triangle.cpp

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00001 
00008 /*****************************************************************************/
00009 /*                                                                           */
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00012 /*         888    888    888       88b 888  888 888 888 888 d888  88b        */
00013 /*         888    888    888  o88^o888 888  888 "88888" 888 8888oo888        */
00014 /*         888    888    888 C888  888 888  888  /      888 q888             */
00015 /*         888    888    888  "88o^888 888  888 Cb      888  "88oooo"        */
00016 /*                                              "8oo8D                       */
00017 /*                                                                           */
00018 /*  A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator.      */
00019 /*  (triangle.c)                                                             */
00020 /*                                                                           */
00021 /*  Version 1.6                                                              */
00022 /*  July 28, 2005                                                            */
00023 /*                                                                           */
00024 /*  Copyright 1993, 1995, 1997, 1998, 2002, 2005                             */
00025 /*  Jonathan Richard Shewchuk                                                */
00026 /*  2360 Woolsey #H                                                          */
00027 /*  Berkeley, California  94705-1927                                         */
00028 /*  jrs@cs.berkeley.edu                                                      */
00029 /*                                                                           */
00030 /*  This program may be freely redistributed under the condition that the    */
00031 /*    copyright notices (including this entire header and the copyright      */
00032 /*    notice printed when the `-h' switch is selected) are not removed, and  */
00033 /*    no compensation is received.  Private, research, and institutional     */
00034 /*    use is free.  You may distribute modified versions of this code UNDER  */
00035 /*    THE CONDITION THAT THIS CODE AND ANY MODIFICATIONS MADE TO IT IN THE   */
00036 /*    SAME FILE REMAIN UNDER COPYRIGHT OF THE ORIGINAL AUTHOR, BOTH SOURCE   */
00037 /*    AND OBJECT CODE ARE MADE FREELY AVAILABLE WITHOUT CHARGE, AND CLEAR    */
00038 /*    NOTICE IS GIVEN OF THE MODIFICATIONS.  Distribution of this code as    */
00039 /*    part of a commercial system is permissible ONLY BY DIRECT ARRANGEMENT  */
00040 /*    WITH THE AUTHOR.  (If you are not directly supplying this code to a    */
00041 /*    customer, and you are instead telling them how they can obtain it for  */
00042 /*    free, then you are not required to make any arrangement with me.)      */
00043 /*                                                                           */
00044 /*  Hypertext instructions for Triangle are available on the Web at          */
00045 /*                                                                           */
00046 /*      http://www.cs.cmu.edu/~quake/triangle.html                           */
00047 /*                                                                           */
00048 /*  Disclaimer:  Neither I nor Carnegie Mellon warrant this code in any way  */
00049 /*    whatsoever.  This code is provided "as-is".  Use at your own risk.     */
00050 /*                                                                           */
00051 /*  Some of the references listed below are marked with an asterisk.  [*]    */
00052 /*    These references are available for downloading from the Web page       */
00053 /*                                                                           */
00054 /*      http://www.cs.cmu.edu/~quake/triangle.research.html                  */
00055 /*                                                                           */
00056 /*  Three papers discussing aspects of Triangle are available.  A short      */
00057 /*    overview appears in "Triangle:  Engineering a 2D Quality Mesh          */
00058 /*    Generator and Delaunay Triangulator," in Applied Computational         */
00059 /*    Geometry:  Towards Geometric Engineering, Ming C. Lin and Dinesh       */
00060 /*    Manocha, editors, Lecture Notes in Computer Science volume 1148,       */
00061 /*    pages 203-222, Springer-Verlag, Berlin, May 1996 (from the First ACM   */
00062 /*    Workshop on Applied Computational Geometry).  [*]                      */
00063 /*                                                                           */
00064 /*    The algorithms are discussed in the greatest detail in "Delaunay       */
00065 /*    Refinement Algorithms for Triangular Mesh Generation," Computational   */
00066 /*    Geometry:  Theory and Applications 22(1-3):21-74, May 2002.  [*]       */
00067 /*                                                                           */
00068 /*    More detail about the data structures may be found in my dissertation: */
00069 /*    "Delaunay Refinement Mesh Generation," Ph.D. thesis, Technical Report  */
00070 /*    CMU-CS-97-137, School of Computer Science, Carnegie Mellon University, */
00071 /*    Pittsburgh, Pennsylvania, 18 May 1997.  [*]                            */
00072 /*                                                                           */
00073 /*  Triangle was created as part of the Quake Project in the School of       */
00074 /*    Computer Science at Carnegie Mellon University.  For further           */
00075 /*    information, see Hesheng Bao, Jacobo Bielak, Omar Ghattas, Loukas F.   */
00076 /*    Kallivokas, David R. O'Hallaron, Jonathan R. Shewchuk, and Jifeng Xu,  */
00077 /*    "Large-scale Simulation of Elastic Wave Propagation in Heterogeneous   */
00078 /*    Media on Parallel Computers," Computer Methods in Applied Mechanics    */
00079 /*    and Engineering 152(1-2):85-102, 22 January 1998.                      */
00080 /*                                                                           */
00081 /*  Triangle's Delaunay refinement algorithm for quality mesh generation is  */
00082 /*    a hybrid of one due to Jim Ruppert, "A Delaunay Refinement Algorithm   */
00083 /*    for Quality 2-Dimensional Mesh Generation," Journal of Algorithms      */
00084 /*    18(3):548-585, May 1995 [*], and one due to L. Paul Chew, "Guaranteed- */
00085 /*    Quality Mesh Generation for Curved Surfaces," Proceedings of the Ninth */
00086 /*    Annual Symposium on Computational Geometry (San Diego, California),    */
00087 /*    pages 274-280, Association for Computing Machinery, May 1993,          */
00088 /*    http://portal.acm.org/citation.cfm?id=161150 .                         */
00089 /*                                                                           */
00090 /*  The Delaunay refinement algorithm has been modified so that it meshes    */
00091 /*    domains with small input angles well, as described in Gary L. Miller,  */
00092 /*    Steven E. Pav, and Noel J. Walkington, "When and Why Ruppert's         */
00093 /*    Algorithm Works," Twelfth International Meshing Roundtable, pages      */
00094 /*    91-102, Sandia National Laboratories, September 2003.  [*]             */
00095 /*                                                                           */
00096 /*  My implementation of the divide-and-conquer and incremental Delaunay     */
00097 /*    triangulation algorithms follows closely the presentation of Guibas    */
00098 /*    and Stolfi, even though I use a triangle-based data structure instead  */
00099 /*    of their quad-edge data structure.  (In fact, I originally implemented */
00100 /*    Triangle using the quad-edge data structure, but the switch to a       */
00101 /*    triangle-based data structure sped Triangle by a factor of two.)  The  */
00102 /*    mesh manipulation primitives and the two aforementioned Delaunay       */
00103 /*    triangulation algorithms are described by Leonidas J. Guibas and Jorge */
00104 /*    Stolfi, "Primitives for the Manipulation of General Subdivisions and   */
00105 /*    the Computation of Voronoi Diagrams," ACM Transactions on Graphics     */
00106 /*    4(2):74-123, April 1985, http://portal.acm.org/citation.cfm?id=282923 .*/
00107 /*                                                                           */
00108 /*  Their O(n log n) divide-and-conquer algorithm is adapted from Der-Tsai   */
00109 /*    Lee and Bruce J. Schachter, "Two Algorithms for Constructing the       */
00110 /*    Delaunay Triangulation," International Journal of Computer and         */
00111 /*    Information Science 9(3):219-242, 1980.  Triangle's improvement of the */
00112 /*    divide-and-conquer algorithm by alternating between vertical and       */
00113 /*    horizontal cuts was introduced by Rex A. Dwyer, "A Faster Divide-and-  */
00114 /*    Conquer Algorithm for Constructing Delaunay Triangulations,"           */
00115 /*    Algorithmica 2(2):137-151, 1987.                                       */
00116 /*                                                                           */
00117 /*  The incremental insertion algorithm was first proposed by C. L. Lawson,  */
00118 /*    "Software for C1 Surface Interpolation," in Mathematical Software III, */
00119 /*    John R. Rice, editor, Academic Press, New York, pp. 161-194, 1977.     */
00120 /*    For point location, I use the algorithm of Ernst P. Mucke, Isaac       */
00121 /*    Saias, and Binhai Zhu, "Fast Randomized Point Location Without         */
00122 /*    Preprocessing in Two- and Three-Dimensional Delaunay Triangulations,"  */
00123 /*    Proceedings of the Twelfth Annual Symposium on Computational Geometry, */
00124 /*    ACM, May 1996.  [*]  If I were to randomize the order of vertex        */
00125 /*    insertion (I currently don't bother), their result combined with the   */
00126 /*    result of Kenneth L. Clarkson and Peter W. Shor, "Applications of      */
00127 /*    Random Sampling in Computational Geometry II," Discrete &              */
00128 /*    Computational Geometry 4(1):387-421, 1989, would yield an expected     */
00129 /*    O(n^{4/3}) bound on running time.                                      */
00130 /*                                                                           */
00131 /*  The O(n log n) sweepline Delaunay triangulation algorithm is taken from  */
00132 /*    Steven Fortune, "A Sweepline Algorithm for Voronoi Diagrams",          */
00133 /*    Algorithmica 2(2):153-174, 1987.  A random sample of edges on the      */
00134 /*    boundary of the triangulation are maintained in a splay tree for the   */
00135 /*    purpose of point location.  Splay trees are described by Daniel        */
00136 /*    Dominic Sleator and Robert Endre Tarjan, "Self-Adjusting Binary Search */
00137 /*    Trees," Journal of the ACM 32(3):652-686, July 1985,                   */
00138 /*    http://portal.acm.org/citation.cfm?id=3835 .                           */
00139 /*                                                                           */
00140 /*  The algorithms for exact computation of the signs of determinants are    */
00141 /*    described in Jonathan Richard Shewchuk, "Adaptive Precision Floating-  */
00142 /*    Point Arithmetic and Fast Robust Geometric Predicates," Discrete &     */
00143 /*    Computational Geometry 18(3):305-363, October 1997.  (Also available   */
00144 /*    as Technical Report CMU-CS-96-140, School of Computer Science,         */
00145 /*    Carnegie Mellon University, Pittsburgh, Pennsylvania, May 1996.)  [*]  */
00146 /*    An abbreviated version appears as Jonathan Richard Shewchuk, "Robust   */
00147 /*    Adaptive Floating-Point Geometric Predicates," Proceedings of the      */
00148 /*    Twelfth Annual Symposium on Computational Geometry, ACM, May 1996. [*] */
00149 /*    Many of the ideas for my exact arithmetic routines originate with      */
00150 /*    Douglas M. Priest, "Algorithms for Arbitrary Precision Floating Point  */
00151 /*    Arithmetic," Tenth Symposium on Computer Arithmetic, pp. 132-143, IEEE */
00152 /*    Computer Society Press, 1991.  [*]  Many of the ideas for the correct  */
00153 /*    evaluation of the signs of determinants are taken from Steven Fortune  */
00154 /*    and Christopher J. Van Wyk, "Efficient Exact Arithmetic for Computa-   */
00155 /*    tional Geometry," Proceedings of the Ninth Annual Symposium on         */
00156 /*    Computational Geometry, ACM, pp. 163-172, May 1993, and from Steven    */
00157 /*    Fortune, "Numerical Stability of Algorithms for 2D Delaunay Triangu-   */
00158 /*    lations," International Journal of Computational Geometry & Applica-   */
00159 /*    tions 5(1-2):193-213, March-June 1995.                                 */
00160 /*                                                                           */
00161 /*  The method of inserting new vertices off-center (not precisely at the    */
00162 /*    circumcenter of every poor-quality triangle) is from Alper Ungor,      */
00163 /*    "Off-centers:  A New Type of Steiner Points for Computing Size-Optimal */
00164 /*    Quality-Guaranteed Delaunay Triangulations," Proceedings of LATIN      */
00165 /*    2004 (Buenos Aires, Argentina), April 2004.                            */
00166 /*                                                                           */
00167 /*  For definitions of and results involving Delaunay triangulations,        */
00168 /*    constrained and conforming versions thereof, and other aspects of      */
00169 /*    triangular mesh generation, see the excellent survey by Marshall Bern  */
00170 /*    and David Eppstein, "Mesh Generation and Optimal Triangulation," in    */
00171 /*    Computing and Euclidean Geometry, Ding-Zhu Du and Frank Hwang,         */
00172 /*    editors, World Scientific, Singapore, pp. 23-90, 1992.  [*]            */
00173 /*                                                                           */
00174 /*  The time for incrementally adding PSLG (planar straight line graph)      */
00175 /*    segments to create a constrained Delaunay triangulation is probably    */
00176 /*    O(t^2) per segment in the worst case and O(t) per segment in the       */
00177 /*    common case, where t is the number of triangles that intersect the     */
00178 /*    segment before it is inserted.  This doesn't count point location,     */
00179 /*    which can be much more expensive.  I could improve this to O(d log d)  */
00180 /*    time, but d is usually quite small, so it's not worth the bother.      */
00181 /*    (This note does not apply when the -s switch is used, invoking a       */
00182 /*    different method is used to insert segments.)                          */
00183 /*                                                                           */
00184 /*  The time for deleting a vertex from a Delaunay triangulation is O(d^2)   */
00185 /*    in the worst case and O(d) in the common case, where d is the degree   */
00186 /*    of the vertex being deleted.  I could improve this to O(d log d) time, */
00187 /*    but d is usually quite small, so it's not worth the bother.            */
00188 /*                                                                           */
00189 /*  Ruppert's Delaunay refinement algorithm typically generates triangles    */
00190 /*    at a linear rate (constant time per triangle) after the initial        */
00191 /*    triangulation is formed.  There may be pathological cases where        */
00192 /*    quadratic time is required, but these never arise in practice.         */
00193 /*                                                                           */
00194 /*  The geometric predicates (circumcenter calculations, segment             */
00195 /*    intersection formulae, etc.) appear in my "Lecture Notes on Geometric  */
00196 /*    Robustness" at http://www.cs.berkeley.edu/~jrs/mesh .                  */
00197 /*                                                                           */
00198 /*  If you make any improvements to this code, please please please let me   */
00199 /*    know, so that I may obtain the improvements.  Even if you don't change */
00200 /*    the code, I'd still love to hear what it's being used for.             */
00201 /*                                                                           */
00202 /*****************************************************************************/
00203 
00204 /* For single precision (which will save some memory and reduce paging),     */
00205 /*   define the symbol SINGLE by using the -DSINGLE compiler switch or by    */
00206 /*   writing "#define SINGLE" below.                                         */
00207 /*                                                                           */
00208 /* For double precision (which will allow you to refine meshes to a smaller  */
00209 /*   edge length), leave SINGLE undefined.                                   */
00210 /*                                                                           */
00211 /* Double precision uses more memory, but improves the resolution of the     */
00212 /*   meshes you can generate with Triangle.  It also reduces the likelihood  */
00213 /*   of a floating exception due to overflow.  Finally, it is much faster    */
00214 /*   than single precision on 64-bit architectures like the DEC Alpha.  I    */
00215 /*   recommend double precision unless you want to generate a mesh for which */
00216 /*   you do not have enough memory.                                          */
00217 
00218 /* #define SINGLE */
00219 
00220 #ifdef SINGLE
00221 #define REAL float
00222 #else /* not SINGLE */
00223 #define REAL double
00224 #endif /* not SINGLE */
00225 
00226 /* If yours is not a Unix system, define the NO_TIMER compiler switch to     */
00227 /*   remove the Unix-specific timing code.                                   */
00228 
00229 /* #define NO_TIMER */
00230 
00231 /* To insert lots of self-checks for internal errors, define the SELF_CHECK  */
00232 /*   symbol.  This will slow down the program significantly.  It is best to  */
00233 /*   define the symbol using the -DSELF_CHECK compiler switch, but you could */
00234 /*   write "#define SELF_CHECK" below.  If you are modifying this code, I    */
00235 /*   recommend you turn self-checks on until your work is debugged.          */
00236 
00237 /* #define SELF_CHECK */
00238 
00239 /* To compile Triangle as a callable object library (triangle.o), define the */
00240 /*   TRILIBRARY symbol.  Read the file triangle.h for details on how to call */
00241 /*   the procedure triangulate() that results.                               */
00242 
00243 /* #define TRILIBRARY */
00244 
00245 /* It is possible to generate a smaller version of Triangle using one or     */
00246 /*   both of the following symbols.  Define the REDUCED symbol to eliminate  */
00247 /*   all features that are primarily of research interest; specifically, the */
00248 /*   -i, -F, -s, and -C switches.  Define the CDT_ONLY symbol to eliminate   */
00249 /*   all meshing algorithms above and beyond constrained Delaunay            */
00250 /*   triangulation; specifically, the -r, -q, -a, -u, -D, -S, and -s         */
00251 /*   switches.  These reductions are most likely to be useful when           */
00252 /*   generating an object library (triangle.o) by defining the TRILIBRARY    */
00253 /*   symbol.                                                                 */
00254 
00255 /* #define REDUCED */
00256 /* #define CDT_ONLY */
00257 
00258 /* On some machines, my exact arithmetic routines might be defeated by the   */
00259 /*   use of internal extended precision floating-point registers.  The best  */
00260 /*   way to solve this problem is to set the floating-point registers to use */
00261 /*   single or double precision internally.  On 80x86 processors, this may   */
00262 /*   be accomplished by setting the CPU86 symbol for the Microsoft C         */
00263 /*   compiler, or the LINUX symbol for the gcc compiler running on Linux.    */
00264 /*                                                                           */
00265 /* An inferior solution is to declare certain values as `volatile', thus     */
00266 /*   forcing them to be stored to memory and rounded off.  Unfortunately,    */
00267 /*   this solution might slow Triangle down quite a bit.  To use volatile    */
00268 /*   values, write "#define INEXACT volatile" below.  Normally, however,     */
00269 /*   INEXACT should be defined to be nothing.  ("#define INEXACT".)          */
00270 /*                                                                           */
00271 /* For more discussion, see http://www.cs.cmu.edu/~quake/robust.pc.html .    */
00272 /*   For yet more discussion, see Section 5 of my paper, "Adaptive Precision */
00273 /*   Floating-Point Arithmetic and Fast Robust Geometric Predicates" (also   */
00274 /*   available as Section 6.6 of my dissertation).                           */
00275 
00276 /* #define CPU86 */
00277 /* #define LINUX */
00278 
00279 #define INEXACT /* Nothing */
00280 /* #define INEXACT volatile */
00281 
00282 /* Maximum number of characters in a file name (including the null).         */
00283 
00284 #define FILENAMESIZE 2048
00285 
00286 /* Maximum number of characters in a line read from a file (including the    */
00287 /*   null).                                                                  */
00288 
00289 #define INPUTLINESIZE 1024
00290 
00291 /* For efficiency, a variety of data structures are allocated in bulk.  The  */
00292 /*   following constants determine how many of each structure is allocated   */
00293 /*   at once.                                                                */
00294 
00295 #define TRIPERBLOCK 4092           /* Number of triangles allocated at once. */
00296 #define SUBSEGPERBLOCK 508       /* Number of subsegments allocated at once. */
00297 #define VERTEXPERBLOCK 4092         /* Number of vertices allocated at once. */
00298 #define VIRUSPERBLOCK 1020   /* Number of virus triangles allocated at once. */
00299 /* Number of encroached subsegments allocated at once. */
00300 #define BADSUBSEGPERBLOCK 252
00301 /* Number of skinny triangles allocated at once. */
00302 #define BADTRIPERBLOCK 4092
00303 /* Number of flipped triangles allocated at once. */
00304 #define FLIPSTACKERPERBLOCK 252
00305 /* Number of splay tree nodes allocated at once. */
00306 #define SPLAYNODEPERBLOCK 508
00307 
00308 /* The vertex types.   A DEADVERTEX has been deleted entirely.  An           */
00309 /*   UNDEADVERTEX is not part of the mesh, but is written to the output      */
00310 /*   .node file and affects the node indexing in the other output files.     */
00311 
00312 #define INPUTVERTEX 0
00313 #define SEGMENTVERTEX 1
00314 #define FREEVERTEX 2
00315 #define DEADVERTEX -32768
00316 #define UNDEADVERTEX -32767
00317 
00318 /* The next line is used to outsmart some very stupid compilers.  If your    */
00319 /*   compiler is smarter, feel free to replace the "int" with "void".        */
00320 /*   Not that it matters.                                                    */
00321 
00322 #define VOID int
00323 
00324 /* Two constants for algorithms based on random sampling.  Both constants    */
00325 /*   have been chosen empirically to optimize their respective algorithms.   */
00326 
00327 /* Used for the point location scheme of Mucke, Saias, and Zhu, to decide    */
00328 /*   how large a random sample of triangles to inspect.                      */
00329 
00330 #define SAMPLEFACTOR 11
00331 
00332 /* Used in Fortune's sweepline Delaunay algorithm to determine what fraction */
00333 /*   of boundary edges should be maintained in the splay tree for point      */
00334 /*   location on the front.                                                  */
00335 
00336 #define SAMPLERATE 10
00337 
00338 /* A number that speaks for itself, every kissable digit.                    */
00339 
00340 #define PI 3.141592653589793238462643383279502884197169399375105820974944592308
00341 
00342 /* Another fave.                                                             */
00343 
00344 #define SQUAREROOTTWO 1.4142135623730950488016887242096980785696718753769480732
00345 
00346 /* And here's one for those of you who are intimidated by math.              */
00347 
00348 #define ONETHIRD 0.333333333333333333333333333333333333333333333333333333333333
00349 
00350 #include <stdio.h>
00351 #include <stdlib.h>
00352 #include <string.h>
00353 #include <math.h>
00354 #ifndef NO_TIMER
00355 #include <sys/time.h>
00356 #endif /* not NO_TIMER */
00357 #ifdef CPU86
00358 #include <float.h>
00359 #endif /* CPU86 */
00360 #ifdef LINUX
00361 #include <fpu_control.h>
00362 #endif /* LINUX */
00363 #ifdef TRILIBRARY
00364 #include "triangle.h"
00365 #endif /* TRILIBRARY */
00366 
00367 /* A few forward declarations.                                               */
00368 
00369 #ifndef TRILIBRARY
00370 char *readline();
00371 char *findfield();
00372 #endif /* not TRILIBRARY */
00373 
00374 /* Labels that signify the result of point location.  The result of a        */
00375 /*   search indicates that the point falls in the interior of a triangle, on */
00376 /*   an edge, on a vertex, or outside the mesh.                              */
00377 
00378 enum locateresult {INTRIANGLE, ONEDGE, ONVERTEX, OUTSIDE};
00379 
00380 /* Labels that signify the result of vertex insertion.  The result indicates */
00381 /*   that the vertex was inserted with complete success, was inserted but    */
00382 /*   encroaches upon a subsegment, was not inserted because it lies on a     */
00383 /*   segment, or was not inserted because another vertex occupies the same   */
00384 /*   location.                                                               */
00385 
00386 enum insertvertexresult {SUCCESSFULVERTEX, ENCROACHINGVERTEX, VIOLATINGVERTEX,
00387                          DUPLICATEVERTEX};
00388 
00389 /* Labels that signify the result of direction finding.  The result          */
00390 /*   indicates that a segment connecting the two query points falls within   */
00391 /*   the direction triangle, along the left edge of the direction triangle,  */
00392 /*   or along the right edge of the direction triangle.                      */
00393 
00394 enum finddirectionresult {WITHIN, LEFTCOLLINEAR, RIGHTCOLLINEAR};
00395 
00396 /*****************************************************************************/
00397 /*                                                                           */
00398 /*  The basic mesh data structures                                           */
00399 /*                                                                           */
00400 /*  There are three:  vertices, triangles, and subsegments (abbreviated      */
00401 /*  `subseg').  These three data structures, linked by pointers, comprise    */
00402 /*  the mesh.  A vertex simply represents a mesh vertex and its properties.  */
00403 /*  A triangle is a triangle.  A subsegment is a special data structure used */
00404 /*  to represent an impenetrable edge of the mesh (perhaps on the outer      */
00405 /*  boundary, on the boundary of a hole, or part of an internal boundary     */
00406 /*  separating two triangulated regions).  Subsegments represent boundaries, */
00407 /*  defined by the user, that triangles may not lie across.                  */
00408 /*                                                                           */
00409 /*  A triangle consists of a list of three vertices, a list of three         */
00410 /*  adjoining triangles, a list of three adjoining subsegments (when         */
00411 /*  segments exist), an arbitrary number of optional user-defined            */
00412 /*  floating-point attributes, and an optional area constraint.  The latter  */
00413 /*  is an upper bound on the permissible area of each triangle in a region,  */
00414 /*  used for mesh refinement.                                                */
00415 /*                                                                           */
00416 /*  For a triangle on a boundary of the mesh, some or all of the neighboring */
00417 /*  triangles may not be present.  For a triangle in the interior of the     */
00418 /*  mesh, often no neighboring subsegments are present.  Such absent         */
00419 /*  triangles and subsegments are never represented by NULL pointers; they   */
00420 /*  are represented by two special records:  `dummytri', the triangle that   */
00421 /*  fills "outer space", and `dummysub', the omnipresent subsegment.         */
00422 /*  `dummytri' and `dummysub' are used for several reasons; for instance,    */
00423 /*  they can be dereferenced and their contents examined without violating   */
00424 /*  protected memory.                                                        */
00425 /*                                                                           */
00426 /*  However, it is important to understand that a triangle includes other    */
00427 /*  information as well.  The pointers to adjoining vertices, triangles, and */
00428 /*  subsegments are ordered in a way that indicates their geometric relation */
00429 /*  to each other.  Furthermore, each of these pointers contains orientation */
00430 /*  information.  Each pointer to an adjoining triangle indicates which face */
00431 /*  of that triangle is contacted.  Similarly, each pointer to an adjoining  */
00432 /*  subsegment indicates which side of that subsegment is contacted, and how */
00433 /*  the subsegment is oriented relative to the triangle.                     */
00434 /*                                                                           */
00435 /*  The data structure representing a subsegment may be thought to be        */
00436 /*  abutting the edge of one or two triangle data structures:  either        */
00437 /*  sandwiched between two triangles, or resting against one triangle on an  */
00438 /*  exterior boundary or hole boundary.                                      */
00439 /*                                                                           */
00440 /*  A subsegment consists of a list of four vertices--the vertices of the    */
00441 /*  subsegment, and the vertices of the segment it is a part of--a list of   */
00442 /*  two adjoining subsegments, and a list of two adjoining triangles.  One   */
00443 /*  of the two adjoining triangles may not be present (though there should   */
00444 /*  always be one), and neighboring subsegments might not be present.        */
00445 /*  Subsegments also store a user-defined integer "boundary marker".         */
00446 /*  Typically, this integer is used to indicate what boundary conditions are */
00447 /*  to be applied at that location in a finite element simulation.           */
00448 /*                                                                           */
00449 /*  Like triangles, subsegments maintain information about the relative      */
00450 /*  orientation of neighboring objects.                                      */
00451 /*                                                                           */
00452 /*  Vertices are relatively simple.  A vertex is a list of floating-point    */
00453 /*  numbers, starting with the x, and y coordinates, followed by an          */
00454 /*  arbitrary number of optional user-defined floating-point attributes,     */
00455 /*  followed by an integer boundary marker.  During the segment insertion    */
00456 /*  phase, there is also a pointer from each vertex to a triangle that may   */
00457 /*  contain it.  Each pointer is not always correct, but when one is, it     */
00458 /*  speeds up segment insertion.  These pointers are assigned values once    */
00459 /*  at the beginning of the segment insertion phase, and are not used or     */
00460 /*  updated except during this phase.  Edge flipping during segment          */
00461 /*  insertion will render some of them incorrect.  Hence, don't rely upon    */
00462 /*  them for anything.                                                       */
00463 /*                                                                           */
00464 /*  Other than the exception mentioned above, vertices have no information   */
00465 /*  about what triangles, subfacets, or subsegments they are linked to.      */
00466 /*                                                                           */
00467 /*****************************************************************************/
00468 
00469 /*****************************************************************************/
00470 /*                                                                           */
00471 /*  Handles                                                                  */
00472 /*                                                                           */
00473 /*  The oriented triangle (`otri') and oriented subsegment (`osub') data     */
00474 /*  structures defined below do not themselves store any part of the mesh.   */
00475 /*  The mesh itself is made of `triangle's, `subseg's, and `vertex's.        */
00476 /*                                                                           */
00477 /*  Oriented triangles and oriented subsegments will usually be referred to  */
00478 /*  as "handles."  A handle is essentially a pointer into the mesh; it       */
00479 /*  allows you to "hold" one particular part of the mesh.  Handles are used  */
00480 /*  to specify the regions in which one is traversing and modifying the mesh.*/
00481 /*  A single `triangle' may be held by many handles, or none at all.  (The   */
00482 /*  latter case is not a memory leak, because the triangle is still          */
00483 /*  connected to other triangles in the mesh.)                               */
00484 /*                                                                           */
00485 /*  An `otri' is a handle that holds a triangle.  It holds a specific edge   */
00486 /*  of the triangle.  An `osub' is a handle that holds a subsegment.  It     */
00487 /*  holds either the left or right side of the subsegment.                   */
00488 /*                                                                           */
00489 /*  Navigation about the mesh is accomplished through a set of mesh          */
00490 /*  manipulation primitives, further below.  Many of these primitives take   */
00491 /*  a handle and produce a new handle that holds the mesh near the first     */
00492 /*  handle.  Other primitives take two handles and glue the corresponding    */
00493 /*  parts of the mesh together.  The orientation of the handles is           */
00494 /*  important.  For instance, when two triangles are glued together by the   */
00495 /*  bond() primitive, they are glued at the edges on which the handles lie.  */
00496 /*                                                                           */
00497 /*  Because vertices have no information about which triangles they are      */
00498 /*  attached to, I commonly represent a vertex by use of a handle whose      */
00499 /*  origin is the vertex.  A single handle can simultaneously represent a    */
00500 /*  triangle, an edge, and a vertex.                                         */
00501 /*                                                                           */
00502 /*****************************************************************************/
00503 
00504 /* The triangle data structure.  Each triangle contains three pointers to    */
00505 /*   adjoining triangles, plus three pointers to vertices, plus three        */
00506 /*   pointers to subsegments (declared below; these pointers are usually     */
00507 /*   `dummysub').  It may or may not also contain user-defined attributes    */
00508 /*   and/or a floating-point "area constraint."  It may also contain extra   */
00509 /*   pointers for nodes, when the user asks for high-order elements.         */
00510 /*   Because the size and structure of a `triangle' is not decided until     */
00511 /*   runtime, I haven't simply declared the type `triangle' as a struct.     */
00512 
00513 typedef REAL **triangle;            /* Really:  typedef triangle *triangle   */
00514 
00515 /* An oriented triangle:  includes a pointer to a triangle and orientation.  */
00516 /*   The orientation denotes an edge of the triangle.  Hence, there are      */
00517 /*   three possible orientations.  By convention, each edge always points    */
00518 /*   counterclockwise about the corresponding triangle.                      */
00519 
00520 struct otri {
00521   triangle *tri;
00522   int orient;                                         /* Ranges from 0 to 2. */
00523 };
00524 
00525 /* The subsegment data structure.  Each subsegment contains two pointers to  */
00526 /*   adjoining subsegments, plus four pointers to vertices, plus two         */
00527 /*   pointers to adjoining triangles, plus one boundary marker, plus one     */
00528 /*   segment number.                                                         */
00529 
00530 typedef REAL **subseg;                  /* Really:  typedef subseg *subseg   */
00531 
00532 /* An oriented subsegment:  includes a pointer to a subsegment and an        */
00533 /*   orientation.  The orientation denotes a side of the edge.  Hence, there */
00534 /*   are two possible orientations.  By convention, the edge is always       */
00535 /*   directed so that the "side" denoted is the right side of the edge.      */
00536 
00537 struct osub {
00538   subseg *ss;
00539   int ssorient;                                       /* Ranges from 0 to 1. */
00540 };
00541 
00542 /* The vertex data structure.  Each vertex is actually an array of REALs.    */
00543 /*   The number of REALs is unknown until runtime.  An integer boundary      */
00544 /*   marker, and sometimes a pointer to a triangle, is appended after the    */
00545 /*   REALs.                                                                  */
00546 
00547 typedef REAL *vertex;
00548 
00549 /* A queue used to store encroached subsegments.  Each subsegment's vertices */
00550 /*   are stored so that we can check whether a subsegment is still the same. */
00551 
00552 struct badsubseg {
00553   subseg encsubseg;                             /* An encroached subsegment. */
00554   vertex subsegorg, subsegdest;                         /* Its two vertices. */
00555 };
00556 
00557 /* A queue used to store bad triangles.  The key is the square of the cosine */
00558 /*   of the smallest angle of the triangle.  Each triangle's vertices are    */
00559 /*   stored so that one can check whether a triangle is still the same.      */
00560 
00561 struct badtriang {
00562   triangle poortri;                       /* A skinny or too-large triangle. */
00563   REAL key;                             /* cos^2 of smallest (apical) angle. */
00564   vertex triangorg, triangdest, triangapex;           /* Its three vertices. */
00565   struct badtriang *nexttriang;             /* Pointer to next bad triangle. */
00566 };
00567 
00568 /* A stack of triangles flipped during the most recent vertex insertion.     */
00569 /*   The stack is used to undo the vertex insertion if the vertex encroaches */
00570 /*   upon a subsegment.                                                      */
00571 
00572 struct flipstacker {
00573   triangle flippedtri;                       /* A recently flipped triangle. */
00574   struct flipstacker *prevflip;               /* Previous flip in the stack. */
00575 };
00576 
00577 /* A node in a heap used to store events for the sweepline Delaunay          */
00578 /*   algorithm.  Nodes do not point directly to their parents or children in */
00579 /*   the heap.  Instead, each node knows its position in the heap, and can   */
00580 /*   look up its parent and children in a separate array.  The `eventptr'    */
00581 /*   points either to a `vertex' or to a triangle (in encoded format, so     */
00582 /*   that an orientation is included).  In the latter case, the origin of    */
00583 /*   the oriented triangle is the apex of a "circle event" of the sweepline  */
00584 /*   algorithm.  To distinguish site events from circle events, all circle   */
00585 /*   events are given an invalid (smaller than `xmin') x-coordinate `xkey'.  */
00586 
00587 struct event {
00588   REAL xkey, ykey;                              /* Coordinates of the event. */
00589   VOID *eventptr;      /* Can be a vertex or the location of a circle event. */
00590   int heapposition;              /* Marks this event's position in the heap. */
00591 };
00592 
00593 /* A node in the splay tree.  Each node holds an oriented ghost triangle     */
00594 /*   that represents a boundary edge of the growing triangulation.  When a   */
00595 /*   circle event covers two boundary edges with a triangle, so that they    */
00596 /*   are no longer boundary edges, those edges are not immediately deleted   */
00597 /*   from the tree; rather, they are lazily deleted when they are next       */
00598 /*   encountered.  (Since only a random sample of boundary edges are kept    */
00599 /*   in the tree, lazy deletion is faster.)  `keydest' is used to verify     */
00600 /*   that a triangle is still the same as when it entered the splay tree; if */
00601 /*   it has been rotated (due to a circle event), it no longer represents a  */
00602 /*   boundary edge and should be deleted.                                    */
00603 
00604 struct splaynode {
00605   struct otri keyedge;                     /* Lprev of an edge on the front. */
00606   vertex keydest;           /* Used to verify that splay node is still live. */
00607   struct splaynode *lchild, *rchild;              /* Children in splay tree. */
00608 };
00609 
00610 /* A type used to allocate memory.  firstblock is the first block of items.  */
00611 /*   nowblock is the block from which items are currently being allocated.   */
00612 /*   nextitem points to the next slab of free memory for an item.            */
00613 /*   deaditemstack is the head of a linked list (stack) of deallocated items */
00614 /*   that can be recycled.  unallocateditems is the number of items that     */
00615 /*   remain to be allocated from nowblock.                                   */
00616 /*                                                                           */
00617 /* Traversal is the process of walking through the entire list of items, and */
00618 /*   is separate from allocation.  Note that a traversal will visit items on */
00619 /*   the "deaditemstack" stack as well as live items.  pathblock points to   */
00620 /*   the block currently being traversed.  pathitem points to the next item  */
00621 /*   to be traversed.  pathitemsleft is the number of items that remain to   */
00622 /*   be traversed in pathblock.                                              */
00623 /*                                                                           */
00624 /* alignbytes determines how new records should be aligned in memory.        */
00625 /*   itembytes is the length of a record in bytes (after rounding up).       */
00626 /*   itemsperblock is the number of items allocated at once in a single      */
00627 /*   block.  itemsfirstblock is the number of items in the first block,      */
00628 /*   which can vary from the others.  items is the number of currently       */
00629 /*   allocated items.  maxitems is the maximum number of items that have     */
00630 /*   been allocated at once; it is the current number of items plus the      */
00631 /*   number of records kept on deaditemstack.                                */
00632 
00633 struct memorypool {
00634   VOID **firstblock, **nowblock;
00635   VOID *nextitem;
00636   VOID *deaditemstack;
00637   VOID **pathblock;
00638   VOID *pathitem;
00639   int alignbytes;
00640   int itembytes;
00641   int itemsperblock;
00642   int itemsfirstblock;
00643   long items, maxitems;
00644   int unallocateditems;
00645   int pathitemsleft;
00646 };
00647 
00648 
00649 /* Global constants.                                                         */
00650 
00651 REAL splitter;       /* Used to split REAL factors for exact multiplication. */
00652 REAL epsilon;                             /* Floating-point machine epsilon. */
00653 REAL resulterrbound;
00654 REAL ccwerrboundA, ccwerrboundB, ccwerrboundC;
00655 REAL iccerrboundA, iccerrboundB, iccerrboundC;
00656 REAL o3derrboundA, o3derrboundB, o3derrboundC;
00657 
00658 /* Random number seed is not constant, but I've made it global anyway.       */
00659 
00660 unsigned long randomseed;                     /* Current random number seed. */
00661 
00662 
00663 /* Mesh data structure.  Triangle operates on only one mesh, but the mesh    */
00664 /*   structure is used (instead of global variables) to allow reentrancy.    */
00665 
00666 struct mesh {
00667 
00668 /* Variables used to allocate memory for triangles, subsegments, vertices,   */
00669 /*   viri (triangles being eaten), encroached segments, bad (skinny or too   */
00670 /*   large) triangles, and splay tree nodes.                                 */
00671 
00672   struct memorypool triangles;
00673   struct memorypool subsegs;
00674   struct memorypool vertices;
00675   struct memorypool viri;
00676   struct memorypool badsubsegs;
00677   struct memorypool badtriangles;
00678   struct memorypool flipstackers;
00679   struct memorypool splaynodes;
00680 
00681 /* Variables that maintain the bad triangle queues.  The queues are          */
00682 /*   ordered from 4095 (highest priority) to 0 (lowest priority).            */
00683 
00684   struct badtriang *queuefront[4096];
00685   struct badtriang *queuetail[4096];
00686   int nextnonemptyq[4096];
00687   int firstnonemptyq;
00688 
00689 /* Variable that maintains the stack of recently flipped triangles.          */
00690 
00691   struct flipstacker *lastflip;
00692 
00693 /* Other variables. */
00694 
00695   REAL xmin, xmax, ymin, ymax;                            /* x and y bounds. */
00696   REAL xminextreme;      /* Nonexistent x value used as a flag in sweepline. */
00697   int invertices;                               /* Number of input vertices. */
00698   int inelements;                              /* Number of input triangles. */
00699   int insegments;                               /* Number of input segments. */
00700   int holes;                                       /* Number of input holes. */
00701   int regions;                                   /* Number of input regions. */
00702   int undeads;    /* Number of input vertices that don't appear in the mesh. */
00703   long edges;                                     /* Number of output edges. */
00704   int mesh_dim;                                /* Dimension (ought to be 2). */
00705   int nextras;                           /* Number of attributes per vertex. */
00706   int eextras;                         /* Number of attributes per triangle. */
00707   long hullsize;                          /* Number of edges in convex hull. */
00708   int steinerleft;                 /* Number of Steiner points not yet used. */
00709   int vertexmarkindex;         /* Index to find boundary marker of a vertex. */
00710   int vertex2triindex;     /* Index to find a triangle adjacent to a vertex. */
00711   int highorderindex;  /* Index to find extra nodes for high-order elements. */
00712   int elemattribindex;            /* Index to find attributes of a triangle. */
00713   int areaboundindex;             /* Index to find area bound of a triangle. */
00714   int checksegments;         /* Are there segments in the triangulation yet? */
00715   int checkquality;                  /* Has quality triangulation begun yet? */
00716   int readnodefile;                           /* Has a .node file been read? */
00717   long samples;              /* Number of random samples for point location. */
00718 
00719   long incirclecount;                 /* Number of incircle tests performed. */
00720   long counterclockcount;     /* Number of counterclockwise tests performed. */
00721   long orient3dcount;           /* Number of 3D orientation tests performed. */
00722   long hyperbolacount;      /* Number of right-of-hyperbola tests performed. */
00723   long circumcentercount;  /* Number of circumcenter calculations performed. */
00724   long circletopcount;       /* Number of circle top calculations performed. */
00725 
00726 /* Triangular bounding box vertices.                                         */
00727 
00728   vertex infvertex1, infvertex2, infvertex3;
00729 
00730 /* Pointer to the `triangle' that occupies all of "outer space."             */
00731 
00732   triangle *dummytri;
00733   triangle *dummytribase;    /* Keep base address so we can free() it later. */
00734 
00735 /* Pointer to the omnipresent subsegment.  Referenced by any triangle or     */
00736 /*   subsegment that isn't really connected to a subsegment at that          */
00737 /*   location.                                                               */
00738 
00739   subseg *dummysub;
00740   subseg *dummysubbase;      /* Keep base address so we can free() it later. */
00741 
00742 /* Pointer to a recently visited triangle.  Improves point location if       */
00743 /*   proximate vertices are inserted sequentially.                           */
00744 
00745   struct otri recenttri;
00746 
00747 };                                                  /* End of `struct mesh'. */
00748 
00749 
00750 /* Data structure for command line switches and file names.  This structure  */
00751 /*   is used (instead of global variables) to allow reentrancy.              */
00752 
00753 struct behavior {
00754 
00755 /* Switches for the triangulator.                                            */
00756 /*   poly: -p switch.  refine: -r switch.                                    */
00757 /*   quality: -q switch.                                                     */
00758 /*     minangle: minimum angle bound, specified after -q switch.             */
00759 /*     goodangle: cosine squared of minangle.                                */
00760 /*     offconstant: constant used to place off-center Steiner points.        */
00761 /*   vararea: -a switch without number.                                      */
00762 /*   fixedarea: -a switch with number.                                       */
00763 /*     maxarea: maximum area bound, specified after -a switch.               */
00764 /*   usertest: -u switch.                                                    */
00765 /*   regionattrib: -A switch.  convex: -c switch.                            */
00766 /*   weighted: 1 for -w switch, 2 for -W switch.  jettison: -j switch        */
00767 /*   firstnumber: inverse of -z switch.  All items are numbered starting     */
00768 /*     from `firstnumber'.                                                   */
00769 /*   edgesout: -e switch.  voronoi: -v switch.                               */
00770 /*   neighbors: -n switch.  geomview: -g switch.                             */
00771 /*   nobound: -B switch.  nopolywritten: -P switch.                          */
00772 /*   nonodewritten: -N switch.  noelewritten: -E switch.                     */
00773 /*   noiterationnum: -I switch.  noholes: -O switch.                         */
00774 /*   noexact: -X switch.                                                     */
00775 /*   order: element order, specified after -o switch.                        */
00776 /*   nobisect: count of how often -Y switch is selected.                     */
00777 /*   steiner: maximum number of Steiner points, specified after -S switch.   */
00778 /*   incremental: -i switch.  sweepline: -F switch.                          */
00779 /*   dwyer: inverse of -l switch.                                            */
00780 /*   splitseg: -s switch.                                                    */
00781 /*   conformdel: -D switch.  docheck: -C switch.                             */
00782 /*   quiet: -Q switch.  verbose: count of how often -V switch is selected.   */
00783 /*   usesegments: -p, -r, -q, or -c switch; determines whether segments are  */
00784 /*     used at all.                                                          */
00785 /*                                                                           */
00786 /* Read the instructions to find out the meaning of these switches.          */
00787 
00788   int poly, refine, quality, vararea, fixedarea, usertest;
00789   int regionattrib, convex, weighted, jettison;
00790   int firstnumber;
00791   int edgesout, voronoi, neighbors, geomview;
00792   int nobound, nopolywritten, nonodewritten, noelewritten, noiterationnum;
00793   int noholes, noexact, conformdel;
00794   int incremental, sweepline, dwyer;
00795   int splitseg;
00796   int docheck;
00797   int quiet, verbose;
00798   int usesegments;
00799   int order;
00800   int nobisect;
00801   int steiner;
00802   REAL minangle, goodangle, offconstant;
00803   REAL maxarea;
00804 
00805 /* Variables for file names.                                                 */
00806 
00807 #ifndef TRILIBRARY
00808   char innodefilename[FILENAMESIZE];
00809   char inelefilename[FILENAMESIZE];
00810   char inpolyfilename[FILENAMESIZE];
00811   char areafilename[FILENAMESIZE];
00812   char outnodefilename[FILENAMESIZE];
00813   char outelefilename[FILENAMESIZE];
00814   char outpolyfilename[FILENAMESIZE];
00815   char edgefilename[FILENAMESIZE];
00816   char vnodefilename[FILENAMESIZE];
00817   char vedgefilename[FILENAMESIZE];
00818   char neighborfilename[FILENAMESIZE];
00819   char offfilename[FILENAMESIZE];
00820 #endif /* not TRILIBRARY */
00821 
00822 };                                              /* End of `struct behavior'. */
00823 
00824 
00825 /*****************************************************************************/
00826 /*                                                                           */
00827 /*  Mesh manipulation primitives.  Each triangle contains three pointers to  */
00828 /*  other triangles, with orientations.  Each pointer points not to the      */
00829 /*  first byte of a triangle, but to one of the first three bytes of a       */
00830 /*  triangle.  It is necessary to extract both the triangle itself and the   */
00831 /*  orientation.  To save memory, I keep both pieces of information in one   */
00832 /*  pointer.  To make this possible, I assume that all triangles are aligned */
00833 /*  to four-byte boundaries.  The decode() routine below decodes a pointer,  */
00834 /*  extracting an orientation (in the range 0 to 2) and a pointer to the     */
00835 /*  beginning of a triangle.  The encode() routine compresses a pointer to a */
00836 /*  triangle and an orientation into a single pointer.  My assumptions that  */
00837 /*  triangles are four-byte-aligned and that the `unsigned long' type is     */
00838 /*  long enough to hold a pointer are two of the few kludges in this program.*/
00839 /*                                                                           */
00840 /*  Subsegments are manipulated similarly.  A pointer to a subsegment        */
00841 /*  carries both an address and an orientation in the range 0 to 1.          */
00842 /*                                                                           */
00843 /*  The other primitives take an oriented triangle or oriented subsegment,   */
00844 /*  and return an oriented triangle or oriented subsegment or vertex; or     */
00845 /*  they change the connections in the data structure.                       */
00846 /*                                                                           */
00847 /*  Below, triangles and subsegments are denoted by their vertices.  The     */
00848 /*  triangle abc has origin (org) a, destination (dest) b, and apex (apex)   */
00849 /*  c.  These vertices occur in counterclockwise order about the triangle.   */
00850 /*  The handle abc may simultaneously denote vertex a, edge ab, and triangle */
00851 /*  abc.                                                                     */
00852 /*                                                                           */
00853 /*  Similarly, the subsegment ab has origin (sorg) a and destination (sdest) */
00854 /*  b.  If ab is thought to be directed upward (with b directly above a),    */
00855 /*  then the handle ab is thought to grasp the right side of ab, and may     */
00856 /*  simultaneously denote vertex a and edge ab.                              */
00857 /*                                                                           */
00858 /*  An asterisk (*) denotes a vertex whose identity is unknown.              */
00859 /*                                                                           */
00860 /*  Given this notation, a partial list of mesh manipulation primitives      */
00861 /*  follows.                                                                 */
00862 /*                                                                           */
00863 /*                                                                           */
00864 /*  For triangles:                                                           */
00865 /*                                                                           */
00866 /*  sym:  Find the abutting triangle; same edge.                             */
00867 /*  sym(abc) -> ba*                                                          */
00868 /*                                                                           */
00869 /*  lnext:  Find the next edge (counterclockwise) of a triangle.             */
00870 /*  lnext(abc) -> bca                                                        */
00871 /*                                                                           */
00872 /*  lprev:  Find the previous edge (clockwise) of a triangle.                */
00873 /*  lprev(abc) -> cab                                                        */
00874 /*                                                                           */
00875 /*  onext:  Find the next edge counterclockwise with the same origin.        */
00876 /*  onext(abc) -> ac*                                                        */
00877 /*                                                                           */
00878 /*  oprev:  Find the next edge clockwise with the same origin.               */
00879 /*  oprev(abc) -> a*b                                                        */
00880 /*                                                                           */
00881 /*  dnext:  Find the next edge counterclockwise with the same destination.   */
00882 /*  dnext(abc) -> *ba                                                        */
00883 /*                                                                           */
00884 /*  dprev:  Find the next edge clockwise with the same destination.          */
00885 /*  dprev(abc) -> cb*                                                        */
00886 /*                                                                           */
00887 /*  rnext:  Find the next edge (counterclockwise) of the adjacent triangle.  */
00888 /*  rnext(abc) -> *a*                                                        */
00889 /*                                                                           */
00890 /*  rprev:  Find the previous edge (clockwise) of the adjacent triangle.     */
00891 /*  rprev(abc) -> b**                                                        */
00892 /*                                                                           */
00893 /*  org:  Origin          dest:  Destination          apex:  Apex            */
00894 /*  org(abc) -> a         dest(abc) -> b              apex(abc) -> c         */
00895 /*                                                                           */
00896 /*  bond:  Bond two triangles together at the resepective handles.           */
00897 /*  bond(abc, bad)                                                           */
00898 /*                                                                           */
00899 /*                                                                           */
00900 /*  For subsegments:                                                         */
00901 /*                                                                           */
00902 /*  ssym:  Reverse the orientation of a subsegment.                          */
00903 /*  ssym(ab) -> ba                                                           */
00904 /*                                                                           */
00905 /*  spivot:  Find adjoining subsegment with the same origin.                 */
00906 /*  spivot(ab) -> a*                                                         */
00907 /*                                                                           */
00908 /*  snext:  Find next subsegment in sequence.                                */
00909 /*  snext(ab) -> b*                                                          */
00910 /*                                                                           */
00911 /*  sorg:  Origin                      sdest:  Destination                   */
00912 /*  sorg(ab) -> a                      sdest(ab) -> b                        */
00913 /*                                                                           */
00914 /*  sbond:  Bond two subsegments together at the respective origins.         */
00915 /*  sbond(ab, ac)                                                            */
00916 /*                                                                           */
00917 /*                                                                           */
00918 /*  For interacting tetrahedra and subfacets:                                */
00919 /*                                                                           */
00920 /*  tspivot:  Find a subsegment abutting a triangle.                         */
00921 /*  tspivot(abc) -> ba                                                       */
00922 /*                                                                           */
00923 /*  stpivot:  Find a triangle abutting a subsegment.                         */
00924 /*  stpivot(ab) -> ba*                                                       */
00925 /*                                                                           */
00926 /*  tsbond:  Bond a triangle to a subsegment.                                */
00927 /*  tsbond(abc, ba)                                                          */
00928 /*                                                                           */
00929 /*****************************************************************************/
00930 
00931 /********* Mesh manipulation primitives begin here                   *********/
00935 /* Fast lookup arrays to speed some of the mesh manipulation primitives.     */
00936 
00937 int plus1mod3[3] = {1, 2, 0};
00938 int minus1mod3[3] = {2, 0, 1};
00939 
00940 /********* Primitives for triangles                                  *********/
00941 /*                                                                           */
00942 /*                                                                           */
00943 
00944 /* decode() converts a pointer to an oriented triangle.  The orientation is  */
00945 /*   extracted from the two least significant bits of the pointer.           */
00946 
00947 #define decode(ptr, otri)                                                     \
00948   (otri).orient = (int) ((unsigned long) (ptr) & (unsigned long) 3l);         \
00949   (otri).tri = (triangle *)                                                   \
00950                   ((unsigned long) (ptr) ^ (unsigned long) (otri).orient)
00951 
00952 /* encode() compresses an oriented triangle into a single pointer.  It       */
00953 /*   relies on the assumption that all triangles are aligned to four-byte    */
00954 /*   boundaries, so the two least significant bits of (otri).tri are zero.   */
00955 
00956 #define encode(otri)                                                          \
00957   (triangle) ((unsigned long) (otri).tri | (unsigned long) (otri).orient)
00958 
00959 /* The following handle manipulation primitives are all described by Guibas  */
00960 /*   and Stolfi.  However, Guibas and Stolfi use an edge-based data          */
00961 /*   structure, whereas I use a triangle-based data structure.               */
00962 
00963 /* sym() finds the abutting triangle, on the same edge.  Note that the edge  */
00964 /*   direction is necessarily reversed, because the handle specified by an   */
00965 /*   oriented triangle is directed counterclockwise around the triangle.     */
00966 
00967 #define sym(otri1, otri2)                                                     \
00968   ptr = (otri1).tri[(otri1).orient];                                          \
00969   decode(ptr, otri2);
00970 
00971 #define symself(otri)                                                         \
00972   ptr = (otri).tri[(otri).orient];                                            \
00973   decode(ptr, otri);
00974 
00975 /* lnext() finds the next edge (counterclockwise) of a triangle.             */
00976 
00977 #define lnext(otri1, otri2)                                                   \
00978   (otri2).tri = (otri1).tri;                                                  \
00979   (otri2).orient = plus1mod3[(otri1).orient]
00980 
00981 #define lnextself(otri)                                                       \
00982   (otri).orient = plus1mod3[(otri).orient]
00983 
00984 /* lprev() finds the previous edge (clockwise) of a triangle.                */
00985 
00986 #define lprev(otri1, otri2)                                                   \
00987   (otri2).tri = (otri1).tri;                                                  \
00988   (otri2).orient = minus1mod3[(otri1).orient]
00989 
00990 #define lprevself(otri)                                                       \
00991   (otri).orient = minus1mod3[(otri).orient]
00992 
00993 /* onext() spins counterclockwise around a vertex; that is, it finds the     */
00994 /*   next edge with the same origin in the counterclockwise direction.  This */
00995 /*   edge is part of a different triangle.                                   */
00996 
00997 #define onext(otri1, otri2)                                                   \
00998   lprev(otri1, otri2);                                                        \
00999   symself(otri2);
01000 
01001 #define onextself(otri)                                                       \
01002   lprevself(otri);                                                            \
01003   symself(otri);
01004 
01005 /* oprev() spins clockwise around a vertex; that is, it finds the next edge  */
01006 /*   with the same origin in the clockwise direction.  This edge is part of  */
01007 /*   a different triangle.                                                   */
01008 
01009 #define oprev(otri1, otri2)                                                   \
01010   sym(otri1, otri2);                                                          \
01011   lnextself(otri2);
01012 
01013 #define oprevself(otri)                                                       \
01014   symself(otri);                                                              \
01015   lnextself(otri);
01016 
01017 /* dnext() spins counterclockwise around a vertex; that is, it finds the     */
01018 /*   next edge with the same destination in the counterclockwise direction.  */
01019 /*   This edge is part of a different triangle.                              */
01020 
01021 #define dnext(otri1, otri2)                                                   \
01022   sym(otri1, otri2);                                                          \
01023   lprevself(otri2);
01024 
01025 #define dnextself(otri)                                                       \
01026   symself(otri);                                                              \
01027   lprevself(otri);
01028 
01029 /* dprev() spins clockwise around a vertex; that is, it finds the next edge  */
01030 /*   with the same destination in the clockwise direction.  This edge is     */
01031 /*   part of a different triangle.                                           */
01032 
01033 #define dprev(otri1, otri2)                                                   \
01034   lnext(otri1, otri2);                                                        \
01035   symself(otri2);
01036 
01037 #define dprevself(otri)                                                       \
01038   lnextself(otri);                                                            \
01039   symself(otri);
01040 
01041 /* rnext() moves one edge counterclockwise about the adjacent triangle.      */
01042 /*   (It's best understood by reading Guibas and Stolfi.  It involves        */
01043 /*   changing triangles twice.)                                              */
01044 
01045 #define rnext(otri1, otri2)                                                   \
01046   sym(otri1, otri2);                                                          \
01047   lnextself(otri2);                                                           \
01048   symself(otri2);
01049 
01050 #define rnextself(otri)                                                       \
01051   symself(otri);                                                              \
01052   lnextself(otri);                                                            \
01053   symself(otri);
01054 
01055 /* rprev() moves one edge clockwise about the adjacent triangle.             */
01056 /*   (It's best understood by reading Guibas and Stolfi.  It involves        */
01057 /*   changing triangles twice.)                                              */
01058 
01059 #define rprev(otri1, otri2)                                                   \
01060   sym(otri1, otri2);                                                          \
01061   lprevself(otri2);                                                           \
01062   symself(otri2);
01063 
01064 #define rprevself(otri)                                                       \
01065   symself(otri);                                                              \
01066   lprevself(otri);                                                            \
01067   symself(otri);
01068 
01069 /* These primitives determine or set the origin, destination, or apex of a   */
01070 /* triangle.                                                                 */
01071 
01072 #define org(otri, vertexptr)                                                  \
01073   vertexptr = (vertex) (otri).tri[plus1mod3[(otri).orient] + 3]
01074 
01075 #define dest(otri, vertexptr)                                                 \
01076   vertexptr = (vertex) (otri).tri[minus1mod3[(otri).orient] + 3]
01077 
01078 #define apex(otri, vertexptr)                                                 \
01079   vertexptr = (vertex) (otri).tri[(otri).orient + 3]
01080 
01081 #define setorg(otri, vertexptr)                                               \
01082   (otri).tri[plus1mod3[(otri).orient] + 3] = (triangle) vertexptr
01083 
01084 #define setdest(otri, vertexptr)                                              \
01085   (otri).tri[minus1mod3[(otri).orient] + 3] = (triangle) vertexptr
01086 
01087 #define setapex(otri, vertexptr)                                              \
01088   (otri).tri[(otri).orient + 3] = (triangle) vertexptr
01089 
01090 /* Bond two triangles together.                                              */
01091 
01092 #define bond(otri1, otri2)                                                    \
01093   (otri1).tri[(otri1).orient] = encode(otri2);                                \
01094   (otri2).tri[(otri2).orient] = encode(otri1)
01095 
01096 /* Dissolve a bond (from one side).  Note that the other triangle will still */
01097 /*   think it's connected to this triangle.  Usually, however, the other     */
01098 /*   triangle is being deleted entirely, or bonded to another triangle, so   */
01099 /*   it doesn't matter.                                                      */
01100 
01101 #define dissolve(otri)                                                        \
01102   (otri).tri[(otri).orient] = (triangle) m->dummytri
01103 
01104 /* Copy an oriented triangle.                                                */
01105 
01106 #define otricopy(otri1, otri2)                                                \
01107   (otri2).tri = (otri1).tri;                                                  \
01108   (otri2).orient = (otri1).orient
01109 
01110 /* Test for equality of oriented triangles.                                  */
01111 
01112 #define otriequal(otri1, otri2)                                               \
01113   (((otri1).tri == (otri2).tri) &&                                            \
01114    ((otri1).orient == (otri2).orient))
01115 
01116 /* Primitives to infect or cure a triangle with the virus.  These rely on    */
01117 /*   the assumption that all subsegments are aligned to four-byte boundaries.*/
01118 
01119 #define infect(otri)                                                          \
01120   (otri).tri[6] = (triangle)                                                  \
01121                     ((unsigned long) (otri).tri[6] | (unsigned long) 2l)
01122 
01123 #define uninfect(otri)                                                        \
01124   (otri).tri[6] = (triangle)                                                  \
01125                     ((unsigned long) (otri).tri[6] & ~ (unsigned long) 2l)
01126 
01127 /* Test a triangle for viral infection.                                      */
01128 
01129 #define infected(otri)                                                        \
01130   (((unsigned long) (otri).tri[6] & (unsigned long) 2l) != 0l)
01131 
01132 /* Check or set a triangle's attributes.                                     */
01133 
01134 #define elemattribute(otri, attnum)                                           \
01135   ((REAL *) (otri).tri)[m->elemattribindex + (attnum)]
01136 
01137 #define setelemattribute(otri, attnum, value)                                 \
01138   ((REAL *) (otri).tri)[m->elemattribindex + (attnum)] = value
01139 
01140 /* Check or set a triangle's maximum area bound.                             */
01141 
01142 #define areabound(otri)  ((REAL *) (otri).tri)[m->areaboundindex]
01143 
01144 #define setareabound(otri, value)                                             \
01145   ((REAL *) (otri).tri)[m->areaboundindex] = value
01146 
01147 /* Check or set a triangle's deallocation.  Its second pointer is set to     */
01148 /*   NULL to indicate that it is not allocated.  (Its first pointer is used  */
01149 /*   for the stack of dead items.)  Its fourth pointer (its first vertex)    */
01150 /*   is set to NULL in case a `badtriang' structure points to it.            */
01151 
01152 #define deadtri(tria)  ((tria)[1] == (triangle) NULL)
01153 
01154 #define killtri(tria)                                                         \
01155   (tria)[1] = (triangle) NULL;                                                \
01156   (tria)[3] = (triangle) NULL
01157 
01158 /********* Primitives for subsegments                                *********/
01159 /*                                                                           */
01160 /*                                                                           */
01161 
01162 /* sdecode() converts a pointer to an oriented subsegment.  The orientation  */
01163 /*   is extracted from the least significant bit of the pointer.  The two    */
01164 /*   least significant bits (one for orientation, one for viral infection)   */
01165 /*   are masked out to produce the real pointer.                             */
01166 
01167 #define sdecode(sptr, osub)                                                   \
01168   (osub).ssorient = (int) ((unsigned long) (sptr) & (unsigned long) 1l);      \
01169   (osub).ss = (subseg *)                                                      \
01170               ((unsigned long) (sptr) & ~ (unsigned long) 3l)
01171 
01172 /* sencode() compresses an oriented subsegment into a single pointer.  It    */
01173 /*   relies on the assumption that all subsegments are aligned to two-byte   */
01174 /*   boundaries, so the least significant bit of (osub).ss is zero.          */
01175 
01176 #define sencode(osub)                                                         \
01177   (subseg) ((unsigned long) (osub).ss | (unsigned long) (osub).ssorient)
01178 
01179 /* ssym() toggles the orientation of a subsegment.                           */
01180 
01181 #define ssym(osub1, osub2)                                                    \
01182   (osub2).ss = (osub1).ss;                                                    \
01183   (osub2).ssorient = 1 - (osub1).ssorient
01184 
01185 #define ssymself(osub)                                                        \
01186   (osub).ssorient = 1 - (osub).ssorient
01187 
01188 /* spivot() finds the other subsegment (from the same segment) that shares   */
01189 /*   the same origin.                                                        */
01190 
01191 #define spivot(osub1, osub2)                                                  \
01192   sptr = (osub1).ss[(osub1).ssorient];                                        \
01193   sdecode(sptr, osub2)
01194 
01195 #define spivotself(osub)                                                      \
01196   sptr = (osub).ss[(osub).ssorient];                                          \
01197   sdecode(sptr, osub)
01198 
01199 /* snext() finds the next subsegment (from the same segment) in sequence;    */
01200 /*   one whose origin is the input subsegment's destination.                 */
01201 
01202 #define snext(osub1, osub2)                                                   \
01203   sptr = (osub1).ss[1 - (osub1).ssorient];                                    \
01204   sdecode(sptr, osub2)
01205 
01206 #define snextself(osub)                                                       \
01207   sptr = (osub).ss[1 - (osub).ssorient];                                      \
01208   sdecode(sptr, osub)
01209 
01210 /* These primitives determine or set the origin or destination of a          */
01211 /*   subsegment or the segment that includes it.                             */
01212 
01213 #define sorg(osub, vertexptr)                                                 \
01214   vertexptr = (vertex) (osub).ss[2 + (osub).ssorient]
01215 
01216 #define sdest(osub, vertexptr)                                                \
01217   vertexptr = (vertex) (osub).ss[3 - (osub).ssorient]
01218 
01219 #define setsorg(osub, vertexptr)                                              \
01220   (osub).ss[2 + (osub).ssorient] = (subseg) vertexptr
01221 
01222 #define setsdest(osub, vertexptr)                                             \
01223   (osub).ss[3 - (osub).ssorient] = (subseg) vertexptr
01224 
01225 #define segorg(osub, vertexptr)                                               \
01226   vertexptr = (vertex) (osub).ss[4 + (osub).ssorient]
01227 
01228 #define segdest(osub, vertexptr)                                              \
01229   vertexptr = (vertex) (osub).ss[5 - (osub).ssorient]
01230 
01231 #define setsegorg(osub, vertexptr)                                            \
01232   (osub).ss[4 + (osub).ssorient] = (subseg) vertexptr
01233 
01234 #define setsegdest(osub, vertexptr)                                           \
01235   (osub).ss[5 - (osub).ssorient] = (subseg) vertexptr
01236 
01237 /* These primitives read or set a boundary marker.  Boundary markers are     */
01238 /*   used to hold user-defined tags for setting boundary conditions in       */
01239 /*   finite element solvers.                                                 */
01240 
01241 #define mark(osub)  (* (int *) ((osub).ss + 8))
01242 
01243 #define setmark(osub, value)                                                  \
01244   * (int *) ((osub).ss + 8) = value
01245 
01246 /* Bond two subsegments together.                                            */
01247 
01248 #define sbond(osub1, osub2)                                                   \
01249   (osub1).ss[(osub1).ssorient] = sencode(osub2);                              \
01250   (osub2).ss[(osub2).ssorient] = sencode(osub1)
01251 
01252 /* Dissolve a subsegment bond (from one side).  Note that the other          */
01253 /*   subsegment will still think it's connected to this subsegment.          */
01254 
01255 #define sdissolve(osub)                                                       \
01256   (osub).ss[(osub).ssorient] = (subseg) m->dummysub
01257 
01258 /* Copy a subsegment.                                                        */
01259 
01260 #define subsegcopy(osub1, osub2)                                              \
01261   (osub2).ss = (osub1).ss;                                                    \
01262   (osub2).ssorient = (osub1).ssorient
01263 
01264 /* Test for equality of subsegments.                                         */
01265 
01266 #define subsegequal(osub1, osub2)                                             \
01267   (((osub1).ss == (osub2).ss) &&                                              \
01268    ((osub1).ssorient == (osub2).ssorient))
01269 
01270 /* Check or set a subsegment's deallocation.  Its second pointer is set to   */
01271 /*   NULL to indicate that it is not allocated.  (Its first pointer is used  */
01272 /*   for the stack of dead items.)  Its third pointer (its first vertex)     */
01273 /*   is set to NULL in case a `badsubseg' structure points to it.            */
01274 
01275 #define deadsubseg(sub)  ((sub)[1] == (subseg) NULL)
01276 
01277 #define killsubseg(sub)                                                       \
01278   (sub)[1] = (subseg) NULL;                                                   \
01279   (sub)[2] = (subseg) NULL
01280 
01281 /********* Primitives for interacting triangles and subsegments      *********/
01282 /*                                                                           */
01283 /*                                                                           */
01284 
01285 /* tspivot() finds a subsegment abutting a triangle.                         */
01286 
01287 #define tspivot(otri, osub)                                                   \
01288   sptr = (subseg) (otri).tri[6 + (otri).orient];                              \
01289   sdecode(sptr, osub)
01290 
01291 /* stpivot() finds a triangle abutting a subsegment.  It requires that the   */
01292 /*   variable `ptr' of type `triangle' be defined.                           */
01293 
01294 #define stpivot(osub, otri)                                                   \
01295   ptr = (triangle) (osub).ss[6 + (osub).ssorient];                            \
01296   decode(ptr, otri)
01297 
01298 /* Bond a triangle to a subsegment.                                          */
01299 
01300 #define tsbond(otri, osub)                                                    \
01301   (otri).tri[6 + (otri).orient] = (triangle) sencode(osub);                   \
01302   (osub).ss[6 + (osub).ssorient] = (subseg) encode(otri)
01303 
01304 /* Dissolve a bond (from the triangle side).                                 */
01305 
01306 #define tsdissolve(otri)                                                      \
01307   (otri).tri[6 + (otri).orient] = (triangle) m->dummysub
01308 
01309 /* Dissolve a bond (from the subsegment side).                               */
01310 
01311 #define stdissolve(osub)                                                      \
01312   (osub).ss[6 + (osub).ssorient] = (subseg) m->dummytri
01313 
01314 /********* Primitives for vertices                                   *********/
01315 /*                                                                           */
01316 /*                                                                           */
01317 
01318 #define vertexmark(vx)  ((int *) (vx))[m->vertexmarkindex]
01319 
01320 #define setvertexmark(vx, value)                                              \
01321   ((int *) (vx))[m->vertexmarkindex] = value
01322 
01323 #define vertextype(vx)  ((int *) (vx))[m->vertexmarkindex + 1]
01324 
01325 #define setvertextype(vx, value)                                              \
01326   ((int *) (vx))[m->vertexmarkindex + 1] = value
01327 
01328 #define vertex2tri(vx)  ((triangle *) (vx))[m->vertex2triindex]
01329 
01330 #define setvertex2tri(vx, value)                                              \
01331   ((triangle *) (vx))[m->vertex2triindex] = value
01332 
01335 /********* Mesh manipulation primitives end here                     *********/
01336 
01337 /********* User-defined triangle evaluation routine begins here      *********/
01341 /*****************************************************************************/
01342 /*                                                                           */
01343 /*  triunsuitable()   Determine if a triangle is unsuitable, and thus must   */
01344 /*                    be further refined.                                    */
01345 /*                                                                           */
01346 /*  You may write your own procedure that decides whether or not a selected  */
01347 /*  triangle is too big (and needs to be refined).  There are two ways to do */
01348 /*  this.                                                                    */
01349 /*                                                                           */
01350 /*  (1)  Modify the procedure `triunsuitable' below, then recompile          */
01351 /*  Triangle.                                                                */
01352 /*                                                                           */
01353 /*  (2)  Define the symbol EXTERNAL_TEST (either by adding the definition    */
01354 /*  to this file, or by using the appropriate compiler switch).  This way,   */
01355 /*  you can compile triangle.c separately from your test.  Write your own    */
01356 /*  `triunsuitable' procedure in a separate C file (using the same prototype */
01357 /*  as below).  Compile it and link the object code with triangle.o.         */
01358 /*                                                                           */
01359 /*  This procedure returns 1 if the triangle is too large and should be      */
01360 /*  refined; 0 otherwise.                                                    */
01361 /*                                                                           */
01362 /*****************************************************************************/
01363 
01364 #ifdef EXTERNAL_TEST
01365 
01366 int triunsuitable();
01367 
01368 #else /* not EXTERNAL_TEST */
01369 
01370 #ifdef ANSI_DECLARATORS
01371 int triunsuitable(vertex triorg, vertex tridest, vertex triapex, REAL area)
01372 #else /* not ANSI_DECLARATORS */
01373 int triunsuitable(triorg, tridest, triapex, area)
01374 vertex triorg;                              /* The triangle's origin vertex. */
01375 vertex tridest;                        /* The triangle's destination vertex. */
01376 vertex triapex;                               /* The triangle's apex vertex. */
01377 REAL area;                                      /* The area of the triangle. */
01378 #endif /* not ANSI_DECLARATORS */
01379 
01380 {
01381   REAL dxoa, dxda, dxod;
01382   REAL dyoa, dyda, dyod;
01383   REAL oalen, dalen, odlen;
01384   REAL maxlen;
01385 
01386   dxoa = triorg[0] - triapex[0];
01387   dyoa = triorg[1] - triapex[1];
01388   dxda = tridest[0] - triapex[0];
01389   dyda = tridest[1] - triapex[1];
01390   dxod = triorg[0] - tridest[0];
01391   dyod = triorg[1] - tridest[1];
01392   /* Find the squares of the lengths of the triangle's three edges. */
01393   oalen = dxoa * dxoa + dyoa * dyoa;
01394   dalen = dxda * dxda + dyda * dyda;
01395   odlen = dxod * dxod + dyod * dyod;
01396   /* Find the square of the length of the longest edge. */
01397   maxlen = (dalen > oalen) ? dalen : oalen;
01398   maxlen = (odlen > maxlen) ? odlen : maxlen;
01399 
01400   if (maxlen > 0.05 * (triorg[0] * triorg[0] + triorg[1] * triorg[1]) + 0.02) {
01401     return 1;
01402   } else {
01403     return 0;
01404   }
01405 }
01406 
01407 #endif /* not EXTERNAL_TEST */
01408 
01411 /********* User-defined triangle evaluation routine ends here        *********/
01412 
01413 /********* Memory allocation and program exit wrappers begin here    *********/
01417 #ifdef ANSI_DECLARATORS
01418 void triexit(int status)
01419 #else /* not ANSI_DECLARATORS */
01420 void triexit(status)
01421 int status;
01422 #endif /* not ANSI_DECLARATORS */
01423 
01424 {
01425   exit(status);
01426 }
01427 
01428 #ifdef ANSI_DECLARATORS
01429 VOID *trimalloc(int size)
01430 #else /* not ANSI_DECLARATORS */
01431 VOID *trimalloc(size)
01432 int size;
01433 #endif /* not ANSI_DECLARATORS */
01434 
01435 {
01436   VOID *memptr;
01437 
01438   memptr = (VOID *) malloc((unsigned int) size);
01439   if (memptr == (VOID *) NULL) {
01440     printf("Error:  Out of memory.\n");
01441     triexit(1);
01442   }
01443   return(memptr);
01444 }
01445 
01446 #ifdef ANSI_DECLARATORS
01447 void trifree(VOID *memptr)
01448 #else /* not ANSI_DECLARATORS */
01449 void trifree(memptr)
01450 VOID *memptr;
01451 #endif /* not ANSI_DECLARATORS */
01452 
01453 {
01454   free(memptr);
01455 }
01456 
01459 /********* Memory allocation and program exit wrappers end here      *********/
01460 
01461 /********* User interaction routines begin here                      *********/
01465 /*****************************************************************************/
01466 /*                                                                           */
01467 /*  syntax()   Print list of command line switches.                          */
01468 /*                                                                           */
01469 /*****************************************************************************/
01470 
01471 #ifndef TRILIBRARY
01472 
01473 void syntax()
01474 {
01475 #ifdef CDT_ONLY
01476 #ifdef REDUCED
01477   printf("triangle [-pAcjevngBPNEIOXzo_lQVh] input_file\n");
01478 #else /* not REDUCED */
01479   printf("triangle [-pAcjevngBPNEIOXzo_iFlCQVh] input_file\n");
01480 #endif /* not REDUCED */
01481 #else /* not CDT_ONLY */
01482 #ifdef REDUCED
01483   printf("triangle [-prq__a__uAcDjevngBPNEIOXzo_YS__lQVh] input_file\n");
01484 #else /* not REDUCED */
01485   printf("triangle [-prq__a__uAcDjevngBPNEIOXzo_YS__iFlsCQVh] input_file\n");
01486 #endif /* not REDUCED */
01487 #endif /* not CDT_ONLY */
01488 
01489   printf("    -p  Triangulates a Planar Straight Line Graph (.poly file).\n");
01490 #ifndef CDT_ONLY
01491   printf("    -r  Refines a previously generated mesh.\n");
01492   printf(
01493     "    -q  Quality mesh generation.  A minimum angle may be specified.\n");
01494   printf("    -a  Applies a maximum triangle area constraint.\n");
01495   printf("    -u  Applies a user-defined triangle constraint.\n");
01496 #endif /* not CDT_ONLY */
01497   printf(
01498     "    -A  Applies attributes to identify triangles in certain regions.\n");
01499   printf("    -c  Encloses the convex hull with segments.\n");
01500 #ifndef CDT_ONLY
01501   printf("    -D  Conforming Delaunay:  all triangles are truly Delaunay.\n");
01502 #endif /* not CDT_ONLY */
01503 /*
01504   printf("    -w  Weighted Delaunay triangulation.\n");
01505   printf("    -W  Regular triangulation (lower hull of a height field).\n");
01506 */
01507   printf("    -j  Jettison unused vertices from output .node file.\n");
01508   printf("    -e  Generates an edge list.\n");
01509   printf("    -v  Generates a Voronoi diagram.\n");
01510   printf("    -n  Generates a list of triangle neighbors.\n");
01511   printf("    -g  Generates an .off file for Geomview.\n");
01512   printf("    -B  Suppresses output of boundary information.\n");
01513   printf("    -P  Suppresses output of .poly file.\n");
01514   printf("    -N  Suppresses output of .node file.\n");
01515   printf("    -E  Suppresses output of .ele file.\n");
01516   printf("    -I  Suppresses mesh iteration numbers.\n");
01517   printf("    -O  Ignores holes in .poly file.\n");
01518   printf("    -X  Suppresses use of exact arithmetic.\n");
01519   printf("    -z  Numbers all items starting from zero (rather than one).\n");
01520   printf("    -o2 Generates second-order subparametric elements.\n");
01521 #ifndef CDT_ONLY
01522   printf("    -Y  Suppresses boundary segment splitting.\n");
01523   printf("    -S  Specifies maximum number of added Steiner points.\n");
01524 #endif /* not CDT_ONLY */
01525 #ifndef REDUCED
01526   printf("    -i  Uses incremental method, rather than divide-and-conquer.\n");
01527   printf("    -F  Uses Fortune's sweepline algorithm, rather than d-and-c.\n");
01528 #endif /* not REDUCED */
01529   printf("    -l  Uses vertical cuts only, rather than alternating cuts.\n");
01530 #ifndef REDUCED
01531 #ifndef CDT_ONLY
01532   printf(
01533     "    -s  Force segments into mesh by splitting (instead of using CDT).\n");
01534 #endif /* not CDT_ONLY */
01535   printf("    -C  Check consistency of final mesh.\n");
01536 #endif /* not REDUCED */
01537   printf("    -Q  Quiet:  No terminal output except errors.\n");
01538   printf("    -V  Verbose:  Detailed information on what I'm doing.\n");
01539   printf("    -h  Help:  Detailed instructions for Triangle.\n");
01540   triexit(0);
01541 }
01542 
01543 #endif /* not TRILIBRARY */
01544 
01545 /*****************************************************************************/
01546 /*                                                                           */
01547 /*  info()   Print out complete instructions.                                */
01548 /*                                                                           */
01549 /*****************************************************************************/
01550 
01551 #ifndef TRILIBRARY
01552 
01553 void info()
01554 {
01555   printf("Triangle\n");
01556   printf(
01557 "A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator.\n");
01558   printf("Version 1.6\n\n");
01559   printf(
01560 "Copyright 1993, 1995, 1997, 1998, 2002, 2005 Jonathan Richard Shewchuk\n");
01561   printf("2360 Woolsey #H / Berkeley, California 94705-1927\n");
01562   printf("Bugs/comments to jrs@cs.berkeley.edu\n");
01563   printf(
01564 "Created as part of the Quake project (tools for earthquake simulation).\n");
01565   printf(
01566 "Supported in part by NSF Grant CMS-9318163 and an NSERC 1967 Scholarship.\n");
01567   printf("There is no warranty whatsoever.  Use at your own risk.\n");
01568 #ifdef SINGLE
01569   printf("This executable is compiled for single precision arithmetic.\n\n\n");
01570 #else /* not SINGLE */
01571   printf("This executable is compiled for double precision arithmetic.\n\n\n");
01572 #endif /* not SINGLE */
01573   printf(
01574 "Triangle generates exact Delaunay triangulations, constrained Delaunay\n");
01575   printf(
01576 "triangulations, conforming Delaunay triangulations, Voronoi diagrams, and\n");
01577   printf(
01578 "high-quality triangular meshes.  The latter can be generated with no small\n"
01579 );
01580   printf(
01581 "or large angles, and are thus suitable for finite element analysis.  If no\n"
01582 );
01583   printf(
01584 "command line switch is specified, your .node input file is read, and the\n");
01585   printf(
01586 "Delaunay triangulation is returned in .node and .ele output files.  The\n");
01587   printf("command syntax is:\n\n");
01588   printf("triangle [-prq__a__uAcDjevngBPNEIOXzo_YS__iFlsCQVh] input_file\n\n");
01589   printf(
01590 "Underscores indicate that numbers may optionally follow certain switches.\n");
01591   printf(
01592 "Do not leave any space between a switch and its numeric parameter.\n");
01593   printf(
01594 "input_file must be a file with extension .node, or extension .poly if the\n");
01595   printf(
01596 "-p switch is used.  If -r is used, you must supply .node and .ele files,\n");
01597   printf(
01598 "and possibly a .poly file and an .area file as well.  The formats of these\n"
01599 );
01600   printf("files are described below.\n\n");
01601   printf("Command Line Switches:\n\n");
01602   printf(
01603 "    -p  Reads a Planar Straight Line Graph (.poly file), which can specify\n"
01604 );
01605   printf(
01606 "        vertices, segments, holes, regional attributes, and regional area\n");
01607   printf(
01608 "        constraints.  Generates a constrained Delaunay triangulation (CDT)\n"
01609 );
01610   printf(
01611 "        fitting the input; or, if -s, -q, -a, or -u is used, a conforming\n");
01612   printf(
01613 "        constrained Delaunay triangulation (CCDT).  If you want a truly\n");
01614   printf(
01615 "        Delaunay (not just constrained Delaunay) triangulation, use -D as\n");
01616   printf(
01617 "        well.  When -p is not used, Triangle reads a .node file by default.\n"
01618 );
01619   printf(
01620 "    -r  Refines a previously generated mesh.  The mesh is read from a .node\n"
01621 );
01622   printf(
01623 "        file and an .ele file.  If -p is also used, a .poly file is read\n");
01624   printf(
01625 "        and used to constrain segments in the mesh.  If -a is also used\n");
01626   printf(
01627 "        (with no number following), an .area file is read and used to\n");
01628   printf(
01629 "        impose area constraints on the mesh.  Further details on refinement\n"
01630 );
01631   printf("        appear below.\n");
01632   printf(
01633 "    -q  Quality mesh generation by Delaunay refinement (a hybrid of Paul\n");
01634   printf(
01635 "        Chew's and Jim Ruppert's algorithms).  Adds vertices to the mesh to\n"
01636 );
01637   printf(
01638 "        ensure that all angles are between 20 and 140 degrees.  An\n");
01639   printf(
01640 "        alternative bound on the minimum angle, replacing 20 degrees, may\n");
01641   printf(
01642 "        be specified after the `q'.  The specified angle may include a\n");
01643   printf(
01644 "        decimal point, but not exponential notation.  Note that a bound of\n"
01645 );
01646   printf(
01647 "        theta degrees on the smallest angle also implies a bound of\n");
01648   printf(
01649 "        (180 - 2 theta) on the largest angle.  If the minimum angle is 28.6\n"
01650 );
01651   printf(
01652 "        degrees or smaller, Triangle is mathematically guaranteed to\n");
01653   printf(
01654 "        terminate (assuming infinite precision arithmetic--Triangle may\n");
01655   printf(
01656 "        fail to terminate if you run out of precision).  In practice,\n");
01657   printf(
01658 "        Triangle often succeeds for minimum angles up to 34 degrees.  For\n");
01659   printf(
01660 "        some meshes, however, you might need to reduce the minimum angle to\n"
01661 );
01662   printf(
01663 "        avoid problems associated with insufficient floating-point\n");
01664   printf("        precision.\n");
01665   printf(
01666 "    -a  Imposes a maximum triangle area.  If a number follows the `a', no\n");
01667   printf(
01668 "        triangle is generated whose area is larger than that number.  If no\n"
01669 );
01670   printf(
01671 "        number is specified, an .area file (if -r is used) or .poly file\n");
01672   printf(
01673 "        (if -r is not used) specifies a set of maximum area constraints.\n");
01674   printf(
01675 "        An .area file contains a separate area constraint for each\n");
01676   printf(
01677 "        triangle, and is useful for refining a finite element mesh based on\n"
01678 );
01679   printf(
01680 "        a posteriori error estimates.  A .poly file can optionally contain\n"
01681 );
01682   printf(
01683 "        an area constraint for each segment-bounded region, thereby\n");
01684   printf(
01685 "        controlling triangle densities in a first triangulation of a PSLG.\n"
01686 );
01687   printf(
01688 "        You can impose both a fixed area constraint and a varying area\n");
01689   printf(
01690 "        constraint by invoking the -a switch twice, once with and once\n");
01691   printf(
01692 "        without a number following.  Each area specified may include a\n");
01693   printf("        decimal point.\n");
01694   printf(
01695 "    -u  Imposes a user-defined constraint on triangle size.  There are two\n"
01696 );
01697   printf(
01698 "        ways to use this feature.  One is to edit the triunsuitable()\n");
01699   printf(
01700 "        procedure in triangle.c to encode any constraint you like, then\n");
01701   printf(
01702 "        recompile Triangle.  The other is to compile triangle.c with the\n");
01703   printf(
01704 "        EXTERNAL_TEST symbol set (compiler switch -DEXTERNAL_TEST), then\n");
01705   printf(
01706 "        link Triangle with a separate object file that implements\n");
01707   printf(
01708 "        triunsuitable().  In either case, the -u switch causes the user-\n");
01709   printf("        defined test to be applied to every triangle.\n");
01710   printf(
01711 "    -A  Assigns an additional floating-point attribute to each triangle\n");
01712   printf(
01713 "        that identifies what segment-bounded region each triangle belongs\n");
01714   printf(
01715 "        to.  Attributes are assigned to regions by the .poly file.  If a\n");
01716   printf(
01717 "        region is not explicitly marked by the .poly file, triangles in\n");
01718   printf(
01719 "        that region are assigned an attribute of zero.  The -A switch has\n");
01720   printf(
01721 "        an effect only when the -p switch is used and the -r switch is not.\n"
01722 );
01723   printf(
01724 "    -c  Creates segments on the convex hull of the triangulation.  If you\n");
01725   printf(
01726 "        are triangulating a vertex set, this switch causes a .poly file to\n"
01727 );
01728   printf(
01729 "        be written, containing all edges of the convex hull.  If you are\n");
01730   printf(
01731 "        triangulating a PSLG, this switch specifies that the whole convex\n");
01732   printf(
01733 "        hull of the PSLG should be triangulated, regardless of what\n");
01734   printf(
01735 "        segments the PSLG has.  If you do not use this switch when\n");
01736   printf(
01737 "        triangulating a PSLG, Triangle assumes that you have identified the\n"
01738 );
01739   printf(
01740 "        region to be triangulated by surrounding it with segments of the\n");
01741   printf(
01742 "        input PSLG.  Beware:  if you are not careful, this switch can cause\n"
01743 );
01744   printf(
01745 "        the introduction of an extremely thin angle between a PSLG segment\n"
01746 );
01747   printf(
01748 "        and a convex hull segment, which can cause overrefinement (and\n");
01749   printf(
01750 "        possibly failure if Triangle runs out of precision).  If you are\n");
01751   printf(
01752 "        refining a mesh, the -c switch works differently:  it causes a\n");
01753   printf(
01754 "        .poly file to be written containing the boundary edges of the mesh\n"
01755 );
01756   printf("        (useful if no .poly file was read).\n");
01757   printf(
01758 "    -D  Conforming Delaunay triangulation:  use this switch if you want to\n"
01759 );
01760   printf(
01761 "        ensure that all the triangles in the mesh are Delaunay, and not\n");
01762   printf(
01763 "        merely constrained Delaunay; or if you want to ensure that all the\n"
01764 );
01765   printf(
01766 "        Voronoi vertices lie within the triangulation.  (Some finite volume\n"
01767 );
01768   printf(
01769 "        methods have this requirement.)  This switch invokes Ruppert's\n");
01770   printf(
01771 "        original algorithm, which splits every subsegment whose diametral\n");
01772   printf(
01773 "        circle is encroached.  It usually increases the number of vertices\n"
01774 );
01775   printf("        and triangles.\n");
01776   printf(
01777 "    -j  Jettisons vertices that are not part of the final triangulation\n");
01778   printf(
01779 "        from the output .node file.  By default, Triangle copies all\n");
01780   printf(
01781 "        vertices in the input .node file to the output .node file, in the\n");
01782   printf(
01783 "        same order, so their indices do not change.  The -j switch prevents\n"
01784 );
01785   printf(
01786 "        duplicated input vertices, or vertices `eaten' by holes, from\n");
01787   printf(
01788 "        appearing in the output .node file.  Thus, if two input vertices\n");
01789   printf(
01790 "        have exactly the same coordinates, only the first appears in the\n");
01791   printf(
01792 "        output.  If any vertices are jettisoned, the vertex numbering in\n");
01793   printf(
01794 "        the output .node file differs from that of the input .node file.\n");
01795   printf(
01796 "    -e  Outputs (to an .edge file) a list of edges of the triangulation.\n");
01797   printf(
01798 "    -v  Outputs the Voronoi diagram associated with the triangulation.\n");
01799   printf(
01800 "        Does not attempt to detect degeneracies, so some Voronoi vertices\n");
01801   printf(
01802 "        may be duplicated.  See the discussion of Voronoi diagrams below.\n");
01803   printf(
01804 "    -n  Outputs (to a .neigh file) a list of triangles neighboring each\n");
01805   printf("        triangle.\n");
01806   printf(
01807 "    -g  Outputs the mesh to an Object File Format (.off) file, suitable for\n"
01808 );
01809   printf("        viewing with the Geometry Center's Geomview package.\n");
01810   printf(
01811 "    -B  No boundary markers in the output .node, .poly, and .edge output\n");
01812   printf(
01813 "        files.  See the detailed discussion of boundary markers below.\n");
01814   printf(
01815 "    -P  No output .poly file.  Saves disk space, but you lose the ability\n");
01816   printf(
01817 "        to maintain constraining segments on later refinements of the mesh.\n"
01818 );
01819   printf("    -N  No output .node file.\n");
01820   printf("    -E  No output .ele file.\n");
01821   printf(
01822 "    -I  No iteration numbers.  Suppresses the output of .node and .poly\n");
01823   printf(
01824 "        files, so your input files won't be overwritten.  (If your input is\n"
01825 );
01826   printf(
01827 "        a .poly file only, a .node file is written.)  Cannot be used with\n");
01828   printf(
01829 "        the -r switch, because that would overwrite your input .ele file.\n");
01830   printf(
01831 "        Shouldn't be used with the -q, -a, -u, or -s switch if you are\n");
01832   printf(
01833 "        using a .node file for input, because no .node file is written, so\n"
01834 );
01835   printf("        there is no record of any added Steiner points.\n");
01836   printf("    -O  No holes.  Ignores the holes in the .poly file.\n");
01837   printf(
01838 "    -X  No exact arithmetic.  Normally, Triangle uses exact floating-point\n"
01839 );
01840   printf(
01841 "        arithmetic for certain tests if it thinks the inexact tests are not\n"
01842 );
01843   printf(
01844 "        accurate enough.  Exact arithmetic ensures the robustness of the\n");
01845   printf(
01846 "        triangulation algorithms, despite floating-point roundoff error.\n");
01847   printf(
01848 "        Disabling exact arithmetic with the -X switch causes a small\n");
01849   printf(
01850 "        improvement in speed and creates the possibility that Triangle will\n"
01851 );
01852   printf("        fail to produce a valid mesh.  Not recommended.\n");
01853   printf(
01854 "    -z  Numbers all items starting from zero (rather than one).  Note that\n"
01855 );
01856   printf(
01857 "        this switch is normally overridden by the value used to number the\n"
01858 );
01859   printf(
01860 "        first vertex of the input .node or .poly file.  However, this\n");
01861   printf(
01862 "        switch is useful when calling Triangle from another program.\n");
01863   printf(
01864 "    -o2 Generates second-order subparametric elements with six nodes each.\n"
01865 );
01866   printf(
01867 "    -Y  No new vertices on the boundary.  This switch is useful when the\n");
01868   printf(
01869 "        mesh boundary must be preserved so that it conforms to some\n");
01870   printf(
01871 "        adjacent mesh.  Be forewarned that you will probably sacrifice much\n"
01872 );
01873   printf(
01874 "        of the quality of the mesh; Triangle will try, but the resulting\n");
01875   printf(
01876 "        mesh may contain poorly shaped triangles.  Works well if all the\n");
01877   printf(
01878 "        boundary vertices are closely spaced.  Specify this switch twice\n");
01879   printf(
01880 "        (`-YY') to prevent all segment splitting, including internal\n");
01881   printf("        boundaries.\n");
01882   printf(
01883 "    -S  Specifies the maximum number of Steiner points (vertices that are\n");
01884   printf(
01885 "        not in the input, but are added to meet the constraints on minimum\n"
01886 );
01887   printf(
01888 "        angle and maximum area).  The default is to allow an unlimited\n");
01889   printf(
01890 "        number.  If you specify this switch with no number after it,\n");
01891   printf(
01892 "        the limit is set to zero.  Triangle always adds vertices at segment\n"
01893 );
01894   printf(
01895 "        intersections, even if it needs to use more vertices than the limit\n"
01896 );
01897   printf(
01898 "        you set.  When Triangle inserts segments by splitting (-s), it\n");
01899   printf(
01900 "        always adds enough vertices to ensure that all the segments of the\n"
01901 );
01902   printf("        PLSG are recovered, ignoring the limit if necessary.\n");
01903   printf(
01904 "    -i  Uses an incremental rather than a divide-and-conquer algorithm to\n");
01905   printf(
01906 "        construct a Delaunay triangulation.  Try it if the divide-and-\n");
01907   printf("        conquer algorithm fails.\n");
01908   printf(
01909 "    -F  Uses Steven Fortune's sweepline algorithm to construct a Delaunay\n");
01910   printf(
01911 "        triangulation.  Warning:  does not use exact arithmetic for all\n");
01912   printf("        calculations.  An exact result is not guaranteed.\n");
01913   printf(
01914 "    -l  Uses only vertical cuts in the divide-and-conquer algorithm.  By\n");
01915   printf(
01916 "        default, Triangle alternates between vertical and horizontal cuts,\n"
01917 );
01918   printf(
01919 "        which usually improve the speed except with vertex sets that are\n");
01920   printf(
01921 "        small or short and wide.  This switch is primarily of theoretical\n");
01922   printf("        interest.\n");
01923   printf(
01924 "    -s  Specifies that segments should be forced into the triangulation by\n"
01925 );
01926   printf(
01927 "        recursively splitting them at their midpoints, rather than by\n");
01928   printf(
01929 "        generating a constrained Delaunay triangulation.  Segment splitting\n"
01930 );
01931   printf(
01932 "        is true to Ruppert's original algorithm, but can create needlessly\n"
01933 );
01934   printf(
01935 "        small triangles.  This switch is primarily of theoretical interest.\n"
01936 );
01937   printf(
01938 "    -C  Check the consistency of the final mesh.  Uses exact arithmetic for\n"
01939 );
01940   printf(
01941 "        checking, even if the -X switch is used.  Useful if you suspect\n");
01942   printf("        Triangle is buggy.\n");
01943   printf(
01944 "    -Q  Quiet:  Suppresses all explanation of what Triangle is doing,\n");
01945   printf("        unless an error occurs.\n");
01946   printf(
01947 "    -V  Verbose:  Gives detailed information about what Triangle is doing.\n"
01948 );
01949   printf(
01950 "        Add more `V's for increasing amount of detail.  `-V' is most\n");
01951   printf(
01952 "        useful; itgives information on algorithmic progress and much more\n");
01953   printf(
01954 "        detailed statistics.  `-VV' gives vertex-by-vertex details, and\n");
01955   printf(
01956 "        prints so much that Triangle runs much more slowly.  `-VVVV' gives\n"
01957 );
01958   printf("        information only a debugger could love.\n");
01959   printf("    -h  Help:  Displays these instructions.\n");
01960   printf("\n");
01961   printf("Definitions:\n");
01962   printf("\n");
01963   printf(
01964 "  A Delaunay triangulation of a vertex set is a triangulation whose\n");
01965   printf(
01966 "  vertices are the vertex set, that covers the convex hull of the vertex\n");
01967   printf(
01968 "  set.  A Delaunay triangulation has the property that no vertex lies\n");
01969   printf(
01970 "  inside the circumscribing circle (circle that passes through all three\n");
01971   printf("  vertices) of any triangle in the triangulation.\n\n");
01972   printf(
01973 "  A Voronoi diagram of a vertex set is a subdivision of the plane into\n");
01974   printf(
01975 "  polygonal cells (some of which may be unbounded, meaning infinitely\n");
01976   printf(
01977 "  large), where each cell is the set of points in the plane that are closer\n"
01978 );
01979   printf(
01980 "  to some input vertex than to any other input vertex.  The Voronoi diagram\n"
01981 );
01982   printf("  is a geometric dual of the Delaunay triangulation.\n\n");
01983   printf(
01984 "  A Planar Straight Line Graph (PSLG) is a set of vertices and segments.\n");
01985   printf(
01986 "  Segments are simply edges, whose endpoints are all vertices in the PSLG.\n"
01987 );
01988   printf(
01989 "  Segments may intersect each other only at their endpoints.  The file\n");
01990   printf("  format for PSLGs (.poly files) is described below.\n\n");
01991   printf(
01992 "  A constrained Delaunay triangulation (CDT) of a PSLG is similar to a\n");
01993   printf(
01994 "  Delaunay triangulation, but each PSLG segment is present as a single edge\n"
01995 );
01996   printf(
01997 "  of the CDT.  (A constrained Delaunay triangulation is not truly a\n");
01998   printf(
01999 "  Delaunay triangulation, because some of its triangles might not be\n");
02000   printf(
02001 "  Delaunay.)  By definition, a CDT does not have any vertices other than\n");
02002   printf(
02003 "  those specified in the input PSLG.  Depending on context, a CDT might\n");
02004   printf(
02005 "  cover the convex hull of the PSLG, or it might cover only a segment-\n");
02006   printf("  bounded region (e.g. a polygon).\n\n");
02007   printf(
02008 "  A conforming Delaunay triangulation of a PSLG is a triangulation in which\n"
02009 );
02010   printf(
02011 "  each triangle is truly Delaunay, and each PSLG segment is represented by\n"
02012 );
02013   printf(
02014 "  a linear contiguous sequence of edges of the triangulation.  New vertices\n"
02015 );
02016   printf(
02017 "  (not part of the PSLG) may appear, and each input segment may have been\n");
02018   printf(
02019 "  subdivided into shorter edges (subsegments) by these additional vertices.\n"
02020 );
02021   printf(
02022 "  The new vertices are frequently necessary to maintain the Delaunay\n");
02023   printf("  property while ensuring that every segment is represented.\n\n");
02024   printf(
02025 "  A conforming constrained Delaunay triangulation (CCDT) of a PSLG is a\n");
02026   printf(
02027 "  triangulation of a PSLG whose triangles are constrained Delaunay.  New\n");
02028   printf("  vertices may appear, and input segments may be subdivided into\n");
02029   printf(
02030 "  subsegments, but not to guarantee that segments are respected; rather, to\n"
02031 );
02032   printf(
02033 "  improve the quality of the triangles.  The high-quality meshes produced\n");
02034   printf(
02035 "  by the -q switch are usually CCDTs, but can be made conforming Delaunay\n");
02036   printf("  with the -D switch.\n\n");
02037   printf("File Formats:\n\n");
02038   printf(
02039 "  All files may contain comments prefixed by the character '#'.  Vertices,\n"
02040 );
02041   printf(
02042 "  triangles, edges, holes, and maximum area constraints must be numbered\n");
02043   printf(
02044 "  consecutively, starting from either 1 or 0.  Whichever you choose, all\n");
02045   printf(
02046 "  input files must be consistent; if the vertices are numbered from 1, so\n");
02047   printf(
02048 "  must be all other objects.  Triangle automatically detects your choice\n");
02049   printf(
02050 "  while reading the .node (or .poly) file.  (When calling Triangle from\n");
02051   printf(
02052 "  another program, use the -z switch if you wish to number objects from\n");
02053   printf("  zero.)  Examples of these file formats are given below.\n\n");
02054   printf("  .node files:\n");
02055   printf(
02056 "    First line:  <# of vertices> <dimension (must be 2)> <# of attributes>\n"
02057 );
02058   printf(
02059 "                                           <# of boundary markers (0 or 1)>\n"
02060 );
02061   printf(
02062 "    Remaining lines:  <vertex #> <x> <y> [attributes] [boundary marker]\n");
02063   printf("\n");
02064   printf(
02065 "    The attributes, which are typically floating-point values of physical\n");
02066   printf(
02067 "    quantities (such as mass or conductivity) associated with the nodes of\n"
02068 );
02069   printf(
02070 "    a finite element mesh, are copied unchanged to the output mesh.  If -q,\n"
02071 );
02072   printf(
02073 "    -a, -u, -D, or -s is selected, each new Steiner point added to the mesh\n"
02074 );
02075   printf("    has attributes assigned to it by linear interpolation.\n\n");
02076   printf(
02077 "    If the fourth entry of the first line is `1', the last column of the\n");
02078   printf(
02079 "    remainder of the file is assumed to contain boundary markers.  Boundary\n"
02080 );
02081   printf(
02082 "    markers are used to identify boundary vertices and vertices resting on\n"
02083 );
02084   printf(
02085 "    PSLG segments; a complete description appears in a section below.  The\n"
02086 );
02087   printf(
02088 "    .node file produced by Triangle contains boundary markers in the last\n");
02089   printf("    column unless they are suppressed by the -B switch.\n\n");
02090   printf("  .ele files:\n");
02091   printf(
02092 "    First line:  <# of triangles> <nodes per triangle> <# of attributes>\n");
02093   printf(
02094 "    Remaining lines:  <triangle #> <node> <node> <node> ... [attributes]\n");
02095   printf("\n");
02096   printf(
02097 "    Nodes are indices into the corresponding .node file.  The first three\n");
02098   printf(
02099 "    nodes are the corner vertices, and are listed in counterclockwise order\n"
02100 );
02101   printf(
02102 "    around each triangle.  (The remaining nodes, if any, depend on the type\n"
02103 );
02104   printf("    of finite element used.)\n\n");
02105   printf(
02106 "    The attributes are just like those of .node files.  Because there is no\n"
02107 );
02108   printf(
02109 "    simple mapping from input to output triangles, Triangle attempts to\n");
02110   printf(
02111 "    interpolate attributes, and may cause a lot of diffusion of attributes\n"
02112 );
02113   printf(
02114 "    among nearby triangles as the triangulation is refined.  Attributes do\n"
02115 );
02116   printf("    not diffuse across segments, so attributes used to identify\n");
02117   printf("    segment-bounded regions remain intact.\n\n");
02118   printf(
02119 "    In .ele files produced by Triangle, each triangular element has three\n");
02120   printf(
02121 "    nodes (vertices) unless the -o2 switch is used, in which case\n");
02122   printf(
02123 "    subparametric quadratic elements with six nodes each are generated.\n");
02124   printf(
02125 "    The first three nodes are the corners in counterclockwise order, and\n");
02126   printf(
02127 "    the fourth, fifth, and sixth nodes lie on the midpoints of the edges\n");
02128   printf(
02129 "    opposite the first, second, and third vertices, respectively.\n");
02130   printf("\n");
02131   printf("  .poly files:\n");
02132   printf(
02133 "    First line:  <# of vertices> <dimension (must be 2)> <# of attributes>\n"
02134 );
02135   printf(
02136 "                                           <# of boundary markers (0 or 1)>\n"
02137 );
02138   printf(
02139 "    Following lines:  <vertex #> <x> <y> [attributes] [boundary marker]\n");
02140   printf("    One line:  <# of segments> <# of boundary markers (0 or 1)>\n");
02141   printf(
02142 "    Following lines:  <segment #> <endpoint> <endpoint> [boundary marker]\n");
02143   printf("    One line:  <# of holes>\n");
02144   printf("    Following lines:  <hole #> <x> <y>\n");
02145   printf(
02146 "    Optional line:  <# of regional attributes and/or area constraints>\n");
02147   printf(
02148 "    Optional following lines:  <region #> <x> <y> <attribute> <max area>\n");
02149   printf("\n");
02150   printf(
02151 "    A .poly file represents a PSLG, as well as some additional information.\n"
02152 );
02153   printf(
02154 "    The first section lists all the vertices, and is identical to the\n");
02155   printf(
02156 "    format of .node files.  <# of vertices> may be set to zero to indicate\n"
02157 );
02158   printf(
02159 "    that the vertices are listed in a separate .node file; .poly files\n");
02160   printf(
02161 "    produced by Triangle always have this format.  A vertex set represented\n"
02162 );
02163   printf(
02164 "    this way has the advantage that it may easily be triangulated with or\n");
02165   printf(
02166 "    without segments (depending on whether the -p switch is invoked).\n");
02167   printf("\n");
02168   printf(
02169 "    The second section lists the segments.  Segments are edges whose\n");
02170   printf(
02171 "    presence in the triangulation is enforced.  (Depending on the choice of\n"
02172 );
02173   printf(
02174 "    switches, segment might be subdivided into smaller edges).  Each\n");
02175   printf(
02176 "    segment is specified by listing the indices of its two endpoints.  This\n"
02177 );
02178   printf(
02179 "    means that you must include its endpoints in the vertex list.  Each\n");
02180   printf("    segment, like each point, may have a boundary marker.\n\n");
02181   printf(
02182 "    If -q, -a, -u, and -s are not selected, Triangle produces a constrained\n"
02183 );
02184   printf(
02185 "    Delaunay triangulation (CDT), in which each segment appears as a single\n"
02186 );
02187   printf(
02188 "    edge in the triangulation.  If -q, -a, -u, or -s is selected, Triangle\n"
02189 );
02190   printf(
02191 "    produces a conforming constrained Delaunay triangulation (CCDT), in\n");
02192   printf(
02193 "    which segments may be subdivided into smaller edges.  If -D is\n");
02194   printf(
02195 "    selected, Triangle produces a conforming Delaunay triangulation, so\n");
02196   printf(
02197 "    that every triangle is Delaunay, and not just constrained Delaunay.\n");
02198   printf("\n");
02199   printf(
02200 "    The third section lists holes (and concavities, if -c is selected) in\n");
02201   printf(
02202 "    the triangulation.  Holes are specified by identifying a point inside\n");
02203   printf(
02204 "    each hole.  After the triangulation is formed, Triangle creates holes\n");
02205   printf(
02206 "    by eating triangles, spreading out from each hole point until its\n");
02207   printf(
02208 "    progress is blocked by segments in the PSLG.  You must be careful to\n");
02209   printf(
02210 "    enclose each hole in segments, or your whole triangulation might be\n");
02211   printf(
02212 "    eaten away.  If the two triangles abutting a segment are eaten, the\n");
02213   printf(
02214 "    segment itself is also eaten.  Do not place a hole directly on a\n");
02215   printf("    segment; if you do, Triangle chooses one side of the segment\n");
02216   printf("    arbitrarily.\n\n");
02217   printf(
02218 "    The optional fourth section lists regional attributes (to be assigned\n");
02219   printf(
02220 "    to all triangles in a region) and regional constraints on the maximum\n");
02221   printf(
02222 "    triangle area.  Triangle reads this section only if the -A switch is\n");
02223   printf(
02224 "    used or the -a switch is used without a number following it, and the -r\n"
02225 );
02226   printf(
02227 "    switch is not used.  Regional attributes and area constraints are\n");
02228   printf(
02229 "    propagated in the same manner as holes:  you specify a point for each\n");
02230   printf(
02231 "    attribute and/or constraint, and the attribute and/or constraint\n");
02232   printf(
02233 "    affects the whole region (bounded by segments) containing the point.\n");
02234   printf(
02235 "    If two values are written on a line after the x and y coordinate, the\n");
02236   printf(
02237 "    first such value is assumed to be a regional attribute (but is only\n");
02238   printf(
02239 "    applied if the -A switch is selected), and the second value is assumed\n"
02240 );
02241   printf(
02242 "    to be a regional area constraint (but is only applied if the -a switch\n"
02243 );
02244   printf(
02245 "    is selected).  You may specify just one value after the coordinates,\n");
02246   printf(
02247 "    which can serve as both an attribute and an area constraint, depending\n"
02248 );
02249   printf(
02250 "    on the choice of switches.  If you are using the -A and -a switches\n");
02251   printf(
02252 "    simultaneously and wish to assign an attribute to some region without\n");
02253   printf("    imposing an area constraint, use a negative maximum area.\n\n");
02254   printf(
02255 "    When a triangulation is created from a .poly file, you must either\n");
02256   printf(
02257 "    enclose the entire region to be triangulated in PSLG segments, or\n");
02258   printf(
02259 "    use the -c switch, which automatically creates extra segments that\n");
02260   printf(
02261 "    enclose the convex hull of the PSLG.  If you do not use the -c switch,\n"
02262 );
02263   printf(
02264 "    Triangle eats all triangles that are not enclosed by segments; if you\n");
02265   printf(
02266 "    are not careful, your whole triangulation may be eaten away.  If you do\n"
02267 );
02268   printf(
02269 "    use the -c switch, you can still produce concavities by the appropriate\n"
02270 );
02271   printf(
02272 "    placement of holes just inside the boundary of the convex hull.\n");
02273   printf("\n");
02274   printf(
02275 "    An ideal PSLG has no intersecting segments, nor any vertices that lie\n");
02276   printf(
02277 "    upon segments (except, of course, the endpoints of each segment).  You\n"
02278 );
02279   printf(
02280 "    aren't required to make your .poly files ideal, but you should be aware\n"
02281 );
02282   printf(
02283 "    of what can go wrong.  Segment intersections are relatively safe--\n");
02284   printf(
02285 "    Triangle calculates the intersection points for you and adds them to\n");
02286   printf(
02287 "    the triangulation--as long as your machine's floating-point precision\n");
02288   printf(
02289 "    doesn't become a problem.  You are tempting the fates if you have three\n"
02290 );
02291   printf(
02292 "    segments that cross at the same location, and expect Triangle to figure\n"
02293 );
02294   printf(
02295 "    out where the intersection point is.  Thanks to floating-point roundoff\n"
02296 );
02297   printf(
02298 "    error, Triangle will probably decide that the three segments intersect\n"
02299 );
02300   printf(
02301 "    at three different points, and you will find a minuscule triangle in\n");
02302   printf(
02303 "    your output--unless Triangle tries to refine the tiny triangle, uses\n");
02304   printf(
02305 "    up the last bit of machine precision, and fails to terminate at all.\n");
02306   printf(
02307 "    You're better off putting the intersection point in the input files,\n");
02308   printf(
02309 "    and manually breaking up each segment into two.  Similarly, if you\n");
02310   printf(
02311 "    place a vertex at the middle of a segment, and hope that Triangle will\n"
02312 );
02313   printf(
02314 "    break up the segment at that vertex, you might get lucky.  On the other\n"
02315 );
02316   printf(
02317 "    hand, Triangle might decide that the vertex doesn't lie precisely on\n");
02318   printf(
02319 "    the segment, and you'll have a needle-sharp triangle in your output--or\n"
02320 );
02321   printf("    a lot of tiny triangles if you're generating a quality mesh.\n");
02322   printf("\n");
02323   printf(
02324 "    When Triangle reads a .poly file, it also writes a .poly file, which\n");
02325   printf(
02326 "    includes all the subsegments--the edges that are parts of input\n");
02327   printf(
02328 "    segments.  If the -c switch is used, the output .poly file also\n");
02329   printf(
02330 "    includes all of the edges on the convex hull.  Hence, the output .poly\n"
02331 );
02332   printf(
02333 "    file is useful for finding edges associated with input segments and for\n"
02334 );
02335   printf(
02336 "    setting boundary conditions in finite element simulations.  Moreover,\n");
02337   printf(
02338 "    you will need the output .poly file if you plan to refine the output\n");
02339   printf(
02340 "    mesh, and don't want segments to be missing in later triangulations.\n");
02341   printf("\n");
02342   printf("  .area files:\n");
02343   printf("    First line:  <# of triangles>\n");
02344   printf("    Following lines:  <triangle #> <maximum area>\n");
02345   printf("\n");
02346   printf(
02347 "    An .area file associates with each triangle a maximum area that is used\n"
02348 );
02349   printf(
02350 "    for mesh refinement.  As with other file formats, every triangle must\n");
02351   printf(
02352 "    be represented, and the triangles must be numbered consecutively.  A\n");
02353   printf(
02354 "    triangle may be left unconstrained by assigning it a negative maximum\n");
02355   printf("    area.\n\n");
02356   printf("  .edge files:\n");
02357   printf("    First line:  <# of edges> <# of boundary markers (0 or 1)>\n");
02358   printf(
02359 "    Following lines:  <edge #> <endpoint> <endpoint> [boundary marker]\n");
02360   printf("\n");
02361   printf(
02362 "    Endpoints are indices into the corresponding .node file.  Triangle can\n"
02363 );
02364   printf(
02365 "    produce .edge files (use the -e switch), but cannot read them.  The\n");
02366   printf(
02367 "    optional column of boundary markers is suppressed by the -B switch.\n");
02368   printf("\n");
02369   printf(
02370 "    In Voronoi diagrams, one also finds a special kind of edge that is an\n");
02371   printf(
02372 "    infinite ray with only one endpoint.  For these edges, a different\n");
02373   printf("    format is used:\n\n");
02374   printf("        <edge #> <endpoint> -1 <direction x> <direction y>\n\n");
02375   printf(
02376 "    The `direction' is a floating-point vector that indicates the direction\n"
02377 );
02378   printf("    of the infinite ray.\n\n");
02379   printf("  .neigh files:\n");
02380   printf(
02381 "    First line:  <# of triangles> <# of neighbors per triangle (always 3)>\n"
02382 );
02383   printf(
02384 "    Following lines:  <triangle #> <neighbor> <neighbor> <neighbor>\n");
02385   printf("\n");
02386   printf(
02387 "    Neighbors are indices into the corresponding .ele file.  An index of -1\n"
02388 );
02389   printf(
02390 "    indicates no neighbor (because the triangle is on an exterior\n");
02391   printf(
02392 "    boundary).  The first neighbor of triangle i is opposite the first\n");
02393   printf("    corner of triangle i, and so on.\n\n");
02394   printf(
02395 "    Triangle can produce .neigh files (use the -n switch), but cannot read\n"
02396 );
02397   printf("    them.\n\n");
02398   printf("Boundary Markers:\n\n");
02399   printf(
02400 "  Boundary markers are tags used mainly to identify which output vertices\n");
02401   printf(
02402 "  and edges are associated with which PSLG segment, and to identify which\n");
02403   printf(
02404 "  vertices and edges occur on a boundary of the triangulation.  A common\n");
02405   printf(
02406 "  use is to determine where boundary conditions should be applied to a\n");
02407   printf(
02408 "  finite element mesh.  You can prevent boundary markers from being written\n"
02409 );
02410   printf("  into files produced by Triangle by using the -B switch.\n\n");
02411   printf(
02412 "  The boundary marker associated with each segment in an output .poly file\n"
02413 );
02414   printf("  and each edge in an output .edge file is chosen as follows:\n");
02415   printf(
02416 "    - If an output edge is part or all of a PSLG segment with a nonzero\n");
02417   printf(
02418 "      boundary marker, then the edge is assigned the same marker.\n");
02419   printf(
02420 "    - Otherwise, if the edge lies on a boundary of the triangulation\n");
02421   printf(
02422 "      (even the boundary of a hole), then the edge is assigned the marker\n");
02423   printf("      one (1).\n");
02424   printf("    - Otherwise, the edge is assigned the marker zero (0).\n");
02425   printf(
02426 "  The boundary marker associated with each vertex in an output .node file\n");
02427   printf("  is chosen as follows:\n");
02428   printf(
02429 "    - If a vertex is assigned a nonzero boundary marker in the input file,\n"
02430 );
02431   printf(
02432 "      then it is assigned the same marker in the output .node file.\n");
02433   printf(
02434 "    - Otherwise, if the vertex lies on a PSLG segment (even if it is an\n");
02435   printf(
02436 "      endpoint of the segment) with a nonzero boundary marker, then the\n");
02437   printf(
02438 "      vertex is assigned the same marker.  If the vertex lies on several\n");
02439   printf("      such segments, one of the markers is chosen arbitrarily.\n");
02440   printf(
02441 "    - Otherwise, if the vertex occurs on a boundary of the triangulation,\n");
02442   printf("      then the vertex is assigned the marker one (1).\n");
02443   printf("    - Otherwise, the vertex is assigned the marker zero (0).\n");
02444   printf("\n");
02445   printf(
02446 "  If you want Triangle to determine for you which vertices and edges are on\n"
02447 );
02448   printf(
02449 "  the boundary, assign them the boundary marker zero (or use no markers at\n"
02450 );
02451   printf(
02452 "  all) in your input files.  In the output files, all boundary vertices,\n");
02453   printf("  edges, and segments will be assigned the value one.\n\n");
02454   printf("Triangulation Iteration Numbers:\n\n");
02455   printf(
02456 "  Because Triangle can read and refine its own triangulations, input\n");
02457   printf(
02458 "  and output files have iteration numbers.  For instance, Triangle might\n");
02459   printf(
02460 "  read the files mesh.3.node, mesh.3.ele, and mesh.3.poly, refine the\n");
02461   printf(
02462 "  triangulation, and output the files mesh.4.node, mesh.4.ele, and\n");
02463   printf("  mesh.4.poly.  Files with no iteration number are treated as if\n");
02464   printf(
02465 "  their iteration number is zero; hence, Triangle might read the file\n");
02466   printf(
02467 "  points.node, triangulate it, and produce the files points.1.node and\n");
02468   printf("  points.1.ele.\n\n");
02469   printf(
02470 "  Iteration numbers allow you to create a sequence of successively finer\n");
02471   printf(
02472 "  meshes suitable for multigrid methods.  They also allow you to produce a\n"
02473 );
02474   printf(
02475 "  sequence of meshes using error estimate-driven mesh refinement.\n");
02476   printf("\n");
02477   printf(
02478 "  If you're not using refinement or quality meshing, and you don't like\n");
02479   printf(
02480 "  iteration numbers, use the -I switch to disable them.  This switch also\n");
02481   printf(
02482 "  disables output of .node and .poly files to prevent your input files from\n"
02483 );
02484   printf(
02485 "  being overwritten.  (If the input is a .poly file that contains its own\n");
02486   printf(
02487 "  points, a .node file is written.  This can be quite convenient for\n");
02488   printf("  computing CDTs or quality meshes.)\n\n");
02489   printf("Examples of How to Use Triangle:\n\n");
02490   printf(
02491 "  `triangle dots' reads vertices from dots.node, and writes their Delaunay\n"
02492 );
02493   printf(
02494 "  triangulation to dots.1.node and dots.1.ele.  (dots.1.node is identical\n");
02495   printf(
02496 "  to dots.node.)  `triangle -I dots' writes the triangulation to dots.ele\n");
02497   printf(
02498 "  instead.  (No additional .node file is needed, so none is written.)\n");
02499   printf("\n");
02500   printf(
02501 "  `triangle -pe object.1' reads a PSLG from object.1.poly (and possibly\n");
02502   printf(
02503 "  object.1.node, if the vertices are omitted from object.1.poly) and writes\n"
02504 );
02505   printf(
02506 "  its constrained Delaunay triangulation to object.2.node and object.2.ele.\n"
02507 );
02508   printf(
02509 "  The segments are copied to object.2.poly, and all edges are written to\n");
02510   printf("  object.2.edge.\n\n");
02511   printf(
02512 "  `triangle -pq31.5a.1 object' reads a PSLG from object.poly (and possibly\n"
02513 );
02514   printf(
02515 "  object.node), generates a mesh whose angles are all between 31.5 and 117\n"
02516 );
02517   printf(
02518 "  degrees and whose triangles all have areas of 0.1 or less, and writes the\n"
02519 );
02520   printf(
02521 "  mesh to object.1.node and object.1.ele.  Each segment may be broken up\n");
02522   printf("  into multiple subsegments; these are written to object.1.poly.\n");
02523   printf("\n");
02524   printf(
02525 "  Here is a sample file `box.poly' describing a square with a square hole:\n"
02526 );
02527   printf("\n");
02528   printf(
02529 "    # A box with eight vertices in 2D, no attributes, one boundary marker.\n"
02530 );
02531   printf("    8 2 0 1\n");
02532   printf("     # Outer box has these vertices:\n");
02533   printf("     1   0 0   0\n");
02534   printf("     2   0 3   0\n");
02535   printf("     3   3 0   0\n");
02536   printf("     4   3 3   33     # A special marker for this vertex.\n");
02537   printf("     # Inner square has these vertices:\n");
02538   printf("     5   1 1   0\n");
02539   printf("     6   1 2   0\n");
02540   printf("     7   2 1   0\n");
02541   printf("     8   2 2   0\n");
02542   printf("    # Five segments with boundary markers.\n");
02543   printf("    5 1\n");
02544   printf("     1   1 2   5      # Left side of outer box.\n");
02545   printf("     # Square hole has these segments:\n");
02546   printf("     2   5 7   0\n");
02547   printf("     3   7 8   0\n");
02548   printf("     4   8 6   10\n");
02549   printf("     5   6 5   0\n");
02550   printf("    # One hole in the middle of the inner square.\n");
02551   printf("    1\n");
02552   printf("     1   1.5 1.5\n");
02553   printf("\n");
02554   printf(
02555 "  Note that some segments are missing from the outer square, so you must\n");
02556   printf(
02557 "  use the `-c' switch.  After `triangle -pqc box.poly', here is the output\n"
02558 );
02559   printf(
02560 "  file `box.1.node', with twelve vertices.  The last four vertices were\n");
02561   printf(
02562 "  added to meet the angle constraint.  Vertices 1, 2, and 9 have markers\n");
02563   printf(
02564 "  from segment 1.  Vertices 6 and 8 have markers from segment 4.  All the\n");
02565   printf(
02566 "  other vertices but 4 have been marked to indicate that they lie on a\n");
02567   printf("  boundary.\n\n");
02568   printf("    12  2  0  1\n");
02569   printf("       1    0   0      5\n");
02570   printf("       2    0   3      5\n");
02571   printf("       3    3   0      1\n");
02572   printf("       4    3   3     33\n");
02573   printf("       5    1   1      1\n");
02574   printf("       6    1   2     10\n");
02575   printf("       7    2   1      1\n");
02576   printf("       8    2   2     10\n");
02577   printf("       9    0   1.5    5\n");
02578   printf("      10    1.5   0    1\n");
02579   printf("      11    3   1.5    1\n");
02580   printf("      12    1.5   3    1\n");
02581   printf("    # Generated by triangle -pqc box.poly\n");
02582   printf("\n");
02583   printf("  Here is the output file `box.1.ele', with twelve triangles.\n");
02584   printf("\n");
02585   printf("    12  3  0\n");
02586   printf("       1     5   6   9\n");
02587   printf("       2    10   3   7\n");
02588   printf("       3     6   8  12\n");
02589   printf("       4     9   1   5\n");
02590   printf("       5     6   2   9\n");
02591   printf("       6     7   3  11\n");
02592   printf("       7    11   4   8\n");
02593   printf("       8     7   5  10\n");
02594   printf("       9    12   2   6\n");
02595   printf("      10     8   7  11\n");
02596   printf("      11     5   1  10\n");
02597   printf("      12     8   4  12\n");
02598   printf("    # Generated by triangle -pqc box.poly\n\n");
02599   printf(
02600 "  Here is the output file `box.1.poly'.  Note that segments have been added\n"
02601 );
02602   printf(
02603 "  to represent the convex hull, and some segments have been subdivided by\n");
02604   printf(
02605 "  newly added vertices.  Note also that <# of vertices> is set to zero to\n");
02606   printf("  indicate that the vertices should be read from the .node file.\n");
02607   printf("\n");
02608   printf("    0  2  0  1\n");
02609   printf("    12  1\n");
02610   printf("       1     1   9     5\n");
02611   printf("       2     5   7     1\n");
02612   printf("       3     8   7     1\n");
02613   printf("       4     6   8    10\n");
02614   printf("       5     5   6     1\n");
02615   printf("       6     3  10     1\n");
02616   printf("       7     4  11     1\n");
02617   printf("       8     2  12     1\n");
02618   printf("       9     9   2     5\n");
02619   printf("      10    10   1     1\n");
02620   printf("      11    11   3     1\n");
02621   printf("      12    12   4     1\n");
02622   printf("    1\n");
02623   printf("       1   1.5 1.5\n");
02624   printf("    # Generated by triangle -pqc box.poly\n");
02625   printf("\n");
02626   printf("Refinement and Area Constraints:\n");
02627   printf("\n");
02628   printf(
02629 "  The -r switch causes a mesh (.node and .ele files) to be read and\n");
02630   printf(
02631 "  refined.  If the -p switch is also used, a .poly file is read and used to\n"
02632 );
02633   printf(
02634 "  specify edges that are constrained and cannot be eliminated (although\n");
02635   printf(
02636 "  they can be subdivided into smaller edges) by the refinement process.\n");
02637   printf("\n");
02638   printf(
02639 "  When you refine a mesh, you generally want to impose tighter constraints.\n"
02640 );
02641   printf(
02642 "  One way to accomplish this is to use -q with a larger angle, or -a\n");
02643   printf(
02644 "  followed by a smaller area than you used to generate the mesh you are\n");
02645   printf(
02646 "  refining.  Another way to do this is to create an .area file, which\n");
02647   printf(
02648 "  specifies a maximum area for each triangle, and use the -a switch\n");
02649   printf(
02650 "  (without a number following).  Each triangle's area constraint is applied\n"
02651 );
02652   printf(
02653 "  to that triangle.  Area constraints tend to diffuse as the mesh is\n");
02654   printf(
02655 "  refined, so if there are large variations in area constraint between\n");
02656   printf(
02657 "  adjacent triangles, you may not get the results you want.  In that case,\n"
02658 );
02659   printf(
02660 "  consider instead using the -u switch and writing a C procedure that\n");
02661   printf("  determines which triangles are too large.\n\n");
02662   printf(
02663 "  If you are refining a mesh composed of linear (three-node) elements, the\n"
02664 );
02665   printf(
02666 "  output mesh contains all the nodes present in the input mesh, in the same\n"
02667 );
02668   printf(
02669 "  order, with new nodes added at the end of the .node file.  However, the\n");
02670   printf(
02671 "  refinement is not hierarchical: there is no guarantee that each output\n");
02672   printf(
02673 "  element is contained in a single input element.  Often, an output element\n"
02674 );
02675   printf(
02676 "  can overlap two or three input elements, and some input edges are not\n");
02677   printf(
02678 "  present in the output mesh.  Hence, a sequence of refined meshes forms a\n"
02679 );
02680   printf(
02681 "  hierarchy of nodes, but not a hierarchy of elements.  If you refine a\n");
02682   printf(
02683 "  mesh of higher-order elements, the hierarchical property applies only to\n"
02684 );
02685   printf(
02686 "  the nodes at the corners of an element; the midpoint nodes on each edge\n");
02687   printf("  are discarded before the mesh is refined.\n\n");
02688   printf(
02689 "  Maximum area constraints in .poly files operate differently from those in\n"
02690 );
02691   printf(
02692 "  .area files.  A maximum area in a .poly file applies to the whole\n");
02693   printf(
02694 "  (segment-bounded) region in which a point falls, whereas a maximum area\n");
02695   printf(
02696 "  in an .area file applies to only one triangle.  Area constraints in .poly\n"
02697 );
02698   printf(
02699 "  files are used only when a mesh is first generated, whereas area\n");
02700   printf(
02701 "  constraints in .area files are used only to refine an existing mesh, and\n"
02702 );
02703   printf(
02704 "  are typically based on a posteriori error estimates resulting from a\n");
02705   printf("  finite element simulation on that mesh.\n\n");
02706   printf(
02707 "  `triangle -rq25 object.1' reads object.1.node and object.1.ele, then\n");
02708   printf(
02709 "  refines the triangulation to enforce a 25 degree minimum angle, and then\n"
02710 );
02711   printf(
02712 "  writes the refined triangulation to object.2.node and object.2.ele.\n");
02713   printf("\n");
02714   printf(
02715 "  `triangle -rpaa6.2 z.3' reads z.3.node, z.3.ele, z.3.poly, and z.3.area.\n"
02716 );
02717   printf(
02718 "  After reconstructing the mesh and its subsegments, Triangle refines the\n");
02719   printf(
02720 "  mesh so that no triangle has area greater than 6.2, and furthermore the\n");
02721   printf(
02722 "  triangles satisfy the maximum area constraints in z.3.area.  No angle\n");
02723   printf(
02724 "  bound is imposed at all.  The output is written to z.4.node, z.4.ele, and\n"
02725 );
02726   printf("  z.4.poly.\n\n");
02727   printf(
02728 "  The sequence `triangle -qa1 x', `triangle -rqa.3 x.1', `triangle -rqa.1\n");
02729   printf(
02730 "  x.2' creates a sequence of successively finer meshes x.1, x.2, and x.3,\n");
02731   printf("  suitable for multigrid.\n\n");
02732   printf("Convex Hulls and Mesh Boundaries:\n\n");
02733   printf(
02734 "  If the input is a vertex set (not a PSLG), Triangle produces its convex\n");
02735   printf(
02736 "  hull as a by-product in the output .poly file if you use the -c switch.\n");
02737   printf(
02738 "  There are faster algorithms for finding a two-dimensional convex hull\n");
02739   printf("  than triangulation, of course, but this one comes for free.\n\n");
02740   printf(
02741 "  If the input is an unconstrained mesh (you are using the -r switch but\n");
02742   printf(
02743 "  not the -p switch), Triangle produces a list of its boundary edges\n");
02744   printf(
02745 "  (including hole boundaries) as a by-product when you use the -c switch.\n");
02746   printf(
02747 "  If you also use the -p switch, the output .poly file contains all the\n");
02748   printf("  segments from the input .poly file as well.\n\n");
02749   printf("Voronoi Diagrams:\n\n");
02750   printf(
02751 "  The -v switch produces a Voronoi diagram, in files suffixed .v.node and\n");
02752   printf(
02753 "  .v.edge.  For example, `triangle -v points' reads points.node, produces\n");
02754   printf(
02755 "  its Delaunay triangulation in points.1.node and points.1.ele, and\n");
02756   printf(
02757 "  produces its Voronoi diagram in points.1.v.node and points.1.v.edge.  The\n"
02758 );
02759   printf(
02760 "  .v.node file contains a list of all Voronoi vertices, and the .v.edge\n");
02761   printf(
02762 "  file contains a list of all Voronoi edges, some of which may be infinite\n"
02763 );
02764   printf(
02765 "  rays.  (The choice of filenames makes it easy to run the set of Voronoi\n");
02766   printf("  vertices through Triangle, if so desired.)\n\n");
02767   printf(
02768 "  This implementation does not use exact arithmetic to compute the Voronoi\n"
02769 );
02770   printf(
02771 "  vertices, and does not check whether neighboring vertices are identical.\n"
02772 );
02773   printf(
02774 "  Be forewarned that if the Delaunay triangulation is degenerate or\n");
02775   printf(
02776 "  near-degenerate, the Voronoi diagram may have duplicate vertices or\n");
02777   printf("  crossing edges.\n\n");
02778   printf(
02779 "  The result is a valid Voronoi diagram only if Triangle's output is a true\n"
02780 );
02781   printf(
02782 "  Delaunay triangulation.  The Voronoi output is usually meaningless (and\n");
02783   printf(
02784 "  may contain crossing edges and other pathology) if the output is a CDT or\n"
02785 );
02786   printf(
02787 "  CCDT, or if it has holes or concavities.  If the triangulated domain is\n");
02788   printf(
02789 "  convex and has no holes, you can use -D switch to force Triangle to\n");
02790   printf(
02791 "  construct a conforming Delaunay triangulation instead of a CCDT, so the\n");
02792   printf("  Voronoi diagram will be valid.\n\n");
02793   printf("Mesh Topology:\n\n");
02794   printf(
02795 "  You may wish to know which triangles are adjacent to a certain Delaunay\n");
02796   printf(
02797 "  edge in an .edge file, which Voronoi cells are adjacent to a certain\n");
02798   printf(
02799 "  Voronoi edge in a .v.edge file, or which Voronoi cells are adjacent to\n");
02800   printf(
02801 "  each other.  All of this information can be found by cross-referencing\n");
02802   printf(
02803 "  output files with the recollection that the Delaunay triangulation and\n");
02804   printf("  the Voronoi diagram are planar duals.\n\n");
02805   printf(
02806 "  Specifically, edge i of an .edge file is the dual of Voronoi edge i of\n");
02807   printf(
02808 "  the corresponding .v.edge file, and is rotated 90 degrees counterclock-\n");
02809   printf(
02810 "  wise from the Voronoi edge.  Triangle j of an .ele file is the dual of\n");
02811   printf(
02812 "  vertex j of the corresponding .v.node file.  Voronoi cell k is the dual\n");
02813   printf("  of vertex k of the corresponding .node file.\n\n");
02814   printf(
02815 "  Hence, to find the triangles adjacent to a Delaunay edge, look at the\n");
02816   printf(
02817 "  vertices of the corresponding Voronoi edge.  If the endpoints of a\n");
02818   printf(
02819 "  Voronoi edge are Voronoi vertices 2 and 6 respectively, then triangles 2\n"
02820 );
02821   printf(
02822 "  and 6 adjoin the left and right sides of the corresponding Delaunay edge,\n"
02823 );
02824   printf(
02825 "  respectively.  To find the Voronoi cells adjacent to a Voronoi edge, look\n"
02826 );
02827   printf(
02828 "  at the endpoints of the corresponding Delaunay edge.  If the endpoints of\n"
02829 );
02830   printf(
02831 "  a Delaunay edge are input vertices 7 and 12, then Voronoi cells 7 and 12\n"
02832 );
02833   printf(
02834 "  adjoin the right and left sides of the corresponding Voronoi edge,\n");
02835   printf(
02836 "  respectively.  To find which Voronoi cells are adjacent to each other,\n");
02837   printf("  just read the list of Delaunay edges.\n\n");
02838   printf(
02839 "  Triangle does not write a list of the edges adjoining each Voronoi cell,\n"
02840 );
02841   printf(
02842 "  but you can reconstructed it straightforwardly.  For instance, to find\n");
02843   printf(
02844 "  all the edges of Voronoi cell 1, search the output .edge file for every\n");
02845   printf(
02846 "  edge that has input vertex 1 as an endpoint.  The corresponding dual\n");
02847   printf(
02848 "  edges in the output .v.edge file form the boundary of Voronoi cell 1.\n");
02849   printf("\n");
02850   printf(
02851 "  For each Voronoi vertex, the .neigh file gives a list of the three\n");
02852   printf(
02853 "  Voronoi vertices attached to it.  You might find this more convenient\n");
02854   printf("  than the .v.edge file.\n\n");
02855   printf("Quadratic Elements:\n\n");
02856   printf(
02857 "  Triangle generates meshes with subparametric quadratic elements if the\n");
02858   printf(
02859 "  -o2 switch is specified.  Quadratic elements have six nodes per element,\n"
02860 );
02861   printf(
02862 "  rather than three.  `Subparametric' means that the edges of the triangles\n"
02863 );
02864   printf(
02865 "  are always straight, so that subparametric quadratic elements are\n");
02866   printf(
02867 "  geometrically identical to linear elements, even though they can be used\n"
02868 );
02869   printf(
02870 "  with quadratic interpolating functions.  The three extra nodes of an\n");
02871   printf(
02872 "  element fall at the midpoints of the three edges, with the fourth, fifth,\n"
02873 );
02874   printf(
02875 "  and sixth nodes appearing opposite the first, second, and third corners\n");
02876   printf("  respectively.\n\n");
02877   printf("Domains with Small Angles:\n\n");
02878   printf(
02879 "  If two input segments adjoin each other at a small angle, clearly the -q\n"
02880 );
02881   printf(
02882 "  switch cannot remove the small angle.  Moreover, Triangle may have no\n");
02883   printf(
02884 "  choice but to generate additional triangles whose smallest angles are\n");
02885   printf(
02886 "  smaller than the specified bound.  However, these triangles only appear\n");
02887   printf(
02888 "  between input segments separated by small angles.  Moreover, if you\n");
02889   printf(
02890 "  request a minimum angle of theta degrees, Triangle will generally produce\n"
02891 );
02892   printf(
02893 "  no angle larger than 180 - 2 theta, even if it is forced to compromise on\n"
02894 );
02895   printf("  the minimum angle.\n\n");
02896   printf("Statistics:\n\n");
02897   printf(
02898 "  After generating a mesh, Triangle prints a count of entities in the\n");
02899   printf(
02900 "  output mesh, including the number of vertices, triangles, edges, exterior\n"
02901 );
02902   printf(
02903 "  boundary edges (i.e. subsegments on the boundary of the triangulation,\n");
02904   printf(
02905 "  including hole boundaries), interior boundary edges (i.e. subsegments of\n"
02906 );
02907   printf(
02908 "  input segments not on the boundary), and total subsegments.  If you've\n");
02909   printf(
02910 "  forgotten the statistics for an existing mesh, run Triangle on that mesh\n"
02911 );
02912   printf(
02913 "  with the -rNEP switches to read the mesh and print the statistics without\n"
02914 );
02915   printf(
02916 "  writing any files.  Use -rpNEP if you've got a .poly file for the mesh.\n");
02917   printf("\n");
02918   printf(
02919 "  The -V switch produces extended statistics, including a rough estimate\n");
02920   printf(
02921 "  of memory use, the number of calls to geometric predicates, and\n");
02922   printf(
02923 "  histograms of the angles and the aspect ratios of the triangles in the\n");
02924   printf("  mesh.\n\n");
02925   printf("Exact Arithmetic:\n\n");
02926   printf(
02927 "  Triangle uses adaptive exact arithmetic to perform what computational\n");
02928   printf(
02929 "  geometers call the `orientation' and `incircle' tests.  If the floating-\n"
02930 );
02931   printf(
02932 "  point arithmetic of your machine conforms to the IEEE 754 standard (as\n");
02933   printf(
02934 "  most workstations do), and does not use extended precision internal\n");
02935   printf(
02936 "  floating-point registers, then your output is guaranteed to be an\n");
02937   printf(
02938 "  absolutely true Delaunay or constrained Delaunay triangulation, roundoff\n"
02939 );
02940   printf(
02941 "  error notwithstanding.  The word `adaptive' implies that these arithmetic\n"
02942 );
02943   printf(
02944 "  routines compute the result only to the precision necessary to guarantee\n"
02945 );
02946   printf(
02947 "  correctness, so they are usually nearly as fast as their approximate\n");
02948   printf("  counterparts.\n\n");
02949   printf(
02950 "  May CPUs, including Intel x86 processors, have extended precision\n");
02951   printf(
02952 "  floating-point registers.  These must be reconfigured so their precision\n"
02953 );
02954   printf(
02955 "  is reduced to memory precision.  Triangle does this if it is compiled\n");
02956   printf("  correctly.  See the makefile for details.\n\n");
02957   printf(
02958 "  The exact tests can be disabled with the -X switch.  On most inputs, this\n"
02959 );
02960   printf(
02961 "  switch reduces the computation time by about eight percent--it's not\n");
02962   printf(
02963 "  worth the risk.  There are rare difficult inputs (having many collinear\n");
02964   printf(
02965 "  and cocircular vertices), however, for which the difference in speed\n");
02966   printf(
02967 "  could be a factor of two.  Be forewarned that these are precisely the\n");
02968   printf(
02969 "  inputs most likely to cause errors if you use the -X switch.  Hence, the\n"
02970 );
02971   printf("  -X switch is not recommended.\n\n");
02972   printf(
02973 "  Unfortunately, the exact tests don't solve every numerical problem.\n");
02974   printf(
02975 "  Exact arithmetic is not used to compute the positions of new vertices,\n");
02976   printf(
02977 "  because the bit complexity of vertex coordinates would grow without\n");
02978   printf(
02979 "  bound.  Hence, segment intersections aren't computed exactly; in very\n");
02980   printf(
02981 "  unusual cases, roundoff error in computing an intersection point might\n");
02982   printf(
02983 "  actually lead to an inverted triangle and an invalid triangulation.\n");
02984   printf(
02985 "  (This is one reason to specify your own intersection points in your .poly\n"
02986 );
02987   printf(
02988 "  files.)  Similarly, exact arithmetic is not used to compute the vertices\n"
02989 );
02990   printf("  of the Voronoi diagram.\n\n");
02991   printf(
02992 "  Another pair of problems not solved by the exact arithmetic routines is\n");
02993   printf(
02994 "  underflow and overflow.  If Triangle is compiled for double precision\n");
02995   printf(
02996 "  arithmetic, I believe that Triangle's geometric predicates work correctly\n"
02997 );
02998   printf(
02999 "  if the exponent of every input coordinate falls in the range [-148, 201].\n"
03000 );
03001   printf(
03002 "  Underflow can silently prevent the orientation and incircle tests from\n");
03003   printf(
03004 "  being performed exactly, while overflow typically causes a floating\n");
03005   printf("  exception.\n\n");
03006   printf("Calling Triangle from Another Program:\n\n");
03007   printf("  Read the file triangle.h for details.\n\n");
03008   printf("Troubleshooting:\n\n");
03009   printf("  Please read this section before mailing me bugs.\n\n");
03010   printf("  `My output mesh has no triangles!'\n\n");
03011   printf(
03012 "    If you're using a PSLG, you've probably failed to specify a proper set\n"
03013 );
03014   printf(
03015 "    of bounding segments, or forgotten to use the -c switch.  Or you may\n");
03016   printf(
03017 "    have placed a hole badly, thereby eating all your triangles.  To test\n");
03018   printf("    these possibilities, try again with the -c and -O switches.\n");
03019   printf(
03020 "    Alternatively, all your input vertices may be collinear, in which case\n"
03021 );
03022   printf("    you can hardly expect to triangulate them.\n\n");
03023   printf("  `Triangle doesn't terminate, or just crashes.'\n\n");
03024   printf(
03025 "    Bad things can happen when triangles get so small that the distance\n");
03026   printf(
03027 "    between their vertices isn't much larger than the precision of your\n");
03028   printf(
03029 "    machine's arithmetic.  If you've compiled Triangle for single-precision\n"
03030 );
03031   printf(
03032 "    arithmetic, you might do better by recompiling it for double-precision.\n"
03033 );
03034   printf(
03035 "    Then again, you might just have to settle for more lenient constraints\n"
03036 );
03037   printf(
03038 "    on the minimum angle and the maximum area than you had planned.\n");
03039   printf("\n");
03040   printf(
03041 "    You can minimize precision problems by ensuring that the origin lies\n");
03042   printf(
03043 "    inside your vertex set, or even inside the densest part of your\n");
03044   printf(
03045 "    mesh.  If you're triangulating an object whose x-coordinates all fall\n");
03046   printf(
03047 "    between 6247133 and 6247134, you're not leaving much floating-point\n");
03048   printf("    precision for Triangle to work with.\n\n");
03049   printf(
03050 "    Precision problems can occur covertly if the input PSLG contains two\n");
03051   printf(
03052 "    segments that meet (or intersect) at an extremely small angle, or if\n");
03053   printf(
03054 "    such an angle is introduced by the -c switch.  If you don't realize\n");
03055   printf(
03056 "    that a tiny angle is being formed, you might never discover why\n");
03057   printf(
03058 "    Triangle is crashing.  To check for this possibility, use the -S switch\n"
03059 );
03060   printf(
03061 "    (with an appropriate limit on the number of Steiner points, found by\n");
03062   printf(
03063 "    trial-and-error) to stop Triangle early, and view the output .poly file\n"
03064 );
03065   printf(
03066 "    with Show Me (described below).  Look carefully for regions where dense\n"
03067 );
03068   printf(
03069 "    clusters of vertices are forming and for small angles between segments.\n"
03070 );
03071   printf(
03072 "    Zoom in closely, as such segments might look like a single segment from\n"
03073 );
03074   printf("    a distance.\n\n");
03075   printf(
03076 "    If some of the input values are too large, Triangle may suffer a\n");
03077   printf(
03078 "    floating exception due to overflow when attempting to perform an\n");
03079   printf(
03080 "    orientation or incircle test.  (Read the section on exact arithmetic\n");
03081   printf(
03082 "    above.)  Again, I recommend compiling Triangle for double (rather\n");
03083   printf("    than single) precision arithmetic.\n\n");
03084   printf(
03085 "    Unexpected problems can arise if you use quality meshing (-q, -a, or\n");
03086   printf(
03087 "    -u) with an input that is not segment-bounded--that is, if your input\n");
03088   printf(
03089 "    is a vertex set, or you're using the -c switch.  If the convex hull of\n"
03090 );
03091   printf(
03092 "    your input vertices has collinear vertices on its boundary, an input\n");
03093   printf(
03094 "    vertex that you think lies on the convex hull might actually lie just\n");
03095   printf(
03096 "    inside the convex hull.  If so, the vertex and the nearby convex hull\n");
03097   printf(
03098 "    edge form an extremely thin triangle.  When Triangle tries to refine\n");
03099   printf(
03100 "    the mesh to enforce angle and area constraints, Triangle might generate\n"
03101 );
03102   printf(
03103 "    extremely tiny triangles, or it might fail because of insufficient\n");
03104   printf("    floating-point precision.\n\n");
03105   printf(
03106 "  `The numbering of the output vertices doesn't match the input vertices.'\n"
03107 );
03108   printf("\n");
03109   printf(
03110 "    You may have had duplicate input vertices, or you may have eaten some\n");
03111   printf(
03112 "    of your input vertices with a hole, or by placing them outside the area\n"
03113 );
03114   printf(
03115 "    enclosed by segments.  In any case, you can solve the problem by not\n");
03116   printf("    using the -j switch.\n\n");
03117   printf(
03118 "  `Triangle executes without incident, but when I look at the resulting\n");
03119   printf(
03120 "  mesh, it has overlapping triangles or other geometric inconsistencies.'\n");
03121   printf("\n");
03122   printf(
03123 "    If you select the -X switch, Triangle occasionally makes mistakes due\n");
03124   printf(
03125 "    to floating-point roundoff error.  Although these errors are rare,\n");
03126   printf(
03127 "    don't use the -X switch.  If you still have problems, please report the\n"
03128 );
03129   printf("    bug.\n\n");
03130   printf(
03131 "  `Triangle executes without incident, but when I look at the resulting\n");
03132   printf("  Voronoi diagram, it has overlapping edges or other geometric\n");
03133   printf("  inconsistencies.'\n");
03134   printf("\n");
03135   printf(
03136 "    If your input is a PSLG (-p), you can only expect a meaningful Voronoi\n"
03137 );
03138   printf(
03139 "    diagram if the domain you are triangulating is convex and free of\n");
03140   printf(
03141 "    holes, and you use the -D switch to construct a conforming Delaunay\n");
03142   printf("    triangulation (instead of a CDT or CCDT).\n\n");
03143   printf(
03144 "  Strange things can happen if you've taken liberties with your PSLG.  Do\n");
03145   printf(
03146 "  you have a vertex lying in the middle of a segment?  Triangle sometimes\n");
03147   printf(
03148 "  copes poorly with that sort of thing.  Do you want to lay out a collinear\n"
03149 );
03150   printf(
03151 "  row of evenly spaced, segment-connected vertices?  Have you simply\n");
03152   printf(
03153 "  defined one long segment connecting the leftmost vertex to the rightmost\n"
03154 );
03155   printf(
03156 "  vertex, and a bunch of vertices lying along it?  This method occasionally\n"
03157 );
03158   printf(
03159 "  works, especially with horizontal and vertical lines, but often it\n");
03160   printf(
03161 "  doesn't, and you'll have to connect each adjacent pair of vertices with a\n"
03162 );
03163   printf("  separate segment.  If you don't like it, tough.\n\n");
03164   printf(
03165 "  Furthermore, if you have segments that intersect other than at their\n");
03166   printf(
03167 "  endpoints, try not to let the intersections fall extremely close to PSLG\n"
03168 );
03169   printf("  vertices or each other.\n\n");
03170   printf(
03171 "  If you have problems refining a triangulation not produced by Triangle:\n");
03172   printf(
03173 "  Are you sure the triangulation is geometrically valid?  Is it formatted\n");
03174   printf(
03175 "  correctly for Triangle?  Are the triangles all listed so the first three\n"
03176 );
03177   printf(
03178 "  vertices are their corners in counterclockwise order?  Are all of the\n");
03179   printf(
03180 "  triangles constrained Delaunay?  Triangle's Delaunay refinement algorithm\n"
03181 );
03182   printf("  assumes that it starts with a CDT.\n\n");
03183   printf("Show Me:\n\n");
03184   printf(
03185 "  Triangle comes with a separate program named `Show Me', whose primary\n");
03186   printf(
03187 "  purpose is to draw meshes on your screen or in PostScript.  Its secondary\n"
03188 );
03189   printf(
03190 "  purpose is to check the validity of your input files, and do so more\n");
03191   printf(
03192 "  thoroughly than Triangle does.  Unlike Triangle, Show Me requires that\n");
03193   printf(
03194 "  you have the X Windows system.  Sorry, Microsoft Windows users.\n");
03195   printf("\n");
03196   printf("Triangle on the Web:\n");
03197   printf("\n");
03198   printf("  To see an illustrated version of these instructions, check out\n");
03199   printf("\n");
03200   printf("    http://www.cs.cmu.edu/~quake/triangle.html\n");
03201   printf("\n");
03202   printf("A Brief Plea:\n");
03203   printf("\n");
03204   printf(
03205 "  If you use Triangle, and especially if you use it to accomplish real\n");
03206   printf(
03207 "  work, I would like very much to hear from you.  A short letter or email\n");
03208   printf(
03209 "  (to jrs@cs.berkeley.edu) describing how you use Triangle will mean a lot\n"
03210 );
03211   printf(
03212 "  to me.  The more people I know are using this program, the more easily I\n"
03213 );
03214   printf(
03215 "  can justify spending time on improvements, which in turn will benefit\n");
03216   printf(
03217 "  you.  Also, I can put you on a list to receive email whenever a new\n");
03218   printf("  version of Triangle is available.\n\n");
03219   printf(
03220 "  If you use a mesh generated by Triangle in a publication, please include\n"
03221 );
03222   printf(
03223 "  an acknowledgment as well.  And please spell Triangle with a capital `T'!\n"
03224 );
03225   printf(
03226 "  If you want to include a citation, use `Jonathan Richard Shewchuk,\n");
03227   printf(
03228 "  ``Triangle: Engineering a 2D Quality Mesh Generator and Delaunay\n");
03229   printf(
03230 "  Triangulator,'' in Applied Computational Geometry:  Towards Geometric\n");
03231   printf(
03232 "  Engineering (Ming C. Lin and Dinesh Manocha, editors), volume 1148 of\n");
03233   printf(
03234 "  Lecture Notes in Computer Science, pages 203-222, Springer-Verlag,\n");
03235   printf(
03236 "  Berlin, May 1996.  (From the First ACM Workshop on Applied Computational\n"
03237 );
03238   printf("  Geometry.)'\n\n");
03239   printf("Research credit:\n\n");
03240   printf(
03241 "  Of course, I can take credit for only a fraction of the ideas that made\n");
03242   printf(
03243 "  this mesh generator possible.  Triangle owes its existence to the efforts\n"
03244 );
03245   printf(
03246 "  of many fine computational geometers and other researchers, including\n");
03247   printf(
03248 "  Marshall Bern, L. Paul Chew, Kenneth L. Clarkson, Boris Delaunay, Rex A.\n"
03249 );
03250   printf(
03251 "  Dwyer, David Eppstein, Steven Fortune, Leonidas J. Guibas, Donald E.\n");
03252   printf(
03253 "  Knuth, Charles L. Lawson, Der-Tsai Lee, Gary L. Miller, Ernst P. Mucke,\n");
03254   printf(
03255 "  Steven E. Pav, Douglas M. Priest, Jim Ruppert, Isaac Saias, Bruce J.\n");
03256   printf(
03257 "  Schachter, Micha Sharir, Peter W. Shor, Daniel D. Sleator, Jorge Stolfi,\n"
03258 );
03259   printf("  Robert E. Tarjan, Alper Ungor, Christopher J. Van Wyk, Noel J.\n");
03260   printf(
03261 "  Walkington, and Binhai Zhu.  See the comments at the beginning of the\n");
03262   printf("  source code for references.\n\n");
03263   triexit(0);
03264 }
03265 
03266 #endif /* not TRILIBRARY */
03267 
03268 /*****************************************************************************/
03269 /*                                                                           */
03270 /*  internalerror()   Ask the user to send me the defective product.  Exit.  */
03271 /*                                                                           */
03272 /*****************************************************************************/
03273 
03274 void internalerror()
03275 {
03276   printf("  Please report this bug to jrs@cs.berkeley.edu\n");
03277   printf("  Include the message above, your input data set, and the exact\n");
03278   printf("    command line you used to run Triangle.\n");
03279   triexit(1);
03280 }
03281 
03282 /*****************************************************************************/
03283 /*                                                                           */
03284 /*  parsecommandline()   Read the command line, identify switches, and set   */
03285 /*                       up options and file names.                          */
03286 /*                                                                           */
03287 /*****************************************************************************/
03288 
03289 #ifdef ANSI_DECLARATORS
03290 void parsecommandline(int argc, char **argv, struct behavior *b)
03291 #else /* not ANSI_DECLARATORS */
03292 void parsecommandline(argc, argv, b)
03293 int argc;
03294 char **argv;
03295 struct behavior *b;
03296 #endif /* not ANSI_DECLARATORS */
03297 
03298 {
03299 #ifdef TRILIBRARY
03300 #define STARTINDEX 0
03301 #else /* not TRILIBRARY */
03302 #define STARTINDEX 1
03303   int increment;
03304   int meshnumber;
03305 #endif /* not TRILIBRARY */
03306   int i, j, k;
03307   char workstring[FILENAMESIZE];
03308 
03309   b->poly = b->refine = b->quality = 0;
03310   b->vararea = b->fixedarea = b->usertest = 0;
03311   b->regionattrib = b->convex = b->weighted = b->jettison = 0;
03312   b->firstnumber = 1;
03313   b->edgesout = b->voronoi = b->neighbors = b->geomview = 0;
03314   b->nobound = b->nopolywritten = b->nonodewritten = b->noelewritten = 0;
03315   b->noiterationnum = 0;
03316   b->noholes = b->noexact = 0;
03317   b->incremental = b->sweepline = 0;
03318   b->dwyer = 1;
03319   b->splitseg = 0;
03320   b->docheck = 0;
03321   b->nobisect = 0;
03322   b->conformdel = 0;
03323   b->steiner = -1;
03324   b->order = 1;
03325   b->minangle = 0.0;
03326   b->maxarea = -1.0;
03327   b->quiet = b->verbose = 0;
03328 #ifndef TRILIBRARY
03329   b->innodefilename[0] = '\0';
03330 #endif /* not TRILIBRARY */
03331 
03332   for (i = STARTINDEX; i < argc; i++) {
03333 #ifndef TRILIBRARY
03334     if (argv[i][0] == '-') {
03335 #endif /* not TRILIBRARY */
03336       for (j = STARTINDEX; argv[i][j] != '\0'; j++) {
03337         if (argv[i][j] == 'p') {
03338           b->poly = 1;
03339     }
03340 #ifndef CDT_ONLY
03341         if (argv[i][j] == 'r') {
03342           b->refine = 1;
03343     }
03344         if (argv[i][j] == 'q') {
03345           b->quality = 1;
03346           if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
03347               (argv[i][j + 1] == '.')) {
03348             k = 0;
03349             while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
03350                    (argv[i][j + 1] == '.')) {
03351               j++;
03352               workstring[k] = argv[i][j];
03353               k++;
03354             }
03355             workstring[k] = '\0';
03356             b->minangle = (REAL) strtod(workstring, (char **) NULL);
03357       } else {
03358             b->minangle = 20.0;
03359       }
03360     }
03361         if (argv[i][j] == 'a') {
03362           b->quality = 1;
03363           if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
03364               (argv[i][j + 1] == '.')) {
03365             b->fixedarea = 1;
03366             k = 0;
03367             while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
03368                    (argv[i][j + 1] == '.')) {
03369               j++;
03370               workstring[k] = argv[i][j];
03371               k++;
03372             }
03373             workstring[k] = '\0';
03374             b->maxarea = (REAL) strtod(workstring, (char **) NULL);
03375             if (b->maxarea <= 0.0) {
03376               printf("Error:  Maximum area must be greater than zero.\n");
03377               triexit(1);
03378         }
03379       } else {
03380             b->vararea = 1;
03381       }
03382     }
03383         if (argv[i][j] == 'u') {
03384           b->quality = 1;
03385           b->usertest = 1;
03386         }
03387 #endif /* not CDT_ONLY */
03388         if (argv[i][j] == 'A') {
03389           b->regionattrib = 1;
03390         }
03391         if (argv[i][j] == 'c') {
03392           b->convex = 1;
03393         }
03394         if (argv[i][j] == 'w') {
03395           b->weighted = 1;
03396         }
03397         if (argv[i][j] == 'W') {
03398           b->weighted = 2;
03399         }
03400         if (argv[i][j] == 'j') {
03401           b->jettison = 1;
03402         }
03403         if (argv[i][j] == 'z') {
03404           b->firstnumber = 0;
03405         }
03406         if (argv[i][j] == 'e') {
03407           b->edgesout = 1;
03408     }
03409         if (argv[i][j] == 'v') {
03410           b->voronoi = 1;
03411     }
03412         if (argv[i][j] == 'n') {
03413           b->neighbors = 1;
03414     }
03415         if (argv[i][j] == 'g') {
03416           b->geomview = 1;
03417     }
03418         if (argv[i][j] == 'B') {
03419           b->nobound = 1;
03420     }
03421         if (argv[i][j] == 'P') {
03422           b->nopolywritten = 1;
03423     }
03424         if (argv[i][j] == 'N') {
03425           b->nonodewritten = 1;
03426     }
03427         if (argv[i][j] == 'E') {
03428           b->noelewritten = 1;
03429     }
03430 #ifndef TRILIBRARY
03431         if (argv[i][j] == 'I') {
03432           b->noiterationnum = 1;
03433     }
03434 #endif /* not TRILIBRARY */
03435         if (argv[i][j] == 'O') {
03436           b->noholes = 1;
03437     }
03438         if (argv[i][j] == 'X') {
03439           b->noexact = 1;
03440     }
03441         if (argv[i][j] == 'o') {
03442           if (argv[i][j + 1] == '2') {
03443             j++;
03444             b->order = 2;
03445           }
03446     }
03447 #ifndef CDT_ONLY
03448         if (argv[i][j] == 'Y') {
03449           b->nobisect++;
03450     }
03451         if (argv[i][j] == 'S') {
03452           b->steiner = 0;
03453           while ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) {
03454             j++;
03455             b->steiner = b->steiner * 10 + (int) (argv[i][j] - '0');
03456           }
03457         }
03458 #endif /* not CDT_ONLY */
03459 #ifndef REDUCED
03460         if (argv[i][j] == 'i') {
03461           b->incremental = 1;
03462         }
03463         if (argv[i][j] == 'F') {
03464           b->sweepline = 1;
03465         }
03466 #endif /* not REDUCED */
03467         if (argv[i][j] == 'l') {
03468           b->dwyer = 0;
03469         }
03470 #ifndef REDUCED
03471 #ifndef CDT_ONLY
03472         if (argv[i][j] == 's') {
03473           b->splitseg = 1;
03474         }
03475         if ((argv[i][j] == 'D') || (argv[i][j] == 'L')) {
03476           b->quality = 1;
03477           b->conformdel = 1;
03478         }
03479 #endif /* not CDT_ONLY */
03480         if (argv[i][j] == 'C') {
03481           b->docheck = 1;
03482         }
03483 #endif /* not REDUCED */
03484         if (argv[i][j] == 'Q') {
03485           b->quiet = 1;
03486         }
03487         if (argv[i][j] == 'V') {
03488           b->verbose++;
03489         }
03490 #ifndef TRILIBRARY
03491         if ((argv[i][j] == 'h') || (argv[i][j] == 'H') ||
03492             (argv[i][j] == '?')) {
03493           info();
03494     }
03495 #endif /* not TRILIBRARY */
03496       }
03497 #ifndef TRILIBRARY
03498     } else {
03499       strncpy(b->innodefilename, argv[i], FILENAMESIZE - 1);
03500       b->innodefilename[FILENAMESIZE - 1] = '\0';
03501     }
03502 #endif /* not TRILIBRARY */
03503   }
03504 #ifndef TRILIBRARY
03505   if (b->innodefilename[0] == '\0') {
03506     syntax();
03507   }
03508   if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 5], ".node")) {
03509     b->innodefilename[strlen(b->innodefilename) - 5] = '\0';
03510   }
03511   if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 5], ".poly")) {
03512     b->innodefilename[strlen(b->innodefilename) - 5] = '\0';
03513     b->poly = 1;
03514   }
03515 #ifndef CDT_ONLY
03516   if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 4], ".ele")) {
03517     b->innodefilename[strlen(b->innodefilename) - 4] = '\0';
03518     b->refine = 1;
03519   }
03520   if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 5], ".area")) {
03521     b->innodefilename[strlen(b->innodefilename) - 5] = '\0';
03522     b->refine = 1;
03523     b->quality = 1;
03524     b->vararea = 1;
03525   }
03526 #endif /* not CDT_ONLY */
03527 #endif /* not TRILIBRARY */
03528   b->usesegments = b->poly || b->refine || b->quality || b->convex;
03529   b->goodangle = cos(b->minangle * PI / 180.0);
03530   if (b->goodangle == 1.0) {
03531     b->offconstant = 0.0;
03532   } else {
03533     b->offconstant = 0.475 * sqrt((1.0 + b->goodangle) / (1.0 - b->goodangle));
03534   }
03535   b->goodangle *= b->goodangle;
03536   if (b->refine && b->noiterationnum) {
03537     printf(
03538       "Error:  You cannot use the -I switch when refining a triangulation.\n");
03539     triexit(1);
03540   }
03541   /* Be careful not to allocate space for element area constraints that */
03542   /*   will never be assigned any value (other than the default -1.0).  */
03543   if (!b->refine && !b->poly) {
03544     b->vararea = 0;
03545   }
03546   /* Be careful not to add an extra attribute to each element unless the */
03547   /*   input supports it (PSLG in, but not refining a preexisting mesh). */
03548   if (b->refine || !b->poly) {
03549     b->regionattrib = 0;
03550   }
03551   /* Regular/weighted triangulations are incompatible with PSLGs */
03552   /*   and meshing.                                              */
03553   if (b->weighted && (b->poly || b->quality)) {
03554     b->weighted = 0;
03555     if (!b->quiet) {
03556       printf("Warning:  weighted triangulations (-w, -W) are incompatible\n");
03557       printf("  with PSLGs (-p) and meshing (-q, -a, -u).  Weights ignored.\n"
03558              );
03559     }
03560   }
03561   if (b->jettison && b->nonodewritten && !b->quiet) {
03562     printf("Warning:  -j and -N switches are somewhat incompatible.\n");
03563     printf("  If any vertices are jettisoned, you will need the output\n");
03564     printf("  .node file to reconstruct the new node indices.");
03565   }
03566 
03567 #ifndef TRILIBRARY
03568   strcpy(b->inpolyfilename, b->innodefilename);
03569   strcpy(b->inelefilename, b->innodefilename);
03570   strcpy(b->areafilename, b->innodefilename);
03571   increment = 0;
03572   strcpy(workstring, b->innodefilename);
03573   j = 1;
03574   while (workstring[j] != '\0') {
03575     if ((workstring[j] == '.') && (workstring[j + 1] != '\0')) {
03576       increment = j + 1;
03577     }
03578     j++;
03579   }
03580   meshnumber = 0;
03581   if (increment > 0) {
03582     j = increment;
03583     do {
03584       if ((workstring[j] >= '0') && (workstring[j] <= '9')) {
03585         meshnumber = meshnumber * 10 + (int) (workstring[j] - '0');
03586       } else {
03587         increment = 0;
03588       }
03589       j++;
03590     } while (workstring[j] != '\0');
03591   }
03592   if (b->noiterationnum) {
03593     strcpy(b->outnodefilename, b->innodefilename);
03594     strcpy(b->outelefilename, b->innodefilename);
03595     strcpy(b->edgefilename, b->innodefilename);
03596     strcpy(b->vnodefilename, b->innodefilename);
03597     strcpy(b->vedgefilename, b->innodefilename);
03598     strcpy(b->neighborfilename, b->innodefilename);
03599     strcpy(b->offfilename, b->innodefilename);
03600     strcat(b->outnodefilename, ".node");
03601     strcat(b->outelefilename, ".ele");
03602     strcat(b->edgefilename, ".edge");
03603     strcat(b->vnodefilename, ".v.node");
03604     strcat(b->vedgefilename, ".v.edge");
03605     strcat(b->neighborfilename, ".neigh");
03606     strcat(b->offfilename, ".off");
03607   } else if (increment == 0) {
03608     strcpy(b->outnodefilename, b->innodefilename);
03609     strcpy(b->outpolyfilename, b->innodefilename);
03610     strcpy(b->outelefilename, b->innodefilename);
03611     strcpy(b->edgefilename, b->innodefilename);
03612     strcpy(b->vnodefilename, b->innodefilename);
03613     strcpy(b->vedgefilename, b->innodefilename);
03614     strcpy(b->neighborfilename, b->innodefilename);
03615     strcpy(b->offfilename, b->innodefilename);
03616     strcat(b->outnodefilename, ".1.node");
03617     strcat(b->outpolyfilename, ".1.poly");
03618     strcat(b->outelefilename, ".1.ele");
03619     strcat(b->edgefilename, ".1.edge");
03620     strcat(b->vnodefilename, ".1.v.node");
03621     strcat(b->vedgefilename, ".1.v.edge");
03622     strcat(b->neighborfilename, ".1.neigh");
03623     strcat(b->offfilename, ".1.off");
03624   } else {
03625     workstring[increment] = '%';
03626     workstring[increment + 1] = 'd';
03627     workstring[increment + 2] = '\0';
03628     sprintf(b->outnodefilename, workstring, meshnumber + 1);
03629     strcpy(b->outpolyfilename, b->outnodefilename);
03630     strcpy(b->outelefilename, b->outnodefilename);
03631     strcpy(b->edgefilename, b->outnodefilename);
03632     strcpy(b->vnodefilename, b->outnodefilename);
03633     strcpy(b->vedgefilename, b->outnodefilename);
03634     strcpy(b->neighborfilename, b->outnodefilename);
03635     strcpy(b->offfilename, b->outnodefilename);
03636     strcat(b->outnodefilename, ".node");
03637     strcat(b->outpolyfilename, ".poly");
03638     strcat(b->outelefilename, ".ele");
03639     strcat(b->edgefilename, ".edge");
03640     strcat(b->vnodefilename, ".v.node");
03641     strcat(b->vedgefilename, ".v.edge");
03642     strcat(b->neighborfilename, ".neigh");
03643     strcat(b->offfilename, ".off");
03644   }
03645   strcat(b->innodefilename, ".node");
03646   strcat(b->inpolyfilename, ".poly");
03647   strcat(b->inelefilename, ".ele");
03648   strcat(b->areafilename, ".area");
03649 #endif /* not TRILIBRARY */
03650 }
03651 
03654 /********* User interaction routines begin here                      *********/
03655 
03656 /********* Debugging routines begin here                             *********/
03660 /*****************************************************************************/
03661 /*                                                                           */
03662 /*  printtriangle()   Print out the details of an oriented triangle.         */
03663 /*                                                                           */
03664 /*  I originally wrote this procedure to simplify debugging; it can be       */
03665 /*  called directly from the debugger, and presents information about an     */
03666 /*  oriented triangle in digestible form.  It's also used when the           */
03667 /*  highest level of verbosity (`-VVV') is specified.                        */
03668 /*                                                                           */
03669 /*****************************************************************************/
03670 
03671 #ifdef ANSI_DECLARATORS
03672 void printtriangle(struct mesh *m, struct behavior *b, struct otri *t)
03673 #else /* not ANSI_DECLARATORS */
03674 void printtriangle(m, b, t)
03675 struct mesh *m;
03676 struct behavior *b;
03677 struct otri *t;
03678 #endif /* not ANSI_DECLARATORS */
03679 
03680 {
03681   struct otri printtri;
03682   struct osub printsh;
03683   vertex printvertex;
03684 
03685   printf("triangle x%lx with orientation %d:\n", (unsigned long) t->tri,
03686          t->orient);
03687   decode(t->tri[0], printtri);
03688   if (printtri.tri == m->dummytri) {
03689     printf("    [0] = Outer space\n");
03690   } else {
03691     printf("    [0] = x%lx  %d\n", (unsigned long) printtri.tri,
03692            printtri.orient);
03693   }
03694   decode(t->tri[1], printtri);
03695   if (printtri.tri == m->dummytri) {
03696     printf("    [1] = Outer space\n");
03697   } else {
03698     printf("    [1] = x%lx  %d\n", (unsigned long) printtri.tri,
03699            printtri.orient);
03700   }
03701   decode(t->tri[2], printtri);
03702   if (printtri.tri == m->dummytri) {
03703     printf("    [2] = Outer space\n");
03704   } else {
03705     printf("    [2] = x%lx  %d\n", (unsigned long) printtri.tri,
03706            printtri.orient);
03707   }
03708 
03709   org(*t, printvertex);
03710   if (printvertex == (vertex) NULL)
03711     printf("    Origin[%d] = NULL\n", (t->orient + 1) % 3 + 3);
03712   else
03713     printf("    Origin[%d] = x%lx  (%.12g, %.12g)\n",
03714            (t->orient + 1) % 3 + 3, (unsigned long) printvertex,
03715            printvertex[0], printvertex[1]);
03716   dest(*t, printvertex);
03717   if (printvertex == (vertex) NULL)
03718     printf("    Dest  [%d] = NULL\n", (t->orient + 2) % 3 + 3);
03719   else
03720     printf("    Dest  [%d] = x%lx  (%.12g, %.12g)\n",
03721            (t->orient + 2) % 3 + 3, (unsigned long) printvertex,
03722            printvertex[0], printvertex[1]);
03723   apex(*t, printvertex);
03724   if (printvertex == (vertex) NULL)
03725     printf("    Apex  [%d] = NULL\n", t->orient + 3);
03726   else
03727     printf("    Apex  [%d] = x%lx  (%.12g, %.12g)\n",
03728            t->orient + 3, (unsigned long) printvertex,
03729            printvertex[0], printvertex[1]);
03730 
03731   if (b->usesegments) {
03732     sdecode(t->tri[6], printsh);
03733     if (printsh.ss != m->dummysub) {
03734       printf("    [6] = x%lx  %d\n", (unsigned long) printsh.ss,
03735              printsh.ssorient);
03736     }
03737     sdecode(t->tri[7], printsh);
03738     if (printsh.ss != m->dummysub) {
03739       printf("    [7] = x%lx  %d\n", (unsigned long) printsh.ss,
03740              printsh.ssorient);
03741     }
03742     sdecode(t->tri[8], printsh);
03743     if (printsh.ss != m->dummysub) {
03744       printf("    [8] = x%lx  %d\n", (unsigned long) printsh.ss,
03745              printsh.ssorient);
03746     }
03747   }
03748 
03749   if (b->vararea) {
03750     printf("    Area constraint:  %.4g\n", areabound(*t));
03751   }
03752 }
03753 
03754 /*****************************************************************************/
03755 /*                                                                           */
03756 /*  printsubseg()   Print out the details of an oriented subsegment.         */
03757 /*                                                                           */
03758 /*  I originally wrote this procedure to simplify debugging; it can be       */
03759 /*  called directly from the debugger, and presents information about an     */
03760 /*  oriented subsegment in digestible form.  It's also used when the highest */
03761 /*  level of verbosity (`-VVV') is specified.                                */
03762 /*                                                                           */
03763 /*****************************************************************************/
03764 
03765 #ifdef ANSI_DECLARATORS
03766 void printsubseg(struct mesh *m, struct behavior *b, struct osub *s)
03767 #else /* not ANSI_DECLARATORS */
03768 void printsubseg(m, b, s)
03769 struct mesh *m;
03770 struct behavior *b;
03771 struct osub *s;
03772 #endif /* not ANSI_DECLARATORS */
03773 
03774 {
03775   struct osub printsh;
03776   struct otri printtri;
03777   vertex printvertex;
03778 
03779   printf("subsegment x%lx with orientation %d and mark %d:\n",
03780          (unsigned long) s->ss, s->ssorient, mark(*s));
03781   sdecode(s->ss[0], printsh);
03782   if (printsh.ss == m->dummysub) {
03783     printf("    [0] = No subsegment\n");
03784   } else {
03785     printf("    [0] = x%lx  %d\n", (unsigned long) printsh.ss,
03786            printsh.ssorient);
03787   }
03788   sdecode(s->ss[1], printsh);
03789   if (printsh.ss == m->dummysub) {
03790     printf("    [1] = No subsegment\n");
03791   } else {
03792     printf("    [1] = x%lx  %d\n", (unsigned long) printsh.ss,
03793            printsh.ssorient);
03794   }
03795 
03796   sorg(*s, printvertex);
03797   if (printvertex == (vertex) NULL)
03798     printf("    Origin[%d] = NULL\n", 2 + s->ssorient);
03799   else
03800     printf("    Origin[%d] = x%lx  (%.12g, %.12g)\n",
03801            2 + s->ssorient, (unsigned long) printvertex,
03802            printvertex[0], printvertex[1]);
03803   sdest(*s, printvertex);
03804   if (printvertex == (vertex) NULL)
03805     printf("    Dest  [%d] = NULL\n", 3 - s->ssorient);
03806   else
03807     printf("    Dest  [%d] = x%lx  (%.12g, %.12g)\n",
03808            3 - s->ssorient, (unsigned long) printvertex,
03809            printvertex[0], printvertex[1]);
03810 
03811   decode(s->ss[6], printtri);
03812   if (printtri.tri == m->dummytri) {
03813     printf("    [6] = Outer space\n");
03814   } else {
03815     printf("    [6] = x%lx  %d\n", (unsigned long) printtri.tri,
03816            printtri.orient);
03817   }
03818   decode(s->ss[7], printtri);
03819   if (printtri.tri == m->dummytri) {
03820     printf("    [7] = Outer space\n");
03821   } else {
03822     printf("    [7] = x%lx  %d\n", (unsigned long) printtri.tri,
03823            printtri.orient);
03824   }
03825 
03826   segorg(*s, printvertex);
03827   if (printvertex == (vertex) NULL)
03828     printf("    Segment origin[%d] = NULL\n", 4 + s->ssorient);
03829   else
03830     printf("    Segment origin[%d] = x%lx  (%.12g, %.12g)\n",
03831            4 + s->ssorient, (unsigned long) printvertex,
03832            printvertex[0], printvertex[1]);
03833   segdest(*s, printvertex);
03834   if (printvertex == (vertex) NULL)
03835     printf("    Segment dest  [%d] = NULL\n", 5 - s->ssorient);
03836   else
03837     printf("    Segment dest  [%d] = x%lx  (%.12g, %.12g)\n",
03838            5 - s->ssorient, (unsigned long) printvertex,
03839            printvertex[0], printvertex[1]);
03840 }
03841 
03844 /********* Debugging routines end here                               *********/
03845 
03846 /********* Memory management routines begin here                     *********/
03850 /*****************************************************************************/
03851 /*                                                                           */
03852 /*  poolzero()   Set all of a pool's fields to zero.                         */
03853 /*                                                                           */
03854 /*  This procedure should never be called on a pool that has any memory      */
03855 /*  allocated to it, as that memory would leak.                              */
03856 /*                                                                           */
03857 /*****************************************************************************/
03858 
03859 #ifdef ANSI_DECLARATORS
03860 void poolzero(struct memorypool *pool)
03861 #else /* not ANSI_DECLARATORS */
03862 void poolzero(pool)
03863 struct memorypool *pool;
03864 #endif /* not ANSI_DECLARATORS */
03865 
03866 {
03867   pool->firstblock = (VOID **) NULL;
03868   pool->nowblock = (VOID **) NULL;
03869   pool->nextitem = (VOID *) NULL;
03870   pool->deaditemstack = (VOID *) NULL;
03871   pool->pathblock = (VOID **) NULL;
03872   pool->pathitem = (VOID *) NULL;
03873   pool->alignbytes = 0;
03874   pool->itembytes = 0;
03875   pool->itemsperblock = 0;
03876   pool->itemsfirstblock = 0;
03877   pool->items = 0;
03878   pool->maxitems = 0;
03879   pool->unallocateditems = 0;
03880   pool->pathitemsleft = 0;
03881 }
03882 
03883 /*****************************************************************************/
03884 /*                                                                           */
03885 /*  poolrestart()   Deallocate all items in a pool.                          */
03886 /*                                                                           */
03887 /*  The pool is returned to its starting state, except that no memory is     */
03888 /*  freed to the operating system.  Rather, the previously allocated blocks  */
03889 /*  are ready to be reused.                                                  */
03890 /*                                                                           */
03891 /*****************************************************************************/
03892 
03893 #ifdef ANSI_DECLARATORS
03894 void poolrestart(struct memorypool *pool)
03895 #else /* not ANSI_DECLARATORS */
03896 void poolrestart(pool)
03897 struct memorypool *pool;
03898 #endif /* not ANSI_DECLARATORS */
03899 
03900 {
03901   unsigned long alignptr;
03902 
03903   pool->items = 0;
03904   pool->maxitems = 0;
03905 
03906   /* Set the currently active block. */
03907   pool->nowblock = pool->firstblock;
03908   /* Find the first item in the pool.  Increment by the size of (VOID *). */
03909   alignptr = (unsigned long) (pool->nowblock + 1);
03910   /* Align the item on an `alignbytes'-byte boundary. */
03911   pool->nextitem = (VOID *)
03912     (alignptr + (unsigned long) pool->alignbytes -
03913      (alignptr % (unsigned long) pool->alignbytes));
03914   /* There are lots of unallocated items left in this block. */
03915   pool->unallocateditems = pool->itemsfirstblock;
03916   /* The stack of deallocated items is empty. */
03917   pool->deaditemstack = (VOID *) NULL;
03918 }
03919 
03920 /*****************************************************************************/
03921 /*                                                                           */
03922 /*  poolinit()   Initialize a pool of memory for allocation of items.        */
03923 /*                                                                           */
03924 /*  This routine initializes the machinery for allocating items.  A `pool'   */
03925 /*  is created whose records have size at least `bytecount'.  Items will be  */
03926 /*  allocated in `itemcount'-item blocks.  Each item is assumed to be a      */
03927 /*  collection of words, and either pointers or floating-point values are    */
03928 /*  assumed to be the "primary" word type.  (The "primary" word type is used */
03929 /*  to determine alignment of items.)  If `alignment' isn't zero, all items  */
03930 /*  will be `alignment'-byte aligned in memory.  `alignment' must be either  */
03931 /*  a multiple or a factor of the primary word size; powers of two are safe. */
03932 /*  `alignment' is normally used to create a few unused bits at the bottom   */
03933 /*  of each item's pointer, in which information may be stored.              */
03934 /*                                                                           */
03935 /*  Don't change this routine unless you understand it.                      */
03936 /*                                                                           */
03937 /*****************************************************************************/
03938 
03939 #ifdef ANSI_DECLARATORS
03940 void poolinit(struct memorypool *pool, int bytecount, int itemcount,
03941               int firstitemcount, unsigned alignment)
03942 #else /* not ANSI_DECLARATORS */
03943 void poolinit(pool, bytecount, itemcount, firstitemcount, alignment)
03944 struct memorypool *pool;
03945 int bytecount;
03946 int itemcount;
03947 int firstitemcount;
03948 unsigned alignment;
03949 #endif /* not ANSI_DECLARATORS */
03950 
03951 {
03952   /* Find the proper alignment, which must be at least as large as:   */
03953   /*   - The parameter `alignment'.                                   */
03954   /*   - sizeof(VOID *), so the stack of dead items can be maintained */
03955   /*       without unaligned accesses.                                */
03956   if (alignment > sizeof(VOID *)) {
03957     pool->alignbytes = alignment;
03958   } else {
03959     pool->alignbytes = sizeof(VOID *);
03960   }
03961   pool->itembytes = ((bytecount - 1) / pool->alignbytes + 1) *
03962                     pool->alignbytes;
03963   pool->itemsperblock = itemcount;
03964   if (firstitemcount == 0) {
03965     pool->itemsfirstblock = itemcount;
03966   } else {
03967     pool->itemsfirstblock = firstitemcount;
03968   }
03969 
03970   /* Allocate a block of items.  Space for `itemsfirstblock' items and one  */
03971   /*   pointer (to point to the next block) are allocated, as well as space */
03972   /*   to ensure alignment of the items.                                    */
03973   pool->firstblock = (VOID **)
03974     trimalloc(pool->itemsfirstblock * pool->itembytes + (int) sizeof(VOID *) +
03975               pool->alignbytes);
03976   /* Set the next block pointer to NULL. */
03977   *(pool->firstblock) = (VOID *) NULL;
03978   poolrestart(pool);
03979 }
03980 
03981 /*****************************************************************************/
03982 /*                                                                           */
03983 /*  pooldeinit()   Free to the operating system all memory taken by a pool.  */
03984 /*                                                                           */
03985 /*****************************************************************************/
03986 
03987 #ifdef ANSI_DECLARATORS
03988 void pooldeinit(struct memorypool *pool)
03989 #else /* not ANSI_DECLARATORS */
03990 void pooldeinit(pool)
03991 struct memorypool *pool;
03992 #endif /* not ANSI_DECLARATORS */
03993 
03994 {
03995   while (pool->firstblock != (VOID **) NULL) {
03996     pool->nowblock = (VOID **) *(pool->firstblock);
03997     trifree((VOID *) pool->firstblock);
03998     pool->firstblock = pool->nowblock;
03999   }
04000 }
04001 
04002 /*****************************************************************************/
04003 /*                                                                           */
04004 /*  poolalloc()   Allocate space for an item.                                */
04005 /*                                                                           */
04006 /*****************************************************************************/
04007 
04008 #ifdef ANSI_DECLARATORS
04009 VOID *poolalloc(struct memorypool *pool)
04010 #else /* not ANSI_DECLARATORS */
04011 VOID *poolalloc(pool)
04012 struct memorypool *pool;
04013 #endif /* not ANSI_DECLARATORS */
04014 
04015 {
04016   VOID *newitem;
04017   VOID **newblock;
04018   unsigned long alignptr;
04019 
04020   /* First check the linked list of dead items.  If the list is not   */
04021   /*   empty, allocate an item from the list rather than a fresh one. */
04022   if (pool->deaditemstack != (VOID *) NULL) {
04023     newitem = pool->deaditemstack;               /* Take first item in list. */
04024     pool->deaditemstack = * (VOID **) pool->deaditemstack;
04025   } else {
04026     /* Check if there are any free items left in the current block. */
04027     if (pool->unallocateditems == 0) {
04028       /* Check if another block must be allocated. */
04029       if (*(pool->nowblock) == (VOID *) NULL) {
04030         /* Allocate a new block of items, pointed to by the previous block. */
04031         newblock = (VOID **) trimalloc(pool->itemsperblock * pool->itembytes +
04032                                        (int) sizeof(VOID *) +
04033                                        pool->alignbytes);
04034         *(pool->nowblock) = (VOID *) newblock;
04035         /* The next block pointer is NULL. */
04036         *newblock = (VOID *) NULL;
04037       }
04038 
04039       /* Move to the new block. */
04040       pool->nowblock = (VOID **) *(pool->nowblock);
04041       /* Find the first item in the block.    */
04042       /*   Increment by the size of (VOID *). */
04043       alignptr = (unsigned long) (pool->nowblock + 1);
04044       /* Align the item on an `alignbytes'-byte boundary. */
04045       pool->nextitem = (VOID *)
04046         (alignptr + (unsigned long) pool->alignbytes -
04047          (alignptr % (unsigned long) pool->alignbytes));
04048       /* There are lots of unallocated items left in this block. */
04049       pool->unallocateditems = pool->itemsperblock;
04050     }
04051 
04052     /* Allocate a new item. */
04053     newitem = pool->nextitem;
04054     /* Advance `nextitem' pointer to next free item in block. */
04055     pool->nextitem = (VOID *) ((char *) pool->nextitem + pool->itembytes);
04056     pool->unallocateditems--;
04057     pool->maxitems++;
04058   }
04059   pool->items++;
04060   return newitem;
04061 }
04062 
04063 /*****************************************************************************/
04064 /*                                                                           */
04065 /*  pooldealloc()   Deallocate space for an item.                            */
04066 /*                                                                           */
04067 /*  The deallocated space is stored in a queue for later reuse.              */
04068 /*                                                                           */
04069 /*****************************************************************************/
04070 
04071 #ifdef ANSI_DECLARATORS
04072 void pooldealloc(struct memorypool *pool, VOID *dyingitem)
04073 #else /* not ANSI_DECLARATORS */
04074 void pooldealloc(pool, dyingitem)
04075 struct memorypool *pool;
04076 VOID *dyingitem;
04077 #endif /* not ANSI_DECLARATORS */
04078 
04079 {
04080   /* Push freshly killed item onto stack. */
04081   *((VOID **) dyingitem) = pool->deaditemstack;
04082   pool->deaditemstack = dyingitem;
04083   pool->items--;
04084 }
04085 
04086 /*****************************************************************************/
04087 /*                                                                           */
04088 /*  traversalinit()   Prepare to traverse the entire list of items.          */
04089 /*                                                                           */
04090 /*  This routine is used in conjunction with traverse().                     */
04091 /*                                                                           */
04092 /*****************************************************************************/
04093 
04094 #ifdef ANSI_DECLARATORS
04095 void traversalinit(struct memorypool *pool)
04096 #else /* not ANSI_DECLARATORS */
04097 void traversalinit(pool)
04098 struct memorypool *pool;
04099 #endif /* not ANSI_DECLARATORS */
04100 
04101 {
04102   unsigned long alignptr;
04103 
04104   /* Begin the traversal in the first block. */
04105   pool->pathblock = pool->firstblock;
04106   /* Find the first item in the block.  Increment by the size of (VOID *). */
04107   alignptr = (unsigned long) (pool->pathblock + 1);
04108   /* Align with item on an `alignbytes'-byte boundary. */
04109   pool->pathitem = (VOID *)
04110     (alignptr + (unsigned long) pool->alignbytes -
04111      (alignptr % (unsigned long) pool->alignbytes));
04112   /* Set the number of items left in the current block. */
04113   pool->pathitemsleft = pool->itemsfirstblock;
04114 }
04115 
04116 /*****************************************************************************/
04117 /*                                                                           */
04118 /*  traverse()   Find the next item in the list.                             */
04119 /*                                                                           */
04120 /*  This routine is used in conjunction with traversalinit().  Be forewarned */
04121 /*  that this routine successively returns all items in the list, including  */
04122 /*  deallocated ones on the deaditemqueue.  It's up to you to figure out     */
04123 /*  which ones are actually dead.  Why?  I don't want to allocate extra      */
04124 /*  space just to demarcate dead items.  It can usually be done more         */
04125 /*  space-efficiently by a routine that knows something about the structure  */
04126 /*  of the item.                                                             */
04127 /*                                                                           */
04128 /*****************************************************************************/
04129 
04130 #ifdef ANSI_DECLARATORS
04131 VOID *traverse(struct memorypool *pool)
04132 #else /* not ANSI_DECLARATORS */
04133 VOID *traverse(pool)
04134 struct memorypool *pool;
04135 #endif /* not ANSI_DECLARATORS */
04136 
04137 {
04138   VOID *newitem;
04139   unsigned long alignptr;
04140 
04141   /* Stop upon exhausting the list of items. */
04142   if (pool->pathitem == pool->nextitem) {
04143     return (VOID *) NULL;
04144   }
04145 
04146   /* Check whether any untraversed items remain in the current block. */
04147   if (pool->pathitemsleft == 0) {
04148     /* Find the next block. */
04149     pool->pathblock = (VOID **) *(pool->pathblock);
04150     /* Find the first item in the block.  Increment by the size of (VOID *). */
04151     alignptr = (unsigned long) (pool->pathblock + 1);
04152     /* Align with item on an `alignbytes'-byte boundary. */
04153     pool->pathitem = (VOID *)
04154       (alignptr + (unsigned long) pool->alignbytes -
04155        (alignptr % (unsigned long) pool->alignbytes));
04156     /* Set the number of items left in the current block. */
04157     pool->pathitemsleft = pool->itemsperblock;
04158   }
04159 
04160   newitem = pool->pathitem;
04161   /* Find the next item in the block. */
04162   pool->pathitem = (VOID *) ((char *) pool->pathitem + pool->itembytes);
04163   pool->pathitemsleft--;
04164   return newitem;
04165 }
04166 
04167 /*****************************************************************************/
04168 /*                                                                           */
04169 /*  dummyinit()   Initialize the triangle that fills "outer space" and the   */
04170 /*                omnipresent subsegment.                                    */
04171 /*                                                                           */
04172 /*  The triangle that fills "outer space," called `dummytri', is pointed to  */
04173 /*  by every triangle and subsegment on a boundary (be it outer or inner) of */
04174 /*  the triangulation.  Also, `dummytri' points to one of the triangles on   */
04175 /*  the convex hull (until the holes and concavities are carved), making it  */
04176 /*  possible to find a starting triangle for point location.                 */
04177 /*                                                                           */
04178 /*  The omnipresent subsegment, `dummysub', is pointed to by every triangle  */
04179 /*  or subsegment that doesn't have a full complement of real subsegments    */
04180 /*  to point to.                                                             */
04181 /*                                                                           */
04182 /*  `dummytri' and `dummysub' are generally required to fulfill only a few   */
04183 /*  invariants:  their vertices must remain NULL and `dummytri' must always  */
04184 /*  be bonded (at offset zero) to some triangle on the convex hull of the    */
04185 /*  mesh, via a boundary edge.  Otherwise, the connections of `dummytri' and */
04186 /*  `dummysub' may change willy-nilly.  This makes it possible to avoid      */
04187 /*  writing a good deal of special-case code (in the edge flip, for example) */
04188 /*  for dealing with the boundary of the mesh, places where no subsegment is */
04189 /*  present, and so forth.  Other entities are frequently bonded to          */
04190 /*  `dummytri' and `dummysub' as if they were real mesh entities, with no    */
04191 /*  harm done.                                                               */
04192 /*                                                                           */
04193 /*****************************************************************************/
04194 
04195 #ifdef ANSI_DECLARATORS
04196 void dummyinit(struct mesh *m, struct behavior *b, int trianglebytes,
04197                int subsegbytes)
04198 #else /* not ANSI_DECLARATORS */
04199 void dummyinit(m, b, trianglebytes, subsegbytes)
04200 struct mesh *m;
04201 struct behavior *b;
04202 int trianglebytes;
04203 int subsegbytes;
04204 #endif /* not ANSI_DECLARATORS */
04205 
04206 {
04207   unsigned long alignptr;
04208 
04209   /* Set up `dummytri', the `triangle' that occupies "outer space." */
04210   m->dummytribase = (triangle *) trimalloc(trianglebytes +
04211                                            m->triangles.alignbytes);
04212   /* Align `dummytri' on a `triangles.alignbytes'-byte boundary. */
04213   alignptr = (unsigned long) m->dummytribase;
04214   m->dummytri = (triangle *)
04215     (alignptr + (unsigned long) m->triangles.alignbytes -
04216      (alignptr % (unsigned long) m->triangles.alignbytes));
04217   /* Initialize the three adjoining triangles to be "outer space."  These  */
04218   /*   will eventually be changed by various bonding operations, but their */
04219   /*   values don't really matter, as long as they can legally be          */
04220   /*   dereferenced.                                                       */
04221   m->dummytri[0] = (triangle) m->dummytri;
04222   m->dummytri[1] = (triangle) m->dummytri;
04223   m->dummytri[2] = (triangle) m->dummytri;
04224   /* Three NULL vertices. */
04225   m->dummytri[3] = (triangle) NULL;
04226   m->dummytri[4] = (triangle) NULL;
04227   m->dummytri[5] = (triangle) NULL;
04228 
04229   if (b->usesegments) {
04230     /* Set up `dummysub', the omnipresent subsegment pointed to by any */
04231     /*   triangle side or subsegment end that isn't attached to a real */
04232     /*   subsegment.                                                   */
04233     m->dummysubbase = (subseg *) trimalloc(subsegbytes +
04234                                            m->subsegs.alignbytes);
04235     /* Align `dummysub' on a `subsegs.alignbytes'-byte boundary. */
04236     alignptr = (unsigned long) m->dummysubbase;
04237     m->dummysub = (subseg *)
04238       (alignptr + (unsigned long) m->subsegs.alignbytes -
04239        (alignptr % (unsigned long) m->subsegs.alignbytes));
04240     /* Initialize the two adjoining subsegments to be the omnipresent      */
04241     /*   subsegment.  These will eventually be changed by various bonding  */
04242     /*   operations, but their values don't really matter, as long as they */
04243     /*   can legally be dereferenced.                                      */
04244     m->dummysub[0] = (subseg) m->dummysub;
04245     m->dummysub[1] = (subseg) m->dummysub;
04246     /* Four NULL vertices. */
04247     m->dummysub[2] = (subseg) NULL;
04248     m->dummysub[3] = (subseg) NULL;
04249     m->dummysub[4] = (subseg) NULL;
04250     m->dummysub[5] = (subseg) NULL;
04251     /* Initialize the two adjoining triangles to be "outer space." */
04252     m->dummysub[6] = (subseg) m->dummytri;
04253     m->dummysub[7] = (subseg) m->dummytri;
04254     /* Set the boundary marker to zero. */
04255     * (int *) (m->dummysub + 8) = 0;
04256 
04257     /* Initialize the three adjoining subsegments of `dummytri' to be */
04258     /*   the omnipresent subsegment.                                  */
04259     m->dummytri[6] = (triangle) m->dummysub;
04260     m->dummytri[7] = (triangle) m->dummysub;
04261     m->dummytri[8] = (triangle) m->dummysub;
04262   }
04263 }
04264 
04265 /*****************************************************************************/
04266 /*                                                                           */
04267 /*  initializevertexpool()   Calculate the size of the vertex data structure */
04268 /*                           and initialize its memory pool.                 */
04269 /*                                                                           */
04270 /*  This routine also computes the `vertexmarkindex' and `vertex2triindex'   */
04271 /*  indices used to find values within each vertex.                          */
04272 /*                                                                           */
04273 /*****************************************************************************/
04274 
04275 #ifdef ANSI_DECLARATORS
04276 void initializevertexpool(struct mesh *m, struct behavior *b)
04277 #else /* not ANSI_DECLARATORS */
04278 void initializevertexpool(m, b)
04279 struct mesh *m;
04280 struct behavior *b;
04281 #endif /* not ANSI_DECLARATORS */
04282 
04283 {
04284   int vertexsize;
04285 
04286   /* The index within each vertex at which the boundary marker is found,    */
04287   /*   followed by the vertex type.  Ensure the vertex marker is aligned to */
04288   /*   a sizeof(int)-byte address.                                          */
04289   m->vertexmarkindex = ((m->mesh_dim + m->nextras) * sizeof(REAL) +
04290                         sizeof(int) - 1) /
04291                        sizeof(int);
04292   vertexsize = (m->vertexmarkindex + 2) * sizeof(int);
04293   if (b->poly) {
04294     /* The index within each vertex at which a triangle pointer is found.  */
04295     /*   Ensure the pointer is aligned to a sizeof(triangle)-byte address. */
04296     m->vertex2triindex = (vertexsize + sizeof(triangle) - 1) /
04297                          sizeof(triangle);
04298     vertexsize = (m->vertex2triindex + 1) * sizeof(triangle);
04299   }
04300 
04301   /* Initialize the pool of vertices. */
04302   poolinit(&m->vertices, vertexsize, VERTEXPERBLOCK,
04303            m->invertices > VERTEXPERBLOCK ? m->invertices : VERTEXPERBLOCK,
04304            sizeof(REAL));
04305 }
04306 
04307 /*****************************************************************************/
04308 /*                                                                           */
04309 /*  initializetrisubpools()   Calculate the sizes of the triangle and        */
04310 /*                            subsegment data structures and initialize      */
04311 /*                            their memory pools.                            */
04312 /*                                                                           */
04313 /*  This routine also computes the `highorderindex', `elemattribindex', and  */
04314 /*  `areaboundindex' indices used to find values within each triangle.       */
04315 /*                                                                           */
04316 /*****************************************************************************/
04317 
04318 #ifdef ANSI_DECLARATORS
04319 void initializetrisubpools(struct mesh *m, struct behavior *b)
04320 #else /* not ANSI_DECLARATORS */
04321 void initializetrisubpools(m, b)
04322 struct mesh *m;
04323 struct behavior *b;
04324 #endif /* not ANSI_DECLARATORS */
04325 
04326 {
04327   unsigned trisize;
04328 
04329   /* The index within each triangle at which the extra nodes (above three)  */
04330   /*   associated with high order elements are found.  There are three      */
04331   /*   pointers to other triangles, three pointers to corners, and possibly */
04332   /*   three pointers to subsegments before the extra nodes.                */
04333   m->highorderindex = 6 + (b->usesegments * 3);
04334   /* The number of bytes occupied by a triangle. */
04335   trisize = ((b->order + 1) * (b->order + 2) / 2 + (m->highorderindex - 3)) *
04336             sizeof(triangle);
04337   /* The index within each triangle at which its attributes are found, */
04338   /*   where the index is measured in REALs.                           */
04339   m->elemattribindex = (trisize + sizeof(REAL) - 1) / sizeof(REAL);
04340   /* The index within each triangle at which the maximum area constraint  */
04341   /*   is found, where the index is measured in REALs.  Note that if the  */
04342   /*   `regionattrib' flag is set, an additional attribute will be added. */
04343   m->areaboundindex = m->elemattribindex + m->eextras + b->regionattrib;
04344   /* If triangle attributes or an area bound are needed, increase the number */
04345   /*   of bytes occupied by a triangle.                                      */
04346   if (b->vararea) {
04347     trisize = (m->areaboundindex + 1) * sizeof(REAL);
04348   } else if (m->eextras + b->regionattrib > 0) {
04349     trisize = m->areaboundindex * sizeof(REAL);
04350   }
04351   /* If a Voronoi diagram or triangle neighbor graph is requested, make    */
04352   /*   sure there's room to store an integer index in each triangle.  This */
04353   /*   integer index can occupy the same space as the subsegment pointers  */
04354   /*   or attributes or area constraint or extra nodes.                    */
04355   if ((b->voronoi || b->neighbors) &&
04356       (trisize < 6 * sizeof(triangle) + sizeof(int))) {
04357     trisize = 6 * sizeof(triangle) + sizeof(int);
04358   }
04359 
04360   /* Having determined the memory size of a triangle, initialize the pool. */
04361   poolinit(&m->triangles, trisize, TRIPERBLOCK,
04362            (2 * m->invertices - 2) > TRIPERBLOCK ? (2 * m->invertices - 2) :
04363            TRIPERBLOCK, 4);
04364 
04365   if (b->usesegments) {
04366     /* Initialize the pool of subsegments.  Take into account all eight */
04367     /*   pointers and one boundary marker.                              */
04368     poolinit(&m->subsegs, 8 * sizeof(triangle) + sizeof(int),
04369              SUBSEGPERBLOCK, SUBSEGPERBLOCK, 4);
04370 
04371     /* Initialize the "outer space" triangle and omnipresent subsegment. */
04372     dummyinit(m, b, m->triangles.itembytes, m->subsegs.itembytes);
04373   } else {
04374     /* Initialize the "outer space" triangle. */
04375     dummyinit(m, b, m->triangles.itembytes, 0);
04376   }
04377 }
04378 
04379 /*****************************************************************************/
04380 /*                                                                           */
04381 /*  triangledealloc()   Deallocate space for a triangle, marking it dead.    */
04382 /*                                                                           */
04383 /*****************************************************************************/
04384 
04385 #ifdef ANSI_DECLARATORS
04386 void triangledealloc(struct mesh *m, triangle *dyingtriangle)
04387 #else /* not ANSI_DECLARATORS */
04388 void triangledealloc(m, dyingtriangle)
04389 struct mesh *m;
04390 triangle *dyingtriangle;
04391 #endif /* not ANSI_DECLARATORS */
04392 
04393 {
04394   /* Mark the triangle as dead.  This makes it possible to detect dead */
04395   /*   triangles when traversing the list of all triangles.            */
04396   killtri(dyingtriangle);
04397   pooldealloc(&m->triangles, (VOID *) dyingtriangle);
04398 }
04399 
04400 /*****************************************************************************/
04401 /*                                                                           */
04402 /*  triangletraverse()   Traverse the triangles, skipping dead ones.         */
04403 /*                                                                           */
04404 /*****************************************************************************/
04405 
04406 #ifdef ANSI_DECLARATORS
04407 triangle *triangletraverse(struct mesh *m)
04408 #else /* not ANSI_DECLARATORS */
04409 triangle *triangletraverse(m)
04410 struct mesh *m;
04411 #endif /* not ANSI_DECLARATORS */
04412 
04413 {
04414   triangle *newtriangle;
04415 
04416   do {
04417     newtriangle = (triangle *) traverse(&m->triangles);
04418     if (newtriangle == (triangle *) NULL) {
04419       return (triangle *) NULL;
04420     }
04421   } while (deadtri(newtriangle));                         /* Skip dead ones. */
04422   return newtriangle;
04423 }
04424 
04425 /*****************************************************************************/
04426 /*                                                                           */
04427 /*  subsegdealloc()   Deallocate space for a subsegment, marking it dead.    */
04428 /*                                                                           */
04429 /*****************************************************************************/
04430 
04431 #ifdef ANSI_DECLARATORS
04432 void subsegdealloc(struct mesh *m, subseg *dyingsubseg)
04433 #else /* not ANSI_DECLARATORS */
04434 void subsegdealloc(m, dyingsubseg)
04435 struct mesh *m;
04436 subseg *dyingsubseg;
04437 #endif /* not ANSI_DECLARATORS */
04438 
04439 {
04440   /* Mark the subsegment as dead.  This makes it possible to detect dead */
04441   /*   subsegments when traversing the list of all subsegments.          */
04442   killsubseg(dyingsubseg);
04443   pooldealloc(&m->subsegs, (VOID *) dyingsubseg);
04444 }
04445 
04446 /*****************************************************************************/
04447 /*                                                                           */
04448 /*  subsegtraverse()   Traverse the subsegments, skipping dead ones.         */
04449 /*                                                                           */
04450 /*****************************************************************************/
04451 
04452 #ifdef ANSI_DECLARATORS
04453 subseg *subsegtraverse(struct mesh *m)
04454 #else /* not ANSI_DECLARATORS */
04455 subseg *subsegtraverse(m)
04456 struct mesh *m;
04457 #endif /* not ANSI_DECLARATORS */
04458 
04459 {
04460   subseg *newsubseg;
04461 
04462   do {
04463     newsubseg = (subseg *) traverse(&m->subsegs);
04464     if (newsubseg == (subseg *) NULL) {
04465       return (subseg *) NULL;
04466     }
04467   } while (deadsubseg(newsubseg));                        /* Skip dead ones. */
04468   return newsubseg;
04469 }
04470 
04471 /*****************************************************************************/
04472 /*                                                                           */
04473 /*  vertexdealloc()   Deallocate space for a vertex, marking it dead.        */
04474 /*                                                                           */
04475 /*****************************************************************************/
04476 
04477 #ifdef ANSI_DECLARATORS
04478 void vertexdealloc(struct mesh *m, vertex dyingvertex)
04479 #else /* not ANSI_DECLARATORS */
04480 void vertexdealloc(m, dyingvertex)
04481 struct mesh *m;
04482 vertex dyingvertex;
04483 #endif /* not ANSI_DECLARATORS */
04484 
04485 {
04486   /* Mark the vertex as dead.  This makes it possible to detect dead */
04487   /*   vertices when traversing the list of all vertices.            */
04488   setvertextype(dyingvertex, DEADVERTEX);
04489   pooldealloc(&m->vertices, (VOID *) dyingvertex);
04490 }
04491 
04492 /*****************************************************************************/
04493 /*                                                                           */
04494 /*  vertextraverse()   Traverse the vertices, skipping dead ones.            */
04495 /*                                                                           */
04496 /*****************************************************************************/
04497 
04498 #ifdef ANSI_DECLARATORS
04499 vertex vertextraverse(struct mesh *m)
04500 #else /* not ANSI_DECLARATORS */
04501 vertex vertextraverse(m)
04502 struct mesh *m;
04503 #endif /* not ANSI_DECLARATORS */
04504 
04505 {
04506   vertex newvertex;
04507 
04508   do {
04509     newvertex = (vertex) traverse(&m->vertices);
04510     if (newvertex == (vertex) NULL) {
04511       return (vertex) NULL;
04512     }
04513   } while (vertextype(newvertex) == DEADVERTEX);          /* Skip dead ones. */
04514   return newvertex;
04515 }
04516 
04517 /*****************************************************************************/
04518 /*                                                                           */
04519 /*  badsubsegdealloc()   Deallocate space for a bad subsegment, marking it   */
04520 /*                       dead.                                               */
04521 /*                                                                           */
04522 /*****************************************************************************/
04523 
04524 #ifndef CDT_ONLY
04525 
04526 #ifdef ANSI_DECLARATORS
04527 void badsubsegdealloc(struct mesh *m, struct badsubseg *dyingseg)
04528 #else /* not ANSI_DECLARATORS */
04529 void badsubsegdealloc(m, dyingseg)
04530 struct mesh *m;
04531 struct badsubseg *dyingseg;
04532 #endif /* not ANSI_DECLARATORS */
04533 
04534 {
04535   /* Set subsegment's origin to NULL.  This makes it possible to detect dead */
04536   /*   badsubsegs when traversing the list of all badsubsegs             .   */
04537   dyingseg->subsegorg = (vertex) NULL;
04538   pooldealloc(&m->badsubsegs, (VOID *) dyingseg);
04539 }
04540 
04541 #endif /* not CDT_ONLY */
04542 
04543 /*****************************************************************************/
04544 /*                                                                           */
04545 /*  badsubsegtraverse()   Traverse the bad subsegments, skipping dead ones.  */
04546 /*                                                                           */
04547 /*****************************************************************************/
04548 
04549 #ifndef CDT_ONLY
04550 
04551 #ifdef ANSI_DECLARATORS
04552 struct badsubseg *badsubsegtraverse(struct mesh *m)
04553 #else /* not ANSI_DECLARATORS */
04554 struct badsubseg *badsubsegtraverse(m)
04555 struct mesh *m;
04556 #endif /* not ANSI_DECLARATORS */
04557 
04558 {
04559   struct badsubseg *newseg;
04560 
04561   do {
04562     newseg = (struct badsubseg *) traverse(&m->badsubsegs);
04563     if (newseg == (struct badsubseg *) NULL) {
04564       return (struct badsubseg *) NULL;
04565     }
04566   } while (newseg->subsegorg == (vertex) NULL);           /* Skip dead ones. */
04567   return newseg;
04568 }
04569 
04570 #endif /* not CDT_ONLY */
04571 
04572 /*****************************************************************************/
04573 /*                                                                           */
04574 /*  getvertex()   Get a specific vertex, by number, from the list.           */
04575 /*                                                                           */
04576 /*  The first vertex is number 'firstnumber'.                                */
04577 /*                                                                           */
04578 /*  Note that this takes O(n) time (with a small constant, if VERTEXPERBLOCK */
04579 /*  is large).  I don't care to take the trouble to make it work in constant */
04580 /*  time.                                                                    */
04581 /*                                                                           */
04582 /*****************************************************************************/
04583 
04584 #ifdef ANSI_DECLARATORS
04585 vertex getvertex(struct mesh *m, struct behavior *b, int number)
04586 #else /* not ANSI_DECLARATORS */
04587 vertex getvertex(m, b, number)
04588 struct mesh *m;
04589 struct behavior *b;
04590 int number;
04591 #endif /* not ANSI_DECLARATORS */
04592 
04593 {
04594   VOID **getblock;
04595   char *foundvertex;
04596   unsigned long alignptr;
04597   int current;
04598 
04599   getblock = m->vertices.firstblock;
04600   current = b->firstnumber;
04601 
04602   /* Find the right block. */
04603   if (current + m->vertices.itemsfirstblock <= number) {
04604     getblock = (VOID **) *getblock;
04605     current += m->vertices.itemsfirstblock;
04606     while (current + m->vertices.itemsperblock <= number) {
04607       getblock = (VOID **) *getblock;
04608       current += m->vertices.itemsperblock;
04609     }
04610   }
04611 
04612   /* Now find the right vertex. */
04613   alignptr = (unsigned long) (getblock + 1);
04614   foundvertex = (char *) (alignptr + (unsigned long) m->vertices.alignbytes -
04615                           (alignptr % (unsigned long) m->vertices.alignbytes));
04616   return (vertex) (foundvertex + m->vertices.itembytes * (number - current));
04617 }
04618 
04619 /*****************************************************************************/
04620 /*                                                                           */
04621 /*  triangledeinit()   Free all remaining allocated memory.                  */
04622 /*                                                                           */
04623 /*****************************************************************************/
04624 
04625 #ifdef ANSI_DECLARATORS
04626 void triangledeinit(struct mesh *m, struct behavior *b)
04627 #else /* not ANSI_DECLARATORS */
04628 void triangledeinit(m, b)
04629 struct mesh *m;
04630 struct behavior *b;
04631 #endif /* not ANSI_DECLARATORS */
04632 
04633 {
04634   pooldeinit(&m->triangles);
04635   trifree((VOID *) m->dummytribase);
04636   if (b->usesegments) {
04637     pooldeinit(&m->subsegs);
04638     trifree((VOID *) m->dummysubbase);
04639   }
04640   pooldeinit(&m->vertices);
04641 #ifndef CDT_ONLY
04642   if (b->quality) {
04643     pooldeinit(&m->badsubsegs);
04644     if ((b->minangle > 0.0) || b->vararea || b->fixedarea || b->usertest) {
04645       pooldeinit(&m->badtriangles);
04646       pooldeinit(&m->flipstackers);
04647     }
04648   }
04649 #endif /* not CDT_ONLY */
04650 }
04651 
04654 /********* Memory management routines end here                       *********/
04655 
04656 /********* Constructors begin here                                   *********/
04660 /*****************************************************************************/
04661 /*                                                                           */
04662 /*  maketriangle()   Create a new triangle with orientation zero.            */
04663 /*                                                                           */
04664 /*****************************************************************************/
04665 
04666 #ifdef ANSI_DECLARATORS
04667 void maketriangle(struct mesh *m, struct behavior *b, struct otri *newotri)
04668 #else /* not ANSI_DECLARATORS */
04669 void maketriangle(m, b, newotri)
04670 struct mesh *m;
04671 struct behavior *b;
04672 struct otri *newotri;
04673 #endif /* not ANSI_DECLARATORS */
04674 
04675 {
04676   int i;
04677 
04678   newotri->tri = (triangle *) poolalloc(&m->triangles);
04679   /* Initialize the three adjoining triangles to be "outer space". */
04680   newotri->tri[0] = (triangle) m->dummytri;
04681   newotri->tri[1] = (triangle) m->dummytri;
04682   newotri->tri[2] = (triangle) m->dummytri;
04683   /* Three NULL vertices. */
04684   newotri->tri[3] = (triangle) NULL;
04685   newotri->tri[4] = (triangle) NULL;
04686   newotri->tri[5] = (triangle) NULL;
04687   if (b->usesegments) {
04688     /* Initialize the three adjoining subsegments to be the omnipresent */
04689     /*   subsegment.                                                    */
04690     newotri->tri[6] = (triangle) m->dummysub;
04691     newotri->tri[7] = (triangle) m->dummysub;
04692     newotri->tri[8] = (triangle) m->dummysub;
04693   }
04694   for (i = 0; i < m->eextras; i++) {
04695     setelemattribute(*newotri, i, 0.0);
04696   }
04697   if (b->vararea) {
04698     setareabound(*newotri, -1.0);
04699   }
04700 
04701   newotri->orient = 0;
04702 }
04703 
04704 /*****************************************************************************/
04705 /*                                                                           */
04706 /*  makesubseg()   Create a new subsegment with orientation zero.            */
04707 /*                                                                           */
04708 /*****************************************************************************/
04709 
04710 #ifdef ANSI_DECLARATORS
04711 void makesubseg(struct mesh *m, struct osub *newsubseg)
04712 #else /* not ANSI_DECLARATORS */
04713 void makesubseg(m, newsubseg)
04714 struct mesh *m;
04715 struct osub *newsubseg;
04716 #endif /* not ANSI_DECLARATORS */
04717 
04718 {
04719   newsubseg->ss = (subseg *) poolalloc(&m->subsegs);
04720   /* Initialize the two adjoining subsegments to be the omnipresent */
04721   /*   subsegment.                                                  */
04722   newsubseg->ss[0] = (subseg) m->dummysub;
04723   newsubseg->ss[1] = (subseg) m->dummysub;
04724   /* Four NULL vertices. */
04725   newsubseg->ss[2] = (subseg) NULL;
04726   newsubseg->ss[3] = (subseg) NULL;
04727   newsubseg->ss[4] = (subseg) NULL;
04728   newsubseg->ss[5] = (subseg) NULL;
04729   /* Initialize the two adjoining triangles to be "outer space." */
04730   newsubseg->ss[6] = (subseg) m->dummytri;
04731   newsubseg->ss[7] = (subseg) m->dummytri;
04732   /* Set the boundary marker to zero. */
04733   setmark(*newsubseg, 0);
04734 
04735   newsubseg->ssorient = 0;
04736 }
04737 
04740 /********* Constructors end here                                     *********/
04741 
04742 /********* Geometric primitives begin here                           *********/
04746 /* The adaptive exact arithmetic geometric predicates implemented herein are */
04747 /*   described in detail in my paper, "Adaptive Precision Floating-Point     */
04748 /*   Arithmetic and Fast Robust Geometric Predicates."  See the header for a */
04749 /*   full citation.                                                          */
04750 
04751 /* Which of the following two methods of finding the absolute values is      */
04752 /*   fastest is compiler-dependent.  A few compilers can inline and optimize */
04753 /*   the fabs() call; but most will incur the overhead of a function call,   */
04754 /*   which is disastrously slow.  A faster way on IEEE machines might be to  */
04755 /*   mask the appropriate bit, but that's difficult to do in C without       */
04756 /*   forcing the value to be stored to memory (rather than be kept in the    */
04757 /*   register to which the optimizer assigned it).                           */
04758 
04759 #define Absolute(a)  ((a) >= 0.0 ? (a) : -(a))
04760 /* #define Absolute(a)  fabs(a) */
04761 
04762 /* Many of the operations are broken up into two pieces, a main part that    */
04763 /*   performs an approximate operation, and a "tail" that computes the       */
04764 /*   roundoff error of that operation.                                       */
04765 /*                                                                           */
04766 /* The operations Fast_Two_Sum(), Fast_Two_Diff(), Two_Sum(), Two_Diff(),    */
04767 /*   Split(), and Two_Product() are all implemented as described in the      */
04768 /*   reference.  Each of these macros requires certain variables to be       */
04769 /*   defined in the calling routine.  The variables `bvirt', `c', `abig',    */
04770 /*   `_i', `_j', `_k', `_l', `_m', and `_n' are declared `INEXACT' because   */
04771 /*   they store the result of an operation that may incur roundoff error.    */
04772 /*   The input parameter `x' (or the highest numbered `x_' parameter) must   */
04773 /*   also be declared `INEXACT'.                                             */
04774 
04775 #define Fast_Two_Sum_Tail(a, b, x, y) \
04776   bvirt = x - a; \
04777   y = b - bvirt
04778 
04779 #define Fast_Two_Sum(a, b, x, y) \
04780   x = (REAL) (a + b); \
04781   Fast_Two_Sum_Tail(a, b, x, y)
04782 
04783 #define Two_Sum_Tail(a, b, x, y) \
04784   bvirt = (REAL) (x - a); \
04785   avirt = x - bvirt; \
04786   bround = b - bvirt; \
04787   around = a - avirt; \
04788   y = around + bround
04789 
04790 #define Two_Sum(a, b, x, y) \
04791   x = (REAL) (a + b); \
04792   Two_Sum_Tail(a, b, x, y)
04793 
04794 #define Two_Diff_Tail(a, b, x, y) \
04795   bvirt = (REAL) (a - x); \
04796   avirt = x + bvirt; \
04797   bround = bvirt - b; \
04798   around = a - avirt; \
04799   y = around + bround
04800 
04801 #define Two_Diff(a, b, x, y) \
04802   x = (REAL) (a - b); \
04803   Two_Diff_Tail(a, b, x, y)
04804 
04805 #define Split(a, ahi, alo) \
04806   c = (REAL) (splitter * a); \
04807   abig = (REAL) (c - a); \
04808   ahi = c - abig; \
04809   alo = a - ahi
04810 
04811 #define Two_Product_Tail(a, b, x, y) \
04812   Split(a, ahi, alo); \
04813   Split(b, bhi, blo); \
04814   err1 = x - (ahi * bhi); \
04815   err2 = err1 - (alo * bhi); \
04816   err3 = err2 - (ahi * blo); \
04817   y = (alo * blo) - err3
04818 
04819 #define Two_Product(a, b, x, y) \
04820   x = (REAL) (a * b); \
04821   Two_Product_Tail(a, b, x, y)
04822 
04823 /* Two_Product_Presplit() is Two_Product() where one of the inputs has       */
04824 /*   already been split.  Avoids redundant splitting.                        */
04825 
04826 #define Two_Product_Presplit(a, b, bhi, blo, x, y) \
04827   x = (REAL) (a * b); \
04828   Split(a, ahi, alo); \
04829   err1 = x - (ahi * bhi); \
04830   err2 = err1 - (alo * bhi); \
04831   err3 = err2 - (ahi * blo); \
04832   y = (alo * blo) - err3
04833 
04834 /* Square() can be done more quickly than Two_Product().                     */
04835 
04836 #define Square_Tail(a, x, y) \
04837   Split(a, ahi, alo); \
04838   err1 = x - (ahi * ahi); \
04839   err3 = err1 - ((ahi + ahi) * alo); \
04840   y = (alo * alo) - err3
04841 
04842 #define Square(a, x, y) \
04843   x = (REAL) (a * a); \
04844   Square_Tail(a, x, y)
04845 
04846 /* Macros for summing expansions of various fixed lengths.  These are all    */
04847 /*   unrolled versions of Expansion_Sum().                                   */
04848 
04849 #define Two_One_Sum(a1, a0, b, x2, x1, x0) \
04850   Two_Sum(a0, b , _i, x0); \
04851   Two_Sum(a1, _i, x2, x1)
04852 
04853 #define Two_One_Diff(a1, a0, b, x2, x1, x0) \
04854   Two_Diff(a0, b , _i, x0); \
04855   Two_Sum( a1, _i, x2, x1)
04856 
04857 #define Two_Two_Sum(a1, a0, b1, b0, x3, x2, x1, x0) \
04858   Two_One_Sum(a1, a0, b0, _j, _0, x0); \
04859   Two_One_Sum(_j, _0, b1, x3, x2, x1)
04860 
04861 #define Two_Two_Diff(a1, a0, b1, b0, x3, x2, x1, x0) \
04862   Two_One_Diff(a1, a0, b0, _j, _0, x0); \
04863   Two_One_Diff(_j, _0, b1, x3, x2, x1)
04864 
04865 /* Macro for multiplying a two-component expansion by a single component.    */
04866 
04867 #define Two_One_Product(a1, a0, b, x3, x2, x1, x0) \
04868   Split(b, bhi, blo); \
04869   Two_Product_Presplit(a0, b, bhi, blo, _i, x0); \
04870   Two_Product_Presplit(a1, b, bhi, blo, _j, _0); \
04871   Two_Sum(_i, _0, _k, x1); \
04872   Fast_Two_Sum(_j, _k, x3, x2)
04873 
04874 /*****************************************************************************/
04875 /*                                                                           */
04876 /*  exactinit()   Initialize the variables used for exact arithmetic.        */
04877 /*                                                                           */
04878 /*  `epsilon' is the largest power of two such that 1.0 + epsilon = 1.0 in   */
04879 /*  floating-point arithmetic.  `epsilon' bounds the relative roundoff       */
04880 /*  error.  It is used for floating-point error analysis.                    */
04881 /*                                                                           */
04882 /*  `splitter' is used to split floating-point numbers into two half-        */
04883 /*  length significands for exact multiplication.                            */
04884 /*                                                                           */
04885 /*  I imagine that a highly optimizing compiler might be too smart for its   */
04886 /*  own good, and somehow cause this routine to fail, if it pretends that    */
04887 /*  floating-point arithmetic is too much like real arithmetic.              */
04888 /*                                                                           */
04889 /*  Don't change this routine unless you fully understand it.                */
04890 /*                                                                           */
04891 /*****************************************************************************/
04892 
04893 void exactinit()
04894 {
04895   REAL half;
04896   REAL check, lastcheck;
04897   int every_other;
04898 #ifdef LINUX
04899   int cword;
04900 #endif /* LINUX */
04901 
04902 #ifdef CPU86
04903 #ifdef SINGLE
04904   _control87(_PC_24, _MCW_PC); /* Set FPU control word for single precision. */
04905 #else /* not SINGLE */
04906   _control87(_PC_53, _MCW_PC); /* Set FPU control word for double precision. */
04907 #endif /* not SINGLE */
04908 #endif /* CPU86 */
04909 #ifdef LINUX
04910 #ifdef SINGLE
04911   /*  cword = 4223; */
04912   cword = 4210;                 /* set FPU control word for single precision */
04913 #else /* not SINGLE */
04914   /*  cword = 4735; */
04915   cword = 4722;                 /* set FPU control word for double precision */
04916 #endif /* not SINGLE */
04917   _FPU_SETCW(cword);
04918 #endif /* LINUX */
04919 
04920   every_other = 1;
04921   half = 0.5;
04922   epsilon = 1.0;
04923   splitter = 1.0;
04924   check = 1.0;
04925   /* Repeatedly divide `epsilon' by two until it is too small to add to      */
04926   /*   one without causing roundoff.  (Also check if the sum is equal to     */
04927   /*   the previous sum, for machines that round up instead of using exact   */
04928   /*   rounding.  Not that these routines will work on such machines.)       */
04929   do {
04930     lastcheck = check;
04931     epsilon *= half;
04932     if (every_other) {
04933       splitter *= 2.0;
04934     }
04935     every_other = !every_other;
04936     check = 1.0 + epsilon;
04937   } while ((check != 1.0) && (check != lastcheck));
04938   splitter += 1.0;
04939   /* Error bounds for orientation and incircle tests. */
04940   resulterrbound = (3.0 + 8.0 * epsilon) * epsilon;
04941   ccwerrboundA = (3.0 + 16.0 * epsilon) * epsilon;
04942   ccwerrboundB = (2.0 + 12.0 * epsilon) * epsilon;
04943   ccwerrboundC = (9.0 + 64.0 * epsilon) * epsilon * epsilon;
04944   iccerrboundA = (10.0 + 96.0 * epsilon) * epsilon;
04945   iccerrboundB = (4.0 + 48.0 * epsilon) * epsilon;
04946   iccerrboundC = (44.0 + 576.0 * epsilon) * epsilon * epsilon;
04947   o3derrboundA = (7.0 + 56.0 * epsilon) * epsilon;
04948   o3derrboundB = (3.0 + 28.0 * epsilon) * epsilon;
04949   o3derrboundC = (26.0 + 288.0 * epsilon) * epsilon * epsilon;
04950 }
04951 
04952 /*****************************************************************************/
04953 /*                                                                           */
04954 /*  fast_expansion_sum_zeroelim()   Sum two expansions, eliminating zero     */
04955 /*                                  components from the output expansion.    */
04956 /*                                                                           */
04957 /*  Sets h = e + f.  See my Robust Predicates paper for details.             */
04958 /*                                                                           */
04959 /*  If round-to-even is used (as with IEEE 754), maintains the strongly      */
04960 /*  nonoverlapping property.  (That is, if e is strongly nonoverlapping, h   */
04961 /*  will be also.)  Does NOT maintain the nonoverlapping or nonadjacent      */
04962 /*  properties.                                                              */
04963 /*                                                                           */
04964 /*****************************************************************************/
04965 
04966 #ifdef ANSI_DECLARATORS
04967 int fast_expansion_sum_zeroelim(int elen, REAL *e, int flen, REAL *f, REAL *h)
04968 #else /* not ANSI_DECLARATORS */
04969 int fast_expansion_sum_zeroelim(elen, e, flen, f, h)  /* h cannot be e or f. */
04970 int elen;
04971 REAL *e;
04972 int flen;
04973 REAL *f;
04974 REAL *h;
04975 #endif /* not ANSI_DECLARATORS */
04976 
04977 {
04978   REAL Q;
04979   INEXACT REAL Qnew;
04980   INEXACT REAL hh;
04981   INEXACT REAL bvirt;
04982   REAL avirt, bround, around;
04983   int eindex, findex, hindex;
04984   REAL enow, fnow;
04985 
04986   enow = e[0];
04987   fnow = f[0];
04988   eindex = findex = 0;
04989   if ((fnow > enow) == (fnow > -enow)) {
04990     Q = enow;
04991     enow = e[++eindex];
04992   } else {
04993     Q = fnow;
04994     fnow = f[++findex];
04995   }
04996   hindex = 0;
04997   if ((eindex < elen) && (findex < flen)) {
04998     if ((fnow > enow) == (fnow > -enow)) {
04999       Fast_Two_Sum(enow, Q, Qnew, hh);
05000       enow = e[++eindex];
05001     } else {
05002       Fast_Two_Sum(fnow, Q, Qnew, hh);
05003       fnow = f[++findex];
05004     }
05005     Q = Qnew;
05006     if (hh != 0.0) {
05007       h[hindex++] = hh;
05008     }
05009     while ((eindex < elen) && (findex < flen)) {
05010       if ((fnow > enow) == (fnow > -enow)) {
05011         Two_Sum(Q, enow, Qnew, hh);
05012         enow = e[++eindex];
05013       } else {
05014         Two_Sum(Q, fnow, Qnew, hh);
05015         fnow = f[++findex];
05016       }
05017       Q = Qnew;
05018       if (hh != 0.0) {
05019         h[hindex++] = hh;
05020       }
05021     }
05022   }
05023   while (eindex < elen) {
05024     Two_Sum(Q, enow, Qnew, hh);
05025     enow = e[++eindex];
05026     Q = Qnew;
05027     if (hh != 0.0) {
05028       h[hindex++] = hh;
05029     }
05030   }
05031   while (findex < flen) {
05032     Two_Sum(Q, fnow, Qnew, hh);
05033     fnow = f[++findex];
05034     Q = Qnew;
05035     if (hh != 0.0) {
05036       h[hindex++] = hh;
05037     }
05038   }
05039   if ((Q != 0.0) || (hindex == 0)) {
05040     h[hindex++] = Q;
05041   }
05042   return hindex;
05043 }
05044 
05045 /*****************************************************************************/
05046 /*                                                                           */
05047 /*  scale_expansion_zeroelim()   Multiply an expansion by a scalar,          */
05048 /*                               eliminating zero components from the        */
05049 /*                               output expansion.                           */
05050 /*                                                                           */
05051 /*  Sets h = be.  See my Robust Predicates paper for details.                */
05052 /*                                                                           */
05053 /*  Maintains the nonoverlapping property.  If round-to-even is used (as     */
05054 /*  with IEEE 754), maintains the strongly nonoverlapping and nonadjacent    */
05055 /*  properties as well.  (That is, if e has one of these properties, so      */
05056 /*  will h.)                                                                 */
05057 /*                                                                           */
05058 /*****************************************************************************/
05059 
05060 #ifdef ANSI_DECLARATORS
05061 int scale_expansion_zeroelim(int elen, REAL *e, REAL b, REAL *h)
05062 #else /* not ANSI_DECLARATORS */
05063 int scale_expansion_zeroelim(elen, e, b, h)   /* e and h cannot be the same. */
05064 int elen;
05065 REAL *e;
05066 REAL b;
05067 REAL *h;
05068 #endif /* not ANSI_DECLARATORS */
05069 
05070 {
05071   INEXACT REAL Q, sum;
05072   REAL hh;
05073   INEXACT REAL product1;
05074   REAL product0;
05075   int eindex, hindex;
05076   REAL enow;
05077   INEXACT REAL bvirt;
05078   REAL avirt, bround, around;
05079   INEXACT REAL c;
05080   INEXACT REAL abig;
05081   REAL ahi, alo, bhi, blo;
05082   REAL err1, err2, err3;
05083 
05084   Split(b, bhi, blo);
05085   Two_Product_Presplit(e[0], b, bhi, blo, Q, hh);
05086   hindex = 0;
05087   if (hh != 0) {
05088     h[hindex++] = hh;
05089   }
05090   for (eindex = 1; eindex < elen; eindex++) {
05091     enow = e[eindex];
05092     Two_Product_Presplit(enow, b, bhi, blo, product1, product0);
05093     Two_Sum(Q, product0, sum, hh);
05094     if (hh != 0) {
05095       h[hindex++] = hh;
05096     }
05097     Fast_Two_Sum(product1, sum, Q, hh);
05098     if (hh != 0) {
05099       h[hindex++] = hh;
05100     }
05101   }
05102   if ((Q != 0.0) || (hindex == 0)) {
05103     h[hindex++] = Q;
05104   }
05105   return hindex;
05106 }
05107 
05108 /*****************************************************************************/
05109 /*                                                                           */
05110 /*  estimate()   Produce a one-word estimate of an expansion's value.        */
05111 /*                                                                           */
05112 /*  See my Robust Predicates paper for details.                              */
05113 /*                                                                           */
05114 /*****************************************************************************/
05115 
05116 #ifdef ANSI_DECLARATORS
05117 REAL estimate(int elen, REAL *e)
05118 #else /* not ANSI_DECLARATORS */
05119 REAL estimate(elen, e)
05120 int elen;
05121 REAL *e;
05122 #endif /* not ANSI_DECLARATORS */
05123 
05124 {
05125   REAL Q;
05126   int eindex;
05127 
05128   Q = e[0];
05129   for (eindex = 1; eindex < elen; eindex++) {
05130     Q += e[eindex];
05131   }
05132   return Q;
05133 }
05134 
05135 /*****************************************************************************/
05136 /*                                                                           */
05137 /*  counterclockwise()   Return a positive value if the points pa, pb, and   */
05138 /*                       pc occur in counterclockwise order; a negative      */
05139 /*                       value if they occur in clockwise order; and zero    */
05140 /*                       if they are collinear.  The result is also a rough  */
05141 /*                       approximation of twice the signed area of the       */
05142 /*                       triangle defined by the three points.               */
05143 /*                                                                           */
05144 /*  Uses exact arithmetic if necessary to ensure a correct answer.  The      */
05145 /*  result returned is the determinant of a matrix.  This determinant is     */
05146 /*  computed adaptively, in the sense that exact arithmetic is used only to  */
05147 /*  the degree it is needed to ensure that the returned value has the        */
05148 /*  correct sign.  Hence, this function is usually quite fast, but will run  */
05149 /*  more slowly when the input points are collinear or nearly so.            */
05150 /*                                                                           */
05151 /*  See my Robust Predicates paper for details.                              */
05152 /*                                                                           */
05153 /*****************************************************************************/
05154 
05155 #ifdef ANSI_DECLARATORS
05156 REAL counterclockwiseadapt(vertex pa, vertex pb, vertex pc, REAL detsum)
05157 #else /* not ANSI_DECLARATORS */
05158 REAL counterclockwiseadapt(pa, pb, pc, detsum)
05159 vertex pa;
05160 vertex pb;
05161 vertex pc;
05162 REAL detsum;
05163 #endif /* not ANSI_DECLARATORS */
05164 
05165 {
05166   INEXACT REAL acx, acy, bcx, bcy;
05167   REAL acxtail, acytail, bcxtail, bcytail;
05168   INEXACT REAL detleft, detright;
05169   REAL detlefttail, detrighttail;
05170   REAL det, errbound;
05171   REAL B[4], C1[8], C2[12], D[16];
05172   INEXACT REAL B3;
05173   int C1length, C2length, Dlength;
05174   REAL u[4];
05175   INEXACT REAL u3;
05176   INEXACT REAL s1, t1;
05177   REAL s0, t0;
05178 
05179   INEXACT REAL bvirt;
05180   REAL avirt, bround, around;
05181   INEXACT REAL c;
05182   INEXACT REAL abig;
05183   REAL ahi, alo, bhi, blo;
05184   REAL err1, err2, err3;
05185   INEXACT REAL _i, _j;
05186   REAL _0;
05187 
05188   acx = (REAL) (pa[0] - pc[0]);
05189   bcx = (REAL) (pb[0] - pc[0]);
05190   acy = (REAL) (pa[1] - pc[1]);
05191   bcy = (REAL) (pb[1] - pc[1]);
05192 
05193   Two_Product(acx, bcy, detleft, detlefttail);
05194   Two_Product(acy, bcx, detright, detrighttail);
05195 
05196   Two_Two_Diff(detleft, detlefttail, detright, detrighttail,
05197                B3, B[2], B[1], B[0]);
05198   B[3] = B3;
05199 
05200   det = estimate(4, B);
05201   errbound = ccwerrboundB * detsum;
05202   if ((det >= errbound) || (-det >= errbound)) {
05203     return det;
05204   }
05205 
05206   Two_Diff_Tail(pa[0], pc[0], acx, acxtail);
05207   Two_Diff_Tail(pb[0], pc[0], bcx, bcxtail);
05208   Two_Diff_Tail(pa[1], pc[1], acy, acytail);
05209   Two_Diff_Tail(pb[1], pc[1], bcy, bcytail);
05210 
05211   if ((acxtail == 0.0) && (acytail == 0.0)
05212       && (bcxtail == 0.0) && (bcytail == 0.0)) {
05213     return det;
05214   }
05215 
05216   errbound = ccwerrboundC * detsum + resulterrbound * Absolute(det);
05217   det += (acx * bcytail + bcy * acxtail)
05218        - (acy * bcxtail + bcx * acytail);
05219   if ((det >= errbound) || (-det >= errbound)) {
05220     return det;
05221   }
05222 
05223   Two_Product(acxtail, bcy, s1, s0);
05224   Two_Product(acytail, bcx, t1, t0);
05225   Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
05226   u[3] = u3;
05227   C1length = fast_expansion_sum_zeroelim(4, B, 4, u, C1);
05228 
05229   Two_Product(acx, bcytail, s1, s0);
05230   Two_Product(acy, bcxtail, t1, t0);
05231   Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
05232   u[3] = u3;
05233   C2length = fast_expansion_sum_zeroelim(C1length, C1, 4, u, C2);
05234 
05235   Two_Product(acxtail, bcytail, s1, s0);
05236   Two_Product(acytail, bcxtail, t1, t0);
05237   Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
05238   u[3] = u3;
05239   Dlength = fast_expansion_sum_zeroelim(C2length, C2, 4, u, D);
05240 
05241   return(D[Dlength - 1]);
05242 }
05243 
05244 #ifdef ANSI_DECLARATORS
05245 REAL counterclockwise(struct mesh *m, struct behavior *b,
05246                       vertex pa, vertex pb, vertex pc)
05247 #else /* not ANSI_DECLARATORS */
05248 REAL counterclockwise(m, b, pa, pb, pc)
05249 struct mesh *m;
05250 struct behavior *b;
05251 vertex pa;
05252 vertex pb;
05253 vertex pc;
05254 #endif /* not ANSI_DECLARATORS */
05255 
05256 {
05257   REAL detleft, detright, det;
05258   REAL detsum, errbound;
05259 
05260   m->counterclockcount++;
05261 
05262   detleft = (pa[0] - pc[0]) * (pb[1] - pc[1]);
05263   detright = (pa[1] - pc[1]) * (pb[0] - pc[0]);
05264   det = detleft - detright;
05265 
05266   if (b->noexact) {
05267     return det;
05268   }
05269 
05270   if (detleft > 0.0) {
05271     if (detright <= 0.0) {
05272       return det;
05273     } else {
05274       detsum = detleft + detright;
05275     }
05276   } else if (detleft < 0.0) {
05277     if (detright >= 0.0) {
05278       return det;
05279     } else {
05280       detsum = -detleft - detright;
05281     }
05282   } else {
05283     return det;
05284   }
05285 
05286   errbound = ccwerrboundA * detsum;
05287   if ((det >= errbound) || (-det >= errbound)) {
05288     return det;
05289   }
05290 
05291   return counterclockwiseadapt(pa, pb, pc, detsum);
05292 }
05293 
05294 /*****************************************************************************/
05295 /*                                                                           */
05296 /*  incircle()   Return a positive value if the point pd lies inside the     */
05297 /*               circle passing through pa, pb, and pc; a negative value if  */
05298 /*               it lies outside; and zero if the four points are cocircular.*/
05299 /*               The points pa, pb, and pc must be in counterclockwise       */
05300 /*               order, or the sign of the result will be reversed.          */
05301 /*                                                                           */
05302 /*  Uses exact arithmetic if necessary to ensure a correct answer.  The      */
05303 /*  result returned is the determinant of a matrix.  This determinant is     */
05304 /*  computed adaptively, in the sense that exact arithmetic is used only to  */
05305 /*  the degree it is needed to ensure that the returned value has the        */
05306 /*  correct sign.  Hence, this function is usually quite fast, but will run  */
05307 /*  more slowly when the input points are cocircular or nearly so.           */
05308 /*                                                                           */
05309 /*  See my Robust Predicates paper for details.                              */
05310 /*                                                                           */
05311 /*****************************************************************************/
05312 
05313 #ifdef ANSI_DECLARATORS
05314 REAL incircleadapt(vertex pa, vertex pb, vertex pc, vertex pd, REAL permanent)
05315 #else /* not ANSI_DECLARATORS */
05316 REAL incircleadapt(pa, pb, pc, pd, permanent)
05317 vertex pa;
05318 vertex pb;
05319 vertex pc;
05320 vertex pd;
05321 REAL permanent;
05322 #endif /* not ANSI_DECLARATORS */
05323 
05324 {
05325   INEXACT REAL adx, bdx, cdx, ady, bdy, cdy;
05326   REAL det, errbound;
05327 
05328   INEXACT REAL bdxcdy1, cdxbdy1, cdxady1, adxcdy1, adxbdy1, bdxady1;
05329   REAL bdxcdy0, cdxbdy0, cdxady0, adxcdy0, adxbdy0, bdxady0;
05330   REAL bc[4], ca[4], ab[4];
05331   INEXACT REAL bc3, ca3, ab3;
05332   REAL axbc[8], axxbc[16], aybc[8], ayybc[16], adet[32];
05333   int axbclen, axxbclen, aybclen, ayybclen, alen;
05334   REAL bxca[8], bxxca[16], byca[8], byyca[16], bdet[32];
05335   int bxcalen, bxxcalen, bycalen, byycalen, blen;
05336   REAL cxab[8], cxxab[16], cyab[8], cyyab[16], cdet[32];
05337   int cxablen, cxxablen, cyablen, cyyablen, clen;
05338   REAL abdet[64];
05339   int ablen;
05340   REAL fin1[1152], fin2[1152];
05341   REAL *finnow, *finother, *finswap;
05342   int finlength;
05343 
05344   REAL adxtail, bdxtail, cdxtail, adytail, bdytail, cdytail;
05345   INEXACT REAL adxadx1, adyady1, bdxbdx1, bdybdy1, cdxcdx1, cdycdy1;
05346   REAL adxadx0, adyady0, bdxbdx0, bdybdy0, cdxcdx0, cdycdy0;
05347   REAL aa[4], bb[4], cc[4];
05348   INEXACT REAL aa3, bb3, cc3;
05349   INEXACT REAL ti1, tj1;
05350   REAL ti0, tj0;
05351   REAL u[4], v[4];
05352   INEXACT REAL u3, v3;
05353   REAL temp8[8], temp16a[16], temp16b[16], temp16c[16];
05354   REAL temp32a[32], temp32b[32], temp48[48], temp64[64];
05355   int temp8len, temp16alen, temp16blen, temp16clen;
05356   int temp32alen, temp32blen, temp48len, temp64len;
05357   REAL axtbb[8], axtcc[8], aytbb[8], aytcc[8];
05358   int axtbblen, axtcclen, aytbblen, aytcclen;
05359   REAL bxtaa[8], bxtcc[8], bytaa[8], bytcc[8];
05360   int bxtaalen, bxtcclen, bytaalen, bytcclen;
05361   REAL cxtaa[8], cxtbb[8], cytaa[8], cytbb[8];
05362   int cxtaalen, cxtbblen, cytaalen, cytbblen;
05363   REAL axtbc[8], aytbc[8], bxtca[8], bytca[8], cxtab[8], cytab[8];
05364   int axtbclen=0, aytbclen=0, bxtcalen=0, bytcalen=0, cxtablen=0, cytablen=0;
05365   REAL axtbct[16], aytbct[16], bxtcat[16], bytcat[16], cxtabt[16], cytabt[16];
05366   int axtbctlen, aytbctlen, bxtcatlen, bytcatlen, cxtabtlen, cytabtlen;
05367   REAL axtbctt[8], aytbctt[8], bxtcatt[8];
05368   REAL bytcatt[8], cxtabtt[8], cytabtt[8];
05369   int axtbcttlen, aytbcttlen, bxtcattlen, bytcattlen, cxtabttlen, cytabttlen;
05370   REAL abt[8], bct[8], cat[8];
05371   int abtlen, bctlen, catlen;
05372   REAL abtt[4], bctt[4], catt[4];
05373   int abttlen, bcttlen, cattlen;
05374   INEXACT REAL abtt3, bctt3, catt3;
05375   REAL negate;
05376 
05377   INEXACT REAL bvirt;
05378   REAL avirt, bround, around;
05379   INEXACT REAL c;
05380   INEXACT REAL abig;
05381   REAL ahi, alo, bhi, blo;
05382   REAL err1, err2, err3;
05383   INEXACT REAL _i, _j;
05384   REAL _0;
05385 
05386   adx = (REAL) (pa[0] - pd[0]);
05387   bdx = (REAL) (pb[0] - pd[0]);
05388   cdx = (REAL) (pc[0] - pd[0]);
05389   ady = (REAL) (pa[1] - pd[1]);
05390   bdy = (REAL) (pb[1] - pd[1]);
05391   cdy = (REAL) (pc[1] - pd[1]);
05392 
05393   Two_Product(bdx, cdy, bdxcdy1, bdxcdy0);
05394   Two_Product(cdx, bdy, cdxbdy1, cdxbdy0);
05395   Two_Two_Diff(bdxcdy1, bdxcdy0, cdxbdy1, cdxbdy0, bc3, bc[2], bc[1], bc[0]);
05396   bc[3] = bc3;
05397   axbclen = scale_expansion_zeroelim(4, bc, adx, axbc);
05398   axxbclen = scale_expansion_zeroelim(axbclen, axbc, adx, axxbc);
05399   aybclen = scale_expansion_zeroelim(4, bc, ady, aybc);
05400   ayybclen = scale_expansion_zeroelim(aybclen, aybc, ady, ayybc);
05401   alen = fast_expansion_sum_zeroelim(axxbclen, axxbc, ayybclen, ayybc, adet);
05402 
05403   Two_Product(cdx, ady, cdxady1, cdxady0);
05404   Two_Product(adx, cdy, adxcdy1, adxcdy0);
05405   Two_Two_Diff(cdxady1, cdxady0, adxcdy1, adxcdy0, ca3, ca[2], ca[1], ca[0]);
05406   ca[3] = ca3;
05407   bxcalen = scale_expansion_zeroelim(4, ca, bdx, bxca);
05408   bxxcalen = scale_expansion_zeroelim(bxcalen, bxca, bdx, bxxca);
05409   bycalen = scale_expansion_zeroelim(4, ca, bdy, byca);
05410   byycalen = scale_expansion_zeroelim(bycalen, byca, bdy, byyca);
05411   blen = fast_expansion_sum_zeroelim(bxxcalen, bxxca, byycalen, byyca, bdet);
05412 
05413   Two_Product(adx, bdy, adxbdy1, adxbdy0);
05414   Two_Product(bdx, ady, bdxady1, bdxady0);
05415   Two_Two_Diff(adxbdy1, adxbdy0, bdxady1, bdxady0, ab3, ab[2], ab[1], ab[0]);
05416   ab[3] = ab3;
05417   cxablen = scale_expansion_zeroelim(4, ab, cdx, cxab);
05418   cxxablen = scale_expansion_zeroelim(cxablen, cxab, cdx, cxxab);
05419   cyablen = scale_expansion_zeroelim(4, ab, cdy, cyab);
05420   cyyablen = scale_expansion_zeroelim(cyablen, cyab, cdy, cyyab);
05421   clen = fast_expansion_sum_zeroelim(cxxablen, cxxab, cyyablen, cyyab, cdet);
05422 
05423   ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
05424   finlength = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, fin1);
05425 
05426   det = estimate(finlength, fin1);
05427   errbound = iccerrboundB * permanent;
05428   if ((det >= errbound) || (-det >= errbound)) {
05429     return det;
05430   }
05431 
05432   Two_Diff_Tail(pa[0], pd[0], adx, adxtail);
05433   Two_Diff_Tail(pa[1], pd[1], ady, adytail);
05434   Two_Diff_Tail(pb[0], pd[0], bdx, bdxtail);
05435   Two_Diff_Tail(pb[1], pd[1], bdy, bdytail);
05436   Two_Diff_Tail(pc[0], pd[0], cdx, cdxtail);
05437   Two_Diff_Tail(pc[1], pd[1], cdy, cdytail);
05438   if ((adxtail == 0.0) && (bdxtail == 0.0) && (cdxtail == 0.0)
05439       && (adytail == 0.0) && (bdytail == 0.0) && (cdytail == 0.0)) {
05440     return det;
05441   }
05442 
05443   errbound = iccerrboundC * permanent + resulterrbound * Absolute(det);
05444   det += ((adx * adx + ady * ady) * ((bdx * cdytail + cdy * bdxtail)
05445                                      - (bdy * cdxtail + cdx * bdytail))
05446           + 2.0 * (adx * adxtail + ady * adytail) * (bdx * cdy - bdy * cdx))
05447        + ((bdx * bdx + bdy * bdy) * ((cdx * adytail + ady * cdxtail)
05448                                      - (cdy * adxtail + adx * cdytail))
05449           + 2.0 * (bdx * bdxtail + bdy * bdytail) * (cdx * ady - cdy * adx))
05450        + ((cdx * cdx + cdy * cdy) * ((adx * bdytail + bdy * adxtail)
05451                                      - (ady * bdxtail + bdx * adytail))
05452           + 2.0 * (cdx * cdxtail + cdy * cdytail) * (adx * bdy - ady * bdx));
05453   if ((det >= errbound) || (-det >= errbound)) {
05454     return det;
05455   }
05456 
05457   finnow = fin1;
05458   finother = fin2;
05459 
05460   if ((bdxtail != 0.0) || (bdytail != 0.0)
05461       || (cdxtail != 0.0) || (cdytail != 0.0)) {
05462     Square(adx, adxadx1, adxadx0);
05463     Square(ady, adyady1, adyady0);
05464     Two_Two_Sum(adxadx1, adxadx0, adyady1, adyady0, aa3, aa[2], aa[1], aa[0]);
05465     aa[3] = aa3;
05466   }
05467   if ((cdxtail != 0.0) || (cdytail != 0.0)
05468       || (adxtail != 0.0) || (adytail != 0.0)) {
05469     Square(bdx, bdxbdx1, bdxbdx0);
05470     Square(bdy, bdybdy1, bdybdy0);
05471     Two_Two_Sum(bdxbdx1, bdxbdx0, bdybdy1, bdybdy0, bb3, bb[2], bb[1], bb[0]);
05472     bb[3] = bb3;
05473   }
05474   if ((adxtail != 0.0) || (adytail != 0.0)
05475       || (bdxtail != 0.0) || (bdytail != 0.0)) {
05476     Square(cdx, cdxcdx1, cdxcdx0);
05477     Square(cdy, cdycdy1, cdycdy0);
05478     Two_Two_Sum(cdxcdx1, cdxcdx0, cdycdy1, cdycdy0, cc3, cc[2], cc[1], cc[0]);
05479     cc[3] = cc3;
05480   }
05481 
05482   if (adxtail != 0.0) {
05483     axtbclen = scale_expansion_zeroelim(4, bc, adxtail, axtbc);
05484     temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, 2.0 * adx,
05485                                           temp16a);
05486 
05487     axtcclen = scale_expansion_zeroelim(4, cc, adxtail, axtcc);
05488     temp16blen = scale_expansion_zeroelim(axtcclen, axtcc, bdy, temp16b);
05489 
05490     axtbblen = scale_expansion_zeroelim(4, bb, adxtail, axtbb);
05491     temp16clen = scale_expansion_zeroelim(axtbblen, axtbb, -cdy, temp16c);
05492 
05493     temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
05494                                             temp16blen, temp16b, temp32a);
05495     temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
05496                                             temp32alen, temp32a, temp48);
05497     finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
05498                                             temp48, finother);
05499     finswap = finnow; finnow = finother; finother = finswap;
05500   }
05501   if (adytail != 0.0) {
05502     aytbclen = scale_expansion_zeroelim(4, bc, adytail, aytbc);
05503     temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, 2.0 * ady,
05504                                           temp16a);
05505 
05506     aytbblen = scale_expansion_zeroelim(4, bb, adytail, aytbb);
05507     temp16blen = scale_expansion_zeroelim(aytbblen, aytbb, cdx, temp16b);
05508 
05509     aytcclen = scale_expansion_zeroelim(4, cc, adytail, aytcc);
05510     temp16clen = scale_expansion_zeroelim(aytcclen, aytcc, -bdx, temp16c);
05511 
05512     temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
05513                                             temp16blen, temp16b, temp32a);
05514     temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
05515                                             temp32alen, temp32a, temp48);
05516     finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
05517                                             temp48, finother);
05518     finswap = finnow; finnow = finother; finother = finswap;
05519   }
05520   if (bdxtail != 0.0) {
05521     bxtcalen = scale_expansion_zeroelim(4, ca, bdxtail, bxtca);
05522     temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, 2.0 * bdx,
05523                                           temp16a);
05524 
05525     bxtaalen = scale_expansion_zeroelim(4, aa, bdxtail, bxtaa);
05526     temp16blen = scale_expansion_zeroelim(bxtaalen, bxtaa, cdy, temp16b);
05527 
05528     bxtcclen = scale_expansion_zeroelim(4, cc, bdxtail, bxtcc);
05529     temp16clen = scale_expansion_zeroelim(bxtcclen, bxtcc, -ady, temp16c);
05530 
05531     temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
05532                                             temp16blen, temp16b, temp32a);
05533     temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
05534                                             temp32alen, temp32a, temp48);
05535     finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
05536                                             temp48, finother);
05537     finswap = finnow; finnow = finother; finother = finswap;
05538   }
05539   if (bdytail != 0.0) {
05540     bytcalen = scale_expansion_zeroelim(4, ca, bdytail, bytca);
05541     temp16alen = scale_expansion_zeroelim(bytcalen, bytca, 2.0 * bdy,
05542                                           temp16a);
05543 
05544     bytcclen = scale_expansion_zeroelim(4, cc, bdytail, bytcc);
05545     temp16blen = scale_expansion_zeroelim(bytcclen, bytcc, adx, temp16b);
05546 
05547     bytaalen = scale_expansion_zeroelim(4, aa, bdytail, bytaa);
05548     temp16clen = scale_expansion_zeroelim(bytaalen, bytaa, -cdx, temp16c);
05549 
05550     temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
05551                                             temp16blen, temp16b, temp32a);
05552     temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
05553                                             temp32alen, temp32a, temp48);
05554     finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
05555                                             temp48, finother);
05556     finswap = finnow; finnow = finother; finother = finswap;
05557   }
05558   if (cdxtail != 0.0) {
05559     cxtablen = scale_expansion_zeroelim(4, ab, cdxtail, cxtab);
05560     temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, 2.0 * cdx,
05561                                           temp16a);
05562 
05563     cxtbblen = scale_expansion_zeroelim(4, bb, cdxtail, cxtbb);
05564     temp16blen = scale_expansion_zeroelim(cxtbblen, cxtbb, ady, temp16b);
05565 
05566     cxtaalen = scale_expansion_zeroelim(4, aa, cdxtail, cxtaa);
05567     temp16clen = scale_expansion_zeroelim(cxtaalen, cxtaa, -bdy, temp16c);
05568 
05569     temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
05570                                             temp16blen, temp16b, temp32a);
05571     temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
05572                                             temp32alen, temp32a, temp48);
05573     finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
05574                                             temp48, finother);
05575     finswap = finnow; finnow = finother; finother = finswap;
05576   }
05577   if (cdytail != 0.0) {
05578     cytablen = scale_expansion_zeroelim(4, ab, cdytail, cytab);
05579     temp16alen = scale_expansion_zeroelim(cytablen, cytab, 2.0 * cdy,
05580                                           temp16a);
05581 
05582     cytaalen = scale_expansion_zeroelim(4, aa, cdytail, cytaa);
05583     temp16blen = scale_expansion_zeroelim(cytaalen, cytaa, bdx, temp16b);
05584 
05585     cytbblen = scale_expansion_zeroelim(4, bb, cdytail, cytbb);
05586     temp16clen = scale_expansion_zeroelim(cytbblen, cytbb, -adx, temp16c);
05587 
05588     temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
05589                                             temp16blen, temp16b, temp32a);
05590     temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
05591                                             temp32alen, temp32a, temp48);
05592     finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
05593                                             temp48, finother);
05594     finswap = finnow; finnow = finother; finother = finswap;
05595   }
05596 
05597   if ((adxtail != 0.0) || (adytail != 0.0)) {
05598     if ((bdxtail != 0.0) || (bdytail != 0.0)
05599         || (cdxtail != 0.0) || (cdytail != 0.0)) {
05600       Two_Product(bdxtail, cdy, ti1, ti0);
05601       Two_Product(bdx, cdytail, tj1, tj0);
05602       Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
05603       u[3] = u3;
05604       negate = -bdy;
05605       Two_Product(cdxtail, negate, ti1, ti0);
05606       negate = -bdytail;
05607       Two_Product(cdx, negate, tj1, tj0);
05608       Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
05609       v[3] = v3;
05610       bctlen = fast_expansion_sum_zeroelim(4, u, 4, v, bct);
05611 
05612       Two_Product(bdxtail, cdytail, ti1, ti0);
05613       Two_Product(cdxtail, bdytail, tj1, tj0);
05614       Two_Two_Diff(ti1, ti0, tj1, tj0, bctt3, bctt[2], bctt[1], bctt[0]);
05615       bctt[3] = bctt3;
05616       bcttlen = 4;
05617     } else {
05618       bct[0] = 0.0;
05619       bctlen = 1;
05620       bctt[0] = 0.0;
05621       bcttlen = 1;
05622     }
05623 
05624     if (adxtail != 0.0) {
05625       temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, adxtail, temp16a);
05626       axtbctlen = scale_expansion_zeroelim(bctlen, bct, adxtail, axtbct);
05627       temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, 2.0 * adx,
05628                                             temp32a);
05629       temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
05630                                               temp32alen, temp32a, temp48);
05631       finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
05632                                               temp48, finother);
05633       finswap = finnow; finnow = finother; finother = finswap;
05634       if (bdytail != 0.0) {
05635         temp8len = scale_expansion_zeroelim(4, cc, adxtail, temp8);
05636         temp16alen = scale_expansion_zeroelim(temp8len, temp8, bdytail,
05637                                               temp16a);
05638         finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
05639                                                 temp16a, finother);
05640         finswap = finnow; finnow = finother; finother = finswap;
05641       }
05642       if (cdytail != 0.0) {
05643         temp8len = scale_expansion_zeroelim(4, bb, -adxtail, temp8);
05644         temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail,
05645                                               temp16a);
05646         finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
05647                                                 temp16a, finother);
05648         finswap = finnow; finnow = finother; finother = finswap;
05649       }
05650 
05651       temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, adxtail,
05652                                             temp32a);
05653       axtbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adxtail, axtbctt);
05654       temp16alen = scale_expansion_zeroelim(axtbcttlen, axtbctt, 2.0 * adx,
05655                                             temp16a);
05656       temp16blen = scale_expansion_zeroelim(axtbcttlen, axtbctt, adxtail,
05657                                             temp16b);
05658       temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
05659                                               temp16blen, temp16b, temp32b);
05660       temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
05661                                               temp32blen, temp32b, temp64);
05662       finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
05663                                               temp64, finother);
05664       finswap = finnow; finnow = finother; finother = finswap;
05665     }
05666     if (adytail != 0.0) {
05667       temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, adytail, temp16a);
05668       aytbctlen = scale_expansion_zeroelim(bctlen, bct, adytail, aytbct);
05669       temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, 2.0 * ady,
05670                                             temp32a);
05671       temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
05672                                               temp32alen, temp32a, temp48);
05673       finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
05674                                               temp48, finother);
05675       finswap = finnow; finnow = finother; finother = finswap;
05676 
05677 
05678       temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, adytail,
05679                                             temp32a);
05680       aytbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adytail, aytbctt);
05681       temp16alen = scale_expansion_zeroelim(aytbcttlen, aytbctt, 2.0 * ady,
05682                                             temp16a);
05683       temp16blen = scale_expansion_zeroelim(aytbcttlen, aytbctt, adytail,
05684                                             temp16b);
05685       temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
05686                                               temp16blen, temp16b, temp32b);
05687       temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
05688                                               temp32blen, temp32b, temp64);
05689       finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
05690                                               temp64, finother);
05691       finswap = finnow; finnow = finother; finother = finswap;
05692     }
05693   }
05694   if ((bdxtail != 0.0) || (bdytail != 0.0)) {
05695     if ((cdxtail != 0.0) || (cdytail != 0.0)
05696         || (adxtail != 0.0) || (adytail != 0.0)) {
05697       Two_Product(cdxtail, ady, ti1, ti0);
05698       Two_Product(cdx, adytail, tj1, tj0);
05699       Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
05700       u[3] = u3;
05701       negate = -cdy;
05702       Two_Product(adxtail, negate, ti1, ti0);
05703       negate = -cdytail;
05704       Two_Product(adx, negate, tj1, tj0);
05705       Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
05706       v[3] = v3;
05707       catlen = fast_expansion_sum_zeroelim(4, u, 4, v, cat);
05708 
05709       Two_Product(cdxtail, adytail, ti1, ti0);
05710       Two_Product(adxtail, cdytail, tj1, tj0);
05711       Two_Two_Diff(ti1, ti0, tj1, tj0, catt3, catt[2], catt[1], catt[0]);
05712       catt[3] = catt3;
05713       cattlen = 4;
05714     } else {
05715       cat[0] = 0.0;
05716       catlen = 1;
05717       catt[0] = 0.0;
05718       cattlen = 1;
05719     }
05720 
05721     if (bdxtail != 0.0) {
05722       temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, bdxtail, temp16a);
05723       bxtcatlen = scale_expansion_zeroelim(catlen, cat, bdxtail, bxtcat);
05724       temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, 2.0 * bdx,
05725                                             temp32a);
05726       temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
05727                                               temp32alen, temp32a, temp48);
05728       finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
05729                                               temp48, finother);
05730       finswap = finnow; finnow = finother; finother = finswap;
05731       if (cdytail != 0.0) {
05732         temp8len = scale_expansion_zeroelim(4, aa, bdxtail, temp8);
05733         temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail,
05734                                               temp16a);
05735         finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
05736                                                 temp16a, finother);
05737         finswap = finnow; finnow = finother; finother = finswap;
05738       }
05739       if (adytail != 0.0) {
05740         temp8len = scale_expansion_zeroelim(4, cc, -bdxtail, temp8);
05741         temp16alen = scale_expansion_zeroelim(temp8len, temp8, adytail,
05742                                               temp16a);
05743         finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
05744                                                 temp16a, finother);
05745         finswap = finnow; finnow = finother; finother = finswap;
05746       }
05747 
05748       temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, bdxtail,
05749                                             temp32a);
05750       bxtcattlen = scale_expansion_zeroelim(cattlen, catt, bdxtail, bxtcatt);
05751       temp16alen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, 2.0 * bdx,
05752                                             temp16a);
05753       temp16blen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, bdxtail,
05754                                             temp16b);
05755       temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
05756                                               temp16blen, temp16b, temp32b);
05757       temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
05758                                               temp32blen, temp32b, temp64);
05759       finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
05760                                               temp64, finother);
05761       finswap = finnow; finnow = finother; finother = finswap;
05762     }
05763     if (bdytail != 0.0) {
05764       temp16alen = scale_expansion_zeroelim(bytcalen, bytca, bdytail, temp16a);
05765       bytcatlen = scale_expansion_zeroelim(catlen, cat, bdytail, bytcat);
05766       temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, 2.0 * bdy,
05767                                             temp32a);
05768       temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
05769                                               temp32alen, temp32a, temp48);
05770       finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
05771                                               temp48, finother);
05772       finswap = finnow; finnow = finother; finother = finswap;
05773 
05774 
05775       temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, bdytail,
05776                                             temp32a);
05777       bytcattlen = scale_expansion_zeroelim(cattlen, catt, bdytail, bytcatt);
05778       temp16alen = scale_expansion_zeroelim(bytcattlen, bytcatt, 2.0 * bdy,
05779                                             temp16a);
05780       temp16blen = scale_expansion_zeroelim(bytcattlen, bytcatt, bdytail,
05781                                             temp16b);
05782       temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
05783                                               temp16blen, temp16b, temp32b);
05784       temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
05785                                               temp32blen, temp32b, temp64);
05786       finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
05787                                               temp64, finother);
05788       finswap = finnow; finnow = finother; finother = finswap;
05789     }
05790   }
05791   if ((cdxtail != 0.0) || (cdytail != 0.0)) {
05792     if ((adxtail != 0.0) || (adytail != 0.0)
05793         || (bdxtail != 0.0) || (bdytail != 0.0)) {
05794       Two_Product(adxtail, bdy, ti1, ti0);
05795       Two_Product(adx, bdytail, tj1, tj0);
05796       Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
05797       u[3] = u3;
05798       negate = -ady;
05799       Two_Product(bdxtail, negate, ti1, ti0);
05800       negate = -adytail;
05801       Two_Product(bdx, negate, tj1, tj0);
05802       Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
05803       v[3] = v3;
05804       abtlen = fast_expansion_sum_zeroelim(4, u, 4, v, abt);
05805 
05806       Two_Product(adxtail, bdytail, ti1, ti0);
05807       Two_Product(bdxtail, adytail, tj1, tj0);
05808       Two_Two_Diff(ti1, ti0, tj1, tj0, abtt3, abtt[2], abtt[1], abtt[0]);
05809       abtt[3] = abtt3;
05810       abttlen = 4;
05811     } else {
05812       abt[0] = 0.0;
05813       abtlen = 1;
05814       abtt[0] = 0.0;
05815       abttlen = 1;
05816     }
05817 
05818     if (cdxtail != 0.0) {
05819       temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, cdxtail, temp16a);
05820       cxtabtlen = scale_expansion_zeroelim(abtlen, abt, cdxtail, cxtabt);
05821       temp32alen = scale_expansion_zeroelim(cxtabtlen, cxtabt, 2.0 * cdx,
05822                                             temp32a);
05823       temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
05824                                               temp32alen, temp32a, temp48);
05825       finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
05826                                               temp48, finother);
05827       finswap = finnow; finnow = finother; finother = finswap;
05828       if (adytail != 0.0) {
05829         temp8len = scale_expansion_zeroelim(4, bb, cdxtail, temp8);
05830         temp16alen = scale_expansion_zeroelim(temp8len, temp8, adytail,
05831                                               temp16a);
05832         finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
05833                                                 temp16a, finother);
05834         finswap = finnow; finnow = finother; finother = finswap;
05835       }
05836       if (bdytail != 0.0) {
05837         temp8len = scale_expansion_zeroelim(4, aa, -cdxtail, temp8);
05838         temp16alen = scale_expansion_zeroelim(temp8len, temp8, bdytail,
05839                                               temp16a);
05840         finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
05841                                                 temp16a, finother);
05842         finswap = finnow; finnow = finother; finother = finswap;
05843       }
05844 
05845       temp32alen = scale_expansion_zeroelim(cxtabtlen, cxtabt, cdxtail,
05846                                             temp32a);
05847       cxtabttlen = scale_expansion_zeroelim(abttlen, abtt, cdxtail, cxtabtt);
05848       temp16alen = scale_expansion_zeroelim(cxtabttlen, cxtabtt, 2.0 * cdx,
05849                                             temp16a);
05850       temp16blen = scale_expansion_zeroelim(cxtabttlen, cxtabtt, cdxtail,
05851                                             temp16b);
05852       temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
05853                                               temp16blen, temp16b, temp32b);
05854       temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
05855                                               temp32blen, temp32b, temp64);
05856       finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
05857                                               temp64, finother);
05858       finswap = finnow; finnow = finother; finother = finswap;
05859     }
05860     if (cdytail != 0.0) {
05861       temp16alen = scale_expansion_zeroelim(cytablen, cytab, cdytail, temp16a);
05862       cytabtlen = scale_expansion_zeroelim(abtlen, abt, cdytail, cytabt);
05863       temp32alen = scale_expansion_zeroelim(cytabtlen, cytabt, 2.0 * cdy,
05864                                             temp32a);
05865       temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
05866                                               temp32alen, temp32a, temp48);
05867       finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
05868                                               temp48, finother);
05869       finswap = finnow; finnow = finother; finother = finswap;
05870 
05871 
05872       temp32alen = scale_expansion_zeroelim(cytabtlen, cytabt, cdytail,
05873                                             temp32a);
05874       cytabttlen = scale_expansion_zeroelim(abttlen, abtt, cdytail, cytabtt);
05875       temp16alen = scale_expansion_zeroelim(cytabttlen, cytabtt, 2.0 * cdy,
05876                                             temp16a);
05877       temp16blen = scale_expansion_zeroelim(cytabttlen, cytabtt, cdytail,
05878                                             temp16b);
05879       temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
05880                                               temp16blen, temp16b, temp32b);
05881       temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
05882                                               temp32blen, temp32b, temp64);
05883       finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
05884                                               temp64, finother);
05885       finswap = finnow; finnow = finother; finother = finswap;
05886     }
05887   }
05888 
05889   return finnow[finlength - 1];
05890 }
05891 
05892 #ifdef ANSI_DECLARATORS
05893 REAL incircle(struct mesh *m, struct behavior *b,
05894               vertex pa, vertex pb, vertex pc, vertex pd)
05895 #else /* not ANSI_DECLARATORS */
05896 REAL incircle(m, b, pa, pb, pc, pd)
05897 struct mesh *m;
05898 struct behavior *b;
05899 vertex pa;
05900 vertex pb;
05901 vertex pc;
05902 vertex pd;
05903 #endif /* not ANSI_DECLARATORS */
05904 
05905 {
05906   REAL adx, bdx, cdx, ady, bdy, cdy;
05907   REAL bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady;
05908   REAL alift, blift, clift;
05909   REAL det;
05910   REAL permanent, errbound;
05911 
05912   m->incirclecount++;
05913 
05914   adx = pa[0] - pd[0];
05915   bdx = pb[0] - pd[0];
05916   cdx = pc[0] - pd[0];
05917   ady = pa[1] - pd[1];
05918   bdy = pb[1] - pd[1];
05919   cdy = pc[1] - pd[1];
05920 
05921   bdxcdy = bdx * cdy;
05922   cdxbdy = cdx * bdy;
05923   alift = adx * adx + ady * ady;
05924 
05925   cdxady = cdx * ady;
05926   adxcdy = adx * cdy;
05927   blift = bdx * bdx + bdy * bdy;
05928 
05929   adxbdy = adx * bdy;
05930   bdxady = bdx * ady;
05931   clift = cdx * cdx + cdy * cdy;
05932 
05933   det = alift * (bdxcdy - cdxbdy)
05934       + blift * (cdxady - adxcdy)
05935       + clift * (adxbdy - bdxady);
05936 
05937   if (b->noexact) {
05938     return det;
05939   }
05940 
05941   permanent = (Absolute(bdxcdy) + Absolute(cdxbdy)) * alift
05942             + (Absolute(cdxady) + Absolute(adxcdy)) * blift
05943             + (Absolute(adxbdy) + Absolute(bdxady)) * clift;
05944   errbound = iccerrboundA * permanent;
05945   if ((det > errbound) || (-det > errbound)) {
05946     return det;
05947   }
05948 
05949   return incircleadapt(pa, pb, pc, pd, permanent);
05950 }
05951 
05952 /*****************************************************************************/
05953 /*                                                                           */
05954 /*  orient3d()   Return a positive value if the point pd lies below the      */
05955 /*               plane passing through pa, pb, and pc; "below" is defined so */
05956 /*               that pa, pb, and pc appear in counterclockwise order when   */
05957 /*               viewed from above the plane.  Returns a negative value if   */
05958 /*               pd lies above the plane.  Returns zero if the points are    */
05959 /*               coplanar.  The result is also a rough approximation of six  */
05960 /*               times the signed volume of the tetrahedron defined by the   */
05961 /*               four points.                                                */
05962 /*                                                                           */
05963 /*  Uses exact arithmetic if necessary to ensure a correct answer.  The      */
05964 /*  result returned is the determinant of a matrix.  This determinant is     */
05965 /*  computed adaptively, in the sense that exact arithmetic is used only to  */
05966 /*  the degree it is needed to ensure that the returned value has the        */
05967 /*  correct sign.  Hence, this function is usually quite fast, but will run  */
05968 /*  more slowly when the input points are coplanar or nearly so.             */
05969 /*                                                                           */
05970 /*  See my Robust Predicates paper for details.                              */
05971 /*                                                                           */
05972 /*****************************************************************************/
05973 
05974 #ifdef ANSI_DECLARATORS
05975 REAL orient3dadapt(vertex pa, vertex pb, vertex pc, vertex pd,
05976                    REAL aheight, REAL bheight, REAL cheight, REAL dheight,
05977                    REAL permanent)
05978 #else /* not ANSI_DECLARATORS */
05979 REAL orient3dadapt(pa, pb, pc, pd,
05980                    aheight, bheight, cheight, dheight, permanent)
05981 vertex pa;
05982 vertex pb;
05983 vertex pc;
05984 vertex pd;
05985 REAL aheight;
05986 REAL bheight;
05987 REAL cheight;
05988 REAL dheight;
05989 REAL permanent;
05990 #endif /* not ANSI_DECLARATORS */
05991 
05992 {
05993   INEXACT REAL adx, bdx, cdx, ady, bdy, cdy, adheight, bdheight, cdheight;
05994   REAL det, errbound;
05995 
05996   INEXACT REAL bdxcdy1, cdxbdy1, cdxady1, adxcdy1, adxbdy1, bdxady1;
05997   REAL bdxcdy0, cdxbdy0, cdxady0, adxcdy0, adxbdy0, bdxady0;
05998   REAL bc[4], ca[4], ab[4];
05999   INEXACT REAL bc3, ca3, ab3;
06000   REAL adet[8], bdet[8], cdet[8];
06001   int alen, blen, clen;
06002   REAL abdet[16];
06003   int ablen;
06004   REAL *finnow, *finother, *finswap;
06005   REAL fin1[192], fin2[192];
06006   int finlength;
06007 
06008   REAL adxtail, bdxtail, cdxtail;
06009   REAL adytail, bdytail, cdytail;
06010   REAL adheighttail, bdheighttail, cdheighttail;
06011   INEXACT REAL at_blarge, at_clarge;
06012   INEXACT REAL bt_clarge, bt_alarge;
06013   INEXACT REAL ct_alarge, ct_blarge;
06014   REAL at_b[4], at_c[4], bt_c[4], bt_a[4], ct_a[4], ct_b[4];
06015   int at_blen, at_clen, bt_clen, bt_alen, ct_alen, ct_blen;
06016   INEXACT REAL bdxt_cdy1, cdxt_bdy1, cdxt_ady1;
06017   INEXACT REAL adxt_cdy1, adxt_bdy1, bdxt_ady1;
06018   REAL bdxt_cdy0, cdxt_bdy0, cdxt_ady0;
06019   REAL adxt_cdy0, adxt_bdy0, bdxt_ady0;
06020   INEXACT REAL bdyt_cdx1, cdyt_bdx1, cdyt_adx1;
06021   INEXACT REAL adyt_cdx1, adyt_bdx1, bdyt_adx1;
06022   REAL bdyt_cdx0, cdyt_bdx0, cdyt_adx0;
06023   REAL adyt_cdx0, adyt_bdx0, bdyt_adx0;
06024   REAL bct[8], cat[8], abt[8];
06025   int bctlen, catlen, abtlen;
06026   INEXACT REAL bdxt_cdyt1, cdxt_bdyt1, cdxt_adyt1;
06027   INEXACT REAL adxt_cdyt1, adxt_bdyt1, bdxt_adyt1;
06028   REAL bdxt_cdyt0, cdxt_bdyt0, cdxt_adyt0;
06029   REAL adxt_cdyt0, adxt_bdyt0, bdxt_adyt0;
06030   REAL u[4], v[12], w[16];
06031   INEXACT REAL u3;
06032   int vlength, wlength;
06033   REAL negate;
06034 
06035   INEXACT REAL bvirt;
06036   REAL avirt, bround, around;
06037   INEXACT REAL c;
06038   INEXACT REAL abig;
06039   REAL ahi, alo, bhi, blo;
06040   REAL err1, err2, err3;
06041   INEXACT REAL _i, _j, _k;
06042   REAL _0;
06043 
06044   adx = (REAL) (pa[0] - pd[0]);
06045   bdx = (REAL) (pb[0] - pd[0]);
06046   cdx = (REAL) (pc[0] - pd[0]);
06047   ady = (REAL) (pa[1] - pd[1]);
06048   bdy = (REAL) (pb[1] - pd[1]);
06049   cdy = (REAL) (pc[1] - pd[1]);
06050   adheight = (REAL) (aheight - dheight);
06051   bdheight = (REAL) (bheight - dheight);
06052   cdheight = (REAL) (cheight - dheight);
06053 
06054   Two_Product(bdx, cdy, bdxcdy1, bdxcdy0);
06055   Two_Product(cdx, bdy, cdxbdy1, cdxbdy0);
06056   Two_Two_Diff(bdxcdy1, bdxcdy0, cdxbdy1, cdxbdy0, bc3, bc[2], bc[1], bc[0]);
06057   bc[3] = bc3;
06058   alen = scale_expansion_zeroelim(4, bc, adheight, adet);
06059 
06060   Two_Product(cdx, ady, cdxady1, cdxady0);
06061   Two_Product(adx, cdy, adxcdy1, adxcdy0);
06062   Two_Two_Diff(cdxady1, cdxady0, adxcdy1, adxcdy0, ca3, ca[2], ca[1], ca[0]);
06063   ca[3] = ca3;
06064   blen = scale_expansion_zeroelim(4, ca, bdheight, bdet);
06065 
06066   Two_Product(adx, bdy, adxbdy1, adxbdy0);
06067   Two_Product(bdx, ady, bdxady1, bdxady0);
06068   Two_Two_Diff(adxbdy1, adxbdy0, bdxady1, bdxady0, ab3, ab[2], ab[1], ab[0]);
06069   ab[3] = ab3;
06070   clen = scale_expansion_zeroelim(4, ab, cdheight, cdet);
06071 
06072   ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
06073   finlength = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, fin1);
06074 
06075   det = estimate(finlength, fin1);
06076   errbound = o3derrboundB * permanent;
06077   if ((det >= errbound) || (-det >= errbound)) {
06078     return det;
06079   }
06080 
06081   Two_Diff_Tail(pa[0], pd[0], adx, adxtail);
06082   Two_Diff_Tail(pb[0], pd[0], bdx, bdxtail);
06083   Two_Diff_Tail(pc[0], pd[0], cdx, cdxtail);
06084   Two_Diff_Tail(pa[1], pd[1], ady, adytail);
06085   Two_Diff_Tail(pb[1], pd[1], bdy, bdytail);
06086   Two_Diff_Tail(pc[1], pd[1], cdy, cdytail);
06087   Two_Diff_Tail(aheight, dheight, adheight, adheighttail);
06088   Two_Diff_Tail(bheight, dheight, bdheight, bdheighttail);
06089   Two_Diff_Tail(cheight, dheight, cdheight, cdheighttail);
06090 
06091   if ((adxtail == 0.0) && (bdxtail == 0.0) && (cdxtail == 0.0) &&
06092       (adytail == 0.0) && (bdytail == 0.0) && (cdytail == 0.0) &&
06093       (adheighttail == 0.0) &&
06094       (bdheighttail == 0.0) &&
06095       (cdheighttail == 0.0)) {
06096     return det;
06097   }
06098 
06099   errbound = o3derrboundC * permanent + resulterrbound * Absolute(det);
06100   det += (adheight * ((bdx * cdytail + cdy * bdxtail) -
06101                       (bdy * cdxtail + cdx * bdytail)) +
06102           adheighttail * (bdx * cdy - bdy * cdx)) +
06103          (bdheight * ((cdx * adytail + ady * cdxtail) -
06104                       (cdy * adxtail + adx * cdytail)) +
06105           bdheighttail * (cdx * ady - cdy * adx)) +
06106          (cdheight * ((adx * bdytail + bdy * adxtail) -
06107                       (ady * bdxtail + bdx * adytail)) +
06108           cdheighttail * (adx * bdy - ady * bdx));
06109   if ((det >= errbound) || (-det >= errbound)) {
06110     return det;
06111   }
06112 
06113   finnow = fin1;
06114   finother = fin2;
06115 
06116   if (adxtail == 0.0) {
06117     if (adytail == 0.0) {
06118       at_b[0] = 0.0;
06119       at_blen = 1;
06120       at_c[0] = 0.0;
06121       at_clen = 1;
06122     } else {
06123       negate = -adytail;
06124       Two_Product(negate, bdx, at_blarge, at_b[0]);
06125       at_b[1] = at_blarge;
06126       at_blen = 2;
06127       Two_Product(adytail, cdx, at_clarge, at_c[0]);
06128       at_c[1] = at_clarge;
06129       at_clen = 2;
06130     }
06131   } else {
06132     if (adytail == 0.0) {
06133       Two_Product(adxtail, bdy, at_blarge, at_b[0]);
06134       at_b[1] = at_blarge;
06135       at_blen = 2;
06136       negate = -adxtail;
06137       Two_Product(negate, cdy, at_clarge, at_c[0]);
06138       at_c[1] = at_clarge;
06139       at_clen = 2;
06140     } else {
06141       Two_Product(adxtail, bdy, adxt_bdy1, adxt_bdy0);
06142       Two_Product(adytail, bdx, adyt_bdx1, adyt_bdx0);
06143       Two_Two_Diff(adxt_bdy1, adxt_bdy0, adyt_bdx1, adyt_bdx0,
06144                    at_blarge, at_b[2], at_b[1], at_b[0]);
06145       at_b[3] = at_blarge;
06146       at_blen = 4;
06147       Two_Product(adytail, cdx, adyt_cdx1, adyt_cdx0);
06148       Two_Product(adxtail, cdy, adxt_cdy1, adxt_cdy0);
06149       Two_Two_Diff(adyt_cdx1, adyt_cdx0, adxt_cdy1, adxt_cdy0,
06150                    at_clarge, at_c[2], at_c[1], at_c[0]);
06151       at_c[3] = at_clarge;
06152       at_clen = 4;
06153     }
06154   }
06155   if (bdxtail == 0.0) {
06156     if (bdytail == 0.0) {
06157       bt_c[0] = 0.0;
06158       bt_clen = 1;
06159       bt_a[0] = 0.0;
06160       bt_alen = 1;
06161     } else {
06162       negate = -bdytail;
06163       Two_Product(negate, cdx, bt_clarge, bt_c[0]);
06164       bt_c[1] = bt_clarge;
06165       bt_clen = 2;
06166       Two_Product(bdytail, adx, bt_alarge, bt_a[0]);
06167       bt_a[1] = bt_alarge;
06168       bt_alen = 2;
06169     }
06170   } else {
06171     if (bdytail == 0.0) {
06172       Two_Product(bdxtail, cdy, bt_clarge, bt_c[0]);
06173       bt_c[1] = bt_clarge;
06174       bt_clen = 2;
06175       negate = -bdxtail;
06176       Two_Product(negate, ady, bt_alarge, bt_a[0]);
06177       bt_a[1] = bt_alarge;
06178       bt_alen = 2;
06179     } else {
06180       Two_Product(bdxtail, cdy, bdxt_cdy1, bdxt_cdy0);
06181       Two_Product(bdytail, cdx, bdyt_cdx1, bdyt_cdx0);
06182       Two_Two_Diff(bdxt_cdy1, bdxt_cdy0, bdyt_cdx1, bdyt_cdx0,
06183                    bt_clarge, bt_c[2], bt_c[1], bt_c[0]);
06184       bt_c[3] = bt_clarge;
06185       bt_clen = 4;
06186       Two_Product(bdytail, adx, bdyt_adx1, bdyt_adx0);
06187       Two_Product(bdxtail, ady, bdxt_ady1, bdxt_ady0);
06188       Two_Two_Diff(bdyt_adx1, bdyt_adx0, bdxt_ady1, bdxt_ady0,
06189                   bt_alarge, bt_a[2], bt_a[1], bt_a[0]);
06190       bt_a[3] = bt_alarge;
06191       bt_alen = 4;
06192     }
06193   }
06194   if (cdxtail == 0.0) {
06195     if (cdytail == 0.0) {
06196       ct_a[0] = 0.0;
06197       ct_alen = 1;
06198       ct_b[0] = 0.0;
06199       ct_blen = 1;
06200     } else {
06201       negate = -cdytail;
06202       Two_Product(negate, adx, ct_alarge, ct_a[0]);
06203       ct_a[1] = ct_alarge;
06204       ct_alen = 2;
06205       Two_Product(cdytail, bdx, ct_blarge, ct_b[0]);
06206       ct_b[1] = ct_blarge;
06207       ct_blen = 2;
06208     }
06209   } else {
06210     if (cdytail == 0.0) {
06211       Two_Product(cdxtail, ady, ct_alarge, ct_a[0]);
06212       ct_a[1] = ct_alarge;
06213       ct_alen = 2;
06214       negate = -cdxtail;
06215       Two_Product(negate, bdy, ct_blarge, ct_b[0]);
06216       ct_b[1] = ct_blarge;
06217       ct_blen = 2;
06218     } else {
06219       Two_Product(cdxtail, ady, cdxt_ady1, cdxt_ady0);
06220       Two_Product(cdytail, adx, cdyt_adx1, cdyt_adx0);
06221       Two_Two_Diff(cdxt_ady1, cdxt_ady0, cdyt_adx1, cdyt_adx0,
06222                    ct_alarge, ct_a[2], ct_a[1], ct_a[0]);
06223       ct_a[3] = ct_alarge;
06224       ct_alen = 4;
06225       Two_Product(cdytail, bdx, cdyt_bdx1, cdyt_bdx0);
06226       Two_Product(cdxtail, bdy, cdxt_bdy1, cdxt_bdy0);
06227       Two_Two_Diff(cdyt_bdx1, cdyt_bdx0, cdxt_bdy1, cdxt_bdy0,
06228                    ct_blarge, ct_b[2], ct_b[1], ct_b[0]);
06229       ct_b[3] = ct_blarge;
06230       ct_blen = 4;
06231     }
06232   }
06233 
06234   bctlen = fast_expansion_sum_zeroelim(bt_clen, bt_c, ct_blen, ct_b, bct);
06235   wlength = scale_expansion_zeroelim(bctlen, bct, adheight, w);
06236   finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
06237                                           finother);
06238   finswap = finnow; finnow = finother; finother = finswap;
06239 
06240   catlen = fast_expansion_sum_zeroelim(ct_alen, ct_a, at_clen, at_c, cat);
06241   wlength = scale_expansion_zeroelim(catlen, cat, bdheight, w);
06242   finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
06243                                           finother);
06244   finswap = finnow; finnow = finother; finother = finswap;
06245 
06246   abtlen = fast_expansion_sum_zeroelim(at_blen, at_b, bt_alen, bt_a, abt);
06247   wlength = scale_expansion_zeroelim(abtlen, abt, cdheight, w);
06248   finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
06249                                           finother);
06250   finswap = finnow; finnow = finother; finother = finswap;
06251 
06252   if (adheighttail != 0.0) {
06253     vlength = scale_expansion_zeroelim(4, bc, adheighttail, v);
06254     finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v,
06255                                             finother);
06256     finswap = finnow; finnow = finother; finother = finswap;
06257   }
06258   if (bdheighttail != 0.0) {
06259     vlength = scale_expansion_zeroelim(4, ca, bdheighttail, v);
06260     finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v,
06261                                             finother);
06262     finswap = finnow; finnow = finother; finother = finswap;
06263   }
06264   if (cdheighttail != 0.0) {
06265     vlength = scale_expansion_zeroelim(4, ab, cdheighttail, v);
06266     finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v,
06267                                             finother);
06268     finswap = finnow; finnow = finother; finother = finswap;
06269   }
06270 
06271   if (adxtail != 0.0) {
06272     if (bdytail != 0.0) {
06273       Two_Product(adxtail, bdytail, adxt_bdyt1, adxt_bdyt0);
06274       Two_One_Product(adxt_bdyt1, adxt_bdyt0, cdheight, u3, u[2], u[1], u[0]);
06275       u[3] = u3;
06276       finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
06277                                               finother);
06278       finswap = finnow; finnow = finother; finother = finswap;
06279       if (cdheighttail != 0.0) {
06280         Two_One_Product(adxt_bdyt1, adxt_bdyt0, cdheighttail,
06281                         u3, u[2], u[1], u[0]);
06282         u[3] = u3;
06283         finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
06284                                                 finother);
06285         finswap = finnow; finnow = finother; finother = finswap;
06286       }
06287     }
06288     if (cdytail != 0.0) {
06289       negate = -adxtail;
06290       Two_Product(negate, cdytail, adxt_cdyt1, adxt_cdyt0);
06291       Two_One_Product(adxt_cdyt1, adxt_cdyt0, bdheight, u3, u[2], u[1], u[0]);
06292       u[3] = u3;
06293       finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
06294                                               finother);
06295       finswap = finnow; finnow = finother; finother = finswap;
06296       if (bdheighttail != 0.0) {
06297         Two_One_Product(adxt_cdyt1, adxt_cdyt0, bdheighttail,
06298                         u3, u[2], u[1], u[0]);
06299         u[3] = u3;
06300         finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
06301                                                 finother);
06302         finswap = finnow; finnow = finother; finother = finswap;
06303       }
06304     }
06305   }
06306   if (bdxtail != 0.0) {
06307     if (cdytail != 0.0) {
06308       Two_Product(bdxtail, cdytail, bdxt_cdyt1, bdxt_cdyt0);
06309       Two_One_Product(bdxt_cdyt1, bdxt_cdyt0, adheight, u3, u[2], u[1], u[0]);
06310       u[3] = u3;
06311       finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
06312                                               finother);
06313       finswap = finnow; finnow = finother; finother = finswap;
06314       if (adheighttail != 0.0) {
06315         Two_One_Product(bdxt_cdyt1, bdxt_cdyt0, adheighttail,
06316                         u3, u[2], u[1], u[0]);
06317         u[3] = u3;
06318         finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
06319                                                 finother);
06320         finswap = finnow; finnow = finother; finother = finswap;
06321       }
06322     }
06323     if (adytail != 0.0) {
06324       negate = -bdxtail;
06325       Two_Product(negate, adytail, bdxt_adyt1, bdxt_adyt0);
06326       Two_One_Product(bdxt_adyt1, bdxt_adyt0, cdheight, u3, u[2], u[1], u[0]);
06327       u[3] = u3;
06328       finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
06329                                               finother);
06330       finswap = finnow; finnow = finother; finother = finswap;
06331       if (cdheighttail != 0.0) {
06332         Two_One_Product(bdxt_adyt1, bdxt_adyt0, cdheighttail,
06333                         u3, u[2], u[1], u[0]);
06334         u[3] = u3;
06335         finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
06336                                                 finother);
06337         finswap = finnow; finnow = finother; finother = finswap;
06338       }
06339     }
06340   }
06341   if (cdxtail != 0.0) {
06342     if (adytail != 0.0) {
06343       Two_Product(cdxtail, adytail, cdxt_adyt1, cdxt_adyt0);
06344       Two_One_Product(cdxt_adyt1, cdxt_adyt0, bdheight, u3, u[2], u[1], u[0]);
06345       u[3] = u3;
06346       finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
06347                                               finother);
06348       finswap = finnow; finnow = finother; finother = finswap;
06349       if (bdheighttail != 0.0) {
06350         Two_One_Product(cdxt_adyt1, cdxt_adyt0, bdheighttail,
06351                         u3, u[2], u[1], u[0]);
06352         u[3] = u3;
06353         finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
06354                                                 finother);
06355         finswap = finnow; finnow = finother; finother = finswap;
06356       }
06357     }
06358     if (bdytail != 0.0) {
06359       negate = -cdxtail;
06360       Two_Product(negate, bdytail, cdxt_bdyt1, cdxt_bdyt0);
06361       Two_One_Product(cdxt_bdyt1, cdxt_bdyt0, adheight, u3, u[2], u[1], u[0]);
06362       u[3] = u3;
06363       finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
06364                                               finother);
06365       finswap = finnow; finnow = finother; finother = finswap;
06366       if (adheighttail != 0.0) {
06367         Two_One_Product(cdxt_bdyt1, cdxt_bdyt0, adheighttail,
06368                         u3, u[2], u[1], u[0]);
06369         u[3] = u3;
06370         finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
06371                                                 finother);
06372         finswap = finnow; finnow = finother; finother = finswap;
06373       }
06374     }
06375   }
06376 
06377   if (adheighttail != 0.0) {
06378     wlength = scale_expansion_zeroelim(bctlen, bct, adheighttail, w);
06379     finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
06380                                             finother);
06381     finswap = finnow; finnow = finother; finother = finswap;
06382   }
06383   if (bdheighttail != 0.0) {
06384     wlength = scale_expansion_zeroelim(catlen, cat, bdheighttail, w);
06385     finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
06386                                             finother);
06387     finswap = finnow; finnow = finother; finother = finswap;
06388   }
06389   if (cdheighttail != 0.0) {
06390     wlength = scale_expansion_zeroelim(abtlen, abt, cdheighttail, w);
06391     finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
06392                                             finother);
06393     finswap = finnow; finnow = finother; finother = finswap;
06394   }
06395 
06396   return finnow[finlength - 1];
06397 }
06398 
06399 #ifdef ANSI_DECLARATORS
06400 REAL orient3d(struct mesh *m, struct behavior *b,
06401               vertex pa, vertex pb, vertex pc, vertex pd,
06402               REAL aheight, REAL bheight, REAL cheight, REAL dheight)
06403 #else /* not ANSI_DECLARATORS */
06404 REAL orient3d(m, b, pa, pb, pc, pd, aheight, bheight, cheight, dheight)
06405 struct mesh *m;
06406 struct behavior *b;
06407 vertex pa;
06408 vertex pb;
06409 vertex pc;
06410 vertex pd;
06411 REAL aheight;
06412 REAL bheight;
06413 REAL cheight;
06414 REAL dheight;
06415 #endif /* not ANSI_DECLARATORS */
06416 
06417 {
06418   REAL adx, bdx, cdx, ady, bdy, cdy, adheight, bdheight, cdheight;
06419   REAL bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady;
06420   REAL det;
06421   REAL permanent, errbound;
06422 
06423   m->orient3dcount++;
06424 
06425   adx = pa[0] - pd[0];
06426   bdx = pb[0] - pd[0];
06427   cdx = pc[0] - pd[0];
06428   ady = pa[1] - pd[1];
06429   bdy = pb[1] - pd[1];
06430   cdy = pc[1] - pd[1];
06431   adheight = aheight - dheight;
06432   bdheight = bheight - dheight;
06433   cdheight = cheight - dheight;
06434 
06435   bdxcdy = bdx * cdy;
06436   cdxbdy = cdx * bdy;
06437 
06438   cdxady = cdx * ady;
06439   adxcdy = adx * cdy;
06440 
06441   adxbdy = adx * bdy;
06442   bdxady = bdx * ady;
06443 
06444   det = adheight * (bdxcdy - cdxbdy)
06445       + bdheight * (cdxady - adxcdy)
06446       + cdheight * (adxbdy - bdxady);
06447 
06448   if (b->noexact) {
06449     return det;
06450   }
06451 
06452   permanent = (Absolute(bdxcdy) + Absolute(cdxbdy)) * Absolute(adheight)
06453             + (Absolute(cdxady) + Absolute(adxcdy)) * Absolute(bdheight)
06454             + (Absolute(adxbdy) + Absolute(bdxady)) * Absolute(cdheight);
06455   errbound = o3derrboundA * permanent;
06456   if ((det > errbound) || (-det > errbound)) {
06457     return det;
06458   }
06459 
06460   return orient3dadapt(pa, pb, pc, pd, aheight, bheight, cheight, dheight,
06461                        permanent);
06462 }
06463 
06464 /*****************************************************************************/
06465 /*                                                                           */
06466 /*  nonregular()   Return a positive value if the point pd is incompatible   */
06467 /*                 with the circle or plane passing through pa, pb, and pc   */
06468 /*                 (meaning that pd is inside the circle or below the        */
06469 /*                 plane); a negative value if it is compatible; and zero if */
06470 /*                 the four points are cocircular/coplanar.  The points pa,  */
06471 /*                 pb, and pc must be in counterclockwise order, or the sign */
06472 /*                 of the result will be reversed.                           */
06473 /*                                                                           */
06474 /*  If the -w switch is used, the points are lifted onto the parabolic       */
06475 /*  lifting map, then they are dropped according to their weights, then the  */
06476 /*  3D orientation test is applied.  If the -W switch is used, the points'   */
06477 /*  heights are already provided, so the 3D orientation test is applied      */
06478 /*  directly.  If neither switch is used, the incircle test is applied.      */
06479 /*                                                                           */
06480 /*****************************************************************************/
06481 
06482 #ifdef ANSI_DECLARATORS
06483 REAL nonregular(struct mesh *m, struct behavior *b,
06484                 vertex pa, vertex pb, vertex pc, vertex pd)
06485 #else /* not ANSI_DECLARATORS */
06486 REAL nonregular(m, b, pa, pb, pc, pd)
06487 struct mesh *m;
06488 struct behavior *b;
06489 vertex pa;
06490 vertex pb;
06491 vertex pc;
06492 vertex pd;
06493 #endif /* not ANSI_DECLARATORS */
06494 
06495 {
06496   if (b->weighted == 0) {
06497     return incircle(m, b, pa, pb, pc, pd);
06498   } else if (b->weighted == 1) {
06499     return orient3d(m, b, pa, pb, pc, pd,
06500                     pa[0] * pa[0] + pa[1] * pa[1] - pa[2],
06501                     pb[0] * pb[0] + pb[1] * pb[1] - pb[2],
06502                     pc[0] * pc[0] + pc[1] * pc[1] - pc[2],
06503                     pd[0] * pd[0] + pd[1] * pd[1] - pd[2]);
06504   } else {
06505     return orient3d(m, b, pa, pb, pc, pd, pa[2], pb[2], pc[2], pd[2]);
06506   }
06507 }
06508 
06509 /*****************************************************************************/
06510 /*                                                                           */
06511 /*  findcircumcenter()   Find the circumcenter of a triangle.                */
06512 /*                                                                           */
06513 /*  The result is returned both in terms of x-y coordinates and xi-eta       */
06514 /*  (barycentric) coordinates.  The xi-eta coordinate system is defined in   */
06515 /*  terms of the triangle:  the origin of the triangle is the origin of the  */
06516 /*  coordinate system; the destination of the triangle is one unit along the */
06517 /*  xi axis; and the apex of the triangle is one unit along the eta axis.    */
06518 /*  This procedure also returns the square of the length of the triangle's   */
06519 /*  shortest edge.                                                           */
06520 /*                                                                           */
06521 /*****************************************************************************/
06522 
06523 #ifdef ANSI_DECLARATORS
06524 void findcircumcenter(struct mesh *m, struct behavior *b,
06525                       vertex torg, vertex tdest, vertex tapex,
06526                       vertex circumcenter, REAL *xi, REAL *eta, int offcenter)
06527 #else /* not ANSI_DECLARATORS */
06528 void findcircumcenter(m, b, torg, tdest, tapex, circumcenter, xi, eta,
06529                       offcenter)
06530 struct mesh *m;
06531 struct behavior *b;
06532 vertex torg;
06533 vertex tdest;
06534 vertex tapex;
06535 vertex circumcenter;
06536 REAL *xi;
06537 REAL *eta;
06538 int offcenter;
06539 #endif /* not ANSI_DECLARATORS */
06540 
06541 {
06542   REAL xdo, ydo, xao, yao;
06543   REAL dodist, aodist, dadist;
06544   REAL denominator;
06545   REAL dx, dy, dxoff, dyoff;
06546 
06547   m->circumcentercount++;
06548 
06549   /* Compute the circumcenter of the triangle. */
06550   xdo = tdest[0] - torg[0];
06551   ydo = tdest[1] - torg[1];
06552   xao = tapex[0] - torg[0];
06553   yao = tapex[1] - torg[1];
06554   dodist = xdo * xdo + ydo * ydo;
06555   aodist = xao * xao + yao * yao;
06556   dadist = (tdest[0] - tapex[0]) * (tdest[0] - tapex[0]) +
06557            (tdest[1] - tapex[1]) * (tdest[1] - tapex[1]);
06558   if (b->noexact) {
06559     denominator = 0.5 / (xdo * yao - xao * ydo);
06560   } else {
06561     /* Use the counterclockwise() routine to ensure a positive (and */
06562     /*   reasonably accurate) result, avoiding any possibility of   */
06563     /*   division by zero.                                          */
06564     denominator = 0.5 / counterclockwise(m, b, tdest, tapex, torg);
06565     /* Don't count the above as an orientation test. */
06566     m->counterclockcount--;
06567   }
06568   dx = (yao * dodist - ydo * aodist) * denominator;
06569   dy = (xdo * aodist - xao * dodist) * denominator;
06570 
06571   /* Find the (squared) length of the triangle's shortest edge.  This   */
06572   /*   serves as a conservative estimate of the insertion radius of the */
06573   /*   circumcenter's parent.  The estimate is used to ensure that      */
06574   /*   the algorithm terminates even if very small angles appear in     */
06575   /*   the input PSLG.                                                  */
06576   if ((dodist < aodist) && (dodist < dadist)) {
06577     if (offcenter && (b->offconstant > 0.0)) {
06578       /* Find the position of the off-center, as described by Alper Ungor. */
06579       dxoff = 0.5 * xdo - b->offconstant * ydo;
06580       dyoff = 0.5 * ydo + b->offconstant * xdo;
06581       /* If the off-center is closer to the origin than the */
06582       /*   circumcenter, use the off-center instead.        */
06583       if (dxoff * dxoff + dyoff * dyoff < dx * dx + dy * dy) {
06584         dx = dxoff;
06585         dy = dyoff;
06586       }
06587     }
06588   } else if (aodist < dadist) {
06589     if (offcenter && (b->offconstant > 0.0)) {
06590       dxoff = 0.5 * xao + b->offconstant * yao;
06591       dyoff = 0.5 * yao - b->offconstant * xao;
06592       /* If the off-center is closer to the origin than the */
06593       /*   circumcenter, use the off-center instead.        */
06594       if (dxoff * dxoff + dyoff * dyoff < dx * dx + dy * dy) {
06595         dx = dxoff;
06596         dy = dyoff;
06597       }
06598     }
06599   } else {
06600     if (offcenter && (b->offconstant > 0.0)) {
06601       dxoff = 0.5 * (tapex[0] - tdest[0]) -
06602               b->offconstant * (tapex[1] - tdest[1]);
06603       dyoff = 0.5 * (tapex[1] - tdest[1]) +
06604               b->offconstant * (tapex[0] - tdest[0]);
06605       /* If the off-center is closer to the destination than the */
06606       /*   circumcenter, use the off-center instead.             */
06607       if (dxoff * dxoff + dyoff * dyoff <
06608           (dx - xdo) * (dx - xdo) + (dy - ydo) * (dy - ydo)) {
06609         dx = xdo + dxoff;
06610         dy = ydo + dyoff;
06611       }
06612     }
06613   }
06614 
06615   circumcenter[0] = torg[0] + dx;
06616   circumcenter[1] = torg[1] + dy;
06617 
06618   /* To interpolate vertex attributes for the new vertex inserted at */
06619   /*   the circumcenter, define a coordinate system with a xi-axis,  */
06620   /*   directed from the triangle's origin to its destination, and   */
06621   /*   an eta-axis, directed from its origin to its apex.            */
06622   /*   Calculate the xi and eta coordinates of the circumcenter.     */
06623   *xi = (yao * dx - xao * dy) * (2.0 * denominator);
06624   *eta = (xdo * dy - ydo * dx) * (2.0 * denominator);
06625 }
06626 
06629 /********* Geometric primitives end here                             *********/
06630 
06631 /*****************************************************************************/
06632 /*                                                                           */
06633 /*  triangleinit()   Initialize some variables.                              */
06634 /*                                                                           */
06635 /*****************************************************************************/
06636 
06637 #ifdef ANSI_DECLARATORS
06638 void triangleinit(struct mesh *m)
06639 #else /* not ANSI_DECLARATORS */
06640 void triangleinit(m)
06641 struct mesh *m;
06642 #endif /* not ANSI_DECLARATORS */
06643 
06644 {
06645   poolzero(&m->vertices);
06646   poolzero(&m->triangles);
06647   poolzero(&m->subsegs);
06648   poolzero(&m->viri);
06649   poolzero(&m->badsubsegs);
06650   poolzero(&m->badtriangles);
06651   poolzero(&m->flipstackers);
06652   poolzero(&m->splaynodes);
06653 
06654   m->recenttri.tri = (triangle *) NULL; /* No triangle has been visited yet. */
06655   m->undeads = 0;                       /* No eliminated input vertices yet. */
06656   m->samples = 1;         /* Point location should take at least one sample. */
06657   m->checksegments = 0;   /* There are no segments in the triangulation yet. */
06658   m->checkquality = 0;     /* The quality triangulation stage has not begun. */
06659   m->incirclecount = m->counterclockcount = m->orient3dcount = 0;
06660   m->hyperbolacount = m->circletopcount = m->circumcentercount = 0;
06661   randomseed = 1;
06662 
06663   exactinit();                     /* Initialize exact arithmetic constants. */
06664 }
06665 
06666 /*****************************************************************************/
06667 /*                                                                           */
06668 /*  randomnation()   Generate a random number between 0 and `choices' - 1.   */
06669 /*                                                                           */
06670 /*  This is a simple linear congruential random number generator.  Hence, it */
06671 /*  is a bad random number generator, but good enough for most randomized    */
06672 /*  geometric algorithms.                                                    */
06673 /*                                                                           */
06674 /*****************************************************************************/
06675 
06676 #ifdef ANSI_DECLARATORS
06677 unsigned long randomnation(unsigned int choices)
06678 #else /* not ANSI_DECLARATORS */
06679 unsigned long randomnation(choices)
06680 unsigned int choices;
06681 #endif /* not ANSI_DECLARATORS */
06682 
06683 {
06684   randomseed = (randomseed * 1366l + 150889l) % 714025l;
06685   return randomseed / (714025l / choices + 1);
06686 }
06687 
06688 /********* Mesh quality testing routines begin here                  *********/
06692 /*****************************************************************************/
06693 /*                                                                           */
06694 /*  checkmesh()   Test the mesh for topological consistency.                 */
06695 /*                                                                           */
06696 /*****************************************************************************/
06697 
06698 #ifndef REDUCED
06699 
06700 #ifdef ANSI_DECLARATORS
06701 void checkmesh(struct mesh *m, struct behavior *b)
06702 #else /* not ANSI_DECLARATORS */
06703 void checkmesh(m, b)
06704 struct mesh *m;
06705 struct behavior *b;
06706 #endif /* not ANSI_DECLARATORS */
06707 
06708 {
06709   struct otri triangleloop;
06710   struct otri oppotri, oppooppotri;
06711   vertex triorg, tridest, triapex;
06712   vertex oppoorg, oppodest;
06713   int horrors;
06714   int saveexact;
06715   triangle ptr;                         /* Temporary variable used by sym(). */
06716 
06717   /* Temporarily turn on exact arithmetic if it's off. */
06718   saveexact = b->noexact;
06719   b->noexact = 0;
06720   if (!b->quiet) {
06721     printf("  Checking consistency of mesh...\n");
06722   }
06723   horrors = 0;
06724   /* Run through the list of triangles, checking each one. */
06725   traversalinit(&m->triangles);
06726   triangleloop.tri = triangletraverse(m);
06727   while (triangleloop.tri != (triangle *) NULL) {
06728     /* Check all three edges of the triangle. */
06729     for (triangleloop.orient = 0; triangleloop.orient < 3;
06730          triangleloop.orient++) {
06731       org(triangleloop, triorg);
06732       dest(triangleloop, tridest);
06733       if (triangleloop.orient == 0) {       /* Only test for inversion once. */
06734         /* Test if the triangle is flat or inverted. */
06735         apex(triangleloop, triapex);
06736         if (counterclockwise(m, b, triorg, tridest, triapex) <= 0.0) {
06737           printf("  !! !! Inverted ");
06738           printtriangle(m, b, &triangleloop);
06739           horrors++;
06740         }
06741       }
06742       /* Find the neighboring triangle on this edge. */
06743       sym(triangleloop, oppotri);
06744       if (oppotri.tri != m->dummytri) {
06745         /* Check that the triangle's neighbor knows it's a neighbor. */
06746         sym(oppotri, oppooppotri);
06747         if ((triangleloop.tri != oppooppotri.tri)
06748             || (triangleloop.orient != oppooppotri.orient)) {
06749           printf("  !! !! Asymmetric triangle-triangle bond:\n");
06750           if (triangleloop.tri == oppooppotri.tri) {
06751             printf("   (Right triangle, wrong orientation)\n");
06752           }
06753           printf("    First ");
06754           printtriangle(m, b, &triangleloop);
06755           printf("    Second (nonreciprocating) ");
06756           printtriangle(m, b, &oppotri);
06757           horrors++;
06758         }
06759         /* Check that both triangles agree on the identities */
06760         /*   of their shared vertices.                       */
06761         org(oppotri, oppoorg);
06762         dest(oppotri, oppodest);
06763         if ((triorg != oppodest) || (tridest != oppoorg)) {
06764           printf("  !! !! Mismatched edge coordinates between two triangles:\n"
06765                  );
06766           printf("    First mismatched ");
06767           printtriangle(m, b, &triangleloop);
06768           printf("    Second mismatched ");
06769           printtriangle(m, b, &oppotri);
06770           horrors++;
06771         }
06772       }
06773     }
06774     triangleloop.tri = triangletraverse(m);
06775   }
06776   if (horrors == 0) {
06777     if (!b->quiet) {
06778       printf("  In my studied opinion, the mesh appears to be consistent.\n");
06779     }
06780   } else if (horrors == 1) {
06781     printf("  !! !! !! !! Precisely one festering wound discovered.\n");
06782   } else {
06783     printf("  !! !! !! !! %d abominations witnessed.\n", horrors);
06784   }
06785   /* Restore the status of exact arithmetic. */
06786   b->noexact = saveexact;
06787 }
06788 
06789 #endif /* not REDUCED */
06790 
06791 /*****************************************************************************/
06792 /*                                                                           */
06793 /*  checkdelaunay()   Ensure that the mesh is (constrained) Delaunay.        */
06794 /*                                                                           */
06795 /*****************************************************************************/
06796 
06797 #ifndef REDUCED
06798 
06799 #ifdef ANSI_DECLARATORS
06800 void checkdelaunay(struct mesh *m, struct behavior *b)
06801 #else /* not ANSI_DECLARATORS */
06802 void checkdelaunay(m, b)
06803 struct mesh *m;
06804 struct behavior *b;
06805 #endif /* not ANSI_DECLARATORS */
06806 
06807 {
06808   struct otri triangleloop;
06809   struct otri oppotri;
06810   struct osub opposubseg;
06811   vertex triorg, tridest, triapex;
06812   vertex oppoapex;
06813   int shouldbedelaunay;
06814   int horrors;
06815   int saveexact;
06816   triangle ptr;                         /* Temporary variable used by sym(). */
06817   subseg sptr;                      /* Temporary variable used by tspivot(). */
06818 
06819   /* Temporarily turn on exact arithmetic if it's off. */
06820   saveexact = b->noexact;
06821   b->noexact = 0;
06822   if (!b->quiet) {
06823     printf("  Checking Delaunay property of mesh...\n");
06824   }
06825   horrors = 0;
06826   /* Run through the list of triangles, checking each one. */
06827   traversalinit(&m->triangles);
06828   triangleloop.tri = triangletraverse(m);
06829   while (triangleloop.tri != (triangle *) NULL) {
06830     /* Check all three edges of the triangle. */
06831     for (triangleloop.orient = 0; triangleloop.orient < 3;
06832          triangleloop.orient++) {
06833       org(triangleloop, triorg);
06834       dest(triangleloop, tridest);
06835       apex(triangleloop, triapex);
06836       sym(triangleloop, oppotri);
06837       apex(oppotri, oppoapex);
06838       /* Only test that the edge is locally Delaunay if there is an   */
06839       /*   adjoining triangle whose pointer is larger (to ensure that */
06840       /*   each pair isn't tested twice).                             */
06841       shouldbedelaunay = (oppotri.tri != m->dummytri) &&
06842             !deadtri(oppotri.tri) && (triangleloop.tri < oppotri.tri) &&
06843             (triorg != m->infvertex1) && (triorg != m->infvertex2) &&
06844             (triorg != m->infvertex3) &&
06845             (tridest != m->infvertex1) && (tridest != m->infvertex2) &&
06846             (tridest != m->infvertex3) &&
06847             (triapex != m->infvertex1) && (triapex != m->infvertex2) &&
06848             (triapex != m->infvertex3) &&
06849             (oppoapex != m->infvertex1) && (oppoapex != m->infvertex2) &&
06850             (oppoapex != m->infvertex3);
06851       if (m->checksegments && shouldbedelaunay) {
06852         /* If a subsegment separates the triangles, then the edge is */
06853         /*   constrained, so no local Delaunay test should be done.  */
06854         tspivot(triangleloop, opposubseg);
06855         if (opposubseg.ss != m->dummysub){
06856           shouldbedelaunay = 0;
06857         }
06858       }
06859       if (shouldbedelaunay) {
06860         if (nonregular(m, b, triorg, tridest, triapex, oppoapex) > 0.0) {
06861           if (!b->weighted) {
06862             printf("  !! !! Non-Delaunay pair of triangles:\n");
06863             printf("    First non-Delaunay ");
06864             printtriangle(m, b, &triangleloop);
06865             printf("    Second non-Delaunay ");
06866           } else {
06867             printf("  !! !! Non-regular pair of triangles:\n");
06868             printf("    First non-regular ");
06869             printtriangle(m, b, &triangleloop);
06870             printf("    Second non-regular ");
06871           }
06872           printtriangle(m, b, &oppotri);
06873           horrors++;
06874         }
06875       }
06876     }
06877     triangleloop.tri = triangletraverse(m);
06878   }
06879   if (horrors == 0) {
06880     if (!b->quiet) {
06881       printf(
06882   "  By virtue of my perceptive intelligence, I declare the mesh Delaunay.\n");
06883     }
06884   } else if (horrors == 1) {
06885     printf(
06886          "  !! !! !! !! Precisely one terrifying transgression identified.\n");
06887   } else {
06888     printf("  !! !! !! !! %d obscenities viewed with horror.\n", horrors);
06889   }
06890   /* Restore the status of exact arithmetic. */
06891   b->noexact = saveexact;
06892 }
06893 
06894 #endif /* not REDUCED */
06895 
06896 /*****************************************************************************/
06897 /*                                                                           */
06898 /*  enqueuebadtriang()   Add a bad triangle data structure to the end of a   */
06899 /*                       queue.                                              */
06900 /*                                                                           */
06901 /*  The queue is actually a set of 4096 queues.  I use multiple queues to    */
06902 /*  give priority to smaller angles.  I originally implemented a heap, but   */
06903 /*  the queues are faster by a larger margin than I'd suspected.             */
06904 /*                                                                           */
06905 /*****************************************************************************/
06906 
06907 #ifndef CDT_ONLY
06908 
06909 #ifdef ANSI_DECLARATORS
06910 void enqueuebadtriang(struct mesh *m, struct behavior *b,
06911                       struct badtriang *badtri)
06912 #else /* not ANSI_DECLARATORS */
06913 void enqueuebadtriang(m, b, badtri)
06914 struct mesh *m;
06915 struct behavior *b;
06916 struct badtriang *badtri;
06917 #endif /* not ANSI_DECLARATORS */
06918 
06919 {
06920   REAL length, multiplier;
06921   int exponent, expincrement;
06922   int queuenumber;
06923   int posexponent;
06924   int i;
06925 
06926   if (b->verbose > 2) {
06927     printf("  Queueing bad triangle:\n");
06928     printf("    (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
06929            badtri->triangorg[0], badtri->triangorg[1],
06930            badtri->triangdest[0], badtri->triangdest[1],
06931            badtri->triangapex[0], badtri->triangapex[1]);
06932   }
06933 
06934   /* Determine the appropriate queue to put the bad triangle into.    */
06935   /*   Recall that the key is the square of its shortest edge length. */
06936   if (badtri->key >= 1.0) {
06937     length = badtri->key;
06938     posexponent = 1;
06939   } else {
06940     /* `badtri->key' is 2.0 to a negative exponent, so we'll record that */
06941     /*   fact and use the reciprocal of `badtri->key', which is > 1.0.   */
06942     length = 1.0 / badtri->key;
06943     posexponent = 0;
06944   }
06945   /* `length' is approximately 2.0 to what exponent?  The following code */
06946   /*   determines the answer in time logarithmic in the exponent.        */
06947   exponent = 0;
06948   while (length > 2.0) {
06949     /* Find an approximation by repeated squaring of two. */
06950     expincrement = 1;
06951     multiplier = 0.5;
06952     while (length * multiplier * multiplier > 1.0) {
06953       expincrement *= 2;
06954       multiplier *= multiplier;
06955     }
06956     /* Reduce the value of `length', then iterate if necessary. */
06957     exponent += expincrement;
06958     length *= multiplier;
06959   }
06960   /* `length' is approximately squareroot(2.0) to what exponent? */
06961   exponent = 2 * exponent + (length > SQUAREROOTTWO);
06962   /* `exponent' is now in the range 0...2047 for IEEE double precision.   */
06963   /*   Choose a queue in the range 0...4095.  The shortest edges have the */
06964   /*   highest priority (queue 4095).                                     */
06965   if (posexponent) {
06966     queuenumber = 2047 - exponent;
06967   } else {
06968     queuenumber = 2048 + exponent;
06969   }
06970 
06971   /* Are we inserting into an empty queue? */
06972   if (m->queuefront[queuenumber] == (struct badtriang *) NULL) {
06973     /* Yes, we are inserting into an empty queue.     */
06974     /*   Will this become the highest-priority queue? */
06975     if (queuenumber > m->firstnonemptyq) {
06976       /* Yes, this is the highest-priority queue. */
06977       m->nextnonemptyq[queuenumber] = m->firstnonemptyq;
06978       m->firstnonemptyq = queuenumber;
06979     } else {
06980       /* No, this is not the highest-priority queue. */
06981       /*   Find the queue with next higher priority. */
06982       i = queuenumber + 1;
06983       while (m->queuefront[i] == (struct badtriang *) NULL) {
06984         i++;
06985       }
06986       /* Mark the newly nonempty queue as following a higher-priority queue. */
06987       m->nextnonemptyq[queuenumber] = m->nextnonemptyq[i];
06988       m->nextnonemptyq[i] = queuenumber;
06989     }
06990     /* Put the bad triangle at the beginning of the (empty) queue. */
06991     m->queuefront[queuenumber] = badtri;
06992   } else {
06993     /* Add the bad triangle to the end of an already nonempty queue. */
06994     m->queuetail[queuenumber]->nexttriang = badtri;
06995   }
06996   /* Maintain a pointer to the last triangle of the queue. */
06997   m->queuetail[queuenumber] = badtri;
06998   /* Newly enqueued bad triangle has no successor in the queue. */
06999   badtri->nexttriang = (struct badtriang *) NULL;
07000 }
07001 
07002 #endif /* not CDT_ONLY */
07003 
07004 /*****************************************************************************/
07005 /*                                                                           */
07006 /*  enqueuebadtri()   Add a bad triangle to the end of a queue.              */
07007 /*                                                                           */
07008 /*  Allocates a badtriang data structure for the triangle, then passes it to */
07009 /*  enqueuebadtriang().                                                      */
07010 /*                                                                           */
07011 /*****************************************************************************/
07012 
07013 #ifndef CDT_ONLY
07014 
07015 #ifdef ANSI_DECLARATORS
07016 void enqueuebadtri(struct mesh *m, struct behavior *b, struct otri *enqtri,
07017                    REAL minedge, vertex enqapex, vertex enqorg, vertex enqdest)
07018 #else /* not ANSI_DECLARATORS */
07019 void enqueuebadtri(m, b, enqtri, minedge, enqapex, enqorg, enqdest)
07020 struct mesh *m;
07021 struct behavior *b;
07022 struct otri *enqtri;
07023 REAL minedge;
07024 vertex enqapex;
07025 vertex enqorg;
07026 vertex enqdest;
07027 #endif /* not ANSI_DECLARATORS */
07028 
07029 {
07030   struct badtriang *newbad;
07031 
07032   /* Allocate space for the bad triangle. */
07033   newbad = (struct badtriang *) poolalloc(&m->badtriangles);
07034   newbad->poortri = encode(*enqtri);
07035   newbad->key = minedge;
07036   newbad->triangapex = enqapex;
07037   newbad->triangorg = enqorg;
07038   newbad->triangdest = enqdest;
07039   enqueuebadtriang(m, b, newbad);
07040 }
07041 
07042 #endif /* not CDT_ONLY */
07043 
07044 /*****************************************************************************/
07045 /*                                                                           */
07046 /*  dequeuebadtriang()   Remove a triangle from the front of the queue.      */
07047 /*                                                                           */
07048 /*****************************************************************************/
07049 
07050 #ifndef CDT_ONLY
07051 
07052 #ifdef ANSI_DECLARATORS
07053 struct badtriang *dequeuebadtriang(struct mesh *m)
07054 #else /* not ANSI_DECLARATORS */
07055 struct badtriang *dequeuebadtriang(m)
07056 struct mesh *m;
07057 #endif /* not ANSI_DECLARATORS */
07058 
07059 {
07060   struct badtriang *result;
07061 
07062   /* If no queues are nonempty, return NULL. */
07063   if (m->firstnonemptyq < 0) {
07064     return (struct badtriang *) NULL;
07065   }
07066   /* Find the first triangle of the highest-priority queue. */
07067   result = m->queuefront[m->firstnonemptyq];
07068   /* Remove the triangle from the queue. */
07069   m->queuefront[m->firstnonemptyq] = result->nexttriang;
07070   /* If this queue is now empty, note the new highest-priority */
07071   /*   nonempty queue.                                         */
07072   if (result == m->queuetail[m->firstnonemptyq]) {
07073     m->firstnonemptyq = m->nextnonemptyq[m->firstnonemptyq];
07074   }
07075   return result;
07076 }
07077 
07078 #endif /* not CDT_ONLY */
07079 
07080 /*****************************************************************************/
07081 /*                                                                           */
07082 /*  checkseg4encroach()   Check a subsegment to see if it is encroached; add */
07083 /*                        it to the list if it is.                           */
07084 /*                                                                           */
07085 /*  A subsegment is encroached if there is a vertex in its diametral lens.   */
07086 /*  For Ruppert's algorithm (-D switch), the "diametral lens" is the         */
07087 /*  diametral circle.  For Chew's algorithm (default), the diametral lens is */
07088 /*  just big enough to enclose two isosceles triangles whose bases are the   */
07089 /*  subsegment.  Each of the two isosceles triangles has two angles equal    */
07090 /*  to `b->minangle'.                                                        */
07091 /*                                                                           */
07092 /*  Chew's algorithm does not require diametral lenses at all--but they save */
07093 /*  time.  Any vertex inside a subsegment's diametral lens implies that the  */
07094 /*  triangle adjoining the subsegment will be too skinny, so it's only a     */
07095 /*  matter of time before the encroaching vertex is deleted by Chew's        */
07096 /*  algorithm.  It's faster to simply not insert the doomed vertex in the    */
07097 /*  first place, which is why I use diametral lenses with Chew's algorithm.  */
07098 /*                                                                           */
07099 /*  Returns a nonzero value if the subsegment is encroached.                 */
07100 /*                                                                           */
07101 /*****************************************************************************/
07102 
07103 #ifndef CDT_ONLY
07104 
07105 #ifdef ANSI_DECLARATORS
07106 int checkseg4encroach(struct mesh *m, struct behavior *b,
07107                       struct osub *testsubseg)
07108 #else /* not ANSI_DECLARATORS */
07109 int checkseg4encroach(m, b, testsubseg)
07110 struct mesh *m;
07111 struct behavior *b;
07112 struct osub *testsubseg;
07113 #endif /* not ANSI_DECLARATORS */
07114 
07115 {
07116   struct otri neighbortri;
07117   struct osub testsym;
07118   struct badsubseg *encroachedseg;
07119   REAL dotproduct;
07120   int encroached;
07121   int sides;
07122   vertex eorg, edest, eapex;
07123   triangle ptr;                     /* Temporary variable used by stpivot(). */
07124 
07125   encroached = 0;
07126   sides = 0;
07127 
07128   sorg(*testsubseg, eorg);
07129   sdest(*testsubseg, edest);
07130   /* Check one neighbor of the subsegment. */
07131   stpivot(*testsubseg, neighbortri);
07132   /* Does the neighbor exist, or is this a boundary edge? */
07133   if (neighbortri.tri != m->dummytri) {
07134     sides++;
07135     /* Find a vertex opposite this subsegment. */
07136     apex(neighbortri, eapex);
07137     /* Check whether the apex is in the diametral lens of the subsegment */
07138     /*   (the diametral circle if `conformdel' is set).  A dot product   */
07139     /*   of two sides of the triangle is used to check whether the angle */
07140     /*   at the apex is greater than (180 - 2 `minangle') degrees (for   */
07141     /*   lenses; 90 degrees for diametral circles).                      */
07142     dotproduct = (eorg[0] - eapex[0]) * (edest[0] - eapex[0]) +
07143                  (eorg[1] - eapex[1]) * (edest[1] - eapex[1]);
07144     if (dotproduct < 0.0) {
07145       if (b->conformdel ||
07146           (dotproduct * dotproduct >=
07147            (2.0 * b->goodangle - 1.0) * (2.0 * b->goodangle - 1.0) *
07148            ((eorg[0] - eapex[0]) * (eorg[0] - eapex[0]) +
07149             (eorg[1] - eapex[1]) * (eorg[1] - eapex[1])) *
07150            ((edest[0] - eapex[0]) * (edest[0] - eapex[0]) +
07151             (edest[1] - eapex[1]) * (edest[1] - eapex[1])))) {
07152         encroached = 1;
07153       }
07154     }
07155   }
07156   /* Check the other neighbor of the subsegment. */
07157   ssym(*testsubseg, testsym);
07158   stpivot(testsym, neighbortri);
07159   /* Does the neighbor exist, or is this a boundary edge? */
07160   if (neighbortri.tri != m->dummytri) {
07161     sides++;
07162     /* Find the other vertex opposite this subsegment. */
07163     apex(neighbortri, eapex);
07164     /* Check whether the apex is in the diametral lens of the subsegment */
07165     /*   (or the diametral circle, if `conformdel' is set).              */
07166     dotproduct = (eorg[0] - eapex[0]) * (edest[0] - eapex[0]) +
07167                  (eorg[1] - eapex[1]) * (edest[1] - eapex[1]);
07168     if (dotproduct < 0.0) {
07169       if (b->conformdel ||
07170           (dotproduct * dotproduct >=
07171            (2.0 * b->goodangle - 1.0) * (2.0 * b->goodangle - 1.0) *
07172            ((eorg[0] - eapex[0]) * (eorg[0] - eapex[0]) +
07173             (eorg[1] - eapex[1]) * (eorg[1] - eapex[1])) *
07174            ((edest[0] - eapex[0]) * (edest[0] - eapex[0]) +
07175             (edest[1] - eapex[1]) * (edest[1] - eapex[1])))) {
07176         encroached += 2;
07177       }
07178     }
07179   }
07180 
07181   if (encroached && (!b->nobisect || ((b->nobisect == 1) && (sides == 2)))) {
07182     if (b->verbose > 2) {
07183       printf(
07184         "  Queueing encroached subsegment (%.12g, %.12g) (%.12g, %.12g).\n",
07185         eorg[0], eorg[1], edest[0], edest[1]);
07186     }
07187     /* Add the subsegment to the list of encroached subsegments. */
07188     /*   Be sure to get the orientation right.                   */
07189     encroachedseg = (struct badsubseg *) poolalloc(&m->badsubsegs);
07190     if (encroached == 1) {
07191       encroachedseg->encsubseg = sencode(*testsubseg);
07192       encroachedseg->subsegorg = eorg;
07193       encroachedseg->subsegdest = edest;
07194     } else {
07195       encroachedseg->encsubseg = sencode(testsym);
07196       encroachedseg->subsegorg = edest;
07197       encroachedseg->subsegdest = eorg;
07198     }
07199   }
07200 
07201   return encroached;
07202 }
07203 
07204 #endif /* not CDT_ONLY */
07205 
07206 /*****************************************************************************/
07207 /*                                                                           */
07208 /*  testtriangle()   Test a triangle for quality and size.                   */
07209 /*                                                                           */
07210 /*  Tests a triangle to see if it satisfies the minimum angle condition and  */
07211 /*  the maximum area condition.  Triangles that aren't up to spec are added  */
07212 /*  to the bad triangle queue.                                               */
07213 /*                                                                           */
07214 /*****************************************************************************/
07215 
07216 #ifndef CDT_ONLY
07217 
07218 #ifdef ANSI_DECLARATORS
07219 void testtriangle(struct mesh *m, struct behavior *b, struct otri *testtri)
07220 #else /* not ANSI_DECLARATORS */
07221 void testtriangle(m, b, testtri)
07222 struct mesh *m;
07223 struct behavior *b;
07224 struct otri *testtri;
07225 #endif /* not ANSI_DECLARATORS */
07226 
07227 {
07228   struct otri tri1, tri2;
07229   struct osub testsub;
07230   vertex torg, tdest, tapex;
07231   vertex base1, base2;
07232   vertex org1, dest1, org2, dest2;
07233   vertex joinvertex;
07234   REAL dxod, dyod, dxda, dyda, dxao, dyao;
07235   REAL dxod2, dyod2, dxda2, dyda2, dxao2, dyao2;
07236   REAL apexlen, orglen, destlen, minedge;
07237   REAL angle;
07238   REAL area;
07239   REAL dist1, dist2;
07240   subseg sptr;                      /* Temporary variable used by tspivot(). */
07241   triangle ptr;           /* Temporary variable used by oprev() and dnext(). */
07242 
07243   org(*testtri, torg);
07244   dest(*testtri, tdest);
07245   apex(*testtri, tapex);
07246   dxod = torg[0] - tdest[0];
07247   dyod = torg[1] - tdest[1];
07248   dxda = tdest[0] - tapex[0];
07249   dyda = tdest[1] - tapex[1];
07250   dxao = tapex[0] - torg[0];
07251   dyao = tapex[1] - torg[1];
07252   dxod2 = dxod * dxod;
07253   dyod2 = dyod * dyod;
07254   dxda2 = dxda * dxda;
07255   dyda2 = dyda * dyda;
07256   dxao2 = dxao * dxao;
07257   dyao2 = dyao * dyao;
07258   /* Find the lengths of the triangle's three edges. */
07259   apexlen = dxod2 + dyod2;
07260   orglen = dxda2 + dyda2;
07261   destlen = dxao2 + dyao2;
07262 
07263   if ((apexlen < orglen) && (apexlen < destlen)) {
07264     /* The edge opposite the apex is shortest. */
07265     minedge = apexlen;
07266     /* Find the square of the cosine of the angle at the apex. */
07267     angle = dxda * dxao + dyda * dyao;
07268     angle = angle * angle / (orglen * destlen);
07269     base1 = torg;
07270     base2 = tdest;
07271     otricopy(*testtri, tri1);
07272   } else if (orglen < destlen) {
07273     /* The edge opposite the origin is shortest. */
07274     minedge = orglen;
07275     /* Find the square of the cosine of the angle at the origin. */
07276     angle = dxod * dxao + dyod * dyao;
07277     angle = angle * angle / (apexlen * destlen);
07278     base1 = tdest;
07279     base2 = tapex;
07280     lnext(*testtri, tri1);
07281   } else {
07282     /* The edge opposite the destination is shortest. */
07283     minedge = destlen;
07284     /* Find the square of the cosine of the angle at the destination. */
07285     angle = dxod * dxda + dyod * dyda;
07286     angle = angle * angle / (apexlen * orglen);
07287     base1 = tapex;
07288     base2 = torg;
07289     lprev(*testtri, tri1);
07290   }
07291 
07292   if (b->vararea || b->fixedarea || b->usertest) {
07293     /* Check whether the area is larger than permitted. */
07294     area = 0.5 * (dxod * dyda - dyod * dxda);
07295     if (b->fixedarea && (area > b->maxarea)) {
07296       /* Add this triangle to the list of bad triangles. */
07297       enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest);
07298       return;
07299     }
07300 
07301     /* Nonpositive area constraints are treated as unconstrained. */
07302     if ((b->vararea) && (area > areabound(*testtri)) &&
07303         (areabound(*testtri) > 0.0)) {
07304       /* Add this triangle to the list of bad triangles. */
07305       enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest);
07306       return;
07307     }
07308 
07309     if (b->usertest) {
07310       /* Check whether the user thinks this triangle is too large. */
07311       if (triunsuitable(torg, tdest, tapex, area)) {
07312         enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest);
07313         return;
07314       }
07315     }
07316   }
07317 
07318   /* Check whether the angle is smaller than permitted. */
07319   if (angle > b->goodangle) {
07320     /* Use the rules of Miller, Pav, and Walkington to decide that certain */
07321     /*   triangles should not be split, even if they have bad angles.      */
07322     /*   A skinny triangle is not split if its shortest edge subtends a    */
07323     /*   small input angle, and both endpoints of the edge lie on a        */
07324     /*   concentric circular shell.  For convenience, I make a small       */
07325     /*   adjustment to that rule:  I check if the endpoints of the edge    */
07326     /*   both lie in segment interiors, equidistant from the apex where    */
07327     /*   the two segments meet.                                            */
07328     /* First, check if both points lie in segment interiors.               */
07329     if ((vertextype(base1) == SEGMENTVERTEX) &&
07330         (vertextype(base2) == SEGMENTVERTEX)) {
07331       /* Check if both points lie in a common segment.  If they do, the */
07332       /*   skinny triangle is enqueued to be split as usual.            */
07333       tspivot(tri1, testsub);
07334       if (testsub.ss == m->dummysub) {
07335         /* No common segment.  Find a subsegment that contains `torg'. */
07336         otricopy(tri1, tri2);
07337         do {
07338           oprevself(tri1);
07339           tspivot(tri1, testsub);
07340         } while (testsub.ss == m->dummysub);
07341         /* Find the endpoints of the containing segment. */
07342         segorg(testsub, org1);
07343         segdest(testsub, dest1);
07344         /* Find a subsegment that contains `tdest'. */
07345         do {
07346           dnextself(tri2);
07347           tspivot(tri2, testsub);
07348         } while (testsub.ss == m->dummysub);
07349         /* Find the endpoints of the containing segment. */
07350         segorg(testsub, org2);
07351         segdest(testsub, dest2);
07352         /* Check if the two containing segments have an endpoint in common. */
07353         joinvertex = (vertex) NULL;
07354         if ((dest1[0] == org2[0]) && (dest1[1] == org2[1])) {
07355           joinvertex = dest1;
07356         } else if ((org1[0] == dest2[0]) && (org1[1] == dest2[1])) {
07357           joinvertex = org1;
07358         }
07359         if (joinvertex != (vertex) NULL) {
07360           /* Compute the distance from the common endpoint (of the two  */
07361           /*   segments) to each of the endpoints of the shortest edge. */
07362           dist1 = ((base1[0] - joinvertex[0]) * (base1[0] - joinvertex[0]) +
07363                    (base1[1] - joinvertex[1]) * (base1[1] - joinvertex[1]));
07364           dist2 = ((base2[0] - joinvertex[0]) * (base2[0] - joinvertex[0]) +
07365                    (base2[1] - joinvertex[1]) * (base2[1] - joinvertex[1]));
07366           /* If the two distances are equal, don't split the triangle. */
07367           if ((dist1 < 1.001 * dist2) && (dist1 > 0.999 * dist2)) {
07368             /* Return now to avoid enqueueing the bad triangle. */
07369             return;
07370           }
07371         }
07372       }
07373     }
07374 
07375     /* Add this triangle to the list of bad triangles. */
07376     enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest);
07377   }
07378 }
07379 
07380 #endif /* not CDT_ONLY */
07381 
07384 /********* Mesh quality testing routines end here                    *********/
07385 
07386 /********* Point location routines begin here                        *********/
07390 /*****************************************************************************/
07391 /*                                                                           */
07392 /*  makevertexmap()   Construct a mapping from vertices to triangles to      */
07393 /*                    improve the speed of point location for segment        */
07394 /*                    insertion.                                             */
07395 /*                                                                           */
07396 /*  Traverses all the triangles, and provides each corner of each triangle   */
07397 /*  with a pointer to that triangle.  Of course, pointers will be            */
07398 /*  overwritten by other pointers because (almost) each vertex is a corner   */
07399 /*  of several triangles, but in the end every vertex will point to some     */
07400 /*  triangle that contains it.                                               */
07401 /*                                                                           */
07402 /*****************************************************************************/
07403 
07404 #ifdef ANSI_DECLARATORS
07405 void makevertexmap(struct mesh *m, struct behavior *b)
07406 #else /* not ANSI_DECLARATORS */
07407 void makevertexmap(m, b)
07408 struct mesh *m;
07409 struct behavior *b;
07410 #endif /* not ANSI_DECLARATORS */
07411 
07412 {
07413   struct otri triangleloop;
07414   vertex triorg;
07415 
07416   if (b->verbose) {
07417     printf("    Constructing mapping from vertices to triangles.\n");
07418   }
07419   traversalinit(&m->triangles);
07420   triangleloop.tri = triangletraverse(m);
07421   while (triangleloop.tri != (triangle *) NULL) {
07422     /* Check all three vertices of the triangle. */
07423     for (triangleloop.orient = 0; triangleloop.orient < 3;
07424          triangleloop.orient++) {
07425       org(triangleloop, triorg);
07426       setvertex2tri(triorg, encode(triangleloop));
07427     }
07428     triangleloop.tri = triangletraverse(m);
07429   }
07430 }
07431 
07432 /*****************************************************************************/
07433 /*                                                                           */
07434 /*  preciselocate()   Find a triangle or edge containing a given point.      */
07435 /*                                                                           */
07436 /*  Begins its search from `searchtri'.  It is important that `searchtri'    */
07437 /*  be a handle with the property that `searchpoint' is strictly to the left */
07438 /*  of the edge denoted by `searchtri', or is collinear with that edge and   */
07439 /*  does not intersect that edge.  (In particular, `searchpoint' should not  */
07440 /*  be the origin or destination of that edge.)                              */
07441 /*                                                                           */
07442 /*  These conditions are imposed because preciselocate() is normally used in */
07443 /*  one of two situations:                                                   */
07444 /*                                                                           */
07445 /*  (1)  To try to find the location to insert a new point.  Normally, we    */
07446 /*       know an edge that the point is strictly to the left of.  In the     */
07447 /*       incremental Delaunay algorithm, that edge is a bounding box edge.   */
07448 /*       In Ruppert's Delaunay refinement algorithm for quality meshing,     */
07449 /*       that edge is the shortest edge of the triangle whose circumcenter   */
07450 /*       is being inserted.                                                  */
07451 /*                                                                           */
07452 /*  (2)  To try to find an existing point.  In this case, any edge on the    */
07453 /*       convex hull is a good starting edge.  You must screen out the       */
07454 /*       possibility that the vertex sought is an endpoint of the starting   */
07455 /*       edge before you call preciselocate().                               */
07456 /*                                                                           */
07457 /*  On completion, `searchtri' is a triangle that contains `searchpoint'.    */
07458 /*                                                                           */
07459 /*  This implementation differs from that given by Guibas and Stolfi.  It    */
07460 /*  walks from triangle to triangle, crossing an edge only if `searchpoint'  */
07461 /*  is on the other side of the line containing that edge.  After entering   */
07462 /*  a triangle, there are two edges by which one can leave that triangle.    */
07463 /*  If both edges are valid (`searchpoint' is on the other side of both      */
07464 /*  edges), one of the two is chosen by drawing a line perpendicular to      */
07465 /*  the entry edge (whose endpoints are `forg' and `fdest') passing through  */
07466 /*  `fapex'.  Depending on which side of this perpendicular `searchpoint'    */
07467 /*  falls on, an exit edge is chosen.                                        */
07468 /*                                                                           */
07469 /*  This implementation is empirically faster than the Guibas and Stolfi     */
07470 /*  point location routine (which I originally used), which tends to spiral  */
07471 /*  in toward its target.                                                    */
07472 /*                                                                           */
07473 /*  Returns ONVERTEX if the point lies on an existing vertex.  `searchtri'   */
07474 /*  is a handle whose origin is the existing vertex.                         */
07475 /*                                                                           */
07476 /*  Returns ONEDGE if the point lies on a mesh edge.  `searchtri' is a       */
07477 /*  handle whose primary edge is the edge on which the point lies.           */
07478 /*                                                                           */
07479 /*  Returns INTRIANGLE if the point lies strictly within a triangle.         */
07480 /*  `searchtri' is a handle on the triangle that contains the point.         */
07481 /*                                                                           */
07482 /*  Returns OUTSIDE if the point lies outside the mesh.  `searchtri' is a    */
07483 /*  handle whose primary edge the point is to the right of.  This might      */
07484 /*  occur when the circumcenter of a triangle falls just slightly outside    */
07485 /*  the mesh due to floating-point roundoff error.  It also occurs when      */
07486 /*  seeking a hole or region point that a foolish user has placed outside    */
07487 /*  the mesh.                                                                */
07488 /*                                                                           */
07489 /*  If `stopatsubsegment' is nonzero, the search will stop if it tries to    */
07490 /*  walk through a subsegment, and will return OUTSIDE.                      */
07491 /*                                                                           */
07492 /*  WARNING:  This routine is designed for convex triangulations, and will   */
07493 /*  not generally work after the holes and concavities have been carved.     */
07494 /*  However, it can still be used to find the circumcenter of a triangle, as */
07495 /*  long as the search is begun from the triangle in question.               */
07496 /*                                                                           */
07497 /*****************************************************************************/
07498 
07499 #ifdef ANSI_DECLARATORS
07500 enum locateresult preciselocate(struct mesh *m, struct behavior *b,
07501                                 vertex searchpoint, struct otri *searchtri,
07502                                 int stopatsubsegment)
07503 #else /* not ANSI_DECLARATORS */
07504 enum locateresult preciselocate(m, b, searchpoint, searchtri, stopatsubsegment)
07505 struct mesh *m;
07506 struct behavior *b;
07507 vertex searchpoint;
07508 struct otri *searchtri;
07509 int stopatsubsegment;
07510 #endif /* not ANSI_DECLARATORS */
07511 
07512 {
07513   struct otri backtracktri;
07514   struct osub checkedge;
07515   vertex forg, fdest, fapex;
07516   REAL orgorient, destorient;
07517   int moveleft;
07518   triangle ptr;                         /* Temporary variable used by sym(). */
07519   subseg sptr;                      /* Temporary variable used by tspivot(). */
07520 
07521   if (b->verbose > 2) {
07522     printf("  Searching for point (%.12g, %.12g).\n",
07523            searchpoint[0], searchpoint[1]);
07524   }
07525   /* Where are we? */
07526   org(*searchtri, forg);
07527   dest(*searchtri, fdest);
07528   apex(*searchtri, fapex);
07529   while (1) {
07530     if (b->verbose > 2) {
07531       printf("    At (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
07532              forg[0], forg[1], fdest[0], fdest[1], fapex[0], fapex[1]);
07533     }
07534     /* Check whether the apex is the point we seek. */
07535     if ((fapex[0] == searchpoint[0]) && (fapex[1] == searchpoint[1])) {
07536       lprevself(*searchtri);
07537       return ONVERTEX;
07538     }
07539     /* Does the point lie on the other side of the line defined by the */
07540     /*   triangle edge opposite the triangle's destination?            */
07541     destorient = counterclockwise(m, b, forg, fapex, searchpoint);
07542     /* Does the point lie on the other side of the line defined by the */
07543     /*   triangle edge opposite the triangle's origin?                 */
07544     orgorient = counterclockwise(m, b, fapex, fdest, searchpoint);
07545     if (destorient > 0.0) {
07546       if (orgorient > 0.0) {
07547         /* Move left if the inner product of (fapex - searchpoint) and  */
07548         /*   (fdest - forg) is positive.  This is equivalent to drawing */
07549         /*   a line perpendicular to the line (forg, fdest) and passing */
07550         /*   through `fapex', and determining which side of this line   */
07551         /*   `searchpoint' falls on.                                    */
07552         moveleft = (fapex[0] - searchpoint[0]) * (fdest[0] - forg[0]) +
07553                    (fapex[1] - searchpoint[1]) * (fdest[1] - forg[1]) > 0.0;
07554       } else {
07555         moveleft = 1;
07556       }
07557     } else {
07558       if (orgorient > 0.0) {
07559         moveleft = 0;
07560       } else {
07561         /* The point we seek must be on the boundary of or inside this */
07562         /*   triangle.                                                 */
07563         if (destorient == 0.0) {
07564           lprevself(*searchtri);
07565           return ONEDGE;
07566         }
07567         if (orgorient == 0.0) {
07568           lnextself(*searchtri);
07569           return ONEDGE;
07570         }
07571         return INTRIANGLE;
07572       }
07573     }
07574 
07575     /* Move to another triangle.  Leave a trace `backtracktri' in case */
07576     /*   floating-point roundoff or some such bogey causes us to walk  */
07577     /*   off a boundary of the triangulation.                          */
07578     if (moveleft) {
07579       lprev(*searchtri, backtracktri);
07580       fdest = fapex;
07581     } else {
07582       lnext(*searchtri, backtracktri);
07583       forg = fapex;
07584     }
07585     sym(backtracktri, *searchtri);
07586 
07587     if (m->checksegments && stopatsubsegment) {
07588       /* Check for walking through a subsegment. */
07589       tspivot(backtracktri, checkedge);
07590       if (checkedge.ss != m->dummysub) {
07591         /* Go back to the last triangle. */
07592         otricopy(backtracktri, *searchtri);
07593         return OUTSIDE;
07594       }
07595     }
07596     /* Check for walking right out of the triangulation. */
07597     if (searchtri->tri == m->dummytri) {
07598       /* Go back to the last triangle. */
07599       otricopy(backtracktri, *searchtri);
07600       return OUTSIDE;
07601     }
07602 
07603     apex(*searchtri, fapex);
07604   }
07605 }
07606 
07607 /*****************************************************************************/
07608 /*                                                                           */
07609 /*  locate()   Find a triangle or edge containing a given point.             */
07610 /*                                                                           */
07611 /*  Searching begins from one of:  the input `searchtri', a recently         */
07612 /*  encountered triangle `recenttri', or from a triangle chosen from a       */
07613 /*  random sample.  The choice is made by determining which triangle's       */
07614 /*  origin is closest to the point we are searching for.  Normally,          */
07615 /*  `searchtri' should be a handle on the convex hull of the triangulation.  */
07616 /*                                                                           */
07617 /*  Details on the random sampling method can be found in the Mucke, Saias,  */
07618 /*  and Zhu paper cited in the header of this code.                          */
07619 /*                                                                           */
07620 /*  On completion, `searchtri' is a triangle that contains `searchpoint'.    */
07621 /*                                                                           */
07622 /*  Returns ONVERTEX if the point lies on an existing vertex.  `searchtri'   */
07623 /*  is a handle whose origin is the existing vertex.                         */
07624 /*                                                                           */
07625 /*  Returns ONEDGE if the point lies on a mesh edge.  `searchtri' is a       */
07626 /*  handle whose primary edge is the edge on which the point lies.           */
07627 /*                                                                           */
07628 /*  Returns INTRIANGLE if the point lies strictly within a triangle.         */
07629 /*  `searchtri' is a handle on the triangle that contains the point.         */
07630 /*                                                                           */
07631 /*  Returns OUTSIDE if the point lies outside the mesh.  `searchtri' is a    */
07632 /*  handle whose primary edge the point is to the right of.  This might      */
07633 /*  occur when the circumcenter of a triangle falls just slightly outside    */
07634 /*  the mesh due to floating-point roundoff error.  It also occurs when      */
07635 /*  seeking a hole or region point that a foolish user has placed outside    */
07636 /*  the mesh.                                                                */
07637 /*                                                                           */
07638 /*  WARNING:  This routine is designed for convex triangulations, and will   */
07639 /*  not generally work after the holes and concavities have been carved.     */
07640 /*                                                                           */
07641 /*****************************************************************************/
07642 
07643 #ifdef ANSI_DECLARATORS
07644 enum locateresult locate(struct mesh *m, struct behavior *b,
07645                          vertex searchpoint, struct otri *searchtri)
07646 #else /* not ANSI_DECLARATORS */
07647 enum locateresult locate(m, b, searchpoint, searchtri)
07648 struct mesh *m;
07649 struct behavior *b;
07650 vertex searchpoint;
07651 struct otri *searchtri;
07652 #endif /* not ANSI_DECLARATORS */
07653 
07654 {
07655   VOID **sampleblock;
07656   char *firsttri;
07657   struct otri sampletri;
07658   vertex torg, tdest;
07659   unsigned long alignptr;
07660   REAL searchdist, dist;
07661   REAL ahead;
07662   long samplesperblock, totalsamplesleft, samplesleft;
07663   long population, totalpopulation;
07664   triangle ptr;                         /* Temporary variable used by sym(). */
07665 
07666   if (b->verbose > 2) {
07667     printf("  Randomly sampling for a triangle near point (%.12g, %.12g).\n",
07668            searchpoint[0], searchpoint[1]);
07669   }
07670   /* Record the distance from the suggested starting triangle to the */
07671   /*   point we seek.                                                */
07672   org(*searchtri, torg);
07673   searchdist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) +
07674                (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]);
07675   if (b->verbose > 2) {
07676     printf("    Boundary triangle has origin (%.12g, %.12g).\n",
07677            torg[0], torg[1]);
07678   }
07679 
07680   /* If a recently encountered triangle has been recorded and has not been */
07681   /*   deallocated, test it as a good starting point.                      */
07682   if (m->recenttri.tri != (triangle *) NULL) {
07683     if (!deadtri(m->recenttri.tri)) {
07684       org(m->recenttri, torg);
07685       if ((torg[0] == searchpoint[0]) && (torg[1] == searchpoint[1])) {
07686         otricopy(m->recenttri, *searchtri);
07687         return ONVERTEX;
07688       }
07689       dist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) +
07690              (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]);
07691       if (dist < searchdist) {
07692         otricopy(m->recenttri, *searchtri);
07693         searchdist = dist;
07694         if (b->verbose > 2) {
07695           printf("    Choosing recent triangle with origin (%.12g, %.12g).\n",
07696                  torg[0], torg[1]);
07697         }
07698       }
07699     }
07700   }
07701 
07702   /* The number of random samples taken is proportional to the cube root of */
07703   /*   the number of triangles in the mesh.  The next bit of code assumes   */
07704   /*   that the number of triangles increases monotonically (or at least    */
07705   /*   doesn't decrease enough to matter).                                  */
07706   while (SAMPLEFACTOR * m->samples * m->samples * m->samples <
07707          m->triangles.items) {
07708     m->samples++;
07709   }
07710 
07711   /* We'll draw ceiling(samples * TRIPERBLOCK / maxitems) random samples  */
07712   /*   from each block of triangles (except the first)--until we meet the */
07713   /*   sample quota.  The ceiling means that blocks at the end might be   */
07714   /*   neglected, but I don't care.                                       */
07715   samplesperblock = (m->samples * TRIPERBLOCK - 1) / m->triangles.maxitems + 1;
07716   /* We'll draw ceiling(samples * itemsfirstblock / maxitems) random samples */
07717   /*   from the first block of triangles.                                    */
07718   samplesleft = (m->samples * m->triangles.itemsfirstblock - 1) /
07719                 m->triangles.maxitems + 1;
07720   totalsamplesleft = m->samples;
07721   population = m->triangles.itemsfirstblock;
07722   totalpopulation = m->triangles.maxitems;
07723   sampleblock = m->triangles.firstblock;
07724   sampletri.orient = 0;
07725   while (totalsamplesleft > 0) {
07726     /* If we're in the last block, `population' needs to be corrected. */
07727     if (population > totalpopulation) {
07728       population = totalpopulation;
07729     }
07730     /* Find a pointer to the first triangle in the block. */
07731     alignptr = (unsigned long) (sampleblock + 1);
07732     firsttri = (char *) (alignptr +
07733                          (unsigned long) m->triangles.alignbytes -
07734                          (alignptr %
07735                           (unsigned long) m->triangles.alignbytes));
07736 
07737     /* Choose `samplesleft' randomly sampled triangles in this block. */
07738     do {
07739       sampletri.tri = (triangle *) (firsttri +
07740                                     (randomnation((unsigned int) population) *
07741                                      m->triangles.itembytes));
07742       if (!deadtri(sampletri.tri)) {
07743         org(sampletri, torg);
07744         dist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) +
07745                (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]);
07746         if (dist < searchdist) {
07747           otricopy(sampletri, *searchtri);
07748           searchdist = dist;
07749           if (b->verbose > 2) {
07750             printf("    Choosing triangle with origin (%.12g, %.12g).\n",
07751                    torg[0], torg[1]);
07752           }
07753         }
07754       }
07755 
07756       samplesleft--;
07757       totalsamplesleft--;
07758     } while ((samplesleft > 0) && (totalsamplesleft > 0));
07759 
07760     if (totalsamplesleft > 0) {
07761       sampleblock = (VOID **) *sampleblock;
07762       samplesleft = samplesperblock;
07763       totalpopulation -= population;
07764       population = TRIPERBLOCK;
07765     }
07766   }
07767 
07768   /* Where are we? */
07769   org(*searchtri, torg);
07770   dest(*searchtri, tdest);
07771   /* Check the starting triangle's vertices. */
07772   if ((torg[0] == searchpoint[0]) && (torg[1] == searchpoint[1])) {
07773     return ONVERTEX;
07774   }
07775   if ((tdest[0] == searchpoint[0]) && (tdest[1] == searchpoint[1])) {
07776     lnextself(*searchtri);
07777     return ONVERTEX;
07778   }
07779   /* Orient `searchtri' to fit the preconditions of calling preciselocate(). */
07780   ahead = counterclockwise(m, b, torg, tdest, searchpoint);
07781   if (ahead < 0.0) {
07782     /* Turn around so that `searchpoint' is to the left of the */
07783     /*   edge specified by `searchtri'.                        */
07784     symself(*searchtri);
07785   } else if (ahead == 0.0) {
07786     /* Check if `searchpoint' is between `torg' and `tdest'. */
07787     if (((torg[0] < searchpoint[0]) == (searchpoint[0] < tdest[0])) &&
07788         ((torg[1] < searchpoint[1]) == (searchpoint[1] < tdest[1]))) {
07789       return ONEDGE;
07790     }
07791   }
07792   return preciselocate(m, b, searchpoint, searchtri, 0);
07793 }
07794 
07797 /********* Point location routines end here                          *********/
07798 
07799 /********* Mesh transformation routines begin here                   *********/
07803 /*****************************************************************************/
07804 /*                                                                           */
07805 /*  insertsubseg()   Create a new subsegment and insert it between two       */
07806 /*                   triangles.                                              */
07807 /*                                                                           */
07808 /*  The new subsegment is inserted at the edge described by the handle       */
07809 /*  `tri'.  Its vertices are properly initialized.  The marker `subsegmark'  */
07810 /*  is applied to the subsegment and, if appropriate, its vertices.          */
07811 /*                                                                           */
07812 /*****************************************************************************/
07813 
07814 #ifdef ANSI_DECLARATORS
07815 void insertsubseg(struct mesh *m, struct behavior *b, struct otri *tri,
07816                   int subsegmark)
07817 #else /* not ANSI_DECLARATORS */
07818 void insertsubseg(m, b, tri, subsegmark)
07819 struct mesh *m;
07820 struct behavior *b;
07821 struct otri *tri;             /* Edge at which to insert the new subsegment. */
07822 int subsegmark;                            /* Marker for the new subsegment. */
07823 #endif /* not ANSI_DECLARATORS */
07824 
07825 {
07826   struct otri oppotri;
07827   struct osub newsubseg;
07828   vertex triorg, tridest;
07829   triangle ptr;                         /* Temporary variable used by sym(). */
07830   subseg sptr;                      /* Temporary variable used by tspivot(). */
07831 
07832   org(*tri, triorg);
07833   dest(*tri, tridest);
07834   /* Mark vertices if possible. */
07835   if (vertexmark(triorg) == 0) {
07836     setvertexmark(triorg, subsegmark);
07837   }
07838   if (vertexmark(tridest) == 0) {
07839     setvertexmark(tridest, subsegmark);
07840   }
07841   /* Check if there's already a subsegment here. */
07842   tspivot(*tri, newsubseg);
07843   if (newsubseg.ss == m->dummysub) {
07844     /* Make new subsegment and initialize its vertices. */
07845     makesubseg(m, &newsubseg);
07846     setsorg(newsubseg, tridest);
07847     setsdest(newsubseg, triorg);
07848     setsegorg(newsubseg, tridest);
07849     setsegdest(newsubseg, triorg);
07850     /* Bond new subsegment to the two triangles it is sandwiched between. */
07851     /*   Note that the facing triangle `oppotri' might be equal to        */
07852     /*   `dummytri' (outer space), but the new subsegment is bonded to it */
07853     /*   all the same.                                                    */
07854     tsbond(*tri, newsubseg);
07855     sym(*tri, oppotri);
07856     ssymself(newsubseg);
07857     tsbond(oppotri, newsubseg);
07858     setmark(newsubseg, subsegmark);
07859     if (b->verbose > 2) {
07860       printf("  Inserting new ");
07861       printsubseg(m, b, &newsubseg);
07862     }
07863   } else {
07864     if (mark(newsubseg) == 0) {
07865       setmark(newsubseg, subsegmark);
07866     }
07867   }
07868 }
07869 
07870 /*****************************************************************************/
07871 /*                                                                           */
07872 /*  Terminology                                                              */
07873 /*                                                                           */
07874 /*  A "local transformation" replaces a small set of triangles with another  */
07875 /*  set of triangles.  This may or may not involve inserting or deleting a   */
07876 /*  vertex.                                                                  */
07877 /*                                                                           */
07878 /*  The term "casing" is used to describe the set of triangles that are      */
07879 /*  attached to the triangles being transformed, but are not transformed     */
07880 /*  themselves.  Think of the casing as a fixed hollow structure inside      */
07881 /*  which all the action happens.  A "casing" is only defined relative to    */
07882 /*  a single transformation; each occurrence of a transformation will        */
07883 /*  involve a different casing.                                              */
07884 /*                                                                           */
07885 /*****************************************************************************/
07886 
07887 /*****************************************************************************/
07888 /*                                                                           */
07889 /*  flip()   Transform two triangles to two different triangles by flipping  */
07890 /*           an edge counterclockwise within a quadrilateral.                */
07891 /*                                                                           */
07892 /*  Imagine the original triangles, abc and bad, oriented so that the        */
07893 /*  shared edge ab lies in a horizontal plane, with the vertex b on the left */
07894 /*  and the vertex a on the right.  The vertex c lies below the edge, and    */
07895 /*  the vertex d lies above the edge.  The `flipedge' handle holds the edge  */
07896 /*  ab of triangle abc, and is directed left, from vertex a to vertex b.     */
07897 /*                                                                           */
07898 /*  The triangles abc and bad are deleted and replaced by the triangles cdb  */
07899 /*  and dca.  The triangles that represent abc and bad are NOT deallocated;  */
07900 /*  they are reused for dca and cdb, respectively.  Hence, any handles that  */
07901 /*  may have held the original triangles are still valid, although not       */
07902 /*  directed as they were before.                                            */
07903 /*                                                                           */
07904 /*  Upon completion of this routine, the `flipedge' handle holds the edge    */
07905 /*  dc of triangle dca, and is directed down, from vertex d to vertex c.     */
07906 /*  (Hence, the two triangles have rotated counterclockwise.)                */
07907 /*                                                                           */
07908 /*  WARNING:  This transformation is geometrically valid only if the         */
07909 /*  quadrilateral adbc is convex.  Furthermore, this transformation is       */
07910 /*  valid only if there is not a subsegment between the triangles abc and    */
07911 /*  bad.  This routine does not check either of these preconditions, and     */
07912 /*  it is the responsibility of the calling routine to ensure that they are  */
07913 /*  met.  If they are not, the streets shall be filled with wailing and      */
07914 /*  gnashing of teeth.                                                       */
07915 /*                                                                           */
07916 /*****************************************************************************/
07917 
07918 #ifdef ANSI_DECLARATORS
07919 void flip(struct mesh *m, struct behavior *b, struct otri *flipedge)
07920 #else /* not ANSI_DECLARATORS */
07921 void flip(m, b, flipedge)
07922 struct mesh *m;
07923 struct behavior *b;
07924 struct otri *flipedge;                    /* Handle for the triangle abc. */
07925 #endif /* not ANSI_DECLARATORS */
07926 
07927 {
07928   struct otri botleft, botright;
07929   struct otri topleft, topright;
07930   struct otri top;
07931   struct otri botlcasing, botrcasing;
07932   struct otri toplcasing, toprcasing;
07933   struct osub botlsubseg, botrsubseg;
07934   struct osub toplsubseg, toprsubseg;
07935   vertex leftvertex, rightvertex, botvertex;
07936   vertex farvertex;
07937   triangle ptr;                         /* Temporary variable used by sym(). */
07938   subseg sptr;                      /* Temporary variable used by tspivot(). */
07939 
07940   /* Identify the vertices of the quadrilateral. */
07941   org(*flipedge, rightvertex);
07942   dest(*flipedge, leftvertex);
07943   apex(*flipedge, botvertex);
07944   sym(*flipedge, top);
07945 #ifdef SELF_CHECK
07946   if (top.tri == m->dummytri) {
07947     printf("Internal error in flip():  Attempt to flip on boundary.\n");
07948     lnextself(*flipedge);
07949     return;
07950   }
07951   if (m->checksegments) {
07952     tspivot(*flipedge, toplsubseg);
07953     if (toplsubseg.ss != m->dummysub) {
07954       printf("Internal error in flip():  Attempt to flip a segment.\n");
07955       lnextself(*flipedge);
07956       return;
07957     }
07958   }
07959 #endif /* SELF_CHECK */
07960   apex(top, farvertex);
07961 
07962   /* Identify the casing of the quadrilateral. */
07963   lprev(top, topleft);
07964   sym(topleft, toplcasing);
07965   lnext(top, topright);
07966   sym(topright, toprcasing);
07967   lnext(*flipedge, botleft);
07968   sym(botleft, botlcasing);
07969   lprev(*flipedge, botright);
07970   sym(botright, botrcasing);
07971   /* Rotate the quadrilateral one-quarter turn counterclockwise. */
07972   bond(topleft, botlcasing);
07973   bond(botleft, botrcasing);
07974   bond(botright, toprcasing);
07975   bond(topright, toplcasing);
07976 
07977   if (m->checksegments) {
07978     /* Check for subsegments and rebond them to the quadrilateral. */
07979     tspivot(topleft, toplsubseg);
07980     tspivot(botleft, botlsubseg);
07981     tspivot(botright, botrsubseg);
07982     tspivot(topright, toprsubseg);
07983     if (toplsubseg.ss == m->dummysub) {
07984       tsdissolve(topright);
07985     } else {
07986       tsbond(topright, toplsubseg);
07987     }
07988     if (botlsubseg.ss == m->dummysub) {
07989       tsdissolve(topleft);
07990     } else {
07991       tsbond(topleft, botlsubseg);
07992     }
07993     if (botrsubseg.ss == m->dummysub) {
07994       tsdissolve(botleft);
07995     } else {
07996       tsbond(botleft, botrsubseg);
07997     }
07998     if (toprsubseg.ss == m->dummysub) {
07999       tsdissolve(botright);
08000     } else {
08001       tsbond(botright, toprsubseg);
08002     }
08003   }
08004 
08005   /* New vertex assignments for the rotated quadrilateral. */
08006   setorg(*flipedge, farvertex);
08007   setdest(*flipedge, botvertex);
08008   setapex(*flipedge, rightvertex);
08009   setorg(top, botvertex);
08010   setdest(top, farvertex);
08011   setapex(top, leftvertex);
08012   if (b->verbose > 2) {
08013     printf("  Edge flip results in left ");
08014     printtriangle(m, b, &top);
08015     printf("  and right ");
08016     printtriangle(m, b, flipedge);
08017   }
08018 }
08019 
08020 /*****************************************************************************/
08021 /*                                                                           */
08022 /*  unflip()   Transform two triangles to two different triangles by         */
08023 /*             flipping an edge clockwise within a quadrilateral.  Reverses  */
08024 /*             the flip() operation so that the data structures representing */
08025 /*             the triangles are back where they were before the flip().     */
08026 /*                                                                           */
08027 /*  Imagine the original triangles, abc and bad, oriented so that the        */
08028 /*  shared edge ab lies in a horizontal plane, with the vertex b on the left */
08029 /*  and the vertex a on the right.  The vertex c lies below the edge, and    */
08030 /*  the vertex d lies above the edge.  The `flipedge' handle holds the edge  */
08031 /*  ab of triangle abc, and is directed left, from vertex a to vertex b.     */
08032 /*                                                                           */
08033 /*  The triangles abc and bad are deleted and replaced by the triangles cdb  */
08034 /*  and dca.  The triangles that represent abc and bad are NOT deallocated;  */
08035 /*  they are reused for cdb and dca, respectively.  Hence, any handles that  */
08036 /*  may have held the original triangles are still valid, although not       */
08037 /*  directed as they were before.                                            */
08038 /*                                                                           */
08039 /*  Upon completion of this routine, the `flipedge' handle holds the edge    */
08040 /*  cd of triangle cdb, and is directed up, from vertex c to vertex d.       */
08041 /*  (Hence, the two triangles have rotated clockwise.)                       */
08042 /*                                                                           */
08043 /*  WARNING:  This transformation is geometrically valid only if the         */
08044 /*  quadrilateral adbc is convex.  Furthermore, this transformation is       */
08045 /*  valid only if there is not a subsegment between the triangles abc and    */
08046 /*  bad.  This routine does not check either of these preconditions, and     */
08047 /*  it is the responsibility of the calling routine to ensure that they are  */
08048 /*  met.  If they are not, the streets shall be filled with wailing and      */
08049 /*  gnashing of teeth.                                                       */
08050 /*                                                                           */
08051 /*****************************************************************************/
08052 
08053 #ifdef ANSI_DECLARATORS
08054 void unflip(struct mesh *m, struct behavior *b, struct otri *flipedge)
08055 #else /* not ANSI_DECLARATORS */
08056 void unflip(m, b, flipedge)
08057 struct mesh *m;
08058 struct behavior *b;
08059 struct otri *flipedge;                    /* Handle for the triangle abc. */
08060 #endif /* not ANSI_DECLARATORS */
08061 
08062 {
08063   struct otri botleft, botright;
08064   struct otri topleft, topright;
08065   struct otri top;
08066   struct otri botlcasing, botrcasing;
08067   struct otri toplcasing, toprcasing;
08068   struct osub botlsubseg, botrsubseg;
08069   struct osub toplsubseg, toprsubseg;
08070   vertex leftvertex, rightvertex, botvertex;
08071   vertex farvertex;
08072   triangle ptr;                         /* Temporary variable used by sym(). */
08073   subseg sptr;                      /* Temporary variable used by tspivot(). */
08074 
08075   /* Identify the vertices of the quadrilateral. */
08076   org(*flipedge, rightvertex);
08077   dest(*flipedge, leftvertex);
08078   apex(*flipedge, botvertex);
08079   sym(*flipedge, top);
08080 #ifdef SELF_CHECK
08081   if (top.tri == m->dummytri) {
08082     printf("Internal error in unflip():  Attempt to flip on boundary.\n");
08083     lnextself(*flipedge);
08084     return;
08085   }
08086   if (m->checksegments) {
08087     tspivot(*flipedge, toplsubseg);
08088     if (toplsubseg.ss != m->dummysub) {
08089       printf("Internal error in unflip():  Attempt to flip a subsegment.\n");
08090       lnextself(*flipedge);
08091       return;
08092     }
08093   }
08094 #endif /* SELF_CHECK */
08095   apex(top, farvertex);
08096 
08097   /* Identify the casing of the quadrilateral. */
08098   lprev(top, topleft);
08099   sym(topleft, toplcasing);
08100   lnext(top, topright);
08101   sym(topright, toprcasing);
08102   lnext(*flipedge, botleft);
08103   sym(botleft, botlcasing);
08104   lprev(*flipedge, botright);
08105   sym(botright, botrcasing);
08106   /* Rotate the quadrilateral one-quarter turn clockwise. */
08107   bond(topleft, toprcasing);
08108   bond(botleft, toplcasing);
08109   bond(botright, botlcasing);
08110   bond(topright, botrcasing);
08111 
08112   if (m->checksegments) {
08113     /* Check for subsegments and rebond them to the quadrilateral. */
08114     tspivot(topleft, toplsubseg);
08115     tspivot(botleft, botlsubseg);
08116     tspivot(botright, botrsubseg);
08117     tspivot(topright, toprsubseg);
08118     if (toplsubseg.ss == m->dummysub) {
08119       tsdissolve(botleft);
08120     } else {
08121       tsbond(botleft, toplsubseg);
08122     }
08123     if (botlsubseg.ss == m->dummysub) {
08124       tsdissolve(botright);
08125     } else {
08126       tsbond(botright, botlsubseg);
08127     }
08128     if (botrsubseg.ss == m->dummysub) {
08129       tsdissolve(topright);
08130     } else {
08131       tsbond(topright, botrsubseg);
08132     }
08133     if (toprsubseg.ss == m->dummysub) {
08134       tsdissolve(topleft);
08135     } else {
08136       tsbond(topleft, toprsubseg);
08137     }
08138   }
08139 
08140   /* New vertex assignments for the rotated quadrilateral. */
08141   setorg(*flipedge, botvertex);
08142   setdest(*flipedge, farvertex);
08143   setapex(*flipedge, leftvertex);
08144   setorg(top, farvertex);
08145   setdest(top, botvertex);
08146   setapex(top, rightvertex);
08147   if (b->verbose > 2) {
08148     printf("  Edge unflip results in left ");
08149     printtriangle(m, b, flipedge);
08150     printf("  and right ");
08151     printtriangle(m, b, &top);
08152   }
08153 }
08154 
08155 /*****************************************************************************/
08156 /*                                                                           */
08157 /*  insertvertex()   Insert a vertex into a Delaunay triangulation,          */
08158 /*                   performing flips as necessary to maintain the Delaunay  */
08159 /*                   property.                                               */
08160 /*                                                                           */
08161 /*  The point `insertvertex' is located.  If `searchtri.tri' is not NULL,    */
08162 /*  the search for the containing triangle begins from `searchtri'.  If      */
08163 /*  `searchtri.tri' is NULL, a full point location procedure is called.      */
08164 /*  If `insertvertex' is found inside a triangle, the triangle is split into */
08165 /*  three; if `insertvertex' lies on an edge, the edge is split in two,      */
08166 /*  thereby splitting the two adjacent triangles into four.  Edge flips are  */
08167 /*  used to restore the Delaunay property.  If `insertvertex' lies on an     */
08168 /*  existing vertex, no action is taken, and the value DUPLICATEVERTEX is    */
08169 /*  returned.  On return, `searchtri' is set to a handle whose origin is the */
08170 /*  existing vertex.                                                         */
08171 /*                                                                           */
08172 /*  Normally, the parameter `splitseg' is set to NULL, implying that no      */
08173 /*  subsegment should be split.  In this case, if `insertvertex' is found to */
08174 /*  lie on a segment, no action is taken, and the value VIOLATINGVERTEX is   */
08175 /*  returned.  On return, `searchtri' is set to a handle whose primary edge  */
08176 /*  is the violated subsegment.                                              */
08177 /*                                                                           */
08178 /*  If the calling routine wishes to split a subsegment by inserting a       */
08179 /*  vertex in it, the parameter `splitseg' should be that subsegment.  In    */
08180 /*  this case, `searchtri' MUST be the triangle handle reached by pivoting   */
08181 /*  from that subsegment; no point location is done.                         */
08182 /*                                                                           */
08183 /*  `segmentflaws' and `triflaws' are flags that indicate whether or not     */
08184 /*  there should be checks for the creation of encroached subsegments or bad */
08185 /*  quality triangles.  If a newly inserted vertex encroaches upon           */
08186 /*  subsegments, these subsegments are added to the list of subsegments to   */
08187 /*  be split if `segmentflaws' is set.  If bad triangles are created, these  */
08188 /*  are added to the queue if `triflaws' is set.                             */
08189 /*                                                                           */
08190 /*  If a duplicate vertex or violated segment does not prevent the vertex    */
08191 /*  from being inserted, the return value will be ENCROACHINGVERTEX if the   */
08192 /*  vertex encroaches upon a subsegment (and checking is enabled), or        */
08193 /*  SUCCESSFULVERTEX otherwise.  In either case, `searchtri' is set to a     */
08194 /*  handle whose origin is the newly inserted vertex.                        */
08195 /*                                                                           */
08196 /*  insertvertex() does not use flip() for reasons of speed; some            */
08197 /*  information can be reused from edge flip to edge flip, like the          */
08198 /*  locations of subsegments.                                                */
08199 /*                                                                           */
08200 /*****************************************************************************/
08201 
08202 #ifdef ANSI_DECLARATORS
08203 enum insertvertexresult insertvertex(struct mesh *m, struct behavior *b,
08204                                      vertex newvertex, struct otri *searchtri,
08205                                      struct osub *splitseg,
08206                                      int segmentflaws, int triflaws)
08207 #else /* not ANSI_DECLARATORS */
08208 enum insertvertexresult insertvertex(m, b, newvertex, searchtri, splitseg,
08209                                      segmentflaws, triflaws)
08210 struct mesh *m;
08211 struct behavior *b;
08212 vertex newvertex;
08213 struct otri *searchtri;
08214 struct osub *splitseg;
08215 int segmentflaws;
08216 int triflaws;
08217 #endif /* not ANSI_DECLARATORS */
08218 
08219 {
08220   struct otri horiz;
08221   struct otri top;
08222   struct otri botleft, botright;
08223   struct otri topleft, topright;
08224   struct otri newbotleft, newbotright;
08225   struct otri newtopright;
08226   struct otri botlcasing, botrcasing;
08227   struct otri toplcasing={NULL, 0}, toprcasing={NULL, 0};
08228   struct otri testtri;
08229   struct osub botlsubseg, botrsubseg;
08230   struct osub toplsubseg, toprsubseg;
08231   struct osub brokensubseg;
08232   struct osub checksubseg;
08233   struct osub rightsubseg;
08234   struct osub newsubseg;
08235   struct badsubseg *encroached;
08236   struct flipstacker *newflip;
08237   vertex first;
08238   vertex leftvertex, rightvertex, botvertex, topvertex, farvertex;
08239   vertex segmentorg, segmentdest;
08240   REAL attrib;
08241   REAL area;
08242   enum insertvertexresult success;
08243   enum locateresult intersect;
08244   int doflip;
08245   int mirrorflag;
08246   int enq;
08247   int i;
08248   triangle ptr;                         /* Temporary variable used by sym(). */
08249   subseg sptr;         /* Temporary variable used by spivot() and tspivot(). */
08250 
08251   if (b->verbose > 1) {
08252     printf("  Inserting (%.12g, %.12g).\n", newvertex[0], newvertex[1]);
08253   }
08254 
08255   if (splitseg == (struct osub *) NULL) {
08256     /* Find the location of the vertex to be inserted.  Check if a good */
08257     /*   starting triangle has already been provided by the caller.     */
08258     if (searchtri->tri == m->dummytri) {
08259       /* Find a boundary triangle. */
08260       horiz.tri = m->dummytri;
08261       horiz.orient = 0;
08262       symself(horiz);
08263       /* Search for a triangle containing `newvertex'. */
08264       intersect = locate(m, b, newvertex, &horiz);
08265     } else {
08266       /* Start searching from the triangle provided by the caller. */
08267       otricopy(*searchtri, horiz);
08268       intersect = preciselocate(m, b, newvertex, &horiz, 1);
08269     }
08270   } else {
08271     /* The calling routine provides the subsegment in which */
08272     /*   the vertex is inserted.                             */
08273     otricopy(*searchtri, horiz);
08274     intersect = ONEDGE;
08275   }
08276 
08277   if (intersect == ONVERTEX) {
08278     /* There's already a vertex there.  Return in `searchtri' a triangle */
08279     /*   whose origin is the existing vertex.                            */
08280     otricopy(horiz, *searchtri);
08281     otricopy(horiz, m->recenttri);
08282     return DUPLICATEVERTEX;
08283   }
08284   if ((intersect == ONEDGE) || (intersect == OUTSIDE)) {
08285     /* The vertex falls on an edge or boundary. */
08286     if (m->checksegments && (splitseg == (struct osub *) NULL)) {
08287       /* Check whether the vertex falls on a subsegment. */
08288       tspivot(horiz, brokensubseg);
08289       if (brokensubseg.ss != m->dummysub) {
08290         /* The vertex falls on a subsegment, and hence will not be inserted. */
08291         if (segmentflaws) {
08292           enq = b->nobisect != 2;
08293           if (enq && (b->nobisect == 1)) {
08294             /* This subsegment may be split only if it is an */
08295             /*   internal boundary.                          */
08296             sym(horiz, testtri);
08297             enq = testtri.tri != m->dummytri;
08298           }
08299           if (enq) {
08300             /* Add the subsegment to the list of encroached subsegments. */
08301             encroached = (struct badsubseg *) poolalloc(&m->badsubsegs);
08302             encroached->encsubseg = sencode(brokensubseg);
08303             sorg(brokensubseg, encroached->subsegorg);
08304             sdest(brokensubseg, encroached->subsegdest);
08305             if (b->verbose > 2) {
08306               printf(
08307           "  Queueing encroached subsegment (%.12g, %.12g) (%.12g, %.12g).\n",
08308                      encroached->subsegorg[0], encroached->subsegorg[1],
08309                      encroached->subsegdest[0], encroached->subsegdest[1]);
08310             }
08311           }
08312         }
08313         /* Return a handle whose primary edge contains the vertex, */
08314         /*   which has not been inserted.                          */
08315         otricopy(horiz, *searchtri);
08316         otricopy(horiz, m->recenttri);
08317         return VIOLATINGVERTEX;
08318       }
08319     }
08320 
08321     /* Insert the vertex on an edge, dividing one triangle into two (if */
08322     /*   the edge lies on a boundary) or two triangles into four.       */
08323     lprev(horiz, botright);
08324     sym(botright, botrcasing);
08325     sym(horiz, topright);
08326     /* Is there a second triangle?  (Or does this edge lie on a boundary?) */
08327     mirrorflag = topright.tri != m->dummytri;
08328     if (mirrorflag) {
08329       lnextself(topright);
08330       sym(topright, toprcasing);
08331       maketriangle(m, b, &newtopright);
08332     } else {
08333       /* Splitting a boundary edge increases the number of boundary edges. */
08334       m->hullsize++;
08335     }
08336     maketriangle(m, b, &newbotright);
08337 
08338     /* Set the vertices of changed and new triangles. */
08339     org(horiz, rightvertex);
08340     dest(horiz, leftvertex);
08341     apex(horiz, botvertex);
08342     setorg(newbotright, botvertex);
08343     setdest(newbotright, rightvertex);
08344     setapex(newbotright, newvertex);
08345     setorg(horiz, newvertex);
08346     for (i = 0; i < m->eextras; i++) {
08347       /* Set the element attributes of a new triangle. */
08348       setelemattribute(newbotright, i, elemattribute(botright, i));
08349     }
08350     if (b->vararea) {
08351       /* Set the area constraint of a new triangle. */
08352       setareabound(newbotright, areabound(botright));
08353     }
08354     if (mirrorflag) {
08355       dest(topright, topvertex);
08356       setorg(newtopright, rightvertex);
08357       setdest(newtopright, topvertex);
08358       setapex(newtopright, newvertex);
08359       setorg(topright, newvertex);
08360       for (i = 0; i < m->eextras; i++) {
08361         /* Set the element attributes of another new triangle. */
08362         setelemattribute(newtopright, i, elemattribute(topright, i));
08363       }
08364       if (b->vararea) {
08365         /* Set the area constraint of another new triangle. */
08366         setareabound(newtopright, areabound(topright));
08367       }
08368     }
08369 
08370     /* There may be subsegments that need to be bonded */
08371     /*   to the new triangle(s).                       */
08372     if (m->checksegments) {
08373       tspivot(botright, botrsubseg);
08374       if (botrsubseg.ss != m->dummysub) {
08375         tsdissolve(botright);
08376         tsbond(newbotright, botrsubseg);
08377       }
08378       if (mirrorflag) {
08379         tspivot(topright, toprsubseg);
08380         if (toprsubseg.ss != m->dummysub) {
08381           tsdissolve(topright);
08382           tsbond(newtopright, toprsubseg);
08383         }
08384       }
08385     }
08386 
08387     /* Bond the new triangle(s) to the surrounding triangles. */
08388     bond(newbotright, botrcasing);
08389     lprevself(newbotright);
08390     bond(newbotright, botright);
08391     lprevself(newbotright);
08392     if (mirrorflag) {
08393       bond(newtopright, toprcasing);
08394       lnextself(newtopright);
08395       bond(newtopright, topright);
08396       lnextself(newtopright);
08397       bond(newtopright, newbotright);
08398     }
08399 
08400     if (splitseg != (struct osub *) NULL) {
08401       /* Split the subsegment into two. */
08402       setsdest(*splitseg, newvertex);
08403       segorg(*splitseg, segmentorg);
08404       segdest(*splitseg, segmentdest);
08405       ssymself(*splitseg);
08406       spivot(*splitseg, rightsubseg);
08407       insertsubseg(m, b, &newbotright, mark(*splitseg));
08408       tspivot(newbotright, newsubseg);
08409       setsegorg(newsubseg, segmentorg);
08410       setsegdest(newsubseg, segmentdest);
08411       sbond(*splitseg, newsubseg);
08412       ssymself(newsubseg);
08413       sbond(newsubseg, rightsubseg);
08414       ssymself(*splitseg);
08415       /* Transfer the subsegment's boundary marker to the vertex */
08416       /*   if required.                                          */
08417       if (vertexmark(newvertex) == 0) {
08418         setvertexmark(newvertex, mark(*splitseg));
08419       }
08420     }
08421 
08422     if (m->checkquality) {
08423       poolrestart(&m->flipstackers);
08424       m->lastflip = (struct flipstacker *) poolalloc(&m->flipstackers);
08425       m->lastflip->flippedtri = encode(horiz);
08426       m->lastflip->prevflip = (struct flipstacker *) &insertvertex;
08427     }
08428 
08429 #ifdef SELF_CHECK
08430     if (counterclockwise(m, b, rightvertex, leftvertex, botvertex) < 0.0) {
08431       printf("Internal error in insertvertex():\n");
08432       printf(
08433             "  Clockwise triangle prior to edge vertex insertion (bottom).\n");
08434     }
08435     if (mirrorflag) {
08436       if (counterclockwise(m, b, leftvertex, rightvertex, topvertex) < 0.0) {
08437         printf("Internal error in insertvertex():\n");
08438         printf("  Clockwise triangle prior to edge vertex insertion (top).\n");
08439       }
08440       if (counterclockwise(m, b, rightvertex, topvertex, newvertex) < 0.0) {
08441         printf("Internal error in insertvertex():\n");
08442         printf(
08443             "  Clockwise triangle after edge vertex insertion (top right).\n");
08444       }
08445       if (counterclockwise(m, b, topvertex, leftvertex, newvertex) < 0.0) {
08446         printf("Internal error in insertvertex():\n");
08447         printf(
08448             "  Clockwise triangle after edge vertex insertion (top left).\n");
08449       }
08450     }
08451     if (counterclockwise(m, b, leftvertex, botvertex, newvertex) < 0.0) {
08452       printf("Internal error in insertvertex():\n");
08453       printf(
08454           "  Clockwise triangle after edge vertex insertion (bottom left).\n");
08455     }
08456     if (counterclockwise(m, b, botvertex, rightvertex, newvertex) < 0.0) {
08457       printf("Internal error in insertvertex():\n");
08458       printf(
08459         "  Clockwise triangle after edge vertex insertion (bottom right).\n");
08460     }
08461 #endif /* SELF_CHECK */
08462     if (b->verbose > 2) {
08463       printf("  Updating bottom left ");
08464       printtriangle(m, b, &botright);
08465       if (mirrorflag) {
08466         printf("  Updating top left ");
08467         printtriangle(m, b, &topright);
08468         printf("  Creating top right ");
08469         printtriangle(m, b, &newtopright);
08470       }
08471       printf("  Creating bottom right ");
08472       printtriangle(m, b, &newbotright);
08473     }
08474 
08475     /* Position `horiz' on the first edge to check for */
08476     /*   the Delaunay property.                        */
08477     lnextself(horiz);
08478   } else {
08479     /* Insert the vertex in a triangle, splitting it into three. */
08480     lnext(horiz, botleft);
08481     lprev(horiz, botright);
08482     sym(botleft, botlcasing);
08483     sym(botright, botrcasing);
08484     maketriangle(m, b, &newbotleft);
08485     maketriangle(m, b, &newbotright);
08486 
08487     /* Set the vertices of changed and new triangles. */
08488     org(horiz, rightvertex);
08489     dest(horiz, leftvertex);
08490     apex(horiz, botvertex);
08491     setorg(newbotleft, leftvertex);
08492     setdest(newbotleft, botvertex);
08493     setapex(newbotleft, newvertex);
08494     setorg(newbotright, botvertex);
08495     setdest(newbotright, rightvertex);
08496     setapex(newbotright, newvertex);
08497     setapex(horiz, newvertex);
08498     for (i = 0; i < m->eextras; i++) {
08499       /* Set the element attributes of the new triangles. */
08500       attrib = elemattribute(horiz, i);
08501       setelemattribute(newbotleft, i, attrib);
08502       setelemattribute(newbotright, i, attrib);
08503     }
08504     if (b->vararea) {
08505       /* Set the area constraint of the new triangles. */
08506       area = areabound(horiz);
08507       setareabound(newbotleft, area);
08508       setareabound(newbotright, area);
08509     }
08510 
08511     /* There may be subsegments that need to be bonded */
08512     /*   to the new triangles.                         */
08513     if (m->checksegments) {
08514       tspivot(botleft, botlsubseg);
08515       if (botlsubseg.ss != m->dummysub) {
08516         tsdissolve(botleft);
08517         tsbond(newbotleft, botlsubseg);
08518       }
08519       tspivot(botright, botrsubseg);
08520       if (botrsubseg.ss != m->dummysub) {
08521         tsdissolve(botright);
08522         tsbond(newbotright, botrsubseg);
08523       }
08524     }
08525 
08526     /* Bond the new triangles to the surrounding triangles. */
08527     bond(newbotleft, botlcasing);
08528     bond(newbotright, botrcasing);
08529     lnextself(newbotleft);
08530     lprevself(newbotright);
08531     bond(newbotleft, newbotright);
08532     lnextself(newbotleft);
08533     bond(botleft, newbotleft);
08534     lprevself(newbotright);
08535     bond(botright, newbotright);
08536 
08537     if (m->checkquality) {
08538       poolrestart(&m->flipstackers);
08539       m->lastflip = (struct flipstacker *) poolalloc(&m->flipstackers);
08540       m->lastflip->flippedtri = encode(horiz);
08541       m->lastflip->prevflip = (struct flipstacker *) NULL;
08542     }
08543 
08544 #ifdef SELF_CHECK
08545     if (counterclockwise(m, b, rightvertex, leftvertex, botvertex) < 0.0) {
08546       printf("Internal error in insertvertex():\n");
08547       printf("  Clockwise triangle prior to vertex insertion.\n");
08548     }
08549     if (counterclockwise(m, b, rightvertex, leftvertex, newvertex) < 0.0) {
08550       printf("Internal error in insertvertex():\n");
08551       printf("  Clockwise triangle after vertex insertion (top).\n");
08552     }
08553     if (counterclockwise(m, b, leftvertex, botvertex, newvertex) < 0.0) {
08554       printf("Internal error in insertvertex():\n");
08555       printf("  Clockwise triangle after vertex insertion (left).\n");
08556     }
08557     if (counterclockwise(m, b, botvertex, rightvertex, newvertex) < 0.0) {
08558       printf("Internal error in insertvertex():\n");
08559       printf("  Clockwise triangle after vertex insertion (right).\n");
08560     }
08561 #endif /* SELF_CHECK */
08562     if (b->verbose > 2) {
08563       printf("  Updating top ");
08564       printtriangle(m, b, &horiz);
08565       printf("  Creating left ");
08566       printtriangle(m, b, &newbotleft);
08567       printf("  Creating right ");
08568       printtriangle(m, b, &newbotright);
08569     }
08570   }
08571 
08572   /* The insertion is successful by default, unless an encroached */
08573   /*   subsegment is found.                                       */
08574   success = SUCCESSFULVERTEX;
08575   /* Circle around the newly inserted vertex, checking each edge opposite */
08576   /*   it for the Delaunay property.  Non-Delaunay edges are flipped.     */
08577   /*   `horiz' is always the edge being checked.  `first' marks where to  */
08578   /*   stop circling.                                                     */
08579   org(horiz, first);
08580   rightvertex = first;
08581   dest(horiz, leftvertex);
08582   /* Circle until finished. */
08583   while (1) {
08584     /* By default, the edge will be flipped. */
08585     doflip = 1;
08586 
08587     if (m->checksegments) {
08588       /* Check for a subsegment, which cannot be flipped. */
08589       tspivot(horiz, checksubseg);
08590       if (checksubseg.ss != m->dummysub) {
08591         /* The edge is a subsegment and cannot be flipped. */
08592         doflip = 0;
08593 #ifndef CDT_ONLY
08594         if (segmentflaws) {
08595           /* Does the new vertex encroach upon this subsegment? */
08596           if (checkseg4encroach(m, b, &checksubseg)) {
08597             success = ENCROACHINGVERTEX;
08598           }
08599         }
08600 #endif /* not CDT_ONLY */
08601       }
08602     }
08603 
08604     if (doflip) {
08605       /* Check if the edge is a boundary edge. */
08606       sym(horiz, top);
08607       if (top.tri == m->dummytri) {
08608         /* The edge is a boundary edge and cannot be flipped. */
08609         doflip = 0;
08610       } else {
08611         /* Find the vertex on the other side of the edge. */
08612         apex(top, farvertex);
08613         /* In the incremental Delaunay triangulation algorithm, any of      */
08614         /*   `leftvertex', `rightvertex', and `farvertex' could be vertices */
08615         /*   of the triangular bounding box.  These vertices must be        */
08616         /*   treated as if they are infinitely distant, even though their   */
08617         /*   "coordinates" are not.                                         */
08618         if ((leftvertex == m->infvertex1) || (leftvertex == m->infvertex2) ||
08619             (leftvertex == m->infvertex3)) {
08620           /* `leftvertex' is infinitely distant.  Check the convexity of  */
08621           /*   the boundary of the triangulation.  'farvertex' might be   */
08622           /*   infinite as well, but trust me, this same condition should */
08623           /*   be applied.                                                */
08624           doflip = counterclockwise(m, b, newvertex, rightvertex, farvertex)
08625                    > 0.0;
08626         } else if ((rightvertex == m->infvertex1) ||
08627                    (rightvertex == m->infvertex2) ||
08628                    (rightvertex == m->infvertex3)) {
08629           /* `rightvertex' is infinitely distant.  Check the convexity of */
08630           /*   the boundary of the triangulation.  'farvertex' might be   */
08631           /*   infinite as well, but trust me, this same condition should */
08632           /*   be applied.                                                */
08633           doflip = counterclockwise(m, b, farvertex, leftvertex, newvertex)
08634                    > 0.0;
08635         } else if ((farvertex == m->infvertex1) ||
08636                    (farvertex == m->infvertex2) ||
08637                    (farvertex == m->infvertex3)) {
08638           /* `farvertex' is infinitely distant and cannot be inside */
08639           /*   the circumcircle of the triangle `horiz'.            */
08640           doflip = 0;
08641         } else {
08642           /* Test whether the edge is locally Delaunay. */
08643           doflip = incircle(m, b, leftvertex, newvertex, rightvertex,
08644                             farvertex) > 0.0;
08645         }
08646         if (doflip) {
08647           /* We made it!  Flip the edge `horiz' by rotating its containing */
08648           /*   quadrilateral (the two triangles adjacent to `horiz').      */
08649           /* Identify the casing of the quadrilateral. */
08650           lprev(top, topleft);
08651           sym(topleft, toplcasing);
08652           lnext(top, topright);
08653           sym(topright, toprcasing);
08654           lnext(horiz, botleft);
08655           sym(botleft, botlcasing);
08656           lprev(horiz, botright);
08657           sym(botright, botrcasing);
08658           /* Rotate the quadrilateral one-quarter turn counterclockwise. */
08659           bond(topleft, botlcasing);
08660           bond(botleft, botrcasing);
08661           bond(botright, toprcasing);
08662           bond(topright, toplcasing);
08663           if (m->checksegments) {
08664             /* Check for subsegments and rebond them to the quadrilateral. */
08665             tspivot(topleft, toplsubseg);
08666             tspivot(botleft, botlsubseg);
08667             tspivot(botright, botrsubseg);
08668             tspivot(topright, toprsubseg);
08669             if (toplsubseg.ss == m->dummysub) {
08670               tsdissolve(topright);
08671             } else {
08672               tsbond(topright, toplsubseg);
08673             }
08674             if (botlsubseg.ss == m->dummysub) {
08675               tsdissolve(topleft);
08676             } else {
08677               tsbond(topleft, botlsubseg);
08678             }
08679             if (botrsubseg.ss == m->dummysub) {
08680               tsdissolve(botleft);
08681             } else {
08682               tsbond(botleft, botrsubseg);
08683             }
08684             if (toprsubseg.ss == m->dummysub) {
08685               tsdissolve(botright);
08686             } else {
08687               tsbond(botright, toprsubseg);
08688             }
08689           }
08690           /* New vertex assignments for the rotated quadrilateral. */
08691           setorg(horiz, farvertex);
08692           setdest(horiz, newvertex);
08693           setapex(horiz, rightvertex);
08694           setorg(top, newvertex);
08695           setdest(top, farvertex);
08696           setapex(top, leftvertex);
08697           for (i = 0; i < m->eextras; i++) {
08698             /* Take the average of the two triangles' attributes. */
08699             attrib = 0.5 * (elemattribute(top, i) + elemattribute(horiz, i));
08700             setelemattribute(top, i, attrib);
08701             setelemattribute(horiz, i, attrib);
08702           }
08703           if (b->vararea) {
08704             if ((areabound(top) <= 0.0) || (areabound(horiz) <= 0.0)) {
08705               area = -1.0;
08706             } else {
08707               /* Take the average of the two triangles' area constraints.    */
08708               /*   This prevents small area constraints from migrating a     */
08709               /*   long, long way from their original location due to flips. */
08710               area = 0.5 * (areabound(top) + areabound(horiz));
08711             }
08712             setareabound(top, area);
08713             setareabound(horiz, area);
08714           }
08715 
08716           if (m->checkquality) {
08717             newflip = (struct flipstacker *) poolalloc(&m->flipstackers);
08718             newflip->flippedtri = encode(horiz);
08719             newflip->prevflip = m->lastflip;
08720             m->lastflip = newflip;
08721           }
08722 
08723 #ifdef SELF_CHECK
08724           if (newvertex != (vertex) NULL) {
08725             if (counterclockwise(m, b, leftvertex, newvertex, rightvertex) <
08726                 0.0) {
08727               printf("Internal error in insertvertex():\n");
08728               printf("  Clockwise triangle prior to edge flip (bottom).\n");
08729             }
08730             /* The following test has been removed because constrainededge() */
08731             /*   sometimes generates inverted triangles that insertvertex()  */
08732             /*   removes.                                                    */
08733 /*
08734             if (counterclockwise(m, b, rightvertex, farvertex, leftvertex) <
08735                 0.0) {
08736               printf("Internal error in insertvertex():\n");
08737               printf("  Clockwise triangle prior to edge flip (top).\n");
08738             }
08739 */
08740             if (counterclockwise(m, b, farvertex, leftvertex, newvertex) <
08741                 0.0) {
08742               printf("Internal error in insertvertex():\n");
08743               printf("  Clockwise triangle after edge flip (left).\n");
08744             }
08745             if (counterclockwise(m, b, newvertex, rightvertex, farvertex) <
08746                 0.0) {
08747               printf("Internal error in insertvertex():\n");
08748               printf("  Clockwise triangle after edge flip (right).\n");
08749             }
08750           }
08751 #endif /* SELF_CHECK */
08752           if (b->verbose > 2) {
08753             printf("  Edge flip results in left ");
08754             lnextself(topleft);
08755             printtriangle(m, b, &topleft);
08756             printf("  and right ");
08757             printtriangle(m, b, &horiz);
08758           }
08759           /* On the next iterations, consider the two edges that were  */
08760           /*   exposed (this is, are now visible to the newly inserted */
08761           /*   vertex) by the edge flip.                               */
08762           lprevself(horiz);
08763           leftvertex = farvertex;
08764         }
08765       }
08766     }
08767     if (!doflip) {
08768       /* The handle `horiz' is accepted as locally Delaunay. */
08769 #ifndef CDT_ONLY
08770       if (triflaws) {
08771         /* Check the triangle `horiz' for quality. */
08772         testtriangle(m, b, &horiz);
08773       }
08774 #endif /* not CDT_ONLY */
08775       /* Look for the next edge around the newly inserted vertex. */
08776       lnextself(horiz);
08777       sym(horiz, testtri);
08778       /* Check for finishing a complete revolution about the new vertex, or */
08779       /*   falling outside  of the triangulation.  The latter will happen   */
08780       /*   when a vertex is inserted at a boundary.                         */
08781       if ((leftvertex == first) || (testtri.tri == m->dummytri)) {
08782         /* We're done.  Return a triangle whose origin is the new vertex. */
08783         lnext(horiz, *searchtri);
08784         lnext(horiz, m->recenttri);
08785         return success;
08786       }
08787       /* Finish finding the next edge around the newly inserted vertex. */
08788       lnext(testtri, horiz);
08789       rightvertex = leftvertex;
08790       dest(horiz, leftvertex);
08791     }
08792   }
08793 }
08794 
08795 /*****************************************************************************/
08796 /*                                                                           */
08797 /*  triangulatepolygon()   Find the Delaunay triangulation of a polygon that */
08798 /*                         has a certain "nice" shape.  This includes the    */
08799 /*                         polygons that result from deletion of a vertex or */
08800 /*                         insertion of a segment.                           */
08801 /*                                                                           */
08802 /*  This is a conceptually difficult routine.  The starting assumption is    */
08803 /*  that we have a polygon with n sides.  n - 1 of these sides are currently */
08804 /*  represented as edges in the mesh.  One side, called the "base", need not */
08805 /*  be.                                                                      */
08806 /*                                                                           */
08807 /*  Inside the polygon is a structure I call a "fan", consisting of n - 1    */
08808 /*  triangles that share a common origin.  For each of these triangles, the  */
08809 /*  edge opposite the origin is one of the sides of the polygon.  The        */
08810 /*  primary edge of each triangle is the edge directed from the origin to    */
08811 /*  the destination; note that this is not the same edge that is a side of   */
08812 /*  the polygon.  `firstedge' is the primary edge of the first triangle.     */
08813 /*  From there, the triangles follow in counterclockwise order about the     */
08814 /*  polygon, until `lastedge', the primary edge of the last triangle.        */
08815 /*  `firstedge' and `lastedge' are probably connected to other triangles     */
08816 /*  beyond the extremes of the fan, but their identity is not important, as  */
08817 /*  long as the fan remains connected to them.                               */
08818 /*                                                                           */
08819 /*  Imagine the polygon oriented so that its base is at the bottom.  This    */
08820 /*  puts `firstedge' on the far right, and `lastedge' on the far left.       */
08821 /*  The right vertex of the base is the destination of `firstedge', and the  */
08822 /*  left vertex of the base is the apex of `lastedge'.                       */
08823 /*                                                                           */
08824 /*  The challenge now is to find the right sequence of edge flips to         */
08825 /*  transform the fan into a Delaunay triangulation of the polygon.  Each    */
08826 /*  edge flip effectively removes one triangle from the fan, committing it   */
08827 /*  to the polygon.  The resulting polygon has one fewer edge.  If `doflip'  */
08828 /*  is set, the final flip will be performed, resulting in a fan of one      */
08829 /*  (useless?) triangle.  If `doflip' is not set, the final flip is not      */
08830 /*  performed, resulting in a fan of two triangles, and an unfinished        */
08831 /*  triangular polygon that is not yet filled out with a single triangle.    */
08832 /*  On completion of the routine, `lastedge' is the last remaining triangle, */
08833 /*  or the leftmost of the last two.                                         */
08834 /*                                                                           */
08835 /*  Although the flips are performed in the order described above, the       */
08836 /*  decisions about what flips to perform are made in precisely the reverse  */
08837 /*  order.  The recursive triangulatepolygon() procedure makes a decision,   */
08838 /*  uses up to two recursive calls to triangulate the "subproblems"          */
08839 /*  (polygons with fewer edges), and then performs an edge flip.             */
08840 /*                                                                           */
08841 /*  The "decision" it makes is which vertex of the polygon should be         */
08842 /*  connected to the base.  This decision is made by testing every possible  */
08843 /*  vertex.  Once the best vertex is found, the two edges that connect this  */
08844 /*  vertex to the base become the bases for two smaller polygons.  These     */
08845 /*  are triangulated recursively.  Unfortunately, this approach can take     */
08846 /*  O(n^2) time not only in the worst case, but in many common cases.  It's  */
08847 /*  rarely a big deal for vertex deletion, where n is rarely larger than     */
08848 /*  ten, but it could be a big deal for segment insertion, especially if     */
08849 /*  there's a lot of long segments that each cut many triangles.  I ought to */
08850 /*  code a faster algorithm some day.                                        */
08851 /*                                                                           */
08852 /*  The `edgecount' parameter is the number of sides of the polygon,         */
08853 /*  including its base.  `triflaws' is a flag that determines whether the    */
08854 /*  new triangles should be tested for quality, and enqueued if they are     */
08855 /*  bad.                                                                     */
08856 /*                                                                           */
08857 /*****************************************************************************/
08858 
08859 #ifdef ANSI_DECLARATORS
08860 void triangulatepolygon(struct mesh *m, struct behavior *b,
08861                         struct otri *firstedge, struct otri *lastedge,
08862                         int edgecount, int doflip, int triflaws)
08863 #else /* not ANSI_DECLARATORS */
08864 void triangulatepolygon(m, b, firstedge, lastedge, edgecount, doflip, triflaws)
08865 struct mesh *m;
08866 struct behavior *b;
08867 struct otri *firstedge;
08868 struct otri *lastedge;
08869 int edgecount;
08870 int doflip;
08871 int triflaws;
08872 #endif /* not ANSI_DECLARATORS */
08873 
08874 {
08875   struct otri testtri;
08876   struct otri besttri;
08877   struct otri tempedge;
08878   vertex leftbasevertex, rightbasevertex;
08879   vertex testvertex;
08880   vertex bestvertex;
08881   int bestnumber;
08882   int i;
08883   triangle ptr;   /* Temporary variable used by sym(), onext(), and oprev(). */
08884 
08885   /* Identify the base vertices. */
08886   apex(*lastedge, leftbasevertex);
08887   dest(*firstedge, rightbasevertex);
08888   if (b->verbose > 2) {
08889     printf("  Triangulating interior polygon at edge\n");
08890     printf("    (%.12g, %.12g) (%.12g, %.12g)\n", leftbasevertex[0],
08891            leftbasevertex[1], rightbasevertex[0], rightbasevertex[1]);
08892   }
08893   /* Find the best vertex to connect the base to. */
08894   onext(*firstedge, besttri);
08895   dest(besttri, bestvertex);
08896   otricopy(besttri, testtri);
08897   bestnumber = 1;
08898   for (i = 2; i <= edgecount - 2; i++) {
08899     onextself(testtri);
08900     dest(testtri, testvertex);
08901     /* Is this a better vertex? */
08902     if (incircle(m, b, leftbasevertex, rightbasevertex, bestvertex,
08903                  testvertex) > 0.0) {
08904       otricopy(testtri, besttri);
08905       bestvertex = testvertex;
08906       bestnumber = i;
08907     }
08908   }
08909   if (b->verbose > 2) {
08910     printf("    Connecting edge to (%.12g, %.12g)\n", bestvertex[0],
08911            bestvertex[1]);
08912   }
08913   if (bestnumber > 1) {
08914     /* Recursively triangulate the smaller polygon on the right. */
08915     oprev(besttri, tempedge);
08916     triangulatepolygon(m, b, firstedge, &tempedge, bestnumber + 1, 1,
08917                        triflaws);
08918   }
08919   if (bestnumber < edgecount - 2) {
08920     /* Recursively triangulate the smaller polygon on the left. */
08921     sym(besttri, tempedge);
08922     triangulatepolygon(m, b, &besttri, lastedge, edgecount - bestnumber, 1,
08923                        triflaws);
08924     /* Find `besttri' again; it may have been lost to edge flips. */
08925     sym(tempedge, besttri);
08926   }
08927   if (doflip) {
08928     /* Do one final edge flip. */
08929     flip(m, b, &besttri);
08930 #ifndef CDT_ONLY
08931     if (triflaws) {
08932       /* Check the quality of the newly committed triangle. */
08933       sym(besttri, testtri);
08934       testtriangle(m, b, &testtri);
08935     }
08936 #endif /* not CDT_ONLY */
08937   }
08938   /* Return the base triangle. */
08939   otricopy(besttri, *lastedge);
08940 }
08941 
08942 /*****************************************************************************/
08943 /*                                                                           */
08944 /*  deletevertex()   Delete a vertex from a Delaunay triangulation, ensuring */
08945 /*                   that the triangulation remains Delaunay.                */
08946 /*                                                                           */
08947 /*  The origin of `deltri' is deleted.  The union of the triangles adjacent  */
08948 /*  to this vertex is a polygon, for which the Delaunay triangulation is     */
08949 /*  found.  Two triangles are removed from the mesh.                         */
08950 /*                                                                           */
08951 /*  Only interior vertices that do not lie on segments or boundaries may be  */
08952 /*  deleted.                                                                 */
08953 /*                                                                           */
08954 /*****************************************************************************/
08955 
08956 #ifndef CDT_ONLY
08957 
08958 #ifdef ANSI_DECLARATORS
08959 void deletevertex(struct mesh *m, struct behavior *b, struct otri *deltri)
08960 #else /* not ANSI_DECLARATORS */
08961 void deletevertex(m, b, deltri)
08962 struct mesh *m;
08963 struct behavior *b;
08964 struct otri *deltri;
08965 #endif /* not ANSI_DECLARATORS */
08966 
08967 {
08968   struct otri countingtri;
08969   struct otri firstedge, lastedge;
08970   struct otri deltriright;
08971   struct otri lefttri, righttri;
08972   struct otri leftcasing, rightcasing;
08973   struct osub leftsubseg, rightsubseg;
08974   vertex delvertex;
08975   vertex neworg;
08976   int edgecount;
08977   triangle ptr;   /* Temporary variable used by sym(), onext(), and oprev(). */
08978   subseg sptr;                      /* Temporary variable used by tspivot(). */
08979 
08980   org(*deltri, delvertex);
08981   if (b->verbose > 1) {
08982     printf("  Deleting (%.12g, %.12g).\n", delvertex[0], delvertex[1]);
08983   }
08984   vertexdealloc(m, delvertex);
08985 
08986   /* Count the degree of the vertex being deleted. */
08987   onext(*deltri, countingtri);
08988   edgecount = 1;
08989   while (!otriequal(*deltri, countingtri)) {
08990 #ifdef SELF_CHECK
08991     if (countingtri.tri == m->dummytri) {
08992       printf("Internal error in deletevertex():\n");
08993       printf("  Attempt to delete boundary vertex.\n");
08994       internalerror();
08995     }
08996 #endif /* SELF_CHECK */
08997     edgecount++;
08998     onextself(countingtri);
08999   }
09000 
09001 #ifdef SELF_CHECK
09002   if (edgecount < 3) {
09003     printf("Internal error in deletevertex():\n  Vertex has degree %d.\n",
09004            edgecount);
09005     internalerror();
09006   }
09007 #endif /* SELF_CHECK */
09008   if (edgecount > 3) {
09009     /* Triangulate the polygon defined by the union of all triangles */
09010     /*   adjacent to the vertex being deleted.  Check the quality of */
09011     /*   the resulting triangles.                                    */
09012     onext(*deltri, firstedge);
09013     oprev(*deltri, lastedge);
09014     triangulatepolygon(m, b, &firstedge, &lastedge, edgecount, 0,
09015                        !b->nobisect);
09016   }
09017   /* Splice out two triangles. */
09018   lprev(*deltri, deltriright);
09019   dnext(*deltri, lefttri);
09020   sym(lefttri, leftcasing);
09021   oprev(deltriright, righttri);
09022   sym(righttri, rightcasing);
09023   bond(*deltri, leftcasing);
09024   bond(deltriright, rightcasing);
09025   tspivot(lefttri, leftsubseg);
09026   if (leftsubseg.ss != m->dummysub) {
09027     tsbond(*deltri, leftsubseg);
09028   }
09029   tspivot(righttri, rightsubseg);
09030   if (rightsubseg.ss != m->dummysub) {
09031     tsbond(deltriright, rightsubseg);
09032   }
09033 
09034   /* Set the new origin of `deltri' and check its quality. */
09035   org(lefttri, neworg);
09036   setorg(*deltri, neworg);
09037   if (!b->nobisect) {
09038     testtriangle(m, b, deltri);
09039   }
09040 
09041   /* Delete the two spliced-out triangles. */
09042   triangledealloc(m, lefttri.tri);
09043   triangledealloc(m, righttri.tri);
09044 }
09045 
09046 #endif /* not CDT_ONLY */
09047 
09048 /*****************************************************************************/
09049 /*                                                                           */
09050 /*  undovertex()   Undo the most recent vertex insertion.                    */
09051 /*                                                                           */
09052 /*  Walks through the list of transformations (flips and a vertex insertion) */
09053 /*  in the reverse of the order in which they were done, and undoes them.    */
09054 /*  The inserted vertex is removed from the triangulation and deallocated.   */
09055 /*  Two triangles (possibly just one) are also deallocated.                  */
09056 /*                                                                           */
09057 /*****************************************************************************/
09058 
09059 #ifndef CDT_ONLY
09060 
09061 #ifdef ANSI_DECLARATORS
09062 void undovertex(struct mesh *m, struct behavior *b)
09063 #else /* not ANSI_DECLARATORS */
09064 void undovertex(m, b)
09065 struct mesh *m;
09066 struct behavior *b;
09067 #endif /* not ANSI_DECLARATORS */
09068 
09069 {
09070   struct otri fliptri;
09071   struct otri botleft, botright, topright;
09072   struct otri botlcasing, botrcasing, toprcasing;
09073   struct otri gluetri;
09074   struct osub botlsubseg, botrsubseg, toprsubseg;
09075   vertex botvertex, rightvertex;
09076   triangle ptr;                         /* Temporary variable used by sym(). */
09077   subseg sptr;                      /* Temporary variable used by tspivot(). */
09078 
09079   /* Walk through the list of transformations (flips and a vertex insertion) */
09080   /*   in the reverse of the order in which they were done, and undo them.   */
09081   while (m->lastflip != (struct flipstacker *) NULL) {
09082     /* Find a triangle involved in the last unreversed transformation. */
09083     decode(m->lastflip->flippedtri, fliptri);
09084 
09085     /* We are reversing one of three transformations:  a trisection of one */
09086     /*   triangle into three (by inserting a vertex in the triangle), a    */
09087     /*   bisection of two triangles into four (by inserting a vertex in an */
09088     /*   edge), or an edge flip.                                           */
09089     if (m->lastflip->prevflip == (struct flipstacker *) NULL) {
09090       /* Restore a triangle that was split into three triangles, */
09091       /*   so it is again one triangle.                          */
09092       dprev(fliptri, botleft);
09093       lnextself(botleft);
09094       onext(fliptri, botright);
09095       lprevself(botright);
09096       sym(botleft, botlcasing);
09097       sym(botright, botrcasing);
09098       dest(botleft, botvertex);
09099 
09100       setapex(fliptri, botvertex);
09101       lnextself(fliptri);
09102       bond(fliptri, botlcasing);
09103       tspivot(botleft, botlsubseg);
09104       tsbond(fliptri, botlsubseg);
09105       lnextself(fliptri);
09106       bond(fliptri, botrcasing);
09107       tspivot(botright, botrsubseg);
09108       tsbond(fliptri, botrsubseg);
09109 
09110       /* Delete the two spliced-out triangles. */
09111       triangledealloc(m, botleft.tri);
09112       triangledealloc(m, botright.tri);
09113     } else if (m->lastflip->prevflip == (struct flipstacker *) &insertvertex) {
09114       /* Restore two triangles that were split into four triangles, */
09115       /*   so they are again two triangles.                         */
09116       lprev(fliptri, gluetri);
09117       sym(gluetri, botright);
09118       lnextself(botright);
09119       sym(botright, botrcasing);
09120       dest(botright, rightvertex);
09121 
09122       setorg(fliptri, rightvertex);
09123       bond(gluetri, botrcasing);
09124       tspivot(botright, botrsubseg);
09125       tsbond(gluetri, botrsubseg);
09126 
09127       /* Delete the spliced-out triangle. */
09128       triangledealloc(m, botright.tri);
09129 
09130       sym(fliptri, gluetri);
09131       if (gluetri.tri != m->dummytri) {
09132         lnextself(gluetri);
09133         dnext(gluetri, topright);
09134         sym(topright, toprcasing);
09135 
09136         setorg(gluetri, rightvertex);
09137         bond(gluetri, toprcasing);
09138         tspivot(topright, toprsubseg);
09139         tsbond(gluetri, toprsubseg);
09140 
09141         /* Delete the spliced-out triangle. */
09142         triangledealloc(m, topright.tri);
09143       }
09144 
09145       /* This is the end of the list, sneakily encoded. */
09146       m->lastflip->prevflip = (struct flipstacker *) NULL;
09147     } else {
09148       /* Undo an edge flip. */
09149       unflip(m, b, &fliptri);
09150     }
09151 
09152     /* Go on and process the next transformation. */
09153     m->lastflip = m->lastflip->prevflip;
09154   }
09155 }
09156 
09157 #endif /* not CDT_ONLY */
09158 
09161 /********* Mesh transformation routines end here                     *********/
09162 
09163 /********* Divide-and-conquer Delaunay triangulation begins here     *********/
09167 /*****************************************************************************/
09168 /*                                                                           */
09169 /*  The divide-and-conquer bounding box                                      */
09170 /*                                                                           */
09171 /*  I originally implemented the divide-and-conquer and incremental Delaunay */
09172 /*  triangulations using the edge-based data structure presented by Guibas   */
09173 /*  and Stolfi.  Switching to a triangle-based data structure doubled the    */
09174 /*  speed.  However, I had to think of a few extra tricks to maintain the    */
09175 /*  elegance of the original algorithms.                                     */
09176 /*                                                                           */
09177 /*  The "bounding box" used by my variant of the divide-and-conquer          */
09178 /*  algorithm uses one triangle for each edge of the convex hull of the      */
09179 /*  triangulation.  These bounding triangles all share a common apical       */
09180 /*  vertex, which is represented by NULL and which represents nothing.       */
09181 /*  The bounding triangles are linked in a circular fan about this NULL      */
09182 /*  vertex, and the edges on the convex hull of the triangulation appear     */
09183 /*  opposite the NULL vertex.  You might find it easiest to imagine that     */
09184 /*  the NULL vertex is a point in 3D space behind the center of the          */
09185 /*  triangulation, and that the bounding triangles form a sort of cone.      */
09186 /*                                                                           */
09187 /*  This bounding box makes it easy to represent degenerate cases.  For      */
09188 /*  instance, the triangulation of two vertices is a single edge.  This edge */
09189 /*  is represented by two bounding box triangles, one on each "side" of the  */
09190 /*  edge.  These triangles are also linked together in a fan about the NULL  */
09191 /*  vertex.                                                                  */
09192 /*                                                                           */
09193 /*  The bounding box also makes it easy to traverse the convex hull, as the  */
09194 /*  divide-and-conquer algorithm needs to do.                                */
09195 /*                                                                           */
09196 /*****************************************************************************/
09197 
09198 /*****************************************************************************/
09199 /*                                                                           */
09200 /*  vertexsort()   Sort an array of vertices by x-coordinate, using the      */
09201 /*                 y-coordinate as a secondary key.                          */
09202 /*                                                                           */
09203 /*  Uses quicksort.  Randomized O(n log n) time.  No, I did not make any of  */
09204 /*  the usual quicksort mistakes.                                            */
09205 /*                                                                           */
09206 /*****************************************************************************/
09207 
09208 #ifdef ANSI_DECLARATORS
09209 void vertexsort(vertex *sortarray, int arraysize)
09210 #else /* not ANSI_DECLARATORS */
09211 void vertexsort(sortarray, arraysize)
09212 vertex *sortarray;
09213 int arraysize;
09214 #endif /* not ANSI_DECLARATORS */
09215 
09216 {
09217   int left, right;
09218   int pivot;
09219   REAL pivotx, pivoty;
09220   vertex temp;
09221 
09222   if (arraysize == 2) {
09223     /* Recursive base case. */
09224     if ((sortarray[0][0] > sortarray[1][0]) ||
09225         ((sortarray[0][0] == sortarray[1][0]) &&
09226          (sortarray[0][1] > sortarray[1][1]))) {
09227       temp = sortarray[1];
09228       sortarray[1] = sortarray[0];
09229       sortarray[0] = temp;
09230     }
09231     return;
09232   }
09233   /* Choose a random pivot to split the array. */
09234   pivot = (int) randomnation((unsigned int) arraysize);
09235   pivotx = sortarray[pivot][0];
09236   pivoty = sortarray[pivot][1];
09237   /* Split the array. */
09238   left = -1;
09239   right = arraysize;
09240   while (left < right) {
09241     /* Search for a vertex whose x-coordinate is too large for the left. */
09242     do {
09243       left++;
09244     } while ((left <= right) && ((sortarray[left][0] < pivotx) ||
09245                                  ((sortarray[left][0] == pivotx) &&
09246                                   (sortarray[left][1] < pivoty))));
09247     /* Search for a vertex whose x-coordinate is too small for the right. */
09248     do {
09249       right--;
09250     } while ((left <= right) && ((sortarray[right][0] > pivotx) ||
09251                                  ((sortarray[right][0] == pivotx) &&
09252                                   (sortarray[right][1] > pivoty))));
09253     if (left < right) {
09254       /* Swap the left and right vertices. */
09255       temp = sortarray[left];
09256       sortarray[left] = sortarray[right];
09257       sortarray[right] = temp;
09258     }
09259   }
09260   if (left > 1) {
09261     /* Recursively sort the left subset. */
09262     vertexsort(sortarray, left);
09263   }
09264   if (right < arraysize - 2) {
09265     /* Recursively sort the right subset. */
09266     vertexsort(&sortarray[right + 1], arraysize - right - 1);
09267   }
09268 }
09269 
09270 /*****************************************************************************/
09271 /*                                                                           */
09272 /*  vertexmedian()   An order statistic algorithm, almost.  Shuffles an      */
09273 /*                   array of vertices so that the first `median' vertices   */
09274 /*                   occur lexicographically before the remaining vertices.  */
09275 /*                                                                           */
09276 /*  Uses the x-coordinate as the primary key if axis == 0; the y-coordinate  */
09277 /*  if axis == 1.  Very similar to the vertexsort() procedure, but runs in   */
09278 /*  randomized linear time.                                                  */
09279 /*                                                                           */
09280 /*****************************************************************************/
09281 
09282 #ifdef ANSI_DECLARATORS
09283 void vertexmedian(vertex *sortarray, int arraysize, int median, int axis)
09284 #else /* not ANSI_DECLARATORS */
09285 void vertexmedian(sortarray, arraysize, median, axis)
09286 vertex *sortarray;
09287 int arraysize;
09288 int median;
09289 int axis;
09290 #endif /* not ANSI_DECLARATORS */
09291 
09292 {
09293   int left, right;
09294   int pivot;
09295   REAL pivot1, pivot2;
09296   vertex temp;
09297 
09298   if (arraysize == 2) {
09299     /* Recursive base case. */
09300     if ((sortarray[0][axis] > sortarray[1][axis]) ||
09301         ((sortarray[0][axis] == sortarray[1][axis]) &&
09302          (sortarray[0][1 - axis] > sortarray[1][1 - axis]))) {
09303       temp = sortarray[1];
09304       sortarray[1] = sortarray[0];
09305       sortarray[0] = temp;
09306     }
09307     return;
09308   }
09309   /* Choose a random pivot to split the array. */
09310   pivot = (int) randomnation((unsigned int) arraysize);
09311   pivot1 = sortarray[pivot][axis];
09312   pivot2 = sortarray[pivot][1 - axis];
09313   /* Split the array. */
09314   left = -1;
09315   right = arraysize;
09316   while (left < right) {
09317     /* Search for a vertex whose x-coordinate is too large for the left. */
09318     do {
09319       left++;
09320     } while ((left <= right) && ((sortarray[left][axis] < pivot1) ||
09321                                  ((sortarray[left][axis] == pivot1) &&
09322                                   (sortarray[left][1 - axis] < pivot2))));
09323     /* Search for a vertex whose x-coordinate is too small for the right. */
09324     do {
09325       right--;
09326     } while ((left <= right) && ((sortarray[right][axis] > pivot1) ||
09327                                  ((sortarray[right][axis] == pivot1) &&
09328                                   (sortarray[right][1 - axis] > pivot2))));
09329     if (left < right) {
09330       /* Swap the left and right vertices. */
09331       temp = sortarray[left];
09332       sortarray[left] = sortarray[right];
09333       sortarray[right] = temp;
09334     }
09335   }
09336   /* Unlike in vertexsort(), at most one of the following */
09337   /*   conditionals is true.                             */
09338   if (left > median) {
09339     /* Recursively shuffle the left subset. */
09340     vertexmedian(sortarray, left, median, axis);
09341   }
09342   if (right < median - 1) {
09343     /* Recursively shuffle the right subset. */
09344     vertexmedian(&sortarray[right + 1], arraysize - right - 1,
09345                  median - right - 1, axis);
09346   }
09347 }
09348 
09349 /*****************************************************************************/
09350 /*                                                                           */
09351 /*  alternateaxes()   Sorts the vertices as appropriate for the divide-and-  */
09352 /*                    conquer algorithm with alternating cuts.               */
09353 /*                                                                           */
09354 /*  Partitions by x-coordinate if axis == 0; by y-coordinate if axis == 1.   */
09355 /*  For the base case, subsets containing only two or three vertices are     */
09356 /*  always sorted by x-coordinate.                                           */
09357 /*                                                                           */
09358 /*****************************************************************************/
09359 
09360 #ifdef ANSI_DECLARATORS
09361 void alternateaxes(vertex *sortarray, int arraysize, int axis)
09362 #else /* not ANSI_DECLARATORS */
09363 void alternateaxes(sortarray, arraysize, axis)
09364 vertex *sortarray;
09365 int arraysize;
09366 int axis;
09367 #endif /* not ANSI_DECLARATORS */
09368 
09369 {
09370   int divider;
09371 
09372   divider = arraysize >> 1;
09373   if (arraysize <= 3) {
09374     /* Recursive base case:  subsets of two or three vertices will be    */
09375     /*   handled specially, and should always be sorted by x-coordinate. */
09376     axis = 0;
09377   }
09378   /* Partition with a horizontal or vertical cut. */
09379   vertexmedian(sortarray, arraysize, divider, axis);
09380   /* Recursively partition the subsets with a cross cut. */
09381   if (arraysize - divider >= 2) {
09382     if (divider >= 2) {
09383       alternateaxes(sortarray, divider, 1 - axis);
09384     }
09385     alternateaxes(&sortarray[divider], arraysize - divider, 1 - axis);
09386   }
09387 }
09388 
09389 /*****************************************************************************/
09390 /*                                                                           */
09391 /*  mergehulls()   Merge two adjacent Delaunay triangulations into a         */
09392 /*                 single Delaunay triangulation.                            */
09393 /*                                                                           */
09394 /*  This is similar to the algorithm given by Guibas and Stolfi, but uses    */
09395 /*  a triangle-based, rather than edge-based, data structure.                */
09396 /*                                                                           */
09397 /*  The algorithm walks up the gap between the two triangulations, knitting  */
09398 /*  them together.  As they are merged, some of their bounding triangles     */
09399 /*  are converted into real triangles of the triangulation.  The procedure   */
09400 /*  pulls each hull's bounding triangles apart, then knits them together     */
09401 /*  like the teeth of two gears.  The Delaunay property determines, at each  */
09402 /*  step, whether the next "tooth" is a bounding triangle of the left hull   */
09403 /*  or the right.  When a bounding triangle becomes real, its apex is        */
09404 /*  changed from NULL to a real vertex.                                      */
09405 /*                                                                           */
09406 /*  Only two new triangles need to be allocated.  These become new bounding  */
09407 /*  triangles at the top and bottom of the seam.  They are used to connect   */
09408 /*  the remaining bounding triangles (those that have not been converted     */
09409 /*  into real triangles) into a single fan.                                  */
09410 /*                                                                           */
09411 /*  On entry, `farleft' and `innerleft' are bounding triangles of the left   */
09412 /*  triangulation.  The origin of `farleft' is the leftmost vertex, and      */
09413 /*  the destination of `innerleft' is the rightmost vertex of the            */
09414 /*  triangulation.  Similarly, `innerright' and `farright' are bounding      */
09415 /*  triangles of the right triangulation.  The origin of `innerright' and    */
09416 /*  destination of `farright' are the leftmost and rightmost vertices.       */
09417 /*                                                                           */
09418 /*  On completion, the origin of `farleft' is the leftmost vertex of the     */
09419 /*  merged triangulation, and the destination of `farright' is the rightmost */
09420 /*  vertex.                                                                  */
09421 /*                                                                           */
09422 /*****************************************************************************/
09423 
09424 #ifdef ANSI_DECLARATORS
09425 void mergehulls(struct mesh *m, struct behavior *b, struct otri *farleft,
09426                 struct otri *innerleft, struct otri *innerright,
09427                 struct otri *farright, int axis)
09428 #else /* not ANSI_DECLARATORS */
09429 void mergehulls(m, b, farleft, innerleft, innerright, farright, axis)
09430 struct mesh *m;
09431 struct behavior *b;
09432 struct otri *farleft;
09433 struct otri *innerleft;
09434 struct otri *innerright;
09435 struct otri *farright;
09436 int axis;
09437 #endif /* not ANSI_DECLARATORS */
09438 
09439 {
09440   struct otri leftcand, rightcand;
09441   struct otri baseedge;
09442   struct otri nextedge;
09443   struct otri sidecasing, topcasing, outercasing;
09444   struct otri checkedge;
09445   vertex innerleftdest;
09446   vertex innerrightorg;
09447   vertex innerleftapex, innerrightapex;
09448   vertex farleftpt, farrightpt;
09449   vertex farleftapex, farrightapex;
09450   vertex lowerleft, lowerright;
09451   vertex upperleft, upperright;
09452   vertex nextapex;
09453   vertex checkvertex;
09454   int changemade;
09455   int badedge;
09456   int leftfinished, rightfinished;
09457   triangle ptr;                         /* Temporary variable used by sym(). */
09458 
09459   dest(*innerleft, innerleftdest);
09460   apex(*innerleft, innerleftapex);
09461   org(*innerright, innerrightorg);
09462   apex(*innerright, innerrightapex);
09463   /* Special treatment for horizontal cuts. */
09464   if (b->dwyer && (axis == 1)) {
09465     org(*farleft, farleftpt);
09466     apex(*farleft, farleftapex);
09467     dest(*farright, farrightpt);
09468     apex(*farright, farrightapex);
09469     /* The pointers to the extremal vertices are shifted to point to the */
09470     /*   topmost and bottommost vertex of each hull, rather than the     */
09471     /*   leftmost and rightmost vertices.                                */
09472     while (farleftapex[1] < farleftpt[1]) {
09473       lnextself(*farleft);
09474       symself(*farleft);
09475       farleftpt = farleftapex;
09476       apex(*farleft, farleftapex);
09477     }
09478     sym(*innerleft, checkedge);
09479     apex(checkedge, checkvertex);
09480     while (checkvertex[1] > innerleftdest[1]) {
09481       lnext(checkedge, *innerleft);
09482       innerleftapex = innerleftdest;
09483       innerleftdest = checkvertex;
09484       sym(*innerleft, checkedge);
09485       apex(checkedge, checkvertex);
09486     }
09487     while (innerrightapex[1] < innerrightorg[1]) {
09488       lnextself(*innerright);
09489       symself(*innerright);
09490       innerrightorg = innerrightapex;
09491       apex(*innerright, innerrightapex);
09492     }
09493     sym(*farright, checkedge);
09494     apex(checkedge, checkvertex);
09495     while (checkvertex[1] > farrightpt[1]) {
09496       lnext(checkedge, *farright);
09497       farrightapex = farrightpt;
09498       farrightpt = checkvertex;
09499       sym(*farright, checkedge);
09500       apex(checkedge, checkvertex);
09501     }
09502   }
09503   /* Find a line tangent to and below both hulls. */
09504   do {
09505     changemade = 0;
09506     /* Make innerleftdest the "bottommost" vertex of the left hull. */
09507     if (counterclockwise(m, b, innerleftdest, innerleftapex, innerrightorg) >
09508         0.0) {
09509       lprevself(*innerleft);
09510       symself(*innerleft);
09511       innerleftdest = innerleftapex;
09512       apex(*innerleft, innerleftapex);
09513       changemade = 1;
09514     }
09515     /* Make innerrightorg the "bottommost" vertex of the right hull. */
09516     if (counterclockwise(m, b, innerrightapex, innerrightorg, innerleftdest) >
09517         0.0) {
09518       lnextself(*innerright);
09519       symself(*innerright);
09520       innerrightorg = innerrightapex;
09521       apex(*innerright, innerrightapex);
09522       changemade = 1;
09523     }
09524   } while (changemade);
09525   /* Find the two candidates to be the next "gear tooth." */
09526   sym(*innerleft, leftcand);
09527   sym(*innerright, rightcand);
09528   /* Create the bottom new bounding triangle. */
09529   maketriangle(m, b, &baseedge);
09530   /* Connect it to the bounding boxes of the left and right triangulations. */
09531   bond(baseedge, *innerleft);
09532   lnextself(baseedge);
09533   bond(baseedge, *innerright);
09534   lnextself(baseedge);
09535   setorg(baseedge, innerrightorg);
09536   setdest(baseedge, innerleftdest);
09537   /* Apex is intentionally left NULL. */
09538   if (b->verbose > 2) {
09539     printf("  Creating base bounding ");
09540     printtriangle(m, b, &baseedge);
09541   }
09542   /* Fix the extreme triangles if necessary. */
09543   org(*farleft, farleftpt);
09544   if (innerleftdest == farleftpt) {
09545     lnext(baseedge, *farleft);
09546   }
09547   dest(*farright, farrightpt);
09548   if (innerrightorg == farrightpt) {
09549     lprev(baseedge, *farright);
09550   }
09551   /* The vertices of the current knitting edge. */
09552   lowerleft = innerleftdest;
09553   lowerright = innerrightorg;
09554   /* The candidate vertices for knitting. */
09555   apex(leftcand, upperleft);
09556   apex(rightcand, upperright);
09557   /* Walk up the gap between the two triangulations, knitting them together. */
09558   while (1) {
09559     /* Have we reached the top?  (This isn't quite the right question,       */
09560     /*   because even though the left triangulation might seem finished now, */
09561     /*   moving up on the right triangulation might reveal a new vertex of   */
09562     /*   the left triangulation.  And vice-versa.)                           */
09563     leftfinished = counterclockwise(m, b, upperleft, lowerleft, lowerright) <=
09564                    0.0;
09565     rightfinished = counterclockwise(m, b, upperright, lowerleft, lowerright)
09566                  <= 0.0;
09567     if (leftfinished && rightfinished) {
09568       /* Create the top new bounding triangle. */
09569       maketriangle(m, b, &nextedge);
09570       setorg(nextedge, lowerleft);
09571       setdest(nextedge, lowerright);
09572       /* Apex is intentionally left NULL. */
09573       /* Connect it to the bounding boxes of the two triangulations. */
09574       bond(nextedge, baseedge);
09575       lnextself(nextedge);
09576       bond(nextedge, rightcand);
09577       lnextself(nextedge);
09578       bond(nextedge, leftcand);
09579       if (b->verbose > 2) {
09580         printf("  Creating top bounding ");
09581         printtriangle(m, b, &nextedge);
09582       }
09583       /* Special treatment for horizontal cuts. */
09584       if (b->dwyer && (axis == 1)) {
09585         org(*farleft, farleftpt);
09586         apex(*farleft, farleftapex);
09587         dest(*farright, farrightpt);
09588         apex(*farright, farrightapex);
09589         sym(*farleft, checkedge);
09590         apex(checkedge, checkvertex);
09591         /* The pointers to the extremal vertices are restored to the  */
09592         /*   leftmost and rightmost vertices (rather than topmost and */
09593         /*   bottommost).                                             */
09594         while (checkvertex[0] < farleftpt[0]) {
09595           lprev(checkedge, *farleft);
09596           farleftapex = farleftpt;
09597           farleftpt = checkvertex;
09598           sym(*farleft, checkedge);
09599           apex(checkedge, checkvertex);
09600         }
09601         while (farrightapex[0] > farrightpt[0]) {
09602           lprevself(*farright);
09603           symself(*farright);
09604           farrightpt = farrightapex;
09605           apex(*farright, farrightapex);
09606         }
09607       }
09608       return;
09609     }
09610     /* Consider eliminating edges from the left triangulation. */
09611     if (!leftfinished) {
09612       /* What vertex would be exposed if an edge were deleted? */
09613       lprev(leftcand, nextedge);
09614       symself(nextedge);
09615       apex(nextedge, nextapex);
09616       /* If nextapex is NULL, then no vertex would be exposed; the */
09617       /*   triangulation would have been eaten right through.      */
09618       if (nextapex != (vertex) NULL) {
09619         /* Check whether the edge is Delaunay. */
09620         badedge = incircle(m, b, lowerleft, lowerright, upperleft, nextapex) >
09621                   0.0;
09622         while (badedge) {
09623           /* Eliminate the edge with an edge flip.  As a result, the    */
09624           /*   left triangulation will have one more boundary triangle. */
09625           lnextself(nextedge);
09626           sym(nextedge, topcasing);
09627           lnextself(nextedge);
09628           sym(nextedge, sidecasing);
09629           bond(nextedge, topcasing);
09630           bond(leftcand, sidecasing);
09631           lnextself(leftcand);
09632           sym(leftcand, outercasing);
09633           lprevself(nextedge);
09634           bond(nextedge, outercasing);
09635           /* Correct the vertices to reflect the edge flip. */
09636           setorg(leftcand, lowerleft);
09637           setdest(leftcand, NULL);
09638           setapex(leftcand, nextapex);
09639           setorg(nextedge, NULL);
09640           setdest(nextedge, upperleft);
09641           setapex(nextedge, nextapex);
09642           /* Consider the newly exposed vertex. */
09643           upperleft = nextapex;
09644           /* What vertex would be exposed if another edge were deleted? */
09645           otricopy(sidecasing, nextedge);
09646           apex(nextedge, nextapex);
09647           if (nextapex != (vertex) NULL) {
09648             /* Check whether the edge is Delaunay. */
09649             badedge = incircle(m, b, lowerleft, lowerright, upperleft,
09650                                nextapex) > 0.0;
09651           } else {
09652             /* Avoid eating right through the triangulation. */
09653             badedge = 0;
09654           }
09655         }
09656       }
09657     }
09658     /* Consider eliminating edges from the right triangulation. */
09659     if (!rightfinished) {
09660       /* What vertex would be exposed if an edge were deleted? */
09661       lnext(rightcand, nextedge);
09662       symself(nextedge);
09663       apex(nextedge, nextapex);
09664       /* If nextapex is NULL, then no vertex would be exposed; the */
09665       /*   triangulation would have been eaten right through.      */
09666       if (nextapex != (vertex) NULL) {
09667         /* Check whether the edge is Delaunay. */
09668         badedge = incircle(m, b, lowerleft, lowerright, upperright, nextapex) >
09669                   0.0;
09670         while (badedge) {
09671           /* Eliminate the edge with an edge flip.  As a result, the     */
09672           /*   right triangulation will have one more boundary triangle. */
09673           lprevself(nextedge);
09674           sym(nextedge, topcasing);
09675           lprevself(nextedge);
09676           sym(nextedge, sidecasing);
09677           bond(nextedge, topcasing);
09678           bond(rightcand, sidecasing);
09679           lprevself(rightcand);
09680           sym(rightcand, outercasing);
09681           lnextself(nextedge);
09682           bond(nextedge, outercasing);
09683           /* Correct the vertices to reflect the edge flip. */
09684           setorg(rightcand, NULL);
09685           setdest(rightcand, lowerright);
09686           setapex(rightcand, nextapex);
09687           setorg(nextedge, upperright);
09688           setdest(nextedge, NULL);
09689           setapex(nextedge, nextapex);
09690           /* Consider the newly exposed vertex. */
09691           upperright = nextapex;
09692           /* What vertex would be exposed if another edge were deleted? */
09693           otricopy(sidecasing, nextedge);
09694           apex(nextedge, nextapex);
09695           if (nextapex != (vertex) NULL) {
09696             /* Check whether the edge is Delaunay. */
09697             badedge = incircle(m, b, lowerleft, lowerright, upperright,
09698                                nextapex) > 0.0;
09699           } else {
09700             /* Avoid eating right through the triangulation. */
09701             badedge = 0;
09702           }
09703         }
09704       }
09705     }
09706     if (leftfinished || (!rightfinished &&
09707            (incircle(m, b, upperleft, lowerleft, lowerright, upperright) >
09708             0.0))) {
09709       /* Knit the triangulations, adding an edge from `lowerleft' */
09710       /*   to `upperright'.                                       */
09711       bond(baseedge, rightcand);
09712       lprev(rightcand, baseedge);
09713       setdest(baseedge, lowerleft);
09714       lowerright = upperright;
09715       sym(baseedge, rightcand);
09716       apex(rightcand, upperright);
09717     } else {
09718       /* Knit the triangulations, adding an edge from `upperleft' */
09719       /*   to `lowerright'.                                       */
09720       bond(baseedge, leftcand);
09721       lnext(leftcand, baseedge);
09722       setorg(baseedge, lowerright);
09723       lowerleft = upperleft;
09724       sym(baseedge, leftcand);
09725       apex(leftcand, upperleft);
09726     }
09727     if (b->verbose > 2) {
09728       printf("  Connecting ");
09729       printtriangle(m, b, &baseedge);
09730     }
09731   }
09732 }
09733 
09734 /*****************************************************************************/
09735 /*                                                                           */
09736 /*  divconqrecurse()   Recursively form a Delaunay triangulation by the      */
09737 /*                     divide-and-conquer method.                            */
09738 /*                                                                           */
09739 /*  Recursively breaks down the problem into smaller pieces, which are       */
09740 /*  knitted together by mergehulls().  The base cases (problems of two or    */
09741 /*  three vertices) are handled specially here.                              */
09742 /*                                                                           */
09743 /*  On completion, `farleft' and `farright' are bounding triangles such that */
09744 /*  the origin of `farleft' is the leftmost vertex (breaking ties by         */
09745 /*  choosing the highest leftmost vertex), and the destination of            */
09746 /*  `farright' is the rightmost vertex (breaking ties by choosing the        */
09747 /*  lowest rightmost vertex).                                                */
09748 /*                                                                           */
09749 /*****************************************************************************/
09750 
09751 #ifdef ANSI_DECLARATORS
09752 void divconqrecurse(struct mesh *m, struct behavior *b, vertex *sortarray,
09753                     int vertices, int axis,
09754                     struct otri *farleft, struct otri *farright)
09755 #else /* not ANSI_DECLARATORS */
09756 void divconqrecurse(m, b, sortarray, vertices, axis, farleft, farright)
09757 struct mesh *m;
09758 struct behavior *b;
09759 vertex *sortarray;
09760 int vertices;
09761 int axis;
09762 struct otri *farleft;
09763 struct otri *farright;
09764 #endif /* not ANSI_DECLARATORS */
09765 
09766 {
09767   struct otri midtri, tri1, tri2, tri3;
09768   struct otri innerleft, innerright;
09769   REAL area;
09770   int divider;
09771 
09772   if (b->verbose > 2) {
09773     printf("  Triangulating %d vertices.\n", vertices);
09774   }
09775   if (vertices == 2) {
09776     /* The triangulation of two vertices is an edge.  An edge is */
09777     /*   represented by two bounding triangles.                  */
09778     maketriangle(m, b, farleft);
09779     setorg(*farleft, sortarray[0]);
09780     setdest(*farleft, sortarray[1]);
09781     /* The apex is intentionally left NULL. */
09782     maketriangle(m, b, farright);
09783     setorg(*farright, sortarray[1]);
09784     setdest(*farright, sortarray[0]);
09785     /* The apex is intentionally left NULL. */
09786     bond(*farleft, *farright);
09787     lprevself(*farleft);
09788     lnextself(*farright);
09789     bond(*farleft, *farright);
09790     lprevself(*farleft);
09791     lnextself(*farright);
09792     bond(*farleft, *farright);
09793     if (b->verbose > 2) {
09794       printf("  Creating ");
09795       printtriangle(m, b, farleft);
09796       printf("  Creating ");
09797       printtriangle(m, b, farright);
09798     }
09799     /* Ensure that the origin of `farleft' is sortarray[0]. */
09800     lprev(*farright, *farleft);
09801     return;
09802   } else if (vertices == 3) {
09803     /* The triangulation of three vertices is either a triangle (with */
09804     /*   three bounding triangles) or two edges (with four bounding   */
09805     /*   triangles).  In either case, four triangles are created.     */
09806     maketriangle(m, b, &midtri);
09807     maketriangle(m, b, &tri1);
09808     maketriangle(m, b, &tri2);
09809     maketriangle(m, b, &tri3);
09810     area = counterclockwise(m, b, sortarray[0], sortarray[1], sortarray[2]);
09811     if (area == 0.0) {
09812       /* Three collinear vertices; the triangulation is two edges. */
09813       setorg(midtri, sortarray[0]);
09814       setdest(midtri, sortarray[1]);
09815       setorg(tri1, sortarray[1]);
09816       setdest(tri1, sortarray[0]);
09817       setorg(tri2, sortarray[2]);
09818       setdest(tri2, sortarray[1]);
09819       setorg(tri3, sortarray[1]);
09820       setdest(tri3, sortarray[2]);
09821       /* All apices are intentionally left NULL. */
09822       bond(midtri, tri1);
09823       bond(tri2, tri3);
09824       lnextself(midtri);
09825       lprevself(tri1);
09826       lnextself(tri2);
09827       lprevself(tri3);
09828       bond(midtri, tri3);
09829       bond(tri1, tri2);
09830       lnextself(midtri);
09831       lprevself(tri1);
09832       lnextself(tri2);
09833       lprevself(tri3);
09834       bond(midtri, tri1);
09835       bond(tri2, tri3);
09836       /* Ensure that the origin of `farleft' is sortarray[0]. */
09837       otricopy(tri1, *farleft);
09838       /* Ensure that the destination of `farright' is sortarray[2]. */
09839       otricopy(tri2, *farright);
09840     } else {
09841       /* The three vertices are not collinear; the triangulation is one */
09842       /*   triangle, namely `midtri'.                                   */
09843       setorg(midtri, sortarray[0]);
09844       setdest(tri1, sortarray[0]);
09845       setorg(tri3, sortarray[0]);
09846       /* Apices of tri1, tri2, and tri3 are left NULL. */
09847       if (area > 0.0) {
09848         /* The vertices are in counterclockwise order. */
09849         setdest(midtri, sortarray[1]);
09850         setorg(tri1, sortarray[1]);
09851         setdest(tri2, sortarray[1]);
09852         setapex(midtri, sortarray[2]);
09853         setorg(tri2, sortarray[2]);
09854         setdest(tri3, sortarray[2]);
09855       } else {
09856         /* The vertices are in clockwise order. */
09857         setdest(midtri, sortarray[2]);
09858         setorg(tri1, sortarray[2]);
09859         setdest(tri2, sortarray[2]);
09860         setapex(midtri, sortarray[1]);
09861         setorg(tri2, sortarray[1]);
09862         setdest(tri3, sortarray[1]);
09863       }
09864       /* The topology does not depend on how the vertices are ordered. */
09865       bond(midtri, tri1);
09866       lnextself(midtri);
09867       bond(midtri, tri2);
09868       lnextself(midtri);
09869       bond(midtri, tri3);
09870       lprevself(tri1);
09871       lnextself(tri2);
09872       bond(tri1, tri2);
09873       lprevself(tri1);
09874       lprevself(tri3);
09875       bond(tri1, tri3);
09876       lnextself(tri2);
09877       lprevself(tri3);
09878       bond(tri2, tri3);
09879       /* Ensure that the origin of `farleft' is sortarray[0]. */
09880       otricopy(tri1, *farleft);
09881       /* Ensure that the destination of `farright' is sortarray[2]. */
09882       if (area > 0.0) {
09883         otricopy(tri2, *farright);
09884       } else {
09885         lnext(*farleft, *farright);
09886       }
09887     }
09888     if (b->verbose > 2) {
09889       printf("  Creating ");
09890       printtriangle(m, b, &midtri);
09891       printf("  Creating ");
09892       printtriangle(m, b, &tri1);
09893       printf("  Creating ");
09894       printtriangle(m, b, &tri2);
09895       printf("  Creating ");
09896       printtriangle(m, b, &tri3);
09897     }
09898     return;
09899   } else {
09900     /* Split the vertices in half. */
09901     divider = vertices >> 1;
09902     /* Recursively triangulate each half. */
09903     divconqrecurse(m, b, sortarray, divider, 1 - axis, farleft, &innerleft);
09904     divconqrecurse(m, b, &sortarray[divider], vertices - divider, 1 - axis,
09905                    &innerright, farright);
09906     if (b->verbose > 1) {
09907       printf("  Joining triangulations with %d and %d vertices.\n", divider,
09908              vertices - divider);
09909     }
09910     /* Merge the two triangulations into one. */
09911     mergehulls(m, b, farleft, &innerleft, &innerright, farright, axis);
09912   }
09913 }
09914 
09915 #ifdef ANSI_DECLARATORS
09916 long removeghosts(struct mesh *m, struct behavior *b, struct otri *startghost)
09917 #else /* not ANSI_DECLARATORS */
09918 long removeghosts(m, b, startghost)
09919 struct mesh *m;
09920 struct behavior *b;
09921 struct otri *startghost;
09922 #endif /* not ANSI_DECLARATORS */
09923 
09924 {
09925   struct otri searchedge;
09926   struct otri dissolveedge;
09927   struct otri deadtriangle;
09928   vertex markorg;
09929   long hullsize;
09930   triangle ptr;                         /* Temporary variable used by sym(). */
09931 
09932   if (b->verbose) {
09933     printf("  Removing ghost triangles.\n");
09934   }
09935   /* Find an edge on the convex hull to start point location from. */
09936   lprev(*startghost, searchedge);
09937   symself(searchedge);
09938   m->dummytri[0] = encode(searchedge);
09939   /* Remove the bounding box and count the convex hull edges. */
09940   otricopy(*startghost, dissolveedge);
09941   hullsize = 0;
09942   do {
09943     hullsize++;
09944     lnext(dissolveedge, deadtriangle);
09945     lprevself(dissolveedge);
09946     symself(dissolveedge);
09947     /* If no PSLG is involved, set the boundary markers of all the vertices */
09948     /*   on the convex hull.  If a PSLG is used, this step is done later.   */
09949     if (!b->poly) {
09950       /* Watch out for the case where all the input vertices are collinear. */
09951       if (dissolveedge.tri != m->dummytri) {
09952         org(dissolveedge, markorg);
09953         if (vertexmark(markorg) == 0) {
09954           setvertexmark(markorg, 1);
09955         }
09956       }
09957     }
09958     /* Remove a bounding triangle from a convex hull triangle. */
09959     dissolve(dissolveedge);
09960     /* Find the next bounding triangle. */
09961     sym(deadtriangle, dissolveedge);
09962     /* Delete the bounding triangle. */
09963     triangledealloc(m, deadtriangle.tri);
09964   } while (!otriequal(dissolveedge, *startghost));
09965   return hullsize;
09966 }
09967 
09968 /*****************************************************************************/
09969 /*                                                                           */
09970 /*  divconqdelaunay()   Form a Delaunay triangulation by the divide-and-     */
09971 /*                      conquer method.                                      */
09972 /*                                                                           */
09973 /*  Sorts the vertices, calls a recursive procedure to triangulate them, and */
09974 /*  removes the bounding box, setting boundary markers as appropriate.       */
09975 /*                                                                           */
09976 /*****************************************************************************/
09977 
09978 #ifdef ANSI_DECLARATORS
09979 long divconqdelaunay(struct mesh *m, struct behavior *b)
09980 #else /* not ANSI_DECLARATORS */
09981 long divconqdelaunay(m, b)
09982 struct mesh *m;
09983 struct behavior *b;
09984 #endif /* not ANSI_DECLARATORS */
09985 
09986 {
09987   vertex *sortarray;
09988   struct otri hullleft, hullright;
09989   int divider;
09990   int i, j;
09991 
09992   if (b->verbose) {
09993     printf("  Sorting vertices.\n");
09994   }
09995 
09996   /* Allocate an array of pointers to vertices for sorting. */
09997   sortarray = (vertex *) trimalloc(m->invertices * (int) sizeof(vertex));
09998   traversalinit(&m->vertices);
09999   for (i = 0; i < m->invertices; i++) {
10000     sortarray[i] = vertextraverse(m);
10001   }
10002   /* Sort the vertices. */
10003   vertexsort(sortarray, m->invertices);
10004   /* Discard duplicate vertices, which can really mess up the algorithm. */
10005   i = 0;
10006   for (j = 1; j < m->invertices; j++) {
10007     if ((sortarray[i][0] == sortarray[j][0])
10008         && (sortarray[i][1] == sortarray[j][1])) {
10009       if (!b->quiet) {
10010         printf(
10011 "Warning:  A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n",
10012                sortarray[j][0], sortarray[j][1]);
10013       }
10014       setvertextype(sortarray[j], UNDEADVERTEX);
10015       m->undeads++;
10016     } else {
10017       i++;
10018       sortarray[i] = sortarray[j];
10019     }
10020   }
10021   i++;
10022   if (b->dwyer) {
10023     /* Re-sort the array of vertices to accommodate alternating cuts. */
10024     divider = i >> 1;
10025     if (i - divider >= 2) {
10026       if (divider >= 2) {
10027         alternateaxes(sortarray, divider, 1);
10028       }
10029       alternateaxes(&sortarray[divider], i - divider, 1);
10030     }
10031   }
10032 
10033   if (b->verbose) {
10034     printf("  Forming triangulation.\n");
10035   }
10036 
10037   /* Form the Delaunay triangulation. */
10038   divconqrecurse(m, b, sortarray, i, 0, &hullleft, &hullright);
10039   trifree((VOID *) sortarray);
10040 
10041   return removeghosts(m, b, &hullleft);
10042 }
10043 
10046 /********* Divide-and-conquer Delaunay triangulation ends here       *********/
10047 
10048 /********* Incremental Delaunay triangulation begins here            *********/
10052 /*****************************************************************************/
10053 /*                                                                           */
10054 /*  boundingbox()   Form an "infinite" bounding triangle to insert vertices  */
10055 /*                  into.                                                    */
10056 /*                                                                           */
10057 /*  The vertices at "infinity" are assigned finite coordinates, which are    */
10058 /*  used by the point location routines, but (mostly) ignored by the         */
10059 /*  Delaunay edge flip routines.                                             */
10060 /*                                                                           */
10061 /*****************************************************************************/
10062 
10063 #ifndef REDUCED
10064 
10065 #ifdef ANSI_DECLARATORS
10066 void boundingbox(struct mesh *m, struct behavior *b)
10067 #else /* not ANSI_DECLARATORS */
10068 void boundingbox(m, b)
10069 struct mesh *m;
10070 struct behavior *b;
10071 #endif /* not ANSI_DECLARATORS */
10072 
10073 {
10074   struct otri inftri;          /* Handle for the triangular bounding box. */
10075   REAL width;
10076 
10077   if (b->verbose) {
10078     printf("  Creating triangular bounding box.\n");
10079   }
10080   /* Find the width (or height, whichever is larger) of the triangulation. */
10081   width = m->xmax - m->xmin;
10082   if (m->ymax - m->ymin > width) {
10083     width = m->ymax - m->ymin;
10084   }
10085   if (width == 0.0) {
10086     width = 1.0;
10087   }
10088   /* Create the vertices of the bounding box. */
10089   m->infvertex1 = (vertex) trimalloc(m->vertices.itembytes);
10090   m->infvertex2 = (vertex) trimalloc(m->vertices.itembytes);
10091   m->infvertex3 = (vertex) trimalloc(m->vertices.itembytes);
10092   m->infvertex1[0] = m->xmin - 50.0 * width;
10093   m->infvertex1[1] = m->ymin - 40.0 * width;
10094   m->infvertex2[0] = m->xmax + 50.0 * width;
10095   m->infvertex2[1] = m->ymin - 40.0 * width;
10096   m->infvertex3[0] = 0.5 * (m->xmin + m->xmax);
10097   m->infvertex3[1] = m->ymax + 60.0 * width;
10098 
10099   /* Create the bounding box. */
10100   maketriangle(m, b, &inftri);
10101   setorg(inftri, m->infvertex1);
10102   setdest(inftri, m->infvertex2);
10103   setapex(inftri, m->infvertex3);
10104   /* Link dummytri to the bounding box so we can always find an */
10105   /*   edge to begin searching (point location) from.           */
10106   m->dummytri[0] = (triangle) inftri.tri;
10107   if (b->verbose > 2) {
10108     printf("  Creating ");
10109     printtriangle(m, b, &inftri);
10110   }
10111 }
10112 
10113 #endif /* not REDUCED */
10114 
10115 /*****************************************************************************/
10116 /*                                                                           */
10117 /*  removebox()   Remove the "infinite" bounding triangle, setting boundary  */
10118 /*                markers as appropriate.                                    */
10119 /*                                                                           */
10120 /*  The triangular bounding box has three boundary triangles (one for each   */
10121 /*  side of the bounding box), and a bunch of triangles fanning out from     */
10122 /*  the three bounding box vertices (one triangle for each edge of the       */
10123 /*  convex hull of the inner mesh).  This routine removes these triangles.   */
10124 /*                                                                           */
10125 /*  Returns the number of edges on the convex hull of the triangulation.     */
10126 /*                                                                           */
10127 /*****************************************************************************/
10128 
10129 #ifndef REDUCED
10130 
10131 #ifdef ANSI_DECLARATORS
10132 long removebox(struct mesh *m, struct behavior *b)
10133 #else /* not ANSI_DECLARATORS */
10134 long removebox(m, b)
10135 struct mesh *m;
10136 struct behavior *b;
10137 #endif /* not ANSI_DECLARATORS */
10138 
10139 {
10140   struct otri deadtriangle;
10141   struct otri searchedge;
10142   struct otri checkedge;
10143   struct otri nextedge, finaledge, dissolveedge;
10144   vertex markorg;
10145   long hullsize;
10146   triangle ptr;                         /* Temporary variable used by sym(). */
10147 
10148   if (b->verbose) {
10149     printf("  Removing triangular bounding box.\n");
10150   }
10151   /* Find a boundary triangle. */
10152   nextedge.tri = m->dummytri;
10153   nextedge.orient = 0;
10154   symself(nextedge);
10155   /* Mark a place to stop. */
10156   lprev(nextedge, finaledge);
10157   lnextself(nextedge);
10158   symself(nextedge);
10159   /* Find a triangle (on the boundary of the vertex set) that isn't */
10160   /*   a bounding box triangle.                                     */
10161   lprev(nextedge, searchedge);
10162   symself(searchedge);
10163   /* Check whether nextedge is another boundary triangle */
10164   /*   adjacent to the first one.                        */
10165   lnext(nextedge, checkedge);
10166   symself(checkedge);
10167   if (checkedge.tri == m->dummytri) {
10168     /* Go on to the next triangle.  There are only three boundary   */
10169     /*   triangles, and this next triangle cannot be the third one, */
10170     /*   so it's safe to stop here.                                 */
10171     lprevself(searchedge);
10172     symself(searchedge);
10173   }
10174   /* Find a new boundary edge to search from, as the current search */
10175   /*   edge lies on a bounding box triangle and will be deleted.    */
10176   m->dummytri[0] = encode(searchedge);
10177   hullsize = -2l;
10178   while (!otriequal(nextedge, finaledge)) {
10179     hullsize++;
10180     lprev(nextedge, dissolveedge);
10181     symself(dissolveedge);
10182     /* If not using a PSLG, the vertices should be marked now. */
10183     /*   (If using a PSLG, markhull() will do the job.)        */
10184     if (!b->poly) {
10185       /* Be careful!  One must check for the case where all the input     */
10186       /*   vertices are collinear, and thus all the triangles are part of */
10187       /*   the bounding box.  Otherwise, the setvertexmark() call below   */
10188       /*   will cause a bad pointer reference.                            */
10189       if (dissolveedge.tri != m->dummytri) {
10190         org(dissolveedge, markorg);
10191         if (vertexmark(markorg) == 0) {
10192           setvertexmark(markorg, 1);
10193         }
10194       }
10195     }
10196     /* Disconnect the bounding box triangle from the mesh triangle. */
10197     dissolve(dissolveedge);
10198     lnext(nextedge, deadtriangle);
10199     sym(deadtriangle, nextedge);
10200     /* Get rid of the bounding box triangle. */
10201     triangledealloc(m, deadtriangle.tri);
10202     /* Do we need to turn the corner? */
10203     if (nextedge.tri == m->dummytri) {
10204       /* Turn the corner. */
10205       otricopy(dissolveedge, nextedge);
10206     }
10207   }
10208   triangledealloc(m, finaledge.tri);
10209 
10210   trifree((VOID *) m->infvertex1);  /* Deallocate the bounding box vertices. */
10211   trifree((VOID *) m->infvertex2);
10212   trifree((VOID *) m->infvertex3);
10213 
10214   return hullsize;
10215 }
10216 
10217 #endif /* not REDUCED */
10218 
10219 /*****************************************************************************/
10220 /*                                                                           */
10221 /*  incrementaldelaunay()   Form a Delaunay triangulation by incrementally   */
10222 /*                          inserting vertices.                              */
10223 /*                                                                           */
10224 /*  Returns the number of edges on the convex hull of the triangulation.     */
10225 /*                                                                           */
10226 /*****************************************************************************/
10227 
10228 #ifndef REDUCED
10229 
10230 #ifdef ANSI_DECLARATORS
10231 long incrementaldelaunay(struct mesh *m, struct behavior *b)
10232 #else /* not ANSI_DECLARATORS */
10233 long incrementaldelaunay(m, b)
10234 struct mesh *m;
10235 struct behavior *b;
10236 #endif /* not ANSI_DECLARATORS */
10237 
10238 {
10239   struct otri starttri;
10240   vertex vertexloop;
10241 
10242   /* Create a triangular bounding box. */
10243   boundingbox(m, b);
10244   if (b->verbose) {
10245     printf("  Incrementally inserting vertices.\n");
10246   }
10247   traversalinit(&m->vertices);
10248   vertexloop = vertextraverse(m);
10249   while (vertexloop != (vertex) NULL) {
10250     starttri.tri = m->dummytri;
10251     if (insertvertex(m, b, vertexloop, &starttri, (struct osub *) NULL, 0, 0)
10252         == DUPLICATEVERTEX) {
10253       if (!b->quiet) {
10254         printf(
10255 "Warning:  A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n",
10256                vertexloop[0], vertexloop[1]);
10257       }
10258       setvertextype(vertexloop, UNDEADVERTEX);
10259       m->undeads++;
10260     }
10261     vertexloop = vertextraverse(m);
10262   }
10263   /* Remove the bounding box. */
10264   return removebox(m, b);
10265 }
10266 
10267 #endif /* not REDUCED */
10268 
10271 /********* Incremental Delaunay triangulation ends here              *********/
10272 
10273 /********* Sweepline Delaunay triangulation begins here              *********/
10277 #ifndef REDUCED
10278 
10279 #ifdef ANSI_DECLARATORS
10280 void eventheapinsert(struct event **heap, int heapsize, struct event *newevent)
10281 #else /* not ANSI_DECLARATORS */
10282 void eventheapinsert(heap, heapsize, newevent)
10283 struct event **heap;
10284 int heapsize;
10285 struct event *newevent;
10286 #endif /* not ANSI_DECLARATORS */
10287 
10288 {
10289   REAL eventx, eventy;
10290   int eventnum;
10291   int parent;
10292   int notdone;
10293 
10294   eventx = newevent->xkey;
10295   eventy = newevent->ykey;
10296   eventnum = heapsize;
10297   notdone = eventnum > 0;
10298   while (notdone) {
10299     parent = (eventnum - 1) >> 1;
10300     if ((heap[parent]->ykey < eventy) ||
10301         ((heap[parent]->ykey == eventy)
10302          && (heap[parent]->xkey <= eventx))) {
10303       notdone = 0;
10304     } else {
10305       heap[eventnum] = heap[parent];
10306       heap[eventnum]->heapposition = eventnum;
10307 
10308       eventnum = parent;
10309       notdone = eventnum > 0;
10310     }
10311   }
10312   heap[eventnum] = newevent;
10313   newevent->heapposition = eventnum;
10314 }
10315 
10316 #endif /* not REDUCED */
10317 
10318 #ifndef REDUCED
10319 
10320 #ifdef ANSI_DECLARATORS
10321 void eventheapify(struct event **heap, int heapsize, int eventnum)
10322 #else /* not ANSI_DECLARATORS */
10323 void eventheapify(heap, heapsize, eventnum)
10324 struct event **heap;
10325 int heapsize;
10326 int eventnum;
10327 #endif /* not ANSI_DECLARATORS */
10328 
10329 {
10330   struct event *thisevent;
10331   REAL eventx, eventy;
10332   int leftchild, rightchild;
10333   int smallest;
10334   int notdone;
10335 
10336   thisevent = heap[eventnum];
10337   eventx = thisevent->xkey;
10338   eventy = thisevent->ykey;
10339   leftchild = 2 * eventnum + 1;
10340   notdone = leftchild < heapsize;
10341   while (notdone) {
10342     if ((heap[leftchild]->ykey < eventy) ||
10343         ((heap[leftchild]->ykey == eventy)
10344          && (heap[leftchild]->xkey < eventx))) {
10345       smallest = leftchild;
10346     } else {
10347       smallest = eventnum;
10348     }
10349     rightchild = leftchild + 1;
10350     if (rightchild < heapsize) {
10351       if ((heap[rightchild]->ykey < heap[smallest]->ykey) ||
10352           ((heap[rightchild]->ykey == heap[smallest]->ykey)
10353            && (heap[rightchild]->xkey < heap[smallest]->xkey))) {
10354         smallest = rightchild;
10355       }
10356     }
10357     if (smallest == eventnum) {
10358       notdone = 0;
10359     } else {
10360       heap[eventnum] = heap[smallest];
10361       heap[eventnum]->heapposition = eventnum;
10362       heap[smallest] = thisevent;
10363       thisevent->heapposition = smallest;
10364 
10365       eventnum = smallest;
10366       leftchild = 2 * eventnum + 1;
10367       notdone = leftchild < heapsize;
10368     }
10369   }
10370 }
10371 
10372 #endif /* not REDUCED */
10373 
10374 #ifndef REDUCED
10375 
10376 #ifdef ANSI_DECLARATORS
10377 void eventheapdelete(struct event **heap, int heapsize, int eventnum)
10378 #else /* not ANSI_DECLARATORS */
10379 void eventheapdelete(heap, heapsize, eventnum)
10380 struct event **heap;
10381 int heapsize;
10382 int eventnum;
10383 #endif /* not ANSI_DECLARATORS */
10384 
10385 {
10386   struct event *moveevent;
10387   REAL eventx, eventy;
10388   int parent;
10389   int notdone;
10390 
10391   moveevent = heap[heapsize - 1];
10392   if (eventnum > 0) {
10393     eventx = moveevent->xkey;
10394     eventy = moveevent->ykey;
10395     do {
10396       parent = (eventnum - 1) >> 1;
10397       if ((heap[parent]->ykey < eventy) ||
10398           ((heap[parent]->ykey == eventy)
10399            && (heap[parent]->xkey <= eventx))) {
10400         notdone = 0;
10401       } else {
10402         heap[eventnum] = heap[parent];
10403         heap[eventnum]->heapposition = eventnum;
10404 
10405         eventnum = parent;
10406         notdone = eventnum > 0;
10407       }
10408     } while (notdone);
10409   }
10410   heap[eventnum] = moveevent;
10411   moveevent->heapposition = eventnum;
10412   eventheapify(heap, heapsize - 1, eventnum);
10413 }
10414 
10415 #endif /* not REDUCED */
10416 
10417 #ifndef REDUCED
10418 
10419 #ifdef ANSI_DECLARATORS
10420 void createeventheap(struct mesh *m, struct event ***eventheap,
10421                      struct event **events, struct event **freeevents)
10422 #else /* not ANSI_DECLARATORS */
10423 void createeventheap(m, eventheap, events, freeevents)
10424 struct mesh *m;
10425 struct event ***eventheap;
10426 struct event **events;
10427 struct event **freeevents;
10428 #endif /* not ANSI_DECLARATORS */
10429 
10430 {
10431   vertex thisvertex;
10432   int maxevents;
10433   int i;
10434 
10435   maxevents = (3 * m->invertices) / 2;
10436   *eventheap = (struct event **) trimalloc(maxevents *
10437                                            (int) sizeof(struct event *));
10438   *events = (struct event *) trimalloc(maxevents * (int) sizeof(struct event));
10439   traversalinit(&m->vertices);
10440   for (i = 0; i < m->invertices; i++) {
10441     thisvertex = vertextraverse(m);
10442     (*events)[i].eventptr = (VOID *) thisvertex;
10443     (*events)[i].xkey = thisvertex[0];
10444     (*events)[i].ykey = thisvertex[1];
10445     eventheapinsert(*eventheap, i, *events + i);
10446   }
10447   *freeevents = (struct event *) NULL;
10448   for (i = maxevents - 1; i >= m->invertices; i--) {
10449     (*events)[i].eventptr = (VOID *) *freeevents;
10450     *freeevents = *events + i;
10451   }
10452 }
10453 
10454 #endif /* not REDUCED */
10455 
10456 #ifndef REDUCED
10457 
10458 #ifdef ANSI_DECLARATORS
10459 int rightofhyperbola(struct mesh *m, struct otri *fronttri, vertex newsite)
10460 #else /* not ANSI_DECLARATORS */
10461 int rightofhyperbola(m, fronttri, newsite)
10462 struct mesh *m;
10463 struct otri *fronttri;
10464 vertex newsite;
10465 #endif /* not ANSI_DECLARATORS */
10466 
10467 {
10468   vertex leftvertex, rightvertex;
10469   REAL dxa, dya, dxb, dyb;
10470 
10471   m->hyperbolacount++;
10472 
10473   dest(*fronttri, leftvertex);
10474   apex(*fronttri, rightvertex);
10475   if ((leftvertex[1] < rightvertex[1]) ||
10476       ((leftvertex[1] == rightvertex[1]) &&
10477        (leftvertex[0] < rightvertex[0]))) {
10478     if (newsite[0] >= rightvertex[0]) {
10479       return 1;
10480     }
10481   } else {
10482     if (newsite[0] <= leftvertex[0]) {
10483       return 0;
10484     }
10485   }
10486   dxa = leftvertex[0] - newsite[0];
10487   dya = leftvertex[1] - newsite[1];
10488   dxb = rightvertex[0] - newsite[0];
10489   dyb = rightvertex[1] - newsite[1];
10490   return dya * (dxb * dxb + dyb * dyb) > dyb * (dxa * dxa + dya * dya);
10491 }
10492 
10493 #endif /* not REDUCED */
10494 
10495 #ifndef REDUCED
10496 
10497 #ifdef ANSI_DECLARATORS
10498 REAL circletop(struct mesh *m, vertex pa, vertex pb, vertex pc, REAL ccwabc)
10499 #else /* not ANSI_DECLARATORS */
10500 REAL circletop(m, pa, pb, pc, ccwabc)
10501 struct mesh *m;
10502 vertex pa;
10503 vertex pb;
10504 vertex pc;
10505 REAL ccwabc;
10506 #endif /* not ANSI_DECLARATORS */
10507 
10508 {
10509   REAL xac, yac, xbc, ybc, xab, yab;
10510   REAL aclen2, bclen2, ablen2;
10511 
10512   m->circletopcount++;
10513 
10514   xac = pa[0] - pc[0];
10515   yac = pa[1] - pc[1];
10516   xbc = pb[0] - pc[0];
10517   ybc = pb[1] - pc[1];
10518   xab = pa[0] - pb[0];
10519   yab = pa[1] - pb[1];
10520   aclen2 = xac * xac + yac * yac;
10521   bclen2 = xbc * xbc + ybc * ybc;
10522   ablen2 = xab * xab + yab * yab;
10523   return pc[1] + (xac * bclen2 - xbc * aclen2 + sqrt(aclen2 * bclen2 * ablen2))
10524                / (2.0 * ccwabc);
10525 }
10526 
10527 #endif /* not REDUCED */
10528 
10529 #ifndef REDUCED
10530 
10531 #ifdef ANSI_DECLARATORS
10532 void check4deadevent(struct otri *checktri, struct event **freeevents,
10533                      struct event **eventheap, int *heapsize)
10534 #else /* not ANSI_DECLARATORS */
10535 void check4deadevent(checktri, freeevents, eventheap, heapsize)
10536 struct otri *checktri;
10537 struct event **freeevents;
10538 struct event **eventheap;
10539 int *heapsize;
10540 #endif /* not ANSI_DECLARATORS */
10541 
10542 {
10543   struct event *deadevent;
10544   vertex eventvertex;
10545   int eventnum;
10546 
10547   org(*checktri, eventvertex);
10548   if (eventvertex != (vertex) NULL) {
10549     deadevent = (struct event *) eventvertex;
10550     eventnum = deadevent->heapposition;
10551     deadevent->eventptr = (VOID *) *freeevents;
10552     *freeevents = deadevent;
10553     eventheapdelete(eventheap, *heapsize, eventnum);
10554     (*heapsize)--;
10555     setorg(*checktri, NULL);
10556   }
10557 }
10558 
10559 #endif /* not REDUCED */
10560 
10561 #ifndef REDUCED
10562 
10563 #ifdef ANSI_DECLARATORS
10564 struct splaynode *splay(struct mesh *m, struct splaynode *splaytree,
10565                         vertex searchpoint, struct otri *searchtri)
10566 #else /* not ANSI_DECLARATORS */
10567 struct splaynode *splay(m, splaytree, searchpoint, searchtri)
10568 struct mesh *m;
10569 struct splaynode *splaytree;
10570 vertex searchpoint;
10571 struct otri *searchtri;
10572 #endif /* not ANSI_DECLARATORS */
10573 
10574 {
10575   struct splaynode *child, *grandchild;
10576   struct splaynode *lefttree, *righttree;
10577   struct splaynode *leftright;
10578   vertex checkvertex;
10579   int rightofroot, rightofchild;
10580 
10581   if (splaytree == (struct splaynode *) NULL) {
10582     return (struct splaynode *) NULL;
10583   }
10584   dest(splaytree->keyedge, checkvertex);
10585   if (checkvertex == splaytree->keydest) {
10586     rightofroot = rightofhyperbola(m, &splaytree->keyedge, searchpoint);
10587     if (rightofroot) {
10588       otricopy(splaytree->keyedge, *searchtri);
10589       child = splaytree->rchild;
10590     } else {
10591       child = splaytree->lchild;
10592     }
10593     if (child == (struct splaynode *) NULL) {
10594       return splaytree;
10595     }
10596     dest(child->keyedge, checkvertex);
10597     if (checkvertex != child->keydest) {
10598       child = splay(m, child, searchpoint, searchtri);
10599       if (child == (struct splaynode *) NULL) {
10600         if (rightofroot) {
10601           splaytree->rchild = (struct splaynode *) NULL;
10602         } else {
10603           splaytree->lchild = (struct splaynode *) NULL;
10604         }
10605         return splaytree;
10606       }
10607     }
10608     rightofchild = rightofhyperbola(m, &child->keyedge, searchpoint);
10609     if (rightofchild) {
10610       otricopy(child->keyedge, *searchtri);
10611       grandchild = splay(m, child->rchild, searchpoint, searchtri);
10612       child->rchild = grandchild;
10613     } else {
10614       grandchild = splay(m, child->lchild, searchpoint, searchtri);
10615       child->lchild = grandchild;
10616     }
10617     if (grandchild == (struct splaynode *) NULL) {
10618       if (rightofroot) {
10619         splaytree->rchild = child->lchild;
10620         child->lchild = splaytree;
10621       } else {
10622         splaytree->lchild = child->rchild;
10623         child->rchild = splaytree;
10624       }
10625       return child;
10626     }
10627     if (rightofchild) {
10628       if (rightofroot) {
10629         splaytree->rchild = child->lchild;
10630         child->lchild = splaytree;
10631       } else {
10632         splaytree->lchild = grandchild->rchild;
10633         grandchild->rchild = splaytree;
10634       }
10635       child->rchild = grandchild->lchild;
10636       grandchild->lchild = child;
10637     } else {
10638       if (rightofroot) {
10639         splaytree->rchild = grandchild->lchild;
10640         grandchild->lchild = splaytree;
10641       } else {
10642         splaytree->lchild = child->rchild;
10643         child->rchild = splaytree;
10644       }
10645       child->lchild = grandchild->rchild;
10646       grandchild->rchild = child;
10647     }
10648     return grandchild;
10649   } else {
10650     lefttree = splay(m, splaytree->lchild, searchpoint, searchtri);
10651     righttree = splay(m, splaytree->rchild, searchpoint, searchtri);
10652 
10653     pooldealloc(&m->splaynodes, (VOID *) splaytree);
10654     if (lefttree == (struct splaynode *) NULL) {
10655       return righttree;
10656     } else if (righttree == (struct splaynode *) NULL) {
10657       return lefttree;
10658     } else if (lefttree->rchild == (struct splaynode *) NULL) {
10659       lefttree->rchild = righttree->lchild;
10660       righttree->lchild = lefttree;
10661       return righttree;
10662     } else if (righttree->lchild == (struct splaynode *) NULL) {
10663       righttree->lchild = lefttree->rchild;
10664       lefttree->rchild = righttree;
10665       return lefttree;
10666     } else {
10667 /*      printf("Holy Toledo!!!\n"); */
10668       leftright = lefttree->rchild;
10669       while (leftright->rchild != (struct splaynode *) NULL) {
10670         leftright = leftright->rchild;
10671       }
10672       leftright->rchild = righttree;
10673       return lefttree;
10674     }
10675   }
10676 }
10677 
10678 #endif /* not REDUCED */
10679 
10680 #ifndef REDUCED
10681 
10682 #ifdef ANSI_DECLARATORS
10683 struct splaynode *splayinsert(struct mesh *m, struct splaynode *splayroot,
10684                               struct otri *newkey, vertex searchpoint)
10685 #else /* not ANSI_DECLARATORS */
10686 struct splaynode *splayinsert(m, splayroot, newkey, searchpoint)
10687 struct mesh *m;
10688 struct splaynode *splayroot;
10689 struct otri *newkey;
10690 vertex searchpoint;
10691 #endif /* not ANSI_DECLARATORS */
10692 
10693 {
10694   struct splaynode *newsplaynode;
10695 
10696   newsplaynode = (struct splaynode *) poolalloc(&m->splaynodes);
10697   otricopy(*newkey, newsplaynode->keyedge);
10698   dest(*newkey, newsplaynode->keydest);
10699   if (splayroot == (struct splaynode *) NULL) {
10700     newsplaynode->lchild = (struct splaynode *) NULL;
10701     newsplaynode->rchild = (struct splaynode *) NULL;
10702   } else if (rightofhyperbola(m, &splayroot->keyedge, searchpoint)) {
10703     newsplaynode->lchild = splayroot;
10704     newsplaynode->rchild = splayroot->rchild;
10705     splayroot->rchild = (struct splaynode *) NULL;
10706   } else {
10707     newsplaynode->lchild = splayroot->lchild;
10708     newsplaynode->rchild = splayroot;
10709     splayroot->lchild = (struct splaynode *) NULL;
10710   }
10711   return newsplaynode;
10712 }
10713 
10714 #endif /* not REDUCED */
10715 
10716 #ifndef REDUCED
10717 
10718 #ifdef ANSI_DECLARATORS
10719 struct splaynode *circletopinsert(struct mesh *m, struct behavior *b,
10720                                   struct splaynode *splayroot,
10721                                   struct otri *newkey,
10722                                   vertex pa, vertex pb, vertex pc, REAL topy)
10723 #else /* not ANSI_DECLARATORS */
10724 struct splaynode *circletopinsert(m, b, splayroot, newkey, pa, pb, pc, topy)
10725 struct mesh *m;
10726 struct behavior *b;
10727 struct splaynode *splayroot;
10728 struct otri *newkey;
10729 vertex pa;
10730 vertex pb;
10731 vertex pc;
10732 REAL topy;
10733 #endif /* not ANSI_DECLARATORS */
10734 
10735 {
10736   REAL ccwabc;
10737   REAL xac, yac, xbc, ybc;
10738   REAL aclen2, bclen2;
10739   REAL searchpoint[2];
10740   struct otri dummytri;
10741 
10742   ccwabc = counterclockwise(m, b, pa, pb, pc);
10743   xac = pa[0] - pc[0];
10744   yac = pa[1] - pc[1];
10745   xbc = pb[0] - pc[0];
10746   ybc = pb[1] - pc[1];
10747   aclen2 = xac * xac + yac * yac;
10748   bclen2 = xbc * xbc + ybc * ybc;
10749   searchpoint[0] = pc[0] - (yac * bclen2 - ybc * aclen2) / (2.0 * ccwabc);
10750   searchpoint[1] = topy;
10751   return splayinsert(m, splay(m, splayroot, (vertex) searchpoint, &dummytri),
10752                      newkey, (vertex) searchpoint);
10753 }
10754 
10755 #endif /* not REDUCED */
10756 
10757 #ifndef REDUCED
10758 
10759 #ifdef ANSI_DECLARATORS
10760 struct splaynode *frontlocate(struct mesh *m, struct splaynode *splayroot,
10761                               struct otri *bottommost, vertex searchvertex,
10762                               struct otri *searchtri, int *farright)
10763 #else /* not ANSI_DECLARATORS */
10764 struct splaynode *frontlocate(m, splayroot, bottommost, searchvertex,
10765                               searchtri, farright)
10766 struct mesh *m;
10767 struct splaynode *splayroot;
10768 struct otri *bottommost;
10769 vertex searchvertex;
10770 struct otri *searchtri;
10771 int *farright;
10772 #endif /* not ANSI_DECLARATORS */
10773 
10774 {
10775   int farrightflag;
10776   triangle ptr;                       /* Temporary variable used by onext(). */
10777 
10778   otricopy(*bottommost, *searchtri);
10779   splayroot = splay(m, splayroot, searchvertex, searchtri);
10780 
10781   farrightflag = 0;
10782   while (!farrightflag && rightofhyperbola(m, searchtri, searchvertex)) {
10783     onextself(*searchtri);
10784     farrightflag = otriequal(*searchtri, *bottommost);
10785   }
10786   *farright = farrightflag;
10787   return splayroot;
10788 }
10789 
10790 #endif /* not REDUCED */
10791 
10792 #ifndef REDUCED
10793 
10794 #ifdef ANSI_DECLARATORS
10795 long sweeplinedelaunay(struct mesh *m, struct behavior *b)
10796 #else /* not ANSI_DECLARATORS */
10797 long sweeplinedelaunay(m, b)
10798 struct mesh *m;
10799 struct behavior *b;
10800 #endif /* not ANSI_DECLARATORS */
10801 
10802 {
10803   struct event **eventheap;
10804   struct event *events;
10805   struct event *freeevents;
10806   struct event *nextevent;
10807   struct event *newevent;
10808   struct splaynode *splayroot;
10809   struct otri bottommost;
10810   struct otri searchtri;
10811   struct otri fliptri;
10812   struct otri lefttri, righttri, farlefttri, farrighttri;
10813   struct otri inserttri;
10814   vertex firstvertex, secondvertex;
10815   vertex nextvertex, lastvertex;
10816   vertex connectvertex;
10817   vertex leftvertex, midvertex, rightvertex;
10818   REAL lefttest, righttest;
10819   int heapsize;
10820   int check4events, farrightflag;
10821   triangle ptr;   /* Temporary variable used by sym(), onext(), and oprev(). */
10822 
10823   poolinit(&m->splaynodes, sizeof(struct splaynode), SPLAYNODEPERBLOCK,
10824            SPLAYNODEPERBLOCK, 0);
10825   splayroot = (struct splaynode *) NULL;
10826 
10827   if (b->verbose) {
10828     printf("  Placing vertices in event heap.\n");
10829   }
10830   createeventheap(m, &eventheap, &events, &freeevents);
10831   heapsize = m->invertices;
10832 
10833   if (b->verbose) {
10834     printf("  Forming triangulation.\n");
10835   }
10836   maketriangle(m, b, &lefttri);
10837   maketriangle(m, b, &righttri);
10838   bond(lefttri, righttri);
10839   lnextself(lefttri);
10840   lprevself(righttri);
10841   bond(lefttri, righttri);
10842   lnextself(lefttri);
10843   lprevself(righttri);
10844   bond(lefttri, righttri);
10845   firstvertex = (vertex) eventheap[0]->eventptr;
10846   eventheap[0]->eventptr = (VOID *) freeevents;
10847   freeevents = eventheap[0];
10848   eventheapdelete(eventheap, heapsize, 0);
10849   heapsize--;
10850   do {
10851     if (heapsize == 0) {
10852       printf("Error:  Input vertices are all identical.\n");
10853       triexit(1);
10854     }
10855     secondvertex = (vertex) eventheap[0]->eventptr;
10856     eventheap[0]->eventptr = (VOID *) freeevents;
10857     freeevents = eventheap[0];
10858     eventheapdelete(eventheap, heapsize, 0);
10859     heapsize--;
10860     if ((firstvertex[0] == secondvertex[0]) &&
10861         (firstvertex[1] == secondvertex[1])) {
10862       if (!b->quiet) {
10863         printf(
10864 "Warning:  A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n",
10865                secondvertex[0], secondvertex[1]);
10866       }
10867       setvertextype(secondvertex, UNDEADVERTEX);
10868       m->undeads++;
10869     }
10870   } while ((firstvertex[0] == secondvertex[0]) &&
10871            (firstvertex[1] == secondvertex[1]));
10872   setorg(lefttri, firstvertex);
10873   setdest(lefttri, secondvertex);
10874   setorg(righttri, secondvertex);
10875   setdest(righttri, firstvertex);
10876   lprev(lefttri, bottommost);
10877   lastvertex = secondvertex;
10878   while (heapsize > 0) {
10879     nextevent = eventheap[0];
10880     eventheapdelete(eventheap, heapsize, 0);
10881     heapsize--;
10882     check4events = 1;
10883     if (nextevent->xkey < m->xmin) {
10884       decode(nextevent->eventptr, fliptri);
10885       oprev(fliptri, farlefttri);
10886       check4deadevent(&farlefttri, &freeevents, eventheap, &heapsize);
10887       onext(fliptri, farrighttri);
10888       check4deadevent(&farrighttri, &freeevents, eventheap, &heapsize);
10889 
10890       if (otriequal(farlefttri, bottommost)) {
10891         lprev(fliptri, bottommost);
10892       }
10893       flip(m, b, &fliptri);
10894       setapex(fliptri, NULL);
10895       lprev(fliptri, lefttri);
10896       lnext(fliptri, righttri);
10897       sym(lefttri, farlefttri);
10898 
10899       if (randomnation(SAMPLERATE) == 0) {
10900         symself(fliptri);
10901         dest(fliptri, leftvertex);
10902         apex(fliptri, midvertex);
10903         org(fliptri, rightvertex);
10904         splayroot = circletopinsert(m, b, splayroot, &lefttri, leftvertex,
10905                                     midvertex, rightvertex, nextevent->ykey);
10906       }
10907     } else {
10908       nextvertex = (vertex) nextevent->eventptr;
10909       if ((nextvertex[0] == lastvertex[0]) &&
10910           (nextvertex[1] == lastvertex[1])) {
10911         if (!b->quiet) {
10912           printf(
10913 "Warning:  A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n",
10914                  nextvertex[0], nextvertex[1]);
10915         }
10916         setvertextype(nextvertex, UNDEADVERTEX);
10917         m->undeads++;
10918         check4events = 0;
10919       } else {
10920         lastvertex = nextvertex;
10921 
10922         splayroot = frontlocate(m, splayroot, &bottommost, nextvertex,
10923                                 &searchtri, &farrightflag);
10924 /*
10925         otricopy(bottommost, searchtri);
10926         farrightflag = 0;
10927         while (!farrightflag && rightofhyperbola(m, &searchtri, nextvertex)) {
10928           onextself(searchtri);
10929           farrightflag = otriequal(searchtri, bottommost);
10930         }
10931 */
10932 
10933         check4deadevent(&searchtri, &freeevents, eventheap, &heapsize);
10934 
10935         otricopy(searchtri, farrighttri);
10936         sym(searchtri, farlefttri);
10937         maketriangle(m, b, &lefttri);
10938         maketriangle(m, b, &righttri);
10939         dest(farrighttri, connectvertex);
10940         setorg(lefttri, connectvertex);
10941         setdest(lefttri, nextvertex);
10942         setorg(righttri, nextvertex);
10943         setdest(righttri, connectvertex);
10944         bond(lefttri, righttri);
10945         lnextself(lefttri);
10946         lprevself(righttri);
10947         bond(lefttri, righttri);
10948         lnextself(lefttri);
10949         lprevself(righttri);
10950         bond(lefttri, farlefttri);
10951         bond(righttri, farrighttri);
10952         if (!farrightflag && otriequal(farrighttri, bottommost)) {
10953           otricopy(lefttri, bottommost);
10954         }
10955 
10956         if (randomnation(SAMPLERATE) == 0) {
10957           splayroot = splayinsert(m, splayroot, &lefttri, nextvertex);
10958         } else if (randomnation(SAMPLERATE) == 0) {
10959           lnext(righttri, inserttri);
10960           splayroot = splayinsert(m, splayroot, &inserttri, nextvertex);
10961         }
10962       }
10963     }
10964     nextevent->eventptr = (VOID *) freeevents;
10965     freeevents = nextevent;
10966 
10967     if (check4events) {
10968       apex(farlefttri, leftvertex);
10969       dest(lefttri, midvertex);
10970       apex(lefttri, rightvertex);
10971       lefttest = counterclockwise(m, b, leftvertex, midvertex, rightvertex);
10972       if (lefttest > 0.0) {
10973         newevent = freeevents;
10974         freeevents = (struct event *) freeevents->eventptr;
10975         newevent->xkey = m->xminextreme;
10976         newevent->ykey = circletop(m, leftvertex, midvertex, rightvertex,
10977                                    lefttest);
10978         newevent->eventptr = (VOID *) encode(lefttri);
10979         eventheapinsert(eventheap, heapsize, newevent);
10980         heapsize++;
10981         setorg(lefttri, newevent);
10982       }
10983       apex(righttri, leftvertex);
10984       org(righttri, midvertex);
10985       apex(farrighttri, rightvertex);
10986       righttest = counterclockwise(m, b, leftvertex, midvertex, rightvertex);
10987       if (righttest > 0.0) {
10988         newevent = freeevents;
10989         freeevents = (struct event *) freeevents->eventptr;
10990         newevent->xkey = m->xminextreme;
10991         newevent->ykey = circletop(m, leftvertex, midvertex, rightvertex,
10992                                    righttest);
10993         newevent->eventptr = (VOID *) encode(farrighttri);
10994         eventheapinsert(eventheap, heapsize, newevent);
10995         heapsize++;
10996         setorg(farrighttri, newevent);
10997       }
10998     }
10999   }
11000 
11001   pooldeinit(&m->splaynodes);
11002   lprevself(bottommost);
11003   return removeghosts(m, b, &bottommost);
11004 }
11005 
11006 #endif /* not REDUCED */
11007 
11010 /********* Sweepline Delaunay triangulation ends here                *********/
11011 
11012 /********* General mesh construction routines begin here             *********/
11016 /*****************************************************************************/
11017 /*                                                                           */
11018 /*  delaunay()   Form a Delaunay triangulation.                              */
11019 /*                                                                           */
11020 /*****************************************************************************/
11021 
11022 #ifdef ANSI_DECLARATORS
11023 long delaunay(struct mesh *m, struct behavior *b)
11024 #else /* not ANSI_DECLARATORS */
11025 long delaunay(m, b)
11026 struct mesh *m;
11027 struct behavior *b;
11028 #endif /* not ANSI_DECLARATORS */
11029 
11030 {
11031   long hulledges;
11032 
11033   m->eextras = 0;
11034   initializetrisubpools(m, b);
11035 
11036 #ifdef REDUCED
11037   if (!b->quiet) {
11038     printf(
11039       "Constructing Delaunay triangulation by divide-and-conquer method.\n");
11040   }
11041   hulledges = divconqdelaunay(m, b);
11042 #else /* not REDUCED */
11043   if (!b->quiet) {
11044     printf("Constructing Delaunay triangulation ");
11045     if (b->incremental) {
11046       printf("by incremental method.\n");
11047     } else if (b->sweepline) {
11048       printf("by sweepline method.\n");
11049     } else {
11050       printf("by divide-and-conquer method.\n");
11051     }
11052   }
11053   if (b->incremental) {
11054     hulledges = incrementaldelaunay(m, b);
11055   } else if (b->sweepline) {
11056     hulledges = sweeplinedelaunay(m, b);
11057   } else {
11058     hulledges = divconqdelaunay(m, b);
11059   }
11060 #endif /* not REDUCED */
11061 
11062   if (m->triangles.items == 0) {
11063     /* The input vertices were all collinear, so there are no triangles. */
11064     return 0l;
11065   } else {
11066     return hulledges;
11067   }
11068 }
11069 
11070 /*****************************************************************************/
11071 /*                                                                           */
11072 /*  reconstruct()   Reconstruct a triangulation from its .ele (and possibly  */
11073 /*                  .poly) file.  Used when the -r switch is used.           */
11074 /*                                                                           */
11075 /*  Reads an .ele file and reconstructs the original mesh.  If the -p switch */
11076 /*  is used, this procedure will also read a .poly file and reconstruct the  */
11077 /*  subsegments of the original mesh.  If the -a switch is used, this        */
11078 /*  procedure will also read an .area file and set a maximum area constraint */
11079 /*  on each triangle.                                                        */
11080 /*                                                                           */
11081 /*  Vertices that are not corners of triangles, such as nodes on edges of    */
11082 /*  subparametric elements, are discarded.                                   */
11083 /*                                                                           */
11084 /*  This routine finds the adjacencies between triangles (and subsegments)   */
11085 /*  by forming one stack of triangles for each vertex.  Each triangle is on  */
11086 /*  three different stacks simultaneously.  Each triangle's subsegment       */
11087 /*  pointers are used to link the items in each stack.  This memory-saving   */
11088 /*  feature makes the code harder to read.  The most important thing to keep */
11089 /*  in mind is that each triangle is removed from a stack precisely when     */
11090 /*  the corresponding pointer is adjusted to refer to a subsegment rather    */
11091 /*  than the next triangle of the stack.                                     */
11092 /*                                                                           */
11093 /*****************************************************************************/
11094 
11095 #ifndef CDT_ONLY
11096 
11097 #ifdef TRILIBRARY
11098 
11099 #ifdef ANSI_DECLARATORS
11100 int reconstruct(struct mesh *m, struct behavior *b, int *trianglelist,
11101                 REAL *triangleattriblist, REAL *trianglearealist,
11102                 int elements, int corners, int attribs,
11103                 int *segmentlist,int *segmentmarkerlist, int numberofsegments)
11104 #else /* not ANSI_DECLARATORS */
11105 int reconstruct(m, b, trianglelist, triangleattriblist, trianglearealist,
11106                 elements, corners, attribs, segmentlist, segmentmarkerlist,
11107                 numberofsegments)
11108 struct mesh *m;
11109 struct behavior *b;
11110 int *trianglelist;
11111 REAL *triangleattriblist;
11112 REAL *trianglearealist;
11113 int elements;
11114 int corners;
11115 int attribs;
11116 int *segmentlist;
11117 int *segmentmarkerlist;
11118 int numberofsegments;
11119 #endif /* not ANSI_DECLARATORS */
11120 
11121 #else /* not TRILIBRARY */
11122 
11123 #ifdef ANSI_DECLARATORS
11124 long reconstruct(struct mesh *m, struct behavior *b, char *elefilename,
11125                  char *areafilename, char *polyfilename, FILE *polyfile)
11126 #else /* not ANSI_DECLARATORS */
11127 long reconstruct(m, b, elefilename, areafilename, polyfilename, polyfile)
11128 struct mesh *m;
11129 struct behavior *b;
11130 char *elefilename;
11131 char *areafilename;
11132 char *polyfilename;
11133 FILE *polyfile;
11134 #endif /* not ANSI_DECLARATORS */
11135 
11136 #endif /* not TRILIBRARY */
11137 
11138 {
11139 #ifdef TRILIBRARY
11140   int vertexindex;
11141   int attribindex;
11142 #else /* not TRILIBRARY */
11143   FILE *elefile;
11144   FILE *areafile;
11145   char inputline[INPUTLINESIZE];
11146   char *stringptr;
11147   int areaelements;
11148 #endif /* not TRILIBRARY */
11149   struct otri triangleloop;
11150   struct otri triangleleft;
11151   struct otri checktri;
11152   struct otri checkleft;
11153   struct otri checkneighbor;
11154   struct osub subsegloop;
11155   triangle *vertexarray;
11156   triangle *prevlink;
11157   triangle nexttri;
11158   vertex tdest, tapex;
11159   vertex checkdest, checkapex;
11160   vertex shorg;
11161   vertex killvertex;
11162   vertex segmentorg, segmentdest;
11163   REAL area;
11164   int corner[3];
11165   int end[2];
11166   int killvertexindex;
11167   int incorners;
11168   int segmentmarkers;
11169   int boundmarker;
11170   int aroundvertex;
11171   long hullsize;
11172   int notfound;
11173   long elementnumber, segmentnumber;
11174   int i, j;
11175   triangle ptr;                         /* Temporary variable used by sym(). */
11176 
11177 #ifdef TRILIBRARY
11178   m->inelements = elements;
11179   incorners = corners;
11180   if (incorners < 3) {
11181     printf("Error:  Triangles must have at least 3 vertices.\n");
11182     triexit(1);
11183   }
11184   m->eextras = attribs;
11185 #else /* not TRILIBRARY */
11186   /* Read the triangles from an .ele file. */
11187   if (!b->quiet) {
11188     printf("Opening %s.\n", elefilename);
11189   }
11190   elefile = fopen(elefilename, "r");
11191   if (elefile == (FILE *) NULL) {
11192     printf("  Error:  Cannot access file %s.\n", elefilename);
11193     triexit(1);
11194   }
11195   /* Read number of triangles, number of vertices per triangle, and */
11196   /*   number of triangle attributes from .ele file.                */
11197   stringptr = readline(inputline, elefile, elefilename);
11198   m->inelements = (int) strtol(stringptr, &stringptr, 0);
11199   stringptr = findfield(stringptr);
11200   if (*stringptr == '\0') {
11201     incorners = 3;
11202   } else {
11203     incorners = (int) strtol(stringptr, &stringptr, 0);
11204     if (incorners < 3) {
11205       printf("Error:  Triangles in %s must have at least 3 vertices.\n",
11206              elefilename);
11207       triexit(1);
11208     }
11209   }
11210   stringptr = findfield(stringptr);
11211   if (*stringptr == '\0') {
11212     m->eextras = 0;
11213   } else {
11214     m->eextras = (int) strtol(stringptr, &stringptr, 0);
11215   }
11216 #endif /* not TRILIBRARY */
11217 
11218   initializetrisubpools(m, b);
11219 
11220   /* Create the triangles. */
11221   for (elementnumber = 1; elementnumber <= m->inelements; elementnumber++) {
11222     maketriangle(m, b, &triangleloop);
11223     /* Mark the triangle as living. */
11224     triangleloop.tri[3] = (triangle) triangleloop.tri;
11225   }
11226 
11227   segmentmarkers = 0;
11228   if (b->poly) {
11229 #ifdef TRILIBRARY
11230     m->insegments = numberofsegments;
11231     segmentmarkers = segmentmarkerlist != (int *) NULL;
11232 #else /* not TRILIBRARY */
11233     /* Read number of segments and number of segment */
11234     /*   boundary markers from .poly file.           */
11235     stringptr = readline(inputline, polyfile, b->inpolyfilename);
11236     m->insegments = (int) strtol(stringptr, &stringptr, 0);
11237     stringptr = findfield(stringptr);
11238     if (*stringptr != '\0') {
11239       segmentmarkers = (int) strtol(stringptr, &stringptr, 0);
11240     }
11241 #endif /* not TRILIBRARY */
11242 
11243     /* Create the subsegments. */
11244     for (segmentnumber = 1; segmentnumber <= m->insegments; segmentnumber++) {
11245       makesubseg(m, &subsegloop);
11246       /* Mark the subsegment as living. */
11247       subsegloop.ss[2] = (subseg) subsegloop.ss;
11248     }
11249   }
11250 
11251 #ifdef TRILIBRARY
11252   vertexindex = 0;
11253   attribindex = 0;
11254 #else /* not TRILIBRARY */
11255   if (b->vararea) {
11256     /* Open an .area file, check for consistency with the .ele file. */
11257     if (!b->quiet) {
11258       printf("Opening %s.\n", areafilename);
11259     }
11260     areafile = fopen(areafilename, "r");
11261     if (areafile == (FILE *) NULL) {
11262       printf("  Error:  Cannot access file %s.\n", areafilename);
11263       triexit(1);
11264     }
11265     stringptr = readline(inputline, areafile, areafilename);
11266     areaelements = (int) strtol(stringptr, &stringptr, 0);
11267     if (areaelements != m->inelements) {
11268       printf("Error:  %s and %s disagree on number of triangles.\n",
11269              elefilename, areafilename);
11270       triexit(1);
11271     }
11272   }
11273 #endif /* not TRILIBRARY */
11274 
11275   if (!b->quiet) {
11276     printf("Reconstructing mesh.\n");
11277   }
11278   /* Allocate a temporary array that maps each vertex to some adjacent */
11279   /*   triangle.  I took care to allocate all the permanent memory for */
11280   /*   triangles and subsegments first.                                */
11281   vertexarray = (triangle *) trimalloc(m->vertices.items *
11282                                        (int) sizeof(triangle));
11283   /* Each vertex is initially unrepresented. */
11284   for (i = 0; i < m->vertices.items; i++) {
11285     vertexarray[i] = (triangle) m->dummytri;
11286   }
11287 
11288   if (b->verbose) {
11289     printf("  Assembling triangles.\n");
11290   }
11291   /* Read the triangles from the .ele file, and link */
11292   /*   together those that share an edge.            */
11293   traversalinit(&m->triangles);
11294   triangleloop.tri = triangletraverse(m);
11295   elementnumber = b->firstnumber;
11296   while (triangleloop.tri != (triangle *) NULL) {
11297 #ifdef TRILIBRARY
11298     /* Copy the triangle's three corners. */
11299     for (j = 0; j < 3; j++) {
11300       corner[j] = trianglelist[vertexindex++];
11301       if ((corner[j] < b->firstnumber) ||
11302           (corner[j] >= b->firstnumber + m->invertices)) {
11303         printf("Error:  Triangle %ld has an invalid vertex index.\n",
11304                elementnumber);
11305         triexit(1);
11306       }
11307     }
11308 #else /* not TRILIBRARY */
11309     /* Read triangle number and the triangle's three corners. */
11310     stringptr = readline(inputline, elefile, elefilename);
11311     for (j = 0; j < 3; j++) {
11312       stringptr = findfield(stringptr);
11313       if (*stringptr == '\0') {
11314         printf("Error:  Triangle %ld is missing vertex %d in %s.\n",
11315                elementnumber, j + 1, elefilename);
11316         triexit(1);
11317       } else {
11318         corner[j] = (int) strtol(stringptr, &stringptr, 0);
11319         if ((corner[j] < b->firstnumber) ||
11320             (corner[j] >= b->firstnumber + m->invertices)) {
11321           printf("Error:  Triangle %ld has an invalid vertex index.\n",
11322                  elementnumber);
11323           triexit(1);
11324         }
11325       }
11326     }
11327 #endif /* not TRILIBRARY */
11328 
11329     /* Find out about (and throw away) extra nodes. */
11330     for (j = 3; j < incorners; j++) {
11331 #ifdef TRILIBRARY
11332       killvertexindex = trianglelist[vertexindex++];
11333 #else /* not TRILIBRARY */
11334       stringptr = findfield(stringptr);
11335       if (*stringptr != '\0') {
11336         killvertexindex = (int) strtol(stringptr, &stringptr, 0);
11337 #endif /* not TRILIBRARY */
11338         if ((killvertexindex >= b->firstnumber) &&
11339             (killvertexindex < b->firstnumber + m->invertices)) {
11340           /* Delete the non-corner vertex if it's not already deleted. */
11341           killvertex = getvertex(m, b, killvertexindex);
11342           if (vertextype(killvertex) != DEADVERTEX) {
11343             vertexdealloc(m, killvertex);
11344           }
11345         }
11346 #ifndef TRILIBRARY
11347       }
11348 #endif /* not TRILIBRARY */
11349     }
11350 
11351     /* Read the triangle's attributes. */
11352     for (j = 0; j < m->eextras; j++) {
11353 #ifdef TRILIBRARY
11354       setelemattribute(triangleloop, j, triangleattriblist[attribindex++]);
11355 #else /* not TRILIBRARY */
11356       stringptr = findfield(stringptr);
11357       if (*stringptr == '\0') {
11358         setelemattribute(triangleloop, j, 0);
11359       } else {
11360         setelemattribute(triangleloop, j,
11361                          (REAL) strtod(stringptr, &stringptr));
11362       }
11363 #endif /* not TRILIBRARY */
11364     }
11365 
11366     if (b->vararea) {
11367 #ifdef TRILIBRARY
11368       area = trianglearealist[elementnumber - b->firstnumber];
11369 #else /* not TRILIBRARY */
11370       /* Read an area constraint from the .area file. */
11371       stringptr = readline(inputline, areafile, areafilename);
11372       stringptr = findfield(stringptr);
11373       if (*stringptr == '\0') {
11374         area = -1.0;                      /* No constraint on this triangle. */
11375       } else {
11376         area = (REAL) strtod(stringptr, &stringptr);
11377       }
11378 #endif /* not TRILIBRARY */
11379       setareabound(triangleloop, area);
11380     }
11381 
11382     /* Set the triangle's vertices. */
11383     triangleloop.orient = 0;
11384     setorg(triangleloop, getvertex(m, b, corner[0]));
11385     setdest(triangleloop, getvertex(m, b, corner[1]));
11386     setapex(triangleloop, getvertex(m, b, corner[2]));
11387     /* Try linking the triangle to others that share these vertices. */
11388     for (triangleloop.orient = 0; triangleloop.orient < 3;
11389          triangleloop.orient++) {
11390       /* Take the number for the origin of triangleloop. */
11391       aroundvertex = corner[triangleloop.orient];
11392       /* Look for other triangles having this vertex. */
11393       nexttri = vertexarray[aroundvertex - b->firstnumber];
11394       /* Link the current triangle to the next one in the stack. */
11395       triangleloop.tri[6 + triangleloop.orient] = nexttri;
11396       /* Push the current triangle onto the stack. */
11397       vertexarray[aroundvertex - b->firstnumber] = encode(triangleloop);
11398       decode(nexttri, checktri);
11399       if (checktri.tri != m->dummytri) {
11400         dest(triangleloop, tdest);
11401         apex(triangleloop, tapex);
11402         /* Look for other triangles that share an edge. */
11403         do {
11404           dest(checktri, checkdest);
11405           apex(checktri, checkapex);
11406           if (tapex == checkdest) {
11407             /* The two triangles share an edge; bond them together. */
11408             lprev(triangleloop, triangleleft);
11409             bond(triangleleft, checktri);
11410           }
11411           if (tdest == checkapex) {
11412             /* The two triangles share an edge; bond them together. */
11413             lprev(checktri, checkleft);
11414             bond(triangleloop, checkleft);
11415           }
11416           /* Find the next triangle in the stack. */
11417           nexttri = checktri.tri[6 + checktri.orient];
11418           decode(nexttri, checktri);
11419         } while (checktri.tri != m->dummytri);
11420       }
11421     }
11422     triangleloop.tri = triangletraverse(m);
11423     elementnumber++;
11424   }
11425 
11426 #ifdef TRILIBRARY
11427   vertexindex = 0;
11428 #else /* not TRILIBRARY */
11429   fclose(elefile);
11430   if (b->vararea) {
11431     fclose(areafile);
11432   }
11433 #endif /* not TRILIBRARY */
11434 
11435   hullsize = 0;                      /* Prepare to count the boundary edges. */
11436   if (b->poly) {
11437     if (b->verbose) {
11438       printf("  Marking segments in triangulation.\n");
11439     }
11440     /* Read the segments from the .poly file, and link them */
11441     /*   to their neighboring triangles.                    */
11442     boundmarker = 0;
11443     traversalinit(&m->subsegs);
11444     subsegloop.ss = subsegtraverse(m);
11445     segmentnumber = b->firstnumber;
11446     while (subsegloop.ss != (subseg *) NULL) {
11447 #ifdef TRILIBRARY
11448       end[0] = segmentlist[vertexindex++];
11449       end[1] = segmentlist[vertexindex++];
11450       if (segmentmarkers) {
11451         boundmarker = segmentmarkerlist[segmentnumber - b->firstnumber];
11452       }
11453 #else /* not TRILIBRARY */
11454       /* Read the endpoints of each segment, and possibly a boundary marker. */
11455       stringptr = readline(inputline, polyfile, b->inpolyfilename);
11456       /* Skip the first (segment number) field. */
11457       stringptr = findfield(stringptr);
11458       if (*stringptr == '\0') {
11459         printf("Error:  Segment %ld has no endpoints in %s.\n", segmentnumber,
11460                polyfilename);
11461         triexit(1);
11462       } else {
11463         end[0] = (int) strtol(stringptr, &stringptr, 0);
11464       }
11465       stringptr = findfield(stringptr);
11466       if (*stringptr == '\0') {
11467         printf("Error:  Segment %ld is missing its second endpoint in %s.\n",
11468                segmentnumber, polyfilename);
11469         triexit(1);
11470       } else {
11471         end[1] = (int) strtol(stringptr, &stringptr, 0);
11472       }
11473       if (segmentmarkers) {
11474         stringptr = findfield(stringptr);
11475         if (*stringptr == '\0') {
11476           boundmarker = 0;
11477         } else {
11478           boundmarker = (int) strtol(stringptr, &stringptr, 0);
11479         }
11480       }
11481 #endif /* not TRILIBRARY */
11482       for (j = 0; j < 2; j++) {
11483         if ((end[j] < b->firstnumber) ||
11484             (end[j] >= b->firstnumber + m->invertices)) {
11485           printf("Error:  Segment %ld has an invalid vertex index.\n",
11486                  segmentnumber);
11487           triexit(1);
11488         }
11489       }
11490 
11491       /* set the subsegment's vertices. */
11492       subsegloop.ssorient = 0;
11493       segmentorg = getvertex(m, b, end[0]);
11494       segmentdest = getvertex(m, b, end[1]);
11495       setsorg(subsegloop, segmentorg);
11496       setsdest(subsegloop, segmentdest);
11497       setsegorg(subsegloop, segmentorg);
11498       setsegdest(subsegloop, segmentdest);
11499       setmark(subsegloop, boundmarker);
11500       /* Try linking the subsegment to triangles that share these vertices. */
11501       for (subsegloop.ssorient = 0; subsegloop.ssorient < 2;
11502            subsegloop.ssorient++) {
11503         /* Take the number for the destination of subsegloop. */
11504         aroundvertex = end[1 - subsegloop.ssorient];
11505         /* Look for triangles having this vertex. */
11506         prevlink = &vertexarray[aroundvertex - b->firstnumber];
11507         nexttri = vertexarray[aroundvertex - b->firstnumber];
11508         decode(nexttri, checktri);
11509         sorg(subsegloop, shorg);
11510         notfound = 1;
11511         /* Look for triangles having this edge.  Note that I'm only       */
11512         /*   comparing each triangle's destination with the subsegment;   */
11513         /*   each triangle's apex is handled through a different vertex.  */
11514         /*   Because each triangle appears on three vertices' lists, each */
11515         /*   occurrence of a triangle on a list can (and does) represent  */
11516         /*   an edge.  In this way, most edges are represented twice, and */
11517         /*   every triangle-subsegment bond is represented once.          */
11518         while (notfound && (checktri.tri != m->dummytri)) {
11519           dest(checktri, checkdest);
11520           if (shorg == checkdest) {
11521             /* We have a match.  Remove this triangle from the list. */
11522             *prevlink = checktri.tri[6 + checktri.orient];
11523             /* Bond the subsegment to the triangle. */
11524             tsbond(checktri, subsegloop);
11525             /* Check if this is a boundary edge. */
11526             sym(checktri, checkneighbor);
11527             if (checkneighbor.tri == m->dummytri) {
11528               /* The next line doesn't insert a subsegment (because there's */
11529               /*   already one there), but it sets the boundary markers of  */
11530               /*   the existing subsegment and its vertices.                */
11531               insertsubseg(m, b, &checktri, 1);
11532               hullsize++;
11533             }
11534             notfound = 0;
11535           }
11536           /* Find the next triangle in the stack. */
11537           prevlink = &checktri.tri[6 + checktri.orient];
11538           nexttri = checktri.tri[6 + checktri.orient];
11539           decode(nexttri, checktri);
11540         }
11541       }
11542       subsegloop.ss = subsegtraverse(m);
11543       segmentnumber++;
11544     }
11545   }
11546 
11547   /* Mark the remaining edges as not being attached to any subsegment. */
11548   /* Also, count the (yet uncounted) boundary edges.                   */
11549   for (i = 0; i < m->vertices.items; i++) {
11550     /* Search the stack of triangles adjacent to a vertex. */
11551     nexttri = vertexarray[i];
11552     decode(nexttri, checktri);
11553     while (checktri.tri != m->dummytri) {
11554       /* Find the next triangle in the stack before this */
11555       /*   information gets overwritten.                 */
11556       nexttri = checktri.tri[6 + checktri.orient];
11557       /* No adjacent subsegment.  (This overwrites the stack info.) */
11558       tsdissolve(checktri);
11559       sym(checktri, checkneighbor);
11560       if (checkneighbor.tri == m->dummytri) {
11561         insertsubseg(m, b, &checktri, 1);
11562         hullsize++;
11563       }
11564       decode(nexttri, checktri);
11565     }
11566   }
11567 
11568   trifree((VOID *) vertexarray);
11569   return hullsize;
11570 }
11571 
11572 #endif /* not CDT_ONLY */
11573 
11576 /********* General mesh construction routines end here               *********/
11577 
11578 /********* Segment insertion begins here                             *********/
11582 /*****************************************************************************/
11583 /*                                                                           */
11584 /*  finddirection()   Find the first triangle on the path from one point     */
11585 /*                    to another.                                            */
11586 /*                                                                           */
11587 /*  Finds the triangle that intersects a line segment drawn from the         */
11588 /*  origin of `searchtri' to the point `searchpoint', and returns the result */
11589 /*  in `searchtri'.  The origin of `searchtri' does not change, even though  */
11590 /*  the triangle returned may differ from the one passed in.  This routine   */
11591 /*  is used to find the direction to move in to get from one point to        */
11592 /*  another.                                                                 */
11593 /*                                                                           */
11594 /*  The return value notes whether the destination or apex of the found      */
11595 /*  triangle is collinear with the two points in question.                   */
11596 /*                                                                           */
11597 /*****************************************************************************/
11598 
11599 #ifdef ANSI_DECLARATORS
11600 enum finddirectionresult finddirection(struct mesh *m, struct behavior *b,
11601                                        struct otri *searchtri,
11602                                        vertex searchpoint)
11603 #else /* not ANSI_DECLARATORS */
11604 enum finddirectionresult finddirection(m, b, searchtri, searchpoint)
11605 struct mesh *m;
11606 struct behavior *b;
11607 struct otri *searchtri;
11608 vertex searchpoint;
11609 #endif /* not ANSI_DECLARATORS */
11610 
11611 {
11612   struct otri checktri;
11613   vertex startvertex;
11614   vertex leftvertex, rightvertex;
11615   REAL leftccw, rightccw;
11616   int leftflag, rightflag;
11617   triangle ptr;           /* Temporary variable used by onext() and oprev(). */
11618 
11619   org(*searchtri, startvertex);
11620   dest(*searchtri, rightvertex);
11621   apex(*searchtri, leftvertex);
11622   /* Is `searchpoint' to the left? */
11623   leftccw = counterclockwise(m, b, searchpoint, startvertex, leftvertex);
11624   leftflag = leftccw > 0.0;
11625   /* Is `searchpoint' to the right? */
11626   rightccw = counterclockwise(m, b, startvertex, searchpoint, rightvertex);
11627   rightflag = rightccw > 0.0;
11628   if (leftflag && rightflag) {
11629     /* `searchtri' faces directly away from `searchpoint'.  We could go left */
11630     /*   or right.  Ask whether it's a triangle or a boundary on the left.   */
11631     onext(*searchtri, checktri);
11632     if (checktri.tri == m->dummytri) {
11633       leftflag = 0;
11634     } else {
11635       rightflag = 0;
11636     }
11637   }
11638   while (leftflag) {
11639     /* Turn left until satisfied. */
11640     onextself(*searchtri);
11641     if (searchtri->tri == m->dummytri) {
11642       printf("Internal error in finddirection():  Unable to find a\n");
11643       printf("  triangle leading from (%.12g, %.12g) to", startvertex[0],
11644              startvertex[1]);
11645       printf("  (%.12g, %.12g).\n", searchpoint[0], searchpoint[1]);
11646       internalerror();
11647     }
11648     apex(*searchtri, leftvertex);
11649     rightccw = leftccw;
11650     leftccw = counterclockwise(m, b, searchpoint, startvertex, leftvertex);
11651     leftflag = leftccw > 0.0;
11652   }
11653   while (rightflag) {
11654     /* Turn right until satisfied. */
11655     oprevself(*searchtri);
11656     if (searchtri->tri == m->dummytri) {
11657       printf("Internal error in finddirection():  Unable to find a\n");
11658       printf("  triangle leading from (%.12g, %.12g) to", startvertex[0],
11659              startvertex[1]);
11660       printf("  (%.12g, %.12g).\n", searchpoint[0], searchpoint[1]);
11661       internalerror();
11662     }
11663     dest(*searchtri, rightvertex);
11664     leftccw = rightccw;
11665     rightccw = counterclockwise(m, b, startvertex, searchpoint, rightvertex);
11666     rightflag = rightccw > 0.0;
11667   }
11668   if (leftccw == 0.0) {
11669     return LEFTCOLLINEAR;
11670   } else if (rightccw == 0.0) {
11671     return RIGHTCOLLINEAR;
11672   } else {
11673     return WITHIN;
11674   }
11675 }
11676 
11677 /*****************************************************************************/
11678 /*                                                                           */
11679 /*  segmentintersection()   Find the intersection of an existing segment     */
11680 /*                          and a segment that is being inserted.  Insert    */
11681 /*                          a vertex at the intersection, splitting an       */
11682 /*                          existing subsegment.                             */
11683 /*                                                                           */
11684 /*  The segment being inserted connects the apex of splittri to endpoint2.   */
11685 /*  splitsubseg is the subsegment being split, and MUST adjoin splittri.     */
11686 /*  Hence, endpoints of the subsegment being split are the origin and        */
11687 /*  destination of splittri.                                                 */
11688 /*                                                                           */
11689 /*  On completion, splittri is a handle having the newly inserted            */
11690 /*  intersection point as its origin, and endpoint1 as its destination.      */
11691 /*                                                                           */
11692 /*****************************************************************************/
11693 
11694 #ifdef ANSI_DECLARATORS
11695 void segmentintersection(struct mesh *m, struct behavior *b,
11696                          struct otri *splittri, struct osub *splitsubseg,
11697                          vertex endpoint2)
11698 #else /* not ANSI_DECLARATORS */
11699 void segmentintersection(m, b, splittri, splitsubseg, endpoint2)
11700 struct mesh *m;
11701 struct behavior *b;
11702 struct otri *splittri;
11703 struct osub *splitsubseg;
11704 vertex endpoint2;
11705 #endif /* not ANSI_DECLARATORS */
11706 
11707 {
11708   struct osub opposubseg;
11709   vertex endpoint1;
11710   vertex torg, tdest;
11711   vertex leftvertex, rightvertex;
11712   vertex newvertex;
11713   enum insertvertexresult success;
11714   enum finddirectionresult collinear;
11715   REAL ex, ey;
11716   REAL tx, ty;
11717   REAL etx, ety;
11718   REAL split, denom;
11719   int i;
11720   triangle ptr;                       /* Temporary variable used by onext(). */
11721   subseg sptr;                        /* Temporary variable used by snext(). */
11722 
11723   /* Find the other three segment endpoints. */
11724   apex(*splittri, endpoint1);
11725   org(*splittri, torg);
11726   dest(*splittri, tdest);
11727   /* Segment intersection formulae; see the Antonio reference. */
11728   tx = tdest[0] - torg[0];
11729   ty = tdest[1] - torg[1];
11730   ex = endpoint2[0] - endpoint1[0];
11731   ey = endpoint2[1] - endpoint1[1];
11732   etx = torg[0] - endpoint2[0];
11733   ety = torg[1] - endpoint2[1];
11734   denom = ty * ex - tx * ey;
11735   if (denom == 0.0) {
11736     printf("Internal error in segmentintersection():");
11737     printf("  Attempt to find intersection of parallel segments.\n");
11738     internalerror();
11739   }
11740   split = (ey * etx - ex * ety) / denom;
11741   /* Create the new vertex. */
11742   newvertex = (vertex) poolalloc(&m->vertices);
11743   /* Interpolate its coordinate and attributes. */
11744   for (i = 0; i < 2 + m->nextras; i++) {
11745     newvertex[i] = torg[i] + split * (tdest[i] - torg[i]);
11746   }
11747   setvertexmark(newvertex, mark(*splitsubseg));
11748   setvertextype(newvertex, INPUTVERTEX);
11749   if (b->verbose > 1) {
11750     printf(
11751   "  Splitting subsegment (%.12g, %.12g) (%.12g, %.12g) at (%.12g, %.12g).\n",
11752            torg[0], torg[1], tdest[0], tdest[1], newvertex[0], newvertex[1]);
11753   }
11754   /* Insert the intersection vertex.  This should always succeed. */
11755   success = insertvertex(m, b, newvertex, splittri, splitsubseg, 0, 0);
11756   if (success != SUCCESSFULVERTEX) {
11757     printf("Internal error in segmentintersection():\n");
11758     printf("  Failure to split a segment.\n");
11759     internalerror();
11760   }
11761   /* Record a triangle whose origin is the new vertex. */
11762   setvertex2tri(newvertex, encode(*splittri));
11763   if (m->steinerleft > 0) {
11764     m->steinerleft--;
11765   }
11766 
11767   /* Divide the segment into two, and correct the segment endpoints. */
11768   ssymself(*splitsubseg);
11769   spivot(*splitsubseg, opposubseg);
11770   sdissolve(*splitsubseg);
11771   sdissolve(opposubseg);
11772   do {
11773     setsegorg(*splitsubseg, newvertex);
11774     snextself(*splitsubseg);
11775   } while (splitsubseg->ss != m->dummysub);
11776   do {
11777     setsegorg(opposubseg, newvertex);
11778     snextself(opposubseg);
11779   } while (opposubseg.ss != m->dummysub);
11780 
11781   /* Inserting the vertex may have caused edge flips.  We wish to rediscover */
11782   /*   the edge connecting endpoint1 to the new intersection vertex.         */
11783   collinear = finddirection(m, b, splittri, endpoint1);
11784   dest(*splittri, rightvertex);
11785   apex(*splittri, leftvertex);
11786   if ((leftvertex[0] == endpoint1[0]) && (leftvertex[1] == endpoint1[1])) {
11787     onextself(*splittri);
11788   } else if ((rightvertex[0] != endpoint1[0]) ||
11789              (rightvertex[1] != endpoint1[1])) {
11790     printf("Internal error in segmentintersection():\n");
11791     printf("  Topological inconsistency after splitting a segment.\n");
11792     internalerror();
11793   }
11794   /* `splittri' should have destination endpoint1. */
11795 }
11796 
11797 /*****************************************************************************/
11798 /*                                                                           */
11799 /*  scoutsegment()   Scout the first triangle on the path from one endpoint  */
11800 /*                   to another, and check for completion (reaching the      */
11801 /*                   second endpoint), a collinear vertex, or the            */
11802 /*                   intersection of two segments.                           */
11803 /*                                                                           */
11804 /*  Returns one if the entire segment is successfully inserted, and zero if  */
11805 /*  the job must be finished by conformingedge() or constrainededge().       */
11806 /*                                                                           */
11807 /*  If the first triangle on the path has the second endpoint as its         */
11808 /*  destination or apex, a subsegment is inserted and the job is done.       */
11809 /*                                                                           */
11810 /*  If the first triangle on the path has a destination or apex that lies on */
11811 /*  the segment, a subsegment is inserted connecting the first endpoint to   */
11812 /*  the collinear vertex, and the search is continued from the collinear     */
11813 /*  vertex.                                                                  */
11814 /*                                                                           */
11815 /*  If the first triangle on the path has a subsegment opposite its origin,  */
11816 /*  then there is a segment that intersects the segment being inserted.      */
11817 /*  Their intersection vertex is inserted, splitting the subsegment.         */
11818 /*                                                                           */
11819 /*****************************************************************************/
11820 
11821 #ifdef ANSI_DECLARATORS
11822 int scoutsegment(struct mesh *m, struct behavior *b, struct otri *searchtri,
11823                  vertex endpoint2, int newmark)
11824 #else /* not ANSI_DECLARATORS */
11825 int scoutsegment(m, b, searchtri, endpoint2, newmark)
11826 struct mesh *m;
11827 struct behavior *b;
11828 struct otri *searchtri;
11829 vertex endpoint2;
11830 int newmark;
11831 #endif /* not ANSI_DECLARATORS */
11832 
11833 {
11834   struct otri crosstri;
11835   struct osub crosssubseg;
11836   vertex leftvertex, rightvertex;
11837   enum finddirectionresult collinear;
11838   subseg sptr;                      /* Temporary variable used by tspivot(). */
11839 
11840   collinear = finddirection(m, b, searchtri, endpoint2);
11841   dest(*searchtri, rightvertex);
11842   apex(*searchtri, leftvertex);
11843   if (((leftvertex[0] == endpoint2[0]) && (leftvertex[1] == endpoint2[1])) ||
11844       ((rightvertex[0] == endpoint2[0]) && (rightvertex[1] == endpoint2[1]))) {
11845     /* The segment is already an edge in the mesh. */
11846     if ((leftvertex[0] == endpoint2[0]) && (leftvertex[1] == endpoint2[1])) {
11847       lprevself(*searchtri);
11848     }
11849     /* Insert a subsegment, if there isn't already one there. */
11850     insertsubseg(m, b, searchtri, newmark);
11851     return 1;
11852   } else if (collinear == LEFTCOLLINEAR) {
11853     /* We've collided with a vertex between the segment's endpoints. */
11854     /* Make the collinear vertex be the triangle's origin. */
11855     lprevself(*searchtri);
11856     insertsubseg(m, b, searchtri, newmark);
11857     /* Insert the remainder of the segment. */
11858     return scoutsegment(m, b, searchtri, endpoint2, newmark);
11859   } else if (collinear == RIGHTCOLLINEAR) {
11860     /* We've collided with a vertex between the segment's endpoints. */
11861     insertsubseg(m, b, searchtri, newmark);
11862     /* Make the collinear vertex be the triangle's origin. */
11863     lnextself(*searchtri);
11864     /* Insert the remainder of the segment. */
11865     return scoutsegment(m, b, searchtri, endpoint2, newmark);
11866   } else {
11867     lnext(*searchtri, crosstri);
11868     tspivot(crosstri, crosssubseg);
11869     /* Check for a crossing segment. */
11870     if (crosssubseg.ss == m->dummysub) {
11871       return 0;
11872     } else {
11873       /* Insert a vertex at the intersection. */
11874       segmentintersection(m, b, &crosstri, &crosssubseg, endpoint2);
11875       otricopy(crosstri, *searchtri);
11876       insertsubseg(m, b, searchtri, newmark);
11877       /* Insert the remainder of the segment. */
11878       return scoutsegment(m, b, searchtri, endpoint2, newmark);
11879     }
11880   }
11881 }
11882 
11883 /*****************************************************************************/
11884 /*                                                                           */
11885 /*  conformingedge()   Force a segment into a conforming Delaunay            */
11886 /*                     triangulation by inserting a vertex at its midpoint,  */
11887 /*                     and recursively forcing in the two half-segments if   */
11888 /*                     necessary.                                            */
11889 /*                                                                           */
11890 /*  Generates a sequence of subsegments connecting `endpoint1' to            */
11891 /*  `endpoint2'.  `newmark' is the boundary marker of the segment, assigned  */
11892 /*  to each new splitting vertex and subsegment.                             */
11893 /*                                                                           */
11894 /*  Note that conformingedge() does not always maintain the conforming       */
11895 /*  Delaunay property.  Once inserted, segments are locked into place;       */
11896 /*  vertices inserted later (to force other segments in) may render these    */
11897 /*  fixed segments non-Delaunay.  The conforming Delaunay property will be   */
11898 /*  restored by enforcequality() by splitting encroached subsegments.        */
11899 /*                                                                           */
11900 /*****************************************************************************/
11901 
11902 #ifndef REDUCED
11903 #ifndef CDT_ONLY
11904 
11905 #ifdef ANSI_DECLARATORS
11906 void conformingedge(struct mesh *m, struct behavior *b,
11907                     vertex endpoint1, vertex endpoint2, int newmark)
11908 #else /* not ANSI_DECLARATORS */
11909 void conformingedge(m, b, endpoint1, endpoint2, newmark)
11910 struct mesh *m;
11911 struct behavior *b;
11912 vertex endpoint1;
11913 vertex endpoint2;
11914 int newmark;
11915 #endif /* not ANSI_DECLARATORS */
11916 
11917 {
11918   struct otri searchtri1, searchtri2;
11919   struct osub brokensubseg;
11920   vertex newvertex;
11921   vertex midvertex1, midvertex2;
11922   enum insertvertexresult success;
11923   int i;
11924   subseg sptr;                      /* Temporary variable used by tspivot(). */
11925 
11926   if (b->verbose > 2) {
11927     printf("Forcing segment into triangulation by recursive splitting:\n");
11928     printf("  (%.12g, %.12g) (%.12g, %.12g)\n", endpoint1[0], endpoint1[1],
11929            endpoint2[0], endpoint2[1]);
11930   }
11931   /* Create a new vertex to insert in the middle of the segment. */
11932   newvertex = (vertex) poolalloc(&m->vertices);
11933   /* Interpolate coordinates and attributes. */
11934   for (i = 0; i < 2 + m->nextras; i++) {
11935     newvertex[i] = 0.5 * (endpoint1[i] + endpoint2[i]);
11936   }
11937   setvertexmark(newvertex, newmark);
11938   setvertextype(newvertex, SEGMENTVERTEX);
11939   /* No known triangle to search from. */
11940   searchtri1.tri = m->dummytri;
11941   /* Attempt to insert the new vertex. */
11942   success = insertvertex(m, b, newvertex, &searchtri1, (struct osub *) NULL,
11943                          0, 0);
11944   if (success == DUPLICATEVERTEX) {
11945     if (b->verbose > 2) {
11946       printf("  Segment intersects existing vertex (%.12g, %.12g).\n",
11947              newvertex[0], newvertex[1]);
11948     }
11949     /* Use the vertex that's already there. */
11950     vertexdealloc(m, newvertex);
11951     org(searchtri1, newvertex);
11952   } else {
11953     if (success == VIOLATINGVERTEX) {
11954       if (b->verbose > 2) {
11955         printf("  Two segments intersect at (%.12g, %.12g).\n",
11956                newvertex[0], newvertex[1]);
11957       }
11958       /* By fluke, we've landed right on another segment.  Split it. */
11959       tspivot(searchtri1, brokensubseg);
11960       success = insertvertex(m, b, newvertex, &searchtri1, &brokensubseg,
11961                              0, 0);
11962       if (success != SUCCESSFULVERTEX) {
11963         printf("Internal error in conformingedge():\n");
11964         printf("  Failure to split a segment.\n");
11965         internalerror();
11966       }
11967     }
11968     /* The vertex has been inserted successfully. */
11969     if (m->steinerleft > 0) {
11970       m->steinerleft--;
11971     }
11972   }
11973   otricopy(searchtri1, searchtri2);
11974   /* `searchtri1' and `searchtri2' are fastened at their origins to         */
11975   /*   `newvertex', and will be directed toward `endpoint1' and `endpoint2' */
11976   /*   respectively.  First, we must get `searchtri2' out of the way so it  */
11977   /*   won't be invalidated during the insertion of the first half of the   */
11978   /*   segment.                                                             */
11979   finddirection(m, b, &searchtri2, endpoint2);
11980   if (!scoutsegment(m, b, &searchtri1, endpoint1, newmark)) {
11981     /* The origin of searchtri1 may have changed if a collision with an */
11982     /*   intervening vertex on the segment occurred.                    */
11983     org(searchtri1, midvertex1);
11984     conformingedge(m, b, midvertex1, endpoint1, newmark);
11985   }
11986   if (!scoutsegment(m, b, &searchtri2, endpoint2, newmark)) {
11987     /* The origin of searchtri2 may have changed if a collision with an */
11988     /*   intervening vertex on the segment occurred.                    */
11989     org(searchtri2, midvertex2);
11990     conformingedge(m, b, midvertex2, endpoint2, newmark);
11991   }
11992 }
11993 
11994 #endif /* not CDT_ONLY */
11995 #endif /* not REDUCED */
11996 
11997 /*****************************************************************************/
11998 /*                                                                           */
11999 /*  delaunayfixup()   Enforce the Delaunay condition at an edge, fanning out */
12000 /*                    recursively from an existing vertex.  Pay special      */
12001 /*                    attention to stacking inverted triangles.              */
12002 /*                                                                           */
12003 /*  This is a support routine for inserting segments into a constrained      */
12004 /*  Delaunay triangulation.                                                  */
12005 /*                                                                           */
12006 /*  The origin of fixuptri is treated as if it has just been inserted, and   */
12007 /*  the local Delaunay condition needs to be enforced.  It is only enforced  */
12008 /*  in one sector, however, that being the angular range defined by          */
12009 /*  fixuptri.                                                                */
12010 /*                                                                           */
12011 /*  This routine also needs to make decisions regarding the "stacking" of    */
12012 /*  triangles.  (Read the description of constrainededge() below before      */
12013 /*  reading on here, so you understand the algorithm.)  If the position of   */
12014 /*  the new vertex (the origin of fixuptri) indicates that the vertex before */
12015 /*  it on the polygon is a reflex vertex, then "stack" the triangle by       */
12016 /*  doing nothing.  (fixuptri is an inverted triangle, which is how stacked  */
12017 /*  triangles are identified.)                                               */
12018 /*                                                                           */
12019 /*  Otherwise, check whether the vertex before that was a reflex vertex.     */
12020 /*  If so, perform an edge flip, thereby eliminating an inverted triangle    */
12021 /*  (popping it off the stack).  The edge flip may result in the creation    */
12022 /*  of a new inverted triangle, depending on whether or not the new vertex   */
12023 /*  is visible to the vertex three edges behind on the polygon.              */
12024 /*                                                                           */
12025 /*  If neither of the two vertices behind the new vertex are reflex          */
12026 /*  vertices, fixuptri and fartri, the triangle opposite it, are not         */
12027 /*  inverted; hence, ensure that the edge between them is locally Delaunay.  */
12028 /*                                                                           */
12029 /*  `leftside' indicates whether or not fixuptri is to the left of the       */
12030 /*  segment being inserted.  (Imagine that the segment is pointing up from   */
12031 /*  endpoint1 to endpoint2.)                                                 */
12032 /*                                                                           */
12033 /*****************************************************************************/
12034 
12035 #ifdef ANSI_DECLARATORS
12036 void delaunayfixup(struct mesh *m, struct behavior *b,
12037                    struct otri *fixuptri, int leftside)
12038 #else /* not ANSI_DECLARATORS */
12039 void delaunayfixup(m, b, fixuptri, leftside)
12040 struct mesh *m;
12041 struct behavior *b;
12042 struct otri *fixuptri;
12043 int leftside;
12044 #endif /* not ANSI_DECLARATORS */
12045 
12046 {
12047   struct otri neartri;
12048   struct otri fartri;
12049   struct osub faredge;
12050   vertex nearvertex, leftvertex, rightvertex, farvertex;
12051   triangle ptr;                         /* Temporary variable used by sym(). */
12052   subseg sptr;                      /* Temporary variable used by tspivot(). */
12053 
12054   lnext(*fixuptri, neartri);
12055   sym(neartri, fartri);
12056   /* Check if the edge opposite the origin of fixuptri can be flipped. */
12057   if (fartri.tri == m->dummytri) {
12058     return;
12059   }
12060   tspivot(neartri, faredge);
12061   if (faredge.ss != m->dummysub) {
12062     return;
12063   }
12064   /* Find all the relevant vertices. */
12065   apex(neartri, nearvertex);
12066   org(neartri, leftvertex);
12067   dest(neartri, rightvertex);
12068   apex(fartri, farvertex);
12069   /* Check whether the previous polygon vertex is a reflex vertex. */
12070   if (leftside) {
12071     if (counterclockwise(m, b, nearvertex, leftvertex, farvertex) <= 0.0) {
12072       /* leftvertex is a reflex vertex too.  Nothing can */
12073       /*   be done until a convex section is found.      */
12074       return;
12075     }
12076   } else {
12077     if (counterclockwise(m, b, farvertex, rightvertex, nearvertex) <= 0.0) {
12078       /* rightvertex is a reflex vertex too.  Nothing can */
12079       /*   be done until a convex section is found.       */
12080       return;
12081     }
12082   }
12083   if (counterclockwise(m, b, rightvertex, leftvertex, farvertex) > 0.0) {
12084     /* fartri is not an inverted triangle, and farvertex is not a reflex */
12085     /*   vertex.  As there are no reflex vertices, fixuptri isn't an     */
12086     /*   inverted triangle, either.  Hence, test the edge between the    */
12087     /*   triangles to ensure it is locally Delaunay.                     */
12088     if (incircle(m, b, leftvertex, farvertex, rightvertex, nearvertex) <=
12089         0.0) {
12090       return;
12091     }
12092     /* Not locally Delaunay; go on to an edge flip. */
12093   }        /* else fartri is inverted; remove it from the stack by flipping. */
12094   flip(m, b, &neartri);
12095   lprevself(*fixuptri);    /* Restore the origin of fixuptri after the flip. */
12096   /* Recursively process the two triangles that result from the flip. */
12097   delaunayfixup(m, b, fixuptri, leftside);
12098   delaunayfixup(m, b, &fartri, leftside);
12099 }
12100 
12101 /*****************************************************************************/
12102 /*                                                                           */
12103 /*  constrainededge()   Force a segment into a constrained Delaunay          */
12104 /*                      triangulation by deleting the triangles it           */
12105 /*                      intersects, and triangulating the polygons that      */
12106 /*                      form on each side of it.                             */
12107 /*                                                                           */
12108 /*  Generates a single subsegment connecting `endpoint1' to `endpoint2'.     */
12109 /*  The triangle `starttri' has `endpoint1' as its origin.  `newmark' is the */
12110 /*  boundary marker of the segment.                                          */
12111 /*                                                                           */
12112 /*  To insert a segment, every triangle whose interior intersects the        */
12113 /*  segment is deleted.  The union of these deleted triangles is a polygon   */
12114 /*  (which is not necessarily monotone, but is close enough), which is       */
12115 /*  divided into two polygons by the new segment.  This routine's task is    */
12116 /*  to generate the Delaunay triangulation of these two polygons.            */
12117 /*                                                                           */
12118 /*  You might think of this routine's behavior as a two-step process.  The   */
12119 /*  first step is to walk from endpoint1 to endpoint2, flipping each edge    */
12120 /*  encountered.  This step creates a fan of edges connected to endpoint1,   */
12121 /*  including the desired edge to endpoint2.  The second step enforces the   */
12122 /*  Delaunay condition on each side of the segment in an incremental manner: */
12123 /*  proceeding along the polygon from endpoint1 to endpoint2 (this is done   */
12124 /*  independently on each side of the segment), each vertex is "enforced"    */
12125 /*  as if it had just been inserted, but affecting only the previous         */
12126 /*  vertices.  The result is the same as if the vertices had been inserted   */
12127 /*  in the order they appear on the polygon, so the result is Delaunay.      */
12128 /*                                                                           */
12129 /*  In truth, constrainededge() interleaves these two steps.  The procedure  */
12130 /*  walks from endpoint1 to endpoint2, and each time an edge is encountered  */
12131 /*  and flipped, the newly exposed vertex (at the far end of the flipped     */
12132 /*  edge) is "enforced" upon the previously flipped edges, usually affecting */
12133 /*  only one side of the polygon (depending upon which side of the segment   */
12134 /*  the vertex falls on).                                                    */
12135 /*                                                                           */
12136 /*  The algorithm is complicated by the need to handle polygons that are not */
12137 /*  convex.  Although the polygon is not necessarily monotone, it can be     */
12138 /*  triangulated in a manner similar to the stack-based algorithms for       */
12139 /*  monotone polygons.  For each reflex vertex (local concavity) of the      */
12140 /*  polygon, there will be an inverted triangle formed by one of the edge    */
12141 /*  flips.  (An inverted triangle is one with negative area - that is, its   */
12142 /*  vertices are arranged in clockwise order - and is best thought of as a   */
12143 /*  wrinkle in the fabric of the mesh.)  Each inverted triangle can be       */
12144 /*  thought of as a reflex vertex pushed on the stack, waiting to be fixed   */
12145 /*  later.                                                                   */
12146 /*                                                                           */
12147 /*  A reflex vertex is popped from the stack when a vertex is inserted that  */
12148 /*  is visible to the reflex vertex.  (However, if the vertex behind the     */
12149 /*  reflex vertex is not visible to the reflex vertex, a new inverted        */
12150 /*  triangle will take its place on the stack.)  These details are handled   */
12151 /*  by the delaunayfixup() routine above.                                    */
12152 /*                                                                           */
12153 /*****************************************************************************/
12154 
12155 #ifdef ANSI_DECLARATORS
12156 void constrainededge(struct mesh *m, struct behavior *b,
12157                      struct otri *starttri, vertex endpoint2, int newmark)
12158 #else /* not ANSI_DECLARATORS */
12159 void constrainededge(m, b, starttri, endpoint2, newmark)
12160 struct mesh *m;
12161 struct behavior *b;
12162 struct otri *starttri;
12163 vertex endpoint2;
12164 int newmark;
12165 #endif /* not ANSI_DECLARATORS */
12166 
12167 {
12168   struct otri fixuptri, fixuptri2;
12169   struct osub crosssubseg;
12170   vertex endpoint1;
12171   vertex farvertex;
12172   REAL area;
12173   int collision;
12174   int done;
12175   triangle ptr;             /* Temporary variable used by sym() and oprev(). */
12176   subseg sptr;                      /* Temporary variable used by tspivot(). */
12177 
12178   org(*starttri, endpoint1);
12179   lnext(*starttri, fixuptri);
12180   flip(m, b, &fixuptri);
12181   /* `collision' indicates whether we have found a vertex directly */
12182   /*   between endpoint1 and endpoint2.                            */
12183   collision = 0;
12184   done = 0;
12185   do {
12186     org(fixuptri, farvertex);
12187     /* `farvertex' is the extreme point of the polygon we are "digging" */
12188     /*   to get from endpoint1 to endpoint2.                           */
12189     if ((farvertex[0] == endpoint2[0]) && (farvertex[1] == endpoint2[1])) {
12190       oprev(fixuptri, fixuptri2);
12191       /* Enforce the Delaunay condition around endpoint2. */
12192       delaunayfixup(m, b, &fixuptri, 0);
12193       delaunayfixup(m, b, &fixuptri2, 1);
12194       done = 1;
12195     } else {
12196       /* Check whether farvertex is to the left or right of the segment */
12197       /*   being inserted, to decide which edge of fixuptri to dig      */
12198       /*   through next.                                                */
12199       area = counterclockwise(m, b, endpoint1, endpoint2, farvertex);
12200       if (area == 0.0) {
12201         /* We've collided with a vertex between endpoint1 and endpoint2. */
12202         collision = 1;
12203         oprev(fixuptri, fixuptri2);
12204         /* Enforce the Delaunay condition around farvertex. */
12205         delaunayfixup(m, b, &fixuptri, 0);
12206         delaunayfixup(m, b, &fixuptri2, 1);
12207         done = 1;
12208       } else {
12209         if (area > 0.0) {        /* farvertex is to the left of the segment. */
12210           oprev(fixuptri, fixuptri2);
12211           /* Enforce the Delaunay condition around farvertex, on the */
12212           /*   left side of the segment only.                        */
12213           delaunayfixup(m, b, &fixuptri2, 1);
12214           /* Flip the edge that crosses the segment.  After the edge is */
12215           /*   flipped, one of its endpoints is the fan vertex, and the */
12216           /*   destination of fixuptri is the fan vertex.               */
12217           lprevself(fixuptri);
12218         } else {                /* farvertex is to the right of the segment. */
12219           delaunayfixup(m, b, &fixuptri, 0);
12220           /* Flip the edge that crosses the segment.  After the edge is */
12221           /*   flipped, one of its endpoints is the fan vertex, and the */
12222           /*   destination of fixuptri is the fan vertex.               */
12223           oprevself(fixuptri);
12224         }
12225         /* Check for two intersecting segments. */
12226         tspivot(fixuptri, crosssubseg);
12227         if (crosssubseg.ss == m->dummysub) {
12228           flip(m, b, &fixuptri);    /* May create inverted triangle at left. */
12229         } else {
12230           /* We've collided with a segment between endpoint1 and endpoint2. */
12231           collision = 1;
12232           /* Insert a vertex at the intersection. */
12233           segmentintersection(m, b, &fixuptri, &crosssubseg, endpoint2);
12234           done = 1;
12235         }
12236       }
12237     }
12238   } while (!done);
12239   /* Insert a subsegment to make the segment permanent. */
12240   insertsubseg(m, b, &fixuptri, newmark);
12241   /* If there was a collision with an interceding vertex, install another */
12242   /*   segment connecting that vertex with endpoint2.                     */
12243   if (collision) {
12244     /* Insert the remainder of the segment. */
12245     if (!scoutsegment(m, b, &fixuptri, endpoint2, newmark)) {
12246       constrainededge(m, b, &fixuptri, endpoint2, newmark);
12247     }
12248   }
12249 }
12250 
12251 /*****************************************************************************/
12252 /*                                                                           */
12253 /*  insertsegment()   Insert a PSLG segment into a triangulation.            */
12254 /*                                                                           */
12255 /*****************************************************************************/
12256 
12257 #ifdef ANSI_DECLARATORS
12258 void insertsegment(struct mesh *m, struct behavior *b,
12259                    vertex endpoint1, vertex endpoint2, int newmark)
12260 #else /* not ANSI_DECLARATORS */
12261 void insertsegment(m, b, endpoint1, endpoint2, newmark)
12262 struct mesh *m;
12263 struct behavior *b;
12264 vertex endpoint1;
12265 vertex endpoint2;
12266 int newmark;
12267 #endif /* not ANSI_DECLARATORS */
12268 
12269 {
12270   struct otri searchtri1, searchtri2;
12271   triangle encodedtri;
12272   vertex checkvertex;
12273   triangle ptr;                         /* Temporary variable used by sym(). */
12274 
12275   if (b->verbose > 1) {
12276     printf("  Connecting (%.12g, %.12g) to (%.12g, %.12g).\n",
12277            endpoint1[0], endpoint1[1], endpoint2[0], endpoint2[1]);
12278   }
12279 
12280   /* Find a triangle whose origin is the segment's first endpoint. */
12281   checkvertex = (vertex) NULL;
12282   encodedtri = vertex2tri(endpoint1);
12283   if (encodedtri != (triangle) NULL) {
12284     decode(encodedtri, searchtri1);
12285     org(searchtri1, checkvertex);
12286   }
12287   if (checkvertex != endpoint1) {
12288     /* Find a boundary triangle to search from. */
12289     searchtri1.tri = m->dummytri;
12290     searchtri1.orient = 0;
12291     symself(searchtri1);
12292     /* Search for the segment's first endpoint by point location. */
12293     if (locate(m, b, endpoint1, &searchtri1) != ONVERTEX) {
12294       printf(
12295         "Internal error in insertsegment():  Unable to locate PSLG vertex\n");
12296       printf("  (%.12g, %.12g) in triangulation.\n",
12297              endpoint1[0], endpoint1[1]);
12298       internalerror();
12299     }
12300   }
12301   /* Remember this triangle to improve subsequent point location. */
12302   otricopy(searchtri1, m->recenttri);
12303   /* Scout the beginnings of a path from the first endpoint */
12304   /*   toward the second.                                   */
12305   if (scoutsegment(m, b, &searchtri1, endpoint2, newmark)) {
12306     /* The segment was easily inserted. */
12307     return;
12308   }
12309   /* The first endpoint may have changed if a collision with an intervening */
12310   /*   vertex on the segment occurred.                                      */
12311   org(searchtri1, endpoint1);
12312 
12313   /* Find a triangle whose origin is the segment's second endpoint. */
12314   checkvertex = (vertex) NULL;
12315   encodedtri = vertex2tri(endpoint2);
12316   if (encodedtri != (triangle) NULL) {
12317     decode(encodedtri, searchtri2);
12318     org(searchtri2, checkvertex);
12319   }
12320   if (checkvertex != endpoint2) {
12321     /* Find a boundary triangle to search from. */
12322     searchtri2.tri = m->dummytri;
12323     searchtri2.orient = 0;
12324     symself(searchtri2);
12325     /* Search for the segment's second endpoint by point location. */
12326     if (locate(m, b, endpoint2, &searchtri2) != ONVERTEX) {
12327       printf(
12328         "Internal error in insertsegment():  Unable to locate PSLG vertex\n");
12329       printf("  (%.12g, %.12g) in triangulation.\n",
12330              endpoint2[0], endpoint2[1]);
12331       internalerror();
12332     }
12333   }
12334   /* Remember this triangle to improve subsequent point location. */
12335   otricopy(searchtri2, m->recenttri);
12336   /* Scout the beginnings of a path from the second endpoint */
12337   /*   toward the first.                                     */
12338   if (scoutsegment(m, b, &searchtri2, endpoint1, newmark)) {
12339     /* The segment was easily inserted. */
12340     return;
12341   }
12342   /* The second endpoint may have changed if a collision with an intervening */
12343   /*   vertex on the segment occurred.                                       */
12344   org(searchtri2, endpoint2);
12345 
12346 #ifndef REDUCED
12347 #ifndef CDT_ONLY
12348   if (b->splitseg) {
12349     /* Insert vertices to force the segment into the triangulation. */
12350     conformingedge(m, b, endpoint1, endpoint2, newmark);
12351   } else {
12352 #endif /* not CDT_ONLY */
12353 #endif /* not REDUCED */
12354     /* Insert the segment directly into the triangulation. */
12355     constrainededge(m, b, &searchtri1, endpoint2, newmark);
12356 #ifndef REDUCED
12357 #ifndef CDT_ONLY
12358   }
12359 #endif /* not CDT_ONLY */
12360 #endif /* not REDUCED */
12361 }
12362 
12363 /*****************************************************************************/
12364 /*                                                                           */
12365 /*  markhull()   Cover the convex hull of a triangulation with subsegments.  */
12366 /*                                                                           */
12367 /*****************************************************************************/
12368 
12369 #ifdef ANSI_DECLARATORS
12370 void markhull(struct mesh *m, struct behavior *b)
12371 #else /* not ANSI_DECLARATORS */
12372 void markhull(m, b)
12373 struct mesh *m;
12374 struct behavior *b;
12375 #endif /* not ANSI_DECLARATORS */
12376 
12377 {
12378   struct otri hulltri;
12379   struct otri nexttri;
12380   struct otri starttri;
12381   triangle ptr;             /* Temporary variable used by sym() and oprev(). */
12382 
12383   /* Find a triangle handle on the hull. */
12384   hulltri.tri = m->dummytri;
12385   hulltri.orient = 0;
12386   symself(hulltri);
12387   /* Remember where we started so we know when to stop. */
12388   otricopy(hulltri, starttri);
12389   /* Go once counterclockwise around the convex hull. */
12390   do {
12391     /* Create a subsegment if there isn't already one here. */
12392     insertsubseg(m, b, &hulltri, 1);
12393     /* To find the next hull edge, go clockwise around the next vertex. */
12394     lnextself(hulltri);
12395     oprev(hulltri, nexttri);
12396     while (nexttri.tri != m->dummytri) {
12397       otricopy(nexttri, hulltri);
12398       oprev(hulltri, nexttri);
12399     }
12400   } while (!otriequal(hulltri, starttri));
12401 }
12402 
12403 /*****************************************************************************/
12404 /*                                                                           */
12405 /*  formskeleton()   Create the segments of a triangulation, including PSLG  */
12406 /*                   segments and edges on the convex hull.                  */
12407 /*                                                                           */
12408 /*  The PSLG segments are read from a .poly file.  The return value is the   */
12409 /*  number of segments in the file.                                          */
12410 /*                                                                           */
12411 /*****************************************************************************/
12412 
12413 #ifdef TRILIBRARY
12414 
12415 #ifdef ANSI_DECLARATORS
12416 void formskeleton(struct mesh *m, struct behavior *b, int *segmentlist,
12417                   int *segmentmarkerlist, int numberofsegments)
12418 #else /* not ANSI_DECLARATORS */
12419 void formskeleton(m, b, segmentlist, segmentmarkerlist, numberofsegments)
12420 struct mesh *m;
12421 struct behavior *b;
12422 int *segmentlist;
12423 int *segmentmarkerlist;
12424 int numberofsegments;
12425 #endif /* not ANSI_DECLARATORS */
12426 
12427 #else /* not TRILIBRARY */
12428 
12429 #ifdef ANSI_DECLARATORS
12430 void formskeleton(struct mesh *m, struct behavior *b,
12431                   FILE *polyfile, char *polyfilename)
12432 #else /* not ANSI_DECLARATORS */
12433 void formskeleton(m, b, polyfile, polyfilename)
12434 struct mesh *m;
12435 struct behavior *b;
12436 FILE *polyfile;
12437 char *polyfilename;
12438 #endif /* not ANSI_DECLARATORS */
12439 
12440 #endif /* not TRILIBRARY */
12441 
12442 {
12443 #ifdef TRILIBRARY
12444   char polyfilename[6];
12445   int index;
12446 #else /* not TRILIBRARY */
12447   char inputline[INPUTLINESIZE];
12448   char *stringptr;
12449 #endif /* not TRILIBRARY */
12450   vertex endpoint1, endpoint2;
12451   int segmentmarkers;
12452   int end1, end2;
12453   int boundmarker;
12454   int i;
12455 
12456   if (b->poly) {
12457     if (!b->quiet) {
12458       printf("Recovering segments in Delaunay triangulation.\n");
12459     }
12460 #ifdef TRILIBRARY
12461     strcpy(polyfilename, "input");
12462     m->insegments = numberofsegments;
12463     segmentmarkers = segmentmarkerlist != (int *) NULL;
12464     index = 0;
12465 #else /* not TRILIBRARY */
12466     /* Read the segments from a .poly file. */
12467     /* Read number of segments and number of boundary markers. */
12468     stringptr = readline(inputline, polyfile, polyfilename);
12469     m->insegments = (int) strtol(stringptr, &stringptr, 0);
12470     stringptr = findfield(stringptr);
12471     if (*stringptr == '\0') {
12472       segmentmarkers = 0;
12473     } else {
12474       segmentmarkers = (int) strtol(stringptr, &stringptr, 0);
12475     }
12476 #endif /* not TRILIBRARY */
12477     /* If the input vertices are collinear, there is no triangulation, */
12478     /*   so don't try to insert segments.                              */
12479     if (m->triangles.items == 0) {
12480       return;
12481     }
12482 
12483     /* If segments are to be inserted, compute a mapping */
12484     /*   from vertices to triangles.                     */
12485     if (m->insegments > 0) {
12486       makevertexmap(m, b);
12487       if (b->verbose) {
12488         printf("  Recovering PSLG segments.\n");
12489       }
12490     }
12491 
12492     boundmarker = 0;
12493     /* Read and insert the segments. */
12494     for (i = 0; i < m->insegments; i++) {
12495 #ifdef TRILIBRARY
12496       end1 = segmentlist[index++];
12497       end2 = segmentlist[index++];
12498       if (segmentmarkers) {
12499         boundmarker = segmentmarkerlist[i];
12500       }
12501 #else /* not TRILIBRARY */
12502       stringptr = readline(inputline, polyfile, b->inpolyfilename);
12503       stringptr = findfield(stringptr);
12504       if (*stringptr == '\0') {
12505         printf("Error:  Segment %d has no endpoints in %s.\n",
12506                b->firstnumber + i, polyfilename);
12507         triexit(1);
12508       } else {
12509         end1 = (int) strtol(stringptr, &stringptr, 0);
12510       }
12511       stringptr = findfield(stringptr);
12512       if (*stringptr == '\0') {
12513         printf("Error:  Segment %d is missing its second endpoint in %s.\n",
12514                b->firstnumber + i, polyfilename);
12515         triexit(1);
12516       } else {
12517         end2 = (int) strtol(stringptr, &stringptr, 0);
12518       }
12519       if (segmentmarkers) {
12520         stringptr = findfield(stringptr);
12521         if (*stringptr == '\0') {
12522           boundmarker = 0;
12523         } else {
12524           boundmarker = (int) strtol(stringptr, &stringptr, 0);
12525         }
12526       }
12527 #endif /* not TRILIBRARY */
12528       if ((end1 < b->firstnumber) ||
12529           (end1 >= b->firstnumber + m->invertices)) {
12530         if (!b->quiet) {
12531           printf("Warning:  Invalid first endpoint of segment %d in %s.\n",
12532                  b->firstnumber + i, polyfilename);
12533         }
12534       } else if ((end2 < b->firstnumber) ||
12535                  (end2 >= b->firstnumber + m->invertices)) {
12536         if (!b->quiet) {
12537           printf("Warning:  Invalid second endpoint of segment %d in %s.\n",
12538                  b->firstnumber + i, polyfilename);
12539         }
12540       } else {
12541         /* Find the vertices numbered `end1' and `end2'. */
12542         endpoint1 = getvertex(m, b, end1);
12543         endpoint2 = getvertex(m, b, end2);
12544         if ((endpoint1[0] == endpoint2[0]) && (endpoint1[1] == endpoint2[1])) {
12545           if (!b->quiet) {
12546             printf("Warning:  Endpoints of segment %d are coincident in %s.\n",
12547                    b->firstnumber + i, polyfilename);
12548           }
12549         } else {
12550           insertsegment(m, b, endpoint1, endpoint2, boundmarker);
12551         }
12552       }
12553     }
12554   } else {
12555     m->insegments = 0;
12556   }
12557   if (b->convex || !b->poly) {
12558     /* Enclose the convex hull with subsegments. */
12559     if (b->verbose) {
12560       printf("  Enclosing convex hull with segments.\n");
12561     }
12562     markhull(m, b);
12563   }
12564 }
12565 
12568 /********* Segment insertion ends here                               *********/
12569 
12570 /********* Carving out holes and concavities begins here             *********/
12574 /*****************************************************************************/
12575 /*                                                                           */
12576 /*  infecthull()   Virally infect all of the triangles of the convex hull    */
12577 /*                 that are not protected by subsegments.  Where there are   */
12578 /*                 subsegments, set boundary markers as appropriate.         */
12579 /*                                                                           */
12580 /*****************************************************************************/
12581 
12582 #ifdef ANSI_DECLARATORS
12583 void infecthull(struct mesh *m, struct behavior *b)
12584 #else /* not ANSI_DECLARATORS */
12585 void infecthull(m, b)
12586 struct mesh *m;
12587 struct behavior *b;
12588 #endif /* not ANSI_DECLARATORS */
12589 
12590 {
12591   struct otri hulltri;
12592   struct otri nexttri;
12593   struct otri starttri;
12594   struct osub hullsubseg;
12595   triangle **deadtriangle;
12596   vertex horg, hdest;
12597   triangle ptr;                         /* Temporary variable used by sym(). */
12598   subseg sptr;                      /* Temporary variable used by tspivot(). */
12599 
12600   if (b->verbose) {
12601     printf("  Marking concavities (external triangles) for elimination.\n");
12602   }
12603   /* Find a triangle handle on the hull. */
12604   hulltri.tri = m->dummytri;
12605   hulltri.orient = 0;
12606   symself(hulltri);
12607   /* Remember where we started so we know when to stop. */
12608   otricopy(hulltri, starttri);
12609   /* Go once counterclockwise around the convex hull. */
12610   do {
12611     /* Ignore triangles that are already infected. */
12612     if (!infected(hulltri)) {
12613       /* Is the triangle protected by a subsegment? */
12614       tspivot(hulltri, hullsubseg);
12615       if (hullsubseg.ss == m->dummysub) {
12616         /* The triangle is not protected; infect it. */
12617         if (!infected(hulltri)) {
12618           infect(hulltri);
12619           deadtriangle = (triangle **) poolalloc(&m->viri);
12620           *deadtriangle = hulltri.tri;
12621         }
12622       } else {
12623         /* The triangle is protected; set boundary markers if appropriate. */
12624         if (mark(hullsubseg) == 0) {
12625           setmark(hullsubseg, 1);
12626           org(hulltri, horg);
12627           dest(hulltri, hdest);
12628           if (vertexmark(horg) == 0) {
12629             setvertexmark(horg, 1);
12630           }
12631           if (vertexmark(hdest) == 0) {
12632             setvertexmark(hdest, 1);
12633           }
12634         }
12635       }
12636     }
12637     /* To find the next hull edge, go clockwise around the next vertex. */
12638     lnextself(hulltri);
12639     oprev(hulltri, nexttri);
12640     while (nexttri.tri != m->dummytri) {
12641       otricopy(nexttri, hulltri);
12642       oprev(hulltri, nexttri);
12643     }
12644   } while (!otriequal(hulltri, starttri));
12645 }
12646 
12647 /*****************************************************************************/
12648 /*                                                                           */
12649 /*  plague()   Spread the virus from all infected triangles to any neighbors */
12650 /*             not protected by subsegments.  Delete all infected triangles. */
12651 /*                                                                           */
12652 /*  This is the procedure that actually creates holes and concavities.       */
12653 /*                                                                           */
12654 /*  This procedure operates in two phases.  The first phase identifies all   */
12655 /*  the triangles that will die, and marks them as infected.  They are       */
12656 /*  marked to ensure that each triangle is added to the virus pool only      */
12657 /*  once, so the procedure will terminate.                                   */
12658 /*                                                                           */
12659 /*  The second phase actually eliminates the infected triangles.  It also    */
12660 /*  eliminates orphaned vertices.                                            */
12661 /*                                                                           */
12662 /*****************************************************************************/
12663 
12664 #ifdef ANSI_DECLARATORS
12665 void plague(struct mesh *m, struct behavior *b)
12666 #else /* not ANSI_DECLARATORS */
12667 void plague(m, b)
12668 struct mesh *m;
12669 struct behavior *b;
12670 #endif /* not ANSI_DECLARATORS */
12671 
12672 {
12673   struct otri testtri;
12674   struct otri neighbor;
12675   triangle **virusloop;
12676   triangle **deadtriangle;
12677   struct osub neighborsubseg;
12678   vertex testvertex;
12679   vertex norg, ndest;
12680   vertex deadorg, deaddest, deadapex;
12681   int killorg;
12682   triangle ptr;             /* Temporary variable used by sym() and onext(). */
12683   subseg sptr;                      /* Temporary variable used by tspivot(). */
12684 
12685   if (b->verbose) {
12686     printf("  Marking neighbors of marked triangles.\n");
12687   }
12688   /* Loop through all the infected triangles, spreading the virus to */
12689   /*   their neighbors, then to their neighbors' neighbors.          */
12690   traversalinit(&m->viri);
12691   virusloop = (triangle **) traverse(&m->viri);
12692   while (virusloop != (triangle **) NULL) {
12693     testtri.tri = *virusloop;
12694     /* A triangle is marked as infected by messing with one of its pointers */
12695     /*   to subsegments, setting it to an illegal value.  Hence, we have to */
12696     /*   temporarily uninfect this triangle so that we can examine its      */
12697     /*   adjacent subsegments.                                              */
12698     uninfect(testtri);
12699     if (b->verbose > 2) {
12700       /* Assign the triangle an orientation for convenience in */
12701       /*   checking its vertices.                              */
12702       testtri.orient = 0;
12703       org(testtri, deadorg);
12704       dest(testtri, deaddest);
12705       apex(testtri, deadapex);
12706       printf("    Checking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
12707              deadorg[0], deadorg[1], deaddest[0], deaddest[1],
12708              deadapex[0], deadapex[1]);
12709     }
12710     /* Check each of the triangle's three neighbors. */
12711     for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
12712       /* Find the neighbor. */
12713       sym(testtri, neighbor);
12714       /* Check for a subsegment between the triangle and its neighbor. */
12715       tspivot(testtri, neighborsubseg);
12716       /* Check if the neighbor is nonexistent or already infected. */
12717       if ((neighbor.tri == m->dummytri) || infected(neighbor)) {
12718         if (neighborsubseg.ss != m->dummysub) {
12719           /* There is a subsegment separating the triangle from its      */
12720           /*   neighbor, but both triangles are dying, so the subsegment */
12721           /*   dies too.                                                 */
12722           subsegdealloc(m, neighborsubseg.ss);
12723           if (neighbor.tri != m->dummytri) {
12724             /* Make sure the subsegment doesn't get deallocated again */
12725             /*   later when the infected neighbor is visited.         */
12726             uninfect(neighbor);
12727             tsdissolve(neighbor);
12728             infect(neighbor);
12729           }
12730         }
12731       } else {                   /* The neighbor exists and is not infected. */
12732         if (neighborsubseg.ss == m->dummysub) {
12733           /* There is no subsegment protecting the neighbor, so */
12734           /*   the neighbor becomes infected.                   */
12735           if (b->verbose > 2) {
12736             org(neighbor, deadorg);
12737             dest(neighbor, deaddest);
12738             apex(neighbor, deadapex);
12739             printf(
12740               "    Marking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
12741                    deadorg[0], deadorg[1], deaddest[0], deaddest[1],
12742                    deadapex[0], deadapex[1]);
12743           }
12744           infect(neighbor);
12745           /* Ensure that the neighbor's neighbors will be infected. */
12746           deadtriangle = (triangle **) poolalloc(&m->viri);
12747           *deadtriangle = neighbor.tri;
12748         } else {               /* The neighbor is protected by a subsegment. */
12749           /* Remove this triangle from the subsegment. */
12750           stdissolve(neighborsubseg);
12751           /* The subsegment becomes a boundary.  Set markers accordingly. */
12752           if (mark(neighborsubseg) == 0) {
12753             setmark(neighborsubseg, 1);
12754           }
12755           org(neighbor, norg);
12756           dest(neighbor, ndest);
12757           if (vertexmark(norg) == 0) {
12758             setvertexmark(norg, 1);
12759           }
12760           if (vertexmark(ndest) == 0) {
12761             setvertexmark(ndest, 1);
12762           }
12763         }
12764       }
12765     }
12766     /* Remark the triangle as infected, so it doesn't get added to the */
12767     /*   virus pool again.                                             */
12768     infect(testtri);
12769     virusloop = (triangle **) traverse(&m->viri);
12770   }
12771 
12772   if (b->verbose) {
12773     printf("  Deleting marked triangles.\n");
12774   }
12775 
12776   traversalinit(&m->viri);
12777   virusloop = (triangle **) traverse(&m->viri);
12778   while (virusloop != (triangle **) NULL) {
12779     testtri.tri = *virusloop;
12780 
12781     /* Check each of the three corners of the triangle for elimination. */
12782     /*   This is done by walking around each vertex, checking if it is  */
12783     /*   still connected to at least one live triangle.                 */
12784     for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
12785       org(testtri, testvertex);
12786       /* Check if the vertex has already been tested. */
12787       if (testvertex != (vertex) NULL) {
12788         killorg = 1;
12789         /* Mark the corner of the triangle as having been tested. */
12790         setorg(testtri, NULL);
12791         /* Walk counterclockwise about the vertex. */
12792         onext(testtri, neighbor);
12793         /* Stop upon reaching a boundary or the starting triangle. */
12794         while ((neighbor.tri != m->dummytri) &&
12795                (!otriequal(neighbor, testtri))) {
12796           if (infected(neighbor)) {
12797             /* Mark the corner of this triangle as having been tested. */
12798             setorg(neighbor, NULL);
12799           } else {
12800             /* A live triangle.  The vertex survives. */
12801             killorg = 0;
12802           }
12803           /* Walk counterclockwise about the vertex. */
12804           onextself(neighbor);
12805         }
12806         /* If we reached a boundary, we must walk clockwise as well. */
12807         if (neighbor.tri == m->dummytri) {
12808           /* Walk clockwise about the vertex. */
12809           oprev(testtri, neighbor);
12810           /* Stop upon reaching a boundary. */
12811           while (neighbor.tri != m->dummytri) {
12812             if (infected(neighbor)) {
12813             /* Mark the corner of this triangle as having been tested. */
12814               setorg(neighbor, NULL);
12815             } else {
12816               /* A live triangle.  The vertex survives. */
12817               killorg = 0;
12818             }
12819             /* Walk clockwise about the vertex. */
12820             oprevself(neighbor);
12821           }
12822         }
12823         if (killorg) {
12824           if (b->verbose > 1) {
12825             printf("    Deleting vertex (%.12g, %.12g)\n",
12826                    testvertex[0], testvertex[1]);
12827           }
12828           setvertextype(testvertex, UNDEADVERTEX);
12829           m->undeads++;
12830         }
12831       }
12832     }
12833 
12834     /* Record changes in the number of boundary edges, and disconnect */
12835     /*   dead triangles from their neighbors.                         */
12836     for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
12837       sym(testtri, neighbor);
12838       if (neighbor.tri == m->dummytri) {
12839         /* There is no neighboring triangle on this edge, so this edge    */
12840         /*   is a boundary edge.  This triangle is being deleted, so this */
12841         /*   boundary edge is deleted.                                    */
12842         m->hullsize--;
12843       } else {
12844         /* Disconnect the triangle from its neighbor. */
12845         dissolve(neighbor);
12846         /* There is a neighboring triangle on this edge, so this edge */
12847         /*   becomes a boundary edge when this triangle is deleted.   */
12848         m->hullsize++;
12849       }
12850     }
12851     /* Return the dead triangle to the pool of triangles. */
12852     triangledealloc(m, testtri.tri);
12853     virusloop = (triangle **) traverse(&m->viri);
12854   }
12855   /* Empty the virus pool. */
12856   poolrestart(&m->viri);
12857 }
12858 
12859 /*****************************************************************************/
12860 /*                                                                           */
12861 /*  regionplague()   Spread regional attributes and/or area constraints      */
12862 /*                   (from a .poly file) throughout the mesh.                */
12863 /*                                                                           */
12864 /*  This procedure operates in two phases.  The first phase spreads an       */
12865 /*  attribute and/or an area constraint through a (segment-bounded) region.  */
12866 /*  The triangles are marked to ensure that each triangle is added to the    */
12867 /*  virus pool only once, so the procedure will terminate.                   */
12868 /*                                                                           */
12869 /*  The second phase uninfects all infected triangles, returning them to     */
12870 /*  normal.                                                                  */
12871 /*                                                                           */
12872 /*****************************************************************************/
12873 
12874 #ifdef ANSI_DECLARATORS
12875 void regionplague(struct mesh *m, struct behavior *b,
12876                   REAL attribute, REAL area)
12877 #else /* not ANSI_DECLARATORS */
12878 void regionplague(m, b, attribute, area)
12879 struct mesh *m;
12880 struct behavior *b;
12881 REAL attribute;
12882 REAL area;
12883 #endif /* not ANSI_DECLARATORS */
12884 
12885 {
12886   struct otri testtri;
12887   struct otri neighbor;
12888   triangle **virusloop;
12889   triangle **regiontri;
12890   struct osub neighborsubseg;
12891   vertex regionorg, regiondest, regionapex;
12892   triangle ptr;             /* Temporary variable used by sym() and onext(). */
12893   subseg sptr;                      /* Temporary variable used by tspivot(). */
12894 
12895   if (b->verbose > 1) {
12896     printf("  Marking neighbors of marked triangles.\n");
12897   }
12898   /* Loop through all the infected triangles, spreading the attribute      */
12899   /*   and/or area constraint to their neighbors, then to their neighbors' */
12900   /*   neighbors.                                                          */
12901   traversalinit(&m->viri);
12902   virusloop = (triangle **) traverse(&m->viri);
12903   while (virusloop != (triangle **) NULL) {
12904     testtri.tri = *virusloop;
12905     /* A triangle is marked as infected by messing with one of its pointers */
12906     /*   to subsegments, setting it to an illegal value.  Hence, we have to */
12907     /*   temporarily uninfect this triangle so that we can examine its      */
12908     /*   adjacent subsegments.                                              */
12909     uninfect(testtri);
12910     if (b->regionattrib) {
12911       /* Set an attribute. */
12912       setelemattribute(testtri, m->eextras, attribute);
12913     }
12914     if (b->vararea) {
12915       /* Set an area constraint. */
12916       setareabound(testtri, area);
12917     }
12918     if (b->verbose > 2) {
12919       /* Assign the triangle an orientation for convenience in */
12920       /*   checking its vertices.                              */
12921       testtri.orient = 0;
12922       org(testtri, regionorg);
12923       dest(testtri, regiondest);
12924       apex(testtri, regionapex);
12925       printf("    Checking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
12926              regionorg[0], regionorg[1], regiondest[0], regiondest[1],
12927              regionapex[0], regionapex[1]);
12928     }
12929     /* Check each of the triangle's three neighbors. */
12930     for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
12931       /* Find the neighbor. */
12932       sym(testtri, neighbor);
12933       /* Check for a subsegment between the triangle and its neighbor. */
12934       tspivot(testtri, neighborsubseg);
12935       /* Make sure the neighbor exists, is not already infected, and */
12936       /*   isn't protected by a subsegment.                          */
12937       if ((neighbor.tri != m->dummytri) && !infected(neighbor)
12938           && (neighborsubseg.ss == m->dummysub)) {
12939         if (b->verbose > 2) {
12940           org(neighbor, regionorg);
12941           dest(neighbor, regiondest);
12942           apex(neighbor, regionapex);
12943           printf("    Marking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
12944                  regionorg[0], regionorg[1], regiondest[0], regiondest[1],
12945                  regionapex[0], regionapex[1]);
12946         }
12947         /* Infect the neighbor. */
12948         infect(neighbor);
12949         /* Ensure that the neighbor's neighbors will be infected. */
12950         regiontri = (triangle **) poolalloc(&m->viri);
12951         *regiontri = neighbor.tri;
12952       }
12953     }
12954     /* Remark the triangle as infected, so it doesn't get added to the */
12955     /*   virus pool again.                                             */
12956     infect(testtri);
12957     virusloop = (triangle **) traverse(&m->viri);
12958   }
12959 
12960   /* Uninfect all triangles. */
12961   if (b->verbose > 1) {
12962     printf("  Unmarking marked triangles.\n");
12963   }
12964   traversalinit(&m->viri);
12965   virusloop = (triangle **) traverse(&m->viri);
12966   while (virusloop != (triangle **) NULL) {
12967     testtri.tri = *virusloop;
12968     uninfect(testtri);
12969     virusloop = (triangle **) traverse(&m->viri);
12970   }
12971   /* Empty the virus pool. */
12972   poolrestart(&m->viri);
12973 }
12974 
12975 /*****************************************************************************/
12976 /*                                                                           */
12977 /*  carveholes()   Find the holes and infect them.  Find the area            */
12978 /*                 constraints and infect them.  Infect the convex hull.     */
12979 /*                 Spread the infection and kill triangles.  Spread the      */
12980 /*                 area constraints.                                         */
12981 /*                                                                           */
12982 /*  This routine mainly calls other routines to carry out all these          */
12983 /*  functions.                                                               */
12984 /*                                                                           */
12985 /*****************************************************************************/
12986 
12987 #ifdef ANSI_DECLARATORS
12988 void carveholes(struct mesh *m, struct behavior *b, REAL *holelist, int holes,
12989                 REAL *regionlist, int regions)
12990 #else /* not ANSI_DECLARATORS */
12991 void carveholes(m, b, holelist, holes, regionlist, regions)
12992 struct mesh *m;
12993 struct behavior *b;
12994 REAL *holelist;
12995 int holes;
12996 REAL *regionlist;
12997 int regions;
12998 #endif /* not ANSI_DECLARATORS */
12999 
13000 {
13001   struct otri searchtri;
13002   struct otri triangleloop;
13003   struct otri *regiontris;
13004   triangle **holetri;
13005   triangle **regiontri;
13006   vertex searchorg, searchdest;
13007   enum locateresult intersect;
13008   int i;
13009   triangle ptr;                         /* Temporary variable used by sym(). */
13010 
13011   if (!(b->quiet || (b->noholes && b->convex))) {
13012     printf("Removing unwanted triangles.\n");
13013     if (b->verbose && (holes > 0)) {
13014       printf("  Marking holes for elimination.\n");
13015     }
13016   }
13017 
13018   if (regions > 0) {
13019     /* Allocate storage for the triangles in which region points fall. */
13020     regiontris = (struct otri *) trimalloc(regions *
13021                                            (int) sizeof(struct otri));
13022   } else {
13023     regiontris = (struct otri *) NULL;
13024   }
13025 
13026   if (((holes > 0) && !b->noholes) || !b->convex || (regions > 0)) {
13027     /* Initialize a pool of viri to be used for holes, concavities, */
13028     /*   regional attributes, and/or regional area constraints.     */
13029     poolinit(&m->viri, sizeof(triangle *), VIRUSPERBLOCK, VIRUSPERBLOCK, 0);
13030   }
13031 
13032   if (!b->convex) {
13033     /* Mark as infected any unprotected triangles on the boundary. */
13034     /*   This is one way by which concavities are created.         */
13035     infecthull(m, b);
13036   }
13037 
13038   if ((holes > 0) && !b->noholes) {
13039     /* Infect each triangle in which a hole lies. */
13040     for (i = 0; i < 2 * holes; i += 2) {
13041       /* Ignore holes that aren't within the bounds of the mesh. */
13042       if ((holelist[i] >= m->xmin) && (holelist[i] <= m->xmax)
13043           && (holelist[i + 1] >= m->ymin) && (holelist[i + 1] <= m->ymax)) {
13044         /* Start searching from some triangle on the outer boundary. */
13045         searchtri.tri = m->dummytri;
13046         searchtri.orient = 0;
13047         symself(searchtri);
13048         /* Ensure that the hole is to the left of this boundary edge; */
13049         /*   otherwise, locate() will falsely report that the hole    */
13050         /*   falls within the starting triangle.                      */
13051         org(searchtri, searchorg);
13052         dest(searchtri, searchdest);
13053         if (counterclockwise(m, b, searchorg, searchdest, &holelist[i]) >
13054             0.0) {
13055           /* Find a triangle that contains the hole. */
13056           intersect = locate(m, b, &holelist[i], &searchtri);
13057           if ((intersect != OUTSIDE) && (!infected(searchtri))) {
13058             /* Infect the triangle.  This is done by marking the triangle  */
13059             /*   as infected and including the triangle in the virus pool. */
13060             infect(searchtri);
13061             holetri = (triangle **) poolalloc(&m->viri);
13062             *holetri = searchtri.tri;
13063           }
13064         }
13065       }
13066     }
13067   }
13068 
13069   /* Now, we have to find all the regions BEFORE we carve the holes, because */
13070   /*   locate() won't work when the triangulation is no longer convex.       */
13071   /*   (Incidentally, this is the reason why regional attributes and area    */
13072   /*   constraints can't be used when refining a preexisting mesh, which     */
13073   /*   might not be convex; they can only be used with a freshly             */
13074   /*   triangulated PSLG.)                                                   */
13075   if (regions > 0) {
13076     /* Find the starting triangle for each region. */
13077     for (i = 0; i < regions; i++) {
13078       regiontris[i].tri = m->dummytri;
13079       /* Ignore region points that aren't within the bounds of the mesh. */
13080       if ((regionlist[4 * i] >= m->xmin) && (regionlist[4 * i] <= m->xmax) &&
13081           (regionlist[4 * i + 1] >= m->ymin) &&
13082           (regionlist[4 * i + 1] <= m->ymax)) {
13083         /* Start searching from some triangle on the outer boundary. */
13084         searchtri.tri = m->dummytri;
13085         searchtri.orient = 0;
13086         symself(searchtri);
13087         /* Ensure that the region point is to the left of this boundary */
13088         /*   edge; otherwise, locate() will falsely report that the     */
13089         /*   region point falls within the starting triangle.           */
13090         org(searchtri, searchorg);
13091         dest(searchtri, searchdest);
13092         if (counterclockwise(m, b, searchorg, searchdest, &regionlist[4 * i]) >
13093             0.0) {
13094           /* Find a triangle that contains the region point. */
13095           intersect = locate(m, b, &regionlist[4 * i], &searchtri);
13096           if ((intersect != OUTSIDE) && (!infected(searchtri))) {
13097             /* Record the triangle for processing after the */
13098             /*   holes have been carved.                    */
13099             otricopy(searchtri, regiontris[i]);
13100           }
13101         }
13102       }
13103     }
13104   }
13105 
13106   if (m->viri.items > 0) {
13107     /* Carve the holes and concavities. */
13108     plague(m, b);
13109   }
13110   /* The virus pool should be empty now. */
13111 
13112   if (regions > 0) {
13113     if (!b->quiet) {
13114       if (b->regionattrib) {
13115         if (b->vararea) {
13116           printf("Spreading regional attributes and area constraints.\n");
13117         } else {
13118           printf("Spreading regional attributes.\n");
13119         }
13120       } else {
13121         printf("Spreading regional area constraints.\n");
13122       }
13123     }
13124     if (b->regionattrib && !b->refine) {
13125       /* Assign every triangle a regional attribute of zero. */
13126       traversalinit(&m->triangles);
13127       triangleloop.orient = 0;
13128       triangleloop.tri = triangletraverse(m);
13129       while (triangleloop.tri != (triangle *) NULL) {
13130         setelemattribute(triangleloop, m->eextras, 0.0);
13131         triangleloop.tri = triangletraverse(m);
13132       }
13133     }
13134     for (i = 0; i < regions; i++) {
13135       if (regiontris[i].tri != m->dummytri) {
13136         /* Make sure the triangle under consideration still exists. */
13137         /*   It may have been eaten by the virus.                   */
13138         if (!deadtri(regiontris[i].tri)) {
13139           /* Put one triangle in the virus pool. */
13140           infect(regiontris[i]);
13141           regiontri = (triangle **) poolalloc(&m->viri);
13142           *regiontri = regiontris[i].tri;
13143           /* Apply one region's attribute and/or area constraint. */
13144           regionplague(m, b, regionlist[4 * i + 2], regionlist[4 * i + 3]);
13145           /* The virus pool should be empty now. */
13146         }
13147       }
13148     }
13149     if (b->regionattrib && !b->refine) {
13150       /* Note the fact that each triangle has an additional attribute. */
13151       m->eextras++;
13152     }
13153   }
13154 
13155   /* Free up memory. */
13156   if (((holes > 0) && !b->noholes) || !b->convex || (regions > 0)) {
13157     pooldeinit(&m->viri);
13158   }
13159   if (regions > 0) {
13160     trifree((VOID *) regiontris);
13161   }
13162 }
13163 
13166 /********* Carving out holes and concavities ends here               *********/
13167 
13168 /********* Mesh quality maintenance begins here                      *********/
13172 /*****************************************************************************/
13173 /*                                                                           */
13174 /*  tallyencs()   Traverse the entire list of subsegments, and check each    */
13175 /*                to see if it is encroached.  If so, add it to the list.    */
13176 /*                                                                           */
13177 /*****************************************************************************/
13178 
13179 #ifndef CDT_ONLY
13180 
13181 #ifdef ANSI_DECLARATORS
13182 void tallyencs(struct mesh *m, struct behavior *b)
13183 #else /* not ANSI_DECLARATORS */
13184 void tallyencs(m, b)
13185 struct mesh *m;
13186 struct behavior *b;
13187 #endif /* not ANSI_DECLARATORS */
13188 
13189 {
13190   struct osub subsegloop;
13191   int dummy;
13192 
13193   traversalinit(&m->subsegs);
13194   subsegloop.ssorient = 0;
13195   subsegloop.ss = subsegtraverse(m);
13196   while (subsegloop.ss != (subseg *) NULL) {
13197     /* If the segment is encroached, add it to the list. */
13198     dummy = checkseg4encroach(m, b, &subsegloop);
13199     subsegloop.ss = subsegtraverse(m);
13200   }
13201 }
13202 
13203 #endif /* not CDT_ONLY */
13204 
13205 /*****************************************************************************/
13206 /*                                                                           */
13207 /*  precisionerror()  Print an error message for precision problems.         */
13208 /*                                                                           */
13209 /*****************************************************************************/
13210 
13211 #ifndef CDT_ONLY
13212 
13213 void precisionerror()
13214 {
13215   printf("Try increasing the area criterion and/or reducing the minimum\n");
13216   printf("  allowable angle so that tiny triangles are not created.\n");
13217 #ifdef SINGLE
13218   printf("Alternatively, try recompiling me with double precision\n");
13219   printf("  arithmetic (by removing \"#define SINGLE\" from the\n");
13220   printf("  source file or \"-DSINGLE\" from the makefile).\n");
13221 #endif /* SINGLE */
13222 }
13223 
13224 #endif /* not CDT_ONLY */
13225 
13226 /*****************************************************************************/
13227 /*                                                                           */
13228 /*  splitencsegs()   Split all the encroached subsegments.                   */
13229 /*                                                                           */
13230 /*  Each encroached subsegment is repaired by splitting it - inserting a     */
13231 /*  vertex at or near its midpoint.  Newly inserted vertices may encroach    */
13232 /*  upon other subsegments; these are also repaired.                         */
13233 /*                                                                           */
13234 /*  `triflaws' is a flag that specifies whether one should take note of new  */
13235 /*  bad triangles that result from inserting vertices to repair encroached   */
13236 /*  subsegments.                                                             */
13237 /*                                                                           */
13238 /*****************************************************************************/
13239 
13240 #ifndef CDT_ONLY
13241 
13242 #ifdef ANSI_DECLARATORS
13243 void splitencsegs(struct mesh *m, struct behavior *b, int triflaws)
13244 #else /* not ANSI_DECLARATORS */
13245 void splitencsegs(m, b, triflaws)
13246 struct mesh *m;
13247 struct behavior *b;
13248 int triflaws;
13249 #endif /* not ANSI_DECLARATORS */
13250 
13251 {
13252   struct otri enctri;
13253   struct otri testtri;
13254   struct osub testsh;
13255   struct osub currentenc;
13256   struct badsubseg *encloop;
13257   vertex eorg, edest, eapex;
13258   vertex newvertex;
13259   enum insertvertexresult success;
13260   REAL segmentlength, nearestpoweroftwo;
13261   REAL split;
13262   REAL multiplier, divisor;
13263   int acuteorg, acuteorg2, acutedest, acutedest2;
13264   int dummy;
13265   int i;
13266   triangle ptr;                     /* Temporary variable used by stpivot(). */
13267   subseg sptr;                        /* Temporary variable used by snext(). */
13268 
13269   /* Note that steinerleft == -1 if an unlimited number */
13270   /*   of Steiner points is allowed.                    */
13271   while ((m->badsubsegs.items > 0) && (m->steinerleft != 0)) {
13272     traversalinit(&m->badsubsegs);
13273     encloop = badsubsegtraverse(m);
13274     while ((encloop != (struct badsubseg *) NULL) && (m->steinerleft != 0)) {
13275       sdecode(encloop->encsubseg, currentenc);
13276       sorg(currentenc, eorg);
13277       sdest(currentenc, edest);
13278       /* Make sure that this segment is still the same segment it was   */
13279       /*   when it was determined to be encroached.  If the segment was */
13280       /*   enqueued multiple times (because several newly inserted      */
13281       /*   vertices encroached it), it may have already been split.     */
13282       if (!deadsubseg(currentenc.ss) &&
13283           (eorg == encloop->subsegorg) && (edest == encloop->subsegdest)) {
13284         /* To decide where to split a segment, we need to know if the   */
13285         /*   segment shares an endpoint with an adjacent segment.       */
13286         /*   The concern is that, if we simply split every encroached   */
13287         /*   segment in its center, two adjacent segments with a small  */
13288         /*   angle between them might lead to an infinite loop; each    */
13289         /*   vertex added to split one segment will encroach upon the   */
13290         /*   other segment, which must then be split with a vertex that */
13291         /*   will encroach upon the first segment, and so on forever.   */
13292         /* To avoid this, imagine a set of concentric circles, whose    */
13293         /*   radii are powers of two, about each segment endpoint.      */
13294         /*   These concentric circles determine where the segment is    */
13295         /*   split.  (If both endpoints are shared with adjacent        */
13296         /*   segments, split the segment in the middle, and apply the   */
13297         /*   concentric circles for later splittings.)                  */
13298 
13299         /* Is the origin shared with another segment? */
13300         stpivot(currentenc, enctri);
13301         lnext(enctri, testtri);
13302         tspivot(testtri, testsh);
13303         acuteorg = testsh.ss != m->dummysub;
13304         /* Is the destination shared with another segment? */
13305         lnextself(testtri);
13306         tspivot(testtri, testsh);
13307         acutedest = testsh.ss != m->dummysub;
13308 
13309         /* If we're using Chew's algorithm (rather than Ruppert's) */
13310         /*   to define encroachment, delete free vertices from the */
13311         /*   subsegment's diametral circle.                        */
13312         if (!b->conformdel && !acuteorg && !acutedest) {
13313           apex(enctri, eapex);
13314           while ((vertextype(eapex) == FREEVERTEX) &&
13315                  ((eorg[0] - eapex[0]) * (edest[0] - eapex[0]) +
13316                   (eorg[1] - eapex[1]) * (edest[1] - eapex[1]) < 0.0)) {
13317             deletevertex(m, b, &testtri);
13318             stpivot(currentenc, enctri);
13319             apex(enctri, eapex);
13320             lprev(enctri, testtri);
13321           }
13322         }
13323 
13324         /* Now, check the other side of the segment, if there's a triangle */
13325         /*   there.                                                        */
13326         sym(enctri, testtri);
13327         if (testtri.tri != m->dummytri) {
13328           /* Is the destination shared with another segment? */
13329           lnextself(testtri);
13330           tspivot(testtri, testsh);
13331           acutedest2 = testsh.ss != m->dummysub;
13332           acutedest = acutedest || acutedest2;
13333           /* Is the origin shared with another segment? */
13334           lnextself(testtri);
13335           tspivot(testtri, testsh);
13336           acuteorg2 = testsh.ss != m->dummysub;
13337           acuteorg = acuteorg || acuteorg2;
13338 
13339           /* Delete free vertices from the subsegment's diametral circle. */
13340           if (!b->conformdel && !acuteorg2 && !acutedest2) {
13341             org(testtri, eapex);
13342             while ((vertextype(eapex) == FREEVERTEX) &&
13343                    ((eorg[0] - eapex[0]) * (edest[0] - eapex[0]) +
13344                     (eorg[1] - eapex[1]) * (edest[1] - eapex[1]) < 0.0)) {
13345               deletevertex(m, b, &testtri);
13346               sym(enctri, testtri);
13347               apex(testtri, eapex);
13348               lprevself(testtri);
13349             }
13350           }
13351         }
13352 
13353         /* Use the concentric circles if exactly one endpoint is shared */
13354         /*   with another adjacent segment.                             */
13355         if (acuteorg || acutedest) {
13356           segmentlength = sqrt((edest[0] - eorg[0]) * (edest[0] - eorg[0]) +
13357                                (edest[1] - eorg[1]) * (edest[1] - eorg[1]));
13358           /* Find the power of two that most evenly splits the segment.  */
13359           /*   The worst case is a 2:1 ratio between subsegment lengths. */
13360           nearestpoweroftwo = 1.0;
13361           while (segmentlength > 3.0 * nearestpoweroftwo) {
13362             nearestpoweroftwo *= 2.0;
13363           }
13364           while (segmentlength < 1.5 * nearestpoweroftwo) {
13365             nearestpoweroftwo *= 0.5;
13366           }
13367           /* Where do we split the segment? */
13368           split = nearestpoweroftwo / segmentlength;
13369           if (acutedest) {
13370             split = 1.0 - split;
13371           }
13372         } else {
13373           /* If we're not worried about adjacent segments, split */
13374           /*   this segment in the middle.                       */
13375           split = 0.5;
13376         }
13377 
13378         /* Create the new vertex. */
13379         newvertex = (vertex) poolalloc(&m->vertices);
13380         /* Interpolate its coordinate and attributes. */
13381         for (i = 0; i < 2 + m->nextras; i++) {
13382           newvertex[i] = eorg[i] + split * (edest[i] - eorg[i]);
13383         }
13384 
13385         if (!b->noexact) {
13386           /* Roundoff in the above calculation may yield a `newvertex'   */
13387           /*   that is not precisely collinear with `eorg' and `edest'.  */
13388           /*   Improve collinearity by one step of iterative refinement. */
13389           multiplier = counterclockwise(m, b, eorg, edest, newvertex);
13390           divisor = ((eorg[0] - edest[0]) * (eorg[0] - edest[0]) +
13391                      (eorg[1] - edest[1]) * (eorg[1] - edest[1]));
13392           if ((multiplier != 0.0) && (divisor != 0.0)) {
13393             multiplier = multiplier / divisor;
13394             /* Watch out for NANs. */
13395             if (multiplier == multiplier) {
13396               newvertex[0] += multiplier * (edest[1] - eorg[1]);
13397               newvertex[1] += multiplier * (eorg[0] - edest[0]);
13398             }
13399           }
13400         }
13401 
13402         setvertexmark(newvertex, mark(currentenc));
13403         setvertextype(newvertex, SEGMENTVERTEX);
13404         if (b->verbose > 1) {
13405           printf(
13406   "  Splitting subsegment (%.12g, %.12g) (%.12g, %.12g) at (%.12g, %.12g).\n",
13407                  eorg[0], eorg[1], edest[0], edest[1],
13408                  newvertex[0], newvertex[1]);
13409         }
13410         /* Check whether the new vertex lies on an endpoint. */
13411         if (((newvertex[0] == eorg[0]) && (newvertex[1] == eorg[1])) ||
13412             ((newvertex[0] == edest[0]) && (newvertex[1] == edest[1]))) {
13413           printf("Error:  Ran out of precision at (%.12g, %.12g).\n",
13414                  newvertex[0], newvertex[1]);
13415           printf("I attempted to split a segment to a smaller size than\n");
13416           printf("  can be accommodated by the finite precision of\n");
13417           printf("  floating point arithmetic.\n");
13418           precisionerror();
13419           triexit(1);
13420         }
13421         /* Insert the splitting vertex.  This should always succeed. */
13422         success = insertvertex(m, b, newvertex, &enctri, &currentenc,
13423                                1, triflaws);
13424         if ((success != SUCCESSFULVERTEX) && (success != ENCROACHINGVERTEX)) {
13425           printf("Internal error in splitencsegs():\n");
13426           printf("  Failure to split a segment.\n");
13427           internalerror();
13428         }
13429         if (m->steinerleft > 0) {
13430           m->steinerleft--;
13431         }
13432         /* Check the two new subsegments to see if they're encroached. */
13433         dummy = checkseg4encroach(m, b, &currentenc);
13434         snextself(currentenc);
13435         dummy = checkseg4encroach(m, b, &currentenc);
13436       }
13437 
13438       badsubsegdealloc(m, encloop);
13439       encloop = badsubsegtraverse(m);
13440     }
13441   }
13442 }
13443 
13444 #endif /* not CDT_ONLY */
13445 
13446 /*****************************************************************************/
13447 /*                                                                           */
13448 /*  tallyfaces()   Test every triangle in the mesh for quality measures.     */
13449 /*                                                                           */
13450 /*****************************************************************************/
13451 
13452 #ifndef CDT_ONLY
13453 
13454 #ifdef ANSI_DECLARATORS
13455 void tallyfaces(struct mesh *m, struct behavior *b)
13456 #else /* not ANSI_DECLARATORS */
13457 void tallyfaces(m, b)
13458 struct mesh *m;
13459 struct behavior *b;
13460 #endif /* not ANSI_DECLARATORS */
13461 
13462 {
13463   struct otri triangleloop;
13464 
13465   if (b->verbose) {
13466     printf("  Making a list of bad triangles.\n");
13467   }
13468   traversalinit(&m->triangles);
13469   triangleloop.orient = 0;
13470   triangleloop.tri = triangletraverse(m);
13471   while (triangleloop.tri != (triangle *) NULL) {
13472     /* If the triangle is bad, enqueue it. */
13473     testtriangle(m, b, &triangleloop);
13474     triangleloop.tri = triangletraverse(m);
13475   }
13476 }
13477 
13478 #endif /* not CDT_ONLY */
13479 
13480 /*****************************************************************************/
13481 /*                                                                           */
13482 /*  splittriangle()   Inserts a vertex at the circumcenter of a triangle.    */
13483 /*                    Deletes the newly inserted vertex if it encroaches     */
13484 /*                    upon a segment.                                        */
13485 /*                                                                           */
13486 /*****************************************************************************/
13487 
13488 #ifndef CDT_ONLY
13489 
13490 #ifdef ANSI_DECLARATORS
13491 void splittriangle(struct mesh *m, struct behavior *b,
13492                    struct badtriang *badtri)
13493 #else /* not ANSI_DECLARATORS */
13494 void splittriangle(m, b, badtri)
13495 struct mesh *m;
13496 struct behavior *b;
13497 struct badtriang *badtri;
13498 #endif /* not ANSI_DECLARATORS */
13499 
13500 {
13501   struct otri badotri;
13502   vertex borg, bdest, bapex;
13503   vertex newvertex;
13504   REAL xi, eta;
13505   enum insertvertexresult success;
13506   int errorflag;
13507   int i;
13508 
13509   decode(badtri->poortri, badotri);
13510   org(badotri, borg);
13511   dest(badotri, bdest);
13512   apex(badotri, bapex);
13513   /* Make sure that this triangle is still the same triangle it was      */
13514   /*   when it was tested and determined to be of bad quality.           */
13515   /*   Subsequent transformations may have made it a different triangle. */
13516   if (!deadtri(badotri.tri) && (borg == badtri->triangorg) &&
13517       (bdest == badtri->triangdest) && (bapex == badtri->triangapex)) {
13518     if (b->verbose > 1) {
13519       printf("  Splitting this triangle at its circumcenter:\n");
13520       printf("    (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", borg[0],
13521              borg[1], bdest[0], bdest[1], bapex[0], bapex[1]);
13522     }
13523 
13524     errorflag = 0;
13525     /* Create a new vertex at the triangle's circumcenter. */
13526     newvertex = (vertex) poolalloc(&m->vertices);
13527     findcircumcenter(m, b, borg, bdest, bapex, newvertex, &xi, &eta, 1);
13528 
13529     /* Check whether the new vertex lies on a triangle vertex. */
13530     if (((newvertex[0] == borg[0]) && (newvertex[1] == borg[1])) ||
13531         ((newvertex[0] == bdest[0]) && (newvertex[1] == bdest[1])) ||
13532         ((newvertex[0] == bapex[0]) && (newvertex[1] == bapex[1]))) {
13533       if (!b->quiet) {
13534         printf(
13535              "Warning:  New vertex (%.12g, %.12g) falls on existing vertex.\n",
13536                newvertex[0], newvertex[1]);
13537         errorflag = 1;
13538       }
13539       vertexdealloc(m, newvertex);
13540     } else {
13541       for (i = 2; i < 2 + m->nextras; i++) {
13542         /* Interpolate the vertex attributes at the circumcenter. */
13543         newvertex[i] = borg[i] + xi * (bdest[i] - borg[i])
13544                               + eta * (bapex[i] - borg[i]);
13545       }
13546       /* The new vertex must be in the interior, and therefore is a */
13547       /*   free vertex with a marker of zero.                       */
13548       setvertexmark(newvertex, 0);
13549       setvertextype(newvertex, FREEVERTEX);
13550 
13551       /* Ensure that the handle `badotri' does not represent the longest  */
13552       /*   edge of the triangle.  This ensures that the circumcenter must */
13553       /*   fall to the left of this edge, so point location will work.    */
13554       /*   (If the angle org-apex-dest exceeds 90 degrees, then the       */
13555       /*   circumcenter lies outside the org-dest edge, and eta is        */
13556       /*   negative.  Roundoff error might prevent eta from being         */
13557       /*   negative when it should be, so I test eta against xi.)         */
13558       if (eta < xi) {
13559         lprevself(badotri);
13560       }
13561 
13562       /* Insert the circumcenter, searching from the edge of the triangle, */
13563       /*   and maintain the Delaunay property of the triangulation.        */
13564       success = insertvertex(m, b, newvertex, &badotri, (struct osub *) NULL,
13565                              1, 1);
13566       if (success == SUCCESSFULVERTEX) {
13567         if (m->steinerleft > 0) {
13568           m->steinerleft--;
13569         }
13570       } else if (success == ENCROACHINGVERTEX) {
13571         /* If the newly inserted vertex encroaches upon a subsegment, */
13572         /*   delete the new vertex.                                   */
13573         undovertex(m, b);
13574         if (b->verbose > 1) {
13575           printf("  Rejecting (%.12g, %.12g).\n", newvertex[0], newvertex[1]);
13576         }
13577         vertexdealloc(m, newvertex);
13578       } else if (success == VIOLATINGVERTEX) {
13579         /* Failed to insert the new vertex, but some subsegment was */
13580         /*   marked as being encroached.                            */
13581         vertexdealloc(m, newvertex);
13582       } else {                                 /* success == DUPLICATEVERTEX */
13583         /* Couldn't insert the new vertex because a vertex is already there. */
13584         if (!b->quiet) {
13585           printf(
13586             "Warning:  New vertex (%.12g, %.12g) falls on existing vertex.\n",
13587                  newvertex[0], newvertex[1]);
13588           errorflag = 1;
13589         }
13590         vertexdealloc(m, newvertex);
13591       }
13592     }
13593     if (errorflag) {
13594       if (b->verbose) {
13595         printf("  The new vertex is at the circumcenter of triangle\n");
13596         printf("    (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
13597                borg[0], borg[1], bdest[0], bdest[1], bapex[0], bapex[1]);
13598       }
13599       printf("This probably means that I am trying to refine triangles\n");
13600       printf("  to a smaller size than can be accommodated by the finite\n");
13601       printf("  precision of floating point arithmetic.  (You can be\n");
13602       printf("  sure of this if I fail to terminate.)\n");
13603       precisionerror();
13604     }
13605   }
13606 }
13607 
13608 #endif /* not CDT_ONLY */
13609 
13610 /*****************************************************************************/
13611 /*                                                                           */
13612 /*  enforcequality()   Remove all the encroached subsegments and bad         */
13613 /*                     triangles from the triangulation.                     */
13614 /*                                                                           */
13615 /*****************************************************************************/
13616 
13617 #ifndef CDT_ONLY
13618 
13619 #ifdef ANSI_DECLARATORS
13620 void enforcequality(struct mesh *m, struct behavior *b)
13621 #else /* not ANSI_DECLARATORS */
13622 void enforcequality(m, b)
13623 struct mesh *m;
13624 struct behavior *b;
13625 #endif /* not ANSI_DECLARATORS */
13626 
13627 {
13628   struct badtriang *badtri;
13629   int i;
13630 
13631   if (!b->quiet) {
13632     printf("Adding Steiner points to enforce quality.\n");
13633   }
13634   /* Initialize the pool of encroached subsegments. */
13635   poolinit(&m->badsubsegs, sizeof(struct badsubseg), BADSUBSEGPERBLOCK,
13636            BADSUBSEGPERBLOCK, 0);
13637   if (b->verbose) {
13638     printf("  Looking for encroached subsegments.\n");
13639   }
13640   /* Test all segments to see if they're encroached. */
13641   tallyencs(m, b);
13642   if (b->verbose && (m->badsubsegs.items > 0)) {
13643     printf("  Splitting encroached subsegments.\n");
13644   }
13645   /* Fix encroached subsegments without noting bad triangles. */
13646   splitencsegs(m, b, 0);
13647   /* At this point, if we haven't run out of Steiner points, the */
13648   /*   triangulation should be (conforming) Delaunay.            */
13649 
13650   /* Next, we worry about enforcing triangle quality. */
13651   if ((b->minangle > 0.0) || b->vararea || b->fixedarea || b->usertest) {
13652     /* Initialize the pool of bad triangles. */
13653     poolinit(&m->badtriangles, sizeof(struct badtriang), BADTRIPERBLOCK,
13654              BADTRIPERBLOCK, 0);
13655     /* Initialize the queues of bad triangles. */
13656     for (i = 0; i < 4096; i++) {
13657       m->queuefront[i] = (struct badtriang *) NULL;
13658     }
13659     m->firstnonemptyq = -1;
13660     /* Test all triangles to see if they're bad. */
13661     tallyfaces(m, b);
13662     /* Initialize the pool of recently flipped triangles. */
13663     poolinit(&m->flipstackers, sizeof(struct flipstacker), FLIPSTACKERPERBLOCK,
13664              FLIPSTACKERPERBLOCK, 0);
13665     m->checkquality = 1;
13666     if (b->verbose) {
13667       printf("  Splitting bad triangles.\n");
13668     }
13669     while ((m->badtriangles.items > 0) && (m->steinerleft != 0)) {
13670       /* Fix one bad triangle by inserting a vertex at its circumcenter. */
13671       badtri = dequeuebadtriang(m);
13672       splittriangle(m, b, badtri);
13673       if (m->badsubsegs.items > 0) {
13674         /* Put bad triangle back in queue for another try later. */
13675         enqueuebadtriang(m, b, badtri);
13676         /* Fix any encroached subsegments that resulted. */
13677         /*   Record any new bad triangles that result.   */
13678         splitencsegs(m, b, 1);
13679       } else {
13680         /* Return the bad triangle to the pool. */
13681         pooldealloc(&m->badtriangles, (VOID *) badtri);
13682       }
13683     }
13684   }
13685   /* At this point, if the "-D" switch was selected and we haven't run out  */
13686   /*   of Steiner points, the triangulation should be (conforming) Delaunay */
13687   /*   and have no low-quality triangles.                                   */
13688 
13689   /* Might we have run out of Steiner points too soon? */
13690   if (!b->quiet && b->conformdel && (m->badsubsegs.items > 0) &&
13691       (m->steinerleft == 0)) {
13692     printf("\nWarning:  I ran out of Steiner points, but the mesh has\n");
13693     if (m->badsubsegs.items == 1) {
13694       printf("  one encroached subsegment, and therefore might not be truly\n"
13695              );
13696     } else {
13697       printf("  %ld encroached subsegments, and therefore might not be truly\n"
13698              , m->badsubsegs.items);
13699     }
13700     printf("  Delaunay.  If the Delaunay property is important to you,\n");
13701     printf("  try increasing the number of Steiner points (controlled by\n");
13702     printf("  the -S switch) slightly and try again.\n\n");
13703   }
13704 }
13705 
13706 #endif /* not CDT_ONLY */
13707 
13710 /********* Mesh quality maintenance ends here                        *********/
13711 
13712 /*****************************************************************************/
13713 /*                                                                           */
13714 /*  highorder()   Create extra nodes for quadratic subparametric elements.   */
13715 /*                                                                           */
13716 /*****************************************************************************/
13717 
13718 #ifdef ANSI_DECLARATORS
13719 void highorder(struct mesh *m, struct behavior *b)
13720 #else /* not ANSI_DECLARATORS */
13721 void highorder(m, b)
13722 struct mesh *m;
13723 struct behavior *b;
13724 #endif /* not ANSI_DECLARATORS */
13725 
13726 {
13727   struct otri triangleloop, trisym;
13728   struct osub checkmark;
13729   vertex newvertex;
13730   vertex torg, tdest;
13731   int i;
13732   triangle ptr;                         /* Temporary variable used by sym(). */
13733   subseg sptr;                      /* Temporary variable used by tspivot(). */
13734 
13735   if (!b->quiet) {
13736     printf("Adding vertices for second-order triangles.\n");
13737   }
13738   /* The following line ensures that dead items in the pool of nodes    */
13739   /*   cannot be allocated for the extra nodes associated with high     */
13740   /*   order elements.  This ensures that the primary nodes (at the     */
13741   /*   corners of elements) will occur earlier in the output files, and */
13742   /*   have lower indices, than the extra nodes.                        */
13743   m->vertices.deaditemstack = (VOID *) NULL;
13744 
13745   traversalinit(&m->triangles);
13746   triangleloop.tri = triangletraverse(m);
13747   /* To loop over the set of edges, loop over all triangles, and look at   */
13748   /*   the three edges of each triangle.  If there isn't another triangle  */
13749   /*   adjacent to the edge, operate on the edge.  If there is another     */
13750   /*   adjacent triangle, operate on the edge only if the current triangle */
13751   /*   has a smaller pointer than its neighbor.  This way, each edge is    */
13752   /*   considered only once.                                               */
13753   while (triangleloop.tri != (triangle *) NULL) {
13754     for (triangleloop.orient = 0; triangleloop.orient < 3;
13755          triangleloop.orient++) {
13756       sym(triangleloop, trisym);
13757       if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) {
13758         org(triangleloop, torg);
13759         dest(triangleloop, tdest);
13760         /* Create a new node in the middle of the edge.  Interpolate */
13761         /*   its attributes.                                         */
13762         newvertex = (vertex) poolalloc(&m->vertices);
13763         for (i = 0; i < 2 + m->nextras; i++) {
13764           newvertex[i] = 0.5 * (torg[i] + tdest[i]);
13765         }
13766         /* Set the new node's marker to zero or one, depending on */
13767         /*   whether it lies on a boundary.                       */
13768         setvertexmark(newvertex, trisym.tri == m->dummytri);
13769         setvertextype(newvertex,
13770                       trisym.tri == m->dummytri ? FREEVERTEX : SEGMENTVERTEX);
13771         if (b->usesegments) {
13772           tspivot(triangleloop, checkmark);
13773           /* If this edge is a segment, transfer the marker to the new node. */
13774           if (checkmark.ss != m->dummysub) {
13775             setvertexmark(newvertex, mark(checkmark));
13776             setvertextype(newvertex, SEGMENTVERTEX);
13777           }
13778         }
13779         if (b->verbose > 1) {
13780           printf("  Creating (%.12g, %.12g).\n", newvertex[0], newvertex[1]);
13781         }
13782         /* Record the new node in the (one or two) adjacent elements. */
13783         triangleloop.tri[m->highorderindex + triangleloop.orient] =
13784                 (triangle) newvertex;
13785         if (trisym.tri != m->dummytri) {
13786           trisym.tri[m->highorderindex + trisym.orient] = (triangle) newvertex;
13787         }
13788       }
13789     }
13790     triangleloop.tri = triangletraverse(m);
13791   }
13792 }
13793 
13794 /********* File I/O routines begin here                              *********/
13798 /*****************************************************************************/
13799 /*                                                                           */
13800 /*  readline()   Read a nonempty line from a file.                           */
13801 /*                                                                           */
13802 /*  A line is considered "nonempty" if it contains something that looks like */
13803 /*  a number.  Comments (prefaced by `#') are ignored.                       */
13804 /*                                                                           */
13805 /*****************************************************************************/
13806 
13807 #ifndef TRILIBRARY
13808 
13809 #ifdef ANSI_DECLARATORS
13810 char *readline(char *string, FILE *infile, char *infilename)
13811 #else /* not ANSI_DECLARATORS */
13812 char *readline(string, infile, infilename)
13813 char *string;
13814 FILE *infile;
13815 char *infilename;
13816 #endif /* not ANSI_DECLARATORS */
13817 
13818 {
13819   char *result;
13820 
13821   /* Search for something that looks like a number. */
13822   do {
13823     result = fgets(string, INPUTLINESIZE, infile);
13824     if (result == (char *) NULL) {
13825       printf("  Error:  Unexpected end of file in %s.\n", infilename);
13826       triexit(1);
13827     }
13828     /* Skip anything that doesn't look like a number, a comment, */
13829     /*   or the end of a line.                                   */
13830     while ((*result != '\0') && (*result != '#')
13831            && (*result != '.') && (*result != '+') && (*result != '-')
13832            && ((*result < '0') || (*result > '9'))) {
13833       result++;
13834     }
13835   /* If it's a comment or end of line, read another line and try again. */
13836   } while ((*result == '#') || (*result == '\0'));
13837   return result;
13838 }
13839 
13840 #endif /* not TRILIBRARY */
13841 
13842 /*****************************************************************************/
13843 /*                                                                           */
13844 /*  findfield()   Find the next field of a string.                           */
13845 /*                                                                           */
13846 /*  Jumps past the current field by searching for whitespace, then jumps     */
13847 /*  past the whitespace to find the next field.                              */
13848 /*                                                                           */
13849 /*****************************************************************************/
13850 
13851 #ifndef TRILIBRARY
13852 
13853 #ifdef ANSI_DECLARATORS
13854 char *findfield(char *string)
13855 #else /* not ANSI_DECLARATORS */
13856 char *findfield(string)
13857 char *string;
13858 #endif /* not ANSI_DECLARATORS */
13859 
13860 {
13861   char *result;
13862 
13863   result = string;
13864   /* Skip the current field.  Stop upon reaching whitespace. */
13865   while ((*result != '\0') && (*result != '#')
13866          && (*result != ' ') && (*result != '\t')) {
13867     result++;
13868   }
13869   /* Now skip the whitespace and anything else that doesn't look like a */
13870   /*   number, a comment, or the end of a line.                         */
13871   while ((*result != '\0') && (*result != '#')
13872          && (*result != '.') && (*result != '+') && (*result != '-')
13873          && ((*result < '0') || (*result > '9'))) {
13874     result++;
13875   }
13876   /* Check for a comment (prefixed with `#'). */
13877   if (*result == '#') {
13878     *result = '\0';
13879   }
13880   return result;
13881 }
13882 
13883 #endif /* not TRILIBRARY */
13884 
13885 /*****************************************************************************/
13886 /*                                                                           */
13887 /*  readnodes()   Read the vertices from a file, which may be a .node or     */
13888 /*                .poly file.                                                */
13889 /*                                                                           */
13890 /*****************************************************************************/
13891 
13892 #ifndef TRILIBRARY
13893 
13894 #ifdef ANSI_DECLARATORS
13895 void readnodes(struct mesh *m, struct behavior *b, char *nodefilename,
13896                char *polyfilename, FILE **polyfile)
13897 #else /* not ANSI_DECLARATORS */
13898 void readnodes(m, b, nodefilename, polyfilename, polyfile)
13899 struct mesh *m;
13900 struct behavior *b;
13901 char *nodefilename;
13902 char *polyfilename;
13903 FILE **polyfile;
13904 #endif /* not ANSI_DECLARATORS */
13905 
13906 {
13907   FILE *infile;
13908   vertex vertexloop;
13909   char inputline[INPUTLINESIZE];
13910   char *stringptr;
13911   char *infilename;
13912   REAL x, y;
13913   int firstnode;
13914   int nodemarkers;
13915   int currentmarker;
13916   int i, j;
13917 
13918   if (b->poly) {
13919     /* Read the vertices from a .poly file. */
13920     if (!b->quiet) {
13921       printf("Opening %s.\n", polyfilename);
13922     }
13923     *polyfile = fopen(polyfilename, "r");
13924     if (*polyfile == (FILE *) NULL) {
13925       printf("  Error:  Cannot access file %s.\n", polyfilename);
13926       triexit(1);
13927     }
13928     /* Read number of vertices, number of dimensions, number of vertex */
13929     /*   attributes, and number of boundary markers.                   */
13930     stringptr = readline(inputline, *polyfile, polyfilename);
13931     m->invertices = (int) strtol(stringptr, &stringptr, 0);
13932     stringptr = findfield(stringptr);
13933     if (*stringptr == '\0') {
13934       m->mesh_dim = 2;
13935     } else {
13936       m->mesh_dim = (int) strtol(stringptr, &stringptr, 0);
13937     }
13938     stringptr = findfield(stringptr);
13939     if (*stringptr == '\0') {
13940       m->nextras = 0;
13941     } else {
13942       m->nextras = (int) strtol(stringptr, &stringptr, 0);
13943     }
13944     stringptr = findfield(stringptr);
13945     if (*stringptr == '\0') {
13946       nodemarkers = 0;
13947     } else {
13948       nodemarkers = (int) strtol(stringptr, &stringptr, 0);
13949     }
13950     if (m->invertices > 0) {
13951       infile = *polyfile;
13952       infilename = polyfilename;
13953       m->readnodefile = 0;
13954     } else {
13955       /* If the .poly file claims there are zero vertices, that means that */
13956       /*   the vertices should be read from a separate .node file.         */
13957       m->readnodefile = 1;
13958       infilename = nodefilename;
13959     }
13960   } else {
13961     m->readnodefile = 1;
13962     infilename = nodefilename;
13963     *polyfile = (FILE *) NULL;
13964   }
13965 
13966   if (m->readnodefile) {
13967     /* Read the vertices from a .node file. */
13968     if (!b->quiet) {
13969       printf("Opening %s.\n", nodefilename);
13970     }
13971     infile = fopen(nodefilename, "r");
13972     if (infile == (FILE *) NULL) {
13973       printf("  Error:  Cannot access file %s.\n", nodefilename);
13974       triexit(1);
13975     }
13976     /* Read number of vertices, number of dimensions, number of vertex */
13977     /*   attributes, and number of boundary markers.                   */
13978     stringptr = readline(inputline, infile, nodefilename);
13979     m->invertices = (int) strtol(stringptr, &stringptr, 0);
13980     stringptr = findfield(stringptr);
13981     if (*stringptr == '\0') {
13982       m->mesh_dim = 2;
13983     } else {
13984       m->mesh_dim = (int) strtol(stringptr, &stringptr, 0);
13985     }
13986     stringptr = findfield(stringptr);
13987     if (*stringptr == '\0') {
13988       m->nextras = 0;
13989     } else {
13990       m->nextras = (int) strtol(stringptr, &stringptr, 0);
13991     }
13992     stringptr = findfield(stringptr);
13993     if (*stringptr == '\0') {
13994       nodemarkers = 0;
13995     } else {
13996       nodemarkers = (int) strtol(stringptr, &stringptr, 0);
13997     }
13998   }
13999 
14000   if (m->invertices < 3) {
14001     printf("Error:  Input must have at least three input vertices.\n");
14002     triexit(1);
14003   }
14004   if (m->mesh_dim != 2) {
14005     printf("Error:  Triangle only works with two-dimensional meshes.\n");
14006     triexit(1);
14007   }
14008   if (m->nextras == 0) {
14009     b->weighted = 0;
14010   }
14011 
14012   initializevertexpool(m, b);
14013 
14014   /* Read the vertices. */
14015   for (i = 0; i < m->invertices; i++) {
14016     vertexloop = (vertex) poolalloc(&m->vertices);
14017     stringptr = readline(inputline, infile, infilename);
14018     if (i == 0) {
14019       firstnode = (int) strtol(stringptr, &stringptr, 0);
14020       if ((firstnode == 0) || (firstnode == 1)) {
14021         b->firstnumber = firstnode;
14022       }
14023     }
14024     stringptr = findfield(stringptr);
14025     if (*stringptr == '\0') {
14026       printf("Error:  Vertex %d has no x coordinate.\n", b->firstnumber + i);
14027       triexit(1);
14028     }
14029     x = (REAL) strtod(stringptr, &stringptr);
14030     stringptr = findfield(stringptr);
14031     if (*stringptr == '\0') {
14032       printf("Error:  Vertex %d has no y coordinate.\n", b->firstnumber + i);
14033       triexit(1);
14034     }
14035     y = (REAL) strtod(stringptr, &stringptr);
14036     vertexloop[0] = x;
14037     vertexloop[1] = y;
14038     /* Read the vertex attributes. */
14039     for (j = 2; j < 2 + m->nextras; j++) {
14040       stringptr = findfield(stringptr);
14041       if (*stringptr == '\0') {
14042         vertexloop[j] = 0.0;
14043       } else {
14044         vertexloop[j] = (REAL) strtod(stringptr, &stringptr);
14045       }
14046     }
14047     if (nodemarkers) {
14048       /* Read a vertex marker. */
14049       stringptr = findfield(stringptr);
14050       if (*stringptr == '\0') {
14051         setvertexmark(vertexloop, 0);
14052       } else {
14053         currentmarker = (int) strtol(stringptr, &stringptr, 0);
14054         setvertexmark(vertexloop, currentmarker);
14055       }
14056     } else {
14057       /* If no markers are specified in the file, they default to zero. */
14058       setvertexmark(vertexloop, 0);
14059     }
14060     setvertextype(vertexloop, INPUTVERTEX);
14061     /* Determine the smallest and largest x and y coordinates. */
14062     if (i == 0) {
14063       m->xmin = m->xmax = x;
14064       m->ymin = m->ymax = y;
14065     } else {
14066       m->xmin = (x < m->xmin) ? x : m->xmin;
14067       m->xmax = (x > m->xmax) ? x : m->xmax;
14068       m->ymin = (y < m->ymin) ? y : m->ymin;
14069       m->ymax = (y > m->ymax) ? y : m->ymax;
14070     }
14071   }
14072   if (m->readnodefile) {
14073     fclose(infile);
14074   }
14075 
14076   /* Nonexistent x value used as a flag to mark circle events in sweepline */
14077   /*   Delaunay algorithm.                                                 */
14078   m->xminextreme = 10 * m->xmin - 9 * m->xmax;
14079 }
14080 
14081 #endif /* not TRILIBRARY */
14082 
14083 /*****************************************************************************/
14084 /*                                                                           */
14085 /*  transfernodes()   Read the vertices from memory.                         */
14086 /*                                                                           */
14087 /*****************************************************************************/
14088 
14089 #ifdef TRILIBRARY
14090 
14091 #ifdef ANSI_DECLARATORS
14092 void transfernodes(struct mesh *m, struct behavior *b, REAL *pointlist,
14093                    REAL *pointattriblist, int *pointmarkerlist,
14094                    int numberofpoints, int numberofpointattribs)
14095 #else /* not ANSI_DECLARATORS */
14096 void transfernodes(m, b, pointlist, pointattriblist, pointmarkerlist,
14097                    numberofpoints, numberofpointattribs)
14098 struct mesh *m;
14099 struct behavior *b;
14100 REAL *pointlist;
14101 REAL *pointattriblist;
14102 int *pointmarkerlist;
14103 int numberofpoints;
14104 int numberofpointattribs;
14105 #endif /* not ANSI_DECLARATORS */
14106 
14107 {
14108   vertex vertexloop;
14109   REAL x, y;
14110   int i, j;
14111   int coordindex;
14112   int attribindex;
14113 
14114   m->invertices = numberofpoints;
14115   m->mesh_dim = 2;
14116   m->nextras = numberofpointattribs;
14117   m->readnodefile = 0;
14118   if (m->invertices < 3) {
14119     printf("Error:  Input must have at least three input vertices.\n");
14120     triexit(1);
14121   }
14122   if (m->nextras == 0) {
14123     b->weighted = 0;
14124   }
14125 
14126   initializevertexpool(m, b);
14127 
14128   /* Read the vertices. */
14129   coordindex = 0;
14130   attribindex = 0;
14131   for (i = 0; i < m->invertices; i++) {
14132     vertexloop = (vertex) poolalloc(&m->vertices);
14133     /* Read the vertex coordinates. */
14134     x = vertexloop[0] = pointlist[coordindex++];
14135     y = vertexloop[1] = pointlist[coordindex++];
14136     /* Read the vertex attributes. */
14137     for (j = 0; j < numberofpointattribs; j++) {
14138       vertexloop[2 + j] = pointattriblist[attribindex++];
14139     }
14140     if (pointmarkerlist != (int *) NULL) {
14141       /* Read a vertex marker. */
14142       setvertexmark(vertexloop, pointmarkerlist[i]);
14143     } else {
14144       /* If no markers are specified, they default to zero. */
14145       setvertexmark(vertexloop, 0);
14146     }
14147     setvertextype(vertexloop, INPUTVERTEX);
14148     /* Determine the smallest and largest x and y coordinates. */
14149     if (i == 0) {
14150       m->xmin = m->xmax = x;
14151       m->ymin = m->ymax = y;
14152     } else {
14153       m->xmin = (x < m->xmin) ? x : m->xmin;
14154       m->xmax = (x > m->xmax) ? x : m->xmax;
14155       m->ymin = (y < m->ymin) ? y : m->ymin;
14156       m->ymax = (y > m->ymax) ? y : m->ymax;
14157     }
14158   }
14159 
14160   /* Nonexistent x value used as a flag to mark circle events in sweepline */
14161   /*   Delaunay algorithm.                                                 */
14162   m->xminextreme = 10 * m->xmin - 9 * m->xmax;
14163 }
14164 
14165 #endif /* TRILIBRARY */
14166 
14167 /*****************************************************************************/
14168 /*                                                                           */
14169 /*  readholes()   Read the holes, and possibly regional attributes and area  */
14170 /*                constraints, from a .poly file.                            */
14171 /*                                                                           */
14172 /*****************************************************************************/
14173 
14174 #ifndef TRILIBRARY
14175 
14176 #ifdef ANSI_DECLARATORS
14177 void readholes(struct mesh *m, struct behavior *b,
14178                FILE *polyfile, char *polyfilename, REAL **hlist, int *holes,
14179                REAL **rlist, int *regions)
14180 #else /* not ANSI_DECLARATORS */
14181 void readholes(m, b, polyfile, polyfilename, hlist, holes, rlist, regions)
14182 struct mesh *m;
14183 struct behavior *b;
14184 FILE *polyfile;
14185 char *polyfilename;
14186 REAL **hlist;
14187 int *holes;
14188 REAL **rlist;
14189 int *regions;
14190 #endif /* not ANSI_DECLARATORS */
14191 
14192 {
14193   REAL *holelist;
14194   REAL *regionlist;
14195   char inputline[INPUTLINESIZE];
14196   char *stringptr;
14197   int index;
14198   int i;
14199 
14200   /* Read the holes. */
14201   stringptr = readline(inputline, polyfile, polyfilename);
14202   *holes = (int) strtol(stringptr, &stringptr, 0);
14203   if (*holes > 0) {
14204     holelist = (REAL *) trimalloc(2 * *holes * (int) sizeof(REAL));
14205     *hlist = holelist;
14206     for (i = 0; i < 2 * *holes; i += 2) {
14207       stringptr = readline(inputline, polyfile, polyfilename);
14208       stringptr = findfield(stringptr);
14209       if (*stringptr == '\0') {
14210         printf("Error:  Hole %d has no x coordinate.\n",
14211                b->firstnumber + (i >> 1));
14212         triexit(1);
14213       } else {
14214         holelist[i] = (REAL) strtod(stringptr, &stringptr);
14215       }
14216       stringptr = findfield(stringptr);
14217       if (*stringptr == '\0') {
14218         printf("Error:  Hole %d has no y coordinate.\n",
14219                b->firstnumber + (i >> 1));
14220         triexit(1);
14221       } else {
14222         holelist[i + 1] = (REAL) strtod(stringptr, &stringptr);
14223       }
14224     }
14225   } else {
14226     *hlist = (REAL *) NULL;
14227   }
14228 
14229 #ifndef CDT_ONLY
14230   if ((b->regionattrib || b->vararea) && !b->refine) {
14231     /* Read the area constraints. */
14232     stringptr = readline(inputline, polyfile, polyfilename);
14233     *regions = (int) strtol(stringptr, &stringptr, 0);
14234     if (*regions > 0) {
14235       regionlist = (REAL *) trimalloc(4 * *regions * (int) sizeof(REAL));
14236       *rlist = regionlist;
14237       index = 0;
14238       for (i = 0; i < *regions; i++) {
14239         stringptr = readline(inputline, polyfile, polyfilename);
14240         stringptr = findfield(stringptr);
14241         if (*stringptr == '\0') {
14242           printf("Error:  Region %d has no x coordinate.\n",
14243                  b->firstnumber + i);
14244           triexit(1);
14245         } else {
14246           regionlist[index++] = (REAL) strtod(stringptr, &stringptr);
14247         }
14248         stringptr = findfield(stringptr);
14249         if (*stringptr == '\0') {
14250           printf("Error:  Region %d has no y coordinate.\n",
14251                  b->firstnumber + i);
14252           triexit(1);
14253         } else {
14254           regionlist[index++] = (REAL) strtod(stringptr, &stringptr);
14255         }
14256         stringptr = findfield(stringptr);
14257         if (*stringptr == '\0') {
14258           printf(
14259             "Error:  Region %d has no region attribute or area constraint.\n",
14260                  b->firstnumber + i);
14261           triexit(1);
14262         } else {
14263           regionlist[index++] = (REAL) strtod(stringptr, &stringptr);
14264         }
14265         stringptr = findfield(stringptr);
14266         if (*stringptr == '\0') {
14267           regionlist[index] = regionlist[index - 1];
14268         } else {
14269           regionlist[index] = (REAL) strtod(stringptr, &stringptr);
14270         }
14271         index++;
14272       }
14273     }
14274   } else {
14275     /* Set `*regions' to zero to avoid an accidental free() later. */
14276     *regions = 0;
14277     *rlist = (REAL *) NULL;
14278   }
14279 #endif /* not CDT_ONLY */
14280 
14281   fclose(polyfile);
14282 }
14283 
14284 #endif /* not TRILIBRARY */
14285 
14286 /*****************************************************************************/
14287 /*                                                                           */
14288 /*  finishfile()   Write the command line to the output file so the user     */
14289 /*                 can remember how the file was generated.  Close the file. */
14290 /*                                                                           */
14291 /*****************************************************************************/
14292 
14293 #ifndef TRILIBRARY
14294 
14295 #ifdef ANSI_DECLARATORS
14296 void finishfile(FILE *outfile, int argc, char **argv)
14297 #else /* not ANSI_DECLARATORS */
14298 void finishfile(outfile, argc, argv)
14299 FILE *outfile;
14300 int argc;
14301 char **argv;
14302 #endif /* not ANSI_DECLARATORS */
14303 
14304 {
14305   int i;
14306 
14307   fprintf(outfile, "# Generated by");
14308   for (i = 0; i < argc; i++) {
14309     fprintf(outfile, " ");
14310     fputs(argv[i], outfile);
14311   }
14312   fprintf(outfile, "\n");
14313   fclose(outfile);
14314 }
14315 
14316 #endif /* not TRILIBRARY */
14317 
14318 /*****************************************************************************/
14319 /*                                                                           */
14320 /*  writenodes()   Number the vertices and write them to a .node file.       */
14321 /*                                                                           */
14322 /*  To save memory, the vertex numbers are written over the boundary markers */
14323 /*  after the vertices are written to a file.                                */
14324 /*                                                                           */
14325 /*****************************************************************************/
14326 
14327 #ifdef TRILIBRARY
14328 
14329 #ifdef ANSI_DECLARATORS
14330 void writenodes(struct mesh *m, struct behavior *b, REAL **pointlist,
14331                 REAL **pointattriblist, int **pointmarkerlist)
14332 #else /* not ANSI_DECLARATORS */
14333 void writenodes(m, b, pointlist, pointattriblist, pointmarkerlist)
14334 struct mesh *m;
14335 struct behavior *b;
14336 REAL **pointlist;
14337 REAL **pointattriblist;
14338 int **pointmarkerlist;
14339 #endif /* not ANSI_DECLARATORS */
14340 
14341 #else /* not TRILIBRARY */
14342 
14343 #ifdef ANSI_DECLARATORS
14344 void writenodes(struct mesh *m, struct behavior *b, char *nodefilename,
14345                 int argc, char **argv)
14346 #else /* not ANSI_DECLARATORS */
14347 void writenodes(m, b, nodefilename, argc, argv)
14348 struct mesh *m;
14349 struct behavior *b;
14350 char *nodefilename;
14351 int argc;
14352 char **argv;
14353 #endif /* not ANSI_DECLARATORS */
14354 
14355 #endif /* not TRILIBRARY */
14356 
14357 {
14358 #ifdef TRILIBRARY
14359   REAL *plist;
14360   REAL *palist;
14361   int *pmlist;
14362   int coordindex;
14363   int attribindex;
14364 #else /* not TRILIBRARY */
14365   FILE *outfile;
14366 #endif /* not TRILIBRARY */
14367   vertex vertexloop;
14368   long outvertices;
14369   int vertexnumber;
14370   int i;
14371 
14372   if (b->jettison) {
14373     outvertices = m->vertices.items - m->undeads;
14374   } else {
14375     outvertices = m->vertices.items;
14376   }
14377 
14378 #ifdef TRILIBRARY
14379   if (!b->quiet) {
14380     printf("Writing vertices.\n");
14381   }
14382   /* Allocate memory for output vertices if necessary. */
14383   if (*pointlist == (REAL *) NULL) {
14384     *pointlist = (REAL *) trimalloc((int) (outvertices * 2 * sizeof(REAL)));
14385   }
14386   /* Allocate memory for output vertex attributes if necessary. */
14387   if ((m->nextras > 0) && (*pointattriblist == (REAL *) NULL)) {
14388     *pointattriblist = (REAL *) trimalloc((int) (outvertices * m->nextras *
14389                                                  sizeof(REAL)));
14390   }
14391   /* Allocate memory for output vertex markers if necessary. */
14392   if (!b->nobound && (*pointmarkerlist == (int *) NULL)) {
14393     *pointmarkerlist = (int *) trimalloc((int) (outvertices * sizeof(int)));
14394   }
14395   plist = *pointlist;
14396   palist = *pointattriblist;
14397   pmlist = *pointmarkerlist;
14398   coordindex = 0;
14399   attribindex = 0;
14400 #else /* not TRILIBRARY */
14401   if (!b->quiet) {
14402     printf("Writing %s.\n", nodefilename);
14403   }
14404   outfile = fopen(nodefilename, "w");
14405   if (outfile == (FILE *) NULL) {
14406     printf("  Error:  Cannot create file %s.\n", nodefilename);
14407     triexit(1);
14408   }
14409   /* Number of vertices, number of dimensions, number of vertex attributes, */
14410   /*   and number of boundary markers (zero or one).                        */
14411   fprintf(outfile, "%ld  %d  %d  %d\n", outvertices, m->mesh_dim,
14412           m->nextras, 1 - b->nobound);
14413 #endif /* not TRILIBRARY */
14414 
14415   traversalinit(&m->vertices);
14416   vertexnumber = b->firstnumber;
14417   vertexloop = vertextraverse(m);
14418   while (vertexloop != (vertex) NULL) {
14419     if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) {
14420 #ifdef TRILIBRARY
14421       /* X and y coordinates. */
14422       plist[coordindex++] = vertexloop[0];
14423       plist[coordindex++] = vertexloop[1];
14424       /* Vertex attributes. */
14425       for (i = 0; i < m->nextras; i++) {
14426         palist[attribindex++] = vertexloop[2 + i];
14427       }
14428       if (!b->nobound) {
14429         /* Copy the boundary marker. */
14430         pmlist[vertexnumber - b->firstnumber] = vertexmark(vertexloop);
14431       }
14432 #else /* not TRILIBRARY */
14433       /* Vertex number, x and y coordinates. */
14434       fprintf(outfile, "%4d    %.17g  %.17g", vertexnumber, vertexloop[0],
14435               vertexloop[1]);
14436       for (i = 0; i < m->nextras; i++) {
14437         /* Write an attribute. */
14438         fprintf(outfile, "  %.17g", vertexloop[i + 2]);
14439       }
14440       if (b->nobound) {
14441         fprintf(outfile, "\n");
14442       } else {
14443         /* Write the boundary marker. */
14444         fprintf(outfile, "    %d\n", vertexmark(vertexloop));
14445       }
14446 #endif /* not TRILIBRARY */
14447 
14448       setvertexmark(vertexloop, vertexnumber);
14449       vertexnumber++;
14450     }
14451     vertexloop = vertextraverse(m);
14452   }
14453 
14454 #ifndef TRILIBRARY
14455   finishfile(outfile, argc, argv);
14456 #endif /* not TRILIBRARY */
14457 }
14458 
14459 /*****************************************************************************/
14460 /*                                                                           */
14461 /*  numbernodes()   Number the vertices.                                     */
14462 /*                                                                           */
14463 /*  Each vertex is assigned a marker equal to its number.                    */
14464 /*                                                                           */
14465 /*  Used when writenodes() is not called because no .node file is written.   */
14466 /*                                                                           */
14467 /*****************************************************************************/
14468 
14469 #ifdef ANSI_DECLARATORS
14470 void numbernodes(struct mesh *m, struct behavior *b)
14471 #else /* not ANSI_DECLARATORS */
14472 void numbernodes(m, b)
14473 struct mesh *m;
14474 struct behavior *b;
14475 #endif /* not ANSI_DECLARATORS */
14476 
14477 {
14478   vertex vertexloop;
14479   int vertexnumber;
14480 
14481   traversalinit(&m->vertices);
14482   vertexnumber = b->firstnumber;
14483   vertexloop = vertextraverse(m);
14484   while (vertexloop != (vertex) NULL) {
14485     setvertexmark(vertexloop, vertexnumber);
14486     if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) {
14487       vertexnumber++;
14488     }
14489     vertexloop = vertextraverse(m);
14490   }
14491 }
14492 
14493 /*****************************************************************************/
14494 /*                                                                           */
14495 /*  writeelements()   Write the triangles to an .ele file.                   */
14496 /*                                                                           */
14497 /*****************************************************************************/
14498 
14499 #ifdef TRILIBRARY
14500 
14501 #ifdef ANSI_DECLARATORS
14502 void writeelements(struct mesh *m, struct behavior *b,
14503                    int **trianglelist, REAL **triangleattriblist)
14504 #else /* not ANSI_DECLARATORS */
14505 void writeelements(m, b, trianglelist, triangleattriblist)
14506 struct mesh *m;
14507 struct behavior *b;
14508 int **trianglelist;
14509 REAL **triangleattriblist;
14510 #endif /* not ANSI_DECLARATORS */
14511 
14512 #else /* not TRILIBRARY */
14513 
14514 #ifdef ANSI_DECLARATORS
14515 void writeelements(struct mesh *m, struct behavior *b, char *elefilename,
14516                    int argc, char **argv)
14517 #else /* not ANSI_DECLARATORS */
14518 void writeelements(m, b, elefilename, argc, argv)
14519 struct mesh *m;
14520 struct behavior *b;
14521 char *elefilename;
14522 int argc;
14523 char **argv;
14524 #endif /* not ANSI_DECLARATORS */
14525 
14526 #endif /* not TRILIBRARY */
14527 
14528 {
14529 #ifdef TRILIBRARY
14530   int *tlist;
14531   REAL *talist;
14532   int vertexindex;
14533   int attribindex;
14534 #else /* not TRILIBRARY */
14535   FILE *outfile;
14536 #endif /* not TRILIBRARY */
14537   struct otri triangleloop;
14538   vertex p1, p2, p3;
14539   vertex mid1, mid2, mid3;
14540   long elementnumber;
14541   int i;
14542 
14543 #ifdef TRILIBRARY
14544   if (!b->quiet) {
14545     printf("Writing triangles.\n");
14546   }
14547   /* Allocate memory for output triangles if necessary. */
14548   if (*trianglelist == (int *) NULL) {
14549     *trianglelist = (int *) trimalloc((int) (m->triangles.items *
14550                                              ((b->order + 1) * (b->order + 2) /
14551                                               2) * sizeof(int)));
14552   }
14553   /* Allocate memory for output triangle attributes if necessary. */
14554   if ((m->eextras > 0) && (*triangleattriblist == (REAL *) NULL)) {
14555     *triangleattriblist = (REAL *) trimalloc((int) (m->triangles.items *
14556                                                     m->eextras *
14557                                                     sizeof(REAL)));
14558   }
14559   tlist = *trianglelist;
14560   talist = *triangleattriblist;
14561   vertexindex = 0;
14562   attribindex = 0;
14563 #else /* not TRILIBRARY */
14564   if (!b->quiet) {
14565     printf("Writing %s.\n", elefilename);
14566   }
14567   outfile = fopen(elefilename, "w");
14568   if (outfile == (FILE *) NULL) {
14569     printf("  Error:  Cannot create file %s.\n", elefilename);
14570     triexit(1);
14571   }
14572   /* Number of triangles, vertices per triangle, attributes per triangle. */
14573   fprintf(outfile, "%ld  %d  %d\n", m->triangles.items,
14574           (b->order + 1) * (b->order + 2) / 2, m->eextras);
14575 #endif /* not TRILIBRARY */
14576 
14577   traversalinit(&m->triangles);
14578   triangleloop.tri = triangletraverse(m);
14579   triangleloop.orient = 0;
14580   elementnumber = b->firstnumber;
14581   while (triangleloop.tri != (triangle *) NULL) {
14582     org(triangleloop, p1);
14583     dest(triangleloop, p2);
14584     apex(triangleloop, p3);
14585     if (b->order == 1) {
14586 #ifdef TRILIBRARY
14587       tlist[vertexindex++] = vertexmark(p1);
14588       tlist[vertexindex++] = vertexmark(p2);
14589       tlist[vertexindex++] = vertexmark(p3);
14590 #else /* not TRILIBRARY */
14591       /* Triangle number, indices for three vertices. */
14592       fprintf(outfile, "%4ld    %4d  %4d  %4d", elementnumber,
14593               vertexmark(p1), vertexmark(p2), vertexmark(p3));
14594 #endif /* not TRILIBRARY */
14595     } else {
14596       mid1 = (vertex) triangleloop.tri[m->highorderindex + 1];
14597       mid2 = (vertex) triangleloop.tri[m->highorderindex + 2];
14598       mid3 = (vertex) triangleloop.tri[m->highorderindex];
14599 #ifdef TRILIBRARY
14600       tlist[vertexindex++] = vertexmark(p1);
14601       tlist[vertexindex++] = vertexmark(p2);
14602       tlist[vertexindex++] = vertexmark(p3);
14603       tlist[vertexindex++] = vertexmark(mid1);
14604       tlist[vertexindex++] = vertexmark(mid2);
14605       tlist[vertexindex++] = vertexmark(mid3);
14606 #else /* not TRILIBRARY */
14607       /* Triangle number, indices for six vertices. */
14608       fprintf(outfile, "%4ld    %4d  %4d  %4d  %4d  %4d  %4d", elementnumber,
14609               vertexmark(p1), vertexmark(p2), vertexmark(p3), vertexmark(mid1),
14610               vertexmark(mid2), vertexmark(mid3));
14611 #endif /* not TRILIBRARY */
14612     }
14613 
14614 #ifdef TRILIBRARY
14615     for (i = 0; i < m->eextras; i++) {
14616       talist[attribindex++] = elemattribute(triangleloop, i);
14617     }
14618 #else /* not TRILIBRARY */
14619     for (i = 0; i < m->eextras; i++) {
14620       fprintf(outfile, "  %.17g", elemattribute(triangleloop, i));
14621     }
14622     fprintf(outfile, "\n");
14623 #endif /* not TRILIBRARY */
14624 
14625     triangleloop.tri = triangletraverse(m);
14626     elementnumber++;
14627   }
14628 
14629 #ifndef TRILIBRARY
14630   finishfile(outfile, argc, argv);
14631 #endif /* not TRILIBRARY */
14632 }
14633 
14634 /*****************************************************************************/
14635 /*                                                                           */
14636 /*  writepoly()   Write the segments and holes to a .poly file.              */
14637 /*                                                                           */
14638 /*****************************************************************************/
14639 
14640 #ifdef TRILIBRARY
14641 
14642 #ifdef ANSI_DECLARATORS
14643 void writepoly(struct mesh *m, struct behavior *b,
14644                int **segmentlist, int **segmentmarkerlist)
14645 #else /* not ANSI_DECLARATORS */
14646 void writepoly(m, b, segmentlist, segmentmarkerlist)
14647 struct mesh *m;
14648 struct behavior *b;
14649 int **segmentlist;
14650 int **segmentmarkerlist;
14651 #endif /* not ANSI_DECLARATORS */
14652 
14653 #else /* not TRILIBRARY */
14654 
14655 #ifdef ANSI_DECLARATORS
14656 void writepoly(struct mesh *m, struct behavior *b, char *polyfilename,
14657                REAL *holelist, int holes, REAL *regionlist, int regions,
14658                int argc, char **argv)
14659 #else /* not ANSI_DECLARATORS */
14660 void writepoly(m, b, polyfilename, holelist, holes, regionlist, regions,
14661                argc, argv)
14662 struct mesh *m;
14663 struct behavior *b;
14664 char *polyfilename;
14665 REAL *holelist;
14666 int holes;
14667 REAL *regionlist;
14668 int regions;
14669 int argc;
14670 char **argv;
14671 #endif /* not ANSI_DECLARATORS */
14672 
14673 #endif /* not TRILIBRARY */
14674 
14675 {
14676 #ifdef TRILIBRARY
14677   int *slist;
14678   int *smlist;
14679   int index;
14680 #else /* not TRILIBRARY */
14681   FILE *outfile;
14682   long holenumber, regionnumber;
14683 #endif /* not TRILIBRARY */
14684   struct osub subsegloop;
14685   vertex endpoint1, endpoint2;
14686   long subsegnumber;
14687 
14688 #ifdef TRILIBRARY
14689   if (!b->quiet) {
14690     printf("Writing segments.\n");
14691   }
14692   /* Allocate memory for output segments if necessary. */
14693   if (*segmentlist == (int *) NULL) {
14694     *segmentlist = (int *) trimalloc((int) (m->subsegs.items * 2 *
14695                                             sizeof(int)));
14696   }
14697   /* Allocate memory for output segment markers if necessary. */
14698   if (!b->nobound && (*segmentmarkerlist == (int *) NULL)) {
14699     *segmentmarkerlist = (int *) trimalloc((int) (m->subsegs.items *
14700                                                   sizeof(int)));
14701   }
14702   slist = *segmentlist;
14703   smlist = *segmentmarkerlist;
14704   index = 0;
14705 #else /* not TRILIBRARY */
14706   if (!b->quiet) {
14707     printf("Writing %s.\n", polyfilename);
14708   }
14709   outfile = fopen(polyfilename, "w");
14710   if (outfile == (FILE *) NULL) {
14711     printf("  Error:  Cannot create file %s.\n", polyfilename);
14712     triexit(1);
14713   }
14714   /* The zero indicates that the vertices are in a separate .node file. */
14715   /*   Followed by number of dimensions, number of vertex attributes,   */
14716   /*   and number of boundary markers (zero or one).                    */
14717   fprintf(outfile, "%d  %d  %d  %d\n", 0, m->mesh_dim, m->nextras,
14718           1 - b->nobound);
14719   /* Number of segments, number of boundary markers (zero or one). */
14720   fprintf(outfile, "%ld  %d\n", m->subsegs.items, 1 - b->nobound);
14721 #endif /* not TRILIBRARY */
14722 
14723   traversalinit(&m->subsegs);
14724   subsegloop.ss = subsegtraverse(m);
14725   subsegloop.ssorient = 0;
14726   subsegnumber = b->firstnumber;
14727   while (subsegloop.ss != (subseg *) NULL) {
14728     sorg(subsegloop, endpoint1);
14729     sdest(subsegloop, endpoint2);
14730 #ifdef TRILIBRARY
14731     /* Copy indices of the segment's two endpoints. */
14732     slist[index++] = vertexmark(endpoint1);
14733     slist[index++] = vertexmark(endpoint2);
14734     if (!b->nobound) {
14735       /* Copy the boundary marker. */
14736       smlist[subsegnumber - b->firstnumber] = mark(subsegloop);
14737     }
14738 #else /* not TRILIBRARY */
14739     /* Segment number, indices of its two endpoints, and possibly a marker. */
14740     if (b->nobound) {
14741       fprintf(outfile, "%4ld    %4d  %4d\n", subsegnumber,
14742               vertexmark(endpoint1), vertexmark(endpoint2));
14743     } else {
14744       fprintf(outfile, "%4ld    %4d  %4d    %4d\n", subsegnumber,
14745               vertexmark(endpoint1), vertexmark(endpoint2), mark(subsegloop));
14746     }
14747 #endif /* not TRILIBRARY */
14748 
14749     subsegloop.ss = subsegtraverse(m);
14750     subsegnumber++;
14751   }
14752 
14753 #ifndef TRILIBRARY
14754 #ifndef CDT_ONLY
14755   fprintf(outfile, "%d\n", holes);
14756   if (holes > 0) {
14757     for (holenumber = 0; holenumber < holes; holenumber++) {
14758       /* Hole number, x and y coordinates. */
14759       fprintf(outfile, "%4ld   %.17g  %.17g\n", b->firstnumber + holenumber,
14760               holelist[2 * holenumber], holelist[2 * holenumber + 1]);
14761     }
14762   }
14763   if (regions > 0) {
14764     fprintf(outfile, "%d\n", regions);
14765     for (regionnumber = 0; regionnumber < regions; regionnumber++) {
14766       /* Region number, x and y coordinates, attribute, maximum area. */
14767       fprintf(outfile, "%4ld   %.17g  %.17g  %.17g  %.17g\n",
14768               b->firstnumber + regionnumber,
14769               regionlist[4 * regionnumber], regionlist[4 * regionnumber + 1],
14770               regionlist[4 * regionnumber + 2],
14771               regionlist[4 * regionnumber + 3]);
14772     }
14773   }
14774 #endif /* not CDT_ONLY */
14775 
14776   finishfile(outfile, argc, argv);
14777 #endif /* not TRILIBRARY */
14778 }
14779 
14780 /*****************************************************************************/
14781 /*                                                                           */
14782 /*  writeedges()   Write the edges to an .edge file.                         */
14783 /*                                                                           */
14784 /*****************************************************************************/
14785 
14786 #ifdef TRILIBRARY
14787 
14788 #ifdef ANSI_DECLARATORS
14789 void writeedges(struct mesh *m, struct behavior *b,
14790                 int **edgelist, int **edgemarkerlist)
14791 #else /* not ANSI_DECLARATORS */
14792 void writeedges(m, b, edgelist, edgemarkerlist)
14793 struct mesh *m;
14794 struct behavior *b;
14795 int **edgelist;
14796 int **edgemarkerlist;
14797 #endif /* not ANSI_DECLARATORS */
14798 
14799 #else /* not TRILIBRARY */
14800 
14801 #ifdef ANSI_DECLARATORS
14802 void writeedges(struct mesh *m, struct behavior *b, char *edgefilename,
14803                 int argc, char **argv)
14804 #else /* not ANSI_DECLARATORS */
14805 void writeedges(m, b, edgefilename, argc, argv)
14806 struct mesh *m;
14807 struct behavior *b;
14808 char *edgefilename;
14809 int argc;
14810 char **argv;
14811 #endif /* not ANSI_DECLARATORS */
14812 
14813 #endif /* not TRILIBRARY */
14814 
14815 {
14816 #ifdef TRILIBRARY
14817   int *elist;
14818   int *emlist;
14819   int index;
14820 #else /* not TRILIBRARY */
14821   FILE *outfile;
14822 #endif /* not TRILIBRARY */
14823   struct otri triangleloop, trisym;
14824   struct osub checkmark;
14825   vertex p1, p2;
14826   long edgenumber;
14827   triangle ptr;                         /* Temporary variable used by sym(). */
14828   subseg sptr;                      /* Temporary variable used by tspivot(). */
14829 
14830 #ifdef TRILIBRARY
14831   if (!b->quiet) {
14832     printf("Writing edges.\n");
14833   }
14834   /* Allocate memory for edges if necessary. */
14835   if (*edgelist == (int *) NULL) {
14836     *edgelist = (int *) trimalloc((int) (m->edges * 2 * sizeof(int)));
14837   }
14838   /* Allocate memory for edge markers if necessary. */
14839   if (!b->nobound && (*edgemarkerlist == (int *) NULL)) {
14840     *edgemarkerlist = (int *) trimalloc((int) (m->edges * sizeof(int)));
14841   }
14842   elist = *edgelist;
14843   emlist = *edgemarkerlist;
14844   index = 0;
14845 #else /* not TRILIBRARY */
14846   if (!b->quiet) {
14847     printf("Writing %s.\n", edgefilename);
14848   }
14849   outfile = fopen(edgefilename, "w");
14850   if (outfile == (FILE *) NULL) {
14851     printf("  Error:  Cannot create file %s.\n", edgefilename);
14852     triexit(1);
14853   }
14854   /* Number of edges, number of boundary markers (zero or one). */
14855   fprintf(outfile, "%ld  %d\n", m->edges, 1 - b->nobound);
14856 #endif /* not TRILIBRARY */
14857 
14858   traversalinit(&m->triangles);
14859   triangleloop.tri = triangletraverse(m);
14860   edgenumber = b->firstnumber;
14861   /* To loop over the set of edges, loop over all triangles, and look at   */
14862   /*   the three edges of each triangle.  If there isn't another triangle  */
14863   /*   adjacent to the edge, operate on the edge.  If there is another     */
14864   /*   adjacent triangle, operate on the edge only if the current triangle */
14865   /*   has a smaller pointer than its neighbor.  This way, each edge is    */
14866   /*   considered only once.                                               */
14867   while (triangleloop.tri != (triangle *) NULL) {
14868     for (triangleloop.orient = 0; triangleloop.orient < 3;
14869          triangleloop.orient++) {
14870       sym(triangleloop, trisym);
14871       if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) {
14872         org(triangleloop, p1);
14873         dest(triangleloop, p2);
14874 #ifdef TRILIBRARY
14875         elist[index++] = vertexmark(p1);
14876         elist[index++] = vertexmark(p2);
14877 #endif /* TRILIBRARY */
14878         if (b->nobound) {
14879 #ifndef TRILIBRARY
14880           /* Edge number, indices of two endpoints. */
14881           fprintf(outfile, "%4ld   %d  %d\n", edgenumber,
14882                   vertexmark(p1), vertexmark(p2));
14883 #endif /* not TRILIBRARY */
14884         } else {
14885           /* Edge number, indices of two endpoints, and a boundary marker. */
14886           /*   If there's no subsegment, the boundary marker is zero.      */
14887           if (b->usesegments) {
14888             tspivot(triangleloop, checkmark);
14889             if (checkmark.ss == m->dummysub) {
14890 #ifdef TRILIBRARY
14891               emlist[edgenumber - b->firstnumber] = 0;
14892 #else /* not TRILIBRARY */
14893               fprintf(outfile, "%4ld   %d  %d  %d\n", edgenumber,
14894                       vertexmark(p1), vertexmark(p2), 0);
14895 #endif /* not TRILIBRARY */
14896             } else {
14897 #ifdef TRILIBRARY
14898               emlist[edgenumber - b->firstnumber] = mark(checkmark);
14899 #else /* not TRILIBRARY */
14900               fprintf(outfile, "%4ld   %d  %d  %d\n", edgenumber,
14901                       vertexmark(p1), vertexmark(p2), mark(checkmark));
14902 #endif /* not TRILIBRARY */
14903             }
14904           } else {
14905 #ifdef TRILIBRARY
14906             emlist[edgenumber - b->firstnumber] = trisym.tri == m->dummytri;
14907 #else /* not TRILIBRARY */
14908             fprintf(outfile, "%4ld   %d  %d  %d\n", edgenumber,
14909                     vertexmark(p1), vertexmark(p2), trisym.tri == m->dummytri);
14910 #endif /* not TRILIBRARY */
14911           }
14912         }
14913         edgenumber++;
14914       }
14915     }
14916     triangleloop.tri = triangletraverse(m);
14917   }
14918 
14919 #ifndef TRILIBRARY
14920   finishfile(outfile, argc, argv);
14921 #endif /* not TRILIBRARY */
14922 }
14923 
14924 /*****************************************************************************/
14925 /*                                                                           */
14926 /*  writevoronoi()   Write the Voronoi diagram to a .v.node and .v.edge      */
14927 /*                   file.                                                   */
14928 /*                                                                           */
14929 /*  The Voronoi diagram is the geometric dual of the Delaunay triangulation. */
14930 /*  Hence, the Voronoi vertices are listed by traversing the Delaunay        */
14931 /*  triangles, and the Voronoi edges are listed by traversing the Delaunay   */
14932 /*  edges.                                                                   */
14933 /*                                                                           */
14934 /*  WARNING:  In order to assign numbers to the Voronoi vertices, this       */
14935 /*  procedure messes up the subsegments or the extra nodes of every          */
14936 /*  element.  Hence, you should call this procedure last.                    */
14937 /*                                                                           */
14938 /*****************************************************************************/
14939 
14940 #ifdef TRILIBRARY
14941 
14942 #ifdef ANSI_DECLARATORS
14943 void writevoronoi(struct mesh *m, struct behavior *b, REAL **vpointlist,
14944                   REAL **vpointattriblist, int **vpointmarkerlist,
14945                   int **vedgelist, int **vedgemarkerlist, REAL **vnormlist)
14946 #else /* not ANSI_DECLARATORS */
14947 void writevoronoi(m, b, vpointlist, vpointattriblist, vpointmarkerlist,
14948                   vedgelist, vedgemarkerlist, vnormlist)
14949 struct mesh *m;
14950 struct behavior *b;
14951 REAL **vpointlist;
14952 REAL **vpointattriblist;
14953 int **vpointmarkerlist;
14954 int **vedgelist;
14955 int **vedgemarkerlist;
14956 REAL **vnormlist;
14957 #endif /* not ANSI_DECLARATORS */
14958 
14959 #else /* not TRILIBRARY */
14960 
14961 #ifdef ANSI_DECLARATORS
14962 void writevoronoi(struct mesh *m, struct behavior *b, char *vnodefilename,
14963                   char *vedgefilename, int argc, char **argv)
14964 #else /* not ANSI_DECLARATORS */
14965 void writevoronoi(m, b, vnodefilename, vedgefilename, argc, argv)
14966 struct mesh *m;
14967 struct behavior *b;
14968 char *vnodefilename;
14969 char *vedgefilename;
14970 int argc;
14971 char **argv;
14972 #endif /* not ANSI_DECLARATORS */
14973 
14974 #endif /* not TRILIBRARY */
14975 
14976 {
14977 #ifdef TRILIBRARY
14978   REAL *plist;
14979   REAL *palist;
14980   int *elist;
14981   REAL *normlist;
14982   int coordindex;
14983   int attribindex;
14984 #else /* not TRILIBRARY */
14985   FILE *outfile;
14986 #endif /* not TRILIBRARY */
14987   struct otri triangleloop, trisym;
14988   vertex torg, tdest, tapex;
14989   REAL circumcenter[2];
14990   REAL xi, eta;
14991   long vnodenumber, vedgenumber;
14992   int p1, p2;
14993   int i;
14994   triangle ptr;                         /* Temporary variable used by sym(). */
14995 
14996 #ifdef TRILIBRARY
14997   if (!b->quiet) {
14998     printf("Writing Voronoi vertices.\n");
14999   }
15000   /* Allocate memory for Voronoi vertices if necessary. */
15001   if (*vpointlist == (REAL *) NULL) {
15002     *vpointlist = (REAL *) trimalloc((int) (m->triangles.items * 2 *
15003                                             sizeof(REAL)));
15004   }
15005   /* Allocate memory for Voronoi vertex attributes if necessary. */
15006   if (*vpointattriblist == (REAL *) NULL) {
15007     *vpointattriblist = (REAL *) trimalloc((int) (m->triangles.items *
15008                                                   m->nextras * sizeof(REAL)));
15009   }
15010   *vpointmarkerlist = (int *) NULL;
15011   plist = *vpointlist;
15012   palist = *vpointattriblist;
15013   coordindex = 0;
15014   attribindex = 0;
15015 #else /* not TRILIBRARY */
15016   if (!b->quiet) {
15017     printf("Writing %s.\n", vnodefilename);
15018   }
15019   outfile = fopen(vnodefilename, "w");
15020   if (outfile == (FILE *) NULL) {
15021     printf("  Error:  Cannot create file %s.\n", vnodefilename);
15022     triexit(1);
15023   }
15024   /* Number of triangles, two dimensions, number of vertex attributes, */
15025   /*   no markers.                                                     */
15026   fprintf(outfile, "%ld  %d  %d  %d\n", m->triangles.items, 2, m->nextras, 0);
15027 #endif /* not TRILIBRARY */
15028 
15029   traversalinit(&m->triangles);
15030   triangleloop.tri = triangletraverse(m);
15031   triangleloop.orient = 0;
15032   vnodenumber = b->firstnumber;
15033   while (triangleloop.tri != (triangle *) NULL) {
15034     org(triangleloop, torg);
15035     dest(triangleloop, tdest);
15036     apex(triangleloop, tapex);
15037     findcircumcenter(m, b, torg, tdest, tapex, circumcenter, &xi, &eta, 0);
15038 #ifdef TRILIBRARY
15039     /* X and y coordinates. */
15040     plist[coordindex++] = circumcenter[0];
15041     plist[coordindex++] = circumcenter[1];
15042     for (i = 2; i < 2 + m->nextras; i++) {
15043       /* Interpolate the vertex attributes at the circumcenter. */
15044       palist[attribindex++] = torg[i] + xi * (tdest[i] - torg[i])
15045                                      + eta * (tapex[i] - torg[i]);
15046     }
15047 #else /* not TRILIBRARY */
15048     /* Voronoi vertex number, x and y coordinates. */
15049     fprintf(outfile, "%4ld    %.17g  %.17g", vnodenumber, circumcenter[0],
15050             circumcenter[1]);
15051     for (i = 2; i < 2 + m->nextras; i++) {
15052       /* Interpolate the vertex attributes at the circumcenter. */
15053       fprintf(outfile, "  %.17g", torg[i] + xi * (tdest[i] - torg[i])
15054                                          + eta * (tapex[i] - torg[i]));
15055     }
15056     fprintf(outfile, "\n");
15057 #endif /* not TRILIBRARY */
15058 
15059     * (int *) (triangleloop.tri + 6) = (int) vnodenumber;
15060     triangleloop.tri = triangletraverse(m);
15061     vnodenumber++;
15062   }
15063 
15064 #ifndef TRILIBRARY
15065   finishfile(outfile, argc, argv);
15066 #endif /* not TRILIBRARY */
15067 
15068 #ifdef TRILIBRARY
15069   if (!b->quiet) {
15070     printf("Writing Voronoi edges.\n");
15071   }
15072   /* Allocate memory for output Voronoi edges if necessary. */
15073   if (*vedgelist == (int *) NULL) {
15074     *vedgelist = (int *) trimalloc((int) (m->edges * 2 * sizeof(int)));
15075   }
15076   *vedgemarkerlist = (int *) NULL;
15077   /* Allocate memory for output Voronoi norms if necessary. */
15078   if (*vnormlist == (REAL *) NULL) {
15079     *vnormlist = (REAL *) trimalloc((int) (m->edges * 2 * sizeof(REAL)));
15080   }
15081   elist = *vedgelist;
15082   normlist = *vnormlist;
15083   coordindex = 0;
15084 #else /* not TRILIBRARY */
15085   if (!b->quiet) {
15086     printf("Writing %s.\n", vedgefilename);
15087   }
15088   outfile = fopen(vedgefilename, "w");
15089   if (outfile == (FILE *) NULL) {
15090     printf("  Error:  Cannot create file %s.\n", vedgefilename);
15091     triexit(1);
15092   }
15093   /* Number of edges, zero boundary markers. */
15094   fprintf(outfile, "%ld  %d\n", m->edges, 0);
15095 #endif /* not TRILIBRARY */
15096 
15097   traversalinit(&m->triangles);
15098   triangleloop.tri = triangletraverse(m);
15099   vedgenumber = b->firstnumber;
15100   /* To loop over the set of edges, loop over all triangles, and look at   */
15101   /*   the three edges of each triangle.  If there isn't another triangle  */
15102   /*   adjacent to the edge, operate on the edge.  If there is another     */
15103   /*   adjacent triangle, operate on the edge only if the current triangle */
15104   /*   has a smaller pointer than its neighbor.  This way, each edge is    */
15105   /*   considered only once.                                               */
15106   while (triangleloop.tri != (triangle *) NULL) {
15107     for (triangleloop.orient = 0; triangleloop.orient < 3;
15108          triangleloop.orient++) {
15109       sym(triangleloop, trisym);
15110       if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) {
15111         /* Find the number of this triangle (and Voronoi vertex). */
15112         p1 = * (int *) (triangleloop.tri + 6);
15113         if (trisym.tri == m->dummytri) {
15114           org(triangleloop, torg);
15115           dest(triangleloop, tdest);
15116 #ifdef TRILIBRARY
15117           /* Copy an infinite ray.  Index of one endpoint, and -1. */
15118           elist[coordindex] = p1;
15119           normlist[coordindex++] = tdest[1] - torg[1];
15120           elist[coordindex] = -1;
15121           normlist[coordindex++] = torg[0] - tdest[0];
15122 #else /* not TRILIBRARY */
15123           /* Write an infinite ray.  Edge number, index of one endpoint, -1, */
15124           /*   and x and y coordinates of a vector representing the          */
15125           /*   direction of the ray.                                         */
15126           fprintf(outfile, "%4ld   %d  %d   %.17g  %.17g\n", vedgenumber,
15127                   p1, -1, tdest[1] - torg[1], torg[0] - tdest[0]);
15128 #endif /* not TRILIBRARY */
15129         } else {
15130           /* Find the number of the adjacent triangle (and Voronoi vertex). */
15131           p2 = * (int *) (trisym.tri + 6);
15132           /* Finite edge.  Write indices of two endpoints. */
15133 #ifdef TRILIBRARY
15134           elist[coordindex] = p1;
15135           normlist[coordindex++] = 0.0;
15136           elist[coordindex] = p2;
15137           normlist[coordindex++] = 0.0;
15138 #else /* not TRILIBRARY */
15139           fprintf(outfile, "%4ld   %d  %d\n", vedgenumber, p1, p2);
15140 #endif /* not TRILIBRARY */
15141         }
15142         vedgenumber++;
15143       }
15144     }
15145     triangleloop.tri = triangletraverse(m);
15146   }
15147 
15148 #ifndef TRILIBRARY
15149   finishfile(outfile, argc, argv);
15150 #endif /* not TRILIBRARY */
15151 }
15152 
15153 #ifdef TRILIBRARY
15154 
15155 #ifdef ANSI_DECLARATORS
15156 void writeneighbors(struct mesh *m, struct behavior *b, int **neighborlist)
15157 #else /* not ANSI_DECLARATORS */
15158 void writeneighbors(m, b, neighborlist)
15159 struct mesh *m;
15160 struct behavior *b;
15161 int **neighborlist;
15162 #endif /* not ANSI_DECLARATORS */
15163 
15164 #else /* not TRILIBRARY */
15165 
15166 #ifdef ANSI_DECLARATORS
15167 void writeneighbors(struct mesh *m, struct behavior *b, char *neighborfilename,
15168                     int argc, char **argv)
15169 #else /* not ANSI_DECLARATORS */
15170 void writeneighbors(m, b, neighborfilename, argc, argv)
15171 struct mesh *m;
15172 struct behavior *b;
15173 char *neighborfilename;
15174 int argc;
15175 char **argv;
15176 #endif /* not ANSI_DECLARATORS */
15177 
15178 #endif /* not TRILIBRARY */
15179 
15180 {
15181 #ifdef TRILIBRARY
15182   int *nlist;
15183   int index;
15184 #else /* not TRILIBRARY */
15185   FILE *outfile;
15186 #endif /* not TRILIBRARY */
15187   struct otri triangleloop, trisym;
15188   long elementnumber;
15189   int neighbor1, neighbor2, neighbor3;
15190   triangle ptr;                         /* Temporary variable used by sym(). */
15191 
15192 #ifdef TRILIBRARY
15193   if (!b->quiet) {
15194     printf("Writing neighbors.\n");
15195   }
15196   /* Allocate memory for neighbors if necessary. */
15197   if (*neighborlist == (int *) NULL) {
15198     *neighborlist = (int *) trimalloc((int) (m->triangles.items * 3 *
15199                                              sizeof(int)));
15200   }
15201   nlist = *neighborlist;
15202   index = 0;
15203 #else /* not TRILIBRARY */
15204   if (!b->quiet) {
15205     printf("Writing %s.\n", neighborfilename);
15206   }
15207   outfile = fopen(neighborfilename, "w");
15208   if (outfile == (FILE *) NULL) {
15209     printf("  Error:  Cannot create file %s.\n", neighborfilename);
15210     triexit(1);
15211   }
15212   /* Number of triangles, three neighbors per triangle. */
15213   fprintf(outfile, "%ld  %d\n", m->triangles.items, 3);
15214 #endif /* not TRILIBRARY */
15215 
15216   traversalinit(&m->triangles);
15217   triangleloop.tri = triangletraverse(m);
15218   triangleloop.orient = 0;
15219   elementnumber = b->firstnumber;
15220   while (triangleloop.tri != (triangle *) NULL) {
15221     * (int *) (triangleloop.tri + 6) = (int) elementnumber;
15222     triangleloop.tri = triangletraverse(m);
15223     elementnumber++;
15224   }
15225   * (int *) (m->dummytri + 6) = -1;
15226 
15227   traversalinit(&m->triangles);
15228   triangleloop.tri = triangletraverse(m);
15229   elementnumber = b->firstnumber;
15230   while (triangleloop.tri != (triangle *) NULL) {
15231     triangleloop.orient = 1;
15232     sym(triangleloop, trisym);
15233     neighbor1 = * (int *) (trisym.tri + 6);
15234     triangleloop.orient = 2;
15235     sym(triangleloop, trisym);
15236     neighbor2 = * (int *) (trisym.tri + 6);
15237     triangleloop.orient = 0;
15238     sym(triangleloop, trisym);
15239     neighbor3 = * (int *) (trisym.tri + 6);
15240 #ifdef TRILIBRARY
15241     nlist[index++] = neighbor1;
15242     nlist[index++] = neighbor2;
15243     nlist[index++] = neighbor3;
15244 #else /* not TRILIBRARY */
15245     /* Triangle number, neighboring triangle numbers. */
15246     fprintf(outfile, "%4ld    %d  %d  %d\n", elementnumber,
15247             neighbor1, neighbor2, neighbor3);
15248 #endif /* not TRILIBRARY */
15249 
15250     triangleloop.tri = triangletraverse(m);
15251     elementnumber++;
15252   }
15253 
15254 #ifndef TRILIBRARY
15255   finishfile(outfile, argc, argv);
15256 #endif /* not TRILIBRARY */
15257 }
15258 
15259 /*****************************************************************************/
15260 /*                                                                           */
15261 /*  writeoff()   Write the triangulation to an .off file.                    */
15262 /*                                                                           */
15263 /*  OFF stands for the Object File Format, a format used by the Geometry     */
15264 /*  Center's Geomview package.                                               */
15265 /*                                                                           */
15266 /*****************************************************************************/
15267 
15268 #ifndef TRILIBRARY
15269 
15270 #ifdef ANSI_DECLARATORS
15271 void writeoff(struct mesh *m, struct behavior *b, char *offfilename,
15272               int argc, char **argv)
15273 #else /* not ANSI_DECLARATORS */
15274 void writeoff(m, b, offfilename, argc, argv)
15275 struct mesh *m;
15276 struct behavior *b;
15277 char *offfilename;
15278 int argc;
15279 char **argv;
15280 #endif /* not ANSI_DECLARATORS */
15281 
15282 {
15283   FILE *outfile;
15284   struct otri triangleloop;
15285   vertex vertexloop;
15286   vertex p1, p2, p3;
15287   long outvertices;
15288 
15289   if (!b->quiet) {
15290     printf("Writing %s.\n", offfilename);
15291   }
15292 
15293   if (b->jettison) {
15294     outvertices = m->vertices.items - m->undeads;
15295   } else {
15296     outvertices = m->vertices.items;
15297   }
15298 
15299   outfile = fopen(offfilename, "w");
15300   if (outfile == (FILE *) NULL) {
15301     printf("  Error:  Cannot create file %s.\n", offfilename);
15302     triexit(1);
15303   }
15304   /* Number of vertices, triangles, and edges. */
15305   fprintf(outfile, "OFF\n%ld  %ld  %ld\n", outvertices, m->triangles.items,
15306           m->edges);
15307 
15308   /* Write the vertices. */
15309   traversalinit(&m->vertices);
15310   vertexloop = vertextraverse(m);
15311   while (vertexloop != (vertex) NULL) {
15312     if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) {
15313       /* The "0.0" is here because the OFF format uses 3D coordinates. */
15314       fprintf(outfile, " %.17g  %.17g  %.17g\n", vertexloop[0], vertexloop[1],
15315               0.0);
15316     }
15317     vertexloop = vertextraverse(m);
15318   }
15319 
15320   /* Write the triangles. */
15321   traversalinit(&m->triangles);
15322   triangleloop.tri = triangletraverse(m);
15323   triangleloop.orient = 0;
15324   while (triangleloop.tri != (triangle *) NULL) {
15325     org(triangleloop, p1);
15326     dest(triangleloop, p2);
15327     apex(triangleloop, p3);
15328     /* The "3" means a three-vertex polygon. */
15329     fprintf(outfile, " 3   %4d  %4d  %4d\n", vertexmark(p1) - b->firstnumber,
15330             vertexmark(p2) - b->firstnumber, vertexmark(p3) - b->firstnumber);
15331     triangleloop.tri = triangletraverse(m);
15332   }
15333   finishfile(outfile, argc, argv);
15334 }
15335 
15336 #endif /* not TRILIBRARY */
15337 
15340 /********* File I/O routines end here                                *********/
15341 
15342 /*****************************************************************************/
15343 /*                                                                           */
15344 /*  quality_statistics()   Print statistics about the quality of the mesh.   */
15345 /*                                                                           */
15346 /*****************************************************************************/
15347 
15348 #ifdef ANSI_DECLARATORS
15349 void quality_statistics(struct mesh *m, struct behavior *b)
15350 #else /* not ANSI_DECLARATORS */
15351 void quality_statistics(m, b)
15352 struct mesh *m;
15353 struct behavior *b;
15354 #endif /* not ANSI_DECLARATORS */
15355 
15356 {
15357   struct otri triangleloop;
15358   vertex p[3];
15359   REAL cossquaretable[8];
15360   REAL ratiotable[16];
15361   REAL dx[3], dy[3];
15362   REAL edgelength[3];
15363   REAL dotproduct;
15364   REAL cossquare;
15365   REAL triarea;
15366   REAL shortest, longest;
15367   REAL trilongest2;
15368   REAL smallestarea, biggestarea;
15369   REAL triminaltitude2;
15370   REAL minaltitude;
15371   REAL triaspect2;
15372   REAL worstaspect;
15373   REAL smallestangle, biggestangle;
15374   REAL radconst, degconst;
15375   int angletable[18];
15376   int aspecttable[16];
15377   int aspectindex;
15378   int tendegree;
15379   int acutebiggest;
15380   int i, ii, j, k;
15381 
15382   printf("Mesh quality statistics:\n\n");
15383   radconst = PI / 18.0;
15384   degconst = 180.0 / PI;
15385   for (i = 0; i < 8; i++) {
15386     cossquaretable[i] = cos(radconst * (REAL) (i + 1));
15387     cossquaretable[i] = cossquaretable[i] * cossquaretable[i];
15388   }
15389   for (i = 0; i < 18; i++) {
15390     angletable[i] = 0;
15391   }
15392 
15393   ratiotable[0]  =      1.5;      ratiotable[1]  =     2.0;
15394   ratiotable[2]  =      2.5;      ratiotable[3]  =     3.0;
15395   ratiotable[4]  =      4.0;      ratiotable[5]  =     6.0;
15396   ratiotable[6]  =     10.0;      ratiotable[7]  =    15.0;
15397   ratiotable[8]  =     25.0;      ratiotable[9]  =    50.0;
15398   ratiotable[10] =    100.0;      ratiotable[11] =   300.0;
15399   ratiotable[12] =   1000.0;      ratiotable[13] = 10000.0;
15400   ratiotable[14] = 100000.0;      ratiotable[15] =     0.0;
15401   for (i = 0; i < 16; i++) {
15402     aspecttable[i] = 0;
15403   }
15404 
15405   worstaspect = 0.0;
15406   minaltitude = m->xmax - m->xmin + m->ymax - m->ymin;
15407   minaltitude = minaltitude * minaltitude;
15408   shortest = minaltitude;
15409   longest = 0.0;
15410   smallestarea = minaltitude;
15411   biggestarea = 0.0;
15412   worstaspect = 0.0;
15413   smallestangle = 0.0;
15414   biggestangle = 2.0;
15415   acutebiggest = 1;
15416 
15417   traversalinit(&m->triangles);
15418   triangleloop.tri = triangletraverse(m);
15419   triangleloop.orient = 0;
15420   while (triangleloop.tri != (triangle *) NULL) {
15421     org(triangleloop, p[0]);
15422     dest(triangleloop, p[1]);
15423     apex(triangleloop, p[2]);
15424     trilongest2 = 0.0;
15425 
15426     for (i = 0; i < 3; i++) {
15427       j = plus1mod3[i];
15428       k = minus1mod3[i];
15429       dx[i] = p[j][0] - p[k][0];
15430       dy[i] = p[j][1] - p[k][1];
15431       edgelength[i] = dx[i] * dx[i] + dy[i] * dy[i];
15432       if (edgelength[i] > trilongest2) {
15433         trilongest2 = edgelength[i];
15434       }
15435       if (edgelength[i] > longest) {
15436         longest = edgelength[i];
15437       }
15438       if (edgelength[i] < shortest) {
15439         shortest = edgelength[i];
15440       }
15441     }
15442 
15443     triarea = counterclockwise(m, b, p[0], p[1], p[2]);
15444     if (triarea < smallestarea) {
15445       smallestarea = triarea;
15446     }
15447     if (triarea > biggestarea) {
15448       biggestarea = triarea;
15449     }
15450     triminaltitude2 = triarea * triarea / trilongest2;
15451     if (triminaltitude2 < minaltitude) {
15452       minaltitude = triminaltitude2;
15453     }
15454     triaspect2 = trilongest2 / triminaltitude2;
15455     if (triaspect2 > worstaspect) {
15456       worstaspect = triaspect2;
15457     }
15458     aspectindex = 0;
15459     while ((triaspect2 > ratiotable[aspectindex] * ratiotable[aspectindex])
15460            && (aspectindex < 15)) {
15461       aspectindex++;
15462     }
15463     aspecttable[aspectindex]++;
15464 
15465     for (i = 0; i < 3; i++) {
15466       j = plus1mod3[i];
15467       k = minus1mod3[i];
15468       dotproduct = dx[j] * dx[k] + dy[j] * dy[k];
15469       cossquare = dotproduct * dotproduct / (edgelength[j] * edgelength[k]);
15470       tendegree = 8;
15471       for (ii = 7; ii >= 0; ii--) {
15472         if (cossquare > cossquaretable[ii]) {
15473           tendegree = ii;
15474         }
15475       }
15476       if (dotproduct <= 0.0) {
15477         angletable[tendegree]++;
15478         if (cossquare > smallestangle) {
15479           smallestangle = cossquare;
15480         }
15481         if (acutebiggest && (cossquare < biggestangle)) {
15482           biggestangle = cossquare;
15483         }
15484       } else {
15485         angletable[17 - tendegree]++;
15486         if (acutebiggest || (cossquare > biggestangle)) {
15487           biggestangle = cossquare;
15488           acutebiggest = 0;
15489         }
15490       }
15491     }
15492     triangleloop.tri = triangletraverse(m);
15493   }
15494 
15495   shortest = sqrt(shortest);
15496   longest = sqrt(longest);
15497   minaltitude = sqrt(minaltitude);
15498   worstaspect = sqrt(worstaspect);
15499   smallestarea *= 0.5;
15500   biggestarea *= 0.5;
15501   if (smallestangle >= 1.0) {
15502     smallestangle = 0.0;
15503   } else {
15504     smallestangle = degconst * acos(sqrt(smallestangle));
15505   }
15506   if (biggestangle >= 1.0) {
15507     biggestangle = 180.0;
15508   } else {
15509     if (acutebiggest) {
15510       biggestangle = degconst * acos(sqrt(biggestangle));
15511     } else {
15512       biggestangle = 180.0 - degconst * acos(sqrt(biggestangle));
15513     }
15514   }
15515 
15516   printf("  Smallest area: %16.5g   |  Largest area: %16.5g\n",
15517          smallestarea, biggestarea);
15518   printf("  Shortest edge: %16.5g   |  Longest edge: %16.5g\n",
15519          shortest, longest);
15520   printf("  Shortest altitude: %12.5g   |  Largest aspect ratio: %8.5g\n\n",
15521          minaltitude, worstaspect);
15522 
15523   printf("  Triangle aspect ratio histogram:\n");
15524   printf("  1.1547 - %-6.6g    :  %8d    | %6.6g - %-6.6g     :  %8d\n",
15525          ratiotable[0], aspecttable[0], ratiotable[7], ratiotable[8],
15526          aspecttable[8]);
15527   for (i = 1; i < 7; i++) {
15528     printf("  %6.6g - %-6.6g    :  %8d    | %6.6g - %-6.6g     :  %8d\n",
15529            ratiotable[i - 1], ratiotable[i], aspecttable[i],
15530            ratiotable[i + 7], ratiotable[i + 8], aspecttable[i + 8]);
15531   }
15532   printf("  %6.6g - %-6.6g    :  %8d    | %6.6g -            :  %8d\n",
15533          ratiotable[6], ratiotable[7], aspecttable[7], ratiotable[14],
15534          aspecttable[15]);
15535   printf("  (Aspect ratio is longest edge divided by shortest altitude)\n\n");
15536 
15537   printf("  Smallest angle: %15.5g   |  Largest angle: %15.5g\n\n",
15538          smallestangle, biggestangle);
15539 
15540   printf("  Angle histogram:\n");
15541   for (i = 0; i < 9; i++) {
15542     printf("    %3d - %3d degrees:  %8d    |    %3d - %3d degrees:  %8d\n",
15543            i * 10, i * 10 + 10, angletable[i],
15544            i * 10 + 90, i * 10 + 100, angletable[i + 9]);
15545   }
15546   printf("\n");
15547 }
15548 
15549 /*****************************************************************************/
15550 /*                                                                           */
15551 /*  statistics()   Print all sorts of cool facts.                            */
15552 /*                                                                           */
15553 /*****************************************************************************/
15554 
15555 #ifdef ANSI_DECLARATORS
15556 void statistics(struct mesh *m, struct behavior *b)
15557 #else /* not ANSI_DECLARATORS */
15558 void statistics(m, b)
15559 struct mesh *m;
15560 struct behavior *b;
15561 #endif /* not ANSI_DECLARATORS */
15562 
15563 {
15564   printf("\nStatistics:\n\n");
15565   printf("  Input vertices: %d\n", m->invertices);
15566   if (b->refine) {
15567     printf("  Input triangles: %d\n", m->inelements);
15568   }
15569   if (b->poly) {
15570     printf("  Input segments: %d\n", m->insegments);
15571     if (!b->refine) {
15572       printf("  Input holes: %d\n", m->holes);
15573     }
15574   }
15575 
15576   printf("\n  Mesh vertices: %ld\n", m->vertices.items - m->undeads);
15577   printf("  Mesh triangles: %ld\n", m->triangles.items);
15578   printf("  Mesh edges: %ld\n", m->edges);
15579   printf("  Mesh exterior boundary edges: %ld\n", m->hullsize);
15580   if (b->poly || b->refine) {
15581     printf("  Mesh interior boundary edges: %ld\n",
15582            m->subsegs.items - m->hullsize);
15583     printf("  Mesh subsegments (constrained edges): %ld\n",
15584            m->subsegs.items);
15585   }
15586   printf("\n");
15587 
15588   if (b->verbose) {
15589     quality_statistics(m, b);
15590     printf("Memory allocation statistics:\n\n");
15591     printf("  Maximum number of vertices: %ld\n", m->vertices.maxitems);
15592     printf("  Maximum number of triangles: %ld\n", m->triangles.maxitems);
15593     if (m->subsegs.maxitems > 0) {
15594       printf("  Maximum number of subsegments: %ld\n", m->subsegs.maxitems);
15595     }
15596     if (m->viri.maxitems > 0) {
15597       printf("  Maximum number of viri: %ld\n", m->viri.maxitems);
15598     }
15599     if (m->badsubsegs.maxitems > 0) {
15600       printf("  Maximum number of encroached subsegments: %ld\n",
15601              m->badsubsegs.maxitems);
15602     }
15603     if (m->badtriangles.maxitems > 0) {
15604       printf("  Maximum number of bad triangles: %ld\n",
15605              m->badtriangles.maxitems);
15606     }
15607     if (m->flipstackers.maxitems > 0) {
15608       printf("  Maximum number of stacked triangle flips: %ld\n",
15609              m->flipstackers.maxitems);
15610     }
15611     if (m->splaynodes.maxitems > 0) {
15612       printf("  Maximum number of splay tree nodes: %ld\n",
15613              m->splaynodes.maxitems);
15614     }
15615     printf("  Approximate heap memory use (bytes): %ld\n\n",
15616            m->vertices.maxitems * m->vertices.itembytes +
15617            m->triangles.maxitems * m->triangles.itembytes +
15618            m->subsegs.maxitems * m->subsegs.itembytes +
15619            m->viri.maxitems * m->viri.itembytes +
15620            m->badsubsegs.maxitems * m->badsubsegs.itembytes +
15621            m->badtriangles.maxitems * m->badtriangles.itembytes +
15622            m->flipstackers.maxitems * m->flipstackers.itembytes +
15623            m->splaynodes.maxitems * m->splaynodes.itembytes);
15624 
15625     printf("Algorithmic statistics:\n\n");
15626     if (!b->weighted) {
15627       printf("  Number of incircle tests: %ld\n", m->incirclecount);
15628     } else {
15629       printf("  Number of 3D orientation tests: %ld\n", m->orient3dcount);
15630     }
15631     printf("  Number of 2D orientation tests: %ld\n", m->counterclockcount);
15632     if (m->hyperbolacount > 0) {
15633       printf("  Number of right-of-hyperbola tests: %ld\n",
15634              m->hyperbolacount);
15635     }
15636     if (m->circletopcount > 0) {
15637       printf("  Number of circle top computations: %ld\n",
15638              m->circletopcount);
15639     }
15640     if (m->circumcentercount > 0) {
15641       printf("  Number of triangle circumcenter computations: %ld\n",
15642              m->circumcentercount);
15643     }
15644     printf("\n");
15645   }
15646 }
15647 
15648 /*****************************************************************************/
15649 /*                                                                           */
15650 /*  main() or triangulate()   Gosh, do everything.                           */
15651 /*                                                                           */
15652 /*  The sequence is roughly as follows.  Many of these steps can be skipped, */
15653 /*  depending on the command line switches.                                  */
15654 /*                                                                           */
15655 /*  - Initialize constants and parse the command line.                       */
15656 /*  - Read the vertices from a file and either                               */
15657 /*    - triangulate them (no -r), or                                         */
15658 /*    - read an old mesh from files and reconstruct it (-r).                 */
15659 /*  - Insert the PSLG segments (-p), and possibly segments on the convex     */
15660 /*      hull (-c).                                                           */
15661 /*  - Read the holes (-p), regional attributes (-pA), and regional area      */
15662 /*      constraints (-pa).  Carve the holes and concavities, and spread the  */
15663 /*      regional attributes and area constraints.                            */
15664 /*  - Enforce the constraints on minimum angle (-q) and maximum area (-a).   */
15665 /*      Also enforce the conforming Delaunay property (-q and -a).           */
15666 /*  - Compute the number of edges in the resulting mesh.                     */
15667 /*  - Promote the mesh's linear triangles to higher order elements (-o).     */
15668 /*  - Write the output files and print the statistics.                       */
15669 /*  - Check the consistency and Delaunay property of the mesh (-C).          */
15670 /*                                                                           */
15671 /*****************************************************************************/
15672 
15673 #ifdef TRILIBRARY
15674 
15675 #ifdef ANSI_DECLARATORS
15676 void triangulate(char *triswitches, struct triangulateio *in,
15677                  struct triangulateio *out, struct triangulateio *vorout)
15678 #else /* not ANSI_DECLARATORS */
15679 void triangulate(triswitches, in, out, vorout)
15680 char *triswitches;
15681 struct triangulateio *in;
15682 struct triangulateio *out;
15683 struct triangulateio *vorout;
15684 #endif /* not ANSI_DECLARATORS */
15685 
15686 #else /* not TRILIBRARY */
15687 
15688 #ifdef ANSI_DECLARATORS
15689 int main(int argc, char **argv)
15690 #else /* not ANSI_DECLARATORS */
15691 int main(argc, argv)
15692 int argc;
15693 char **argv;
15694 #endif /* not ANSI_DECLARATORS */
15695 
15696 #endif /* not TRILIBRARY */
15697 
15698 {
15699   struct mesh m;
15700   struct behavior b;
15701   REAL *holearray;                                        /* Array of holes. */
15702   REAL *regionarray;   /* Array of regional attributes and area constraints. */
15703 #ifndef TRILIBRARY
15704   FILE *polyfile;
15705 #endif /* not TRILIBRARY */
15706 #ifndef NO_TIMER
15707   /* Variables for timing the performance of Triangle.  The types are */
15708   /*   defined in sys/time.h.                                         */
15709   struct timeval tv0, tv1, tv2, tv3, tv4, tv5, tv6;
15710   struct timezone tz;
15711 #endif /* not NO_TIMER */
15712 
15713 #ifndef NO_TIMER
15714   gettimeofday(&tv0, &tz);
15715 #endif /* not NO_TIMER */
15716 
15717   triangleinit(&m);
15718 #ifdef TRILIBRARY
15719   parsecommandline(1, &triswitches, &b);
15720 #else /* not TRILIBRARY */
15721   parsecommandline(argc, argv, &b);
15722 #endif /* not TRILIBRARY */
15723   m.steinerleft = b.steiner;
15724 
15725 #ifdef TRILIBRARY
15726   transfernodes(&m, &b, in->pointlist, in->pointattributelist,
15727                 in->pointmarkerlist, in->numberofpoints,
15728                 in->numberofpointattributes);
15729 #else /* not TRILIBRARY */
15730   readnodes(&m, &b, b.innodefilename, b.inpolyfilename, &polyfile);
15731 #endif /* not TRILIBRARY */
15732 
15733 #ifndef NO_TIMER
15734   if (!b.quiet) {
15735     gettimeofday(&tv1, &tz);
15736   }
15737 #endif /* not NO_TIMER */
15738 
15739 #ifdef CDT_ONLY
15740   m.hullsize = delaunay(&m, &b);                /* Triangulate the vertices. */
15741 #else /* not CDT_ONLY */
15742   if (b.refine) {
15743     /* Read and reconstruct a mesh. */
15744 #ifdef TRILIBRARY
15745     m.hullsize = reconstruct(&m, &b, in->trianglelist,
15746                              in->triangleattributelist, in->trianglearealist,
15747                              in->numberoftriangles, in->numberofcorners,
15748                              in->numberoftriangleattributes,
15749                              in->segmentlist, in->segmentmarkerlist,
15750                              in->numberofsegments);
15751 #else /* not TRILIBRARY */
15752     m.hullsize = reconstruct(&m, &b, b.inelefilename, b.areafilename,
15753                              b.inpolyfilename, polyfile);
15754 #endif /* not TRILIBRARY */
15755   } else {
15756     m.hullsize = delaunay(&m, &b);              /* Triangulate the vertices. */
15757   }
15758 #endif /* not CDT_ONLY */
15759 
15760 #ifndef NO_TIMER
15761   if (!b.quiet) {
15762     gettimeofday(&tv2, &tz);
15763     if (b.refine) {
15764       printf("Mesh reconstruction");
15765     } else {
15766       printf("Delaunay");
15767     }
15768     printf(" milliseconds:  %ld\n", 1000l * (tv2.tv_sec - tv1.tv_sec) +
15769            (tv2.tv_usec - tv1.tv_usec) / 1000l);
15770   }
15771 #endif /* not NO_TIMER */
15772 
15773   /* Ensure that no vertex can be mistaken for a triangular bounding */
15774   /*   box vertex in insertvertex().                                 */
15775   m.infvertex1 = (vertex) NULL;
15776   m.infvertex2 = (vertex) NULL;
15777   m.infvertex3 = (vertex) NULL;
15778 
15779   if (b.usesegments) {
15780     m.checksegments = 1;                /* Segments will be introduced next. */
15781     if (!b.refine) {
15782       /* Insert PSLG segments and/or convex hull segments. */
15783 #ifdef TRILIBRARY
15784       formskeleton(&m, &b, in->segmentlist,
15785                    in->segmentmarkerlist, in->numberofsegments);
15786 #else /* not TRILIBRARY */
15787       formskeleton(&m, &b, polyfile, b.inpolyfilename);
15788 #endif /* not TRILIBRARY */
15789     }
15790   }
15791 
15792 #ifndef NO_TIMER
15793   if (!b.quiet) {
15794     gettimeofday(&tv3, &tz);
15795     if (b.usesegments && !b.refine) {
15796       printf("Segment milliseconds:  %ld\n",
15797              1000l * (tv3.tv_sec - tv2.tv_sec) +
15798              (tv3.tv_usec - tv2.tv_usec) / 1000l);
15799     }
15800   }
15801 #endif /* not NO_TIMER */
15802 
15803   if (b.poly && (m.triangles.items > 0)) {
15804 #ifdef TRILIBRARY
15805     holearray = in->holelist;
15806     m.holes = in->numberofholes;
15807     regionarray = in->regionlist;
15808     m.regions = in->numberofregions;
15809 #else /* not TRILIBRARY */
15810     readholes(&m, &b, polyfile, b.inpolyfilename, &holearray, &m.holes,
15811               &regionarray, &m.regions);
15812 #endif /* not TRILIBRARY */
15813     if (!b.refine) {
15814       /* Carve out holes and concavities. */
15815       carveholes(&m, &b, holearray, m.holes, regionarray, m.regions);
15816     }
15817   } else {
15818     /* Without a PSLG, there can be no holes or regional attributes   */
15819     /*   or area constraints.  The following are set to zero to avoid */
15820     /*   an accidental free() later.                                  */
15821     m.holes = 0;
15822     m.regions = 0;
15823   }
15824 
15825 #ifndef NO_TIMER
15826   if (!b.quiet) {
15827     gettimeofday(&tv4, &tz);
15828     if (b.poly && !b.refine) {
15829       printf("Hole milliseconds:  %ld\n", 1000l * (tv4.tv_sec - tv3.tv_sec) +
15830              (tv4.tv_usec - tv3.tv_usec) / 1000l);
15831     }
15832   }
15833 #endif /* not NO_TIMER */
15834 
15835 #ifndef CDT_ONLY
15836   if (b.quality && (m.triangles.items > 0)) {
15837     enforcequality(&m, &b);           /* Enforce angle and area constraints. */
15838   }
15839 #endif /* not CDT_ONLY */
15840 
15841 #ifndef NO_TIMER
15842   if (!b.quiet) {
15843     gettimeofday(&tv5, &tz);
15844 #ifndef CDT_ONLY
15845     if (b.quality) {
15846       printf("Quality milliseconds:  %ld\n",
15847              1000l * (tv5.tv_sec - tv4.tv_sec) +
15848              (tv5.tv_usec - tv4.tv_usec) / 1000l);
15849     }
15850 #endif /* not CDT_ONLY */
15851   }
15852 #endif /* not NO_TIMER */
15853 
15854   /* Calculate the number of edges. */
15855   m.edges = (3l * m.triangles.items + m.hullsize) / 2l;
15856 
15857   if (b.order > 1) {
15858     highorder(&m, &b);       /* Promote elements to higher polynomial order. */
15859   }
15860   if (!b.quiet) {
15861     printf("\n");
15862   }
15863 
15864 #ifdef TRILIBRARY
15865   if (b.jettison) {
15866     out->numberofpoints = m.vertices.items - m.undeads;
15867   } else {
15868     out->numberofpoints = m.vertices.items;
15869   }
15870   out->numberofpointattributes = m.nextras;
15871   out->numberoftriangles = m.triangles.items;
15872   out->numberofcorners = (b.order + 1) * (b.order + 2) / 2;
15873   out->numberoftriangleattributes = m.eextras;
15874   out->numberofedges = m.edges;
15875   if (b.usesegments) {
15876     out->numberofsegments = m.subsegs.items;
15877   } else {
15878     out->numberofsegments = m.hullsize;
15879   }
15880   if (vorout != (struct triangulateio *) NULL) {
15881     vorout->numberofpoints = m.triangles.items;
15882     vorout->numberofpointattributes = m.nextras;
15883     vorout->numberofedges = m.edges;
15884   }
15885 #endif /* TRILIBRARY */
15886   /* If not using iteration numbers, don't write a .node file if one was */
15887   /*   read, because the original one would be overwritten!              */
15888   if (b.nonodewritten || (b.noiterationnum && m.readnodefile)) {
15889     if (!b.quiet) {
15890 #ifdef TRILIBRARY
15891       printf("NOT writing vertices.\n");
15892 #else /* not TRILIBRARY */
15893       printf("NOT writing a .node file.\n");
15894 #endif /* not TRILIBRARY */
15895     }
15896     numbernodes(&m, &b);         /* We must remember to number the vertices. */
15897   } else {
15898     /* writenodes() numbers the vertices too. */
15899 #ifdef TRILIBRARY
15900     writenodes(&m, &b, &out->pointlist, &out->pointattributelist,
15901                &out->pointmarkerlist);
15902 #else /* not TRILIBRARY */
15903     writenodes(&m, &b, b.outnodefilename, argc, argv);
15904 #endif /* TRILIBRARY */
15905   }
15906   if (b.noelewritten) {
15907     if (!b.quiet) {
15908 #ifdef TRILIBRARY
15909       printf("NOT writing triangles.\n");
15910 #else /* not TRILIBRARY */
15911       printf("NOT writing an .ele file.\n");
15912 #endif /* not TRILIBRARY */
15913     }
15914   } else {
15915 #ifdef TRILIBRARY
15916     writeelements(&m, &b, &out->trianglelist, &out->triangleattributelist);
15917 #else /* not TRILIBRARY */
15918     writeelements(&m, &b, b.outelefilename, argc, argv);
15919 #endif /* not TRILIBRARY */
15920   }
15921   /* The -c switch (convex switch) causes a PSLG to be written */
15922   /*   even if none was read.                                  */
15923   if (b.poly || b.convex) {
15924     /* If not using iteration numbers, don't overwrite the .poly file. */
15925     if (b.nopolywritten || b.noiterationnum) {
15926       if (!b.quiet) {
15927 #ifdef TRILIBRARY
15928         printf("NOT writing segments.\n");
15929 #else /* not TRILIBRARY */
15930         printf("NOT writing a .poly file.\n");
15931 #endif /* not TRILIBRARY */
15932       }
15933     } else {
15934 #ifdef TRILIBRARY
15935       writepoly(&m, &b, &out->segmentlist, &out->segmentmarkerlist);
15936       out->numberofholes = m.holes;
15937       out->numberofregions = m.regions;
15938       if (b.poly) {
15939         out->holelist = in->holelist;
15940         out->regionlist = in->regionlist;
15941       } else {
15942         out->holelist = (REAL *) NULL;
15943         out->regionlist = (REAL *) NULL;
15944       }
15945 #else /* not TRILIBRARY */
15946       writepoly(&m, &b, b.outpolyfilename, holearray, m.holes, regionarray,
15947                 m.regions, argc, argv);
15948 #endif /* not TRILIBRARY */
15949     }
15950   }
15951 #ifndef TRILIBRARY
15952 #ifndef CDT_ONLY
15953   if (m.regions > 0) {
15954     trifree((VOID *) regionarray);
15955   }
15956 #endif /* not CDT_ONLY */
15957   if (m.holes > 0) {
15958     trifree((VOID *) holearray);
15959   }
15960   if (b.geomview) {
15961     writeoff(&m, &b, b.offfilename, argc, argv);
15962   }
15963 #endif /* not TRILIBRARY */
15964   if (b.edgesout) {
15965 #ifdef TRILIBRARY
15966     writeedges(&m, &b, &out->edgelist, &out->edgemarkerlist);
15967 #else /* not TRILIBRARY */
15968     writeedges(&m, &b, b.edgefilename, argc, argv);
15969 #endif /* not TRILIBRARY */
15970   }
15971   if (b.voronoi) {
15972 #ifdef TRILIBRARY
15973     writevoronoi(&m, &b, &vorout->pointlist, &vorout->pointattributelist,
15974                  &vorout->pointmarkerlist, &vorout->edgelist,
15975                  &vorout->edgemarkerlist, &vorout->normlist);
15976 #else /* not TRILIBRARY */
15977     writevoronoi(&m, &b, b.vnodefilename, b.vedgefilename, argc, argv);
15978 #endif /* not TRILIBRARY */
15979   }
15980   if (b.neighbors) {
15981 #ifdef TRILIBRARY
15982     writeneighbors(&m, &b, &out->neighborlist);
15983 #else /* not TRILIBRARY */
15984     writeneighbors(&m, &b, b.neighborfilename, argc, argv);
15985 #endif /* not TRILIBRARY */
15986   }
15987 
15988   if (!b.quiet) {
15989 #ifndef NO_TIMER
15990     gettimeofday(&tv6, &tz);
15991     printf("\nOutput milliseconds:  %ld\n",
15992            1000l * (tv6.tv_sec - tv5.tv_sec) +
15993            (tv6.tv_usec - tv5.tv_usec) / 1000l);
15994     printf("Total running milliseconds:  %ld\n",
15995            1000l * (tv6.tv_sec - tv0.tv_sec) +
15996            (tv6.tv_usec - tv0.tv_usec) / 1000l);
15997 #endif /* not NO_TIMER */
15998 
15999     statistics(&m, &b);
16000   }
16001 
16002 #ifndef REDUCED
16003   if (b.docheck) {
16004     checkmesh(&m, &b);
16005     checkdelaunay(&m, &b);
16006   }
16007 #endif /* not REDUCED */
16008 
16009   triangledeinit(&m, &b);
16010 #ifndef TRILIBRARY
16011   return 0;
16012 #endif /* not TRILIBRARY */
16013 }

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