text: /*****************************************************************************/
  /*                                                                           */
  /*      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.             */
  /*                                                                           */
  /*****************************************************************************/
  
  #define ANSI_DECLARATORS
  
  /* 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 VOID 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.                                               */
  
  /* 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. */
  	VOID *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 {
  	VOID **firstblock, **nowblock;
  	VOID *nextitem;
  	VOID *deaditemstack;
  	VOID **pathblock;
  	VOID *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.                                                 */
  };                                              /* 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.*/
  /*                                                                           */
  /*  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) (ptr) & (unsigned long) 3l);         \
  	(otri).tri = (triangle *)                                                   \
  	((unsigned long) (ptr) ^ (unsigned 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) (otri).tri | (unsigned 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) (otri).tri[6] | (unsigned long) 2l)
  
  #define uninfect(otri)                                                        \
  	(otri).tri[6] = (triangle)                                                  \
  	((unsigned long) (otri).tri[6] & ~ (unsigned long) 2l)
  
  /* Test a triangle for viral infection.                                      */
  
  #define infected(otri)                                                        \
  	(((unsigned long) (otri).tri[6] & (unsigned long) 2l) != 0l)
  
  /* 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) (sptr) & (unsigned long) 1l);      \
  	(osub).ss = (subseg *)                                                      \
  	((unsigned long) (sptr) & ~ (unsigned long) 3l)
  
  /* 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) (osub).ss | (unsigned 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
  VOID *trimalloc(int size)
  #else /* not ANSI_DECLARATORS */
  VOID *trimalloc(size)
  int size;
  #endif /* not ANSI_DECLARATORS */
  
  {
  	VOID *memptr;
  
  	memptr = (VOID *) malloc((unsigned int) size);
  	if (memptr == (VOID *) NULL) {
  		printf("Error:  Out of memory.\n");
  		triexit(1);
  	}
  	return(memptr);
  }
  
  #ifdef ANSI_DECLARATORS
  void trifree(VOID *memptr)
  #else /* not ANSI_DECLARATORS */
  void trifree(memptr)
  VOID *memptr;
  #endif /* not ANSI_DECLARATORS */
  
  {
  	free(memptr);
  }
  
  /**                                                                         **/
  /**                                                                         **/
  /********* Memory allocation and program exit wrappers end here      *********/
  
  /********* User interaction routines begin here                      *********/
  /**                                                                         **/
  /**                                                                         **/
  
  /*****************************************************************************/
  /*                                                                           */
  /*  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, const 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 */
  
  {
  #define STARTINDEX 0
  	int i, j;
  
  	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;
  
  	for (i = STARTINDEX; i < argc; i++) {
  			for (j = STARTINDEX; argv[i][j] != '\0'; j++) {
  				if (argv[i][j] == 'p') {
  					b->poly = 1;
  				}
  				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;
  				}
  				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;
  					}
  				}
  				if (argv[i][j] == 'l') {
  					b->dwyer = 0;
  				}
  				if (argv[i][j] == 'Q') {
  					b->quiet = 1;
  				}
  				if (argv[i][j] == 'V') {
  					b->verbose++;
  				}
  			}
  	}
  	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.");
  	}
  }
  
  /**                                                                         **/
  /**                                                                         **/
  /********* 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%lx with orientation %d:\n", (unsigned long) t->tri,
  		t->orient);
  	decode(t->tri[0], printtri);
  	if (printtri.tri == m->dummytri) {
  		printf("    [0] = Outer space\n");
  	} else {
  		printf("    [0] = x%lx  %d\n", (unsigned long) printtri.tri,
  			printtri.orient);
  	}
  	decode(t->tri[1], printtri);
  	if (printtri.tri == m->dummytri) {
  		printf("    [1] = Outer space\n");
  	} else {
  		printf("    [1] = x%lx  %d\n", (unsigned long) printtri.tri,
  			printtri.orient);
  	}
  	decode(t->tri[2], printtri);
  	if (printtri.tri == m->dummytri) {
  		printf("    [2] = Outer space\n");
  	} else {
  		printf("    [2] = x%lx  %d\n", (unsigned 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%lx  (%.12g, %.12g)\n",
  		(t->orient + 1) % 3 + 3, (unsigned 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%lx  (%.12g, %.12g)\n",
  		(t->orient + 2) % 3 + 3, (unsigned 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%lx  (%.12g, %.12g)\n",
  		t->orient + 3, (unsigned long) printvertex,
  		printvertex[0], printvertex[1]);
  
  	if (b->usesegments) {
  		sdecode(t->tri[6], printsh);
  		if (printsh.ss != m->dummysub) {
  			printf("    [6] = x%lx  %d\n", (unsigned long) printsh.ss,
  				printsh.ssorient);
  		}
  		sdecode(t->tri[7], printsh);
  		if (printsh.ss != m->dummysub) {
  			printf("    [7] = x%lx  %d\n", (unsigned long) printsh.ss,
  				printsh.ssorient);
  		}
  		sdecode(t->tri[8], printsh);
  		if (printsh.ss != m->dummysub) {
  			printf("    [8] = x%lx  %d\n", (unsigned 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%lx with orientation %d and mark %d:\n",
  		(unsigned 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%lx  %d\n", (unsigned long) printsh.ss,
  			printsh.ssorient);
  	}
  	sdecode(s->ss[1], printsh);
  	if (printsh.ss == m->dummysub) {
  		printf("    [1] = No subsegment\n");
  	} else {
  		printf("    [1] = x%lx  %d\n", (unsigned 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%lx  (%.12g, %.12g)\n",
  		2 + s->ssorient, (unsigned 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%lx  (%.12g, %.12g)\n",
  		3 - s->ssorient, (unsigned 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%lx  %d\n", (unsigned long) printtri.tri,
  			printtri.orient);
  	}
  	decode(s->ss[7], printtri);
  	if (printtri.tri == m->dummytri) {
  		printf("    [7] = Outer space\n");
  	} else {
  		printf("    [7] = x%lx  %d\n", (unsigned 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%lx  (%.12g, %.12g)\n",
  		4 + s->ssorient, (unsigned 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%lx  (%.12g, %.12g)\n",
  		5 - s->ssorient, (unsigned 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 = (VOID **) NULL;
  	pool->nowblock = (VOID **) NULL;
  	pool->nextitem = (VOID *) NULL;
  	pool->deaditemstack = (VOID *) NULL;
  	pool->pathblock = (VOID **) NULL;
  	pool->pathitem = (VOID *) 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 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 (VOID *). */
  	alignptr = (unsigned long) (pool->nowblock + 1);
  	/* Align the item on an `alignbytes'-byte boundary. */
  	pool->nextitem = (VOID *)
  		(alignptr + (unsigned long) pool->alignbytes -
  		(alignptr % (unsigned 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 = (VOID *) 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(VOID *), so the stack of dead items can be maintained */
  	/*       without unaligned accesses.                                */
  	if (alignment > sizeof(VOID *)) {
  		pool->alignbytes = alignment;
  	} else {
  		pool->alignbytes = sizeof(VOID *);
  	}
  	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 = (VOID **)
  		trimalloc(pool->itemsfirstblock * pool->itembytes + (int) sizeof(VOID *) +
  		pool->alignbytes);
  	/* Set the next block pointer to NULL. */
  	*(pool->firstblock) = (VOID *) 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 != (VOID **) NULL) {
  		pool->nowblock = (VOID **) *(pool->firstblock);
  		trifree((VOID *) pool->firstblock);
  		pool->firstblock = pool->nowblock;
  	}
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  poolalloc()   Allocate space for an item.                                */
  /*                                                                           */
  /*****************************************************************************/
  
  #ifdef ANSI_DECLARATORS
  VOID *poolalloc(struct memorypool *pool)
  #else /* not ANSI_DECLARATORS */
  VOID *poolalloc(pool)
  struct memorypool *pool;
  #endif /* not ANSI_DECLARATORS */
  
  {
  	VOID *newitem;
  	VOID **newblock;
  	unsigned 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 != (VOID *) NULL) {
  		newitem = pool->deaditemstack;               /* Take first item in list. */
  		pool->deaditemstack = * (VOID **) 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) == (VOID *) NULL) {
  				/* Allocate a new block of items, pointed to by the previous block. */
  				newblock = (VOID **) trimalloc(pool->itemsperblock * pool->itembytes +
  					(int) sizeof(VOID *) +
  					pool->alignbytes);
  				*(pool->nowblock) = (VOID *) newblock;
  				/* The next block pointer is NULL. */
  				*newblock = (VOID *) NULL;
  			}
  
  			/* Move to the new block. */
  			pool->nowblock = (VOID **) *(pool->nowblock);
  			/* Find the first item in the block.    */
  			/*   Increment by the size of (VOID *). */
  			alignptr = (unsigned long) (pool->nowblock + 1);
  			/* Align the item on an `alignbytes'-byte boundary. */
  			pool->nextitem = (VOID *)
  				(alignptr + (unsigned long) pool->alignbytes -
  				(alignptr % (unsigned 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 = (VOID *) ((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, VOID *dyingitem)
  #else /* not ANSI_DECLARATORS */
  void pooldealloc(pool, dyingitem)
  struct memorypool *pool;
  VOID *dyingitem;
  #endif /* not ANSI_DECLARATORS */
  
  {
  	/* Push freshly killed item onto stack. */
  	*((VOID **) 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 alignptr;
  
  	/* Begin the traversal in the first block. */
  	pool->pathblock = pool->firstblock;
  	/* Find the first item in the block.  Increment by the size of (VOID *). */
  	alignptr = (unsigned long) (pool->pathblock + 1);
  	/* Align with item on an `alignbytes'-byte boundary. */
  	pool->pathitem = (VOID *)
  		(alignptr + (unsigned long) pool->alignbytes -
  		(alignptr % (unsigned 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
  VOID *traverse(struct memorypool *pool)
  #else /* not ANSI_DECLARATORS */
  VOID *traverse(pool)
  struct memorypool *pool;
  #endif /* not ANSI_DECLARATORS */
  
  {
  	VOID *newitem;
  	unsigned long alignptr;
  
  	/* Stop upon exhausting the list of items. */
  	if (pool->pathitem == pool->nextitem) {
  		return (VOID *) NULL;
  	}
  
  	/* Check whether any untraversed items remain in the current block. */
  	if (pool->pathitemsleft == 0) {
  		/* Find the next block. */
  		pool->pathblock = (VOID **) *(pool->pathblock);
  		/* Find the first item in the block.  Increment by the size of (VOID *). */
  		alignptr = (unsigned long) (pool->pathblock + 1);
  		/* Align with item on an `alignbytes'-byte boundary. */
  		pool->pathitem = (VOID *)
  			(alignptr + (unsigned long) pool->alignbytes -
  			(alignptr % (unsigned 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 = (VOID *) ((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 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) m->dummytribase;
  	m->dummytri = (triangle *)
  		(alignptr + (unsigned long) m->triangles.alignbytes -
  		(alignptr % (unsigned 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) m->dummysubbase;
  		m->dummysub = (subseg *)
  			(alignptr + (unsigned long) m->subsegs.alignbytes -
  			(alignptr % (unsigned 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, (VOID *) 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, (VOID *) 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, (VOID *) 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;
  }
  
  
  /*****************************************************************************/
  /*                                                                           */
  /*  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 */
  
  {
  	VOID **getblock;
  	char *foundvertex;
  	unsigned long alignptr;
  	int current;
  
  	getblock = m->vertices.firstblock;
  	current = b->firstnumber;
  
  	/* Find the right block. */
  	if (current + m->vertices.itemsfirstblock <= number) {
  		getblock = (VOID **) *getblock;
  		current += m->vertices.itemsfirstblock;
  		while (current + m->vertices.itemsperblock <= number) {
  			getblock = (VOID **) *getblock;
  			current += m->vertices.itemsperblock;
  		}
  	}
  
  	/* Now find the right vertex. */
  	alignptr = (unsigned long) (getblock + 1);
  	foundvertex = (char *) (alignptr + (unsigned long) m->vertices.alignbytes -
  		(alignptr % (unsigned 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((VOID *) m->dummytribase);
  	if (b->usesegments) {
  		pooldeinit(&m->subsegs);
  		trifree((VOID *) m->dummysubbase);
  	}
  	pooldeinit(&m->vertices);
  }
  
  /**                                                                         **/
  /**                                                                         **/
  /********* 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);
  }
  
  /********* 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 */
  
  {
  	VOID **sampleblock;
  	char *firsttri;
  	struct otri sampletri;
  	vertex torg, tdest;
  	unsigned 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) (sampleblock + 1);
  		firsttri = (char *) (alignptr +
  			(unsigned long) m->triangles.alignbytes -
  			(alignptr %
  			(unsigned 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 = (VOID **) *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;
  			}
  		}
  
  		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. */
  			/* 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);
  	}
  	/* Return the base triangle. */
  	otricopy(besttri, *lastedge);
  }
  
  /**                                                                         **/
  /**                                                                         **/
  /********* 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((VOID *) sortarray);
  
  	return removeghosts(m, b, &hullleft);
  }
  
  /**                                                                         **/
  /**                                                                         **/
  /********* Divide-and-conquer 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);
  
  	if (!b->quiet) {
  		printf(
  			"Constructing Delaunay triangulation by divide-and-conquer method.\n");
  	}
  	hulledges = divconqdelaunay(m, b);
  
  	if (m->triangles.items == 0) {
  		/* The input vertices were all collinear, so there are no triangles. */
  		return 0l;
  	} else {
  		return hulledges;
  	}
  }
  
  /**                                                                         **/
  /**                                                                         **/
  /********* 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);
  		}
  	}
  }
  
  
  /*****************************************************************************/
  /*                                                                           */
  /*  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);
  
  		/* Insert the segment directly into the triangulation. */
  		constrainededge(m, b, &searchtri1, endpoint2, newmark);
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  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 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 */
  
  {
  	char polyfilename[6];
  	int index;
  
  	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");
  		}
  		strcpy(polyfilename, "input");
  		m->insegments = numberofsegments;
  		segmentmarkers = segmentmarkerlist != (int *) NULL;
  		index = 0;
  
  		/* 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++) {
  			end1 = segmentlist[index++];
  			end2 = segmentlist[index++];
  			if (segmentmarkers) {
  				boundmarker = segmentmarkerlist[i];
  			}
  
  			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((VOID *) regiontris);
  	}
  }
  
  /**                                                                         **/
  /**                                                                         **/
  /********* Carving out holes and concavities 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 = (VOID *) 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                              *********/
  /**                                                                         **/
  /**                                                                         **/
  
  /*****************************************************************************/
  /*                                                                           */
  /*  transfernodes()   Read the vertices from memory.                         */
  /*                                                                           */
  /*****************************************************************************/
  
  #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;
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  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 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 */
  
  {
  	REAL *plist;
  	REAL *palist;
  	int *pmlist;
  	int coordindex;
  	int attribindex;
  
  	vertex vertexloop;
  	long outvertices;
  	int vertexnumber;
  	int i;
  
  	if (b->jettison) {
  		outvertices = m->vertices.items - m->undeads;
  	} else {
  		outvertices = m->vertices.items;
  	}
  
  	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;
  
  
  	traversalinit(&m->vertices);
  	vertexnumber = b->firstnumber;
  	vertexloop = vertextraverse(m);
  	while (vertexloop != (vertex) NULL) {
  		if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) {
  			/* 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);
  			}
  
  
  			setvertexmark(vertexloop, vertexnumber);
  			vertexnumber++;
  		}
  		vertexloop = vertextraverse(m);
  	}
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  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 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 */
  
  {
  	int *tlist;
  	REAL *talist;
  	int vertexindex;
  	int attribindex;
  
  	struct otri triangleloop;
  	vertex p1, p2, p3;
  	vertex mid1, mid2, mid3;
  	long elementnumber;
  	int i;
  
  	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;
  
  	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) {
  			tlist[vertexindex++] = vertexmark(p1);
  			tlist[vertexindex++] = vertexmark(p2);
  			tlist[vertexindex++] = vertexmark(p3);
  
  		} else {
  			mid1 = (vertex) triangleloop.tri[m->highorderindex + 1];
  			mid2 = (vertex) triangleloop.tri[m->highorderindex + 2];
  			mid3 = (vertex) triangleloop.tri[m->highorderindex];
  
  			tlist[vertexindex++] = vertexmark(p1);
  			tlist[vertexindex++] = vertexmark(p2);
  			tlist[vertexindex++] = vertexmark(p3);
  			tlist[vertexindex++] = vertexmark(mid1);
  			tlist[vertexindex++] = vertexmark(mid2);
  			tlist[vertexindex++] = vertexmark(mid3);
  		}
  
  		for (i = 0; i < m->eextras; i++) {
  			talist[attribindex++] = elemattribute(triangleloop, i);
  		}
  
  		triangleloop.tri = triangletraverse(m);
  		elementnumber++;
  	}
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  writepoly()   Write the segments and holes to a .poly file.              */
  /*                                                                           */
  /*****************************************************************************/
  
  #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 */
  
  {
  	int *slist;
  	int *smlist;
  	int index;
  
  	struct osub subsegloop;
  	vertex endpoint1, endpoint2;
  	long subsegnumber;
  
  	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;
  
  	traversalinit(&m->subsegs);
  	subsegloop.ss = subsegtraverse(m);
  	subsegloop.ssorient = 0;
  	subsegnumber = b->firstnumber;
  	while (subsegloop.ss != (subseg *) NULL) {
  		sorg(subsegloop, endpoint1);
  		sdest(subsegloop, endpoint2);
  		/* 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);
  		}
  
  		subsegloop.ss = subsegtraverse(m);
  		subsegnumber++;
  	}
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  writeedges()   Write the edges to an .edge file.                         */
  /*                                                                           */
  /*****************************************************************************/
  
  #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 */
  
  {
  	int *elist;
  	int *emlist;
  	int index;
  
  	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(). */
  
  	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;
  
  	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);
  
  					elist[index++] = vertexmark(p1);
  					elist[index++] = vertexmark(p2);
  
  					if (b->nobound) {
  					} 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) {
  								emlist[edgenumber - b->firstnumber] = 0;
  							} else {
  								emlist[edgenumber - b->firstnumber] = mark(checkmark);
  							}
  						} else {
  							emlist[edgenumber - b->firstnumber] = trisym.tri == m->dummytri;
  						}
  					}
  					edgenumber++;
  				}
  		}
  		triangleloop.tri = triangletraverse(m);
  	}
  }
  
  /*****************************************************************************/
  /*                                                                           */
  /*  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 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 */
  
  {
  	REAL *plist;
  	REAL *palist;
  	int *elist;
  	REAL *normlist;
  	int coordindex;
  	int attribindex;
  
  	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(). */
  
  	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;
  
  	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);
  
  		/* 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]);
  		}
  
  		* (int *) (triangleloop.tri + 6) = (int) vnodenumber;
  		triangleloop.tri = triangletraverse(m);
  		vnodenumber++;
  	}
  
  	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;
  
  	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);
  
  						/* 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 {
  						/* Find the number of the adjacent triangle (and Voronoi vertex). */
  						p2 = * (int *) (trisym.tri + 6);
  						/* Finite edge.  Write indices of two endpoints. */
  						elist[coordindex] = p1;
  						normlist[coordindex++] = 0.0;
  						elist[coordindex] = p2;
  						normlist[coordindex++] = 0.0;
  					}
  					vedgenumber++;
  				}
  		}
  		triangleloop.tri = triangletraverse(m);
  	}
  }
  
  
  #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 */
  
  {
  	int *nlist;
  	int index;
  
  	struct otri triangleloop, trisym;
  	long elementnumber;
  	int neighbor1, neighbor2, neighbor3;
  	triangle ptr;                         /* Temporary variable used by sym(). */
  
  	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;
  
  	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);
  
  		nlist[index++] = neighbor1;
  		nlist[index++] = neighbor2;
  		nlist[index++] = neighbor3;
  
  		triangleloop.tri = triangletraverse(m);
  		elementnumber++;
  	}
  }
  
  /**                                                                         **/
  /**                                                                         **/
  /********* 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 ANSI_DECLARATORS
  void triangulate(const 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 */
  
  {
  	struct mesh m;
  	struct behavior b;
  	REAL *holearray;                                        /* Array of holes. */
  	REAL *regionarray;   /* Array of regional attributes and area constraints. */
  
  #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);
  	parsecommandline(1, &triswitches, &b);
  	m.steinerleft = b.steiner;
  
  	transfernodes(&m, &b, in->pointlist, in->pointattributelist,
  		in->pointmarkerlist, in->numberofpoints,
  		in->numberofpointattributes);
  
  #ifndef NO_TIMER
  	if (!b.quiet) {
  		gettimeofday(&tv1, &tz);
  	}
  #endif /* not NO_TIMER */
  
  	m.hullsize = delaunay(&m, &b);                /* Triangulate the vertices. */
  
  #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. */
  			formskeleton(&m, &b, in->segmentlist,
  				in->segmentmarkerlist, in->numberofsegments);
  		}
  	}
  
  #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)) {
  		holearray = in->holelist;
  		m.holes = in->numberofholes;
  		regionarray = in->regionlist;
  		m.regions = in->numberofregions;
  
  		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 NO_TIMER
  	if (!b.quiet) {
  		gettimeofday(&tv5, &tz);
  	}
  #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");
  	}
  
  	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;
  	}
  	/* 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) {
  			printf("NOT writing vertices.\n");
  		}
  		numbernodes(&m, &b);         /* We must remember to number the vertices. */
  	} else {
  		/* writenodes() numbers the vertices too. */
  		writenodes(&m, &b, &out->pointlist, &out->pointattributelist,
  			&out->pointmarkerlist);
  	}
  	if (b.noelewritten) {
  		if (!b.quiet) {
  			printf("NOT writing triangles.\n");
  		}
  	} else {
  		writeelements(&m, &b, &out->trianglelist, &out->triangleattributelist);
  	}
  	/* 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) {
  				printf("NOT writing segments.\n");
  			}
  		} else {
  			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;
  			}
  		}
  	}
  	if (b.edgesout) {
  		writeedges(&m, &b, &out->edgelist, &out->edgemarkerlist);
  	}
  	if (b.voronoi) {
  		writevoronoi(&m, &b, &vorout->pointlist, &vorout->pointattributelist,
  			&vorout->pointmarkerlist, &vorout->edgelist,
  			&vorout->edgemarkerlist, &vorout->normlist);
  	}
  	if (b.neighbors) {
  		writeneighbors(&m, &b, &out->neighborlist);
  	}
  
  	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);
  	}
  
  	triangledeinit(&m, &b);
  }
  