	/*****************************************************************************/
	/*                                                                           */
	/*      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.             */
	/*                                                                           */
	/*****************************************************************************/


	/* 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 int

	/* 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>
#ifdef CPU86
#include <float.h>
#endif /* CPU86 */
#ifdef LINUX
#include <fpu_control.h>
#endif /* LINUX */

#ifdef CPU86
template< typename Real > void control87( void );
template<> void control87< float  >( _control87(_PC_24, _MCW_PC) );
template<> void control87< double >( _control87(_PC_53, _MCW_PC) );
#endif /* CPU86 */



template< typename Real >
struct Shewchuk
{
	/* 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. */
		int *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 {
		int **firstblock, **nowblock;
		int *nextitem;
		int *deaditemstack;
		int **pathblock;
		int *pathitem;
		int alignbytes;
		int itembytes;
		int itemsperblock;
		int itemsfirstblock;
		long items, maxitems;
		int unallocateditems;
		int pathitemsleft;
	};


	/* Global constants.                                                         */

	static Real splitter;       /* Used to split Real factors for exact multiplication. */
	static Real epsilon;                             /* Floating-point machine epsilon. */
	static Real resulterrbound;
	static Real ccwerrboundA, ccwerrboundB, ccwerrboundC;
	static Real iccerrboundA, iccerrboundB, iccerrboundC;
	static Real o3derrboundA, o3derrboundB, o3derrboundC;

#ifdef LINUX
	static const int CWORD;
#endif /* LINUX */


	/* Random number seed is not constant, but I've made it global anyway.       */

	static size_t 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;
	};                                              /* 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 `size_t' 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.     */

	static const int plus1mod3[];
	static const int minus1mod3[];

	/********* 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) ((size_t) (ptr) & (size_t) 3l);         \
  (otri).tri = (triangle *)                                                   \
                  ((size_t) (ptr) ^ (size_t) (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) ((size_t) (otri).tri | (size_t) (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)                                                  \
                    ((size_t) (otri).tri[6] | (size_t) 2l)

#define uninfect(otri)                                                        \
  (otri).tri[6] = (triangle)                                                  \
                    ((size_t) (otri).tri[6] & ~ (size_t) 2l)

	/* Test a triangle for viral infection.                                      */

#define infected(otri)                                                        \
  (((size_t) (otri).tri[6] & (size_t) 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) ((size_t) (sptr) & (size_t) 1l);      \
  (osub).ss = (subseg *)                                                      \
              ((size_t) (sptr) & ~ (size_t) 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) ((size_t) (osub).ss | (size_t) (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

	static int triunsuitable();

#else /* not EXTERNAL_TEST */

	static int triunsuitable(vertex triorg, vertex tridest, vertex triapex, Real area)

	{
		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    *********/
	/**                                                                         **/
	/**                                                                         **/

	static void triexit(int status)

	{
		exit(status);
	}

	static int *trimalloc(int size)

	{
		int *memptr;

		memptr = (int *) malloc((unsigned int) size);
		if (memptr == (int *) NULL) {
			printf("Error:  Out of memory.\n");
			triexit(1);
		}
		return(memptr);
	}

	static void trifree(int *memptr)

	{
		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.  */
	/*                                                                           */
	/*****************************************************************************/

	static 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.                          */
	/*                                                                           */
	/*****************************************************************************/

	static void parsecommandline(int argc, char **argv, struct behavior *b)

	{
#define STARTINDEX 0
		int i, j, k;
		char workstring[FILENAMESIZE];

		b->poly = b->refine = b->quality = 0;
		b->vararea = b->fixedarea = b->usertest = 0;
		b->regionattrib = b->convex = b->weighted = b->jettison = 0;
		b->firstnumber = 1;
		b->edgesout = b->voronoi = b->neighbors = b->geomview = 0;
		b->nobound = b->nopolywritten = b->nonodewritten = b->noelewritten = 0;
		b->noiterationnum = 0;
		b->noholes = b->noexact = 0;
		b->incremental = b->sweepline = 0;
		b->dwyer = 1;
		b->splitseg = 0;
		b->docheck = 0;
		b->nobisect = 0;
		b->conformdel = 0;
		b->steiner = -1;
		b->order = 1;
		b->minangle = 0.0;
		b->maxarea = -1.0;
		b->quiet = b->verbose = 0;

		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] == 'r') {
					b->refine = 1;
				}
				if (argv[i][j] == 'q') {
					b->quality = 1;
					if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
						(argv[i][j + 1] == '.')) {
						k = 0;
						while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
							(argv[i][j + 1] == '.')) {
							j++;
							workstring[k] = argv[i][j];
							k++;
						}
						workstring[k] = '\0';
						b->minangle = (Real) strtod(workstring, (char **) NULL);
					} else {
						b->minangle = 20.0;
					}
				}
				if (argv[i][j] == 'a') {
					b->quality = 1;
					if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
						(argv[i][j + 1] == '.')) {
						b->fixedarea = 1;
						k = 0;
						while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
							(argv[i][j + 1] == '.')) {
							j++;
							workstring[k] = argv[i][j];
							k++;
						}
						workstring[k] = '\0';
						b->maxarea = (Real) strtod(workstring, (char **) NULL);
						if (b->maxarea <= 0.0) {
							printf("Error:  Maximum area must be greater than zero.\n");
							triexit(1);
						}
					} else {
						b->vararea = 1;
					}
				}
				if (argv[i][j] == 'u') {
					b->quality = 1;
					b->usertest = 1;
				}
				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] == 'Y') {
					b->nobisect++;
				}
				if (argv[i][j] == 'S') {
					b->steiner = 0;
					while ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) {
						j++;
						b->steiner = b->steiner * 10 + (int) (argv[i][j] - '0');
					}
				}
				if (argv[i][j] == 'i') {
					b->incremental = 1;
				}
				if (argv[i][j] == 'F') {
					b->sweepline = 1;
				}
				if (argv[i][j] == 'l') {
					b->dwyer = 0;
				}
				if (argv[i][j] == 's') {
					b->splitseg = 1;
				}
				if ((argv[i][j] == 'D') || (argv[i][j] == 'L')) {
					b->quality = 1;
					b->conformdel = 1;
				}
				if (argv[i][j] == 'C') {
					b->docheck = 1;
				}
				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.                        */
	/*                                                                           */
	/*****************************************************************************/

	static void printtriangle(struct mesh *m, struct behavior *b, struct otri *t)
	{
		struct otri printtri;
		struct osub printsh;
		vertex printvertex;

		printf("triangle x%llx with orientation %d:\n", (size_t) t->tri,
			t->orient);
		decode(t->tri[0], printtri);
		if (printtri.tri == m->dummytri) {
			printf("    [0] = Outer space\n");
		} else {
			printf("    [0] = x%llx  %d\n", (size_t) printtri.tri,
				printtri.orient);
		}
		decode(t->tri[1], printtri);
		if (printtri.tri == m->dummytri) {
			printf("    [1] = Outer space\n");
		} else {
			printf("    [1] = x%llx  %d\n", (size_t) printtri.tri,
				printtri.orient);
		}
		decode(t->tri[2], printtri);
		if (printtri.tri == m->dummytri) {
			printf("    [2] = Outer space\n");
		} else {
			printf("    [2] = x%llx  %d\n", (size_t) printtri.tri,
				printtri.orient);
		}

		org(*t, printvertex);
		if (printvertex == (vertex) NULL)
			printf("    Origin[%d] = NULL\n", (t->orient + 1) % 3 + 3);
		else
			printf("    Origin[%d] = x%llx  (%.12g, %.12g)\n",
			(t->orient + 1) % 3 + 3, (size_t) printvertex,
				printvertex[0], printvertex[1]);
		dest(*t, printvertex);
		if (printvertex == (vertex) NULL)
			printf("    Dest  [%d] = NULL\n", (t->orient + 2) % 3 + 3);
		else
			printf("    Dest  [%d] = x%llx  (%.12g, %.12g)\n",
			(t->orient + 2) % 3 + 3, (size_t) printvertex,
				printvertex[0], printvertex[1]);
		apex(*t, printvertex);
		if (printvertex == (vertex) NULL)
			printf("    Apex  [%d] = NULL\n", t->orient + 3);
		else
			printf("    Apex  [%d] = x%llx  (%.12g, %.12g)\n",
				t->orient + 3, (size_t) printvertex,
				printvertex[0], printvertex[1]);

		if (b->usesegments) {
			sdecode(t->tri[6], printsh);
			if (printsh.ss != m->dummysub) {
				printf("    [6] = x%llx  %d\n", (size_t) printsh.ss,
					printsh.ssorient);
			}
			sdecode(t->tri[7], printsh);
			if (printsh.ss != m->dummysub) {
				printf("    [7] = x%llx  %d\n", (size_t) printsh.ss,
					printsh.ssorient);
			}
			sdecode(t->tri[8], printsh);
			if (printsh.ss != m->dummysub) {
				printf("    [8] = x%llx  %d\n", (size_t) 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.                                */
	/*                                                                           */
	/*****************************************************************************/

	static void printsubseg(struct mesh *m, struct behavior *b, struct osub *s)
	{
		struct osub printsh;
		struct otri printtri;
		vertex printvertex;

		printf("subsegment x%llx with orientation %d and mark %d:\n",
			(size_t) s->ss, s->ssorient, mark(*s));
		sdecode(s->ss[0], printsh);
		if (printsh.ss == m->dummysub) {
			printf("    [0] = No subsegment\n");
		} else {
			printf("    [0] = x%llx  %d\n", (size_t) printsh.ss,
				printsh.ssorient);
		}
		sdecode(s->ss[1], printsh);
		if (printsh.ss == m->dummysub) {
			printf("    [1] = No subsegment\n");
		} else {
			printf("    [1] = x%llx  %d\n", (size_t) printsh.ss,
				printsh.ssorient);
		}

		sorg(*s, printvertex);
		if (printvertex == (vertex) NULL)
			printf("    Origin[%d] = NULL\n", 2 + s->ssorient);
		else
			printf("    Origin[%d] = x%llx  (%.12g, %.12g)\n",
				2 + s->ssorient, (size_t) printvertex,
				printvertex[0], printvertex[1]);
		sdest(*s, printvertex);
		if (printvertex == (vertex) NULL)
			printf("    Dest  [%d] = NULL\n", 3 - s->ssorient);
		else
			printf("    Dest  [%d] = x%llx  (%.12g, %.12g)\n",
				3 - s->ssorient, (size_t) printvertex,
				printvertex[0], printvertex[1]);

		decode(s->ss[6], printtri);
		if (printtri.tri == m->dummytri) {
			printf("    [6] = Outer space\n");
		} else {
			printf("    [6] = x%llx  %d\n", (size_t) printtri.tri,
				printtri.orient);
		}
		decode(s->ss[7], printtri);
		if (printtri.tri == m->dummytri) {
			printf("    [7] = Outer space\n");
		} else {
			printf("    [7] = x%llx  %d\n", (size_t) printtri.tri,
				printtri.orient);
		}

		segorg(*s, printvertex);
		if (printvertex == (vertex) NULL)
			printf("    Segment origin[%d] = NULL\n", 4 + s->ssorient);
		else
			printf("    Segment origin[%d] = x%llx  (%.12g, %.12g)\n",
				4 + s->ssorient, (size_t) printvertex,
				printvertex[0], printvertex[1]);
		segdest(*s, printvertex);
		if (printvertex == (vertex) NULL)
			printf("    Segment dest  [%d] = NULL\n", 5 - s->ssorient);
		else
			printf("    Segment dest  [%d] = x%llx  (%.12g, %.12g)\n",
				5 - s->ssorient, (size_t) 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.                              */
	/*                                                                           */
	/*****************************************************************************/

	static void poolzero(struct memorypool *pool)
	{
		pool->firstblock = (int **) NULL;
		pool->nowblock = (int **) NULL;
		pool->nextitem = (int *) NULL;
		pool->deaditemstack = (int *) NULL;
		pool->pathblock = (int **) NULL;
		pool->pathitem = (int *) 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.                                                  */
	/*                                                                           */
	/*****************************************************************************/

	static void poolrestart(struct memorypool *pool)
	{
		size_t 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 (int *). */
		alignptr = (size_t) (pool->nowblock + 1);
		/* Align the item on an `alignbytes'-byte boundary. */
		pool->nextitem = (int *)
			(alignptr + (size_t) pool->alignbytes -
			(alignptr % (size_t) 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 = (int *) 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.                      */
	/*                                                                           */
	/*****************************************************************************/

	static void poolinit(struct memorypool *pool, int bytecount, int itemcount,
		int firstitemcount, int alignment)
	{
		/* Find the proper alignment, which must be at least as large as:   */
		/*   - The parameter `alignment'.                                   */
		/*   - sizeof(int *), so the stack of dead items can be maintained */
		/*       without unaligned accesses.                                */
		if (alignment > sizeof(int *)) {
			pool->alignbytes = alignment;
		} else {
			pool->alignbytes = sizeof(int *);
		}
		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 = (int **)
			trimalloc(pool->itemsfirstblock * pool->itembytes + (int) sizeof(int *) +
				pool->alignbytes);
		/* Set the next block pointer to NULL. */
		*(pool->firstblock) = (int *) NULL;
		poolrestart(pool);
	}

	/*****************************************************************************/
	/*                                                                           */
	/*  pooldeinit()   Free to the operating system all memory taken by a pool.  */
	/*                                                                           */
	/*****************************************************************************/

	static void pooldeinit(struct memorypool *pool)
	{
		while (pool->firstblock != (int **) NULL) {
			pool->nowblock = (int **) *(pool->firstblock);
			trifree((int *) pool->firstblock);
			pool->firstblock = pool->nowblock;
		}
	}

	/*****************************************************************************/
	/*                                                                           */
	/*  poolalloc()   Allocate space for an item.                                */
	/*                                                                           */
	/*****************************************************************************/

	static int *poolalloc(struct memorypool *pool)
	{
		int *newitem;
		int **newblock;
		size_t 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 != (int *) NULL) {
			newitem = pool->deaditemstack;               /* Take first item in list. */
			pool->deaditemstack = * (int **) 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) == (int *) NULL) {
					/* Allocate a new block of items, pointed to by the previous block. */
					newblock = (int **) trimalloc(pool->itemsperblock * pool->itembytes +
						(int) sizeof(int *) +
						pool->alignbytes);
					*(pool->nowblock) = (int *) newblock;
					/* The next block pointer is NULL. */
					*newblock = (int *) NULL;
				}

				/* Move to the new block. */
				pool->nowblock = (int **) *(pool->nowblock);
				/* Find the first item in the block.    */
				/*   Increment by the size of (int *). */
				alignptr = (size_t) (pool->nowblock + 1);
				/* Align the item on an `alignbytes'-byte boundary. */
				pool->nextitem = (int *)
					(alignptr + (size_t) pool->alignbytes -
					(alignptr % (size_t) 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 = (int *) ((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.              */
	/*                                                                           */
	/*****************************************************************************/

	static void pooldealloc(struct memorypool *pool, int *dyingitem)
	{
		/* Push freshly killed item onto stack. */
		*((int **) 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().                     */
	/*                                                                           */
	/*****************************************************************************/

	static void traversalinit(struct memorypool *pool)
	{
		size_t alignptr;

		/* Begin the traversal in the first block. */
		pool->pathblock = pool->firstblock;
		/* Find the first item in the block.  Increment by the size of (int *). */
		alignptr = (size_t) (pool->pathblock + 1);
		/* Align with item on an `alignbytes'-byte boundary. */
		pool->pathitem = (int *)
			(alignptr + (size_t) pool->alignbytes -
			(alignptr % (size_t) 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.                                                             */
	/*                                                                           */
	/*****************************************************************************/

	static int *traverse(struct memorypool *pool)
	{
		int *newitem;
		size_t alignptr;

		/* Stop upon exhausting the list of items. */
		if (pool->pathitem == pool->nextitem) {
			return (int *) NULL;
		}

		/* Check whether any untraversed items remain in the current block. */
		if (pool->pathitemsleft == 0) {
			/* Find the next block. */
			pool->pathblock = (int **) *(pool->pathblock);
			/* Find the first item in the block.  Increment by the size of (int *). */
			alignptr = (size_t) (pool->pathblock + 1);
			/* Align with item on an `alignbytes'-byte boundary. */
			pool->pathitem = (int *)
				(alignptr + (size_t) pool->alignbytes -
				(alignptr % (size_t) 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 = (int *) ((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.                                                               */
	/*                                                                           */
	/*****************************************************************************/

	static void dummyinit(struct mesh *m, struct behavior *b, int trianglebytes,
		int subsegbytes)
	{
		size_t 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 = (size_t) m->dummytribase;
		m->dummytri = (triangle *)
			(alignptr + (size_t) m->triangles.alignbytes -
			(alignptr % (size_t) 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 = (size_t) m->dummysubbase;
			m->dummysub = (subseg *)
				(alignptr + (size_t) m->subsegs.alignbytes -
				(alignptr % (size_t) 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.                          */
	/*                                                                           */
	/*****************************************************************************/

	static void initializevertexpool(struct mesh *m, struct behavior *b)
	{
		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.       */
	/*                                                                           */
	/*****************************************************************************/

	static void initializetrisubpools(struct mesh *m, struct behavior *b)
	{
		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.    */
	/*                                                                           */
	/*****************************************************************************/

	static void triangledealloc(struct mesh *m, triangle *dyingtriangle)
	{
		/* 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, (int *) dyingtriangle);
	}

	/*****************************************************************************/
	/*                                                                           */
	/*  triangletraverse()   Traverse the triangles, skipping dead ones.         */
	/*                                                                           */
	/*****************************************************************************/

	static triangle *triangletraverse(struct mesh *m)
	{
		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.    */
	/*                                                                           */
	/*****************************************************************************/

	static void subsegdealloc(struct mesh *m, subseg *dyingsubseg)
	{
		/* 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, (int *) dyingsubseg);
	}

	/*****************************************************************************/
	/*                                                                           */
	/*  subsegtraverse()   Traverse the subsegments, skipping dead ones.         */
	/*                                                                           */
	/*****************************************************************************/

	static subseg *subsegtraverse(struct mesh *m)
	{
		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.        */
	/*                                                                           */
	/*****************************************************************************/

	static void vertexdealloc(struct mesh *m, vertex dyingvertex)
	{
		/* 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, (int *) dyingvertex);
	}

	/*****************************************************************************/
	/*                                                                           */
	/*  vertextraverse()   Traverse the vertices, skipping dead ones.            */
	/*                                                                           */
	/*****************************************************************************/

	static vertex vertextraverse(struct mesh *m)
	{
		vertex newvertex;

		do {
			newvertex = (vertex) traverse(&m->vertices);
			if (newvertex == (vertex) NULL) {
				return (vertex) NULL;
			}
		} while (vertextype(newvertex) == DEADVERTEX);          /* Skip dead ones. */
		return newvertex;
	}

	/*****************************************************************************/
	/*                                                                           */
	/*  badsubsegdealloc()   Deallocate space for a bad subsegment, marking it   */
	/*                       dead.                                               */
	/*                                                                           */
	/*****************************************************************************/

	static void badsubsegdealloc(struct mesh *m, struct badsubseg *dyingseg)
	{
		/* Set subsegment's origin to NULL.  This makes it possible to detect dead */
		/*   badsubsegs when traversing the list of all badsubsegs             .   */
		dyingseg->subsegorg = (vertex) NULL;
		pooldealloc(&m->badsubsegs, (int *) dyingseg);
	}

	/*****************************************************************************/
	/*                                                                           */
	/*  badsubsegtraverse()   Traverse the bad subsegments, skipping dead ones.  */
	/*                                                                           */
	/*****************************************************************************/

	static struct badsubseg *badsubsegtraverse(struct mesh *m)
	{
		struct badsubseg *newseg;

		do {
			newseg = (struct badsubseg *) traverse(&m->badsubsegs);
			if (newseg == (struct badsubseg *) NULL) {
				return (struct badsubseg *) NULL;
			}
		} while (newseg->subsegorg == (vertex) NULL);           /* Skip dead ones. */
		return newseg;
	}

	/*****************************************************************************/
	/*                                                                           */
	/*  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.                                                                    */
	/*                                                                           */
	/*****************************************************************************/

	static vertex getvertex(struct mesh *m, struct behavior *b, int number)
	{
		int **getblock;
		char *foundvertex;
		size_t alignptr;
		int current;

		getblock = m->vertices.firstblock;
		current = b->firstnumber;

		/* Find the right block. */
		if (current + m->vertices.itemsfirstblock <= number) {
			getblock = (int **) *getblock;
			current += m->vertices.itemsfirstblock;
			while (current + m->vertices.itemsperblock <= number) {
				getblock = (int **) *getblock;
				current += m->vertices.itemsperblock;
			}
		}

		/* Now find the right vertex. */
		alignptr = (size_t) (getblock + 1);
		foundvertex = (char *) (alignptr + (size_t) m->vertices.alignbytes -
			(alignptr % (size_t) m->vertices.alignbytes));
		return (vertex) (foundvertex + m->vertices.itembytes * (number - current));
	}

	/*****************************************************************************/
	/*                                                                           */
	/*  triangledeinit()   Free all remaining allocated memory.                  */
	/*                                                                           */
	/*****************************************************************************/

	static void triangledeinit(struct mesh *m, struct behavior *b)
	{
		pooldeinit(&m->triangles);
		trifree((int *) m->dummytribase);
		if (b->usesegments) {
			pooldeinit(&m->subsegs);
			trifree((int *) m->dummysubbase);
		}
		pooldeinit(&m->vertices);
		if (b->quality) {
			pooldeinit(&m->badsubsegs);
			if ((b->minangle > 0.0) || b->vararea || b->fixedarea || b->usertest) {
				pooldeinit(&m->badtriangles);
				pooldeinit(&m->flipstackers);
			}
		}
	}

	/**                                                                         **/
	/**                                                                         **/
	/********* Memory management routines end here                       *********/

	/********* Constructors begin here                                   *********/
	/**                                                                         **/
	/**                                                                         **/

	/*****************************************************************************/
	/*                                                                           */
	/*  maketriangle()   Create a new triangle with orientation zero.            */
	/*                                                                           */
	/*****************************************************************************/

	static void maketriangle(struct mesh *m, struct behavior *b, struct otri *newotri)
	{
		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.            */
	/*                                                                           */
	/*****************************************************************************/

	static void makesubseg(struct mesh *m, struct osub *newsubseg)
	{
		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.                */
	/*                                                                           */
	/*****************************************************************************/

	static void exactinit()
	{
		Real half;
		Real check, lastcheck;
		int every_other;

#ifdef CPU86
		control87();
#endif /* CPU86 */
#ifdef LINUX
		_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.                                                              */
	/*                                                                           */
	/*****************************************************************************/

	static int fast_expansion_sum_zeroelim(int elen, Real *e, int flen, Real *f, Real *h)
	{
		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.)                                                                 */
	/*                                                                           */
	/*****************************************************************************/

	static int scale_expansion_zeroelim(int elen, Real *e, Real b, Real *h)
	{
		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.                              */
	/*                                                                           */
	/*****************************************************************************/

	static Real estimate(int elen, Real *e)
	{
		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.                              */
	/*                                                                           */
	/*****************************************************************************/

	static Real counterclockwiseadapt(vertex pa, vertex pb, vertex pc, Real detsum)
	{
		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]);
	}

	static Real counterclockwise(struct mesh *m, struct behavior *b,
		vertex pa, vertex pb, vertex pc)
	{
		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.                              */
	/*                                                                           */
	/*****************************************************************************/

	static Real incircleadapt(vertex pa, vertex pb, vertex pc, vertex pd, Real permanent)
	{
		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];
	}

	static Real incircle(struct mesh *m, struct behavior *b,
		vertex pa, vertex pb, vertex pc, vertex pd)
	{
		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.                              */
	/*                                                                           */
	/*****************************************************************************/

	static Real orient3dadapt(vertex pa, vertex pb, vertex pc, vertex pd,
		Real aheight, Real bheight, Real cheight, Real dheight,
		Real permanent)
	{
		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];
	}

	static Real orient3d(struct mesh *m, struct behavior *b,
		vertex pa, vertex pb, vertex pc, vertex pd,
		Real aheight, Real bheight, Real cheight, Real dheight)
	{
		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.      */
	/*                                                                           */
	/*****************************************************************************/

	static Real nonregular(struct mesh *m, struct behavior *b,
		vertex pa, vertex pb, vertex pc, vertex pd)
	{
		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.                                                           */
	/*                                                                           */
	/*****************************************************************************/

	static void findcircumcenter(struct mesh *m, struct behavior *b,
		vertex torg, vertex tdest, vertex tapex,
		vertex circumcenter, Real *xi, Real *eta, int offcenter)
	{
		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.                              */
	/*                                                                           */
	/*****************************************************************************/

	static void triangleinit(struct mesh *m)
	{
		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.                                                    */
	/*                                                                           */
	/*****************************************************************************/

	static size_t randomnation(unsigned int choices)
	{
		randomseed = (randomseed * 1366l + 150889l) % 714025l;
		return randomseed / (714025l / choices + 1);
	}

	/********* Mesh quality testing routines begin here                  *********/
	/**                                                                         **/
	/**                                                                         **/

	/*****************************************************************************/
	/*                                                                           */
	/*  checkmesh()   Test the mesh for topological consistency.                 */
	/*                                                                           */
	/*****************************************************************************/

	static void checkmesh(struct mesh *m, struct behavior *b)
	{
		struct otri triangleloop;
		struct otri oppotri, oppooppotri;
		vertex triorg, tridest, triapex;
		vertex oppoorg, oppodest;
		int horrors;
		int saveexact;
		triangle ptr;                         /* Temporary variable used by sym(). */

											  /* Temporarily turn on exact arithmetic if it's off. */
		saveexact = b->noexact;
		b->noexact = 0;
		if (!b->quiet) {
			printf("  Checking consistency of mesh...\n");
		}
		horrors = 0;
		/* Run through the list of triangles, checking each one. */
		traversalinit(&m->triangles);
		triangleloop.tri = triangletraverse(m);
		while (triangleloop.tri != (triangle *) NULL) {
			/* Check all three edges of the triangle. */
			for (triangleloop.orient = 0; triangleloop.orient < 3;
				triangleloop.orient++) {
				org(triangleloop, triorg);
				dest(triangleloop, tridest);
				if (triangleloop.orient == 0) {       /* Only test for inversion once. */
													  /* Test if the triangle is flat or inverted. */
					apex(triangleloop, triapex);
					if (counterclockwise(m, b, triorg, tridest, triapex) <= 0.0) {
						printf("  !! !! Inverted ");
						printtriangle(m, b, &triangleloop);
						horrors++;
					}
				}
				/* Find the neighboring triangle on this edge. */
				sym(triangleloop, oppotri);
				if (oppotri.tri != m->dummytri) {
					/* Check that the triangle's neighbor knows it's a neighbor. */
					sym(oppotri, oppooppotri);
					if ((triangleloop.tri != oppooppotri.tri)
						|| (triangleloop.orient != oppooppotri.orient)) {
						printf("  !! !! Asymmetric triangle-triangle bond:\n");
						if (triangleloop.tri == oppooppotri.tri) {
							printf("   (Right triangle, wrong orientation)\n");
						}
						printf("    First ");
						printtriangle(m, b, &triangleloop);
						printf("    Second (nonreciprocating) ");
						printtriangle(m, b, &oppotri);
						horrors++;
					}
					/* Check that both triangles agree on the identities */
					/*   of their shared vertices.                       */
					org(oppotri, oppoorg);
					dest(oppotri, oppodest);
					if ((triorg != oppodest) || (tridest != oppoorg)) {
						printf("  !! !! Mismatched edge coordinates between two triangles:\n"
						);
						printf("    First mismatched ");
						printtriangle(m, b, &triangleloop);
						printf("    Second mismatched ");
						printtriangle(m, b, &oppotri);
						horrors++;
					}
				}
			}
			triangleloop.tri = triangletraverse(m);
		}
		if (horrors == 0) {
			if (!b->quiet) {
				printf("  In my studied opinion, the mesh appears to be consistent.\n");
			}
		} else if (horrors == 1) {
			printf("  !! !! !! !! Precisely one festering wound discovered.\n");
		} else {
			printf("  !! !! !! !! %d abominations witnessed.\n", horrors);
		}
		/* Restore the status of exact arithmetic. */
		b->noexact = saveexact;
	}

	/*****************************************************************************/
	/*                                                                           */
	/*  checkdelaunay()   Ensure that the mesh is (constrained) Delaunay.        */
	/*                                                                           */
	/*****************************************************************************/

	static void checkdelaunay(struct mesh *m, struct behavior *b)
	{
		struct otri triangleloop;
		struct otri oppotri;
		struct osub opposubseg;
		vertex triorg, tridest, triapex;
		vertex oppoapex;
		int shouldbedelaunay;
		int horrors;
		int saveexact;
		triangle ptr;                         /* Temporary variable used by sym(). */
		subseg sptr;                      /* Temporary variable used by tspivot(). */

										  /* Temporarily turn on exact arithmetic if it's off. */
		saveexact = b->noexact;
		b->noexact = 0;
		if (!b->quiet) {
			printf("  Checking Delaunay property of mesh...\n");
		}
		horrors = 0;
		/* Run through the list of triangles, checking each one. */
		traversalinit(&m->triangles);
		triangleloop.tri = triangletraverse(m);
		while (triangleloop.tri != (triangle *) NULL) {
			/* Check all three edges of the triangle. */
			for (triangleloop.orient = 0; triangleloop.orient < 3;
				triangleloop.orient++) {
				org(triangleloop, triorg);
				dest(triangleloop, tridest);
				apex(triangleloop, triapex);
				sym(triangleloop, oppotri);
				apex(oppotri, oppoapex);
				/* Only test that the edge is locally Delaunay if there is an   */
				/*   adjoining triangle whose pointer is larger (to ensure that */
				/*   each pair isn't tested twice).                             */
				shouldbedelaunay = (oppotri.tri != m->dummytri) &&
					!deadtri(oppotri.tri) && (triangleloop.tri < oppotri.tri) &&
					(triorg != m->infvertex1) && (triorg != m->infvertex2) &&
					(triorg != m->infvertex3) &&
					(tridest != m->infvertex1) && (tridest != m->infvertex2) &&
					(tridest != m->infvertex3) &&
					(triapex != m->infvertex1) && (triapex != m->infvertex2) &&
					(triapex != m->infvertex3) &&
					(oppoapex != m->infvertex1) && (oppoapex != m->infvertex2) &&
					(oppoapex != m->infvertex3);
				if (m->checksegments && shouldbedelaunay) {
					/* If a subsegment separates the triangles, then the edge is */
					/*   constrained, so no local Delaunay test should be done.  */
					tspivot(triangleloop, opposubseg);
					if (opposubseg.ss != m->dummysub){
						shouldbedelaunay = 0;
					}
				}
				if (shouldbedelaunay) {
					if (nonregular(m, b, triorg, tridest, triapex, oppoapex) > 0.0) {
						if (!b->weighted) {
							printf("  !! !! Non-Delaunay pair of triangles:\n");
							printf("    First non-Delaunay ");
							printtriangle(m, b, &triangleloop);
							printf("    Second non-Delaunay ");
						} else {
							printf("  !! !! Non-regular pair of triangles:\n");
							printf("    First non-regular ");
							printtriangle(m, b, &triangleloop);
							printf("    Second non-regular ");
						}
						printtriangle(m, b, &oppotri);
						horrors++;
					}
				}
			}
			triangleloop.tri = triangletraverse(m);
		}
		if (horrors == 0) {
			if (!b->quiet) {
				printf(
					"  By virtue of my perceptive intelligence, I declare the mesh Delaunay.\n");
			}
		} else if (horrors == 1) {
			printf(
				"  !! !! !! !! Precisely one terrifying transgression identified.\n");
		} else {
			printf("  !! !! !! !! %d obscenities viewed with horror.\n", horrors);
		}
		/* Restore the status of exact arithmetic. */
		b->noexact = saveexact;
	}

	/*****************************************************************************/
	/*                                                                           */
	/*  enqueuebadtriang()   Add a bad triangle data structure to the end of a   */
	/*                       queue.                                              */
	/*                                                                           */
	/*  The queue is actually a set of 4096 queues.  I use multiple queues to    */
	/*  give priority to smaller angles.  I originally implemented a heap, but   */
	/*  the queues are faster by a larger margin than I'd suspected.             */
	/*                                                                           */
	/*****************************************************************************/

	static void enqueuebadtriang(struct mesh *m, struct behavior *b,
		struct badtriang *badtri)
	{
		Real length, multiplier;
		int exponent, expincrement;
		int queuenumber;
		int posexponent;
		int i;

		if (b->verbose > 2) {
			printf("  Queueing bad triangle:\n");
			printf("    (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
				badtri->triangorg[0], badtri->triangorg[1],
				badtri->triangdest[0], badtri->triangdest[1],
				badtri->triangapex[0], badtri->triangapex[1]);
		}

		/* Determine the appropriate queue to put the bad triangle into.    */
		/*   Recall that the key is the square of its shortest edge length. */
		if (badtri->key >= 1.0) {
			length = badtri->key;
			posexponent = 1;
		} else {
			/* `badtri->key' is 2.0 to a negative exponent, so we'll record that */
			/*   fact and use the reciprocal of `badtri->key', which is > 1.0.   */
			length = 1.0 / badtri->key;
			posexponent = 0;
		}
		/* `length' is approximately 2.0 to what exponent?  The following code */
		/*   determines the answer in time logarithmic in the exponent.        */
		exponent = 0;
		while (length > 2.0) {
			/* Find an approximation by repeated squaring of two. */
			expincrement = 1;
			multiplier = 0.5;
			while (length * multiplier * multiplier > 1.0) {
				expincrement *= 2;
				multiplier *= multiplier;
			}
			/* Reduce the value of `length', then iterate if necessary. */
			exponent += expincrement;
			length *= multiplier;
		}
		/* `length' is approximately squareroot(2.0) to what exponent? */
		exponent = (int)(2.0 * exponent + (length > SQUAREROOTTWO));
		/* `exponent' is now in the range 0...2047 for IEEE double precision.   */
		/*   Choose a queue in the range 0...4095.  The shortest edges have the */
		/*   highest priority (queue 4095).                                     */
		if (posexponent) {
			queuenumber = 2047 - exponent;
		} else {
			queuenumber = 2048 + exponent;
		}

		/* Are we inserting into an empty queue? */
		if (m->queuefront[queuenumber] == (struct badtriang *) NULL) {
			/* Yes, we are inserting into an empty queue.     */
			/*   Will this become the highest-priority queue? */
			if (queuenumber > m->firstnonemptyq) {
				/* Yes, this is the highest-priority queue. */
				m->nextnonemptyq[queuenumber] = m->firstnonemptyq;
				m->firstnonemptyq = queuenumber;
			} else {
				/* No, this is not the highest-priority queue. */
				/*   Find the queue with next higher priority. */
				i = queuenumber + 1;
				while (m->queuefront[i] == (struct badtriang *) NULL) {
					i++;
				}
				/* Mark the newly nonempty queue as following a higher-priority queue. */
				m->nextnonemptyq[queuenumber] = m->nextnonemptyq[i];
				m->nextnonemptyq[i] = queuenumber;
			}
			/* Put the bad triangle at the beginning of the (empty) queue. */
			m->queuefront[queuenumber] = badtri;
		} else {
			/* Add the bad triangle to the end of an already nonempty queue. */
			m->queuetail[queuenumber]->nexttriang = badtri;
		}
		/* Maintain a pointer to the last triangle of the queue. */
		m->queuetail[queuenumber] = badtri;
		/* Newly enqueued bad triangle has no successor in the queue. */
		badtri->nexttriang = (struct badtriang *) NULL;
	}

	/*****************************************************************************/
	/*                                                                           */
	/*  enqueuebadtri()   Add a bad triangle to the end of a queue.              */
	/*                                                                           */
	/*  Allocates a badtriang data structure for the triangle, then passes it to */
	/*  enqueuebadtriang().                                                      */
	/*                                                                           */
	/*****************************************************************************/

	static void enqueuebadtri(struct mesh *m, struct behavior *b, struct otri *enqtri,
		Real minedge, vertex enqapex, vertex enqorg, vertex enqdest)
	{
		struct badtriang *newbad;

		/* Allocate space for the bad triangle. */
		newbad = (struct badtriang *) poolalloc(&m->badtriangles);
		newbad->poortri = encode(*enqtri);
		newbad->key = minedge;
		newbad->triangapex = enqapex;
		newbad->triangorg = enqorg;
		newbad->triangdest = enqdest;
		enqueuebadtriang(m, b, newbad);
	}

	/*****************************************************************************/
	/*                                                                           */
	/*  dequeuebadtriang()   Remove a triangle from the front of the queue.      */
	/*                                                                           */
	/*****************************************************************************/

	static struct badtriang *dequeuebadtriang(struct mesh *m)
	{
		struct badtriang *result;

		/* If no queues are nonempty, return NULL. */
		if (m->firstnonemptyq < 0) {
			return (struct badtriang *) NULL;
		}
		/* Find the first triangle of the highest-priority queue. */
		result = m->queuefront[m->firstnonemptyq];
		/* Remove the triangle from the queue. */
		m->queuefront[m->firstnonemptyq] = result->nexttriang;
		/* If this queue is now empty, note the new highest-priority */
		/*   nonempty queue.                                         */
		if (result == m->queuetail[m->firstnonemptyq]) {
			m->firstnonemptyq = m->nextnonemptyq[m->firstnonemptyq];
		}
		return result;
	}

	/*****************************************************************************/
	/*                                                                           */
	/*  checkseg4encroach()   Check a subsegment to see if it is encroached; add */
	/*                        it to the list if it is.                           */
	/*                                                                           */
	/*  A subsegment is encroached if there is a vertex in its diametral lens.   */
	/*  For Ruppert's algorithm (-D switch), the "diametral lens" is the         */
	/*  diametral circle.  For Chew's algorithm (default), the diametral lens is */
	/*  just big enough to enclose two isosceles triangles whose bases are the   */
	/*  subsegment.  Each of the two isosceles triangles has two angles equal    */
	/*  to `b->minangle'.                                                        */
	/*                                                                           */
	/*  Chew's algorithm does not require diametral lenses at all--but they save */
	/*  time.  Any vertex inside a subsegment's diametral lens implies that the  */
	/*  triangle adjoining the subsegment will be too skinny, so it's only a     */
	/*  matter of time before the encroaching vertex is deleted by Chew's        */
	/*  algorithm.  It's faster to simply not insert the doomed vertex in the    */
	/*  first place, which is why I use diametral lenses with Chew's algorithm.  */
	/*                                                                           */
	/*  Returns a nonzero value if the subsegment is encroached.                 */
	/*                                                                           */
	/*****************************************************************************/

	static int checkseg4encroach(struct mesh *m, struct behavior *b,
		struct osub *testsubseg)
	{
		struct otri neighbortri;
		struct osub testsym;
		struct badsubseg *encroachedseg;
		Real dotproduct;
		int encroached;
		int sides;
		vertex eorg, edest, eapex;
		triangle ptr;                     /* Temporary variable used by stpivot(). */

		encroached = 0;
		sides = 0;

		sorg(*testsubseg, eorg);
		sdest(*testsubseg, edest);
		/* Check one neighbor of the subsegment. */
		stpivot(*testsubseg, neighbortri);
		/* Does the neighbor exist, or is this a boundary edge? */
		if (neighbortri.tri != m->dummytri) {
			sides++;
			/* Find a vertex opposite this subsegment. */
			apex(neighbortri, eapex);
			/* Check whether the apex is in the diametral lens of the subsegment */
			/*   (the diametral circle if `conformdel' is set).  A dot product   */
			/*   of two sides of the triangle is used to check whether the angle */
			/*   at the apex is greater than (180 - 2 `minangle') degrees (for   */
			/*   lenses; 90 degrees for diametral circles).                      */
			dotproduct = (eorg[0] - eapex[0]) * (edest[0] - eapex[0]) +
				(eorg[1] - eapex[1]) * (edest[1] - eapex[1]);
			if (dotproduct < 0.0) {
				if (b->conformdel ||
					(dotproduct * dotproduct >=
					(2.0 * b->goodangle - 1.0) * (2.0 * b->goodangle - 1.0) *
						((eorg[0] - eapex[0]) * (eorg[0] - eapex[0]) +
						(eorg[1] - eapex[1]) * (eorg[1] - eapex[1])) *
							((edest[0] - eapex[0]) * (edest[0] - eapex[0]) +
						(edest[1] - eapex[1]) * (edest[1] - eapex[1])))) {
					encroached = 1;
				}
			}
		}
		/* Check the other neighbor of the subsegment. */
		ssym(*testsubseg, testsym);
		stpivot(testsym, neighbortri);
		/* Does the neighbor exist, or is this a boundary edge? */
		if (neighbortri.tri != m->dummytri) {
			sides++;
			/* Find the other vertex opposite this subsegment. */
			apex(neighbortri, eapex);
			/* Check whether the apex is in the diametral lens of the subsegment */
			/*   (or the diametral circle, if `conformdel' is set).              */
			dotproduct = (eorg[0] - eapex[0]) * (edest[0] - eapex[0]) +
				(eorg[1] - eapex[1]) * (edest[1] - eapex[1]);
			if (dotproduct < 0.0) {
				if (b->conformdel ||
					(dotproduct * dotproduct >=
					(2.0 * b->goodangle - 1.0) * (2.0 * b->goodangle - 1.0) *
						((eorg[0] - eapex[0]) * (eorg[0] - eapex[0]) +
						(eorg[1] - eapex[1]) * (eorg[1] - eapex[1])) *
							((edest[0] - eapex[0]) * (edest[0] - eapex[0]) +
						(edest[1] - eapex[1]) * (edest[1] - eapex[1])))) {
					encroached += 2;
				}
			}
		}

		if (encroached && (!b->nobisect || ((b->nobisect == 1) && (sides == 2)))) {
			if (b->verbose > 2) {
				printf(
					"  Queueing encroached subsegment (%.12g, %.12g) (%.12g, %.12g).\n",
					eorg[0], eorg[1], edest[0], edest[1]);
			}
			/* Add the subsegment to the list of encroached subsegments. */
			/*   Be sure to get the orientation right.                   */
			encroachedseg = (struct badsubseg *) poolalloc(&m->badsubsegs);
			if (encroached == 1) {
				encroachedseg->encsubseg = sencode(*testsubseg);
				encroachedseg->subsegorg = eorg;
				encroachedseg->subsegdest = edest;
			} else {
				encroachedseg->encsubseg = sencode(testsym);
				encroachedseg->subsegorg = edest;
				encroachedseg->subsegdest = eorg;
			}
		}

		return encroached;
	}

	/*****************************************************************************/
	/*                                                                           */
	/*  testtriangle()   Test a triangle for quality and size.                   */
	/*                                                                           */
	/*  Tests a triangle to see if it satisfies the minimum angle condition and  */
	/*  the maximum area condition.  Triangles that aren't up to spec are added  */
	/*  to the bad triangle queue.                                               */
	/*                                                                           */
	/*****************************************************************************/

	static void testtriangle(struct mesh *m, struct behavior *b, struct otri *testtri)
	{
		struct otri tri1, tri2;
		struct osub testsub;
		vertex torg, tdest, tapex;
		vertex base1, base2;
		vertex org1, dest1, org2, dest2;
		vertex joinvertex;
		Real dxod, dyod, dxda, dyda, dxao, dyao;
		Real dxod2, dyod2, dxda2, dyda2, dxao2, dyao2;
		Real apexlen, orglen, destlen, minedge;
		Real angle;
		Real area;
		Real dist1, dist2;
		subseg sptr;                      /* Temporary variable used by tspivot(). */
		triangle ptr;           /* Temporary variable used by oprev() and dnext(). */

		org(*testtri, torg);
		dest(*testtri, tdest);
		apex(*testtri, tapex);
		dxod = torg[0] - tdest[0];
		dyod = torg[1] - tdest[1];
		dxda = tdest[0] - tapex[0];
		dyda = tdest[1] - tapex[1];
		dxao = tapex[0] - torg[0];
		dyao = tapex[1] - torg[1];
		dxod2 = dxod * dxod;
		dyod2 = dyod * dyod;
		dxda2 = dxda * dxda;
		dyda2 = dyda * dyda;
		dxao2 = dxao * dxao;
		dyao2 = dyao * dyao;
		/* Find the lengths of the triangle's three edges. */
		apexlen = dxod2 + dyod2;
		orglen = dxda2 + dyda2;
		destlen = dxao2 + dyao2;

		if ((apexlen < orglen) && (apexlen < destlen)) {
			/* The edge opposite the apex is shortest. */
			minedge = apexlen;
			/* Find the square of the cosine of the angle at the apex. */
			angle = dxda * dxao + dyda * dyao;
			angle = angle * angle / (orglen * destlen);
			base1 = torg;
			base2 = tdest;
			otricopy(*testtri, tri1);
		} else if (orglen < destlen) {
			/* The edge opposite the origin is shortest. */
			minedge = orglen;
			/* Find the square of the cosine of the angle at the origin. */
			angle = dxod * dxao + dyod * dyao;
			angle = angle * angle / (apexlen * destlen);
			base1 = tdest;
			base2 = tapex;
			lnext(*testtri, tri1);
		} else {
			/* The edge opposite the destination is shortest. */
			minedge = destlen;
			/* Find the square of the cosine of the angle at the destination. */
			angle = dxod * dxda + dyod * dyda;
			angle = angle * angle / (apexlen * orglen);
			base1 = tapex;
			base2 = torg;
			lprev(*testtri, tri1);
		}

		if (b->vararea || b->fixedarea || b->usertest) {
			/* Check whether the area is larger than permitted. */
			area = 0.5 * (dxod * dyda - dyod * dxda);
			if (b->fixedarea && (area > b->maxarea)) {
				/* Add this triangle to the list of bad triangles. */
				enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest);
				return;
			}

			/* Nonpositive area constraints are treated as unconstrained. */
			if ((b->vararea) && (area > areabound(*testtri)) &&
				(areabound(*testtri) > 0.0)) {
				/* Add this triangle to the list of bad triangles. */
				enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest);
				return;
			}

			if (b->usertest) {
				/* Check whether the user thinks this triangle is too large. */
				if (triunsuitable(torg, tdest, tapex, area)) {
					enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest);
					return;
				}
			}
		}

		/* Check whether the angle is smaller than permitted. */
		if (angle > b->goodangle) {
			/* Use the rules of Miller, Pav, and Walkington to decide that certain */
			/*   triangles should not be split, even if they have bad angles.      */
			/*   A skinny triangle is not split if its shortest edge subtends a    */
			/*   small input angle, and both endpoints of the edge lie on a        */
			/*   concentric circular shell.  For convenience, I make a small       */
			/*   adjustment to that rule:  I check if the endpoints of the edge    */
			/*   both lie in segment interiors, equidistant from the apex where    */
			/*   the two segments meet.                                            */
			/* First, check if both points lie in segment interiors.               */
			if ((vertextype(base1) == SEGMENTVERTEX) &&
				(vertextype(base2) == SEGMENTVERTEX)) {
				/* Check if both points lie in a common segment.  If they do, the */
				/*   skinny triangle is enqueued to be split as usual.            */
				tspivot(tri1, testsub);
				if (testsub.ss == m->dummysub) {
					/* No common segment.  Find a subsegment that contains `torg'. */
					otricopy(tri1, tri2);
					do {
						oprevself(tri1);
						tspivot(tri1, testsub);
					} while (testsub.ss == m->dummysub);
					/* Find the endpoints of the containing segment. */
					segorg(testsub, org1);
					segdest(testsub, dest1);
					/* Find a subsegment that contains `tdest'. */
					do {
						dnextself(tri2);
						tspivot(tri2, testsub);
					} while (testsub.ss == m->dummysub);
					/* Find the endpoints of the containing segment. */
					segorg(testsub, org2);
					segdest(testsub, dest2);
					/* Check if the two containing segments have an endpoint in common. */
					joinvertex = (vertex) NULL;
					if ((dest1[0] == org2[0]) && (dest1[1] == org2[1])) {
						joinvertex = dest1;
					} else if ((org1[0] == dest2[0]) && (org1[1] == dest2[1])) {
						joinvertex = org1;
					}
					if (joinvertex != (vertex) NULL) {
						/* Compute the distance from the common endpoint (of the two  */
						/*   segments) to each of the endpoints of the shortest edge. */
						dist1 = ((base1[0] - joinvertex[0]) * (base1[0] - joinvertex[0]) +
							(base1[1] - joinvertex[1]) * (base1[1] - joinvertex[1]));
						dist2 = ((base2[0] - joinvertex[0]) * (base2[0] - joinvertex[0]) +
							(base2[1] - joinvertex[1]) * (base2[1] - joinvertex[1]));
						/* If the two distances are equal, don't split the triangle. */
						if ((dist1 < 1.001 * dist2) && (dist1 > 0.999 * dist2)) {
							/* Return now to avoid enqueueing the bad triangle. */
							return;
						}
					}
				}
			}

			/* Add this triangle to the list of bad triangles. */
			enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest);
		}
	}

	/**                                                                         **/
	/**                                                                         **/
	/********* Mesh quality testing routines end here                    *********/

	/********* Point location routines begin here                        *********/
	/**                                                                         **/
	/**                                                                         **/

	/*****************************************************************************/
	/*                                                                           */
	/*  makevertexmap()   Construct a mapping from vertices to triangles to      */
	/*                    improve the speed of point location for segment        */
	/*                    insertion.                                             */
	/*                                                                           */
	/*  Traverses all the triangles, and provides each corner of each triangle   */
	/*  with a pointer to that triangle.  Of course, pointers will be            */
	/*  overwritten by other pointers because (almost) each vertex is a corner   */
	/*  of several triangles, but in the end every vertex will point to some     */
	/*  triangle that contains it.                                               */
	/*                                                                           */
	/*****************************************************************************/

	static void makevertexmap(struct mesh *m, struct behavior *b)
	{
		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.               */
	/*                                                                           */
	/*****************************************************************************/

	static enum locateresult preciselocate(struct mesh *m, struct behavior *b,
		vertex searchpoint, struct otri *searchtri,
		int stopatsubsegment)
	{
		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.     */
	/*                                                                           */
	/*****************************************************************************/

	static enum locateresult locate(struct mesh *m, struct behavior *b,
		vertex searchpoint, struct otri *searchtri)
	{
		int **sampleblock;
		char *firsttri;
		struct otri sampletri;
		vertex torg, tdest;
		size_t 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 = (size_t) (sampleblock + 1);
			firsttri = (char *) (alignptr +
				(size_t) m->triangles.alignbytes -
				(alignptr %
				(size_t) 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 = (int **) *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.          */
	/*                                                                           */
	/*****************************************************************************/

	static void insertsubseg(struct mesh *m, struct behavior *b, struct otri *tri,
		int subsegmark)
	{
		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.                                                       */
	/*                                                                           */
	/*****************************************************************************/

	static void flip(struct mesh *m, struct behavior *b, struct otri *flipedge)
	{
		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);
		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.                                                       */
	/*                                                                           */
	/*****************************************************************************/

	static void unflip(struct mesh *m, struct behavior *b, struct otri *flipedge)
	{
		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);
		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.                                                */
	/*                                                                           */
	/*****************************************************************************/

	static enum insertvertexresult insertvertex(struct mesh *m, struct behavior *b,
		vertex newvertex, struct otri *searchtri,
		struct osub *splitseg,
		int segmentflaws, int triflaws)
	{
		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;
			}

			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;
			}

			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 (segmentflaws) {
						/* Does the new vertex encroach upon this subsegment? */
						if (checkseg4encroach(m, b, &checksubseg)) {
							success = ENCROACHINGVERTEX;
						}
					}
				}
			}

			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;
						}

						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. */
				if (triflaws) {
					/* Check the triangle `horiz' for quality. */
					testtriangle(m, b, &horiz);
				}
				/* 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.                                                                     */
	/*                                                                           */
	/*****************************************************************************/

	static void triangulatepolygon(struct mesh *m, struct behavior *b,
		struct otri *firstedge, struct otri *lastedge,
		int edgecount, int doflip, int triflaws)
	{
		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);
			if (triflaws) {
				/* Check the quality of the newly committed triangle. */
				sym(besttri, testtri);
				testtriangle(m, b, &testtri);
			}
		}
		/* Return the base triangle. */
		otricopy(besttri, *lastedge);
	}

	/*****************************************************************************/
	/*                                                                           */
	/*  deletevertex()   Delete a vertex from a Delaunay triangulation, ensuring */
	/*                   that the triangulation remains Delaunay.                */
	/*                                                                           */
	/*  The origin of `deltri' is deleted.  The union of the triangles adjacent  */
	/*  to this vertex is a polygon, for which the Delaunay triangulation is     */
	/*  found.  Two triangles are removed from the mesh.                         */
	/*                                                                           */
	/*  Only interior vertices that do not lie on segments or boundaries may be  */
	/*  deleted.                                                                 */
	/*                                                                           */
	/*****************************************************************************/

	static void deletevertex(struct mesh *m, struct behavior *b, struct otri *deltri)
	{
		struct otri countingtri;
		struct otri firstedge, lastedge;
		struct otri deltriright;
		struct otri lefttri, righttri;
		struct otri leftcasing, rightcasing;
		struct osub leftsubseg, rightsubseg;
		vertex delvertex;
		vertex neworg;
		int edgecount;
		triangle ptr;   /* Temporary variable used by sym(), onext(), and oprev(). */
		subseg sptr;                      /* Temporary variable used by tspivot(). */

		org(*deltri, delvertex);
		if (b->verbose > 1) {
			printf("  Deleting (%.12g, %.12g).\n", delvertex[0], delvertex[1]);
		}
		vertexdealloc(m, delvertex);

		/* Count the degree of the vertex being deleted. */
		onext(*deltri, countingtri);
		edgecount = 1;
		while (!otriequal(*deltri, countingtri)) {
			edgecount++;
			onextself(countingtri);
		}

		if (edgecount > 3) {
			/* Triangulate the polygon defined by the union of all triangles */
			/*   adjacent to the vertex being deleted.  Check the quality of */
			/*   the resulting triangles.                                    */
			onext(*deltri, firstedge);
			oprev(*deltri, lastedge);
			triangulatepolygon(m, b, &firstedge, &lastedge, edgecount, 0,
				!b->nobisect);
		}
		/* Splice out two triangles. */
		lprev(*deltri, deltriright);
		dnext(*deltri, lefttri);
		sym(lefttri, leftcasing);
		oprev(deltriright, righttri);
		sym(righttri, rightcasing);
		bond(*deltri, leftcasing);
		bond(deltriright, rightcasing);
		tspivot(lefttri, leftsubseg);
		if (leftsubseg.ss != m->dummysub) {
			tsbond(*deltri, leftsubseg);
		}
		tspivot(righttri, rightsubseg);
		if (rightsubseg.ss != m->dummysub) {
			tsbond(deltriright, rightsubseg);
		}

		/* Set the new origin of `deltri' and check its quality. */
		org(lefttri, neworg);
		setorg(*deltri, neworg);
		if (!b->nobisect) {
			testtriangle(m, b, deltri);
		}

		/* Delete the two spliced-out triangles. */
		triangledealloc(m, lefttri.tri);
		triangledealloc(m, righttri.tri);
	}

	/*****************************************************************************/
	/*                                                                           */
	/*  undovertex()   Undo the most recent vertex insertion.                    */
	/*                                                                           */
	/*  Walks through the list of transformations (flips and a vertex insertion) */
	/*  in the reverse of the order in which they were done, and undoes them.    */
	/*  The inserted vertex is removed from the triangulation and deallocated.   */
	/*  Two triangles (possibly just one) are also deallocated.                  */
	/*                                                                           */
	/*****************************************************************************/

	static void undovertex(struct mesh *m, struct behavior *b)
	{
		struct otri fliptri;
		struct otri botleft, botright, topright;
		struct otri botlcasing, botrcasing, toprcasing;
		struct otri gluetri;
		struct osub botlsubseg, botrsubseg, toprsubseg;
		vertex botvertex, rightvertex;
		triangle ptr;                         /* Temporary variable used by sym(). */
		subseg sptr;                      /* Temporary variable used by tspivot(). */

										  /* Walk through the list of transformations (flips and a vertex insertion) */
										  /*   in the reverse of the order in which they were done, and undo them.   */
		while (m->lastflip != (struct flipstacker *) NULL) {
			/* Find a triangle involved in the last unreversed transformation. */
			decode(m->lastflip->flippedtri, fliptri);

			/* We are reversing one of three transformations:  a trisection of one */
			/*   triangle into three (by inserting a vertex in the triangle), a    */
			/*   bisection of two triangles into four (by inserting a vertex in an */
			/*   edge), or an edge flip.                                           */
			if (m->lastflip->prevflip == (struct flipstacker *) NULL) {
				/* Restore a triangle that was split into three triangles, */
				/*   so it is again one triangle.                          */
				dprev(fliptri, botleft);
				lnextself(botleft);
				onext(fliptri, botright);
				lprevself(botright);
				sym(botleft, botlcasing);
				sym(botright, botrcasing);
				dest(botleft, botvertex);

				setapex(fliptri, botvertex);
				lnextself(fliptri);
				bond(fliptri, botlcasing);
				tspivot(botleft, botlsubseg);
				tsbond(fliptri, botlsubseg);
				lnextself(fliptri);
				bond(fliptri, botrcasing);
				tspivot(botright, botrsubseg);
				tsbond(fliptri, botrsubseg);

				/* Delete the two spliced-out triangles. */
				triangledealloc(m, botleft.tri);
				triangledealloc(m, botright.tri);
			} else if (m->lastflip->prevflip == (struct flipstacker *) &insertvertex) {
				/* Restore two triangles that were split into four triangles, */
				/*   so they are again two triangles.                         */
				lprev(fliptri, gluetri);
				sym(gluetri, botright);
				lnextself(botright);
				sym(botright, botrcasing);
				dest(botright, rightvertex);

				setorg(fliptri, rightvertex);
				bond(gluetri, botrcasing);
				tspivot(botright, botrsubseg);
				tsbond(gluetri, botrsubseg);

				/* Delete the spliced-out triangle. */
				triangledealloc(m, botright.tri);

				sym(fliptri, gluetri);
				if (gluetri.tri != m->dummytri) {
					lnextself(gluetri);
					dnext(gluetri, topright);
					sym(topright, toprcasing);

					setorg(gluetri, rightvertex);
					bond(gluetri, toprcasing);
					tspivot(topright, toprsubseg);
					tsbond(gluetri, toprsubseg);

					/* Delete the spliced-out triangle. */
					triangledealloc(m, topright.tri);
				}

				/* This is the end of the list, sneakily encoded. */
				m->lastflip->prevflip = (struct flipstacker *) NULL;
			} else {
				/* Undo an edge flip. */
				unflip(m, b, &fliptri);
			}

			/* Go on and process the next transformation. */
			m->lastflip = m->lastflip->prevflip;
		}
	}

	/**                                                                         **/
	/**                                                                         **/
	/********* 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.                                            */
	/*                                                                           */
	/*****************************************************************************/

	static void vertexsort(vertex *sortarray, int arraysize)
	{
		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.                                                  */
	/*                                                                           */
	/*****************************************************************************/

	static void vertexmedian(vertex *sortarray, int arraysize, int median, int axis)
	{
		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.                                           */
	/*                                                                           */
	/*****************************************************************************/

	static void alternateaxes(vertex *sortarray, int arraysize, int axis)
	{
		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.                                                                  */
	/*                                                                           */
	/*****************************************************************************/

	static void mergehulls(struct mesh *m, struct behavior *b, struct otri *farleft,
		struct otri *innerleft, struct otri *innerright,
		struct otri *farright, int axis)
	{
		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).                                                */
	/*                                                                           */
	/*****************************************************************************/

	static void divconqrecurse(struct mesh *m, struct behavior *b, vertex *sortarray,
		int vertices, int axis,
		struct otri *farleft, struct otri *farright)
	{
		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);
		}
	}

	static long removeghosts(struct mesh *m, struct behavior *b, struct otri *startghost)
	{
		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.       */
	/*                                                                           */
	/*****************************************************************************/

	static long divconqdelaunay(struct mesh *m, struct behavior *b)
	{
		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((int *) sortarray);

		return removeghosts(m, b, &hullleft);
	}

	/**                                                                         **/
	/**                                                                         **/
	/********* Divide-and-conquer Delaunay triangulation ends here       *********/

	/********* Incremental Delaunay triangulation begins here            *********/
	/**                                                                         **/
	/**                                                                         **/

	/*****************************************************************************/
	/*                                                                           */
	/*  boundingbox()   Form an "infinite" bounding triangle to insert vertices  */
	/*                  into.                                                    */
	/*                                                                           */
	/*  The vertices at "infinity" are assigned finite coordinates, which are    */
	/*  used by the point location routines, but (mostly) ignored by the         */
	/*  Delaunay edge flip routines.                                             */
	/*                                                                           */
	/*****************************************************************************/

	static void boundingbox(struct mesh *m, struct behavior *b)
	{
		struct otri inftri;          /* Handle for the triangular bounding box. */
		Real width;

		if (b->verbose) {
			printf("  Creating triangular bounding box.\n");
		}
		/* Find the width (or height, whichever is larger) of the triangulation. */
		width = m->xmax - m->xmin;
		if (m->ymax - m->ymin > width) {
			width = m->ymax - m->ymin;
		}
		if (width == 0.0) {
			width = 1.0;
		}
		/* Create the vertices of the bounding box. */
		m->infvertex1 = (vertex) trimalloc(m->vertices.itembytes);
		m->infvertex2 = (vertex) trimalloc(m->vertices.itembytes);
		m->infvertex3 = (vertex) trimalloc(m->vertices.itembytes);
		m->infvertex1[0] = m->xmin - 50.0 * width;
		m->infvertex1[1] = m->ymin - 40.0 * width;
		m->infvertex2[0] = m->xmax + 50.0 * width;
		m->infvertex2[1] = m->ymin - 40.0 * width;
		m->infvertex3[0] = 0.5 * (m->xmin + m->xmax);
		m->infvertex3[1] = m->ymax + 60.0 * width;

		/* Create the bounding box. */
		maketriangle(m, b, &inftri);
		setorg(inftri, m->infvertex1);
		setdest(inftri, m->infvertex2);
		setapex(inftri, m->infvertex3);
		/* Link dummytri to the bounding box so we can always find an */
		/*   edge to begin searching (point location) from.           */
		m->dummytri[0] = (triangle) inftri.tri;
		if (b->verbose > 2) {
			printf("  Creating ");
			printtriangle(m, b, &inftri);
		}
	}

	/*****************************************************************************/
	/*                                                                           */
	/*  removebox()   Remove the "infinite" bounding triangle, setting boundary  */
	/*                markers as appropriate.                                    */
	/*                                                                           */
	/*  The triangular bounding box has three boundary triangles (one for each   */
	/*  side of the bounding box), and a bunch of triangles fanning out from     */
	/*  the three bounding box vertices (one triangle for each edge of the       */
	/*  convex hull of the inner mesh).  This routine removes these triangles.   */
	/*                                                                           */
	/*  Returns the number of edges on the convex hull of the triangulation.     */
	/*                                                                           */
	/*****************************************************************************/

	static long removebox(struct mesh *m, struct behavior *b)
	{
		struct otri deadtriangle;
		struct otri searchedge;
		struct otri checkedge;
		struct otri nextedge, finaledge, dissolveedge;
		vertex markorg;
		long hullsize;
		triangle ptr;                         /* Temporary variable used by sym(). */

		if (b->verbose) {
			printf("  Removing triangular bounding box.\n");
		}
		/* Find a boundary triangle. */
		nextedge.tri = m->dummytri;
		nextedge.orient = 0;
		symself(nextedge);
		/* Mark a place to stop. */
		lprev(nextedge, finaledge);
		lnextself(nextedge);
		symself(nextedge);
		/* Find a triangle (on the boundary of the vertex set) that isn't */
		/*   a bounding box triangle.                                     */
		lprev(nextedge, searchedge);
		symself(searchedge);
		/* Check whether nextedge is another boundary triangle */
		/*   adjacent to the first one.                        */
		lnext(nextedge, checkedge);
		symself(checkedge);
		if (checkedge.tri == m->dummytri) {
			/* Go on to the next triangle.  There are only three boundary   */
			/*   triangles, and this next triangle cannot be the third one, */
			/*   so it's safe to stop here.                                 */
			lprevself(searchedge);
			symself(searchedge);
		}
		/* Find a new boundary edge to search from, as the current search */
		/*   edge lies on a bounding box triangle and will be deleted.    */
		m->dummytri[0] = encode(searchedge);
		hullsize = -2l;
		while (!otriequal(nextedge, finaledge)) {
			hullsize++;
			lprev(nextedge, dissolveedge);
			symself(dissolveedge);
			/* If not using a PSLG, the vertices should be marked now. */
			/*   (If using a PSLG, markhull() will do the job.)        */
			if (!b->poly) {
				/* Be careful!  One must check for the case where all the input     */
				/*   vertices are collinear, and thus all the triangles are part of */
				/*   the bounding box.  Otherwise, the setvertexmark() call below   */
				/*   will cause a bad pointer reference.                            */
				if (dissolveedge.tri != m->dummytri) {
					org(dissolveedge, markorg);
					if (vertexmark(markorg) == 0) {
						setvertexmark(markorg, 1);
					}
				}
			}
			/* Disconnect the bounding box triangle from the mesh triangle. */
			dissolve(dissolveedge);
			lnext(nextedge, deadtriangle);
			sym(deadtriangle, nextedge);
			/* Get rid of the bounding box triangle. */
			triangledealloc(m, deadtriangle.tri);
			/* Do we need to turn the corner? */
			if (nextedge.tri == m->dummytri) {
				/* Turn the corner. */
				otricopy(dissolveedge, nextedge);
			}
		}
		triangledealloc(m, finaledge.tri);

		trifree((int *) m->infvertex1);  /* Deallocate the bounding box vertices. */
		trifree((int *) m->infvertex2);
		trifree((int *) m->infvertex3);

		return hullsize;
	}

	/*****************************************************************************/
	/*                                                                           */
	/*  incrementaldelaunay()   Form a Delaunay triangulation by incrementally   */
	/*                          inserting vertices.                              */
	/*                                                                           */
	/*  Returns the number of edges on the convex hull of the triangulation.     */
	/*                                                                           */
	/*****************************************************************************/

	static long incrementaldelaunay(struct mesh *m, struct behavior *b)
	{
		struct otri starttri;
		vertex vertexloop;

		/* Create a triangular bounding box. */
		boundingbox(m, b);
		if (b->verbose) {
			printf("  Incrementally inserting vertices.\n");
		}
		traversalinit(&m->vertices);
		vertexloop = vertextraverse(m);
		while (vertexloop != (vertex) NULL) {
			starttri.tri = m->dummytri;
			if (insertvertex(m, b, vertexloop, &starttri, (struct osub *) NULL, 0, 0)
				== DUPLICATEVERTEX) {
				if (!b->quiet) {
					printf(
						"Warning:  A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n",
						vertexloop[0], vertexloop[1]);
				}
				setvertextype(vertexloop, UNDEADVERTEX);
				m->undeads++;
			}
			vertexloop = vertextraverse(m);
		}
		/* Remove the bounding box. */
		return removebox(m, b);
	}

	/**                                                                         **/
	/**                                                                         **/
	/********* Incremental Delaunay triangulation ends here              *********/

	/********* Sweepline Delaunay triangulation begins here              *********/
	/**                                                                         **/
	/**                                                                         **/

	static void eventheapinsert(struct event **heap, int heapsize, struct event *newevent)
	{
		Real eventx, eventy;
		int eventnum;
		int parent;
		int notdone;

		eventx = newevent->xkey;
		eventy = newevent->ykey;
		eventnum = heapsize;
		notdone = eventnum > 0;
		while (notdone) {
			parent = (eventnum - 1) >> 1;
			if ((heap[parent]->ykey < eventy) ||
				((heap[parent]->ykey == eventy)
					&& (heap[parent]->xkey <= eventx))) {
				notdone = 0;
			} else {
				heap[eventnum] = heap[parent];
				heap[eventnum]->heapposition = eventnum;

				eventnum = parent;
				notdone = eventnum > 0;
			}
		}
		heap[eventnum] = newevent;
		newevent->heapposition = eventnum;
	}

	static void eventheapify(struct event **heap, int heapsize, int eventnum)
	{
		struct event *thisevent;
		Real eventx, eventy;
		int leftchild, rightchild;
		int smallest;
		int notdone;

		thisevent = heap[eventnum];
		eventx = thisevent->xkey;
		eventy = thisevent->ykey;
		leftchild = 2 * eventnum + 1;
		notdone = leftchild < heapsize;
		while (notdone) {
			if ((heap[leftchild]->ykey < eventy) ||
				((heap[leftchild]->ykey == eventy)
					&& (heap[leftchild]->xkey < eventx))) {
				smallest = leftchild;
			} else {
				smallest = eventnum;
			}
			rightchild = leftchild + 1;
			if (rightchild < heapsize) {
				if ((heap[rightchild]->ykey < heap[smallest]->ykey) ||
					((heap[rightchild]->ykey == heap[smallest]->ykey)
						&& (heap[rightchild]->xkey < heap[smallest]->xkey))) {
					smallest = rightchild;
				}
			}
			if (smallest == eventnum) {
				notdone = 0;
			} else {
				heap[eventnum] = heap[smallest];
				heap[eventnum]->heapposition = eventnum;
				heap[smallest] = thisevent;
				thisevent->heapposition = smallest;

				eventnum = smallest;
				leftchild = 2 * eventnum + 1;
				notdone = leftchild < heapsize;
			}
		}
	}

	static void eventheapdelete(struct event **heap, int heapsize, int eventnum)
	{
		struct event *moveevent;
		Real eventx, eventy;
		int parent;
		int notdone;

		moveevent = heap[heapsize - 1];
		if (eventnum > 0) {
			eventx = moveevent->xkey;
			eventy = moveevent->ykey;
			do {
				parent = (eventnum - 1) >> 1;
				if ((heap[parent]->ykey < eventy) ||
					((heap[parent]->ykey == eventy)
						&& (heap[parent]->xkey <= eventx))) {
					notdone = 0;
				} else {
					heap[eventnum] = heap[parent];
					heap[eventnum]->heapposition = eventnum;

					eventnum = parent;
					notdone = eventnum > 0;
				}
			} while (notdone);
		}
		heap[eventnum] = moveevent;
		moveevent->heapposition = eventnum;
		eventheapify(heap, heapsize - 1, eventnum);
	}

	static void createeventheap(struct mesh *m, struct event ***eventheap,
		struct event **events, struct event **freeevents)
	{
		vertex thisvertex;
		int maxevents;
		int i;

		maxevents = (3 * m->invertices) / 2;
		*eventheap = (struct event **) trimalloc(maxevents *
			(int) sizeof(struct event *));
		*events = (struct event *) trimalloc(maxevents * (int) sizeof(struct event));
		traversalinit(&m->vertices);
		for (i = 0; i < m->invertices; i++) {
			thisvertex = vertextraverse(m);
			(*events)[i].eventptr = (int *) thisvertex;
			(*events)[i].xkey = thisvertex[0];
			(*events)[i].ykey = thisvertex[1];
			eventheapinsert(*eventheap, i, *events + i);
		}
		*freeevents = (struct event *) NULL;
		for (i = maxevents - 1; i >= m->invertices; i--) {
			(*events)[i].eventptr = (int *) *freeevents;
			*freeevents = *events + i;
		}
	}

	static int rightofhyperbola(struct mesh *m, struct otri *fronttri, vertex newsite)
	{
		vertex leftvertex, rightvertex;
		Real dxa, dya, dxb, dyb;

		m->hyperbolacount++;

		dest(*fronttri, leftvertex);
		apex(*fronttri, rightvertex);
		if ((leftvertex[1] < rightvertex[1]) ||
			((leftvertex[1] == rightvertex[1]) &&
			(leftvertex[0] < rightvertex[0]))) {
			if (newsite[0] >= rightvertex[0]) {
				return 1;
			}
		} else {
			if (newsite[0] <= leftvertex[0]) {
				return 0;
			}
		}
		dxa = leftvertex[0] - newsite[0];
		dya = leftvertex[1] - newsite[1];
		dxb = rightvertex[0] - newsite[0];
		dyb = rightvertex[1] - newsite[1];
		return dya * (dxb * dxb + dyb * dyb) > dyb * (dxa * dxa + dya * dya);
	}

	static Real circletop(struct mesh *m, vertex pa, vertex pb, vertex pc, Real ccwabc)
	{
		Real xac, yac, xbc, ybc, xab, yab;
		Real aclen2, bclen2, ablen2;

		m->circletopcount++;

		xac = pa[0] - pc[0];
		yac = pa[1] - pc[1];
		xbc = pb[0] - pc[0];
		ybc = pb[1] - pc[1];
		xab = pa[0] - pb[0];
		yab = pa[1] - pb[1];
		aclen2 = xac * xac + yac * yac;
		bclen2 = xbc * xbc + ybc * ybc;
		ablen2 = xab * xab + yab * yab;
		return pc[1] + (xac * bclen2 - xbc * aclen2 + sqrt(aclen2 * bclen2 * ablen2))
			/ (2.0 * ccwabc);
	}

	static void check4deadevent(struct otri *checktri, struct event **freeevents,
		struct event **eventheap, int *heapsize)
	{
		struct event *deadevent;
		vertex eventvertex;
		int eventnum;

		org(*checktri, eventvertex);
		if (eventvertex != (vertex) NULL) {
			deadevent = (struct event *) eventvertex;
			eventnum = deadevent->heapposition;
			deadevent->eventptr = (int *) *freeevents;
			*freeevents = deadevent;
			eventheapdelete(eventheap, *heapsize, eventnum);
			(*heapsize)--;
			setorg(*checktri, NULL);
		}
	}

	static struct splaynode *splay(struct mesh *m, struct splaynode *splaytree,
		vertex searchpoint, struct otri *searchtri)
	{
		struct splaynode *child, *grandchild;
		struct splaynode *lefttree, *righttree;
		struct splaynode *leftright;
		vertex checkvertex;
		int rightofroot, rightofchild;

		if (splaytree == (struct splaynode *) NULL) {
			return (struct splaynode *) NULL;
		}
		dest(splaytree->keyedge, checkvertex);
		if (checkvertex == splaytree->keydest) {
			rightofroot = rightofhyperbola(m, &splaytree->keyedge, searchpoint);
			if (rightofroot) {
				otricopy(splaytree->keyedge, *searchtri);
				child = splaytree->rchild;
			} else {
				child = splaytree->lchild;
			}
			if (child == (struct splaynode *) NULL) {
				return splaytree;
			}
			dest(child->keyedge, checkvertex);
			if (checkvertex != child->keydest) {
				child = splay(m, child, searchpoint, searchtri);
				if (child == (struct splaynode *) NULL) {
					if (rightofroot) {
						splaytree->rchild = (struct splaynode *) NULL;
					} else {
						splaytree->lchild = (struct splaynode *) NULL;
					}
					return splaytree;
				}
			}
			rightofchild = rightofhyperbola(m, &child->keyedge, searchpoint);
			if (rightofchild) {
				otricopy(child->keyedge, *searchtri);
				grandchild = splay(m, child->rchild, searchpoint, searchtri);
				child->rchild = grandchild;
			} else {
				grandchild = splay(m, child->lchild, searchpoint, searchtri);
				child->lchild = grandchild;
			}
			if (grandchild == (struct splaynode *) NULL) {
				if (rightofroot) {
					splaytree->rchild = child->lchild;
					child->lchild = splaytree;
				} else {
					splaytree->lchild = child->rchild;
					child->rchild = splaytree;
				}
				return child;
			}
			if (rightofchild) {
				if (rightofroot) {
					splaytree->rchild = child->lchild;
					child->lchild = splaytree;
				} else {
					splaytree->lchild = grandchild->rchild;
					grandchild->rchild = splaytree;
				}
				child->rchild = grandchild->lchild;
				grandchild->lchild = child;
			} else {
				if (rightofroot) {
					splaytree->rchild = grandchild->lchild;
					grandchild->lchild = splaytree;
				} else {
					splaytree->lchild = child->rchild;
					child->rchild = splaytree;
				}
				child->lchild = grandchild->rchild;
				grandchild->rchild = child;
			}
			return grandchild;
		} else {
			lefttree = splay(m, splaytree->lchild, searchpoint, searchtri);
			righttree = splay(m, splaytree->rchild, searchpoint, searchtri);

			pooldealloc(&m->splaynodes, (int *) splaytree);
			if (lefttree == (struct splaynode *) NULL) {
				return righttree;
			} else if (righttree == (struct splaynode *) NULL) {
				return lefttree;
			} else if (lefttree->rchild == (struct splaynode *) NULL) {
				lefttree->rchild = righttree->lchild;
				righttree->lchild = lefttree;
				return righttree;
			} else if (righttree->lchild == (struct splaynode *) NULL) {
				righttree->lchild = lefttree->rchild;
				lefttree->rchild = righttree;
				return lefttree;
			} else {
				/*      printf("Holy Toledo!!!\n"); */
				leftright = lefttree->rchild;
				while (leftright->rchild != (struct splaynode *) NULL) {
					leftright = leftright->rchild;
				}
				leftright->rchild = righttree;
				return lefttree;
			}
		}
	}

	static struct splaynode *splayinsert(struct mesh *m, struct splaynode *splayroot,
		struct otri *newkey, vertex searchpoint)
	{
		struct splaynode *newsplaynode;

		newsplaynode = (struct splaynode *) poolalloc(&m->splaynodes);
		otricopy(*newkey, newsplaynode->keyedge);
		dest(*newkey, newsplaynode->keydest);
		if (splayroot == (struct splaynode *) NULL) {
			newsplaynode->lchild = (struct splaynode *) NULL;
			newsplaynode->rchild = (struct splaynode *) NULL;
		} else if (rightofhyperbola(m, &splayroot->keyedge, searchpoint)) {
			newsplaynode->lchild = splayroot;
			newsplaynode->rchild = splayroot->rchild;
			splayroot->rchild = (struct splaynode *) NULL;
		} else {
			newsplaynode->lchild = splayroot->lchild;
			newsplaynode->rchild = splayroot;
			splayroot->lchild = (struct splaynode *) NULL;
		}
		return newsplaynode;
	}

	static struct splaynode *circletopinsert(struct mesh *m, struct behavior *b,
		struct splaynode *splayroot,
		struct otri *newkey,
		vertex pa, vertex pb, vertex pc, Real topy)
	{
		Real ccwabc;
		Real xac, yac, xbc, ybc;
		Real aclen2, bclen2;
		Real searchpoint[2];
		struct otri dummytri;

		ccwabc = counterclockwise(m, b, pa, pb, pc);
		xac = pa[0] - pc[0];
		yac = pa[1] - pc[1];
		xbc = pb[0] - pc[0];
		ybc = pb[1] - pc[1];
		aclen2 = xac * xac + yac * yac;
		bclen2 = xbc * xbc + ybc * ybc;
		searchpoint[0] = pc[0] - (yac * bclen2 - ybc * aclen2) / (2.0 * ccwabc);
		searchpoint[1] = topy;
		return splayinsert(m, splay(m, splayroot, (vertex) searchpoint, &dummytri),
			newkey, (vertex) searchpoint);
	}

	static struct splaynode *frontlocate(struct mesh *m, struct splaynode *splayroot,
		struct otri *bottommost, vertex searchvertex,
		struct otri *searchtri, int *farright)
	{
		int farrightflag;
		triangle ptr;                       /* Temporary variable used by onext(). */

		otricopy(*bottommost, *searchtri);
		splayroot = splay(m, splayroot, searchvertex, searchtri);

		farrightflag = 0;
		while (!farrightflag && rightofhyperbola(m, searchtri, searchvertex)) {
			onextself(*searchtri);
			farrightflag = otriequal(*searchtri, *bottommost);
		}
		*farright = farrightflag;
		return splayroot;
	}

	static long sweeplinedelaunay(struct mesh *m, struct behavior *b)
	{
		struct event **eventheap;
		struct event *events;
		struct event *freeevents;
		struct event *nextevent;
		struct event *newevent;
		struct splaynode *splayroot;
		struct otri bottommost;
		struct otri searchtri;
		struct otri fliptri;
		struct otri lefttri, righttri, farlefttri, farrighttri;
		struct otri inserttri;
		vertex firstvertex, secondvertex;
		vertex nextvertex, lastvertex;
		vertex connectvertex;
		vertex leftvertex, midvertex, rightvertex;
		Real lefttest, righttest;
		int heapsize;
		int check4events, farrightflag;
		triangle ptr;   /* Temporary variable used by sym(), onext(), and oprev(). */

		poolinit(&m->splaynodes, sizeof(struct splaynode), SPLAYNODEPERBLOCK,
			SPLAYNODEPERBLOCK, 0);
		splayroot = (struct splaynode *) NULL;

		if (b->verbose) {
			printf("  Placing vertices in event heap.\n");
		}
		createeventheap(m, &eventheap, &events, &freeevents);
		heapsize = m->invertices;

		if (b->verbose) {
			printf("  Forming triangulation.\n");
		}
		maketriangle(m, b, &lefttri);
		maketriangle(m, b, &righttri);
		bond(lefttri, righttri);
		lnextself(lefttri);
		lprevself(righttri);
		bond(lefttri, righttri);
		lnextself(lefttri);
		lprevself(righttri);
		bond(lefttri, righttri);
		firstvertex = (vertex) eventheap[0]->eventptr;
		eventheap[0]->eventptr = (int *) freeevents;
		freeevents = eventheap[0];
		eventheapdelete(eventheap, heapsize, 0);
		heapsize--;
		do {
			if (heapsize == 0) {
				printf("Error:  Input vertices are all identical.\n");
				triexit(1);
			}
			secondvertex = (vertex) eventheap[0]->eventptr;
			eventheap[0]->eventptr = (int *) freeevents;
			freeevents = eventheap[0];
			eventheapdelete(eventheap, heapsize, 0);
			heapsize--;
			if ((firstvertex[0] == secondvertex[0]) &&
				(firstvertex[1] == secondvertex[1])) {
				if (!b->quiet) {
					printf(
						"Warning:  A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n",
						secondvertex[0], secondvertex[1]);
				}
				setvertextype(secondvertex, UNDEADVERTEX);
				m->undeads++;
			}
		} while ((firstvertex[0] == secondvertex[0]) &&
			(firstvertex[1] == secondvertex[1]));
		setorg(lefttri, firstvertex);
		setdest(lefttri, secondvertex);
		setorg(righttri, secondvertex);
		setdest(righttri, firstvertex);
		lprev(lefttri, bottommost);
		lastvertex = secondvertex;
		while (heapsize > 0) {
			nextevent = eventheap[0];
			eventheapdelete(eventheap, heapsize, 0);
			heapsize--;
			check4events = 1;
			if (nextevent->xkey < m->xmin) {
				decode(nextevent->eventptr, fliptri);
				oprev(fliptri, farlefttri);
				check4deadevent(&farlefttri, &freeevents, eventheap, &heapsize);
				onext(fliptri, farrighttri);
				check4deadevent(&farrighttri, &freeevents, eventheap, &heapsize);

				if (otriequal(farlefttri, bottommost)) {
					lprev(fliptri, bottommost);
				}
				flip(m, b, &fliptri);
				setapex(fliptri, NULL);
				lprev(fliptri, lefttri);
				lnext(fliptri, righttri);
				sym(lefttri, farlefttri);

				if (randomnation(SAMPLERATE) == 0) {
					symself(fliptri);
					dest(fliptri, leftvertex);
					apex(fliptri, midvertex);
					org(fliptri, rightvertex);
					splayroot = circletopinsert(m, b, splayroot, &lefttri, leftvertex,
						midvertex, rightvertex, nextevent->ykey);
				}
			} else {
				nextvertex = (vertex) nextevent->eventptr;
				if ((nextvertex[0] == lastvertex[0]) &&
					(nextvertex[1] == lastvertex[1])) {
					if (!b->quiet) {
						printf(
							"Warning:  A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n",
							nextvertex[0], nextvertex[1]);
					}
					setvertextype(nextvertex, UNDEADVERTEX);
					m->undeads++;
					check4events = 0;
				} else {
					lastvertex = nextvertex;

					splayroot = frontlocate(m, splayroot, &bottommost, nextvertex,
						&searchtri, &farrightflag);
					/*
					otricopy(bottommost, searchtri);
					farrightflag = 0;
					while (!farrightflag && rightofhyperbola(m, &searchtri, nextvertex)) {
					onextself(searchtri);
					farrightflag = otriequal(searchtri, bottommost);
					}
					*/

					check4deadevent(&searchtri, &freeevents, eventheap, &heapsize);

					otricopy(searchtri, farrighttri);
					sym(searchtri, farlefttri);
					maketriangle(m, b, &lefttri);
					maketriangle(m, b, &righttri);
					dest(farrighttri, connectvertex);
					setorg(lefttri, connectvertex);
					setdest(lefttri, nextvertex);
					setorg(righttri, nextvertex);
					setdest(righttri, connectvertex);
					bond(lefttri, righttri);
					lnextself(lefttri);
					lprevself(righttri);
					bond(lefttri, righttri);
					lnextself(lefttri);
					lprevself(righttri);
					bond(lefttri, farlefttri);
					bond(righttri, farrighttri);
					if (!farrightflag && otriequal(farrighttri, bottommost)) {
						otricopy(lefttri, bottommost);
					}

					if (randomnation(SAMPLERATE) == 0) {
						splayroot = splayinsert(m, splayroot, &lefttri, nextvertex);
					} else if (randomnation(SAMPLERATE) == 0) {
						lnext(righttri, inserttri);
						splayroot = splayinsert(m, splayroot, &inserttri, nextvertex);
					}
				}
			}
			nextevent->eventptr = (int *) freeevents;
			freeevents = nextevent;

			if (check4events) {
				apex(farlefttri, leftvertex);
				dest(lefttri, midvertex);
				apex(lefttri, rightvertex);
				lefttest = counterclockwise(m, b, leftvertex, midvertex, rightvertex);
				if (lefttest > 0.0) {
					newevent = freeevents;
					freeevents = (struct event *) freeevents->eventptr;
					newevent->xkey = m->xminextreme;
					newevent->ykey = circletop(m, leftvertex, midvertex, rightvertex,
						lefttest);
					newevent->eventptr = (int *) encode(lefttri);
					eventheapinsert(eventheap, heapsize, newevent);
					heapsize++;
					setorg(lefttri, newevent);
				}
				apex(righttri, leftvertex);
				org(righttri, midvertex);
				apex(farrighttri, rightvertex);
				righttest = counterclockwise(m, b, leftvertex, midvertex, rightvertex);
				if (righttest > 0.0) {
					newevent = freeevents;
					freeevents = (struct event *) freeevents->eventptr;
					newevent->xkey = m->xminextreme;
					newevent->ykey = circletop(m, leftvertex, midvertex, rightvertex,
						righttest);
					newevent->eventptr = (int *) encode(farrighttri);
					eventheapinsert(eventheap, heapsize, newevent);
					heapsize++;
					setorg(farrighttri, newevent);
				}
			}
		}

		pooldeinit(&m->splaynodes);
		lprevself(bottommost);
		return removeghosts(m, b, &bottommost);
	}

	/**                                                                         **/
	/**                                                                         **/
	/********* Sweepline Delaunay triangulation ends here                *********/

	/********* General mesh construction routines begin here             *********/
	/**                                                                         **/
	/**                                                                         **/

	/*****************************************************************************/
	/*                                                                           */
	/*  delaunay()   Form a Delaunay triangulation.                              */
	/*                                                                           */
	/*****************************************************************************/

	static long delaunay(struct mesh *m, struct behavior *b)
	{
		long hulledges;

		m->eextras = 0;
		initializetrisubpools(m, b);

		if (!b->quiet) {
			printf("Constructing Delaunay triangulation ");
			if (b->incremental) {
				printf("by incremental method.\n");
			} else if (b->sweepline) {
				printf("by sweepline method.\n");
			} else {
				printf("by divide-and-conquer method.\n");
			}
		}
		if (b->incremental) {
			hulledges = incrementaldelaunay(m, b);
		} else if (b->sweepline) {
			hulledges = sweeplinedelaunay(m, b);
		} else {
			hulledges = divconqdelaunay(m, b);
		}

		if (m->triangles.items == 0) {
			/* The input vertices were all collinear, so there are no triangles. */
			return 0l;
		} else {
			return hulledges;
		}
	}

	/*****************************************************************************/
	/*                                                                           */
	/*  reconstruct()   Reconstruct a triangulation from its .ele (and possibly  */
	/*                  .poly) file.  Used when the -r switch is used.           */
	/*                                                                           */
	/*  Reads an .ele file and reconstructs the original mesh.  If the -p switch */
	/*  is used, this procedure will also read a .poly file and reconstruct the  */
	/*  subsegments of the original mesh.  If the -a switch is used, this        */
	/*  procedure will also read an .area file and set a maximum area constraint */
	/*  on each triangle.                                                        */
	/*                                                                           */
	/*  Vertices that are not corners of triangles, such as nodes on edges of    */
	/*  subparametric elements, are discarded.                                   */
	/*                                                                           */
	/*  This routine finds the adjacencies between triangles (and subsegments)   */
	/*  by forming one stack of triangles for each vertex.  Each triangle is on  */
	/*  three different stacks simultaneously.  Each triangle's subsegment       */
	/*  pointers are used to link the items in each stack.  This memory-saving   */
	/*  feature makes the code harder to read.  The most important thing to keep */
	/*  in mind is that each triangle is removed from a stack precisely when     */
	/*  the corresponding pointer is adjusted to refer to a subsegment rather    */
	/*  than the next triangle of the stack.                                     */
	/*                                                                           */
	/*****************************************************************************/

	static int reconstruct(struct mesh *m, struct behavior *b, int *trianglelist,
		Real *triangleattriblist, Real *trianglearealist,
		int elements, int corners, int attribs,
		int *segmentlist,int *segmentmarkerlist, int numberofsegments)
	{
		int vertexindex;
		int attribindex;
		struct otri triangleloop;
		struct otri triangleleft;
		struct otri checktri;
		struct otri checkleft;
		struct otri checkneighbor;
		struct osub subsegloop;
		triangle *vertexarray;
		triangle *prevlink;
		triangle nexttri;
		vertex tdest, tapex;
		vertex checkdest, checkapex;
		vertex shorg;
		vertex killvertex;
		vertex segmentorg, segmentdest;
		Real area;
		int corner[3];
		int end[2];
		int killvertexindex;
		int incorners;
		int segmentmarkers;
		int boundmarker;
		int aroundvertex;
		long hullsize;
		int notfound;
		long elementnumber, segmentnumber;
		int i, j;
		triangle ptr;                         /* Temporary variable used by sym(). */

		m->inelements = elements;
		incorners = corners;
		if (incorners < 3) {
			printf("Error:  Triangles must have at least 3 vertices.\n");
			triexit(1);
		}
		m->eextras = attribs;

		initializetrisubpools(m, b);

		/* Create the triangles. */
		for (elementnumber = 1; elementnumber <= m->inelements; elementnumber++) {
			maketriangle(m, b, &triangleloop);
			/* Mark the triangle as living. */
			triangleloop.tri[3] = (triangle) triangleloop.tri;
		}

		segmentmarkers = 0;
		if (b->poly) {
			m->insegments = numberofsegments;
			segmentmarkers = segmentmarkerlist != (int *) NULL;

			/* Create the subsegments. */
			for (segmentnumber = 1; segmentnumber <= m->insegments; segmentnumber++) {
				makesubseg(m, &subsegloop);
				/* Mark the subsegment as living. */
				subsegloop.ss[2] = (subseg) subsegloop.ss;
			}
		}

		vertexindex = 0;
		attribindex = 0;

		if (!b->quiet) {
			printf("Reconstructing mesh.\n");
		}
		/* Allocate a temporary array that maps each vertex to some adjacent */
		/*   triangle.  I took care to allocate all the permanent memory for */
		/*   triangles and subsegments first.                                */
		vertexarray = (triangle *) trimalloc(m->vertices.items *
			(int) sizeof(triangle));
		/* Each vertex is initially unrepresented. */
		for (i = 0; i < m->vertices.items; i++) {
			vertexarray[i] = (triangle) m->dummytri;
		}

		if (b->verbose) {
			printf("  Assembling triangles.\n");
		}
		/* Read the triangles from the .ele file, and link */
		/*   together those that share an edge.            */
		traversalinit(&m->triangles);
		triangleloop.tri = triangletraverse(m);
		elementnumber = b->firstnumber;
		while (triangleloop.tri != (triangle *) NULL) {
			/* Copy the triangle's three corners. */
			for (j = 0; j < 3; j++) {
				corner[j] = trianglelist[vertexindex++];
				if ((corner[j] < b->firstnumber) ||
					(corner[j] >= b->firstnumber + m->invertices)) {
					printf("Error:  Triangle %ld has an invalid vertex index.\n",
						elementnumber);
					triexit(1);
				}
			}

			/* Find out about (and throw away) extra nodes. */
			for (j = 3; j < incorners; j++) {
				killvertexindex = trianglelist[vertexindex++];
				if ((killvertexindex >= b->firstnumber) &&
					(killvertexindex < b->firstnumber + m->invertices)) {
					/* Delete the non-corner vertex if it's not already deleted. */
					killvertex = getvertex(m, b, killvertexindex);
					if (vertextype(killvertex) != DEADVERTEX) {
						vertexdealloc(m, killvertex);
					}
				}
			}

			/* Read the triangle's attributes. */
			for (j = 0; j < m->eextras; j++) {
				setelemattribute(triangleloop, j, triangleattriblist[attribindex++]);
			}

			if (b->vararea) {
				area = trianglearealist[elementnumber - b->firstnumber];
				setareabound(triangleloop, area);
			}

			/* Set the triangle's vertices. */
			triangleloop.orient = 0;
			setorg(triangleloop, getvertex(m, b, corner[0]));
			setdest(triangleloop, getvertex(m, b, corner[1]));
			setapex(triangleloop, getvertex(m, b, corner[2]));
			/* Try linking the triangle to others that share these vertices. */
			for (triangleloop.orient = 0; triangleloop.orient < 3;
				triangleloop.orient++) {
				/* Take the number for the origin of triangleloop. */
				aroundvertex = corner[triangleloop.orient];
				/* Look for other triangles having this vertex. */
				nexttri = vertexarray[aroundvertex - b->firstnumber];
				/* Link the current triangle to the next one in the stack. */
				triangleloop.tri[6 + triangleloop.orient] = nexttri;
				/* Push the current triangle onto the stack. */
				vertexarray[aroundvertex - b->firstnumber] = encode(triangleloop);
				decode(nexttri, checktri);
				if (checktri.tri != m->dummytri) {
					dest(triangleloop, tdest);
					apex(triangleloop, tapex);
					/* Look for other triangles that share an edge. */
					do {
						dest(checktri, checkdest);
						apex(checktri, checkapex);
						if (tapex == checkdest) {
							/* The two triangles share an edge; bond them together. */
							lprev(triangleloop, triangleleft);
							bond(triangleleft, checktri);
						}
						if (tdest == checkapex) {
							/* The two triangles share an edge; bond them together. */
							lprev(checktri, checkleft);
							bond(triangleloop, checkleft);
						}
						/* Find the next triangle in the stack. */
						nexttri = checktri.tri[6 + checktri.orient];
						decode(nexttri, checktri);
					} while (checktri.tri != m->dummytri);
				}
			}
			triangleloop.tri = triangletraverse(m);
			elementnumber++;
		}

		vertexindex = 0;

		hullsize = 0;                      /* Prepare to count the boundary edges. */
		if (b->poly) {
			if (b->verbose) {
				printf("  Marking segments in triangulation.\n");
			}
			/* Read the segments from the .poly file, and link them */
			/*   to their neighboring triangles.                    */
			boundmarker = 0;
			traversalinit(&m->subsegs);
			subsegloop.ss = subsegtraverse(m);
			segmentnumber = b->firstnumber;
			while (subsegloop.ss != (subseg *) NULL) {
				end[0] = segmentlist[vertexindex++];
				end[1] = segmentlist[vertexindex++];
				if (segmentmarkers) {
					boundmarker = segmentmarkerlist[segmentnumber - b->firstnumber];
				}
				for (j = 0; j < 2; j++) {
					if ((end[j] < b->firstnumber) ||
						(end[j] >= b->firstnumber + m->invertices)) {
						printf("Error:  Segment %ld has an invalid vertex index.\n", 
							segmentnumber);
						triexit(1);
					}
				}

				/* set the subsegment's vertices. */
				subsegloop.ssorient = 0;
				segmentorg = getvertex(m, b, end[0]);
				segmentdest = getvertex(m, b, end[1]);
				setsorg(subsegloop, segmentorg);
				setsdest(subsegloop, segmentdest);
				setsegorg(subsegloop, segmentorg);
				setsegdest(subsegloop, segmentdest);
				setmark(subsegloop, boundmarker);
				/* Try linking the subsegment to triangles that share these vertices. */
				for (subsegloop.ssorient = 0; subsegloop.ssorient < 2;
					subsegloop.ssorient++) {
					/* Take the number for the destination of subsegloop. */
					aroundvertex = end[1 - subsegloop.ssorient];
					/* Look for triangles having this vertex. */
					prevlink = &vertexarray[aroundvertex - b->firstnumber];
					nexttri = vertexarray[aroundvertex - b->firstnumber];
					decode(nexttri, checktri);
					sorg(subsegloop, shorg);
					notfound = 1;
					/* Look for triangles having this edge.  Note that I'm only       */
					/*   comparing each triangle's destination with the subsegment;   */
					/*   each triangle's apex is handled through a different vertex.  */
					/*   Because each triangle appears on three vertices' lists, each */
					/*   occurrence of a triangle on a list can (and does) represent  */
					/*   an edge.  In this way, most edges are represented twice, and */
					/*   every triangle-subsegment bond is represented once.          */
					while (notfound && (checktri.tri != m->dummytri)) {
						dest(checktri, checkdest);
						if (shorg == checkdest) {
							/* We have a match.  Remove this triangle from the list. */
							*prevlink = checktri.tri[6 + checktri.orient];
							/* Bond the subsegment to the triangle. */
							tsbond(checktri, subsegloop);
							/* Check if this is a boundary edge. */
							sym(checktri, checkneighbor);
							if (checkneighbor.tri == m->dummytri) {
								/* The next line doesn't insert a subsegment (because there's */
								/*   already one there), but it sets the boundary markers of  */
								/*   the existing subsegment and its vertices.                */
								insertsubseg(m, b, &checktri, 1);
								hullsize++;
							}
							notfound = 0;
						}
						/* Find the next triangle in the stack. */
						prevlink = &checktri.tri[6 + checktri.orient];
						nexttri = checktri.tri[6 + checktri.orient];
						decode(nexttri, checktri);
					}
				}
				subsegloop.ss = subsegtraverse(m);
				segmentnumber++;
			}
		}

		/* Mark the remaining edges as not being attached to any subsegment. */
		/* Also, count the (yet uncounted) boundary edges.                   */
		for (i = 0; i < m->vertices.items; i++) {
			/* Search the stack of triangles adjacent to a vertex. */
			nexttri = vertexarray[i];
			decode(nexttri, checktri);
			while (checktri.tri != m->dummytri) {
				/* Find the next triangle in the stack before this */
				/*   information gets overwritten.                 */
				nexttri = checktri.tri[6 + checktri.orient];
				/* No adjacent subsegment.  (This overwrites the stack info.) */
				tsdissolve(checktri);
				sym(checktri, checkneighbor);
				if (checkneighbor.tri == m->dummytri) {
					insertsubseg(m, b, &checktri, 1);
					hullsize++;
				}
				decode(nexttri, checktri);
			}
		}

		trifree((int *) vertexarray);
		return hullsize;
	}

	/**                                                                         **/
	/**                                                                         **/
	/********* 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.                   */
	/*                                                                           */
	/*****************************************************************************/

	static enum finddirectionresult finddirection(struct mesh *m, struct behavior *b,
		struct otri *searchtri,
		vertex searchpoint)
	{
		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.      */
	/*                                                                           */
	/*****************************************************************************/

	static void segmentintersection(struct mesh *m, struct behavior *b,
		struct otri *splittri, struct osub *splitsubseg,
		vertex endpoint2)
	{
		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.         */
	/*                                                                           */
	/*****************************************************************************/

	static int scoutsegment(struct mesh *m, struct behavior *b, struct otri *searchtri,
		vertex endpoint2, int newmark)
	{
		struct otri crosstri;
		struct osub crosssubseg;
		vertex leftvertex, rightvertex;
		enum finddirectionresult collinear;
		subseg sptr;                      /* Temporary variable used by tspivot(). */

		collinear = finddirection(m, b, searchtri, endpoint2);
		dest(*searchtri, rightvertex);
		apex(*searchtri, leftvertex);
		if (((leftvertex[0] == endpoint2[0]) && (leftvertex[1] == endpoint2[1])) ||
			((rightvertex[0] == endpoint2[0]) && (rightvertex[1] == endpoint2[1]))) {
			/* The segment is already an edge in the mesh. */
			if ((leftvertex[0] == endpoint2[0]) && (leftvertex[1] == endpoint2[1])) {
				lprevself(*searchtri);
			}
			/* Insert a subsegment, if there isn't already one there. */
			insertsubseg(m, b, searchtri, newmark);
			return 1;
		} else if (collinear == LEFTCOLLINEAR) {
			/* We've collided with a vertex between the segment's endpoints. */
			/* Make the collinear vertex be the triangle's origin. */
			lprevself(*searchtri);
			insertsubseg(m, b, searchtri, newmark);
			/* Insert the remainder of the segment. */
			return scoutsegment(m, b, searchtri, endpoint2, newmark);
		} else if (collinear == RIGHTCOLLINEAR) {
			/* We've collided with a vertex between the segment's endpoints. */
			insertsubseg(m, b, searchtri, newmark);
			/* Make the collinear vertex be the triangle's origin. */
			lnextself(*searchtri);
			/* Insert the remainder of the segment. */
			return scoutsegment(m, b, searchtri, endpoint2, newmark);
		} else {
			lnext(*searchtri, crosstri);
			tspivot(crosstri, crosssubseg);
			/* Check for a crossing segment. */
			if (crosssubseg.ss == m->dummysub) {
				return 0;
			} else {
				/* Insert a vertex at the intersection. */
				segmentintersection(m, b, &crosstri, &crosssubseg, endpoint2);
				otricopy(crosstri, *searchtri);
				insertsubseg(m, b, searchtri, newmark);
				/* Insert the remainder of the segment. */
				return scoutsegment(m, b, searchtri, endpoint2, newmark);
			}
		}
	}

	/*****************************************************************************/
	/*                                                                           */
	/*  conformingedge()   Force a segment into a conforming Delaunay            */
	/*                     triangulation by inserting a vertex at its midpoint,  */
	/*                     and recursively forcing in the two half-segments if   */
	/*                     necessary.                                            */
	/*                                                                           */
	/*  Generates a sequence of subsegments connecting `endpoint1' to            */
	/*  `endpoint2'.  `newmark' is the boundary marker of the segment, assigned  */
	/*  to each new splitting vertex and subsegment.                             */
	/*                                                                           */
	/*  Note that conformingedge() does not always maintain the conforming       */
	/*  Delaunay property.  Once inserted, segments are locked into place;       */
	/*  vertices inserted later (to force other segments in) may render these    */
	/*  fixed segments non-Delaunay.  The conforming Delaunay property will be   */
	/*  restored by enforcequality() by splitting encroached subsegments.        */
	/*                                                                           */
	/*****************************************************************************/

	static void conformingedge(struct mesh *m, struct behavior *b,
		vertex endpoint1, vertex endpoint2, int newmark)
	{
		struct otri searchtri1, searchtri2;
		struct osub brokensubseg;
		vertex newvertex;
		vertex midvertex1, midvertex2;
		enum insertvertexresult success;
		int i;
		subseg sptr;                      /* Temporary variable used by tspivot(). */

		if (b->verbose > 2) {
			printf("Forcing segment into triangulation by recursive splitting:\n");
			printf("  (%.12g, %.12g) (%.12g, %.12g)\n", endpoint1[0], endpoint1[1],
				endpoint2[0], endpoint2[1]);
		}
		/* Create a new vertex to insert in the middle of the segment. */
		newvertex = (vertex) poolalloc(&m->vertices);
		/* Interpolate coordinates and attributes. */
		for (i = 0; i < 2 + m->nextras; i++) {
			newvertex[i] = 0.5 * (endpoint1[i] + endpoint2[i]);
		}
		setvertexmark(newvertex, newmark);
		setvertextype(newvertex, SEGMENTVERTEX);
		/* No known triangle to search from. */
		searchtri1.tri = m->dummytri;
		/* Attempt to insert the new vertex. */
		success = insertvertex(m, b, newvertex, &searchtri1, (struct osub *) NULL,
			0, 0);
		if (success == DUPLICATEVERTEX) {
			if (b->verbose > 2) {
				printf("  Segment intersects existing vertex (%.12g, %.12g).\n",
					newvertex[0], newvertex[1]);
			}
			/* Use the vertex that's already there. */
			vertexdealloc(m, newvertex);
			org(searchtri1, newvertex);
		} else {
			if (success == VIOLATINGVERTEX) {
				if (b->verbose > 2) {
					printf("  Two segments intersect at (%.12g, %.12g).\n",
						newvertex[0], newvertex[1]);
				}
				/* By fluke, we've landed right on another segment.  Split it. */
				tspivot(searchtri1, brokensubseg);
				success = insertvertex(m, b, newvertex, &searchtri1, &brokensubseg,
					0, 0);
				if (success != SUCCESSFULVERTEX) {
					printf("Internal error in conformingedge():\n");
					printf("  Failure to split a segment.\n");
					internalerror();
				}
			}
			/* The vertex has been inserted successfully. */
			if (m->steinerleft > 0) {
				m->steinerleft--;
			}
		}
		otricopy(searchtri1, searchtri2);
		/* `searchtri1' and `searchtri2' are fastened at their origins to         */
		/*   `newvertex', and will be directed toward `endpoint1' and `endpoint2' */
		/*   respectively.  First, we must get `searchtri2' out of the way so it  */
		/*   won't be invalidated during the insertion of the first half of the   */
		/*   segment.                                                             */
		finddirection(m, b, &searchtri2, endpoint2);
		if (!scoutsegment(m, b, &searchtri1, endpoint1, newmark)) {
			/* The origin of searchtri1 may have changed if a collision with an */
			/*   intervening vertex on the segment occurred.                    */
			org(searchtri1, midvertex1);
			conformingedge(m, b, midvertex1, endpoint1, newmark);
		}
		if (!scoutsegment(m, b, &searchtri2, endpoint2, newmark)) {
			/* The origin of searchtri2 may have changed if a collision with an */
			/*   intervening vertex on the segment occurred.                    */
			org(searchtri2, midvertex2);
			conformingedge(m, b, midvertex2, endpoint2, newmark);
		}
	}

	/*****************************************************************************/
	/*                                                                           */
	/*  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.)                                                 */
	/*                                                                           */
	/*****************************************************************************/

	static void delaunayfixup(struct mesh *m, struct behavior *b,
		struct otri *fixuptri, int leftside)
	{
		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.                                    */
	/*                                                                           */
	/*****************************************************************************/

	static void constrainededge(struct mesh *m, struct behavior *b,
		struct otri *starttri, vertex endpoint2, int newmark)
	{
		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.            */
	/*                                                                           */
	/*****************************************************************************/

	static void insertsegment(struct mesh *m, struct behavior *b,
		vertex endpoint1, vertex endpoint2, int newmark)
	{
		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);

		if (b->splitseg) {
			/* Insert vertices to force the segment into the triangulation. */
			conformingedge(m, b, endpoint1, endpoint2, newmark);
		} else {
			/* Insert the segment directly into the triangulation. */
			constrainededge(m, b, &searchtri1, endpoint2, newmark);
		}
	}

	/*****************************************************************************/
	/*                                                                           */
	/*  markhull()   Cover the convex hull of a triangulation with subsegments.  */
	/*                                                                           */
	/*****************************************************************************/

	static void markhull(struct mesh *m, struct behavior *b)
	{
		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.                                          */
	/*                                                                           */
	/*****************************************************************************/

	static void formskeleton(struct mesh *m, struct behavior *b, int *segmentlist,
		int *segmentmarkerlist, int numberofsegments)
	{
		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.         */
	/*                                                                           */
	/*****************************************************************************/

	static void infecthull(struct mesh *m, struct behavior *b)
	{
		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.                                            */
	/*                                                                           */
	/*****************************************************************************/

	static void plague(struct mesh *m, struct behavior *b)
	{
		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.                                                                  */
	/*                                                                           */
	/*****************************************************************************/

	static void regionplague(struct mesh *m, struct behavior *b,
		Real attribute, Real area)
	{
		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.                                                               */
	/*                                                                           */
	/*****************************************************************************/

	static void carveholes(struct mesh *m, struct behavior *b, Real *holelist, int holes,
		Real *regionlist, int regions)
	{
		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((int *) regiontris);
		}
	}

	/**                                                                         **/
	/**                                                                         **/
	/********* Carving out holes and concavities ends here               *********/

	/********* Mesh quality maintenance begins here                      *********/
	/**                                                                         **/
	/**                                                                         **/

	/*****************************************************************************/
	/*                                                                           */
	/*  tallyencs()   Traverse the entire list of subsegments, and check each    */
	/*                to see if it is encroached.  If so, add it to the list.    */
	/*                                                                           */
	/*****************************************************************************/

	static void tallyencs(struct mesh *m, struct behavior *b)
	{
		struct osub subsegloop;
		int dummy;

		traversalinit(&m->subsegs);
		subsegloop.ssorient = 0;
		subsegloop.ss = subsegtraverse(m);
		while (subsegloop.ss != (subseg *) NULL) {
			/* If the segment is encroached, add it to the list. */
			dummy = checkseg4encroach(m, b, &subsegloop);
			subsegloop.ss = subsegtraverse(m);
		}
	}

	/*****************************************************************************/
	/*                                                                           */
	/*  precisionerror()  Print an error message for precision problems.         */
	/*                                                                           */
	/*****************************************************************************/

	// [MK] Specialized declaration pushed to the end
	static void precisionerror( void );

	/*****************************************************************************/
	/*                                                                           */
	/*  splitencsegs()   Split all the encroached subsegments.                   */
	/*                                                                           */
	/*  Each encroached subsegment is repaired by splitting it - inserting a     */
	/*  vertex at or near its midpoint.  Newly inserted vertices may encroach    */
	/*  upon other subsegments; these are also repaired.                         */
	/*                                                                           */
	/*  `triflaws' is a flag that specifies whether one should take note of new  */
	/*  bad triangles that result from inserting vertices to repair encroached   */
	/*  subsegments.                                                             */
	/*                                                                           */
	/*****************************************************************************/

	static void splitencsegs(struct mesh *m, struct behavior *b, int triflaws)
	{
		struct otri enctri;
		struct otri testtri;
		struct osub testsh;
		struct osub currentenc;
		struct badsubseg *encloop;
		vertex eorg, edest, eapex;
		vertex newvertex;
		enum insertvertexresult success;
		Real segmentlength, nearestpoweroftwo;
		Real split;
		Real multiplier, divisor;
		int acuteorg, acuteorg2, acutedest, acutedest2;
		int dummy;
		int i;
		triangle ptr;                     /* Temporary variable used by stpivot(). */
		subseg sptr;                        /* Temporary variable used by snext(). */

											/* Note that steinerleft == -1 if an unlimited number */
											/*   of Steiner points is allowed.                    */
		while ((m->badsubsegs.items > 0) && (m->steinerleft != 0)) {
			traversalinit(&m->badsubsegs);
			encloop = badsubsegtraverse(m);
			while ((encloop != (struct badsubseg *) NULL) && (m->steinerleft != 0)) {
				sdecode(encloop->encsubseg, currentenc);
				sorg(currentenc, eorg);
				sdest(currentenc, edest);
				/* Make sure that this segment is still the same segment it was   */
				/*   when it was determined to be encroached.  If the segment was */
				/*   enqueued multiple times (because several newly inserted      */
				/*   vertices encroached it), it may have already been split.     */
				if (!deadsubseg(currentenc.ss) &&
					(eorg == encloop->subsegorg) && (edest == encloop->subsegdest)) {
					/* To decide where to split a segment, we need to know if the   */
					/*   segment shares an endpoint with an adjacent segment.       */
					/*   The concern is that, if we simply split every encroached   */
					/*   segment in its center, two adjacent segments with a small  */
					/*   angle between them might lead to an infinite loop; each    */
					/*   vertex added to split one segment will encroach upon the   */
					/*   other segment, which must then be split with a vertex that */
					/*   will encroach upon the first segment, and so on forever.   */
					/* To avoid this, imagine a set of concentric circles, whose    */
					/*   radii are powers of two, about each segment endpoint.      */
					/*   These concentric circles determine where the segment is    */
					/*   split.  (If both endpoints are shared with adjacent        */
					/*   segments, split the segment in the middle, and apply the   */
					/*   concentric circles for later splittings.)                  */

					/* Is the origin shared with another segment? */
					stpivot(currentenc, enctri);
					lnext(enctri, testtri);
					tspivot(testtri, testsh);
					acuteorg = testsh.ss != m->dummysub;
					/* Is the destination shared with another segment? */
					lnextself(testtri);
					tspivot(testtri, testsh);
					acutedest = testsh.ss != m->dummysub;

					/* If we're using Chew's algorithm (rather than Ruppert's) */
					/*   to define encroachment, delete free vertices from the */
					/*   subsegment's diametral circle.                        */
					if (!b->conformdel && !acuteorg && !acutedest) {
						apex(enctri, eapex);
						while ((vertextype(eapex) == FREEVERTEX) &&
							((eorg[0] - eapex[0]) * (edest[0] - eapex[0]) +
							(eorg[1] - eapex[1]) * (edest[1] - eapex[1]) < 0.0)) {
							deletevertex(m, b, &testtri);
							stpivot(currentenc, enctri);
							apex(enctri, eapex);
							lprev(enctri, testtri);
						}
					}

					/* Now, check the other side of the segment, if there's a triangle */
					/*   there.                                                        */
					sym(enctri, testtri);
					if (testtri.tri != m->dummytri) {
						/* Is the destination shared with another segment? */
						lnextself(testtri);
						tspivot(testtri, testsh);
						acutedest2 = testsh.ss != m->dummysub;
						acutedest = acutedest || acutedest2;
						/* Is the origin shared with another segment? */
						lnextself(testtri);
						tspivot(testtri, testsh);
						acuteorg2 = testsh.ss != m->dummysub;
						acuteorg = acuteorg || acuteorg2;

						/* Delete free vertices from the subsegment's diametral circle. */
						if (!b->conformdel && !acuteorg2 && !acutedest2) {
							org(testtri, eapex);
							while ((vertextype(eapex) == FREEVERTEX) &&
								((eorg[0] - eapex[0]) * (edest[0] - eapex[0]) +
								(eorg[1] - eapex[1]) * (edest[1] - eapex[1]) < 0.0)) {
								deletevertex(m, b, &testtri);
								sym(enctri, testtri);
								apex(testtri, eapex);
								lprevself(testtri);
							}
						}
					}

					/* Use the concentric circles if exactly one endpoint is shared */
					/*   with another adjacent segment.                             */
					if (acuteorg || acutedest) {
						segmentlength = sqrt((edest[0] - eorg[0]) * (edest[0] - eorg[0]) +
							(edest[1] - eorg[1]) * (edest[1] - eorg[1]));
						/* Find the power of two that most evenly splits the segment.  */
						/*   The worst case is a 2:1 ratio between subsegment lengths. */
						nearestpoweroftwo = 1.0;
						while (segmentlength > 3.0 * nearestpoweroftwo) {
							nearestpoweroftwo *= 2.0;
						}
						while (segmentlength < 1.5 * nearestpoweroftwo) {
							nearestpoweroftwo *= 0.5;
						}
						/* Where do we split the segment? */
						split = nearestpoweroftwo / segmentlength;
						if (acutedest) {
							split = 1.0 - split;
						}
					} else {
						/* If we're not worried about adjacent segments, split */
						/*   this segment in the middle.                       */
						split = 0.5;
					}

					/* Create the new vertex. */
					newvertex = (vertex) poolalloc(&m->vertices);
					/* Interpolate its coordinate and attributes. */
					for (i = 0; i < 2 + m->nextras; i++) {
						newvertex[i] = eorg[i] + split * (edest[i] - eorg[i]);
					}

					if (!b->noexact) {
						/* Roundoff in the above calculation may yield a `newvertex'   */
						/*   that is not precisely collinear with `eorg' and `edest'.  */
						/*   Improve collinearity by one step of iterative refinement. */
						multiplier = counterclockwise(m, b, eorg, edest, newvertex);
						divisor = ((eorg[0] - edest[0]) * (eorg[0] - edest[0]) +
							(eorg[1] - edest[1]) * (eorg[1] - edest[1]));
						if ((multiplier != 0.0) && (divisor != 0.0)) {
							multiplier = multiplier / divisor;
							/* Watch out for NANs. */
							if (multiplier == multiplier) {
								newvertex[0] += multiplier * (edest[1] - eorg[1]);
								newvertex[1] += multiplier * (eorg[0] - edest[0]);
							}
						}
					}

					setvertexmark(newvertex, mark(currentenc));
					setvertextype(newvertex, SEGMENTVERTEX);
					if (b->verbose > 1) {
						printf(
							"  Splitting subsegment (%.12g, %.12g) (%.12g, %.12g) at (%.12g, %.12g).\n",
							eorg[0], eorg[1], edest[0], edest[1],
							newvertex[0], newvertex[1]);
					}
					/* Check whether the new vertex lies on an endpoint. */
					if (((newvertex[0] == eorg[0]) && (newvertex[1] == eorg[1])) ||
						((newvertex[0] == edest[0]) && (newvertex[1] == edest[1]))) {
						printf("Error:  Ran out of precision at (%.12g, %.12g).\n",
							newvertex[0], newvertex[1]);
						printf("I attempted to split a segment to a smaller size than\n");
						printf("  can be accommodated by the finite precision of\n");
						printf("  floating point arithmetic.\n");
						precisionerror();
						triexit(1);
					}
					/* Insert the splitting vertex.  This should always succeed. */
					success = insertvertex(m, b, newvertex, &enctri, &currentenc,
						1, triflaws);
					if ((success != SUCCESSFULVERTEX) && (success != ENCROACHINGVERTEX)) {
						printf("Internal error in splitencsegs():\n");
						printf("  Failure to split a segment.\n");
						internalerror();
					}
					if (m->steinerleft > 0) {
						m->steinerleft--;
					}
					/* Check the two new subsegments to see if they're encroached. */
					dummy = checkseg4encroach(m, b, &currentenc);
					snextself(currentenc);
					dummy = checkseg4encroach(m, b, &currentenc);
				}

				badsubsegdealloc(m, encloop);
				encloop = badsubsegtraverse(m);
			}
		}
	}

	/*****************************************************************************/
	/*                                                                           */
	/*  tallyfaces()   Test every triangle in the mesh for quality measures.     */
	/*                                                                           */
	/*****************************************************************************/

	static void tallyfaces(struct mesh *m, struct behavior *b)
	{
		struct otri triangleloop;

		if (b->verbose) {
			printf("  Making a list of bad triangles.\n");
		}
		traversalinit(&m->triangles);
		triangleloop.orient = 0;
		triangleloop.tri = triangletraverse(m);
		while (triangleloop.tri != (triangle *) NULL) {
			/* If the triangle is bad, enqueue it. */
			testtriangle(m, b, &triangleloop);
			triangleloop.tri = triangletraverse(m);
		}
	}

	/*****************************************************************************/
	/*                                                                           */
	/*  splittriangle()   Inserts a vertex at the circumcenter of a triangle.    */
	/*                    Deletes the newly inserted vertex if it encroaches     */
	/*                    upon a segment.                                        */
	/*                                                                           */
	/*****************************************************************************/

	static void splittriangle(struct mesh *m, struct behavior *b,
		struct badtriang *badtri)
	{
		struct otri badotri;
		vertex borg, bdest, bapex;
		vertex newvertex;
		Real xi, eta;
		enum insertvertexresult success;
		int errorflag;
		int i;

		decode(badtri->poortri, badotri);
		org(badotri, borg);
		dest(badotri, bdest);
		apex(badotri, bapex);
		/* Make sure that this triangle is still the same triangle it was      */
		/*   when it was tested and determined to be of bad quality.           */
		/*   Subsequent transformations may have made it a different triangle. */
		if (!deadtri(badotri.tri) && (borg == badtri->triangorg) &&
			(bdest == badtri->triangdest) && (bapex == badtri->triangapex)) {
			if (b->verbose > 1) {
				printf("  Splitting this triangle at its circumcenter:\n");
				printf("    (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", borg[0],
					borg[1], bdest[0], bdest[1], bapex[0], bapex[1]);
			}

			errorflag = 0;
			/* Create a new vertex at the triangle's circumcenter. */
			newvertex = (vertex) poolalloc(&m->vertices);
			findcircumcenter(m, b, borg, bdest, bapex, newvertex, &xi, &eta, 1);

			/* Check whether the new vertex lies on a triangle vertex. */
			if (((newvertex[0] == borg[0]) && (newvertex[1] == borg[1])) ||
				((newvertex[0] == bdest[0]) && (newvertex[1] == bdest[1])) ||
				((newvertex[0] == bapex[0]) && (newvertex[1] == bapex[1]))) {
				if (!b->quiet) {
					printf(
						"Warning:  New vertex (%.12g, %.12g) falls on existing vertex.\n",
						newvertex[0], newvertex[1]);
					errorflag = 1;
				}
				vertexdealloc(m, newvertex);
			} else {
				for (i = 2; i < 2 + m->nextras; i++) {
					/* Interpolate the vertex attributes at the circumcenter. */
					newvertex[i] = borg[i] + xi * (bdest[i] - borg[i])
						+ eta * (bapex[i] - borg[i]);
				}
				/* The new vertex must be in the interior, and therefore is a */
				/*   free vertex with a marker of zero.                       */
				setvertexmark(newvertex, 0);
				setvertextype(newvertex, FREEVERTEX);

				/* Ensure that the handle `badotri' does not represent the longest  */
				/*   edge of the triangle.  This ensures that the circumcenter must */
				/*   fall to the left of this edge, so point location will work.    */
				/*   (If the angle org-apex-dest exceeds 90 degrees, then the       */
				/*   circumcenter lies outside the org-dest edge, and eta is        */
				/*   negative.  Roundoff error might prevent eta from being         */
				/*   negative when it should be, so I test eta against xi.)         */
				if (eta < xi) {
					lprevself(badotri);
				}

				/* Insert the circumcenter, searching from the edge of the triangle, */
				/*   and maintain the Delaunay property of the triangulation.        */
				success = insertvertex(m, b, newvertex, &badotri, (struct osub *) NULL,
					1, 1);
				if (success == SUCCESSFULVERTEX) {
					if (m->steinerleft > 0) {
						m->steinerleft--;
					}
				} else if (success == ENCROACHINGVERTEX) {
					/* If the newly inserted vertex encroaches upon a subsegment, */
					/*   delete the new vertex.                                   */
					undovertex(m, b);
					if (b->verbose > 1) {
						printf("  Rejecting (%.12g, %.12g).\n", newvertex[0], newvertex[1]);
					}
					vertexdealloc(m, newvertex);
				} else if (success == VIOLATINGVERTEX) {
					/* Failed to insert the new vertex, but some subsegment was */
					/*   marked as being encroached.                            */
					vertexdealloc(m, newvertex);
				} else {                                 /* success == DUPLICATEVERTEX */
														 /* Couldn't insert the new vertex because a vertex is already there. */
					if (!b->quiet) {
						printf(
							"Warning:  New vertex (%.12g, %.12g) falls on existing vertex.\n",
							newvertex[0], newvertex[1]);
						errorflag = 1;
					}
					vertexdealloc(m, newvertex);
				}
			}
			if (errorflag) {
				if (b->verbose) {
					printf("  The new vertex is at the circumcenter of triangle\n");
					printf("    (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
						borg[0], borg[1], bdest[0], bdest[1], bapex[0], bapex[1]);
				}
				printf("This probably means that I am trying to refine triangles\n");
				printf("  to a smaller size than can be accommodated by the finite\n");
				printf("  precision of floating point arithmetic.  (You can be\n");
				printf("  sure of this if I fail to terminate.)\n");
				precisionerror();
			}
		}
	}

	/*****************************************************************************/
	/*                                                                           */
	/*  enforcequality()   Remove all the encroached subsegments and bad         */
	/*                     triangles from the triangulation.                     */
	/*                                                                           */
	/*****************************************************************************/

	static void enforcequality(struct mesh *m, struct behavior *b)
	{
		struct badtriang *badtri;
		int i;

		if (!b->quiet) {
			printf("Adding Steiner points to enforce quality.\n");
		}
		/* Initialize the pool of encroached subsegments. */
		poolinit(&m->badsubsegs, sizeof(struct badsubseg), BADSUBSEGPERBLOCK,
			BADSUBSEGPERBLOCK, 0);
		if (b->verbose) {
			printf("  Looking for encroached subsegments.\n");
		}
		/* Test all segments to see if they're encroached. */
		tallyencs(m, b);
		if (b->verbose && (m->badsubsegs.items > 0)) {
			printf("  Splitting encroached subsegments.\n");
		}
		/* Fix encroached subsegments without noting bad triangles. */
		splitencsegs(m, b, 0);
		/* At this point, if we haven't run out of Steiner points, the */
		/*   triangulation should be (conforming) Delaunay.            */

		/* Next, we worry about enforcing triangle quality. */
		if ((b->minangle > 0.0) || b->vararea || b->fixedarea || b->usertest) {
			/* Initialize the pool of bad triangles. */
			poolinit(&m->badtriangles, sizeof(struct badtriang), BADTRIPERBLOCK,
				BADTRIPERBLOCK, 0);
			/* Initialize the queues of bad triangles. */
			for (i = 0; i < 4096; i++) {
				m->queuefront[i] = (struct badtriang *) NULL;
			}
			m->firstnonemptyq = -1;
			/* Test all triangles to see if they're bad. */
			tallyfaces(m, b);
			/* Initialize the pool of recently flipped triangles. */
			poolinit(&m->flipstackers, sizeof(struct flipstacker), FLIPSTACKERPERBLOCK,
				FLIPSTACKERPERBLOCK, 0);
			m->checkquality = 1;
			if (b->verbose) {
				printf("  Splitting bad triangles.\n");
			}
			while ((m->badtriangles.items > 0) && (m->steinerleft != 0)) {
				/* Fix one bad triangle by inserting a vertex at its circumcenter. */
				badtri = dequeuebadtriang(m);
				splittriangle(m, b, badtri);
				if (m->badsubsegs.items > 0) {
					/* Put bad triangle back in queue for another try later. */
					enqueuebadtriang(m, b, badtri);
					/* Fix any encroached subsegments that resulted. */
					/*   Record any new bad triangles that result.   */
					splitencsegs(m, b, 1);
				} else {
					/* Return the bad triangle to the pool. */
					pooldealloc(&m->badtriangles, (int *) badtri);
				}
			}
		}
		/* At this point, if the "-D" switch was selected and we haven't run out  */
		/*   of Steiner points, the triangulation should be (conforming) Delaunay */
		/*   and have no low-quality triangles.                                   */

		/* Might we have run out of Steiner points too soon? */
		if (!b->quiet && b->conformdel && (m->badsubsegs.items > 0) &&
			(m->steinerleft == 0)) {
			printf("\nWarning:  I ran out of Steiner points, but the mesh has\n");
			if (m->badsubsegs.items == 1) {
				printf("  one encroached subsegment, and therefore might not be truly\n"
				);
			} else {
				printf("  %ld encroached subsegments, and therefore might not be truly\n"
					, m->badsubsegs.items);
			}
			printf("  Delaunay.  If the Delaunay property is important to you,\n");
			printf("  try increasing the number of Steiner points (controlled by\n");
			printf("  the -S switch) slightly and try again.\n\n");
		}
	}

	/**                                                                         **/
	/**                                                                         **/
	/********* Mesh quality maintenance ends here                        *********/

	/*****************************************************************************/
	/*                                                                           */
	/*  highorder()   Create extra nodes for quadratic subparametric elements.   */
	/*                                                                           */
	/*****************************************************************************/

	static void highorder(struct mesh *m, struct behavior *b)
	{
		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 = (int *) 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.                         */
	/*                                                                           */
	/*****************************************************************************/

	static void transfernodes(struct mesh *m, struct behavior *b, Real *pointlist,
		Real *pointattriblist, int *pointmarkerlist,
		int numberofpoints, int numberofpointattribs)
	{
		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.                                */
	/*                                                                           */
	/*****************************************************************************/

	static void writenodes(struct mesh *m, struct behavior *b, Real **pointlist,
		Real **pointattriblist, int **pointmarkerlist)
	{
		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.   */
	/*                                                                           */
	/*****************************************************************************/

	static void numbernodes(struct mesh *m, struct behavior *b)
	{
		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.                   */
	/*                                                                           */
	/*****************************************************************************/

	static void writeelements(struct mesh *m, struct behavior *b,
		int **trianglelist, Real **triangleattriblist)
	{
		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.              */
	/*                                                                           */
	/*****************************************************************************/

	static void writepoly(struct mesh *m, struct behavior *b,
		int **segmentlist, int **segmentmarkerlist)
	{
		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.                         */
	/*                                                                           */
	/*****************************************************************************/

	static void writeedges(struct mesh *m, struct behavior *b,
		int **edgelist, int **edgemarkerlist)
	{
		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.                    */
	/*                                                                           */
	/*****************************************************************************/

	static void writevoronoi(struct mesh *m, struct behavior *b, Real **vpointlist,
		Real **vpointattriblist, int **vpointmarkerlist,
		int **vedgelist, int **vedgemarkerlist, Real **vnormlist)
	{
		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);
		}
	}

	static void writeneighbors(struct mesh *m, struct behavior *b, int **neighborlist)
	{
		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.   */
	/*                                                                           */
	/*****************************************************************************/

	static void quality_statistics(struct mesh *m, struct behavior *b)
	{
		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.                            */
	/*                                                                           */
	/*****************************************************************************/

	static void statistics(struct mesh *m, struct behavior *b)
	{
		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).          */
	/*                                                                           */
	/*****************************************************************************/

	static void triangulate(char *triswitches, struct triangulateio< Real > *in,
		struct triangulateio< Real > *out, struct triangulateio< Real > *vorout)
	{
		struct mesh m;
		struct behavior b;
		Real *holearray;                                        /* Array of holes. */
		Real *regionarray;   /* Array of regional attributes and area constraints. */

		triangleinit(&m);
		parsecommandline(1, &triswitches, &b);
		m.steinerleft = b.steiner;

		transfernodes(&m, &b, in->pointlist, in->pointattributelist,
			in->pointmarkerlist, in->numberofpoints,
			in->numberofpointattributes);

		if (b.refine) {
			/* Read and reconstruct a mesh. */
			m.hullsize = reconstruct(&m, &b, in->trianglelist,
				in->triangleattributelist, in->trianglearealist,
				in->numberoftriangles, in->numberofcorners,
				in->numberoftriangleattributes,
				in->segmentlist, in->segmentmarkerlist,
				in->numberofsegments);
		} else {
			m.hullsize = delaunay(&m, &b);              /* Triangulate the vertices. */
		}

		/* 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);
			}
		}

		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;
		}

		if (b.quality && (m.triangles.items > 0)) {
			enforcequality(&m, &b);           /* Enforce angle and area constraints. */
		}

		/* 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< Real > *) 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) {
			statistics(&m, &b);
		}

		if (b.docheck) {
			checkmesh(&m, &b);
			checkdelaunay(&m, &b);
		}

		triangledeinit(&m, &b);
	}
};
template< typename Real > const int Shewchuk< Real >::plus1mod3[] = {1, 2, 0};
template< typename Real > const int Shewchuk< Real >::minus1mod3[] = {2, 0, 1};
template< typename Real > Real Shewchuk< Real >::splitter;
template< typename Real > Real Shewchuk< Real >::epsilon;
template< typename Real > Real Shewchuk< Real >::resulterrbound;
template< typename Real > Real Shewchuk< Real >::ccwerrboundA;
template< typename Real > Real Shewchuk< Real >::ccwerrboundB;
template< typename Real > Real Shewchuk< Real >::ccwerrboundC;
template< typename Real > Real Shewchuk< Real >::iccerrboundA;
template< typename Real > Real Shewchuk< Real >::iccerrboundB;
template< typename Real > Real Shewchuk< Real >::iccerrboundC;
template< typename Real > Real Shewchuk< Real >::o3derrboundA;
template< typename Real > Real Shewchuk< Real >::o3derrboundB;
template< typename Real > Real Shewchuk< Real >::o3derrboundC;
template< typename Real > size_t Shewchuk< Real >::randomseed;

#ifdef LINUX
template<> const int Shewchuk< float  >::CWORD = 4210;
template<> const int Shewchuk< double >::CWORD = 4722;
#endif /* LINUX */

template<> void Shewchuk< float >::precisionerror( void )
{
	printf("Try increasing the area criterion and/or reducing the minimum\n");
	printf("  allowable angle so that tiny triangles are not created.\n");
	printf("Alternatively, try recompiling me with double precision\n");
	printf("  arithmetic (by removing \"#define SINGLE\" from the\n");
	printf("  source file or \"-DSINGLE\" from the makefile).\n");
}
template<> void Shewchuk< double >::precisionerror( void )
{
	printf("Try increasing the area criterion and/or reducing the minimum\n");
	printf("  allowable angle so that tiny triangles are not created.\n");
}
