/contrib/gtkgensurf/triangle.c

#define ANSI_DECLARATORS
/*****************************************************************************/
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/*      888888888        ,o,                          / 888                  */
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/*         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 1.3                                                              */
/*  July 19, 1996                                                            */
/*                                                                           */
/*  Copyright 1996                                                           */
/*  Jonathan Richard Shewchuk                                                */
/*  School of Computer Science                                               */
/*  Carnegie Mellon University                                               */
/*  5000 Forbes Avenue                                                       */
/*  Pittsburgh, Pennsylvania  15213-3891                                     */
/*  jrs@cs.cmu.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                           */
/*                                                                           */
/*  Some of the references listed below are marked [*].  These are available */
/*    for downloading from the Web page                                      */
/*                                                                           */
/*      http://www.cs.cmu.edu/~quake/triangle.research.html                  */
/*                                                                           */
/*  A paper discussing some aspects of Triangle is available.  See Jonathan  */
/*    Richard Shewchuk, "Triangle:  Engineering a 2D Quality Mesh Generator  */
/*    and Delaunay Triangulator," First Workshop on Applied Computational    */
/*    Geometry, ACM, May 1996.  [*]                                          */
/*                                                                           */
/*  Triangle was created as part of the Archimedes project in the School of  */
/*    Computer Science at Carnegie Mellon University.  Archimedes is a       */
/*    system for compiling parallel finite element solvers.  For further     */
/*    information, see Anja Feldmann, Omar Ghattas, John R. Gilbert, Gary L. */
/*    Miller, David R. O'Hallaron, Eric J. Schwabe, Jonathan R. Shewchuk,    */
/*    and Shang-Hua Teng, "Automated Parallel Solution of Unstructured PDE   */
/*    Problems."  To appear in Communications of the ACM, we hope.           */
/*                                                                           */
/*  The quality mesh generation algorithm is due to Jim Ruppert, "A          */
/*    Delaunay Refinement Algorithm for Quality 2-Dimensional Mesh           */
/*    Generation," Journal of Algorithms 18(3):548-585, May 1995.  [*]       */
/*                                                                           */
/*  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 switching 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.                                               */
/*                                                                           */
/*  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.  The idea to improve 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 point         */
/*    insertion (I currently don't bother), their result combined with the   */
/*    result of Leonidas J. Guibas, Donald E. Knuth, and Micha Sharir,       */
/*    "Randomized Incremental Construction of Delaunay and Voronoi           */
/*    Diagrams," Algorithmica 7(4):381-413, 1992, 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.                   */
/*                                                                           */
/*  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," Technical      */
/*    Report CMU-CS-96-140, School of Computer Science, Carnegie Mellon      */
/*    University, Pittsburgh, Pennsylvania, May 1996.  [*]  (Submitted to    */
/*    Discrete & Computational Geometry.)  An abbreviated version appears as */
/*    Jonathan Richard Shewchuk, "Robust Adaptive Floating-Point Geometric   */
/*    Predicates," Proceedings of the Twelfth Annual Symposium on Computa-   */
/*    tional 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, 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 Computational 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 Triangulations," International Journal   */
/*    of Computational Geometry & Applications 5(1-2):193-213, March-June    */
/*    1995.                                                                  */
/*                                                                           */
/*  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(n^2) per segment in the worst case and O(n) per edge in the common   */
/*    case, where n 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.  (This note does not apply to conforming       */
/*    Delaunay triangulations, for which a different method is used to       */
/*    insert segments.)                                                      */
/*                                                                           */
/*  The time for adding segments to a conforming Delaunay triangulation is   */
/*    not clear, but does not depend upon n alone.  In some cases, very      */
/*    small features (like a point lying next to a segment) can cause a      */
/*    single segment to be split an arbitrary number of times.  Of course,   */
/*    floating-point precision is a practical barrier to how much this can   */
/*    happen.                                                                */
/*                                                                           */
/*  The time for deleting a point from a Delaunay triangulation is O(n^2) in */
/*    the worst case and O(n) in the common case, where n is the degree of   */
/*    the point being deleted.  I could improve this to expected O(n) time   */
/*    by "inserting" the neighboring vertices in random order, but n is      */
/*    usually quite small, so it's not worth the bother.  (The O(n) time     */
/*    for random insertion follows from L. Paul Chew, "Building Voronoi      */
/*    Diagrams for Convex Polygons in Linear Expected Time," Technical       */
/*    Report PCS-TR90-147, Department of Mathematics and Computer Science,   */
/*    Dartmouth College, 1990.                                               */
/*                                                                           */
/*  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 more   */
/*    time is required, but these never arise in practice.                   */
/*                                                                           */
/*  The segment intersection formulae are straightforward.  If you want to   */
/*    see them derived, see Franklin Antonio.  "Faster Line Segment          */
/*    Intersection."  In Graphics Gems III (David Kirk, editor), pp. 199-    */
/*    202.  Academic Press, Boston, 1992.                                    */
/*                                                                           */
/*  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.             */
/*                                                                           */
/*  Disclaimer:  Neither I nor Carnegie Mellon warrant this code in any way  */
/*    whatsoever.  This code is provided "as-is".  Use at your own risk.     */
/*                                                                           */
/*****************************************************************************/

/* For single precision (which will save some memory and reduce paging),     */
/*   define the symbol SINGLE by using the -DSINGLE compiler switch or by    */
/*   writing "#define SINGLE" below.                                         */
/*                                                                           */
/* For double precision (which will allow you to refine meshes to a smaller  */
/*   edge length), leave SINGLE undefined.                                   */
/*                                                                           */
/* Double precision uses more memory, but improves the resolution of the     */
/*   meshes you can generate with Triangle.  It also reduces the likelihood  */
/*   of a floating exception due to overflow.  Finally, it is much faster    */
/*   than single precision on 64-bit architectures like the DEC Alpha.  I    */
/*   recommend double precision unless you want to generate a mesh for which */
/*   you do not have enough memory.                                          */

#define SINGLE

#ifdef SINGLE
#define REAL float
#else /* not SINGLE */
#define REAL double
#endif /* not SINGLE */

/* If yours is not a Unix system, define the NO_TIMER compiler switch to     */
/*   remove the Unix-specific timing code.                                   */

#define NO_TIMER

/* To insert lots of self-checks for internal errors, define the SELF_CHECK  */
/*   symbol.  This will slow down the program significantly.  It is best to  */
/*   define the symbol using the -DSELF_CHECK compiler switch, but you could */
/*   write "#define SELF_CHECK" below.  If you are modifying this code, I    */
/*   recommend you turn self-checks on.                                      */

/* #define SELF_CHECK */

/* To compile Triangle as a callable object library (triangle.o), define the */
/*   TRILIBRARY symbol.  Read the file triangle.h for details on how to call */
/*   the procedure triangulate() that results.                               */

#define TRILIBRARY

/* It is possible to generate a smaller version of Triangle using one or     */
/*   both of the following symbols.  Define the REDUCED symbol to eliminate  */
/*   all features that are primarily of research interest; specifically, the */
/*   -i, -F, -s, and -C switches.  Define the CDT_ONLY symbol to eliminate   */
/*   all meshing algorithms above and beyond constrained Delaunay            */
/*   triangulation; specifically, the -r, -q, -a, -S, and -s switches.       */
/*   These reductions are most likely to be useful when generating an object */
/*   library (triangle.o) by defining the TRILIBRARY symbol.                 */

#define REDUCED
#define CDT_ONLY

/* On some machines, the exact arithmetic routines might be defeated by the  */
/*   use of internal extended precision floating-point registers.  Sometimes */
/*   this problem can be fixed by defining certain values to be volatile,    */
/*   thus forcing them to be stored to memory and rounded off.  This isn't   */
/*   a great solution, though, as it slows Triangle down.                    */
/*                                                                           */
/* To try this out, write "#define INEXACT volatile" below.  Normally,       */
/*   however, INEXACT should be defined to be nothing.  ("#define INEXACT".) */

#define INEXACT /* Nothing */
/* #define INEXACT volatile */

/* Maximum number of characters in a file name (including the null).         */

#define FILENAMESIZE 512

/* Maximum number of characters in a line read from a file (including the    */
/*   null).                                                                  */

#define INPUTLINESIZE 512

/* 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 SHELLEPERBLOCK 508       /* Number of shell edges allocated at once. */
#define POINTPERBLOCK 4092            /* Number of points allocated at once. */
#define VIRUSPERBLOCK 1020   /* Number of virus triangles allocated at once. */
/* Number of encroached segments allocated at once. */
#define BADSEGMENTPERBLOCK 252
/* Number of skinny triangles allocated at once. */
#define BADTRIPERBLOCK 4092
/* Number of splay tree nodes allocated at once. */
#define SPLAYNODEPERBLOCK 508

/* The point marker DEADPOINT is an arbitrary number chosen large enough to  */
/*   (hopefully) not conflict with user boundary markers.  Make sure that it */
/*   is small enough to fit into your machine's integer size.                */

#define DEADPOINT -1073741824

/* 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 <string.h>
#include <math.h>
#ifndef NO_TIMER
#include <sys/time.h>
#endif /* NO_TIMER */
#ifdef TRILIBRARY
#include "triangle.h"
#endif /* TRILIBRARY */

/* The following obscenity seems to be necessary to ensure that this program */
/* will port to Dec Alphas running OSF/1, because their stdio.h file commits */
/* the unpardonable sin of including stdlib.h.  Hence, malloc(), free(), and */
/* exit() may or may not already be defined at this point.  I declare these  */
/* functions explicitly because some non-ANSI C compilers lack stdlib.h.     */

#ifndef _STDLIB_H_
extern void *malloc();
extern void free();
extern void exit();
extern double strtod();
extern long strtol();
#endif /* _STDLIB_H_ */

/* A few forward declarations.                                               */

void poolrestart();
#ifndef TRILIBRARY
char *readline();
char *findfield();
#endif /* not TRILIBRARY */

/* Labels that signify whether a record consists primarily of pointers or of */
/*   floating-point words.  Used to make decisions about data alignment.     */

enum wordtype {POINTER, FLOATINGPOINT};

/* 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 site insertion.  The result indicates   */
/*   that the point was inserted with complete success, was inserted but     */
/*   encroaches on a segment, was not inserted because it lies on a segment, */
/*   or was not inserted because another point occupies the same location.   */

enum insertsiteresult {SUCCESSFULPOINT, ENCROACHINGPOINT, VIOLATINGPOINT,
					   DUPLICATEPOINT};

/* 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};

/* Labels that signify the result of the circumcenter computation routine.   */
/*   The return value indicates which edge of the triangle is shortest.      */

enum circumcenterresult {OPPOSITEORG, OPPOSITEDEST, OPPOSITEAPEX};

/*****************************************************************************/
/*                                                                           */
/*  The basic mesh data structures                                           */
/*                                                                           */
/*  There are three:  points, triangles, and shell edges (abbreviated        */
/*  `shelle').  These three data structures, linked by pointers, comprise    */
/*  the mesh.  A point simply represents a point in space and its properties.*/
/*  A triangle is a triangle.  A shell edge is a special data structure used */
/*  to represent impenetrable segments in the mesh (including the outer      */
/*  boundary, boundaries of holes, and internal boundaries separating two    */
/*  triangulated regions).  Shell edges 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 shell edges (when shell   */
/*  edges are used), 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 shell edges are present.  Such absent         */
/*  triangles and shell edges are never represented by NULL pointers; they   */
/*  are represented by two special records:  `dummytri', the triangle that   */
/*  fills "outer space", and `dummysh', the omnipresent shell edge.          */
/*  `dummytri' and `dummysh' are used for several reasons; for instance,     */
/*  they can be dereferenced and their contents examined without causing the */
/*  memory protection exception that would occur if NULL were dereferenced.  */
/*                                                                           */
/*  However, it is important to understand that a triangle includes other    */
/*  information as well.  The pointers to adjoining vertices, triangles, and */
/*  shell edges 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  */
/*  shell edge indicates which side of that shell edge is contacted, and how */
/*  the shell edge is oriented relative to the triangle.                     */
/*                                                                           */
/*  Shell edges are found abutting edges of triangles; either sandwiched     */
/*  between two triangles, or resting against one triangle on an exterior    */
/*  boundary or hole boundary.                                               */
/*                                                                           */
/*  A shell edge consists of a list of two vertices, a list of two           */
/*  adjoining shell edges, 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 shell edges might not be present.        */
/*  Shell edges also store a user-defined integer "boundary marker".         */
/*  Typically, this integer is used to indicate what sort of boundary        */
/*  conditions are to be applied at that location in a finite element        */
/*  simulation.                                                              */
/*                                                                           */
/*  Like triangles, shell edges maintain information about the relative      */
/*  orientation of neighboring objects.                                      */
/*                                                                           */
/*  Points are relatively simple.  A point 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 point 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 at any other time.  Edge swapping during segment insertion will  */
/*  render some of them incorrect.  Hence, don't rely upon them for          */
/*  anything.  For the most part, points do not have any information about   */
/*  what triangles or shell edges they are linked to.                        */
/*                                                                           */
/*****************************************************************************/

/*****************************************************************************/
/*                                                                           */
/*  Handles                                                                  */
/*                                                                           */
/*  The oriented triangle (`triedge') and oriented shell edge (`edge') data  */
/*  structures defined below do not themselves store any part of the mesh.   */
/*  The mesh itself is made of `triangle's, `shelle's, and `point's.         */
/*                                                                           */
/*  Oriented triangles and oriented shell edges 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.)                               */
/*                                                                           */
/*  A `triedge' is a handle that holds a triangle.  It holds a specific side */
/*  of the triangle.  An `edge' is a handle that holds a shell edge.  It     */
/*  holds either the left or right side of the edge.                         */
/*                                                                           */
/*  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 exact position of the handles is        */
/*  important.  For instance, when two triangles are glued together by the   */
/*  bond() primitive, they are glued by the sides on which the handles lie.  */
/*                                                                           */
/*  Because points have no information about which triangles they are        */
/*  attached to, I commonly represent a point by use of a handle whose       */
/*  origin is the point.  A single handle can simultaneously represent a     */
/*  triangle, an edge, and a point.                                          */
/*                                                                           */
/*****************************************************************************/

/* The triangle data structure.  Each triangle contains three pointers to    */
/*   adjoining triangles, plus three pointers to vertex points, plus three   */
/*   pointers to shell edges (defined below; these pointers are usually      */
/*   `dummysh').  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 defined the type `triangle' to be 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 is always        */
/*   directed to point counterclockwise about the corresponding triangle.    */

struct triedge {
	triangle *tri;
	int orient;                                       /* Ranges from 0 to 2. */
};

/* The shell data structure.  Each shell edge contains two pointers to       */
/*   adjoining shell edges, plus two pointers to vertex points, plus two     */
/*   pointers to adjoining triangles, plus one shell marker.                 */

typedef REAL **shelle;                  /* Really:  typedef shelle *shelle   */

/* An oriented shell edge:  includes a pointer to a shell edge 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 edge {
	shelle *sh;
	int shorient;                                     /* Ranges from 0 to 1. */
};

/* The point data structure.  Each point 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 *point;

/* A queue used to store encroached segments.  Each segment's vertices are   */
/*   stored so that one can check whether a segment is still the same.       */

struct badsegment {
	struct edge encsegment;                        /* An encroached segment. */
	point segorg, segdest;                              /* The two vertices. */
	struct badsegment *nextsegment;   /* Pointer to next encroached segment. */
};

/* 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 badface {
	struct triedge badfacetri;                            /* A bad triangle. */
	REAL key;                           /* cos^2 of smallest (apical) angle. */
	point faceorg, facedest, faceapex;                /* The three vertices. */
	struct badface *nextface;               /* Pointer to next bad triangle. */
};

/* 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 `point' or to a triangle (in encoded format, so that */
/*   an orientation is included).  In the latter case, the origin of the     */
/*   oriented triangle is the apex of a "circle event" of the sweepline      */
/*   algorithm.  To distinguish site events from circle events, all circle   */
/*   events are given an invalid (smaller than `xmin') x-coordinate `xkey'.  */

struct event {
	REAL xkey, ykey;                            /* Coordinates of the event. */
	VOID *eventptr;     /* Can be a point 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 triedge keyedge;                /* Lprev of an edge on the front. */
	point 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.                                              */
/*                                                                           */
/* itemwordtype is set to POINTER or FLOATINGPOINT, and is used to suggest   */
/*   what sort of word the record is primarily made up of.  alignbytes       */
/*   determines how new records should be aligned in memory.  itembytes and  */
/*   itemwords are the length of a record in bytes (after rounding up) and   */
/*   words.  itemsperblock is the number of items allocated at once in a     */
/*   single block.  items is the number of currently allocated items.        */
/*   maxitems is the maximum number of items that have been allocated at     */
/*   once; it is the current number of items plus the number of records kept */
/*   on deaditemstack.                                                       */

struct memorypool {
	VOID **firstblock, **nowblock;
	VOID *nextitem;
	VOID *deaditemstack;
	VOID **pathblock;
	VOID *pathitem;
	enum wordtype itemwordtype;
	int alignbytes;
	int itembytes, itemwords;
	int itemsperblock;
	long items, maxitems;
	int unallocateditems;
	int pathitemsleft;
};

/* Variables used to allocate memory for triangles, shell edges, points,     */
/*   viri (triangles being eaten), bad (encroached) segments, bad (skinny    */
/*   or too large) triangles, and splay tree nodes.                          */

static struct memorypool triangles;
static struct memorypool shelles;
static struct memorypool points;
static struct memorypool viri;
static struct memorypool badsegments;
static struct memorypool badtriangles;
static struct memorypool splaynodes;

/* Variables that maintain the bad triangle queues.  The tails are pointers  */
/*   to the pointers that have to be filled in to enqueue an item.           */

static struct badface *queuefront[64];
static struct badface **queuetail[64];

static REAL xmin, xmax, ymin, ymax;                              /* x and y bounds. */
static REAL xminextreme;        /* Nonexistent x value used as a flag in sweepline. */
static int inpoints;                                     /* Number of input points. */
static int inelements;                                /* Number of input triangles. */
static int insegments;                                 /* Number of input segments. */
static int holes;                                         /* Number of input holes. */
static int regions;                                     /* Number of input regions. */
static long edges;                                       /* Number of output edges. */
static int mesh_dim;                                  /* Dimension (ought to be 2). */
static int nextras;                              /* Number of attributes per point. */
static int eextras;                           /* Number of attributes per triangle. */
static long hullsize;                            /* Number of edges of convex hull. */
static int triwords;                                   /* Total words per triangle. */
static int shwords;                                  /* Total words per shell edge. */
static int pointmarkindex;             /* Index to find boundary marker of a point. */
static int point2triindex;         /* Index to find a triangle adjacent to a point. */
static int highorderindex;    /* Index to find extra nodes for high-order elements. */
static int elemattribindex;              /* Index to find attributes of a triangle. */
static int areaboundindex;               /* Index to find area bound of a triangle. */
static int checksegments;           /* Are there segments in the triangulation yet? */
static int readnodefile;                             /* Has a .node file been read? */
static long samples;                /* Number of random samples for point location. */
static unsigned long randomseed;                     /* Current random number seed. */

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 long incirclecount;                   /* Number of incircle tests performed. */
static long counterclockcount;       /* Number of counterclockwise tests performed. */
static long hyperbolacount;        /* Number of right-of-hyperbola tests performed. */
static long circumcentercount;    /* Number of circumcenter calculations performed. */
static long circletopcount;         /* Number of circle top calculations performed. */

/* 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.                                */
/*   vararea: -a switch without number.                                      */
/*   fixedarea: -a switch with number.                                       */
/*     maxarea: maximum area bound, specified after -a switch.               */
/*   regionattrib: -A switch.  convex: -c 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.   */
/*     steinerleft: number of Steiner points not yet used.                   */
/*   incremental: -i switch.  sweepline: -F switch.                          */
/*   dwyer: inverse of -l switch.                                            */
/*   splitseg: -s switch.                                                    */
/*   docheck: -C switch.                                                     */
/*   quiet: -Q switch.  verbose: count of how often -V switch is selected.   */
/*   useshelles: -p, -r, -q, or -c switch; determines whether shell edges    */
/*     are used at all.                                                      */
/*                                                                           */
/* Read the instructions to find out the meaning of these switches.          */

static int poly, refine, quality, vararea, fixedarea, regionattrib, convex;
static int firstnumber;
static int edgesout, voronoi, neighbors, geomview;
static int nobound, nopolywritten, nonodewritten, noelewritten, noiterationnum;
static int noholes, noexact;
static int incremental, sweepline, dwyer;
static int splitseg;
static int docheck;
static int quiet, verbose;
static int useshelles;
static int order;
static int nobisect;
static int steiner, steinerleft;
static REAL minangle, goodangle;
static REAL maxarea;

/* Variables for file names.                                                 */

#ifndef TRILIBRARY
char innodefilename[FILENAMESIZE];
char inelefilename[FILENAMESIZE];
char inpolyfilename[FILENAMESIZE];
char areafilename[FILENAMESIZE];
char outnodefilename[FILENAMESIZE];
char outelefilename[FILENAMESIZE];
char outpolyfilename[FILENAMESIZE];
char edgefilename[FILENAMESIZE];
char vnodefilename[FILENAMESIZE];
char vedgefilename[FILENAMESIZE];
char neighborfilename[FILENAMESIZE];
char offfilename[FILENAMESIZE];
#endif /* not TRILIBRARY */

/* Triangular bounding box points.                                           */

static point infpoint1, infpoint2, infpoint3;

/* Pointer to the `triangle' that occupies all of "outer space".             */

static triangle *dummytri;
static triangle *dummytribase;      /* Keep base address so we can free() it later. */

/* Pointer to the omnipresent shell edge.  Referenced by any triangle or     */
/*   shell edge that isn't really connected to a shell edge at that          */
/*   location.                                                               */

static shelle *dummysh;
static shelle *dummyshbase;         /* Keep base address so we can free() it later. */

/* Pointer to a recently visited triangle.  Improves point location if       */
/*   proximate points are inserted sequentially.                             */

static struct triedge recenttri;

/*****************************************************************************/
/*                                                                           */
/*  Mesh manipulation primitives.  Each triangle contains three pointers to  */
/*  other triangles, with orientations.  Each pointer points not to the      */
/*  first byte of a triangle, but to one of the first three bytes of a       */
/*  triangle.  It is necessary to extract both the triangle itself and the   */
/*  orientation.  To save memory, I keep both pieces of information in one   */
/*  pointer.  To make this possible, I assume that all triangles are aligned */
/*  to four-byte boundaries.  The `decode' routine below decodes a pointer,  */
/*  extracting an orientation (in the range 0 to 2) and a pointer to the     */
/*  beginning of a triangle.  The `encode' routine compresses a pointer to a */
/*  triangle and an orientation into a single pointer.  My assumptions that  */
/*  triangles are four-byte-aligned and that the `unsigned long' type is     */
/*  long enough to hold a pointer are two of the few kludges in this program.*/
/*                                                                           */
/*  Shell edges are manipulated similarly.  A pointer to a shell edge        */
/*  carries both an address and an orientation in the range 0 to 1.          */
/*                                                                           */
/*  The other primitives take an oriented triangle or oriented shell edge,   */
/*  and return an oriented triangle or oriented shell edge or point; or they */
/*  change the connections in the data structure.                            */
/*                                                                           */
/*****************************************************************************/

/********* Mesh manipulation primitives begin here                   *********/
/**                                                                         **/
/**                                                                         **/

/* Fast lookup arrays to speed some of the mesh manipulation primitives.     */

int plus1mod3[3] = {1, 2, 0};
int minus1mod3[3] = {2, 0, 1};

/********* Primitives for triangles                                  *********/
/*                                                                           */
/*                                                                           */

/* decode() converts a pointer to an oriented triangle.  The orientation is  */
/*   extracted from the two least significant bits of the pointer.           */

#define decode( ptr, triedge )													\
	( triedge ).orient = (int) ( (unsigned long) ( ptr ) & (unsigned long) 3l );	  \
	( triedge ).tri = (triangle *)												  \
					  ( (unsigned long) ( ptr ) ^ (unsigned long) ( triedge ).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 (triedge).tri are zero.*/

#define encode( triedge )														\
	(triangle) ( (unsigned long) ( triedge ).tri | (unsigned long) ( triedge ).orient )

/* The following edge manipulation primitives are all described by Guibas    */
/*   and Stolfi.  However, they use an edge-based data structure, whereas I  */
/*   am using a triangle-based data structure.                               */

/* sym() finds the abutting triangle, on the same edge.  Note that the       */
/*   edge direction is necessarily reversed, because triangle/edge handles   */
/*   are always directed counterclockwise around the triangle.               */

#define sym( triedge1, triedge2 )												\
	ptr = ( triedge1 ).tri[( triedge1 ).orient];									\
	decode( ptr, triedge2 );

#define symself( triedge )														\
	ptr = ( triedge ).tri[( triedge ).orient];										\
	decode( ptr, triedge );

/* lnext() finds the next edge (counterclockwise) of a triangle.             */

#define lnext( triedge1, triedge2 )												\
	( triedge2 ).tri = ( triedge1 ).tri;											\
	( triedge2 ).orient = plus1mod3[( triedge1 ).orient]

#define lnextself( triedge )													\
	( triedge ).orient = plus1mod3[( triedge ).orient]

/* lprev() finds the previous edge (clockwise) of a triangle.                */

#define lprev( triedge1, triedge2 )												\
	( triedge2 ).tri = ( triedge1 ).tri;											\
	( triedge2 ).orient = minus1mod3[( triedge1 ).orient]

#define lprevself( triedge )													\
	( triedge ).orient = minus1mod3[( triedge ).orient]

/* onext() spins counterclockwise around a point; that is, it finds the next */
/*   edge with the same origin in the counterclockwise direction.  This edge */
/*   will be part of a different triangle.                                   */

#define onext( triedge1, triedge2 )												\
	lprev( triedge1, triedge2 );												  \
	symself( triedge2 );

#define onextself( triedge )													\
	lprevself( triedge );														  \
	symself( triedge );

/* oprev() spins clockwise around a point; that is, it finds the next edge   */
/*   with the same origin in the clockwise direction.  This edge will be     */
/*   part of a different triangle.                                           */

#define oprev( triedge1, triedge2 )												\
	sym( triedge1, triedge2 );													  \
	lnextself( triedge2 );

#define oprevself( triedge )													\
	symself( triedge );															  \
	lnextself( triedge );

/* dnext() spins counterclockwise around a point; that is, it finds the next */
/*   edge with the same destination in the counterclockwise direction.  This */
/*   edge will be part of a different triangle.                              */

#define dnext( triedge1, triedge2 )												\
	sym( triedge1, triedge2 );													  \
	lprevself( triedge2 );

#define dnextself( triedge )													\
	symself( triedge );															  \
	lprevself( triedge );

/* dprev() spins clockwise around a point; that is, it finds the next edge   */
/*   with the same destination in the clockwise direction.  This edge will   */
/*   be part of a different triangle.                                        */

#define dprev( triedge1, triedge2 )												\
	lnext( triedge1, triedge2 );												  \
	symself( triedge2 );

#define dprevself( triedge )													\
	lnextself( triedge );														  \
	symself( triedge );

/* 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( triedge1, triedge2 )												\
	sym( triedge1, triedge2 );													  \
	lnextself( triedge2 );														  \
	symself( triedge2 );

#define rnextself( triedge )													\
	symself( triedge );															  \
	lnextself( triedge );														  \
	symself( triedge );

/* rnext() moves one edge clockwise about the adjacent triangle.             */
/*   (It's best understood by reading Guibas and Stolfi.  It involves        */
/*   changing triangles twice.)                                              */

#define rprev( triedge1, triedge2 )												\
	sym( triedge1, triedge2 );													  \
	lprevself( triedge2 );														  \
	symself( triedge2 );

#define rprevself( triedge )													\
	symself( triedge );															  \
	lprevself( triedge );														  \
	symself( triedge );

/* These primitives determine or set the origin, destination, or apex of a   */
/* triangle.                                                                 */

#define org( triedge, pointptr )												\
	pointptr = (point) ( triedge ).tri[plus1mod3[( triedge ).orient] + 3]

#define dest( triedge, pointptr )												\
	pointptr = (point) ( triedge ).tri[minus1mod3[( triedge ).orient] + 3]

#define apex( triedge, pointptr )												\
	pointptr = (point) ( triedge ).tri[( triedge ).orient + 3]

#define setorg( triedge, pointptr )												\
	( triedge ).tri[plus1mod3[( triedge ).orient] + 3] = (triangle) pointptr

#define setdest( triedge, pointptr )											\
	( triedge ).tri[minus1mod3[( triedge ).orient] + 3] = (triangle) pointptr

#define setapex( triedge, pointptr )											\
	( triedge ).tri[( triedge ).orient + 3] = (triangle) pointptr

#define setvertices2null( triedge )												\
	( triedge ).tri[3] = (triangle) NULL;										  \
	( triedge ).tri[4] = (triangle) NULL;										  \
	( triedge ).tri[5] = (triangle) NULL;

/* Bond two triangles together.                                              */

#define bond( triedge1, triedge2 )												\
	( triedge1 ).tri[( triedge1 ).orient] = encode( triedge2 );						  \
	( triedge2 ).tri[( triedge2 ).orient] = encode( triedge1 )

/* 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( triedge )														\
	( triedge ).tri[( triedge ).orient] = (triangle) dummytri

/* Copy a triangle/edge handle.                                              */

#define triedgecopy( triedge1, triedge2 )										\
	( triedge2 ).tri = ( triedge1 ).tri;											\
	( triedge2 ).orient = ( triedge1 ).orient

/* Test for equality of triangle/edge handles.                               */

#define triedgeequal( triedge1, triedge2 )										\
	( ( ( triedge1 ).tri == ( triedge2 ).tri ) &&									   \
	  ( ( triedge1 ).orient == ( triedge2 ).orient ) )

/* Primitives to infect or cure a triangle with the virus.  These rely on    */
/*   the assumption that all shell edges are aligned to four-byte boundaries.*/

#define infect( triedge )														\
	( triedge ).tri[6] = (triangle)												  \
						 ( (unsigned long) ( triedge ).tri[6] | (unsigned long) 2l )

#define uninfect( triedge )														\
	( triedge ).tri[6] = (triangle)												  \
						 ( (unsigned long) ( triedge ).tri[6] & ~(unsigned long) 2l )

/* Test a triangle for viral infection.                                      */

#define infected( triedge )														\
	( ( (unsigned long) ( triedge ).tri[6] & (unsigned long) 2l ) != 0 )

/* Check or set a triangle's attributes.                                     */

#define elemattribute( triedge, attnum )										\
	( (REAL *) ( triedge ).tri )[elemattribindex + ( attnum )]

#define setelemattribute( triedge, attnum, value )								\
	( (REAL *) ( triedge ).tri )[elemattribindex + ( attnum )] = (REAL)value

/* Check or set a triangle's maximum area bound.                             */

#define areabound( triedge )  ( (REAL *) ( triedge ).tri )[areaboundindex]

#define setareabound( triedge, value )											\
	( (REAL *) ( triedge ).tri )[areaboundindex] = (REAL)value

/********* Primitives for shell edges                                *********/
/*                                                                           */
/*                                                                           */

/* sdecode() converts a pointer to an oriented shell edge.  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, edge )													\
	( edge ).shorient = (int) ( (unsigned long) ( sptr ) & (unsigned long) 1l );	  \
	( edge ).sh = (shelle *)													  \
				  ( (unsigned long) ( sptr ) & ~(unsigned long) 3l )

/* sencode() compresses an oriented shell edge into a single pointer.  It    */
/*   relies on the assumption that all shell edges are aligned to two-byte   */
/*   boundaries, so the least significant bit of (edge).sh is zero.          */

#define sencode( edge )															\
	(shelle) ( (unsigned long) ( edge ).sh | (unsigned long) ( edge ).shorient )

/* ssym() toggles the orientation of a shell edge.                           */

#define ssym( edge1, edge2 )													\
	( edge2 ).sh = ( edge1 ).sh;													\
	( edge2 ).shorient = 1 - ( edge1 ).shorient

#define ssymself( edge )														\
	( edge ).shorient = 1 - ( edge ).shorient

/* spivot() finds the other shell edge (from the same segment) that shares   */
/*   the same origin.                                                        */

#define spivot( edge1, edge2 )													\
	sptr = ( edge1 ).sh[( edge1 ).shorient];										\
	sdecode( sptr, edge2 )

#define spivotself( edge )														\
	sptr = ( edge ).sh[( edge ).shorient];											\
	sdecode( sptr, edge )

/* snext() finds the next shell edge (from the same segment) in sequence;    */
/*   one whose origin is the input shell edge's destination.                 */

#define snext( edge1, edge2 )													\
	sptr = ( edge1 ).sh[1 - ( edge1 ).shorient];									\
	sdecode( sptr, edge2 )

#define snextself( edge )														\
	sptr = ( edge ).sh[1 - ( edge ).shorient];										\
	sdecode( sptr, edge )

/* These primitives determine or set the origin or destination of a shell    */
/*   edge.                                                                   */

#define sorg( edge, pointptr )													\
	pointptr = (point) ( edge ).sh[2 + ( edge ).shorient]

#define sdest( edge, pointptr )													\
	pointptr = (point) ( edge ).sh[3 - ( edge ).shorient]

#define setsorg( edge, pointptr )												\
	( edge ).sh[2 + ( edge ).shorient] = (shelle) pointptr

#define setsdest( edge, pointptr )												\
	( edge ).sh[3 - ( edge ).shorient] = (shelle) pointptr

/* These primitives read or set a shell marker.  Shell markers are used to   */
/*   hold user boundary information.                                         */

#define mark( edge )  ( *(int *) ( ( edge ).sh + 6 ) )

#define setmark( edge, value )													\
	*(int *) ( ( edge ).sh + 6 ) = value

/* Bond two shell edges together.                                            */

#define sbond( edge1, edge2 )													\
	( edge1 ).sh[( edge1 ).shorient] = sencode( edge2 );							  \
	( edge2 ).sh[( edge2 ).shorient] = sencode( edge1 )

/* Dissolve a shell edge bond (from one side).  Note that the other shell    */
/*   edge will still think it's connected to this shell edge.                */

#define sdissolve( edge )														\
	( edge ).sh[( edge ).shorient] = (shelle) dummysh

/* Copy a shell edge.                                                        */

#define shellecopy( edge1, edge2 )												\
	( edge2 ).sh = ( edge1 ).sh;													\
	( edge2 ).shorient = ( edge1 ).shorient

/* Test for equality of shell edges.                                         */

#define shelleequal( edge1, edge2 )												\
	( ( ( edge1 ).sh == ( edge2 ).sh ) &&											   \
	  ( ( edge1 ).shorient == ( edge2 ).shorient ) )

/********* Primitives for interacting triangles and shell edges      *********/
/*                                                                           */
/*                                                                           */

/* tspivot() finds a shell edge abutting a triangle.                         */

#define tspivot( triedge, edge )												\
	sptr = (shelle) ( triedge ).tri[6 + ( triedge ).orient];						\
	sdecode( sptr, edge )

/* stpivot() finds a triangle abutting a shell edge.  It requires that the   */
/*   variable `ptr' of type `triangle' be defined.                           */

#define stpivot( edge, triedge )												\
	ptr = (triangle) ( edge ).sh[4 + ( edge ).shorient];							\
	decode( ptr, triedge )

/* Bond a triangle to a shell edge.                                          */

#define tsbond( triedge, edge )													\
	( triedge ).tri[6 + ( triedge ).orient] = (triangle) sencode( edge );			  \
	( edge ).sh[4 + ( edge ).shorient] = (shelle) encode( triedge )

/* Dissolve a bond (from the triangle side).                                 */

#define tsdissolve( triedge )													\
	( triedge ).tri[6 + ( triedge ).orient] = (triangle) dummysh

/* Dissolve a bond (from the shell edge side).                               */

#define stdissolve( edge )														\
	( edge ).sh[4 + ( edge ).shorient] = (shelle) dummytri

/********* Primitives for points                                     *********/
/*                                                                           */
/*                                                                           */

#define pointmark( pt )  ( (int *) ( pt ) )[pointmarkindex]

#define setpointmark( pt, value )												\
	( (int *) ( pt ) )[pointmarkindex] = value

#define point2tri( pt )  ( (triangle *) ( pt ) )[point2triindex]

#define setpoint2tri( pt, value )												\
	( (triangle *) ( pt ) )[point2triindex] = value

/**                                                                         **/
/**                                                                         **/
/********* Mesh manipulation primitives end here                     *********/

/********* User interaction routines begin here                      *********/
/**                                                                         **/
/**                                                                         **/

/*****************************************************************************/
/*                                                                           */
/*  syntax()   Print list of command line switches.                          */
/*                                                                           */
/*****************************************************************************/

#ifndef TRILIBRARY

void syntax(){
#ifdef CDT_ONLY
#ifdef REDUCED
	printf( "triangle [-pAcevngBPNEIOXzo_lQVh] input_file\n" );
#else /* not REDUCED */
	printf( "triangle [-pAcevngBPNEIOXzo_iFlCQVh] input_file\n" );
#endif /* not REDUCED */
#else /* not CDT_ONLY */
#ifdef REDUCED
	printf( "triangle [-prq__a__AcevngBPNEIOXzo_YS__lQVh] input_file\n" );
#else /* not REDUCED */
	printf( "triangle [-prq__a__AcevngBPNEIOXzo_YS__iFlsCQVh] input_file\n" );
#endif /* not REDUCED */
#endif /* not CDT_ONLY */

	printf( "    -p  Triangulates a Planar Straight Line Graph (.poly file).\n" );
#ifndef CDT_ONLY
	printf( "    -r  Refines a previously generated mesh.\n" );
	printf(
		"    -q  Quality mesh generation.  A minimum angle may be specified.\n" );
	printf( "    -a  Applies a maximum triangle area constraint.\n" );
#endif /* not CDT_ONLY */
	printf(
		"    -A  Applies attributes to identify elements in certain regions.\n" );
	printf( "    -c  Encloses the convex hull with segments.\n" );
	printf( "    -e  Generates an edge list.\n" );
	printf( "    -v  Generates a Voronoi diagram.\n" );
	printf( "    -n  Generates a list of triangle neighbors.\n" );
	printf( "    -g  Generates an .off file for Geomview.\n" );
	printf( "    -B  Suppresses output of boundary information.\n" );
	printf( "    -P  Suppresses output of .poly file.\n" );
	printf( "    -N  Suppresses output of .node file.\n" );
	printf( "    -E  Suppresses output of .ele file.\n" );
	printf( "    -I  Suppresses mesh iteration numbers.\n" );
	printf( "    -O  Ignores holes in .poly file.\n" );
	printf( "    -X  Suppresses use of exact arithmetic.\n" );
	printf( "    -z  Numbers all items starting from zero (rather than one).\n" );
	printf( "    -o2 Generates second-order subparametric elements.\n" );
#ifndef CDT_ONLY
	printf( "    -Y  Suppresses boundary segment splitting.\n" );
	printf( "    -S  Specifies maximum number of added Steiner points.\n" );
#endif /* not CDT_ONLY */
#ifndef REDUCED
	printf( "    -i  Uses incremental method, rather than divide-and-conquer.\n" );
	printf( "    -F  Uses Fortune's sweepline algorithm, rather than d-and-c.\n" );
#endif /* not REDUCED */
	printf( "    -l  Uses vertical cuts only, rather than alternating cuts.\n" );
#ifndef REDUCED
#ifndef CDT_ONLY
	printf(
		"    -s  Force segments into mesh by splitting (instead of using CDT).\n" );
#endif /* not CDT_ONLY */
	printf( "    -C  Check consistency of final mesh.\n" );
#endif /* not REDUCED */
	printf( "    -Q  Quiet:  No terminal output except errors.\n" );
	printf( "    -V  Verbose:  Detailed information on what I'm doing.\n" );
	printf( "    -h  Help:  Detailed instructions for Triangle.\n" );
	exit( 0 );
}

#endif /* not TRILIBRARY */

/*****************************************************************************/
/*                                                                           */
/*  info()   Print out complete instructions.                                */
/*                                                                           */
/*****************************************************************************/

#ifndef TRILIBRARY

void info(){
	printf( "Triangle\n" );
	printf(
		"A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator.\n" );
	printf( "Version 1.3\n\n" );
	printf(
		"Copyright 1996 Jonathan Richard Shewchuk  (bugs/comments to jrs@cs.cmu.edu)\n"
		);
	printf( "School of Computer Science / Carnegie Mellon University\n" );
	printf( "5000 Forbes Avenue / Pittsburgh, Pennsylvania  15213-3891\n" );
	printf(
		"Created as part of the Archimedes project (tools for parallel FEM).\n" );
	printf(
		"Supported in part by NSF Grant CMS-9318163 and an NSERC 1967 Scholarship.\n" );
	printf( "There is no warranty whatsoever.  Use at your own risk.\n" );
#ifdef SINGLE
	printf( "This executable is compiled for single precision arithmetic.\n\n\n" );
#else /* not SINGLE */
	printf( "This executable is compiled for double precision arithmetic.\n\n\n" );
#endif /* not SINGLE */
	printf(
		"Triangle generates exact Delaunay triangulations, constrained Delaunay\n" );
	printf(
		"triangulations, and quality conforming Delaunay triangulations.  The latter\n"
		);
	printf(
		"can be generated with no small angles, and are thus suitable for finite\n" );
	printf(
		"element analysis.  If no command line switches are specified, your .node\n" );
	printf(
		"input file will be read, and the Delaunay triangulation will be returned in\n"
		);
	printf( ".node and .ele output files.  The command syntax is:\n\n" );
#ifdef CDT_ONLY
#ifdef REDUCED
	printf( "triangle [-pAcevngBPNEIOXzo_lQVh] input_file\n\n" );
#else /* not REDUCED */
	printf( "triangle [-pAcevngBPNEIOXzo_iFlCQVh] input_file\n\n" );
#endif /* not REDUCED */
#else /* not CDT_ONLY */
#ifdef REDUCED
	printf( "triangle [-prq__a__AcevngBPNEIOXzo_YS__lQVh] input_file\n\n" );
#else /* not REDUCED */
	printf( "triangle [-prq__a__AcevngBPNEIOXzo_YS__iFlsCQVh] input_file\n\n" );
#endif /* not REDUCED */
#endif /* not CDT_ONLY */
	printf(
		"Underscores indicate that numbers may optionally follow certain switches;\n" );
	printf(
		"do not leave any space between a switch and its numeric parameter.\n" );
	printf(
		"input_file must be a file with extension .node, or extension .poly if the\n" );
	printf(
		"-p switch is used.  If -r is used, you must supply .node and .ele files,\n" );
	printf(
		"and possibly a .poly file and .area file as well.  The formats of these\n" );
	printf( "files are described below.\n\n" );
	printf( "Command Line Switches:\n\n" );
	printf(
		"    -p  Reads a Planar Straight Line Graph (.poly file), which can specify\n"
		);
	printf(
		"        points, segments, holes, and regional attributes and area\n" );
	printf(
		"        constraints.  Will generate a constrained Delaunay triangulation\n" );
	printf(
		"        fitting the input; or, if -s, -q, or -a is used, a conforming\n" );
	printf(
		"        Delaunay triangulation.  If -p is not used, Triangle reads a .node\n"
		);
	printf( "        file by default.\n" );
	printf(
		"    -r  Refines a previously generated mesh.  The mesh is read from a .node\n"
		);
	printf(
		"        file and an .ele file.  If -p is also used, a .poly file is read\n" );
	printf(
		"        and used to constrain edges in the mesh.  Further details on\n" );
	printf( "        refinement are given below.\n" );
	printf(
		"    -q  Quality mesh generation by Jim Ruppert's Delaunay refinement\n" );
	printf(
		"        algorithm.  Adds points to the mesh to ensure that no angles\n" );
	printf(
		"        smaller than 20 degrees occur.  An alternative minimum angle may be\n"
		);
	printf(
		"        specified after the `q'.  If the minimum angle is 20.7 degrees or\n" );
	printf(
		"        smaller, the triangulation algorithm is theoretically guaranteed to\n"
		);
	printf(
		"        terminate (assuming infinite precision arithmetic - Triangle may\n" );
	printf(
		"        fail to terminate if you run out of precision).  In practice, the\n" );
	printf(
		"        algorithm often succeeds for minimum angles up to 33.8 degrees.\n" );
	printf(
		"        For highly refined meshes, however, it may be necessary to reduce\n" );
	printf(
		"        the minimum angle to well below 20 to avoid problems associated\n" );
	printf(
		"        with insufficient floating-point precision.  The specified angle\n" );
	printf( "        may include a decimal point.\n" );
	printf(
		"    -a  Imposes a maximum triangle area.  If a number follows the `a', no\n" );
	printf(
		"        triangle will be generated whose area is larger than that number.\n" );
	printf(
		"        If no number is specified, an .area file (if -r is used) or .poly\n" );
	printf(
		"        file (if -r is not used) specifies a number of maximum area\n" );
	printf(
		"        constraints.  An .area file contains a separate area constraint for\n"
		);
	printf(
		"        each triangle, and is useful for refining a finite element mesh\n" );
	printf(
		"        based on a posteriori error estimates.  A .poly file can optionally\n"
		);
	printf(
		"        contain an area constraint for each segment-bounded region, thereby\n"
		);
	printf(
		"        enforcing triangle densities in a first triangulation.  You can\n" );
	printf(
		"        impose both a fixed area constraint and a varying area constraint\n" );
	printf(
		"        by invoking the -a switch twice, once with and once without a\n" );
	printf(
		"        number following.  Each area specified may include a decimal point.\n"
		);
	printf(
		"    -A  Assigns an additional attribute to each triangle that identifies\n" );
	printf(
		"        what segment-bounded region each triangle belongs to.  Attributes\n" );
	printf(
		"        are assigned to regions by the .poly file.  If a region is not\n" );
	printf(
		"        explicitly marked by the .poly file, triangles in that region are\n" );
	printf(
		"        assigned an attribute of zero.  The -A switch has an effect only\n" );
	printf( "        when the -p switch is used and the -r switch is not.\n" );
	printf(
		"    -c  Creates segments on the convex hull of the triangulation.  If you\n" );
	printf(
		"        are triangulating a point set, this switch causes a .poly file to\n" );
	printf(
		"        be written, containing all edges in the convex hull.  (By default,\n"
		);
	printf(
		"        a .poly file is written only if a .poly file is read.)  If you are\n"
		);
	printf(
		"        triangulating a PSLG, this switch specifies that the interior of\n" );
	printf(
		"        the convex hull of the PSLG should be triangulated.  If you do not\n"
		);
	printf(
		"        use this switch when triangulating a PSLG, it is assumed that you\n" );
	printf(
		"        have identified the region to be triangulated by surrounding it\n" );
	printf(
		"        with segments of the input PSLG.  Beware:  if you are not careful,\n"
		);
	printf(
		"        this switch can cause the introduction of an extremely thin angle\n" );
	printf(
		"        between a PSLG segment and a convex hull segment, which can cause\n" );
	printf(
		"        overrefinement or failure if Triangle runs out of precision.  If\n" );
	printf(
		"        you are refining a mesh, the -c switch works differently; it\n" );
	printf(
		"        generates the set of boundary edges of the mesh, rather than the\n" );
	printf( "        convex hull.\n" );
	printf(
		"    -e  Outputs (to an .edge file) a list of edges of the triangulation.\n" );
	printf(
		"    -v  Outputs the Voronoi diagram associated with the triangulation.\n" );
	printf( "        Does not attempt to detect degeneracies.\n" );
	printf(
		"    -n  Outputs (to a .neigh file) a list of triangles neighboring each\n" );
	printf( "        triangle.\n" );
	printf(
		"    -g  Outputs the mesh to an Object File Format (.off) file, suitable for\n"
		);
	printf( "        viewing with the Geometry Center's Geomview package.\n" );
	printf(
		"    -B  No boundary markers in the output .node, .poly, and .edge output\n" );
	printf(
		"        files.  See the detailed discussion of boundary markers below.\n" );
	printf(
		"    -P  No output .poly file.  Saves disk space, but you lose the ability\n" );
	printf(
		"        to impose segment constraints on later refinements of the mesh.\n" );
	printf( "    -N  No output .node file.\n" );
	printf( "    -E  No output .ele file.\n" );
	printf(
		"    -I  No iteration numbers.  Suppresses the output of .node and .poly\n" );
	printf(
		"        files, so your input files won't be overwritten.  (If your input is\n"
		);
	printf(
		"        a .poly file only, a .node file will be written.)  Cannot be used\n" );
	printf(
		"        with the -r switch, because that would overwrite your input .ele\n" );
	printf(
		"        file.  Shouldn't be used with the -s, -q, or -a switch if you are\n" );
	printf(
		"        using a .node file for input, because no .node file will be\n" );
	printf( "        written, so there will be no record of any added points.\n" );
	printf( "    -O  No holes.  Ignores the holes in the .poly file.\n" );
	printf(
		"    -X  No exact arithmetic.  Normally, Triangle uses exact floating-point\n"
		);
	printf(
		"        arithmetic for certain tests if it thinks the inexact tests are not\n"
		);
	printf(
		"        accurate enough.  Exact arithmetic ensures the robustness of the\n" );
	printf(
		"        triangulation algorithms, despite floating-point roundoff error.\n" );
	printf(
		"        Disabling exact arithmetic with the -X switch will cause a small\n" );
	printf(
		"        improvement in speed and create the possibility (albeit small) that\n"
		);
	printf(
		"        Triangle will fail to produce a valid mesh.  Not recommended.\n" );
	printf(
		"    -z  Numbers all items starting from zero (rather than one).  Note that\n"
		);
	printf(
		"        this switch is normally overrided by the value used to number the\n" );
	printf(
		"        first point of the input .node or .poly file.  However, this switch\n"
		);
	printf( "        is useful when calling Triangle from another program.\n" );
	printf(
		"    -o2 Generates second-order subparametric elements with six nodes each.\n"
		);
	printf(
		"    -Y  No new points on the boundary.  This switch is useful when the mesh\n"
		);
	printf(
		"        boundary must be preserved so that it conforms to some adjacent\n" );
	printf(
		"        mesh.  Be forewarned that you will probably sacrifice some of the\n" );
	printf(
		"        quality of the mesh; Triangle will try, but the resulting mesh may\n"
		);
	printf(
		"        contain triangles of poor aspect ratio.  Works well if all the\n" );
	printf(
		"        boundary points are closely spaced.  Specify this switch twice\n" );
	printf(
		"        (`-YY') to prevent all segment splitting, including internal\n" );
	printf( "        boundaries.\n" );
	printf(
		"    -S  Specifies the maximum number of Steiner points (points that are not\n"
		);
	printf(
		"        in the input, but are added to meet the constraints of minimum\n" );
	printf(
		"        angle and maximum area).  The default is to allow an unlimited\n" );
	printf(
		"        number.  If you specify this switch with no number after it,\n" );
	printf(
		"        the limit is set to zero.  Triangle always adds points at segment\n" );
	printf(
		"        intersections, even if it needs to use more points than the limit\n" );
	printf(
		"        you set.  When Triangle inserts segments by splitting (-s), it\n" );
	printf(
		"        always adds enough points to ensure that all the segments appear in\n"
		);
	printf(
		"        the triangulation, again ignoring the limit.  Be forewarned that\n" );
	printf(
		"        the -S switch may result in a conforming triangulation that is not\n"
		);
	printf(
		"        truly Delaunay, because Triangle may be forced to stop adding\n" );
	printf(
		"        points when the mesh is in a state where a segment is non-Delaunay\n"
		);
	printf(
		"        and needs to be split.  If so, Triangle will print a warning.\n" );
	printf(
		"    -i  Uses an incremental rather than divide-and-conquer algorithm to\n" );
	printf(
		"        form a Delaunay triangulation.  Try it if the divide-and-conquer\n" );
	printf( "        algorithm fails.\n" );
	printf(
		"    -F  Uses Steven Fortune's sweepline algorithm to form a Delaunay\n" );
	printf(
		"        triangulation.  Warning:  does not use exact arithmetic for all\n" );
	printf( "        calculations.  An exact result is not guaranteed.\n" );
	printf(
		"    -l  Uses only vertical cuts in the divide-and-conquer algorithm.  By\n" );
	printf(
		"        default, Triangle uses alternating vertical and horizontal cuts,\n" );
	printf(
		"        which usually improve the speed except with point sets that are\n" );
	printf(
		"        small or short and wide.  This switch is primarily of theoretical\n" );
	printf( "        interest.\n" );
	printf(
		"    -s  Specifies that segments should be forced into the triangulation by\n"
		);
	printf(
		"        recursively splitting them at their midpoints, rather than by\n" );
	printf(
		"        generating a constrained Delaunay triangulation.  Segment splitting\n"
		);
	printf(
		"        is true to Ruppert's original algorithm, but can create needlessly\n"
		);
	printf( "        small triangles near external small features.\n" );
	printf(
		"    -C  Check the consistency of the final mesh.  Uses exact arithmetic for\n"
		);
	printf(
		"        checking, even if the -X switch is used.  Useful if you suspect\n" );
	printf( "        Triangle is buggy.\n" );
	printf(
		"    -Q  Quiet: Suppresses all explanation of what Triangle is doing, unless\n"
		);
	printf( "        an error occurs.\n" );
	printf(
		"    -V  Verbose: Gives detailed information about what Triangle is doing.\n" );
	printf(
		"        Add more `V's for increasing amount of detail.  `-V' gives\n" );
	printf(
		"        information on algorithmic progress and more detailed statistics.\n" );
	printf(
		"        `-VV' gives point-by-point details, and will print so much that\n" );
	printf(
		"        Triangle will run much more slowly.  `-VVV' gives information only\n"
		);
	printf( "        a debugger could love.\n" );
	printf( "    -h  Help:  Displays these instructions.\n" );
	printf( "\n" );
	printf( "Definitions:\n" );
	printf( "\n" );
	printf(
		"  A Delaunay triangulation of a point set is a triangulation whose vertices\n"
		);
	printf(
		"  are the point set, having the property that no point in the point set\n" );
	printf(
		"  falls in the interior of the circumcircle (circle that passes through all\n"
		);
	printf( "  three vertices) of any triangle in the triangulation.\n\n" );
	printf(
		"  A Voronoi diagram of a point set is a subdivision of the plane into\n" );
	printf(
		"  polygonal regions (some of which may be infinite), where each region is\n" );
	printf(
		"  the set of points in the plane that are closer to some input point than\n" );
	printf(
		"  to any other input point.  (The Voronoi diagram is the geometric dual of\n"
		);
	printf( "  the Delaunay triangulation.)\n\n" );
	printf(
		"  A Planar Straight Line Graph (PSLG) is a collection of points and\n" );
	printf(
		"  segments.  Segments are simply edges, whose endpoints are points in the\n" );
	printf(
		"  PSLG.  The file format for PSLGs (.poly files) is described below.\n" );
	printf( "\n" );
	printf(
		"  A constrained Delaunay triangulation of a PSLG is similar to a Delaunay\n" );
	printf(
		"  triangulation, but each PSLG segment is present as a single edge in the\n" );
	printf(
		"  triangulation.  (A constrained Delaunay triangulation is not truly a\n" );
	printf( "  Delaunay triangulation.)\n\n" );
	printf(
		"  A conforming Delaunay triangulation of a PSLG is a true Delaunay\n" );
	printf(
		"  triangulation in which each PSLG segment may have been subdivided into\n" );
	printf(
		"  several edges by the insertion of additional points.  These inserted\n" );
	printf(
		"  points are necessary to allow the segments to exist in the mesh while\n" );
	printf( "  maintaining the Delaunay property.\n\n" );
	printf( "File Formats:\n\n" );
	printf(
		"  All files may contain comments prefixed by the character '#'.  Points,\n" );
	printf(
		"  triangles, edges, holes, and maximum area constraints must be numbered\n" );
	printf(
		"  consecutively, starting from either 1 or 0.  Whichever you choose, all\n" );
	printf(
		"  input files must be consistent; if the nodes are numbered from 1, so must\n"
		);
	printf(
		"  be all other objects.  Triangle automatically detects your choice while\n" );
	printf(
		"  reading the .node (or .poly) file.  (When calling Triangle from another\n" );
	printf(
		"  program, use the -z switch if you wish to number objects from zero.)\n" );
	printf( "  Examples of these file formats are given below.\n\n" );
	printf( "  .node files:\n" );
	printf(
		"    First line:  <# of points> <dimension (must be 2)> <# of attributes>\n" );
	printf(
		"                                           <# of boundary markers (0 or 1)>\n"
		);
	printf(
		"    Remaining lines:  <point #> <x> <y> [attributes] [boundary marker]\n" );
	printf( "\n" );
	printf(
		"    The attributes, which are typically floating-point values of physical\n" );
	printf(
		"    quantities (such as mass or conductivity) associated with the nodes of\n"
		);
	printf(
		"    a finite element mesh, are copied unchanged to the output mesh.  If -s,\n"
		);
	printf(
		"    -q, or -a is selected, each new Steiner point added to the mesh will\n" );
	printf( "    have attributes assigned to it by linear interpolation.\n\n" );
	printf(
		"    If the fourth entry of the first line is `1', the last column of the\n" );
	printf(
		"    remainder of the file is assumed to contain boundary markers.  Boundary\n"
		);
	printf(
		"    markers are used to identify boundary points and points resting on PSLG\n"
		);
	printf(
		"    segments; a complete description appears in a section below.  The .node\n"
		);
	printf(
		"    file produced by Triangle will contain boundary markers in the last\n" );
	printf( "    column unless they are suppressed by the -B switch.\n\n" );
	printf( "  .ele files:\n" );
	printf(
		"    First line:  <# of triangles> <points per triangle> <# of attributes>\n" );
	printf(
		"    Remaining lines:  <triangle #> <point> <point> <point> ... [attributes]\n"
		);
	printf( "\n" );
	printf(
		"    Points are indices into the corresponding .node file.  The first three\n"
		);
	printf(
		"    points are the corners, and are listed in counterclockwise order around\n"
		);
	printf(
		"    each triangle.  (The remaining points, if any, depend on the type of\n" );
	printf(
		"    finite element used.)  The attributes are just like those of .node\n" );
	printf(
		"    files.  Because there is no simple mapping from input to output\n" );
	printf(
		"    triangles, an attempt is made to interpolate attributes, which may\n" );
	printf(
		"    result in a good deal of diffusion of attributes among nearby triangles\n"
		);
	printf(
		"    as the triangulation is refined.  Diffusion does not occur across\n" );
	printf(
		"    segments, so attributes used to identify segment-bounded regions remain\n"
		);
	printf(
		"    intact.  In output .ele files, all triangles have three points each\n" );
	printf(
		"    unless the -o2 switch is used, in which case they have six, and the\n" );
	printf(
		"    fourth, fifth, and sixth points lie on the midpoints of the edges\n" );
	printf( "    opposite the first, second, and third corners.\n\n" );
	printf( "  .poly files:\n" );
	printf(
		"    First line:  <# of points> <dimension (must be 2)> <# of attributes>\n" );
	printf(
		"                                           <# of boundary markers (0 or 1)>\n"
		);
	printf(
		"    Following lines:  <point #> <x> <y> [attributes] [boundary marker]\n" );
	printf( "    One line:  <# of segments> <# of boundary markers (0 or 1)>\n" );
	printf(
		"    Following lines:  <segment #> <endpoint> <endpoint> [boundary marker]\n" );
	printf( "    One line:  <# of holes>\n" );
	printf( "    Following lines:  <hole #> <x> <y>\n" );
	printf(
		"    Optional line:  <# of regional attributes and/or area constraints>\n" );
	printf(
		"    Optional following lines:  <constraint #> <x> <y> <attrib> <max area>\n" );
	printf( "\n" );
	printf(
		"    A .poly file represents a PSLG, as well as some additional information.\n"
		);
	printf(
		"    The first section lists all the points, and is identical to the format\n"
		);
	printf(
		"    of .node files.  <# of points> may be set to zero to indicate that the\n"
		);
	printf(
		"    points are listed in a separate .node file; .poly files produced by\n" );
	printf(
		"    Triangle always have this format.  This has the advantage that a point\n"
		);
	printf(
		"    set may easily be triangulated with or without segments.  (The same\n" );
	printf(
		"    effect can be achieved, albeit using more disk space, by making a copy\n"
		);
	printf(
		"    of the .poly file with the extension .node; all sections of the file\n" );
	printf( "    but the first are ignored.)\n\n" );
	printf(
		"    The second section lists the segments.  Segments are edges whose\n" );
	printf(
		"    presence in the triangulation is enforced.  Each segment is specified\n" );
	printf(
		"    by listing the indices of its two endpoints.  This means that you must\n"
		);
	printf(
		"    include its endpoints in the point list.  If -s, -q, and -a are not\n" );
	printf(
		"    selected, Triangle will produce a constrained Delaunay triangulation,\n" );
	printf(
		"    in which each segment appears as a single edge in the triangulation.\n" );
	printf(
		"    If -q or -a is selected, Triangle will produce a conforming Delaunay\n" );
	printf(
		"    triangulation, in which segments may be subdivided into smaller edges.\n"
		);
	printf( "    Each segment, like each point, may have a boundary marker.\n\n" );
	printf(
		"    The third section lists holes (and concavities, if -c is selected) in\n" );
	printf(
		"    the triangulation.  Holes are specified by identifying a point inside\n" );
	printf(
		"    each hole.  After the triangulation is formed, Triangle creates holes\n" );
	printf(
		"    by eating triangles, spreading out from each hole point until its\n" );
	printf(
		"    progress is blocked by PSLG segments; you must be careful to enclose\n" );
	printf(
		"    each hole in segments, or your whole triangulation may be eaten away.\n" );
	printf(
		"    If the two triangles abutting a segment are eaten, the segment itself\n" );
	printf(
		"    is also eaten.  Do not place a hole directly on a segment; if you do,\n" );
	printf( "    Triangle will choose one side of the segment arbitrarily.\n\n" );
	printf(
		"    The optional fourth section lists regional attributes (to be assigned\n" );
	printf(
		"    to all triangles in a region) and regional constraints on the maximum\n" );
	printf(
		"    triangle area.  Triangle will read this section only if the -A switch\n" );
	printf(
		"    is used or the -a switch is used without a number following it, and the\n"
		);
	printf(
		"    -r switch is not used.  Regional attributes and area constraints are\n" );
	printf(
		"    propagated in the same manner as holes; you specify a point for each\n" );
	printf(
		"    attribute and/or constraint, and the attribute and/or constraint will\n" );
	printf(
		"    affect the whole region (bounded by segments) containing the point.  If\n"
		);
	printf(
		"    two values are written on a line after the x and y coordinate, the\n" );
	printf(
		"    former is assumed to be a regional attribute (but will only be applied\n"
		);
	printf(
		"    if the -A switch is selected), and the latter is assumed to be a\n" );
	printf(
		"    regional area constraint (but will only be applied if the -a switch is\n"
		);
	printf(
		"    selected).  You may also specify just one value after the coordinates,\n"
		);
	printf(
		"    which can serve as both an attribute and an area constraint, depending\n"
		);
	printf(
		"    on the choice of switches.  If you are using the -A and -a switches\n" );
	printf(
		"    simultaneously and wish to assign an attribute to some region without\n" );
	printf( "    imposing an area constraint, use a negative maximum area.\n\n" );
	printf(
		"    When a triangulation is created from a .poly file, you must either\n" );
	printf(
		"    enclose the entire region to be triangulated in PSLG segments, or\n" );
	printf(
		"    use the -c switch, which encloses the convex hull of the input point\n" );
	printf(
		"    set.  If you do not use the -c switch, Triangle will eat all triangles\n"
		);
	printf(
		"    on the outer boundary that are not protected by segments; if you are\n" );
	printf(
		"    not careful, your whole triangulation may be eaten away.  If you do\n" );
	printf(
		"    use the -c switch, you can still produce concavities by appropriate\n" );
	printf( "    placement of holes just inside the convex hull.\n\n" );
	printf(
		"    An ideal PSLG has no intersecting segments, nor any points that lie\n" );
	printf(
		"    upon segments (except, of course, the endpoints of each segment.)  You\n"
		);
	printf(
		"    aren't required to make your .poly files ideal, but you should be aware\n"
		);
	printf(
		"    of what can go wrong.  Segment intersections are relatively safe -\n" );
	printf(
		"    Triangle will calculate the intersection points for you and add them to\n"
		);
	printf(
		"    the triangulation - as long as your machine's floating-point precision\n"
		);
	printf(
		"    doesn't become a problem.  You are tempting the fates if you have three\n"
		);
	printf(
		"    segments that cross at the same location, and expect Triangle to figure\n"
		);
	printf(
		"    out where the intersection point is.  Thanks to floating-point roundoff\n"
		);
	printf(
		"    error, Triangle will probably decide that the three segments intersect\n"
		);
	printf(
		"    at three different points, and you will find a minuscule triangle in\n" );
	printf(
		"    your output - unless Triangle tries to refine the tiny triangle, uses\n" );
	printf(
		"    up the last bit of machine precision, and fails to terminate at all.\n" );
	printf(
		"    You're better off putting the intersection point in the input files,\n" );
	printf(
		"    and manually breaking up each segment into two.  Similarly, if you\n" );
	printf(
		"    place a point at the middle of a segment, and hope that Triangle will\n" );
	printf(
		"    break up the segment at that point, you might get lucky.  On the other\n"
		);
	printf(
		"    hand, Triangle might decide that the point doesn't lie precisely on the\n"
		);
	printf(
		"    line, and you'll have a needle-sharp triangle in your output - or a lot\n"
		);
	printf( "    of tiny triangles if you're generating a quality mesh.\n\n" );
	printf(
		"    When Triangle reads a .poly file, it also writes a .poly file, which\n" );
	printf(
		"    includes all edges that are part of input segments.  If the -c switch\n" );
	printf(
		"    is used, the output .poly file will also include all of the edges on\n" );
	printf(
		"    the convex hull.  Hence, the output .poly file is useful for finding\n" );
	printf(
		"    edges associated with input segments and setting boundary conditions in\n"
		);
	printf(
		"    finite element simulations.  More importantly, you will need it if you\n"
		);
	printf(
		"    plan to refine the output mesh, and don't want segments to be missing\n" );
	printf( "    in later triangulations.\n\n" );
	printf( "  .area files:\n" );
	printf( "    First line:  <# of triangles>\n" );
	printf( "    Following lines:  <triangle #> <maximum area>\n\n" );
	printf(
		"    An .area file associates with each triangle a maximum area that is used\n"
		);
	printf(
		"    for mesh refinement.  As with other file formats, every triangle must\n" );
	printf(
		"    be represented, and they must be numbered consecutively.  A triangle\n" );
	printf(
		"    may be left unconstrained by assigning it a negative maximum area.\n" );
	printf( "\n" );
	printf( "  .edge files:\n" );
	printf( "    First line:  <# of edges> <# of boundary markers (0 or 1)>\n" );
	printf(
		"    Following lines:  <edge #> <endpoint> <endpoint> [boundary marker]\n" );
	printf( "\n" );
	printf(
		"    Endpoints are indices into the corresponding .node file.  Triangle can\n"
		);
	printf(
		"    produce .edge files (use the -e switch), but cannot read them.  The\n" );
	printf(
		"    optional column of boundary markers is suppressed by the -B switch.\n" );
	printf( "\n" );
	printf(
		"    In Voronoi diagrams, one also finds a special kind of edge that is an\n" );
	printf(
		"    infinite ray with only one endpoint.  For these edges, a different\n" );
	printf( "    format is used:\n\n" );
	printf( "        <edge #> <endpoint> -1 <direction x> <direction y>\n\n" );
	printf(
		"    The `direction' is a floating-point vector that indicates the direction\n"
		);
	printf( "    of the infinite ray.\n\n" );
	printf( "  .neigh files:\n" );
	printf(
		"    First line:  <# of triangles> <# of neighbors per triangle (always 3)>\n"
		);
	printf(
		"    Following lines:  <triangle #> <neighbor> <neighbor> <neighbor>\n" );
	printf( "\n" );
	printf(
		"    Neighbors are indices into the corresponding .ele file.  An index of -1\n"
		);
	printf(
		"    indicates a mesh boundary, and therefore no neighbor.  Triangle can\n" );
	printf(
		"    produce .neigh files (use the -n switch), but cannot read them.\n" );
	printf( "\n" );
	printf(
		"    The first neighbor of triangle i is opposite the first corner of\n" );
	printf( "    triangle i, and so on.\n\n" );
	printf( "Boundary Markers:\n\n" );
	printf(
		"  Boundary markers are tags used mainly to identify which output points and\n"
		);
	printf(
		"  edges are associated with which PSLG segment, and to identify which\n" );
	printf(
		"  points and edges occur on a boundary of the triangulation.  A common use\n"
		);
	printf(
		"  is to determine where boundary conditions should be applied to a finite\n" );
	printf(
		"  element mesh.  You can prevent boundary markers from being written into\n" );
	printf( "  files produced by Triangle by using the -B switch.\n\n" );
	printf(
		"  The boundary marker associated with each segment in an output .poly file\n"
		);
	printf( "  or edge in an output .edge file is chosen as follows:\n" );
	printf(
		"    - If an output edge is part or all of a PSLG segment with a nonzero\n" );
	printf(
		"      boundary marker, then the edge is assigned the same marker.\n" );
	printf(
		"    - Otherwise, if the edge occurs on a boundary of the triangulation\n" );
	printf(
		"      (including boundaries of holes), then the edge is assigned the marker\n"
		);
	printf( "      one (1).\n" );
	printf( "    - Otherwise, the edge is assigned the marker zero (0).\n" );
	printf(
		"  The boundary marker associated with each point in an output .node file is\n"
		);
	printf( "  chosen as follows:\n" );
	printf(
		"    - If a point is assigned a nonzero boundary marker in the input file,\n" );
	printf(
		"      then it is assigned the same marker in the output .node file.\n" );
	printf(
		"    - Otherwise, if the point lies on a PSLG segment (including the\n" );
	printf(
		"      segment's endpoints) with a nonzero boundary marker, then the point\n" );
	printf(
		"      is assigned the same marker.  If the point lies on several such\n" );
	printf( "      segments, one of the markers is chosen arbitrarily.\n" );
	printf(
		"    - Otherwise, if the point occurs on a boundary of the triangulation,\n" );
	printf( "      then the point is assigned the marker one (1).\n" );
	printf( "    - Otherwise, the point is assigned the marker zero (0).\n" );
	printf( "\n" );
	printf(
		"  If you want Triangle to determine for you which points and edges are on\n" );
	printf(
		"  the boundary, assign them the boundary marker zero (or use no markers at\n"
		);
	printf(
		"  all) in your input files.  Alternatively, you can mark some of them and\n" );
	printf( "  leave others marked zero, allowing Triangle to label them.\n\n" );
	printf( "Triangulation Iteration Numbers:\n\n" );
	printf(
		"  Because Triangle can read and refine its own triangulations, input\n" );
	printf(
		"  and output files have iteration numbers.  For instance, Triangle might\n" );
	printf(
		"  read the files mesh.3.node, mesh.3.ele, and mesh.3.poly, refine the\n" );
	printf(
		"  triangulation, and output the files mesh.4.node, mesh.4.ele, and\n" );
	printf( "  mesh.4.poly.  Files with no iteration number are treated as if\n" );
	printf(
		"  their iteration number is zero; hence, Triangle might read the file\n" );
	printf(
		"  points.node, triangulate it, and produce the files points.1.node and\n" );
	printf( "  points.1.ele.\n\n" );
	printf(
		"  Iteration numbers allow you to create a sequence of successively finer\n" );
	printf(
		"  meshes suitable for multigrid methods.  They also allow you to produce a\n"
		);
	printf(
		"  sequence of meshes using error estimate-driven mesh refinement.\n" );
	printf( "\n" );
	printf(
		"  If you're not using refinement or quality meshing, and you don't like\n" );
	printf(
		"  iteration numbers, use the -I switch to disable them.  This switch will\n" );
	printf(
		"  also disable output of .node and .poly files to prevent your input files\n"
		);
	printf(
		"  from being overwritten.  (If the input is a .poly file that contains its\n"
		);
	printf( "  own points, a .node file will be written.)\n\n" );
	printf( "Examples of How to Use Triangle:\n\n" );
	printf(
		"  `triangle dots' will read points from dots.node, and write their Delaunay\n"
		);
	printf(
		"  triangulation to dots.1.node and dots.1.ele.  (dots.1.node will be\n" );
	printf(
		"  identical to dots.node.)  `triangle -I dots' writes the triangulation to\n"
		);
	printf(
		"  dots.ele instead.  (No additional .node file is needed, so none is\n" );
	printf( "  written.)\n\n" );
	printf(
		"  `triangle -pe object.1' will read a PSLG from object.1.poly (and possibly\n"
		);
	printf(
		"  object.1.node, if the points are omitted from object.1.poly) and write\n" );
	printf( "  their constrained Delaunay triangulation to object.2.node and\n" );
	printf(
		"  object.2.ele.  The segments will be copied to object.2.poly, and all\n" );
	printf( "  edges will be written to object.2.edge.\n\n" );
	printf(
		"  `triangle -pq31.5a.1 object' will read a PSLG from object.poly (and\n" );
	printf(
		"  possibly object.node), generate a mesh whose angles are all greater than\n"
		);
	printf(
		"  31.5 degrees and whose triangles all have area smaller than 0.1, and\n" );
	printf(
		"  write the mesh to object.1.node and object.1.ele.  Each segment may have\n"
		);
	printf(
		"  been broken up into multiple edges; the resulting constrained edges are\n" );
	printf( "  written to object.1.poly.\n\n" );
	printf(
		"  Here is a sample file `box.poly' describing a square with a square hole:\n"
		);
	printf( "\n" );
	printf(
		"    # A box with eight points in 2D, no attributes, one boundary marker.\n" );
	printf( "    8 2 0 1\n" );
	printf( "    # Outer box has these vertices:\n" );
	printf( "     1   0 0   0\n" );
	printf( "     2   0 3   0\n" );
	printf( "     3   3 0   0\n" );
	printf( "     4   3 3   33     # A special marker for this point.\n" );
	printf( "    # Inner square has these vertices:\n" );
	printf( "     5   1 1   0\n" );
	printf( "     6   1 2   0\n" );
	printf( "     7   2 1   0\n" );
	printf( "     8   2 2   0\n" );
	printf( "    # Five segments with boundary markers.\n" );
	printf( "    5 1\n" );
	printf( "     1   1 2   5      # Left side of outer box.\n" );
	printf( "     2   5 7   0      # Segments 2 through 5 enclose the hole.\n" );
	printf( "     3   7 8   0\n" );
	printf( "     4   8 6   10\n" );
	printf( "     5   6 5   0\n" );
	printf( "    # One hole in the middle of the inner square.\n" );
	printf( "    1\n" );
	printf( "     1   1.5 1.5\n\n" );
	printf(
		"  Note that some segments are missing from the outer square, so one must\n" );
	printf(
		"  use the `-c' switch.  After `triangle -pqc box.poly', here is the output\n"
		);
	printf(
		"  file `box.1.node', with twelve points.  The last four points were added\n" );
	printf(
		"  to meet the angle constraint.  Points 1, 2, and 9 have markers from\n" );
	printf(
		"  segment 1.  Points 6 and 8 have markers from segment 4.  All the other\n" );
	printf(
		"  points but 4 have been marked to indicate that they lie on a boundary.\n" );
	printf( "\n" );
	printf( "    12  2  0  1\n" );
	printf( "       1    0   0      5\n" );
	printf( "       2    0   3      5\n" );
	printf( "       3    3   0      1\n" );
	printf( "       4    3   3     33\n" );
	printf( "       5    1   1      1\n" );
	printf( "       6    1   2     10\n" );
	printf( "       7    2   1      1\n" );
	printf( "       8    2   2     10\n" );
	printf( "       9    0   1.5    5\n" );
	printf( "      10    1.5   0    1\n" );
	printf( "      11    3   1.5    1\n" );
	printf( "      12    1.5   3    1\n" );
	printf( "    # Generated by triangle -pqc box.poly\n\n" );
	printf( "  Here is the output file `box.1.ele', with twelve triangles.\n\n" );
	printf( "    12  3  0\n" );
	printf( "       1     5   6   9\n" );
	printf( "       2    10   3   7\n" );
	printf( "       3     6   8  12\n" );
	printf( "       4     9   1   5\n" );
	printf( "       5     6   2   9\n" );
	printf( "       6     7   3  11\n" );
	printf( "       7    11   4   8\n" );
	printf( "       8     7   5  10\n" );
	printf( "       9    12   2   6\n" );
	printf( "      10     8   7  11\n" );
	printf( "      11     5   1  10\n" );
	printf( "      12     8   4  12\n" );
	printf( "    # Generated by triangle -pqc box.poly\n\n" );
	printf(
		"  Here is the output file `box.1.poly'.  Note that segments have been added\n"
		);
	printf(
		"  to represent the convex hull, and some segments have been split by newly\n"
		);
	printf(
		"  added points.  Note also that <# of points> is set to zero to indicate\n" );
	printf( "  that the points should be read from the .node file.\n\n" );
	printf( "    0  2  0  1\n" );
	printf( "    12  1\n" );
	printf( "       1     1   9     5\n" );
	printf( "       2     5   7     1\n" );
	printf( "       3     8   7     1\n" );
	printf( "       4     6   8    10\n" );
	printf( "       5     5   6     1\n" );
	printf( "       6     3  10     1\n" );
	printf( "       7     4  11     1\n" );
	printf( "       8     2  12     1\n" );
	printf( "       9     9   2     5\n" );
	printf( "      10    10   1     1\n" );
	printf( "      11    11   3     1\n" );
	printf( "      12    12   4     1\n" );
	printf( "    1\n" );
	printf( "       1   1.5 1.5\n" );
	printf( "    # Generated by triangle -pqc box.poly\n\n" );
	printf( "Refinement and Area Constraints:\n\n" );
	printf(
		"  The -r switch causes a mesh (.node and .ele files) to be read and\n" );
	printf(
		"  refined.  If the -p switch is also used, a .poly file is read and used to\n"
		);
	printf(
		"  specify edges that are constrained and cannot be eliminated (although\n" );
	printf(
		"  they can be divided into smaller edges) by the refinement process.\n" );
	printf( "\n" );
	printf(
		"  When you refine a mesh, you generally want to impose tighter quality\n" );
	printf(
		"  constraints.  One way to accomplish this is to use -q with a larger\n" );
	printf(
		"  angle, or -a followed by a smaller area than you used to generate the\n" );
	printf(
		"  mesh you are refining.  Another way to do this is to create an .area\n" );
	printf(
		"  file, which specifies a maximum area for each triangle, and use the -a\n" );
	printf(
		"  switch (without a number following).  Each triangle's area constraint is\n"
		);
	printf(
		"  applied to that triangle.  Area constraints tend to diffuse as the mesh\n" );
	printf(
		"  is refined, so if there are large variations in area constraint between\n" );
	printf( "  adjacent triangles, you may not get the results you want.\n\n" );
	printf(
		"  If you are refining a mesh composed of linear (three-node) elements, the\n"
		);
	printf(
		"  output mesh will contain all the nodes present in the input mesh, in the\n"
		);
	printf(
		"  same order, with new nodes added at the end of the .node file.  However,\n"
		);
	printf(
		"  there is no guarantee that each output element is contained in a single\n" );
	printf(
		"  input element.  Often, output elements will overlap two input elements,\n" );
	printf(
		"  and input edges are not present in the output mesh.  Hence, a sequence of\n"
		);
	printf(
		"  refined meshes will form a hierarchy of nodes, but not a hierarchy of\n" );
	printf(
		"  elements.  If you a refining a mesh of higher-order elements, the\n" );
	printf(
		"  hierarchical property applies only to the nodes at the corners of an\n" );
	printf( "  element; other nodes may not be present in the refined mesh.\n\n" );
	printf(
		"  It is important to understand that maximum area constraints in .poly\n" );
	printf(
		"  files are handled differently from those in .area files.  A maximum area\n"
		);
	printf(
		"  in a .poly file applies to the whole (segment-bounded) region in which a\n"
		);
	printf(
		"  point falls, whereas a maximum area in an .area file applies to only one\n"
		);
	printf(
		"  triangle.  Area constraints in .poly files are used only when a mesh is\n" );
	printf(
		"  first generated, whereas area constraints in .area files are used only to\n"
		);
	printf(
		"  refine an existing mesh, and are typically based on a posteriori error\n" );
	printf(
		"  estimates resulting from a finite element simulation on that mesh.\n" );
	printf( "\n" );
	printf(
		"  `triangle -rq25 object.1' will read object.1.node and object.1.ele, then\n"
		);
	printf(
		"  refine the triangulation to enforce a 25 degree minimum angle, and then\n" );
	printf(
		"  write the refined triangulation to object.2.node and object.2.ele.\n" );
	printf( "\n" );
	printf(
		"  `triangle -rpaa6.2 z.3' will read z.3.node, z.3.ele, z.3.poly, and\n" );
	printf(
		"  z.3.area.  After reconstructing the mesh and its segments, Triangle will\n"
		);
	printf(
		"  refine the mesh so that no triangle has area greater than 6.2, and\n" );
	printf(
		"  furthermore the triangles satisfy the maximum area constraints in\n" );
	printf(
		"  z.3.area.  The output is written to z.4.node, z.4.ele, and z.4.poly.\n" );
	printf( "\n" );
	printf(
		"  The sequence `triangle -qa1 x', `triangle -rqa.3 x.1', `triangle -rqa.1\n" );
	printf(
		"  x.2' creates a sequence of successively finer meshes x.1, x.2, and x.3,\n" );
	printf( "  suitable for multigrid.\n\n" );
	printf( "Convex Hulls and Mesh Boundaries:\n\n" );
	printf(
		"  If the input is a point set (rather than a PSLG), Triangle produces its\n" );
	printf(
		"  convex hull as a by-product in the output .poly file if you use the -c\n" );
	printf(
		"  switch.  There are faster algorithms for finding a two-dimensional convex\n"
		);
	printf(
		"  hull than triangulation, of course, but this one comes for free.  If the\n"
		);
	printf(
		"  input is an unconstrained mesh (you are using the -r switch but not the\n" );
	printf(
		"  -p switch), Triangle produces a list of its boundary edges (including\n" );
	printf( "  hole boundaries) as a by-product if you use the -c switch.\n\n" );
	printf( "Voronoi Diagrams:\n\n" );
	printf(
		"  The -v switch produces a Voronoi diagram, in files suffixed .v.node and\n" );
	printf(
		"  .v.edge.  For example, `triangle -v points' will read points.node,\n" );
	printf(
		"  produce its Delaunay triangulation in points.1.node and points.1.ele,\n" );
	printf(
		"  and produce its Voronoi diagram in points.1.v.node and points.1.v.edge.\n" );
	printf(
		"  The .v.node file contains a list of all Voronoi vertices, and the .v.edge\n"
		);
	printf(
		"  file contains a list of all Voronoi edges, some of which may be infinite\n"
		);
	printf(
		"  rays.  (The choice of filenames makes it easy to run the set of Voronoi\n" );
	printf( "  vertices through Triangle, if so desired.)\n\n" );
	printf(
		"  This implementation does not use exact arithmetic to compute the Voronoi\n"
		);
	printf(
		"  vertices, and does not check whether neighboring vertices are identical.\n"
		);
	printf(
		"  Be forewarned that if the Delaunay triangulation is degenerate or\n" );
	printf(
		"  near-degenerate, the Voronoi diagram may have duplicate points, crossing\n"
		);
	printf(
		"  edges, or infinite rays whose direction vector is zero.  Also, if you\n" );
	printf(
		"  generate a constrained (as opposed to conforming) Delaunay triangulation,\n"
		);
	printf(
		"  or if the triangulation has holes, the corresponding Voronoi diagram is\n" );
	printf( "  likely to have crossing edges and unlikely to make sense.\n\n" );
	printf( "Mesh Topology:\n\n" );
	printf(
		"  You may wish to know which triangles are adjacent to a certain Delaunay\n" );
	printf(
		"  edge in an .edge file, which Voronoi regions are adjacent to a certain\n" );
	printf(
		"  Voronoi edge in a .v.edge file, or which Voronoi regions are adjacent to\n"
		);
	printf(
		"  each other.  All of this information can be found by cross-referencing\n" );
	printf(
		"  output files with the recollection that the Delaunay triangulation and\n" );
	printf( "  the Voronoi diagrams are planar duals.\n\n" );
	printf(
		"  Specifically, edge i of an .edge file is the dual of Voronoi edge i of\n" );
	printf(
		"  the corresponding .v.edge file, and is rotated 90 degrees counterclock-\n" );
	printf(
		"  wise from the Voronoi edge.  Triangle j of an .ele file is the dual of\n" );
	printf(
		"  vertex j of the corresponding .v.node file; and Voronoi region k is the\n" );
	printf( "  dual of point k of the corresponding .node file.\n\n" );
	printf(
		"  Hence, to find the triangles adjacent to a Delaunay edge, look at the\n" );
	printf(
		"  vertices of the corresponding Voronoi edge; their dual triangles are on\n" );
	printf(
		"  the left and right of the Delaunay edge, respectively.  To find the\n" );
	printf(
		"  Voronoi regions adjacent to a Voronoi edge, look at the endpoints of the\n"
		);
	printf(
		"  corresponding Delaunay edge; their dual regions are on the right and left\n"
		);
	printf(
		"  of the Voronoi edge, respectively.  To find which Voronoi regions are\n" );
	printf( "  adjacent to each other, just read the list of Delaunay edges.\n" );
	printf( "\n" );
	printf( "Statistics:\n" );
	printf( "\n" );
	printf(
		"  After generating a mesh, Triangle prints a count of the number of points,\n"
		);
	printf(
		"  triangles, edges, boundary edges, and segments in the output mesh.  If\n" );
	printf(
		"  you've forgotten the statistics for an existing mesh, the -rNEP switches\n"
		);
	printf(
		"  (or -rpNEP if you've got a .poly file for the existing mesh) will\n" );
	printf( "  regenerate these statistics without writing any output.\n\n" );
	printf(
		"  The -V switch produces extended statistics, including a rough estimate\n" );
	printf(
		"  of memory use and a histogram of triangle aspect ratios and angles in the\n"
		);
	printf( "  mesh.\n\n" );
	printf( "Exact Arithmetic:\n\n" );
	printf(
		"  Triangle uses adaptive exact arithmetic to perform what computational\n" );
	printf(
		"  geometers call the `orientation' and `incircle' tests.  If the floating-\n"
		);
	printf(
		"  point arithmetic of your machine conforms to the IEEE 754 standard (as\n" );
	printf(
		"  most workstations do), and does not use extended precision internal\n" );
	printf(
		"  registers, then your output is guaranteed to be an absolutely true\n" );
	printf( "  Delaunay or conforming Delaunay triangulation, roundoff error\n" );
	printf(
		"  notwithstanding.  The word `adaptive' implies that these arithmetic\n" );
	printf(
		"  routines compute the result only to the precision necessary to guarantee\n"
		);
	printf(
		"  correctness, so they are usually nearly as fast as their approximate\n" );
	printf(
		"  counterparts.  The exact tests can be disabled with the -X switch.  On\n" );
	printf(
		"  most inputs, this switch will reduce the computation time by about eight\n"
		);
	printf(
		"  percent - it's not worth the risk.  There are rare difficult inputs\n" );
	printf(
		"  (having many collinear and cocircular points), however, for which the\n" );
	printf(
		"  difference could be a factor of two.  These are precisely the inputs most\n"
		);
	printf( "  likely to cause errors if you use the -X switch.\n\n" );
	printf(
		"  Unfortunately, these routines don't solve every numerical problem.  Exact\n"
		);
	printf(
		"  arithmetic is not used to compute the positions of points, because the\n" );
	printf(
		"  bit complexity of point coordinates would grow without bound.  Hence,\n" );
	printf(
		"  segment intersections aren't computed exactly; in very unusual cases,\n" );
	printf(
		"  roundoff error in computing an intersection point might actually lead to\n"
		);
	printf(
		"  an inverted triangle and an invalid triangulation.  (This is one reason\n" );
	printf(
		"  to compute your own intersection points in your .poly files.)  Similarly,\n"
		);
	printf(
		"  exact arithmetic is not used to compute the vertices of the Voronoi\n" );
	printf( "  diagram.\n\n" );
	printf(
		"  Underflow and overflow can also cause difficulties; the exact arithmetic\n"
		);
	printf(
		"  routines do not ameliorate out-of-bounds exponents, which can arise\n" );
	printf(
		"  during the orientation and incircle tests.  As a rule of thumb, you\n" );
	printf(
		"  should ensure that your input values are within a range such that their\n" );
	printf(
		"  third powers can be taken without underflow or overflow.  Underflow can\n" );
	printf(
		"  silently prevent the tests from being performed exactly, while overflow\n" );
	printf( "  will typically cause a floating exception.\n\n" );
	printf( "Calling Triangle from Another Program:\n\n" );
	printf( "  Read the file triangle.h for details.\n\n" );
	printf( "Troubleshooting:\n\n" );
	printf( "  Please read this section before mailing me bugs.\n\n" );
	printf( "  `My output mesh has no triangles!'\n\n" );
	printf(
		"    If you're using a PSLG, you've probably failed to specify a proper set\n"
		);
	printf(
		"    of bounding segments, or forgotten to use the -c switch.  Or you may\n" );
	printf(
		"    have placed a hole badly.  To test these possibilities, try again with\n"
		);
	printf(
		"    the -c and -O switches.  Alternatively, all your input points may be\n" );
	printf(
		"    collinear, in which case you can hardly expect to triangulate them.\n" );
	printf( "\n" );
	printf( "  `Triangle doesn't terminate, or just crashes.'\n" );
	printf( "\n" );
	printf(
		"    Bad things can happen when triangles get so small that the distance\n" );
	printf(
		"    between their vertices isn't much larger than the precision of your\n" );
	printf(
		"    machine's arithmetic.  If you've compiled Triangle for single-precision\n"
		);
	printf(
		"    arithmetic, you might do better by recompiling it for double-precision.\n"
		);
	printf(
		"    Then again, you might just have to settle for more lenient constraints\n"
		);
	printf(
		"    on the minimum angle and the maximum area than you had planned.\n" );
	printf( "\n" );
	printf(
		"    You can minimize precision problems by ensuring that the origin lies\n" );
	printf(
		"    inside your point set, or even inside the densest part of your\n" );
	printf(
		"    mesh.  On the other hand, if you're triangulating an object whose x\n" );
	printf(
		"    coordinates all fall between 6247133 and 6247134, you're not leaving\n" );
	printf( "    much floating-point precision for Triangle to work with.\n\n" );
	printf(
		"    Precision problems can occur covertly if the input PSLG contains two\n" );
	printf(
		"    segments that meet (or intersect) at a very small angle, or if such an\n"
		);
	printf(
		"    angle is introduced by the -c switch, which may occur if a point lies\n" );
	printf(
		"    ever-so-slightly inside the convex hull, and is connected by a PSLG\n" );
	printf(
		"    segment to a point on the convex hull.  If you don't realize that a\n" );
	printf(
		"    small angle is being formed, you might never discover why Triangle is\n" );
	printf(
		"    crashing.  To check for this possibility, use the -S switch (with an\n" );
	printf(
		"    appropriate limit on the number of Steiner points, found by trial-and-\n"
		);
	printf(
		"    error) to stop Triangle early, and view the output .poly file with\n" );
	printf(
		"    Show Me (described below).  Look carefully for small angles between\n" );
	printf(
		"    segments; zoom in closely, as such segments might look like a single\n" );
	printf( "    segment from a distance.\n\n" );
	printf(
		"    If some of the input values are too large, Triangle may suffer a\n" );
	printf(
		"    floating exception due to overflow when attempting to perform an\n" );
	printf(
		"    orientation or incircle test.  (Read the section on exact arithmetic\n" );
	printf(
		"    above.)  Again, I recommend compiling Triangle for double (rather\n" );
	printf( "    than single) precision arithmetic.\n\n" );
	printf(
		"  `The numbering of the output points doesn't match the input points.'\n" );
	printf( "\n" );
	printf(
		"    You may have eaten some of your input points with a hole, or by placing\n"
		);
	printf( "    them outside the area enclosed by segments.\n\n" );
	printf(
		"  `Triangle executes without incident, but when I look at the resulting\n" );
	printf(
		"  mesh, it has overlapping triangles or other geometric inconsistencies.'\n" );
	printf( "\n" );
	printf(
		"    If you select the -X switch, Triangle's divide-and-conquer Delaunay\n" );
	printf(
		"    triangulation algorithm occasionally makes mistakes due to floating-\n" );
	printf(
		"    point roundoff error.  Although these errors are rare, don't use the -X\n"
		);
	printf( "    switch.  If you still have problems, please report the bug.\n" );
	printf( "\n" );
	printf(
		"  Strange things can happen if you've taken liberties with your PSLG.  Do\n" );
	printf(
		"  you have a point lying in the middle of a segment?  Triangle sometimes\n" );
	printf(
		"  copes poorly with that sort of thing.  Do you want to lay out a collinear\n"
		);
	printf(
		"  row of evenly spaced, segment-connected points?  Have you simply defined\n"
		);
	printf(
		"  one long segment connecting the leftmost point to the rightmost point,\n" );
	printf(
		"  and a bunch of points lying along it?  This method occasionally works,\n" );
	printf(
		"  especially with horizontal and vertical lines, but often it doesn't, and\n"
		);
	printf(
		"  you'll have to connect each adjacent pair of points with a separate\n" );
	printf( "  segment.  If you don't like it, tough.\n\n" );
	printf(
		"  Furthermore, if you have segments that intersect other than at their\n" );
	printf(
		"  endpoints, try not to let the intersections fall extremely close to PSLG\n"
		);
	printf( "  points or each other.\n\n" );
	printf(
		"  If you have problems refining a triangulation not produced by Triangle:\n" );
	printf(
		"  Are you sure the triangulation is geometrically valid?  Is it formatted\n" );
	printf(
		"  correctly for Triangle?  Are the triangles all listed so the first three\n"
		);
	printf( "  points are their corners in counterclockwise order?\n\n" );
	printf( "Show Me:\n\n" );
	printf(
		"  Triangle comes with a separate program named `Show Me', whose primary\n" );
	printf(
		"  purpose is to draw meshes on your screen or in PostScript.  Its secondary\n"
		);
	printf(
		"  purpose is to check the validity of your input files, and do so more\n" );
	printf(
		"  thoroughly than Triangle does.  Show Me requires that you have the X\n" );
	printf(
		"  Windows system.  If you didn't receive Show Me with Triangle, complain to\n"
		);
	printf( "  whomever you obtained Triangle from, then send me mail.\n\n" );
	printf( "Triangle on the Web:\n\n" );
	printf(
		"  To see an illustrated, updated version of these instructions, check out\n" );
	printf( "\n" );
	printf( "    http://www.cs.cmu.edu/~quake/triangle.html\n" );
	printf( "\n" );
	printf( "A Brief Plea:\n" );
	printf( "\n" );
	printf(
		"  If you use Triangle, and especially if you use it to accomplish real\n" );
	printf(
		"  work, I would like very much to hear from you.  A short letter or email\n" );
	printf(
		"  (to jrs@cs.cmu.edu) describing how you use Triangle will mean a lot to\n" );
	printf(
		"  me.  The more people I know are using this program, the more easily I can\n"
		);
	printf(
		"  justify spending time on improvements and on the three-dimensional\n" );
	printf(
		"  successor to Triangle, which in turn will benefit you.  Also, I can put\n" );
	printf(
		"  you on a list to receive email whenever a new version of Triangle is\n" );
	printf( "  available.\n\n" );
	printf(
		"  If you use a mesh generated by Triangle in a publication, please include\n"
		);
	printf( "  an acknowledgment as well.\n\n" );
	printf( "Research credit:\n\n" );
	printf(
		"  Of course, I can take credit for only a fraction of the ideas that made\n" );
	printf(
		"  this mesh generator possible.  Triangle owes its existence to the efforts\n"
		);
	printf(
		"  of many fine computational geometers and other researchers, including\n" );
	printf(
		"  Marshall Bern, L. Paul Chew, Boris Delaunay, Rex A. Dwyer, David\n" );
	printf(
		"  Eppstein, Steven Fortune, Leonidas J. Guibas, Donald E. Knuth, C. L.\n" );
	printf(
		"  Lawson, Der-Tsai Lee, Ernst P. Mucke, Douglas M. Priest, Jim Ruppert,\n" );
	printf(
		"  Isaac Saias, Bruce J. Schachter, Micha Sharir, Jorge Stolfi, Christopher\n"
		);
	printf(
		"  J. Van Wyk, David F. Watson, and Binhai Zhu.  See the comments at the\n" );
	printf( "  beginning of the source code for references.\n\n" );
	exit( 0 );
}

#endif /* not TRILIBRARY */

/*****************************************************************************/
/*                                                                           */
/*  internalerror()   Ask the user to send me the defective product.  Exit.  */
/*                                                                           */
/*****************************************************************************/

void internalerror(){
	printf( "  Please report this bug to jrs@cs.cmu.edu\n" );
	printf( "  Include the message above, your input data set, and the exact\n" );
	printf( "    command line you used to run Triangle.\n" );
	exit( 1 );
}

/*****************************************************************************/
/*                                                                           */
/*  parsecommandline()   Read the command line, identify switches, and set   */
/*                       up options and file names.                          */
/*                                                                           */
/*  The effects of this routine are felt entirely through global variables.  */
/*                                                                           */
/*****************************************************************************/

void parsecommandline( argc, argv )
int argc;
char **argv;
{
#ifdef TRILIBRARY
#define STARTINDEX 0
#else /* not TRILIBRARY */
#define STARTINDEX 1
	int increment;
	int meshnumber;
#endif /* not TRILIBRARY */
	int i, j;
#ifndef CDT_ONLY
	int k;
	char workstring[FILENAMESIZE];
#endif

	poly = refine = quality = vararea = fixedarea = regionattrib = convex = 0;
	firstnumber = 1;
	edgesout = voronoi = neighbors = geomview = 0;
	nobound = nopolywritten = nonodewritten = noelewritten = noiterationnum = 0;
	noholes = noexact = 0;
	incremental = sweepline = 0;
	dwyer = 1;
	splitseg = 0;
	docheck = 0;
	nobisect = 0;
	steiner = -1;
	order = 1;
	minangle = 0.0;
	maxarea = -1.0;
	quiet = verbose = 0;
#ifndef TRILIBRARY
	innodefilename[0] = '\0';
#endif /* not TRILIBRARY */

	for ( i = STARTINDEX; i < argc; i++ ) {
#ifndef TRILIBRARY
		if ( argv[i][0] == '-' ) {
#endif /* not TRILIBRARY */
		for ( j = STARTINDEX; argv[i][j] != '\0'; j++ ) {
			if ( argv[i][j] == 'p' ) {
				poly = 1;
			}
#ifndef CDT_ONLY
			if ( argv[i][j] == 'r' ) {
				refine = 1;
			}
			if ( argv[i][j] == 'q' ) {
				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';
					minangle = (REAL) strtod( workstring, (char **) NULL );
				}
				else {
					minangle = 20.0;
				}
			}
			if ( argv[i][j] == 'a' ) {
				quality = 1;
				if ( ( ( argv[i][j + 1] >= '0' ) && ( argv[i][j + 1] <= '9' ) ) ||
					 ( argv[i][j + 1] == '.' ) ) {
					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';
					maxarea = (REAL) strtod( workstring, (char **) NULL );
					if ( maxarea <= 0.0 ) {
						printf( "Error:  Maximum area must be greater than zero.\n" );
						exit( 1 );
					}
				}
				else {
					vararea = 1;
				}
			}
#endif /* not CDT_ONLY */
			if ( argv[i][j] == 'A' ) {
				regionattrib = 1;
			}
			if ( argv[i][j] == 'c' ) {
				convex = 1;
			}
			if ( argv[i][j] == 'z' ) {
				firstnumber = 0;
			}
			if ( argv[i][j] == 'e' ) {
				edgesout = 1;
			}
			if ( argv[i][j] == 'v' ) {
				voronoi = 1;
			}
			if ( argv[i][j] == 'n' ) {
				neighbors = 1;
			}
			if ( argv[i][j] == 'g' ) {
				geomview = 1;
			}
			if ( argv[i][j] == 'B' ) {
				nobound = 1;
			}
			if ( argv[i][j] == 'P' ) {
				nopolywritten = 1;
			}
			if ( argv[i][j] == 'N' ) {
				nonodewritten = 1;
			}
			if ( argv[i][j] == 'E' ) {
				noelewritten = 1;
			}
#ifndef TRILIBRARY
			if ( argv[i][j] == 'I' ) {
				noiterationnum = 1;
			}
#endif /* not TRILIBRARY */
			if ( argv[i][j] == 'O' ) {
				noholes = 1;
			}
			if ( argv[i][j] == 'X' ) {
				noexact = 1;
			}
			if ( argv[i][j] == 'o' ) {
				if ( argv[i][j + 1] == '2' ) {
					j++;
					order = 2;
				}
			}
#ifndef CDT_ONLY
			if ( argv[i][j] == 'Y' ) {
				nobisect++;
			}
			if ( argv[i][j] == 'S' ) {
				steiner = 0;
				while ( ( argv[i][j + 1] >= '0' ) && ( argv[i][j + 1] <= '9' ) ) {
					j++;
					steiner = steiner * 10 + (int) ( argv[i][j] - '0' );
				}
			}
#endif /* not CDT_ONLY */
#ifndef REDUCED
			if ( argv[i][j] == 'i' ) {
				incremental = 1;
			}
			if ( argv[i][j] == 'F' ) {
				sweepline = 1;
			}
#endif /* not REDUCED */
			if ( argv[i][j] == 'l' ) {
				dwyer = 0;
			}
#ifndef REDUCED
#ifndef CDT_ONLY
			if ( argv[i][j] == 's' ) {
				splitseg = 1;
			}
#endif /* not CDT_ONLY */
			if ( argv[i][j] == 'C' ) {
				docheck = 1;
			}
#endif /* not REDUCED */
			if ( argv[i][j] == 'Q' ) {
				quiet = 1;
			}
			if ( argv[i][j] == 'V' ) {
				verbose++;
			}
#ifndef TRILIBRARY
			if ( ( argv[i][j] == 'h' ) || ( argv[i][j] == 'H' ) ||
				 ( argv[i][j] == '?' ) ) {
				info();
			}
#endif /* not TRILIBRARY */
		}
#ifndef TRILIBRARY
	} else {
		strncpy( innodefilename, argv[i], FILENAMESIZE - 1 );
		innodefilename[FILENAMESIZE - 1] = '\0';
	}
#endif /* not TRILIBRARY */
	}
#ifndef TRILIBRARY
	if ( innodefilename[0] == '\0' ) {
		syntax();
	}
	if ( !strcmp( &innodefilename[strlen( innodefilename ) - 5], ".node" ) ) {
		innodefilename[strlen( innodefilename ) - 5] = '\0';
	}
	if ( !strcmp( &innodefilename[strlen( innodefilename ) - 5], ".poly" ) ) {
		innodefilename[strlen( innodefilename ) - 5] = '\0';
		poly = 1;
	}
#ifndef CDT_ONLY
	if ( !strcmp( &innodefilename[strlen( innodefilename ) - 4], ".ele" ) ) {
		innodefilename[strlen( innodefilename ) - 4] = '\0';
		refine = 1;
	}
	if ( !strcmp( &innodefilename[strlen( innodefilename ) - 5], ".area" ) ) {
		innodefilename[strlen( innodefilename ) - 5] = '\0';
		refine = 1;
		quality = 1;
		vararea = 1;
	}
#endif /* not CDT_ONLY */
#endif /* not TRILIBRARY */
	steinerleft = steiner;
	useshelles = poly || refine || quality || convex;
	goodangle = (REAL)cos( minangle * PI / 180.0 );
	goodangle *= goodangle;
	if ( refine && noiterationnum ) {
		printf(
			"Error:  You cannot use the -I switch when refining a triangulation.\n" );
		exit( 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 ( !refine && !poly ) {
		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 ( refine || !poly ) {
		regionattrib = 0;
	}

#ifndef TRILIBRARY
	strcpy( inpolyfilename, innodefilename );
	strcpy( inelefilename, innodefilename );
	strcpy( areafilename, innodefilename );
	increment = 0;
	strcpy( workstring, innodefilename );
	j = 1;
	while ( workstring[j] != '\0' ) {
		if ( ( workstring[j] == '.' ) && ( workstring[j + 1] != '\0' ) ) {
			increment = j + 1;
		}
		j++;
	}
	meshnumber = 0;
	if ( increment > 0 ) {
		j = increment;
		do {
			if ( ( workstring[j] >= '0' ) && ( workstring[j] <= '9' ) ) {
				meshnumber = meshnumber * 10 + (int) ( workstring[j] - '0' );
			}
			else {
				increment = 0;
			}
			j++;
		} while ( workstring[j] != '\0' );
	}
	if ( noiterationnum ) {
		strcpy( outnodefilename, innodefilename );
		strcpy( outelefilename, innodefilename );
		strcpy( edgefilename, innodefilename );
		strcpy( vnodefilename, innodefilename );
		strcpy( vedgefilename, innodefilename );
		strcpy( neighborfilename, innodefilename );
		strcpy( offfilename, innodefilename );
		strcat( outnodefilename, ".node" );
		strcat( outelefilename, ".ele" );
		strcat( edgefilename, ".edge" );
		strcat( vnodefilename, ".v.node" );
		strcat( vedgefilename, ".v.edge" );
		strcat( neighborfilename, ".neigh" );
		strcat( offfilename, ".off" );
	}
	else if ( increment == 0 ) {
		strcpy( outnodefilename, innodefilename );
		strcpy( outpolyfilename, innodefilename );
		strcpy( outelefilename, innodefilename );
		strcpy( edgefilename, innodefilename );
		strcpy( vnodefilename, innodefilename );
		strcpy( vedgefilename, innodefilename );
		strcpy( neighborfilename, innodefilename );
		strcpy( offfilename, innodefilename );
		strcat( outnodefilename, ".1.node" );
		strcat( outpolyfilename, ".1.poly" );
		strcat( outelefilename, ".1.ele" );
		strcat( edgefilename, ".1.edge" );
		strcat( vnodefilename, ".1.v.node" );
		strcat( vedgefilename, ".1.v.edge" );
		strcat( neighborfilename, ".1.neigh" );
		strcat( offfilename, ".1.off" );
	}
	else {
		workstring[increment] = '%';
		workstring[increment + 1] = 'd';
		workstring[increment + 2] = '\0';
		sprintf( outnodefilename, workstring, meshnumber + 1 );
		strcpy( outpolyfilename, outnodefilename );
		strcpy( outelefilename, outnodefilename );
		strcpy( edgefilename, outnodefilename );
		strcpy( vnodefilename, outnodefilename );
		strcpy( vedgefilename, outnodefilename );
		strcpy( neighborfilename, outnodefilename );
		strcpy( offfilename, outnodefilename );
		strcat( outnodefilename, ".node" );
		strcat( outpolyfilename, ".poly" );
		strcat( outelefilename, ".ele" );
		strcat( edgefilename, ".edge" );
		strcat( vnodefilename, ".v.node" );
		strcat( vedgefilename, ".v.edge" );
		strcat( neighborfilename, ".neigh" );
		strcat( offfilename, ".off" );
	}
	strcat( innodefilename, ".node" );
	strcat( inpolyfilename, ".poly" );
	strcat( inelefilename, ".ele" );
	strcat( areafilename, ".area" );
#endif /* not TRILIBRARY */
}

/**                                                                         **/
/**                                                                         **/
/********* User interaction routines begin here                      *********/

/********* Debugging routines begin here                             *********/
/**                                                                         **/
/**                                                                         **/

/*****************************************************************************/
/*                                                                           */
/*  printtriangle()   Print out the details of a triangle/edge handle.       */
/*                                                                           */
/*  I originally wrote this procedure to simplify debugging; it can be       */
/*  called directly from the debugger, and presents information about a      */
/*  triangle/edge handle in digestible form.  It's also used when the        */
/*  highest level of verbosity (`-VVV') is specified.                        */
/*                                                                           */
/*****************************************************************************/

void printtriangle( t )
struct triedge *t;
{
	struct triedge printtri;
	struct edge printsh;
	point printpoint;

	printf( "triangle x%lx with orientation %d:\n", (unsigned long) t->tri,
			t->orient );
	decode( t->tri[0], printtri );
	if ( printtri.tri == dummytri ) {
		printf( "    [0] = Outer space\n" );
	}
	else {
		printf( "    [0] = x%lx  %d\n", (unsigned long) printtri.tri,
				printtri.orient );
	}
	decode( t->tri[1], printtri );
	if ( printtri.tri == dummytri ) {
		printf( "    [1] = Outer space\n" );
	}
	else {
		printf( "    [1] = x%lx  %d\n", (unsigned long) printtri.tri,
				printtri.orient );
	}
	decode( t->tri[2], printtri );
	if ( printtri.tri == dummytri ) {
		printf( "    [2] = Outer space\n" );
	}
	else {
		printf( "    [2] = x%lx  %d\n", (unsigned long) printtri.tri,
				printtri.orient );
	}
	org( *t, printpoint );
	if ( printpoint == (point) NULL ) {
		printf( "    Origin[%d] = NULL\n", ( t->orient + 1 ) % 3 + 3 );
	}
	else{
		printf( "    Origin[%d] = x%lx  (%.12g, %.12g)\n",
				( t->orient + 1 ) % 3 + 3, (unsigned long) printpoint,
				printpoint[0], printpoint[1] );
	}
	dest( *t, printpoint );
	if ( printpoint == (point) NULL ) {
		printf( "    Dest  [%d] = NULL\n", ( t->orient + 2 ) % 3 + 3 );
	}
	else{
		printf( "    Dest  [%d] = x%lx  (%.12g, %.12g)\n",
				( t->orient + 2 ) % 3 + 3, (unsigned long) printpoint,
				printpoint[0], printpoint[1] );
	}
	apex( *t, printpoint );
	if ( printpoint == (point) NULL ) {
		printf( "    Apex  [%d] = NULL\n", t->orient + 3 );
	}
	else{
		printf( "    Apex  [%d] = x%lx  (%.12g, %.12g)\n",
				t->orient + 3, (unsigned long) printpoint,
				printpoint[0], printpoint[1] );
	}
	if ( useshelles ) {
		sdecode( t->tri[6], printsh );
		if ( printsh.sh != dummysh ) {
			printf( "    [6] = x%lx  %d\n", (unsigned long) printsh.sh,
					printsh.shorient );
		}
		sdecode( t->tri[7], printsh );
		if ( printsh.sh != dummysh ) {
			printf( "    [7] = x%lx  %d\n", (unsigned long) printsh.sh,
					printsh.shorient );
		}
		sdecode( t->tri[8], printsh );
		if ( printsh.sh != dummysh ) {
			printf( "    [8] = x%lx  %d\n", (unsigned long) printsh.sh,
					printsh.shorient );
		}
	}
	if ( vararea ) {
		printf( "    Area constraint:  %.4g\n", areabound( *t ) );
	}
}

/*****************************************************************************/
/*                                                                           */
/*  printshelle()   Print out the details of a shell edge handle.            */
/*                                                                           */
/*  I originally wrote this procedure to simplify debugging; it can be       */
/*  called directly from the debugger, and presents information about a      */
/*  shell edge handle in digestible form.  It's also used when the highest   */
/*  level of verbosity (`-VVV') is specified.                                */
/*                                                                           */
/*****************************************************************************/

void printshelle( s )
struct edge *s;
{
	struct edge printsh;
	struct triedge printtri;
	point printpoint;

	printf( "shell edge x%lx with orientation %d and mark %d:\n",
			(unsigned long) s->sh, s->shorient, mark( *s ) );
	sdecode( s->sh[0], printsh );
	if ( printsh.sh == dummysh ) {
		printf( "    [0] = No shell\n" );
	}
	else {
		printf( "    [0] = x%lx  %d\n", (unsigned long) printsh.sh,
				printsh.shorient );
	}
	sdecode( s->sh[1], printsh );
	if ( printsh.sh == dummysh ) {
		printf( "    [1] = No shell\n" );
	}
	else {
		printf( "    [1] = x%lx  %d\n", (unsigned long) printsh.sh,
				printsh.shorient );
	}
	sorg( *s, printpoint );
	if ( printpoint == (point) NULL ) {
		printf( "    Origin[%d] = NULL\n", 2 + s->shorient );
	}
	else{
		printf( "    Origin[%d] = x%lx  (%.12g, %.12g)\n",
				2 + s->shorient, (unsigned long) printpoint,
				printpoint[0], printpoint[1] );
	}
	sdest( *s, printpoint );
	if ( printpoint == (point) NULL ) {
		printf( "    Dest  [%d] = NULL\n", 3 - s->shorient );
	}
	else{
		printf( "    Dest  [%d] = x%lx  (%.12g, %.12g)\n",
				3 - s->shorient, (unsigned long) printpoint,
				printpoint[0], printpoint[1] );
	}
	decode( s->sh[4], printtri );
	if ( printtri.tri == dummytri ) {
		printf( "    [4] = Outer space\n" );
	}
	else {
		printf( "    [4] = x%lx  %d\n", (unsigned long) printtri.tri,
				printtri.orient );
	}
	decode( s->sh[5], printtri );
	if ( printtri.tri == dummytri ) {
		printf( "    [5] = Outer space\n" );
	}
	else {
		printf( "    [5] = x%lx  %d\n", (unsigned long) printtri.tri,
				printtri.orient );
	}
}

/**                                                                         **/
/**                                                                         **/
/********* Debugging routines end here                               *********/

/********* Memory management routines begin here                     *********/
/**                                                                         **/
/**                                                                         **/

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

void poolinit( pool, bytecount, itemcount, wtype, alignment )
struct memorypool *pool;
int bytecount;
int itemcount;
enum wordtype wtype;
int alignment;
{
	int wordsize;

	/* Initialize values in the pool. */
	pool->itemwordtype = wtype;
	wordsize = ( pool->itemwordtype == POINTER ) ? sizeof( VOID * ) : sizeof( REAL );
	/* Find the proper alignment, which must be at least as large as:   */
	/*   - The parameter `alignment'.                                   */
	/*   - The primary word type, to avoid unaligned accesses.          */
	/*   - sizeof(VOID *), so the stack of dead items can be maintained */
	/*       without unaligned accesses.                                */
	if ( alignment > wordsize ) {
		pool->alignbytes = alignment;
	}
	else {
		pool->alignbytes = wordsize;
	}
	if ( sizeof( VOID * ) > pool->alignbytes ) {
		pool->alignbytes = sizeof( VOID * );
	}
	pool->itemwords = ( ( bytecount + pool->alignbytes - 1 ) / pool->alignbytes )
					  * ( pool->alignbytes / wordsize );
	pool->itembytes = pool->itemwords * wordsize;
	pool->itemsperblock = itemcount;

	/* Allocate a block of items.  Space for `itemsperblock' items and one    */
	/*   pointer (to point to the next block) are allocated, as well as space */
	/*   to ensure alignment of the items.                                    */
	pool->firstblock = (VOID **) malloc( pool->itemsperblock * pool->itembytes
										 + sizeof( VOID * ) + pool->alignbytes );
	if ( pool->firstblock == (VOID **) NULL ) {
		printf( "Error:  Out of memory.\n" );
		exit( 1 );
	}
	/* Set the next block pointer to NULL. */
	*( pool->firstblock ) = (VOID *) NULL;
	poolrestart( pool );
}

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

void poolrestart( pool )
struct memorypool *pool;
{
	unsigned long alignptr;

	pool->items = 0;
	pool->maxitems = 0;

	/* Set the currently active block. */
	pool->nowblock = pool->firstblock;
	/* Find the first item in the pool.  Increment by the size of (VOID *). */
	alignptr = (unsigned long) ( pool->nowblock + 1 );
	/* Align the item on an `alignbytes'-byte boundary. */
	pool->nextitem = (VOID *)
					 ( alignptr + (unsigned long) pool->alignbytes
					   - ( alignptr % (unsigned long) pool->alignbytes ) );
	/* There are lots of unallocated items left in this block. */
	pool->unallocateditems = pool->itemsperblock;
	/* The stack of deallocated items is empty. */
	pool->deaditemstack = (VOID *) NULL;
}

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

void pooldeinit( pool )
struct memorypool *pool;
{
	while ( pool->firstblock != (VOID **) NULL ) {
		pool->nowblock = (VOID **) *( pool->firstblock );
		free( pool->firstblock );
		pool->firstblock = pool->nowblock;
	}
}

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

VOID *poolalloc( pool )
struct memorypool *pool;
{
	VOID *newitem;
	VOID **newblock;
	unsigned long alignptr;

	/* First check the linked list of dead items.  If the list is not   */
	/*   empty, allocate an item from the list rather than a fresh one. */
	if ( pool->deaditemstack != (VOID *) NULL ) {
		newitem = pool->deaditemstack;           /* Take first item in list. */
		pool->deaditemstack = *(VOID **) pool->deaditemstack;
	}
	else {
		/* Check if there are any free items left in the current block. */
		if ( pool->unallocateditems == 0 ) {
			/* Check if another block must be allocated. */
			if ( *( pool->nowblock ) == (VOID *) NULL ) {
				/* Allocate a new block of items, pointed to by the previous block. */
				newblock = (VOID **) malloc( pool->itemsperblock * pool->itembytes
											 + sizeof( VOID * ) + pool->alignbytes );
				if ( newblock == (VOID **) NULL ) {
					printf( "Error:  Out of memory.\n" );
					exit( 1 );
				}
				*( pool->nowblock ) = (VOID *) newblock;
				/* The next block pointer is NULL. */
				*newblock = (VOID *) NULL;
			}
			/* Move to the new block. */
			pool->nowblock = (VOID **) *( pool->nowblock );
			/* Find the first item in the block.    */
			/*   Increment by the size of (VOID *). */
			alignptr = (unsigned long) ( pool->nowblock + 1 );
			/* Align the item on an `alignbytes'-byte boundary. */
			pool->nextitem = (VOID *)
							 ( alignptr + (unsigned long) pool->alignbytes
							   - ( alignptr % (unsigned long) pool->alignbytes ) );
			/* There are lots of unallocated items left in this block. */
			pool->unallocateditems = pool->itemsperblock;
		}
		/* Allocate a new item. */
		newitem = pool->nextitem;
		/* Advance `nextitem' pointer to next free item in block. */
		if ( pool->itemwordtype == POINTER ) {
			pool->nextitem = (VOID *) ( (VOID **) pool->nextitem + pool->itemwords );
		}
		else {
			pool->nextitem = (VOID *) ( (REAL *) pool->nextitem + pool->itemwords );
		}
		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.              */
/*                                                                           */
/*****************************************************************************/

void pooldealloc( pool, dyingitem )
struct memorypool *pool;
VOID *dyingitem;
{
	/* Push freshly killed item onto stack. */
	*( (VOID **) dyingitem ) = pool->deaditemstack;
	pool->deaditemstack = dyingitem;
	pool->items--;
}

/*****************************************************************************/
/*                                                                           */
/*  traversalinit()   Prepare to traverse the entire list of items.          */
/*                                                                           */
/*  This routine is used in conjunction with traverse().                     */
/*                                                                           */
/*****************************************************************************/

void traversalinit( pool )
struct memorypool *pool;
{
	unsigned long alignptr;

	/* Begin the traversal in the first block. */
	pool->pathblock = pool->firstblock;
	/* Find the first item in the block.  Increment by the size of (VOID *). */
	alignptr = (unsigned long) ( pool->pathblock + 1 );
	/* Align with item on an `alignbytes'-byte boundary. */
	pool->pathitem = (VOID *)
					 ( alignptr + (unsigned long) pool->alignbytes
					   - ( alignptr % (unsigned long) pool->alignbytes ) );
	/* Set the number of items left in the current block. */
	pool->pathitemsleft = pool->itemsperblock;
}

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

VOID *traverse( pool )
struct memorypool *pool;
{
	VOID *newitem;
	unsigned long alignptr;

	/* Stop upon exhausting the list of items. */
	if ( pool->pathitem == pool->nextitem ) {
		return (VOID *) NULL;
	}
	/* Check whether any untraversed items remain in the current block. */
	if ( pool->pathitemsleft == 0 ) {
		/* Find the next block. */
		pool->pathblock = (VOID **) *( pool->pathblock );
		/* Find the first item in the block.  Increment by the size of (VOID *). */
		alignptr = (unsigned long) ( pool->pathblock + 1 );
		/* Align with item on an `alignbytes'-byte boundary. */
		pool->pathitem = (VOID *)
						 ( alignptr + (unsigned long) pool->alignbytes
						   - ( alignptr % (unsigned long) pool->alignbytes ) );
		/* Set the number of items left in the current block. */
		pool->pathitemsleft = pool->itemsperblock;
	}
	newitem = pool->pathitem;
	/* Find the next item in the block. */
	if ( pool->itemwordtype == POINTER ) {
		pool->pathitem = (VOID *) ( (VOID **) pool->pathitem + pool->itemwords );
	}
	else {
		pool->pathitem = (VOID *) ( (REAL *) pool->pathitem + pool->itemwords );
	}
	pool->pathitemsleft--;
	return newitem;
}

/*****************************************************************************/
/*                                                                           */
/*  dummyinit()   Initialize the triangle that fills "outer space" and the   */
/*                omnipresent shell edge.                                    */
/*                                                                           */
/*  The triangle that fills "outer space", called `dummytri', is pointed to  */
/*  by every triangle and shell edge 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 shell edge, `dummysh', is pointed to by every triangle   */
/*  or shell edge that doesn't have a full complement of real shell edges    */
/*  to point to.                                                             */
/*                                                                           */
/*****************************************************************************/

void dummyinit( trianglewords, shellewords )
int trianglewords;
int shellewords;
{
	unsigned long alignptr;

	/* `triwords' and `shwords' are used by the mesh manipulation primitives */
	/*   to extract orientations of triangles and shell edges from pointers. */
	triwords = trianglewords;     /* Initialize `triwords' once and for all. */
	shwords = shellewords;         /* Initialize `shwords' once and for all. */

	/* Set up `dummytri', the `triangle' that occupies "outer space". */
	dummytribase = (triangle *) malloc( triwords * sizeof( triangle )
										+ triangles.alignbytes );
	if ( dummytribase == (triangle *) NULL ) {
		printf( "Error:  Out of memory.\n" );
		exit( 1 );
	}
	/* Align `dummytri' on a `triangles.alignbytes'-byte boundary. */
	alignptr = (unsigned long) dummytribase;
	dummytri = (triangle *)
			   ( alignptr + (unsigned long) triangles.alignbytes
				 - ( alignptr % (unsigned long) 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.                                                       */
	dummytri[0] = (triangle) dummytri;
	dummytri[1] = (triangle) dummytri;
	dummytri[2] = (triangle) dummytri;
	/* Three NULL vertex points. */
	dummytri[3] = (triangle) NULL;
	dummytri[4] = (triangle) NULL;
	dummytri[5] = (triangle) NULL;

	if ( useshelles ) {
		/* Set up `dummysh', the omnipresent "shell edge" pointed to by any      */
		/*   triangle side or shell edge end that isn't attached to a real shell */
		/*   edge.                                                               */
		dummyshbase = (shelle *) malloc( shwords * sizeof( shelle )
										 + shelles.alignbytes );
		if ( dummyshbase == (shelle *) NULL ) {
			printf( "Error:  Out of memory.\n" );
			exit( 1 );
		}
		/* Align `dummysh' on a `shelles.alignbytes'-byte boundary. */
		alignptr = (unsigned long) dummyshbase;
		dummysh = (shelle *)
				  ( alignptr + (unsigned long) shelles.alignbytes
					- ( alignptr % (unsigned long) shelles.alignbytes ) );
		/* Initialize the two adjoining shell edges to be the omnipresent shell */
		/*   edge.  These will eventually be changed by various bonding         */
		/*   operations, but their values don't really matter, as long as they  */
		/*   can legally be dereferenced.                                       */
		dummysh[0] = (shelle) dummysh;
		dummysh[1] = (shelle) dummysh;
		/* Two NULL vertex points. */
		dummysh[2] = (shelle) NULL;
		dummysh[3] = (shelle) NULL;
		/* Initialize the two adjoining triangles to be "outer space". */
		dummysh[4] = (shelle) dummytri;
		dummysh[5] = (shelle) dummytri;
		/* Set the boundary marker to zero. */
		*(int *) ( dummysh + 6 ) = 0;

		/* Initialize the three adjoining shell edges of `dummytri' to be */
		/*   the omnipresent shell edge.                                  */
		dummytri[6] = (triangle) dummysh;
		dummytri[7] = (triangle) dummysh;
		dummytri[8] = (triangle) dummysh;
	}
}

/*****************************************************************************/
/*                                                                           */
/*  initializepointpool()   Calculate the size of the point data structure   */
/*                          and initialize its memory pool.                  */
/*                                                                           */
/*  This routine also computes the `pointmarkindex' and `point2triindex'     */
/*  indices used to find values within each point.                           */
/*                                                                           */
/*****************************************************************************/

void initializepointpool(){
	int pointsize;

	/* The index within each point at which the boundary marker is found.  */
	/*   Ensure the point marker is aligned to a sizeof(int)-byte address. */
	pointmarkindex = ( ( mesh_dim + nextras ) * sizeof( REAL ) + sizeof( int ) - 1 )
					 / sizeof( int );
	pointsize = ( pointmarkindex + 1 ) * sizeof( int );
	if ( poly ) {
		/* The index within each point at which a triangle pointer is found.   */
		/*   Ensure the pointer is aligned to a sizeof(triangle)-byte address. */
		point2triindex = ( pointsize + sizeof( triangle ) - 1 ) / sizeof( triangle );
		pointsize = ( point2triindex + 1 ) * sizeof( triangle );
	}
	/* Initialize the pool of points. */
	poolinit( &points, pointsize, POINTPERBLOCK,
			  ( sizeof( REAL ) >= sizeof( triangle ) ) ? FLOATINGPOINT : POINTER, 0 );
}

/*****************************************************************************/
/*                                                                           */
/*  initializetrisegpools()   Calculate the sizes of the triangle and shell  */
/*                            edge data structures and initialize their      */
/*                            memory pools.                                  */
/*                                                                           */
/*  This routine also computes the `highorderindex', `elemattribindex', and  */
/*  `areaboundindex' indices used to find values within each triangle.       */
/*                                                                           */
/*****************************************************************************/

void initializetrisegpools(){
	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 shell edges before the extra nodes.                */
	highorderindex = 6 + ( useshelles * 3 );
	/* The number of bytes occupied by a triangle. */
	trisize = ( ( order + 1 ) * ( order + 2 ) / 2 + ( highorderindex - 3 ) ) *
			  sizeof( triangle );
	/* The index within each triangle at which its attributes are found, */
	/*   where the index is measured in REALs.                           */
	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. */
	areaboundindex = elemattribindex + eextras + regionattrib;
	/* If triangle attributes or an area bound are needed, increase the number */
	/*   of bytes occupied by a triangle.                                      */
	if ( vararea ) {
		trisize = ( areaboundindex + 1 ) * sizeof( REAL );
	}
	else if ( eextras + regionattrib > 0 ) {
		trisize = 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 shell edges or       */
	/*   attributes or area constraint or extra nodes.                       */
	if ( ( voronoi || 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( &triangles, trisize, TRIPERBLOCK, POINTER, 4 );

	if ( useshelles ) {
		/* Initialize the pool of shell edges. */
		poolinit( &shelles, 6 * sizeof( triangle ) + sizeof( int ), SHELLEPERBLOCK,
				  POINTER, 4 );

		/* Initialize the "outer space" triangle and omnipresent shell edge. */
		dummyinit( triangles.itemwords, shelles.itemwords );
	}
	else {
		/* Initialize the "outer space" triangle. */
		dummyinit( triangles.itemwords, 0 );
	}
}

/*****************************************************************************/
/*                                                                           */
/*  triangledealloc()   Deallocate space for a triangle, marking it dead.    */
/*                                                                           */
/*****************************************************************************/

void triangledealloc( dyingtriangle )
triangle * dyingtriangle;
{
	/* Set triangle's vertices to NULL.  This makes it possible to        */
	/*   detect dead triangles when traversing the list of all triangles. */
	dyingtriangle[3] = (triangle) NULL;
	dyingtriangle[4] = (triangle) NULL;
	dyingtriangle[5] = (triangle) NULL;
	pooldealloc( &triangles, (VOID *) dyingtriangle );
}

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

triangle *triangletraverse(){
	triangle *newtriangle;

	do {
		newtriangle = (triangle *) traverse( &triangles );
		if ( newtriangle == (triangle *) NULL ) {
			return (triangle *) NULL;
		}
	} while ( newtriangle[3] == (triangle) NULL );        /* Skip dead ones. */
	return newtriangle;
}

/*****************************************************************************/
/*                                                                           */
/*  shelledealloc()   Deallocate space for a shell edge, marking it dead.    */
/*                                                                           */
/*****************************************************************************/

void shelledealloc( dyingshelle )
shelle * dyingshelle;
{
	/* Set shell edge's vertices to NULL.  This makes it possible to */
	/*   detect dead shells when traversing the list of all shells.  */
	dyingshelle[2] = (shelle) NULL;
	dyingshelle[3] = (shelle) NULL;
	pooldealloc( &shelles, (VOID *) dyingshelle );
}

/*****************************************************************************/
/*                                                                           */
/*  shelletraverse()   Traverse the shell edges, skipping dead ones.         */
/*                                                                           */
/*****************************************************************************/

shelle *shelletraverse(){
	shelle *newshelle;

	do {
		newshelle = (shelle *) traverse( &shelles );
		if ( newshelle == (shelle *) NULL ) {
			return (shelle *) NULL;
		}
	} while ( newshelle[2] == (shelle) NULL );            /* Skip dead ones. */
	return newshelle;
}

/*****************************************************************************/
/*                                                                           */
/*  pointdealloc()   Deallocate space for a point, marking it dead.          */
/*                                                                           */
/*****************************************************************************/

void pointdealloc( dyingpoint )
point dyingpoint;
{
	/* Mark the point as dead.  This makes it possible to detect dead points */
	/*   when traversing the list of all points.                             */
	setpointmark( dyingpoint, DEADPOINT );
	pooldealloc( &points, (VOID *) dyingpoint );
}

/*****************************************************************************/
/*                                                                           */
/*  pointtraverse()   Traverse the points, skipping dead ones.               */
/*                                                                           */
/*****************************************************************************/

point pointtraverse(){
	point newpoint;

	do {
		newpoint = (point) traverse( &points );
		if ( newpoint == (point) NULL ) {
			return (point) NULL;
		}
	} while ( pointmark( newpoint ) == DEADPOINT );       /* Skip dead ones. */
	return newpoint;
}

/*****************************************************************************/
/*                                                                           */
/*  badsegmentdealloc()   Deallocate space for a bad segment, marking it     */
/*                        dead.                                              */
/*                                                                           */
/*****************************************************************************/

#ifndef CDT_ONLY

void badsegmentdealloc( dyingseg )
struct edge *dyingseg;
{
	/* Set segment's orientation to -1.  This makes it possible to      */
	/*   detect dead segments when traversing the list of all segments. */
	dyingseg->shorient = -1;
	pooldealloc( &badsegments, (VOID *) dyingseg );
}

#endif /* not CDT_ONLY */

/*****************************************************************************/
/*                                                                           */
/*  badsegmenttraverse()   Traverse the bad segments, skipping dead ones.    */
/*                                                                           */
/*****************************************************************************/

#ifndef CDT_ONLY

struct edge *badsegmenttraverse(){
	struct edge *newseg;

	do {
		newseg = (struct edge *) traverse( &badsegments );
		if ( newseg == (struct edge *) NULL ) {
			return (struct edge *) NULL;
		}
	} while ( newseg->shorient == -1 );                   /* Skip dead ones. */
	return newseg;
}

#endif /* not CDT_ONLY */

/*****************************************************************************/
/*                                                                           */
/*  getpoint()   Get a specific point, by number, from the list.             */
/*                                                                           */
/*  The first point is number 'firstnumber'.                                 */
/*                                                                           */
/*  Note that this takes O(n) time (with a small constant, if POINTPERBLOCK  */
/*  is large).  I don't care to take the trouble to make it work in constant */
/*  time.                                                                    */
/*                                                                           */
/*****************************************************************************/

point getpoint( number )
int number;
{
	VOID **getblock;
	point foundpoint;
	unsigned long alignptr;
	int current;

	getblock = points.firstblock;
	current = firstnumber;
	/* Find the right block. */
	while ( current + points.itemsperblock <= number ) {
		getblock = (VOID **) *getblock;
		current += points.itemsperblock;
	}
	/* Now find the right point. */
	alignptr = (unsigned long) ( getblock + 1 );
	foundpoint = (point) ( alignptr + (unsigned long) points.alignbytes
						   - ( alignptr % (unsigned long) points.alignbytes ) );
	while ( current < number ) {
		foundpoint += points.itemwords;
		current++;
	}
	return foundpoint;
}

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

void triangledeinit(){
	pooldeinit( &triangles );
	free( dummytribase );
	if ( useshelles ) {
		pooldeinit( &shelles );
		free( dummyshbase );
	}
	pooldeinit( &points );
#ifndef CDT_ONLY
	if ( quality ) {
		pooldeinit( &badsegments );
		if ( ( minangle > 0.0 ) || vararea || fixedarea ) {
			pooldeinit( &badtriangles );
		}
	}
#endif /* not CDT_ONLY */
}

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

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

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

void maketriangle( newtriedge )
struct triedge *newtriedge;
{
	int i;

	newtriedge->tri = (triangle *) poolalloc( &triangles );
	/* Initialize the three adjoining triangles to be "outer space". */
	newtriedge->tri[0] = (triangle) dummytri;
	newtriedge->tri[1] = (triangle) dummytri;
	newtriedge->tri[2] = (triangle) dummytri;
	/* Three NULL vertex points. */
	newtriedge->tri[3] = (triangle) NULL;
	newtriedge->tri[4] = (triangle) NULL;
	newtriedge->tri[5] = (triangle) NULL;
	/* Initialize the three adjoining shell edges to be the omnipresent */
	/*   shell edge.                                                    */
	if ( useshelles ) {
		newtriedge->tri[6] = (triangle) dummysh;
		newtriedge->tri[7] = (triangle) dummysh;
		newtriedge->tri[8] = (triangle) dummysh;
	}
	for ( i = 0; i < eextras; i++ ) {
		setelemattribute( *newtriedge, i, 0.0 );
	}
	if ( vararea ) {
		setareabound( *newtriedge, -1.0 );
	}

	newtriedge->orient = 0;
}

/*****************************************************************************/
/*                                                                           */
/*  makeshelle()   Create a new shell edge with orientation zero.            */
/*                                                                           */
/*****************************************************************************/

void makeshelle( newedge )
struct edge *newedge;
{
	newedge->sh = (shelle *) poolalloc( &shelles );
	/* Initialize the two adjoining shell edges to be the omnipresent */
	/*   shell edge.                                                  */
	newedge->sh[0] = (shelle) dummysh;
	newedge->sh[1] = (shelle) dummysh;
	/* Two NULL vertex points. */
	newedge->sh[2] = (shelle) NULL;
	newedge->sh[3] = (shelle) NULL;
	/* Initialize the two adjoining triangles to be "outer space". */
	newedge->sh[4] = (shelle) dummytri;
	newedge->sh[5] = (shelle) dummytri;
	/* Set the boundary marker to zero. */
	setmark( *newedge, 0 );

	newedge->shorient = 0;
}

/**                                                                         **/
/**                                                                         **/
/********* Constructors end here                                     *********/

/********* Determinant evaluation routines begin here                *********/
/**                                                                         **/
/**                                                                         **/

/* The adaptive exact arithmetic geometric predicates implemented herein are */
/*   described in detail in my Technical Report CMU-CS-96-140.  The complete */
/*   reference is given in the header.                                       */

/* 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.              */

#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 = (REAL)( c - abig ); \
	alo = (REAL)( 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 )

/*****************************************************************************/
/*                                                                           */
/*  exactinit()   Initialize the variables used for exact arithmetic.        */
/*                                                                           */
/*  `epsilon' is the largest power of two such that 1.0 + epsilon = 1.0 in   */
/*  floating-point arithmetic.  `epsilon' bounds the relative roundoff       */
/*  error.  It is used for floating-point error analysis.                    */
/*                                                                           */
/*  `splitter' is used to split floating-point numbers into two half-        */
/*  length significands for exact multiplication.                            */
/*                                                                           */
/*  I imagine that a highly optimizing compiler might be too smart for its   */
/*  own good, and somehow cause this routine to fail, if it pretends that    */
/*  floating-point arithmetic is too much like real arithmetic.              */
/*                                                                           */
/*  Don't change this routine unless you fully understand it.                */
/*                                                                           */
/*****************************************************************************/

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

	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 anyway. */
	do {
		lastcheck = check;
		epsilon *= half;
		if ( every_other ) {
			splitter *= 2.0;
		}
		every_other = !every_other;
		check = (REAL)( 1.0 + epsilon );
	} while ( ( check != 1.0 ) && ( check != lastcheck ) );
	splitter += 1.0;
	if ( verbose > 1 ) {
		printf( "Floating point roundoff is of magnitude %.17g\n", epsilon );
		printf( "Floating point splitter is %.17g\n", splitter );
	}
	/* Error bounds for orientation and incircle tests. */
	resulterrbound = (REAL)( ( 3.0 + 8.0 * epsilon ) * epsilon );
	ccwerrboundA = (REAL)( ( 3.0 + 16.0 * epsilon ) * epsilon );
	ccwerrboundB = (REAL)( ( 2.0 + 12.0 * epsilon ) * epsilon );
	ccwerrboundC = (REAL)( ( 9.0 + 64.0 * epsilon ) * epsilon * epsilon );
	iccerrboundA = (REAL)( ( 10.0 + 96.0 * epsilon ) * epsilon );
	iccerrboundB = (REAL)( ( 4.0 + 48.0 * epsilon ) * epsilon );
	iccerrboundC = (REAL)( ( 44.0 + 576.0 * 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.                                                              */
/*                                                                           */
/*****************************************************************************/

int fast_expansion_sum_zeroelim( elen, e, flen, f, h )  /* h cannot be e or f. */
int elen;
REAL *e;
int flen;
REAL *f;
REAL *h;
{
	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.)                                                                 */
/*                                                                           */
/*****************************************************************************/

int scale_expansion_zeroelim( elen, e, b, h )   /* e and h cannot be the same. */
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.                              */
/*                                                                           */
/*****************************************************************************/

REAL estimate( elen, e )
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.                              */
/*                                                                           */
/*****************************************************************************/

REAL counterclockwiseadapt( pa, pb, pc, detsum )
point pa;
point pb;
point 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 = (REAL)( 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 = (REAL)( 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] );
}

REAL counterclockwise( pa, pb, pc )
point pa;
point pb;
point pc;
{
	REAL detleft, detright, det;
	REAL detsum, errbound;

	counterclockcount++;

	detleft = ( pa[0] - pc[0] ) * ( pb[1] - pc[1] );
	detright = ( pa[1] - pc[1] ) * ( pb[0] - pc[0] );
	det = detleft - detright;

	if ( 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.                              */
/*                                                                           */
/*****************************************************************************/

REAL incircleadapt( pa, pb, pc, pd, permanent )
point pa;
point pb;
point pc;
point 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 = (REAL)( 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 = (REAL)( iccerrboundC * permanent + resulterrbound * Absolute( det ) );
	det += (REAL)( ( ( 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];
}

REAL incircle( pa, pb, pc, pd )
point pa;
point pb;
point pc;
point pd;
{
	REAL adx, bdx, cdx, ady, bdy, cdy;
	REAL bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady;
	REAL alift, blift, clift;
	REAL det;
	REAL permanent, errbound;

	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 ( 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 );
}

/**                                                                         **/
/**                                                                         **/
/********* Determinant evaluation routines end here                  *********/

/*****************************************************************************/
/*                                                                           */
/*  triangleinit()   Initialize some variables.                              */
/*                                                                           */
/*****************************************************************************/

void triangleinit(){
	points.maxitems = triangles.maxitems = shelles.maxitems = viri.maxitems =
																  badsegments.maxitems = badtriangles.maxitems = splaynodes.maxitems = 0l;
	points.itembytes = triangles.itembytes = shelles.itembytes = viri.itembytes =
																	 badsegments.itembytes = badtriangles.itembytes = splaynodes.itembytes = 0;
	recenttri.tri = (triangle *) NULL;  /* No triangle has been visited yet. */
	samples = 1;          /* Point location should take at least one sample. */
	checksegments = 0;    /* There are no segments in the triangulation yet. */
	incirclecount = counterclockcount = hyperbolacount = 0;
	circumcentercount = circletopcount = 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.                                                    */
/*                                                                           */
/*****************************************************************************/

unsigned long randomnation( choices )
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.                 */
/*                                                                           */
/*****************************************************************************/

#ifndef REDUCED

void checkmesh(){
	struct triedge triangleloop;
	struct triedge oppotri, oppooppotri;
	point triorg, tridest, triapex;
	point oppoorg, oppodest;
	int horrors;
	int saveexact;
	triangle ptr;                       /* Temporary variable used by sym(). */

	/* Temporarily turn on exact arithmetic if it's off. */
	saveexact = noexact;
	noexact = 0;
	if ( !quiet ) {
		printf( "  Checking consistency of mesh...\n" );
	}
	horrors = 0;
	/* Run through the list of triangles, checking each one. */
	traversalinit( &triangles );
	triangleloop.tri = triangletraverse();
	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( triorg, tridest, triapex ) <= 0.0 ) {
					printf( "  !! !! Inverted " );
					printtriangle( &triangleloop );
					horrors++;
				}
			}
			/* Find the neighboring triangle on this edge. */
			sym( triangleloop, oppotri );
			if ( oppotri.tri != 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( &triangleloop );
					printf( "    Second (nonreciprocating) " );
					printtriangle( &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( &triangleloop );
					printf( "    Second mismatched " );
					printtriangle( &oppotri );
					horrors++;
				}
			}
		}
		triangleloop.tri = triangletraverse();
	}
	if ( horrors == 0 ) {
		if ( !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. */
	noexact = saveexact;
}

#endif /* not REDUCED */

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

#ifndef REDUCED

void checkdelaunay(){
	struct triedge triangleloop;
	struct triedge oppotri;
	struct edge opposhelle;
	point triorg, tridest, triapex;
	point oppoapex;
	int shouldbedelaunay;
	int horrors;
	int saveexact;
	triangle ptr;                       /* Temporary variable used by sym(). */
	shelle sptr;                    /* Temporary variable used by tspivot(). */

	/* Temporarily turn on exact arithmetic if it's off. */
	saveexact = noexact;
	noexact = 0;
	if ( !quiet ) {
		printf( "  Checking Delaunay property of mesh...\n" );
	}
	horrors = 0;
	/* Run through the list of triangles, checking each one. */
	traversalinit( &triangles );
	triangleloop.tri = triangletraverse();
	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 != dummytri )
							   && ( triapex != (point) NULL ) && ( oppoapex != (point) NULL )
							   && ( triangleloop.tri < oppotri.tri );
			if ( checksegments && shouldbedelaunay ) {
				/* If a shell edge separates the triangles, then the edge is */
				/*   constrained, so no local Delaunay test should be done.  */
				tspivot( triangleloop, opposhelle );
				if ( opposhelle.sh != dummysh ) {
					shouldbedelaunay = 0;
				}
			}
			if ( shouldbedelaunay ) {
				if ( incircle( triorg, tridest, triapex, oppoapex ) > 0.0 ) {
					printf( "  !! !! Non-Delaunay pair of triangles:\n" );
					printf( "    First non-Delaunay " );
					printtriangle( &triangleloop );
					printf( "    Second non-Delaunay " );
					printtriangle( &oppotri );
					horrors++;
				}
			}
		}
		triangleloop.tri = triangletraverse();
	}
	if ( horrors == 0 ) {
		if ( !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. */
	noexact = saveexact;
}

#endif /* not REDUCED */

/*****************************************************************************/
/*                                                                           */
/*  enqueuebadtri()   Add a bad triangle to the end of a queue.              */
/*                                                                           */
/*  The queue is actually a set of 64 queues.  I use multiple queues to give */
/*  priority to smaller angles.  I originally implemented a heap, but the    */
/*  queues are (to my surprise) much faster.                                 */
/*                                                                           */
/*****************************************************************************/

#ifndef CDT_ONLY

void enqueuebadtri( instri, angle, insapex, insorg, insdest )
struct triedge *instri;
REAL angle;
point insapex;
point insorg;
point insdest;
{
	struct badface *newface;
	int queuenumber;

	if ( verbose > 2 ) {
		printf( "  Queueing bad triangle:\n" );
		printf( "    (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", insorg[0],
				insorg[1], insdest[0], insdest[1], insapex[0], insapex[1] );
	}
	/* Allocate space for the bad triangle. */
	newface = (struct badface *) poolalloc( &badtriangles );
	triedgecopy( *instri, newface->badfacetri );
	newface->key = angle;
	newface->faceapex = insapex;
	newface->faceorg = insorg;
	newface->facedest = insdest;
	newface->nextface = (struct badface *) NULL;
	/* Determine the appropriate queue to put the bad triangle into. */
	if ( angle > 0.6 ) {
		queuenumber = (int) ( 160.0 * ( angle - 0.6 ) );
		if ( queuenumber > 63 ) {
			queuenumber = 63;
		}
	}
	else {
		/* It's not a bad angle; put the triangle in the lowest-priority queue. */
		queuenumber = 0;
	}
	/* Add the triangle to the end of a queue. */
	*queuetail[queuenumber] = newface;
	/* Maintain a pointer to the NULL pointer at the end of the queue. */
	queuetail[queuenumber] = &newface->nextface;
}

#endif /* not CDT_ONLY */

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

#ifndef CDT_ONLY

struct badface *dequeuebadtri(){
	struct badface *result;
	int queuenumber;

	/* Look for a nonempty queue. */
	for ( queuenumber = 63; queuenumber >= 0; queuenumber-- ) {
		result = queuefront[queuenumber];
		if ( result != (struct badface *) NULL ) {
			/* Remove the triangle from the queue. */
			queuefront[queuenumber] = result->nextface;
			/* Maintain a pointer to the NULL pointer at the end of the queue. */
			if ( queuefront[queuenumber] == (struct badface *) NULL ) {
				queuetail[queuenumber] = &queuefront[queuenumber];
			}
			return result;
		}
	}
	return (struct badface *) NULL;
}

#endif /* not CDT_ONLY */

/*****************************************************************************/
/*                                                                           */
/*  checkedge4encroach()   Check a segment to see if it is encroached; add   */
/*                         it to the list if it is.                          */
/*                                                                           */
/*  An encroached segment is an unflippable edge that has a point in its     */
/*  diametral circle (that is, it faces an angle greater than 90 degrees).   */
/*  This definition is due to Ruppert.                                       */
/*                                                                           */
/*  Returns a nonzero value if the edge is encroached.                       */
/*                                                                           */
/*****************************************************************************/

#ifndef CDT_ONLY

int checkedge4encroach( testedge )
struct edge *testedge;
{
	struct triedge neighbortri;
	struct edge testsym;
	struct edge *badedge;
	int addtolist;
	int sides;
	point eorg, edest, eapex;
	triangle ptr;                   /* Temporary variable used by stpivot(). */

	addtolist = 0;
	sides = 0;

	sorg( *testedge, eorg );
	sdest( *testedge, edest );
	/* Check one neighbor of the shell edge. */
	stpivot( *testedge, neighbortri );
	/* Does the neighbor exist, or is this a boundary edge? */
	if ( neighbortri.tri != dummytri ) {
		sides++;
		/* Find a vertex opposite this edge. */
		apex( neighbortri, eapex );
		/* Check whether the vertex is inside the diametral circle of the  */
		/*   shell edge.  Pythagoras' Theorem is used to check whether the */
		/*   angle at the vertex is greater than 90 degrees.               */
		if ( eapex[0] * ( eorg[0] + edest[0] ) + eapex[1] * ( eorg[1] + edest[1] ) >
			 eapex[0] * eapex[0] + eorg[0] * edest[0] +
			 eapex[1] * eapex[1] + eorg[1] * edest[1] ) {
			addtolist = 1;
		}
	}
	/* Check the other neighbor of the shell edge. */
	ssym( *testedge, testsym );
	stpivot( testsym, neighbortri );
	/* Does the neighbor exist, or is this a boundary edge? */
	if ( neighbortri.tri != dummytri ) {
		sides++;
		/* Find the other vertex opposite this edge. */
		apex( neighbortri, eapex );
		/* Check whether the vertex is inside the diametral circle of the  */
		/*   shell edge.  Pythagoras' Theorem is used to check whether the */
		/*   angle at the vertex is greater than 90 degrees.               */
		if ( eapex[0] * ( eorg[0] + edest[0] ) +
			 eapex[1] * ( eorg[1] + edest[1] ) >
			 eapex[0] * eapex[0] + eorg[0] * edest[0] +
			 eapex[1] * eapex[1] + eorg[1] * edest[1] ) {
			addtolist += 2;
		}
	}

	if ( addtolist && ( !nobisect || ( ( nobisect == 1 ) && ( sides == 2 ) ) ) ) {
		if ( verbose > 2 ) {
			printf( "  Queueing encroached segment (%.12g, %.12g) (%.12g, %.12g).\n",
					eorg[0], eorg[1], edest[0], edest[1] );
		}
		/* Add the shell edge to the list of encroached segments. */
		/*   Be sure to get the orientation right.                */
		badedge = (struct edge *) poolalloc( &badsegments );
		if ( addtolist == 1 ) {
			shellecopy( *testedge, *badedge );
		}
		else {
			shellecopy( testsym, *badedge );
		}
	}
	return addtolist;
}

#endif /* not CDT_ONLY */

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

#ifndef CDT_ONLY

void testtriangle( testtri )
struct triedge *testtri;
{
	struct triedge sametesttri;
	struct edge edge1, edge2;
	point torg, tdest, tapex;
	point anglevertex;
	REAL dxod, dyod, dxda, dyda, dxao, dyao;
	REAL dxod2, dyod2, dxda2, dyda2, dxao2, dyao2;
	REAL apexlen, orglen, destlen;
	REAL angle;
	REAL area;
	shelle sptr;                    /* Temporary variable used by tspivot(). */

	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. */
		/* Find the square of the cosine of the angle at the apex. */
		angle = dxda * dxao + dyda * dyao;
		angle = angle * angle / ( orglen * destlen );
		anglevertex = tapex;
		lnext( *testtri, sametesttri );
		tspivot( sametesttri, edge1 );
		lnextself( sametesttri );
		tspivot( sametesttri, edge2 );
	}
	else if ( orglen < destlen ) {
		/* The edge opposite the origin is shortest. */
		/* Find the square of the cosine of the angle at the origin. */
		angle = dxod * dxao + dyod * dyao;
		angle = angle * angle / ( apexlen * destlen );
		anglevertex = torg;
		tspivot( *testtri, edge1 );
		lprev( *testtri, sametesttri );
		tspivot( sametesttri, edge2 );
	}
	else {
		/* The edge opposite the destination is shortest. */
		/* Find the square of the cosine of the angle at the destination. */
		angle = dxod * dxda + dyod * dyda;
		angle = angle * angle / ( apexlen * orglen );
		anglevertex = tdest;
		tspivot( *testtri, edge1 );
		lnext( *testtri, sametesttri );
		tspivot( sametesttri, edge2 );
	}
	/* Check if both edges that form the angle are segments. */
	if ( ( edge1.sh != dummysh ) && ( edge2.sh != dummysh ) ) {
		/* The angle is a segment intersection. */
		if ( ( angle > 0.9924 ) && !quiet ) {          /* Roughly 5 degrees. */
			if ( angle > 1.0 ) {
				/* Beware of a floating exception in acos(). */
				angle = 1.0;
			}
			/* Find the actual angle in degrees, for printing. */
			angle = acos( sqrt( angle ) ) * ( 180.0 / PI );
			printf(
				"Warning:  Small angle (%.4g degrees) between segments at point\n",
				angle );
			printf( "  (%.12g, %.12g)\n", anglevertex[0], anglevertex[1] );
		}
		/* Don't add this bad triangle to the list; there's nothing that */
		/*   can be done about a small angle between two segments.       */
		angle = 0.0;
	}
	/* Check whether the angle is smaller than permitted. */
	if ( angle > goodangle ) {
		/* Add this triangle to the list of bad triangles. */
		enqueuebadtri( testtri, angle, tapex, torg, tdest );
		return;
	}
	if ( vararea || fixedarea ) {
		/* Check whether the area is larger than permitted. */
		area = 0.5 * ( dxod * dyda - dyod * dxda );
		if ( fixedarea && ( area > maxarea ) ) {
			/* Add this triangle to the list of bad triangles. */
			enqueuebadtri( testtri, angle, tapex, torg, tdest );
		}
		else if ( vararea ) {
			/* Nonpositive area constraints are treated as unconstrained. */
			if ( ( area > areabound( *testtri ) ) && ( areabound( *testtri ) > 0.0 ) ) {
				/* Add this triangle to the list of bad triangles. */
				enqueuebadtri( testtri, angle, tapex, torg, tdest );
			}
		}
	}
}

#endif /* not CDT_ONLY */

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

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

/*****************************************************************************/
/*                                                                           */
/*  makepointmap()   Construct a mapping from points 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 point is a corner    */
/*  of several triangles, but in the end every point will point to some      */
/*  triangle that contains it.                                               */
/*                                                                           */
/*****************************************************************************/

void makepointmap(){
	struct triedge triangleloop;
	point triorg;

	if ( verbose ) {
		printf( "    Constructing mapping from points to triangles.\n" );
	}
	traversalinit( &triangles );
	triangleloop.tri = triangletraverse();
	while ( triangleloop.tri != (triangle *) NULL ) {
		/* Check all three points of the triangle. */
		for ( triangleloop.orient = 0; triangleloop.orient < 3;
			  triangleloop.orient++ ) {
			org( triangleloop, triorg );
			setpoint2tri( triorg, encode( triangleloop ) );
		}
		triangleloop.tri = triangletraverse();
	}
}

/*****************************************************************************/
/*                                                                           */
/*  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.  The possibility that the      */
/*       vertex one seeks is an endpoint of the starting edge must be        */
/*       screened out before preciselocate() is called.                      */
/*                                                                           */
/*  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.                                                                */
/*                                                                           */
/*  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.               */
/*                                                                           */
/*****************************************************************************/

enum locateresult preciselocate( searchpoint, searchtri )
point searchpoint;
struct triedge *searchtri;
{
	struct triedge backtracktri;
	point forg, fdest, fapex;
	point swappoint;
	REAL orgorient, destorient;
	int moveleft;
	triangle ptr;                       /* Temporary variable used by sym(). */

	if ( 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 ( 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( 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( 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) 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.  We can just bounce off  */
		/*   the boundary as if it were an elastic band.                   */
		if ( moveleft ) {
			lprev( *searchtri, backtracktri );
			fdest = fapex;
		}
		else {
			lnext( *searchtri, backtracktri );
			forg = fapex;
		}
		sym( backtracktri, *searchtri );

		/* Check for walking off the edge. */
		if ( searchtri->tri == dummytri ) {
			/* Turn around. */
			triedgecopy( backtracktri, *searchtri );
			swappoint = forg;
			forg = fdest;
			fdest = swappoint;
			apex( *searchtri, fapex );
			/* Check if the point really is beyond the triangulation boundary. */
			destorient = counterclockwise( forg, fapex, searchpoint );
			orgorient = counterclockwise( fapex, fdest, searchpoint );
			if ( ( orgorient < 0.0 ) && ( destorient < 0.0 ) ) {
				return OUTSIDE;
			}
		}
		else {
			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 searcing 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.     */
/*                                                                           */
/*****************************************************************************/

enum locateresult locate( searchpoint, searchtri )
point searchpoint;
struct triedge *searchtri;
{
	VOID **sampleblock;
	triangle *firsttri;
	struct triedge sampletri;
	point torg, tdest;
	unsigned long alignptr;
	REAL searchdist, dist;
	REAL ahead;
	long sampleblocks, samplesperblock, samplenum;
	long triblocks;
	long i, j;
	triangle ptr;                       /* Temporary variable used by sym(). */

	if ( 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 ( 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 ( recenttri.tri != (triangle *) NULL ) {
		if ( recenttri.tri[3] != (triangle) NULL ) {
			org( recenttri, torg );
			if ( ( torg[0] == searchpoint[0] ) && ( torg[1] == searchpoint[1] ) ) {
				triedgecopy( recenttri, *searchtri );
				return ONVERTEX;
			}
			dist = ( searchpoint[0] - torg[0] ) * ( searchpoint[0] - torg[0] )
				   + ( searchpoint[1] - torg[1] ) * ( searchpoint[1] - torg[1] );
			if ( dist < searchdist ) {
				triedgecopy( recenttri, *searchtri );
				searchdist = dist;
				if ( 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.                */
	while ( SAMPLEFACTOR * samples * samples * samples < triangles.items ) {
		samples++;
	}
	triblocks = ( triangles.maxitems + TRIPERBLOCK - 1 ) / TRIPERBLOCK;
	samplesperblock = 1 + ( samples / triblocks );
	sampleblocks = samples / samplesperblock;
	sampleblock = triangles.firstblock;
	sampletri.orient = 0;
	for ( i = 0; i < sampleblocks; i++ ) {
		alignptr = (unsigned long) ( sampleblock + 1 );
		firsttri = (triangle *) ( alignptr + (unsigned long) triangles.alignbytes
								  - ( alignptr % (unsigned long) triangles.alignbytes ) );
		for ( j = 0; j < samplesperblock; j++ ) {
			if ( i == triblocks - 1 ) {
				samplenum = randomnation( (int)
										  ( triangles.maxitems - ( i * TRIPERBLOCK ) ) );
			}
			else {
				samplenum = randomnation( TRIPERBLOCK );
			}
			sampletri.tri = (triangle *)
							( firsttri + ( samplenum * triangles.itemwords ) );
			if ( sampletri.tri[3] != (triangle) NULL ) {
				org( sampletri, torg );
				dist = ( searchpoint[0] - torg[0] ) * ( searchpoint[0] - torg[0] )
					   + ( searchpoint[1] - torg[1] ) * ( searchpoint[1] - torg[1] );
				if ( dist < searchdist ) {
					triedgecopy( sampletri, *searchtri );
					searchdist = dist;
					if ( verbose > 2 ) {
						printf( "    Choosing triangle with origin (%.12g, %.12g).\n",
								torg[0], torg[1] );
					}
				}
			}
		}
		sampleblock = (VOID **) *sampleblock;
	}
	/* 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( 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( searchpoint, searchtri );
}

/**                                                                         **/
/**                                                                         **/
/********* Point location routines end here                          *********/

/********* Mesh transformation routines begin here                   *********/
/**                                                                         **/
/**                                                                         **/

/*****************************************************************************/
/*                                                                           */
/*  insertshelle()   Create a new shell edge and insert it between two       */
/*                   triangles.                                              */
/*                                                                           */
/*  The new shell edge is inserted at the edge described by the handle       */
/*  `tri'.  Its vertices are properly initialized.  The marker `shellemark'  */
/*  is applied to the shell edge and, if appropriate, its vertices.          */
/*                                                                           */
/*****************************************************************************/

void insertshelle( tri, shellemark )
struct triedge *tri;          /* Edge at which to insert the new shell edge. */
int shellemark;                            /* Marker for the new shell edge. */
{
	struct triedge oppotri;
	struct edge newshelle;
	point triorg, tridest;
	triangle ptr;                       /* Temporary variable used by sym(). */
	shelle sptr;                    /* Temporary variable used by tspivot(). */

	/* Mark points if possible. */
	org( *tri, triorg );
	dest( *tri, tridest );
	if ( pointmark( triorg ) == 0 ) {
		setpointmark( triorg, shellemark );
	}
	if ( pointmark( tridest ) == 0 ) {
		setpointmark( tridest, shellemark );
	}
	/* Check if there's already a shell edge here. */
	tspivot( *tri, newshelle );
	if ( newshelle.sh == dummysh ) {
		/* Make new shell edge and initialize its vertices. */
		makeshelle( &newshelle );
		setsorg( newshelle, tridest );
		setsdest( newshelle, triorg );
		/* Bond new shell edge to the two triangles it is sandwiched between. */
		/*   Note that the facing triangle `oppotri' might be equal to        */
		/*   `dummytri' (outer space), but the new shell edge is bonded to it */
		/*   all the same.                                                    */
		tsbond( *tri, newshelle );
		sym( *tri, oppotri );
		ssymself( newshelle );
		tsbond( oppotri, newshelle );
		setmark( newshelle, shellemark );
		if ( verbose > 2 ) {
			printf( "  Inserting new " );
			printshelle( &newshelle );
		}
	}
	else {
		if ( mark( newshelle ) == 0 ) {
			setmark( newshelle, shellemark );
		}
	}
}

/*****************************************************************************/
/*                                                                           */
/*  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   */
/*  point.                                                                   */
/*                                                                           */
/*  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.                                              */
/*                                                                           */
/*  A "shell" is similar to a "casing".  The term "shell" describes the set  */
/*  of shell edges (if any) that are attached to the triangles being         */
/*  transformed.  However, I sometimes use "shell" to refer to a single      */
/*  shell edge, so don't get confused.                                       */
/*                                                                           */
/*****************************************************************************/

/*****************************************************************************/
/*                                                                           */
/*  flip()   Transform two triangles to two different triangles by flipping  */
/*           an edge within a quadrilateral.                                 */
/*                                                                           */
/*  Imagine the original triangles, abc and bad, oriented so that the        */
/*  shared edge ab lies in a horizontal plane, with the point b on the left  */
/*  and the point a on the right.  The point c lies below the edge, and the  */
/*  point 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 shell edge 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.                                                       */
/*                                                                           */
/*****************************************************************************/

void flip( flipedge )
struct triedge *flipedge;                    /* Handle for the triangle abc. */
{
	struct triedge botleft, botright;
	struct triedge topleft, topright;
	struct triedge top;
	struct triedge botlcasing, botrcasing;
	struct triedge toplcasing, toprcasing;
	struct edge botlshelle, botrshelle;
	struct edge toplshelle, toprshelle;
	point leftpoint, rightpoint, botpoint;
	point farpoint;
	triangle ptr;                       /* Temporary variable used by sym(). */
	shelle sptr;                    /* Temporary variable used by tspivot(). */

	/* Identify the vertices of the quadrilateral. */
	org( *flipedge, rightpoint );
	dest( *flipedge, leftpoint );
	apex( *flipedge, botpoint );
	sym( *flipedge, top );
#ifdef SELF_CHECK
	if ( top.tri == dummytri ) {
		printf( "Internal error in flip():  Attempt to flip on boundary.\n" );
		lnextself( *flipedge );
		return;
	}
	if ( checksegments ) {
		tspivot( *flipedge, toplshelle );
		if ( toplshelle.sh != dummysh ) {
			printf( "Internal error in flip():  Attempt to flip a segment.\n" );
			lnextself( *flipedge );
			return;
		}
	}
#endif /* SELF_CHECK */
	apex( top, farpoint );

	/* 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 ( checksegments ) {
		/* Check for shell edges and rebond them to the quadrilateral. */
		tspivot( topleft, toplshelle );
		tspivot( botleft, botlshelle );
		tspivot( botright, botrshelle );
		tspivot( topright, toprshelle );
		if ( toplshelle.sh == dummysh ) {
			tsdissolve( topright );
		}
		else {
			tsbond( topright, toplshelle );
		}
		if ( botlshelle.sh == dummysh ) {
			tsdissolve( topleft );
		}
		else {
			tsbond( topleft, botlshelle );
		}
		if ( botrshelle.sh == dummysh ) {
			tsdissolve( botleft );
		}
		else {
			tsbond( botleft, botrshelle );
		}
		if ( toprshelle.sh == dummysh ) {
			tsdissolve( botright );
		}
		else {
			tsbond( botright, toprshelle );
		}
	}

	/* New point assignments for the rotated quadrilateral. */
	setorg( *flipedge, farpoint );
	setdest( *flipedge, botpoint );
	setapex( *flipedge, rightpoint );
	setorg( top, botpoint );
	setdest( top, farpoint );
	setapex( top, leftpoint );
	if ( verbose > 2 ) {
		printf( "  Edge flip results in left " );
		lnextself( topleft );
		printtriangle( &topleft );
		printf( "  and right " );
		printtriangle( flipedge );
	}
}

/*****************************************************************************/
/*                                                                           */
/*  insertsite()   Insert a vertex into a Delaunay triangulation,            */
/*                 performing flips as necessary to maintain the Delaunay    */
/*                 property.                                                 */
/*                                                                           */
/*  The point `insertpoint' 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 `insertpoint' is found inside a triangle, the triangle is split into  */
/*  three; if `insertpoint' 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 `insertpoint' lies on an      */
/*  existing vertex, no action is taken, and the value DUPLICATEPOINT is     */
/*  returned.  On return, `searchtri' is set to a handle whose origin is the */
/*  existing vertex.                                                         */
/*                                                                           */
/*  Normally, the parameter `splitedge' is set to NULL, implying that no     */
/*  segment should be split.  In this case, if `insertpoint' is found to     */
/*  lie on a segment, no action is taken, and the value VIOLATINGPOINT is    */
/*  returned.  On return, `searchtri' is set to a handle whose primary edge  */
/*  is the violated segment.                                                 */
/*                                                                           */
/*  If the calling routine wishes to split a segment by inserting a point in */
/*  it, the parameter `splitedge' should be that segment.  In this case,     */
/*  `searchtri' MUST be the triangle handle reached by pivoting from that    */
/*  segment; no point location is done.                                      */
/*                                                                           */
/*  `segmentflaws' and `triflaws' are flags that indicate whether or not     */
/*  there should be checks for the creation of encroached segments or bad    */
/*  quality faces.  If a newly inserted point encroaches upon segments,      */
/*  these segments are added to the list of segments 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 point or violated segment does not prevent the point      */
/*  from being inserted, the return value will be ENCROACHINGPOINT if the    */
/*  point encroaches upon a segment (and checking is enabled), or            */
/*  SUCCESSFULPOINT otherwise.  In either case, `searchtri' is set to a      */
/*  handle whose origin is the newly inserted vertex.                        */
/*                                                                           */
/*  insertsite() does not use flip() for reasons of speed; some              */
/*  information can be reused from edge flip to edge flip, like the          */
/*  locations of shell edges.                                                */
/*                                                                           */
/*****************************************************************************/

enum insertsiteresult insertsite( insertpoint, searchtri, splitedge,
								  segmentflaws, triflaws )
point insertpoint;
struct triedge *searchtri;
struct edge *splitedge;
int segmentflaws;
int triflaws;
{
	struct triedge horiz;
	struct triedge top;
	struct triedge botleft, botright;
	struct triedge topleft, topright;
	struct triedge newbotleft, newbotright;
	struct triedge newtopright;
	struct triedge botlcasing, botrcasing;
	struct triedge toplcasing, toprcasing;
	struct triedge testtri;
	struct edge botlshelle, botrshelle;
	struct edge toplshelle, toprshelle;
	struct edge brokenshelle;
	struct edge checkshelle;
	struct edge rightedge;
	struct edge newedge;
	struct edge *encroached;
	point first;
	point leftpoint, rightpoint, botpoint, toppoint, farpoint;
	REAL attrib;
	REAL area;
	enum insertsiteresult success;
	enum locateresult intersect;
	int doflip;
	int mirrorflag;
	int i;
	triangle ptr;                       /* Temporary variable used by sym(). */
	shelle sptr;       /* Temporary variable used by spivot() and tspivot(). */

	if ( verbose > 1 ) {
		printf( "  Inserting (%.12g, %.12g).\n", insertpoint[0], insertpoint[1] );
	}
	if ( splitedge == (struct edge *) NULL ) {
		/* Find the location of the point to be inserted.  Check if a good */
		/*   starting triangle has already been provided by the caller.    */
		if ( searchtri->tri == (triangle *) NULL ) {
			/* Find a boundary triangle. */
			horiz.tri = dummytri;
			horiz.orient = 0;
			symself( horiz );
			/* Search for a triangle containing `insertpoint'. */
			intersect = locate( insertpoint, &horiz );
		}
		else {
			/* Start searching from the triangle provided by the caller. */
			triedgecopy( *searchtri, horiz );
			intersect = preciselocate( insertpoint, &horiz );
		}
	}
	else {
		/* The calling routine provides the edge in which the point is inserted. */
		triedgecopy( *searchtri, horiz );
		intersect = ONEDGE;
	}
	if ( intersect == ONVERTEX ) {
		/* There's already a vertex there.  Return in `searchtri' a triangle */
		/*   whose origin is the existing vertex.                            */
		triedgecopy( horiz, *searchtri );
		triedgecopy( horiz, recenttri );
		return DUPLICATEPOINT;
	}
	if ( ( intersect == ONEDGE ) || ( intersect == OUTSIDE ) ) {
		/* The vertex falls on an edge or boundary. */
		if ( checksegments && ( splitedge == (struct edge *) NULL ) ) {
			/* Check whether the vertex falls on a shell edge. */
			tspivot( horiz, brokenshelle );
			if ( brokenshelle.sh != dummysh ) {
				/* The vertex falls on a shell edge. */
				if ( segmentflaws ) {
					if ( nobisect == 0 ) {
						/* Add the shell edge to the list of encroached segments. */
						encroached = (struct edge *) poolalloc( &badsegments );
						shellecopy( brokenshelle, *encroached );
					}
					else if ( ( nobisect == 1 ) && ( intersect == ONEDGE ) ) {
						/* This segment may be split only if it is an internal boundary. */
						sym( horiz, testtri );
						if ( testtri.tri != dummytri ) {
							/* Add the shell edge to the list of encroached segments. */
							encroached = (struct edge *) poolalloc( &badsegments );
							shellecopy( brokenshelle, *encroached );
						}
					}
				}
				/* Return a handle whose primary edge contains the point, */
				/*   which has not been inserted.                         */
				triedgecopy( horiz, *searchtri );
				triedgecopy( horiz, recenttri );
				return VIOLATINGPOINT;
			}
		}
		/* Insert the point 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 != dummytri;
		if ( mirrorflag ) {
			lnextself( topright );
			sym( topright, toprcasing );
			maketriangle( &newtopright );
		}
		else {
			/* Splitting the boundary edge increases the number of boundary edges. */
			hullsize++;
		}
		maketriangle( &newbotright );

		/* Set the vertices of changed and new triangles. */
		org( horiz, rightpoint );
		dest( horiz, leftpoint );
		apex( horiz, botpoint );
		setorg( newbotright, botpoint );
		setdest( newbotright, rightpoint );
		setapex( newbotright, insertpoint );
		setorg( horiz, insertpoint );
		for ( i = 0; i < eextras; i++ ) {
			/* Set the element attributes of a new triangle. */
			setelemattribute( newbotright, i, elemattribute( botright, i ) );
		}
		if ( vararea ) {
			/* Set the area constraint of a new triangle. */
			setareabound( newbotright, areabound( botright ) );
		}
		if ( mirrorflag ) {
			dest( topright, toppoint );
			setorg( newtopright, rightpoint );
			setdest( newtopright, toppoint );
			setapex( newtopright, insertpoint );
			setorg( topright, insertpoint );
			for ( i = 0; i < eextras; i++ ) {
				/* Set the element attributes of another new triangle. */
				setelemattribute( newtopright, i, elemattribute( topright, i ) );
			}
			if ( vararea ) {
				/* Set the area constraint of another new triangle. */
				setareabound( newtopright, areabound( topright ) );
			}
		}

		/* There may be shell edges that need to be bonded */
		/*   to the new triangle(s).                       */
		if ( checksegments ) {
			tspivot( botright, botrshelle );
			if ( botrshelle.sh != dummysh ) {
				tsdissolve( botright );
				tsbond( newbotright, botrshelle );
			}
			if ( mirrorflag ) {
				tspivot( topright, toprshelle );
				if ( toprshelle.sh != dummysh ) {
					tsdissolve( topright );
					tsbond( newtopright, toprshelle );
				}
			}
		}

		/* 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 ( splitedge != (struct edge *) NULL ) {
			/* Split the shell edge into two. */
			setsdest( *splitedge, insertpoint );
			ssymself( *splitedge );
			spivot( *splitedge, rightedge );
			insertshelle( &newbotright, mark( *splitedge ) );
			tspivot( newbotright, newedge );
			sbond( *splitedge, newedge );
			ssymself( newedge );
			sbond( newedge, rightedge );
			ssymself( *splitedge );
		}

#ifdef SELF_CHECK
		if ( counterclockwise( rightpoint, leftpoint, botpoint ) < 0.0 ) {
			printf( "Internal error in insertsite():\n" );
			printf( "  Clockwise triangle prior to edge point insertion (bottom).\n" );
		}
		if ( mirrorflag ) {
			if ( counterclockwise( leftpoint, rightpoint, toppoint ) < 0.0 ) {
				printf( "Internal error in insertsite():\n" );
				printf( "  Clockwise triangle prior to edge point insertion (top).\n" );
			}
			if ( counterclockwise( rightpoint, toppoint, insertpoint ) < 0.0 ) {
				printf( "Internal error in insertsite():\n" );
				printf( "  Clockwise triangle after edge point insertion (top right).\n"
						);
			}
			if ( counterclockwise( toppoint, leftpoint, insertpoint ) < 0.0 ) {
				printf( "Internal error in insertsite():\n" );
				printf( "  Clockwise triangle after edge point insertion (top left).\n"
						);
			}
		}
		if ( counterclockwise( leftpoint, botpoint, insertpoint ) < 0.0 ) {
			printf( "Internal error in insertsite():\n" );
			printf( "  Clockwise triangle after edge point insertion (bottom left).\n"
					);
		}
		if ( counterclockwise( botpoint, rightpoint, insertpoint ) < 0.0 ) {
			printf( "Internal error in insertsite():\n" );
			printf(
				"  Clockwise triangle after edge point insertion (bottom right).\n" );
		}
#endif /* SELF_CHECK */
		if ( verbose > 2 ) {
			printf( "  Updating bottom left " );
			printtriangle( &botright );
			if ( mirrorflag ) {
				printf( "  Updating top left " );
				printtriangle( &topright );
				printf( "  Creating top right " );
				printtriangle( &newtopright );
			}
			printf( "  Creating bottom right " );
			printtriangle( &newbotright );
		}

		/* Position `horiz' on the first edge to check for */
		/*   the Delaunay property.                        */
		lnextself( horiz );
	}
	else {
		/* Insert the point in a triangle, splitting it into three. */
		lnext( horiz, botleft );
		lprev( horiz, botright );
		sym( botleft, botlcasing );
		sym( botright, botrcasing );
		maketriangle( &newbotleft );
		maketriangle( &newbotright );

		/* Set the vertices of changed and new triangles. */
		org( horiz, rightpoint );
		dest( horiz, leftpoint );
		apex( horiz, botpoint );
		setorg( newbotleft, leftpoint );
		setdest( newbotleft, botpoint );
		setapex( newbotleft, insertpoint );
		setorg( newbotright, botpoint );
		setdest( newbotright, rightpoint );
		setapex( newbotright, insertpoint );
		setapex( horiz, insertpoint );
		for ( i = 0; i < eextras; i++ ) {
			/* Set the element attributes of the new triangles. */
			attrib = elemattribute( horiz, i );
			setelemattribute( newbotleft, i, attrib );
			setelemattribute( newbotright, i, attrib );
		}
		if ( vararea ) {
			/* Set the area constraint of the new triangles. */
			area = areabound( horiz );
			setareabound( newbotleft, area );
			setareabound( newbotright, area );
		}

		/* There may be shell edges that need to be bonded */
		/*   to the new triangles.                         */
		if ( checksegments ) {
			tspivot( botleft, botlshelle );
			if ( botlshelle.sh != dummysh ) {
				tsdissolve( botleft );
				tsbond( newbotleft, botlshelle );
			}
			tspivot( botright, botrshelle );
			if ( botrshelle.sh != dummysh ) {
				tsdissolve( botright );
				tsbond( newbotright, botrshelle );
			}
		}

		/* 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 );

#ifdef SELF_CHECK
		if ( counterclockwise( rightpoint, leftpoint, botpoint ) < 0.0 ) {
			printf( "Internal error in insertsite():\n" );
			printf( "  Clockwise triangle prior to point insertion.\n" );
		}
		if ( counterclockwise( rightpoint, leftpoint, insertpoint ) < 0.0 ) {
			printf( "Internal error in insertsite():\n" );
			printf( "  Clockwise triangle after point insertion (top).\n" );
		}
		if ( counterclockwise( leftpoint, botpoint, insertpoint ) < 0.0 ) {
			printf( "Internal error in insertsite():\n" );
			printf( "  Clockwise triangle after point insertion (left).\n" );
		}
		if ( counterclockwise( botpoint, rightpoint, insertpoint ) < 0.0 ) {
			printf( "Internal error in insertsite():\n" );
			printf( "  Clockwise triangle after point insertion (right).\n" );
		}
#endif /* SELF_CHECK */
		if ( verbose > 2 ) {
			printf( "  Updating top " );
			printtriangle( &horiz );
			printf( "  Creating left " );
			printtriangle( &newbotleft );
			printf( "  Creating right " );
			printtriangle( &newbotright );
		}
	}

	/* The insertion is successful by default, unless an encroached */
	/*   edge is found.                                             */
	success = SUCCESSFULPOINT;
	/* 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 );
	rightpoint = first;
	dest( horiz, leftpoint );
	/* Circle until finished. */
	while ( 1 ) {
		/* By default, the edge will be flipped. */
		doflip = 1;
		if ( checksegments ) {
			/* Check for a segment, which cannot be flipped. */
			tspivot( horiz, checkshelle );
			if ( checkshelle.sh != dummysh ) {
				/* The edge is a segment and cannot be flipped. */
				doflip = 0;
#ifndef CDT_ONLY
				if ( segmentflaws ) {
					/* Does the new point encroach upon this segment? */
					if ( checkedge4encroach( &checkshelle ) ) {
						success = ENCROACHINGPOINT;
					}
				}
#endif /* not CDT_ONLY */
			}
		}
		if ( doflip ) {
			/* Check if the edge is a boundary edge. */
			sym( horiz, top );
			if ( top.tri == dummytri ) {
				/* The edge is a boundary edge and cannot be flipped. */
				doflip = 0;
			}
			else {
				/* Find the point on the other side of the edge. */
				apex( top, farpoint );
				/* In the incremental Delaunay triangulation algorithm, any of    */
				/*   `leftpoint', `rightpoint', and `farpoint' 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 ( ( leftpoint == infpoint1 ) || ( leftpoint == infpoint2 )
					 || ( leftpoint == infpoint3 ) ) {
					/* `leftpoint' is infinitely distant.  Check the convexity of */
					/*   the boundary of the triangulation.  'farpoint' might be  */
					/*   infinite as well, but trust me, this same condition      */
					/*   should be applied.                                       */
					doflip = counterclockwise( insertpoint, rightpoint, farpoint ) > 0.0;
				}
				else if ( ( rightpoint == infpoint1 ) || ( rightpoint == infpoint2 )
						  || ( rightpoint == infpoint3 ) ) {
					/* `rightpoint' is infinitely distant.  Check the convexity of */
					/*   the boundary of the triangulation.  'farpoint' might be  */
					/*   infinite as well, but trust me, this same condition      */
					/*   should be applied.                                       */
					doflip = counterclockwise( farpoint, leftpoint, insertpoint ) > 0.0;
				}
				else if ( ( farpoint == infpoint1 ) || ( farpoint == infpoint2 )
						  || ( farpoint == infpoint3 ) ) {
					/* `farpoint' 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( leftpoint, insertpoint, rightpoint, farpoint )
							 > 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 ( checksegments ) {
						/* Check for shell edges and rebond them to the quadrilateral. */
						tspivot( topleft, toplshelle );
						tspivot( botleft, botlshelle );
						tspivot( botright, botrshelle );
						tspivot( topright, toprshelle );
						if ( toplshelle.sh == dummysh ) {
							tsdissolve( topright );
						}
						else {
							tsbond( topright, toplshelle );
						}
						if ( botlshelle.sh == dummysh ) {
							tsdissolve( topleft );
						}
						else {
							tsbond( topleft, botlshelle );
						}
						if ( botrshelle.sh == dummysh ) {
							tsdissolve( botleft );
						}
						else {
							tsbond( botleft, botrshelle );
						}
						if ( toprshelle.sh == dummysh ) {
							tsdissolve( botright );
						}
						else {
							tsbond( botright, toprshelle );
						}
					}
					/* New point assignments for the rotated quadrilateral. */
					setorg( horiz, farpoint );
					setdest( horiz, insertpoint );
					setapex( horiz, rightpoint );
					setorg( top, insertpoint );
					setdest( top, farpoint );
					setapex( top, leftpoint );
					for ( i = 0; i < eextras; i++ ) {
						/* Take the average of the two triangles' attributes. */
						attrib = (REAL)( 0.5 * ( elemattribute( top, i ) + elemattribute( horiz, i ) ) );
						setelemattribute( top, i, attrib );
						setelemattribute( horiz, i, attrib );
					}
					if ( 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 = (REAL)( 0.5 * ( areabound( top ) + areabound( horiz ) ) );
						}
						setareabound( top, area );
						setareabound( horiz, area );
					}
#ifdef SELF_CHECK
					if ( insertpoint != (point) NULL ) {
						if ( counterclockwise( leftpoint, insertpoint, rightpoint ) < 0.0 ) {
							printf( "Internal error in insertsite():\n" );
							printf( "  Clockwise triangle prior to edge flip (bottom).\n" );
						}
						/* The following test has been removed because constrainededge() */
						/*   sometimes generates inverted triangles that insertsite()    */
						/*   removes.                                                    */
/*
            if (counterclockwise(rightpoint, farpoint, leftpoint) < 0.0) {
              printf("Internal error in insertsite():\n");
              printf("  Clockwise triangle prior to edge flip (top).\n");
            }
 */
						if ( counterclockwise( farpoint, leftpoint, insertpoint ) < 0.0 ) {
							printf( "Internal error in insertsite():\n" );
							printf( "  Clockwise triangle after edge flip (left).\n" );
						}
						if ( counterclockwise( insertpoint, rightpoint, farpoint ) < 0.0 ) {
							printf( "Internal error in insertsite():\n" );
							printf( "  Clockwise triangle after edge flip (right).\n" );
						}
					}
#endif /* SELF_CHECK */
					if ( verbose > 2 ) {
						printf( "  Edge flip results in left " );
						lnextself( topleft );
						printtriangle( &topleft );
						printf( "  and right " );
						printtriangle( &horiz );
					}
					/* On the next iterations, consider the two edges that were  */
					/*   exposed (this is, are now visible to the newly inserted */
					/*   point) by the edge flip.                                */
					lprevself( horiz );
					leftpoint = farpoint;
				}
			}
		}
		if ( !doflip ) {
			/* The handle `horiz' is accepted as locally Delaunay. */
#ifndef CDT_ONLY
			if ( triflaws ) {
				/* Check the triangle `horiz' for quality. */
				testtriangle( &horiz );
			}
#endif /* not CDT_ONLY */
			/* Look for the next edge around the newly inserted point. */
			lnextself( horiz );
			sym( horiz, testtri );
			/* Check for finishing a complete revolution about the new point, or */
			/*   falling off the edge of the triangulation.  The latter will     */
			/*   happen when a point is inserted at a boundary.                  */
			if ( ( leftpoint == first ) || ( testtri.tri == dummytri ) ) {
				/* We're done.  Return a triangle whose origin is the new point. */
				lnext( horiz, *searchtri );
				lnext( horiz, recenttri );
				return success;
			}
			/* Finish finding the next edge around the newly inserted point. */
			lnext( testtri, horiz );
			rightpoint = leftpoint;
			dest( horiz, leftpoint );
		}
	}
}

/*****************************************************************************/
/*                                                                           */
/*  triangulatepolygon()   Find the Delaunay triangulation of a polygon that */
/*                         has a certain "nice" shape.  This includes the    */
/*                         polygons that result from deletion of a point 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 point 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 time.                                            */
/*                                                                           */
/*  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.                                                                     */
/*                                                                           */
/*****************************************************************************/

void triangulatepolygon( firstedge, lastedge, edgecount, doflip, triflaws )
struct triedge *firstedge;
struct triedge *lastedge;
int edgecount;
int doflip;
int triflaws;
{
	struct triedge testtri;
	struct triedge besttri;
	struct triedge tempedge;
	point leftbasepoint, rightbasepoint;
	point testpoint;
	point bestpoint;
	int bestnumber;
	int i;
	triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */

	/* Identify the base vertices. */
	apex( *lastedge, leftbasepoint );
	dest( *firstedge, rightbasepoint );
	if ( verbose > 2 ) {
		printf( "  Triangulating interior polygon at edge\n" );
		printf( "    (%.12g, %.12g) (%.12g, %.12g)\n", leftbasepoint[0],
				leftbasepoint[1], rightbasepoint[0], rightbasepoint[1] );
	}
	/* Find the best vertex to connect the base to. */
	onext( *firstedge, besttri );
	dest( besttri, bestpoint );
	triedgecopy( besttri, testtri );
	bestnumber = 1;
	for ( i = 2; i <= edgecount - 2; i++ ) {
		onextself( testtri );
		dest( testtri, testpoint );
		/* Is this a better vertex? */
		if ( incircle( leftbasepoint, rightbasepoint, bestpoint, testpoint ) > 0.0 ) {
			triedgecopy( testtri, besttri );
			bestpoint = testpoint;
			bestnumber = i;
		}
	}
	if ( verbose > 2 ) {
		printf( "    Connecting edge to (%.12g, %.12g)\n", bestpoint[0],
				bestpoint[1] );
	}
	if ( bestnumber > 1 ) {
		/* Recursively triangulate the smaller polygon on the right. */
		oprev( besttri, tempedge );
		triangulatepolygon( firstedge, &tempedge, bestnumber + 1, 1, triflaws );
	}
	if ( bestnumber < edgecount - 2 ) {
		/* Recursively triangulate the smaller polygon on the left. */
		sym( besttri, tempedge );
		triangulatepolygon( &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( &besttri );
#ifndef CDT_ONLY
		if ( triflaws ) {
			/* Check the quality of the newly committed triangle. */
			sym( besttri, testtri );
			testtriangle( &testtri );
		}
#endif /* not CDT_ONLY */
	}
	/* Return the base triangle. */
	triedgecopy( besttri, *lastedge );
}

/*****************************************************************************/
/*                                                                           */
/*  deletesite()   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 point is a polygon, for which the Delaunay triangulation is      */
/*  found.  Two triangles are removed from the mesh.                         */
/*                                                                           */
/*  Only interior points that do not lie on segments (shell edges) or        */
/*  boundaries may be deleted.                                               */
/*                                                                           */
/*****************************************************************************/

#ifndef CDT_ONLY

void deletesite( deltri )
struct triedge *deltri;
{
	struct triedge countingtri;
	struct triedge firstedge, lastedge;
	struct triedge deltriright;
	struct triedge lefttri, righttri;
	struct triedge leftcasing, rightcasing;
	struct edge leftshelle, rightshelle;
	point delpoint;
	point neworg;
	int edgecount;
	triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */
	shelle sptr;                    /* Temporary variable used by tspivot(). */

	org( *deltri, delpoint );
	if ( verbose > 1 ) {
		printf( "  Deleting (%.12g, %.12g).\n", delpoint[0], delpoint[1] );
	}
	pointdealloc( delpoint );

	/* Count the degree of the point being deleted. */
	onext( *deltri, countingtri );
	edgecount = 1;
	while ( !triedgeequal( *deltri, countingtri ) ) {
#ifdef SELF_CHECK
		if ( countingtri.tri == dummytri ) {
			printf( "Internal error in deletesite():\n" );
			printf( "  Attempt to delete boundary point.\n" );
			internalerror();
		}
#endif /* SELF_CHECK */
		edgecount++;
		onextself( countingtri );
	}

#ifdef SELF_CHECK
	if ( edgecount < 3 ) {
		printf( "Internal error in deletesite():\n  Point has degree %d.\n",
				edgecount );
		internalerror();
	}
#endif /* SELF_CHECK */
	if ( edgecount > 3 ) {
		/* Triangulate the polygon defined by the union of all triangles */
		/*   adjacent to the point being deleted.  Check the quality of  */
		/*   the resulting triangles.                                    */
		onext( *deltri, firstedge );
		oprev( *deltri, lastedge );
		triangulatepolygon( &firstedge, &lastedge, edgecount, 0, !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, leftshelle );
	if ( leftshelle.sh != dummysh ) {
		tsbond( *deltri, leftshelle );
	}
	tspivot( righttri, rightshelle );
	if ( rightshelle.sh != dummysh ) {
		tsbond( deltriright, rightshelle );
	}

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

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

#endif /* not CDT_ONLY */

/**                                                                         **/
/**                                                                         **/
/********* Mesh transformation routines end here                     *********/

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

/*****************************************************************************/
/*                                                                           */
/*  The divide-and-conquer bounding box                                      */
/*                                                                           */
/*  I originally implemented the divide-and-conquer and incremental Delaunay */
/*  triangulations using the edge-based data structure presented by Guibas   */
/*  and Stolfi.  Switching to a triangle-based data structure doubled the    */
/*  speed.  However, I had to think of a few extra tricks to maintain the    */
/*  elegance of the original algorithms.                                     */
/*                                                                           */
/*  The "bounding box" used by my variant of the divide-and-conquer          */
/*  algorithm uses one triangle for each edge of the convex hull of the      */
/*  triangulation.  These bounding triangles all share a common apical       */
/*  vertex, which is represented by NULL and which represents nothing.       */
/*  The bounding triangles are linked in a circular fan about this NULL      */
/*  vertex, and the edges on the convex hull of the triangulation appear     */
/*  opposite the NULL vertex.  You might find it easiest to imagine that     */
/*  the NULL vertex is a point in 3D space behind the center of the          */
/*  triangulation, and that the bounding triangles form a sort of cone.      */
/*                                                                           */
/*  This bounding box makes it easy to represent degenerate cases.  For      */
/*  instance, the triangulation of two vertices is a single edge.  This edge */
/*  is represented by two bounding box triangles, one on each "side" of the  */
/*  edge.  These triangles are also linked together in a fan about the NULL  */
/*  vertex.                                                                  */
/*                                                                           */
/*  The bounding box also makes it easy to traverse the convex hull, as the  */
/*  divide-and-conquer algorithm needs to do.                                */
/*                                                                           */
/*****************************************************************************/

/*****************************************************************************/
/*                                                                           */
/*  pointsort()   Sort an array of points 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.                                            */
/*                                                                           */
/*****************************************************************************/

void pointsort( sortarray, arraysize )
point * sortarray;
int arraysize;
{
	int left, right;
	int pivot;
	REAL pivotx, pivoty;
	point 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( arraysize );
	pivotx = sortarray[pivot][0];
	pivoty = sortarray[pivot][1];
	/* Split the array. */
	left = -1;
	right = arraysize;
	while ( left < right ) {
		/* Search for a point 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 point 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 points. */
			temp = sortarray[left];
			sortarray[left] = sortarray[right];
			sortarray[right] = temp;
		}
	}
	if ( left > 1 ) {
		/* Recursively sort the left subset. */
		pointsort( sortarray, left );
	}
	if ( right < arraysize - 2 ) {
		/* Recursively sort the right subset. */
		pointsort( &sortarray[right + 1], arraysize - right - 1 );
	}
}

/*****************************************************************************/
/*                                                                           */
/*  pointmedian()   An order statistic algorithm, almost.  Shuffles an array */
/*                  of points so that the first `median' points occur        */
/*                  lexicographically before the remaining points.           */
/*                                                                           */
/*  Uses the x-coordinate as the primary key if axis == 0; the y-coordinate  */
/*  if axis == 1.  Very similar to the pointsort() procedure, but runs in    */
/*  randomized linear time.                                                  */
/*                                                                           */
/*****************************************************************************/

void pointmedian( sortarray, arraysize, median, axis )
point * sortarray;
int arraysize;
int median;
int axis;
{
	int left, right;
	int pivot;
	REAL pivot1, pivot2;
	point 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( arraysize );
	pivot1 = sortarray[pivot][axis];
	pivot2 = sortarray[pivot][1 - axis];
	/* Split the array. */
	left = -1;
	right = arraysize;
	while ( left < right ) {
		/* Search for a point 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 point 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 points. */
			temp = sortarray[left];
			sortarray[left] = sortarray[right];
			sortarray[right] = temp;
		}
	}
	/* Unlike in pointsort(), at most one of the following */
	/*   conditionals is true.                             */
	if ( left > median ) {
		/* Recursively shuffle the left subset. */
		pointmedian( sortarray, left, median, axis );
	}
	if ( right < median - 1 ) {
		/* Recursively shuffle the right subset. */
		pointmedian( &sortarray[right + 1], arraysize - right - 1,
					 median - right - 1, axis );
	}
}

/*****************************************************************************/
/*                                                                           */
/*  alternateaxes()   Sorts the points 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 points are       */
/*  always sorted by x-coordinate.                                           */
/*                                                                           */
/*****************************************************************************/

void alternateaxes( sortarray, arraysize, axis )
point * sortarray;
int arraysize;
int axis;
{
	int divider;

	divider = arraysize >> 1;
	if ( arraysize <= 3 ) {
		/* Recursive base case:  subsets of two or three points will be      */
		/*   handled specially, and should always be sorted by x-coordinate. */
		axis = 0;
	}
	/* Partition with a horizontal or vertical cut. */
	pointmedian( 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 point.                                       */
/*                                                                           */
/*  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.                                                                  */
/*                                                                           */
/*****************************************************************************/

void mergehulls( farleft, innerleft, innerright, farright, axis )
struct triedge *farleft;
struct triedge *innerleft;
struct triedge *innerright;
struct triedge *farright;
int axis;
{
	struct triedge leftcand, rightcand;
	struct triedge baseedge;
	struct triedge nextedge;
	struct triedge sidecasing, topcasing, outercasing;
	struct triedge checkedge;
	point innerleftdest;
	point innerrightorg;
	point innerleftapex, innerrightapex;
	point farleftpt, farrightpt;
	point farleftapex, farrightapex;
	point lowerleft, lowerright;
	point upperleft, upperright;
	point nextapex;
	point 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 ( dwyer && ( axis == 1 ) ) {
		org( *farleft, farleftpt );
		apex( *farleft, farleftapex );
		dest( *farright, farrightpt );
		apex( *farright, farrightapex );
		/* The pointers to the extremal points are shifted to point to the */
		/*   topmost and bottommost point of each hull, rather than the    */
		/*   leftmost and rightmost points.                                */
		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" point of the left hull. */
		if ( counterclockwise( innerleftdest, innerleftapex, innerrightorg ) > 0.0 ) {
			lprevself( *innerleft );
			symself( *innerleft );
			innerleftdest = innerleftapex;
			apex( *innerleft, innerleftapex );
			changemade = 1;
		}
		/* Make innerrightorg the "bottommost" point of the right hull. */
		if ( counterclockwise( 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( &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 ( verbose > 2 ) {
		printf( "  Creating base bounding " );
		printtriangle( &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 point of    */
		/*   the left triangulation.  And vice-versa.)                           */
		leftfinished = counterclockwise( upperleft, lowerleft, lowerright ) <= 0.0;
		rightfinished = counterclockwise( upperright, lowerleft, lowerright ) <= 0.0;
		if ( leftfinished && rightfinished ) {
			/* Create the top new bounding triangle. */
			maketriangle( &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 ( verbose > 2 ) {
				printf( "  Creating top bounding " );
				printtriangle( &baseedge );
			}
			/* Special treatment for horizontal cuts. */
			if ( 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 points are restored to the leftmost */
				/*   and rightmost points (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 != (point) NULL ) {
				/* Check whether the edge is Delaunay. */
				badedge = incircle( 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? */
					triedgecopy( sidecasing, nextedge );
					apex( nextedge, nextapex );
					if ( nextapex != (point) NULL ) {
						/* Check whether the edge is Delaunay. */
						badedge = incircle( 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 != (point) NULL ) {
				/* Check whether the edge is Delaunay. */
				badedge = incircle( 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? */
					triedgecopy( sidecasing, nextedge );
					apex( nextedge, nextapex );
					if ( nextapex != (point) NULL ) {
						/* Check whether the edge is Delaunay. */
						badedge = incircle( lowerleft, lowerright, upperright, nextapex )
								  > 0.0;
					}
					else {
						/* Avoid eating right through the triangulation. */
						badedge = 0;
					}
				}
			}
		}
		if ( leftfinished || ( !rightfinished &&
							   ( incircle( 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 ( verbose > 2 ) {
			printf( "  Connecting " );
			printtriangle( &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 points) 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).                                                */
/*                                                                           */
/*****************************************************************************/

void divconqrecurse( sortarray, vertices, axis, farleft, farright )
point * sortarray;
int vertices;
int axis;
struct triedge *farleft;
struct triedge *farright;
{
	struct triedge midtri, tri1, tri2, tri3;
	struct triedge innerleft, innerright;
	REAL area;
	int divider;

	if ( verbose > 2 ) {
		printf( "  Triangulating %d points.\n", vertices );
	}
	if ( vertices == 2 ) {
		/* The triangulation of two vertices is an edge.  An edge is */
		/*   represented by two bounding triangles.                  */
		maketriangle( farleft );
		setorg( *farleft, sortarray[0] );
		setdest( *farleft, sortarray[1] );
		/* The apex is intentionally left NULL. */
		maketriangle( 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 ( verbose > 2 ) {
			printf( "  Creating " );
			printtriangle( farleft );
			printf( "  Creating " );
			printtriangle( 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( &midtri );
		maketriangle( &tri1 );
		maketriangle( &tri2 );
		maketriangle( &tri3 );
		area = counterclockwise( sortarray[0], sortarray[1], sortarray[2] );
		if ( area == 0.0 ) {
			/* Three collinear points; 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]. */
			triedgecopy( tri1, *farleft );
			/* Ensure that the destination of `farright' is sortarray[2]. */
			triedgecopy( tri2, *farright );
		}
		else {
			/* The three points 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]. */
			triedgecopy( tri1, *farleft );
			/* Ensure that the destination of `farright' is sortarray[2]. */
			if ( area > 0.0 ) {
				triedgecopy( tri2, *farright );
			}
			else {
				lnext( *farleft, *farright );
			}
		}
		if ( verbose > 2 ) {
			printf( "  Creating " );
			printtriangle( &midtri );
			printf( "  Creating " );
			printtriangle( &tri1 );
			printf( "  Creating " );
			printtriangle( &tri2 );
			printf( "  Creating " );
			printtriangle( &tri3 );
		}
		return;
	}
	else {
		/* Split the vertices in half. */
		divider = vertices >> 1;
		/* Recursively triangulate each half. */
		divconqrecurse( sortarray, divider, 1 - axis, farleft, &innerleft );
		divconqrecurse( &sortarray[divider], vertices - divider, 1 - axis,
						&innerright, farright );
		if ( verbose > 1 ) {
			printf( "  Joining triangulations with %d and %d vertices.\n", divider,
					vertices - divider );
		}
		/* Merge the two triangulations into one. */
		mergehulls( farleft, &innerleft, &innerright, farright, axis );
	}
}

long removeghosts( startghost )
struct triedge *startghost;
{
	struct triedge searchedge;
	struct triedge dissolveedge;
	struct triedge deadtri;
	point markorg;
	long hullsize;
	triangle ptr;                       /* Temporary variable used by sym(). */

	if ( verbose ) {
		printf( "  Removing ghost triangles.\n" );
	}
	/* Find an edge on the convex hull to start point location from. */
	lprev( *startghost, searchedge );
	symself( searchedge );
	dummytri[0] = encode( searchedge );
	/* Remove the bounding box and count the convex hull edges. */
	triedgecopy( *startghost, dissolveedge );
	hullsize = 0;
	do {
		hullsize++;
		lnext( dissolveedge, deadtri );
		lprevself( dissolveedge );
		symself( dissolveedge );
		/* If no PSLG is involved, set the boundary markers of all the points */
		/*   on the convex hull.  If a PSLG is used, this step is done later. */
		if ( !poly ) {
			/* Watch out for the case where all the input points are collinear. */
			if ( dissolveedge.tri != dummytri ) {
				org( dissolveedge, markorg );
				if ( pointmark( markorg ) == 0 ) {
					setpointmark( markorg, 1 );
				}
			}
		}
		/* Remove a bounding triangle from a convex hull triangle. */
		dissolve( dissolveedge );
		/* Find the next bounding triangle. */
		sym( deadtri, dissolveedge );
		/* Delete the bounding triangle. */
		triangledealloc( deadtri.tri );
	} while ( !triedgeequal( dissolveedge, *startghost ) );
	return hullsize;
}

/*****************************************************************************/
/*                                                                           */
/*  divconqdelaunay()   Form a Delaunay triangulation by the divide-and-     */
/*                      conquer method.                                      */
/*                                                                           */
/*  Sorts the points, calls a recursive procedure to triangulate them, and   */
/*  removes the bounding box, setting boundary markers as appropriate.       */
/*                                                                           */
/*****************************************************************************/

long divconqdelaunay(){
	point *sortarray;
	struct triedge hullleft, hullright;
	int divider;
	int i, j;

	/* Allocate an array of pointers to points for sorting. */
	sortarray = (point *) malloc( inpoints * sizeof( point ) );
	if ( sortarray == (point *) NULL ) {
		printf( "Error:  Out of memory.\n" );
		exit( 1 );
	}
	traversalinit( &points );
	for ( i = 0; i < inpoints; i++ ) {
		sortarray[i] = pointtraverse();
	}
	if ( verbose ) {
		printf( "  Sorting points.\n" );
	}
	/* Sort the points. */
	pointsort( sortarray, inpoints );
	/* Discard duplicate points, which can really mess up the algorithm. */
	i = 0;
	for ( j = 1; j < inpoints; j++ ) {
		if ( ( sortarray[i][0] == sortarray[j][0] )
			 && ( sortarray[i][1] == sortarray[j][1] ) ) {
			if ( !quiet ) {
				printf(
					"Warning:  A duplicate point at (%.12g, %.12g) appeared and was ignored.\n",
					sortarray[j][0], sortarray[j][1] );
			}
/*  Commented out - would eliminate point from output .node file, but causes
    a failure if some segment has this point as an endpoint.
      setpointmark(sortarray[j], DEADPOINT);
 */
		}
		else {
			i++;
			sortarray[i] = sortarray[j];
		}
	}
	i++;
	if ( dwyer ) {
		/* Re-sort the array of points 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 ( verbose ) {
		printf( "  Forming triangulation.\n" );
	}
	/* Form the Delaunay triangulation. */
	divconqrecurse( sortarray, i, 0, &hullleft, &hullright );
	free( sortarray );

	return removeghosts( &hullleft );
}

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

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

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

#ifndef REDUCED

void boundingbox(){
	struct triedge inftri;        /* Handle for the triangular bounding box. */
	REAL width;

	if ( verbose ) {
		printf( "  Creating triangular bounding box.\n" );
	}
	/* Find the width (or height, whichever is larger) of the triangulation. */
	width = xmax - xmin;
	if ( ymax - ymin > width ) {
		width = ymax - ymin;
	}
	if ( width == 0.0 ) {
		width = 1.0;
	}
	/* Create the vertices of the bounding box. */
	infpoint1 = (point) malloc( points.itembytes );
	infpoint2 = (point) malloc( points.itembytes );
	infpoint3 = (point) malloc( points.itembytes );
	if ( ( infpoint1 == (point) NULL ) || ( infpoint2 == (point) NULL )
		 || ( infpoint3 == (point) NULL ) ) {
		printf( "Error:  Out of memory.\n" );
		exit( 1 );
	}
	infpoint1[0] = xmin - 50.0 * width;
	infpoint1[1] = ymin - 40.0 * width;
	infpoint2[0] = xmax + 50.0 * width;
	infpoint2[1] = ymin - 40.0 * width;
	infpoint3[0] = 0.5 * ( xmin + xmax );
	infpoint3[1] = ymax + 60.0 * width;

	/* Create the bounding box. */
	maketriangle( &inftri );
	setorg( inftri, infpoint1 );
	setdest( inftri, infpoint2 );
	setapex( inftri, infpoint3 );
	/* Link dummytri to the bounding box so we can always find an */
	/*   edge to begin searching (point location) from.           */
	dummytri[0] = (triangle) inftri.tri;
	if ( verbose > 2 ) {
		printf( "  Creating " );
		printtriangle( &inftri );
	}
}

#endif /* not REDUCED */

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

#ifndef REDUCED

long removebox(){
	struct triedge deadtri;
	struct triedge searchedge;
	struct triedge checkedge;
	struct triedge nextedge, finaledge, dissolveedge;
	point markorg;
	long hullsize;
	triangle ptr;                       /* Temporary variable used by sym(). */

	if ( verbose ) {
		printf( "  Removing triangular bounding box.\n" );
	}
	/* Find a boundary triangle. */
	nextedge.tri = 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 point 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 == 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.    */
	dummytri[0] = encode( searchedge );
	hullsize = -2l;
	while ( !triedgeequal( 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 ( !poly ) {
			/* Be careful!  One must check for the case where all the input   */
			/*   points are collinear, and thus all the triangles are part of */
			/*   the bounding box.  Otherwise, the setpointmark() call below  */
			/*   will cause a bad pointer reference.                          */
			if ( dissolveedge.tri != dummytri ) {
				org( dissolveedge, markorg );
				if ( pointmark( markorg ) == 0 ) {
					setpointmark( markorg, 1 );
				}
			}
		}
		/* Disconnect the bounding box triangle from the mesh triangle. */
		dissolve( dissolveedge );
		lnext( nextedge, deadtri );
		sym( deadtri, nextedge );
		/* Get rid of the bounding box triangle. */
		triangledealloc( deadtri.tri );
		/* Do we need to turn the corner? */
		if ( nextedge.tri == dummytri ) {
			/* Turn the corner. */
			triedgecopy( dissolveedge, nextedge );
		}
	}
	triangledealloc( finaledge.tri );

	free( infpoint1 );              /* Deallocate the bounding box vertices. */
	free( infpoint2 );
	free( infpoint3 );

	return hullsize;
}

#endif /* not REDUCED */

/*****************************************************************************/
/*                                                                           */
/*  incrementaldelaunay()   Form a Delaunay triangulation by incrementally   */
/*                          adding vertices.                                 */
/*                                                                           */
/*****************************************************************************/

#ifndef REDUCED

long incrementaldelaunay(){
	struct triedge starttri;
	point pointloop;
	int i;

	/* Create a triangular bounding box. */
	boundingbox();
	if ( verbose ) {
		printf( "  Incrementally inserting points.\n" );
	}
	traversalinit( &points );
	pointloop = pointtraverse();
	i = 1;
	while ( pointloop != (point) NULL ) {
		/* Find a boundary triangle to search from. */
		starttri.tri = (triangle *) NULL;
		if ( insertsite( pointloop, &starttri, (struct edge *) NULL, 0, 0 ) ==
			 DUPLICATEPOINT ) {
			if ( !quiet ) {
				printf(
					"Warning:  A duplicate point at (%.12g, %.12g) appeared and was ignored.\n",
					pointloop[0], pointloop[1] );
			}
/*  Commented out - would eliminate point from output .node file.
      setpointmark(pointloop, DEADPOINT);
 */
		}
		pointloop = pointtraverse();
		i++;
	}
	/* Remove the bounding box. */
	return removebox();
}

#endif /* not REDUCED */

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

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

#ifndef REDUCED

void eventheapinsert( heap, heapsize, newevent )
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;
}

#endif /* not REDUCED */

#ifndef REDUCED

void eventheapify( heap, heapsize, eventnum )
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;
		}
	}
}

#endif /* not REDUCED */

#ifndef REDUCED

void eventheapdelete( heap, heapsize, eventnum )
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 );
}

#endif /* not REDUCED */

#ifndef REDUCED

void createeventheap( eventheap, events, freeevents )
struct event ***eventheap;
struct event **events;
struct event **freeevents;
{
	point thispoint;
	int maxevents;
	int i;

	maxevents = ( 3 * inpoints ) / 2;
	*eventheap = (struct event **) malloc( maxevents * sizeof( struct event * ) );
	if ( *eventheap == (struct event **) NULL ) {
		printf( "Error:  Out of memory.\n" );
		exit( 1 );
	}
	*events = (struct event *) malloc( maxevents * sizeof( struct event ) );
	if ( *events == (struct event *) NULL ) {
		printf( "Error:  Out of memory.\n" );
		exit( 1 );
	}
	traversalinit( &points );
	for ( i = 0; i < inpoints; i++ ) {
		thispoint = pointtraverse();
		( *events )[i].eventptr = (VOID *) thispoint;
		( *events )[i].xkey = thispoint[0];
		( *events )[i].ykey = thispoint[1];
		eventheapinsert( *eventheap, i, *events + i );
	}
	*freeevents = (struct event *) NULL;
	for ( i = maxevents - 1; i >= inpoints; i-- ) {
		( *events )[i].eventptr = (VOID *) *freeevents;
		*freeevents = *events + i;
	}
}

#endif /* not REDUCED */

#ifndef REDUCED

int rightofhyperbola( fronttri, newsite )
struct triedge *fronttri;
point newsite;
{
	point leftpoint, rightpoint;
	REAL dxa, dya, dxb, dyb;

	hyperbolacount++;

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

#endif /* not REDUCED */

#ifndef REDUCED

REAL circletop( pa, pb, pc, ccwabc )
point pa;
point pb;
point pc;
REAL ccwabc;
{
	REAL xac, yac, xbc, ybc, xab, yab;
	REAL aclen2, bclen2, ablen2;

	circletopcount++;

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

#endif /* not REDUCED */

#ifndef REDUCED

void check4deadevent( checktri, freeevents, eventheap, heapsize )
struct triedge *checktri;
struct event **freeevents;
struct event **eventheap;
int *heapsize;
{
	struct event *deadevent;
	point eventpoint;
	int eventnum;

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

#endif /* not REDUCED */

#ifndef REDUCED

struct splaynode *splay( splaytree, searchpoint, searchtri )
struct splaynode *splaytree;
point searchpoint;
struct triedge *searchtri;
{
	struct splaynode *child, *grandchild;
	struct splaynode *lefttree, *righttree;
	struct splaynode *leftright;
	point checkpoint;
	int rightofroot, rightofchild;

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

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

#endif /* not REDUCED */

#ifndef REDUCED

struct splaynode *splayinsert( splayroot, newkey, searchpoint )
struct splaynode *splayroot;
struct triedge *newkey;
point searchpoint;
{
	struct splaynode *newsplaynode;

	newsplaynode = (struct splaynode *) poolalloc( &splaynodes );
	triedgecopy( *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( &splayroot->keyedge, searchpoint ) ) {
		newsplaynode->lchild = splayroot;
		newsplaynode->rchild = splayroot->rchild;
		splayroot->rchild = (struct splaynode *) NULL;
	}
	else {
		newsplaynode->lchild = splayroot->lchild;
		newsplaynode->rchild = splayroot;
		splayroot->lchild = (struct splaynode *) NULL;
	}
	return newsplaynode;
}

#endif /* not REDUCED */

#ifndef REDUCED

struct splaynode *circletopinsert( splayroot, newkey, pa, pb, pc, topy )
struct splaynode *splayroot;
struct triedge *newkey;
point pa;
point pb;
point pc;
REAL topy;
{
	REAL ccwabc;
	REAL xac, yac, xbc, ybc;
	REAL aclen2, bclen2;
	REAL searchpoint[2];
	struct triedge dummytri;

	ccwabc = counterclockwise( 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( splay( splayroot, (point) searchpoint, &dummytri ), newkey,
						(point) searchpoint );
}

#endif /* not REDUCED */

#ifndef REDUCED

struct splaynode *frontlocate( splayroot, bottommost, searchpoint, searchtri,
							   farright )
struct splaynode *splayroot;
struct triedge *bottommost;
point searchpoint;
struct triedge *searchtri;
int *farright;
{
	int farrightflag;
	triangle ptr;                     /* Temporary variable used by onext(). */

	triedgecopy( *bottommost, *searchtri );
	splayroot = splay( splayroot, searchpoint, searchtri );

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

#endif /* not REDUCED */

#ifndef REDUCED

long sweeplinedelaunay(){
	struct event **eventheap;
	struct event *events;
	struct event *freeevents;
	struct event *nextevent;
	struct event *newevent;
	struct splaynode *splayroot;
	struct triedge bottommost;
	struct triedge searchtri;
	struct triedge fliptri;
	struct triedge lefttri, righttri, farlefttri, farrighttri;
	struct triedge inserttri;
	point firstpoint, secondpoint;
	point nextpoint, lastpoint;
	point connectpoint;
	point leftpoint, midpoint, rightpoint;
	REAL lefttest, righttest;
	int heapsize;
	int check4events, farrightflag;
	triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */

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

	if ( verbose ) {
		printf( "  Placing points in event heap.\n" );
	}
	createeventheap( &eventheap, &events, &freeevents );
	heapsize = inpoints;

	if ( verbose ) {
		printf( "  Forming triangulation.\n" );
	}
	maketriangle( &lefttri );
	maketriangle( &righttri );
	bond( lefttri, righttri );
	lnextself( lefttri );
	lprevself( righttri );
	bond( lefttri, righttri );
	lnextself( lefttri );
	lprevself( righttri );
	bond( lefttri, righttri );
	firstpoint = (point) eventheap[0]->eventptr;
	eventheap[0]->eventptr = (VOID *) freeevents;
	freeevents = eventheap[0];
	eventheapdelete( eventheap, heapsize, 0 );
	heapsize--;
	do {
		if ( heapsize == 0 ) {
			printf( "Error:  Input points are all identical.\n" );
			exit( 1 );
		}
		secondpoint = (point) eventheap[0]->eventptr;
		eventheap[0]->eventptr = (VOID *) freeevents;
		freeevents = eventheap[0];
		eventheapdelete( eventheap, heapsize, 0 );
		heapsize--;
		if ( ( firstpoint[0] == secondpoint[0] )
			 && ( firstpoint[1] == secondpoint[1] ) ) {
			printf(
				"Warning:  A duplicate point at (%.12g, %.12g) appeared and was ignored.\n",
				secondpoint[0], secondpoint[1] );
/*  Commented out - would eliminate point from output .node file.
      setpointmark(secondpoint, DEADPOINT);
 */
		}
	} while ( ( firstpoint[0] == secondpoint[0] )
			  && ( firstpoint[1] == secondpoint[1] ) );
	setorg( lefttri, firstpoint );
	setdest( lefttri, secondpoint );
	setorg( righttri, secondpoint );
	setdest( righttri, firstpoint );
	lprev( lefttri, bottommost );
	lastpoint = secondpoint;
	while ( heapsize > 0 ) {
		nextevent = eventheap[0];
		eventheapdelete( eventheap, heapsize, 0 );
		heapsize--;
		check4events = 1;
		if ( nextevent->xkey < xmin ) {
			decode( nextevent->eventptr, fliptri );
			oprev( fliptri, farlefttri );
			check4deadevent( &farlefttri, &freeevents, eventheap, &heapsize );
			onext( fliptri, farrighttri );
			check4deadevent( &farrighttri, &freeevents, eventheap, &heapsize );

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

			if ( randomnation( SAMPLERATE ) == 0 ) {
				symself( fliptri );
				dest( fliptri, leftpoint );
				apex( fliptri, midpoint );
				org( fliptri, rightpoint );
				splayroot = circletopinsert( splayroot, &lefttri, leftpoint, midpoint,
											 rightpoint, nextevent->ykey );
			}
		}
		else {
			nextpoint = (point) nextevent->eventptr;
			if ( ( nextpoint[0] == lastpoint[0] ) && ( nextpoint[1] == lastpoint[1] ) ) {
				printf(
					"Warning:  A duplicate point at (%.12g, %.12g) appeared and was ignored.\n",
					nextpoint[0], nextpoint[1] );
/*  Commented out - would eliminate point from output .node file.
        setpointmark(nextpoint, DEADPOINT);
 */
				check4events = 0;
			}
			else {
				lastpoint = nextpoint;

				splayroot = frontlocate( splayroot, &bottommost, nextpoint, &searchtri,
										 &farrightflag );
/*
        triedgecopy(bottommost, searchtri);
        farrightflag = 0;
        while (!farrightflag && rightofhyperbola(&searchtri, nextpoint)) {
          onextself(searchtri);
          farrightflag = triedgeequal(searchtri, bottommost);
        }
 */

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

				triedgecopy( searchtri, farrighttri );
				sym( searchtri, farlefttri );
				maketriangle( &lefttri );
				maketriangle( &righttri );
				dest( farrighttri, connectpoint );
				setorg( lefttri, connectpoint );
				setdest( lefttri, nextpoint );
				setorg( righttri, nextpoint );
				setdest( righttri, connectpoint );
				bond( lefttri, righttri );
				lnextself( lefttri );
				lprevself( righttri );
				bond( lefttri, righttri );
				lnextself( lefttri );
				lprevself( righttri );
				bond( lefttri, farlefttri );
				bond( righttri, farrighttri );
				if ( !farrightflag && triedgeequal( farrighttri, bottommost ) ) {
					triedgecopy( lefttri, bottommost );
				}

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

		if ( check4events ) {
			apex( farlefttri, leftpoint );
			dest( lefttri, midpoint );
			apex( lefttri, rightpoint );
			lefttest = counterclockwise( leftpoint, midpoint, rightpoint );
			if ( lefttest > 0.0 ) {
				newevent = freeevents;
				freeevents = (struct event *) freeevents->eventptr;
				newevent->xkey = xminextreme;
				newevent->ykey = circletop( leftpoint, midpoint, rightpoint,
											lefttest );
				newevent->eventptr = (VOID *) encode( lefttri );
				eventheapinsert( eventheap, heapsize, newevent );
				heapsize++;
				setorg( lefttri, newevent );
			}
			apex( righttri, leftpoint );
			org( righttri, midpoint );
			apex( farrighttri, rightpoint );
			righttest = counterclockwise( leftpoint, midpoint, rightpoint );
			if ( righttest > 0.0 ) {
				newevent = freeevents;
				freeevents = (struct event *) freeevents->eventptr;
				newevent->xkey = xminextreme;
				newevent->ykey = circletop( leftpoint, midpoint, rightpoint,
											righttest );
				newevent->eventptr = (VOID *) encode( farrighttri );
				eventheapinsert( eventheap, heapsize, newevent );
				heapsize++;
				setorg( farrighttri, newevent );
			}
		}
	}

	pooldeinit( &splaynodes );
	lprevself( bottommost );
	return removeghosts( &bottommost );
}

#endif /* not REDUCED */

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

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

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

long delaunay(){
	eextras = 0;
	initializetrisegpools();

#ifdef REDUCED
	if ( !quiet ) {
		printf(
			"Constructing Delaunay triangulation by divide-and-conquer method.\n" );
	}
	return divconqdelaunay();
#else /* not REDUCED */
	if ( !quiet ) {
		printf( "Constructing Delaunay triangulation " );
		if ( incremental ) {
			printf( "by incremental method.\n" );
		}
		else if ( sweepline ) {
			printf( "by sweepline method.\n" );
		}
		else {
			printf( "by divide-and-conquer method.\n" );
		}
	}
	if ( incremental ) {
		return incrementaldelaunay();
	}
	else if ( sweepline ) {
		return sweeplinedelaunay();
	}
	else {
		return divconqdelaunay();
	}
#endif /* not REDUCED */
}

/*****************************************************************************/
/*                                                                           */
/*  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  */
/*  shell edges 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.                                                        */
/*                                                                           */
/*  Points that are not corners of triangles, such as nodes on edges of      */
/*  subparametric elements, are discarded.                                   */
/*                                                                           */
/*  This routine finds the adjacencies between triangles (and shell edges)   */
/*  by forming one stack of triangles for each vertex.  Each triangle is on  */
/*  three different stacks simultaneously.  Each triangle's shell edge       */
/*  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 shell edge rather    */
/*  than the next triangle of the stack.                                     */
/*                                                                           */
/*****************************************************************************/

#ifndef CDT_ONLY

#ifdef TRILIBRARY

int reconstruct( trianglelist, triangleattriblist, trianglearealist, elements,
				 corners, attribs, segmentlist, segmentmarkerlist,
				 numberofsegments )
int *trianglelist;
REAL *triangleattriblist;
REAL *trianglearealist;
int elements;
int corners;
int attribs;
int *segmentlist;
int *segmentmarkerlist;
int numberofsegments;

#else /* not TRILIBRARY */

long reconstruct( elefilename, areafilename, polyfilename, polyfile )
char *elefilename;
char *areafilename;
char *polyfilename;
FILE *polyfile;

#endif /* not TRILIBRARY */

{
#ifdef TRILIBRARY
	int pointindex;
	int attribindex;
#else /* not TRILIBRARY */
	FILE *elefile;
	FILE *areafile;
	char inputline[INPUTLINESIZE];
	char *stringptr;
	int areaelements;
#endif /* not TRILIBRARY */
	struct triedge triangleloop;
	struct triedge triangleleft;
	struct triedge checktri;
	struct triedge checkleft;
	struct triedge checkneighbor;
	struct edge shelleloop;
	triangle *vertexarray;
	triangle *prevlink;
	triangle nexttri;
	point tdest, tapex;
	point checkdest, checkapex;
	point shorg;
	point killpoint;
	REAL area;
	int corner[3];
	int end[2];
	int killpointindex;
	int incorners;
	int segmentmarkers;
	int boundmarker;
	int aroundpoint;
	long hullsize;
	int notfound;
	int elementnumber, segmentnumber;
	int i, j;
	triangle ptr;                       /* Temporary variable used by sym(). */

#ifdef TRILIBRARY
	inelements = elements;
	incorners = corners;
	if ( incorners < 3 ) {
		printf( "Error:  Triangles must have at least 3 points.\n" );
		exit( 1 );
	}
	eextras = attribs;
#else /* not TRILIBRARY */
	/* Read the triangles from an .ele file. */
	if ( !quiet ) {
		printf( "Opening %s.\n", elefilename );
	}
	elefile = fopen( elefilename, "r" );
	if ( elefile == (FILE *) NULL ) {
		printf( "  Error:  Cannot access file %s.\n", elefilename );
		exit( 1 );
	}
	/* Read number of triangles, number of points per triangle, and */
	/*   number of triangle attributes from .ele file.              */
	stringptr = readline( inputline, elefile, elefilename );
	inelements = (int) strtol( stringptr, &stringptr, 0 );
	stringptr = findfield( stringptr );
	if ( *stringptr == '\0' ) {
		incorners = 3;
	}
	else {
		incorners = (int) strtol( stringptr, &stringptr, 0 );
		if ( incorners < 3 ) {
			printf( "Error:  Triangles in %s must have at least 3 points.\n",
					elefilename );
			exit( 1 );
		}
	}
	stringptr = findfield( stringptr );
	if ( *stringptr == '\0' ) {
		eextras = 0;
	}
	else {
		eextras = (int) strtol( stringptr, &stringptr, 0 );
	}
#endif /* not TRILIBRARY */

	initializetrisegpools();

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

	if ( poly ) {
#ifdef TRILIBRARY
		insegments = numberofsegments;
		segmentmarkers = segmentmarkerlist != (int *) NULL;
#else /* not TRILIBRARY */
		/* Read number of segments and number of segment */
		/*   boundary markers from .poly file.           */
		stringptr = readline( inputline, polyfile, inpolyfilename );
		insegments = (int) strtol( stringptr, &stringptr, 0 );
		stringptr = findfield( stringptr );
		if ( *stringptr == '\0' ) {
			segmentmarkers = 0;
		}
		else {
			segmentmarkers = (int) strtol( stringptr, &stringptr, 0 );
		}
#endif /* not TRILIBRARY */

		/* Create the shell edges. */
		for ( segmentnumber = 1; segmentnumber <= insegments; segmentnumber++ ) {
			makeshelle( &shelleloop );
			/* Mark the shell edge as living. */
			shelleloop.sh[2] = (shelle) shelleloop.sh;
		}
	}

#ifdef TRILIBRARY
	pointindex = 0;
	attribindex = 0;
#else /* not TRILIBRARY */
	if ( vararea ) {
		/* Open an .area file, check for consistency with the .ele file. */
		if ( !quiet ) {
			printf( "Opening %s.\n", areafilename );
		}
		areafile = fopen( areafilename, "r" );
		if ( areafile == (FILE *) NULL ) {
			printf( "  Error:  Cannot access file %s.\n", areafilename );
			exit( 1 );
		}
		stringptr = readline( inputline, areafile, areafilename );
		areaelements = (int) strtol( stringptr, &stringptr, 0 );
		if ( areaelements != inelements ) {
			printf( "Error:  %s and %s disagree on number of triangles.\n",
					elefilename, areafilename );
			exit( 1 );
		}
	}
#endif /* not TRILIBRARY */

	if ( !quiet ) {
		printf( "Reconstructing mesh.\n" );
	}
	/* Allocate a temporary array that maps each point to some adjacent  */
	/*   triangle.  I took care to allocate all the permanent memory for */
	/*   triangles and shell edges first.                                */
	vertexarray = (triangle *) malloc( points.items * sizeof( triangle ) );
	if ( vertexarray == (triangle *) NULL ) {
		printf( "Error:  Out of memory.\n" );
		exit( 1 );
	}
	/* Each point is initially unrepresented. */
	for ( i = 0; i < points.items; i++ ) {
		vertexarray[i] = (triangle) dummytri;
	}

	if ( verbose ) {
		printf( "  Assembling triangles.\n" );
	}
	/* Read the triangles from the .ele file, and link */
	/*   together those that share an edge.            */
	traversalinit( &triangles );
	triangleloop.tri = triangletraverse();
	elementnumber = firstnumber;
	while ( triangleloop.tri != (triangle *) NULL ) {
#ifdef TRILIBRARY
		/* Copy the triangle's three corners. */
		for ( j = 0; j < 3; j++ ) {
			corner[j] = trianglelist[pointindex++];
			if ( ( corner[j] < firstnumber ) || ( corner[j] >= firstnumber + inpoints ) ) {
				printf( "Error:  Triangle %d has an invalid vertex index.\n",
						elementnumber );
				exit( 1 );
			}
		}
#else /* not TRILIBRARY */
		/* Read triangle number and the triangle's three corners. */
		stringptr = readline( inputline, elefile, elefilename );
		for ( j = 0; j < 3; j++ ) {
			stringptr = findfield( stringptr );
			if ( *stringptr == '\0' ) {
				printf( "Error:  Triangle %d is missing point %d in %s.\n",
						elementnumber, j + 1, elefilename );
				exit( 1 );
			}
			else {
				corner[j] = (int) strtol( stringptr, &stringptr, 0 );
				if ( ( corner[j] < firstnumber ) ||
					 ( corner[j] >= firstnumber + inpoints ) ) {
					printf( "Error:  Triangle %d has an invalid vertex index.\n",
							elementnumber );
					exit( 1 );
				}
			}
		}
#endif /* not TRILIBRARY */

		/* Find out about (and throw away) extra nodes. */
		for ( j = 3; j < incorners; j++ ) {
#ifdef TRILIBRARY
			killpointindex = trianglelist[pointindex++];
#else /* not TRILIBRARY */
			stringptr = findfield( stringptr );
			if ( *stringptr != '\0' ) {
				killpointindex = (int) strtol( stringptr, &stringptr, 0 );
#endif /* not TRILIBRARY */
			if ( ( killpointindex >= firstnumber ) &&
				 ( killpointindex < firstnumber + inpoints ) ) {
				/* Delete the non-corner point if it's not already deleted. */
				killpoint = getpoint( killpointindex );
				if ( pointmark( killpoint ) != DEADPOINT ) {
					pointdealloc( killpoint );
				}
			}
#ifndef TRILIBRARY
		}
#endif /* not TRILIBRARY */
		}

		/* Read the triangle's attributes. */
		for ( j = 0; j < eextras; j++ ) {
#ifdef TRILIBRARY
			setelemattribute( triangleloop, j, triangleattriblist[attribindex++] );
#else /* not TRILIBRARY */
			stringptr = findfield( stringptr );
			if ( *stringptr == '\0' ) {
				setelemattribute( triangleloop, j, 0 );
			}
			else {
				setelemattribute( triangleloop, j,
								  (REAL) strtod( stringptr, &stringptr ) );
			}
#endif /* not TRILIBRARY */
		}

		if ( vararea ) {
#ifdef TRILIBRARY
			area = trianglearealist[elementnumber - firstnumber];
#else /* not TRILIBRARY */
			/* Read an area constraint from the .area file. */
			stringptr = readline( inputline, areafile, areafilename );
			stringptr = findfield( stringptr );
			if ( *stringptr == '\0' ) {
				area = -1.0;              /* No constraint on this triangle. */
			}
			else {
				area = (REAL) strtod( stringptr, &stringptr );
			}
#endif /* not TRILIBRARY */
			setareabound( triangleloop, area );
		}

		/* Set the triangle's vertices. */
		triangleloop.orient = 0;
		setorg( triangleloop, getpoint( corner[0] ) );
		setdest( triangleloop, getpoint( corner[1] ) );
		setapex( triangleloop, getpoint( 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. */
			aroundpoint = corner[triangleloop.orient];
			/* Look for other triangles having this vertex. */
			nexttri = vertexarray[aroundpoint - 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[aroundpoint - firstnumber] = encode( triangleloop );
			decode( nexttri, checktri );
			if ( checktri.tri != 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 != dummytri );
			}
		}
		triangleloop.tri = triangletraverse();
		elementnumber++;
	}

#ifdef TRILIBRARY
	pointindex = 0;
#else /* not TRILIBRARY */
	fclose( elefile );
	if ( vararea ) {
		fclose( areafile );
	}
#endif /* not TRILIBRARY */

	hullsize = 0;                    /* Prepare to count the boundary edges. */
	if ( poly ) {
		if ( verbose ) {
			printf( "  Marking segments in triangulation.\n" );
		}
		/* Read the segments from the .poly file, and link them */
		/*   to their neighboring triangles.                    */
		boundmarker = 0;
		traversalinit( &shelles );
		shelleloop.sh = shelletraverse();
		segmentnumber = firstnumber;
		while ( shelleloop.sh != (shelle *) NULL ) {
#ifdef TRILIBRARY
			end[0] = segmentlist[pointindex++];
			end[1] = segmentlist[pointindex++];
			if ( segmentmarkers ) {
				boundmarker = segmentmarkerlist[segmentnumber - firstnumber];
			}
#else /* not TRILIBRARY */
			/* Read the endpoints of each segment, and possibly a boundary marker. */
			stringptr = readline( inputline, polyfile, inpolyfilename );
			/* Skip the first (segment number) field. */
			stringptr = findfield( stringptr );
			if ( *stringptr == '\0' ) {
				printf( "Error:  Segment %d has no endpoints in %s.\n", segmentnumber,
						polyfilename );
				exit( 1 );
			}
			else {
				end[0] = (int) strtol( stringptr, &stringptr, 0 );
			}
			stringptr = findfield( stringptr );
			if ( *stringptr == '\0' ) {
				printf( "Error:  Segment %d is missing its second endpoint in %s.\n",
						segmentnumber, polyfilename );
				exit( 1 );
			}
			else {
				end[1] = (int) strtol( stringptr, &stringptr, 0 );
			}
			if ( segmentmarkers ) {
				stringptr = findfield( stringptr );
				if ( *stringptr == '\0' ) {
					boundmarker = 0;
				}
				else {
					boundmarker = (int) strtol( stringptr, &stringptr, 0 );
				}
			}
#endif /* not TRILIBRARY */
			for ( j = 0; j < 2; j++ ) {
				if ( ( end[j] < firstnumber ) || ( end[j] >= firstnumber + inpoints ) ) {
					printf( "Error:  Segment %d has an invalid vertex index.\n",
							segmentnumber );
					exit( 1 );
				}
			}

			/* set the shell edge's vertices. */
			shelleloop.shorient = 0;
			setsorg( shelleloop, getpoint( end[0] ) );
			setsdest( shelleloop, getpoint( end[1] ) );
			setmark( shelleloop, boundmarker );
			/* Try linking the shell edge to triangles that share these vertices. */
			for ( shelleloop.shorient = 0; shelleloop.shorient < 2;
				  shelleloop.shorient++ ) {
				/* Take the number for the destination of shelleloop. */
				aroundpoint = end[1 - shelleloop.shorient];
				/* Look for triangles having this vertex. */
				prevlink = &vertexarray[aroundpoint - firstnumber];
				nexttri = vertexarray[aroundpoint - firstnumber];
				decode( nexttri, checktri );
				sorg( shelleloop, shorg );
				notfound = 1;
				/* Look for triangles having this edge.  Note that I'm only       */
				/*   comparing each triangle's destination with the shell edge;   */
				/*   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-segment bond is represented once.             */
				while ( notfound && ( checktri.tri != 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 shell edge to the triangle. */
						tsbond( checktri, shelleloop );
						/* Check if this is a boundary edge. */
						sym( checktri, checkneighbor );
						if ( checkneighbor.tri == dummytri ) {
							/* The next line doesn't insert a shell edge (because there's */
							/*   already one there), but it sets the boundary markers of  */
							/*   the existing shell edge and its vertices.                */
							insertshelle( &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 );
				}
			}
			shelleloop.sh = shelletraverse();
			segmentnumber++;
		}
	}

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

	free( vertexarray );
	return hullsize;
}

#endif /* not CDT_ONLY */

/**                                                                         **/
/**                                                                         **/
/********* General mesh construction routines end here               *********/

/********* Segment (shell edge) 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 `endpoint', 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.                   */
/*                                                                           */
/*****************************************************************************/

enum finddirectionresult finddirection( searchtri, endpoint )
struct triedge *searchtri;
point endpoint;
{
	struct triedge checktri;
	point startpoint;
	point leftpoint, rightpoint;
	REAL leftccw, rightccw;
	int leftflag, rightflag;
	triangle ptr;         /* Temporary variable used by onext() and oprev(). */

	org( *searchtri, startpoint );
	dest( *searchtri, rightpoint );
	apex( *searchtri, leftpoint );
	/* Is `endpoint' to the left? */
	leftccw = counterclockwise( endpoint, startpoint, leftpoint );
	leftflag = leftccw > 0.0;
	/* Is `endpoint' to the right? */
	rightccw = counterclockwise( startpoint, endpoint, rightpoint );
	rightflag = rightccw > 0.0;
	if ( leftflag && rightflag ) {
		/* `searchtri' faces directly away from `endpoint'.  We could go */
		/*   left or right.  Ask whether it's a triangle or a boundary   */
		/*   on the left.                                                */
		onext( *searchtri, checktri );
		if ( checktri.tri == dummytri ) {
			leftflag = 0;
		}
		else {
			rightflag = 0;
		}
	}
	while ( leftflag ) {
		/* Turn left until satisfied. */
		onextself( *searchtri );
		if ( searchtri->tri == dummytri ) {
			printf( "Internal error in finddirection():  Unable to find a\n" );
			printf( "  triangle leading from (%.12g, %.12g) to", startpoint[0],
					startpoint[1] );
			printf( "  (%.12g, %.12g).\n", endpoint[0], endpoint[1] );
			internalerror();
		}
		apex( *searchtri, leftpoint );
		rightccw = leftccw;
		leftccw = counterclockwise( endpoint, startpoint, leftpoint );
		leftflag = leftccw > 0.0;
	}
	while ( rightflag ) {
		/* Turn right until satisfied. */
		oprevself( *searchtri );
		if ( searchtri->tri == dummytri ) {
			printf( "Internal error in finddirection():  Unable to find a\n" );
			printf( "  triangle leading from (%.12g, %.12g) to", startpoint[0],
					startpoint[1] );
			printf( "  (%.12g, %.12g).\n", endpoint[0], endpoint[1] );
			internalerror();
		}
		dest( *searchtri, rightpoint );
		leftccw = rightccw;
		rightccw = counterclockwise( startpoint, endpoint, rightpoint );
		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 point at the intersection, splitting an        */
/*                          existing shell edge.                             */
/*                                                                           */
/*  The segment being inserted connects the apex of splittri to endpoint2.   */
/*  splitshelle is the shell edge being split, and MUST be opposite          */
/*  splittri.  Hence, the edge being split connects 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.      */
/*                                                                           */
/*****************************************************************************/

void segmentintersection( splittri, splitshelle, endpoint2 )
struct triedge *splittri;
struct edge *splitshelle;
point endpoint2;
{
	point endpoint1;
	point torg, tdest;
	point leftpoint, rightpoint;
	point newpoint;
	enum insertsiteresult 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(). */

	/* 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 point. */
	newpoint = (point) poolalloc( &points );
	/* Interpolate its coordinate and attributes. */
	for ( i = 0; i < 2 + nextras; i++ ) {
		newpoint[i] = torg[i] + split * ( tdest[i] - torg[i] );
	}
	setpointmark( newpoint, mark( *splitshelle ) );
	if ( verbose > 1 ) {
		printf(
			"  Splitting edge (%.12g, %.12g) (%.12g, %.12g) at (%.12g, %.12g).\n",
			torg[0], torg[1], tdest[0], tdest[1], newpoint[0], newpoint[1] );
	}
	/* Insert the intersection point.  This should always succeed. */
	success = insertsite( newpoint, splittri, splitshelle, 0, 0 );
	if ( success != SUCCESSFULPOINT ) {
		printf( "Internal error in segmentintersection():\n" );
		printf( "  Failure to split a segment.\n" );
		internalerror();
	}
	if ( steinerleft > 0 ) {
		steinerleft--;
	}
	/* Inserting the point may have caused edge flips.  We wish to rediscover */
	/*   the edge connecting endpoint1 to the new intersection point.         */
	collinear = finddirection( splittri, endpoint1 );
	dest( *splittri, rightpoint );
	apex( *splittri, leftpoint );
	if ( ( leftpoint[0] == endpoint1[0] ) && ( leftpoint[1] == endpoint1[1] ) ) {
		onextself( *splittri );
	}
	else if ( ( rightpoint[0] != endpoint1[0] ) ||
			  ( rightpoint[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 point, and 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 shell edge 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 shell edge is inserted connecting the first endpoint to   */
/*  the collinear point, and the search is continued from the collinear      */
/*  point.                                                                   */
/*                                                                           */
/*  If the first triangle on the path has a shell edge opposite its origin,  */
/*  then there is a segment that intersects the segment being inserted.      */
/*  Their intersection point is inserted, splitting the shell edge.          */
/*                                                                           */
/*  Otherwise, return zero.                                                  */
/*                                                                           */
/*****************************************************************************/

int scoutsegment( searchtri, endpoint2, newmark )
struct triedge *searchtri;
point endpoint2;
int newmark;
{
	struct triedge crosstri;
	struct edge crossedge;
	point leftpoint, rightpoint;
	point endpoint1;
	enum finddirectionresult collinear;
	shelle sptr;                    /* Temporary variable used by tspivot(). */

	collinear = finddirection( searchtri, endpoint2 );
	dest( *searchtri, rightpoint );
	apex( *searchtri, leftpoint );
	if ( ( ( leftpoint[0] == endpoint2[0] ) && ( leftpoint[1] == endpoint2[1] ) ) ||
		 ( ( rightpoint[0] == endpoint2[0] ) && ( rightpoint[1] == endpoint2[1] ) ) ) {
		/* The segment is already an edge in the mesh. */
		if ( ( leftpoint[0] == endpoint2[0] ) && ( leftpoint[1] == endpoint2[1] ) ) {
			lprevself( *searchtri );
		}
		/* Insert a shell edge, if there isn't already one there. */
		insertshelle( searchtri, newmark );
		return 1;
	}
	else if ( collinear == LEFTCOLLINEAR ) {
		/* We've collided with a point between the segment's endpoints. */
		/* Make the collinear point be the triangle's origin. */
		lprevself( *searchtri );
		insertshelle( searchtri, newmark );
		/* Insert the remainder of the segment. */
		return scoutsegment( searchtri, endpoint2, newmark );
	}
	else if ( collinear == RIGHTCOLLINEAR ) {
		/* We've collided with a point between the segment's endpoints. */
		insertshelle( searchtri, newmark );
		/* Make the collinear point be the triangle's origin. */
		lnextself( *searchtri );
		/* Insert the remainder of the segment. */
		return scoutsegment( searchtri, endpoint2, newmark );
	}
	else {
		lnext( *searchtri, crosstri );
		tspivot( crosstri, crossedge );
		/* Check for a crossing segment. */
		if ( crossedge.sh == dummysh ) {
			return 0;
		}
		else {
			org( *searchtri, endpoint1 );
			/* Insert a point at the intersection. */
			segmentintersection( &crosstri, &crossedge, endpoint2 );
			triedgecopy( crosstri, *searchtri );
			insertshelle( searchtri, newmark );
			/* Insert the remainder of the segment. */
			return scoutsegment( searchtri, endpoint2, newmark );
		}
	}
}

/*****************************************************************************/
/*                                                                           */
/*  conformingedge()   Force a segment into a conforming Delaunay            */
/*                     triangulation by inserting a point at its midpoint,   */
/*                     and recursively forcing in the two half-segments if   */
/*                     necessary.                                            */
/*                                                                           */
/*  Generates a sequence of edges connecting `endpoint1' to `endpoint2'.     */
/*  `newmark' is the boundary marker of the segment, assigned to each new    */
/*  splitting point and shell edge.                                          */
/*                                                                           */
/*  Note that conformingedge() does not always maintain the conforming       */
/*  Delaunay property.  Once inserted, segments are locked into place;       */
/*  points 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 segments.           */
/*                                                                           */
/*****************************************************************************/

#ifndef REDUCED
#ifndef CDT_ONLY

void conformingedge( endpoint1, endpoint2, newmark )
point endpoint1;
point endpoint2;
int newmark;
{
	struct triedge searchtri1, searchtri2;
	struct edge brokenshelle;
	point newpoint;
	point midpoint1, midpoint2;
	enum insertsiteresult success;
	int result1, result2;
	int i;
	shelle sptr;                    /* Temporary variable used by tspivot(). */

	if ( 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 point to insert in the middle of the segment. */
	newpoint = (point) poolalloc( &points );
	/* Interpolate coordinates and attributes. */
	for ( i = 0; i < 2 + nextras; i++ ) {
		newpoint[i] = 0.5 * ( endpoint1[i] + endpoint2[i] );
	}
	setpointmark( newpoint, newmark );
	/* Find a boundary triangle to search from. */
	searchtri1.tri = (triangle *) NULL;
	/* Attempt to insert the new point. */
	success = insertsite( newpoint, &searchtri1, (struct edge *) NULL, 0, 0 );
	if ( success == DUPLICATEPOINT ) {
		if ( verbose > 2 ) {
			printf( "  Segment intersects existing point (%.12g, %.12g).\n",
					newpoint[0], newpoint[1] );
		}
		/* Use the point that's already there. */
		pointdealloc( newpoint );
		org( searchtri1, newpoint );
	}
	else {
		if ( success == VIOLATINGPOINT ) {
			if ( verbose > 2 ) {
				printf( "  Two segments intersect at (%.12g, %.12g).\n",
						newpoint[0], newpoint[1] );
			}
			/* By fluke, we've landed right on another segment.  Split it. */
			tspivot( searchtri1, brokenshelle );
			success = insertsite( newpoint, &searchtri1, &brokenshelle, 0, 0 );
			if ( success != SUCCESSFULPOINT ) {
				printf( "Internal error in conformingedge():\n" );
				printf( "  Failure to split a segment.\n" );
				internalerror();
			}
		}
		/* The point has been inserted successfully. */
		if ( steinerleft > 0 ) {
			steinerleft--;
		}
	}
	triedgecopy( searchtri1, searchtri2 );
	result1 = scoutsegment( &searchtri1, endpoint1, newmark );
	result2 = scoutsegment( &searchtri2, endpoint2, newmark );
	if ( !result1 ) {
		/* The origin of searchtri1 may have changed if a collision with an */
		/*   intervening vertex on the segment occurred.                    */
		org( searchtri1, midpoint1 );
		conformingedge( midpoint1, endpoint1, newmark );
	}
	if ( !result2 ) {
		/* The origin of searchtri2 may have changed if a collision with an */
		/*   intervening vertex on the segment occurred.                    */
		org( searchtri2, midpoint2 );
		conformingedge( midpoint2, endpoint2, newmark );
	}
}

#endif /* not CDT_ONLY */
#endif /* not REDUCED */

/*****************************************************************************/
/*                                                                           */
/*  delaunayfixup()   Enforce the Delaunay condition at an edge, fanning out */
/*                    recursively from an existing point.  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 point (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.)                                                 */
/*                                                                           */
/*****************************************************************************/

void delaunayfixup( fixuptri, leftside )
struct triedge *fixuptri;
int leftside;
{
	struct triedge neartri;
	struct triedge fartri;
	struct edge faredge;
	point nearpoint, leftpoint, rightpoint, farpoint;
	triangle ptr;                       /* Temporary variable used by sym(). */
	shelle 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 == dummytri ) {
		return;
	}
	tspivot( neartri, faredge );
	if ( faredge.sh != dummysh ) {
		return;
	}
	/* Find all the relevant vertices. */
	apex( neartri, nearpoint );
	org( neartri, leftpoint );
	dest( neartri, rightpoint );
	apex( fartri, farpoint );
	/* Check whether the previous polygon vertex is a reflex vertex. */
	if ( leftside ) {
		if ( counterclockwise( nearpoint, leftpoint, farpoint ) <= 0.0 ) {
			/* leftpoint is a reflex vertex too.  Nothing can */
			/*   be done until a convex section is found.     */
			return;
		}
	}
	else {
		if ( counterclockwise( farpoint, rightpoint, nearpoint ) <= 0.0 ) {
			/* rightpoint is a reflex vertex too.  Nothing can */
			/*   be done until a convex section is found.      */
			return;
		}
	}
	if ( counterclockwise( rightpoint, leftpoint, farpoint ) > 0.0 ) {
		/* fartri is not an inverted triangle, and farpoint 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( leftpoint, farpoint, rightpoint, nearpoint ) <= 0.0 ) {
			return;
		}
		/* Not locally Delaunay; go on to an edge flip. */
	}      /* else fartri is inverted; remove it from the stack by flipping. */
	flip( &neartri );
	lprevself( *fixuptri ); /* Restore the origin of fixuptri after the flip. */
	/* Recursively process the two triangles that result from the flip. */
	delaunayfixup( fixuptri, leftside );
	delaunayfixup( &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 edge 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.                                    */
/*                                                                           */
/*****************************************************************************/

void constrainededge( starttri, endpoint2, newmark )
struct triedge *starttri;
point endpoint2;
int newmark;
{
	struct triedge fixuptri, fixuptri2;
	struct edge fixupedge;
	point endpoint1;
	point farpoint;
	REAL area;
	int collision;
	int done;
	triangle ptr;           /* Temporary variable used by sym() and oprev(). */
	shelle sptr;                    /* Temporary variable used by tspivot(). */

	org( *starttri, endpoint1 );
	lnext( *starttri, fixuptri );
	flip( &fixuptri );
	/* `collision' indicates whether we have found a point directly */
	/*   between endpoint1 and endpoint2.                           */
	collision = 0;
	done = 0;
	do {
		org( fixuptri, farpoint );
		/* `farpoint' is the extreme point of the polygon we are "digging" */
		/*   to get from endpoint1 to endpoint2.                           */
		if ( ( farpoint[0] == endpoint2[0] ) && ( farpoint[1] == endpoint2[1] ) ) {
			oprev( fixuptri, fixuptri2 );
			/* Enforce the Delaunay condition around endpoint2. */
			delaunayfixup( &fixuptri, 0 );
			delaunayfixup( &fixuptri2, 1 );
			done = 1;
		}
		else {
			/* Check whether farpoint is to the left or right of the segment */
			/*   being inserted, to decide which edge of fixuptri to dig     */
			/*   through next.                                               */
			area = counterclockwise( endpoint1, endpoint2, farpoint );
			if ( area == 0.0 ) {
				/* We've collided with a point between endpoint1 and endpoint2. */
				collision = 1;
				oprev( fixuptri, fixuptri2 );
				/* Enforce the Delaunay condition around farpoint. */
				delaunayfixup( &fixuptri, 0 );
				delaunayfixup( &fixuptri2, 1 );
				done = 1;
			}
			else {
				if ( area > 0.0 ) { /* farpoint is to the left of the segment. */
					oprev( fixuptri, fixuptri2 );
					/* Enforce the Delaunay condition around farpoint, on the */
					/*   left side of the segment only.                       */
					delaunayfixup( &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 {           /* farpoint is to the right of the segment. */
					delaunayfixup( &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, fixupedge );
				if ( fixupedge.sh == dummysh ) {
					flip( &fixuptri ); /* May create an inverted triangle on the left. */
				}
				else {
					/* We've collided with a segment between endpoint1 and endpoint2. */
					collision = 1;
					/* Insert a point at the intersection. */
					segmentintersection( &fixuptri, &fixupedge, endpoint2 );
					done = 1;
				}
			}
		}
	} while ( !done );
	/* Insert a shell edge to make the segment permanent. */
	insertshelle( &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( &fixuptri, endpoint2, newmark ) ) {
			constrainededge( &fixuptri, endpoint2, newmark );
		}
	}
}

/*****************************************************************************/
/*                                                                           */
/*  insertsegment()   Insert a PSLG segment into a triangulation.            */
/*                                                                           */
/*****************************************************************************/

void insertsegment( endpoint1, endpoint2, newmark )
point endpoint1;
point endpoint2;
int newmark;
{
	struct triedge searchtri1, searchtri2;
	triangle encodedtri;
	point checkpoint;
	triangle ptr;                       /* Temporary variable used by sym(). */

	if ( 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. */
	checkpoint = (point) NULL;
	encodedtri = point2tri( endpoint1 );
	if ( encodedtri != (triangle) NULL ) {
		decode( encodedtri, searchtri1 );
		org( searchtri1, checkpoint );
	}
	if ( checkpoint != endpoint1 ) {
		/* Find a boundary triangle to search from. */
		searchtri1.tri = dummytri;
		searchtri1.orient = 0;
		symself( searchtri1 );
		/* Search for the segment's first endpoint by point location. */
		if ( locate( endpoint1, &searchtri1 ) != ONVERTEX ) {
			printf(
				"Internal error in insertsegment():  Unable to locate PSLG point\n" );
			printf( "  (%.12g, %.12g) in triangulation.\n",
					endpoint1[0], endpoint1[1] );
			internalerror();
		}
	}
	/* Remember this triangle to improve subsequent point location. */
	triedgecopy( searchtri1, recenttri );
	/* Scout the beginnings of a path from the first endpoint */
	/*   toward the second.                                   */
	if ( scoutsegment( &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. */
	checkpoint = (point) NULL;
	encodedtri = point2tri( endpoint2 );
	if ( encodedtri != (triangle) NULL ) {
		decode( encodedtri, searchtri2 );
		org( searchtri2, checkpoint );
	}
	if ( checkpoint != endpoint2 ) {
		/* Find a boundary triangle to search from. */
		searchtri2.tri = dummytri;
		searchtri2.orient = 0;
		symself( searchtri2 );
		/* Search for the segment's second endpoint by point location. */
		if ( locate( endpoint2, &searchtri2 ) != ONVERTEX ) {
			printf(
				"Internal error in insertsegment():  Unable to locate PSLG point\n" );
			printf( "  (%.12g, %.12g) in triangulation.\n",
					endpoint2[0], endpoint2[1] );
			internalerror();
		}
	}
	/* Remember this triangle to improve subsequent point location. */
	triedgecopy( searchtri2, recenttri );
	/* Scout the beginnings of a path from the second endpoint */
	/*   toward the first.                                     */
	if ( scoutsegment( &searchtri2, endpoint1, newmark ) ) {
		/* The segment was easily inserted. */
		return;
	}
	/* The second endpoint may have changed if a collision with an intervening */
	/*   vertex on the segment occurred.                                       */
	org( searchtri2, endpoint2 );

#ifndef REDUCED
#ifndef CDT_ONLY
	if ( splitseg ) {
		/* Insert vertices to force the segment into the triangulation. */
		conformingedge( endpoint1, endpoint2, newmark );
	}
	else {
#endif /* not CDT_ONLY */
#endif /* not REDUCED */
	   /* Insert the segment directly into the triangulation. */
	constrainededge( &searchtri1, endpoint2, newmark );
#ifndef REDUCED
#ifndef CDT_ONLY
}
#endif /* not CDT_ONLY */
#endif /* not REDUCED */
}

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

void markhull(){
	struct triedge hulltri;
	struct triedge nexttri;
	struct triedge starttri;
	triangle ptr;           /* Temporary variable used by sym() and oprev(). */

	/* Find a triangle handle on the hull. */
	hulltri.tri = dummytri;
	hulltri.orient = 0;
	symself( hulltri );
	/* Remember where we started so we know when to stop. */
	triedgecopy( hulltri, starttri );
	/* Go once counterclockwise around the convex hull. */
	do {
		/* Create a shell edge if there isn't already one here. */
		insertshelle( &hulltri, 1 );
		/* To find the next hull edge, go clockwise around the next vertex. */
		lnextself( hulltri );
		oprev( hulltri, nexttri );
		while ( nexttri.tri != dummytri ) {
			triedgecopy( nexttri, hulltri );
			oprev( hulltri, nexttri );
		}
	} while ( !triedgeequal( hulltri, starttri ) );
}

/*****************************************************************************/
/*                                                                           */
/*  formskeleton()   Create the shell edges of a triangulation, including    */
/*                   PSLG edges and edges on the convex hull.                */
/*                                                                           */
/*  The PSLG edges are read from a .poly file.  The return value is the      */
/*  number of segments in the file.                                          */
/*                                                                           */
/*****************************************************************************/

#ifdef TRILIBRARY

int formskeleton( segmentlist, segmentmarkerlist, numberofsegments )
int *segmentlist;
int *segmentmarkerlist;
int numberofsegments;

#else /* not TRILIBRARY */

int formskeleton( polyfile, polyfilename )
FILE * polyfile;
char *polyfilename;

#endif /* not TRILIBRARY */

{
#ifdef TRILIBRARY
	char polyfilename[6];
	int index;
#else /* not TRILIBRARY */
	char inputline[INPUTLINESIZE];
	char *stringptr;
#endif /* not TRILIBRARY */
	point endpoint1, endpoint2;
	int segments;
	int segmentmarkers;
	int end1, end2;
	int boundmarker;
	int i;

	if ( poly ) {
		if ( !quiet ) {
			printf( "Inserting segments into Delaunay triangulation.\n" );
		}
#ifdef TRILIBRARY
		strcpy( polyfilename, "input" );
		segments = numberofsegments;
		segmentmarkers = segmentmarkerlist != (int *) NULL;
		index = 0;
#else /* not TRILIBRARY */
		/* Read the segments from a .poly file. */
		/* Read number of segments and number of boundary markers. */
		stringptr = readline( inputline, polyfile, polyfilename );
		segments = (int) strtol( stringptr, &stringptr, 0 );
		stringptr = findfield( stringptr );
		if ( *stringptr == '\0' ) {
			segmentmarkers = 0;
		}
		else {
			segmentmarkers = (int) strtol( stringptr, &stringptr, 0 );
		}
#endif /* not TRILIBRARY */
		/* If segments are to be inserted, compute a mapping */
		/*   from points to triangles.                       */
		if ( segments > 0 ) {
			if ( verbose ) {
				printf( "  Inserting PSLG segments.\n" );
			}
			makepointmap();
		}

		boundmarker = 0;
		/* Read and insert the segments. */
		for ( i = 1; i <= segments; i++ ) {
#ifdef TRILIBRARY
			end1 = segmentlist[index++];
			end2 = segmentlist[index++];
			if ( segmentmarkers ) {
				boundmarker = segmentmarkerlist[i - 1];
			}
#else /* not TRILIBRARY */
			stringptr = readline( inputline, polyfile, inpolyfilename );
			stringptr = findfield( stringptr );
			if ( *stringptr == '\0' ) {
				printf( "Error:  Segment %d has no endpoints in %s.\n", i,
						polyfilename );
				exit( 1 );
			}
			else {
				end1 = (int) strtol( stringptr, &stringptr, 0 );
			}
			stringptr = findfield( stringptr );
			if ( *stringptr == '\0' ) {
				printf( "Error:  Segment %d is missing its second endpoint in %s.\n", i,
						polyfilename );
				exit( 1 );
			}
			else {
				end2 = (int) strtol( stringptr, &stringptr, 0 );
			}
			if ( segmentmarkers ) {
				stringptr = findfield( stringptr );
				if ( *stringptr == '\0' ) {
					boundmarker = 0;
				}
				else {
					boundmarker = (int) strtol( stringptr, &stringptr, 0 );
				}
			}
#endif /* not TRILIBRARY */
			if ( ( end1 < firstnumber ) || ( end1 >= firstnumber + inpoints ) ) {
				if ( !quiet ) {
					printf( "Warning:  Invalid first endpoint of segment %d in %s.\n", i,
							polyfilename );
				}
			}
			else if ( ( end2 < firstnumber ) || ( end2 >= firstnumber + inpoints ) ) {
				if ( !quiet ) {
					printf( "Warning:  Invalid second endpoint of segment %d in %s.\n", i,
							polyfilename );
				}
			}
			else {
				endpoint1 = getpoint( end1 );
				endpoint2 = getpoint( end2 );
				if ( ( endpoint1[0] == endpoint2[0] ) && ( endpoint1[1] == endpoint2[1] ) ) {
					if ( !quiet ) {
						printf( "Warning:  Endpoints of segment %d are coincident in %s.\n",
								i, polyfilename );
					}
				}
				else {
					insertsegment( endpoint1, endpoint2, boundmarker );
				}
			}
		}
	}
	else {
		segments = 0;
	}
	if ( convex || !poly ) {
		/* Enclose the convex hull with shell edges. */
		if ( verbose ) {
			printf( "  Enclosing convex hull with segments.\n" );
		}
		markhull();
	}
	return segments;
}

/**                                                                         **/
/**                                                                         **/
/********* Segment (shell edge) 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 shell edges.  Where there are   */
/*                 shell edges, set boundary markers as appropriate.         */
/*                                                                           */
/*****************************************************************************/

void infecthull(){
	struct triedge hulltri;
	struct triedge nexttri;
	struct triedge starttri;
	struct edge hulledge;
	triangle **deadtri;
	point horg, hdest;
	triangle ptr;                       /* Temporary variable used by sym(). */
	shelle sptr;                    /* Temporary variable used by tspivot(). */

	if ( verbose ) {
		printf( "  Marking concavities (external triangles) for elimination.\n" );
	}
	/* Find a triangle handle on the hull. */
	hulltri.tri = dummytri;
	hulltri.orient = 0;
	symself( hulltri );
	/* Remember where we started so we know when to stop. */
	triedgecopy( 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 shell edge? */
			tspivot( hulltri, hulledge );
			if ( hulledge.sh == dummysh ) {
				/* The triangle is not protected; infect it. */
				infect( hulltri );
				deadtri = (triangle **) poolalloc( &viri );
				*deadtri = hulltri.tri;
			}
			else {
				/* The triangle is protected; set boundary markers if appropriate. */
				if ( mark( hulledge ) == 0 ) {
					setmark( hulledge, 1 );
					org( hulltri, horg );
					dest( hulltri, hdest );
					if ( pointmark( horg ) == 0 ) {
						setpointmark( horg, 1 );
					}
					if ( pointmark( hdest ) == 0 ) {
						setpointmark( hdest, 1 );
					}
				}
			}
		}
		/* To find the next hull edge, go clockwise around the next vertex. */
		lnextself( hulltri );
		oprev( hulltri, nexttri );
		while ( nexttri.tri != dummytri ) {
			triedgecopy( nexttri, hulltri );
			oprev( hulltri, nexttri );
		}
	} while ( !triedgeequal( hulltri, starttri ) );
}

/*****************************************************************************/
/*                                                                           */
/*  plague()   Spread the virus from all infected triangles to any neighbors */
/*             not protected by shell edges.  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 points.                                              */
/*                                                                           */
/*****************************************************************************/

void plague(){
	struct triedge testtri;
	struct triedge neighbor;
	triangle **virusloop;
	triangle **deadtri;
	struct edge neighborshelle;
	point testpoint;
	point norg, ndest;
	point deadorg, deaddest, deadapex;
	int killorg;
	triangle ptr;           /* Temporary variable used by sym() and onext(). */
	shelle sptr;                    /* Temporary variable used by tspivot(). */

	if ( 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( &viri );
	virusloop = (triangle **) traverse( &viri );
	while ( virusloop != (triangle **) NULL ) {
		testtri.tri = *virusloop;
		/* A triangle is marked as infected by messing with one of its shell */
		/*   edges, setting it to an illegal value.  Hence, we have to       */
		/*   temporarily uninfect this triangle so that we can examine its   */
		/*   adjacent shell edges.                                           */
		uninfect( testtri );
		if ( verbose > 2 ) {
			/* Assign the triangle an orientation for convenience in */
			/*   checking its points.                                */
			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 shell between the triangle and its neighbor. */
			tspivot( testtri, neighborshelle );
			/* Check if the neighbor is nonexistent or already infected. */
			if ( ( neighbor.tri == dummytri ) || infected( neighbor ) ) {
				if ( neighborshelle.sh != dummysh ) {
					/* There is a shell edge separating the triangle from its */
					/*   neighbor, but both triangles are dying, so the shell */
					/*   edge dies too.                                       */
					shelledealloc( neighborshelle.sh );
					if ( neighbor.tri != dummytri ) {
						/* Make sure the shell edge 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 ( neighborshelle.sh == dummysh ) {
					/* There is no shell edge protecting the neighbor, so */
					/*   the neighbor becomes infected.                   */
					if ( 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. */
					deadtri = (triangle **) poolalloc( &viri );
					*deadtri = neighbor.tri;
				}
				else {         /* The neighbor is protected by a shell edge. */
					/* Remove this triangle from the shell edge. */
					stdissolve( neighborshelle );
					/* The shell edge becomes a boundary.  Set markers accordingly. */
					if ( mark( neighborshelle ) == 0 ) {
						setmark( neighborshelle, 1 );
					}
					org( neighbor, norg );
					dest( neighbor, ndest );
					if ( pointmark( norg ) == 0 ) {
						setpointmark( norg, 1 );
					}
					if ( pointmark( ndest ) == 0 ) {
						setpointmark( ndest, 1 );
					}
				}
			}
		}
		/* Remark the triangle as infected, so it doesn't get added to the */
		/*   virus pool again.                                             */
		infect( testtri );
		virusloop = (triangle **) traverse( &viri );
	}

	if ( verbose ) {
		printf( "  Deleting marked triangles.\n" );
	}
	traversalinit( &viri );
	virusloop = (triangle **) traverse( &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 point, checking if it is   */
		/*   still connected to at least one live triangle.                 */
		for ( testtri.orient = 0; testtri.orient < 3; testtri.orient++ ) {
			org( testtri, testpoint );
			/* Check if the point has already been tested. */
			if ( testpoint != (point) NULL ) {
				killorg = 1;
				/* Mark the corner of the triangle as having been tested. */
				setorg( testtri, NULL );
				/* Walk counterclockwise about the point. */
				onext( testtri, neighbor );
				/* Stop upon reaching a boundary or the starting triangle. */
				while ( ( neighbor.tri != dummytri )
						&& ( !triedgeequal( neighbor, testtri ) ) ) {
					if ( infected( neighbor ) ) {
						/* Mark the corner of this triangle as having been tested. */
						setorg( neighbor, NULL );
					}
					else {
						/* A live triangle.  The point survives. */
						killorg = 0;
					}
					/* Walk counterclockwise about the point. */
					onextself( neighbor );
				}
				/* If we reached a boundary, we must walk clockwise as well. */
				if ( neighbor.tri == dummytri ) {
					/* Walk clockwise about the point. */
					oprev( testtri, neighbor );
					/* Stop upon reaching a boundary. */
					while ( neighbor.tri != dummytri ) {
						if ( infected( neighbor ) ) {
							/* Mark the corner of this triangle as having been tested. */
							setorg( neighbor, NULL );
						}
						else {
							/* A live triangle.  The point survives. */
							killorg = 0;
						}
						/* Walk clockwise about the point. */
						oprevself( neighbor );
					}
				}
				if ( killorg ) {
					if ( verbose > 1 ) {
						printf( "    Deleting point (%.12g, %.12g)\n",
								testpoint[0], testpoint[1] );
					}
					pointdealloc( testpoint );
				}
			}
		}

		/* 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 == 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.                                    */
				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.   */
				hullsize++;
			}
		}
		/* Return the dead triangle to the pool of triangles. */
		triangledealloc( testtri.tri );
		virusloop = (triangle **) traverse( &viri );
	}
	/* Empty the virus pool. */
	poolrestart( &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.                                                                  */
/*                                                                           */
/*****************************************************************************/

void regionplague( attribute, area )
REAL attribute;
REAL area;
{
	struct triedge testtri;
	struct triedge neighbor;
	triangle **virusloop;
	triangle **regiontri;
	struct edge neighborshelle;
	point regionorg, regiondest, regionapex;
	triangle ptr;           /* Temporary variable used by sym() and onext(). */
	shelle sptr;                    /* Temporary variable used by tspivot(). */

	if ( 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( &viri );
	virusloop = (triangle **) traverse( &viri );
	while ( virusloop != (triangle **) NULL ) {
		testtri.tri = *virusloop;
		/* A triangle is marked as infected by messing with one of its shell */
		/*   edges, setting it to an illegal value.  Hence, we have to       */
		/*   temporarily uninfect this triangle so that we can examine its   */
		/*   adjacent shell edges.                                           */
		uninfect( testtri );
		if ( regionattrib ) {
			/* Set an attribute. */
			setelemattribute( testtri, eextras, attribute );
		}
		if ( vararea ) {
			/* Set an area constraint. */
			setareabound( testtri, area );
		}
		if ( verbose > 2 ) {
			/* Assign the triangle an orientation for convenience in */
			/*   checking its points.                                */
			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 shell between the triangle and its neighbor. */
			tspivot( testtri, neighborshelle );
			/* Make sure the neighbor exists, is not already infected, and */
			/*   isn't protected by a shell edge.                          */
			if ( ( neighbor.tri != dummytri ) && !infected( neighbor )
				 && ( neighborshelle.sh == dummysh ) ) {
				if ( 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( &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( &viri );
	}

	/* Uninfect all triangles. */
	if ( verbose > 1 ) {
		printf( "  Unmarking marked triangles.\n" );
	}
	traversalinit( &viri );
	virusloop = (triangle **) traverse( &viri );
	while ( virusloop != (triangle **) NULL ) {
		testtri.tri = *virusloop;
		uninfect( testtri );
		virusloop = (triangle **) traverse( &viri );
	}
	/* Empty the virus pool. */
	poolrestart( &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.                                                               */
/*                                                                           */
/*****************************************************************************/

void carveholes( holelist, holes, regionlist, regions )
REAL * holelist;
int holes;
REAL *regionlist;
int regions;
{
	struct triedge searchtri;
	struct triedge triangleloop;
	struct triedge *regiontris;
	triangle **holetri;
	triangle **regiontri;
	point searchorg, searchdest;
	enum locateresult intersect;
	int i;
	triangle ptr;                       /* Temporary variable used by sym(). */

	if ( !( quiet || ( noholes && convex ) ) ) {
		printf( "Removing unwanted triangles.\n" );
		if ( verbose && ( holes > 0 ) ) {
			printf( "  Marking holes for elimination.\n" );
		}
	}

	if ( regions > 0 ) {
		/* Allocate storage for the triangles in which region points fall. */
		regiontris = (struct triedge *) malloc( regions * sizeof( struct triedge ) );
		if ( regiontris == (struct triedge *) NULL ) {
			printf( "Error:  Out of memory.\n" );
			exit( 1 );
		}
	}

	if ( ( ( holes > 0 ) && !noholes ) || !convex || ( regions > 0 ) ) {
		/* Initialize a pool of viri to be used for holes, concavities, */
		/*   regional attributes, and/or regional area constraints.     */
		poolinit( &viri, sizeof( triangle * ), VIRUSPERBLOCK, POINTER, 0 );
	}

	if ( !convex ) {
		/* Mark as infected any unprotected triangles on the boundary. */
		/*   This is one way by which concavities are created.         */
		infecthull();
	}

	if ( ( holes > 0 ) && !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] >= xmin ) && ( holelist[i] <= xmax )
				 && ( holelist[i + 1] >= ymin ) && ( holelist[i + 1] <= ymax ) ) {
				/* Start searching from some triangle on the outer boundary. */
				searchtri.tri = 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( searchorg, searchdest, &holelist[i] ) > 0.0 ) {
					/* Find a triangle that contains the hole. */
					intersect = locate( &holelist[i], &searchtri );
					if ( ( intersect != OUTSIDE ) && ( !infected( searchtri ) ) ) {
						/* Infect the triangle.  This is done by marking the triangle */
						/*   as infect and including the triangle in the virus pool.  */
						infect( searchtri );
						holetri = (triangle **) poolalloc( &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 = dummytri;
			/* Ignore region points that aren't within the bounds of the mesh. */
			if ( ( regionlist[4 * i] >= xmin ) && ( regionlist[4 * i] <= xmax ) &&
				 ( regionlist[4 * i + 1] >= ymin ) && ( regionlist[4 * i + 1] <= ymax ) ) {
				/* Start searching from some triangle on the outer boundary. */
				searchtri.tri = 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( searchorg, searchdest, &regionlist[4 * i] ) >
					 0.0 ) {
					/* Find a triangle that contains the region point. */
					intersect = locate( &regionlist[4 * i], &searchtri );
					if ( ( intersect != OUTSIDE ) && ( !infected( searchtri ) ) ) {
						/* Record the triangle for processing after the */
						/*   holes have been carved.                    */
						triedgecopy( searchtri, regiontris[i] );
					}
				}
			}
		}
	}

	if ( viri.items > 0 ) {
		/* Carve the holes and concavities. */
		plague();
	}
	/* The virus pool should be empty now. */

	if ( regions > 0 ) {
		if ( !quiet ) {
			if ( regionattrib ) {
				if ( vararea ) {
					printf( "Spreading regional attributes and area constraints.\n" );
				}
				else {
					printf( "Spreading regional attributes.\n" );
				}
			}
			else {
				printf( "Spreading regional area constraints.\n" );
			}
		}
		if ( regionattrib && !refine ) {
			/* Assign every triangle a regional attribute of zero. */
			traversalinit( &triangles );
			triangleloop.orient = 0;
			triangleloop.tri = triangletraverse();
			while ( triangleloop.tri != (triangle *) NULL ) {
				setelemattribute( triangleloop, eextras, 0.0 );
				triangleloop.tri = triangletraverse();
			}
		}
		for ( i = 0; i < regions; i++ ) {
			if ( regiontris[i].tri != dummytri ) {
				/* Make sure the triangle under consideration still exists. */
				/*   It may have been eaten by the virus.                   */
				if ( regiontris[i].tri[3] != (triangle) NULL ) {
					/* Put one triangle in the virus pool. */
					infect( regiontris[i] );
					regiontri = (triangle **) poolalloc( &viri );
					*regiontri = regiontris[i].tri;
					/* Apply one region's attribute and/or area constraint. */
					regionplague( regionlist[4 * i + 2], regionlist[4 * i + 3] );
					/* The virus pool should be empty now. */
				}
			}
		}
		if ( regionattrib && !refine ) {
			/* Note the fact that each triangle has an additional attribute. */
			eextras++;
		}
	}

	/* Free up memory. */
	if ( ( ( holes > 0 ) && !noholes ) || !convex || ( regions > 0 ) ) {
		pooldeinit( &viri );
	}
	if ( regions > 0 ) {
		free( regiontris );
	}
}

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

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

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

#ifndef CDT_ONLY

void tallyencs(){
	struct edge edgeloop;
	int dummy;

	traversalinit( &shelles );
	edgeloop.shorient = 0;
	edgeloop.sh = shelletraverse();
	while ( edgeloop.sh != (shelle *) NULL ) {
		/* If the segment is encroached, add it to the list. */
		dummy = checkedge4encroach( &edgeloop );
		edgeloop.sh = shelletraverse();
	}
}

#endif /* not CDT_ONLY */

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

#ifndef CDT_ONLY

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

#endif /* not CDT_ONLY */

/*****************************************************************************/
/*                                                                           */
/*  repairencs()   Find and repair all the encroached segments.              */
/*                                                                           */
/*  Encroached segments are repaired by splitting them by inserting a point  */
/*  at or near their centers.                                                */
/*                                                                           */
/*  `flaws' is a flag that specifies whether one should take note of new     */
/*  encroached segments and bad triangles that result from inserting points  */
/*  to repair existing encroached segments.                                  */
/*                                                                           */
/*  When a segment is split, the two resulting subsegments are always        */
/*  tested to see if they are encroached upon, regardless of the value       */
/*  of `flaws'.                                                              */
/*                                                                           */
/*****************************************************************************/

#ifndef CDT_ONLY

void repairencs( flaws )
int flaws;
{
	struct triedge enctri;
	struct triedge testtri;
	struct edge *encloop;
	struct edge testsh;
	point eorg, edest;
	point newpoint;
	enum insertsiteresult success;
	REAL segmentlength, nearestpoweroftwo;
	REAL split;
	int acuteorg, acutedest;
	int dummy;
	int i;
	triangle ptr;                   /* Temporary variable used by stpivot(). */
	shelle sptr;                      /* Temporary variable used by snext(). */

	while ( ( badsegments.items > 0 ) && ( steinerleft != 0 ) ) {
		traversalinit( &badsegments );
		encloop = badsegmenttraverse();
		while ( ( encloop != (struct edge *) NULL ) && ( steinerleft != 0 ) ) {
			/* 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   */
			/*   point added to split one segment will encroach upon the   */
			/*   other segment, which must then be split with a point 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 shells for later splittings.)                  */

			/* Is the origin shared with another segment? */
			stpivot( *encloop, enctri );
			lnext( enctri, testtri );
			tspivot( testtri, testsh );
			acuteorg = testsh.sh != dummysh;
			/* Is the destination shared with another segment? */
			lnextself( testtri );
			tspivot( testtri, testsh );
			acutedest = testsh.sh != dummysh;
			/* Now, check the other side of the segment, if there's a triangle */
			/*   there.                                                        */
			sym( enctri, testtri );
			if ( testtri.tri != dummytri ) {
				/* Is the destination shared with another segment? */
				lnextself( testtri );
				tspivot( testtri, testsh );
				acutedest = acutedest || ( testsh.sh != dummysh );
				/* Is the origin shared with another segment? */
				lnextself( testtri );
				tspivot( testtri, testsh );
				acuteorg = acuteorg || ( testsh.sh != dummysh );
			}

			sorg( *encloop, eorg );
			sdest( *encloop, edest );
			/* 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 nearest the segment's length. */
				nearestpoweroftwo = 1.0;
				while ( segmentlength > SQUAREROOTTWO * nearestpoweroftwo ) {
					nearestpoweroftwo *= 2.0;
				}
				while ( segmentlength < ( 0.5 * SQUAREROOTTWO ) * nearestpoweroftwo ) {
					nearestpoweroftwo *= 0.5;
				}
				/* Where do we split the segment? */
				split = 0.5 * 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 point. */
			newpoint = (point) poolalloc( &points );
			/* Interpolate its coordinate and attributes. */
			for ( i = 0; i < 2 + nextras; i++ ) {
				newpoint[i] = ( 1.0 - split ) * eorg[i] + split * edest[i];
			}
			setpointmark( newpoint, mark( *encloop ) );
			if ( verbose > 1 ) {
				printf(
					"  Splitting edge (%.12g, %.12g) (%.12g, %.12g) at (%.12g, %.12g).\n",
					eorg[0], eorg[1], edest[0], edest[1], newpoint[0], newpoint[1] );
			}
			/* Check whether the new point lies on an endpoint. */
			if ( ( ( newpoint[0] == eorg[0] ) && ( newpoint[1] == eorg[1] ) )
				 || ( ( newpoint[0] == edest[0] ) && ( newpoint[1] == edest[1] ) ) ) {
				printf( "Error:  Ran out of precision at (%.12g, %.12g).\n",
						newpoint[0], newpoint[1] );
				printf( "I attempted to split a segment to a smaller size than can\n" );
				printf( "  be accommodated by the finite precision of floating point\n"
						);
				printf( "  arithmetic.\n" );
				precisionerror();
				exit( 1 );
			}
			/* Insert the splitting point.  This should always succeed. */
			success = insertsite( newpoint, &enctri, encloop, flaws, flaws );
			if ( ( success != SUCCESSFULPOINT ) && ( success != ENCROACHINGPOINT ) ) {
				printf( "Internal error in repairencs():\n" );
				printf( "  Failure to split a segment.\n" );
				internalerror();
			}
			if ( steinerleft > 0 ) {
				steinerleft--;
			}
			/* Check the two new subsegments to see if they're encroached. */
			dummy = checkedge4encroach( encloop );
			snextself( *encloop );
			dummy = checkedge4encroach( encloop );

			badsegmentdealloc( encloop );
			encloop = badsegmenttraverse();
		}
	}
}

#endif /* not CDT_ONLY */

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

#ifndef CDT_ONLY

void tallyfaces(){
	struct triedge triangleloop;

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

#endif /* not CDT_ONLY */

/*****************************************************************************/
/*                                                                           */
/*  findcircumcenter()   Find the circumcenter of a triangle.                */
/*                                                                           */
/*  The result is returned both in terms of x-y coordinates and xi-eta       */
/*  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.             */
/*                                                                           */
/*  The return value indicates which edge of the triangle is shortest.       */
/*                                                                           */
/*****************************************************************************/

enum circumcenterresult findcircumcenter( torg, tdest, tapex, circumcenter,
										  xi, eta )
point torg;
point tdest;
point tapex;
point circumcenter;
REAL *xi;
REAL *eta;
{
	REAL xdo, ydo, xao, yao, xad, yad;
	REAL dodist, aodist, addist;
	REAL denominator;
	REAL dx, dy;

	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;
	if ( noexact ) {
		denominator = (REAL)( 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 = (REAL)( 0.5 / counterclockwise( tdest, tapex, torg ) );
		/* Don't count the above as an orientation test. */
		counterclockcount--;
	}
	circumcenter[0] = torg[0] - ( ydo * aodist - yao * dodist ) * denominator;
	circumcenter[1] = torg[1] + ( xdo * aodist - xao * dodist ) * denominator;

	/* To interpolate point attributes for the new point 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.    */
	dx = circumcenter[0] - torg[0];
	dy = circumcenter[1] - torg[1];
	*xi = (REAL)( ( dx * yao - xao * dy ) * ( 2.0 * denominator ) );
	*eta = (REAL)( ( xdo * dy - dx * ydo ) * ( 2.0 * denominator ) );

	xad = tapex[0] - tdest[0];
	yad = tapex[1] - tdest[1];
	addist = xad * xad + yad * yad;
	if ( ( addist < dodist ) && ( addist < aodist ) ) {
		return OPPOSITEORG;
	}
	else if ( dodist < aodist ) {
		return OPPOSITEAPEX;
	}
	else {
		return OPPOSITEDEST;
	}
}

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

#ifndef CDT_ONLY

void splittriangle( badtri )
struct badface *badtri;
{
	point borg, bdest, bapex;
	point newpoint;
	REAL xi, eta;
	enum insertsiteresult success;
	enum circumcenterresult shortedge;
	int errorflag;
	int i;

	org( badtri->badfacetri, borg );
	dest( badtri->badfacetri, bdest );
	apex( badtri->badfacetri, 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 ( ( borg == badtri->faceorg ) && ( bdest == badtri->facedest ) &&
		 ( bapex == badtri->faceapex ) ) {
		if ( 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 point at the triangle's circumcenter. */
		newpoint = (point) poolalloc( &points );
		shortedge = findcircumcenter( borg, bdest, bapex, newpoint, &xi, &eta );
		/* Check whether the new point lies on a triangle vertex. */
		if ( ( ( newpoint[0] == borg[0] ) && ( newpoint[1] == borg[1] ) )
			 || ( ( newpoint[0] == bdest[0] ) && ( newpoint[1] == bdest[1] ) )
			 || ( ( newpoint[0] == bapex[0] ) && ( newpoint[1] == bapex[1] ) ) ) {
			if ( !quiet ) {
				printf( "Warning:  New point (%.12g, %.12g) falls on existing vertex.\n"
						, newpoint[0], newpoint[1] );
				errorflag = 1;
			}
			pointdealloc( newpoint );
		}
		else {
			for ( i = 2; i < 2 + nextras; i++ ) {
				/* Interpolate the point attributes at the circumcenter. */
				newpoint[i] = borg[i] + xi * ( bdest[i] - borg[i] )
							  + eta * ( bapex[i] - borg[i] );
			}
			/* The new point must be in the interior, and have a marker of zero. */
			setpointmark( newpoint, 0 );
			/* Ensure that the handle `badtri->badfacetri' represents the shortest */
			/*   edge of the triangle.  This ensures that the circumcenter must    */
			/*   fall to the left of this edge, so point location will work.       */
			if ( shortedge == OPPOSITEORG ) {
				lnextself( badtri->badfacetri );
			}
			else if ( shortedge == OPPOSITEDEST ) {
				lprevself( badtri->badfacetri );
			}
			/* Insert the circumcenter, searching from the edge of the triangle, */
			/*   and maintain the Delaunay property of the triangulation.        */
			success = insertsite( newpoint, &( badtri->badfacetri ),
								  (struct edge *) NULL, 1, 1 );
			if ( success == SUCCESSFULPOINT ) {
				if ( steinerleft > 0 ) {
					steinerleft--;
				}
			}
			else if ( success == ENCROACHINGPOINT ) {
				/* If the newly inserted point encroaches upon a segment, delete it. */
				deletesite( &( badtri->badfacetri ) );
			}
			else if ( success == VIOLATINGPOINT ) {
				/* Failed to insert the new point, but some segment was */
				/*   marked as being encroached.                        */
				pointdealloc( newpoint );
			}
			else {                              /* success == DUPLICATEPOINT */
				/* Failed to insert the new point because a vertex is already there. */
				if ( !quiet ) {
					printf(
						"Warning:  New point (%.12g, %.12g) falls on existing vertex.\n"
						, newpoint[0], newpoint[1] );
					errorflag = 1;
				}
				pointdealloc( newpoint );
			}
		}
		if ( errorflag ) {
			if ( verbose ) {
				printf( "  The new point 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();
		}
	}
	/* Return the bad triangle to the pool. */
	pooldealloc( &badtriangles, (VOID *) badtri );
}

#endif /* not CDT_ONLY */

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

#ifndef CDT_ONLY

void enforcequality(){
	int i;

	if ( !quiet ) {
		printf( "Adding Steiner points to enforce quality.\n" );
	}
	/* Initialize the pool of encroached segments. */
	poolinit( &badsegments, sizeof( struct edge ), BADSEGMENTPERBLOCK, POINTER, 0 );
	if ( verbose ) {
		printf( "  Looking for encroached segments.\n" );
	}
	/* Test all segments to see if they're encroached. */
	tallyencs();
	if ( verbose && ( badsegments.items > 0 ) ) {
		printf( "  Splitting encroached segments.\n" );
	}
	/* Note that steinerleft == -1 if an unlimited number */
	/*   of Steiner points is allowed.                    */
	while ( ( badsegments.items > 0 ) && ( steinerleft != 0 ) ) {
		/* Fix the segments without noting newly encroached segments or   */
		/*   bad triangles.  The reason we don't want to note newly       */
		/*   encroached segments is because some encroached segments are  */
		/*   likely to be noted multiple times, and would then be blindly */
		/*   split multiple times.  I should fix that some time.          */
		repairencs( 0 );
		/* Now, find all the segments that became encroached while adding */
		/*   points to split encroached segments.                         */
		tallyencs();
	}
	/* 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 ( ( minangle > 0.0 ) || vararea || fixedarea ) {
		/* Initialize the pool of bad triangles. */
		poolinit( &badtriangles, sizeof( struct badface ), BADTRIPERBLOCK, POINTER,
				  0 );
		/* Initialize the queues of bad triangles. */
		for ( i = 0; i < 64; i++ ) {
			queuefront[i] = (struct badface *) NULL;
			queuetail[i] = &queuefront[i];
		}
		/* Test all triangles to see if they're bad. */
		tallyfaces();
		if ( verbose ) {
			printf( "  Splitting bad triangles.\n" );
		}
		while ( ( badtriangles.items > 0 ) && ( steinerleft != 0 ) ) {
			/* Fix one bad triangle by inserting a point at its circumcenter. */
			splittriangle( dequeuebadtri() );
			/* Fix any encroached segments that may have resulted.  Record */
			/*   any new bad triangles or encroached segments that result. */
			if ( badsegments.items > 0 ) {
				repairencs( 1 );
			}
		}
	}
	/* At this point, if 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 ( !quiet && ( badsegments.items > 0 ) && ( steinerleft == 0 ) ) {
		printf( "\nWarning:  I ran out of Steiner points, but the mesh has\n" );
		if ( badsegments.items == 1 ) {
			printf( "  an encroached segment, and therefore might not be truly\n" );
		}
		else {
			printf( "  %ld encroached segments, and therefore might not be truly\n",
					badsegments.items );
		}
		printf( "  Delaunay.  If the Delaunay property is important to you,\n" );
		printf( "  try increasing the number of Steiner points (controlled by\n" );
		printf( "  the -S switch) slightly and try again.\n\n" );
	}
}

#endif /* not CDT_ONLY */

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

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

void highorder(){
	struct triedge triangleloop, trisym;
	struct edge checkmark;
	point newpoint;
	point torg, tdest;
	int i;
	triangle ptr;                       /* Temporary variable used by sym(). */
	shelle sptr;                    /* Temporary variable used by tspivot(). */

	if ( !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.                        */
	points.deaditemstack = (VOID *) NULL;

	traversalinit( &triangles );
	triangleloop.tri = triangletraverse();
	/* 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 == dummytri ) ) {
				org( triangleloop, torg );
				dest( triangleloop, tdest );
				/* Create a new node in the middle of the edge.  Interpolate */
				/*   its attributes.                                         */
				newpoint = (point) poolalloc( &points );
				for ( i = 0; i < 2 + nextras; i++ ) {
					newpoint[i] = (REAL)( 0.5 * ( torg[i] + tdest[i] ) );
				}
				/* Set the new node's marker to zero or one, depending on */
				/*   whether it lies on a boundary.                       */
				setpointmark( newpoint, trisym.tri == dummytri );
				if ( useshelles ) {
					tspivot( triangleloop, checkmark );
					/* If this edge is a segment, transfer the marker to the new node. */
					if ( checkmark.sh != dummysh ) {
						setpointmark( newpoint, mark( checkmark ) );
					}
				}
				if ( verbose > 1 ) {
					printf( "  Creating (%.12g, %.12g).\n", newpoint[0], newpoint[1] );
				}
				/* Record the new node in the (one or two) adjacent elements. */
				triangleloop.tri[highorderindex + triangleloop.orient] =
					(triangle) newpoint;
				if ( trisym.tri != dummytri ) {
					trisym.tri[highorderindex + trisym.orient] = (triangle) newpoint;
				}
			}
		}
		triangleloop.tri = triangletraverse();
	}
}

/********* File I/O routines begin here                              *********/
/**                                                                         **/
/**                                                                         **/

/*****************************************************************************/
/*                                                                           */
/*  readline()   Read a nonempty line from a file.                           */
/*                                                                           */
/*  A line is considered "nonempty" if it contains something that looks like */
/*  a number.                                                                */
/*                                                                           */
/*****************************************************************************/

#ifndef TRILIBRARY

char *readline( string, infile, infilename )
char *string;
FILE *infile;
char *infilename;
{
	char *result;

	/* Search for something that looks like a number. */
	do {
		result = fgets( string, INPUTLINESIZE, infile );
		if ( result == (char *) NULL ) {
			printf( "  Error:  Unexpected end of file in %s.\n", infilename );
			exit( 1 );
		}
		/* Skip anything that doesn't look like a number, a comment, */
		/*   or the end of a line.                                   */
		while ( ( *result != '\0' ) && ( *result != '#' )
				&& ( *result != '.' ) && ( *result != '+' ) && ( *result != '-' )
				&& ( ( *result < '0' ) || ( *result > '9' ) ) ) {
			result++;
		}
		/* If it's a comment or end of line, read another line and try again. */
	} while ( ( *result == '#' ) || ( *result == '\0' ) );
	return result;
}

#endif /* not TRILIBRARY */

/*****************************************************************************/
/*                                                                           */
/*  findfield()   Find the next field of a string.                           */
/*                                                                           */
/*  Jumps past the current field by searching for whitespace, then jumps     */
/*  past the whitespace to find the next field.                              */
/*                                                                           */
/*****************************************************************************/

#ifndef TRILIBRARY

char *findfield( string )
char *string;
{
	char *result;

	result = string;
	/* Skip the current field.  Stop upon reaching whitespace. */
	while ( ( *result != '\0' ) && ( *result != '#' )
			&& ( *result != ' ' ) && ( *result != '\t' ) ) {
		result++;
	}
	/* Now skip the whitespace and anything else that doesn't look like a */
	/*   number, a comment, or the end of a line.                         */
	while ( ( *result != '\0' ) && ( *result != '#' )
			&& ( *result != '.' ) && ( *result != '+' ) && ( *result != '-' )
			&& ( ( *result < '0' ) || ( *result > '9' ) ) ) {
		result++;
	}
	/* Check for a comment (prefixed with `#'). */
	if ( *result == '#' ) {
		*result = '\0';
	}
	return result;
}

#endif /* not TRILIBRARY */

/*****************************************************************************/
/*                                                                           */
/*  readnodes()   Read the points from a file, which may be a .node or .poly */
/*                file.                                                      */
/*                                                                           */
/*****************************************************************************/

#ifndef TRILIBRARY

void readnodes( nodefilename, polyfilename, polyfile )
char *nodefilename;
char *polyfilename;
FILE **polyfile;
{
	FILE *infile;
	point pointloop;
	char inputline[INPUTLINESIZE];
	char *stringptr;
	char *infilename;
	REAL x, y;
	int firstnode;
	int nodemarkers;
	int currentmarker;
	int i, j;

	if ( poly ) {
		/* Read the points from a .poly file. */
		if ( !quiet ) {
			printf( "Opening %s.\n", polyfilename );
		}
		*polyfile = fopen( polyfilename, "r" );
		if ( *polyfile == (FILE *) NULL ) {
			printf( "  Error:  Cannot access file %s.\n", polyfilename );
			exit( 1 );
		}
		/* Read number of points, number of dimensions, number of point */
		/*   attributes, and number of boundary markers.                */
		stringptr = readline( inputline, *polyfile, polyfilename );
		inpoints = (int) strtol( stringptr, &stringptr, 0 );
		stringptr = findfield( stringptr );
		if ( *stringptr == '\0' ) {
			mesh_dim = 2;
		}
		else {
			mesh_dim = (int) strtol( stringptr, &stringptr, 0 );
		}
		stringptr = findfield( stringptr );
		if ( *stringptr == '\0' ) {
			nextras = 0;
		}
		else {
			nextras = (int) strtol( stringptr, &stringptr, 0 );
		}
		stringptr = findfield( stringptr );
		if ( *stringptr == '\0' ) {
			nodemarkers = 0;
		}
		else {
			nodemarkers = (int) strtol( stringptr, &stringptr, 0 );
		}
		if ( inpoints > 0 ) {
			infile = *polyfile;
			infilename = polyfilename;
			readnodefile = 0;
		}
		else {
			/* If the .poly file claims there are zero points, that means that */
			/*   the points should be read from a separate .node file.         */
			readnodefile = 1;
			infilename = innodefilename;
		}
	}
	else {
		readnodefile = 1;
		infilename = innodefilename;
		*polyfile = (FILE *) NULL;
	}

	if ( readnodefile ) {
		/* Read the points from a .node file. */
		if ( !quiet ) {
			printf( "Opening %s.\n", innodefilename );
		}
		infile = fopen( innodefilename, "r" );
		if ( infile == (FILE *) NULL ) {
			printf( "  Error:  Cannot access file %s.\n", innodefilename );
			exit( 1 );
		}
		/* Read number of points, number of dimensions, number of point */
		/*   attributes, and number of boundary markers.                */
		stringptr = readline( inputline, infile, innodefilename );
		inpoints = (int) strtol( stringptr, &stringptr, 0 );
		stringptr = findfield( stringptr );
		if ( *stringptr == '\0' ) {
			mesh_dim = 2;
		}
		else {
			mesh_dim = (int) strtol( stringptr, &stringptr, 0 );
		}
		stringptr = findfield( stringptr );
		if ( *stringptr == '\0' ) {
			nextras = 0;
		}
		else {
			nextras = (int) strtol( stringptr, &stringptr, 0 );
		}
		stringptr = findfield( stringptr );
		if ( *stringptr == '\0' ) {
			nodemarkers = 0;
		}
		else {
			nodemarkers = (int) strtol( stringptr, &stringptr, 0 );
		}
	}

	if ( inpoints < 3 ) {
		printf( "Error:  Input must have at least three input points.\n" );
		exit( 1 );
	}
	if ( mesh_dim != 2 ) {
		printf( "Error:  Triangle only works with two-dimensional meshes.\n" );
		exit( 1 );
	}

	initializepointpool();

	/* Read the points. */
	for ( i = 0; i < inpoints; i++ ) {
		pointloop = (point) poolalloc( &points );
		stringptr = readline( inputline, infile, infilename );
		if ( i == 0 ) {
			firstnode = (int) strtol( stringptr, &stringptr, 0 );
			if ( ( firstnode == 0 ) || ( firstnode == 1 ) ) {
				firstnumber = firstnode;
			}
		}
		stringptr = findfield( stringptr );
		if ( *stringptr == '\0' ) {
			printf( "Error:  Point %d has no x coordinate.\n", firstnumber + i );
			exit( 1 );
		}
		x = (REAL) strtod( stringptr, &stringptr );
		stringptr = findfield( stringptr );
		if ( *stringptr == '\0' ) {
			printf( "Error:  Point %d has no y coordinate.\n", firstnumber + i );
			exit( 1 );
		}
		y = (REAL) strtod( stringptr, &stringptr );
		pointloop[0] = x;
		pointloop[1] = y;
		/* Read the point attributes. */
		for ( j = 2; j < 2 + nextras; j++ ) {
			stringptr = findfield( stringptr );
			if ( *stringptr == '\0' ) {
				pointloop[j] = 0.0;
			}
			else {
				pointloop[j] = (REAL) strtod( stringptr, &stringptr );
			}
		}
		if ( nodemarkers ) {
			/* Read a point marker. */
			stringptr = findfield( stringptr );
			if ( *stringptr == '\0' ) {
				setpointmark( pointloop, 0 );
			}
			else {
				currentmarker = (int) strtol( stringptr, &stringptr, 0 );
				setpointmark( pointloop, currentmarker );
			}
		}
		else {
			/* If no markers are specified in the file, they default to zero. */
			setpointmark( pointloop, 0 );
		}
		/* Determine the smallest and largest x and y coordinates. */
		if ( i == 0 ) {
			xmin = xmax = x;
			ymin = ymax = y;
		}
		else {
			xmin = ( x < xmin ) ? x : xmin;
			xmax = ( x > xmax ) ? x : xmax;
			ymin = ( y < ymin ) ? y : ymin;
			ymax = ( y > ymax ) ? y : ymax;
		}
	}
	if ( readnodefile ) {
		fclose( infile );
	}

	/* Nonexistent x value used as a flag to mark circle events in sweepline */
	/*   Delaunay algorithm.                                                 */
	xminextreme = 10 * xmin - 9 * xmax;
}

#endif /* not TRILIBRARY */

/*****************************************************************************/
/*                                                                           */
/*  transfernodes()   Read the points from memory.                           */
/*                                                                           */
/*****************************************************************************/

#ifdef TRILIBRARY

void transfernodes( pointlist, pointattriblist, pointmarkerlist, numberofpoints,
					numberofpointattribs )
REAL * pointlist;
REAL *pointattriblist;
int *pointmarkerlist;
int numberofpoints;
int numberofpointattribs;
{
	point pointloop;
	REAL x, y;
	int i, j;
	int coordindex;
	int attribindex;

	inpoints = numberofpoints;
	mesh_dim = 2;
	nextras = numberofpointattribs;
	readnodefile = 0;
	if ( inpoints < 3 ) {
		printf( "Error:  Input must have at least three input points.\n" );
		exit( 1 );
	}

	initializepointpool();

	/* Read the points. */
	coordindex = 0;
	attribindex = 0;
	for ( i = 0; i < inpoints; i++ ) {
		pointloop = (point) poolalloc( &points );
		/* Read the point coordinates. */
		x = pointloop[0] = pointlist[coordindex++];
		y = pointloop[1] = pointlist[coordindex++];
		/* Read the point attributes. */
		for ( j = 0; j < numberofpointattribs; j++ ) {
			pointloop[2 + j] = pointattriblist[attribindex++];
		}
		if ( pointmarkerlist != (int *) NULL ) {
			/* Read a point marker. */
			setpointmark( pointloop, pointmarkerlist[i] );
		}
		else {
			/* If no markers are specified, they default to zero. */
			setpointmark( pointloop, 0 );
		}
		x = pointloop[0];
		y = pointloop[1];
		/* Determine the smallest and largest x and y coordinates. */
		if ( i == 0 ) {
			xmin = xmax = x;
			ymin = ymax = y;
		}
		else {
			xmin = ( x < xmin ) ? x : xmin;
			xmax = ( x > xmax ) ? x : xmax;
			ymin = ( y < ymin ) ? y : ymin;
			ymax = ( y > ymax ) ? y : ymax;
		}
	}

	/* Nonexistent x value used as a flag to mark circle events in sweepline */
	/*   Delaunay algorithm.                                                 */
	xminextreme = 10 * xmin - 9 * xmax;
}

#endif /* TRILIBRARY */

/*****************************************************************************/
/*                                                                           */
/*  readholes()   Read the holes, and possibly regional attributes and area  */
/*                constraints, from a .poly file.                            */
/*                                                                           */
/*****************************************************************************/

#ifndef TRILIBRARY

void readholes( polyfile, polyfilename, hlist, holes, rlist, regions )
FILE * polyfile;
char *polyfilename;
REAL **hlist;
int *holes;
REAL **rlist;
int *regions;
{
	REAL *holelist;
	REAL *regionlist;
	char inputline[INPUTLINESIZE];
	char *stringptr;
	int index;
	int i;

	/* Read the holes. */
	stringptr = readline( inputline, polyfile, polyfilename );
	*holes = (int) strtol( stringptr, &stringptr, 0 );
	if ( *holes > 0 ) {
		holelist = (REAL *) malloc( 2 * *holes * sizeof( REAL ) );
		*hlist = holelist;
		if ( holelist == (REAL *) NULL ) {
			printf( "Error:  Out of memory.\n" );
			exit( 1 );
		}
		for ( i = 0; i < 2 * *holes; i += 2 ) {
			stringptr = readline( inputline, polyfile, polyfilename );
			stringptr = findfield( stringptr );
			if ( *stringptr == '\0' ) {
				printf( "Error:  Hole %d has no x coordinate.\n",
						firstnumber + ( i >> 1 ) );
				exit( 1 );
			}
			else {
				holelist[i] = (REAL) strtod( stringptr, &stringptr );
			}
			stringptr = findfield( stringptr );
			if ( *stringptr == '\0' ) {
				printf( "Error:  Hole %d has no y coordinate.\n",
						firstnumber + ( i >> 1 ) );
				exit( 1 );
			}
			else {
				holelist[i + 1] = (REAL) strtod( stringptr, &stringptr );
			}
		}
	}
	else {
		*hlist = (REAL *) NULL;
	}

#ifndef CDT_ONLY
	if ( ( regionattrib || vararea ) && !refine ) {
		/* Read the area constraints. */
		stringptr = readline( inputline, polyfile, polyfilename );
		*regions = (int) strtol( stringptr, &stringptr, 0 );
		if ( *regions > 0 ) {
			regionlist = (REAL *) malloc( 4 * *regions * sizeof( REAL ) );
			*rlist = regionlist;
			if ( regionlist == (REAL *) NULL ) {
				printf( "Error:  Out of memory.\n" );
				exit( 1 );
			}
			index = 0;
			for ( i = 0; i < *regions; i++ ) {
				stringptr = readline( inputline, polyfile, polyfilename );
				stringptr = findfield( stringptr );
				if ( *stringptr == '\0' ) {
					printf( "Error:  Region %d has no x coordinate.\n",
							firstnumber + i );
					exit( 1 );
				}
				else {
					regionlist[index++] = (REAL) strtod( stringptr, &stringptr );
				}
				stringptr = findfield( stringptr );
				if ( *stringptr == '\0' ) {
					printf( "Error:  Region %d has no y coordinate.\n",
							firstnumber + i );
					exit( 1 );
				}
				else {
					regionlist[index++] = (REAL) strtod( stringptr, &stringptr );
				}
				stringptr = findfield( stringptr );
				if ( *stringptr == '\0' ) {
					printf(
						"Error:  Region %d has no region attribute or area constraint.\n",
						firstnumber + i );
					exit( 1 );
				}
				else {
					regionlist[index++] = (REAL) strtod( stringptr, &stringptr );
				}
				stringptr = findfield( stringptr );
				if ( *stringptr == '\0' ) {
					regionlist[index] = regionlist[index - 1];
				}
				else {
					regionlist[index] = (REAL) strtod( stringptr, &stringptr );
				}
				index++;
			}
		}
	}
	else {
		/* Set `*regions' to zero to avoid an accidental free() later. */
		*regions = 0;
		*rlist = (REAL *) NULL;
	}
#endif /* not CDT_ONLY */

	fclose( polyfile );
}

#endif /* not TRILIBRARY */

/*****************************************************************************/
/*                                                                           */
/*  finishfile()   Write the command line to the output file so the user     */
/*                 can remember how the file was generated.  Close the file. */
/*                                                                           */
/*****************************************************************************/

#ifndef TRILIBRARY

void finishfile( outfile, argc, argv )
FILE * outfile;
int argc;
char **argv;
{
	int i;

	fprintf( outfile, "# Generated by" );
	for ( i = 0; i < argc; i++ ) {
		fprintf( outfile, " " );
		fputs( argv[i], outfile );
	}
	fprintf( outfile, "\n" );
	fclose( outfile );
}

#endif /* not TRILIBRARY */

/*****************************************************************************/
/*                                                                           */
/*  writenodes()   Number the points and write them to a .node file.         */
/*                                                                           */
/*  To save memory, the point numbers are written over the shell markers     */
/*  after the points are written to a file.                                  */
/*                                                                           */
/*****************************************************************************/

#ifdef TRILIBRARY

void writenodes( pointlist, pointattriblist, pointmarkerlist )
REAL * *pointlist;
REAL **pointattriblist;
int **pointmarkerlist;

#else /* not TRILIBRARY */

void writenodes( nodefilename, argc, argv )
char *nodefilename;
int argc;
char **argv;

#endif /* not TRILIBRARY */

{
#ifdef TRILIBRARY
	REAL *plist;
	REAL *palist;
	int *pmlist;
	int coordindex;
	int attribindex;
#else /* not TRILIBRARY */
	FILE *outfile;
#endif /* not TRILIBRARY */
	point pointloop;
	int pointnumber;
	int i;

#ifdef TRILIBRARY
	if ( !quiet ) {
		printf( "Writing points.\n" );
	}
	/* Allocate memory for output points if necessary. */
	if ( *pointlist == (REAL *) NULL ) {
		*pointlist = (REAL *) malloc( points.items * 2 * sizeof( REAL ) );
		if ( *pointlist == (REAL *) NULL ) {
			printf( "Error:  Out of memory.\n" );
			exit( 1 );
		}
	}
	/* Allocate memory for output point attributes if necessary. */
	if ( ( nextras > 0 ) && ( *pointattriblist == (REAL *) NULL ) ) {
		*pointattriblist = (REAL *) malloc( points.items * nextras * sizeof( REAL ) );
		if ( *pointattriblist == (REAL *) NULL ) {
			printf( "Error:  Out of memory.\n" );
			exit( 1 );
		}
	}
	/* Allocate memory for output point markers if necessary. */
	if ( !nobound && ( *pointmarkerlist == (int *) NULL ) ) {
		*pointmarkerlist = (int *) malloc( points.items * sizeof( int ) );
		if ( *pointmarkerlist == (int *) NULL ) {
			printf( "Error:  Out of memory.\n" );
			exit( 1 );
		}
	}
	plist = *pointlist;
	palist = *pointattriblist;
	pmlist = *pointmarkerlist;
	coordindex = 0;
	attribindex = 0;
#else /* not TRILIBRARY */
	if ( !quiet ) {
		printf( "Writing %s.\n", nodefilename );
	}
	outfile = fopen( nodefilename, "w" );
	if ( outfile == (FILE *) NULL ) {
		printf( "  Error:  Cannot create file %s.\n", nodefilename );
		exit( 1 );
	}
	/* Number of points, number of dimensions, number of point attributes, */
	/*   and number of boundary markers (zero or one).                     */
	fprintf( outfile, "%ld  %d  %d  %d\n", points.items, mesh_dim, nextras,
			 1 - nobound );
#endif /* not TRILIBRARY */

	traversalinit( &points );
	pointloop = pointtraverse();
	pointnumber = firstnumber;
	while ( pointloop != (point) NULL ) {
#ifdef TRILIBRARY
		/* X and y coordinates. */
		plist[coordindex++] = pointloop[0];
		plist[coordindex++] = pointloop[1];
		/* Point attributes. */
		for ( i = 0; i < nextras; i++ ) {
			palist[attribindex++] = pointloop[2 + i];
		}
		if ( !nobound ) {
			/* Copy the boundary marker. */
			pmlist[pointnumber - firstnumber] = pointmark( pointloop );
		}
#else /* not TRILIBRARY */
		/* Point number, x and y coordinates. */
		fprintf( outfile, "%4d    %.17g  %.17g", pointnumber, pointloop[0],
				 pointloop[1] );
		for ( i = 0; i < nextras; i++ ) {
			/* Write an attribute. */
			fprintf( outfile, "  %.17g", pointloop[i + 2] );
		}
		if ( nobound ) {
			fprintf( outfile, "\n" );
		}
		else {
			/* Write the boundary marker. */
			fprintf( outfile, "    %d\n", pointmark( pointloop ) );
		}
#endif /* not TRILIBRARY */

		setpointmark( pointloop, pointnumber );
		pointloop = pointtraverse();
		pointnumber++;
	}

#ifndef TRILIBRARY
	finishfile( outfile, argc, argv );
#endif /* not TRILIBRARY */
}

/*****************************************************************************/
/*                                                                           */
/*  numbernodes()   Number the points.                                       */
/*                                                                           */
/*  Each point is assigned a marker equal to its number.                     */
/*                                                                           */
/*  Used when writenodes() is not called because no .node file is written.   */
/*                                                                           */
/*****************************************************************************/

void numbernodes(){
	point pointloop;
	int pointnumber;

	traversalinit( &points );
	pointloop = pointtraverse();
	pointnumber = firstnumber;
	while ( pointloop != (point) NULL ) {
		setpointmark( pointloop, pointnumber );
		pointloop = pointtraverse();
		pointnumber++;
	}
}

/*****************************************************************************/
/*                                                                           */
/*  writeelements()   Write the triangles to an .ele file.                   */
/*                                                                           */
/*****************************************************************************/

#ifdef TRILIBRARY

void writeelements( trianglelist, triangleattriblist )
int **trianglelist;
REAL **triangleattriblist;

#else /* not TRILIBRARY */

void writeelements( elefilename, argc, argv )
char *elefilename;
int argc;
char **argv;

#endif /* not TRILIBRARY */

{
#ifdef TRILIBRARY
	int *tlist;
	REAL *talist;
	int pointindex;
	int attribindex;
#else /* not TRILIBRARY */
	FILE *outfile;
#endif /* not TRILIBRARY */
	struct triedge triangleloop;
	point p1, p2, p3;
	point mid1, mid2, mid3;
	int elementnumber;
	int i;

#ifdef TRILIBRARY
	if ( !quiet ) {
		printf( "Writing triangles.\n" );
	}
	/* Allocate memory for output triangles if necessary. */
	if ( *trianglelist == (int *) NULL ) {
		*trianglelist = (int *) malloc( triangles.items *
										( ( order + 1 ) * ( order + 2 ) / 2 ) * sizeof( int ) );
		if ( *trianglelist == (int *) NULL ) {
			printf( "Error:  Out of memory.\n" );
			exit( 1 );
		}
	}
	/* Allocate memory for output triangle attributes if necessary. */
	if ( ( eextras > 0 ) && ( *triangleattriblist == (REAL *) NULL ) ) {
		*triangleattriblist = (REAL *) malloc( triangles.items * eextras *
											   sizeof( REAL ) );
		if ( *triangleattriblist == (REAL *) NULL ) {
			printf( "Error:  Out of memory.\n" );
			exit( 1 );
		}
	}
	tlist = *trianglelist;
	talist = *triangleattriblist;
	pointindex = 0;
	attribindex = 0;
#else /* not TRILIBRARY */
	if ( !quiet ) {
		printf( "Writing %s.\n", elefilename );
	}
	outfile = fopen( elefilename, "w" );
	if ( outfile == (FILE *) NULL ) {
		printf( "  Error:  Cannot create file %s.\n", elefilename );
		exit( 1 );
	}
	/* Number of triangles, points per triangle, attributes per triangle. */
	fprintf( outfile, "%ld  %d  %d\n", triangles.items,
			 ( order + 1 ) * ( order + 2 ) / 2, eextras );
#endif /* not TRILIBRARY */

	traversalinit( &triangles );
	triangleloop.tri = triangletraverse();
	triangleloop.orient = 0;
	elementnumber = firstnumber;
	while ( triangleloop.tri != (triangle *) NULL ) {
		org( triangleloop, p1 );
		dest( triangleloop, p2 );
		apex( triangleloop, p3 );
		if ( order == 1 ) {
#ifdef TRILIBRARY
			tlist[pointindex++] = pointmark( p1 );
			tlist[pointindex++] = pointmark( p2 );
			tlist[pointindex++] = pointmark( p3 );
#else /* not TRILIBRARY */
			/* Triangle number, indices for three points. */
			fprintf( outfile, "%4d    %4d  %4d  %4d", elementnumber,
					 pointmark( p1 ), pointmark( p2 ), pointmark( p3 ) );
#endif /* not TRILIBRARY */
		}
		else {
			mid1 = (point) triangleloop.tri[highorderindex + 1];
			mid2 = (point) triangleloop.tri[highorderindex + 2];
			mid3 = (point) triangleloop.tri[highorderindex];
#ifdef TRILIBRARY
			tlist[pointindex++] = pointmark( p1 );
			tlist[pointindex++] = pointmark( p2 );
			tlist[pointindex++] = pointmark( p3 );
			tlist[pointindex++] = pointmark( mid1 );
			tlist[pointindex++] = pointmark( mid2 );
			tlist[pointindex++] = pointmark( mid3 );
#else /* not TRILIBRARY */
			/* Triangle number, indices for six points. */
			fprintf( outfile, "%4d    %4d  %4d  %4d  %4d  %4d  %4d", elementnumber,
					 pointmark( p1 ), pointmark( p2 ), pointmark( p3 ), pointmark( mid1 ),
					 pointmark( mid2 ), pointmark( mid3 ) );
#endif /* not TRILIBRARY */
		}

#ifdef TRILIBRARY
		for ( i = 0; i < eextras; i++ ) {
			talist[attribindex++] = elemattribute( triangleloop, i );
		}
#else /* not TRILIBRARY */
		for ( i = 0; i < eextras; i++ ) {
			fprintf( outfile, "  %.17g", elemattribute( triangleloop, i ) );
		}
		fprintf( outfile, "\n" );
#endif /* not TRILIBRARY */

		triangleloop.tri = triangletraverse();
		elementnumber++;
	}

#ifndef TRILIBRARY
	finishfile( outfile, argc, argv );
#endif /* not TRILIBRARY */
}

/*****************************************************************************/
/*                                                                           */
/*  writepoly()   Write the segments and holes to a .poly file.              */
/*                                                                           */
/*****************************************************************************/

#ifdef TRILIBRARY

void writepoly( segmentlist, segmentmarkerlist )
int **segmentlist;
int **segmentmarkerlist;

#else /* not TRILIBRARY */

void writepoly( polyfilename, holelist, holes, regionlist, regions, argc, argv )
char *polyfilename;
REAL *holelist;
int holes;
REAL *regionlist;
int regions;
int argc;
char **argv;

#endif /* not TRILIBRARY */

{
#ifdef TRILIBRARY
	int *slist;
	int *smlist;
	int index;
#else /* not TRILIBRARY */
	FILE *outfile;
	int i;
#endif /* not TRILIBRARY */
	struct edge shelleloop;
	point endpoint1, endpoint2;
	int shellenumber;

#ifdef TRILIBRARY
	if ( !quiet ) {
		printf( "Writing segments.\n" );
	}
	/* Allocate memory for output segments if necessary. */
	if ( *segmentlist == (int *) NULL ) {
		*segmentlist = (int *) malloc( shelles.items * 2 * sizeof( int ) );
		if ( *segmentlist == (int *) NULL ) {
			printf( "Error:  Out of memory.\n" );
			exit( 1 );
		}
	}
	/* Allocate memory for output segment markers if necessary. */
	if ( !nobound && ( *segmentmarkerlist == (int *) NULL ) ) {
		*segmentmarkerlist = (int *) malloc( shelles.items * sizeof( int ) );
		if ( *segmentmarkerlist == (int *) NULL ) {
			printf( "Error:  Out of memory.\n" );
			exit( 1 );
		}
	}
	slist = *segmentlist;
	smlist = *segmentmarkerlist;
	index = 0;
#else /* not TRILIBRARY */
	if ( !quiet ) {
		printf( "Writing %s.\n", polyfilename );
	}
	outfile = fopen( polyfilename, "w" );
	if ( outfile == (FILE *) NULL ) {
		printf( "  Error:  Cannot create file %s.\n", polyfilename );
		exit( 1 );
	}
	/* The zero indicates that the points are in a separate .node file. */
	/*   Followed by number of dimensions, number of point attributes,  */
	/*   and number of boundary markers (zero or one).                  */
	fprintf( outfile, "%d  %d  %d  %d\n", 0, mesh_dim, nextras, 1 - nobound );
	/* Number of segments, number of boundary markers (zero or one). */
	fprintf( outfile, "%ld  %d\n", shelles.items, 1 - nobound );
#endif /* not TRILIBRARY */

	traversalinit( &shelles );
	shelleloop.sh = shelletraverse();
	shelleloop.shorient = 0;
	shellenumber = firstnumber;
	while ( shelleloop.sh != (shelle *) NULL ) {
		sorg( shelleloop, endpoint1 );
		sdest( shelleloop, endpoint2 );
#ifdef TRILIBRARY
		/* Copy indices of the segment's two endpoints. */
		slist[index++] = pointmark( endpoint1 );
		slist[index++] = pointmark( endpoint2 );
		if ( !nobound ) {
			/* Copy the boundary marker. */
			smlist[shellenumber - firstnumber] = mark( shelleloop );
		}
#else /* not TRILIBRARY */
		/* Segment number, indices of its two endpoints, and possibly a marker. */
		if ( nobound ) {
			fprintf( outfile, "%4d    %4d  %4d\n", shellenumber,
					 pointmark( endpoint1 ), pointmark( endpoint2 ) );
		}
		else {
			fprintf( outfile, "%4d    %4d  %4d    %4d\n", shellenumber,
					 pointmark( endpoint1 ), pointmark( endpoint2 ), mark( shelleloop ) );
		}
#endif /* not TRILIBRARY */

		shelleloop.sh = shelletraverse();
		shellenumber++;
	}

#ifndef TRILIBRARY
#ifndef CDT_ONLY
	fprintf( outfile, "%d\n", holes );
	if ( holes > 0 ) {
		for ( i = 0; i < holes; i++ ) {
			/* Hole number, x and y coordinates. */
			fprintf( outfile, "%4d   %.17g  %.17g\n", firstnumber + i,
					 holelist[2 * i], holelist[2 * i + 1] );
		}
	}
	if ( regions > 0 ) {
		fprintf( outfile, "%d\n", regions );
		for ( i = 0; i < regions; i++ ) {
			/* Region number, x and y coordinates, attribute, maximum area. */
			fprintf( outfile, "%4d   %.17g  %.17g  %.17g  %.17g\n", firstnumber + i,
					 regionlist[4 * i], regionlist[4 * i + 1],
					 regionlist[4 * i + 2], regionlist[4 * i + 3] );
		}
	}
#endif /* not CDT_ONLY */

	finishfile( outfile, argc, argv );
#endif /* not TRILIBRARY */
}

/*****************************************************************************/
/*                                                                           */
/*  writeedges()   Write the edges to a .edge file.                          */
/*                                                                           */
/*****************************************************************************/

#ifdef TRILIBRARY

void writeedges( edgelist, edgemarkerlist )
int **edgelist;
int **edgemarkerlist;

#else /* not TRILIBRARY */

void writeedges( edgefilename, argc, argv )
char *edgefilename;
int argc;
char **argv;

#endif /* not TRILIBRARY */

{
#ifdef TRILIBRARY
	int *elist;
	int *emlist;
	int index;
#else /* not TRILIBRARY */
	FILE *outfile;
#endif /* not TRILIBRARY */
	struct triedge triangleloop, trisym;
	struct edge checkmark;
	point p1, p2;
	int edgenumber;
	triangle ptr;                       /* Temporary variable used by sym(). */
	shelle sptr;                    /* Temporary variable used by tspivot(). */

#ifdef TRILIBRARY
	if ( !quiet ) {
		printf( "Writing edges.\n" );
	}
	/* Allocate memory for edges if necessary. */
	if ( *edgelist == (int *) NULL ) {
		*edgelist = (int *) malloc( edges * 2 * sizeof( int ) );
		if ( *edgelist == (int *) NULL ) {
			printf( "Error:  Out of memory.\n" );
			exit( 1 );
		}
	}
	/* Allocate memory for edge markers if necessary. */
	if ( !nobound && ( *edgemarkerlist == (int *) NULL ) ) {
		*edgemarkerlist = (int *) malloc( edges * sizeof( int ) );
		if ( *edgemarkerlist == (int *) NULL ) {
			printf( "Error:  Out of memory.\n" );
			exit( 1 );
		}
	}
	elist = *edgelist;
	emlist = *edgemarkerlist;
	index = 0;
#else /* not TRILIBRARY */
	if ( !quiet ) {
		printf( "Writing %s.\n", edgefilename );
	}
	outfile = fopen( edgefilename, "w" );
	if ( outfile == (FILE *) NULL ) {
		printf( "  Error:  Cannot create file %s.\n", edgefilename );
		exit( 1 );
	}
	/* Number of edges, number of boundary markers (zero or one). */
	fprintf( outfile, "%ld  %d\n", edges, 1 - nobound );
#endif /* not TRILIBRARY */

	traversalinit( &triangles );
	triangleloop.tri = triangletraverse();
	edgenumber = 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 == dummytri ) ) {
				org( triangleloop, p1 );
				dest( triangleloop, p2 );
#ifdef TRILIBRARY
				elist[index++] = pointmark( p1 );
				elist[index++] = pointmark( p2 );
#endif /* TRILIBRARY */
				if ( nobound ) {
#ifndef TRILIBRARY
					/* Edge number, indices of two endpoints. */
					fprintf( outfile, "%4d   %d  %d\n", edgenumber,
							 pointmark( p1 ), pointmark( p2 ) );
#endif /* not TRILIBRARY */
				}
				else {
					/* Edge number, indices of two endpoints, and a boundary marker. */
					/*   If there's no shell edge, the boundary marker is zero.      */
					if ( useshelles ) {
						tspivot( triangleloop, checkmark );
						if ( checkmark.sh == dummysh ) {
#ifdef TRILIBRARY
							emlist[edgenumber - firstnumber] = 0;
#else /* not TRILIBRARY */
							fprintf( outfile, "%4d   %d  %d  %d\n", edgenumber,
									 pointmark( p1 ), pointmark( p2 ), 0 );
#endif /* not TRILIBRARY */
						}
						else {
#ifdef TRILIBRARY
							emlist[edgenumber - firstnumber] = mark( checkmark );
#else /* not TRILIBRARY */
							fprintf( outfile, "%4d   %d  %d  %d\n", edgenumber,
									 pointmark( p1 ), pointmark( p2 ), mark( checkmark ) );
#endif /* not TRILIBRARY */
						}
					}
					else {
#ifdef TRILIBRARY
						emlist[edgenumber - firstnumber] = trisym.tri == dummytri;
#else /* not TRILIBRARY */
						fprintf( outfile, "%4d   %d  %d  %d\n", edgenumber,
								 pointmark( p1 ), pointmark( p2 ), trisym.tri == dummytri );
#endif /* not TRILIBRARY */
					}
				}
				edgenumber++;
			}
		}
		triangleloop.tri = triangletraverse();
	}

#ifndef TRILIBRARY
	finishfile( outfile, argc, argv );
#endif /* not TRILIBRARY */
}

/*****************************************************************************/
/*                                                                           */
/*  writevoronoi()   Write the Voronoi diagram to a .v.node and .v.edge      */
/*                   file.                                                   */
/*                                                                           */
/*  The Voronoi diagram is the geometric dual of the Delaunay triangulation. */
/*  Hence, the Voronoi vertices are listed by traversing the Delaunay        */
/*  triangles, and the Voronoi edges are listed by traversing the Delaunay   */
/*  edges.                                                                   */
/*                                                                           */
/*  WARNING:  In order to assign numbers to the Voronoi vertices, this       */
/*  procedure messes up the shell edges or the extra nodes of every          */
/*  element.  Hence, you should call this procedure last.                    */
/*                                                                           */
/*****************************************************************************/

#ifdef TRILIBRARY

void writevoronoi( vpointlist, vpointattriblist, vpointmarkerlist, vedgelist,
				   vedgemarkerlist, vnormlist )
REAL * *vpointlist;
REAL **vpointattriblist;
int **vpointmarkerlist;
int **vedgelist;
int **vedgemarkerlist;
REAL **vnormlist;

#else /* not TRILIBRARY */

void writevoronoi( vnodefilename, vedgefilename, argc, argv )
char *vnodefilename;
char *vedgefilename;
int argc;
char **argv;

#endif /* not TRILIBRARY */

{
#ifdef TRILIBRARY
	REAL *plist;
	REAL *palist;
	int *elist;
	REAL *normlist;
	int coordindex;
	int attribindex;
#else /* not TRILIBRARY */
	FILE *outfile;
#endif /* not TRILIBRARY */
	struct triedge triangleloop, trisym;
	point torg, tdest, tapex;
	REAL circumcenter[2];
	REAL xi, eta;
	int vnodenumber, vedgenumber;
	int p1, p2;
	int i;
	triangle ptr;                       /* Temporary variable used by sym(). */

#ifdef TRILIBRARY
	if ( !quiet ) {
		printf( "Writing Voronoi vertices.\n" );
	}
	/* Allocate memory for Voronoi vertices if necessary. */
	if ( *vpointlist == (REAL *) NULL ) {
		*vpointlist = (REAL *) malloc( triangles.items * 2 * sizeof( REAL ) );
		if ( *vpointlist == (REAL *) NULL ) {
			printf( "Error:  Out of memory.\n" );
			exit( 1 );
		}
	}
	/* Allocate memory for Voronoi vertex attributes if necessary. */
	if ( *vpointattriblist == (REAL *) NULL ) {
		*vpointattriblist = (REAL *) malloc( triangles.items * nextras *
											 sizeof( REAL ) );
		if ( *vpointattriblist == (REAL *) NULL ) {
			printf( "Error:  Out of memory.\n" );
			exit( 1 );
		}
	}
	*vpointmarkerlist = (int *) NULL;
	plist = *vpointlist;
	palist = *vpointattriblist;
	coordindex = 0;
	attribindex = 0;
#else /* not TRILIBRARY */
	if ( !quiet ) {
		printf( "Writing %s.\n", vnodefilename );
	}
	outfile = fopen( vnodefilename, "w" );
	if ( outfile == (FILE *) NULL ) {
		printf( "  Error:  Cannot create file %s.\n", vnodefilename );
		exit( 1 );
	}
	/* Number of triangles, two dimensions, number of point attributes, */
	/*   zero markers.                                                  */
	fprintf( outfile, "%ld  %d  %d  %d\n", triangles.items, 2, nextras, 0 );
#endif /* not TRILIBRARY */

	traversalinit( &triangles );
	triangleloop.tri = triangletraverse();
	triangleloop.orient = 0;
	vnodenumber = firstnumber;
	while ( triangleloop.tri != (triangle *) NULL ) {
		org( triangleloop, torg );
		dest( triangleloop, tdest );
		apex( triangleloop, tapex );
		findcircumcenter( torg, tdest, tapex, circumcenter, &xi, &eta );
#ifdef TRILIBRARY
		/* X and y coordinates. */
		plist[coordindex++] = circumcenter[0];
		plist[coordindex++] = circumcenter[1];
		for ( i = 2; i < 2 + nextras; i++ ) {
			/* Interpolate the point attributes at the circumcenter. */
			palist[attribindex++] = torg[i] + xi * ( tdest[i] - torg[i] )
									+ eta * ( tapex[i] - torg[i] );
		}
#else /* not TRILIBRARY */
		/* Voronoi vertex number, x and y coordinates. */
		fprintf( outfile, "%4d    %.17g  %.17g", vnodenumber, circumcenter[0],
				 circumcenter[1] );
		for ( i = 2; i < 2 + nextras; i++ ) {
			/* Interpolate the point attributes at the circumcenter. */
			fprintf( outfile, "  %.17g", torg[i] + xi * ( tdest[i] - torg[i] )
					 + eta * ( tapex[i] - torg[i] ) );
		}
		fprintf( outfile, "\n" );
#endif /* not TRILIBRARY */

		*(int *) ( triangleloop.tri + 6 ) = vnodenumber;
		triangleloop.tri = triangletraverse();
		vnodenumber++;
	}

#ifndef TRILIBRARY
	finishfile( outfile, argc, argv );
#endif /* not TRILIBRARY */

#ifdef TRILIBRARY
	if ( !quiet ) {
		printf( "Writing Voronoi edges.\n" );
	}
	/* Allocate memory for output Voronoi edges if necessary. */
	if ( *vedgelist == (int *) NULL ) {
		*vedgelist = (int *) malloc( edges * 2 * sizeof( int ) );
		if ( *vedgelist == (int *) NULL ) {
			printf( "Error:  Out of memory.\n" );
			exit( 1 );
		}
	}
	*vedgemarkerlist = (int *) NULL;
	/* Allocate memory for output Voronoi norms if necessary. */
	if ( *vnormlist == (REAL *) NULL ) {
		*vnormlist = (REAL *) malloc( edges * 2 * sizeof( REAL ) );
		if ( *vnormlist == (REAL *) NULL ) {
			printf( "Error:  Out of memory.\n" );
			exit( 1 );
		}
	}
	elist = *vedgelist;
	normlist = *vnormlist;
	coordindex = 0;
#else /* not TRILIBRARY */
	if ( !quiet ) {
		printf( "Writing %s.\n", vedgefilename );
	}
	outfile = fopen( vedgefilename, "w" );
	if ( outfile == (FILE *) NULL ) {
		printf( "  Error:  Cannot create file %s.\n", vedgefilename );
		exit( 1 );
	}
	/* Number of edges, zero boundary markers. */
	fprintf( outfile, "%ld  %d\n", edges, 0 );
#endif /* not TRILIBRARY */

	traversalinit( &triangles );
	triangleloop.tri = triangletraverse();
	vedgenumber = 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 == dummytri ) ) {
				/* Find the number of this triangle (and Voronoi vertex). */
				p1 = *(int *) ( triangleloop.tri + 6 );
				if ( trisym.tri == dummytri ) {
					org( triangleloop, torg );
					dest( triangleloop, tdest );
#ifdef TRILIBRARY
					/* Copy an infinite ray.  Index of one endpoint, and -1. */
					elist[coordindex] = p1;
					normlist[coordindex++] = tdest[1] - torg[1];
					elist[coordindex] = -1;
					normlist[coordindex++] = torg[0] - tdest[0];
#else /* not TRILIBRARY */
					/* Write an infinite ray.  Edge number, index of one endpoint, -1, */
					/*   and x and y coordinates of a vector representing the          */
					/*   direction of the ray.                                         */
					fprintf( outfile, "%4d   %d  %d   %.17g  %.17g\n", vedgenumber,
							 p1, -1, tdest[1] - torg[1], torg[0] - tdest[0] );
#endif /* not TRILIBRARY */
				}
				else {
					/* Find the number of the adjacent triangle (and Voronoi vertex). */
					p2 = *(int *) ( trisym.tri + 6 );
					/* Finite edge.  Write indices of two endpoints. */
#ifdef TRILIBRARY
					elist[coordindex] = p1;
					normlist[coordindex++] = 0.0;
					elist[coordindex] = p2;
					normlist[coordindex++] = 0.0;
#else /* not TRILIBRARY */
					fprintf( outfile, "%4d   %d  %d\n", vedgenumber, p1, p2 );
#endif /* not TRILIBRARY */
				}
				vedgenumber++;
			}
		}
		triangleloop.tri = triangletraverse();
	}

#ifndef TRILIBRARY
	finishfile( outfile, argc, argv );
#endif /* not TRILIBRARY */
}

#ifdef TRILIBRARY

void writeneighbors( neighborlist )
int **neighborlist;

#else /* not TRILIBRARY */

void writeneighbors( neighborfilename, argc, argv )
char *neighborfilename;
int argc;
char **argv;

#endif /* not TRILIBRARY */

{
#ifdef TRILIBRARY
	int *nlist;
	int index;
#else /* not TRILIBRARY */
	FILE *outfile;
#endif /* not TRILIBRARY */
	struct triedge triangleloop, trisym;
	int elementnumber;
	int neighbor1, neighbor2, neighbor3;
	triangle ptr;                       /* Temporary variable used by sym(). */