1 /*****************************************************************************/
2 /* */
3 /* 888888888 ,o, / 888 */
4 /* 888 88o88o " o8888o 88o8888o o88888o 888 o88888o */
5 /* 888 888 888 88b 888 888 888 888 888 d888 88b */
6 /* 888 888 888 o88^o888 888 888 "88888" 888 8888oo888 */
7 /* 888 888 888 C888 888 888 888 / 888 q888 */
8 /* 888 888 888 "88o^888 888 888 Cb 888 "88oooo" */
9 /* "8oo8D */
10 /* */
11 /* A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator. */
12 /* (triangle.c) */
13 /* */
14 /* Version 1.3 */
15 /* July 19, 1996 */
16 /* */
17 /* Copyright 1996 */
18 /* Jonathan Richard Shewchuk */
19 /* School of Computer Science */
20 /* Carnegie Mellon University */
21 /* 5000 Forbes Avenue */
22 /* Pittsburgh, Pennsylvania 15213-3891 */
23 /* jrs@cs.cmu.edu */
24 /* */
25 /* This program may be freely redistributed under the condition that the */
26 /* copyright notices (including this entire header and the copyright */
27 /* notice printed when the `-h' switch is selected) are not removed, and */
28 /* no compensation is received. Private, research, and institutional */
29 /* use is free. You may distribute modified versions of this code UNDER */
30 /* THE CONDITION THAT THIS CODE AND ANY MODIFICATIONS MADE TO IT IN THE */
31 /* SAME FILE REMAIN UNDER COPYRIGHT OF THE ORIGINAL AUTHOR, BOTH SOURCE */
32 /* AND OBJECT CODE ARE MADE FREELY AVAILABLE WITHOUT CHARGE, AND CLEAR */
33 /* NOTICE IS GIVEN OF THE MODIFICATIONS. Distribution of this code as */
34 /* part of a commercial system is permissible ONLY BY DIRECT ARRANGEMENT */
35 /* WITH THE AUTHOR. (If you are not directly supplying this code to a */
36 /* customer, and you are instead telling them how they can obtain it for */
37 /* free, then you are not required to make any arrangement with me.) */
38 /* */
39 /* Hypertext instructions for Triangle are available on the Web at */
40 /* */
41 /* http://www.cs.cmu.edu/~quake/triangle.html */
42 /* */
43 /* Some of the references listed below are marked [*]. These are available */
44 /* for downloading from the Web page */
45 /* */
46 /* http://www.cs.cmu.edu/~quake/triangle.research.html */
47 /* */
48 /* A paper discussing some aspects of Triangle is available. See Jonathan */
49 /* Richard Shewchuk, "Triangle: Engineering a 2D Quality Mesh Generator */
50 /* and Delaunay Triangulator," First Workshop on Applied Computational */
51 /* Geometry, ACM, May 1996. [*] */
52 /* */
53 /* Triangle was created as part of the Archimedes project in the School of */
54 /* Computer Science at Carnegie Mellon University. Archimedes is a */
55 /* system for compiling parallel finite element solvers. For further */
56 /* information, see Anja Feldmann, Omar Ghattas, John R. Gilbert, Gary L. */
57 /* Miller, David R. O'Hallaron, Eric J. Schwabe, Jonathan R. Shewchuk, */
58 /* and Shang-Hua Teng, "Automated Parallel Solution of Unstructured PDE */
59 /* Problems." To appear in Communications of the ACM, we hope. */
60 /* */
61 /* The quality mesh generation algorithm is due to Jim Ruppert, "A */
62 /* Delaunay Refinement Algorithm for Quality 2-Dimensional Mesh */
63 /* Generation," Journal of Algorithms 18(3):548-585, May 1995. [*] */
64 /* */
65 /* My implementation of the divide-and-conquer and incremental Delaunay */
66 /* triangulation algorithms follows closely the presentation of Guibas */
67 /* and Stolfi, even though I use a triangle-based data structure instead */
68 /* of their quad-edge data structure. (In fact, I originally implemented */
69 /* Triangle using the quad-edge data structure, but switching to a */
70 /* triangle-based data structure sped Triangle by a factor of two.) The */
71 /* mesh manipulation primitives and the two aforementioned Delaunay */
72 /* triangulation algorithms are described by Leonidas J. Guibas and Jorge */
73 /* Stolfi, "Primitives for the Manipulation of General Subdivisions and */
74 /* the Computation of Voronoi Diagrams," ACM Transactions on Graphics */
75 /* 4(2):74-123, April 1985. */
76 /* */
77 /* Their O(n log n) divide-and-conquer algorithm is adapted from Der-Tsai */
78 /* Lee and Bruce J. Schachter, "Two Algorithms for Constructing the */
79 /* Delaunay Triangulation," International Journal of Computer and */
80 /* Information Science 9(3):219-242, 1980. The idea to improve the */
81 /* divide-and-conquer algorithm by alternating between vertical and */
82 /* horizontal cuts was introduced by Rex A. Dwyer, "A Faster Divide-and- */
83 /* Conquer Algorithm for Constructing Delaunay Triangulations," */
84 /* Algorithmica 2(2):137-151, 1987. */
85 /* */
86 /* The incremental insertion algorithm was first proposed by C. L. Lawson, */
87 /* "Software for C1 Surface Interpolation," in Mathematical Software III, */
88 /* John R. Rice, editor, Academic Press, New York, pp. 161-194, 1977. */
89 /* For point location, I use the algorithm of Ernst P. Mucke, Isaac */
90 /* Saias, and Binhai Zhu, "Fast Randomized Point Location Without */
91 /* Preprocessing in Two- and Three-dimensional Delaunay Triangulations," */
92 /* Proceedings of the Twelfth Annual Symposium on Computational Geometry, */
93 /* ACM, May 1996. [*] If I were to randomize the order of point */
94 /* insertion (I currently don't bother), their result combined with the */
95 /* result of Leonidas J. Guibas, Donald E. Knuth, and Micha Sharir, */
96 /* "Randomized Incremental Construction of Delaunay and Voronoi */
97 /* Diagrams," Algorithmica 7(4):381-413, 1992, would yield an expected */
98 /* O(n^{4/3}) bound on running time. */
99 /* */
100 /* The O(n log n) sweepline Delaunay triangulation algorithm is taken from */
101 /* Steven Fortune, "A Sweepline Algorithm for Voronoi Diagrams", */
102 /* Algorithmica 2(2):153-174, 1987. A random sample of edges on the */
103 /* boundary of the triangulation are maintained in a splay tree for the */
104 /* purpose of point location. Splay trees are described by Daniel */
105 /* Dominic Sleator and Robert Endre Tarjan, "Self-Adjusting Binary Search */
106 /* Trees," Journal of the ACM 32(3):652-686, July 1985. */
107 /* */
108 /* The algorithms for exact computation of the signs of determinants are */
109 /* described in Jonathan Richard Shewchuk, "Adaptive Precision Floating- */
110 /* Point Arithmetic and Fast Robust Geometric Predicates," Technical */
111 /* Report CMU-CS-96-140, School of Computer Science, Carnegie Mellon */
112 /* University, Pittsburgh, Pennsylvania, May 1996. [*] (Submitted to */
113 /* Discrete & Computational Geometry.) An abbreviated version appears as */
114 /* Jonathan Richard Shewchuk, "Robust Adaptive Floating-Point Geometric */
115 /* Predicates," Proceedings of the Twelfth Annual Symposium on Computa- */
116 /* tional Geometry, ACM, May 1996. [*] Many of the ideas for my exact */
117 /* arithmetic routines originate with Douglas M. Priest, "Algorithms for */
118 /* Arbitrary Precision Floating Point Arithmetic," Tenth Symposium on */
119 /* Computer Arithmetic, 132-143, IEEE Computer Society Press, 1991. [*] */
120 /* Many of the ideas for the correct evaluation of the signs of */
121 /* determinants are taken from Steven Fortune and Christopher J. Van Wyk, */
122 /* "Efficient Exact Arithmetic for Computational Geometry," Proceedings */
123 /* of the Ninth Annual Symposium on Computational Geometry, ACM, */
124 /* pp. 163-172, May 1993, and from Steven Fortune, "Numerical Stability */
125 /* of Algorithms for 2D Delaunay Triangulations," International Journal */
126 /* of Computational Geometry & Applications 5(1-2):193-213, March-June */
127 /* 1995. */
128 /* */
129 /* For definitions of and results involving Delaunay triangulations, */
130 /* constrained and conforming versions thereof, and other aspects of */
131 /* triangular mesh generation, see the excellent survey by Marshall Bern */
132 /* and David Eppstein, "Mesh Generation and Optimal Triangulation," in */
133 /* Computing and Euclidean Geometry, Ding-Zhu Du and Frank Hwang, */
134 /* editors, World Scientific, Singapore, pp. 23-90, 1992. */
135 /* */
136 /* The time for incrementally adding PSLG (planar straight line graph) */
137 /* segments to create a constrained Delaunay triangulation is probably */
138 /* O(n^2) per segment in the worst case and O(n) per edge in the common */
139 /* case, where n is the number of triangles that intersect the segment */
140 /* before it is inserted. This doesn't count point location, which can */
141 /* be much more expensive. (This note does not apply to conforming */
142 /* Delaunay triangulations, for which a different method is used to */
143 /* insert segments.) */
144 /* */
145 /* The time for adding segments to a conforming Delaunay triangulation is */
146 /* not clear, but does not depend upon n alone. In some cases, very */
147 /* small features (like a point lying next to a segment) can cause a */
148 /* single segment to be split an arbitrary number of times. Of course, */
149 /* floating-point precision is a practical barrier to how much this can */
150 /* happen. */
151 /* */
152 /* The time for deleting a point from a Delaunay triangulation is O(n^2) in */
153 /* the worst case and O(n) in the common case, where n is the degree of */
154 /* the point being deleted. I could improve this to expected O(n) time */
155 /* by "inserting" the neighboring vertices in random order, but n is */
156 /* usually quite small, so it's not worth the bother. (The O(n) time */
157 /* for random insertion follows from L. Paul Chew, "Building Voronoi */
158 /* Diagrams for Convex Polygons in Linear Expected Time," Technical */
159 /* Report PCS-TR90-147, Department of Mathematics and Computer Science, */
160 /* Dartmouth College, 1990. */
161 /* */
162 /* Ruppert's Delaunay refinement algorithm typically generates triangles */
163 /* at a linear rate (constant time per triangle) after the initial */
164 /* triangulation is formed. There may be pathological cases where more */
165 /* time is required, but these never arise in practice. */
166 /* */
167 /* The segment intersection formulae are straightforward. If you want to */
168 /* see them derived, see Franklin Antonio. "Faster Line Segment */
169 /* Intersection." In Graphics Gems III (David Kirk, editor), pp. 199- */
170 /* 202. Academic Press, Boston, 1992. */
171 /* */
172 /* If you make any improvements to this code, please please please let me */
173 /* know, so that I may obtain the improvements. Even if you don't change */
174 /* the code, I'd still love to hear what it's being used for. */
175 /* */
176 /* Disclaimer: Neither I nor Carnegie Mellon warrant this code in any way */
177 /* whatsoever. This code is provided "as-is". Use at your own risk. */
178 /* */
179 /*****************************************************************************/
180
181 /* For single precision (which will save some memory and reduce paging), */
182 /* define the symbol SINGLE by using the -DSINGLE compiler switch or by */
183 /* writing "#define SINGLE" below. */
184 /* */
185 /* For double precision (which will allow you to refine meshes to a smaller */
186 /* edge length), leave SINGLE undefined. */
187 /* */
188 /* Double precision uses more memory, but improves the resolution of the */
189 /* meshes you can generate with Triangle. It also reduces the likelihood */
190 /* of a floating exception due to overflow. Finally, it is much faster */
191 /* than single precision on 64-bit architectures like the DEC Alpha. I */
192 /* recommend double precision unless you want to generate a mesh for which */
193 /* you do not have enough memory. */
194
195 /* #define SINGLE */
196
197 #ifdef SINGLE
198 #define REAL float
199 #else /* not SINGLE */
200 #define REAL double
201 #endif /* not SINGLE */
202
203 /* If yours is not a Unix system, define the NO_TIMER compiler switch to */
204 /* remove the Unix-specific timing code. */
205
206 /* #define NO_TIMER */
207
208 /* To insert lots of self-checks for internal errors, define the SELF_CHECK */
209 /* symbol. This will slow down the program significantly. It is best to */
210 /* define the symbol using the -DSELF_CHECK compiler switch, but you could */
211 /* write "#define SELF_CHECK" below. If you are modifying this code, I */
212 /* recommend you turn self-checks on. */
213
214 /* #define SELF_CHECK */
215
216 /* To compile Triangle as a callable object library (triangle.o), define the */
217 /* TRILIBRARY symbol. Read the file triangle.h for details on how to call */
218 /* the procedure triangulate() that results. */
219
220 #define TRILIBRARY
221
222 /* It is possible to generate a smaller version of Triangle using one or */
223 /* both of the following symbols. Define the REDUCED symbol to eliminate */
224 /* all features that are primarily of research interest; specifically, the */
225 /* -i, -F, -s, and -C switches. Define the CDT_ONLY symbol to eliminate */
226 /* all meshing algorithms above and beyond constrained Delaunay */
227 /* triangulation; specifically, the -r, -q, -a, -S, and -s switches. */
228 /* These reductions are most likely to be useful when generating an object */
229 /* library (triangle.o) by defining the TRILIBRARY symbol. */
230
231 #define REDUCED
232 #define CDT_ONLY
233
234 /* On some machines, the exact arithmetic routines might be defeated by the */
235 /* use of internal extended precision floating-point registers. Sometimes */
236 /* this problem can be fixed by defining certain values to be volatile, */
237 /* thus forcing them to be stored to memory and rounded off. This isn't */
238 /* a great solution, though, as it slows Triangle down. */
239 /* */
240 /* To try this out, write "#define INEXACT volatile" below. Normally, */
241 /* however, INEXACT should be defined to be nothing. ("#define INEXACT".) */
242
243 #define INEXACT /* Nothing */
244 /* #define INEXACT volatile */
245
246 /* Maximum number of characters in a file name (including the null). */
247
248 #define FILENAMESIZE 512
249
250 /* Maximum number of characters in a line read from a file (including the */
251 /* null). */
252
253 #define INPUTLINESIZE 512
254
255 /* For efficiency, a variety of data structures are allocated in bulk. The */
256 /* following constants determine how many of each structure is allocated */
257 /* at once. */
258
259 #define TRIPERBLOCK 4092 /* Number of triangles allocated at once. */
260 #define SHELLEPERBLOCK 508 /* Number of shell edges allocated at once. */
261 #define POINTPERBLOCK 4092 /* Number of points allocated at once. */
262 #define VIRUSPERBLOCK 1020 /* Number of virus triangles allocated at once. */
263 /* Number of encroached segments allocated at once. */
264 #define BADSEGMENTPERBLOCK 252
265 /* Number of skinny triangles allocated at once. */
266 #define BADTRIPERBLOCK 4092
267 /* Number of splay tree nodes allocated at once. */
268 #define SPLAYNODEPERBLOCK 508
269
270 /* The point marker DEADPOINT is an arbitrary number chosen large enough to */
271 /* (hopefully) not conflict with user boundary markers. Make sure that it */
272 /* is small enough to fit into your machine's integer size. */
273
274 #define DEADPOINT -1073741824
275
276 /* The next line is used to outsmart some very stupid compilers. If your */
277 /* compiler is smarter, feel free to replace the "int" with "void". */
278 /* Not that it matters. */
279
280 #define VOID int
281
282 /* Two constants for algorithms based on random sampling. Both constants */
283 /* have been chosen empirically to optimize their respective algorithms. */
284
285 /* Used for the point location scheme of Mucke, Saias, and Zhu, to decide */
286 /* how large a random sample of triangles to inspect. */
287 #define SAMPLEFACTOR 11
288 /* Used in Fortune's sweepline Delaunay algorithm to determine what fraction */
289 /* of boundary edges should be maintained in the splay tree for point */
290 /* location on the front. */
291 #define SAMPLERATE 10
292
293 /* A number that speaks for itself, every kissable digit. */
294
295 #define PI 3.141592653589793238462643383279502884197169399375105820974944592308
296
297 /* Another fave. */
298
299 #define SQUAREROOTTWO 1.4142135623730950488016887242096980785696718753769480732
300
301 /* And here's one for those of you who are intimidated by math. */
302
303 #define ONETHIRD 0.333333333333333333333333333333333333333333333333333333333333
304
305 #include <stdio.h>
306 #include <string.h>
307 #include <math.h>
308 #ifndef NO_TIMER
309 #include <sys/time.h>
310 #endif /* NO_TIMER */
311 #ifdef TRILIBRARY
312 #include <tina/triangle.h>
313 #endif /* TRILIBRARY */
314
315 /* The following obscenity seems to be necessary to ensure that this program */
316 /* will port to Dec Alphas running OSF/1, because their stdio.h file commits */
317 /* the unpardonable sin of including stdlib.h. Hence, malloc(), free(), and */
318 /* exit() may or may not already be defined at this point. I declare these */
319 /* functions explicitly because some non-ANSI C compilers lack stdlib.h. */
320
321 #ifndef _STDLIB_H_
322 extern void *malloc();
323 extern void free();
324 extern void exit();
325 extern double strtod();
326 extern long strtol();
327 #endif /* _STDLIB_H_ */
328
329 /* A few forward declarations. */
330
331 void poolrestart();
332 #ifndef TRILIBRARY
333 char *freadline();
334 char *findfield();
335 #endif /* not TRILIBRARY */
336
337 /* Labels that signify whether a record consists primarily of pointers or of */
338 /* floating-point words. Used to make decisions about data alignment. */
339
340 enum wordtype {POINTER, FLOATINGPOINT};
341
342 /* Labels that signify the result of point location. The result of a */
343 /* search indicates that the point falls in the interior of a triangle, on */
344 /* an edge, on a vertex, or outside the mesh. */
345
346 enum locateresult {INTRIANGLE, ONEDGE, ONVERTEX, OUTSIDE};
347
348 /* Labels that signify the result of site insertion. The result indicates */
349 /* that the point was inserted with complete success, was inserted but */
350 /* encroaches on a segment, was not inserted because it lies on a segment, */
351 /* or was not inserted because another point occupies the same location. */
352
353 enum insertsiteresult {SUCCESSFULPOINT, ENCROACHINGPOINT, VIOLATINGPOINT,
354 DUPLICATEPOINT};
355
356 /* Labels that signify the result of direction finding. The result */
357 /* indicates that a segment connecting the two query points falls within */
358 /* the direction triangle, along the left edge of the direction triangle, */
359 /* or along the right edge of the direction triangle. */
360
361 enum finddirectionresult {WITHIN, LEFTCOLLINEAR, RIGHTCOLLINEAR};
362
363 /* Labels that signify the result of the circumcenter computation routine. */
364 /* The return value indicates which edge of the triangle is shortest. */
365
366 enum circumcenterresult {OPPOSITEORG, OPPOSITEDEST, OPPOSITEAPEX};
367
368 /*****************************************************************************/
369 /* */
370 /* The basic mesh data structures */
371 /* */
372 /* There are three: points, triangles, and shell edges (abbreviated */
373 /* `shelle'). These three data structures, linked by pointers, comprise */
374 /* the mesh. A point simply represents a point in space and its properties.*/
375 /* A triangle is a triangle. A shell edge is a special data structure used */
376 /* to represent impenetrable segments in the mesh (including the outer */
377 /* boundary, boundaries of holes, and internal boundaries separating two */
378 /* triangulated regions). Shell edges represent boundaries defined by the */
379 /* user that triangles may not lie across. */
380 /* */
381 /* A triangle consists of a list of three vertices, a list of three */
382 /* adjoining triangles, a list of three adjoining shell edges (when shell */
383 /* edges are used), an arbitrary number of optional user-defined floating- */
384 /* point attributes, and an optional area constraint. The latter is an */
385 /* upper bound on the permissible area of each triangle in a region, used */
386 /* for mesh refinement. */
387 /* */
388 /* For a triangle on a boundary of the mesh, some or all of the neighboring */
389 /* triangles may not be present. For a triangle in the interior of the */
390 /* mesh, often no neighboring shell edges are present. Such absent */
391 /* triangles and shell edges are never represented by NULL pointers; they */
392 /* are represented by two special records: `dummytri', the triangle that */
393 /* fills "outer space", and `dummysh', the omnipresent shell edge. */
394 /* `dummytri' and `dummysh' are used for several reasons; for instance, */
395 /* they can be dereferenced and their contents examined without causing the */
396 /* memory protection exception that would occur if NULL were dereferenced. */
397 /* */
398 /* However, it is important to understand that a triangle includes other */
399 /* information as well. The pointers to adjoining vertices, triangles, and */
400 /* shell edges are ordered in a way that indicates their geometric relation */
401 /* to each other. Furthermore, each of these pointers contains orientation */
402 /* information. Each pointer to an adjoining triangle indicates which face */
403 /* of that triangle is contacted. Similarly, each pointer to an adjoining */
404 /* shell edge indicates which side of that shell edge is contacted, and how */
405 /* the shell edge is oriented relative to the triangle. */
406 /* */
407 /* Shell edges are found abutting edges of triangles; either sandwiched */
408 /* between two triangles, or resting against one triangle on an exterior */
409 /* boundary or hole boundary. */
410 /* */
411 /* A shell edge consists of a list of two vertices, a list of two */
412 /* adjoining shell edges, and a list of two adjoining triangles. One of */
413 /* the two adjoining triangles may not be present (though there should */
414 /* always be one), and neighboring shell edges might not be present. */
415 /* Shell edges also store a user-defined integer "boundary marker". */
416 /* Typically, this integer is used to indicate what sort of boundary */
417 /* conditions are to be applied at that location in a finite element */
418 /* simulation. */
419 /* */
420 /* Like triangles, shell edges maintain information about the relative */
421 /* orientation of neighboring objects. */
422 /* */
423 /* Points are relatively simple. A point is a list of floating point */
424 /* numbers, starting with the x, and y coordinates, followed by an */
425 /* arbitrary number of optional user-defined floating-point attributes, */
426 /* followed by an integer boundary marker. During the segment insertion */
427 /* phase, there is also a pointer from each point to a triangle that may */
428 /* contain it. Each pointer is not always correct, but when one is, it */
429 /* speeds up segment insertion. These pointers are assigned values once */
430 /* at the beginning of the segment insertion phase, and are not used or */
431 /* updated at any other time. Edge swapping during segment insertion will */
432 /* render some of them incorrect. Hence, don't rely upon them for */
433 /* anything. For the most part, points do not have any information about */
434 /* what triangles or shell edges they are linked to. */
435 /* */
436 /*****************************************************************************/
437
438 /*****************************************************************************/
439 /* */
440 /* Handles */
441 /* */
442 /* The oriented triangle (`triedge') and oriented shell edge (`edge') data */
443 /* structures defined below do not themselves store any part of the mesh. */
444 /* The mesh itself is made of `triangle's, `shelle's, and `point's. */
445 /* */
446 /* Oriented triangles and oriented shell edges will usually be referred to */
447 /* as "handles". A handle is essentially a pointer into the mesh; it */
448 /* allows you to "hold" one particular part of the mesh. Handles are used */
449 /* to specify the regions in which one is traversing and modifying the mesh.*/
450 /* A single `triangle' may be held by many handles, or none at all. (The */
451 /* latter case is not a memory leak, because the triangle is still */
452 /* connected to other triangles in the mesh.) */
453 /* */
454 /* A `triedge' is a handle that holds a triangle. It holds a specific side */
455 /* of the triangle. An `edge' is a handle that holds a shell edge. It */
456 /* holds either the left or right side of the edge. */
457 /* */
458 /* Navigation about the mesh is accomplished through a set of mesh */
459 /* manipulation primitives, further below. Many of these primitives take */
460 /* a handle and produce a new handle that holds the mesh near the first */
461 /* handle. Other primitives take two handles and glue the corresponding */
462 /* parts of the mesh together. The exact position of the handles is */
463 /* important. For instance, when two triangles are glued together by the */
464 /* bond() primitive, they are glued by the sides on which the handles lie. */
465 /* */
466 /* Because points have no information about which triangles they are */
467 /* attached to, I commonly represent a point by use of a handle whose */
468 /* origin is the point. A single handle can simultaneously represent a */
469 /* triangle, an edge, and a point. */
470 /* */
471 /*****************************************************************************/
472
473 /* The triangle data structure. Each triangle contains three pointers to */
474 /* adjoining triangles, plus three pointers to vertex points, plus three */
475 /* pointers to shell edges (defined below; these pointers are usually */
476 /* `dummysh'). It may or may not also contain user-defined attributes */
477 /* and/or a floating-point "area constraint". It may also contain extra */
478 /* pointers for nodes, when the user asks for high-order elements. */
479 /* Because the size and structure of a `triangle' is not decided until */
480 /* runtime, I haven't simply defined the type `triangle' to be a struct. */
481
482 typedef REAL **triangle; /* Really: typedef triangle *triangle */
483
484 /* An oriented triangle: includes a pointer to a triangle and orientation. */
485 /* The orientation denotes an edge of the triangle. Hence, there are */
486 /* three possible orientations. By convention, each edge is always */
487 /* directed to point counterclockwise about the corresponding triangle. */
488
489 struct triedge {
490 triangle *tri;
491 int orient; /* Ranges from 0 to 2. */
492 };
493
494 /* The shell data structure. Each shell edge contains two pointers to */
495 /* adjoining shell edges, plus two pointers to vertex points, plus two */
496 /* pointers to adjoining triangles, plus one shell marker. */
497
498 typedef REAL **shelle; /* Really: typedef shelle *shelle */
499
500 /* An oriented shell edge: includes a pointer to a shell edge and an */
501 /* orientation. The orientation denotes a side of the edge. Hence, there */
502 /* are two possible orientations. By convention, the edge is always */
503 /* directed so that the "side" denoted is the right side of the edge. */
504
505 struct edge {
506 shelle *sh;
507 int shorient; /* Ranges from 0 to 1. */
508 };
509
510 /* The point data structure. Each point is actually an array of REALs. */
511 /* The number of REALs is unknown until runtime. An integer boundary */
512 /* marker, and sometimes a pointer to a triangle, is appended after the */
513 /* REALs. */
514
515 typedef REAL *point;
516
517 /* A queue used to store encroached segments. Each segment's vertices are */
518 /* stored so that one can check whether a segment is still the same. */
519
520 struct badsegment {
521 struct edge encsegment; /* An encroached segment. */
522 point segorg, segdest; /* The two vertices. */
523 struct badsegment *nextsegment; /* Pointer to next encroached segment. */
524 };
525
526 /* A queue used to store bad triangles. The key is the square of the cosine */
527 /* of the smallest angle of the triangle. Each triangle's vertices are */
528 /* stored so that one can check whether a triangle is still the same. */
529
530 struct badface {
531 struct triedge badfacetri; /* A bad triangle. */
532 REAL key; /* cos^2 of smallest (apical) angle. */
533 point faceorg, facedest, faceapex; /* The three vertices. */
534 struct badface *nextface; /* Pointer to next bad triangle. */
535 };
536
537 /* A node in a heap used to store events for the sweepline Delaunay */
538 /* algorithm. Nodes do not point directly to their parents or children in */
539 /* the heap. Instead, each node knows its position in the heap, and can */
540 /* look up its parent and children in a separate array. The `eventptr' */
541 /* points either to a `point' or to a triangle (in encoded format, so that */
542 /* an orientation is included). In the latter case, the origin of the */
543 /* oriented triangle is the apex of a "circle event" of the sweepline */
544 /* algorithm. To distinguish site events from circle events, all circle */
545 /* events are given an invalid (smaller than `xmin') x-coordinate `xkey'. */
546
547 struct event {
548 REAL xkey, ykey; /* Coordinates of the event. */
549 VOID *eventptr; /* Can be a point or the location of a circle event. */
550 int heapposition; /* Marks this event's position in the heap. */
551 };
552
553 /* A node in the splay tree. Each node holds an oriented ghost triangle */
554 /* that represents a boundary edge of the growing triangulation. When a */
555 /* circle event covers two boundary edges with a triangle, so that they */
556 /* are no longer boundary edges, those edges are not immediately deleted */
557 /* from the tree; rather, they are lazily deleted when they are next */
558 /* encountered. (Since only a random sample of boundary edges are kept */
559 /* in the tree, lazy deletion is faster.) `keydest' is used to verify */
560 /* that a triangle is still the same as when it entered the splay tree; if */
561 /* it has been rotated (due to a circle event), it no longer represents a */
562 /* boundary edge and should be deleted. */
563
564 struct splaynode {
565 struct triedge keyedge; /* Lprev of an edge on the front. */
566 point keydest; /* Used to verify that splay node is still live. */
567 struct splaynode *lchild, *rchild; /* Children in splay tree. */
568 };
569
570 /* A type used to allocate memory. firstblock is the first block of items. */
571 /* nowblock is the block from which items are currently being allocated. */
572 /* nextitem points to the next slab of free memory for an item. */
573 /* deaditemstack is the head of a linked list (stack) of deallocated items */
574 /* that can be recycled. unallocateditems is the number of items that */
575 /* remain to be allocated from nowblock. */
576 /* */
577 /* Traversal is the process of walking through the entire list of items, and */
578 /* is separate from allocation. Note that a traversal will visit items on */
579 /* the "deaditemstack" stack as well as live items. pathblock points to */
580 /* the block currently being traversed. pathitem points to the next item */
581 /* to be traversed. pathitemsleft is the number of items that remain to */
582 /* be traversed in pathblock. */
583 /* */
584 /* itemwordtype is set to POINTER or FLOATINGPOINT, and is used to suggest */
585 /* what sort of word the record is primarily made up of. alignbytes */
586 /* determines how new records should be aligned in memory. itembytes and */
587 /* itemwords are the length of a record in bytes (after rounding up) and */
588 /* words. itemsperblock is the number of items allocated at once in a */
589 /* single block. items is the number of currently allocated items. */
590 /* maxitems is the maximum number of items that have been allocated at */
591 /* once; it is the current number of items plus the number of records kept */
592 /* on deaditemstack. */
593
594 struct memorypool {
595 VOID **firstblock, **nowblock;
596 VOID *nextitem;
597 VOID *deaditemstack;
598 VOID **pathblock;
599 VOID *pathitem;
600 enum wordtype itemwordtype;
601 int alignbytes;
602 int itembytes, itemwords;
603 int itemsperblock;
604 long items, maxitems;
605 int unallocateditems;
606 int pathitemsleft;
607 };
608
609 /* Variables used to allocate memory for triangles, shell edges, points, */
610 /* viri (triangles being eaten), bad (encroached) segments, bad (skinny */
611 /* or too large) triangles, and splay tree nodes. */
612
613 struct memorypool triangles;
614 struct memorypool shelles;
615 struct memorypool points;
616 struct memorypool viri;
617 struct memorypool badsegments;
618 struct memorypool badtriangles;
619 struct memorypool splaynodes;
620
621 /* Variables that maintain the bad triangle queues. The tails are pointers */
622 /* to the pointers that have to be filled in to enqueue an item. */
623
624 struct badface *queuefront[64];
625 struct badface **queuetail[64];
626
627 REAL xmin, xmax, ymin, ymax; /* x and y bounds. */
628 REAL xminextreme; /* Nonexistent x value used as a flag in sweepline. */
629 int inpoints; /* Number of input points. */
630 int inelements; /* Number of input triangles. */
631 int insegments; /* Number of input segments. */
632 int holes; /* Number of input holes. */
633 int regions; /* Number of input regions. */
634 long edges; /* Number of output edges. */
635 int mesh_dim; /* Dimension (ought to be 2). */
636 int nextras; /* Number of attributes per point. */
637 int eextras; /* Number of attributes per triangle. */
638 long hullsize; /* Number of edges of convex hull. */
639 int triwords; /* Total words per triangle. */
640 int shwords; /* Total words per shell edge. */
641 int pointmarkindex; /* Index to find boundary marker of a point. */
642 int point2triindex; /* Index to find a triangle adjacent to a point. */
643 int highorderindex; /* Index to find extra nodes for high-order elements. */
644 int elemattribindex; /* Index to find attributes of a triangle. */
645 int areaboundindex; /* Index to find area bound of a triangle. */
646 int checksegments; /* Are there segments in the triangulation yet? */
647 int readnodefile; /* Has a .node file been read? */
648 long samples; /* Number of random samples for point location. */
649 unsigned long randomseed; /* Current random number seed. */
650
651 REAL splitter; /* Used to split REAL factors for exact multiplication. */
652 REAL epsilon; /* Floating-point machine epsilon. */
653 REAL resulterrbound;
654 REAL ccwerrboundA, ccwerrboundB, ccwerrboundC;
655 REAL iccerrboundA, iccerrboundB, iccerrboundC;
656
657 long incirclecount; /* Number of incircle tests performed. */
658 long counterclockcount; /* Number of counterclockwise tests performed. */
659 long hyperbolacount; /* Number of right-of-hyperbola tests performed. */
660 long circumcentercount; /* Number of circumcenter calculations performed. */
661 long circletopcount; /* Number of circle top calculations performed. */
662
663 /* Switches for the triangulator. */
664 /* poly: -p switch. refine: -r switch. */
665 /* quality: -q switch. */
666 /* minangle: minimum angle bound, specified after -q switch. */
667 /* goodangle: cosine squared of minangle. */
668 /* vararea: -a switch without number. */
669 /* fixedarea: -a switch with number. */
670 /* maxarea: maximum area bound, specified after -a switch. */
671 /* regionattrib: -A switch. convex: -c switch. */
672 /* firstnumber: inverse of -z switch. All items are numbered starting */
673 /* from firstnumber. */
674 /* edgesout: -e switch. voronoi: -v switch. */
675 /* neighbors: -n switch. geomview: -g switch. */
676 /* nobound: -B switch. nopolywritten: -P switch. */
677 /* nonodewritten: -N switch. noelewritten: -E switch. */
678 /* noiterationnum: -I switch. noholes: -O switch. */
679 /* noexact: -X switch. */
680 /* order: element order, specified after -o switch. */
681 /* nobisect: count of how often -Y switch is selected. */
682 /* steiner: maximum number of Steiner points, specified after -S switch. */
683 /* steinerleft: number of Steiner points not yet used. */
684 /* incremental: -i switch. sweepline: -F switch. */
685 /* dwyer: inverse of -l switch. */
686 /* splitseg: -s switch. */
687 /* docheck: -C switch. */
688 /* quiet: -Q switch. verbose: count of how often -V switch is selected. */
689 /* useshelles: -p, -r, -q, or -c switch; determines whether shell edges */
690 /* are used at all. */
691 /* */
692 /* Read the instructions to find out the meaning of these switches. */
693
694 int poly, refine, quality, vararea, fixedarea, regionattrib, convex;
695 int firstnumber;
696 int edgesout, voronoi, neighbors, geomview;
697 int nobound, nopolywritten, nonodewritten, noelewritten, noiterationnum;
698 int noholes, noexact;
699 int incremental, sweepline, dwyer;
700 int splitseg;
701 int docheck;
702 int quiet, verbose;
703 int useshelles;
704 int order;
705 int nobisect;
706 int steiner, steinerleft;
707 REAL minangle, goodangle;
708 REAL maxarea;
709
710 /* Variables for file names. */
711
712 #ifndef TRILIBRARY
713 char innodefilename[FILENAMESIZE];
714 char inelefilename[FILENAMESIZE];
715 char inpolyfilename[FILENAMESIZE];
716 char areafilename[FILENAMESIZE];
717 char outnodefilename[FILENAMESIZE];
718 char outelefilename[FILENAMESIZE];
719 char outpolyfilename[FILENAMESIZE];
720 char edgefilename[FILENAMESIZE];
721 char vnodefilename[FILENAMESIZE];
722 char vedgefilename[FILENAMESIZE];
723 char neighborfilename[FILENAMESIZE];
724 char offfilename[FILENAMESIZE];
725 #endif /* not TRILIBRARY */
726
727 /* Triangular bounding box points. */
728
729 point infpoint1, infpoint2, infpoint3;
730
731 /* Pointer to the `triangle' that occupies all of "outer space". */
732
733 triangle *dummytri;
734 triangle *dummytribase; /* Keep base address so we can free() it later. */
735
736 /* Pointer to the omnipresent shell edge. Referenced by any triangle or */
737 /* shell edge that isn't really connected to a shell edge at that */
738 /* location. */
739
740 shelle *dummysh;
741 shelle *dummyshbase; /* Keep base address so we can free() it later. */
742
743 /* Pointer to a recently visited triangle. Improves point location if */
744 /* proximate points are inserted sequentially. */
745
746 struct triedge recenttri;
747
748 /*****************************************************************************/
749 /* */
750 /* Mesh manipulation primitives. Each triangle contains three pointers to */
751 /* other triangles, with orientations. Each pointer points not to the */
752 /* first byte of a triangle, but to one of the first three bytes of a */
753 /* triangle. It is necessary to extract both the triangle itself and the */
754 /* orientation. To save memory, I keep both pieces of information in one */
755 /* pointer. To make this possible, I assume that all triangles are aligned */
756 /* to four-byte boundaries. The `decode' routine below decodes a pointer, */
757 /* extracting an orientation (in the range 0 to 2) and a pointer to the */
758 /* beginning of a triangle. The `encode' routine compresses a pointer to a */
759 /* triangle and an orientation into a single pointer. My assumptions that */
760 /* triangles are four-byte-aligned and that the `unsigned long' type is */
761 /* long enough to hold a pointer are two of the few kludges in this program.*/
762 /* */
763 /* Shell edges are manipulated similarly. A pointer to a shell edge */
764 /* carries both an address and an orientation in the range 0 to 1. */
765 /* */
766 /* The other primitives take an oriented triangle or oriented shell edge, */
767 /* and return an oriented triangle or oriented shell edge or point; or they */
768 /* change the connections in the data structure. */
769 /* */
770 /*****************************************************************************/
771
772 /********* Mesh manipulation primitives begin here *********/
773 /** **/
774 /** **/
775
776 /* Fast lookup arrays to speed some of the mesh manipulation primitives. */
777
778 int plus1mod3[3] = {1, 2, 0};
779 int minus1mod3[3] = {2, 0, 1};
780
781 /********* Primitives for triangles *********/
782 /* */
783 /* */
784
785 /* decode() converts a pointer to an oriented triangle. The orientation is */
786 /* extracted from the two least significant bits of the pointer. */
787
788 #define decode(ptr, triedge) \
789 (triedge).orient = (int) ((unsigned long) (ptr) & (unsigned long) 3l); \
790 (triedge).tri = (triangle *) \
791 ((unsigned long) (ptr) ^ (unsigned long) (triedge).orient)
792
793 /* encode() compresses an oriented triangle into a single pointer. It */
794 /* relies on the assumption that all triangles are aligned to four-byte */
795 /* boundaries, so the two least significant bits of (triedge).tri are zero.*/
796
797 #define encode(triedge) \
798 (triangle) ((unsigned long) (triedge).tri | (unsigned long) (triedge).orient)
799
800 /* The following edge manipulation primitives are all described by Guibas */
801 /* and Stolfi. However, they use an edge-based data structure, whereas I */
802 /* am using a triangle-based data structure. */
803
804 /* sym() finds the abutting triangle, on the same edge. Note that the */
805 /* edge direction is necessarily reversed, because triangle/edge handles */
806 /* are always directed counterclockwise around the triangle. */
807
808 #define sym(triedge1, triedge2) \
809 ptr = (triedge1).tri[(triedge1).orient]; \
810 decode(ptr, triedge2);
811
812 #define symself(triedge) \
813 ptr = (triedge).tri[(triedge).orient]; \
814 decode(ptr, triedge);
815
816 /* lnext() finds the next edge (counterclockwise) of a triangle. */
817
818 #define lnext(triedge1, triedge2) \
819 (triedge2).tri = (triedge1).tri; \
820 (triedge2).orient = plus1mod3[(triedge1).orient]
821
822 #define lnextself(triedge) \
823 (triedge).orient = plus1mod3[(triedge).orient]
824
825 /* lprev() finds the previous edge (clockwise) of a triangle. */
826
827 #define lprev(triedge1, triedge2) \
828 (triedge2).tri = (triedge1).tri; \
829 (triedge2).orient = minus1mod3[(triedge1).orient]
830
831 #define lprevself(triedge) \
832 (triedge).orient = minus1mod3[(triedge).orient]
833
834 /* onext() spins counterclockwise around a point; that is, it finds the next */
835 /* edge with the same origin in the counterclockwise direction. This edge */
836 /* will be part of a different triangle. */
837
838 #define onext(triedge1, triedge2) \
839 lprev(triedge1, triedge2); \
840 symself(triedge2);
841
842 #define onextself(triedge) \
843 lprevself(triedge); \
844 symself(triedge);
845
846 /* oprev() spins clockwise around a point; that is, it finds the next edge */
847 /* with the same origin in the clockwise direction. This edge will be */
848 /* part of a different triangle. */
849
850 #define oprev(triedge1, triedge2) \
851 sym(triedge1, triedge2); \
852 lnextself(triedge2);
853
854 #define oprevself(triedge) \
855 symself(triedge); \
856 lnextself(triedge);
857
858 /* dnext() spins counterclockwise around a point; that is, it finds the next */
859 /* edge with the same destination in the counterclockwise direction. This */
860 /* edge will be part of a different triangle. */
861
862 #define dnext(triedge1, triedge2) \
863 sym(triedge1, triedge2); \
864 lprevself(triedge2);
865
866 #define dnextself(triedge) \
867 symself(triedge); \
868 lprevself(triedge);
869
870 /* dprev() spins clockwise around a point; that is, it finds the next edge */
871 /* with the same destination in the clockwise direction. This edge will */
872 /* be part of a different triangle. */
873
874 #define dprev(triedge1, triedge2) \
875 lnext(triedge1, triedge2); \
876 symself(triedge2);
877
878 #define dprevself(triedge) \
879 lnextself(triedge); \
880 symself(triedge);
881
882 /* rnext() moves one edge counterclockwise about the adjacent triangle. */
883 /* (It's best understood by reading Guibas and Stolfi. It involves */
884 /* changing triangles twice.) */
885
886 #define rnext(triedge1, triedge2) \
887 sym(triedge1, triedge2); \
888 lnextself(triedge2); \
889 symself(triedge2);
890
891 #define rnextself(triedge) \
892 symself(triedge); \
893 lnextself(triedge); \
894 symself(triedge);
895
896 /* rnext() moves one edge clockwise about the adjacent triangle. */
897 /* (It's best understood by reading Guibas and Stolfi. It involves */
898 /* changing triangles twice.) */
899
900 #define rprev(triedge1, triedge2) \
901 sym(triedge1, triedge2); \
902 lprevself(triedge2); \
903 symself(triedge2);
904
905 #define rprevself(triedge) \
906 symself(triedge); \
907 lprevself(triedge); \
908 symself(triedge);
909
910 /* These primitives determine or set the origin, destination, or apex of a */
911 /* triangle. */
912
913 #define org(triedge, pointptr) \
914 pointptr = (point) (triedge).tri[plus1mod3[(triedge).orient] + 3]
915
916 #define dest(triedge, pointptr) \
917 pointptr = (point) (triedge).tri[minus1mod3[(triedge).orient] + 3]
918
919 #define apex(triedge, pointptr) \
920 pointptr = (point) (triedge).tri[(triedge).orient + 3]
921
922 #define setorg(triedge, pointptr) \
923 (triedge).tri[plus1mod3[(triedge).orient] + 3] = (triangle) pointptr
924
925 #define setdest(triedge, pointptr) \
926 (triedge).tri[minus1mod3[(triedge).orient] + 3] = (triangle) pointptr
927
928 #define setapex(triedge, pointptr) \
929 (triedge).tri[(triedge).orient + 3] = (triangle) pointptr
930
931 #define setvertices2null(triedge) \
932 (triedge).tri[3] = (triangle) NULL; \
933 (triedge).tri[4] = (triangle) NULL; \
934 (triedge).tri[5] = (triangle) NULL;
935
936 /* Bond two triangles together. */
937
938 #define bond(triedge1, triedge2) \
939 (triedge1).tri[(triedge1).orient] = encode(triedge2); \
940 (triedge2).tri[(triedge2).orient] = encode(triedge1)
941
942 /* Dissolve a bond (from one side). Note that the other triangle will still */
943 /* think it's connected to this triangle. Usually, however, the other */
944 /* triangle is being deleted entirely, or bonded to another triangle, so */
945 /* it doesn't matter. */
946
947 #define dissolve(triedge) \
948 (triedge).tri[(triedge).orient] = (triangle) dummytri
949
950 /* Copy a triangle/edge handle. */
951
952 #define triedgecopy(triedge1, triedge2) \
953 (triedge2).tri = (triedge1).tri; \
954 (triedge2).orient = (triedge1).orient
955
956 /* Test for equality of triangle/edge handles. */
957
958 #define triedgeequal(triedge1, triedge2) \
959 (((triedge1).tri == (triedge2).tri) && \
960 ((triedge1).orient == (triedge2).orient))
961
962 /* Primitives to infect or cure a triangle with the virus. These rely on */
963 /* the assumption that all shell edges are aligned to four-byte boundaries.*/
964
965 #define infect(triedge) \
966 (triedge).tri[6] = (triangle) \
967 ((unsigned long) (triedge).tri[6] | (unsigned long) 2l)
968
969 #define uninfect(triedge) \
970 (triedge).tri[6] = (triangle) \
971 ((unsigned long) (triedge).tri[6] & ~ (unsigned long) 2l)
972
973 /* Test a triangle for viral infection. */
974
975 #define infected(triedge) \
976 (((unsigned long) (triedge).tri[6] & (unsigned long) 2l) != 0)
977
978 /* Check or set a triangle's attributes. */
979
980 #define elemattribute(triedge, attnum) \
981 ((REAL *) (triedge).tri)[elemattribindex + (attnum)]
982
983 #define setelemattribute(triedge, attnum, value) \
984 ((REAL *) (triedge).tri)[elemattribindex + (attnum)] = value
985
986 /* Check or set a triangle's maximum area bound. */
987
988 #define areabound(triedge) ((REAL *) (triedge).tri)[areaboundindex]
989
990 #define setareabound(triedge, value) \
991 ((REAL *) (triedge).tri)[areaboundindex] = value
992
993 /********* Primitives for shell edges *********/
994 /* */
995 /* */
996
997 /* sdecode() converts a pointer to an oriented shell edge. The orientation */
998 /* is extracted from the least significant bit of the pointer. The two */
999 /* least significant bits (one for orientation, one for viral infection) */
1000 /* are masked out to produce the real pointer. */
1001
1002 #define sdecode(sptr, edge) \
1003 (edge).shorient = (int) ((unsigned long) (sptr) & (unsigned long) 1l); \
1004 (edge).sh = (shelle *) \
1005 ((unsigned long) (sptr) & ~ (unsigned long) 3l)
1006
1007 /* sencode() compresses an oriented shell edge into a single pointer. It */
1008 /* relies on the assumption that all shell edges are aligned to two-byte */
1009 /* boundaries, so the least significant bit of (edge).sh is zero. */
1010
1011 #define sencode(edge) \
1012 (shelle) ((unsigned long) (edge).sh | (unsigned long) (edge).shorient)
1013
1014 /* ssym() toggles the orientation of a shell edge. */
1015
1016 #define ssym(edge1, edge2) \
1017 (edge2).sh = (edge1).sh; \
1018 (edge2).shorient = 1 - (edge1).shorient
1019
1020 #define ssymself(edge) \
1021 (edge).shorient = 1 - (edge).shorient
1022
1023 /* spivot() finds the other shell edge (from the same segment) that shares */
1024 /* the same origin. */
1025
1026 #define spivot(edge1, edge2) \
1027 sptr = (edge1).sh[(edge1).shorient]; \
1028 sdecode(sptr, edge2)
1029
1030 #define spivotself(edge) \
1031 sptr = (edge).sh[(edge).shorient]; \
1032 sdecode(sptr, edge)
1033
1034 /* snext() finds the next shell edge (from the same segment) in sequence; */
1035 /* one whose origin is the input shell edge's destination. */
1036
1037 #define snext(edge1, edge2) \
1038 sptr = (edge1).sh[1 - (edge1).shorient]; \
1039 sdecode(sptr, edge2)
1040
1041 #define snextself(edge) \
1042 sptr = (edge).sh[1 - (edge).shorient]; \
1043 sdecode(sptr, edge)
1044
1045 /* These primitives determine or set the origin or destination of a shell */
1046 /* edge. */
1047
1048 #define sorg(edge, pointptr) \
1049 pointptr = (point) (edge).sh[2 + (edge).shorient]
1050
1051 #define sdest(edge, pointptr) \
1052 pointptr = (point) (edge).sh[3 - (edge).shorient]
1053
1054 #define setsorg(edge, pointptr) \
1055 (edge).sh[2 + (edge).shorient] = (shelle) pointptr
1056
1057 #define setsdest(edge, pointptr) \
1058 (edge).sh[3 - (edge).shorient] = (shelle) pointptr
1059
1060 /* These primitives read or set a shell marker. Shell markers are used to */
1061 /* hold user boundary information. */
1062
1063 #define mark(edge) (* (int *) ((edge).sh + 6))
1064
1065 #define setmark(edge, value) \
1066 * (int *) ((edge).sh + 6) = value
1067
1068 /* Bond two shell edges together. */
1069
1070 #define sbond(edge1, edge2) \
1071 (edge1).sh[(edge1).shorient] = sencode(edge2); \
1072 (edge2).sh[(edge2).shorient] = sencode(edge1)
1073
1074 /* Dissolve a shell edge bond (from one side). Note that the other shell */
1075 /* edge will still think it's connected to this shell edge. */
1076
1077 #define sdissolve(edge) \
1078 (edge).sh[(edge).shorient] = (shelle) dummysh
1079
1080 /* Copy a shell edge. */
1081
1082 #define shellecopy(edge1, edge2) \
1083 (edge2).sh = (edge1).sh; \
1084 (edge2).shorient = (edge1).shorient
1085
1086 /* Test for equality of shell edges. */
1087
1088 #define shelleequal(edge1, edge2) \
1089 (((edge1).sh == (edge2).sh) && \
1090 ((edge1).shorient == (edge2).shorient))
1091
1092 /********* Primitives for interacting triangles and shell edges *********/
1093 /* */
1094 /* */
1095
1096 /* tspivot() finds a shell edge abutting a triangle. */
1097
1098 #define tspivot(triedge, edge) \
1099 sptr = (shelle) (triedge).tri[6 + (triedge).orient]; \
1100 sdecode(sptr, edge)
1101
1102 /* stpivot() finds a triangle abutting a shell edge. It requires that the */
1103 /* variable `ptr' of type `triangle' be defined. */
1104
1105 #define stpivot(edge, triedge) \
1106 ptr = (triangle) (edge).sh[4 + (edge).shorient]; \
1107 decode(ptr, triedge)
1108
1109 /* Bond a triangle to a shell edge. */
1110
1111 #define tsbond(triedge, edge) \
1112 (triedge).tri[6 + (triedge).orient] = (triangle) sencode(edge); \
1113 (edge).sh[4 + (edge).shorient] = (shelle) encode(triedge)
1114
1115 /* Dissolve a bond (from the triangle side). */
1116
1117 #define tsdissolve(triedge) \
1118 (triedge).tri[6 + (triedge).orient] = (triangle) dummysh
1119
1120 /* Dissolve a bond (from the shell edge side). */
1121
1122 #define stdissolve(edge) \
1123 (edge).sh[4 + (edge).shorient] = (shelle) dummytri
1124
1125 /********* Primitives for points *********/
1126 /* */
1127 /* */
1128
1129 #define pointmark(pt) ((int *) (pt))[pointmarkindex]
1130
1131 #define setpointmark(pt, value) \
1132 ((int *) (pt))[pointmarkindex] = value
1133
1134 #define point2tri(pt) ((triangle *) (pt))[point2triindex]
1135
1136 #define setpoint2tri(pt, value) \
1137 ((triangle *) (pt))[point2triindex] = value
1138
1139 /** **/
1140 /** **/
1141 /********* Mesh manipulation primitives end here *********/
1142
1143 /********* User interaction routines begin here *********/
1144 /** **/
1145 /** **/
1146
1147 /*****************************************************************************/
1148 /* */
1149 /* syntax() Print list of command line switches. */
1150 /* */
1151 /*****************************************************************************/
1152
1153 #ifndef TRILIBRARY
1154
1155 void syntax()
1156 {
1157 #ifdef CDT_ONLY
1158 #ifdef REDUCED
1159 printf("triangle [-pAcevngBPNEIOXzo_lQVh] input_file\n");
1160 #else /* not REDUCED */
1161 printf("triangle [-pAcevngBPNEIOXzo_iFlCQVh] input_file\n");
1162 #endif /* not REDUCED */
1163 #else /* not CDT_ONLY */
1164 #ifdef REDUCED
1165 printf("triangle [-prq__a__AcevngBPNEIOXzo_YS__lQVh] input_file\n");
1166 #else /* not REDUCED */
1167 printf("triangle [-prq__a__AcevngBPNEIOXzo_YS__iFlsCQVh] input_file\n");
1168 #endif /* not REDUCED */
1169 #endif /* not CDT_ONLY */
1170
1171 printf(" -p Triangulates a Planar Straight Line Graph (.poly file).\n");
1172 #ifndef CDT_ONLY
1173 printf(" -r Refines a previously generated mesh.\n");
1174 printf(
1175 " -q Quality mesh generation. A minimum angle may be specified.\n");
1176 printf(" -a Applies a maximum triangle area constraint.\n");
1177 #endif /* not CDT_ONLY */
1178 printf(
1179 " -A Applies attributes to identify elements in certain regions.\n");
1180 printf(" -c Encloses the convex hull with segments.\n");
1181 printf(" -e Generates an edge list.\n");
1182 printf(" -v Generates a Voronoi diagram.\n");
1183 printf(" -n Generates a list of triangle neighbors.\n");
1184 printf(" -g Generates an .off file for Geomview.\n");
1185 printf(" -B Suppresses output of boundary information.\n");
1186 printf(" -P Suppresses output of .poly file.\n");
1187 printf(" -N Suppresses output of .node file.\n");
1188 printf(" -E Suppresses output of .ele file.\n");
1189 printf(" -I Suppresses mesh iteration numbers.\n");
1190 printf(" -O Ignores holes in .poly file.\n");
1191 printf(" -X Suppresses use of exact arithmetic.\n");
1192 printf(" -z Numbers all items starting from zero (rather than one).\n");
1193 printf(" -o2 Generates second-order subparametric elements.\n");
1194 #ifndef CDT_ONLY
1195 printf(" -Y Suppresses boundary segment splitting.\n");
1196 printf(" -S Specifies maximum number of added Steiner points.\n");
1197 #endif /* not CDT_ONLY */
1198 #ifndef REDUCED
1199 printf(" -i Uses incremental method, rather than divide-and-conquer.\n");
1200 printf(" -F Uses Fortune's sweepline algorithm, rather than d-and-c.\n");
1201 #endif /* not REDUCED */
1202 printf(" -l Uses vertical cuts only, rather than alternating cuts.\n");
1203 #ifndef REDUCED
1204 #ifndef CDT_ONLY
1205 printf(
1206 " -s Force segments into mesh by splitting (instead of using CDT).\n");
1207 #endif /* not CDT_ONLY */
1208 printf(" -C Check consistency of final mesh.\n");
1209 #endif /* not REDUCED */
1210 printf(" -Q Quiet: No terminal output except errors.\n");
1211 printf(" -V Verbose: Detailed information on what I'm doing.\n");
1212 printf(" -h Help: Detailed instructions for Triangle.\n");
1213 exit(0);
1214 }
1215
1216 #endif /* not TRILIBRARY */
1217
1218 /*****************************************************************************/
1219 /* */
1220 /* info() Print out complete instructions. */
1221 /* */
1222 /*****************************************************************************/
1223
1224 #ifndef TRILIBRARY
1225
1226 void info()
1227 {
1228 printf("Triangle\n");
1229 printf(
1230 "A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator.\n");
1231 printf("Version 1.3\n\n");
1232 printf(
1233 "Copyright 1996 Jonathan Richard Shewchuk (bugs/comments to jrs@cs.cmu.edu)\n"
1234 );
1235 printf("School of Computer Science / Carnegie Mellon University\n");
1236 printf("5000 Forbes Avenue / Pittsburgh, Pennsylvania 15213-3891\n");
1237 printf(
1238 "Created as part of the Archimedes project (tools for parallel FEM).\n");
1239 printf(
1240 "Supported in part by NSF Grant CMS-9318163 and an NSERC 1967 Scholarship.\n");
1241 printf("There is no warranty whatsoever. Use at your own risk.\n");
1242 #ifdef SINGLE
1243 printf("This executable is compiled for single precision arithmetic.\n\n\n");
1244 #else /* not SINGLE */
1245 printf("This executable is compiled for double precision arithmetic.\n\n\n");
1246 #endif /* not SINGLE */
1247 printf(
1248 "Triangle generates exact Delaunay triangulations, constrained Delaunay\n");
1249 printf(
1250 "triangulations, and quality conforming Delaunay triangulations. The latter\n"
1251 );
1252 printf(
1253 "can be generated with no small angles, and are thus suitable for finite\n");
1254 printf(
1255 "element analysis. If no command line switches are specified, your .node\n");
1256 printf(
1257 "input file will be read, and the Delaunay triangulation will be returned in\n"
1258 );
1259 printf(".node and .ele output files. The command syntax is:\n\n");
1260 #ifdef CDT_ONLY
1261 #ifdef REDUCED
1262 printf("triangle [-pAcevngBPNEIOXzo_lQVh] input_file\n\n");
1263 #else /* not REDUCED */
1264 printf("triangle [-pAcevngBPNEIOXzo_iFlCQVh] input_file\n\n");
1265 #endif /* not REDUCED */
1266 #else /* not CDT_ONLY */
1267 #ifdef REDUCED
1268 printf("triangle [-prq__a__AcevngBPNEIOXzo_YS__lQVh] input_file\n\n");
1269 #else /* not REDUCED */
1270 printf("triangle [-prq__a__AcevngBPNEIOXzo_YS__iFlsCQVh] input_file\n\n");
1271 #endif /* not REDUCED */
1272 #endif /* not CDT_ONLY */
1273 printf(
1274 "Underscores indicate that numbers may optionally follow certain switches;\n");
1275 printf(
1276 "do not leave any space between a switch and its numeric parameter.\n");
1277 printf(
1278 "input_file must be a file with extension .node, or extension .poly if the\n");
1279 printf(
1280 "-p switch is used. If -r is used, you must supply .node and .ele files,\n");
1281 printf(
1282 "and possibly a .poly file and .area file as well. The formats of these\n");
1283 printf("files are described below.\n\n");
1284 printf("Command Line Switches:\n\n");
1285 printf(
1286 " -p Reads a Planar Straight Line Graph (.poly file), which can specify\n"
1287 );
1288 printf(
1289 " points, segments, holes, and regional attributes and area\n");
1290 printf(
1291 " constraints. Will generate a constrained Delaunay triangulation\n");
1292 printf(
1293 " fitting the input; or, if -s, -q, or -a is used, a conforming\n");
1294 printf(
1295 " Delaunay triangulation. If -p is not used, Triangle reads a .node\n"
1296 );
1297 printf(" file by default.\n");
1298 printf(
1299 " -r Refines a previously generated mesh. The mesh is read from a .node\n"
1300 );
1301 printf(
1302 " file and an .ele file. If -p is also used, a .poly file is read\n");
1303 printf(
1304 " and used to constrain edges in the mesh. Further details on\n");
1305 printf(" refinement are given below.\n");
1306 printf(
1307 " -q Quality mesh generation by Jim Ruppert's Delaunay refinement\n");
1308 printf(
1309 " algorithm. Adds points to the mesh to ensure that no angles\n");
1310 printf(
1311 " smaller than 20 degrees occur. An alternative minimum angle may be\n"
1312 );
1313 printf(
1314 " specified after the `q'. If the minimum angle is 20.7 degrees or\n");
1315 printf(
1316 " smaller, the triangulation algorithm is theoretically guaranteed to\n"
1317 );
1318 printf(
1319 " terminate (assuming infinite precision arithmetic - Triangle may\n");
1320 printf(
1321 " fail to terminate if you run out of precision). In practice, the\n");
1322 printf(
1323 " algorithm often succeeds for minimum angles up to 33.8 degrees.\n");
1324 printf(
1325 " For highly refined meshes, however, it may be necessary to reduce\n");
1326 printf(
1327 " the minimum angle to well below 20 to avoid problems associated\n");
1328 printf(
1329 " with insufficient floating-point precision. The specified angle\n");
1330 printf(" may include a decimal point.\n");
1331 printf(
1332 " -a Imposes a maximum triangle area. If a number follows the `a', no\n");
1333 printf(
1334 " triangle will be generated whose area is larger than that number.\n");
1335 printf(
1336 " If no number is specified, an .area file (if -r is used) or .poly\n");
1337 printf(
1338 " file (if -r is not used) specifies a number of maximum area\n");
1339 printf(
1340 " constraints. An .area file contains a separate area constraint for\n"
1341 );
1342 printf(
1343 " each triangle, and is useful for refining a finite element mesh\n");
1344 printf(
1345 " based on a posteriori error estimates. A .poly file can optionally\n"
1346 );
1347 printf(
1348 " contain an area constraint for each segment-bounded region, thereby\n"
1349 );
1350 printf(
1351 " enforcing triangle densities in a first triangulation. You can\n");
1352 printf(
1353 " impose both a fixed area constraint and a varying area constraint\n");
1354 printf(
1355 " by invoking the -a switch twice, once with and once without a\n");
1356 printf(
1357 " number following. Each area specified may include a decimal point.\n"
1358 );
1359 printf(
1360 " -A Assigns an additional attribute to each triangle that identifies\n");
1361 printf(
1362 " what segment-bounded region each triangle belongs to. Attributes\n");
1363 printf(
1364 " are assigned to regions by the .poly file. If a region is not\n");
1365 printf(
1366 " explicitly marked by the .poly file, triangles in that region are\n");
1367 printf(
1368 " assigned an attribute of zero. The -A switch has an effect only\n");
1369 printf(" when the -p switch is used and the -r switch is not.\n");
1370 printf(
1371 " -c Creates segments on the convex hull of the triangulation. If you\n");
1372 printf(
1373 " are triangulating a point set, this switch causes a .poly file to\n");
1374 printf(
1375 " be written, containing all edges in the convex hull. (By default,\n"
1376 );
1377 printf(
1378 " a .poly file is written only if a .poly file is read.) If you are\n"
1379 );
1380 printf(
1381 " triangulating a PSLG, this switch specifies that the interior of\n");
1382 printf(
1383 " the convex hull of the PSLG should be triangulated. If you do not\n"
1384 );
1385 printf(
1386 " use this switch when triangulating a PSLG, it is assumed that you\n");
1387 printf(
1388 " have identified the region to be triangulated by surrounding it\n");
1389 printf(
1390 " with segments of the input PSLG. Beware: if you are not careful,\n"
1391 );
1392 printf(
1393 " this switch can cause the introduction of an extremely thin angle\n");
1394 printf(
1395 " between a PSLG segment and a convex hull segment, which can cause\n");
1396 printf(
1397 " overrefinement or failure if Triangle runs out of precision. If\n");
1398 printf(
1399 " you are refining a mesh, the -c switch works differently; it\n");
1400 printf(
1401 " generates the set of boundary edges of the mesh, rather than the\n");
1402 printf(" convex hull.\n");
1403 printf(
1404 " -e Outputs (to an .edge file) a list of edges of the triangulation.\n");
1405 printf(
1406 " -v Outputs the Voronoi diagram associated with the triangulation.\n");
1407 printf(" Does not attempt to detect degeneracies.\n");
1408 printf(
1409 " -n Outputs (to a .neigh file) a list of triangles neighboring each\n");
1410 printf(" triangle.\n");
1411 printf(
1412 " -g Outputs the mesh to an Object File Format (.off) file, suitable for\n"
1413 );
1414 printf(" viewing with the Geometry Center's Geomview package.\n");
1415 printf(
1416 " -B No boundary markers in the output .node, .poly, and .edge output\n");
1417 printf(
1418 " files. See the detailed discussion of boundary markers below.\n");
1419 printf(
1420 " -P No output .poly file. Saves disk space, but you lose the ability\n");
1421 printf(
1422 " to impose segment constraints on later refinements of the mesh.\n");
1423 printf(" -N No output .node file.\n");
1424 printf(" -E No output .ele file.\n");
1425 printf(
1426 " -I No iteration numbers. Suppresses the output of .node and .poly\n");
1427 printf(
1428 " files, so your input files won't be overwritten. (If your input is\n"
1429 );
1430 printf(
1431 " a .poly file only, a .node file will be written.) Cannot be used\n");
1432 printf(
1433 " with the -r switch, because that would overwrite your input .ele\n");
1434 printf(
1435 " file. Shouldn't be used with the -s, -q, or -a switch if you are\n");
1436 printf(
1437 " using a .node file for input, because no .node file will be\n");
1438 printf(" written, so there will be no record of any added points.\n");
1439 printf(" -O No holes. Ignores the holes in the .poly file.\n");
1440 printf(
1441 " -X No exact arithmetic. Normally, Triangle uses exact floating-point\n"
1442 );
1443 printf(
1444 " arithmetic for certain tests if it thinks the inexact tests are not\n"
1445 );
1446 printf(
1447 " accurate enough. Exact arithmetic ensures the robustness of the\n");
1448 printf(
1449 " triangulation algorithms, despite floating-point roundoff error.\n");
1450 printf(
1451 " Disabling exact arithmetic with the -X switch will cause a small\n");
1452 printf(
1453 " improvement in speed and create the possibility (albeit small) that\n"
1454 );
1455 printf(
1456 " Triangle will fail to produce a valid mesh. Not recommended.\n");
1457 printf(
1458 " -z Numbers all items starting from zero (rather than one). Note that\n"
1459 );
1460 printf(
1461 " this switch is normally overrided by the value used to number the\n");
1462 printf(
1463 " first point of the input .node or .poly file. However, this switch\n"
1464 );
1465 printf(" is useful when calling Triangle from another program.\n");
1466 printf(
1467 " -o2 Generates second-order subparametric elements with six nodes each.\n"
1468 );
1469 printf(
1470 " -Y No new points on the boundary. This switch is useful when the mesh\n"
1471 );
1472 printf(
1473 " boundary must be preserved so that it conforms to some adjacent\n");
1474 printf(
1475 " mesh. Be forewarned that you will probably sacrifice some of the\n");
1476 printf(
1477 " quality of the mesh; Triangle will try, but the resulting mesh may\n"
1478 );
1479 printf(
1480 " contain triangles of poor aspect ratio. Works well if all the\n");
1481 printf(
1482 " boundary points are closely spaced. Specify this switch twice\n");
1483 printf(
1484 " (`-YY') to prevent all segment splitting, including internal\n");
1485 printf(" boundaries.\n");
1486 printf(
1487 " -S Specifies the maximum number of Steiner points (points that are not\n"
1488 );
1489 printf(
1490 " in the input, but are added to meet the constraints of minimum\n");
1491 printf(
1492 " angle and maximum area). The default is to allow an unlimited\n");
1493 printf(
1494 " number. If you specify this switch with no number after it,\n");
1495 printf(
1496 " the limit is set to zero. Triangle always adds points at segment\n");
1497 printf(
1498 " intersections, even if it needs to use more points than the limit\n");
1499 printf(
1500 " you set. When Triangle inserts segments by splitting (-s), it\n");
1501 printf(
1502 " always adds enough points to ensure that all the segments appear in\n"
1503 );
1504 printf(
1505 " the triangulation, again ignoring the limit. Be forewarned that\n");
1506 printf(
1507 " the -S switch may result in a conforming triangulation that is not\n"
1508 );
1509 printf(
1510 " truly Delaunay, because Triangle may be forced to stop adding\n");
1511 printf(
1512 " points when the mesh is in a state where a segment is non-Delaunay\n"
1513 );
1514 printf(
1515 " and needs to be split. If so, Triangle will print a warning.\n");
1516 printf(
1517 " -i Uses an incremental rather than divide-and-conquer algorithm to\n");
1518 printf(
1519 " form a Delaunay triangulation. Try it if the divide-and-conquer\n");
1520 printf(" algorithm fails.\n");
1521 printf(
1522 " -F Uses Steven Fortune's sweepline algorithm to form a Delaunay\n");
1523 printf(
1524 " triangulation. Warning: does not use exact arithmetic for all\n");
1525 printf(" calculations. An exact result is not guaranteed.\n");
1526 printf(
1527 " -l Uses only vertical cuts in the divide-and-conquer algorithm. By\n");
1528 printf(
1529 " default, Triangle uses alternating vertical and horizontal cuts,\n");
1530 printf(
1531 " which usually improve the speed except with point sets that are\n");
1532 printf(
1533 " small or short and wide. This switch is primarily of theoretical\n");
1534 printf(" interest.\n");
1535 printf(
1536 " -s Specifies that segments should be forced into the triangulation by\n"
1537 );
1538 printf(
1539 " recursively splitting them at their midpoints, rather than by\n");
1540 printf(
1541 " generating a constrained Delaunay triangulation. Segment splitting\n"
1542 );
1543 printf(
1544 " is true to Ruppert's original algorithm, but can create needlessly\n"
1545 );
1546 printf(" small triangles near external small features.\n");
1547 printf(
1548 " -C Check the consistency of the final mesh. Uses exact arithmetic for\n"
1549 );
1550 printf(
1551 " checking, even if the -X switch is used. Useful if you suspect\n");
1552 printf(" Triangle is buggy.\n");
1553 printf(
1554 " -Q Quiet: Suppresses all explanation of what Triangle is doing, unless\n"
1555 );
1556 printf(" an error occurs.\n");
1557 printf(
1558 " -V Verbose: Gives detailed information about what Triangle is doing.\n");
1559 printf(
1560 " Add more `V's for increasing amount of detail. `-V' gives\n");
1561 printf(
1562 " information on algorithmic progress and more detailed statistics.\n");
1563 printf(
1564 " `-VV' gives point-by-point details, and will print so much that\n");
1565 printf(
1566 " Triangle will run much more slowly. `-VVV' gives information only\n"
1567 );
1568 printf(" a debugger could love.\n");
1569 printf(" -h Help: Displays these instructions.\n");
1570 printf("\n");
1571 printf("Definitions:\n");
1572 printf("\n");
1573 printf(
1574 " A Delaunay triangulation of a point set is a triangulation whose vertices\n"
1575 );
1576 printf(
1577 " are the point set, having the property that no point in the point set\n");
1578 printf(
1579 " falls in the interior of the circumcircle (circle that passes through all\n"
1580 );
1581 printf(" three vertices) of any triangle in the triangulation.\n\n");
1582 printf(
1583 " A Voronoi diagram of a point set is a subdivision of the plane into\n");
1584 printf(
1585 " polygonal regions (some of which may be infinite), where each region is\n");
1586 printf(
1587 " the set of points in the plane that are closer to some input point than\n");
1588 printf(
1589 " to any other input point. (The Voronoi diagram is the geometric dual of\n"
1590 );
1591 printf(" the Delaunay triangulation.)\n\n");
1592 printf(
1593 " A Planar Straight Line Graph (PSLG) is a collection of points and\n");
1594 printf(
1595 " segments. Segments are simply edges, whose endpoints are points in the\n");
1596 printf(
1597 " PSLG. The file format for PSLGs (.poly files) is described below.\n");
1598 printf("\n");
1599 printf(
1600 " A constrained Delaunay triangulation of a PSLG is similar to a Delaunay\n");
1601 printf(
1602 " triangulation, but each PSLG segment is present as a single edge in the\n");
1603 printf(
1604 " triangulation. (A constrained Delaunay triangulation is not truly a\n");
1605 printf(" Delaunay triangulation.)\n\n");
1606 printf(
1607 " A conforming Delaunay triangulation of a PSLG is a true Delaunay\n");
1608 printf(
1609 " triangulation in which each PSLG segment may have been subdivided into\n");
1610 printf(
1611 " several edges by the insertion of additional points. These inserted\n");
1612 printf(
1613 " points are necessary to allow the segments to exist in the mesh while\n");
1614 printf(" maintaining the Delaunay property.\n\n");
1615 printf("File Formats:\n\n");
1616 printf(
1617 " All files may contain comments prefixed by the character '#'. Points,\n");
1618 printf(
1619 " triangles, edges, holes, and maximum area constraints must be numbered\n");
1620 printf(
1621 " consecutively, starting from either 1 or 0. Whichever you choose, all\n");
1622 printf(
1623 " input files must be consistent; if the nodes are numbered from 1, so must\n"
1624 );
1625 printf(
1626 " be all other objects. Triangle automatically detects your choice while\n");
1627 printf(
1628 " reading the .node (or .poly) file. (When calling Triangle from another\n");
1629 printf(
1630 " program, use the -z switch if you wish to number objects from zero.)\n");
1631 printf(" Examples of these file formats are given below.\n\n");
1632 printf(" .node files:\n");
1633 printf(
1634 " First line: <# of points> <dimension (must be 2)> <# of attributes>\n");
1635 printf(
1636 " <# of boundary markers (0 or 1)>\n"
1637 );
1638 printf(
1639 " Remaining lines: <point #> <x> <y> [attributes] [boundary marker]\n");
1640 printf("\n");
1641 printf(
1642 " The attributes, which are typically floating-point values of physical\n");
1643 printf(
1644 " quantities (such as mass or conductivity) associated with the nodes of\n"
1645 );
1646 printf(
1647 " a finite element mesh, are copied unchanged to the output mesh. If -s,\n"
1648 );
1649 printf(
1650 " -q, or -a is selected, each new Steiner point added to the mesh will\n");
1651 printf(" have attributes assigned to it by linear interpolation.\n\n");
1652 printf(
1653 " If the fourth entry of the first line is `1', the last column of the\n");
1654 printf(
1655 " remainder of the file is assumed to contain boundary markers. Boundary\n"
1656 );
1657 printf(
1658 " markers are used to identify boundary points and points resting on PSLG\n"
1659 );
1660 printf(
1661 " segments; a complete description appears in a section below. The .node\n"
1662 );
1663 printf(
1664 " file produced by Triangle will contain boundary markers in the last\n");
1665 printf(" column unless they are suppressed by the -B switch.\n\n");
1666 printf(" .ele files:\n");
1667 printf(
1668 " First line: <# of triangles> <points per triangle> <# of attributes>\n");
1669 printf(
1670 " Remaining lines: <triangle #> <point> <point> <point> ... [attributes]\n"
1671 );
1672 printf("\n");
1673 printf(
1674 " Points are indices into the corresponding .node file. The first three\n"
1675 );
1676 printf(
1677 " points are the corners, and are listed in counterclockwise order around\n"
1678 );
1679 printf(
1680 " each triangle. (The remaining points, if any, depend on the type of\n");
1681 printf(
1682 " finite element used.) The attributes are just like those of .node\n");
1683 printf(
1684 " files. Because there is no simple mapping from input to output\n");
1685 printf(
1686 " triangles, an attempt is made to interpolate attributes, which may\n");
1687 printf(
1688 " result in a good deal of diffusion of attributes among nearby triangles\n"
1689 );
1690 printf(
1691 " as the triangulation is refined. Diffusion does not occur across\n");
1692 printf(
1693 " segments, so attributes used to identify segment-bounded regions remain\n"
1694 );
1695 printf(
1696 " intact. In output .ele files, all triangles have three points each\n");
1697 printf(
1698 " unless the -o2 switch is used, in which case they have six, and the\n");
1699 printf(
1700 " fourth, fifth, and sixth points lie on the midpoints of the edges\n");
1701 printf(" opposite the first, second, and third corners.\n\n");
1702 printf(" .poly files:\n");
1703 printf(
1704 " First line: <# of points> <dimension (must be 2)> <# of attributes>\n");
1705 printf(
1706 " <# of boundary markers (0 or 1)>\n"
1707 );
1708 printf(
1709 " Following lines: <point #> <x> <y> [attributes] [boundary marker]\n");
1710 printf(" One line: <# of segments> <# of boundary markers (0 or 1)>\n");
1711 printf(
1712 " Following lines: <segment #> <endpoint> <endpoint> [boundary marker]\n");
1713 printf(" One line: <# of holes>\n");
1714 printf(" Following lines: <hole #> <x> <y>\n");
1715 printf(
1716 " Optional line: <# of regional attributes and/or area constraints>\n");
1717 printf(
1718 " Optional following lines: <constraint #> <x> <y> <attrib> <max area>\n");
1719 printf("\n");
1720 printf(
1721 " A .poly file represents a PSLG, as well as some additional information.\n"
1722 );
1723 printf(
1724 " The first section lists all the points, and is identical to the format\n"
1725 );
1726 printf(
1727 " of .node files. <# of points> may be set to zero to indicate that the\n"
1728 );
1729 printf(
1730 " points are listed in a separate .node file; .poly files produced by\n");
1731 printf(
1732 " Triangle always have this format. This has the advantage that a point\n"
1733 );
1734 printf(
1735 " set may easily be triangulated with or without segments. (The same\n");
1736 printf(
1737 " effect can be achieved, albeit using more disk space, by making a copy\n"
1738 );
1739 printf(
1740 " of the .poly file with the extension .node; all sections of the file\n");
1741 printf(" but the first are ignored.)\n\n");
1742 printf(
1743 " The second section lists the segments. Segments are edges whose\n");
1744 printf(
1745 " presence in the triangulation is enforced. Each segment is specified\n");
1746 printf(
1747 " by listing the indices of its two endpoints. This means that you must\n"
1748 );
1749 printf(
1750 " include its endpoints in the point list. If -s, -q, and -a are not\n");
1751 printf(
1752 " selected, Triangle will produce a constrained Delaunay triangulation,\n");
1753 printf(
1754 " in which each segment appears as a single edge in the triangulation.\n");
1755 printf(
1756 " If -q or -a is selected, Triangle will produce a conforming Delaunay\n");
1757 printf(
1758 " triangulation, in which segments may be subdivided into smaller edges.\n"
1759 );
1760 printf(" Each segment, like each point, may have a boundary marker.\n\n");
1761 printf(
1762 " The third section lists holes (and concavities, if -c is selected) in\n");
1763 printf(
1764 " the triangulation. Holes are specified by identifying a point inside\n");
1765 printf(
1766 " each hole. After the triangulation is formed, Triangle creates holes\n");
1767 printf(
1768 " by eating triangles, spreading out from each hole point until its\n");
1769 printf(
1770 " progress is blocked by PSLG segments; you must be careful to enclose\n");
1771 printf(
1772 " each hole in segments, or your whole triangulation may be eaten away.\n");
1773 printf(
1774 " If the two triangles abutting a segment are eaten, the segment itself\n");
1775 printf(
1776 " is also eaten. Do not place a hole directly on a segment; if you do,\n");
1777 printf(" Triangle will choose one side of the segment arbitrarily.\n\n");
1778 printf(
1779 " The optional fourth section lists regional attributes (to be assigned\n");
1780 printf(
1781 " to all triangles in a region) and regional constraints on the maximum\n");
1782 printf(
1783 " triangle area. Triangle will read this section only if the -A switch\n");
1784 printf(
1785 " is used or the -a switch is used without a number following it, and the\n"
1786 );
1787 printf(
1788 " -r switch is not used. Regional attributes and area constraints are\n");
1789 printf(
1790 " propagated in the same manner as holes; you specify a point for each\n");
1791 printf(
1792 " attribute and/or constraint, and the attribute and/or constraint will\n");
1793 printf(
1794 " affect the whole region (bounded by segments) containing the point. If\n"
1795 );
1796 printf(
1797 " two values are written on a line after the x and y coordinate, the\n");
1798 printf(
1799 " former is assumed to be a regional attribute (but will only be applied\n"
1800 );
1801 printf(
1802 " if the -A switch is selected), and the latter is assumed to be a\n");
1803 printf(
1804 " regional area constraint (but will only be applied if the -a switch is\n"
1805 );
1806 printf(
1807 " selected). You may also specify just one value after the coordinates,\n"
1808 );
1809 printf(
1810 " which can serve as both an attribute and an area constraint, depending\n"
1811 );
1812 printf(
1813 " on the choice of switches. If you are using the -A and -a switches\n");
1814 printf(
1815 " simultaneously and wish to assign an attribute to some region without\n");
1816 printf(" imposing an area constraint, use a negative maximum area.\n\n");
1817 printf(
1818 " When a triangulation is created from a .poly file, you must either\n");
1819 printf(
1820 " enclose the entire region to be triangulated in PSLG segments, or\n");
1821 printf(
1822 " use the -c switch, which encloses the convex hull of the input point\n");
1823 printf(
1824 " set. If you do not use the -c switch, Triangle will eat all triangles\n"
1825 );
1826 printf(
1827 " on the outer boundary that are not protected by segments; if you are\n");
1828 printf(
1829 " not careful, your whole triangulation may be eaten away. If you do\n");
1830 printf(
1831 " use the -c switch, you can still produce concavities by appropriate\n");
1832 printf(" placement of holes just inside the convex hull.\n\n");
1833 printf(
1834 " An ideal PSLG has no intersecting segments, nor any points that lie\n");
1835 printf(
1836 " upon segments (except, of course, the endpoints of each segment.) You\n"
1837 );
1838 printf(
1839 " aren't required to make your .poly files ideal, but you should be aware\n"
1840 );
1841 printf(
1842 " of what can go wrong. Segment intersections are relatively safe -\n");
1843 printf(
1844 " Triangle will calculate the intersection points for you and add them to\n"
1845 );
1846 printf(
1847 " the triangulation - as long as your machine's floating-point precision\n"
1848 );
1849 printf(
1850 " doesn't become a problem. You are tempting the fates if you have three\n"
1851 );
1852 printf(
1853 " segments that cross at the same location, and expect Triangle to figure\n"
1854 );
1855 printf(
1856 " out where the intersection point is. Thanks to floating-point roundoff\n"
1857 );
1858 printf(
1859 " error, Triangle will probably decide that the three segments intersect\n"
1860 );
1861 printf(
1862 " at three different points, and you will find a minuscule triangle in\n");
1863 printf(
1864 " your output - unless Triangle tries to refine the tiny triangle, uses\n");
1865 printf(
1866 " up the last bit of machine precision, and fails to terminate at all.\n");
1867 printf(
1868 " You're better off putting the intersection point in the input files,\n");
1869 printf(
1870 " and manually breaking up each segment into two. Similarly, if you\n");
1871 printf(
1872 " place a point at the middle of a segment, and hope that Triangle will\n");
1873 printf(
1874 " break up the segment at that point, you might get lucky. On the other\n"
1875 );
1876 printf(
1877 " hand, Triangle might decide that the point doesn't lie precisely on the\n"
1878 );
1879 printf(
1880 " line, and you'll have a needle-sharp triangle in your output - or a lot\n"
1881 );
1882 printf(" of tiny triangles if you're generating a quality mesh.\n\n");
1883 printf(
1884 " When Triangle reads a .poly file, it also writes a .poly file, which\n");
1885 printf(
1886 " includes all edges that are part of input segments. If the -c switch\n");
1887 printf(
1888 " is used, the output .poly file will also include all of the edges on\n");
1889 printf(
1890 " the convex hull. Hence, the output .poly file is useful for finding\n");
1891 printf(
1892 " edges associated with input segments and setting boundary conditions in\n"
1893 );
1894 printf(
1895 " finite element simulations. More importantly, you will need it if you\n"
1896 );
1897 printf(
1898 " plan to refine the output mesh, and don't want segments to be missing\n");
1899 printf(" in later triangulations.\n\n");
1900 printf(" .area files:\n");
1901 printf(" First line: <# of triangles>\n");
1902 printf(" Following lines: <triangle #> <maximum area>\n\n");
1903 printf(
1904 " An .area file associates with each triangle a maximum area that is used\n"
1905 );
1906 printf(
1907 " for mesh refinement. As with other file formats, every triangle must\n");
1908 printf(
1909 " be represented, and they must be numbered consecutively. A triangle\n");
1910 printf(
1911 " may be left unconstrained by assigning it a negative maximum area.\n");
1912 printf("\n");
1913 printf(" .edge files:\n");
1914 printf(" First line: <# of edges> <# of boundary markers (0 or 1)>\n");
1915 printf(
1916 " Following lines: <edge #> <endpoint> <endpoint> [boundary marker]\n");
1917 printf("\n");
1918 printf(
1919 " Endpoints are indices into the corresponding .node file. Triangle can\n"
1920 );
1921 printf(
1922 " produce .edge files (use the -e switch), but cannot read them. The\n");
1923 printf(
1924 " optional column of boundary markers is suppressed by the -B switch.\n");
1925 printf("\n");
1926 printf(
1927 " In Voronoi diagrams, one also finds a special kind of edge that is an\n");
1928 printf(
1929 " infinite ray with only one endpoint. For these edges, a different\n");
1930 printf(" format is used:\n\n");
1931 printf(" <edge #> <endpoint> -1 <direction x> <direction y>\n\n");
1932 printf(
1933 " The `direction' is a floating-point vector that indicates the direction\n"
1934 );
1935 printf(" of the infinite ray.\n\n");
1936 printf(" .neigh files:\n");
1937 printf(
1938 " First line: <# of triangles> <# of neighbors per triangle (always 3)>\n"
1939 );
1940 printf(
1941 " Following lines: <triangle #> <neighbor> <neighbor> <neighbor>\n");
1942 printf("\n");
1943 printf(
1944 " Neighbors are indices into the corresponding .ele file. An index of -1\n"
1945 );
1946 printf(
1947 " indicates a mesh boundary, and therefore no neighbor. Triangle can\n");
1948 printf(
1949 " produce .neigh files (use the -n switch), but cannot read them.\n");
1950 printf("\n");
1951 printf(
1952 " The first neighbor of triangle i is opposite the first corner of\n");
1953 printf(" triangle i, and so on.\n\n");
1954 printf("Boundary Markers:\n\n");
1955 printf(
1956 " Boundary markers are tags used mainly to identify which output points and\n"
1957 );
1958 printf(
1959 " edges are associated with which PSLG segment, and to identify which\n");
1960 printf(
1961 " points and edges occur on a boundary of the triangulation. A common use\n"
1962 );
1963 printf(
1964 " is to determine where boundary conditions should be applied to a finite\n");
1965 printf(
1966 " element mesh. You can prevent boundary markers from being written into\n");
1967 printf(" files produced by Triangle by using the -B switch.\n\n");
1968 printf(
1969 " The boundary marker associated with each segment in an output .poly file\n"
1970 );
1971 printf(" or edge in an output .edge file is chosen as follows:\n");
1972 printf(
1973 " - If an output edge is part or all of a PSLG segment with a nonzero\n");
1974 printf(
1975 " boundary marker, then the edge is assigned the same marker.\n");
1976 printf(
1977 " - Otherwise, if the edge occurs on a boundary of the triangulation\n");
1978 printf(
1979 " (including boundaries of holes), then the edge is assigned the marker\n"
1980 );
1981 printf(" one (1).\n");
1982 printf(" - Otherwise, the edge is assigned the marker zero (0).\n");
1983 printf(
1984 " The boundary marker associated with each point in an output .node file is\n"
1985 );
1986 printf(" chosen as follows:\n");
1987 printf(
1988 " - If a point is assigned a nonzero boundary marker in the input file,\n");
1989 printf(
1990 " then it is assigned the same marker in the output .node file.\n");
1991 printf(
1992 " - Otherwise, if the point lies on a PSLG segment (including the\n");
1993 printf(
1994 " segment's endpoints) with a nonzero boundary marker, then the point\n");
1995 printf(
1996 " is assigned the same marker. If the point lies on several such\n");
1997 printf(" segments, one of the markers is chosen arbitrarily.\n");
1998 printf(
1999 " - Otherwise, if the point occurs on a boundary of the triangulation,\n");
2000 printf(" then the point is assigned the marker one (1).\n");
2001 printf(" - Otherwise, the point is assigned the marker zero (0).\n");
2002 printf("\n");
2003 printf(
2004 " If you want Triangle to determine for you which points and edges are on\n");
2005 printf(
2006 " the boundary, assign them the boundary marker zero (or use no markers at\n"
2007 );
2008 printf(
2009 " all) in your input files. Alternatively, you can mark some of them and\n");
2010 printf(" leave others marked zero, allowing Triangle to label them.\n\n");
2011 printf("Triangulation Iteration Numbers:\n\n");
2012 printf(
2013 " Because Triangle can read and refine its own triangulations, input\n");
2014 printf(
2015 " and output files have iteration numbers. For instance, Triangle might\n");
2016 printf(
2017 " read the files mesh.3.node, mesh.3.ele, and mesh.3.poly, refine the\n");
2018 printf(
2019 " triangulation, and output the files mesh.4.node, mesh.4.ele, and\n");
2020 printf(" mesh.4.poly. Files with no iteration number are treated as if\n");
2021 printf(
2022 " their iteration number is zero; hence, Triangle might read the file\n");
2023 printf(
2024 " points.node, triangulate it, and produce the files points.1.node and\n");
2025 printf(" points.1.ele.\n\n");
2026 printf(
2027 " Iteration numbers allow you to create a sequence of successively finer\n");
2028 printf(
2029 " meshes suitable for multigrid methods. They also allow you to produce a\n"
2030 );
2031 printf(
2032 " sequence of meshes using error estimate-driven mesh refinement.\n");
2033 printf("\n");
2034 printf(
2035 " If you're not using refinement or quality meshing, and you don't like\n");
2036 printf(
2037 " iteration numbers, use the -I switch to disable them. This switch will\n");
2038 printf(
2039 " also disable output of .node and .poly files to prevent your input files\n"
2040 );
2041 printf(
2042 " from being overwritten. (If the input is a .poly file that contains its\n"
2043 );
2044 printf(" own points, a .node file will be written.)\n\n");
2045 printf("Examples of How to Use Triangle:\n\n");
2046 printf(
2047 " `triangle dots' will read points from dots.node, and write their Delaunay\n"
2048 );
2049 printf(
2050 " triangulation to dots.1.node and dots.1.ele. (dots.1.node will be\n");
2051 printf(
2052 " identical to dots.node.) `triangle -I dots' writes the triangulation to\n"
2053 );
2054 printf(
2055 " dots.ele instead. (No additional .node file is needed, so none is\n");
2056 printf(" written.)\n\n");
2057 printf(
2058 " `triangle -pe object.1' will read a PSLG from object.1.poly (and possibly\n"
2059 );
2060 printf(
2061 " object.1.node, if the points are omitted from object.1.poly) and write\n");
2062 printf(" their constrained Delaunay triangulation to object.2.node and\n");
2063 printf(
2064 " object.2.ele. The segments will be copied to object.2.poly, and all\n");
2065 printf(" edges will be written to object.2.edge.\n\n");
2066 printf(
2067 " `triangle -pq31.5a.1 object' will read a PSLG from object.poly (and\n");
2068 printf(
2069 " possibly object.node), generate a mesh whose angles are all greater than\n"
2070 );
2071 printf(
2072 " 31.5 degrees and whose triangles all have area smaller than 0.1, and\n");
2073 printf(
2074 " write the mesh to object.1.node and object.1.ele. Each segment may have\n"
2075 );
2076 printf(
2077 " been broken up into multiple edges; the resulting constrained edges are\n");
2078 printf(" written to object.1.poly.\n\n");
2079 printf(
2080 " Here is a sample file `box.poly' describing a square with a square hole:\n"
2081 );
2082 printf("\n");
2083 printf(
2084 " # A box with eight points in 2D, no attributes, one boundary marker.\n");
2085 printf(" 8 2 0 1\n");
2086 printf(" # Outer box has these vertices:\n");
2087 printf(" 1 0 0 0\n");
2088 printf(" 2 0 3 0\n");
2089 printf(" 3 3 0 0\n");
2090 printf(" 4 3 3 33 # A special marker for this point.\n");
2091 printf(" # Inner square has these vertices:\n");
2092 printf(" 5 1 1 0\n");
2093 printf(" 6 1 2 0\n");
2094 printf(" 7 2 1 0\n");
2095 printf(" 8 2 2 0\n");
2096 printf(" # Five segments with boundary markers.\n");
2097 printf(" 5 1\n");
2098 printf(" 1 1 2 5 # Left side of outer box.\n");
2099 printf(" 2 5 7 0 # Segments 2 through 5 enclose the hole.\n");
2100 printf(" 3 7 8 0\n");
2101 printf(" 4 8 6 10\n");
2102 printf(" 5 6 5 0\n");
2103 printf(" # One hole in the middle of the inner square.\n");
2104 printf(" 1\n");
2105 printf(" 1 1.5 1.5\n\n");
2106 printf(
2107 " Note that some segments are missing from the outer square, so one must\n");
2108 printf(
2109 " use the `-c' switch. After `triangle -pqc box.poly', here is the output\n"
2110 );
2111 printf(
2112 " file `box.1.node', with twelve points. The last four points were added\n");
2113 printf(
2114 " to meet the angle constraint. Points 1, 2, and 9 have markers from\n");
2115 printf(
2116 " segment 1. Points 6 and 8 have markers from segment 4. All the other\n");
2117 printf(
2118 " points but 4 have been marked to indicate that they lie on a boundary.\n");
2119 printf("\n");
2120 printf(" 12 2 0 1\n");
2121 printf(" 1 0 0 5\n");
2122 printf(" 2 0 3 5\n");
2123 printf(" 3 3 0 1\n");
2124 printf(" 4 3 3 33\n");
2125 printf(" 5 1 1 1\n");
2126 printf(" 6 1 2 10\n");
2127 printf(" 7 2 1 1\n");
2128 printf(" 8 2 2 10\n");
2129 printf(" 9 0 1.5 5\n");
2130 printf(" 10 1.5 0 1\n");
2131 printf(" 11 3 1.5 1\n");
2132 printf(" 12 1.5 3 1\n");
2133 printf(" # Generated by triangle -pqc box.poly\n\n");
2134 printf(" Here is the output file `box.1.ele', with twelve triangles.\n\n");
2135 printf(" 12 3 0\n");
2136 printf(" 1 5 6 9\n");
2137 printf(" 2 10 3 7\n");
2138 printf(" 3 6 8 12\n");
2139 printf(" 4 9 1 5\n");
2140 printf(" 5 6 2 9\n");
2141 printf(" 6 7 3 11\n");
2142 printf(" 7 11 4 8\n");
2143 printf(" 8 7 5 10\n");
2144 printf(" 9 12 2 6\n");
2145 printf(" 10 8 7 11\n");
2146 printf(" 11 5 1 10\n");
2147 printf(" 12 8 4 12\n");
2148 printf(" # Generated by triangle -pqc box.poly\n\n");
2149 printf(
2150 " Here is the output file `box.1.poly'. Note that segments have been added\n"
2151 );
2152 printf(
2153 " to represent the convex hull, and some segments have been split by newly\n"
2154 );
2155 printf(
2156 " added points. Note also that <# of points> is set to zero to indicate\n");
2157 printf(" that the points should be read from the .node file.\n\n");
2158 printf(" 0 2 0 1\n");
2159 printf(" 12 1\n");
2160 printf(" 1 1 9 5\n");
2161 printf(" 2 5 7 1\n");
2162 printf(" 3 8 7 1\n");
2163 printf(" 4 6 8 10\n");
2164 printf(" 5 5 6 1\n");
2165 printf(" 6 3 10 1\n");
2166 printf(" 7 4 11 1\n");
2167 printf(" 8 2 12 1\n");
2168 printf(" 9 9 2 5\n");
2169 printf(" 10 10 1 1\n");
2170 printf(" 11 11 3 1\n");
2171 printf(" 12 12 4 1\n");
2172 printf(" 1\n");
2173 printf(" 1 1.5 1.5\n");
2174 printf(" # Generated by triangle -pqc box.poly\n\n");
2175 printf("Refinement and Area Constraints:\n\n");
2176 printf(
2177 " The -r switch causes a mesh (.node and .ele files) to be read and\n");
2178 printf(
2179 " refined. If the -p switch is also used, a .poly file is read and used to\n"
2180 );
2181 printf(
2182 " specify edges that are constrained and cannot be eliminated (although\n");
2183 printf(
2184 " they can be divided into smaller edges) by the refinement process.\n");
2185 printf("\n");
2186 printf(
2187 " When you refine a mesh, you generally want to impose tighter quality\n");
2188 printf(
2189 " constraints. One way to accomplish this is to use -q with a larger\n");
2190 printf(
2191 " angle, or -a followed by a smaller area than you used to generate the\n");
2192 printf(
2193 " mesh you are refining. Another way to do this is to create an .area\n");
2194 printf(
2195 " file, which specifies a maximum area for each triangle, and use the -a\n");
2196 printf(
2197 " switch (without a number following). Each triangle's area constraint is\n"
2198 );
2199 printf(
2200 " applied to that triangle. Area constraints tend to diffuse as the mesh\n");
2201 printf(
2202 " is refined, so if there are large variations in area constraint between\n");
2203 printf(" adjacent triangles, you may not get the results you want.\n\n");
2204 printf(
2205 " If you are refining a mesh composed of linear (three-node) elements, the\n"
2206 );
2207 printf(
2208 " output mesh will contain all the nodes present in the input mesh, in the\n"
2209 );
2210 printf(
2211 " same order, with new nodes added at the end of the .node file. However,\n"
2212 );
2213 printf(
2214 " there is no guarantee that each output element is contained in a single\n");
2215 printf(
2216 " input element. Often, output elements will overlap two input elements,\n");
2217 printf(
2218 " and input edges are not present in the output mesh. Hence, a sequence of\n"
2219 );
2220 printf(
2221 " refined meshes will form a hierarchy of nodes, but not a hierarchy of\n");
2222 printf(
2223 " elements. If you a refining a mesh of higher-order elements, the\n");
2224 printf(
2225 " hierarchical property applies only to the nodes at the corners of an\n");
2226 printf(" element; other nodes may not be present in the refined mesh.\n\n");
2227 printf(
2228 " It is important to understand that maximum area constraints in .poly\n");
2229 printf(
2230 " files are handled differently from those in .area files. A maximum area\n"
2231 );
2232 printf(
2233 " in a .poly file applies to the whole (segment-bounded) region in which a\n"
2234 );
2235 printf(
2236 " point falls, whereas a maximum area in an .area file applies to only one\n"
2237 );
2238 printf(
2239 " triangle. Area constraints in .poly files are used only when a mesh is\n");
2240 printf(
2241 " first generated, whereas area constraints in .area files are used only to\n"
2242 );
2243 printf(
2244 " refine an existing mesh, and are typically based on a posteriori error\n");
2245 printf(
2246 " estimates resulting from a finite element simulation on that mesh.\n");
2247 printf("\n");
2248 printf(
2249 " `triangle -rq25 object.1' will read object.1.node and object.1.ele, then\n"
2250 );
2251 printf(
2252 " refine the triangulation to enforce a 25 degree minimum angle, and then\n");
2253 printf(
2254 " write the refined triangulation to object.2.node and object.2.ele.\n");
2255 printf("\n");
2256 printf(
2257 " `triangle -rpaa6.2 z.3' will read z.3.node, z.3.ele, z.3.poly, and\n");
2258 printf(
2259 " z.3.area. After reconstructing the mesh and its segments, Triangle will\n"
2260 );
2261 printf(
2262 " refine the mesh so that no triangle has area greater than 6.2, and\n");
2263 printf(
2264 " furthermore the triangles satisfy the maximum area constraints in\n");
2265 printf(
2266 " z.3.area. The output is written to z.4.node, z.4.ele, and z.4.poly.\n");
2267 printf("\n");
2268 printf(
2269 " The sequence `triangle -qa1 x', `triangle -rqa.3 x.1', `triangle -rqa.1\n");
2270 printf(
2271 " x.2' creates a sequence of successively finer meshes x.1, x.2, and x.3,\n");
2272 printf(" suitable for multigrid.\n\n");
2273 printf("Convex Hulls and Mesh Boundaries:\n\n");
2274 printf(
2275 " If the input is a point set (rather than a PSLG), Triangle produces its\n");
2276 printf(
2277 " convex hull as a by-product in the output .poly file if you use the -c\n");
2278 printf(
2279 " switch. There are faster algorithms for finding a two-dimensional convex\n"
2280 );
2281 printf(
2282 " hull than triangulation, of course, but this one comes for free. If the\n"
2283 );
2284 printf(
2285 " input is an unconstrained mesh (you are using the -r switch but not the\n");
2286 printf(
2287 " -p switch), Triangle produces a list of its boundary edges (including\n");
2288 printf(" hole boundaries) as a by-product if you use the -c switch.\n\n");
2289 printf("Voronoi Diagrams:\n\n");
2290 printf(
2291 " The -v switch produces a Voronoi diagram, in files suffixed .v.node and\n");
2292 printf(
2293 " .v.edge. For example, `triangle -v points' will read points.node,\n");
2294 printf(
2295 " produce its Delaunay triangulation in points.1.node and points.1.ele,\n");
2296 printf(
2297 " and produce its Voronoi diagram in points.1.v.node and points.1.v.edge.\n");
2298 printf(
2299 " The .v.node file contains a list of all Voronoi vertices, and the .v.edge\n"
2300 );
2301 printf(
2302 " file contains a list of all Voronoi edges, some of which may be infinite\n"
2303 );
2304 printf(
2305 " rays. (The choice of filenames makes it easy to run the set of Voronoi\n");
2306 printf(" vertices through Triangle, if so desired.)\n\n");
2307 printf(
2308 " This implementation does not use exact arithmetic to compute the Voronoi\n"
2309 );
2310 printf(
2311 " vertices, and does not check whether neighboring vertices are identical.\n"
2312 );
2313 printf(
2314 " Be forewarned that if the Delaunay triangulation is degenerate or\n");
2315 printf(
2316 " near-degenerate, the Voronoi diagram may have duplicate points, crossing\n"
2317 );
2318 printf(
2319 " edges, or infinite rays whose direction vector is zero. Also, if you\n");
2320 printf(
2321 " generate a constrained (as opposed to conforming) Delaunay triangulation,\n"
2322 );
2323 printf(
2324 " or if the triangulation has holes, the corresponding Voronoi diagram is\n");
2325 printf(" likely to have crossing edges and unlikely to make sense.\n\n");
2326 printf("Mesh Topology:\n\n");
2327 printf(
2328 " You may wish to know which triangles are adjacent to a certain Delaunay\n");
2329 printf(
2330 " edge in an .edge file, which Voronoi regions are adjacent to a certain\n");
2331 printf(
2332 " Voronoi edge in a .v.edge file, or which Voronoi regions are adjacent to\n"
2333 );
2334 printf(
2335 " each other. All of this information can be found by cross-referencing\n");
2336 printf(
2337 " output files with the recollection that the Delaunay triangulation and\n");
2338 printf(" the Voronoi diagrams are planar duals.\n\n");
2339 printf(
2340 " Specifically, edge i of an .edge file is the dual of Voronoi edge i of\n");
2341 printf(
2342 " the corresponding .v.edge file, and is rotated 90 degrees counterclock-\n");
2343 printf(
2344 " wise from the Voronoi edge. Triangle j of an .ele file is the dual of\n");
2345 printf(
2346 " vertex j of the corresponding .v.node file; and Voronoi region k is the\n");
2347 printf(" dual of point k of the corresponding .node file.\n\n");
2348 printf(
2349 " Hence, to find the triangles adjacent to a Delaunay edge, look at the\n");
2350 printf(
2351 " vertices of the corresponding Voronoi edge; their dual triangles are on\n");
2352 printf(
2353 " the left and right of the Delaunay edge, respectively. To find the\n");
2354 printf(
2355 " Voronoi regions adjacent to a Voronoi edge, look at the endpoints of the\n"
2356 );
2357 printf(
2358 " corresponding Delaunay edge; their dual regions are on the right and left\n"
2359 );
2360 printf(
2361 " of the Voronoi edge, respectively. To find which Voronoi regions are\n");
2362 printf(" adjacent to each other, just read the list of Delaunay edges.\n");
2363 printf("\n");
2364 printf("Statistics:\n");
2365 printf("\n");
2366 printf(
2367 " After generating a mesh, Triangle prints a count of the number of points,\n"
2368 );
2369 printf(
2370 " triangles, edges, boundary edges, and segments in the output mesh. If\n");
2371 printf(
2372 " you've forgotten the statistics for an existing mesh, the -rNEP switches\n"
2373 );
2374 printf(
2375 " (or -rpNEP if you've got a .poly file for the existing mesh) will\n");
2376 printf(" regenerate these statistics without writing any output.\n\n");
2377 printf(
2378 " The -V switch produces extended statistics, including a rough estimate\n");
2379 printf(
2380 " of memory use and a histogram of triangle aspect ratios and angles in the\n"
2381 );
2382 printf(" mesh.\n\n");
2383 printf("Exact Arithmetic:\n\n");
2384 printf(
2385 " Triangle uses adaptive exact arithmetic to perform what computational\n");
2386 printf(
2387 " geometers call the `orientation' and `incircle' tests. If the floating-\n"
2388 );
2389 printf(
2390 " point arithmetic of your machine conforms to the IEEE 754 standard (as\n");
2391 printf(
2392 " most workstations do), and does not use extended precision internal\n");
2393 printf(
2394 " registers, then your output is guaranteed to be an absolutely true\n");
2395 printf(" Delaunay or conforming Delaunay triangulation, roundoff error\n");
2396 printf(
2397 " notwithstanding. The word `adaptive' implies that these arithmetic\n");
2398 printf(
2399 " routines compute the result only to the precision necessary to guarantee\n"
2400 );
2401 printf(
2402 " correctness, so they are usually nearly as fast as their approximate\n");
2403 printf(
2404 " counterparts. The exact tests can be disabled with the -X switch. On\n");
2405 printf(
2406 " most inputs, this switch will reduce the computation time by about eight\n"
2407 );
2408 printf(
2409 " percent - it's not worth the risk. There are rare difficult inputs\n");
2410 printf(
2411 " (having many collinear and cocircular points), however, for which the\n");
2412 printf(
2413 " difference could be a factor of two. These are precisely the inputs most\n"
2414 );
2415 printf(" likely to cause errors if you use the -X switch.\n\n");
2416 printf(
2417 " Unfortunately, these routines don't solve every numerical problem. Exact\n"
2418 );
2419 printf(
2420 " arithmetic is not used to compute the positions of points, because the\n");
2421 printf(
2422 " bit complexity of point coordinates would grow without bound. Hence,\n");
2423 printf(
2424 " segment intersections aren't computed exactly; in very unusual cases,\n");
2425 printf(
2426 " roundoff error in computing an intersection point might actually lead to\n"
2427 );
2428 printf(
2429 " an inverted triangle and an invalid triangulation. (This is one reason\n");
2430 printf(
2431 " to compute your own intersection points in your .poly files.) Similarly,\n"
2432 );
2433 printf(
2434 " exact arithmetic is not used to compute the vertices of the Voronoi\n");
2435 printf(" diagram.\n\n");
2436 printf(
2437 " Underflow and overflow can also cause difficulties; the exact arithmetic\n"
2438 );
2439 printf(
2440 " routines do not ameliorate out-of-bounds exponents, which can arise\n");
2441 printf(
2442 " during the orientation and incircle tests. As a rule of thumb, you\n");
2443 printf(
2444 " should ensure that your input values are within a range such that their\n");
2445 printf(
2446 " third powers can be taken without underflow or overflow. Underflow can\n");
2447 printf(
2448 " silently prevent the tests from being performed exactly, while overflow\n");
2449 printf(" will typically cause a floating exception.\n\n");
2450 printf("Calling Triangle from Another Program:\n\n");
2451 printf(" Read the file triangle.h for details.\n\n");
2452 printf("Troubleshooting:\n\n");
2453 printf(" Please read this section before mailing me bugs.\n\n");
2454 printf(" `My output mesh has no triangles!'\n\n");
2455 printf(
2456 " If you're using a PSLG, you've probably failed to specify a proper set\n"
2457 );
2458 printf(
2459 " of bounding segments, or forgotten to use the -c switch. Or you may\n");
2460 printf(
2461 " have placed a hole badly. To test these possibilities, try again with\n"
2462 );
2463 printf(
2464 " the -c and -O switches. Alternatively, all your input points may be\n");
2465 printf(
2466 " collinear, in which case you can hardly expect to triangulate them.\n");
2467 printf("\n");
2468 printf(" `Triangle doesn't terminate, or just crashes.'\n");
2469 printf("\n");
2470 printf(
2471 " Bad things can happen when triangles get so small that the distance\n");
2472 printf(
2473 " between their vertices isn't much larger than the precision of your\n");
2474 printf(
2475 " machine's arithmetic. If you've compiled Triangle for single-precision\n"
2476 );
2477 printf(
2478 " arithmetic, you might do better by recompiling it for double-precision.\n"
2479 );
2480 printf(
2481 " Then again, you might just have to settle for more lenient constraints\n"
2482 );
2483 printf(
2484 " on the minimum angle and the maximum area than you had planned.\n");
2485 printf("\n");
2486 printf(
2487 " You can minimize precision problems by ensuring that the origin lies\n");
2488 printf(
2489 " inside your point set, or even inside the densest part of your\n");
2490 printf(
2491 " mesh. On the other hand, if you're triangulating an object whose x\n");
2492 printf(
2493 " coordinates all fall between 6247133 and 6247134, you're not leaving\n");
2494 printf(" much floating-point precision for Triangle to work with.\n\n");
2495 printf(
2496 " Precision problems can occur covertly if the input PSLG contains two\n");
2497 printf(
2498 " segments that meet (or intersect) at a very small angle, or if such an\n"
2499 );
2500 printf(
2501 " angle is introduced by the -c switch, which may occur if a point lies\n");
2502 printf(
2503 " ever-so-slightly inside the convex hull, and is connected by a PSLG\n");
2504 printf(
2505 " segment to a point on the convex hull. If you don't realize that a\n");
2506 printf(
2507 " small angle is being formed, you might never discover why Triangle is\n");
2508 printf(
2509 " crashing. To check for this possibility, use the -S switch (with an\n");
2510 printf(
2511 " appropriate limit on the number of Steiner points, found by trial-and-\n"
2512 );
2513 printf(
2514 " error) to stop Triangle early, and view the output .poly file with\n");
2515 printf(
2516 " Show Me (described below). Look carefully for small angles between\n");
2517 printf(
2518 " segments; zoom in closely, as such segments might look like a single\n");
2519 printf(" segment from a distance.\n\n");
2520 printf(
2521 " If some of the input values are too large, Triangle may suffer a\n");
2522 printf(
2523 " floating exception due to overflow when attempting to perform an\n");
2524 printf(
2525 " orientation or incircle test. (Read the section on exact arithmetic\n");
2526 printf(
2527 " above.) Again, I recommend compiling Triangle for double (rather\n");
2528 printf(" than single) precision arithmetic.\n\n");
2529 printf(
2530 " `The numbering of the output points doesn't match the input points.'\n");
2531 printf("\n");
2532 printf(
2533 " You may have eaten some of your input points with a hole, or by placing\n"
2534 );
2535 printf(" them outside the area enclosed by segments.\n\n");
2536 printf(
2537 " `Triangle executes without incident, but when I look at the resulting\n");
2538 printf(
2539 " mesh, it has overlapping triangles or other geometric inconsistencies.'\n");
2540 printf("\n");
2541 printf(
2542 " If you select the -X switch, Triangle's divide-and-conquer Delaunay\n");
2543 printf(
2544 " triangulation algorithm occasionally makes mistakes due to floating-\n");
2545 printf(
2546 " point roundoff error. Although these errors are rare, don't use the -X\n"
2547 );
2548 printf(" switch. If you still have problems, please report the bug.\n");
2549 printf("\n");
2550 printf(
2551 " Strange things can happen if you've taken liberties with your PSLG. Do\n");
2552 printf(
2553 " you have a point lying in the middle of a segment? Triangle sometimes\n");
2554 printf(
2555 " copes poorly with that sort of thing. Do you want to lay out a collinear\n"
2556 );
2557 printf(
2558 " row of evenly spaced, segment-connected points? Have you simply defined\n"
2559 );
2560 printf(
2561 " one long segment connecting the leftmost point to the rightmost point,\n");
2562 printf(
2563 " and a bunch of points lying along it? This method occasionally works,\n");
2564 printf(
2565 " especially with horizontal and vertical lines, but often it doesn't, and\n"
2566 );
2567 printf(
2568 " you'll have to connect each adjacent pair of points with a separate\n");
2569 printf(" segment. If you don't like it, tough.\n\n");
2570 printf(
2571 " Furthermore, if you have segments that intersect other than at their\n");
2572 printf(
2573 " endpoints, try not to let the intersections fall extremely close to PSLG\n"
2574 );
2575 printf(" points or each other.\n\n");
2576 printf(
2577 " If you have problems refining a triangulation not produced by Triangle:\n");
2578 printf(
2579 " Are you sure the triangulation is geometrically valid? Is it formatted\n");
2580 printf(
2581 " correctly for Triangle? Are the triangles all listed so the first three\n"
2582 );
2583 printf(" points are their corners in counterclockwise order?\n\n");
2584 printf("Show Me:\n\n");
2585 printf(
2586 " Triangle comes with a separate program named `Show Me', whose primary\n");
2587 printf(
2588 " purpose is to draw meshes on your screen or in PostScript. Its secondary\n"
2589 );
2590 printf(
2591 " purpose is to check the validity of your input files, and do so more\n");
2592 printf(
2593 " thoroughly than Triangle does. Show Me requires that you have the X\n");
2594 printf(
2595 " Windows system. If you didn't receive Show Me with Triangle, complain to\n"
2596 );
2597 printf(" whomever you obtained Triangle from, then send me mail.\n\n");
2598 printf("Triangle on the Web:\n\n");
2599 printf(
2600 " To see an illustrated, updated version of these instructions, check out\n");
2601 printf("\n");
2602 printf(" http://www.cs.cmu.edu/~quake/triangle.html\n");
2603 printf("\n");
2604 printf("A Brief Plea:\n");
2605 printf("\n");
2606 printf(
2607 " If you use Triangle, and especially if you use it to accomplish real\n");
2608 printf(
2609 " work, I would like very much to hear from you. A short letter or email\n");
2610 printf(
2611 " (to jrs@cs.cmu.edu) describing how you use Triangle will mean a lot to\n");
2612 printf(
2613 " me. The more people I know are using this program, the more easily I can\n"
2614 );
2615 printf(
2616 " justify spending time on improvements and on the three-dimensional\n");
2617 printf(
2618 " successor to Triangle, which in turn will benefit you. Also, I can put\n");
2619 printf(
2620 " you on a list to receive email whenever a new version of Triangle is\n");
2621 printf(" available.\n\n");
2622 printf(
2623 " If you use a mesh generated by Triangle in a publication, please include\n"
2624 );
2625 printf(" an acknowledgment as well.\n\n");
2626 printf("Research credit:\n\n");
2627 printf(
2628 " Of course, I can take credit for only a fraction of the ideas that made\n");
2629 printf(
2630 " this mesh generator possible. Triangle owes its existence to the efforts\n"
2631 );
2632 printf(
2633 " of many fine computational geometers and other researchers, including\n");
2634 printf(
2635 " Marshall Bern, L. Paul Chew, Boris Delaunay, Rex A. Dwyer, David\n");
2636 printf(
2637 " Eppstein, Steven Fortune, Leonidas J. Guibas, Donald E. Knuth, C. L.\n");
2638 printf(
2639 " Lawson, Der-Tsai Lee, Ernst P. Mucke, Douglas M. Priest, Jim Ruppert,\n");
2640 printf(
2641 " Isaac Saias, Bruce J. Schachter, Micha Sharir, Jorge Stolfi, Christopher\n"
2642 );
2643 printf(
2644 " J. Van Wyk, David F. Watson, and Binhai Zhu. See the comments at the\n");
2645 printf(" beginning of the source code for references.\n\n");
2646 exit(0);
2647 }
2648
2649 #endif /* not TRILIBRARY */
2650
2651 /*****************************************************************************/
2652 /* */
2653 /* internalerror() Ask the user to send me the defective product. Exit. */
2654 /* */
2655 /*****************************************************************************/
2656
2657 void internalerror()
2658 {
2659 printf(" Please report this bug to jrs@cs.cmu.edu\n");
2660 printf(" Include the message above, your input data set, and the exact\n");
2661 printf(" command line you used to run Triangle.\n");
2662 exit(1);
2663 }
2664
2665 /*****************************************************************************/
2666 /* */
2667 /* parsecommandline() Read the command line, identify switches, and set */
2668 /* up options and file names. */
2669 /* */
2670 /* The effects of this routine are felt entirely through global variables. */
2671 /* */
2672 /*****************************************************************************/
2673
2674 void parsecommandline(argc, argv)
2675 int argc;
2676 char **argv;
2677 {
2678 #ifdef TRILIBRARY
2679 #define STARTINDEX 0
2680 #else /* not TRILIBRARY */
2681 #define STARTINDEX 1
2682 int increment;
2683 int meshnumber;
2684 #endif /* not TRILIBRARY */
2685 int i, j, k;
2686 char workstring[FILENAMESIZE];
2687
2688 poly = refine = quality = vararea = fixedarea = regionattrib = convex = 0;
2689 firstnumber = 1;
2690 edgesout = voronoi = neighbors = geomview = 0;
2691 nobound = nopolywritten = nonodewritten = noelewritten = noiterationnum = 0;
2692 noholes = noexact = 0;
2693 incremental = sweepline = 0;
2694 dwyer = 1;
2695 splitseg = 0;
2696 docheck = 0;
2697 nobisect = 0;
2698 steiner = -1;
2699 order = 1;
2700 minangle = 0.0;
2701 maxarea = -1.0;
2702 quiet = verbose = 0;
2703 #ifndef TRILIBRARY
2704 innodefilename[0] = '\0';
2705 #endif /* not TRILIBRARY */
2706
2707 for (i = STARTINDEX; i < argc; i++) {
2708 #ifndef TRILIBRARY
2709 if (argv[i][0] == '-') {
2710 #endif /* not TRILIBRARY */
2711 for (j = STARTINDEX; argv[i][j] != '\0'; j++) {
2712 if (argv[i][j] == 'p') {
2713 poly = 1;
2714 }
2715 #ifndef CDT_ONLY
2716 if (argv[i][j] == 'r') {
2717 refine = 1;
2718 }
2719 if (argv[i][j] == 'q') {
2720 quality = 1;
2721 if (((argv[i][j + 1] >= '') && (argv[i][j + 1] <= '9')) ||
2722 (argv[i][j + 1] == '.')) {
2723 k = 0;
2724 while (((argv[i][j + 1] >= '') && (argv[i][j + 1] <= '9')) ||
2725 (argv[i][j + 1] == '.')) {
2726 j++;
2727 workstring[k] = argv[i][j];
2728 k++;
2729 }
2730 workstring[k] = '\0';
2731 minangle = (REAL) strtod(workstring, (char **) NULL);
2732 } else {
2733 minangle = 20.0;
2734 }
2735 }
2736 if (argv[i][j] == 'a') {
2737 quality = 1;
2738 if (((argv[i][j + 1] >= '') && (argv[i][j + 1] <= '9')) ||
2739 (argv[i][j + 1] == '.')) {
2740 fixedarea = 1;
2741 k = 0;
2742 while (((argv[i][j + 1] >= '') && (argv[i][j + 1] <= '9')) ||
2743 (argv[i][j + 1] == '.')) {
2744 j++;
2745 workstring[k] = argv[i][j];
2746 k++;
2747 }
2748 workstring[k] = '\0';
2749 maxarea = (REAL) strtod(workstring, (char **) NULL);
2750 if (maxarea <= 0.0) {
2751 printf("Error: Maximum area must be greater than zero.\n");
2752 exit(1);
2753 }
2754 } else {
2755 vararea = 1;
2756 }
2757 }
2758 #endif /* not CDT_ONLY */
2759 if (argv[i][j] == 'A') {
2760 regionattrib = 1;
2761 }
2762 if (argv[i][j] == 'c') {
2763 convex = 1;
2764 }
2765 if (argv[i][j] == 'z') {
2766 firstnumber = 0;
2767 }
2768 if (argv[i][j] == 'e') {
2769 edgesout = 1;
2770 }
2771 if (argv[i][j] == 'v') {
2772 voronoi = 1;
2773 }
2774 if (argv[i][j] == 'n') {
2775 neighbors = 1;
2776 }
2777 if (argv[i][j] == 'g') {
2778 geomview = 1;
2779 }
2780 if (argv[i][j] == 'B') {
2781 nobound = 1;
2782 }
2783 if (argv[i][j] == 'P') {
2784 nopolywritten = 1;
2785 }
2786 if (argv[i][j] == 'N') {
2787 nonodewritten = 1;
2788 }
2789 if (argv[i][j] == 'E') {
2790 noelewritten = 1;
2791 }
2792 #ifndef TRILIBRARY
2793 if (argv[i][j] == 'I') {
2794 noiterationnum = 1;
2795 }
2796 #endif /* not TRILIBRARY */
2797 if (argv[i][j] == 'O') {
2798 noholes = 1;
2799 }
2800 if (argv[i][j] == 'X') {
2801 noexact = 1;
2802 }
2803 if (argv[i][j] == 'o') {
2804 if (argv[i][j + 1] == '2') {
2805 j++;
2806 order = 2;
2807 }
2808 }
2809 #ifndef CDT_ONLY
2810 if (argv[i][j] == 'Y') {
2811 nobisect++;
2812 }
2813 if (argv[i][j] == 'S') {
2814 steiner = 0;
2815 while ((argv[i][j + 1] >= '') && (argv[i][j + 1] <= '9')) {
2816 j++;
2817 steiner = steiner * 10 + (int) (argv[i][j] - '');
2818 }
2819 }
2820 #endif /* not CDT_ONLY */
2821 #ifndef REDUCED
2822 if (argv[i][j] == 'i') {
2823 incremental = 1;
2824 }
2825 if (argv[i][j] == 'F') {
2826 sweepline = 1;
2827 }
2828 #endif /* not REDUCED */
2829 if (argv[i][j] == 'l') {
2830 dwyer = 0;
2831 }
2832 #ifndef REDUCED
2833 #ifndef CDT_ONLY
2834 if (argv[i][j] == 's') {
2835 splitseg = 1;
2836 }
2837 #endif /* not CDT_ONLY */
2838 if (argv[i][j] == 'C') {
2839 docheck = 1;
2840 }
2841 #endif /* not REDUCED */
2842 if (argv[i][j] == 'Q') {
2843 quiet = 1;
2844 }
2845 if (argv[i][j] == 'V') {
2846 verbose++;
2847 }
2848 #ifndef TRILIBRARY
2849 if ((argv[i][j] == 'h') || (argv[i][j] == 'H') ||
2850 (argv[i][j] == '?')) {
2851 info();
2852 }
2853 #endif /* not TRILIBRARY */
2854 }
2855 #ifndef TRILIBRARY
2856 } else {
2857 strncpy(innodefilename, argv[i], FILENAMESIZE - 1);
2858 innodefilename[FILENAMESIZE - 1] = '\0';
2859 }
2860 #endif /* not TRILIBRARY */
2861 }
2862 #ifndef TRILIBRARY
2863 if (innodefilename[0] == '\0') {
2864 syntax();
2865 }
2866 if (!strcmp(&innodefilename[strlen(innodefilename) - 5], ".node")) {
2867 innodefilename[strlen(innodefilename) - 5] = '\0';
2868 }
2869 if (!strcmp(&innodefilename[strlen(innodefilename) - 5], ".poly")) {
2870 innodefilename[strlen(innodefilename) - 5] = '\0';
2871 poly = 1;
2872 }
2873 #ifndef CDT_ONLY
2874 if (!strcmp(&innodefilename[strlen(innodefilename) - 4], ".ele")) {
2875 innodefilename[strlen(innodefilename) - 4] = '\0';
2876 refine = 1;
2877 }
2878 if (!strcmp(&innodefilename[strlen(innodefilename) - 5], ".area")) {
2879 innodefilename[strlen(innodefilename) - 5] = '\0';
2880 refine = 1;
2881 quality = 1;
2882 vararea = 1;
2883 }
2884 #endif /* not CDT_ONLY */
2885 #endif /* not TRILIBRARY */
2886 steinerleft = steiner;
2887 useshelles = poly || refine || quality || convex;
2888 goodangle = cos(minangle * PI / 180.0);
2889 goodangle *= goodangle;
2890 if (refine && noiterationnum) {
2891 printf(
2892 "Error: You cannot use the -I switch when refining a triangulation.\n");
2893 exit(1);
2894 }
2895 /* Be careful not to allocate space for element area constraints that */
2896 /* will never be assigned any value (other than the default -1.0). */
2897 if (!refine && !poly) {
2898 vararea = 0;
2899 }
2900 /* Be careful not to add an extra attribute to each element unless the */
2901 /* input supports it (PSLG in, but not refining a preexisting mesh). */
2902 if (refine || !poly) {
2903 regionattrib = 0;
2904 }
2905
2906 #ifndef TRILIBRARY
2907 strcpy(inpolyfilename, innodefilename);
2908 strcpy(inelefilename, innodefilename);
2909 strcpy(areafilename, innodefilename);
2910 increment = 0;
2911 strcpy(workstring, innodefilename);
2912 j = 1;
2913 while (workstring[j] != '\0') {
2914 if ((workstring[j] == '.') && (workstring[j + 1] != '\0')) {
2915 increment = j + 1;
2916 }
2917 j++;
2918 }
2919 meshnumber = 0;
2920 if (increment > 0) {
2921 j = increment;
2922 do {
2923 if ((workstring[j] >= '') && (workstring[j] <= '9')) {
2924 meshnumber = meshnumber * 10 + (int) (workstring[j] - '');
2925 } else {
2926 increment = 0;
2927 }
2928 j++;
2929 } while (workstring[j] != '\0');
2930 }
2931 if (noiterationnum) {
2932 strcpy(outnodefilename, innodefilename);
2933 strcpy(outelefilename, innodefilename);
2934 strcpy(edgefilename, innodefilename);
2935 strcpy(vnodefilename, innodefilename);
2936 strcpy(vedgefilename, innodefilename);
2937 strcpy(neighborfilename, innodefilename);
2938 strcpy(offfilename, innodefilename);
2939 strcat(outnodefilename, ".node");
2940 strcat(outelefilename, ".ele");
2941 strcat(edgefilename, ".edge");
2942 strcat(vnodefilename, ".v.node");
2943 strcat(vedgefilename, ".v.edge");
2944 strcat(neighborfilename, ".neigh");
2945 strcat(offfilename, ".off");
2946 } else if (increment == 0) {
2947 strcpy(outnodefilename, innodefilename);
2948 strcpy(outpolyfilename, innodefilename);
2949 strcpy(outelefilename, innodefilename);
2950 strcpy(edgefilename, innodefilename);
2951 strcpy(vnodefilename, innodefilename);
2952 strcpy(vedgefilename, innodefilename);
2953 strcpy(neighborfilename, innodefilename);
2954 strcpy(offfilename, innodefilename);
2955 strcat(outnodefilename, ".1.node");
2956 strcat(outpolyfilename, ".1.poly");
2957 strcat(outelefilename, ".1.ele");
2958 strcat(edgefilename, ".1.edge");
2959 strcat(vnodefilename, ".1.v.node");
2960 strcat(vedgefilename, ".1.v.edge");
2961 strcat(neighborfilename, ".1.neigh");
2962 strcat(offfilename, ".1.off");
2963 } else {
2964 workstring[increment] = '%';
2965 workstring[increment + 1] = 'd';
2966 workstring[increment + 2] = '\0';
2967 sprintf(outnodefilename, workstring, meshnumber + 1);
2968 strcpy(outpolyfilename, outnodefilename);
2969 strcpy(outelefilename, outnodefilename);
2970 strcpy(edgefilename, outnodefilename);
2971 strcpy(vnodefilename, outnodefilename);
2972 strcpy(vedgefilename, outnodefilename);
2973 strcpy(neighborfilename, outnodefilename);
2974 strcpy(offfilename, outnodefilename);
2975 strcat(outnodefilename, ".node");
2976 strcat(outpolyfilename, ".poly");
2977 strcat(outelefilename, ".ele");
2978 strcat(edgefilename, ".edge");
2979 strcat(vnodefilename, ".v.node");
2980 strcat(vedgefilename, ".v.edge");
2981 strcat(neighborfilename, ".neigh");
2982 strcat(offfilename, ".off");
2983 }
2984 strcat(innodefilename, ".node");
2985 strcat(inpolyfilename, ".poly");
2986 strcat(inelefilename, ".ele");
2987 strcat(areafilename, ".area");
2988 #endif /* not TRILIBRARY */
2989 }
2990
2991 /** **/
2992 /** **/
2993 /********* User interaction routines begin here *********/
2994
2995 /********* Debugging routines begin here *********/
2996 /** **/
2997 /** **/
2998
2999 /*****************************************************************************/
3000 /* */
3001 /* printtriangle() Print out the details of a triangle/edge handle. */
3002 /* */
3003 /* I originally wrote this procedure to simplify debugging; it can be */
3004 /* called directly from the debugger, and presents information about a */
3005 /* triangle/edge handle in digestible form. It's also used when the */
3006 /* highest level of verbosity (`-VVV') is specified. */
3007 /* */
3008 /*****************************************************************************/
3009
3010 void printtriangle(t)
3011 struct triedge *t;
3012 {
3013 struct triedge printtri;
3014 struct edge printsh;
3015 point printpoint;
3016
3017 printf("triangle x%lx with orientation %d:\n", (unsigned long) t->tri,
3018 t->orient);
3019 decode(t->tri[0], printtri);
3020 if (printtri.tri == dummytri) {
3021 printf(" [0] = Outer space\n");
3022 } else {
3023 printf(" [0] = x%lx %d\n", (unsigned long) printtri.tri,
3024 printtri.orient);
3025 }
3026 decode(t->tri[1], printtri);
3027 if (printtri.tri == dummytri) {
3028 printf(" [1] = Outer space\n");
3029 } else {
3030 printf(" [1] = x%lx %d\n", (unsigned long) printtri.tri,
3031 printtri.orient);
3032 }
3033 decode(t->tri[2], printtri);
3034 if (printtri.tri == dummytri) {
3035 printf(" [2] = Outer space\n");
3036 } else {
3037 printf(" [2] = x%lx %d\n", (unsigned long) printtri.tri,
3038 printtri.orient);
3039 }
3040 org(*t, printpoint);
3041 if (printpoint == (point) NULL)
3042 printf(" Origin[%d] = NULL\n", (t->orient + 1) % 3 + 3);
3043 else
3044 printf(" Origin[%d] = x%lx (%.12g, %.12g)\n",
3045 (t->orient + 1) % 3 + 3, (unsigned long) printpoint,
3046 printpoint[0], printpoint[1]);
3047 dest(*t, printpoint);
3048 if (printpoint == (point) NULL)
3049 printf(" Dest [%d] = NULL\n", (t->orient + 2) % 3 + 3);
3050 else
3051 printf(" Dest [%d] = x%lx (%.12g, %.12g)\n",
3052 (t->orient + 2) % 3 + 3, (unsigned long) printpoint,
3053 printpoint[0], printpoint[1]);
3054 apex(*t, printpoint);
3055 if (printpoint == (point) NULL)
3056 printf(" Apex [%d] = NULL\n", t->orient + 3);
3057 else
3058 printf(" Apex [%d] = x%lx (%.12g, %.12g)\n",
3059 t->orient + 3, (unsigned long) printpoint,
3060 printpoint[0], printpoint[1]);
3061 if (useshelles) {
3062 sdecode(t->tri[6], printsh);
3063 if (printsh.sh != dummysh) {
3064 printf(" [6] = x%lx %d\n", (unsigned long) printsh.sh,
3065 printsh.shorient);
3066 }
3067 sdecode(t->tri[7], printsh);
3068 if (printsh.sh != dummysh) {
3069 printf(" [7] = x%lx %d\n", (unsigned long) printsh.sh,
3070 printsh.shorient);
3071 }
3072 sdecode(t->tri[8], printsh);
3073 if (printsh.sh != dummysh) {
3074 printf(" [8] = x%lx %d\n", (unsigned long) printsh.sh,
3075 printsh.shorient);
3076 }
3077 }
3078 if (vararea) {
3079 printf(" Area constraint: %.4g\n", areabound(*t));
3080 }
3081 }
3082
3083 /*****************************************************************************/
3084 /* */
3085 /* printshelle() Print out the details of a shell edge handle. */
3086 /* */
3087 /* I originally wrote this procedure to simplify debugging; it can be */
3088 /* called directly from the debugger, and presents information about a */
3089 /* shell edge handle in digestible form. It's also used when the highest */
3090 /* level of verbosity (`-VVV') is specified. */
3091 /* */
3092 /*****************************************************************************/
3093
3094 void printshelle(s)
3095 struct edge *s;
3096 {
3097 struct edge printsh;
3098 struct triedge printtri;
3099 point printpoint;
3100
3101 printf("shell edge x%lx with orientation %d and mark %d:\n",
3102 (unsigned long) s->sh, s->shorient, mark(*s));
3103 sdecode(s->sh[0], printsh);
3104 if (printsh.sh == dummysh) {
3105 printf(" [0] = No shell\n");
3106 } else {
3107 printf(" [0] = x%lx %d\n", (unsigned long) printsh.sh,
3108 printsh.shorient);
3109 }
3110 sdecode(s->sh[1], printsh);
3111 if (printsh.sh == dummysh) {
3112 printf(" [1] = No shell\n");
3113 } else {
3114 printf(" [1] = x%lx %d\n", (unsigned long) printsh.sh,
3115 printsh.shorient);
3116 }
3117 sorg(*s, printpoint);
3118 if (printpoint == (point) NULL)
3119 printf(" Origin[%d] = NULL\n", 2 + s->shorient);
3120 else
3121 printf(" Origin[%d] = x%lx (%.12g, %.12g)\n",
3122 2 + s->shorient, (unsigned long) printpoint,
3123 printpoint[0], printpoint[1]);
3124 sdest(*s, printpoint);
3125 if (printpoint == (point) NULL)
3126 printf(" Dest [%d] = NULL\n", 3 - s->shorient);
3127 else
3128 printf(" Dest [%d] = x%lx (%.12g, %.12g)\n",
3129 3 - s->shorient, (unsigned long) printpoint,
3130 printpoint[0], printpoint[1]);
3131 decode(s->sh[4], printtri);
3132 if (printtri.tri == dummytri) {
3133 printf(" [4] = Outer space\n");
3134 } else {
3135 printf(" [4] = x%lx %d\n", (unsigned long) printtri.tri,
3136 printtri.orient);
3137 }
3138 decode(s->sh[5], printtri);
3139 if (printtri.tri == dummytri) {
3140 printf(" [5] = Outer space\n");
3141 } else {
3142 printf(" [5] = x%lx %d\n", (unsigned long) printtri.tri,
3143 printtri.orient);
3144 }
3145 }
3146
3147 /** **/
3148 /** **/
3149 /********* Debugging routines end here *********/
3150
3151 /********* Memory management routines begin here *********/
3152 /** **/
3153 /** **/
3154
3155 /*****************************************************************************/
3156 /* */
3157 /* poolinit() Initialize a pool of memory for allocation of items. */
3158 /* */
3159 /* This routine initializes the machinery for allocating items. A `pool' */
3160 /* is created whose records have size at least `bytecount'. Items will be */
3161 /* allocated in `itemcount'-item blocks. Each item is assumed to be a */
3162 /* collection of words, and either pointers or floating-point values are */
3163 /* assumed to be the "primary" word type. (The "primary" word type is used */
3164 /* to determine alignment of items.) If `alignment' isn't zero, all items */
3165 /* will be `alignment'-byte aligned in memory. `alignment' must be either */
3166 /* a multiple or a factor of the primary word size; powers of two are safe. */
3167 /* `alignment' is normally used to create a few unused bits at the bottom */
3168 /* of each item's pointer, in which information may be stored. */
3169 /* */
3170 /* Don't change this routine unless you understand it. */
3171 /* */
3172 /*****************************************************************************/
3173
3174 void poolinit(pool, bytecount, itemcount, wtype, alignment)
3175 struct memorypool *pool;
3176 int bytecount;
3177 int itemcount;
3178 enum wordtype wtype;
3179 int alignment;
3180 {
3181 int wordsize;
3182
3183 /* Initialize values in the pool. */
3184 pool->itemwordtype = wtype;
3185 wordsize = (pool->itemwordtype == POINTER) ? sizeof(VOID *) : sizeof(REAL);
3186 /* Find the proper alignment, which must be at least as large as: */
3187 /* - The parameter `alignment'. */
3188 /* - The primary word type, to avoid unaligned accesses. */
3189 /* - sizeof(VOID *), so the stack of dead items can be maintained */
3190 /* without unaligned accesses. */
3191 if (alignment > wordsize) {
3192 pool->alignbytes = alignment;
3193 } else {
3194 pool->alignbytes = wordsize;
3195 }
3196 if (sizeof(VOID *) > pool->alignbytes) {
3197 pool->alignbytes = sizeof(VOID *);
3198 }
3199 pool->itemwords = ((bytecount + pool->alignbytes - 1) / pool->alignbytes)
3200 * (pool->alignbytes / wordsize);
3201 pool->itembytes = pool->itemwords * wordsize;
3202 pool->itemsperblock = itemcount;
3203
3204 /* Allocate a block of items. Space for `itemsperblock' items and one */
3205 /* pointer (to point to the next block) are allocated, as well as space */
3206 /* to ensure alignment of the items. */
3207 pool->firstblock = (VOID **) malloc(pool->itemsperblock * pool->itembytes
3208 + sizeof(VOID *) + pool->alignbytes);
3209 if (pool->firstblock == (VOID **) NULL) {
3210 printf("Error: Out of memory.\n");
3211 exit(1);
3212 }
3213 /* Set the next block pointer to NULL. */
3214 *(pool->firstblock) = (VOID *) NULL;
3215 poolrestart(pool);
3216 }
3217
3218 /*****************************************************************************/
3219 /* */
3220 /* poolrestart() Deallocate all items in a pool. */
3221 /* */
3222 /* The pool is returned to its starting state, except that no memory is */
3223 /* freed to the operating system. Rather, the previously allocated blocks */
3224 /* are ready to be reused. */
3225 /* */
3226 /*****************************************************************************/
3227
3228 void poolrestart(pool)
3229 struct memorypool *pool;
3230 {
3231 unsigned long alignptr;
3232
3233 pool->items = 0;
3234 pool->maxitems = 0;
3235
3236 /* Set the currently active block. */
3237 pool->nowblock = pool->firstblock;
3238 /* Find the first item in the pool. Increment by the size of (VOID *). */
3239 alignptr = (unsigned long) (pool->nowblock + 1);
3240 /* Align the item on an `alignbytes'-byte boundary. */
3241 pool->nextitem = (VOID *)
3242 (alignptr + (unsigned long) pool->alignbytes
3243 - (alignptr % (unsigned long) pool->alignbytes));
3244 /* There are lots of unallocated items left in this block. */
3245 pool->unallocateditems = pool->itemsperblock;
3246 /* The stack of deallocated items is empty. */
3247 pool->deaditemstack = (VOID *) NULL;
3248 }
3249
3250 /*****************************************************************************/
3251 /* */
3252 /* pooldeinit() Free to the operating system all memory taken by a pool. */
3253 /* */
3254 /*****************************************************************************/
3255
3256 void pooldeinit(pool)
3257 struct memorypool *pool;
3258 {
3259 while (pool->firstblock != (VOID **) NULL) {
3260 pool->nowblock = (VOID **) *(pool->firstblock);
3261 free(pool->firstblock);
3262 pool->firstblock = pool->nowblock;
3263 }
3264 }
3265
3266 /*****************************************************************************/
3267 /* */
3268 /* poolalloc() Allocate space for an item. */
3269 /* */
3270 /*****************************************************************************/
3271
3272 VOID *poolalloc(pool)
3273 struct memorypool *pool;
3274 {
3275 VOID *newitem;
3276 VOID **newblock;
3277 unsigned long alignptr;
3278
3279 /* First check the linked list of dead items. If the list is not */
3280 /* empty, allocate an item from the list rather than a fresh one. */
3281 if (pool->deaditemstack != (VOID *) NULL) {
3282 newitem = pool->deaditemstack; /* Take first item in list. */
3283 pool->deaditemstack = * (VOID **) pool->deaditemstack;
3284 } else {
3285 /* Check if there are any free items left in the current block. */
3286 if (pool->unallocateditems == 0) {
3287 /* Check if another block must be allocated. */
3288 if (*(pool->nowblock) == (VOID *) NULL) {
3289 /* Allocate a new block of items, pointed to by the previous block. */
3290 newblock = (VOID **) malloc(pool->itemsperblock * pool->itembytes
3291 + sizeof(VOID *) + pool->alignbytes);
3292 if (newblock == (VOID **) NULL) {
3293 printf("Error: Out of memory.\n");
3294 exit(1);
3295 }
3296 *(pool->nowblock) = (VOID *) newblock;
3297 /* The next block pointer is NULL. */
3298 *newblock = (VOID *) NULL;
3299 }
3300 /* Move to the new block. */
3301 pool->nowblock = (VOID **) *(pool->nowblock);
3302 /* Find the first item in the block. */
3303 /* Increment by the size of (VOID *). */
3304 alignptr = (unsigned long) (pool->nowblock + 1);
3305 /* Align the item on an `alignbytes'-byte boundary. */
3306 pool->nextitem = (VOID *)
3307 (alignptr + (unsigned long) pool->alignbytes
3308 - (alignptr % (unsigned long) pool->alignbytes));
3309 /* There are lots of unallocated items left in this block. */
3310 pool->unallocateditems = pool->itemsperblock;
3311 }
3312 /* Allocate a new item. */
3313 newitem = pool->nextitem;
3314 /* Advance `nextitem' pointer to next free item in block. */
3315 if (pool->itemwordtype == POINTER) {
3316 pool->nextitem = (VOID *) ((VOID **) pool->nextitem + pool->itemwords);
3317 } else {
3318 pool->nextitem = (VOID *) ((REAL *) pool->nextitem + pool->itemwords);
3319 }
3320 pool->unallocateditems--;
3321 pool->maxitems++;
3322 }
3323 pool->items++;
3324 return newitem;
3325 }
3326
3327 /*****************************************************************************/
3328 /* */
3329 /* pooldealloc() Deallocate space for an item. */
3330 /* */
3331 /* The deallocated space is stored in a queue for later reuse. */
3332 /* */
3333 /*****************************************************************************/
3334
3335 void pooldealloc(pool, dyingitem)
3336 struct memorypool *pool;
3337 VOID *dyingitem;
3338 {
3339 /* Push freshly killed item onto stack. */
3340 *((VOID **) dyingitem) = pool->deaditemstack;
3341 pool->deaditemstack = dyingitem;
3342 pool->items--;
3343 }
3344
3345 /*****************************************************************************/
3346 /* */
3347 /* traversalinit() Prepare to traverse the entire list of items. */
3348 /* */
3349 /* This routine is used in conjunction with traverse(). */
3350 /* */
3351 /*****************************************************************************/
3352
3353 void traversalinit(pool)
3354 struct memorypool *pool;
3355 {
3356 unsigned long alignptr;
3357
3358 /* Begin the traversal in the first block. */
3359 pool->pathblock = pool->firstblock;
3360 /* Find the first item in the block. Increment by the size of (VOID *). */
3361 alignptr = (unsigned long) (pool->pathblock + 1);
3362 /* Align with item on an `alignbytes'-byte boundary. */
3363 pool->pathitem = (VOID *)
3364 (alignptr + (unsigned long) pool->alignbytes
3365 - (alignptr % (unsigned long) pool->alignbytes));
3366 /* Set the number of items left in the current block. */
3367 pool->pathitemsleft = pool->itemsperblock;
3368 }
3369
3370 /*****************************************************************************/
3371 /* */
3372 /* traverse() Find the next item in the list. */
3373 /* */
3374 /* This routine is used in conjunction with traversalinit(). Be forewarned */
3375 /* that this routine successively returns all items in the list, including */
3376 /* deallocated ones on the deaditemqueue. It's up to you to figure out */
3377 /* which ones are actually dead. Why? I don't want to allocate extra */
3378 /* space just to demarcate dead items. It can usually be done more */
3379 /* space-efficiently by a routine that knows something about the structure */
3380 /* of the item. */
3381 /* */
3382 /*****************************************************************************/
3383
3384 VOID *traverse(pool)
3385 struct memorypool *pool;
3386 {
3387 VOID *newitem;
3388 unsigned long alignptr;
3389
3390 /* Stop upon exhausting the list of items. */
3391 if (pool->pathitem == pool->nextitem) {
3392 return (VOID *) NULL;
3393 }
3394 /* Check whether any untraversed items remain in the current block. */
3395 if (pool->pathitemsleft == 0) {
3396 /* Find the next block. */
3397 pool->pathblock = (VOID **) *(pool->pathblock);
3398 /* Find the first item in the block. Increment by the size of (VOID *). */
3399 alignptr = (unsigned long) (pool->pathblock + 1);
3400 /* Align with item on an `alignbytes'-byte boundary. */
3401 pool->pathitem = (VOID *)
3402 (alignptr + (unsigned long) pool->alignbytes
3403 - (alignptr % (unsigned long) pool->alignbytes));
3404 /* Set the number of items left in the current block. */
3405 pool->pathitemsleft = pool->itemsperblock;
3406 }
3407 newitem = pool->pathitem;
3408 /* Find the next item in the block. */
3409 if (pool->itemwordtype == POINTER) {
3410 pool->pathitem = (VOID *) ((VOID **) pool->pathitem + pool->itemwords);
3411 } else {
3412 pool->pathitem = (VOID *) ((REAL *) pool->pathitem + pool->itemwords);
3413 }
3414 pool->pathitemsleft--;
3415 return newitem;
3416 }
3417
3418 /*****************************************************************************/
3419 /* */
3420 /* dummyinit() Initialize the triangle that fills "outer space" and the */
3421 /* omnipresent shell edge. */
3422 /* */
3423 /* The triangle that fills "outer space", called `dummytri', is pointed to */
3424 /* by every triangle and shell edge on a boundary (be it outer or inner) of */
3425 /* the triangulation. Also, `dummytri' points to one of the triangles on */
3426 /* the convex hull (until the holes and concavities are carved), making it */
3427 /* possible to find a starting triangle for point location. */
3428 /* */
3429 /* The omnipresent shell edge, `dummysh', is pointed to by every triangle */
3430 /* or shell edge that doesn't have a full complement of real shell edges */
3431 /* to point to. */
3432 /* */
3433 /*****************************************************************************/
3434
3435 void dummyinit(trianglewords, shellewords)
3436 int trianglewords;
3437 int shellewords;
3438 {
3439 unsigned long alignptr;
3440
3441 /* `triwords' and `shwords' are used by the mesh manipulation primitives */
3442 /* to extract orientations of triangles and shell edges from pointers. */
3443 triwords = trianglewords; /* Initialize `triwords' once and for all. */
3444 shwords = shellewords; /* Initialize `shwords' once and for all. */
3445
3446 /* Set up `dummytri', the `triangle' that occupies "outer space". */
3447 dummytribase = (triangle *) malloc(triwords * sizeof(triangle)
3448 + triangles.alignbytes);
3449 if (dummytribase == (triangle *) NULL) {
3450 printf("Error: Out of memory.\n");
3451 exit(1);
3452 }
3453 /* Align `dummytri' on a `triangles.alignbytes'-byte boundary. */
3454 alignptr = (unsigned long) dummytribase;
3455 dummytri = (triangle *)
3456 (alignptr + (unsigned long) triangles.alignbytes
3457 - (alignptr % (unsigned long) triangles.alignbytes));
3458 /* Initialize the three adjoining triangles to be "outer space". These */
3459 /* will eventually be changed by various bonding operations, but their */
3460 /* values don't really matter, as long as they can legally be */
3461 /* dereferenced. */
3462 dummytri[0] = (triangle) dummytri;
3463 dummytri[1] = (triangle) dummytri;
3464 dummytri[2] = (triangle) dummytri;
3465 /* Three NULL vertex points. */
3466 dummytri[3] = (triangle) NULL;
3467 dummytri[4] = (triangle) NULL;
3468 dummytri[5] = (triangle) NULL;
3469
3470 if (useshelles) {
3471 /* Set up `dummysh', the omnipresent "shell edge" pointed to by any */
3472 /* triangle side or shell edge end that isn't attached to a real shell */
3473 /* edge. */
3474 dummyshbase = (shelle *) malloc(shwords * sizeof(shelle)
3475 + shelles.alignbytes);
3476 if (dummyshbase == (shelle *) NULL) {
3477 printf("Error: Out of memory.\n");
3478 exit(1);
3479 }
3480 /* Align `dummysh' on a `shelles.alignbytes'-byte boundary. */
3481 alignptr = (unsigned long) dummyshbase;
3482 dummysh = (shelle *)
3483 (alignptr + (unsigned long) shelles.alignbytes
3484 - (alignptr % (unsigned long) shelles.alignbytes));
3485 /* Initialize the two adjoining shell edges to be the omnipresent shell */
3486 /* edge. These will eventually be changed by various bonding */
3487 /* operations, but their values don't really matter, as long as they */
3488 /* can legally be dereferenced. */
3489 dummysh[0] = (shelle) dummysh;
3490 dummysh[1] = (shelle) dummysh;
3491 /* Two NULL vertex points. */
3492 dummysh[2] = (shelle) NULL;
3493 dummysh[3] = (shelle) NULL;
3494 /* Initialize the two adjoining triangles to be "outer space". */
3495 dummysh[4] = (shelle) dummytri;
3496 dummysh[5] = (shelle) dummytri;
3497 /* Set the boundary marker to zero. */
3498 * (int *) (dummysh + 6) = 0;
3499
3500 /* Initialize the three adjoining shell edges of `dummytri' to be */
3501 /* the omnipresent shell edge. */
3502 dummytri[6] = (triangle) dummysh;
3503 dummytri[7] = (triangle) dummysh;
3504 dummytri[8] = (triangle) dummysh;
3505 }
3506 }
3507
3508 /*****************************************************************************/
3509 /* */
3510 /* initializepointpool() Calculate the size of the point data structure */
3511 /* and initialize its memory pool. */
3512 /* */
3513 /* This routine also computes the `pointmarkindex' and `point2triindex' */
3514 /* indices used to find values within each point. */
3515 /* */
3516 /*****************************************************************************/
3517
3518 void initializepointpool()
3519 {
3520 int pointsize;
3521
3522 /* The index within each point at which the boundary marker is found. */
3523 /* Ensure the point marker is aligned to a sizeof(int)-byte address. */
3524 pointmarkindex = ((mesh_dim + nextras) * sizeof(REAL) + sizeof(int) - 1)
3525 / sizeof(int);
3526 pointsize = (pointmarkindex + 1) * sizeof(int);
3527 if (poly) {
3528 /* The index within each point at which a triangle pointer is found. */
3529 /* Ensure the pointer is aligned to a sizeof(triangle)-byte address. */
3530 point2triindex = (pointsize + sizeof(triangle) - 1) / sizeof(triangle);
3531 pointsize = (point2triindex + 1) * sizeof(triangle);
3532 }
3533 /* Initialize the pool of points. */
3534 poolinit(&points, pointsize, POINTPERBLOCK,
3535 (sizeof(REAL) >= sizeof(triangle)) ? FLOATINGPOINT : POINTER, 0);
3536 }
3537
3538 /*****************************************************************************/
3539 /* */
3540 /* initializetrisegpools() Calculate the sizes of the triangle and shell */
3541 /* edge data structures and initialize their */
3542 /* memory pools. */
3543 /* */
3544 /* This routine also computes the `highorderindex', `elemattribindex', and */
3545 /* `areaboundindex' indices used to find values within each triangle. */
3546 /* */
3547 /*****************************************************************************/
3548
3549 void initializetrisegpools()
3550 {
3551 int trisize;
3552
3553 /* The index within each triangle at which the extra nodes (above three) */
3554 /* associated with high order elements are found. There are three */
3555 /* pointers to other triangles, three pointers to corners, and possibly */
3556 /* three pointers to shell edges before the extra nodes. */
3557 highorderindex = 6 + (useshelles * 3);
3558 /* The number of bytes occupied by a triangle. */
3559 trisize = ((order + 1) * (order + 2) / 2 + (highorderindex - 3)) *
3560 sizeof(triangle);
3561 /* The index within each triangle at which its attributes are found, */
3562 /* where the index is measured in REALs. */
3563 elemattribindex = (trisize + sizeof(REAL) - 1) / sizeof(REAL);
3564 /* The index within each triangle at which the maximum area constraint */
3565 /* is found, where the index is measured in REALs. Note that if the */
3566 /* `regionattrib' flag is set, an additional attribute will be added. */
3567 areaboundindex = elemattribindex + eextras + regionattrib;
3568 /* If triangle attributes or an area bound are needed, increase the number */
3569 /* of bytes occupied by a triangle. */
3570 if (vararea) {
3571 trisize = (areaboundindex + 1) * sizeof(REAL);
3572 } else if (eextras + regionattrib > 0) {
3573 trisize = areaboundindex * sizeof(REAL);
3574 }
3575 /* If a Voronoi diagram or triangle neighbor graph is requested, make */
3576 /* sure there's room to store an integer index in each triangle. This */
3577 /* integer index can occupy the same space as the shell edges or */
3578 /* attributes or area constraint or extra nodes. */
3579 if ((voronoi || neighbors) &&
3580 (trisize < 6 * sizeof(triangle) + sizeof(int))) {
3581 trisize = 6 * sizeof(triangle) + sizeof(int);
3582 }
3583 /* Having determined the memory size of a triangle, initialize the pool. */
3584 poolinit(&triangles, trisize, TRIPERBLOCK, POINTER, 4);
3585
3586 if (useshelles) {
3587 /* Initialize the pool of shell edges. */
3588 poolinit(&shelles, 6 * sizeof(triangle) + sizeof(int), SHELLEPERBLOCK,
3589 POINTER, 4);
3590
3591 /* Initialize the "outer space" triangle and omnipresent shell edge. */
3592 dummyinit(triangles.itemwords, shelles.itemwords);
3593 } else {
3594 /* Initialize the "outer space" triangle. */
3595 dummyinit(triangles.itemwords, 0);
3596 }
3597 }
3598
3599 /*****************************************************************************/
3600 /* */
3601 /* triangledealloc() Deallocate space for a triangle, marking it dead. */
3602 /* */
3603 /*****************************************************************************/
3604
3605 void triangledealloc(dyingtriangle)
3606 triangle *dyingtriangle;
3607 {
3608 /* Set triangle's vertices to NULL. This makes it possible to */
3609 /* detect dead triangles when traversing the list of all triangles. */
3610 dyingtriangle[3] = (triangle) NULL;
3611 dyingtriangle[4] = (triangle) NULL;
3612 dyingtriangle[5] = (triangle) NULL;
3613 pooldealloc(&triangles, (VOID *) dyingtriangle);
3614 }
3615
3616 /*****************************************************************************/
3617 /* */
3618 /* triangletraverse() Traverse the triangles, skipping dead ones. */
3619 /* */
3620 /*****************************************************************************/
3621
3622 triangle *triangletraverse()
3623 {
3624 triangle *newtriangle;
3625
3626 do {
3627 newtriangle = (triangle *) traverse(&triangles);
3628 if (newtriangle == (triangle *) NULL) {
3629 return (triangle *) NULL;
3630 }
3631 } while (newtriangle[3] == (triangle) NULL); /* Skip dead ones. */
3632 return newtriangle;
3633 }
3634
3635 /*****************************************************************************/
3636 /* */
3637 /* shelledealloc() Deallocate space for a shell edge, marking it dead. */
3638 /* */
3639 /*****************************************************************************/
3640
3641 void shelledealloc(dyingshelle)
3642 shelle *dyingshelle;
3643 {
3644 /* Set shell edge's vertices to NULL. This makes it possible to */
3645 /* detect dead shells when traversing the list of all shells. */
3646 dyingshelle[2] = (shelle) NULL;
3647 dyingshelle[3] = (shelle) NULL;
3648 pooldealloc(&shelles, (VOID *) dyingshelle);
3649 }
3650
3651 /*****************************************************************************/
3652 /* */
3653 /* shelletraverse() Traverse the shell edges, skipping dead ones. */
3654 /* */
3655 /*****************************************************************************/
3656
3657 shelle *shelletraverse()
3658 {
3659 shelle *newshelle;
3660
3661 do {
3662 newshelle = (shelle *) traverse(&shelles);
3663 if (newshelle == (shelle *) NULL) {
3664 return (shelle *) NULL;
3665 }
3666 } while (newshelle[2] == (shelle) NULL); /* Skip dead ones. */
3667 return newshelle;
3668 }
3669
3670 /*****************************************************************************/
3671 /* */
3672 /* pointdealloc() Deallocate space for a point, marking it dead. */
3673 /* */
3674 /*****************************************************************************/
3675
3676 void pointdealloc(dyingpoint)
3677 point dyingpoint;
3678 {
3679 /* Mark the point as dead. This makes it possible to detect dead points */
3680 /* when traversing the list of all points. */
3681 setpointmark(dyingpoint, DEADPOINT);
3682 pooldealloc(&points, (VOID *) dyingpoint);
3683 }
3684
3685 /*****************************************************************************/
3686 /* */
3687 /* pointtraverse() Traverse the points, skipping dead ones. */
3688 /* */
3689 /*****************************************************************************/
3690
3691 point pointtraverse()
3692 {
3693 point newpoint;
3694
3695 do {
3696 newpoint = (point) traverse(&points);
3697 if (newpoint == (point) NULL) {
3698 return (point) NULL;
3699 }
3700 } while (pointmark(newpoint) == DEADPOINT); /* Skip dead ones. */
3701 return newpoint;
3702 }
3703
3704 /*****************************************************************************/
3705 /* */
3706 /* badsegmentdealloc() Deallocate space for a bad segment, marking it */
3707 /* dead. */
3708 /* */
3709 /*****************************************************************************/
3710
3711 #ifndef CDT_ONLY
3712
3713 void badsegmentdealloc(dyingseg)
3714 struct edge *dyingseg;
3715 {
3716 /* Set segment's orientation to -1. This makes it possible to */
3717 /* detect dead segments when traversing the list of all segments. */
3718 dyingseg->shorient = -1;
3719 pooldealloc(&badsegments, (VOID *) dyingseg);
3720 }
3721
3722 #endif /* not CDT_ONLY */
3723
3724 /*****************************************************************************/
3725 /* */
3726 /* badsegmenttraverse() Traverse the bad segments, skipping dead ones. */
3727 /* */
3728 /*****************************************************************************/
3729
3730 #ifndef CDT_ONLY
3731
3732 struct edge *badsegmenttraverse()
3733 {
3734 struct edge *newseg;
3735
3736 do {
3737 newseg = (struct edge *) traverse(&badsegments);
3738 if (newseg == (struct edge *) NULL) {
3739 return (struct edge *) NULL;
3740 }
3741 } while (newseg->shorient == -1); /* Skip dead ones. */
3742 return newseg;
3743 }
3744
3745 #endif /* not CDT_ONLY */
3746
3747 /*****************************************************************************/
3748 /* */
3749 /* getpoint() Get a specific point, by number, from the list. */
3750 /* */
3751 /* The first point is number 'firstnumber'. */
3752 /* */
3753 /* Note that this takes O(n) time (with a small constant, if POINTPERBLOCK */
3754 /* is large). I don't care to take the trouble to make it work in constant */
3755 /* time. */
3756 /* */
3757 /*****************************************************************************/
3758
3759 point getpoint(number)
3760 int number;
3761 {
3762 VOID **getblock;
3763 point foundpoint;
3764 unsigned long alignptr;
3765 int current;
3766
3767 getblock = points.firstblock;
3768 current = firstnumber;
3769 /* Find the right block. */
3770 while (current + points.itemsperblock <= number) {
3771 getblock = (VOID **) *getblock;
3772 current += points.itemsperblock;
3773 }
3774 /* Now find the right point. */
3775 alignptr = (unsigned long) (getblock + 1);
3776 foundpoint = (point) (alignptr + (unsigned long) points.alignbytes
3777 - (alignptr % (unsigned long) points.alignbytes));
3778 while (current < number) {
3779 foundpoint += points.itemwords;
3780 current++;
3781 }
3782 return foundpoint;
3783 }
3784
3785 /*****************************************************************************/
3786 /* */
3787 /* triangledeinit() Free all remaining allocated memory. */
3788 /* */
3789 /*****************************************************************************/
3790
3791 void triangledeinit()
3792 {
3793 pooldeinit(&triangles);
3794 free(dummytribase);
3795 if (useshelles) {
3796 pooldeinit(&shelles);
3797 free(dummyshbase);
3798 }
3799 pooldeinit(&points);
3800 #ifndef CDT_ONLY
3801 if (quality) {
3802 pooldeinit(&badsegments);
3803 if ((minangle > 0.0) || vararea || fixedarea) {
3804 pooldeinit(&badtriangles);
3805 }
3806 }
3807 #endif /* not CDT_ONLY */
3808 }
3809
3810 /** **/
3811 /** **/
3812 /********* Memory management routines end here *********/
3813
3814 /********* Constructors begin here *********/
3815 /** **/
3816 /** **/
3817
3818 /*****************************************************************************/
3819 /* */
3820 /* maketriangle() Create a new triangle with orientation zero. */
3821 /* */
3822 /*****************************************************************************/
3823
3824 void maketriangle(newtriedge)
3825 struct triedge *newtriedge;
3826 {
3827 int i;
3828
3829 newtriedge->tri = (triangle *) poolalloc(&triangles);
3830 /* Initialize the three adjoining triangles to be "outer space". */
3831 newtriedge->tri[0] = (triangle) dummytri;
3832 newtriedge->tri[1] = (triangle) dummytri;
3833 newtriedge->tri[2] = (triangle) dummytri;
3834 /* Three NULL vertex points. */
3835 newtriedge->tri[3] = (triangle) NULL;
3836 newtriedge->tri[4] = (triangle) NULL;
3837 newtriedge->tri[5] = (triangle) NULL;
3838 /* Initialize the three adjoining shell edges to be the omnipresent */
3839 /* shell edge. */
3840 if (useshelles) {
3841 newtriedge->tri[6] = (triangle) dummysh;
3842 newtriedge->tri[7] = (triangle) dummysh;
3843 newtriedge->tri[8] = (triangle) dummysh;
3844 }
3845 for (i = 0; i < eextras; i++) {
3846 setelemattribute(*newtriedge, i, 0.0);
3847 }
3848 if (vararea) {
3849 setareabound(*newtriedge, -1.0);
3850 }
3851
3852 newtriedge->orient = 0;
3853 }
3854
3855 /*****************************************************************************/
3856 /* */
3857 /* makeshelle() Create a new shell edge with orientation zero. */
3858 /* */
3859 /*****************************************************************************/
3860
3861 void makeshelle(newedge)
3862 struct edge *newedge;
3863 {
3864 newedge->sh = (shelle *) poolalloc(&shelles);
3865 /* Initialize the two adjoining shell edges to be the omnipresent */
3866 /* shell edge. */
3867 newedge->sh[0] = (shelle) dummysh;
3868 newedge->sh[1] = (shelle) dummysh;
3869 /* Two NULL vertex points. */
3870 newedge->sh[2] = (shelle) NULL;
3871 newedge->sh[3] = (shelle) NULL;
3872 /* Initialize the two adjoining triangles to be "outer space". */
3873 newedge->sh[4] = (shelle) dummytri;
3874 newedge->sh[5] = (shelle) dummytri;
3875 /* Set the boundary marker to zero. */
3876 setmark(*newedge, 0);
3877
3878 newedge->shorient = 0;
3879 }
3880
3881 /** **/
3882 /** **/
3883 /********* Constructors end here *********/
3884
3885 /********* Determinant evaluation routines begin here *********/
3886 /** **/
3887 /** **/
3888
3889 /* The adaptive exact arithmetic geometric predicates implemented herein are */
3890 /* described in detail in my Technical Report CMU-CS-96-140. The complete */
3891 /* reference is given in the header. */
3892
3893 /* Which of the following two methods of finding the absolute values is */
3894 /* fastest is compiler-dependent. A few compilers can inline and optimize */
3895 /* the fabs() call; but most will incur the overhead of a function call, */
3896 /* which is disastrously slow. A faster way on IEEE machines might be to */
3897 /* mask the appropriate bit, but that's difficult to do in C. */
3898
3899 #define Absolute(a) ((a) >= 0.0 ? (a) : -(a))
3900 /* #define Absolute(a) fabs(a) */
3901
3902 /* Many of the operations are broken up into two pieces, a main part that */
3903 /* performs an approximate operation, and a "tail" that computes the */
3904 /* roundoff error of that operation. */
3905 /* */
3906 /* The operations Fast_Two_Sum(), Fast_Two_Diff(), Two_Sum(), Two_Diff(), */
3907 /* Split(), and Two_Product() are all implemented as described in the */
3908 /* reference. Each of these macros requires certain variables to be */
3909 /* defined in the calling routine. The variables `bvirt', `c', `abig', */
3910 /* `_i', `_j', `_k', `_l', `_m', and `_n' are declared `INEXACT' because */
3911 /* they store the result of an operation that may incur roundoff error. */
3912 /* The input parameter `x' (or the highest numbered `x_' parameter) must */
3913 /* also be declared `INEXACT'. */
3914
3915 #define Fast_Two_Sum_Tail(a, b, x, y) \
3916 bvirt = x - a; \
3917 y = b - bvirt
3918
3919 #define Fast_Two_Sum(a, b, x, y) \
3920 x = (REAL) (a + b); \
3921 Fast_Two_Sum_Tail(a, b, x, y)
3922
3923 #define Two_Sum_Tail(a, b, x, y) \
3924 bvirt = (REAL) (x - a); \
3925 avirt = x - bvirt; \
3926 bround = b - bvirt; \
3927 around = a - avirt; \
3928 y = around + bround
3929
3930 #define Two_Sum(a, b, x, y) \
3931 x = (REAL) (a + b); \
3932 Two_Sum_Tail(a, b, x, y)
3933
3934 #define Two_Diff_Tail(a, b, x, y) \
3935 bvirt = (REAL) (a - x); \
3936 avirt = x + bvirt; \
3937 bround = bvirt - b; \
3938 around = a - avirt; \
3939 y = around + bround
3940
3941 #define Two_Diff(a, b, x, y) \
3942 x = (REAL) (a - b); \
3943 Two_Diff_Tail(a, b, x, y)
3944
3945 #define Split(a, ahi, alo) \
3946 c = (REAL) (splitter * a); \
3947 abig = (REAL) (c - a); \
3948 ahi = c - abig; \
3949 alo = a - ahi
3950
3951 #define Two_Product_Tail(a, b, x, y) \
3952 Split(a, ahi, alo); \
3953 Split(b, bhi, blo); \
3954 err1 = x - (ahi * bhi); \
3955 err2 = err1 - (alo * bhi); \
3956 err3 = err2 - (ahi * blo); \
3957 y = (alo * blo) - err3
3958
3959 #define Two_Product(a, b, x, y) \
3960 x = (REAL) (a * b); \
3961 Two_Product_Tail(a, b, x, y)
3962
3963 /* Two_Product_Presplit() is Two_Product() where one of the inputs has */
3964 /* already been split. Avoids redundant splitting. */
3965
3966 #define Two_Product_Presplit(a, b, bhi, blo, x, y) \
3967 x = (REAL) (a * b); \
3968 Split(a, ahi, alo); \
3969 err1 = x - (ahi * bhi); \
3970 err2 = err1 - (alo * bhi); \
3971 err3 = err2 - (ahi * blo); \
3972 y = (alo * blo) - err3
3973
3974 /* Square() can be done more quickly than Two_Product(). */
3975
3976 #define Square_Tail(a, x, y) \
3977 Split(a, ahi, alo); \
3978 err1 = x - (ahi * ahi); \
3979 err3 = err1 - ((ahi + ahi) * alo); \
3980 y = (alo * alo) - err3
3981
3982 #define Square(a, x, y) \
3983 x = (REAL) (a * a); \
3984 Square_Tail(a, x, y)
3985
3986 /* Macros for summing expansions of various fixed lengths. These are all */
3987 /* unrolled versions of Expansion_Sum(). */
3988
3989 #define Two_One_Sum(a1, a0, b, x2, x1, x0) \
3990 Two_Sum(a0, b , _i, x0); \
3991 Two_Sum(a1, _i, x2, x1)
3992
3993 #define Two_One_Diff(a1, a0, b, x2, x1, x0) \
3994 Two_Diff(a0, b , _i, x0); \
3995 Two_Sum( a1, _i, x2, x1)
3996
3997 #define Two_Two_Sum(a1, a0, b1, b0, x3, x2, x1, x0) \
3998