triangle.cpp

/*****************************************************************************/
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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             */
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/*  A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator.      */
/*  (triangle.c)                                                             */
/*                                                                           */
/*  Version 1.6                                                              */
/*  July 28, 2005                                                            */
/*                                                                           */
/*  Copyright 1993, 1995, 1997, 1998, 2002, 2005                             */
/*  Jonathan Richard Shewchuk                                                */
/*  2360 Woolsey #H                                                          */
/*  Berkeley, California  94705-1927                                         */
/*  jrs@cs.berkeley.edu                                                      */
/*                                                                           */
/*  Modified by Andreas Geiger, 2011                                         */
/*                                                                           */
/*  This program may be freely redistributed under the condition that the    */
/*    copyright notices (including this entire header and the copyright      */
/*    notice printed when the `-h' switch is selected) are not removed, and  */
/*    no compensation is received.  Private, research, and institutional     */
/*    use is free.  You may distribute modified versions of this code UNDER  */
/*    THE CONDITION THAT THIS CODE AND ANY MODIFICATIONS MADE TO IT IN THE   */
/*    SAME FILE REMAIN UNDER COPYRIGHT OF THE ORIGINAL AUTHOR, BOTH SOURCE   */
/*    AND OBJECT CODE ARE MADE FREELY AVAILABLE WITHOUT CHARGE, AND CLEAR    */
/*    NOTICE IS GIVEN OF THE MODIFICATIONS.  Distribution of this code as    */
/*    part of a commercial system is permissible ONLY BY DIRECT ARRANGEMENT  */
/*    WITH THE AUTHOR.  (If you are not directly supplying this code to a    */
/*    customer, and you are instead telling them how they can obtain it for  */
/*    free, then you are not required to make any arrangement with me.)      */
/*                                                                           */
/*  Hypertext instructions for Triangle are available on the Web at          */
/*                                                                           */
/*      http://www.cs.cmu.edu/~quake/triangle.html                           */
/*                                                                           */
/*  Disclaimer:  Neither I nor Carnegie Mellon warrant this code in any way  */
/*    whatsoever.  This code is provided "as-is".  Use at your own risk.     */
/*                                                                           */
/*  Some of the references listed below are marked with an asterisk.  [*]    */
/*    These references are available for downloading from the Web page       */
/*                                                                           */
/*      http://www.cs.cmu.edu/~quake/triangle.research.html                  */
/*                                                                           */
/*  Three papers discussing aspects of Triangle are available.  A short      */
/*    overview appears in "Triangle:  Engineering a 2D Quality Mesh          */
/*    Generator and Delaunay Triangulator," in Applied Computational         */
/*    Geometry:  Towards Geometric Engineering, Ming C. Lin and Dinesh       */
/*    Manocha, editors, Lecture Notes in Computer Science volume 1148,       */
/*    pages 203-222, Springer-Verlag, Berlin, May 1996 (from the First ACM   */
/*    Workshop on Applied Computational Geometry).  [*]                      */
/*                                                                           */
/*    The algorithms are discussed in the greatest detail in "Delaunay       */
/*    Refinement Algorithms for Triangular Mesh Generation," Computational   */
/*    Geometry:  Theory and Applications 22(1-3):21-74, May 2002.  [*]       */
/*                                                                           */
/*    More detail about the data structures may be found in my dissertation: */
/*    "Delaunay Refinement Mesh Generation," Ph.D. thesis, Technical Report  */
/*    CMU-CS-97-137, School of Computer Science, Carnegie Mellon University, */
/*    Pittsburgh, Pennsylvania, 18 May 1997.  [*]                            */
/*                                                                           */
/*  Triangle was created as part of the Quake Project in the School of       */
/*    Computer Science at Carnegie Mellon University.  For further           */
/*    information, see Hesheng Bao, Jacobo Bielak, Omar Ghattas, Loukas F.   */
/*    Kallivokas, David R. O'Hallaron, Jonathan R. Shewchuk, and Jifeng Xu,  */
/*    "Large-scale Simulation of Elastic Wave Propagation in Heterogeneous   */
/*    Media on Parallel Computers," Computer Methods in Applied Mechanics    */
/*    and Engineering 152(1-2):85-102, 22 January 1998.                      */
/*                                                                           */
/*  Triangle's Delaunay refinement algorithm for quality mesh generation is  */
/*    a hybrid of one due to Jim Ruppert, "A Delaunay Refinement Algorithm   */
/*    for Quality 2-Dimensional Mesh Generation," Journal of Algorithms      */
/*    18(3):548-585, May 1995 [*], and one due to L. Paul Chew, "Guaranteed- */
/*    Quality Mesh Generation for Curved Surfaces," Proceedings of the Ninth */
/*    Annual Symposium on Computational Geometry (San Diego, California),    */
/*    pages 274-280, Association for Computing Machinery, May 1993,          */
/*    http://portal.acm.org/citation.cfm?id=161150 .                         */
/*                                                                           */
/*  The Delaunay refinement algorithm has been modified so that it meshes    */
/*    domains with small input angles well, as described in Gary L. Miller,  */
/*    Steven E. Pav, and Noel J. Walkington, "When and Why Ruppert's         */
/*    Algorithm Works," Twelfth International Meshing Roundtable, pages      */
/*    91-102, Sandia National Laboratories, September 2003.  [*]             */
/*                                                                           */
/*  My implementation of the divide-and-conquer and incremental Delaunay     */
/*    triangulation algorithms follows closely the presentation of Guibas    */
/*    and Stolfi, even though I use a triangle-based data structure instead  */
/*    of their quad-edge data structure.  (In fact, I originally implemented */
/*    Triangle using the quad-edge data structure, but the switch to a       */
/*    triangle-based data structure sped Triangle by a factor of two.)  The  */
/*    mesh manipulation primitives and the two aforementioned Delaunay       */
/*    triangulation algorithms are described by Leonidas J. Guibas and Jorge */
/*    Stolfi, "Primitives for the Manipulation of General Subdivisions and   */
/*    the Computation of Voronoi Diagrams," ACM Transactions on Graphics     */
/*    4(2):74-123, April 1985, http://portal.acm.org/citation.cfm?id=282923 .*/
/*                                                                           */
/*  Their O(n log n) divide-and-conquer algorithm is adapted from Der-Tsai   */
/*    Lee and Bruce J. Schachter, "Two Algorithms for Constructing the       */
/*    Delaunay Triangulation," International Journal of Computer and         */
/*    Information Science 9(3):219-242, 1980.  Triangle's improvement of the */
/*    divide-and-conquer algorithm by alternating between vertical and       */
/*    horizontal cuts was introduced by Rex A. Dwyer, "A Faster Divide-and-  */
/*    Conquer Algorithm for Constructing Delaunay Triangulations,"           */
/*    Algorithmica 2(2):137-151, 1987.                                       */
/*                                                                           */
/*  The incremental insertion algorithm was first proposed by C. L. Lawson,  */
/*    "Software for C1 Surface Interpolation," in Mathematical Software III, */
/*    John R. Rice, editor, Academic Press, New York, pp. 161-194, 1977.     */
/*    For point location, I use the algorithm of Ernst P. Mucke, Isaac       */
/*    Saias, and Binhai Zhu, "Fast Randomized Point Location Without         */
/*    Preprocessing in Two- and Three-Dimensional Delaunay Triangulations,"  */
/*    Proceedings of the Twelfth Annual Symposium on Computational Geometry, */
/*    ACM, May 1996.  [*]  If I were to randomize the order of vertex        */
/*    insertion (I currently don't bother), their result combined with the   */
/*    result of Kenneth L. Clarkson and Peter W. Shor, "Applications of      */
/*    Random Sampling in Computational Geometry II," Discrete &              */
/*    Computational Geometry 4(1):387-421, 1989, would yield an expected     */
/*    O(n^{4/3}) bound on running time.                                      */
/*                                                                           */
/*  The O(n log n) sweepline Delaunay triangulation algorithm is taken from  */
/*    Steven Fortune, "A Sweepline Algorithm for Voronoi Diagrams",          */
/*    Algorithmica 2(2):153-174, 1987.  A random sample of edges on the      */
/*    boundary of the triangulation are maintained in a splay tree for the   */
/*    purpose of point location.  Splay trees are described by Daniel        */
/*    Dominic Sleator and Robert Endre Tarjan, "Self-Adjusting Binary Search */
/*    Trees," Journal of the ACM 32(3):652-686, July 1985,                   */
/*    http://portal.acm.org/citation.cfm?id=3835 .                           */
/*                                                                           */
/*  The algorithms for exact computation of the signs of determinants are    */
/*    described in Jonathan Richard Shewchuk, "Adaptive Precision Floating-  */
/*    Point Arithmetic and Fast Robust Geometric Predicates," Discrete &     */
/*    Computational Geometry 18(3):305-363, October 1997.  (Also available   */
/*    as Technical Report CMU-CS-96-140, School of Computer Science,         */
/*    Carnegie Mellon University, Pittsburgh, Pennsylvania, May 1996.)  [*]  */
/*    An abbreviated version appears as Jonathan Richard Shewchuk, "Robust   */
/*    Adaptive Floating-Point Geometric Predicates," Proceedings of the      */
/*    Twelfth Annual Symposium on Computational Geometry, ACM, May 1996. [*] */
/*    Many of the ideas for my exact arithmetic routines originate with      */
/*    Douglas M. Priest, "Algorithms for Arbitrary Precision Floating Point  */
/*    Arithmetic," Tenth Symposium on Computer Arithmetic, pp. 132-143, IEEE */
/*    Computer Society Press, 1991.  [*]  Many of the ideas for the correct  */
/*    evaluation of the signs of determinants are taken from Steven Fortune  */
/*    and Christopher J. Van Wyk, "Efficient Exact Arithmetic for Computa-   */
/*    tional Geometry," Proceedings of the Ninth Annual Symposium on         */
/*    Computational Geometry, ACM, pp. 163-172, May 1993, and from Steven    */
/*    Fortune, "Numerical Stability of Algorithms for 2D Delaunay Triangu-   */
/*    lations," International Journal of Computational Geometry & Applica-   */
/*    tions 5(1-2):193-213, March-June 1995.                                 */
/*                                                                           */
/*  The method of inserting new vertices off-center (not precisely at the    */
/*    circumcenter of every poor-quality triangle) is from Alper Ungor,      */
/*    "Off-centers:  A New Type of Steiner Points for Computing Size-Optimal */
/*    Quality-Guaranteed Delaunay Triangulations," Proceedings of LATIN      */
/*    2004 (Buenos Aires, Argentina), April 2004.                            */
/*                                                                           */
/*  For definitions of and results involving Delaunay triangulations,        */
/*    constrained and conforming versions thereof, and other aspects of      */
/*    triangular mesh generation, see the excellent survey by Marshall Bern  */
/*    and David Eppstein, "Mesh Generation and Optimal Triangulation," in    */
/*    Computing and Euclidean Geometry, Ding-Zhu Du and Frank Hwang,         */
/*    editors, World Scientific, Singapore, pp. 23-90, 1992.  [*]            */
/*                                                                           */
/*  The time for incrementally adding PSLG (planar straight line graph)      */
/*    segments to create a constrained Delaunay triangulation is probably    */
/*    O(t^2) per segment in the worst case and O(t) per segment in the       */
/*    common case, where t is the number of triangles that intersect the     */
/*    segment before it is inserted.  This doesn't count point location,     */
/*    which can be much more expensive.  I could improve this to O(d log d)  */
/*    time, but d is usually quite small, so it's not worth the bother.      */
/*    (This note does not apply when the -s switch is used, invoking a       */
/*    different method is used to insert segments.)                          */
/*                                                                           */
/*  The time for deleting a vertex from a Delaunay triangulation is O(d^2)   */
/*    in the worst case and O(d) in the common case, where d is the degree   */
/*    of the vertex being deleted.  I could improve this to O(d log d) time, */
/*    but d is usually quite small, so it's not worth the bother.            */
/*                                                                           */
/*  Ruppert's Delaunay refinement algorithm typically generates triangles    */
/*    at a linear rate (constant time per triangle) after the initial        */
/*    triangulation is formed.  There may be pathological cases where        */
/*    quadratic time is required, but these never arise in practice.         */
/*                                                                           */
/*  The geometric predicates (circumcenter calculations, segment             */
/*    intersection formulae, etc.) appear in my "Lecture Notes on Geometric  */
/*    Robustness" at http://www.cs.berkeley.edu/~jrs/mesh .                  */
/*                                                                           */
/*  If you make any improvements to this code, please please please let me   */
/*    know, so that I may obtain the improvements.  Even if you don't change */
/*    the code, I'd still love to hear what it's being used for.             */
/*                                                                           */
/*****************************************************************************/
 
/* Maximum number of characters in a file name (including the null).         */
 
#define FILENAMESIZE 2048
 
/* Maximum number of characters in a line read from a file (including the    */
/*   null).                                                                  */
 
#define INPUTLINESIZE 1024
 
/* For efficiency, a variety of data structures are allocated in bulk.  The  */
/*   following constants determine how many of each structure is allocated   */
/*   at once.                                                                */
 
#define TRIPERBLOCK 4092           /* Number of triangles allocated at once. */
#define SUBSEGPERBLOCK 508       /* Number of subsegments allocated at once. */
#define VERTEXPERBLOCK 4092         /* Number of vertices allocated at once. */
#define VIRUSPERBLOCK 1020   /* Number of virus triangles allocated at once. */
#define BADSUBSEGPERBLOCK 252 /* Number of encroached subsegments allocated at once. */
#define BADTRIPERBLOCK 4092 /* Number of skinny triangles allocated at once. */
#define FLIPSTACKERPERBLOCK 252 /* Number of flipped triangles allocated at once. */
#define SPLAYNODEPERBLOCK 508 /* Number of splay tree nodes allocated at once. */
 
/* The vertex types.   A DEADVERTEX has been deleted entirely.  An           */
/*   UNDEADVERTEX is not part of the mesh, but is written to the output      */
/*   .node file and affects the node indexing in the other output files.     */
 
#define INPUTVERTEX 0
#define SEGMENTVERTEX 1
#define FREEVERTEX 2
#define DEADVERTEX -32768
#define UNDEADVERTEX -32767
 
/* Two constants for algorithms based on random sampling.  Both constants    */
/*   have been chosen empirically to optimize their respective algorithms.   */
 
/* Used for the point location scheme of Mucke, Saias, and Zhu, to decide    */
/*   how large a random sample of triangles to inspect.                      */
 
#define SAMPLEFACTOR 11
 
/* Used in Fortune's sweepline Delaunay algorithm to determine what fraction */
/*   of boundary edges should be maintained in the splay tree for point      */
/*   location on the front.                                                  */
 
#define SAMPLERATE 10
 
/* A number that speaks for itself, every kissable digit.                    */
 
#define PI 3.141592653589793238462643383279502884197169399375105820974944592308
 
/* Another fave.                                                             */
 
#define SQUAREROOTTWO 1.4142135623730950488016887242096980785696718753769480732
 
/* And here's one for those of you who are intimidated by math.              */
 
#define ONETHIRD 0.333333333333333333333333333333333333333333333333333333333333
 
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
 
#include "triangle.h"
 
/* Labels that signify the result of point location.  The result of a        */
/*   search indicates that the point falls in the interior of a triangle, on */
/*   an edge, on a vertex, or outside the mesh.                              */
 
enum locateresult {INTRIANGLE, ONEDGE, ONVERTEX, OUTSIDE};
 
/* Labels that signify the result of vertex insertion.  The result indicates */
/*   that the vertex was inserted with complete success, was inserted but    */
/*   encroaches upon a subsegment, was not inserted because it lies on a     */
/*   segment, or was not inserted because another vertex occupies the same   */
/*   location.                                                               */
 
enum insertvertexresult {SUCCESSFULVERTEX, ENCROACHINGVERTEX, VIOLATINGVERTEX,
                         DUPLICATEVERTEX};
 
/* Labels that signify the result of direction finding.  The result          */
/*   indicates that a segment connecting the two query points falls within   */
/*   the direction triangle, along the left edge of the direction triangle,  */
/*   or along the right edge of the direction triangle.                      */
 
enum finddirectionresult {WITHIN, LEFTCOLLINEAR, RIGHTCOLLINEAR};
 
/*****************************************************************************/
/*                                                                           */
/*  The basic mesh data structures                                           */
/*                                                                           */
/*  There are three:  vertices, triangles, and subsegments (abbreviated      */
/*  `subseg').  These three data structures, linked by pointers, comprise    */
/*  the mesh.  A vertex simply represents a mesh vertex and its properties.  */
/*  A triangle is a triangle.  A subsegment is a special data structure used */
/*  to represent an impenetrable edge of the mesh (perhaps on the outer      */
/*  boundary, on the boundary of a hole, or part of an internal boundary     */
/*  separating two triangulated regions).  Subsegments represent boundaries, */
/*  defined by the user, that triangles may not lie across.                  */
/*                                                                           */
/*  A triangle consists of a list of three vertices, a list of three         */
/*  adjoining triangles, a list of three adjoining subsegments (when         */
/*  segments exist), an arbitrary number of optional user-defined            */
/*  floating-point attributes, and an optional area constraint.  The latter  */
/*  is an upper bound on the permissible area of each triangle in a region,  */
/*  used for mesh refinement.                                                */
/*                                                                           */
/*  For a triangle on a boundary of the mesh, some or all of the neighboring */
/*  triangles may not be present.  For a triangle in the interior of the     */
/*  mesh, often no neighboring subsegments are present.  Such absent         */
/*  triangles and subsegments are never represented by NULL pointers; they   */
/*  are represented by two special records:  `dummytri', the triangle that   */
/*  fills "outer space", and `dummysub', the omnipresent subsegment.         */
/*  `dummytri' and `dummysub' are used for several reasons; for instance,    */
/*  they can be dereferenced and their contents examined without violating   */
/*  protected memory.                                                        */
/*                                                                           */
/*  However, it is important to understand that a triangle includes other    */
/*  information as well.  The pointers to adjoining vertices, triangles, and */
/*  subsegments are ordered in a way that indicates their geometric relation */
/*  to each other.  Furthermore, each of these pointers contains orientation */
/*  information.  Each pointer to an adjoining triangle indicates which face */
/*  of that triangle is contacted.  Similarly, each pointer to an adjoining  */
/*  subsegment indicates which side of that subsegment is contacted, and how */
/*  the subsegment is oriented relative to the triangle.                     */
/*                                                                           */
/*  The data structure representing a subsegment may be thought to be        */
/*  abutting the edge of one or two triangle data structures:  either        */
/*  sandwiched between two triangles, or resting against one triangle on an  */
/*  exterior boundary or hole boundary.                                      */
/*                                                                           */
/*  A subsegment consists of a list of four vertices--the vertices of the    */
/*  subsegment, and the vertices of the segment it is a part of--a list of   */
/*  two adjoining subsegments, and a list of two adjoining triangles.  One   */
/*  of the two adjoining triangles may not be present (though there should   */
/*  always be one), and neighboring subsegments might not be present.        */
/*  Subsegments also store a user-defined integer "boundary marker".         */
/*  Typically, this integer is used to indicate what boundary conditions are */
/*  to be applied at that location in a finite element simulation.           */
/*                                                                           */
/*  Like triangles, subsegments maintain information about the relative      */
/*  orientation of neighboring objects.                                      */
/*                                                                           */
/*  Vertices are relatively simple.  A vertex is a list of floating-point    */
/*  numbers, starting with the x, and y coordinates, followed by an          */
/*  arbitrary number of optional user-defined floating-point attributes,     */
/*  followed by an integer boundary marker.  During the segment insertion    */
/*  phase, there is also a pointer from each vertex to a triangle that may   */
/*  contain it.  Each pointer is not always correct, but when one is, it     */
/*  speeds up segment insertion.  These pointers are assigned values once    */
/*  at the beginning of the segment insertion phase, and are not used or     */
/*  updated except during this phase.  Edge flipping during segment          */
/*  insertion will render some of them incorrect.  Hence, don't rely upon    */
/*  them for anything.                                                       */
/*                                                                           */
/*  Other than the exception mentioned above, vertices have no information   */
/*  about what triangles, subfacets, or subsegments they are linked to.      */
/*                                                                           */
/*****************************************************************************/
 
/*****************************************************************************/
/*                                                                           */
/*  Handles                                                                  */
/*                                                                           */
/*  The oriented triangle (`otri') and oriented subsegment (`osub') data     */
/*  structures defined below do not themselves store any part of the mesh.   */
/*  The mesh itself is made of `triangle's, `subseg's, and `vertex's.        */
/*                                                                           */
/*  Oriented triangles and oriented subsegments will usually be referred to  */
/*  as "handles."  A handle is essentially a pointer into the mesh; it       */
/*  allows you to "hold" one particular part of the mesh.  Handles are used  */
/*  to specify the regions in which one is traversing and modifying the mesh.*/
/*  A single `triangle' may be held by many handles, or none at all.  (The   */
/*  latter case is not a memory leak, because the triangle is still          */
/*  connected to other triangles in the mesh.)                               */
/*                                                                           */
/*  An `otri' is a handle that holds a triangle.  It holds a specific edge   */
/*  of the triangle.  An `osub' is a handle that holds a subsegment.  It     */
/*  holds either the left or right side of the subsegment.                   */
/*                                                                           */
/*  Navigation about the mesh is accomplished through a set of mesh          */
/*  manipulation primitives, further below.  Many of these primitives take   */
/*  a handle and produce a new handle that holds the mesh near the first     */
/*  handle.  Other primitives take two handles and glue the corresponding    */
/*  parts of the mesh together.  The orientation of the handles is           */
/*  important.  For instance, when two triangles are glued together by the   */
/*  bond() primitive, they are glued at the edges on which the handles lie.  */
/*                                                                           */
/*  Because vertices have no information about which triangles they are      */
/*  attached to, I commonly represent a vertex by use of a handle whose      */
/*  origin is the vertex.  A single handle can simultaneously represent a    */
/*  triangle, an edge, and a vertex.                                         */
/*                                                                           */
/*****************************************************************************/
 
/* The triangle data structure.  Each triangle contains three pointers to    */
/*   adjoining triangles, plus three pointers to vertices, plus three        */
/*   pointers to subsegments (declared below; these pointers are usually     */
/*   `dummysub').  It may or may not also contain user-defined attributes    */
/*   and/or a floating-point "area constraint."  It may also contain extra   */
/*   pointers for nodes, when the user asks for high-order elements.         */
/*   Because the size and structure of a `triangle' is not decided until     */
/*   runtime, I haven't simply declared the type `triangle' as a struct.     */
 
typedef float **triangle;            /* Really:  typedef triangle *triangle   */
 
/* An oriented triangle:  includes a pointer to a triangle and orientation.  */
/*   The orientation denotes an edge of the triangle.  Hence, there are      */
/*   three possible orientations.  By convention, each edge always points    */
/*   counterclockwise about the corresponding triangle.                      */
 
struct otri {
  triangle *tri;
  int orient;                                         /* Ranges from 0 to 2. */
};
 
/* The subsegment data structure.  Each subsegment contains two pointers to  */
/*   adjoining subsegments, plus four pointers to vertices, plus two         */
/*   pointers to adjoining triangles, plus one boundary marker, plus one     */
/*   segment number.                                                         */
 
typedef float **subseg;                  /* Really:  typedef subseg *subseg   */
 
/* An oriented subsegment:  includes a pointer to a subsegment and an        */
/*   orientation.  The orientation denotes a side of the edge.  Hence, there */
/*   are two possible orientations.  By convention, the edge is always       */
/*   directed so that the "side" denoted is the right side of the edge.      */
 
struct osub {
  subseg *ss;
  int ssorient;                                       /* Ranges from 0 to 1. */
};
 
/* The vertex data structure.  Each vertex is actually an array of floats.    */
/*   The number of floats is unknown until runtime.  An integer boundary      */
/*   marker, and sometimes a pointer to a triangle, is appended after the    */
/*   floats.                                                                  */
 
typedef float *vertex;
 
/* A queue used to store encroached subsegments.  Each subsegment's vertices */
/*   are stored so that we can check whether a subsegment is still the same. */
 
struct badsubseg {
  subseg encsubseg;                             /* An encroached subsegment. */
  vertex subsegorg, subsegdest;                         /* Its two vertices. */
};
 
/* A queue used to store bad triangles.  The key is the square of the cosine */
/*   of the smallest angle of the triangle.  Each triangle's vertices are    */
/*   stored so that one can check whether a triangle is still the same.      */
 
struct badtriang {
  triangle poortri;                       /* A skinny or too-large triangle. */
  float key;                             /* cos^2 of smallest (apical) angle. */
  vertex triangorg, triangdest, triangapex;           /* Its three vertices. */
  struct badtriang *nexttriang;             /* Pointer to next bad triangle. */
};
 
/* A stack of triangles flipped during the most recent vertex insertion.     */
/*   The stack is used to undo the vertex insertion if the vertex encroaches */
/*   upon a subsegment.                                                      */
 
struct flipstacker {
  triangle flippedtri;                       /* A recently flipped triangle. */
  struct flipstacker *prevflip;               /* Previous flip in the stack. */
};
 
/* A node in a heap used to store events for the sweepline Delaunay          */
/*   algorithm.  Nodes do not point directly to their parents or children in */
/*   the heap.  Instead, each node knows its position in the heap, and can   */
/*   look up its parent and children in a separate array.  The `eventptr'    */
/*   points either to a `vertex' or to a triangle (in encoded format, so     */
/*   that an orientation is included).  In the latter case, the origin of    */
/*   the oriented triangle is the apex of a "circle event" of the sweepline  */
/*   algorithm.  To distinguish site events from circle events, all circle   */
/*   events are given an invalid (smaller than `xmin') x-coordinate `xkey'.  */
 
struct event {
  float xkey, ykey;                              /* Coordinates of the event. */
  int *eventptr;      /* Can be a vertex or the location of a circle event. */
  int heapposition;              /* Marks this event's position in the heap. */
};
 
/* A node in the splay tree.  Each node holds an oriented ghost triangle     */
/*   that represents a boundary edge of the growing triangulation.  When a   */
/*   circle event covers two boundary edges with a triangle, so that they    */
/*   are no longer boundary edges, those edges are not immediately deleted   */
/*   from the tree; rather, they are lazily deleted when they are next       */
/*   encountered.  (Since only a random sample of boundary edges are kept    */
/*   in the tree, lazy deletion is faster.)  `keydest' is used to verify     */
/*   that a triangle is still the same as when it entered the splay tree; if */
/*   it has been rotated (due to a circle event), it no longer represents a  */
/*   boundary edge and should be deleted.                                    */
 
struct splaynode {
  struct otri keyedge;                     /* Lprev of an edge on the front. */
  vertex keydest;           /* Used to verify that splay node is still live. */
  struct splaynode *lchild, *rchild;              /* Children in splay tree. */
};
 
/* A type used to allocate memory.  firstblock is the first block of items.  */
/*   nowblock is the block from which items are currently being allocated.   */
/*   nextitem points to the next slab of free memory for an item.            */
/*   deaditemstack is the head of a linked list (stack) of deallocated items */
/*   that can be recycled.  unallocateditems is the number of items that     */
/*   remain to be allocated from nowblock.                                   */
/*                                                                           */
/* Traversal is the process of walking through the entire list of items, and */
/*   is separate from allocation.  Note that a traversal will visit items on */
/*   the "deaditemstack" stack as well as live items.  pathblock points to   */
/*   the block currently being traversed.  pathitem points to the next item  */
/*   to be traversed.  pathitemsleft is the number of items that remain to   */
/*   be traversed in pathblock.                                              */
/*                                                                           */
/* alignbytes determines how new records should be aligned in memory.        */
/*   itembytes is the length of a record in bytes (after rounding up).       */
/*   itemsperblock is the number of items allocated at once in a single      */
/*   block.  itemsfirstblock is the number of items in the first block,      */
/*   which can vary from the others.  items is the number of currently       */
/*   allocated items.  maxitems is the maximum number of items that have     */
/*   been allocated at once; it is the current number of items plus the      */
/*   number of records kept on deaditemstack.                                */
 
struct memorypool {
  int **firstblock, **nowblock;
  int *nextitem;
  int *deaditemstack;
  int **pathblock;
  int *pathitem;
  int alignbytes;
  int itembytes;
  int itemsperblock;
  int itemsfirstblock;
  long items, maxitems;
  int unallocateditems;
  int pathitemsleft;
};
 
 
/* Global constants.                                                         */
 
float splitter;       /* Used to split float factors for exact multiplication. */
float epsilon;                             /* Floating-point machine epsilon. */
float resulterrbound;
float ccwerrboundA, ccwerrboundB, ccwerrboundC;
float iccerrboundA, iccerrboundB, iccerrboundC;
float o3derrboundA, o3derrboundB, o3derrboundC;
 
/* Random number seed is not constant, but I've made it global anyway.       */
 
unsigned long randomseed;                     /* Current random number seed. */
 
 
/* Mesh data structure.  Triangle operates on only one mesh, but the mesh    */
/*   structure is used (instead of global variables) to allow reentrancy.    */
 
struct mesh {
 
/* Variables used to allocate memory for triangles, subsegments, vertices,   */
/*   viri (triangles being eaten), encroached segments, bad (skinny or too   */
/*   large) triangles, and splay tree nodes.                                 */
 
  struct memorypool triangles;
  struct memorypool subsegs;
  struct memorypool vertices;
  struct memorypool viri;
  struct memorypool badsubsegs;
  struct memorypool badtriangles;
  struct memorypool flipstackers;
  struct memorypool splaynodes;
 
/* Variables that maintain the bad triangle queues.  The queues are          */
/*   ordered from 4095 (highest priority) to 0 (lowest priority).            */
 
  struct badtriang *queuefront[4096];
  struct badtriang *queuetail[4096];
  int nextnonemptyq[4096];
  int firstnonemptyq;
 
/* Variable that maintains the stack of recently flipped triangles.          */
 
  struct flipstacker *lastflip;
 
/* Other variables. */
 
  float xmin, xmax, ymin, ymax;                            /* x and y bounds. */
  float xminextreme;      /* Nonexistent x value used as a flag in sweepline. */
  int invertices;                               /* Number of input vertices. */
  int inelements;                              /* Number of input triangles. */
  int insegments;                               /* Number of input segments. */
  int holes;                                       /* Number of input holes. */
  int regions;                                   /* Number of input regions. */
  int undeads;    /* Number of input vertices that don't appear in the mesh. */
  long edges;                                     /* Number of output edges. */
  int mesh_dim;                                /* Dimension (ought to be 2). */
  int nextras;                           /* Number of attributes per vertex. */
  int eextras;                         /* Number of attributes per triangle. */
  long hullsize;                          /* Number of edges in convex hull. */
  int steinerleft;                 /* Number of Steiner points not yet used. */
  int vertexmarkindex;         /* Index to find boundary marker of a vertex. */
  int vertex2triindex;     /* Index to find a triangle adjacent to a vertex. */
  int highorderindex;  /* Index to find extra nodes for high-order elements. */
  int elemattribindex;            /* Index to find attributes of a triangle. */
  int areaboundindex;             /* Index to find area bound of a triangle. */
  int checksegments;         /* Are there segments in the triangulation yet? */
  int checkquality;                  /* Has quality triangulation begun yet? */
  int readnodefile;                           /* Has a .node file been read? */
  long samples;              /* Number of random samples for point location. */
 
  long incirclecount;                 /* Number of incircle tests performed. */
  long counterclockcount;     /* Number of counterclockwise tests performed. */
  long orient3dcount;           /* Number of 3D orientation tests performed. */
  long hyperbolacount;      /* Number of right-of-hyperbola tests performed. */
  long circumcentercount;  /* Number of circumcenter calculations performed. */
  long circletopcount;       /* Number of circle top calculations performed. */
 
/* Triangular bounding box vertices.                                         */
 
  vertex infvertex1, infvertex2, infvertex3;
 
/* Pointer to the `triangle' that occupies all of "outer space."             */
 
  triangle *dummytri;
  triangle *dummytribase;    /* Keep base address so we can free() it later. */
 
/* Pointer to the omnipresent subsegment.  Referenced by any triangle or     */
/*   subsegment that isn't really connected to a subsegment at that          */
/*   location.                                                               */
 
  subseg *dummysub;
  subseg *dummysubbase;      /* Keep base address so we can free() it later. */
 
/* Pointer to a recently visited triangle.  Improves point location if       */
/*   proximate vertices are inserted sequentially.                           */
 
  struct otri recenttri;
 
};                                                  /* End of `struct mesh'. */
 
 
/* Data structure for command line switches and file names.  This structure  */
/*   is used (instead of global variables) to allow reentrancy.              */
 
struct behavior {
 
/* Switches for the triangulator.                                            */
/*   poly: -p switch.  refine: -r switch.                                    */
/*   quality: -q switch.                                                     */
/*     minangle: minimum angle bound, specified after -q switch.             */
/*     goodangle: cosine squared of minangle.                                */
/*     offconstant: constant used to place off-center Steiner points.        */
/*   vararea: -a switch without number.                                      */
/*   fixedarea: -a switch with number.                                       */
/*     maxarea: maximum area bound, specified after -a switch.               */
/*   usertest: -u switch.                                                    */
/*   regionattrib: -A switch.  convex: -c switch.                            */
/*   weighted: 1 for -w switch, 2 for -W switch.  jettison: -j switch        */
/*   firstnumber: inverse of -z switch.  All items are numbered starting     */
/*     from `firstnumber'.                                                   */
/*   edgesout: -e switch.  voronoi: -v switch.                               */
/*   neighbors: -n switch.  geomview: -g switch.                             */
/*   nobound: -B switch.  nopolywritten: -P switch.                          */
/*   nonodewritten: -N switch.  noelewritten: -E switch.                     */
/*   noiterationnum: -I switch.  noholes: -O switch.                         */
/*   noexact: -X switch.                                                     */
/*   order: element order, specified after -o switch.                        */
/*   nobisect: count of how often -Y switch is selected.                     */
/*   steiner: maximum number of Steiner points, specified after -S switch.   */
/*   incremental: -i switch.  sweepline: -F switch.                          */
/*   dwyer: inverse of -l switch.                                            */
/*   splitseg: -s switch.                                                    */
/*   conformdel: -D switch.  docheck: -C switch.                             */
/*   quiet: -Q switch.  verbose: count of how often -V switch is selected.   */
/*   usesegments: -p, -r, -q, or -c switch; determines whether segments are  */
/*     used at all.                                                          */
/*                                                                           */
/* Read the instructions to find out the meaning of these switches.          */
 
  int poly, refine, quality, vararea, fixedarea, usertest;
  int regionattrib, convex, weighted, jettison;
  int firstnumber;
  int edgesout, voronoi, neighbors, geomview;
  int nobound, nopolywritten, nonodewritten, noelewritten, noiterationnum;
  int noholes, noexact, conformdel;
  int incremental, sweepline, dwyer;
  int splitseg;
  int docheck;
  int quiet, verbose;
  int usesegments;
  int order;
  int nobisect;
  int steiner;
  float minangle, goodangle, offconstant;
  float maxarea;
 
/* Variables for file names.                                                 */
 
};                                              /* End of `struct behavior'. */
 
 
/*****************************************************************************/
/*                                                                           */
/*  Mesh manipulation primitives.  Each triangle contains three pointers to  */
/*  other triangles, with orientations.  Each pointer points not to the      */
/*  first byte of a triangle, but to one of the first three bytes of a       */
/*  triangle.  It is necessary to extract both the triangle itself and the   */
/*  orientation.  To save memory, I keep both pieces of information in one   */
/*  pointer.  To make this possible, I assume that all triangles are aligned */
/*  to four-byte boundaries.  The decode() routine below decodes a pointer,  */
/*  extracting an orientation (in the range 0 to 2) and a pointer to the     */
/*  beginning of a triangle.  The encode() routine compresses a pointer to a */
/*  triangle and an orientation into a single pointer.  My assumptions that  */
/*  triangles are four-byte-aligned and that the `unsigned long' type is     */
/*  long enough to hold a pointer are two of the few kludges in this program.*/
/*                                                                           */
/*  Subsegments are manipulated similarly.  A pointer to a subsegment        */
/*  carries both an address and an orientation in the range 0 to 1.          */
/*                                                                           */
/*  The other primitives take an oriented triangle or oriented subsegment,   */
/*  and return an oriented triangle or oriented subsegment or vertex; or     */
/*  they change the connections in the data structure.                       */
/*                                                                           */
/*  Below, triangles and subsegments are denoted by their vertices.  The     */
/*  triangle abc has origin (org) a, destination (dest) b, and apex (apex)   */
/*  c.  These vertices occur in counterclockwise order about the triangle.   */
/*  The handle abc may simultaneously denote vertex a, edge ab, and triangle */
/*  abc.                                                                     */
/*                                                                           */
/*  Similarly, the subsegment ab has origin (sorg) a and destination (sdest) */
/*  b.  If ab is thought to be directed upward (with b directly above a),    */
/*  then the handle ab is thought to grasp the right side of ab, and may     */
/*  simultaneously denote vertex a and edge ab.                              */
/*                                                                           */
/*  An asterisk (*) denotes a vertex whose identity is unknown.              */
/*                                                                           */
/*  Given this notation, a partial list of mesh manipulation primitives      */
/*  follows.                                                                 */
/*                                                                           */
/*                                                                           */
/*  For triangles:                                                           */
/*                                                                           */
/*  sym:  Find the abutting triangle; same edge.                             */
/*  sym(abc) -> ba*                                                          */
/*                                                                           */
/*  lnext:  Find the next edge (counterclockwise) of a triangle.             */
/*  lnext(abc) -> bca                                                        */
/*                                                                           */
/*  lprev:  Find the previous edge (clockwise) of a triangle.                */
/*  lprev(abc) -> cab                                                        */
/*                                                                           */
/*  onext:  Find the next edge counterclockwise with the same origin.        */
/*  onext(abc) -> ac*                                                        */
/*                                                                           */
/*  oprev:  Find the next edge clockwise with the same origin.               */
/*  oprev(abc) -> a*b                                                        */
/*                                                                           */
/*  dnext:  Find the next edge counterclockwise with the same destination.   */
/*  dnext(abc) -> *ba                                                        */
/*                                                                           */
/*  dprev:  Find the next edge clockwise with the same destination.          */
/*  dprev(abc) -> cb*                                                        */
/*                                                                           */
/*  rnext:  Find the next edge (counterclockwise) of the adjacent triangle.  */
/*  rnext(abc) -> *a*                                                        */
/*                                                                           */
/*  rprev:  Find the previous edge (clockwise) of the adjacent triangle.     */
/*  rprev(abc) -> b**                                                        */
/*                                                                           */
/*  org:  Origin          dest:  Destination          apex:  Apex            */
/*  org(abc) -> a         dest(abc) -> b              apex(abc) -> c         */
/*                                                                           */
/*  bond:  Bond two triangles together at the resepective handles.           */
/*  bond(abc, bad)                                                           */
/*                                                                           */
/*                                                                           */
/*  For subsegments:                                                         */
/*                                                                           */
/*  ssym:  Reverse the orientation of a subsegment.                          */
/*  ssym(ab) -> ba                                                           */
/*                                                                           */
/*  spivot:  Find adjoining subsegment with the same origin.                 */
/*  spivot(ab) -> a*                                                         */
/*                                                                           */
/*  snext:  Find next subsegment in sequence.                                */
/*  snext(ab) -> b*                                                          */
/*                                                                           */
/*  sorg:  Origin                      sdest:  Destination                   */
/*  sorg(ab) -> a                      sdest(ab) -> b                        */
/*                                                                           */
/*  sbond:  Bond two subsegments together at the respective origins.         */
/*  sbond(ab, ac)                                                            */
/*                                                                           */
/*                                                                           */
/*  For interacting tetrahedra and subfacets:                                */
/*                                                                           */
/*  tspivot:  Find a subsegment abutting a triangle.                         */
/*  tspivot(abc) -> ba                                                       */
/*                                                                           */
/*  stpivot:  Find a triangle abutting a subsegment.                         */
/*  stpivot(ab) -> ba*                                                       */
/*                                                                           */
/*  tsbond:  Bond a triangle to a subsegment.                                */
/*  tsbond(abc, ba)                                                          */
/*                                                                           */
/*****************************************************************************/
 
/********* Mesh manipulation primitives begin here                   *********/
/* Fast lookup arrays to speed some of the mesh manipulation primitives.     */
 
int plus1mod3[3] = {1, 2, 0};
int minus1mod3[3] = {2, 0, 1};
 
/********* Primitives for triangles                                  *********/
/*                                                                           */
/*                                                                           */
 
/* decode() converts a pointer to an oriented triangle.  The orientation is  */
/*   extracted from the two least significant bits of the pointer.           */
 
#define decode(ptr, otri)                                                     \
  (otri).orient = (int) ((unsigned long) (ptr) & (unsigned long) 3l);         \
  (otri).tri = (triangle *)                                                   \
                  ((unsigned long) (ptr) ^ (unsigned long) (otri).orient)
 
/* encode() compresses an oriented triangle into a single pointer.  It       */
/*   relies on the assumption that all triangles are aligned to four-byte    */
/*   boundaries, so the two least significant bits of (otri).tri are zero.   */
 
#define encode(otri)                                                          \
  (triangle) ((unsigned long) (otri).tri | (unsigned long) (otri).orient)
 
/* The following handle manipulation primitives are all described by Guibas  */
/*   and Stolfi.  However, Guibas and Stolfi use an edge-based data          */
/*   structure, whereas I use a triangle-based data structure.               */
 
/* sym() finds the abutting triangle, on the same edge.  Note that the edge  */
/*   direction is necessarily reversed, because the handle specified by an   */
/*   oriented triangle is directed counterclockwise around the triangle.     */
 
#define sym(otri1, otri2)                                                     \
  ptr = (otri1).tri[(otri1).orient];                                          \
  decode(ptr, otri2);
 
#define symself(otri)                                                         \
  ptr = (otri).tri[(otri).orient];                                            \
  decode(ptr, otri);
 
/* lnext() finds the next edge (counterclockwise) of a triangle.             */
 
#define lnext(otri1, otri2)                                                   \
  (otri2).tri = (otri1).tri;                                                  \
  (otri2).orient = plus1mod3[(otri1).orient]
 
#define lnextself(otri)                                                       \
  (otri).orient = plus1mod3[(otri).orient]
 
/* lprev() finds the previous edge (clockwise) of a triangle.                */
 
#define lprev(otri1, otri2)                                                   \
  (otri2).tri = (otri1).tri;                                                  \
  (otri2).orient = minus1mod3[(otri1).orient]
 
#define lprevself(otri)                                                       \
  (otri).orient = minus1mod3[(otri).orient]
 
/* onext() spins counterclockwise around a vertex; that is, it finds the     */
/*   next edge with the same origin in the counterclockwise direction.  This */
/*   edge is part of a different triangle.                                   */
 
#define onext(otri1, otri2)                                                   \
  lprev(otri1, otri2);                                                        \
  symself(otri2);
 
#define onextself(otri)                                                       \
  lprevself(otri);                                                            \
  symself(otri);
 
/* oprev() spins clockwise around a vertex; that is, it finds the next edge  */
/*   with the same origin in the clockwise direction.  This edge is part of  */
/*   a different triangle.                                                   */
 
#define oprev(otri1, otri2)                                                   \
  sym(otri1, otri2);                                                          \
  lnextself(otri2);
 
#define oprevself(otri)                                                       \
  symself(otri);                                                              \
  lnextself(otri);
 
/* dnext() spins counterclockwise around a vertex; that is, it finds the     */
/*   next edge with the same destination in the counterclockwise direction.  */
/*   This edge is part of a different triangle.                              */
 
#define dnext(otri1, otri2)                                                   \
  sym(otri1, otri2);                                                          \
  lprevself(otri2);
 
#define dnextself(otri)                                                       \
  symself(otri);                                                              \
  lprevself(otri);
 
/* dprev() spins clockwise around a vertex; that is, it finds the next edge  */
/*   with the same destination in the clockwise direction.  This edge is     */
/*   part of a different triangle.                                           */
 
#define dprev(otri1, otri2)                                                   \
  lnext(otri1, otri2);                                                        \
  symself(otri2);
 
#define dprevself(otri)                                                       \
  lnextself(otri);                                                            \
  symself(otri);
 
/* rnext() moves one edge counterclockwise about the adjacent triangle.      */
/*   (It's best understood by reading Guibas and Stolfi.  It involves        */
/*   changing triangles twice.)                                              */
 
#define rnext(otri1, otri2)                                                   \
  sym(otri1, otri2);                                                          \
  lnextself(otri2);                                                           \
  symself(otri2);
 
#define rnextself(otri)                                                       \
  symself(otri);                                                              \
  lnextself(otri);                                                            \
  symself(otri);
 
/* rprev() moves one edge clockwise about the adjacent triangle.             */
/*   (It's best understood by reading Guibas and Stolfi.  It involves        */
/*   changing triangles twice.)                                              */
 
#define rprev(otri1, otri2)                                                   \
  sym(otri1, otri2);                                                          \
  lprevself(otri2);                                                           \
  symself(otri2);
 
#define rprevself(otri)                                                       \
  symself(otri);                                                              \
  lprevself(otri);                                                            \
  symself(otri);
 
/* These primitives determine or set the origin, destination, or apex of a   */
/* triangle.                                                                 */
 
#define org(otri, vertexptr)                                                  \
  vertexptr = (vertex) (otri).tri[plus1mod3[(otri).orient] + 3]
 
#define dest(otri, vertexptr)                                                 \
  vertexptr = (vertex) (otri).tri[minus1mod3[(otri).orient] + 3]
 
#define apex(otri, vertexptr)                                                 \
  vertexptr = (vertex) (otri).tri[(otri).orient + 3]
 
#define setorg(otri, vertexptr)                                               \
  (otri).tri[plus1mod3[(otri).orient] + 3] = (triangle) vertexptr
 
#define setdest(otri, vertexptr)                                              \
  (otri).tri[minus1mod3[(otri).orient] + 3] = (triangle) vertexptr
 
#define setapex(otri, vertexptr)                                              \
  (otri).tri[(otri).orient + 3] = (triangle) vertexptr
 
/* Bond two triangles together.                                              */
 
#define bond(otri1, otri2)                                                    \
  (otri1).tri[(otri1).orient] = encode(otri2);                                \
  (otri2).tri[(otri2).orient] = encode(otri1)
 
/* Dissolve a bond (from one side).  Note that the other triangle will still */
/*   think it's connected to this triangle.  Usually, however, the other     */
/*   triangle is being deleted entirely, or bonded to another triangle, so   */
/*   it doesn't matter.                                                      */
 
#define dissolve(otri)                                                        \
  (otri).tri[(otri).orient] = (triangle) m->dummytri
 
/* Copy an oriented triangle.                                                */
 
#define otricopy(otri1, otri2)                                                \
  (otri2).tri = (otri1).tri;                                                  \
  (otri2).orient = (otri1).orient
 
/* Test for equality of oriented triangles.                                  */
 
#define otriequal(otri1, otri2)                                               \
  (((otri1).tri == (otri2).tri) &&                                            \
   ((otri1).orient == (otri2).orient))
 
/* Primitives to infect or cure a triangle with the virus.  These rely on    */
/*   the assumption that all subsegments are aligned to four-byte boundaries.*/
 
#define infect(otri)                                                          \
  (otri).tri[6] = (triangle)                                                  \
                    ((unsigned long) (otri).tri[6] | (unsigned long) 2l)
 
#define uninfect(otri)                                                        \
  (otri).tri[6] = (triangle)                                                  \
                    ((unsigned long) (otri).tri[6] & ~ (unsigned long) 2l)
 
/* Test a triangle for viral infection.                                      */
 
#define infected(otri)                                                        \
  (((unsigned long) (otri).tri[6] & (unsigned long) 2l) != 0l)
 
/* Check or set a triangle's attributes.                                     */
 
#define elemattribute(otri, attnum)                                           \
  ((float *) (otri).tri)[m->elemattribindex + (attnum)]
 
#define setelemattribute(otri, attnum, value)                                 \
  ((float *) (otri).tri)[m->elemattribindex + (attnum)] = value
 
/* Check or set a triangle's maximum area bound.                             */
 
#define areabound(otri)  ((float *) (otri).tri)[m->areaboundindex]
 
#define setareabound(otri, value)                                             \
  ((float *) (otri).tri)[m->areaboundindex] = value
 
/* Check or set a triangle's deallocation.  Its second pointer is set to     */
/*   NULL to indicate that it is not allocated.  (Its first pointer is used  */
/*   for the stack of dead items.)  Its fourth pointer (its first vertex)    */
/*   is set to NULL in case a `badtriang' structure points to it.            */
 
#define deadtri(tria)  ((tria)[1] == (triangle) NULL)
 
#define killtri(tria)                                                         \
  (tria)[1] = (triangle) NULL;                                                \
  (tria)[3] = (triangle) NULL
 
/********* Primitives for subsegments                                *********/
/*                                                                           */
/*                                                                           */
 
/* sdecode() converts a pointer to an oriented subsegment.  The orientation  */
/*   is extracted from the least significant bit of the pointer.  The two    */
/*   least significant bits (one for orientation, one for viral infection)   */
/*   are masked out to produce the real pointer.                             */
 
#define sdecode(sptr, osub)                                                   \
  (osub).ssorient = (int) ((unsigned long) (sptr) & (unsigned long) 1l);      \
  (osub).ss = (subseg *)                                                      \
              ((unsigned long) (sptr) & ~ (unsigned long) 3l)
 
/* sencode() compresses an oriented subsegment into a single pointer.  It    */
/*   relies on the assumption that all subsegments are aligned to two-byte   */
/*   boundaries, so the least significant bit of (osub).ss is zero.          */
 
#define sencode(osub)                                                         \
  (subseg) ((unsigned long) (osub).ss | (unsigned long) (osub).ssorient)
 
/* ssym() toggles the orientation of a subsegment.                           */
 
#define ssym(osub1, osub2)                                                    \
  (osub2).ss = (osub1).ss;                                                    \
  (osub2).ssorient = 1 - (osub1).ssorient
 
#define ssymself(osub)                                                        \
  (osub).ssorient = 1 - (osub).ssorient
 
/* spivot() finds the other subsegment (from the same segment) that shares   */
/*   the same origin.                                                        */
 
#define spivot(osub1, osub2)                                                  \
  sptr = (osub1).ss[(osub1).ssorient];                                        \
  sdecode(sptr, osub2)
 
#define spivotself(osub)                                                      \
  sptr = (osub).ss[(osub).ssorient];                                          \
  sdecode(sptr, osub)
 
/* snext() finds the next subsegment (from the same segment) in sequence;    */
/*   one whose origin is the input subsegment's destination.                 */
 
#define snext(osub1, osub2)                                                   \
  sptr = (osub1).ss[1 - (osub1).ssorient];                                    \
  sdecode(sptr, osub2)
 
#define snextself(osub)                                                       \
  sptr = (osub).ss[1 - (osub).ssorient];                                      \
  sdecode(sptr, osub)
 
/* These primitives determine or set the origin or destination of a          */
/*   subsegment or the segment that includes it.                             */
 
#define sorg(osub, vertexptr)                                                 \
  vertexptr = (vertex) (osub).ss[2 + (osub).ssorient]
 
#define sdest(osub, vertexptr)                                                \
  vertexptr = (vertex) (osub).ss[3 - (osub).ssorient]
 
#define setsorg(osub, vertexptr)                                              \
  (osub).ss[2 + (osub).ssorient] = (subseg) vertexptr
 
#define setsdest(osub, vertexptr)                                             \
  (osub).ss[3 - (osub).ssorient] = (subseg) vertexptr
 
#define segorg(osub, vertexptr)                                               \
  vertexptr = (vertex) (osub).ss[4 + (osub).ssorient]
 
#define segdest(osub, vertexptr)                                              \
  vertexptr = (vertex) (osub).ss[5 - (osub).ssorient]
 
#define setsegorg(osub, vertexptr)                                            \
  (osub).ss[4 + (osub).ssorient] = (subseg) vertexptr
 
#define setsegdest(osub, vertexptr)                                           \
  (osub).ss[5 - (osub).ssorient] = (subseg) vertexptr
 
/* These primitives read or set a boundary marker.  Boundary markers are     */
/*   used to hold user-defined tags for setting boundary conditions in       */
/*   finite element solvers.                                                 */
 
#define mark(osub)  (* (int *) ((osub).ss + 8))
 
#define setmark(osub, value)                                                  \
  * (int *) ((osub).ss + 8) = value
 
/* Bond two subsegments together.                                            */
 
#define sbond(osub1, osub2)                                                   \
  (osub1).ss[(osub1).ssorient] = sencode(osub2);                              \
  (osub2).ss[(osub2).ssorient] = sencode(osub1)
 
/* Dissolve a subsegment bond (from one side).  Note that the other          */
/*   subsegment will still think it's connected to this subsegment.          */
 
#define sdissolve(osub)                                                       \
  (osub).ss[(osub).ssorient] = (subseg) m->dummysub
 
/* Copy a subsegment.                                                        */
 
#define subsegcopy(osub1, osub2)                                              \
  (osub2).ss = (osub1).ss;                                                    \
  (osub2).ssorient = (osub1).ssorient
 
/* Test for equality of subsegments.                                         */
 
#define subsegequal(osub1, osub2)                                             \
  (((osub1).ss == (osub2).ss) &&                                              \
   ((osub1).ssorient == (osub2).ssorient))
 
/* Check or set a subsegment's deallocation.  Its second pointer is set to   */
/*   NULL to indicate that it is not allocated.  (Its first pointer is used  */
/*   for the stack of dead items.)  Its third pointer (its first vertex)     */
/*   is set to NULL in case a `badsubseg' structure points to it.            */
 
#define deadsubseg(sub)  ((sub)[1] == (subseg) NULL)
 
#define killsubseg(sub)                                                       \
  (sub)[1] = (subseg) NULL;                                                   \
  (sub)[2] = (subseg) NULL
 
/********* Primitives for interacting triangles and subsegments      *********/
/*                                                                           */
/*                                                                           */
 
/* tspivot() finds a subsegment abutting a triangle.                         */
 
#define tspivot(otri, osub)                                                   \
  sptr = (subseg) (otri).tri[6 + (otri).orient];                              \
  sdecode(sptr, osub)
 
/* stpivot() finds a triangle abutting a subsegment.  It requires that the   */
/*   variable `ptr' of type `triangle' be defined.                           */
 
#define stpivot(osub, otri)                                                   \
  ptr = (triangle) (osub).ss[6 + (osub).ssorient];                            \
  decode(ptr, otri)
 
/* Bond a triangle to a subsegment.                                          */
 
#define tsbond(otri, osub)                                                    \
  (otri).tri[6 + (otri).orient] = (triangle) sencode(osub);                   \
  (osub).ss[6 + (osub).ssorient] = (subseg) encode(otri)
 
/* Dissolve a bond (from the triangle side).                                 */
 
#define tsdissolve(otri)                                                      \
  (otri).tri[6 + (otri).orient] = (triangle) m->dummysub
 
/* Dissolve a bond (from the subsegment side).                               */
 
#define stdissolve(osub)                                                      \
  (osub).ss[6 + (osub).ssorient] = (subseg) m->dummytri
 
/********* Primitives for vertices                                   *********/
/*                                                                           */
/*                                                                           */
 
#define vertexmark(vx)  ((int *) (vx))[m->vertexmarkindex]
 
#define setvertexmark(vx, value)                                              \
  ((int *) (vx))[m->vertexmarkindex] = value
 
#define vertextype(vx)  ((int *) (vx))[m->vertexmarkindex + 1]
 
#define setvertextype(vx, value)                                              \
  ((int *) (vx))[m->vertexmarkindex + 1] = value
 
#define vertex2tri(vx)  ((triangle *) (vx))[m->vertex2triindex]
 
#define setvertex2tri(vx, value)                                              \
  ((triangle *) (vx))[m->vertex2triindex] = value
 
/********* Mesh manipulation primitives end here                     *********/
 
/********* Memory allocation and program exit wrappers begin here    *********/
void triexit(int status)
{
  exit(status);
}
 
int *trimalloc(int size)
{
  int *memptr;
 
  memptr = (int *) malloc((unsigned int) size);
  if (memptr == (int *) NULL) {
    printf("Error:  Out of memory.\n");
    triexit(1);
  }
  return(memptr);
}
 
void trifree(int *memptr)
{
  free(memptr);
}
 
/********* Memory allocation and program exit wrappers end here      *********/
 
/*****************************************************************************/
/*                                                                           */
/*  internalerror()   Ask the user to send me the defective product.  Exit.  */
/*                                                                           */
/*****************************************************************************/
 
void internalerror()
{
  printf("  Please report this bug to jrs@cs.berkeley.edu\n");
  printf("  Include the message above, your input data set, and the exact\n");
  printf("    command line you used to run Triangle.\n");
  triexit(1);
}
 
/*****************************************************************************/
/*                                                                           */
/*  parsecommandline()   Read the command line, identify switches, and set   */
/*                       up options and file names.                          */
/*                                                                           */
/*****************************************************************************/
 
void parsecommandline(int argc, char **argv, struct behavior *b) {
  int i, j, k;
  char workstring[FILENAMESIZE];
 
  b->poly = b->refine = b->quality = 0;
  b->vararea = b->fixedarea = b->usertest = 0;
  b->regionattrib = b->convex = b->weighted = b->jettison = 0;
  b->firstnumber = 1;
  b->edgesout = b->voronoi = b->neighbors = b->geomview = 0;
  b->nobound = b->nopolywritten = b->nonodewritten = b->noelewritten = 0;
  b->noiterationnum = 0;
  b->noholes = b->noexact = 0;
  b->incremental = b->sweepline = 0;
  b->dwyer = 1;
  b->splitseg = 0;
  b->docheck = 0;
  b->nobisect = 0;
  b->conformdel = 0;
  b->steiner = -1;
  b->order = 1;
  b->minangle = 0.0;
  b->maxarea = -1.0;
  b->quiet = b->verbose = 0;
 
  for (i = 0; i < argc; i++) {
    for (j = 0; argv[i][j] != '\0'; j++) {
      if (argv[i][j] == 'p') {
        b->poly = 1;
      }
      if (argv[i][j] == 'A') {
        b->regionattrib = 1;
      }
      if (argv[i][j] == 'c') {
        b->convex = 1;
      }
      if (argv[i][j] == 'w') {
        b->weighted = 1;
      }
      if (argv[i][j] == 'W') {
        b->weighted = 2;
      }
      if (argv[i][j] == 'j') {
        b->jettison = 1;
      }
      if (argv[i][j] == 'z') {
        b->firstnumber = 0;
      }
      if (argv[i][j] == 'e') {
        b->edgesout = 1;
      }
      if (argv[i][j] == 'v') {
        b->voronoi = 1;
      }
      if (argv[i][j] == 'n') {
        b->neighbors = 1;
      }
      if (argv[i][j] == 'g') {
        b->geomview = 1;
      }
      if (argv[i][j] == 'B') {
        b->nobound = 1;
      }
      if (argv[i][j] == 'P') {
        b->nopolywritten = 1;
      }
      if (argv[i][j] == 'N') {
        b->nonodewritten = 1;
      }
      if (argv[i][j] == 'E') {
        b->noelewritten = 1;
      }
      if (argv[i][j] == 'O') {
        b->noholes = 1;
      }
      if (argv[i][j] == 'X') {
        b->noexact = 1;
      }
      if (argv[i][j] == 'o') {
        if (argv[i][j + 1] == '2') {
          j++;
          b->order = 2;
        }
      }
      if (argv[i][j] == 'l') {
        b->dwyer = 0;
      }
      if (argv[i][j] == 'Q') {
        b->quiet = 1;
      }
      if (argv[i][j] == 'V') {
        b->verbose++;
      }
    }
  }
  b->usesegments = b->poly || b->refine || b->quality || b->convex;
  b->goodangle = cos(b->minangle * PI / 180.0);
  if (b->goodangle == 1.0) {
    b->offconstant = 0.0;
  } else {
    b->offconstant = 0.475 * sqrt((1.0 + b->goodangle) / (1.0 - b->goodangle));
  }
  b->goodangle *= b->goodangle;
  if (b->refine && b->noiterationnum) {
    printf(
      "Error:  You cannot use the -I switch when refining a triangulation.\n");
    triexit(1);
  }
  /* Be careful not to allocate space for element area constraints that */
  /*   will never be assigned any value (other than the default -1.0).  */
  if (!b->refine && !b->poly) {
    b->vararea = 0;
  }
  /* Be careful not to add an extra attribute to each element unless the */
  /*   input supports it (PSLG in, but not refining a preexisting mesh). */
  if (b->refine || !b->poly) {
    b->regionattrib = 0;
  }
  /* Regular/weighted triangulations are incompatible with PSLGs */
  /*   and meshing.                                              */
  if (b->weighted && (b->poly || b->quality)) {
    b->weighted = 0;
    if (!b->quiet) {
      printf("Warning:  weighted triangulations (-w, -W) are incompatible\n");
      printf("  with PSLGs (-p) and meshing (-q, -a, -u).  Weights ignored.\n"
             );
    }
  }
  if (b->jettison && b->nonodewritten && !b->quiet) {
    printf("Warning:  -j and -N switches are somewhat incompatible.\n");
    printf("  If any vertices are jettisoned, you will need the output\n");
    printf("  .node file to reconstruct the new node indices.");
  }
}
 
/********* User interaction routines begin here                      *********/
 
/********* Debugging routines begin here                             *********/
/*****************************************************************************/
/*                                                                           */
/*  printtriangle()   Print out the details of an oriented triangle.         */
/*                                                                           */
/*  I originally wrote this procedure to simplify debugging; it can be       */
/*  called directly from the debugger, and presents information about an     */
/*  oriented triangle in digestible form.  It's also used when the           */
/*  highest level of verbosity (`-VVV') is specified.                        */
/*                                                                           */
/*****************************************************************************/
 
void printtriangle(struct mesh *m, struct behavior *b, struct otri *t)
{
  struct otri printtri;
  struct osub printsh;
  vertex printvertex;
 
  printf("triangle x%lx with orientation %d:\n", (unsigned long) t->tri,
         t->orient);
  decode(t->tri[0], printtri);
  if (printtri.tri == m->dummytri) {
    printf("    [0] = Outer space\n");
  } else {
    printf("    [0] = x%lx  %d\n", (unsigned long) printtri.tri,
           printtri.orient);
  }
  decode(t->tri[1], printtri);
  if (printtri.tri == m->dummytri) {
    printf("    [1] = Outer space\n");
  } else {
    printf("    [1] = x%lx  %d\n", (unsigned long) printtri.tri,
           printtri.orient);
  }
  decode(t->tri[2], printtri);
  if (printtri.tri == m->dummytri) {
    printf("    [2] = Outer space\n");
  } else {
    printf("    [2] = x%lx  %d\n", (unsigned long) printtri.tri,
           printtri.orient);
  }
 
  org(*t, printvertex);
  if (printvertex == (vertex) NULL)
    printf("    Origin[%d] = NULL\n", (t->orient + 1) % 3 + 3);
  else
    printf("    Origin[%d] = x%lx  (%.12g, %.12g)\n",
           (t->orient + 1) % 3 + 3, (unsigned long) printvertex,
           printvertex[0], printvertex[1]);
  dest(*t, printvertex);
  if (printvertex == (vertex) NULL)
    printf("    Dest  [%d] = NULL\n", (t->orient + 2) % 3 + 3);
  else
    printf("    Dest  [%d] = x%lx  (%.12g, %.12g)\n",
           (t->orient + 2) % 3 + 3, (unsigned long) printvertex,
           printvertex[0], printvertex[1]);
  apex(*t, printvertex);
  if (printvertex == (vertex) NULL)
    printf("    Apex  [%d] = NULL\n", t->orient + 3);
  else
    printf("    Apex  [%d] = x%lx  (%.12g, %.12g)\n",
           t->orient + 3, (unsigned long) printvertex,
           printvertex[0], printvertex[1]);
 
  if (b->usesegments) {
    sdecode(t->tri[6], printsh);
    if (printsh.ss != m->dummysub) {
      printf("    [6] = x%lx  %d\n", (unsigned long) printsh.ss,
             printsh.ssorient);
    }
    sdecode(t->tri[7], printsh);
    if (printsh.ss != m->dummysub) {
      printf("    [7] = x%lx  %d\n", (unsigned long) printsh.ss,
             printsh.ssorient);
    }
    sdecode(t->tri[8], printsh);
    if (printsh.ss != m->dummysub) {
      printf("    [8] = x%lx  %d\n", (unsigned long) printsh.ss,
             printsh.ssorient);
    }
  }
 
  if (b->vararea) {
    printf("    Area constraint:  %.4g\n", areabound(*t));
  }
}
 
/*****************************************************************************/
/*                                                                           */
/*  printsubseg()   Print out the details of an oriented subsegment.         */
/*                                                                           */
/*  I originally wrote this procedure to simplify debugging; it can be       */
/*  called directly from the debugger, and presents information about an     */
/*  oriented subsegment in digestible form.  It's also used when the highest */
/*  level of verbosity (`-VVV') is specified.                                */
/*                                                                           */
/*****************************************************************************/
 
void printsubseg(struct mesh *m, struct behavior *b, struct osub *s)
{
  struct osub printsh;
  struct otri printtri;
  vertex printvertex;
 
  printf("subsegment x%lx with orientation %d and mark %d:\n",
         (unsigned long) s->ss, s->ssorient, mark(*s));
  sdecode(s->ss[0], printsh);
  if (printsh.ss == m->dummysub) {
    printf("    [0] = No subsegment\n");
  } else {
    printf("    [0] = x%lx  %d\n", (unsigned long) printsh.ss,
           printsh.ssorient);
  }
  sdecode(s->ss[1], printsh);
  if (printsh.ss == m->dummysub) {
    printf("    [1] = No subsegment\n");
  } else {
    printf("    [1] = x%lx  %d\n", (unsigned long) printsh.ss,
           printsh.ssorient);
  }
 
  sorg(*s, printvertex);
  if (printvertex == (vertex) NULL)
    printf("    Origin[%d] = NULL\n", 2 + s->ssorient);
  else
    printf("    Origin[%d] = x%lx  (%.12g, %.12g)\n",
           2 + s->ssorient, (unsigned long) printvertex,
           printvertex[0], printvertex[1]);
  sdest(*s, printvertex);
  if (printvertex == (vertex) NULL)
    printf("    Dest  [%d] = NULL\n", 3 - s->ssorient);
  else
    printf("    Dest  [%d] = x%lx  (%.12g, %.12g)\n",
           3 - s->ssorient, (unsigned long) printvertex,
           printvertex[0], printvertex[1]);
 
  decode(s->ss[6], printtri);
  if (printtri.tri == m->dummytri) {
    printf("    [6] = Outer space\n");
  } else {
    printf("    [6] = x%lx  %d\n", (unsigned long) printtri.tri,
           printtri.orient);
  }
  decode(s->ss[7], printtri);
  if (printtri.tri == m->dummytri) {
    printf("    [7] = Outer space\n");
  } else {
    printf("    [7] = x%lx  %d\n", (unsigned long) printtri.tri,
           printtri.orient);
  }
 
  segorg(*s, printvertex);
  if (printvertex == (vertex) NULL)
    printf("    Segment origin[%d] = NULL\n", 4 + s->ssorient);
  else
    printf("    Segment origin[%d] = x%lx  (%.12g, %.12g)\n",
           4 + s->ssorient, (unsigned long) printvertex,
           printvertex[0], printvertex[1]);
  segdest(*s, printvertex);
  if (printvertex == (vertex) NULL)
    printf("    Segment dest  [%d] = NULL\n", 5 - s->ssorient);
  else
    printf("    Segment dest  [%d] = x%lx  (%.12g, %.12g)\n",
           5 - s->ssorient, (unsigned long) printvertex,
           printvertex[0], printvertex[1]);
}
 
/********* Debugging routines end here                               *********/
 
/********* Memory management routines begin here                     *********/
/*****************************************************************************/
/*                                                                           */
/*  poolzero()   Set all of a pool's fields to zero.                         */
/*                                                                           */
/*  This procedure should never be called on a pool that has any memory      */
/*  allocated to it, as that memory would leak.                              */
/*                                                                           */
/*****************************************************************************/
 
void poolzero(struct memorypool *pool)
{
  pool->firstblock = (int **) NULL;
  pool->nowblock = (int **) NULL;
  pool->nextitem = (int *) NULL;
  pool->deaditemstack = (int *) NULL;
  pool->pathblock = (int **) NULL;
  pool->pathitem = (int *) NULL;
  pool->alignbytes = 0;
  pool->itembytes = 0;
  pool->itemsperblock = 0;
  pool->itemsfirstblock = 0;
  pool->items = 0;
  pool->maxitems = 0;
  pool->unallocateditems = 0;
  pool->pathitemsleft = 0;
}
 
/*****************************************************************************/
/*                                                                           */
/*  poolrestart()   Deallocate all items in a pool.                          */
/*                                                                           */
/*  The pool is returned to its starting state, except that no memory is     */
/*  freed to the operating system.  Rather, the previously allocated blocks  */
/*  are ready to be reused.                                                  */
/*                                                                           */
/*****************************************************************************/
 
void poolrestart(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 (int *). */
  alignptr = (unsigned long) (pool->nowblock + 1);
  /* Align the item on an `alignbytes'-byte boundary. */
  pool->nextitem = (int *)
    (alignptr + (unsigned long) pool->alignbytes -
     (alignptr % (unsigned long) pool->alignbytes));
  /* There are lots of unallocated items left in this block. */
  pool->unallocateditems = pool->itemsfirstblock;
  /* The stack of deallocated items is empty. */
  pool->deaditemstack = (int *) NULL;
}
 
/*****************************************************************************/
/*                                                                           */
/*  poolinit()   Initialize a pool of memory for allocation of items.        */
/*                                                                           */
/*  This routine initializes the machinery for allocating items.  A `pool'   */
/*  is created whose records have size at least `bytecount'.  Items will be  */
/*  allocated in `itemcount'-item blocks.  Each item is assumed to be a      */
/*  collection of words, and either pointers or floating-point values are    */
/*  assumed to be the "primary" word type.  (The "primary" word type is used */
/*  to determine alignment of items.)  If `alignment' isn't zero, all items  */
/*  will be `alignment'-byte aligned in memory.  `alignment' must be either  */
/*  a multiple or a factor of the primary word size; powers of two are safe. */
/*  `alignment' is normally used to create a few unused bits at the bottom   */
/*  of each item's pointer, in which information may be stored.              */
/*                                                                           */
/*  Don't change this routine unless you understand it.                      */
/*                                                                           */
/*****************************************************************************/
 
void poolinit(struct memorypool *pool, int bytecount, int itemcount,
              int firstitemcount, int alignment)
{
  /* Find the proper alignment, which must be at least as large as:   */
  /*   - The parameter `alignment'.                                   */
  /*   - sizeof(int *), so the stack of dead items can be maintained */
  /*       without unaligned accesses.                                */
  if (alignment > sizeof(int *)) {
    pool->alignbytes = alignment;
  } else {
    pool->alignbytes = sizeof(int *);
  }
  pool->itembytes = ((bytecount - 1) / pool->alignbytes + 1) *
                    pool->alignbytes;
  pool->itemsperblock = itemcount;
  if (firstitemcount == 0) {
    pool->itemsfirstblock = itemcount;
  } else {
    pool->itemsfirstblock = firstitemcount;
  }
 
  /* Allocate a block of items.  Space for `itemsfirstblock' items and one  */
  /*   pointer (to point to the next block) are allocated, as well as space */
  /*   to ensure alignment of the items.                                    */
  pool->firstblock = (int **)
    trimalloc(pool->itemsfirstblock * pool->itembytes + (int) sizeof(int *) +
              pool->alignbytes);
  /* Set the next block pointer to NULL. */
  *(pool->firstblock) = (int *) NULL;
  poolrestart(pool);
}
 
/*****************************************************************************/
/*                                                                           */
/*  pooldeinit()   Free to the operating system all memory taken by a pool.  */
/*                                                                           */
/*****************************************************************************/
 
void pooldeinit(struct memorypool *pool)
{
  while (pool->firstblock != (int **) NULL) {
    pool->nowblock = (int **) *(pool->firstblock);
    trifree((int *) pool->firstblock);
    pool->firstblock = pool->nowblock;
  }
}
 
/*****************************************************************************/
/*                                                                           */
/*  poolalloc()   Allocate space for an item.                                */
/*                                                                           */
/*****************************************************************************/
 
int *poolalloc(struct memorypool *pool)
{
  int *newitem;
  int **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 != (int *) NULL) {
    newitem = pool->deaditemstack;               /* Take first item in list. */
    pool->deaditemstack = * (int **) pool->deaditemstack;
  } else {
    /* Check if there are any free items left in the current block. */
    if (pool->unallocateditems == 0) {
      /* Check if another block must be allocated. */
      if (*(pool->nowblock) == (int *) NULL) {
        /* Allocate a new block of items, pointed to by the previous block. */
        newblock = (int **) trimalloc(pool->itemsperblock * pool->itembytes +
                                       (int) sizeof(int *) +
                                       pool->alignbytes);
        *(pool->nowblock) = (int *) newblock;
        /* The next block pointer is NULL. */
        *newblock = (int *) NULL;
      }
 
      /* Move to the new block. */
      pool->nowblock = (int **) *(pool->nowblock);
      /* Find the first item in the block.    */
      /*   Increment by the size of (int *). */
      alignptr = (unsigned long) (pool->nowblock + 1);
      /* Align the item on an `alignbytes'-byte boundary. */
      pool->nextitem = (int *)
        (alignptr + (unsigned long) pool->alignbytes -
         (alignptr % (unsigned long) pool->alignbytes));
      /* There are lots of unallocated items left in this block. */
      pool->unallocateditems = pool->itemsperblock;
    }
 
    /* Allocate a new item. */
    newitem = pool->nextitem;
    /* Advance `nextitem' pointer to next free item in block. */
    pool->nextitem = (int *) ((char *) pool->nextitem + pool->itembytes);
    pool->unallocateditems--;
    pool->maxitems++;
  }
  pool->items++;
  return newitem;
}
 
/*****************************************************************************/
/*                                                                           */
/*  pooldealloc()   Deallocate space for an item.                            */
/*                                                                           */
/*  The deallocated space is stored in a queue for later reuse.              */
/*                                                                           */
/*****************************************************************************/
 
void pooldealloc(struct memorypool *pool, int *dyingitem)
{
  /* Push freshly killed item onto stack. */
  *((int **) dyingitem) = pool->deaditemstack;
  pool->deaditemstack = dyingitem;
  pool->items--;
}
 
/*****************************************************************************/
/*                                                                           */
/*  traversalinit()   Prepare to traverse the entire list of items.          */
/*                                                                           */
/*  This routine is used in conjunction with traverse().                     */
/*                                                                           */
/*****************************************************************************/
 
void traversalinit(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 (int *). */
  alignptr = (unsigned long) (pool->pathblock + 1);
  /* Align with item on an `alignbytes'-byte boundary. */
  pool->pathitem = (int *)
    (alignptr + (unsigned long) pool->alignbytes -
     (alignptr % (unsigned long) pool->alignbytes));
  /* Set the number of items left in the current block. */
  pool->pathitemsleft = pool->itemsfirstblock;
}
 
/*****************************************************************************/
/*                                                                           */
/*  traverse()   Find the next item in the list.                             */
/*                                                                           */
/*  This routine is used in conjunction with traversalinit().  Be forewarned */
/*  that this routine successively returns all items in the list, including  */
/*  deallocated ones on the deaditemqueue.  It's up to you to figure out     */
/*  which ones are actually dead.  Why?  I don't want to allocate extra      */
/*  space just to demarcate dead items.  It can usually be done more         */
/*  space-efficiently by a routine that knows something about the structure  */
/*  of the item.                                                             */
/*                                                                           */
/*****************************************************************************/
 
int *traverse(struct memorypool *pool)
{
  int *newitem;
  unsigned long alignptr;
 
  /* Stop upon exhausting the list of items. */
  if (pool->pathitem == pool->nextitem) {
    return (int *) NULL;
  }
 
  /* Check whether any untraversed items remain in the current block. */
  if (pool->pathitemsleft == 0) {
    /* Find the next block. */
    pool->pathblock = (int **) *(pool->pathblock);
    /* Find the first item in the block.  Increment by the size of (int *). */
    alignptr = (unsigned long) (pool->pathblock + 1);
    /* Align with item on an `alignbytes'-byte boundary. */
    pool->pathitem = (int *)
      (alignptr + (unsigned long) pool->alignbytes -
       (alignptr % (unsigned long) pool->alignbytes));
    /* Set the number of items left in the current block. */
    pool->pathitemsleft = pool->itemsperblock;
  }
 
  newitem = pool->pathitem;
  /* Find the next item in the block. */
  pool->pathitem = (int *) ((char *) pool->pathitem + pool->itembytes);
  pool->pathitemsleft--;
  return newitem;
}
 
/*****************************************************************************/
/*                                                                           */
/*  dummyinit()   Initialize the triangle that fills "outer space" and the   */
/*                omnipresent subsegment.                                    */
/*                                                                           */
/*  The triangle that fills "outer space," called `dummytri', is pointed to  */
/*  by every triangle and subsegment on a boundary (be it outer or inner) of */
/*  the triangulation.  Also, `dummytri' points to one of the triangles on   */
/*  the convex hull (until the holes and concavities are carved), making it  */
/*  possible to find a starting triangle for point location.                 */
/*                                                                           */
/*  The omnipresent subsegment, `dummysub', is pointed to by every triangle  */
/*  or subsegment that doesn't have a full complement of real subsegments    */
/*  to point to.                                                             */
/*                                                                           */
/*  `dummytri' and `dummysub' are generally required to fulfill only a few   */
/*  invariants:  their vertices must remain NULL and `dummytri' must always  */
/*  be bonded (at offset zero) to some triangle on the convex hull of the    */
/*  mesh, via a boundary edge.  Otherwise, the connections of `dummytri' and */
/*  `dummysub' may change willy-nilly.  This makes it possible to avoid      */
/*  writing a good deal of special-case code (in the edge flip, for example) */
/*  for dealing with the boundary of the mesh, places where no subsegment is */
/*  present, and so forth.  Other entities are frequently bonded to          */
/*  `dummytri' and `dummysub' as if they were real mesh entities, with no    */
/*  harm done.                                                               */
/*                                                                           */
/*****************************************************************************/
 
void dummyinit(struct mesh *m, struct behavior *b, int trianglebytes,
               int subsegbytes)
{
  unsigned long alignptr;
 
  /* Set up `dummytri', the `triangle' that occupies "outer space." */
  m->dummytribase = (triangle *) trimalloc(trianglebytes +
                                           m->triangles.alignbytes);
  /* Align `dummytri' on a `triangles.alignbytes'-byte boundary. */
  alignptr = (unsigned long) m->dummytribase;
  m->dummytri = (triangle *)
    (alignptr + (unsigned long) m->triangles.alignbytes -
     (alignptr % (unsigned long) m->triangles.alignbytes));
  /* Initialize the three adjoining triangles to be "outer space."  These  */
  /*   will eventually be changed by various bonding operations, but their */
  /*   values don't really matter, as long as they can legally be          */
  /*   dereferenced.                                                       */
  m->dummytri[0] = (triangle) m->dummytri;
  m->dummytri[1] = (triangle) m->dummytri;
  m->dummytri[2] = (triangle) m->dummytri;
  /* Three NULL vertices. */
  m->dummytri[3] = (triangle) NULL;
  m->dummytri[4] = (triangle) NULL;
  m->dummytri[5] = (triangle) NULL;
 
  if (b->usesegments) {
    /* Set up `dummysub', the omnipresent subsegment pointed to by any */
    /*   triangle side or subsegment end that isn't attached to a real */
    /*   subsegment.                                                   */
    m->dummysubbase = (subseg *) trimalloc(subsegbytes +
                                           m->subsegs.alignbytes);
    /* Align `dummysub' on a `subsegs.alignbytes'-byte boundary. */
    alignptr = (unsigned long) m->dummysubbase;
    m->dummysub = (subseg *)
      (alignptr + (unsigned long) m->subsegs.alignbytes -
       (alignptr % (unsigned long) m->subsegs.alignbytes));
    /* Initialize the two adjoining subsegments to be the omnipresent      */
    /*   subsegment.  These will eventually be changed by various bonding  */
    /*   operations, but their values don't really matter, as long as they */
    /*   can legally be dereferenced.                                      */
    m->dummysub[0] = (subseg) m->dummysub;
    m->dummysub[1] = (subseg) m->dummysub;
    /* Four NULL vertices. */
    m->dummysub[2] = (subseg) NULL;
    m->dummysub[3] = (subseg) NULL;
    m->dummysub[4] = (subseg) NULL;
    m->dummysub[5] = (subseg) NULL;
    /* Initialize the two adjoining triangles to be "outer space." */
    m->dummysub[6] = (subseg) m->dummytri;
    m->dummysub[7] = (subseg) m->dummytri;
    /* Set the boundary marker to zero. */
    * (int *) (m->dummysub + 8) = 0;
 
    /* Initialize the three adjoining subsegments of `dummytri' to be */
    /*   the omnipresent subsegment.                                  */
    m->dummytri[6] = (triangle) m->dummysub;
    m->dummytri[7] = (triangle) m->dummysub;
    m->dummytri[8] = (triangle) m->dummysub;
  }
}
 
/*****************************************************************************/
/*                                                                           */
/*  initializevertexpool()   Calculate the size of the vertex data structure */
/*                           and initialize its memory pool.                 */
/*                                                                           */
/*  This routine also computes the `vertexmarkindex' and `vertex2triindex'   */
/*  indices used to find values within each vertex.                          */
/*                                                                           */
/*****************************************************************************/
 
void initializevertexpool(struct mesh *m, struct behavior *b)
{
  int vertexsize;
 
  /* The index within each vertex at which the boundary marker is found,    */
  /*   followed by the vertex type.  Ensure the vertex marker is aligned to */
  /*   a sizeof(int)-byte address.                                          */
  m->vertexmarkindex = ((m->mesh_dim + m->nextras) * sizeof(float) +
                        sizeof(int) - 1) /
                       sizeof(int);
  vertexsize = (m->vertexmarkindex + 2) * sizeof(int);
  if (b->poly) {
    /* The index within each vertex at which a triangle pointer is found.  */
    /*   Ensure the pointer is aligned to a sizeof(triangle)-byte address. */
    m->vertex2triindex = (vertexsize + sizeof(triangle) - 1) /
                         sizeof(triangle);
    vertexsize = (m->vertex2triindex + 1) * sizeof(triangle);
  }
 
  /* Initialize the pool of vertices. */
  poolinit(&m->vertices, vertexsize, VERTEXPERBLOCK,
           m->invertices > VERTEXPERBLOCK ? m->invertices : VERTEXPERBLOCK,
           sizeof(float));
}
 
/*****************************************************************************/
/*                                                                           */
/*  initializetrisubpools()   Calculate the sizes of the triangle and        */
/*                            subsegment data structures and initialize      */
/*                            their memory pools.                            */
/*                                                                           */
/*  This routine also computes the `highorderindex', `elemattribindex', and  */
/*  `areaboundindex' indices used to find values within each triangle.       */
/*                                                                           */
/*****************************************************************************/
 
void initializetrisubpools(struct mesh *m, struct behavior *b)
{
  int trisize;
 
  /* The index within each triangle at which the extra nodes (above three)  */
  /*   associated with high order elements are found.  There are three      */
  /*   pointers to other triangles, three pointers to corners, and possibly */
  /*   three pointers to subsegments before the extra nodes.                */
  m->highorderindex = 6 + (b->usesegments * 3);
  /* The number of bytes occupied by a triangle. */
  trisize = ((b->order + 1) * (b->order + 2) / 2 + (m->highorderindex - 3)) *
            sizeof(triangle);
  /* The index within each triangle at which its attributes are found, */
  /*   where the index is measured in floats.                           */
  m->elemattribindex = (trisize + sizeof(float) - 1) / sizeof(float);
  /* The index within each triangle at which the maximum area constraint  */
  /*   is found, where the index is measured in floats.  Note that if the  */
  /*   `regionattrib' flag is set, an additional attribute will be added. */
  m->areaboundindex = m->elemattribindex + m->eextras + b->regionattrib;
  /* If triangle attributes or an area bound are needed, increase the number */
  /*   of bytes occupied by a triangle.                                      */
  if (b->vararea) {
    trisize = (m->areaboundindex + 1) * sizeof(float);
  } else if (m->eextras + b->regionattrib > 0) {
    trisize = m->areaboundindex * sizeof(float);
  }
  /* If a Voronoi diagram or triangle neighbor graph is requested, make    */
  /*   sure there's room to store an integer index in each triangle.  This */
  /*   integer index can occupy the same space as the subsegment pointers  */
  /*   or attributes or area constraint or extra nodes.                    */
  if ((b->voronoi || b->neighbors) &&
      (trisize < 6 * sizeof(triangle) + sizeof(int))) {
    trisize = 6 * sizeof(triangle) + sizeof(int);
  }
 
  /* Having determined the memory size of a triangle, initialize the pool. */
  poolinit(&m->triangles, trisize, TRIPERBLOCK,
           (2 * m->invertices - 2) > TRIPERBLOCK ? (2 * m->invertices - 2) :
           TRIPERBLOCK, 4);
 
  if (b->usesegments) {
    /* Initialize the pool of subsegments.  Take into account all eight */
    /*   pointers and one boundary marker.                              */
    poolinit(&m->subsegs, 8 * sizeof(triangle) + sizeof(int),
             SUBSEGPERBLOCK, SUBSEGPERBLOCK, 4);
 
    /* Initialize the "outer space" triangle and omnipresent subsegment. */
    dummyinit(m, b, m->triangles.itembytes, m->subsegs.itembytes);
  } else {
    /* Initialize the "outer space" triangle. */
    dummyinit(m, b, m->triangles.itembytes, 0);
  }
}
 
/*****************************************************************************/
/*                                                                           */
/*  triangledealloc()   Deallocate space for a triangle, marking it dead.    */
/*                                                                           */
/*****************************************************************************/
 
void triangledealloc(struct mesh *m, triangle *dyingtriangle)
{
  /* Mark the triangle as dead.  This makes it possible to detect dead */
  /*   triangles when traversing the list of all triangles.            */
  killtri(dyingtriangle);
  pooldealloc(&m->triangles, (int *) dyingtriangle);
}
 
/*****************************************************************************/
/*                                                                           */
/*  triangletraverse()   Traverse the triangles, skipping dead ones.         */
/*                                                                           */
/*****************************************************************************/
 
triangle *triangletraverse(struct mesh *m)
{
  triangle *newtriangle;
 
  do {
    newtriangle = (triangle *) traverse(&m->triangles);
    if (newtriangle == (triangle *) NULL) {
      return (triangle *) NULL;
    }
  } while (deadtri(newtriangle));                         /* Skip dead ones. */
  return newtriangle;
}
 
/*****************************************************************************/
/*                                                                           */
/*  subsegdealloc()   Deallocate space for a subsegment, marking it dead.    */
/*                                                                           */
/*****************************************************************************/
 
void subsegdealloc(struct mesh *m, subseg *dyingsubseg)
{
  /* Mark the subsegment as dead.  This makes it possible to detect dead */
  /*   subsegments when traversing the list of all subsegments.          */
  killsubseg(dyingsubseg);
  pooldealloc(&m->subsegs, (int *) dyingsubseg);
}
 
/*****************************************************************************/
/*                                                                           */
/*  subsegtraverse()   Traverse the subsegments, skipping dead ones.         */
/*                                                                           */
/*****************************************************************************/
 
subseg *subsegtraverse(struct mesh *m)
{
  subseg *newsubseg;
 
  do {
    newsubseg = (subseg *) traverse(&m->subsegs);
    if (newsubseg == (subseg *) NULL) {
      return (subseg *) NULL;
    }
  } while (deadsubseg(newsubseg));                        /* Skip dead ones. */
  return newsubseg;
}
 
/*****************************************************************************/
/*                                                                           */
/*  vertexdealloc()   Deallocate space for a vertex, marking it dead.        */
/*                                                                           */
/*****************************************************************************/
 
void vertexdealloc(struct mesh *m, vertex dyingvertex)
{
  /* Mark the vertex as dead.  This makes it possible to detect dead */
  /*   vertices when traversing the list of all vertices.            */
  setvertextype(dyingvertex, DEADVERTEX);
  pooldealloc(&m->vertices, (int *) dyingvertex);
}
 
/*****************************************************************************/
/*                                                                           */
/*  vertextraverse()   Traverse the vertices, skipping dead ones.            */
/*                                                                           */
/*****************************************************************************/
 
vertex vertextraverse(struct mesh *m)
{
  vertex newvertex;
 
  do {
    newvertex = (vertex) traverse(&m->vertices);
    if (newvertex == (vertex) NULL) {
      return (vertex) NULL;
    }
  } while (vertextype(newvertex) == DEADVERTEX);          /* Skip dead ones. */
  return newvertex;
}
 
/*****************************************************************************/
/*                                                                           */
/*  getvertex()   Get a specific vertex, by number, from the list.           */
/*                                                                           */
/*  The first vertex is number 'firstnumber'.                                */
/*                                                                           */
/*  Note that this takes O(n) time (with a small constant, if VERTEXPERBLOCK */
/*  is large).  I don't care to take the trouble to make it work in constant */
/*  time.                                                                    */
/*                                                                           */
/*****************************************************************************/
 
vertex getvertex(struct mesh *m, struct behavior *b, int number)
{
  int **getblock;
  char *foundvertex;
  unsigned long alignptr;
  int current;
 
  getblock = m->vertices.firstblock;
  current = b->firstnumber;
 
  /* Find the right block. */
  if (current + m->vertices.itemsfirstblock <= number) {
    getblock = (int **) *getblock;
    current += m->vertices.itemsfirstblock;
    while (current + m->vertices.itemsperblock <= number) {
      getblock = (int **) *getblock;
      current += m->vertices.itemsperblock;
    }
  }
 
  /* Now find the right vertex. */
  alignptr = (unsigned long) (getblock + 1);
  foundvertex = (char *) (alignptr + (unsigned long) m->vertices.alignbytes -
                          (alignptr % (unsigned long) m->vertices.alignbytes));
  return (vertex) (foundvertex + m->vertices.itembytes * (number - current));
}
 
/*****************************************************************************/
/*                                                                           */
/*  triangledeinit()   Free all remaining allocated memory.                  */
/*                                                                           */
/*****************************************************************************/
 
void triangledeinit(struct mesh *m, struct behavior *b)
{
  pooldeinit(&m->triangles);
  trifree((int *) m->dummytribase);
  if (b->usesegments) {
    pooldeinit(&m->subsegs);
    trifree((int *) m->dummysubbase);
  }
  pooldeinit(&m->vertices);
}
 
/********* Memory management routines end here                       *********/
 
/********* Constructors begin here                                   *********/
/*****************************************************************************/
/*                                                                           */
/*  maketriangle()   Create a new triangle with orientation zero.            */
/*                                                                           */
/*****************************************************************************/
 
void maketriangle(struct mesh *m, struct behavior *b, struct otri *newotri)
{
  int i;
 
  newotri->tri = (triangle *) poolalloc(&m->triangles);
  /* Initialize the three adjoining triangles to be "outer space". */
  newotri->tri[0] = (triangle) m->dummytri;
  newotri->tri[1] = (triangle) m->dummytri;
  newotri->tri[2] = (triangle) m->dummytri;
  /* Three NULL vertices. */
  newotri->tri[3] = (triangle) NULL;
  newotri->tri[4] = (triangle) NULL;
  newotri->tri[5] = (triangle) NULL;
  if (b->usesegments) {
    /* Initialize the three adjoining subsegments to be the omnipresent */
    /*   subsegment.                                                    */
    newotri->tri[6] = (triangle) m->dummysub;
    newotri->tri[7] = (triangle) m->dummysub;
    newotri->tri[8] = (triangle) m->dummysub;
  }
  for (i = 0; i < m->eextras; i++) {
    setelemattribute(*newotri, i, 0.0);
  }
  if (b->vararea) {
    setareabound(*newotri, -1.0);
  }
 
  newotri->orient = 0;
}
 
/*****************************************************************************/
/*                                                                           */
/*  makesubseg()   Create a new subsegment with orientation zero.            */
/*                                                                           */
/*****************************************************************************/
 
void makesubseg(struct mesh *m, struct osub *newsubseg)
{
  newsubseg->ss = (subseg *) poolalloc(&m->subsegs);
  /* Initialize the two adjoining subsegments to be the omnipresent */
  /*   subsegment.                                                  */
  newsubseg->ss[0] = (subseg) m->dummysub;
  newsubseg->ss[1] = (subseg) m->dummysub;
  /* Four NULL vertices. */
  newsubseg->ss[2] = (subseg) NULL;
  newsubseg->ss[3] = (subseg) NULL;
  newsubseg->ss[4] = (subseg) NULL;
  newsubseg->ss[5] = (subseg) NULL;
  /* Initialize the two adjoining triangles to be "outer space." */
  newsubseg->ss[6] = (subseg) m->dummytri;
  newsubseg->ss[7] = (subseg) m->dummytri;
  /* Set the boundary marker to zero. */
  setmark(*newsubseg, 0);
 
  newsubseg->ssorient = 0;
}
 
/********* Constructors end here                                     *********/
 
/********* Geometric primitives begin here                           *********/
/* The adaptive exact arithmetic geometric predicates implemented herein are */
/*   described in detail in my paper, "Adaptive Precision Floating-Point     */
/*   Arithmetic and Fast Robust Geometric Predicates."  See the header for a */
/*   full citation.                                                          */
 
/* Which of the following two methods of finding the absolute values is      */
/*   fastest is compiler-dependent.  A few compilers can inline and optimize */
/*   the fabs() call; but most will incur the overhead of a function call,   */
/*   which is disastrously slow.  A faster way on IEEE machines might be to  */
/*   mask the appropriate bit, but that's difficult to do in C without       */
/*   forcing the value to be stored to memory (rather than be kept in the    */
/*   register to which the optimizer assigned it).                           */
 
#define Absolute(a)  ((a) >= 0.0 ? (a) : -(a))
/* #define Absolute(a)  fabs(a) */
 
/* Many of the operations are broken up into two pieces, a main part that    */
/*   performs an approximate operation, and a "tail" that computes the       */
/*   roundoff error of that operation.                                       */
/*                                                                           */
/* The operations Fast_Two_Sum(), Fast_Two_Diff(), Two_Sum(), Two_Diff(),    */
/*   Split(), and Two_Product() are all implemented as described in the      */
/*   reference.  Each of these macros requires certain variables to be       */
/*   defined in the calling routine.  The variables `bvirt', `c', `abig',    */
/*   `_i', `_j', `_k', `_l', `_m', and `_n' are declared `INEXACT' because   */
/*   they store the result of an operation that may incur roundoff error.    */
/*   The input parameter `x' (or the highest numbered `x_' parameter) must   */
/*   also be declared `INEXACT'.                                             */
 
#define Fast_Two_Sum_Tail(a, b, x, y) \
  bvirt = x - a; \
  y = b - bvirt
 
#define Fast_Two_Sum(a, b, x, y) \
  x = (float) (a + b); \
  Fast_Two_Sum_Tail(a, b, x, y)
 
#define Two_Sum_Tail(a, b, x, y) \
  bvirt = (float) (x - a); \
  avirt = x - bvirt; \
  bround = b - bvirt; \
  around = a - avirt; \
  y = around + bround
 
#define Two_Sum(a, b, x, y) \
  x = (float) (a + b); \
  Two_Sum_Tail(a, b, x, y)
 
#define Two_Diff_Tail(a, b, x, y) \
  bvirt = (float) (a - x); \
  avirt = x + bvirt; \
  bround = bvirt - b; \
  around = a - avirt; \
  y = around + bround
 
#define Two_Diff(a, b, x, y) \
  x = (float) (a - b); \
  Two_Diff_Tail(a, b, x, y)
 
#define Split(a, ahi, alo) \
  c = (float) (splitter * a); \
  abig = (float) (c - a); \
  ahi = c - abig; \
  alo = a - ahi
 
#define Two_Product_Tail(a, b, x, y) \
  Split(a, ahi, alo); \
  Split(b, bhi, blo); \
  err1 = x - (ahi * bhi); \
  err2 = err1 - (alo * bhi); \
  err3 = err2 - (ahi * blo); \
  y = (alo * blo) - err3
 
#define Two_Product(a, b, x, y) \
  x = (float) (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 = (float) (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 = (float) (a * a); \
  Square_Tail(a, x, y)
 
/* Macros for summing expansions of various fixed lengths.  These are all    */
/*   unrolled versions of Expansion_Sum().                                   */
 
#define Two_One_Sum(a1, a0, b, x2, x1, x0) \
  Two_Sum(a0, b , _i, x0); \
  Two_Sum(a1, _i, x2, x1)
 
#define Two_One_Diff(a1, a0, b, x2, x1, x0) \
  Two_Diff(a0, b , _i, x0); \
  Two_Sum( a1, _i, x2, x1)
 
#define Two_Two_Sum(a1, a0, b1, b0, x3, x2, x1, x0) \
  Two_One_Sum(a1, a0, b0, _j, _0, x0); \
  Two_One_Sum(_j, _0, b1, x3, x2, x1)
 
#define Two_Two_Diff(a1, a0, b1, b0, x3, x2, x1, x0) \
  Two_One_Diff(a1, a0, b0, _j, _0, x0); \
  Two_One_Diff(_j, _0, b1, x3, x2, x1)
 
/* Macro for multiplying a two-component expansion by a single component.    */
 
#define Two_One_Product(a1, a0, b, x3, x2, x1, x0) \
  Split(b, bhi, blo); \
  Two_Product_Presplit(a0, b, bhi, blo, _i, x0); \
  Two_Product_Presplit(a1, b, bhi, blo, _j, _0); \
  Two_Sum(_i, _0, _k, x1); \
  Fast_Two_Sum(_j, _k, x3, x2)
 
/*****************************************************************************/
/*                                                                           */
/*  exactinit()   Initialize the variables used for exact arithmetic.        */
/*                                                                           */
/*  `epsilon' is the largest power of two such that 1.0 + epsilon = 1.0 in   */
/*  floating-point arithmetic.  `epsilon' bounds the relative roundoff       */
/*  error.  It is used for floating-point error analysis.                    */
/*                                                                           */
/*  `splitter' is used to split floating-point numbers into two half-        */
/*  length significands for exact multiplication.                            */
/*                                                                           */
/*  I imagine that a highly optimizing compiler might be too smart for its   */
/*  own good, and somehow cause this routine to fail, if it pretends that    */
/*  floating-point arithmetic is too much like real arithmetic.              */
/*                                                                           */
/*  Don't change this routine unless you fully understand it.                */
/*                                                                           */
/*****************************************************************************/
 
void exactinit()
{
  float half;
  float 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.)       */
  do {
    lastcheck = check;
    epsilon *= half;
    if (every_other) {
      splitter *= 2.0;
    }
    every_other = !every_other;
    check = 1.0 + epsilon;
  } while ((check != 1.0) && (check != lastcheck));
  splitter += 1.0;
  /* Error bounds for orientation and incircle tests. */
  resulterrbound = (3.0 + 8.0 * epsilon) * epsilon;
  ccwerrboundA = (3.0 + 16.0 * epsilon) * epsilon;
  ccwerrboundB = (2.0 + 12.0 * epsilon) * epsilon;
  ccwerrboundC = (9.0 + 64.0 * epsilon) * epsilon * epsilon;
  iccerrboundA = (10.0 + 96.0 * epsilon) * epsilon;
  iccerrboundB = (4.0 + 48.0 * epsilon) * epsilon;
  iccerrboundC = (44.0 + 576.0 * epsilon) * epsilon * epsilon;
  o3derrboundA = (7.0 + 56.0 * epsilon) * epsilon;
  o3derrboundB = (3.0 + 28.0 * epsilon) * epsilon;
  o3derrboundC = (26.0 + 288.0 * epsilon) * epsilon * epsilon;
}
 
/*****************************************************************************/
/*                                                                           */
/*  fast_expansion_sum_zeroelim()   Sum two expansions, eliminating zero     */
/*                                  components from the output expansion.    */
/*                                                                           */
/*  Sets h = e + f.  See my Robust Predicates paper for details.             */
/*                                                                           */
/*  If round-to-even is used (as with IEEE 754), maintains the strongly      */
/*  nonoverlapping property.  (That is, if e is strongly nonoverlapping, h   */
/*  will be also.)  Does NOT maintain the nonoverlapping or nonadjacent      */
/*  properties.                                                              */
/*                                                                           */
/*****************************************************************************/
 
int fast_expansion_sum_zeroelim(int elen, float *e, int flen, float *f, float *h)
{
  float Q;
  float Qnew;
  float hh;
  float bvirt;
  float avirt, bround, around;
  int eindex, findex, hindex;
  float 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(int elen, float *e, float b, float *h)
{
  float Q, sum;
  float hh;
  float product1;
  float product0;
  int eindex, hindex;
  float enow;
  float bvirt;
  float avirt, bround, around;
  float c;
  float abig;
  float ahi, alo, bhi, blo;
  float 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.                              */
/*                                                                           */
/*****************************************************************************/
 
float estimate(int elen, float *e)
{
  float 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.                              */
/*                                                                           */
/*****************************************************************************/
 
float counterclockwiseadapt(vertex pa, vertex pb, vertex pc, float detsum)
{
  float acx, acy, bcx, bcy;
  float acxtail, acytail, bcxtail, bcytail;
  float detleft, detright;
  float detlefttail, detrighttail;
  float det, errbound;
  float B[4], C1[8], C2[12], D[16];
  float B3;
  int C1length, C2length, Dlength;
  float u[4];
  float u3;
  float s1, t1;
  float s0, t0;
 
  float bvirt;
  float avirt, bround, around;
  float c;
  float abig;
  float ahi, alo, bhi, blo;
  float err1, err2, err3;
  float _i, _j;
  float _0;
 
  acx = (float) (pa[0] - pc[0]);
  bcx = (float) (pb[0] - pc[0]);
  acy = (float) (pa[1] - pc[1]);
  bcy = (float) (pb[1] - pc[1]);
 
  Two_Product(acx, bcy, detleft, detlefttail);
  Two_Product(acy, bcx, detright, detrighttail);
 
  Two_Two_Diff(detleft, detlefttail, detright, detrighttail,
               B3, B[2], B[1], B[0]);
  B[3] = B3;
 
  det = estimate(4, B);
  errbound = ccwerrboundB * detsum;
  if ((det >= errbound) || (-det >= errbound)) {
    return det;
  }
 
  Two_Diff_Tail(pa[0], pc[0], acx, acxtail);
  Two_Diff_Tail(pb[0], pc[0], bcx, bcxtail);
  Two_Diff_Tail(pa[1], pc[1], acy, acytail);
  Two_Diff_Tail(pb[1], pc[1], bcy, bcytail);
 
  if ((acxtail == 0.0) && (acytail == 0.0)
      && (bcxtail == 0.0) && (bcytail == 0.0)) {
    return det;
  }
 
  errbound = ccwerrboundC * detsum + resulterrbound * Absolute(det);
  det += (acx * bcytail + bcy * acxtail)
       - (acy * bcxtail + bcx * acytail);
  if ((det >= errbound) || (-det >= errbound)) {
    return det;
  }
 
  Two_Product(acxtail, bcy, s1, s0);
  Two_Product(acytail, bcx, t1, t0);
  Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
  u[3] = u3;
  C1length = fast_expansion_sum_zeroelim(4, B, 4, u, C1);
 
  Two_Product(acx, bcytail, s1, s0);
  Two_Product(acy, bcxtail, t1, t0);
  Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
  u[3] = u3;
  C2length = fast_expansion_sum_zeroelim(C1length, C1, 4, u, C2);
 
  Two_Product(acxtail, bcytail, s1, s0);
  Two_Product(acytail, bcxtail, t1, t0);
  Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
  u[3] = u3;
  Dlength = fast_expansion_sum_zeroelim(C2length, C2, 4, u, D);
 
  return(D[Dlength - 1]);
}
 
float counterclockwise(struct mesh *m, struct behavior *b,
                      vertex pa, vertex pb, vertex pc)
{
  float detleft, detright, det;
  float detsum, errbound;
 
  m->counterclockcount++;
 
  detleft = (pa[0] - pc[0]) * (pb[1] - pc[1]);
  detright = (pa[1] - pc[1]) * (pb[0] - pc[0]);
  det = detleft - detright;
 
  if (b->noexact) {
    return det;
  }
 
  if (detleft > 0.0) {
    if (detright <= 0.0) {
      return det;
    } else {
      detsum = detleft + detright;
    }
  } else if (detleft < 0.0) {
    if (detright >= 0.0) {
      return det;
    } else {
      detsum = -detleft - detright;
    }
  } else {
    return det;
  }
 
  errbound = ccwerrboundA * detsum;
  if ((det >= errbound) || (-det >= errbound)) {
    return det;
  }
 
  return counterclockwiseadapt(pa, pb, pc, detsum);
}
 
/*****************************************************************************/
/*                                                                           */
/*  incircle()   Return a positive value if the point pd lies inside the     */
/*               circle passing through pa, pb, and pc; a negative value if  */
/*               it lies outside; and zero if the four points are cocircular.*/
/*               The points pa, pb, and pc must be in counterclockwise       */
/*               order, or the sign of the result will be reversed.          */
/*                                                                           */
/*  Uses exact arithmetic if necessary to ensure a correct answer.  The      */
/*  result returned is the determinant of a matrix.  This determinant is     */
/*  computed adaptively, in the sense that exact arithmetic is used only to  */
/*  the degree it is needed to ensure that the returned value has the        */
/*  correct sign.  Hence, this function is usually quite fast, but will run  */
/*  more slowly when the input points are cocircular or nearly so.           */
/*                                                                           */
/*  See my Robust Predicates paper for details.                              */
/*                                                                           */
/*****************************************************************************/
 
float incircleadapt(vertex pa, vertex pb, vertex pc, vertex pd, float permanent)
{
  float adx, bdx, cdx, ady, bdy, cdy;
  float det, errbound;
 
  float bdxcdy1, cdxbdy1, cdxady1, adxcdy1, adxbdy1, bdxady1;
  float bdxcdy0, cdxbdy0, cdxady0, adxcdy0, adxbdy0, bdxady0;
  float bc[4], ca[4], ab[4];
  float bc3, ca3, ab3;
  float axbc[8], axxbc[16], aybc[8], ayybc[16], adet[32];
  int axbclen, axxbclen, aybclen, ayybclen, alen;
  float bxca[8], bxxca[16], byca[8], byyca[16], bdet[32];
  int bxcalen, bxxcalen, bycalen, byycalen, blen;
  float cxab[8], cxxab[16], cyab[8], cyyab[16], cdet[32];
  int cxablen, cxxablen, cyablen, cyyablen, clen;
  float abdet[64];
  int ablen;
  float fin1[1152], fin2[1152];
  float *finnow, *finother, *finswap;
  int finlength;
 
  float adxtail, bdxtail, cdxtail, adytail, bdytail, cdytail;
  float adxadx1, adyady1, bdxbdx1, bdybdy1, cdxcdx1, cdycdy1;
  float adxadx0, adyady0, bdxbdx0, bdybdy0, cdxcdx0, cdycdy0;
  float aa[4], bb[4], cc[4];
  float aa3, bb3, cc3;
  float ti1, tj1;
  float ti0, tj0;
  float u[4], v[4];
  float u3, v3;
  float temp8[8], temp16a[16], temp16b[16], temp16c[16];
  float temp32a[32], temp32b[32], temp48[48], temp64[64];
  int temp8len, temp16alen, temp16blen, temp16clen;
  int temp32alen, temp32blen, temp48len, temp64len;
  float axtbb[8], axtcc[8], aytbb[8], aytcc[8];
  int axtbblen, axtcclen, aytbblen, aytcclen;
  float bxtaa[8], bxtcc[8], bytaa[8], bytcc[8];
  int bxtaalen, bxtcclen, bytaalen, bytcclen;
  float cxtaa[8], cxtbb[8], cytaa[8], cytbb[8];
  int cxtaalen, cxtbblen, cytaalen, cytbblen;
  float axtbc[8], aytbc[8], bxtca[8], bytca[8], cxtab[8], cytab[8];
  int axtbclen, aytbclen, bxtcalen, bytcalen, cxtablen, cytablen;
  float axtbct[16], aytbct[16], bxtcat[16], bytcat[16], cxtabt[16], cytabt[16];
  int axtbctlen, aytbctlen, bxtcatlen, bytcatlen, cxtabtlen, cytabtlen;
  float axtbctt[8], aytbctt[8], bxtcatt[8];
  float bytcatt[8], cxtabtt[8], cytabtt[8];
  int axtbcttlen, aytbcttlen, bxtcattlen, bytcattlen, cxtabttlen, cytabttlen;
  float abt[8], bct[8], cat[8];
  int abtlen, bctlen, catlen;
  float abtt[4], bctt[4], catt[4];
  int abttlen, bcttlen, cattlen;
  float abtt3, bctt3, catt3;
  float negate;
 
  float bvirt;
  float avirt, bround, around;
  float c;
  float abig;
  float ahi, alo, bhi, blo;
  float err1, err2, err3;
  float _i, _j;
  float _0;
 
  adx = (float) (pa[0] - pd[0]);
  bdx = (float) (pb[0] - pd[0]);
  cdx = (float) (pc[0] - pd[0]);
  ady = (float) (pa[1] - pd[1]);
  bdy = (float) (pb[1] - pd[1]);
  cdy = (float) (pc[1] - pd[1]);
 
  Two_Product(bdx, cdy, bdxcdy1, bdxcdy0);
  Two_Product(cdx, bdy, cdxbdy1, cdxbdy0);
  Two_Two_Diff(bdxcdy1, bdxcdy0, cdxbdy1, cdxbdy0, bc3, bc[2], bc[1], bc[0]);
  bc[3] = bc3;
  axbclen = scale_expansion_zeroelim(4, bc, adx, axbc);
  axxbclen = scale_expansion_zeroelim(axbclen, axbc, adx, axxbc);
  aybclen = scale_expansion_zeroelim(4, bc, ady, aybc);
  ayybclen = scale_expansion_zeroelim(aybclen, aybc, ady, ayybc);
  alen = fast_expansion_sum_zeroelim(axxbclen, axxbc, ayybclen, ayybc, adet);
 
  Two_Product(cdx, ady, cdxady1, cdxady0);
  Two_Product(adx, cdy, adxcdy1, adxcdy0);
  Two_Two_Diff(cdxady1, cdxady0, adxcdy1, adxcdy0, ca3, ca[2], ca[1], ca[0]);
  ca[3] = ca3;
  bxcalen = scale_expansion_zeroelim(4, ca, bdx, bxca);
  bxxcalen = scale_expansion_zeroelim(bxcalen, bxca, bdx, bxxca);
  bycalen = scale_expansion_zeroelim(4, ca, bdy, byca);
  byycalen = scale_expansion_zeroelim(bycalen, byca, bdy, byyca);
  blen = fast_expansion_sum_zeroelim(bxxcalen, bxxca, byycalen, byyca, bdet);
 
  Two_Product(adx, bdy, adxbdy1, adxbdy0);
  Two_Product(bdx, ady, bdxady1, bdxady0);
  Two_Two_Diff(adxbdy1, adxbdy0, bdxady1, bdxady0, ab3, ab[2], ab[1], ab[0]);
  ab[3] = ab3;
  cxablen = scale_expansion_zeroelim(4, ab, cdx, cxab);
  cxxablen = scale_expansion_zeroelim(cxablen, cxab, cdx, cxxab);
  cyablen = scale_expansion_zeroelim(4, ab, cdy, cyab);
  cyyablen = scale_expansion_zeroelim(cyablen, cyab, cdy, cyyab);
  clen = fast_expansion_sum_zeroelim(cxxablen, cxxab, cyyablen, cyyab, cdet);
 
  ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
  finlength = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, fin1);
 
  det = estimate(finlength, fin1);
  errbound = iccerrboundB * permanent;
  if ((det >= errbound) || (-det >= errbound)) {
    return det;
  }
 
  Two_Diff_Tail(pa[0], pd[0], adx, adxtail);
  Two_Diff_Tail(pa[1], pd[1], ady, adytail);
  Two_Diff_Tail(pb[0], pd[0], bdx, bdxtail);
  Two_Diff_Tail(pb[1], pd[1], bdy, bdytail);
  Two_Diff_Tail(pc[0], pd[0], cdx, cdxtail);
  Two_Diff_Tail(pc[1], pd[1], cdy, cdytail);
  if ((adxtail == 0.0) && (bdxtail == 0.0) && (cdxtail == 0.0)
      && (adytail == 0.0) && (bdytail == 0.0) && (cdytail == 0.0)) {
    return det;
  }
 
  errbound = iccerrboundC * permanent + resulterrbound * Absolute(det);
  det += ((adx * adx + ady * ady) * ((bdx * cdytail + cdy * bdxtail)
                                     - (bdy * cdxtail + cdx * bdytail))
          + 2.0 * (adx * adxtail + ady * adytail) * (bdx * cdy - bdy * cdx))
       + ((bdx * bdx + bdy * bdy) * ((cdx * adytail + ady * cdxtail)
                                     - (cdy * adxtail + adx * cdytail))
          + 2.0 * (bdx * bdxtail + bdy * bdytail) * (cdx * ady - cdy * adx))
       + ((cdx * cdx + cdy * cdy) * ((adx * bdytail + bdy * adxtail)
                                     - (ady * bdxtail + bdx * adytail))
          + 2.0 * (cdx * cdxtail + cdy * cdytail) * (adx * bdy - ady * bdx));
  if ((det >= errbound) || (-det >= errbound)) {
    return det;
  }
 
  finnow = fin1;
  finother = fin2;
 
  if ((bdxtail != 0.0) || (bdytail != 0.0)
      || (cdxtail != 0.0) || (cdytail != 0.0)) {
    Square(adx, adxadx1, adxadx0);
    Square(ady, adyady1, adyady0);
    Two_Two_Sum(adxadx1, adxadx0, adyady1, adyady0, aa3, aa[2], aa[1], aa[0]);
    aa[3] = aa3;
  }
  if ((cdxtail != 0.0) || (cdytail != 0.0)
      || (adxtail != 0.0) || (adytail != 0.0)) {
    Square(bdx, bdxbdx1, bdxbdx0);
    Square(bdy, bdybdy1, bdybdy0);
    Two_Two_Sum(bdxbdx1, bdxbdx0, bdybdy1, bdybdy0, bb3, bb[2], bb[1], bb[0]);
    bb[3] = bb3;
  }
  if ((adxtail != 0.0) || (adytail != 0.0)
      || (bdxtail != 0.0) || (bdytail != 0.0)) {
    Square(cdx, cdxcdx1, cdxcdx0);
    Square(cdy, cdycdy1, cdycdy0);
    Two_Two_Sum(cdxcdx1, cdxcdx0, cdycdy1, cdycdy0, cc3, cc[2], cc[1], cc[0]);
    cc[3] = cc3;
  }
 
  if (adxtail != 0.0) {
    axtbclen = scale_expansion_zeroelim(4, bc, adxtail, axtbc);
    temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, 2.0 * adx,
                                          temp16a);
 
    axtcclen = scale_expansion_zeroelim(4, cc, adxtail, axtcc);
    temp16blen = scale_expansion_zeroelim(axtcclen, axtcc, bdy, temp16b);
 
    axtbblen = scale_expansion_zeroelim(4, bb, adxtail, axtbb);
    temp16clen = scale_expansion_zeroelim(axtbblen, axtbb, -cdy, temp16c);
 
    temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
                                            temp16blen, temp16b, temp32a);
    temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
                                            temp32alen, temp32a, temp48);
    finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
                                            temp48, finother);
    finswap = finnow; finnow = finother; finother = finswap;
  }
  if (adytail != 0.0) {
    aytbclen = scale_expansion_zeroelim(4, bc, adytail, aytbc);
    temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, 2.0 * ady,
                                          temp16a);
 
    aytbblen = scale_expansion_zeroelim(4, bb, adytail, aytbb);
    temp16blen = scale_expansion_zeroelim(aytbblen, aytbb, cdx, temp16b);
 
    aytcclen = scale_expansion_zeroelim(4, cc, adytail, aytcc);
    temp16clen = scale_expansion_zeroelim(aytcclen, aytcc, -bdx, temp16c);
 
    temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
                                            temp16blen, temp16b, temp32a);
    temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
                                            temp32alen, temp32a, temp48);
    finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
                                            temp48, finother);
    finswap = finnow; finnow = finother; finother = finswap;
  }
  if (bdxtail != 0.0) {
    bxtcalen = scale_expansion_zeroelim(4, ca, bdxtail, bxtca);
    temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, 2.0 * bdx,
                                          temp16a);
 
    bxtaalen = scale_expansion_zeroelim(4, aa, bdxtail, bxtaa);
    temp16blen = scale_expansion_zeroelim(bxtaalen, bxtaa, cdy, temp16b);
 
    bxtcclen = scale_expansion_zeroelim(4, cc, bdxtail, bxtcc);
    temp16clen = scale_expansion_zeroelim(bxtcclen, bxtcc, -ady, temp16c);
 
    temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
                                            temp16blen, temp16b, temp32a);
    temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
                                            temp32alen, temp32a, temp48);
    finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
                                            temp48, finother);
    finswap = finnow; finnow = finother; finother = finswap;
  }
  if (bdytail != 0.0) {
    bytcalen = scale_expansion_zeroelim(4, ca, bdytail, bytca);
    temp16alen = scale_expansion_zeroelim(bytcalen, bytca, 2.0 * bdy,
                                          temp16a);
 
    bytcclen = scale_expansion_zeroelim(4, cc, bdytail, bytcc);
    temp16blen = scale_expansion_zeroelim(bytcclen, bytcc, adx, temp16b);
 
    bytaalen = scale_expansion_zeroelim(4, aa, bdytail, bytaa);
    temp16clen = scale_expansion_zeroelim(bytaalen, bytaa, -cdx, temp16c);
 
    temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
                                            temp16blen, temp16b, temp32a);
    temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
                                            temp32alen, temp32a, temp48);
    finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
                                            temp48, finother);
    finswap = finnow; finnow = finother; finother = finswap;
  }
  if (cdxtail != 0.0) {
    cxtablen = scale_expansion_zeroelim(4, ab, cdxtail, cxtab);
    temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, 2.0 * cdx,
                                          temp16a);
 
    cxtbblen = scale_expansion_zeroelim(4, bb, cdxtail, cxtbb);
    temp16blen = scale_expansion_zeroelim(cxtbblen, cxtbb, ady, temp16b);
 
    cxtaalen = scale_expansion_zeroelim(4, aa, cdxtail, cxtaa);
    temp16clen = scale_expansion_zeroelim(cxtaalen, cxtaa, -bdy, temp16c);
 
    temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
                                            temp16blen, temp16b, temp32a);
    temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
                                            temp32alen, temp32a, temp48);
    finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
                                            temp48, finother);
    finswap = finnow; finnow = finother; finother = finswap;
  }
  if (cdytail != 0.0) {
    cytablen = scale_expansion_zeroelim(4, ab, cdytail, cytab);
    temp16alen = scale_expansion_zeroelim(cytablen, cytab, 2.0 * cdy,
                                          temp16a);
 
    cytaalen = scale_expansion_zeroelim(4, aa, cdytail, cytaa);
    temp16blen = scale_expansion_zeroelim(cytaalen, cytaa, bdx, temp16b);
 
    cytbblen = scale_expansion_zeroelim(4, bb, cdytail, cytbb);
    temp16clen = scale_expansion_zeroelim(cytbblen, cytbb, -adx, temp16c);
 
    temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
                                            temp16blen, temp16b, temp32a);
    temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
                                            temp32alen, temp32a, temp48);
    finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
                                            temp48, finother);
    finswap = finnow; finnow = finother; finother = finswap;
  }
 
  if ((adxtail != 0.0) || (adytail != 0.0)) {
    if ((bdxtail != 0.0) || (bdytail != 0.0)
        || (cdxtail != 0.0) || (cdytail != 0.0)) {
      Two_Product(bdxtail, cdy, ti1, ti0);
      Two_Product(bdx, cdytail, tj1, tj0);
      Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
      u[3] = u3;
      negate = -bdy;
      Two_Product(cdxtail, negate, ti1, ti0);
      negate = -bdytail;
      Two_Product(cdx, negate, tj1, tj0);
      Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
      v[3] = v3;
      bctlen = fast_expansion_sum_zeroelim(4, u, 4, v, bct);
 
      Two_Product(bdxtail, cdytail, ti1, ti0);
      Two_Product(cdxtail, bdytail, tj1, tj0);
      Two_Two_Diff(ti1, ti0, tj1, tj0, bctt3, bctt[2], bctt[1], bctt[0]);
      bctt[3] = bctt3;
      bcttlen = 4;
    } else {
      bct[0] = 0.0;
      bctlen = 1;
      bctt[0] = 0.0;
      bcttlen = 1;
    }
 
    if (adxtail != 0.0) {
      temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, adxtail, temp16a);
      axtbctlen = scale_expansion_zeroelim(bctlen, bct, adxtail, axtbct);
      temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, 2.0 * adx,
                                            temp32a);
      temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
                                              temp32alen, temp32a, temp48);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
                                              temp48, finother);
      finswap = finnow; finnow = finother; finother = finswap;
      if (bdytail != 0.0) {
        temp8len = scale_expansion_zeroelim(4, cc, adxtail, temp8);
        temp16alen = scale_expansion_zeroelim(temp8len, temp8, bdytail,
                                              temp16a);
        finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
                                                temp16a, finother);
        finswap = finnow; finnow = finother; finother = finswap;
      }
      if (cdytail != 0.0) {
        temp8len = scale_expansion_zeroelim(4, bb, -adxtail, temp8);
        temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail,
                                              temp16a);
        finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
                                                temp16a, finother);
        finswap = finnow; finnow = finother; finother = finswap;
      }
 
      temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, adxtail,
                                            temp32a);
      axtbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adxtail, axtbctt);
      temp16alen = scale_expansion_zeroelim(axtbcttlen, axtbctt, 2.0 * adx,
                                            temp16a);
      temp16blen = scale_expansion_zeroelim(axtbcttlen, axtbctt, adxtail,
                                            temp16b);
      temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
                                              temp16blen, temp16b, temp32b);
      temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
                                              temp32blen, temp32b, temp64);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
                                              temp64, finother);
      finswap = finnow; finnow = finother; finother = finswap;
    }
    if (adytail != 0.0) {
      temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, adytail, temp16a);
      aytbctlen = scale_expansion_zeroelim(bctlen, bct, adytail, aytbct);
      temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, 2.0 * ady,
                                            temp32a);
      temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
                                              temp32alen, temp32a, temp48);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
                                              temp48, finother);
      finswap = finnow; finnow = finother; finother = finswap;
 
 
      temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, adytail,
                                            temp32a);
      aytbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adytail, aytbctt);
      temp16alen = scale_expansion_zeroelim(aytbcttlen, aytbctt, 2.0 * ady,
                                            temp16a);
      temp16blen = scale_expansion_zeroelim(aytbcttlen, aytbctt, adytail,
                                            temp16b);
      temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
                                              temp16blen, temp16b, temp32b);
      temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
                                              temp32blen, temp32b, temp64);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
                                              temp64, finother);
      finswap = finnow; finnow = finother; finother = finswap;
    }
  }
  if ((bdxtail != 0.0) || (bdytail != 0.0)) {
    if ((cdxtail != 0.0) || (cdytail != 0.0)
        || (adxtail != 0.0) || (adytail != 0.0)) {
      Two_Product(cdxtail, ady, ti1, ti0);
      Two_Product(cdx, adytail, tj1, tj0);
      Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
      u[3] = u3;
      negate = -cdy;
      Two_Product(adxtail, negate, ti1, ti0);
      negate = -cdytail;
      Two_Product(adx, negate, tj1, tj0);
      Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
      v[3] = v3;
      catlen = fast_expansion_sum_zeroelim(4, u, 4, v, cat);
 
      Two_Product(cdxtail, adytail, ti1, ti0);
      Two_Product(adxtail, cdytail, tj1, tj0);
      Two_Two_Diff(ti1, ti0, tj1, tj0, catt3, catt[2], catt[1], catt[0]);
      catt[3] = catt3;
      cattlen = 4;
    } else {
      cat[0] = 0.0;
      catlen = 1;
      catt[0] = 0.0;
      cattlen = 1;
    }
 
    if (bdxtail != 0.0) {
      temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, bdxtail, temp16a);
      bxtcatlen = scale_expansion_zeroelim(catlen, cat, bdxtail, bxtcat);
      temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, 2.0 * bdx,
                                            temp32a);
      temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
                                              temp32alen, temp32a, temp48);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
                                              temp48, finother);
      finswap = finnow; finnow = finother; finother = finswap;
      if (cdytail != 0.0) {
        temp8len = scale_expansion_zeroelim(4, aa, bdxtail, temp8);
        temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail,
                                              temp16a);
        finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
                                                temp16a, finother);
        finswap = finnow; finnow = finother; finother = finswap;
      }
      if (adytail != 0.0) {
        temp8len = scale_expansion_zeroelim(4, cc, -bdxtail, temp8);
        temp16alen = scale_expansion_zeroelim(temp8len, temp8, adytail,
                                              temp16a);
        finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
                                                temp16a, finother);
        finswap = finnow; finnow = finother; finother = finswap;
      }
 
      temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, bdxtail,
                                            temp32a);
      bxtcattlen = scale_expansion_zeroelim(cattlen, catt, bdxtail, bxtcatt);
      temp16alen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, 2.0 * bdx,
                                            temp16a);
      temp16blen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, bdxtail,
                                            temp16b);
      temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
                                              temp16blen, temp16b, temp32b);
      temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
                                              temp32blen, temp32b, temp64);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
                                              temp64, finother);
      finswap = finnow; finnow = finother; finother = finswap;
    }
    if (bdytail != 0.0) {
      temp16alen = scale_expansion_zeroelim(bytcalen, bytca, bdytail, temp16a);
      bytcatlen = scale_expansion_zeroelim(catlen, cat, bdytail, bytcat);
      temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, 2.0 * bdy,
                                            temp32a);
      temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
                                              temp32alen, temp32a, temp48);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
                                              temp48, finother);
      finswap = finnow; finnow = finother; finother = finswap;
 
 
      temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, bdytail,
                                            temp32a);
      bytcattlen = scale_expansion_zeroelim(cattlen, catt, bdytail, bytcatt);
      temp16alen = scale_expansion_zeroelim(bytcattlen, bytcatt, 2.0 * bdy,
                                            temp16a);
      temp16blen = scale_expansion_zeroelim(bytcattlen, bytcatt, bdytail,
                                            temp16b);
      temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
                                              temp16blen, temp16b, temp32b);
      temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
                                              temp32blen, temp32b, temp64);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
                                              temp64, finother);
      finswap = finnow; finnow = finother; finother = finswap;
    }
  }
  if ((cdxtail != 0.0) || (cdytail != 0.0)) {
    if ((adxtail != 0.0) || (adytail != 0.0)
        || (bdxtail != 0.0) || (bdytail != 0.0)) {
      Two_Product(adxtail, bdy, ti1, ti0);
      Two_Product(adx, bdytail, tj1, tj0);
      Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
      u[3] = u3;
      negate = -ady;
      Two_Product(bdxtail, negate, ti1, ti0);
      negate = -adytail;
      Two_Product(bdx, negate, tj1, tj0);
      Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
      v[3] = v3;
      abtlen = fast_expansion_sum_zeroelim(4, u, 4, v, abt);
 
      Two_Product(adxtail, bdytail, ti1, ti0);
      Two_Product(bdxtail, adytail, tj1, tj0);
      Two_Two_Diff(ti1, ti0, tj1, tj0, abtt3, abtt[2], abtt[1], abtt[0]);
      abtt[3] = abtt3;
      abttlen = 4;
    } else {
      abt[0] = 0.0;
      abtlen = 1;
      abtt[0] = 0.0;
      abttlen = 1;
    }
 
    if (cdxtail != 0.0) {
      temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, cdxtail, temp16a);
      cxtabtlen = scale_expansion_zeroelim(abtlen, abt, cdxtail, cxtabt);
      temp32alen = scale_expansion_zeroelim(cxtabtlen, cxtabt, 2.0 * cdx,
                                            temp32a);
      temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
                                              temp32alen, temp32a, temp48);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
                                              temp48, finother);
      finswap = finnow; finnow = finother; finother = finswap;
      if (adytail != 0.0) {
        temp8len = scale_expansion_zeroelim(4, bb, cdxtail, temp8);
        temp16alen = scale_expansion_zeroelim(temp8len, temp8, adytail,
                                              temp16a);
        finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
                                                temp16a, finother);
        finswap = finnow; finnow = finother; finother = finswap;
      }
      if (bdytail != 0.0) {
        temp8len = scale_expansion_zeroelim(4, aa, -cdxtail, temp8);
        temp16alen = scale_expansion_zeroelim(temp8len, temp8, bdytail,
                                              temp16a);
        finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
                                                temp16a, finother);
        finswap = finnow; finnow = finother; finother = finswap;
      }
 
      temp32alen = scale_expansion_zeroelim(cxtabtlen, cxtabt, cdxtail,
                                            temp32a);
      cxtabttlen = scale_expansion_zeroelim(abttlen, abtt, cdxtail, cxtabtt);
      temp16alen = scale_expansion_zeroelim(cxtabttlen, cxtabtt, 2.0 * cdx,
                                            temp16a);
      temp16blen = scale_expansion_zeroelim(cxtabttlen, cxtabtt, cdxtail,
                                            temp16b);
      temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
                                              temp16blen, temp16b, temp32b);
      temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
                                              temp32blen, temp32b, temp64);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
                                              temp64, finother);
      finswap = finnow; finnow = finother; finother = finswap;
    }
    if (cdytail != 0.0) {
      temp16alen = scale_expansion_zeroelim(cytablen, cytab, cdytail, temp16a);
      cytabtlen = scale_expansion_zeroelim(abtlen, abt, cdytail, cytabt);
      temp32alen = scale_expansion_zeroelim(cytabtlen, cytabt, 2.0 * cdy,
                                            temp32a);
      temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
                                              temp32alen, temp32a, temp48);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
                                              temp48, finother);
      finswap = finnow; finnow = finother; finother = finswap;
 
 
      temp32alen = scale_expansion_zeroelim(cytabtlen, cytabt, cdytail,
                                            temp32a);
      cytabttlen = scale_expansion_zeroelim(abttlen, abtt, cdytail, cytabtt);
      temp16alen = scale_expansion_zeroelim(cytabttlen, cytabtt, 2.0 * cdy,
                                            temp16a);
      temp16blen = scale_expansion_zeroelim(cytabttlen, cytabtt, cdytail,
                                            temp16b);
      temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
                                              temp16blen, temp16b, temp32b);
      temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
                                              temp32blen, temp32b, temp64);
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
                                              temp64, finother);
      finswap = finnow; finnow = finother; finother = finswap;
    }
  }
 
  return finnow[finlength - 1];
}
 
float incircle(struct mesh *m, struct behavior *b,
              vertex pa, vertex pb, vertex pc, vertex pd)
{
  float adx, bdx, cdx, ady, bdy, cdy;
  float bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady;
  float alift, blift, clift;
  float det;
  float permanent, errbound;
 
  m->incirclecount++;
 
  adx = pa[0] - pd[0];
  bdx = pb[0] - pd[0];
  cdx = pc[0] - pd[0];
  ady = pa[1] - pd[1];
  bdy = pb[1] - pd[1];
  cdy = pc[1] - pd[1];
 
  bdxcdy = bdx * cdy;
  cdxbdy = cdx * bdy;
  alift = adx * adx + ady * ady;
 
  cdxady = cdx * ady;
  adxcdy = adx * cdy;
  blift = bdx * bdx + bdy * bdy;
 
  adxbdy = adx * bdy;
  bdxady = bdx * ady;
  clift = cdx * cdx + cdy * cdy;
 
  det = alift * (bdxcdy - cdxbdy)
      + blift * (cdxady - adxcdy)
      + clift * (adxbdy - bdxady);
 
  if (b->noexact) {
    return det;
  }
 
  permanent = (Absolute(bdxcdy) + Absolute(cdxbdy)) * alift
            + (Absolute(cdxady) + Absolute(adxcdy)) * blift
            + (Absolute(adxbdy) + Absolute(bdxady)) * clift;
  errbound = iccerrboundA * permanent;
  if ((det > errbound) || (-det > errbound)) {
    return det;
  }
 
  return incircleadapt(pa, pb, pc, pd, permanent);
}
 
/*****************************************************************************/
/*                                                                           */
/*  orient3d()   Return a positive value if the point pd lies below the      */
/*               plane passing through pa, pb, and pc; "below" is defined so */
/*               that pa, pb, and pc appear in counterclockwise order when   */
/*               viewed from above the plane.  Returns a negative value if   */
/*               pd lies above the plane.  Returns zero if the points are    */
/*               coplanar.  The result is also a rough approximation of six  */
/*               times the signed volume of the tetrahedron defined by the   */
/*               four points.                                                */
/*                                                                           */
/*  Uses exact arithmetic if necessary to ensure a correct answer.  The      */
/*  result returned is the determinant of a matrix.  This determinant is     */
/*  computed adaptively, in the sense that exact arithmetic is used only to  */
/*  the degree it is needed to ensure that the returned value has the        */
/*  correct sign.  Hence, this function is usually quite fast, but will run  */
/*  more slowly when the input points are coplanar or nearly so.             */
/*                                                                           */
/*  See my Robust Predicates paper for details.                              */
/*                                                                           */
/*****************************************************************************/
 
float orient3dadapt(vertex pa, vertex pb, vertex pc, vertex pd,
                   float aheight, float bheight, float cheight, float dheight,
                   float permanent)
{
  float adx, bdx, cdx, ady, bdy, cdy, adheight, bdheight, cdheight;
  float det, errbound;
 
  float bdxcdy1, cdxbdy1, cdxady1, adxcdy1, adxbdy1, bdxady1;
  float bdxcdy0, cdxbdy0, cdxady0, adxcdy0, adxbdy0, bdxady0;
  float bc[4], ca[4], ab[4];
  float bc3, ca3, ab3;
  float adet[8], bdet[8], cdet[8];
  int alen, blen, clen;
  float abdet[16];
  int ablen;
  float *finnow, *finother, *finswap;
  float fin1[192], fin2[192];
  int finlength;
 
  float adxtail, bdxtail, cdxtail;
  float adytail, bdytail, cdytail;
  float adheighttail, bdheighttail, cdheighttail;
  float at_blarge, at_clarge;
  float bt_clarge, bt_alarge;
  float ct_alarge, ct_blarge;
  float at_b[4], at_c[4], bt_c[4], bt_a[4], ct_a[4], ct_b[4];
  int at_blen, at_clen, bt_clen, bt_alen, ct_alen, ct_blen;
  float bdxt_cdy1, cdxt_bdy1, cdxt_ady1;
  float adxt_cdy1, adxt_bdy1, bdxt_ady1;
  float bdxt_cdy0, cdxt_bdy0, cdxt_ady0;
  float adxt_cdy0, adxt_bdy0, bdxt_ady0;
  float bdyt_cdx1, cdyt_bdx1, cdyt_adx1;
  float adyt_cdx1, adyt_bdx1, bdyt_adx1;
  float bdyt_cdx0, cdyt_bdx0, cdyt_adx0;
  float adyt_cdx0, adyt_bdx0, bdyt_adx0;
  float bct[8], cat[8], abt[8];
  int bctlen, catlen, abtlen;
  float bdxt_cdyt1, cdxt_bdyt1, cdxt_adyt1;
  float adxt_cdyt1, adxt_bdyt1, bdxt_adyt1;
  float bdxt_cdyt0, cdxt_bdyt0, cdxt_adyt0;
  float adxt_cdyt0, adxt_bdyt0, bdxt_adyt0;
  float u[4], v[12], w[16];
  float u3;
  int vlength, wlength;
  float negate;
 
  float bvirt;
  float avirt, bround, around;
  float c;
  float abig;
  float ahi, alo, bhi, blo;
  float err1, err2, err3;
  float _i, _j, _k;
  float _0;
 
  adx = (float) (pa[0] - pd[0]);
  bdx = (float) (pb[0] - pd[0]);
  cdx = (float) (pc[0] - pd[0]);
  ady = (float) (pa[1] - pd[1]);
  bdy = (float) (pb[1] - pd[1]);
  cdy = (float) (pc[1] - pd[1]);
  adheight = (float) (aheight - dheight);
  bdheight = (float) (bheight - dheight);
  cdheight = (float) (cheight - dheight);
 
  Two_Product(bdx, cdy, bdxcdy1, bdxcdy0);
  Two_Product(cdx, bdy, cdxbdy1, cdxbdy0);
  Two_Two_Diff(bdxcdy1, bdxcdy0, cdxbdy1, cdxbdy0, bc3, bc[2], bc[1], bc[0]);
  bc[3] = bc3;
  alen = scale_expansion_zeroelim(4, bc, adheight, adet);
 
  Two_Product(cdx, ady, cdxady1, cdxady0);
  Two_Product(adx, cdy, adxcdy1, adxcdy0);
  Two_Two_Diff(cdxady1, cdxady0, adxcdy1, adxcdy0, ca3, ca[2], ca[1], ca[0]);
  ca[3] = ca3;
  blen = scale_expansion_zeroelim(4, ca, bdheight, bdet);
 
  Two_Product(adx, bdy, adxbdy1, adxbdy0);
  Two_Product(bdx, ady, bdxady1, bdxady0);
  Two_Two_Diff(adxbdy1, adxbdy0, bdxady1, bdxady0, ab3, ab[2], ab[1], ab[0]);
  ab[3] = ab3;
  clen = scale_expansion_zeroelim(4, ab, cdheight, cdet);
 
  ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
  finlength = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, fin1);
 
  det = estimate(finlength, fin1);
  errbound = o3derrboundB * permanent;
  if ((det >= errbound) || (-det >= errbound)) {
    return det;
  }
 
  Two_Diff_Tail(pa[0], pd[0], adx, adxtail);
  Two_Diff_Tail(pb[0], pd[0], bdx, bdxtail);
  Two_Diff_Tail(pc[0], pd[0], cdx, cdxtail);
  Two_Diff_Tail(pa[1], pd[1], ady, adytail);
  Two_Diff_Tail(pb[1], pd[1], bdy, bdytail);
  Two_Diff_Tail(pc[1], pd[1], cdy, cdytail);
  Two_Diff_Tail(aheight, dheight, adheight, adheighttail);
  Two_Diff_Tail(bheight, dheight, bdheight, bdheighttail);
  Two_Diff_Tail(cheight, dheight, cdheight, cdheighttail);
 
  if ((adxtail == 0.0) && (bdxtail == 0.0) && (cdxtail == 0.0) &&
      (adytail == 0.0) && (bdytail == 0.0) && (cdytail == 0.0) &&
      (adheighttail == 0.0) &&
      (bdheighttail == 0.0) &&
      (cdheighttail == 0.0)) {
    return det;
  }
 
  errbound = o3derrboundC * permanent + resulterrbound * Absolute(det);
  det += (adheight * ((bdx * cdytail + cdy * bdxtail) -
                      (bdy * cdxtail + cdx * bdytail)) +
          adheighttail * (bdx * cdy - bdy * cdx)) +
         (bdheight * ((cdx * adytail + ady * cdxtail) -
                      (cdy * adxtail + adx * cdytail)) +
          bdheighttail * (cdx * ady - cdy * adx)) +
         (cdheight * ((adx * bdytail + bdy * adxtail) -
                      (ady * bdxtail + bdx * adytail)) +
          cdheighttail * (adx * bdy - ady * bdx));
  if ((det >= errbound) || (-det >= errbound)) {
    return det;
  }
 
  finnow = fin1;
  finother = fin2;
 
  if (adxtail == 0.0) {
    if (adytail == 0.0) {
      at_b[0] = 0.0;
      at_blen = 1;
      at_c[0] = 0.0;
      at_clen = 1;
    } else {
      negate = -adytail;
      Two_Product(negate, bdx, at_blarge, at_b[0]);
      at_b[1] = at_blarge;
      at_blen = 2;
      Two_Product(adytail, cdx, at_clarge, at_c[0]);
      at_c[1] = at_clarge;
      at_clen = 2;
    }
  } else {
    if (adytail == 0.0) {
      Two_Product(adxtail, bdy, at_blarge, at_b[0]);
      at_b[1] = at_blarge;
      at_blen = 2;
      negate = -adxtail;
      Two_Product(negate, cdy, at_clarge, at_c[0]);
      at_c[1] = at_clarge;
      at_clen = 2;
    } else {
      Two_Product(adxtail, bdy, adxt_bdy1, adxt_bdy0);
      Two_Product(adytail, bdx, adyt_bdx1, adyt_bdx0);
      Two_Two_Diff(adxt_bdy1, adxt_bdy0, adyt_bdx1, adyt_bdx0,
                   at_blarge, at_b[2], at_b[1], at_b[0]);
      at_b[3] = at_blarge;
      at_blen = 4;
      Two_Product(adytail, cdx, adyt_cdx1, adyt_cdx0);
      Two_Product(adxtail, cdy, adxt_cdy1, adxt_cdy0);
      Two_Two_Diff(adyt_cdx1, adyt_cdx0, adxt_cdy1, adxt_cdy0,
                   at_clarge, at_c[2], at_c[1], at_c[0]);
      at_c[3] = at_clarge;
      at_clen = 4;
    }
  }
  if (bdxtail == 0.0) {
    if (bdytail == 0.0) {
      bt_c[0] = 0.0;
      bt_clen = 1;
      bt_a[0] = 0.0;
      bt_alen = 1;
    } else {
      negate = -bdytail;
      Two_Product(negate, cdx, bt_clarge, bt_c[0]);
      bt_c[1] = bt_clarge;
      bt_clen = 2;
      Two_Product(bdytail, adx, bt_alarge, bt_a[0]);
      bt_a[1] = bt_alarge;
      bt_alen = 2;
    }
  } else {
    if (bdytail == 0.0) {
      Two_Product(bdxtail, cdy, bt_clarge, bt_c[0]);
      bt_c[1] = bt_clarge;
      bt_clen = 2;
      negate = -bdxtail;
      Two_Product(negate, ady, bt_alarge, bt_a[0]);
      bt_a[1] = bt_alarge;
      bt_alen = 2;
    } else {
      Two_Product(bdxtail, cdy, bdxt_cdy1, bdxt_cdy0);
      Two_Product(bdytail, cdx, bdyt_cdx1, bdyt_cdx0);
      Two_Two_Diff(bdxt_cdy1, bdxt_cdy0, bdyt_cdx1, bdyt_cdx0,
                   bt_clarge, bt_c[2], bt_c[1], bt_c[0]);
      bt_c[3] = bt_clarge;
      bt_clen = 4;
      Two_Product(bdytail, adx, bdyt_adx1, bdyt_adx0);
      Two_Product(bdxtail, ady, bdxt_ady1, bdxt_ady0);
      Two_Two_Diff(bdyt_adx1, bdyt_adx0, bdxt_ady1, bdxt_ady0,
                  bt_alarge, bt_a[2], bt_a[1], bt_a[0]);
      bt_a[3] = bt_alarge;
      bt_alen = 4;
    }
  }
  if (cdxtail == 0.0) {
    if (cdytail == 0.0) {
      ct_a[0] = 0.0;
      ct_alen = 1;
      ct_b[0] = 0.0;
      ct_blen = 1;
    } else {
      negate = -cdytail;
      Two_Product(negate, adx, ct_alarge, ct_a[0]);
      ct_a[1] = ct_alarge;
      ct_alen = 2;
      Two_Product(cdytail, bdx, ct_blarge, ct_b[0]);
      ct_b[1] = ct_blarge;
      ct_blen = 2;
    }
  } else {
    if (cdytail == 0.0) {
      Two_Product(cdxtail, ady, ct_alarge, ct_a[0]);
      ct_a[1] = ct_alarge;
      ct_alen = 2;
      negate = -cdxtail;
      Two_Product(negate, bdy, ct_blarge, ct_b[0]);
      ct_b[1] = ct_blarge;
      ct_blen = 2;
    } else {
      Two_Product(cdxtail, ady, cdxt_ady1, cdxt_ady0);
      Two_Product(cdytail, adx, cdyt_adx1, cdyt_adx0);
      Two_Two_Diff(cdxt_ady1, cdxt_ady0, cdyt_adx1, cdyt_adx0,
                   ct_alarge, ct_a[2], ct_a[1], ct_a[0]);
      ct_a[3] = ct_alarge;
      ct_alen = 4;
      Two_Product(cdytail, bdx, cdyt_bdx1, cdyt_bdx0);
      Two_Product(cdxtail, bdy, cdxt_bdy1, cdxt_bdy0);
      Two_Two_Diff(cdyt_bdx1, cdyt_bdx0, cdxt_bdy1, cdxt_bdy0,
                   ct_blarge, ct_b[2], ct_b[1], ct_b[0]);
      ct_b[3] = ct_blarge;
      ct_blen = 4;
    }
  }
 
  bctlen = fast_expansion_sum_zeroelim(bt_clen, bt_c, ct_blen, ct_b, bct);
  wlength = scale_expansion_zeroelim(bctlen, bct, adheight, w);
  finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
                                          finother);
  finswap = finnow; finnow = finother; finother = finswap;
 
  catlen = fast_expansion_sum_zeroelim(ct_alen, ct_a, at_clen, at_c, cat);
  wlength = scale_expansion_zeroelim(catlen, cat, bdheight, w);
  finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
                                          finother);
  finswap = finnow; finnow = finother; finother = finswap;
 
  abtlen = fast_expansion_sum_zeroelim(at_blen, at_b, bt_alen, bt_a, abt);
  wlength = scale_expansion_zeroelim(abtlen, abt, cdheight, w);
  finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
                                          finother);
  finswap = finnow; finnow = finother; finother = finswap;
 
  if (adheighttail != 0.0) {
    vlength = scale_expansion_zeroelim(4, bc, adheighttail, v);
    finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v,
                                            finother);
    finswap = finnow; finnow = finother; finother = finswap;
  }
  if (bdheighttail != 0.0) {
    vlength = scale_expansion_zeroelim(4, ca, bdheighttail, v);
    finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v,
                                            finother);
    finswap = finnow; finnow = finother; finother = finswap;
  }
  if (cdheighttail != 0.0) {
    vlength = scale_expansion_zeroelim(4, ab, cdheighttail, v);
    finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v,
                                            finother);
    finswap = finnow; finnow = finother; finother = finswap;
  }
 
  if (adxtail != 0.0) {
    if (bdytail != 0.0) {
      Two_Product(adxtail, bdytail, adxt_bdyt1, adxt_bdyt0);
      Two_One_Product(adxt_bdyt1, adxt_bdyt0, cdheight, u3, u[2], u[1], u[0]);
      u[3] = u3;
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
                                              finother);
      finswap = finnow; finnow = finother; finother = finswap;
      if (cdheighttail != 0.0) {
        Two_One_Product(adxt_bdyt1, adxt_bdyt0, cdheighttail,
                        u3, u[2], u[1], u[0]);
        u[3] = u3;
        finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
                                                finother);
        finswap = finnow; finnow = finother; finother = finswap;
      }
    }
    if (cdytail != 0.0) {
      negate = -adxtail;
      Two_Product(negate, cdytail, adxt_cdyt1, adxt_cdyt0);
      Two_One_Product(adxt_cdyt1, adxt_cdyt0, bdheight, u3, u[2], u[1], u[0]);
      u[3] = u3;
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
                                              finother);
      finswap = finnow; finnow = finother; finother = finswap;
      if (bdheighttail != 0.0) {
        Two_One_Product(adxt_cdyt1, adxt_cdyt0, bdheighttail,
                        u3, u[2], u[1], u[0]);
        u[3] = u3;
        finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
                                                finother);
        finswap = finnow; finnow = finother; finother = finswap;
      }
    }
  }
  if (bdxtail != 0.0) {
    if (cdytail != 0.0) {
      Two_Product(bdxtail, cdytail, bdxt_cdyt1, bdxt_cdyt0);
      Two_One_Product(bdxt_cdyt1, bdxt_cdyt0, adheight, u3, u[2], u[1], u[0]);
      u[3] = u3;
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
                                              finother);
      finswap = finnow; finnow = finother; finother = finswap;
      if (adheighttail != 0.0) {
        Two_One_Product(bdxt_cdyt1, bdxt_cdyt0, adheighttail,
                        u3, u[2], u[1], u[0]);
        u[3] = u3;
        finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
                                                finother);
        finswap = finnow; finnow = finother; finother = finswap;
      }
    }
    if (adytail != 0.0) {
      negate = -bdxtail;
      Two_Product(negate, adytail, bdxt_adyt1, bdxt_adyt0);
      Two_One_Product(bdxt_adyt1, bdxt_adyt0, cdheight, u3, u[2], u[1], u[0]);
      u[3] = u3;
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
                                              finother);
      finswap = finnow; finnow = finother; finother = finswap;
      if (cdheighttail != 0.0) {
        Two_One_Product(bdxt_adyt1, bdxt_adyt0, cdheighttail,
                        u3, u[2], u[1], u[0]);
        u[3] = u3;
        finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
                                                finother);
        finswap = finnow; finnow = finother; finother = finswap;
      }
    }
  }
  if (cdxtail != 0.0) {
    if (adytail != 0.0) {
      Two_Product(cdxtail, adytail, cdxt_adyt1, cdxt_adyt0);
      Two_One_Product(cdxt_adyt1, cdxt_adyt0, bdheight, u3, u[2], u[1], u[0]);
      u[3] = u3;
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
                                              finother);
      finswap = finnow; finnow = finother; finother = finswap;
      if (bdheighttail != 0.0) {
        Two_One_Product(cdxt_adyt1, cdxt_adyt0, bdheighttail,
                        u3, u[2], u[1], u[0]);
        u[3] = u3;
        finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
                                                finother);
        finswap = finnow; finnow = finother; finother = finswap;
      }
    }
    if (bdytail != 0.0) {
      negate = -cdxtail;
      Two_Product(negate, bdytail, cdxt_bdyt1, cdxt_bdyt0);
      Two_One_Product(cdxt_bdyt1, cdxt_bdyt0, adheight, u3, u[2], u[1], u[0]);
      u[3] = u3;
      finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
                                              finother);
      finswap = finnow; finnow = finother; finother = finswap;
      if (adheighttail != 0.0) {
        Two_One_Product(cdxt_bdyt1, cdxt_bdyt0, adheighttail,
                        u3, u[2], u[1], u[0]);
        u[3] = u3;
        finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
                                                finother);
        finswap = finnow; finnow = finother; finother = finswap;
      }
    }
  }
 
  if (adheighttail != 0.0) {
    wlength = scale_expansion_zeroelim(bctlen, bct, adheighttail, w);
    finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
                                            finother);
    finswap = finnow; finnow = finother; finother = finswap;
  }
  if (bdheighttail != 0.0) {
    wlength = scale_expansion_zeroelim(catlen, cat, bdheighttail, w);
    finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
                                            finother);
    finswap = finnow; finnow = finother; finother = finswap;
  }
  if (cdheighttail != 0.0) {
    wlength = scale_expansion_zeroelim(abtlen, abt, cdheighttail, w);
    finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
                                            finother);
    finswap = finnow; finnow = finother; finother = finswap;
  }
 
  return finnow[finlength - 1];
}
 
float orient3d(struct mesh *m, struct behavior *b,
              vertex pa, vertex pb, vertex pc, vertex pd,
              float aheight, float bheight, float cheight, float dheight)
{
  float adx, bdx, cdx, ady, bdy, cdy, adheight, bdheight, cdheight;
  float bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady;
  float det;
  float permanent, errbound;
 
  m->orient3dcount++;
 
  adx = pa[0] - pd[0];
  bdx = pb[0] - pd[0];
  cdx = pc[0] - pd[0];
  ady = pa[1] - pd[1];
  bdy = pb[1] - pd[1];
  cdy = pc[1] - pd[1];
  adheight = aheight - dheight;
  bdheight = bheight - dheight;
  cdheight = cheight - dheight;
 
  bdxcdy = bdx * cdy;
  cdxbdy = cdx * bdy;
 
  cdxady = cdx * ady;
  adxcdy = adx * cdy;
 
  adxbdy = adx * bdy;
  bdxady = bdx * ady;
 
  det = adheight * (bdxcdy - cdxbdy) 
      + bdheight * (cdxady - adxcdy)
      + cdheight * (adxbdy - bdxady);
 
  if (b->noexact) {
    return det;
  }
 
  permanent = (Absolute(bdxcdy) + Absolute(cdxbdy)) * Absolute(adheight)
            + (Absolute(cdxady) + Absolute(adxcdy)) * Absolute(bdheight)
            + (Absolute(adxbdy) + Absolute(bdxady)) * Absolute(cdheight);
  errbound = o3derrboundA * permanent;
  if ((det > errbound) || (-det > errbound)) {
    return det;
  }
 
  return orient3dadapt(pa, pb, pc, pd, aheight, bheight, cheight, dheight,
                       permanent);
}
 
/*****************************************************************************/
/*                                                                           */
/*  nonregular()   Return a positive value if the point pd is incompatible   */
/*                 with the circle or plane passing through pa, pb, and pc   */
/*                 (meaning that pd is inside the circle or below the        */
/*                 plane); a negative value if it is compatible; and zero if */
/*                 the four points are cocircular/coplanar.  The points pa,  */
/*                 pb, and pc must be in counterclockwise order, or the sign */
/*                 of the result will be reversed.                           */
/*                                                                           */
/*  If the -w switch is used, the points are lifted onto the parabolic       */
/*  lifting map, then they are dropped according to their weights, then the  */
/*  3D orientation test is applied.  If the -W switch is used, the points'   */
/*  heights are already provided, so the 3D orientation test is applied      */
/*  directly.  If neither switch is used, the incircle test is applied.      */
/*                                                                           */
/*****************************************************************************/
 
float nonregular(struct mesh *m, struct behavior *b,
                vertex pa, vertex pb, vertex pc, vertex pd)
{
  if (b->weighted == 0) {
    return incircle(m, b, pa, pb, pc, pd);
  } else if (b->weighted == 1) {
    return orient3d(m, b, pa, pb, pc, pd,
                    pa[0] * pa[0] + pa[1] * pa[1] - pa[2],
                    pb[0] * pb[0] + pb[1] * pb[1] - pb[2],
                    pc[0] * pc[0] + pc[1] * pc[1] - pc[2],
                    pd[0] * pd[0] + pd[1] * pd[1] - pd[2]);
  } else {
    return orient3d(m, b, pa, pb, pc, pd, pa[2], pb[2], pc[2], pd[2]);
  }
}
 
/*****************************************************************************/
/*                                                                           */
/*  findcircumcenter()   Find the circumcenter of a triangle.                */
/*                                                                           */
/*  The result is returned both in terms of x-y coordinates and xi-eta       */
/*  (barycentric) coordinates.  The xi-eta coordinate system is defined in   */
/*  terms of the triangle:  the origin of the triangle is the origin of the  */
/*  coordinate system; the destination of the triangle is one unit along the */
/*  xi axis; and the apex of the triangle is one unit along the eta axis.    */
/*  This procedure also returns the square of the length of the triangle's   */
/*  shortest edge.                                                           */
/*                                                                           */
/*****************************************************************************/
 
void findcircumcenter(struct mesh *m, struct behavior *b,
                      vertex torg, vertex tdest, vertex tapex,
                      vertex circumcenter, float *xi, float *eta, int offcenter)
{
  float xdo, ydo, xao, yao;
  float dodist, aodist, dadist;
  float denominator;
  float dx, dy, dxoff, dyoff;
 
  m->circumcentercount++;
 
  /* Compute the circumcenter of the triangle. */
  xdo = tdest[0] - torg[0];
  ydo = tdest[1] - torg[1];
  xao = tapex[0] - torg[0];
  yao = tapex[1] - torg[1];
  dodist = xdo * xdo + ydo * ydo;
  aodist = xao * xao + yao * yao;
  dadist = (tdest[0] - tapex[0]) * (tdest[0] - tapex[0]) +
           (tdest[1] - tapex[1]) * (tdest[1] - tapex[1]);
  if (b->noexact) {
    denominator = 0.5 / (xdo * yao - xao * ydo);
  } else {
    /* Use the counterclockwise() routine to ensure a positive (and */
    /*   reasonably accurate) result, avoiding any possibility of   */
    /*   division by zero.                                          */
    denominator = 0.5 / counterclockwise(m, b, tdest, tapex, torg);
    /* Don't count the above as an orientation test. */
    m->counterclockcount--;
  }
  dx = (yao * dodist - ydo * aodist) * denominator;
  dy = (xdo * aodist - xao * dodist) * denominator;
 
  /* Find the (squared) length of the triangle's shortest edge.  This   */
  /*   serves as a conservative estimate of the insertion radius of the */
  /*   circumcenter's parent.  The estimate is used to ensure that      */
  /*   the algorithm terminates even if very small angles appear in     */
  /*   the input PSLG.                                                  */
  if ((dodist < aodist) && (dodist < dadist)) {
    if (offcenter && (b->offconstant > 0.0)) {
      /* Find the position of the off-center, as described by Alper Ungor. */
      dxoff = 0.5 * xdo - b->offconstant * ydo;
      dyoff = 0.5 * ydo + b->offconstant * xdo;
      /* If the off-center is closer to the origin than the */
      /*   circumcenter, use the off-center instead.        */
      if (dxoff * dxoff + dyoff * dyoff < dx * dx + dy * dy) {
        dx = dxoff;
        dy = dyoff;
      }
    }
  } else if (aodist < dadist) {
    if (offcenter && (b->offconstant > 0.0)) {
      dxoff = 0.5 * xao + b->offconstant * yao;
      dyoff = 0.5 * yao - b->offconstant * xao;
      /* If the off-center is closer to the origin than the */
      /*   circumcenter, use the off-center instead.        */
      if (dxoff * dxoff + dyoff * dyoff < dx * dx + dy * dy) {
        dx = dxoff;
        dy = dyoff;
      }
    }
  } else {
    if (offcenter && (b->offconstant > 0.0)) {
      dxoff = 0.5 * (tapex[0] - tdest[0]) -
              b->offconstant * (tapex[1] - tdest[1]);
      dyoff = 0.5 * (tapex[1] - tdest[1]) +
              b->offconstant * (tapex[0] - tdest[0]);
      /* If the off-center is closer to the destination than the */
      /*   circumcenter, use the off-center instead.             */
      if (dxoff * dxoff + dyoff * dyoff <
          (dx - xdo) * (dx - xdo) + (dy - ydo) * (dy - ydo)) {
        dx = xdo + dxoff;
        dy = ydo + dyoff;
      }
    }
  }
 
  circumcenter[0] = torg[0] + dx;
  circumcenter[1] = torg[1] + dy;
 
  /* To interpolate vertex attributes for the new vertex inserted at */
  /*   the circumcenter, define a coordinate system with a xi-axis,  */
  /*   directed from the triangle's origin to its destination, and   */
  /*   an eta-axis, directed from its origin to its apex.            */
  /*   Calculate the xi and eta coordinates of the circumcenter.     */
  *xi = (yao * dx - xao * dy) * (2.0 * denominator);
  *eta = (xdo * dy - ydo * dx) * (2.0 * denominator);
}
 
/********* Geometric primitives end here                             *********/
 
/*****************************************************************************/
/*                                                                           */
/*  triangleinit()   Initialize some variables.                              */
/*                                                                           */
/*****************************************************************************/
 
void triangleinit(struct mesh *m)
{
  poolzero(&m->vertices);
  poolzero(&m->triangles);
  poolzero(&m->subsegs);
  poolzero(&m->viri);
  poolzero(&m->badsubsegs);
  poolzero(&m->badtriangles);
  poolzero(&m->flipstackers);
  poolzero(&m->splaynodes);
 
  m->recenttri.tri = (triangle *) NULL; /* No triangle has been visited yet. */
  m->undeads = 0;                       /* No eliminated input vertices yet. */
  m->samples = 1;         /* Point location should take at least one sample. */
  m->checksegments = 0;   /* There are no segments in the triangulation yet. */
  m->checkquality = 0;     /* The quality triangulation stage has not begun. */
  m->incirclecount = m->counterclockcount = m->orient3dcount = 0;
  m->hyperbolacount = m->circletopcount = m->circumcentercount = 0;
  randomseed = 1;
 
  exactinit();                     /* Initialize exact arithmetic constants. */
}
 
/*****************************************************************************/
/*                                                                           */
/*  randomnation()   Generate a random number between 0 and `choices' - 1.   */
/*                                                                           */
/*  This is a simple linear congruential random number generator.  Hence, it */
/*  is a bad random number generator, but good enough for most randomized    */
/*  geometric algorithms.                                                    */
/*                                                                           */
/*****************************************************************************/
 
unsigned long randomnation(unsigned int choices)
{
  randomseed = (randomseed * 1366l + 150889l) % 714025l;
  return randomseed / (714025l / choices + 1);
}
 
/********* Point location routines begin here                        *********/
/*****************************************************************************/
/*                                                                           */
/*  makevertexmap()   Construct a mapping from vertices to triangles to      */
/*                    improve the speed of point location for segment        */
/*                    insertion.                                             */
/*                                                                           */
/*  Traverses all the triangles, and provides each corner of each triangle   */
/*  with a pointer to that triangle.  Of course, pointers will be            */
/*  overwritten by other pointers because (almost) each vertex is a corner   */
/*  of several triangles, but in the end every vertex will point to some     */
/*  triangle that contains it.                                               */
/*                                                                           */
/*****************************************************************************/
 
void makevertexmap(struct mesh *m, struct behavior *b)
{
  struct otri triangleloop;
  vertex triorg;
 
  if (b->verbose) {
    printf("    Constructing mapping from vertices to triangles.\n");
  }
  traversalinit(&m->triangles);
  triangleloop.tri = triangletraverse(m);
  while (triangleloop.tri != (triangle *) NULL) {
    /* Check all three vertices of the triangle. */
    for (triangleloop.orient = 0; triangleloop.orient < 3;
         triangleloop.orient++) {
      org(triangleloop, triorg);
      setvertex2tri(triorg, encode(triangleloop));
    }
    triangleloop.tri = triangletraverse(m);
  }
}
 
/*****************************************************************************/
/*                                                                           */
/*  preciselocate()   Find a triangle or edge containing a given point.      */
/*                                                                           */
/*  Begins its search from `searchtri'.  It is important that `searchtri'    */
/*  be a handle with the property that `searchpoint' is strictly to the left */
/*  of the edge denoted by `searchtri', or is collinear with that edge and   */
/*  does not intersect that edge.  (In particular, `searchpoint' should not  */
/*  be the origin or destination of that edge.)                              */
/*                                                                           */
/*  These conditions are imposed because preciselocate() is normally used in */
/*  one of two situations:                                                   */
/*                                                                           */
/*  (1)  To try to find the location to insert a new point.  Normally, we    */
/*       know an edge that the point is strictly to the left of.  In the     */
/*       incremental Delaunay algorithm, that edge is a bounding box edge.   */
/*       In Ruppert's Delaunay refinement algorithm for quality meshing,     */
/*       that edge is the shortest edge of the triangle whose circumcenter   */
/*       is being inserted.                                                  */
/*                                                                           */
/*  (2)  To try to find an existing point.  In this case, any edge on the    */
/*       convex hull is a good starting edge.  You must screen out the       */
/*       possibility that the vertex sought is an endpoint of the starting   */
/*       edge before you call preciselocate().                               */
/*                                                                           */
/*  On completion, `searchtri' is a triangle that contains `searchpoint'.    */
/*                                                                           */
/*  This implementation differs from that given by Guibas and Stolfi.  It    */
/*  walks from triangle to triangle, crossing an edge only if `searchpoint'  */
/*  is on the other side of the line containing that edge.  After entering   */
/*  a triangle, there are two edges by which one can leave that triangle.    */
/*  If both edges are valid (`searchpoint' is on the other side of both      */
/*  edges), one of the two is chosen by drawing a line perpendicular to      */
/*  the entry edge (whose endpoints are `forg' and `fdest') passing through  */
/*  `fapex'.  Depending on which side of this perpendicular `searchpoint'    */
/*  falls on, an exit edge is chosen.                                        */
/*                                                                           */
/*  This implementation is empirically faster than the Guibas and Stolfi     */
/*  point location routine (which I originally used), which tends to spiral  */
/*  in toward its target.                                                    */
/*                                                                           */
/*  Returns ONVERTEX if the point lies on an existing vertex.  `searchtri'   */
/*  is a handle whose origin is the existing vertex.                         */
/*                                                                           */
/*  Returns ONEDGE if the point lies on a mesh edge.  `searchtri' is a       */
/*  handle whose primary edge is the edge on which the point lies.           */
/*                                                                           */
/*  Returns INTRIANGLE if the point lies strictly within a triangle.         */
/*  `searchtri' is a handle on the triangle that contains the point.         */
/*                                                                           */
/*  Returns OUTSIDE if the point lies outside the mesh.  `searchtri' is a    */
/*  handle whose primary edge the point is to the right of.  This might      */
/*  occur when the circumcenter of a triangle falls just slightly outside    */
/*  the mesh due to floating-point roundoff error.  It also occurs when      */
/*  seeking a hole or region point that a foolish user has placed outside    */
/*  the mesh.                                                                */
/*                                                                           */
/*  If `stopatsubsegment' is nonzero, the search will stop if it tries to    */
/*  walk through a subsegment, and will return OUTSIDE.                      */
/*                                                                           */
/*  WARNING:  This routine is designed for convex triangulations, and will   */
/*  not generally work after the holes and concavities have been carved.     */
/*  However, it can still be used to find the circumcenter of a triangle, as */
/*  long as the search is begun from the triangle in question.               */
/*                                                                           */
/*****************************************************************************/
 
enum locateresult preciselocate(struct mesh *m, struct behavior *b,
                                vertex searchpoint, struct otri *searchtri,
                                int stopatsubsegment)
{
  struct otri backtracktri;
  struct osub checkedge;
  vertex forg, fdest, fapex;
  float orgorient, destorient;
  int moveleft;
  triangle ptr;                         /* Temporary variable used by sym(). */
  subseg sptr;                      /* Temporary variable used by tspivot(). */
 
  if (b->verbose > 2) {
    printf("  Searching for point (%.12g, %.12g).\n",
           searchpoint[0], searchpoint[1]);
  }
  /* Where are we? */
  org(*searchtri, forg);
  dest(*searchtri, fdest);
  apex(*searchtri, fapex);
  while (1) {
    if (b->verbose > 2) {
      printf("    At (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
             forg[0], forg[1], fdest[0], fdest[1], fapex[0], fapex[1]);
    }
    /* Check whether the apex is the point we seek. */
    if ((fapex[0] == searchpoint[0]) && (fapex[1] == searchpoint[1])) {
      lprevself(*searchtri);
      return ONVERTEX;
    }
    /* Does the point lie on the other side of the line defined by the */
    /*   triangle edge opposite the triangle's destination?            */
    destorient = counterclockwise(m, b, forg, fapex, searchpoint);
    /* Does the point lie on the other side of the line defined by the */
    /*   triangle edge opposite the triangle's origin?                 */
    orgorient = counterclockwise(m, b, fapex, fdest, searchpoint);
    if (destorient > 0.0) {
      if (orgorient > 0.0) {
        /* Move left if the inner product of (fapex - searchpoint) and  */
        /*   (fdest - forg) is positive.  This is equivalent to drawing */
        /*   a line perpendicular to the line (forg, fdest) and passing */
        /*   through `fapex', and determining which side of this line   */
        /*   `searchpoint' falls on.                                    */
        moveleft = (fapex[0] - searchpoint[0]) * (fdest[0] - forg[0]) +
                   (fapex[1] - searchpoint[1]) * (fdest[1] - forg[1]) > 0.0;
      } else {
        moveleft = 1;
      }
    } else {
      if (orgorient > 0.0) {
        moveleft = 0;
      } else {
        /* The point we seek must be on the boundary of or inside this */
        /*   triangle.                                                 */
        if (destorient == 0.0) {
          lprevself(*searchtri);
          return ONEDGE;
        }
        if (orgorient == 0.0) {
          lnextself(*searchtri);
          return ONEDGE;
        }
        return INTRIANGLE;
      }
    }
 
    /* Move to another triangle.  Leave a trace `backtracktri' in case */
    /*   floating-point roundoff or some such bogey causes us to walk  */
    /*   off a boundary of the triangulation.                          */
    if (moveleft) {
      lprev(*searchtri, backtracktri);
      fdest = fapex;
    } else {
      lnext(*searchtri, backtracktri);
      forg = fapex;
    }
    sym(backtracktri, *searchtri);
 
    if (m->checksegments && stopatsubsegment) {
      /* Check for walking through a subsegment. */
      tspivot(backtracktri, checkedge);
      if (checkedge.ss != m->dummysub) {
        /* Go back to the last triangle. */
        otricopy(backtracktri, *searchtri);
        return OUTSIDE;
      }
    }
    /* Check for walking right out of the triangulation. */
    if (searchtri->tri == m->dummytri) {
      /* Go back to the last triangle. */
      otricopy(backtracktri, *searchtri);
      return OUTSIDE;
    }
 
    apex(*searchtri, fapex);
  }
}
 
/*****************************************************************************/
/*                                                                           */
/*  locate()   Find a triangle or edge containing a given point.             */
/*                                                                           */
/*  Searching begins from one of:  the input `searchtri', a recently         */
/*  encountered triangle `recenttri', or from a triangle chosen from a       */
/*  random sample.  The choice is made by determining which triangle's       */
/*  origin is closest to the point we are searching for.  Normally,          */
/*  `searchtri' should be a handle on the convex hull of the triangulation.  */
/*                                                                           */
/*  Details on the random sampling method can be found in the Mucke, Saias,  */
/*  and Zhu paper cited in the header of this code.                          */
/*                                                                           */
/*  On completion, `searchtri' is a triangle that contains `searchpoint'.    */
/*                                                                           */
/*  Returns ONVERTEX if the point lies on an existing vertex.  `searchtri'   */
/*  is a handle whose origin is the existing vertex.                         */
/*                                                                           */
/*  Returns ONEDGE if the point lies on a mesh edge.  `searchtri' is a       */
/*  handle whose primary edge is the edge on which the point lies.           */
/*                                                                           */
/*  Returns INTRIANGLE if the point lies strictly within a triangle.         */
/*  `searchtri' is a handle on the triangle that contains the point.         */
/*                                                                           */
/*  Returns OUTSIDE if the point lies outside the mesh.  `searchtri' is a    */
/*  handle whose primary edge the point is to the right of.  This might      */
/*  occur when the circumcenter of a triangle falls just slightly outside    */
/*  the mesh due to floating-point roundoff error.  It also occurs when      */
/*  seeking a hole or region point that a foolish user has placed outside    */
/*  the mesh.                                                                */
/*                                                                           */
/*  WARNING:  This routine is designed for convex triangulations, and will   */
/*  not generally work after the holes and concavities have been carved.     */
/*                                                                           */
/*****************************************************************************/
 
enum locateresult locate(struct mesh *m, struct behavior *b,
                         vertex searchpoint, struct otri *searchtri)
{
  int **sampleblock;
  char *firsttri;
  struct otri sampletri;
  vertex torg, tdest;
  unsigned long alignptr;
  float searchdist, dist;
  float ahead;
  long samplesperblock, totalsamplesleft, samplesleft;
  long population, totalpopulation;
  triangle ptr;                         /* Temporary variable used by sym(). */
 
  if (b->verbose > 2) {
    printf("  Randomly sampling for a triangle near point (%.12g, %.12g).\n",
           searchpoint[0], searchpoint[1]);
  }
  /* Record the distance from the suggested starting triangle to the */
  /*   point we seek.                                                */
  org(*searchtri, torg);
  searchdist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) +
               (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]);
  if (b->verbose > 2) {
    printf("    Boundary triangle has origin (%.12g, %.12g).\n",
           torg[0], torg[1]);
  }
 
  /* If a recently encountered triangle has been recorded and has not been */
  /*   deallocated, test it as a good starting point.                      */
  if (m->recenttri.tri != (triangle *) NULL) {
    if (!deadtri(m->recenttri.tri)) {
      org(m->recenttri, torg);
      if ((torg[0] == searchpoint[0]) && (torg[1] == searchpoint[1])) {
        otricopy(m->recenttri, *searchtri);
        return ONVERTEX;
      }
      dist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) +
             (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]);
      if (dist < searchdist) {
        otricopy(m->recenttri, *searchtri);
        searchdist = dist;
        if (b->verbose > 2) {
          printf("    Choosing recent triangle with origin (%.12g, %.12g).\n",
                 torg[0], torg[1]);
        }
      }
    }
  }
 
  /* The number of random samples taken is proportional to the cube root of */
  /*   the number of triangles in the mesh.  The next bit of code assumes   */
  /*   that the number of triangles increases monotonically (or at least    */
  /*   doesn't decrease enough to matter).                                  */
  while (SAMPLEFACTOR * m->samples * m->samples * m->samples <
         m->triangles.items) {
    m->samples++;
  }
 
  /* We'll draw ceiling(samples * TRIPERBLOCK / maxitems) random samples  */
  /*   from each block of triangles (except the first)--until we meet the */
  /*   sample quota.  The ceiling means that blocks at the end might be   */
  /*   neglected, but I don't care.                                       */
  samplesperblock = (m->samples * TRIPERBLOCK - 1) / m->triangles.maxitems + 1;
  /* We'll draw ceiling(samples * itemsfirstblock / maxitems) random samples */
  /*   from the first block of triangles.                                    */
  samplesleft = (m->samples * m->triangles.itemsfirstblock - 1) /
                m->triangles.maxitems + 1;
  totalsamplesleft = m->samples;
  population = m->triangles.itemsfirstblock;
  totalpopulation = m->triangles.maxitems;
  sampleblock = m->triangles.firstblock;
  sampletri.orient = 0;
  while (totalsamplesleft > 0) {
    /* If we're in the last block, `population' needs to be corrected. */
    if (population > totalpopulation) {
      population = totalpopulation;
    }
    /* Find a pointer to the first triangle in the block. */
    alignptr = (unsigned long) (sampleblock + 1);
    firsttri = (char *) (alignptr +
                         (unsigned long) m->triangles.alignbytes -
                         (alignptr %
                          (unsigned long) m->triangles.alignbytes));
 
    /* Choose `samplesleft' randomly sampled triangles in this block. */
    do {
      sampletri.tri = (triangle *) (firsttri +
                                    (randomnation((unsigned int) population) *
                                     m->triangles.itembytes));
      if (!deadtri(sampletri.tri)) {
        org(sampletri, torg);
        dist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) +
               (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]);
        if (dist < searchdist) {
          otricopy(sampletri, *searchtri);
          searchdist = dist;
          if (b->verbose > 2) {
            printf("    Choosing triangle with origin (%.12g, %.12g).\n",
                   torg[0], torg[1]);
          }
        }
      }
 
      samplesleft--;
      totalsamplesleft--;
    } while ((samplesleft > 0) && (totalsamplesleft > 0));
 
    if (totalsamplesleft > 0) {
      sampleblock = (int **) *sampleblock;
      samplesleft = samplesperblock;
      totalpopulation -= population;
      population = TRIPERBLOCK;
    }
  }
 
  /* Where are we? */
  org(*searchtri, torg);
  dest(*searchtri, tdest);
  /* Check the starting triangle's vertices. */
  if ((torg[0] == searchpoint[0]) && (torg[1] == searchpoint[1])) {
    return ONVERTEX;
  }
  if ((tdest[0] == searchpoint[0]) && (tdest[1] == searchpoint[1])) {
    lnextself(*searchtri);
    return ONVERTEX;
  }
  /* Orient `searchtri' to fit the preconditions of calling preciselocate(). */
  ahead = counterclockwise(m, b, torg, tdest, searchpoint);
  if (ahead < 0.0) {
    /* Turn around so that `searchpoint' is to the left of the */
    /*   edge specified by `searchtri'.                        */
    symself(*searchtri);
  } else if (ahead == 0.0) {
    /* Check if `searchpoint' is between `torg' and `tdest'. */
    if (((torg[0] < searchpoint[0]) == (searchpoint[0] < tdest[0])) &&
        ((torg[1] < searchpoint[1]) == (searchpoint[1] < tdest[1]))) {
      return ONEDGE;
    }
  }
  return preciselocate(m, b, searchpoint, searchtri, 0);
}
 
/********* Point location routines end here                          *********/
 
/********* Mesh transformation routines begin here                   *********/
/*****************************************************************************/
/*                                                                           */
/*  insertsubseg()   Create a new subsegment and insert it between two       */
/*                   triangles.                                              */
/*                                                                           */
/*  The new subsegment is inserted at the edge described by the handle       */
/*  `tri'.  Its vertices are properly initialized.  The marker `subsegmark'  */
/*  is applied to the subsegment and, if appropriate, its vertices.          */
/*                                                                           */
/*****************************************************************************/
 
void insertsubseg(struct mesh *m, struct behavior *b, struct otri *tri,
                  int subsegmark)
{
  struct otri oppotri;
  struct osub newsubseg;
  vertex triorg, tridest;
  triangle ptr;                         /* Temporary variable used by sym(). */
  subseg sptr;                      /* Temporary variable used by tspivot(). */
 
  org(*tri, triorg);
  dest(*tri, tridest);
  /* Mark vertices if possible. */
  if (vertexmark(triorg) == 0) {
    setvertexmark(triorg, subsegmark);
  }
  if (vertexmark(tridest) == 0) {
    setvertexmark(tridest, subsegmark);
  }
  /* Check if there's already a subsegment here. */
  tspivot(*tri, newsubseg);
  if (newsubseg.ss == m->dummysub) {
    /* Make new subsegment and initialize its vertices. */
    makesubseg(m, &newsubseg);
    setsorg(newsubseg, tridest);
    setsdest(newsubseg, triorg);
    setsegorg(newsubseg, tridest);
    setsegdest(newsubseg, triorg);
    /* Bond new subsegment to the two triangles it is sandwiched between. */
    /*   Note that the facing triangle `oppotri' might be equal to        */
    /*   `dummytri' (outer space), but the new subsegment is bonded to it */
    /*   all the same.                                                    */
    tsbond(*tri, newsubseg);
    sym(*tri, oppotri);
    ssymself(newsubseg);
    tsbond(oppotri, newsubseg);
    setmark(newsubseg, subsegmark);
    if (b->verbose > 2) {
      printf("  Inserting new ");
      printsubseg(m, b, &newsubseg);
    }
  } else {
    if (mark(newsubseg) == 0) {
      setmark(newsubseg, subsegmark);
    }
  }
}
 
/*****************************************************************************/
/*                                                                           */
/*  Terminology                                                              */
/*                                                                           */
/*  A "local transformation" replaces a small set of triangles with another  */
/*  set of triangles.  This may or may not involve inserting or deleting a   */
/*  vertex.                                                                  */
/*                                                                           */
/*  The term "casing" is used to describe the set of triangles that are      */
/*  attached to the triangles being transformed, but are not transformed     */
/*  themselves.  Think of the casing as a fixed hollow structure inside      */
/*  which all the action happens.  A "casing" is only defined relative to    */
/*  a single transformation; each occurrence of a transformation will        */
/*  involve a different casing.                                              */
/*                                                                           */
/*****************************************************************************/
 
/*****************************************************************************/
/*                                                                           */
/*  flip()   Transform two triangles to two different triangles by flipping  */
/*           an edge counterclockwise within a quadrilateral.                */
/*                                                                           */
/*  Imagine the original triangles, abc and bad, oriented so that the        */
/*  shared edge ab lies in a horizontal plane, with the vertex b on the left */
/*  and the vertex a on the right.  The vertex c lies below the edge, and    */
/*  the vertex d lies above the edge.  The `flipedge' handle holds the edge  */
/*  ab of triangle abc, and is directed left, from vertex a to vertex b.     */
/*                                                                           */
/*  The triangles abc and bad are deleted and replaced by the triangles cdb  */
/*  and dca.  The triangles that represent abc and bad are NOT deallocated;  */
/*  they are reused for dca and cdb, respectively.  Hence, any handles that  */
/*  may have held the original triangles are still valid, although not       */
/*  directed as they were before.                                            */
/*                                                                           */
/*  Upon completion of this routine, the `flipedge' handle holds the edge    */
/*  dc of triangle dca, and is directed down, from vertex d to vertex c.     */
/*  (Hence, the two triangles have rotated counterclockwise.)                */
/*                                                                           */
/*  WARNING:  This transformation is geometrically valid only if the         */
/*  quadrilateral adbc is convex.  Furthermore, this transformation is       */
/*  valid only if there is not a subsegment between the triangles abc and    */
/*  bad.  This routine does not check either of these preconditions, and     */
/*  it is the responsibility of the calling routine to ensure that they are  */
/*  met.  If they are not, the streets shall be filled with wailing and      */
/*  gnashing of teeth.                                                       */
/*                                                                           */
/*****************************************************************************/
 
void flip(struct mesh *m, struct behavior *b, struct otri *flipedge)
{
  struct otri botleft, botright;
  struct otri topleft, topright;
  struct otri top;
  struct otri botlcasing, botrcasing;
  struct otri toplcasing, toprcasing;
  struct osub botlsubseg, botrsubseg;
  struct osub toplsubseg, toprsubseg;
  vertex leftvertex, rightvertex, botvertex;
  vertex farvertex;
  triangle ptr;                         /* Temporary variable used by sym(). */
  subseg sptr;                      /* Temporary variable used by tspivot(). */
 
  /* Identify the vertices of the quadrilateral. */
  org(*flipedge, rightvertex);
  dest(*flipedge, leftvertex);
  apex(*flipedge, botvertex);
  sym(*flipedge, top);
  apex(top, farvertex);
 
  /* Identify the casing of the quadrilateral. */
  lprev(top, topleft);
  sym(topleft, toplcasing);
  lnext(top, topright);
  sym(topright, toprcasing);
  lnext(*flipedge, botleft);
  sym(botleft, botlcasing);
  lprev(*flipedge, botright);
  sym(botright, botrcasing);
  /* Rotate the quadrilateral one-quarter turn counterclockwise. */
  bond(topleft, botlcasing);
  bond(botleft, botrcasing);
  bond(botright, toprcasing);
  bond(topright, toplcasing);
 
  if (m->checksegments) {
    /* Check for subsegments and rebond them to the quadrilateral. */
    tspivot(topleft, toplsubseg);
    tspivot(botleft, botlsubseg);
    tspivot(botright, botrsubseg);
    tspivot(topright, toprsubseg);
    if (toplsubseg.ss == m->dummysub) {
      tsdissolve(topright);
    } else {
      tsbond(topright, toplsubseg);
    }
    if (botlsubseg.ss == m->dummysub) {
      tsdissolve(topleft);
    } else {
      tsbond(topleft, botlsubseg);
    }
    if (botrsubseg.ss == m->dummysub) {
      tsdissolve(botleft);
    } else {
      tsbond(botleft, botrsubseg);
    }
    if (toprsubseg.ss == m->dummysub) {
      tsdissolve(botright);
    } else {
      tsbond(botright, toprsubseg);
    }
  }
 
  /* New vertex assignments for the rotated quadrilateral. */
  setorg(*flipedge, farvertex);
  setdest(*flipedge, botvertex);
  setapex(*flipedge, rightvertex);
  setorg(top, botvertex);
  setdest(top, farvertex);
  setapex(top, leftvertex);
  if (b->verbose > 2) {
    printf("  Edge flip results in left ");
    printtriangle(m, b, &top);
    printf("  and right ");
    printtriangle(m, b, flipedge);
  }
}
 
/*****************************************************************************/
/*                                                                           */
/*  unflip()   Transform two triangles to two different triangles by         */
/*             flipping an edge clockwise within a quadrilateral.  Reverses  */
/*             the flip() operation so that the data structures representing */
/*             the triangles are back where they were before the flip().     */
/*                                                                           */
/*  Imagine the original triangles, abc and bad, oriented so that the        */
/*  shared edge ab lies in a horizontal plane, with the vertex b on the left */
/*  and the vertex a on the right.  The vertex c lies below the edge, and    */
/*  the vertex d lies above the edge.  The `flipedge' handle holds the edge  */
/*  ab of triangle abc, and is directed left, from vertex a to vertex b.     */
/*                                                                           */
/*  The triangles abc and bad are deleted and replaced by the triangles cdb  */
/*  and dca.  The triangles that represent abc and bad are NOT deallocated;  */
/*  they are reused for cdb and dca, respectively.  Hence, any handles that  */
/*  may have held the original triangles are still valid, although not       */
/*  directed as they were before.                                            */
/*                                                                           */
/*  Upon completion of this routine, the `flipedge' handle holds the edge    */
/*  cd of triangle cdb, and is directed up, from vertex c to vertex d.       */
/*  (Hence, the two triangles have rotated clockwise.)                       */
/*                                                                           */
/*  WARNING:  This transformation is geometrically valid only if the         */
/*  quadrilateral adbc is convex.  Furthermore, this transformation is       */
/*  valid only if there is not a subsegment between the triangles abc and    */
/*  bad.  This routine does not check either of these preconditions, and     */
/*  it is the responsibility of the calling routine to ensure that they are  */
/*  met.  If they are not, the streets shall be filled with wailing and      */
/*  gnashing of teeth.                                                       */
/*                                                                           */
/*****************************************************************************/
 
void unflip(struct mesh *m, struct behavior *b, struct otri *flipedge)
{
  struct otri botleft, botright;
  struct otri topleft, topright;
  struct otri top;
  struct otri botlcasing, botrcasing;
  struct otri toplcasing, toprcasing;
  struct osub botlsubseg, botrsubseg;
  struct osub toplsubseg, toprsubseg;
  vertex leftvertex, rightvertex, botvertex;
  vertex farvertex;
  triangle ptr;                         /* Temporary variable used by sym(). */
  subseg sptr;                      /* Temporary variable used by tspivot(). */
 
  /* Identify the vertices of the quadrilateral. */
  org(*flipedge, rightvertex);
  dest(*flipedge, leftvertex);
  apex(*flipedge, botvertex);
  sym(*flipedge, top);
  apex(top, farvertex);
 
  /* Identify the casing of the quadrilateral. */
  lprev(top, topleft);
  sym(topleft, toplcasing);
  lnext(top, topright);
  sym(topright, toprcasing);
  lnext(*flipedge, botleft);
  sym(botleft, botlcasing);
  lprev(*flipedge, botright);
  sym(botright, botrcasing);
  /* Rotate the quadrilateral one-quarter turn clockwise. */
  bond(topleft, toprcasing);
  bond(botleft, toplcasing);
  bond(botright, botlcasing);
  bond(topright, botrcasing);
 
  if (m->checksegments) {
    /* Check for subsegments and rebond them to the quadrilateral. */
    tspivot(topleft, toplsubseg);
    tspivot(botleft, botlsubseg);
    tspivot(botright, botrsubseg);
    tspivot(topright, toprsubseg);
    if (toplsubseg.ss == m->dummysub) {
      tsdissolve(botleft);
    } else {
      tsbond(botleft, toplsubseg);
    }
    if (botlsubseg.ss == m->dummysub) {
      tsdissolve(botright);
    } else {
      tsbond(botright, botlsubseg);
    }
    if (botrsubseg.ss == m->dummysub) {
      tsdissolve(topright);
    } else {
      tsbond(topright, botrsubseg);
    }
    if (toprsubseg.ss == m->dummysub) {
      tsdissolve(topleft);
    } else {
      tsbond(topleft, toprsubseg);
    }
  }
 
  /* New vertex assignments for the rotated quadrilateral. */
  setorg(*flipedge, botvertex);
  setdest(*flipedge, farvertex);
  setapex(*flipedge, leftvertex);
  setorg(top, farvertex);
  setdest(top, botvertex);
  setapex(top, rightvertex);
  if (b->verbose > 2) {
    printf("  Edge unflip results in left ");
    printtriangle(m, b, flipedge);
    printf("  and right ");
    printtriangle(m, b, &top);
  }
}
 
/*****************************************************************************/
/*                                                                           */
/*  insertvertex()   Insert a vertex into a Delaunay triangulation,          */
/*                   performing flips as necessary to maintain the Delaunay  */
/*                   property.                                               */
/*                                                                           */
/*  The point `insertvertex' is located.  If `searchtri.tri' is not NULL,    */
/*  the search for the containing triangle begins from `searchtri'.  If      */
/*  `searchtri.tri' is NULL, a full point location procedure is called.      */
/*  If `insertvertex' is found inside a triangle, the triangle is split into */
/*  three; if `insertvertex' lies on an edge, the edge is split in two,      */
/*  thereby splitting the two adjacent triangles into four.  Edge flips are  */
/*  used to restore the Delaunay property.  If `insertvertex' lies on an     */
/*  existing vertex, no action is taken, and the value DUPLICATEVERTEX is    */
/*  returned.  On return, `searchtri' is set to a handle whose origin is the */
/*  existing vertex.                                                         */
/*                                                                           */
/*  Normally, the parameter `splitseg' is set to NULL, implying that no      */
/*  subsegment should be split.  In this case, if `insertvertex' is found to */
/*  lie on a segment, no action is taken, and the value VIOLATINGVERTEX is   */
/*  returned.  On return, `searchtri' is set to a handle whose primary edge  */
/*  is the violated subsegment.                                              */
/*                                                                           */
/*  If the calling routine wishes to split a subsegment by inserting a       */
/*  vertex in it, the parameter `splitseg' should be that subsegment.  In    */
/*  this case, `searchtri' MUST be the triangle handle reached by pivoting   */
/*  from that subsegment; no point location is done.                         */
/*                                                                           */
/*  `segmentflaws' and `triflaws' are flags that indicate whether or not     */
/*  there should be checks for the creation of encroached subsegments or bad */
/*  quality triangles.  If a newly inserted vertex encroaches upon           */
/*  subsegments, these subsegments are added to the list of subsegments to   */
/*  be split if `segmentflaws' is set.  If bad triangles are created, these  */
/*  are added to the queue if `triflaws' is set.                             */
/*                                                                           */
/*  If a duplicate vertex or violated segment does not prevent the vertex    */
/*  from being inserted, the return value will be ENCROACHINGVERTEX if the   */
/*  vertex encroaches upon a subsegment (and checking is enabled), or        */
/*  SUCCESSFULVERTEX otherwise.  In either case, `searchtri' is set to a     */
/*  handle whose origin is the newly inserted vertex.                        */
/*                                                                           */
/*  insertvertex() does not use flip() for reasons of speed; some            */
/*  information can be reused from edge flip to edge flip, like the          */
/*  locations of subsegments.                                                */
/*                                                                           */
/*****************************************************************************/
 
enum insertvertexresult insertvertex(struct mesh *m, struct behavior *b,
                                     vertex newvertex, struct otri *searchtri,
                                     struct osub *splitseg,
                                     int segmentflaws, int triflaws)
{
  struct otri horiz;
  struct otri top;
  struct otri botleft, botright;
  struct otri topleft, topright;
  struct otri newbotleft, newbotright;
  struct otri newtopright;
  struct otri botlcasing, botrcasing;
  struct otri toplcasing, toprcasing;
  struct otri testtri;
  struct osub botlsubseg, botrsubseg;
  struct osub toplsubseg, toprsubseg;
  struct osub brokensubseg;
  struct osub checksubseg;
  struct osub rightsubseg;
  struct osub newsubseg;
  struct badsubseg *encroached;
  struct flipstacker *newflip;
  vertex first;
  vertex leftvertex, rightvertex, botvertex, topvertex, farvertex;
  vertex segmentorg, segmentdest;
  float attrib;
  float area;
  enum insertvertexresult success;
  enum locateresult intersect;
  int doflip;
  int mirrorflag;
  int enq;
  int i;
  triangle ptr;                         /* Temporary variable used by sym(). */
  subseg sptr;         /* Temporary variable used by spivot() and tspivot(). */
 
  if (b->verbose > 1) {
    printf("  Inserting (%.12g, %.12g).\n", newvertex[0], newvertex[1]);
  }
 
  if (splitseg == (struct osub *) NULL) {
    /* Find the location of the vertex to be inserted.  Check if a good */
    /*   starting triangle has already been provided by the caller.     */
    if (searchtri->tri == m->dummytri) {
      /* Find a boundary triangle. */
      horiz.tri = m->dummytri;
      horiz.orient = 0;
      symself(horiz);
      /* Search for a triangle containing `newvertex'. */
      intersect = locate(m, b, newvertex, &horiz);
    } else {
      /* Start searching from the triangle provided by the caller. */
      otricopy(*searchtri, horiz);
      intersect = preciselocate(m, b, newvertex, &horiz, 1);
    }
  } else {
    /* The calling routine provides the subsegment in which */
    /*   the vertex is inserted.                             */
    otricopy(*searchtri, horiz);
    intersect = ONEDGE;
  }
 
  if (intersect == ONVERTEX) {
    /* There's already a vertex there.  Return in `searchtri' a triangle */
    /*   whose origin is the existing vertex.                            */
    otricopy(horiz, *searchtri);
    otricopy(horiz, m->recenttri);
    return DUPLICATEVERTEX;
  }
  if ((intersect == ONEDGE) || (intersect == OUTSIDE)) {
    /* The vertex falls on an edge or boundary. */
    if (m->checksegments && (splitseg == (struct osub *) NULL)) {
      /* Check whether the vertex falls on a subsegment. */
      tspivot(horiz, brokensubseg);
      if (brokensubseg.ss != m->dummysub) {
        /* The vertex falls on a subsegment, and hence will not be inserted. */
        if (segmentflaws) {
          enq = b->nobisect != 2;
          if (enq && (b->nobisect == 1)) {
            /* This subsegment may be split only if it is an */
            /*   internal boundary.                          */
            sym(horiz, testtri);
            enq = testtri.tri != m->dummytri;
          }
          if (enq) {
            /* Add the subsegment to the list of encroached subsegments. */
            encroached = (struct badsubseg *) poolalloc(&m->badsubsegs);
            encroached->encsubseg = sencode(brokensubseg);
            sorg(brokensubseg, encroached->subsegorg);
            sdest(brokensubseg, encroached->subsegdest);
            if (b->verbose > 2) {
              printf(
          "  Queueing encroached subsegment (%.12g, %.12g) (%.12g, %.12g).\n",
                     encroached->subsegorg[0], encroached->subsegorg[1],
                     encroached->subsegdest[0], encroached->subsegdest[1]);
            }
          }
        }
        /* Return a handle whose primary edge contains the vertex, */
        /*   which has not been inserted.                          */
        otricopy(horiz, *searchtri);
        otricopy(horiz, m->recenttri);
        return VIOLATINGVERTEX;
      }
    }
 
    /* Insert the vertex on an edge, dividing one triangle into two (if */
    /*   the edge lies on a boundary) or two triangles into four.       */
    lprev(horiz, botright);
    sym(botright, botrcasing);
    sym(horiz, topright);
    /* Is there a second triangle?  (Or does this edge lie on a boundary?) */
    mirrorflag = topright.tri != m->dummytri;
    if (mirrorflag) {
      lnextself(topright);
      sym(topright, toprcasing);
      maketriangle(m, b, &newtopright);
    } else {
      /* Splitting a boundary edge increases the number of boundary edges. */
      m->hullsize++;
    }
    maketriangle(m, b, &newbotright);
 
    /* Set the vertices of changed and new triangles. */
    org(horiz, rightvertex);
    dest(horiz, leftvertex);
    apex(horiz, botvertex);
    setorg(newbotright, botvertex);
    setdest(newbotright, rightvertex);
    setapex(newbotright, newvertex);
    setorg(horiz, newvertex);
    for (i = 0; i < m->eextras; i++) {
      /* Set the element attributes of a new triangle. */
      setelemattribute(newbotright, i, elemattribute(botright, i));
    }
    if (b->vararea) {
      /* Set the area constraint of a new triangle. */
      setareabound(newbotright, areabound(botright));
    }
    if (mirrorflag) {
      dest(topright, topvertex);
      setorg(newtopright, rightvertex);
      setdest(newtopright, topvertex);
      setapex(newtopright, newvertex);
      setorg(topright, newvertex);
      for (i = 0; i < m->eextras; i++) {
        /* Set the element attributes of another new triangle. */
        setelemattribute(newtopright, i, elemattribute(topright, i));
      }
      if (b->vararea) {
        /* Set the area constraint of another new triangle. */
        setareabound(newtopright, areabound(topright));
      }
    }
 
    /* There may be subsegments that need to be bonded */
    /*   to the new triangle(s).                       */
    if (m->checksegments) {
      tspivot(botright, botrsubseg);
      if (botrsubseg.ss != m->dummysub) {
        tsdissolve(botright);
        tsbond(newbotright, botrsubseg);
      }
      if (mirrorflag) {
        tspivot(topright, toprsubseg);
        if (toprsubseg.ss != m->dummysub) {
          tsdissolve(topright);
          tsbond(newtopright, toprsubseg);
        }
      }
    }
 
    /* Bond the new triangle(s) to the surrounding triangles. */
    bond(newbotright, botrcasing);
    lprevself(newbotright);
    bond(newbotright, botright);
    lprevself(newbotright);
    if (mirrorflag) {
      bond(newtopright, toprcasing);
      lnextself(newtopright);
      bond(newtopright, topright);
      lnextself(newtopright);
      bond(newtopright, newbotright);
    }
 
    if (splitseg != (struct osub *) NULL) {
      /* Split the subsegment into two. */
      setsdest(*splitseg, newvertex);
      segorg(*splitseg, segmentorg);
      segdest(*splitseg, segmentdest);
      ssymself(*splitseg);
      spivot(*splitseg, rightsubseg);
      insertsubseg(m, b, &newbotright, mark(*splitseg));
      tspivot(newbotright, newsubseg);
      setsegorg(newsubseg, segmentorg);
      setsegdest(newsubseg, segmentdest);
      sbond(*splitseg, newsubseg);
      ssymself(newsubseg);
      sbond(newsubseg, rightsubseg);
      ssymself(*splitseg);
      /* Transfer the subsegment's boundary marker to the vertex */
      /*   if required.                                          */
      if (vertexmark(newvertex) == 0) {
        setvertexmark(newvertex, mark(*splitseg));
      }
    }
 
    if (m->checkquality) {
      poolrestart(&m->flipstackers);
      m->lastflip = (struct flipstacker *) poolalloc(&m->flipstackers);
      m->lastflip->flippedtri = encode(horiz);
      m->lastflip->prevflip = (struct flipstacker *) &insertvertex;
    }
    if (b->verbose > 2) {
      printf("  Updating bottom left ");
      printtriangle(m, b, &botright);
      if (mirrorflag) {
        printf("  Updating top left ");
        printtriangle(m, b, &topright);
        printf("  Creating top right ");
        printtriangle(m, b, &newtopright);
      }
      printf("  Creating bottom right ");
      printtriangle(m, b, &newbotright);
    }
 
    /* Position `horiz' on the first edge to check for */
    /*   the Delaunay property.                        */
    lnextself(horiz);
  } else {
    /* Insert the vertex in a triangle, splitting it into three. */
    lnext(horiz, botleft);
    lprev(horiz, botright);
    sym(botleft, botlcasing);
    sym(botright, botrcasing);
    maketriangle(m, b, &newbotleft);
    maketriangle(m, b, &newbotright);
 
    /* Set the vertices of changed and new triangles. */
    org(horiz, rightvertex);
    dest(horiz, leftvertex);
    apex(horiz, botvertex);
    setorg(newbotleft, leftvertex);
    setdest(newbotleft, botvertex);
    setapex(newbotleft, newvertex);
    setorg(newbotright, botvertex);
    setdest(newbotright, rightvertex);
    setapex(newbotright, newvertex);
    setapex(horiz, newvertex);
    for (i = 0; i < m->eextras; i++) {
      /* Set the element attributes of the new triangles. */
      attrib = elemattribute(horiz, i);
      setelemattribute(newbotleft, i, attrib);
      setelemattribute(newbotright, i, attrib);
    }
    if (b->vararea) {
      /* Set the area constraint of the new triangles. */
      area = areabound(horiz);
      setareabound(newbotleft, area);
      setareabound(newbotright, area);
    }
 
    /* There may be subsegments that need to be bonded */
    /*   to the new triangles.                         */
    if (m->checksegments) {
      tspivot(botleft, botlsubseg);
      if (botlsubseg.ss != m->dummysub) {
        tsdissolve(botleft);
        tsbond(newbotleft, botlsubseg);
      }
      tspivot(botright, botrsubseg);
      if (botrsubseg.ss != m->dummysub) {
        tsdissolve(botright);
        tsbond(newbotright, botrsubseg);
      }
    }
 
    /* Bond the new triangles to the surrounding triangles. */
    bond(newbotleft, botlcasing);
    bond(newbotright, botrcasing);
    lnextself(newbotleft);
    lprevself(newbotright);
    bond(newbotleft, newbotright);
    lnextself(newbotleft);
    bond(botleft, newbotleft);
    lprevself(newbotright);
    bond(botright, newbotright);
 
    if (m->checkquality) {
      poolrestart(&m->flipstackers);
      m->lastflip = (struct flipstacker *) poolalloc(&m->flipstackers);
      m->lastflip->flippedtri = encode(horiz);
      m->lastflip->prevflip = (struct flipstacker *) NULL;
    }
    if (b->verbose > 2) {
      printf("  Updating top ");
      printtriangle(m, b, &horiz);
      printf("  Creating left ");
      printtriangle(m, b, &newbotleft);
      printf("  Creating right ");
      printtriangle(m, b, &newbotright);
    }
  }
 
  /* The insertion is successful by default, unless an encroached */
  /*   subsegment is found.                                       */
  success = SUCCESSFULVERTEX;
  /* Circle around the newly inserted vertex, checking each edge opposite */
  /*   it for the Delaunay property.  Non-Delaunay edges are flipped.     */
  /*   `horiz' is always the edge being checked.  `first' marks where to  */
  /*   stop circling.                                                     */
  org(horiz, first);
  rightvertex = first;
  dest(horiz, leftvertex);
  /* Circle until finished. */
  while (1) {
    /* By default, the edge will be flipped. */
    doflip = 1;
 
    if (m->checksegments) {
      /* Check for a subsegment, which cannot be flipped. */
      tspivot(horiz, checksubseg);
      if (checksubseg.ss != m->dummysub) {
        /* The edge is a subsegment and cannot be flipped. */
        doflip = 0;
      }
    }
 
    if (doflip) {
      /* Check if the edge is a boundary edge. */
      sym(horiz, top);
      if (top.tri == m->dummytri) {
        /* The edge is a boundary edge and cannot be flipped. */
        doflip = 0;
      } else {
        /* Find the vertex on the other side of the edge. */
        apex(top, farvertex);
        /* In the incremental Delaunay triangulation algorithm, any of      */
        /*   `leftvertex', `rightvertex', and `farvertex' could be vertices */
        /*   of the triangular bounding box.  These vertices must be        */
        /*   treated as if they are infinitely distant, even though their   */
        /*   "coordinates" are not.                                         */
        if ((leftvertex == m->infvertex1) || (leftvertex == m->infvertex2) ||
            (leftvertex == m->infvertex3)) {
          /* `leftvertex' is infinitely distant.  Check the convexity of  */
          /*   the boundary of the triangulation.  'farvertex' might be   */
          /*   infinite as well, but trust me, this same condition should */
          /*   be applied.                                                */
          doflip = counterclockwise(m, b, newvertex, rightvertex, farvertex)
                   > 0.0;
        } else if ((rightvertex == m->infvertex1) ||
                   (rightvertex == m->infvertex2) ||
                   (rightvertex == m->infvertex3)) {
          /* `rightvertex' is infinitely distant.  Check the convexity of */
          /*   the boundary of the triangulation.  'farvertex' might be   */
          /*   infinite as well, but trust me, this same condition should */
          /*   be applied.                                                */
          doflip = counterclockwise(m, b, farvertex, leftvertex, newvertex)
                   > 0.0;
        } else if ((farvertex == m->infvertex1) ||
                   (farvertex == m->infvertex2) ||
                   (farvertex == m->infvertex3)) {
          /* `farvertex' is infinitely distant and cannot be inside */
          /*   the circumcircle of the triangle `horiz'.            */
          doflip = 0;
        } else {
          /* Test whether the edge is locally Delaunay. */
          doflip = incircle(m, b, leftvertex, newvertex, rightvertex,
                            farvertex) > 0.0;
        }
        if (doflip) {
          /* We made it!  Flip the edge `horiz' by rotating its containing */
          /*   quadrilateral (the two triangles adjacent to `horiz').      */
          /* Identify the casing of the quadrilateral. */
          lprev(top, topleft);
          sym(topleft, toplcasing);
          lnext(top, topright);
          sym(topright, toprcasing);
          lnext(horiz, botleft);
          sym(botleft, botlcasing);
          lprev(horiz, botright);
          sym(botright, botrcasing);
          /* Rotate the quadrilateral one-quarter turn counterclockwise. */
          bond(topleft, botlcasing);
          bond(botleft, botrcasing);
          bond(botright, toprcasing);
          bond(topright, toplcasing);
          if (m->checksegments) {
            /* Check for subsegments and rebond them to the quadrilateral. */
            tspivot(topleft, toplsubseg);
            tspivot(botleft, botlsubseg);
            tspivot(botright, botrsubseg);
            tspivot(topright, toprsubseg);
            if (toplsubseg.ss == m->dummysub) {
              tsdissolve(topright);
            } else {
              tsbond(topright, toplsubseg);
            }
            if (botlsubseg.ss == m->dummysub) {
              tsdissolve(topleft);
            } else {
              tsbond(topleft, botlsubseg);
            }
            if (botrsubseg.ss == m->dummysub) {
              tsdissolve(botleft);
            } else {
              tsbond(botleft, botrsubseg);
            }
            if (toprsubseg.ss == m->dummysub) {
              tsdissolve(botright);
            } else {
              tsbond(botright, toprsubseg);
            }
          }
          /* New vertex assignments for the rotated quadrilateral. */
          setorg(horiz, farvertex);
          setdest(horiz, newvertex);
          setapex(horiz, rightvertex);
          setorg(top, newvertex);
          setdest(top, farvertex);
          setapex(top, leftvertex);
          for (i = 0; i < m->eextras; i++) {
            /* Take the average of the two triangles' attributes. */
            attrib = 0.5 * (elemattribute(top, i) + elemattribute(horiz, i));
            setelemattribute(top, i, attrib);
            setelemattribute(horiz, i, attrib);
          }
          if (b->vararea) {
            if ((areabound(top) <= 0.0) || (areabound(horiz) <= 0.0)) {
              area = -1.0;
            } else {
              /* Take the average of the two triangles' area constraints.    */
              /*   This prevents small area constraints from migrating a     */
              /*   long, long way from their original location due to flips. */
              area = 0.5 * (areabound(top) + areabound(horiz));
            }
            setareabound(top, area);
            setareabound(horiz, area);
          }
 
          if (m->checkquality) {
            newflip = (struct flipstacker *) poolalloc(&m->flipstackers);
            newflip->flippedtri = encode(horiz);
            newflip->prevflip = m->lastflip;
            m->lastflip = newflip;
          }
          if (b->verbose > 2) {
            printf("  Edge flip results in left ");
            lnextself(topleft);
            printtriangle(m, b, &topleft);
            printf("  and right ");
            printtriangle(m, b, &horiz);
          }
          /* On the next iterations, consider the two edges that were  */
          /*   exposed (this is, are now visible to the newly inserted */
          /*   vertex) by the edge flip.                               */
          lprevself(horiz);
          leftvertex = farvertex;
        }
      }
    }
    if (!doflip) {
      /* The handle `horiz' is accepted as locally Delaunay. */
      /* Look for the next edge around the newly inserted vertex. */
      lnextself(horiz);
      sym(horiz, testtri);
      /* Check for finishing a complete revolution about the new vertex, or */
      /*   falling outside  of the triangulation.  The latter will happen   */
      /*   when a vertex is inserted at a boundary.                         */
      if ((leftvertex == first) || (testtri.tri == m->dummytri)) {
        /* We're done.  Return a triangle whose origin is the new vertex. */
        lnext(horiz, *searchtri);
        lnext(horiz, m->recenttri);
        return success;
      }
      /* Finish finding the next edge around the newly inserted vertex. */
      lnext(testtri, horiz);
      rightvertex = leftvertex;
      dest(horiz, leftvertex);
    }
  }
}
 
/*****************************************************************************/
/*                                                                           */
/*  triangulatepolygon()   Find the Delaunay triangulation of a polygon that */
/*                         has a certain "nice" shape.  This includes the    */
/*                         polygons that result from deletion of a vertex or */
/*                         insertion of a segment.                           */
/*                                                                           */
/*  This is a conceptually difficult routine.  The starting assumption is    */
/*  that we have a polygon with n sides.  n - 1 of these sides are currently */
/*  represented as edges in the mesh.  One side, called the "base", need not */
/*  be.                                                                      */
/*                                                                           */
/*  Inside the polygon is a structure I call a "fan", consisting of n - 1    */
/*  triangles that share a common origin.  For each of these triangles, the  */
/*  edge opposite the origin is one of the sides of the polygon.  The        */
/*  primary edge of each triangle is the edge directed from the origin to    */
/*  the destination; note that this is not the same edge that is a side of   */
/*  the polygon.  `firstedge' is the primary edge of the first triangle.     */
/*  From there, the triangles follow in counterclockwise order about the     */
/*  polygon, until `lastedge', the primary edge of the last triangle.        */
/*  `firstedge' and `lastedge' are probably connected to other triangles     */
/*  beyond the extremes of the fan, but their identity is not important, as  */
/*  long as the fan remains connected to them.                               */
/*                                                                           */
/*  Imagine the polygon oriented so that its base is at the bottom.  This    */
/*  puts `firstedge' on the far right, and `lastedge' on the far left.       */
/*  The right vertex of the base is the destination of `firstedge', and the  */
/*  left vertex of the base is the apex of `lastedge'.                       */
/*                                                                           */
/*  The challenge now is to find the right sequence of edge flips to         */
/*  transform the fan into a Delaunay triangulation of the polygon.  Each    */
/*  edge flip effectively removes one triangle from the fan, committing it   */
/*  to the polygon.  The resulting polygon has one fewer edge.  If `doflip'  */
/*  is set, the final flip will be performed, resulting in a fan of one      */
/*  (useless?) triangle.  If `doflip' is not set, the final flip is not      */
/*  performed, resulting in a fan of two triangles, and an unfinished        */
/*  triangular polygon that is not yet filled out with a single triangle.    */
/*  On completion of the routine, `lastedge' is the last remaining triangle, */
/*  or the leftmost of the last two.                                         */
/*                                                                           */
/*  Although the flips are performed in the order described above, the       */
/*  decisions about what flips to perform are made in precisely the reverse  */
/*  order.  The recursive triangulatepolygon() procedure makes a decision,   */
/*  uses up to two recursive calls to triangulate the "subproblems"          */
/*  (polygons with fewer edges), and then performs an edge flip.             */
/*                                                                           */
/*  The "decision" it makes is which vertex of the polygon should be         */
/*  connected to the base.  This decision is made by testing every possible  */
/*  vertex.  Once the best vertex is found, the two edges that connect this  */
/*  vertex to the base become the bases for two smaller polygons.  These     */
/*  are triangulated recursively.  Unfortunately, this approach can take     */
/*  O(n^2) time not only in the worst case, but in many common cases.  It's  */
/*  rarely a big deal for vertex deletion, where n is rarely larger than     */
/*  ten, but it could be a big deal for segment insertion, especially if     */
/*  there's a lot of long segments that each cut many triangles.  I ought to */
/*  code a faster algorithm some day.                                        */
/*                                                                           */
/*  The `edgecount' parameter is the number of sides of the polygon,         */
/*  including its base.  `triflaws' is a flag that determines whether the    */
/*  new triangles should be tested for quality, and enqueued if they are     */
/*  bad.                                                                     */
/*                                                                           */
/*****************************************************************************/
 
void triangulatepolygon(struct mesh *m, struct behavior *b,
                        struct otri *firstedge, struct otri *lastedge,
                        int edgecount, int doflip, int triflaws)
{
  struct otri testtri;
  struct otri besttri;
  struct otri tempedge;
  vertex leftbasevertex, rightbasevertex;
  vertex testvertex;
  vertex bestvertex;
  int bestnumber;
  int i;
  triangle ptr;   /* Temporary variable used by sym(), onext(), and oprev(). */
 
  /* Identify the base vertices. */
  apex(*lastedge, leftbasevertex);
  dest(*firstedge, rightbasevertex);
  if (b->verbose > 2) {
    printf("  Triangulating interior polygon at edge\n");
    printf("    (%.12g, %.12g) (%.12g, %.12g)\n", leftbasevertex[0],
           leftbasevertex[1], rightbasevertex[0], rightbasevertex[1]);
  }
  /* Find the best vertex to connect the base to. */
  onext(*firstedge, besttri);
  dest(besttri, bestvertex);
  otricopy(besttri, testtri);
  bestnumber = 1;
  for (i = 2; i <= edgecount - 2; i++) {
    onextself(testtri);
    dest(testtri, testvertex);
    /* Is this a better vertex? */
    if (incircle(m, b, leftbasevertex, rightbasevertex, bestvertex,
                 testvertex) > 0.0) {
      otricopy(testtri, besttri);
      bestvertex = testvertex;
      bestnumber = i;
    }
  }
  if (b->verbose > 2) {
    printf("    Connecting edge to (%.12g, %.12g)\n", bestvertex[0],
           bestvertex[1]);
  }
  if (bestnumber > 1) {
    /* Recursively triangulate the smaller polygon on the right. */
    oprev(besttri, tempedge);
    triangulatepolygon(m, b, firstedge, &tempedge, bestnumber + 1, 1,
                       triflaws);
  }
  if (bestnumber < edgecount - 2) {
    /* Recursively triangulate the smaller polygon on the left. */
    sym(besttri, tempedge);
    triangulatepolygon(m, b, &besttri, lastedge, edgecount - bestnumber, 1,
                       triflaws);
    /* Find `besttri' again; it may have been lost to edge flips. */
    sym(tempedge, besttri);
  }
  if (doflip) {
    /* Do one final edge flip. */
    flip(m, b, &besttri);
  }
  /* Return the base triangle. */
  otricopy(besttri, *lastedge);
}
 
/********* Mesh transformation routines end here                     *********/
 
/********* Divide-and-conquer Delaunay triangulation begins here     *********/
/*****************************************************************************/
/*                                                                           */
/*  The divide-and-conquer bounding box                                      */
/*                                                                           */
/*  I originally implemented the divide-and-conquer and incremental Delaunay */
/*  triangulations using the edge-based data structure presented by Guibas   */
/*  and Stolfi.  Switching to a triangle-based data structure doubled the    */
/*  speed.  However, I had to think of a few extra tricks to maintain the    */
/*  elegance of the original algorithms.                                     */
/*                                                                           */
/*  The "bounding box" used by my variant of the divide-and-conquer          */
/*  algorithm uses one triangle for each edge of the convex hull of the      */
/*  triangulation.  These bounding triangles all share a common apical       */
/*  vertex, which is represented by NULL and which represents nothing.       */
/*  The bounding triangles are linked in a circular fan about this NULL      */
/*  vertex, and the edges on the convex hull of the triangulation appear     */
/*  opposite the NULL vertex.  You might find it easiest to imagine that     */
/*  the NULL vertex is a point in 3D space behind the center of the          */
/*  triangulation, and that the bounding triangles form a sort of cone.      */
/*                                                                           */
/*  This bounding box makes it easy to represent degenerate cases.  For      */
/*  instance, the triangulation of two vertices is a single edge.  This edge */
/*  is represented by two bounding box triangles, one on each "side" of the  */
/*  edge.  These triangles are also linked together in a fan about the NULL  */
/*  vertex.                                                                  */
/*                                                                           */
/*  The bounding box also makes it easy to traverse the convex hull, as the  */
/*  divide-and-conquer algorithm needs to do.                                */
/*                                                                           */
/*****************************************************************************/
 
/*****************************************************************************/
/*                                                                           */
/*  vertexsort()   Sort an array of vertices by x-coordinate, using the      */
/*                 y-coordinate as a secondary key.                          */
/*                                                                           */
/*  Uses quicksort.  Randomized O(n log n) time.  No, I did not make any of  */
/*  the usual quicksort mistakes.                                            */
/*                                                                           */
/*****************************************************************************/
 
void vertexsort(vertex *sortarray, int arraysize)
{
  int left, right;
  int pivot;
  float pivotx, pivoty;
  vertex temp;
 
  if (arraysize == 2) {
    /* Recursive base case. */
    if ((sortarray[0][0] > sortarray[1][0]) ||
        ((sortarray[0][0] == sortarray[1][0]) &&
         (sortarray[0][1] > sortarray[1][1]))) {
      temp = sortarray[1];
      sortarray[1] = sortarray[0];
      sortarray[0] = temp;
    }
    return;
  }
  /* Choose a random pivot to split the array. */
  pivot = (int) randomnation((unsigned int) arraysize);
  pivotx = sortarray[pivot][0];
  pivoty = sortarray[pivot][1];
  /* Split the array. */
  left = -1;
  right = arraysize;
  while (left < right) {
    /* Search for a vertex whose x-coordinate is too large for the left. */
    do {
      left++;
    } while ((left <= right) && ((sortarray[left][0] < pivotx) ||
                                 ((sortarray[left][0] == pivotx) &&
                                  (sortarray[left][1] < pivoty))));
    /* Search for a vertex whose x-coordinate is too small for the right. */
    do {
      right--;
    } while ((left <= right) && ((sortarray[right][0] > pivotx) ||
                                 ((sortarray[right][0] == pivotx) &&
                                  (sortarray[right][1] > pivoty))));
    if (left < right) {
      /* Swap the left and right vertices. */
      temp = sortarray[left];
      sortarray[left] = sortarray[right];
      sortarray[right] = temp;
    }
  }
  if (left > 1) {
    /* Recursively sort the left subset. */
    vertexsort(sortarray, left);
  }
  if (right < arraysize - 2) {
    /* Recursively sort the right subset. */
    vertexsort(&sortarray[right + 1], arraysize - right - 1);
  }
}
 
/*****************************************************************************/
/*                                                                           */
/*  vertexmedian()   An order statistic algorithm, almost.  Shuffles an      */
/*                   array of vertices so that the first `median' vertices   */
/*                   occur lexicographically before the remaining vertices.  */
/*                                                                           */
/*  Uses the x-coordinate as the primary key if axis == 0; the y-coordinate  */
/*  if axis == 1.  Very similar to the vertexsort() procedure, but runs in   */
/*  randomized linear time.                                                  */
/*                                                                           */
/*****************************************************************************/
 
void vertexmedian(vertex *sortarray, int arraysize, int median, int axis)
{
  int left, right;
  int pivot;
  float pivot1, pivot2;
  vertex temp;
 
  if (arraysize == 2) {
    /* Recursive base case. */
    if ((sortarray[0][axis] > sortarray[1][axis]) ||
        ((sortarray[0][axis] == sortarray[1][axis]) &&
         (sortarray[0][1 - axis] > sortarray[1][1 - axis]))) {
      temp = sortarray[1];
      sortarray[1] = sortarray[0];
      sortarray[0] = temp;
    }
    return;
  }
  /* Choose a random pivot to split the array. */
  pivot = (int) randomnation((unsigned int) arraysize);
  pivot1 = sortarray[pivot][axis];
  pivot2 = sortarray[pivot][1 - axis];
  /* Split the array. */
  left = -1;
  right = arraysize;
  while (left < right) {
    /* Search for a vertex whose x-coordinate is too large for the left. */
    do {
      left++;
    } while ((left <= right) && ((sortarray[left][axis] < pivot1) ||
                                 ((sortarray[left][axis] == pivot1) &&
                                  (sortarray[left][1 - axis] < pivot2))));
    /* Search for a vertex whose x-coordinate is too small for the right. */
    do {
      right--;
    } while ((left <= right) && ((sortarray[right][axis] > pivot1) ||
                                 ((sortarray[right][axis] == pivot1) &&
                                  (sortarray[right][1 - axis] > pivot2))));
    if (left < right) {
      /* Swap the left and right vertices. */
      temp = sortarray[left];
      sortarray[left] = sortarray[right];
      sortarray[right] = temp;
    }
  }
  /* Unlike in vertexsort(), at most one of the following */
  /*   conditionals is true.                             */
  if (left > median) {
    /* Recursively shuffle the left subset. */
    vertexmedian(sortarray, left, median, axis);
  }
  if (right < median - 1) {
    /* Recursively shuffle the right subset. */
    vertexmedian(&sortarray[right + 1], arraysize - right - 1,
                 median - right - 1, axis);
  }
}
 
/*****************************************************************************/
/*                                                                           */
/*  alternateaxes()   Sorts the vertices as appropriate for the divide-and-  */
/*                    conquer algorithm with alternating cuts.               */
/*                                                                           */
/*  Partitions by x-coordinate if axis == 0; by y-coordinate if axis == 1.   */
/*  For the base case, subsets containing only two or three vertices are     */
/*  always sorted by x-coordinate.                                           */
/*                                                                           */
/*****************************************************************************/
 
void alternateaxes(vertex *sortarray, int arraysize, int axis)
{
  int divider;
 
  divider = arraysize >> 1;
  if (arraysize <= 3) {
    /* Recursive base case:  subsets of two or three vertices will be    */
    /*   handled specially, and should always be sorted by x-coordinate. */
    axis = 0;
  }
  /* Partition with a horizontal or vertical cut. */
  vertexmedian(sortarray, arraysize, divider, axis);
  /* Recursively partition the subsets with a cross cut. */
  if (arraysize - divider >= 2) {
    if (divider >= 2) {
      alternateaxes(sortarray, divider, 1 - axis);
    }
    alternateaxes(&sortarray[divider], arraysize - divider, 1 - axis);
  }
}
 
/*****************************************************************************/
/*                                                                           */
/*  mergehulls()   Merge two adjacent Delaunay triangulations into a         */
/*                 single Delaunay triangulation.                            */
/*                                                                           */
/*  This is similar to the algorithm given by Guibas and Stolfi, but uses    */
/*  a triangle-based, rather than edge-based, data structure.                */
/*                                                                           */
/*  The algorithm walks up the gap between the two triangulations, knitting  */
/*  them together.  As they are merged, some of their bounding triangles     */
/*  are converted into real triangles of the triangulation.  The procedure   */
/*  pulls each hull's bounding triangles apart, then knits them together     */
/*  like the teeth of two gears.  The Delaunay property determines, at each  */
/*  step, whether the next "tooth" is a bounding triangle of the left hull   */
/*  or the right.  When a bounding triangle becomes real, its apex is        */
/*  changed from NULL to a real vertex.                                      */
/*                                                                           */
/*  Only two new triangles need to be allocated.  These become new bounding  */
/*  triangles at the top and bottom of the seam.  They are used to connect   */
/*  the remaining bounding triangles (those that have not been converted     */
/*  into real triangles) into a single fan.                                  */
/*                                                                           */
/*  On entry, `farleft' and `innerleft' are bounding triangles of the left   */
/*  triangulation.  The origin of `farleft' is the leftmost vertex, and      */
/*  the destination of `innerleft' is the rightmost vertex of the            */
/*  triangulation.  Similarly, `innerright' and `farright' are bounding      */
/*  triangles of the right triangulation.  The origin of `innerright' and    */
/*  destination of `farright' are the leftmost and rightmost vertices.       */
/*                                                                           */
/*  On completion, the origin of `farleft' is the leftmost vertex of the     */
/*  merged triangulation, and the destination of `farright' is the rightmost */
/*  vertex.                                                                  */
/*                                                                           */
/*****************************************************************************/
 
void mergehulls(struct mesh *m, struct behavior *b, struct otri *farleft,
                struct otri *innerleft, struct otri *innerright,
                struct otri *farright, int axis)
{
  struct otri leftcand, rightcand;
  struct otri baseedge;
  struct otri nextedge;
  struct otri sidecasing, topcasing, outercasing;
  struct otri checkedge;
  vertex innerleftdest;
  vertex innerrightorg;
  vertex innerleftapex, innerrightapex;
  vertex farleftpt, farrightpt;
  vertex farleftapex, farrightapex;
  vertex lowerleft, lowerright;
  vertex upperleft, upperright;
  vertex nextapex;
  vertex checkvertex;
  int changemade;
  int badedge;
  int leftfinished, rightfinished;
  triangle ptr;                         /* Temporary variable used by sym(). */
 
  dest(*innerleft, innerleftdest);
  apex(*innerleft, innerleftapex);
  org(*innerright, innerrightorg);
  apex(*innerright, innerrightapex);
  /* Special treatment for horizontal cuts. */
  if (b->dwyer && (axis == 1)) {
    org(*farleft, farleftpt);
    apex(*farleft, farleftapex);
    dest(*farright, farrightpt);
    apex(*farright, farrightapex);
    /* The pointers to the extremal vertices are shifted to point to the */
    /*   topmost and bottommost vertex of each hull, rather than the     */
    /*   leftmost and rightmost vertices.                                */
    while (farleftapex[1] < farleftpt[1]) {
      lnextself(*farleft);
      symself(*farleft);
      farleftpt = farleftapex;
      apex(*farleft, farleftapex);
    }
    sym(*innerleft, checkedge);
    apex(checkedge, checkvertex);
    while (checkvertex[1] > innerleftdest[1]) {
      lnext(checkedge, *innerleft);
      innerleftapex = innerleftdest;
      innerleftdest = checkvertex;
      sym(*innerleft, checkedge);
      apex(checkedge, checkvertex);
    }
    while (innerrightapex[1] < innerrightorg[1]) {
      lnextself(*innerright);
      symself(*innerright);
      innerrightorg = innerrightapex;
      apex(*innerright, innerrightapex);
    }
    sym(*farright, checkedge);
    apex(checkedge, checkvertex);
    while (checkvertex[1] > farrightpt[1]) {
      lnext(checkedge, *farright);
      farrightapex = farrightpt;
      farrightpt = checkvertex;
      sym(*farright, checkedge);
      apex(checkedge, checkvertex);
    }
  }
  /* Find a line tangent to and below both hulls. */
  do {
    changemade = 0;
    /* Make innerleftdest the "bottommost" vertex of the left hull. */
    if (counterclockwise(m, b, innerleftdest, innerleftapex, innerrightorg) >
        0.0) {
      lprevself(*innerleft);
      symself(*innerleft);
      innerleftdest = innerleftapex;
      apex(*innerleft, innerleftapex);
      changemade = 1;
    }
    /* Make innerrightorg the "bottommost" vertex of the right hull. */
    if (counterclockwise(m, b, innerrightapex, innerrightorg, innerleftdest) >
        0.0) {
      lnextself(*innerright);
      symself(*innerright);
      innerrightorg = innerrightapex;
      apex(*innerright, innerrightapex);
      changemade = 1;
    }
  } while (changemade);
  /* Find the two candidates to be the next "gear tooth." */
  sym(*innerleft, leftcand);
  sym(*innerright, rightcand);
  /* Create the bottom new bounding triangle. */
  maketriangle(m, b, &baseedge);
  /* Connect it to the bounding boxes of the left and right triangulations. */
  bond(baseedge, *innerleft);
  lnextself(baseedge);
  bond(baseedge, *innerright);
  lnextself(baseedge);
  setorg(baseedge, innerrightorg);
  setdest(baseedge, innerleftdest);
  /* Apex is intentionally left NULL. */
  if (b->verbose > 2) {
    printf("  Creating base bounding ");
    printtriangle(m, b, &baseedge);
  }
  /* Fix the extreme triangles if necessary. */
  org(*farleft, farleftpt);
  if (innerleftdest == farleftpt) {
    lnext(baseedge, *farleft);
  }
  dest(*farright, farrightpt);
  if (innerrightorg == farrightpt) {
    lprev(baseedge, *farright);
  }
  /* The vertices of the current knitting edge. */
  lowerleft = innerleftdest;
  lowerright = innerrightorg;
  /* The candidate vertices for knitting. */
  apex(leftcand, upperleft);
  apex(rightcand, upperright);
  /* Walk up the gap between the two triangulations, knitting them together. */
  while (1) {
    /* Have we reached the top?  (This isn't quite the right question,       */
    /*   because even though the left triangulation might seem finished now, */
    /*   moving up on the right triangulation might reveal a new vertex of   */
    /*   the left triangulation.  And vice-versa.)                           */
    leftfinished = counterclockwise(m, b, upperleft, lowerleft, lowerright) <=
                   0.0;
    rightfinished = counterclockwise(m, b, upperright, lowerleft, lowerright)
                 <= 0.0;
    if (leftfinished && rightfinished) {
      /* Create the top new bounding triangle. */
      maketriangle(m, b, &nextedge);
      setorg(nextedge, lowerleft);
      setdest(nextedge, lowerright);
      /* Apex is intentionally left NULL. */
      /* Connect it to the bounding boxes of the two triangulations. */
      bond(nextedge, baseedge);
      lnextself(nextedge);
      bond(nextedge, rightcand);
      lnextself(nextedge);
      bond(nextedge, leftcand);
      if (b->verbose > 2) {
        printf("  Creating top bounding ");
        printtriangle(m, b, &nextedge);
      }
      /* Special treatment for horizontal cuts. */
      if (b->dwyer && (axis == 1)) {
        org(*farleft, farleftpt);
        apex(*farleft, farleftapex);
        dest(*farright, farrightpt);
        apex(*farright, farrightapex);
        sym(*farleft, checkedge);
        apex(checkedge, checkvertex);
        /* The pointers to the extremal vertices are restored to the  */
        /*   leftmost and rightmost vertices (rather than topmost and */
        /*   bottommost).                                             */
        while (checkvertex[0] < farleftpt[0]) {
          lprev(checkedge, *farleft);
          farleftapex = farleftpt;
          farleftpt = checkvertex;
          sym(*farleft, checkedge);
          apex(checkedge, checkvertex);
        }
        while (farrightapex[0] > farrightpt[0]) {
          lprevself(*farright);
          symself(*farright);
          farrightpt = farrightapex;
          apex(*farright, farrightapex);
        }
      }
      return;
    }
    /* Consider eliminating edges from the left triangulation. */
    if (!leftfinished) {
      /* What vertex would be exposed if an edge were deleted? */
      lprev(leftcand, nextedge);
      symself(nextedge);
      apex(nextedge, nextapex);
      /* If nextapex is NULL, then no vertex would be exposed; the */
      /*   triangulation would have been eaten right through.      */
      if (nextapex != (vertex) NULL) {
        /* Check whether the edge is Delaunay. */
        badedge = incircle(m, b, lowerleft, lowerright, upperleft, nextapex) >
                  0.0;
        while (badedge) {
          /* Eliminate the edge with an edge flip.  As a result, the    */
          /*   left triangulation will have one more boundary triangle. */
          lnextself(nextedge);
          sym(nextedge, topcasing);
          lnextself(nextedge);
          sym(nextedge, sidecasing);
          bond(nextedge, topcasing);
          bond(leftcand, sidecasing);
          lnextself(leftcand);
          sym(leftcand, outercasing);
          lprevself(nextedge);
          bond(nextedge, outercasing);
          /* Correct the vertices to reflect the edge flip. */
          setorg(leftcand, lowerleft);
          setdest(leftcand, NULL);
          setapex(leftcand, nextapex);
          setorg(nextedge, NULL);
          setdest(nextedge, upperleft);
          setapex(nextedge, nextapex);
          /* Consider the newly exposed vertex. */
          upperleft = nextapex;
          /* What vertex would be exposed if another edge were deleted? */
          otricopy(sidecasing, nextedge);
          apex(nextedge, nextapex);
          if (nextapex != (vertex) NULL) {
            /* Check whether the edge is Delaunay. */
            badedge = incircle(m, b, lowerleft, lowerright, upperleft,
                               nextapex) > 0.0;
          } else {
            /* Avoid eating right through the triangulation. */
            badedge = 0;
          }
        }
      }
    }
    /* Consider eliminating edges from the right triangulation. */
    if (!rightfinished) {
      /* What vertex would be exposed if an edge were deleted? */
      lnext(rightcand, nextedge);
      symself(nextedge);
      apex(nextedge, nextapex);
      /* If nextapex is NULL, then no vertex would be exposed; the */
      /*   triangulation would have been eaten right through.      */
      if (nextapex != (vertex) NULL) {
        /* Check whether the edge is Delaunay. */
        badedge = incircle(m, b, lowerleft, lowerright, upperright, nextapex) >
                  0.0;
        while (badedge) {
          /* Eliminate the edge with an edge flip.  As a result, the     */
          /*   right triangulation will have one more boundary triangle. */
          lprevself(nextedge);
          sym(nextedge, topcasing);
          lprevself(nextedge);
          sym(nextedge, sidecasing);
          bond(nextedge, topcasing);
          bond(rightcand, sidecasing);
          lprevself(rightcand);
          sym(rightcand, outercasing);
          lnextself(nextedge);
          bond(nextedge, outercasing);
          /* Correct the vertices to reflect the edge flip. */
          setorg(rightcand, NULL);
          setdest(rightcand, lowerright);
          setapex(rightcand, nextapex);
          setorg(nextedge, upperright);
          setdest(nextedge, NULL);
          setapex(nextedge, nextapex);
          /* Consider the newly exposed vertex. */
          upperright = nextapex;
          /* What vertex would be exposed if another edge were deleted? */
          otricopy(sidecasing, nextedge);
          apex(nextedge, nextapex);
          if (nextapex != (vertex) NULL) {
            /* Check whether the edge is Delaunay. */
            badedge = incircle(m, b, lowerleft, lowerright, upperright,
                               nextapex) > 0.0;
          } else {
            /* Avoid eating right through the triangulation. */
            badedge = 0;
          }
        }
      }
    }
    if (leftfinished || (!rightfinished &&
           (incircle(m, b, upperleft, lowerleft, lowerright, upperright) >
            0.0))) {
      /* Knit the triangulations, adding an edge from `lowerleft' */
      /*   to `upperright'.                                       */
      bond(baseedge, rightcand);
      lprev(rightcand, baseedge);
      setdest(baseedge, lowerleft);
      lowerright = upperright;
      sym(baseedge, rightcand);
      apex(rightcand, upperright);
    } else {
      /* Knit the triangulations, adding an edge from `upperleft' */
      /*   to `lowerright'.                                       */
      bond(baseedge, leftcand);
      lnext(leftcand, baseedge);
      setorg(baseedge, lowerright);
      lowerleft = upperleft;
      sym(baseedge, leftcand);
      apex(leftcand, upperleft);
    }
    if (b->verbose > 2) {
      printf("  Connecting ");
      printtriangle(m, b, &baseedge);
    }
  }
}
 
/*****************************************************************************/
/*                                                                           */
/*  divconqrecurse()   Recursively form a Delaunay triangulation by the      */
/*                     divide-and-conquer method.                            */
/*                                                                           */
/*  Recursively breaks down the problem into smaller pieces, which are       */
/*  knitted together by mergehulls().  The base cases (problems of two or    */
/*  three vertices) are handled specially here.                              */
/*                                                                           */
/*  On completion, `farleft' and `farright' are bounding triangles such that */
/*  the origin of `farleft' is the leftmost vertex (breaking ties by         */
/*  choosing the highest leftmost vertex), and the destination of            */
/*  `farright' is the rightmost vertex (breaking ties by choosing the        */
/*  lowest rightmost vertex).                                                */
/*                                                                           */
/*****************************************************************************/
 
void divconqrecurse(struct mesh *m, struct behavior *b, vertex *sortarray,
                    int vertices, int axis,
                    struct otri *farleft, struct otri *farright)
{
  struct otri midtri, tri1, tri2, tri3;
  struct otri innerleft, innerright;
  float area;
  int divider;
 
  if (b->verbose > 2) {
    printf("  Triangulating %d vertices.\n", vertices);
  }
  if (vertices == 2) {
    /* The triangulation of two vertices is an edge.  An edge is */
    /*   represented by two bounding triangles.                  */
    maketriangle(m, b, farleft);
    setorg(*farleft, sortarray[0]);
    setdest(*farleft, sortarray[1]);
    /* The apex is intentionally left NULL. */
    maketriangle(m, b, farright);
    setorg(*farright, sortarray[1]);
    setdest(*farright, sortarray[0]);
    /* The apex is intentionally left NULL. */
    bond(*farleft, *farright);
    lprevself(*farleft);
    lnextself(*farright);
    bond(*farleft, *farright);
    lprevself(*farleft);
    lnextself(*farright);
    bond(*farleft, *farright);
    if (b->verbose > 2) {
      printf("  Creating ");
      printtriangle(m, b, farleft);
      printf("  Creating ");
      printtriangle(m, b, farright);
    }
    /* Ensure that the origin of `farleft' is sortarray[0]. */
    lprev(*farright, *farleft);
    return;
  } else if (vertices == 3) {
    /* The triangulation of three vertices is either a triangle (with */
    /*   three bounding triangles) or two edges (with four bounding   */
    /*   triangles).  In either case, four triangles are created.     */
    maketriangle(m, b, &midtri);
    maketriangle(m, b, &tri1);
    maketriangle(m, b, &tri2);
    maketriangle(m, b, &tri3);
    area = counterclockwise(m, b, sortarray[0], sortarray[1], sortarray[2]);
    if (area == 0.0) {
      /* Three collinear vertices; the triangulation is two edges. */
      setorg(midtri, sortarray[0]);
      setdest(midtri, sortarray[1]);
      setorg(tri1, sortarray[1]);
      setdest(tri1, sortarray[0]);
      setorg(tri2, sortarray[2]);
      setdest(tri2, sortarray[1]);
      setorg(tri3, sortarray[1]);
      setdest(tri3, sortarray[2]);
      /* All apices are intentionally left NULL. */
      bond(midtri, tri1);
      bond(tri2, tri3);
      lnextself(midtri);
      lprevself(tri1);
      lnextself(tri2);
      lprevself(tri3);
      bond(midtri, tri3);
      bond(tri1, tri2);
      lnextself(midtri);
      lprevself(tri1);
      lnextself(tri2);
      lprevself(tri3);
      bond(midtri, tri1);
      bond(tri2, tri3);
      /* Ensure that the origin of `farleft' is sortarray[0]. */
      otricopy(tri1, *farleft);
      /* Ensure that the destination of `farright' is sortarray[2]. */
      otricopy(tri2, *farright);
    } else {
      /* The three vertices are not collinear; the triangulation is one */
      /*   triangle, namely `midtri'.                                   */
      setorg(midtri, sortarray[0]);
      setdest(tri1, sortarray[0]);
      setorg(tri3, sortarray[0]);
      /* Apices of tri1, tri2, and tri3 are left NULL. */
      if (area > 0.0) {
        /* The vertices are in counterclockwise order. */
        setdest(midtri, sortarray[1]);
        setorg(tri1, sortarray[1]);
        setdest(tri2, sortarray[1]);
        setapex(midtri, sortarray[2]);
        setorg(tri2, sortarray[2]);
        setdest(tri3, sortarray[2]);
      } else {
        /* The vertices are in clockwise order. */
        setdest(midtri, sortarray[2]);
        setorg(tri1, sortarray[2]);
        setdest(tri2, sortarray[2]);
        setapex(midtri, sortarray[1]);
        setorg(tri2, sortarray[1]);
        setdest(tri3, sortarray[1]);
      }
      /* The topology does not depend on how the vertices are ordered. */
      bond(midtri, tri1);
      lnextself(midtri);
      bond(midtri, tri2);
      lnextself(midtri);
      bond(midtri, tri3);
      lprevself(tri1);
      lnextself(tri2);
      bond(tri1, tri2);
      lprevself(tri1);
      lprevself(tri3);
      bond(tri1, tri3);
      lnextself(tri2);
      lprevself(tri3);
      bond(tri2, tri3);
      /* Ensure that the origin of `farleft' is sortarray[0]. */
      otricopy(tri1, *farleft);
      /* Ensure that the destination of `farright' is sortarray[2]. */
      if (area > 0.0) {
        otricopy(tri2, *farright);
      } else {
        lnext(*farleft, *farright);
      }
    }
    if (b->verbose > 2) {
      printf("  Creating ");
      printtriangle(m, b, &midtri);
      printf("  Creating ");
      printtriangle(m, b, &tri1);
      printf("  Creating ");
      printtriangle(m, b, &tri2);
      printf("  Creating ");
      printtriangle(m, b, &tri3);
    }
    return;
  } else {
    /* Split the vertices in half. */
    divider = vertices >> 1;
    /* Recursively triangulate each half. */
    divconqrecurse(m, b, sortarray, divider, 1 - axis, farleft, &innerleft);
    divconqrecurse(m, b, &sortarray[divider], vertices - divider, 1 - axis,
                   &innerright, farright);
    if (b->verbose > 1) {
      printf("  Joining triangulations with %d and %d vertices.\n", divider,
             vertices - divider);
    }
    /* Merge the two triangulations into one. */
    mergehulls(m, b, farleft, &innerleft, &innerright, farright, axis);
  }
}
 
long removeghosts(struct mesh *m, struct behavior *b, struct otri *startghost)
{
  struct otri searchedge;
  struct otri dissolveedge;
  struct otri deadtriangle;
  vertex markorg;
  long hullsize;
  triangle ptr;                         /* Temporary variable used by sym(). */
 
  if (b->verbose) {
    printf("  Removing ghost triangles.\n");
  }
  /* Find an edge on the convex hull to start point location from. */
  lprev(*startghost, searchedge);
  symself(searchedge);
  m->dummytri[0] = encode(searchedge);
  /* Remove the bounding box and count the convex hull edges. */
  otricopy(*startghost, dissolveedge);
  hullsize = 0;
  do {
    hullsize++;
    lnext(dissolveedge, deadtriangle);
    lprevself(dissolveedge);
    symself(dissolveedge);
    /* If no PSLG is involved, set the boundary markers of all the vertices */
    /*   on the convex hull.  If a PSLG is used, this step is done later.   */
    if (!b->poly) {
      /* Watch out for the case where all the input vertices are collinear. */
      if (dissolveedge.tri != m->dummytri) {
        org(dissolveedge, markorg);
        if (vertexmark(markorg) == 0) {
          setvertexmark(markorg, 1);
        }
      }
    }
    /* Remove a bounding triangle from a convex hull triangle. */
    dissolve(dissolveedge);
    /* Find the next bounding triangle. */
    sym(deadtriangle, dissolveedge);
    /* Delete the bounding triangle. */
    triangledealloc(m, deadtriangle.tri);
  } while (!otriequal(dissolveedge, *startghost));
  return hullsize;
}
 
/*****************************************************************************/
/*                                                                           */
/*  divconqdelaunay()   Form a Delaunay triangulation by the divide-and-     */
/*                      conquer method.                                      */
/*                                                                           */
/*  Sorts the vertices, calls a recursive procedure to triangulate them, and */
/*  removes the bounding box, setting boundary markers as appropriate.       */
/*                                                                           */
/*****************************************************************************/
 
long divconqdelaunay(struct mesh *m, struct behavior *b)
{
  vertex *sortarray;
  struct otri hullleft, hullright;
  int divider;
  int i, j;
 
  if (b->verbose) {
    printf("  Sorting vertices.\n");
  }
 
  /* Allocate an array of pointers to vertices for sorting. */
  sortarray = (vertex *) trimalloc(m->invertices * (int) sizeof(vertex));
  traversalinit(&m->vertices);
  for (i = 0; i < m->invertices; i++) {
    sortarray[i] = vertextraverse(m);
  }
  /* Sort the vertices. */
  vertexsort(sortarray, m->invertices);
  /* Discard duplicate vertices, which can really mess up the algorithm. */
  i = 0;
  for (j = 1; j < m->invertices; j++) {
    if ((sortarray[i][0] == sortarray[j][0])
        && (sortarray[i][1] == sortarray[j][1])) {
      if (!b->quiet) {
        printf(
"Warning:  A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n",
               sortarray[j][0], sortarray[j][1]);
      }
      setvertextype(sortarray[j], UNDEADVERTEX);
      m->undeads++;
    } else {
      i++;
      sortarray[i] = sortarray[j];
    }
  }
  i++;
  if (b->dwyer) {
    /* Re-sort the array of vertices to accommodate alternating cuts. */
    divider = i >> 1;
    if (i - divider >= 2) {
      if (divider >= 2) {
        alternateaxes(sortarray, divider, 1);
      }
      alternateaxes(&sortarray[divider], i - divider, 1);
    }
  }
 
  if (b->verbose) {
    printf("  Forming triangulation.\n");
  }
 
  /* Form the Delaunay triangulation. */
  divconqrecurse(m, b, sortarray, i, 0, &hullleft, &hullright);
  trifree((int *) sortarray);
 
  return removeghosts(m, b, &hullleft);
}
 
/********* Divide-and-conquer Delaunay triangulation ends here       *********/
 
/********* General mesh construction routines begin here             *********/
/*****************************************************************************/
/*                                                                           */
/*  delaunay()   Form a Delaunay triangulation.                              */
/*                                                                           */
/*****************************************************************************/
 
long delaunay(struct mesh *m, struct behavior *b)
{
  long hulledges;
 
  m->eextras = 0;
  initializetrisubpools(m, b);
 
  if (!b->quiet) {
    printf(
      "Constructing Delaunay triangulation by divide-and-conquer method.\n");
  }
  hulledges = divconqdelaunay(m, b);
 
  if (m->triangles.items == 0) {
    /* The input vertices were all collinear, so there are no triangles. */
    return 0l;
  } else {
    return hulledges;
  }
}
 
/********* General mesh construction routines end here               *********/
 
/********* Segment insertion begins here                             *********/
/*****************************************************************************/
/*                                                                           */
/*  finddirection()   Find the first triangle on the path from one point     */
/*                    to another.                                            */
/*                                                                           */
/*  Finds the triangle that intersects a line segment drawn from the         */
/*  origin of `searchtri' to the point `searchpoint', and returns the result */
/*  in `searchtri'.  The origin of `searchtri' does not change, even though  */
/*  the triangle returned may differ from the one passed in.  This routine   */
/*  is used to find the direction to move in to get from one point to        */
/*  another.                                                                 */
/*                                                                           */
/*  The return value notes whether the destination or apex of the found      */
/*  triangle is collinear with the two points in question.                   */
/*                                                                           */
/*****************************************************************************/
 
enum finddirectionresult finddirection(struct mesh *m, struct behavior *b,
                                       struct otri *searchtri,
                                       vertex searchpoint)
{
  struct otri checktri;
  vertex startvertex;
  vertex leftvertex, rightvertex;
  float leftccw, rightccw;
  int leftflag, rightflag;
  triangle ptr;           /* Temporary variable used by onext() and oprev(). */
 
  org(*searchtri, startvertex);
  dest(*searchtri, rightvertex);
  apex(*searchtri, leftvertex);
  /* Is `searchpoint' to the left? */
  leftccw = counterclockwise(m, b, searchpoint, startvertex, leftvertex);
  leftflag = leftccw > 0.0;
  /* Is `searchpoint' to the right? */
  rightccw = counterclockwise(m, b, startvertex, searchpoint, rightvertex);
  rightflag = rightccw > 0.0;
  if (leftflag && rightflag) {
    /* `searchtri' faces directly away from `searchpoint'.  We could go left */
    /*   or right.  Ask whether it's a triangle or a boundary on the left.   */
    onext(*searchtri, checktri);
    if (checktri.tri == m->dummytri) {
      leftflag = 0;
    } else {
      rightflag = 0;
    }
  }
  while (leftflag) {
    /* Turn left until satisfied. */
    onextself(*searchtri);
    if (searchtri->tri == m->dummytri) {
      printf("Internal error in finddirection():  Unable to find a\n");
      printf("  triangle leading from (%.12g, %.12g) to", startvertex[0],
             startvertex[1]);
      printf("  (%.12g, %.12g).\n", searchpoint[0], searchpoint[1]);
      internalerror();
    }
    apex(*searchtri, leftvertex);
    rightccw = leftccw;
    leftccw = counterclockwise(m, b, searchpoint, startvertex, leftvertex);
    leftflag = leftccw > 0.0;
  }
  while (rightflag) {
    /* Turn right until satisfied. */
    oprevself(*searchtri);
    if (searchtri->tri == m->dummytri) {
      printf("Internal error in finddirection():  Unable to find a\n");
      printf("  triangle leading from (%.12g, %.12g) to", startvertex[0],
             startvertex[1]);
      printf("  (%.12g, %.12g).\n", searchpoint[0], searchpoint[1]);
      internalerror();
    }
    dest(*searchtri, rightvertex);
    leftccw = rightccw;
    rightccw = counterclockwise(m, b, startvertex, searchpoint, rightvertex);
    rightflag = rightccw > 0.0;
  }
  if (leftccw == 0.0) {
    return LEFTCOLLINEAR;
  } else if (rightccw == 0.0) {
    return RIGHTCOLLINEAR;
  } else {
    return WITHIN;
  }
}
 
/*****************************************************************************/
/*                                                                           */
/*  segmentintersection()   Find the intersection of an existing segment     */
/*                          and a segment that is being inserted.  Insert    */
/*                          a vertex at the intersection, splitting an       */
/*                          existing subsegment.                             */
/*                                                                           */
/*  The segment being inserted connects the apex of splittri to endpoint2.   */
/*  splitsubseg is the subsegment being split, and MUST adjoin splittri.     */
/*  Hence, endpoints of the subsegment being split are the origin and        */
/*  destination of splittri.                                                 */
/*                                                                           */
/*  On completion, splittri is a handle having the newly inserted            */
/*  intersection point as its origin, and endpoint1 as its destination.      */
/*                                                                           */
/*****************************************************************************/
 
void segmentintersection(struct mesh *m, struct behavior *b,
                         struct otri *splittri, struct osub *splitsubseg,
                         vertex endpoint2)
{
  struct osub opposubseg;
  vertex endpoint1;
  vertex torg, tdest;
  vertex leftvertex, rightvertex;
  vertex newvertex;
  enum insertvertexresult success;
  enum finddirectionresult collinear;
  float ex, ey;
  float tx, ty;
  float etx, ety;
  float split, denom;
  int i;
  triangle ptr;                       /* Temporary variable used by onext(). */
  subseg sptr;                        /* Temporary variable used by snext(). */
 
  /* Find the other three segment endpoints. */
  apex(*splittri, endpoint1);
  org(*splittri, torg);
  dest(*splittri, tdest);
  /* Segment intersection formulae; see the Antonio reference. */
  tx = tdest[0] - torg[0];
  ty = tdest[1] - torg[1];
  ex = endpoint2[0] - endpoint1[0];
  ey = endpoint2[1] - endpoint1[1];
  etx = torg[0] - endpoint2[0];
  ety = torg[1] - endpoint2[1];
  denom = ty * ex - tx * ey;
  if (denom == 0.0) {
    printf("Internal error in segmentintersection():");
    printf("  Attempt to find intersection of parallel segments.\n");
    internalerror();
  }
  split = (ey * etx - ex * ety) / denom;
  /* Create the new vertex. */
  newvertex = (vertex) poolalloc(&m->vertices);
  /* Interpolate its coordinate and attributes. */
  for (i = 0; i < 2 + m->nextras; i++) {
    newvertex[i] = torg[i] + split * (tdest[i] - torg[i]);
  }
  setvertexmark(newvertex, mark(*splitsubseg));
  setvertextype(newvertex, INPUTVERTEX);
  if (b->verbose > 1) {
    printf(
  "  Splitting subsegment (%.12g, %.12g) (%.12g, %.12g) at (%.12g, %.12g).\n",
           torg[0], torg[1], tdest[0], tdest[1], newvertex[0], newvertex[1]);
  }
  /* Insert the intersection vertex.  This should always succeed. */
  success = insertvertex(m, b, newvertex, splittri, splitsubseg, 0, 0);
  if (success != SUCCESSFULVERTEX) {
    printf("Internal error in segmentintersection():\n");
    printf("  Failure to split a segment.\n");
    internalerror();
  }
  /* Record a triangle whose origin is the new vertex. */
  setvertex2tri(newvertex, encode(*splittri));
  if (m->steinerleft > 0) {
    m->steinerleft--;
  }
 
  /* Divide the segment into two, and correct the segment endpoints. */
  ssymself(*splitsubseg);
  spivot(*splitsubseg, opposubseg);
  sdissolve(*splitsubseg);
  sdissolve(opposubseg);
  do {
    setsegorg(*splitsubseg, newvertex);
    snextself(*splitsubseg);
  } while (splitsubseg->ss != m->dummysub);
  do {
    setsegorg(opposubseg, newvertex);
    snextself(opposubseg);
  } while (opposubseg.ss != m->dummysub);
 
  /* Inserting the vertex may have caused edge flips.  We wish to rediscover */
  /*   the edge connecting endpoint1 to the new intersection vertex.         */
  collinear = finddirection(m, b, splittri, endpoint1);
  dest(*splittri, rightvertex);
  apex(*splittri, leftvertex);
  if ((leftvertex[0] == endpoint1[0]) && (leftvertex[1] == endpoint1[1])) {
    onextself(*splittri);
  } else if ((rightvertex[0] != endpoint1[0]) ||
             (rightvertex[1] != endpoint1[1])) {
    printf("Internal error in segmentintersection():\n");
    printf("  Topological inconsistency after splitting a segment.\n");
    internalerror();
  }
  /* `splittri' should have destination endpoint1. */
}
 
/*****************************************************************************/
/*                                                                           */
/*  scoutsegment()   Scout the first triangle on the path from one endpoint  */
/*                   to another, and check for completion (reaching the      */
/*                   second endpoint), a collinear vertex, or the            */
/*                   intersection of two segments.                           */
/*                                                                           */
/*  Returns one if the entire segment is successfully inserted, and zero if  */
/*  the job must be finished by conformingedge() or constrainededge().       */
/*                                                                           */
/*  If the first triangle on the path has the second endpoint as its         */
/*  destination or apex, a subsegment is inserted and the job is done.       */
/*                                                                           */
/*  If the first triangle on the path has a destination or apex that lies on */
/*  the segment, a subsegment is inserted connecting the first endpoint to   */
/*  the collinear vertex, and the search is continued from the collinear     */
/*  vertex.                                                                  */
/*                                                                           */
/*  If the first triangle on the path has a subsegment opposite its origin,  */
/*  then there is a segment that intersects the segment being inserted.      */
/*  Their intersection vertex is inserted, splitting the subsegment.         */
/*                                                                           */
/*****************************************************************************/
 
int scoutsegment(struct mesh *m, struct behavior *b, struct otri *searchtri,
                 vertex endpoint2, int newmark)
{
  struct otri crosstri;
  struct osub crosssubseg;
  vertex leftvertex, rightvertex;
  enum finddirectionresult collinear;
  subseg sptr;                      /* Temporary variable used by tspivot(). */
 
  collinear = finddirection(m, b, searchtri, endpoint2);
  dest(*searchtri, rightvertex);
  apex(*searchtri, leftvertex);
  if (((leftvertex[0] == endpoint2[0]) && (leftvertex[1] == endpoint2[1])) ||
      ((rightvertex[0] == endpoint2[0]) && (rightvertex[1] == endpoint2[1]))) {
    /* The segment is already an edge in the mesh. */
    if ((leftvertex[0] == endpoint2[0]) && (leftvertex[1] == endpoint2[1])) {
      lprevself(*searchtri);
    }
    /* Insert a subsegment, if there isn't already one there. */
    insertsubseg(m, b, searchtri, newmark);
    return 1;
  } else if (collinear == LEFTCOLLINEAR) {
    /* We've collided with a vertex between the segment's endpoints. */
    /* Make the collinear vertex be the triangle's origin. */
    lprevself(*searchtri);
    insertsubseg(m, b, searchtri, newmark);
    /* Insert the remainder of the segment. */
    return scoutsegment(m, b, searchtri, endpoint2, newmark);
  } else if (collinear == RIGHTCOLLINEAR) {
    /* We've collided with a vertex between the segment's endpoints. */
    insertsubseg(m, b, searchtri, newmark);
    /* Make the collinear vertex be the triangle's origin. */
    lnextself(*searchtri);
    /* Insert the remainder of the segment. */
    return scoutsegment(m, b, searchtri, endpoint2, newmark);
  } else {
    lnext(*searchtri, crosstri);
    tspivot(crosstri, crosssubseg);
    /* Check for a crossing segment. */
    if (crosssubseg.ss == m->dummysub) {
      return 0;
    } else {
      /* Insert a vertex at the intersection. */
      segmentintersection(m, b, &crosstri, &crosssubseg, endpoint2);
      otricopy(crosstri, *searchtri);
      insertsubseg(m, b, searchtri, newmark);
      /* Insert the remainder of the segment. */
      return scoutsegment(m, b, searchtri, endpoint2, newmark);
    }
  }
}
 
/*****************************************************************************/
/*                                                                           */
/*  delaunayfixup()   Enforce the Delaunay condition at an edge, fanning out */
/*                    recursively from an existing vertex.  Pay special      */
/*                    attention to stacking inverted triangles.              */
/*                                                                           */
/*  This is a support routine for inserting segments into a constrained      */
/*  Delaunay triangulation.                                                  */
/*                                                                           */
/*  The origin of fixuptri is treated as if it has just been inserted, and   */
/*  the local Delaunay condition needs to be enforced.  It is only enforced  */
/*  in one sector, however, that being the angular range defined by          */
/*  fixuptri.                                                                */
/*                                                                           */
/*  This routine also needs to make decisions regarding the "stacking" of    */
/*  triangles.  (Read the description of constrainededge() below before      */
/*  reading on here, so you understand the algorithm.)  If the position of   */
/*  the new vertex (the origin of fixuptri) indicates that the vertex before */
/*  it on the polygon is a reflex vertex, then "stack" the triangle by       */
/*  doing nothing.  (fixuptri is an inverted triangle, which is how stacked  */
/*  triangles are identified.)                                               */
/*                                                                           */
/*  Otherwise, check whether the vertex before that was a reflex vertex.     */
/*  If so, perform an edge flip, thereby eliminating an inverted triangle    */
/*  (popping it off the stack).  The edge flip may result in the creation    */
/*  of a new inverted triangle, depending on whether or not the new vertex   */
/*  is visible to the vertex three edges behind on the polygon.              */
/*                                                                           */
/*  If neither of the two vertices behind the new vertex are reflex          */
/*  vertices, fixuptri and fartri, the triangle opposite it, are not         */
/*  inverted; hence, ensure that the edge between them is locally Delaunay.  */
/*                                                                           */
/*  `leftside' indicates whether or not fixuptri is to the left of the       */
/*  segment being inserted.  (Imagine that the segment is pointing up from   */
/*  endpoint1 to endpoint2.)                                                 */
/*                                                                           */
/*****************************************************************************/
 
void delaunayfixup(struct mesh *m, struct behavior *b,
                   struct otri *fixuptri, int leftside)
{
  struct otri neartri;
  struct otri fartri;
  struct osub faredge;
  vertex nearvertex, leftvertex, rightvertex, farvertex;
  triangle ptr;                         /* Temporary variable used by sym(). */
  subseg sptr;                      /* Temporary variable used by tspivot(). */
 
  lnext(*fixuptri, neartri);
  sym(neartri, fartri);
  /* Check if the edge opposite the origin of fixuptri can be flipped. */
  if (fartri.tri == m->dummytri) {
    return;
  }
  tspivot(neartri, faredge);
  if (faredge.ss != m->dummysub) {
    return;
  }
  /* Find all the relevant vertices. */
  apex(neartri, nearvertex);
  org(neartri, leftvertex);
  dest(neartri, rightvertex);
  apex(fartri, farvertex);
  /* Check whether the previous polygon vertex is a reflex vertex. */
  if (leftside) {
    if (counterclockwise(m, b, nearvertex, leftvertex, farvertex) <= 0.0) {
      /* leftvertex is a reflex vertex too.  Nothing can */
      /*   be done until a convex section is found.      */
      return;
    }
  } else {
    if (counterclockwise(m, b, farvertex, rightvertex, nearvertex) <= 0.0) {
      /* rightvertex is a reflex vertex too.  Nothing can */
      /*   be done until a convex section is found.       */
      return;
    }
  }
  if (counterclockwise(m, b, rightvertex, leftvertex, farvertex) > 0.0) {
    /* fartri is not an inverted triangle, and farvertex is not a reflex */
    /*   vertex.  As there are no reflex vertices, fixuptri isn't an     */
    /*   inverted triangle, either.  Hence, test the edge between the    */
    /*   triangles to ensure it is locally Delaunay.                     */
    if (incircle(m, b, leftvertex, farvertex, rightvertex, nearvertex) <=
        0.0) {
      return;
    }
    /* Not locally Delaunay; go on to an edge flip. */
  }        /* else fartri is inverted; remove it from the stack by flipping. */
  flip(m, b, &neartri);
  lprevself(*fixuptri);    /* Restore the origin of fixuptri after the flip. */
  /* Recursively process the two triangles that result from the flip. */
  delaunayfixup(m, b, fixuptri, leftside);
  delaunayfixup(m, b, &fartri, leftside);
}
 
/*****************************************************************************/
/*                                                                           */
/*  constrainededge()   Force a segment into a constrained Delaunay          */
/*                      triangulation by deleting the triangles it           */
/*                      intersects, and triangulating the polygons that      */
/*                      form on each side of it.                             */
/*                                                                           */
/*  Generates a single subsegment connecting `endpoint1' to `endpoint2'.     */
/*  The triangle `starttri' has `endpoint1' as its origin.  `newmark' is the */
/*  boundary marker of the segment.                                          */
/*                                                                           */
/*  To insert a segment, every triangle whose interior intersects the        */
/*  segment is deleted.  The union of these deleted triangles is a polygon   */
/*  (which is not necessarily monotone, but is close enough), which is       */
/*  divided into two polygons by the new segment.  This routine's task is    */
/*  to generate the Delaunay triangulation of these two polygons.            */
/*                                                                           */
/*  You might think of this routine's behavior as a two-step process.  The   */
/*  first step is to walk from endpoint1 to endpoint2, flipping each edge    */
/*  encountered.  This step creates a fan of edges connected to endpoint1,   */
/*  including the desired edge to endpoint2.  The second step enforces the   */
/*  Delaunay condition on each side of the segment in an incremental manner: */
/*  proceeding along the polygon from endpoint1 to endpoint2 (this is done   */
/*  independently on each side of the segment), each vertex is "enforced"    */
/*  as if it had just been inserted, but affecting only the previous         */
/*  vertices.  The result is the same as if the vertices had been inserted   */
/*  in the order they appear on the polygon, so the result is Delaunay.      */
/*                                                                           */
/*  In truth, constrainededge() interleaves these two steps.  The procedure  */
/*  walks from endpoint1 to endpoint2, and each time an edge is encountered  */
/*  and flipped, the newly exposed vertex (at the far end of the flipped     */
/*  edge) is "enforced" upon the previously flipped edges, usually affecting */
/*  only one side of the polygon (depending upon which side of the segment   */
/*  the vertex falls on).                                                    */
/*                                                                           */
/*  The algorithm is complicated by the need to handle polygons that are not */
/*  convex.  Although the polygon is not necessarily monotone, it can be     */
/*  triangulated in a manner similar to the stack-based algorithms for       */
/*  monotone polygons.  For each reflex vertex (local concavity) of the      */
/*  polygon, there will be an inverted triangle formed by one of the edge    */
/*  flips.  (An inverted triangle is one with negative area - that is, its   */
/*  vertices are arranged in clockwise order - and is best thought of as a   */
/*  wrinkle in the fabric of the mesh.)  Each inverted triangle can be       */
/*  thought of as a reflex vertex pushed on the stack, waiting to be fixed   */
/*  later.                                                                   */
/*                                                                           */
/*  A reflex vertex is popped from the stack when a vertex is inserted that  */
/*  is visible to the reflex vertex.  (However, if the vertex behind the     */
/*  reflex vertex is not visible to the reflex vertex, a new inverted        */
/*  triangle will take its place on the stack.)  These details are handled   */
/*  by the delaunayfixup() routine above.                                    */
/*                                                                           */
/*****************************************************************************/
 
void constrainededge(struct mesh *m, struct behavior *b,
                     struct otri *starttri, vertex endpoint2, int newmark)
{
  struct otri fixuptri, fixuptri2;
  struct osub crosssubseg;
  vertex endpoint1;
  vertex farvertex;
  float area;
  int collision;
  int done;
  triangle ptr;             /* Temporary variable used by sym() and oprev(). */
  subseg sptr;                      /* Temporary variable used by tspivot(). */
 
  org(*starttri, endpoint1);
  lnext(*starttri, fixuptri);
  flip(m, b, &fixuptri);
  /* `collision' indicates whether we have found a vertex directly */
  /*   between endpoint1 and endpoint2.                            */
  collision = 0;
  done = 0;
  do {
    org(fixuptri, farvertex);
    /* `farvertex' is the extreme point of the polygon we are "digging" */
    /*   to get from endpoint1 to endpoint2.                           */
    if ((farvertex[0] == endpoint2[0]) && (farvertex[1] == endpoint2[1])) {
      oprev(fixuptri, fixuptri2);
      /* Enforce the Delaunay condition around endpoint2. */
      delaunayfixup(m, b, &fixuptri, 0);
      delaunayfixup(m, b, &fixuptri2, 1);
      done = 1;
    } else {
      /* Check whether farvertex is to the left or right of the segment */
      /*   being inserted, to decide which edge of fixuptri to dig      */
      /*   through next.                                                */
      area = counterclockwise(m, b, endpoint1, endpoint2, farvertex);
      if (area == 0.0) {
        /* We've collided with a vertex between endpoint1 and endpoint2. */
        collision = 1;
        oprev(fixuptri, fixuptri2);
        /* Enforce the Delaunay condition around farvertex. */
        delaunayfixup(m, b, &fixuptri, 0);
        delaunayfixup(m, b, &fixuptri2, 1);
        done = 1;
      } else {
        if (area > 0.0) {        /* farvertex is to the left of the segment. */
          oprev(fixuptri, fixuptri2);
          /* Enforce the Delaunay condition around farvertex, on the */
          /*   left side of the segment only.                        */
          delaunayfixup(m, b, &fixuptri2, 1);
          /* Flip the edge that crosses the segment.  After the edge is */
          /*   flipped, one of its endpoints is the fan vertex, and the */
          /*   destination of fixuptri is the fan vertex.               */
          lprevself(fixuptri);
        } else {                /* farvertex is to the right of the segment. */
          delaunayfixup(m, b, &fixuptri, 0);
          /* Flip the edge that crosses the segment.  After the edge is */
          /*   flipped, one of its endpoints is the fan vertex, and the */
          /*   destination of fixuptri is the fan vertex.               */
          oprevself(fixuptri);
        }
        /* Check for two intersecting segments. */
        tspivot(fixuptri, crosssubseg);
        if (crosssubseg.ss == m->dummysub) {
          flip(m, b, &fixuptri);    /* May create inverted triangle at left. */
        } else {
          /* We've collided with a segment between endpoint1 and endpoint2. */
          collision = 1;
          /* Insert a vertex at the intersection. */
          segmentintersection(m, b, &fixuptri, &crosssubseg, endpoint2);
          done = 1;
        }
      }
    }
  } while (!done);
  /* Insert a subsegment to make the segment permanent. */
  insertsubseg(m, b, &fixuptri, newmark);
  /* If there was a collision with an interceding vertex, install another */
  /*   segment connecting that vertex with endpoint2.                     */
  if (collision) {
    /* Insert the remainder of the segment. */
    if (!scoutsegment(m, b, &fixuptri, endpoint2, newmark)) {
      constrainededge(m, b, &fixuptri, endpoint2, newmark);
    }
  }
}
 
/*****************************************************************************/
/*                                                                           */
/*  insertsegment()   Insert a PSLG segment into a triangulation.            */
/*                                                                           */
/*****************************************************************************/
 
void insertsegment(struct mesh *m, struct behavior *b,
                   vertex endpoint1, vertex endpoint2, int newmark)
{
  struct otri searchtri1, searchtri2;
  triangle encodedtri;
  vertex checkvertex;
  triangle ptr;                         /* Temporary variable used by sym(). */
 
  if (b->verbose > 1) {
    printf("  Connecting (%.12g, %.12g) to (%.12g, %.12g).\n",
           endpoint1[0], endpoint1[1], endpoint2[0], endpoint2[1]);
  }
 
  /* Find a triangle whose origin is the segment's first endpoint. */
  checkvertex = (vertex) NULL;
  encodedtri = vertex2tri(endpoint1);
  if (encodedtri != (triangle) NULL) {
    decode(encodedtri, searchtri1);
    org(searchtri1, checkvertex);
  }
  if (checkvertex != endpoint1) {
    /* Find a boundary triangle to search from. */
    searchtri1.tri = m->dummytri;
    searchtri1.orient = 0;
    symself(searchtri1);
    /* Search for the segment's first endpoint by point location. */
    if (locate(m, b, endpoint1, &searchtri1) != ONVERTEX) {
      printf(
        "Internal error in insertsegment():  Unable to locate PSLG vertex\n");
      printf("  (%.12g, %.12g) in triangulation.\n",
             endpoint1[0], endpoint1[1]);
      internalerror();
    }
  }
  /* Remember this triangle to improve subsequent point location. */
  otricopy(searchtri1, m->recenttri);
  /* Scout the beginnings of a path from the first endpoint */
  /*   toward the second.                                   */
  if (scoutsegment(m, b, &searchtri1, endpoint2, newmark)) {
    /* The segment was easily inserted. */
    return;
  }
  /* The first endpoint may have changed if a collision with an intervening */
  /*   vertex on the segment occurred.                                      */
  org(searchtri1, endpoint1);
 
  /* Find a triangle whose origin is the segment's second endpoint. */
  checkvertex = (vertex) NULL;
  encodedtri = vertex2tri(endpoint2);
  if (encodedtri != (triangle) NULL) {
    decode(encodedtri, searchtri2);
    org(searchtri2, checkvertex);
  }
  if (checkvertex != endpoint2) {
    /* Find a boundary triangle to search from. */
    searchtri2.tri = m->dummytri;
    searchtri2.orient = 0;
    symself(searchtri2);
    /* Search for the segment's second endpoint by point location. */
    if (locate(m, b, endpoint2, &searchtri2) != ONVERTEX) {
      printf(
        "Internal error in insertsegment():  Unable to locate PSLG vertex\n");
      printf("  (%.12g, %.12g) in triangulation.\n",
             endpoint2[0], endpoint2[1]);
      internalerror();
    }
  }
  /* Remember this triangle to improve subsequent point location. */
  otricopy(searchtri2, m->recenttri);
  /* Scout the beginnings of a path from the second endpoint */
  /*   toward the first.                                     */
  if (scoutsegment(m, b, &searchtri2, endpoint1, newmark)) {
    /* The segment was easily inserted. */
    return;
  }
  /* The second endpoint may have changed if a collision with an intervening */
  /*   vertex on the segment occurred.                                       */
  org(searchtri2, endpoint2);
 
    /* Insert the segment directly into the triangulation. */
    constrainededge(m, b, &searchtri1, endpoint2, newmark);
}
 
/*****************************************************************************/
/*                                                                           */
/*  markhull()   Cover the convex hull of a triangulation with subsegments.  */
/*                                                                           */
/*****************************************************************************/
 
void markhull(struct mesh *m, struct behavior *b)
{
  struct otri hulltri;
  struct otri nexttri;
  struct otri starttri;
  triangle ptr;             /* Temporary variable used by sym() and oprev(). */
 
  /* Find a triangle handle on the hull. */
  hulltri.tri = m->dummytri;
  hulltri.orient = 0;
  symself(hulltri);
  /* Remember where we started so we know when to stop. */
  otricopy(hulltri, starttri);
  /* Go once counterclockwise around the convex hull. */
  do {
    /* Create a subsegment if there isn't already one here. */
    insertsubseg(m, b, &hulltri, 1);
    /* To find the next hull edge, go clockwise around the next vertex. */
    lnextself(hulltri);
    oprev(hulltri, nexttri);
    while (nexttri.tri != m->dummytri) {
      otricopy(nexttri, hulltri);
      oprev(hulltri, nexttri);
    }
  } while (!otriequal(hulltri, starttri));
}
 
/*****************************************************************************/
/*                                                                           */
/*  formskeleton()   Create the segments of a triangulation, including PSLG  */
/*                   segments and edges on the convex hull.                  */
/*                                                                           */
/*  The PSLG segments are read from a .poly file.  The return value is the   */
/*  number of segments in the file.                                          */
/*                                                                           */
/*****************************************************************************/
 
void formskeleton(struct mesh *m, struct behavior *b, int *segmentlist,
                  int *segmentmarkerlist, int numberofsegments)
{
  char polyfilename[6];
  int index;
  vertex endpoint1, endpoint2;
  int segmentmarkers;
  int end1, end2;
  int boundmarker;
  int i;
 
  if (b->poly) {
    if (!b->quiet) {
      printf("Recovering segments in Delaunay triangulation.\n");
    }
    strcpy(polyfilename, "input");
    m->insegments = numberofsegments;
    segmentmarkers = segmentmarkerlist != (int *) NULL;
    index = 0;
    /* If the input vertices are collinear, there is no triangulation, */
    /*   so don't try to insert segments.                              */
    if (m->triangles.items == 0) {
      return;
    }
 
    /* If segments are to be inserted, compute a mapping */
    /*   from vertices to triangles.                     */
    if (m->insegments > 0) {
      makevertexmap(m, b);
      if (b->verbose) {
        printf("  Recovering PSLG segments.\n");
      }
    }
 
    boundmarker = 0;
    /* Read and insert the segments. */
    for (i = 0; i < m->insegments; i++) {
      end1 = segmentlist[index++];
      end2 = segmentlist[index++];
      if (segmentmarkers) {
        boundmarker = segmentmarkerlist[i];
      }
      if ((end1 < b->firstnumber) ||
          (end1 >= b->firstnumber + m->invertices)) {
        if (!b->quiet) {
          printf("Warning:  Invalid first endpoint of segment %d in %s.\n",
                 b->firstnumber + i, polyfilename);
        }
      } else if ((end2 < b->firstnumber) ||
                 (end2 >= b->firstnumber + m->invertices)) {
        if (!b->quiet) {
          printf("Warning:  Invalid second endpoint of segment %d in %s.\n",
                 b->firstnumber + i, polyfilename);
        }
      } else {
        /* Find the vertices numbered `end1' and `end2'. */
        endpoint1 = getvertex(m, b, end1);
        endpoint2 = getvertex(m, b, end2);
        if ((endpoint1[0] == endpoint2[0]) && (endpoint1[1] == endpoint2[1])) {
          if (!b->quiet) {
            printf("Warning:  Endpoints of segment %d are coincident in %s.\n",
                   b->firstnumber + i, polyfilename);
          }
        } else {
          insertsegment(m, b, endpoint1, endpoint2, boundmarker);
        }
      }
    }
  } else {
    m->insegments = 0;
  }
  if (b->convex || !b->poly) {
    /* Enclose the convex hull with subsegments. */
    if (b->verbose) {
      printf("  Enclosing convex hull with segments.\n");
    }
    markhull(m, b);
  }
}
 
/********* Segment insertion ends here                               *********/
 
/********* Carving out holes and concavities begins here             *********/
/*****************************************************************************/
/*                                                                           */
/*  infecthull()   Virally infect all of the triangles of the convex hull    */
/*                 that are not protected by subsegments.  Where there are   */
/*                 subsegments, set boundary markers as appropriate.         */
/*                                                                           */
/*****************************************************************************/
 
void infecthull(struct mesh *m, struct behavior *b)
{
  struct otri hulltri;
  struct otri nexttri;
  struct otri starttri;
  struct osub hullsubseg;
  triangle **deadtriangle;
  vertex horg, hdest;
  triangle ptr;                         /* Temporary variable used by sym(). */
  subseg sptr;                      /* Temporary variable used by tspivot(). */
 
  if (b->verbose) {
    printf("  Marking concavities (external triangles) for elimination.\n");
  }
  /* Find a triangle handle on the hull. */
  hulltri.tri = m->dummytri;
  hulltri.orient = 0;
  symself(hulltri);
  /* Remember where we started so we know when to stop. */
  otricopy(hulltri, starttri);
  /* Go once counterclockwise around the convex hull. */
  do {
    /* Ignore triangles that are already infected. */
    if (!infected(hulltri)) {
      /* Is the triangle protected by a subsegment? */
      tspivot(hulltri, hullsubseg);
      if (hullsubseg.ss == m->dummysub) {
        /* The triangle is not protected; infect it. */
        if (!infected(hulltri)) {
          infect(hulltri);
          deadtriangle = (triangle **) poolalloc(&m->viri);
          *deadtriangle = hulltri.tri;
        }
      } else {
        /* The triangle is protected; set boundary markers if appropriate. */
        if (mark(hullsubseg) == 0) {
          setmark(hullsubseg, 1);
          org(hulltri, horg);
          dest(hulltri, hdest);
          if (vertexmark(horg) == 0) {
            setvertexmark(horg, 1);
          }
          if (vertexmark(hdest) == 0) {
            setvertexmark(hdest, 1);
          }
        }
      }
    }
    /* To find the next hull edge, go clockwise around the next vertex. */
    lnextself(hulltri);
    oprev(hulltri, nexttri);
    while (nexttri.tri != m->dummytri) {
      otricopy(nexttri, hulltri);
      oprev(hulltri, nexttri);
    }
  } while (!otriequal(hulltri, starttri));
}
 
/*****************************************************************************/
/*                                                                           */
/*  plague()   Spread the virus from all infected triangles to any neighbors */
/*             not protected by subsegments.  Delete all infected triangles. */
/*                                                                           */
/*  This is the procedure that actually creates holes and concavities.       */
/*                                                                           */
/*  This procedure operates in two phases.  The first phase identifies all   */
/*  the triangles that will die, and marks them as infected.  They are       */
/*  marked to ensure that each triangle is added to the virus pool only      */
/*  once, so the procedure will terminate.                                   */
/*                                                                           */
/*  The second phase actually eliminates the infected triangles.  It also    */
/*  eliminates orphaned vertices.                                            */
/*                                                                           */
/*****************************************************************************/
 
void plague(struct mesh *m, struct behavior *b)
{
  struct otri testtri;
  struct otri neighbor;
  triangle **virusloop;
  triangle **deadtriangle;
  struct osub neighborsubseg;
  vertex testvertex;
  vertex norg, ndest;
  vertex deadorg, deaddest, deadapex;
  int killorg;
  triangle ptr;             /* Temporary variable used by sym() and onext(). */
  subseg sptr;                      /* Temporary variable used by tspivot(). */
 
  if (b->verbose) {
    printf("  Marking neighbors of marked triangles.\n");
  }
  /* Loop through all the infected triangles, spreading the virus to */
  /*   their neighbors, then to their neighbors' neighbors.          */
  traversalinit(&m->viri);
  virusloop = (triangle **) traverse(&m->viri);
  while (virusloop != (triangle **) NULL) {
    testtri.tri = *virusloop;
    /* A triangle is marked as infected by messing with one of its pointers */
    /*   to subsegments, setting it to an illegal value.  Hence, we have to */
    /*   temporarily uninfect this triangle so that we can examine its      */
    /*   adjacent subsegments.                                              */
    uninfect(testtri);
    if (b->verbose > 2) {
      /* Assign the triangle an orientation for convenience in */
      /*   checking its vertices.                              */
      testtri.orient = 0;
      org(testtri, deadorg);
      dest(testtri, deaddest);
      apex(testtri, deadapex);
      printf("    Checking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
             deadorg[0], deadorg[1], deaddest[0], deaddest[1],
             deadapex[0], deadapex[1]);
    }
    /* Check each of the triangle's three neighbors. */
    for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
      /* Find the neighbor. */
      sym(testtri, neighbor);
      /* Check for a subsegment between the triangle and its neighbor. */
      tspivot(testtri, neighborsubseg);
      /* Check if the neighbor is nonexistent or already infected. */
      if ((neighbor.tri == m->dummytri) || infected(neighbor)) {
        if (neighborsubseg.ss != m->dummysub) {
          /* There is a subsegment separating the triangle from its      */
          /*   neighbor, but both triangles are dying, so the subsegment */
          /*   dies too.                                                 */
          subsegdealloc(m, neighborsubseg.ss);
          if (neighbor.tri != m->dummytri) {
            /* Make sure the subsegment doesn't get deallocated again */
            /*   later when the infected neighbor is visited.         */
            uninfect(neighbor);
            tsdissolve(neighbor);
            infect(neighbor);
          }
        }
      } else {                   /* The neighbor exists and is not infected. */
        if (neighborsubseg.ss == m->dummysub) {
          /* There is no subsegment protecting the neighbor, so */
          /*   the neighbor becomes infected.                   */
          if (b->verbose > 2) {
            org(neighbor, deadorg);
            dest(neighbor, deaddest);
            apex(neighbor, deadapex);
            printf(
              "    Marking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
                   deadorg[0], deadorg[1], deaddest[0], deaddest[1],
                   deadapex[0], deadapex[1]);
          }
          infect(neighbor);
          /* Ensure that the neighbor's neighbors will be infected. */
          deadtriangle = (triangle **) poolalloc(&m->viri);
          *deadtriangle = neighbor.tri;
        } else {               /* The neighbor is protected by a subsegment. */
          /* Remove this triangle from the subsegment. */
          stdissolve(neighborsubseg);
          /* The subsegment becomes a boundary.  Set markers accordingly. */
          if (mark(neighborsubseg) == 0) {
            setmark(neighborsubseg, 1);
          }
          org(neighbor, norg);
          dest(neighbor, ndest);
          if (vertexmark(norg) == 0) {
            setvertexmark(norg, 1);
          }
          if (vertexmark(ndest) == 0) {
            setvertexmark(ndest, 1);
          }
        }
      }
    }
    /* Remark the triangle as infected, so it doesn't get added to the */
    /*   virus pool again.                                             */
    infect(testtri);
    virusloop = (triangle **) traverse(&m->viri);
  }
 
  if (b->verbose) {
    printf("  Deleting marked triangles.\n");
  }
 
  traversalinit(&m->viri);
  virusloop = (triangle **) traverse(&m->viri);
  while (virusloop != (triangle **) NULL) {
    testtri.tri = *virusloop;
 
    /* Check each of the three corners of the triangle for elimination. */
    /*   This is done by walking around each vertex, checking if it is  */
    /*   still connected to at least one live triangle.                 */
    for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
      org(testtri, testvertex);
      /* Check if the vertex has already been tested. */
      if (testvertex != (vertex) NULL) {
        killorg = 1;
        /* Mark the corner of the triangle as having been tested. */
        setorg(testtri, NULL);
        /* Walk counterclockwise about the vertex. */
        onext(testtri, neighbor);
        /* Stop upon reaching a boundary or the starting triangle. */
        while ((neighbor.tri != m->dummytri) &&
               (!otriequal(neighbor, testtri))) {
          if (infected(neighbor)) {
            /* Mark the corner of this triangle as having been tested. */
            setorg(neighbor, NULL);
          } else {
            /* A live triangle.  The vertex survives. */
            killorg = 0;
          }
          /* Walk counterclockwise about the vertex. */
          onextself(neighbor);
        }
        /* If we reached a boundary, we must walk clockwise as well. */
        if (neighbor.tri == m->dummytri) {
          /* Walk clockwise about the vertex. */
          oprev(testtri, neighbor);
          /* Stop upon reaching a boundary. */
          while (neighbor.tri != m->dummytri) {
            if (infected(neighbor)) {
            /* Mark the corner of this triangle as having been tested. */
              setorg(neighbor, NULL);
            } else {
              /* A live triangle.  The vertex survives. */
              killorg = 0;
            }
            /* Walk clockwise about the vertex. */
            oprevself(neighbor);
          }
        }
        if (killorg) {
          if (b->verbose > 1) {
            printf("    Deleting vertex (%.12g, %.12g)\n",
                   testvertex[0], testvertex[1]);
          }
          setvertextype(testvertex, UNDEADVERTEX);
          m->undeads++;
        }
      }
    }
 
    /* Record changes in the number of boundary edges, and disconnect */
    /*   dead triangles from their neighbors.                         */
    for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
      sym(testtri, neighbor);
      if (neighbor.tri == m->dummytri) {
        /* There is no neighboring triangle on this edge, so this edge    */
        /*   is a boundary edge.  This triangle is being deleted, so this */
        /*   boundary edge is deleted.                                    */
        m->hullsize--;
      } else {
        /* Disconnect the triangle from its neighbor. */
        dissolve(neighbor);
        /* There is a neighboring triangle on this edge, so this edge */
        /*   becomes a boundary edge when this triangle is deleted.   */
        m->hullsize++;
      }
    }
    /* Return the dead triangle to the pool of triangles. */
    triangledealloc(m, testtri.tri);
    virusloop = (triangle **) traverse(&m->viri);
  }
  /* Empty the virus pool. */
  poolrestart(&m->viri);
}
 
/*****************************************************************************/
/*                                                                           */
/*  regionplague()   Spread regional attributes and/or area constraints      */
/*                   (from a .poly file) throughout the mesh.                */
/*                                                                           */
/*  This procedure operates in two phases.  The first phase spreads an       */
/*  attribute and/or an area constraint through a (segment-bounded) region.  */
/*  The triangles are marked to ensure that each triangle is added to the    */
/*  virus pool only once, so the procedure will terminate.                   */
/*                                                                           */
/*  The second phase uninfects all infected triangles, returning them to     */
/*  normal.                                                                  */
/*                                                                           */
/*****************************************************************************/
 
void regionplague(struct mesh *m, struct behavior *b,
                  float attribute, float area)
{
  struct otri testtri;
  struct otri neighbor;
  triangle **virusloop;
  triangle **regiontri;
  struct osub neighborsubseg;
  vertex regionorg, regiondest, regionapex;
  triangle ptr;             /* Temporary variable used by sym() and onext(). */
  subseg sptr;                      /* Temporary variable used by tspivot(). */
 
  if (b->verbose > 1) {
    printf("  Marking neighbors of marked triangles.\n");
  }
  /* Loop through all the infected triangles, spreading the attribute      */
  /*   and/or area constraint to their neighbors, then to their neighbors' */
  /*   neighbors.                                                          */
  traversalinit(&m->viri);
  virusloop = (triangle **) traverse(&m->viri);
  while (virusloop != (triangle **) NULL) {
    testtri.tri = *virusloop;
    /* A triangle is marked as infected by messing with one of its pointers */
    /*   to subsegments, setting it to an illegal value.  Hence, we have to */
    /*   temporarily uninfect this triangle so that we can examine its      */
    /*   adjacent subsegments.                                              */
    uninfect(testtri);
    if (b->regionattrib) {
      /* Set an attribute. */
      setelemattribute(testtri, m->eextras, attribute);
    }
    if (b->vararea) {
      /* Set an area constraint. */
      setareabound(testtri, area);
    }
    if (b->verbose > 2) {
      /* Assign the triangle an orientation for convenience in */
      /*   checking its vertices.                              */
      testtri.orient = 0;
      org(testtri, regionorg);
      dest(testtri, regiondest);
      apex(testtri, regionapex);
      printf("    Checking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
             regionorg[0], regionorg[1], regiondest[0], regiondest[1],
             regionapex[0], regionapex[1]);
    }
    /* Check each of the triangle's three neighbors. */
    for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
      /* Find the neighbor. */
      sym(testtri, neighbor);
      /* Check for a subsegment between the triangle and its neighbor. */
      tspivot(testtri, neighborsubseg);
      /* Make sure the neighbor exists, is not already infected, and */
      /*   isn't protected by a subsegment.                          */
      if ((neighbor.tri != m->dummytri) && !infected(neighbor)
          && (neighborsubseg.ss == m->dummysub)) {
        if (b->verbose > 2) {
          org(neighbor, regionorg);
          dest(neighbor, regiondest);
          apex(neighbor, regionapex);
          printf("    Marking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
                 regionorg[0], regionorg[1], regiondest[0], regiondest[1],
                 regionapex[0], regionapex[1]);
        }
        /* Infect the neighbor. */
        infect(neighbor);
        /* Ensure that the neighbor's neighbors will be infected. */
        regiontri = (triangle **) poolalloc(&m->viri);
        *regiontri = neighbor.tri;
      }
    }
    /* Remark the triangle as infected, so it doesn't get added to the */
    /*   virus pool again.                                             */
    infect(testtri);
    virusloop = (triangle **) traverse(&m->viri);
  }
 
  /* Uninfect all triangles. */
  if (b->verbose > 1) {
    printf("  Unmarking marked triangles.\n");
  }
  traversalinit(&m->viri);
  virusloop = (triangle **) traverse(&m->viri);
  while (virusloop != (triangle **) NULL) {
    testtri.tri = *virusloop;
    uninfect(testtri);
    virusloop = (triangle **) traverse(&m->viri);
  }
  /* Empty the virus pool. */
  poolrestart(&m->viri);
}
 
/*****************************************************************************/
/*                                                                           */
/*  carveholes()   Find the holes and infect them.  Find the area            */
/*                 constraints and infect them.  Infect the convex hull.     */
/*                 Spread the infection and kill triangles.  Spread the      */
/*                 area constraints.                                         */
/*                                                                           */
/*  This routine mainly calls other routines to carry out all these          */
/*  functions.                                                               */
/*                                                                           */
/*****************************************************************************/
 
void carveholes(struct mesh *m, struct behavior *b, float *holelist, int holes,
                float *regionlist, int regions)
{
  struct otri searchtri;
  struct otri triangleloop;
  struct otri *regiontris;
  triangle **holetri;
  triangle **regiontri;
  vertex searchorg, searchdest;
  enum locateresult intersect;
  int i;
  triangle ptr;                         /* Temporary variable used by sym(). */
 
  if (!(b->quiet || (b->noholes && b->convex))) {
    printf("Removing unwanted triangles.\n");
    if (b->verbose && (holes > 0)) {
      printf("  Marking holes for elimination.\n");
    }
  }
 
  if (regions > 0) {
    /* Allocate storage for the triangles in which region points fall. */
    regiontris = (struct otri *) trimalloc(regions *
                                           (int) sizeof(struct otri));
  } else {
    regiontris = (struct otri *) NULL;
  }
 
  if (((holes > 0) && !b->noholes) || !b->convex || (regions > 0)) {
    /* Initialize a pool of viri to be used for holes, concavities, */
    /*   regional attributes, and/or regional area constraints.     */
    poolinit(&m->viri, sizeof(triangle *), VIRUSPERBLOCK, VIRUSPERBLOCK, 0);
  }
 
  if (!b->convex) {
    /* Mark as infected any unprotected triangles on the boundary. */
    /*   This is one way by which concavities are created.         */
    infecthull(m, b);
  }
 
  if ((holes > 0) && !b->noholes) {
    /* Infect each triangle in which a hole lies. */
    for (i = 0; i < 2 * holes; i += 2) {
      /* Ignore holes that aren't within the bounds of the mesh. */
      if ((holelist[i] >= m->xmin) && (holelist[i] <= m->xmax)
          && (holelist[i + 1] >= m->ymin) && (holelist[i + 1] <= m->ymax)) {
        /* Start searching from some triangle on the outer boundary. */
        searchtri.tri = m->dummytri;
        searchtri.orient = 0;
        symself(searchtri);
        /* Ensure that the hole is to the left of this boundary edge; */
        /*   otherwise, locate() will falsely report that the hole    */
        /*   falls within the starting triangle.                      */
        org(searchtri, searchorg);
        dest(searchtri, searchdest);
        if (counterclockwise(m, b, searchorg, searchdest, &holelist[i]) >
            0.0) {
          /* Find a triangle that contains the hole. */
          intersect = locate(m, b, &holelist[i], &searchtri);
          if ((intersect != OUTSIDE) && (!infected(searchtri))) {
            /* Infect the triangle.  This is done by marking the triangle  */
            /*   as infected and including the triangle in the virus pool. */
            infect(searchtri);
            holetri = (triangle **) poolalloc(&m->viri);
            *holetri = searchtri.tri;
          }
        }
      }
    }
  }
 
  /* Now, we have to find all the regions BEFORE we carve the holes, because */
  /*   locate() won't work when the triangulation is no longer convex.       */
  /*   (Incidentally, this is the reason why regional attributes and area    */
  /*   constraints can't be used when refining a preexisting mesh, which     */
  /*   might not be convex; they can only be used with a freshly             */
  /*   triangulated PSLG.)                                                   */
  if (regions > 0) {
    /* Find the starting triangle for each region. */
    for (i = 0; i < regions; i++) {
      regiontris[i].tri = m->dummytri;
      /* Ignore region points that aren't within the bounds of the mesh. */
      if ((regionlist[4 * i] >= m->xmin) && (regionlist[4 * i] <= m->xmax) &&
          (regionlist[4 * i + 1] >= m->ymin) &&
          (regionlist[4 * i + 1] <= m->ymax)) {
        /* Start searching from some triangle on the outer boundary. */
        searchtri.tri = m->dummytri;
        searchtri.orient = 0;
        symself(searchtri);
        /* Ensure that the region point is to the left of this boundary */
        /*   edge; otherwise, locate() will falsely report that the     */
        /*   region point falls within the starting triangle.           */
        org(searchtri, searchorg);
        dest(searchtri, searchdest);
        if (counterclockwise(m, b, searchorg, searchdest, &regionlist[4 * i]) >
            0.0) {
          /* Find a triangle that contains the region point. */
          intersect = locate(m, b, &regionlist[4 * i], &searchtri);
          if ((intersect != OUTSIDE) && (!infected(searchtri))) {
            /* Record the triangle for processing after the */
            /*   holes have been carved.                    */
            otricopy(searchtri, regiontris[i]);
          }
        }
      }
    }
  }
 
  if (m->viri.items > 0) {
    /* Carve the holes and concavities. */
    plague(m, b);
  }
  /* The virus pool should be empty now. */
 
  if (regions > 0) {
    if (!b->quiet) {
      if (b->regionattrib) {
        if (b->vararea) {
          printf("Spreading regional attributes and area constraints.\n");
        } else {
          printf("Spreading regional attributes.\n");
        }
      } else { 
        printf("Spreading regional area constraints.\n");
      }
    }
    if (b->regionattrib && !b->refine) {
      /* Assign every triangle a regional attribute of zero. */
      traversalinit(&m->triangles);
      triangleloop.orient = 0;
      triangleloop.tri = triangletraverse(m);
      while (triangleloop.tri != (triangle *) NULL) {
        setelemattribute(triangleloop, m->eextras, 0.0);
        triangleloop.tri = triangletraverse(m);
      }
    }
    for (i = 0; i < regions; i++) {
      if (regiontris[i].tri != m->dummytri) {
        /* Make sure the triangle under consideration still exists. */
        /*   It may have been eaten by the virus.                   */
        if (!deadtri(regiontris[i].tri)) {
          /* Put one triangle in the virus pool. */
          infect(regiontris[i]);
          regiontri = (triangle **) poolalloc(&m->viri);
          *regiontri = regiontris[i].tri;
          /* Apply one region's attribute and/or area constraint. */
          regionplague(m, b, regionlist[4 * i + 2], regionlist[4 * i + 3]);
          /* The virus pool should be empty now. */
        }
      }
    }
    if (b->regionattrib && !b->refine) {
      /* Note the fact that each triangle has an additional attribute. */
      m->eextras++;
    }
  }
 
  /* Free up memory. */
  if (((holes > 0) && !b->noholes) || !b->convex || (regions > 0)) {
    pooldeinit(&m->viri);
  }
  if (regions > 0) {
    trifree((int *) regiontris);
  }
}
 
/********* Carving out holes and concavities ends here               *********/
 
/*****************************************************************************/
/*                                                                           */
/*  highorder()   Create extra nodes for quadratic subparametric elements.   */
/*                                                                           */
/*****************************************************************************/
 
void highorder(struct mesh *m, struct behavior *b)
{
  struct otri triangleloop, trisym;
  struct osub checkmark;
  vertex newvertex;
  vertex torg, tdest;
  int i;
  triangle ptr;                         /* Temporary variable used by sym(). */
  subseg sptr;                      /* Temporary variable used by tspivot(). */
 
  if (!b->quiet) {
    printf("Adding vertices for second-order triangles.\n");
  }
  /* The following line ensures that dead items in the pool of nodes    */
  /*   cannot be allocated for the extra nodes associated with high     */
  /*   order elements.  This ensures that the primary nodes (at the     */
  /*   corners of elements) will occur earlier in the output files, and */
  /*   have lower indices, than the extra nodes.                        */
  m->vertices.deaditemstack = (int *) NULL;
 
  traversalinit(&m->triangles);
  triangleloop.tri = triangletraverse(m);
  /* To loop over the set of edges, loop over all triangles, and look at   */
  /*   the three edges of each triangle.  If there isn't another triangle  */
  /*   adjacent to the edge, operate on the edge.  If there is another     */
  /*   adjacent triangle, operate on the edge only if the current triangle */
  /*   has a smaller pointer than its neighbor.  This way, each edge is    */
  /*   considered only once.                                               */
  while (triangleloop.tri != (triangle *) NULL) {
    for (triangleloop.orient = 0; triangleloop.orient < 3;
         triangleloop.orient++) {
      sym(triangleloop, trisym);
      if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) {
        org(triangleloop, torg);
        dest(triangleloop, tdest);
        /* Create a new node in the middle of the edge.  Interpolate */
        /*   its attributes.                                         */
        newvertex = (vertex) poolalloc(&m->vertices);
        for (i = 0; i < 2 + m->nextras; i++) {
          newvertex[i] = 0.5 * (torg[i] + tdest[i]);
        }
        /* Set the new node's marker to zero or one, depending on */
        /*   whether it lies on a boundary.                       */
        setvertexmark(newvertex, trisym.tri == m->dummytri);
        setvertextype(newvertex,
                      trisym.tri == m->dummytri ? FREEVERTEX : SEGMENTVERTEX);
        if (b->usesegments) {
          tspivot(triangleloop, checkmark);
          /* If this edge is a segment, transfer the marker to the new node. */
          if (checkmark.ss != m->dummysub) {
            setvertexmark(newvertex, mark(checkmark));
            setvertextype(newvertex, SEGMENTVERTEX);
          }
        }
        if (b->verbose > 1) {
          printf("  Creating (%.12g, %.12g).\n", newvertex[0], newvertex[1]);
        }
        /* Record the new node in the (one or two) adjacent elements. */
        triangleloop.tri[m->highorderindex + triangleloop.orient] =
                (triangle) newvertex;
        if (trisym.tri != m->dummytri) {
          trisym.tri[m->highorderindex + trisym.orient] = (triangle) newvertex;
        }
      }
    }
    triangleloop.tri = triangletraverse(m);
  }
}
 
/********* File I/O routines begin here                              *********/
/*****************************************************************************/
/*                                                                           */
/*  transfernodes()   Read the vertices from memory.                         */
/*                                                                           */
/*****************************************************************************/
 
void transfernodes(struct mesh *m, struct behavior *b, float *pointlist,
                   float *pointattriblist, int *pointmarkerlist,
                   int numberofpoints, int numberofpointattribs)
{
  vertex vertexloop;
  float x, y;
  int i, j;
  int coordindex;
  int attribindex;
 
  m->invertices = numberofpoints;
  m->mesh_dim = 2;
  m->nextras = numberofpointattribs;
  m->readnodefile = 0;
  if (m->invertices < 3) {
    printf("Error:  Input must have at least three input vertices.\n");
    triexit(1);
  }
  if (m->nextras == 0) {
    b->weighted = 0;
  }
 
  initializevertexpool(m, b);
 
  /* Read the vertices. */
  coordindex = 0;
  attribindex = 0;
  for (i = 0; i < m->invertices; i++) {
    vertexloop = (vertex) poolalloc(&m->vertices);
    /* Read the vertex coordinates. */
    x = vertexloop[0] = pointlist[coordindex++];
    y = vertexloop[1] = pointlist[coordindex++];
    /* Read the vertex attributes. */
    for (j = 0; j < numberofpointattribs; j++) {
      vertexloop[2 + j] = pointattriblist[attribindex++];
    }
    if (pointmarkerlist != (int *) NULL) {
      /* Read a vertex marker. */
      setvertexmark(vertexloop, pointmarkerlist[i]);
    } else {
      /* If no markers are specified, they default to zero. */
      setvertexmark(vertexloop, 0);
    }
    setvertextype(vertexloop, INPUTVERTEX);
    /* Determine the smallest and largest x and y coordinates. */
    if (i == 0) {
      m->xmin = m->xmax = x;
      m->ymin = m->ymax = y;
    } else {
      m->xmin = (x < m->xmin) ? x : m->xmin;
      m->xmax = (x > m->xmax) ? x : m->xmax;
      m->ymin = (y < m->ymin) ? y : m->ymin;
      m->ymax = (y > m->ymax) ? y : m->ymax;
    }
  }
 
  /* Nonexistent x value used as a flag to mark circle events in sweepline */
  /*   Delaunay algorithm.                                                 */
  m->xminextreme = 10 * m->xmin - 9 * m->xmax;
}
 
/*****************************************************************************/
/*                                                                           */
/*  writenodes()   Number the vertices and write them to a .node file.       */
/*                                                                           */
/*  To save memory, the vertex numbers are written over the boundary markers */
/*  after the vertices are written to a file.                                */
/*                                                                           */
/*****************************************************************************/
 
void writenodes(struct mesh *m, struct behavior *b, float **pointlist,
                float **pointattriblist, int **pointmarkerlist)
{
  float *plist;
  float *palist;
  int *pmlist;
  int coordindex;
  int attribindex;
  vertex vertexloop;
  long outvertices;
  int vertexnumber;
  int i;
 
  if (b->jettison) {
    outvertices = m->vertices.items - m->undeads;
  } else {
    outvertices = m->vertices.items;
  }
 
  if (!b->quiet) {
    printf("Writing vertices.\n");
  }
  /* Allocate memory for output vertices if necessary. */
  if (*pointlist == (float *) NULL) {
    *pointlist = (float *) trimalloc((int) (outvertices * 2 * sizeof(float)));
  }
  /* Allocate memory for output vertex attributes if necessary. */
  if ((m->nextras > 0) && (*pointattriblist == (float *) NULL)) {
    *pointattriblist = (float *) trimalloc((int) (outvertices * m->nextras *
                                                 sizeof(float)));
  }
  /* Allocate memory for output vertex markers if necessary. */
  if (!b->nobound && (*pointmarkerlist == (int *) NULL)) {
    *pointmarkerlist = (int *) trimalloc((int) (outvertices * sizeof(int)));
  }
  plist = *pointlist;
  palist = *pointattriblist;
  pmlist = *pointmarkerlist;
  coordindex = 0;
  attribindex = 0;
  traversalinit(&m->vertices);
  vertexnumber = b->firstnumber;
  vertexloop = vertextraverse(m);
  while (vertexloop != (vertex) NULL) {
    if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) {
      /* X and y coordinates. */
      plist[coordindex++] = vertexloop[0];
      plist[coordindex++] = vertexloop[1];
      /* Vertex attributes. */
      for (i = 0; i < m->nextras; i++) {
        palist[attribindex++] = vertexloop[2 + i];
      }
      if (!b->nobound) {
        /* Copy the boundary marker. */
        pmlist[vertexnumber - b->firstnumber] = vertexmark(vertexloop);
      }
      setvertexmark(vertexloop, vertexnumber);
      vertexnumber++;
    }
    vertexloop = vertextraverse(m);
  }
}
 
/*****************************************************************************/
/*                                                                           */
/*  numbernodes()   Number the vertices.                                     */
/*                                                                           */
/*  Each vertex is assigned a marker equal to its number.                    */
/*                                                                           */
/*  Used when writenodes() is not called because no .node file is written.   */
/*                                                                           */
/*****************************************************************************/
 
void numbernodes(struct mesh *m, struct behavior *b)
{
  vertex vertexloop;
  int vertexnumber;
 
  traversalinit(&m->vertices);
  vertexnumber = b->firstnumber;
  vertexloop = vertextraverse(m);
  while (vertexloop != (vertex) NULL) {
    setvertexmark(vertexloop, vertexnumber);
    if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) {
      vertexnumber++;
    }
    vertexloop = vertextraverse(m);
  }
}
 
/*****************************************************************************/
/*                                                                           */
/*  writeelements()   Write the triangles to an .ele file.                   */
/*                                                                           */
/*****************************************************************************/
 
void writeelements(struct mesh *m, struct behavior *b,
                   int **trianglelist, float **triangleattriblist)
{
  int *tlist;
  float *talist;
  int vertexindex;
  int attribindex;
  struct otri triangleloop;
  vertex p1, p2, p3;
  vertex mid1, mid2, mid3;
  long elementnumber;
  int i;
 
  if (!b->quiet) {
    printf("Writing triangles.\n");
  }
  /* Allocate memory for output triangles if necessary. */
  if (*trianglelist == (int *) NULL) {
    *trianglelist = (int *) trimalloc((int) (m->triangles.items *
                                             ((b->order + 1) * (b->order + 2) /
                                              2) * sizeof(int)));
  }
  /* Allocate memory for output triangle attributes if necessary. */
  if ((m->eextras > 0) && (*triangleattriblist == (float *) NULL)) {
    *triangleattriblist = (float *) trimalloc((int) (m->triangles.items *
                                                    m->eextras *
                                                    sizeof(float)));
  }
  tlist = *trianglelist;
  talist = *triangleattriblist;
  vertexindex = 0;
  attribindex = 0;
  traversalinit(&m->triangles);
  triangleloop.tri = triangletraverse(m);
  triangleloop.orient = 0;
  elementnumber = b->firstnumber;
  while (triangleloop.tri != (triangle *) NULL) {
    org(triangleloop, p1);
    dest(triangleloop, p2);
    apex(triangleloop, p3);
    if (b->order == 1) {
      tlist[vertexindex++] = vertexmark(p1);
      tlist[vertexindex++] = vertexmark(p2);
      tlist[vertexindex++] = vertexmark(p3);
    } else {
      mid1 = (vertex) triangleloop.tri[m->highorderindex + 1];
      mid2 = (vertex) triangleloop.tri[m->highorderindex + 2];
      mid3 = (vertex) triangleloop.tri[m->highorderindex];
      tlist[vertexindex++] = vertexmark(p1);
      tlist[vertexindex++] = vertexmark(p2);
      tlist[vertexindex++] = vertexmark(p3);
      tlist[vertexindex++] = vertexmark(mid1);
      tlist[vertexindex++] = vertexmark(mid2);
      tlist[vertexindex++] = vertexmark(mid3);
    }
 
    for (i = 0; i < m->eextras; i++) {
      talist[attribindex++] = elemattribute(triangleloop, i);
    }
    triangleloop.tri = triangletraverse(m);
    elementnumber++;
  }
}
 
/*****************************************************************************/
/*                                                                           */
/*  writepoly()   Write the segments and holes to a .poly file.              */
/*                                                                           */
/*****************************************************************************/
 
void writepoly(struct mesh *m, struct behavior *b,
               int **segmentlist, int **segmentmarkerlist)
{
  int *slist;
  int *smlist;
  int index;
  struct osub subsegloop;
  vertex endpoint1, endpoint2;
  long subsegnumber;
 
  if (!b->quiet) {
    printf("Writing segments.\n");
  }
  /* Allocate memory for output segments if necessary. */
  if (*segmentlist == (int *) NULL) {
    *segmentlist = (int *) trimalloc((int) (m->subsegs.items * 2 *
                                            sizeof(int)));
  }
  /* Allocate memory for output segment markers if necessary. */
  if (!b->nobound && (*segmentmarkerlist == (int *) NULL)) {
    *segmentmarkerlist = (int *) trimalloc((int) (m->subsegs.items *
                                                  sizeof(int)));
  }
  slist = *segmentlist;
  smlist = *segmentmarkerlist;
  index = 0;
  
  traversalinit(&m->subsegs);
  subsegloop.ss = subsegtraverse(m);
  subsegloop.ssorient = 0;
  subsegnumber = b->firstnumber;
  while (subsegloop.ss != (subseg *) NULL) {
    sorg(subsegloop, endpoint1);
    sdest(subsegloop, endpoint2);
    /* Copy indices of the segment's two endpoints. */
    slist[index++] = vertexmark(endpoint1);
    slist[index++] = vertexmark(endpoint2);
    if (!b->nobound) {
      /* Copy the boundary marker. */
      smlist[subsegnumber - b->firstnumber] = mark(subsegloop);
    }
    subsegloop.ss = subsegtraverse(m);
    subsegnumber++;
  }
}
 
/*****************************************************************************/
/*                                                                           */
/*  writeedges()   Write the edges to an .edge file.                         */
/*                                                                           */
/*****************************************************************************/
 
void writeedges(struct mesh *m, struct behavior *b,
                int **edgelist, int **edgemarkerlist)
{
  int *elist;
  int *emlist;
  int index;
  struct otri triangleloop, trisym;
  struct osub checkmark;
  vertex p1, p2;
  long edgenumber;
  triangle ptr;                         /* Temporary variable used by sym(). */
  subseg sptr;                      /* Temporary variable used by tspivot(). */
 
  if (!b->quiet) {
    printf("Writing edges.\n");
  }
  /* Allocate memory for edges if necessary. */
  if (*edgelist == (int *) NULL) {
    *edgelist = (int *) trimalloc((int) (m->edges * 2 * sizeof(int)));
  }
  /* Allocate memory for edge markers if necessary. */
  if (!b->nobound && (*edgemarkerlist == (int *) NULL)) {
    *edgemarkerlist = (int *) trimalloc((int) (m->edges * sizeof(int)));
  }
  elist = *edgelist;
  emlist = *edgemarkerlist;
  index = 0;
 
  traversalinit(&m->triangles);
  triangleloop.tri = triangletraverse(m);
  edgenumber = b->firstnumber;
  /* To loop over the set of edges, loop over all triangles, and look at   */
  /*   the three edges of each triangle.  If there isn't another triangle  */
  /*   adjacent to the edge, operate on the edge.  If there is another     */
  /*   adjacent triangle, operate on the edge only if the current triangle */
  /*   has a smaller pointer than its neighbor.  This way, each edge is    */
  /*   considered only once.                                               */
  while (triangleloop.tri != (triangle *) NULL) {
    for (triangleloop.orient = 0; triangleloop.orient < 3;
         triangleloop.orient++) {
      sym(triangleloop, trisym);
      if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) {
        org(triangleloop, p1);
        dest(triangleloop, p2);
        elist[index++] = vertexmark(p1);
        elist[index++] = vertexmark(p2);
        if (b->nobound) {
        } else {
          /* Edge number, indices of two endpoints, and a boundary marker. */
          /*   If there's no subsegment, the boundary marker is zero.      */
          if (b->usesegments) {
            tspivot(triangleloop, checkmark);
            if (checkmark.ss == m->dummysub) {
              emlist[edgenumber - b->firstnumber] = 0;
            } else {
              emlist[edgenumber - b->firstnumber] = mark(checkmark);
            }
          } else {
            emlist[edgenumber - b->firstnumber] = trisym.tri == m->dummytri;
          }
        }
        edgenumber++;
      }
    }
    triangleloop.tri = triangletraverse(m);
  }
}
 
/*****************************************************************************/
/*                                                                           */
/*  writevoronoi()   Write the Voronoi diagram to a .v.node and .v.edge      */
/*                   file.                                                   */
/*                                                                           */
/*  The Voronoi diagram is the geometric dual of the Delaunay triangulation. */
/*  Hence, the Voronoi vertices are listed by traversing the Delaunay        */
/*  triangles, and the Voronoi edges are listed by traversing the Delaunay   */
/*  edges.                                                                   */
/*                                                                           */
/*  WARNING:  In order to assign numbers to the Voronoi vertices, this       */
/*  procedure messes up the subsegments or the extra nodes of every          */
/*  element.  Hence, you should call this procedure last.                    */
/*                                                                           */
/*****************************************************************************/
 
void writevoronoi(struct mesh *m, struct behavior *b, float **vpointlist,
                  float **vpointattriblist, int **vpointmarkerlist,
                  int **vedgelist, int **vedgemarkerlist, float **vnormlist)
{
  float *plist;
  float *palist;
  int *elist;
  float *normlist;
  int coordindex;
  int attribindex;
  struct otri triangleloop, trisym;
  vertex torg, tdest, tapex;
  float circumcenter[2];
  float xi, eta;
  long vnodenumber, vedgenumber;
  int p1, p2;
  int i;
  triangle ptr;                         /* Temporary variable used by sym(). */
 
  if (!b->quiet) {
    printf("Writing Voronoi vertices.\n");
  }
  /* Allocate memory for Voronoi vertices if necessary. */
  if (*vpointlist == (float *) NULL) {
    *vpointlist = (float *) trimalloc((int) (m->triangles.items * 2 *
                                            sizeof(float)));
  }
  /* Allocate memory for Voronoi vertex attributes if necessary. */
  if (*vpointattriblist == (float *) NULL) {
    *vpointattriblist = (float *) trimalloc((int) (m->triangles.items *
                                                  m->nextras * sizeof(float)));
  }
  *vpointmarkerlist = (int *) NULL;
  plist = *vpointlist;
  palist = *vpointattriblist;
  coordindex = 0;
  attribindex = 0;
 
  traversalinit(&m->triangles);
  triangleloop.tri = triangletraverse(m);
  triangleloop.orient = 0;
  vnodenumber = b->firstnumber;
  while (triangleloop.tri != (triangle *) NULL) {
    org(triangleloop, torg);
    dest(triangleloop, tdest);
    apex(triangleloop, tapex);
    findcircumcenter(m, b, torg, tdest, tapex, circumcenter, &xi, &eta, 0);
 
    /* X and y coordinates. */
    plist[coordindex++] = circumcenter[0];
    plist[coordindex++] = circumcenter[1];
    for (i = 2; i < 2 + m->nextras; i++) {
      /* Interpolate the vertex attributes at the circumcenter. */
      palist[attribindex++] = torg[i] + xi * (tdest[i] - torg[i])
                                     + eta * (tapex[i] - torg[i]);
    }
 
    * (int *) (triangleloop.tri + 6) = (int) vnodenumber;
    triangleloop.tri = triangletraverse(m);
    vnodenumber++;
  }
 
  if (!b->quiet) {
    printf("Writing Voronoi edges.\n");
  }
  /* Allocate memory for output Voronoi edges if necessary. */
  if (*vedgelist == (int *) NULL) {
    *vedgelist = (int *) trimalloc((int) (m->edges * 2 * sizeof(int)));
  }
  *vedgemarkerlist = (int *) NULL;
  /* Allocate memory for output Voronoi norms if necessary. */
  if (*vnormlist == (float *) NULL) {
    *vnormlist = (float *) trimalloc((int) (m->edges * 2 * sizeof(float)));
  }
  elist = *vedgelist;
  normlist = *vnormlist;
  coordindex = 0;
 
  traversalinit(&m->triangles);
  triangleloop.tri = triangletraverse(m);
  vedgenumber = b->firstnumber;
  /* To loop over the set of edges, loop over all triangles, and look at   */
  /*   the three edges of each triangle.  If there isn't another triangle  */
  /*   adjacent to the edge, operate on the edge.  If there is another     */
  /*   adjacent triangle, operate on the edge only if the current triangle */
  /*   has a smaller pointer than its neighbor.  This way, each edge is    */
  /*   considered only once.                                               */
  while (triangleloop.tri != (triangle *) NULL) {
    for (triangleloop.orient = 0; triangleloop.orient < 3;
         triangleloop.orient++) {
      sym(triangleloop, trisym);
      if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) {
        /* Find the number of this triangle (and Voronoi vertex). */
        p1 = * (int *) (triangleloop.tri + 6);
        if (trisym.tri == m->dummytri) {
          org(triangleloop, torg);
          dest(triangleloop, tdest);
          /* Copy an infinite ray.  Index of one endpoint, and -1. */
          elist[coordindex] = p1;
          normlist[coordindex++] = tdest[1] - torg[1];
          elist[coordindex] = -1;
          normlist[coordindex++] = torg[0] - tdest[0];
        } else {
          /* Find the number of the adjacent triangle (and Voronoi vertex). */
          p2 = * (int *) (trisym.tri + 6);
          /* Finite edge.  Write indices of two endpoints. */
          elist[coordindex] = p1;
          normlist[coordindex++] = 0.0;
          elist[coordindex] = p2;
          normlist[coordindex++] = 0.0;
        }
        vedgenumber++;
      }
    }
    triangleloop.tri = triangletraverse(m);
  }
}
 
 
void writeneighbors(struct mesh *m, struct behavior *b, int **neighborlist)
{
  int *nlist;
  int index;
  struct otri triangleloop, trisym;
  long elementnumber;
  int neighbor1, neighbor2, neighbor3;
  triangle ptr;                         /* Temporary variable used by sym(). */
 
  if (!b->quiet) {
    printf("Writing neighbors.\n");
  }
  /* Allocate memory for neighbors if necessary. */
  if (*neighborlist == (int *) NULL) {
    *neighborlist = (int *) trimalloc((int) (m->triangles.items * 3 *
                                             sizeof(int)));
  }
  nlist = *neighborlist;
  index = 0;
 
  traversalinit(&m->triangles);
  triangleloop.tri = triangletraverse(m);
  triangleloop.orient = 0;
  elementnumber = b->firstnumber;
  while (triangleloop.tri != (triangle *) NULL) {
    * (int *) (triangleloop.tri + 6) = (int) elementnumber;
    triangleloop.tri = triangletraverse(m);
    elementnumber++;
  }
  * (int *) (m->dummytri + 6) = -1;
 
  traversalinit(&m->triangles);
  triangleloop.tri = triangletraverse(m);
  elementnumber = b->firstnumber;
  while (triangleloop.tri != (triangle *) NULL) {
    triangleloop.orient = 1;
    sym(triangleloop, trisym);
    neighbor1 = * (int *) (trisym.tri + 6);
    triangleloop.orient = 2;
    sym(triangleloop, trisym);
    neighbor2 = * (int *) (trisym.tri + 6);
    triangleloop.orient = 0;
    sym(triangleloop, trisym);
    neighbor3 = * (int *) (trisym.tri + 6);
    nlist[index++] = neighbor1;
    nlist[index++] = neighbor2;
    nlist[index++] = neighbor3;
 
    triangleloop.tri = triangletraverse(m);
    elementnumber++;
  }
}
 
/********* File I/O routines end here                                *********/
 
/*****************************************************************************/
/*                                                                           */
/*  quality_statistics()   Print statistics about the quality of the mesh.   */
/*                                                                           */
/*****************************************************************************/
 
void quality_statistics(struct mesh *m, struct behavior *b)
{
  struct otri triangleloop;
  vertex p[3];
  float cossquaretable[8];
  float ratiotable[16];
  float dx[3], dy[3];
  float edgelength[3];
  float dotproduct;
  float cossquare;
  float triarea;
  float shortest, longest;
  float trilongest2;
  float smallestarea, biggestarea;
  float triminaltitude2;
  float minaltitude;
  float triaspect2;
  float worstaspect;
  float smallestangle, biggestangle;
  float radconst, degconst;
  int angletable[18];
  int aspecttable[16];
  int aspectindex;
  int tendegree;
  int acutebiggest;
  int i, ii, j, k;
 
  printf("Mesh quality statistics:\n\n");
  radconst = PI / 18.0;
  degconst = 180.0 / PI;
  for (i = 0; i < 8; i++) {
    cossquaretable[i] = cos(radconst * (float) (i + 1));
    cossquaretable[i] = cossquaretable[i] * cossquaretable[i];
  }
  for (i = 0; i < 18; i++) {
    angletable[i] = 0;
  }
 
  ratiotable[0]  =      1.5;      ratiotable[1]  =     2.0;
  ratiotable[2]  =      2.5;      ratiotable[3]  =     3.0;
  ratiotable[4]  =      4.0;      ratiotable[5]  =     6.0;
  ratiotable[6]  =     10.0;      ratiotable[7]  =    15.0;
  ratiotable[8]  =     25.0;      ratiotable[9]  =    50.0;
  ratiotable[10] =    100.0;      ratiotable[11] =   300.0;
  ratiotable[12] =   1000.0;      ratiotable[13] = 10000.0;
  ratiotable[14] = 100000.0;      ratiotable[15] =     0.0;
  for (i = 0; i < 16; i++) {
    aspecttable[i] = 0;
  }
 
  worstaspect = 0.0;
  minaltitude = m->xmax - m->xmin + m->ymax - m->ymin;
  minaltitude = minaltitude * minaltitude;
  shortest = minaltitude;
  longest = 0.0;
  smallestarea = minaltitude;
  biggestarea = 0.0;
  worstaspect = 0.0;
  smallestangle = 0.0;
  biggestangle = 2.0;
  acutebiggest = 1;
 
  traversalinit(&m->triangles);
  triangleloop.tri = triangletraverse(m);
  triangleloop.orient = 0;
  while (triangleloop.tri != (triangle *) NULL) {
    org(triangleloop, p[0]);
    dest(triangleloop, p[1]);
    apex(triangleloop, p[2]);
    trilongest2 = 0.0;
 
    for (i = 0; i < 3; i++) {
      j = plus1mod3[i];
      k = minus1mod3[i];
      dx[i] = p[j][0] - p[k][0];
      dy[i] = p[j][1] - p[k][1];
      edgelength[i] = dx[i] * dx[i] + dy[i] * dy[i];
      if (edgelength[i] > trilongest2) {
        trilongest2 = edgelength[i];
      }
      if (edgelength[i] > longest) {
        longest = edgelength[i];
      }
      if (edgelength[i] < shortest) {
        shortest = edgelength[i];
      }
    }
 
    triarea = counterclockwise(m, b, p[0], p[1], p[2]);
    if (triarea < smallestarea) {
      smallestarea = triarea;
    }
    if (triarea > biggestarea) {
      biggestarea = triarea;
    }
    triminaltitude2 = triarea * triarea / trilongest2;
    if (triminaltitude2 < minaltitude) {
      minaltitude = triminaltitude2;
    }
    triaspect2 = trilongest2 / triminaltitude2;
    if (triaspect2 > worstaspect) {
      worstaspect = triaspect2;
    }
    aspectindex = 0;
    while ((triaspect2 > ratiotable[aspectindex] * ratiotable[aspectindex])
           && (aspectindex < 15)) {
      aspectindex++;
    }
    aspecttable[aspectindex]++;
 
    for (i = 0; i < 3; i++) {
      j = plus1mod3[i];
      k = minus1mod3[i];
      dotproduct = dx[j] * dx[k] + dy[j] * dy[k];
      cossquare = dotproduct * dotproduct / (edgelength[j] * edgelength[k]);
      tendegree = 8;
      for (ii = 7; ii >= 0; ii--) {
        if (cossquare > cossquaretable[ii]) {
          tendegree = ii;
        }
      }
      if (dotproduct <= 0.0) {
        angletable[tendegree]++;
        if (cossquare > smallestangle) {
          smallestangle = cossquare;
        }
        if (acutebiggest && (cossquare < biggestangle)) {
          biggestangle = cossquare;
        }
      } else {
        angletable[17 - tendegree]++;
        if (acutebiggest || (cossquare > biggestangle)) {
          biggestangle = cossquare;
          acutebiggest = 0;
        }
      }
    }
    triangleloop.tri = triangletraverse(m);
  }
 
  shortest = sqrt(shortest);
  longest = sqrt(longest);
  minaltitude = sqrt(minaltitude);
  worstaspect = sqrt(worstaspect);
  smallestarea *= 0.5;
  biggestarea *= 0.5;
  if (smallestangle >= 1.0) {
    smallestangle = 0.0;
  } else {
    smallestangle = degconst * acos(sqrt(smallestangle));
  }
  if (biggestangle >= 1.0) {
    biggestangle = 180.0;
  } else {
    if (acutebiggest) {
      biggestangle = degconst * acos(sqrt(biggestangle));
    } else {
      biggestangle = 180.0 - degconst * acos(sqrt(biggestangle));
    }
  }
 
  printf("  Smallest area: %16.5g   |  Largest area: %16.5g\n",
         smallestarea, biggestarea);
  printf("  Shortest edge: %16.5g   |  Longest edge: %16.5g\n",
         shortest, longest);
  printf("  Shortest altitude: %12.5g   |  Largest aspect ratio: %8.5g\n\n",
         minaltitude, worstaspect);
 
  printf("  Triangle aspect ratio histogram:\n");
  printf("  1.1547 - %-6.6g    :  %8d    | %6.6g - %-6.6g     :  %8d\n",
         ratiotable[0], aspecttable[0], ratiotable[7], ratiotable[8],
         aspecttable[8]);
  for (i = 1; i < 7; i++) {
    printf("  %6.6g - %-6.6g    :  %8d    | %6.6g - %-6.6g     :  %8d\n",
           ratiotable[i - 1], ratiotable[i], aspecttable[i],
           ratiotable[i + 7], ratiotable[i + 8], aspecttable[i + 8]);
  }
  printf("  %6.6g - %-6.6g    :  %8d    | %6.6g -            :  %8d\n",
         ratiotable[6], ratiotable[7], aspecttable[7], ratiotable[14],
         aspecttable[15]);
  printf("  (Aspect ratio is longest edge divided by shortest altitude)\n\n");
 
  printf("  Smallest angle: %15.5g   |  Largest angle: %15.5g\n\n",
         smallestangle, biggestangle);
 
  printf("  Angle histogram:\n");
  for (i = 0; i < 9; i++) {
    printf("    %3d - %3d degrees:  %8d    |    %3d - %3d degrees:  %8d\n",
           i * 10, i * 10 + 10, angletable[i],
           i * 10 + 90, i * 10 + 100, angletable[i + 9]);
  }
  printf("\n");
}
 
/*****************************************************************************/
/*                                                                           */
/*  statistics()   Print all sorts of cool facts.                            */
/*                                                                           */
/*****************************************************************************/
 
void statistics(struct mesh *m, struct behavior *b)
{
  printf("\nStatistics:\n\n");
  printf("  Input vertices: %d\n", m->invertices);
  if (b->refine) {
    printf("  Input triangles: %d\n", m->inelements);
  }
  if (b->poly) {
    printf("  Input segments: %d\n", m->insegments);
    if (!b->refine) {
      printf("  Input holes: %d\n", m->holes);
    }
  }
 
  printf("\n  Mesh vertices: %ld\n", m->vertices.items - m->undeads);
  printf("  Mesh triangles: %ld\n", m->triangles.items);
  printf("  Mesh edges: %ld\n", m->edges);
  printf("  Mesh exterior boundary edges: %ld\n", m->hullsize);
  if (b->poly || b->refine) {
    printf("  Mesh interior boundary edges: %ld\n",
           m->subsegs.items - m->hullsize);
    printf("  Mesh subsegments (constrained edges): %ld\n",
           m->subsegs.items);
  }
  printf("\n");
 
  if (b->verbose) {
    quality_statistics(m, b);
    printf("Memory allocation statistics:\n\n");
    printf("  Maximum number of vertices: %ld\n", m->vertices.maxitems);
    printf("  Maximum number of triangles: %ld\n", m->triangles.maxitems);
    if (m->subsegs.maxitems > 0) {
      printf("  Maximum number of subsegments: %ld\n", m->subsegs.maxitems);
    }
    if (m->viri.maxitems > 0) {
      printf("  Maximum number of viri: %ld\n", m->viri.maxitems);
    }
    if (m->badsubsegs.maxitems > 0) {
      printf("  Maximum number of encroached subsegments: %ld\n",
             m->badsubsegs.maxitems);
    }
    if (m->badtriangles.maxitems > 0) {
      printf("  Maximum number of bad triangles: %ld\n",
             m->badtriangles.maxitems);
    }
    if (m->flipstackers.maxitems > 0) {
      printf("  Maximum number of stacked triangle flips: %ld\n",
             m->flipstackers.maxitems);
    }
    if (m->splaynodes.maxitems > 0) {
      printf("  Maximum number of splay tree nodes: %ld\n",
             m->splaynodes.maxitems);
    }
    printf("  Approximate heap memory use (bytes): %ld\n\n",
           m->vertices.maxitems * m->vertices.itembytes +
           m->triangles.maxitems * m->triangles.itembytes +
           m->subsegs.maxitems * m->subsegs.itembytes +
           m->viri.maxitems * m->viri.itembytes +
           m->badsubsegs.maxitems * m->badsubsegs.itembytes +
           m->badtriangles.maxitems * m->badtriangles.itembytes +
           m->flipstackers.maxitems * m->flipstackers.itembytes +
           m->splaynodes.maxitems * m->splaynodes.itembytes);
 
    printf("Algorithmic statistics:\n\n");
    if (!b->weighted) {
      printf("  Number of incircle tests: %ld\n", m->incirclecount);
    } else {
      printf("  Number of 3D orientation tests: %ld\n", m->orient3dcount);
    }
    printf("  Number of 2D orientation tests: %ld\n", m->counterclockcount);
    if (m->hyperbolacount > 0) {
      printf("  Number of right-of-hyperbola tests: %ld\n",
             m->hyperbolacount);
    }
    if (m->circletopcount > 0) {
      printf("  Number of circle top computations: %ld\n",
             m->circletopcount);
    }
    if (m->circumcentercount > 0) {
      printf("  Number of triangle circumcenter computations: %ld\n",
             m->circumcentercount);
    }
    printf("\n");
  }
}
 
/*****************************************************************************/
/*                                                                           */
/*  main() or triangulate()   Gosh, do everything.                           */
/*                                                                           */
/*  The sequence is roughly as follows.  Many of these steps can be skipped, */
/*  depending on the command line switches.                                  */
/*                                                                           */
/*  - Initialize constants and parse the command line.                       */
/*  - Read the vertices from a file and either                               */
/*    - triangulate them (no -r), or                                         */
/*    - read an old mesh from files and reconstruct it (-r).                 */
/*  - Insert the PSLG segments (-p), and possibly segments on the convex     */
/*      hull (-c).                                                           */
/*  - Read the holes (-p), regional attributes (-pA), and regional area      */
/*      constraints (-pa).  Carve the holes and concavities, and spread the  */
/*      regional attributes and area constraints.                            */
/*  - Enforce the constraints on minimum angle (-q) and maximum area (-a).   */
/*      Also enforce the conforming Delaunay property (-q and -a).           */
/*  - Compute the number of edges in the resulting mesh.                     */
/*  - Promote the mesh's linear triangles to higher order elements (-o).     */
/*  - Write the output files and print the statistics.                       */
/*  - Check the consistency and Delaunay property of the mesh (-C).          */
/*                                                                           */
/*****************************************************************************/
 
void triangulate(char *triswitches, struct triangulateio *in,
                 struct triangulateio *out, struct triangulateio *vorout)
{
  struct mesh m;
  struct behavior b;
  float *holearray;                                        /* Array of holes. */
  float *regionarray;   /* Array of regional attributes and area constraints. */
  
  triangleinit(&m);
  parsecommandline(1, &triswitches, &b);
  m.steinerleft = b.steiner;
 
  transfernodes(&m, &b, in->pointlist, in->pointattributelist,
                in->pointmarkerlist, in->numberofpoints,
                in->numberofpointattributes);
 
  m.hullsize = delaunay(&m, &b);                /* Triangulate the vertices. */
  /* Ensure that no vertex can be mistaken for a triangular bounding */
  /*   box vertex in insertvertex().                                 */
  m.infvertex1 = (vertex) NULL;
  m.infvertex2 = (vertex) NULL;
  m.infvertex3 = (vertex) NULL;
 
  if (b.usesegments) {
    m.checksegments = 1;                /* Segments will be introduced next. */
    if (!b.refine) {
      /* Insert PSLG segments and/or convex hull segments. */
      formskeleton(&m, &b, in->segmentlist,
                   in->segmentmarkerlist, in->numberofsegments);
    }
  }
 
  if (b.poly && (m.triangles.items > 0)) {
    holearray = in->holelist;
    m.holes = in->numberofholes;
    regionarray = in->regionlist;
    m.regions = in->numberofregions;
    if (!b.refine) {
      /* Carve out holes and concavities. */
      carveholes(&m, &b, holearray, m.holes, regionarray, m.regions);
    }
  } else {
    /* Without a PSLG, there can be no holes or regional attributes   */
    /*   or area constraints.  The following are set to zero to avoid */
    /*   an accidental free() later.                                  */
    m.holes = 0;
    m.regions = 0;
  }
 
  /* Calculate the number of edges. */
  m.edges = (3l * m.triangles.items + m.hullsize) / 2l;
 
  if (b.order > 1) {
    highorder(&m, &b);       /* Promote elements to higher polynomial order. */
  }
  if (!b.quiet) {
    printf("\n");
  }
 
  if (b.jettison) {
    out->numberofpoints = m.vertices.items - m.undeads;
  } else {
    out->numberofpoints = m.vertices.items;
  }
  out->numberofpointattributes = m.nextras;
  out->numberoftriangles = m.triangles.items;
  out->numberofcorners = (b.order + 1) * (b.order + 2) / 2;
  out->numberoftriangleattributes = m.eextras;
  out->numberofedges = m.edges;
  if (b.usesegments) {
    out->numberofsegments = m.subsegs.items;
  } else {
    out->numberofsegments = m.hullsize;
  }
  if (vorout != (struct triangulateio *) NULL) {
    vorout->numberofpoints = m.triangles.items;
    vorout->numberofpointattributes = m.nextras;
    vorout->numberofedges = m.edges;
  }
  /* If not using iteration numbers, don't write a .node file if one was */
  /*   read, because the original one would be overwritten!              */
  if (b.nonodewritten || (b.noiterationnum && m.readnodefile)) {
    if (!b.quiet) {
      printf("NOT writing vertices.\n");
    }
    numbernodes(&m, &b);         /* We must remember to number the vertices. */
  } else {
    /* writenodes() numbers the vertices too. */
    writenodes(&m, &b, &out->pointlist, &out->pointattributelist,
               &out->pointmarkerlist);
  }
  if (b.noelewritten) {
    if (!b.quiet) {
      printf("NOT writing triangles.\n");
    }
  } else {
    writeelements(&m, &b, &out->trianglelist, &out->triangleattributelist);
  }
  /* The -c switch (convex switch) causes a PSLG to be written */
  /*   even if none was read.                                  */
  if (b.poly || b.convex) {
    /* If not using iteration numbers, don't overwrite the .poly file. */
    if (b.nopolywritten || b.noiterationnum) {
      if (!b.quiet) {
        printf("NOT writing segments.\n");
      }
    } else {
      writepoly(&m, &b, &out->segmentlist, &out->segmentmarkerlist);
      out->numberofholes = m.holes;
      out->numberofregions = m.regions;
      if (b.poly) {
        out->holelist = in->holelist;
        out->regionlist = in->regionlist;
      } else {
        out->holelist = (float *) NULL;
        out->regionlist = (float *) NULL;
      }
    }
  }
  if (b.edgesout) {
    writeedges(&m, &b, &out->edgelist, &out->edgemarkerlist);
  }
  if (b.voronoi) {
    writevoronoi(&m, &b, &vorout->pointlist, &vorout->pointattributelist,
                 &vorout->pointmarkerlist, &vorout->edgelist,
                 &vorout->edgemarkerlist, &vorout->normlist);
  }
  if (b.neighbors) {
    writeneighbors(&m, &b, &out->neighborlist);
  }
 
  if (!b.quiet) {
    statistics(&m, &b);
  }
 
  triangledeinit(&m, &b);
}