triangle prints a count of entities in the\n");
2902 printf(
2903 " output mesh, including the number of vertices, triangles, edges, exterior\n"
2904 );
2905 printf(
2906 " boundary edges (i.e. subsegments on the boundary of the triangulation,\n");
2907 printf(
2908 " including hole boundaries), interior boundary edges (i.e. subsegments of\n"
2909 );
2910 printf(
2911 " input segments not on the boundary), and total subsegments. If you've\n");
2912 printf(
2913 " forgotten the statistics for an existing mesh, run Triangle on that mesh\n"
2914 );
2915 printf(
2916 " with the -rNEP switches to read the mesh and print the statistics without\n"
2917 );
2918 printf(
2919 " writing any files. Use -rpNEP if you've got a .poly file for the mesh.\n");
2920 printf("\n");
2921 printf(
2922 " The -V switch produces extended statistics, including a rough estimate\n");
2923 printf(
2924 " of memory use, the number of calls to geometric predicates, and\n");
2925 printf(
2926 " histograms of the angles and the aspect ratios of the triangles in the\n");
2927 printf(" mesh.\n\n");
2928 printf("Exact Arithmetic:\n\n");
2929 printf(
2930 " Triangle uses adaptive exact arithmetic to perform what computational\n");
2931 printf(
2932 " geometers call the `orientation' and `incircle' tests. If the floating-\n"
2933 );
2934 printf(
2935 " point arithmetic of your machine conforms to the IEEE 754 standard (as\n");
2936 printf(
2937 " most workstations do), and does not use extended precision internal\n");
2938 printf(
2939 " floating-point registers, then your output is guaranteed to be an\n");
2940 printf(
2941 " absolutely true Delaunay or constrained Delaunay triangulation, roundoff\n"
2942 );
2943 printf(
2944 " error notwithstanding. The word `adaptive' implies that these arithmetic\n"
2945 );
2946 printf(
2947 " routines compute the result only to the precision necessary to guarantee\n"
2948 );
2949 printf(
2950 " correctness, so they are usually nearly as fast as their approximate\n");
2951 printf(" counterparts.\n\n");
2952 printf(
2953 " May CPUs, including Intel x86 processors, have extended precision\n");
2954 printf(
2955 " floating-point registers. These must be reconfigured so their precision\n"
2956 );
2957 printf(
2958 " is reduced to memory precision. Triangle does this if it is compiled\n");
2959 printf(" correctly. See the makefile for details.\n\n");
2960 printf(
2961 " The exact tests can be disabled with the -X switch. On most inputs, this\n"
2962 );
2963 printf(
2964 " switch reduces the computation time by about eight percent--it's not\n");
2965 printf(
2966 " worth the risk. There are rare difficult inputs (having many collinear\n");
2967 printf(
2968 " and cocircular vertices), however, for which the difference in speed\n");
2969 printf(
2970 " could be a factor of two. Be forewarned that these are precisely the\n");
2971 printf(
2972 " inputs most likely to cause errors if you use the -X switch. Hence, the\n"
2973 );
2974 printf(" -X switch is not recommended.\n\n");
2975 printf(
2976 " Unfortunately, the exact tests don't solve every numerical problem.\n");
2977 printf(
2978 " Exact arithmetic is not used to compute the positions of new vertices,\n");
2979 printf(
2980 " because the bit complexity of vertex coordinates would grow without\n");
2981 printf(
2982 " bound. Hence, segment intersections aren't computed exactly; in very\n");
2983 printf(
2984 " unusual cases, roundoff error in computing an intersection point might\n");
2985 printf(
2986 " actually lead to an inverted triangle and an invalid triangulation.\n");
2987 printf(
2988 " (This is one reason to specify your own intersection points in your .poly\n"
2989 );
2990 printf(
2991 " files.) Similarly, exact arithmetic is not used to compute the vertices\n"
2992 );
2993 printf(" of the Voronoi diagram.\n\n");
2994 printf(
2995 " Another pair of problems not solved by the exact arithmetic routines is\n");
2996 printf(
2997 " underflow and overflow. If Triangle is compiled for double precision\n");
2998 printf(
2999 " arithmetic, I believe that Triangle's geometric predicates work correctly\n"
3000 );
3001 printf(
3002 " if the exponent of every input coordinate falls in the range [-148, 201].\n"
3003 );
3004 printf(
3005 " Underflow can silently prevent the orientation and incircle tests from\n");
3006 printf(
3007 " being performed exactly, while overflow typically causes a floating\n");
3008 printf(" exception.\n\n");
3009 printf("Calling Triangle from Another Program:\n\n");
3010 printf(" Read the file triangle.h for details.\n\n");
3011 printf("Troubleshooting:\n\n");
3012 printf(" Please read this section before mailing me bugs.\n\n");
3013 printf(" `My output mesh has no triangles!'\n\n");
3014 printf(
3015 " If you're using a PSLG, you've probably failed to specify a proper set\n"
3016 );
3017 printf(
3018 " of bounding segments, or forgotten to use the -c switch. Or you may\n");
3019 printf(
3020 " have placed a hole badly, thereby eating all your triangles. To test\n");
3021 printf(" these possibilities, try again with the -c and -O switches.\n");
3022 printf(
3023 " Alternatively, all your input vertices may be collinear, in which case\n"
3024 );
3025 printf(" you can hardly expect to triangulate them.\n\n");
3026 printf(" `Triangle doesn't terminate, or just crashes.'\n\n");
3027 printf(
3028 " Bad things can happen when triangles get so small that the distance\n");
3029 printf(
3030 " between their vertices isn't much larger than the precision of your\n");
3031 printf(
3032 " machine's arithmetic. If you've compiled Triangle for single-precision\n"
3033 );
3034 printf(
3035 " arithmetic, you might do better by recompiling it for double-precision.\n"
3036 );
3037 printf(
3038 " Then again, you might just have to settle for more lenient constraints\n"
3039 );
3040 printf(
3041 " on the minimum angle and the maximum area than you had planned.\n");
3042 printf("\n");
3043 printf(
3044 " You can minimize precision problems by ensuring that the origin lies\n");
3045 printf(
3046 " inside your vertex set, or even inside the densest part of your\n");
3047 printf(
3048 " mesh. If you're triangulating an object whose x-coordinates all fall\n");
3049 printf(
3050 " between 6247133 and 6247134, you're not leaving much floating-point\n");
3051 printf(" precision for Triangle to work with.\n\n");
3052 printf(
3053 " Precision problems can occur covertly if the input PSLG contains two\n");
3054 printf(
3055 " segments that meet (or intersect) at an extremely small angle, or if\n");
3056 printf(
3057 " such an angle is introduced by the -c switch. If you don't realize\n");
3058 printf(
3059 " that a tiny angle is being formed, you might never discover why\n");
3060 printf(
3061 " Triangle is crashing. To check for this possibility, use the -S switch\n"
3062 );
3063 printf(
3064 " (with an appropriate limit on the number of Steiner points, found by\n");
3065 printf(
3066 " trial-and-error) to stop Triangle early, and view the output .poly file\n"
3067 );
3068 printf(
3069 " with Show Me (described below). Look carefully for regions where dense\n"
3070 );
3071 printf(
3072 " clusters of vertices are forming and for small angles between segments.\n"
3073 );
3074 printf(
3075 " Zoom in closely, as such segments might look like a single segment from\n"
3076 );
3077 printf(" a distance.\n\n");
3078 printf(
3079 " If some of the input values are too large, Triangle may suffer a\n");
3080 printf(
3081 " floating exception due to overflow when attempting to perform an\n");
3082 printf(
3083 " orientation or incircle test. (Read the section on exact arithmetic\n");
3084 printf(
3085 " above.) Again, I recommend compiling Triangle for double (rather\n");
3086 printf(" than single) precision arithmetic.\n\n");
3087 printf(
3088 " Unexpected problems can arise if you use quality meshing (-q, -a, or\n");
3089 printf(
3090 " -u) with an input that is not segment-bounded--that is, if your input\n");
3091 printf(
3092 " is a vertex set, or you're using the -c switch. If the convex hull of\n"
3093 );
3094 printf(
3095 " your input vertices has collinear vertices on its boundary, an input\n");
3096 printf(
3097 " vertex that you think lies on the convex hull might actually lie just\n");
3098 printf(
3099 " inside the convex hull. If so, the vertex and the nearby convex hull\n");
3100 printf(
3101 " edge form an extremely thin triangle. When Triangle tries to refine\n");
3102 printf(
3103 " the mesh to enforce angle and area constraints, Triangle might generate\n"
3104 );
3105 printf(
3106 " extremely tiny triangles, or it might fail because of insufficient\n");
3107 printf(" floating-point precision.\n\n");
3108 printf(
3109 " `The numbering of the output vertices doesn't match the input vertices.'\n"
3110 );
3111 printf("\n");
3112 printf(
3113 " You may have had duplicate input vertices, or you may have eaten some\n");
3114 printf(
3115 " of your input vertices with a hole, or by placing them outside the area\n"
3116 );
3117 printf(
3118 " enclosed by segments. In any case, you can solve the problem by not\n");
3119 printf(" using the -j switch.\n\n");
3120 printf(
3121 " `Triangle executes without incident, but when I look at the resulting\n");
3122 printf(
3123 " mesh, it has overlapping triangles or other geometric inconsistencies.'\n");
3124 printf("\n");
3125 printf(
3126 " If you select the -X switch, Triangle occasionally makes mistakes due\n");
3127 printf(
3128 " to floating-point roundoff error. Although these errors are rare,\n");
3129 printf(
3130 " don't use the -X switch. If you still have problems, please report the\n"
3131 );
3132 printf(" bug.\n\n");
3133 printf(
3134 " `Triangle executes without incident, but when I look at the resulting\n");
3135 printf(" Voronoi diagram, it has overlapping edges or other geometric\n");
3136 printf(" inconsistencies.'\n");
3137 printf("\n");
3138 printf(
3139 " If your input is a PSLG (-p), you can only expect a meaningful Voronoi\n"
3140 );
3141 printf(
3142 " diagram if the domain you are triangulating is convex and free of\n");
3143 printf(
3144 " holes, and you use the -D switch to construct a conforming Delaunay\n");
3145 printf(" triangulation (instead of a CDT or CCDT).\n\n");
3146 printf(
3147 " Strange things can happen if you've taken liberties with your PSLG. Do\n");
3148 printf(
3149 " you have a vertex lying in the middle of a segment? Triangle sometimes\n");
3150 printf(
3151 " copes poorly with that sort of thing. Do you want to lay out a collinear\n"
3152 );
3153 printf(
3154 " row of evenly spaced, segment-connected vertices? Have you simply\n");
3155 printf(
3156 " defined one long segment connecting the leftmost vertex to the rightmost\n"
3157 );
3158 printf(
3159 " vertex, and a bunch of vertices lying along it? This method occasionally\n"
3160 );
3161 printf(
3162 " works, especially with horizontal and vertical lines, but often it\n");
3163 printf(
3164 " doesn't, and you'll have to connect each adjacent pair of vertices with a\n"
3165 );
3166 printf(" separate segment. If you don't like it, tough.\n\n");
3167 printf(
3168 " Furthermore, if you have segments that intersect other than at their\n");
3169 printf(
3170 " endpoints, try not to let the intersections fall extremely close to PSLG\n"
3171 );
3172 printf(" vertices or each other.\n\n");
3173 printf(
3174 " If you have problems refining a triangulation not produced by Triangle:\n");
3175 printf(
3176 " Are you sure the triangulation is geometrically valid? Is it formatted\n");
3177 printf(
3178 " correctly for Triangle? Are the triangles all listed so the first three\n"
3179 );
3180 printf(
3181 " vertices are their corners in counterclockwise order? Are all of the\n");
3182 printf(
3183 " triangles constrained Delaunay? Triangle's Delaunay refinement algorithm\n"
3184 );
3185 printf(" assumes that it starts with a CDT.\n\n");
3186 printf("Show Me:\n\n");
3187 printf(
3188 " Triangle comes with a separate program named `Show Me', whose primary\n");
3189 printf(
3190 " purpose is to draw meshes on your screen or in PostScript. Its secondary\n"
3191 );
3192 printf(
3193 " purpose is to check the validity of your input files, and do so more\n");
3194 printf(
3195 " thoroughly than Triangle does. Unlike Triangle, Show Me requires that\n");
3196 printf(
3197 " you have the X Windows system. Sorry, Microsoft Windows users.\n");
3198 printf("\n");
3199 printf("Triangle on the Web:\n");
3200 printf("\n");
3201 printf(" To see an illustrated version of these instructions, check out\n");
3202 printf("\n");
3203 printf(" http://www.cs.cmu.edu/~quake/triangle.html\n");
3204 printf("\n");
3205 printf("A Brief Plea:\n");
3206 printf("\n");
3207 printf(
3208 " If you use Triangle, and especially if you use it to accomplish real\n");
3209 printf(
3210 " work, I would like very much to hear from you. A short letter or email\n");
3211 printf(
3212 " (to jrs@cs.berkeley.edu) describing how you use Triangle will mean a lot\n"
3213 );
3214 printf(
3215 " to me. The more people I know are using this program, the more easily I\n"
3216 );
3217 printf(
3218 " can justify spending time on improvements, which in turn will benefit\n");
3219 printf(
3220 " you. Also, I can put you on a list to receive email whenever a new\n");
3221 printf(" version of Triangle is available.\n\n");
3222 printf(
3223 " If you use a mesh generated by Triangle in a publication, please include\n"
3224 );
3225 printf(
3226 " an acknowledgment as well. And please spell Triangle with a capital `T'!\n"
3227 );
3228 printf(
3229 " If you want to include a citation, use `Jonathan Richard Shewchuk,\n");
3230 printf(
3231 " ``Triangle: Engineering a 2D Quality Mesh Generator and Delaunay\n");
3232 printf(
3233 " Triangulator,'' in Applied Computational Geometry: Towards Geometric\n");
3234 printf(
3235 " Engineering (Ming C. Lin and Dinesh Manocha, editors), volume 1148 of\n");
3236 printf(
3237 " Lecture Notes in Computer Science, pages 203-222, Springer-Verlag,\n");
3238 printf(
3239 " Berlin, May 1996. (From the First ACM Workshop on Applied Computational\n"
3240 );
3241 printf(" Geometry.)'\n\n");
3242 printf("Research credit:\n\n");
3243 printf(
3244 " Of course, I can take credit for only a fraction of the ideas that made\n");
3245 printf(
3246 " this mesh generator possible. Triangle owes its existence to the efforts\n"
3247 );
3248 printf(
3249 " of many fine computational geometers and other researchers, including\n");
3250 printf(
3251 " Marshall Bern, L. Paul Chew, Kenneth L. Clarkson, Boris Delaunay, Rex A.\n"
3252 );
3253 printf(
3254 " Dwyer, David Eppstein, Steven Fortune, Leonidas J. Guibas, Donald E.\n");
3255 printf(
3256 " Knuth, Charles L. Lawson, Der-Tsai Lee, Gary L. Miller, Ernst P. Mucke,\n");
3257 printf(
3258 " Steven E. Pav, Douglas M. Priest, Jim Ruppert, Isaac Saias, Bruce J.\n");
3259 printf(
3260 " Schachter, Micha Sharir, Peter W. Shor, Daniel D. Sleator, Jorge Stolfi,\n"
3261 );
3262 printf(" Robert E. Tarjan, Alper Ungor, Christopher J. Van Wyk, Noel J.\n");
3263 printf(
3264 " Walkington, and Binhai Zhu. See the comments at the beginning of the\n");
3265 printf(" source code for references.\n\n");
3266 triexit(0);
3267 }
3268
3269 #endif /* not TRILIBRARY */
3270
3271 /*****************************************************************************/
3272 /* */
3273 /* internalerror() Ask the user to send me the defective product. Exit. */
3274 /* */
3275 /*****************************************************************************/
3276
internalerror()3277 void internalerror()
3278 {
3279 printf(" Please report this bug to jrs@cs.berkeley.edu\n");
3280 printf(" Include the message above, your input data set, and the exact\n");
3281 printf(" command line you used to run Triangle.\n");
3282 triexit(1);
3283 }
3284
3285 /*****************************************************************************/
3286 /* */
3287 /* parsecommandline() Read the command line, identify switches, and set */
3288 /* up options and file names. */
3289 /* */
3290 /*****************************************************************************/
3291
3292 #ifdef ANSI_DECLARATORS
3293 void parsecommandline(int argc, char **argv, struct behavior *b)
3294 #else /* not ANSI_DECLARATORS */
3295 void parsecommandline(argc, argv, b)
3296 int argc;
3297 char **argv;
3298 struct behavior *b;
3299 #endif /* not ANSI_DECLARATORS */
3300
3301 {
3302 #ifdef TRILIBRARY
3303 #define STARTINDEX 0
3304 #else /* not TRILIBRARY */
3305 #define STARTINDEX 1
3306 int increment;
3307 int meshnumber;
3308 #endif /* not TRILIBRARY */
3309 int i, j, k;
3310 char workstring[FILENAMESIZE];
3311
3312 b->poly = b->refine = b->quality = 0;
3313 b->vararea = b->fixedarea = b->usertest = 0;
3314 b->regionattrib = b->convex = b->weighted = b->jettison = 0;
3315 b->firstnumber = 1;
3316 b->edgesout = b->voronoi = b->neighbors = b->geomview = 0;
3317 b->nobound = b->nopolywritten = b->nonodewritten = b->noelewritten = 0;
3318 b->noiterationnum = 0;
3319 b->noholes = b->noexact = 0;
3320 b->incremental = b->sweepline = 0;
3321 b->dwyer = 1;
3322 b->splitseg = 0;
3323 b->docheck = 0;
3324 b->nobisect = 0;
3325 b->conformdel = 0;
3326 b->steiner = -1;
3327 b->order = 1;
3328 b->minangle = 0.0;
3329 b->maxarea = -1.0;
3330 b->quiet = b->verbose = 0;
3331 #ifndef TRILIBRARY
3332 b->innodefilename[0] = '\0';
3333 #endif /* not TRILIBRARY */
3334
3335 for (i = STARTINDEX; i < argc; i++) {
3336 #ifndef TRILIBRARY
3337 if (argv[i][0] == '-') {
3338 #endif /* not TRILIBRARY */
3339 for (j = STARTINDEX; argv[i][j] != '\0'; j++) {
3340 if (argv[i][j] == 'p') {
3341 b->poly = 1;
3342 }
3343 #ifndef CDT_ONLY
3344 if (argv[i][j] == 'r') {
3345 b->refine = 1;
3346 }
3347 if (argv[i][j] == 'q') {
3348 b->quality = 1;
3349 if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
3350 (argv[i][j + 1] == '.')) {
3351 k = 0;
3352 while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
3353 (argv[i][j + 1] == '.')) {
3354 j++;
3355 workstring[k] = argv[i][j];
3356 k++;
3357 }
3358 workstring[k] = '\0';
3359 b->minangle = (REAL) strtod(workstring, (char **) NULL);
3360 } else {
3361 b->minangle = 20.0;
3362 }
3363 }
3364 if (argv[i][j] == 'a') {
3365 b->quality = 1;
3366 if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
3367 (argv[i][j + 1] == '.')) {
3368 b->fixedarea = 1;
3369 k = 0;
3370 while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
3371 (argv[i][j + 1] == '.')) {
3372 j++;
3373 workstring[k] = argv[i][j];
3374 k++;
3375 }
3376 workstring[k] = '\0';
3377 b->maxarea = (REAL) strtod(workstring, (char **) NULL);
3378 if (b->maxarea <= 0.0) {
3379 printf("Error: Maximum area must be greater than zero.\n");
3380 triexit(1);
3381 }
3382 } else {
3383 b->vararea = 1;
3384 }
3385 }
3386 if (argv[i][j] == 'u') {
3387 b->quality = 1;
3388 b->usertest = 1;
3389 }
3390 #endif /* not CDT_ONLY */
3391 if (argv[i][j] == 'A') {
3392 b->regionattrib = 1;
3393 }
3394 if (argv[i][j] == 'c') {
3395 b->convex = 1;
3396 }
3397 if (argv[i][j] == 'w') {
3398 b->weighted = 1;
3399 }
3400 if (argv[i][j] == 'W') {
3401 b->weighted = 2;
3402 }
3403 if (argv[i][j] == 'j') {
3404 b->jettison = 1;
3405 }
3406 if (argv[i][j] == 'z') {
3407 b->firstnumber = 0;
3408 }
3409 if (argv[i][j] == 'e') {
3410 b->edgesout = 1;
3411 }
3412 if (argv[i][j] == 'v') {
3413 b->voronoi = 1;
3414 }
3415 if (argv[i][j] == 'n') {
3416 b->neighbors = 1;
3417 }
3418 if (argv[i][j] == 'g') {
3419 b->geomview = 1;
3420 }
3421 if (argv[i][j] == 'B') {
3422 b->nobound = 1;
3423 }
3424 if (argv[i][j] == 'P') {
3425 b->nopolywritten = 1;
3426 }
3427 if (argv[i][j] == 'N') {
3428 b->nonodewritten = 1;
3429 }
3430 if (argv[i][j] == 'E') {
3431 b->noelewritten = 1;
3432 }
3433 #ifndef TRILIBRARY
3434 if (argv[i][j] == 'I') {
3435 b->noiterationnum = 1;
3436 }
3437 #endif /* not TRILIBRARY */
3438 if (argv[i][j] == 'O') {
3439 b->noholes = 1;
3440 }
3441 if (argv[i][j] == 'X') {
3442 b->noexact = 1;
3443 }
3444 if (argv[i][j] == 'o') {
3445 if (argv[i][j + 1] == '2') {
3446 j++;
3447 b->order = 2;
3448 }
3449 }
3450 #ifndef CDT_ONLY
3451 if (argv[i][j] == 'Y') {
3452 b->nobisect++;
3453 }
3454 if (argv[i][j] == 'S') {
3455 b->steiner = 0;
3456 while ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) {
3457 j++;
3458 b->steiner = b->steiner * 10 + (int) (argv[i][j] - '0');
3459 }
3460 }
3461 #endif /* not CDT_ONLY */
3462 #ifndef REDUCED
3463 if (argv[i][j] == 'i') {
3464 b->incremental = 1;
3465 }
3466 if (argv[i][j] == 'F') {
3467 b->sweepline = 1;
3468 }
3469 #endif /* not REDUCED */
3470 if (argv[i][j] == 'l') {
3471 b->dwyer = 0;
3472 }
3473 #ifndef REDUCED
3474 #ifndef CDT_ONLY
3475 if (argv[i][j] == 's') {
3476 b->splitseg = 1;
3477 }
3478 if ((argv[i][j] == 'D') || (argv[i][j] == 'L')) {
3479 b->quality = 1;
3480 b->conformdel = 1;
3481 }
3482 #endif /* not CDT_ONLY */
3483 if (argv[i][j] == 'C') {
3484 b->docheck = 1;
3485 }
3486 #endif /* not REDUCED */
3487 if (argv[i][j] == 'Q') {
3488 b->quiet = 1;
3489 }
3490 if (argv[i][j] == 'V') {
3491 b->verbose++;
3492 }
3493 #ifndef TRILIBRARY
3494 if ((argv[i][j] == 'h') || (argv[i][j] == 'H') ||
3495 (argv[i][j] == '?')) {
3496 info();
3497 }
3498 #endif /* not TRILIBRARY */
3499 }
3500 #ifndef TRILIBRARY
3501 } else {
3502 strncpy(b->innodefilename, argv[i], FILENAMESIZE - 1);
3503 b->innodefilename[FILENAMESIZE - 1] = '\0';
3504 }
3505 #endif /* not TRILIBRARY */
3506 }
3507 #ifndef TRILIBRARY
3508 if (b->innodefilename[0] == '\0') {
3509 syntax();
3510 }
3511 if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 5], ".node")) {
3512 b->innodefilename[strlen(b->innodefilename) - 5] = '\0';
3513 }
3514 if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 5], ".poly")) {
3515 b->innodefilename[strlen(b->innodefilename) - 5] = '\0';
3516 b->poly = 1;
3517 }
3518 #ifndef CDT_ONLY
3519 if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 4], ".ele")) {
3520 b->innodefilename[strlen(b->innodefilename) - 4] = '\0';
3521 b->refine = 1;
3522 }
3523 if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 5], ".area")) {
3524 b->innodefilename[strlen(b->innodefilename) - 5] = '\0';
3525 b->refine = 1;
3526 b->quality = 1;
3527 b->vararea = 1;
3528 }
3529 #endif /* not CDT_ONLY */
3530 #endif /* not TRILIBRARY */
3531 b->usesegments = b->poly || b->refine || b->quality || b->convex;
3532 b->goodangle = cos(b->minangle * PI / 180.0);
3533 if (b->goodangle == 1.0) {
3534 b->offconstant = 0.0;
3535 } else {
3536 b->offconstant = 0.475 * sqrt((1.0 + b->goodangle) / (1.0 - b->goodangle));
3537 }
3538 b->goodangle *= b->goodangle;
3539 if (b->refine && b->noiterationnum) {
3540 printf(
3541 "Error: You cannot use the -I switch when refining a triangulation.\n");
3542 triexit(1);
3543 }
3544 /* Be careful not to allocate space for element area constraints that */
3545 /* will never be assigned any value (other than the default -1.0). */
3546 if (!b->refine && !b->poly) {
3547 b->vararea = 0;
3548 }
3549 /* Be careful not to add an extra attribute to each element unless the */
3550 /* input supports it (PSLG in, but not refining a preexisting mesh). */
3551 if (b->refine || !b->poly) {
3552 b->regionattrib = 0;
3553 }
3554 /* Regular/weighted triangulations are incompatible with PSLGs */
3555 /* and meshing. */
3556 if (b->weighted && (b->poly || b->quality)) {
3557 b->weighted = 0;
3558 if (!b->quiet) {
3559 printf("Warning: weighted triangulations (-w, -W) are incompatible\n");
3560 printf(" with PSLGs (-p) and meshing (-q, -a, -u). Weights ignored.\n"
3561 );
3562 }
3563 }
3564 if (b->jettison && b->nonodewritten && !b->quiet) {
3565 printf("Warning: -j and -N switches are somewhat incompatible.\n");
3566 printf(" If any vertices are jettisoned, you will need the output\n");
3567 printf(" .node file to reconstruct the new node indices.");
3568 }
3569
3570 #ifndef TRILIBRARY
3571 strcpy(b->inpolyfilename, b->innodefilename);
3572 strcpy(b->inelefilename, b->innodefilename);
3573 strcpy(b->areafilename, b->innodefilename);
3574 increment = 0;
3575 strcpy(workstring, b->innodefilename);
3576 j = 1;
3577 while (workstring[j] != '\0') {
3578 if ((workstring[j] == '.') && (workstring[j + 1] != '\0')) {
3579 increment = j + 1;
3580 }
3581 j++;
3582 }
3583 meshnumber = 0;
3584 if (increment > 0) {
3585 j = increment;
3586 do {
3587 if ((workstring[j] >= '0') && (workstring[j] <= '9')) {
3588 meshnumber = meshnumber * 10 + (int) (workstring[j] - '0');
3589 } else {
3590 increment = 0;
3591 }
3592 j++;
3593 } while (workstring[j] != '\0');
3594 }
3595 if (b->noiterationnum) {
3596 strcpy(b->outnodefilename, b->innodefilename);
3597 strcpy(b->outelefilename, b->innodefilename);
3598 strcpy(b->edgefilename, b->innodefilename);
3599 strcpy(b->vnodefilename, b->innodefilename);
3600 strcpy(b->vedgefilename, b->innodefilename);
3601 strcpy(b->neighborfilename, b->innodefilename);
3602 strcpy(b->offfilename, b->innodefilename);
3603 strcat(b->outnodefilename, ".node");
3604 strcat(b->outelefilename, ".ele");
3605 strcat(b->edgefilename, ".edge");
3606 strcat(b->vnodefilename, ".v.node");
3607 strcat(b->vedgefilename, ".v.edge");
3608 strcat(b->neighborfilename, ".neigh");
3609 strcat(b->offfilename, ".off");
3610 } else if (increment == 0) {
3611 strcpy(b->outnodefilename, b->innodefilename);
3612 strcpy(b->outpolyfilename, b->innodefilename);
3613 strcpy(b->outelefilename, b->innodefilename);
3614 strcpy(b->edgefilename, b->innodefilename);
3615 strcpy(b->vnodefilename, b->innodefilename);
3616 strcpy(b->vedgefilename, b->innodefilename);
3617 strcpy(b->neighborfilename, b->innodefilename);
3618 strcpy(b->offfilename, b->innodefilename);
3619 strcat(b->outnodefilename, ".1.node");
3620 strcat(b->outpolyfilename, ".1.poly");
3621 strcat(b->outelefilename, ".1.ele");
3622 strcat(b->edgefilename, ".1.edge");
3623 strcat(b->vnodefilename, ".1.v.node");
3624 strcat(b->vedgefilename, ".1.v.edge");
3625 strcat(b->neighborfilename, ".1.neigh");
3626 strcat(b->offfilename, ".1.off");
3627 } else {
3628 workstring[increment] = '%';
3629 workstring[increment + 1] = 'd';
3630 workstring[increment + 2] = '\0';
3631 sprintf(b->outnodefilename, workstring, meshnumber + 1);
3632 strcpy(b->outpolyfilename, b->outnodefilename);
3633 strcpy(b->outelefilename, b->outnodefilename);
3634 strcpy(b->edgefilename, b->outnodefilename);
3635 strcpy(b->vnodefilename, b->outnodefilename);
3636 strcpy(b->vedgefilename, b->outnodefilename);
3637 strcpy(b->neighborfilename, b->outnodefilename);
3638 strcpy(b->offfilename, b->outnodefilename);
3639 strcat(b->outnodefilename, ".node");
3640 strcat(b->outpolyfilename, ".poly");
3641 strcat(b->outelefilename, ".ele");
3642 strcat(b->edgefilename, ".edge");
3643 strcat(b->vnodefilename, ".v.node");
3644 strcat(b->vedgefilename, ".v.edge");
3645 strcat(b->neighborfilename, ".neigh");
3646 strcat(b->offfilename, ".off");
3647 }
3648 strcat(b->innodefilename, ".node");
3649 strcat(b->inpolyfilename, ".poly");
3650 strcat(b->inelefilename, ".ele");
3651 strcat(b->areafilename, ".area");
3652 #endif /* not TRILIBRARY */
3653 }
3654
3655 /** **/
3656 /** **/
3657 /********* User interaction routines begin here *********/
3658
3659 /********* Debugging routines begin here *********/
3660 /** **/
3661 /** **/
3662
3663 /*****************************************************************************/
3664 /* */
3665 /* printtriangle() Print out the details of an oriented triangle. */
3666 /* */
3667 /* I originally wrote this procedure to simplify debugging; it can be */
3668 /* called directly from the debugger, and presents information about an */
3669 /* oriented triangle in digestible form. It's also used when the */
3670 /* highest level of verbosity (`-VVV') is specified. */
3671 /* */
3672 /*****************************************************************************/
3673
3674 #ifdef ANSI_DECLARATORS
3675 void printtriangle(struct mesh *m, struct behavior *b, struct otri *t)
3676 #else /* not ANSI_DECLARATORS */
3677 void printtriangle(m, b, t)
3678 struct mesh *m;
3679 struct behavior *b;
3680 struct otri *t;
3681 #endif /* not ANSI_DECLARATORS */
3682
3683 {
3684 struct otri printtri;
3685 struct osub printsh;
3686 vertex printvertex;
3687
3688 printf("triangle x%lx with orientation %d:\n", (unsigned long) t->tri,
3689 t->orient);
3690 decode(t->tri[0], printtri);
3691 if (printtri.tri == m->dummytri) {
3692 printf(" [0] = Outer space\n");
3693 } else {
3694 printf(" [0] = x%lx %d\n", (unsigned long) printtri.tri,
3695 printtri.orient);
3696 }
3697 decode(t->tri[1], printtri);
3698 if (printtri.tri == m->dummytri) {
3699 printf(" [1] = Outer space\n");
3700 } else {
3701 printf(" [1] = x%lx %d\n", (unsigned long) printtri.tri,
3702 printtri.orient);
3703 }
3704 decode(t->tri[2], printtri);
3705 if (printtri.tri == m->dummytri) {
3706 printf(" [2] = Outer space\n");
3707 } else {
3708 printf(" [2] = x%lx %d\n", (unsigned long) printtri.tri,
3709 printtri.orient);
3710 }
3711
3712 org(*t, printvertex);
3713 if (printvertex == (vertex) NULL)
3714 printf(" Origin[%d] = NULL\n", (t->orient + 1) % 3 + 3);
3715 else
3716 printf(" Origin[%d] = x%lx (%.12g, %.12g)\n",
3717 (t->orient + 1) % 3 + 3, (unsigned long) printvertex,
3718 (double)printvertex[0], (double)printvertex[1]);
3719 dest(*t, printvertex);
3720 if (printvertex == (vertex) NULL)
3721 printf(" Dest [%d] = NULL\n", (t->orient + 2) % 3 + 3);
3722 else
3723 printf(" Dest [%d] = x%lx (%.12g, %.12g)\n",
3724 (t->orient + 2) % 3 + 3, (unsigned long) printvertex,
3725 (double)printvertex[0], (double)printvertex[1]);
3726 apex(*t, printvertex);
3727 if (printvertex == (vertex) NULL)
3728 printf(" Apex [%d] = NULL\n", t->orient + 3);
3729 else
3730 printf(" Apex [%d] = x%lx (%.12g, %.12g)\n",
3731 t->orient + 3, (unsigned long) printvertex,
3732 (double)printvertex[0], (double)printvertex[1]);
3733
3734 if (b->usesegments) {
3735 sdecode(t->tri[6], printsh);
3736 if (printsh.ss != m->dummysub) {
3737 printf(" [6] = x%lx %d\n", (unsigned long) printsh.ss,
3738 printsh.ssorient);
3739 }
3740 sdecode(t->tri[7], printsh);
3741 if (printsh.ss != m->dummysub) {
3742 printf(" [7] = x%lx %d\n", (unsigned long) printsh.ss,
3743 printsh.ssorient);
3744 }
3745 sdecode(t->tri[8], printsh);
3746 if (printsh.ss != m->dummysub) {
3747 printf(" [8] = x%lx %d\n", (unsigned long) printsh.ss,
3748 printsh.ssorient);
3749 }
3750 }
3751
3752 if (b->vararea) {
3753 printf(" Area constraint: %.4g\n", (double)areabound(*t));
3754 }
3755 }
3756
3757 /*****************************************************************************/
3758 /* */
3759 /* printsubseg() Print out the details of an oriented subsegment. */
3760 /* */
3761 /* I originally wrote this procedure to simplify debugging; it can be */
3762 /* called directly from the debugger, and presents information about an */
3763 /* oriented subsegment in digestible form. It's also used when the highest */
3764 /* level of verbosity (`-VVV') is specified. */
3765 /* */
3766 /*****************************************************************************/
3767
3768 #ifdef ANSI_DECLARATORS
3769 void printsubseg(struct mesh *m, struct behavior *b, struct osub *s)
3770 #else /* not ANSI_DECLARATORS */
3771 void printsubseg(m, b, s)
3772 struct mesh *m;
3773 struct behavior *b;
3774 struct osub *s;
3775 #endif /* not ANSI_DECLARATORS */
3776
3777 {
3778 struct osub printsh;
3779 struct otri printtri;
3780 vertex printvertex;
3781
3782 printf("subsegment x%lx with orientation %d and mark %d:\n",
3783 (unsigned long) s->ss, s->ssorient, mark(*s));
3784 sdecode(s->ss[0], printsh);
3785 if (printsh.ss == m->dummysub) {
3786 printf(" [0] = No subsegment\n");
3787 } else {
3788 printf(" [0] = x%lx %d\n", (unsigned long) printsh.ss,
3789 printsh.ssorient);
3790 }
3791 sdecode(s->ss[1], printsh);
3792 if (printsh.ss == m->dummysub) {
3793 printf(" [1] = No subsegment\n");
3794 } else {
3795 printf(" [1] = x%lx %d\n", (unsigned long) printsh.ss,
3796 printsh.ssorient);
3797 }
3798
3799 sorg(*s, printvertex);
3800 if (printvertex == (vertex) NULL)
3801 printf(" Origin[%d] = NULL\n", 2 + s->ssorient);
3802 else
3803 printf(" Origin[%d] = x%lx (%.12g, %.12g)\n",
3804 2 + s->ssorient, (unsigned long) printvertex,
3805 (double)printvertex[0], (double)printvertex[1]);
3806 sdest(*s, printvertex);
3807 if (printvertex == (vertex) NULL)
3808 printf(" Dest [%d] = NULL\n", 3 - s->ssorient);
3809 else
3810 printf(" Dest [%d] = x%lx (%.12g, %.12g)\n",
3811 3 - s->ssorient, (unsigned long) printvertex,
3812 (double)printvertex[0], (double)printvertex[1]);
3813
3814 decode(s->ss[6], printtri);
3815 if (printtri.tri == m->dummytri) {
3816 printf(" [6] = Outer space\n");
3817 } else {
3818 printf(" [6] = x%lx %d\n", (unsigned long) printtri.tri,
3819 printtri.orient);
3820 }
3821 decode(s->ss[7], printtri);
3822 if (printtri.tri == m->dummytri) {
3823 printf(" [7] = Outer space\n");
3824 } else {
3825 printf(" [7] = x%lx %d\n", (unsigned long) printtri.tri,
3826 printtri.orient);
3827 }
3828
3829 segorg(*s, printvertex);
3830 if (printvertex == (vertex) NULL)
3831 printf(" Segment origin[%d] = NULL\n", 4 + s->ssorient);
3832 else
3833 printf(" Segment origin[%d] = x%lx (%.12g, %.12g)\n",
3834 4 + s->ssorient, (unsigned long) printvertex,
3835 (double)printvertex[0], (double)printvertex[1]);
3836 segdest(*s, printvertex);
3837 if (printvertex == (vertex) NULL)
3838 printf(" Segment dest [%d] = NULL\n", 5 - s->ssorient);
3839 else
3840 printf(" Segment dest [%d] = x%lx (%.12g, %.12g)\n",
3841 5 - s->ssorient, (unsigned long) printvertex,
3842 (double)printvertex[0], (double)printvertex[1]);
3843 }
3844
3845 /** **/
3846 /** **/
3847 /********* Debugging routines end here *********/
3848
3849 /********* Memory management routines begin here *********/
3850 /** **/
3851 /** **/
3852
3853 /*****************************************************************************/
3854 /* */
3855 /* poolzero() Set all of a pool's fields to zero. */
3856 /* */
3857 /* This procedure should never be called on a pool that has any memory */
3858 /* allocated to it, as that memory would leak. */
3859 /* */
3860 /*****************************************************************************/
3861
3862 #ifdef ANSI_DECLARATORS
3863 void poolzero(struct memorypool *pool)
3864 #else /* not ANSI_DECLARATORS */
3865 void poolzero(pool)
3866 struct memorypool *pool;
3867 #endif /* not ANSI_DECLARATORS */
3868
3869 {
3870 pool->firstblock = (VOID **) NULL;
3871 pool->nowblock = (VOID **) NULL;
3872 pool->nextitem = (VOID *) NULL;
3873 pool->deaditemstack = (VOID *) NULL;
3874 pool->pathblock = (VOID **) NULL;
3875 pool->pathitem = (VOID *) NULL;
3876 pool->alignbytes = 0;
3877 pool->itembytes = 0;
3878 pool->itemsperblock = 0;
3879 pool->itemsfirstblock = 0;
3880 pool->items = 0;
3881 pool->maxitems = 0;
3882 pool->unallocateditems = 0;
3883 pool->pathitemsleft = 0;
3884 }
3885
3886 /*****************************************************************************/
3887 /* */
3888 /* poolrestart() Deallocate all items in a pool. */
3889 /* */
3890 /* The pool is returned to its starting state, except that no memory is */
3891 /* freed to the operating system. Rather, the previously allocated blocks */
3892 /* are ready to be reused. */
3893 /* */
3894 /*****************************************************************************/
3895
3896 #ifdef ANSI_DECLARATORS
3897 void poolrestart(struct memorypool *pool)
3898 #else /* not ANSI_DECLARATORS */
3899 void poolrestart(pool)
3900 struct memorypool *pool;
3901 #endif /* not ANSI_DECLARATORS */
3902
3903 {
3904 unsigned long alignptr;
3905
3906 pool->items = 0;
3907 pool->maxitems = 0;
3908
3909 /* Set the currently active block. */
3910 pool->nowblock = pool->firstblock;
3911 /* Find the first item in the pool. Increment by the size of (VOID *). */
3912 alignptr = (unsigned long) (pool->nowblock + 1);
3913 /* Align the item on an `alignbytes'-byte boundary. */
3914 pool->nextitem = (VOID *)
3915 (alignptr + (unsigned long) pool->alignbytes -
3916 (alignptr % (unsigned long) pool->alignbytes));
3917 /* There are lots of unallocated items left in this block. */
3918 pool->unallocateditems = pool->itemsfirstblock;
3919 /* The stack of deallocated items is empty. */
3920 pool->deaditemstack = (VOID *) NULL;
3921 }
3922
3923 /*****************************************************************************/
3924 /* */
3925 /* poolinit() Initialize a pool of memory for allocation of items. */
3926 /* */
3927 /* This routine initializes the machinery for allocating items. A `pool' */
3928 /* is created whose records have size at least `bytecount'. Items will be */
3929 /* allocated in `itemcount'-item blocks. Each item is assumed to be a */
3930 /* collection of words, and either pointers or floating-point values are */
3931 /* assumed to be the "primary" word type. (The "primary" word type is used */
3932 /* to determine alignment of items.) If `alignment' isn't zero, all items */
3933 /* will be `alignment'-byte aligned in memory. `alignment' must be either */
3934 /* a multiple or a factor of the primary word size; powers of two are safe. */
3935 /* `alignment' is normally used to create a few unused bits at the bottom */
3936 /* of each item's pointer, in which information may be stored. */
3937 /* */
3938 /* Don't change this routine unless you understand it. */
3939 /* */
3940 /*****************************************************************************/
3941
3942 #ifdef ANSI_DECLARATORS
3943 void poolinit(struct memorypool *pool, int bytecount, int itemcount,
3944 int firstitemcount, int alignment)
3945 #else /* not ANSI_DECLARATORS */
3946 void poolinit(pool, bytecount, itemcount, firstitemcount, alignment)
3947 struct memorypool *pool;
3948 int bytecount;
3949 int itemcount;
3950 int firstitemcount;
3951 int alignment;
3952 #endif /* not ANSI_DECLARATORS */
3953
3954 {
3955 /* Find the proper alignment, which must be at least as large as: */
3956 /* - The parameter `alignment'. */
3957 /* - sizeof(VOID *), so the stack of dead items can be maintained */
3958 /* without unaligned accesses. */
3959 if (alignment > sizeof(VOID *)) {
3960 pool->alignbytes = alignment;
3961 } else {
3962 pool->alignbytes = sizeof(VOID *);
3963 }
3964 pool->itembytes = ((bytecount - 1) / pool->alignbytes + 1) *
3965 pool->alignbytes;
3966 pool->itemsperblock = itemcount;
3967 if (firstitemcount == 0) {
3968 pool->itemsfirstblock = itemcount;
3969 } else {
3970 pool->itemsfirstblock = firstitemcount;
3971 }
3972
3973 /* Allocate a block of items. Space for `itemsfirstblock' items and one */
3974 /* pointer (to point to the next block) are allocated, as well as space */
3975 /* to ensure alignment of the items. */
3976 pool->firstblock = (VOID **)
3977 trimalloc(pool->itemsfirstblock * pool->itembytes + (int) sizeof(VOID *) +
3978 pool->alignbytes);
3979 /* Set the next block pointer to NULL. */
3980 *(pool->firstblock) = (VOID *) NULL;
3981 poolrestart(pool);
3982 }
3983
3984 /*****************************************************************************/
3985 /* */
3986 /* pooldeinit() Free to the operating system all memory taken by a pool. */
3987 /* */
3988 /*****************************************************************************/
3989
3990 #ifdef ANSI_DECLARATORS
3991 void pooldeinit(struct memorypool *pool)
3992 #else /* not ANSI_DECLARATORS */
3993 void pooldeinit(pool)
3994 struct memorypool *pool;
3995 #endif /* not ANSI_DECLARATORS */
3996
3997 {
3998 while (pool->firstblock != (VOID **) NULL) {
3999 pool->nowblock = (VOID **) *(pool->firstblock);
4000 trifree((VOID *) pool->firstblock);
4001 pool->firstblock = pool->nowblock;
4002 }
4003 }
4004
4005 /*****************************************************************************/
4006 /* */
4007 /* poolalloc() Allocate space for an item. */
4008 /* */
4009 /*****************************************************************************/
4010
4011 #ifdef ANSI_DECLARATORS
4012 VOID *poolalloc(struct memorypool *pool)
4013 #else /* not ANSI_DECLARATORS */
4014 VOID *poolalloc(pool)
4015 struct memorypool *pool;
4016 #endif /* not ANSI_DECLARATORS */
4017
4018 {
4019 VOID *newitem;
4020 VOID **newblock;
4021 unsigned long alignptr;
4022
4023 /* First check the linked list of dead items. If the list is not */
4024 /* empty, allocate an item from the list rather than a fresh one. */
4025 if (pool->deaditemstack != (VOID *) NULL) {
4026 newitem = pool->deaditemstack; /* Take first item in list. */
4027 pool->deaditemstack = * (VOID **) pool->deaditemstack;
4028 } else {
4029 /* Check if there are any free items left in the current block. */
4030 if (pool->unallocateditems == 0) {
4031 /* Check if another block must be allocated. */
4032 if (*(pool->nowblock) == (VOID *) NULL) {
4033 /* Allocate a new block of items, pointed to by the previous block. */
4034 newblock = (VOID **) trimalloc(pool->itemsperblock * pool->itembytes +
4035 (int) sizeof(VOID *) +
4036 pool->alignbytes);
4037 *(pool->nowblock) = (VOID *) newblock;
4038 /* The next block pointer is NULL. */
4039 *newblock = (VOID *) NULL;
4040 }
4041
4042 /* Move to the new block. */
4043 pool->nowblock = (VOID **) *(pool->nowblock);
4044 /* Find the first item in the block. */
4045 /* Increment by the size of (VOID *). */
4046 alignptr = (unsigned long) (pool->nowblock + 1);
4047 /* Align the item on an `alignbytes'-byte boundary. */
4048 pool->nextitem = (VOID *)
4049 (alignptr + (unsigned long) pool->alignbytes -
4050 (alignptr % (unsigned long) pool->alignbytes));
4051 /* There are lots of unallocated items left in this block. */
4052 pool->unallocateditems = pool->itemsperblock;
4053 }
4054
4055 /* Allocate a new item. */
4056 newitem = pool->nextitem;
4057 /* Advance `nextitem' pointer to next free item in block. */
4058 pool->nextitem = (VOID *) ((char *) pool->nextitem + pool->itembytes);
4059 pool->unallocateditems--;
4060 pool->maxitems++;
4061 }
4062 pool->items++;
4063 return newitem;
4064 }
4065
4066 /*****************************************************************************/
4067 /* */
4068 /* pooldealloc() Deallocate space for an item. */
4069 /* */
4070 /* The deallocated space is stored in a queue for later reuse. */
4071 /* */
4072 /*****************************************************************************/
4073
4074 #ifdef ANSI_DECLARATORS
4075 void pooldealloc(struct memorypool *pool, VOID *dyingitem)
4076 #else /* not ANSI_DECLARATORS */
4077 void pooldealloc(pool, dyingitem)
4078 struct memorypool *pool;
4079 VOID *dyingitem;
4080 #endif /* not ANSI_DECLARATORS */
4081
4082 {
4083 /* Push freshly killed item onto stack. */
4084 *((VOID **) dyingitem) = pool->deaditemstack;
4085 pool->deaditemstack = dyingitem;
4086 pool->items--;
4087 }
4088
4089 /*****************************************************************************/
4090 /* */
4091 /* traversalinit() Prepare to traverse the entire list of items. */
4092 /* */
4093 /* This routine is used in conjunction with traverse(). */
4094 /* */
4095 /*****************************************************************************/
4096
4097 #ifdef ANSI_DECLARATORS
4098 void traversalinit(struct memorypool *pool)
4099 #else /* not ANSI_DECLARATORS */
4100 void traversalinit(pool)
4101 struct memorypool *pool;
4102 #endif /* not ANSI_DECLARATORS */
4103
4104 {
4105 unsigned long alignptr;
4106
4107 /* Begin the traversal in the first block. */
4108 pool->pathblock = pool->firstblock;
4109 /* Find the first item in the block. Increment by the size of (VOID *). */
4110 alignptr = (unsigned long) (pool->pathblock + 1);
4111 /* Align with item on an `alignbytes'-byte boundary. */
4112 pool->pathitem = (VOID *)
4113 (alignptr + (unsigned long) pool->alignbytes -
4114 (alignptr % (unsigned long) pool->alignbytes));
4115 /* Set the number of items left in the current block. */
4116 pool->pathitemsleft = pool->itemsfirstblock;
4117 }
4118
4119 /*****************************************************************************/
4120 /* */
4121 /* traverse() Find the next item in the list. */
4122 /* */
4123 /* This routine is used in conjunction with traversalinit(). Be forewarned */
4124 /* that this routine successively returns all items in the list, including */
4125 /* deallocated ones on the deaditemqueue. It's up to you to figure out */
4126 /* which ones are actually dead. Why? I don't want to allocate extra */
4127 /* space just to demarcate dead items. It can usually be done more */
4128 /* space-efficiently by a routine that knows something about the structure */
4129 /* of the item. */
4130 /* */
4131 /*****************************************************************************/
4132
4133 #ifdef ANSI_DECLARATORS
4134 VOID *traverse(struct memorypool *pool)
4135 #else /* not ANSI_DECLARATORS */
4136 VOID *traverse(pool)
4137 struct memorypool *pool;
4138 #endif /* not ANSI_DECLARATORS */
4139
4140 {
4141 VOID *newitem;
4142 unsigned long alignptr;
4143
4144 /* Stop upon exhausting the list of items. */
4145 if (pool->pathitem == pool->nextitem) {
4146 return (VOID *) NULL;
4147 }
4148
4149 /* Check whether any untraversed items remain in the current block. */
4150 if (pool->pathitemsleft == 0) {
4151 /* Find the next block. */
4152 pool->pathblock = (VOID **) *(pool->pathblock);
4153 /* Find the first item in the block. Increment by the size of (VOID *). */
4154 alignptr = (unsigned long) (pool->pathblock + 1);
4155 /* Align with item on an `alignbytes'-byte boundary. */
4156 pool->pathitem = (VOID *)
4157 (alignptr + (unsigned long) pool->alignbytes -
4158 (alignptr % (unsigned long) pool->alignbytes));
4159 /* Set the number of items left in the current block. */
4160 pool->pathitemsleft = pool->itemsperblock;
4161 }
4162
4163 newitem = pool->pathitem;
4164 /* Find the next item in the block. */
4165 pool->pathitem = (VOID *) ((char *) pool->pathitem + pool->itembytes);
4166 pool->pathitemsleft--;
4167 return newitem;
4168 }
4169
4170 /*****************************************************************************/
4171 /* */
4172 /* dummyinit() Initialize the triangle that fills "outer space" and the */
4173 /* omnipresent subsegment. */
4174 /* */
4175 /* The triangle that fills "outer space," called `dummytri', is pointed to */
4176 /* by every triangle and subsegment on a boundary (be it outer or inner) of */
4177 /* the triangulation. Also, `dummytri' points to one of the triangles on */
4178 /* the convex hull (until the holes and concavities are carved), making it */
4179 /* possible to find a starting triangle for point location. */
4180 /* */
4181 /* The omnipresent subsegment, `dummysub', is pointed to by every triangle */
4182 /* or subsegment that doesn't have a full complement of real subsegments */
4183 /* to point to. */
4184 /* */
4185 /* `dummytri' and `dummysub' are generally required to fulfill only a few */
4186 /* invariants: their vertices must remain NULL and `dummytri' must always */
4187 /* be bonded (at offset zero) to some triangle on the convex hull of the */
4188 /* mesh, via a boundary edge. Otherwise, the connections of `dummytri' and */
4189 /* `dummysub' may change willy-nilly. This makes it possible to avoid */
4190 /* writing a good deal of special-case code (in the edge flip, for example) */
4191 /* for dealing with the boundary of the mesh, places where no subsegment is */
4192 /* present, and so forth. Other entities are frequently bonded to */
4193 /* `dummytri' and `dummysub' as if they were real mesh entities, with no */
4194 /* harm done. */
4195 /* */
4196 /*****************************************************************************/
4197
4198 #ifdef ANSI_DECLARATORS
4199 void dummyinit(struct mesh *m, struct behavior *b, int trianglebytes,
4200 int subsegbytes)
4201 #else /* not ANSI_DECLARATORS */
4202 void dummyinit(m, b, trianglebytes, subsegbytes)
4203 struct mesh *m;
4204 struct behavior *b;
4205 int trianglebytes;
4206 int subsegbytes;
4207 #endif /* not ANSI_DECLARATORS */
4208
4209 {
4210 unsigned long alignptr;
4211
4212 /* Set up `dummytri', the `triangle' that occupies "outer space." */
4213 m->dummytribase = (triangle *) trimalloc(trianglebytes +
4214 m->triangles.alignbytes);
4215 /* Align `dummytri' on a `triangles.alignbytes'-byte boundary. */
4216 alignptr = (unsigned long) m->dummytribase;
4217 m->dummytri = (triangle *)
4218 (alignptr + (unsigned long) m->triangles.alignbytes -
4219 (alignptr % (unsigned long) m->triangles.alignbytes));
4220 /* Initialize the three adjoining triangles to be "outer space." These */
4221 /* will eventually be changed by various bonding operations, but their */
4222 /* values don't really matter, as long as they can legally be */
4223 /* dereferenced. */
4224 m->dummytri[0] = (triangle) m->dummytri;
4225 m->dummytri[1] = (triangle) m->dummytri;
4226 m->dummytri[2] = (triangle) m->dummytri;
4227 /* Three NULL vertices. */
4228 m->dummytri[3] = (triangle) NULL;
4229 m->dummytri[4] = (triangle) NULL;
4230 m->dummytri[5] = (triangle) NULL;
4231
4232 if (b->usesegments) {
4233 /* Set up `dummysub', the omnipresent subsegment pointed to by any */
4234 /* triangle side or subsegment end that isn't attached to a real */
4235 /* subsegment. */
4236 m->dummysubbase = (subseg *) trimalloc(subsegbytes +
4237 m->subsegs.alignbytes);
4238 /* Align `dummysub' on a `subsegs.alignbytes'-byte boundary. */
4239 alignptr = (unsigned long) m->dummysubbase;
4240 m->dummysub = (subseg *)
4241 (alignptr + (unsigned long) m->subsegs.alignbytes -
4242 (alignptr % (unsigned long) m->subsegs.alignbytes));
4243 /* Initialize the two adjoining subsegments to be the omnipresent */
4244 /* subsegment. These will eventually be changed by various bonding */
4245 /* operations, but their values don't really matter, as long as they */
4246 /* can legally be dereferenced. */
4247 m->dummysub[0] = (subseg) m->dummysub;
4248 m->dummysub[1] = (subseg) m->dummysub;
4249 /* Four NULL vertices. */
4250 m->dummysub[2] = (subseg) NULL;
4251 m->dummysub[3] = (subseg) NULL;
4252 m->dummysub[4] = (subseg) NULL;
4253 m->dummysub[5] = (subseg) NULL;
4254 /* Initialize the two adjoining triangles to be "outer space." */
4255 m->dummysub[6] = (subseg) m->dummytri;
4256 m->dummysub[7] = (subseg) m->dummytri;
4257 /* Set the boundary marker to zero. */
4258 * (int *) (m->dummysub + 8) = 0;
4259
4260 /* Initialize the three adjoining subsegments of `dummytri' to be */
4261 /* the omnipresent subsegment. */
4262 m->dummytri[6] = (triangle) m->dummysub;
4263 m->dummytri[7] = (triangle) m->dummysub;
4264 m->dummytri[8] = (triangle) m->dummysub;
4265 }
4266 }
4267
4268 /*****************************************************************************/
4269 /* */
4270 /* initializevertexpool() Calculate the size of the vertex data structure */
4271 /* and initialize its memory pool. */
4272 /* */
4273 /* This routine also computes the `vertexmarkindex' and `vertex2triindex' */
4274 /* indices used to find values within each vertex. */
4275 /* */
4276 /*****************************************************************************/
4277
4278 #ifdef ANSI_DECLARATORS
4279 void initializevertexpool(struct mesh *m, struct behavior *b)
4280 #else /* not ANSI_DECLARATORS */
4281 void initializevertexpool(m, b)
4282 struct mesh *m;
4283 struct behavior *b;
4284 #endif /* not ANSI_DECLARATORS */
4285
4286 {
4287 int vertexsize;
4288
4289 /* The index within each vertex at which the boundary marker is found, */
4290 /* followed by the vertex type. Ensure the vertex marker is aligned to */
4291 /* a sizeof(int)-byte address. */
4292 m->vertexmarkindex = ((m->mesh_dim + m->nextras) * sizeof(REAL) +
4293 sizeof(int) - 1) /
4294 sizeof(int);
4295 vertexsize = (m->vertexmarkindex + 2) * sizeof(int);
4296 if (b->poly) {
4297 /* The index within each vertex at which a triangle pointer is found. */
4298 /* Ensure the pointer is aligned to a sizeof(triangle)-byte address. */
4299 m->vertex2triindex = (vertexsize + sizeof(triangle) - 1) /
4300 sizeof(triangle);
4301 vertexsize = (m->vertex2triindex + 1) * sizeof(triangle);
4302 }
4303
4304 /* Initialize the pool of vertices. */
4305 poolinit(&m->vertices, vertexsize, VERTEXPERBLOCK,
4306 m->invertices > VERTEXPERBLOCK ? m->invertices : VERTEXPERBLOCK,
4307 sizeof(REAL));
4308 }
4309
4310 /*****************************************************************************/
4311 /* */
4312 /* initializetrisubpools() Calculate the sizes of the triangle and */
4313 /* subsegment data structures and initialize */
4314 /* their memory pools. */
4315 /* */
4316 /* This routine also computes the `highorderindex', `elemattribindex', and */
4317 /* `areaboundindex' indices used to find values within each triangle. */
4318 /* */
4319 /*****************************************************************************/
4320
4321 #ifdef ANSI_DECLARATORS
4322 void initializetrisubpools(struct mesh *m, struct behavior *b)
4323 #else /* not ANSI_DECLARATORS */
4324 void initializetrisubpools(m, b)
4325 struct mesh *m;
4326 struct behavior *b;
4327 #endif /* not ANSI_DECLARATORS */
4328
4329 {
4330 int trisize;
4331
4332 /* The index within each triangle at which the extra nodes (above three) */
4333 /* associated with high order elements are found. There are three */
4334 /* pointers to other triangles, three pointers to corners, and possibly */
4335 /* three pointers to subsegments before the extra nodes. */
4336 m->highorderindex = 6 + (b->usesegments * 3);
4337 /* The number of bytes occupied by a triangle. */
4338 trisize = ((b->order + 1) * (b->order + 2) / 2 + (m->highorderindex - 3)) *
4339 sizeof(triangle);
4340 /* The index within each triangle at which its attributes are found, */
4341 /* where the index is measured in REALs. */
4342 m->elemattribindex = (trisize + sizeof(REAL) - 1) / sizeof(REAL);
4343 /* The index within each triangle at which the maximum area constraint */
4344 /* is found, where the index is measured in REALs. Note that if the */
4345 /* `regionattrib' flag is set, an additional attribute will be added. */
4346 m->areaboundindex = m->elemattribindex + m->eextras + b->regionattrib;
4347 /* If triangle attributes or an area bound are needed, increase the number */
4348 /* of bytes occupied by a triangle. */
4349 if (b->vararea) {
4350 trisize = (m->areaboundindex + 1) * sizeof(REAL);
4351 } else if (m->eextras + b->regionattrib > 0) {
4352 trisize = m->areaboundindex * sizeof(REAL);
4353 }
4354 /* If a Voronoi diagram or triangle neighbor graph is requested, make */
4355 /* sure there's room to store an integer index in each triangle. This */
4356 /* integer index can occupy the same space as the subsegment pointers */
4357 /* or attributes or area constraint or extra nodes. */
4358 if ((b->voronoi || b->neighbors) &&
4359 (trisize < 6 * sizeof(triangle) + sizeof(int))) {
4360 trisize = 6 * sizeof(triangle) + sizeof(int);
4361 }
4362
4363 /* Having determined the memory size of a triangle, initialize the pool. */
4364 poolinit(&m->triangles, trisize, TRIPERBLOCK,
4365 (2 * m->invertices - 2) > TRIPERBLOCK ? (2 * m->invertices - 2) :
4366 TRIPERBLOCK, 4);
4367
4368 if (b->usesegments) {
4369 /* Initialize the pool of subsegments. Take into account all eight */
4370 /* pointers and one boundary marker. */
4371 poolinit(&m->subsegs, 8 * sizeof(triangle) + sizeof(int),
4372 SUBSEGPERBLOCK, SUBSEGPERBLOCK, 4);
4373
4374 /* Initialize the "outer space" triangle and omnipresent subsegment. */
4375 dummyinit(m, b, m->triangles.itembytes, m->subsegs.itembytes);
4376 } else {
4377 /* Initialize the "outer space" triangle. */
4378 dummyinit(m, b, m->triangles.itembytes, 0);
4379 }
4380 }
4381
4382 /*****************************************************************************/
4383 /* */
4384 /* triangledealloc() Deallocate space for a triangle, marking it dead. */
4385 /* */
4386 /*****************************************************************************/
4387
4388 #ifdef ANSI_DECLARATORS
4389 void triangledealloc(struct mesh *m, triangle *dyingtriangle)
4390 #else /* not ANSI_DECLARATORS */
4391 void triangledealloc(m, dyingtriangle)
4392 struct mesh *m;
4393 triangle *dyingtriangle;
4394 #endif /* not ANSI_DECLARATORS */
4395
4396 {
4397 /* Mark the triangle as dead. This makes it possible to detect dead */
4398 /* triangles when traversing the list of all triangles. */
4399 killtri(dyingtriangle);
4400 pooldealloc(&m->triangles, (VOID *) dyingtriangle);
4401 }
4402
4403 /*****************************************************************************/
4404 /* */
4405 /* triangletraverse() Traverse the triangles, skipping dead ones. */
4406 /* */
4407 /*****************************************************************************/
4408
4409 #ifdef ANSI_DECLARATORS
4410 triangle *triangletraverse(struct mesh *m)
4411 #else /* not ANSI_DECLARATORS */
4412 triangle *triangletraverse(m)
4413 struct mesh *m;
4414 #endif /* not ANSI_DECLARATORS */
4415
4416 {
4417 triangle *newtriangle;
4418
4419 do {
4420 newtriangle = (triangle *) traverse(&m->triangles);
4421 if (newtriangle == (triangle *) NULL) {
4422 return (triangle *) NULL;
4423 }
4424 } while (deadtri(newtriangle)); /* Skip dead ones. */
4425 return newtriangle;
4426 }
4427
4428 /*****************************************************************************/
4429 /* */
4430 /* subsegdealloc() Deallocate space for a subsegment, marking it dead. */
4431 /* */
4432 /*****************************************************************************/
4433
4434 #ifdef ANSI_DECLARATORS
4435 void subsegdealloc(struct mesh *m, subseg *dyingsubseg)
4436 #else /* not ANSI_DECLARATORS */
4437 void subsegdealloc(m, dyingsubseg)
4438 struct mesh *m;
4439 subseg *dyingsubseg;
4440 #endif /* not ANSI_DECLARATORS */
4441
4442 {
4443 /* Mark the subsegment as dead. This makes it possible to detect dead */
4444 /* subsegments when traversing the list of all subsegments. */
4445 killsubseg(dyingsubseg);
4446 pooldealloc(&m->subsegs, (VOID *) dyingsubseg);
4447 }
4448
4449 /*****************************************************************************/
4450 /* */
4451 /* subsegtraverse() Traverse the subsegments, skipping dead ones. */
4452 /* */
4453 /*****************************************************************************/
4454
4455 #ifdef ANSI_DECLARATORS
4456 subseg *subsegtraverse(struct mesh *m)
4457 #else /* not ANSI_DECLARATORS */
4458 subseg *subsegtraverse(m)
4459 struct mesh *m;
4460 #endif /* not ANSI_DECLARATORS */
4461
4462 {
4463 subseg *newsubseg;
4464
4465 do {
4466 newsubseg = (subseg *) traverse(&m->subsegs);
4467 if (newsubseg == (subseg *) NULL) {
4468 return (subseg *) NULL;
4469 }
4470 } while (deadsubseg(newsubseg)); /* Skip dead ones. */
4471 return newsubseg;
4472 }
4473
4474 /*****************************************************************************/
4475 /* */
4476 /* vertexdealloc() Deallocate space for a vertex, marking it dead. */
4477 /* */
4478 /*****************************************************************************/
4479
4480 #ifdef ANSI_DECLARATORS
4481 void vertexdealloc(struct mesh *m, vertex dyingvertex)
4482 #else /* not ANSI_DECLARATORS */
4483 void vertexdealloc(m, dyingvertex)
4484 struct mesh *m;
4485 vertex dyingvertex;
4486 #endif /* not ANSI_DECLARATORS */
4487
4488 {
4489 /* Mark the vertex as dead. This makes it possible to detect dead */
4490 /* vertices when traversing the list of all vertices. */
4491 setvertextype(dyingvertex, DEADVERTEX);
4492 pooldealloc(&m->vertices, (VOID *) dyingvertex);
4493 }
4494
4495 /*****************************************************************************/
4496 /* */
4497 /* vertextraverse() Traverse the vertices, skipping dead ones. */
4498 /* */
4499 /*****************************************************************************/
4500
4501 #ifdef ANSI_DECLARATORS
4502 vertex vertextraverse(struct mesh *m)
4503 #else /* not ANSI_DECLARATORS */
4504 vertex vertextraverse(m)
4505 struct mesh *m;
4506 #endif /* not ANSI_DECLARATORS */
4507
4508 {
4509 vertex newvertex;
4510
4511 do {
4512 newvertex = (vertex) traverse(&m->vertices);
4513 if (newvertex == (vertex) NULL) {
4514 return (vertex) NULL;
4515 }
4516 } while (vertextype(newvertex) == DEADVERTEX); /* Skip dead ones. */
4517 return newvertex;
4518 }
4519
4520 /*****************************************************************************/
4521 /* */
4522 /* badsubsegdealloc() Deallocate space for a bad subsegment, marking it */
4523 /* dead. */
4524 /* */
4525 /*****************************************************************************/
4526
4527 #ifndef CDT_ONLY
4528
4529 #ifdef ANSI_DECLARATORS
4530 void badsubsegdealloc(struct mesh *m, struct badsubseg *dyingseg)
4531 #else /* not ANSI_DECLARATORS */
4532 void badsubsegdealloc(m, dyingseg)
4533 struct mesh *m;
4534 struct badsubseg *dyingseg;
4535 #endif /* not ANSI_DECLARATORS */
4536
4537 {
4538 /* Set subsegment's origin to NULL. This makes it possible to detect dead */
4539 /* badsubsegs when traversing the list of all badsubsegs . */
4540 dyingseg->subsegorg = (vertex) NULL;
4541 pooldealloc(&m->badsubsegs, (VOID *) dyingseg);
4542 }
4543
4544 #endif /* not CDT_ONLY */
4545
4546 /*****************************************************************************/
4547 /* */
4548 /* badsubsegtraverse() Traverse the bad subsegments, skipping dead ones. */
4549 /* */
4550 /*****************************************************************************/
4551
4552 #ifndef CDT_ONLY
4553
4554 #ifdef ANSI_DECLARATORS
4555 struct badsubseg *badsubsegtraverse(struct mesh *m)
4556 #else /* not ANSI_DECLARATORS */
4557 struct badsubseg *badsubsegtraverse(m)
4558 struct mesh *m;
4559 #endif /* not ANSI_DECLARATORS */
4560
4561 {
4562 struct badsubseg *newseg;
4563
4564 do {
4565 newseg = (struct badsubseg *) traverse(&m->badsubsegs);
4566 if (newseg == (struct badsubseg *) NULL) {
4567 return (struct badsubseg *) NULL;
4568 }
4569 } while (newseg->subsegorg == (vertex) NULL); /* Skip dead ones. */
4570 return newseg;
4571 }
4572
4573 #endif /* not CDT_ONLY */
4574
4575 /*****************************************************************************/
4576 /* */
4577 /* getvertex() Get a specific vertex, by number, from the list. */
4578 /* */
4579 /* The first vertex is number 'firstnumber'. */
4580 /* */
4581 /* Note that this takes O(n) time (with a small constant, if VERTEXPERBLOCK */
4582 /* is large). I don't care to take the trouble to make it work in constant */
4583 /* time. */
4584 /* */
4585 /*****************************************************************************/
4586
4587 #ifdef ANSI_DECLARATORS
4588 vertex getvertex(struct mesh *m, struct behavior *b, int number)
4589 #else /* not ANSI_DECLARATORS */
4590 vertex getvertex(m, b, number)
4591 struct mesh *m;
4592 struct behavior *b;
4593 int number;
4594 #endif /* not ANSI_DECLARATORS */
4595
4596 {
4597 VOID **getblock;
4598 char *foundvertex;
4599 unsigned long alignptr;
4600 int current;
4601
4602 getblock = m->vertices.firstblock;
4603 current = b->firstnumber;
4604
4605 /* Find the right block. */
4606 if (current + m->vertices.itemsfirstblock <= number) {
4607 getblock = (VOID **) *getblock;
4608 current += m->vertices.itemsfirstblock;
4609 while (current + m->vertices.itemsperblock <= number) {
4610 getblock = (VOID **) *getblock;
4611 current += m->vertices.itemsperblock;
4612 }
4613 }
4614
4615 /* Now find the right vertex. */
4616 alignptr = (unsigned long) (getblock + 1);
4617 foundvertex = (char *) (alignptr + (unsigned long) m->vertices.alignbytes -
4618 (alignptr % (unsigned long) m->vertices.alignbytes));
4619 return (vertex) (foundvertex + m->vertices.itembytes * (number - current));
4620 }
4621
4622 /*****************************************************************************/
4623 /* */
4624 /* triangledeinit() Free all remaining allocated memory. */
4625 /* */
4626 /*****************************************************************************/
4627
4628 #ifdef ANSI_DECLARATORS
4629 void triangledeinit(struct mesh *m, struct behavior *b)
4630 #else /* not ANSI_DECLARATORS */
4631 void triangledeinit(m, b)
4632 struct mesh *m;
4633 struct behavior *b;
4634 #endif /* not ANSI_DECLARATORS */
4635
4636 {
4637 pooldeinit(&m->triangles);
4638 trifree((VOID *) m->dummytribase);
4639 if (b->usesegments) {
4640 pooldeinit(&m->subsegs);
4641 trifree((VOID *) m->dummysubbase);
4642 }
4643 pooldeinit(&m->vertices);
4644 #ifndef CDT_ONLY
4645 if (b->quality) {
4646 pooldeinit(&m->badsubsegs);
4647 if ((b->minangle > 0.0) || b->vararea || b->fixedarea || b->usertest) {
4648 pooldeinit(&m->badtriangles);
4649 pooldeinit(&m->flipstackers);
4650 }
4651 }
4652 #endif /* not CDT_ONLY */
4653 }
4654
4655 /** **/
4656 /** **/
4657 /********* Memory management routines end here *********/
4658
4659 /********* Constructors begin here *********/
4660 /** **/
4661 /** **/
4662
4663 /*****************************************************************************/
4664 /* */
4665 /* maketriangle() Create a new triangle with orientation zero. */
4666 /* */
4667 /*****************************************************************************/
4668
4669 #ifdef ANSI_DECLARATORS
4670 void maketriangle(struct mesh *m, struct behavior *b, struct otri *newotri)
4671 #else /* not ANSI_DECLARATORS */
4672 void maketriangle(m, b, newotri)
4673 struct mesh *m;
4674 struct behavior *b;
4675 struct otri *newotri;
4676 #endif /* not ANSI_DECLARATORS */
4677
4678 {
4679 int i;
4680
4681 newotri->tri = (triangle *) poolalloc(&m->triangles);
4682 /* Initialize the three adjoining triangles to be "outer space". */
4683 newotri->tri[0] = (triangle) m->dummytri;
4684 newotri->tri[1] = (triangle) m->dummytri;
4685 newotri->tri[2] = (triangle) m->dummytri;
4686 /* Three NULL vertices. */
4687 newotri->tri[3] = (triangle) NULL;
4688 newotri->tri[4] = (triangle) NULL;
4689 newotri->tri[5] = (triangle) NULL;
4690 if (b->usesegments) {
4691 /* Initialize the three adjoining subsegments to be the omnipresent */
4692 /* subsegment. */
4693 newotri->tri[6] = (triangle) m->dummysub;
4694 newotri->tri[7] = (triangle) m->dummysub;
4695 newotri->tri[8] = (triangle) m->dummysub;
4696 }
4697 for (i = 0; i < m->eextras; i++) {
4698 setelemattribute(*newotri, i, 0.0);
4699 }
4700 if (b->vararea) {
4701 setareabound(*newotri, -1.0);
4702 }
4703
4704 newotri->orient = 0;
4705 }
4706
4707 /*****************************************************************************/
4708 /* */
4709 /* makesubseg() Create a new subsegment with orientation zero. */
4710 /* */
4711 /*****************************************************************************/
4712
4713 #ifdef ANSI_DECLARATORS
4714 void makesubseg(struct mesh *m, struct osub *newsubseg)
4715 #else /* not ANSI_DECLARATORS */
4716 void makesubseg(m, newsubseg)
4717 struct mesh *m;
4718 struct osub *newsubseg;
4719 #endif /* not ANSI_DECLARATORS */
4720
4721 {
4722 newsubseg->ss = (subseg *) poolalloc(&m->subsegs);
4723 /* Initialize the two adjoining subsegments to be the omnipresent */
4724 /* subsegment. */
4725 newsubseg->ss[0] = (subseg) m->dummysub;
4726 newsubseg->ss[1] = (subseg) m->dummysub;
4727 /* Four NULL vertices. */
4728 newsubseg->ss[2] = (subseg) NULL;
4729 newsubseg->ss[3] = (subseg) NULL;
4730 newsubseg->ss[4] = (subseg) NULL;
4731 newsubseg->ss[5] = (subseg) NULL;
4732 /* Initialize the two adjoining triangles to be "outer space." */
4733 newsubseg->ss[6] = (subseg) m->dummytri;
4734 newsubseg->ss[7] = (subseg) m->dummytri;
4735 /* Set the boundary marker to zero. */
4736 setmark(*newsubseg, 0);
4737
4738 newsubseg->ssorient = 0;
4739 }
4740
4741 /** **/
4742 /** **/
4743 /********* Constructors end here *********/
4744
4745 /********* Geometric primitives begin here *********/
4746 /** **/
4747 /** **/
4748
4749 /* The adaptive exact arithmetic geometric predicates implemented herein are */
4750 /* described in detail in my paper, "Adaptive Precision Floating-Point */
4751 /* Arithmetic and Fast Robust Geometric Predicates." See the header for a */
4752 /* full citation. */
4753
4754 /* Which of the following two methods of finding the absolute values is */
4755 /* fastest is compiler-dependent. A few compilers can inline and optimize */
4756 /* the fabs() call; but most will incur the overhead of a function call, */
4757 /* which is disastrously slow. A faster way on IEEE machines might be to */
4758 /* mask the appropriate bit, but that's difficult to do in C without */
4759 /* forcing the value to be stored to memory (rather than be kept in the */
4760 /* register to which the optimizer assigned it). */
4761
4762 #define Absolute(a) ((a) >= 0.0 ? (a) : -(a))
4763 /* #define Absolute(a) fabs(a) */
4764
4765 /* Many of the operations are broken up into two pieces, a main part that */
4766 /* performs an approximate operation, and a "tail" that computes the */
4767 /* roundoff error of that operation. */
4768 /* */
4769 /* The operations Fast_Two_Sum(), Fast_Two_Diff(), Two_Sum(), Two_Diff(), */
4770 /* Split(), and Two_Product() are all implemented as described in the */
4771 /* reference. Each of these macros requires certain variables to be */
4772 /* defined in the calling routine. The variables `bvirt', `c', `abig', */
4773 /* `_i', `_j', `_k', `_l', `_m', and `_n' are declared `INEXACT' because */
4774 /* they store the result of an operation that may incur roundoff error. */
4775 /* The input parameter `x' (or the highest numbered `x_' parameter) must */
4776 /* also be declared `INEXACT'. */
4777
4778 #define Fast_Two_Sum_Tail(a, b, x, y) \
4779 bvirt = x - a; \
4780 y = b - bvirt
4781
4782 #define Fast_Two_Sum(a, b, x, y) \
4783 x = (REAL) (a + b); \
4784 Fast_Two_Sum_Tail(a, b, x, y)
4785
4786 #define Two_Sum_Tail(a, b, x, y) \
4787 bvirt = (REAL) (x - a); \
4788 avirt = x - bvirt; \
4789 bround = b - bvirt; \
4790 around = a - avirt; \
4791 y = around + bround
4792
4793 #define Two_Sum(a, b, x, y) \
4794 x = (REAL) (a + b); \
4795 Two_Sum_Tail(a, b, x, y)
4796
4797 #define Two_Diff_Tail(a, b, x, y) \
4798 bvirt = (REAL) (a - x); \
4799 avirt = x + bvirt; \
4800 bround = bvirt - b; \
4801 around = a - avirt; \
4802 y = around + bround
4803
4804 #define Two_Diff(a, b, x, y) \
4805 x = (REAL) (a - b); \
4806 Two_Diff_Tail(a, b, x, y)
4807
4808 #define Split(a, ahi, alo) \
4809 c = (REAL) (splitter * a); \
4810 abig = (REAL) (c - a); \
4811 ahi = c - abig; \
4812 alo = a - ahi
4813
4814 #define Two_Product_Tail(a, b, x, y) \
4815 Split(a, ahi, alo); \
4816 Split(b, bhi, blo); \
4817 err1 = x - (ahi * bhi); \
4818 err2 = err1 - (alo * bhi); \
4819 err3 = err2 - (ahi * blo); \
4820 y = (alo * blo) - err3
4821
4822 #define Two_Product(a, b, x, y) \
4823 x = (REAL) (a * b); \
4824 Two_Product_Tail(a, b, x, y)
4825
4826 /* Two_Product_Presplit() is Two_Product() where one of the inputs has */
4827 /* already been split. Avoids redundant splitting. */
4828
4829 #define Two_Product_Presplit(a, b, bhi, blo, x, y) \
4830 x = (REAL) (a * b); \
4831 Split(a, ahi, alo); \
4832 err1 = x - (ahi * bhi); \
4833 err2 = err1 - (alo * bhi); \
4834 err3 = err2 - (ahi * blo); \
4835 y = (alo * blo) - err3
4836
4837 /* Square() can be done more quickly than Two_Product(). */
4838
4839 #define Square_Tail(a, x, y) \
4840 Split(a, ahi, alo); \
4841 err1 = x - (ahi * ahi); \
4842 err3 = err1 - ((ahi + ahi) * alo); \
4843 y = (alo * alo) - err3
4844
4845 #define Square(a, x, y) \
4846 x = (REAL) (a * a); \
4847 Square_Tail(a, x, y)
4848
4849 /* Macros for summing expansions of various fixed lengths. These are all */
4850 /* unrolled versions of Expansion_Sum(). */
4851
4852 #define Two_One_Sum(a1, a0, b, x2, x1, x0) \
4853 Two_Sum(a0, b , _i, x0); \
4854 Two_Sum(a1, _i, x2, x1)
4855
4856 #define Two_One_Diff(a1, a0, b, x2, x1, x0) \
4857 Two_Diff(a0, b , _i, x0); \
4858 Two_Sum( a1, _i, x2, x1)
4859
4860 #define Two_Two_Sum(a1, a0, b1, b0, x3, x2, x1, x0) \
4861 Two_One_Sum(a1, a0, b0, _j, _0, x0); \
4862 Two_One_Sum(_j, _0, b1, x3, x2, x1)
4863
4864 #define Two_Two_Diff(a1, a0, b1, b0, x3, x2, x1, x0) \
4865 Two_One_Diff(a1, a0, b0, _j, _0, x0); \
4866 Two_One_Diff(_j, _0, b1, x3, x2, x1)
4867
4868 /* Macro for multiplying a two-component expansion by a single component. */
4869
4870 #define Two_One_Product(a1, a0, b, x3, x2, x1, x0) \
4871 Split(b, bhi, blo); \
4872 Two_Product_Presplit(a0, b, bhi, blo, _i, x0); \
4873 Two_Product_Presplit(a1, b, bhi, blo, _j, _0); \
4874 Two_Sum(_i, _0, _k, x1); \
4875 Fast_Two_Sum(_j, _k, x3, x2)
4876
4877 /*****************************************************************************/
4878 /* */
4879 /* exactinit() Initialize the variables used for exact arithmetic. */
4880 /* */
4881 /* `epsilon' is the largest power of two such that 1.0 + epsilon = 1.0 in */
4882 /* floating-point arithmetic. `epsilon' bounds the relative roundoff */
4883 /* error. It is used for floating-point error analysis. */
4884 /* */
4885 /* `splitter' is used to split floating-point numbers into two half- */
4886 /* length significands for exact multiplication. */
4887 /* */
4888 /* I imagine that a highly optimizing compiler might be too smart for its */
4889 /* own good, and somehow cause this routine to fail, if it pretends that */
4890 /* floating-point arithmetic is too much like real arithmetic. */
4891 /* */
4892 /* Don't change this routine unless you fully understand it. */
4893 /* */
4894 /*****************************************************************************/
4895
exactinit()4896 void exactinit()
4897 {
4898 REAL half;
4899 REAL check, lastcheck;
4900 int every_other;
4901 #ifdef LINUX
4902 int cword;
4903 #endif /* LINUX */
4904
4905 #ifdef CPU86
4906 #ifdef SINGLE
4907 _control87(_PC_24, _MCW_PC); /* Set FPU control word for single precision. */
4908 #else /* not SINGLE */
4909 _control87(_PC_53, _MCW_PC); /* Set FPU control word for double precision. */
4910 #endif /* not SINGLE */
4911 #endif /* CPU86 */
4912 #ifdef LINUX
4913 #ifdef SINGLE
4914 /* cword = 4223; */
4915 cword = 4210; /* set FPU control word for single precision */
4916 #else /* not SINGLE */
4917 /* cword = 4735; */
4918 cword = 4722; /* set FPU control word for double precision */
4919 #endif /* not SINGLE */
4920 _FPU_SETCW(cword);
4921 #endif /* LINUX */
4922
4923 every_other = 1;
4924 half = 0.5;
4925 epsilon = 1.0;
4926 splitter = 1.0;
4927 check = 1.0;
4928 /* Repeatedly divide `epsilon' by two until it is too small to add to */
4929 /* one without causing roundoff. (Also check if the sum is equal to */
4930 /* the previous sum, for machines that round up instead of using exact */
4931 /* rounding. Not that these routines will work on such machines.) */
4932 do {
4933 lastcheck = check;
4934 epsilon *= half;
4935 if (every_other) {
4936 splitter *= 2.0;
4937 }
4938 every_other = !every_other;
4939 check = 1.0 + epsilon;
4940 } while ((check != 1.0) && (check != lastcheck));
4941 splitter += 1.0;
4942 /* Error bounds for orientation and incircle tests. */
4943 resulterrbound = (3.0 + 8.0 * epsilon) * epsilon;
4944 ccwerrboundA = (3.0 + 16.0 * epsilon) * epsilon;
4945 ccwerrboundB = (2.0 + 12.0 * epsilon) * epsilon;
4946 ccwerrboundC = (9.0 + 64.0 * epsilon) * epsilon * epsilon;
4947 iccerrboundA = (10.0 + 96.0 * epsilon) * epsilon;
4948 iccerrboundB = (4.0 + 48.0 * epsilon) * epsilon;
4949 iccerrboundC = (44.0 + 576.0 * epsilon) * epsilon * epsilon;
4950 o3derrboundA = (7.0 + 56.0 * epsilon) * epsilon;
4951 o3derrboundB = (3.0 + 28.0 * epsilon) * epsilon;
4952 o3derrboundC = (26.0 + 288.0 * epsilon) * epsilon * epsilon;
4953 }
4954
4955 /*****************************************************************************/
4956 /* */
4957 /* fast_expansion_sum_zeroelim() Sum two expansions, eliminating zero */
4958 /* components from the output expansion. */
4959 /* */
4960 /* Sets h = e + f. See my Robust Predicates paper for details. */
4961 /* */
4962 /* If round-to-even is used (as with IEEE 754), maintains the strongly */
4963 /* nonoverlapping property. (That is, if e is strongly nonoverlapping, h */
4964 /* will be also.) Does NOT maintain the nonoverlapping or nonadjacent */
4965 /* properties. */
4966 /* */
4967 /*****************************************************************************/
4968
4969 #ifdef ANSI_DECLARATORS
4970 int fast_expansion_sum_zeroelim(int elen, REAL *e, int flen, REAL *f, REAL *h)
4971 #else /* not ANSI_DECLARATORS */
4972 int fast_expansion_sum_zeroelim(elen, e, flen, f, h) /* h cannot be e or f. */
4973 int elen;
4974 REAL *e;
4975 int flen;
4976 REAL *f;
4977 REAL *h;
4978 #endif /* not ANSI_DECLARATORS */
4979
4980 {
4981 REAL Q;
4982 INEXACT REAL Qnew;
4983 INEXACT REAL hh;
4984 INEXACT REAL bvirt;
4985 REAL avirt, bround, around;
4986 int eindex, findex, hindex;
4987 REAL enow, fnow;
4988
4989 enow = e[0];
4990 fnow = f[0];
4991 eindex = findex = 0;
4992 if ((fnow > enow) == (fnow > -enow)) {
4993 Q = enow;
4994 enow = e[++eindex];
4995 } else {
4996 Q = fnow;
4997 fnow = f[++findex];
4998 }
4999 hindex = 0;
5000 if ((eindex < elen) && (findex < flen)) {
5001 if ((fnow > enow) == (fnow > -enow)) {
5002 Fast_Two_Sum(enow, Q, Qnew, hh);
5003 enow = e[++eindex];
5004 } else {
5005 Fast_Two_Sum(fnow, Q, Qnew, hh);
5006 fnow = f[++findex];
5007 }
5008 Q = Qnew;
5009 if (hh != 0.0) {
5010 h[hindex++] = hh;
5011 }
5012 while ((eindex < elen) && (findex < flen)) {
5013 if ((fnow > enow) == (fnow > -enow)) {
5014 Two_Sum(Q, enow, Qnew, hh);
5015 enow = e[++eindex];
5016 } else {
5017 Two_Sum(Q, fnow, Qnew, hh);
5018 fnow = f[++findex];
5019 }
5020 Q = Qnew;
5021 if (hh != 0.0) {
5022 h[hindex++] = hh;
5023 }
5024 }
5025 }
5026 while (eindex < elen) {
5027 Two_Sum(Q, enow, Qnew, hh);
5028 enow = e[++eindex];
5029 Q = Qnew;
5030 if (hh != 0.0) {
5031 h[hindex++] = hh;
5032 }
5033 }
5034 while (findex < flen) {
5035 Two_Sum(Q, fnow, Qnew, hh);
5036 fnow = f[++findex];
5037 Q = Qnew;
5038 if (hh != 0.0) {
5039 h[hindex++] = hh;
5040 }
5041 }
5042 if ((Q != 0.0) || (hindex == 0)) {
5043 h[hindex++] = Q;
5044 }
5045 return hindex;
5046 }
5047
5048 /*****************************************************************************/
5049 /* */
5050 /* scale_expansion_zeroelim() Multiply an expansion by a scalar, */
5051 /* eliminating zero components from the */
5052 /* output expansion. */
5053 /* */
5054 /* Sets h = be. See my Robust Predicates paper for details. */
5055 /* */
5056 /* Maintains the nonoverlapping property. If round-to-even is used (as */
5057 /* with IEEE 754), maintains the strongly nonoverlapping and nonadjacent */
5058 /* properties as well. (That is, if e has one of these properties, so */
5059 /* will h.) */
5060 /* */
5061 /*****************************************************************************/
5062
5063 #ifdef ANSI_DECLARATORS
5064 int scale_expansion_zeroelim(int elen, REAL *e, REAL b, REAL *h)
5065 #else /* not ANSI_DECLARATORS */
5066 int scale_expansion_zeroelim(elen, e, b, h) /* e and h cannot be the same. */
5067 int elen;
5068 REAL *e;
5069 REAL b;
5070 REAL *h;
5071 #endif /* not ANSI_DECLARATORS */
5072
5073 {
5074 INEXACT REAL Q, sum;
5075 REAL hh;
5076 INEXACT REAL product1;
5077 REAL product0;
5078 int eindex, hindex;
5079 REAL enow;
5080 INEXACT REAL bvirt;
5081 REAL avirt, bround, around;
5082 INEXACT REAL c;
5083 INEXACT REAL abig;
5084 REAL ahi, alo, bhi, blo;
5085 REAL err1, err2, err3;
5086
5087 Split(b, bhi, blo);
5088 Two_Product_Presplit(e[0], b, bhi, blo, Q, hh);
5089 hindex = 0;
5090 if (hh != 0) {
5091 h[hindex++] = hh;
5092 }
5093 for (eindex = 1; eindex < elen; eindex++) {
5094 enow = e[eindex];
5095 Two_Product_Presplit(enow, b, bhi, blo, product1, product0);
5096 Two_Sum(Q, product0, sum, hh);
5097 if (hh != 0) {
5098 h[hindex++] = hh;
5099 }
5100 Fast_Two_Sum(product1, sum, Q, hh);
5101 if (hh != 0) {
5102 h[hindex++] = hh;
5103 }
5104 }
5105 if ((Q != 0.0) || (hindex == 0)) {
5106 h[hindex++] = Q;
5107 }
5108 return hindex;
5109 }
5110
5111 /*****************************************************************************/
5112 /* */
5113 /* estimate() Produce a one-word estimate of an expansion's value. */
5114 /* */
5115 /* See my Robust Predicates paper for details. */
5116 /* */
5117 /*****************************************************************************/
5118
5119 #ifdef ANSI_DECLARATORS
5120 REAL estimate(int elen, REAL *e)
5121 #else /* not ANSI_DECLARATORS */
5122 REAL estimate(elen, e)
5123 int elen;
5124 REAL *e;
5125 #endif /* not ANSI_DECLARATORS */
5126
5127 {
5128 REAL Q;
5129 int eindex;
5130
5131 Q = e[0];
5132 for (eindex = 1; eindex < elen; eindex++) {
5133 Q += e[eindex];
5134 }
5135 return Q;
5136 }
5137
5138 /*****************************************************************************/
5139 /* */
5140 /* counterclockwise() Return a positive value if the points pa, pb, and */
5141 /* pc occur in counterclockwise order; a negative */
5142 /* value if they occur in clockwise order; and zero */
5143 /* if they are collinear. The result is also a rough */
5144 /* approximation of twice the signed area of the */
5145 /* triangle defined by the three points. */
5146 /* */
5147 /* Uses exact arithmetic if necessary to ensure a correct answer. The */
5148 /* result returned is the determinant of a matrix. This determinant is */
5149 /* computed adaptively, in the sense that exact arithmetic is used only to */
5150 /* the degree it is needed to ensure that the returned value has the */
5151 /* correct sign. Hence, this function is usually quite fast, but will run */
5152 /* more slowly when the input points are collinear or nearly so. */
5153 /* */
5154 /* See my Robust Predicates paper for details. */
5155 /* */
5156 /*****************************************************************************/
5157
5158 #ifdef ANSI_DECLARATORS
5159 REAL counterclockwiseadapt(vertex pa, vertex pb, vertex pc, REAL detsum)
5160 #else /* not ANSI_DECLARATORS */
5161 REAL counterclockwiseadapt(pa, pb, pc, detsum)
5162 vertex pa;
5163 vertex pb;
5164 vertex pc;
5165 REAL detsum;
5166 #endif /* not ANSI_DECLARATORS */
5167
5168 {
5169 INEXACT REAL acx, acy, bcx, bcy;
5170 REAL acxtail, acytail, bcxtail, bcytail;
5171 INEXACT REAL detleft, detright;
5172 REAL detlefttail, detrighttail;
5173 REAL det, errbound;
5174 REAL B[4], C1[8], C2[12], D[16];
5175 INEXACT REAL B3;
5176 int C1length, C2length, Dlength;
5177 REAL u[4];
5178 INEXACT REAL u3;
5179 INEXACT REAL s1, t1;
5180 REAL s0, t0;
5181
5182 INEXACT REAL bvirt;
5183 REAL avirt, bround, around;
5184 INEXACT REAL c;
5185 INEXACT REAL abig;
5186 REAL ahi, alo, bhi, blo;
5187 REAL err1, err2, err3;
5188 INEXACT REAL _i, _j;
5189 REAL _0;
5190
5191 acx = (REAL) (pa[0] - pc[0]);
5192 bcx = (REAL) (pb[0] - pc[0]);
5193 acy = (REAL) (pa[1] - pc[1]);
5194 bcy = (REAL) (pb[1] - pc[1]);
5195
5196 Two_Product(acx, bcy, detleft, detlefttail);
5197 Two_Product(acy, bcx, detright, detrighttail);
5198
5199 Two_Two_Diff(detleft, detlefttail, detright, detrighttail,
5200 B3, B[2], B[1], B[0]);
5201 B[3] = B3;
5202
5203 det = estimate(4, B);
5204 errbound = ccwerrboundB * detsum;
5205 if ((det >= errbound) || (-det >= errbound)) {
5206 return det;
5207 }
5208
5209 Two_Diff_Tail(pa[0], pc[0], acx, acxtail);
5210 Two_Diff_Tail(pb[0], pc[0], bcx, bcxtail);
5211 Two_Diff_Tail(pa[1], pc[1], acy, acytail);
5212 Two_Diff_Tail(pb[1], pc[1], bcy, bcytail);
5213
5214 if ((acxtail == 0.0) && (acytail == 0.0)
5215 && (bcxtail == 0.0) && (bcytail == 0.0)) {
5216 return det;
5217 }
5218
5219 errbound = ccwerrboundC * detsum + resulterrbound * Absolute(det);
5220 det += (acx * bcytail + bcy * acxtail)
5221 - (acy * bcxtail + bcx * acytail);
5222 if ((det >= errbound) || (-det >= errbound)) {
5223 return det;
5224 }
5225
5226 Two_Product(acxtail, bcy, s1, s0);
5227 Two_Product(acytail, bcx, t1, t0);
5228 Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
5229 u[3] = u3;
5230 C1length = fast_expansion_sum_zeroelim(4, B, 4, u, C1);
5231
5232 Two_Product(acx, bcytail, s1, s0);
5233 Two_Product(acy, bcxtail, t1, t0);
5234 Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
5235 u[3] = u3;
5236 C2length = fast_expansion_sum_zeroelim(C1length, C1, 4, u, C2);
5237
5238 Two_Product(acxtail, bcytail, s1, s0);
5239 Two_Product(acytail, bcxtail, t1, t0);
5240 Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
5241 u[3] = u3;
5242 Dlength = fast_expansion_sum_zeroelim(C2length, C2, 4, u, D);
5243
5244 return(D[Dlength - 1]);
5245 }
5246
5247 #ifdef ANSI_DECLARATORS
5248 REAL counterclockwise(struct mesh *m, struct behavior *b,
5249 vertex pa, vertex pb, vertex pc)
5250 #else /* not ANSI_DECLARATORS */
5251 REAL counterclockwise(m, b, pa, pb, pc)
5252 struct mesh *m;
5253 struct behavior *b;
5254 vertex pa;
5255 vertex pb;
5256 vertex pc;
5257 #endif /* not ANSI_DECLARATORS */
5258
5259 {
5260 REAL detleft, detright, det;
5261 REAL detsum, errbound;
5262
5263 m->counterclockcount++;
5264
5265 detleft = (pa[0] - pc[0]) * (pb[1] - pc[1]);
5266 detright = (pa[1] - pc[1]) * (pb[0] - pc[0]);
5267 det = detleft - detright;
5268
5269 if (b->noexact) {
5270 return det;
5271 }
5272
5273 if (detleft > 0.0) {
5274 if (detright <= 0.0) {
5275 return det;
5276 } else {
5277 detsum = detleft + detright;
5278 }
5279 } else if (detleft < 0.0) {
5280 if (detright >= 0.0) {
5281 return det;
5282 } else {
5283 detsum = -detleft - detright;
5284 }
5285 } else {
5286 return det;
5287 }
5288
5289 errbound = ccwerrboundA * detsum;
5290 if ((det >= errbound) || (-det >= errbound)) {
5291 return det;
5292 }
5293
5294 return counterclockwiseadapt(pa, pb, pc, detsum);
5295 }
5296
5297 /*****************************************************************************/
5298 /* */
5299 /* incircle() Return a positive value if the point pd lies inside the */
5300 /* circle passing through pa, pb, and pc; a negative value if */
5301 /* it lies outside; and zero if the four points are cocircular.*/
5302 /* The points pa, pb, and pc must be in counterclockwise */
5303 /* order, or the sign of the result will be reversed. */
5304 /* */
5305 /* Uses exact arithmetic if necessary to ensure a correct answer. The */
5306 /* result returned is the determinant of a matrix. This determinant is */
5307 /* computed adaptively, in the sense that exact arithmetic is used only to */
5308 /* the degree it is needed to ensure that the returned value has the */
5309 /* correct sign. Hence, this function is usually quite fast, but will run */
5310 /* more slowly when the input points are cocircular or nearly so. */
5311 /* */
5312 /* See my Robust Predicates paper for details. */
5313 /* */
5314 /*****************************************************************************/
5315
5316 #ifdef ANSI_DECLARATORS
5317 REAL incircleadapt(vertex pa, vertex pb, vertex pc, vertex pd, REAL permanent)
5318 #else /* not ANSI_DECLARATORS */
5319 REAL incircleadapt(pa, pb, pc, pd, permanent)
5320 vertex pa;
5321 vertex pb;
5322 vertex pc;
5323 vertex pd;
5324 REAL permanent;
5325 #endif /* not ANSI_DECLARATORS */
5326
5327 {
5328 INEXACT REAL adx, bdx, cdx, ady, bdy, cdy;
5329 REAL det, errbound;
5330
5331 INEXACT REAL bdxcdy1, cdxbdy1, cdxady1, adxcdy1, adxbdy1, bdxady1;
5332 REAL bdxcdy0, cdxbdy0, cdxady0, adxcdy0, adxbdy0, bdxady0;
5333 REAL bc[4], ca[4], ab[4];
5334 INEXACT REAL bc3, ca3, ab3;
5335 REAL axbc[8], axxbc[16], aybc[8], ayybc[16], adet[32];
5336 int axbclen, axxbclen, aybclen, ayybclen, alen;
5337 REAL bxca[8], bxxca[16], byca[8], byyca[16], bdet[32];
5338 int bxcalen, bxxcalen, bycalen, byycalen, blen;
5339 REAL cxab[8], cxxab[16], cyab[8], cyyab[16], cdet[32];
5340 int cxablen, cxxablen, cyablen, cyyablen, clen;
5341 REAL abdet[64];
5342 int ablen;
5343 REAL fin1[1152], fin2[1152];
5344 REAL *finnow, *finother, *finswap;
5345 int finlength;
5346
5347 REAL adxtail, bdxtail, cdxtail, adytail, bdytail, cdytail;
5348 INEXACT REAL adxadx1, adyady1, bdxbdx1, bdybdy1, cdxcdx1, cdycdy1;
5349 REAL adxadx0, adyady0, bdxbdx0, bdybdy0, cdxcdx0, cdycdy0;
5350 REAL aa[4], bb[4], cc[4];
5351 INEXACT REAL aa3, bb3, cc3;
5352 INEXACT REAL ti1, tj1;
5353 REAL ti0, tj0;
5354 REAL u[4], v[4];
5355 INEXACT REAL u3, v3;
5356 REAL temp8[8], temp16a[16], temp16b[16], temp16c[16];
5357 REAL temp32a[32], temp32b[32], temp48[48], temp64[64];
5358 int temp8len, temp16alen, temp16blen, temp16clen;
5359 int temp32alen, temp32blen, temp48len, temp64len;
5360 REAL axtbb[8], axtcc[8], aytbb[8], aytcc[8];
5361 int axtbblen, axtcclen, aytbblen, aytcclen;
5362 REAL bxtaa[8], bxtcc[8], bytaa[8], bytcc[8];
5363 int bxtaalen, bxtcclen, bytaalen, bytcclen;
5364 REAL cxtaa[8], cxtbb[8], cytaa[8], cytbb[8];
5365 int cxtaalen, cxtbblen, cytaalen, cytbblen;
5366 REAL axtbc[8], aytbc[8], bxtca[8], bytca[8], cxtab[8], cytab[8];
5367 int axtbclen=0, aytbclen=0, bxtcalen=0, bytcalen=0, cxtablen=0, cytablen=0;
5368 REAL axtbct[16], aytbct[16], bxtcat[16], bytcat[16], cxtabt[16], cytabt[16];
5369 int axtbctlen, aytbctlen, bxtcatlen, bytcatlen, cxtabtlen, cytabtlen;
5370 REAL axtbctt[8], aytbctt[8], bxtcatt[8];
5371 REAL bytcatt[8], cxtabtt[8], cytabtt[8];
5372 int axtbcttlen, aytbcttlen, bxtcattlen, bytcattlen, cxtabttlen, cytabttlen;
5373 REAL abt[8], bct[8], cat[8];
5374 int abtlen, bctlen, catlen;
5375 REAL abtt[4], bctt[4], catt[4];
5376 int abttlen, bcttlen, cattlen;
5377 INEXACT REAL abtt3, bctt3, catt3;
5378 REAL negate;
5379
5380 INEXACT REAL bvirt;
5381 REAL avirt, bround, around;
5382 INEXACT REAL c;
5383 INEXACT REAL abig;
5384 REAL ahi, alo, bhi, blo;
5385 REAL err1, err2, err3;
5386 INEXACT REAL _i, _j;
5387 REAL _0;
5388
5389 adx = (REAL) (pa[0] - pd[0]);
5390 bdx = (REAL) (pb[0] - pd[0]);
5391 cdx = (REAL) (pc[0] - pd[0]);
5392 ady = (REAL) (pa[1] - pd[1]);
5393 bdy = (REAL) (pb[1] - pd[1]);
5394 cdy = (REAL) (pc[1] - pd[1]);
5395
5396 Two_Product(bdx, cdy, bdxcdy1, bdxcdy0);
5397 Two_Product(cdx, bdy, cdxbdy1, cdxbdy0);
5398 Two_Two_Diff(bdxcdy1, bdxcdy0, cdxbdy1, cdxbdy0, bc3, bc[2], bc[1], bc[0]);
5399 bc[3] = bc3;
5400 axbclen = scale_expansion_zeroelim(4, bc, adx, axbc);
5401 axxbclen = scale_expansion_zeroelim(axbclen, axbc, adx, axxbc);
5402 aybclen = scale_expansion_zeroelim(4, bc, ady, aybc);
5403 ayybclen = scale_expansion_zeroelim(aybclen, aybc, ady, ayybc);
5404 alen = fast_expansion_sum_zeroelim(axxbclen, axxbc, ayybclen, ayybc, adet);
5405
5406 Two_Product(cdx, ady, cdxady1, cdxady0);
5407 Two_Product(adx, cdy, adxcdy1, adxcdy0);
5408 Two_Two_Diff(cdxady1, cdxady0, adxcdy1, adxcdy0, ca3, ca[2], ca[1], ca[0]);
5409 ca[3] = ca3;
5410 bxcalen = scale_expansion_zeroelim(4, ca, bdx, bxca);
5411 bxxcalen = scale_expansion_zeroelim(bxcalen, bxca, bdx, bxxca);
5412 bycalen = scale_expansion_zeroelim(4, ca, bdy, byca);
5413 byycalen = scale_expansion_zeroelim(bycalen, byca, bdy, byyca);
5414 blen = fast_expansion_sum_zeroelim(bxxcalen, bxxca, byycalen, byyca, bdet);
5415
5416 Two_Product(adx, bdy, adxbdy1, adxbdy0);
5417 Two_Product(bdx, ady, bdxady1, bdxady0);
5418 Two_Two_Diff(adxbdy1, adxbdy0, bdxady1, bdxady0, ab3, ab[2], ab[1], ab[0]);
5419 ab[3] = ab3;
5420 cxablen = scale_expansion_zeroelim(4, ab, cdx, cxab);
5421 cxxablen = scale_expansion_zeroelim(cxablen, cxab, cdx, cxxab);
5422 cyablen = scale_expansion_zeroelim(4, ab, cdy, cyab);
5423 cyyablen = scale_expansion_zeroelim(cyablen, cyab, cdy, cyyab);
5424 clen = fast_expansion_sum_zeroelim(cxxablen, cxxab, cyyablen, cyyab, cdet);
5425
5426 ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
5427 finlength = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, fin1);
5428
5429 det = estimate(finlength, fin1);
5430 errbound = iccerrboundB * permanent;
5431 if ((det >= errbound) || (-det >= errbound)) {
5432 return det;
5433 }
5434
5435 Two_Diff_Tail(pa[0], pd[0], adx, adxtail);
5436 Two_Diff_Tail(pa[1], pd[1], ady, adytail);
5437 Two_Diff_Tail(pb[0], pd[0], bdx, bdxtail);
5438 Two_Diff_Tail(pb[1], pd[1], bdy, bdytail);
5439 Two_Diff_Tail(pc[0], pd[0], cdx, cdxtail);
5440 Two_Diff_Tail(pc[1], pd[1], cdy, cdytail);
5441 if ((adxtail == 0.0) && (bdxtail == 0.0) && (cdxtail == 0.0)
5442 && (adytail == 0.0) && (bdytail == 0.0) && (cdytail == 0.0)) {
5443 return det;
5444 }
5445
5446 errbound = iccerrboundC * permanent + resulterrbound * Absolute(det);
5447 det += ((adx * adx + ady * ady) * ((bdx * cdytail + cdy * bdxtail)
5448 - (bdy * cdxtail + cdx * bdytail))
5449 + 2.0 * (adx * adxtail + ady * adytail) * (bdx * cdy - bdy * cdx))
5450 + ((bdx * bdx + bdy * bdy) * ((cdx * adytail + ady * cdxtail)
5451 - (cdy * adxtail + adx * cdytail))
5452 + 2.0 * (bdx * bdxtail + bdy * bdytail) * (cdx * ady - cdy * adx))
5453 + ((cdx * cdx + cdy * cdy) * ((adx * bdytail + bdy * adxtail)
5454 - (ady * bdxtail + bdx * adytail))
5455 + 2.0 * (cdx * cdxtail + cdy * cdytail) * (adx * bdy - ady * bdx));
5456 if ((det >= errbound) || (-det >= errbound)) {
5457 return det;
5458 }
5459
5460 finnow = fin1;
5461 finother = fin2;
5462
5463 if ((bdxtail != 0.0) || (bdytail != 0.0)
5464 || (cdxtail != 0.0) || (cdytail != 0.0)) {
5465 Square(adx, adxadx1, adxadx0);
5466 Square(ady, adyady1, adyady0);
5467 Two_Two_Sum(adxadx1, adxadx0, adyady1, adyady0, aa3, aa[2], aa[1], aa[0]);
5468 aa[3] = aa3;
5469 }
5470 if ((cdxtail != 0.0) || (cdytail != 0.0)
5471 || (adxtail != 0.0) || (adytail != 0.0)) {
5472 Square(bdx, bdxbdx1, bdxbdx0);
5473 Square(bdy, bdybdy1, bdybdy0);
5474 Two_Two_Sum(bdxbdx1, bdxbdx0, bdybdy1, bdybdy0, bb3, bb[2], bb[1], bb[0]);
5475 bb[3] = bb3;
5476 }
5477 if ((adxtail != 0.0) || (adytail != 0.0)
5478 || (bdxtail != 0.0) || (bdytail != 0.0)) {
5479 Square(cdx, cdxcdx1, cdxcdx0);
5480 Square(cdy, cdycdy1, cdycdy0);
5481 Two_Two_Sum(cdxcdx1, cdxcdx0, cdycdy1, cdycdy0, cc3, cc[2], cc[1], cc[0]);
5482 cc[3] = cc3;
5483 }
5484
5485 if (adxtail != 0.0) {
5486 axtbclen = scale_expansion_zeroelim(4, bc, adxtail, axtbc);
5487 temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, 2.0 * adx,
5488 temp16a);
5489
5490 axtcclen = scale_expansion_zeroelim(4, cc, adxtail, axtcc);
5491 temp16blen = scale_expansion_zeroelim(axtcclen, axtcc, bdy, temp16b);
5492
5493 axtbblen = scale_expansion_zeroelim(4, bb, adxtail, axtbb);
5494 temp16clen = scale_expansion_zeroelim(axtbblen, axtbb, -cdy, temp16c);
5495
5496 temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5497 temp16blen, temp16b, temp32a);
5498 temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
5499 temp32alen, temp32a, temp48);
5500 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
5501 temp48, finother);
5502 finswap = finnow; finnow = finother; finother = finswap;
5503 }
5504 if (adytail != 0.0) {
5505 aytbclen = scale_expansion_zeroelim(4, bc, adytail, aytbc);
5506 temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, 2.0 * ady,
5507 temp16a);
5508
5509 aytbblen = scale_expansion_zeroelim(4, bb, adytail, aytbb);
5510 temp16blen = scale_expansion_zeroelim(aytbblen, aytbb, cdx, temp16b);
5511
5512 aytcclen = scale_expansion_zeroelim(4, cc, adytail, aytcc);
5513 temp16clen = scale_expansion_zeroelim(aytcclen, aytcc, -bdx, temp16c);
5514
5515 temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5516 temp16blen, temp16b, temp32a);
5517 temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
5518 temp32alen, temp32a, temp48);
5519 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
5520 temp48, finother);
5521 finswap = finnow; finnow = finother; finother = finswap;
5522 }
5523 if (bdxtail != 0.0) {
5524 bxtcalen = scale_expansion_zeroelim(4, ca, bdxtail, bxtca);
5525 temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, 2.0 * bdx,
5526 temp16a);
5527
5528 bxtaalen = scale_expansion_zeroelim(4, aa, bdxtail, bxtaa);
5529 temp16blen = scale_expansion_zeroelim(bxtaalen, bxtaa, cdy, temp16b);
5530
5531 bxtcclen = scale_expansion_zeroelim(4, cc, bdxtail, bxtcc);
5532 temp16clen = scale_expansion_zeroelim(bxtcclen, bxtcc, -ady, temp16c);
5533
5534 temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5535 temp16blen, temp16b, temp32a);
5536 temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
5537 temp32alen, temp32a, temp48);
5538 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
5539 temp48, finother);
5540 finswap = finnow; finnow = finother; finother = finswap;
5541 }
5542 if (bdytail != 0.0) {
5543 bytcalen = scale_expansion_zeroelim(4, ca, bdytail, bytca);
5544 temp16alen = scale_expansion_zeroelim(bytcalen, bytca, 2.0 * bdy,
5545 temp16a);
5546
5547 bytcclen = scale_expansion_zeroelim(4, cc, bdytail, bytcc);
5548 temp16blen = scale_expansion_zeroelim(bytcclen, bytcc, adx, temp16b);
5549
5550 bytaalen = scale_expansion_zeroelim(4, aa, bdytail, bytaa);
5551 temp16clen = scale_expansion_zeroelim(bytaalen, bytaa, -cdx, temp16c);
5552
5553 temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5554 temp16blen, temp16b, temp32a);
5555 temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
5556 temp32alen, temp32a, temp48);
5557 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
5558 temp48, finother);
5559 finswap = finnow; finnow = finother; finother = finswap;
5560 }
5561 if (cdxtail != 0.0) {
5562 cxtablen = scale_expansion_zeroelim(4, ab, cdxtail, cxtab);
5563 temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, 2.0 * cdx,
5564 temp16a);
5565
5566 cxtbblen = scale_expansion_zeroelim(4, bb, cdxtail, cxtbb);
5567 temp16blen = scale_expansion_zeroelim(cxtbblen, cxtbb, ady, temp16b);
5568
5569 cxtaalen = scale_expansion_zeroelim(4, aa, cdxtail, cxtaa);
5570 temp16clen = scale_expansion_zeroelim(cxtaalen, cxtaa, -bdy, temp16c);
5571
5572 temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5573 temp16blen, temp16b, temp32a);
5574 temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
5575 temp32alen, temp32a, temp48);
5576 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
5577 temp48, finother);
5578 finswap = finnow; finnow = finother; finother = finswap;
5579 }
5580 if (cdytail != 0.0) {
5581 cytablen = scale_expansion_zeroelim(4, ab, cdytail, cytab);
5582 temp16alen = scale_expansion_zeroelim(cytablen, cytab, 2.0 * cdy,
5583 temp16a);
5584
5585 cytaalen = scale_expansion_zeroelim(4, aa, cdytail, cytaa);
5586 temp16blen = scale_expansion_zeroelim(cytaalen, cytaa, bdx, temp16b);
5587
5588 cytbblen = scale_expansion_zeroelim(4, bb, cdytail, cytbb);
5589 temp16clen = scale_expansion_zeroelim(cytbblen, cytbb, -adx, temp16c);
5590
5591 temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5592 temp16blen, temp16b, temp32a);
5593 temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
5594 temp32alen, temp32a, temp48);
5595 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
5596 temp48, finother);
5597 finswap = finnow; finnow = finother; finother = finswap;
5598 }
5599
5600 if ((adxtail != 0.0) || (adytail != 0.0)) {
5601 if ((bdxtail != 0.0) || (bdytail != 0.0)
5602 || (cdxtail != 0.0) || (cdytail != 0.0)) {
5603 Two_Product(bdxtail, cdy, ti1, ti0);
5604 Two_Product(bdx, cdytail, tj1, tj0);
5605 Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
5606 u[3] = u3;
5607 negate = -bdy;
5608 Two_Product(cdxtail, negate, ti1, ti0);
5609 negate = -bdytail;
5610 Two_Product(cdx, negate, tj1, tj0);
5611 Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
5612 v[3] = v3;
5613 bctlen = fast_expansion_sum_zeroelim(4, u, 4, v, bct);
5614
5615 Two_Product(bdxtail, cdytail, ti1, ti0);
5616 Two_Product(cdxtail, bdytail, tj1, tj0);
5617 Two_Two_Diff(ti1, ti0, tj1, tj0, bctt3, bctt[2], bctt[1], bctt[0]);
5618 bctt[3] = bctt3;
5619 bcttlen = 4;
5620 } else {
5621 bct[0] = 0.0;
5622 bctlen = 1;
5623 bctt[0] = 0.0;
5624 bcttlen = 1;
5625 }
5626
5627 if (adxtail != 0.0) {
5628 temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, adxtail, temp16a);
5629 axtbctlen = scale_expansion_zeroelim(bctlen, bct, adxtail, axtbct);
5630 temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, 2.0 * adx,
5631 temp32a);
5632 temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5633 temp32alen, temp32a, temp48);
5634 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
5635 temp48, finother);
5636 finswap = finnow; finnow = finother; finother = finswap;
5637 if (bdytail != 0.0) {
5638 temp8len = scale_expansion_zeroelim(4, cc, adxtail, temp8);
5639 temp16alen = scale_expansion_zeroelim(temp8len, temp8, bdytail,
5640 temp16a);
5641 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
5642 temp16a, finother);
5643 finswap = finnow; finnow = finother; finother = finswap;
5644 }
5645 if (cdytail != 0.0) {
5646 temp8len = scale_expansion_zeroelim(4, bb, -adxtail, temp8);
5647 temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail,
5648 temp16a);
5649 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
5650 temp16a, finother);
5651 finswap = finnow; finnow = finother; finother = finswap;
5652 }
5653
5654 temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, adxtail,
5655 temp32a);
5656 axtbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adxtail, axtbctt);
5657 temp16alen = scale_expansion_zeroelim(axtbcttlen, axtbctt, 2.0 * adx,
5658 temp16a);
5659 temp16blen = scale_expansion_zeroelim(axtbcttlen, axtbctt, adxtail,
5660 temp16b);
5661 temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5662 temp16blen, temp16b, temp32b);
5663 temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
5664 temp32blen, temp32b, temp64);
5665 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
5666 temp64, finother);
5667 finswap = finnow; finnow = finother; finother = finswap;
5668 }
5669 if (adytail != 0.0) {
5670 temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, adytail, temp16a);
5671 aytbctlen = scale_expansion_zeroelim(bctlen, bct, adytail, aytbct);
5672 temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, 2.0 * ady,
5673 temp32a);
5674 temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5675 temp32alen, temp32a, temp48);
5676 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
5677 temp48, finother);
5678 finswap = finnow; finnow = finother; finother = finswap;
5679
5680
5681 temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, adytail,
5682 temp32a);
5683 aytbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adytail, aytbctt);
5684 temp16alen = scale_expansion_zeroelim(aytbcttlen, aytbctt, 2.0 * ady,
5685 temp16a);
5686 temp16blen = scale_expansion_zeroelim(aytbcttlen, aytbctt, adytail,
5687 temp16b);
5688 temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5689 temp16blen, temp16b, temp32b);
5690 temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
5691 temp32blen, temp32b, temp64);
5692 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
5693 temp64, finother);
5694 finswap = finnow; finnow = finother; finother = finswap;
5695 }
5696 }
5697 if ((bdxtail != 0.0) || (bdytail != 0.0)) {
5698 if ((cdxtail != 0.0) || (cdytail != 0.0)
5699 || (adxtail != 0.0) || (adytail != 0.0)) {
5700 Two_Product(cdxtail, ady, ti1, ti0);
5701 Two_Product(cdx, adytail, tj1, tj0);
5702 Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
5703 u[3] = u3;
5704 negate = -cdy;
5705 Two_Product(adxtail, negate, ti1, ti0);
5706 negate = -cdytail;
5707 Two_Product(adx, negate, tj1, tj0);
5708 Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
5709 v[3] = v3;
5710 catlen = fast_expansion_sum_zeroelim(4, u, 4, v, cat);
5711
5712 Two_Product(cdxtail, adytail, ti1, ti0);
5713 Two_Product(adxtail, cdytail, tj1, tj0);
5714 Two_Two_Diff(ti1, ti0, tj1, tj0, catt3, catt[2], catt[1], catt[0]);
5715 catt[3] = catt3;
5716 cattlen = 4;
5717 } else {
5718 cat[0] = 0.0;
5719 catlen = 1;
5720 catt[0] = 0.0;
5721 cattlen = 1;
5722 }
5723
5724 if (bdxtail != 0.0) {
5725 temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, bdxtail, temp16a);
5726 bxtcatlen = scale_expansion_zeroelim(catlen, cat, bdxtail, bxtcat);
5727 temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, 2.0 * bdx,
5728 temp32a);
5729 temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5730 temp32alen, temp32a, temp48);
5731 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
5732 temp48, finother);
5733 finswap = finnow; finnow = finother; finother = finswap;
5734 if (cdytail != 0.0) {
5735 temp8len = scale_expansion_zeroelim(4, aa, bdxtail, temp8);
5736 temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail,
5737 temp16a);
5738 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
5739 temp16a, finother);
5740 finswap = finnow; finnow = finother; finother = finswap;
5741 }
5742 if (adytail != 0.0) {
5743 temp8len = scale_expansion_zeroelim(4, cc, -bdxtail, temp8);
5744 temp16alen = scale_expansion_zeroelim(temp8len, temp8, adytail,
5745 temp16a);
5746 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
5747 temp16a, finother);
5748 finswap = finnow; finnow = finother; finother = finswap;
5749 }
5750
5751 temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, bdxtail,
5752 temp32a);
5753 bxtcattlen = scale_expansion_zeroelim(cattlen, catt, bdxtail, bxtcatt);
5754 temp16alen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, 2.0 * bdx,
5755 temp16a);
5756 temp16blen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, bdxtail,
5757 temp16b);
5758 temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5759 temp16blen, temp16b, temp32b);
5760 temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
5761 temp32blen, temp32b, temp64);
5762 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
5763 temp64, finother);
5764 finswap = finnow; finnow = finother; finother = finswap;
5765 }
5766 if (bdytail != 0.0) {
5767 temp16alen = scale_expansion_zeroelim(bytcalen, bytca, bdytail, temp16a);
5768 bytcatlen = scale_expansion_zeroelim(catlen, cat, bdytail, bytcat);
5769 temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, 2.0 * bdy,
5770 temp32a);
5771 temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5772 temp32alen, temp32a, temp48);
5773 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
5774 temp48, finother);
5775 finswap = finnow; finnow = finother; finother = finswap;
5776
5777
5778 temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, bdytail,
5779 temp32a);
5780 bytcattlen = scale_expansion_zeroelim(cattlen, catt, bdytail, bytcatt);
5781 temp16alen = scale_expansion_zeroelim(bytcattlen, bytcatt, 2.0 * bdy,
5782 temp16a);
5783 temp16blen = scale_expansion_zeroelim(bytcattlen, bytcatt, bdytail,
5784 temp16b);
5785 temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5786 temp16blen, temp16b, temp32b);
5787 temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
5788 temp32blen, temp32b, temp64);
5789 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
5790 temp64, finother);
5791 finswap = finnow; finnow = finother; finother = finswap;
5792 }
5793 }
5794 if ((cdxtail != 0.0) || (cdytail != 0.0)) {
5795 if ((adxtail != 0.0) || (adytail != 0.0)
5796 || (bdxtail != 0.0) || (bdytail != 0.0)) {
5797 Two_Product(adxtail, bdy, ti1, ti0);
5798 Two_Product(adx, bdytail, tj1, tj0);
5799 Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
5800 u[3] = u3;
5801 negate = -ady;
5802 Two_Product(bdxtail, negate, ti1, ti0);
5803 negate = -adytail;
5804 Two_Product(bdx, negate, tj1, tj0);
5805 Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
5806 v[3] = v3;
5807 abtlen = fast_expansion_sum_zeroelim(4, u, 4, v, abt);
5808
5809 Two_Product(adxtail, bdytail, ti1, ti0);
5810 Two_Product(bdxtail, adytail, tj1, tj0);
5811 Two_Two_Diff(ti1, ti0, tj1, tj0, abtt3, abtt[2], abtt[1], abtt[0]);
5812 abtt[3] = abtt3;
5813 abttlen = 4;
5814 } else {
5815 abt[0] = 0.0;
5816 abtlen = 1;
5817 abtt[0] = 0.0;
5818 abttlen = 1;
5819 }
5820
5821 if (cdxtail != 0.0) {
5822 temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, cdxtail, temp16a);
5823 cxtabtlen = scale_expansion_zeroelim(abtlen, abt, cdxtail, cxtabt);
5824 temp32alen = scale_expansion_zeroelim(cxtabtlen, cxtabt, 2.0 * cdx,
5825 temp32a);
5826 temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5827 temp32alen, temp32a, temp48);
5828 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
5829 temp48, finother);
5830 finswap = finnow; finnow = finother; finother = finswap;
5831 if (adytail != 0.0) {
5832 temp8len = scale_expansion_zeroelim(4, bb, cdxtail, temp8);
5833 temp16alen = scale_expansion_zeroelim(temp8len, temp8, adytail,
5834 temp16a);
5835 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
5836 temp16a, finother);
5837 finswap = finnow; finnow = finother; finother = finswap;
5838 }
5839 if (bdytail != 0.0) {
5840 temp8len = scale_expansion_zeroelim(4, aa, -cdxtail, temp8);
5841 temp16alen = scale_expansion_zeroelim(temp8len, temp8, bdytail,
5842 temp16a);
5843 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
5844 temp16a, finother);
5845 finswap = finnow; finnow = finother; finother = finswap;
5846 }
5847
5848 temp32alen = scale_expansion_zeroelim(cxtabtlen, cxtabt, cdxtail,
5849 temp32a);
5850 cxtabttlen = scale_expansion_zeroelim(abttlen, abtt, cdxtail, cxtabtt);
5851 temp16alen = scale_expansion_zeroelim(cxtabttlen, cxtabtt, 2.0 * cdx,
5852 temp16a);
5853 temp16blen = scale_expansion_zeroelim(cxtabttlen, cxtabtt, cdxtail,
5854 temp16b);
5855 temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5856 temp16blen, temp16b, temp32b);
5857 temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
5858 temp32blen, temp32b, temp64);
5859 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
5860 temp64, finother);
5861 finswap = finnow; finnow = finother; finother = finswap;
5862 }
5863 if (cdytail != 0.0) {
5864 temp16alen = scale_expansion_zeroelim(cytablen, cytab, cdytail, temp16a);
5865 cytabtlen = scale_expansion_zeroelim(abtlen, abt, cdytail, cytabt);
5866 temp32alen = scale_expansion_zeroelim(cytabtlen, cytabt, 2.0 * cdy,
5867 temp32a);
5868 temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5869 temp32alen, temp32a, temp48);
5870 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
5871 temp48, finother);
5872 finswap = finnow; finnow = finother; finother = finswap;
5873
5874
5875 temp32alen = scale_expansion_zeroelim(cytabtlen, cytabt, cdytail,
5876 temp32a);
5877 cytabttlen = scale_expansion_zeroelim(abttlen, abtt, cdytail, cytabtt);
5878 temp16alen = scale_expansion_zeroelim(cytabttlen, cytabtt, 2.0 * cdy,
5879 temp16a);
5880 temp16blen = scale_expansion_zeroelim(cytabttlen, cytabtt, cdytail,
5881 temp16b);
5882 temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
5883 temp16blen, temp16b, temp32b);
5884 temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
5885 temp32blen, temp32b, temp64);
5886 finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
5887 temp64, finother);
5888 finswap = finnow; finnow = finother; finother = finswap;
5889 }
5890 }
5891
5892 return finnow[finlength - 1];
5893 }
5894
5895 #ifdef ANSI_DECLARATORS
5896 REAL incircle(struct mesh *m, struct behavior *b,
5897 vertex pa, vertex pb, vertex pc, vertex pd)
5898 #else /* not ANSI_DECLARATORS */
5899 REAL incircle(m, b, pa, pb, pc, pd)
5900 struct mesh *m;
5901 struct behavior *b;
5902 vertex pa;
5903 vertex pb;
5904 vertex pc;
5905 vertex pd;
5906 #endif /* not ANSI_DECLARATORS */
5907
5908 {
5909 REAL adx, bdx, cdx, ady, bdy, cdy;
5910 REAL bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady;
5911 REAL alift, blift, clift;
5912 REAL det;
5913 REAL permanent, errbound;
5914
5915 m->incirclecount++;
5916
5917 adx = pa[0] - pd[0];
5918 bdx = pb[0] - pd[0];
5919 cdx = pc[0] - pd[0];
5920 ady = pa[1] - pd[1];
5921 bdy = pb[1] - pd[1];
5922 cdy = pc[1] - pd[1];
5923
5924 bdxcdy = bdx * cdy;
5925 cdxbdy = cdx * bdy;
5926 alift = adx * adx + ady * ady;
5927
5928 cdxady = cdx * ady;
5929 adxcdy = adx * cdy;
5930 blift = bdx * bdx + bdy * bdy;
5931
5932 adxbdy = adx * bdy;
5933 bdxady = bdx * ady;
5934 clift = cdx * cdx + cdy * cdy;
5935
5936 det = alift * (bdxcdy - cdxbdy)
5937 + blift * (cdxady - adxcdy)
5938 + clift * (adxbdy - bdxady);
5939
5940 if (b->noexact) {
5941 return det;
5942 }
5943
5944 permanent = (Absolute(bdxcdy) + Absolute(cdxbdy)) * alift
5945 + (Absolute(cdxady) + Absolute(adxcdy)) * blift
5946 + (Absolute(adxbdy) + Absolute(bdxady)) * clift;
5947 errbound = iccerrboundA * permanent;
5948 if ((det > errbound) || (-det > errbound)) {
5949 return det;
5950 }
5951
5952 return incircleadapt(pa, pb, pc, pd, permanent);
5953 }
5954
5955 /*****************************************************************************/
5956 /* */
5957 /* orient3d() Return a positive value if the point pd lies below the */
5958 /* plane passing through pa, pb, and pc; "below" is defined so */
5959 /* that pa, pb, and pc appear in counterclockwise order when */
5960 /* viewed from above the plane. Returns a negative value if */
5961 /* pd lies above the plane. Returns zero if the points are */
5962 /* coplanar. The result is also a rough approximation of six */
5963 /* times the signed volume of the tetrahedron defined by the */
5964 /* four points. */
5965 /* */
5966 /* Uses exact arithmetic if necessary to ensure a correct answer. The */
5967 /* result returned is the determinant of a matrix. This determinant is */
5968 /* computed adaptively, in the sense that exact arithmetic is used only to */
5969 /* the degree it is needed to ensure that the returned value has the */
5970 /* correct sign. Hence, this function is usually quite fast, but will run */
5971 /* more slowly when the input points are coplanar or nearly so. */
5972 /* */
5973 /* See my Robust Predicates paper for details. */
5974 /* */
5975 /*****************************************************************************/
5976
5977 #ifdef ANSI_DECLARATORS
5978 REAL orient3dadapt(vertex pa, vertex pb, vertex pc, vertex pd,
5979 REAL aheight, REAL bheight, REAL cheight, REAL dheight,
5980 REAL permanent)
5981 #else /* not ANSI_DECLARATORS */
5982 REAL orient3dadapt(pa, pb, pc, pd,
5983 aheight, bheight, cheight, dheight, permanent)
5984 vertex pa;
5985 vertex pb;
5986 vertex pc;
5987 vertex pd;
5988 REAL aheight;
5989 REAL bheight;
5990 REAL cheight;
5991 REAL dheight;
5992 REAL permanent;
5993 #endif /* not ANSI_DECLARATORS */
5994
5995 {
5996 INEXACT REAL adx, bdx, cdx, ady, bdy, cdy, adheight, bdheight, cdheight;
5997 REAL det, errbound;
5998
5999 INEXACT REAL bdxcdy1, cdxbdy1, cdxady1, adxcdy1, adxbdy1, bdxady1;
6000 REAL bdxcdy0, cdxbdy0, cdxady0, adxcdy0, adxbdy0, bdxady0;
6001 REAL bc[4], ca[4], ab[4];
6002 INEXACT REAL bc3, ca3, ab3;
6003 REAL adet[8], bdet[8], cdet[8];
6004 int alen, blen, clen;
6005 REAL abdet[16];
6006 int ablen;
6007 REAL *finnow, *finother, *finswap;
6008 REAL fin1[192], fin2[192];
6009 int finlength;
6010
6011 REAL adxtail, bdxtail, cdxtail;
6012 REAL adytail, bdytail, cdytail;
6013 REAL adheighttail, bdheighttail, cdheighttail;
6014 INEXACT REAL at_blarge, at_clarge;
6015 INEXACT REAL bt_clarge, bt_alarge;
6016 INEXACT REAL ct_alarge, ct_blarge;
6017 REAL at_b[4], at_c[4], bt_c[4], bt_a[4], ct_a[4], ct_b[4];
6018 int at_blen, at_clen, bt_clen, bt_alen, ct_alen, ct_blen;
6019 INEXACT REAL bdxt_cdy1, cdxt_bdy1, cdxt_ady1;
6020 INEXACT REAL adxt_cdy1, adxt_bdy1, bdxt_ady1;
6021 REAL bdxt_cdy0, cdxt_bdy0, cdxt_ady0;
6022 REAL adxt_cdy0, adxt_bdy0, bdxt_ady0;
6023 INEXACT REAL bdyt_cdx1, cdyt_bdx1, cdyt_adx1;
6024 INEXACT REAL adyt_cdx1, adyt_bdx1, bdyt_adx1;
6025 REAL bdyt_cdx0, cdyt_bdx0, cdyt_adx0;
6026 REAL adyt_cdx0, adyt_bdx0, bdyt_adx0;
6027 REAL bct[8], cat[8], abt[8];
6028 int bctlen, catlen, abtlen;
6029 INEXACT REAL bdxt_cdyt1, cdxt_bdyt1, cdxt_adyt1;
6030 INEXACT REAL adxt_cdyt1, adxt_bdyt1, bdxt_adyt1;
6031 REAL bdxt_cdyt0, cdxt_bdyt0, cdxt_adyt0;
6032 REAL adxt_cdyt0, adxt_bdyt0, bdxt_adyt0;
6033 REAL u[4], v[12], w[16];
6034 INEXACT REAL u3;
6035 int vlength, wlength;
6036 REAL negate;
6037
6038 INEXACT REAL bvirt;
6039 REAL avirt, bround, around;
6040 INEXACT REAL c;
6041 INEXACT REAL abig;
6042 REAL ahi, alo, bhi, blo;
6043 REAL err1, err2, err3;
6044 INEXACT REAL _i, _j, _k;
6045 REAL _0;
6046
6047 adx = (REAL) (pa[0] - pd[0]);
6048 bdx = (REAL) (pb[0] - pd[0]);
6049 cdx = (REAL) (pc[0] - pd[0]);
6050 ady = (REAL) (pa[1] - pd[1]);
6051 bdy = (REAL) (pb[1] - pd[1]);
6052 cdy = (REAL) (pc[1] - pd[1]);
6053 adheight = (REAL) (aheight - dheight);
6054 bdheight = (REAL) (bheight - dheight);
6055 cdheight = (REAL) (cheight - dheight);
6056
6057 Two_Product(bdx, cdy, bdxcdy1, bdxcdy0);
6058 Two_Product(cdx, bdy, cdxbdy1, cdxbdy0);
6059 Two_Two_Diff(bdxcdy1, bdxcdy0, cdxbdy1, cdxbdy0, bc3, bc[2], bc[1], bc[0]);
6060 bc[3] = bc3;
6061 alen = scale_expansion_zeroelim(4, bc, adheight, adet);
6062
6063 Two_Product(cdx, ady, cdxady1, cdxady0);
6064 Two_Product(adx, cdy, adxcdy1, adxcdy0);
6065 Two_Two_Diff(cdxady1, cdxady0, adxcdy1, adxcdy0, ca3, ca[2], ca[1], ca[0]);
6066 ca[3] = ca3;
6067 blen = scale_expansion_zeroelim(4, ca, bdheight, bdet);
6068
6069 Two_Product(adx, bdy, adxbdy1, adxbdy0);
6070 Two_Product(bdx, ady, bdxady1, bdxady0);
6071 Two_Two_Diff(adxbdy1, adxbdy0, bdxady1, bdxady0, ab3, ab[2], ab[1], ab[0]);
6072 ab[3] = ab3;
6073 clen = scale_expansion_zeroelim(4, ab, cdheight, cdet);
6074
6075 ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
6076 finlength = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, fin1);
6077
6078 det = estimate(finlength, fin1);
6079 errbound = o3derrboundB * permanent;
6080 if ((det >= errbound) || (-det >= errbound)) {
6081 return det;
6082 }
6083
6084 Two_Diff_Tail(pa[0], pd[0], adx, adxtail);
6085 Two_Diff_Tail(pb[0], pd[0], bdx, bdxtail);
6086 Two_Diff_Tail(pc[0], pd[0], cdx, cdxtail);
6087 Two_Diff_Tail(pa[1], pd[1], ady, adytail);
6088 Two_Diff_Tail(pb[1], pd[1], bdy, bdytail);
6089 Two_Diff_Tail(pc[1], pd[1], cdy, cdytail);
6090 Two_Diff_Tail(aheight, dheight, adheight, adheighttail);
6091 Two_Diff_Tail(bheight, dheight, bdheight, bdheighttail);
6092 Two_Diff_Tail(cheight, dheight, cdheight, cdheighttail);
6093
6094 if ((adxtail == 0.0) && (bdxtail == 0.0) && (cdxtail == 0.0) &&
6095 (adytail == 0.0) && (bdytail == 0.0) && (cdytail == 0.0) &&
6096 (adheighttail == 0.0) &&
6097 (bdheighttail == 0.0) &&
6098 (cdheighttail == 0.0)) {
6099 return det;
6100 }
6101
6102 errbound = o3derrboundC * permanent + resulterrbound * Absolute(det);
6103 det += (adheight * ((bdx * cdytail + cdy * bdxtail) -
6104 (bdy * cdxtail + cdx * bdytail)) +
6105 adheighttail * (bdx * cdy - bdy * cdx)) +
6106 (bdheight * ((cdx * adytail + ady * cdxtail) -
6107 (cdy * adxtail + adx * cdytail)) +
6108 bdheighttail * (cdx * ady - cdy * adx)) +
6109 (cdheight * ((adx * bdytail + bdy * adxtail) -
6110 (ady * bdxtail + bdx * adytail)) +
6111 cdheighttail * (adx * bdy - ady * bdx));
6112 if ((det >= errbound) || (-det >= errbound)) {
6113 return det;
6114 }
6115
6116 finnow = fin1;
6117 finother = fin2;
6118
6119 if (adxtail == 0.0) {
6120 if (adytail == 0.0) {
6121 at_b[0] = 0.0;
6122 at_blen = 1;
6123 at_c[0] = 0.0;
6124 at_clen = 1;
6125 } else {
6126 negate = -adytail;
6127 Two_Product(negate, bdx, at_blarge, at_b[0]);
6128 at_b[1] = at_blarge;
6129 at_blen = 2;
6130 Two_Product(adytail, cdx, at_clarge, at_c[0]);
6131 at_c[1] = at_clarge;
6132 at_clen = 2;
6133 }
6134 } else {
6135 if (adytail == 0.0) {
6136 Two_Product(adxtail, bdy, at_blarge, at_b[0]);
6137 at_b[1] = at_blarge;
6138 at_blen = 2;
6139 negate = -adxtail;
6140 Two_Product(negate, cdy, at_clarge, at_c[0]);
6141 at_c[1] = at_clarge;
6142 at_clen = 2;
6143 } else {
6144 Two_Product(adxtail, bdy, adxt_bdy1, adxt_bdy0);
6145 Two_Product(adytail, bdx, adyt_bdx1, adyt_bdx0);
6146 Two_Two_Diff(adxt_bdy1, adxt_bdy0, adyt_bdx1, adyt_bdx0,
6147 at_blarge, at_b[2], at_b[1], at_b[0]);
6148 at_b[3] = at_blarge;
6149 at_blen = 4;
6150 Two_Product(adytail, cdx, adyt_cdx1, adyt_cdx0);
6151 Two_Product(adxtail, cdy, adxt_cdy1, adxt_cdy0);
6152 Two_Two_Diff(adyt_cdx1, adyt_cdx0, adxt_cdy1, adxt_cdy0,
6153 at_clarge, at_c[2], at_c[1], at_c[0]);
6154 at_c[3] = at_clarge;
6155 at_clen = 4;
6156 }
6157 }
6158 if (bdxtail == 0.0) {
6159 if (bdytail == 0.0) {
6160 bt_c[0] = 0.0;
6161 bt_clen = 1;
6162 bt_a[0] = 0.0;
6163 bt_alen = 1;
6164 } else {
6165 negate = -bdytail;
6166 Two_Product(negate, cdx, bt_clarge, bt_c[0]);
6167 bt_c[1] = bt_clarge;
6168 bt_clen = 2;
6169 Two_Product(bdytail, adx, bt_alarge, bt_a[0]);
6170 bt_a[1] = bt_alarge;
6171 bt_alen = 2;
6172 }
6173 } else {
6174 if (bdytail == 0.0) {
6175 Two_Product(bdxtail, cdy, bt_clarge, bt_c[0]);
6176 bt_c[1] = bt_clarge;
6177 bt_clen = 2;
6178 negate = -bdxtail;
6179 Two_Product(negate, ady, bt_alarge, bt_a[0]);
6180 bt_a[1] = bt_alarge;
6181 bt_alen = 2;
6182 } else {
6183 Two_Product(bdxtail, cdy, bdxt_cdy1, bdxt_cdy0);
6184 Two_Product(bdytail, cdx, bdyt_cdx1, bdyt_cdx0);
6185 Two_Two_Diff(bdxt_cdy1, bdxt_cdy0, bdyt_cdx1, bdyt_cdx0,
6186 bt_clarge, bt_c[2], bt_c[1], bt_c[0]);
6187 bt_c[3] = bt_clarge;
6188 bt_clen = 4;
6189 Two_Product(bdytail, adx, bdyt_adx1, bdyt_adx0);
6190 Two_Product(bdxtail, ady, bdxt_ady1, bdxt_ady0);
6191 Two_Two_Diff(bdyt_adx1, bdyt_adx0, bdxt_ady1, bdxt_ady0,
6192 bt_alarge, bt_a[2], bt_a[1], bt_a[0]);
6193 bt_a[3] = bt_alarge;
6194 bt_alen = 4;
6195 }
6196 }
6197 if (cdxtail == 0.0) {
6198 if (cdytail == 0.0) {
6199 ct_a[0] = 0.0;
6200 ct_alen = 1;
6201 ct_b[0] = 0.0;
6202 ct_blen = 1;
6203 } else {
6204 negate = -cdytail;
6205 Two_Product(negate, adx, ct_alarge, ct_a[0]);
6206 ct_a[1] = ct_alarge;
6207 ct_alen = 2;
6208 Two_Product(cdytail, bdx, ct_blarge, ct_b[0]);
6209 ct_b[1] = ct_blarge;
6210 ct_blen = 2;
6211 }
6212 } else {
6213 if (cdytail == 0.0) {
6214 Two_Product(cdxtail, ady, ct_alarge, ct_a[0]);
6215 ct_a[1] = ct_alarge;
6216 ct_alen = 2;
6217 negate = -cdxtail;
6218 Two_Product(negate, bdy, ct_blarge, ct_b[0]);
6219 ct_b[1] = ct_blarge;
6220 ct_blen = 2;
6221 } else {
6222 Two_Product(cdxtail, ady, cdxt_ady1, cdxt_ady0);
6223 Two_Product(cdytail, adx, cdyt_adx1, cdyt_adx0);
6224 Two_Two_Diff(cdxt_ady1, cdxt_ady0, cdyt_adx1, cdyt_adx0,
6225 ct_alarge, ct_a[2], ct_a[1], ct_a[0]);
6226 ct_a[3] = ct_alarge;
6227 ct_alen = 4;
6228 Two_Product(cdytail, bdx, cdyt_bdx1, cdyt_bdx0);
6229 Two_Product(cdxtail, bdy, cdxt_bdy1, cdxt_bdy0);
6230 Two_Two_Diff(cdyt_bdx1, cdyt_bdx0, cdxt_bdy1, cdxt_bdy0,
6231 ct_blarge, ct_b[2], ct_b[1], ct_b[0]);
6232 ct_b[3] = ct_blarge;
6233 ct_blen = 4;
6234 }
6235 }
6236
6237 bctlen = fast_expansion_sum_zeroelim(bt_clen, bt_c, ct_blen, ct_b, bct);
6238 wlength = scale_expansion_zeroelim(bctlen, bct, adheight, w);
6239 finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
6240 finother);
6241 finswap = finnow; finnow = finother; finother = finswap;
6242
6243 catlen = fast_expansion_sum_zeroelim(ct_alen, ct_a, at_clen, at_c, cat);
6244 wlength = scale_expansion_zeroelim(catlen, cat, bdheight, w);
6245 finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
6246 finother);
6247 finswap = finnow; finnow = finother; finother = finswap;
6248
6249 abtlen = fast_expansion_sum_zeroelim(at_blen, at_b, bt_alen, bt_a, abt);
6250 wlength = scale_expansion_zeroelim(abtlen, abt, cdheight, w);
6251 finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
6252 finother);
6253 finswap = finnow; finnow = finother; finother = finswap;
6254
6255 if (adheighttail != 0.0) {
6256 vlength = scale_expansion_zeroelim(4, bc, adheighttail, v);
6257 finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v,
6258 finother);
6259 finswap = finnow; finnow = finother; finother = finswap;
6260 }
6261 if (bdheighttail != 0.0) {
6262 vlength = scale_expansion_zeroelim(4, ca, bdheighttail, v);
6263 finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v,
6264 finother);
6265 finswap = finnow; finnow = finother; finother = finswap;
6266 }
6267 if (cdheighttail != 0.0) {
6268 vlength = scale_expansion_zeroelim(4, ab, cdheighttail, v);
6269 finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v,
6270 finother);
6271 finswap = finnow; finnow = finother; finother = finswap;
6272 }
6273
6274 if (adxtail != 0.0) {
6275 if (bdytail != 0.0) {
6276 Two_Product(adxtail, bdytail, adxt_bdyt1, adxt_bdyt0);
6277 Two_One_Product(adxt_bdyt1, adxt_bdyt0, cdheight, u3, u[2], u[1], u[0]);
6278 u[3] = u3;
6279 finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
6280 finother);
6281 finswap = finnow; finnow = finother; finother = finswap;
6282 if (cdheighttail != 0.0) {
6283 Two_One_Product(adxt_bdyt1, adxt_bdyt0, cdheighttail,
6284 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 }
6290 }
6291 if (cdytail != 0.0) {
6292 negate = -adxtail;
6293 Two_Product(negate, cdytail, adxt_cdyt1, adxt_cdyt0);
6294 Two_One_Product(adxt_cdyt1, adxt_cdyt0, bdheight, u3, u[2], u[1], u[0]);
6295 u[3] = u3;
6296 finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
6297 finother);
6298 finswap = finnow; finnow = finother; finother = finswap;
6299 if (bdheighttail != 0.0) {
6300 Two_One_Product(adxt_cdyt1, adxt_cdyt0, bdheighttail,
6301 u3, u[2], u[1], u[0]);
6302 u[3] = u3;
6303 finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
6304 finother);
6305 finswap = finnow; finnow = finother; finother = finswap;
6306 }
6307 }
6308 }
6309 if (bdxtail != 0.0) {
6310 if (cdytail != 0.0) {
6311 Two_Product(bdxtail, cdytail, bdxt_cdyt1, bdxt_cdyt0);
6312 Two_One_Product(bdxt_cdyt1, bdxt_cdyt0, adheight, u3, u[2], u[1], u[0]);
6313 u[3] = u3;
6314 finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
6315 finother);
6316 finswap = finnow; finnow = finother; finother = finswap;
6317 if (adheighttail != 0.0) {
6318 Two_One_Product(bdxt_cdyt1, bdxt_cdyt0, adheighttail,
6319 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 }
6325 }
6326 if (adytail != 0.0) {
6327 negate = -bdxtail;
6328 Two_Product(negate, adytail, bdxt_adyt1, bdxt_adyt0);
6329 Two_One_Product(bdxt_adyt1, bdxt_adyt0, cdheight, u3, u[2], u[1], u[0]);
6330 u[3] = u3;
6331 finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
6332 finother);
6333 finswap = finnow; finnow = finother; finother = finswap;
6334 if (cdheighttail != 0.0) {
6335 Two_One_Product(bdxt_adyt1, bdxt_adyt0, cdheighttail,
6336 u3, u[2], u[1], u[0]);
6337 u[3] = u3;
6338 finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
6339 finother);
6340 finswap = finnow; finnow = finother; finother = finswap;
6341 }
6342 }
6343 }
6344 if (cdxtail != 0.0) {
6345 if (adytail != 0.0) {
6346 Two_Product(cdxtail, adytail, cdxt_adyt1, cdxt_adyt0);
6347 Two_One_Product(cdxt_adyt1, cdxt_adyt0, bdheight, u3, u[2], u[1], u[0]);
6348 u[3] = u3;
6349 finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
6350 finother);
6351 finswap = finnow; finnow = finother; finother = finswap;
6352 if (bdheighttail != 0.0) {
6353 Two_One_Product(cdxt_adyt1, cdxt_adyt0, bdheighttail,
6354 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 }
6360 }
6361 if (bdytail != 0.0) {
6362 negate = -cdxtail;
6363 Two_Product(negate, bdytail, cdxt_bdyt1, cdxt_bdyt0);
6364 Two_One_Product(cdxt_bdyt1, cdxt_bdyt0, adheight, u3, u[2], u[1], u[0]);
6365 u[3] = u3;
6366 finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
6367 finother);
6368 finswap = finnow; finnow = finother; finother = finswap;
6369 if (adheighttail != 0.0) {
6370 Two_One_Product(cdxt_bdyt1, cdxt_bdyt0, adheighttail,
6371 u3, u[2], u[1], u[0]);
6372 u[3] = u3;
6373 finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
6374 finother);
6375 finswap = finnow; finnow = finother; finother = finswap;
6376 }
6377 }
6378 }
6379
6380 if (adheighttail != 0.0) {
6381 wlength = scale_expansion_zeroelim(bctlen, bct, adheighttail, w);
6382 finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
6383 finother);
6384 finswap = finnow; finnow = finother; finother = finswap;
6385 }
6386 if (bdheighttail != 0.0) {
6387 wlength = scale_expansion_zeroelim(catlen, cat, bdheighttail, w);
6388 finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
6389 finother);
6390 finswap = finnow; finnow = finother; finother = finswap;
6391 }
6392 if (cdheighttail != 0.0) {
6393 wlength = scale_expansion_zeroelim(abtlen, abt, cdheighttail, w);
6394 finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
6395 finother);
6396 finswap = finnow; finnow = finother; finother = finswap;
6397 }
6398
6399 return finnow[finlength - 1];
6400 }
6401
6402 #ifdef ANSI_DECLARATORS
6403 REAL orient3d(struct mesh *m, struct behavior *b,
6404 vertex pa, vertex pb, vertex pc, vertex pd,
6405 REAL aheight, REAL bheight, REAL cheight, REAL dheight)
6406 #else /* not ANSI_DECLARATORS */
6407 REAL orient3d(m, b, pa, pb, pc, pd, aheight, bheight, cheight, dheight)
6408 struct mesh *m;
6409 struct behavior *b;
6410 vertex pa;
6411 vertex pb;
6412 vertex pc;
6413 vertex pd;
6414 REAL aheight;
6415 REAL bheight;
6416 REAL cheight;
6417 REAL dheight;
6418 #endif /* not ANSI_DECLARATORS */
6419
6420 {
6421 REAL adx, bdx, cdx, ady, bdy, cdy, adheight, bdheight, cdheight;
6422 REAL bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady;
6423 REAL det;
6424 REAL permanent, errbound;
6425
6426 m->orient3dcount++;
6427
6428 adx = pa[0] - pd[0];
6429 bdx = pb[0] - pd[0];
6430 cdx = pc[0] - pd[0];
6431 ady = pa[1] - pd[1];
6432 bdy = pb[1] - pd[1];
6433 cdy = pc[1] - pd[1];
6434 adheight = aheight - dheight;
6435 bdheight = bheight - dheight;
6436 cdheight = cheight - dheight;
6437
6438 bdxcdy = bdx * cdy;
6439 cdxbdy = cdx * bdy;
6440
6441 cdxady = cdx * ady;
6442 adxcdy = adx * cdy;
6443
6444 adxbdy = adx * bdy;
6445 bdxady = bdx * ady;
6446
6447 det = adheight * (bdxcdy - cdxbdy)
6448 + bdheight * (cdxady - adxcdy)
6449 + cdheight * (adxbdy - bdxady);
6450
6451 if (b->noexact) {
6452 return det;
6453 }
6454
6455 permanent = (Absolute(bdxcdy) + Absolute(cdxbdy)) * Absolute(adheight)
6456 + (Absolute(cdxady) + Absolute(adxcdy)) * Absolute(bdheight)
6457 + (Absolute(adxbdy) + Absolute(bdxady)) * Absolute(cdheight);
6458 errbound = o3derrboundA * permanent;
6459 if ((det > errbound) || (-det > errbound)) {
6460 return det;
6461 }
6462
6463 return orient3dadapt(pa, pb, pc, pd, aheight, bheight, cheight, dheight,
6464 permanent);
6465 }
6466
6467 /*****************************************************************************/
6468 /* */
6469 /* nonregular() Return a positive value if the point pd is incompatible */
6470 /* with the circle or plane passing through pa, pb, and pc */
6471 /* (meaning that pd is inside the circle or below the */
6472 /* plane); a negative value if it is compatible; and zero if */
6473 /* the four points are cocircular/coplanar. The points pa, */
6474 /* pb, and pc must be in counterclockwise order, or the sign */
6475 /* of the result will be reversed. */
6476 /* */
6477 /* If the -w switch is used, the points are lifted onto the parabolic */
6478 /* lifting map, then they are dropped according to their weights, then the */
6479 /* 3D orientation test is applied. If the -W switch is used, the points' */
6480 /* heights are already provided, so the 3D orientation test is applied */
6481 /* directly. If neither switch is used, the incircle test is applied. */
6482 /* */
6483 /*****************************************************************************/
6484
6485 #ifdef ANSI_DECLARATORS
6486 REAL nonregular(struct mesh *m, struct behavior *b,
6487 vertex pa, vertex pb, vertex pc, vertex pd)
6488 #else /* not ANSI_DECLARATORS */
6489 REAL nonregular(m, b, pa, pb, pc, pd)
6490 struct mesh *m;
6491 struct behavior *b;
6492 vertex pa;
6493 vertex pb;
6494 vertex pc;
6495 vertex pd;
6496 #endif /* not ANSI_DECLARATORS */
6497
6498 {
6499 if (b->weighted == 0) {
6500 return incircle(m, b, pa, pb, pc, pd);
6501 } else if (b->weighted == 1) {
6502 return orient3d(m, b, pa, pb, pc, pd,
6503 pa[0] * pa[0] + pa[1] * pa[1] - pa[2],
6504 pb[0] * pb[0] + pb[1] * pb[1] - pb[2],
6505 pc[0] * pc[0] + pc[1] * pc[1] - pc[2],
6506 pd[0] * pd[0] + pd[1] * pd[1] - pd[2]);
6507 } else {
6508 return orient3d(m, b, pa, pb, pc, pd, pa[2], pb[2], pc[2], pd[2]);
6509 }
6510 }
6511
6512 /*****************************************************************************/
6513 /* */
6514 /* findcircumcenter() Find the circumcenter of a triangle. */
6515 /* */
6516 /* The result is returned both in terms of x-y coordinates and xi-eta */
6517 /* (barycentric) coordinates. The xi-eta coordinate system is defined in */
6518 /* terms of the triangle: the origin of the triangle is the origin of the */
6519 /* coordinate system; the destination of the triangle is one unit along the */
6520 /* xi axis; and the apex of the triangle is one unit along the eta axis. */
6521 /* This procedure also returns the square of the length of the triangle's */
6522 /* shortest edge. */
6523 /* */
6524 /*****************************************************************************/
6525
6526 #ifdef ANSI_DECLARATORS
6527 void findcircumcenter(struct mesh *m, struct behavior *b,
6528 vertex torg, vertex tdest, vertex tapex,
6529 vertex circumcenter, REAL *xi, REAL *eta, int offcenter)
6530 #else /* not ANSI_DECLARATORS */
6531 void findcircumcenter(m, b, torg, tdest, tapex, circumcenter, xi, eta,
6532 offcenter)
6533 struct mesh *m;
6534 struct behavior *b;
6535 vertex torg;
6536 vertex tdest;
6537 vertex tapex;
6538 vertex circumcenter;
6539 REAL *xi;
6540 REAL *eta;
6541 int offcenter;
6542 #endif /* not ANSI_DECLARATORS */
6543
6544 {
6545 REAL xdo, ydo, xao, yao;
6546 REAL dodist, aodist, dadist;
6547 REAL denominator;
6548 REAL dx, dy, dxoff, dyoff;
6549
6550 m->circumcentercount++;
6551
6552 /* Compute the circumcenter of the triangle. */
6553 xdo = tdest[0] - torg[0];
6554 ydo = tdest[1] - torg[1];
6555 xao = tapex[0] - torg[0];
6556 yao = tapex[1] - torg[1];
6557 dodist = xdo * xdo + ydo * ydo;
6558 aodist = xao * xao + yao * yao;
6559 dadist = (tdest[0] - tapex[0]) * (tdest[0] - tapex[0]) +
6560 (tdest[1] - tapex[1]) * (tdest[1] - tapex[1]);
6561 if (b->noexact) {
6562 denominator = 0.5 / (xdo * yao - xao * ydo);
6563 } else {
6564 /* Use the counterclockwise() routine to ensure a positive (and */
6565 /* reasonably accurate) result, avoiding any possibility of */
6566 /* division by zero. */
6567 denominator = 0.5 / counterclockwise(m, b, tdest, tapex, torg);
6568 /* Don't count the above as an orientation test. */
6569 m->counterclockcount--;
6570 }
6571 dx = (yao * dodist - ydo * aodist) * denominator;
6572 dy = (xdo * aodist - xao * dodist) * denominator;
6573
6574 /* Find the (squared) length of the triangle's shortest edge. This */
6575 /* serves as a conservative estimate of the insertion radius of the */
6576 /* circumcenter's parent. The estimate is used to ensure that */
6577 /* the algorithm terminates even if very small angles appear in */
6578 /* the input PSLG. */
6579 if ((dodist < aodist) && (dodist < dadist)) {
6580 if (offcenter && (b->offconstant > 0.0)) {
6581 /* Find the position of the off-center, as described by Alper Ungor. */
6582 dxoff = 0.5 * xdo - b->offconstant * ydo;
6583 dyoff = 0.5 * ydo + b->offconstant * xdo;
6584 /* If the off-center is closer to the origin than the */
6585 /* circumcenter, use the off-center instead. */
6586 if (dxoff * dxoff + dyoff * dyoff < dx * dx + dy * dy) {
6587 dx = dxoff;
6588 dy = dyoff;
6589 }
6590 }
6591 } else if (aodist < dadist) {
6592 if (offcenter && (b->offconstant > 0.0)) {
6593 dxoff = 0.5 * xao + b->offconstant * yao;
6594 dyoff = 0.5 * yao - b->offconstant * xao;
6595 /* If the off-center is closer to the origin than the */
6596 /* circumcenter, use the off-center instead. */
6597 if (dxoff * dxoff + dyoff * dyoff < dx * dx + dy * dy) {
6598 dx = dxoff;
6599 dy = dyoff;
6600 }
6601 }
6602 } else {
6603 if (offcenter && (b->offconstant > 0.0)) {
6604 dxoff = 0.5 * (tapex[0] - tdest[0]) -
6605 b->offconstant * (tapex[1] - tdest[1]);
6606 dyoff = 0.5 * (tapex[1] - tdest[1]) +
6607 b->offconstant * (tapex[0] - tdest[0]);
6608 /* If the off-center is closer to the destination than the */
6609 /* circumcenter, use the off-center instead. */
6610 if (dxoff * dxoff + dyoff * dyoff <
6611 (dx - xdo) * (dx - xdo) + (dy - ydo) * (dy - ydo)) {
6612 dx = xdo + dxoff;
6613 dy = ydo + dyoff;
6614 }
6615 }
6616 }
6617
6618 circumcenter[0] = torg[0] + dx;
6619 circumcenter[1] = torg[1] + dy;
6620
6621 /* To interpolate vertex attributes for the new vertex inserted at */
6622 /* the circumcenter, define a coordinate system with a xi-axis, */
6623 /* directed from the triangle's origin to its destination, and */
6624 /* an eta-axis, directed from its origin to its apex. */
6625 /* Calculate the xi and eta coordinates of the circumcenter. */
6626 *xi = (yao * dx - xao * dy) * (2.0 * denominator);
6627 *eta = (xdo * dy - ydo * dx) * (2.0 * denominator);
6628 }
6629
6630 /** **/
6631 /** **/
6632 /********* Geometric primitives end here *********/
6633
6634 /*****************************************************************************/
6635 /* */
6636 /* triangleinit() Initialize some variables. */
6637 /* */
6638 /*****************************************************************************/
6639
6640 #ifdef ANSI_DECLARATORS
6641 void triangleinit(struct mesh *m)
6642 #else /* not ANSI_DECLARATORS */
6643 void triangleinit(m)
6644 struct mesh *m;
6645 #endif /* not ANSI_DECLARATORS */
6646
6647 {
6648 poolzero(&m->vertices);
6649 poolzero(&m->triangles);
6650 poolzero(&m->subsegs);
6651 poolzero(&m->viri);
6652 poolzero(&m->badsubsegs);
6653 poolzero(&m->badtriangles);
6654 poolzero(&m->flipstackers);
6655 poolzero(&m->splaynodes);
6656
6657 m->recenttri.tri = (triangle *) NULL; /* No triangle has been visited yet. */
6658 m->undeads = 0; /* No eliminated input vertices yet. */
6659 m->samples = 1; /* Point location should take at least one sample. */
6660 m->checksegments = 0; /* There are no segments in the triangulation yet. */
6661 m->checkquality = 0; /* The quality triangulation stage has not begun. */
6662 m->incirclecount = m->counterclockcount = m->orient3dcount = 0;
6663 m->hyperbolacount = m->circletopcount = m->circumcentercount = 0;
6664 randomseed = 1;
6665
6666 exactinit(); /* Initialize exact arithmetic constants. */
6667 }
6668
6669 /*****************************************************************************/
6670 /* */
6671 /* randomnation() Generate a random number between 0 and `choices' - 1. */
6672 /* */
6673 /* This is a simple linear congruential random number generator. Hence, it */
6674 /* is a bad random number generator, but good enough for most randomized */
6675 /* geometric algorithms. */
6676 /* */
6677 /*****************************************************************************/
6678
6679 #ifdef ANSI_DECLARATORS
6680 unsigned long randomnation(unsigned int choices)
6681 #else /* not ANSI_DECLARATORS */
6682 unsigned long randomnation(choices)
6683 unsigned int choices;
6684 #endif /* not ANSI_DECLARATORS */
6685
6686 {
6687 randomseed = (randomseed * 1366l + 150889l) % 714025l;
6688 return randomseed / (714025l / choices + 1);
6689 }
6690
6691 /********* Mesh quality testing routines begin here *********/
6692 /** **/
6693 /** **/
6694
6695 /*****************************************************************************/
6696 /* */
6697 /* checkmesh() Test the mesh for topological consistency. */
6698 /* */
6699 /*****************************************************************************/
6700
6701 #ifndef REDUCED
6702
6703 #ifdef ANSI_DECLARATORS
6704 void checkmesh(struct mesh *m, struct behavior *b)
6705 #else /* not ANSI_DECLARATORS */
6706 void checkmesh(m, b)
6707 struct mesh *m;
6708 struct behavior *b;
6709 #endif /* not ANSI_DECLARATORS */
6710
6711 {
6712 struct otri triangleloop;
6713 struct otri oppotri, oppooppotri;
6714 vertex triorg, tridest, triapex;
6715 vertex oppoorg, oppodest;
6716 int horrors;
6717 int saveexact;
6718 triangle ptr; /* Temporary variable used by sym(). */
6719
6720 /* Temporarily turn on exact arithmetic if it's off. */
6721 saveexact = b->noexact;
6722 b->noexact = 0;
6723 if (!b->quiet) {
6724 printf(" Checking consistency of mesh...\n");
6725 }
6726 horrors = 0;
6727 /* Run through the list of triangles, checking each one. */
6728 traversalinit(&m->triangles);
6729 triangleloop.tri = triangletraverse(m);
6730 while (triangleloop.tri != (triangle *) NULL) {
6731 /* Check all three edges of the triangle. */
6732 for (triangleloop.orient = 0; triangleloop.orient < 3;
6733 triangleloop.orient++) {
6734 org(triangleloop, triorg);
6735 dest(triangleloop, tridest);
6736 if (triangleloop.orient == 0) { /* Only test for inversion once. */
6737 /* Test if the triangle is flat or inverted. */
6738 apex(triangleloop, triapex);
6739 if (counterclockwise(m, b, triorg, tridest, triapex) <= 0.0) {
6740 printf(" !! !! Inverted ");
6741 printtriangle(m, b, &triangleloop);
6742 horrors++;
6743 }
6744 }
6745 /* Find the neighboring triangle on this edge. */
6746 sym(triangleloop, oppotri);
6747 if (oppotri.tri != m->dummytri) {
6748 /* Check that the triangle's neighbor knows it's a neighbor. */
6749 sym(oppotri, oppooppotri);
6750 if ((triangleloop.tri != oppooppotri.tri)
6751 || (triangleloop.orient != oppooppotri.orient)) {
6752 printf(" !! !! Asymmetric triangle-triangle bond:\n");
6753 if (triangleloop.tri == oppooppotri.tri) {
6754 printf(" (Right triangle, wrong orientation)\n");
6755 }
6756 printf(" First ");
6757 printtriangle(m, b, &triangleloop);
6758 printf(" Second (nonreciprocating) ");
6759 printtriangle(m, b, &oppotri);
6760 horrors++;
6761 }
6762 /* Check that both triangles agree on the identities */
6763 /* of their shared vertices. */
6764 org(oppotri, oppoorg);
6765 dest(oppotri, oppodest);
6766 if ((triorg != oppodest) || (tridest != oppoorg)) {
6767 printf(" !! !! Mismatched edge coordinates between two triangles:\n"
6768 );
6769 printf(" First mismatched ");
6770 printtriangle(m, b, &triangleloop);
6771 printf(" Second mismatched ");
6772 printtriangle(m, b, &oppotri);
6773 horrors++;
6774 }
6775 }
6776 }
6777 triangleloop.tri = triangletraverse(m);
6778 }
6779 if (horrors == 0) {
6780 if (!b->quiet) {
6781 printf(" In my studied opinion, the mesh appears to be consistent.\n");
6782 }
6783 } else if (horrors == 1) {
6784 printf(" !! !! !! !! Precisely one festering wound discovered.\n");
6785 } else {
6786 printf(" !! !! !! !! %d abominations witnessed.\n", horrors);
6787 }
6788 /* Restore the status of exact arithmetic. */
6789 b->noexact = saveexact;
6790 }
6791
6792 #endif /* not REDUCED */
6793
6794 /*****************************************************************************/
6795 /* */
6796 /* checkdelaunay() Ensure that the mesh is (constrained) Delaunay. */
6797 /* */
6798 /*****************************************************************************/
6799
6800 #ifndef REDUCED
6801
6802 #ifdef ANSI_DECLARATORS
6803 void checkdelaunay(struct mesh *m, struct behavior *b)
6804 #else /* not ANSI_DECLARATORS */
6805 void checkdelaunay(m, b)
6806 struct mesh *m;
6807 struct behavior *b;
6808 #endif /* not ANSI_DECLARATORS */
6809
6810 {
6811 struct otri triangleloop;
6812 struct otri oppotri;
6813 struct osub opposubseg;
6814 vertex triorg, tridest, triapex;
6815 vertex oppoapex;
6816 int shouldbedelaunay;
6817 int horrors;
6818 int saveexact;
6819 triangle ptr; /* Temporary variable used by sym(). */
6820 subseg sptr; /* Temporary variable used by tspivot(). */
6821
6822 /* Temporarily turn on exact arithmetic if it's off. */
6823 saveexact = b->noexact;
6824 b->noexact = 0;
6825 if (!b->quiet) {
6826 printf(" Checking Delaunay property of mesh...\n");
6827 }
6828 horrors = 0;
6829 /* Run through the list of triangles, checking each one. */
6830 traversalinit(&m->triangles);
6831 triangleloop.tri = triangletraverse(m);
6832 while (triangleloop.tri != (triangle *) NULL) {
6833 /* Check all three edges of the triangle. */
6834 for (triangleloop.orient = 0; triangleloop.orient < 3;
6835 triangleloop.orient++) {
6836 org(triangleloop, triorg);
6837 dest(triangleloop, tridest);
6838 apex(triangleloop, triapex);
6839 sym(triangleloop, oppotri);
6840 apex(oppotri, oppoapex);
6841 /* Only test that the edge is locally Delaunay if there is an */
6842 /* adjoining triangle whose pointer is larger (to ensure that */
6843 /* each pair isn't tested twice). */
6844 shouldbedelaunay = (oppotri.tri != m->dummytri) &&
6845 !deadtri(oppotri.tri) && (triangleloop.tri < oppotri.tri) &&
6846 (triorg != m->infvertex1) && (triorg != m->infvertex2) &&
6847 (triorg != m->infvertex3) &&
6848 (tridest != m->infvertex1) && (tridest != m->infvertex2) &&
6849 (tridest != m->infvertex3) &&
6850 (triapex != m->infvertex1) && (triapex != m->infvertex2) &&
6851 (triapex != m->infvertex3) &&
6852 (oppoapex != m->infvertex1) && (oppoapex != m->infvertex2) &&
6853 (oppoapex != m->infvertex3);
6854 if (m->checksegments && shouldbedelaunay) {
6855 /* If a subsegment separates the triangles, then the edge is */
6856 /* constrained, so no local Delaunay test should be done. */
6857 tspivot(triangleloop, opposubseg);
6858 if (opposubseg.ss != m->dummysub){
6859 shouldbedelaunay = 0;
6860 }
6861 }
6862 if (shouldbedelaunay) {
6863 if (nonregular(m, b, triorg, tridest, triapex, oppoapex) > 0.0) {
6864 if (!b->weighted) {
6865 printf(" !! !! Non-Delaunay pair of triangles:\n");
6866 printf(" First non-Delaunay ");
6867 printtriangle(m, b, &triangleloop);
6868 printf(" Second non-Delaunay ");
6869 } else {
6870 printf(" !! !! Non-regular pair of triangles:\n");
6871 printf(" First non-regular ");
6872 printtriangle(m, b, &triangleloop);
6873 printf(" Second non-regular ");
6874 }
6875 printtriangle(m, b, &oppotri);
6876 horrors++;
6877 }
6878 }
6879 }
6880 triangleloop.tri = triangletraverse(m);
6881 }
6882 if (horrors == 0) {
6883 if (!b->quiet) {
6884 printf(
6885 " By virtue of my perceptive intelligence, I declare the mesh Delaunay.\n");
6886 }
6887 } else if (horrors == 1) {
6888 printf(
6889 " !! !! !! !! Precisely one terrifying transgression identified.\n");
6890 } else {
6891 printf(" !! !! !! !! %d obscenities viewed with horror.\n", horrors);
6892 }
6893 /* Restore the status of exact arithmetic. */
6894 b->noexact = saveexact;
6895 }
6896
6897 #endif /* not REDUCED */
6898
6899 /*****************************************************************************/
6900 /* */
6901 /* enqueuebadtriang() Add a bad triangle data structure to the end of a */
6902 /* queue. */
6903 /* */
6904 /* The queue is actually a set of 4096 queues. I use multiple queues to */
6905 /* give priority to smaller angles. I originally implemented a heap, but */
6906 /* the queues are faster by a larger margin than I'd suspected. */
6907 /* */
6908 /*****************************************************************************/
6909
6910 #ifndef CDT_ONLY
6911
6912 #ifdef ANSI_DECLARATORS
6913 void enqueuebadtriang(struct mesh *m, struct behavior *b,
6914 struct badtriang *badtri)
6915 #else /* not ANSI_DECLARATORS */
6916 void enqueuebadtriang(m, b, badtri)
6917 struct mesh *m;
6918 struct behavior *b;
6919 struct badtriang *badtri;
6920 #endif /* not ANSI_DECLARATORS */
6921
6922 {
6923 REAL length, multiplier;
6924 int exponent, expincrement;
6925 int queuenumber;
6926 int posexponent;
6927 int i;
6928
6929 if (b->verbose > 2) {
6930 printf(" Queueing bad triangle:\n");
6931 printf(" (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
6932 (double)badtri->triangorg[0], (double)badtri->triangorg[1],
6933 (double)badtri->triangdest[0], (double)badtri->triangdest[1],
6934 (double)badtri->triangapex[0], (double)badtri->triangapex[1]);
6935 }
6936
6937 /* Determine the appropriate queue to put the bad triangle into. */
6938 /* Recall that the key is the square of its shortest edge length. */
6939 if (badtri->key >= 1.0) {
6940 length = badtri->key;
6941 posexponent = 1;
6942 } else {
6943 /* `badtri->key' is 2.0 to a negative exponent, so we'll record that */
6944 /* fact and use the reciprocal of `badtri->key', which is > 1.0. */
6945 length = 1.0 / badtri->key;
6946 posexponent = 0;
6947 }
6948 /* `length' is approximately 2.0 to what exponent? The following code */
6949 /* determines the answer in time logarithmic in the exponent. */
6950 exponent = 0;
6951 while (length > 2.0) {
6952 /* Find an approximation by repeated squaring of two. */
6953 expincrement = 1;
6954 multiplier = 0.5;
6955 while (length * multiplier * multiplier > 1.0) {
6956 expincrement *= 2;
6957 multiplier *= multiplier;
6958 }
6959 /* Reduce the value of `length', then iterate if necessary. */
6960 exponent += expincrement;
6961 length *= multiplier;
6962 }
6963 /* `length' is approximately squareroot(2.0) to what exponent? */
6964 exponent = 2.0 * exponent + (length > SQUAREROOTTWO);
6965 /* `exponent' is now in the range 0...2047 for IEEE double precision. */
6966 /* Choose a queue in the range 0...4095. The shortest edges have the */
6967 /* highest priority (queue 4095). */
6968 if (posexponent) {
6969 queuenumber = 2047 - exponent;
6970 } else {
6971 queuenumber = 2048 + exponent;
6972 }
6973
6974 /* Are we inserting into an empty queue? */
6975 if (m->queuefront[queuenumber] == (struct badtriang *) NULL) {
6976 /* Yes, we are inserting into an empty queue. */
6977 /* Will this become the highest-priority queue? */
6978 if (queuenumber > m->firstnonemptyq) {
6979 /* Yes, this is the highest-priority queue. */
6980 m->nextnonemptyq[queuenumber] = m->firstnonemptyq;
6981 m->firstnonemptyq = queuenumber;
6982 } else {
6983 /* No, this is not the highest-priority queue. */
6984 /* Find the queue with next higher priority. */
6985 i = queuenumber + 1;
6986 while (m->queuefront[i] == (struct badtriang *) NULL) {
6987 i++;
6988 }
6989 /* Mark the newly nonempty queue as following a higher-priority queue. */
6990 m->nextnonemptyq[queuenumber] = m->nextnonemptyq[i];
6991 m->nextnonemptyq[i] = queuenumber;
6992 }
6993 /* Put the bad triangle at the beginning of the (empty) queue. */
6994 m->queuefront[queuenumber] = badtri;
6995 } else {
6996 /* Add the bad triangle to the end of an already nonempty queue. */
6997 m->queuetail[queuenumber]->nexttriang = badtri;
6998 }
6999 /* Maintain a pointer to the last triangle of the queue. */
7000 m->queuetail[queuenumber] = badtri;
7001 /* Newly enqueued bad triangle has no successor in the queue. */
7002 badtri->nexttriang = (struct badtriang *) NULL;
7003 }
7004
7005 #endif /* not CDT_ONLY */
7006
7007 /*****************************************************************************/
7008 /* */
7009 /* enqueuebadtri() Add a bad triangle to the end of a queue. */
7010 /* */
7011 /* Allocates a badtriang data structure for the triangle, then passes it to */
7012 /* enqueuebadtriang(). */
7013 /* */
7014 /*****************************************************************************/
7015
7016 #ifndef CDT_ONLY
7017
7018 #ifdef ANSI_DECLARATORS
7019 void enqueuebadtri(struct mesh *m, struct behavior *b, struct otri *enqtri,
7020 REAL minedge, vertex enqapex, vertex enqorg, vertex enqdest)
7021 #else /* not ANSI_DECLARATORS */
7022 void enqueuebadtri(m, b, enqtri, minedge, enqapex, enqorg, enqdest)
7023 struct mesh *m;
7024 struct behavior *b;
7025 struct otri *enqtri;
7026 REAL minedge;
7027 vertex enqapex;
7028 vertex enqorg;
7029 vertex enqdest;
7030 #endif /* not ANSI_DECLARATORS */
7031
7032 {
7033 struct badtriang *newbad;
7034
7035 /* Allocate space for the bad triangle. */
7036 newbad = (struct badtriang *) poolalloc(&m->badtriangles);
7037 newbad->poortri = encode(*enqtri);
7038 newbad->key = minedge;
7039 newbad->triangapex = enqapex;
7040 newbad->triangorg = enqorg;
7041 newbad->triangdest = enqdest;
7042 enqueuebadtriang(m, b, newbad);
7043 }
7044
7045 #endif /* not CDT_ONLY */
7046
7047 /*****************************************************************************/
7048 /* */
7049 /* dequeuebadtriang() Remove a triangle from the front of the queue. */
7050 /* */
7051 /*****************************************************************************/
7052
7053 #ifndef CDT_ONLY
7054
7055 #ifdef ANSI_DECLARATORS
7056 struct badtriang *dequeuebadtriang(struct mesh *m)
7057 #else /* not ANSI_DECLARATORS */
7058 struct badtriang *dequeuebadtriang(m)
7059 struct mesh *m;
7060 #endif /* not ANSI_DECLARATORS */
7061
7062 {
7063 struct badtriang *result;
7064
7065 /* If no queues are nonempty, return NULL. */
7066 if (m->firstnonemptyq < 0) {
7067 return (struct badtriang *) NULL;
7068 }
7069 /* Find the first triangle of the highest-priority queue. */
7070 result = m->queuefront[m->firstnonemptyq];
7071 /* Remove the triangle from the queue. */
7072 m->queuefront[m->firstnonemptyq] = result->nexttriang;
7073 /* If this queue is now empty, note the new highest-priority */
7074 /* nonempty queue. */
7075 if (result == m->queuetail[m->firstnonemptyq]) {
7076 m->firstnonemptyq = m->nextnonemptyq[m->firstnonemptyq];
7077 }
7078 return result;
7079 }
7080
7081 #endif /* not CDT_ONLY */
7082
7083 /*****************************************************************************/
7084 /* */
7085 /* checkseg4encroach() Check a subsegment to see if it is encroached; add */
7086 /* it to the list if it is. */
7087 /* */
7088 /* A subsegment is encroached if there is a vertex in its diametral lens. */
7089 /* For Ruppert's algorithm (-D switch), the "diametral lens" is the */
7090 /* diametral circle. For Chew's algorithm (default), the diametral lens is */
7091 /* just big enough to enclose two isosceles triangles whose bases are the */
7092 /* subsegment. Each of the two isosceles triangles has two angles equal */
7093 /* to `b->minangle'. */
7094 /* */
7095 /* Chew's algorithm does not require diametral lenses at all--but they save */
7096 /* time. Any vertex inside a subsegment's diametral lens implies that the */
7097 /* triangle adjoining the subsegment will be too skinny, so it's only a */
7098 /* matter of time before the encroaching vertex is deleted by Chew's */
7099 /* algorithm. It's faster to simply not insert the doomed vertex in the */
7100 /* first place, which is why I use diametral lenses with Chew's algorithm. */
7101 /* */
7102 /* Returns a nonzero value if the subsegment is encroached. */
7103 /* */
7104 /*****************************************************************************/
7105
7106 #ifndef CDT_ONLY
7107
7108 #ifdef ANSI_DECLARATORS
7109 int checkseg4encroach(struct mesh *m, struct behavior *b,
7110 struct osub *testsubseg)
7111 #else /* not ANSI_DECLARATORS */
7112 int checkseg4encroach(m, b, testsubseg)
7113 struct mesh *m;
7114 struct behavior *b;
7115 struct osub *testsubseg;
7116 #endif /* not ANSI_DECLARATORS */
7117
7118 {
7119 struct otri neighbortri;
7120 struct osub testsym;
7121 struct badsubseg *encroachedseg;
7122 REAL dotproduct;
7123 int encroached;
7124 int sides;
7125 vertex eorg, edest, eapex;
7126 triangle ptr; /* Temporary variable used by stpivot(). */
7127
7128 encroached = 0;
7129 sides = 0;
7130
7131 sorg(*testsubseg, eorg);
7132 sdest(*testsubseg, edest);
7133 /* Check one neighbor of the subsegment. */
7134 stpivot(*testsubseg, neighbortri);
7135 /* Does the neighbor exist, or is this a boundary edge? */
7136 if (neighbortri.tri != m->dummytri) {
7137 sides++;
7138 /* Find a vertex opposite this subsegment. */
7139 apex(neighbortri, eapex);
7140 /* Check whether the apex is in the diametral lens of the subsegment */
7141 /* (the diametral circle if `conformdel' is set). A dot product */
7142 /* of two sides of the triangle is used to check whether the angle */
7143 /* at the apex is greater than (180 - 2 `minangle') degrees (for */
7144 /* lenses; 90 degrees for diametral circles). */
7145 dotproduct = (eorg[0] - eapex[0]) * (edest[0] - eapex[0]) +
7146 (eorg[1] - eapex[1]) * (edest[1] - eapex[1]);
7147 if (dotproduct < 0.0) {
7148 if (b->conformdel ||
7149 (dotproduct * dotproduct >=
7150 (2.0 * b->goodangle - 1.0) * (2.0 * b->goodangle - 1.0) *
7151 ((eorg[0] - eapex[0]) * (eorg[0] - eapex[0]) +
7152 (eorg[1] - eapex[1]) * (eorg[1] - eapex[1])) *
7153 ((edest[0] - eapex[0]) * (edest[0] - eapex[0]) +
7154 (edest[1] - eapex[1]) * (edest[1] - eapex[1])))) {
7155 encroached = 1;
7156 }
7157 }
7158 }
7159 /* Check the other neighbor of the subsegment. */
7160 ssym(*testsubseg, testsym);
7161 stpivot(testsym, neighbortri);
7162 /* Does the neighbor exist, or is this a boundary edge? */
7163 if (neighbortri.tri != m->dummytri) {
7164 sides++;
7165 /* Find the other vertex opposite this subsegment. */
7166 apex(neighbortri, eapex);
7167 /* Check whether the apex is in the diametral lens of the subsegment */
7168 /* (or the diametral circle, if `conformdel' is set). */
7169 dotproduct = (eorg[0] - eapex[0]) * (edest[0] - eapex[0]) +
7170 (eorg[1] - eapex[1]) * (edest[1] - eapex[1]);
7171 if (dotproduct < 0.0) {
7172 if (b->conformdel ||
7173 (dotproduct * dotproduct >=
7174 (2.0 * b->goodangle - 1.0) * (2.0 * b->goodangle - 1.0) *
7175 ((eorg[0] - eapex[0]) * (eorg[0] - eapex[0]) +
7176 (eorg[1] - eapex[1]) * (eorg[1] - eapex[1])) *
7177 ((edest[0] - eapex[0]) * (edest[0] - eapex[0]) +
7178 (edest[1] - eapex[1]) * (edest[1] - eapex[1])))) {
7179 encroached += 2;
7180 }
7181 }
7182 }
7183
7184 if (encroached && (!b->nobisect || ((b->nobisect == 1) && (sides == 2)))) {
7185 if (b->verbose > 2) {
7186 printf(
7187 " Queueing encroached subsegment (%.12g, %.12g) (%.12g, %.12g).\n",
7188 (double)eorg[0], (double)eorg[1], (double)edest[0], (double)edest[1]);
7189 }
7190 /* Add the subsegment to the list of encroached subsegments. */
7191 /* Be sure to get the orientation right. */
7192 encroachedseg = (struct badsubseg *) poolalloc(&m->badsubsegs);
7193 if (encroached == 1) {
7194 encroachedseg->encsubseg = sencode(*testsubseg);
7195 encroachedseg->subsegorg = eorg;
7196 encroachedseg->subsegdest = edest;
7197 } else {
7198 encroachedseg->encsubseg = sencode(testsym);
7199 encroachedseg->subsegorg = edest;
7200 encroachedseg->subsegdest = eorg;
7201 }
7202 }
7203
7204 return encroached;
7205 }
7206
7207 #endif /* not CDT_ONLY */
7208
7209 /*****************************************************************************/
7210 /* */
7211 /* testtriangle() Test a triangle for quality and size. */
7212 /* */
7213 /* Tests a triangle to see if it satisfies the minimum angle condition and */
7214 /* the maximum area condition. Triangles that aren't up to spec are added */
7215 /* to the bad triangle queue. */
7216 /* */
7217 /*****************************************************************************/
7218
7219 #ifndef CDT_ONLY
7220
7221 #ifdef ANSI_DECLARATORS
7222 void testtriangle(struct mesh *m, struct behavior *b, struct otri *testtri)
7223 #else /* not ANSI_DECLARATORS */
7224 void testtriangle(m, b, testtri)
7225 struct mesh *m;
7226 struct behavior *b;
7227 struct otri *testtri;
7228 #endif /* not ANSI_DECLARATORS */
7229
7230 {
7231 struct otri tri1, tri2;
7232 struct osub testsub;
7233 vertex torg, tdest, tapex;
7234 vertex base1, base2;
7235 vertex org1, dest1, org2, dest2;
7236 vertex joinvertex;
7237 REAL dxod, dyod, dxda, dyda, dxao, dyao;
7238 REAL dxod2, dyod2, dxda2, dyda2, dxao2, dyao2;
7239 REAL apexlen, orglen, destlen, minedge;
7240 REAL angle;
7241 REAL area;
7242 REAL dist1, dist2;
7243 subseg sptr; /* Temporary variable used by tspivot(). */
7244 triangle ptr; /* Temporary variable used by oprev() and dnext(). */
7245
7246 org(*testtri, torg);
7247 dest(*testtri, tdest);
7248 apex(*testtri, tapex);
7249 dxod = torg[0] - tdest[0];
7250 dyod = torg[1] - tdest[1];
7251 dxda = tdest[0] - tapex[0];
7252 dyda = tdest[1] - tapex[1];
7253 dxao = tapex[0] - torg[0];
7254 dyao = tapex[1] - torg[1];
7255 dxod2 = dxod * dxod;
7256 dyod2 = dyod * dyod;
7257 dxda2 = dxda * dxda;
7258 dyda2 = dyda * dyda;
7259 dxao2 = dxao * dxao;
7260 dyao2 = dyao * dyao;
7261 /* Find the lengths of the triangle's three edges. */
7262 apexlen = dxod2 + dyod2;
7263 orglen = dxda2 + dyda2;
7264 destlen = dxao2 + dyao2;
7265
7266 if ((apexlen < orglen) && (apexlen < destlen)) {
7267 /* The edge opposite the apex is shortest. */
7268 minedge = apexlen;
7269 /* Find the square of the cosine of the angle at the apex. */
7270 angle = dxda * dxao + dyda * dyao;
7271 angle = angle * angle / (orglen * destlen);
7272 base1 = torg;
7273 base2 = tdest;
7274 otricopy(*testtri, tri1);
7275 } else if (orglen < destlen) {
7276 /* The edge opposite the origin is shortest. */
7277 minedge = orglen;
7278 /* Find the square of the cosine of the angle at the origin. */
7279 angle = dxod * dxao + dyod * dyao;
7280 angle = angle * angle / (apexlen * destlen);
7281 base1 = tdest;
7282 base2 = tapex;
7283 lnext(*testtri, tri1);
7284 } else {
7285 /* The edge opposite the destination is shortest. */
7286 minedge = destlen;
7287 /* Find the square of the cosine of the angle at the destination. */
7288 angle = dxod * dxda + dyod * dyda;
7289 angle = angle * angle / (apexlen * orglen);
7290 base1 = tapex;
7291 base2 = torg;
7292 lprev(*testtri, tri1);
7293 }
7294
7295 if (b->vararea || b->fixedarea || b->usertest) {
7296 /* Check whether the area is larger than permitted. */
7297 area = 0.5 * (dxod * dyda - dyod * dxda);
7298 if (b->fixedarea && (area > b->maxarea)) {
7299 /* Add this triangle to the list of bad triangles. */
7300 enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest);
7301 return;
7302 }
7303
7304 /* Nonpositive area constraints are treated as unconstrained. */
7305 if ((b->vararea) && (area > areabound(*testtri)) &&
7306 (areabound(*testtri) > 0.0)) {
7307 /* Add this triangle to the list of bad triangles. */
7308 enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest);
7309 return;
7310 }
7311
7312 if (b->usertest) {
7313 /* Check whether the user thinks this triangle is too large. */
7314 if (triunsuitable(torg, tdest, tapex, area)) {
7315 enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest);
7316 return;
7317 }
7318 }
7319 }
7320
7321 /* Check whether the angle is smaller than permitted. */
7322 if (angle > b->goodangle) {
7323 /* Use the rules of Miller, Pav, and Walkington to decide that certain */
7324 /* triangles should not be split, even if they have bad angles. */
7325 /* A skinny triangle is not split if its shortest edge subtends a */
7326 /* small input angle, and both endpoints of the edge lie on a */
7327 /* concentric circular shell. For convenience, I make a small */
7328 /* adjustment to that rule: I check if the endpoints of the edge */
7329 /* both lie in segment interiors, equidistant from the apex where */
7330 /* the two segments meet. */
7331 /* First, check if both points lie in segment interiors. */
7332 if ((vertextype(base1) == SEGMENTVERTEX) &&
7333 (vertextype(base2) == SEGMENTVERTEX)) {
7334 /* Check if both points lie in a common segment. If they do, the */
7335 /* skinny triangle is enqueued to be split as usual. */
7336 tspivot(tri1, testsub);
7337 if (testsub.ss == m->dummysub) {
7338 /* No common segment. Find a subsegment that contains `torg'. */
7339 otricopy(tri1, tri2);
7340 do {
7341 oprevself(tri1);
7342 tspivot(tri1, testsub);
7343 } while (testsub.ss == m->dummysub);
7344 /* Find the endpoints of the containing segment. */
7345 segorg(testsub, org1);
7346 segdest(testsub, dest1);
7347 /* Find a subsegment that contains `tdest'. */
7348 do {
7349 dnextself(tri2);
7350 tspivot(tri2, testsub);
7351 } while (testsub.ss == m->dummysub);
7352 /* Find the endpoints of the containing segment. */
7353 segorg(testsub, org2);
7354 segdest(testsub, dest2);
7355 /* Check if the two containing segments have an endpoint in common. */
7356 joinvertex = (vertex) NULL;
7357 if ((dest1[0] == org2[0]) && (dest1[1] == org2[1])) {
7358 joinvertex = dest1;
7359 } else if ((org1[0] == dest2[0]) && (org1[1] == dest2[1])) {
7360 joinvertex = org1;
7361 }
7362 if (joinvertex != (vertex) NULL) {
7363 /* Compute the distance from the common endpoint (of the two */
7364 /* segments) to each of the endpoints of the shortest edge. */
7365 dist1 = ((base1[0] - joinvertex[0]) * (base1[0] - joinvertex[0]) +
7366 (base1[1] - joinvertex[1]) * (base1[1] - joinvertex[1]));
7367 dist2 = ((base2[0] - joinvertex[0]) * (base2[0] - joinvertex[0]) +
7368 (base2[1] - joinvertex[1]) * (base2[1] - joinvertex[1]));
7369 /* If the two distances are equal, don't split the triangle. */
7370 if ((dist1 < 1.001 * dist2) && (dist1 > 0.999 * dist2)) {
7371 /* Return now to avoid enqueueing the bad triangle. */
7372 return;
7373 }
7374 }
7375 }
7376 }
7377
7378 /* Add this triangle to the list of bad triangles. */
7379 enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest);
7380 }
7381 }
7382
7383 #endif /* not CDT_ONLY */
7384
7385 /** **/
7386 /** **/
7387 /********* Mesh quality testing routines end here *********/
7388
7389 /********* Point location routines begin here *********/
7390 /** **/
7391 /** **/
7392
7393 /*****************************************************************************/
7394 /* */
7395 /* makevertexmap() Construct a mapping from vertices to triangles to */
7396 /* improve the speed of point location for segment */
7397 /* insertion. */
7398 /* */
7399 /* Traverses all the triangles, and provides each corner of each triangle */
7400 /* with a pointer to that triangle. Of course, pointers will be */
7401 /* overwritten by other pointers because (almost) each vertex is a corner */
7402 /* of several triangles, but in the end every vertex will point to some */
7403 /* triangle that contains it. */
7404 /* */
7405 /*****************************************************************************/
7406
7407 #ifdef ANSI_DECLARATORS
7408 void makevertexmap(struct mesh *m, struct behavior *b)
7409 #else /* not ANSI_DECLARATORS */
7410 void makevertexmap(m, b)
7411 struct mesh *m;
7412 struct behavior *b;
7413 #endif /* not ANSI_DECLARATORS */
7414
7415 {
7416 struct otri triangleloop;
7417 vertex triorg;
7418
7419 if (b->verbose) {
7420 printf(" Constructing mapping from vertices to triangles.\n");
7421 }
7422 traversalinit(&m->triangles);
7423 triangleloop.tri = triangletraverse(m);
7424 while (triangleloop.tri != (triangle *) NULL) {
7425 /* Check all three vertices of the triangle. */
7426 for (triangleloop.orient = 0; triangleloop.orient < 3;
7427 triangleloop.orient++) {
7428 org(triangleloop, triorg);
7429 setvertex2tri(triorg, encode(triangleloop));
7430 }
7431 triangleloop.tri = triangletraverse(m);
7432 }
7433 }
7434
7435 /*****************************************************************************/
7436 /* */
7437 /* preciselocate() Find a triangle or edge containing a given point. */
7438 /* */
7439 /* Begins its search from `searchtri'. It is important that `searchtri' */
7440 /* be a handle with the property that `searchpoint' is strictly to the left */
7441 /* of the edge denoted by `searchtri', or is collinear with that edge and */
7442 /* does not intersect that edge. (In particular, `searchpoint' should not */
7443 /* be the origin or destination of that edge.) */
7444 /* */
7445 /* These conditions are imposed because preciselocate() is normally used in */
7446 /* one of two situations: */
7447 /* */
7448 /* (1) To try to find the location to insert a new point. Normally, we */
7449 /* know an edge that the point is strictly to the left of. In the */
7450 /* incremental Delaunay algorithm, that edge is a bounding box edge. */
7451 /* In Ruppert's Delaunay refinement algorithm for quality meshing, */
7452 /* that edge is the shortest edge of the triangle whose circumcenter */
7453 /* is being inserted. */
7454 /* */
7455 /* (2) To try to find an existing point. In this case, any edge on the */
7456 /* convex hull is a good starting edge. You must screen out the */
7457 /* possibility that the vertex sought is an endpoint of the starting */
7458 /* edge before you call preciselocate(). */
7459 /* */
7460 /* On completion, `searchtri' is a triangle that contains `searchpoint'. */
7461 /* */
7462 /* This implementation differs from that given by Guibas and Stolfi. It */
7463 /* walks from triangle to triangle, crossing an edge only if `searchpoint' */
7464 /* is on the other side of the line containing that edge. After entering */
7465 /* a triangle, there are two edges by which one can leave that triangle. */
7466 /* If both edges are valid (`searchpoint' is on the other side of both */
7467 /* edges), one of the two is chosen by drawing a line perpendicular to */
7468 /* the entry edge (whose endpoints are `forg' and `fdest') passing through */
7469 /* `fapex'. Depending on which side of this perpendicular `searchpoint' */
7470 /* falls on, an exit edge is chosen. */
7471 /* */
7472 /* This implementation is empirically faster than the Guibas and Stolfi */
7473 /* point location routine (which I originally used), which tends to spiral */
7474 /* in toward its target. */
7475 /* */
7476 /* Returns ONVERTEX if the point lies on an existing vertex. `searchtri' */
7477 /* is a handle whose origin is the existing vertex. */
7478 /* */
7479 /* Returns ONEDGE if the point lies on a mesh edge. `searchtri' is a */
7480 /* handle whose primary edge is the edge on which the point lies. */
7481 /* */
7482 /* Returns INTRIANGLE if the point lies strictly within a triangle. */
7483 /* `searchtri' is a handle on the triangle that contains the point. */
7484 /* */
7485 /* Returns OUTSIDE if the point lies outside the mesh. `searchtri' is a */
7486 /* handle whose primary edge the point is to the right of. This might */
7487 /* occur when the circumcenter of a triangle falls just slightly outside */
7488 /* the mesh due to floating-point roundoff error. It also occurs when */
7489 /* seeking a hole or region point that a foolish user has placed outside */
7490 /* the mesh. */
7491 /* */
7492 /* If `stopatsubsegment' is nonzero, the search will stop if it tries to */
7493 /* walk through a subsegment, and will return OUTSIDE. */
7494 /* */
7495 /* WARNING: This routine is designed for convex triangulations, and will */
7496 /* not generally work after the holes and concavities have been carved. */
7497 /* However, it can still be used to find the circumcenter of a triangle, as */
7498 /* long as the search is begun from the triangle in question. */
7499 /* */
7500 /*****************************************************************************/
7501
7502 #ifdef ANSI_DECLARATORS
7503 enum locateresult preciselocate(struct mesh *m, struct behavior *b,
7504 vertex searchpoint, struct otri *searchtri,
7505 int stopatsubsegment)
7506 #else /* not ANSI_DECLARATORS */
7507 enum locateresult preciselocate(m, b, searchpoint, searchtri, stopatsubsegment)
7508 struct mesh *m;
7509 struct behavior *b;
7510 vertex searchpoint;
7511 struct otri *searchtri;
7512 int stopatsubsegment;
7513 #endif /* not ANSI_DECLARATORS */
7514
7515 {
7516 struct otri backtracktri;
7517 struct osub checkedge;
7518 vertex forg, fdest, fapex;
7519 REAL orgorient, destorient;
7520 int moveleft;
7521 triangle ptr; /* Temporary variable used by sym(). */
7522 subseg sptr; /* Temporary variable used by tspivot(). */
7523
7524 if (b->verbose > 2) {
7525 printf(" Searching for point (%.12g, %.12g).\n",
7526 (double)searchpoint[0], (double)searchpoint[1]);
7527 }
7528 /* Where are we? */
7529 org(*searchtri, forg);
7530 dest(*searchtri, fdest);
7531 apex(*searchtri, fapex);
7532 while (1) {
7533 if (b->verbose > 2) {
7534 printf(" At (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
7535 (double)forg[0], (double)forg[1],
7536 (double)fdest[0], (double)fdest[1],
7537 (double)fapex[0], (double)fapex[1]);
7538 }
7539 /* Check whether the apex is the point we seek. */
7540 if ((fapex[0] == searchpoint[0]) && (fapex[1] == searchpoint[1])) {
7541 lprevself(*searchtri);
7542 return ONVERTEX;
7543 }
7544 /* Does the point lie on the other side of the line defined by the */
7545 /* triangle edge opposite the triangle's destination? */
7546 destorient = counterclockwise(m, b, forg, fapex, searchpoint);
7547 /* Does the point lie on the other side of the line defined by the */
7548 /* triangle edge opposite the triangle's origin? */
7549 orgorient = counterclockwise(m, b, fapex, fdest, searchpoint);
7550 if (destorient > 0.0) {
7551 if (orgorient > 0.0) {
7552 /* Move left if the inner product of (fapex - searchpoint) and */
7553 /* (fdest - forg) is positive. This is equivalent to drawing */
7554 /* a line perpendicular to the line (forg, fdest) and passing */
7555 /* through `fapex', and determining which side of this line */
7556 /* `searchpoint' falls on. */
7557 moveleft = (fapex[0] - searchpoint[0]) * (fdest[0] - forg[0]) +
7558 (fapex[1] - searchpoint[1]) * (fdest[1] - forg[1]) > 0.0;
7559 } else {
7560 moveleft = 1;
7561 }
7562 } else {
7563 if (orgorient > 0.0) {
7564 moveleft = 0;
7565 } else {
7566 /* The point we seek must be on the boundary of or inside this */
7567 /* triangle. */
7568 if (destorient == 0.0) {
7569 lprevself(*searchtri);
7570 return ONEDGE;
7571 }
7572 if (orgorient == 0.0) {
7573 lnextself(*searchtri);
7574 return ONEDGE;
7575 }
7576 return INTRIANGLE;
7577 }
7578 }
7579
7580 /* Move to another triangle. Leave a trace `backtracktri' in case */
7581 /* floating-point roundoff or some such bogey causes us to walk */
7582 /* off a boundary of the triangulation. */
7583 if (moveleft) {
7584 lprev(*searchtri, backtracktri);
7585 fdest = fapex;
7586 } else {
7587 lnext(*searchtri, backtracktri);
7588 forg = fapex;
7589 }
7590 sym(backtracktri, *searchtri);
7591
7592 if (m->checksegments && stopatsubsegment) {
7593 /* Check for walking through a subsegment. */
7594 tspivot(backtracktri, checkedge);
7595 if (checkedge.ss != m->dummysub) {
7596 /* Go back to the last triangle. */
7597 otricopy(backtracktri, *searchtri);
7598 return OUTSIDE;
7599 }
7600 }
7601 /* Check for walking right out of the triangulation. */
7602 if (searchtri->tri == m->dummytri) {
7603 /* Go back to the last triangle. */
7604 otricopy(backtracktri, *searchtri);
7605 return OUTSIDE;
7606 }
7607
7608 apex(*searchtri, fapex);
7609 }
7610 }
7611
7612 /*****************************************************************************/
7613 /* */
7614 /* locate() Find a triangle or edge containing a given point. */
7615 /* */
7616 /* Searching begins from one of: the input `searchtri', a recently */
7617 /* encountered triangle `recenttri', or from a triangle chosen from a */
7618 /* random sample. The choice is made by determining which triangle's */
7619 /* origin is closest to the point we are searching for. Normally, */
7620 /* `searchtri' should be a handle on the convex hull of the triangulation. */
7621 /* */
7622 /* Details on the random sampling method can be found in the Mucke, Saias, */
7623 /* and Zhu paper cited in the header of this code. */
7624 /* */
7625 /* On completion, `searchtri' is a triangle that contains `searchpoint'. */
7626 /* */
7627 /* Returns ONVERTEX if the point lies on an existing vertex. `searchtri' */
7628 /* is a handle whose origin is the existing vertex. */
7629 /* */
7630 /* Returns ONEDGE if the point lies on a mesh edge. `searchtri' is a */
7631 /* handle whose primary edge is the edge on which the point lies. */
7632 /* */
7633 /* Returns INTRIANGLE if the point lies strictly within a triangle. */
7634 /* `searchtri' is a handle on the triangle that contains the point. */
7635 /* */
7636 /* Returns OUTSIDE if the point lies outside the mesh. `searchtri' is a */
7637 /* handle whose primary edge the point is to the right of. This might */
7638 /* occur when the circumcenter of a triangle falls just slightly outside */
7639 /* the mesh due to floating-point roundoff error. It also occurs when */
7640 /* seeking a hole or region point that a foolish user has placed outside */
7641 /* the mesh. */
7642 /* */
7643 /* WARNING: This routine is designed for convex triangulations, and will */
7644 /* not generally work after the holes and concavities have been carved. */
7645 /* */
7646 /*****************************************************************************/
7647
7648 #ifdef ANSI_DECLARATORS
7649 enum locateresult locate(struct mesh *m, struct behavior *b,
7650 vertex searchpoint, struct otri *searchtri)
7651 #else /* not ANSI_DECLARATORS */
7652 enum locateresult locate(m, b, searchpoint, searchtri)
7653 struct mesh *m;
7654 struct behavior *b;
7655 vertex searchpoint;
7656 struct otri *searchtri;
7657 #endif /* not ANSI_DECLARATORS */
7658
7659 {
7660 VOID **sampleblock;
7661 char *firsttri;
7662 struct otri sampletri;
7663 vertex torg, tdest;
7664 unsigned long alignptr;
7665 REAL searchdist, dist;
7666 REAL ahead;
7667 long samplesperblock, totalsamplesleft, samplesleft;
7668 long population, totalpopulation;
7669 triangle ptr; /* Temporary variable used by sym(). */
7670
7671 if (b->verbose > 2) {
7672 printf(" Randomly sampling for a triangle near point (%.12g, %.12g).\n",
7673 (double)searchpoint[0], (double)searchpoint[1]);
7674 }
7675 /* Record the distance from the suggested starting triangle to the */
7676 /* point we seek. */
7677 org(*searchtri, torg);
7678 searchdist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) +
7679 (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]);
7680 if (b->verbose > 2) {
7681 printf(" Boundary triangle has origin (%.12g, %.12g).\n",
7682 (double)torg[0], (double)torg[1]);
7683 }
7684
7685 /* If a recently encountered triangle has been recorded and has not been */
7686 /* deallocated, test it as a good starting point. */
7687 if (m->recenttri.tri != (triangle *) NULL) {
7688 if (!deadtri(m->recenttri.tri)) {
7689 org(m->recenttri, torg);
7690 if ((torg[0] == searchpoint[0]) && (torg[1] == searchpoint[1])) {
7691 otricopy(m->recenttri, *searchtri);
7692 return ONVERTEX;
7693 }
7694 dist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) +
7695 (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]);
7696 if (dist < searchdist) {
7697 otricopy(m->recenttri, *searchtri);
7698 searchdist = dist;
7699 if (b->verbose > 2) {
7700 printf(" Choosing recent triangle with origin (%.12g, %.12g).\n",
7701 (double)torg[0], (double)torg[1]);
7702 }
7703 }
7704 }
7705 }
7706
7707 /* The number of random samples taken is proportional to the cube root of */
7708 /* the number of triangles in the mesh. The next bit of code assumes */
7709 /* that the number of triangles increases monotonically (or at least */
7710 /* doesn't decrease enough to matter). */
7711 while (SAMPLEFACTOR * m->samples * m->samples * m->samples <
7712 m->triangles.items) {
7713 m->samples++;
7714 }
7715
7716 /* We'll draw ceiling(samples * TRIPERBLOCK / maxitems) random samples */
7717 /* from each block of triangles (except the first)--until we meet the */
7718 /* sample quota. The ceiling means that blocks at the end might be */
7719 /* neglected, but I don't care. */
7720 samplesperblock = (m->samples * TRIPERBLOCK - 1) / m->triangles.maxitems + 1;
7721 /* We'll draw ceiling(samples * itemsfirstblock / maxitems) random samples */
7722 /* from the first block of triangles. */
7723 samplesleft = (m->samples * m->triangles.itemsfirstblock - 1) /
7724 m->triangles.maxitems + 1;
7725 totalsamplesleft = m->samples;
7726 population = m->triangles.itemsfirstblock;
7727 totalpopulation = m->triangles.maxitems;
7728 sampleblock = m->triangles.firstblock;
7729 sampletri.orient = 0;
7730 while (totalsamplesleft > 0) {
7731 /* If we're in the last block, `population' needs to be corrected. */
7732 if (population > totalpopulation) {
7733 population = totalpopulation;
7734 }
7735 /* Find a pointer to the first triangle in the block. */
7736 alignptr = (unsigned long) (sampleblock + 1);
7737 firsttri = (char *) (alignptr +
7738 (unsigned long) m->triangles.alignbytes -
7739 (alignptr %
7740 (unsigned long) m->triangles.alignbytes));
7741
7742 /* Choose `samplesleft' randomly sampled triangles in this block. */
7743 do {
7744 sampletri.tri = (triangle *) (firsttri +
7745 (randomnation((unsigned int) population) *
7746 m->triangles.itembytes));
7747 if (!deadtri(sampletri.tri)) {
7748 org(sampletri, torg);
7749 dist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) +
7750 (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]);
7751 if (dist < searchdist) {
7752 otricopy(sampletri, *searchtri);
7753 searchdist = dist;
7754 if (b->verbose > 2) {
7755 printf(" Choosing triangle with origin (%.12g, %.12g).\n",
7756 (double)torg[0], (double)torg[1]);
7757 }
7758 }
7759 }
7760
7761 samplesleft--;
7762 totalsamplesleft--;
7763 } while ((samplesleft > 0) && (totalsamplesleft > 0));
7764
7765 if (totalsamplesleft > 0) {
7766 sampleblock = (VOID **) *sampleblock;
7767 samplesleft = samplesperblock;
7768 totalpopulation -= population;
7769 population = TRIPERBLOCK;
7770 }
7771 }
7772
7773 /* Where are we? */
7774 org(*searchtri, torg);
7775 dest(*searchtri, tdest);
7776 /* Check the starting triangle's vertices. */
7777 if ((torg[0] == searchpoint[0]) && (torg[1] == searchpoint[1])) {
7778 return ONVERTEX;
7779 }
7780 if ((tdest[0] == searchpoint[0]) && (tdest[1] == searchpoint[1])) {
7781 lnextself(*searchtri);
7782 return ONVERTEX;
7783 }
7784 /* Orient `searchtri' to fit the preconditions of calling preciselocate(). */
7785 ahead = counterclockwise(m, b, torg, tdest, searchpoint);
7786 if (ahead < 0.0) {
7787 /* Turn around so that `searchpoint' is to the left of the */
7788 /* edge specified by `searchtri'. */
7789 symself(*searchtri);
7790 } else if (ahead == 0.0) {
7791 /* Check if `searchpoint' is between `torg' and `tdest'. */
7792 if (((torg[0] < searchpoint[0]) == (searchpoint[0] < tdest[0])) &&
7793 ((torg[1] < searchpoint[1]) == (searchpoint[1] < tdest[1]))) {
7794 return ONEDGE;
7795 }
7796 }
7797 return preciselocate(m, b, searchpoint, searchtri, 0);
7798 }
7799
7800 /** **/
7801 /** **/
7802 /********* Point location routines end here *********/
7803
7804 /********* Mesh transformation routines begin here *********/
7805 /** **/
7806 /** **/
7807
7808 /*****************************************************************************/
7809 /* */
7810 /* insertsubseg() Create a new subsegment and insert it between two */
7811 /* triangles. */
7812 /* */
7813 /* The new subsegment is inserted at the edge described by the handle */
7814 /* `tri'. Its vertices are properly initialized. The marker `subsegmark' */
7815 /* is applied to the subsegment and, if appropriate, its vertices. */
7816 /* */
7817 /*****************************************************************************/
7818
7819 #ifdef ANSI_DECLARATORS
7820 void insertsubseg(struct mesh *m, struct behavior *b, struct otri *tri,
7821 int subsegmark)
7822 #else /* not ANSI_DECLARATORS */
7823 void insertsubseg(m, b, tri, subsegmark)
7824 struct mesh *m;
7825 struct behavior *b;
7826 struct otri *tri; /* Edge at which to insert the new subsegment. */
7827 int subsegmark; /* Marker for the new subsegment. */
7828 #endif /* not ANSI_DECLARATORS */
7829
7830 {
7831 struct otri oppotri;
7832 struct osub newsubseg;
7833 vertex triorg, tridest;
7834 triangle ptr; /* Temporary variable used by sym(). */
7835 subseg sptr; /* Temporary variable used by tspivot(). */
7836
7837 org(*tri, triorg);
7838 dest(*tri, tridest);
7839 /* Mark vertices if possible. */
7840 if (vertexmark(triorg) == 0) {
7841 setvertexmark(triorg, subsegmark);
7842 }
7843 if (vertexmark(tridest) == 0) {
7844 setvertexmark(tridest, subsegmark);
7845 }
7846 /* Check if there's already a subsegment here. */
7847 tspivot(*tri, newsubseg);
7848 if (newsubseg.ss == m->dummysub) {
7849 /* Make new subsegment and initialize its vertices. */
7850 makesubseg(m, &newsubseg);
7851 setsorg(newsubseg, tridest);
7852 setsdest(newsubseg, triorg);
7853 setsegorg(newsubseg, tridest);
7854 setsegdest(newsubseg, triorg);
7855 /* Bond new subsegment to the two triangles it is sandwiched between. */
7856 /* Note that the facing triangle `oppotri' might be equal to */
7857 /* `dummytri' (outer space), but the new subsegment is bonded to it */
7858 /* all the same. */
7859 tsbond(*tri, newsubseg);
7860 sym(*tri, oppotri);
7861 ssymself(newsubseg);
7862 tsbond(oppotri, newsubseg);
7863 setmark(newsubseg, subsegmark);
7864 if (b->verbose > 2) {
7865 printf(" Inserting new ");
7866 printsubseg(m, b, &newsubseg);
7867 }
7868 } else {
7869 if (mark(newsubseg) == 0) {
7870 setmark(newsubseg, subsegmark);
7871 }
7872 }
7873 }
7874
7875 /*****************************************************************************/
7876 /* */
7877 /* Terminology */
7878 /* */
7879 /* A "local transformation" replaces a small set of triangles with another */
7880 /* set of triangles. This may or may not involve inserting or deleting a */
7881 /* vertex. */
7882 /* */
7883 /* The term "casing" is used to describe the set of triangles that are */
7884 /* attached to the triangles being transformed, but are not transformed */
7885 /* themselves. Think of the casing as a fixed hollow structure inside */
7886 /* which all the action happens. A "casing" is only defined relative to */
7887 /* a single transformation; each occurrence of a transformation will */
7888 /* involve a different casing. */
7889 /* */
7890 /*****************************************************************************/
7891
7892 /*****************************************************************************/
7893 /* */
7894 /* flip() Transform two triangles to two different triangles by flipping */
7895 /* an edge counterclockwise within a quadrilateral. */
7896 /* */
7897 /* Imagine the original triangles, abc and bad, oriented so that the */
7898 /* shared edge ab lies in a horizontal plane, with the vertex b on the left */
7899 /* and the vertex a on the right. The vertex c lies below the edge, and */
7900 /* the vertex d lies above the edge. The `flipedge' handle holds the edge */
7901 /* ab of triangle abc, and is directed left, from vertex a to vertex b. */
7902 /* */
7903 /* The triangles abc and bad are deleted and replaced by the triangles cdb */
7904 /* and dca. The triangles that represent abc and bad are NOT deallocated; */
7905 /* they are reused for dca and cdb, respectively. Hence, any handles that */
7906 /* may have held the original triangles are still valid, although not */
7907 /* directed as they were before. */
7908 /* */
7909 /* Upon completion of this routine, the `flipedge' handle holds the edge */
7910 /* dc of triangle dca, and is directed down, from vertex d to vertex c. */
7911 /* (Hence, the two triangles have rotated counterclockwise.) */
7912 /* */
7913 /* WARNING: This transformation is geometrically valid only if the */
7914 /* quadrilateral adbc is convex. Furthermore, this transformation is */
7915 /* valid only if there is not a subsegment between the triangles abc and */
7916 /* bad. This routine does not check either of these preconditions, and */
7917 /* it is the responsibility of the calling routine to ensure that they are */
7918 /* met. If they are not, the streets shall be filled with wailing and */
7919 /* gnashing of teeth. */
7920 /* */
7921 /*****************************************************************************/
7922
7923 #ifdef ANSI_DECLARATORS
7924 void flip(struct mesh *m, struct behavior *b, struct otri *flipedge)
7925 #else /* not ANSI_DECLARATORS */
7926 void flip(m, b, flipedge)
7927 struct mesh *m;
7928 struct behavior *b;
7929 struct otri *flipedge; /* Handle for the triangle abc. */
7930 #endif /* not ANSI_DECLARATORS */
7931
7932 {
7933 struct otri botleft, botright;
7934 struct otri topleft, topright;
7935 struct otri top;
7936 struct otri botlcasing, botrcasing;
7937 struct otri toplcasing, toprcasing;
7938 struct osub botlsubseg, botrsubseg;
7939 struct osub toplsubseg, toprsubseg;
7940 vertex leftvertex, rightvertex, botvertex;
7941 vertex farvertex;
7942 triangle ptr; /* Temporary variable used by sym(). */
7943 subseg sptr; /* Temporary variable used by tspivot(). */
7944
7945 /* Identify the vertices of the quadrilateral. */
7946 org(*flipedge, rightvertex);
7947 dest(*flipedge, leftvertex);
7948 apex(*flipedge, botvertex);
7949 sym(*flipedge, top);
7950 #ifdef SELF_CHECK
7951 if (top.tri == m->dummytri) {
7952 printf("Internal error in flip(): Attempt to flip on boundary.\n");
7953 lnextself(*flipedge);
7954 return;
7955 }
7956 if (m->checksegments) {
7957 tspivot(*flipedge, toplsubseg);
7958 if (toplsubseg.ss != m->dummysub) {
7959 printf("Internal error in flip(): Attempt to flip a segment.\n");
7960 lnextself(*flipedge);
7961 return;
7962 }
7963 }
7964 #endif /* SELF_CHECK */
7965 apex(top, farvertex);
7966
7967 /* Identify the casing of the quadrilateral. */
7968 lprev(top, topleft);
7969 sym(topleft, toplcasing);
7970 lnext(top, topright);
7971 sym(topright, toprcasing);
7972 lnext(*flipedge, botleft);
7973 sym(botleft, botlcasing);
7974 lprev(*flipedge, botright);
7975 sym(botright, botrcasing);
7976 /* Rotate the quadrilateral one-quarter turn counterclockwise. */
7977 bond(topleft, botlcasing);
7978 bond(botleft, botrcasing);
7979 bond(botright, toprcasing);
7980 bond(topright, toplcasing);
7981
7982 if (m->checksegments) {
7983 /* Check for subsegments and rebond them to the quadrilateral. */
7984 tspivot(topleft, toplsubseg);
7985 tspivot(botleft, botlsubseg);
7986 tspivot(botright, botrsubseg);
7987 tspivot(topright, toprsubseg);
7988 if (toplsubseg.ss == m->dummysub) {
7989 tsdissolve(topright);
7990 } else {
7991 tsbond(topright, toplsubseg);
7992 }
7993 if (botlsubseg.ss == m->dummysub) {
7994 tsdissolve(topleft);
7995 } else {
7996 tsbond(topleft, botlsubseg);
7997 }
7998 if (botrsubseg.ss == m->dummysub) {
7999 tsdissolve(botleft);
8000 } else {
8001 tsbond(botleft, botrsubseg);
8002 }
8003 if (toprsubseg.ss == m->dummysub) {
8004 tsdissolve(botright);
8005 } else {
8006 tsbond(botright, toprsubseg);
8007 }
8008 }
8009
8010 /* New vertex assignments for the rotated quadrilateral. */
8011 setorg(*flipedge, farvertex);
8012 setdest(*flipedge, botvertex);
8013 setapex(*flipedge, rightvertex);
8014 setorg(top, botvertex);
8015 setdest(top, farvertex);
8016 setapex(top, leftvertex);
8017 if (b->verbose > 2) {
8018 printf(" Edge flip results in left ");
8019 printtriangle(m, b, &top);
8020 printf(" and right ");
8021 printtriangle(m, b, flipedge);
8022 }
8023 }
8024
8025 /*****************************************************************************/
8026 /* */
8027 /* unflip() Transform two triangles to two different triangles by */
8028 /* flipping an edge clockwise within a quadrilateral. Reverses */
8029 /* the flip() operation so that the data structures representing */
8030 /* the triangles are back where they were before the flip(). */
8031 /* */
8032 /* Imagine the original triangles, abc and bad, oriented so that the */
8033 /* shared edge ab lies in a horizontal plane, with the vertex b on the left */
8034 /* and the vertex a on the right. The vertex c lies below the edge, and */
8035 /* the vertex d lies above the edge. The `flipedge' handle holds the edge */
8036 /* ab of triangle abc, and is directed left, from vertex a to vertex b. */
8037 /* */
8038 /* The triangles abc and bad are deleted and replaced by the triangles cdb */
8039 /* and dca. The triangles that represent abc and bad are NOT deallocated; */
8040 /* they are reused for cdb and dca, respectively. Hence, any handles that */
8041 /* may have held the original triangles are still valid, although not */
8042 /* directed as they were before. */
8043 /* */
8044 /* Upon completion of this routine, the `flipedge' handle holds the edge */
8045 /* cd of triangle cdb, and is directed up, from vertex c to vertex d. */
8046 /* (Hence, the two triangles have rotated clockwise.) */
8047 /* */
8048 /* WARNING: This transformation is geometrically valid only if the */
8049 /* quadrilateral adbc is convex. Furthermore, this transformation is */
8050 /* valid only if there is not a subsegment between the triangles abc and */
8051 /* bad. This routine does not check either of these preconditions, and */
8052 /* it is the responsibility of the calling routine to ensure that they are */
8053 /* met. If they are not, the streets shall be filled with wailing and */
8054 /* gnashing of teeth. */
8055 /* */
8056 /*****************************************************************************/
8057
8058 #ifdef ANSI_DECLARATORS
8059 void unflip(struct mesh *m, struct behavior *b, struct otri *flipedge)
8060 #else /* not ANSI_DECLARATORS */
8061 void unflip(m, b, flipedge)
8062 struct mesh *m;
8063 struct behavior *b;
8064 struct otri *flipedge; /* Handle for the triangle abc. */
8065 #endif /* not ANSI_DECLARATORS */
8066
8067 {
8068 struct otri botleft, botright;
8069 struct otri topleft, topright;
8070 struct otri top;
8071 struct otri botlcasing, botrcasing;
8072 struct otri toplcasing, toprcasing;
8073 struct osub botlsubseg, botrsubseg;
8074 struct osub toplsubseg, toprsubseg;
8075 vertex leftvertex, rightvertex, botvertex;
8076 vertex farvertex;
8077 triangle ptr; /* Temporary variable used by sym(). */
8078 subseg sptr; /* Temporary variable used by tspivot(). */
8079
8080 /* Identify the vertices of the quadrilateral. */
8081 org(*flipedge, rightvertex);
8082 dest(*flipedge, leftvertex);
8083 apex(*flipedge, botvertex);
8084 sym(*flipedge, top);
8085 #ifdef SELF_CHECK
8086 if (top.tri == m->dummytri) {
8087 printf("Internal error in unflip(): Attempt to flip on boundary.\n");
8088 lnextself(*flipedge);
8089 return;
8090 }
8091 if (m->checksegments) {
8092 tspivot(*flipedge, toplsubseg);
8093 if (toplsubseg.ss != m->dummysub) {
8094 printf("Internal error in unflip(): Attempt to flip a subsegment.\n");
8095 lnextself(*flipedge);
8096 return;
8097 }
8098 }
8099 #endif /* SELF_CHECK */
8100 apex(top, farvertex);
8101
8102 /* Identify the casing of the quadrilateral. */
8103 lprev(top, topleft);
8104 sym(topleft, toplcasing);
8105 lnext(top, topright);
8106 sym(topright, toprcasing);
8107 lnext(*flipedge, botleft);
8108 sym(botleft, botlcasing);
8109 lprev(*flipedge, botright);
8110 sym(botright, botrcasing);
8111 /* Rotate the quadrilateral one-quarter turn clockwise. */
8112 bond(topleft, toprcasing);
8113 bond(botleft, toplcasing);
8114 bond(botright, botlcasing);
8115 bond(topright, botrcasing);
8116
8117 if (m->checksegments) {
8118 /* Check for subsegments and rebond them to the quadrilateral. */
8119 tspivot(topleft, toplsubseg);
8120 tspivot(botleft, botlsubseg);
8121 tspivot(botright, botrsubseg);
8122 tspivot(topright, toprsubseg);
8123 if (toplsubseg.ss == m->dummysub) {
8124 tsdissolve(botleft);
8125 } else {
8126 tsbond(botleft, toplsubseg);
8127 }
8128 if (botlsubseg.ss == m->dummysub) {
8129 tsdissolve(botright);
8130 } else {
8131 tsbond(botright, botlsubseg);
8132 }
8133 if (botrsubseg.ss == m->dummysub) {
8134 tsdissolve(topright);
8135 } else {
8136 tsbond(topright, botrsubseg);
8137 }
8138 if (toprsubseg.ss == m->dummysub) {
8139 tsdissolve(topleft);
8140 } else {
8141 tsbond(topleft, toprsubseg);
8142 }
8143 }
8144
8145 /* New vertex assignments for the rotated quadrilateral. */
8146 setorg(*flipedge, botvertex);
8147 setdest(*flipedge, farvertex);
8148 setapex(*flipedge, leftvertex);
8149 setorg(top, farvertex);
8150 setdest(top, botvertex);
8151 setapex(top, rightvertex);
8152 if (b->verbose > 2) {
8153 printf(" Edge unflip results in left ");
8154 printtriangle(m, b, flipedge);
8155 printf(" and right ");
8156 printtriangle(m, b, &top);
8157 }
8158 }
8159
8160 /*****************************************************************************/
8161 /* */
8162 /* insertvertex() Insert a vertex into a Delaunay triangulation, */
8163 /* performing flips as necessary to maintain the Delaunay */
8164 /* property. */
8165 /* */
8166 /* The point `insertvertex' is located. If `searchtri.tri' is not NULL, */
8167 /* the search for the containing triangle begins from `searchtri'. If */
8168 /* `searchtri.tri' is NULL, a full point location procedure is called. */
8169 /* If `insertvertex' is found inside a triangle, the triangle is split into */
8170 /* three; if `insertvertex' lies on an edge, the edge is split in two, */
8171 /* thereby splitting the two adjacent triangles into four. Edge flips are */
8172 /* used to restore the Delaunay property. If `insertvertex' lies on an */
8173 /* existing vertex, no action is taken, and the value DUPLICATEVERTEX is */
8174 /* returned. On return, `searchtri' is set to a handle whose origin is the */
8175 /* existing vertex. */
8176 /* */
8177 /* Normally, the parameter `splitseg' is set to NULL, implying that no */
8178 /* subsegment should be split. In this case, if `insertvertex' is found to */
8179 /* lie on a segment, no action is taken, and the value VIOLATINGVERTEX is */
8180 /* returned. On return, `searchtri' is set to a handle whose primary edge */
8181 /* is the violated subsegment. */
8182 /* */
8183 /* If the calling routine wishes to split a subsegment by inserting a */
8184 /* vertex in it, the parameter `splitseg' should be that subsegment. In */
8185 /* this case, `searchtri' MUST be the triangle handle reached by pivoting */
8186 /* from that subsegment; no point location is done. */
8187 /* */
8188 /* `segmentflaws' and `triflaws' are flags that indicate whether or not */
8189 /* there should be checks for the creation of encroached subsegments or bad */
8190 /* quality triangles. If a newly inserted vertex encroaches upon */
8191 /* subsegments, these subsegments are added to the list of subsegments to */
8192 /* be split if `segmentflaws' is set. If bad triangles are created, these */
8193 /* are added to the queue if `triflaws' is set. */
8194 /* */
8195 /* If a duplicate vertex or violated segment does not prevent the vertex */
8196 /* from being inserted, the return value will be ENCROACHINGVERTEX if the */
8197 /* vertex encroaches upon a subsegment (and checking is enabled), or */
8198 /* SUCCESSFULVERTEX otherwise. In either case, `searchtri' is set to a */
8199 /* handle whose origin is the newly inserted vertex. */
8200 /* */
8201 /* insertvertex() does not use flip() for reasons of speed; some */
8202 /* information can be reused from edge flip to edge flip, like the */
8203 /* locations of subsegments. */
8204 /* */
8205 /*****************************************************************************/
8206
8207 #ifdef ANSI_DECLARATORS
8208 enum insertvertexresult insertvertex(struct mesh *m, struct behavior *b,
8209 vertex newvertex, struct otri *searchtri,
8210 struct osub *splitseg,
8211 int segmentflaws, int triflaws)
8212 #else /* not ANSI_DECLARATORS */
8213 enum insertvertexresult insertvertex(m, b, newvertex, searchtri, splitseg,
8214 segmentflaws, triflaws)
8215 struct mesh *m;
8216 struct behavior *b;
8217 vertex newvertex;
8218 struct otri *searchtri;
8219 struct osub *splitseg;
8220 int segmentflaws;
8221 int triflaws;
8222 #endif /* not ANSI_DECLARATORS */
8223
8224 {
8225 struct otri horiz;
8226 struct otri top;
8227 struct otri botleft, botright;
8228 struct otri topleft, topright;
8229 struct otri newbotleft, newbotright;
8230 struct otri newtopright;
8231 struct otri botlcasing, botrcasing;
8232 struct otri toplcasing, toprcasing;
8233 struct otri testtri;
8234 struct osub botlsubseg, botrsubseg;
8235 struct osub toplsubseg, toprsubseg;
8236 struct osub brokensubseg;
8237 struct osub checksubseg;
8238 struct osub rightsubseg;
8239 struct osub newsubseg;
8240 struct badsubseg *encroached;
8241 struct flipstacker *newflip;
8242 vertex first;
8243 vertex leftvertex, rightvertex, botvertex, topvertex, farvertex;
8244 vertex segmentorg, segmentdest;
8245 REAL attrib;
8246 REAL area;
8247 enum insertvertexresult success;
8248 enum locateresult intersect;
8249 int doflip;
8250 int mirrorflag;
8251 int enq;
8252 int i;
8253 triangle ptr; /* Temporary variable used by sym(). */
8254 subseg sptr; /* Temporary variable used by spivot() and tspivot(). */
8255
8256 /* Avoid compiler warnings about uninitialized variables */
8257 toprcasing.tri = NULL;
8258 toprcasing.orient = 0;
8259
8260 if (b->verbose > 1) {
8261 printf(" Inserting (%.12g, %.12g).\n", (double)newvertex[0], (double)newvertex[1]);
8262 }
8263
8264 if (splitseg == (struct osub *) NULL) {
8265 /* Find the location of the vertex to be inserted. Check if a good */
8266 /* starting triangle has already been provided by the caller. */
8267 if (searchtri->tri == m->dummytri) {
8268 /* Find a boundary triangle. */
8269 horiz.tri = m->dummytri;
8270 horiz.orient = 0;
8271 symself(horiz);
8272 /* Search for a triangle containing `newvertex'. */
8273 intersect = locate(m, b, newvertex, &horiz);
8274 } else {
8275 /* Start searching from the triangle provided by the caller. */
8276 otricopy(*searchtri, horiz);
8277 intersect = preciselocate(m, b, newvertex, &horiz, 1);
8278 }
8279 } else {
8280 /* The calling routine provides the subsegment in which */
8281 /* the vertex is inserted. */
8282 otricopy(*searchtri, horiz);
8283 intersect = ONEDGE;
8284 }
8285
8286 if (intersect == ONVERTEX) {
8287 /* There's already a vertex there. Return in `searchtri' a triangle */
8288 /* whose origin is the existing vertex. */
8289 otricopy(horiz, *searchtri);
8290 otricopy(horiz, m->recenttri);
8291 return DUPLICATEVERTEX;
8292 }
8293 if ((intersect == ONEDGE) || (intersect == OUTSIDE)) {
8294 /* The vertex falls on an edge or boundary. */
8295 if (m->checksegments && (splitseg == (struct osub *) NULL)) {
8296 /* Check whether the vertex falls on a subsegment. */
8297 tspivot(horiz, brokensubseg);
8298 if (brokensubseg.ss != m->dummysub) {
8299 /* The vertex falls on a subsegment, and hence will not be inserted. */
8300 if (segmentflaws) {
8301 enq = b->nobisect != 2;
8302 if (enq && (b->nobisect == 1)) {
8303 /* This subsegment may be split only if it is an */
8304 /* internal boundary. */
8305 sym(horiz, testtri);
8306 enq = testtri.tri != m->dummytri;
8307 }
8308 if (enq) {
8309 /* Add the subsegment to the list of encroached subsegments. */
8310 encroached = (struct badsubseg *) poolalloc(&m->badsubsegs);
8311 encroached->encsubseg = sencode(brokensubseg);
8312 sorg(brokensubseg, encroached->subsegorg);
8313 sdest(brokensubseg, encroached->subsegdest);
8314 if (b->verbose > 2) {
8315 printf(
8316 " Queueing encroached subsegment (%.12g, %.12g) (%.12g, %.12g).\n",
8317 (double)encroached->subsegorg[0], (double)encroached->subsegorg[1],
8318 (double)encroached->subsegdest[0], (double)encroached->subsegdest[1]);
8319 }
8320 }
8321 }
8322 /* Return a handle whose primary edge contains the vertex, */
8323 /* which has not been inserted. */
8324 otricopy(horiz, *searchtri);
8325 otricopy(horiz, m->recenttri);
8326 return VIOLATINGVERTEX;
8327 }
8328 }
8329
8330 /* Insert the vertex on an edge, dividing one triangle into two (if */
8331 /* the edge lies on a boundary) or two triangles into four. */
8332 lprev(horiz, botright);
8333 sym(botright, botrcasing);
8334 sym(horiz, topright);
8335 /* Is there a second triangle? (Or does this edge lie on a boundary?) */
8336 mirrorflag = topright.tri != m->dummytri;
8337 if (mirrorflag) {
8338 lnextself(topright);
8339 sym(topright, toprcasing);
8340 maketriangle(m, b, &newtopright);
8341 } else {
8342 /* Splitting a boundary edge increases the number of boundary edges. */
8343 m->hullsize++;
8344 }
8345 maketriangle(m, b, &newbotright);
8346
8347 /* Set the vertices of changed and new triangles. */
8348 org(horiz, rightvertex);
8349 dest(horiz, leftvertex);
8350 apex(horiz, botvertex);
8351 setorg(newbotright, botvertex);
8352 setdest(newbotright, rightvertex);
8353 setapex(newbotright, newvertex);
8354 setorg(horiz, newvertex);
8355 for (i = 0; i < m->eextras; i++) {
8356 /* Set the element attributes of a new triangle. */
8357 setelemattribute(newbotright, i, elemattribute(botright, i));
8358 }
8359 if (b->vararea) {
8360 /* Set the area constraint of a new triangle. */
8361 setareabound(newbotright, areabound(botright));
8362 }
8363 if (mirrorflag) {
8364 dest(topright, topvertex);
8365 setorg(newtopright, rightvertex);
8366 setdest(newtopright, topvertex);
8367 setapex(newtopright, newvertex);
8368 setorg(topright, newvertex);
8369 for (i = 0; i < m->eextras; i++) {
8370 /* Set the element attributes of another new triangle. */
8371 setelemattribute(newtopright, i, elemattribute(topright, i));
8372 }
8373 if (b->vararea) {
8374 /* Set the area constraint of another new triangle. */
8375 setareabound(newtopright, areabound(topright));
8376 }
8377 }
8378
8379 /* There may be subsegments that need to be bonded */
8380 /* to the new triangle(s). */
8381 if (m->checksegments) {
8382 tspivot(botright, botrsubseg);
8383 if (botrsubseg.ss != m->dummysub) {
8384 tsdissolve(botright);
8385 tsbond(newbotright, botrsubseg);
8386 }
8387 if (mirrorflag) {
8388 tspivot(topright, toprsubseg);
8389 if (toprsubseg.ss != m->dummysub) {
8390 tsdissolve(topright);
8391 tsbond(newtopright, toprsubseg);
8392 }
8393 }
8394 }
8395
8396 /* Bond the new triangle(s) to the surrounding triangles. */
8397 bond(newbotright, botrcasing);
8398 lprevself(newbotright);
8399 bond(newbotright, botright);
8400 lprevself(newbotright);
8401 if (mirrorflag) {
8402 bond(newtopright, toprcasing);
8403 lnextself(newtopright);
8404 bond(newtopright, topright);
8405 lnextself(newtopright);
8406 bond(newtopright, newbotright);
8407 }
8408
8409 if (splitseg != (struct osub *) NULL) {
8410 /* Split the subsegment into two. */
8411 setsdest(*splitseg, newvertex);
8412 segorg(*splitseg, segmentorg);
8413 segdest(*splitseg, segmentdest);
8414 ssymself(*splitseg);
8415 spivot(*splitseg, rightsubseg);
8416 insertsubseg(m, b, &newbotright, mark(*splitseg));
8417 tspivot(newbotright, newsubseg);
8418 setsegorg(newsubseg, segmentorg);
8419 setsegdest(newsubseg, segmentdest);
8420 sbond(*splitseg, newsubseg);
8421 ssymself(newsubseg);
8422 sbond(newsubseg, rightsubseg);
8423 ssymself(*splitseg);
8424 /* Transfer the subsegment's boundary marker to the vertex */
8425 /* if required. */
8426 if (vertexmark(newvertex) == 0) {
8427 setvertexmark(newvertex, mark(*splitseg));
8428 }
8429 }
8430
8431 if (m->checkquality) {
8432 poolrestart(&m->flipstackers);
8433 m->lastflip = (struct flipstacker *) poolalloc(&m->flipstackers);
8434 m->lastflip->flippedtri = encode(horiz);
8435 m->lastflip->prevflip = (struct flipstacker *) &insertvertex;
8436 }
8437
8438 #ifdef SELF_CHECK
8439 if (counterclockwise(m, b, rightvertex, leftvertex, botvertex) < 0.0) {
8440 printf("Internal error in insertvertex():\n");
8441 printf(
8442 " Clockwise triangle prior to edge vertex insertion (bottom).\n");
8443 }
8444 if (mirrorflag) {
8445 if (counterclockwise(m, b, leftvertex, rightvertex, topvertex) < 0.0) {
8446 printf("Internal error in insertvertex():\n");
8447 printf(" Clockwise triangle prior to edge vertex insertion (top).\n");
8448 }
8449 if (counterclockwise(m, b, rightvertex, topvertex, newvertex) < 0.0) {
8450 printf("Internal error in insertvertex():\n");
8451 printf(
8452 " Clockwise triangle after edge vertex insertion (top right).\n");
8453 }
8454 if (counterclockwise(m, b, topvertex, leftvertex, newvertex) < 0.0) {
8455 printf("Internal error in insertvertex():\n");
8456 printf(
8457 " Clockwise triangle after edge vertex insertion (top left).\n");
8458 }
8459 }
8460 if (counterclockwise(m, b, leftvertex, botvertex, newvertex) < 0.0) {
8461 printf("Internal error in insertvertex():\n");
8462 printf(
8463 " Clockwise triangle after edge vertex insertion (bottom left).\n");
8464 }
8465 if (counterclockwise(m, b, botvertex, rightvertex, newvertex) < 0.0) {
8466 printf("Internal error in insertvertex():\n");
8467 printf(
8468 " Clockwise triangle after edge vertex insertion (bottom right).\n");
8469 }
8470 #endif /* SELF_CHECK */
8471 if (b->verbose > 2) {
8472 printf(" Updating bottom left ");
8473 printtriangle(m, b, &botright);
8474 if (mirrorflag) {
8475 printf(" Updating top left ");
8476 printtriangle(m, b, &topright);
8477 printf(" Creating top right ");
8478 printtriangle(m, b, &newtopright);
8479 }
8480 printf(" Creating bottom right ");
8481 printtriangle(m, b, &newbotright);
8482 }
8483
8484 /* Position `horiz' on the first edge to check for */
8485 /* the Delaunay property. */
8486 lnextself(horiz);
8487 } else {
8488 /* Insert the vertex in a triangle, splitting it into three. */
8489 lnext(horiz, botleft);
8490 lprev(horiz, botright);
8491 sym(botleft, botlcasing);
8492 sym(botright, botrcasing);
8493 maketriangle(m, b, &newbotleft);
8494 maketriangle(m, b, &newbotright);
8495
8496 /* Set the vertices of changed and new triangles. */
8497 org(horiz, rightvertex);
8498 dest(horiz, leftvertex);
8499 apex(horiz, botvertex);
8500 setorg(newbotleft, leftvertex);
8501 setdest(newbotleft, botvertex);
8502 setapex(newbotleft, newvertex);
8503 setorg(newbotright, botvertex);
8504 setdest(newbotright, rightvertex);
8505 setapex(newbotright, newvertex);
8506 setapex(horiz, newvertex);
8507 for (i = 0; i < m->eextras; i++) {
8508 /* Set the element attributes of the new triangles. */
8509 attrib = elemattribute(horiz, i);
8510 setelemattribute(newbotleft, i, attrib);
8511 setelemattribute(newbotright, i, attrib);
8512 }
8513 if (b->vararea) {
8514 /* Set the area constraint of the new triangles. */
8515 area = areabound(horiz);
8516 setareabound(newbotleft, area);
8517 setareabound(newbotright, area);
8518 }
8519
8520 /* There may be subsegments that need to be bonded */
8521 /* to the new triangles. */
8522 if (m->checksegments) {
8523 tspivot(botleft, botlsubseg);
8524 if (botlsubseg.ss != m->dummysub) {
8525 tsdissolve(botleft);
8526 tsbond(newbotleft, botlsubseg);
8527 }
8528 tspivot(botright, botrsubseg);
8529 if (botrsubseg.ss != m->dummysub) {
8530 tsdissolve(botright);
8531 tsbond(newbotright, botrsubseg);
8532 }
8533 }
8534
8535 /* Bond the new triangles to the surrounding triangles. */
8536 bond(newbotleft, botlcasing);
8537 bond(newbotright, botrcasing);
8538 lnextself(newbotleft);
8539 lprevself(newbotright);
8540 bond(newbotleft, newbotright);
8541 lnextself(newbotleft);
8542 bond(botleft, newbotleft);
8543 lprevself(newbotright);
8544 bond(botright, newbotright);
8545
8546 if (m->checkquality) {
8547 poolrestart(&m->flipstackers);
8548 m->lastflip = (struct flipstacker *) poolalloc(&m->flipstackers);
8549 m->lastflip->flippedtri = encode(horiz);
8550 m->lastflip->prevflip = (struct flipstacker *) NULL;
8551 }
8552
8553 #ifdef SELF_CHECK
8554 if (counterclockwise(m, b, rightvertex, leftvertex, botvertex) < 0.0) {
8555 printf("Internal error in insertvertex():\n");
8556 printf(" Clockwise triangle prior to vertex insertion.\n");
8557 }
8558 if (counterclockwise(m, b, rightvertex, leftvertex, newvertex) < 0.0) {
8559 printf("Internal error in insertvertex():\n");
8560 printf(" Clockwise triangle after vertex insertion (top).\n");
8561 }
8562 if (counterclockwise(m, b, leftvertex, botvertex, newvertex) < 0.0) {
8563 printf("Internal error in insertvertex():\n");
8564 printf(" Clockwise triangle after vertex insertion (left).\n");
8565 }
8566 if (counterclockwise(m, b, botvertex, rightvertex, newvertex) < 0.0) {
8567 printf("Internal error in insertvertex():\n");
8568 printf(" Clockwise triangle after vertex insertion (right).\n");
8569 }
8570 #endif /* SELF_CHECK */
8571 if (b->verbose > 2) {
8572 printf(" Updating top ");
8573 printtriangle(m, b, &horiz);
8574 printf(" Creating left ");
8575 printtriangle(m, b, &newbotleft);
8576 printf(" Creating right ");
8577 printtriangle(m, b, &newbotright);
8578 }
8579 }
8580
8581 /* The insertion is successful by default, unless an encroached */
8582 /* subsegment is found. */
8583 success = SUCCESSFULVERTEX;
8584 /* Circle around the newly inserted vertex, checking each edge opposite */
8585 /* it for the Delaunay property. Non-Delaunay edges are flipped. */
8586 /* `horiz' is always the edge being checked. `first' marks where to */
8587 /* stop circling. */
8588 org(horiz, first);
8589 rightvertex = first;
8590 dest(horiz, leftvertex);
8591 /* Circle until finished. */
8592 while (1) {
8593 /* By default, the edge will be flipped. */
8594 doflip = 1;
8595
8596 if (m->checksegments) {
8597 /* Check for a subsegment, which cannot be flipped. */
8598 tspivot(horiz, checksubseg);
8599 if (checksubseg.ss != m->dummysub) {
8600 /* The edge is a subsegment and cannot be flipped. */
8601 doflip = 0;
8602 #ifndef CDT_ONLY
8603 if (segmentflaws) {
8604 /* Does the new vertex encroach upon this subsegment? */
8605 if (checkseg4encroach(m, b, &checksubseg)) {
8606 success = ENCROACHINGVERTEX;
8607 }
8608 }
8609 #endif /* not CDT_ONLY */
8610 }
8611 }
8612
8613 if (doflip) {
8614 /* Check if the edge is a boundary edge. */
8615 sym(horiz, top);
8616 if (top.tri == m->dummytri) {
8617 /* The edge is a boundary edge and cannot be flipped. */
8618 doflip = 0;
8619 } else {
8620 /* Find the vertex on the other side of the edge. */
8621 apex(top, farvertex);
8622 /* In the incremental Delaunay triangulation algorithm, any of */
8623 /* `leftvertex', `rightvertex', and `farvertex' could be vertices */
8624 /* of the triangular bounding box. These vertices must be */
8625 /* treated as if they are infinitely distant, even though their */
8626 /* "coordinates" are not. */
8627 if ((leftvertex == m->infvertex1) || (leftvertex == m->infvertex2) ||
8628 (leftvertex == m->infvertex3)) {
8629 /* `leftvertex' is infinitely distant. Check the convexity of */
8630 /* the boundary of the triangulation. 'farvertex' might be */
8631 /* infinite as well, but trust me, this same condition should */
8632 /* be applied. */
8633 doflip = counterclockwise(m, b, newvertex, rightvertex, farvertex)
8634 > 0.0;
8635 } else if ((rightvertex == m->infvertex1) ||
8636 (rightvertex == m->infvertex2) ||
8637 (rightvertex == m->infvertex3)) {
8638 /* `rightvertex' is infinitely distant. Check the convexity of */
8639 /* the boundary of the triangulation. 'farvertex' might be */
8640 /* infinite as well, but trust me, this same condition should */
8641 /* be applied. */
8642 doflip = counterclockwise(m, b, farvertex, leftvertex, newvertex)
8643 > 0.0;
8644 } else if ((farvertex == m->infvertex1) ||
8645 (farvertex == m->infvertex2) ||
8646 (farvertex == m->infvertex3)) {
8647 /* `farvertex' is infinitely distant and cannot be inside */
8648 /* the circumcircle of the triangle `horiz'. */
8649 doflip = 0;
8650 } else {
8651 /* Test whether the edge is locally Delaunay. */
8652 doflip = incircle(m, b, leftvertex, newvertex, rightvertex,
8653 farvertex) > 0.0;
8654 }
8655 if (doflip) {
8656 /* We made it! Flip the edge `horiz' by rotating its containing */
8657 /* quadrilateral (the two triangles adjacent to `horiz'). */
8658 /* Identify the casing of the quadrilateral. */
8659 lprev(top, topleft);
8660 sym(topleft, toplcasing);
8661 lnext(top, topright);
8662 sym(topright, toprcasing);
8663 lnext(horiz, botleft);
8664 sym(botleft, botlcasing);
8665 lprev(horiz, botright);
8666 sym(botright, botrcasing);
8667 /* Rotate the quadrilateral one-quarter turn counterclockwise. */
8668 bond(topleft, botlcasing);
8669 bond(botleft, botrcasing);
8670 bond(botright, toprcasing);
8671 bond(topright, toplcasing);
8672 if (m->checksegments) {
8673 /* Check for subsegments and rebond them to the quadrilateral. */
8674 tspivot(topleft, toplsubseg);
8675 tspivot(botleft, botlsubseg);
8676 tspivot(botright, botrsubseg);
8677 tspivot(topright, toprsubseg);
8678 if (toplsubseg.ss == m->dummysub) {
8679 tsdissolve(topright);
8680 } else {
8681 tsbond(topright, toplsubseg);
8682 }
8683 if (botlsubseg.ss == m->dummysub) {
8684 tsdissolve(topleft);
8685 } else {
8686 tsbond(topleft, botlsubseg);
8687 }
8688 if (botrsubseg.ss == m->dummysub) {
8689 tsdissolve(botleft);
8690 } else {
8691 tsbond(botleft, botrsubseg);
8692 }
8693 if (toprsubseg.ss == m->dummysub) {
8694 tsdissolve(botright);
8695 } else {
8696 tsbond(botright, toprsubseg);
8697 }
8698 }
8699 /* New vertex assignments for the rotated quadrilateral. */
8700 setorg(horiz, farvertex);
8701 setdest(horiz, newvertex);
8702 setapex(horiz, rightvertex);
8703 setorg(top, newvertex);
8704 setdest(top, farvertex);
8705 setapex(top, leftvertex);
8706 for (i = 0; i < m->eextras; i++) {
8707 /* Take the average of the two triangles' attributes. */
8708 attrib = 0.5 * (elemattribute(top, i) + elemattribute(horiz, i));
8709 setelemattribute(top, i, attrib);
8710 setelemattribute(horiz, i, attrib);
8711 }
8712 if (b->vararea) {
8713 if ((areabound(top) <= 0.0) || (areabound(horiz) <= 0.0)) {
8714 area = -1.0;
8715 } else {
8716 /* Take the average of the two triangles' area constraints. */
8717 /* This prevents small area constraints from migrating a */
8718 /* long, long way from their original location due to flips. */
8719 area = 0.5 * (areabound(top) + areabound(horiz));
8720 }
8721 setareabound(top, area);
8722 setareabound(horiz, area);
8723 }
8724
8725 if (m->checkquality) {
8726 newflip = (struct flipstacker *) poolalloc(&m->flipstackers);
8727 newflip->flippedtri = encode(horiz);
8728 newflip->prevflip = m->lastflip;
8729 m->lastflip = newflip;
8730 }
8731
8732 #ifdef SELF_CHECK
8733 if (newvertex != (vertex) NULL) {
8734 if (counterclockwise(m, b, leftvertex, newvertex, rightvertex) <
8735 0.0) {
8736 printf("Internal error in insertvertex():\n");
8737 printf(" Clockwise triangle prior to edge flip (bottom).\n");
8738 }
8739 /* The following test has been removed because constrainededge() */
8740 /* sometimes generates inverted triangles that insertvertex() */
8741 /* removes. */
8742 /*
8743 if (counterclockwise(m, b, rightvertex, farvertex, leftvertex) <
8744 0.0) {
8745 printf("Internal error in insertvertex():\n");
8746 printf(" Clockwise triangle prior to edge flip (top).\n");
8747 }
8748 */
8749 if (counterclockwise(m, b, farvertex, leftvertex, newvertex) <
8750 0.0) {
8751 printf("Internal error in insertvertex():\n");
8752 printf(" Clockwise triangle after edge flip (left).\n");
8753 }
8754 if (counterclockwise(m, b, newvertex, rightvertex, farvertex) <
8755 0.0) {
8756 printf("Internal error in insertvertex():\n");
8757 printf(" Clockwise triangle after edge flip (right).\n");
8758 }
8759 }
8760 #endif /* SELF_CHECK */
8761 if (b->verbose > 2) {
8762 printf(" Edge flip results in left ");
8763 lnextself(topleft);
8764 printtriangle(m, b, &topleft);
8765 printf(" and right ");
8766 printtriangle(m, b, &horiz);
8767 }
8768 /* On the next iterations, consider the two edges that were */
8769 /* exposed (this is, are now visible to the newly inserted */
8770 /* vertex) by the edge flip. */
8771 lprevself(horiz);
8772 leftvertex = farvertex;
8773 }
8774 }
8775 }
8776 if (!doflip) {
8777 /* The handle `horiz' is accepted as locally Delaunay. */
8778 #ifndef CDT_ONLY
8779 if (triflaws) {
8780 /* Check the triangle `horiz' for quality. */
8781 testtriangle(m, b, &horiz);
8782 }
8783 #endif /* not CDT_ONLY */
8784 /* Look for the next edge around the newly inserted vertex. */
8785 lnextself(horiz);
8786 sym(horiz, testtri);
8787 /* Check for finishing a complete revolution about the new vertex, or */
8788 /* falling outside of the triangulation. The latter will happen */
8789 /* when a vertex is inserted at a boundary. */
8790 if ((leftvertex == first) || (testtri.tri == m->dummytri)) {
8791 /* We're done. Return a triangle whose origin is the new vertex. */
8792 lnext(horiz, *searchtri);
8793 lnext(horiz, m->recenttri);
8794 return success;
8795 }
8796 /* Finish finding the next edge around the newly inserted vertex. */
8797 lnext(testtri, horiz);
8798 rightvertex = leftvertex;
8799 dest(horiz, leftvertex);
8800 }
8801 }
8802 }
8803
8804 /*****************************************************************************/
8805 /* */
8806 /* triangulatepolygon() Find the Delaunay triangulation of a polygon that */
8807 /* has a certain "nice" shape. This includes the */
8808 /* polygons that result from deletion of a vertex or */
8809 /* insertion of a segment. */
8810 /* */
8811 /* This is a conceptually difficult routine. The starting assumption is */
8812 /* that we have a polygon with n sides. n - 1 of these sides are currently */
8813 /* represented as edges in the mesh. One side, called the "base", need not */
8814 /* be. */
8815 /* */
8816 /* Inside the polygon is a structure I call a "fan", consisting of n - 1 */
8817 /* triangles that share a common origin. For each of these triangles, the */
8818 /* edge opposite the origin is one of the sides of the polygon. The */
8819 /* primary edge of each triangle is the edge directed from the origin to */
8820 /* the destination; note that this is not the same edge that is a side of */
8821 /* the polygon. `firstedge' is the primary edge of the first triangle. */
8822 /* From there, the triangles follow in counterclockwise order about the */
8823 /* polygon, until `lastedge', the primary edge of the last triangle. */
8824 /* `firstedge' and `lastedge' are probably connected to other triangles */
8825 /* beyond the extremes of the fan, but their identity is not important, as */
8826 /* long as the fan remains connected to them. */
8827 /* */
8828 /* Imagine the polygon oriented so that its base is at the bottom. This */
8829 /* puts `firstedge' on the far right, and `lastedge' on the far left. */
8830 /* The right vertex of the base is the destination of `firstedge', and the */
8831 /* left vertex of the base is the apex of `lastedge'. */
8832 /* */
8833 /* The challenge now is to find the right sequence of edge flips to */
8834 /* transform the fan into a Delaunay triangulation of the polygon. Each */
8835 /* edge flip effectively removes one triangle from the fan, committing it */
8836 /* to the polygon. The resulting polygon has one fewer edge. If `doflip' */
8837 /* is set, the final flip will be performed, resulting in a fan of one */
8838 /* (useless?) triangle. If `doflip' is not set, the final flip is not */
8839 /* performed, resulting in a fan of two triangles, and an unfinished */
8840 /* triangular polygon that is not yet filled out with a single triangle. */
8841 /* On completion of the routine, `lastedge' is the last remaining triangle, */
8842 /* or the leftmost of the last two. */
8843 /* */
8844 /* Although the flips are performed in the order described above, the */
8845 /* decisions about what flips to perform are made in precisely the reverse */
8846 /* order. The recursive triangulatepolygon() procedure makes a decision, */
8847 /* uses up to two recursive calls to triangulate the "subproblems" */
8848 /* (polygons with fewer edges), and then performs an edge flip. */
8849 /* */
8850 /* The "decision" it makes is which vertex of the polygon should be */
8851 /* connected to the base. This decision is made by testing every possible */
8852 /* vertex. Once the best vertex is found, the two edges that connect this */
8853 /* vertex to the base become the bases for two smaller polygons. These */
8854 /* are triangulated recursively. Unfortunately, this approach can take */
8855 /* O(n^2) time not only in the worst case, but in many common cases. It's */
8856 /* rarely a big deal for vertex deletion, where n is rarely larger than */
8857 /* ten, but it could be a big deal for segment insertion, especially if */
8858 /* there's a lot of long segments that each cut many triangles. I ought to */
8859 /* code a faster algorithm some day. */
8860 /* */
8861 /* The `edgecount' parameter is the number of sides of the polygon, */
8862 /* including its base. `triflaws' is a flag that determines whether the */
8863 /* new triangles should be tested for quality, and enqueued if they are */
8864 /* bad. */
8865 /* */
8866 /*****************************************************************************/
8867
8868 #ifdef ANSI_DECLARATORS
8869 void triangulatepolygon(struct mesh *m, struct behavior *b,
8870 struct otri *firstedge, struct otri *lastedge,
8871 int edgecount, int doflip, int triflaws)
8872 #else /* not ANSI_DECLARATORS */
8873 void triangulatepolygon(m, b, firstedge, lastedge, edgecount, doflip, triflaws)
8874 struct mesh *m;
8875 struct behavior *b;
8876 struct otri *firstedge;
8877 struct otri *lastedge;
8878 int edgecount;
8879 int doflip;
8880 int triflaws;
8881 #endif /* not ANSI_DECLARATORS */
8882
8883 {
8884 struct otri testtri;
8885 struct otri besttri;
8886 struct otri tempedge;
8887 vertex leftbasevertex, rightbasevertex;
8888 vertex testvertex;
8889 vertex bestvertex;
8890 int bestnumber;
8891 int i;
8892 triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */
8893
8894 /* Identify the base vertices. */
8895 apex(*lastedge, leftbasevertex);
8896 dest(*firstedge, rightbasevertex);
8897 if (b->verbose > 2) {
8898 printf(" Triangulating interior polygon at edge\n");
8899 printf(" (%.12g, %.12g) (%.12g, %.12g)\n", (double)leftbasevertex[0],
8900 (double)leftbasevertex[1], (double)rightbasevertex[0], (double)rightbasevertex[1]);
8901 }
8902 /* Find the best vertex to connect the base to. */
8903 onext(*firstedge, besttri);
8904 dest(besttri, bestvertex);
8905 otricopy(besttri, testtri);
8906 bestnumber = 1;
8907 for (i = 2; i <= edgecount - 2; i++) {
8908 onextself(testtri);
8909 dest(testtri, testvertex);
8910 /* Is this a better vertex? */
8911 if (incircle(m, b, leftbasevertex, rightbasevertex, bestvertex,
8912 testvertex) > 0.0) {
8913 otricopy(testtri, besttri);
8914 bestvertex = testvertex;
8915 bestnumber = i;
8916 }
8917 }
8918 if (b->verbose > 2) {
8919 printf(" Connecting edge to (%.12g, %.12g)\n", (double)bestvertex[0],
8920 (double)bestvertex[1]);
8921 }
8922 if (bestnumber > 1) {
8923 /* Recursively triangulate the smaller polygon on the right. */
8924 oprev(besttri, tempedge);
8925 triangulatepolygon(m, b, firstedge, &tempedge, bestnumber + 1, 1,
8926 triflaws);
8927 }
8928 if (bestnumber < edgecount - 2) {
8929 /* Recursively triangulate the smaller polygon on the left. */
8930 sym(besttri, tempedge);
8931 triangulatepolygon(m, b, &besttri, lastedge, edgecount - bestnumber, 1,
8932 triflaws);
8933 /* Find `besttri' again; it may have been lost to edge flips. */
8934 sym(tempedge, besttri);
8935 }
8936 if (doflip) {
8937 /* Do one final edge flip. */
8938 flip(m, b, &besttri);
8939 #ifndef CDT_ONLY
8940 if (triflaws) {
8941 /* Check the quality of the newly committed triangle. */
8942 sym(besttri, testtri);
8943 testtriangle(m, b, &testtri);
8944 }
8945 #endif /* not CDT_ONLY */
8946 }
8947 /* Return the base triangle. */
8948 otricopy(besttri, *lastedge);
8949 }
8950
8951 /*****************************************************************************/
8952 /* */
8953 /* deletevertex() Delete a vertex from a Delaunay triangulation, ensuring */
8954 /* that the triangulation remains Delaunay. */
8955 /* */
8956 /* The origin of `deltri' is deleted. The union of the triangles adjacent */
8957 /* to this vertex is a polygon, for which the Delaunay triangulation is */
8958 /* found. Two triangles are removed from the mesh. */
8959 /* */
8960 /* Only interior vertices that do not lie on segments or boundaries may be */
8961 /* deleted. */
8962 /* */
8963 /*****************************************************************************/
8964
8965 #ifndef CDT_ONLY
8966
8967 #ifdef ANSI_DECLARATORS
8968 void deletevertex(struct mesh *m, struct behavior *b, struct otri *deltri)
8969 #else /* not ANSI_DECLARATORS */
8970 void deletevertex(m, b, deltri)
8971 struct mesh *m;
8972 struct behavior *b;
8973 struct otri *deltri;
8974 #endif /* not ANSI_DECLARATORS */
8975
8976 {
8977 struct otri countingtri;
8978 struct otri firstedge, lastedge;
8979 struct otri deltriright;
8980 struct otri lefttri, righttri;
8981 struct otri leftcasing, rightcasing;
8982 struct osub leftsubseg, rightsubseg;
8983 vertex delvertex;
8984 vertex neworg;
8985 int edgecount;
8986 triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */
8987 subseg sptr; /* Temporary variable used by tspivot(). */
8988
8989 org(*deltri, delvertex);
8990 if (b->verbose > 1) {
8991 printf(" Deleting (%.12g, %.12g).\n", (double)delvertex[0], (double)delvertex[1]);
8992 }
8993 vertexdealloc(m, delvertex);
8994
8995 /* Count the degree of the vertex being deleted. */
8996 onext(*deltri, countingtri);
8997 edgecount = 1;
8998 while (!otriequal(*deltri, countingtri)) {
8999 #ifdef SELF_CHECK
9000 if (countingtri.tri == m->dummytri) {
9001 printf("Internal error in deletevertex():\n");
9002 printf(" Attempt to delete boundary vertex.\n");
9003 internalerror();
9004 }
9005 #endif /* SELF_CHECK */
9006 edgecount++;
9007 onextself(countingtri);
9008 }
9009
9010 #ifdef SELF_CHECK
9011 if (edgecount < 3) {
9012 printf("Internal error in deletevertex():\n Vertex has degree %d.\n",
9013 edgecount);
9014 internalerror();
9015 }
9016 #endif /* SELF_CHECK */
9017 if (edgecount > 3) {
9018 /* Triangulate the polygon defined by the union of all triangles */
9019 /* adjacent to the vertex being deleted. Check the quality of */
9020 /* the resulting triangles. */
9021 onext(*deltri, firstedge);
9022 oprev(*deltri, lastedge);
9023 triangulatepolygon(m, b, &firstedge, &lastedge, edgecount, 0,
9024 !b->nobisect);
9025 }
9026 /* Splice out two triangles. */
9027 lprev(*deltri, deltriright);
9028 dnext(*deltri, lefttri);
9029 sym(lefttri, leftcasing);
9030 oprev(deltriright, righttri);
9031 sym(righttri, rightcasing);
9032 bond(*deltri, leftcasing);
9033 bond(deltriright, rightcasing);
9034 tspivot(lefttri, leftsubseg);
9035 if (leftsubseg.ss != m->dummysub) {
9036 tsbond(*deltri, leftsubseg);
9037 }
9038 tspivot(righttri, rightsubseg);
9039 if (rightsubseg.ss != m->dummysub) {
9040 tsbond(deltriright, rightsubseg);
9041 }
9042
9043 /* Set the new origin of `deltri' and check its quality. */
9044 org(lefttri, neworg);
9045 setorg(*deltri, neworg);
9046 if (!b->nobisect) {
9047 testtriangle(m, b, deltri);
9048 }
9049
9050 /* Delete the two spliced-out triangles. */
9051 triangledealloc(m, lefttri.tri);
9052 triangledealloc(m, righttri.tri);
9053 }
9054
9055 #endif /* not CDT_ONLY */
9056
9057 /*****************************************************************************/
9058 /* */
9059 /* undovertex() Undo the most recent vertex insertion. */
9060 /* */
9061 /* Walks through the list of transformations (flips and a vertex insertion) */
9062 /* in the reverse of the order in which they were done, and undoes them. */
9063 /* The inserted vertex is removed from the triangulation and deallocated. */
9064 /* Two triangles (possibly just one) are also deallocated. */
9065 /* */
9066 /*****************************************************************************/
9067
9068 #ifndef CDT_ONLY
9069
9070 #ifdef ANSI_DECLARATORS
9071 void undovertex(struct mesh *m, struct behavior *b)
9072 #else /* not ANSI_DECLARATORS */
9073 void undovertex(m, b)
9074 struct mesh *m;
9075 struct behavior *b;
9076 #endif /* not ANSI_DECLARATORS */
9077
9078 {
9079 struct otri fliptri;
9080 struct otri botleft, botright, topright;
9081 struct otri botlcasing, botrcasing, toprcasing;
9082 struct otri gluetri;
9083 struct osub botlsubseg, botrsubseg, toprsubseg;
9084 vertex botvertex, rightvertex;
9085 triangle ptr; /* Temporary variable used by sym(). */
9086 subseg sptr; /* Temporary variable used by tspivot(). */
9087
9088 /* Walk through the list of transformations (flips and a vertex insertion) */
9089 /* in the reverse of the order in which they were done, and undo them. */
9090 while (m->lastflip != (struct flipstacker *) NULL) {
9091 /* Find a triangle involved in the last unreversed transformation. */
9092 decode(m->lastflip->flippedtri, fliptri);
9093
9094 /* We are reversing one of three transformations: a trisection of one */
9095 /* triangle into three (by inserting a vertex in the triangle), a */
9096 /* bisection of two triangles into four (by inserting a vertex in an */
9097 /* edge), or an edge flip. */
9098 if (m->lastflip->prevflip == (struct flipstacker *) NULL) {
9099 /* Restore a triangle that was split into three triangles, */
9100 /* so it is again one triangle. */
9101 dprev(fliptri, botleft);
9102 lnextself(botleft);
9103 onext(fliptri, botright);
9104 lprevself(botright);
9105 sym(botleft, botlcasing);
9106 sym(botright, botrcasing);
9107 dest(botleft, botvertex);
9108
9109 setapex(fliptri, botvertex);
9110 lnextself(fliptri);
9111 bond(fliptri, botlcasing);
9112 tspivot(botleft, botlsubseg);
9113 tsbond(fliptri, botlsubseg);
9114 lnextself(fliptri);
9115 bond(fliptri, botrcasing);
9116 tspivot(botright, botrsubseg);
9117 tsbond(fliptri, botrsubseg);
9118
9119 /* Delete the two spliced-out triangles. */
9120 triangledealloc(m, botleft.tri);
9121 triangledealloc(m, botright.tri);
9122 } else if (m->lastflip->prevflip == (struct flipstacker *) &insertvertex) {
9123 /* Restore two triangles that were split into four triangles, */
9124 /* so they are again two triangles. */
9125 lprev(fliptri, gluetri);
9126 sym(gluetri, botright);
9127 lnextself(botright);
9128 sym(botright, botrcasing);
9129 dest(botright, rightvertex);
9130
9131 setorg(fliptri, rightvertex);
9132 bond(gluetri, botrcasing);
9133 tspivot(botright, botrsubseg);
9134 tsbond(gluetri, botrsubseg);
9135
9136 /* Delete the spliced-out triangle. */
9137 triangledealloc(m, botright.tri);
9138
9139 sym(fliptri, gluetri);
9140 if (gluetri.tri != m->dummytri) {
9141 lnextself(gluetri);
9142 dnext(gluetri, topright);
9143 sym(topright, toprcasing);
9144
9145 setorg(gluetri, rightvertex);
9146 bond(gluetri, toprcasing);
9147 tspivot(topright, toprsubseg);
9148 tsbond(gluetri, toprsubseg);
9149
9150 /* Delete the spliced-out triangle. */
9151 triangledealloc(m, topright.tri);
9152 }
9153
9154 /* This is the end of the list, sneakily encoded. */
9155 m->lastflip->prevflip = (struct flipstacker *) NULL;
9156 } else {
9157 /* Undo an edge flip. */
9158 unflip(m, b, &fliptri);
9159 }
9160
9161 /* Go on and process the next transformation. */
9162 m->lastflip = m->lastflip->prevflip;
9163 }
9164 }
9165
9166 #endif /* not CDT_ONLY */
9167
9168 /** **/
9169 /** **/
9170 /********* Mesh transformation routines end here *********/
9171
9172 /********* Divide-and-conquer Delaunay triangulation begins here *********/
9173 /** **/
9174 /** **/
9175
9176 /*****************************************************************************/
9177 /* */
9178 /* The divide-and-conquer bounding box */
9179 /* */
9180 /* I originally implemented the divide-and-conquer and incremental Delaunay */
9181 /* triangulations using the edge-based data structure presented by Guibas */
9182 /* and Stolfi. Switching to a triangle-based data structure doubled the */
9183 /* speed. However, I had to think of a few extra tricks to maintain the */
9184 /* elegance of the original algorithms. */
9185 /* */
9186 /* The "bounding box" used by my variant of the divide-and-conquer */
9187 /* algorithm uses one triangle for each edge of the convex hull of the */
9188 /* triangulation. These bounding triangles all share a common apical */
9189 /* vertex, which is represented by NULL and which represents nothing. */
9190 /* The bounding triangles are linked in a circular fan about this NULL */
9191 /* vertex, and the edges on the convex hull of the triangulation appear */
9192 /* opposite the NULL vertex. You might find it easiest to imagine that */
9193 /* the NULL vertex is a point in 3D space behind the center of the */
9194 /* triangulation, and that the bounding triangles form a sort of cone. */
9195 /* */
9196 /* This bounding box makes it easy to represent degenerate cases. For */
9197 /* instance, the triangulation of two vertices is a single edge. This edge */
9198 /* is represented by two bounding box triangles, one on each "side" of the */
9199 /* edge. These triangles are also linked together in a fan about the NULL */
9200 /* vertex. */
9201 /* */
9202 /* The bounding box also makes it easy to traverse the convex hull, as the */
9203 /* divide-and-conquer algorithm needs to do. */
9204 /* */
9205 /*****************************************************************************/
9206
9207 /*****************************************************************************/
9208 /* */
9209 /* vertexsort() Sort an array of vertices by x-coordinate, using the */
9210 /* y-coordinate as a secondary key. */
9211 /* */
9212 /* Uses quicksort. Randomized O(n log n) time. No, I did not make any of */
9213 /* the usual quicksort mistakes. */
9214 /* */
9215 /*****************************************************************************/
9216
9217 #ifdef ANSI_DECLARATORS
9218 void vertexsort(vertex *sortarray, int arraysize)
9219 #else /* not ANSI_DECLARATORS */
9220 void vertexsort(sortarray, arraysize)
9221 vertex *sortarray;
9222 int arraysize;
9223 #endif /* not ANSI_DECLARATORS */
9224
9225 {
9226 int left, right;
9227 int pivot;
9228 REAL pivotx, pivoty;
9229 vertex temp;
9230
9231 if (arraysize == 2) {
9232 /* Recursive base case. */
9233 if ((sortarray[0][0] > sortarray[1][0]) ||
9234 ((sortarray[0][0] == sortarray[1][0]) &&
9235 (sortarray[0][1] > sortarray[1][1]))) {
9236 temp = sortarray[1];
9237 sortarray[1] = sortarray[0];
9238 sortarray[0] = temp;
9239 }
9240 return;
9241 }
9242 /* Choose a random pivot to split the array. */
9243 pivot = (int) randomnation((unsigned int) arraysize);
9244 pivotx = sortarray[pivot][0];
9245 pivoty = sortarray[pivot][1];
9246 /* Split the array. */
9247 left = -1;
9248 right = arraysize;
9249 while (left < right) {
9250 /* Search for a vertex whose x-coordinate is too large for the left. */
9251 do {
9252 left++;
9253 } while ((left <= right) && ((sortarray[left][0] < pivotx) ||
9254 ((sortarray[left][0] == pivotx) &&
9255 (sortarray[left][1] < pivoty))));
9256 /* Search for a vertex whose x-coordinate is too small for the right. */
9257 do {
9258 right--;
9259 } while ((left <= right) && ((sortarray[right][0] > pivotx) ||
9260 ((sortarray[right][0] == pivotx) &&
9261 (sortarray[right][1] > pivoty))));
9262 if (left < right) {
9263 /* Swap the left and right vertices. */
9264 temp = sortarray[left];
9265 sortarray[left] = sortarray[right];
9266 sortarray[right] = temp;
9267 }
9268 }
9269 if (left > 1) {
9270 /* Recursively sort the left subset. */
9271 vertexsort(sortarray, left);
9272 }
9273 if (right < arraysize - 2) {
9274 /* Recursively sort the right subset. */
9275 vertexsort(&sortarray[right + 1], arraysize - right - 1);
9276 }
9277 }
9278
9279 /*****************************************************************************/
9280 /* */
9281 /* vertexmedian() An order statistic algorithm, almost. Shuffles an */
9282 /* array of vertices so that the first `median' vertices */
9283 /* occur lexicographically before the remaining vertices. */
9284 /* */
9285 /* Uses the x-coordinate as the primary key if axis == 0; the y-coordinate */
9286 /* if axis == 1. Very similar to the vertexsort() procedure, but runs in */
9287 /* randomized linear time. */
9288 /* */
9289 /*****************************************************************************/
9290
9291 #ifdef ANSI_DECLARATORS
9292 void vertexmedian(vertex *sortarray, int arraysize, int median, int axis)
9293 #else /* not ANSI_DECLARATORS */
9294 void vertexmedian(sortarray, arraysize, median, axis)
9295 vertex *sortarray;
9296 int arraysize;
9297 int median;
9298 int axis;
9299 #endif /* not ANSI_DECLARATORS */
9300
9301 {
9302 int left, right;
9303 int pivot;
9304 REAL pivot1, pivot2;
9305 vertex temp;
9306
9307 if (arraysize == 2) {
9308 /* Recursive base case. */
9309 if ((sortarray[0][axis] > sortarray[1][axis]) ||
9310 ((sortarray[0][axis] == sortarray[1][axis]) &&
9311 (sortarray[0][1 - axis] > sortarray[1][1 - axis]))) {
9312 temp = sortarray[1];
9313 sortarray[1] = sortarray[0];
9314 sortarray[0] = temp;
9315 }
9316 return;
9317 }
9318 /* Choose a random pivot to split the array. */
9319 pivot = (int) randomnation((unsigned int) arraysize);
9320 pivot1 = sortarray[pivot][axis];
9321 pivot2 = sortarray[pivot][1 - axis];
9322 /* Split the array. */
9323 left = -1;
9324 right = arraysize;
9325 while (left < right) {
9326 /* Search for a vertex whose x-coordinate is too large for the left. */
9327 do {
9328 left++;
9329 } while ((left <= right) && ((sortarray[left][axis] < pivot1) ||
9330 ((sortarray[left][axis] == pivot1) &&
9331 (sortarray[left][1 - axis] < pivot2))));
9332 /* Search for a vertex whose x-coordinate is too small for the right. */
9333 do {
9334 right--;
9335 } while ((left <= right) && ((sortarray[right][axis] > pivot1) ||
9336 ((sortarray[right][axis] == pivot1) &&
9337 (sortarray[right][1 - axis] > pivot2))));
9338 if (left < right) {
9339 /* Swap the left and right vertices. */
9340 temp = sortarray[left];
9341 sortarray[left] = sortarray[right];
9342 sortarray[right] = temp;
9343 }
9344 }
9345 /* Unlike in vertexsort(), at most one of the following */
9346 /* conditionals is true. */
9347 if (left > median) {
9348 /* Recursively shuffle the left subset. */
9349 vertexmedian(sortarray, left, median, axis);
9350 }
9351 if (right < median - 1) {
9352 /* Recursively shuffle the right subset. */
9353 vertexmedian(&sortarray[right + 1], arraysize - right - 1,
9354 median - right - 1, axis);
9355 }
9356 }
9357
9358 /*****************************************************************************/
9359 /* */
9360 /* alternateaxes() Sorts the vertices as appropriate for the divide-and- */
9361 /* conquer algorithm with alternating cuts. */
9362 /* */
9363 /* Partitions by x-coordinate if axis == 0; by y-coordinate if axis == 1. */
9364 /* For the base case, subsets containing only two or three vertices are */
9365 /* always sorted by x-coordinate. */
9366 /* */
9367 /*****************************************************************************/
9368
9369 #ifdef ANSI_DECLARATORS
9370 void alternateaxes(vertex *sortarray, int arraysize, int axis)
9371 #else /* not ANSI_DECLARATORS */
9372 void alternateaxes(sortarray, arraysize, axis)
9373 vertex *sortarray;
9374 int arraysize;
9375 int axis;
9376 #endif /* not ANSI_DECLARATORS */
9377
9378 {
9379 int divider;
9380
9381 divider = arraysize >> 1;
9382 if (arraysize <= 3) {
9383 /* Recursive base case: subsets of two or three vertices will be */
9384 /* handled specially, and should always be sorted by x-coordinate. */
9385 axis = 0;
9386 }
9387 /* Partition with a horizontal or vertical cut. */
9388 vertexmedian(sortarray, arraysize, divider, axis);
9389 /* Recursively partition the subsets with a cross cut. */
9390 if (arraysize - divider >= 2) {
9391 if (divider >= 2) {
9392 alternateaxes(sortarray, divider, 1 - axis);
9393 }
9394 alternateaxes(&sortarray[divider], arraysize - divider, 1 - axis);
9395 }
9396 }
9397
9398 /*****************************************************************************/
9399 /* */
9400 /* mergehulls() Merge two adjacent Delaunay triangulations into a */
9401 /* single Delaunay triangulation. */
9402 /* */
9403 /* This is similar to the algorithm given by Guibas and Stolfi, but uses */
9404 /* a triangle-based, rather than edge-based, data structure. */
9405 /* */
9406 /* The algorithm walks up the gap between the two triangulations, knitting */
9407 /* them together. As they are merged, some of their bounding triangles */
9408 /* are converted into real triangles of the triangulation. The procedure */
9409 /* pulls each hull's bounding triangles apart, then knits them together */
9410 /* like the teeth of two gears. The Delaunay property determines, at each */
9411 /* step, whether the next "tooth" is a bounding triangle of the left hull */
9412 /* or the right. When a bounding triangle becomes real, its apex is */
9413 /* changed from NULL to a real vertex. */
9414 /* */
9415 /* Only two new triangles need to be allocated. These become new bounding */
9416 /* triangles at the top and bottom of the seam. They are used to connect */
9417 /* the remaining bounding triangles (those that have not been converted */
9418 /* into real triangles) into a single fan. */
9419 /* */
9420 /* On entry, `farleft' and `innerleft' are bounding triangles of the left */
9421 /* triangulation. The origin of `farleft' is the leftmost vertex, and */
9422 /* the destination of `innerleft' is the rightmost vertex of the */
9423 /* triangulation. Similarly, `innerright' and `farright' are bounding */
9424 /* triangles of the right triangulation. The origin of `innerright' and */
9425 /* destination of `farright' are the leftmost and rightmost vertices. */
9426 /* */
9427 /* On completion, the origin of `farleft' is the leftmost vertex of the */
9428 /* merged triangulation, and the destination of `farright' is the rightmost */
9429 /* vertex. */
9430 /* */
9431 /*****************************************************************************/
9432
9433 #ifdef ANSI_DECLARATORS
9434 void mergehulls(struct mesh *m, struct behavior *b, struct otri *farleft,
9435 struct otri *innerleft, struct otri *innerright,
9436 struct otri *farright, int axis)
9437 #else /* not ANSI_DECLARATORS */
9438 void mergehulls(m, b, farleft, innerleft, innerright, farright, axis)
9439 struct mesh *m;
9440 struct behavior *b;
9441 struct otri *farleft;
9442 struct otri *innerleft;
9443 struct otri *innerright;
9444 struct otri *farright;
9445 int axis;
9446 #endif /* not ANSI_DECLARATORS */
9447
9448 {
9449 struct otri leftcand, rightcand;
9450 struct otri baseedge;
9451 struct otri nextedge;
9452 struct otri sidecasing, topcasing, outercasing;
9453 struct otri checkedge;
9454 vertex innerleftdest;
9455 vertex innerrightorg;
9456 vertex innerleftapex, innerrightapex;
9457 vertex farleftpt, farrightpt;
9458 vertex farleftapex, farrightapex;
9459 vertex lowerleft, lowerright;
9460 vertex upperleft, upperright;
9461 vertex nextapex;
9462 vertex checkvertex;
9463 int changemade;
9464 int badedge;
9465 int leftfinished, rightfinished;
9466 triangle ptr; /* Temporary variable used by sym(). */
9467
9468 dest(*innerleft, innerleftdest);
9469 apex(*innerleft, innerleftapex);
9470 org(*innerright, innerrightorg);
9471 apex(*innerright, innerrightapex);
9472 /* Special treatment for horizontal cuts. */
9473 if (b->dwyer && (axis == 1)) {
9474 org(*farleft, farleftpt);
9475 apex(*farleft, farleftapex);
9476 dest(*farright, farrightpt);
9477 apex(*farright, farrightapex);
9478 /* The pointers to the extremal vertices are shifted to point to the */
9479 /* topmost and bottommost vertex of each hull, rather than the */
9480 /* leftmost and rightmost vertices. */
9481 while (farleftapex[1] < farleftpt[1]) {
9482 lnextself(*farleft);
9483 symself(*farleft);
9484 farleftpt = farleftapex;
9485 apex(*farleft, farleftapex);
9486 }
9487 sym(*innerleft, checkedge);
9488 apex(checkedge, checkvertex);
9489 while (checkvertex[1] > innerleftdest[1]) {
9490 lnext(checkedge, *innerleft);
9491 innerleftapex = innerleftdest;
9492 innerleftdest = checkvertex;
9493 sym(*innerleft, checkedge);
9494 apex(checkedge, checkvertex);
9495 }
9496 while (innerrightapex[1] < innerrightorg[1]) {
9497 lnextself(*innerright);
9498 symself(*innerright);
9499 innerrightorg = innerrightapex;
9500 apex(*innerright, innerrightapex);
9501 }
9502 sym(*farright, checkedge);
9503 apex(checkedge, checkvertex);
9504 while (checkvertex[1] > farrightpt[1]) {
9505 lnext(checkedge, *farright);
9506 farrightapex = farrightpt;
9507 farrightpt = checkvertex;
9508 sym(*farright, checkedge);
9509 apex(checkedge, checkvertex);
9510 }
9511 }
9512 /* Find a line tangent to and below both hulls. */
9513 do {
9514 changemade = 0;
9515 /* Make innerleftdest the "bottommost" vertex of the left hull. */
9516 if (counterclockwise(m, b, innerleftdest, innerleftapex, innerrightorg) >
9517 0.0) {
9518 lprevself(*innerleft);
9519 symself(*innerleft);
9520 innerleftdest = innerleftapex;
9521 apex(*innerleft, innerleftapex);
9522 changemade = 1;
9523 }
9524 /* Make innerrightorg the "bottommost" vertex of the right hull. */
9525 if (counterclockwise(m, b, innerrightapex, innerrightorg, innerleftdest) >
9526 0.0) {
9527 lnextself(*innerright);
9528 symself(*innerright);
9529 innerrightorg = innerrightapex;
9530 apex(*innerright, innerrightapex);
9531 changemade = 1;
9532 }
9533 } while (changemade);
9534 /* Find the two candidates to be the next "gear tooth." */
9535 sym(*innerleft, leftcand);
9536 sym(*innerright, rightcand);
9537 /* Create the bottom new bounding triangle. */
9538 maketriangle(m, b, &baseedge);
9539 /* Connect it to the bounding boxes of the left and right triangulations. */
9540 bond(baseedge, *innerleft);
9541 lnextself(baseedge);
9542 bond(baseedge, *innerright);
9543 lnextself(baseedge);
9544 setorg(baseedge, innerrightorg);
9545 setdest(baseedge, innerleftdest);
9546 /* Apex is intentionally left NULL. */
9547 if (b->verbose > 2) {
9548 printf(" Creating base bounding ");
9549 printtriangle(m, b, &baseedge);
9550 }
9551 /* Fix the extreme triangles if necessary. */
9552 org(*farleft, farleftpt);
9553 if (innerleftdest == farleftpt) {
9554 lnext(baseedge, *farleft);
9555 }
9556 dest(*farright, farrightpt);
9557 if (innerrightorg == farrightpt) {
9558 lprev(baseedge, *farright);
9559 }
9560 /* The vertices of the current knitting edge. */
9561 lowerleft = innerleftdest;
9562 lowerright = innerrightorg;
9563 /* The candidate vertices for knitting. */
9564 apex(leftcand, upperleft);
9565 apex(rightcand, upperright);
9566 /* Walk up the gap between the two triangulations, knitting them together. */
9567 while (1) {
9568 /* Have we reached the top? (This isn't quite the right question, */
9569 /* because even though the left triangulation might seem finished now, */
9570 /* moving up on the right triangulation might reveal a new vertex of */
9571 /* the left triangulation. And vice-versa.) */
9572 leftfinished = counterclockwise(m, b, upperleft, lowerleft, lowerright) <=
9573 0.0;
9574 rightfinished = counterclockwise(m, b, upperright, lowerleft, lowerright)
9575 <= 0.0;
9576 if (leftfinished && rightfinished) {
9577 /* Create the top new bounding triangle. */
9578 maketriangle(m, b, &nextedge);
9579 setorg(nextedge, lowerleft);
9580 setdest(nextedge, lowerright);
9581 /* Apex is intentionally left NULL. */
9582 /* Connect it to the bounding boxes of the two triangulations. */
9583 bond(nextedge, baseedge);
9584 lnextself(nextedge);
9585 bond(nextedge, rightcand);
9586 lnextself(nextedge);
9587 bond(nextedge, leftcand);
9588 if (b->verbose > 2) {
9589 printf(" Creating top bounding ");
9590 printtriangle(m, b, &nextedge);
9591 }
9592 /* Special treatment for horizontal cuts. */
9593 if (b->dwyer && (axis == 1)) {
9594 org(*farleft, farleftpt);
9595 apex(*farleft, farleftapex);
9596 dest(*farright, farrightpt);
9597 apex(*farright, farrightapex);
9598 sym(*farleft, checkedge);
9599 apex(checkedge, checkvertex);
9600 /* The pointers to the extremal vertices are restored to the */
9601 /* leftmost and rightmost vertices (rather than topmost and */
9602 /* bottommost). */
9603 while (checkvertex[0] < farleftpt[0]) {
9604 lprev(checkedge, *farleft);
9605 farleftapex = farleftpt;
9606 farleftpt = checkvertex;
9607 sym(*farleft, checkedge);
9608 apex(checkedge, checkvertex);
9609 }
9610 while (farrightapex[0] > farrightpt[0]) {
9611 lprevself(*farright);
9612 symself(*farright);
9613 farrightpt = farrightapex;
9614 apex(*farright, farrightapex);
9615 }
9616 }
9617 return;
9618 }
9619 /* Consider eliminating edges from the left triangulation. */
9620 if (!leftfinished) {
9621 /* What vertex would be exposed if an edge were deleted? */
9622 lprev(leftcand, nextedge);
9623 symself(nextedge);
9624 apex(nextedge, nextapex);
9625 /* If nextapex is NULL, then no vertex would be exposed; the */
9626 /* triangulation would have been eaten right through. */
9627 if (nextapex != (vertex) NULL) {
9628 /* Check whether the edge is Delaunay. */
9629 badedge = incircle(m, b, lowerleft, lowerright, upperleft, nextapex) >
9630 0.0;
9631 while (badedge) {
9632 /* Eliminate the edge with an edge flip. As a result, the */
9633 /* left triangulation will have one more boundary triangle. */
9634 lnextself(nextedge);
9635 sym(nextedge, topcasing);
9636 lnextself(nextedge);
9637 sym(nextedge, sidecasing);
9638 bond(nextedge, topcasing);
9639 bond(leftcand, sidecasing);
9640 lnextself(leftcand);
9641 sym(leftcand, outercasing);
9642 lprevself(nextedge);
9643 bond(nextedge, outercasing);
9644 /* Correct the vertices to reflect the edge flip. */
9645 setorg(leftcand, lowerleft);
9646 setdest(leftcand, NULL);
9647 setapex(leftcand, nextapex);
9648 setorg(nextedge, NULL);
9649 setdest(nextedge, upperleft);
9650 setapex(nextedge, nextapex);
9651 /* Consider the newly exposed vertex. */
9652 upperleft = nextapex;
9653 /* What vertex would be exposed if another edge were deleted? */
9654 otricopy(sidecasing, nextedge);
9655 apex(nextedge, nextapex);
9656 if (nextapex != (vertex) NULL) {
9657 /* Check whether the edge is Delaunay. */
9658 badedge = incircle(m, b, lowerleft, lowerright, upperleft,
9659 nextapex) > 0.0;
9660 } else {
9661 /* Avoid eating right through the triangulation. */
9662 badedge = 0;
9663 }
9664 }
9665 }
9666 }
9667 /* Consider eliminating edges from the right triangulation. */
9668 if (!rightfinished) {
9669 /* What vertex would be exposed if an edge were deleted? */
9670 lnext(rightcand, nextedge);
9671 symself(nextedge);
9672 apex(nextedge, nextapex);
9673 /* If nextapex is NULL, then no vertex would be exposed; the */
9674 /* triangulation would have been eaten right through. */
9675 if (nextapex != (vertex) NULL) {
9676 /* Check whether the edge is Delaunay. */
9677 badedge = incircle(m, b, lowerleft, lowerright, upperright, nextapex) >
9678 0.0;
9679 while (badedge) {
9680 /* Eliminate the edge with an edge flip. As a result, the */
9681 /* right triangulation will have one more boundary triangle. */
9682 lprevself(nextedge);
9683 sym(nextedge, topcasing);
9684 lprevself(nextedge);
9685 sym(nextedge, sidecasing);
9686 bond(nextedge, topcasing);
9687 bond(rightcand, sidecasing);
9688 lprevself(rightcand);
9689 sym(rightcand, outercasing);
9690 lnextself(nextedge);
9691 bond(nextedge, outercasing);
9692 /* Correct the vertices to reflect the edge flip. */
9693 setorg(rightcand, NULL);
9694 setdest(rightcand, lowerright);
9695 setapex(rightcand, nextapex);
9696 setorg(nextedge, upperright);
9697 setdest(nextedge, NULL);
9698 setapex(nextedge, nextapex);
9699 /* Consider the newly exposed vertex. */
9700 upperright = nextapex;
9701 /* What vertex would be exposed if another edge were deleted? */
9702 otricopy(sidecasing, nextedge);
9703 apex(nextedge, nextapex);
9704 if (nextapex != (vertex) NULL) {
9705 /* Check whether the edge is Delaunay. */
9706 badedge = incircle(m, b, lowerleft, lowerright, upperright,
9707 nextapex) > 0.0;
9708 } else {
9709 /* Avoid eating right through the triangulation. */
9710 badedge = 0;
9711 }
9712 }
9713 }
9714 }
9715 if (leftfinished || (!rightfinished &&
9716 (incircle(m, b, upperleft, lowerleft, lowerright, upperright) >
9717 0.0))) {
9718 /* Knit the triangulations, adding an edge from `lowerleft' */
9719 /* to `upperright'. */
9720 bond(baseedge, rightcand);
9721 lprev(rightcand, baseedge);
9722 setdest(baseedge, lowerleft);
9723 lowerright = upperright;
9724 sym(baseedge, rightcand);
9725 apex(rightcand, upperright);
9726 } else {
9727 /* Knit the triangulations, adding an edge from `upperleft' */
9728 /* to `lowerright'. */
9729 bond(baseedge, leftcand);
9730 lnext(leftcand, baseedge);
9731 setorg(baseedge, lowerright);
9732 lowerleft = upperleft;
9733 sym(baseedge, leftcand);
9734 apex(leftcand, upperleft);
9735 }
9736 if (b->verbose > 2) {
9737 printf(" Connecting ");
9738 printtriangle(m, b, &baseedge);
9739 }
9740 }
9741 }
9742
9743 /*****************************************************************************/
9744 /* */
9745 /* divconqrecurse() Recursively form a Delaunay triangulation by the */
9746 /* divide-and-conquer method. */
9747 /* */
9748 /* Recursively breaks down the problem into smaller pieces, which are */
9749 /* knitted together by mergehulls(). The base cases (problems of two or */
9750 /* three vertices) are handled specially here. */
9751 /* */
9752 /* On completion, `farleft' and `farright' are bounding triangles such that */
9753 /* the origin of `farleft' is the leftmost vertex (breaking ties by */
9754 /* choosing the highest leftmost vertex), and the destination of */
9755 /* `farright' is the rightmost vertex (breaking ties by choosing the */
9756 /* lowest rightmost vertex). */
9757 /* */
9758 /*****************************************************************************/
9759
9760 #ifdef ANSI_DECLARATORS
9761 void divconqrecurse(struct mesh *m, struct behavior *b, vertex *sortarray,
9762 int vertices, int axis,
9763 struct otri *farleft, struct otri *farright)
9764 #else /* not ANSI_DECLARATORS */
9765 void divconqrecurse(m, b, sortarray, vertices, axis, farleft, farright)
9766 struct mesh *m;
9767 struct behavior *b;
9768 vertex *sortarray;
9769 int vertices;
9770 int axis;
9771 struct otri *farleft;
9772 struct otri *farright;
9773 #endif /* not ANSI_DECLARATORS */
9774
9775 {
9776 struct otri midtri, tri1, tri2, tri3;
9777 struct otri innerleft, innerright;
9778 REAL area;
9779 int divider;
9780
9781 if (b->verbose > 2) {
9782 printf(" Triangulating %d vertices.\n", vertices);
9783 }
9784 if (vertices == 2) {
9785 /* The triangulation of two vertices is an edge. An edge is */
9786 /* represented by two bounding triangles. */
9787 maketriangle(m, b, farleft);
9788 setorg(*farleft, sortarray[0]);
9789 setdest(*farleft, sortarray[1]);
9790 /* The apex is intentionally left NULL. */
9791 maketriangle(m, b, farright);
9792 setorg(*farright, sortarray[1]);
9793 setdest(*farright, sortarray[0]);
9794 /* The apex is intentionally left NULL. */
9795 bond(*farleft, *farright);
9796 lprevself(*farleft);
9797 lnextself(*farright);
9798 bond(*farleft, *farright);
9799 lprevself(*farleft);
9800 lnextself(*farright);
9801 bond(*farleft, *farright);
9802 if (b->verbose > 2) {
9803 printf(" Creating ");
9804 printtriangle(m, b, farleft);
9805 printf(" Creating ");
9806 printtriangle(m, b, farright);
9807 }
9808 /* Ensure that the origin of `farleft' is sortarray[0]. */
9809 lprev(*farright, *farleft);
9810 return;
9811 } else if (vertices == 3) {
9812 /* The triangulation of three vertices is either a triangle (with */
9813 /* three bounding triangles) or two edges (with four bounding */
9814 /* triangles). In either case, four triangles are created. */
9815 maketriangle(m, b, &midtri);
9816 maketriangle(m, b, &tri1);
9817 maketriangle(m, b, &tri2);
9818 maketriangle(m, b, &tri3);
9819 area = counterclockwise(m, b, sortarray[0], sortarray[1], sortarray[2]);
9820 if (area == 0.0) {
9821 /* Three collinear vertices; the triangulation is two edges. */
9822 setorg(midtri, sortarray[0]);
9823 setdest(midtri, sortarray[1]);
9824 setorg(tri1, sortarray[1]);
9825 setdest(tri1, sortarray[0]);
9826 setorg(tri2, sortarray[2]);
9827 setdest(tri2, sortarray[1]);
9828 setorg(tri3, sortarray[1]);
9829 setdest(tri3, sortarray[2]);
9830 /* All apices are intentionally left NULL. */
9831 bond(midtri, tri1);
9832 bond(tri2, tri3);
9833 lnextself(midtri);
9834 lprevself(tri1);
9835 lnextself(tri2);
9836 lprevself(tri3);
9837 bond(midtri, tri3);
9838 bond(tri1, tri2);
9839 lnextself(midtri);
9840 lprevself(tri1);
9841 lnextself(tri2);
9842 lprevself(tri3);
9843 bond(midtri, tri1);
9844 bond(tri2, tri3);
9845 /* Ensure that the origin of `farleft' is sortarray[0]. */
9846 otricopy(tri1, *farleft);
9847 /* Ensure that the destination of `farright' is sortarray[2]. */
9848 otricopy(tri2, *farright);
9849 } else {
9850 /* The three vertices are not collinear; the triangulation is one */
9851 /* triangle, namely `midtri'. */
9852 setorg(midtri, sortarray[0]);
9853 setdest(tri1, sortarray[0]);
9854 setorg(tri3, sortarray[0]);
9855 /* Apices of tri1, tri2, and tri3 are left NULL. */
9856 if (area > 0.0) {
9857 /* The vertices are in counterclockwise order. */
9858 setdest(midtri, sortarray[1]);
9859 setorg(tri1, sortarray[1]);
9860 setdest(tri2, sortarray[1]);
9861 setapex(midtri, sortarray[2]);
9862 setorg(tri2, sortarray[2]);
9863 setdest(tri3, sortarray[2]);
9864 } else {
9865 /* The vertices are in clockwise order. */
9866 setdest(midtri, sortarray[2]);
9867 setorg(tri1, sortarray[2]);
9868 setdest(tri2, sortarray[2]);
9869 setapex(midtri, sortarray[1]);
9870 setorg(tri2, sortarray[1]);
9871 setdest(tri3, sortarray[1]);
9872 }
9873 /* The topology does not depend on how the vertices are ordered. */
9874 bond(midtri, tri1);
9875 lnextself(midtri);
9876 bond(midtri, tri2);
9877 lnextself(midtri);
9878 bond(midtri, tri3);
9879 lprevself(tri1);
9880 lnextself(tri2);
9881 bond(tri1, tri2);
9882 lprevself(tri1);
9883 lprevself(tri3);
9884 bond(tri1, tri3);
9885 lnextself(tri2);
9886 lprevself(tri3);
9887 bond(tri2, tri3);
9888 /* Ensure that the origin of `farleft' is sortarray[0]. */
9889 otricopy(tri1, *farleft);
9890 /* Ensure that the destination of `farright' is sortarray[2]. */
9891 if (area > 0.0) {
9892 otricopy(tri2, *farright);
9893 } else {
9894 lnext(*farleft, *farright);
9895 }
9896 }
9897 if (b->verbose > 2) {
9898 printf(" Creating ");
9899 printtriangle(m, b, &midtri);
9900 printf(" Creating ");
9901 printtriangle(m, b, &tri1);
9902 printf(" Creating ");
9903 printtriangle(m, b, &tri2);
9904 printf(" Creating ");
9905 printtriangle(m, b, &tri3);
9906 }
9907 return;
9908 } else {
9909 /* Split the vertices in half. */
9910 divider = vertices >> 1;
9911 /* Recursively triangulate each half. */
9912 divconqrecurse(m, b, sortarray, divider, 1 - axis, farleft, &innerleft);
9913 divconqrecurse(m, b, &sortarray[divider], vertices - divider, 1 - axis,
9914 &innerright, farright);
9915 if (b->verbose > 1) {
9916 printf(" Joining triangulations with %d and %d vertices.\n", divider,
9917 vertices - divider);
9918 }
9919 /* Merge the two triangulations into one. */
9920 mergehulls(m, b, farleft, &innerleft, &innerright, farright, axis);
9921 }
9922 }
9923
9924 #ifdef ANSI_DECLARATORS
9925 long removeghosts(struct mesh *m, struct behavior *b, struct otri *startghost)
9926 #else /* not ANSI_DECLARATORS */
9927 long removeghosts(m, b, startghost)
9928 struct mesh *m;
9929 struct behavior *b;
9930 struct otri *startghost;
9931 #endif /* not ANSI_DECLARATORS */
9932
9933 {
9934 struct otri searchedge;
9935 struct otri dissolveedge;
9936 struct otri deadtriangle;
9937 vertex markorg;
9938 long hullsize;
9939 triangle ptr; /* Temporary variable used by sym(). */
9940
9941 if (b->verbose) {
9942 printf(" Removing ghost triangles.\n");
9943 }
9944 /* Find an edge on the convex hull to start point location from. */
9945 lprev(*startghost, searchedge);
9946 symself(searchedge);
9947 m->dummytri[0] = encode(searchedge);
9948 /* Remove the bounding box and count the convex hull edges. */
9949 otricopy(*startghost, dissolveedge);
9950 hullsize = 0;
9951 do {
9952 hullsize++;
9953 lnext(dissolveedge, deadtriangle);
9954 lprevself(dissolveedge);
9955 symself(dissolveedge);
9956 /* If no PSLG is involved, set the boundary markers of all the vertices */
9957 /* on the convex hull. If a PSLG is used, this step is done later. */
9958 if (!b->poly) {
9959 /* Watch out for the case where all the input vertices are collinear. */
9960 if (dissolveedge.tri != m->dummytri) {
9961 org(dissolveedge, markorg);
9962 if (vertexmark(markorg) == 0) {
9963 setvertexmark(markorg, 1);
9964 }
9965 }
9966 }
9967 /* Remove a bounding triangle from a convex hull triangle. */
9968 dissolve(dissolveedge);
9969 /* Find the next bounding triangle. */
9970 sym(deadtriangle, dissolveedge);
9971 /* Delete the bounding triangle. */
9972 triangledealloc(m, deadtriangle.tri);
9973 } while (!otriequal(dissolveedge, *startghost));
9974 return hullsize;
9975 }
9976
9977 /*****************************************************************************/
9978 /* */
9979 /* divconqdelaunay() Form a Delaunay triangulation by the divide-and- */
9980 /* conquer method. */
9981 /* */
9982 /* Sorts the vertices, calls a recursive procedure to triangulate them, and */
9983 /* removes the bounding box, setting boundary markers as appropriate. */
9984 /* */
9985 /*****************************************************************************/
9986
9987 #ifdef ANSI_DECLARATORS
9988 long divconqdelaunay(struct mesh *m, struct behavior *b)
9989 #else /* not ANSI_DECLARATORS */
9990 long divconqdelaunay(m, b)
9991 struct mesh *m;
9992 struct behavior *b;
9993 #endif /* not ANSI_DECLARATORS */
9994
9995 {
9996 vertex *sortarray;
9997 struct otri hullleft, hullright;
9998 int divider;
9999 int i, j;
10000
10001 if (b->verbose) {
10002 printf(" Sorting vertices.\n");
10003 }
10004
10005 /* Allocate an array of pointers to vertices for sorting. */
10006 sortarray = (vertex *) trimalloc(m->invertices * (int) sizeof(vertex));
10007 traversalinit(&m->vertices);
10008 for (i = 0; i < m->invertices; i++) {
10009 sortarray[i] = vertextraverse(m);
10010 }
10011 /* Sort the vertices. */
10012 vertexsort(sortarray, m->invertices);
10013 /* Discard duplicate vertices, which can really mess up the algorithm. */
10014 i = 0;
10015 for (j = 1; j < m->invertices; j++) {
10016 if ((sortarray[i][0] == sortarray[j][0])
10017 && (sortarray[i][1] == sortarray[j][1])) {
10018 if (!b->quiet) {
10019 printf(
10020 "Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n",
10021 (double)sortarray[j][0], (double)sortarray[j][1]);
10022 }
10023 setvertextype(sortarray[j], UNDEADVERTEX);
10024 m->undeads++;
10025 } else {
10026 i++;
10027 sortarray[i] = sortarray[j];
10028 }
10029 }
10030 i++;
10031 if (b->dwyer) {
10032 /* Re-sort the array of vertices to accommodate alternating cuts. */
10033 divider = i >> 1;
10034 if (i - divider >= 2) {
10035 if (divider >= 2) {
10036 alternateaxes(sortarray, divider, 1);
10037 }
10038 alternateaxes(&sortarray[divider], i - divider, 1);
10039 }
10040 }
10041
10042 if (b->verbose) {
10043 printf(" Forming triangulation.\n");
10044 }
10045
10046 /* Form the Delaunay triangulation. */
10047 divconqrecurse(m, b, sortarray, i, 0, &hullleft, &hullright);
10048 trifree((VOID *) sortarray);
10049
10050 return removeghosts(m, b, &hullleft);
10051 }
10052
10053 /** **/
10054 /** **/
10055 /********* Divide-and-conquer Delaunay triangulation ends here *********/
10056
10057 /********* Incremental Delaunay triangulation begins here *********/
10058 /** **/
10059 /** **/
10060
10061 /*****************************************************************************/
10062 /* */
10063 /* boundingbox() Form an "infinite" bounding triangle to insert vertices */
10064 /* into. */
10065 /* */
10066 /* The vertices at "infinity" are assigned finite coordinates, which are */
10067 /* used by the point location routines, but (mostly) ignored by the */
10068 /* Delaunay edge flip routines. */
10069 /* */
10070 /*****************************************************************************/
10071
10072 #ifndef REDUCED
10073
10074 #ifdef ANSI_DECLARATORS
10075 void boundingbox(struct mesh *m, struct behavior *b)
10076 #else /* not ANSI_DECLARATORS */
10077 void boundingbox(m, b)
10078 struct mesh *m;
10079 struct behavior *b;
10080 #endif /* not ANSI_DECLARATORS */
10081
10082 {
10083 struct otri inftri; /* Handle for the triangular bounding box. */
10084 REAL width;
10085
10086 if (b->verbose) {
10087 printf(" Creating triangular bounding box.\n");
10088 }
10089 /* Find the width (or height, whichever is larger) of the triangulation. */
10090 width = m->xmax - m->xmin;
10091 if (m->ymax - m->ymin > width) {
10092 width = m->ymax - m->ymin;
10093 }
10094 if (width == 0.0) {
10095 width = 1.0;
10096 }
10097 /* Create the vertices of the bounding box. */
10098 m->infvertex1 = (vertex) trimalloc(m->vertices.itembytes);
10099 m->infvertex2 = (vertex) trimalloc(m->vertices.itembytes);
10100 m->infvertex3 = (vertex) trimalloc(m->vertices.itembytes);
10101 m->infvertex1[0] = m->xmin - 50.0 * width;
10102 m->infvertex1[1] = m->ymin - 40.0 * width;
10103 m->infvertex2[0] = m->xmax + 50.0 * width;
10104 m->infvertex2[1] = m->ymin - 40.0 * width;
10105 m->infvertex3[0] = 0.5 * (m->xmin + m->xmax);
10106 m->infvertex3[1] = m->ymax + 60.0 * width;
10107
10108 /* Create the bounding box. */
10109 maketriangle(m, b, &inftri);
10110 setorg(inftri, m->infvertex1);
10111 setdest(inftri, m->infvertex2);
10112 setapex(inftri, m->infvertex3);
10113 /* Link dummytri to the bounding box so we can always find an */
10114 /* edge to begin searching (point location) from. */
10115 m->dummytri[0] = (triangle) inftri.tri;
10116 if (b->verbose > 2) {
10117 printf(" Creating ");
10118 printtriangle(m, b, &inftri);
10119 }
10120 }
10121
10122 #endif /* not REDUCED */
10123
10124 /*****************************************************************************/
10125 /* */
10126 /* removebox() Remove the "infinite" bounding triangle, setting boundary */
10127 /* markers as appropriate. */
10128 /* */
10129 /* The triangular bounding box has three boundary triangles (one for each */
10130 /* side of the bounding box), and a bunch of triangles fanning out from */
10131 /* the three bounding box vertices (one triangle for each edge of the */
10132 /* convex hull of the inner mesh). This routine removes these triangles. */
10133 /* */
10134 /* Returns the number of edges on the convex hull of the triangulation. */
10135 /* */
10136 /*****************************************************************************/
10137
10138 #ifndef REDUCED
10139
10140 #ifdef ANSI_DECLARATORS
10141 long removebox(struct mesh *m, struct behavior *b)
10142 #else /* not ANSI_DECLARATORS */
10143 long removebox(m, b)
10144 struct mesh *m;
10145 struct behavior *b;
10146 #endif /* not ANSI_DECLARATORS */
10147
10148 {
10149 struct otri deadtriangle;
10150 struct otri searchedge;
10151 struct otri checkedge;
10152 struct otri nextedge, finaledge, dissolveedge;
10153 vertex markorg;
10154 long hullsize;
10155 triangle ptr; /* Temporary variable used by sym(). */
10156
10157 if (b->verbose) {
10158 printf(" Removing triangular bounding box.\n");
10159 }
10160 /* Find a boundary triangle. */
10161 nextedge.tri = m->dummytri;
10162 nextedge.orient = 0;
10163 symself(nextedge);
10164 /* Mark a place to stop. */
10165 lprev(nextedge, finaledge);
10166 lnextself(nextedge);
10167 symself(nextedge);
10168 /* Find a triangle (on the boundary of the vertex set) that isn't */
10169 /* a bounding box triangle. */
10170 lprev(nextedge, searchedge);
10171 symself(searchedge);
10172 /* Check whether nextedge is another boundary triangle */
10173 /* adjacent to the first one. */
10174 lnext(nextedge, checkedge);
10175 symself(checkedge);
10176 if (checkedge.tri == m->dummytri) {
10177 /* Go on to the next triangle. There are only three boundary */
10178 /* triangles, and this next triangle cannot be the third one, */
10179 /* so it's safe to stop here. */
10180 lprevself(searchedge);
10181 symself(searchedge);
10182 }
10183 /* Find a new boundary edge to search from, as the current search */
10184 /* edge lies on a bounding box triangle and will be deleted. */
10185 m->dummytri[0] = encode(searchedge);
10186 hullsize = -2l;
10187 while (!otriequal(nextedge, finaledge)) {
10188 hullsize++;
10189 lprev(nextedge, dissolveedge);
10190 symself(dissolveedge);
10191 /* If not using a PSLG, the vertices should be marked now. */
10192 /* (If using a PSLG, markhull() will do the job.) */
10193 if (!b->poly) {
10194 /* Be careful! One must check for the case where all the input */
10195 /* vertices are collinear, and thus all the triangles are part of */
10196 /* the bounding box. Otherwise, the setvertexmark() call below */
10197 /* will cause a bad pointer reference. */
10198 if (dissolveedge.tri != m->dummytri) {
10199 org(dissolveedge, markorg);
10200 if (vertexmark(markorg) == 0) {
10201 setvertexmark(markorg, 1);
10202 }
10203 }
10204 }
10205 /* Disconnect the bounding box triangle from the mesh triangle. */
10206 dissolve(dissolveedge);
10207 lnext(nextedge, deadtriangle);
10208 sym(deadtriangle, nextedge);
10209 /* Get rid of the bounding box triangle. */
10210 triangledealloc(m, deadtriangle.tri);
10211 /* Do we need to turn the corner? */
10212 if (nextedge.tri == m->dummytri) {
10213 /* Turn the corner. */
10214 otricopy(dissolveedge, nextedge);
10215 }
10216 }
10217 triangledealloc(m, finaledge.tri);
10218
10219 trifree((VOID *) m->infvertex1); /* Deallocate the bounding box vertices. */
10220 trifree((VOID *) m->infvertex2);
10221 trifree((VOID *) m->infvertex3);
10222
10223 return hullsize;
10224 }
10225
10226 #endif /* not REDUCED */
10227
10228 /*****************************************************************************/
10229 /* */
10230 /* incrementaldelaunay() Form a Delaunay triangulation by incrementally */
10231 /* inserting vertices. */
10232 /* */
10233 /* Returns the number of edges on the convex hull of the triangulation. */
10234 /* */
10235 /*****************************************************************************/
10236
10237 #ifndef REDUCED
10238
10239 #ifdef ANSI_DECLARATORS
10240 long incrementaldelaunay(struct mesh *m, struct behavior *b)
10241 #else /* not ANSI_DECLARATORS */
10242 long incrementaldelaunay(m, b)
10243 struct mesh *m;
10244 struct behavior *b;
10245 #endif /* not ANSI_DECLARATORS */
10246
10247 {
10248 struct otri starttri;
10249 vertex vertexloop;
10250
10251 /* Create a triangular bounding box. */
10252 boundingbox(m, b);
10253 if (b->verbose) {
10254 printf(" Incrementally inserting vertices.\n");
10255 }
10256 traversalinit(&m->vertices);
10257 vertexloop = vertextraverse(m);
10258 while (vertexloop != (vertex) NULL) {
10259 starttri.tri = m->dummytri;
10260 if (insertvertex(m, b, vertexloop, &starttri, (struct osub *) NULL, 0, 0)
10261 == DUPLICATEVERTEX) {
10262 if (!b->quiet) {
10263 printf(
10264 "Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n",
10265 (double)vertexloop[0], (double)vertexloop[1]);
10266 }
10267 setvertextype(vertexloop, UNDEADVERTEX);
10268 m->undeads++;
10269 }
10270 vertexloop = vertextraverse(m);
10271 }
10272 /* Remove the bounding box. */
10273 return removebox(m, b);
10274 }
10275
10276 #endif /* not REDUCED */
10277
10278 /** **/
10279 /** **/
10280 /********* Incremental Delaunay triangulation ends here *********/
10281
10282 /********* Sweepline Delaunay triangulation begins here *********/
10283 /** **/
10284 /** **/
10285
10286 #ifndef REDUCED
10287
10288 #ifdef ANSI_DECLARATORS
10289 void eventheapinsert(struct event **heap, int heapsize, struct event *newevent)
10290 #else /* not ANSI_DECLARATORS */
10291 void eventheapinsert(heap, heapsize, newevent)
10292 struct event **heap;
10293 int heapsize;
10294 struct event *newevent;
10295 #endif /* not ANSI_DECLARATORS */
10296
10297 {
10298 REAL eventx, eventy;
10299 int eventnum;
10300 int parent;
10301 int notdone;
10302
10303 eventx = newevent->xkey;
10304 eventy = newevent->ykey;
10305 eventnum = heapsize;
10306 notdone = eventnum > 0;
10307 while (notdone) {
10308 parent = (eventnum - 1) >> 1;
10309 if ((heap[parent]->ykey < eventy) ||
10310 ((heap[parent]->ykey == eventy)
10311 && (heap[parent]->xkey <= eventx))) {
10312 notdone = 0;
10313 } else {
10314 heap[eventnum] = heap[parent];
10315 heap[eventnum]->heapposition = eventnum;
10316
10317 eventnum = parent;
10318 notdone = eventnum > 0;
10319 }
10320 }
10321 heap[eventnum] = newevent;
10322 newevent->heapposition = eventnum;
10323 }
10324
10325 #endif /* not REDUCED */
10326
10327 #ifndef REDUCED
10328
10329 #ifdef ANSI_DECLARATORS
10330 void eventheapify(struct event **heap, int heapsize, int eventnum)
10331 #else /* not ANSI_DECLARATORS */
10332 void eventheapify(heap, heapsize, eventnum)
10333 struct event **heap;
10334 int heapsize;
10335 int eventnum;
10336 #endif /* not ANSI_DECLARATORS */
10337
10338 {
10339 struct event *thisevent;
10340 REAL eventx, eventy;
10341 int leftchild, rightchild;
10342 int smallest;
10343 int notdone;
10344
10345 thisevent = heap[eventnum];
10346 eventx = thisevent->xkey;
10347 eventy = thisevent->ykey;
10348 leftchild = 2 * eventnum + 1;
10349 notdone = leftchild < heapsize;
10350 while (notdone) {
10351 if ((heap[leftchild]->ykey < eventy) ||
10352 ((heap[leftchild]->ykey == eventy)
10353 && (heap[leftchild]->xkey < eventx))) {
10354 smallest = leftchild;
10355 } else {
10356 smallest = eventnum;
10357 }
10358 rightchild = leftchild + 1;
10359 if (rightchild < heapsize) {
10360 if ((heap[rightchild]->ykey < heap[smallest]->ykey) ||
10361 ((heap[rightchild]->ykey == heap[smallest]->ykey)
10362 && (heap[rightchild]->xkey < heap[smallest]->xkey))) {
10363 smallest = rightchild;
10364 }
10365 }
10366 if (smallest == eventnum) {
10367 notdone = 0;
10368 } else {
10369 heap[eventnum] = heap[smallest];
10370 heap[eventnum]->heapposition = eventnum;
10371 heap[smallest] = thisevent;
10372 thisevent->heapposition = smallest;
10373
10374 eventnum = smallest;
10375 leftchild = 2 * eventnum + 1;
10376 notdone = leftchild < heapsize;
10377 }
10378 }
10379 }
10380
10381 #endif /* not REDUCED */
10382
10383 #ifndef REDUCED
10384
10385 #ifdef ANSI_DECLARATORS
10386 void eventheapdelete(struct event **heap, int heapsize, int eventnum)
10387 #else /* not ANSI_DECLARATORS */
10388 void eventheapdelete(heap, heapsize, eventnum)
10389 struct event **heap;
10390 int heapsize;
10391 int eventnum;
10392 #endif /* not ANSI_DECLARATORS */
10393
10394 {
10395 struct event *moveevent;
10396 REAL eventx, eventy;
10397 int parent;
10398 int notdone;
10399
10400 moveevent = heap[heapsize - 1];
10401 if (eventnum > 0) {
10402 eventx = moveevent->xkey;
10403 eventy = moveevent->ykey;
10404 do {
10405 parent = (eventnum - 1) >> 1;
10406 if ((heap[parent]->ykey < eventy) ||
10407 ((heap[parent]->ykey == eventy)
10408 && (heap[parent]->xkey <= eventx))) {
10409 notdone = 0;
10410 } else {
10411 heap[eventnum] = heap[parent];
10412 heap[eventnum]->heapposition = eventnum;
10413
10414 eventnum = parent;
10415 notdone = eventnum > 0;
10416 }
10417 } while (notdone);
10418 }
10419 heap[eventnum] = moveevent;
10420 moveevent->heapposition = eventnum;
10421 eventheapify(heap, heapsize - 1, eventnum);
10422 }
10423
10424 #endif /* not REDUCED */
10425
10426 #ifndef REDUCED
10427
10428 #ifdef ANSI_DECLARATORS
10429 void createeventheap(struct mesh *m, struct event ***eventheap,
10430 struct event **events, struct event **freeevents)
10431 #else /* not ANSI_DECLARATORS */
10432 void createeventheap(m, eventheap, events, freeevents)
10433 struct mesh *m;
10434 struct event ***eventheap;
10435 struct event **events;
10436 struct event **freeevents;
10437 #endif /* not ANSI_DECLARATORS */
10438
10439 {
10440 vertex thisvertex;
10441 int maxevents;
10442 int i;
10443
10444 maxevents = (3 * m->invertices) / 2;
10445 *eventheap = (struct event **) trimalloc(maxevents *
10446 (int) sizeof(struct event *));
10447 *events = (struct event *) trimalloc(maxevents * (int) sizeof(struct event));
10448 traversalinit(&m->vertices);
10449 for (i = 0; i < m->invertices; i++) {
10450 thisvertex = vertextraverse(m);
10451 (*events)[i].eventptr = (VOID *) thisvertex;
10452 (*events)[i].xkey = thisvertex[0];
10453 (*events)[i].ykey = thisvertex[1];
10454 eventheapinsert(*eventheap, i, *events + i);
10455 }
10456 *freeevents = (struct event *) NULL;
10457 for (i = maxevents - 1; i >= m->invertices; i--) {
10458 (*events)[i].eventptr = (VOID *) *freeevents;
10459 *freeevents = *events + i;
10460 }
10461 }
10462
10463 #endif /* not REDUCED */
10464
10465 #ifndef REDUCED
10466
10467 #ifdef ANSI_DECLARATORS
10468 int rightofhyperbola(struct mesh *m, struct otri *fronttri, vertex newsite)
10469 #else /* not ANSI_DECLARATORS */
10470 int rightofhyperbola(m, fronttri, newsite)
10471 struct mesh *m;
10472 struct otri *fronttri;
10473 vertex newsite;
10474 #endif /* not ANSI_DECLARATORS */
10475
10476 {
10477 vertex leftvertex, rightvertex;
10478 REAL dxa, dya, dxb, dyb;
10479
10480 m->hyperbolacount++;
10481
10482 dest(*fronttri, leftvertex);
10483 apex(*fronttri, rightvertex);
10484 if ((leftvertex[1] < rightvertex[1]) ||
10485 ((leftvertex[1] == rightvertex[1]) &&
10486 (leftvertex[0] < rightvertex[0]))) {
10487 if (newsite[0] >= rightvertex[0]) {
10488 return 1;
10489 }
10490 } else {
10491 if (newsite[0] <= leftvertex[0]) {
10492 return 0;
10493 }
10494 }
10495 dxa = leftvertex[0] - newsite[0];
10496 dya = leftvertex[1] - newsite[1];
10497 dxb = rightvertex[0] - newsite[0];
10498 dyb = rightvertex[1] - newsite[1];
10499 return dya * (dxb * dxb + dyb * dyb) > dyb * (dxa * dxa + dya * dya);
10500 }
10501
10502 #endif /* not REDUCED */
10503
10504 #ifndef REDUCED
10505
10506 #ifdef ANSI_DECLARATORS
10507 REAL circletop(struct mesh *m, vertex pa, vertex pb, vertex pc, REAL ccwabc)
10508 #else /* not ANSI_DECLARATORS */
10509 REAL circletop(m, pa, pb, pc, ccwabc)
10510 struct mesh *m;
10511 vertex pa;
10512 vertex pb;
10513 vertex pc;
10514 REAL ccwabc;
10515 #endif /* not ANSI_DECLARATORS */
10516
10517 {
10518 REAL xac, yac, xbc, ybc, xab, yab;
10519 REAL aclen2, bclen2, ablen2;
10520
10521 m->circletopcount++;
10522
10523 xac = pa[0] - pc[0];
10524 yac = pa[1] - pc[1];
10525 xbc = pb[0] - pc[0];
10526 ybc = pb[1] - pc[1];
10527 xab = pa[0] - pb[0];
10528 yab = pa[1] - pb[1];
10529 aclen2 = xac * xac + yac * yac;
10530 bclen2 = xbc * xbc + ybc * ybc;
10531 ablen2 = xab * xab + yab * yab;
10532 return pc[1] + (xac * bclen2 - xbc * aclen2 + sqrt(aclen2 * bclen2 * ablen2))
10533 / (2.0 * ccwabc);
10534 }
10535
10536 #endif /* not REDUCED */
10537
10538 #ifndef REDUCED
10539
10540 #ifdef ANSI_DECLARATORS
10541 void check4deadevent(struct otri *checktri, struct event **freeevents,
10542 struct event **eventheap, int *heapsize)
10543 #else /* not ANSI_DECLARATORS */
10544 void check4deadevent(checktri, freeevents, eventheap, heapsize)
10545 struct otri *checktri;
10546 struct event **freeevents;
10547 struct event **eventheap;
10548 int *heapsize;
10549 #endif /* not ANSI_DECLARATORS */
10550
10551 {
10552 struct event *deadevent;
10553 vertex eventvertex;
10554 int eventnum;
10555
10556 org(*checktri, eventvertex);
10557 if (eventvertex != (vertex) NULL) {
10558 deadevent = (struct event *) eventvertex;
10559 eventnum = deadevent->heapposition;
10560 deadevent->eventptr = (VOID *) *freeevents;
10561 *freeevents = deadevent;
10562 eventheapdelete(eventheap, *heapsize, eventnum);
10563 (*heapsize)--;
10564 setorg(*checktri, NULL);
10565 }
10566 }
10567
10568 #endif /* not REDUCED */
10569
10570 #ifndef REDUCED
10571
10572 #ifdef ANSI_DECLARATORS
10573 struct splaynode *splay(struct mesh *m, struct splaynode *splaytree,
10574 vertex searchpoint, struct otri *searchtri)
10575 #else /* not ANSI_DECLARATORS */
10576 struct splaynode *splay(m, splaytree, searchpoint, searchtri)
10577 struct mesh *m;
10578 struct splaynode *splaytree;
10579 vertex searchpoint;
10580 struct otri *searchtri;
10581 #endif /* not ANSI_DECLARATORS */
10582
10583 {
10584 struct splaynode *child, *grandchild;
10585 struct splaynode *lefttree, *righttree;
10586 struct splaynode *leftright;
10587 vertex checkvertex;
10588 int rightofroot, rightofchild;
10589
10590 if (splaytree == (struct splaynode *) NULL) {
10591 return (struct splaynode *) NULL;
10592 }
10593 dest(splaytree->keyedge, checkvertex);
10594 if (checkvertex == splaytree->keydest) {
10595 rightofroot = rightofhyperbola(m, &splaytree->keyedge, searchpoint);
10596 if (rightofroot) {
10597 otricopy(splaytree->keyedge, *searchtri);
10598 child = splaytree->rchild;
10599 } else {
10600 child = splaytree->lchild;
10601 }
10602 if (child == (struct splaynode *) NULL) {
10603 return splaytree;
10604 }
10605 dest(child->keyedge, checkvertex);
10606 if (checkvertex != child->keydest) {
10607 child = splay(m, child, searchpoint, searchtri);
10608 if (child == (struct splaynode *) NULL) {
10609 if (rightofroot) {
10610 splaytree->rchild = (struct splaynode *) NULL;
10611 } else {
10612 splaytree->lchild = (struct splaynode *) NULL;
10613 }
10614 return splaytree;
10615 }
10616 }
10617 rightofchild = rightofhyperbola(m, &child->keyedge, searchpoint);
10618 if (rightofchild) {
10619 otricopy(child->keyedge, *searchtri);
10620 grandchild = splay(m, child->rchild, searchpoint, searchtri);
10621 child->rchild = grandchild;
10622 } else {
10623 grandchild = splay(m, child->lchild, searchpoint, searchtri);
10624 child->lchild = grandchild;
10625 }
10626 if (grandchild == (struct splaynode *) NULL) {
10627 if (rightofroot) {
10628 splaytree->rchild = child->lchild;
10629 child->lchild = splaytree;
10630 } else {
10631 splaytree->lchild = child->rchild;
10632 child->rchild = splaytree;
10633 }
10634 return child;
10635 }
10636 if (rightofchild) {
10637 if (rightofroot) {
10638 splaytree->rchild = child->lchild;
10639 child->lchild = splaytree;
10640 } else {
10641 splaytree->lchild = grandchild->rchild;
10642 grandchild->rchild = splaytree;
10643 }
10644 child->rchild = grandchild->lchild;
10645 grandchild->lchild = child;
10646 } else {
10647 if (rightofroot) {
10648 splaytree->rchild = grandchild->lchild;
10649 grandchild->lchild = splaytree;
10650 } else {
10651 splaytree->lchild = child->rchild;
10652 child->rchild = splaytree;
10653 }
10654 child->lchild = grandchild->rchild;
10655 grandchild->rchild = child;
10656 }
10657 return grandchild;
10658 } else {
10659 lefttree = splay(m, splaytree->lchild, searchpoint, searchtri);
10660 righttree = splay(m, splaytree->rchild, searchpoint, searchtri);
10661
10662 pooldealloc(&m->splaynodes, (VOID *) splaytree);
10663 if (lefttree == (struct splaynode *) NULL) {
10664 return righttree;
10665 } else if (righttree == (struct splaynode *) NULL) {
10666 return lefttree;
10667 } else if (lefttree->rchild == (struct splaynode *) NULL) {
10668 lefttree->rchild = righttree->lchild;
10669 righttree->lchild = lefttree;
10670 return righttree;
10671 } else if (righttree->lchild == (struct splaynode *) NULL) {
10672 righttree->lchild = lefttree->rchild;
10673 lefttree->rchild = righttree;
10674 return lefttree;
10675 } else {
10676 /* printf("Holy Toledo!!!\n"); */
10677 leftright = lefttree->rchild;
10678 while (leftright->rchild != (struct splaynode *) NULL) {
10679 leftright = leftright->rchild;
10680 }
10681 leftright->rchild = righttree;
10682 return lefttree;
10683 }
10684 }
10685 }
10686
10687 #endif /* not REDUCED */
10688
10689 #ifndef REDUCED
10690
10691 #ifdef ANSI_DECLARATORS
10692 struct splaynode *splayinsert(struct mesh *m, struct splaynode *splayroot,
10693 struct otri *newkey, vertex searchpoint)
10694 #else /* not ANSI_DECLARATORS */
10695 struct splaynode *splayinsert(m, splayroot, newkey, searchpoint)
10696 struct mesh *m;
10697 struct splaynode *splayroot;
10698 struct otri *newkey;
10699 vertex searchpoint;
10700 #endif /* not ANSI_DECLARATORS */
10701
10702 {
10703 struct splaynode *newsplaynode;
10704
10705 newsplaynode = (struct splaynode *) poolalloc(&m->splaynodes);
10706 otricopy(*newkey, newsplaynode->keyedge);
10707 dest(*newkey, newsplaynode->keydest);
10708 if (splayroot == (struct splaynode *) NULL) {
10709 newsplaynode->lchild = (struct splaynode *) NULL;
10710 newsplaynode->rchild = (struct splaynode *) NULL;
10711 } else if (rightofhyperbola(m, &splayroot->keyedge, searchpoint)) {
10712 newsplaynode->lchild = splayroot;
10713 newsplaynode->rchild = splayroot->rchild;
10714 splayroot->rchild = (struct splaynode *) NULL;
10715 } else {
10716 newsplaynode->lchild = splayroot->lchild;
10717 newsplaynode->rchild = splayroot;
10718 splayroot->lchild = (struct splaynode *) NULL;
10719 }
10720 return newsplaynode;
10721 }
10722
10723 #endif /* not REDUCED */
10724
10725 #ifndef REDUCED
10726
10727 #ifdef ANSI_DECLARATORS
10728 struct splaynode *circletopinsert(struct mesh *m, struct behavior *b,
10729 struct splaynode *splayroot,
10730 struct otri *newkey,
10731 vertex pa, vertex pb, vertex pc, REAL topy)
10732 #else /* not ANSI_DECLARATORS */
10733 struct splaynode *circletopinsert(m, b, splayroot, newkey, pa, pb, pc, topy)
10734 struct mesh *m;
10735 struct behavior *b;
10736 struct splaynode *splayroot;
10737 struct otri *newkey;
10738 vertex pa;
10739 vertex pb;
10740 vertex pc;
10741 REAL topy;
10742 #endif /* not ANSI_DECLARATORS */
10743
10744 {
10745 REAL ccwabc;
10746 REAL xac, yac, xbc, ybc;
10747 REAL aclen2, bclen2;
10748 REAL searchpoint[2];
10749 struct otri dummytri;
10750
10751 ccwabc = counterclockwise(m, b, pa, pb, pc);
10752 xac = pa[0] - pc[0];
10753 yac = pa[1] - pc[1];
10754 xbc = pb[0] - pc[0];
10755 ybc = pb[1] - pc[1];
10756 aclen2 = xac * xac + yac * yac;
10757 bclen2 = xbc * xbc + ybc * ybc;
10758 searchpoint[0] = pc[0] - (yac * bclen2 - ybc * aclen2) / (2.0 * ccwabc);
10759 searchpoint[1] = topy;
10760 return splayinsert(m, splay(m, splayroot, (vertex) searchpoint, &dummytri),
10761 newkey, (vertex) searchpoint);
10762 }
10763
10764 #endif /* not REDUCED */
10765
10766 #ifndef REDUCED
10767
10768 #ifdef ANSI_DECLARATORS
10769 struct splaynode *frontlocate(struct mesh *m, struct splaynode *splayroot,
10770 struct otri *bottommost, vertex searchvertex,
10771 struct otri *searchtri, int *farright)
10772 #else /* not ANSI_DECLARATORS */
10773 struct splaynode *frontlocate(m, splayroot, bottommost, searchvertex,
10774 searchtri, farright)
10775 struct mesh *m;
10776 struct splaynode *splayroot;
10777 struct otri *bottommost;
10778 vertex searchvertex;
10779 struct otri *searchtri;
10780 int *farright;
10781 #endif /* not ANSI_DECLARATORS */
10782
10783 {
10784 int farrightflag;
10785 triangle ptr; /* Temporary variable used by onext(). */
10786
10787 otricopy(*bottommost, *searchtri);
10788 splayroot = splay(m, splayroot, searchvertex, searchtri);
10789
10790 farrightflag = 0;
10791 while (!farrightflag && rightofhyperbola(m, searchtri, searchvertex)) {
10792 onextself(*searchtri);
10793 farrightflag = otriequal(*searchtri, *bottommost);
10794 }
10795 *farright = farrightflag;
10796 return splayroot;
10797 }
10798
10799 #endif /* not REDUCED */
10800
10801 #ifndef REDUCED
10802
10803 #ifdef ANSI_DECLARATORS
10804 long sweeplinedelaunay(struct mesh *m, struct behavior *b)
10805 #else /* not ANSI_DECLARATORS */
10806 long sweeplinedelaunay(m, b)
10807 struct mesh *m;
10808 struct behavior *b;
10809 #endif /* not ANSI_DECLARATORS */
10810
10811 {
10812 struct event **eventheap;
10813 struct event *events;
10814 struct event *freeevents;
10815 struct event *nextevent;
10816 struct event *newevent;
10817 struct splaynode *splayroot;
10818 struct otri bottommost;
10819 struct otri searchtri;
10820 struct otri fliptri;
10821 struct otri lefttri, righttri, farlefttri, farrighttri;
10822 struct otri inserttri;
10823 vertex firstvertex, secondvertex;
10824 vertex nextvertex, lastvertex;
10825 vertex connectvertex;
10826 vertex leftvertex, midvertex, rightvertex;
10827 REAL lefttest, righttest;
10828 int heapsize;
10829 int check4events, farrightflag;
10830 triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */
10831
10832 poolinit(&m->splaynodes, sizeof(struct splaynode), SPLAYNODEPERBLOCK,
10833 SPLAYNODEPERBLOCK, 0);
10834 splayroot = (struct splaynode *) NULL;
10835
10836 if (b->verbose) {
10837 printf(" Placing vertices in event heap.\n");
10838 }
10839 createeventheap(m, &eventheap, &events, &freeevents);
10840 heapsize = m->invertices;
10841
10842 if (b->verbose) {
10843 printf(" Forming triangulation.\n");
10844 }
10845 maketriangle(m, b, &lefttri);
10846 maketriangle(m, b, &righttri);
10847 bond(lefttri, righttri);
10848 lnextself(lefttri);
10849 lprevself(righttri);
10850 bond(lefttri, righttri);
10851 lnextself(lefttri);
10852 lprevself(righttri);
10853 bond(lefttri, righttri);
10854 firstvertex = (vertex) eventheap[0]->eventptr;
10855 eventheap[0]->eventptr = (VOID *) freeevents;
10856 freeevents = eventheap[0];
10857 eventheapdelete(eventheap, heapsize, 0);
10858 heapsize--;
10859 do {
10860 if (heapsize == 0) {
10861 printf("Error: Input vertices are all identical.\n");
10862 triexit(1);
10863 }
10864 secondvertex = (vertex) eventheap[0]->eventptr;
10865 eventheap[0]->eventptr = (VOID *) freeevents;
10866 freeevents = eventheap[0];
10867 eventheapdelete(eventheap, heapsize, 0);
10868 heapsize--;
10869 if ((firstvertex[0] == secondvertex[0]) &&
10870 (firstvertex[1] == secondvertex[1])) {
10871 if (!b->quiet) {
10872 printf(
10873 "Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n",
10874 (double)secondvertex[0], (double)secondvertex[1]);
10875 }
10876 setvertextype(secondvertex, UNDEADVERTEX);
10877 m->undeads++;
10878 }
10879 } while ((firstvertex[0] == secondvertex[0]) &&
10880 (firstvertex[1] == secondvertex[1]));
10881 setorg(lefttri, firstvertex);
10882 setdest(lefttri, secondvertex);
10883 setorg(righttri, secondvertex);
10884 setdest(righttri, firstvertex);
10885 lprev(lefttri, bottommost);
10886 lastvertex = secondvertex;
10887 while (heapsize > 0) {
10888 nextevent = eventheap[0];
10889 eventheapdelete(eventheap, heapsize, 0);
10890 heapsize--;
10891 check4events = 1;
10892 if (nextevent->xkey < m->xmin) {
10893 decode(nextevent->eventptr, fliptri);
10894 oprev(fliptri, farlefttri);
10895 check4deadevent(&farlefttri, &freeevents, eventheap, &heapsize);
10896 onext(fliptri, farrighttri);
10897 check4deadevent(&farrighttri, &freeevents, eventheap, &heapsize);
10898
10899 if (otriequal(farlefttri, bottommost)) {
10900 lprev(fliptri, bottommost);
10901 }
10902 flip(m, b, &fliptri);
10903 setapex(fliptri, NULL);
10904 lprev(fliptri, lefttri);
10905 lnext(fliptri, righttri);
10906 sym(lefttri, farlefttri);
10907
10908 if (randomnation(SAMPLERATE) == 0) {
10909 symself(fliptri);
10910 dest(fliptri, leftvertex);
10911 apex(fliptri, midvertex);
10912 org(fliptri, rightvertex);
10913 splayroot = circletopinsert(m, b, splayroot, &lefttri, leftvertex,
10914 midvertex, rightvertex, nextevent->ykey);
10915 }
10916 } else {
10917 nextvertex = (vertex) nextevent->eventptr;
10918 if ((nextvertex[0] == lastvertex[0]) &&
10919 (nextvertex[1] == lastvertex[1])) {
10920 if (!b->quiet) {
10921 printf(
10922 "Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n",
10923 (double)nextvertex[0], (double)nextvertex[1]);
10924 }
10925 setvertextype(nextvertex, UNDEADVERTEX);
10926 m->undeads++;
10927 check4events = 0;
10928 } else {
10929 lastvertex = nextvertex;
10930
10931 splayroot = frontlocate(m, splayroot, &bottommost, nextvertex,
10932 &searchtri, &farrightflag);
10933 /*
10934 otricopy(bottommost, searchtri);
10935 farrightflag = 0;
10936 while (!farrightflag && rightofhyperbola(m, &searchtri, nextvertex)) {
10937 onextself(searchtri);
10938 farrightflag = otriequal(searchtri, bottommost);
10939 }
10940 */
10941
10942 check4deadevent(&searchtri, &freeevents, eventheap, &heapsize);
10943
10944 otricopy(searchtri, farrighttri);
10945 sym(searchtri, farlefttri);
10946 maketriangle(m, b, &lefttri);
10947 maketriangle(m, b, &righttri);
10948 dest(farrighttri, connectvertex);
10949 setorg(lefttri, connectvertex);
10950 setdest(lefttri, nextvertex);
10951 setorg(righttri, nextvertex);
10952 setdest(righttri, connectvertex);
10953 bond(lefttri, righttri);
10954 lnextself(lefttri);
10955 lprevself(righttri);
10956 bond(lefttri, righttri);
10957 lnextself(lefttri);
10958 lprevself(righttri);
10959 bond(lefttri, farlefttri);
10960 bond(righttri, farrighttri);
10961 if (!farrightflag && otriequal(farrighttri, bottommost)) {
10962 otricopy(lefttri, bottommost);
10963 }
10964
10965 if (randomnation(SAMPLERATE) == 0) {
10966 splayroot = splayinsert(m, splayroot, &lefttri, nextvertex);
10967 } else if (randomnation(SAMPLERATE) == 0) {
10968 lnext(righttri, inserttri);
10969 splayroot = splayinsert(m, splayroot, &inserttri, nextvertex);
10970 }
10971 }
10972 }
10973 nextevent->eventptr = (VOID *) freeevents;
10974 freeevents = nextevent;
10975
10976 if (check4events) {
10977 apex(farlefttri, leftvertex);
10978 dest(lefttri, midvertex);
10979 apex(lefttri, rightvertex);
10980 lefttest = counterclockwise(m, b, leftvertex, midvertex, rightvertex);
10981 if (lefttest > 0.0) {
10982 newevent = freeevents;
10983 freeevents = (struct event *) freeevents->eventptr;
10984 newevent->xkey = m->xminextreme;
10985 newevent->ykey = circletop(m, leftvertex, midvertex, rightvertex,
10986 lefttest);
10987 newevent->eventptr = (VOID *) encode(lefttri);
10988 eventheapinsert(eventheap, heapsize, newevent);
10989 heapsize++;
10990 setorg(lefttri, newevent);
10991 }
10992 apex(righttri, leftvertex);
10993 org(righttri, midvertex);
10994 apex(farrighttri, rightvertex);
10995 righttest = counterclockwise(m, b, leftvertex, midvertex, rightvertex);
10996 if (righttest > 0.0) {
10997 newevent = freeevents;
10998 freeevents = (struct event *) freeevents->eventptr;
10999 newevent->xkey = m->xminextreme;
11000 newevent->ykey = circletop(m, leftvertex, midvertex, rightvertex,
11001 righttest);
11002 newevent->eventptr = (VOID *) encode(farrighttri);
11003 eventheapinsert(eventheap, heapsize, newevent);
11004 heapsize++;
11005 setorg(farrighttri, newevent);
11006 }
11007 }
11008 }
11009
11010 pooldeinit(&m->splaynodes);
11011 lprevself(bottommost);
11012 return removeghosts(m, b, &bottommost);
11013 }
11014
11015 #endif /* not REDUCED */
11016
11017 /** **/
11018 /** **/
11019 /********* Sweepline Delaunay triangulation ends here *********/
11020
11021 /********* General mesh construction routines begin here *********/
11022 /** **/
11023 /** **/
11024
11025 /*****************************************************************************/
11026 /* */
11027 /* delaunay() Form a Delaunay triangulation. */
11028 /* */
11029 /*****************************************************************************/
11030
11031 #ifdef ANSI_DECLARATORS
11032 long delaunay(struct mesh *m, struct behavior *b)
11033 #else /* not ANSI_DECLARATORS */
11034 long delaunay(m, b)
11035 struct mesh *m;
11036 struct behavior *b;
11037 #endif /* not ANSI_DECLARATORS */
11038
11039 {
11040 long hulledges;
11041
11042 m->eextras = 0;
11043 initializetrisubpools(m, b);
11044
11045 #ifdef REDUCED
11046 if (!b->quiet) {
11047 printf(
11048 "Constructing Delaunay triangulation by divide-and-conquer method.\n");
11049 }
11050 hulledges = divconqdelaunay(m, b);
11051 #else /* not REDUCED */
11052 if (!b->quiet) {
11053 printf("Constructing Delaunay triangulation ");
11054 if (b->incremental) {
11055 printf("by incremental method.\n");
11056 } else if (b->sweepline) {
11057 printf("by sweepline method.\n");
11058 } else {
11059 printf("by divide-and-conquer method.\n");
11060 }
11061 }
11062 if (b->incremental) {
11063 hulledges = incrementaldelaunay(m, b);
11064 } else if (b->sweepline) {
11065 hulledges = sweeplinedelaunay(m, b);
11066 } else {
11067 hulledges = divconqdelaunay(m, b);
11068 }
11069 #endif /* not REDUCED */
11070
11071 if (m->triangles.items == 0) {
11072 /* The input vertices were all collinear, so there are no triangles. */
11073 return 0l;
11074 } else {
11075 return hulledges;
11076 }
11077 }
11078
11079 /*****************************************************************************/
11080 /* */
11081 /* reconstruct() Reconstruct a triangulation from its .ele (and possibly */
11082 /* .poly) file. Used when the -r switch is used. */
11083 /* */
11084 /* Reads an .ele file and reconstructs the original mesh. If the -p switch */
11085 /* is used, this procedure will also read a .poly file and reconstruct the */
11086 /* subsegments of the original mesh. If the -a switch is used, this */
11087 /* procedure will also read an .area file and set a maximum area constraint */
11088 /* on each triangle. */
11089 /* */
11090 /* Vertices that are not corners of triangles, such as nodes on edges of */
11091 /* subparametric elements, are discarded. */
11092 /* */
11093 /* This routine finds the adjacencies between triangles (and subsegments) */
11094 /* by forming one stack of triangles for each vertex. Each triangle is on */
11095 /* three different stacks simultaneously. Each triangle's subsegment */
11096 /* pointers are used to link the items in each stack. This memory-saving */
11097 /* feature makes the code harder to read. The most important thing to keep */
11098 /* in mind is that each triangle is removed from a stack precisely when */
11099 /* the corresponding pointer is adjusted to refer to a subsegment rather */
11100 /* than the next triangle of the stack. */
11101 /* */
11102 /*****************************************************************************/
11103
11104 #ifndef CDT_ONLY
11105
11106 #ifdef TRILIBRARY
11107
11108 #ifdef ANSI_DECLARATORS
11109 int reconstruct(struct mesh *m, struct behavior *b, int *trianglelist,
11110 REAL *triangleattriblist, REAL *trianglearealist,
11111 int elements, int corners, int attribs,
11112 int *segmentlist,int *segmentmarkerlist, int numberofsegments)
11113 #else /* not ANSI_DECLARATORS */
11114 int reconstruct(m, b, trianglelist, triangleattriblist, trianglearealist,
11115 elements, corners, attribs, segmentlist, segmentmarkerlist,
11116 numberofsegments)
11117 struct mesh *m;
11118 struct behavior *b;
11119 int *trianglelist;
11120 REAL *triangleattriblist;
11121 REAL *trianglearealist;
11122 int elements;
11123 int corners;
11124 int attribs;
11125 int *segmentlist;
11126 int *segmentmarkerlist;
11127 int numberofsegments;
11128 #endif /* not ANSI_DECLARATORS */
11129
11130 #else /* not TRILIBRARY */
11131
11132 #ifdef ANSI_DECLARATORS
11133 long reconstruct(struct mesh *m, struct behavior *b, char *elefilename,
11134 char *areafilename, char *polyfilename, FILE *polyfile)
11135 #else /* not ANSI_DECLARATORS */
11136 long reconstruct(m, b, elefilename, areafilename, polyfilename, polyfile)
11137 struct mesh *m;
11138 struct behavior *b;
11139 char *elefilename;
11140 char *areafilename;
11141 char *polyfilename;
11142 FILE *polyfile;
11143 #endif /* not ANSI_DECLARATORS */
11144
11145 #endif /* not TRILIBRARY */
11146
11147 {
11148 #ifdef TRILIBRARY
11149 int vertexindex;
11150 int attribindex;
11151 #else /* not TRILIBRARY */
11152 FILE *elefile;
11153 FILE *areafile;
11154 char inputline[INPUTLINESIZE];
11155 char *stringptr;
11156 int areaelements;
11157 #endif /* not TRILIBRARY */
11158 struct otri triangleloop;
11159 struct otri triangleleft;
11160 struct otri checktri;
11161 struct otri checkleft;
11162 struct otri checkneighbor;
11163 struct osub subsegloop;
11164 triangle *vertexarray;
11165 triangle *prevlink;
11166 triangle nexttri;
11167 vertex tdest, tapex;
11168 vertex checkdest, checkapex;
11169 vertex shorg;
11170 vertex killvertex;
11171 vertex segmentorg, segmentdest;
11172 REAL area;
11173 int corner[3];
11174 int end[2];
11175 int killvertexindex;
11176 int incorners;
11177 int segmentmarkers;
11178 int boundmarker;
11179 int aroundvertex;
11180 long hullsize;
11181 int notfound;
11182 long elementnumber, segmentnumber;
11183 int i, j;
11184 triangle ptr; /* Temporary variable used by sym(). */
11185
11186 #ifdef TRILIBRARY
11187 m->inelements = elements;
11188 incorners = corners;
11189 if (incorners < 3) {
11190 printf("Error: Triangles must have at least 3 vertices.\n");
11191 triexit(1);
11192 }
11193 m->eextras = attribs;
11194 #else /* not TRILIBRARY */
11195 /* Read the triangles from an .ele file. */
11196 if (!b->quiet) {
11197 printf("Opening %s.\n", elefilename);
11198 }
11199 elefile = fopen(elefilename, "r");
11200 if (elefile == (FILE *) NULL) {
11201 printf(" Error: Cannot access file %s.\n", elefilename);
11202 triexit(1);
11203 }
11204 /* Read number of triangles, number of vertices per triangle, and */
11205 /* number of triangle attributes from .ele file. */
11206 stringptr = readline(inputline, elefile, elefilename);
11207 m->inelements = (int) strtol(stringptr, &stringptr, 0);
11208 stringptr = findfield(stringptr);
11209 if (*stringptr == '\0') {
11210 incorners = 3;
11211 } else {
11212 incorners = (int) strtol(stringptr, &stringptr, 0);
11213 if (incorners < 3) {
11214 printf("Error: Triangles in %s must have at least 3 vertices.\n",
11215 elefilename);
11216 triexit(1);
11217 }
11218 }
11219 stringptr = findfield(stringptr);
11220 if (*stringptr == '\0') {
11221 m->eextras = 0;
11222 } else {
11223 m->eextras = (int) strtol(stringptr, &stringptr, 0);
11224 }
11225 #endif /* not TRILIBRARY */
11226
11227 initializetrisubpools(m, b);
11228
11229 /* Create the triangles. */
11230 for (elementnumber = 1; elementnumber <= m->inelements; elementnumber++) {
11231 maketriangle(m, b, &triangleloop);
11232 /* Mark the triangle as living. */
11233 triangleloop.tri[3] = (triangle) triangleloop.tri;
11234 }
11235
11236 segmentmarkers = 0;
11237 if (b->poly) {
11238 #ifdef TRILIBRARY
11239 m->insegments = numberofsegments;
11240 segmentmarkers = segmentmarkerlist != (int *) NULL;
11241 #else /* not TRILIBRARY */
11242 /* Read number of segments and number of segment */
11243 /* boundary markers from .poly file. */
11244 stringptr = readline(inputline, polyfile, b->inpolyfilename);
11245 m->insegments = (int) strtol(stringptr, &stringptr, 0);
11246 stringptr = findfield(stringptr);
11247 if (*stringptr != '\0') {
11248 segmentmarkers = (int) strtol(stringptr, &stringptr, 0);
11249 }
11250 #endif /* not TRILIBRARY */
11251
11252 /* Create the subsegments. */
11253 for (segmentnumber = 1; segmentnumber <= m->insegments; segmentnumber++) {
11254 makesubseg(m, &subsegloop);
11255 /* Mark the subsegment as living. */
11256 subsegloop.ss[2] = (subseg) subsegloop.ss;
11257 }
11258 }
11259
11260 #ifdef TRILIBRARY
11261 vertexindex = 0;
11262 attribindex = 0;
11263 #else /* not TRILIBRARY */
11264 if (b->vararea) {
11265 /* Open an .area file, check for consistency with the .ele file. */
11266 if (!b->quiet) {
11267 printf("Opening %s.\n", areafilename);
11268 }
11269 areafile = fopen(areafilename, "r");
11270 if (areafile == (FILE *) NULL) {
11271 printf(" Error: Cannot access file %s.\n", areafilename);
11272 triexit(1);
11273 }
11274 stringptr = readline(inputline, areafile, areafilename);
11275 areaelements = (int) strtol(stringptr, &stringptr, 0);
11276 if (areaelements != m->inelements) {
11277 printf("Error: %s and %s disagree on number of triangles.\n",
11278 elefilename, areafilename);
11279 triexit(1);
11280 }
11281 }
11282 #endif /* not TRILIBRARY */
11283
11284 if (!b->quiet) {
11285 printf("Reconstructing mesh.\n");
11286 }
11287 /* Allocate a temporary array that maps each vertex to some adjacent */
11288 /* triangle. I took care to allocate all the permanent memory for */
11289 /* triangles and subsegments first. */
11290 vertexarray = (triangle *) trimalloc(m->vertices.items *
11291 (int) sizeof(triangle));
11292 /* Each vertex is initially unrepresented. */
11293 for (i = 0; i < m->vertices.items; i++) {
11294 vertexarray[i] = (triangle) m->dummytri;
11295 }
11296
11297 if (b->verbose) {
11298 printf(" Assembling triangles.\n");
11299 }
11300 /* Read the triangles from the .ele file, and link */
11301 /* together those that share an edge. */
11302 traversalinit(&m->triangles);
11303 triangleloop.tri = triangletraverse(m);
11304 elementnumber = b->firstnumber;
11305 while (triangleloop.tri != (triangle *) NULL) {
11306 #ifdef TRILIBRARY
11307 /* Copy the triangle's three corners. */
11308 for (j = 0; j < 3; j++) {
11309 corner[j] = trianglelist[vertexindex++];
11310 if ((corner[j] < b->firstnumber) ||
11311 (corner[j] >= b->firstnumber + m->invertices)) {
11312 printf("Error: Triangle %ld has an invalid vertex index.\n",
11313 elementnumber);
11314 triexit(1);
11315 }
11316 }
11317 #else /* not TRILIBRARY */
11318 /* Read triangle number and the triangle's three corners. */
11319 stringptr = readline(inputline, elefile, elefilename);
11320 for (j = 0; j < 3; j++) {
11321 stringptr = findfield(stringptr);
11322 if (*stringptr == '\0') {
11323 printf("Error: Triangle %ld is missing vertex %d in %s.\n",
11324 elementnumber, j + 1, elefilename);
11325 triexit(1);
11326 } else {
11327 corner[j] = (int) strtol(stringptr, &stringptr, 0);
11328 if ((corner[j] < b->firstnumber) ||
11329 (corner[j] >= b->firstnumber + m->invertices)) {
11330 printf("Error: Triangle %ld has an invalid vertex index.\n",
11331 elementnumber);
11332 triexit(1);
11333 }
11334 }
11335 }
11336 #endif /* not TRILIBRARY */
11337
11338 /* Find out about (and throw away) extra nodes. */
11339 for (j = 3; j < incorners; j++) {
11340 #ifdef TRILIBRARY
11341 killvertexindex = trianglelist[vertexindex++];
11342 #else /* not TRILIBRARY */
11343 stringptr = findfield(stringptr);
11344 if (*stringptr != '\0') {
11345 killvertexindex = (int) strtol(stringptr, &stringptr, 0);
11346 #endif /* not TRILIBRARY */
11347 if ((killvertexindex >= b->firstnumber) &&
11348 (killvertexindex < b->firstnumber + m->invertices)) {
11349 /* Delete the non-corner vertex if it's not already deleted. */
11350 killvertex = getvertex(m, b, killvertexindex);
11351 if (vertextype(killvertex) != DEADVERTEX) {
11352 vertexdealloc(m, killvertex);
11353 }
11354 }
11355 #ifndef TRILIBRARY
11356 }
11357 #endif /* not TRILIBRARY */
11358 }
11359
11360 /* Read the triangle's attributes. */
11361 for (j = 0; j < m->eextras; j++) {
11362 #ifdef TRILIBRARY
11363 setelemattribute(triangleloop, j, triangleattriblist[attribindex++]);
11364 #else /* not TRILIBRARY */
11365 stringptr = findfield(stringptr);
11366 if (*stringptr == '\0') {
11367 setelemattribute(triangleloop, j, 0);
11368 } else {
11369 setelemattribute(triangleloop, j,
11370 (REAL) strtod(stringptr, &stringptr));
11371 }
11372 #endif /* not TRILIBRARY */
11373 }
11374
11375 if (b->vararea) {
11376 #ifdef TRILIBRARY
11377 area = trianglearealist[elementnumber - b->firstnumber];
11378 #else /* not TRILIBRARY */
11379 /* Read an area constraint from the .area file. */
11380 stringptr = readline(inputline, areafile, areafilename);
11381 stringptr = findfield(stringptr);
11382 if (*stringptr == '\0') {
11383 area = -1.0; /* No constraint on this triangle. */
11384 } else {
11385 area = (REAL) strtod(stringptr, &stringptr);
11386 }
11387 #endif /* not TRILIBRARY */
11388 setareabound(triangleloop, area);
11389 }
11390
11391 /* Set the triangle's vertices. */
11392 triangleloop.orient = 0;
11393 setorg(triangleloop, getvertex(m, b, corner[0]));
11394 setdest(triangleloop, getvertex(m, b, corner[1]));
11395 setapex(triangleloop, getvertex(m, b, corner[2]));
11396 /* Try linking the triangle to others that share these vertices. */
11397 for (triangleloop.orient = 0; triangleloop.orient < 3;
11398 triangleloop.orient++) {
11399 /* Take the number for the origin of triangleloop. */
11400 aroundvertex = corner[triangleloop.orient];
11401 /* Look for other triangles having this vertex. */
11402 nexttri = vertexarray[aroundvertex - b->firstnumber];
11403 /* Link the current triangle to the next one in the stack. */
11404 triangleloop.tri[6 + triangleloop.orient] = nexttri;
11405 /* Push the current triangle onto the stack. */
11406 vertexarray[aroundvertex - b->firstnumber] = encode(triangleloop);
11407 decode(nexttri, checktri);
11408 if (checktri.tri != m->dummytri) {
11409 dest(triangleloop, tdest);
11410 apex(triangleloop, tapex);
11411 /* Look for other triangles that share an edge. */
11412 do {
11413 dest(checktri, checkdest);
11414 apex(checktri, checkapex);
11415 if (tapex == checkdest) {
11416 /* The two triangles share an edge; bond them together. */
11417 lprev(triangleloop, triangleleft);
11418 bond(triangleleft, checktri);
11419 }
11420 if (tdest == checkapex) {
11421 /* The two triangles share an edge; bond them together. */
11422 lprev(checktri, checkleft);
11423 bond(triangleloop, checkleft);
11424 }
11425 /* Find the next triangle in the stack. */
11426 nexttri = checktri.tri[6 + checktri.orient];
11427 decode(nexttri, checktri);
11428 } while (checktri.tri != m->dummytri);
11429 }
11430 }
11431 triangleloop.tri = triangletraverse(m);
11432 elementnumber++;
11433 }
11434
11435 #ifdef TRILIBRARY
11436 vertexindex = 0;
11437 #else /* not TRILIBRARY */
11438 fclose(elefile);
11439 if (b->vararea) {
11440 fclose(areafile);
11441 }
11442 #endif /* not TRILIBRARY */
11443
11444 hullsize = 0; /* Prepare to count the boundary edges. */
11445 if (b->poly) {
11446 if (b->verbose) {
11447 printf(" Marking segments in triangulation.\n");
11448 }
11449 /* Read the segments from the .poly file, and link them */
11450 /* to their neighboring triangles. */
11451 boundmarker = 0;
11452 traversalinit(&m->subsegs);
11453 subsegloop.ss = subsegtraverse(m);
11454 segmentnumber = b->firstnumber;
11455 while (subsegloop.ss != (subseg *) NULL) {
11456 #ifdef TRILIBRARY
11457 end[0] = segmentlist[vertexindex++];
11458 end[1] = segmentlist[vertexindex++];
11459 if (segmentmarkers) {
11460 boundmarker = segmentmarkerlist[segmentnumber - b->firstnumber];
11461 }
11462 #else /* not TRILIBRARY */
11463 /* Read the endpoints of each segment, and possibly a boundary marker. */
11464 stringptr = readline(inputline, polyfile, b->inpolyfilename);
11465 /* Skip the first (segment number) field. */
11466 stringptr = findfield(stringptr);
11467 if (*stringptr == '\0') {
11468 printf("Error: Segment %ld has no endpoints in %s.\n", segmentnumber,
11469 polyfilename);
11470 triexit(1);
11471 } else {
11472 end[0] = (int) strtol(stringptr, &stringptr, 0);
11473 }
11474 stringptr = findfield(stringptr);
11475 if (*stringptr == '\0') {
11476 printf("Error: Segment %ld is missing its second endpoint in %s.\n",
11477 segmentnumber, polyfilename);
11478 triexit(1);
11479 } else {
11480 end[1] = (int) strtol(stringptr, &stringptr, 0);
11481 }
11482 if (segmentmarkers) {
11483 stringptr = findfield(stringptr);
11484 if (*stringptr == '\0') {
11485 boundmarker = 0;
11486 } else {
11487 boundmarker = (int) strtol(stringptr, &stringptr, 0);
11488 }
11489 }
11490 #endif /* not TRILIBRARY */
11491 for (j = 0; j < 2; j++) {
11492 if ((end[j] < b->firstnumber) ||
11493 (end[j] >= b->firstnumber + m->invertices)) {
11494 printf("Error: Segment %ld has an invalid vertex index.\n",
11495 segmentnumber);
11496 triexit(1);
11497 }
11498 }
11499
11500 /* set the subsegment's vertices. */
11501 subsegloop.ssorient = 0;
11502 segmentorg = getvertex(m, b, end[0]);
11503 segmentdest = getvertex(m, b, end[1]);
11504 setsorg(subsegloop, segmentorg);
11505 setsdest(subsegloop, segmentdest);
11506 setsegorg(subsegloop, segmentorg);
11507 setsegdest(subsegloop, segmentdest);
11508 setmark(subsegloop, boundmarker);
11509 /* Try linking the subsegment to triangles that share these vertices. */
11510 for (subsegloop.ssorient = 0; subsegloop.ssorient < 2;
11511 subsegloop.ssorient++) {
11512 /* Take the number for the destination of subsegloop. */
11513 aroundvertex = end[1 - subsegloop.ssorient];
11514 /* Look for triangles having this vertex. */
11515 prevlink = &vertexarray[aroundvertex - b->firstnumber];
11516 nexttri = vertexarray[aroundvertex - b->firstnumber];
11517 decode(nexttri, checktri);
11518 sorg(subsegloop, shorg);
11519 notfound = 1;
11520 /* Look for triangles having this edge. Note that I'm only */
11521 /* comparing each triangle's destination with the subsegment; */
11522 /* each triangle's apex is handled through a different vertex. */
11523 /* Because each triangle appears on three vertices' lists, each */
11524 /* occurrence of a triangle on a list can (and does) represent */
11525 /* an edge. In this way, most edges are represented twice, and */
11526 /* every triangle-subsegment bond is represented once. */
11527 while (notfound && (checktri.tri != m->dummytri)) {
11528 dest(checktri, checkdest);
11529 if (shorg == checkdest) {
11530 /* We have a match. Remove this triangle from the list. */
11531 *prevlink = checktri.tri[6 + checktri.orient];
11532 /* Bond the subsegment to the triangle. */
11533 tsbond(checktri, subsegloop);
11534 /* Check if this is a boundary edge. */
11535 sym(checktri, checkneighbor);
11536 if (checkneighbor.tri == m->dummytri) {
11537 /* The next line doesn't insert a subsegment (because there's */
11538 /* already one there), but it sets the boundary markers of */
11539 /* the existing subsegment and its vertices. */
11540 insertsubseg(m, b, &checktri, 1);
11541 hullsize++;
11542 }
11543 notfound = 0;
11544 }
11545 /* Find the next triangle in the stack. */
11546 prevlink = &checktri.tri[6 + checktri.orient];
11547 nexttri = checktri.tri[6 + checktri.orient];
11548 decode(nexttri, checktri);
11549 }
11550 }
11551 subsegloop.ss = subsegtraverse(m);
11552 segmentnumber++;
11553 }
11554 }
11555
11556 /* Mark the remaining edges as not being attached to any subsegment. */
11557 /* Also, count the (yet uncounted) boundary edges. */
11558 for (i = 0; i < m->vertices.items; i++) {
11559 /* Search the stack of triangles adjacent to a vertex. */
11560 nexttri = vertexarray[i];
11561 decode(nexttri, checktri);
11562 while (checktri.tri != m->dummytri) {
11563 /* Find the next triangle in the stack before this */
11564 /* information gets overwritten. */
11565 nexttri = checktri.tri[6 + checktri.orient];
11566 /* No adjacent subsegment. (This overwrites the stack info.) */
11567 tsdissolve(checktri);
11568 sym(checktri, checkneighbor);
11569 if (checkneighbor.tri == m->dummytri) {
11570 insertsubseg(m, b, &checktri, 1);
11571 hullsize++;
11572 }
11573 decode(nexttri, checktri);
11574 }
11575 }
11576
11577 trifree((VOID *) vertexarray);
11578 return hullsize;
11579 }
11580
11581 #endif /* not CDT_ONLY */
11582
11583 /** **/
11584 /** **/
11585 /********* General mesh construction routines end here *********/
11586
11587 /********* Segment insertion begins here *********/
11588 /** **/
11589 /** **/
11590
11591 /*****************************************************************************/
11592 /* */
11593 /* finddirection() Find the first triangle on the path from one point */
11594 /* to another. */
11595 /* */
11596 /* Finds the triangle that intersects a line segment drawn from the */
11597 /* origin of `searchtri' to the point `searchpoint', and returns the result */
11598 /* in `searchtri'. The origin of `searchtri' does not change, even though */
11599 /* the triangle returned may differ from the one passed in. This routine */
11600 /* is used to find the direction to move in to get from one point to */
11601 /* another. */
11602 /* */
11603 /* The return value notes whether the destination or apex of the found */
11604 /* triangle is collinear with the two points in question. */
11605 /* */
11606 /*****************************************************************************/
11607
11608 #ifdef ANSI_DECLARATORS
11609 enum finddirectionresult finddirection(struct mesh *m, struct behavior *b,
11610 struct otri *searchtri,
11611 vertex searchpoint)
11612 #else /* not ANSI_DECLARATORS */
11613 enum finddirectionresult finddirection(m, b, searchtri, searchpoint)
11614 struct mesh *m;
11615 struct behavior *b;
11616 struct otri *searchtri;
11617 vertex searchpoint;
11618 #endif /* not ANSI_DECLARATORS */
11619
11620 {
11621 struct otri checktri;
11622 vertex startvertex;
11623 vertex leftvertex, rightvertex;
11624 REAL leftccw, rightccw;
11625 int leftflag, rightflag;
11626 triangle ptr; /* Temporary variable used by onext() and oprev(). */
11627
11628 org(*searchtri, startvertex);
11629 dest(*searchtri, rightvertex);
11630 apex(*searchtri, leftvertex);
11631 /* Is `searchpoint' to the left? */
11632 leftccw = counterclockwise(m, b, searchpoint, startvertex, leftvertex);
11633 leftflag = leftccw > 0.0;
11634 /* Is `searchpoint' to the right? */
11635 rightccw = counterclockwise(m, b, startvertex, searchpoint, rightvertex);
11636 rightflag = rightccw > 0.0;
11637 if (leftflag && rightflag) {
11638 /* `searchtri' faces directly away from `searchpoint'. We could go left */
11639 /* or right. Ask whether it's a triangle or a boundary on the left. */
11640 onext(*searchtri, checktri);
11641 if (checktri.tri == m->dummytri) {
11642 leftflag = 0;
11643 } else {
11644 rightflag = 0;
11645 }
11646 }
11647 while (leftflag) {
11648 /* Turn left until satisfied. */
11649 onextself(*searchtri);
11650 if (searchtri->tri == m->dummytri) {
11651 printf("Internal error in finddirection(): Unable to find a\n");
11652 printf(" triangle leading from (%.12g, %.12g) to", (double)startvertex[0],
11653 (double)startvertex[1]);
11654 printf(" (%.12g, %.12g).\n", (double)searchpoint[0], (double)searchpoint[1]);
11655 internalerror();
11656 }
11657 apex(*searchtri, leftvertex);
11658 rightccw = leftccw;
11659 leftccw = counterclockwise(m, b, searchpoint, startvertex, leftvertex);
11660 leftflag = leftccw > 0.0;
11661 }
11662 while (rightflag) {
11663 /* Turn right until satisfied. */
11664 oprevself(*searchtri);
11665 if (searchtri->tri == m->dummytri) {
11666 printf("Internal error in finddirection(): Unable to find a\n");
11667 printf(" triangle leading from (%.12g, %.12g) to", (double)startvertex[0],
11668 (double)startvertex[1]);
11669 printf(" (%.12g, %.12g).\n", (double)searchpoint[0], (double)searchpoint[1]);
11670 internalerror();
11671 }
11672 dest(*searchtri, rightvertex);
11673 leftccw = rightccw;
11674 rightccw = counterclockwise(m, b, startvertex, searchpoint, rightvertex);
11675 rightflag = rightccw > 0.0;
11676 }
11677 if (leftccw == 0.0) {
11678 return LEFTCOLLINEAR;
11679 } else if (rightccw == 0.0) {
11680 return RIGHTCOLLINEAR;
11681 } else {
11682 return WITHIN;
11683 }
11684 }
11685
11686 /*****************************************************************************/
11687 /* */
11688 /* segmentintersection() Find the intersection of an existing segment */
11689 /* and a segment that is being inserted. Insert */
11690 /* a vertex at the intersection, splitting an */
11691 /* existing subsegment. */
11692 /* */
11693 /* The segment being inserted connects the apex of splittri to endpoint2. */
11694 /* splitsubseg is the subsegment being split, and MUST adjoin splittri. */
11695 /* Hence, endpoints of the subsegment being split are the origin and */
11696 /* destination of splittri. */
11697 /* */
11698 /* On completion, splittri is a handle having the newly inserted */
11699 /* intersection point as its origin, and endpoint1 as its destination. */
11700 /* */
11701 /*****************************************************************************/
11702
11703 #ifdef ANSI_DECLARATORS
11704 void segmentintersection(struct mesh *m, struct behavior *b,
11705 struct otri *splittri, struct osub *splitsubseg,
11706 vertex endpoint2)
11707 #else /* not ANSI_DECLARATORS */
11708 void segmentintersection(m, b, splittri, splitsubseg, endpoint2)
11709 struct mesh *m;
11710 struct behavior *b;
11711 struct otri *splittri;
11712 struct osub *splitsubseg;
11713 vertex endpoint2;
11714 #endif /* not ANSI_DECLARATORS */
11715
11716 {
11717 struct osub opposubseg;
11718 vertex endpoint1;
11719 vertex torg, tdest;
11720 vertex leftvertex, rightvertex;
11721 vertex newvertex;
11722 enum insertvertexresult success;
11723 enum finddirectionresult collinear;
11724 REAL ex, ey;
11725 REAL tx, ty;
11726 REAL etx, ety;
11727 REAL split, denom;
11728 int i;
11729 triangle ptr; /* Temporary variable used by onext(). */
11730 subseg sptr; /* Temporary variable used by snext(). */
11731
11732 /* Find the other three segment endpoints. */
11733 apex(*splittri, endpoint1);
11734 org(*splittri, torg);
11735 dest(*splittri, tdest);
11736 /* Segment intersection formulae; see the Antonio reference. */
11737 tx = tdest[0] - torg[0];
11738 ty = tdest[1] - torg[1];
11739 ex = endpoint2[0] - endpoint1[0];
11740 ey = endpoint2[1] - endpoint1[1];
11741 etx = torg[0] - endpoint2[0];
11742 ety = torg[1] - endpoint2[1];
11743 denom = ty * ex - tx * ey;
11744 if (denom == 0.0) {
11745 printf("Internal error in segmentintersection():");
11746 printf(" Attempt to find intersection of parallel segments.\n");
11747 internalerror();
11748 }
11749 split = (ey * etx - ex * ety) / denom;
11750 /* Create the new vertex. */
11751 newvertex = (vertex) poolalloc(&m->vertices);
11752 /* Interpolate its coordinate and attributes. */
11753 for (i = 0; i < 2 + m->nextras; i++) {
11754 newvertex[i] = torg[i] + split * (tdest[i] - torg[i]);
11755 }
11756 setvertexmark(newvertex, mark(*splitsubseg));
11757 setvertextype(newvertex, INPUTVERTEX);
11758 if (b->verbose > 1) {
11759 printf(
11760 " Splitting subsegment (%.12g, %.12g) (%.12g, %.12g) at (%.12g, %.12g).\n",
11761 (double)torg[0], (double)torg[1], (double)tdest[0], (double)tdest[1], (double)newvertex[0], (double)newvertex[1]);
11762 }
11763 /* Insert the intersection vertex. This should always succeed. */
11764 success = insertvertex(m, b, newvertex, splittri, splitsubseg, 0, 0);
11765 if (success != SUCCESSFULVERTEX) {
11766 printf("Internal error in segmentintersection():\n");
11767 printf(" Failure to split a segment.\n");
11768 internalerror();
11769 }
11770 /* Record a triangle whose origin is the new vertex. */
11771 setvertex2tri(newvertex, encode(*splittri));
11772 if (m->steinerleft > 0) {
11773 m->steinerleft--;
11774 }
11775
11776 /* Divide the segment into two, and correct the segment endpoints. */
11777 ssymself(*splitsubseg);
11778 spivot(*splitsubseg, opposubseg);
11779 sdissolve(*splitsubseg);
11780 sdissolve(opposubseg);
11781 do {
11782 setsegorg(*splitsubseg, newvertex);
11783 snextself(*splitsubseg);
11784 } while (splitsubseg->ss != m->dummysub);
11785 do {
11786 setsegorg(opposubseg, newvertex);
11787 snextself(opposubseg);
11788 } while (opposubseg.ss != m->dummysub);
11789
11790 /* Inserting the vertex may have caused edge flips. We wish to rediscover */
11791 /* the edge connecting endpoint1 to the new intersection vertex. */
11792 collinear = finddirection(m, b, splittri, endpoint1);
11793 dest(*splittri, rightvertex);
11794 apex(*splittri, leftvertex);
11795 if ((leftvertex[0] == endpoint1[0]) && (leftvertex[1] == endpoint1[1])) {
11796 onextself(*splittri);
11797 } else if ((rightvertex[0] != endpoint1[0]) ||
11798 (rightvertex[1] != endpoint1[1])) {
11799 printf("Internal error in segmentintersection():\n");
11800 printf(" Topological inconsistency after splitting a segment.\n");
11801 internalerror();
11802 }
11803 /* `splittri' should have destination endpoint1. */
11804 }
11805
11806 /*****************************************************************************/
11807 /* */
11808 /* scoutsegment() Scout the first triangle on the path from one endpoint */
11809 /* to another, and check for completion (reaching the */
11810 /* second endpoint), a collinear vertex, or the */
11811 /* intersection of two segments. */
11812 /* */
11813 /* Returns one if the entire segment is successfully inserted, and zero if */
11814 /* the job must be finished by conformingedge() or constrainededge(). */
11815 /* */
11816 /* If the first triangle on the path has the second endpoint as its */
11817 /* destination or apex, a subsegment is inserted and the job is done. */
11818 /* */
11819 /* If the first triangle on the path has a destination or apex that lies on */
11820 /* the segment, a subsegment is inserted connecting the first endpoint to */
11821 /* the collinear vertex, and the search is continued from the collinear */
11822 /* vertex. */
11823 /* */
11824 /* If the first triangle on the path has a subsegment opposite its origin, */
11825 /* then there is a segment that intersects the segment being inserted. */
11826 /* Their intersection vertex is inserted, splitting the subsegment. */
11827 /* */
11828 /*****************************************************************************/
11829
11830 #ifdef ANSI_DECLARATORS
11831 int scoutsegment(struct mesh *m, struct behavior *b, struct otri *searchtri,
11832 vertex endpoint2, int newmark)
11833 #else /* not ANSI_DECLARATORS */
11834 int scoutsegment(m, b, searchtri, endpoint2, newmark)
11835 struct mesh *m;
11836 struct behavior *b;
11837 struct otri *searchtri;
11838 vertex endpoint2;
11839 int newmark;
11840 #endif /* not ANSI_DECLARATORS */
11841
11842 {
11843 struct otri crosstri;
11844 struct osub crosssubseg;
11845 vertex leftvertex, rightvertex;
11846 enum finddirectionresult collinear;
11847 subseg sptr; /* Temporary variable used by tspivot(). */
11848
11849 collinear = finddirection(m, b, searchtri, endpoint2);
11850 dest(*searchtri, rightvertex);
11851 apex(*searchtri, leftvertex);
11852 if (((leftvertex[0] == endpoint2[0]) && (leftvertex[1] == endpoint2[1])) ||
11853 ((rightvertex[0] == endpoint2[0]) && (rightvertex[1] == endpoint2[1]))) {
11854 /* The segment is already an edge in the mesh. */
11855 if ((leftvertex[0] == endpoint2[0]) && (leftvertex[1] == endpoint2[1])) {
11856 lprevself(*searchtri);
11857 }
11858 /* Insert a subsegment, if there isn't already one there. */
11859 insertsubseg(m, b, searchtri, newmark);
11860 return 1;
11861 } else if (collinear == LEFTCOLLINEAR) {
11862 /* We've collided with a vertex between the segment's endpoints. */
11863 /* Make the collinear vertex be the triangle's origin. */
11864 lprevself(*searchtri);
11865 insertsubseg(m, b, searchtri, newmark);
11866 /* Insert the remainder of the segment. */
11867 return scoutsegment(m, b, searchtri, endpoint2, newmark);
11868 } else if (collinear == RIGHTCOLLINEAR) {
11869 /* We've collided with a vertex between the segment's endpoints. */
11870 insertsubseg(m, b, searchtri, newmark);
11871 /* Make the collinear vertex be the triangle's origin. */
11872 lnextself(*searchtri);
11873 /* Insert the remainder of the segment. */
11874 return scoutsegment(m, b, searchtri, endpoint2, newmark);
11875 } else {
11876 lnext(*searchtri, crosstri);
11877 tspivot(crosstri, crosssubseg);
11878 /* Check for a crossing segment. */
11879 if (crosssubseg.ss == m->dummysub) {
11880 return 0;
11881 } else {
11882 /* Insert a vertex at the intersection. */
11883 segmentintersection(m, b, &crosstri, &crosssubseg, endpoint2);
11884 otricopy(crosstri, *searchtri);
11885 insertsubseg(m, b, searchtri, newmark);
11886 /* Insert the remainder of the segment. */
11887 return scoutsegment(m, b, searchtri, endpoint2, newmark);
11888 }
11889 }
11890 }
11891
11892 /*****************************************************************************/
11893 /* */
11894 /* conformingedge() Force a segment into a conforming Delaunay */
11895 /* triangulation by inserting a vertex at its midpoint, */
11896 /* and recursively forcing in the two half-segments if */
11897 /* necessary. */
11898 /* */
11899 /* Generates a sequence of subsegments connecting `endpoint1' to */
11900 /* `endpoint2'. `newmark' is the boundary marker of the segment, assigned */
11901 /* to each new splitting vertex and subsegment. */
11902 /* */
11903 /* Note that conformingedge() does not always maintain the conforming */
11904 /* Delaunay property. Once inserted, segments are locked into place; */
11905 /* vertices inserted later (to force other segments in) may render these */
11906 /* fixed segments non-Delaunay. The conforming Delaunay property will be */
11907 /* restored by enforcequality() by splitting encroached subsegments. */
11908 /* */
11909 /*****************************************************************************/
11910
11911 #ifndef REDUCED
11912 #ifndef CDT_ONLY
11913
11914 #ifdef ANSI_DECLARATORS
11915 void conformingedge(struct mesh *m, struct behavior *b,
11916 vertex endpoint1, vertex endpoint2, int newmark)
11917 #else /* not ANSI_DECLARATORS */
11918 void conformingedge(m, b, endpoint1, endpoint2, newmark)
11919 struct mesh *m;
11920 struct behavior *b;
11921 vertex endpoint1;
11922 vertex endpoint2;
11923 int newmark;
11924 #endif /* not ANSI_DECLARATORS */
11925
11926 {
11927 struct otri searchtri1, searchtri2;
11928 struct osub brokensubseg;
11929 vertex newvertex;
11930 vertex midvertex1, midvertex2;
11931 enum insertvertexresult success;
11932 int i;
11933 subseg sptr; /* Temporary variable used by tspivot(). */
11934
11935 if (b->verbose > 2) {
11936 printf("Forcing segment into triangulation by recursive splitting:\n");
11937 printf(" (%.12g, %.12g) (%.12g, %.12g)\n", (double)endpoint1[0], (double)endpoint1[1],
11938 (double)endpoint2[0], (double)endpoint2[1]);
11939 }
11940 /* Create a new vertex to insert in the middle of the segment. */
11941 newvertex = (vertex) poolalloc(&m->vertices);
11942 /* Interpolate coordinates and attributes. */
11943 for (i = 0; i < 2 + m->nextras; i++) {
11944 newvertex[i] = 0.5 * (endpoint1[i] + endpoint2[i]);
11945 }
11946 setvertexmark(newvertex, newmark);
11947 setvertextype(newvertex, SEGMENTVERTEX);
11948 /* No known triangle to search from. */
11949 searchtri1.tri = m->dummytri;
11950 /* Attempt to insert the new vertex. */
11951 success = insertvertex(m, b, newvertex, &searchtri1, (struct osub *) NULL,
11952 0, 0);
11953 if (success == DUPLICATEVERTEX) {
11954 if (b->verbose > 2) {
11955 printf(" Segment intersects existing vertex (%.12g, %.12g).\n",
11956 (double)newvertex[0], (double)newvertex[1]);
11957 }
11958 /* Use the vertex that's already there. */
11959 vertexdealloc(m, newvertex);
11960 org(searchtri1, newvertex);
11961 } else {
11962 if (success == VIOLATINGVERTEX) {
11963 if (b->verbose > 2) {
11964 printf(" Two segments intersect at (%.12g, %.12g).\n",
11965 (double)newvertex[0], (double)newvertex[1]);
11966 }
11967 /* By fluke, we've landed right on another segment. Split it. */
11968 tspivot(searchtri1, brokensubseg);
11969 success = insertvertex(m, b, newvertex, &searchtri1, &brokensubseg,
11970 0, 0);
11971 if (success != SUCCESSFULVERTEX) {
11972 printf("Internal error in conformingedge():\n");
11973 printf(" Failure to split a segment.\n");
11974 internalerror();
11975 }
11976 }
11977 /* The vertex has been inserted successfully. */
11978 if (m->steinerleft > 0) {
11979 m->steinerleft--;
11980 }
11981 }
11982 otricopy(searchtri1, searchtri2);
11983 /* `searchtri1' and `searchtri2' are fastened at their origins to */
11984 /* `newvertex', and will be directed toward `endpoint1' and `endpoint2' */
11985 /* respectively. First, we must get `searchtri2' out of the way so it */
11986 /* won't be invalidated during the insertion of the first half of the */
11987 /* segment. */
11988 finddirection(m, b, &searchtri2, endpoint2);
11989 if (!scoutsegment(m, b, &searchtri1, endpoint1, newmark)) {
11990 /* The origin of searchtri1 may have changed if a collision with an */
11991 /* intervening vertex on the segment occurred. */
11992 org(searchtri1, midvertex1);
11993 conformingedge(m, b, midvertex1, endpoint1, newmark);
11994 }
11995 if (!scoutsegment(m, b, &searchtri2, endpoint2, newmark)) {
11996 /* The origin of searchtri2 may have changed if a collision with an */
11997 /* intervening vertex on the segment occurred. */
11998 org(searchtri2, midvertex2);
11999 conformingedge(m, b, midvertex2, endpoint2, newmark);
12000 }
12001 }
12002
12003 #endif /* not CDT_ONLY */
12004 #endif /* not REDUCED */
12005
12006 /*****************************************************************************/
12007 /* */
12008 /* delaunayfixup() Enforce the Delaunay condition at an edge, fanning out */
12009 /* recursively from an existing vertex. Pay special */
12010 /* attention to stacking inverted triangles. */
12011 /* */
12012 /* This is a support routine for inserting segments into a constrained */
12013 /* Delaunay triangulation. */
12014 /* */
12015 /* The origin of fixuptri is treated as if it has just been inserted, and */
12016 /* the local Delaunay condition needs to be enforced. It is only enforced */
12017 /* in one sector, however, that being the angular range defined by */
12018 /* fixuptri. */
12019 /* */
12020 /* This routine also needs to make decisions regarding the "stacking" of */
12021 /* triangles. (Read the description of constrainededge() below before */
12022 /* reading on here, so you understand the algorithm.) If the position of */
12023 /* the new vertex (the origin of fixuptri) indicates that the vertex before */
12024 /* it on the polygon is a reflex vertex, then "stack" the triangle by */
12025 /* doing nothing. (fixuptri is an inverted triangle, which is how stacked */
12026 /* triangles are identified.) */
12027 /* */
12028 /* Otherwise, check whether the vertex before that was a reflex vertex. */
12029 /* If so, perform an edge flip, thereby eliminating an inverted triangle */
12030 /* (popping it off the stack). The edge flip may result in the creation */
12031 /* of a new inverted triangle, depending on whether or not the new vertex */
12032 /* is visible to the vertex three edges behind on the polygon. */
12033 /* */
12034 /* If neither of the two vertices behind the new vertex are reflex */
12035 /* vertices, fixuptri and fartri, the triangle opposite it, are not */
12036 /* inverted; hence, ensure that the edge between them is locally Delaunay. */
12037 /* */
12038 /* `leftside' indicates whether or not fixuptri is to the left of the */
12039 /* segment being inserted. (Imagine that the segment is pointing up from */
12040 /* endpoint1 to endpoint2.) */
12041 /* */
12042 /*****************************************************************************/
12043
12044 #ifdef ANSI_DECLARATORS
12045 void delaunayfixup(struct mesh *m, struct behavior *b,
12046 struct otri *fixuptri, int leftside)
12047 #else /* not ANSI_DECLARATORS */
12048 void delaunayfixup(m, b, fixuptri, leftside)
12049 struct mesh *m;
12050 struct behavior *b;
12051 struct otri *fixuptri;
12052 int leftside;
12053 #endif /* not ANSI_DECLARATORS */
12054
12055 {
12056 struct otri neartri;
12057 struct otri fartri;
12058 struct osub faredge;
12059 vertex nearvertex, leftvertex, rightvertex, farvertex;
12060 triangle ptr; /* Temporary variable used by sym(). */
12061 subseg sptr; /* Temporary variable used by tspivot(). */
12062
12063 lnext(*fixuptri, neartri);
12064 sym(neartri, fartri);
12065 /* Check if the edge opposite the origin of fixuptri can be flipped. */
12066 if (fartri.tri == m->dummytri) {
12067 return;
12068 }
12069 tspivot(neartri, faredge);
12070 if (faredge.ss != m->dummysub) {
12071 return;
12072 }
12073 /* Find all the relevant vertices. */
12074 apex(neartri, nearvertex);
12075 org(neartri, leftvertex);
12076 dest(neartri, rightvertex);
12077 apex(fartri, farvertex);
12078 /* Check whether the previous polygon vertex is a reflex vertex. */
12079 if (leftside) {
12080 if (counterclockwise(m, b, nearvertex, leftvertex, farvertex) <= 0.0) {
12081 /* leftvertex is a reflex vertex too. Nothing can */
12082 /* be done until a convex section is found. */
12083 return;
12084 }
12085 } else {
12086 if (counterclockwise(m, b, farvertex, rightvertex, nearvertex) <= 0.0) {
12087 /* rightvertex is a reflex vertex too. Nothing can */
12088 /* be done until a convex section is found. */
12089 return;
12090 }
12091 }
12092 if (counterclockwise(m, b, rightvertex, leftvertex, farvertex) > 0.0) {
12093 /* fartri is not an inverted triangle, and farvertex is not a reflex */
12094 /* vertex. As there are no reflex vertices, fixuptri isn't an */
12095 /* inverted triangle, either. Hence, test the edge between the */
12096 /* triangles to ensure it is locally Delaunay. */
12097 if (incircle(m, b, leftvertex, farvertex, rightvertex, nearvertex) <=
12098 0.0) {
12099 return;
12100 }
12101 /* Not locally Delaunay; go on to an edge flip. */
12102 } /* else fartri is inverted; remove it from the stack by flipping. */
12103 flip(m, b, &neartri);
12104 lprevself(*fixuptri); /* Restore the origin of fixuptri after the flip. */
12105 /* Recursively process the two triangles that result from the flip. */
12106 delaunayfixup(m, b, fixuptri, leftside);
12107 delaunayfixup(m, b, &fartri, leftside);
12108 }
12109
12110 /*****************************************************************************/
12111 /* */
12112 /* constrainededge() Force a segment into a constrained Delaunay */
12113 /* triangulation by deleting the triangles it */
12114 /* intersects, and triangulating the polygons that */
12115 /* form on each side of it. */
12116 /* */
12117 /* Generates a single subsegment connecting `endpoint1' to `endpoint2'. */
12118 /* The triangle `starttri' has `endpoint1' as its origin. `newmark' is the */
12119 /* boundary marker of the segment. */
12120 /* */
12121 /* To insert a segment, every triangle whose interior intersects the */
12122 /* segment is deleted. The union of these deleted triangles is a polygon */
12123 /* (which is not necessarily monotone, but is close enough), which is */
12124 /* divided into two polygons by the new segment. This routine's task is */
12125 /* to generate the Delaunay triangulation of these two polygons. */
12126 /* */
12127 /* You might think of this routine's behavior as a two-step process. The */
12128 /* first step is to walk from endpoint1 to endpoint2, flipping each edge */
12129 /* encountered. This step creates a fan of edges connected to endpoint1, */
12130 /* including the desired edge to endpoint2. The second step enforces the */
12131 /* Delaunay condition on each side of the segment in an incremental manner: */
12132 /* proceeding along the polygon from endpoint1 to endpoint2 (this is done */
12133 /* independently on each side of the segment), each vertex is "enforced" */
12134 /* as if it had just been inserted, but affecting only the previous */
12135 /* vertices. The result is the same as if the vertices had been inserted */
12136 /* in the order they appear on the polygon, so the result is Delaunay. */
12137 /* */
12138 /* In truth, constrainededge() interleaves these two steps. The procedure */
12139 /* walks from endpoint1 to endpoint2, and each time an edge is encountered */
12140 /* and flipped, the newly exposed vertex (at the far end of the flipped */
12141 /* edge) is "enforced" upon the previously flipped edges, usually affecting */
12142 /* only one side of the polygon (depending upon which side of the segment */
12143 /* the vertex falls on). */
12144 /* */
12145 /* The algorithm is complicated by the need to handle polygons that are not */
12146 /* convex. Although the polygon is not necessarily monotone, it can be */
12147 /* triangulated in a manner similar to the stack-based algorithms for */
12148 /* monotone polygons. For each reflex vertex (local concavity) of the */
12149 /* polygon, there will be an inverted triangle formed by one of the edge */
12150 /* flips. (An inverted triangle is one with negative area - that is, its */
12151 /* vertices are arranged in clockwise order - and is best thought of as a */
12152 /* wrinkle in the fabric of the mesh.) Each inverted triangle can be */
12153 /* thought of as a reflex vertex pushed on the stack, waiting to be fixed */
12154 /* later. */
12155 /* */
12156 /* A reflex vertex is popped from the stack when a vertex is inserted that */
12157 /* is visible to the reflex vertex. (However, if the vertex behind the */
12158 /* reflex vertex is not visible to the reflex vertex, a new inverted */
12159 /* triangle will take its place on the stack.) These details are handled */
12160 /* by the delaunayfixup() routine above. */
12161 /* */
12162 /*****************************************************************************/
12163
12164 #ifdef ANSI_DECLARATORS
12165 void constrainededge(struct mesh *m, struct behavior *b,
12166 struct otri *starttri, vertex endpoint2, int newmark)
12167 #else /* not ANSI_DECLARATORS */
12168 void constrainededge(m, b, starttri, endpoint2, newmark)
12169 struct mesh *m;
12170 struct behavior *b;
12171 struct otri *starttri;
12172 vertex endpoint2;
12173 int newmark;
12174 #endif /* not ANSI_DECLARATORS */
12175
12176 {
12177 struct otri fixuptri, fixuptri2;
12178 struct osub crosssubseg;
12179 vertex endpoint1;
12180 vertex farvertex;
12181 REAL area;
12182 int collision;
12183 int done;
12184 triangle ptr; /* Temporary variable used by sym() and oprev(). */
12185 subseg sptr; /* Temporary variable used by tspivot(). */
12186
12187 org(*starttri, endpoint1);
12188 lnext(*starttri, fixuptri);
12189 flip(m, b, &fixuptri);
12190 /* `collision' indicates whether we have found a vertex directly */
12191 /* between endpoint1 and endpoint2. */
12192 collision = 0;
12193 done = 0;
12194 do {
12195 org(fixuptri, farvertex);
12196 /* `farvertex' is the extreme point of the polygon we are "digging" */
12197 /* to get from endpoint1 to endpoint2. */
12198 if ((farvertex[0] == endpoint2[0]) && (farvertex[1] == endpoint2[1])) {
12199 oprev(fixuptri, fixuptri2);
12200 /* Enforce the Delaunay condition around endpoint2. */
12201 delaunayfixup(m, b, &fixuptri, 0);
12202 delaunayfixup(m, b, &fixuptri2, 1);
12203 done = 1;
12204 } else {
12205 /* Check whether farvertex is to the left or right of the segment */
12206 /* being inserted, to decide which edge of fixuptri to dig */
12207 /* through next. */
12208 area = counterclockwise(m, b, endpoint1, endpoint2, farvertex);
12209 if (area == 0.0) {
12210 /* We've collided with a vertex between endpoint1 and endpoint2. */
12211 collision = 1;
12212 oprev(fixuptri, fixuptri2);
12213 /* Enforce the Delaunay condition around farvertex. */
12214 delaunayfixup(m, b, &fixuptri, 0);
12215 delaunayfixup(m, b, &fixuptri2, 1);
12216 done = 1;
12217 } else {
12218 if (area > 0.0) { /* farvertex is to the left of the segment. */
12219 oprev(fixuptri, fixuptri2);
12220 /* Enforce the Delaunay condition around farvertex, on the */
12221 /* left side of the segment only. */
12222 delaunayfixup(m, b, &fixuptri2, 1);
12223 /* Flip the edge that crosses the segment. After the edge is */
12224 /* flipped, one of its endpoints is the fan vertex, and the */
12225 /* destination of fixuptri is the fan vertex. */
12226 lprevself(fixuptri);
12227 } else { /* farvertex is to the right of the segment. */
12228 delaunayfixup(m, b, &fixuptri, 0);
12229 /* Flip the edge that crosses the segment. After the edge is */
12230 /* flipped, one of its endpoints is the fan vertex, and the */
12231 /* destination of fixuptri is the fan vertex. */
12232 oprevself(fixuptri);
12233 }
12234 /* Check for two intersecting segments. */
12235 tspivot(fixuptri, crosssubseg);
12236 if (crosssubseg.ss == m->dummysub) {
12237 flip(m, b, &fixuptri); /* May create inverted triangle at left. */
12238 } else {
12239 /* We've collided with a segment between endpoint1 and endpoint2. */
12240 collision = 1;
12241 /* Insert a vertex at the intersection. */
12242 segmentintersection(m, b, &fixuptri, &crosssubseg, endpoint2);
12243 done = 1;
12244 }
12245 }
12246 }
12247 } while (!done);
12248 /* Insert a subsegment to make the segment permanent. */
12249 insertsubseg(m, b, &fixuptri, newmark);
12250 /* If there was a collision with an interceding vertex, install another */
12251 /* segment connecting that vertex with endpoint2. */
12252 if (collision) {
12253 /* Insert the remainder of the segment. */
12254 if (!scoutsegment(m, b, &fixuptri, endpoint2, newmark)) {
12255 constrainededge(m, b, &fixuptri, endpoint2, newmark);
12256 }
12257 }
12258 }
12259
12260 /*****************************************************************************/
12261 /* */
12262 /* insertsegment() Insert a PSLG segment into a triangulation. */
12263 /* */
12264 /*****************************************************************************/
12265
12266 #ifdef ANSI_DECLARATORS
12267 void insertsegment(struct mesh *m, struct behavior *b,
12268 vertex endpoint1, vertex endpoint2, int newmark)
12269 #else /* not ANSI_DECLARATORS */
12270 void insertsegment(m, b, endpoint1, endpoint2, newmark)
12271 struct mesh *m;
12272 struct behavior *b;
12273 vertex endpoint1;
12274 vertex endpoint2;
12275 int newmark;
12276 #endif /* not ANSI_DECLARATORS */
12277
12278 {
12279 struct otri searchtri1, searchtri2;
12280 triangle encodedtri;
12281 vertex checkvertex;
12282 triangle ptr; /* Temporary variable used by sym(). */
12283
12284 if (b->verbose > 1) {
12285 printf(" Connecting (%.12g, %.12g) to (%.12g, %.12g).\n",
12286 (double)endpoint1[0], (double)endpoint1[1], (double)endpoint2[0], (double)endpoint2[1]);
12287 }
12288
12289 /* Find a triangle whose origin is the segment's first endpoint. */
12290 checkvertex = (vertex) NULL;
12291 encodedtri = vertex2tri(endpoint1);
12292 if (encodedtri != (triangle) NULL) {
12293 decode(encodedtri, searchtri1);
12294 org(searchtri1, checkvertex);
12295 }
12296 if (checkvertex != endpoint1) {
12297 /* Find a boundary triangle to search from. */
12298 searchtri1.tri = m->dummytri;
12299 searchtri1.orient = 0;
12300 symself(searchtri1);
12301 /* Search for the segment's first endpoint by point location. */
12302 if (locate(m, b, endpoint1, &searchtri1) != ONVERTEX) {
12303 printf(
12304 "Internal error in insertsegment(): Unable to locate PSLG vertex\n");
12305 printf(" (%.12g, %.12g) in triangulation.\n",
12306 (double)endpoint1[0], (double)endpoint1[1]);
12307 internalerror();
12308 }
12309 }
12310 /* Remember this triangle to improve subsequent point location. */
12311 otricopy(searchtri1, m->recenttri);
12312 /* Scout the beginnings of a path from the first endpoint */
12313 /* toward the second. */
12314 if (scoutsegment(m, b, &searchtri1, endpoint2, newmark)) {
12315 /* The segment was easily inserted. */
12316 return;
12317 }
12318 /* The first endpoint may have changed if a collision with an intervening */
12319 /* vertex on the segment occurred. */
12320 org(searchtri1, endpoint1);
12321
12322 /* Find a triangle whose origin is the segment's second endpoint. */
12323 checkvertex = (vertex) NULL;
12324 encodedtri = vertex2tri(endpoint2);
12325 if (encodedtri != (triangle) NULL) {
12326 decode(encodedtri, searchtri2);
12327 org(searchtri2, checkvertex);
12328 }
12329 if (checkvertex != endpoint2) {
12330 /* Find a boundary triangle to search from. */
12331 searchtri2.tri = m->dummytri;
12332 searchtri2.orient = 0;
12333 symself(searchtri2);
12334 /* Search for the segment's second endpoint by point location. */
12335 if (locate(m, b, endpoint2, &searchtri2) != ONVERTEX) {
12336 printf(
12337 "Internal error in insertsegment(): Unable to locate PSLG vertex\n");
12338 printf(" (%.12g, %.12g) in triangulation.\n",
12339 (double)endpoint2[0], (double)endpoint2[1]);
12340 internalerror();
12341 }
12342 }
12343 /* Remember this triangle to improve subsequent point location. */
12344 otricopy(searchtri2, m->recenttri);
12345 /* Scout the beginnings of a path from the second endpoint */
12346 /* toward the first. */
12347 if (scoutsegment(m, b, &searchtri2, endpoint1, newmark)) {
12348 /* The segment was easily inserted. */
12349 return;
12350 }
12351 /* The second endpoint may have changed if a collision with an intervening */
12352 /* vertex on the segment occurred. */
12353 org(searchtri2, endpoint2);
12354
12355 #ifndef REDUCED
12356 #ifndef CDT_ONLY
12357 if (b->splitseg) {
12358 /* Insert vertices to force the segment into the triangulation. */
12359 conformingedge(m, b, endpoint1, endpoint2, newmark);
12360 } else {
12361 #endif /* not CDT_ONLY */
12362 #endif /* not REDUCED */
12363 /* Insert the segment directly into the triangulation. */
12364 constrainededge(m, b, &searchtri1, endpoint2, newmark);
12365 #ifndef REDUCED
12366 #ifndef CDT_ONLY
12367 }
12368 #endif /* not CDT_ONLY */
12369 #endif /* not REDUCED */
12370 }
12371
12372 /*****************************************************************************/
12373 /* */
12374 /* markhull() Cover the convex hull of a triangulation with subsegments. */
12375 /* */
12376 /*****************************************************************************/
12377
12378 #ifdef ANSI_DECLARATORS
12379 void markhull(struct mesh *m, struct behavior *b)
12380 #else /* not ANSI_DECLARATORS */
12381 void markhull(m, b)
12382 struct mesh *m;
12383 struct behavior *b;
12384 #endif /* not ANSI_DECLARATORS */
12385
12386 {
12387 struct otri hulltri;
12388 struct otri nexttri;
12389 struct otri starttri;
12390 triangle ptr; /* Temporary variable used by sym() and oprev(). */
12391
12392 /* Find a triangle handle on the hull. */
12393 hulltri.tri = m->dummytri;
12394 hulltri.orient = 0;
12395 symself(hulltri);
12396 /* Remember where we started so we know when to stop. */
12397 otricopy(hulltri, starttri);
12398 /* Go once counterclockwise around the convex hull. */
12399 do {
12400 /* Create a subsegment if there isn't already one here. */
12401 insertsubseg(m, b, &hulltri, 1);
12402 /* To find the next hull edge, go clockwise around the next vertex. */
12403 lnextself(hulltri);
12404 oprev(hulltri, nexttri);
12405 while (nexttri.tri != m->dummytri) {
12406 otricopy(nexttri, hulltri);
12407 oprev(hulltri, nexttri);
12408 }
12409 } while (!otriequal(hulltri, starttri));
12410 }
12411
12412 /*****************************************************************************/
12413 /* */
12414 /* formskeleton() Create the segments of a triangulation, including PSLG */
12415 /* segments and edges on the convex hull. */
12416 /* */
12417 /* The PSLG segments are read from a .poly file. The return value is the */
12418 /* number of segments in the file. */
12419 /* */
12420 /*****************************************************************************/
12421
12422 #ifdef TRILIBRARY
12423
12424 #ifdef ANSI_DECLARATORS
12425 void formskeleton(struct mesh *m, struct behavior *b, int *segmentlist,
12426 int *segmentmarkerlist, int numberofsegments)
12427 #else /* not ANSI_DECLARATORS */
12428 void formskeleton(m, b, segmentlist, segmentmarkerlist, numberofsegments)
12429 struct mesh *m;
12430 struct behavior *b;
12431 int *segmentlist;
12432 int *segmentmarkerlist;
12433 int numberofsegments;
12434 #endif /* not ANSI_DECLARATORS */
12435
12436 #else /* not TRILIBRARY */
12437
12438 #ifdef ANSI_DECLARATORS
12439 void formskeleton(struct mesh *m, struct behavior *b,
12440 FILE *polyfile, char *polyfilename)
12441 #else /* not ANSI_DECLARATORS */
12442 void formskeleton(m, b, polyfile, polyfilename)
12443 struct mesh *m;
12444 struct behavior *b;
12445 FILE *polyfile;
12446 char *polyfilename;
12447 #endif /* not ANSI_DECLARATORS */
12448
12449 #endif /* not TRILIBRARY */
12450
12451 {
12452 #ifdef TRILIBRARY
12453 char polyfilename[6];
12454 int index;
12455 #else /* not TRILIBRARY */
12456 char inputline[INPUTLINESIZE];
12457 char *stringptr;
12458 #endif /* not TRILIBRARY */
12459 vertex endpoint1, endpoint2;
12460 int segmentmarkers;
12461 int end1, end2;
12462 int boundmarker;
12463 int i;
12464
12465 if (b->poly) {
12466 if (!b->quiet) {
12467 printf("Recovering segments in Delaunay triangulation.\n");
12468 }
12469 #ifdef TRILIBRARY
12470 strcpy(polyfilename, "input");
12471 m->insegments = numberofsegments;
12472 segmentmarkers = segmentmarkerlist != (int *) NULL;
12473 index = 0;
12474 #else /* not TRILIBRARY */
12475 /* Read the segments from a .poly file. */
12476 /* Read number of segments and number of boundary markers. */
12477 stringptr = readline(inputline, polyfile, polyfilename);
12478 m->insegments = (int) strtol(stringptr, &stringptr, 0);
12479 stringptr = findfield(stringptr);
12480 if (*stringptr == '\0') {
12481 segmentmarkers = 0;
12482 } else {
12483 segmentmarkers = (int) strtol(stringptr, &stringptr, 0);
12484 }
12485 #endif /* not TRILIBRARY */
12486 /* If the input vertices are collinear, there is no triangulation, */
12487 /* so don't try to insert segments. */
12488 if (m->triangles.items == 0) {
12489 return;
12490 }
12491
12492 /* If segments are to be inserted, compute a mapping */
12493 /* from vertices to triangles. */
12494 if (m->insegments > 0) {
12495 makevertexmap(m, b);
12496 if (b->verbose) {
12497 printf(" Recovering PSLG segments.\n");
12498 }
12499 }
12500
12501 boundmarker = 0;
12502 /* Read and insert the segments. */
12503 for (i = 0; i < m->insegments; i++) {
12504 #ifdef TRILIBRARY
12505 end1 = segmentlist[index++];
12506 end2 = segmentlist[index++];
12507 if (segmentmarkers) {
12508 boundmarker = segmentmarkerlist[i];
12509 }
12510 #else /* not TRILIBRARY */
12511 stringptr = readline(inputline, polyfile, b->inpolyfilename);
12512 stringptr = findfield(stringptr);
12513 if (*stringptr == '\0') {
12514 printf("Error: Segment %d has no endpoints in %s.\n",
12515 b->firstnumber + i, polyfilename);
12516 triexit(1);
12517 } else {
12518 end1 = (int) strtol(stringptr, &stringptr, 0);
12519 }
12520 stringptr = findfield(stringptr);
12521 if (*stringptr == '\0') {
12522 printf("Error: Segment %d is missing its second endpoint in %s.\n",
12523 b->firstnumber + i, polyfilename);
12524 triexit(1);
12525 } else {
12526 end2 = (int) strtol(stringptr, &stringptr, 0);
12527 }
12528 if (segmentmarkers) {
12529 stringptr = findfield(stringptr);
12530 if (*stringptr == '\0') {
12531 boundmarker = 0;
12532 } else {
12533 boundmarker = (int) strtol(stringptr, &stringptr, 0);
12534 }
12535 }
12536 #endif /* not TRILIBRARY */
12537 if ((end1 < b->firstnumber) ||
12538 (end1 >= b->firstnumber + m->invertices)) {
12539 if (!b->quiet) {
12540 printf("Warning: Invalid first endpoint of segment %d in %s.\n",
12541 b->firstnumber + i, polyfilename);
12542 }
12543 } else if ((end2 < b->firstnumber) ||
12544 (end2 >= b->firstnumber + m->invertices)) {
12545 if (!b->quiet) {
12546 printf("Warning: Invalid second endpoint of segment %d in %s.\n",
12547 b->firstnumber + i, polyfilename);
12548 }
12549 } else {
12550 /* Find the vertices numbered `end1' and `end2'. */
12551 endpoint1 = getvertex(m, b, end1);
12552 endpoint2 = getvertex(m, b, end2);
12553 if ((endpoint1[0] == endpoint2[0]) && (endpoint1[1] == endpoint2[1])) {
12554 if (!b->quiet) {
12555 printf("Warning: Endpoints of segment %d are coincident in %s.\n",
12556 b->firstnumber + i, polyfilename);
12557 }
12558 } else {
12559 insertsegment(m, b, endpoint1, endpoint2, boundmarker);
12560 }
12561 }
12562 }
12563 } else {
12564 m->insegments = 0;
12565 }
12566 if (b->convex || !b->poly) {
12567 /* Enclose the convex hull with subsegments. */
12568 if (b->verbose) {
12569 printf(" Enclosing convex hull with segments.\n");
12570 }
12571 markhull(m, b);
12572 }
12573 }
12574
12575 /** **/
12576 /** **/
12577 /********* Segment insertion ends here *********/
12578
12579 /********* Carving out holes and concavities begins here *********/
12580 /** **/
12581 /** **/
12582
12583 /*****************************************************************************/
12584 /* */
12585 /* infecthull() Virally infect all of the triangles of the convex hull */
12586 /* that are not protected by subsegments. Where there are */
12587 /* subsegments, set boundary markers as appropriate. */
12588 /* */
12589 /*****************************************************************************/
12590
12591 #ifdef ANSI_DECLARATORS
12592 void infecthull(struct mesh *m, struct behavior *b)
12593 #else /* not ANSI_DECLARATORS */
12594 void infecthull(m, b)
12595 struct mesh *m;
12596 struct behavior *b;
12597 #endif /* not ANSI_DECLARATORS */
12598
12599 {
12600 struct otri hulltri;
12601 struct otri nexttri;
12602 struct otri starttri;
12603 struct osub hullsubseg;
12604 triangle **deadtriangle;
12605 vertex horg, hdest;
12606 triangle ptr; /* Temporary variable used by sym(). */
12607 subseg sptr; /* Temporary variable used by tspivot(). */
12608
12609 if (b->verbose) {
12610 printf(" Marking concavities (external triangles) for elimination.\n");
12611 }
12612 /* Find a triangle handle on the hull. */
12613 hulltri.tri = m->dummytri;
12614 hulltri.orient = 0;
12615 symself(hulltri);
12616 /* Remember where we started so we know when to stop. */
12617 otricopy(hulltri, starttri);
12618 /* Go once counterclockwise around the convex hull. */
12619 do {
12620 /* Ignore triangles that are already infected. */
12621 if (!infected(hulltri)) {
12622 /* Is the triangle protected by a subsegment? */
12623 tspivot(hulltri, hullsubseg);
12624 if (hullsubseg.ss == m->dummysub) {
12625 /* The triangle is not protected; infect it. */
12626 if (!infected(hulltri)) {
12627 infect(hulltri);
12628 deadtriangle = (triangle **) poolalloc(&m->viri);
12629 *deadtriangle = hulltri.tri;
12630 }
12631 } else {
12632 /* The triangle is protected; set boundary markers if appropriate. */
12633 if (mark(hullsubseg) == 0) {
12634 setmark(hullsubseg, 1);
12635 org(hulltri, horg);
12636 dest(hulltri, hdest);
12637 if (vertexmark(horg) == 0) {
12638 setvertexmark(horg, 1);
12639 }
12640 if (vertexmark(hdest) == 0) {
12641 setvertexmark(hdest, 1);
12642 }
12643 }
12644 }
12645 }
12646 /* To find the next hull edge, go clockwise around the next vertex. */
12647 lnextself(hulltri);
12648 oprev(hulltri, nexttri);
12649 while (nexttri.tri != m->dummytri) {
12650 otricopy(nexttri, hulltri);
12651 oprev(hulltri, nexttri);
12652 }
12653 } while (!otriequal(hulltri, starttri));
12654 }
12655
12656 /*****************************************************************************/
12657 /* */
12658 /* plague() Spread the virus from all infected triangles to any neighbors */
12659 /* not protected by subsegments. Delete all infected triangles. */
12660 /* */
12661 /* This is the procedure that actually creates holes and concavities. */
12662 /* */
12663 /* This procedure operates in two phases. The first phase identifies all */
12664 /* the triangles that will die, and marks them as infected. They are */
12665 /* marked to ensure that each triangle is added to the virus pool only */
12666 /* once, so the procedure will terminate. */
12667 /* */
12668 /* The second phase actually eliminates the infected triangles. It also */
12669 /* eliminates orphaned vertices. */
12670 /* */
12671 /*****************************************************************************/
12672
12673 #ifdef ANSI_DECLARATORS
12674 void plague(struct mesh *m, struct behavior *b)
12675 #else /* not ANSI_DECLARATORS */
12676 void plague(m, b)
12677 struct mesh *m;
12678 struct behavior *b;
12679 #endif /* not ANSI_DECLARATORS */
12680
12681 {
12682 struct otri testtri;
12683 struct otri neighbor;
12684 triangle **virusloop;
12685 triangle **deadtriangle;
12686 struct osub neighborsubseg;
12687 vertex testvertex;
12688 vertex norg, ndest;
12689 vertex deadorg, deaddest, deadapex;
12690 int killorg;
12691 triangle ptr; /* Temporary variable used by sym() and onext(). */
12692 subseg sptr; /* Temporary variable used by tspivot(). */
12693
12694 if (b->verbose) {
12695 printf(" Marking neighbors of marked triangles.\n");
12696 }
12697 /* Loop through all the infected triangles, spreading the virus to */
12698 /* their neighbors, then to their neighbors' neighbors. */
12699 traversalinit(&m->viri);
12700 virusloop = (triangle **) traverse(&m->viri);
12701 while (virusloop != (triangle **) NULL) {
12702 testtri.tri = *virusloop;
12703 /* A triangle is marked as infected by messing with one of its pointers */
12704 /* to subsegments, setting it to an illegal value. Hence, we have to */
12705 /* temporarily uninfect this triangle so that we can examine its */
12706 /* adjacent subsegments. */
12707 uninfect(testtri);
12708 if (b->verbose > 2) {
12709 /* Assign the triangle an orientation for convenience in */
12710 /* checking its vertices. */
12711 testtri.orient = 0;
12712 org(testtri, deadorg);
12713 dest(testtri, deaddest);
12714 apex(testtri, deadapex);
12715 printf(" Checking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
12716 (double)deadorg[0], (double)deadorg[1], (double)deaddest[0], (double)deaddest[1],
12717 (double)deadapex[0], (double)deadapex[1]);
12718 }
12719 /* Check each of the triangle's three neighbors. */
12720 for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
12721 /* Find the neighbor. */
12722 sym(testtri, neighbor);
12723 /* Check for a subsegment between the triangle and its neighbor. */
12724 tspivot(testtri, neighborsubseg);
12725 /* Check if the neighbor is nonexistent or already infected. */
12726 if ((neighbor.tri == m->dummytri) || infected(neighbor)) {
12727 if (neighborsubseg.ss != m->dummysub) {
12728 /* There is a subsegment separating the triangle from its */
12729 /* neighbor, but both triangles are dying, so the subsegment */
12730 /* dies too. */
12731 subsegdealloc(m, neighborsubseg.ss);
12732 if (neighbor.tri != m->dummytri) {
12733 /* Make sure the subsegment doesn't get deallocated again */
12734 /* later when the infected neighbor is visited. */
12735 uninfect(neighbor);
12736 tsdissolve(neighbor);
12737 infect(neighbor);
12738 }
12739 }
12740 } else { /* The neighbor exists and is not infected. */
12741 if (neighborsubseg.ss == m->dummysub) {
12742 /* There is no subsegment protecting the neighbor, so */
12743 /* the neighbor becomes infected. */
12744 if (b->verbose > 2) {
12745 org(neighbor, deadorg);
12746 dest(neighbor, deaddest);
12747 apex(neighbor, deadapex);
12748 printf(
12749 " Marking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
12750 (double)deadorg[0], (double)deadorg[1], (double)deaddest[0], (double)deaddest[1],
12751 (double)deadapex[0], (double)deadapex[1]);
12752 }
12753 infect(neighbor);
12754 /* Ensure that the neighbor's neighbors will be infected. */
12755 deadtriangle = (triangle **) poolalloc(&m->viri);
12756 *deadtriangle = neighbor.tri;
12757 } else { /* The neighbor is protected by a subsegment. */
12758 /* Remove this triangle from the subsegment. */
12759 stdissolve(neighborsubseg);
12760 /* The subsegment becomes a boundary. Set markers accordingly. */
12761 if (mark(neighborsubseg) == 0) {
12762 setmark(neighborsubseg, 1);
12763 }
12764 org(neighbor, norg);
12765 dest(neighbor, ndest);
12766 if (vertexmark(norg) == 0) {
12767 setvertexmark(norg, 1);
12768 }
12769 if (vertexmark(ndest) == 0) {
12770 setvertexmark(ndest, 1);
12771 }
12772 }
12773 }
12774 }
12775 /* Remark the triangle as infected, so it doesn't get added to the */
12776 /* virus pool again. */
12777 infect(testtri);
12778 virusloop = (triangle **) traverse(&m->viri);
12779 }
12780
12781 if (b->verbose) {
12782 printf(" Deleting marked triangles.\n");
12783 }
12784
12785 traversalinit(&m->viri);
12786 virusloop = (triangle **) traverse(&m->viri);
12787 while (virusloop != (triangle **) NULL) {
12788 testtri.tri = *virusloop;
12789
12790 /* Check each of the three corners of the triangle for elimination. */
12791 /* This is done by walking around each vertex, checking if it is */
12792 /* still connected to at least one live triangle. */
12793 for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
12794 org(testtri, testvertex);
12795 /* Check if the vertex has already been tested. */
12796 if (testvertex != (vertex) NULL) {
12797 killorg = 1;
12798 /* Mark the corner of the triangle as having been tested. */
12799 setorg(testtri, NULL);
12800 /* Walk counterclockwise about the vertex. */
12801 onext(testtri, neighbor);
12802 /* Stop upon reaching a boundary or the starting triangle. */
12803 while ((neighbor.tri != m->dummytri) &&
12804 (!otriequal(neighbor, testtri))) {
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 counterclockwise about the vertex. */
12813 onextself(neighbor);
12814 }
12815 /* If we reached a boundary, we must walk clockwise as well. */
12816 if (neighbor.tri == m->dummytri) {
12817 /* Walk clockwise about the vertex. */
12818 oprev(testtri, neighbor);
12819 /* Stop upon reaching a boundary. */
12820 while (neighbor.tri != m->dummytri) {
12821 if (infected(neighbor)) {
12822 /* Mark the corner of this triangle as having been tested. */
12823 setorg(neighbor, NULL);
12824 } else {
12825 /* A live triangle. The vertex survives. */
12826 killorg = 0;
12827 }
12828 /* Walk clockwise about the vertex. */
12829 oprevself(neighbor);
12830 }
12831 }
12832 if (killorg) {
12833 if (b->verbose > 1) {
12834 printf(" Deleting vertex (%.12g, %.12g)\n",
12835 (double)testvertex[0], (double)testvertex[1]);
12836 }
12837 setvertextype(testvertex, UNDEADVERTEX);
12838 m->undeads++;
12839 }
12840 }
12841 }
12842
12843 /* Record changes in the number of boundary edges, and disconnect */
12844 /* dead triangles from their neighbors. */
12845 for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
12846 sym(testtri, neighbor);
12847 if (neighbor.tri == m->dummytri) {
12848 /* There is no neighboring triangle on this edge, so this edge */
12849 /* is a boundary edge. This triangle is being deleted, so this */
12850 /* boundary edge is deleted. */
12851 m->hullsize--;
12852 } else {
12853 /* Disconnect the triangle from its neighbor. */
12854 dissolve(neighbor);
12855 /* There is a neighboring triangle on this edge, so this edge */
12856 /* becomes a boundary edge when this triangle is deleted. */
12857 m->hullsize++;
12858 }
12859 }
12860 /* Return the dead triangle to the pool of triangles. */
12861 triangledealloc(m, testtri.tri);
12862 virusloop = (triangle **) traverse(&m->viri);
12863 }
12864 /* Empty the virus pool. */
12865 poolrestart(&m->viri);
12866 }
12867
12868 /*****************************************************************************/
12869 /* */
12870 /* regionplague() Spread regional attributes and/or area constraints */
12871 /* (from a .poly file) throughout the mesh. */
12872 /* */
12873 /* This procedure operates in two phases. The first phase spreads an */
12874 /* attribute and/or an area constraint through a (segment-bounded) region. */
12875 /* The triangles are marked to ensure that each triangle is added to the */
12876 /* virus pool only once, so the procedure will terminate. */
12877 /* */
12878 /* The second phase uninfects all infected triangles, returning them to */
12879 /* normal. */
12880 /* */
12881 /*****************************************************************************/
12882
12883 #ifdef ANSI_DECLARATORS
12884 void regionplague(struct mesh *m, struct behavior *b,
12885 REAL attribute, REAL area)
12886 #else /* not ANSI_DECLARATORS */
12887 void regionplague(m, b, attribute, area)
12888 struct mesh *m;
12889 struct behavior *b;
12890 REAL attribute;
12891 REAL area;
12892 #endif /* not ANSI_DECLARATORS */
12893
12894 {
12895 struct otri testtri;
12896 struct otri neighbor;
12897 triangle **virusloop;
12898 triangle **regiontri;
12899 struct osub neighborsubseg;
12900 vertex regionorg, regiondest, regionapex;
12901 triangle ptr; /* Temporary variable used by sym() and onext(). */
12902 subseg sptr; /* Temporary variable used by tspivot(). */
12903
12904 if (b->verbose > 1) {
12905 printf(" Marking neighbors of marked triangles.\n");
12906 }
12907 /* Loop through all the infected triangles, spreading the attribute */
12908 /* and/or area constraint to their neighbors, then to their neighbors' */
12909 /* neighbors. */
12910 traversalinit(&m->viri);
12911 virusloop = (triangle **) traverse(&m->viri);
12912 while (virusloop != (triangle **) NULL) {
12913 testtri.tri = *virusloop;
12914 /* A triangle is marked as infected by messing with one of its pointers */
12915 /* to subsegments, setting it to an illegal value. Hence, we have to */
12916 /* temporarily uninfect this triangle so that we can examine its */
12917 /* adjacent subsegments. */
12918 uninfect(testtri);
12919 if (b->regionattrib) {
12920 /* Set an attribute. */
12921 setelemattribute(testtri, m->eextras, attribute);
12922 }
12923 if (b->vararea) {
12924 /* Set an area constraint. */
12925 setareabound(testtri, area);
12926 }
12927 if (b->verbose > 2) {
12928 /* Assign the triangle an orientation for convenience in */
12929 /* checking its vertices. */
12930 testtri.orient = 0;
12931 org(testtri, regionorg);
12932 dest(testtri, regiondest);
12933 apex(testtri, regionapex);
12934 printf(" Checking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
12935 (double)regionorg[0], (double)regionorg[1], (double)regiondest[0], (double)regiondest[1],
12936 (double)regionapex[0], (double)regionapex[1]);
12937 }
12938 /* Check each of the triangle's three neighbors. */
12939 for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
12940 /* Find the neighbor. */
12941 sym(testtri, neighbor);
12942 /* Check for a subsegment between the triangle and its neighbor. */
12943 tspivot(testtri, neighborsubseg);
12944 /* Make sure the neighbor exists, is not already infected, and */
12945 /* isn't protected by a subsegment. */
12946 if ((neighbor.tri != m->dummytri) && !infected(neighbor)
12947 && (neighborsubseg.ss == m->dummysub)) {
12948 if (b->verbose > 2) {
12949 org(neighbor, regionorg);
12950 dest(neighbor, regiondest);
12951 apex(neighbor, regionapex);
12952 printf(" Marking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
12953 (double)regionorg[0], (double)regionorg[1], (double)regiondest[0], (double)regiondest[1],
12954 (double)regionapex[0], (double)regionapex[1]);
12955 }
12956 /* Infect the neighbor. */
12957 infect(neighbor);
12958 /* Ensure that the neighbor's neighbors will be infected. */
12959 regiontri = (triangle **) poolalloc(&m->viri);
12960 *regiontri = neighbor.tri;
12961 }
12962 }
12963 /* Remark the triangle as infected, so it doesn't get added to the */
12964 /* virus pool again. */
12965 infect(testtri);
12966 virusloop = (triangle **) traverse(&m->viri);
12967 }
12968
12969 /* Uninfect all triangles. */
12970 if (b->verbose > 1) {
12971 printf(" Unmarking marked triangles.\n");
12972 }
12973 traversalinit(&m->viri);
12974 virusloop = (triangle **) traverse(&m->viri);
12975 while (virusloop != (triangle **) NULL) {
12976 testtri.tri = *virusloop;
12977 uninfect(testtri);
12978 virusloop = (triangle **) traverse(&m->viri);
12979 }
12980 /* Empty the virus pool. */
12981 poolrestart(&m->viri);
12982 }
12983
12984 /*****************************************************************************/
12985 /* */
12986 /* carveholes() Find the holes and infect them. Find the area */
12987 /* constraints and infect them. Infect the convex hull. */
12988 /* Spread the infection and kill triangles. Spread the */
12989 /* area constraints. */
12990 /* */
12991 /* This routine mainly calls other routines to carry out all these */
12992 /* functions. */
12993 /* */
12994 /*****************************************************************************/
12995
12996 #ifdef ANSI_DECLARATORS
12997 void carveholes(struct mesh *m, struct behavior *b, REAL *holelist, int holes,
12998 REAL *regionlist, int regions)
12999 #else /* not ANSI_DECLARATORS */
13000 void carveholes(m, b, holelist, holes, regionlist, regions)
13001 struct mesh *m;
13002 struct behavior *b;
13003 REAL *holelist;
13004 int holes;
13005 REAL *regionlist;
13006 int regions;
13007 #endif /* not ANSI_DECLARATORS */
13008
13009 {
13010 struct otri searchtri;
13011 struct otri triangleloop;
13012 struct otri *regiontris;
13013 triangle **holetri;
13014 triangle **regiontri;
13015 vertex searchorg, searchdest;
13016 enum locateresult intersect;
13017 int i;
13018 triangle ptr; /* Temporary variable used by sym(). */
13019
13020 if (!(b->quiet || (b->noholes && b->convex))) {
13021 printf("Removing unwanted triangles.\n");
13022 if (b->verbose && (holes > 0)) {
13023 printf(" Marking holes for elimination.\n");
13024 }
13025 }
13026
13027 if (regions > 0) {
13028 /* Allocate storage for the triangles in which region points fall. */
13029 regiontris = (struct otri *) trimalloc(regions *
13030 (int) sizeof(struct otri));
13031 } else {
13032 regiontris = (struct otri *) NULL;
13033 }
13034
13035 if (((holes > 0) && !b->noholes) || !b->convex || (regions > 0)) {
13036 /* Initialize a pool of viri to be used for holes, concavities, */
13037 /* regional attributes, and/or regional area constraints. */
13038 poolinit(&m->viri, sizeof(triangle *), VIRUSPERBLOCK, VIRUSPERBLOCK, 0);
13039 }
13040
13041 if (!b->convex) {
13042 /* Mark as infected any unprotected triangles on the boundary. */
13043 /* This is one way by which concavities are created. */
13044 infecthull(m, b);
13045 }
13046
13047 if ((holes > 0) && !b->noholes) {
13048 /* Infect each triangle in which a hole lies. */
13049 for (i = 0; i < 2 * holes; i += 2) {
13050 /* Ignore holes that aren't within the bounds of the mesh. */
13051 if ((holelist[i] >= m->xmin) && (holelist[i] <= m->xmax)
13052 && (holelist[i + 1] >= m->ymin) && (holelist[i + 1] <= m->ymax)) {
13053 /* Start searching from some triangle on the outer boundary. */
13054 searchtri.tri = m->dummytri;
13055 searchtri.orient = 0;
13056 symself(searchtri);
13057 /* Ensure that the hole is to the left of this boundary edge; */
13058 /* otherwise, locate() will falsely report that the hole */
13059 /* falls within the starting triangle. */
13060 org(searchtri, searchorg);
13061 dest(searchtri, searchdest);
13062 if (counterclockwise(m, b, searchorg, searchdest, &holelist[i]) >
13063 0.0) {
13064 /* Find a triangle that contains the hole. */
13065 intersect = locate(m, b, &holelist[i], &searchtri);
13066 if ((intersect != OUTSIDE) && (!infected(searchtri))) {
13067 /* Infect the triangle. This is done by marking the triangle */
13068 /* as infected and including the triangle in the virus pool. */
13069 infect(searchtri);
13070 holetri = (triangle **) poolalloc(&m->viri);
13071 *holetri = searchtri.tri;
13072 }
13073 }
13074 }
13075 }
13076 }
13077
13078 /* Now, we have to find all the regions BEFORE we carve the holes, because */
13079 /* locate() won't work when the triangulation is no longer convex. */
13080 /* (Incidentally, this is the reason why regional attributes and area */
13081 /* constraints can't be used when refining a preexisting mesh, which */
13082 /* might not be convex; they can only be used with a freshly */
13083 /* triangulated PSLG.) */
13084 if (regions > 0) {
13085 /* Find the starting triangle for each region. */
13086 for (i = 0; i < regions; i++) {
13087 regiontris[i].tri = m->dummytri;
13088 /* Ignore region points that aren't within the bounds of the mesh. */
13089 if ((regionlist[4 * i] >= m->xmin) && (regionlist[4 * i] <= m->xmax) &&
13090 (regionlist[4 * i + 1] >= m->ymin) &&
13091 (regionlist[4 * i + 1] <= m->ymax)) {
13092 /* Start searching from some triangle on the outer boundary. */
13093 searchtri.tri = m->dummytri;
13094 searchtri.orient = 0;
13095 symself(searchtri);
13096 /* Ensure that the region point is to the left of this boundary */
13097 /* edge; otherwise, locate() will falsely report that the */
13098 /* region point falls within the starting triangle. */
13099 org(searchtri, searchorg);
13100 dest(searchtri, searchdest);
13101 if (counterclockwise(m, b, searchorg, searchdest, ®ionlist[4 * i]) >
13102 0.0) {
13103 /* Find a triangle that contains the region point. */
13104 intersect = locate(m, b, ®ionlist[4 * i], &searchtri);
13105 if ((intersect != OUTSIDE) && (!infected(searchtri))) {
13106 /* Record the triangle for processing after the */
13107 /* holes have been carved. */
13108 otricopy(searchtri, regiontris[i]);
13109 }
13110 }
13111 }
13112 }
13113 }
13114
13115 if (m->viri.items > 0) {
13116 /* Carve the holes and concavities. */
13117 plague(m, b);
13118 }
13119 /* The virus pool should be empty now. */
13120
13121 if (regions > 0) {
13122 if (!b->quiet) {
13123 if (b->regionattrib) {
13124 if (b->vararea) {
13125 printf("Spreading regional attributes and area constraints.\n");
13126 } else {
13127 printf("Spreading regional attributes.\n");
13128 }
13129 } else {
13130 printf("Spreading regional area constraints.\n");
13131 }
13132 }
13133 if (b->regionattrib && !b->refine) {
13134 /* Assign every triangle a regional attribute of zero. */
13135 traversalinit(&m->triangles);
13136 triangleloop.orient = 0;
13137 triangleloop.tri = triangletraverse(m);
13138 while (triangleloop.tri != (triangle *) NULL) {
13139 setelemattribute(triangleloop, m->eextras, 0.0);
13140 triangleloop.tri = triangletraverse(m);
13141 }
13142 }
13143 for (i = 0; i < regions; i++) {
13144 if (regiontris[i].tri != m->dummytri) {
13145 /* Make sure the triangle under consideration still exists. */
13146 /* It may have been eaten by the virus. */
13147 if (!deadtri(regiontris[i].tri)) {
13148 /* Put one triangle in the virus pool. */
13149 infect(regiontris[i]);
13150 regiontri = (triangle **) poolalloc(&m->viri);
13151 *regiontri = regiontris[i].tri;
13152 /* Apply one region's attribute and/or area constraint. */
13153 regionplague(m, b, regionlist[4 * i + 2], regionlist[4 * i + 3]);
13154 /* The virus pool should be empty now. */
13155 }
13156 }
13157 }
13158 if (b->regionattrib && !b->refine) {
13159 /* Note the fact that each triangle has an additional attribute. */
13160 m->eextras++;
13161 }
13162 }
13163
13164 /* Free up memory. */
13165 if (((holes > 0) && !b->noholes) || !b->convex || (regions > 0)) {
13166 pooldeinit(&m->viri);
13167 }
13168 if (regions > 0) {
13169 trifree((VOID *) regiontris);
13170 }
13171 }
13172
13173 /** **/
13174 /** **/
13175 /********* Carving out holes and concavities ends here *********/
13176
13177 /********* Mesh quality maintenance begins here *********/
13178 /** **/
13179 /** **/
13180
13181 /*****************************************************************************/
13182 /* */
13183 /* tallyencs() Traverse the entire list of subsegments, and check each */
13184 /* to see if it is encroached. If so, add it to the list. */
13185 /* */
13186 /*****************************************************************************/
13187
13188 #ifndef CDT_ONLY
13189
13190 #ifdef ANSI_DECLARATORS
13191 void tallyencs(struct mesh *m, struct behavior *b)
13192 #else /* not ANSI_DECLARATORS */
13193 void tallyencs(m, b)
13194 struct mesh *m;
13195 struct behavior *b;
13196 #endif /* not ANSI_DECLARATORS */
13197
13198 {
13199 struct osub subsegloop;
13200 int dummy;
13201
13202 traversalinit(&m->subsegs);
13203 subsegloop.ssorient = 0;
13204 subsegloop.ss = subsegtraverse(m);
13205 while (subsegloop.ss != (subseg *) NULL) {
13206 /* If the segment is encroached, add it to the list. */
13207 dummy = checkseg4encroach(m, b, &subsegloop);
13208 subsegloop.ss = subsegtraverse(m);
13209 }
13210 }
13211
13212 #endif /* not CDT_ONLY */
13213
13214 /*****************************************************************************/
13215 /* */
13216 /* precisionerror() Print an error message for precision problems. */
13217 /* */
13218 /*****************************************************************************/
13219
13220 #ifndef CDT_ONLY
13221
13222 void precisionerror()
13223 {
13224 printf("Try increasing the area criterion and/or reducing the minimum\n");
13225 printf(" allowable angle so that tiny triangles are not created.\n");
13226 #ifdef SINGLE
13227 printf("Alternatively, try recompiling me with double precision\n");
13228 printf(" arithmetic (by removing \"#define SINGLE\" from the\n");
13229 printf(" source file or \"-DSINGLE\" from the makefile).\n");
13230 #endif /* SINGLE */
13231 }
13232
13233 #endif /* not CDT_ONLY */
13234
13235 /*****************************************************************************/
13236 /* */
13237 /* splitencsegs() Split all the encroached subsegments. */
13238 /* */
13239 /* Each encroached subsegment is repaired by splitting it - inserting a */
13240 /* vertex at or near its midpoint. Newly inserted vertices may encroach */
13241 /* upon other subsegments; these are also repaired. */
13242 /* */
13243 /* `triflaws' is a flag that specifies whether one should take note of new */
13244 /* bad triangles that result from inserting vertices to repair encroached */
13245 /* subsegments. */
13246 /* */
13247 /*****************************************************************************/
13248
13249 #ifndef CDT_ONLY
13250
13251 #ifdef ANSI_DECLARATORS
13252 void splitencsegs(struct mesh *m, struct behavior *b, int triflaws)
13253 #else /* not ANSI_DECLARATORS */
13254 void splitencsegs(m, b, triflaws)
13255 struct mesh *m;
13256 struct behavior *b;
13257 int triflaws;
13258 #endif /* not ANSI_DECLARATORS */
13259
13260 {
13261 struct otri enctri;
13262 struct otri testtri;
13263 struct osub testsh;
13264 struct osub currentenc;
13265 struct badsubseg *encloop;
13266 vertex eorg, edest, eapex;
13267 vertex newvertex;
13268 enum insertvertexresult success;
13269 REAL segmentlength, nearestpoweroftwo;
13270 REAL split;
13271 REAL multiplier, divisor;
13272 int acuteorg, acuteorg2, acutedest, acutedest2;
13273 int dummy;
13274 int i;
13275 triangle ptr; /* Temporary variable used by stpivot(). */
13276 subseg sptr; /* Temporary variable used by snext(). */
13277
13278 /* Note that steinerleft == -1 if an unlimited number */
13279 /* of Steiner points is allowed. */
13280 while ((m->badsubsegs.items > 0) && (m->steinerleft != 0)) {
13281 traversalinit(&m->badsubsegs);
13282 encloop = badsubsegtraverse(m);
13283 while ((encloop != (struct badsubseg *) NULL) && (m->steinerleft != 0)) {
13284 sdecode(encloop->encsubseg, currentenc);
13285 sorg(currentenc, eorg);
13286 sdest(currentenc, edest);
13287 /* Make sure that this segment is still the same segment it was */
13288 /* when it was determined to be encroached. If the segment was */
13289 /* enqueued multiple times (because several newly inserted */
13290 /* vertices encroached it), it may have already been split. */
13291 if (!deadsubseg(currentenc.ss) &&
13292 (eorg == encloop->subsegorg) && (edest == encloop->subsegdest)) {
13293 /* To decide where to split a segment, we need to know if the */
13294 /* segment shares an endpoint with an adjacent segment. */
13295 /* The concern is that, if we simply split every encroached */
13296 /* segment in its center, two adjacent segments with a small */
13297 /* angle between them might lead to an infinite loop; each */
13298 /* vertex added to split one segment will encroach upon the */
13299 /* other segment, which must then be split with a vertex that */
13300 /* will encroach upon the first segment, and so on forever. */
13301 /* To avoid this, imagine a set of concentric circles, whose */
13302 /* radii are powers of two, about each segment endpoint. */
13303 /* These concentric circles determine where the segment is */
13304 /* split. (If both endpoints are shared with adjacent */
13305 /* segments, split the segment in the middle, and apply the */
13306 /* concentric circles for later splittings.) */
13307
13308 /* Is the origin shared with another segment? */
13309 stpivot(currentenc, enctri);
13310 lnext(enctri, testtri);
13311 tspivot(testtri, testsh);
13312 acuteorg = testsh.ss != m->dummysub;
13313 /* Is the destination shared with another segment? */
13314 lnextself(testtri);
13315 tspivot(testtri, testsh);
13316 acutedest = testsh.ss != m->dummysub;
13317
13318 /* If we're using Chew's algorithm (rather than Ruppert's) */
13319 /* to define encroachment, delete free vertices from the */
13320 /* subsegment's diametral circle. */
13321 if (!b->conformdel && !acuteorg && !acutedest) {
13322 apex(enctri, eapex);
13323 while ((vertextype(eapex) == FREEVERTEX) &&
13324 ((eorg[0] - eapex[0]) * (edest[0] - eapex[0]) +
13325 (eorg[1] - eapex[1]) * (edest[1] - eapex[1]) < 0.0)) {
13326 deletevertex(m, b, &testtri);
13327 stpivot(currentenc, enctri);
13328 apex(enctri, eapex);
13329 lprev(enctri, testtri);
13330 }
13331 }
13332
13333 /* Now, check the other side of the segment, if there's a triangle */
13334 /* there. */
13335 sym(enctri, testtri);
13336 if (testtri.tri != m->dummytri) {
13337 /* Is the destination shared with another segment? */
13338 lnextself(testtri);
13339 tspivot(testtri, testsh);
13340 acutedest2 = testsh.ss != m->dummysub;
13341 acutedest = acutedest || acutedest2;
13342 /* Is the origin shared with another segment? */
13343 lnextself(testtri);
13344 tspivot(testtri, testsh);
13345 acuteorg2 = testsh.ss != m->dummysub;
13346 acuteorg = acuteorg || acuteorg2;
13347
13348 /* Delete free vertices from the subsegment's diametral circle. */
13349 if (!b->conformdel && !acuteorg2 && !acutedest2) {
13350 org(testtri, eapex);
13351 while ((vertextype(eapex) == FREEVERTEX) &&
13352 ((eorg[0] - eapex[0]) * (edest[0] - eapex[0]) +
13353 (eorg[1] - eapex[1]) * (edest[1] - eapex[1]) < 0.0)) {
13354 deletevertex(m, b, &testtri);
13355 sym(enctri, testtri);
13356 apex(testtri, eapex);
13357 lprevself(testtri);
13358 }
13359 }
13360 }
13361
13362 /* Use the concentric circles if exactly one endpoint is shared */
13363 /* with another adjacent segment. */
13364 if (acuteorg || acutedest) {
13365 segmentlength = sqrt((edest[0] - eorg[0]) * (edest[0] - eorg[0]) +
13366 (edest[1] - eorg[1]) * (edest[1] - eorg[1]));
13367 /* Find the power of two that most evenly splits the segment. */
13368 /* The worst case is a 2:1 ratio between subsegment lengths. */
13369 nearestpoweroftwo = 1.0;
13370 while (segmentlength > 3.0 * nearestpoweroftwo) {
13371 nearestpoweroftwo *= 2.0;
13372 }
13373 while (segmentlength < 1.5 * nearestpoweroftwo) {
13374 nearestpoweroftwo *= 0.5;
13375 }
13376 /* Where do we split the segment? */
13377 split = nearestpoweroftwo / segmentlength;
13378 if (acutedest) {
13379 split = 1.0 - split;
13380 }
13381 } else {
13382 /* If we're not worried about adjacent segments, split */
13383 /* this segment in the middle. */
13384 split = 0.5;
13385 }
13386
13387 /* Create the new vertex. */
13388 newvertex = (vertex) poolalloc(&m->vertices);
13389 /* Interpolate its coordinate and attributes. */
13390 for (i = 0; i < 2 + m->nextras; i++) {
13391 newvertex[i] = eorg[i] + split * (edest[i] - eorg[i]);
13392 }
13393
13394 if (!b->noexact) {
13395 /* Roundoff in the above calculation may yield a `newvertex' */
13396 /* that is not precisely collinear with `eorg' and `edest'. */
13397 /* Improve collinearity by one step of iterative refinement. */
13398 multiplier = counterclockwise(m, b, eorg, edest, newvertex);
13399 divisor = ((eorg[0] - edest[0]) * (eorg[0] - edest[0]) +
13400 (eorg[1] - edest[1]) * (eorg[1] - edest[1]));
13401 if ((multiplier != 0.0) && (divisor != 0.0)) {
13402 multiplier = multiplier / divisor;
13403 /* Watch out for NANs. */
13404 if (multiplier == multiplier) {
13405 newvertex[0] += multiplier * (edest[1] - eorg[1]);
13406 newvertex[1] += multiplier * (eorg[0] - edest[0]);
13407 }
13408 }
13409 }
13410
13411 setvertexmark(newvertex, mark(currentenc));
13412 setvertextype(newvertex, SEGMENTVERTEX);
13413 if (b->verbose > 1) {
13414 printf(
13415 " Splitting subsegment (%.12g, %.12g) (%.12g, %.12g) at (%.12g, %.12g).\n",
13416 (double)eorg[0], (double)eorg[1], (double)edest[0], (double)edest[1],
13417 (double)newvertex[0], (double)newvertex[1]);
13418 }
13419 /* Check whether the new vertex lies on an endpoint. */
13420 if (((newvertex[0] == eorg[0]) && (newvertex[1] == eorg[1])) ||
13421 ((newvertex[0] == edest[0]) && (newvertex[1] == edest[1]))) {
13422 printf("Error: Ran out of precision at (%.12g, %.12g).\n",
13423 (double)newvertex[0], (double)newvertex[1]);
13424 printf("I attempted to split a segment to a smaller size than\n");
13425 printf(" can be accommodated by the finite precision of\n");
13426 printf(" floating point arithmetic.\n");
13427 precisionerror();
13428 triexit(1);
13429 }
13430 /* Insert the splitting vertex. This should always succeed. */
13431 success = insertvertex(m, b, newvertex, &enctri, ¤tenc,
13432 1, triflaws);
13433 if ((success != SUCCESSFULVERTEX) && (success != ENCROACHINGVERTEX)) {
13434 printf("Internal error in splitencsegs():\n");
13435 printf(" Failure to split a segment.\n");
13436 internalerror();
13437 }
13438 if (m->steinerleft > 0) {
13439 m->steinerleft--;
13440 }
13441 /* Check the two new subsegments to see if they're encroached. */
13442 dummy = checkseg4encroach(m, b, ¤tenc);
13443 snextself(currentenc);
13444 dummy = checkseg4encroach(m, b, ¤tenc);
13445 }
13446
13447 badsubsegdealloc(m, encloop);
13448 encloop = badsubsegtraverse(m);
13449 }
13450 }
13451 }
13452
13453 #endif /* not CDT_ONLY */
13454
13455 /*****************************************************************************/
13456 /* */
13457 /* tallyfaces() Test every triangle in the mesh for quality measures. */
13458 /* */
13459 /*****************************************************************************/
13460
13461 #ifndef CDT_ONLY
13462
13463 #ifdef ANSI_DECLARATORS
13464 void tallyfaces(struct mesh *m, struct behavior *b)
13465 #else /* not ANSI_DECLARATORS */
13466 void tallyfaces(m, b)
13467 struct mesh *m;
13468 struct behavior *b;
13469 #endif /* not ANSI_DECLARATORS */
13470
13471 {
13472 struct otri triangleloop;
13473
13474 if (b->verbose) {
13475 printf(" Making a list of bad triangles.\n");
13476 }
13477 traversalinit(&m->triangles);
13478 triangleloop.orient = 0;
13479 triangleloop.tri = triangletraverse(m);
13480 while (triangleloop.tri != (triangle *) NULL) {
13481 /* If the triangle is bad, enqueue it. */
13482 testtriangle(m, b, &triangleloop);
13483 triangleloop.tri = triangletraverse(m);
13484 }
13485 }
13486
13487 #endif /* not CDT_ONLY */
13488
13489 /*****************************************************************************/
13490 /* */
13491 /* splittriangle() Inserts a vertex at the circumcenter of a triangle. */
13492 /* Deletes the newly inserted vertex if it encroaches */
13493 /* upon a segment. */
13494 /* */
13495 /*****************************************************************************/
13496
13497 #ifndef CDT_ONLY
13498
13499 #ifdef ANSI_DECLARATORS
13500 void splittriangle(struct mesh *m, struct behavior *b,
13501 struct badtriang *badtri)
13502 #else /* not ANSI_DECLARATORS */
13503 void splittriangle(m, b, badtri)
13504 struct mesh *m;
13505 struct behavior *b;
13506 struct badtriang *badtri;
13507 #endif /* not ANSI_DECLARATORS */
13508
13509 {
13510 struct otri badotri;
13511 vertex borg, bdest, bapex;
13512 vertex newvertex;
13513 REAL xi, eta;
13514 enum insertvertexresult success;
13515 int errorflag;
13516 int i;
13517
13518 decode(badtri->poortri, badotri);
13519 org(badotri, borg);
13520 dest(badotri, bdest);
13521 apex(badotri, bapex);
13522 /* Make sure that this triangle is still the same triangle it was */
13523 /* when it was tested and determined to be of bad quality. */
13524 /* Subsequent transformations may have made it a different triangle. */
13525 if (!deadtri(badotri.tri) && (borg == badtri->triangorg) &&
13526 (bdest == badtri->triangdest) && (bapex == badtri->triangapex)) {
13527 if (b->verbose > 1) {
13528 printf(" Splitting this triangle at its circumcenter:\n");
13529 printf(" (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", (double)borg[0],
13530 (double)borg[1], (double)bdest[0], (double)bdest[1], (double)bapex[0], (double)bapex[1]);
13531 }
13532
13533 errorflag = 0;
13534 /* Create a new vertex at the triangle's circumcenter. */
13535 newvertex = (vertex) poolalloc(&m->vertices);
13536 findcircumcenter(m, b, borg, bdest, bapex, newvertex, &xi, &eta, 1);
13537
13538 /* Check whether the new vertex lies on a triangle vertex. */
13539 if (((newvertex[0] == borg[0]) && (newvertex[1] == borg[1])) ||
13540 ((newvertex[0] == bdest[0]) && (newvertex[1] == bdest[1])) ||
13541 ((newvertex[0] == bapex[0]) && (newvertex[1] == bapex[1]))) {
13542 if (!b->quiet) {
13543 printf(
13544 "Warning: New vertex (%.12g, %.12g) falls on existing vertex.\n",
13545 (double)newvertex[0], (double)newvertex[1]);
13546 errorflag = 1;
13547 }
13548 vertexdealloc(m, newvertex);
13549 } else {
13550 for (i = 2; i < 2 + m->nextras; i++) {
13551 /* Interpolate the vertex attributes at the circumcenter. */
13552 newvertex[i] = borg[i] + xi * (bdest[i] - borg[i])
13553 + eta * (bapex[i] - borg[i]);
13554 }
13555 /* The new vertex must be in the interior, and therefore is a */
13556 /* free vertex with a marker of zero. */
13557 setvertexmark(newvertex, 0);
13558 setvertextype(newvertex, FREEVERTEX);
13559
13560 /* Ensure that the handle `badotri' does not represent the longest */
13561 /* edge of the triangle. This ensures that the circumcenter must */
13562 /* fall to the left of this edge, so point location will work. */
13563 /* (If the angle org-apex-dest exceeds 90 degrees, then the */
13564 /* circumcenter lies outside the org-dest edge, and eta is */
13565 /* negative. Roundoff error might prevent eta from being */
13566 /* negative when it should be, so I test eta against xi.) */
13567 if (eta < xi) {
13568 lprevself(badotri);
13569 }
13570
13571 /* Insert the circumcenter, searching from the edge of the triangle, */
13572 /* and maintain the Delaunay property of the triangulation. */
13573 success = insertvertex(m, b, newvertex, &badotri, (struct osub *) NULL,
13574 1, 1);
13575 if (success == SUCCESSFULVERTEX) {
13576 if (m->steinerleft > 0) {
13577 m->steinerleft--;
13578 }
13579 } else if (success == ENCROACHINGVERTEX) {
13580 /* If the newly inserted vertex encroaches upon a subsegment, */
13581 /* delete the new vertex. */
13582 undovertex(m, b);
13583 if (b->verbose > 1) {
13584 printf(" Rejecting (%.12g, %.12g).\n", (double)newvertex[0], (double)newvertex[1]);
13585 }
13586 vertexdealloc(m, newvertex);
13587 } else if (success == VIOLATINGVERTEX) {
13588 /* Failed to insert the new vertex, but some subsegment was */
13589 /* marked as being encroached. */
13590 vertexdealloc(m, newvertex);
13591 } else { /* success == DUPLICATEVERTEX */
13592 /* Couldn't insert the new vertex because a vertex is already there. */
13593 if (!b->quiet) {
13594 printf(
13595 "Warning: New vertex (%.12g, %.12g) falls on existing vertex.\n",
13596 (double)newvertex[0], (double)newvertex[1]);
13597 errorflag = 1;
13598 }
13599 vertexdealloc(m, newvertex);
13600 }
13601 }
13602 if (errorflag) {
13603 if (b->verbose) {
13604 printf(" The new vertex is at the circumcenter of triangle\n");
13605 printf(" (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
13606 (double)borg[0], (double)borg[1], (double)bdest[0], (double)bdest[1], (double)bapex[0], (double)bapex[1]);
13607 }
13608 printf("This probably means that I am trying to refine triangles\n");
13609 printf(" to a smaller size than can be accommodated by the finite\n");
13610 printf(" precision of floating point arithmetic. (You can be\n");
13611 printf(" sure of this if I fail to terminate.)\n");
13612 precisionerror();
13613 }
13614 }
13615 }
13616
13617 #endif /* not CDT_ONLY */
13618
13619 /*****************************************************************************/
13620 /* */
13621 /* enforcequality() Remove all the encroached subsegments and bad */
13622 /* triangles from the triangulation. */
13623 /* */
13624 /*****************************************************************************/
13625
13626 #ifndef CDT_ONLY
13627
13628 #ifdef ANSI_DECLARATORS
13629 void enforcequality(struct mesh *m, struct behavior *b)
13630 #else /* not ANSI_DECLARATORS */
13631 void enforcequality(m, b)
13632 struct mesh *m;
13633 struct behavior *b;
13634 #endif /* not ANSI_DECLARATORS */
13635
13636 {
13637 struct badtriang *badtri;
13638 int i;
13639
13640 if (!b->quiet) {
13641 printf("Adding Steiner points to enforce quality.\n");
13642 }
13643 /* Initialize the pool of encroached subsegments. */
13644 poolinit(&m->badsubsegs, sizeof(struct badsubseg), BADSUBSEGPERBLOCK,
13645 BADSUBSEGPERBLOCK, 0);
13646 if (b->verbose) {
13647 printf(" Looking for encroached subsegments.\n");
13648 }
13649 /* Test all segments to see if they're encroached. */
13650 tallyencs(m, b);
13651 if (b->verbose && (m->badsubsegs.items > 0)) {
13652 printf(" Splitting encroached subsegments.\n");
13653 }
13654 /* Fix encroached subsegments without noting bad triangles. */
13655 splitencsegs(m, b, 0);
13656 /* At this point, if we haven't run out of Steiner points, the */
13657 /* triangulation should be (conforming) Delaunay. */
13658
13659 /* Next, we worry about enforcing triangle quality. */
13660 if ((b->minangle > 0.0) || b->vararea || b->fixedarea || b->usertest) {
13661 /* Initialize the pool of bad triangles. */
13662 poolinit(&m->badtriangles, sizeof(struct badtriang), BADTRIPERBLOCK,
13663 BADTRIPERBLOCK, 0);
13664 /* Initialize the queues of bad triangles. */
13665 for (i = 0; i < 4096; i++) {
13666 m->queuefront[i] = (struct badtriang *) NULL;
13667 }
13668 m->firstnonemptyq = -1;
13669 /* Test all triangles to see if they're bad. */
13670 tallyfaces(m, b);
13671 /* Initialize the pool of recently flipped triangles. */
13672 poolinit(&m->flipstackers, sizeof(struct flipstacker), FLIPSTACKERPERBLOCK,
13673 FLIPSTACKERPERBLOCK, 0);
13674 m->checkquality = 1;
13675 if (b->verbose) {
13676 printf(" Splitting bad triangles.\n");
13677 }
13678 while ((m->badtriangles.items > 0) && (m->steinerleft != 0)) {
13679 /* Fix one bad triangle by inserting a vertex at its circumcenter. */
13680 badtri = dequeuebadtriang(m);
13681 splittriangle(m, b, badtri);
13682 if (m->badsubsegs.items > 0) {
13683 /* Put bad triangle back in queue for another try later. */
13684 enqueuebadtriang(m, b, badtri);
13685 /* Fix any encroached subsegments that resulted. */
13686 /* Record any new bad triangles that result. */
13687 splitencsegs(m, b, 1);
13688 } else {
13689 /* Return the bad triangle to the pool. */
13690 pooldealloc(&m->badtriangles, (VOID *) badtri);
13691 }
13692 }
13693 }
13694 /* At this point, if the "-D" switch was selected and we haven't run out */
13695 /* of Steiner points, the triangulation should be (conforming) Delaunay */
13696 /* and have no low-quality triangles. */
13697
13698 /* Might we have run out of Steiner points too soon? */
13699 if (!b->quiet && b->conformdel && (m->badsubsegs.items > 0) &&
13700 (m->steinerleft == 0)) {
13701 printf("\nWarning: I ran out of Steiner points, but the mesh has\n");
13702 if (m->badsubsegs.items == 1) {
13703 printf(" one encroached subsegment, and therefore might not be truly\n"
13704 );
13705 } else {
13706 printf(" %ld encroached subsegments, and therefore might not be truly\n"
13707 , m->badsubsegs.items);
13708 }
13709 printf(" Delaunay. If the Delaunay property is important to you,\n");
13710 printf(" try increasing the number of Steiner points (controlled by\n");
13711 printf(" the -S switch) slightly and try again.\n\n");
13712 }
13713 }
13714
13715 #endif /* not CDT_ONLY */
13716
13717 /** **/
13718 /** **/
13719 /********* Mesh quality maintenance ends here *********/
13720
13721 /*****************************************************************************/
13722 /* */
13723 /* highorder() Create extra nodes for quadratic subparametric elements. */
13724 /* */
13725 /*****************************************************************************/
13726
13727 #ifdef ANSI_DECLARATORS
13728 void highorder(struct mesh *m, struct behavior *b)
13729 #else /* not ANSI_DECLARATORS */
13730 void highorder(m, b)
13731 struct mesh *m;
13732 struct behavior *b;
13733 #endif /* not ANSI_DECLARATORS */
13734
13735 {
13736 struct otri triangleloop, trisym;
13737 struct osub checkmark;
13738 vertex newvertex;
13739 vertex torg, tdest;
13740 int i;
13741 triangle ptr; /* Temporary variable used by sym(). */
13742 subseg sptr; /* Temporary variable used by tspivot(). */
13743
13744 if (!b->quiet) {
13745 printf("Adding vertices for second-order triangles.\n");
13746 }
13747 /* The following line ensures that dead items in the pool of nodes */
13748 /* cannot be allocated for the extra nodes associated with high */
13749 /* order elements. This ensures that the primary nodes (at the */
13750 /* corners of elements) will occur earlier in the output files, and */
13751 /* have lower indices, than the extra nodes. */
13752 m->vertices.deaditemstack = (VOID *) NULL;
13753
13754 traversalinit(&m->triangles);
13755 triangleloop.tri = triangletraverse(m);
13756 /* To loop over the set of edges, loop over all triangles, and look at */
13757 /* the three edges of each triangle. If there isn't another triangle */
13758 /* adjacent to the edge, operate on the edge. If there is another */
13759 /* adjacent triangle, operate on the edge only if the current triangle */
13760 /* has a smaller pointer than its neighbor. This way, each edge is */
13761 /* considered only once. */
13762 while (triangleloop.tri != (triangle *) NULL) {
13763 for (triangleloop.orient = 0; triangleloop.orient < 3;
13764 triangleloop.orient++) {
13765 sym(triangleloop, trisym);
13766 if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) {
13767 org(triangleloop, torg);
13768 dest(triangleloop, tdest);
13769 /* Create a new node in the middle of the edge. Interpolate */
13770 /* its attributes. */
13771 newvertex = (vertex) poolalloc(&m->vertices);
13772 for (i = 0; i < 2 + m->nextras; i++) {
13773 newvertex[i] = 0.5 * (torg[i] + tdest[i]);
13774 }
13775 /* Set the new node's marker to zero or one, depending on */
13776 /* whether it lies on a boundary. */
13777 setvertexmark(newvertex, trisym.tri == m->dummytri);
13778 setvertextype(newvertex,
13779 trisym.tri == m->dummytri ? FREEVERTEX : SEGMENTVERTEX);
13780 if (b->usesegments) {
13781 tspivot(triangleloop, checkmark);
13782 /* If this edge is a segment, transfer the marker to the new node. */
13783 if (checkmark.ss != m->dummysub) {
13784 setvertexmark(newvertex, mark(checkmark));
13785 setvertextype(newvertex, SEGMENTVERTEX);
13786 }
13787 }
13788 if (b->verbose > 1) {
13789 printf(" Creating (%.12g, %.12g).\n", (double)newvertex[0], (double)newvertex[1]);
13790 }
13791 /* Record the new node in the (one or two) adjacent elements. */
13792 triangleloop.tri[m->highorderindex + triangleloop.orient] =
13793 (triangle) newvertex;
13794 if (trisym.tri != m->dummytri) {
13795 trisym.tri[m->highorderindex + trisym.orient] = (triangle) newvertex;
13796 }
13797 }
13798 }
13799 triangleloop.tri = triangletraverse(m);
13800 }
13801 }
13802
13803 /********* File I/O routines begin here *********/
13804 /** **/
13805 /** **/
13806
13807 /*****************************************************************************/
13808 /* */
13809 /* readline() Read a nonempty line from a file. */
13810 /* */
13811 /* A line is considered "nonempty" if it contains something that looks like */
13812 /* a number. Comments (prefaced by `#') are ignored. */
13813 /* */
13814 /*****************************************************************************/
13815
13816 #ifndef TRILIBRARY
13817
13818 #ifdef ANSI_DECLARATORS
13819 char *readline(char *string, FILE *infile, char *infilename)
13820 #else /* not ANSI_DECLARATORS */
13821 char *readline(string, infile, infilename)
13822 char *string;
13823 FILE *infile;
13824 char *infilename;
13825 #endif /* not ANSI_DECLARATORS */
13826
13827 {
13828 char *result;
13829
13830 /* Search for something that looks like a number. */
13831 do {
13832 result = fgets(string, INPUTLINESIZE, infile);
13833 if (result == (char *) NULL) {
13834 printf(" Error: Unexpected end of file in %s.\n", infilename);
13835 triexit(1);
13836 }
13837 /* Skip anything that doesn't look like a number, a comment, */
13838 /* or the end of a line. */
13839 while ((*result != '\0') && (*result != '#')
13840 && (*result != '.') && (*result != '+') && (*result != '-')
13841 && ((*result < '0') || (*result > '9'))) {
13842 result++;
13843 }
13844 /* If it's a comment or end of line, read another line and try again. */
13845 } while ((*result == '#') || (*result == '\0'));
13846 return result;
13847 }
13848
13849 #endif /* not TRILIBRARY */
13850
13851 /*****************************************************************************/
13852 /* */
13853 /* findfield() Find the next field of a string. */
13854 /* */
13855 /* Jumps past the current field by searching for whitespace, then jumps */
13856 /* past the whitespace to find the next field. */
13857 /* */
13858 /*****************************************************************************/
13859
13860 #ifndef TRILIBRARY
13861
13862 #ifdef ANSI_DECLARATORS
13863 char *findfield(char *string)
13864 #else /* not ANSI_DECLARATORS */
13865 char *findfield(string)
13866 char *string;
13867 #endif /* not ANSI_DECLARATORS */
13868
13869 {
13870 char *result;
13871
13872 result = string;
13873 /* Skip the current field. Stop upon reaching whitespace. */
13874 while ((*result != '\0') && (*result != '#')
13875 && (*result != ' ') && (*result != '\t')) {
13876 result++;
13877 }
13878 /* Now skip the whitespace and anything else that doesn't look like a */
13879 /* number, a comment, or the end of a line. */
13880 while ((*result != '\0') && (*result != '#')
13881 && (*result != '.') && (*result != '+') && (*result != '-')
13882 && ((*result < '0') || (*result > '9'))) {
13883 result++;
13884 }
13885 /* Check for a comment (prefixed with `#'). */
13886 if (*result == '#') {
13887 *result = '\0';
13888 }
13889 return result;
13890 }
13891
13892 #endif /* not TRILIBRARY */
13893
13894 /*****************************************************************************/
13895 /* */
13896 /* readnodes() Read the vertices from a file, which may be a .node or */
13897 /* .poly file. */
13898 /* */
13899 /*****************************************************************************/
13900
13901 #ifndef TRILIBRARY
13902
13903 #ifdef ANSI_DECLARATORS
13904 void readnodes(struct mesh *m, struct behavior *b, char *nodefilename,
13905 char *polyfilename, FILE **polyfile)
13906 #else /* not ANSI_DECLARATORS */
13907 void readnodes(m, b, nodefilename, polyfilename, polyfile)
13908 struct mesh *m;
13909 struct behavior *b;
13910 char *nodefilename;
13911 char *polyfilename;
13912 FILE **polyfile;
13913 #endif /* not ANSI_DECLARATORS */
13914
13915 {
13916 FILE *infile;
13917 vertex vertexloop;
13918 char inputline[INPUTLINESIZE];
13919 char *stringptr;
13920 char *infilename;
13921 REAL x, y;
13922 int firstnode;
13923 int nodemarkers;
13924 int currentmarker;
13925 int i, j;
13926
13927 if (b->poly) {
13928 /* Read the vertices from a .poly file. */
13929 if (!b->quiet) {
13930 printf("Opening %s.\n", polyfilename);
13931 }
13932 *polyfile = fopen(polyfilename, "r");
13933 if (*polyfile == (FILE *) NULL) {
13934 printf(" Error: Cannot access file %s.\n", polyfilename);
13935 triexit(1);
13936 }
13937 /* Read number of vertices, number of dimensions, number of vertex */
13938 /* attributes, and number of boundary markers. */
13939 stringptr = readline(inputline, *polyfile, polyfilename);
13940 m->invertices = (int) strtol(stringptr, &stringptr, 0);
13941 stringptr = findfield(stringptr);
13942 if (*stringptr == '\0') {
13943 m->mesh_dim = 2;
13944 } else {
13945 m->mesh_dim = (int) strtol(stringptr, &stringptr, 0);
13946 }
13947 stringptr = findfield(stringptr);
13948 if (*stringptr == '\0') {
13949 m->nextras = 0;
13950 } else {
13951 m->nextras = (int) strtol(stringptr, &stringptr, 0);
13952 }
13953 stringptr = findfield(stringptr);
13954 if (*stringptr == '\0') {
13955 nodemarkers = 0;
13956 } else {
13957 nodemarkers = (int) strtol(stringptr, &stringptr, 0);
13958 }
13959 if (m->invertices > 0) {
13960 infile = *polyfile;
13961 infilename = polyfilename;
13962 m->readnodefile = 0;
13963 } else {
13964 /* If the .poly file claims there are zero vertices, that means that */
13965 /* the vertices should be read from a separate .node file. */
13966 m->readnodefile = 1;
13967 infilename = nodefilename;
13968 }
13969 } else {
13970 m->readnodefile = 1;
13971 infilename = nodefilename;
13972 *polyfile = (FILE *) NULL;
13973 }
13974
13975 if (m->readnodefile) {
13976 /* Read the vertices from a .node file. */
13977 if (!b->quiet) {
13978 printf("Opening %s.\n", nodefilename);
13979 }
13980 infile = fopen(nodefilename, "r");
13981 if (infile == (FILE *) NULL) {
13982 printf(" Error: Cannot access file %s.\n", nodefilename);
13983 triexit(1);
13984 }
13985 /* Read number of vertices, number of dimensions, number of vertex */
13986 /* attributes, and number of boundary markers. */
13987 stringptr = readline(inputline, infile, nodefilename);
13988 m->invertices = (int) strtol(stringptr, &stringptr, 0);
13989 stringptr = findfield(stringptr);
13990 if (*stringptr == '\0') {
13991 m->mesh_dim = 2;
13992 } else {
13993 m->mesh_dim = (int) strtol(stringptr, &stringptr, 0);
13994 }
13995 stringptr = findfield(stringptr);
13996 if (*stringptr == '\0') {
13997 m->nextras = 0;
13998 } else {
13999 m->nextras = (int) strtol(stringptr, &stringptr, 0);
14000 }
14001 stringptr = findfield(stringptr);
14002 if (*stringptr == '\0') {
14003 nodemarkers = 0;
14004 } else {
14005 nodemarkers = (int) strtol(stringptr, &stringptr, 0);
14006 }
14007 }
14008
14009 if (m->invertices < 3) {
14010 printf("Error: Input must have at least three input vertices.\n");
14011 triexit(1);
14012 }
14013 if (m->mesh_dim != 2) {
14014 printf("Error: Triangle only works with two-dimensional meshes.\n");
14015 triexit(1);
14016 }
14017 if (m->nextras == 0) {
14018 b->weighted = 0;
14019 }
14020
14021 initializevertexpool(m, b);
14022
14023 /* Read the vertices. */
14024 for (i = 0; i < m->invertices; i++) {
14025 vertexloop = (vertex) poolalloc(&m->vertices);
14026 stringptr = readline(inputline, infile, infilename);
14027 if (i == 0) {
14028 firstnode = (int) strtol(stringptr, &stringptr, 0);
14029 if ((firstnode == 0) || (firstnode == 1)) {
14030 b->firstnumber = firstnode;
14031 }
14032 }
14033 stringptr = findfield(stringptr);
14034 if (*stringptr == '\0') {
14035 printf("Error: Vertex %d has no x coordinate.\n", b->firstnumber + i);
14036 triexit(1);
14037 }
14038 x = (REAL) strtod(stringptr, &stringptr);
14039 stringptr = findfield(stringptr);
14040 if (*stringptr == '\0') {
14041 printf("Error: Vertex %d has no y coordinate.\n", b->firstnumber + i);
14042 triexit(1);
14043 }
14044 y = (REAL) strtod(stringptr, &stringptr);
14045 vertexloop[0] = x;
14046 vertexloop[1] = y;
14047 /* Read the vertex attributes. */
14048 for (j = 2; j < 2 + m->nextras; j++) {
14049 stringptr = findfield(stringptr);
14050 if (*stringptr == '\0') {
14051 vertexloop[j] = 0.0;
14052 } else {
14053 vertexloop[j] = (REAL) strtod(stringptr, &stringptr);
14054 }
14055 }
14056 if (nodemarkers) {
14057 /* Read a vertex marker. */
14058 stringptr = findfield(stringptr);
14059 if (*stringptr == '\0') {
14060 setvertexmark(vertexloop, 0);
14061 } else {
14062 currentmarker = (int) strtol(stringptr, &stringptr, 0);
14063 setvertexmark(vertexloop, currentmarker);
14064 }
14065 } else {
14066 /* If no markers are specified in the file, they default to zero. */
14067 setvertexmark(vertexloop, 0);
14068 }
14069 setvertextype(vertexloop, INPUTVERTEX);
14070 /* Determine the smallest and largest x and y coordinates. */
14071 if (i == 0) {
14072 m->xmin = m->xmax = x;
14073 m->ymin = m->ymax = y;
14074 } else {
14075 m->xmin = (x < m->xmin) ? x : m->xmin;
14076 m->xmax = (x > m->xmax) ? x : m->xmax;
14077 m->ymin = (y < m->ymin) ? y : m->ymin;
14078 m->ymax = (y > m->ymax) ? y : m->ymax;
14079 }
14080 }
14081 if (m->readnodefile) {
14082 fclose(infile);
14083 }
14084
14085 /* Nonexistent x value used as a flag to mark circle events in sweepline */
14086 /* Delaunay algorithm. */
14087 m->xminextreme = 10 * m->xmin - 9 * m->xmax;
14088 }
14089
14090 #endif /* not TRILIBRARY */
14091
14092 /*****************************************************************************/
14093 /* */
14094 /* transfernodes() Read the vertices from memory. */
14095 /* */
14096 /*****************************************************************************/
14097
14098 #ifdef TRILIBRARY
14099
14100 #ifdef ANSI_DECLARATORS
14101 void transfernodes(struct mesh *m, struct behavior *b, REAL *pointlist,
14102 REAL *pointattriblist, int *pointmarkerlist,
14103 int numberofpoints, int numberofpointattribs)
14104 #else /* not ANSI_DECLARATORS */
14105 void transfernodes(m, b, pointlist, pointattriblist, pointmarkerlist,
14106 numberofpoints, numberofpointattribs)
14107 struct mesh *m;
14108 struct behavior *b;
14109 REAL *pointlist;
14110 REAL *pointattriblist;
14111 int *pointmarkerlist;
14112 int numberofpoints;
14113 int numberofpointattribs;
14114 #endif /* not ANSI_DECLARATORS */
14115
14116 {
14117 vertex vertexloop;
14118 REAL x, y;
14119 int i, j;
14120 int coordindex;
14121 int attribindex;
14122
14123 m->invertices = numberofpoints;
14124 m->mesh_dim = 2;
14125 m->nextras = numberofpointattribs;
14126 m->readnodefile = 0;
14127 if (m->invertices < 3) {
14128 printf("Error: Input must have at least three input vertices.\n");
14129 triexit(1);
14130 }
14131 if (m->nextras == 0) {
14132 b->weighted = 0;
14133 }
14134
14135 initializevertexpool(m, b);
14136
14137 /* Read the vertices. */
14138 coordindex = 0;
14139 attribindex = 0;
14140 for (i = 0; i < m->invertices; i++) {
14141 vertexloop = (vertex) poolalloc(&m->vertices);
14142 /* Read the vertex coordinates. */
14143 x = vertexloop[0] = pointlist[coordindex++];
14144 y = vertexloop[1] = pointlist[coordindex++];
14145 /* Read the vertex attributes. */
14146 for (j = 0; j < numberofpointattribs; j++) {
14147 vertexloop[2 + j] = pointattriblist[attribindex++];
14148 }
14149 if (pointmarkerlist != (int *) NULL) {
14150 /* Read a vertex marker. */
14151 setvertexmark(vertexloop, pointmarkerlist[i]);
14152 } else {
14153 /* If no markers are specified, they default to zero. */
14154 setvertexmark(vertexloop, 0);
14155 }
14156 setvertextype(vertexloop, INPUTVERTEX);
14157 /* Determine the smallest and largest x and y coordinates. */
14158 if (i == 0) {
14159 m->xmin = m->xmax = x;
14160 m->ymin = m->ymax = y;
14161 } else {
14162 m->xmin = (x < m->xmin) ? x : m->xmin;
14163 m->xmax = (x > m->xmax) ? x : m->xmax;
14164 m->ymin = (y < m->ymin) ? y : m->ymin;
14165 m->ymax = (y > m->ymax) ? y : m->ymax;
14166 }
14167 }
14168
14169 /* Nonexistent x value used as a flag to mark circle events in sweepline */
14170 /* Delaunay algorithm. */
14171 m->xminextreme = 10 * m->xmin - 9 * m->xmax;
14172 }
14173
14174 #endif /* TRILIBRARY */
14175
14176 /*****************************************************************************/
14177 /* */
14178 /* readholes() Read the holes, and possibly regional attributes and area */
14179 /* constraints, from a .poly file. */
14180 /* */
14181 /*****************************************************************************/
14182
14183 #ifndef TRILIBRARY
14184
14185 #ifdef ANSI_DECLARATORS
14186 void readholes(struct mesh *m, struct behavior *b,
14187 FILE *polyfile, char *polyfilename, REAL **hlist, int *holes,
14188 REAL **rlist, int *regions)
14189 #else /* not ANSI_DECLARATORS */
14190 void readholes(m, b, polyfile, polyfilename, hlist, holes, rlist, regions)
14191 struct mesh *m;
14192 struct behavior *b;
14193 FILE *polyfile;
14194 char *polyfilename;
14195 REAL **hlist;
14196 int *holes;
14197 REAL **rlist;
14198 int *regions;
14199 #endif /* not ANSI_DECLARATORS */
14200
14201 {
14202 REAL *holelist;
14203 REAL *regionlist;
14204 char inputline[INPUTLINESIZE];
14205 char *stringptr;
14206 int index;
14207 int i;
14208
14209 /* Read the holes. */
14210 stringptr = readline(inputline, polyfile, polyfilename);
14211 *holes = (int) strtol(stringptr, &stringptr, 0);
14212 if (*holes > 0) {
14213 holelist = (REAL *) trimalloc(2 * *holes * (int) sizeof(REAL));
14214 *hlist = holelist;
14215 for (i = 0; i < 2 * *holes; i += 2) {
14216 stringptr = readline(inputline, polyfile, polyfilename);
14217 stringptr = findfield(stringptr);
14218 if (*stringptr == '\0') {
14219 printf("Error: Hole %d has no x coordinate.\n",
14220 b->firstnumber + (i >> 1));
14221 triexit(1);
14222 } else {
14223 holelist[i] = (REAL) strtod(stringptr, &stringptr);
14224 }
14225 stringptr = findfield(stringptr);
14226 if (*stringptr == '\0') {
14227 printf("Error: Hole %d has no y coordinate.\n",
14228 b->firstnumber + (i >> 1));
14229 triexit(1);
14230 } else {
14231 holelist[i + 1] = (REAL) strtod(stringptr, &stringptr);
14232 }
14233 }
14234 } else {
14235 *hlist = (REAL *) NULL;
14236 }
14237
14238 #ifndef CDT_ONLY
14239 if ((b->regionattrib || b->vararea) && !b->refine) {
14240 /* Read the area constraints. */
14241 stringptr = readline(inputline, polyfile, polyfilename);
14242 *regions = (int) strtol(stringptr, &stringptr, 0);
14243 if (*regions > 0) {
14244 regionlist = (REAL *) trimalloc(4 * *regions * (int) sizeof(REAL));
14245 *rlist = regionlist;
14246 index = 0;
14247 for (i = 0; i < *regions; i++) {
14248 stringptr = readline(inputline, polyfile, polyfilename);
14249 stringptr = findfield(stringptr);
14250 if (*stringptr == '\0') {
14251 printf("Error: Region %d has no x coordinate.\n",
14252 b->firstnumber + i);
14253 triexit(1);
14254 } else {
14255 regionlist[index++] = (REAL) strtod(stringptr, &stringptr);
14256 }
14257 stringptr = findfield(stringptr);
14258 if (*stringptr == '\0') {
14259 printf("Error: Region %d has no y coordinate.\n",
14260 b->firstnumber + i);
14261 triexit(1);
14262 } else {
14263 regionlist[index++] = (REAL) strtod(stringptr, &stringptr);
14264 }
14265 stringptr = findfield(stringptr);
14266 if (*stringptr == '\0') {
14267 printf(
14268 "Error: Region %d has no region attribute or area constraint.\n",
14269 b->firstnumber + i);
14270 triexit(1);
14271 } else {
14272 regionlist[index++] = (REAL) strtod(stringptr, &stringptr);
14273 }
14274 stringptr = findfield(stringptr);
14275 if (*stringptr == '\0') {
14276 regionlist[index] = regionlist[index - 1];
14277 } else {
14278 regionlist[index] = (REAL) strtod(stringptr, &stringptr);
14279 }
14280 index++;
14281 }
14282 }
14283 } else {
14284 /* Set `*regions' to zero to avoid an accidental free() later. */
14285 *regions = 0;
14286 *rlist = (REAL *) NULL;
14287 }
14288 #endif /* not CDT_ONLY */
14289
14290 fclose(polyfile);
14291 }
14292
14293 #endif /* not TRILIBRARY */
14294
14295 /*****************************************************************************/
14296 /* */
14297 /* finishfile() Write the command line to the output file so the user */
14298 /* can remember how the file was generated. Close the file. */
14299 /* */
14300 /*****************************************************************************/
14301
14302 #ifndef TRILIBRARY
14303
14304 #ifdef ANSI_DECLARATORS
14305 void finishfile(FILE *outfile, int argc, char **argv)
14306 #else /* not ANSI_DECLARATORS */
14307 void finishfile(outfile, argc, argv)
14308 FILE *outfile;
14309 int argc;
14310 char **argv;
14311 #endif /* not ANSI_DECLARATORS */
14312
14313 {
14314 int i;
14315
14316 fprintf(outfile, "# Generated by");
14317 for (i = 0; i < argc; i++) {
14318 fprintf(outfile, " ");
14319 fputs(argv[i], outfile);
14320 }
14321 fprintf(outfile, "\n");
14322 fclose(outfile);
14323 }
14324
14325 #endif /* not TRILIBRARY */
14326
14327 /*****************************************************************************/
14328 /* */
14329 /* writenodes() Number the vertices and write them to a .node file. */
14330 /* */
14331 /* To save memory, the vertex numbers are written over the boundary markers */
14332 /* after the vertices are written to a file. */
14333 /* */
14334 /*****************************************************************************/
14335
14336 #ifdef TRILIBRARY
14337
14338 #ifdef ANSI_DECLARATORS
14339 void writenodes(struct mesh *m, struct behavior *b, REAL **pointlist,
14340 REAL **pointattriblist, int **pointmarkerlist)
14341 #else /* not ANSI_DECLARATORS */
14342 void writenodes(m, b, pointlist, pointattriblist, pointmarkerlist)
14343 struct mesh *m;
14344 struct behavior *b;
14345 REAL **pointlist;
14346 REAL **pointattriblist;
14347 int **pointmarkerlist;
14348 #endif /* not ANSI_DECLARATORS */
14349
14350 #else /* not TRILIBRARY */
14351
14352 #ifdef ANSI_DECLARATORS
14353 void writenodes(struct mesh *m, struct behavior *b, char *nodefilename,
14354 int argc, char **argv)
14355 #else /* not ANSI_DECLARATORS */
14356 void writenodes(m, b, nodefilename, argc, argv)
14357 struct mesh *m;
14358 struct behavior *b;
14359 char *nodefilename;
14360 int argc;
14361 char **argv;
14362 #endif /* not ANSI_DECLARATORS */
14363
14364 #endif /* not TRILIBRARY */
14365
14366 {
14367 #ifdef TRILIBRARY
14368 REAL *plist;
14369 REAL *palist;
14370 int *pmlist;
14371 int coordindex;
14372 int attribindex;
14373 #else /* not TRILIBRARY */
14374 FILE *outfile;
14375 #endif /* not TRILIBRARY */
14376 vertex vertexloop;
14377 long outvertices;
14378 int vertexnumber;
14379 int i;
14380
14381 if (b->jettison) {
14382 outvertices = m->vertices.items - m->undeads;
14383 } else {
14384 outvertices = m->vertices.items;
14385 }
14386
14387 #ifdef TRILIBRARY
14388 if (!b->quiet) {
14389 printf("Writing vertices.\n");
14390 }
14391 /* Allocate memory for output vertices if necessary. */
14392 if (*pointlist == (REAL *) NULL) {
14393 *pointlist = (REAL *) trimalloc((int) (outvertices * 2 * sizeof(REAL)));
14394 }
14395 /* Allocate memory for output vertex attributes if necessary. */
14396 if ((m->nextras > 0) && (*pointattriblist == (REAL *) NULL)) {
14397 *pointattriblist = (REAL *) trimalloc((int) (outvertices * m->nextras *
14398 sizeof(REAL)));
14399 }
14400 /* Allocate memory for output vertex markers if necessary. */
14401 if (!b->nobound && (*pointmarkerlist == (int *) NULL)) {
14402 *pointmarkerlist = (int *) trimalloc((int) (outvertices * sizeof(int)));
14403 }
14404 plist = *pointlist;
14405 palist = *pointattriblist;
14406 pmlist = *pointmarkerlist;
14407 coordindex = 0;
14408 attribindex = 0;
14409 #else /* not TRILIBRARY */
14410 if (!b->quiet) {
14411 printf("Writing %s.\n", nodefilename);
14412 }
14413 outfile = fopen(nodefilename, "w");
14414 if (outfile == (FILE *) NULL) {
14415 printf(" Error: Cannot create file %s.\n", nodefilename);
14416 triexit(1);
14417 }
14418 /* Number of vertices, number of dimensions, number of vertex attributes, */
14419 /* and number of boundary markers (zero or one). */
14420 fprintf(outfile, "%ld %d %d %d\n", outvertices, m->mesh_dim,
14421 m->nextras, 1 - b->nobound);
14422 #endif /* not TRILIBRARY */
14423
14424 traversalinit(&m->vertices);
14425 vertexnumber = b->firstnumber;
14426 vertexloop = vertextraverse(m);
14427 while (vertexloop != (vertex) NULL) {
14428 if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) {
14429 #ifdef TRILIBRARY
14430 /* X and y coordinates. */
14431 plist[coordindex++] = vertexloop[0];
14432 plist[coordindex++] = vertexloop[1];
14433 /* Vertex attributes. */
14434 for (i = 0; i < m->nextras; i++) {
14435 palist[attribindex++] = vertexloop[2 + i];
14436 }
14437 if (!b->nobound) {
14438 /* Copy the boundary marker. */
14439 pmlist[vertexnumber - b->firstnumber] = vertexmark(vertexloop);
14440 }
14441 #else /* not TRILIBRARY */
14442 /* Vertex number, x and y coordinates. */
14443 fprintf(outfile, "%4d %.17g %.17g", vertexnumber, vertexloop[0],
14444 vertexloop[1]);
14445 for (i = 0; i < m->nextras; i++) {
14446 /* Write an attribute. */
14447 fprintf(outfile, " %.17g", vertexloop[i + 2]);
14448 }
14449 if (b->nobound) {
14450 fprintf(outfile, "\n");
14451 } else {
14452 /* Write the boundary marker. */
14453 fprintf(outfile, " %d\n", vertexmark(vertexloop));
14454 }
14455 #endif /* not TRILIBRARY */
14456
14457 setvertexmark(vertexloop, vertexnumber);
14458 vertexnumber++;
14459 }
14460 vertexloop = vertextraverse(m);
14461 }
14462
14463 #ifndef TRILIBRARY
14464 finishfile(outfile, argc, argv);
14465 #endif /* not TRILIBRARY */
14466 }
14467
14468 /*****************************************************************************/
14469 /* */
14470 /* numbernodes() Number the vertices. */
14471 /* */
14472 /* Each vertex is assigned a marker equal to its number. */
14473 /* */
14474 /* Used when writenodes() is not called because no .node file is written. */
14475 /* */
14476 /*****************************************************************************/
14477
14478 #ifdef ANSI_DECLARATORS
14479 void numbernodes(struct mesh *m, struct behavior *b)
14480 #else /* not ANSI_DECLARATORS */
14481 void numbernodes(m, b)
14482 struct mesh *m;
14483 struct behavior *b;
14484 #endif /* not ANSI_DECLARATORS */
14485
14486 {
14487 vertex vertexloop;
14488 int vertexnumber;
14489
14490 traversalinit(&m->vertices);
14491 vertexnumber = b->firstnumber;
14492 vertexloop = vertextraverse(m);
14493 while (vertexloop != (vertex) NULL) {
14494 setvertexmark(vertexloop, vertexnumber);
14495 if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) {
14496 vertexnumber++;
14497 }
14498 vertexloop = vertextraverse(m);
14499 }
14500 }
14501
14502 /*****************************************************************************/
14503 /* */
14504 /* writeelements() Write the triangles to an .ele file. */
14505 /* */
14506 /*****************************************************************************/
14507
14508 #ifdef TRILIBRARY
14509
14510 #ifdef ANSI_DECLARATORS
14511 void writeelements(struct mesh *m, struct behavior *b,
14512 int **trianglelist, REAL **triangleattriblist)
14513 #else /* not ANSI_DECLARATORS */
14514 void writeelements(m, b, trianglelist, triangleattriblist)
14515 struct mesh *m;
14516 struct behavior *b;
14517 int **trianglelist;
14518 REAL **triangleattriblist;
14519 #endif /* not ANSI_DECLARATORS */
14520
14521 #else /* not TRILIBRARY */
14522
14523 #ifdef ANSI_DECLARATORS
14524 void writeelements(struct mesh *m, struct behavior *b, char *elefilename,
14525 int argc, char **argv)
14526 #else /* not ANSI_DECLARATORS */
14527 void writeelements(m, b, elefilename, argc, argv)
14528 struct mesh *m;
14529 struct behavior *b;
14530 char *elefilename;
14531 int argc;
14532 char **argv;
14533 #endif /* not ANSI_DECLARATORS */
14534
14535 #endif /* not TRILIBRARY */
14536
14537 {
14538 #ifdef TRILIBRARY
14539 int *tlist;
14540 REAL *talist;
14541 int vertexindex;
14542 int attribindex;
14543 #else /* not TRILIBRARY */
14544 FILE *outfile;
14545 #endif /* not TRILIBRARY */
14546 struct otri triangleloop;
14547 vertex p1, p2, p3;
14548 vertex mid1, mid2, mid3;
14549 long elementnumber;
14550 int i;
14551
14552 #ifdef TRILIBRARY
14553 if (!b->quiet) {
14554 printf("Writing triangles.\n");
14555 }
14556 /* Allocate memory for output triangles if necessary. */
14557 if (*trianglelist == (int *) NULL) {
14558 *trianglelist = (int *) trimalloc((int) (m->triangles.items *
14559 ((b->order + 1) * (b->order + 2) /
14560 2) * sizeof(int)));
14561 }
14562 /* Allocate memory for output triangle attributes if necessary. */
14563 if ((m->eextras > 0) && (*triangleattriblist == (REAL *) NULL)) {
14564 *triangleattriblist = (REAL *) trimalloc((int) (m->triangles.items *
14565 m->eextras *
14566 sizeof(REAL)));
14567 }
14568 tlist = *trianglelist;
14569 talist = *triangleattriblist;
14570 vertexindex = 0;
14571 attribindex = 0;
14572 #else /* not TRILIBRARY */
14573 if (!b->quiet) {
14574 printf("Writing %s.\n", elefilename);
14575 }
14576 outfile = fopen(elefilename, "w");
14577 if (outfile == (FILE *) NULL) {
14578 printf(" Error: Cannot create file %s.\n", elefilename);
14579 triexit(1);
14580 }
14581 /* Number of triangles, vertices per triangle, attributes per triangle. */
14582 fprintf(outfile, "%ld %d %d\n", m->triangles.items,
14583 (b->order + 1) * (b->order + 2) / 2, m->eextras);
14584 #endif /* not TRILIBRARY */
14585
14586 traversalinit(&m->triangles);
14587 triangleloop.tri = triangletraverse(m);
14588 triangleloop.orient = 0;
14589 elementnumber = b->firstnumber;
14590 while (triangleloop.tri != (triangle *) NULL) {
14591 org(triangleloop, p1);
14592 dest(triangleloop, p2);
14593 apex(triangleloop, p3);
14594 if (b->order == 1) {
14595 #ifdef TRILIBRARY
14596 tlist[vertexindex++] = vertexmark(p1);
14597 tlist[vertexindex++] = vertexmark(p2);
14598 tlist[vertexindex++] = vertexmark(p3);
14599 #else /* not TRILIBRARY */
14600 /* Triangle number, indices for three vertices. */
14601 fprintf(outfile, "%4ld %4d %4d %4d", elementnumber,
14602 vertexmark(p1), vertexmark(p2), vertexmark(p3));
14603 #endif /* not TRILIBRARY */
14604 } else {
14605 mid1 = (vertex) triangleloop.tri[m->highorderindex + 1];
14606 mid2 = (vertex) triangleloop.tri[m->highorderindex + 2];
14607 mid3 = (vertex) triangleloop.tri[m->highorderindex];
14608 #ifdef TRILIBRARY
14609 tlist[vertexindex++] = vertexmark(p1);
14610 tlist[vertexindex++] = vertexmark(p2);
14611 tlist[vertexindex++] = vertexmark(p3);
14612 tlist[vertexindex++] = vertexmark(mid1);
14613 tlist[vertexindex++] = vertexmark(mid2);
14614 tlist[vertexindex++] = vertexmark(mid3);
14615 #else /* not TRILIBRARY */
14616 /* Triangle number, indices for six vertices. */
14617 fprintf(outfile, "%4ld %4d %4d %4d %4d %4d %4d", elementnumber,
14618 vertexmark(p1), vertexmark(p2), vertexmark(p3), vertexmark(mid1),
14619 vertexmark(mid2), vertexmark(mid3));
14620 #endif /* not TRILIBRARY */
14621 }
14622
14623 #ifdef TRILIBRARY
14624 for (i = 0; i < m->eextras; i++) {
14625 talist[attribindex++] = elemattribute(triangleloop, i);
14626 }
14627 #else /* not TRILIBRARY */
14628 for (i = 0; i < m->eextras; i++) {
14629 fprintf(outfile, " %.17g", elemattribute(triangleloop, i));
14630 }
14631 fprintf(outfile, "\n");
14632 #endif /* not TRILIBRARY */
14633
14634 triangleloop.tri = triangletraverse(m);
14635 elementnumber++;
14636 }
14637
14638 #ifndef TRILIBRARY
14639 finishfile(outfile, argc, argv);
14640 #endif /* not TRILIBRARY */
14641 }
14642
14643 /*****************************************************************************/
14644 /* */
14645 /* writepoly() Write the segments and holes to a .poly file. */
14646 /* */
14647 /*****************************************************************************/
14648
14649 #ifdef TRILIBRARY
14650
14651 #ifdef ANSI_DECLARATORS
14652 void writepoly(struct mesh *m, struct behavior *b,
14653 int **segmentlist, int **segmentmarkerlist)
14654 #else /* not ANSI_DECLARATORS */
14655 void writepoly(m, b, segmentlist, segmentmarkerlist)
14656 struct mesh *m;
14657 struct behavior *b;
14658 int **segmentlist;
14659 int **segmentmarkerlist;
14660 #endif /* not ANSI_DECLARATORS */
14661
14662 #else /* not TRILIBRARY */
14663
14664 #ifdef ANSI_DECLARATORS
14665 void writepoly(struct mesh *m, struct behavior *b, char *polyfilename,
14666 REAL *holelist, int holes, REAL *regionlist, int regions,
14667 int argc, char **argv)
14668 #else /* not ANSI_DECLARATORS */
14669 void writepoly(m, b, polyfilename, holelist, holes, regionlist, regions,
14670 argc, argv)
14671 struct mesh *m;
14672 struct behavior *b;
14673 char *polyfilename;
14674 REAL *holelist;
14675 int holes;
14676 REAL *regionlist;
14677 int regions;
14678 int argc;
14679 char **argv;
14680 #endif /* not ANSI_DECLARATORS */
14681
14682 #endif /* not TRILIBRARY */
14683
14684 {
14685 #ifdef TRILIBRARY
14686 int *slist;
14687 int *smlist;
14688 int index;
14689 #else /* not TRILIBRARY */
14690 FILE *outfile;
14691 long holenumber, regionnumber;
14692 #endif /* not TRILIBRARY */
14693 struct osub subsegloop;
14694 vertex endpoint1, endpoint2;
14695 long subsegnumber;
14696
14697 #ifdef TRILIBRARY
14698 if (!b->quiet) {
14699 printf("Writing segments.\n");
14700 }
14701 /* Allocate memory for output segments if necessary. */
14702 if (*segmentlist == (int *) NULL) {
14703 *segmentlist = (int *) trimalloc((int) (m->subsegs.items * 2 *
14704 sizeof(int)));
14705 }
14706 /* Allocate memory for output segment markers if necessary. */
14707 if (!b->nobound && (*segmentmarkerlist == (int *) NULL)) {
14708 *segmentmarkerlist = (int *) trimalloc((int) (m->subsegs.items *
14709 sizeof(int)));
14710 }
14711 slist = *segmentlist;
14712 smlist = *segmentmarkerlist;
14713 index = 0;
14714 #else /* not TRILIBRARY */
14715 if (!b->quiet) {
14716 printf("Writing %s.\n", polyfilename);
14717 }
14718 outfile = fopen(polyfilename, "w");
14719 if (outfile == (FILE *) NULL) {
14720 printf(" Error: Cannot create file %s.\n", polyfilename);
14721 triexit(1);
14722 }
14723 /* The zero indicates that the vertices are in a separate .node file. */
14724 /* Followed by number of dimensions, number of vertex attributes, */
14725 /* and number of boundary markers (zero or one). */
14726 fprintf(outfile, "%d %d %d %d\n", 0, m->mesh_dim, m->nextras,
14727 1 - b->nobound);
14728 /* Number of segments, number of boundary markers (zero or one). */
14729 fprintf(outfile, "%ld %d\n", m->subsegs.items, 1 - b->nobound);
14730 #endif /* not TRILIBRARY */
14731
14732 traversalinit(&m->subsegs);
14733 subsegloop.ss = subsegtraverse(m);
14734 subsegloop.ssorient = 0;
14735 subsegnumber = b->firstnumber;
14736 while (subsegloop.ss != (subseg *) NULL) {
14737 sorg(subsegloop, endpoint1);
14738 sdest(subsegloop, endpoint2);
14739 #ifdef TRILIBRARY
14740 /* Copy indices of the segment's two endpoints. */
14741 slist[index++] = vertexmark(endpoint1);
14742 slist[index++] = vertexmark(endpoint2);
14743 if (!b->nobound) {
14744 /* Copy the boundary marker. */
14745 smlist[subsegnumber - b->firstnumber] = mark(subsegloop);
14746 }
14747 #else /* not TRILIBRARY */
14748 /* Segment number, indices of its two endpoints, and possibly a marker. */
14749 if (b->nobound) {
14750 fprintf(outfile, "%4ld %4d %4d\n", subsegnumber,
14751 vertexmark(endpoint1), vertexmark(endpoint2));
14752 } else {
14753 fprintf(outfile, "%4ld %4d %4d %4d\n", subsegnumber,
14754 vertexmark(endpoint1), vertexmark(endpoint2), mark(subsegloop));
14755 }
14756 #endif /* not TRILIBRARY */
14757
14758 subsegloop.ss = subsegtraverse(m);
14759 subsegnumber++;
14760 }
14761
14762 #ifndef TRILIBRARY
14763 #ifndef CDT_ONLY
14764 fprintf(outfile, "%d\n", holes);
14765 if (holes > 0) {
14766 for (holenumber = 0; holenumber < holes; holenumber++) {
14767 /* Hole number, x and y coordinates. */
14768 fprintf(outfile, "%4ld %.17g %.17g\n", b->firstnumber + holenumber,
14769 holelist[2 * holenumber], holelist[2 * holenumber + 1]);
14770 }
14771 }
14772 if (regions > 0) {
14773 fprintf(outfile, "%d\n", regions);
14774 for (regionnumber = 0; regionnumber < regions; regionnumber++) {
14775 /* Region number, x and y coordinates, attribute, maximum area. */
14776 fprintf(outfile, "%4ld %.17g %.17g %.17g %.17g\n",
14777 b->firstnumber + regionnumber,
14778 regionlist[4 * regionnumber], regionlist[4 * regionnumber + 1],
14779 regionlist[4 * regionnumber + 2],
14780 regionlist[4 * regionnumber + 3]);
14781 }
14782 }
14783 #endif /* not CDT_ONLY */
14784
14785 finishfile(outfile, argc, argv);
14786 #endif /* not TRILIBRARY */
14787 }
14788
14789 /*****************************************************************************/
14790 /* */
14791 /* writeedges() Write the edges to an .edge file. */
14792 /* */
14793 /*****************************************************************************/
14794
14795 #ifdef TRILIBRARY
14796
14797 #ifdef ANSI_DECLARATORS
14798 void writeedges(struct mesh *m, struct behavior *b,
14799 int **edgelist, int **edgemarkerlist)
14800 #else /* not ANSI_DECLARATORS */
14801 void writeedges(m, b, edgelist, edgemarkerlist)
14802 struct mesh *m;
14803 struct behavior *b;
14804 int **edgelist;
14805 int **edgemarkerlist;
14806 #endif /* not ANSI_DECLARATORS */
14807
14808 #else /* not TRILIBRARY */
14809
14810 #ifdef ANSI_DECLARATORS
14811 void writeedges(struct mesh *m, struct behavior *b, char *edgefilename,
14812 int argc, char **argv)
14813 #else /* not ANSI_DECLARATORS */
14814 void writeedges(m, b, edgefilename, argc, argv)
14815 struct mesh *m;
14816 struct behavior *b;
14817 char *edgefilename;
14818 int argc;
14819 char **argv;
14820 #endif /* not ANSI_DECLARATORS */
14821
14822 #endif /* not TRILIBRARY */
14823
14824 {
14825 #ifdef TRILIBRARY
14826 int *elist;
14827 int *emlist;
14828 int index;
14829 #else /* not TRILIBRARY */
14830 FILE *outfile;
14831 #endif /* not TRILIBRARY */
14832 struct otri triangleloop, trisym;
14833 struct osub checkmark;
14834 vertex p1, p2;
14835 long edgenumber;
14836 triangle ptr; /* Temporary variable used by sym(). */
14837 subseg sptr; /* Temporary variable used by tspivot(). */
14838
14839 #ifdef TRILIBRARY
14840 if (!b->quiet) {
14841 printf("Writing edges.\n");
14842 }
14843 /* Allocate memory for edges if necessary. */
14844 if (*edgelist == (int *) NULL) {
14845 *edgelist = (int *) trimalloc((int) (m->edges * 2 * sizeof(int)));
14846 }
14847 /* Allocate memory for edge markers if necessary. */
14848 if (!b->nobound && (*edgemarkerlist == (int *) NULL)) {
14849 *edgemarkerlist = (int *) trimalloc((int) (m->edges * sizeof(int)));
14850 }
14851 elist = *edgelist;
14852 emlist = *edgemarkerlist;
14853 index = 0;
14854 #else /* not TRILIBRARY */
14855 if (!b->quiet) {
14856 printf("Writing %s.\n", edgefilename);
14857 }
14858 outfile = fopen(edgefilename, "w");
14859 if (outfile == (FILE *) NULL) {
14860 printf(" Error: Cannot create file %s.\n", edgefilename);
14861 triexit(1);
14862 }
14863 /* Number of edges, number of boundary markers (zero or one). */
14864 fprintf(outfile, "%ld %d\n", m->edges, 1 - b->nobound);
14865 #endif /* not TRILIBRARY */
14866
14867 traversalinit(&m->triangles);
14868 triangleloop.tri = triangletraverse(m);
14869 edgenumber = b->firstnumber;
14870 /* To loop over the set of edges, loop over all triangles, and look at */
14871 /* the three edges of each triangle. If there isn't another triangle */
14872 /* adjacent to the edge, operate on the edge. If there is another */
14873 /* adjacent triangle, operate on the edge only if the current triangle */
14874 /* has a smaller pointer than its neighbor. This way, each edge is */
14875 /* considered only once. */
14876 while (triangleloop.tri != (triangle *) NULL) {
14877 for (triangleloop.orient = 0; triangleloop.orient < 3;
14878 triangleloop.orient++) {
14879 sym(triangleloop, trisym);
14880 if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) {
14881 org(triangleloop, p1);
14882 dest(triangleloop, p2);
14883 #ifdef TRILIBRARY
14884 elist[index++] = vertexmark(p1);
14885 elist[index++] = vertexmark(p2);
14886 #endif /* TRILIBRARY */
14887 if (b->nobound) {
14888 #ifndef TRILIBRARY
14889 /* Edge number, indices of two endpoints. */
14890 fprintf(outfile, "%4ld %d %d\n", edgenumber,
14891 vertexmark(p1), vertexmark(p2));
14892 #endif /* not TRILIBRARY */
14893 } else {
14894 /* Edge number, indices of two endpoints, and a boundary marker. */
14895 /* If there's no subsegment, the boundary marker is zero. */
14896 if (b->usesegments) {
14897 tspivot(triangleloop, checkmark);
14898 if (checkmark.ss == m->dummysub) {
14899 #ifdef TRILIBRARY
14900 emlist[edgenumber - b->firstnumber] = 0;
14901 #else /* not TRILIBRARY */
14902 fprintf(outfile, "%4ld %d %d %d\n", edgenumber,
14903 vertexmark(p1), vertexmark(p2), 0);
14904 #endif /* not TRILIBRARY */
14905 } else {
14906 #ifdef TRILIBRARY
14907 emlist[edgenumber - b->firstnumber] = mark(checkmark);
14908 #else /* not TRILIBRARY */
14909 fprintf(outfile, "%4ld %d %d %d\n", edgenumber,
14910 vertexmark(p1), vertexmark(p2), mark(checkmark));
14911 #endif /* not TRILIBRARY */
14912 }
14913 } else {
14914 #ifdef TRILIBRARY
14915 emlist[edgenumber - b->firstnumber] = trisym.tri == m->dummytri;
14916 #else /* not TRILIBRARY */
14917 fprintf(outfile, "%4ld %d %d %d\n", edgenumber,
14918 vertexmark(p1), vertexmark(p2), trisym.tri == m->dummytri);
14919 #endif /* not TRILIBRARY */
14920 }
14921 }
14922 edgenumber++;
14923 }
14924 }
14925 triangleloop.tri = triangletraverse(m);
14926 }
14927
14928 #ifndef TRILIBRARY
14929 finishfile(outfile, argc, argv);
14930 #endif /* not TRILIBRARY */
14931 }
14932
14933 /*****************************************************************************/
14934 /* */
14935 /* writevoronoi() Write the Voronoi diagram to a .v.node and .v.edge */
14936 /* file. */
14937 /* */
14938 /* The Voronoi diagram is the geometric dual of the Delaunay triangulation. */
14939 /* Hence, the Voronoi vertices are listed by traversing the Delaunay */
14940 /* triangles, and the Voronoi edges are listed by traversing the Delaunay */
14941 /* edges. */
14942 /* */
14943 /* WARNING: In order to assign numbers to the Voronoi vertices, this */
14944 /* procedure messes up the subsegments or the extra nodes of every */
14945 /* element. Hence, you should call this procedure last. */
14946 /* */
14947 /*****************************************************************************/
14948
14949 #ifdef TRILIBRARY
14950
14951 #ifdef ANSI_DECLARATORS
14952 void writevoronoi(struct mesh *m, struct behavior *b, REAL **vpointlist,
14953 REAL **vpointattriblist, int **vpointmarkerlist,
14954 int **vedgelist, int **vedgemarkerlist, REAL **vnormlist)
14955 #else /* not ANSI_DECLARATORS */
14956 void writevoronoi(m, b, vpointlist, vpointattriblist, vpointmarkerlist,
14957 vedgelist, vedgemarkerlist, vnormlist)
14958 struct mesh *m;
14959 struct behavior *b;
14960 REAL **vpointlist;
14961 REAL **vpointattriblist;
14962 int **vpointmarkerlist;
14963 int **vedgelist;
14964 int **vedgemarkerlist;
14965 REAL **vnormlist;
14966 #endif /* not ANSI_DECLARATORS */
14967
14968 #else /* not TRILIBRARY */
14969
14970 #ifdef ANSI_DECLARATORS
14971 void writevoronoi(struct mesh *m, struct behavior *b, char *vnodefilename,
14972 char *vedgefilename, int argc, char **argv)
14973 #else /* not ANSI_DECLARATORS */
14974 void writevoronoi(m, b, vnodefilename, vedgefilename, argc, argv)
14975 struct mesh *m;
14976 struct behavior *b;
14977 char *vnodefilename;
14978 char *vedgefilename;
14979 int argc;
14980 char **argv;
14981 #endif /* not ANSI_DECLARATORS */
14982
14983 #endif /* not TRILIBRARY */
14984
14985 {
14986 #ifdef TRILIBRARY
14987 REAL *plist;
14988 REAL *palist;
14989 int *elist;
14990 REAL *normlist;
14991 int coordindex;
14992 int attribindex;
14993 #else /* not TRILIBRARY */
14994 FILE *outfile;
14995 #endif /* not TRILIBRARY */
14996 struct otri triangleloop, trisym;
14997 vertex torg, tdest, tapex;
14998 REAL circumcenter[2];
14999 REAL xi, eta;
15000 long vnodenumber, vedgenumber;
15001 int p1, p2;
15002 int i;
15003 triangle ptr; /* Temporary variable used by sym(). */
15004
15005 #ifdef TRILIBRARY
15006 if (!b->quiet) {
15007 printf("Writing Voronoi vertices.\n");
15008 }
15009 /* Allocate memory for Voronoi vertices if necessary. */
15010 if (*vpointlist == (REAL *) NULL) {
15011 *vpointlist = (REAL *) trimalloc((int) (m->triangles.items * 2 *
15012 sizeof(REAL)));
15013 }
15014 /* Allocate memory for Voronoi vertex attributes if necessary. */
15015 if (*vpointattriblist == (REAL *) NULL) {
15016 *vpointattriblist = (REAL *) trimalloc((int) (m->triangles.items *
15017 m->nextras * sizeof(REAL)));
15018 }
15019 *vpointmarkerlist = (int *) NULL;
15020 plist = *vpointlist;
15021 palist = *vpointattriblist;
15022 coordindex = 0;
15023 attribindex = 0;
15024 #else /* not TRILIBRARY */
15025 if (!b->quiet) {
15026 printf("Writing %s.\n", vnodefilename);
15027 }
15028 outfile = fopen(vnodefilename, "w");
15029 if (outfile == (FILE *) NULL) {
15030 printf(" Error: Cannot create file %s.\n", vnodefilename);
15031 triexit(1);
15032 }
15033 /* Number of triangles, two dimensions, number of vertex attributes, */
15034 /* no markers. */
15035 fprintf(outfile, "%ld %d %d %d\n", m->triangles.items, 2, m->nextras, 0);
15036 #endif /* not TRILIBRARY */
15037
15038 traversalinit(&m->triangles);
15039 triangleloop.tri = triangletraverse(m);
15040 triangleloop.orient = 0;
15041 vnodenumber = b->firstnumber;
15042 while (triangleloop.tri != (triangle *) NULL) {
15043 org(triangleloop, torg);
15044 dest(triangleloop, tdest);
15045 apex(triangleloop, tapex);
15046 findcircumcenter(m, b, torg, tdest, tapex, circumcenter, &xi, &eta, 0);
15047 #ifdef TRILIBRARY
15048 /* X and y coordinates. */
15049 plist[coordindex++] = circumcenter[0];
15050 plist[coordindex++] = circumcenter[1];
15051 for (i = 2; i < 2 + m->nextras; i++) {
15052 /* Interpolate the vertex attributes at the circumcenter. */
15053 palist[attribindex++] = torg[i] + xi * (tdest[i] - torg[i])
15054 + eta * (tapex[i] - torg[i]);
15055 }
15056 #else /* not TRILIBRARY */
15057 /* Voronoi vertex number, x and y coordinates. */
15058 fprintf(outfile, "%4ld %.17g %.17g", vnodenumber, circumcenter[0],
15059 circumcenter[1]);
15060 for (i = 2; i < 2 + m->nextras; i++) {
15061 /* Interpolate the vertex attributes at the circumcenter. */
15062 fprintf(outfile, " %.17g", torg[i] + xi * (tdest[i] - torg[i])
15063 + eta * (tapex[i] - torg[i]));
15064 }
15065 fprintf(outfile, "\n");
15066 #endif /* not TRILIBRARY */
15067
15068 * (int *) (triangleloop.tri + 6) = (int) vnodenumber;
15069 triangleloop.tri = triangletraverse(m);
15070 vnodenumber++;
15071 }
15072
15073 #ifndef TRILIBRARY
15074 finishfile(outfile, argc, argv);
15075 #endif /* not TRILIBRARY */
15076
15077 #ifdef TRILIBRARY
15078 if (!b->quiet) {
15079 printf("Writing Voronoi edges.\n");
15080 }
15081 /* Allocate memory for output Voronoi edges if necessary. */
15082 if (*vedgelist == (int *) NULL) {
15083 *vedgelist = (int *) trimalloc((int) (m->edges * 2 * sizeof(int)));
15084 }
15085 *vedgemarkerlist = (int *) NULL;
15086 /* Allocate memory for output Voronoi norms if necessary. */
15087 if (*vnormlist == (REAL *) NULL) {
15088 *vnormlist = (REAL *) trimalloc((int) (m->edges * 2 * sizeof(REAL)));
15089 }
15090 elist = *vedgelist;
15091 normlist = *vnormlist;
15092 coordindex = 0;
15093 #else /* not TRILIBRARY */
15094 if (!b->quiet) {
15095 printf("Writing %s.\n", vedgefilename);
15096 }
15097 outfile = fopen(vedgefilename, "w");
15098 if (outfile == (FILE *) NULL) {
15099 printf(" Error: Cannot create file %s.\n", vedgefilename);
15100 triexit(1);
15101 }
15102 /* Number of edges, zero boundary markers. */
15103 fprintf(outfile, "%ld %d\n", m->edges, 0);
15104 #endif /* not TRILIBRARY */
15105
15106 traversalinit(&m->triangles);
15107 triangleloop.tri = triangletraverse(m);
15108 vedgenumber = b->firstnumber;
15109 /* To loop over the set of edges, loop over all triangles, and look at */
15110 /* the three edges of each triangle. If there isn't another triangle */
15111 /* adjacent to the edge, operate on the edge. If there is another */
15112 /* adjacent triangle, operate on the edge only if the current triangle */
15113 /* has a smaller pointer than its neighbor. This way, each edge is */
15114 /* considered only once. */
15115 while (triangleloop.tri != (triangle *) NULL) {
15116 for (triangleloop.orient = 0; triangleloop.orient < 3;
15117 triangleloop.orient++) {
15118 sym(triangleloop, trisym);
15119 if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) {
15120 /* Find the number of this triangle (and Voronoi vertex). */
15121 p1 = * (int *) (triangleloop.tri + 6);
15122 if (trisym.tri == m->dummytri) {
15123 org(triangleloop, torg);
15124 dest(triangleloop, tdest);
15125 #ifdef TRILIBRARY
15126 /* Copy an infinite ray. Index of one endpoint, and -1. */
15127 elist[coordindex] = p1;
15128 normlist[coordindex++] = tdest[1] - torg[1];
15129 elist[coordindex] = -1;
15130 normlist[coordindex++] = torg[0] - tdest[0];
15131 #else /* not TRILIBRARY */
15132 /* Write an infinite ray. Edge number, index of one endpoint, -1, */
15133 /* and x and y coordinates of a vector representing the */
15134 /* direction of the ray. */
15135 fprintf(outfile, "%4ld %d %d %.17g %.17g\n", vedgenumber,
15136 p1, -1, tdest[1] - torg[1], torg[0] - tdest[0]);
15137 #endif /* not TRILIBRARY */
15138 } else {
15139 /* Find the number of the adjacent triangle (and Voronoi vertex). */
15140 p2 = * (int *) (trisym.tri + 6);
15141 /* Finite edge. Write indices of two endpoints. */
15142 #ifdef TRILIBRARY
15143 elist[coordindex] = p1;
15144 normlist[coordindex++] = 0.0;
15145 elist[coordindex] = p2;
15146 normlist[coordindex++] = 0.0;
15147 #else /* not TRILIBRARY */
15148 fprintf(outfile, "%4ld %d %d\n", vedgenumber, p1, p2);
15149 #endif /* not TRILIBRARY */
15150 }
15151 vedgenumber++;
15152 }
15153 }
15154 triangleloop.tri = triangletraverse(m);
15155 }
15156
15157 #ifndef TRILIBRARY
15158 finishfile(outfile, argc, argv);
15159 #endif /* not TRILIBRARY */
15160 }
15161
15162 #ifdef TRILIBRARY
15163
15164 #ifdef ANSI_DECLARATORS
15165 void writeneighbors(struct mesh *m, struct behavior *b, int **neighborlist)
15166 #else /* not ANSI_DECLARATORS */
15167 void writeneighbors(m, b, neighborlist)
15168 struct mesh *m;
15169 struct behavior *b;
15170 int **neighborlist;
15171 #endif /* not ANSI_DECLARATORS */
15172
15173 #else /* not TRILIBRARY */
15174
15175 #ifdef ANSI_DECLARATORS
15176 void writeneighbors(struct mesh *m, struct behavior *b, char *neighborfilename,
15177 int argc, char **argv)
15178 #else /* not ANSI_DECLARATORS */
15179 void writeneighbors(m, b, neighborfilename, argc, argv)
15180 struct mesh *m;
15181 struct behavior *b;
15182 char *neighborfilename;
15183 int argc;
15184 char **argv;
15185 #endif /* not ANSI_DECLARATORS */
15186
15187 #endif /* not TRILIBRARY */
15188
15189 {
15190 #ifdef TRILIBRARY
15191 int *nlist;
15192 int index;
15193 #else /* not TRILIBRARY */
15194 FILE *outfile;
15195 #endif /* not TRILIBRARY */
15196 struct otri triangleloop, trisym;
15197 long elementnumber;
15198 int neighbor1, neighbor2, neighbor3;
15199 triangle ptr; /* Temporary variable used by sym(). */
15200
15201 #ifdef TRILIBRARY
15202 if (!b->quiet) {
15203 printf("Writing neighbors.\n");
15204 }
15205 /* Allocate memory for neighbors if necessary. */
15206 if (*neighborlist == (int *) NULL) {
15207 *neighborlist = (int *) trimalloc((int) (m->triangles.items * 3 *
15208 sizeof(int)));
15209 }
15210 nlist = *neighborlist;
15211 index = 0;
15212 #else /* not TRILIBRARY */
15213 if (!b->quiet) {
15214 printf("Writing %s.\n", neighborfilename);
15215 }
15216 outfile = fopen(neighborfilename, "w");
15217 if (outfile == (FILE *) NULL) {
15218 printf(" Error: Cannot create file %s.\n", neighborfilename);
15219 triexit(1);
15220 }
15221 /* Number of triangles, three neighbors per triangle. */
15222 fprintf(outfile, "%ld %d\n", m->triangles.items, 3);
15223 #endif /* not TRILIBRARY */
15224
15225 traversalinit(&m->triangles);
15226 triangleloop.tri = triangletraverse(m);
15227 triangleloop.orient = 0;
15228 elementnumber = b->firstnumber;
15229 while (triangleloop.tri != (triangle *) NULL) {
15230 * (int *) (triangleloop.tri + 6) = (int) elementnumber;
15231 triangleloop.tri = triangletraverse(m);
15232 elementnumber++;
15233 }
15234 * (int *) (m->dummytri + 6) = -1;
15235
15236 traversalinit(&m->triangles);
15237 triangleloop.tri = triangletraverse(m);
15238 elementnumber = b->firstnumber;
15239 while (triangleloop.tri != (triangle *) NULL) {
15240 triangleloop.orient = 1;
15241 sym(triangleloop, trisym);
15242 neighbor1 = * (int *) (trisym.tri + 6);
15243 triangleloop.orient = 2;
15244 sym(triangleloop, trisym);
15245 neighbor2 = * (int *) (trisym.tri + 6);
15246 triangleloop.orient = 0;
15247 sym(triangleloop, trisym);
15248 neighbor3 = * (int *) (trisym.tri + 6);
15249 #ifdef TRILIBRARY
15250 nlist[index++] = neighbor1;
15251 nlist[index++] = neighbor2;
15252 nlist[index++] = neighbor3;
15253 #else /* not TRILIBRARY */
15254 /* Triangle number, neighboring triangle numbers. */
15255 fprintf(outfile, "%4ld %d %d %d\n", elementnumber,
15256 neighbor1, neighbor2, neighbor3);
15257 #endif /* not TRILIBRARY */
15258
15259 triangleloop.tri = triangletraverse(m);
15260 elementnumber++;
15261 }
15262
15263 #ifndef TRILIBRARY
15264 finishfile(outfile, argc, argv);
15265 #endif /* not TRILIBRARY */
15266 }
15267
15268 /*****************************************************************************/
15269 /* */
15270 /* writeoff() Write the triangulation to an .off file. */
15271 /* */
15272 /* OFF stands for the Object File Format, a format used by the Geometry */
15273 /* Center's Geomview package. */
15274 /* */
15275 /*****************************************************************************/
15276
15277 #ifndef TRILIBRARY
15278
15279 #ifdef ANSI_DECLARATORS
15280 void writeoff(struct mesh *m, struct behavior *b, char *offfilename,
15281 int argc, char **argv)
15282 #else /* not ANSI_DECLARATORS */
15283 void writeoff(m, b, offfilename, argc, argv)
15284 struct mesh *m;
15285 struct behavior *b;
15286 char *offfilename;
15287 int argc;
15288 char **argv;
15289 #endif /* not ANSI_DECLARATORS */
15290
15291 {
15292 FILE *outfile;
15293 struct otri triangleloop;
15294 vertex vertexloop;
15295 vertex p1, p2, p3;
15296 long outvertices;
15297
15298 if (!b->quiet) {
15299 printf("Writing %s.\n", offfilename);
15300 }
15301
15302 if (b->jettison) {
15303 outvertices = m->vertices.items - m->undeads;
15304 } else {
15305 outvertices = m->vertices.items;
15306 }
15307
15308 outfile = fopen(offfilename, "w");
15309 if (outfile == (FILE *) NULL) {
15310 printf(" Error: Cannot create file %s.\n", offfilename);
15311 triexit(1);
15312 }
15313 /* Number of vertices, triangles, and edges. */
15314 fprintf(outfile, "OFF\n%ld %ld %ld\n", outvertices, m->triangles.items,
15315 m->edges);
15316
15317 /* Write the vertices. */
15318 traversalinit(&m->vertices);
15319 vertexloop = vertextraverse(m);
15320 while (vertexloop != (vertex) NULL) {
15321 if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) {
15322 /* The "0.0" is here because the OFF format uses 3D coordinates. */
15323 fprintf(outfile, " %.17g %.17g %.17g\n", vertexloop[0], vertexloop[1],
15324 0.0);
15325 }
15326 vertexloop = vertextraverse(m);
15327 }
15328
15329 /* Write the triangles. */
15330 traversalinit(&m->triangles);
15331 triangleloop.tri = triangletraverse(m);
15332 triangleloop.orient = 0;
15333 while (triangleloop.tri != (triangle *) NULL) {
15334 org(triangleloop, p1);
15335 dest(triangleloop, p2);
15336 apex(triangleloop, p3);
15337 /* The "3" means a three-vertex polygon. */
15338 fprintf(outfile, " 3 %4d %4d %4d\n", vertexmark(p1) - b->firstnumber,
15339 vertexmark(p2) - b->firstnumber, vertexmark(p3) - b->firstnumber);
15340 triangleloop.tri = triangletraverse(m);
15341 }
15342 finishfile(outfile, argc, argv);
15343 }
15344
15345 #endif /* not TRILIBRARY */
15346
15347 /** **/
15348 /** **/
15349 /********* File I/O routines end here *********/
15350
15351 /*****************************************************************************/
15352 /* */
15353 /* quality_statistics() Print statistics about the quality of the mesh. */
15354 /* */
15355 /*****************************************************************************/
15356
15357 #ifdef ANSI_DECLARATORS
15358 void quality_statistics(struct mesh *m, struct behavior *b)
15359 #else /* not ANSI_DECLARATORS */
15360 void quality_statistics(m, b)
15361 struct mesh *m;
15362 struct behavior *b;
15363 #endif /* not ANSI_DECLARATORS */
15364
15365 {
15366 struct otri triangleloop;
15367 vertex p[3];
15368 REAL cossquaretable[8];
15369 REAL ratiotable[16];
15370 REAL dx[3], dy[3];
15371 REAL edgelength[3];
15372 REAL dotproduct;
15373 REAL cossquare;
15374 REAL triarea;
15375 REAL shortest, longest;
15376 REAL trilongest2;
15377 REAL smallestarea, biggestarea;
15378 REAL triminaltitude2;
15379 REAL minaltitude;
15380 REAL triaspect2;
15381 REAL worstaspect;
15382 REAL smallestangle, biggestangle;
15383 REAL radconst, degconst;
15384 int angletable[18];
15385 int aspecttable[16];
15386 int aspectindex;
15387 int tendegree;
15388 int acutebiggest;
15389 int i, ii, j, k;
15390
15391 printf("Mesh quality statistics:\n\n");
15392 radconst = PI / 18.0;
15393 degconst = 180.0 / PI;
15394 for (i = 0; i < 8; i++) {
15395 cossquaretable[i] = cos(radconst * (REAL) (i + 1));
15396 cossquaretable[i] = cossquaretable[i] * cossquaretable[i];
15397 }
15398 for (i = 0; i < 18; i++) {
15399 angletable[i] = 0;
15400 }
15401
15402 ratiotable[0] = 1.5; ratiotable[1] = 2.0;
15403 ratiotable[2] = 2.5; ratiotable[3] = 3.0;
15404 ratiotable[4] = 4.0; ratiotable[5] = 6.0;
15405 ratiotable[6] = 10.0; ratiotable[7] = 15.0;
15406 ratiotable[8] = 25.0; ratiotable[9] = 50.0;
15407 ratiotable[10] = 100.0; ratiotable[11] = 300.0;
15408 ratiotable[12] = 1000.0; ratiotable[13] = 10000.0;
15409 ratiotable[14] = 100000.0; ratiotable[15] = 0.0;
15410 for (i = 0; i < 16; i++) {
15411 aspecttable[i] = 0;
15412 }
15413
15414 worstaspect = 0.0;
15415 minaltitude = m->xmax - m->xmin + m->ymax - m->ymin;
15416 minaltitude = minaltitude * minaltitude;
15417 shortest = minaltitude;
15418 longest = 0.0;
15419 smallestarea = minaltitude;
15420 biggestarea = 0.0;
15421 worstaspect = 0.0;
15422 smallestangle = 0.0;
15423 biggestangle = 2.0;
15424 acutebiggest = 1;
15425
15426 traversalinit(&m->triangles);
15427 triangleloop.tri = triangletraverse(m);
15428 triangleloop.orient = 0;
15429 while (triangleloop.tri != (triangle *) NULL) {
15430 org(triangleloop, p[0]);
15431 dest(triangleloop, p[1]);
15432 apex(triangleloop, p[2]);
15433 trilongest2 = 0.0;
15434
15435 for (i = 0; i < 3; i++) {
15436 j = plus1mod3[i];
15437 k = minus1mod3[i];
15438 dx[i] = p[j][0] - p[k][0];
15439 dy[i] = p[j][1] - p[k][1];
15440 edgelength[i] = dx[i] * dx[i] + dy[i] * dy[i];
15441 if (edgelength[i] > trilongest2) {
15442 trilongest2 = edgelength[i];
15443 }
15444 if (edgelength[i] > longest) {
15445 longest = edgelength[i];
15446 }
15447 if (edgelength[i] < shortest) {
15448 shortest = edgelength[i];
15449 }
15450 }
15451
15452 triarea = counterclockwise(m, b, p[0], p[1], p[2]);
15453 if (triarea < smallestarea) {
15454 smallestarea = triarea;
15455 }
15456 if (triarea > biggestarea) {
15457 biggestarea = triarea;
15458 }
15459 triminaltitude2 = triarea * triarea / trilongest2;
15460 if (triminaltitude2 < minaltitude) {
15461 minaltitude = triminaltitude2;
15462 }
15463 triaspect2 = trilongest2 / triminaltitude2;
15464 if (triaspect2 > worstaspect) {
15465 worstaspect = triaspect2;
15466 }
15467 aspectindex = 0;
15468 while ((triaspect2 > ratiotable[aspectindex] * ratiotable[aspectindex])
15469 && (aspectindex < 15)) {
15470 aspectindex++;
15471 }
15472 aspecttable[aspectindex]++;
15473
15474 for (i = 0; i < 3; i++) {
15475 j = plus1mod3[i];
15476 k = minus1mod3[i];
15477 dotproduct = dx[j] * dx[k] + dy[j] * dy[k];
15478 cossquare = dotproduct * dotproduct / (edgelength[j] * edgelength[k]);
15479 tendegree = 8;
15480 for (ii = 7; ii >= 0; ii--) {
15481 if (cossquare > cossquaretable[ii]) {
15482 tendegree = ii;
15483 }
15484 }
15485 if (dotproduct <= 0.0) {
15486 angletable[tendegree]++;
15487 if (cossquare > smallestangle) {
15488 smallestangle = cossquare;
15489 }
15490 if (acutebiggest && (cossquare < biggestangle)) {
15491 biggestangle = cossquare;
15492 }
15493 } else {
15494 angletable[17 - tendegree]++;
15495 if (acutebiggest || (cossquare > biggestangle)) {
15496 biggestangle = cossquare;
15497 acutebiggest = 0;
15498 }
15499 }
15500 }
15501 triangleloop.tri = triangletraverse(m);
15502 }
15503
15504 shortest = sqrt(shortest);
15505 longest = sqrt(longest);
15506 minaltitude = sqrt(minaltitude);
15507 worstaspect = sqrt(worstaspect);
15508 smallestarea *= 0.5;
15509 biggestarea *= 0.5;
15510 if (smallestangle >= 1.0) {
15511 smallestangle = 0.0;
15512 } else {
15513 smallestangle = degconst * acos(sqrt(smallestangle));
15514 }
15515 if (biggestangle >= 1.0) {
15516 biggestangle = 180.0;
15517 } else {
15518 if (acutebiggest) {
15519 biggestangle = degconst * acos(sqrt(biggestangle));
15520 } else {
15521 biggestangle = 180.0 - degconst * acos(sqrt(biggestangle));
15522 }
15523 }
15524
15525 printf(" Smallest area: %16.5g | Largest area: %16.5g\n",
15526 (double)smallestarea, (double)biggestarea);
15527 printf(" Shortest edge: %16.5g | Longest edge: %16.5g\n",
15528 (double)shortest, (double)longest);
15529 printf(" Shortest altitude: %12.5g | Largest aspect ratio: %8.5g\n\n",
15530 (double)minaltitude, (double)worstaspect);
15531
15532 printf(" Triangle aspect ratio histogram:\n");
15533 printf(" 1.1547 - %-6.6g : %8d | %6.6g - %-6.6g : %8d\n",
15534 (double)ratiotable[0], aspecttable[0], (double)ratiotable[7], (double)ratiotable[8],
15535 aspecttable[8]);
15536 for (i = 1; i < 7; i++) {
15537 printf(" %6.6g - %-6.6g : %8d | %6.6g - %-6.6g : %8d\n",
15538 (double)ratiotable[i - 1], (double)ratiotable[i], aspecttable[i],
15539 (double)ratiotable[i + 7], (double)ratiotable[i + 8], aspecttable[i + 8]);
15540 }
15541 printf(" %6.6g - %-6.6g : %8d | %6.6g - : %8d\n",
15542 (double)ratiotable[6], (double)ratiotable[7], aspecttable[7], (double)ratiotable[14],
15543 aspecttable[15]);
15544 printf(" (Aspect ratio is longest edge divided by shortest altitude)\n\n");
15545
15546 printf(" Smallest angle: %15.5g | Largest angle: %15.5g\n\n",
15547 (double)smallestangle, (double)biggestangle);
15548
15549 printf(" Angle histogram:\n");
15550 for (i = 0; i < 9; i++) {
15551 printf(" %3d - %3d degrees: %8d | %3d - %3d degrees: %8d\n",
15552 i * 10, i * 10 + 10, angletable[i],
15553 i * 10 + 90, i * 10 + 100, angletable[i + 9]);
15554 }
15555 printf("\n");
15556 }
15557
15558 /*****************************************************************************/
15559 /* */
15560 /* statistics() Print all sorts of cool facts. */
15561 /* */
15562 /*****************************************************************************/
15563
15564 #ifdef ANSI_DECLARATORS
15565 void statistics(struct mesh *m, struct behavior *b)
15566 #else /* not ANSI_DECLARATORS */
15567 void statistics(m, b)
15568 struct mesh *m;
15569 struct behavior *b;
15570 #endif /* not ANSI_DECLARATORS */
15571
15572 {
15573 printf("\nStatistics:\n\n");
15574 printf(" Input vertices: %d\n", m->invertices);
15575 if (b->refine) {
15576 printf(" Input triangles: %d\n", m->inelements);
15577 }
15578 if (b->poly) {
15579 printf(" Input segments: %d\n", m->insegments);
15580 if (!b->refine) {
15581 printf(" Input holes: %d\n", m->holes);
15582 }
15583 }
15584
15585 printf("\n Mesh vertices: %ld\n", m->vertices.items - m->undeads);
15586 printf(" Mesh triangles: %ld\n", m->triangles.items);
15587 printf(" Mesh edges: %ld\n", m->edges);
15588 printf(" Mesh exterior boundary edges: %ld\n", m->hullsize);
15589 if (b->poly || b->refine) {
15590 printf(" Mesh interior boundary edges: %ld\n",
15591 m->subsegs.items - m->hullsize);
15592 printf(" Mesh subsegments (constrained edges): %ld\n",
15593 m->subsegs.items);
15594 }
15595 printf("\n");
15596
15597 if (b->verbose) {
15598 quality_statistics(m, b);
15599 printf("Memory allocation statistics:\n\n");
15600 printf(" Maximum number of vertices: %ld\n", m->vertices.maxitems);
15601 printf(" Maximum number of triangles: %ld\n", m->triangles.maxitems);
15602 if (m->subsegs.maxitems > 0) {
15603 printf(" Maximum number of subsegments: %ld\n", m->subsegs.maxitems);
15604 }
15605 if (m->viri.maxitems > 0) {
15606 printf(" Maximum number of viri: %ld\n", m->viri.maxitems);
15607 }
15608 if (m->badsubsegs.maxitems > 0) {
15609 printf(" Maximum number of encroached subsegments: %ld\n",
15610 m->badsubsegs.maxitems);
15611 }
15612 if (m->badtriangles.maxitems > 0) {
15613 printf(" Maximum number of bad triangles: %ld\n",
15614 m->badtriangles.maxitems);
15615 }
15616 if (m->flipstackers.maxitems > 0) {
15617 printf(" Maximum number of stacked triangle flips: %ld\n",
15618 m->flipstackers.maxitems);
15619 }
15620 if (m->splaynodes.maxitems > 0) {
15621 printf(" Maximum number of splay tree nodes: %ld\n",
15622 m->splaynodes.maxitems);
15623 }
15624 printf(" Approximate heap memory use (bytes): %ld\n\n",
15625 m->vertices.maxitems * m->vertices.itembytes +
15626 m->triangles.maxitems * m->triangles.itembytes +
15627 m->subsegs.maxitems * m->subsegs.itembytes +
15628 m->viri.maxitems * m->viri.itembytes +
15629 m->badsubsegs.maxitems * m->badsubsegs.itembytes +
15630 m->badtriangles.maxitems * m->badtriangles.itembytes +
15631 m->flipstackers.maxitems * m->flipstackers.itembytes +
15632 m->splaynodes.maxitems * m->splaynodes.itembytes);
15633
15634 printf("Algorithmic statistics:\n\n");
15635 if (!b->weighted) {
15636 printf(" Number of incircle tests: %ld\n", m->incirclecount);
15637 } else {
15638 printf(" Number of 3D orientation tests: %ld\n", m->orient3dcount);
15639 }
15640 printf(" Number of 2D orientation tests: %ld\n", m->counterclockcount);
15641 if (m->hyperbolacount > 0) {
15642 printf(" Number of right-of-hyperbola tests: %ld\n",
15643 m->hyperbolacount);
15644 }
15645 if (m->circletopcount > 0) {
15646 printf(" Number of circle top computations: %ld\n",
15647 m->circletopcount);
15648 }
15649 if (m->circumcentercount > 0) {
15650 printf(" Number of triangle circumcenter computations: %ld\n",
15651 m->circumcentercount);
15652 }
15653 printf("\n");
15654 }
15655 }
15656
15657 /*****************************************************************************/
15658 /* */
15659 /* main() or triangulate() Gosh, do everything. */
15660 /* */
15661 /* The sequence is roughly as follows. Many of these steps can be skipped, */
15662 /* depending on the command line switches. */
15663 /* */
15664 /* - Initialize constants and parse the command line. */
15665 /* - Read the vertices from a file and either */
15666 /* - triangulate them (no -r), or */
15667 /* - read an old mesh from files and reconstruct it (-r). */
15668 /* - Insert the PSLG segments (-p), and possibly segments on the convex */
15669 /* hull (-c). */
15670 /* - Read the holes (-p), regional attributes (-pA), and regional area */
15671 /* constraints (-pa). Carve the holes and concavities, and spread the */
15672 /* regional attributes and area constraints. */
15673 /* - Enforce the constraints on minimum angle (-q) and maximum area (-a). */
15674 /* Also enforce the conforming Delaunay property (-q and -a). */
15675 /* - Compute the number of edges in the resulting mesh. */
15676 /* - Promote the mesh's linear triangles to higher order elements (-o). */
15677 /* - Write the output files and print the statistics. */
15678 /* - Check the consistency and Delaunay property of the mesh (-C). */
15679 /* */
15680 /*****************************************************************************/
15681
15682 #ifdef TRILIBRARY
15683
15684 #ifdef ANSI_DECLARATORS
15685 void triangulate(char *triswitches, struct triangulateio *in,
15686 struct triangulateio *out, struct triangulateio *vorout)
15687 #else /* not ANSI_DECLARATORS */
15688 void triangulate(triswitches, in, out, vorout)
15689 char *triswitches;
15690 struct triangulateio *in;
15691 struct triangulateio *out;
15692 struct triangulateio *vorout;
15693 #endif /* not ANSI_DECLARATORS */
15694
15695 #else /* not TRILIBRARY */
15696
15697 #ifdef ANSI_DECLARATORS
15698 int main(int argc, char **argv)
15699 #else /* not ANSI_DECLARATORS */
15700 int main(argc, argv)
15701 int argc;
15702 char **argv;
15703 #endif /* not ANSI_DECLARATORS */
15704
15705 #endif /* not TRILIBRARY */
15706
15707 {
15708 struct mesh m;
15709 struct behavior b;
15710 REAL *holearray; /* Array of holes. */
15711 REAL *regionarray; /* Array of regional attributes and area constraints. */
15712 #ifndef TRILIBRARY
15713 FILE *polyfile;
15714 #endif /* not TRILIBRARY */
15715 #ifndef NO_TIMER
15716 /* Variables for timing the performance of Triangle. The types are */
15717 /* defined in sys/time.h. */
15718 struct timeval tv0, tv1, tv2, tv3, tv4, tv5, tv6;
15719 struct timezone tz;
15720 #endif /* not NO_TIMER */
15721
15722 #ifndef NO_TIMER
15723 gettimeofday(&tv0, &tz);
15724 #endif /* not NO_TIMER */
15725
15726 triangleinit(&m);
15727 #ifdef TRILIBRARY
15728 parsecommandline(1, &triswitches, &b);
15729 #else /* not TRILIBRARY */
15730 parsecommandline(argc, argv, &b);
15731 #endif /* not TRILIBRARY */
15732 m.steinerleft = b.steiner;
15733
15734 #ifdef TRILIBRARY
15735 transfernodes(&m, &b, in->pointlist, in->pointattributelist,
15736 in->pointmarkerlist, in->numberofpoints,
15737 in->numberofpointattributes);
15738 #else /* not TRILIBRARY */
15739 readnodes(&m, &b, b.innodefilename, b.inpolyfilename, &polyfile);
15740 #endif /* not TRILIBRARY */
15741
15742 #ifndef NO_TIMER
15743 if (!b.quiet) {
15744 gettimeofday(&tv1, &tz);
15745 }
15746 #endif /* not NO_TIMER */
15747
15748 #ifdef CDT_ONLY
15749 m.hullsize = delaunay(&m, &b); /* Triangulate the vertices. */
15750 #else /* not CDT_ONLY */
15751 if (b.refine) {
15752 /* Read and reconstruct a mesh. */
15753 #ifdef TRILIBRARY
15754 m.hullsize = reconstruct(&m, &b, in->trianglelist,
15755 in->triangleattributelist, in->trianglearealist,
15756 in->numberoftriangles, in->numberofcorners,
15757 in->numberoftriangleattributes,
15758 in->segmentlist, in->segmentmarkerlist,
15759 in->numberofsegments);
15760 #else /* not TRILIBRARY */
15761 m.hullsize = reconstruct(&m, &b, b.inelefilename, b.areafilename,
15762 b.inpolyfilename, polyfile);
15763 #endif /* not TRILIBRARY */
15764 } else {
15765 m.hullsize = delaunay(&m, &b); /* Triangulate the vertices. */
15766 }
15767 #endif /* not CDT_ONLY */
15768
15769 #ifndef NO_TIMER
15770 if (!b.quiet) {
15771 gettimeofday(&tv2, &tz);
15772 if (b.refine) {
15773 printf("Mesh reconstruction");
15774 } else {
15775 printf("Delaunay");
15776 }
15777 printf(" milliseconds: %ld\n", 1000l * (tv2.tv_sec - tv1.tv_sec) +
15778 (tv2.tv_usec - tv1.tv_usec) / 1000l);
15779 }
15780 #endif /* not NO_TIMER */
15781
15782 /* Ensure that no vertex can be mistaken for a triangular bounding */
15783 /* box vertex in insertvertex(). */
15784 m.infvertex1 = (vertex) NULL;
15785 m.infvertex2 = (vertex) NULL;
15786 m.infvertex3 = (vertex) NULL;
15787
15788 if (b.usesegments) {
15789 m.checksegments = 1; /* Segments will be introduced next. */
15790 if (!b.refine) {
15791 /* Insert PSLG segments and/or convex hull segments. */
15792 #ifdef TRILIBRARY
15793 formskeleton(&m, &b, in->segmentlist,
15794 in->segmentmarkerlist, in->numberofsegments);
15795 #else /* not TRILIBRARY */
15796 formskeleton(&m, &b, polyfile, b.inpolyfilename);
15797 #endif /* not TRILIBRARY */
15798 }
15799 }
15800
15801 #ifndef NO_TIMER
15802 if (!b.quiet) {
15803 gettimeofday(&tv3, &tz);
15804 if (b.usesegments && !b.refine) {
15805 printf("Segment milliseconds: %ld\n",
15806 1000l * (tv3.tv_sec - tv2.tv_sec) +
15807 (tv3.tv_usec - tv2.tv_usec) / 1000l);
15808 }
15809 }
15810 #endif /* not NO_TIMER */
15811
15812 if (b.poly && (m.triangles.items > 0)) {
15813 #ifdef TRILIBRARY
15814 holearray = in->holelist;
15815 m.holes = in->numberofholes;
15816 regionarray = in->regionlist;
15817 m.regions = in->numberofregions;
15818 #else /* not TRILIBRARY */
15819 readholes(&m, &b, polyfile, b.inpolyfilename, &holearray, &m.holes,
15820 ®ionarray, &m.regions);
15821 #endif /* not TRILIBRARY */
15822 if (!b.refine) {
15823 /* Carve out holes and concavities. */
15824 carveholes(&m, &b, holearray, m.holes, regionarray, m.regions);
15825 }
15826 } else {
15827 /* Without a PSLG, there can be no holes or regional attributes */
15828 /* or area constraints. The following are set to zero to avoid */
15829 /* an accidental free() later. */
15830 m.holes = 0;
15831 m.regions = 0;
15832 }
15833
15834 #ifndef NO_TIMER
15835 if (!b.quiet) {
15836 gettimeofday(&tv4, &tz);
15837 if (b.poly && !b.refine) {
15838 printf("Hole milliseconds: %ld\n", 1000l * (tv4.tv_sec - tv3.tv_sec) +
15839 (tv4.tv_usec - tv3.tv_usec) / 1000l);
15840 }
15841 }
15842 #endif /* not NO_TIMER */
15843
15844 #ifndef CDT_ONLY
15845 if (b.quality && (m.triangles.items > 0)) {
15846 enforcequality(&m, &b); /* Enforce angle and area constraints. */
15847 }
15848 #endif /* not CDT_ONLY */
15849
15850 #ifndef NO_TIMER
15851 if (!b.quiet) {
15852 gettimeofday(&tv5, &tz);
15853 #ifndef CDT_ONLY
15854 if (b.quality) {
15855 printf("Quality milliseconds: %ld\n",
15856 1000l * (tv5.tv_sec - tv4.tv_sec) +
15857 (tv5.tv_usec - tv4.tv_usec) / 1000l);
15858 }
15859 #endif /* not CDT_ONLY */
15860 }
15861 #endif /* not NO_TIMER */
15862
15863 /* Calculate the number of edges. */
15864 m.edges = (3l * m.triangles.items + m.hullsize) / 2l;
15865
15866 if (b.order > 1) {
15867 highorder(&m, &b); /* Promote elements to higher polynomial order. */
15868 }
15869 if (!b.quiet) {
15870 printf("\n");
15871 }
15872
15873 #ifdef TRILIBRARY
15874 if (b.jettison) {
15875 out->numberofpoints = m.vertices.items - m.undeads;
15876 } else {
15877 out->numberofpoints = m.vertices.items;
15878 }
15879 out->numberofpointattributes = m.nextras;
15880 out->numberoftriangles = m.triangles.items;
15881 out->numberofcorners = (b.order + 1) * (b.order + 2) / 2;
15882 out->numberoftriangleattributes = m.eextras;
15883 out->numberofedges = m.edges;
15884 if (b.usesegments) {
15885 out->numberofsegments = m.subsegs.items;
15886 } else {
15887 out->numberofsegments = m.hullsize;
15888 }
15889 if (vorout != (struct triangulateio *) NULL) {
15890 vorout->numberofpoints = m.triangles.items;
15891 vorout->numberofpointattributes = m.nextras;
15892 vorout->numberofedges = m.edges;
15893 }
15894 #endif /* TRILIBRARY */
15895 /* If not using iteration numbers, don't write a .node file if one was */
15896 /* read, because the original one would be overwritten! */
15897 if (b.nonodewritten || (b.noiterationnum && m.readnodefile)) {
15898 if (!b.quiet) {
15899 #ifdef TRILIBRARY
15900 printf("NOT writing vertices.\n");
15901 #else /* not TRILIBRARY */
15902 printf("NOT writing a .node file.\n");
15903 #endif /* not TRILIBRARY */
15904 }
15905 numbernodes(&m, &b); /* We must remember to number the vertices. */
15906 } else {
15907 /* writenodes() numbers the vertices too. */
15908 #ifdef TRILIBRARY
15909 writenodes(&m, &b, &out->pointlist, &out->pointattributelist,
15910 &out->pointmarkerlist);
15911 #else /* not TRILIBRARY */
15912 writenodes(&m, &b, b.outnodefilename, argc, argv);
15913 #endif /* TRILIBRARY */
15914 }
15915 if (b.noelewritten) {
15916 if (!b.quiet) {
15917 #ifdef TRILIBRARY
15918 printf("NOT writing triangles.\n");
15919 #else /* not TRILIBRARY */
15920 printf("NOT writing an .ele file.\n");
15921 #endif /* not TRILIBRARY */
15922 }
15923 } else {
15924 #ifdef TRILIBRARY
15925 writeelements(&m, &b, &out->trianglelist, &out->triangleattributelist);
15926 #else /* not TRILIBRARY */
15927 writeelements(&m, &b, b.outelefilename, argc, argv);
15928 #endif /* not TRILIBRARY */
15929 }
15930 /* The -c switch (convex switch) causes a PSLG to be written */
15931 /* even if none was read. */
15932 if (b.poly || b.convex) {
15933 /* If not using iteration numbers, don't overwrite the .poly file. */
15934 if (b.nopolywritten || b.noiterationnum) {
15935 if (!b.quiet) {
15936 #ifdef TRILIBRARY
15937 printf("NOT writing segments.\n");
15938 #else /* not TRILIBRARY */
15939 printf("NOT writing a .poly file.\n");
15940 #endif /* not TRILIBRARY */
15941 }
15942 } else {
15943 #ifdef TRILIBRARY
15944 writepoly(&m, &b, &out->segmentlist, &out->segmentmarkerlist);
15945 out->numberofholes = m.holes;
15946 out->numberofregions = m.regions;
15947 if (b.poly) {
15948 out->holelist = in->holelist;
15949 out->regionlist = in->regionlist;
15950 } else {
15951 out->holelist = (REAL *) NULL;
15952 out->regionlist = (REAL *) NULL;
15953 }
15954 #else /* not TRILIBRARY */
15955 writepoly(&m, &b, b.outpolyfilename, holearray, m.holes, regionarray,
15956 m.regions, argc, argv);
15957 #endif /* not TRILIBRARY */
15958 }
15959 }
15960 #ifndef TRILIBRARY
15961 #ifndef CDT_ONLY
15962 if (m.regions > 0) {
15963 trifree((VOID *) regionarray);
15964 }
15965 #endif /* not CDT_ONLY */
15966 if (m.holes > 0) {
15967 trifree((VOID *) holearray);
15968 }
15969 if (b.geomview) {
15970 writeoff(&m, &b, b.offfilename, argc, argv);
15971 }
15972 #endif /* not TRILIBRARY */
15973 if (b.edgesout) {
15974 #ifdef TRILIBRARY
15975 writeedges(&m, &b, &out->edgelist, &out->edgemarkerlist);
15976 #else /* not TRILIBRARY */
15977 writeedges(&m, &b, b.edgefilename, argc, argv);
15978 #endif /* not TRILIBRARY */
15979 }
15980 if (b.voronoi) {
15981 #ifdef TRILIBRARY
15982 writevoronoi(&m, &b, &vorout->pointlist, &vorout->pointattributelist,
15983 &vorout->pointmarkerlist, &vorout->edgelist,
15984 &vorout->edgemarkerlist, &vorout->normlist);
15985 #else /* not TRILIBRARY */
15986 writevoronoi(&m, &b, b.vnodefilename, b.vedgefilename, argc, argv);
15987 #endif /* not TRILIBRARY */
15988 }
15989 if (b.neighbors) {
15990 #ifdef TRILIBRARY
15991 writeneighbors(&m, &b, &out->neighborlist);
15992 #else /* not TRILIBRARY */
15993 writeneighbors(&m, &b, b.neighborfilename, argc, argv);
15994 #endif /* not TRILIBRARY */
15995 }
15996
15997 if (!b.quiet) {
15998 #ifndef NO_TIMER
15999 gettimeofday(&tv6, &tz);
16000 printf("\nOutput milliseconds: %ld\n",
16001 1000l * (tv6.tv_sec - tv5.tv_sec) +
16002 (tv6.tv_usec - tv5.tv_usec) / 1000l);
16003 printf("Total running milliseconds: %ld\n",
16004 1000l * (tv6.tv_sec - tv0.tv_sec) +
16005 (tv6.tv_usec - tv0.tv_usec) / 1000l);
16006 #endif /* not NO_TIMER */
16007
16008 statistics(&m, &b);
16009 }
16010
16011 #ifndef REDUCED
16012 if (b.docheck) {
16013 checkmesh(&m, &b);
16014 checkdelaunay(&m, &b);
16015 }
16016 #endif /* not REDUCED */
16017
16018 triangledeinit(&m, &b);
16019 #ifndef TRILIBRARY
16020 return 0;
16021 #endif /* not TRILIBRARY */
16022 }
16023