text: /*****************************************************************************/
  /*                                                                           */
  /*  This is a slightly modified version of Triangle that simply replaces     */
  /*  most uses of the "unsigned long" type with "unsigned long long". This    */
  /*  is for Microsoft Windows 64 bit platforms where "unsigned long" is only  */
  /*  32 bits, and therfore cannot store the pointers that are manipulated in  */
  /*  Jonathan's efficient storage strategy.                                   */
  /*                                                                           */
  /*  This copy is distributed with the Math::Geometry::Delaunay Perl module,  */
  /*  to support the automated build and install process.                      */
  /*                                                                           */
  /*  See the original copyright and licence terms below.                      */
  /*                                                                           */
  /*                                            -- Mike Sheldrake 02/2013      */
  /*****************************************************************************/
  
  /*****************************************************************************/
  /*                                                                           */
  /*      888888888        ,o,                          / 888                  */
  /*         888    88o88o  "    o8888o  88o8888o o88888o 888  o88888o         */
  /*         888    888    888       88b 888  888 888 888 888 d888  88b        */
  /*         888    888    888  o88^o888 888  888 "88888" 888 8888oo888        */
  /*         888    888    888 C888  888 888  888  /      888 q888             */
  /*         888    888    888  "88o^888 888  888 Cb      888  "88oooo"        */
  /*                                              "8oo8D                       */
  /*                                                                           */
  /*  A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator.      */
  /*  (triangle.c)                                                             */
  /*                                                                           */
  /*  Version 1.6                                                              */
  /*  July 28, 2005                                                            */
  /*                                                                           */
  /*  Copyright 1993, 1995, 1997, 1998, 2002, 2005                             */
  /*  Jonathan Richard Shewchuk                                                */
  /*  2360 Woolsey #H                                                          */
  /*  Berkeley, California  94705-1927                                         */
  /*  jrs@cs.berkeley.edu                                                      */
  /*                                                                           */
  /*  This program may be freely redistributed under the condition that the    */
  /*    copyright notices (including this entire header and the copyright      */
  /*    notice printed when the `-h' switch is selected) are not removed, and  */
  /*    no compensation is received.  Private, research, and institutional     */
  /*    use is free.  You may distribute modified versions of this code UNDER  */
  /*    THE CONDITION THAT THIS CODE AND ANY MODIFICATIONS MADE TO IT IN THE   */
  /*    SAME FILE REMAIN UNDER COPYRIGHT OF THE ORIGINAL AUTHOR, BOTH SOURCE   */
  /*    AND OBJECT CODE ARE MADE FREELY AVAILABLE WITHOUT CHARGE, AND CLEAR    */
  /*    NOTICE IS GIVEN OF THE MODIFICATIONS.  Distribution of this code as    */
  /*    part of a commercial system is permissible ONLY BY DIRECT ARRANGEMENT  */
  /*    WITH THE AUTHOR.  (If you are not directly supplying this code to a    */
  /*    customer, and you are instead telling them how they can obtain it for  */
  /*    free, then you are not required to make any arrangement with me.)      */
  /*                                                                           */
  /*  Hypertext instructions for Triangle are available on the Web at          */
  /*                                                                           */
  /*      http://www.cs.cmu.edu/~quake/triangle.html                           */
  /*                                                                           */
  /*  Disclaimer:  Neither I nor Carnegie Mellon warrant this code in any way  */
  /*    whatsoever.  This code is provided "as-is".  Use at your own risk.     */
  /*                                                                           */
  /*  Some of the references listed below are marked with an asterisk.  [*]    */
  /*    These references are available for downloading from the Web page       */
  /*                                                                           */
  /*      http://www.cs.cmu.edu/~quake/triangle.research.html                  */
  /*                                                                           */
  /*  Three papers discussing aspects of Triangle are available.  A short      */
  /*    overview appears in "Triangle:  Engineering a 2D Quality Mesh          */
  /*    Generator and Delaunay Triangulator," in Applied Computational         */
  /*    Geometry:  Towards Geometric Engineering, Ming C. Lin and Dinesh       */
  /*    Manocha, editors, Lecture Notes in Computer Science volume 1148,       */
  /*    pages 203-222, Springer-Verlag, Berlin, May 1996 (from the First ACM   */
  /*    Workshop on Applied Computational Geometry).  [*]                      */
  /*                                                                           */
  /*    The algorithms are discussed in the greatest detail in "Delaunay       */
  /*    Refinement Algorithms for Triangular Mesh Generation," Computational   */
  /*    Geometry:  Theory and Applications 22(1-3):21-74, May 2002.  [*]       */
  /*                                                                           */
  /*    More detail about the data structures may be found in my dissertation: */
  /*    "Delaunay Refinement Mesh Generation," Ph.D. thesis, Technical Report  */
  /*    CMU-CS-97-137, School of Computer Science, Carnegie Mellon University, */
  /*    Pittsburgh, Pennsylvania, 18 May 1997.  [*]                            */
  /*                                                                           */
  /*  Triangle was created as part of the Quake Project in the School of       */
  /*    Computer Science at Carnegie Mellon University.  For further           */
  /*    information, see Hesheng Bao, Jacobo Bielak, Omar Ghattas, Loukas F.   */
  /*    Kallivokas, David R. O'Hallaron, Jonathan R. Shewchuk, and Jifeng Xu,  */
  /*    "Large-scale Simulation of Elastic Wave Propagation in Heterogeneous   */
  /*    Media on Parallel Computers," Computer Methods in Applied Mechanics    */
  /*    and Engineering 152(1-2):85-102, 22 January 1998.                      */
  /*                                                                           */
  /*  Triangle's Delaunay refinement algorithm for quality mesh generation is  */
  /*    a hybrid of one due to Jim Ruppert, "A Delaunay Refinement Algorithm   */
  /*    for Quality 2-Dimensional Mesh Generation," Journal of Algorithms      */
  /*    18(3):548-585, May 1995 [*], and one due to L. Paul Chew, "Guaranteed- */
  /*    Quality Mesh Generation for Curved Surfaces," Proceedings of the Ninth */
  /*    Annual Symposium on Computational Geometry (San Diego, California),    */
  /*    pages 274-280, Association for Computing Machinery, May 1993,          */
  /*    http://portal.acm.org/citation.cfm?id=161150 .                         */
  /*                                                                           */
  /*  The Delaunay refinement algorithm has been modified so that it meshes    */
  /*    domains with small input angles well, as described in Gary L. Miller,  */
  /*    Steven E. Pav, and Noel J. Walkington, "When and Why Ruppert's         */
  /*    Algorithm Works," Twelfth International Meshing Roundtable, pages      */
  /*    91-102, Sandia National Laboratories, September 2003.  [*]             */
  /*                                                                           */
  /*  My implementation of the divide-and-conquer and incremental Delaunay     */
  /*    triangulation algorithms follows closely the presentation of Guibas    */
  /*    and Stolfi, even though I use a triangle-based data structure instead  */
  /*    of their quad-edge data structure.  (In fact, I originally implemented */
  /*    Triangle using the quad-edge data structure, but the switch to a       */
  /*    triangle-based data structure sped Triangle by a factor of two.)  The  */
  /*    mesh manipulation primitives and the two aforementioned Delaunay       */
  /*    triangulation algorithms are described by Leonidas J. Guibas and Jorge */
  /*    Stolfi, "Primitives for the Manipulation of General Subdivisions and   */
  /*    the Computation of Voronoi Diagrams," ACM Transactions on Graphics     */
  /*    4(2):74-123, April 1985, http://portal.acm.org/citation.cfm?id=282923 .*/
  /*                                                                           */
  /*  Their O(n log n) divide-and-conquer algorithm is adapted from Der-Tsai   */
  /*    Lee and Bruce J. Schachter, "Two Algorithms for Constructing the       */
  /*    Delaunay Triangulation," International Journal of Computer and         */
  /*    Information Science 9(3):219-242, 1980.  Triangle's improvement of the */
  /*    divide-and-conquer algorithm by alternating between vertical and       */
  /*    horizontal cuts was introduced by Rex A. Dwyer, "A Faster Divide-and-  */
  /*    Conquer Algorithm for Constructing Delaunay Triangulations,"           */
  /*    Algorithmica 2(2):137-151, 1987.                                       */
  /*                                                                           */
  /*  The incremental insertion algorithm was first proposed by C. L. Lawson,  */
  /*    "Software for C1 Surface Interpolation," in Mathematical Software III, */
  /*    John R. Rice, editor, Academic Press, New York, pp. 161-194, 1977.     */
  /*    For point location, I use the algorithm of Ernst P. Mucke, Isaac       */
  /*    Saias, and Binhai Zhu, "Fast Randomized Point Location Without         */
  /*    Preprocessing in Two- and Three-Dimensional Delaunay Triangulations,"  */
  /*    Proceedings of the Twelfth Annual Symposium on Computational Geometry, */
  /*    ACM, May 1996.  [*]  If I were to randomize the order of vertex        */
  /*    insertion (I currently don't bother), their result combined with the   */
  /*    result of Kenneth L. Clarkson and Peter W. Shor, "Applications of      */
  /*    Random Sampling in Computational Geometry II," Discrete &              */
  /*    Computational Geometry 4(1):387-421, 1989, would yield an expected     */
  /*    O(n^{4/3}) bound on running time.                                      */
  /*                                                                           */
  /*  The O(n log n) sweepline Delaunay triangulation algorithm is taken from  */
  /*    Steven Fortune, "A Sweepline Algorithm for Voronoi Diagrams",          */
  /*    Algorithmica 2(2):153-174, 1987.  A random sample of edges on the      */
  /*    boundary of the triangulation are maintained in a splay tree for the   */
  /*    purpose of point location.  Splay trees are described by Daniel        */
  /*    Dominic Sleator and Robert Endre Tarjan, "Self-Adjusting Binary Search */
  /*    Trees," Journal of the ACM 32(3):652-686, July 1985,                   */
  /*    http://portal.acm.org/citation.cfm?id=3835 .                           */
  /*                                                                           */
  /*  The algorithms for exact computation of the signs of determinants are    */
  /*    described in Jonathan Richard Shewchuk, "Adaptive Precision Floating-  */
  /*    Point Arithmetic and Fast Robust Geometric Predicates," Discrete &     */
  /*    Computational Geometry 18(3):305-363, October 1997.  (Also available   */
  /*    as Technical Report CMU-CS-96-140, School of Computer Science,         */
  /*    Carnegie Mellon University, Pittsburgh, Pennsylvania, May 1996.)  [*]  */
  /*    An abbreviated version appears as Jonathan Richard Shewchuk, "Robust   */
  /*    Adaptive Floating-Point Geometric Predicates," Proceedings of the      */
  /*    Twelfth Annual Symposium on Computational Geometry, ACM, May 1996. [*] */
  /*    Many of the ideas for my exact arithmetic routines originate with      */
  /*    Douglas M. Priest, "Algorithms for Arbitrary Precision Floating Point  */
  /*    Arithmetic," Tenth Symposium on Computer Arithmetic, pp. 132-143, IEEE */
  /*    Computer Society Press, 1991.  [*]  Many of the ideas for the correct  */
  /*    evaluation of the signs of determinants are taken from Steven Fortune  */
  /*    and Christopher J. Van Wyk, "Efficient Exact Arithmetic for Computa-   */
  /*    tional Geometry," Proceedings of the Ninth Annual Symposium on         */
  /*    Computational Geometry, ACM, pp. 163-172, May 1993, and from Steven    */
  /*    Fortune, "Numerical Stability of Algorithms for 2D Delaunay Triangu-   */
  /*    lations," International Journal of Computational Geometry & Applica-   */
  /*    tions 5(1-2):193-213, March-June 1995.                                 */
  /*                                                                           */
  /*  The method of inserting new vertices off-center (not precisely at the    */
  /*    circumcenter of every poor-quality triangle) is from Alper Ungor,      */
  /*    "Off-centers:  A New Type of Steiner Points for Computing Size-Optimal */
  /*    Quality-Guaranteed Delaunay Triangulations," Proceedings of LATIN      */
  /*    2004 (Buenos Aires, Argentina), April 2004.                            */
  /*                                                                           */
  /*  For definitions of and results involving Delaunay triangulations,        */
  /*    constrained and conforming versions thereof, and other aspects of      */
  /*    triangular mesh generation, see the excellent survey by Marshall Bern  */
  /*    and David Eppstein, "Mesh Generation and Optimal Triangulation," in    */
  /*    Computing and Euclidean Geometry, Ding-Zhu Du and Frank Hwang,         */
  /*    editors, World Scientific, Singapore, pp. 23-90, 1992.  [*]            */
  /*                                                                           */
  /*  The time for incrementally adding PSLG (planar straight line graph)      */
  /*    segments to create a constrained Delaunay triangulation is probably    */
  /*    O(t^2) per segment in the worst case and O(t) per segment in the       */
  /*    common case, where t is the number of triangles that intersect the     */
  /*    segment before it is inserted.  This doesn't count point location,     */
  /*    which can be much more expensive.  I could improve this to O(d log d)  */
  /*    time, but d is usually quite small, so it's not worth the bother.      */
  /*    (This note does not apply when the -s switch is used, invoking a       */
  /*    different method is used to insert segments.)                          */
  /*                                                                           */
  /*  The time for deleting a vertex from a Delaunay triangulation is O(d^2)   */
  /*    in the worst case and O(d) in the common case, where d is the degree   */
  /*    of the vertex being deleted.  I could improve this to O(d log d) time, */
  /*    but d is usually quite small, so it's not worth the bother.            */
  /*                                                                           */
  /*  Ruppert's Delaunay refinement algorithm typically generates triangles    */
  /*    at a linear rate (constant time per triangle) after the initial        */
  /*    triangulation is formed.  There may be pathological cases where        */
  /*    quadratic time is required, but these never arise in practice.         */
  /*                                                                           */
  /*  The geometric predicates (circumcenter calculations, segment             */
  /*    intersection formulae, etc.) appear in my "Lecture Notes on Geometric  */
  /*    Robustness" at http://www.cs.berkeley.edu/~jrs/mesh .                  */
  /*                                                                           */
  /*  If you make any improvements to this code, please please please let me   */
  /*    know, so that I may obtain the improvements.  Even if you don't change */
  /*    the code, I'd still love to hear what it's being used for.             */
  /*                                                                           */
  /*****************************************************************************/
  
  /* For single precision (which will save some memory and reduce paging),     */
  /*   define the symbol SINGLE by using the -DSINGLE compiler switch or by    */
  /*   writing "#define SINGLE" below.                                         */
  /*                                                                           */
  /* For double precision (which will allow you to refine meshes to a smaller  */
  /*   edge length), leave SINGLE undefined.                                   */
  /*                                                                           */
  /* Double precision uses more memory, but improves the resolution of the     */
  /*   meshes you can generate with Triangle.  It also reduces the likelihood  */
  /*   of a floating exception due to overflow.  Finally, it is much faster    */
  /*   than single precision on 64-bit architectures like the DEC Alpha.  I    */
  /*   recommend double precision unless you want to generate a mesh for which */
  /*   you do not have enough memory.                                          */
  
  /* #define SINGLE */
  
  #ifdef SINGLE
  #define REAL float
  #else /* not SINGLE */
  #define REAL double
  #endif /* not SINGLE */
  
  /* If yours is not a Unix system, define the NO_TIMER compiler switch to     */
  /*   remove the Unix-specific timing code.                                   */
  
  /* #define NO_TIMER */
  
  /* To insert lots of self-checks for internal errors, define the SELF_CHECK  */
  /*   symbol.  This will slow down the program significantly.  It is best to  */
  /*   define the symbol using the -DSELF_CHECK compiler switch, but you could */
  /*   write "#define SELF_CHECK" below.  If you are modifying this code, I    */
  /*   recommend you turn self-checks on until your work is debugged.          */
  
  /* #define SELF_CHECK */
  
  /* To compile Triangle as a callable object library (triangle.o), define the */
  /*   TRILIBRARY symbol.  Read the file triangle.h for details on how to call */
  /*   the procedure triangulate() that results.                               */
  
  /* #define TRILIBRARY */
  
  /* It is possible to generate a smaller version of Triangle using one or     */
  /*   both of the following symbols.  Define the REDUCED symbol to eliminate  */
  /*   all features that are primarily of research interest; specifically, the */
  /*   -i, -F, -s, and -C switches.  Define the CDT_ONLY symbol to eliminate   */
  /*   all meshing algorithms above and beyond constrained Delaunay            */
  /*   triangulation; specifically, the -r, -q, -a, -u, -D, -S, and -s         */
  /*   switches.  These reductions are most likely to be useful when           */
  /*   generating an object library (triangle.o) by defining the TRILIBRARY    */
  /*   symbol.                                                                 */
  
  /* #define REDUCED */
  /* #define CDT_ONLY */
  
  /* On some machines, my exact arithmetic routines might be defeated by the   */
  /*   use of internal extended precision floating-point registers.  The best  */
  /*   way to solve this problem is to set the floating-point registers to use */
  /*   single or double precision internally.  On 80x86 processors, this may   */
  /*   be accomplished by setting the CPU86 symbol for the Microsoft C         */
  /*   compiler, or the LINUX symbol for the gcc compiler running on Linux.    */
  /*                                                                           */
  /* An inferior solution is to declare certain values as `volatile', thus     */
  /*   forcing them to be stored to memory and rounded off.  Unfortunately,    */
  /*   this solution might slow Triangle down quite a bit.  To use volatile    */
  /*   values, write "#define INEXACT volatile" below.  Normally, however,     */
  /*   INEXACT should be defined to be nothing.  ("#define INEXACT".)          */
  /*                                                                           */
  /* For more discussion, see http://www.cs.cmu.edu/~quake/robust.pc.html .    */
  /*   For yet more discussion, see Section 5 of my paper, "Adaptive Precision */
  /*   Floating-Point Arithmetic and Fast Robust Geometric Predicates" (also   */
  /*   available as Section 6.6 of my dissertation).                           */
  
  /* #define CPU86 */
  /* #define LINUX */
  
  #define INEXACT /* Nothing */
  /* #define INEXACT volatile */
  
  /* Maximum number of characters in a file name (including the null).         */
  
  #define FILENAMESIZE 2048
  
  /* Maximum number of characters in a line read from a file (including the    */
  /*   null).                                                                  */
  
  #define INPUTLINESIZE 1024
  
  /* For efficiency, a variety of data structures are allocated in bulk.  The  */
  /*   following constants determine how many of each structure is allocated   */
  /*   at once.                                                                */
  
  #define TRIPERBLOCK 4092           /* Number of triangles allocated at once. */
  #define SUBSEGPERBLOCK 508       /* Number of subsegments allocated at once. */
  #define VERTEXPERBLOCK 4092         /* Number of vertices allocated at once. */
  #define VIRUSPERBLOCK 1020   /* Number of virus triangles allocated at once. */
  /* Number of encroached subsegments allocated at once. */
  #define BADSUBSEGPERBLOCK 252
  /* Number of skinny triangles allocated at once. */
  #define BADTRIPERBLOCK 4092
  /* Number of flipped triangles allocated at once. */
  #define FLIPSTACKERPERBLOCK 252
  /* Number of splay tree nodes allocated at once. */
  #define SPLAYNODEPERBLOCK 508
  
  /* The vertex types.   A DEADVERTEX has been deleted entirely.  An           */
  /*   UNDEADVERTEX is not part of the mesh, but is written to the output      */
  /*   .node file and affects the node indexing in the other output files.     */
  
  #define INPUTVERTEX 0
  #define SEGMENTVERTEX 1
  #define FREEVERTEX 2
  #define DEADVERTEX -32768
  #define UNDEADVERTEX -32767
  
  /* The next line is used to outsmart some very stupid compilers.  If your    */
  /*   compiler is smarter, feel free to replace the "int" with "void".        */
  /*   Not that it matters.                                                    */
  
  #define TRIVOID void
  
  /* Two constants for algorithms based on random sampling.  Both constants    */
  /*   have been chosen empirically to optimize their respective algorithms.   */
  
  /* Used for the point location scheme of Mucke, Saias, and Zhu, to decide    */
  /*   how large a random sample of triangles to inspect.                      */
  
  #define SAMPLEFACTOR 11
  
  /* Used in Fortune's sweepline Delaunay algorithm to determine what fraction */
  /*   of boundary edges should be maintained in the splay tree for point      */
  /*   location on the front.                                                  */
  
  #define SAMPLERATE 10
  
  /* A number that speaks for itself, every kissable digit.                    */
  
  #define PI 3.141592653589793238462643383279502884197169399375105820974944592308
  
  /* Another fave.                                                             */
  
  #define SQUAREROOTTWO 1.4142135623730950488016887242096980785696718753769480732
  
  /* And here's one for those of you who are intimidated by math.              */
  
  #define ONETHIRD 0.333333333333333333333333333333333333333333333333333333333333
  
  #include <stdio.h>
  #include <stdlib.h>
  #include <string.h>
  #include <math.h>
  #ifndef NO_TIMER
  #include <sys/time.h>
  #endif /* not NO_TIMER */
  #ifdef CPU86
  #include <float.h>
  #endif /* CPU86 */
  #ifdef LINUX
  #include <fpu_control.h>
  #endif /* LINUX */
  #ifdef TRILIBRARY
  #include "triangle.h"
  #endif /* TRILIBRARY */
  
  /* A few forward declarations.                                               */
  
  #ifndef TRILIBRARY
  char *readline();
  char *findfield();
  #endif /* not TRILIBRARY */
  
  /* Labels that signify the result of point location.  The result of a        */
  /*   search indicates that the point falls in the interior of a triangle, on */
  /*   an edge, on a vertex, or outside the mesh.                              */
  
  enum locateresult {INTRIANGLE, ONEDGE, ONVERTEX, OUTSIDE};
  
  /* Labels that signify the result of vertex insertion.  The result indicates */
  /*   that the vertex was inserted with complete success, was inserted but    */
  /*   encroaches upon a subsegment, was not inserted because it lies on a     */
  /*   segment, or was not inserted because another vertex occupies the same   */
  /*   location.                                                               */
  
  enum insertvertexresult {SUCCESSFULVERTEX, ENCROACHINGVERTEX, VIOLATINGVERTEX,
                           DUPLICATEVERTEX};
  
  /* Labels that signify the result of direction finding.  The result          */
  /*   indicates that a segment connecting the two query points falls within   */
  /*   the direction triangle, along the left edge of the direction triangle,  */
  /*   or along the right edge of the direction triangle.                      */
  
  enum finddirectionresult {WITHIN, LEFTCOLLINEAR, RIGHTCOLLINEAR};
  
  /*****************************************************************************/
  /*                                                                           */
  /*  The basic mesh data structures                                           */
  /*                                                                           */
  /*  There are three:  vertices, triangles, and subsegments (abbreviated      */
  /*  `subseg').  These three data structures, linked by pointers, comprise    */
  /*  the mesh.  A vertex simply represents a mesh vertex and its properties.  */
  /*  A triangle is a triangle.  A subsegment is a special data structure used */
  /*  to represent an impenetrable edge of the mesh (perhaps on the outer      */
  /*  boundary, on the boundary of a hole, or part of an internal boundary     */
  /*  separating two triangulated regions).  Subsegments represent boundaries, */
  /*  defined by the user, that triangles may not lie across.                  */
  /*                                                                           */
  /*  A triangle consists of a list of three vertices, a list of three         */
  /*  adjoining triangles, a list of three adjoining subsegments (when         */
  /*  segments exist), an arbitrary number of optional user-defined            */
  /*  floating-point attributes, and an optional area constraint.  The latter  */
  /*  is an upper bound on the permissible area of each triangle in a region,  */
  /*  used for mesh refinement.                                                */
  /*                                                                           */
  /*  For a triangle on a boundary of the mesh, some or all of the neighboring */
  /*  triangles may not be present.  For a triangle in the interior of the     */
  /*  mesh, often no neighboring subsegments are present.  Such absent         */
  /*  triangles and subsegments are never represented by NULL pointers; they   */
  /*  are represented by two special records:  `dummytri', the triangle that   */
  /*  fills "outer space", and `dummysub', the omnipresent subsegment.         */
  /*  `dummytri' and `dummysub' are used for several reasons; for instance,    */
  /*  they can be dereferenced and their contents examined without violating   */
  /*  protected memory.                                                        */
  /*                                                                           */
  /*  However, it is important to understand that a triangle includes other    */
  /*  information as well.  The pointers to adjoining vertices, triangles, and */
  /*  subsegments are ordered in a way that indicates their geometric relation */
  /*  to each other.  Furthermore, each of these pointers contains orientation */
  /*  information.  Each pointer to an adjoining triangle indicates which face */
  /*  of that triangle is contacted.  Similarly, each pointer to an adjoining  */
  /*  subsegment indicates which side of that subsegment is contacted, and how */
  /*  the subsegment is oriented relative to the triangle.                     */
  /*                                                                           */
  /*  The data structure representing a subsegment may be thought to be        */
  /*  abutting the edge of one or two triangle data structures:  either        */
  /*  sandwiched between two triangles, or resting against one triangle on an  */
  /*  exterior boundary or hole boundary.                                      */
  /*                                                                           */
  /*  A subsegment consists of a list of four vertices--the vertices of the    */
  /*  subsegment, and the vertices of the segment it is a part of--a list of   */
  /*  two adjoining subsegments, and a list of two adjoining triangles.  One   */
  /*  of the two adjoining triangles may not be present (though there should   */
  /*  always be one), and neighboring subsegments might not be present.        */
  /*  Subsegments also store a user-defined integer "boundary marker".         */
  /*  Typically, this integer is used to indicate what boundary conditions are */
  /*  to be applied at that location in a finite element simulation.           */
  /*                                                                           */
  /*  Like triangles, subsegments maintain information about the relative      */
  /*  orientation of neighboring objects.                                      */
  /*                                                                           */
  /*  Vertices are relatively simple.  A vertex is a list of floating-point    */
  /*  numbers, starting with the x, and y coordinates, followed by an          */
  /*  arbitrary number of optional user-defined floating-point attributes,     */
  /*  followed by an integer boundary marker.  During the segment insertion    */
  /*  phase, there is also a pointer from each vertex to a triangle that may   */
  /*  contain it.  Each pointer is not always correct, but when one is, it     */
  /*  speeds up segment insertion.  These pointers are assigned values once    */
  /*  at the beginning of the segment insertion phase, and are not used or     */
  /*  updated except during this phase.  Edge flipping during segment          */
  /*  insertion will render some of them incorrect.  Hence, don't rely upon    */
  /*  them for anything.                                                       */
  /*                                                                           */
  /*  Other than the exception mentioned above, vertices have no information   */
  /*  about what triangles, subfacets, or subsegments they are linked to.      */
  /*                                                                           */
  /*****************************************************************************/
  
  /*****************************************************************************/
  /*                                                                           */
  /*  Handles                                                                  */
  /*                                                                           */
  /*  The oriented triangle (`otri') and oriented subsegment (`osub') data     */
  /*  structures defined below do not themselves store any part of the mesh.   */
  /*  The mesh itself is made of `triangle's, `subseg's, and `vertex's.        */
  /*                                                                           */
  /*  Oriented triangles and oriented subsegments will usually be referred to  */
  /*  as "handles."  A handle is essentially a pointer into the mesh; it       */
  /*  allows you to "hold" one particular part of the mesh.  Handles are used  */
  /*  to specify the regions in which one is traversing and modifying the mesh.*/
  /*  A single `triangle' may be held by many handles, or none at all.  (The   */
  /*  latter case is not a memory leak, because the triangle is still          */
  /*  connected to other triangles in the mesh.)                               */
  /*                                                                           */
  /*  An `otri' is a handle that holds a triangle.  It holds a specific edge   */
  /*  of the triangle.  An `osub' is a handle that holds a subsegment.  It     */
  /*  holds either the left or right side of the subsegment.                   */
  /*                                                                           */
  /*  Navigation about the mesh is accomplished through a set of mesh          */
  /*  manipulation primitives, further below.  Many of these primitives take   */
  /*  a handle and produce a new handle that holds the mesh near the first     */
  /*  handle.  Other primitives take two handles and glue the corresponding    */
  /*  parts of the mesh together.  The orientation of the handles is           */
  /*  important.  For instance, when two triangles are glued together by the   */
  /*  bond() primitive, they are glued at the edges on which the handles lie.  */
  /*                                                                           */
  /*  Because vertices have no information about which triangles they are      */
  /*  attached to, I commonly represent a vertex by use of a handle whose      */
  /*  origin is the vertex.  A single handle can simultaneously represent a    */
  /*  triangle, an edge, and a vertex.                                         */
  /*                                                                           */
  /*****************************************************************************/
  
  /* The triangle data structure.  Each triangle contains three pointers to    */
  /*   adjoining triangles, plus three pointers to vertices, plus three        */
  /*   pointers to subsegments (declared below; these pointers are usually     */
  /*   `dummysub').  It may or may not also contain user-defined attributes    */
  /*   and/or a floating-point "area constraint."  It may also contain extra   */
  /*   pointers for nodes, when the user asks for high-order elements.         */
  /*   Because the size and structure of a `triangle' is not decided until     */
  /*   runtime, I haven't simply declared the type `triangle' as a struct.     */
  
  typedef REAL **triangle;            /* Really:  typedef triangle *triangle   */
  
  /* An oriented triangle:  includes a pointer to a triangle and orientation.  */
  /*   The orientation denotes an edge of the triangle.  Hence, there are      */
  /*   three possible orientations.  By convention, each edge always points    */
  /*   counterclockwise about the corresponding triangle.                      */
  
  struct otri {
    triangle *tri;
    int orient;                                         /* Ranges from 0 to 2. */
  };
  
  /* The subsegment data structure.  Each subsegment contains two pointers to  */
  /*   adjoining subsegments, plus four pointers to vertices, plus two         */
  /*   pointers to adjoining triangles, plus one boundary marker, plus one     */
  /*   segment number.                                                         */
  
  typedef REAL **subseg;                  /* Really:  typedef subseg *subseg   */
  
  /* An oriented subsegment:  includes a pointer to a subsegment and an        */
  /*   orientation.  The orientation denotes a side of the edge.  Hence, there */
  /*   are two possible orientations.  By convention, the edge is always       */
  /*   directed so that the "side" denoted is the right side of the edge.      */
  
  struct osub {
    subseg *ss;
    int ssorient;                                       /* Ranges from 0 to 1. */
  };
  
  /* The vertex data structure.  Each vertex is actually an array of REALs.    */
  /*   The number of REALs is unknown until runtime.  An integer boundary      */
  /*   marker, and sometimes a pointer to a triangle, is appended after the    */
  /*   REALs.                                                                  */
  
  typedef REAL *vertex;
  
  /* A queue used to store encroached subsegments.  Each subsegment's vertices */
  /*   are stored so that we can check whether a subsegment is still the same. */
  
  struct badsubseg {
    subseg encsubseg;                             /* An encroached subsegment. */
    vertex subsegorg, subsegdest;                         /* Its two vertices. */
  };
  
  /* A queue used to store bad triangles.  The key is the square of the cosine */
  /*   of the smallest angle of the triangle.  Each triangle's vertices are    */
  /*   stored so that one can check whether a triangle is still the same.      */
  
  struct badtriang {
    triangle poortri;                       /* A skinny or too-large triangle. */
    REAL key;                             /* cos^2 of smallest (apical) angle. */
    vertex triangorg, triangdest, triangapex;           /* Its three vertices. */
    struct badtriang *nexttriang;             /* Pointer to next bad triangle. */
  };
  
  /* A stack of triangles flipped during the most recent vertex insertion.     */
  /*   The stack is used to undo the vertex insertion if the vertex encroaches */
  /*   upon a subsegment.                                                      */
  
  struct flipstacker {
    triangle flippedtri;                       /* A recently flipped triangle. */
    struct flipstacker *prevflip;               /* Previous flip in the stack. */
  };
  
  /* A node in a heap used to store events for the sweepline Delaunay          */
  /*   algorithm.  Nodes do not point directly to their parents or children in */
  /*   the heap.  Instead, each node knows its position in the heap, and can   */
  /*   look up its parent and children in a separate array.  The `eventptr'    */
  /*   points either to a `vertex' or to a triangle (in encoded format, so     */
  /*   that an orientation is included).  In the latter case, the origin of    */
  /*   the oriented triangle is the apex of a "circle event" of the sweepline  */
  /*   algorithm.  To distinguish site events from circle events, all circle   */
  /*   events are given an invalid (smaller than `xmin') x-coordinate `xkey'.  */
  
  struct event {
    REAL xkey, ykey;                              /* Coordinates of the event. */
    TRIVOID *eventptr;      /* Can be a vertex or the location of a circle event. */
    int heapposition;              /* Marks this event's position in the heap. */
  };
  
  /* A node in the splay tree.  Each node holds an oriented ghost triangle     */
  /*   that represents a boundary edge of the growing triangulation.  When a   */
  /*   circle event covers two boundary edges with a triangle, so that they    */
  /*   are no longer boundary edges, those edges are not immediately deleted   */
  /*   from the tree; rather, they are lazily deleted when they are next       */
  /*   encountered.  (Since only a random sample of boundary edges are kept    */
  /*   in the tree, lazy deletion is faster.)  `keydest' is used to verify     */
  /*   that a triangle is still the same as when it entered the splay tree; if */
  /*   it has been rotated (due to a circle event), it no longer represents a  */
  /*   boundary edge and should be deleted.                                    */
  
  struct splaynode {
    struct otri keyedge;                     /* Lprev of an edge on the front. */
    vertex keydest;           /* Used to verify that splay node is still live. */
    struct splaynode *lchild, *rchild;              /* Children in splay tree. */
  };
  
  /* A type used to allocate memory.  firstblock is the first block of items.  */
  /*   nowblock is the block from which items are currently being allocated.   */
  /*   nextitem points to the next slab of free memory for an item.            */
  /*   deaditemstack is the head of a linked list (stack) of deallocated items */
  /*   that can be recycled.  unallocateditems is the number of items that     */
  /*   remain to be allocated from nowblock.                                   */
  /*                                                                           */
  /* Traversal is the process of walking through the entire list of items, and */
  /*   is separate from allocation.  Note that a traversal will visit items on */
  /*   the "deaditemstack" stack as well as live items.  pathblock points to   */
  /*   the block currently being traversed.  pathitem points to the next item  */
  /*   to be traversed.  pathitemsleft is the number of items that remain to   */
  /*   be traversed in pathblock.                                              */
  /*                                                                           */
  /* alignbytes determines how new records should be aligned in memory.        */
  /*   itembytes is the length of a record in bytes (after rounding up).       */
  /*   itemsperblock is the number of items allocated at once in a single      */
  /*   block.  itemsfirstblock is the number of items in the first block,      */
  /*   which can vary from the others.  items is the number of currently       */
  /*   allocated items.  maxitems is the maximum number of items that have     */
  /*   been allocated at once; it is the current number of items plus the      */
  /*   number of records kept on deaditemstack.                                */
  
  struct memorypool {
    TRIVOID **firstblock, **nowblock;
    TRIVOID *nextitem;
    TRIVOID *deaditemstack;
    TRIVOID **pathblock;
    TRIVOID *pathitem;
    int alignbytes;
    int itembytes;
    int itemsperblock;
    int itemsfirstblock;
    long items, maxitems;
    int unallocateditems;
    int pathitemsleft;
  };
  
  
  /* Global constants.                                                         */
  
  REAL splitter;       /* Used to split REAL factors for exact multiplication. */
  REAL epsilon;                             /* Floating-point machine epsilon. */
  REAL resulterrbound;
  REAL ccwerrboundA, ccwerrboundB, ccwerrboundC;
  REAL iccerrboundA, iccerrboundB, iccerrboundC;
  REAL o3derrboundA, o3derrboundB, o3derrboundC;
  
  /* Random number seed is not constant, but I've made it global anyway.       */
  
  unsigned long randomseed;                     /* Current random number seed. */
  
  
  /* Mesh data structure.  Triangle operates on only one mesh, but the mesh    */
  /*   structure is used (instead of global variables) to allow reentrancy.    */
  
  struct mesh {
  
  /* Variables used to allocate memory for triangles, subsegments, vertices,   */
  /*   viri (triangles being eaten), encroached segments, bad (skinny or too   */
  /*   large) triangles, and splay tree nodes.                                 */
  
    struct memorypool triangles;
    struct memorypool subsegs;
    struct memorypool vertices;
    struct memorypool viri;
    struct memorypool badsubsegs;
    struct memorypool badtriangles;
    struct memorypool flipstackers;
    struct memorypool splaynodes;
  
  /* Variables that maintain the bad triangle queues.  The queues are          */
  /*   ordered from 4095 (highest priority) to 0 (lowest priority).            */
  
    struct badtriang *queuefront[4096];
    struct badtriang *queuetail[4096];
    int nextnonemptyq[4096];
    int firstnonemptyq;
  
  /* Variable that maintains the stack of recently flipped triangles.          */
  
    struct flipstacker *lastflip;
  
  /* Other variables. */
  
    REAL xmin, xmax, ymin, ymax;                            /* x and y bounds. */
    REAL xminextreme;      /* Nonexistent x value used as a flag in sweepline. */
    int invertices;                               /* Number of input vertices. */
    int inelements;                              /* Number of input triangles. */
    int insegments;                               /* Number of input segments. */
    int holes;                                       /* Number of input holes. */
    int regions;                                   /* Number of input regions. */
    int undeads;    /* Number of input vertices that don't appear in the mesh. */
    long edges;                                     /* Number of output edges. */
    int mesh_dim;                                /* Dimension (ought to be 2). */
    int nextras;                           /* Number of attributes per vertex. */
    int eextras;                         /* Number of attributes per triangle. */
    long hullsize;                          /* Number of edges in convex hull. */
    int steinerleft;                 /* Number of Steiner points not yet used. */
    int vertexmarkindex;         /* Index to find boundary marker of a vertex. */
    int vertex2triindex;     /* Index to find a triangle adjacent to a vertex. */
    int highorderindex;  /* Index to find extra nodes for high-order elements. */
    int elemattribindex;            /* Index to find attributes of a triangle. */
    int areaboundindex;             /* Index to find area bound of a triangle. */
    int checksegments;         /* Are there segments in the triangulation yet? */
    int checkquality;                  /* Has quality triangulation begun yet? */
    int readnodefile;                           /* Has a .node file been read? */
    long samples;              /* Number of random samples for point location. */
  
    long incirclecount;                 /* Number of incircle tests performed. */
    long counterclockcount;     /* Number of counterclockwise tests performed. */
    long orient3dcount;           /* Number of 3D orientation tests performed. */
    long hyperbolacount;      /* Number of right-of-hyperbola tests performed. */
    long circumcentercount;  /* Number of circumcenter calculations performed. */
    long circletopcount;       /* Number of circle top calculations performed. */
  
  /* Triangular bounding box vertices.                                         */
  
    vertex infvertex1, infvertex2, infvertex3;
  
  /* Pointer to the `triangle' that occupies all of "outer space."             */
  
    triangle *dummytri;
    triangle *dummytribase;    /* Keep base address so we can free() it later. */
  
  /* Pointer to the omnipresent subsegment.  Referenced by any triangle or     */
  /*   subsegment that isn't really connected to a subsegment at that          */
  /*   location.                                                               */
  
    subseg *dummysub;
    subseg *dummysubbase;      /* Keep base address so we can free() it later. */
  
  /* Pointer to a recently visited triangle.  Improves point location if       */
  /*   proximate vertices are inserted sequentially.                           */
  
    struct otri recenttri;
  
  };                                                  /* End of `struct mesh'. */
  
  
  /* Data structure for command line switches and file names.  This structure  */
  /*   is used (instead of global variables) to allow reentrancy.              */
  
  struct behavior {
  
  /* Switches for the triangulator.                                            */
  /*   poly: -p switch.  refine: -r switch.                                    */
  /*   quality: -q switch.                                                     */
  /*     minangle: minimum angle bound, specified after -q switch.             */
  /*     goodangle: cosine squared of minangle.                                */
  /*     offconstant: constant used to place off-center Steiner points.        */
  /*   vararea: -a switch without number.                                      */
  /*   fixedarea: -a switch with number.                                       */
  /*     maxarea: maximum area bound, specified after -a switch.               */
  /*   usertest: -u switch.                                                    */
  /*   regionattrib: -A switch.  convex: -c switch.                            */
  /*   weighted: 1 for -w switch, 2 for -W switch.  jettison: -j switch        */
  /*   firstnumber: inverse of -z switch.  All items are numbered starting     */
  /*     from `firstnumber'.                                                   */
  /*   edgesout: -e switch.  voronoi: -v switch.                               */
  /*   neighbors: -n switch.  geomview: -g switch.                             */
  /*   nobound: -B switch.  nopolywritten: -P switch.                          */
  /*   nonodewritten: -N switch.  noelewritten: -E switch.                     */
  /*   noiterationnum: -I switch.  noholes: -O switch.                         */
  /*   noexact: -X switch.                                                     */
  /*   order: element order, specified after -o switch.                        */
  /*   nobisect: count of how often -Y switch is selected.                     */
  /*   steiner: maximum number of Steiner points, specified after -S switch.   */
  /*   incremental: -i switch.  sweepline: -F switch.                          */
  /*   dwyer: inverse of -l switch.                                            */
  /*   splitseg: -s switch.                                                    */
  /*   conformdel: -D switch.  docheck: -C switch.                             */
  /*   quiet: -Q switch.  verbose: count of how often -V switch is selected.   */
  /*   usesegments: -p, -r, -q, or -c switch; determines whether segments are  */
  /*     used at all.                                                          */
  /*                                                                           */
  /* Read the instructions to find out the meaning of these switches.          */
  
    int poly, refine, quality, vararea, fixedarea, usertest;
    int regionattrib, convex, weighted, jettison;
    int firstnumber;
    int edgesout, voronoi, neighbors, geomview;
    int nobound, nopolywritten, nonodewritten, noelewritten, noiterationnum;
    int noholes, noexact, conformdel;
    int incremental, sweepline, dwyer;
    int splitseg;
    int docheck;
    int quiet, verbose;
    int usesegments;
    int order;
    int nobisect;
    int steiner;
    REAL minangle, goodangle, offconstant;
    REAL maxarea;
  
  /* Variables for file names.                                                 */
  
  #ifndef TRILIBRARY
    char innodefilename[FILENAMESIZE];
    char inelefilename[FILENAMESIZE];
    char inpolyfilename[FILENAMESIZE];
    char areafilename[FILENAMESIZE];
    char outnodefilename[FILENAMESIZE];
    char outelefilename[FILENAMESIZE];
    char outpolyfilename[FILENAMESIZE];
    char edgefilename[FILENAMESIZE];
    char vnodefilename[FILENAMESIZE];
    char vedgefilename[FILENAMESIZE];
    char neighborfilename[FILENAMESIZE];
    char offfilename[FILENAMESIZE];
  #endif /* not TRILIBRARY */
  
  };                                              /* End of `struct behavior'. */
  
  
  /*****************************************************************************/
  /*                                                                           */
  /*  Mesh manipulation primitives.  Each triangle contains three pointers to  */
  /*  other triangles, with orientations.  Each pointer points not to the      */
  /*  first byte of a triangle, but to one of the first three bytes of a       */
  /*  triangle.  It is necessary to extract both the triangle itself and the   */
  /*  orientation.  To save memory, I keep both pieces of information in one   */
  /*  pointer.  To make this possible, I assume that all triangles are aligned */
  /*  to four-byte boundaries.  The decode() routine below decodes a pointer,  */
  /*  extracting an orientation (in the range 0 to 2) and a pointer to the     */
  /*  beginning of a triangle.  The encode() routine compresses a pointer to a */
  /*  triangle and an orientation into a single pointer.  My assumptions that  */
  /*  triangles are four-byte-aligned and that the `unsigned long' type is     */
  /*  long enough to hold a pointer are two of the few kludges in this program.*/
  /*                                                                           */
  /*    ( Note that this copy for 64 bit Windows, distributed with the    )    */
  /*    (     Math::Geometry::Delaunay Perl module, has replaced          )    */
  /*    (  "unsigned long" (32 bits) with "unsigned long long" (64 bits)  )    */
  /*    (               -- Mike Sheldrake 02/2013                         )    */
  /*                                                                           */
  /*  Subsegments are manipulated similarly.  A pointer to a subsegment        */
  /*  carries both an address and an orientation in the range 0 to 1.          */
  /*                                                                           */
  /*  The other primitives take an oriented triangle or oriented subsegment,   */
  /*  and return an oriented triangle or oriented subsegment or vertex; or     */
  /*  they change the connections in the data structure.                       */
  /*                                                                           */
  /*  Below, triangles and subsegments are denoted by their vertices.  The     */
  /*  triangle abc has origin (org) a, destination (dest) b, and apex (apex)   */
  /*  c.  These vertices occur in counterclockwise order about the triangle.   */
  /*  The handle abc may simultaneously denote vertex a, edge ab, and triangle */
  /*  abc.                                                                     */
  /*                                                                           */
  /*  Similarly, the subsegment ab has origin (sorg) a and destination (sdest) */
  /*  b.  If ab is thought to be directed upward (with b directly above a),    */
  /*  then the handle ab is thought to grasp the right side of ab, and may     */
  /*  simultaneously denote vertex a and edge ab.                              */
  /*                                                                           */
  /*  An asterisk (*) denotes a vertex whose identity is unknown.              */
  /*                                                                           */
  /*  Given this notation, a partial list of mesh manipulation primitives      */
  /*  follows.                                                                 */
  /*                                                                           */
  /*                                                                           */
  /*  For triangles:                                                           */
  /*                                                                           */
  /*  sym:  Find the abutting triangle; same edge.                             */
  /*  sym(abc) -> ba*                                                          */
  /*                                                                           */
  /*  lnext:  Find the next edge (counterclockwise) of a triangle.             */
  /*  lnext(abc) -> bca                                                        */
  /*                                                                           */
  /*  lprev:  Find the previous edge (clockwise) of a triangle.                */
  /*  lprev(abc) -> cab                                                        */
  /*                                                                           */
  /*  onext:  Find the next edge counterclockwise with the same origin.        */
  /*  onext(abc) -> ac*                                                        */
  /*                                                                           */
  /*  oprev:  Find the next edge clockwise with the same origin.               */
  /*  oprev(abc) -> a*b                                                        */
  /*                                                                           */
  /*  dnext:  Find the next edge counterclockwise with the same destination.   */
  /*  dnext(abc) -> *ba                                                        */
  /*                                                                           */
  /*  dprev:  Find the next edge clockwise with the same destination.          */
  /*  dprev(abc) -> cb*                                                        */
  /*                                                                           */
  /*  rnext:  Find the next edge (counterclockwise) of the adjacent triangle.  */
  /*  rnext(abc) -> *a*                                                        */
  /*                                                                           */
  /*  rprev:  Find the previous edge (clockwise) of the adjacent triangle.     */
  /*  rprev(abc) -> b**                                                        */
  /*                                                                           */
  /*  org:  Origin          dest:  Destination          apex:  Apex            */
  /*  org(abc) -> a         dest(abc) -> b              apex(abc) -> c         */
  /*                                                                           */
  /*  bond:  Bond two triangles together at the resepective handles.           */
  /*  bond(abc, bad)                                                           */
  /*                                                                           */
  /*                                                                           */
  /*  For subsegments:                                                         */
  /*                                                                           */
  /*  ssym:  Reverse the orientation of a subsegment.                          */
  /*  ssym(ab) -> ba                                                           */
  /*                                                                           */
  /*  spivot:  Find adjoining subsegment with the same origin.                 */
  /*  spivot(ab) -> a*                                                         */
  /*                                                                           */
  /*  snext:  Find next subsegment in sequence.                                */
  /*  snext(ab) -> b*                                                          */
  /*                                                                           */
  /*  sorg:  Origin                      sdest:  Destination                   */
  /*  sorg(ab) -> a                      sdest(ab) -> b                        */
  /*                                                                           */
  /*  sbond:  Bond two subsegments together at the respective origins.         */
  /*  sbond(ab, ac)                                                            */
  /*                                                                           */
  /*                                                                           */
  /*  For interacting tetrahedra and subfacets:                                */
  /*                                                                           */
  /*  tspivot:  Find a subsegment abutting a triangle.                         */
  /*  tspivot(abc) -> ba                                                       */
  /*                                                                           */
  /*  stpivot:  Find a triangle abutting a subsegment.                         */
  /*  stpivot(ab) -> ba*                                                       */
  /*                                                                           */
  /*  tsbond:  Bond a triangle to a subsegment.                                */
  /*  tsbond(abc, ba)                                                          */
  /*                                                                           */
  /*****************************************************************************/
  
  /********* Mesh manipulation primitives begin here                   *********/
  /**                                                                         **/
  /**                                                                         **/
  
  /* Fast lookup arrays to speed some of the mesh manipulation primitives.     */
  
  int plus1mod3[3] = {1, 2, 0};
  int minus1mod3[3] = {2, 0, 1};
  
  /********* Primitives for triangles                                  *********/
  /*                                                                           */
  /*                                                                           */
  
  /* decode() converts a pointer to an oriented triangle.  The orientation is  */
  /*   extracted from the two least significant bits of the pointer.           */
  
  #define decode(ptr, otri)                                                     \
    (otri).orient = (int) ((unsigned long long) (ptr) & (unsigned long long) 3ll);         \
    (otri).tri = (triangle *)                                                   \
                    ((unsigned long long) (ptr) ^ (unsigned long long) (otri).orient)
  
  /* encode() compresses an oriented triangle into a single pointer.  It       */
  /*   relies on the assumption that all triangles are aligned to four-byte    */
  /*   boundaries, so the two least significant bits of (otri).tri are zero.   */
  
  #define encode(otri)                                                          \
    (triangle) ((unsigned long long) (otri).tri | (unsigned long long) (otri).orient)
  
  /* The following handle manipulation primitives are all described by Guibas  */
  /*   and Stolfi.  However, Guibas and Stolfi use an edge-based data          */
  /*   structure, whereas I use a triangle-based data structure.               */
  
  /* sym() finds the abutting triangle, on the same edge.  Note that the edge  */
  /*   direction is necessarily reversed, because the handle specified by an   */
  /*   oriented triangle is directed counterclockwise around the triangle.     */
  
  #define sym(otri1, otri2)                                                     \
    ptr = (otri1).tri[(otri1).orient];                                          \
    decode(ptr, otri2);
  
  #define symself(otri)                                                         \
    ptr = (otri).tri[(otri).orient];                                            \
    decode(ptr, otri);
  
  /* lnext() finds the next edge (counterclockwise) of a triangle.             */
  
  #define lnext(otri1, otri2)                                                   \
    (otri2).tri = (otri1).tri;                                                  \
    (otri2).orient = plus1mod3[(otri1).orient]
  
  #define lnextself(otri)                                                       \
    (otri).orient = plus1mod3[(otri).orient]
  
  /* lprev() finds the previous edge (clockwise) of a triangle.                */
  
  #define lprev(otri1, otri2)                                                   \
    (otri2).tri = (otri1).tri;                                                  \
    (otri2).orient = minus1mod3[(otri1).orient]
  
  #define lprevself(otri)                                                       \
    (otri).orient = minus1mod3[(otri).orient]
  
  /* onext() spins counterclockwise around a vertex; that is, it finds the     */
  /*   next edge with the same origin in the counterclockwise direction.  This */
  /*   edge is part of a different triangle.                                   */
  
  #define onext(otri1, otri2)                                                   \
    lprev(otri1, otri2);                                                        \
    symself(otri2);
  
  #define onextself(otri)                                                       \
    lprevself(otri);                                                            \
    symself(otri);
  
  /* oprev() spins clockwise around a vertex; that is, it finds the next edge  */
  /*   with the same origin in the clockwise direction.  This edge is part of  */
  /*   a different triangle.                                                   */
  
  #define oprev(otri1, otri2)                                                   \
    sym(otri1, otri2);                                                          \
    lnextself(otri2);
  
  #define oprevself(otri)                                                       \
    symself(otri);                                                              \
    lnextself(otri);
  
  /* dnext() spins counterclockwise around a vertex; that is, it finds the     */
  /*   next edge with the same destination in the counterclockwise direction.  */
  /*   This edge is part of a different triangle.                              */
  
  #define dnext(otri1, otri2)                                                   \
    sym(otri1, otri2);                                                          \
    lprevself(otri2);
  
  #define dnextself(otri)                                                       \
    symself(otri);                                                              \
    lprevself(otri);
  
  /* dprev() spins clockwise around a vertex; that is, it finds the next edge  */
  /*   with the same destination in the clockwise direction.  This edge is     */
  /*   part of a different triangle.                                           */
  
  #define dprev(otri1, otri2)                                                   \
    lnext(otri1, otri2);                                                        \
    symself(otri2);
  
  #define dprevself(otri)                                                       \
    lnextself(otri);                                                            \
    symself(otri);
  
  /* rnext() moves one edge counterclockwise about the adjacent triangle.      */
  /*   (It's best understood by reading Guibas and Stolfi.  It involves        */
  /*   changing triangles twice.)                                              */
  
  #define rnext(otri1, otri2)                                                   \
    sym(otri1, otri2);                                                          \
    lnextself(otri2);                                                           \
    symself(otri2);
  
  #define rnextself(otri)                                                       \
    symself(otri);                                                              \
    lnextself(otri);                                                            \
    symself(otri);
  
  /* rprev() moves one edge clockwise about the adjacent triangle.             */
  /*   (It's best understood by reading Guibas and Stolfi.  It involves        */
  /*   changing triangles twice.)                                              */
  
  #define rprev(otri1, otri2)                                                   \
    sym(otri1, otri2);                                                          \
    lprevself(otri2);                                                           \
    symself(otri2);
  
  #define rprevself(otri)                                                       \
    symself(otri);                                                              \
    lprevself(otri);                                                            \
    symself(otri);
  
  /* These primitives determine or set the origin, destination, or apex of a   */
  /* triangle.                                                                 */
  
  #define org(otri, vertexptr)                                                  \
    vertexptr = (vertex) (otri).tri[plus1mod3[(otri).orient] + 3]
  
  #define dest(otri, vertexptr)                                                 \
    vertexptr = (vertex) (otri).tri[minus1mod3[(otri).orient] + 3]
  
  #define apex(otri, vertexptr)                                                 \
    vertexptr = (vertex) (otri).tri[(otri).orient + 3]
  
  #define setorg(otri, vertexptr)                                               \
    (otri).tri[plus1mod3[(otri).orient] + 3] = (triangle) vertexptr
  
  #define setdest(otri, vertexptr)                                              \
    (otri).tri[minus1mod3[(otri).orient] + 3] = (triangle) vertexptr
  
  #define setapex(otri, vertexptr)                                              \
    (otri).tri[(otri).orient + 3] = (triangle) vertexptr
  
  /* Bond two triangles together.                                              */
  
  #define bond(otri1, otri2)                                                    \
    (otri1).tri[(otri1).orient] = encode(otri2);                                \
    (otri2).tri[(otri2).orient] = encode(otri1)
  
  /* Dissolve a bond (from one side).  Note that the other triangle will still */
  /*   think it's connected to this triangle.  Usually, however, the other     */
  /*   triangle is being deleted entirely, or bonded to another triangle, so   */
  /*   it doesn't matter.                                                      */
  
  #define dissolve(otri)                                                        \
    (otri).tri[(otri).orient] = (triangle) m->dummytri
  
  /* Copy an oriented triangle.                                                */
  
  #define otricopy(otri1, otri2)                                                \
    (otri2).tri = (otri1).tri;                                                  \
    (otri2).orient = (otri1).orient
  
  /* Test for equality of oriented triangles.                                  */
  
  #define otriequal(otri1, otri2)                                               \
    (((otri1).tri == (otri2).tri) &&                                            \
     ((otri1).orient == (otri2).orient))
  
  /* Primitives to infect or cure a triangle with the virus.  These rely on    */
  /*   the assumption that all subsegments are aligned to four-byte boundaries.*/
  
  #define infect(otri)                                                          \
    (otri).tri[6] = (triangle)                                                  \
                      ((unsigned long long) (otri).tri[6] | (unsigned long long) 2ll)
  
  #define uninfect(otri)                                                        \
    (otri).tri[6] = (triangle)                                                  \
                      ((unsigned long long) (otri).tri[6] & ~ (unsigned long long) 2ll)
  
  /* Test a triangle for viral infection.                                      */
  
  #define infected(otri)                                                        \
    (((unsigned long long) (otri).tri[6] & (unsigned long long) 2ll) != 0ll)
  
  /* Check or set a triangle's attributes.                                     */
  
  #define elemattribute(otri, attnum)                                           \
    ((REAL *) (otri).tri)[m->elemattribindex + (attnum)]
  
  #define setelemattribute(otri, attnum, value)                                 \
    ((REAL *) (otri).tri)[m->elemattribindex + (attnum)] = value
  
  /* Check or set a triangle's maximum area bound.                             */
  
  #define areabound(otri)  ((REAL *) (otri).tri)[m->areaboundindex]
  
  #define setareabound(otri, value)                                             \
    ((REAL *) (otri).tri)[m->areaboundindex] = value
  
  /* Check or set a triangle's deallocation.  Its second pointer is set to     */
  /*   NULL to indicate that it is not allocated.  (Its first pointer is used  */
  /*   for the stack of dead items.)  Its fourth pointer (its first vertex)    */
  /*   is set to NULL in case a `badtriang' structure points to it.            */
  
  #define deadtri(tria)  ((tria)[1] == (triangle) NULL)
  
  #define killtri(tria)                                                         \
    (tria)[1] = (triangle) NULL;                                                \
    (tria)[3] = (triangle) NULL
  
  /********* Primitives for subsegments                                *********/
  /*                                                                           */
  /*                                                                           */
  
  /* sdecode() converts a pointer to an oriented subsegment.  The orientation  */
  /*   is extracted from the least significant bit of the pointer.  The two    */
  /*   least significant bits (one for orientation, one for viral infection)   */
  /*   are masked out to produce the real pointer.                             */
  
  #define sdecode(sptr, osub)                                                   \
    (osub).ssorient = (int) ((unsigned long long) (sptr) & (unsigned long long) 1ll);      \
    (osub).ss = (subseg *)                                                      \
                ((unsigned long long) (sptr) & ~ (unsigned long long) 3ll)
  
  /* sencode() compresses an oriented subsegment into a single pointer.  It    */
  /*   relies on the assumption that all subsegments are aligned to two-byte   */
  /*   boundaries, so the least significant bit of (osub).ss is zero.          */
  
  #define sencode(osub)                                                         \
    (subseg) ((unsigned long long) (osub).ss | (unsigned long long) (osub).ssorient)
  
  /* ssym() toggles the orientation of a subsegment.                           */
  
  #define ssym(osub1, osub2)                                                    \
    (osub2).ss = (osub1).ss;                                                    \
    (osub2).ssorient = 1 - (osub1).ssorient
  
  #define ssymself(osub)                                                        \
    (osub).ssorient = 1 - (osub).ssorient
  
  /* spivot() finds the other subsegment (from the same segment) that shares   */
  /*   the same origin.                                                        */
  
  #define spivot(osub1, osub2)                                                  \
    sptr = (osub1).ss[(osub1).ssorient];                                        \
    sdecode(sptr, osub2)
  
  #define spivotself(osub)                                                      \
    sptr = (osub).ss[(osub).ssorient];                                          \
    sdecode(sptr, osub)
  
  /* snext() finds the next subsegment (from the same segment) in sequence;    */
  /*   one whose origin is the input subsegment's destination.                 */
  
  #define snext(osub1, osub2)                                                   \
    sptr = (osub1).ss[1 - (osub1).ssorient];                                    \
    sdecode(sptr, osub2)
  
  #define snextself(osub)                                                       \
    sptr = (osub).ss[1 - (osub).ssorient];                                      \
    sdecode(sptr, osub)
  
  /* These primitives determine or set the origin or destination of a          */
  /*   subsegment or the segment that includes it.                             */
  
  #define sorg(osub, vertexptr)                                                 \
    vertexptr = (vertex) (osub).ss[2 + (osub).ssorient]
  
  #define sdest(osub, vertexptr)                                                \
    vertexptr = (vertex) (osub).ss[3 - (osub).ssorient]
  
  #define setsorg(osub, vertexptr)                                              \
    (osub).ss[2 + (osub).ssorient] = (subseg) vertexptr
  
  #define setsdest(osub, vertexptr)                                             \
    (osub).ss[3 - (osub).ssorient] = (subseg) vertexptr
  
  #define segorg(osub, vertexptr)                                               \
    vertexptr = (vertex) (osub).ss[4 + (osub).ssorient]
  
  #define segdest(osub, vertexptr)                                              \
    vertexptr = (vertex) (osub).ss[5 - (osub).ssorient]
  
  #define setsegorg(osub, vertexptr)                                            \
    (osub).ss[4 + (osub).ssorient] = (subseg) vertexptr
  
  #define setsegdest(osub, vertexptr)                                           \
    (osub).ss[5 - (osub).ssorient] = (subseg) vertexptr
  
  /* These primitives read or set a boundary marker.  Boundary markers are     */
  /*   used to hold user-defined tags for setting boundary conditions in       */
  /*   finite element solvers.                                                 */
  
  #define mark(osub)  (* (int *) ((osub).ss + 8))
  
  #define setmark(osub, value)                                                  \
    * (int *) ((osub).ss + 8) = value
  
  /* Bond two subsegments together.                                            */
  
  #define sbond(osub1, osub2)                                                   \
    (osub1).ss[(osub1).ssorient] = sencode(osub2);                              \
    (osub2).ss[(osub2).ssorient] = sencode(osub1)
  
  /* Dissolve a subsegment bond (from one side).  Note that the other          */
  /*   subsegment will still think it's connected to this subsegment.          */
  
  #define sdissolve(osub)                                                       \
    (osub).ss[(osub).ssorient] = (subseg) m->dummysub
  
  /* Copy a subsegment.                                                        */
  
  #define subsegcopy(osub1, osub2)                                              \
    (osub2).ss = (osub1).ss;                                                    \
    (osub2).ssorient = (osub1).ssorient
  
  /* Test for equality of subsegments.                                         */
  
  #define subsegequal(osub1, osub2)                                             \
    (((osub1).ss == (osub2).ss) &&                                              \
     ((osub1).ssorient == (osub2).ssorient))
  
  /* Check or set a subsegment's deallocation.  Its second pointer is set to   */
  /*   NULL to indicate that it is not allocated.  (Its first pointer is used  */
  /*   for the stack of dead items.)  Its third pointer (its first vertex)     */
  /*   is set to NULL in case a `badsubseg' structure points to it.            */
  
  #define deadsubseg(sub)  ((sub)[1] == (subseg) NULL)
  
  #define killsubseg(sub)                                                       \
    (sub)[1] = (subseg) NULL;                                                   \
    (sub)[2] = (subseg) NULL
  
  /********* Primitives for interacting triangles and subsegments      *********/
  /*                                                                           */
  /*                                                                           */
  
  /* tspivot() finds a subsegment abutting a triangle.                         */
  
  #define tspivot(otri, osub)                                                   \
    sptr = (subseg) (otri).tri[6 + (otri).orient];                              \
    sdecode(sptr, osub)
  
  /* stpivot() finds a triangle abutting a subsegment.  It requires that the   */
  /*   variable `ptr' of type `triangle' be defined.                           */
  
  #define stpivot(osub, otri)                                                   \
    ptr = (triangle) (osub).ss[6 + (osub).ssorient];                            \
    decode(ptr, otri)
  
  /* Bond a triangle to a subsegment.                                          */
  
  #define tsbond(otri, osub)                                                    \
    (otri).tri[6 + (otri).orient] = (triangle) sencode(osub);                   \
    (osub).ss[6 + (osub).ssorient] = (subseg) encode(otri)
  
  /* Dissolve a bond (from the triangle side).                                 */
  
  #define tsdissolve(otri)                                                      \
    (otri).tri[6 + (otri).orient] = (triangle) m->dummysub
  
  /* Dissolve a bond (from the subsegment side).                               */
  
  #define stdissolve(osub)                                                      \
    (osub).ss[6 + (osub).ssorient] = (subseg) m->dummytri
  
  /********* Primitives for vertices                                   *********/
  /*                                                                           */
  /*                                                                           */
  
  #define vertexmark(vx)  ((int *) (vx))[m->vertexmarkindex]
  
  #define setvertexmark(vx, value)                                              \
    ((int *) (vx))[m->vertexmarkindex] = value
  
  #define vertextype(vx)  ((int *) (vx))[m->vertexmarkindex + 1]
  
  #define setvertextype(vx, value)                                              \
    ((int *) (vx))[m->vertexmarkindex + 1] = value
  
  #define vertex2tri(vx)  ((triangle *) (vx))[m->vertex2triindex]
  
  #define setvertex2tri(vx, value)                                              \
    ((triangle *) (vx))[m->vertex2triindex] = value
  
  /**                                                                         **/
  /**                                                                         **/
  /********* Mesh manipulation primitives end here                     *********/
  
  /********* User-defined triangle evaluation routine begins here      *********/
  /**                                                                         **/
  /**                                                                         **/
  
  /*****************************************************************************/
  /*                                                                           */
  /*  triunsuitable()   Determine if a triangle is unsuitable, and thus must   */
  /*                    be further refined.                                    */
  /*                                                                           */
  /*  You may write your own procedure that decides whether or not a selected  */
  /*  triangle is too big (and needs to be refined).  There are two ways to do */
  /*  this.                                                                    */
  /*                                                                           */
  /*  (1)  Modify the procedure `triunsuitable' below, then recompile          */
  /*  Triangle.                                                                */
  /*                                                                           */
  /*  (2)  Define the symbol EXTERNAL_TEST (either by adding the definition    */
  /*  to this file, or by using the appropriate compiler switch).  This way,   */
  /*  you can compile triangle.c separately from your test.  Write your own    */
  /*  `triunsuitable' procedure in a separate C file (using the same prototype */
  /*  as below).  Compile it and link the object code with triangle.o.         */
  /*                                                                           */
  /*  This procedure returns 1 if the triangle is too large and should be      */
  /*  refined; 0 otherwise.                                                    */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef EXTERNAL_TEST
  
  int triunsuitable();
  
  #else /* not EXTERNAL_TEST */
  
  #ifdef ANSI_DECLARATORS
  int triunsuitable(vertex triorg, vertex tridest, vertex triapex, REAL area)
  #else /* not ANSI_DECLARATORS */
  int triunsuitable(triorg, tridest, triapex, area)
  vertex triorg;                              /* The triangle's origin vertex. */
  vertex tridest;                        /* The triangle's destination vertex. */
  vertex triapex;                               /* The triangle's apex vertex. */
  REAL area;                                      /* The area of the triangle. */
  #endif /* not ANSI_DECLARATORS */
  
  {
    REAL dxoa, dxda, dxod;
    REAL dyoa, dyda, dyod;
    REAL oalen, dalen, odlen;
    REAL maxlen;
  
    dxoa = triorg[0] - triapex[0];
    dyoa = triorg[1] - triapex[1];
    dxda = tridest[0] - triapex[0];
    dyda = tridest[1] - triapex[1];
    dxod = triorg[0] - tridest[0];
    dyod = triorg[1] - tridest[1];
    /* Find the squares of the lengths of the triangle's three edges. */
    oalen = dxoa * dxoa + dyoa * dyoa;
    dalen = dxda * dxda + dyda * dyda;
    odlen = dxod * dxod + dyod * dyod;
    /* Find the square of the length of the longest edge. */
    maxlen = (dalen > oalen) ? dalen : oalen;
    maxlen = (odlen > maxlen) ? odlen : maxlen;
  
    if (maxlen > 0.05 * (triorg[0] * triorg[0] + triorg[1] * triorg[1]) + 0.02) {
      return 1;
    } else {
      return 0;
    }
  }
  
  #endif /* not EXTERNAL_TEST */
  
  /**                                                                         **/
  /**                                                                         **/
  /********* User-defined triangle evaluation routine ends here        *********/
  
  /********* Memory allocation and program exit wrappers begin here    *********/
  /**                                                                         **/
  /**                                                                         **/
  
  #ifdef ANSI_DECLARATORS
  void triexit(int status)
  #else /* not ANSI_DECLARATORS */
  void triexit(status)
  int status;
  #endif /* not ANSI_DECLARATORS */
  
  {
    exit(status);
  }
  
  #ifdef ANSI_DECLARATORS
  TRIVOID *trimalloc(int size)
  #else /* not ANSI_DECLARATORS */
  TRIVOID *trimalloc(size)
  int size;
  #endif /* not ANSI_DECLARATORS */
  
  {
    TRIVOID *memptr;
  
    memptr = (TRIVOID *) malloc((unsigned int) size);
    if (memptr == (TRIVOID *) NULL) {
      printf("Error:  Out of memory.\n");
      triexit(1);
    }
    return(memptr);
  }
  
  #ifdef ANSI_DECLARATORS
  void trifree(TRIVOID *memptr)
  #else /* not ANSI_DECLARATORS */
  void trifree(memptr)
  TRIVOID *memptr;
  #endif /* not ANSI_DECLARATORS */
  
  {
    free(memptr);
  }
  
  /**                                                                         **/
  /**                                                                         **/
  /********* Memory allocation and program exit wrappers end here      *********/
  
  /********* User interaction routines begin here                      *********/
  /**                                                                         **/
  /**                                                                         **/
  
  /*****************************************************************************/
  /*                                                                           */
  /*  syntax()   Print list of command line switches.                          */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifndef TRILIBRARY
  
  void syntax()
  {
  #ifdef CDT_ONLY
  #ifdef REDUCED
    printf("triangle [-pAcjevngBPNEIOXzo_lQVh] input_file\n");
  #else /* not REDUCED */
    printf("triangle [-pAcjevngBPNEIOXzo_iFlCQVh] input_file\n");
  #endif /* not REDUCED */
  #else /* not CDT_ONLY */
  #ifdef REDUCED
    printf("triangle [-prq__a__uAcDjevngBPNEIOXzo_YS__lQVh] input_file\n");
  #else /* not REDUCED */
    printf("triangle [-prq__a__uAcDjevngBPNEIOXzo_YS__iFlsCQVh] input_file\n");
  #endif /* not REDUCED */
  #endif /* not CDT_ONLY */
  
    printf("    -p  Triangulates a Planar Straight Line Graph (.poly file).\n");
  #ifndef CDT_ONLY
    printf("    -r  Refines a previously generated mesh.\n");
    printf(
      "    -q  Quality mesh generation.  A minimum angle may be specified.\n");
    printf("    -a  Applies a maximum triangle area constraint.\n");
    printf("    -u  Applies a user-defined triangle constraint.\n");
  #endif /* not CDT_ONLY */
    printf(
      "    -A  Applies attributes to identify triangles in certain regions.\n");
    printf("    -c  Encloses the convex hull with segments.\n");
  #ifndef CDT_ONLY
    printf("    -D  Conforming Delaunay:  all triangles are truly Delaunay.\n");
  #endif /* not CDT_ONLY */
  /*
    printf("    -w  Weighted Delaunay triangulation.\n");
    printf("    -W  Regular triangulation (lower hull of a height field).\n");
  */
    printf("    -j  Jettison unused vertices from output .node file.\n");
    printf("    -e  Generates an edge list.\n");
    printf("    -v  Generates a Voronoi diagram.\n");
    printf("    -n  Generates a list of triangle neighbors.\n");
    printf("    -g  Generates an .off file for Geomview.\n");
    printf("    -B  Suppresses output of boundary information.\n");
    printf("    -P  Suppresses output of .poly file.\n");
    printf("    -N  Suppresses output of .node file.\n");
    printf("    -E  Suppresses output of .ele file.\n");
    printf("    -I  Suppresses mesh iteration numbers.\n");
    printf("    -O  Ignores holes in .poly file.\n");
    printf("    -X  Suppresses use of exact arithmetic.\n");
    printf("    -z  Numbers all items starting from zero (rather than one).\n");
    printf("    -o2 Generates second-order subparametric elements.\n");
  #ifndef CDT_ONLY
    printf("    -Y  Suppresses boundary segment splitting.\n");
    printf("    -S  Specifies maximum number of added Steiner points.\n");
  #endif /* not CDT_ONLY */
  #ifndef REDUCED
    printf("    -i  Uses incremental method, rather than divide-and-conquer.\n");
    printf("    -F  Uses Fortune's sweepline algorithm, rather than d-and-c.\n");
  #endif /* not REDUCED */
    printf("    -l  Uses vertical cuts only, rather than alternating cuts.\n");
  #ifndef REDUCED
  #ifndef CDT_ONLY
    printf(
      "    -s  Force segments into mesh by splitting (instead of using CDT).\n");
  #endif /* not CDT_ONLY */
    printf("    -C  Check consistency of final mesh.\n");
  #endif /* not REDUCED */
    printf("    -Q  Quiet:  No terminal output except errors.\n");
    printf("    -V  Verbose:  Detailed information on what I'm doing.\n");
    printf("    -h  Help:  Detailed instructions for Triangle.\n");
    triexit(0);
  }
  
  #endif /* not TRILIBRARY */
  
  /*****************************************************************************/
  /*                                                                           */
  /*  info()   Print out complete instructions.                                */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifndef TRILIBRARY
  
  void info()
  {
    printf("Triangle\n");
    printf(
  "A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator.\n");
    printf("Version 1.6\n\n");
    printf(
  "Copyright 1993, 1995, 1997, 1998, 2002, 2005 Jonathan Richard Shewchuk\n");
    printf("2360 Woolsey #H / Berkeley, California 94705-1927\n");
    printf("Bugs/comments to jrs@cs.berkeley.edu\n");
    printf(
  "Created as part of the Quake project (tools for earthquake simulation).\n");
    printf(
  "Supported in part by NSF Grant CMS-9318163 and an NSERC 1967 Scholarship.\n");
    printf("There is no warranty whatsoever.  Use at your own risk.\n");
  #ifdef SINGLE
    printf("This executable is compiled for single precision arithmetic.\n\n\n");
  #else /* not SINGLE */
    printf("This executable is compiled for double precision arithmetic.\n\n\n");
  #endif /* not SINGLE */
    printf(
  "Triangle generates exact Delaunay triangulations, constrained Delaunay\n");
    printf(
  "triangulations, conforming Delaunay triangulations, Voronoi diagrams, and\n");
    printf(
  "high-quality triangular meshes.  The latter can be generated with no small\n"
  );
    printf(
  "or large angles, and are thus suitable for finite element analysis.  If no\n"
  );
    printf(
  "command line switch is specified, your .node input file is read, and the\n");
    printf(
  "Delaunay triangulation is returned in .node and .ele output files.  The\n");
    printf("command syntax is:\n\n");
    printf("triangle [-prq__a__uAcDjevngBPNEIOXzo_YS__iFlsCQVh] input_file\n\n");
    printf(
  "Underscores indicate that numbers may optionally follow certain switches.\n");
    printf(
  "Do not leave any space between a switch and its numeric parameter.\n");
    printf(
  "input_file must be a file with extension .node, or extension .poly if the\n");
    printf(
  "-p switch is used.  If -r is used, you must supply .node and .ele files,\n");
    printf(
  "and possibly a .poly file and an .area file as well.  The formats of these\n"
  );
    printf("files are described below.\n\n");
    printf("Command Line Switches:\n\n");
    printf(
  "    -p  Reads a Planar Straight Line Graph (.poly file), which can specify\n"
  );
    printf(
  "        vertices, segments, holes, regional attributes, and regional area\n");
    printf(
  "        constraints.  Generates a constrained Delaunay triangulation (CDT)\n"
  );
    printf(
  "        fitting the input; or, if -s, -q, -a, or -u is used, a conforming\n");
    printf(
  "        constrained Delaunay triangulation (CCDT).  If you want a truly\n");
    printf(
  "        Delaunay (not just constrained Delaunay) triangulation, use -D as\n");
    printf(
  "        well.  When -p is not used, Triangle reads a .node file by default.\n"
  );
    printf(
  "    -r  Refines a previously generated mesh.  The mesh is read from a .node\n"
  );
    printf(
  "        file and an .ele file.  If -p is also used, a .poly file is read\n");
    printf(
  "        and used to constrain segments in the mesh.  If -a is also used\n");
    printf(
  "        (with no number following), an .area file is read and used to\n");
    printf(
  "        impose area constraints on the mesh.  Further details on refinement\n"
  );
    printf("        appear below.\n");
    printf(
  "    -q  Quality mesh generation by Delaunay refinement (a hybrid of Paul\n");
    printf(
  "        Chew's and Jim Ruppert's algorithms).  Adds vertices to the mesh to\n"
  );
    printf(
  "        ensure that all angles are between 20 and 140 degrees.  An\n");
    printf(
  "        alternative bound on the minimum angle, replacing 20 degrees, may\n");
    printf(
  "        be specified after the `q'.  The specified angle may include a\n");
    printf(
  "        decimal point, but not exponential notation.  Note that a bound of\n"
  );
    printf(
  "        theta degrees on the smallest angle also implies a bound of\n");
    printf(
  "        (180 - 2 theta) on the largest angle.  If the minimum angle is 28.6\n"
  );
    printf(
  "        degrees or smaller, Triangle is mathematically guaranteed to\n");
    printf(
  "        terminate (assuming infinite precision arithmetic--Triangle may\n");
    printf(
  "        fail to terminate if you run out of precision).  In practice,\n");
    printf(
  "        Triangle often succeeds for minimum angles up to 34 degrees.  For\n");
    printf(
  "        some meshes, however, you might need to reduce the minimum angle to\n"
  );
    printf(
  "        avoid problems associated with insufficient floating-point\n");
    printf("        precision.\n");
    printf(
  "    -a  Imposes a maximum triangle area.  If a number follows the `a', no\n");
    printf(
  "        triangle is generated whose area is larger than that number.  If no\n"
  );
    printf(
  "        number is specified, an .area file (if -r is used) or .poly file\n");
    printf(
  "        (if -r is not used) specifies a set of maximum area constraints.\n");
    printf(
  "        An .area file contains a separate area constraint for each\n");
    printf(
  "        triangle, and is useful for refining a finite element mesh based on\n"
  );
    printf(
  "        a posteriori error estimates.  A .poly file can optionally contain\n"
  );
    printf(
  "        an area constraint for each segment-bounded region, thereby\n");
    printf(
  "        controlling triangle densities in a first triangulation of a PSLG.\n"
  );
    printf(
  "        You can impose both a fixed area constraint and a varying area\n");
    printf(
  "        constraint by invoking the -a switch twice, once with and once\n");
    printf(
  "        without a number following.  Each area specified may include a\n");
    printf("        decimal point.\n");
    printf(
  "    -u  Imposes a user-defined constraint on triangle size.  There are two\n"
  );
    printf(
  "        ways to use this feature.  One is to edit the triunsuitable()\n");
    printf(
  "        procedure in triangle.c to encode any constraint you like, then\n");
    printf(
  "        recompile Triangle.  The other is to compile triangle.c with the\n");
    printf(
  "        EXTERNAL_TEST symbol set (compiler switch -DEXTERNAL_TEST), then\n");
    printf(
  "        link Triangle with a separate object file that implements\n");
    printf(
  "        triunsuitable().  In either case, the -u switch causes the user-\n");
    printf("        defined test to be applied to every triangle.\n");
    printf(
  "    -A  Assigns an additional floating-point attribute to each triangle\n");
    printf(
  "        that identifies what segment-bounded region each triangle belongs\n");
    printf(
  "        to.  Attributes are assigned to regions by the .poly file.  If a\n");
    printf(
  "        region is not explicitly marked by the .poly file, triangles in\n");
    printf(
  "        that region are assigned an attribute of zero.  The -A switch has\n");
    printf(
  "        an effect only when the -p switch is used and the -r switch is not.\n"
  );
    printf(
  "    -c  Creates segments on the convex hull of the triangulation.  If you\n");
    printf(
  "        are triangulating a vertex set, this switch causes a .poly file to\n"
  );
    printf(
  "        be written, containing all edges of the convex hull.  If you are\n");
    printf(
  "        triangulating a PSLG, this switch specifies that the whole convex\n");
    printf(
  "        hull of the PSLG should be triangulated, regardless of what\n");
    printf(
  "        segments the PSLG has.  If you do not use this switch when\n");
    printf(
  "        triangulating a PSLG, Triangle assumes that you have identified the\n"
  );
    printf(
  "        region to be triangulated by surrounding it with segments of the\n");
    printf(
  "        input PSLG.  Beware:  if you are not careful, this switch can cause\n"
  );
    printf(
  "        the introduction of an extremely thin angle between a PSLG segment\n"
  );
    printf(
  "        and a convex hull segment, which can cause overrefinement (and\n");
    printf(
  "        possibly failure if Triangle runs out of precision).  If you are\n");
    printf(
  "        refining a mesh, the -c switch works differently:  it causes a\n");
    printf(
  "        .poly file to be written containing the boundary edges of the mesh\n"
  );
    printf("        (useful if no .poly file was read).\n");
    printf(
  "    -D  Conforming Delaunay triangulation:  use this switch if you want to\n"
  );
    printf(
  "        ensure that all the triangles in the mesh are Delaunay, and not\n");
    printf(
  "        merely constrained Delaunay; or if you want to ensure that all the\n"
  );
    printf(
  "        Voronoi vertices lie within the triangulation.  (Some finite volume\n"
  );
    printf(
  "        methods have this requirement.)  This switch invokes Ruppert's\n");
    printf(
  "        original algorithm, which splits every subsegment whose diametral\n");
    printf(
  "        circle is encroached.  It usually increases the number of vertices\n"
  );
    printf("        and triangles.\n");
    printf(
  "    -j  Jettisons vertices that are not part of the final triangulation\n");
    printf(
  "        from the output .node file.  By default, Triangle copies all\n");
    printf(
  "        vertices in the input .node file to the output .node file, in the\n");
    printf(
  "        same order, so their indices do not change.  The -j switch prevents\n"
  );
    printf(
  "        duplicated input vertices, or vertices `eaten' by holes, from\n");
    printf(
  "        appearing in the output .node file.  Thus, if two input vertices\n");
    printf(
  "        have exactly the same coordinates, only the first appears in the\n");
    printf(
  "        output.  If any vertices are jettisoned, the vertex numbering in\n");
    printf(
  "        the output .node file differs from that of the input .node file.\n");
    printf(
  "    -e  Outputs (to an .edge file) a list of edges of the triangulation.\n");
    printf(
  "    -v  Outputs the Voronoi diagram associated with the triangulation.\n");
    printf(
  "        Does not attempt to detect degeneracies, so some Voronoi vertices\n");
    printf(
  "        may be duplicated.  See the discussion of Voronoi diagrams below.\n");
    printf(
  "    -n  Outputs (to a .neigh file) a list of triangles neighboring each\n");
    printf("        triangle.\n");
    printf(
  "    -g  Outputs the mesh to an Object File Format (.off) file, suitable for\n"
  );
    printf("        viewing with the Geometry Center's Geomview package.\n");
    printf(
  "    -B  No boundary markers in the output .node, .poly, and .edge output\n");
    printf(
  "        files.  See the detailed discussion of boundary markers below.\n");
    printf(
  "    -P  No output .poly file.  Saves disk space, but you lose the ability\n");
    printf(
  "        to maintain constraining segments on later refinements of the mesh.\n"
  );
    printf("    -N  No output .node file.\n");
    printf("    -E  No output .ele file.\n");
    printf(
  "    -I  No iteration numbers.  Suppresses the output of .node and .poly\n");
    printf(
  "        files, so your input files won't be overwritten.  (If your input is\n"
  );
    printf(
  "        a .poly file only, a .node file is written.)  Cannot be used with\n");
    printf(
  "        the -r switch, because that would overwrite your input .ele file.\n");
    printf(
  "        Shouldn't be used with the -q, -a, -u, or -s switch if you are\n");
    printf(
  "        using a .node file for input, because no .node file is written, so\n"
  );
    printf("        there is no record of any added Steiner points.\n");
    printf("    -O  No holes.  Ignores the holes in the .poly file.\n");
    printf(
  "    -X  No exact arithmetic.  Normally, Triangle uses exact floating-point\n"
  );
    printf(
  "        arithmetic for certain tests if it thinks the inexact tests are not\n"
  );
    printf(
  "        accurate enough.  Exact arithmetic ensures the robustness of the\n");
    printf(
  "        triangulation algorithms, despite floating-point roundoff error.\n");
    printf(
  "        Disabling exact arithmetic with the -X switch causes a small\n");
    printf(
  "        improvement in speed and creates the possibility that Triangle will\n"
  );
    printf("        fail to produce a valid mesh.  Not recommended.\n");
    printf(
  "    -z  Numbers all items starting from zero (rather than one).  Note that\n"
  );
    printf(
  "        this switch is normally overridden by the value used to number the\n"
  );
    printf(
  "        first vertex of the input .node or .poly file.  However, this\n");
    printf(
  "        switch is useful when calling Triangle from another program.\n");
    printf(
  "    -o2 Generates second-order subparametric elements with six nodes each.\n"
  );
    printf(
  "    -Y  No new vertices on the boundary.  This switch is useful when the\n");
    printf(
  "        mesh boundary must be preserved so that it conforms to some\n");
    printf(
  "        adjacent mesh.  Be forewarned that you will probably sacrifice much\n"
  );
    printf(
  "        of the quality of the mesh; Triangle will try, but the resulting\n");
    printf(
  "        mesh may contain poorly shaped triangles.  Works well if all the\n");
    printf(
  "        boundary vertices are closely spaced.  Specify this switch twice\n");
    printf(
  "        (`-YY') to prevent all segment splitting, including internal\n");
    printf("        boundaries.\n");
    printf(
  "    -S  Specifies the maximum number of Steiner points (vertices that are\n");
    printf(
  "        not in the input, but are added to meet the constraints on minimum\n"
  );
    printf(
  "        angle and maximum area).  The default is to allow an unlimited\n");
    printf(
  "        number.  If you specify this switch with no number after it,\n");
    printf(
  "        the limit is set to zero.  Triangle always adds vertices at segment\n"
  );
    printf(
  "        intersections, even if it needs to use more vertices than the limit\n"
  );
    printf(
  "        you set.  When Triangle inserts segments by splitting (-s), it\n");
    printf(
  "        always adds enough vertices to ensure that all the segments of the\n"
  );
    printf("        PLSG are recovered, ignoring the limit if necessary.\n");
    printf(
  "    -i  Uses an incremental rather than a divide-and-conquer algorithm to\n");
    printf(
  "        construct a Delaunay triangulation.  Try it if the divide-and-\n");
    printf("        conquer algorithm fails.\n");
    printf(
  "    -F  Uses Steven Fortune's sweepline algorithm to construct a Delaunay\n");
    printf(
  "        triangulation.  Warning:  does not use exact arithmetic for all\n");
    printf("        calculations.  An exact result is not guaranteed.\n");
    printf(
  "    -l  Uses only vertical cuts in the divide-and-conquer algorithm.  By\n");
    printf(
  "        default, Triangle alternates between vertical and horizontal cuts,\n"
  );
    printf(
  "        which usually improve the speed except with vertex sets that are\n");
    printf(
  "        small or short and wide.  This switch is primarily of theoretical\n");
    printf("        interest.\n");
    printf(
  "    -s  Specifies that segments should be forced into the triangulation by\n"
  );
    printf(
  "        recursively splitting them at their midpoints, rather than by\n");
    printf(
  "        generating a constrained Delaunay triangulation.  Segment splitting\n"
  );
    printf(
  "        is true to Ruppert's original algorithm, but can create needlessly\n"
  );
    printf(
  "        small triangles.  This switch is primarily of theoretical interest.\n"
  );
    printf(
  "    -C  Check the consistency of the final mesh.  Uses exact arithmetic for\n"
  );
    printf(
  "        checking, even if the -X switch is used.  Useful if you suspect\n");
    printf("        Triangle is buggy.\n");
    printf(
  "    -Q  Quiet:  Suppresses all explanation of what Triangle is doing,\n");
    printf("        unless an error occurs.\n");
    printf(
  "    -V  Verbose:  Gives detailed information about what Triangle is doing.\n"
  );
    printf(
  "        Add more `V's for increasing amount of detail.  `-V' is most\n");
    printf(
  "        useful; itgives information on algorithmic progress and much more\n");
    printf(
  "        detailed statistics.  `-VV' gives vertex-by-vertex details, and\n");
    printf(
  "        prints so much that Triangle runs much more slowly.  `-VVVV' gives\n"
  );
    printf("        information only a debugger could love.\n");
    printf("    -h  Help:  Displays these instructions.\n");
    printf("\n");
    printf("Definitions:\n");
    printf("\n");
    printf(
  "  A Delaunay triangulation of a vertex set is a triangulation whose\n");
    printf(
  "  vertices are the vertex set, that covers the convex hull of the vertex\n");
    printf(
  "  set.  A Delaunay triangulation has the property that no vertex lies\n");
    printf(
  "  inside the circumscribing circle (circle that passes through all three\n");
    printf("  vertices) of any triangle in the triangulation.\n\n");
    printf(
  "  A Voronoi diagram of a vertex set is a subdivision of the plane into\n");
    printf(
  "  polygonal cells (some of which may be unbounded, meaning infinitely\n");
    printf(
  "  large), where each cell is the set of points in the plane that are closer\n"
  );
    printf(
  "  to some input vertex than to any other input vertex.  The Voronoi diagram\n"
  );
    printf("  is a geometric dual of the Delaunay triangulation.\n\n");
    printf(
  "  A Planar Straight Line Graph (PSLG) is a set of vertices and segments.\n");
    printf(
  "  Segments are simply edges, whose endpoints are all vertices in the PSLG.\n"
  );
    printf(
  "  Segments may intersect each other only at their endpoints.  The file\n");
    printf("  format for PSLGs (.poly files) is described below.\n\n");
    printf(
  "  A constrained Delaunay triangulation (CDT) of a PSLG is similar to a\n");
    printf(
  "  Delaunay triangulation, but each PSLG segment is present as a single edge\n"
  );
    printf(
  "  of the CDT.  (A constrained Delaunay triangulation is not truly a\n");
    printf(
  "  Delaunay triangulation, because some of its triangles might not be\n");
    printf(
  "  Delaunay.)  By definition, a CDT does not have any vertices other than\n");
    printf(
  "  those specified in the input PSLG.  Depending on context, a CDT might\n");
    printf(
  "  cover the convex hull of the PSLG, or it might cover only a segment-\n");
    printf("  bounded region (e.g. a polygon).\n\n");
    printf(
  "  A conforming Delaunay triangulation of a PSLG is a triangulation in which\n"
  );
    printf(
  "  each triangle is truly Delaunay, and each PSLG segment is represented by\n"
  );
    printf(
  "  a linear contiguous sequence of edges of the triangulation.  New vertices\n"
  );
    printf(
  "  (not part of the PSLG) may appear, and each input segment may have been\n");
    printf(
  "  subdivided into shorter edges (subsegments) by these additional vertices.\n"
  );
    printf(
  "  The new vertices are frequently necessary to maintain the Delaunay\n");
    printf("  property while ensuring that every segment is represented.\n\n");
    printf(
  "  A conforming constrained Delaunay triangulation (CCDT) of a PSLG is a\n");
    printf(
  "  triangulation of a PSLG whose triangles are constrained Delaunay.  New\n");
    printf("  vertices may appear, and input segments may be subdivided into\n");
    printf(
  "  subsegments, but not to guarantee that segments are respected; rather, to\n"
  );
    printf(
  "  improve the quality of the triangles.  The high-quality meshes produced\n");
    printf(
  "  by the -q switch are usually CCDTs, but can be made conforming Delaunay\n");
    printf("  with the -D switch.\n\n");
    printf("File Formats:\n\n");
    printf(
  "  All files may contain comments prefixed by the character '#'.  Vertices,\n"
  );
    printf(
  "  triangles, edges, holes, and maximum area constraints must be numbered\n");
    printf(
  "  consecutively, starting from either 1 or 0.  Whichever you choose, all\n");
    printf(
  "  input files must be consistent; if the vertices are numbered from 1, so\n");
    printf(
  "  must be all other objects.  Triangle automatically detects your choice\n");
    printf(
  "  while reading the .node (or .poly) file.  (When calling Triangle from\n");
    printf(
  "  another program, use the -z switch if you wish to number objects from\n");
    printf("  zero.)  Examples of these file formats are given below.\n\n");
    printf("  .node files:\n");
    printf(
  "    First line:  <# of vertices> <dimension (must be 2)> <# of attributes>\n"
  );
    printf(
  "                                           <# of boundary markers (0 or 1)>\n"
  );
    printf(
  "    Remaining lines:  <vertex #> <x> <y> [attributes] [boundary marker]\n");
    printf("\n");
    printf(
  "    The attributes, which are typically floating-point values of physical\n");
    printf(
  "    quantities (such as mass or conductivity) associated with the nodes of\n"
  );
    printf(
  "    a finite element mesh, are copied unchanged to the output mesh.  If -q,\n"
  );
    printf(
  "    -a, -u, -D, or -s is selected, each new Steiner point added to the mesh\n"
  );
    printf("    has attributes assigned to it by linear interpolation.\n\n");
    printf(
  "    If the fourth entry of the first line is `1', the last column of the\n");
    printf(
  "    remainder of the file is assumed to contain boundary markers.  Boundary\n"
  );
    printf(
  "    markers are used to identify boundary vertices and vertices resting on\n"
  );
    printf(
  "    PSLG segments; a complete description appears in a section below.  The\n"
  );
    printf(
  "    .node file produced by Triangle contains boundary markers in the last\n");
    printf("    column unless they are suppressed by the -B switch.\n\n");
    printf("  .ele files:\n");
    printf(
  "    First line:  <# of triangles> <nodes per triangle> <# of attributes>\n");
    printf(
  "    Remaining lines:  <triangle #> <node> <node> <node> ... [attributes]\n");
    printf("\n");
    printf(
  "    Nodes are indices into the corresponding .node file.  The first three\n");
    printf(
  "    nodes are the corner vertices, and are listed in counterclockwise order\n"
  );
    printf(
  "    around each triangle.  (The remaining nodes, if any, depend on the type\n"
  );
    printf("    of finite element used.)\n\n");
    printf(
  "    The attributes are just like those of .node files.  Because there is no\n"
  );
    printf(
  "    simple mapping from input to output triangles, Triangle attempts to\n");
    printf(
  "    interpolate attributes, and may cause a lot of diffusion of attributes\n"
  );
    printf(
  "    among nearby triangles as the triangulation is refined.  Attributes do\n"
  );
    printf("    not diffuse across segments, so attributes used to identify\n");
    printf("    segment-bounded regions remain intact.\n\n");
    printf(
  "    In .ele files produced by Triangle, each triangular element has three\n");
    printf(
  "    nodes (vertices) unless the -o2 switch is used, in which case\n");
    printf(
  "    subparametric quadratic elements with six nodes each are generated.\n");
    printf(
  "    The first three nodes are the corners in counterclockwise order, and\n");
    printf(
  "    the fourth, fifth, and sixth nodes lie on the midpoints of the edges\n");
    printf(
  "    opposite the first, second, and third vertices, respectively.\n");
    printf("\n");
    printf("  .poly files:\n");
    printf(
  "    First line:  <# of vertices> <dimension (must be 2)> <# of attributes>\n"
  );
    printf(
  "                                           <# of boundary markers (0 or 1)>\n"
  );
    printf(
  "    Following lines:  <vertex #> <x> <y> [attributes] [boundary marker]\n");
    printf("    One line:  <# of segments> <# of boundary markers (0 or 1)>\n");
    printf(
  "    Following lines:  <segment #> <endpoint> <endpoint> [boundary marker]\n");
    printf("    One line:  <# of holes>\n");
    printf("    Following lines:  <hole #> <x> <y>\n");
    printf(
  "    Optional line:  <# of regional attributes and/or area constraints>\n");
    printf(
  "    Optional following lines:  <region #> <x> <y> <attribute> <max area>\n");
    printf("\n");
    printf(
  "    A .poly file represents a PSLG, as well as some additional information.\n"
  );
    printf(
  "    The first section lists all the vertices, and is identical to the\n");
    printf(
  "    format of .node files.  <# of vertices> may be set to zero to indicate\n"
  );
    printf(
  "    that the vertices are listed in a separate .node file; .poly files\n");
    printf(
  "    produced by Triangle always have this format.  A vertex set represented\n"
  );
    printf(
  "    this way has the advantage that it may easily be triangulated with or\n");
    printf(
  "    without segments (depending on whether the -p switch is invoked).\n");
    printf("\n");
    printf(
  "    The second section lists the segments.  Segments are edges whose\n");
    printf(
  "    presence in the triangulation is enforced.  (Depending on the choice of\n"
  );
    printf(
  "    switches, segment might be subdivided into smaller edges).  Each\n");
    printf(
  "    segment is specified by listing the indices of its two endpoints.  This\n"
  );
    printf(
  "    means that you must include its endpoints in the vertex list.  Each\n");
    printf("    segment, like each point, may have a boundary marker.\n\n");
    printf(
  "    If -q, -a, -u, and -s are not selected, Triangle produces a constrained\n"
  );
    printf(
  "    Delaunay triangulation (CDT), in which each segment appears as a single\n"
  );
    printf(
  "    edge in the triangulation.  If -q, -a, -u, or -s is selected, Triangle\n"
  );
    printf(
  "    produces a conforming constrained Delaunay triangulation (CCDT), in\n");
    printf(
  "    which segments may be subdivided into smaller edges.  If -D is\n");
    printf(
  "    selected, Triangle produces a conforming Delaunay triangulation, so\n");
    printf(
  "    that every triangle is Delaunay, and not just constrained Delaunay.\n");
    printf("\n");
    printf(
  "    The third section lists holes (and concavities, if -c is selected) in\n");
    printf(
  "    the triangulation.  Holes are specified by identifying a point inside\n");
    printf(
  "    each hole.  After the triangulation is formed, Triangle creates holes\n");
    printf(
  "    by eating triangles, spreading out from each hole point until its\n");
    printf(
  "    progress is blocked by segments in the PSLG.  You must be careful to\n");
    printf(
  "    enclose each hole in segments, or your whole triangulation might be\n");
    printf(
  "    eaten away.  If the two triangles abutting a segment are eaten, the\n");
    printf(
  "    segment itself is also eaten.  Do not place a hole directly on a\n");
    printf("    segment; if you do, Triangle chooses one side of the segment\n");
    printf("    arbitrarily.\n\n");
    printf(
  "    The optional fourth section lists regional attributes (to be assigned\n");
    printf(
  "    to all triangles in a region) and regional constraints on the maximum\n");
    printf(
  "    triangle area.  Triangle reads this section only if the -A switch is\n");
    printf(
  "    used or the -a switch is used without a number following it, and the -r\n"
  );
    printf(
  "    switch is not used.  Regional attributes and area constraints are\n");
    printf(
  "    propagated in the same manner as holes:  you specify a point for each\n");
    printf(
  "    attribute and/or constraint, and the attribute and/or constraint\n");
    printf(
  "    affects the whole region (bounded by segments) containing the point.\n");
    printf(
  "    If two values are written on a line after the x and y coordinate, the\n");
    printf(
  "    first such value is assumed to be a regional attribute (but is only\n");
    printf(
  "    applied if the -A switch is selected), and the second value is assumed\n"
  );
    printf(
  "    to be a regional area constraint (but is only applied if the -a switch\n"
  );
    printf(
  "    is selected).  You may specify just one value after the coordinates,\n");
    printf(
  "    which can serve as both an attribute and an area constraint, depending\n"
  );
    printf(
  "    on the choice of switches.  If you are using the -A and -a switches\n");
    printf(
  "    simultaneously and wish to assign an attribute to some region without\n");
    printf("    imposing an area constraint, use a negative maximum area.\n\n");
    printf(
  "    When a triangulation is created from a .poly file, you must either\n");
    printf(
  "    enclose the entire region to be triangulated in PSLG segments, or\n");
    printf(
  "    use the -c switch, which automatically creates extra segments that\n");
    printf(
  "    enclose the convex hull of the PSLG.  If you do not use the -c switch,\n"
  );
    printf(
  "    Triangle eats all triangles that are not enclosed by segments; if you\n");
    printf(
  "    are not careful, your whole triangulation may be eaten away.  If you do\n"
  );
    printf(
  "    use the -c switch, you can still produce concavities by the appropriate\n"
  );
    printf(
  "    placement of holes just inside the boundary of the convex hull.\n");
    printf("\n");
    printf(
  "    An ideal PSLG has no intersecting segments, nor any vertices that lie\n");
    printf(
  "    upon segments (except, of course, the endpoints of each segment).  You\n"
  );
    printf(
  "    aren't required to make your .poly files ideal, but you should be aware\n"
  );
    printf(
  "    of what can go wrong.  Segment intersections are relatively safe--\n");
    printf(
  "    Triangle calculates the intersection points for you and adds them to\n");
    printf(
  "    the triangulation--as long as your machine's floating-point precision\n");
    printf(
  "    doesn't become a problem.  You are tempting the fates if you have three\n"
  );
    printf(
  "    segments that cross at the same location, and expect Triangle to figure\n"
  );
    printf(
  "    out where the intersection point is.  Thanks to floating-point roundoff\n"
  );
    printf(
  "    error, Triangle will probably decide that the three segments intersect\n"
  );
    printf(
  "    at three different points, and you will find a minuscule triangle in\n");
    printf(
  "    your output--unless Triangle tries to refine the tiny triangle, uses\n");
    printf(
  "    up the last bit of machine precision, and fails to terminate at all.\n");
    printf(
  "    You're better off putting the intersection point in the input files,\n");
    printf(
  "    and manually breaking up each segment into two.  Similarly, if you\n");
    printf(
  "    place a vertex at the middle of a segment, and hope that Triangle will\n"
  );
    printf(
  "    break up the segment at that vertex, you might get lucky.  On the other\n"
  );
    printf(
  "    hand, Triangle might decide that the vertex doesn't lie precisely on\n");
    printf(
  "    the segment, and you'll have a needle-sharp triangle in your output--or\n"
  );
    printf("    a lot of tiny triangles if you're generating a quality mesh.\n");
    printf("\n");
    printf(
  "    When Triangle reads a .poly file, it also writes a .poly file, which\n");
    printf(
  "    includes all the subsegments--the edges that are parts of input\n");
    printf(
  "    segments.  If the -c switch is used, the output .poly file also\n");
    printf(
  "    includes all of the edges on the convex hull.  Hence, the output .poly\n"
  );
    printf(
  "    file is useful for finding edges associated with input segments and for\n"
  );
    printf(
  "    setting boundary conditions in finite element simulations.  Moreover,\n");
    printf(
  "    you will need the output .poly file if you plan to refine the output\n");
    printf(
  "    mesh, and don't want segments to be missing in later triangulations.\n");
    printf("\n");
    printf("  .area files:\n");
    printf("    First line:  <# of triangles>\n");
    printf("    Following lines:  <triangle #> <maximum area>\n");
    printf("\n");
    printf(
  "    An .area file associates with each triangle a maximum area that is used\n"
  );
    printf(
  "    for mesh refinement.  As with other file formats, every triangle must\n");
    printf(
  "    be represented, and the triangles must be numbered consecutively.  A\n");
    printf(
  "    triangle may be left unconstrained by assigning it a negative maximum\n");
    printf("    area.\n\n");
    printf("  .edge files:\n");
    printf("    First line:  <# of edges> <# of boundary markers (0 or 1)>\n");
    printf(
  "    Following lines:  <edge #> <endpoint> <endpoint> [boundary marker]\n");
    printf("\n");
    printf(
  "    Endpoints are indices into the corresponding .node file.  Triangle can\n"
  );
    printf(
  "    produce .edge files (use the -e switch), but cannot read them.  The\n");
    printf(
  "    optional column of boundary markers is suppressed by the -B switch.\n");
    printf("\n");
    printf(
  "    In Voronoi diagrams, one also finds a special kind of edge that is an\n");
    printf(
  "    infinite ray with only one endpoint.  For these edges, a different\n");
    printf("    format is used:\n\n");
    printf("        <edge #> <endpoint> -1 <direction x> <direction y>\n\n");
    printf(
  "    The `direction' is a floating-point vector that indicates the direction\n"
  );
    printf("    of the infinite ray.\n\n");
    printf("  .neigh files:\n");
    printf(
  "    First line:  <# of triangles> <# of neighbors per triangle (always 3)>\n"
  );
    printf(
  "    Following lines:  <triangle #> <neighbor> <neighbor> <neighbor>\n");
    printf("\n");
    printf(
  "    Neighbors are indices into the corresponding .ele file.  An index of -1\n"
  );
    printf(
  "    indicates no neighbor (because the triangle is on an exterior\n");
    printf(
  "    boundary).  The first neighbor of triangle i is opposite the first\n");
    printf("    corner of triangle i, and so on.\n\n");
    printf(
  "    Triangle can produce .neigh files (use the -n switch), but cannot read\n"
  );
    printf("    them.\n\n");
    printf("Boundary Markers:\n\n");
    printf(
  "  Boundary markers are tags used mainly to identify which output vertices\n");
    printf(
  "  and edges are associated with which PSLG segment, and to identify which\n");
    printf(
  "  vertices and edges occur on a boundary of the triangulation.  A common\n");
    printf(
  "  use is to determine where boundary conditions should be applied to a\n");
    printf(
  "  finite element mesh.  You can prevent boundary markers from being written\n"
  );
    printf("  into files produced by Triangle by using the -B switch.\n\n");
    printf(
  "  The boundary marker associated with each segment in an output .poly file\n"
  );
    printf("  and each edge in an output .edge file is chosen as follows:\n");
    printf(
  "    - If an output edge is part or all of a PSLG segment with a nonzero\n");
    printf(
  "      boundary marker, then the edge is assigned the same marker.\n");
    printf(
  "    - Otherwise, if the edge lies on a boundary of the triangulation\n");
    printf(
  "      (even the boundary of a hole), then the edge is assigned the marker\n");
    printf("      one (1).\n");
    printf("    - Otherwise, the edge is assigned the marker zero (0).\n");
    printf(
  "  The boundary marker associated with each vertex in an output .node file\n");
    printf("  is chosen as follows:\n");
    printf(
  "    - If a vertex is assigned a nonzero boundary marker in the input file,\n"
  );
    printf(
  "      then it is assigned the same marker in the output .node file.\n");
    printf(
  "    - Otherwise, if the vertex lies on a PSLG segment (even if it is an\n");
    printf(
  "      endpoint of the segment) with a nonzero boundary marker, then the\n");
    printf(
  "      vertex is assigned the same marker.  If the vertex lies on several\n");
    printf("      such segments, one of the markers is chosen arbitrarily.\n");
    printf(
  "    - Otherwise, if the vertex occurs on a boundary of the triangulation,\n");
    printf("      then the vertex is assigned the marker one (1).\n");
    printf("    - Otherwise, the vertex is assigned the marker zero (0).\n");
    printf("\n");
    printf(
  "  If you want Triangle to determine for you which vertices and edges are on\n"
  );
    printf(
  "  the boundary, assign them the boundary marker zero (or use no markers at\n"
  );
    printf(
  "  all) in your input files.  In the output files, all boundary vertices,\n");
    printf("  edges, and segments will be assigned the value one.\n\n");
    printf("Triangulation Iteration Numbers:\n\n");
    printf(
  "  Because Triangle can read and refine its own triangulations, input\n");
    printf(
  "  and output files have iteration numbers.  For instance, Triangle might\n");
    printf(
  "  read the files mesh.3.node, mesh.3.ele, and mesh.3.poly, refine the\n");
    printf(
  "  triangulation, and output the files mesh.4.node, mesh.4.ele, and\n");
    printf("  mesh.4.poly.  Files with no iteration number are treated as if\n");
    printf(
  "  their iteration number is zero; hence, Triangle might read the file\n");
    printf(
  "  points.node, triangulate it, and produce the files points.1.node and\n");
    printf("  points.1.ele.\n\n");
    printf(
  "  Iteration numbers allow you to create a sequence of successively finer\n");
    printf(
  "  meshes suitable for multigrid methods.  They also allow you to produce a\n"
  );
    printf(
  "  sequence of meshes using error estimate-driven mesh refinement.\n");
    printf("\n");
    printf(
  "  If you're not using refinement or quality meshing, and you don't like\n");
    printf(
  "  iteration numbers, use the -I switch to disable them.  This switch also\n");
    printf(
  "  disables output of .node and .poly files to prevent your input files from\n"
  );
    printf(
  "  being overwritten.  (If the input is a .poly file that contains its own\n");
    printf(
  "  points, a .node file is written.  This can be quite convenient for\n");
    printf("  computing CDTs or quality meshes.)\n\n");
    printf("Examples of How to Use Triangle:\n\n");
    printf(
  "  `triangle dots' reads vertices from dots.node, and writes their Delaunay\n"
  );
    printf(
  "  triangulation to dots.1.node and dots.1.ele.  (dots.1.node is identical\n");
    printf(
  "  to dots.node.)  `triangle -I dots' writes the triangulation to dots.ele\n");
    printf(
  "  instead.  (No additional .node file is needed, so none is written.)\n");
    printf("\n");
    printf(
  "  `triangle -pe object.1' reads a PSLG from object.1.poly (and possibly\n");
    printf(
  "  object.1.node, if the vertices are omitted from object.1.poly) and writes\n"
  );
    printf(
  "  its constrained Delaunay triangulation to object.2.node and object.2.ele.\n"
  );
    printf(
  "  The segments are copied to object.2.poly, and all edges are written to\n");
    printf("  object.2.edge.\n\n");
    printf(
  "  `triangle -pq31.5a.1 object' reads a PSLG from object.poly (and possibly\n"
  );
    printf(
  "  object.node), generates a mesh whose angles are all between 31.5 and 117\n"
  );
    printf(
  "  degrees and whose triangles all have areas of 0.1 or less, and writes the\n"
  );
    printf(
  "  mesh to object.1.node and object.1.ele.  Each segment may be broken up\n");
    printf("  into multiple subsegments; these are written to object.1.poly.\n");
    printf("\n");
    printf(
  "  Here is a sample file `box.poly' describing a square with a square hole:\n"
  );
    printf("\n");
    printf(
  "    # A box with eight vertices in 2D, no attributes, one boundary marker.\n"
  );
    printf("    8 2 0 1\n");
    printf("     # Outer box has these vertices:\n");
    printf("     1   0 0   0\n");
    printf("     2   0 3   0\n");
    printf("     3   3 0   0\n");
    printf("     4   3 3   33     # A special marker for this vertex.\n");
    printf("     # Inner square has these vertices:\n");
    printf("     5   1 1   0\n");
    printf("     6   1 2   0\n");
    printf("     7   2 1   0\n");
    printf("     8   2 2   0\n");
    printf("    # Five segments with boundary markers.\n");
    printf("    5 1\n");
    printf("     1   1 2   5      # Left side of outer box.\n");
    printf("     # Square hole has these segments:\n");
    printf("     2   5 7   0\n");
    printf("     3   7 8   0\n");
    printf("     4   8 6   10\n");
    printf("     5   6 5   0\n");
    printf("    # One hole in the middle of the inner square.\n");
    printf("    1\n");
    printf("     1   1.5 1.5\n");
    printf("\n");
    printf(
  "  Note that some segments are missing from the outer square, so you must\n");
    printf(
  "  use the `-c' switch.  After `triangle -pqc box.poly', here is the output\n"
  );
    printf(
  "  file `box.1.node', with twelve vertices.  The last four vertices were\n");
    printf(
  "  added to meet the angle constraint.  Vertices 1, 2, and 9 have markers\n");
    printf(
  "  from segment 1.  Vertices 6 and 8 have markers from segment 4.  All the\n");
    printf(
  "  other vertices but 4 have been marked to indicate that they lie on a\n");
    printf("  boundary.\n\n");
    printf("    12  2  0  1\n");
    printf("       1    0   0      5\n");
    printf("       2    0   3      5\n");
    printf("       3    3   0      1\n");
    printf("       4    3   3     33\n");
    printf("       5    1   1      1\n");
    printf("       6    1   2     10\n");
    printf("       7    2   1      1\n");
    printf("       8    2   2     10\n");
    printf("       9    0   1.5    5\n");
    printf("      10    1.5   0    1\n");
    printf("      11    3   1.5    1\n");
    printf("      12    1.5   3    1\n");
    printf("    # Generated by triangle -pqc box.poly\n");
    printf("\n");
    printf("  Here is the output file `box.1.ele', with twelve triangles.\n");
    printf("\n");
    printf("    12  3  0\n");
    printf("       1     5   6   9\n");
    printf("       2    10   3   7\n");
    printf("       3     6   8  12\n");
    printf("       4     9   1   5\n");
    printf("       5     6   2   9\n");
    printf("       6     7   3  11\n");
    printf("       7    11   4   8\n");
    printf("       8     7   5  10\n");
    printf("       9    12   2   6\n");
    printf("      10     8   7  11\n");
    printf("      11     5   1  10\n");
    printf("      12     8   4  12\n");
    printf("    # Generated by triangle -pqc box.poly\n\n");
    printf(
  "  Here is the output file `box.1.poly'.  Note that segments have been added\n"
  );
    printf(
  "  to represent the convex hull, and some segments have been subdivided by\n");
    printf(
  "  newly added vertices.  Note also that <# of vertices> is set to zero to\n");
    printf("  indicate that the vertices should be read from the .node file.\n");
    printf("\n");
    printf("    0  2  0  1\n");
    printf("    12  1\n");
    printf("       1     1   9     5\n");
    printf("       2     5   7     1\n");
    printf("       3     8   7     1\n");
    printf("       4     6   8    10\n");
    printf("       5     5   6     1\n");
    printf("       6     3  10     1\n");
    printf("       7     4  11     1\n");
    printf("       8     2  12     1\n");
    printf("       9     9   2     5\n");
    printf("      10    10   1     1\n");
    printf("      11    11   3     1\n");
    printf("      12    12   4     1\n");
    printf("    1\n");
    printf("       1   1.5 1.5\n");
    printf("    # Generated by triangle -pqc box.poly\n");
    printf("\n");
    printf("Refinement and Area Constraints:\n");
    printf("\n");
    printf(
  "  The -r switch causes a mesh (.node and .ele files) to be read and\n");
    printf(
  "  refined.  If the -p switch is also used, a .poly file is read and used to\n"
  );
    printf(
  "  specify edges that are constrained and cannot be eliminated (although\n");
    printf(
  "  they can be subdivided into smaller edges) by the refinement process.\n");
    printf("\n");
    printf(
  "  When you refine a mesh, you generally want to impose tighter constraints.\n"
  );
    printf(
  "  One way to accomplish this is to use -q with a larger angle, or -a\n");
    printf(
  "  followed by a smaller area than you used to generate the mesh you are\n");
    printf(
  "  refining.  Another way to do this is to create an .area file, which\n");
    printf(
  "  specifies a maximum area for each triangle, and use the -a switch\n");
    printf(
  "  (without a number following).  Each triangle's area constraint is applied\n"
  );
    printf(
  "  to that triangle.  Area constraints tend to diffuse as the mesh is\n");
    printf(
  "  refined, so if there are large variations in area constraint between\n");
    printf(
  "  adjacent triangles, you may not get the results you want.  In that case,\n"
  );
    printf(
  "  consider instead using the -u switch and writing a C procedure that\n");
    printf("  determines which triangles are too large.\n\n");
    printf(
  "  If you are refining a mesh composed of linear (three-node) elements, the\n"
  );
    printf(
  "  output mesh contains all the nodes present in the input mesh, in the same\n"
  );
    printf(
  "  order, with new nodes added at the end of the .node file.  However, the\n");
    printf(
  "  refinement is not hierarchical: there is no guarantee that each output\n");
    printf(
  "  element is contained in a single input element.  Often, an output element\n"
  );
    printf(
  "  can overlap two or three input elements, and some input edges are not\n");
    printf(
  "  present in the output mesh.  Hence, a sequence of refined meshes forms a\n"
  );
    printf(
  "  hierarchy of nodes, but not a hierarchy of elements.  If you refine a\n");
    printf(
  "  mesh of higher-order elements, the hierarchical property applies only to\n"
  );
    printf(
  "  the nodes at the corners of an element; the midpoint nodes on each edge\n");
    printf("  are discarded before the mesh is refined.\n\n");
    printf(
  "  Maximum area constraints in .poly files operate differently from those in\n"
  );
    printf(
  "  .area files.  A maximum area in a .poly file applies to the whole\n");
    printf(
  "  (segment-bounded) region in which a point falls, whereas a maximum area\n");
    printf(
  "  in an .area file applies to only one triangle.  Area constraints in .poly\n"
  );
    printf(
  "  files are used only when a mesh is first generated, whereas area\n");
    printf(
  "  constraints in .area files are used only to refine an existing mesh, and\n"
  );
    printf(
  "  are typically based on a posteriori error estimates resulting from a\n");
    printf("  finite element simulation on that mesh.\n\n");
    printf(
  "  `triangle -rq25 object.1' reads object.1.node and object.1.ele, then\n");
    printf(
  "  refines the triangulation to enforce a 25 degree minimum angle, and then\n"
  );
    printf(
  "  writes the refined triangulation to object.2.node and object.2.ele.\n");
    printf("\n");
    printf(
  "  `triangle -rpaa6.2 z.3' reads z.3.node, z.3.ele, z.3.poly, and z.3.area.\n"
  );
    printf(
  "  After reconstructing the mesh and its subsegments, Triangle refines the\n");
    printf(
  "  mesh so that no triangle has area greater than 6.2, and furthermore the\n");
    printf(
  "  triangles satisfy the maximum area constraints in z.3.area.  No angle\n");
    printf(
  "  bound is imposed at all.  The output is written to z.4.node, z.4.ele, and\n"
  );
    printf("  z.4.poly.\n\n");
    printf(
  "  The sequence `triangle -qa1 x', `triangle -rqa.3 x.1', `triangle -rqa.1\n");
    printf(
  "  x.2' creates a sequence of successively finer meshes x.1, x.2, and x.3,\n");
    printf("  suitable for multigrid.\n\n");
    printf("Convex Hulls and Mesh Boundaries:\n\n");
    printf(
  "  If the input is a vertex set (not a PSLG), Triangle produces its convex\n");
    printf(
  "  hull as a by-product in the output .poly file if you use the -c switch.\n");
    printf(
  "  There are faster algorithms for finding a two-dimensional convex hull\n");
    printf("  than triangulation, of course, but this one comes for free.\n\n");
    printf(
  "  If the input is an unconstrained mesh (you are using the -r switch but\n");
    printf(
  "  not the -p switch), Triangle produces a list of its boundary edges\n");
    printf(
  "  (including hole boundaries) as a by-product when you use the -c switch.\n");
    printf(
  "  If you also use the -p switch, the output .poly file contains all the\n");
    printf("  segments from the input .poly file as well.\n\n");
    printf("Voronoi Diagrams:\n\n");
    printf(
  "  The -v switch produces a Voronoi diagram, in files suffixed .v.node and\n");
    printf(
  "  .v.edge.  For example, `triangle -v points' reads points.node, produces\n");
    printf(
  "  its Delaunay triangulation in points.1.node and points.1.ele, and\n");
    printf(
  "  produces its Voronoi diagram in points.1.v.node and points.1.v.edge.  The\n"
  );
    printf(
  "  .v.node file contains a list of all Voronoi vertices, and the .v.edge\n");
    printf(
  "  file contains a list of all Voronoi edges, some of which may be infinite\n"
  );
    printf(
  "  rays.  (The choice of filenames makes it easy to run the set of Voronoi\n");
    printf("  vertices through Triangle, if so desired.)\n\n");
    printf(
  "  This implementation does not use exact arithmetic to compute the Voronoi\n"
  );
    printf(
  "  vertices, and does not check whether neighboring vertices are identical.\n"
  );
    printf(
  "  Be forewarned that if the Delaunay triangulation is degenerate or\n");
    printf(
  "  near-degenerate, the Voronoi diagram may have duplicate vertices or\n");
    printf("  crossing edges.\n\n");
    printf(
  "  The result is a valid Voronoi diagram only if Triangle's output is a true\n"
  );
    printf(
  "  Delaunay triangulation.  The Voronoi output is usually meaningless (and\n");
    printf(
  "  may contain crossing edges and other pathology) if the output is a CDT or\n"
  );
    printf(
  "  CCDT, or if it has holes or concavities.  If the triangulated domain is\n");
    printf(
  "  convex and has no holes, you can use -D switch to force Triangle to\n");
    printf(
  "  construct a conforming Delaunay triangulation instead of a CCDT, so the\n");
    printf("  Voronoi diagram will be valid.\n\n");
    printf("Mesh Topology:\n\n");
    printf(
  "  You may wish to know which triangles are adjacent to a certain Delaunay\n");
    printf(
  "  edge in an .edge file, which Voronoi cells are adjacent to a certain\n");
    printf(
  "  Voronoi edge in a .v.edge file, or which Voronoi cells are adjacent to\n");
    printf(
  "  each other.  All of this information can be found by cross-referencing\n");
    printf(
  "  output files with the recollection that the Delaunay triangulation and\n");
    printf("  the Voronoi diagram are planar duals.\n\n");
    printf(
  "  Specifically, edge i of an .edge file is the dual of Voronoi edge i of\n");
    printf(
  "  the corresponding .v.edge file, and is rotated 90 degrees counterclock-\n");
    printf(
  "  wise from the Voronoi edge.  Triangle j of an .ele file is the dual of\n");
    printf(
  "  vertex j of the corresponding .v.node file.  Voronoi cell k is the dual\n");
    printf("  of vertex k of the corresponding .node file.\n\n");
    printf(
  "  Hence, to find the triangles adjacent to a Delaunay edge, look at the\n");
    printf(
  "  vertices of the corresponding Voronoi edge.  If the endpoints of a\n");
    printf(
  "  Voronoi edge are Voronoi vertices 2 and 6 respectively, then triangles 2\n"
  );
    printf(
  "  and 6 adjoin the left and right sides of the corresponding Delaunay edge,\n"
  );
    printf(
  "  respectively.  To find the Voronoi cells adjacent to a Voronoi edge, look\n"
  );
    printf(
  "  at the endpoints of the corresponding Delaunay edge.  If the endpoints of\n"
  );
    printf(
  "  a Delaunay edge are input vertices 7 and 12, then Voronoi cells 7 and 12\n"
  );
    printf(
  "  adjoin the right and left sides of the corresponding Voronoi edge,\n");
    printf(
  "  respectively.  To find which Voronoi cells are adjacent to each other,\n");
    printf("  just read the list of Delaunay edges.\n\n");
    printf(
  "  Triangle does not write a list of the edges adjoining each Voronoi cell,\n"
  );
    printf(
  "  but you can reconstructed it straightforwardly.  For instance, to find\n");
    printf(
  "  all the edges of Voronoi cell 1, search the output .edge file for every\n");
    printf(
  "  edge that has input vertex 1 as an endpoint.  The corresponding dual\n");
    printf(
  "  edges in the output .v.edge file form the boundary of Voronoi cell 1.\n");
    printf("\n");
    printf(
  "  For each Voronoi vertex, the .neigh file gives a list of the three\n");
    printf(
  "  Voronoi vertices attached to it.  You might find this more convenient\n");
    printf("  than the .v.edge file.\n\n");
    printf("Quadratic Elements:\n\n");
    printf(
  "  Triangle generates meshes with subparametric quadratic elements if the\n");
    printf(
  "  -o2 switch is specified.  Quadratic elements have six nodes per element,\n"
  );
    printf(
  "  rather than three.  `Subparametric' means that the edges of the triangles\n"
  );
    printf(
  "  are always straight, so that subparametric quadratic elements are\n");
    printf(
  "  geometrically identical to linear elements, even though they can be used\n"
  );
    printf(
  "  with quadratic interpolating functions.  The three extra nodes of an\n");
    printf(
  "  element fall at the midpoints of the three edges, with the fourth, fifth,\n"
  );
    printf(
  "  and sixth nodes appearing opposite the first, second, and third corners\n");
    printf("  respectively.\n\n");
    printf("Domains with Small Angles:\n\n");
    printf(
  "  If two input segments adjoin each other at a small angle, clearly the -q\n"
  );
    printf(
  "  switch cannot remove the small angle.  Moreover, Triangle may have no\n");
    printf(
  "  choice but to generate additional triangles whose smallest angles are\n");
    printf(
  "  smaller than the specified bound.  However, these triangles only appear\n");
    printf(
  "  between input segments separated by small angles.  Moreover, if you\n");
    printf(
  "  request a minimum angle of theta degrees, Triangle will generally produce\n"
  );
    printf(
  "  no angle larger than 180 - 2 theta, even if it is forced to compromise on\n"
  );
    printf("  the minimum angle.\n\n");
    printf("Statistics:\n\n");
    printf(
  "  After generating a mesh, Triangle prints a count of entities in the\n");
    printf(
  "  output mesh, including the number of vertices, triangles, edges, exterior\n"
  );
    printf(
  "  boundary edges (i.e. subsegments on the boundary of the triangulation,\n");
    printf(
  "  including hole boundaries), interior boundary edges (i.e. subsegments of\n"
  );
    printf(
  "  input segments not on the boundary), and total subsegments.  If you've\n");
    printf(
  "  forgotten the statistics for an existing mesh, run Triangle on that mesh\n"
  );
    printf(
  "  with the -rNEP switches to read the mesh and print the statistics without\n"
  );
    printf(
  "  writing any files.  Use -rpNEP if you've got a .poly file for the mesh.\n");
    printf("\n");
    printf(
  "  The -V switch produces extended statistics, including a rough estimate\n");
    printf(
  "  of memory use, the number of calls to geometric predicates, and\n");
    printf(
  "  histograms of the angles and the aspect ratios of the triangles in the\n");
    printf("  mesh.\n\n");
    printf("Exact Arithmetic:\n\n");
    printf(
  "  Triangle uses adaptive exact arithmetic to perform what computational\n");
    printf(
  "  geometers call the `orientation' and `incircle' tests.  If the floating-\n"
  );
    printf(
  "  point arithmetic of your machine conforms to the IEEE 754 standard (as\n");
    printf(
  "  most workstations do), and does not use extended precision internal\n");
    printf(
  "  floating-point registers, then your output is guaranteed to be an\n");
    printf(
  "  absolutely true Delaunay or constrained Delaunay triangulation, roundoff\n"
  );
    printf(
  "  error notwithstanding.  The word `adaptive' implies that these arithmetic\n"
  );
    printf(
  "  routines compute the result only to the precision necessary to guarantee\n"
  );
    printf(
  "  correctness, so they are usually nearly as fast as their approximate\n");
    printf("  counterparts.\n\n");
    printf(
  "  May CPUs, including Intel x86 processors, have extended precision\n");
    printf(
  "  floating-point registers.  These must be reconfigured so their precision\n"
  );
    printf(
  "  is reduced to memory precision.  Triangle does this if it is compiled\n");
    printf("  correctly.  See the makefile for details.\n\n");
    printf(
  "  The exact tests can be disabled with the -X switch.  On most inputs, this\n"
  );
    printf(
  "  switch reduces the computation time by about eight percent--it's not\n");
    printf(
  "  worth the risk.  There are rare difficult inputs (having many collinear\n");
    printf(
  "  and cocircular vertices), however, for which the difference in speed\n");
    printf(
  "  could be a factor of two.  Be forewarned that these are precisely the\n");
    printf(
  "  inputs most likely to cause errors if you use the -X switch.  Hence, the\n"
  );
    printf("  -X switch is not recommended.\n\n");
    printf(
  "  Unfortunately, the exact tests don't solve every numerical problem.\n");
    printf(
  "  Exact arithmetic is not used to compute the positions of new vertices,\n");
    printf(
  "  because the bit complexity of vertex coordinates would grow without\n");
    printf(
  "  bound.  Hence, segment intersections aren't computed exactly; in very\n");
    printf(
  "  unusual cases, roundoff error in computing an intersection point might\n");
    printf(
  "  actually lead to an inverted triangle and an invalid triangulation.\n");
    printf(
  "  (This is one reason to specify your own intersection points in your .poly\n"
  );
    printf(
  "  files.)  Similarly, exact arithmetic is not used to compute the vertices\n"
  );
    printf("  of the Voronoi diagram.\n\n");
    printf(
  "  Another pair of problems not solved by the exact arithmetic routines is\n");
    printf(
  "  underflow and overflow.  If Triangle is compiled for double precision\n");
    printf(
  "  arithmetic, I believe that Triangle's geometric predicates work correctly\n"
  );
    printf(
  "  if the exponent of every input coordinate falls in the range [-148, 201].\n"
  );
    printf(
  "  Underflow can silently prevent the orientation and incircle tests from\n");
    printf(
  "  being performed exactly, while overflow typically causes a floating\n");
    printf("  exception.\n\n");
    printf("Calling Triangle from Another Program:\n\n");
    printf("  Read the file triangle.h for details.\n\n");
    printf("Troubleshooting:\n\n");
    printf("  Please read this section before mailing me bugs.\n\n");
    printf("  `My output mesh has no triangles!'\n\n");
    printf(
  "    If you're using a PSLG, you've probably failed to specify a proper set\n"
  );
    printf(
  "    of bounding segments, or forgotten to use the -c switch.  Or you may\n");
    printf(
  "    have placed a hole badly, thereby eating all your triangles.  To test\n");
    printf("    these possibilities, try again with the -c and -O switches.\n");
    printf(
  "    Alternatively, all your input vertices may be collinear, in which case\n"
  );
    printf("    you can hardly expect to triangulate them.\n\n");
    printf("  `Triangle doesn't terminate, or just crashes.'\n\n");
    printf(
  "    Bad things can happen when triangles get so small that the distance\n");
    printf(
  "    between their vertices isn't much larger than the precision of your\n");
    printf(
  "    machine's arithmetic.  If you've compiled Triangle for single-precision\n"
  );
    printf(
  "    arithmetic, you might do better by recompiling it for double-precision.\n"
  );
    printf(
  "    Then again, you might just have to settle for more lenient constraints\n"
  );
    printf(
  "    on the minimum angle and the maximum area than you had planned.\n");
    printf("\n");
    printf(
  "    You can minimize precision problems by ensuring that the origin lies\n");
    printf(
  "    inside your vertex set, or even inside the densest part of your\n");
    printf(
  "    mesh.  If you're triangulating an object whose x-coordinates all fall\n");
    printf(
  "    between 6247133 and 6247134, you're not leaving much floating-point\n");
    printf("    precision for Triangle to work with.\n\n");
    printf(
  "    Precision problems can occur covertly if the input PSLG contains two\n");
    printf(
  "    segments that meet (or intersect) at an extremely small angle, or if\n");
    printf(
  "    such an angle is introduced by the -c switch.  If you don't realize\n");
    printf(
  "    that a tiny angle is being formed, you might never discover why\n");
    printf(
  "    Triangle is crashing.  To check for this possibility, use the -S switch\n"
  );
    printf(
  "    (with an appropriate limit on the number of Steiner points, found by\n");
    printf(
  "    trial-and-error) to stop Triangle early, and view the output .poly file\n"
  );
    printf(
  "    with Show Me (described below).  Look carefully for regions where dense\n"
  );
    printf(
  "    clusters of vertices are forming and for small angles between segments.\n"
  );
    printf(
  "    Zoom in closely, as such segments might look like a single segment from\n"
  );
    printf("    a distance.\n\n");
    printf(
  "    If some of the input values are too large, Triangle may suffer a\n");
    printf(
  "    floating exception due to overflow when attempting to perform an\n");
    printf(
  "    orientation or incircle test.  (Read the section on exact arithmetic\n");
    printf(
  "    above.)  Again, I recommend compiling Triangle for double (rather\n");
    printf("    than single) precision arithmetic.\n\n");
    printf(
  "    Unexpected problems can arise if you use quality meshing (-q, -a, or\n");
    printf(
  "    -u) with an input that is not segment-bounded--that is, if your input\n");
    printf(
  "    is a vertex set, or you're using the -c switch.  If the convex hull of\n"
  );
    printf(
  "    your input vertices has collinear vertices on its boundary, an input\n");
    printf(
  "    vertex that you think lies on the convex hull might actually lie just\n");
    printf(
  "    inside the convex hull.  If so, the vertex and the nearby convex hull\n");
    printf(
  "    edge form an extremely thin triangle.  When Triangle tries to refine\n");
    printf(
  "    the mesh to enforce angle and area constraints, Triangle might generate\n"
  );
    printf(
  "    extremely tiny triangles, or it might fail because of insufficient\n");
    printf("    floating-point precision.\n\n");
    printf(
  "  `The numbering of the output vertices doesn't match the input vertices.'\n"
  );
    printf("\n");
    printf(
  "    You may have had duplicate input vertices, or you may have eaten some\n");
    printf(
  "    of your input vertices with a hole, or by placing them outside the area\n"
  );
    printf(
  "    enclosed by segments.  In any case, you can solve the problem by not\n");
    printf("    using the -j switch.\n\n");
    printf(
  "  `Triangle executes without incident, but when I look at the resulting\n");
    printf(
  "  mesh, it has overlapping triangles or other geometric inconsistencies.'\n");
    printf("\n");
    printf(
  "    If you select the -X switch, Triangle occasionally makes mistakes due\n");
    printf(
  "    to floating-point roundoff error.  Although these errors are rare,\n");
    printf(
  "    don't use the -X switch.  If you still have problems, please report the\n"
  );
    printf("    bug.\n\n");
    printf(
  "  `Triangle executes without incident, but when I look at the resulting\n");
    printf("  Voronoi diagram, it has overlapping edges or other geometric\n");
    printf("  inconsistencies.'\n");
    printf("\n");
    printf(
  "    If your input is a PSLG (-p), you can only expect a meaningful Voronoi\n"
  );
    printf(
  "    diagram if the domain you are triangulating is convex and free of\n");
    printf(
  "    holes, and you use the -D switch to construct a conforming Delaunay\n");
    printf("    triangulation (instead of a CDT or CCDT).\n\n");
    printf(
  "  Strange things can happen if you've taken liberties with your PSLG.  Do\n");
    printf(
  "  you have a vertex lying in the middle of a segment?  Triangle sometimes\n");
    printf(
  "  copes poorly with that sort of thing.  Do you want to lay out a collinear\n"
  );
    printf(
  "  row of evenly spaced, segment-connected vertices?  Have you simply\n");
    printf(
  "  defined one long segment connecting the leftmost vertex to the rightmost\n"
  );
    printf(
  "  vertex, and a bunch of vertices lying along it?  This method occasionally\n"
  );
    printf(
  "  works, especially with horizontal and vertical lines, but often it\n");
    printf(
  "  doesn't, and you'll have to connect each adjacent pair of vertices with a\n"
  );
    printf("  separate segment.  If you don't like it, tough.\n\n");
    printf(
  "  Furthermore, if you have segments that intersect other than at their\n");
    printf(
  "  endpoints, try not to let the intersections fall extremely close to PSLG\n"
  );
    printf("  vertices or each other.\n\n");
    printf(
  "  If you have problems refining a triangulation not produced by Triangle:\n");
    printf(
  "  Are you sure the triangulation is geometrically valid?  Is it formatted\n");
    printf(
  "  correctly for Triangle?  Are the triangles all listed so the first three\n"
  );
    printf(
  "  vertices are their corners in counterclockwise order?  Are all of the\n");
    printf(
  "  triangles constrained Delaunay?  Triangle's Delaunay refinement algorithm\n"
  );
    printf("  assumes that it starts with a CDT.\n\n");
    printf("Show Me:\n\n");
    printf(
  "  Triangle comes with a separate program named `Show Me', whose primary\n");
    printf(
  "  purpose is to draw meshes on your screen or in PostScript.  Its secondary\n"
  );
    printf(
  "  purpose is to check the validity of your input files, and do so more\n");
    printf(
  "  thoroughly than Triangle does.  Unlike Triangle, Show Me requires that\n");
    printf(
  "  you have the X Windows system.  Sorry, Microsoft Windows users.\n");
    printf("\n");
    printf("Triangle on the Web:\n");
    printf("\n");
    printf("  To see an illustrated version of these instructions, check out\n");
    printf("\n");
    printf("    http://www.cs.cmu.edu/~quake/triangle.html\n");
    printf("\n");
    printf("A Brief Plea:\n");
    printf("\n");
    printf(
  "  If you use Triangle, and especially if you use it to accomplish real\n");
    printf(
  "  work, I would like very much to hear from you.  A short letter or email\n");
    printf(
  "  (to jrs@cs.berkeley.edu) describing how you use Triangle will mean a lot\n"
  );
    printf(
  "  to me.  The more people I know are using this program, the more easily I\n"
  );
    printf(
  "  can justify spending time on improvements, which in turn will benefit\n");
    printf(
  "  you.  Also, I can put you on a list to receive email whenever a new\n");
    printf("  version of Triangle is available.\n\n");
    printf(
  "  If you use a mesh generated by Triangle in a publication, please include\n"
  );
    printf(
  "  an acknowledgment as well.  And please spell Triangle with a capital `T'!\n"
  );
    printf(
  "  If you want to include a citation, use `Jonathan Richard Shewchuk,\n");
    printf(
  "  ``Triangle: Engineering a 2D Quality Mesh Generator and Delaunay\n");
    printf(
  "  Triangulator,'' in Applied Computational Geometry:  Towards Geometric\n");
    printf(
  "  Engineering (Ming C. Lin and Dinesh Manocha, editors), volume 1148 of\n");
    printf(
  "  Lecture Notes in Computer Science, pages 203-222, Springer-Verlag,\n");
    printf(
  "  Berlin, May 1996.  (From the First ACM Workshop on Applied Computational\n"
  );
    printf("  Geometry.)'\n\n");
    printf("Research credit:\n\n");
    printf(
  "  Of course, I can take credit for only a fraction of the ideas that made\n");
    printf(
  "  this mesh generator possible.  Triangle owes its existence to the efforts\n"
  );
    printf(
  "  of many fine computational geometers and other researchers, including\n");
    printf(
  "  Marshall Bern, L. Paul Chew, Kenneth L. Clarkson, Boris Delaunay, Rex A.\n"
  );
    printf(
  "  Dwyer, David Eppstein, Steven Fortune, Leonidas J. Guibas, Donald E.\n");
    printf(
  "  Knuth, Charles L. Lawson, Der-Tsai Lee, Gary L. Miller, Ernst P. Mucke,\n");
    printf(
  "  Steven E. Pav, Douglas M. Priest, Jim Ruppert, Isaac Saias, Bruce J.\n");
    printf(
  "  Schachter, Micha Sharir, Peter W. Shor, Daniel D. Sleator, Jorge Stolfi,\n"
  );
    printf("  Robert E. Tarjan, Alper Ungor, Christopher J. Van Wyk, Noel J.\n");
    printf(
  "  Walkington, and Binhai Zhu.  See the comments at the beginning of the\n");
    printf("  source code for references.\n\n");
    triexit(0);
  }
  
  #endif /* not TRILIBRARY */
  
  /*****************************************************************************/
  /*                                                                           */
  /*  internalerror()   Ask the user to send me the defective product.  Exit.  */
  /*                                                                           */
  /*****************************************************************************/
  
  void internalerror()
  {
    printf("  Please report this bug to jrs@cs.berkeley.edu\n");
    printf("  Include the message above, your input data set, and the exact\n");
    printf("    command line you used to run Triangle.\n");
    triexit(1);
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  parsecommandline()   Read the command line, identify switches, and set   */
  /*                       up options and file names.                          */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  void parsecommandline(int argc, char **argv, struct behavior *b)
  #else /* not ANSI_DECLARATORS */
  void parsecommandline(argc, argv, b)
  int argc;
  char **argv;
  struct behavior *b;
  #endif /* not ANSI_DECLARATORS */
  
  {
  #ifdef TRILIBRARY
  #define STARTINDEX 0
  #else /* not TRILIBRARY */
  #define STARTINDEX 1
    int increment;
    int meshnumber;
  #endif /* not TRILIBRARY */
    int i, j, k;
    char workstring[FILENAMESIZE];
  
    b->poly = b->refine = b->quality = 0;
    b->vararea = b->fixedarea = b->usertest = 0;
    b->regionattrib = b->convex = b->weighted = b->jettison = 0;
    b->firstnumber = 1;
    b->edgesout = b->voronoi = b->neighbors = b->geomview = 0;
    b->nobound = b->nopolywritten = b->nonodewritten = b->noelewritten = 0;
    b->noiterationnum = 0;
    b->noholes = b->noexact = 0;
    b->incremental = b->sweepline = 0;
    b->dwyer = 1;
    b->splitseg = 0;
    b->docheck = 0;
    b->nobisect = 0;
    b->conformdel = 0;
    b->steiner = -1;
    b->order = 1;
    b->minangle = 0.0;
    b->maxarea = -1.0;
    b->quiet = b->verbose = 0;
  #ifndef TRILIBRARY
    b->innodefilename[0] = '\0';
  #endif /* not TRILIBRARY */
  
    for (i = STARTINDEX; i < argc; i++) {
  #ifndef TRILIBRARY
      if (argv[i][0] == '-') {
  #endif /* not TRILIBRARY */
        for (j = STARTINDEX; argv[i][j] != '\0'; j++) {
          if (argv[i][j] == 'p') {
            b->poly = 1;
  	}
  #ifndef CDT_ONLY
          if (argv[i][j] == 'r') {
            b->refine = 1;
  	}
          if (argv[i][j] == 'q') {
            b->quality = 1;
            if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
                (argv[i][j + 1] == '.')) {
              k = 0;
              while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
                     (argv[i][j + 1] == '.')) {
                j++;
                workstring[k] = argv[i][j];
                k++;
              }
              workstring[k] = '\0';
              b->minangle = (REAL) strtod(workstring, (char **) NULL);
  	  } else {
              b->minangle = 20.0;
  	  }
  	}
          if (argv[i][j] == 'a') {
            b->quality = 1;
            if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
                (argv[i][j + 1] == '.')) {
              b->fixedarea = 1;
              k = 0;
              while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
                     (argv[i][j + 1] == '.')) {
                j++;
                workstring[k] = argv[i][j];
                k++;
              }
              workstring[k] = '\0';
              b->maxarea = (REAL) strtod(workstring, (char **) NULL);
              if (b->maxarea <= 0.0) {
                printf("Error:  Maximum area must be greater than zero.\n");
                triexit(1);
  	    }
  	  } else {
              b->vararea = 1;
  	  }
  	}
          if (argv[i][j] == 'u') {
            b->quality = 1;
            b->usertest = 1;
          }
  #endif /* not CDT_ONLY */
          if (argv[i][j] == 'A') {
            b->regionattrib = 1;
          }
          if (argv[i][j] == 'c') {
            b->convex = 1;
          }
          if (argv[i][j] == 'w') {
            b->weighted = 1;
          }
          if (argv[i][j] == 'W') {
            b->weighted = 2;
          }
          if (argv[i][j] == 'j') {
            b->jettison = 1;
          }
          if (argv[i][j] == 'z') {
            b->firstnumber = 0;
          }
          if (argv[i][j] == 'e') {
            b->edgesout = 1;
  	}
          if (argv[i][j] == 'v') {
            b->voronoi = 1;
  	}
          if (argv[i][j] == 'n') {
            b->neighbors = 1;
  	}
          if (argv[i][j] == 'g') {
            b->geomview = 1;
  	}
          if (argv[i][j] == 'B') {
            b->nobound = 1;
  	}
          if (argv[i][j] == 'P') {
            b->nopolywritten = 1;
  	}
          if (argv[i][j] == 'N') {
            b->nonodewritten = 1;
  	}
          if (argv[i][j] == 'E') {
            b->noelewritten = 1;
  	}
  #ifndef TRILIBRARY
          if (argv[i][j] == 'I') {
            b->noiterationnum = 1;
  	}
  #endif /* not TRILIBRARY */
          if (argv[i][j] == 'O') {
            b->noholes = 1;
  	}
          if (argv[i][j] == 'X') {
            b->noexact = 1;
  	}
          if (argv[i][j] == 'o') {
            if (argv[i][j + 1] == '2') {
              j++;
              b->order = 2;
            }
  	}
  #ifndef CDT_ONLY
          if (argv[i][j] == 'Y') {
            b->nobisect++;
  	}
          if (argv[i][j] == 'S') {
            b->steiner = 0;
            while ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) {
              j++;
              b->steiner = b->steiner * 10 + (int) (argv[i][j] - '0');
            }
          }
  #endif /* not CDT_ONLY */
  #ifndef REDUCED
          if (argv[i][j] == 'i') {
            b->incremental = 1;
          }
          if (argv[i][j] == 'F') {
            b->sweepline = 1;
          }
  #endif /* not REDUCED */
          if (argv[i][j] == 'l') {
            b->dwyer = 0;
          }
  #ifndef REDUCED
  #ifndef CDT_ONLY
          if (argv[i][j] == 's') {
            b->splitseg = 1;
          }
          if ((argv[i][j] == 'D') || (argv[i][j] == 'L')) {
            b->quality = 1;
            b->conformdel = 1;
          }
  #endif /* not CDT_ONLY */
          if (argv[i][j] == 'C') {
            b->docheck = 1;
          }
  #endif /* not REDUCED */
          if (argv[i][j] == 'Q') {
            b->quiet = 1;
          }
          if (argv[i][j] == 'V') {
            b->verbose++;
          }
  #ifndef TRILIBRARY
          if ((argv[i][j] == 'h') || (argv[i][j] == 'H') ||
              (argv[i][j] == '?')) {
            info();
  	}
  #endif /* not TRILIBRARY */
        }
  #ifndef TRILIBRARY
      } else {
        strncpy(b->innodefilename, argv[i], FILENAMESIZE - 1);
        b->innodefilename[FILENAMESIZE - 1] = '\0';
      }
  #endif /* not TRILIBRARY */
    }
  #ifndef TRILIBRARY
    if (b->innodefilename[0] == '\0') {
      syntax();
    }
    if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 5], ".node")) {
      b->innodefilename[strlen(b->innodefilename) - 5] = '\0';
    }
    if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 5], ".poly")) {
      b->innodefilename[strlen(b->innodefilename) - 5] = '\0';
      b->poly = 1;
    }
  #ifndef CDT_ONLY
    if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 4], ".ele")) {
      b->innodefilename[strlen(b->innodefilename) - 4] = '\0';
      b->refine = 1;
    }
    if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 5], ".area")) {
      b->innodefilename[strlen(b->innodefilename) - 5] = '\0';
      b->refine = 1;
      b->quality = 1;
      b->vararea = 1;
    }
  #endif /* not CDT_ONLY */
  #endif /* not TRILIBRARY */
    b->usesegments = b->poly || b->refine || b->quality || b->convex;
    b->goodangle = cos(b->minangle * PI / 180.0);
    if (b->goodangle == 1.0) {
      b->offconstant = 0.0;
    } else {
      b->offconstant = 0.475 * sqrt((1.0 + b->goodangle) / (1.0 - b->goodangle));
    }
    b->goodangle *= b->goodangle;
    if (b->refine && b->noiterationnum) {
      printf(
        "Error:  You cannot use the -I switch when refining a triangulation.\n");
      triexit(1);
    }
    /* Be careful not to allocate space for element area constraints that */
    /*   will never be assigned any value (other than the default -1.0).  */
    if (!b->refine && !b->poly) {
      b->vararea = 0;
    }
    /* Be careful not to add an extra attribute to each element unless the */
    /*   input supports it (PSLG in, but not refining a preexisting mesh). */
    if (b->refine || !b->poly) {
      b->regionattrib = 0;
    }
    /* Regular/weighted triangulations are incompatible with PSLGs */
    /*   and meshing.                                              */
    if (b->weighted && (b->poly || b->quality)) {
      b->weighted = 0;
      if (!b->quiet) {
        printf("Warning:  weighted triangulations (-w, -W) are incompatible\n");
        printf("  with PSLGs (-p) and meshing (-q, -a, -u).  Weights ignored.\n"
               );
      }
    }
    if (b->jettison && b->nonodewritten && !b->quiet) {
      printf("Warning:  -j and -N switches are somewhat incompatible.\n");
      printf("  If any vertices are jettisoned, you will need the output\n");
      printf("  .node file to reconstruct the new node indices.");
    }
  
  #ifndef TRILIBRARY
    strcpy(b->inpolyfilename, b->innodefilename);
    strcpy(b->inelefilename, b->innodefilename);
    strcpy(b->areafilename, b->innodefilename);
    increment = 0;
    strcpy(workstring, b->innodefilename);
    j = 1;
    while (workstring[j] != '\0') {
      if ((workstring[j] == '.') && (workstring[j + 1] != '\0')) {
        increment = j + 1;
      }
      j++;
    }
    meshnumber = 0;
    if (increment > 0) {
      j = increment;
      do {
        if ((workstring[j] >= '0') && (workstring[j] <= '9')) {
          meshnumber = meshnumber * 10 + (int) (workstring[j] - '0');
        } else {
          increment = 0;
        }
        j++;
      } while (workstring[j] != '\0');
    }
    if (b->noiterationnum) {
      strcpy(b->outnodefilename, b->innodefilename);
      strcpy(b->outelefilename, b->innodefilename);
      strcpy(b->edgefilename, b->innodefilename);
      strcpy(b->vnodefilename, b->innodefilename);
      strcpy(b->vedgefilename, b->innodefilename);
      strcpy(b->neighborfilename, b->innodefilename);
      strcpy(b->offfilename, b->innodefilename);
      strcat(b->outnodefilename, ".node");
      strcat(b->outelefilename, ".ele");
      strcat(b->edgefilename, ".edge");
      strcat(b->vnodefilename, ".v.node");
      strcat(b->vedgefilename, ".v.edge");
      strcat(b->neighborfilename, ".neigh");
      strcat(b->offfilename, ".off");
    } else if (increment == 0) {
      strcpy(b->outnodefilename, b->innodefilename);
      strcpy(b->outpolyfilename, b->innodefilename);
      strcpy(b->outelefilename, b->innodefilename);
      strcpy(b->edgefilename, b->innodefilename);
      strcpy(b->vnodefilename, b->innodefilename);
      strcpy(b->vedgefilename, b->innodefilename);
      strcpy(b->neighborfilename, b->innodefilename);
      strcpy(b->offfilename, b->innodefilename);
      strcat(b->outnodefilename, ".1.node");
      strcat(b->outpolyfilename, ".1.poly");
      strcat(b->outelefilename, ".1.ele");
      strcat(b->edgefilename, ".1.edge");
      strcat(b->vnodefilename, ".1.v.node");
      strcat(b->vedgefilename, ".1.v.edge");
      strcat(b->neighborfilename, ".1.neigh");
      strcat(b->offfilename, ".1.off");
    } else {
      workstring[increment] = '%';
      workstring[increment + 1] = 'd';
      workstring[increment + 2] = '\0';
      sprintf(b->outnodefilename, workstring, meshnumber + 1);
      strcpy(b->outpolyfilename, b->outnodefilename);
      strcpy(b->outelefilename, b->outnodefilename);
      strcpy(b->edgefilename, b->outnodefilename);
      strcpy(b->vnodefilename, b->outnodefilename);
      strcpy(b->vedgefilename, b->outnodefilename);
      strcpy(b->neighborfilename, b->outnodefilename);
      strcpy(b->offfilename, b->outnodefilename);
      strcat(b->outnodefilename, ".node");
      strcat(b->outpolyfilename, ".poly");
      strcat(b->outelefilename, ".ele");
      strcat(b->edgefilename, ".edge");
      strcat(b->vnodefilename, ".v.node");
      strcat(b->vedgefilename, ".v.edge");
      strcat(b->neighborfilename, ".neigh");
      strcat(b->offfilename, ".off");
    }
    strcat(b->innodefilename, ".node");
    strcat(b->inpolyfilename, ".poly");
    strcat(b->inelefilename, ".ele");
    strcat(b->areafilename, ".area");
  #endif /* not TRILIBRARY */
  }
  
  /**                                                                         **/
  /**                                                                         **/
  /********* User interaction routines begin here                      *********/
  
  /********* Debugging routines begin here                             *********/
  /**                                                                         **/
  /**                                                                         **/
  
  /*****************************************************************************/
  /*                                                                           */
  /*  printtriangle()   Print out the details of an oriented triangle.         */
  /*                                                                           */
  /*  I originally wrote this procedure to simplify debugging; it can be       */
  /*  called directly from the debugger, and presents information about an     */
  /*  oriented triangle in digestible form.  It's also used when the           */
  /*  highest level of verbosity (`-VVV') is specified.                        */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  void printtriangle(struct mesh *m, struct behavior *b, struct otri *t)
  #else /* not ANSI_DECLARATORS */
  void printtriangle(m, b, t)
  struct mesh *m;
  struct behavior *b;
  struct otri *t;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct otri printtri;
    struct osub printsh;
    vertex printvertex;
  
    printf("triangle x%llx with orientation %d:\n", (unsigned long long) t->tri,
           t->orient);
    decode(t->tri[0], printtri);
    if (printtri.tri == m->dummytri) {
      printf("    [0] = Outer space\n");
    } else {
      printf("    [0] = x%llx  %d\n", (unsigned long long) printtri.tri,
             printtri.orient);
    }
    decode(t->tri[1], printtri);
    if (printtri.tri == m->dummytri) {
      printf("    [1] = Outer space\n");
    } else {
      printf("    [1] = x%llx  %d\n", (unsigned long long) printtri.tri,
             printtri.orient);
    }
    decode(t->tri[2], printtri);
    if (printtri.tri == m->dummytri) {
      printf("    [2] = Outer space\n");
    } else {
      printf("    [2] = x%llx  %d\n", (unsigned long long) printtri.tri,
             printtri.orient);
    }
  
    org(*t, printvertex);
    if (printvertex == (vertex) NULL)
      printf("    Origin[%d] = NULL\n", (t->orient + 1) % 3 + 3);
    else
      printf("    Origin[%d] = x%llx  (%.12g, %.12g)\n",
             (t->orient + 1) % 3 + 3, (unsigned long long) printvertex,
             printvertex[0], printvertex[1]);
    dest(*t, printvertex);
    if (printvertex == (vertex) NULL)
      printf("    Dest  [%d] = NULL\n", (t->orient + 2) % 3 + 3);
    else
      printf("    Dest  [%d] = x%llx  (%.12g, %.12g)\n",
             (t->orient + 2) % 3 + 3, (unsigned long long) printvertex,
             printvertex[0], printvertex[1]);
    apex(*t, printvertex);
    if (printvertex == (vertex) NULL)
      printf("    Apex  [%d] = NULL\n", t->orient + 3);
    else
      printf("    Apex  [%d] = x%llx  (%.12g, %.12g)\n",
             t->orient + 3, (unsigned long long) printvertex,
             printvertex[0], printvertex[1]);
  
    if (b->usesegments) {
      sdecode(t->tri[6], printsh);
      if (printsh.ss != m->dummysub) {
        printf("    [6] = x%llx  %d\n", (unsigned long long) printsh.ss,
               printsh.ssorient);
      }
      sdecode(t->tri[7], printsh);
      if (printsh.ss != m->dummysub) {
        printf("    [7] = x%llx  %d\n", (unsigned long long) printsh.ss,
               printsh.ssorient);
      }
      sdecode(t->tri[8], printsh);
      if (printsh.ss != m->dummysub) {
        printf("    [8] = x%llx  %d\n", (unsigned long long) printsh.ss,
               printsh.ssorient);
      }
    }
  
    if (b->vararea) {
      printf("    Area constraint:  %.4g\n", areabound(*t));
    }
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  printsubseg()   Print out the details of an oriented subsegment.         */
  /*                                                                           */
  /*  I originally wrote this procedure to simplify debugging; it can be       */
  /*  called directly from the debugger, and presents information about an     */
  /*  oriented subsegment in digestible form.  It's also used when the highest */
  /*  level of verbosity (`-VVV') is specified.                                */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  void printsubseg(struct mesh *m, struct behavior *b, struct osub *s)
  #else /* not ANSI_DECLARATORS */
  void printsubseg(m, b, s)
  struct mesh *m;
  struct behavior *b;
  struct osub *s;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct osub printsh;
    struct otri printtri;
    vertex printvertex;
  
    printf("subsegment x%llx with orientation %d and mark %d:\n",
           (unsigned long long) s->ss, s->ssorient, mark(*s));
    sdecode(s->ss[0], printsh);
    if (printsh.ss == m->dummysub) {
      printf("    [0] = No subsegment\n");
    } else {
      printf("    [0] = x%llx  %d\n", (unsigned long long) printsh.ss,
             printsh.ssorient);
    }
    sdecode(s->ss[1], printsh);
    if (printsh.ss == m->dummysub) {
      printf("    [1] = No subsegment\n");
    } else {
      printf("    [1] = x%llx  %d\n", (unsigned long long) printsh.ss,
             printsh.ssorient);
    }
  
    sorg(*s, printvertex);
    if (printvertex == (vertex) NULL)
      printf("    Origin[%d] = NULL\n", 2 + s->ssorient);
    else
      printf("    Origin[%d] = x%llx  (%.12g, %.12g)\n",
             2 + s->ssorient, (unsigned long long) printvertex,
             printvertex[0], printvertex[1]);
    sdest(*s, printvertex);
    if (printvertex == (vertex) NULL)
      printf("    Dest  [%d] = NULL\n", 3 - s->ssorient);
    else
      printf("    Dest  [%d] = x%llx  (%.12g, %.12g)\n",
             3 - s->ssorient, (unsigned long long) printvertex,
             printvertex[0], printvertex[1]);
  
    decode(s->ss[6], printtri);
    if (printtri.tri == m->dummytri) {
      printf("    [6] = Outer space\n");
    } else {
      printf("    [6] = x%llx  %d\n", (unsigned long long) printtri.tri,
             printtri.orient);
    }
    decode(s->ss[7], printtri);
    if (printtri.tri == m->dummytri) {
      printf("    [7] = Outer space\n");
    } else {
      printf("    [7] = x%llx  %d\n", (unsigned long long) printtri.tri,
             printtri.orient);
    }
  
    segorg(*s, printvertex);
    if (printvertex == (vertex) NULL)
      printf("    Segment origin[%d] = NULL\n", 4 + s->ssorient);
    else
      printf("    Segment origin[%d] = x%llx  (%.12g, %.12g)\n",
             4 + s->ssorient, (unsigned long long) printvertex,
             printvertex[0], printvertex[1]);
    segdest(*s, printvertex);
    if (printvertex == (vertex) NULL)
      printf("    Segment dest  [%d] = NULL\n", 5 - s->ssorient);
    else
      printf("    Segment dest  [%d] = x%llx  (%.12g, %.12g)\n",
             5 - s->ssorient, (unsigned long long) printvertex,
             printvertex[0], printvertex[1]);
  }
  
  /**                                                                         **/
  /**                                                                         **/
  /********* Debugging routines end here                               *********/
  
  /********* Memory management routines begin here                     *********/
  /**                                                                         **/
  /**                                                                         **/
  
  /*****************************************************************************/
  /*                                                                           */
  /*  poolzero()   Set all of a pool's fields to zero.                         */
  /*                                                                           */
  /*  This procedure should never be called on a pool that has any memory      */
  /*  allocated to it, as that memory would leak.                              */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  void poolzero(struct memorypool *pool)
  #else /* not ANSI_DECLARATORS */
  void poolzero(pool)
  struct memorypool *pool;
  #endif /* not ANSI_DECLARATORS */
  
  {
    pool->firstblock = (TRIVOID **) NULL;
    pool->nowblock = (TRIVOID **) NULL;
    pool->nextitem = (TRIVOID *) NULL;
    pool->deaditemstack = (TRIVOID *) NULL;
    pool->pathblock = (TRIVOID **) NULL;
    pool->pathitem = (TRIVOID *) NULL;
    pool->alignbytes = 0;
    pool->itembytes = 0;
    pool->itemsperblock = 0;
    pool->itemsfirstblock = 0;
    pool->items = 0;
    pool->maxitems = 0;
    pool->unallocateditems = 0;
    pool->pathitemsleft = 0;
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  poolrestart()   Deallocate all items in a pool.                          */
  /*                                                                           */
  /*  The pool is returned to its starting state, except that no memory is     */
  /*  freed to the operating system.  Rather, the previously allocated blocks  */
  /*  are ready to be reused.                                                  */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  void poolrestart(struct memorypool *pool)
  #else /* not ANSI_DECLARATORS */
  void poolrestart(pool)
  struct memorypool *pool;
  #endif /* not ANSI_DECLARATORS */
  
  {
    unsigned long long alignptr;
  
    pool->items = 0;
    pool->maxitems = 0;
  
    /* Set the currently active block. */
    pool->nowblock = pool->firstblock;
    /* Find the first item in the pool.  Increment by the size of (TRIVOID *). */
    alignptr = (unsigned long long) (pool->nowblock + 1);
    /* Align the item on an `alignbytes'-byte boundary. */
    pool->nextitem = (TRIVOID *)
      (alignptr + (unsigned long long) pool->alignbytes -
       (alignptr % (unsigned long long) pool->alignbytes));
    /* There are lots of unallocated items left in this block. */
    pool->unallocateditems = pool->itemsfirstblock;
    /* The stack of deallocated items is empty. */
    pool->deaditemstack = (TRIVOID *) NULL;
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  poolinit()   Initialize a pool of memory for allocation of items.        */
  /*                                                                           */
  /*  This routine initializes the machinery for allocating items.  A `pool'   */
  /*  is created whose records have size at least `bytecount'.  Items will be  */
  /*  allocated in `itemcount'-item blocks.  Each item is assumed to be a      */
  /*  collection of words, and either pointers or floating-point values are    */
  /*  assumed to be the "primary" word type.  (The "primary" word type is used */
  /*  to determine alignment of items.)  If `alignment' isn't zero, all items  */
  /*  will be `alignment'-byte aligned in memory.  `alignment' must be either  */
  /*  a multiple or a factor of the primary word size; powers of two are safe. */
  /*  `alignment' is normally used to create a few unused bits at the bottom   */
  /*  of each item's pointer, in which information may be stored.              */
  /*                                                                           */
  /*  Don't change this routine unless you understand it.                      */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  void poolinit(struct memorypool *pool, int bytecount, int itemcount,
                int firstitemcount, int alignment)
  #else /* not ANSI_DECLARATORS */
  void poolinit(pool, bytecount, itemcount, firstitemcount, alignment)
  struct memorypool *pool;
  int bytecount;
  int itemcount;
  int firstitemcount;
  int alignment;
  #endif /* not ANSI_DECLARATORS */
  
  {
    /* Find the proper alignment, which must be at least as large as:   */
    /*   - The parameter `alignment'.                                   */
    /*   - sizeof(TRIVOID *), so the stack of dead items can be maintained */
    /*       without unaligned accesses.                                */
    if (alignment > sizeof(TRIVOID *)) {
      pool->alignbytes = alignment;
    } else {
      pool->alignbytes = sizeof(TRIVOID *);
    }
    pool->itembytes = ((bytecount - 1) / pool->alignbytes + 1) *
                      pool->alignbytes;
    pool->itemsperblock = itemcount;
    if (firstitemcount == 0) {
      pool->itemsfirstblock = itemcount;
    } else {
      pool->itemsfirstblock = firstitemcount;
    }
  
    /* Allocate a block of items.  Space for `itemsfirstblock' items and one  */
    /*   pointer (to point to the next block) are allocated, as well as space */
    /*   to ensure alignment of the items.                                    */
    pool->firstblock = (TRIVOID **)
      trimalloc(pool->itemsfirstblock * pool->itembytes + (int) sizeof(TRIVOID *) +
                pool->alignbytes);
    /* Set the next block pointer to NULL. */
    *(pool->firstblock) = (TRIVOID *) NULL;
    poolrestart(pool);
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  pooldeinit()   Free to the operating system all memory taken by a pool.  */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  void pooldeinit(struct memorypool *pool)
  #else /* not ANSI_DECLARATORS */
  void pooldeinit(pool)
  struct memorypool *pool;
  #endif /* not ANSI_DECLARATORS */
  
  {
    while (pool->firstblock != (TRIVOID **) NULL) {
      pool->nowblock = (TRIVOID **) *(pool->firstblock);
      trifree((TRIVOID *) pool->firstblock);
      pool->firstblock = pool->nowblock;
    }
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  poolalloc()   Allocate space for an item.                                */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  TRIVOID *poolalloc(struct memorypool *pool)
  #else /* not ANSI_DECLARATORS */
  TRIVOID *poolalloc(pool)
  struct memorypool *pool;
  #endif /* not ANSI_DECLARATORS */
  
  {
    TRIVOID *newitem;
    TRIVOID **newblock;
    unsigned long long alignptr;
  
    /* First check the linked list of dead items.  If the list is not   */
    /*   empty, allocate an item from the list rather than a fresh one. */
    if (pool->deaditemstack != (TRIVOID *) NULL) {
      newitem = pool->deaditemstack;               /* Take first item in list. */
      pool->deaditemstack = * (TRIVOID **) pool->deaditemstack;
    } else {
      /* Check if there are any free items left in the current block. */
      if (pool->unallocateditems == 0) {
        /* Check if another block must be allocated. */
        if (*(pool->nowblock) == (TRIVOID *) NULL) {
          /* Allocate a new block of items, pointed to by the previous block. */
          newblock = (TRIVOID **) trimalloc(pool->itemsperblock * pool->itembytes +
                                         (int) sizeof(TRIVOID *) +
                                         pool->alignbytes);
          *(pool->nowblock) = (TRIVOID *) newblock;
          /* The next block pointer is NULL. */
          *newblock = (TRIVOID *) NULL;
        }
  
        /* Move to the new block. */
        pool->nowblock = (TRIVOID **) *(pool->nowblock);
        /* Find the first item in the block.    */
        /*   Increment by the size of (TRIVOID *). */
        alignptr = (unsigned long long) (pool->nowblock + 1);
        /* Align the item on an `alignbytes'-byte boundary. */
        pool->nextitem = (TRIVOID *)
          (alignptr + (unsigned long long) pool->alignbytes -
           (alignptr % (unsigned long long) pool->alignbytes));
        /* There are lots of unallocated items left in this block. */
        pool->unallocateditems = pool->itemsperblock;
      }
  
      /* Allocate a new item. */
      newitem = pool->nextitem;
      /* Advance `nextitem' pointer to next free item in block. */
      pool->nextitem = (TRIVOID *) ((char *) pool->nextitem + pool->itembytes);
      pool->unallocateditems--;
      pool->maxitems++;
    }
    pool->items++;
    return newitem;
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  pooldealloc()   Deallocate space for an item.                            */
  /*                                                                           */
  /*  The deallocated space is stored in a queue for later reuse.              */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  void pooldealloc(struct memorypool *pool, TRIVOID *dyingitem)
  #else /* not ANSI_DECLARATORS */
  void pooldealloc(pool, dyingitem)
  struct memorypool *pool;
  TRIVOID *dyingitem;
  #endif /* not ANSI_DECLARATORS */
  
  {
    /* Push freshly killed item onto stack. */
    *((TRIVOID **) dyingitem) = pool->deaditemstack;
    pool->deaditemstack = dyingitem;
    pool->items--;
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  traversalinit()   Prepare to traverse the entire list of items.          */
  /*                                                                           */
  /*  This routine is used in conjunction with traverse().                     */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  void traversalinit(struct memorypool *pool)
  #else /* not ANSI_DECLARATORS */
  void traversalinit(pool)
  struct memorypool *pool;
  #endif /* not ANSI_DECLARATORS */
  
  {
    unsigned long long alignptr;
  
    /* Begin the traversal in the first block. */
    pool->pathblock = pool->firstblock;
    /* Find the first item in the block.  Increment by the size of (TRIVOID *). */
    alignptr = (unsigned long long) (pool->pathblock + 1);
    /* Align with item on an `alignbytes'-byte boundary. */
    pool->pathitem = (TRIVOID *)
      (alignptr + (unsigned long long) pool->alignbytes -
       (alignptr % (unsigned long long) pool->alignbytes));
    /* Set the number of items left in the current block. */
    pool->pathitemsleft = pool->itemsfirstblock;
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  traverse()   Find the next item in the list.                             */
  /*                                                                           */
  /*  This routine is used in conjunction with traversalinit().  Be forewarned */
  /*  that this routine successively returns all items in the list, including  */
  /*  deallocated ones on the deaditemqueue.  It's up to you to figure out     */
  /*  which ones are actually dead.  Why?  I don't want to allocate extra      */
  /*  space just to demarcate dead items.  It can usually be done more         */
  /*  space-efficiently by a routine that knows something about the structure  */
  /*  of the item.                                                             */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  TRIVOID *traverse(struct memorypool *pool)
  #else /* not ANSI_DECLARATORS */
  TRIVOID *traverse(pool)
  struct memorypool *pool;
  #endif /* not ANSI_DECLARATORS */
  
  {
    TRIVOID *newitem;
    unsigned long long alignptr;
  
    /* Stop upon exhausting the list of items. */
    if (pool->pathitem == pool->nextitem) {
      return (TRIVOID *) NULL;
    }
  
    /* Check whether any untraversed items remain in the current block. */
    if (pool->pathitemsleft == 0) {
      /* Find the next block. */
      pool->pathblock = (TRIVOID **) *(pool->pathblock);
      /* Find the first item in the block.  Increment by the size of (TRIVOID *). */
      alignptr = (unsigned long long) (pool->pathblock + 1);
      /* Align with item on an `alignbytes'-byte boundary. */
      pool->pathitem = (TRIVOID *)
        (alignptr + (unsigned long long) pool->alignbytes -
         (alignptr % (unsigned long long) pool->alignbytes));
      /* Set the number of items left in the current block. */
      pool->pathitemsleft = pool->itemsperblock;
    }
  
    newitem = pool->pathitem;
    /* Find the next item in the block. */
    pool->pathitem = (TRIVOID *) ((char *) pool->pathitem + pool->itembytes);
    pool->pathitemsleft--;
    return newitem;
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  dummyinit()   Initialize the triangle that fills "outer space" and the   */
  /*                omnipresent subsegment.                                    */
  /*                                                                           */
  /*  The triangle that fills "outer space," called `dummytri', is pointed to  */
  /*  by every triangle and subsegment on a boundary (be it outer or inner) of */
  /*  the triangulation.  Also, `dummytri' points to one of the triangles on   */
  /*  the convex hull (until the holes and concavities are carved), making it  */
  /*  possible to find a starting triangle for point location.                 */
  /*                                                                           */
  /*  The omnipresent subsegment, `dummysub', is pointed to by every triangle  */
  /*  or subsegment that doesn't have a full complement of real subsegments    */
  /*  to point to.                                                             */
  /*                                                                           */
  /*  `dummytri' and `dummysub' are generally required to fulfill only a few   */
  /*  invariants:  their vertices must remain NULL and `dummytri' must always  */
  /*  be bonded (at offset zero) to some triangle on the convex hull of the    */
  /*  mesh, via a boundary edge.  Otherwise, the connections of `dummytri' and */
  /*  `dummysub' may change willy-nilly.  This makes it possible to avoid      */
  /*  writing a good deal of special-case code (in the edge flip, for example) */
  /*  for dealing with the boundary of the mesh, places where no subsegment is */
  /*  present, and so forth.  Other entities are frequently bonded to          */
  /*  `dummytri' and `dummysub' as if they were real mesh entities, with no    */
  /*  harm done.                                                               */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  void dummyinit(struct mesh *m, struct behavior *b, int trianglebytes,
                 int subsegbytes)
  #else /* not ANSI_DECLARATORS */
  void dummyinit(m, b, trianglebytes, subsegbytes)
  struct mesh *m;
  struct behavior *b;
  int trianglebytes;
  int subsegbytes;
  #endif /* not ANSI_DECLARATORS */
  
  {
    unsigned long long alignptr;
  
    /* Set up `dummytri', the `triangle' that occupies "outer space." */
    m->dummytribase = (triangle *) trimalloc(trianglebytes +
                                             m->triangles.alignbytes);
    /* Align `dummytri' on a `triangles.alignbytes'-byte boundary. */
    alignptr = (unsigned long long) m->dummytribase;
    m->dummytri = (triangle *)
      (alignptr + (unsigned long long) m->triangles.alignbytes -
       (alignptr % (unsigned long long) m->triangles.alignbytes));
    /* Initialize the three adjoining triangles to be "outer space."  These  */
    /*   will eventually be changed by various bonding operations, but their */
    /*   values don't really matter, as long as they can legally be          */
    /*   dereferenced.                                                       */
    m->dummytri[0] = (triangle) m->dummytri;
    m->dummytri[1] = (triangle) m->dummytri;
    m->dummytri[2] = (triangle) m->dummytri;
    /* Three NULL vertices. */
    m->dummytri[3] = (triangle) NULL;
    m->dummytri[4] = (triangle) NULL;
    m->dummytri[5] = (triangle) NULL;
  
    if (b->usesegments) {
      /* Set up `dummysub', the omnipresent subsegment pointed to by any */
      /*   triangle side or subsegment end that isn't attached to a real */
      /*   subsegment.                                                   */
      m->dummysubbase = (subseg *) trimalloc(subsegbytes +
                                             m->subsegs.alignbytes);
      /* Align `dummysub' on a `subsegs.alignbytes'-byte boundary. */
      alignptr = (unsigned long long) m->dummysubbase;
      m->dummysub = (subseg *)
        (alignptr + (unsigned long long) m->subsegs.alignbytes -
         (alignptr % (unsigned long long) m->subsegs.alignbytes));
      /* Initialize the two adjoining subsegments to be the omnipresent      */
      /*   subsegment.  These will eventually be changed by various bonding  */
      /*   operations, but their values don't really matter, as long as they */
      /*   can legally be dereferenced.                                      */
      m->dummysub[0] = (subseg) m->dummysub;
      m->dummysub[1] = (subseg) m->dummysub;
      /* Four NULL vertices. */
      m->dummysub[2] = (subseg) NULL;
      m->dummysub[3] = (subseg) NULL;
      m->dummysub[4] = (subseg) NULL;
      m->dummysub[5] = (subseg) NULL;
      /* Initialize the two adjoining triangles to be "outer space." */
      m->dummysub[6] = (subseg) m->dummytri;
      m->dummysub[7] = (subseg) m->dummytri;
      /* Set the boundary marker to zero. */
      * (int *) (m->dummysub + 8) = 0;
  
      /* Initialize the three adjoining subsegments of `dummytri' to be */
      /*   the omnipresent subsegment.                                  */
      m->dummytri[6] = (triangle) m->dummysub;
      m->dummytri[7] = (triangle) m->dummysub;
      m->dummytri[8] = (triangle) m->dummysub;
    }
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  initializevertexpool()   Calculate the size of the vertex data structure */
  /*                           and initialize its memory pool.                 */
  /*                                                                           */
  /*  This routine also computes the `vertexmarkindex' and `vertex2triindex'   */
  /*  indices used to find values within each vertex.                          */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  void initializevertexpool(struct mesh *m, struct behavior *b)
  #else /* not ANSI_DECLARATORS */
  void initializevertexpool(m, b)
  struct mesh *m;
  struct behavior *b;
  #endif /* not ANSI_DECLARATORS */
  
  {
    int vertexsize;
  
    /* The index within each vertex at which the boundary marker is found,    */
    /*   followed by the vertex type.  Ensure the vertex marker is aligned to */
    /*   a sizeof(int)-byte address.                                          */
    m->vertexmarkindex = ((m->mesh_dim + m->nextras) * sizeof(REAL) +
                          sizeof(int) - 1) /
                         sizeof(int);
    vertexsize = (m->vertexmarkindex + 2) * sizeof(int);
    if (b->poly) {
      /* The index within each vertex at which a triangle pointer is found.  */
      /*   Ensure the pointer is aligned to a sizeof(triangle)-byte address. */
      m->vertex2triindex = (vertexsize + sizeof(triangle) - 1) /
                           sizeof(triangle);
      vertexsize = (m->vertex2triindex + 1) * sizeof(triangle);
    }
  
    /* Initialize the pool of vertices. */
    poolinit(&m->vertices, vertexsize, VERTEXPERBLOCK,
             m->invertices > VERTEXPERBLOCK ? m->invertices : VERTEXPERBLOCK,
             sizeof(REAL));
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  initializetrisubpools()   Calculate the sizes of the triangle and        */
  /*                            subsegment data structures and initialize      */
  /*                            their memory pools.                            */
  /*                                                                           */
  /*  This routine also computes the `highorderindex', `elemattribindex', and  */
  /*  `areaboundindex' indices used to find values within each triangle.       */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  void initializetrisubpools(struct mesh *m, struct behavior *b)
  #else /* not ANSI_DECLARATORS */
  void initializetrisubpools(m, b)
  struct mesh *m;
  struct behavior *b;
  #endif /* not ANSI_DECLARATORS */
  
  {
    int trisize;
  
    /* The index within each triangle at which the extra nodes (above three)  */
    /*   associated with high order elements are found.  There are three      */
    /*   pointers to other triangles, three pointers to corners, and possibly */
    /*   three pointers to subsegments before the extra nodes.                */
    m->highorderindex = 6 + (b->usesegments * 3);
    /* The number of bytes occupied by a triangle. */
    trisize = ((b->order + 1) * (b->order + 2) / 2 + (m->highorderindex - 3)) *
              sizeof(triangle);
    /* The index within each triangle at which its attributes are found, */
    /*   where the index is measured in REALs.                           */
    m->elemattribindex = (trisize + sizeof(REAL) - 1) / sizeof(REAL);
    /* The index within each triangle at which the maximum area constraint  */
    /*   is found, where the index is measured in REALs.  Note that if the  */
    /*   `regionattrib' flag is set, an additional attribute will be added. */
    m->areaboundindex = m->elemattribindex + m->eextras + b->regionattrib;
    /* If triangle attributes or an area bound are needed, increase the number */
    /*   of bytes occupied by a triangle.                                      */
    if (b->vararea) {
      trisize = (m->areaboundindex + 1) * sizeof(REAL);
    } else if (m->eextras + b->regionattrib > 0) {
      trisize = m->areaboundindex * sizeof(REAL);
    }
    /* If a Voronoi diagram or triangle neighbor graph is requested, make    */
    /*   sure there's room to store an integer index in each triangle.  This */
    /*   integer index can occupy the same space as the subsegment pointers  */
    /*   or attributes or area constraint or extra nodes.                    */
    if ((b->voronoi || b->neighbors) &&
        (trisize < 6 * sizeof(triangle) + sizeof(int))) {
      trisize = 6 * sizeof(triangle) + sizeof(int);
    }
  
    /* Having determined the memory size of a triangle, initialize the pool. */
    poolinit(&m->triangles, trisize, TRIPERBLOCK,
             (2 * m->invertices - 2) > TRIPERBLOCK ? (2 * m->invertices - 2) :
             TRIPERBLOCK, 4);
  
    if (b->usesegments) {
      /* Initialize the pool of subsegments.  Take into account all eight */
      /*   pointers and one boundary marker.                              */
      poolinit(&m->subsegs, 8 * sizeof(triangle) + sizeof(int),
               SUBSEGPERBLOCK, SUBSEGPERBLOCK, 4);
  
      /* Initialize the "outer space" triangle and omnipresent subsegment. */
      dummyinit(m, b, m->triangles.itembytes, m->subsegs.itembytes);
    } else {
      /* Initialize the "outer space" triangle. */
      dummyinit(m, b, m->triangles.itembytes, 0);
    }
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  triangledealloc()   Deallocate space for a triangle, marking it dead.    */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  void triangledealloc(struct mesh *m, triangle *dyingtriangle)
  #else /* not ANSI_DECLARATORS */
  void triangledealloc(m, dyingtriangle)
  struct mesh *m;
  triangle *dyingtriangle;
  #endif /* not ANSI_DECLARATORS */
  
  {
    /* Mark the triangle as dead.  This makes it possible to detect dead */
    /*   triangles when traversing the list of all triangles.            */
    killtri(dyingtriangle);
    pooldealloc(&m->triangles, (TRIVOID *) dyingtriangle);
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  triangletraverse()   Traverse the triangles, skipping dead ones.         */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  triangle *triangletraverse(struct mesh *m)
  #else /* not ANSI_DECLARATORS */
  triangle *triangletraverse(m)
  struct mesh *m;
  #endif /* not ANSI_DECLARATORS */
  
  {
    triangle *newtriangle;
  
    do {
      newtriangle = (triangle *) traverse(&m->triangles);
      if (newtriangle == (triangle *) NULL) {
        return (triangle *) NULL;
      }
    } while (deadtri(newtriangle));                         /* Skip dead ones. */
    return newtriangle;
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  subsegdealloc()   Deallocate space for a subsegment, marking it dead.    */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  void subsegdealloc(struct mesh *m, subseg *dyingsubseg)
  #else /* not ANSI_DECLARATORS */
  void subsegdealloc(m, dyingsubseg)
  struct mesh *m;
  subseg *dyingsubseg;
  #endif /* not ANSI_DECLARATORS */
  
  {
    /* Mark the subsegment as dead.  This makes it possible to detect dead */
    /*   subsegments when traversing the list of all subsegments.          */
    killsubseg(dyingsubseg);
    pooldealloc(&m->subsegs, (TRIVOID *) dyingsubseg);
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  subsegtraverse()   Traverse the subsegments, skipping dead ones.         */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  subseg *subsegtraverse(struct mesh *m)
  #else /* not ANSI_DECLARATORS */
  subseg *subsegtraverse(m)
  struct mesh *m;
  #endif /* not ANSI_DECLARATORS */
  
  {
    subseg *newsubseg;
  
    do {
      newsubseg = (subseg *) traverse(&m->subsegs);
      if (newsubseg == (subseg *) NULL) {
        return (subseg *) NULL;
      }
    } while (deadsubseg(newsubseg));                        /* Skip dead ones. */
    return newsubseg;
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  vertexdealloc()   Deallocate space for a vertex, marking it dead.        */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  void vertexdealloc(struct mesh *m, vertex dyingvertex)
  #else /* not ANSI_DECLARATORS */
  void vertexdealloc(m, dyingvertex)
  struct mesh *m;
  vertex dyingvertex;
  #endif /* not ANSI_DECLARATORS */
  
  {
    /* Mark the vertex as dead.  This makes it possible to detect dead */
    /*   vertices when traversing the list of all vertices.            */
    setvertextype(dyingvertex, DEADVERTEX);
    pooldealloc(&m->vertices, (TRIVOID *) dyingvertex);
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  vertextraverse()   Traverse the vertices, skipping dead ones.            */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  vertex vertextraverse(struct mesh *m)
  #else /* not ANSI_DECLARATORS */
  vertex vertextraverse(m)
  struct mesh *m;
  #endif /* not ANSI_DECLARATORS */
  
  {
    vertex newvertex;
  
    do {
      newvertex = (vertex) traverse(&m->vertices);
      if (newvertex == (vertex) NULL) {
        return (vertex) NULL;
      }
    } while (vertextype(newvertex) == DEADVERTEX);          /* Skip dead ones. */
    return newvertex;
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  badsubsegdealloc()   Deallocate space for a bad subsegment, marking it   */
  /*                       dead.                                               */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifndef CDT_ONLY
  
  #ifdef ANSI_DECLARATORS
  void badsubsegdealloc(struct mesh *m, struct badsubseg *dyingseg)
  #else /* not ANSI_DECLARATORS */
  void badsubsegdealloc(m, dyingseg)
  struct mesh *m;
  struct badsubseg *dyingseg;
  #endif /* not ANSI_DECLARATORS */
  
  {
    /* Set subsegment's origin to NULL.  This makes it possible to detect dead */
    /*   badsubsegs when traversing the list of all badsubsegs             .   */
    dyingseg->subsegorg = (vertex) NULL;
    pooldealloc(&m->badsubsegs, (TRIVOID *) dyingseg);
  }
  
  #endif /* not CDT_ONLY */
  
  /*****************************************************************************/
  /*                                                                           */
  /*  badsubsegtraverse()   Traverse the bad subsegments, skipping dead ones.  */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifndef CDT_ONLY
  
  #ifdef ANSI_DECLARATORS
  struct badsubseg *badsubsegtraverse(struct mesh *m)
  #else /* not ANSI_DECLARATORS */
  struct badsubseg *badsubsegtraverse(m)
  struct mesh *m;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct badsubseg *newseg;
  
    do {
      newseg = (struct badsubseg *) traverse(&m->badsubsegs);
      if (newseg == (struct badsubseg *) NULL) {
        return (struct badsubseg *) NULL;
      }
    } while (newseg->subsegorg == (vertex) NULL);           /* Skip dead ones. */
    return newseg;
  }
  
  #endif /* not CDT_ONLY */
  
  /*****************************************************************************/
  /*                                                                           */
  /*  getvertex()   Get a specific vertex, by number, from the list.           */
  /*                                                                           */
  /*  The first vertex is number 'firstnumber'.                                */
  /*                                                                           */
  /*  Note that this takes O(n) time (with a small constant, if VERTEXPERBLOCK */
  /*  is large).  I don't care to take the trouble to make it work in constant */
  /*  time.                                                                    */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  vertex getvertex(struct mesh *m, struct behavior *b, int number)
  #else /* not ANSI_DECLARATORS */
  vertex getvertex(m, b, number)
  struct mesh *m;
  struct behavior *b;
  int number;
  #endif /* not ANSI_DECLARATORS */
  
  {
    TRIVOID **getblock;
    char *foundvertex;
    unsigned long long alignptr;
    int current;
  
    getblock = m->vertices.firstblock;
    current = b->firstnumber;
  
    /* Find the right block. */
    if (current + m->vertices.itemsfirstblock <= number) {
      getblock = (TRIVOID **) *getblock;
      current += m->vertices.itemsfirstblock;
      while (current + m->vertices.itemsperblock <= number) {
        getblock = (TRIVOID **) *getblock;
        current += m->vertices.itemsperblock;
      }
    }
  
    /* Now find the right vertex. */
    alignptr = (unsigned long long) (getblock + 1);
    foundvertex = (char *) (alignptr + (unsigned long long) m->vertices.alignbytes -
                            (alignptr % (unsigned long long) m->vertices.alignbytes));
    return (vertex) (foundvertex + m->vertices.itembytes * (number - current));
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  triangledeinit()   Free all remaining allocated memory.                  */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  void triangledeinit(struct mesh *m, struct behavior *b)
  #else /* not ANSI_DECLARATORS */
  void triangledeinit(m, b)
  struct mesh *m;
  struct behavior *b;
  #endif /* not ANSI_DECLARATORS */
  
  {
    pooldeinit(&m->triangles);
    trifree((TRIVOID *) m->dummytribase);
    if (b->usesegments) {
      pooldeinit(&m->subsegs);
      trifree((TRIVOID *) m->dummysubbase);
    }
    pooldeinit(&m->vertices);
  #ifndef CDT_ONLY
    if (b->quality) {
      pooldeinit(&m->badsubsegs);
      if ((b->minangle > 0.0) || b->vararea || b->fixedarea || b->usertest) {
        pooldeinit(&m->badtriangles);
        pooldeinit(&m->flipstackers);
      }
    }
  #endif /* not CDT_ONLY */
  }
  
  /**                                                                         **/
  /**                                                                         **/
  /********* Memory management routines end here                       *********/
  
  /********* Constructors begin here                                   *********/
  /**                                                                         **/
  /**                                                                         **/
  
  /*****************************************************************************/
  /*                                                                           */
  /*  maketriangle()   Create a new triangle with orientation zero.            */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  void maketriangle(struct mesh *m, struct behavior *b, struct otri *newotri)
  #else /* not ANSI_DECLARATORS */
  void maketriangle(m, b, newotri)
  struct mesh *m;
  struct behavior *b;
  struct otri *newotri;
  #endif /* not ANSI_DECLARATORS */
  
  {
    int i;
  
    newotri->tri = (triangle *) poolalloc(&m->triangles);
    /* Initialize the three adjoining triangles to be "outer space". */
    newotri->tri[0] = (triangle) m->dummytri;
    newotri->tri[1] = (triangle) m->dummytri;
    newotri->tri[2] = (triangle) m->dummytri;
    /* Three NULL vertices. */
    newotri->tri[3] = (triangle) NULL;
    newotri->tri[4] = (triangle) NULL;
    newotri->tri[5] = (triangle) NULL;
    if (b->usesegments) {
      /* Initialize the three adjoining subsegments to be the omnipresent */
      /*   subsegment.                                                    */
      newotri->tri[6] = (triangle) m->dummysub;
      newotri->tri[7] = (triangle) m->dummysub;
      newotri->tri[8] = (triangle) m->dummysub;
    }
    for (i = 0; i < m->eextras; i++) {
      setelemattribute(*newotri, i, 0.0);
    }
    if (b->vararea) {
      setareabound(*newotri, -1.0);
    }
  
    newotri->orient = 0;
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  makesubseg()   Create a new subsegment with orientation zero.            */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  void makesubseg(struct mesh *m, struct osub *newsubseg)
  #else /* not ANSI_DECLARATORS */
  void makesubseg(m, newsubseg)
  struct mesh *m;
  struct osub *newsubseg;
  #endif /* not ANSI_DECLARATORS */
  
  {
    newsubseg->ss = (subseg *) poolalloc(&m->subsegs);
    /* Initialize the two adjoining subsegments to be the omnipresent */
    /*   subsegment.                                                  */
    newsubseg->ss[0] = (subseg) m->dummysub;
    newsubseg->ss[1] = (subseg) m->dummysub;
    /* Four NULL vertices. */
    newsubseg->ss[2] = (subseg) NULL;
    newsubseg->ss[3] = (subseg) NULL;
    newsubseg->ss[4] = (subseg) NULL;
    newsubseg->ss[5] = (subseg) NULL;
    /* Initialize the two adjoining triangles to be "outer space." */
    newsubseg->ss[6] = (subseg) m->dummytri;
    newsubseg->ss[7] = (subseg) m->dummytri;
    /* Set the boundary marker to zero. */
    setmark(*newsubseg, 0);
  
    newsubseg->ssorient = 0;
  }
  
  /**                                                                         **/
  /**                                                                         **/
  /********* Constructors end here                                     *********/
  
  /********* Geometric primitives begin here                           *********/
  /**                                                                         **/
  /**                                                                         **/
  
  /* The adaptive exact arithmetic geometric predicates implemented herein are */
  /*   described in detail in my paper, "Adaptive Precision Floating-Point     */
  /*   Arithmetic and Fast Robust Geometric Predicates."  See the header for a */
  /*   full citation.                                                          */
  
  /* Which of the following two methods of finding the absolute values is      */
  /*   fastest is compiler-dependent.  A few compilers can inline and optimize */
  /*   the fabs() call; but most will incur the overhead of a function call,   */
  /*   which is disastrously slow.  A faster way on IEEE machines might be to  */
  /*   mask the appropriate bit, but that's difficult to do in C without       */
  /*   forcing the value to be stored to memory (rather than be kept in the    */
  /*   register to which the optimizer assigned it).                           */
  
  #define Absolute(a)  ((a) >= 0.0 ? (a) : -(a))
  /* #define Absolute(a)  fabs(a) */
  
  /* Many of the operations are broken up into two pieces, a main part that    */
  /*   performs an approximate operation, and a "tail" that computes the       */
  /*   roundoff error of that operation.                                       */
  /*                                                                           */
  /* The operations Fast_Two_Sum(), Fast_Two_Diff(), Two_Sum(), Two_Diff(),    */
  /*   Split(), and Two_Product() are all implemented as described in the      */
  /*   reference.  Each of these macros requires certain variables to be       */
  /*   defined in the calling routine.  The variables `bvirt', `c', `abig',    */
  /*   `_i', `_j', `_k', `_l', `_m', and `_n' are declared `INEXACT' because   */
  /*   they store the result of an operation that may incur roundoff error.    */
  /*   The input parameter `x' (or the highest numbered `x_' parameter) must   */
  /*   also be declared `INEXACT'.                                             */
  
  #define Fast_Two_Sum_Tail(a, b, x, y) \
    bvirt = x - a; \
    y = b - bvirt
  
  #define Fast_Two_Sum(a, b, x, y) \
    x = (REAL) (a + b); \
    Fast_Two_Sum_Tail(a, b, x, y)
  
  #define Two_Sum_Tail(a, b, x, y) \
    bvirt = (REAL) (x - a); \
    avirt = x - bvirt; \
    bround = b - bvirt; \
    around = a - avirt; \
    y = around + bround
  
  #define Two_Sum(a, b, x, y) \
    x = (REAL) (a + b); \
    Two_Sum_Tail(a, b, x, y)
  
  #define Two_Diff_Tail(a, b, x, y) \
    bvirt = (REAL) (a - x); \
    avirt = x + bvirt; \
    bround = bvirt - b; \
    around = a - avirt; \
    y = around + bround
  
  #define Two_Diff(a, b, x, y) \
    x = (REAL) (a - b); \
    Two_Diff_Tail(a, b, x, y)
  
  #define Split(a, ahi, alo) \
    c = (REAL) (splitter * a); \
    abig = (REAL) (c - a); \
    ahi = c - abig; \
    alo = a - ahi
  
  #define Two_Product_Tail(a, b, x, y) \
    Split(a, ahi, alo); \
    Split(b, bhi, blo); \
    err1 = x - (ahi * bhi); \
    err2 = err1 - (alo * bhi); \
    err3 = err2 - (ahi * blo); \
    y = (alo * blo) - err3
  
  #define Two_Product(a, b, x, y) \
    x = (REAL) (a * b); \
    Two_Product_Tail(a, b, x, y)
  
  /* Two_Product_Presplit() is Two_Product() where one of the inputs has       */
  /*   already been split.  Avoids redundant splitting.                        */
  
  #define Two_Product_Presplit(a, b, bhi, blo, x, y) \
    x = (REAL) (a * b); \
    Split(a, ahi, alo); \
    err1 = x - (ahi * bhi); \
    err2 = err1 - (alo * bhi); \
    err3 = err2 - (ahi * blo); \
    y = (alo * blo) - err3
  
  /* Square() can be done more quickly than Two_Product().                     */
  
  #define Square_Tail(a, x, y) \
    Split(a, ahi, alo); \
    err1 = x - (ahi * ahi); \
    err3 = err1 - ((ahi + ahi) * alo); \
    y = (alo * alo) - err3
  
  #define Square(a, x, y) \
    x = (REAL) (a * a); \
    Square_Tail(a, x, y)
  
  /* Macros for summing expansions of various fixed lengths.  These are all    */
  /*   unrolled versions of Expansion_Sum().                                   */
  
  #define Two_One_Sum(a1, a0, b, x2, x1, x0) \
    Two_Sum(a0, b , _i, x0); \
    Two_Sum(a1, _i, x2, x1)
  
  #define Two_One_Diff(a1, a0, b, x2, x1, x0) \
    Two_Diff(a0, b , _i, x0); \
    Two_Sum( a1, _i, x2, x1)
  
  #define Two_Two_Sum(a1, a0, b1, b0, x3, x2, x1, x0) \
    Two_One_Sum(a1, a0, b0, _j, _0, x0); \
    Two_One_Sum(_j, _0, b1, x3, x2, x1)
  
  #define Two_Two_Diff(a1, a0, b1, b0, x3, x2, x1, x0) \
    Two_One_Diff(a1, a0, b0, _j, _0, x0); \
    Two_One_Diff(_j, _0, b1, x3, x2, x1)
  
  /* Macro for multiplying a two-component expansion by a single component.    */
  
  #define Two_One_Product(a1, a0, b, x3, x2, x1, x0) \
    Split(b, bhi, blo); \
    Two_Product_Presplit(a0, b, bhi, blo, _i, x0); \
    Two_Product_Presplit(a1, b, bhi, blo, _j, _0); \
    Two_Sum(_i, _0, _k, x1); \
    Fast_Two_Sum(_j, _k, x3, x2)
  
  /*****************************************************************************/
  /*                                                                           */
  /*  exactinit()   Initialize the variables used for exact arithmetic.        */
  /*                                                                           */
  /*  `epsilon' is the largest power of two such that 1.0 + epsilon = 1.0 in   */
  /*  floating-point arithmetic.  `epsilon' bounds the relative roundoff       */
  /*  error.  It is used for floating-point error analysis.                    */
  /*                                                                           */
  /*  `splitter' is used to split floating-point numbers into two half-        */
  /*  length significands for exact multiplication.                            */
  /*                                                                           */
  /*  I imagine that a highly optimizing compiler might be too smart for its   */
  /*  own good, and somehow cause this routine to fail, if it pretends that    */
  /*  floating-point arithmetic is too much like real arithmetic.              */
  /*                                                                           */
  /*  Don't change this routine unless you fully understand it.                */
  /*                                                                           */
  /*****************************************************************************/
  
  void exactinit()
  {
    REAL half;
    REAL check, lastcheck;
    int every_other;
  #ifdef LINUX
    int cword;
  #endif /* LINUX */
  
  #ifdef CPU86
  #ifdef SINGLE
    _control87(_PC_24, _MCW_PC); /* Set FPU control word for single precision. */
  #else /* not SINGLE */
    _control87(_PC_53, _MCW_PC); /* Set FPU control word for double precision. */
  #endif /* not SINGLE */
  #endif /* CPU86 */
  #ifdef LINUX
  #ifdef SINGLE
    /*  cword = 4223; */
    cword = 4210;                 /* set FPU control word for single precision */
  #else /* not SINGLE */
    /*  cword = 4735; */
    cword = 4722;                 /* set FPU control word for double precision */
  #endif /* not SINGLE */
    _FPU_SETCW(cword);
  #endif /* LINUX */
  
    every_other = 1;
    half = 0.5;
    epsilon = 1.0;
    splitter = 1.0;
    check = 1.0;
    /* Repeatedly divide `epsilon' by two until it is too small to add to      */
    /*   one without causing roundoff.  (Also check if the sum is equal to     */
    /*   the previous sum, for machines that round up instead of using exact   */
    /*   rounding.  Not that these routines will work on such machines.)       */
    do {
      lastcheck = check;
      epsilon *= half;
      if (every_other) {
        splitter *= 2.0;
      }
      every_other = !every_other;
      check = 1.0 + epsilon;
    } while ((check != 1.0) && (check != lastcheck));
    splitter += 1.0;
    /* Error bounds for orientation and incircle tests. */
    resulterrbound = (3.0 + 8.0 * epsilon) * epsilon;
    ccwerrboundA = (3.0 + 16.0 * epsilon) * epsilon;
    ccwerrboundB = (2.0 + 12.0 * epsilon) * epsilon;
    ccwerrboundC = (9.0 + 64.0 * epsilon) * epsilon * epsilon;
    iccerrboundA = (10.0 + 96.0 * epsilon) * epsilon;
    iccerrboundB = (4.0 + 48.0 * epsilon) * epsilon;
    iccerrboundC = (44.0 + 576.0 * epsilon) * epsilon * epsilon;
    o3derrboundA = (7.0 + 56.0 * epsilon) * epsilon;
    o3derrboundB = (3.0 + 28.0 * epsilon) * epsilon;
    o3derrboundC = (26.0 + 288.0 * epsilon) * epsilon * epsilon;
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  fast_expansion_sum_zeroelim()   Sum two expansions, eliminating zero     */
  /*                                  components from the output expansion.    */
  /*                                                                           */
  /*  Sets h = e + f.  See my Robust Predicates paper for details.             */
  /*                                                                           */
  /*  If round-to-even is used (as with IEEE 754), maintains the strongly      */
  /*  nonoverlapping property.  (That is, if e is strongly nonoverlapping, h   */
  /*  will be also.)  Does NOT maintain the nonoverlapping or nonadjacent      */
  /*  properties.                                                              */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  int fast_expansion_sum_zeroelim(int elen, REAL *e, int flen, REAL *f, REAL *h)
  #else /* not ANSI_DECLARATORS */
  int fast_expansion_sum_zeroelim(elen, e, flen, f, h)  /* h cannot be e or f. */
  int elen;
  REAL *e;
  int flen;
  REAL *f;
  REAL *h;
  #endif /* not ANSI_DECLARATORS */
  
  {
    REAL Q;
    INEXACT REAL Qnew;
    INEXACT REAL hh;
    INEXACT REAL bvirt;
    REAL avirt, bround, around;
    int eindex, findex, hindex;
    REAL enow, fnow;
  
    enow = e[0];
    fnow = f[0];
    eindex = findex = 0;
    if ((fnow > enow) == (fnow > -enow)) {
      Q = enow;
      enow = e[++eindex];
    } else {
      Q = fnow;
      fnow = f[++findex];
    }
    hindex = 0;
    if ((eindex < elen) && (findex < flen)) {
      if ((fnow > enow) == (fnow > -enow)) {
        Fast_Two_Sum(enow, Q, Qnew, hh);
        enow = e[++eindex];
      } else {
        Fast_Two_Sum(fnow, Q, Qnew, hh);
        fnow = f[++findex];
      }
      Q = Qnew;
      if (hh != 0.0) {
        h[hindex++] = hh;
      }
      while ((eindex < elen) && (findex < flen)) {
        if ((fnow > enow) == (fnow > -enow)) {
          Two_Sum(Q, enow, Qnew, hh);
          enow = e[++eindex];
        } else {
          Two_Sum(Q, fnow, Qnew, hh);
          fnow = f[++findex];
        }
        Q = Qnew;
        if (hh != 0.0) {
          h[hindex++] = hh;
        }
      }
    }
    while (eindex < elen) {
      Two_Sum(Q, enow, Qnew, hh);
      enow = e[++eindex];
      Q = Qnew;
      if (hh != 0.0) {
        h[hindex++] = hh;
      }
    }
    while (findex < flen) {
      Two_Sum(Q, fnow, Qnew, hh);
      fnow = f[++findex];
      Q = Qnew;
      if (hh != 0.0) {
        h[hindex++] = hh;
      }
    }
    if ((Q != 0.0) || (hindex == 0)) {
      h[hindex++] = Q;
    }
    return hindex;
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  scale_expansion_zeroelim()   Multiply an expansion by a scalar,          */
  /*                               eliminating zero components from the        */
  /*                               output expansion.                           */
  /*                                                                           */
  /*  Sets h = be.  See my Robust Predicates paper for details.                */
  /*                                                                           */
  /*  Maintains the nonoverlapping property.  If round-to-even is used (as     */
  /*  with IEEE 754), maintains the strongly nonoverlapping and nonadjacent    */
  /*  properties as well.  (That is, if e has one of these properties, so      */
  /*  will h.)                                                                 */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  int scale_expansion_zeroelim(int elen, REAL *e, REAL b, REAL *h)
  #else /* not ANSI_DECLARATORS */
  int scale_expansion_zeroelim(elen, e, b, h)   /* e and h cannot be the same. */
  int elen;
  REAL *e;
  REAL b;
  REAL *h;
  #endif /* not ANSI_DECLARATORS */
  
  {
    INEXACT REAL Q, sum;
    REAL hh;
    INEXACT REAL product1;
    REAL product0;
    int eindex, hindex;
    REAL enow;
    INEXACT REAL bvirt;
    REAL avirt, bround, around;
    INEXACT REAL c;
    INEXACT REAL abig;
    REAL ahi, alo, bhi, blo;
    REAL err1, err2, err3;
  
    Split(b, bhi, blo);
    Two_Product_Presplit(e[0], b, bhi, blo, Q, hh);
    hindex = 0;
    if (hh != 0) {
      h[hindex++] = hh;
    }
    for (eindex = 1; eindex < elen; eindex++) {
      enow = e[eindex];
      Two_Product_Presplit(enow, b, bhi, blo, product1, product0);
      Two_Sum(Q, product0, sum, hh);
      if (hh != 0) {
        h[hindex++] = hh;
      }
      Fast_Two_Sum(product1, sum, Q, hh);
      if (hh != 0) {
        h[hindex++] = hh;
      }
    }
    if ((Q != 0.0) || (hindex == 0)) {
      h[hindex++] = Q;
    }
    return hindex;
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  estimate()   Produce a one-word estimate of an expansion's value.        */
  /*                                                                           */
  /*  See my Robust Predicates paper for details.                              */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  REAL estimate(int elen, REAL *e)
  #else /* not ANSI_DECLARATORS */
  REAL estimate(elen, e)
  int elen;
  REAL *e;
  #endif /* not ANSI_DECLARATORS */
  
  {
    REAL Q;
    int eindex;
  
    Q = e[0];
    for (eindex = 1; eindex < elen; eindex++) {
      Q += e[eindex];
    }
    return Q;
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  counterclockwise()   Return a positive value if the points pa, pb, and   */
  /*                       pc occur in counterclockwise order; a negative      */
  /*                       value if they occur in clockwise order; and zero    */
  /*                       if they are collinear.  The result is also a rough  */
  /*                       approximation of twice the signed area of the       */
  /*                       triangle defined by the three points.               */
  /*                                                                           */
  /*  Uses exact arithmetic if necessary to ensure a correct answer.  The      */
  /*  result returned is the determinant of a matrix.  This determinant is     */
  /*  computed adaptively, in the sense that exact arithmetic is used only to  */
  /*  the degree it is needed to ensure that the returned value has the        */
  /*  correct sign.  Hence, this function is usually quite fast, but will run  */
  /*  more slowly when the input points are collinear or nearly so.            */
  /*                                                                           */
  /*  See my Robust Predicates paper for details.                              */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  REAL counterclockwiseadapt(vertex pa, vertex pb, vertex pc, REAL detsum)
  #else /* not ANSI_DECLARATORS */
  REAL counterclockwiseadapt(pa, pb, pc, detsum)
  vertex pa;
  vertex pb;
  vertex pc;
  REAL detsum;
  #endif /* not ANSI_DECLARATORS */
  
  {
    INEXACT REAL acx, acy, bcx, bcy;
    REAL acxtail, acytail, bcxtail, bcytail;
    INEXACT REAL detleft, detright;
    REAL detlefttail, detrighttail;
    REAL det, errbound;
    REAL B[4], C1[8], C2[12], D[16];
    INEXACT REAL B3;
    int C1length, C2length, Dlength;
    REAL u[4];
    INEXACT REAL u3;
    INEXACT REAL s1, t1;
    REAL s0, t0;
  
    INEXACT REAL bvirt;
    REAL avirt, bround, around;
    INEXACT REAL c;
    INEXACT REAL abig;
    REAL ahi, alo, bhi, blo;
    REAL err1, err2, err3;
    INEXACT REAL _i, _j;
    REAL _0;
  
    acx = (REAL) (pa[0] - pc[0]);
    bcx = (REAL) (pb[0] - pc[0]);
    acy = (REAL) (pa[1] - pc[1]);
    bcy = (REAL) (pb[1] - pc[1]);
  
    Two_Product(acx, bcy, detleft, detlefttail);
    Two_Product(acy, bcx, detright, detrighttail);
  
    Two_Two_Diff(detleft, detlefttail, detright, detrighttail,
                 B3, B[2], B[1], B[0]);
    B[3] = B3;
  
    det = estimate(4, B);
    errbound = ccwerrboundB * detsum;
    if ((det >= errbound) || (-det >= errbound)) {
      return det;
    }
  
    Two_Diff_Tail(pa[0], pc[0], acx, acxtail);
    Two_Diff_Tail(pb[0], pc[0], bcx, bcxtail);
    Two_Diff_Tail(pa[1], pc[1], acy, acytail);
    Two_Diff_Tail(pb[1], pc[1], bcy, bcytail);
  
    if ((acxtail == 0.0) && (acytail == 0.0)
        && (bcxtail == 0.0) && (bcytail == 0.0)) {
      return det;
    }
  
    errbound = ccwerrboundC * detsum + resulterrbound * Absolute(det);
    det += (acx * bcytail + bcy * acxtail)
         - (acy * bcxtail + bcx * acytail);
    if ((det >= errbound) || (-det >= errbound)) {
      return det;
    }
  
    Two_Product(acxtail, bcy, s1, s0);
    Two_Product(acytail, bcx, t1, t0);
    Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
    u[3] = u3;
    C1length = fast_expansion_sum_zeroelim(4, B, 4, u, C1);
  
    Two_Product(acx, bcytail, s1, s0);
    Two_Product(acy, bcxtail, t1, t0);
    Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
    u[3] = u3;
    C2length = fast_expansion_sum_zeroelim(C1length, C1, 4, u, C2);
  
    Two_Product(acxtail, bcytail, s1, s0);
    Two_Product(acytail, bcxtail, t1, t0);
    Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
    u[3] = u3;
    Dlength = fast_expansion_sum_zeroelim(C2length, C2, 4, u, D);
  
    return(D[Dlength - 1]);
  }
  
  #ifdef ANSI_DECLARATORS
  REAL counterclockwise(struct mesh *m, struct behavior *b,
                        vertex pa, vertex pb, vertex pc)
  #else /* not ANSI_DECLARATORS */
  REAL counterclockwise(m, b, pa, pb, pc)
  struct mesh *m;
  struct behavior *b;
  vertex pa;
  vertex pb;
  vertex pc;
  #endif /* not ANSI_DECLARATORS */
  
  {
    REAL detleft, detright, det;
    REAL detsum, errbound;
  
    m->counterclockcount++;
  
    detleft = (pa[0] - pc[0]) * (pb[1] - pc[1]);
    detright = (pa[1] - pc[1]) * (pb[0] - pc[0]);
    det = detleft - detright;
  
    if (b->noexact) {
      return det;
    }
  
    if (detleft > 0.0) {
      if (detright <= 0.0) {
        return det;
      } else {
        detsum = detleft + detright;
      }
    } else if (detleft < 0.0) {
      if (detright >= 0.0) {
        return det;
      } else {
        detsum = -detleft - detright;
      }
    } else {
      return det;
    }
  
    errbound = ccwerrboundA * detsum;
    if ((det >= errbound) || (-det >= errbound)) {
      return det;
    }
  
    return counterclockwiseadapt(pa, pb, pc, detsum);
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  incircle()   Return a positive value if the point pd lies inside the     */
  /*               circle passing through pa, pb, and pc; a negative value if  */
  /*               it lies outside; and zero if the four points are cocircular.*/
  /*               The points pa, pb, and pc must be in counterclockwise       */
  /*               order, or the sign of the result will be reversed.          */
  /*                                                                           */
  /*  Uses exact arithmetic if necessary to ensure a correct answer.  The      */
  /*  result returned is the determinant of a matrix.  This determinant is     */
  /*  computed adaptively, in the sense that exact arithmetic is used only to  */
  /*  the degree it is needed to ensure that the returned value has the        */
  /*  correct sign.  Hence, this function is usually quite fast, but will run  */
  /*  more slowly when the input points are cocircular or nearly so.           */
  /*                                                                           */
  /*  See my Robust Predicates paper for details.                              */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  REAL incircleadapt(vertex pa, vertex pb, vertex pc, vertex pd, REAL permanent)
  #else /* not ANSI_DECLARATORS */
  REAL incircleadapt(pa, pb, pc, pd, permanent)
  vertex pa;
  vertex pb;
  vertex pc;
  vertex pd;
  REAL permanent;
  #endif /* not ANSI_DECLARATORS */
  
  {
    INEXACT REAL adx, bdx, cdx, ady, bdy, cdy;
    REAL det, errbound;
  
    INEXACT REAL bdxcdy1, cdxbdy1, cdxady1, adxcdy1, adxbdy1, bdxady1;
    REAL bdxcdy0, cdxbdy0, cdxady0, adxcdy0, adxbdy0, bdxady0;
    REAL bc[4], ca[4], ab[4];
    INEXACT REAL bc3, ca3, ab3;
    REAL axbc[8], axxbc[16], aybc[8], ayybc[16], adet[32];
    int axbclen, axxbclen, aybclen, ayybclen, alen;
    REAL bxca[8], bxxca[16], byca[8], byyca[16], bdet[32];
    int bxcalen, bxxcalen, bycalen, byycalen, blen;
    REAL cxab[8], cxxab[16], cyab[8], cyyab[16], cdet[32];
    int cxablen, cxxablen, cyablen, cyyablen, clen;
    REAL abdet[64];
    int ablen;
    REAL fin1[1152], fin2[1152];
    REAL *finnow, *finother, *finswap;
    int finlength;
  
    REAL adxtail, bdxtail, cdxtail, adytail, bdytail, cdytail;
    INEXACT REAL adxadx1, adyady1, bdxbdx1, bdybdy1, cdxcdx1, cdycdy1;
    REAL adxadx0, adyady0, bdxbdx0, bdybdy0, cdxcdx0, cdycdy0;
    REAL aa[4], bb[4], cc[4];
    INEXACT REAL aa3, bb3, cc3;
    INEXACT REAL ti1, tj1;
    REAL ti0, tj0;
    REAL u[4], v[4];
    INEXACT REAL u3, v3;
    REAL temp8[8], temp16a[16], temp16b[16], temp16c[16];
    REAL temp32a[32], temp32b[32], temp48[48], temp64[64];
    int temp8len, temp16alen, temp16blen, temp16clen;
    int temp32alen, temp32blen, temp48len, temp64len;
    REAL axtbb[8], axtcc[8], aytbb[8], aytcc[8];
    int axtbblen, axtcclen, aytbblen, aytcclen;
    REAL bxtaa[8], bxtcc[8], bytaa[8], bytcc[8];
    int bxtaalen, bxtcclen, bytaalen, bytcclen;
    REAL cxtaa[8], cxtbb[8], cytaa[8], cytbb[8];
    int cxtaalen, cxtbblen, cytaalen, cytbblen;
    REAL axtbc[8], aytbc[8], bxtca[8], bytca[8], cxtab[8], cytab[8];
    int axtbclen, aytbclen, bxtcalen, bytcalen, cxtablen, cytablen;
    REAL axtbct[16], aytbct[16], bxtcat[16], bytcat[16], cxtabt[16], cytabt[16];
    int axtbctlen, aytbctlen, bxtcatlen, bytcatlen, cxtabtlen, cytabtlen;
    REAL axtbctt[8], aytbctt[8], bxtcatt[8];
    REAL bytcatt[8], cxtabtt[8], cytabtt[8];
    int axtbcttlen, aytbcttlen, bxtcattlen, bytcattlen, cxtabttlen, cytabttlen;
    REAL abt[8], bct[8], cat[8];
    int abtlen, bctlen, catlen;
    REAL abtt[4], bctt[4], catt[4];
    int abttlen, bcttlen, cattlen;
    INEXACT REAL abtt3, bctt3, catt3;
    REAL negate;
  
    INEXACT REAL bvirt;
    REAL avirt, bround, around;
    INEXACT REAL c;
    INEXACT REAL abig;
    REAL ahi, alo, bhi, blo;
    REAL err1, err2, err3;
    INEXACT REAL _i, _j;
    REAL _0;
  
    adx = (REAL) (pa[0] - pd[0]);
    bdx = (REAL) (pb[0] - pd[0]);
    cdx = (REAL) (pc[0] - pd[0]);
    ady = (REAL) (pa[1] - pd[1]);
    bdy = (REAL) (pb[1] - pd[1]);
    cdy = (REAL) (pc[1] - pd[1]);
  
    Two_Product(bdx, cdy, bdxcdy1, bdxcdy0);
    Two_Product(cdx, bdy, cdxbdy1, cdxbdy0);
    Two_Two_Diff(bdxcdy1, bdxcdy0, cdxbdy1, cdxbdy0, bc3, bc[2], bc[1], bc[0]);
    bc[3] = bc3;
    axbclen = scale_expansion_zeroelim(4, bc, adx, axbc);
    axxbclen = scale_expansion_zeroelim(axbclen, axbc, adx, axxbc);
    aybclen = scale_expansion_zeroelim(4, bc, ady, aybc);
    ayybclen = scale_expansion_zeroelim(aybclen, aybc, ady, ayybc);
    alen = fast_expansion_sum_zeroelim(axxbclen, axxbc, ayybclen, ayybc, adet);
  
    Two_Product(cdx, ady, cdxady1, cdxady0);
    Two_Product(adx, cdy, adxcdy1, adxcdy0);
    Two_Two_Diff(cdxady1, cdxady0, adxcdy1, adxcdy0, ca3, ca[2], ca[1], ca[0]);
    ca[3] = ca3;
    bxcalen = scale_expansion_zeroelim(4, ca, bdx, bxca);
    bxxcalen = scale_expansion_zeroelim(bxcalen, bxca, bdx, bxxca);
    bycalen = scale_expansion_zeroelim(4, ca, bdy, byca);
    byycalen = scale_expansion_zeroelim(bycalen, byca, bdy, byyca);
    blen = fast_expansion_sum_zeroelim(bxxcalen, bxxca, byycalen, byyca, bdet);
  
    Two_Product(adx, bdy, adxbdy1, adxbdy0);
    Two_Product(bdx, ady, bdxady1, bdxady0);
    Two_Two_Diff(adxbdy1, adxbdy0, bdxady1, bdxady0, ab3, ab[2], ab[1], ab[0]);
    ab[3] = ab3;
    cxablen = scale_expansion_zeroelim(4, ab, cdx, cxab);
    cxxablen = scale_expansion_zeroelim(cxablen, cxab, cdx, cxxab);
    cyablen = scale_expansion_zeroelim(4, ab, cdy, cyab);
    cyyablen = scale_expansion_zeroelim(cyablen, cyab, cdy, cyyab);
    clen = fast_expansion_sum_zeroelim(cxxablen, cxxab, cyyablen, cyyab, cdet);
  
    ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
    finlength = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, fin1);
  
    det = estimate(finlength, fin1);
    errbound = iccerrboundB * permanent;
    if ((det >= errbound) || (-det >= errbound)) {
      return det;
    }
  
    Two_Diff_Tail(pa[0], pd[0], adx, adxtail);
    Two_Diff_Tail(pa[1], pd[1], ady, adytail);
    Two_Diff_Tail(pb[0], pd[0], bdx, bdxtail);
    Two_Diff_Tail(pb[1], pd[1], bdy, bdytail);
    Two_Diff_Tail(pc[0], pd[0], cdx, cdxtail);
    Two_Diff_Tail(pc[1], pd[1], cdy, cdytail);
    if ((adxtail == 0.0) && (bdxtail == 0.0) && (cdxtail == 0.0)
        && (adytail == 0.0) && (bdytail == 0.0) && (cdytail == 0.0)) {
      return det;
    }
  
    errbound = iccerrboundC * permanent + resulterrbound * Absolute(det);
    det += ((adx * adx + ady * ady) * ((bdx * cdytail + cdy * bdxtail)
                                       - (bdy * cdxtail + cdx * bdytail))
            + 2.0 * (adx * adxtail + ady * adytail) * (bdx * cdy - bdy * cdx))
         + ((bdx * bdx + bdy * bdy) * ((cdx * adytail + ady * cdxtail)
                                       - (cdy * adxtail + adx * cdytail))
            + 2.0 * (bdx * bdxtail + bdy * bdytail) * (cdx * ady - cdy * adx))
         + ((cdx * cdx + cdy * cdy) * ((adx * bdytail + bdy * adxtail)
                                       - (ady * bdxtail + bdx * adytail))
            + 2.0 * (cdx * cdxtail + cdy * cdytail) * (adx * bdy - ady * bdx));
    if ((det >= errbound) || (-det >= errbound)) {
      return det;
    }
  
    finnow = fin1;
    finother = fin2;
  
    if ((bdxtail != 0.0) || (bdytail != 0.0)
        || (cdxtail != 0.0) || (cdytail != 0.0)) {
      Square(adx, adxadx1, adxadx0);
      Square(ady, adyady1, adyady0);
      Two_Two_Sum(adxadx1, adxadx0, adyady1, adyady0, aa3, aa[2], aa[1], aa[0]);
      aa[3] = aa3;
    }
    if ((cdxtail != 0.0) || (cdytail != 0.0)
        || (adxtail != 0.0) || (adytail != 0.0)) {
      Square(bdx, bdxbdx1, bdxbdx0);
      Square(bdy, bdybdy1, bdybdy0);
      Two_Two_Sum(bdxbdx1, bdxbdx0, bdybdy1, bdybdy0, bb3, bb[2], bb[1], bb[0]);
      bb[3] = bb3;
    }
    if ((adxtail != 0.0) || (adytail != 0.0)
        || (bdxtail != 0.0) || (bdytail != 0.0)) {
      Square(cdx, cdxcdx1, cdxcdx0);
      Square(cdy, cdycdy1, cdycdy0);
      Two_Two_Sum(cdxcdx1, cdxcdx0, cdycdy1, cdycdy0, cc3, cc[2], cc[1], cc[0]);
      cc[3] = cc3;
    }
  
    if (adxtail != 0.0) {
      axtbclen = scale_expansion_zeroelim(4, bc, adxtail, axtbc);
      temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, 2.0 * adx,
                                            temp16a);
  
      axtcclen = scale_expansion_zeroelim(4, cc, adxtail, axtcc);
      temp16blen = scale_expansion_zeroelim(axtcclen, axtcc, bdy, temp16b);
  
      axtbblen = scale_expansion_zeroelim(4, bb, adxtail, axtbb);
      temp16clen = scale_expansion_zeroelim(axtbblen, axtbb, -cdy, temp16c);
  
      temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
                                              temp16blen, temp16b, temp32a);
      temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
                                              temp32alen, temp32a, temp48);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
                                              temp48, finother);
      finswap = finnow; finnow = finother; finother = finswap;
    }
    if (adytail != 0.0) {
      aytbclen = scale_expansion_zeroelim(4, bc, adytail, aytbc);
      temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, 2.0 * ady,
                                            temp16a);
  
      aytbblen = scale_expansion_zeroelim(4, bb, adytail, aytbb);
      temp16blen = scale_expansion_zeroelim(aytbblen, aytbb, cdx, temp16b);
  
      aytcclen = scale_expansion_zeroelim(4, cc, adytail, aytcc);
      temp16clen = scale_expansion_zeroelim(aytcclen, aytcc, -bdx, temp16c);
  
      temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
                                              temp16blen, temp16b, temp32a);
      temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
                                              temp32alen, temp32a, temp48);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
                                              temp48, finother);
      finswap = finnow; finnow = finother; finother = finswap;
    }
    if (bdxtail != 0.0) {
      bxtcalen = scale_expansion_zeroelim(4, ca, bdxtail, bxtca);
      temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, 2.0 * bdx,
                                            temp16a);
  
      bxtaalen = scale_expansion_zeroelim(4, aa, bdxtail, bxtaa);
      temp16blen = scale_expansion_zeroelim(bxtaalen, bxtaa, cdy, temp16b);
  
      bxtcclen = scale_expansion_zeroelim(4, cc, bdxtail, bxtcc);
      temp16clen = scale_expansion_zeroelim(bxtcclen, bxtcc, -ady, temp16c);
  
      temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
                                              temp16blen, temp16b, temp32a);
      temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
                                              temp32alen, temp32a, temp48);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
                                              temp48, finother);
      finswap = finnow; finnow = finother; finother = finswap;
    }
    if (bdytail != 0.0) {
      bytcalen = scale_expansion_zeroelim(4, ca, bdytail, bytca);
      temp16alen = scale_expansion_zeroelim(bytcalen, bytca, 2.0 * bdy,
                                            temp16a);
  
      bytcclen = scale_expansion_zeroelim(4, cc, bdytail, bytcc);
      temp16blen = scale_expansion_zeroelim(bytcclen, bytcc, adx, temp16b);
  
      bytaalen = scale_expansion_zeroelim(4, aa, bdytail, bytaa);
      temp16clen = scale_expansion_zeroelim(bytaalen, bytaa, -cdx, temp16c);
  
      temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
                                              temp16blen, temp16b, temp32a);
      temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
                                              temp32alen, temp32a, temp48);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
                                              temp48, finother);
      finswap = finnow; finnow = finother; finother = finswap;
    }
    if (cdxtail != 0.0) {
      cxtablen = scale_expansion_zeroelim(4, ab, cdxtail, cxtab);
      temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, 2.0 * cdx,
                                            temp16a);
  
      cxtbblen = scale_expansion_zeroelim(4, bb, cdxtail, cxtbb);
      temp16blen = scale_expansion_zeroelim(cxtbblen, cxtbb, ady, temp16b);
  
      cxtaalen = scale_expansion_zeroelim(4, aa, cdxtail, cxtaa);
      temp16clen = scale_expansion_zeroelim(cxtaalen, cxtaa, -bdy, temp16c);
  
      temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
                                              temp16blen, temp16b, temp32a);
      temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
                                              temp32alen, temp32a, temp48);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
                                              temp48, finother);
      finswap = finnow; finnow = finother; finother = finswap;
    }
    if (cdytail != 0.0) {
      cytablen = scale_expansion_zeroelim(4, ab, cdytail, cytab);
      temp16alen = scale_expansion_zeroelim(cytablen, cytab, 2.0 * cdy,
                                            temp16a);
  
      cytaalen = scale_expansion_zeroelim(4, aa, cdytail, cytaa);
      temp16blen = scale_expansion_zeroelim(cytaalen, cytaa, bdx, temp16b);
  
      cytbblen = scale_expansion_zeroelim(4, bb, cdytail, cytbb);
      temp16clen = scale_expansion_zeroelim(cytbblen, cytbb, -adx, temp16c);
  
      temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
                                              temp16blen, temp16b, temp32a);
      temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
                                              temp32alen, temp32a, temp48);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
                                              temp48, finother);
      finswap = finnow; finnow = finother; finother = finswap;
    }
  
    if ((adxtail != 0.0) || (adytail != 0.0)) {
      if ((bdxtail != 0.0) || (bdytail != 0.0)
          || (cdxtail != 0.0) || (cdytail != 0.0)) {
        Two_Product(bdxtail, cdy, ti1, ti0);
        Two_Product(bdx, cdytail, tj1, tj0);
        Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
        u[3] = u3;
        negate = -bdy;
        Two_Product(cdxtail, negate, ti1, ti0);
        negate = -bdytail;
        Two_Product(cdx, negate, tj1, tj0);
        Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
        v[3] = v3;
        bctlen = fast_expansion_sum_zeroelim(4, u, 4, v, bct);
  
        Two_Product(bdxtail, cdytail, ti1, ti0);
        Two_Product(cdxtail, bdytail, tj1, tj0);
        Two_Two_Diff(ti1, ti0, tj1, tj0, bctt3, bctt[2], bctt[1], bctt[0]);
        bctt[3] = bctt3;
        bcttlen = 4;
      } else {
        bct[0] = 0.0;
        bctlen = 1;
        bctt[0] = 0.0;
        bcttlen = 1;
      }
  
      if (adxtail != 0.0) {
        temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, adxtail, temp16a);
        axtbctlen = scale_expansion_zeroelim(bctlen, bct, adxtail, axtbct);
        temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, 2.0 * adx,
                                              temp32a);
        temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
                                                temp32alen, temp32a, temp48);
        finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
                                                temp48, finother);
        finswap = finnow; finnow = finother; finother = finswap;
        if (bdytail != 0.0) {
          temp8len = scale_expansion_zeroelim(4, cc, adxtail, temp8);
          temp16alen = scale_expansion_zeroelim(temp8len, temp8, bdytail,
                                                temp16a);
          finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
                                                  temp16a, finother);
          finswap = finnow; finnow = finother; finother = finswap;
        }
        if (cdytail != 0.0) {
          temp8len = scale_expansion_zeroelim(4, bb, -adxtail, temp8);
          temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail,
                                                temp16a);
          finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
                                                  temp16a, finother);
          finswap = finnow; finnow = finother; finother = finswap;
        }
  
        temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, adxtail,
                                              temp32a);
        axtbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adxtail, axtbctt);
        temp16alen = scale_expansion_zeroelim(axtbcttlen, axtbctt, 2.0 * adx,
                                              temp16a);
        temp16blen = scale_expansion_zeroelim(axtbcttlen, axtbctt, adxtail,
                                              temp16b);
        temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
                                                temp16blen, temp16b, temp32b);
        temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
                                                temp32blen, temp32b, temp64);
        finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
                                                temp64, finother);
        finswap = finnow; finnow = finother; finother = finswap;
      }
      if (adytail != 0.0) {
        temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, adytail, temp16a);
        aytbctlen = scale_expansion_zeroelim(bctlen, bct, adytail, aytbct);
        temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, 2.0 * ady,
                                              temp32a);
        temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
                                                temp32alen, temp32a, temp48);
        finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
                                                temp48, finother);
        finswap = finnow; finnow = finother; finother = finswap;
  
  
        temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, adytail,
                                              temp32a);
        aytbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adytail, aytbctt);
        temp16alen = scale_expansion_zeroelim(aytbcttlen, aytbctt, 2.0 * ady,
                                              temp16a);
        temp16blen = scale_expansion_zeroelim(aytbcttlen, aytbctt, adytail,
                                              temp16b);
        temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
                                                temp16blen, temp16b, temp32b);
        temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
                                                temp32blen, temp32b, temp64);
        finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
                                                temp64, finother);
        finswap = finnow; finnow = finother; finother = finswap;
      }
    }
    if ((bdxtail != 0.0) || (bdytail != 0.0)) {
      if ((cdxtail != 0.0) || (cdytail != 0.0)
          || (adxtail != 0.0) || (adytail != 0.0)) {
        Two_Product(cdxtail, ady, ti1, ti0);
        Two_Product(cdx, adytail, tj1, tj0);
        Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
        u[3] = u3;
        negate = -cdy;
        Two_Product(adxtail, negate, ti1, ti0);
        negate = -cdytail;
        Two_Product(adx, negate, tj1, tj0);
        Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
        v[3] = v3;
        catlen = fast_expansion_sum_zeroelim(4, u, 4, v, cat);
  
        Two_Product(cdxtail, adytail, ti1, ti0);
        Two_Product(adxtail, cdytail, tj1, tj0);
        Two_Two_Diff(ti1, ti0, tj1, tj0, catt3, catt[2], catt[1], catt[0]);
        catt[3] = catt3;
        cattlen = 4;
      } else {
        cat[0] = 0.0;
        catlen = 1;
        catt[0] = 0.0;
        cattlen = 1;
      }
  
      if (bdxtail != 0.0) {
        temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, bdxtail, temp16a);
        bxtcatlen = scale_expansion_zeroelim(catlen, cat, bdxtail, bxtcat);
        temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, 2.0 * bdx,
                                              temp32a);
        temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
                                                temp32alen, temp32a, temp48);
        finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
                                                temp48, finother);
        finswap = finnow; finnow = finother; finother = finswap;
        if (cdytail != 0.0) {
          temp8len = scale_expansion_zeroelim(4, aa, bdxtail, temp8);
          temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail,
                                                temp16a);
          finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
                                                  temp16a, finother);
          finswap = finnow; finnow = finother; finother = finswap;
        }
        if (adytail != 0.0) {
          temp8len = scale_expansion_zeroelim(4, cc, -bdxtail, temp8);
          temp16alen = scale_expansion_zeroelim(temp8len, temp8, adytail,
                                                temp16a);
          finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
                                                  temp16a, finother);
          finswap = finnow; finnow = finother; finother = finswap;
        }
  
        temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, bdxtail,
                                              temp32a);
        bxtcattlen = scale_expansion_zeroelim(cattlen, catt, bdxtail, bxtcatt);
        temp16alen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, 2.0 * bdx,
                                              temp16a);
        temp16blen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, bdxtail,
                                              temp16b);
        temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
                                                temp16blen, temp16b, temp32b);
        temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
                                                temp32blen, temp32b, temp64);
        finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
                                                temp64, finother);
        finswap = finnow; finnow = finother; finother = finswap;
      }
      if (bdytail != 0.0) {
        temp16alen = scale_expansion_zeroelim(bytcalen, bytca, bdytail, temp16a);
        bytcatlen = scale_expansion_zeroelim(catlen, cat, bdytail, bytcat);
        temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, 2.0 * bdy,
                                              temp32a);
        temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
                                                temp32alen, temp32a, temp48);
        finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
                                                temp48, finother);
        finswap = finnow; finnow = finother; finother = finswap;
  
  
        temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, bdytail,
                                              temp32a);
        bytcattlen = scale_expansion_zeroelim(cattlen, catt, bdytail, bytcatt);
        temp16alen = scale_expansion_zeroelim(bytcattlen, bytcatt, 2.0 * bdy,
                                              temp16a);
        temp16blen = scale_expansion_zeroelim(bytcattlen, bytcatt, bdytail,
                                              temp16b);
        temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
                                                temp16blen, temp16b, temp32b);
        temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
                                                temp32blen, temp32b, temp64);
        finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
                                                temp64, finother);
        finswap = finnow; finnow = finother; finother = finswap;
      }
    }
    if ((cdxtail != 0.0) || (cdytail != 0.0)) {
      if ((adxtail != 0.0) || (adytail != 0.0)
          || (bdxtail != 0.0) || (bdytail != 0.0)) {
        Two_Product(adxtail, bdy, ti1, ti0);
        Two_Product(adx, bdytail, tj1, tj0);
        Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
        u[3] = u3;
        negate = -ady;
        Two_Product(bdxtail, negate, ti1, ti0);
        negate = -adytail;
        Two_Product(bdx, negate, tj1, tj0);
        Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
        v[3] = v3;
        abtlen = fast_expansion_sum_zeroelim(4, u, 4, v, abt);
  
        Two_Product(adxtail, bdytail, ti1, ti0);
        Two_Product(bdxtail, adytail, tj1, tj0);
        Two_Two_Diff(ti1, ti0, tj1, tj0, abtt3, abtt[2], abtt[1], abtt[0]);
        abtt[3] = abtt3;
        abttlen = 4;
      } else {
        abt[0] = 0.0;
        abtlen = 1;
        abtt[0] = 0.0;
        abttlen = 1;
      }
  
      if (cdxtail != 0.0) {
        temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, cdxtail, temp16a);
        cxtabtlen = scale_expansion_zeroelim(abtlen, abt, cdxtail, cxtabt);
        temp32alen = scale_expansion_zeroelim(cxtabtlen, cxtabt, 2.0 * cdx,
                                              temp32a);
        temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
                                                temp32alen, temp32a, temp48);
        finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
                                                temp48, finother);
        finswap = finnow; finnow = finother; finother = finswap;
        if (adytail != 0.0) {
          temp8len = scale_expansion_zeroelim(4, bb, cdxtail, temp8);
          temp16alen = scale_expansion_zeroelim(temp8len, temp8, adytail,
                                                temp16a);
          finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
                                                  temp16a, finother);
          finswap = finnow; finnow = finother; finother = finswap;
        }
        if (bdytail != 0.0) {
          temp8len = scale_expansion_zeroelim(4, aa, -cdxtail, temp8);
          temp16alen = scale_expansion_zeroelim(temp8len, temp8, bdytail,
                                                temp16a);
          finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
                                                  temp16a, finother);
          finswap = finnow; finnow = finother; finother = finswap;
        }
  
        temp32alen = scale_expansion_zeroelim(cxtabtlen, cxtabt, cdxtail,
                                              temp32a);
        cxtabttlen = scale_expansion_zeroelim(abttlen, abtt, cdxtail, cxtabtt);
        temp16alen = scale_expansion_zeroelim(cxtabttlen, cxtabtt, 2.0 * cdx,
                                              temp16a);
        temp16blen = scale_expansion_zeroelim(cxtabttlen, cxtabtt, cdxtail,
                                              temp16b);
        temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
                                                temp16blen, temp16b, temp32b);
        temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
                                                temp32blen, temp32b, temp64);
        finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
                                                temp64, finother);
        finswap = finnow; finnow = finother; finother = finswap;
      }
      if (cdytail != 0.0) {
        temp16alen = scale_expansion_zeroelim(cytablen, cytab, cdytail, temp16a);
        cytabtlen = scale_expansion_zeroelim(abtlen, abt, cdytail, cytabt);
        temp32alen = scale_expansion_zeroelim(cytabtlen, cytabt, 2.0 * cdy,
                                              temp32a);
        temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
                                                temp32alen, temp32a, temp48);
        finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
                                                temp48, finother);
        finswap = finnow; finnow = finother; finother = finswap;
  
  
        temp32alen = scale_expansion_zeroelim(cytabtlen, cytabt, cdytail,
                                              temp32a);
        cytabttlen = scale_expansion_zeroelim(abttlen, abtt, cdytail, cytabtt);
        temp16alen = scale_expansion_zeroelim(cytabttlen, cytabtt, 2.0 * cdy,
                                              temp16a);
        temp16blen = scale_expansion_zeroelim(cytabttlen, cytabtt, cdytail,
                                              temp16b);
        temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
                                                temp16blen, temp16b, temp32b);
        temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
                                                temp32blen, temp32b, temp64);
        finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
                                                temp64, finother);
        finswap = finnow; finnow = finother; finother = finswap;
      }
    }
  
    return finnow[finlength - 1];
  }
  
  #ifdef ANSI_DECLARATORS
  REAL incircle(struct mesh *m, struct behavior *b,
                vertex pa, vertex pb, vertex pc, vertex pd)
  #else /* not ANSI_DECLARATORS */
  REAL incircle(m, b, pa, pb, pc, pd)
  struct mesh *m;
  struct behavior *b;
  vertex pa;
  vertex pb;
  vertex pc;
  vertex pd;
  #endif /* not ANSI_DECLARATORS */
  
  {
    REAL adx, bdx, cdx, ady, bdy, cdy;
    REAL bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady;
    REAL alift, blift, clift;
    REAL det;
    REAL permanent, errbound;
  
    m->incirclecount++;
  
    adx = pa[0] - pd[0];
    bdx = pb[0] - pd[0];
    cdx = pc[0] - pd[0];
    ady = pa[1] - pd[1];
    bdy = pb[1] - pd[1];
    cdy = pc[1] - pd[1];
  
    bdxcdy = bdx * cdy;
    cdxbdy = cdx * bdy;
    alift = adx * adx + ady * ady;
  
    cdxady = cdx * ady;
    adxcdy = adx * cdy;
    blift = bdx * bdx + bdy * bdy;
  
    adxbdy = adx * bdy;
    bdxady = bdx * ady;
    clift = cdx * cdx + cdy * cdy;
  
    det = alift * (bdxcdy - cdxbdy)
        + blift * (cdxady - adxcdy)
        + clift * (adxbdy - bdxady);
  
    if (b->noexact) {
      return det;
    }
  
    permanent = (Absolute(bdxcdy) + Absolute(cdxbdy)) * alift
              + (Absolute(cdxady) + Absolute(adxcdy)) * blift
              + (Absolute(adxbdy) + Absolute(bdxady)) * clift;
    errbound = iccerrboundA * permanent;
    if ((det > errbound) || (-det > errbound)) {
      return det;
    }
  
    return incircleadapt(pa, pb, pc, pd, permanent);
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  orient3d()   Return a positive value if the point pd lies below the      */
  /*               plane passing through pa, pb, and pc; "below" is defined so */
  /*               that pa, pb, and pc appear in counterclockwise order when   */
  /*               viewed from above the plane.  Returns a negative value if   */
  /*               pd lies above the plane.  Returns zero if the points are    */
  /*               coplanar.  The result is also a rough approximation of six  */
  /*               times the signed volume of the tetrahedron defined by the   */
  /*               four points.                                                */
  /*                                                                           */
  /*  Uses exact arithmetic if necessary to ensure a correct answer.  The      */
  /*  result returned is the determinant of a matrix.  This determinant is     */
  /*  computed adaptively, in the sense that exact arithmetic is used only to  */
  /*  the degree it is needed to ensure that the returned value has the        */
  /*  correct sign.  Hence, this function is usually quite fast, but will run  */
  /*  more slowly when the input points are coplanar or nearly so.             */
  /*                                                                           */
  /*  See my Robust Predicates paper for details.                              */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  REAL orient3dadapt(vertex pa, vertex pb, vertex pc, vertex pd,
                     REAL aheight, REAL bheight, REAL cheight, REAL dheight,
                     REAL permanent)
  #else /* not ANSI_DECLARATORS */
  REAL orient3dadapt(pa, pb, pc, pd,
                     aheight, bheight, cheight, dheight, permanent)
  vertex pa;
  vertex pb;
  vertex pc;
  vertex pd;
  REAL aheight;
  REAL bheight;
  REAL cheight;
  REAL dheight;
  REAL permanent;
  #endif /* not ANSI_DECLARATORS */
  
  {
    INEXACT REAL adx, bdx, cdx, ady, bdy, cdy, adheight, bdheight, cdheight;
    REAL det, errbound;
  
    INEXACT REAL bdxcdy1, cdxbdy1, cdxady1, adxcdy1, adxbdy1, bdxady1;
    REAL bdxcdy0, cdxbdy0, cdxady0, adxcdy0, adxbdy0, bdxady0;
    REAL bc[4], ca[4], ab[4];
    INEXACT REAL bc3, ca3, ab3;
    REAL adet[8], bdet[8], cdet[8];
    int alen, blen, clen;
    REAL abdet[16];
    int ablen;
    REAL *finnow, *finother, *finswap;
    REAL fin1[192], fin2[192];
    int finlength;
  
    REAL adxtail, bdxtail, cdxtail;
    REAL adytail, bdytail, cdytail;
    REAL adheighttail, bdheighttail, cdheighttail;
    INEXACT REAL at_blarge, at_clarge;
    INEXACT REAL bt_clarge, bt_alarge;
    INEXACT REAL ct_alarge, ct_blarge;
    REAL at_b[4], at_c[4], bt_c[4], bt_a[4], ct_a[4], ct_b[4];
    int at_blen, at_clen, bt_clen, bt_alen, ct_alen, ct_blen;
    INEXACT REAL bdxt_cdy1, cdxt_bdy1, cdxt_ady1;
    INEXACT REAL adxt_cdy1, adxt_bdy1, bdxt_ady1;
    REAL bdxt_cdy0, cdxt_bdy0, cdxt_ady0;
    REAL adxt_cdy0, adxt_bdy0, bdxt_ady0;
    INEXACT REAL bdyt_cdx1, cdyt_bdx1, cdyt_adx1;
    INEXACT REAL adyt_cdx1, adyt_bdx1, bdyt_adx1;
    REAL bdyt_cdx0, cdyt_bdx0, cdyt_adx0;
    REAL adyt_cdx0, adyt_bdx0, bdyt_adx0;
    REAL bct[8], cat[8], abt[8];
    int bctlen, catlen, abtlen;
    INEXACT REAL bdxt_cdyt1, cdxt_bdyt1, cdxt_adyt1;
    INEXACT REAL adxt_cdyt1, adxt_bdyt1, bdxt_adyt1;
    REAL bdxt_cdyt0, cdxt_bdyt0, cdxt_adyt0;
    REAL adxt_cdyt0, adxt_bdyt0, bdxt_adyt0;
    REAL u[4], v[12], w[16];
    INEXACT REAL u3;
    int vlength, wlength;
    REAL negate;
  
    INEXACT REAL bvirt;
    REAL avirt, bround, around;
    INEXACT REAL c;
    INEXACT REAL abig;
    REAL ahi, alo, bhi, blo;
    REAL err1, err2, err3;
    INEXACT REAL _i, _j, _k;
    REAL _0;
  
    adx = (REAL) (pa[0] - pd[0]);
    bdx = (REAL) (pb[0] - pd[0]);
    cdx = (REAL) (pc[0] - pd[0]);
    ady = (REAL) (pa[1] - pd[1]);
    bdy = (REAL) (pb[1] - pd[1]);
    cdy = (REAL) (pc[1] - pd[1]);
    adheight = (REAL) (aheight - dheight);
    bdheight = (REAL) (bheight - dheight);
    cdheight = (REAL) (cheight - dheight);
  
    Two_Product(bdx, cdy, bdxcdy1, bdxcdy0);
    Two_Product(cdx, bdy, cdxbdy1, cdxbdy0);
    Two_Two_Diff(bdxcdy1, bdxcdy0, cdxbdy1, cdxbdy0, bc3, bc[2], bc[1], bc[0]);
    bc[3] = bc3;
    alen = scale_expansion_zeroelim(4, bc, adheight, adet);
  
    Two_Product(cdx, ady, cdxady1, cdxady0);
    Two_Product(adx, cdy, adxcdy1, adxcdy0);
    Two_Two_Diff(cdxady1, cdxady0, adxcdy1, adxcdy0, ca3, ca[2], ca[1], ca[0]);
    ca[3] = ca3;
    blen = scale_expansion_zeroelim(4, ca, bdheight, bdet);
  
    Two_Product(adx, bdy, adxbdy1, adxbdy0);
    Two_Product(bdx, ady, bdxady1, bdxady0);
    Two_Two_Diff(adxbdy1, adxbdy0, bdxady1, bdxady0, ab3, ab[2], ab[1], ab[0]);
    ab[3] = ab3;
    clen = scale_expansion_zeroelim(4, ab, cdheight, cdet);
  
    ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
    finlength = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, fin1);
  
    det = estimate(finlength, fin1);
    errbound = o3derrboundB * permanent;
    if ((det >= errbound) || (-det >= errbound)) {
      return det;
    }
  
    Two_Diff_Tail(pa[0], pd[0], adx, adxtail);
    Two_Diff_Tail(pb[0], pd[0], bdx, bdxtail);
    Two_Diff_Tail(pc[0], pd[0], cdx, cdxtail);
    Two_Diff_Tail(pa[1], pd[1], ady, adytail);
    Two_Diff_Tail(pb[1], pd[1], bdy, bdytail);
    Two_Diff_Tail(pc[1], pd[1], cdy, cdytail);
    Two_Diff_Tail(aheight, dheight, adheight, adheighttail);
    Two_Diff_Tail(bheight, dheight, bdheight, bdheighttail);
    Two_Diff_Tail(cheight, dheight, cdheight, cdheighttail);
  
    if ((adxtail == 0.0) && (bdxtail == 0.0) && (cdxtail == 0.0) &&
        (adytail == 0.0) && (bdytail == 0.0) && (cdytail == 0.0) &&
        (adheighttail == 0.0) &&
        (bdheighttail == 0.0) &&
        (cdheighttail == 0.0)) {
      return det;
    }
  
    errbound = o3derrboundC * permanent + resulterrbound * Absolute(det);
    det += (adheight * ((bdx * cdytail + cdy * bdxtail) -
                        (bdy * cdxtail + cdx * bdytail)) +
            adheighttail * (bdx * cdy - bdy * cdx)) +
           (bdheight * ((cdx * adytail + ady * cdxtail) -
                        (cdy * adxtail + adx * cdytail)) +
            bdheighttail * (cdx * ady - cdy * adx)) +
           (cdheight * ((adx * bdytail + bdy * adxtail) -
                        (ady * bdxtail + bdx * adytail)) +
            cdheighttail * (adx * bdy - ady * bdx));
    if ((det >= errbound) || (-det >= errbound)) {
      return det;
    }
  
    finnow = fin1;
    finother = fin2;
  
    if (adxtail == 0.0) {
      if (adytail == 0.0) {
        at_b[0] = 0.0;
        at_blen = 1;
        at_c[0] = 0.0;
        at_clen = 1;
      } else {
        negate = -adytail;
        Two_Product(negate, bdx, at_blarge, at_b[0]);
        at_b[1] = at_blarge;
        at_blen = 2;
        Two_Product(adytail, cdx, at_clarge, at_c[0]);
        at_c[1] = at_clarge;
        at_clen = 2;
      }
    } else {
      if (adytail == 0.0) {
        Two_Product(adxtail, bdy, at_blarge, at_b[0]);
        at_b[1] = at_blarge;
        at_blen = 2;
        negate = -adxtail;
        Two_Product(negate, cdy, at_clarge, at_c[0]);
        at_c[1] = at_clarge;
        at_clen = 2;
      } else {
        Two_Product(adxtail, bdy, adxt_bdy1, adxt_bdy0);
        Two_Product(adytail, bdx, adyt_bdx1, adyt_bdx0);
        Two_Two_Diff(adxt_bdy1, adxt_bdy0, adyt_bdx1, adyt_bdx0,
                     at_blarge, at_b[2], at_b[1], at_b[0]);
        at_b[3] = at_blarge;
        at_blen = 4;
        Two_Product(adytail, cdx, adyt_cdx1, adyt_cdx0);
        Two_Product(adxtail, cdy, adxt_cdy1, adxt_cdy0);
        Two_Two_Diff(adyt_cdx1, adyt_cdx0, adxt_cdy1, adxt_cdy0,
                     at_clarge, at_c[2], at_c[1], at_c[0]);
        at_c[3] = at_clarge;
        at_clen = 4;
      }
    }
    if (bdxtail == 0.0) {
      if (bdytail == 0.0) {
        bt_c[0] = 0.0;
        bt_clen = 1;
        bt_a[0] = 0.0;
        bt_alen = 1;
      } else {
        negate = -bdytail;
        Two_Product(negate, cdx, bt_clarge, bt_c[0]);
        bt_c[1] = bt_clarge;
        bt_clen = 2;
        Two_Product(bdytail, adx, bt_alarge, bt_a[0]);
        bt_a[1] = bt_alarge;
        bt_alen = 2;
      }
    } else {
      if (bdytail == 0.0) {
        Two_Product(bdxtail, cdy, bt_clarge, bt_c[0]);
        bt_c[1] = bt_clarge;
        bt_clen = 2;
        negate = -bdxtail;
        Two_Product(negate, ady, bt_alarge, bt_a[0]);
        bt_a[1] = bt_alarge;
        bt_alen = 2;
      } else {
        Two_Product(bdxtail, cdy, bdxt_cdy1, bdxt_cdy0);
        Two_Product(bdytail, cdx, bdyt_cdx1, bdyt_cdx0);
        Two_Two_Diff(bdxt_cdy1, bdxt_cdy0, bdyt_cdx1, bdyt_cdx0,
                     bt_clarge, bt_c[2], bt_c[1], bt_c[0]);
        bt_c[3] = bt_clarge;
        bt_clen = 4;
        Two_Product(bdytail, adx, bdyt_adx1, bdyt_adx0);
        Two_Product(bdxtail, ady, bdxt_ady1, bdxt_ady0);
        Two_Two_Diff(bdyt_adx1, bdyt_adx0, bdxt_ady1, bdxt_ady0,
                    bt_alarge, bt_a[2], bt_a[1], bt_a[0]);
        bt_a[3] = bt_alarge;
        bt_alen = 4;
      }
    }
    if (cdxtail == 0.0) {
      if (cdytail == 0.0) {
        ct_a[0] = 0.0;
        ct_alen = 1;
        ct_b[0] = 0.0;
        ct_blen = 1;
      } else {
        negate = -cdytail;
        Two_Product(negate, adx, ct_alarge, ct_a[0]);
        ct_a[1] = ct_alarge;
        ct_alen = 2;
        Two_Product(cdytail, bdx, ct_blarge, ct_b[0]);
        ct_b[1] = ct_blarge;
        ct_blen = 2;
      }
    } else {
      if (cdytail == 0.0) {
        Two_Product(cdxtail, ady, ct_alarge, ct_a[0]);
        ct_a[1] = ct_alarge;
        ct_alen = 2;
        negate = -cdxtail;
        Two_Product(negate, bdy, ct_blarge, ct_b[0]);
        ct_b[1] = ct_blarge;
        ct_blen = 2;
      } else {
        Two_Product(cdxtail, ady, cdxt_ady1, cdxt_ady0);
        Two_Product(cdytail, adx, cdyt_adx1, cdyt_adx0);
        Two_Two_Diff(cdxt_ady1, cdxt_ady0, cdyt_adx1, cdyt_adx0,
                     ct_alarge, ct_a[2], ct_a[1], ct_a[0]);
        ct_a[3] = ct_alarge;
        ct_alen = 4;
        Two_Product(cdytail, bdx, cdyt_bdx1, cdyt_bdx0);
        Two_Product(cdxtail, bdy, cdxt_bdy1, cdxt_bdy0);
        Two_Two_Diff(cdyt_bdx1, cdyt_bdx0, cdxt_bdy1, cdxt_bdy0,
                     ct_blarge, ct_b[2], ct_b[1], ct_b[0]);
        ct_b[3] = ct_blarge;
        ct_blen = 4;
      }
    }
  
    bctlen = fast_expansion_sum_zeroelim(bt_clen, bt_c, ct_blen, ct_b, bct);
    wlength = scale_expansion_zeroelim(bctlen, bct, adheight, w);
    finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
                                            finother);
    finswap = finnow; finnow = finother; finother = finswap;
  
    catlen = fast_expansion_sum_zeroelim(ct_alen, ct_a, at_clen, at_c, cat);
    wlength = scale_expansion_zeroelim(catlen, cat, bdheight, w);
    finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
                                            finother);
    finswap = finnow; finnow = finother; finother = finswap;
  
    abtlen = fast_expansion_sum_zeroelim(at_blen, at_b, bt_alen, bt_a, abt);
    wlength = scale_expansion_zeroelim(abtlen, abt, cdheight, w);
    finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
                                            finother);
    finswap = finnow; finnow = finother; finother = finswap;
  
    if (adheighttail != 0.0) {
      vlength = scale_expansion_zeroelim(4, bc, adheighttail, v);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v,
                                              finother);
      finswap = finnow; finnow = finother; finother = finswap;
    }
    if (bdheighttail != 0.0) {
      vlength = scale_expansion_zeroelim(4, ca, bdheighttail, v);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v,
                                              finother);
      finswap = finnow; finnow = finother; finother = finswap;
    }
    if (cdheighttail != 0.0) {
      vlength = scale_expansion_zeroelim(4, ab, cdheighttail, v);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v,
                                              finother);
      finswap = finnow; finnow = finother; finother = finswap;
    }
  
    if (adxtail != 0.0) {
      if (bdytail != 0.0) {
        Two_Product(adxtail, bdytail, adxt_bdyt1, adxt_bdyt0);
        Two_One_Product(adxt_bdyt1, adxt_bdyt0, cdheight, u3, u[2], u[1], u[0]);
        u[3] = u3;
        finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
                                                finother);
        finswap = finnow; finnow = finother; finother = finswap;
        if (cdheighttail != 0.0) {
          Two_One_Product(adxt_bdyt1, adxt_bdyt0, cdheighttail,
                          u3, u[2], u[1], u[0]);
          u[3] = u3;
          finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
                                                  finother);
          finswap = finnow; finnow = finother; finother = finswap;
        }
      }
      if (cdytail != 0.0) {
        negate = -adxtail;
        Two_Product(negate, cdytail, adxt_cdyt1, adxt_cdyt0);
        Two_One_Product(adxt_cdyt1, adxt_cdyt0, bdheight, u3, u[2], u[1], u[0]);
        u[3] = u3;
        finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
                                                finother);
        finswap = finnow; finnow = finother; finother = finswap;
        if (bdheighttail != 0.0) {
          Two_One_Product(adxt_cdyt1, adxt_cdyt0, bdheighttail,
                          u3, u[2], u[1], u[0]);
          u[3] = u3;
          finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
                                                  finother);
          finswap = finnow; finnow = finother; finother = finswap;
        }
      }
    }
    if (bdxtail != 0.0) {
      if (cdytail != 0.0) {
        Two_Product(bdxtail, cdytail, bdxt_cdyt1, bdxt_cdyt0);
        Two_One_Product(bdxt_cdyt1, bdxt_cdyt0, adheight, u3, u[2], u[1], u[0]);
        u[3] = u3;
        finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
                                                finother);
        finswap = finnow; finnow = finother; finother = finswap;
        if (adheighttail != 0.0) {
          Two_One_Product(bdxt_cdyt1, bdxt_cdyt0, adheighttail,
                          u3, u[2], u[1], u[0]);
          u[3] = u3;
          finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
                                                  finother);
          finswap = finnow; finnow = finother; finother = finswap;
        }
      }
      if (adytail != 0.0) {
        negate = -bdxtail;
        Two_Product(negate, adytail, bdxt_adyt1, bdxt_adyt0);
        Two_One_Product(bdxt_adyt1, bdxt_adyt0, cdheight, u3, u[2], u[1], u[0]);
        u[3] = u3;
        finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
                                                finother);
        finswap = finnow; finnow = finother; finother = finswap;
        if (cdheighttail != 0.0) {
          Two_One_Product(bdxt_adyt1, bdxt_adyt0, cdheighttail,
                          u3, u[2], u[1], u[0]);
          u[3] = u3;
          finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
                                                  finother);
          finswap = finnow; finnow = finother; finother = finswap;
        }
      }
    }
    if (cdxtail != 0.0) {
      if (adytail != 0.0) {
        Two_Product(cdxtail, adytail, cdxt_adyt1, cdxt_adyt0);
        Two_One_Product(cdxt_adyt1, cdxt_adyt0, bdheight, u3, u[2], u[1], u[0]);
        u[3] = u3;
        finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
                                                finother);
        finswap = finnow; finnow = finother; finother = finswap;
        if (bdheighttail != 0.0) {
          Two_One_Product(cdxt_adyt1, cdxt_adyt0, bdheighttail,
                          u3, u[2], u[1], u[0]);
          u[3] = u3;
          finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
                                                  finother);
          finswap = finnow; finnow = finother; finother = finswap;
        }
      }
      if (bdytail != 0.0) {
        negate = -cdxtail;
        Two_Product(negate, bdytail, cdxt_bdyt1, cdxt_bdyt0);
        Two_One_Product(cdxt_bdyt1, cdxt_bdyt0, adheight, u3, u[2], u[1], u[0]);
        u[3] = u3;
        finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
                                                finother);
        finswap = finnow; finnow = finother; finother = finswap;
        if (adheighttail != 0.0) {
          Two_One_Product(cdxt_bdyt1, cdxt_bdyt0, adheighttail,
                          u3, u[2], u[1], u[0]);
          u[3] = u3;
          finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
                                                  finother);
          finswap = finnow; finnow = finother; finother = finswap;
        }
      }
    }
  
    if (adheighttail != 0.0) {
      wlength = scale_expansion_zeroelim(bctlen, bct, adheighttail, w);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
                                              finother);
      finswap = finnow; finnow = finother; finother = finswap;
    }
    if (bdheighttail != 0.0) {
      wlength = scale_expansion_zeroelim(catlen, cat, bdheighttail, w);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
                                              finother);
      finswap = finnow; finnow = finother; finother = finswap;
    }
    if (cdheighttail != 0.0) {
      wlength = scale_expansion_zeroelim(abtlen, abt, cdheighttail, w);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
                                              finother);
      finswap = finnow; finnow = finother; finother = finswap;
    }
  
    return finnow[finlength - 1];
  }
  
  #ifdef ANSI_DECLARATORS
  REAL orient3d(struct mesh *m, struct behavior *b,
                vertex pa, vertex pb, vertex pc, vertex pd,
                REAL aheight, REAL bheight, REAL cheight, REAL dheight)
  #else /* not ANSI_DECLARATORS */
  REAL orient3d(m, b, pa, pb, pc, pd, aheight, bheight, cheight, dheight)
  struct mesh *m;
  struct behavior *b;
  vertex pa;
  vertex pb;
  vertex pc;
  vertex pd;
  REAL aheight;
  REAL bheight;
  REAL cheight;
  REAL dheight;
  #endif /* not ANSI_DECLARATORS */
  
  {
    REAL adx, bdx, cdx, ady, bdy, cdy, adheight, bdheight, cdheight;
    REAL bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady;
    REAL det;
    REAL permanent, errbound;
  
    m->orient3dcount++;
  
    adx = pa[0] - pd[0];
    bdx = pb[0] - pd[0];
    cdx = pc[0] - pd[0];
    ady = pa[1] - pd[1];
    bdy = pb[1] - pd[1];
    cdy = pc[1] - pd[1];
    adheight = aheight - dheight;
    bdheight = bheight - dheight;
    cdheight = cheight - dheight;
  
    bdxcdy = bdx * cdy;
    cdxbdy = cdx * bdy;
  
    cdxady = cdx * ady;
    adxcdy = adx * cdy;
  
    adxbdy = adx * bdy;
    bdxady = bdx * ady;
  
    det = adheight * (bdxcdy - cdxbdy) 
        + bdheight * (cdxady - adxcdy)
        + cdheight * (adxbdy - bdxady);
  
    if (b->noexact) {
      return det;
    }
  
    permanent = (Absolute(bdxcdy) + Absolute(cdxbdy)) * Absolute(adheight)
              + (Absolute(cdxady) + Absolute(adxcdy)) * Absolute(bdheight)
              + (Absolute(adxbdy) + Absolute(bdxady)) * Absolute(cdheight);
    errbound = o3derrboundA * permanent;
    if ((det > errbound) || (-det > errbound)) {
      return det;
    }
  
    return orient3dadapt(pa, pb, pc, pd, aheight, bheight, cheight, dheight,
                         permanent);
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  nonregular()   Return a positive value if the point pd is incompatible   */
  /*                 with the circle or plane passing through pa, pb, and pc   */
  /*                 (meaning that pd is inside the circle or below the        */
  /*                 plane); a negative value if it is compatible; and zero if */
  /*                 the four points are cocircular/coplanar.  The points pa,  */
  /*                 pb, and pc must be in counterclockwise order, or the sign */
  /*                 of the result will be reversed.                           */
  /*                                                                           */
  /*  If the -w switch is used, the points are lifted onto the parabolic       */
  /*  lifting map, then they are dropped according to their weights, then the  */
  /*  3D orientation test is applied.  If the -W switch is used, the points'   */
  /*  heights are already provided, so the 3D orientation test is applied      */
  /*  directly.  If neither switch is used, the incircle test is applied.      */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  REAL nonregular(struct mesh *m, struct behavior *b,
                  vertex pa, vertex pb, vertex pc, vertex pd)
  #else /* not ANSI_DECLARATORS */
  REAL nonregular(m, b, pa, pb, pc, pd)
  struct mesh *m;
  struct behavior *b;
  vertex pa;
  vertex pb;
  vertex pc;
  vertex pd;
  #endif /* not ANSI_DECLARATORS */
  
  {
    if (b->weighted == 0) {
      return incircle(m, b, pa, pb, pc, pd);
    } else if (b->weighted == 1) {
      return orient3d(m, b, pa, pb, pc, pd,
                      pa[0] * pa[0] + pa[1] * pa[1] - pa[2],
                      pb[0] * pb[0] + pb[1] * pb[1] - pb[2],
                      pc[0] * pc[0] + pc[1] * pc[1] - pc[2],
                      pd[0] * pd[0] + pd[1] * pd[1] - pd[2]);
    } else {
      return orient3d(m, b, pa, pb, pc, pd, pa[2], pb[2], pc[2], pd[2]);
    }
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  findcircumcenter()   Find the circumcenter of a triangle.                */
  /*                                                                           */
  /*  The result is returned both in terms of x-y coordinates and xi-eta       */
  /*  (barycentric) coordinates.  The xi-eta coordinate system is defined in   */
  /*  terms of the triangle:  the origin of the triangle is the origin of the  */
  /*  coordinate system; the destination of the triangle is one unit along the */
  /*  xi axis; and the apex of the triangle is one unit along the eta axis.    */
  /*  This procedure also returns the square of the length of the triangle's   */
  /*  shortest edge.                                                           */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  void findcircumcenter(struct mesh *m, struct behavior *b,
                        vertex torg, vertex tdest, vertex tapex,
                        vertex circumcenter, REAL *xi, REAL *eta, int offcenter)
  #else /* not ANSI_DECLARATORS */
  void findcircumcenter(m, b, torg, tdest, tapex, circumcenter, xi, eta,
                        offcenter)
  struct mesh *m;
  struct behavior *b;
  vertex torg;
  vertex tdest;
  vertex tapex;
  vertex circumcenter;
  REAL *xi;
  REAL *eta;
  int offcenter;
  #endif /* not ANSI_DECLARATORS */
  
  {
    REAL xdo, ydo, xao, yao;
    REAL dodist, aodist, dadist;
    REAL denominator;
    REAL dx, dy, dxoff, dyoff;
  
    m->circumcentercount++;
  
    /* Compute the circumcenter of the triangle. */
    xdo = tdest[0] - torg[0];
    ydo = tdest[1] - torg[1];
    xao = tapex[0] - torg[0];
    yao = tapex[1] - torg[1];
    dodist = xdo * xdo + ydo * ydo;
    aodist = xao * xao + yao * yao;
    dadist = (tdest[0] - tapex[0]) * (tdest[0] - tapex[0]) +
             (tdest[1] - tapex[1]) * (tdest[1] - tapex[1]);
    if (b->noexact) {
      denominator = 0.5 / (xdo * yao - xao * ydo);
    } else {
      /* Use the counterclockwise() routine to ensure a positive (and */
      /*   reasonably accurate) result, avoiding any possibility of   */
      /*   division by zero.                                          */
      denominator = 0.5 / counterclockwise(m, b, tdest, tapex, torg);
      /* Don't count the above as an orientation test. */
      m->counterclockcount--;
    }
    dx = (yao * dodist - ydo * aodist) * denominator;
    dy = (xdo * aodist - xao * dodist) * denominator;
  
    /* Find the (squared) length of the triangle's shortest edge.  This   */
    /*   serves as a conservative estimate of the insertion radius of the */
    /*   circumcenter's parent.  The estimate is used to ensure that      */
    /*   the algorithm terminates even if very small angles appear in     */
    /*   the input PSLG.                                                  */
    if ((dodist < aodist) && (dodist < dadist)) {
      if (offcenter && (b->offconstant > 0.0)) {
        /* Find the position of the off-center, as described by Alper Ungor. */
        dxoff = 0.5 * xdo - b->offconstant * ydo;
        dyoff = 0.5 * ydo + b->offconstant * xdo;
        /* If the off-center is closer to the origin than the */
        /*   circumcenter, use the off-center instead.        */
        if (dxoff * dxoff + dyoff * dyoff < dx * dx + dy * dy) {
          dx = dxoff;
          dy = dyoff;
        }
      }
    } else if (aodist < dadist) {
      if (offcenter && (b->offconstant > 0.0)) {
        dxoff = 0.5 * xao + b->offconstant * yao;
        dyoff = 0.5 * yao - b->offconstant * xao;
        /* If the off-center is closer to the origin than the */
        /*   circumcenter, use the off-center instead.        */
        if (dxoff * dxoff + dyoff * dyoff < dx * dx + dy * dy) {
          dx = dxoff;
          dy = dyoff;
        }
      }
    } else {
      if (offcenter && (b->offconstant > 0.0)) {
        dxoff = 0.5 * (tapex[0] - tdest[0]) -
                b->offconstant * (tapex[1] - tdest[1]);
        dyoff = 0.5 * (tapex[1] - tdest[1]) +
                b->offconstant * (tapex[0] - tdest[0]);
        /* If the off-center is closer to the destination than the */
        /*   circumcenter, use the off-center instead.             */
        if (dxoff * dxoff + dyoff * dyoff <
            (dx - xdo) * (dx - xdo) + (dy - ydo) * (dy - ydo)) {
          dx = xdo + dxoff;
          dy = ydo + dyoff;
        }
      }
    }
  
    circumcenter[0] = torg[0] + dx;
    circumcenter[1] = torg[1] + dy;
  
    /* To interpolate vertex attributes for the new vertex inserted at */
    /*   the circumcenter, define a coordinate system with a xi-axis,  */
    /*   directed from the triangle's origin to its destination, and   */
    /*   an eta-axis, directed from its origin to its apex.            */
    /*   Calculate the xi and eta coordinates of the circumcenter.     */
    *xi = (yao * dx - xao * dy) * (2.0 * denominator);
    *eta = (xdo * dy - ydo * dx) * (2.0 * denominator);
  }
  
  /**                                                                         **/
  /**                                                                         **/
  /********* Geometric primitives end here                             *********/
  
  /*****************************************************************************/
  /*                                                                           */
  /*  triangleinit()   Initialize some variables.                              */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  void triangleinit(struct mesh *m)
  #else /* not ANSI_DECLARATORS */
  void triangleinit(m)
  struct mesh *m;
  #endif /* not ANSI_DECLARATORS */
  
  {
    poolzero(&m->vertices);
    poolzero(&m->triangles);
    poolzero(&m->subsegs);
    poolzero(&m->viri);
    poolzero(&m->badsubsegs);
    poolzero(&m->badtriangles);
    poolzero(&m->flipstackers);
    poolzero(&m->splaynodes);
  
    m->recenttri.tri = (triangle *) NULL; /* No triangle has been visited yet. */
    m->undeads = 0;                       /* No eliminated input vertices yet. */
    m->samples = 1;         /* Point location should take at least one sample. */
    m->checksegments = 0;   /* There are no segments in the triangulation yet. */
    m->checkquality = 0;     /* The quality triangulation stage has not begun. */
    m->incirclecount = m->counterclockcount = m->orient3dcount = 0;
    m->hyperbolacount = m->circletopcount = m->circumcentercount = 0;
    randomseed = 1;
  
    exactinit();                     /* Initialize exact arithmetic constants. */
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  randomnation()   Generate a random number between 0 and `choices' - 1.   */
  /*                                                                           */
  /*  This is a simple linear congruential random number generator.  Hence, it */
  /*  is a bad random number generator, but good enough for most randomized    */
  /*  geometric algorithms.                                                    */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  unsigned long randomnation(unsigned int choices)
  #else /* not ANSI_DECLARATORS */
  unsigned long randomnation(choices)
  unsigned int choices;
  #endif /* not ANSI_DECLARATORS */
  
  {
    randomseed = (randomseed * 1366l + 150889l) % 714025l;
    return randomseed / (714025l / choices + 1);
  }
  
  /********* Mesh quality testing routines begin here                  *********/
  /**                                                                         **/
  /**                                                                         **/
  
  /*****************************************************************************/
  /*                                                                           */
  /*  checkmesh()   Test the mesh for topological consistency.                 */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifndef REDUCED
  
  #ifdef ANSI_DECLARATORS
  void checkmesh(struct mesh *m, struct behavior *b)
  #else /* not ANSI_DECLARATORS */
  void checkmesh(m, b)
  struct mesh *m;
  struct behavior *b;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct otri triangleloop;
    struct otri oppotri, oppooppotri;
    vertex triorg, tridest, triapex;
    vertex oppoorg, oppodest;
    int horrors;
    int saveexact;
    triangle ptr;                         /* Temporary variable used by sym(). */
  
    /* Temporarily turn on exact arithmetic if it's off. */
    saveexact = b->noexact;
    b->noexact = 0;
    if (!b->quiet) {
      printf("  Checking consistency of mesh...\n");
    }
    horrors = 0;
    /* Run through the list of triangles, checking each one. */
    traversalinit(&m->triangles);
    triangleloop.tri = triangletraverse(m);
    while (triangleloop.tri != (triangle *) NULL) {
      /* Check all three edges of the triangle. */
      for (triangleloop.orient = 0; triangleloop.orient < 3;
           triangleloop.orient++) {
        org(triangleloop, triorg);
        dest(triangleloop, tridest);
        if (triangleloop.orient == 0) {       /* Only test for inversion once. */
          /* Test if the triangle is flat or inverted. */
          apex(triangleloop, triapex);
          if (counterclockwise(m, b, triorg, tridest, triapex) <= 0.0) {
            printf("  !! !! Inverted ");
            printtriangle(m, b, &triangleloop);
            horrors++;
          }
        }
        /* Find the neighboring triangle on this edge. */
        sym(triangleloop, oppotri);
        if (oppotri.tri != m->dummytri) {
          /* Check that the triangle's neighbor knows it's a neighbor. */
          sym(oppotri, oppooppotri);
          if ((triangleloop.tri != oppooppotri.tri)
              || (triangleloop.orient != oppooppotri.orient)) {
            printf("  !! !! Asymmetric triangle-triangle bond:\n");
            if (triangleloop.tri == oppooppotri.tri) {
              printf("   (Right triangle, wrong orientation)\n");
            }
            printf("    First ");
            printtriangle(m, b, &triangleloop);
            printf("    Second (nonreciprocating) ");
            printtriangle(m, b, &oppotri);
            horrors++;
          }
          /* Check that both triangles agree on the identities */
          /*   of their shared vertices.                       */
          org(oppotri, oppoorg);
          dest(oppotri, oppodest);
          if ((triorg != oppodest) || (tridest != oppoorg)) {
            printf("  !! !! Mismatched edge coordinates between two triangles:\n"
                   );
            printf("    First mismatched ");
            printtriangle(m, b, &triangleloop);
            printf("    Second mismatched ");
            printtriangle(m, b, &oppotri);
            horrors++;
          }
        }
      }
      triangleloop.tri = triangletraverse(m);
    }
    if (horrors == 0) {
      if (!b->quiet) {
        printf("  In my studied opinion, the mesh appears to be consistent.\n");
      }
    } else if (horrors == 1) {
      printf("  !! !! !! !! Precisely one festering wound discovered.\n");
    } else {
      printf("  !! !! !! !! %d abominations witnessed.\n", horrors);
    }
    /* Restore the status of exact arithmetic. */
    b->noexact = saveexact;
  }
  
  #endif /* not REDUCED */
  
  /*****************************************************************************/
  /*                                                                           */
  /*  checkdelaunay()   Ensure that the mesh is (constrained) Delaunay.        */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifndef REDUCED
  
  #ifdef ANSI_DECLARATORS
  void checkdelaunay(struct mesh *m, struct behavior *b)
  #else /* not ANSI_DECLARATORS */
  void checkdelaunay(m, b)
  struct mesh *m;
  struct behavior *b;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct otri triangleloop;
    struct otri oppotri;
    struct osub opposubseg;
    vertex triorg, tridest, triapex;
    vertex oppoapex;
    int shouldbedelaunay;
    int horrors;
    int saveexact;
    triangle ptr;                         /* Temporary variable used by sym(). */
    subseg sptr;                      /* Temporary variable used by tspivot(). */
  
    /* Temporarily turn on exact arithmetic if it's off. */
    saveexact = b->noexact;
    b->noexact = 0;
    if (!b->quiet) {
      printf("  Checking Delaunay property of mesh...\n");
    }
    horrors = 0;
    /* Run through the list of triangles, checking each one. */
    traversalinit(&m->triangles);
    triangleloop.tri = triangletraverse(m);
    while (triangleloop.tri != (triangle *) NULL) {
      /* Check all three edges of the triangle. */
      for (triangleloop.orient = 0; triangleloop.orient < 3;
           triangleloop.orient++) {
        org(triangleloop, triorg);
        dest(triangleloop, tridest);
        apex(triangleloop, triapex);
        sym(triangleloop, oppotri);
        apex(oppotri, oppoapex);
        /* Only test that the edge is locally Delaunay if there is an   */
        /*   adjoining triangle whose pointer is larger (to ensure that */
        /*   each pair isn't tested twice).                             */
        shouldbedelaunay = (oppotri.tri != m->dummytri) &&
              !deadtri(oppotri.tri) && (triangleloop.tri < oppotri.tri) &&
              (triorg != m->infvertex1) && (triorg != m->infvertex2) &&
              (triorg != m->infvertex3) &&
              (tridest != m->infvertex1) && (tridest != m->infvertex2) &&
              (tridest != m->infvertex3) &&
              (triapex != m->infvertex1) && (triapex != m->infvertex2) &&
              (triapex != m->infvertex3) &&
              (oppoapex != m->infvertex1) && (oppoapex != m->infvertex2) &&
              (oppoapex != m->infvertex3);
        if (m->checksegments && shouldbedelaunay) {
          /* If a subsegment separates the triangles, then the edge is */
          /*   constrained, so no local Delaunay test should be done.  */
          tspivot(triangleloop, opposubseg);
          if (opposubseg.ss != m->dummysub){
            shouldbedelaunay = 0;
          }
        }
        if (shouldbedelaunay) {
          if (nonregular(m, b, triorg, tridest, triapex, oppoapex) > 0.0) {
            if (!b->weighted) {
              printf("  !! !! Non-Delaunay pair of triangles:\n");
              printf("    First non-Delaunay ");
              printtriangle(m, b, &triangleloop);
              printf("    Second non-Delaunay ");
            } else {
              printf("  !! !! Non-regular pair of triangles:\n");
              printf("    First non-regular ");
              printtriangle(m, b, &triangleloop);
              printf("    Second non-regular ");
            }
            printtriangle(m, b, &oppotri);
            horrors++;
          }
        }
      }
      triangleloop.tri = triangletraverse(m);
    }
    if (horrors == 0) {
      if (!b->quiet) {
        printf(
    "  By virtue of my perceptive intelligence, I declare the mesh Delaunay.\n");
      }
    } else if (horrors == 1) {
      printf(
           "  !! !! !! !! Precisely one terrifying transgression identified.\n");
    } else {
      printf("  !! !! !! !! %d obscenities viewed with horror.\n", horrors);
    }
    /* Restore the status of exact arithmetic. */
    b->noexact = saveexact;
  }
  
  #endif /* not REDUCED */
  
  /*****************************************************************************/
  /*                                                                           */
  /*  enqueuebadtriang()   Add a bad triangle data structure to the end of a   */
  /*                       queue.                                              */
  /*                                                                           */
  /*  The queue is actually a set of 4096 queues.  I use multiple queues to    */
  /*  give priority to smaller angles.  I originally implemented a heap, but   */
  /*  the queues are faster by a larger margin than I'd suspected.             */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifndef CDT_ONLY
  
  #ifdef ANSI_DECLARATORS
  void enqueuebadtriang(struct mesh *m, struct behavior *b,
                        struct badtriang *badtri)
  #else /* not ANSI_DECLARATORS */
  void enqueuebadtriang(m, b, badtri)
  struct mesh *m;
  struct behavior *b;
  struct badtriang *badtri;
  #endif /* not ANSI_DECLARATORS */
  
  {
    REAL length, multiplier;
    int exponent, expincrement;
    int queuenumber;
    int posexponent;
    int i;
  
    if (b->verbose > 2) {
      printf("  Queueing bad triangle:\n");
      printf("    (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
             badtri->triangorg[0], badtri->triangorg[1],
             badtri->triangdest[0], badtri->triangdest[1],
             badtri->triangapex[0], badtri->triangapex[1]);
    }
  
    /* Determine the appropriate queue to put the bad triangle into.    */
    /*   Recall that the key is the square of its shortest edge length. */
    if (badtri->key >= 1.0) {
      length = badtri->key;
      posexponent = 1;
    } else {
      /* `badtri->key' is 2.0 to a negative exponent, so we'll record that */
      /*   fact and use the reciprocal of `badtri->key', which is > 1.0.   */
      length = 1.0 / badtri->key;
      posexponent = 0;
    }
    /* `length' is approximately 2.0 to what exponent?  The following code */
    /*   determines the answer in time logarithmic in the exponent.        */
    exponent = 0;
    while (length > 2.0) {
      /* Find an approximation by repeated squaring of two. */
      expincrement = 1;
      multiplier = 0.5;
      while (length * multiplier * multiplier > 1.0) {
        expincrement *= 2;
        multiplier *= multiplier;
      }
      /* Reduce the value of `length', then iterate if necessary. */
      exponent += expincrement;
      length *= multiplier;
    }
    /* `length' is approximately squareroot(2.0) to what exponent? */
    exponent = 2.0 * exponent + (length > SQUAREROOTTWO);
    /* `exponent' is now in the range 0...2047 for IEEE double precision.   */
    /*   Choose a queue in the range 0...4095.  The shortest edges have the */
    /*   highest priority (queue 4095).                                     */
    if (posexponent) {
      queuenumber = 2047 - exponent;
    } else {
      queuenumber = 2048 + exponent;
    }
  
    /* Are we inserting into an empty queue? */
    if (m->queuefront[queuenumber] == (struct badtriang *) NULL) {
      /* Yes, we are inserting into an empty queue.     */
      /*   Will this become the highest-priority queue? */
      if (queuenumber > m->firstnonemptyq) {
        /* Yes, this is the highest-priority queue. */
        m->nextnonemptyq[queuenumber] = m->firstnonemptyq;
        m->firstnonemptyq = queuenumber;
      } else {
        /* No, this is not the highest-priority queue. */
        /*   Find the queue with next higher priority. */
        i = queuenumber + 1;
        while (m->queuefront[i] == (struct badtriang *) NULL) {
          i++;
        }
        /* Mark the newly nonempty queue as following a higher-priority queue. */
        m->nextnonemptyq[queuenumber] = m->nextnonemptyq[i];
        m->nextnonemptyq[i] = queuenumber;
      }
      /* Put the bad triangle at the beginning of the (empty) queue. */
      m->queuefront[queuenumber] = badtri;
    } else {
      /* Add the bad triangle to the end of an already nonempty queue. */
      m->queuetail[queuenumber]->nexttriang = badtri;
    }
    /* Maintain a pointer to the last triangle of the queue. */
    m->queuetail[queuenumber] = badtri;
    /* Newly enqueued bad triangle has no successor in the queue. */
    badtri->nexttriang = (struct badtriang *) NULL;
  }
  
  #endif /* not CDT_ONLY */
  
  /*****************************************************************************/
  /*                                                                           */
  /*  enqueuebadtri()   Add a bad triangle to the end of a queue.              */
  /*                                                                           */
  /*  Allocates a badtriang data structure for the triangle, then passes it to */
  /*  enqueuebadtriang().                                                      */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifndef CDT_ONLY
  
  #ifdef ANSI_DECLARATORS
  void enqueuebadtri(struct mesh *m, struct behavior *b, struct otri *enqtri,
                     REAL minedge, vertex enqapex, vertex enqorg, vertex enqdest)
  #else /* not ANSI_DECLARATORS */
  void enqueuebadtri(m, b, enqtri, minedge, enqapex, enqorg, enqdest)
  struct mesh *m;
  struct behavior *b;
  struct otri *enqtri;
  REAL minedge;
  vertex enqapex;
  vertex enqorg;
  vertex enqdest;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct badtriang *newbad;
  
    /* Allocate space for the bad triangle. */
    newbad = (struct badtriang *) poolalloc(&m->badtriangles);
    newbad->poortri = encode(*enqtri);
    newbad->key = minedge;
    newbad->triangapex = enqapex;
    newbad->triangorg = enqorg;
    newbad->triangdest = enqdest;
    enqueuebadtriang(m, b, newbad);
  }
  
  #endif /* not CDT_ONLY */
  
  /*****************************************************************************/
  /*                                                                           */
  /*  dequeuebadtriang()   Remove a triangle from the front of the queue.      */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifndef CDT_ONLY
  
  #ifdef ANSI_DECLARATORS
  struct badtriang *dequeuebadtriang(struct mesh *m)
  #else /* not ANSI_DECLARATORS */
  struct badtriang *dequeuebadtriang(m)
  struct mesh *m;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct badtriang *result;
  
    /* If no queues are nonempty, return NULL. */
    if (m->firstnonemptyq < 0) {
      return (struct badtriang *) NULL;
    }
    /* Find the first triangle of the highest-priority queue. */
    result = m->queuefront[m->firstnonemptyq];
    /* Remove the triangle from the queue. */
    m->queuefront[m->firstnonemptyq] = result->nexttriang;
    /* If this queue is now empty, note the new highest-priority */
    /*   nonempty queue.                                         */
    if (result == m->queuetail[m->firstnonemptyq]) {
      m->firstnonemptyq = m->nextnonemptyq[m->firstnonemptyq];
    }
    return result;
  }
  
  #endif /* not CDT_ONLY */
  
  /*****************************************************************************/
  /*                                                                           */
  /*  checkseg4encroach()   Check a subsegment to see if it is encroached; add */
  /*                        it to the list if it is.                           */
  /*                                                                           */
  /*  A subsegment is encroached if there is a vertex in its diametral lens.   */
  /*  For Ruppert's algorithm (-D switch), the "diametral lens" is the         */
  /*  diametral circle.  For Chew's algorithm (default), the diametral lens is */
  /*  just big enough to enclose two isosceles triangles whose bases are the   */
  /*  subsegment.  Each of the two isosceles triangles has two angles equal    */
  /*  to `b->minangle'.                                                        */
  /*                                                                           */
  /*  Chew's algorithm does not require diametral lenses at all--but they save */
  /*  time.  Any vertex inside a subsegment's diametral lens implies that the  */
  /*  triangle adjoining the subsegment will be too skinny, so it's only a     */
  /*  matter of time before the encroaching vertex is deleted by Chew's        */
  /*  algorithm.  It's faster to simply not insert the doomed vertex in the    */
  /*  first place, which is why I use diametral lenses with Chew's algorithm.  */
  /*                                                                           */
  /*  Returns a nonzero value if the subsegment is encroached.                 */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifndef CDT_ONLY
  
  #ifdef ANSI_DECLARATORS
  int checkseg4encroach(struct mesh *m, struct behavior *b,
                        struct osub *testsubseg)
  #else /* not ANSI_DECLARATORS */
  int checkseg4encroach(m, b, testsubseg)
  struct mesh *m;
  struct behavior *b;
  struct osub *testsubseg;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct otri neighbortri;
    struct osub testsym;
    struct badsubseg *encroachedseg;
    REAL dotproduct;
    int encroached;
    int sides;
    vertex eorg, edest, eapex;
    triangle ptr;                     /* Temporary variable used by stpivot(). */
  
    encroached = 0;
    sides = 0;
  
    sorg(*testsubseg, eorg);
    sdest(*testsubseg, edest);
    /* Check one neighbor of the subsegment. */
    stpivot(*testsubseg, neighbortri);
    /* Does the neighbor exist, or is this a boundary edge? */
    if (neighbortri.tri != m->dummytri) {
      sides++;
      /* Find a vertex opposite this subsegment. */
      apex(neighbortri, eapex);
      /* Check whether the apex is in the diametral lens of the subsegment */
      /*   (the diametral circle if `conformdel' is set).  A dot product   */
      /*   of two sides of the triangle is used to check whether the angle */
      /*   at the apex is greater than (180 - 2 `minangle') degrees (for   */
      /*   lenses; 90 degrees for diametral circles).                      */
      dotproduct = (eorg[0] - eapex[0]) * (edest[0] - eapex[0]) +
                   (eorg[1] - eapex[1]) * (edest[1] - eapex[1]);
      if (dotproduct < 0.0) {
        if (b->conformdel ||
            (dotproduct * dotproduct >=
             (2.0 * b->goodangle - 1.0) * (2.0 * b->goodangle - 1.0) *
             ((eorg[0] - eapex[0]) * (eorg[0] - eapex[0]) +
              (eorg[1] - eapex[1]) * (eorg[1] - eapex[1])) *
             ((edest[0] - eapex[0]) * (edest[0] - eapex[0]) +
              (edest[1] - eapex[1]) * (edest[1] - eapex[1])))) {
          encroached = 1;
        }
      }
    }
    /* Check the other neighbor of the subsegment. */
    ssym(*testsubseg, testsym);
    stpivot(testsym, neighbortri);
    /* Does the neighbor exist, or is this a boundary edge? */
    if (neighbortri.tri != m->dummytri) {
      sides++;
      /* Find the other vertex opposite this subsegment. */
      apex(neighbortri, eapex);
      /* Check whether the apex is in the diametral lens of the subsegment */
      /*   (or the diametral circle, if `conformdel' is set).              */
      dotproduct = (eorg[0] - eapex[0]) * (edest[0] - eapex[0]) +
                   (eorg[1] - eapex[1]) * (edest[1] - eapex[1]);
      if (dotproduct < 0.0) {
        if (b->conformdel ||
            (dotproduct * dotproduct >=
             (2.0 * b->goodangle - 1.0) * (2.0 * b->goodangle - 1.0) *
             ((eorg[0] - eapex[0]) * (eorg[0] - eapex[0]) +
              (eorg[1] - eapex[1]) * (eorg[1] - eapex[1])) *
             ((edest[0] - eapex[0]) * (edest[0] - eapex[0]) +
              (edest[1] - eapex[1]) * (edest[1] - eapex[1])))) {
          encroached += 2;
        }
      }
    }
  
    if (encroached && (!b->nobisect || ((b->nobisect == 1) && (sides == 2)))) {
      if (b->verbose > 2) {
        printf(
          "  Queueing encroached subsegment (%.12g, %.12g) (%.12g, %.12g).\n",
          eorg[0], eorg[1], edest[0], edest[1]);
      }
      /* Add the subsegment to the list of encroached subsegments. */
      /*   Be sure to get the orientation right.                   */
      encroachedseg = (struct badsubseg *) poolalloc(&m->badsubsegs);
      if (encroached == 1) {
        encroachedseg->encsubseg = sencode(*testsubseg);
        encroachedseg->subsegorg = eorg;
        encroachedseg->subsegdest = edest;
      } else {
        encroachedseg->encsubseg = sencode(testsym);
        encroachedseg->subsegorg = edest;
        encroachedseg->subsegdest = eorg;
      }
    }
  
    return encroached;
  }
  
  #endif /* not CDT_ONLY */
  
  /*****************************************************************************/
  /*                                                                           */
  /*  testtriangle()   Test a triangle for quality and size.                   */
  /*                                                                           */
  /*  Tests a triangle to see if it satisfies the minimum angle condition and  */
  /*  the maximum area condition.  Triangles that aren't up to spec are added  */
  /*  to the bad triangle queue.                                               */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifndef CDT_ONLY
  
  #ifdef ANSI_DECLARATORS
  void testtriangle(struct mesh *m, struct behavior *b, struct otri *testtri)
  #else /* not ANSI_DECLARATORS */
  void testtriangle(m, b, testtri)
  struct mesh *m;
  struct behavior *b;
  struct otri *testtri;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct otri tri1, tri2;
    struct osub testsub;
    vertex torg, tdest, tapex;
    vertex base1, base2;
    vertex org1, dest1, org2, dest2;
    vertex joinvertex;
    REAL dxod, dyod, dxda, dyda, dxao, dyao;
    REAL dxod2, dyod2, dxda2, dyda2, dxao2, dyao2;
    REAL apexlen, orglen, destlen, minedge;
    REAL angle;
    REAL area;
    REAL dist1, dist2;
    subseg sptr;                      /* Temporary variable used by tspivot(). */
    triangle ptr;           /* Temporary variable used by oprev() and dnext(). */
  
    org(*testtri, torg);
    dest(*testtri, tdest);
    apex(*testtri, tapex);
    dxod = torg[0] - tdest[0];
    dyod = torg[1] - tdest[1];
    dxda = tdest[0] - tapex[0];
    dyda = tdest[1] - tapex[1];
    dxao = tapex[0] - torg[0];
    dyao = tapex[1] - torg[1];
    dxod2 = dxod * dxod;
    dyod2 = dyod * dyod;
    dxda2 = dxda * dxda;
    dyda2 = dyda * dyda;
    dxao2 = dxao * dxao;
    dyao2 = dyao * dyao;
    /* Find the lengths of the triangle's three edges. */
    apexlen = dxod2 + dyod2;
    orglen = dxda2 + dyda2;
    destlen = dxao2 + dyao2;
  
    if ((apexlen < orglen) && (apexlen < destlen)) {
      /* The edge opposite the apex is shortest. */
      minedge = apexlen;
      /* Find the square of the cosine of the angle at the apex. */
      angle = dxda * dxao + dyda * dyao;
      angle = angle * angle / (orglen * destlen);
      base1 = torg;
      base2 = tdest;
      otricopy(*testtri, tri1);
    } else if (orglen < destlen) {
      /* The edge opposite the origin is shortest. */
      minedge = orglen;
      /* Find the square of the cosine of the angle at the origin. */
      angle = dxod * dxao + dyod * dyao;
      angle = angle * angle / (apexlen * destlen);
      base1 = tdest;
      base2 = tapex;
      lnext(*testtri, tri1);
    } else {
      /* The edge opposite the destination is shortest. */
      minedge = destlen;
      /* Find the square of the cosine of the angle at the destination. */
      angle = dxod * dxda + dyod * dyda;
      angle = angle * angle / (apexlen * orglen);
      base1 = tapex;
      base2 = torg;
      lprev(*testtri, tri1);
    }
  
    if (b->vararea || b->fixedarea || b->usertest) {
      /* Check whether the area is larger than permitted. */
      area = 0.5 * (dxod * dyda - dyod * dxda);
      if (b->fixedarea && (area > b->maxarea)) {
        /* Add this triangle to the list of bad triangles. */
        enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest);
        return;
      }
  
      /* Nonpositive area constraints are treated as unconstrained. */
      if ((b->vararea) && (area > areabound(*testtri)) &&
          (areabound(*testtri) > 0.0)) {
        /* Add this triangle to the list of bad triangles. */
        enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest);
        return;
      }
  
      if (b->usertest) {
        /* Check whether the user thinks this triangle is too large. */
        if (triunsuitable(torg, tdest, tapex, area)) {
          enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest);
          return;
        }
      }
    }
  
    /* Check whether the angle is smaller than permitted. */
    if (angle > b->goodangle) {
      /* Use the rules of Miller, Pav, and Walkington to decide that certain */
      /*   triangles should not be split, even if they have bad angles.      */
      /*   A skinny triangle is not split if its shortest edge subtends a    */
      /*   small input angle, and both endpoints of the edge lie on a        */
      /*   concentric circular shell.  For convenience, I make a small       */
      /*   adjustment to that rule:  I check if the endpoints of the edge    */
      /*   both lie in segment interiors, equidistant from the apex where    */
      /*   the two segments meet.                                            */
      /* First, check if both points lie in segment interiors.               */
      if ((vertextype(base1) == SEGMENTVERTEX) &&
          (vertextype(base2) == SEGMENTVERTEX)) {
        /* Check if both points lie in a common segment.  If they do, the */
        /*   skinny triangle is enqueued to be split as usual.            */
        tspivot(tri1, testsub);
        if (testsub.ss == m->dummysub) {
          /* No common segment.  Find a subsegment that contains `torg'. */
          otricopy(tri1, tri2);
          do {
            oprevself(tri1);
            tspivot(tri1, testsub);
          } while (testsub.ss == m->dummysub);
          /* Find the endpoints of the containing segment. */
          segorg(testsub, org1);
          segdest(testsub, dest1);
          /* Find a subsegment that contains `tdest'. */
          do {
            dnextself(tri2);
            tspivot(tri2, testsub);
          } while (testsub.ss == m->dummysub);
          /* Find the endpoints of the containing segment. */
          segorg(testsub, org2);
          segdest(testsub, dest2);
          /* Check if the two containing segments have an endpoint in common. */
          joinvertex = (vertex) NULL;
          if ((dest1[0] == org2[0]) && (dest1[1] == org2[1])) {
            joinvertex = dest1;
          } else if ((org1[0] == dest2[0]) && (org1[1] == dest2[1])) {
            joinvertex = org1;
          }
          if (joinvertex != (vertex) NULL) {
            /* Compute the distance from the common endpoint (of the two  */
            /*   segments) to each of the endpoints of the shortest edge. */
            dist1 = ((base1[0] - joinvertex[0]) * (base1[0] - joinvertex[0]) +
                     (base1[1] - joinvertex[1]) * (base1[1] - joinvertex[1]));
            dist2 = ((base2[0] - joinvertex[0]) * (base2[0] - joinvertex[0]) +
                     (base2[1] - joinvertex[1]) * (base2[1] - joinvertex[1]));
            /* If the two distances are equal, don't split the triangle. */
            if ((dist1 < 1.001 * dist2) && (dist1 > 0.999 * dist2)) {
              /* Return now to avoid enqueueing the bad triangle. */
              return;
            }
          }
        }
      }
  
      /* Add this triangle to the list of bad triangles. */
      enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest);
    }
  }
  
  #endif /* not CDT_ONLY */
  
  /**                                                                         **/
  /**                                                                         **/
  /********* Mesh quality testing routines end here                    *********/
  
  /********* Point location routines begin here                        *********/
  /**                                                                         **/
  /**                                                                         **/
  
  /*****************************************************************************/
  /*                                                                           */
  /*  makevertexmap()   Construct a mapping from vertices to triangles to      */
  /*                    improve the speed of point location for segment        */
  /*                    insertion.                                             */
  /*                                                                           */
  /*  Traverses all the triangles, and provides each corner of each triangle   */
  /*  with a pointer to that triangle.  Of course, pointers will be            */
  /*  overwritten by other pointers because (almost) each vertex is a corner   */
  /*  of several triangles, but in the end every vertex will point to some     */
  /*  triangle that contains it.                                               */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  void makevertexmap(struct mesh *m, struct behavior *b)
  #else /* not ANSI_DECLARATORS */
  void makevertexmap(m, b)
  struct mesh *m;
  struct behavior *b;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct otri triangleloop;
    vertex triorg;
  
    if (b->verbose) {
      printf("    Constructing mapping from vertices to triangles.\n");
    }
    traversalinit(&m->triangles);
    triangleloop.tri = triangletraverse(m);
    while (triangleloop.tri != (triangle *) NULL) {
      /* Check all three vertices of the triangle. */
      for (triangleloop.orient = 0; triangleloop.orient < 3;
           triangleloop.orient++) {
        org(triangleloop, triorg);
        setvertex2tri(triorg, encode(triangleloop));
      }
      triangleloop.tri = triangletraverse(m);
    }
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  preciselocate()   Find a triangle or edge containing a given point.      */
  /*                                                                           */
  /*  Begins its search from `searchtri'.  It is important that `searchtri'    */
  /*  be a handle with the property that `searchpoint' is strictly to the left */
  /*  of the edge denoted by `searchtri', or is collinear with that edge and   */
  /*  does not intersect that edge.  (In particular, `searchpoint' should not  */
  /*  be the origin or destination of that edge.)                              */
  /*                                                                           */
  /*  These conditions are imposed because preciselocate() is normally used in */
  /*  one of two situations:                                                   */
  /*                                                                           */
  /*  (1)  To try to find the location to insert a new point.  Normally, we    */
  /*       know an edge that the point is strictly to the left of.  In the     */
  /*       incremental Delaunay algorithm, that edge is a bounding box edge.   */
  /*       In Ruppert's Delaunay refinement algorithm for quality meshing,     */
  /*       that edge is the shortest edge of the triangle whose circumcenter   */
  /*       is being inserted.                                                  */
  /*                                                                           */
  /*  (2)  To try to find an existing point.  In this case, any edge on the    */
  /*       convex hull is a good starting edge.  You must screen out the       */
  /*       possibility that the vertex sought is an endpoint of the starting   */
  /*       edge before you call preciselocate().                               */
  /*                                                                           */
  /*  On completion, `searchtri' is a triangle that contains `searchpoint'.    */
  /*                                                                           */
  /*  This implementation differs from that given by Guibas and Stolfi.  It    */
  /*  walks from triangle to triangle, crossing an edge only if `searchpoint'  */
  /*  is on the other side of the line containing that edge.  After entering   */
  /*  a triangle, there are two edges by which one can leave that triangle.    */
  /*  If both edges are valid (`searchpoint' is on the other side of both      */
  /*  edges), one of the two is chosen by drawing a line perpendicular to      */
  /*  the entry edge (whose endpoints are `forg' and `fdest') passing through  */
  /*  `fapex'.  Depending on which side of this perpendicular `searchpoint'    */
  /*  falls on, an exit edge is chosen.                                        */
  /*                                                                           */
  /*  This implementation is empirically faster than the Guibas and Stolfi     */
  /*  point location routine (which I originally used), which tends to spiral  */
  /*  in toward its target.                                                    */
  /*                                                                           */
  /*  Returns ONVERTEX if the point lies on an existing vertex.  `searchtri'   */
  /*  is a handle whose origin is the existing vertex.                         */
  /*                                                                           */
  /*  Returns ONEDGE if the point lies on a mesh edge.  `searchtri' is a       */
  /*  handle whose primary edge is the edge on which the point lies.           */
  /*                                                                           */
  /*  Returns INTRIANGLE if the point lies strictly within a triangle.         */
  /*  `searchtri' is a handle on the triangle that contains the point.         */
  /*                                                                           */
  /*  Returns OUTSIDE if the point lies outside the mesh.  `searchtri' is a    */
  /*  handle whose primary edge the point is to the right of.  This might      */
  /*  occur when the circumcenter of a triangle falls just slightly outside    */
  /*  the mesh due to floating-point roundoff error.  It also occurs when      */
  /*  seeking a hole or region point that a foolish user has placed outside    */
  /*  the mesh.                                                                */
  /*                                                                           */
  /*  If `stopatsubsegment' is nonzero, the search will stop if it tries to    */
  /*  walk through a subsegment, and will return OUTSIDE.                      */
  /*                                                                           */
  /*  WARNING:  This routine is designed for convex triangulations, and will   */
  /*  not generally work after the holes and concavities have been carved.     */
  /*  However, it can still be used to find the circumcenter of a triangle, as */
  /*  long as the search is begun from the triangle in question.               */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  enum locateresult preciselocate(struct mesh *m, struct behavior *b,
                                  vertex searchpoint, struct otri *searchtri,
                                  int stopatsubsegment)
  #else /* not ANSI_DECLARATORS */
  enum locateresult preciselocate(m, b, searchpoint, searchtri, stopatsubsegment)
  struct mesh *m;
  struct behavior *b;
  vertex searchpoint;
  struct otri *searchtri;
  int stopatsubsegment;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct otri backtracktri;
    struct osub checkedge;
    vertex forg, fdest, fapex;
    REAL orgorient, destorient;
    int moveleft;
    triangle ptr;                         /* Temporary variable used by sym(). */
    subseg sptr;                      /* Temporary variable used by tspivot(). */
  
    if (b->verbose > 2) {
      printf("  Searching for point (%.12g, %.12g).\n",
             searchpoint[0], searchpoint[1]);
    }
    /* Where are we? */
    org(*searchtri, forg);
    dest(*searchtri, fdest);
    apex(*searchtri, fapex);
    while (1) {
      if (b->verbose > 2) {
        printf("    At (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
               forg[0], forg[1], fdest[0], fdest[1], fapex[0], fapex[1]);
      }
      /* Check whether the apex is the point we seek. */
      if ((fapex[0] == searchpoint[0]) && (fapex[1] == searchpoint[1])) {
        lprevself(*searchtri);
        return ONVERTEX;
      }
      /* Does the point lie on the other side of the line defined by the */
      /*   triangle edge opposite the triangle's destination?            */
      destorient = counterclockwise(m, b, forg, fapex, searchpoint);
      /* Does the point lie on the other side of the line defined by the */
      /*   triangle edge opposite the triangle's origin?                 */
      orgorient = counterclockwise(m, b, fapex, fdest, searchpoint);
      if (destorient > 0.0) {
        if (orgorient > 0.0) {
          /* Move left if the inner product of (fapex - searchpoint) and  */
          /*   (fdest - forg) is positive.  This is equivalent to drawing */
          /*   a line perpendicular to the line (forg, fdest) and passing */
          /*   through `fapex', and determining which side of this line   */
          /*   `searchpoint' falls on.                                    */
          moveleft = (fapex[0] - searchpoint[0]) * (fdest[0] - forg[0]) +
                     (fapex[1] - searchpoint[1]) * (fdest[1] - forg[1]) > 0.0;
        } else {
          moveleft = 1;
        }
      } else {
        if (orgorient > 0.0) {
          moveleft = 0;
        } else {
          /* The point we seek must be on the boundary of or inside this */
          /*   triangle.                                                 */
          if (destorient == 0.0) {
            lprevself(*searchtri);
            return ONEDGE;
          }
          if (orgorient == 0.0) {
            lnextself(*searchtri);
            return ONEDGE;
          }
          return INTRIANGLE;
        }
      }
  
      /* Move to another triangle.  Leave a trace `backtracktri' in case */
      /*   floating-point roundoff or some such bogey causes us to walk  */
      /*   off a boundary of the triangulation.                          */
      if (moveleft) {
        lprev(*searchtri, backtracktri);
        fdest = fapex;
      } else {
        lnext(*searchtri, backtracktri);
        forg = fapex;
      }
      sym(backtracktri, *searchtri);
  
      if (m->checksegments && stopatsubsegment) {
        /* Check for walking through a subsegment. */
        tspivot(backtracktri, checkedge);
        if (checkedge.ss != m->dummysub) {
          /* Go back to the last triangle. */
          otricopy(backtracktri, *searchtri);
          return OUTSIDE;
        }
      }
      /* Check for walking right out of the triangulation. */
      if (searchtri->tri == m->dummytri) {
        /* Go back to the last triangle. */
        otricopy(backtracktri, *searchtri);
        return OUTSIDE;
      }
  
      apex(*searchtri, fapex);
    }
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  locate()   Find a triangle or edge containing a given point.             */
  /*                                                                           */
  /*  Searching begins from one of:  the input `searchtri', a recently         */
  /*  encountered triangle `recenttri', or from a triangle chosen from a       */
  /*  random sample.  The choice is made by determining which triangle's       */
  /*  origin is closest to the point we are searching for.  Normally,          */
  /*  `searchtri' should be a handle on the convex hull of the triangulation.  */
  /*                                                                           */
  /*  Details on the random sampling method can be found in the Mucke, Saias,  */
  /*  and Zhu paper cited in the header of this code.                          */
  /*                                                                           */
  /*  On completion, `searchtri' is a triangle that contains `searchpoint'.    */
  /*                                                                           */
  /*  Returns ONVERTEX if the point lies on an existing vertex.  `searchtri'   */
  /*  is a handle whose origin is the existing vertex.                         */
  /*                                                                           */
  /*  Returns ONEDGE if the point lies on a mesh edge.  `searchtri' is a       */
  /*  handle whose primary edge is the edge on which the point lies.           */
  /*                                                                           */
  /*  Returns INTRIANGLE if the point lies strictly within a triangle.         */
  /*  `searchtri' is a handle on the triangle that contains the point.         */
  /*                                                                           */
  /*  Returns OUTSIDE if the point lies outside the mesh.  `searchtri' is a    */
  /*  handle whose primary edge the point is to the right of.  This might      */
  /*  occur when the circumcenter of a triangle falls just slightly outside    */
  /*  the mesh due to floating-point roundoff error.  It also occurs when      */
  /*  seeking a hole or region point that a foolish user has placed outside    */
  /*  the mesh.                                                                */
  /*                                                                           */
  /*  WARNING:  This routine is designed for convex triangulations, and will   */
  /*  not generally work after the holes and concavities have been carved.     */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  enum locateresult locate(struct mesh *m, struct behavior *b,
                           vertex searchpoint, struct otri *searchtri)
  #else /* not ANSI_DECLARATORS */
  enum locateresult locate(m, b, searchpoint, searchtri)
  struct mesh *m;
  struct behavior *b;
  vertex searchpoint;
  struct otri *searchtri;
  #endif /* not ANSI_DECLARATORS */
  
  {
    TRIVOID **sampleblock;
    char *firsttri;
    struct otri sampletri;
    vertex torg, tdest;
    unsigned long long alignptr;
    REAL searchdist, dist;
    REAL ahead;
    long samplesperblock, totalsamplesleft, samplesleft;
    long population, totalpopulation;
    triangle ptr;                         /* Temporary variable used by sym(). */
  
    if (b->verbose > 2) {
      printf("  Randomly sampling for a triangle near point (%.12g, %.12g).\n",
             searchpoint[0], searchpoint[1]);
    }
    /* Record the distance from the suggested starting triangle to the */
    /*   point we seek.                                                */
    org(*searchtri, torg);
    searchdist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) +
                 (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]);
    if (b->verbose > 2) {
      printf("    Boundary triangle has origin (%.12g, %.12g).\n",
             torg[0], torg[1]);
    }
  
    /* If a recently encountered triangle has been recorded and has not been */
    /*   deallocated, test it as a good starting point.                      */
    if (m->recenttri.tri != (triangle *) NULL) {
      if (!deadtri(m->recenttri.tri)) {
        org(m->recenttri, torg);
        if ((torg[0] == searchpoint[0]) && (torg[1] == searchpoint[1])) {
          otricopy(m->recenttri, *searchtri);
          return ONVERTEX;
        }
        dist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) +
               (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]);
        if (dist < searchdist) {
          otricopy(m->recenttri, *searchtri);
          searchdist = dist;
          if (b->verbose > 2) {
            printf("    Choosing recent triangle with origin (%.12g, %.12g).\n",
                   torg[0], torg[1]);
          }
        }
      }
    }
  
    /* The number of random samples taken is proportional to the cube root of */
    /*   the number of triangles in the mesh.  The next bit of code assumes   */
    /*   that the number of triangles increases monotonically (or at least    */
    /*   doesn't decrease enough to matter).                                  */
    while (SAMPLEFACTOR * m->samples * m->samples * m->samples <
           m->triangles.items) {
      m->samples++;
    }
  
    /* We'll draw ceiling(samples * TRIPERBLOCK / maxitems) random samples  */
    /*   from each block of triangles (except the first)--until we meet the */
    /*   sample quota.  The ceiling means that blocks at the end might be   */
    /*   neglected, but I don't care.                                       */
    samplesperblock = (m->samples * TRIPERBLOCK - 1) / m->triangles.maxitems + 1;
    /* We'll draw ceiling(samples * itemsfirstblock / maxitems) random samples */
    /*   from the first block of triangles.                                    */
    samplesleft = (m->samples * m->triangles.itemsfirstblock - 1) /
                  m->triangles.maxitems + 1;
    totalsamplesleft = m->samples;
    population = m->triangles.itemsfirstblock;
    totalpopulation = m->triangles.maxitems;
    sampleblock = m->triangles.firstblock;
    sampletri.orient = 0;
    while (totalsamplesleft > 0) {
      /* If we're in the last block, `population' needs to be corrected. */
      if (population > totalpopulation) {
        population = totalpopulation;
      }
      /* Find a pointer to the first triangle in the block. */
      alignptr = (unsigned long long) (sampleblock + 1);
      firsttri = (char *) (alignptr +
                           (unsigned long long) m->triangles.alignbytes -
                           (alignptr %
                            (unsigned long long) m->triangles.alignbytes));
  
      /* Choose `samplesleft' randomly sampled triangles in this block. */
      do {
        sampletri.tri = (triangle *) (firsttri +
                                      (randomnation((unsigned int) population) *
                                       m->triangles.itembytes));
        if (!deadtri(sampletri.tri)) {
          org(sampletri, torg);
          dist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) +
                 (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]);
          if (dist < searchdist) {
            otricopy(sampletri, *searchtri);
            searchdist = dist;
            if (b->verbose > 2) {
              printf("    Choosing triangle with origin (%.12g, %.12g).\n",
                     torg[0], torg[1]);
            }
          }
        }
  
        samplesleft--;
        totalsamplesleft--;
      } while ((samplesleft > 0) && (totalsamplesleft > 0));
  
      if (totalsamplesleft > 0) {
        sampleblock = (TRIVOID **) *sampleblock;
        samplesleft = samplesperblock;
        totalpopulation -= population;
        population = TRIPERBLOCK;
      }
    }
  
    /* Where are we? */
    org(*searchtri, torg);
    dest(*searchtri, tdest);
    /* Check the starting triangle's vertices. */
    if ((torg[0] == searchpoint[0]) && (torg[1] == searchpoint[1])) {
      return ONVERTEX;
    }
    if ((tdest[0] == searchpoint[0]) && (tdest[1] == searchpoint[1])) {
      lnextself(*searchtri);
      return ONVERTEX;
    }
    /* Orient `searchtri' to fit the preconditions of calling preciselocate(). */
    ahead = counterclockwise(m, b, torg, tdest, searchpoint);
    if (ahead < 0.0) {
      /* Turn around so that `searchpoint' is to the left of the */
      /*   edge specified by `searchtri'.                        */
      symself(*searchtri);
    } else if (ahead == 0.0) {
      /* Check if `searchpoint' is between `torg' and `tdest'. */
      if (((torg[0] < searchpoint[0]) == (searchpoint[0] < tdest[0])) &&
          ((torg[1] < searchpoint[1]) == (searchpoint[1] < tdest[1]))) {
        return ONEDGE;
      }
    }
    return preciselocate(m, b, searchpoint, searchtri, 0);
  }
  
  /**                                                                         **/
  /**                                                                         **/
  /********* Point location routines end here                          *********/
  
  /********* Mesh transformation routines begin here                   *********/
  /**                                                                         **/
  /**                                                                         **/
  
  /*****************************************************************************/
  /*                                                                           */
  /*  insertsubseg()   Create a new subsegment and insert it between two       */
  /*                   triangles.                                              */
  /*                                                                           */
  /*  The new subsegment is inserted at the edge described by the handle       */
  /*  `tri'.  Its vertices are properly initialized.  The marker `subsegmark'  */
  /*  is applied to the subsegment and, if appropriate, its vertices.          */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  void insertsubseg(struct mesh *m, struct behavior *b, struct otri *tri,
                    int subsegmark)
  #else /* not ANSI_DECLARATORS */
  void insertsubseg(m, b, tri, subsegmark)
  struct mesh *m;
  struct behavior *b;
  struct otri *tri;             /* Edge at which to insert the new subsegment. */
  int subsegmark;                            /* Marker for the new subsegment. */
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct otri oppotri;
    struct osub newsubseg;
    vertex triorg, tridest;
    triangle ptr;                         /* Temporary variable used by sym(). */
    subseg sptr;                      /* Temporary variable used by tspivot(). */
  
    org(*tri, triorg);
    dest(*tri, tridest);
    /* Mark vertices if possible. */
    if (vertexmark(triorg) == 0) {
      setvertexmark(triorg, subsegmark);
    }
    if (vertexmark(tridest) == 0) {
      setvertexmark(tridest, subsegmark);
    }
    /* Check if there's already a subsegment here. */
    tspivot(*tri, newsubseg);
    if (newsubseg.ss == m->dummysub) {
      /* Make new subsegment and initialize its vertices. */
      makesubseg(m, &newsubseg);
      setsorg(newsubseg, tridest);
      setsdest(newsubseg, triorg);
      setsegorg(newsubseg, tridest);
      setsegdest(newsubseg, triorg);
      /* Bond new subsegment to the two triangles it is sandwiched between. */
      /*   Note that the facing triangle `oppotri' might be equal to        */
      /*   `dummytri' (outer space), but the new subsegment is bonded to it */
      /*   all the same.                                                    */
      tsbond(*tri, newsubseg);
      sym(*tri, oppotri);
      ssymself(newsubseg);
      tsbond(oppotri, newsubseg);
      setmark(newsubseg, subsegmark);
      if (b->verbose > 2) {
        printf("  Inserting new ");
        printsubseg(m, b, &newsubseg);
      }
    } else {
      if (mark(newsubseg) == 0) {
        setmark(newsubseg, subsegmark);
      }
    }
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  Terminology                                                              */
  /*                                                                           */
  /*  A "local transformation" replaces a small set of triangles with another  */
  /*  set of triangles.  This may or may not involve inserting or deleting a   */
  /*  vertex.                                                                  */
  /*                                                                           */
  /*  The term "casing" is used to describe the set of triangles that are      */
  /*  attached to the triangles being transformed, but are not transformed     */
  /*  themselves.  Think of the casing as a fixed hollow structure inside      */
  /*  which all the action happens.  A "casing" is only defined relative to    */
  /*  a single transformation; each occurrence of a transformation will        */
  /*  involve a different casing.                                              */
  /*                                                                           */
  /*****************************************************************************/
  
  /*****************************************************************************/
  /*                                                                           */
  /*  flip()   Transform two triangles to two different triangles by flipping  */
  /*           an edge counterclockwise within a quadrilateral.                */
  /*                                                                           */
  /*  Imagine the original triangles, abc and bad, oriented so that the        */
  /*  shared edge ab lies in a horizontal plane, with the vertex b on the left */
  /*  and the vertex a on the right.  The vertex c lies below the edge, and    */
  /*  the vertex d lies above the edge.  The `flipedge' handle holds the edge  */
  /*  ab of triangle abc, and is directed left, from vertex a to vertex b.     */
  /*                                                                           */
  /*  The triangles abc and bad are deleted and replaced by the triangles cdb  */
  /*  and dca.  The triangles that represent abc and bad are NOT deallocated;  */
  /*  they are reused for dca and cdb, respectively.  Hence, any handles that  */
  /*  may have held the original triangles are still valid, although not       */
  /*  directed as they were before.                                            */
  /*                                                                           */
  /*  Upon completion of this routine, the `flipedge' handle holds the edge    */
  /*  dc of triangle dca, and is directed down, from vertex d to vertex c.     */
  /*  (Hence, the two triangles have rotated counterclockwise.)                */
  /*                                                                           */
  /*  WARNING:  This transformation is geometrically valid only if the         */
  /*  quadrilateral adbc is convex.  Furthermore, this transformation is       */
  /*  valid only if there is not a subsegment between the triangles abc and    */
  /*  bad.  This routine does not check either of these preconditions, and     */
  /*  it is the responsibility of the calling routine to ensure that they are  */
  /*  met.  If they are not, the streets shall be filled with wailing and      */
  /*  gnashing of teeth.                                                       */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  void flip(struct mesh *m, struct behavior *b, struct otri *flipedge)
  #else /* not ANSI_DECLARATORS */
  void flip(m, b, flipedge)
  struct mesh *m;
  struct behavior *b;
  struct otri *flipedge;                    /* Handle for the triangle abc. */
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct otri botleft, botright;
    struct otri topleft, topright;
    struct otri top;
    struct otri botlcasing, botrcasing;
    struct otri toplcasing, toprcasing;
    struct osub botlsubseg, botrsubseg;
    struct osub toplsubseg, toprsubseg;
    vertex leftvertex, rightvertex, botvertex;
    vertex farvertex;
    triangle ptr;                         /* Temporary variable used by sym(). */
    subseg sptr;                      /* Temporary variable used by tspivot(). */
  
    /* Identify the vertices of the quadrilateral. */
    org(*flipedge, rightvertex);
    dest(*flipedge, leftvertex);
    apex(*flipedge, botvertex);
    sym(*flipedge, top);
  #ifdef SELF_CHECK
    if (top.tri == m->dummytri) {
      printf("Internal error in flip():  Attempt to flip on boundary.\n");
      lnextself(*flipedge);
      return;
    }
    if (m->checksegments) {
      tspivot(*flipedge, toplsubseg);
      if (toplsubseg.ss != m->dummysub) {
        printf("Internal error in flip():  Attempt to flip a segment.\n");
        lnextself(*flipedge);
        return;
      }
    }
  #endif /* SELF_CHECK */
    apex(top, farvertex);
  
    /* Identify the casing of the quadrilateral. */
    lprev(top, topleft);
    sym(topleft, toplcasing);
    lnext(top, topright);
    sym(topright, toprcasing);
    lnext(*flipedge, botleft);
    sym(botleft, botlcasing);
    lprev(*flipedge, botright);
    sym(botright, botrcasing);
    /* Rotate the quadrilateral one-quarter turn counterclockwise. */
    bond(topleft, botlcasing);
    bond(botleft, botrcasing);
    bond(botright, toprcasing);
    bond(topright, toplcasing);
  
    if (m->checksegments) {
      /* Check for subsegments and rebond them to the quadrilateral. */
      tspivot(topleft, toplsubseg);
      tspivot(botleft, botlsubseg);
      tspivot(botright, botrsubseg);
      tspivot(topright, toprsubseg);
      if (toplsubseg.ss == m->dummysub) {
        tsdissolve(topright);
      } else {
        tsbond(topright, toplsubseg);
      }
      if (botlsubseg.ss == m->dummysub) {
        tsdissolve(topleft);
      } else {
        tsbond(topleft, botlsubseg);
      }
      if (botrsubseg.ss == m->dummysub) {
        tsdissolve(botleft);
      } else {
        tsbond(botleft, botrsubseg);
      }
      if (toprsubseg.ss == m->dummysub) {
        tsdissolve(botright);
      } else {
        tsbond(botright, toprsubseg);
      }
    }
  
    /* New vertex assignments for the rotated quadrilateral. */
    setorg(*flipedge, farvertex);
    setdest(*flipedge, botvertex);
    setapex(*flipedge, rightvertex);
    setorg(top, botvertex);
    setdest(top, farvertex);
    setapex(top, leftvertex);
    if (b->verbose > 2) {
      printf("  Edge flip results in left ");
      printtriangle(m, b, &top);
      printf("  and right ");
      printtriangle(m, b, flipedge);
    }
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  unflip()   Transform two triangles to two different triangles by         */
  /*             flipping an edge clockwise within a quadrilateral.  Reverses  */
  /*             the flip() operation so that the data structures representing */
  /*             the triangles are back where they were before the flip().     */
  /*                                                                           */
  /*  Imagine the original triangles, abc and bad, oriented so that the        */
  /*  shared edge ab lies in a horizontal plane, with the vertex b on the left */
  /*  and the vertex a on the right.  The vertex c lies below the edge, and    */
  /*  the vertex d lies above the edge.  The `flipedge' handle holds the edge  */
  /*  ab of triangle abc, and is directed left, from vertex a to vertex b.     */
  /*                                                                           */
  /*  The triangles abc and bad are deleted and replaced by the triangles cdb  */
  /*  and dca.  The triangles that represent abc and bad are NOT deallocated;  */
  /*  they are reused for cdb and dca, respectively.  Hence, any handles that  */
  /*  may have held the original triangles are still valid, although not       */
  /*  directed as they were before.                                            */
  /*                                                                           */
  /*  Upon completion of this routine, the `flipedge' handle holds the edge    */
  /*  cd of triangle cdb, and is directed up, from vertex c to vertex d.       */
  /*  (Hence, the two triangles have rotated clockwise.)                       */
  /*                                                                           */
  /*  WARNING:  This transformation is geometrically valid only if the         */
  /*  quadrilateral adbc is convex.  Furthermore, this transformation is       */
  /*  valid only if there is not a subsegment between the triangles abc and    */
  /*  bad.  This routine does not check either of these preconditions, and     */
  /*  it is the responsibility of the calling routine to ensure that they are  */
  /*  met.  If they are not, the streets shall be filled with wailing and      */
  /*  gnashing of teeth.                                                       */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  void unflip(struct mesh *m, struct behavior *b, struct otri *flipedge)
  #else /* not ANSI_DECLARATORS */
  void unflip(m, b, flipedge)
  struct mesh *m;
  struct behavior *b;
  struct otri *flipedge;                    /* Handle for the triangle abc. */
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct otri botleft, botright;
    struct otri topleft, topright;
    struct otri top;
    struct otri botlcasing, botrcasing;
    struct otri toplcasing, toprcasing;
    struct osub botlsubseg, botrsubseg;
    struct osub toplsubseg, toprsubseg;
    vertex leftvertex, rightvertex, botvertex;
    vertex farvertex;
    triangle ptr;                         /* Temporary variable used by sym(). */
    subseg sptr;                      /* Temporary variable used by tspivot(). */
  
    /* Identify the vertices of the quadrilateral. */
    org(*flipedge, rightvertex);
    dest(*flipedge, leftvertex);
    apex(*flipedge, botvertex);
    sym(*flipedge, top);
  #ifdef SELF_CHECK
    if (top.tri == m->dummytri) {
      printf("Internal error in unflip():  Attempt to flip on boundary.\n");
      lnextself(*flipedge);
      return;
    }
    if (m->checksegments) {
      tspivot(*flipedge, toplsubseg);
      if (toplsubseg.ss != m->dummysub) {
        printf("Internal error in unflip():  Attempt to flip a subsegment.\n");
        lnextself(*flipedge);
        return;
      }
    }
  #endif /* SELF_CHECK */
    apex(top, farvertex);
  
    /* Identify the casing of the quadrilateral. */
    lprev(top, topleft);
    sym(topleft, toplcasing);
    lnext(top, topright);
    sym(topright, toprcasing);
    lnext(*flipedge, botleft);
    sym(botleft, botlcasing);
    lprev(*flipedge, botright);
    sym(botright, botrcasing);
    /* Rotate the quadrilateral one-quarter turn clockwise. */
    bond(topleft, toprcasing);
    bond(botleft, toplcasing);
    bond(botright, botlcasing);
    bond(topright, botrcasing);
  
    if (m->checksegments) {
      /* Check for subsegments and rebond them to the quadrilateral. */
      tspivot(topleft, toplsubseg);
      tspivot(botleft, botlsubseg);
      tspivot(botright, botrsubseg);
      tspivot(topright, toprsubseg);
      if (toplsubseg.ss == m->dummysub) {
        tsdissolve(botleft);
      } else {
        tsbond(botleft, toplsubseg);
      }
      if (botlsubseg.ss == m->dummysub) {
        tsdissolve(botright);
      } else {
        tsbond(botright, botlsubseg);
      }
      if (botrsubseg.ss == m->dummysub) {
        tsdissolve(topright);
      } else {
        tsbond(topright, botrsubseg);
      }
      if (toprsubseg.ss == m->dummysub) {
        tsdissolve(topleft);
      } else {
        tsbond(topleft, toprsubseg);
      }
    }
  
    /* New vertex assignments for the rotated quadrilateral. */
    setorg(*flipedge, botvertex);
    setdest(*flipedge, farvertex);
    setapex(*flipedge, leftvertex);
    setorg(top, farvertex);
    setdest(top, botvertex);
    setapex(top, rightvertex);
    if (b->verbose > 2) {
      printf("  Edge unflip results in left ");
      printtriangle(m, b, flipedge);
      printf("  and right ");
      printtriangle(m, b, &top);
    }
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  insertvertex()   Insert a vertex into a Delaunay triangulation,          */
  /*                   performing flips as necessary to maintain the Delaunay  */
  /*                   property.                                               */
  /*                                                                           */
  /*  The point `insertvertex' is located.  If `searchtri.tri' is not NULL,    */
  /*  the search for the containing triangle begins from `searchtri'.  If      */
  /*  `searchtri.tri' is NULL, a full point location procedure is called.      */
  /*  If `insertvertex' is found inside a triangle, the triangle is split into */
  /*  three; if `insertvertex' lies on an edge, the edge is split in two,      */
  /*  thereby splitting the two adjacent triangles into four.  Edge flips are  */
  /*  used to restore the Delaunay property.  If `insertvertex' lies on an     */
  /*  existing vertex, no action is taken, and the value DUPLICATEVERTEX is    */
  /*  returned.  On return, `searchtri' is set to a handle whose origin is the */
  /*  existing vertex.                                                         */
  /*                                                                           */
  /*  Normally, the parameter `splitseg' is set to NULL, implying that no      */
  /*  subsegment should be split.  In this case, if `insertvertex' is found to */
  /*  lie on a segment, no action is taken, and the value VIOLATINGVERTEX is   */
  /*  returned.  On return, `searchtri' is set to a handle whose primary edge  */
  /*  is the violated subsegment.                                              */
  /*                                                                           */
  /*  If the calling routine wishes to split a subsegment by inserting a       */
  /*  vertex in it, the parameter `splitseg' should be that subsegment.  In    */
  /*  this case, `searchtri' MUST be the triangle handle reached by pivoting   */
  /*  from that subsegment; no point location is done.                         */
  /*                                                                           */
  /*  `segmentflaws' and `triflaws' are flags that indicate whether or not     */
  /*  there should be checks for the creation of encroached subsegments or bad */
  /*  quality triangles.  If a newly inserted vertex encroaches upon           */
  /*  subsegments, these subsegments are added to the list of subsegments to   */
  /*  be split if `segmentflaws' is set.  If bad triangles are created, these  */
  /*  are added to the queue if `triflaws' is set.                             */
  /*                                                                           */
  /*  If a duplicate vertex or violated segment does not prevent the vertex    */
  /*  from being inserted, the return value will be ENCROACHINGVERTEX if the   */
  /*  vertex encroaches upon a subsegment (and checking is enabled), or        */
  /*  SUCCESSFULVERTEX otherwise.  In either case, `searchtri' is set to a     */
  /*  handle whose origin is the newly inserted vertex.                        */
  /*                                                                           */
  /*  insertvertex() does not use flip() for reasons of speed; some            */
  /*  information can be reused from edge flip to edge flip, like the          */
  /*  locations of subsegments.                                                */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  enum insertvertexresult insertvertex(struct mesh *m, struct behavior *b,
                                       vertex newvertex, struct otri *searchtri,
                                       struct osub *splitseg,
                                       int segmentflaws, int triflaws)
  #else /* not ANSI_DECLARATORS */
  enum insertvertexresult insertvertex(m, b, newvertex, searchtri, splitseg,
                                       segmentflaws, triflaws)
  struct mesh *m;
  struct behavior *b;
  vertex newvertex;
  struct otri *searchtri;
  struct osub *splitseg;
  int segmentflaws;
  int triflaws;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct otri horiz;
    struct otri top;
    struct otri botleft, botright;
    struct otri topleft, topright;
    struct otri newbotleft, newbotright;
    struct otri newtopright;
    struct otri botlcasing, botrcasing;
    struct otri toplcasing, toprcasing;
    struct otri testtri;
    struct osub botlsubseg, botrsubseg;
    struct osub toplsubseg, toprsubseg;
    struct osub brokensubseg;
    struct osub checksubseg;
    struct osub rightsubseg;
    struct osub newsubseg;
    struct badsubseg *encroached;
    struct flipstacker *newflip;
    vertex first;
    vertex leftvertex, rightvertex, botvertex, topvertex, farvertex;
    vertex segmentorg, segmentdest;
    REAL attrib;
    REAL area;
    enum insertvertexresult success;
    enum locateresult intersect;
    int doflip;
    int mirrorflag;
    int enq;
    int i;
    triangle ptr;                         /* Temporary variable used by sym(). */
    subseg sptr;         /* Temporary variable used by spivot() and tspivot(). */
  
    if (b->verbose > 1) {
      printf("  Inserting (%.12g, %.12g).\n", newvertex[0], newvertex[1]);
    }
  
    if (splitseg == (struct osub *) NULL) {
      /* Find the location of the vertex to be inserted.  Check if a good */
      /*   starting triangle has already been provided by the caller.     */
      if (searchtri->tri == m->dummytri) {
        /* Find a boundary triangle. */
        horiz.tri = m->dummytri;
        horiz.orient = 0;
        symself(horiz);
        /* Search for a triangle containing `newvertex'. */
        intersect = locate(m, b, newvertex, &horiz);
      } else {
        /* Start searching from the triangle provided by the caller. */
        otricopy(*searchtri, horiz);
        intersect = preciselocate(m, b, newvertex, &horiz, 1);
      }
    } else {
      /* The calling routine provides the subsegment in which */
      /*   the vertex is inserted.                             */
      otricopy(*searchtri, horiz);
      intersect = ONEDGE;
    }
  
    if (intersect == ONVERTEX) {
      /* There's already a vertex there.  Return in `searchtri' a triangle */
      /*   whose origin is the existing vertex.                            */
      otricopy(horiz, *searchtri);
      otricopy(horiz, m->recenttri);
      return DUPLICATEVERTEX;
    }
    if ((intersect == ONEDGE) || (intersect == OUTSIDE)) {
      /* The vertex falls on an edge or boundary. */
      if (m->checksegments && (splitseg == (struct osub *) NULL)) {
        /* Check whether the vertex falls on a subsegment. */
        tspivot(horiz, brokensubseg);
        if (brokensubseg.ss != m->dummysub) {
          /* The vertex falls on a subsegment, and hence will not be inserted. */
          if (segmentflaws) {
            enq = b->nobisect != 2;
            if (enq && (b->nobisect == 1)) {
              /* This subsegment may be split only if it is an */
              /*   internal boundary.                          */
              sym(horiz, testtri);
              enq = testtri.tri != m->dummytri;
            }
            if (enq) {
              /* Add the subsegment to the list of encroached subsegments. */
              encroached = (struct badsubseg *) poolalloc(&m->badsubsegs);
              encroached->encsubseg = sencode(brokensubseg);
              sorg(brokensubseg, encroached->subsegorg);
              sdest(brokensubseg, encroached->subsegdest);
              if (b->verbose > 2) {
                printf(
            "  Queueing encroached subsegment (%.12g, %.12g) (%.12g, %.12g).\n",
                       encroached->subsegorg[0], encroached->subsegorg[1],
                       encroached->subsegdest[0], encroached->subsegdest[1]);
              }
            }
          }
          /* Return a handle whose primary edge contains the vertex, */
          /*   which has not been inserted.                          */
          otricopy(horiz, *searchtri);
          otricopy(horiz, m->recenttri);
          return VIOLATINGVERTEX;
        }
      }
  
      /* Insert the vertex on an edge, dividing one triangle into two (if */
      /*   the edge lies on a boundary) or two triangles into four.       */
      lprev(horiz, botright);
      sym(botright, botrcasing);
      sym(horiz, topright);
      /* Is there a second triangle?  (Or does this edge lie on a boundary?) */
      mirrorflag = topright.tri != m->dummytri;
      if (mirrorflag) {
        lnextself(topright);
        sym(topright, toprcasing);
        maketriangle(m, b, &newtopright);
      } else {
        /* Splitting a boundary edge increases the number of boundary edges. */
        m->hullsize++;
      }
      maketriangle(m, b, &newbotright);
  
      /* Set the vertices of changed and new triangles. */
      org(horiz, rightvertex);
      dest(horiz, leftvertex);
      apex(horiz, botvertex);
      setorg(newbotright, botvertex);
      setdest(newbotright, rightvertex);
      setapex(newbotright, newvertex);
      setorg(horiz, newvertex);
      for (i = 0; i < m->eextras; i++) {
        /* Set the element attributes of a new triangle. */
        setelemattribute(newbotright, i, elemattribute(botright, i));
      }
      if (b->vararea) {
        /* Set the area constraint of a new triangle. */
        setareabound(newbotright, areabound(botright));
      }
      if (mirrorflag) {
        dest(topright, topvertex);
        setorg(newtopright, rightvertex);
        setdest(newtopright, topvertex);
        setapex(newtopright, newvertex);
        setorg(topright, newvertex);
        for (i = 0; i < m->eextras; i++) {
          /* Set the element attributes of another new triangle. */
          setelemattribute(newtopright, i, elemattribute(topright, i));
        }
        if (b->vararea) {
          /* Set the area constraint of another new triangle. */
          setareabound(newtopright, areabound(topright));
        }
      }
  
      /* There may be subsegments that need to be bonded */
      /*   to the new triangle(s).                       */
      if (m->checksegments) {
        tspivot(botright, botrsubseg);
        if (botrsubseg.ss != m->dummysub) {
          tsdissolve(botright);
          tsbond(newbotright, botrsubseg);
        }
        if (mirrorflag) {
          tspivot(topright, toprsubseg);
          if (toprsubseg.ss != m->dummysub) {
            tsdissolve(topright);
            tsbond(newtopright, toprsubseg);
          }
        }
      }
  
      /* Bond the new triangle(s) to the surrounding triangles. */
      bond(newbotright, botrcasing);
      lprevself(newbotright);
      bond(newbotright, botright);
      lprevself(newbotright);
      if (mirrorflag) {
        bond(newtopright, toprcasing);
        lnextself(newtopright);
        bond(newtopright, topright);
        lnextself(newtopright);
        bond(newtopright, newbotright);
      }
  
      if (splitseg != (struct osub *) NULL) {
        /* Split the subsegment into two. */
        setsdest(*splitseg, newvertex);
        segorg(*splitseg, segmentorg);
        segdest(*splitseg, segmentdest);
        ssymself(*splitseg);
        spivot(*splitseg, rightsubseg);
        insertsubseg(m, b, &newbotright, mark(*splitseg));
        tspivot(newbotright, newsubseg);
        setsegorg(newsubseg, segmentorg);
        setsegdest(newsubseg, segmentdest);
        sbond(*splitseg, newsubseg);
        ssymself(newsubseg);
        sbond(newsubseg, rightsubseg);
        ssymself(*splitseg);
        /* Transfer the subsegment's boundary marker to the vertex */
        /*   if required.                                          */
        if (vertexmark(newvertex) == 0) {
          setvertexmark(newvertex, mark(*splitseg));
        }
      }
  
      if (m->checkquality) {
        poolrestart(&m->flipstackers);
        m->lastflip = (struct flipstacker *) poolalloc(&m->flipstackers);
        m->lastflip->flippedtri = encode(horiz);
        m->lastflip->prevflip = (struct flipstacker *) &insertvertex;
      }
  
  #ifdef SELF_CHECK
      if (counterclockwise(m, b, rightvertex, leftvertex, botvertex) < 0.0) {
        printf("Internal error in insertvertex():\n");
        printf(
              "  Clockwise triangle prior to edge vertex insertion (bottom).\n");
      }
      if (mirrorflag) {
        if (counterclockwise(m, b, leftvertex, rightvertex, topvertex) < 0.0) {
          printf("Internal error in insertvertex():\n");
          printf("  Clockwise triangle prior to edge vertex insertion (top).\n");
        }
        if (counterclockwise(m, b, rightvertex, topvertex, newvertex) < 0.0) {
          printf("Internal error in insertvertex():\n");
          printf(
              "  Clockwise triangle after edge vertex insertion (top right).\n");
        }
        if (counterclockwise(m, b, topvertex, leftvertex, newvertex) < 0.0) {
          printf("Internal error in insertvertex():\n");
          printf(
              "  Clockwise triangle after edge vertex insertion (top left).\n");
        }
      }
      if (counterclockwise(m, b, leftvertex, botvertex, newvertex) < 0.0) {
        printf("Internal error in insertvertex():\n");
        printf(
            "  Clockwise triangle after edge vertex insertion (bottom left).\n");
      }
      if (counterclockwise(m, b, botvertex, rightvertex, newvertex) < 0.0) {
        printf("Internal error in insertvertex():\n");
        printf(
          "  Clockwise triangle after edge vertex insertion (bottom right).\n");
      }
  #endif /* SELF_CHECK */
      if (b->verbose > 2) {
        printf("  Updating bottom left ");
        printtriangle(m, b, &botright);
        if (mirrorflag) {
          printf("  Updating top left ");
          printtriangle(m, b, &topright);
          printf("  Creating top right ");
          printtriangle(m, b, &newtopright);
        }
        printf("  Creating bottom right ");
        printtriangle(m, b, &newbotright);
      }
  
      /* Position `horiz' on the first edge to check for */
      /*   the Delaunay property.                        */
      lnextself(horiz);
    } else {
      /* Insert the vertex in a triangle, splitting it into three. */
      lnext(horiz, botleft);
      lprev(horiz, botright);
      sym(botleft, botlcasing);
      sym(botright, botrcasing);
      maketriangle(m, b, &newbotleft);
      maketriangle(m, b, &newbotright);
  
      /* Set the vertices of changed and new triangles. */
      org(horiz, rightvertex);
      dest(horiz, leftvertex);
      apex(horiz, botvertex);
      setorg(newbotleft, leftvertex);
      setdest(newbotleft, botvertex);
      setapex(newbotleft, newvertex);
      setorg(newbotright, botvertex);
      setdest(newbotright, rightvertex);
      setapex(newbotright, newvertex);
      setapex(horiz, newvertex);
      for (i = 0; i < m->eextras; i++) {
        /* Set the element attributes of the new triangles. */
        attrib = elemattribute(horiz, i);
        setelemattribute(newbotleft, i, attrib);
        setelemattribute(newbotright, i, attrib);
      }
      if (b->vararea) {
        /* Set the area constraint of the new triangles. */
        area = areabound(horiz);
        setareabound(newbotleft, area);
        setareabound(newbotright, area);
      }
  
      /* There may be subsegments that need to be bonded */
      /*   to the new triangles.                         */
      if (m->checksegments) {
        tspivot(botleft, botlsubseg);
        if (botlsubseg.ss != m->dummysub) {
          tsdissolve(botleft);
          tsbond(newbotleft, botlsubseg);
        }
        tspivot(botright, botrsubseg);
        if (botrsubseg.ss != m->dummysub) {
          tsdissolve(botright);
          tsbond(newbotright, botrsubseg);
        }
      }
  
      /* Bond the new triangles to the surrounding triangles. */
      bond(newbotleft, botlcasing);
      bond(newbotright, botrcasing);
      lnextself(newbotleft);
      lprevself(newbotright);
      bond(newbotleft, newbotright);
      lnextself(newbotleft);
      bond(botleft, newbotleft);
      lprevself(newbotright);
      bond(botright, newbotright);
  
      if (m->checkquality) {
        poolrestart(&m->flipstackers);
        m->lastflip = (struct flipstacker *) poolalloc(&m->flipstackers);
        m->lastflip->flippedtri = encode(horiz);
        m->lastflip->prevflip = (struct flipstacker *) NULL;
      }
  
  #ifdef SELF_CHECK
      if (counterclockwise(m, b, rightvertex, leftvertex, botvertex) < 0.0) {
        printf("Internal error in insertvertex():\n");
        printf("  Clockwise triangle prior to vertex insertion.\n");
      }
      if (counterclockwise(m, b, rightvertex, leftvertex, newvertex) < 0.0) {
        printf("Internal error in insertvertex():\n");
        printf("  Clockwise triangle after vertex insertion (top).\n");
      }
      if (counterclockwise(m, b, leftvertex, botvertex, newvertex) < 0.0) {
        printf("Internal error in insertvertex():\n");
        printf("  Clockwise triangle after vertex insertion (left).\n");
      }
      if (counterclockwise(m, b, botvertex, rightvertex, newvertex) < 0.0) {
        printf("Internal error in insertvertex():\n");
        printf("  Clockwise triangle after vertex insertion (right).\n");
      }
  #endif /* SELF_CHECK */
      if (b->verbose > 2) {
        printf("  Updating top ");
        printtriangle(m, b, &horiz);
        printf("  Creating left ");
        printtriangle(m, b, &newbotleft);
        printf("  Creating right ");
        printtriangle(m, b, &newbotright);
      }
    }
  
    /* The insertion is successful by default, unless an encroached */
    /*   subsegment is found.                                       */
    success = SUCCESSFULVERTEX;
    /* Circle around the newly inserted vertex, checking each edge opposite */
    /*   it for the Delaunay property.  Non-Delaunay edges are flipped.     */
    /*   `horiz' is always the edge being checked.  `first' marks where to  */
    /*   stop circling.                                                     */
    org(horiz, first);
    rightvertex = first;
    dest(horiz, leftvertex);
    /* Circle until finished. */
    while (1) {
      /* By default, the edge will be flipped. */
      doflip = 1;
  
      if (m->checksegments) {
        /* Check for a subsegment, which cannot be flipped. */
        tspivot(horiz, checksubseg);
        if (checksubseg.ss != m->dummysub) {
          /* The edge is a subsegment and cannot be flipped. */
          doflip = 0;
  #ifndef CDT_ONLY
          if (segmentflaws) {
            /* Does the new vertex encroach upon this subsegment? */
            if (checkseg4encroach(m, b, &checksubseg)) {
              success = ENCROACHINGVERTEX;
            }
          }
  #endif /* not CDT_ONLY */
        }
      }
  
      if (doflip) {
        /* Check if the edge is a boundary edge. */
        sym(horiz, top);
        if (top.tri == m->dummytri) {
          /* The edge is a boundary edge and cannot be flipped. */
          doflip = 0;
        } else {
          /* Find the vertex on the other side of the edge. */
          apex(top, farvertex);
          /* In the incremental Delaunay triangulation algorithm, any of      */
          /*   `leftvertex', `rightvertex', and `farvertex' could be vertices */
          /*   of the triangular bounding box.  These vertices must be        */
          /*   treated as if they are infinitely distant, even though their   */
          /*   "coordinates" are not.                                         */
          if ((leftvertex == m->infvertex1) || (leftvertex == m->infvertex2) ||
              (leftvertex == m->infvertex3)) {
            /* `leftvertex' is infinitely distant.  Check the convexity of  */
            /*   the boundary of the triangulation.  'farvertex' might be   */
            /*   infinite as well, but trust me, this same condition should */
            /*   be applied.                                                */
            doflip = counterclockwise(m, b, newvertex, rightvertex, farvertex)
                     > 0.0;
          } else if ((rightvertex == m->infvertex1) ||
                     (rightvertex == m->infvertex2) ||
                     (rightvertex == m->infvertex3)) {
            /* `rightvertex' is infinitely distant.  Check the convexity of */
            /*   the boundary of the triangulation.  'farvertex' might be   */
            /*   infinite as well, but trust me, this same condition should */
            /*   be applied.                                                */
            doflip = counterclockwise(m, b, farvertex, leftvertex, newvertex)
                     > 0.0;
          } else if ((farvertex == m->infvertex1) ||
                     (farvertex == m->infvertex2) ||
                     (farvertex == m->infvertex3)) {
            /* `farvertex' is infinitely distant and cannot be inside */
            /*   the circumcircle of the triangle `horiz'.            */
            doflip = 0;
          } else {
            /* Test whether the edge is locally Delaunay. */
            doflip = incircle(m, b, leftvertex, newvertex, rightvertex,
                              farvertex) > 0.0;
          }
          if (doflip) {
            /* We made it!  Flip the edge `horiz' by rotating its containing */
            /*   quadrilateral (the two triangles adjacent to `horiz').      */
            /* Identify the casing of the quadrilateral. */
            lprev(top, topleft);
            sym(topleft, toplcasing);
            lnext(top, topright);
            sym(topright, toprcasing);
            lnext(horiz, botleft);
            sym(botleft, botlcasing);
            lprev(horiz, botright);
            sym(botright, botrcasing);
            /* Rotate the quadrilateral one-quarter turn counterclockwise. */
            bond(topleft, botlcasing);
            bond(botleft, botrcasing);
            bond(botright, toprcasing);
            bond(topright, toplcasing);
            if (m->checksegments) {
              /* Check for subsegments and rebond them to the quadrilateral. */
              tspivot(topleft, toplsubseg);
              tspivot(botleft, botlsubseg);
              tspivot(botright, botrsubseg);
              tspivot(topright, toprsubseg);
              if (toplsubseg.ss == m->dummysub) {
                tsdissolve(topright);
              } else {
                tsbond(topright, toplsubseg);
              }
              if (botlsubseg.ss == m->dummysub) {
                tsdissolve(topleft);
              } else {
                tsbond(topleft, botlsubseg);
              }
              if (botrsubseg.ss == m->dummysub) {
                tsdissolve(botleft);
              } else {
                tsbond(botleft, botrsubseg);
              }
              if (toprsubseg.ss == m->dummysub) {
                tsdissolve(botright);
              } else {
                tsbond(botright, toprsubseg);
              }
            }
            /* New vertex assignments for the rotated quadrilateral. */
            setorg(horiz, farvertex);
            setdest(horiz, newvertex);
            setapex(horiz, rightvertex);
            setorg(top, newvertex);
            setdest(top, farvertex);
            setapex(top, leftvertex);
            for (i = 0; i < m->eextras; i++) {
              /* Take the average of the two triangles' attributes. */
              attrib = 0.5 * (elemattribute(top, i) + elemattribute(horiz, i));
              setelemattribute(top, i, attrib);
              setelemattribute(horiz, i, attrib);
            }
            if (b->vararea) {
              if ((areabound(top) <= 0.0) || (areabound(horiz) <= 0.0)) {
                area = -1.0;
              } else {
                /* Take the average of the two triangles' area constraints.    */
                /*   This prevents small area constraints from migrating a     */
                /*   long, long way from their original location due to flips. */
                area = 0.5 * (areabound(top) + areabound(horiz));
              }
              setareabound(top, area);
              setareabound(horiz, area);
            }
  
            if (m->checkquality) {
              newflip = (struct flipstacker *) poolalloc(&m->flipstackers);
              newflip->flippedtri = encode(horiz);
              newflip->prevflip = m->lastflip;
              m->lastflip = newflip;
            }
  
  #ifdef SELF_CHECK
            if (newvertex != (vertex) NULL) {
              if (counterclockwise(m, b, leftvertex, newvertex, rightvertex) <
                  0.0) {
                printf("Internal error in insertvertex():\n");
                printf("  Clockwise triangle prior to edge flip (bottom).\n");
              }
              /* The following test has been removed because constrainededge() */
              /*   sometimes generates inverted triangles that insertvertex()  */
              /*   removes.                                                    */
  /*
              if (counterclockwise(m, b, rightvertex, farvertex, leftvertex) <
                  0.0) {
                printf("Internal error in insertvertex():\n");
                printf("  Clockwise triangle prior to edge flip (top).\n");
              }
  */
              if (counterclockwise(m, b, farvertex, leftvertex, newvertex) <
                  0.0) {
                printf("Internal error in insertvertex():\n");
                printf("  Clockwise triangle after edge flip (left).\n");
              }
              if (counterclockwise(m, b, newvertex, rightvertex, farvertex) <
                  0.0) {
                printf("Internal error in insertvertex():\n");
                printf("  Clockwise triangle after edge flip (right).\n");
              }
            }
  #endif /* SELF_CHECK */
            if (b->verbose > 2) {
              printf("  Edge flip results in left ");
              lnextself(topleft);
              printtriangle(m, b, &topleft);
              printf("  and right ");
              printtriangle(m, b, &horiz);
            }
            /* On the next iterations, consider the two edges that were  */
            /*   exposed (this is, are now visible to the newly inserted */
            /*   vertex) by the edge flip.                               */
            lprevself(horiz);
            leftvertex = farvertex;
          }
        }
      }
      if (!doflip) {
        /* The handle `horiz' is accepted as locally Delaunay. */
  #ifndef CDT_ONLY
        if (triflaws) {
          /* Check the triangle `horiz' for quality. */
          testtriangle(m, b, &horiz);
        }
  #endif /* not CDT_ONLY */
        /* Look for the next edge around the newly inserted vertex. */
        lnextself(horiz);
        sym(horiz, testtri);
        /* Check for finishing a complete revolution about the new vertex, or */
        /*   falling outside  of the triangulation.  The latter will happen   */
        /*   when a vertex is inserted at a boundary.                         */
        if ((leftvertex == first) || (testtri.tri == m->dummytri)) {
          /* We're done.  Return a triangle whose origin is the new vertex. */
          lnext(horiz, *searchtri);
          lnext(horiz, m->recenttri);
          return success;
        }
        /* Finish finding the next edge around the newly inserted vertex. */
        lnext(testtri, horiz);
        rightvertex = leftvertex;
        dest(horiz, leftvertex);
      }
    }
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  triangulatepolygon()   Find the Delaunay triangulation of a polygon that */
  /*                         has a certain "nice" shape.  This includes the    */
  /*                         polygons that result from deletion of a vertex or */
  /*                         insertion of a segment.                           */
  /*                                                                           */
  /*  This is a conceptually difficult routine.  The starting assumption is    */
  /*  that we have a polygon with n sides.  n - 1 of these sides are currently */
  /*  represented as edges in the mesh.  One side, called the "base", need not */
  /*  be.                                                                      */
  /*                                                                           */
  /*  Inside the polygon is a structure I call a "fan", consisting of n - 1    */
  /*  triangles that share a common origin.  For each of these triangles, the  */
  /*  edge opposite the origin is one of the sides of the polygon.  The        */
  /*  primary edge of each triangle is the edge directed from the origin to    */
  /*  the destination; note that this is not the same edge that is a side of   */
  /*  the polygon.  `firstedge' is the primary edge of the first triangle.     */
  /*  From there, the triangles follow in counterclockwise order about the     */
  /*  polygon, until `lastedge', the primary edge of the last triangle.        */
  /*  `firstedge' and `lastedge' are probably connected to other triangles     */
  /*  beyond the extremes of the fan, but their identity is not important, as  */
  /*  long as the fan remains connected to them.                               */
  /*                                                                           */
  /*  Imagine the polygon oriented so that its base is at the bottom.  This    */
  /*  puts `firstedge' on the far right, and `lastedge' on the far left.       */
  /*  The right vertex of the base is the destination of `firstedge', and the  */
  /*  left vertex of the base is the apex of `lastedge'.                       */
  /*                                                                           */
  /*  The challenge now is to find the right sequence of edge flips to         */
  /*  transform the fan into a Delaunay triangulation of the polygon.  Each    */
  /*  edge flip effectively removes one triangle from the fan, committing it   */
  /*  to the polygon.  The resulting polygon has one fewer edge.  If `doflip'  */
  /*  is set, the final flip will be performed, resulting in a fan of one      */
  /*  (useless?) triangle.  If `doflip' is not set, the final flip is not      */
  /*  performed, resulting in a fan of two triangles, and an unfinished        */
  /*  triangular polygon that is not yet filled out with a single triangle.    */
  /*  On completion of the routine, `lastedge' is the last remaining triangle, */
  /*  or the leftmost of the last two.                                         */
  /*                                                                           */
  /*  Although the flips are performed in the order described above, the       */
  /*  decisions about what flips to perform are made in precisely the reverse  */
  /*  order.  The recursive triangulatepolygon() procedure makes a decision,   */
  /*  uses up to two recursive calls to triangulate the "subproblems"          */
  /*  (polygons with fewer edges), and then performs an edge flip.             */
  /*                                                                           */
  /*  The "decision" it makes is which vertex of the polygon should be         */
  /*  connected to the base.  This decision is made by testing every possible  */
  /*  vertex.  Once the best vertex is found, the two edges that connect this  */
  /*  vertex to the base become the bases for two smaller polygons.  These     */
  /*  are triangulated recursively.  Unfortunately, this approach can take     */
  /*  O(n^2) time not only in the worst case, but in many common cases.  It's  */
  /*  rarely a big deal for vertex deletion, where n is rarely larger than     */
  /*  ten, but it could be a big deal for segment insertion, especially if     */
  /*  there's a lot of long segments that each cut many triangles.  I ought to */
  /*  code a faster algorithm some day.                                        */
  /*                                                                           */
  /*  The `edgecount' parameter is the number of sides of the polygon,         */
  /*  including its base.  `triflaws' is a flag that determines whether the    */
  /*  new triangles should be tested for quality, and enqueued if they are     */
  /*  bad.                                                                     */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  void triangulatepolygon(struct mesh *m, struct behavior *b,
                          struct otri *firstedge, struct otri *lastedge,
                          int edgecount, int doflip, int triflaws)
  #else /* not ANSI_DECLARATORS */
  void triangulatepolygon(m, b, firstedge, lastedge, edgecount, doflip, triflaws)
  struct mesh *m;
  struct behavior *b;
  struct otri *firstedge;
  struct otri *lastedge;
  int edgecount;
  int doflip;
  int triflaws;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct otri testtri;
    struct otri besttri;
    struct otri tempedge;
    vertex leftbasevertex, rightbasevertex;
    vertex testvertex;
    vertex bestvertex;
    int bestnumber;
    int i;
    triangle ptr;   /* Temporary variable used by sym(), onext(), and oprev(). */
  
    /* Identify the base vertices. */
    apex(*lastedge, leftbasevertex);
    dest(*firstedge, rightbasevertex);
    if (b->verbose > 2) {
      printf("  Triangulating interior polygon at edge\n");
      printf("    (%.12g, %.12g) (%.12g, %.12g)\n", leftbasevertex[0],
             leftbasevertex[1], rightbasevertex[0], rightbasevertex[1]);
    }
    /* Find the best vertex to connect the base to. */
    onext(*firstedge, besttri);
    dest(besttri, bestvertex);
    otricopy(besttri, testtri);
    bestnumber = 1;
    for (i = 2; i <= edgecount - 2; i++) {
      onextself(testtri);
      dest(testtri, testvertex);
      /* Is this a better vertex? */
      if (incircle(m, b, leftbasevertex, rightbasevertex, bestvertex,
                   testvertex) > 0.0) {
        otricopy(testtri, besttri);
        bestvertex = testvertex;
        bestnumber = i;
      }
    }
    if (b->verbose > 2) {
      printf("    Connecting edge to (%.12g, %.12g)\n", bestvertex[0],
             bestvertex[1]);
    }
    if (bestnumber > 1) {
      /* Recursively triangulate the smaller polygon on the right. */
      oprev(besttri, tempedge);
      triangulatepolygon(m, b, firstedge, &tempedge, bestnumber + 1, 1,
                         triflaws);
    }
    if (bestnumber < edgecount - 2) {
      /* Recursively triangulate the smaller polygon on the left. */
      sym(besttri, tempedge);
      triangulatepolygon(m, b, &besttri, lastedge, edgecount - bestnumber, 1,
                         triflaws);
      /* Find `besttri' again; it may have been lost to edge flips. */
      sym(tempedge, besttri);
    }
    if (doflip) {
      /* Do one final edge flip. */
      flip(m, b, &besttri);
  #ifndef CDT_ONLY
      if (triflaws) {
        /* Check the quality of the newly committed triangle. */
        sym(besttri, testtri);
        testtriangle(m, b, &testtri);
      }
  #endif /* not CDT_ONLY */
    }
    /* Return the base triangle. */
    otricopy(besttri, *lastedge);
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  deletevertex()   Delete a vertex from a Delaunay triangulation, ensuring */
  /*                   that the triangulation remains Delaunay.                */
  /*                                                                           */
  /*  The origin of `deltri' is deleted.  The union of the triangles adjacent  */
  /*  to this vertex is a polygon, for which the Delaunay triangulation is     */
  /*  found.  Two triangles are removed from the mesh.                         */
  /*                                                                           */
  /*  Only interior vertices that do not lie on segments or boundaries may be  */
  /*  deleted.                                                                 */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifndef CDT_ONLY
  
  #ifdef ANSI_DECLARATORS
  void deletevertex(struct mesh *m, struct behavior *b, struct otri *deltri)
  #else /* not ANSI_DECLARATORS */
  void deletevertex(m, b, deltri)
  struct mesh *m;
  struct behavior *b;
  struct otri *deltri;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct otri countingtri;
    struct otri firstedge, lastedge;
    struct otri deltriright;
    struct otri lefttri, righttri;
    struct otri leftcasing, rightcasing;
    struct osub leftsubseg, rightsubseg;
    vertex delvertex;
    vertex neworg;
    int edgecount;
    triangle ptr;   /* Temporary variable used by sym(), onext(), and oprev(). */
    subseg sptr;                      /* Temporary variable used by tspivot(). */
  
    org(*deltri, delvertex);
    if (b->verbose > 1) {
      printf("  Deleting (%.12g, %.12g).\n", delvertex[0], delvertex[1]);
    }
    vertexdealloc(m, delvertex);
  
    /* Count the degree of the vertex being deleted. */
    onext(*deltri, countingtri);
    edgecount = 1;
    while (!otriequal(*deltri, countingtri)) {
  #ifdef SELF_CHECK
      if (countingtri.tri == m->dummytri) {
        printf("Internal error in deletevertex():\n");
        printf("  Attempt to delete boundary vertex.\n");
        internalerror();
      }
  #endif /* SELF_CHECK */
      edgecount++;
      onextself(countingtri);
    }
  
  #ifdef SELF_CHECK
    if (edgecount < 3) {
      printf("Internal error in deletevertex():\n  Vertex has degree %d.\n",
             edgecount);
      internalerror();
    }
  #endif /* SELF_CHECK */
    if (edgecount > 3) {
      /* Triangulate the polygon defined by the union of all triangles */
      /*   adjacent to the vertex being deleted.  Check the quality of */
      /*   the resulting triangles.                                    */
      onext(*deltri, firstedge);
      oprev(*deltri, lastedge);
      triangulatepolygon(m, b, &firstedge, &lastedge, edgecount, 0,
                         !b->nobisect);
    }
    /* Splice out two triangles. */
    lprev(*deltri, deltriright);
    dnext(*deltri, lefttri);
    sym(lefttri, leftcasing);
    oprev(deltriright, righttri);
    sym(righttri, rightcasing);
    bond(*deltri, leftcasing);
    bond(deltriright, rightcasing);
    tspivot(lefttri, leftsubseg);
    if (leftsubseg.ss != m->dummysub) {
      tsbond(*deltri, leftsubseg);
    }
    tspivot(righttri, rightsubseg);
    if (rightsubseg.ss != m->dummysub) {
      tsbond(deltriright, rightsubseg);
    }
  
    /* Set the new origin of `deltri' and check its quality. */
    org(lefttri, neworg);
    setorg(*deltri, neworg);
    if (!b->nobisect) {
      testtriangle(m, b, deltri);
    }
  
    /* Delete the two spliced-out triangles. */
    triangledealloc(m, lefttri.tri);
    triangledealloc(m, righttri.tri);
  }
  
  #endif /* not CDT_ONLY */
  
  /*****************************************************************************/
  /*                                                                           */
  /*  undovertex()   Undo the most recent vertex insertion.                    */
  /*                                                                           */
  /*  Walks through the list of transformations (flips and a vertex insertion) */
  /*  in the reverse of the order in which they were done, and undoes them.    */
  /*  The inserted vertex is removed from the triangulation and deallocated.   */
  /*  Two triangles (possibly just one) are also deallocated.                  */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifndef CDT_ONLY
  
  #ifdef ANSI_DECLARATORS
  void undovertex(struct mesh *m, struct behavior *b)
  #else /* not ANSI_DECLARATORS */
  void undovertex(m, b)
  struct mesh *m;
  struct behavior *b;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct otri fliptri;
    struct otri botleft, botright, topright;
    struct otri botlcasing, botrcasing, toprcasing;
    struct otri gluetri;
    struct osub botlsubseg, botrsubseg, toprsubseg;
    vertex botvertex, rightvertex;
    triangle ptr;                         /* Temporary variable used by sym(). */
    subseg sptr;                      /* Temporary variable used by tspivot(). */
  
    /* Walk through the list of transformations (flips and a vertex insertion) */
    /*   in the reverse of the order in which they were done, and undo them.   */
    while (m->lastflip != (struct flipstacker *) NULL) {
      /* Find a triangle involved in the last unreversed transformation. */
      decode(m->lastflip->flippedtri, fliptri);
  
      /* We are reversing one of three transformations:  a trisection of one */
      /*   triangle into three (by inserting a vertex in the triangle), a    */
      /*   bisection of two triangles into four (by inserting a vertex in an */
      /*   edge), or an edge flip.                                           */
      if (m->lastflip->prevflip == (struct flipstacker *) NULL) {
        /* Restore a triangle that was split into three triangles, */
        /*   so it is again one triangle.                          */
        dprev(fliptri, botleft);
        lnextself(botleft);
        onext(fliptri, botright);
        lprevself(botright);
        sym(botleft, botlcasing);
        sym(botright, botrcasing);
        dest(botleft, botvertex);
  
        setapex(fliptri, botvertex);
        lnextself(fliptri);
        bond(fliptri, botlcasing);
        tspivot(botleft, botlsubseg);
        tsbond(fliptri, botlsubseg);
        lnextself(fliptri);
        bond(fliptri, botrcasing);
        tspivot(botright, botrsubseg);
        tsbond(fliptri, botrsubseg);
  
        /* Delete the two spliced-out triangles. */
        triangledealloc(m, botleft.tri);
        triangledealloc(m, botright.tri);
      } else if (m->lastflip->prevflip == (struct flipstacker *) &insertvertex) {
        /* Restore two triangles that were split into four triangles, */
        /*   so they are again two triangles.                         */
        lprev(fliptri, gluetri);
        sym(gluetri, botright);
        lnextself(botright);
        sym(botright, botrcasing);
        dest(botright, rightvertex);
  
        setorg(fliptri, rightvertex);
        bond(gluetri, botrcasing);
        tspivot(botright, botrsubseg);
        tsbond(gluetri, botrsubseg);
  
        /* Delete the spliced-out triangle. */
        triangledealloc(m, botright.tri);
  
        sym(fliptri, gluetri);
        if (gluetri.tri != m->dummytri) {
          lnextself(gluetri);
          dnext(gluetri, topright);
          sym(topright, toprcasing);
  
          setorg(gluetri, rightvertex);
          bond(gluetri, toprcasing);
          tspivot(topright, toprsubseg);
          tsbond(gluetri, toprsubseg);
  
          /* Delete the spliced-out triangle. */
          triangledealloc(m, topright.tri);
        }
  
        /* This is the end of the list, sneakily encoded. */
        m->lastflip->prevflip = (struct flipstacker *) NULL;
      } else {
        /* Undo an edge flip. */
        unflip(m, b, &fliptri);
      }
  
      /* Go on and process the next transformation. */
      m->lastflip = m->lastflip->prevflip;
    }
  }
  
  #endif /* not CDT_ONLY */
  
  /**                                                                         **/
  /**                                                                         **/
  /********* Mesh transformation routines end here                     *********/
  
  /********* Divide-and-conquer Delaunay triangulation begins here     *********/
  /**                                                                         **/
  /**                                                                         **/
  
  /*****************************************************************************/
  /*                                                                           */
  /*  The divide-and-conquer bounding box                                      */
  /*                                                                           */
  /*  I originally implemented the divide-and-conquer and incremental Delaunay */
  /*  triangulations using the edge-based data structure presented by Guibas   */
  /*  and Stolfi.  Switching to a triangle-based data structure doubled the    */
  /*  speed.  However, I had to think of a few extra tricks to maintain the    */
  /*  elegance of the original algorithms.                                     */
  /*                                                                           */
  /*  The "bounding box" used by my variant of the divide-and-conquer          */
  /*  algorithm uses one triangle for each edge of the convex hull of the      */
  /*  triangulation.  These bounding triangles all share a common apical       */
  /*  vertex, which is represented by NULL and which represents nothing.       */
  /*  The bounding triangles are linked in a circular fan about this NULL      */
  /*  vertex, and the edges on the convex hull of the triangulation appear     */
  /*  opposite the NULL vertex.  You might find it easiest to imagine that     */
  /*  the NULL vertex is a point in 3D space behind the center of the          */
  /*  triangulation, and that the bounding triangles form a sort of cone.      */
  /*                                                                           */
  /*  This bounding box makes it easy to represent degenerate cases.  For      */
  /*  instance, the triangulation of two vertices is a single edge.  This edge */
  /*  is represented by two bounding box triangles, one on each "side" of the  */
  /*  edge.  These triangles are also linked together in a fan about the NULL  */
  /*  vertex.                                                                  */
  /*                                                                           */
  /*  The bounding box also makes it easy to traverse the convex hull, as the  */
  /*  divide-and-conquer algorithm needs to do.                                */
  /*                                                                           */
  /*****************************************************************************/
  
  /*****************************************************************************/
  /*                                                                           */
  /*  vertexsort()   Sort an array of vertices by x-coordinate, using the      */
  /*                 y-coordinate as a secondary key.                          */
  /*                                                                           */
  /*  Uses quicksort.  Randomized O(n log n) time.  No, I did not make any of  */
  /*  the usual quicksort mistakes.                                            */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  void vertexsort(vertex *sortarray, int arraysize)
  #else /* not ANSI_DECLARATORS */
  void vertexsort(sortarray, arraysize)
  vertex *sortarray;
  int arraysize;
  #endif /* not ANSI_DECLARATORS */
  
  {
    int left, right;
    int pivot;
    REAL pivotx, pivoty;
    vertex temp;
  
    if (arraysize == 2) {
      /* Recursive base case. */
      if ((sortarray[0][0] > sortarray[1][0]) ||
          ((sortarray[0][0] == sortarray[1][0]) &&
           (sortarray[0][1] > sortarray[1][1]))) {
        temp = sortarray[1];
        sortarray[1] = sortarray[0];
        sortarray[0] = temp;
      }
      return;
    }
    /* Choose a random pivot to split the array. */
    pivot = (int) randomnation((unsigned int) arraysize);
    pivotx = sortarray[pivot][0];
    pivoty = sortarray[pivot][1];
    /* Split the array. */
    left = -1;
    right = arraysize;
    while (left < right) {
      /* Search for a vertex whose x-coordinate is too large for the left. */
      do {
        left++;
      } while ((left <= right) && ((sortarray[left][0] < pivotx) ||
                                   ((sortarray[left][0] == pivotx) &&
                                    (sortarray[left][1] < pivoty))));
      /* Search for a vertex whose x-coordinate is too small for the right. */
      do {
        right--;
      } while ((left <= right) && ((sortarray[right][0] > pivotx) ||
                                   ((sortarray[right][0] == pivotx) &&
                                    (sortarray[right][1] > pivoty))));
      if (left < right) {
        /* Swap the left and right vertices. */
        temp = sortarray[left];
        sortarray[left] = sortarray[right];
        sortarray[right] = temp;
      }
    }
    if (left > 1) {
      /* Recursively sort the left subset. */
      vertexsort(sortarray, left);
    }
    if (right < arraysize - 2) {
      /* Recursively sort the right subset. */
      vertexsort(&sortarray[right + 1], arraysize - right - 1);
    }
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  vertexmedian()   An order statistic algorithm, almost.  Shuffles an      */
  /*                   array of vertices so that the first `median' vertices   */
  /*                   occur lexicographically before the remaining vertices.  */
  /*                                                                           */
  /*  Uses the x-coordinate as the primary key if axis == 0; the y-coordinate  */
  /*  if axis == 1.  Very similar to the vertexsort() procedure, but runs in   */
  /*  randomized linear time.                                                  */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  void vertexmedian(vertex *sortarray, int arraysize, int median, int axis)
  #else /* not ANSI_DECLARATORS */
  void vertexmedian(sortarray, arraysize, median, axis)
  vertex *sortarray;
  int arraysize;
  int median;
  int axis;
  #endif /* not ANSI_DECLARATORS */
  
  {
    int left, right;
    int pivot;
    REAL pivot1, pivot2;
    vertex temp;
  
    if (arraysize == 2) {
      /* Recursive base case. */
      if ((sortarray[0][axis] > sortarray[1][axis]) ||
          ((sortarray[0][axis] == sortarray[1][axis]) &&
           (sortarray[0][1 - axis] > sortarray[1][1 - axis]))) {
        temp = sortarray[1];
        sortarray[1] = sortarray[0];
        sortarray[0] = temp;
      }
      return;
    }
    /* Choose a random pivot to split the array. */
    pivot = (int) randomnation((unsigned int) arraysize);
    pivot1 = sortarray[pivot][axis];
    pivot2 = sortarray[pivot][1 - axis];
    /* Split the array. */
    left = -1;
    right = arraysize;
    while (left < right) {
      /* Search for a vertex whose x-coordinate is too large for the left. */
      do {
        left++;
      } while ((left <= right) && ((sortarray[left][axis] < pivot1) ||
                                   ((sortarray[left][axis] == pivot1) &&
                                    (sortarray[left][1 - axis] < pivot2))));
      /* Search for a vertex whose x-coordinate is too small for the right. */
      do {
        right--;
      } while ((left <= right) && ((sortarray[right][axis] > pivot1) ||
                                   ((sortarray[right][axis] == pivot1) &&
                                    (sortarray[right][1 - axis] > pivot2))));
      if (left < right) {
        /* Swap the left and right vertices. */
        temp = sortarray[left];
        sortarray[left] = sortarray[right];
        sortarray[right] = temp;
      }
    }
    /* Unlike in vertexsort(), at most one of the following */
    /*   conditionals is true.                             */
    if (left > median) {
      /* Recursively shuffle the left subset. */
      vertexmedian(sortarray, left, median, axis);
    }
    if (right < median - 1) {
      /* Recursively shuffle the right subset. */
      vertexmedian(&sortarray[right + 1], arraysize - right - 1,
                   median - right - 1, axis);
    }
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  alternateaxes()   Sorts the vertices as appropriate for the divide-and-  */
  /*                    conquer algorithm with alternating cuts.               */
  /*                                                                           */
  /*  Partitions by x-coordinate if axis == 0; by y-coordinate if axis == 1.   */
  /*  For the base case, subsets containing only two or three vertices are     */
  /*  always sorted by x-coordinate.                                           */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  void alternateaxes(vertex *sortarray, int arraysize, int axis)
  #else /* not ANSI_DECLARATORS */
  void alternateaxes(sortarray, arraysize, axis)
  vertex *sortarray;
  int arraysize;
  int axis;
  #endif /* not ANSI_DECLARATORS */
  
  {
    int divider;
  
    divider = arraysize >> 1;
    if (arraysize <= 3) {
      /* Recursive base case:  subsets of two or three vertices will be    */
      /*   handled specially, and should always be sorted by x-coordinate. */
      axis = 0;
    }
    /* Partition with a horizontal or vertical cut. */
    vertexmedian(sortarray, arraysize, divider, axis);
    /* Recursively partition the subsets with a cross cut. */
    if (arraysize - divider >= 2) {
      if (divider >= 2) {
        alternateaxes(sortarray, divider, 1 - axis);
      }
      alternateaxes(&sortarray[divider], arraysize - divider, 1 - axis);
    }
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  mergehulls()   Merge two adjacent Delaunay triangulations into a         */
  /*                 single Delaunay triangulation.                            */
  /*                                                                           */
  /*  This is similar to the algorithm given by Guibas and Stolfi, but uses    */
  /*  a triangle-based, rather than edge-based, data structure.                */
  /*                                                                           */
  /*  The algorithm walks up the gap between the two triangulations, knitting  */
  /*  them together.  As they are merged, some of their bounding triangles     */
  /*  are converted into real triangles of the triangulation.  The procedure   */
  /*  pulls each hull's bounding triangles apart, then knits them together     */
  /*  like the teeth of two gears.  The Delaunay property determines, at each  */
  /*  step, whether the next "tooth" is a bounding triangle of the left hull   */
  /*  or the right.  When a bounding triangle becomes real, its apex is        */
  /*  changed from NULL to a real vertex.                                      */
  /*                                                                           */
  /*  Only two new triangles need to be allocated.  These become new bounding  */
  /*  triangles at the top and bottom of the seam.  They are used to connect   */
  /*  the remaining bounding triangles (those that have not been converted     */
  /*  into real triangles) into a single fan.                                  */
  /*                                                                           */
  /*  On entry, `farleft' and `innerleft' are bounding triangles of the left   */
  /*  triangulation.  The origin of `farleft' is the leftmost vertex, and      */
  /*  the destination of `innerleft' is the rightmost vertex of the            */
  /*  triangulation.  Similarly, `innerright' and `farright' are bounding      */
  /*  triangles of the right triangulation.  The origin of `innerright' and    */
  /*  destination of `farright' are the leftmost and rightmost vertices.       */
  /*                                                                           */
  /*  On completion, the origin of `farleft' is the leftmost vertex of the     */
  /*  merged triangulation, and the destination of `farright' is the rightmost */
  /*  vertex.                                                                  */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  void mergehulls(struct mesh *m, struct behavior *b, struct otri *farleft,
                  struct otri *innerleft, struct otri *innerright,
                  struct otri *farright, int axis)
  #else /* not ANSI_DECLARATORS */
  void mergehulls(m, b, farleft, innerleft, innerright, farright, axis)
  struct mesh *m;
  struct behavior *b;
  struct otri *farleft;
  struct otri *innerleft;
  struct otri *innerright;
  struct otri *farright;
  int axis;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct otri leftcand, rightcand;
    struct otri baseedge;
    struct otri nextedge;
    struct otri sidecasing, topcasing, outercasing;
    struct otri checkedge;
    vertex innerleftdest;
    vertex innerrightorg;
    vertex innerleftapex, innerrightapex;
    vertex farleftpt, farrightpt;
    vertex farleftapex, farrightapex;
    vertex lowerleft, lowerright;
    vertex upperleft, upperright;
    vertex nextapex;
    vertex checkvertex;
    int changemade;
    int badedge;
    int leftfinished, rightfinished;
    triangle ptr;                         /* Temporary variable used by sym(). */
  
    dest(*innerleft, innerleftdest);
    apex(*innerleft, innerleftapex);
    org(*innerright, innerrightorg);
    apex(*innerright, innerrightapex);
    /* Special treatment for horizontal cuts. */
    if (b->dwyer && (axis == 1)) {
      org(*farleft, farleftpt);
      apex(*farleft, farleftapex);
      dest(*farright, farrightpt);
      apex(*farright, farrightapex);
      /* The pointers to the extremal vertices are shifted to point to the */
      /*   topmost and bottommost vertex of each hull, rather than the     */
      /*   leftmost and rightmost vertices.                                */
      while (farleftapex[1] < farleftpt[1]) {
        lnextself(*farleft);
        symself(*farleft);
        farleftpt = farleftapex;
        apex(*farleft, farleftapex);
      }
      sym(*innerleft, checkedge);
      apex(checkedge, checkvertex);
      while (checkvertex[1] > innerleftdest[1]) {
        lnext(checkedge, *innerleft);
        innerleftapex = innerleftdest;
        innerleftdest = checkvertex;
        sym(*innerleft, checkedge);
        apex(checkedge, checkvertex);
      }
      while (innerrightapex[1] < innerrightorg[1]) {
        lnextself(*innerright);
        symself(*innerright);
        innerrightorg = innerrightapex;
        apex(*innerright, innerrightapex);
      }
      sym(*farright, checkedge);
      apex(checkedge, checkvertex);
      while (checkvertex[1] > farrightpt[1]) {
        lnext(checkedge, *farright);
        farrightapex = farrightpt;
        farrightpt = checkvertex;
        sym(*farright, checkedge);
        apex(checkedge, checkvertex);
      }
    }
    /* Find a line tangent to and below both hulls. */
    do {
      changemade = 0;
      /* Make innerleftdest the "bottommost" vertex of the left hull. */
      if (counterclockwise(m, b, innerleftdest, innerleftapex, innerrightorg) >
          0.0) {
        lprevself(*innerleft);
        symself(*innerleft);
        innerleftdest = innerleftapex;
        apex(*innerleft, innerleftapex);
        changemade = 1;
      }
      /* Make innerrightorg the "bottommost" vertex of the right hull. */
      if (counterclockwise(m, b, innerrightapex, innerrightorg, innerleftdest) >
          0.0) {
        lnextself(*innerright);
        symself(*innerright);
        innerrightorg = innerrightapex;
        apex(*innerright, innerrightapex);
        changemade = 1;
      }
    } while (changemade);
    /* Find the two candidates to be the next "gear tooth." */
    sym(*innerleft, leftcand);
    sym(*innerright, rightcand);
    /* Create the bottom new bounding triangle. */
    maketriangle(m, b, &baseedge);
    /* Connect it to the bounding boxes of the left and right triangulations. */
    bond(baseedge, *innerleft);
    lnextself(baseedge);
    bond(baseedge, *innerright);
    lnextself(baseedge);
    setorg(baseedge, innerrightorg);
    setdest(baseedge, innerleftdest);
    /* Apex is intentionally left NULL. */
    if (b->verbose > 2) {
      printf("  Creating base bounding ");
      printtriangle(m, b, &baseedge);
    }
    /* Fix the extreme triangles if necessary. */
    org(*farleft, farleftpt);
    if (innerleftdest == farleftpt) {
      lnext(baseedge, *farleft);
    }
    dest(*farright, farrightpt);
    if (innerrightorg == farrightpt) {
      lprev(baseedge, *farright);
    }
    /* The vertices of the current knitting edge. */
    lowerleft = innerleftdest;
    lowerright = innerrightorg;
    /* The candidate vertices for knitting. */
    apex(leftcand, upperleft);
    apex(rightcand, upperright);
    /* Walk up the gap between the two triangulations, knitting them together. */
    while (1) {
      /* Have we reached the top?  (This isn't quite the right question,       */
      /*   because even though the left triangulation might seem finished now, */
      /*   moving up on the right triangulation might reveal a new vertex of   */
      /*   the left triangulation.  And vice-versa.)                           */
      leftfinished = counterclockwise(m, b, upperleft, lowerleft, lowerright) <=
                     0.0;
      rightfinished = counterclockwise(m, b, upperright, lowerleft, lowerright)
                   <= 0.0;
      if (leftfinished && rightfinished) {
        /* Create the top new bounding triangle. */
        maketriangle(m, b, &nextedge);
        setorg(nextedge, lowerleft);
        setdest(nextedge, lowerright);
        /* Apex is intentionally left NULL. */
        /* Connect it to the bounding boxes of the two triangulations. */
        bond(nextedge, baseedge);
        lnextself(nextedge);
        bond(nextedge, rightcand);
        lnextself(nextedge);
        bond(nextedge, leftcand);
        if (b->verbose > 2) {
          printf("  Creating top bounding ");
          printtriangle(m, b, &nextedge);
        }
        /* Special treatment for horizontal cuts. */
        if (b->dwyer && (axis == 1)) {
          org(*farleft, farleftpt);
          apex(*farleft, farleftapex);
          dest(*farright, farrightpt);
          apex(*farright, farrightapex);
          sym(*farleft, checkedge);
          apex(checkedge, checkvertex);
          /* The pointers to the extremal vertices are restored to the  */
          /*   leftmost and rightmost vertices (rather than topmost and */
          /*   bottommost).                                             */
          while (checkvertex[0] < farleftpt[0]) {
            lprev(checkedge, *farleft);
            farleftapex = farleftpt;
            farleftpt = checkvertex;
            sym(*farleft, checkedge);
            apex(checkedge, checkvertex);
          }
          while (farrightapex[0] > farrightpt[0]) {
            lprevself(*farright);
            symself(*farright);
            farrightpt = farrightapex;
            apex(*farright, farrightapex);
          }
        }
        return;
      }
      /* Consider eliminating edges from the left triangulation. */
      if (!leftfinished) {
        /* What vertex would be exposed if an edge were deleted? */
        lprev(leftcand, nextedge);
        symself(nextedge);
        apex(nextedge, nextapex);
        /* If nextapex is NULL, then no vertex would be exposed; the */
        /*   triangulation would have been eaten right through.      */
        if (nextapex != (vertex) NULL) {
          /* Check whether the edge is Delaunay. */
          badedge = incircle(m, b, lowerleft, lowerright, upperleft, nextapex) >
                    0.0;
          while (badedge) {
            /* Eliminate the edge with an edge flip.  As a result, the    */
            /*   left triangulation will have one more boundary triangle. */
            lnextself(nextedge);
            sym(nextedge, topcasing);
            lnextself(nextedge);
            sym(nextedge, sidecasing);
            bond(nextedge, topcasing);
            bond(leftcand, sidecasing);
            lnextself(leftcand);
            sym(leftcand, outercasing);
            lprevself(nextedge);
            bond(nextedge, outercasing);
            /* Correct the vertices to reflect the edge flip. */
            setorg(leftcand, lowerleft);
            setdest(leftcand, NULL);
            setapex(leftcand, nextapex);
            setorg(nextedge, NULL);
            setdest(nextedge, upperleft);
            setapex(nextedge, nextapex);
            /* Consider the newly exposed vertex. */
            upperleft = nextapex;
            /* What vertex would be exposed if another edge were deleted? */
            otricopy(sidecasing, nextedge);
            apex(nextedge, nextapex);
            if (nextapex != (vertex) NULL) {
              /* Check whether the edge is Delaunay. */
              badedge = incircle(m, b, lowerleft, lowerright, upperleft,
                                 nextapex) > 0.0;
            } else {
              /* Avoid eating right through the triangulation. */
              badedge = 0;
            }
          }
        }
      }
      /* Consider eliminating edges from the right triangulation. */
      if (!rightfinished) {
        /* What vertex would be exposed if an edge were deleted? */
        lnext(rightcand, nextedge);
        symself(nextedge);
        apex(nextedge, nextapex);
        /* If nextapex is NULL, then no vertex would be exposed; the */
        /*   triangulation would have been eaten right through.      */
        if (nextapex != (vertex) NULL) {
          /* Check whether the edge is Delaunay. */
          badedge = incircle(m, b, lowerleft, lowerright, upperright, nextapex) >
                    0.0;
          while (badedge) {
            /* Eliminate the edge with an edge flip.  As a result, the     */
            /*   right triangulation will have one more boundary triangle. */
            lprevself(nextedge);
            sym(nextedge, topcasing);
            lprevself(nextedge);
            sym(nextedge, sidecasing);
            bond(nextedge, topcasing);
            bond(rightcand, sidecasing);
            lprevself(rightcand);
            sym(rightcand, outercasing);
            lnextself(nextedge);
            bond(nextedge, outercasing);
            /* Correct the vertices to reflect the edge flip. */
            setorg(rightcand, NULL);
            setdest(rightcand, lowerright);
            setapex(rightcand, nextapex);
            setorg(nextedge, upperright);
            setdest(nextedge, NULL);
            setapex(nextedge, nextapex);
            /* Consider the newly exposed vertex. */
            upperright = nextapex;
            /* What vertex would be exposed if another edge were deleted? */
            otricopy(sidecasing, nextedge);
            apex(nextedge, nextapex);
            if (nextapex != (vertex) NULL) {
              /* Check whether the edge is Delaunay. */
              badedge = incircle(m, b, lowerleft, lowerright, upperright,
                                 nextapex) > 0.0;
            } else {
              /* Avoid eating right through the triangulation. */
              badedge = 0;
            }
          }
        }
      }
      if (leftfinished || (!rightfinished &&
             (incircle(m, b, upperleft, lowerleft, lowerright, upperright) >
              0.0))) {
        /* Knit the triangulations, adding an edge from `lowerleft' */
        /*   to `upperright'.                                       */
        bond(baseedge, rightcand);
        lprev(rightcand, baseedge);
        setdest(baseedge, lowerleft);
        lowerright = upperright;
        sym(baseedge, rightcand);
        apex(rightcand, upperright);
      } else {
        /* Knit the triangulations, adding an edge from `upperleft' */
        /*   to `lowerright'.                                       */
        bond(baseedge, leftcand);
        lnext(leftcand, baseedge);
        setorg(baseedge, lowerright);
        lowerleft = upperleft;
        sym(baseedge, leftcand);
        apex(leftcand, upperleft);
      }
      if (b->verbose > 2) {
        printf("  Connecting ");
        printtriangle(m, b, &baseedge);
      }
    }
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  divconqrecurse()   Recursively form a Delaunay triangulation by the      */
  /*                     divide-and-conquer method.                            */
  /*                                                                           */
  /*  Recursively breaks down the problem into smaller pieces, which are       */
  /*  knitted together by mergehulls().  The base cases (problems of two or    */
  /*  three vertices) are handled specially here.                              */
  /*                                                                           */
  /*  On completion, `farleft' and `farright' are bounding triangles such that */
  /*  the origin of `farleft' is the leftmost vertex (breaking ties by         */
  /*  choosing the highest leftmost vertex), and the destination of            */
  /*  `farright' is the rightmost vertex (breaking ties by choosing the        */
  /*  lowest rightmost vertex).                                                */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  void divconqrecurse(struct mesh *m, struct behavior *b, vertex *sortarray,
                      int vertices, int axis,
                      struct otri *farleft, struct otri *farright)
  #else /* not ANSI_DECLARATORS */
  void divconqrecurse(m, b, sortarray, vertices, axis, farleft, farright)
  struct mesh *m;
  struct behavior *b;
  vertex *sortarray;
  int vertices;
  int axis;
  struct otri *farleft;
  struct otri *farright;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct otri midtri, tri1, tri2, tri3;
    struct otri innerleft, innerright;
    REAL area;
    int divider;
  
    if (b->verbose > 2) {
      printf("  Triangulating %d vertices.\n", vertices);
    }
    if (vertices == 2) {
      /* The triangulation of two vertices is an edge.  An edge is */
      /*   represented by two bounding triangles.                  */
      maketriangle(m, b, farleft);
      setorg(*farleft, sortarray[0]);
      setdest(*farleft, sortarray[1]);
      /* The apex is intentionally left NULL. */
      maketriangle(m, b, farright);
      setorg(*farright, sortarray[1]);
      setdest(*farright, sortarray[0]);
      /* The apex is intentionally left NULL. */
      bond(*farleft, *farright);
      lprevself(*farleft);
      lnextself(*farright);
      bond(*farleft, *farright);
      lprevself(*farleft);
      lnextself(*farright);
      bond(*farleft, *farright);
      if (b->verbose > 2) {
        printf("  Creating ");
        printtriangle(m, b, farleft);
        printf("  Creating ");
        printtriangle(m, b, farright);
      }
      /* Ensure that the origin of `farleft' is sortarray[0]. */
      lprev(*farright, *farleft);
      return;
    } else if (vertices == 3) {
      /* The triangulation of three vertices is either a triangle (with */
      /*   three bounding triangles) or two edges (with four bounding   */
      /*   triangles).  In either case, four triangles are created.     */
      maketriangle(m, b, &midtri);
      maketriangle(m, b, &tri1);
      maketriangle(m, b, &tri2);
      maketriangle(m, b, &tri3);
      area = counterclockwise(m, b, sortarray[0], sortarray[1], sortarray[2]);
      if (area == 0.0) {
        /* Three collinear vertices; the triangulation is two edges. */
        setorg(midtri, sortarray[0]);
        setdest(midtri, sortarray[1]);
        setorg(tri1, sortarray[1]);
        setdest(tri1, sortarray[0]);
        setorg(tri2, sortarray[2]);
        setdest(tri2, sortarray[1]);
        setorg(tri3, sortarray[1]);
        setdest(tri3, sortarray[2]);
        /* All apices are intentionally left NULL. */
        bond(midtri, tri1);
        bond(tri2, tri3);
        lnextself(midtri);
        lprevself(tri1);
        lnextself(tri2);
        lprevself(tri3);
        bond(midtri, tri3);
        bond(tri1, tri2);
        lnextself(midtri);
        lprevself(tri1);
        lnextself(tri2);
        lprevself(tri3);
        bond(midtri, tri1);
        bond(tri2, tri3);
        /* Ensure that the origin of `farleft' is sortarray[0]. */
        otricopy(tri1, *farleft);
        /* Ensure that the destination of `farright' is sortarray[2]. */
        otricopy(tri2, *farright);
      } else {
        /* The three vertices are not collinear; the triangulation is one */
        /*   triangle, namely `midtri'.                                   */
        setorg(midtri, sortarray[0]);
        setdest(tri1, sortarray[0]);
        setorg(tri3, sortarray[0]);
        /* Apices of tri1, tri2, and tri3 are left NULL. */
        if (area > 0.0) {
          /* The vertices are in counterclockwise order. */
          setdest(midtri, sortarray[1]);
          setorg(tri1, sortarray[1]);
          setdest(tri2, sortarray[1]);
          setapex(midtri, sortarray[2]);
          setorg(tri2, sortarray[2]);
          setdest(tri3, sortarray[2]);
        } else {
          /* The vertices are in clockwise order. */
          setdest(midtri, sortarray[2]);
          setorg(tri1, sortarray[2]);
          setdest(tri2, sortarray[2]);
          setapex(midtri, sortarray[1]);
          setorg(tri2, sortarray[1]);
          setdest(tri3, sortarray[1]);
        }
        /* The topology does not depend on how the vertices are ordered. */
        bond(midtri, tri1);
        lnextself(midtri);
        bond(midtri, tri2);
        lnextself(midtri);
        bond(midtri, tri3);
        lprevself(tri1);
        lnextself(tri2);
        bond(tri1, tri2);
        lprevself(tri1);
        lprevself(tri3);
        bond(tri1, tri3);
        lnextself(tri2);
        lprevself(tri3);
        bond(tri2, tri3);
        /* Ensure that the origin of `farleft' is sortarray[0]. */
        otricopy(tri1, *farleft);
        /* Ensure that the destination of `farright' is sortarray[2]. */
        if (area > 0.0) {
          otricopy(tri2, *farright);
        } else {
          lnext(*farleft, *farright);
        }
      }
      if (b->verbose > 2) {
        printf("  Creating ");
        printtriangle(m, b, &midtri);
        printf("  Creating ");
        printtriangle(m, b, &tri1);
        printf("  Creating ");
        printtriangle(m, b, &tri2);
        printf("  Creating ");
        printtriangle(m, b, &tri3);
      }
      return;
    } else {
      /* Split the vertices in half. */
      divider = vertices >> 1;
      /* Recursively triangulate each half. */
      divconqrecurse(m, b, sortarray, divider, 1 - axis, farleft, &innerleft);
      divconqrecurse(m, b, &sortarray[divider], vertices - divider, 1 - axis,
                     &innerright, farright);
      if (b->verbose > 1) {
        printf("  Joining triangulations with %d and %d vertices.\n", divider,
               vertices - divider);
      }
      /* Merge the two triangulations into one. */
      mergehulls(m, b, farleft, &innerleft, &innerright, farright, axis);
    }
  }
  
  #ifdef ANSI_DECLARATORS
  long removeghosts(struct mesh *m, struct behavior *b, struct otri *startghost)
  #else /* not ANSI_DECLARATORS */
  long removeghosts(m, b, startghost)
  struct mesh *m;
  struct behavior *b;
  struct otri *startghost;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct otri searchedge;
    struct otri dissolveedge;
    struct otri deadtriangle;
    vertex markorg;
    long hullsize;
    triangle ptr;                         /* Temporary variable used by sym(). */
  
    if (b->verbose) {
      printf("  Removing ghost triangles.\n");
    }
    /* Find an edge on the convex hull to start point location from. */
    lprev(*startghost, searchedge);
    symself(searchedge);
    m->dummytri[0] = encode(searchedge);
    /* Remove the bounding box and count the convex hull edges. */
    otricopy(*startghost, dissolveedge);
    hullsize = 0;
    do {
      hullsize++;
      lnext(dissolveedge, deadtriangle);
      lprevself(dissolveedge);
      symself(dissolveedge);
      /* If no PSLG is involved, set the boundary markers of all the vertices */
      /*   on the convex hull.  If a PSLG is used, this step is done later.   */
      if (!b->poly) {
        /* Watch out for the case where all the input vertices are collinear. */
        if (dissolveedge.tri != m->dummytri) {
          org(dissolveedge, markorg);
          if (vertexmark(markorg) == 0) {
            setvertexmark(markorg, 1);
          }
        }
      }
      /* Remove a bounding triangle from a convex hull triangle. */
      dissolve(dissolveedge);
      /* Find the next bounding triangle. */
      sym(deadtriangle, dissolveedge);
      /* Delete the bounding triangle. */
      triangledealloc(m, deadtriangle.tri);
    } while (!otriequal(dissolveedge, *startghost));
    return hullsize;
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  divconqdelaunay()   Form a Delaunay triangulation by the divide-and-     */
  /*                      conquer method.                                      */
  /*                                                                           */
  /*  Sorts the vertices, calls a recursive procedure to triangulate them, and */
  /*  removes the bounding box, setting boundary markers as appropriate.       */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  long divconqdelaunay(struct mesh *m, struct behavior *b)
  #else /* not ANSI_DECLARATORS */
  long divconqdelaunay(m, b)
  struct mesh *m;
  struct behavior *b;
  #endif /* not ANSI_DECLARATORS */
  
  {
    vertex *sortarray;
    struct otri hullleft, hullright;
    int divider;
    int i, j;
  
    if (b->verbose) {
      printf("  Sorting vertices.\n");
    }
  
    /* Allocate an array of pointers to vertices for sorting. */
    sortarray = (vertex *) trimalloc(m->invertices * (int) sizeof(vertex));
    traversalinit(&m->vertices);
    for (i = 0; i < m->invertices; i++) {
      sortarray[i] = vertextraverse(m);
    }
    /* Sort the vertices. */
    vertexsort(sortarray, m->invertices);
    /* Discard duplicate vertices, which can really mess up the algorithm. */
    i = 0;
    for (j = 1; j < m->invertices; j++) {
      if ((sortarray[i][0] == sortarray[j][0])
          && (sortarray[i][1] == sortarray[j][1])) {
        if (!b->quiet) {
          printf(
  "Warning:  A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n",
                 sortarray[j][0], sortarray[j][1]);
        }
        setvertextype(sortarray[j], UNDEADVERTEX);
        m->undeads++;
      } else {
        i++;
        sortarray[i] = sortarray[j];
      }
    }
    i++;
    if (b->dwyer) {
      /* Re-sort the array of vertices to accommodate alternating cuts. */
      divider = i >> 1;
      if (i - divider >= 2) {
        if (divider >= 2) {
          alternateaxes(sortarray, divider, 1);
        }
        alternateaxes(&sortarray[divider], i - divider, 1);
      }
    }
  
    if (b->verbose) {
      printf("  Forming triangulation.\n");
    }
  
    /* Form the Delaunay triangulation. */
    divconqrecurse(m, b, sortarray, i, 0, &hullleft, &hullright);
    trifree((TRIVOID *) sortarray);
  
    return removeghosts(m, b, &hullleft);
  }
  
  /**                                                                         **/
  /**                                                                         **/
  /********* Divide-and-conquer Delaunay triangulation ends here       *********/
  
  /********* Incremental Delaunay triangulation begins here            *********/
  /**                                                                         **/
  /**                                                                         **/
  
  /*****************************************************************************/
  /*                                                                           */
  /*  boundingbox()   Form an "infinite" bounding triangle to insert vertices  */
  /*                  into.                                                    */
  /*                                                                           */
  /*  The vertices at "infinity" are assigned finite coordinates, which are    */
  /*  used by the point location routines, but (mostly) ignored by the         */
  /*  Delaunay edge flip routines.                                             */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifndef REDUCED
  
  #ifdef ANSI_DECLARATORS
  void boundingbox(struct mesh *m, struct behavior *b)
  #else /* not ANSI_DECLARATORS */
  void boundingbox(m, b)
  struct mesh *m;
  struct behavior *b;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct otri inftri;          /* Handle for the triangular bounding box. */
    REAL width;
  
    if (b->verbose) {
      printf("  Creating triangular bounding box.\n");
    }
    /* Find the width (or height, whichever is larger) of the triangulation. */
    width = m->xmax - m->xmin;
    if (m->ymax - m->ymin > width) {
      width = m->ymax - m->ymin;
    }
    if (width == 0.0) {
      width = 1.0;
    }
    /* Create the vertices of the bounding box. */
    m->infvertex1 = (vertex) trimalloc(m->vertices.itembytes);
    m->infvertex2 = (vertex) trimalloc(m->vertices.itembytes);
    m->infvertex3 = (vertex) trimalloc(m->vertices.itembytes);
    m->infvertex1[0] = m->xmin - 50.0 * width;
    m->infvertex1[1] = m->ymin - 40.0 * width;
    m->infvertex2[0] = m->xmax + 50.0 * width;
    m->infvertex2[1] = m->ymin - 40.0 * width;
    m->infvertex3[0] = 0.5 * (m->xmin + m->xmax);
    m->infvertex3[1] = m->ymax + 60.0 * width;
  
    /* Create the bounding box. */
    maketriangle(m, b, &inftri);
    setorg(inftri, m->infvertex1);
    setdest(inftri, m->infvertex2);
    setapex(inftri, m->infvertex3);
    /* Link dummytri to the bounding box so we can always find an */
    /*   edge to begin searching (point location) from.           */
    m->dummytri[0] = (triangle) inftri.tri;
    if (b->verbose > 2) {
      printf("  Creating ");
      printtriangle(m, b, &inftri);
    }
  }
  
  #endif /* not REDUCED */
  
  /*****************************************************************************/
  /*                                                                           */
  /*  removebox()   Remove the "infinite" bounding triangle, setting boundary  */
  /*                markers as appropriate.                                    */
  /*                                                                           */
  /*  The triangular bounding box has three boundary triangles (one for each   */
  /*  side of the bounding box), and a bunch of triangles fanning out from     */
  /*  the three bounding box vertices (one triangle for each edge of the       */
  /*  convex hull of the inner mesh).  This routine removes these triangles.   */
  /*                                                                           */
  /*  Returns the number of edges on the convex hull of the triangulation.     */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifndef REDUCED
  
  #ifdef ANSI_DECLARATORS
  long removebox(struct mesh *m, struct behavior *b)
  #else /* not ANSI_DECLARATORS */
  long removebox(m, b)
  struct mesh *m;
  struct behavior *b;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct otri deadtriangle;
    struct otri searchedge;
    struct otri checkedge;
    struct otri nextedge, finaledge, dissolveedge;
    vertex markorg;
    long hullsize;
    triangle ptr;                         /* Temporary variable used by sym(). */
  
    if (b->verbose) {
      printf("  Removing triangular bounding box.\n");
    }
    /* Find a boundary triangle. */
    nextedge.tri = m->dummytri;
    nextedge.orient = 0;
    symself(nextedge);
    /* Mark a place to stop. */
    lprev(nextedge, finaledge);
    lnextself(nextedge);
    symself(nextedge);
    /* Find a triangle (on the boundary of the vertex set) that isn't */
    /*   a bounding box triangle.                                     */
    lprev(nextedge, searchedge);
    symself(searchedge);
    /* Check whether nextedge is another boundary triangle */
    /*   adjacent to the first one.                        */
    lnext(nextedge, checkedge);
    symself(checkedge);
    if (checkedge.tri == m->dummytri) {
      /* Go on to the next triangle.  There are only three boundary   */
      /*   triangles, and this next triangle cannot be the third one, */
      /*   so it's safe to stop here.                                 */
      lprevself(searchedge);
      symself(searchedge);
    }
    /* Find a new boundary edge to search from, as the current search */
    /*   edge lies on a bounding box triangle and will be deleted.    */
    m->dummytri[0] = encode(searchedge);
    hullsize = -2l;
    while (!otriequal(nextedge, finaledge)) {
      hullsize++;
      lprev(nextedge, dissolveedge);
      symself(dissolveedge);
      /* If not using a PSLG, the vertices should be marked now. */
      /*   (If using a PSLG, markhull() will do the job.)        */
      if (!b->poly) {
        /* Be careful!  One must check for the case where all the input     */
        /*   vertices are collinear, and thus all the triangles are part of */
        /*   the bounding box.  Otherwise, the setvertexmark() call below   */
        /*   will cause a bad pointer reference.                            */
        if (dissolveedge.tri != m->dummytri) {
          org(dissolveedge, markorg);
          if (vertexmark(markorg) == 0) {
            setvertexmark(markorg, 1);
          }
        }
      }
      /* Disconnect the bounding box triangle from the mesh triangle. */
      dissolve(dissolveedge);
      lnext(nextedge, deadtriangle);
      sym(deadtriangle, nextedge);
      /* Get rid of the bounding box triangle. */
      triangledealloc(m, deadtriangle.tri);
      /* Do we need to turn the corner? */
      if (nextedge.tri == m->dummytri) {
        /* Turn the corner. */
        otricopy(dissolveedge, nextedge);
      }
    }
    triangledealloc(m, finaledge.tri);
  
    trifree((TRIVOID *) m->infvertex1);  /* Deallocate the bounding box vertices. */
    trifree((TRIVOID *) m->infvertex2);
    trifree((TRIVOID *) m->infvertex3);
  
    return hullsize;
  }
  
  #endif /* not REDUCED */
  
  /*****************************************************************************/
  /*                                                                           */
  /*  incrementaldelaunay()   Form a Delaunay triangulation by incrementally   */
  /*                          inserting vertices.                              */
  /*                                                                           */
  /*  Returns the number of edges on the convex hull of the triangulation.     */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifndef REDUCED
  
  #ifdef ANSI_DECLARATORS
  long incrementaldelaunay(struct mesh *m, struct behavior *b)
  #else /* not ANSI_DECLARATORS */
  long incrementaldelaunay(m, b)
  struct mesh *m;
  struct behavior *b;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct otri starttri;
    vertex vertexloop;
  
    /* Create a triangular bounding box. */
    boundingbox(m, b);
    if (b->verbose) {
      printf("  Incrementally inserting vertices.\n");
    }
    traversalinit(&m->vertices);
    vertexloop = vertextraverse(m);
    while (vertexloop != (vertex) NULL) {
      starttri.tri = m->dummytri;
      if (insertvertex(m, b, vertexloop, &starttri, (struct osub *) NULL, 0, 0)
          == DUPLICATEVERTEX) {
        if (!b->quiet) {
          printf(
  "Warning:  A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n",
                 vertexloop[0], vertexloop[1]);
        }
        setvertextype(vertexloop, UNDEADVERTEX);
        m->undeads++;
      }
      vertexloop = vertextraverse(m);
    }
    /* Remove the bounding box. */
    return removebox(m, b);
  }
  
  #endif /* not REDUCED */
  
  /**                                                                         **/
  /**                                                                         **/
  /********* Incremental Delaunay triangulation ends here              *********/
  
  /********* Sweepline Delaunay triangulation begins here              *********/
  /**                                                                         **/
  /**                                                                         **/
  
  #ifndef REDUCED
  
  #ifdef ANSI_DECLARATORS
  void eventheapinsert(struct event **heap, int heapsize, struct event *newevent)
  #else /* not ANSI_DECLARATORS */
  void eventheapinsert(heap, heapsize, newevent)
  struct event **heap;
  int heapsize;
  struct event *newevent;
  #endif /* not ANSI_DECLARATORS */
  
  {
    REAL eventx, eventy;
    int eventnum;
    int parent;
    int notdone;
  
    eventx = newevent->xkey;
    eventy = newevent->ykey;
    eventnum = heapsize;
    notdone = eventnum > 0;
    while (notdone) {
      parent = (eventnum - 1) >> 1;
      if ((heap[parent]->ykey < eventy) ||
          ((heap[parent]->ykey == eventy)
           && (heap[parent]->xkey <= eventx))) {
        notdone = 0;
      } else {
        heap[eventnum] = heap[parent];
        heap[eventnum]->heapposition = eventnum;
  
        eventnum = parent;
        notdone = eventnum > 0;
      }
    }
    heap[eventnum] = newevent;
    newevent->heapposition = eventnum;
  }
  
  #endif /* not REDUCED */
  
  #ifndef REDUCED
  
  #ifdef ANSI_DECLARATORS
  void eventheapify(struct event **heap, int heapsize, int eventnum)
  #else /* not ANSI_DECLARATORS */
  void eventheapify(heap, heapsize, eventnum)
  struct event **heap;
  int heapsize;
  int eventnum;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct event *thisevent;
    REAL eventx, eventy;
    int leftchild, rightchild;
    int smallest;
    int notdone;
  
    thisevent = heap[eventnum];
    eventx = thisevent->xkey;
    eventy = thisevent->ykey;
    leftchild = 2 * eventnum + 1;
    notdone = leftchild < heapsize;
    while (notdone) {
      if ((heap[leftchild]->ykey < eventy) ||
          ((heap[leftchild]->ykey == eventy)
           && (heap[leftchild]->xkey < eventx))) {
        smallest = leftchild;
      } else {
        smallest = eventnum;
      }
      rightchild = leftchild + 1;
      if (rightchild < heapsize) {
        if ((heap[rightchild]->ykey < heap[smallest]->ykey) ||
            ((heap[rightchild]->ykey == heap[smallest]->ykey)
             && (heap[rightchild]->xkey < heap[smallest]->xkey))) {
          smallest = rightchild;
        }
      }
      if (smallest == eventnum) {
        notdone = 0;
      } else {
        heap[eventnum] = heap[smallest];
        heap[eventnum]->heapposition = eventnum;
        heap[smallest] = thisevent;
        thisevent->heapposition = smallest;
  
        eventnum = smallest;
        leftchild = 2 * eventnum + 1;
        notdone = leftchild < heapsize;
      }
    }
  }
  
  #endif /* not REDUCED */
  
  #ifndef REDUCED
  
  #ifdef ANSI_DECLARATORS
  void eventheapdelete(struct event **heap, int heapsize, int eventnum)
  #else /* not ANSI_DECLARATORS */
  void eventheapdelete(heap, heapsize, eventnum)
  struct event **heap;
  int heapsize;
  int eventnum;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct event *moveevent;
    REAL eventx, eventy;
    int parent;
    int notdone;
  
    moveevent = heap[heapsize - 1];
    if (eventnum > 0) {
      eventx = moveevent->xkey;
      eventy = moveevent->ykey;
      do {
        parent = (eventnum - 1) >> 1;
        if ((heap[parent]->ykey < eventy) ||
            ((heap[parent]->ykey == eventy)
             && (heap[parent]->xkey <= eventx))) {
          notdone = 0;
        } else {
          heap[eventnum] = heap[parent];
          heap[eventnum]->heapposition = eventnum;
  
          eventnum = parent;
          notdone = eventnum > 0;
        }
      } while (notdone);
    }
    heap[eventnum] = moveevent;
    moveevent->heapposition = eventnum;
    eventheapify(heap, heapsize - 1, eventnum);
  }
  
  #endif /* not REDUCED */
  
  #ifndef REDUCED
  
  #ifdef ANSI_DECLARATORS
  void createeventheap(struct mesh *m, struct event ***eventheap,
                       struct event **events, struct event **freeevents)
  #else /* not ANSI_DECLARATORS */
  void createeventheap(m, eventheap, events, freeevents)
  struct mesh *m;
  struct event ***eventheap;
  struct event **events;
  struct event **freeevents;
  #endif /* not ANSI_DECLARATORS */
  
  {
    vertex thisvertex;
    int maxevents;
    int i;
  
    maxevents = (3 * m->invertices) / 2;
    *eventheap = (struct event **) trimalloc(maxevents *
                                             (int) sizeof(struct event *));
    *events = (struct event *) trimalloc(maxevents * (int) sizeof(struct event));
    traversalinit(&m->vertices);
    for (i = 0; i < m->invertices; i++) {
      thisvertex = vertextraverse(m);
      (*events)[i].eventptr = (TRIVOID *) thisvertex;
      (*events)[i].xkey = thisvertex[0];
      (*events)[i].ykey = thisvertex[1];
      eventheapinsert(*eventheap, i, *events + i);
    }
    *freeevents = (struct event *) NULL;
    for (i = maxevents - 1; i >= m->invertices; i--) {
      (*events)[i].eventptr = (TRIVOID *) *freeevents;
      *freeevents = *events + i;
    }
  }
  
  #endif /* not REDUCED */
  
  #ifndef REDUCED
  
  #ifdef ANSI_DECLARATORS
  int rightofhyperbola(struct mesh *m, struct otri *fronttri, vertex newsite)
  #else /* not ANSI_DECLARATORS */
  int rightofhyperbola(m, fronttri, newsite)
  struct mesh *m;
  struct otri *fronttri;
  vertex newsite;
  #endif /* not ANSI_DECLARATORS */
  
  {
    vertex leftvertex, rightvertex;
    REAL dxa, dya, dxb, dyb;
  
    m->hyperbolacount++;
  
    dest(*fronttri, leftvertex);
    apex(*fronttri, rightvertex);
    if ((leftvertex[1] < rightvertex[1]) ||
        ((leftvertex[1] == rightvertex[1]) &&
         (leftvertex[0] < rightvertex[0]))) {
      if (newsite[0] >= rightvertex[0]) {
        return 1;
      }
    } else {
      if (newsite[0] <= leftvertex[0]) {
        return 0;
      }
    }
    dxa = leftvertex[0] - newsite[0];
    dya = leftvertex[1] - newsite[1];
    dxb = rightvertex[0] - newsite[0];
    dyb = rightvertex[1] - newsite[1];
    return dya * (dxb * dxb + dyb * dyb) > dyb * (dxa * dxa + dya * dya);
  }
  
  #endif /* not REDUCED */
  
  #ifndef REDUCED
  
  #ifdef ANSI_DECLARATORS
  REAL circletop(struct mesh *m, vertex pa, vertex pb, vertex pc, REAL ccwabc)
  #else /* not ANSI_DECLARATORS */
  REAL circletop(m, pa, pb, pc, ccwabc)
  struct mesh *m;
  vertex pa;
  vertex pb;
  vertex pc;
  REAL ccwabc;
  #endif /* not ANSI_DECLARATORS */
  
  {
    REAL xac, yac, xbc, ybc, xab, yab;
    REAL aclen2, bclen2, ablen2;
  
    m->circletopcount++;
  
    xac = pa[0] - pc[0];
    yac = pa[1] - pc[1];
    xbc = pb[0] - pc[0];
    ybc = pb[1] - pc[1];
    xab = pa[0] - pb[0];
    yab = pa[1] - pb[1];
    aclen2 = xac * xac + yac * yac;
    bclen2 = xbc * xbc + ybc * ybc;
    ablen2 = xab * xab + yab * yab;
    return pc[1] + (xac * bclen2 - xbc * aclen2 + sqrt(aclen2 * bclen2 * ablen2))
                 / (2.0 * ccwabc);
  }
  
  #endif /* not REDUCED */
  
  #ifndef REDUCED
  
  #ifdef ANSI_DECLARATORS
  void check4deadevent(struct otri *checktri, struct event **freeevents,
                       struct event **eventheap, int *heapsize)
  #else /* not ANSI_DECLARATORS */
  void check4deadevent(checktri, freeevents, eventheap, heapsize)
  struct otri *checktri;
  struct event **freeevents;
  struct event **eventheap;
  int *heapsize;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct event *deadevent;
    vertex eventvertex;
    int eventnum;
  
    org(*checktri, eventvertex);
    if (eventvertex != (vertex) NULL) {
      deadevent = (struct event *) eventvertex;
      eventnum = deadevent->heapposition;
      deadevent->eventptr = (TRIVOID *) *freeevents;
      *freeevents = deadevent;
      eventheapdelete(eventheap, *heapsize, eventnum);
      (*heapsize)--;
      setorg(*checktri, NULL);
    }
  }
  
  #endif /* not REDUCED */
  
  #ifndef REDUCED
  
  #ifdef ANSI_DECLARATORS
  struct splaynode *splay(struct mesh *m, struct splaynode *splaytree,
                          vertex searchpoint, struct otri *searchtri)
  #else /* not ANSI_DECLARATORS */
  struct splaynode *splay(m, splaytree, searchpoint, searchtri)
  struct mesh *m;
  struct splaynode *splaytree;
  vertex searchpoint;
  struct otri *searchtri;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct splaynode *child, *grandchild;
    struct splaynode *lefttree, *righttree;
    struct splaynode *leftright;
    vertex checkvertex;
    int rightofroot, rightofchild;
  
    if (splaytree == (struct splaynode *) NULL) {
      return (struct splaynode *) NULL;
    }
    dest(splaytree->keyedge, checkvertex);
    if (checkvertex == splaytree->keydest) {
      rightofroot = rightofhyperbola(m, &splaytree->keyedge, searchpoint);
      if (rightofroot) {
        otricopy(splaytree->keyedge, *searchtri);
        child = splaytree->rchild;
      } else {
        child = splaytree->lchild;
      }
      if (child == (struct splaynode *) NULL) {
        return splaytree;
      }
      dest(child->keyedge, checkvertex);
      if (checkvertex != child->keydest) {
        child = splay(m, child, searchpoint, searchtri);
        if (child == (struct splaynode *) NULL) {
          if (rightofroot) {
            splaytree->rchild = (struct splaynode *) NULL;
          } else {
            splaytree->lchild = (struct splaynode *) NULL;
          }
          return splaytree;
        }
      }
      rightofchild = rightofhyperbola(m, &child->keyedge, searchpoint);
      if (rightofchild) {
        otricopy(child->keyedge, *searchtri);
        grandchild = splay(m, child->rchild, searchpoint, searchtri);
        child->rchild = grandchild;
      } else {
        grandchild = splay(m, child->lchild, searchpoint, searchtri);
        child->lchild = grandchild;
      }
      if (grandchild == (struct splaynode *) NULL) {
        if (rightofroot) {
          splaytree->rchild = child->lchild;
          child->lchild = splaytree;
        } else {
          splaytree->lchild = child->rchild;
          child->rchild = splaytree;
        }
        return child;
      }
      if (rightofchild) {
        if (rightofroot) {
          splaytree->rchild = child->lchild;
          child->lchild = splaytree;
        } else {
          splaytree->lchild = grandchild->rchild;
          grandchild->rchild = splaytree;
        }
        child->rchild = grandchild->lchild;
        grandchild->lchild = child;
      } else {
        if (rightofroot) {
          splaytree->rchild = grandchild->lchild;
          grandchild->lchild = splaytree;
        } else {
          splaytree->lchild = child->rchild;
          child->rchild = splaytree;
        }
        child->lchild = grandchild->rchild;
        grandchild->rchild = child;
      }
      return grandchild;
    } else {
      lefttree = splay(m, splaytree->lchild, searchpoint, searchtri);
      righttree = splay(m, splaytree->rchild, searchpoint, searchtri);
  
      pooldealloc(&m->splaynodes, (TRIVOID *) splaytree);
      if (lefttree == (struct splaynode *) NULL) {
        return righttree;
      } else if (righttree == (struct splaynode *) NULL) {
        return lefttree;
      } else if (lefttree->rchild == (struct splaynode *) NULL) {
        lefttree->rchild = righttree->lchild;
        righttree->lchild = lefttree;
        return righttree;
      } else if (righttree->lchild == (struct splaynode *) NULL) {
        righttree->lchild = lefttree->rchild;
        lefttree->rchild = righttree;
        return lefttree;
      } else {
  /*      printf("Holy Toledo!!!\n"); */
        leftright = lefttree->rchild;
        while (leftright->rchild != (struct splaynode *) NULL) {
          leftright = leftright->rchild;
        }
        leftright->rchild = righttree;
        return lefttree;
      }
    }
  }
  
  #endif /* not REDUCED */
  
  #ifndef REDUCED
  
  #ifdef ANSI_DECLARATORS
  struct splaynode *splayinsert(struct mesh *m, struct splaynode *splayroot,
                                struct otri *newkey, vertex searchpoint)
  #else /* not ANSI_DECLARATORS */
  struct splaynode *splayinsert(m, splayroot, newkey, searchpoint)
  struct mesh *m;
  struct splaynode *splayroot;
  struct otri *newkey;
  vertex searchpoint;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct splaynode *newsplaynode;
  
    newsplaynode = (struct splaynode *) poolalloc(&m->splaynodes);
    otricopy(*newkey, newsplaynode->keyedge);
    dest(*newkey, newsplaynode->keydest);
    if (splayroot == (struct splaynode *) NULL) {
      newsplaynode->lchild = (struct splaynode *) NULL;
      newsplaynode->rchild = (struct splaynode *) NULL;
    } else if (rightofhyperbola(m, &splayroot->keyedge, searchpoint)) {
      newsplaynode->lchild = splayroot;
      newsplaynode->rchild = splayroot->rchild;
      splayroot->rchild = (struct splaynode *) NULL;
    } else {
      newsplaynode->lchild = splayroot->lchild;
      newsplaynode->rchild = splayroot;
      splayroot->lchild = (struct splaynode *) NULL;
    }
    return newsplaynode;
  }
  
  #endif /* not REDUCED */
  
  #ifndef REDUCED
  
  #ifdef ANSI_DECLARATORS
  struct splaynode *circletopinsert(struct mesh *m, struct behavior *b,
                                    struct splaynode *splayroot,
                                    struct otri *newkey,
                                    vertex pa, vertex pb, vertex pc, REAL topy)
  #else /* not ANSI_DECLARATORS */
  struct splaynode *circletopinsert(m, b, splayroot, newkey, pa, pb, pc, topy)
  struct mesh *m;
  struct behavior *b;
  struct splaynode *splayroot;
  struct otri *newkey;
  vertex pa;
  vertex pb;
  vertex pc;
  REAL topy;
  #endif /* not ANSI_DECLARATORS */
  
  {
    REAL ccwabc;
    REAL xac, yac, xbc, ybc;
    REAL aclen2, bclen2;
    REAL searchpoint[2];
    struct otri dummytri;
  
    ccwabc = counterclockwise(m, b, pa, pb, pc);
    xac = pa[0] - pc[0];
    yac = pa[1] - pc[1];
    xbc = pb[0] - pc[0];
    ybc = pb[1] - pc[1];
    aclen2 = xac * xac + yac * yac;
    bclen2 = xbc * xbc + ybc * ybc;
    searchpoint[0] = pc[0] - (yac * bclen2 - ybc * aclen2) / (2.0 * ccwabc);
    searchpoint[1] = topy;
    return splayinsert(m, splay(m, splayroot, (vertex) searchpoint, &dummytri),
                       newkey, (vertex) searchpoint);
  }
  
  #endif /* not REDUCED */
  
  #ifndef REDUCED
  
  #ifdef ANSI_DECLARATORS
  struct splaynode *frontlocate(struct mesh *m, struct splaynode *splayroot,
                                struct otri *bottommost, vertex searchvertex,
                                struct otri *searchtri, int *farright)
  #else /* not ANSI_DECLARATORS */
  struct splaynode *frontlocate(m, splayroot, bottommost, searchvertex,
                                searchtri, farright)
  struct mesh *m;
  struct splaynode *splayroot;
  struct otri *bottommost;
  vertex searchvertex;
  struct otri *searchtri;
  int *farright;
  #endif /* not ANSI_DECLARATORS */
  
  {
    int farrightflag;
    triangle ptr;                       /* Temporary variable used by onext(). */
  
    otricopy(*bottommost, *searchtri);
    splayroot = splay(m, splayroot, searchvertex, searchtri);
  
    farrightflag = 0;
    while (!farrightflag && rightofhyperbola(m, searchtri, searchvertex)) {
      onextself(*searchtri);
      farrightflag = otriequal(*searchtri, *bottommost);
    }
    *farright = farrightflag;
    return splayroot;
  }
  
  #endif /* not REDUCED */
  
  #ifndef REDUCED
  
  #ifdef ANSI_DECLARATORS
  long sweeplinedelaunay(struct mesh *m, struct behavior *b)
  #else /* not ANSI_DECLARATORS */
  long sweeplinedelaunay(m, b)
  struct mesh *m;
  struct behavior *b;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct event **eventheap;
    struct event *events;
    struct event *freeevents;
    struct event *nextevent;
    struct event *newevent;
    struct splaynode *splayroot;
    struct otri bottommost;
    struct otri searchtri;
    struct otri fliptri;
    struct otri lefttri, righttri, farlefttri, farrighttri;
    struct otri inserttri;
    vertex firstvertex, secondvertex;
    vertex nextvertex, lastvertex;
    vertex connectvertex;
    vertex leftvertex, midvertex, rightvertex;
    REAL lefttest, righttest;
    int heapsize;
    int check4events, farrightflag;
    triangle ptr;   /* Temporary variable used by sym(), onext(), and oprev(). */
  
    poolinit(&m->splaynodes, sizeof(struct splaynode), SPLAYNODEPERBLOCK,
             SPLAYNODEPERBLOCK, 0);
    splayroot = (struct splaynode *) NULL;
  
    if (b->verbose) {
      printf("  Placing vertices in event heap.\n");
    }
    createeventheap(m, &eventheap, &events, &freeevents);
    heapsize = m->invertices;
  
    if (b->verbose) {
      printf("  Forming triangulation.\n");
    }
    maketriangle(m, b, &lefttri);
    maketriangle(m, b, &righttri);
    bond(lefttri, righttri);
    lnextself(lefttri);
    lprevself(righttri);
    bond(lefttri, righttri);
    lnextself(lefttri);
    lprevself(righttri);
    bond(lefttri, righttri);
    firstvertex = (vertex) eventheap[0]->eventptr;
    eventheap[0]->eventptr = (TRIVOID *) freeevents;
    freeevents = eventheap[0];
    eventheapdelete(eventheap, heapsize, 0);
    heapsize--;
    do {
      if (heapsize == 0) {
        printf("Error:  Input vertices are all identical.\n");
        triexit(1);
      }
      secondvertex = (vertex) eventheap[0]->eventptr;
      eventheap[0]->eventptr = (TRIVOID *) freeevents;
      freeevents = eventheap[0];
      eventheapdelete(eventheap, heapsize, 0);
      heapsize--;
      if ((firstvertex[0] == secondvertex[0]) &&
          (firstvertex[1] == secondvertex[1])) {
        if (!b->quiet) {
          printf(
  "Warning:  A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n",
                 secondvertex[0], secondvertex[1]);
        }
        setvertextype(secondvertex, UNDEADVERTEX);
        m->undeads++;
      }
    } while ((firstvertex[0] == secondvertex[0]) &&
             (firstvertex[1] == secondvertex[1]));
    setorg(lefttri, firstvertex);
    setdest(lefttri, secondvertex);
    setorg(righttri, secondvertex);
    setdest(righttri, firstvertex);
    lprev(lefttri, bottommost);
    lastvertex = secondvertex;
    while (heapsize > 0) {
      nextevent = eventheap[0];
      eventheapdelete(eventheap, heapsize, 0);
      heapsize--;
      check4events = 1;
      if (nextevent->xkey < m->xmin) {
        decode(nextevent->eventptr, fliptri);
        oprev(fliptri, farlefttri);
        check4deadevent(&farlefttri, &freeevents, eventheap, &heapsize);
        onext(fliptri, farrighttri);
        check4deadevent(&farrighttri, &freeevents, eventheap, &heapsize);
  
        if (otriequal(farlefttri, bottommost)) {
          lprev(fliptri, bottommost);
        }
        flip(m, b, &fliptri);
        setapex(fliptri, NULL);
        lprev(fliptri, lefttri);
        lnext(fliptri, righttri);
        sym(lefttri, farlefttri);
  
        if (randomnation(SAMPLERATE) == 0) {
          symself(fliptri);
          dest(fliptri, leftvertex);
          apex(fliptri, midvertex);
          org(fliptri, rightvertex);
          splayroot = circletopinsert(m, b, splayroot, &lefttri, leftvertex,
                                      midvertex, rightvertex, nextevent->ykey);
        }
      } else {
        nextvertex = (vertex) nextevent->eventptr;
        if ((nextvertex[0] == lastvertex[0]) &&
            (nextvertex[1] == lastvertex[1])) {
          if (!b->quiet) {
            printf(
  "Warning:  A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n",
                   nextvertex[0], nextvertex[1]);
          }
          setvertextype(nextvertex, UNDEADVERTEX);
          m->undeads++;
          check4events = 0;
        } else {
          lastvertex = nextvertex;
  
          splayroot = frontlocate(m, splayroot, &bottommost, nextvertex,
                                  &searchtri, &farrightflag);
  /*
          otricopy(bottommost, searchtri);
          farrightflag = 0;
          while (!farrightflag && rightofhyperbola(m, &searchtri, nextvertex)) {
            onextself(searchtri);
            farrightflag = otriequal(searchtri, bottommost);
          }
  */
  
          check4deadevent(&searchtri, &freeevents, eventheap, &heapsize);
  
          otricopy(searchtri, farrighttri);
          sym(searchtri, farlefttri);
          maketriangle(m, b, &lefttri);
          maketriangle(m, b, &righttri);
          dest(farrighttri, connectvertex);
          setorg(lefttri, connectvertex);
          setdest(lefttri, nextvertex);
          setorg(righttri, nextvertex);
          setdest(righttri, connectvertex);
          bond(lefttri, righttri);
          lnextself(lefttri);
          lprevself(righttri);
          bond(lefttri, righttri);
          lnextself(lefttri);
          lprevself(righttri);
          bond(lefttri, farlefttri);
          bond(righttri, farrighttri);
          if (!farrightflag && otriequal(farrighttri, bottommost)) {
            otricopy(lefttri, bottommost);
          }
  
          if (randomnation(SAMPLERATE) == 0) {
            splayroot = splayinsert(m, splayroot, &lefttri, nextvertex);
          } else if (randomnation(SAMPLERATE) == 0) {
            lnext(righttri, inserttri);
            splayroot = splayinsert(m, splayroot, &inserttri, nextvertex);
          }
        }
      }
      nextevent->eventptr = (TRIVOID *) freeevents;
      freeevents = nextevent;
  
      if (check4events) {
        apex(farlefttri, leftvertex);
        dest(lefttri, midvertex);
        apex(lefttri, rightvertex);
        lefttest = counterclockwise(m, b, leftvertex, midvertex, rightvertex);
        if (lefttest > 0.0) {
          newevent = freeevents;
          freeevents = (struct event *) freeevents->eventptr;
          newevent->xkey = m->xminextreme;
          newevent->ykey = circletop(m, leftvertex, midvertex, rightvertex,
                                     lefttest);
          newevent->eventptr = (TRIVOID *) encode(lefttri);
          eventheapinsert(eventheap, heapsize, newevent);
          heapsize++;
          setorg(lefttri, newevent);
        }
        apex(righttri, leftvertex);
        org(righttri, midvertex);
        apex(farrighttri, rightvertex);
        righttest = counterclockwise(m, b, leftvertex, midvertex, rightvertex);
        if (righttest > 0.0) {
          newevent = freeevents;
          freeevents = (struct event *) freeevents->eventptr;
          newevent->xkey = m->xminextreme;
          newevent->ykey = circletop(m, leftvertex, midvertex, rightvertex,
                                     righttest);
          newevent->eventptr = (TRIVOID *) encode(farrighttri);
          eventheapinsert(eventheap, heapsize, newevent);
          heapsize++;
          setorg(farrighttri, newevent);
        }
      }
    }
  
    pooldeinit(&m->splaynodes);
    lprevself(bottommost);
    return removeghosts(m, b, &bottommost);
  }
  
  #endif /* not REDUCED */
  
  /**                                                                         **/
  /**                                                                         **/
  /********* Sweepline Delaunay triangulation ends here                *********/
  
  /********* General mesh construction routines begin here             *********/
  /**                                                                         **/
  /**                                                                         **/
  
  /*****************************************************************************/
  /*                                                                           */
  /*  delaunay()   Form a Delaunay triangulation.                              */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  long delaunay(struct mesh *m, struct behavior *b)
  #else /* not ANSI_DECLARATORS */
  long delaunay(m, b)
  struct mesh *m;
  struct behavior *b;
  #endif /* not ANSI_DECLARATORS */
  
  {
    long hulledges;
  
    m->eextras = 0;
    initializetrisubpools(m, b);
  
  #ifdef REDUCED
    if (!b->quiet) {
      printf(
        "Constructing Delaunay triangulation by divide-and-conquer method.\n");
    }
    hulledges = divconqdelaunay(m, b);
  #else /* not REDUCED */
    if (!b->quiet) {
      printf("Constructing Delaunay triangulation ");
      if (b->incremental) {
        printf("by incremental method.\n");
      } else if (b->sweepline) {
        printf("by sweepline method.\n");
      } else {
        printf("by divide-and-conquer method.\n");
      }
    }
    if (b->incremental) {
      hulledges = incrementaldelaunay(m, b);
    } else if (b->sweepline) {
      hulledges = sweeplinedelaunay(m, b);
    } else {
      hulledges = divconqdelaunay(m, b);
    }
  #endif /* not REDUCED */
  
    if (m->triangles.items == 0) {
      /* The input vertices were all collinear, so there are no triangles. */
      return 0l;
    } else {
      return hulledges;
    }
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  reconstruct()   Reconstruct a triangulation from its .ele (and possibly  */
  /*                  .poly) file.  Used when the -r switch is used.           */
  /*                                                                           */
  /*  Reads an .ele file and reconstructs the original mesh.  If the -p switch */
  /*  is used, this procedure will also read a .poly file and reconstruct the  */
  /*  subsegments of the original mesh.  If the -a switch is used, this        */
  /*  procedure will also read an .area file and set a maximum area constraint */
  /*  on each triangle.                                                        */
  /*                                                                           */
  /*  Vertices that are not corners of triangles, such as nodes on edges of    */
  /*  subparametric elements, are discarded.                                   */
  /*                                                                           */
  /*  This routine finds the adjacencies between triangles (and subsegments)   */
  /*  by forming one stack of triangles for each vertex.  Each triangle is on  */
  /*  three different stacks simultaneously.  Each triangle's subsegment       */
  /*  pointers are used to link the items in each stack.  This memory-saving   */
  /*  feature makes the code harder to read.  The most important thing to keep */
  /*  in mind is that each triangle is removed from a stack precisely when     */
  /*  the corresponding pointer is adjusted to refer to a subsegment rather    */
  /*  than the next triangle of the stack.                                     */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifndef CDT_ONLY
  
  #ifdef TRILIBRARY
  
  #ifdef ANSI_DECLARATORS
  int reconstruct(struct mesh *m, struct behavior *b, int *trianglelist,
                  REAL *triangleattriblist, REAL *trianglearealist,
                  int elements, int corners, int attribs,
                  int *segmentlist,int *segmentmarkerlist, int numberofsegments)
  #else /* not ANSI_DECLARATORS */
  int reconstruct(m, b, trianglelist, triangleattriblist, trianglearealist,
                  elements, corners, attribs, segmentlist, segmentmarkerlist,
                  numberofsegments)
  struct mesh *m;
  struct behavior *b;
  int *trianglelist;
  REAL *triangleattriblist;
  REAL *trianglearealist;
  int elements;
  int corners;
  int attribs;
  int *segmentlist;
  int *segmentmarkerlist;
  int numberofsegments;
  #endif /* not ANSI_DECLARATORS */
  
  #else /* not TRILIBRARY */
  
  #ifdef ANSI_DECLARATORS
  long reconstruct(struct mesh *m, struct behavior *b, char *elefilename,
                   char *areafilename, char *polyfilename, FILE *polyfile)
  #else /* not ANSI_DECLARATORS */
  long reconstruct(m, b, elefilename, areafilename, polyfilename, polyfile)
  struct mesh *m;
  struct behavior *b;
  char *elefilename;
  char *areafilename;
  char *polyfilename;
  FILE *polyfile;
  #endif /* not ANSI_DECLARATORS */
  
  #endif /* not TRILIBRARY */
  
  {
  #ifdef TRILIBRARY
    int vertexindex;
    int attribindex;
  #else /* not TRILIBRARY */
    FILE *elefile;
    FILE *areafile;
    char inputline[INPUTLINESIZE];
    char *stringptr;
    int areaelements;
  #endif /* not TRILIBRARY */
    struct otri triangleloop;
    struct otri triangleleft;
    struct otri checktri;
    struct otri checkleft;
    struct otri checkneighbor;
    struct osub subsegloop;
    triangle *vertexarray;
    triangle *prevlink;
    triangle nexttri;
    vertex tdest, tapex;
    vertex checkdest, checkapex;
    vertex shorg;
    vertex killvertex;
    vertex segmentorg, segmentdest;
    REAL area;
    int corner[3];
    int end[2];
    int killvertexindex;
    int incorners;
    int segmentmarkers;
    int boundmarker;
    int aroundvertex;
    long hullsize;
    int notfound;
    long elementnumber, segmentnumber;
    int i, j;
    triangle ptr;                         /* Temporary variable used by sym(). */
  
  #ifdef TRILIBRARY
    m->inelements = elements;
    incorners = corners;
    if (incorners < 3) {
      printf("Error:  Triangles must have at least 3 vertices.\n");
      triexit(1);
    }
    m->eextras = attribs;
  #else /* not TRILIBRARY */
    /* Read the triangles from an .ele file. */
    if (!b->quiet) {
      printf("Opening %s.\n", elefilename);
    }
    elefile = fopen(elefilename, "r");
    if (elefile == (FILE *) NULL) {
      printf("  Error:  Cannot access file %s.\n", elefilename);
      triexit(1);
    }
    /* Read number of triangles, number of vertices per triangle, and */
    /*   number of triangle attributes from .ele file.                */
    stringptr = readline(inputline, elefile, elefilename);
    m->inelements = (int) strtol(stringptr, &stringptr, 0);
    stringptr = findfield(stringptr);
    if (*stringptr == '\0') {
      incorners = 3;
    } else {
      incorners = (int) strtol(stringptr, &stringptr, 0);
      if (incorners < 3) {
        printf("Error:  Triangles in %s must have at least 3 vertices.\n",
               elefilename);
        triexit(1);
      }
    }
    stringptr = findfield(stringptr);
    if (*stringptr == '\0') {
      m->eextras = 0;
    } else {
      m->eextras = (int) strtol(stringptr, &stringptr, 0);
    }
  #endif /* not TRILIBRARY */
  
    initializetrisubpools(m, b);
  
    /* Create the triangles. */
    for (elementnumber = 1; elementnumber <= m->inelements; elementnumber++) {
      maketriangle(m, b, &triangleloop);
      /* Mark the triangle as living. */
      triangleloop.tri[3] = (triangle) triangleloop.tri;
    }
  
    segmentmarkers = 0;
    if (b->poly) {
  #ifdef TRILIBRARY
      m->insegments = numberofsegments;
      segmentmarkers = segmentmarkerlist != (int *) NULL;
  #else /* not TRILIBRARY */
      /* Read number of segments and number of segment */
      /*   boundary markers from .poly file.           */
      stringptr = readline(inputline, polyfile, b->inpolyfilename);
      m->insegments = (int) strtol(stringptr, &stringptr, 0);
      stringptr = findfield(stringptr);
      if (*stringptr != '\0') {
        segmentmarkers = (int) strtol(stringptr, &stringptr, 0);
      }
  #endif /* not TRILIBRARY */
  
      /* Create the subsegments. */
      for (segmentnumber = 1; segmentnumber <= m->insegments; segmentnumber++) {
        makesubseg(m, &subsegloop);
        /* Mark the subsegment as living. */
        subsegloop.ss[2] = (subseg) subsegloop.ss;
      }
    }
  
  #ifdef TRILIBRARY
    vertexindex = 0;
    attribindex = 0;
  #else /* not TRILIBRARY */
    if (b->vararea) {
      /* Open an .area file, check for consistency with the .ele file. */
      if (!b->quiet) {
        printf("Opening %s.\n", areafilename);
      }
      areafile = fopen(areafilename, "r");
      if (areafile == (FILE *) NULL) {
        printf("  Error:  Cannot access file %s.\n", areafilename);
        triexit(1);
      }
      stringptr = readline(inputline, areafile, areafilename);
      areaelements = (int) strtol(stringptr, &stringptr, 0);
      if (areaelements != m->inelements) {
        printf("Error:  %s and %s disagree on number of triangles.\n",
               elefilename, areafilename);
        triexit(1);
      }
    }
  #endif /* not TRILIBRARY */
  
    if (!b->quiet) {
      printf("Reconstructing mesh.\n");
    }
    /* Allocate a temporary array that maps each vertex to some adjacent */
    /*   triangle.  I took care to allocate all the permanent memory for */
    /*   triangles and subsegments first.                                */
    vertexarray = (triangle *) trimalloc(m->vertices.items *
                                         (int) sizeof(triangle));
    /* Each vertex is initially unrepresented. */
    for (i = 0; i < m->vertices.items; i++) {
      vertexarray[i] = (triangle) m->dummytri;
    }
  
    if (b->verbose) {
      printf("  Assembling triangles.\n");
    }
    /* Read the triangles from the .ele file, and link */
    /*   together those that share an edge.            */
    traversalinit(&m->triangles);
    triangleloop.tri = triangletraverse(m);
    elementnumber = b->firstnumber;
    while (triangleloop.tri != (triangle *) NULL) {
  #ifdef TRILIBRARY
      /* Copy the triangle's three corners. */
      for (j = 0; j < 3; j++) {
        corner[j] = trianglelist[vertexindex++];
        if ((corner[j] < b->firstnumber) ||
            (corner[j] >= b->firstnumber + m->invertices)) {
          printf("Error:  Triangle %ld has an invalid vertex index.\n",
                 elementnumber);
          triexit(1);
        }
      }
  #else /* not TRILIBRARY */
      /* Read triangle number and the triangle's three corners. */
      stringptr = readline(inputline, elefile, elefilename);
      for (j = 0; j < 3; j++) {
        stringptr = findfield(stringptr);
        if (*stringptr == '\0') {
          printf("Error:  Triangle %ld is missing vertex %d in %s.\n",
                 elementnumber, j + 1, elefilename);
          triexit(1);
        } else {
          corner[j] = (int) strtol(stringptr, &stringptr, 0);
          if ((corner[j] < b->firstnumber) ||
              (corner[j] >= b->firstnumber + m->invertices)) {
            printf("Error:  Triangle %ld has an invalid vertex index.\n",
                   elementnumber);
            triexit(1);
          }
        }
      }
  #endif /* not TRILIBRARY */
  
      /* Find out about (and throw away) extra nodes. */
      for (j = 3; j < incorners; j++) {
  #ifdef TRILIBRARY
        killvertexindex = trianglelist[vertexindex++];
  #else /* not TRILIBRARY */
        stringptr = findfield(stringptr);
        if (*stringptr != '\0') {
          killvertexindex = (int) strtol(stringptr, &stringptr, 0);
  #endif /* not TRILIBRARY */
          if ((killvertexindex >= b->firstnumber) &&
              (killvertexindex < b->firstnumber + m->invertices)) {
            /* Delete the non-corner vertex if it's not already deleted. */
            killvertex = getvertex(m, b, killvertexindex);
            if (vertextype(killvertex) != DEADVERTEX) {
              vertexdealloc(m, killvertex);
            }
          }
  #ifndef TRILIBRARY
        }
  #endif /* not TRILIBRARY */
      }
  
      /* Read the triangle's attributes. */
      for (j = 0; j < m->eextras; j++) {
  #ifdef TRILIBRARY
        setelemattribute(triangleloop, j, triangleattriblist[attribindex++]);
  #else /* not TRILIBRARY */
        stringptr = findfield(stringptr);
        if (*stringptr == '\0') {
          setelemattribute(triangleloop, j, 0);
        } else {
          setelemattribute(triangleloop, j,
                           (REAL) strtod(stringptr, &stringptr));
        }
  #endif /* not TRILIBRARY */
      }
  
      if (b->vararea) {
  #ifdef TRILIBRARY
        area = trianglearealist[elementnumber - b->firstnumber];
  #else /* not TRILIBRARY */
        /* Read an area constraint from the .area file. */
        stringptr = readline(inputline, areafile, areafilename);
        stringptr = findfield(stringptr);
        if (*stringptr == '\0') {
          area = -1.0;                      /* No constraint on this triangle. */
        } else {
          area = (REAL) strtod(stringptr, &stringptr);
        }
  #endif /* not TRILIBRARY */
        setareabound(triangleloop, area);
      }
  
      /* Set the triangle's vertices. */
      triangleloop.orient = 0;
      setorg(triangleloop, getvertex(m, b, corner[0]));
      setdest(triangleloop, getvertex(m, b, corner[1]));
      setapex(triangleloop, getvertex(m, b, corner[2]));
      /* Try linking the triangle to others that share these vertices. */
      for (triangleloop.orient = 0; triangleloop.orient < 3;
           triangleloop.orient++) {
        /* Take the number for the origin of triangleloop. */
        aroundvertex = corner[triangleloop.orient];
        /* Look for other triangles having this vertex. */
        nexttri = vertexarray[aroundvertex - b->firstnumber];
        /* Link the current triangle to the next one in the stack. */
        triangleloop.tri[6 + triangleloop.orient] = nexttri;
        /* Push the current triangle onto the stack. */
        vertexarray[aroundvertex - b->firstnumber] = encode(triangleloop);
        decode(nexttri, checktri);
        if (checktri.tri != m->dummytri) {
          dest(triangleloop, tdest);
          apex(triangleloop, tapex);
          /* Look for other triangles that share an edge. */
          do {
            dest(checktri, checkdest);
            apex(checktri, checkapex);
            if (tapex == checkdest) {
              /* The two triangles share an edge; bond them together. */
              lprev(triangleloop, triangleleft);
              bond(triangleleft, checktri);
            }
            if (tdest == checkapex) {
              /* The two triangles share an edge; bond them together. */
              lprev(checktri, checkleft);
              bond(triangleloop, checkleft);
            }
            /* Find the next triangle in the stack. */
            nexttri = checktri.tri[6 + checktri.orient];
            decode(nexttri, checktri);
          } while (checktri.tri != m->dummytri);
        }
      }
      triangleloop.tri = triangletraverse(m);
      elementnumber++;
    }
  
  #ifdef TRILIBRARY
    vertexindex = 0;
  #else /* not TRILIBRARY */
    fclose(elefile);
    if (b->vararea) {
      fclose(areafile);
    }
  #endif /* not TRILIBRARY */
  
    hullsize = 0;                      /* Prepare to count the boundary edges. */
    if (b->poly) {
      if (b->verbose) {
        printf("  Marking segments in triangulation.\n");
      }
      /* Read the segments from the .poly file, and link them */
      /*   to their neighboring triangles.                    */
      boundmarker = 0;
      traversalinit(&m->subsegs);
      subsegloop.ss = subsegtraverse(m);
      segmentnumber = b->firstnumber;
      while (subsegloop.ss != (subseg *) NULL) {
  #ifdef TRILIBRARY
        end[0] = segmentlist[vertexindex++];
        end[1] = segmentlist[vertexindex++];
        if (segmentmarkers) {
          boundmarker = segmentmarkerlist[segmentnumber - b->firstnumber];
        }
  #else /* not TRILIBRARY */
        /* Read the endpoints of each segment, and possibly a boundary marker. */
        stringptr = readline(inputline, polyfile, b->inpolyfilename);
        /* Skip the first (segment number) field. */
        stringptr = findfield(stringptr);
        if (*stringptr == '\0') {
          printf("Error:  Segment %ld has no endpoints in %s.\n", segmentnumber,
                 polyfilename);
          triexit(1);
        } else {
          end[0] = (int) strtol(stringptr, &stringptr, 0);
        }
        stringptr = findfield(stringptr);
        if (*stringptr == '\0') {
          printf("Error:  Segment %ld is missing its second endpoint in %s.\n",
                 segmentnumber, polyfilename);
          triexit(1);
        } else {
          end[1] = (int) strtol(stringptr, &stringptr, 0);
        }
        if (segmentmarkers) {
          stringptr = findfield(stringptr);
          if (*stringptr == '\0') {
            boundmarker = 0;
          } else {
            boundmarker = (int) strtol(stringptr, &stringptr, 0);
          }
        }
  #endif /* not TRILIBRARY */
        for (j = 0; j < 2; j++) {
          if ((end[j] < b->firstnumber) ||
              (end[j] >= b->firstnumber + m->invertices)) {
            printf("Error:  Segment %ld has an invalid vertex index.\n", 
                   segmentnumber);
            triexit(1);
          }
        }
  
        /* set the subsegment's vertices. */
        subsegloop.ssorient = 0;
        segmentorg = getvertex(m, b, end[0]);
        segmentdest = getvertex(m, b, end[1]);
        setsorg(subsegloop, segmentorg);
        setsdest(subsegloop, segmentdest);
        setsegorg(subsegloop, segmentorg);
        setsegdest(subsegloop, segmentdest);
        setmark(subsegloop, boundmarker);
        /* Try linking the subsegment to triangles that share these vertices. */
        for (subsegloop.ssorient = 0; subsegloop.ssorient < 2;
             subsegloop.ssorient++) {
          /* Take the number for the destination of subsegloop. */
          aroundvertex = end[1 - subsegloop.ssorient];
          /* Look for triangles having this vertex. */
          prevlink = &vertexarray[aroundvertex - b->firstnumber];
          nexttri = vertexarray[aroundvertex - b->firstnumber];
          decode(nexttri, checktri);
          sorg(subsegloop, shorg);
          notfound = 1;
          /* Look for triangles having this edge.  Note that I'm only       */
          /*   comparing each triangle's destination with the subsegment;   */
          /*   each triangle's apex is handled through a different vertex.  */
          /*   Because each triangle appears on three vertices' lists, each */
          /*   occurrence of a triangle on a list can (and does) represent  */
          /*   an edge.  In this way, most edges are represented twice, and */
          /*   every triangle-subsegment bond is represented once.          */
          while (notfound && (checktri.tri != m->dummytri)) {
            dest(checktri, checkdest);
            if (shorg == checkdest) {
              /* We have a match.  Remove this triangle from the list. */
              *prevlink = checktri.tri[6 + checktri.orient];
              /* Bond the subsegment to the triangle. */
              tsbond(checktri, subsegloop);
              /* Check if this is a boundary edge. */
              sym(checktri, checkneighbor);
              if (checkneighbor.tri == m->dummytri) {
                /* The next line doesn't insert a subsegment (because there's */
                /*   already one there), but it sets the boundary markers of  */
                /*   the existing subsegment and its vertices.                */
                insertsubseg(m, b, &checktri, 1);
                hullsize++;
              }
              notfound = 0;
            }
            /* Find the next triangle in the stack. */
            prevlink = &checktri.tri[6 + checktri.orient];
            nexttri = checktri.tri[6 + checktri.orient];
            decode(nexttri, checktri);
          }
        }
        subsegloop.ss = subsegtraverse(m);
        segmentnumber++;
      }
    }
  
    /* Mark the remaining edges as not being attached to any subsegment. */
    /* Also, count the (yet uncounted) boundary edges.                   */
    for (i = 0; i < m->vertices.items; i++) {
      /* Search the stack of triangles adjacent to a vertex. */
      nexttri = vertexarray[i];
      decode(nexttri, checktri);
      while (checktri.tri != m->dummytri) {
        /* Find the next triangle in the stack before this */
        /*   information gets overwritten.                 */
        nexttri = checktri.tri[6 + checktri.orient];
        /* No adjacent subsegment.  (This overwrites the stack info.) */
        tsdissolve(checktri);
        sym(checktri, checkneighbor);
        if (checkneighbor.tri == m->dummytri) {
          insertsubseg(m, b, &checktri, 1);
          hullsize++;
        }
        decode(nexttri, checktri);
      }
    }
  
    trifree((TRIVOID *) vertexarray);
    return hullsize;
  }
  
  #endif /* not CDT_ONLY */
  
  /**                                                                         **/
  /**                                                                         **/
  /********* General mesh construction routines end here               *********/
  
  /********* Segment insertion begins here                             *********/
  /**                                                                         **/
  /**                                                                         **/
  
  /*****************************************************************************/
  /*                                                                           */
  /*  finddirection()   Find the first triangle on the path from one point     */
  /*                    to another.                                            */
  /*                                                                           */
  /*  Finds the triangle that intersects a line segment drawn from the         */
  /*  origin of `searchtri' to the point `searchpoint', and returns the result */
  /*  in `searchtri'.  The origin of `searchtri' does not change, even though  */
  /*  the triangle returned may differ from the one passed in.  This routine   */
  /*  is used to find the direction to move in to get from one point to        */
  /*  another.                                                                 */
  /*                                                                           */
  /*  The return value notes whether the destination or apex of the found      */
  /*  triangle is collinear with the two points in question.                   */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  enum finddirectionresult finddirection(struct mesh *m, struct behavior *b,
                                         struct otri *searchtri,
                                         vertex searchpoint)
  #else /* not ANSI_DECLARATORS */
  enum finddirectionresult finddirection(m, b, searchtri, searchpoint)
  struct mesh *m;
  struct behavior *b;
  struct otri *searchtri;
  vertex searchpoint;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct otri checktri;
    vertex startvertex;
    vertex leftvertex, rightvertex;
    REAL leftccw, rightccw;
    int leftflag, rightflag;
    triangle ptr;           /* Temporary variable used by onext() and oprev(). */
  
    org(*searchtri, startvertex);
    dest(*searchtri, rightvertex);
    apex(*searchtri, leftvertex);
    /* Is `searchpoint' to the left? */
    leftccw = counterclockwise(m, b, searchpoint, startvertex, leftvertex);
    leftflag = leftccw > 0.0;
    /* Is `searchpoint' to the right? */
    rightccw = counterclockwise(m, b, startvertex, searchpoint, rightvertex);
    rightflag = rightccw > 0.0;
    if (leftflag && rightflag) {
      /* `searchtri' faces directly away from `searchpoint'.  We could go left */
      /*   or right.  Ask whether it's a triangle or a boundary on the left.   */
      onext(*searchtri, checktri);
      if (checktri.tri == m->dummytri) {
        leftflag = 0;
      } else {
        rightflag = 0;
      }
    }
    while (leftflag) {
      /* Turn left until satisfied. */
      onextself(*searchtri);
      if (searchtri->tri == m->dummytri) {
        printf("Internal error in finddirection():  Unable to find a\n");
        printf("  triangle leading from (%.12g, %.12g) to", startvertex[0],
               startvertex[1]);
        printf("  (%.12g, %.12g).\n", searchpoint[0], searchpoint[1]);
        internalerror();
      }
      apex(*searchtri, leftvertex);
      rightccw = leftccw;
      leftccw = counterclockwise(m, b, searchpoint, startvertex, leftvertex);
      leftflag = leftccw > 0.0;
    }
    while (rightflag) {
      /* Turn right until satisfied. */
      oprevself(*searchtri);
      if (searchtri->tri == m->dummytri) {
        printf("Internal error in finddirection():  Unable to find a\n");
        printf("  triangle leading from (%.12g, %.12g) to", startvertex[0],
               startvertex[1]);
        printf("  (%.12g, %.12g).\n", searchpoint[0], searchpoint[1]);
        internalerror();
      }
      dest(*searchtri, rightvertex);
      leftccw = rightccw;
      rightccw = counterclockwise(m, b, startvertex, searchpoint, rightvertex);
      rightflag = rightccw > 0.0;
    }
    if (leftccw == 0.0) {
      return LEFTCOLLINEAR;
    } else if (rightccw == 0.0) {
      return RIGHTCOLLINEAR;
    } else {
      return WITHIN;
    }
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  segmentintersection()   Find the intersection of an existing segment     */
  /*                          and a segment that is being inserted.  Insert    */
  /*                          a vertex at the intersection, splitting an       */
  /*                          existing subsegment.                             */
  /*                                                                           */
  /*  The segment being inserted connects the apex of splittri to endpoint2.   */
  /*  splitsubseg is the subsegment being split, and MUST adjoin splittri.     */
  /*  Hence, endpoints of the subsegment being split are the origin and        */
  /*  destination of splittri.                                                 */
  /*                                                                           */
  /*  On completion, splittri is a handle having the newly inserted            */
  /*  intersection point as its origin, and endpoint1 as its destination.      */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  void segmentintersection(struct mesh *m, struct behavior *b,
                           struct otri *splittri, struct osub *splitsubseg,
                           vertex endpoint2)
  #else /* not ANSI_DECLARATORS */
  void segmentintersection(m, b, splittri, splitsubseg, endpoint2)
  struct mesh *m;
  struct behavior *b;
  struct otri *splittri;
  struct osub *splitsubseg;
  vertex endpoint2;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct osub opposubseg;
    vertex endpoint1;
    vertex torg, tdest;
    vertex leftvertex, rightvertex;
    vertex newvertex;
    enum insertvertexresult success;
    enum finddirectionresult collinear;
    REAL ex, ey;
    REAL tx, ty;
    REAL etx, ety;
    REAL split, denom;
    int i;
    triangle ptr;                       /* Temporary variable used by onext(). */
    subseg sptr;                        /* Temporary variable used by snext(). */
  
    /* Find the other three segment endpoints. */
    apex(*splittri, endpoint1);
    org(*splittri, torg);
    dest(*splittri, tdest);
    /* Segment intersection formulae; see the Antonio reference. */
    tx = tdest[0] - torg[0];
    ty = tdest[1] - torg[1];
    ex = endpoint2[0] - endpoint1[0];
    ey = endpoint2[1] - endpoint1[1];
    etx = torg[0] - endpoint2[0];
    ety = torg[1] - endpoint2[1];
    denom = ty * ex - tx * ey;
    if (denom == 0.0) {
      printf("Internal error in segmentintersection():");
      printf("  Attempt to find intersection of parallel segments.\n");
      internalerror();
    }
    split = (ey * etx - ex * ety) / denom;
    /* Create the new vertex. */
    newvertex = (vertex) poolalloc(&m->vertices);
    /* Interpolate its coordinate and attributes. */
    for (i = 0; i < 2 + m->nextras; i++) {
      newvertex[i] = torg[i] + split * (tdest[i] - torg[i]);
    }
    setvertexmark(newvertex, mark(*splitsubseg));
    setvertextype(newvertex, INPUTVERTEX);
    if (b->verbose > 1) {
      printf(
    "  Splitting subsegment (%.12g, %.12g) (%.12g, %.12g) at (%.12g, %.12g).\n",
             torg[0], torg[1], tdest[0], tdest[1], newvertex[0], newvertex[1]);
    }
    /* Insert the intersection vertex.  This should always succeed. */
    success = insertvertex(m, b, newvertex, splittri, splitsubseg, 0, 0);
    if (success != SUCCESSFULVERTEX) {
      printf("Internal error in segmentintersection():\n");
      printf("  Failure to split a segment.\n");
      internalerror();
    }
    /* Record a triangle whose origin is the new vertex. */
    setvertex2tri(newvertex, encode(*splittri));
    if (m->steinerleft > 0) {
      m->steinerleft--;
    }
  
    /* Divide the segment into two, and correct the segment endpoints. */
    ssymself(*splitsubseg);
    spivot(*splitsubseg, opposubseg);
    sdissolve(*splitsubseg);
    sdissolve(opposubseg);
    do {
      setsegorg(*splitsubseg, newvertex);
      snextself(*splitsubseg);
    } while (splitsubseg->ss != m->dummysub);
    do {
      setsegorg(opposubseg, newvertex);
      snextself(opposubseg);
    } while (opposubseg.ss != m->dummysub);
  
    /* Inserting the vertex may have caused edge flips.  We wish to rediscover */
    /*   the edge connecting endpoint1 to the new intersection vertex.         */
    collinear = finddirection(m, b, splittri, endpoint1);
    dest(*splittri, rightvertex);
    apex(*splittri, leftvertex);
    if ((leftvertex[0] == endpoint1[0]) && (leftvertex[1] == endpoint1[1])) {
      onextself(*splittri);
    } else if ((rightvertex[0] != endpoint1[0]) ||
               (rightvertex[1] != endpoint1[1])) {
      printf("Internal error in segmentintersection():\n");
      printf("  Topological inconsistency after splitting a segment.\n");
      internalerror();
    }
    /* `splittri' should have destination endpoint1. */
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  scoutsegment()   Scout the first triangle on the path from one endpoint  */
  /*                   to another, and check for completion (reaching the      */
  /*                   second endpoint), a collinear vertex, or the            */
  /*                   intersection of two segments.                           */
  /*                                                                           */
  /*  Returns one if the entire segment is successfully inserted, and zero if  */
  /*  the job must be finished by conformingedge() or constrainededge().       */
  /*                                                                           */
  /*  If the first triangle on the path has the second endpoint as its         */
  /*  destination or apex, a subsegment is inserted and the job is done.       */
  /*                                                                           */
  /*  If the first triangle on the path has a destination or apex that lies on */
  /*  the segment, a subsegment is inserted connecting the first endpoint to   */
  /*  the collinear vertex, and the search is continued from the collinear     */
  /*  vertex.                                                                  */
  /*                                                                           */
  /*  If the first triangle on the path has a subsegment opposite its origin,  */
  /*  then there is a segment that intersects the segment being inserted.      */
  /*  Their intersection vertex is inserted, splitting the subsegment.         */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  int scoutsegment(struct mesh *m, struct behavior *b, struct otri *searchtri,
                   vertex endpoint2, int newmark)
  #else /* not ANSI_DECLARATORS */
  int scoutsegment(m, b, searchtri, endpoint2, newmark)
  struct mesh *m;
  struct behavior *b;
  struct otri *searchtri;
  vertex endpoint2;
  int newmark;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct otri crosstri;
    struct osub crosssubseg;
    vertex leftvertex, rightvertex;
    enum finddirectionresult collinear;
    subseg sptr;                      /* Temporary variable used by tspivot(). */
  
    collinear = finddirection(m, b, searchtri, endpoint2);
    dest(*searchtri, rightvertex);
    apex(*searchtri, leftvertex);
    if (((leftvertex[0] == endpoint2[0]) && (leftvertex[1] == endpoint2[1])) ||
        ((rightvertex[0] == endpoint2[0]) && (rightvertex[1] == endpoint2[1]))) {
      /* The segment is already an edge in the mesh. */
      if ((leftvertex[0] == endpoint2[0]) && (leftvertex[1] == endpoint2[1])) {
        lprevself(*searchtri);
      }
      /* Insert a subsegment, if there isn't already one there. */
      insertsubseg(m, b, searchtri, newmark);
      return 1;
    } else if (collinear == LEFTCOLLINEAR) {
      /* We've collided with a vertex between the segment's endpoints. */
      /* Make the collinear vertex be the triangle's origin. */
      lprevself(*searchtri);
      insertsubseg(m, b, searchtri, newmark);
      /* Insert the remainder of the segment. */
      return scoutsegment(m, b, searchtri, endpoint2, newmark);
    } else if (collinear == RIGHTCOLLINEAR) {
      /* We've collided with a vertex between the segment's endpoints. */
      insertsubseg(m, b, searchtri, newmark);
      /* Make the collinear vertex be the triangle's origin. */
      lnextself(*searchtri);
      /* Insert the remainder of the segment. */
      return scoutsegment(m, b, searchtri, endpoint2, newmark);
    } else {
      lnext(*searchtri, crosstri);
      tspivot(crosstri, crosssubseg);
      /* Check for a crossing segment. */
      if (crosssubseg.ss == m->dummysub) {
        return 0;
      } else {
        /* Insert a vertex at the intersection. */
        segmentintersection(m, b, &crosstri, &crosssubseg, endpoint2);
        otricopy(crosstri, *searchtri);
        insertsubseg(m, b, searchtri, newmark);
        /* Insert the remainder of the segment. */
        return scoutsegment(m, b, searchtri, endpoint2, newmark);
      }
    }
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  conformingedge()   Force a segment into a conforming Delaunay            */
  /*                     triangulation by inserting a vertex at its midpoint,  */
  /*                     and recursively forcing in the two half-segments if   */
  /*                     necessary.                                            */
  /*                                                                           */
  /*  Generates a sequence of subsegments connecting `endpoint1' to            */
  /*  `endpoint2'.  `newmark' is the boundary marker of the segment, assigned  */
  /*  to each new splitting vertex and subsegment.                             */
  /*                                                                           */
  /*  Note that conformingedge() does not always maintain the conforming       */
  /*  Delaunay property.  Once inserted, segments are locked into place;       */
  /*  vertices inserted later (to force other segments in) may render these    */
  /*  fixed segments non-Delaunay.  The conforming Delaunay property will be   */
  /*  restored by enforcequality() by splitting encroached subsegments.        */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifndef REDUCED
  #ifndef CDT_ONLY
  
  #ifdef ANSI_DECLARATORS
  void conformingedge(struct mesh *m, struct behavior *b,
                      vertex endpoint1, vertex endpoint2, int newmark)
  #else /* not ANSI_DECLARATORS */
  void conformingedge(m, b, endpoint1, endpoint2, newmark)
  struct mesh *m;
  struct behavior *b;
  vertex endpoint1;
  vertex endpoint2;
  int newmark;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct otri searchtri1, searchtri2;
    struct osub brokensubseg;
    vertex newvertex;
    vertex midvertex1, midvertex2;
    enum insertvertexresult success;
    int i;
    subseg sptr;                      /* Temporary variable used by tspivot(). */
  
    if (b->verbose > 2) {
      printf("Forcing segment into triangulation by recursive splitting:\n");
      printf("  (%.12g, %.12g) (%.12g, %.12g)\n", endpoint1[0], endpoint1[1],
             endpoint2[0], endpoint2[1]);
    }
    /* Create a new vertex to insert in the middle of the segment. */
    newvertex = (vertex) poolalloc(&m->vertices);
    /* Interpolate coordinates and attributes. */
    for (i = 0; i < 2 + m->nextras; i++) {
      newvertex[i] = 0.5 * (endpoint1[i] + endpoint2[i]);
    }
    setvertexmark(newvertex, newmark);
    setvertextype(newvertex, SEGMENTVERTEX);
    /* No known triangle to search from. */
    searchtri1.tri = m->dummytri;
    /* Attempt to insert the new vertex. */
    success = insertvertex(m, b, newvertex, &searchtri1, (struct osub *) NULL,
                           0, 0);
    if (success == DUPLICATEVERTEX) {
      if (b->verbose > 2) {
        printf("  Segment intersects existing vertex (%.12g, %.12g).\n",
               newvertex[0], newvertex[1]);
      }
      /* Use the vertex that's already there. */
      vertexdealloc(m, newvertex);
      org(searchtri1, newvertex);
    } else {
      if (success == VIOLATINGVERTEX) {
        if (b->verbose > 2) {
          printf("  Two segments intersect at (%.12g, %.12g).\n",
                 newvertex[0], newvertex[1]);
        }
        /* By fluke, we've landed right on another segment.  Split it. */
        tspivot(searchtri1, brokensubseg);
        success = insertvertex(m, b, newvertex, &searchtri1, &brokensubseg,
                               0, 0);
        if (success != SUCCESSFULVERTEX) {
          printf("Internal error in conformingedge():\n");
          printf("  Failure to split a segment.\n");
          internalerror();
        }
      }
      /* The vertex has been inserted successfully. */
      if (m->steinerleft > 0) {
        m->steinerleft--;
      }
    }
    otricopy(searchtri1, searchtri2);
    /* `searchtri1' and `searchtri2' are fastened at their origins to         */
    /*   `newvertex', and will be directed toward `endpoint1' and `endpoint2' */
    /*   respectively.  First, we must get `searchtri2' out of the way so it  */
    /*   won't be invalidated during the insertion of the first half of the   */
    /*   segment.                                                             */
    finddirection(m, b, &searchtri2, endpoint2);
    if (!scoutsegment(m, b, &searchtri1, endpoint1, newmark)) {
      /* The origin of searchtri1 may have changed if a collision with an */
      /*   intervening vertex on the segment occurred.                    */
      org(searchtri1, midvertex1);
      conformingedge(m, b, midvertex1, endpoint1, newmark);
    }
    if (!scoutsegment(m, b, &searchtri2, endpoint2, newmark)) {
      /* The origin of searchtri2 may have changed if a collision with an */
      /*   intervening vertex on the segment occurred.                    */
      org(searchtri2, midvertex2);
      conformingedge(m, b, midvertex2, endpoint2, newmark);
    }
  }
  
  #endif /* not CDT_ONLY */
  #endif /* not REDUCED */
  
  /*****************************************************************************/
  /*                                                                           */
  /*  delaunayfixup()   Enforce the Delaunay condition at an edge, fanning out */
  /*                    recursively from an existing vertex.  Pay special      */
  /*                    attention to stacking inverted triangles.              */
  /*                                                                           */
  /*  This is a support routine for inserting segments into a constrained      */
  /*  Delaunay triangulation.                                                  */
  /*                                                                           */
  /*  The origin of fixuptri is treated as if it has just been inserted, and   */
  /*  the local Delaunay condition needs to be enforced.  It is only enforced  */
  /*  in one sector, however, that being the angular range defined by          */
  /*  fixuptri.                                                                */
  /*                                                                           */
  /*  This routine also needs to make decisions regarding the "stacking" of    */
  /*  triangles.  (Read the description of constrainededge() below before      */
  /*  reading on here, so you understand the algorithm.)  If the position of   */
  /*  the new vertex (the origin of fixuptri) indicates that the vertex before */
  /*  it on the polygon is a reflex vertex, then "stack" the triangle by       */
  /*  doing nothing.  (fixuptri is an inverted triangle, which is how stacked  */
  /*  triangles are identified.)                                               */
  /*                                                                           */
  /*  Otherwise, check whether the vertex before that was a reflex vertex.     */
  /*  If so, perform an edge flip, thereby eliminating an inverted triangle    */
  /*  (popping it off the stack).  The edge flip may result in the creation    */
  /*  of a new inverted triangle, depending on whether or not the new vertex   */
  /*  is visible to the vertex three edges behind on the polygon.              */
  /*                                                                           */
  /*  If neither of the two vertices behind the new vertex are reflex          */
  /*  vertices, fixuptri and fartri, the triangle opposite it, are not         */
  /*  inverted; hence, ensure that the edge between them is locally Delaunay.  */
  /*                                                                           */
  /*  `leftside' indicates whether or not fixuptri is to the left of the       */
  /*  segment being inserted.  (Imagine that the segment is pointing up from   */
  /*  endpoint1 to endpoint2.)                                                 */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  void delaunayfixup(struct mesh *m, struct behavior *b,
                     struct otri *fixuptri, int leftside)
  #else /* not ANSI_DECLARATORS */
  void delaunayfixup(m, b, fixuptri, leftside)
  struct mesh *m;
  struct behavior *b;
  struct otri *fixuptri;
  int leftside;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct otri neartri;
    struct otri fartri;
    struct osub faredge;
    vertex nearvertex, leftvertex, rightvertex, farvertex;
    triangle ptr;                         /* Temporary variable used by sym(). */
    subseg sptr;                      /* Temporary variable used by tspivot(). */
  
    lnext(*fixuptri, neartri);
    sym(neartri, fartri);
    /* Check if the edge opposite the origin of fixuptri can be flipped. */
    if (fartri.tri == m->dummytri) {
      return;
    }
    tspivot(neartri, faredge);
    if (faredge.ss != m->dummysub) {
      return;
    }
    /* Find all the relevant vertices. */
    apex(neartri, nearvertex);
    org(neartri, leftvertex);
    dest(neartri, rightvertex);
    apex(fartri, farvertex);
    /* Check whether the previous polygon vertex is a reflex vertex. */
    if (leftside) {
      if (counterclockwise(m, b, nearvertex, leftvertex, farvertex) <= 0.0) {
        /* leftvertex is a reflex vertex too.  Nothing can */
        /*   be done until a convex section is found.      */
        return;
      }
    } else {
      if (counterclockwise(m, b, farvertex, rightvertex, nearvertex) <= 0.0) {
        /* rightvertex is a reflex vertex too.  Nothing can */
        /*   be done until a convex section is found.       */
        return;
      }
    }
    if (counterclockwise(m, b, rightvertex, leftvertex, farvertex) > 0.0) {
      /* fartri is not an inverted triangle, and farvertex is not a reflex */
      /*   vertex.  As there are no reflex vertices, fixuptri isn't an     */
      /*   inverted triangle, either.  Hence, test the edge between the    */
      /*   triangles to ensure it is locally Delaunay.                     */
      if (incircle(m, b, leftvertex, farvertex, rightvertex, nearvertex) <=
          0.0) {
        return;
      }
      /* Not locally Delaunay; go on to an edge flip. */
    }        /* else fartri is inverted; remove it from the stack by flipping. */
    flip(m, b, &neartri);
    lprevself(*fixuptri);    /* Restore the origin of fixuptri after the flip. */
    /* Recursively process the two triangles that result from the flip. */
    delaunayfixup(m, b, fixuptri, leftside);
    delaunayfixup(m, b, &fartri, leftside);
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  constrainededge()   Force a segment into a constrained Delaunay          */
  /*                      triangulation by deleting the triangles it           */
  /*                      intersects, and triangulating the polygons that      */
  /*                      form on each side of it.                             */
  /*                                                                           */
  /*  Generates a single subsegment connecting `endpoint1' to `endpoint2'.     */
  /*  The triangle `starttri' has `endpoint1' as its origin.  `newmark' is the */
  /*  boundary marker of the segment.                                          */
  /*                                                                           */
  /*  To insert a segment, every triangle whose interior intersects the        */
  /*  segment is deleted.  The union of these deleted triangles is a polygon   */
  /*  (which is not necessarily monotone, but is close enough), which is       */
  /*  divided into two polygons by the new segment.  This routine's task is    */
  /*  to generate the Delaunay triangulation of these two polygons.            */
  /*                                                                           */
  /*  You might think of this routine's behavior as a two-step process.  The   */
  /*  first step is to walk from endpoint1 to endpoint2, flipping each edge    */
  /*  encountered.  This step creates a fan of edges connected to endpoint1,   */
  /*  including the desired edge to endpoint2.  The second step enforces the   */
  /*  Delaunay condition on each side of the segment in an incremental manner: */
  /*  proceeding along the polygon from endpoint1 to endpoint2 (this is done   */
  /*  independently on each side of the segment), each vertex is "enforced"    */
  /*  as if it had just been inserted, but affecting only the previous         */
  /*  vertices.  The result is the same as if the vertices had been inserted   */
  /*  in the order they appear on the polygon, so the result is Delaunay.      */
  /*                                                                           */
  /*  In truth, constrainededge() interleaves these two steps.  The procedure  */
  /*  walks from endpoint1 to endpoint2, and each time an edge is encountered  */
  /*  and flipped, the newly exposed vertex (at the far end of the flipped     */
  /*  edge) is "enforced" upon the previously flipped edges, usually affecting */
  /*  only one side of the polygon (depending upon which side of the segment   */
  /*  the vertex falls on).                                                    */
  /*                                                                           */
  /*  The algorithm is complicated by the need to handle polygons that are not */
  /*  convex.  Although the polygon is not necessarily monotone, it can be     */
  /*  triangulated in a manner similar to the stack-based algorithms for       */
  /*  monotone polygons.  For each reflex vertex (local concavity) of the      */
  /*  polygon, there will be an inverted triangle formed by one of the edge    */
  /*  flips.  (An inverted triangle is one with negative area - that is, its   */
  /*  vertices are arranged in clockwise order - and is best thought of as a   */
  /*  wrinkle in the fabric of the mesh.)  Each inverted triangle can be       */
  /*  thought of as a reflex vertex pushed on the stack, waiting to be fixed   */
  /*  later.                                                                   */
  /*                                                                           */
  /*  A reflex vertex is popped from the stack when a vertex is inserted that  */
  /*  is visible to the reflex vertex.  (However, if the vertex behind the     */
  /*  reflex vertex is not visible to the reflex vertex, a new inverted        */
  /*  triangle will take its place on the stack.)  These details are handled   */
  /*  by the delaunayfixup() routine above.                                    */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  void constrainededge(struct mesh *m, struct behavior *b,
                       struct otri *starttri, vertex endpoint2, int newmark)
  #else /* not ANSI_DECLARATORS */
  void constrainededge(m, b, starttri, endpoint2, newmark)
  struct mesh *m;
  struct behavior *b;
  struct otri *starttri;
  vertex endpoint2;
  int newmark;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct otri fixuptri, fixuptri2;
    struct osub crosssubseg;
    vertex endpoint1;
    vertex farvertex;
    REAL area;
    int collision;
    int done;
    triangle ptr;             /* Temporary variable used by sym() and oprev(). */
    subseg sptr;                      /* Temporary variable used by tspivot(). */
  
    org(*starttri, endpoint1);
    lnext(*starttri, fixuptri);
    flip(m, b, &fixuptri);
    /* `collision' indicates whether we have found a vertex directly */
    /*   between endpoint1 and endpoint2.                            */
    collision = 0;
    done = 0;
    do {
      org(fixuptri, farvertex);
      /* `farvertex' is the extreme point of the polygon we are "digging" */
      /*   to get from endpoint1 to endpoint2.                           */
      if ((farvertex[0] == endpoint2[0]) && (farvertex[1] == endpoint2[1])) {
        oprev(fixuptri, fixuptri2);
        /* Enforce the Delaunay condition around endpoint2. */
        delaunayfixup(m, b, &fixuptri, 0);
        delaunayfixup(m, b, &fixuptri2, 1);
        done = 1;
      } else {
        /* Check whether farvertex is to the left or right of the segment */
        /*   being inserted, to decide which edge of fixuptri to dig      */
        /*   through next.                                                */
        area = counterclockwise(m, b, endpoint1, endpoint2, farvertex);
        if (area == 0.0) {
          /* We've collided with a vertex between endpoint1 and endpoint2. */
          collision = 1;
          oprev(fixuptri, fixuptri2);
          /* Enforce the Delaunay condition around farvertex. */
          delaunayfixup(m, b, &fixuptri, 0);
          delaunayfixup(m, b, &fixuptri2, 1);
          done = 1;
        } else {
          if (area > 0.0) {        /* farvertex is to the left of the segment. */
            oprev(fixuptri, fixuptri2);
            /* Enforce the Delaunay condition around farvertex, on the */
            /*   left side of the segment only.                        */
            delaunayfixup(m, b, &fixuptri2, 1);
            /* Flip the edge that crosses the segment.  After the edge is */
            /*   flipped, one of its endpoints is the fan vertex, and the */
            /*   destination of fixuptri is the fan vertex.               */
            lprevself(fixuptri);
          } else {                /* farvertex is to the right of the segment. */
            delaunayfixup(m, b, &fixuptri, 0);
            /* Flip the edge that crosses the segment.  After the edge is */
            /*   flipped, one of its endpoints is the fan vertex, and the */
            /*   destination of fixuptri is the fan vertex.               */
            oprevself(fixuptri);
          }
          /* Check for two intersecting segments. */
          tspivot(fixuptri, crosssubseg);
          if (crosssubseg.ss == m->dummysub) {
            flip(m, b, &fixuptri);    /* May create inverted triangle at left. */
          } else {
            /* We've collided with a segment between endpoint1 and endpoint2. */
            collision = 1;
            /* Insert a vertex at the intersection. */
            segmentintersection(m, b, &fixuptri, &crosssubseg, endpoint2);
            done = 1;
          }
        }
      }
    } while (!done);
    /* Insert a subsegment to make the segment permanent. */
    insertsubseg(m, b, &fixuptri, newmark);
    /* If there was a collision with an interceding vertex, install another */
    /*   segment connecting that vertex with endpoint2.                     */
    if (collision) {
      /* Insert the remainder of the segment. */
      if (!scoutsegment(m, b, &fixuptri, endpoint2, newmark)) {
        constrainededge(m, b, &fixuptri, endpoint2, newmark);
      }
    }
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  insertsegment()   Insert a PSLG segment into a triangulation.            */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  void insertsegment(struct mesh *m, struct behavior *b,
                     vertex endpoint1, vertex endpoint2, int newmark)
  #else /* not ANSI_DECLARATORS */
  void insertsegment(m, b, endpoint1, endpoint2, newmark)
  struct mesh *m;
  struct behavior *b;
  vertex endpoint1;
  vertex endpoint2;
  int newmark;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct otri searchtri1, searchtri2;
    triangle encodedtri;
    vertex checkvertex;
    triangle ptr;                         /* Temporary variable used by sym(). */
  
    if (b->verbose > 1) {
      printf("  Connecting (%.12g, %.12g) to (%.12g, %.12g).\n",
             endpoint1[0], endpoint1[1], endpoint2[0], endpoint2[1]);
    }
  
    /* Find a triangle whose origin is the segment's first endpoint. */
    checkvertex = (vertex) NULL;
    encodedtri = vertex2tri(endpoint1);
    if (encodedtri != (triangle) NULL) {
      decode(encodedtri, searchtri1);
      org(searchtri1, checkvertex);
    }
    if (checkvertex != endpoint1) {
      /* Find a boundary triangle to search from. */
      searchtri1.tri = m->dummytri;
      searchtri1.orient = 0;
      symself(searchtri1);
      /* Search for the segment's first endpoint by point location. */
      if (locate(m, b, endpoint1, &searchtri1) != ONVERTEX) {
        printf(
          "Internal error in insertsegment():  Unable to locate PSLG vertex\n");
        printf("  (%.12g, %.12g) in triangulation.\n",
               endpoint1[0], endpoint1[1]);
        internalerror();
      }
    }
    /* Remember this triangle to improve subsequent point location. */
    otricopy(searchtri1, m->recenttri);
    /* Scout the beginnings of a path from the first endpoint */
    /*   toward the second.                                   */
    if (scoutsegment(m, b, &searchtri1, endpoint2, newmark)) {
      /* The segment was easily inserted. */
      return;
    }
    /* The first endpoint may have changed if a collision with an intervening */
    /*   vertex on the segment occurred.                                      */
    org(searchtri1, endpoint1);
  
    /* Find a triangle whose origin is the segment's second endpoint. */
    checkvertex = (vertex) NULL;
    encodedtri = vertex2tri(endpoint2);
    if (encodedtri != (triangle) NULL) {
      decode(encodedtri, searchtri2);
      org(searchtri2, checkvertex);
    }
    if (checkvertex != endpoint2) {
      /* Find a boundary triangle to search from. */
      searchtri2.tri = m->dummytri;
      searchtri2.orient = 0;
      symself(searchtri2);
      /* Search for the segment's second endpoint by point location. */
      if (locate(m, b, endpoint2, &searchtri2) != ONVERTEX) {
        printf(
          "Internal error in insertsegment():  Unable to locate PSLG vertex\n");
        printf("  (%.12g, %.12g) in triangulation.\n",
               endpoint2[0], endpoint2[1]);
        internalerror();
      }
    }
    /* Remember this triangle to improve subsequent point location. */
    otricopy(searchtri2, m->recenttri);
    /* Scout the beginnings of a path from the second endpoint */
    /*   toward the first.                                     */
    if (scoutsegment(m, b, &searchtri2, endpoint1, newmark)) {
      /* The segment was easily inserted. */
      return;
    }
    /* The second endpoint may have changed if a collision with an intervening */
    /*   vertex on the segment occurred.                                       */
    org(searchtri2, endpoint2);
  
  #ifndef REDUCED
  #ifndef CDT_ONLY
    if (b->splitseg) {
      /* Insert vertices to force the segment into the triangulation. */
      conformingedge(m, b, endpoint1, endpoint2, newmark);
    } else {
  #endif /* not CDT_ONLY */
  #endif /* not REDUCED */
      /* Insert the segment directly into the triangulation. */
      constrainededge(m, b, &searchtri1, endpoint2, newmark);
  #ifndef REDUCED
  #ifndef CDT_ONLY
    }
  #endif /* not CDT_ONLY */
  #endif /* not REDUCED */
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  markhull()   Cover the convex hull of a triangulation with subsegments.  */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  void markhull(struct mesh *m, struct behavior *b)
  #else /* not ANSI_DECLARATORS */
  void markhull(m, b)
  struct mesh *m;
  struct behavior *b;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct otri hulltri;
    struct otri nexttri;
    struct otri starttri;
    triangle ptr;             /* Temporary variable used by sym() and oprev(). */
  
    /* Find a triangle handle on the hull. */
    hulltri.tri = m->dummytri;
    hulltri.orient = 0;
    symself(hulltri);
    /* Remember where we started so we know when to stop. */
    otricopy(hulltri, starttri);
    /* Go once counterclockwise around the convex hull. */
    do {
      /* Create a subsegment if there isn't already one here. */
      insertsubseg(m, b, &hulltri, 1);
      /* To find the next hull edge, go clockwise around the next vertex. */
      lnextself(hulltri);
      oprev(hulltri, nexttri);
      while (nexttri.tri != m->dummytri) {
        otricopy(nexttri, hulltri);
        oprev(hulltri, nexttri);
      }
    } while (!otriequal(hulltri, starttri));
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  formskeleton()   Create the segments of a triangulation, including PSLG  */
  /*                   segments and edges on the convex hull.                  */
  /*                                                                           */
  /*  The PSLG segments are read from a .poly file.  The return value is the   */
  /*  number of segments in the file.                                          */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef TRILIBRARY
  
  #ifdef ANSI_DECLARATORS
  void formskeleton(struct mesh *m, struct behavior *b, int *segmentlist,
                    int *segmentmarkerlist, int numberofsegments)
  #else /* not ANSI_DECLARATORS */
  void formskeleton(m, b, segmentlist, segmentmarkerlist, numberofsegments)
  struct mesh *m;
  struct behavior *b;
  int *segmentlist;
  int *segmentmarkerlist;
  int numberofsegments;
  #endif /* not ANSI_DECLARATORS */
  
  #else /* not TRILIBRARY */
  
  #ifdef ANSI_DECLARATORS
  void formskeleton(struct mesh *m, struct behavior *b,
                    FILE *polyfile, char *polyfilename)
  #else /* not ANSI_DECLARATORS */
  void formskeleton(m, b, polyfile, polyfilename)
  struct mesh *m;
  struct behavior *b;
  FILE *polyfile;
  char *polyfilename;
  #endif /* not ANSI_DECLARATORS */
  
  #endif /* not TRILIBRARY */
  
  {
  #ifdef TRILIBRARY
    char polyfilename[6];
    int index;
  #else /* not TRILIBRARY */
    char inputline[INPUTLINESIZE];
    char *stringptr;
  #endif /* not TRILIBRARY */
    vertex endpoint1, endpoint2;
    int segmentmarkers;
    int end1, end2;
    int boundmarker;
    int i;
  
    if (b->poly) {
      if (!b->quiet) {
        printf("Recovering segments in Delaunay triangulation.\n");
      }
  #ifdef TRILIBRARY
      strcpy(polyfilename, "input");
      m->insegments = numberofsegments;
      segmentmarkers = segmentmarkerlist != (int *) NULL;
      index = 0;
  #else /* not TRILIBRARY */
      /* Read the segments from a .poly file. */
      /* Read number of segments and number of boundary markers. */
      stringptr = readline(inputline, polyfile, polyfilename);
      m->insegments = (int) strtol(stringptr, &stringptr, 0);
      stringptr = findfield(stringptr);
      if (*stringptr == '\0') {
        segmentmarkers = 0;
      } else {
        segmentmarkers = (int) strtol(stringptr, &stringptr, 0);
      }
  #endif /* not TRILIBRARY */
      /* If the input vertices are collinear, there is no triangulation, */
      /*   so don't try to insert segments.                              */
      if (m->triangles.items == 0) {
        return;
      }
  
      /* If segments are to be inserted, compute a mapping */
      /*   from vertices to triangles.                     */
      if (m->insegments > 0) {
        makevertexmap(m, b);
        if (b->verbose) {
          printf("  Recovering PSLG segments.\n");
        }
      }
  
      boundmarker = 0;
      /* Read and insert the segments. */
      for (i = 0; i < m->insegments; i++) {
  #ifdef TRILIBRARY
        end1 = segmentlist[index++];
        end2 = segmentlist[index++];
        if (segmentmarkers) {
          boundmarker = segmentmarkerlist[i];
        }
  #else /* not TRILIBRARY */
        stringptr = readline(inputline, polyfile, b->inpolyfilename);
        stringptr = findfield(stringptr);
        if (*stringptr == '\0') {
          printf("Error:  Segment %d has no endpoints in %s.\n",
                 b->firstnumber + i, polyfilename);
          triexit(1);
        } else {
          end1 = (int) strtol(stringptr, &stringptr, 0);
        }
        stringptr = findfield(stringptr);
        if (*stringptr == '\0') {
          printf("Error:  Segment %d is missing its second endpoint in %s.\n",
                 b->firstnumber + i, polyfilename);
          triexit(1);
        } else {
          end2 = (int) strtol(stringptr, &stringptr, 0);
        }
        if (segmentmarkers) {
          stringptr = findfield(stringptr);
          if (*stringptr == '\0') {
            boundmarker = 0;
          } else {
            boundmarker = (int) strtol(stringptr, &stringptr, 0);
          }
        }
  #endif /* not TRILIBRARY */
        if ((end1 < b->firstnumber) ||
            (end1 >= b->firstnumber + m->invertices)) {
          if (!b->quiet) {
            printf("Warning:  Invalid first endpoint of segment %d in %s.\n",
                   b->firstnumber + i, polyfilename);
          }
        } else if ((end2 < b->firstnumber) ||
                   (end2 >= b->firstnumber + m->invertices)) {
          if (!b->quiet) {
            printf("Warning:  Invalid second endpoint of segment %d in %s.\n",
                   b->firstnumber + i, polyfilename);
          }
        } else {
          /* Find the vertices numbered `end1' and `end2'. */
          endpoint1 = getvertex(m, b, end1);
          endpoint2 = getvertex(m, b, end2);
          if ((endpoint1[0] == endpoint2[0]) && (endpoint1[1] == endpoint2[1])) {
            if (!b->quiet) {
              printf("Warning:  Endpoints of segment %d are coincident in %s.\n",
                     b->firstnumber + i, polyfilename);
            }
          } else {
            insertsegment(m, b, endpoint1, endpoint2, boundmarker);
          }
        }
      }
    } else {
      m->insegments = 0;
    }
    if (b->convex || !b->poly) {
      /* Enclose the convex hull with subsegments. */
      if (b->verbose) {
        printf("  Enclosing convex hull with segments.\n");
      }
      markhull(m, b);
    }
  }
  
  /**                                                                         **/
  /**                                                                         **/
  /********* Segment insertion ends here                               *********/
  
  /********* Carving out holes and concavities begins here             *********/
  /**                                                                         **/
  /**                                                                         **/
  
  /*****************************************************************************/
  /*                                                                           */
  /*  infecthull()   Virally infect all of the triangles of the convex hull    */
  /*                 that are not protected by subsegments.  Where there are   */
  /*                 subsegments, set boundary markers as appropriate.         */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  void infecthull(struct mesh *m, struct behavior *b)
  #else /* not ANSI_DECLARATORS */
  void infecthull(m, b)
  struct mesh *m;
  struct behavior *b;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct otri hulltri;
    struct otri nexttri;
    struct otri starttri;
    struct osub hullsubseg;
    triangle **deadtriangle;
    vertex horg, hdest;
    triangle ptr;                         /* Temporary variable used by sym(). */
    subseg sptr;                      /* Temporary variable used by tspivot(). */
  
    if (b->verbose) {
      printf("  Marking concavities (external triangles) for elimination.\n");
    }
    /* Find a triangle handle on the hull. */
    hulltri.tri = m->dummytri;
    hulltri.orient = 0;
    symself(hulltri);
    /* Remember where we started so we know when to stop. */
    otricopy(hulltri, starttri);
    /* Go once counterclockwise around the convex hull. */
    do {
      /* Ignore triangles that are already infected. */
      if (!infected(hulltri)) {
        /* Is the triangle protected by a subsegment? */
        tspivot(hulltri, hullsubseg);
        if (hullsubseg.ss == m->dummysub) {
          /* The triangle is not protected; infect it. */
          if (!infected(hulltri)) {
            infect(hulltri);
            deadtriangle = (triangle **) poolalloc(&m->viri);
            *deadtriangle = hulltri.tri;
          }
        } else {
          /* The triangle is protected; set boundary markers if appropriate. */
          if (mark(hullsubseg) == 0) {
            setmark(hullsubseg, 1);
            org(hulltri, horg);
            dest(hulltri, hdest);
            if (vertexmark(horg) == 0) {
              setvertexmark(horg, 1);
            }
            if (vertexmark(hdest) == 0) {
              setvertexmark(hdest, 1);
            }
          }
        }
      }
      /* To find the next hull edge, go clockwise around the next vertex. */
      lnextself(hulltri);
      oprev(hulltri, nexttri);
      while (nexttri.tri != m->dummytri) {
        otricopy(nexttri, hulltri);
        oprev(hulltri, nexttri);
      }
    } while (!otriequal(hulltri, starttri));
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  plague()   Spread the virus from all infected triangles to any neighbors */
  /*             not protected by subsegments.  Delete all infected triangles. */
  /*                                                                           */
  /*  This is the procedure that actually creates holes and concavities.       */
  /*                                                                           */
  /*  This procedure operates in two phases.  The first phase identifies all   */
  /*  the triangles that will die, and marks them as infected.  They are       */
  /*  marked to ensure that each triangle is added to the virus pool only      */
  /*  once, so the procedure will terminate.                                   */
  /*                                                                           */
  /*  The second phase actually eliminates the infected triangles.  It also    */
  /*  eliminates orphaned vertices.                                            */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  void plague(struct mesh *m, struct behavior *b)
  #else /* not ANSI_DECLARATORS */
  void plague(m, b)
  struct mesh *m;
  struct behavior *b;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct otri testtri;
    struct otri neighbor;
    triangle **virusloop;
    triangle **deadtriangle;
    struct osub neighborsubseg;
    vertex testvertex;
    vertex norg, ndest;
    vertex deadorg, deaddest, deadapex;
    int killorg;
    triangle ptr;             /* Temporary variable used by sym() and onext(). */
    subseg sptr;                      /* Temporary variable used by tspivot(). */
  
    if (b->verbose) {
      printf("  Marking neighbors of marked triangles.\n");
    }
    /* Loop through all the infected triangles, spreading the virus to */
    /*   their neighbors, then to their neighbors' neighbors.          */
    traversalinit(&m->viri);
    virusloop = (triangle **) traverse(&m->viri);
    while (virusloop != (triangle **) NULL) {
      testtri.tri = *virusloop;
      /* A triangle is marked as infected by messing with one of its pointers */
      /*   to subsegments, setting it to an illegal value.  Hence, we have to */
      /*   temporarily uninfect this triangle so that we can examine its      */
      /*   adjacent subsegments.                                              */
      uninfect(testtri);
      if (b->verbose > 2) {
        /* Assign the triangle an orientation for convenience in */
        /*   checking its vertices.                              */
        testtri.orient = 0;
        org(testtri, deadorg);
        dest(testtri, deaddest);
        apex(testtri, deadapex);
        printf("    Checking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
               deadorg[0], deadorg[1], deaddest[0], deaddest[1],
               deadapex[0], deadapex[1]);
      }
      /* Check each of the triangle's three neighbors. */
      for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
        /* Find the neighbor. */
        sym(testtri, neighbor);
        /* Check for a subsegment between the triangle and its neighbor. */
        tspivot(testtri, neighborsubseg);
        /* Check if the neighbor is nonexistent or already infected. */
        if ((neighbor.tri == m->dummytri) || infected(neighbor)) {
          if (neighborsubseg.ss != m->dummysub) {
            /* There is a subsegment separating the triangle from its      */
            /*   neighbor, but both triangles are dying, so the subsegment */
            /*   dies too.                                                 */
            subsegdealloc(m, neighborsubseg.ss);
            if (neighbor.tri != m->dummytri) {
              /* Make sure the subsegment doesn't get deallocated again */
              /*   later when the infected neighbor is visited.         */
              uninfect(neighbor);
              tsdissolve(neighbor);
              infect(neighbor);
            }
          }
        } else {                   /* The neighbor exists and is not infected. */
          if (neighborsubseg.ss == m->dummysub) {
            /* There is no subsegment protecting the neighbor, so */
            /*   the neighbor becomes infected.                   */
            if (b->verbose > 2) {
              org(neighbor, deadorg);
              dest(neighbor, deaddest);
              apex(neighbor, deadapex);
              printf(
                "    Marking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
                     deadorg[0], deadorg[1], deaddest[0], deaddest[1],
                     deadapex[0], deadapex[1]);
            }
            infect(neighbor);
            /* Ensure that the neighbor's neighbors will be infected. */
            deadtriangle = (triangle **) poolalloc(&m->viri);
            *deadtriangle = neighbor.tri;
          } else {               /* The neighbor is protected by a subsegment. */
            /* Remove this triangle from the subsegment. */
            stdissolve(neighborsubseg);
            /* The subsegment becomes a boundary.  Set markers accordingly. */
            if (mark(neighborsubseg) == 0) {
              setmark(neighborsubseg, 1);
            }
            org(neighbor, norg);
            dest(neighbor, ndest);
            if (vertexmark(norg) == 0) {
              setvertexmark(norg, 1);
            }
            if (vertexmark(ndest) == 0) {
              setvertexmark(ndest, 1);
            }
          }
        }
      }
      /* Remark the triangle as infected, so it doesn't get added to the */
      /*   virus pool again.                                             */
      infect(testtri);
      virusloop = (triangle **) traverse(&m->viri);
    }
  
    if (b->verbose) {
      printf("  Deleting marked triangles.\n");
    }
  
    traversalinit(&m->viri);
    virusloop = (triangle **) traverse(&m->viri);
    while (virusloop != (triangle **) NULL) {
      testtri.tri = *virusloop;
  
      /* Check each of the three corners of the triangle for elimination. */
      /*   This is done by walking around each vertex, checking if it is  */
      /*   still connected to at least one live triangle.                 */
      for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
        org(testtri, testvertex);
        /* Check if the vertex has already been tested. */
        if (testvertex != (vertex) NULL) {
          killorg = 1;
          /* Mark the corner of the triangle as having been tested. */
          setorg(testtri, NULL);
          /* Walk counterclockwise about the vertex. */
          onext(testtri, neighbor);
          /* Stop upon reaching a boundary or the starting triangle. */
          while ((neighbor.tri != m->dummytri) &&
                 (!otriequal(neighbor, testtri))) {
            if (infected(neighbor)) {
              /* Mark the corner of this triangle as having been tested. */
              setorg(neighbor, NULL);
            } else {
              /* A live triangle.  The vertex survives. */
              killorg = 0;
            }
            /* Walk counterclockwise about the vertex. */
            onextself(neighbor);
          }
          /* If we reached a boundary, we must walk clockwise as well. */
          if (neighbor.tri == m->dummytri) {
            /* Walk clockwise about the vertex. */
            oprev(testtri, neighbor);
            /* Stop upon reaching a boundary. */
            while (neighbor.tri != m->dummytri) {
              if (infected(neighbor)) {
              /* Mark the corner of this triangle as having been tested. */
                setorg(neighbor, NULL);
              } else {
                /* A live triangle.  The vertex survives. */
                killorg = 0;
              }
              /* Walk clockwise about the vertex. */
              oprevself(neighbor);
            }
          }
          if (killorg) {
            if (b->verbose > 1) {
              printf("    Deleting vertex (%.12g, %.12g)\n",
                     testvertex[0], testvertex[1]);
            }
            setvertextype(testvertex, UNDEADVERTEX);
            m->undeads++;
          }
        }
      }
  
      /* Record changes in the number of boundary edges, and disconnect */
      /*   dead triangles from their neighbors.                         */
      for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
        sym(testtri, neighbor);
        if (neighbor.tri == m->dummytri) {
          /* There is no neighboring triangle on this edge, so this edge    */
          /*   is a boundary edge.  This triangle is being deleted, so this */
          /*   boundary edge is deleted.                                    */
          m->hullsize--;
        } else {
          /* Disconnect the triangle from its neighbor. */
          dissolve(neighbor);
          /* There is a neighboring triangle on this edge, so this edge */
          /*   becomes a boundary edge when this triangle is deleted.   */
          m->hullsize++;
        }
      }
      /* Return the dead triangle to the pool of triangles. */
      triangledealloc(m, testtri.tri);
      virusloop = (triangle **) traverse(&m->viri);
    }
    /* Empty the virus pool. */
    poolrestart(&m->viri);
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  regionplague()   Spread regional attributes and/or area constraints      */
  /*                   (from a .poly file) throughout the mesh.                */
  /*                                                                           */
  /*  This procedure operates in two phases.  The first phase spreads an       */
  /*  attribute and/or an area constraint through a (segment-bounded) region.  */
  /*  The triangles are marked to ensure that each triangle is added to the    */
  /*  virus pool only once, so the procedure will terminate.                   */
  /*                                                                           */
  /*  The second phase uninfects all infected triangles, returning them to     */
  /*  normal.                                                                  */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  void regionplague(struct mesh *m, struct behavior *b,
                    REAL attribute, REAL area)
  #else /* not ANSI_DECLARATORS */
  void regionplague(m, b, attribute, area)
  struct mesh *m;
  struct behavior *b;
  REAL attribute;
  REAL area;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct otri testtri;
    struct otri neighbor;
    triangle **virusloop;
    triangle **regiontri;
    struct osub neighborsubseg;
    vertex regionorg, regiondest, regionapex;
    triangle ptr;             /* Temporary variable used by sym() and onext(). */
    subseg sptr;                      /* Temporary variable used by tspivot(). */
  
    if (b->verbose > 1) {
      printf("  Marking neighbors of marked triangles.\n");
    }
    /* Loop through all the infected triangles, spreading the attribute      */
    /*   and/or area constraint to their neighbors, then to their neighbors' */
    /*   neighbors.                                                          */
    traversalinit(&m->viri);
    virusloop = (triangle **) traverse(&m->viri);
    while (virusloop != (triangle **) NULL) {
      testtri.tri = *virusloop;
      /* A triangle is marked as infected by messing with one of its pointers */
      /*   to subsegments, setting it to an illegal value.  Hence, we have to */
      /*   temporarily uninfect this triangle so that we can examine its      */
      /*   adjacent subsegments.                                              */
      uninfect(testtri);
      if (b->regionattrib) {
        /* Set an attribute. */
        setelemattribute(testtri, m->eextras, attribute);
      }
      if (b->vararea) {
        /* Set an area constraint. */
        setareabound(testtri, area);
      }
      if (b->verbose > 2) {
        /* Assign the triangle an orientation for convenience in */
        /*   checking its vertices.                              */
        testtri.orient = 0;
        org(testtri, regionorg);
        dest(testtri, regiondest);
        apex(testtri, regionapex);
        printf("    Checking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
               regionorg[0], regionorg[1], regiondest[0], regiondest[1],
               regionapex[0], regionapex[1]);
      }
      /* Check each of the triangle's three neighbors. */
      for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
        /* Find the neighbor. */
        sym(testtri, neighbor);
        /* Check for a subsegment between the triangle and its neighbor. */
        tspivot(testtri, neighborsubseg);
        /* Make sure the neighbor exists, is not already infected, and */
        /*   isn't protected by a subsegment.                          */
        if ((neighbor.tri != m->dummytri) && !infected(neighbor)
            && (neighborsubseg.ss == m->dummysub)) {
          if (b->verbose > 2) {
            org(neighbor, regionorg);
            dest(neighbor, regiondest);
            apex(neighbor, regionapex);
            printf("    Marking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
                   regionorg[0], regionorg[1], regiondest[0], regiondest[1],
                   regionapex[0], regionapex[1]);
          }
          /* Infect the neighbor. */
          infect(neighbor);
          /* Ensure that the neighbor's neighbors will be infected. */
          regiontri = (triangle **) poolalloc(&m->viri);
          *regiontri = neighbor.tri;
        }
      }
      /* Remark the triangle as infected, so it doesn't get added to the */
      /*   virus pool again.                                             */
      infect(testtri);
      virusloop = (triangle **) traverse(&m->viri);
    }
  
    /* Uninfect all triangles. */
    if (b->verbose > 1) {
      printf("  Unmarking marked triangles.\n");
    }
    traversalinit(&m->viri);
    virusloop = (triangle **) traverse(&m->viri);
    while (virusloop != (triangle **) NULL) {
      testtri.tri = *virusloop;
      uninfect(testtri);
      virusloop = (triangle **) traverse(&m->viri);
    }
    /* Empty the virus pool. */
    poolrestart(&m->viri);
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  carveholes()   Find the holes and infect them.  Find the area            */
  /*                 constraints and infect them.  Infect the convex hull.     */
  /*                 Spread the infection and kill triangles.  Spread the      */
  /*                 area constraints.                                         */
  /*                                                                           */
  /*  This routine mainly calls other routines to carry out all these          */
  /*  functions.                                                               */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  void carveholes(struct mesh *m, struct behavior *b, REAL *holelist, int holes,
                  REAL *regionlist, int regions)
  #else /* not ANSI_DECLARATORS */
  void carveholes(m, b, holelist, holes, regionlist, regions)
  struct mesh *m;
  struct behavior *b;
  REAL *holelist;
  int holes;
  REAL *regionlist;
  int regions;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct otri searchtri;
    struct otri triangleloop;
    struct otri *regiontris;
    triangle **holetri;
    triangle **regiontri;
    vertex searchorg, searchdest;
    enum locateresult intersect;
    int i;
    triangle ptr;                         /* Temporary variable used by sym(). */
  
    if (!(b->quiet || (b->noholes && b->convex))) {
      printf("Removing unwanted triangles.\n");
      if (b->verbose && (holes > 0)) {
        printf("  Marking holes for elimination.\n");
      }
    }
  
    if (regions > 0) {
      /* Allocate storage for the triangles in which region points fall. */
      regiontris = (struct otri *) trimalloc(regions *
                                             (int) sizeof(struct otri));
    } else {
      regiontris = (struct otri *) NULL;
    }
  
    if (((holes > 0) && !b->noholes) || !b->convex || (regions > 0)) {
      /* Initialize a pool of viri to be used for holes, concavities, */
      /*   regional attributes, and/or regional area constraints.     */
      poolinit(&m->viri, sizeof(triangle *), VIRUSPERBLOCK, VIRUSPERBLOCK, 0);
    }
  
    if (!b->convex) {
      /* Mark as infected any unprotected triangles on the boundary. */
      /*   This is one way by which concavities are created.         */
      infecthull(m, b);
    }
  
    if ((holes > 0) && !b->noholes) {
      /* Infect each triangle in which a hole lies. */
      for (i = 0; i < 2 * holes; i += 2) {
        /* Ignore holes that aren't within the bounds of the mesh. */
        if ((holelist[i] >= m->xmin) && (holelist[i] <= m->xmax)
            && (holelist[i + 1] >= m->ymin) && (holelist[i + 1] <= m->ymax)) {
          /* Start searching from some triangle on the outer boundary. */
          searchtri.tri = m->dummytri;
          searchtri.orient = 0;
          symself(searchtri);
          /* Ensure that the hole is to the left of this boundary edge; */
          /*   otherwise, locate() will falsely report that the hole    */
          /*   falls within the starting triangle.                      */
          org(searchtri, searchorg);
          dest(searchtri, searchdest);
          if (counterclockwise(m, b, searchorg, searchdest, &holelist[i]) >
              0.0) {
            /* Find a triangle that contains the hole. */
            intersect = locate(m, b, &holelist[i], &searchtri);
            if ((intersect != OUTSIDE) && (!infected(searchtri))) {
              /* Infect the triangle.  This is done by marking the triangle  */
              /*   as infected and including the triangle in the virus pool. */
              infect(searchtri);
              holetri = (triangle **) poolalloc(&m->viri);
              *holetri = searchtri.tri;
            }
          }
        }
      }
    }
  
    /* Now, we have to find all the regions BEFORE we carve the holes, because */
    /*   locate() won't work when the triangulation is no longer convex.       */
    /*   (Incidentally, this is the reason why regional attributes and area    */
    /*   constraints can't be used when refining a preexisting mesh, which     */
    /*   might not be convex; they can only be used with a freshly             */
    /*   triangulated PSLG.)                                                   */
    if (regions > 0) {
      /* Find the starting triangle for each region. */
      for (i = 0; i < regions; i++) {
        regiontris[i].tri = m->dummytri;
        /* Ignore region points that aren't within the bounds of the mesh. */
        if ((regionlist[4 * i] >= m->xmin) && (regionlist[4 * i] <= m->xmax) &&
            (regionlist[4 * i + 1] >= m->ymin) &&
            (regionlist[4 * i + 1] <= m->ymax)) {
          /* Start searching from some triangle on the outer boundary. */
          searchtri.tri = m->dummytri;
          searchtri.orient = 0;
          symself(searchtri);
          /* Ensure that the region point is to the left of this boundary */
          /*   edge; otherwise, locate() will falsely report that the     */
          /*   region point falls within the starting triangle.           */
          org(searchtri, searchorg);
          dest(searchtri, searchdest);
          if (counterclockwise(m, b, searchorg, searchdest, &regionlist[4 * i]) >
              0.0) {
            /* Find a triangle that contains the region point. */
            intersect = locate(m, b, &regionlist[4 * i], &searchtri);
            if ((intersect != OUTSIDE) && (!infected(searchtri))) {
              /* Record the triangle for processing after the */
              /*   holes have been carved.                    */
              otricopy(searchtri, regiontris[i]);
            }
          }
        }
      }
    }
  
    if (m->viri.items > 0) {
      /* Carve the holes and concavities. */
      plague(m, b);
    }
    /* The virus pool should be empty now. */
  
    if (regions > 0) {
      if (!b->quiet) {
        if (b->regionattrib) {
          if (b->vararea) {
            printf("Spreading regional attributes and area constraints.\n");
          } else {
            printf("Spreading regional attributes.\n");
          }
        } else { 
          printf("Spreading regional area constraints.\n");
        }
      }
      if (b->regionattrib && !b->refine) {
        /* Assign every triangle a regional attribute of zero. */
        traversalinit(&m->triangles);
        triangleloop.orient = 0;
        triangleloop.tri = triangletraverse(m);
        while (triangleloop.tri != (triangle *) NULL) {
          setelemattribute(triangleloop, m->eextras, 0.0);
          triangleloop.tri = triangletraverse(m);
        }
      }
      for (i = 0; i < regions; i++) {
        if (regiontris[i].tri != m->dummytri) {
          /* Make sure the triangle under consideration still exists. */
          /*   It may have been eaten by the virus.                   */
          if (!deadtri(regiontris[i].tri)) {
            /* Put one triangle in the virus pool. */
            infect(regiontris[i]);
            regiontri = (triangle **) poolalloc(&m->viri);
            *regiontri = regiontris[i].tri;
            /* Apply one region's attribute and/or area constraint. */
            regionplague(m, b, regionlist[4 * i + 2], regionlist[4 * i + 3]);
            /* The virus pool should be empty now. */
          }
        }
      }
      if (b->regionattrib && !b->refine) {
        /* Note the fact that each triangle has an additional attribute. */
        m->eextras++;
      }
    }
  
    /* Free up memory. */
    if (((holes > 0) && !b->noholes) || !b->convex || (regions > 0)) {
      pooldeinit(&m->viri);
    }
    if (regions > 0) {
      trifree((TRIVOID *) regiontris);
    }
  }
  
  /**                                                                         **/
  /**                                                                         **/
  /********* Carving out holes and concavities ends here               *********/
  
  /********* Mesh quality maintenance begins here                      *********/
  /**                                                                         **/
  /**                                                                         **/
  
  /*****************************************************************************/
  /*                                                                           */
  /*  tallyencs()   Traverse the entire list of subsegments, and check each    */
  /*                to see if it is encroached.  If so, add it to the list.    */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifndef CDT_ONLY
  
  #ifdef ANSI_DECLARATORS
  void tallyencs(struct mesh *m, struct behavior *b)
  #else /* not ANSI_DECLARATORS */
  void tallyencs(m, b)
  struct mesh *m;
  struct behavior *b;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct osub subsegloop;
    int dummy;
  
    traversalinit(&m->subsegs);
    subsegloop.ssorient = 0;
    subsegloop.ss = subsegtraverse(m);
    while (subsegloop.ss != (subseg *) NULL) {
      /* If the segment is encroached, add it to the list. */
      dummy = checkseg4encroach(m, b, &subsegloop);
      subsegloop.ss = subsegtraverse(m);
    }
  }
  
  #endif /* not CDT_ONLY */
  
  /*****************************************************************************/
  /*                                                                           */
  /*  precisionerror()  Print an error message for precision problems.         */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifndef CDT_ONLY
  
  void precisionerror()
  {
    printf("Try increasing the area criterion and/or reducing the minimum\n");
    printf("  allowable angle so that tiny triangles are not created.\n");
  #ifdef SINGLE
    printf("Alternatively, try recompiling me with double precision\n");
    printf("  arithmetic (by removing \"#define SINGLE\" from the\n");
    printf("  source file or \"-DSINGLE\" from the makefile).\n");
  #endif /* SINGLE */
  }
  
  #endif /* not CDT_ONLY */
  
  /*****************************************************************************/
  /*                                                                           */
  /*  splitencsegs()   Split all the encroached subsegments.                   */
  /*                                                                           */
  /*  Each encroached subsegment is repaired by splitting it - inserting a     */
  /*  vertex at or near its midpoint.  Newly inserted vertices may encroach    */
  /*  upon other subsegments; these are also repaired.                         */
  /*                                                                           */
  /*  `triflaws' is a flag that specifies whether one should take note of new  */
  /*  bad triangles that result from inserting vertices to repair encroached   */
  /*  subsegments.                                                             */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifndef CDT_ONLY
  
  #ifdef ANSI_DECLARATORS
  void splitencsegs(struct mesh *m, struct behavior *b, int triflaws)
  #else /* not ANSI_DECLARATORS */
  void splitencsegs(m, b, triflaws)
  struct mesh *m;
  struct behavior *b;
  int triflaws;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct otri enctri;
    struct otri testtri;
    struct osub testsh;
    struct osub currentenc;
    struct badsubseg *encloop;
    vertex eorg, edest, eapex;
    vertex newvertex;
    enum insertvertexresult success;
    REAL segmentlength, nearestpoweroftwo;
    REAL split;
    REAL multiplier, divisor;
    int acuteorg, acuteorg2, acutedest, acutedest2;
    int dummy;
    int i;
    triangle ptr;                     /* Temporary variable used by stpivot(). */
    subseg sptr;                        /* Temporary variable used by snext(). */
  
    /* Note that steinerleft == -1 if an unlimited number */
    /*   of Steiner points is allowed.                    */
    while ((m->badsubsegs.items > 0) && (m->steinerleft != 0)) {
      traversalinit(&m->badsubsegs);
      encloop = badsubsegtraverse(m);
      while ((encloop != (struct badsubseg *) NULL) && (m->steinerleft != 0)) {
        sdecode(encloop->encsubseg, currentenc);
        sorg(currentenc, eorg);
        sdest(currentenc, edest);
        /* Make sure that this segment is still the same segment it was   */
        /*   when it was determined to be encroached.  If the segment was */
        /*   enqueued multiple times (because several newly inserted      */
        /*   vertices encroached it), it may have already been split.     */
        if (!deadsubseg(currentenc.ss) &&
            (eorg == encloop->subsegorg) && (edest == encloop->subsegdest)) {
          /* To decide where to split a segment, we need to know if the   */
          /*   segment shares an endpoint with an adjacent segment.       */
          /*   The concern is that, if we simply split every encroached   */
          /*   segment in its center, two adjacent segments with a small  */
          /*   angle between them might lead to an infinite loop; each    */
          /*   vertex added to split one segment will encroach upon the   */
          /*   other segment, which must then be split with a vertex that */
          /*   will encroach upon the first segment, and so on forever.   */
          /* To avoid this, imagine a set of concentric circles, whose    */
          /*   radii are powers of two, about each segment endpoint.      */
          /*   These concentric circles determine where the segment is    */
          /*   split.  (If both endpoints are shared with adjacent        */
          /*   segments, split the segment in the middle, and apply the   */
          /*   concentric circles for later splittings.)                  */
  
          /* Is the origin shared with another segment? */
          stpivot(currentenc, enctri);
          lnext(enctri, testtri);
          tspivot(testtri, testsh);
          acuteorg = testsh.ss != m->dummysub;
          /* Is the destination shared with another segment? */
          lnextself(testtri);
          tspivot(testtri, testsh);
          acutedest = testsh.ss != m->dummysub;
  
          /* If we're using Chew's algorithm (rather than Ruppert's) */
          /*   to define encroachment, delete free vertices from the */
          /*   subsegment's diametral circle.                        */
          if (!b->conformdel && !acuteorg && !acutedest) {
            apex(enctri, eapex);
            while ((vertextype(eapex) == FREEVERTEX) &&
                   ((eorg[0] - eapex[0]) * (edest[0] - eapex[0]) +
                    (eorg[1] - eapex[1]) * (edest[1] - eapex[1]) < 0.0)) {
              deletevertex(m, b, &testtri);
              stpivot(currentenc, enctri);
              apex(enctri, eapex);
              lprev(enctri, testtri);
            }
          }
  
          /* Now, check the other side of the segment, if there's a triangle */
          /*   there.                                                        */
          sym(enctri, testtri);
          if (testtri.tri != m->dummytri) {
            /* Is the destination shared with another segment? */
            lnextself(testtri);
            tspivot(testtri, testsh);
            acutedest2 = testsh.ss != m->dummysub;
            acutedest = acutedest || acutedest2;
            /* Is the origin shared with another segment? */
            lnextself(testtri);
            tspivot(testtri, testsh);
            acuteorg2 = testsh.ss != m->dummysub;
            acuteorg = acuteorg || acuteorg2;
  
            /* Delete free vertices from the subsegment's diametral circle. */
            if (!b->conformdel && !acuteorg2 && !acutedest2) {
              org(testtri, eapex);
              while ((vertextype(eapex) == FREEVERTEX) &&
                     ((eorg[0] - eapex[0]) * (edest[0] - eapex[0]) +
                      (eorg[1] - eapex[1]) * (edest[1] - eapex[1]) < 0.0)) {
                deletevertex(m, b, &testtri);
                sym(enctri, testtri);
                apex(testtri, eapex);
                lprevself(testtri);
              }
            }
          }
  
          /* Use the concentric circles if exactly one endpoint is shared */
          /*   with another adjacent segment.                             */
          if (acuteorg || acutedest) {
            segmentlength = sqrt((edest[0] - eorg[0]) * (edest[0] - eorg[0]) +
                                 (edest[1] - eorg[1]) * (edest[1] - eorg[1]));
            /* Find the power of two that most evenly splits the segment.  */
            /*   The worst case is a 2:1 ratio between subsegment lengths. */
            nearestpoweroftwo = 1.0;
            while (segmentlength > 3.0 * nearestpoweroftwo) {
              nearestpoweroftwo *= 2.0;
            }
            while (segmentlength < 1.5 * nearestpoweroftwo) {
              nearestpoweroftwo *= 0.5;
            }
            /* Where do we split the segment? */
            split = nearestpoweroftwo / segmentlength;
            if (acutedest) {
              split = 1.0 - split;
            }
          } else {
            /* If we're not worried about adjacent segments, split */
            /*   this segment in the middle.                       */
            split = 0.5;
          }
  
          /* Create the new vertex. */
          newvertex = (vertex) poolalloc(&m->vertices);
          /* Interpolate its coordinate and attributes. */
          for (i = 0; i < 2 + m->nextras; i++) {
            newvertex[i] = eorg[i] + split * (edest[i] - eorg[i]);
          }
  
          if (!b->noexact) {
            /* Roundoff in the above calculation may yield a `newvertex'   */
            /*   that is not precisely collinear with `eorg' and `edest'.  */
            /*   Improve collinearity by one step of iterative refinement. */
            multiplier = counterclockwise(m, b, eorg, edest, newvertex);
            divisor = ((eorg[0] - edest[0]) * (eorg[0] - edest[0]) +
                       (eorg[1] - edest[1]) * (eorg[1] - edest[1]));
            if ((multiplier != 0.0) && (divisor != 0.0)) {
              multiplier = multiplier / divisor;
              /* Watch out for NANs. */
              if (multiplier == multiplier) {
                newvertex[0] += multiplier * (edest[1] - eorg[1]);
                newvertex[1] += multiplier * (eorg[0] - edest[0]);
              }
            }
          }
  
          setvertexmark(newvertex, mark(currentenc));
          setvertextype(newvertex, SEGMENTVERTEX);
          if (b->verbose > 1) {
            printf(
    "  Splitting subsegment (%.12g, %.12g) (%.12g, %.12g) at (%.12g, %.12g).\n",
                   eorg[0], eorg[1], edest[0], edest[1],
                   newvertex[0], newvertex[1]);
          }
          /* Check whether the new vertex lies on an endpoint. */
          if (((newvertex[0] == eorg[0]) && (newvertex[1] == eorg[1])) ||
              ((newvertex[0] == edest[0]) && (newvertex[1] == edest[1]))) {
            printf("Error:  Ran out of precision at (%.12g, %.12g).\n",
                   newvertex[0], newvertex[1]);
            printf("I attempted to split a segment to a smaller size than\n");
            printf("  can be accommodated by the finite precision of\n");
            printf("  floating point arithmetic.\n");
            precisionerror();
            triexit(1);
          }
          /* Insert the splitting vertex.  This should always succeed. */
          success = insertvertex(m, b, newvertex, &enctri, &currentenc,
                                 1, triflaws);
          if ((success != SUCCESSFULVERTEX) && (success != ENCROACHINGVERTEX)) {
            printf("Internal error in splitencsegs():\n");
            printf("  Failure to split a segment.\n");
            internalerror();
          }
          if (m->steinerleft > 0) {
            m->steinerleft--;
          }
          /* Check the two new subsegments to see if they're encroached. */
          dummy = checkseg4encroach(m, b, &currentenc);
          snextself(currentenc);
          dummy = checkseg4encroach(m, b, &currentenc);
        }
  
        badsubsegdealloc(m, encloop);
        encloop = badsubsegtraverse(m);
      }
    }
  }
  
  #endif /* not CDT_ONLY */
  
  /*****************************************************************************/
  /*                                                                           */
  /*  tallyfaces()   Test every triangle in the mesh for quality measures.     */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifndef CDT_ONLY
  
  #ifdef ANSI_DECLARATORS
  void tallyfaces(struct mesh *m, struct behavior *b)
  #else /* not ANSI_DECLARATORS */
  void tallyfaces(m, b)
  struct mesh *m;
  struct behavior *b;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct otri triangleloop;
  
    if (b->verbose) {
      printf("  Making a list of bad triangles.\n");
    }
    traversalinit(&m->triangles);
    triangleloop.orient = 0;
    triangleloop.tri = triangletraverse(m);
    while (triangleloop.tri != (triangle *) NULL) {
      /* If the triangle is bad, enqueue it. */
      testtriangle(m, b, &triangleloop);
      triangleloop.tri = triangletraverse(m);
    }
  }
  
  #endif /* not CDT_ONLY */
  
  /*****************************************************************************/
  /*                                                                           */
  /*  splittriangle()   Inserts a vertex at the circumcenter of a triangle.    */
  /*                    Deletes the newly inserted vertex if it encroaches     */
  /*                    upon a segment.                                        */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifndef CDT_ONLY
  
  #ifdef ANSI_DECLARATORS
  void splittriangle(struct mesh *m, struct behavior *b,
                     struct badtriang *badtri)
  #else /* not ANSI_DECLARATORS */
  void splittriangle(m, b, badtri)
  struct mesh *m;
  struct behavior *b;
  struct badtriang *badtri;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct otri badotri;
    vertex borg, bdest, bapex;
    vertex newvertex;
    REAL xi, eta;
    enum insertvertexresult success;
    int errorflag;
    int i;
  
    decode(badtri->poortri, badotri);
    org(badotri, borg);
    dest(badotri, bdest);
    apex(badotri, bapex);
    /* Make sure that this triangle is still the same triangle it was      */
    /*   when it was tested and determined to be of bad quality.           */
    /*   Subsequent transformations may have made it a different triangle. */
    if (!deadtri(badotri.tri) && (borg == badtri->triangorg) &&
        (bdest == badtri->triangdest) && (bapex == badtri->triangapex)) {
      if (b->verbose > 1) {
        printf("  Splitting this triangle at its circumcenter:\n");
        printf("    (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", borg[0],
               borg[1], bdest[0], bdest[1], bapex[0], bapex[1]);
      }
  
      errorflag = 0;
      /* Create a new vertex at the triangle's circumcenter. */
      newvertex = (vertex) poolalloc(&m->vertices);
      findcircumcenter(m, b, borg, bdest, bapex, newvertex, &xi, &eta, 1);
  
      /* Check whether the new vertex lies on a triangle vertex. */
      if (((newvertex[0] == borg[0]) && (newvertex[1] == borg[1])) ||
          ((newvertex[0] == bdest[0]) && (newvertex[1] == bdest[1])) ||
          ((newvertex[0] == bapex[0]) && (newvertex[1] == bapex[1]))) {
        if (!b->quiet) {
          printf(
               "Warning:  New vertex (%.12g, %.12g) falls on existing vertex.\n",
                 newvertex[0], newvertex[1]);
          errorflag = 1;
        }
        vertexdealloc(m, newvertex);
      } else {
        for (i = 2; i < 2 + m->nextras; i++) {
          /* Interpolate the vertex attributes at the circumcenter. */
          newvertex[i] = borg[i] + xi * (bdest[i] - borg[i])
                                + eta * (bapex[i] - borg[i]);
        }
        /* The new vertex must be in the interior, and therefore is a */
        /*   free vertex with a marker of zero.                       */
        setvertexmark(newvertex, 0);
        setvertextype(newvertex, FREEVERTEX);
  
        /* Ensure that the handle `badotri' does not represent the longest  */
        /*   edge of the triangle.  This ensures that the circumcenter must */
        /*   fall to the left of this edge, so point location will work.    */
        /*   (If the angle org-apex-dest exceeds 90 degrees, then the       */
        /*   circumcenter lies outside the org-dest edge, and eta is        */
        /*   negative.  Roundoff error might prevent eta from being         */
        /*   negative when it should be, so I test eta against xi.)         */
        if (eta < xi) {
          lprevself(badotri);
        }
  
        /* Insert the circumcenter, searching from the edge of the triangle, */
        /*   and maintain the Delaunay property of the triangulation.        */
        success = insertvertex(m, b, newvertex, &badotri, (struct osub *) NULL,
                               1, 1);
        if (success == SUCCESSFULVERTEX) {
          if (m->steinerleft > 0) {
            m->steinerleft--;
          }
        } else if (success == ENCROACHINGVERTEX) {
          /* If the newly inserted vertex encroaches upon a subsegment, */
          /*   delete the new vertex.                                   */
          undovertex(m, b);
          if (b->verbose > 1) {
            printf("  Rejecting (%.12g, %.12g).\n", newvertex[0], newvertex[1]);
          }
          vertexdealloc(m, newvertex);
        } else if (success == VIOLATINGVERTEX) {
          /* Failed to insert the new vertex, but some subsegment was */
          /*   marked as being encroached.                            */
          vertexdealloc(m, newvertex);
        } else {                                 /* success == DUPLICATEVERTEX */
          /* Couldn't insert the new vertex because a vertex is already there. */
          if (!b->quiet) {
            printf(
              "Warning:  New vertex (%.12g, %.12g) falls on existing vertex.\n",
                   newvertex[0], newvertex[1]);
            errorflag = 1;
          }
          vertexdealloc(m, newvertex);
        }
      }
      if (errorflag) {
        if (b->verbose) {
          printf("  The new vertex is at the circumcenter of triangle\n");
          printf("    (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
                 borg[0], borg[1], bdest[0], bdest[1], bapex[0], bapex[1]);
        }
        printf("This probably means that I am trying to refine triangles\n");
        printf("  to a smaller size than can be accommodated by the finite\n");
        printf("  precision of floating point arithmetic.  (You can be\n");
        printf("  sure of this if I fail to terminate.)\n");
        precisionerror();
      }
    }
  }
  
  #endif /* not CDT_ONLY */
  
  /*****************************************************************************/
  /*                                                                           */
  /*  enforcequality()   Remove all the encroached subsegments and bad         */
  /*                     triangles from the triangulation.                     */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifndef CDT_ONLY
  
  #ifdef ANSI_DECLARATORS
  void enforcequality(struct mesh *m, struct behavior *b)
  #else /* not ANSI_DECLARATORS */
  void enforcequality(m, b)
  struct mesh *m;
  struct behavior *b;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct badtriang *badtri;
    int i;
  
    if (!b->quiet) {
      printf("Adding Steiner points to enforce quality.\n");
    }
    /* Initialize the pool of encroached subsegments. */
    poolinit(&m->badsubsegs, sizeof(struct badsubseg), BADSUBSEGPERBLOCK,
             BADSUBSEGPERBLOCK, 0);
    if (b->verbose) {
      printf("  Looking for encroached subsegments.\n");
    }
    /* Test all segments to see if they're encroached. */
    tallyencs(m, b);
    if (b->verbose && (m->badsubsegs.items > 0)) {
      printf("  Splitting encroached subsegments.\n");
    }
    /* Fix encroached subsegments without noting bad triangles. */
    splitencsegs(m, b, 0);
    /* At this point, if we haven't run out of Steiner points, the */
    /*   triangulation should be (conforming) Delaunay.            */
  
    /* Next, we worry about enforcing triangle quality. */
    if ((b->minangle > 0.0) || b->vararea || b->fixedarea || b->usertest) {
      /* Initialize the pool of bad triangles. */
      poolinit(&m->badtriangles, sizeof(struct badtriang), BADTRIPERBLOCK,
               BADTRIPERBLOCK, 0);
      /* Initialize the queues of bad triangles. */
      for (i = 0; i < 4096; i++) {
        m->queuefront[i] = (struct badtriang *) NULL;
      }
      m->firstnonemptyq = -1;
      /* Test all triangles to see if they're bad. */
      tallyfaces(m, b);
      /* Initialize the pool of recently flipped triangles. */
      poolinit(&m->flipstackers, sizeof(struct flipstacker), FLIPSTACKERPERBLOCK,
               FLIPSTACKERPERBLOCK, 0);
      m->checkquality = 1;
      if (b->verbose) {
        printf("  Splitting bad triangles.\n");
      }
      while ((m->badtriangles.items > 0) && (m->steinerleft != 0)) {
        /* Fix one bad triangle by inserting a vertex at its circumcenter. */
        badtri = dequeuebadtriang(m);
        splittriangle(m, b, badtri);
        if (m->badsubsegs.items > 0) {
          /* Put bad triangle back in queue for another try later. */
          enqueuebadtriang(m, b, badtri);
          /* Fix any encroached subsegments that resulted. */
          /*   Record any new bad triangles that result.   */
          splitencsegs(m, b, 1);
        } else {
          /* Return the bad triangle to the pool. */
          pooldealloc(&m->badtriangles, (TRIVOID *) badtri);
        }
      }
    }
    /* At this point, if the "-D" switch was selected and we haven't run out  */
    /*   of Steiner points, the triangulation should be (conforming) Delaunay */
    /*   and have no low-quality triangles.                                   */
  
    /* Might we have run out of Steiner points too soon? */
    if (!b->quiet && b->conformdel && (m->badsubsegs.items > 0) &&
        (m->steinerleft == 0)) {
      printf("\nWarning:  I ran out of Steiner points, but the mesh has\n");
      if (m->badsubsegs.items == 1) {
        printf("  one encroached subsegment, and therefore might not be truly\n"
               );
      } else {
        printf("  %ld encroached subsegments, and therefore might not be truly\n"
               , m->badsubsegs.items);
      }
      printf("  Delaunay.  If the Delaunay property is important to you,\n");
      printf("  try increasing the number of Steiner points (controlled by\n");
      printf("  the -S switch) slightly and try again.\n\n");
    }
  }
  
  #endif /* not CDT_ONLY */
  
  /**                                                                         **/
  /**                                                                         **/
  /********* Mesh quality maintenance ends here                        *********/
  
  /*****************************************************************************/
  /*                                                                           */
  /*  highorder()   Create extra nodes for quadratic subparametric elements.   */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  void highorder(struct mesh *m, struct behavior *b)
  #else /* not ANSI_DECLARATORS */
  void highorder(m, b)
  struct mesh *m;
  struct behavior *b;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct otri triangleloop, trisym;
    struct osub checkmark;
    vertex newvertex;
    vertex torg, tdest;
    int i;
    triangle ptr;                         /* Temporary variable used by sym(). */
    subseg sptr;                      /* Temporary variable used by tspivot(). */
  
    if (!b->quiet) {
      printf("Adding vertices for second-order triangles.\n");
    }
    /* The following line ensures that dead items in the pool of nodes    */
    /*   cannot be allocated for the extra nodes associated with high     */
    /*   order elements.  This ensures that the primary nodes (at the     */
    /*   corners of elements) will occur earlier in the output files, and */
    /*   have lower indices, than the extra nodes.                        */
    m->vertices.deaditemstack = (TRIVOID *) NULL;
  
    traversalinit(&m->triangles);
    triangleloop.tri = triangletraverse(m);
    /* To loop over the set of edges, loop over all triangles, and look at   */
    /*   the three edges of each triangle.  If there isn't another triangle  */
    /*   adjacent to the edge, operate on the edge.  If there is another     */
    /*   adjacent triangle, operate on the edge only if the current triangle */
    /*   has a smaller pointer than its neighbor.  This way, each edge is    */
    /*   considered only once.                                               */
    while (triangleloop.tri != (triangle *) NULL) {
      for (triangleloop.orient = 0; triangleloop.orient < 3;
           triangleloop.orient++) {
        sym(triangleloop, trisym);
        if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) {
          org(triangleloop, torg);
          dest(triangleloop, tdest);
          /* Create a new node in the middle of the edge.  Interpolate */
          /*   its attributes.                                         */
          newvertex = (vertex) poolalloc(&m->vertices);
          for (i = 0; i < 2 + m->nextras; i++) {
            newvertex[i] = 0.5 * (torg[i] + tdest[i]);
          }
          /* Set the new node's marker to zero or one, depending on */
          /*   whether it lies on a boundary.                       */
          setvertexmark(newvertex, trisym.tri == m->dummytri);
          setvertextype(newvertex,
                        trisym.tri == m->dummytri ? FREEVERTEX : SEGMENTVERTEX);
          if (b->usesegments) {
            tspivot(triangleloop, checkmark);
            /* If this edge is a segment, transfer the marker to the new node. */
            if (checkmark.ss != m->dummysub) {
              setvertexmark(newvertex, mark(checkmark));
              setvertextype(newvertex, SEGMENTVERTEX);
            }
          }
          if (b->verbose > 1) {
            printf("  Creating (%.12g, %.12g).\n", newvertex[0], newvertex[1]);
          }
          /* Record the new node in the (one or two) adjacent elements. */
          triangleloop.tri[m->highorderindex + triangleloop.orient] =
                  (triangle) newvertex;
          if (trisym.tri != m->dummytri) {
            trisym.tri[m->highorderindex + trisym.orient] = (triangle) newvertex;
          }
        }
      }
      triangleloop.tri = triangletraverse(m);
    }
  }
  
  /********* File I/O routines begin here                              *********/
  /**                                                                         **/
  /**                                                                         **/
  
  /*****************************************************************************/
  /*                                                                           */
  /*  readline()   Read a nonempty line from a file.                           */
  /*                                                                           */
  /*  A line is considered "nonempty" if it contains something that looks like */
  /*  a number.  Comments (prefaced by `#') are ignored.                       */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifndef TRILIBRARY
  
  #ifdef ANSI_DECLARATORS
  char *readline(char *string, FILE *infile, char *infilename)
  #else /* not ANSI_DECLARATORS */
  char *readline(string, infile, infilename)
  char *string;
  FILE *infile;
  char *infilename;
  #endif /* not ANSI_DECLARATORS */
  
  {
    char *result;
  
    /* Search for something that looks like a number. */
    do {
      result = fgets(string, INPUTLINESIZE, infile);
      if (result == (char *) NULL) {
        printf("  Error:  Unexpected end of file in %s.\n", infilename);
        triexit(1);
      }
      /* Skip anything that doesn't look like a number, a comment, */
      /*   or the end of a line.                                   */
      while ((*result != '\0') && (*result != '#')
             && (*result != '.') && (*result != '+') && (*result != '-')
             && ((*result < '0') || (*result > '9'))) {
        result++;
      }
    /* If it's a comment or end of line, read another line and try again. */
    } while ((*result == '#') || (*result == '\0'));
    return result;
  }
  
  #endif /* not TRILIBRARY */
  
  /*****************************************************************************/
  /*                                                                           */
  /*  findfield()   Find the next field of a string.                           */
  /*                                                                           */
  /*  Jumps past the current field by searching for whitespace, then jumps     */
  /*  past the whitespace to find the next field.                              */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifndef TRILIBRARY
  
  #ifdef ANSI_DECLARATORS
  char *findfield(char *string)
  #else /* not ANSI_DECLARATORS */
  char *findfield(string)
  char *string;
  #endif /* not ANSI_DECLARATORS */
  
  {
    char *result;
  
    result = string;
    /* Skip the current field.  Stop upon reaching whitespace. */
    while ((*result != '\0') && (*result != '#')
           && (*result != ' ') && (*result != '\t')) {
      result++;
    }
    /* Now skip the whitespace and anything else that doesn't look like a */
    /*   number, a comment, or the end of a line.                         */
    while ((*result != '\0') && (*result != '#')
           && (*result != '.') && (*result != '+') && (*result != '-')
           && ((*result < '0') || (*result > '9'))) {
      result++;
    }
    /* Check for a comment (prefixed with `#'). */
    if (*result == '#') {
      *result = '\0';
    }
    return result;
  }
  
  #endif /* not TRILIBRARY */
  
  /*****************************************************************************/
  /*                                                                           */
  /*  readnodes()   Read the vertices from a file, which may be a .node or     */
  /*                .poly file.                                                */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifndef TRILIBRARY
  
  #ifdef ANSI_DECLARATORS
  void readnodes(struct mesh *m, struct behavior *b, char *nodefilename,
                 char *polyfilename, FILE **polyfile)
  #else /* not ANSI_DECLARATORS */
  void readnodes(m, b, nodefilename, polyfilename, polyfile)
  struct mesh *m;
  struct behavior *b;
  char *nodefilename;
  char *polyfilename;
  FILE **polyfile;
  #endif /* not ANSI_DECLARATORS */
  
  {
    FILE *infile;
    vertex vertexloop;
    char inputline[INPUTLINESIZE];
    char *stringptr;
    char *infilename;
    REAL x, y;
    int firstnode;
    int nodemarkers;
    int currentmarker;
    int i, j;
  
    if (b->poly) {
      /* Read the vertices from a .poly file. */
      if (!b->quiet) {
        printf("Opening %s.\n", polyfilename);
      }
      *polyfile = fopen(polyfilename, "r");
      if (*polyfile == (FILE *) NULL) {
        printf("  Error:  Cannot access file %s.\n", polyfilename);
        triexit(1);
      }
      /* Read number of vertices, number of dimensions, number of vertex */
      /*   attributes, and number of boundary markers.                   */
      stringptr = readline(inputline, *polyfile, polyfilename);
      m->invertices = (int) strtol(stringptr, &stringptr, 0);
      stringptr = findfield(stringptr);
      if (*stringptr == '\0') {
        m->mesh_dim = 2;
      } else {
        m->mesh_dim = (int) strtol(stringptr, &stringptr, 0);
      }
      stringptr = findfield(stringptr);
      if (*stringptr == '\0') {
        m->nextras = 0;
      } else {
        m->nextras = (int) strtol(stringptr, &stringptr, 0);
      }
      stringptr = findfield(stringptr);
      if (*stringptr == '\0') {
        nodemarkers = 0;
      } else {
        nodemarkers = (int) strtol(stringptr, &stringptr, 0);
      }
      if (m->invertices > 0) {
        infile = *polyfile;
        infilename = polyfilename;
        m->readnodefile = 0;
      } else {
        /* If the .poly file claims there are zero vertices, that means that */
        /*   the vertices should be read from a separate .node file.         */
        m->readnodefile = 1;
        infilename = nodefilename;
      }
    } else {
      m->readnodefile = 1;
      infilename = nodefilename;
      *polyfile = (FILE *) NULL;
    }
  
    if (m->readnodefile) {
      /* Read the vertices from a .node file. */
      if (!b->quiet) {
        printf("Opening %s.\n", nodefilename);
      }
      infile = fopen(nodefilename, "r");
      if (infile == (FILE *) NULL) {
        printf("  Error:  Cannot access file %s.\n", nodefilename);
        triexit(1);
      }
      /* Read number of vertices, number of dimensions, number of vertex */
      /*   attributes, and number of boundary markers.                   */
      stringptr = readline(inputline, infile, nodefilename);
      m->invertices = (int) strtol(stringptr, &stringptr, 0);
      stringptr = findfield(stringptr);
      if (*stringptr == '\0') {
        m->mesh_dim = 2;
      } else {
        m->mesh_dim = (int) strtol(stringptr, &stringptr, 0);
      }
      stringptr = findfield(stringptr);
      if (*stringptr == '\0') {
        m->nextras = 0;
      } else {
        m->nextras = (int) strtol(stringptr, &stringptr, 0);
      }
      stringptr = findfield(stringptr);
      if (*stringptr == '\0') {
        nodemarkers = 0;
      } else {
        nodemarkers = (int) strtol(stringptr, &stringptr, 0);
      }
    }
  
    if (m->invertices < 3) {
      printf("Error:  Input must have at least three input vertices.\n");
      triexit(1);
    }
    if (m->mesh_dim != 2) {
      printf("Error:  Triangle only works with two-dimensional meshes.\n");
      triexit(1);
    }
    if (m->nextras == 0) {
      b->weighted = 0;
    }
  
    initializevertexpool(m, b);
  
    /* Read the vertices. */
    for (i = 0; i < m->invertices; i++) {
      vertexloop = (vertex) poolalloc(&m->vertices);
      stringptr = readline(inputline, infile, infilename);
      if (i == 0) {
        firstnode = (int) strtol(stringptr, &stringptr, 0);
        if ((firstnode == 0) || (firstnode == 1)) {
          b->firstnumber = firstnode;
        }
      }
      stringptr = findfield(stringptr);
      if (*stringptr == '\0') {
        printf("Error:  Vertex %d has no x coordinate.\n", b->firstnumber + i);
        triexit(1);
      }
      x = (REAL) strtod(stringptr, &stringptr);
      stringptr = findfield(stringptr);
      if (*stringptr == '\0') {
        printf("Error:  Vertex %d has no y coordinate.\n", b->firstnumber + i);
        triexit(1);
      }
      y = (REAL) strtod(stringptr, &stringptr);
      vertexloop[0] = x;
      vertexloop[1] = y;
      /* Read the vertex attributes. */
      for (j = 2; j < 2 + m->nextras; j++) {
        stringptr = findfield(stringptr);
        if (*stringptr == '\0') {
          vertexloop[j] = 0.0;
        } else {
          vertexloop[j] = (REAL) strtod(stringptr, &stringptr);
        }
      }
      if (nodemarkers) {
        /* Read a vertex marker. */
        stringptr = findfield(stringptr);
        if (*stringptr == '\0') {
          setvertexmark(vertexloop, 0);
        } else {
          currentmarker = (int) strtol(stringptr, &stringptr, 0);
          setvertexmark(vertexloop, currentmarker);
        }
      } else {
        /* If no markers are specified in the file, they default to zero. */
        setvertexmark(vertexloop, 0);
      }
      setvertextype(vertexloop, INPUTVERTEX);
      /* Determine the smallest and largest x and y coordinates. */
      if (i == 0) {
        m->xmin = m->xmax = x;
        m->ymin = m->ymax = y;
      } else {
        m->xmin = (x < m->xmin) ? x : m->xmin;
        m->xmax = (x > m->xmax) ? x : m->xmax;
        m->ymin = (y < m->ymin) ? y : m->ymin;
        m->ymax = (y > m->ymax) ? y : m->ymax;
      }
    }
    if (m->readnodefile) {
      fclose(infile);
    }
  
    /* Nonexistent x value used as a flag to mark circle events in sweepline */
    /*   Delaunay algorithm.                                                 */
    m->xminextreme = 10 * m->xmin - 9 * m->xmax;
  }
  
  #endif /* not TRILIBRARY */
  
  /*****************************************************************************/
  /*                                                                           */
  /*  transfernodes()   Read the vertices from memory.                         */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef TRILIBRARY
  
  #ifdef ANSI_DECLARATORS
  void transfernodes(struct mesh *m, struct behavior *b, REAL *pointlist,
                     REAL *pointattriblist, int *pointmarkerlist,
                     int numberofpoints, int numberofpointattribs)
  #else /* not ANSI_DECLARATORS */
  void transfernodes(m, b, pointlist, pointattriblist, pointmarkerlist,
                     numberofpoints, numberofpointattribs)
  struct mesh *m;
  struct behavior *b;
  REAL *pointlist;
  REAL *pointattriblist;
  int *pointmarkerlist;
  int numberofpoints;
  int numberofpointattribs;
  #endif /* not ANSI_DECLARATORS */
  
  {
    vertex vertexloop;
    REAL x, y;
    int i, j;
    int coordindex;
    int attribindex;
  
    m->invertices = numberofpoints;
    m->mesh_dim = 2;
    m->nextras = numberofpointattribs;
    m->readnodefile = 0;
    if (m->invertices < 3) {
      printf("Error:  Input must have at least three input vertices.\n");
      triexit(1);
    }
    if (m->nextras == 0) {
      b->weighted = 0;
    }
  
    initializevertexpool(m, b);
  
    /* Read the vertices. */
    coordindex = 0;
    attribindex = 0;
    for (i = 0; i < m->invertices; i++) {
      vertexloop = (vertex) poolalloc(&m->vertices);
      /* Read the vertex coordinates. */
      x = vertexloop[0] = pointlist[coordindex++];
      y = vertexloop[1] = pointlist[coordindex++];
      /* Read the vertex attributes. */
      for (j = 0; j < numberofpointattribs; j++) {
        vertexloop[2 + j] = pointattriblist[attribindex++];
      }
      if (pointmarkerlist != (int *) NULL) {
        /* Read a vertex marker. */
        setvertexmark(vertexloop, pointmarkerlist[i]);
      } else {
        /* If no markers are specified, they default to zero. */
        setvertexmark(vertexloop, 0);
      }
      setvertextype(vertexloop, INPUTVERTEX);
      /* Determine the smallest and largest x and y coordinates. */
      if (i == 0) {
        m->xmin = m->xmax = x;
        m->ymin = m->ymax = y;
      } else {
        m->xmin = (x < m->xmin) ? x : m->xmin;
        m->xmax = (x > m->xmax) ? x : m->xmax;
        m->ymin = (y < m->ymin) ? y : m->ymin;
        m->ymax = (y > m->ymax) ? y : m->ymax;
      }
    }
  
    /* Nonexistent x value used as a flag to mark circle events in sweepline */
    /*   Delaunay algorithm.                                                 */
    m->xminextreme = 10 * m->xmin - 9 * m->xmax;
  }
  
  #endif /* TRILIBRARY */
  
  /*****************************************************************************/
  /*                                                                           */
  /*  readholes()   Read the holes, and possibly regional attributes and area  */
  /*                constraints, from a .poly file.                            */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifndef TRILIBRARY
  
  #ifdef ANSI_DECLARATORS
  void readholes(struct mesh *m, struct behavior *b,
                 FILE *polyfile, char *polyfilename, REAL **hlist, int *holes,
                 REAL **rlist, int *regions)
  #else /* not ANSI_DECLARATORS */
  void readholes(m, b, polyfile, polyfilename, hlist, holes, rlist, regions)
  struct mesh *m;
  struct behavior *b;
  FILE *polyfile;
  char *polyfilename;
  REAL **hlist;
  int *holes;
  REAL **rlist;
  int *regions;
  #endif /* not ANSI_DECLARATORS */
  
  {
    REAL *holelist;
    REAL *regionlist;
    char inputline[INPUTLINESIZE];
    char *stringptr;
    int index;
    int i;
  
    /* Read the holes. */
    stringptr = readline(inputline, polyfile, polyfilename);
    *holes = (int) strtol(stringptr, &stringptr, 0);
    if (*holes > 0) {
      holelist = (REAL *) trimalloc(2 * *holes * (int) sizeof(REAL));
      *hlist = holelist;
      for (i = 0; i < 2 * *holes; i += 2) {
        stringptr = readline(inputline, polyfile, polyfilename);
        stringptr = findfield(stringptr);
        if (*stringptr == '\0') {
          printf("Error:  Hole %d has no x coordinate.\n",
                 b->firstnumber + (i >> 1));
          triexit(1);
        } else {
          holelist[i] = (REAL) strtod(stringptr, &stringptr);
        }
        stringptr = findfield(stringptr);
        if (*stringptr == '\0') {
          printf("Error:  Hole %d has no y coordinate.\n",
                 b->firstnumber + (i >> 1));
          triexit(1);
        } else {
          holelist[i + 1] = (REAL) strtod(stringptr, &stringptr);
        }
      }
    } else {
      *hlist = (REAL *) NULL;
    }
  
  #ifndef CDT_ONLY
    if ((b->regionattrib || b->vararea) && !b->refine) {
      /* Read the area constraints. */
      stringptr = readline(inputline, polyfile, polyfilename);
      *regions = (int) strtol(stringptr, &stringptr, 0);
      if (*regions > 0) {
        regionlist = (REAL *) trimalloc(4 * *regions * (int) sizeof(REAL));
        *rlist = regionlist;
        index = 0;
        for (i = 0; i < *regions; i++) {
          stringptr = readline(inputline, polyfile, polyfilename);
          stringptr = findfield(stringptr);
          if (*stringptr == '\0') {
            printf("Error:  Region %d has no x coordinate.\n",
                   b->firstnumber + i);
            triexit(1);
          } else {
            regionlist[index++] = (REAL) strtod(stringptr, &stringptr);
          }
          stringptr = findfield(stringptr);
          if (*stringptr == '\0') {
            printf("Error:  Region %d has no y coordinate.\n",
                   b->firstnumber + i);
            triexit(1);
          } else {
            regionlist[index++] = (REAL) strtod(stringptr, &stringptr);
          }
          stringptr = findfield(stringptr);
          if (*stringptr == '\0') {
            printf(
              "Error:  Region %d has no region attribute or area constraint.\n",
                   b->firstnumber + i);
            triexit(1);
          } else {
            regionlist[index++] = (REAL) strtod(stringptr, &stringptr);
          }
          stringptr = findfield(stringptr);
          if (*stringptr == '\0') {
            regionlist[index] = regionlist[index - 1];
          } else {
            regionlist[index] = (REAL) strtod(stringptr, &stringptr);
          }
          index++;
        }
      }
    } else {
      /* Set `*regions' to zero to avoid an accidental free() later. */
      *regions = 0;
      *rlist = (REAL *) NULL;
    }
  #endif /* not CDT_ONLY */
  
    fclose(polyfile);
  }
  
  #endif /* not TRILIBRARY */
  
  /*****************************************************************************/
  /*                                                                           */
  /*  finishfile()   Write the command line to the output file so the user     */
  /*                 can remember how the file was generated.  Close the file. */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifndef TRILIBRARY
  
  #ifdef ANSI_DECLARATORS
  void finishfile(FILE *outfile, int argc, char **argv)
  #else /* not ANSI_DECLARATORS */
  void finishfile(outfile, argc, argv)
  FILE *outfile;
  int argc;
  char **argv;
  #endif /* not ANSI_DECLARATORS */
  
  {
    int i;
  
    fprintf(outfile, "# Generated by");
    for (i = 0; i < argc; i++) {
      fprintf(outfile, " ");
      fputs(argv[i], outfile);
    }
    fprintf(outfile, "\n");
    fclose(outfile);
  }
  
  #endif /* not TRILIBRARY */
  
  /*****************************************************************************/
  /*                                                                           */
  /*  writenodes()   Number the vertices and write them to a .node file.       */
  /*                                                                           */
  /*  To save memory, the vertex numbers are written over the boundary markers */
  /*  after the vertices are written to a file.                                */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef TRILIBRARY
  
  #ifdef ANSI_DECLARATORS
  void writenodes(struct mesh *m, struct behavior *b, REAL **pointlist,
                  REAL **pointattriblist, int **pointmarkerlist)
  #else /* not ANSI_DECLARATORS */
  void writenodes(m, b, pointlist, pointattriblist, pointmarkerlist)
  struct mesh *m;
  struct behavior *b;
  REAL **pointlist;
  REAL **pointattriblist;
  int **pointmarkerlist;
  #endif /* not ANSI_DECLARATORS */
  
  #else /* not TRILIBRARY */
  
  #ifdef ANSI_DECLARATORS
  void writenodes(struct mesh *m, struct behavior *b, char *nodefilename,
                  int argc, char **argv)
  #else /* not ANSI_DECLARATORS */
  void writenodes(m, b, nodefilename, argc, argv)
  struct mesh *m;
  struct behavior *b;
  char *nodefilename;
  int argc;
  char **argv;
  #endif /* not ANSI_DECLARATORS */
  
  #endif /* not TRILIBRARY */
  
  {
  #ifdef TRILIBRARY
    REAL *plist;
    REAL *palist;
    int *pmlist;
    int coordindex;
    int attribindex;
  #else /* not TRILIBRARY */
    FILE *outfile;
  #endif /* not TRILIBRARY */
    vertex vertexloop;
    long outvertices;
    int vertexnumber;
    int i;
  
    if (b->jettison) {
      outvertices = m->vertices.items - m->undeads;
    } else {
      outvertices = m->vertices.items;
    }
  
  #ifdef TRILIBRARY
    if (!b->quiet) {
      printf("Writing vertices.\n");
    }
    /* Allocate memory for output vertices if necessary. */
    if (*pointlist == (REAL *) NULL) {
      *pointlist = (REAL *) trimalloc((int) (outvertices * 2 * sizeof(REAL)));
    }
    /* Allocate memory for output vertex attributes if necessary. */
    if ((m->nextras > 0) && (*pointattriblist == (REAL *) NULL)) {
      *pointattriblist = (REAL *) trimalloc((int) (outvertices * m->nextras *
                                                   sizeof(REAL)));
    }
    /* Allocate memory for output vertex markers if necessary. */
    if (!b->nobound && (*pointmarkerlist == (int *) NULL)) {
      *pointmarkerlist = (int *) trimalloc((int) (outvertices * sizeof(int)));
    }
    plist = *pointlist;
    palist = *pointattriblist;
    pmlist = *pointmarkerlist;
    coordindex = 0;
    attribindex = 0;
  #else /* not TRILIBRARY */
    if (!b->quiet) {
      printf("Writing %s.\n", nodefilename);
    }
    outfile = fopen(nodefilename, "w");
    if (outfile == (FILE *) NULL) {
      printf("  Error:  Cannot create file %s.\n", nodefilename);
      triexit(1);
    }
    /* Number of vertices, number of dimensions, number of vertex attributes, */
    /*   and number of boundary markers (zero or one).                        */
    fprintf(outfile, "%ld  %d  %d  %d\n", outvertices, m->mesh_dim,
            m->nextras, 1 - b->nobound);
  #endif /* not TRILIBRARY */
  
    traversalinit(&m->vertices);
    vertexnumber = b->firstnumber;
    vertexloop = vertextraverse(m);
    while (vertexloop != (vertex) NULL) {
      if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) {
  #ifdef TRILIBRARY
        /* X and y coordinates. */
        plist[coordindex++] = vertexloop[0];
        plist[coordindex++] = vertexloop[1];
        /* Vertex attributes. */
        for (i = 0; i < m->nextras; i++) {
          palist[attribindex++] = vertexloop[2 + i];
        }
        if (!b->nobound) {
          /* Copy the boundary marker. */
          pmlist[vertexnumber - b->firstnumber] = vertexmark(vertexloop);
        }
  #else /* not TRILIBRARY */
        /* Vertex number, x and y coordinates. */
        fprintf(outfile, "%4d    %.17g  %.17g", vertexnumber, vertexloop[0],
                vertexloop[1]);
        for (i = 0; i < m->nextras; i++) {
          /* Write an attribute. */
          fprintf(outfile, "  %.17g", vertexloop[i + 2]);
        }
        if (b->nobound) {
          fprintf(outfile, "\n");
        } else {
          /* Write the boundary marker. */
          fprintf(outfile, "    %d\n", vertexmark(vertexloop));
        }
  #endif /* not TRILIBRARY */
  
        setvertexmark(vertexloop, vertexnumber);
        vertexnumber++;
      }
      vertexloop = vertextraverse(m);
    }
  
  #ifndef TRILIBRARY
    finishfile(outfile, argc, argv);
  #endif /* not TRILIBRARY */
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  numbernodes()   Number the vertices.                                     */
  /*                                                                           */
  /*  Each vertex is assigned a marker equal to its number.                    */
  /*                                                                           */
  /*  Used when writenodes() is not called because no .node file is written.   */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  void numbernodes(struct mesh *m, struct behavior *b)
  #else /* not ANSI_DECLARATORS */
  void numbernodes(m, b)
  struct mesh *m;
  struct behavior *b;
  #endif /* not ANSI_DECLARATORS */
  
  {
    vertex vertexloop;
    int vertexnumber;
  
    traversalinit(&m->vertices);
    vertexnumber = b->firstnumber;
    vertexloop = vertextraverse(m);
    while (vertexloop != (vertex) NULL) {
      setvertexmark(vertexloop, vertexnumber);
      if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) {
        vertexnumber++;
      }
      vertexloop = vertextraverse(m);
    }
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  writeelements()   Write the triangles to an .ele file.                   */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef TRILIBRARY
  
  #ifdef ANSI_DECLARATORS
  void writeelements(struct mesh *m, struct behavior *b,
                     int **trianglelist, REAL **triangleattriblist)
  #else /* not ANSI_DECLARATORS */
  void writeelements(m, b, trianglelist, triangleattriblist)
  struct mesh *m;
  struct behavior *b;
  int **trianglelist;
  REAL **triangleattriblist;
  #endif /* not ANSI_DECLARATORS */
  
  #else /* not TRILIBRARY */
  
  #ifdef ANSI_DECLARATORS
  void writeelements(struct mesh *m, struct behavior *b, char *elefilename,
                     int argc, char **argv)
  #else /* not ANSI_DECLARATORS */
  void writeelements(m, b, elefilename, argc, argv)
  struct mesh *m;
  struct behavior *b;
  char *elefilename;
  int argc;
  char **argv;
  #endif /* not ANSI_DECLARATORS */
  
  #endif /* not TRILIBRARY */
  
  {
  #ifdef TRILIBRARY
    int *tlist;
    REAL *talist;
    int vertexindex;
    int attribindex;
  #else /* not TRILIBRARY */
    FILE *outfile;
  #endif /* not TRILIBRARY */
    struct otri triangleloop;
    vertex p1, p2, p3;
    vertex mid1, mid2, mid3;
    long elementnumber;
    int i;
  
  #ifdef TRILIBRARY
    if (!b->quiet) {
      printf("Writing triangles.\n");
    }
    /* Allocate memory for output triangles if necessary. */
    if (*trianglelist == (int *) NULL) {
      *trianglelist = (int *) trimalloc((int) (m->triangles.items *
                                               ((b->order + 1) * (b->order + 2) /
                                                2) * sizeof(int)));
    }
    /* Allocate memory for output triangle attributes if necessary. */
    if ((m->eextras > 0) && (*triangleattriblist == (REAL *) NULL)) {
      *triangleattriblist = (REAL *) trimalloc((int) (m->triangles.items *
                                                      m->eextras *
                                                      sizeof(REAL)));
    }
    tlist = *trianglelist;
    talist = *triangleattriblist;
    vertexindex = 0;
    attribindex = 0;
  #else /* not TRILIBRARY */
    if (!b->quiet) {
      printf("Writing %s.\n", elefilename);
    }
    outfile = fopen(elefilename, "w");
    if (outfile == (FILE *) NULL) {
      printf("  Error:  Cannot create file %s.\n", elefilename);
      triexit(1);
    }
    /* Number of triangles, vertices per triangle, attributes per triangle. */
    fprintf(outfile, "%ld  %d  %d\n", m->triangles.items,
            (b->order + 1) * (b->order + 2) / 2, m->eextras);
  #endif /* not TRILIBRARY */
  
    traversalinit(&m->triangles);
    triangleloop.tri = triangletraverse(m);
    triangleloop.orient = 0;
    elementnumber = b->firstnumber;
    while (triangleloop.tri != (triangle *) NULL) {
      org(triangleloop, p1);
      dest(triangleloop, p2);
      apex(triangleloop, p3);
      if (b->order == 1) {
  #ifdef TRILIBRARY
        tlist[vertexindex++] = vertexmark(p1);
        tlist[vertexindex++] = vertexmark(p2);
        tlist[vertexindex++] = vertexmark(p3);
  #else /* not TRILIBRARY */
        /* Triangle number, indices for three vertices. */
        fprintf(outfile, "%4ld    %4d  %4d  %4d", elementnumber,
                vertexmark(p1), vertexmark(p2), vertexmark(p3));
  #endif /* not TRILIBRARY */
      } else {
        mid1 = (vertex) triangleloop.tri[m->highorderindex + 1];
        mid2 = (vertex) triangleloop.tri[m->highorderindex + 2];
        mid3 = (vertex) triangleloop.tri[m->highorderindex];
  #ifdef TRILIBRARY
        tlist[vertexindex++] = vertexmark(p1);
        tlist[vertexindex++] = vertexmark(p2);
        tlist[vertexindex++] = vertexmark(p3);
        tlist[vertexindex++] = vertexmark(mid1);
        tlist[vertexindex++] = vertexmark(mid2);
        tlist[vertexindex++] = vertexmark(mid3);
  #else /* not TRILIBRARY */
        /* Triangle number, indices for six vertices. */
        fprintf(outfile, "%4ld    %4d  %4d  %4d  %4d  %4d  %4d", elementnumber,
                vertexmark(p1), vertexmark(p2), vertexmark(p3), vertexmark(mid1),
                vertexmark(mid2), vertexmark(mid3));
  #endif /* not TRILIBRARY */
      }
  
  #ifdef TRILIBRARY
      for (i = 0; i < m->eextras; i++) {
        talist[attribindex++] = elemattribute(triangleloop, i);
      }
  #else /* not TRILIBRARY */
      for (i = 0; i < m->eextras; i++) {
        fprintf(outfile, "  %.17g", elemattribute(triangleloop, i));
      }
      fprintf(outfile, "\n");
  #endif /* not TRILIBRARY */
  
      triangleloop.tri = triangletraverse(m);
      elementnumber++;
    }
  
  #ifndef TRILIBRARY
    finishfile(outfile, argc, argv);
  #endif /* not TRILIBRARY */
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  writepoly()   Write the segments and holes to a .poly file.              */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef TRILIBRARY
  
  #ifdef ANSI_DECLARATORS
  void writepoly(struct mesh *m, struct behavior *b,
                 int **segmentlist, int **segmentmarkerlist)
  #else /* not ANSI_DECLARATORS */
  void writepoly(m, b, segmentlist, segmentmarkerlist)
  struct mesh *m;
  struct behavior *b;
  int **segmentlist;
  int **segmentmarkerlist;
  #endif /* not ANSI_DECLARATORS */
  
  #else /* not TRILIBRARY */
  
  #ifdef ANSI_DECLARATORS
  void writepoly(struct mesh *m, struct behavior *b, char *polyfilename,
                 REAL *holelist, int holes, REAL *regionlist, int regions,
                 int argc, char **argv)
  #else /* not ANSI_DECLARATORS */
  void writepoly(m, b, polyfilename, holelist, holes, regionlist, regions,
                 argc, argv)
  struct mesh *m;
  struct behavior *b;
  char *polyfilename;
  REAL *holelist;
  int holes;
  REAL *regionlist;
  int regions;
  int argc;
  char **argv;
  #endif /* not ANSI_DECLARATORS */
  
  #endif /* not TRILIBRARY */
  
  {
  #ifdef TRILIBRARY
    int *slist;
    int *smlist;
    int index;
  #else /* not TRILIBRARY */
    FILE *outfile;
    long holenumber, regionnumber;
  #endif /* not TRILIBRARY */
    struct osub subsegloop;
    vertex endpoint1, endpoint2;
    long subsegnumber;
  
  #ifdef TRILIBRARY
    if (!b->quiet) {
      printf("Writing segments.\n");
    }
    /* Allocate memory for output segments if necessary. */
    if (*segmentlist == (int *) NULL) {
      *segmentlist = (int *) trimalloc((int) (m->subsegs.items * 2 *
                                              sizeof(int)));
    }
    /* Allocate memory for output segment markers if necessary. */
    if (!b->nobound && (*segmentmarkerlist == (int *) NULL)) {
      *segmentmarkerlist = (int *) trimalloc((int) (m->subsegs.items *
                                                    sizeof(int)));
    }
    slist = *segmentlist;
    smlist = *segmentmarkerlist;
    index = 0;
  #else /* not TRILIBRARY */
    if (!b->quiet) {
      printf("Writing %s.\n", polyfilename);
    }
    outfile = fopen(polyfilename, "w");
    if (outfile == (FILE *) NULL) {
      printf("  Error:  Cannot create file %s.\n", polyfilename);
      triexit(1);
    }
    /* The zero indicates that the vertices are in a separate .node file. */
    /*   Followed by number of dimensions, number of vertex attributes,   */
    /*   and number of boundary markers (zero or one).                    */
    fprintf(outfile, "%d  %d  %d  %d\n", 0, m->mesh_dim, m->nextras,
            1 - b->nobound);
    /* Number of segments, number of boundary markers (zero or one). */
    fprintf(outfile, "%ld  %d\n", m->subsegs.items, 1 - b->nobound);
  #endif /* not TRILIBRARY */
  
    traversalinit(&m->subsegs);
    subsegloop.ss = subsegtraverse(m);
    subsegloop.ssorient = 0;
    subsegnumber = b->firstnumber;
    while (subsegloop.ss != (subseg *) NULL) {
      sorg(subsegloop, endpoint1);
      sdest(subsegloop, endpoint2);
  #ifdef TRILIBRARY
      /* Copy indices of the segment's two endpoints. */
      slist[index++] = vertexmark(endpoint1);
      slist[index++] = vertexmark(endpoint2);
      if (!b->nobound) {
        /* Copy the boundary marker. */
        smlist[subsegnumber - b->firstnumber] = mark(subsegloop);
      }
  #else /* not TRILIBRARY */
      /* Segment number, indices of its two endpoints, and possibly a marker. */
      if (b->nobound) {
        fprintf(outfile, "%4ld    %4d  %4d\n", subsegnumber,
                vertexmark(endpoint1), vertexmark(endpoint2));
      } else {
        fprintf(outfile, "%4ld    %4d  %4d    %4d\n", subsegnumber,
                vertexmark(endpoint1), vertexmark(endpoint2), mark(subsegloop));
      }
  #endif /* not TRILIBRARY */
  
      subsegloop.ss = subsegtraverse(m);
      subsegnumber++;
    }
  
  #ifndef TRILIBRARY
  #ifndef CDT_ONLY
    fprintf(outfile, "%d\n", holes);
    if (holes > 0) {
      for (holenumber = 0; holenumber < holes; holenumber++) {
        /* Hole number, x and y coordinates. */
        fprintf(outfile, "%4ld   %.17g  %.17g\n", b->firstnumber + holenumber,
                holelist[2 * holenumber], holelist[2 * holenumber + 1]);
      }
    }
    if (regions > 0) {
      fprintf(outfile, "%d\n", regions);
      for (regionnumber = 0; regionnumber < regions; regionnumber++) {
        /* Region number, x and y coordinates, attribute, maximum area. */
        fprintf(outfile, "%4ld   %.17g  %.17g  %.17g  %.17g\n",
                b->firstnumber + regionnumber,
                regionlist[4 * regionnumber], regionlist[4 * regionnumber + 1],
                regionlist[4 * regionnumber + 2],
                regionlist[4 * regionnumber + 3]);
      }
    }
  #endif /* not CDT_ONLY */
  
    finishfile(outfile, argc, argv);
  #endif /* not TRILIBRARY */
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  writeedges()   Write the edges to an .edge file.                         */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef TRILIBRARY
  
  #ifdef ANSI_DECLARATORS
  void writeedges(struct mesh *m, struct behavior *b,
                  int **edgelist, int **edgemarkerlist)
  #else /* not ANSI_DECLARATORS */
  void writeedges(m, b, edgelist, edgemarkerlist)
  struct mesh *m;
  struct behavior *b;
  int **edgelist;
  int **edgemarkerlist;
  #endif /* not ANSI_DECLARATORS */
  
  #else /* not TRILIBRARY */
  
  #ifdef ANSI_DECLARATORS
  void writeedges(struct mesh *m, struct behavior *b, char *edgefilename,
                  int argc, char **argv)
  #else /* not ANSI_DECLARATORS */
  void writeedges(m, b, edgefilename, argc, argv)
  struct mesh *m;
  struct behavior *b;
  char *edgefilename;
  int argc;
  char **argv;
  #endif /* not ANSI_DECLARATORS */
  
  #endif /* not TRILIBRARY */
  
  {
  #ifdef TRILIBRARY
    int *elist;
    int *emlist;
    int index;
  #else /* not TRILIBRARY */
    FILE *outfile;
  #endif /* not TRILIBRARY */
    struct otri triangleloop, trisym;
    struct osub checkmark;
    vertex p1, p2;
    long edgenumber;
    triangle ptr;                         /* Temporary variable used by sym(). */
    subseg sptr;                      /* Temporary variable used by tspivot(). */
  
  #ifdef TRILIBRARY
    if (!b->quiet) {
      printf("Writing edges.\n");
    }
    /* Allocate memory for edges if necessary. */
    if (*edgelist == (int *) NULL) {
      *edgelist = (int *) trimalloc((int) (m->edges * 2 * sizeof(int)));
    }
    /* Allocate memory for edge markers if necessary. */
    if (!b->nobound && (*edgemarkerlist == (int *) NULL)) {
      *edgemarkerlist = (int *) trimalloc((int) (m->edges * sizeof(int)));
    }
    elist = *edgelist;
    emlist = *edgemarkerlist;
    index = 0;
  #else /* not TRILIBRARY */
    if (!b->quiet) {
      printf("Writing %s.\n", edgefilename);
    }
    outfile = fopen(edgefilename, "w");
    if (outfile == (FILE *) NULL) {
      printf("  Error:  Cannot create file %s.\n", edgefilename);
      triexit(1);
    }
    /* Number of edges, number of boundary markers (zero or one). */
    fprintf(outfile, "%ld  %d\n", m->edges, 1 - b->nobound);
  #endif /* not TRILIBRARY */
  
    traversalinit(&m->triangles);
    triangleloop.tri = triangletraverse(m);
    edgenumber = b->firstnumber;
    /* To loop over the set of edges, loop over all triangles, and look at   */
    /*   the three edges of each triangle.  If there isn't another triangle  */
    /*   adjacent to the edge, operate on the edge.  If there is another     */
    /*   adjacent triangle, operate on the edge only if the current triangle */
    /*   has a smaller pointer than its neighbor.  This way, each edge is    */
    /*   considered only once.                                               */
    while (triangleloop.tri != (triangle *) NULL) {
      for (triangleloop.orient = 0; triangleloop.orient < 3;
           triangleloop.orient++) {
        sym(triangleloop, trisym);
        if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) {
          org(triangleloop, p1);
          dest(triangleloop, p2);
  #ifdef TRILIBRARY
          elist[index++] = vertexmark(p1);
          elist[index++] = vertexmark(p2);
  #endif /* TRILIBRARY */
          if (b->nobound) {
  #ifndef TRILIBRARY
            /* Edge number, indices of two endpoints. */
            fprintf(outfile, "%4ld   %d  %d\n", edgenumber,
                    vertexmark(p1), vertexmark(p2));
  #endif /* not TRILIBRARY */
          } else {
            /* Edge number, indices of two endpoints, and a boundary marker. */
            /*   If there's no subsegment, the boundary marker is zero.      */
            if (b->usesegments) {
              tspivot(triangleloop, checkmark);
              if (checkmark.ss == m->dummysub) {
  #ifdef TRILIBRARY
                emlist[edgenumber - b->firstnumber] = 0;
  #else /* not TRILIBRARY */
                fprintf(outfile, "%4ld   %d  %d  %d\n", edgenumber,
                        vertexmark(p1), vertexmark(p2), 0);
  #endif /* not TRILIBRARY */
              } else {
  #ifdef TRILIBRARY
                emlist[edgenumber - b->firstnumber] = mark(checkmark);
  #else /* not TRILIBRARY */
                fprintf(outfile, "%4ld   %d  %d  %d\n", edgenumber,
                        vertexmark(p1), vertexmark(p2), mark(checkmark));
  #endif /* not TRILIBRARY */
              }
            } else {
  #ifdef TRILIBRARY
              emlist[edgenumber - b->firstnumber] = trisym.tri == m->dummytri;
  #else /* not TRILIBRARY */
              fprintf(outfile, "%4ld   %d  %d  %d\n", edgenumber,
                      vertexmark(p1), vertexmark(p2), trisym.tri == m->dummytri);
  #endif /* not TRILIBRARY */
            }
          }
          edgenumber++;
        }
      }
      triangleloop.tri = triangletraverse(m);
    }
  
  #ifndef TRILIBRARY
    finishfile(outfile, argc, argv);
  #endif /* not TRILIBRARY */
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  writevoronoi()   Write the Voronoi diagram to a .v.node and .v.edge      */
  /*                   file.                                                   */
  /*                                                                           */
  /*  The Voronoi diagram is the geometric dual of the Delaunay triangulation. */
  /*  Hence, the Voronoi vertices are listed by traversing the Delaunay        */
  /*  triangles, and the Voronoi edges are listed by traversing the Delaunay   */
  /*  edges.                                                                   */
  /*                                                                           */
  /*  WARNING:  In order to assign numbers to the Voronoi vertices, this       */
  /*  procedure messes up the subsegments or the extra nodes of every          */
  /*  element.  Hence, you should call this procedure last.                    */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef TRILIBRARY
  
  #ifdef ANSI_DECLARATORS
  void writevoronoi(struct mesh *m, struct behavior *b, REAL **vpointlist,
                    REAL **vpointattriblist, int **vpointmarkerlist,
                    int **vedgelist, int **vedgemarkerlist, REAL **vnormlist)
  #else /* not ANSI_DECLARATORS */
  void writevoronoi(m, b, vpointlist, vpointattriblist, vpointmarkerlist,
                    vedgelist, vedgemarkerlist, vnormlist)
  struct mesh *m;
  struct behavior *b;
  REAL **vpointlist;
  REAL **vpointattriblist;
  int **vpointmarkerlist;
  int **vedgelist;
  int **vedgemarkerlist;
  REAL **vnormlist;
  #endif /* not ANSI_DECLARATORS */
  
  #else /* not TRILIBRARY */
  
  #ifdef ANSI_DECLARATORS
  void writevoronoi(struct mesh *m, struct behavior *b, char *vnodefilename,
                    char *vedgefilename, int argc, char **argv)
  #else /* not ANSI_DECLARATORS */
  void writevoronoi(m, b, vnodefilename, vedgefilename, argc, argv)
  struct mesh *m;
  struct behavior *b;
  char *vnodefilename;
  char *vedgefilename;
  int argc;
  char **argv;
  #endif /* not ANSI_DECLARATORS */
  
  #endif /* not TRILIBRARY */
  
  {
  #ifdef TRILIBRARY
    REAL *plist;
    REAL *palist;
    int *elist;
    REAL *normlist;
    int coordindex;
    int attribindex;
  #else /* not TRILIBRARY */
    FILE *outfile;
  #endif /* not TRILIBRARY */
    struct otri triangleloop, trisym;
    vertex torg, tdest, tapex;
    REAL circumcenter[2];
    REAL xi, eta;
    long vnodenumber, vedgenumber;
    int p1, p2;
    int i;
    triangle ptr;                         /* Temporary variable used by sym(). */
  
  #ifdef TRILIBRARY
    if (!b->quiet) {
      printf("Writing Voronoi vertices.\n");
    }
    /* Allocate memory for Voronoi vertices if necessary. */
    if (*vpointlist == (REAL *) NULL) {
      *vpointlist = (REAL *) trimalloc((int) (m->triangles.items * 2 *
                                              sizeof(REAL)));
    }
    /* Allocate memory for Voronoi vertex attributes if necessary. */
    if (*vpointattriblist == (REAL *) NULL) {
      *vpointattriblist = (REAL *) trimalloc((int) (m->triangles.items *
                                                    m->nextras * sizeof(REAL)));
    }
    *vpointmarkerlist = (int *) NULL;
    plist = *vpointlist;
    palist = *vpointattriblist;
    coordindex = 0;
    attribindex = 0;
  #else /* not TRILIBRARY */
    if (!b->quiet) {
      printf("Writing %s.\n", vnodefilename);
    }
    outfile = fopen(vnodefilename, "w");
    if (outfile == (FILE *) NULL) {
      printf("  Error:  Cannot create file %s.\n", vnodefilename);
      triexit(1);
    }
    /* Number of triangles, two dimensions, number of vertex attributes, */
    /*   no markers.                                                     */
    fprintf(outfile, "%ld  %d  %d  %d\n", m->triangles.items, 2, m->nextras, 0);
  #endif /* not TRILIBRARY */
  
    traversalinit(&m->triangles);
    triangleloop.tri = triangletraverse(m);
    triangleloop.orient = 0;
    vnodenumber = b->firstnumber;
    while (triangleloop.tri != (triangle *) NULL) {
      org(triangleloop, torg);
      dest(triangleloop, tdest);
      apex(triangleloop, tapex);
      findcircumcenter(m, b, torg, tdest, tapex, circumcenter, &xi, &eta, 0);
  #ifdef TRILIBRARY
      /* X and y coordinates. */
      plist[coordindex++] = circumcenter[0];
      plist[coordindex++] = circumcenter[1];
      for (i = 2; i < 2 + m->nextras; i++) {
        /* Interpolate the vertex attributes at the circumcenter. */
        palist[attribindex++] = torg[i] + xi * (tdest[i] - torg[i])
                                       + eta * (tapex[i] - torg[i]);
      }
  #else /* not TRILIBRARY */
      /* Voronoi vertex number, x and y coordinates. */
      fprintf(outfile, "%4ld    %.17g  %.17g", vnodenumber, circumcenter[0],
              circumcenter[1]);
      for (i = 2; i < 2 + m->nextras; i++) {
        /* Interpolate the vertex attributes at the circumcenter. */
        fprintf(outfile, "  %.17g", torg[i] + xi * (tdest[i] - torg[i])
                                           + eta * (tapex[i] - torg[i]));
      }
      fprintf(outfile, "\n");
  #endif /* not TRILIBRARY */
  
      * (int *) (triangleloop.tri + 6) = (int) vnodenumber;
      triangleloop.tri = triangletraverse(m);
      vnodenumber++;
    }
  
  #ifndef TRILIBRARY
    finishfile(outfile, argc, argv);
  #endif /* not TRILIBRARY */
  
  #ifdef TRILIBRARY
    if (!b->quiet) {
      printf("Writing Voronoi edges.\n");
    }
    /* Allocate memory for output Voronoi edges if necessary. */
    if (*vedgelist == (int *) NULL) {
      *vedgelist = (int *) trimalloc((int) (m->edges * 2 * sizeof(int)));
    }
    *vedgemarkerlist = (int *) NULL;
    /* Allocate memory for output Voronoi norms if necessary. */
    if (*vnormlist == (REAL *) NULL) {
      *vnormlist = (REAL *) trimalloc((int) (m->edges * 2 * sizeof(REAL)));
    }
    elist = *vedgelist;
    normlist = *vnormlist;
    coordindex = 0;
  #else /* not TRILIBRARY */
    if (!b->quiet) {
      printf("Writing %s.\n", vedgefilename);
    }
    outfile = fopen(vedgefilename, "w");
    if (outfile == (FILE *) NULL) {
      printf("  Error:  Cannot create file %s.\n", vedgefilename);
      triexit(1);
    }
    /* Number of edges, zero boundary markers. */
    fprintf(outfile, "%ld  %d\n", m->edges, 0);
  #endif /* not TRILIBRARY */
  
    traversalinit(&m->triangles);
    triangleloop.tri = triangletraverse(m);
    vedgenumber = b->firstnumber;
    /* To loop over the set of edges, loop over all triangles, and look at   */
    /*   the three edges of each triangle.  If there isn't another triangle  */
    /*   adjacent to the edge, operate on the edge.  If there is another     */
    /*   adjacent triangle, operate on the edge only if the current triangle */
    /*   has a smaller pointer than its neighbor.  This way, each edge is    */
    /*   considered only once.                                               */
    while (triangleloop.tri != (triangle *) NULL) {
      for (triangleloop.orient = 0; triangleloop.orient < 3;
           triangleloop.orient++) {
        sym(triangleloop, trisym);
        if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) {
          /* Find the number of this triangle (and Voronoi vertex). */
          p1 = * (int *) (triangleloop.tri + 6);
          if (trisym.tri == m->dummytri) {
            org(triangleloop, torg);
            dest(triangleloop, tdest);
  #ifdef TRILIBRARY
            /* Copy an infinite ray.  Index of one endpoint, and -1. */
            elist[coordindex] = p1;
            normlist[coordindex++] = tdest[1] - torg[1];
            elist[coordindex] = -1;
            normlist[coordindex++] = torg[0] - tdest[0];
  #else /* not TRILIBRARY */
            /* Write an infinite ray.  Edge number, index of one endpoint, -1, */
            /*   and x and y coordinates of a vector representing the          */
            /*   direction of the ray.                                         */
            fprintf(outfile, "%4ld   %d  %d   %.17g  %.17g\n", vedgenumber,
                    p1, -1, tdest[1] - torg[1], torg[0] - tdest[0]);
  #endif /* not TRILIBRARY */
          } else {
            /* Find the number of the adjacent triangle (and Voronoi vertex). */
            p2 = * (int *) (trisym.tri + 6);
            /* Finite edge.  Write indices of two endpoints. */
  #ifdef TRILIBRARY
            elist[coordindex] = p1;
            normlist[coordindex++] = 0.0;
            elist[coordindex] = p2;
            normlist[coordindex++] = 0.0;
  #else /* not TRILIBRARY */
            fprintf(outfile, "%4ld   %d  %d\n", vedgenumber, p1, p2);
  #endif /* not TRILIBRARY */
          }
          vedgenumber++;
        }
      }
      triangleloop.tri = triangletraverse(m);
    }
  
  #ifndef TRILIBRARY
    finishfile(outfile, argc, argv);
  #endif /* not TRILIBRARY */
  }
  
  #ifdef TRILIBRARY
  
  #ifdef ANSI_DECLARATORS
  void writeneighbors(struct mesh *m, struct behavior *b, int **neighborlist)
  #else /* not ANSI_DECLARATORS */
  void writeneighbors(m, b, neighborlist)
  struct mesh *m;
  struct behavior *b;
  int **neighborlist;
  #endif /* not ANSI_DECLARATORS */
  
  #else /* not TRILIBRARY */
  
  #ifdef ANSI_DECLARATORS
  void writeneighbors(struct mesh *m, struct behavior *b, char *neighborfilename,
                      int argc, char **argv)
  #else /* not ANSI_DECLARATORS */
  void writeneighbors(m, b, neighborfilename, argc, argv)
  struct mesh *m;
  struct behavior *b;
  char *neighborfilename;
  int argc;
  char **argv;
  #endif /* not ANSI_DECLARATORS */
  
  #endif /* not TRILIBRARY */
  
  {
  #ifdef TRILIBRARY
    int *nlist;
    int index;
  #else /* not TRILIBRARY */
    FILE *outfile;
  #endif /* not TRILIBRARY */
    struct otri triangleloop, trisym;
    long elementnumber;
    int neighbor1, neighbor2, neighbor3;
    triangle ptr;                         /* Temporary variable used by sym(). */
  
  #ifdef TRILIBRARY
    if (!b->quiet) {
      printf("Writing neighbors.\n");
    }
    /* Allocate memory for neighbors if necessary. */
    if (*neighborlist == (int *) NULL) {
      *neighborlist = (int *) trimalloc((int) (m->triangles.items * 3 *
                                               sizeof(int)));
    }
    nlist = *neighborlist;
    index = 0;
  #else /* not TRILIBRARY */
    if (!b->quiet) {
      printf("Writing %s.\n", neighborfilename);
    }
    outfile = fopen(neighborfilename, "w");
    if (outfile == (FILE *) NULL) {
      printf("  Error:  Cannot create file %s.\n", neighborfilename);
      triexit(1);
    }
    /* Number of triangles, three neighbors per triangle. */
    fprintf(outfile, "%ld  %d\n", m->triangles.items, 3);
  #endif /* not TRILIBRARY */
  
    traversalinit(&m->triangles);
    triangleloop.tri = triangletraverse(m);
    triangleloop.orient = 0;
    elementnumber = b->firstnumber;
    while (triangleloop.tri != (triangle *) NULL) {
      * (int *) (triangleloop.tri + 6) = (int) elementnumber;
      triangleloop.tri = triangletraverse(m);
      elementnumber++;
    }
    * (int *) (m->dummytri + 6) = -1;
  
    traversalinit(&m->triangles);
    triangleloop.tri = triangletraverse(m);
    elementnumber = b->firstnumber;
    while (triangleloop.tri != (triangle *) NULL) {
      triangleloop.orient = 1;
      sym(triangleloop, trisym);
      neighbor1 = * (int *) (trisym.tri + 6);
      triangleloop.orient = 2;
      sym(triangleloop, trisym);
      neighbor2 = * (int *) (trisym.tri + 6);
      triangleloop.orient = 0;
      sym(triangleloop, trisym);
      neighbor3 = * (int *) (trisym.tri + 6);
  #ifdef TRILIBRARY
      nlist[index++] = neighbor1;
      nlist[index++] = neighbor2;
      nlist[index++] = neighbor3;
  #else /* not TRILIBRARY */
      /* Triangle number, neighboring triangle numbers. */
      fprintf(outfile, "%4ld    %d  %d  %d\n", elementnumber,
              neighbor1, neighbor2, neighbor3);
  #endif /* not TRILIBRARY */
  
      triangleloop.tri = triangletraverse(m);
      elementnumber++;
    }
  
  #ifndef TRILIBRARY
    finishfile(outfile, argc, argv);
  #endif /* not TRILIBRARY */
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  writeoff()   Write the triangulation to an .off file.                    */
  /*                                                                           */
  /*  OFF stands for the Object File Format, a format used by the Geometry     */
  /*  Center's Geomview package.                                               */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifndef TRILIBRARY
  
  #ifdef ANSI_DECLARATORS
  void writeoff(struct mesh *m, struct behavior *b, char *offfilename,
                int argc, char **argv)
  #else /* not ANSI_DECLARATORS */
  void writeoff(m, b, offfilename, argc, argv)
  struct mesh *m;
  struct behavior *b;
  char *offfilename;
  int argc;
  char **argv;
  #endif /* not ANSI_DECLARATORS */
  
  {
    FILE *outfile;
    struct otri triangleloop;
    vertex vertexloop;
    vertex p1, p2, p3;
    long outvertices;
  
    if (!b->quiet) {
      printf("Writing %s.\n", offfilename);
    }
  
    if (b->jettison) {
      outvertices = m->vertices.items - m->undeads;
    } else {
      outvertices = m->vertices.items;
    }
  
    outfile = fopen(offfilename, "w");
    if (outfile == (FILE *) NULL) {
      printf("  Error:  Cannot create file %s.\n", offfilename);
      triexit(1);
    }
    /* Number of vertices, triangles, and edges. */
    fprintf(outfile, "OFF\n%ld  %ld  %ld\n", outvertices, m->triangles.items,
            m->edges);
  
    /* Write the vertices. */
    traversalinit(&m->vertices);
    vertexloop = vertextraverse(m);
    while (vertexloop != (vertex) NULL) {
      if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) {
        /* The "0.0" is here because the OFF format uses 3D coordinates. */
        fprintf(outfile, " %.17g  %.17g  %.17g\n", vertexloop[0], vertexloop[1],
                0.0);
      }
      vertexloop = vertextraverse(m);
    }
  
    /* Write the triangles. */
    traversalinit(&m->triangles);
    triangleloop.tri = triangletraverse(m);
    triangleloop.orient = 0;
    while (triangleloop.tri != (triangle *) NULL) {
      org(triangleloop, p1);
      dest(triangleloop, p2);
      apex(triangleloop, p3);
      /* The "3" means a three-vertex polygon. */
      fprintf(outfile, " 3   %4d  %4d  %4d\n", vertexmark(p1) - b->firstnumber,
              vertexmark(p2) - b->firstnumber, vertexmark(p3) - b->firstnumber);
      triangleloop.tri = triangletraverse(m);
    }
    finishfile(outfile, argc, argv);
  }
  
  #endif /* not TRILIBRARY */
  
  /**                                                                         **/
  /**                                                                         **/
  /********* File I/O routines end here                                *********/
  
  /*****************************************************************************/
  /*                                                                           */
  /*  quality_statistics()   Print statistics about the quality of the mesh.   */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  void quality_statistics(struct mesh *m, struct behavior *b)
  #else /* not ANSI_DECLARATORS */
  void quality_statistics(m, b)
  struct mesh *m;
  struct behavior *b;
  #endif /* not ANSI_DECLARATORS */
  
  {
    struct otri triangleloop;
    vertex p[3];
    REAL cossquaretable[8];
    REAL ratiotable[16];
    REAL dx[3], dy[3];
    REAL edgelength[3];
    REAL dotproduct;
    REAL cossquare;
    REAL triarea;
    REAL shortest, longest;
    REAL trilongest2;
    REAL smallestarea, biggestarea;
    REAL triminaltitude2;
    REAL minaltitude;
    REAL triaspect2;
    REAL worstaspect;
    REAL smallestangle, biggestangle;
    REAL radconst, degconst;
    int angletable[18];
    int aspecttable[16];
    int aspectindex;
    int tendegree;
    int acutebiggest;
    int i, ii, j, k;
  
    printf("Mesh quality statistics:\n\n");
    radconst = PI / 18.0;
    degconst = 180.0 / PI;
    for (i = 0; i < 8; i++) {
      cossquaretable[i] = cos(radconst * (REAL) (i + 1));
      cossquaretable[i] = cossquaretable[i] * cossquaretable[i];
    }
    for (i = 0; i < 18; i++) {
      angletable[i] = 0;
    }
  
    ratiotable[0]  =      1.5;      ratiotable[1]  =     2.0;
    ratiotable[2]  =      2.5;      ratiotable[3]  =     3.0;
    ratiotable[4]  =      4.0;      ratiotable[5]  =     6.0;
    ratiotable[6]  =     10.0;      ratiotable[7]  =    15.0;
    ratiotable[8]  =     25.0;      ratiotable[9]  =    50.0;
    ratiotable[10] =    100.0;      ratiotable[11] =   300.0;
    ratiotable[12] =   1000.0;      ratiotable[13] = 10000.0;
    ratiotable[14] = 100000.0;      ratiotable[15] =     0.0;
    for (i = 0; i < 16; i++) {
      aspecttable[i] = 0;
    }
  
    worstaspect = 0.0;
    minaltitude = m->xmax - m->xmin + m->ymax - m->ymin;
    minaltitude = minaltitude * minaltitude;
    shortest = minaltitude;
    longest = 0.0;
    smallestarea = minaltitude;
    biggestarea = 0.0;
    worstaspect = 0.0;
    smallestangle = 0.0;
    biggestangle = 2.0;
    acutebiggest = 1;
  
    traversalinit(&m->triangles);
    triangleloop.tri = triangletraverse(m);
    triangleloop.orient = 0;
    while (triangleloop.tri != (triangle *) NULL) {
      org(triangleloop, p[0]);
      dest(triangleloop, p[1]);
      apex(triangleloop, p[2]);
      trilongest2 = 0.0;
  
      for (i = 0; i < 3; i++) {
        j = plus1mod3[i];
        k = minus1mod3[i];
        dx[i] = p[j][0] - p[k][0];
        dy[i] = p[j][1] - p[k][1];
        edgelength[i] = dx[i] * dx[i] + dy[i] * dy[i];
        if (edgelength[i] > trilongest2) {
          trilongest2 = edgelength[i];
        }
        if (edgelength[i] > longest) {
          longest = edgelength[i];
        }
        if (edgelength[i] < shortest) {
          shortest = edgelength[i];
        }
      }
  
      triarea = counterclockwise(m, b, p[0], p[1], p[2]);
      if (triarea < smallestarea) {
        smallestarea = triarea;
      }
      if (triarea > biggestarea) {
        biggestarea = triarea;
      }
      triminaltitude2 = triarea * triarea / trilongest2;
      if (triminaltitude2 < minaltitude) {
        minaltitude = triminaltitude2;
      }
      triaspect2 = trilongest2 / triminaltitude2;
      if (triaspect2 > worstaspect) {
        worstaspect = triaspect2;
      }
      aspectindex = 0;
      while ((triaspect2 > ratiotable[aspectindex] * ratiotable[aspectindex])
             && (aspectindex < 15)) {
        aspectindex++;
      }
      aspecttable[aspectindex]++;
  
      for (i = 0; i < 3; i++) {
        j = plus1mod3[i];
        k = minus1mod3[i];
        dotproduct = dx[j] * dx[k] + dy[j] * dy[k];
        cossquare = dotproduct * dotproduct / (edgelength[j] * edgelength[k]);
        tendegree = 8;
        for (ii = 7; ii >= 0; ii--) {
          if (cossquare > cossquaretable[ii]) {
            tendegree = ii;
          }
        }
        if (dotproduct <= 0.0) {
          angletable[tendegree]++;
          if (cossquare > smallestangle) {
            smallestangle = cossquare;
          }
          if (acutebiggest && (cossquare < biggestangle)) {
            biggestangle = cossquare;
          }
        } else {
          angletable[17 - tendegree]++;
          if (acutebiggest || (cossquare > biggestangle)) {
            biggestangle = cossquare;
            acutebiggest = 0;
          }
        }
      }
      triangleloop.tri = triangletraverse(m);
    }
  
    shortest = sqrt(shortest);
    longest = sqrt(longest);
    minaltitude = sqrt(minaltitude);
    worstaspect = sqrt(worstaspect);
    smallestarea *= 0.5;
    biggestarea *= 0.5;
    if (smallestangle >= 1.0) {
      smallestangle = 0.0;
    } else {
      smallestangle = degconst * acos(sqrt(smallestangle));
    }
    if (biggestangle >= 1.0) {
      biggestangle = 180.0;
    } else {
      if (acutebiggest) {
        biggestangle = degconst * acos(sqrt(biggestangle));
      } else {
        biggestangle = 180.0 - degconst * acos(sqrt(biggestangle));
      }
    }
  
    printf("  Smallest area: %16.5g   |  Largest area: %16.5g\n",
           smallestarea, biggestarea);
    printf("  Shortest edge: %16.5g   |  Longest edge: %16.5g\n",
           shortest, longest);
    printf("  Shortest altitude: %12.5g   |  Largest aspect ratio: %8.5g\n\n",
           minaltitude, worstaspect);
  
    printf("  Triangle aspect ratio histogram:\n");
    printf("  1.1547 - %-6.6g    :  %8d    | %6.6g - %-6.6g     :  %8d\n",
           ratiotable[0], aspecttable[0], ratiotable[7], ratiotable[8],
           aspecttable[8]);
    for (i = 1; i < 7; i++) {
      printf("  %6.6g - %-6.6g    :  %8d    | %6.6g - %-6.6g     :  %8d\n",
             ratiotable[i - 1], ratiotable[i], aspecttable[i],
             ratiotable[i + 7], ratiotable[i + 8], aspecttable[i + 8]);
    }
    printf("  %6.6g - %-6.6g    :  %8d    | %6.6g -            :  %8d\n",
           ratiotable[6], ratiotable[7], aspecttable[7], ratiotable[14],
           aspecttable[15]);
    printf("  (Aspect ratio is longest edge divided by shortest altitude)\n\n");
  
    printf("  Smallest angle: %15.5g   |  Largest angle: %15.5g\n\n",
           smallestangle, biggestangle);
  
    printf("  Angle histogram:\n");
    for (i = 0; i < 9; i++) {
      printf("    %3d - %3d degrees:  %8d    |    %3d - %3d degrees:  %8d\n",
             i * 10, i * 10 + 10, angletable[i],
             i * 10 + 90, i * 10 + 100, angletable[i + 9]);
    }
    printf("\n");
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  statistics()   Print all sorts of cool facts.                            */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  void statistics(struct mesh *m, struct behavior *b)
  #else /* not ANSI_DECLARATORS */
  void statistics(m, b)
  struct mesh *m;
  struct behavior *b;
  #endif /* not ANSI_DECLARATORS */
  
  {
    printf("\nStatistics:\n\n");
    printf("  Input vertices: %d\n", m->invertices);
    if (b->refine) {
      printf("  Input triangles: %d\n", m->inelements);
    }
    if (b->poly) {
      printf("  Input segments: %d\n", m->insegments);
      if (!b->refine) {
        printf("  Input holes: %d\n", m->holes);
      }
    }
  
    printf("\n  Mesh vertices: %ld\n", m->vertices.items - m->undeads);
    printf("  Mesh triangles: %ld\n", m->triangles.items);
    printf("  Mesh edges: %ld\n", m->edges);
    printf("  Mesh exterior boundary edges: %ld\n", m->hullsize);
    if (b->poly || b->refine) {
      printf("  Mesh interior boundary edges: %ld\n",
             m->subsegs.items - m->hullsize);
      printf("  Mesh subsegments (constrained edges): %ld\n",
             m->subsegs.items);
    }
    printf("\n");
  
    if (b->verbose) {
      quality_statistics(m, b);
      printf("Memory allocation statistics:\n\n");
      printf("  Maximum number of vertices: %ld\n", m->vertices.maxitems);
      printf("  Maximum number of triangles: %ld\n", m->triangles.maxitems);
      if (m->subsegs.maxitems > 0) {
        printf("  Maximum number of subsegments: %ld\n", m->subsegs.maxitems);
      }
      if (m->viri.maxitems > 0) {
        printf("  Maximum number of viri: %ld\n", m->viri.maxitems);
      }
      if (m->badsubsegs.maxitems > 0) {
        printf("  Maximum number of encroached subsegments: %ld\n",
               m->badsubsegs.maxitems);
      }
      if (m->badtriangles.maxitems > 0) {
        printf("  Maximum number of bad triangles: %ld\n",
               m->badtriangles.maxitems);
      }
      if (m->flipstackers.maxitems > 0) {
        printf("  Maximum number of stacked triangle flips: %ld\n",
               m->flipstackers.maxitems);
      }
      if (m->splaynodes.maxitems > 0) {
        printf("  Maximum number of splay tree nodes: %ld\n",
               m->splaynodes.maxitems);
      }
      printf("  Approximate heap memory use (bytes): %ld\n\n",
             m->vertices.maxitems * m->vertices.itembytes +
             m->triangles.maxitems * m->triangles.itembytes +
             m->subsegs.maxitems * m->subsegs.itembytes +
             m->viri.maxitems * m->viri.itembytes +
             m->badsubsegs.maxitems * m->badsubsegs.itembytes +
             m->badtriangles.maxitems * m->badtriangles.itembytes +
             m->flipstackers.maxitems * m->flipstackers.itembytes +
             m->splaynodes.maxitems * m->splaynodes.itembytes);
  
      printf("Algorithmic statistics:\n\n");
      if (!b->weighted) {
        printf("  Number of incircle tests: %ld\n", m->incirclecount);
      } else {
        printf("  Number of 3D orientation tests: %ld\n", m->orient3dcount);
      }
      printf("  Number of 2D orientation tests: %ld\n", m->counterclockcount);
      if (m->hyperbolacount > 0) {
        printf("  Number of right-of-hyperbola tests: %ld\n",
               m->hyperbolacount);
      }
      if (m->circletopcount > 0) {
        printf("  Number of circle top computations: %ld\n",
               m->circletopcount);
      }
      if (m->circumcentercount > 0) {
        printf("  Number of triangle circumcenter computations: %ld\n",
               m->circumcentercount);
      }
      printf("\n");
    }
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  main() or triangulate()   Gosh, do everything.                           */
  /*                                                                           */
  /*  The sequence is roughly as follows.  Many of these steps can be skipped, */
  /*  depending on the command line switches.                                  */
  /*                                                                           */
  /*  - Initialize constants and parse the command line.                       */
  /*  - Read the vertices from a file and either                               */
  /*    - triangulate them (no -r), or                                         */
  /*    - read an old mesh from files and reconstruct it (-r).                 */
  /*  - Insert the PSLG segments (-p), and possibly segments on the convex     */
  /*      hull (-c).                                                           */
  /*  - Read the holes (-p), regional attributes (-pA), and regional area      */
  /*      constraints (-pa).  Carve the holes and concavities, and spread the  */
  /*      regional attributes and area constraints.                            */
  /*  - Enforce the constraints on minimum angle (-q) and maximum area (-a).   */
  /*      Also enforce the conforming Delaunay property (-q and -a).           */
  /*  - Compute the number of edges in the resulting mesh.                     */
  /*  - Promote the mesh's linear triangles to higher order elements (-o).     */
  /*  - Write the output files and print the statistics.                       */
  /*  - Check the consistency and Delaunay property of the mesh (-C).          */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef TRILIBRARY
  
  #ifdef ANSI_DECLARATORS
  void triangulate(char *triswitches, struct triangulateio *in,
                   struct triangulateio *out, struct triangulateio *vorout)
  #else /* not ANSI_DECLARATORS */
  void triangulate(triswitches, in, out, vorout)
  char *triswitches;
  struct triangulateio *in;
  struct triangulateio *out;
  struct triangulateio *vorout;
  #endif /* not ANSI_DECLARATORS */
  
  #else /* not TRILIBRARY */
  
  #ifdef ANSI_DECLARATORS
  int main(int argc, char **argv)
  #else /* not ANSI_DECLARATORS */
  int main(argc, argv)
  int argc;
  char **argv;
  #endif /* not ANSI_DECLARATORS */
  
  #endif /* not TRILIBRARY */
  
  {
    struct mesh m;
    struct behavior b;
    REAL *holearray;                                        /* Array of holes. */
    REAL *regionarray;   /* Array of regional attributes and area constraints. */
  #ifndef TRILIBRARY
    FILE *polyfile;
  #endif /* not TRILIBRARY */
  #ifndef NO_TIMER
    /* Variables for timing the performance of Triangle.  The types are */
    /*   defined in sys/time.h.                                         */
    struct timeval tv0, tv1, tv2, tv3, tv4, tv5, tv6;
    struct timezone tz;
  #endif /* not NO_TIMER */
  
  #ifndef NO_TIMER
    gettimeofday(&tv0, &tz);
  #endif /* not NO_TIMER */
  
    triangleinit(&m);
  #ifdef TRILIBRARY
    parsecommandline(1, &triswitches, &b);
  #else /* not TRILIBRARY */
    parsecommandline(argc, argv, &b);
  #endif /* not TRILIBRARY */
    m.steinerleft = b.steiner;
  
  #ifdef TRILIBRARY
    transfernodes(&m, &b, in->pointlist, in->pointattributelist,
                  in->pointmarkerlist, in->numberofpoints,
                  in->numberofpointattributes);
  #else /* not TRILIBRARY */
    readnodes(&m, &b, b.innodefilename, b.inpolyfilename, &polyfile);
  #endif /* not TRILIBRARY */
  
  #ifndef NO_TIMER
    if (!b.quiet) {
      gettimeofday(&tv1, &tz);
    }
  #endif /* not NO_TIMER */
  
  #ifdef CDT_ONLY
    m.hullsize = delaunay(&m, &b);                /* Triangulate the vertices. */
  #else /* not CDT_ONLY */
    if (b.refine) {
      /* Read and reconstruct a mesh. */
  #ifdef TRILIBRARY
      m.hullsize = reconstruct(&m, &b, in->trianglelist,
                               in->triangleattributelist, in->trianglearealist,
                               in->numberoftriangles, in->numberofcorners,
                               in->numberoftriangleattributes,
                               in->segmentlist, in->segmentmarkerlist,
                               in->numberofsegments);
  #else /* not TRILIBRARY */
      m.hullsize = reconstruct(&m, &b, b.inelefilename, b.areafilename,
                               b.inpolyfilename, polyfile);
  #endif /* not TRILIBRARY */
    } else {
      m.hullsize = delaunay(&m, &b);              /* Triangulate the vertices. */
    }
  #endif /* not CDT_ONLY */
  
  #ifndef NO_TIMER
    if (!b.quiet) {
      gettimeofday(&tv2, &tz);
      if (b.refine) {
        printf("Mesh reconstruction");
      } else {
        printf("Delaunay");
      }
      printf(" milliseconds:  %ld\n", 1000l * (tv2.tv_sec - tv1.tv_sec) +
             (tv2.tv_usec - tv1.tv_usec) / 1000l);
    }
  #endif /* not NO_TIMER */
  
    /* Ensure that no vertex can be mistaken for a triangular bounding */
    /*   box vertex in insertvertex().                                 */
    m.infvertex1 = (vertex) NULL;
    m.infvertex2 = (vertex) NULL;
    m.infvertex3 = (vertex) NULL;
  
    if (b.usesegments) {
      m.checksegments = 1;                /* Segments will be introduced next. */
      if (!b.refine) {
        /* Insert PSLG segments and/or convex hull segments. */
  #ifdef TRILIBRARY
        formskeleton(&m, &b, in->segmentlist,
                     in->segmentmarkerlist, in->numberofsegments);
  #else /* not TRILIBRARY */
        formskeleton(&m, &b, polyfile, b.inpolyfilename);
  #endif /* not TRILIBRARY */
      }
    }
  
  #ifndef NO_TIMER
    if (!b.quiet) {
      gettimeofday(&tv3, &tz);
      if (b.usesegments && !b.refine) {
        printf("Segment milliseconds:  %ld\n",
               1000l * (tv3.tv_sec - tv2.tv_sec) +
               (tv3.tv_usec - tv2.tv_usec) / 1000l);
      }
    }
  #endif /* not NO_TIMER */
  
    if (b.poly && (m.triangles.items > 0)) {
  #ifdef TRILIBRARY
      holearray = in->holelist;
      m.holes = in->numberofholes;
      regionarray = in->regionlist;
      m.regions = in->numberofregions;
  #else /* not TRILIBRARY */
      readholes(&m, &b, polyfile, b.inpolyfilename, &holearray, &m.holes,
                &regionarray, &m.regions);
  #endif /* not TRILIBRARY */
      if (!b.refine) {
        /* Carve out holes and concavities. */
        carveholes(&m, &b, holearray, m.holes, regionarray, m.regions);
      }
    } else {
      /* Without a PSLG, there can be no holes or regional attributes   */
      /*   or area constraints.  The following are set to zero to avoid */
      /*   an accidental free() later.                                  */
      m.holes = 0;
      m.regions = 0;
    }
  
  #ifndef NO_TIMER
    if (!b.quiet) {
      gettimeofday(&tv4, &tz);
      if (b.poly && !b.refine) {
        printf("Hole milliseconds:  %ld\n", 1000l * (tv4.tv_sec - tv3.tv_sec) +
               (tv4.tv_usec - tv3.tv_usec) / 1000l);
      }
    }
  #endif /* not NO_TIMER */
  
  #ifndef CDT_ONLY
    if (b.quality && (m.triangles.items > 0)) {
      enforcequality(&m, &b);           /* Enforce angle and area constraints. */
    }
  #endif /* not CDT_ONLY */
  
  #ifndef NO_TIMER
    if (!b.quiet) {
      gettimeofday(&tv5, &tz);
  #ifndef CDT_ONLY
      if (b.quality) {
        printf("Quality milliseconds:  %ld\n",
               1000l * (tv5.tv_sec - tv4.tv_sec) +
               (tv5.tv_usec - tv4.tv_usec) / 1000l);
      }
  #endif /* not CDT_ONLY */
    }
  #endif /* not NO_TIMER */
  
    /* Calculate the number of edges. */
    m.edges = (3l * m.triangles.items + m.hullsize) / 2l;
  
    if (b.order > 1) {
      highorder(&m, &b);       /* Promote elements to higher polynomial order. */
    }
    if (!b.quiet) {
      printf("\n");
    }
  
  #ifdef TRILIBRARY
    if (b.jettison) {
      out->numberofpoints = m.vertices.items - m.undeads;
    } else {
      out->numberofpoints = m.vertices.items;
    }
    out->numberofpointattributes = m.nextras;
    out->numberoftriangles = m.triangles.items;
    out->numberofcorners = (b.order + 1) * (b.order + 2) / 2;
    out->numberoftriangleattributes = m.eextras;
    out->numberofedges = m.edges;
    if (b.usesegments) {
      out->numberofsegments = m.subsegs.items;
    } else {
      out->numberofsegments = m.hullsize;
    }
    if (vorout != (struct triangulateio *) NULL) {
      vorout->numberofpoints = m.triangles.items;
      vorout->numberofpointattributes = m.nextras;
      vorout->numberofedges = m.edges;
    }
  #endif /* TRILIBRARY */
    /* If not using iteration numbers, don't write a .node file if one was */
    /*   read, because the original one would be overwritten!              */
    if (b.nonodewritten || (b.noiterationnum && m.readnodefile)) {
      if (!b.quiet) {
  #ifdef TRILIBRARY
        printf("NOT writing vertices.\n");
  #else /* not TRILIBRARY */
        printf("NOT writing a .node file.\n");
  #endif /* not TRILIBRARY */
      }
      numbernodes(&m, &b);         /* We must remember to number the vertices. */
    } else {
      /* writenodes() numbers the vertices too. */
  #ifdef TRILIBRARY
      writenodes(&m, &b, &out->pointlist, &out->pointattributelist,
                 &out->pointmarkerlist);
  #else /* not TRILIBRARY */
      writenodes(&m, &b, b.outnodefilename, argc, argv);
  #endif /* TRILIBRARY */
    }
    if (b.noelewritten) {
      if (!b.quiet) {
  #ifdef TRILIBRARY
        printf("NOT writing triangles.\n");
  #else /* not TRILIBRARY */
        printf("NOT writing an .ele file.\n");
  #endif /* not TRILIBRARY */
      }
    } else {
  #ifdef TRILIBRARY
      writeelements(&m, &b, &out->trianglelist, &out->triangleattributelist);
  #else /* not TRILIBRARY */
      writeelements(&m, &b, b.outelefilename, argc, argv);
  #endif /* not TRILIBRARY */
    }
    /* The -c switch (convex switch) causes a PSLG to be written */
    /*   even if none was read.                                  */
    if (b.poly || b.convex) {
      /* If not using iteration numbers, don't overwrite the .poly file. */
      if (b.nopolywritten || b.noiterationnum) {
        if (!b.quiet) {
  #ifdef TRILIBRARY
          printf("NOT writing segments.\n");
  #else /* not TRILIBRARY */
          printf("NOT writing a .poly file.\n");
  #endif /* not TRILIBRARY */
        }
      } else {
  #ifdef TRILIBRARY
        writepoly(&m, &b, &out->segmentlist, &out->segmentmarkerlist);
        out->numberofholes = m.holes;
        out->numberofregions = m.regions;
        if (b.poly) {
          out->holelist = in->holelist;
          out->regionlist = in->regionlist;
        } else {
          out->holelist = (REAL *) NULL;
          out->regionlist = (REAL *) NULL;
        }
  #else /* not TRILIBRARY */
        writepoly(&m, &b, b.outpolyfilename, holearray, m.holes, regionarray,
                  m.regions, argc, argv);
  #endif /* not TRILIBRARY */
      }
    }
  #ifndef TRILIBRARY
  #ifndef CDT_ONLY
    if (m.regions > 0) {
      trifree((TRIVOID *) regionarray);
    }
  #endif /* not CDT_ONLY */
    if (m.holes > 0) {
      trifree((TRIVOID *) holearray);
    }
    if (b.geomview) {
      writeoff(&m, &b, b.offfilename, argc, argv);
    }
  #endif /* not TRILIBRARY */
    if (b.edgesout) {
  #ifdef TRILIBRARY
      writeedges(&m, &b, &out->edgelist, &out->edgemarkerlist);
  #else /* not TRILIBRARY */
      writeedges(&m, &b, b.edgefilename, argc, argv);
  #endif /* not TRILIBRARY */
    }
    if (b.voronoi) {
  #ifdef TRILIBRARY
      writevoronoi(&m, &b, &vorout->pointlist, &vorout->pointattributelist,
                   &vorout->pointmarkerlist, &vorout->edgelist,
                   &vorout->edgemarkerlist, &vorout->normlist);
  #else /* not TRILIBRARY */
      writevoronoi(&m, &b, b.vnodefilename, b.vedgefilename, argc, argv);
  #endif /* not TRILIBRARY */
    }
    if (b.neighbors) {
  #ifdef TRILIBRARY
      writeneighbors(&m, &b, &out->neighborlist);
  #else /* not TRILIBRARY */
      writeneighbors(&m, &b, b.neighborfilename, argc, argv);
  #endif /* not TRILIBRARY */
    }
  
    if (!b.quiet) {
  #ifndef NO_TIMER
      gettimeofday(&tv6, &tz);
      printf("\nOutput milliseconds:  %ld\n",
             1000l * (tv6.tv_sec - tv5.tv_sec) +
             (tv6.tv_usec - tv5.tv_usec) / 1000l);
      printf("Total running milliseconds:  %ld\n",
             1000l * (tv6.tv_sec - tv0.tv_sec) +
             (tv6.tv_usec - tv0.tv_usec) / 1000l);
  #endif /* not NO_TIMER */
  
      statistics(&m, &b);
    }
  
  #ifndef REDUCED
    if (b.docheck) {
      checkmesh(&m, &b);
      checkdelaunay(&m, &b);
    }
  #endif /* not REDUCED */
  
    triangledeinit(&m, &b);
  #ifndef TRILIBRARY
    return 0;
  #endif /* not TRILIBRARY */
  }
  