triangle.c

/*****************************************************************************/
/*                                                                           */
/*      888888888        ,o,                          / 888                  */
/*         888    88o88o  "    o8888o  88o8888o o88888o 888  o88888o         */
/*         888    888    888       88b 888  888 888 888 888 d888  88b        */
/*         888    888    888  o88^o888 888  888 "88888" 888 8888oo888        */
/*         888    888    888 C888  888 888  888  /      888 q888             */
/*         888    888    888  "88o^888 888  888 Cb      888  "88oooo"        */
/*                                              "8oo8D                       */
/*                                                                           */
/*  A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator.      */
/*  (triangle.c)                                                             */
/*																			 */

/* #define SINGLE */

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

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

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

#define FILENAMESIZE 2048

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

#define INPUTLINESIZE 1024

/* For efficiency, a variety of data structures are allocated in bulk.  The  */
/*   following constants determine how many of each structure is allocated   */
/*   at once.                                                                */

#define TRIPERBLOCK 4092           /* Number of triangles allocated at once. */
#define SUBSEGPERBLOCK 508       /* Number of subsegments allocated at once. */
#define VERTEXPERBLOCK 4092         /* Number of vertices allocated at once. */
#define VIRUSPERBLOCK 1020   /* Number of virus triangles allocated at once. */
/* Number of encroached subsegments allocated at once. */
#define BADSUBSEGPERBLOCK 252
/* Number of skinny triangles allocated at once. */
#define BADTRIPERBLOCK 4092
/* Number of flipped triangles allocated at once. */
#define FLIPSTACKERPERBLOCK 252
/* Number of splay tree nodes allocated at once. */
#define SPLAYNODEPERBLOCK 508

/* The vertex types.   A DEADVERTEX has been deleted entirely.  An           */
/*   UNDEADVERTEX is not part of the mesh, but is written to the output      */
/*   .node file and affects the node indexing in the other output files.     */

#define INPUTVERTEX 0
#define SEGMENTVERTEX 1
#define FREEVERTEX 2
#define DEADVERTEX -32768
#define UNDEADVERTEX -32767

/* The next line is used to outsmart some very stupid compilers.  If your    */
/*   compiler is smarter, feel free to replace the "int" with "void".        */
/*   Not that it matters.                                                    */

#define VOID int

/* Two constants for algorithms based on random sampling.  Both constants    */
/*   have been chosen empirically to optimize their respective algorithms.   */

/* Used for the point location scheme of Mucke, Saias, and Zhu, to decide    */
/*   how large a random sample of triangles to inspect.                      */

#define SAMPLEFACTOR 11

/* Used in Fortune's sweepline Delaunay algorithm to determine what fraction */
/*   of boundary edges should be maintained in the splay tree for point      */
/*   location on the front.                                                  */

#define SAMPLERATE 10

/* A number that speaks for itself, every kissable digit.                    */

#define PI 3.141592653589793238462643383279502884197169399375105820974944592308

/* Another fave.                                                             */

#define SQUAREROOTTWO 1.4142135623730950488016887242096980785696718753769480732

/* And here's one for those of you who are intimidated by math.              */

#define ONETHIRD 0.333333333333333333333333333333333333333333333333333333333333

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#ifndef NO_TIMER
#include <sys/time.h>
#endif /* not NO_TIMER */
#ifdef CPU86
#include <float.h>
#endif /* CPU86 */
#ifdef LINUX
#include <fpu_control.h>
#endif /* LINUX */
#ifdef TRILIBRARY
#include "triangle.h"
#endif /* TRILIBRARY */

/* A few forward declarations.                                               */

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

/* Labels that signify the result of point location.  The result of a        */
/*   search indicates that the point falls in the interior of a triangle, on */
/*   an edge, on a vertex, or outside the mesh.                              */

enum locateresult { INTRIANGLE, ONEDGE, ONVERTEX, OUTSIDE };

/* Labels that signify the result of vertex insertion.  The result indicates */
/*   that the vertex was inserted with complete success, was inserted but    */
/*   encroaches upon a subsegment, was not inserted because it lies on a     */
/*   segment, or was not inserted because another vertex occupies the same   */
/*   location.                                                               */

enum insertvertexresult {
	SUCCESSFULVERTEX, ENCROACHINGVERTEX, VIOLATINGVERTEX,
	DUPLICATEVERTEX
};

/* Labels that signify the result of direction finding.  The result          */
/*   indicates that a segment connecting the two query points falls within   */
/*   the direction triangle, along the left edge of the direction triangle,  */
/*   or along the right edge of the direction triangle.                      */

enum finddirectionresult { WITHIN, LEFTCOLLINEAR, RIGHTCOLLINEAR };

/*****************************************************************************/
/*                                                                           */
/*  The basic mesh data structures                                           */
/*                                                                           */
/*  There are three:  vertices, triangles, and subsegments (abbreviated      */
/*  `subseg').  These three data structures, linked by pointers, comprise    */
/*  the mesh.  A vertex simply represents a mesh vertex and its properties.  */
/*  A triangle is a triangle.  A subsegment is a special data structure used */
/*  to represent an impenetrable edge of the mesh (perhaps on the outer      */
/*  boundary, on the boundary of a hole, or part of an internal boundary     */
/*  separating two triangulated regions).  Subsegments represent boundaries, */
/*  defined by the user, that triangles may not lie across.                  */
/*                                                                           */
/*  A triangle consists of a list of three vertices, a list of three         */
/*  adjoining triangles, a list of three adjoining subsegments (when         */
/*  segments exist), an arbitrary number of optional user-defined            */
/*  floating-point attributes, and an optional area constraint.  The latter  */
/*  is an upper bound on the permissible area of each triangle in a region,  */
/*  used for mesh refinement.                                                */
/*                                                                           */
/*  For a triangle on a boundary of the mesh, some or all of the neighboring */
/*  triangles may not be present.  For a triangle in the interior of the     */
/*  mesh, often no neighboring subsegments are present.  Such absent         */
/*  triangles and subsegments are never represented by NULL pointers; they   */
/*  are represented by two special records:  `dummytri', the triangle that   */
/*  fills "outer space", and `dummysub', the omnipresent subsegment.         */
/*  `dummytri' and `dummysub' are used for several reasons; for instance,    */
/*  they can be dereferenced and their contents examined without violating   */
/*  protected memory.                                                        */
/*                                                                           */
/*  However, it is important to understand that a triangle includes other    */
/*  information as well.  The pointers to adjoining vertices, triangles, and */
/*  subsegments are ordered in a way that indicates their geometric relation */
/*  to each other.  Furthermore, each of these pointers contains orientation */
/*  information.  Each pointer to an adjoining triangle indicates which face */
/*  of that triangle is contacted.  Similarly, each pointer to an adjoining  */
/*  subsegment indicates which side of that subsegment is contacted, and how */
/*  the subsegment is oriented relative to the triangle.                     */
/*                                                                           */
/*  The data structure representing a subsegment may be thought to be        */
/*  abutting the edge of one or two triangle data structures:  either        */
/*  sandwiched between two triangles, or resting against one triangle on an  */
/*  exterior boundary or hole boundary.                                      */
/*                                                                           */
/*  A subsegment consists of a list of four vertices--the vertices of the    */
/*  subsegment, and the vertices of the segment it is a part of--a list of   */
/*  two adjoining subsegments, and a list of two adjoining triangles.  One   */
/*  of the two adjoining triangles may not be present (though there should   */
/*  always be one), and neighboring subsegments might not be present.        */
/*  Subsegments also store a user-defined integer "boundary marker".         */
/*  Typically, this integer is used to indicate what boundary conditions are */
/*  to be applied at that location in a finite element simulation.           */
/*                                                                           */
/*  Like triangles, subsegments maintain information about the relative      */
/*  orientation of neighboring objects.                                      */
/*                                                                           */
/*  Vertices are relatively simple.  A vertex is a list of floating-point    */
/*  numbers, starting with the x, and y coordinates, followed by an          */
/*  arbitrary number of optional user-defined floating-point attributes,     */
/*  followed by an integer boundary marker.  During the segment insertion    */
/*  phase, there is also a pointer from each vertex to a triangle that may   */
/*  contain it.  Each pointer is not always correct, but when one is, it     */
/*  speeds up segment insertion.  These pointers are assigned values once    */
/*  at the beginning of the segment insertion phase, and are not used or     */
/*  updated except during this phase.  Edge flipping during segment          */
/*  insertion will render some of them incorrect.  Hence, don't rely upon    */
/*  them for anything.                                                       */
/*                                                                           */
/*  Other than the exception mentioned above, vertices have no information   */
/*  about what triangles, subfacets, or subsegments they are linked to.      */
/*                                                                           */
/*****************************************************************************/

/*****************************************************************************/
/*                                                                           */
/*  Handles                                                                  */
/*                                                                           */
/*  The oriented triangle (`otri') and oriented subsegment (`osub') data     */
/*  structures defined below do not themselves store any part of the mesh.   */
/*  The mesh itself is made of `triangle's, `subseg's, and `vertex's.        */
/*                                                                           */
/*  Oriented triangles and oriented subsegments will usually be referred to  */
/*  as "handles."  A handle is essentially a pointer into the mesh; it       */
/*  allows you to "hold" one particular part of the mesh.  Handles are used  */
/*  to specify the regions in which one is traversing and modifying the mesh.*/
/*  A single `triangle' may be held by many handles, or none at all.  (The   */
/*  latter case is not a memory leak, because the triangle is still          */
/*  connected to other triangles in the mesh.)                               */
/*                                                                           */
/*  An `otri' is a handle that holds a triangle.  It holds a specific edge   */
/*  of the triangle.  An `osub' is a handle that holds a subsegment.  It     */
/*  holds either the left or right side of the subsegment.                   */
/*                                                                           */
/*  Navigation about the mesh is accomplished through a set of mesh          */
/*  manipulation primitives, further below.  Many of these primitives take   */
/*  a handle and produce a new handle that holds the mesh near the first     */
/*  handle.  Other primitives take two handles and glue the corresponding    */
/*  parts of the mesh together.  The orientation of the handles is           */
/*  important.  For instance, when two triangles are glued together by the   */
/*  bond() primitive, they are glued at the edges on which the handles lie.  */
/*                                                                           */
/*  Because vertices have no information about which triangles they are      */
/*  attached to, I commonly represent a vertex by use of a handle whose      */
/*  origin is the vertex.  A single handle can simultaneously represent a    */
/*  triangle, an edge, and a vertex.                                         */
/*                                                                           */
/*****************************************************************************/

/* The triangle data structure.  Each triangle contains three pointers to    */
/*   adjoining triangles, plus three pointers to vertices, plus three        */
/*   pointers to subsegments (declared below; these pointers are usually     */
/*   `dummysub').  It may or may not also contain user-defined attributes    */
/*   and/or a floating-point "area constraint."  It may also contain extra   */
/*   pointers for nodes, when the user asks for high-order elements.         */
/*   Because the size and structure of a `triangle' is not decided until     */
/*   runtime, I haven't simply declared the type `triangle' as a struct.     */

typedef REAL **triangle;            /* Really:  typedef triangle *triangle   */

									/* An oriented triangle:  includes a pointer to a triangle and orientation.  */
									/*   The orientation denotes an edge of the triangle.  Hence, there are      */
									/*   three possible orientations.  By convention, each edge always points    */
									/*   counterclockwise about the corresponding triangle.                      */

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

/* The subsegment data structure.  Each subsegment contains two pointers to  */
/*   adjoining subsegments, plus four pointers to vertices, plus two         */
/*   pointers to adjoining triangles, plus one boundary marker, plus one     */
/*   segment number.                                                         */

typedef REAL **subseg;                  /* Really:  typedef subseg *subseg   */

										/* An oriented subsegment:  includes a pointer to a subsegment and an        */
										/*   orientation.  The orientation denotes a side of the edge.  Hence, there */
										/*   are two possible orientations.  By convention, the edge is always       */
										/*   directed so that the "side" denoted is the right side of the edge.      */

struct osub {
	subseg *ss;
	int ssorient;                                       /* Ranges from 0 to 1. */
};

/* The vertex data structure.  Each vertex is actually an array of REALs.    */
/*   The number of REALs is unknown until runtime.  An integer boundary      */
/*   marker, and sometimes a pointer to a triangle, is appended after the    */
/*   REALs.                                                                  */

typedef REAL *vertex;

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

struct badsubseg {
	subseg encsubseg;                             /* An encroached subsegment. */
	vertex subsegorg, subsegdest;                         /* Its two vertices. */
};

/* A queue used to store bad triangles.  The key is the square of the cosine */
/*   of the smallest angle of the triangle.  Each triangle's vertices are    */
/*   stored so that one can check whether a triangle is still the same.      */

struct badtriang {
	triangle poortri;                       /* A skinny or too-large triangle. */
	REAL key;                             /* cos^2 of smallest (apical) angle. */
	vertex triangorg, triangdest, triangapex;           /* Its three vertices. */
	struct badtriang *nexttriang;             /* Pointer to next bad triangle. */
};

/* A stack of triangles flipped during the most recent vertex insertion.     */
/*   The stack is used to undo the vertex insertion if the vertex encroaches */
/*   upon a subsegment.                                                      */

struct flipstacker {
	triangle flippedtri;                       /* A recently flipped triangle. */
	struct flipstacker *prevflip;               /* Previous flip in the stack. */
};

/* A node in a heap used to store events for the sweepline Delaunay          */
/*   algorithm.  Nodes do not point directly to their parents or children in */
/*   the heap.  Instead, each node knows its position in the heap, and can   */
/*   look up its parent and children in a separate array.  The `eventptr'    */
/*   points either to a `vertex' or to a triangle (in encoded format, so     */
/*   that an orientation is included).  In the latter case, the origin of    */
/*   the oriented triangle is the apex of a "circle event" of the sweepline  */
/*   algorithm.  To distinguish site events from circle events, all circle   */
/*   events are given an invalid (smaller than `xmin') x-coordinate `xkey'.  */

struct event {
	REAL xkey, ykey;                              /* Coordinates of the event. */
	VOID *eventptr;      /* Can be a vertex or the location of a circle event. */
	int heapposition;              /* Marks this event's position in the heap. */
};

/* A node in the splay tree.  Each node holds an oriented ghost triangle     */
/*   that represents a boundary edge of the growing triangulation.  When a   */
/*   circle event covers two boundary edges with a triangle, so that they    */
/*   are no longer boundary edges, those edges are not immediately deleted   */
/*   from the tree; rather, they are lazily deleted when they are next       */
/*   encountered.  (Since only a random sample of boundary edges are kept    */
/*   in the tree, lazy deletion is faster.)  `keydest' is used to verify     */
/*   that a triangle is still the same as when it entered the splay tree; if */
/*   it has been rotated (due to a circle event), it no longer represents a  */
/*   boundary edge and should be deleted.                                    */

struct splaynode {
	struct otri keyedge;                     /* Lprev of an edge on the front. */
	vertex keydest;           /* Used to verify that splay node is still live. */
	struct splaynode *lchild, *rchild;              /* Children in splay tree. */
};

/* A type used to allocate memory.  firstblock is the first block of items.  */
/*   nowblock is the block from which items are currently being allocated.   */
/*   nextitem points to the next slab of free memory for an item.            */
/*   deaditemstack is the head of a linked list (stack) of deallocated items */
/*   that can be recycled.  unallocateditems is the number of items that     */
/*   remain to be allocated from nowblock.                                   */
/*                                                                           */
/* Traversal is the process of walking through the entire list of items, and */
/*   is separate from allocation.  Note that a traversal will visit items on */
/*   the "deaditemstack" stack as well as live items.  pathblock points to   */
/*   the block currently being traversed.  pathitem points to the next item  */
/*   to be traversed.  pathitemsleft is the number of items that remain to   */
/*   be traversed in pathblock.                                              */
/*                                                                           */
/* alignbytes determines how new records should be aligned in memory.        */
/*   itembytes is the length of a record in bytes (after rounding up).       */
/*   itemsperblock is the number of items allocated at once in a single      */
/*   block.  itemsfirstblock is the number of items in the first block,      */
/*   which can vary from the others.  items is the number of currently       */
/*   allocated items.  maxitems is the maximum number of items that have     */
/*   been allocated at once; it is the current number of items plus the      */
/*   number of records kept on deaditemstack.                                */

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


/* Global constants.                                                         */

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

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

unsigned long randomseed;                     /* Current random number seed. */


											  /* Mesh data structure.  Triangle operates on only one mesh, but the mesh    */
											  /*   structure is used (instead of global variables) to allow reentrancy.    */

struct mesh {

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

	struct memorypool triangles;
	struct memorypool subsegs;
	struct memorypool vertices;
	struct memorypool viri;
	struct memorypool badsubsegs;
	struct memorypool badtriangles;
	struct memorypool flipstackers;
	struct memorypool splaynodes;

	/* Variables that maintain the bad triangle queues.  The queues are          */
	/*   ordered from 4095 (highest priority) to 0 (lowest priority).            */

	struct badtriang *queuefront[4096];
	struct badtriang *queuetail[4096];
	int nextnonemptyq[4096];
	int firstnonemptyq;

	/* Variable that maintains the stack of recently flipped triangles.          */

	struct flipstacker *lastflip;

	/* Other variables. */

	REAL xmin, xmax, ymin, ymax;                            /* x and y bounds. */
	REAL xminextreme;      /* Nonexistent x value used as a flag in sweepline. */
	int invertices;                               /* Number of input vertices. */
	int inelements;                              /* Number of input triangles. */
	int insegments;                               /* Number of input segments. */
	int holes;                                       /* Number of input holes. */
	int regions;                                   /* Number of input regions. */
	int undeads;    /* Number of input vertices that don't appear in the mesh. */
	long edges;                                     /* Number of output edges. */
	int mesh_dim;                                /* Dimension (ought to be 2). */
	int nextras;                           /* Number of attributes per vertex. */
	int eextras;                         /* Number of attributes per triangle. */
	long hullsize;                          /* Number of edges in convex hull. */
	int steinerleft;                 /* Number of Steiner points not yet used. */
	int vertexmarkindex;         /* Index to find boundary marker of a vertex. */
	int vertex2triindex;     /* Index to find a triangle adjacent to a vertex. */
	int highorderindex;  /* Index to find extra nodes for high-order elements. */
	int elemattribindex;            /* Index to find attributes of a triangle. */
	int areaboundindex;             /* Index to find area bound of a triangle. */
	int checksegments;         /* Are there segments in the triangulation yet? */
	int checkquality;                  /* Has quality triangulation begun yet? */
	int readnodefile;                           /* Has a .node file been read? */
	long samples;              /* Number of random samples for point location. */

	long incirclecount;                 /* Number of incircle tests performed. */
	long counterclockcount;     /* Number of counterclockwise tests performed. */
	long orient3dcount;           /* Number of 3D orientation tests performed. */
	long hyperbolacount;      /* Number of right-of-hyperbola tests performed. */
	long circumcentercount;  /* Number of circumcenter calculations performed. */
	long circletopcount;       /* Number of circle top calculations performed. */

							   /* Triangular bounding box vertices.                                         */

	vertex infvertex1, infvertex2, infvertex3;

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

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

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

	subseg *dummysub;
	subseg *dummysubbase;      /* Keep base address so we can free() it later. */

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

	struct otri recenttri;

};                                                  /* End of `struct mesh'. */


													/* Data structure for command line switches and file names.  This structure  */
													/*   is used (instead of global variables) to allow reentrancy.              */

struct behavior {

	/* Switches for the triangulator.                                            */
	/*   poly: -p switch.  refine: -r switch.                                    */
	/*   quality: -q switch.                                                     */
	/*     minangle: minimum angle bound, specified after -q switch.             */
	/*     goodangle: cosine squared of minangle.                                */
	/*     offconstant: constant used to place off-center Steiner points.        */
	/*   vararea: -a switch without number.                                      */
	/*   fixedarea: -a switch with number.                                       */
	/*     maxarea: maximum area bound, specified after -a switch.               */
	/*   usertest: -u switch.                                                    */
	/*   regionattrib: -A switch.  convex: -c switch.                            */
	/*   weighted: 1 for -w switch, 2 for -W switch.  jettison: -j switch        */
	/*   firstnumber: inverse of -z switch.  All items are numbered starting     */
	/*     from `firstnumber'.                                                   */
	/*   edgesout: -e switch.  voronoi: -v switch.                               */
	/*   neighbors: -n switch.  geomview: -g switch.                             */
	/*   nobound: -B switch.  nopolywritten: -P switch.                          */
	/*   nonodewritten: -N switch.  noelewritten: -E switch.                     */
	/*   noiterationnum: -I switch.  noholes: -O switch.                         */
	/*   noexact: -X switch.                                                     */
	/*   order: element order, specified after -o switch.                        */
	/*   nobisect: count of how often -Y switch is selected.                     */
	/*   steiner: maximum number of Steiner points, specified after -S switch.   */
	/*   incremental: -i switch.  sweepline: -F switch.                          */
	/*   dwyer: inverse of -l switch.                                            */
	/*   splitseg: -s switch.                                                    */
	/*   conformdel: -D switch.  docheck: -C switch.                             */
	/*   quiet: -Q switch.  verbose: count of how often -V switch is selected.   */
	/*   usesegments: -p, -r, -q, or -c switch; determines whether segments are  */
	/*     used at all.                                                          */
	/*                                                                           */
	/* Read the instructions to find out the meaning of these switches.          */

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

	/* Variables for file names.                                                 */

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

};                                              /* End of `struct behavior'. */


												/*****************************************************************************/
												/*                                                                           */
												/*  Mesh manipulation primitives.  Each triangle contains three pointers to  */
												/*  other triangles, with orientations.  Each pointer points not to the      */
												/*  first byte of a triangle, but to one of the first three bytes of a       */
												/*  triangle.  It is necessary to extract both the triangle itself and the   */
												/*  orientation.  To save memory, I keep both pieces of information in one   */
												/*  pointer.  To make this possible, I assume that all triangles are aligned */
												/*  to four-byte boundaries.  The decode() routine below decodes a pointer,  */
												/*  extracting an orientation (in the range 0 to 2) and a pointer to the     */
												/*  beginning of a triangle.  The encode() routine compresses a pointer to a */
												/*  triangle and an orientation into a single pointer.  My assumptions that  */
												/*  triangles are four-byte-aligned and that the `unsigned long' type is     */
												/*  long enough to hold a pointer are two of the few kludges in this program.*/
												/*                                                                           */
												/*  Subsegments are manipulated similarly.  A pointer to a subsegment        */
												/*  carries both an address and an orientation in the range 0 to 1.          */
												/*                                                                           */
												/*  The other primitives take an oriented triangle or oriented subsegment,   */
												/*  and return an oriented triangle or oriented subsegment or vertex; or     */
												/*  they change the connections in the data structure.                       */
												/*                                                                           */
												/*  Below, triangles and subsegments are denoted by their vertices.  The     */
												/*  triangle abc has origin (org) a, destination (dest) b, and apex (apex)   */
												/*  c.  These vertices occur in counterclockwise order about the triangle.   */
												/*  The handle abc may simultaneously denote vertex a, edge ab, and triangle */
												/*  abc.                                                                     */
												/*                                                                           */
												/*  Similarly, the subsegment ab has origin (sorg) a and destination (sdest) */
												/*  b.  If ab is thought to be directed upward (with b directly above a),    */
												/*  then the handle ab is thought to grasp the right side of ab, and may     */
												/*  simultaneously denote vertex a and edge ab.                              */
												/*                                                                           */
												/*  An asterisk (*) denotes a vertex whose identity is unknown.              */
												/*                                                                           */
												/*  Given this notation, a partial list of mesh manipulation primitives      */
												/*  follows.                                                                 */
												/*                                                                           */
												/*                                                                           */
												/*  For triangles:                                                           */
												/*                                                                           */
												/*  sym:  Find the abutting triangle; same edge.                             */
												/*  sym(abc) -> ba*                                                          */
												/*                                                                           */
												/*  lnext:  Find the next edge (counterclockwise) of a triangle.             */
												/*  lnext(abc) -> bca                                                        */
												/*                                                                           */
												/*  lprev:  Find the previous edge (clockwise) of a triangle.                */
												/*  lprev(abc) -> cab                                                        */
												/*                                                                           */
												/*  onext:  Find the next edge counterclockwise with the same origin.        */
												/*  onext(abc) -> ac*                                                        */
												/*                                                                           */
												/*  oprev:  Find the next edge clockwise with the same origin.               */
												/*  oprev(abc) -> a*b                                                        */
												/*                                                                           */
												/*  dnext:  Find the next edge counterclockwise with the same destination.   */
												/*  dnext(abc) -> *ba                                                        */
												/*                                                                           */
												/*  dprev:  Find the next edge clockwise with the same destination.          */
												/*  dprev(abc) -> cb*                                                        */
												/*                                                                           */
												/*  rnext:  Find the next edge (counterclockwise) of the adjacent triangle.  */
												/*  rnext(abc) -> *a*                                                        */
												/*                                                                           */
												/*  rprev:  Find the previous edge (clockwise) of the adjacent triangle.     */
												/*  rprev(abc) -> b**                                                        */
												/*                                                                           */
												/*  org:  Origin          dest:  Destination          apex:  Apex            */
												/*  org(abc) -> a         dest(abc) -> b              apex(abc) -> c         */
												/*                                                                           */
												/*  bond:  Bond two triangles together at the resepective handles.           */
												/*  bond(abc, bad)                                                           */
												/*                                                                           */
												/*                                                                           */
												/*  For subsegments:                                                         */
												/*                                                                           */
												/*  ssym:  Reverse the orientation of a subsegment.                          */
												/*  ssym(ab) -> ba                                                           */
												/*                                                                           */
												/*  spivot:  Find adjoining subsegment with the same origin.                 */
												/*  spivot(ab) -> a*                                                         */
												/*                                                                           */
												/*  snext:  Find next subsegment in sequence.                                */
												/*  snext(ab) -> b*                                                          */
												/*                                                                           */
												/*  sorg:  Origin                      sdest:  Destination                   */
												/*  sorg(ab) -> a                      sdest(ab) -> b                        */
												/*                                                                           */
												/*  sbond:  Bond two subsegments together at the respective origins.         */
												/*  sbond(ab, ac)                                                            */
												/*                                                                           */
												/*                                                                           */
												/*  For interacting tetrahedra and subfacets:                                */
												/*                                                                           */
												/*  tspivot:  Find a subsegment abutting a triangle.                         */
												/*  tspivot(abc) -> ba                                                       */
												/*                                                                           */
												/*  stpivot:  Find a triangle abutting a subsegment.                         */
												/*  stpivot(ab) -> ba*                                                       */
												/*                                                                           */
												/*  tsbond:  Bond a triangle to a subsegment.                                */
												/*  tsbond(abc, ba)                                                          */
												/*                                                                           */
												/*****************************************************************************/

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

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

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

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

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

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

/* encode() compresses an oriented triangle into a single pointer.  It       */
/*   relies on the assumption that all triangles are aligned to four-byte    */
/*   boundaries, so the two least significant bits of (otri).tri are zero.   */

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

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

/* sym() finds the abutting triangle, on the same edge.  Note that the edge  */
/*   direction is necessarily reversed, because the handle specified by an   */
/*   oriented triangle is directed counterclockwise around the triangle.     */

#define sym(otri1, otri2)                                                     \
  ptr = (otri1).tri[(otri1).orient];                                          \
  decode(ptr, otri2);

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

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

#define lnext(otri1, otri2)                                                   \
  (otri2).tri = (otri1).tri;                                                  \
  (otri2).orient = plus1mod3[(otri1).orient]

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

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

#define lprev(otri1, otri2)                                                   \
  (otri2).tri = (otri1).tri;                                                  \
  (otri2).orient = minus1mod3[(otri1).orient]

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

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

#define onext(otri1, otri2)                                                   \
  lprev(otri1, otri2);                                                        \
  symself(otri2);

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

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

#define oprev(otri1, otri2)                                                   \
  sym(otri1, otri2);                                                          \
  lnextself(otri2);

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

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

#define dnext(otri1, otri2)                                                   \
  sym(otri1, otri2);                                                          \
  lprevself(otri2);

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

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

#define dprev(otri1, otri2)                                                   \
  lnext(otri1, otri2);                                                        \
  symself(otri2);

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

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

#define rnext(otri1, otri2)                                                   \
  sym(otri1, otri2);                                                          \
  lnextself(otri2);                                                           \
  symself(otri2);

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

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

#define rprev(otri1, otri2)                                                   \
  sym(otri1, otri2);                                                          \
  lprevself(otri2);                                                           \
  symself(otri2);

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

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

#define org(otri, vertexptr)                                                  \
  vertexptr = (vertex) (otri).tri[plus1mod3[(otri).orient] + 3]

#define dest(otri, vertexptr)                                                 \
  vertexptr = (vertex) (otri).tri[minus1mod3[(otri).orient] + 3]

#define apex(otri, vertexptr)                                                 \
  vertexptr = (vertex) (otri).tri[(otri).orient + 3]

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

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

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

/* Bond two triangles together.                                              */

#define bond(otri1, otri2)                                                    \
  (otri1).tri[(otri1).orient] = encode(otri2);                                \
  (otri2).tri[(otri2).orient] = encode(otri1)

/* Dissolve a bond (from one side).  Note that the other triangle will still */
/*   think it's connected to this triangle.  Usually, however, the other     */
/*   triangle is being deleted entirely, or bonded to another triangle, so   */
/*   it doesn't matter.                                                      */

#define dissolve(otri)                                                        \
  (otri).tri[(otri).orient] = (triangle) m->dummytri

/* Copy an oriented triangle.                                                */

#define otricopy(otri1, otri2)                                                \
  (otri2).tri = (otri1).tri;                                                  \
  (otri2).orient = (otri1).orient

/* Test for equality of oriented triangles.                                  */

#define otriequal(otri1, otri2)                                               \
  (((otri1).tri == (otri2).tri) &&                                            \
   ((otri1).orient == (otri2).orient))

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

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

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

/* Test a triangle for viral infection.                                      */

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

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

#define elemattribute(otri, attnum)                                           \
  ((REAL *) (otri).tri)[m->elemattribindex + (attnum)]

#define setelemattribute(otri, attnum, value)                                 \
  ((REAL *) (otri).tri)[m->elemattribindex + (attnum)] = value

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

#define areabound(otri)  ((REAL *) (otri).tri)[m->areaboundindex]

#define setareabound(otri, value)                                             \
  ((REAL *) (otri).tri)[m->areaboundindex] = value

/* Check or set a triangle's deallocation.  Its second pointer is set to     */
/*   NULL to indicate that it is not allocated.  (Its first pointer is used  */
/*   for the stack of dead items.)  Its fourth pointer (its first vertex)    */
/*   is set to NULL in case a `badtriang' structure points to it.            */

#define deadtri(tria)  ((tria)[1] == (triangle) NULL)

#define killtri(tria)                                                         \
  (tria)[1] = (triangle) NULL;                                                \
  (tria)[3] = (triangle) NULL

/********* Primitives for subsegments                                *********/
/*                                                                           */
/*                                                                           */

/* sdecode() converts a pointer to an oriented subsegment.  The orientation  */
/*   is extracted from the least significant bit of the pointer.  The two    */
/*   least significant bits (one for orientation, one for viral infection)   */
/*   are masked out to produce the real pointer.                             */

#define sdecode(sptr, osub)                                                   \
  (osub).ssorient = (int) ((unsigned long) (sptr) & (unsigned long) 1l);      \
  (osub).ss = (subseg *)                                                      \
              ((unsigned long) (sptr) & ~ (unsigned long) 3l)

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

#define sencode(osub)                                                         \
  (subseg) ((unsigned long) (osub).ss | (unsigned long) (osub).ssorient)

/* ssym() toggles the orientation of a subsegment.                           */

#define ssym(osub1, osub2)                                                    \
  (osub2).ss = (osub1).ss;                                                    \
  (osub2).ssorient = 1 - (osub1).ssorient

#define ssymself(osub)                                                        \
  (osub).ssorient = 1 - (osub).ssorient

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

#define spivot(osub1, osub2)                                                  \
  sptr = (osub1).ss[(osub1).ssorient];                                        \
  sdecode(sptr, osub2)

#define spivotself(osub)                                                      \
  sptr = (osub).ss[(osub).ssorient];                                          \
  sdecode(sptr, osub)

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

#define snext(osub1, osub2)                                                   \
  sptr = (osub1).ss[1 - (osub1).ssorient];                                    \
  sdecode(sptr, osub2)

#define snextself(osub)                                                       \
  sptr = (osub).ss[1 - (osub).ssorient];                                      \
  sdecode(sptr, osub)

/* These primitives determine or set the origin or destination of a          */
/*   subsegment or the segment that includes it.                             */

#define sorg(osub, vertexptr)                                                 \
  vertexptr = (vertex) (osub).ss[2 + (osub).ssorient]

#define sdest(osub, vertexptr)                                                \
  vertexptr = (vertex) (osub).ss[3 - (osub).ssorient]

#define setsorg(osub, vertexptr)                                              \
  (osub).ss[2 + (osub).ssorient] = (subseg) vertexptr

#define setsdest(osub, vertexptr)                                             \
  (osub).ss[3 - (osub).ssorient] = (subseg) vertexptr

#define segorg(osub, vertexptr)                                               \
  vertexptr = (vertex) (osub).ss[4 + (osub).ssorient]

#define segdest(osub, vertexptr)                                              \
  vertexptr = (vertex) (osub).ss[5 - (osub).ssorient]

#define setsegorg(osub, vertexptr)                                            \
  (osub).ss[4 + (osub).ssorient] = (subseg) vertexptr

#define setsegdest(osub, vertexptr)                                           \
  (osub).ss[5 - (osub).ssorient] = (subseg) vertexptr

/* These primitives read or set a boundary marker.  Boundary markers are     */
/*   used to hold user-defined tags for setting boundary conditions in       */
/*   finite element solvers.                                                 */

#define mark(osub)  (* (int *) ((osub).ss + 8))

#define setmark(osub, value)                                                  \
  * (int *) ((osub).ss + 8) = value

/* Bond two subsegments together.                                            */

#define sbond(osub1, osub2)                                                   \
  (osub1).ss[(osub1).ssorient] = sencode(osub2);                              \
  (osub2).ss[(osub2).ssorient] = sencode(osub1)

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

#define sdissolve(osub)                                                       \
  (osub).ss[(osub).ssorient] = (subseg) m->dummysub

/* Copy a subsegment.                                                        */

#define subsegcopy(osub1, osub2)                                              \
  (osub2).ss = (osub1).ss;                                                    \
  (osub2).ssorient = (osub1).ssorient

/* Test for equality of subsegments.                                         */

#define subsegequal(osub1, osub2)                                             \
  (((osub1).ss == (osub2).ss) &&                                              \
   ((osub1).ssorient == (osub2).ssorient))

/* Check or set a subsegment's deallocation.  Its second pointer is set to   */
/*   NULL to indicate that it is not allocated.  (Its first pointer is used  */
/*   for the stack of dead items.)  Its third pointer (its first vertex)     */
/*   is set to NULL in case a `badsubseg' structure points to it.            */

#define deadsubseg(sub)  ((sub)[1] == (subseg) NULL)

#define killsubseg(sub)                                                       \
  (sub)[1] = (subseg) NULL;                                                   \
  (sub)[2] = (subseg) NULL

/********* Primitives for interacting triangles and subsegments      *********/
/*                                                                           */
/*                                                                           */

/* tspivot() finds a subsegment abutting a triangle.                         */

#define tspivot(otri, osub)                                                   \
  sptr = (subseg) (otri).tri[6 + (otri).orient];                              \
  sdecode(sptr, osub)

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

#define stpivot(osub, otri)                                                   \
  ptr = (triangle) (osub).ss[6 + (osub).ssorient];                            \
  decode(ptr, otri)

/* Bond a triangle to a subsegment.                                          */

#define tsbond(otri, osub)                                                    \
  (otri).tri[6 + (otri).orient] = (triangle) sencode(osub);                   \
  (osub).ss[6 + (osub).ssorient] = (subseg) encode(otri)

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

#define tsdissolve(otri)                                                      \
  (otri).tri[6 + (otri).orient] = (triangle) m->dummysub

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

#define stdissolve(osub)                                                      \
  (osub).ss[6 + (osub).ssorient] = (subseg) m->dummytri

/********* Primitives for vertices                                   *********/
/*                                                                           */
/*                                                                           */

#define vertexmark(vx)  ((int *) (vx))[m->vertexmarkindex]

#define setvertexmark(vx, value)                                              \
  ((int *) (vx))[m->vertexmarkindex] = value

#define vertextype(vx)  ((int *) (vx))[m->vertexmarkindex + 1]

#define setvertextype(vx, value)                                              \
  ((int *) (vx))[m->vertexmarkindex + 1] = value

#define vertex2tri(vx)  ((triangle *) (vx))[m->vertex2triindex]

#define setvertex2tri(vx, value)                                              \
  ((triangle *) (vx))[m->vertex2triindex] = value

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

/********* User-defined triangle evaluation routine begins here      *********/
/**                                                                         **/
/**                                                                         **/

/*****************************************************************************/
/*                                                                           */
/*  triunsuitable()   Determine if a triangle is unsuitable, and thus must   */
/*                    be further refined.                                    */
/*                                                                           */
/*  You may write your own procedure that decides whether or not a selected  */
/*  triangle is too big (and needs to be refined).  There are two ways to do */
/*  this.                                                                    */
/*                                                                           */
/*  (1)  Modify the procedure `triunsuitable' below, then recompile          */
/*  Triangle.                                                                */
/*                                                                           */
/*  (2)  Define the symbol EXTERNAL_TEST (either by adding the definition    */
/*  to this file, or by using the appropriate compiler switch).  This way,   */
/*  you can compile triangle.c separately from your test.  Write your own    */
/*  `triunsuitable' procedure in a separate C file (using the same prototype */
/*  as below).  Compile it and link the object code with triangle.o.         */
/*                                                                           */
/*  This procedure returns 1 if the triangle is too large and should be      */
/*  refined; 0 otherwise.                                                    */
/*                                                                           */
/*****************************************************************************/

#ifdef EXTERNAL_TEST

int triunsuitable();

#else /* not EXTERNAL_TEST */

#ifdef ANSI_DECLARATORS
int triunsuitable(vertex triorg, vertex tridest, vertex triapex, REAL area)
#else /* not ANSI_DECLARATORS */
int triunsuitable(triorg, tridest, triapex, area)
vertex triorg;                              /* The triangle's origin vertex. */
vertex tridest;                        /* The triangle's destination vertex. */
vertex triapex;                               /* The triangle's apex vertex. */
REAL area;                                      /* The area of the triangle. */
#endif /* not ANSI_DECLARATORS */

{
	REAL dxoa, dxda, dxod;
	REAL dyoa, dyda, dyod;
	REAL oalen, dalen, odlen;
	REAL maxlen;

	dxoa = triorg[0] - triapex[0];
	dyoa = triorg[1] - triapex[1];
	dxda = tridest[0] - triapex[0];
	dyda = tridest[1] - triapex[1];
	dxod = triorg[0] - tridest[0];
	dyod = triorg[1] - tridest[1];
	/* Find the squares of the lengths of the triangle's three edges. */
	oalen = dxoa * dxoa + dyoa * dyoa;
	dalen = dxda * dxda + dyda * dyda;
	odlen = dxod * dxod + dyod * dyod;
	/* Find the square of the length of the longest edge. */
	maxlen = (dalen > oalen) ? dalen : oalen;
	maxlen = (odlen > maxlen) ? odlen : maxlen;

	if (maxlen > 0.05 * (triorg[0] * triorg[0] + triorg[1] * triorg[1]) + 0.02) {
		return 1;
	}
	else {
		return 0;
	}
}

#endif /* not EXTERNAL_TEST */

/**                                                                         **/
/**                                                                         **/
/********* User-defined triangle evaluation routine ends here        *********/

/********* Memory allocation and program exit wrappers begin here    *********/
/**                                                                         **/
/**                                                                         **/

#ifdef ANSI_DECLARATORS
void triexit(int status)
#else /* not ANSI_DECLARATORS */
void triexit(status)
int status;
#endif /* not ANSI_DECLARATORS */

{
	exit(status);
}

#ifdef ANSI_DECLARATORS
VOID *trimalloc(int size)
#else /* not ANSI_DECLARATORS */
VOID *trimalloc(size)
int size;
#endif /* not ANSI_DECLARATORS */

{
	VOID *memptr;

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

#ifdef ANSI_DECLARATORS
void trifree(void *memptr)
#else /* not ANSI_DECLARATORS */
void trifree(memptr)
VOID *memptr;
#endif /* not ANSI_DECLARATORS */
{
	free(memptr);
}

/**                                                                         **/
/**                                                                         **/
/********* Memory allocation and program exit wrappers end here      *********/

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

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

#ifndef TRILIBRARY

void syntax()
{
#ifdef CDT_ONLY
#ifdef REDUCED
	printf("triangle [-pAcjevngBPNEIOXzo_lQVh] input_file\n");
#else /* not REDUCED */
	printf("triangle [-pAcjevngBPNEIOXzo_iFlCQVh] input_file\n");
#endif /* not REDUCED */
#else /* not CDT_ONLY */
#ifdef REDUCED
	printf("triangle [-prq__a__uAcDjevngBPNEIOXzo_YS__lQVh] input_file\n");
#else /* not REDUCED */
	printf("triangle [-prq__a__uAcDjevngBPNEIOXzo_YS__iFlsCQVh] input_file\n");
#endif /* not REDUCED */
#endif /* not CDT_ONLY */

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

#endif /* not TRILIBRARY */

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

#ifndef TRILIBRARY

void info()
{
	printf("Triangle\n");
	printf(
		"A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator.\n");
	printf("Version 1.6\n\n");
	printf(
		"Copyright 1993, 1995, 1997, 1998, 2002, 2005 Jonathan Richard Shewchuk\n");
	printf("2360 Woolsey #H / Berkeley, California 94705-1927\n");
	printf("Bugs/comments to jrs@cs.berkeley.edu\n");
	printf(
		"Created as part of the Quake project (tools for earthquake simulation).\n");
	printf(
		"Supported in part by NSF Grant CMS-9318163 and an NSERC 1967 Scholarship.\n");
	printf("There is no warranty whatsoever.  Use at your own risk.\n");
#ifdef SINGLE
	printf("This executable is compiled for single precision arithmetic.\n\n\n");
#else /* not SINGLE */
	printf("This executable is compiled for double precision arithmetic.\n\n\n");
#endif /* not SINGLE */
	printf(
		"Triangle generates exact Delaunay triangulations, constrained Delaunay\n");
	printf(
		"triangulations, conforming Delaunay triangulations, Voronoi diagrams, and\n");
	printf(
		"high-quality triangular meshes.  The latter can be generated with no small\n"
		);
	printf(
		"or large angles, and are thus suitable for finite element analysis.  If no\n"
		);
	printf(
		"command line switch is specified, your .node input file is read, and the\n");
	printf(
		"Delaunay triangulation is returned in .node and .ele output files.  The\n");
	printf("command syntax is:\n\n");
	printf("triangle [-prq__a__uAcDjevngBPNEIOXzo_YS__iFlsCQVh] input_file\n\n");
	printf(
		"Underscores indicate that numbers may optionally follow certain switches.\n");
	printf(
		"Do not leave any space between a switch and its numeric parameter.\n");
	printf(
		"input_file must be a file with extension .node, or extension .poly if the\n");
	printf(
		"-p switch is used.  If -r is used, you must supply .node and .ele files,\n");
	printf(
		"and possibly a .poly file and an .area file as well.  The formats of these\n"
		);
	printf("files are described below.\n\n");
	printf("Command Line Switches:\n\n");
	printf(
		"    -p  Reads a Planar Straight Line Graph (.poly file), which can specify\n"
		);
	printf(
		"        vertices, segments, holes, regional attributes, and regional area\n");
	printf(
		"        constraints.  Generates a constrained Delaunay triangulation (CDT)\n"
		);
	printf(
		"        fitting the input; or, if -s, -q, -a, or -u is used, a conforming\n");
	printf(
		"        constrained Delaunay triangulation (CCDT).  If you want a truly\n");
	printf(
		"        Delaunay (not just constrained Delaunay) triangulation, use -D as\n");
	printf(
		"        well.  When -p is not used, Triangle reads a .node file by default.\n"
		);
	printf(
		"    -r  Refines a previously generated mesh.  The mesh is read from a .node\n"
		);
	printf(
		"        file and an .ele file.  If -p is also used, a .poly file is read\n");
	printf(
		"        and used to constrain segments in the mesh.  If -a is also used\n");
	printf(
		"        (with no number following), an .area file is read and used to\n");
	printf(
		"        impose area constraints on the mesh.  Further details on refinement\n"
		);
	printf("        appear below.\n");
	printf(
		"    -q  Quality mesh generation by Delaunay refinement (a hybrid of Paul\n");
	printf(
		"        Chew's and Jim Ruppert's algorithms).  Adds vertices to the mesh to\n"
		);
	printf(
		"        ensure that all angles are between 20 and 140 degrees.  An\n");
	printf(
		"        alternative bound on the minimum angle, replacing 20 degrees, may\n");
	printf(
		"        be specified after the `q'.  The specified angle may include a\n");
	printf(
		"        decimal point, but not exponential notation.  Note that a bound of\n"
		);
	printf(
		"        theta degrees on the smallest angle also implies a bound of\n");
	printf(
		"        (180 - 2 theta) on the largest angle.  If the minimum angle is 28.6\n"
		);
	printf(
		"        degrees or smaller, Triangle is mathematically guaranteed to\n");
	printf(
		"        terminate (assuming infinite precision arithmetic--Triangle may\n");
	printf(
		"        fail to terminate if you run out of precision).  In practice,\n");
	printf(
		"        Triangle often succeeds for minimum angles up to 34 degrees.  For\n");
	printf(
		"        some meshes, however, you might need to reduce the minimum angle to\n"
		);
	printf(
		"        avoid problems associated with insufficient floating-point\n");
	printf("        precision.\n");
	printf(
		"    -a  Imposes a maximum triangle area.  If a number follows the `a', no\n");
	printf(
		"        triangle is generated whose area is larger than that number.  If no\n"
		);
	printf(
		"        number is specified, an .area file (if -r is used) or .poly file\n");
	printf(
		"        (if -r is not used) specifies a set of maximum area constraints.\n");
	printf(
		"        An .area file contains a separate area constraint for each\n");
	printf(
		"        triangle, and is useful for refining a finite element mesh based on\n"
		);
	printf(
		"        a posteriori error estimates.  A .poly file can optionally contain\n"
		);
	printf(
		"        an area constraint for each segment-bounded region, thereby\n");
	printf(
		"        controlling triangle densities in a first triangulation of a PSLG.\n"
		);
	printf(
		"        You can impose both a fixed area constraint and a varying area\n");
	printf(
		"        constraint by invoking the -a switch twice, once with and once\n");
	printf(
		"        without a number following.  Each area specified may include a\n");
	printf("        decimal point.\n");
	printf(
		"    -u  Imposes a user-defined constraint on triangle size.  There are two\n"
		);
	printf(
		"        ways to use this feature.  One is to edit the triunsuitable()\n");
	printf(
		"        procedure in triangle.c to encode any constraint you like, then\n");
	printf(
		"        recompile Triangle.  The other is to compile triangle.c with the\n");
	printf(
		"        EXTERNAL_TEST symbol set (compiler switch -DEXTERNAL_TEST), then\n");
	printf(
		"        link Triangle with a separate object file that implements\n");
	printf(
		"        triunsuitable().  In either case, the -u switch causes the user-\n");
	printf("        defined test to be applied to every triangle.\n");
	printf(
		"    -A  Assigns an additional floating-point attribute to each triangle\n");
	printf(
		"        that identifies what segment-bounded region each triangle belongs\n");
	printf(
		"        to.  Attributes are assigned to regions by the .poly file.  If a\n");
	printf(
		"        region is not explicitly marked by the .poly file, triangles in\n");
	printf(
		"        that region are assigned an attribute of zero.  The -A switch has\n");
	printf(
		"        an effect only when the -p switch is used and the -r switch is not.\n"
		);
	printf(
		"    -c  Creates segments on the convex hull of the triangulation.  If you\n");
	printf(
		"        are triangulating a vertex set, this switch causes a .poly file to\n"
		);
	printf(
		"        be written, containing all edges of the convex hull.  If you are\n");
	printf(
		"        triangulating a PSLG, this switch specifies that the whole convex\n");
	printf(
		"        hull of the PSLG should be triangulated, regardless of what\n");
	printf(
		"        segments the PSLG has.  If you do not use this switch when\n");
	printf(
		"        triangulating a PSLG, Triangle assumes that you have identified the\n"
		);
	printf(
		"        region to be triangulated by surrounding it with segments of the\n");
	printf(
		"        input PSLG.  Beware:  if you are not careful, this switch can cause\n"
		);
	printf(
		"        the introduction of an extremely thin angle between a PSLG segment\n"
		);
	printf(
		"        and a convex hull segment, which can cause overrefinement (and\n");
	printf(
		"        possibly failure if Triangle runs out of precision).  If you are\n");
	printf(
		"        refining a mesh, the -c switch works differently:  it causes a\n");
	printf(
		"        .poly file to be written containing the boundary edges of the mesh\n"
		);
	printf("        (useful if no .poly file was read).\n");
	printf(
		"    -D  Conforming Delaunay triangulation:  use this switch if you want to\n"
		);
	printf(
		"        ensure that all the triangles in the mesh are Delaunay, and not\n");
	printf(
		"        merely constrained Delaunay; or if you want to ensure that all the\n"
		);
	printf(
		"        Voronoi vertices lie within the triangulation.  (Some finite volume\n"
		);
	printf(
		"        methods have this requirement.)  This switch invokes Ruppert's\n");
	printf(
		"        original algorithm, which splits every subsegment whose diametral\n");
	printf(
		"        circle is encroached.  It usually increases the number of vertices\n"
		);
	printf("        and triangles.\n");
	printf(
		"    -j  Jettisons vertices that are not part of the final triangulation\n");
	printf(
		"        from the output .node file.  By default, Triangle copies all\n");
	printf(
		"        vertices in the input .node file to the output .node file, in the\n");
	printf(
		"        same order, so their indices do not change.  The -j switch prevents\n"
		);
	printf(
		"        duplicated input vertices, or vertices `eaten' by holes, from\n");
	printf(
		"        appearing in the output .node file.  Thus, if two input vertices\n");
	printf(
		"        have exactly the same coordinates, only the first appears in the\n");
	printf(
		"        output.  If any vertices are jettisoned, the vertex numbering in\n");
	printf(
		"        the output .node file differs from that of the input .node file.\n");
	printf(
		"    -e  Outputs (to an .edge file) a list of edges of the triangulation.\n");
	printf(
		"    -v  Outputs the Voronoi diagram associated with the triangulation.\n");
	printf(
		"        Does not attempt to detect degeneracies, so some Voronoi vertices\n");
	printf(
		"        may be duplicated.  See the discussion of Voronoi diagrams below.\n");
	printf(
		"    -n  Outputs (to a .neigh file) a list of triangles neighboring each\n");
	printf("        triangle.\n");
	printf(
		"    -g  Outputs the mesh to an Object File Format (.off) file, suitable for\n"
		);
	printf("        viewing with the Geometry Center's Geomview package.\n");
	printf(
		"    -B  No boundary markers in the output .node, .poly, and .edge output\n");
	printf(
		"        files.  See the detailed discussion of boundary markers below.\n");
	printf(
		"    -P  No output .poly file.  Saves disk space, but you lose the ability\n");
	printf(
		"        to maintain constraining segments on later refinements of the mesh.\n"
		);
	printf("    -N  No output .node file.\n");
	printf("    -E  No output .ele file.\n");
	printf(
		"    -I  No iteration numbers.  Suppresses the output of .node and .poly\n");
	printf(
		"        files, so your input files won't be overwritten.  (If your input is\n"
		);
	printf(
		"        a .poly file only, a .node file is written.)  Cannot be used with\n");
	printf(
		"        the -r switch, because that would overwrite your input .ele file.\n");
	printf(
		"        Shouldn't be used with the -q, -a, -u, or -s switch if you are\n");
	printf(
		"        using a .node file for input, because no .node file is written, so\n"
		);
	printf("        there is no record of any added Steiner points.\n");
	printf("    -O  No holes.  Ignores the holes in the .poly file.\n");
	printf(
		"    -X  No exact arithmetic.  Normally, Triangle uses exact floating-point\n"
		);
	printf(
		"        arithmetic for certain tests if it thinks the inexact tests are not\n"
		);
	printf(
		"        accurate enough.  Exact arithmetic ensures the robustness of the\n");
	printf(
		"        triangulation algorithms, despite floating-point roundoff error.\n");
	printf(
		"        Disabling exact arithmetic with the -X switch causes a small\n");
	printf(
		"        improvement in speed and creates the possibility that Triangle will\n"
		);
	printf("        fail to produce a valid mesh.  Not recommended.\n");
	printf(
		"    -z  Numbers all items starting from zero (rather than one).  Note that\n"
		);
	printf(
		"        this switch is normally overridden by the value used to number the\n"
		);
	printf(
		"        first vertex of the input .node or .poly file.  However, this\n");
	printf(
		"        switch is useful when calling Triangle from another program.\n");
	printf(
		"    -o2 Generates second-order subparametric elements with six nodes each.\n"
		);
	printf(
		"    -Y  No new vertices on the boundary.  This switch is useful when the\n");
	printf(
		"        mesh boundary must be preserved so that it conforms to some\n");
	printf(
		"        adjacent mesh.  Be forewarned that you will probably sacrifice much\n"
		);
	printf(
		"        of the quality of the mesh; Triangle will try, but the resulting\n");
	printf(
		"        mesh may contain poorly shaped triangles.  Works well if all the\n");
	printf(
		"        boundary vertices are closely spaced.  Specify this switch twice\n");
	printf(
		"        (`-YY') to prevent all segment splitting, including internal\n");
	printf("        boundaries.\n");
	printf(
		"    -S  Specifies the maximum number of Steiner points (vertices that are\n");
	printf(
		"        not in the input, but are added to meet the constraints on minimum\n"
		);
	printf(
		"        angle and maximum area).  The default is to allow an unlimited\n");
	printf(
		"        number.  If you specify this switch with no number after it,\n");
	printf(
		"        the limit is set to zero.  Triangle always adds vertices at segment\n"
		);
	printf(
		"        intersections, even if it needs to use more vertices than the limit\n"
		);
	printf(
		"        you set.  When Triangle inserts segments by splitting (-s), it\n");
	printf(
		"        always adds enough vertices to ensure that all the segments of the\n"
		);
	printf("        PLSG are recovered, ignoring the limit if necessary.\n");
	printf(
		"    -i  Uses an incremental rather than a divide-and-conquer algorithm to\n");
	printf(
		"        construct a Delaunay triangulation.  Try it if the divide-and-\n");
	printf("        conquer algorithm fails.\n");
	printf(
		"    -F  Uses Steven Fortune's sweepline algorithm to construct a Delaunay\n");
	printf(
		"        triangulation.  Warning:  does not use exact arithmetic for all\n");
	printf("        calculations.  An exact result is not guaranteed.\n");
	printf(
		"    -l  Uses only vertical cuts in the divide-and-conquer algorithm.  By\n");
	printf(
		"        default, Triangle alternates between vertical and horizontal cuts,\n"
		);
	printf(
		"        which usually improve the speed except with vertex sets that are\n");
	printf(
		"        small or short and wide.  This switch is primarily of theoretical\n");
	printf("        interest.\n");
	printf(
		"    -s  Specifies that segments should be forced into the triangulation by\n"
		);
	printf(
		"        recursively splitting them at their midpoints, rather than by\n");
	printf(
		"        generating a constrained Delaunay triangulation.  Segment splitting\n"
		);
	printf(
		"        is true to Ruppert's original algorithm, but can create needlessly\n"
		);
	printf(
		"        small triangles.  This switch is primarily of theoretical interest.\n"
		);
	printf(
		"    -C  Check the consistency of the final mesh.  Uses exact arithmetic for\n"
		);
	printf(
		"        checking, even if the -X switch is used.  Useful if you suspect\n");
	printf("        Triangle is buggy.\n");
	printf(
		"    -Q  Quiet:  Suppresses all explanation of what Triangle is doing,\n");
	printf("        unless an error occurs.\n");
	printf(
		"    -V  Verbose:  Gives detailed information about what Triangle is doing.\n"
		);
	printf(
		"        Add more `V's for increasing amount of detail.  `-V' is most\n");
	printf(
		"        useful; itgives information on algorithmic progress and much more\n");
	printf(
		"        detailed statistics.  `-VV' gives vertex-by-vertex details, and\n");
	printf(
		"        prints so much that Triangle runs much more slowly.  `-VVVV' gives\n"
		);
	printf("        information only a debugger could love.\n");
	printf("    -h  Help:  Displays these instructions.\n");
	printf("\n");
	printf("Definitions:\n");
	printf("\n");
	printf(
		"  A Delaunay triangulation of a vertex set is a triangulation whose\n");
	printf(
		"  vertices are the vertex set, that covers the convex hull of the vertex\n");
	printf(
		"  set.  A Delaunay triangulation has the property that no vertex lies\n");
	printf(
		"  inside the circumscribing circle (circle that passes through all three\n");
	printf("  vertices) of any triangle in the triangulation.\n\n");
	printf(
		"  A Voronoi diagram of a vertex set is a subdivision of the plane into\n");
	printf(
		"  polygonal cells (some of which may be unbounded, meaning infinitely\n");
	printf(
		"  large), where each cell is the set of points in the plane that are closer\n"
		);
	printf(
		"  to some input vertex than to any other input vertex.  The Voronoi diagram\n"
		);
	printf("  is a geometric dual of the Delaunay triangulation.\n\n");
	printf(
		"  A Planar Straight Line Graph (PSLG) is a set of vertices and segments.\n");
	printf(
		"  Segments are simply edges, whose endpoints are all vertices in the PSLG.\n"
		);
	printf(
		"  Segments may intersect each other only at their endpoints.  The file\n");
	printf("  format for PSLGs (.poly files) is described below.\n\n");
	printf(
		"  A constrained Delaunay triangulation (CDT) of a PSLG is similar to a\n");
	printf(
		"  Delaunay triangulation, but each PSLG segment is present as a single edge\n"
		);
	printf(
		"  of the CDT.  (A constrained Delaunay triangulation is not truly a\n");
	printf(
		"  Delaunay triangulation, because some of its triangles might not be\n");
	printf(
		"  Delaunay.)  By definition, a CDT does not have any vertices other than\n");
	printf(
		"  those specified in the input PSLG.  Depending on context, a CDT might\n");
	printf(
		"  cover the convex hull of the PSLG, or it might cover only a segment-\n");
	printf("  bounded region (e.g. a polygon).\n\n");
	printf(
		"  A conforming Delaunay triangulation of a PSLG is a triangulation in which\n"
		);
	printf(
		"  each triangle is truly Delaunay, and each PSLG segment is represented by\n"
		);
	printf(
		"  a linear contiguous sequence of edges of the triangulation.  New vertices\n"
		);
	printf(
		"  (not part of the PSLG) may appear, and each input segment may have been\n");
	printf(
		"  subdivided into shorter edges (subsegments) by these additional vertices.\n"
		);
	printf(
		"  The new vertices are frequently necessary to maintain the Delaunay\n");
	printf("  property while ensuring that every segment is represented.\n\n");
	printf(
		"  A conforming constrained Delaunay triangulation (CCDT) of a PSLG is a\n");
	printf(
		"  triangulation of a PSLG whose triangles are constrained Delaunay.  New\n");
	printf("  vertices may appear, and input segments may be subdivided into\n");
	printf(
		"  subsegments, but not to guarantee that segments are respected; rather, to\n"
		);
	printf(
		"  improve the quality of the triangles.  The high-quality meshes produced\n");
	printf(
		"  by the -q switch are usually CCDTs, but can be made conforming Delaunay\n");
	printf("  with the -D switch.\n\n");
	printf("File Formats:\n\n");
	printf(
		"  All files may contain comments prefixed by the character '#'.  Vertices,\n"
		);
	printf(
		"  triangles, edges, holes, and maximum area constraints must be numbered\n");
	printf(
		"  consecutively, starting from either 1 or 0.  Whichever you choose, all\n");
	printf(
		"  input files must be consistent; if the vertices are numbered from 1, so\n");
	printf(
		"  must be all other objects.  Triangle automatically detects your choice\n");
	printf(
		"  while reading the .node (or .poly) file.  (When calling Triangle from\n");
	printf(
		"  another program, use the -z switch if you wish to number objects from\n");
	printf("  zero.)  Examples of these file formats are given below.\n\n");
	printf("  .node files:\n");
	printf(
		"    First line:  <# of vertices> <dimension (must be 2)> <# of attributes>\n"
		);
	printf(
		"                                           <# of boundary markers (0 or 1)>\n"
		);
	printf(
		"    Remaining lines:  <vertex #> <x> <y> [attributes] [boundary marker]\n");
	printf("\n");
	printf(
		"    The attributes, which are typically floating-point values of physical\n");
	printf(
		"    quantities (such as mass or conductivity) associated with the nodes of\n"
		);
	printf(
		"    a finite element mesh, are copied unchanged to the output mesh.  If -q,\n"
		);
	printf(
		"    -a, -u, -D, or -s is selected, each new Steiner point added to the mesh\n"
		);
	printf("    has attributes assigned to it by linear interpolation.\n\n");
	printf(
		"    If the fourth entry of the first line is `1', the last column of the\n");
	printf(
		"    remainder of the file is assumed to contain boundary markers.  Boundary\n"
		);
	printf(
		"    markers are used to identify boundary vertices and vertices resting on\n"
		);
	printf(
		"    PSLG segments; a complete description appears in a section below.  The\n"
		);
	printf(
		"    .node file produced by Triangle contains boundary markers in the last\n");
	printf("    column unless they are suppressed by the -B switch.\n\n");
	printf("  .ele files:\n");
	printf(
		"    First line:  <# of triangles> <nodes per triangle> <# of attributes>\n");
	printf(
		"    Remaining lines:  <triangle #> <node> <node> <node> ... [attributes]\n");
	printf("\n");
	printf(
		"    Nodes are indices into the corresponding .node file.  The first three\n");
	printf(
		"    nodes are the corner vertices, and are listed in counterclockwise order\n"
		);
	printf(
		"    around each triangle.  (The remaining nodes, if any, depend on the type\n"
		);
	printf("    of finite element used.)\n\n");
	printf(
		"    The attributes are just like those of .node files.  Because there is no\n"
		);
	printf(
		"    simple mapping from input to output triangles, Triangle attempts to\n");
	printf(
		"    interpolate attributes, and may cause a lot of diffusion of attributes\n"
		);
	printf(
		"    among nearby triangles as the triangulation is refined.  Attributes do\n"
		);
	printf("    not diffuse across segments, so attributes used to identify\n");
	printf("    segment-bounded regions remain intact.\n\n");
	printf(
		"    In .ele files produced by Triangle, each triangular element has three\n");
	printf(
		"    nodes (vertices) unless the -o2 switch is used, in which case\n");
	printf(
		"    subparametric quadratic elements with six nodes each are generated.\n");
	printf(
		"    The first three nodes are the corners in counterclockwise order, and\n");
	printf(
		"    the fourth, fifth, and sixth nodes lie on the midpoints of the edges\n");
	printf(
		"    opposite the first, second, and third vertices, respectively.\n");
	printf("\n");
	printf("  .poly files:\n");
	printf(
		"    First line:  <# of vertices> <dimension (must be 2)> <# of attributes>\n"
		);
	printf(
		"                                           <# of boundary markers (0 or 1)>\n"
		);
	printf(
		"    Following lines:  <vertex #> <x> <y> [attributes] [boundary marker]\n");
	printf("    One line:  <# of segments> <# of boundary markers (0 or 1)>\n");
	printf(
		"    Following lines:  <segment #> <endpoint> <endpoint> [boundary marker]\n");
	printf("    One line:  <# of holes>\n");
	printf("    Following lines:  <hole #> <x> <y>\n");
	printf(
		"    Optional line:  <# of regional attributes and/or area constraints>\n");
	printf(
		"    Optional following lines:  <region #> <x> <y> <attribute> <max area>\n");
	printf("\n");
	printf(
		"    A .poly file represents a PSLG, as well as some additional information.\n"
		);
	printf(
		"    The first section lists all the vertices, and is identical to the\n");
	printf(
		"    format of .node files.  <# of vertices> may be set to zero to indicate\n"
		);
	printf(
		"    that the vertices are listed in a separate .node file; .poly files\n");
	printf(
		"    produced by Triangle always have this format.  A vertex set represented\n"
		);
	printf(
		"    this way has the advantage that it may easily be triangulated with or\n");
	printf(
		"    without segments (depending on whether the -p switch is invoked).\n");
	printf("\n");
	printf(
		"    The second section lists the segments.  Segments are edges whose\n");
	printf(
		"    presence in the triangulation is enforced.  (Depending on the choice of\n"
		);
	printf(
		"    switches, segment might be subdivided into smaller edges).  Each\n");
	printf(
		"    segment is specified by listing the indices of its two endpoints.  This\n"
		);
	printf(
		"    means that you must include its endpoints in the vertex list.  Each\n");
	printf("    segment, like each point, may have a boundary marker.\n\n");
	printf(
		"    If -q, -a, -u, and -s are not selected, Triangle produces a constrained\n"
		);
	printf(
		"    Delaunay triangulation (CDT), in which each segment appears as a single\n"
		);
	printf(
		"    edge in the triangulation.  If -q, -a, -u, or -s is selected, Triangle\n"
		);
	printf(
		"    produces a conforming constrained Delaunay triangulation (CCDT), in\n");
	printf(
		"    which segments may be subdivided into smaller edges.  If -D is\n");
	printf(
		"    selected, Triangle produces a conforming Delaunay triangulation, so\n");
	printf(
		"    that every triangle is Delaunay, and not just constrained Delaunay.\n");
	printf("\n");
	printf(
		"    The third section lists holes (and concavities, if -c is selected) in\n");
	printf(
		"    the triangulation.  Holes are specified by identifying a point inside\n");
	printf(
		"    each hole.  After the triangulation is formed, Triangle creates holes\n");
	printf(
		"    by eating triangles, spreading out from each hole point until its\n");
	printf(
		"    progress is blocked by segments in the PSLG.  You must be careful to\n");
	printf(
		"    enclose each hole in segments, or your whole triangulation might be\n");
	printf(
		"    eaten away.  If the two triangles abutting a segment are eaten, the\n");
	printf(
		"    segment itself is also eaten.  Do not place a hole directly on a\n");
	printf("    segment; if you do, Triangle chooses one side of the segment\n");
	printf("    arbitrarily.\n\n");
	printf(
		"    The optional fourth section lists regional attributes (to be assigned\n");
	printf(
		"    to all triangles in a region) and regional constraints on the maximum\n");
	printf(
		"    triangle area.  Triangle reads this section only if the -A switch is\n");
	printf(
		"    used or the -a switch is used without a number following it, and the -r\n"
		);
	printf(
		"    switch is not used.  Regional attributes and area constraints are\n");
	printf(
		"    propagated in the same manner as holes:  you specify a point for each\n");
	printf(
		"    attribute and/or constraint, and the attribute and/or constraint\n");
	printf(
		"    affects the whole region (bounded by segments) containing the point.\n");
	printf(
		"    If two values are written on a line after the x and y coordinate, the\n");
	printf(
		"    first such value is assumed to be a regional attribute (but is only\n");
	printf(
		"    applied if the -A switch is selected), and the second value is assumed\n"
		);
	printf(
		"    to be a regional area constraint (but is only applied if the -a switch\n"
		);
	printf(
		"    is selected).  You may specify just one value after the coordinates,\n");
	printf(
		"    which can serve as both an attribute and an area constraint, depending\n"
		);
	printf(
		"    on the choice of switches.  If you are using the -A and -a switches\n");
	printf(
		"    simultaneously and wish to assign an attribute to some region without\n");
	printf("    imposing an area constraint, use a negative maximum area.\n\n");
	printf(
		"    When a triangulation is created from a .poly file, you must either\n");
	printf(
		"    enclose the entire region to be triangulated in PSLG segments, or\n");
	printf(
		"    use the -c switch, which automatically creates extra segments that\n");
	printf(
		"    enclose the convex hull of the PSLG.  If you do not use the -c switch,\n"
		);
	printf(
		"    Triangle eats all triangles that are not enclosed by segments; if you\n");
	printf(
		"    are not careful, your whole triangulation may be eaten away.  If you do\n"
		);
	printf(
		"    use the -c switch, you can still produce concavities by the appropriate\n"
		);
	printf(
		"    placement of holes just inside the boundary of the convex hull.\n");
	printf("\n");
	printf(
		"    An ideal PSLG has no intersecting segments, nor any vertices that lie\n");
	printf(
		"    upon segments (except, of course, the endpoints of each segment).  You\n"
		);
	printf(
		"    aren't required to make your .poly files ideal, but you should be aware\n"
		);
	printf(
		"    of what can go wrong.  Segment intersections are relatively safe--\n");
	printf(
		"    Triangle calculates the intersection points for you and adds them to\n");
	printf(
		"    the triangulation--as long as your machine's floating-point precision\n");
	printf(
		"    doesn't become a problem.  You are tempting the fates if you have three\n"
		);
	printf(
		"    segments that cross at the same location, and expect Triangle to figure\n"
		);
	printf(
		"    out where the intersection point is.  Thanks to floating-point roundoff\n"
		);
	printf(
		"    error, Triangle will probably decide that the three segments intersect\n"
		);
	printf(
		"    at three different points, and you will find a minuscule triangle in\n");
	printf(
		"    your output--unless Triangle tries to refine the tiny triangle, uses\n");
	printf(
		"    up the last bit of machine precision, and fails to terminate at all.\n");
	printf(
		"    You're better off putting the intersection point in the input files,\n");
	printf(
		"    and manually breaking up each segment into two.  Similarly, if you\n");
	printf(
		"    place a vertex at the middle of a segment, and hope that Triangle will\n"
		);
	printf(
		"    break up the segment at that vertex, you might get lucky.  On the other\n"
		);
	printf(
		"    hand, Triangle might decide that the vertex doesn't lie precisely on\n");
	printf(
		"    the segment, and you'll have a needle-sharp triangle in your output--or\n"
		);
	printf("    a lot of tiny triangles if you're generating a quality mesh.\n");
	printf("\n");
	printf(
		"    When Triangle reads a .poly file, it also writes a .poly file, which\n");
	printf(
		"    includes all the subsegments--the edges that are parts of input\n");
	printf(
		"    segments.  If the -c switch is used, the output .poly file also\n");
	printf(
		"    includes all of the edges on the convex hull.  Hence, the output .poly\n"
		);
	printf(
		"    file is useful for finding edges associated with input segments and for\n"
		);
	printf(
		"    setting boundary conditions in finite element simulations.  Moreover,\n");
	printf(
		"    you will need the output .poly file if you plan to refine the output\n");
	printf(
		"    mesh, and don't want segments to be missing in later triangulations.\n");
	printf("\n");
	printf("  .area files:\n");
	printf("    First line:  <# of triangles>\n");
	printf("    Following lines:  <triangle #> <maximum area>\n");
	printf("\n");
	printf(
		"    An .area file associates with each triangle a maximum area that is used\n"
		);
	printf(
		"    for mesh refinement.  As with other file formats, every triangle must\n");
	printf(
		"    be represented, and the triangles must be numbered consecutively.  A\n");
	printf(
		"    triangle may be left unconstrained by assigning it a negative maximum\n");
	printf("    area.\n\n");
	printf("  .edge files:\n");
	printf("    First line:  <# of edges> <# of boundary markers (0 or 1)>\n");
	printf(
		"    Following lines:  <edge #> <endpoint> <endpoint> [boundary marker]\n");
	printf("\n");
	printf(
		"    Endpoints are indices into the corresponding .node file.  Triangle can\n"
		);
	printf(
		"    produce .edge files (use the -e switch), but cannot read them.  The\n");
	printf(
		"    optional column of boundary markers is suppressed by the -B switch.\n");
	printf("\n");
	printf(
		"    In Voronoi diagrams, one also finds a special kind of edge that is an\n");
	printf(
		"    infinite ray with only one endpoint.  For these edges, a different\n");
	printf("    format is used:\n\n");
	printf("        <edge #> <endpoint> -1 <direction x> <direction y>\n\n");
	printf(
		"    The `direction' is a floating-point vector that indicates the direction\n"
		);
	printf("    of the infinite ray.\n\n");
	printf("  .neigh files:\n");
	printf(
		"    First line:  <# of triangles> <# of neighbors per triangle (always 3)>\n"
		);
	printf(
		"    Following lines:  <triangle #> <neighbor> <neighbor> <neighbor>\n");
	printf("\n");
	printf(
		"    Neighbors are indices into the corresponding .ele file.  An index of -1\n"
		);
	printf(
		"    indicates no neighbor (because the triangle is on an exterior\n");
	printf(
		"    boundary).  The first neighbor of triangle i is opposite the first\n");
	printf("    corner of triangle i, and so on.\n\n");
	printf(
		"    Triangle can produce .neigh files (use the -n switch), but cannot read\n"
		);
	printf("    them.\n\n");
	printf("Boundary Markers:\n\n");
	printf(
		"  Boundary markers are tags used mainly to identify which output vertices\n");
	printf(
		"  and edges are associated with which PSLG segment, and to identify which\n");
	printf(
		"  vertices and edges occur on a boundary of the triangulation.  A common\n");
	printf(
		"  use is to determine where boundary conditions should be applied to a\n");
	printf(
		"  finite element mesh.  You can prevent boundary markers from being written\n"
		);
	printf("  into files produced by Triangle by using the -B switch.\n\n");
	printf(
		"  The boundary marker associated with each segment in an output .poly file\n"
		);
	printf("  and each edge in an output .edge file is chosen as follows:\n");
	printf(
		"    - If an output edge is part or all of a PSLG segment with a nonzero\n");
	printf(
		"      boundary marker, then the edge is assigned the same marker.\n");
	printf(
		"    - Otherwise, if the edge lies on a boundary of the triangulation\n");
	printf(
		"      (even the boundary of a hole), then the edge is assigned the marker\n");
	printf("      one (1).\n");
	printf("    - Otherwise, the edge is assigned the marker zero (0).\n");
	printf(
		"  The boundary marker associated with each vertex in an output .node file\n");
	printf("  is chosen as follows:\n");
	printf(
		"    - If a vertex is assigned a nonzero boundary marker in the input file,\n"
		);
	printf(
		"      then it is assigned the same marker in the output .node file.\n");
	printf(
		"    - Otherwise, if the vertex lies on a PSLG segment (even if it is an\n");
	printf(
		"      endpoint of the segment) with a nonzero boundary marker, then the\n");
	printf(
		"      vertex is assigned the same marker.  If the vertex lies on several\n");
	printf("      such segments, one of the markers is chosen arbitrarily.\n");
	printf(
		"    - Otherwise, if the vertex occurs on a boundary of the triangulation,\n");
	printf("      then the vertex is assigned the marker one (1).\n");
	printf("    - Otherwise, the vertex is assigned the marker zero (0).\n");
	printf("\n");
	printf(
		"  If you want Triangle to determine for you which vertices and edges are on\n"
		);
	printf(
		"  the boundary, assign them the boundary marker zero (or use no markers at\n"
		);
	printf(
		"  all) in your input files.  In the output files, all boundary vertices,\n");
	printf("  edges, and segments will be assigned the value one.\n\n");
	printf("Triangulation Iteration Numbers:\n\n");
	printf(
		"  Because Triangle can read and refine its own triangulations, input\n");
	printf(
		"  and output files have iteration numbers.  For instance, Triangle might\n");
	printf(
		"  read the files mesh.3.node, mesh.3.ele, and mesh.3.poly, refine the\n");
	printf(
		"  triangulation, and output the files mesh.4.node, mesh.4.ele, and\n");
	printf("  mesh.4.poly.  Files with no iteration number are treated as if\n");
	printf(
		"  their iteration number is zero; hence, Triangle might read the file\n");
	printf(
		"  points.node, triangulate it, and produce the files points.1.node and\n");
	printf("  points.1.ele.\n\n");
	printf(
		"  Iteration numbers allow you to create a sequence of successively finer\n");
	printf(
		"  meshes suitable for multigrid methods.  They also allow you to produce a\n"
		);
	printf(
		"  sequence of meshes using error estimate-driven mesh refinement.\n");
	printf("\n");
	printf(
		"  If you're not using refinement or quality meshing, and you don't like\n");
	printf(
		"  iteration numbers, use the -I switch to disable them.  This switch also\n");
	printf(
		"  disables output of .node and .poly files to prevent your input files from\n"
		);
	printf(
		"  being overwritten.  (If the input is a .poly file that contains its own\n");
	printf(
		"  points, a .node file is written.  This can be quite convenient for\n");
	printf("  computing CDTs or quality meshes.)\n\n");
	printf("Examples of How to Use Triangle:\n\n");
	printf(
		"  `triangle dots' reads vertices from dots.node, and writes their Delaunay\n"
		);
	printf(
		"  triangulation to dots.1.node and dots.1.ele.  (dots.1.node is identical\n");
	printf(
		"  to dots.node.)  `triangle -I dots' writes the triangulation to dots.ele\n");
	printf(
		"  instead.  (No additional .node file is needed, so none is written.)\n");
	printf("\n");
	printf(
		"  `triangle -pe object.1' reads a PSLG from object.1.poly (and possibly\n");
	printf(
		"  object.1.node, if the vertices are omitted from object.1.poly) and writes\n"
		);
	printf(
		"  its constrained Delaunay triangulation to object.2.node and object.2.ele.\n"
		);
	printf(
		"  The segments are copied to object.2.poly, and all edges are written to\n");
	printf("  object.2.edge.\n\n");
	printf(
		"  `triangle -pq31.5a.1 object' reads a PSLG from object.poly (and possibly\n"
		);
	printf(
		"  object.node), generates a mesh whose angles are all between 31.5 and 117\n"
		);
	printf(
		"  degrees and whose triangles all have areas of 0.1 or less, and writes the\n"
		);
	printf(
		"  mesh to object.1.node and object.1.ele.  Each segment may be broken up\n");
	printf("  into multiple subsegments; these are written to object.1.poly.\n");
	printf("\n");
	printf(
		"  Here is a sample file `box.poly' describing a square with a square hole:\n"
		);
	printf("\n");
	printf(
		"    # A box with eight vertices in 2D, no attributes, one boundary marker.\n"
		);
	printf("    8 2 0 1\n");
	printf("     # Outer box has these vertices:\n");
	printf("     1   0 0   0\n");
	printf("     2   0 3   0\n");
	printf("     3   3 0   0\n");
	printf("     4   3 3   33     # A special marker for this vertex.\n");
	printf("     # Inner square has these vertices:\n");
	printf("     5   1 1   0\n");
	printf("     6   1 2   0\n");
	printf("     7   2 1   0\n");
	printf("     8   2 2   0\n");
	printf("    # Five segments with boundary markers.\n");
	printf("    5 1\n");
	printf("     1   1 2   5      # Left side of outer box.\n");
	printf("     # Square hole has these segments:\n");
	printf("     2   5 7   0\n");
	printf("     3   7 8   0\n");
	printf("     4   8 6   10\n");
	printf("     5   6 5   0\n");
	printf("    # One hole in the middle of the inner square.\n");
	printf("    1\n");
	printf("     1   1.5 1.5\n");
	printf("\n");
	printf(
		"  Note that some segments are missing from the outer square, so you must\n");
	printf(
		"  use the `-c' switch.  After `triangle -pqc box.poly', here is the output\n"
		);
	printf(
		"  file `box.1.node', with twelve vertices.  The last four vertices were\n");
	printf(
		"  added to meet the angle constraint.  Vertices 1, 2, and 9 have markers\n");
	printf(
		"  from segment 1.  Vertices 6 and 8 have markers from segment 4.  All the\n");
	printf(
		"  other vertices but 4 have been marked to indicate that they lie on a\n");
	printf("  boundary.\n\n");
	printf("    12  2  0  1\n");
	printf("       1    0   0      5\n");
	printf("       2    0   3      5\n");
	printf("       3    3   0      1\n");
	printf("       4    3   3     33\n");
	printf("       5    1   1      1\n");
	printf("       6    1   2     10\n");
	printf("       7    2   1      1\n");
	printf("       8    2   2     10\n");
	printf("       9    0   1.5    5\n");
	printf("      10    1.5   0    1\n");
	printf("      11    3   1.5    1\n");
	printf("      12    1.5   3    1\n");
	printf("    # Generated by triangle -pqc box.poly\n");
	printf("\n");
	printf("  Here is the output file `box.1.ele', with twelve triangles.\n");
	printf("\n");
	printf("    12  3  0\n");
	printf("       1     5   6   9\n");
	printf("       2    10   3   7\n");
	printf("       3     6   8  12\n");
	printf("       4     9   1   5\n");
	printf("       5     6   2   9\n");
	printf("       6     7   3  11\n");
	printf("       7    11   4   8\n");
	printf("       8     7   5  10\n");
	printf("       9    12   2   6\n");
	printf("      10     8   7  11\n");
	printf("      11     5   1  10\n");
	printf("      12     8   4  12\n");
	printf("    # Generated by triangle -pqc box.poly\n\n");
	printf(
		"  Here is the output file `box.1.poly'.  Note that segments have been added\n"
		);
	printf(
		"  to represent the convex hull, and some segments have been subdivided by\n");
	printf(
		"  newly added vertices.  Note also that <# of vertices> is set to zero to\n");
	printf("  indicate that the vertices should be read from the .node file.\n");
	printf("\n");
	printf("    0  2  0  1\n");
	printf("    12  1\n");
	printf("       1     1   9     5\n");
	printf("       2     5   7     1\n");
	printf("       3     8   7     1\n");
	printf("       4     6   8    10\n");
	printf("       5     5   6     1\n");
	printf("       6     3  10     1\n");
	printf("       7     4  11     1\n");
	printf("       8     2  12     1\n");
	printf("       9     9   2     5\n");
	printf("      10    10   1     1\n");
	printf("      11    11   3     1\n");
	printf("      12    12   4     1\n");
	printf("    1\n");
	printf("       1   1.5 1.5\n");
	printf("    # Generated by triangle -pqc box.poly\n");
	printf("\n");
	printf("Refinement and Area Constraints:\n");
	printf("\n");
	printf(
		"  The -r switch causes a mesh (.node and .ele files) to be read and\n");
	printf(
		"  refined.  If the -p switch is also used, a .poly file is read and used to\n"
		);
	printf(
		"  specify edges that are constrained and cannot be eliminated (although\n");
	printf(
		"  they can be subdivided into smaller edges) by the refinement process.\n");
	printf("\n");
	printf(
		"  When you refine a mesh, you generally want to impose tighter constraints.\n"
		);
	printf(
		"  One way to accomplish this is to use -q with a larger angle, or -a\n");
	printf(
		"  followed by a smaller area than you used to generate the mesh you are\n");
	printf(
		"  refining.  Another way to do this is to create an .area file, which\n");
	printf(
		"  specifies a maximum area for each triangle, and use the -a switch\n");
	printf(
		"  (without a number following).  Each triangle's area constraint is applied\n"
		);
	printf(
		"  to that triangle.  Area constraints tend to diffuse as the mesh is\n");
	printf(
		"  refined, so if there are large variations in area constraint between\n");
	printf(
		"  adjacent triangles, you may not get the results you want.  In that case,\n"
		);
	printf(
		"  consider instead using the -u switch and writing a C procedure that\n");
	printf("  determines which triangles are too large.\n\n");
	printf(
		"  If you are refining a mesh composed of linear (three-node) elements, the\n"
		);
	printf(
		"  output mesh contains all the nodes present in the input mesh, in the same\n"
		);
	printf(
		"  order, with new nodes added at the end of the .node file.  However, the\n");
	printf(
		"  refinement is not hierarchical: there is no guarantee that each output\n");
	printf(
		"  element is contained in a single input element.  Often, an output element\n"
		);
	printf(
		"  can overlap two or three input elements, and some input edges are not\n");
	printf(
		"  present in the output mesh.  Hence, a sequence of refined meshes forms a\n"
		);
	printf(
		"  hierarchy of nodes, but not a hierarchy of elements.  If you refine a\n");
	printf(
		"  mesh of higher-order elements, the hierarchical property applies only to\n"
		);
	printf(
		"  the nodes at the corners of an element; the midpoint nodes on each edge\n");
	printf("  are discarded before the mesh is refined.\n\n");
	printf(
		"  Maximum area constraints in .poly files operate differently from those in\n"
		);
	printf(
		"  .area files.  A maximum area in a .poly file applies to the whole\n");
	printf(
		"  (segment-bounded) region in which a point falls, whereas a maximum area\n");
	printf(
		"  in an .area file applies to only one triangle.  Area constraints in .poly\n"
		);
	printf(
		"  files are used only when a mesh is first generated, whereas area\n");
	printf(
		"  constraints in .area files are used only to refine an existing mesh, and\n"
		);
	printf(
		"  are typically based on a posteriori error estimates resulting from a\n");
	printf("  finite element simulation on that mesh.\n\n");
	printf(
		"  `triangle -rq25 object.1' reads object.1.node and object.1.ele, then\n");
	printf(
		"  refines the triangulation to enforce a 25 degree minimum angle, and then\n"
		);
	printf(
		"  writes the refined triangulation to object.2.node and object.2.ele.\n");
	printf("\n");
	printf(
		"  `triangle -rpaa6.2 z.3' reads z.3.node, z.3.ele, z.3.poly, and z.3.area.\n"
		);
	printf(
		"  After reconstructing the mesh and its subsegments, Triangle refines the\n");
	printf(
		"  mesh so that no triangle has area greater than 6.2, and furthermore the\n");
	printf(
		"  triangles satisfy the maximum area constraints in z.3.area.  No angle\n");
	printf(
		"  bound is imposed at all.  The output is written to z.4.node, z.4.ele, and\n"
		);
	printf("  z.4.poly.\n\n");
	printf(
		"  The sequence `triangle -qa1 x', `triangle -rqa.3 x.1', `triangle -rqa.1\n");
	printf(
		"  x.2' creates a sequence of successively finer meshes x.1, x.2, and x.3,\n");
	printf("  suitable for multigrid.\n\n");
	printf("Convex Hulls and Mesh Boundaries:\n\n");
	printf(
		"  If the input is a vertex set (not a PSLG), Triangle produces its convex\n");
	printf(
		"  hull as a by-product in the output .poly file if you use the -c switch.\n");
	printf(
		"  There are faster algorithms for finding a two-dimensional convex hull\n");
	printf("  than triangulation, of course, but this one comes for free.\n\n");
	printf(
		"  If the input is an unconstrained mesh (you are using the -r switch but\n");
	printf(
		"  not the -p switch), Triangle produces a list of its boundary edges\n");
	printf(
		"  (including hole boundaries) as a by-product when you use the -c switch.\n");
	printf(
		"  If you also use the -p switch, the output .poly file contains all the\n");
	printf("  segments from the input .poly file as well.\n\n");
	printf("Voronoi Diagrams:\n\n");
	printf(
		"  The -v switch produces a Voronoi diagram, in files suffixed .v.node and\n");
	printf(
		"  .v.edge.  For example, `triangle -v points' reads points.node, produces\n");
	printf(
		"  its Delaunay triangulation in points.1.node and points.1.ele, and\n");
	printf(
		"  produces its Voronoi diagram in points.1.v.node and points.1.v.edge.  The\n"
		);
	printf(
		"  .v.node file contains a list of all Voronoi vertices, and the .v.edge\n");
	printf(
		"  file contains a list of all Voronoi edges, some of which may be infinite\n"
		);
	printf(
		"  rays.  (The choice of filenames makes it easy to run the set of Voronoi\n");
	printf("  vertices through Triangle, if so desired.)\n\n");
	printf(
		"  This implementation does not use exact arithmetic to compute the Voronoi\n"
		);
	printf(
		"  vertices, and does not check whether neighboring vertices are identical.\n"
		);
	printf(
		"  Be forewarned that if the Delaunay triangulation is degenerate or\n");
	printf(
		"  near-degenerate, the Voronoi diagram may have duplicate vertices or\n");
	printf("  crossing edges.\n\n");
	printf(
		"  The result is a valid Voronoi diagram only if Triangle's output is a true\n"
		);
	printf(
		"  Delaunay triangulation.  The Voronoi output is usually meaningless (and\n");
	printf(
		"  may contain crossing edges and other pathology) if the output is a CDT or\n"
		);
	printf(
		"  CCDT, or if it has holes or concavities.  If the triangulated domain is\n");
	printf(
		"  convex and has no holes, you can use -D switch to force Triangle to\n");
	printf(
		"  construct a conforming Delaunay triangulation instead of a CCDT, so the\n");
	printf("  Voronoi diagram will be valid.\n\n");
	printf("Mesh Topology:\n\n");
	printf(
		"  You may wish to know which triangles are adjacent to a certain Delaunay\n");
	printf(
		"  edge in an .edge file, which Voronoi cells are adjacent to a certain\n");
	printf(
		"  Voronoi edge in a .v.edge file, or which Voronoi cells are adjacent to\n");
	printf(
		"  each other.  All of this information can be found by cross-referencing\n");
	printf(
		"  output files with the recollection that the Delaunay triangulation and\n");
	printf("  the Voronoi diagram are planar duals.\n\n");
	printf(
		"  Specifically, edge i of an .edge file is the dual of Voronoi edge i of\n");
	printf(
		"  the corresponding .v.edge file, and is rotated 90 degrees counterclock-\n");
	printf(
		"  wise from the Voronoi edge.  Triangle j of an .ele file is the dual of\n");
	printf(
		"  vertex j of the corresponding .v.node file.  Voronoi cell k is the dual\n");
	printf("  of vertex k of the corresponding .node file.\n\n");
	printf(
		"  Hence, to find the triangles adjacent to a Delaunay edge, look at the\n");
	printf(
		"  vertices of the corresponding Voronoi edge.  If the endpoints of a\n");
	printf(
		"  Voronoi edge are Voronoi vertices 2 and 6 respectively, then triangles 2\n"
		);
	printf(
		"  and 6 adjoin the left and right sides of the corresponding Delaunay edge,\n"
		);
	printf(
		"  respectively.  To find the Voronoi cells adjacent to a Voronoi edge, look\n"
		);
	printf(
		"  at the endpoints of the corresponding Delaunay edge.  If the endpoints of\n"
		);
	printf(
		"  a Delaunay edge are input vertices 7 and 12, then Voronoi cells 7 and 12\n"
		);
	printf(
		"  adjoin the right and left sides of the corresponding Voronoi edge,\n");
	printf(
		"  respectively.  To find which Voronoi cells are adjacent to each other,\n");
	printf("  just read the list of Delaunay edges.\n\n");
	printf(
		"  Triangle does not write a list of the edges adjoining each Voronoi cell,\n"
		);
	printf(
		"  but you can reconstructed it straightforwardly.  For instance, to find\n");
	printf(
		"  all the edges of Voronoi cell 1, search the output .edge file for every\n");
	printf(
		"  edge that has input vertex 1 as an endpoint.  The corresponding dual\n");
	printf(
		"  edges in the output .v.edge file form the boundary of Voronoi cell 1.\n");
	printf("\n");
	printf(
		"  For each Voronoi vertex, the .neigh file gives a list of the three\n");
	printf(
		"  Voronoi vertices attached to it.  You might find this more convenient\n");
	printf("  than the .v.edge file.\n\n");
	printf("Quadratic Elements:\n\n");
	printf(
		"  Triangle generates meshes with subparametric quadratic elements if the\n");
	printf(
		"  -o2 switch is specified.  Quadratic elements have six nodes per element,\n"
		);
	printf(
		"  rather than three.  `Subparametric' means that the edges of the triangles\n"
		);
	printf(
		"  are always straight, so that subparametric quadratic elements are\n");
	printf(
		"  geometrically identical to linear elements, even though they can be used\n"
		);
	printf(
		"  with quadratic interpolating functions.  The three extra nodes of an\n");
	printf(
		"  element fall at the midpoints of the three edges, with the fourth, fifth,\n"
		);
	printf(
		"  and sixth nodes appearing opposite the first, second, and third corners\n");
	printf("  respectively.\n\n");
	printf("Domains with Small Angles:\n\n");
	printf(
		"  If two input segments adjoin each other at a small angle, clearly the -q\n"
		);
	printf(
		"  switch cannot remove the small angle.  Moreover, Triangle may have no\n");
	printf(
		"  choice but to generate additional triangles whose smallest angles are\n");
	printf(
		"  smaller than the specified bound.  However, these triangles only appear\n");
	printf(
		"  between input segments separated by small angles.  Moreover, if you\n");
	printf(
		"  request a minimum angle of theta degrees, Triangle will generally produce\n"
		);
	printf(
		"  no angle larger than 180 - 2 theta, even if it is forced to compromise on\n"
		);
	printf("  the minimum angle.\n\n");
	printf("Statistics:\n\n");
	printf(
		"  After generating a mesh, Triangle prints a count of entities in the\n");
	printf(
		"  output mesh, including the number of vertices, triangles, edges, exterior\n"
		);
	printf(
		"  boundary edges (i.e. subsegments on the boundary of the triangulation,\n");
	printf(
		"  including hole boundaries), interior boundary edges (i.e. subsegments of\n"
		);
	printf(
		"  input segments not on the boundary), and total subsegments.  If you've\n");
	printf(
		"  forgotten the statistics for an existing mesh, run Triangle on that mesh\n"
		);
	printf(
		"  with the -rNEP switches to read the mesh and print the statistics without\n"
		);
	printf(
		"  writing any files.  Use -rpNEP if you've got a .poly file for the mesh.\n");
	printf("\n");
	printf(
		"  The -V switch produces extended statistics, including a rough estimate\n");
	printf(
		"  of memory use, the number of calls to geometric predicates, and\n");
	printf(
		"  histograms of the angles and the aspect ratios of the triangles in the\n");
	printf("  mesh.\n\n");
	printf("Exact Arithmetic:\n\n");
	printf(
		"  Triangle uses adaptive exact arithmetic to perform what computational\n");
	printf(
		"  geometers call the `orientation' and `incircle' tests.  If the floating-\n"
		);
	printf(
		"  point arithmetic of your machine conforms to the IEEE 754 standard (as\n");
	printf(
		"  most workstations do), and does not use extended precision internal\n");
	printf(
		"  floating-point registers, then your output is guaranteed to be an\n");
	printf(
		"  absolutely true Delaunay or constrained Delaunay triangulation, roundoff\n"
		);
	printf(
		"  error notwithstanding.  The word `adaptive' implies that these arithmetic\n"
		);
	printf(
		"  routines compute the result only to the precision necessary to guarantee\n"
		);
	printf(
		"  correctness, so they are usually nearly as fast as their approximate\n");
	printf("  counterparts.\n\n");
	printf(
		"  May CPUs, including Intel x86 processors, have extended precision\n");
	printf(
		"  floating-point registers.  These must be reconfigured so their precision\n"
		);
	printf(
		"  is reduced to memory precision.  Triangle does this if it is compiled\n");
	printf("  correctly.  See the makefile for details.\n\n");
	printf(
		"  The exact tests can be disabled with the -X switch.  On most inputs, this\n"
		);
	printf(
		"  switch reduces the computation time by about eight percent--it's not\n");
	printf(
		"  worth the risk.  There are rare difficult inputs (having many collinear\n");
	printf(
		"  and cocircular vertices), however, for which the difference in speed\n");
	printf(
		"  could be a factor of two.  Be forewarned that these are precisely the\n");
	printf(
		"  inputs most likely to cause errors if you use the -X switch.  Hence, the\n"
		);
	printf("  -X switch is not recommended.\n\n");
	printf(
		"  Unfortunately, the exact tests don't solve every numerical problem.\n");
	printf(
		"  Exact arithmetic is not used to compute the positions of new vertices,\n");
	printf(
		"  because the bit complexity of vertex coordinates would grow without\n");
	printf(
		"  bound.  Hence, segment intersections aren't computed exactly; in very\n");
	printf(
		"  unusual cases, roundoff error in computing an intersection point might\n");
	printf(
		"  actually lead to an inverted triangle and an invalid triangulation.\n");
	printf(
		"  (This is one reason to specify your own intersection points in your .poly\n"
		);
	printf(
		"  files.)  Similarly, exact arithmetic is not used to compute the vertices\n"
		);
	printf("  of the Voronoi diagram.\n\n");
	printf(
		"  Another pair of problems not solved by the exact arithmetic routines is\n");
	printf(
		"  underflow and overflow.  If Triangle is compiled for double precision\n");
	printf(
		"  arithmetic, I believe that Triangle's geometric predicates work correctly\n"
		);
	printf(
		"  if the exponent of every input coordinate falls in the range [-148, 201].\n"
		);
	printf(
		"  Underflow can silently prevent the orientation and incircle tests from\n");
	printf(
		"  being performed exactly, while overflow typically causes a floating\n");
	printf("  exception.\n\n");
	printf("Calling Triangle from Another Program:\n\n");
	printf("  Read the file triangle.h for details.\n\n");
	printf("Troubleshooting:\n\n");
	printf("  Please read this section before mailing me bugs.\n\n");
	printf("  `My output mesh has no triangles!'\n\n");
	printf(
		"    If you're using a PSLG, you've probably failed to specify a proper set\n"
		);
	printf(
		"    of bounding segments, or forgotten to use the -c switch.  Or you may\n");
	printf(
		"    have placed a hole badly, thereby eating all your triangles.  To test\n");
	printf("    these possibilities, try again with the -c and -O switches.\n");
	printf(
		"    Alternatively, all your input vertices may be collinear, in which case\n"
		);
	printf("    you can hardly expect to triangulate them.\n\n");
	printf("  `Triangle doesn't terminate, or just crashes.'\n\n");
	printf(
		"    Bad things can happen when triangles get so small that the distance\n");
	printf(
		"    between their vertices isn't much larger than the precision of your\n");
	printf(
		"    machine's arithmetic.  If you've compiled Triangle for single-precision\n"
		);
	printf(
		"    arithmetic, you might do better by recompiling it for double-precision.\n"
		);
	printf(
		"    Then again, you might just have to settle for more lenient constraints\n"
		);
	printf(
		"    on the minimum angle and the maximum area than you had planned.\n");
	printf("\n");
	printf(
		"    You can minimize precision problems by ensuring that the origin lies\n");
	printf(
		"    inside your vertex set, or even inside the densest part of your\n");
	printf(
		"    mesh.  If you're triangulating an object whose x-coordinates all fall\n");
	printf(
		"    between 6247133 and 6247134, you're not leaving much floating-point\n");
	printf("    precision for Triangle to work with.\n\n");
	printf(
		"    Precision problems can occur covertly if the input PSLG contains two\n");
	printf(
		"    segments that meet (or intersect) at an extremely small angle, or if\n");
	printf(
		"    such an angle is introduced by the -c switch.  If you don't realize\n");
	printf(
		"    that a tiny angle is being formed, you might never discover why\n");
	printf(
		"    Triangle is crashing.  To check for this possibility, use the -S switch\n"
		);
	printf(
		"    (with an appropriate limit on the number of Steiner points, found by\n");
	printf(
		"    trial-and-error) to stop Triangle early, and view the output .poly file\n"
		);
	printf(
		"    with Show Me (described below).  Look carefully for regions where dense\n"
		);
	printf(
		"    clusters of vertices are forming and for small angles between segments.\n"
		);
	printf(
		"    Zoom in closely, as such segments might look like a single segment from\n"
		);
	printf("    a distance.\n\n");
	printf(
		"    If some of the input values are too large, Triangle may suffer a\n");
	printf(
		"    floating exception due to overflow when attempting to perform an\n");
	printf(
		"    orientation or incircle test.  (Read the section on exact arithmetic\n");
	printf(
		"    above.)  Again, I recommend compiling Triangle for double (rather\n");
	printf("    than single) precision arithmetic.\n\n");
	printf(
		"    Unexpected problems can arise if you use quality meshing (-q, -a, or\n");
	printf(
		"    -u) with an input that is not segment-bounded--that is, if your input\n");
	printf(
		"    is a vertex set, or you're using the -c switch.  If the convex hull of\n"
		);
	printf(
		"    your input vertices has collinear vertices on its boundary, an input\n");
	printf(
		"    vertex that you think lies on the convex hull might actually lie just\n");
	printf(
		"    inside the convex hull.  If so, the vertex and the nearby convex hull\n");
	printf(
		"    edge form an extremely thin triangle.  When Triangle tries to refine\n");
	printf(
		"    the mesh to enforce angle and area constraints, Triangle might generate\n"
		);
	printf(
		"    extremely tiny triangles, or it might fail because of insufficient\n");
	printf("    floating-point precision.\n\n");
	printf(
		"  `The numbering of the output vertices doesn't match the input vertices.'\n"
		);
	printf("\n");
	printf(
		"    You may have had duplicate input vertices, or you may have eaten some\n");
	printf(
		"    of your input vertices with a hole, or by placing them outside the area\n"
		);
	printf(
		"    enclosed by segments.  In any case, you can solve the problem by not\n");
	printf("    using the -j switch.\n\n");
	printf(
		"  `Triangle executes without incident, but when I look at the resulting\n");
	printf(
		"  mesh, it has overlapping triangles or other geometric inconsistencies.'\n");
	printf("\n");
	printf(
		"    If you select the -X switch, Triangle occasionally makes mistakes due\n");
	printf(
		"    to floating-point roundoff error.  Although these errors are rare,\n");
	printf(
		"    don't use the -X switch.  If you still have problems, please report the\n"
		);
	printf("    bug.\n\n");
	printf(
		"  `Triangle executes without incident, but when I look at the resulting\n");
	printf("  Voronoi diagram, it has overlapping edges or other geometric\n");
	printf("  inconsistencies.'\n");
	printf("\n");
	printf(
		"    If your input is a PSLG (-p), you can only expect a meaningful Voronoi\n"
		);
	printf(
		"    diagram if the domain you are triangulating is convex and free of\n");
	printf(
		"    holes, and you use the -D switch to construct a conforming Delaunay\n");
	printf("    triangulation (instead of a CDT or CCDT).\n\n");
	printf(
		"  Strange things can happen if you've taken liberties with your PSLG.  Do\n");
	printf(
		"  you have a vertex lying in the middle of a segment?  Triangle sometimes\n");
	printf(
		"  copes poorly with that sort of thing.  Do you want to lay out a collinear\n"
		);
	printf(
		"  row of evenly spaced, segment-connected vertices?  Have you simply\n");
	printf(
		"  defined one long segment connecting the leftmost vertex to the rightmost\n"
		);
	printf(
		"  vertex, and a bunch of vertices lying along it?  This method occasionally\n"
		);
	printf(
		"  works, especially with horizontal and vertical lines, but often it\n");
	printf(
		"  doesn't, and you'll have to connect each adjacent pair of vertices with a\n"
		);
	printf("  separate segment.  If you don't like it, tough.\n\n");
	printf(
		"  Furthermore, if you have segments that intersect other than at their\n");
	printf(
		"  endpoints, try not to let the intersections fall extremely close to PSLG\n"
		);
	printf("  vertices or each other.\n\n");
	printf(
		"  If you have problems refining a triangulation not produced by Triangle:\n");
	printf(
		"  Are you sure the triangulation is geometrically valid?  Is it formatted\n");
	printf(
		"  correctly for Triangle?  Are the triangles all listed so the first three\n"
		);
	printf(
		"  vertices are their corners in counterclockwise order?  Are all of the\n");
	printf(
		"  triangles constrained Delaunay?  Triangle's Delaunay refinement algorithm\n"
		);
	printf("  assumes that it starts with a CDT.\n\n");
	printf("Show Me:\n\n");
	printf(
		"  Triangle comes with a separate program named `Show Me', whose primary\n");
	printf(
		"  purpose is to draw meshes on your screen or in PostScript.  Its secondary\n"
		);
	printf(
		"  purpose is to check the validity of your input files, and do so more\n");
	printf(
		"  thoroughly than Triangle does.  Unlike Triangle, Show Me requires that\n");
	printf(
		"  you have the X Windows system.  Sorry, Microsoft Windows users.\n");
	printf("\n");
	printf("Triangle on the Web:\n");
	printf("\n");
	printf("  To see an illustrated version of these instructions, check out\n");
	printf("\n");
	printf("    http://www.cs.cmu.edu/~quake/triangle.html\n");
	printf("\n");
	printf("A Brief Plea:\n");
	printf("\n");
	printf(
		"  If you use Triangle, and especially if you use it to accomplish real\n");
	printf(
		"  work, I would like very much to hear from you.  A short letter or email\n");
	printf(
		"  (to jrs@cs.berkeley.edu) describing how you use Triangle will mean a lot\n"
		);
	printf(
		"  to me.  The more people I know are using this program, the more easily I\n"
		);
	printf(
		"  can justify spending time on improvements, which in turn will benefit\n");
	printf(
		"  you.  Also, I can put you on a list to receive email whenever a new\n");
	printf("  version of Triangle is available.\n\n");
	printf(
		"  If you use a mesh generated by Triangle in a publication, please include\n"
		);
	printf(
		"  an acknowledgment as well.  And please spell Triangle with a capital `T'!\n"
		);
	printf(
		"  If you want to include a citation, use `Jonathan Richard Shewchuk,\n");
	printf(
		"  ``Triangle: Engineering a 2D Quality Mesh Generator and Delaunay\n");
	printf(
		"  Triangulator,'' in Applied Computational Geometry:  Towards Geometric\n");
	printf(
		"  Engineering (Ming C. Lin and Dinesh Manocha, editors), volume 1148 of\n");
	printf(
		"  Lecture Notes in Computer Science, pages 203-222, Springer-Verlag,\n");
	printf(
		"  Berlin, May 1996.  (From the First ACM Workshop on Applied Computational\n"
		);
	printf("  Geometry.)'\n\n");
	printf("Research credit:\n\n");
	printf(
		"  Of course, I can take credit for only a fraction of the ideas that made\n");
	printf(
		"  this mesh generator possible.  Triangle owes its existence to the efforts\n"
		);
	printf(
		"  of many fine computational geometers and other researchers, including\n");
	printf(
		"  Marshall Bern, L. Paul Chew, Kenneth L. Clarkson, Boris Delaunay, Rex A.\n"
		);
	printf(
		"  Dwyer, David Eppstein, Steven Fortune, Leonidas J. Guibas, Donald E.\n");
	printf(
		"  Knuth, Charles L. Lawson, Der-Tsai Lee, Gary L. Miller, Ernst P. Mucke,\n");
	printf(
		"  Steven E. Pav, Douglas M. Priest, Jim Ruppert, Isaac Saias, Bruce J.\n");
	printf(
		"  Schachter, Micha Sharir, Peter W. Shor, Daniel D. Sleator, Jorge Stolfi,\n"
		);
	printf("  Robert E. Tarjan, Alper Ungor, Christopher J. Van Wyk, Noel J.\n");
	printf(
		"  Walkington, and Binhai Zhu.  See the comments at the beginning of the\n");
	printf("  source code for references.\n\n");
	triexit(0);
}

#endif /* not TRILIBRARY */

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

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

/*****************************************************************************/
/*                                                                           */
/*  parsecommandline()   Read the command line, identify switches, and set   */
/*                       up options and file names.                          */
/*                                                                           */
/*****************************************************************************/

#ifdef ANSI_DECLARATORS
void parsecommandline(int argc, char **argv, struct behavior *b)
#else /* not ANSI_DECLARATORS */
void parsecommandline(argc, argv, b)
int argc;
char **argv;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */

{
#ifdef TRILIBRARY
#define STARTINDEX 0
#else /* not TRILIBRARY */
#define STARTINDEX 1
	int increment;
	int meshnumber;
#endif /* not TRILIBRARY */
	int i, j, k;
	char workstring[FILENAMESIZE];

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

	for (i = STARTINDEX; i < argc; i++) {
#ifndef TRILIBRARY
		if (argv[i][0] == '-') {
#endif /* not TRILIBRARY */
			for (j = STARTINDEX; argv[i][j] != '\0'; j++) {
				if (argv[i][j] == 'p') {
					b->poly = 1;
				}
#ifndef CDT_ONLY
				if (argv[i][j] == 'r') {
					b->refine = 1;
				}
				if (argv[i][j] == 'q') {
					b->quality = 1;
					if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
						(argv[i][j + 1] == '.')) {
						k = 0;
						while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
							(argv[i][j + 1] == '.')) {
							j++;
							workstring[k] = argv[i][j];
							k++;
						}
						workstring[k] = '\0';
						b->minangle = (REAL)strtod(workstring, (char **)NULL);
					}
					else {
						b->minangle = 20.0;
					}
				}
				if (argv[i][j] == 'a') {
					b->quality = 1;
					if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
						(argv[i][j + 1] == '.')) {
						b->fixedarea = 1;
						k = 0;
						while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
							(argv[i][j + 1] == '.')) {
							j++;
							workstring[k] = argv[i][j];
							k++;
						}
						workstring[k] = '\0';
						b->maxarea = (REAL)strtod(workstring, (char **)NULL);
						if (b->maxarea <= 0.0) {
							printf("Error:  Maximum area must be greater than zero.\n");
							triexit(1);
						}
					}
					else {
						b->vararea = 1;
					}
				}
				if (argv[i][j] == 'u') {
					b->quality = 1;
					b->usertest = 1;
				}
#endif /* not CDT_ONLY */
				if (argv[i][j] == 'A') {
					b->regionattrib = 1;
				}
				if (argv[i][j] == 'c') {
					b->convex = 1;
				}
				if (argv[i][j] == 'w') {
					b->weighted = 1;
				}
				if (argv[i][j] == 'W') {
					b->weighted = 2;
				}
				if (argv[i][j] == 'j') {
					b->jettison = 1;
				}
				if (argv[i][j] == 'z') {
					b->firstnumber = 0;
				}
				if (argv[i][j] == 'e') {
					b->edgesout = 1;
				}
				if (argv[i][j] == 'v') {
					b->voronoi = 1;
				}
				if (argv[i][j] == 'n') {
					b->neighbors = 1;
				}
				if (argv[i][j] == 'g') {
					b->geomview = 1;
				}
				if (argv[i][j] == 'B') {
					b->nobound = 1;
				}
				if (argv[i][j] == 'P') {
					b->nopolywritten = 1;
				}
				if (argv[i][j] == 'N') {
					b->nonodewritten = 1;
				}
				if (argv[i][j] == 'E') {
					b->noelewritten = 1;
				}
#ifndef TRILIBRARY
				if (argv[i][j] == 'I') {
					b->noiterationnum = 1;
				}
#endif /* not TRILIBRARY */
				if (argv[i][j] == 'O') {
					b->noholes = 1;
				}
				if (argv[i][j] == 'X') {
					b->noexact = 1;
				}
				if (argv[i][j] == 'o') {
					if (argv[i][j + 1] == '2') {
						j++;
						b->order = 2;
					}
				}
#ifndef CDT_ONLY
				if (argv[i][j] == 'Y') {
					b->nobisect++;
				}
				if (argv[i][j] == 'S') {
					b->steiner = 0;
					while ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) {
						j++;
						b->steiner = b->steiner * 10 + (int)(argv[i][j] - '0');
					}
				}
#endif /* not CDT_ONLY */
#ifndef REDUCED
				if (argv[i][j] == 'i') {
					b->incremental = 1;
				}
				if (argv[i][j] == 'F') {
					b->sweepline = 1;
				}
#endif /* not REDUCED */
				if (argv[i][j] == 'l') {
					b->dwyer = 0;
				}
#ifndef REDUCED
#ifndef CDT_ONLY
				if (argv[i][j] == 's') {
					b->splitseg = 1;
				}
				if ((argv[i][j] == 'D') || (argv[i][j] == 'L')) {
					b->quality = 1;
					b->conformdel = 1;
				}
#endif /* not CDT_ONLY */
				if (argv[i][j] == 'C') {
					b->docheck = 1;
				}
#endif /* not REDUCED */
				if (argv[i][j] == 'Q') {
					b->quiet = 1;
				}
				if (argv[i][j] == 'V') {
					b->verbose++;
				}
#ifndef TRILIBRARY
				if ((argv[i][j] == 'h') || (argv[i][j] == 'H') ||
					(argv[i][j] == '?')) {
					info();
				}
#endif /* not TRILIBRARY */
			}
#ifndef TRILIBRARY
		}
		else {
			strncpy(b->innodefilename, argv[i], FILENAMESIZE - 1);
			b->innodefilename[FILENAMESIZE - 1] = '\0';
		}
#endif /* not TRILIBRARY */
	}
#ifndef TRILIBRARY
	if (b->innodefilename[0] == '\0') {
		syntax();
	}
	if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 5], ".node")) {
		b->innodefilename[strlen(b->innodefilename) - 5] = '\0';
	}
	if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 5], ".poly")) {
		b->innodefilename[strlen(b->innodefilename) - 5] = '\0';
		b->poly = 1;
	}
#ifndef CDT_ONLY
	if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 4], ".ele")) {
		b->innodefilename[strlen(b->innodefilename) - 4] = '\0';
		b->refine = 1;
	}
	if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 5], ".area")) {
		b->innodefilename[strlen(b->innodefilename) - 5] = '\0';
		b->refine = 1;
		b->quality = 1;
		b->vararea = 1;
	}
#endif /* not CDT_ONLY */
#endif /* not TRILIBRARY */
	b->usesegments = b->poly || b->refine || b->quality || b->convex;
	b->goodangle = cos(b->minangle * PI / 180.0);
	if (b->goodangle == 1.0) {
		b->offconstant = 0.0;
	}
	else {
		b->offconstant = 0.475 * sqrt((1.0 + b->goodangle) / (1.0 - b->goodangle));
	}
	b->goodangle *= b->goodangle;
	if (b->refine && b->noiterationnum) {
		printf(
			"Error:  You cannot use the -I switch when refining a triangulation.\n");
		triexit(1);
	}
	/* Be careful not to allocate space for element area constraints that */
	/*   will never be assigned any value (other than the default -1.0).  */
	if (!b->refine && !b->poly) {
		b->vararea = 0;
	}
	/* Be careful not to add an extra attribute to each element unless the */
	/*   input supports it (PSLG in, but not refining a preexisting mesh). */
	if (b->refine || !b->poly) {
		b->regionattrib = 0;
	}
	/* Regular/weighted triangulations are incompatible with PSLGs */
	/*   and meshing.                                              */
	if (b->weighted && (b->poly || b->quality)) {
		b->weighted = 0;
		if (!b->quiet) {
			printf("Warning:  weighted triangulations (-w, -W) are incompatible\n");
			printf("  with PSLGs (-p) and meshing (-q, -a, -u).  Weights ignored.\n"
				);
		}
	}
	if (b->jettison && b->nonodewritten && !b->quiet) {
		printf("Warning:  -j and -N switches are somewhat incompatible.\n");
		printf("  If any vertices are jettisoned, you will need the output\n");
		printf("  .node file to reconstruct the new node indices.");
	}

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

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

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

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

#ifdef ANSI_DECLARATORS
void printtriangle(struct mesh *m, struct behavior *b, struct otri *t)
#else /* not ANSI_DECLARATORS */
void printtriangle(m, b, t)
struct mesh *m;
struct behavior *b;
struct otri *t;
#endif /* not ANSI_DECLARATORS */

{
	struct otri printtri;
	struct osub printsh;
	vertex printvertex;

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

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

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

	if (b->vararea) {
		printf("    Area constraint:  %.4g\n", areabound(*t));
	}
}

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

#ifdef ANSI_DECLARATORS
void printsubseg(struct mesh *m, struct behavior *b, struct osub *s)
#else /* not ANSI_DECLARATORS */
void printsubseg(m, b, s)
struct mesh *m;
struct behavior *b;
struct osub *s;
#endif /* not ANSI_DECLARATORS */

{
	struct osub printsh;
	struct otri printtri;
	vertex printvertex;

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

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

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

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

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

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

/*****************************************************************************/
/*                                                                           */
/*  poolzero()   Set all of a pool's fields to zero.                         */
/*                                                                           */
/*  This procedure should never be called on a pool that has any memory      */
/*  allocated to it, as that memory would leak.                              */
/*                                                                           */
/*****************************************************************************/

#ifdef ANSI_DECLARATORS
void poolzero(struct memorypool *pool)
#else /* not ANSI_DECLARATORS */
void poolzero(pool)
struct memorypool *pool;
#endif /* not ANSI_DECLARATORS */

{
	pool->firstblock = (VOID **)NULL;
	pool->nowblock = (VOID **)NULL;
	pool->nextitem = (VOID *)NULL;
	pool->deaditemstack = (VOID *)NULL;
	pool->pathblock = (VOID **)NULL;
	pool->pathitem = (VOID *)NULL;
	pool->alignbytes = 0;
	pool->itembytes = 0;
	pool->itemsperblock = 0;
	pool->itemsfirstblock = 0;
	pool->items = 0;
	pool->maxitems = 0;
	pool->unallocateditems = 0;
	pool->pathitemsleft = 0;
}

/*****************************************************************************/
/*                                                                           */
/*  poolrestart()   Deallocate all items in a pool.                          */
/*                                                                           */
/*  The pool is returned to its starting state, except that no memory is     */
/*  freed to the operating system.  Rather, the previously allocated blocks  */
/*  are ready to be reused.                                                  */
/*                                                                           */
/*****************************************************************************/

#ifdef ANSI_DECLARATORS
void poolrestart(struct memorypool *pool)
#else /* not ANSI_DECLARATORS */
void poolrestart(pool)
struct memorypool *pool;
#endif /* not ANSI_DECLARATORS */

{
	unsigned long alignptr;

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

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

/*****************************************************************************/
/*                                                                           */
/*  poolinit()   Initialize a pool of memory for allocation of items.        */
/*                                                                           */
/*  This routine initializes the machinery for allocating items.  A `pool'   */
/*  is created whose records have size at least `bytecount'.  Items will be  */
/*  allocated in `itemcount'-item blocks.  Each item is assumed to be a      */
/*  collection of words, and either pointers or floating-point values are    */
/*  assumed to be the "primary" word type.  (The "primary" word type is used */
/*  to determine alignment of items.)  If `alignment' isn't zero, all items  */
/*  will be `alignment'-byte aligned in memory.  `alignment' must be either  */
/*  a multiple or a factor of the primary word size; powers of two are safe. */
/*  `alignment' is normally used to create a few unused bits at the bottom   */
/*  of each item's pointer, in which information may be stored.              */
/*                                                                           */
/*  Don't change this routine unless you understand it.                      */
/*                                                                           */
/*****************************************************************************/

#ifdef ANSI_DECLARATORS
void poolinit(struct memorypool *pool, int bytecount, int itemcount,
	int firstitemcount, int alignment)
#else /* not ANSI_DECLARATORS */
void poolinit(pool, bytecount, itemcount, firstitemcount, alignment)
struct memorypool *pool;
int bytecount;
int itemcount;
int firstitemcount;
int alignment;
#endif /* not ANSI_DECLARATORS */

{
	/* Find the proper alignment, which must be at least as large as:   */
	/*   - The parameter `alignment'.                                   */
	/*   - sizeof(VOID *), so the stack of dead items can be maintained */
	/*       without unaligned accesses.                                */
	if (alignment > sizeof(VOID *)) {
		pool->alignbytes = alignment;
	}
	else {
		pool->alignbytes = sizeof(VOID *);
	}
	pool->itembytes = ((bytecount - 1) / pool->alignbytes + 1) *
		pool->alignbytes;
	pool->itemsperblock = itemcount;
	if (firstitemcount == 0) {
		pool->itemsfirstblock = itemcount;
	}
	else {
		pool->itemsfirstblock = firstitemcount;
	}

	/* Allocate a block of items.  Space for `itemsfirstblock' items and one  */
	/*   pointer (to point to the next block) are allocated, as well as space */
	/*   to ensure alignment of the items.                                    */
	pool->firstblock = (VOID **)
		trimalloc(pool->itemsfirstblock * pool->itembytes + (int) sizeof(VOID *) +
			pool->alignbytes);
	/* Set the next block pointer to NULL. */
	*(pool->firstblock) = (VOID *)NULL;
	poolrestart(pool);
}

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

#ifdef ANSI_DECLARATORS
void pooldeinit(struct memorypool *pool)
#else /* not ANSI_DECLARATORS */
void pooldeinit(pool)
struct memorypool *pool;
#endif /* not ANSI_DECLARATORS */

{
	while (pool->firstblock != (VOID **)NULL) {
		pool->nowblock = (VOID **)*(pool->firstblock);
		trifree((VOID *)pool->firstblock);
		pool->firstblock = pool->nowblock;
	}
}

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

#ifdef ANSI_DECLARATORS
VOID *poolalloc(struct memorypool *pool)
#else /* not ANSI_DECLARATORS */
VOID *poolalloc(pool)
struct memorypool *pool;
#endif /* not ANSI_DECLARATORS */

{
	VOID *newitem;
	VOID **newblock;
	unsigned long alignptr;

	/* First check the linked list of dead items.  If the list is not   */
	/*   empty, allocate an item from the list rather than a fresh one. */
	if (pool->deaditemstack != (VOID *)NULL) {
		newitem = pool->deaditemstack;               /* Take first item in list. */
		pool->deaditemstack = *(VOID **)pool->deaditemstack;
	}
	else {
		/* Check if there are any free items left in the current block. */
		if (pool->unallocateditems == 0) {
			/* Check if another block must be allocated. */
			if (*(pool->nowblock) == (VOID *)NULL) {
				/* Allocate a new block of items, pointed to by the previous block. */
				newblock = (VOID **)trimalloc(pool->itemsperblock * pool->itembytes +
					(int) sizeof(VOID *) +
					pool->alignbytes);
				*(pool->nowblock) = (VOID *)newblock;
				/* The next block pointer is NULL. */
				*newblock = (VOID *)NULL;
			}

			/* Move to the new block. */
			pool->nowblock = (VOID **)*(pool->nowblock);
			/* Find the first item in the block.    */
			/*   Increment by the size of (VOID *). */
			alignptr = (unsigned long)(pool->nowblock + 1);
			/* Align the item on an `alignbytes'-byte boundary. */
			pool->nextitem = (VOID *)
				(alignptr + (unsigned long)pool->alignbytes -
					(alignptr % (unsigned long)pool->alignbytes));
			/* There are lots of unallocated items left in this block. */
			pool->unallocateditems = pool->itemsperblock;
		}

		/* Allocate a new item. */
		newitem = pool->nextitem;
		/* Advance `nextitem' pointer to next free item in block. */
		pool->nextitem = (VOID *)((char *)pool->nextitem + pool->itembytes);
		pool->unallocateditems--;
		pool->maxitems++;
	}
	pool->items++;
	return newitem;
}

/*****************************************************************************/
/*                                                                           */
/*  pooldealloc()   Deallocate space for an item.                            */
/*                                                                           */
/*  The deallocated space is stored in a queue for later reuse.              */
/*                                                                           */
/*****************************************************************************/

#ifdef ANSI_DECLARATORS
void pooldealloc(struct memorypool *pool, VOID *dyingitem)
#else /* not ANSI_DECLARATORS */
void pooldealloc(pool, dyingitem)
struct memorypool *pool;
VOID *dyingitem;
#endif /* not ANSI_DECLARATORS */

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

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

#ifdef ANSI_DECLARATORS
void traversalinit(struct memorypool *pool)
#else /* not ANSI_DECLARATORS */
void traversalinit(pool)
struct memorypool *pool;
#endif /* not ANSI_DECLARATORS */

{
	unsigned long alignptr;

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

/*****************************************************************************/
/*                                                                           */
/*  traverse()   Find the next item in the list.                             */
/*                                                                           */
/*  This routine is used in conjunction with traversalinit().  Be forewarned */
/*  that this routine successively returns all items in the list, including  */
/*  deallocated ones on the deaditemqueue.  It's up to you to figure out     */
/*  which ones are actually dead.  Why?  I don't want to allocate extra      */
/*  space just to demarcate dead items.  It can usually be done more         */
/*  space-efficiently by a routine that knows something about the structure  */
/*  of the item.                                                             */
/*                                                                           */
/*****************************************************************************/

#ifdef ANSI_DECLARATORS
VOID *traverse(struct memorypool *pool)
#else /* not ANSI_DECLARATORS */
VOID *traverse(pool)
struct memorypool *pool;
#endif /* not ANSI_DECLARATORS */

{
	VOID *newitem;
	unsigned long alignptr;

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

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

	newitem = pool->pathitem;
	/* Find the next item in the block. */
	pool->pathitem = (VOID *)((char *)pool->pathitem + pool->itembytes);
	pool->pathitemsleft--;
	return newitem;
}

/*****************************************************************************/
/*                                                                           */
/*  dummyinit()   Initialize the triangle that fills "outer space" and the   */
/*                omnipresent subsegment.                                    */
/*                                                                           */
/*  The triangle that fills "outer space," called `dummytri', is pointed to  */
/*  by every triangle and subsegment on a boundary (be it outer or inner) of */
/*  the triangulation.  Also, `dummytri' points to one of the triangles on   */
/*  the convex hull (until the holes and concavities are carved), making it  */
/*  possible to find a starting triangle for point location.                 */
/*                                                                           */
/*  The omnipresent subsegment, `dummysub', is pointed to by every triangle  */
/*  or subsegment that doesn't have a full complement of real subsegments    */
/*  to point to.                                                             */
/*                                                                           */
/*  `dummytri' and `dummysub' are generally required to fulfill only a few   */
/*  invariants:  their vertices must remain NULL and `dummytri' must always  */
/*  be bonded (at offset zero) to some triangle on the convex hull of the    */
/*  mesh, via a boundary edge.  Otherwise, the connections of `dummytri' and */
/*  `dummysub' may change willy-nilly.  This makes it possible to avoid      */
/*  writing a good deal of special-case code (in the edge flip, for example) */
/*  for dealing with the boundary of the mesh, places where no subsegment is */
/*  present, and so forth.  Other entities are frequently bonded to          */
/*  `dummytri' and `dummysub' as if they were real mesh entities, with no    */
/*  harm done.                                                               */
/*                                                                           */
/*****************************************************************************/

#ifdef ANSI_DECLARATORS
void dummyinit(struct mesh *m, struct behavior *b, int trianglebytes,
	int subsegbytes)
#else /* not ANSI_DECLARATORS */
void dummyinit(m, b, trianglebytes, subsegbytes)
struct mesh *m;
struct behavior *b;
int trianglebytes;
int subsegbytes;
#endif /* not ANSI_DECLARATORS */

{
	unsigned long alignptr;

	/* Set up `dummytri', the `triangle' that occupies "outer space." */
	m->dummytribase = (triangle *)trimalloc(trianglebytes +
		m->triangles.alignbytes);
	/* Align `dummytri' on a `triangles.alignbytes'-byte boundary. */
	alignptr = (unsigned long)m->dummytribase;
	m->dummytri = (triangle *)
		(alignptr + (unsigned long)m->triangles.alignbytes -
			(alignptr % (unsigned long)m->triangles.alignbytes));
	/* Initialize the three adjoining triangles to be "outer space."  These  */
	/*   will eventually be changed by various bonding operations, but their */
	/*   values don't really matter, as long as they can legally be          */
	/*   dereferenced.                                                       */
	m->dummytri[0] = (triangle)m->dummytri;
	m->dummytri[1] = (triangle)m->dummytri;
	m->dummytri[2] = (triangle)m->dummytri;
	/* Three NULL vertices. */
	m->dummytri[3] = (triangle)NULL;
	m->dummytri[4] = (triangle)NULL;
	m->dummytri[5] = (triangle)NULL;

	if (b->usesegments) {
		/* Set up `dummysub', the omnipresent subsegment pointed to by any */
		/*   triangle side or subsegment end that isn't attached to a real */
		/*   subsegment.                                                   */
		m->dummysubbase = (subseg *)trimalloc(subsegbytes +
			m->subsegs.alignbytes);
		/* Align `dummysub' on a `subsegs.alignbytes'-byte boundary. */
		alignptr = (unsigned long)m->dummysubbase;
		m->dummysub = (subseg *)
			(alignptr + (unsigned long)m->subsegs.alignbytes -
				(alignptr % (unsigned long)m->subsegs.alignbytes));
		/* Initialize the two adjoining subsegments to be the omnipresent      */
		/*   subsegment.  These will eventually be changed by various bonding  */
		/*   operations, but their values don't really matter, as long as they */
		/*   can legally be dereferenced.                                      */
		m->dummysub[0] = (subseg)m->dummysub;
		m->dummysub[1] = (subseg)m->dummysub;
		/* Four NULL vertices. */
		m->dummysub[2] = (subseg)NULL;
		m->dummysub[3] = (subseg)NULL;
		m->dummysub[4] = (subseg)NULL;
		m->dummysub[5] = (subseg)NULL;
		/* Initialize the two adjoining triangles to be "outer space." */
		m->dummysub[6] = (subseg)m->dummytri;
		m->dummysub[7] = (subseg)m->dummytri;
		/* Set the boundary marker to zero. */
		*(int *)(m->dummysub + 8) = 0;

		/* Initialize the three adjoining subsegments of `dummytri' to be */
		/*   the omnipresent subsegment.                                  */
		m->dummytri[6] = (triangle)m->dummysub;
		m->dummytri[7] = (triangle)m->dummysub;
		m->dummytri[8] = (triangle)m->dummysub;
	}
}

/*****************************************************************************/
/*                                                                           */
/*  initializevertexpool()   Calculate the size of the vertex data structure */
/*                           and initialize its memory pool.                 */
/*                                                                           */
/*  This routine also computes the `vertexmarkindex' and `vertex2triindex'   */
/*  indices used to find values within each vertex.                          */
/*                                                                           */
/*****************************************************************************/

#ifdef ANSI_DECLARATORS
void initializevertexpool(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
void initializevertexpool(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */

{
	int vertexsize;

	/* The index within each vertex at which the boundary marker is found,    */
	/*   followed by the vertex type.  Ensure the vertex marker is aligned to */
	/*   a sizeof(int)-byte address.                                          */
	m->vertexmarkindex = ((m->mesh_dim + m->nextras) * sizeof(REAL) +
		sizeof(int) - 1) /
		sizeof(int);
	vertexsize = (m->vertexmarkindex + 2) * sizeof(int);
	if (b->poly) {
		/* The index within each vertex at which a triangle pointer is found.  */
		/*   Ensure the pointer is aligned to a sizeof(triangle)-byte address. */
		m->vertex2triindex = (vertexsize + sizeof(triangle) - 1) /
			sizeof(triangle);
		vertexsize = (m->vertex2triindex + 1) * sizeof(triangle);
	}

	/* Initialize the pool of vertices. */
	poolinit(&m->vertices, vertexsize, VERTEXPERBLOCK,
		m->invertices > VERTEXPERBLOCK ? m->invertices : VERTEXPERBLOCK,
		sizeof(REAL));
}

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

#ifdef ANSI_DECLARATORS
void initializetrisubpools(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
void initializetrisubpools(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */

{
	int trisize;

	/* The index within each triangle at which the extra nodes (above three)  */
	/*   associated with high order elements are found.  There are three      */
	/*   pointers to other triangles, three pointers to corners, and possibly */
	/*   three pointers to subsegments before the extra nodes.                */
	m->highorderindex = 6 + (b->usesegments * 3);
	/* The number of bytes occupied by a triangle. */
	trisize = ((b->order + 1) * (b->order + 2) / 2 + (m->highorderindex - 3)) *
		sizeof(triangle);
	/* The index within each triangle at which its attributes are found, */
	/*   where the index is measured in REALs.                           */
	m->elemattribindex = (trisize + sizeof(REAL) - 1) / sizeof(REAL);
	/* The index within each triangle at which the maximum area constraint  */
	/*   is found, where the index is measured in REALs.  Note that if the  */
	/*   `regionattrib' flag is set, an additional attribute will be added. */
	m->areaboundindex = m->elemattribindex + m->eextras + b->regionattrib;
	/* If triangle attributes or an area bound are needed, increase the number */
	/*   of bytes occupied by a triangle.                                      */
	if (b->vararea) {
		trisize = (m->areaboundindex + 1) * sizeof(REAL);
	}
	else if (m->eextras + b->regionattrib > 0) {
		trisize = m->areaboundindex * sizeof(REAL);
	}
	/* If a Voronoi diagram or triangle neighbor graph is requested, make    */
	/*   sure there's room to store an integer index in each triangle.  This */
	/*   integer index can occupy the same space as the subsegment pointers  */
	/*   or attributes or area constraint or extra nodes.                    */
	if ((b->voronoi || b->neighbors) &&
		(trisize < 6 * sizeof(triangle) + sizeof(int))) {
		trisize = 6 * sizeof(triangle) + sizeof(int);
	}

	/* Having determined the memory size of a triangle, initialize the pool. */
	poolinit(&m->triangles, trisize, TRIPERBLOCK,
		(2 * m->invertices - 2) > TRIPERBLOCK ? (2 * m->invertices - 2) :
		TRIPERBLOCK, 4);

	if (b->usesegments) {
		/* Initialize the pool of subsegments.  Take into account all eight */
		/*   pointers and one boundary marker.                              */
		poolinit(&m->subsegs, 8 * sizeof(triangle) + sizeof(int),
			SUBSEGPERBLOCK, SUBSEGPERBLOCK, 4);

		/* Initialize the "outer space" triangle and omnipresent subsegment. */
		dummyinit(m, b, m->triangles.itembytes, m->subsegs.itembytes);
	}
	else {
		/* Initialize the "outer space" triangle. */
		dummyinit(m, b, m->triangles.itembytes, 0);
	}
}

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

#ifdef ANSI_DECLARATORS
void triangledealloc(struct mesh *m, triangle *dyingtriangle)
#else /* not ANSI_DECLARATORS */
void triangledealloc(m, dyingtriangle)
struct mesh *m;
triangle *dyingtriangle;
#endif /* not ANSI_DECLARATORS */

{
	/* Mark the triangle as dead.  This makes it possible to detect dead */
	/*   triangles when traversing the list of all triangles.            */
	killtri(dyingtriangle);
	pooldealloc(&m->triangles, (VOID *)dyingtriangle);
}

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

#ifdef ANSI_DECLARATORS
triangle *triangletraverse(struct mesh *m)
#else /* not ANSI_DECLARATORS */
triangle *triangletraverse(m)
struct mesh *m;
#endif /* not ANSI_DECLARATORS */

{
	triangle *newtriangle;

	do {
		newtriangle = (triangle *)traverse(&m->triangles);
		if (newtriangle == (triangle *)NULL) {
			return (triangle *)NULL;
		}
	} while (deadtri(newtriangle));                         /* Skip dead ones. */
	return newtriangle;
}

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

#ifdef ANSI_DECLARATORS
void subsegdealloc(struct mesh *m, subseg *dyingsubseg)
#else /* not ANSI_DECLARATORS */
void subsegdealloc(m, dyingsubseg)
struct mesh *m;
subseg *dyingsubseg;
#endif /* not ANSI_DECLARATORS */

{
	/* Mark the subsegment as dead.  This makes it possible to detect dead */
	/*   subsegments when traversing the list of all subsegments.          */
	killsubseg(dyingsubseg);
	pooldealloc(&m->subsegs, (VOID *)dyingsubseg);
}

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

#ifdef ANSI_DECLARATORS
subseg *subsegtraverse(struct mesh *m)
#else /* not ANSI_DECLARATORS */
subseg *subsegtraverse(m)
struct mesh *m;
#endif /* not ANSI_DECLARATORS */

{
	subseg *newsubseg;

	do {
		newsubseg = (subseg *)traverse(&m->subsegs);
		if (newsubseg == (subseg *)NULL) {
			return (subseg *)NULL;
		}
	} while (deadsubseg(newsubseg));                        /* Skip dead ones. */
	return newsubseg;
}

/*****************************************************************************/
/*                                                                           */
/*  vertexdealloc()   Deallocate space for a vertex, marking it dead.        */
/*                                                                           */
/*****************************************************************************/

#ifdef ANSI_DECLARATORS
void vertexdealloc(struct mesh *m, vertex dyingvertex)
#else /* not ANSI_DECLARATORS */
void vertexdealloc(m, dyingvertex)
struct mesh *m;
vertex dyingvertex;
#endif /* not ANSI_DECLARATORS */

{
	/* Mark the vertex as dead.  This makes it possible to detect dead */
	/*   vertices when traversing the list of all vertices.            */
	setvertextype(dyingvertex, DEADVERTEX);
	pooldealloc(&m->vertices, (VOID *)dyingvertex);
}

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

#ifdef ANSI_DECLARATORS
vertex vertextraverse(struct mesh *m)
#else /* not ANSI_DECLARATORS */
vertex vertextraverse(m)
struct mesh *m;
#endif /* not ANSI_DECLARATORS */

{
	vertex newvertex;

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

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

#ifndef CDT_ONLY

#ifdef ANSI_DECLARATORS
void badsubsegdealloc(struct mesh *m, struct badsubseg *dyingseg)
#else /* not ANSI_DECLARATORS */
void badsubsegdealloc(m, dyingseg)
struct mesh *m;
struct badsubseg *dyingseg;
#endif /* not ANSI_DECLARATORS */

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

#endif /* not CDT_ONLY */

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

#ifndef CDT_ONLY

#ifdef ANSI_DECLARATORS
struct badsubseg *badsubsegtraverse(struct mesh *m)
#else /* not ANSI_DECLARATORS */
struct badsubseg *badsubsegtraverse(m)
struct mesh *m;
#endif /* not ANSI_DECLARATORS */

{
	struct badsubseg *newseg;

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

#endif /* not CDT_ONLY */

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

#ifdef ANSI_DECLARATORS
vertex getvertex(struct mesh *m, struct behavior *b, int number)
#else /* not ANSI_DECLARATORS */
vertex getvertex(m, b, number)
struct mesh *m;
struct behavior *b;
int number;
#endif /* not ANSI_DECLARATORS */

{
	VOID **getblock;
	char *foundvertex;
	unsigned long alignptr;
	int current;

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

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

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

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

#ifdef ANSI_DECLARATORS
void triangledeinit(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
void triangledeinit(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */

{
	pooldeinit(&m->triangles);
	trifree((VOID *)m->dummytribase);
	if (b->usesegments) {
		pooldeinit(&m->subsegs);
		trifree((VOID *)m->dummysubbase);
	}
	pooldeinit(&m->vertices);
#ifndef CDT_ONLY
	if (b->quality) {
		pooldeinit(&m->badsubsegs);
		if ((b->minangle > 0.0) || b->vararea || b->fixedarea || b->usertest) {
			pooldeinit(&m->badtriangles);
			pooldeinit(&m->flipstackers);
		}
	}
#endif /* not CDT_ONLY */
}

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

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

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

#ifdef ANSI_DECLARATORS
void maketriangle(struct mesh *m, struct behavior *b, struct otri *newotri)
#else /* not ANSI_DECLARATORS */
void maketriangle(m, b, newotri)
struct mesh *m;
struct behavior *b;
struct otri *newotri;
#endif /* not ANSI_DECLARATORS */

{
	int i;

	newotri->tri = (triangle *)poolalloc(&m->triangles);
	/* Initialize the three adjoining triangles to be "outer space". */
	newotri->tri[0] = (triangle)m->dummytri;
	newotri->tri[1] = (triangle)m->dummytri;
	newotri->tri[2] = (triangle)m->dummytri;
	/* Three NULL vertices. */
	newotri->tri[3] = (triangle)NULL;
	newotri->tri[4] = (triangle)NULL;
	newotri->tri[5] = (triangle)NULL;
	if (b->usesegments) {
		/* Initialize the three adjoining subsegments to be the omnipresent */
		/*   subsegment.                                                    */
		newotri->tri[6] = (triangle)m->dummysub;
		newotri->tri[7] = (triangle)m->dummysub;
		newotri->tri[8] = (triangle)m->dummysub;
	}
	for (i = 0; i < m->eextras; i++) {
		setelemattribute(*newotri, i, 0.0);
	}
	if (b->vararea) {
		setareabound(*newotri, -1.0);
	}

	newotri->orient = 0;
}

/*****************************************************************************/
/*                                                                           */
/*  makesubseg()   Create a new subsegment with orientation zero.            */
/*                                                                           */
/*****************************************************************************/

#ifdef ANSI_DECLARATORS
void makesubseg(struct mesh *m, struct osub *newsubseg)
#else /* not ANSI_DECLARATORS */
void makesubseg(m, newsubseg)
struct mesh *m;
struct osub *newsubseg;
#endif /* not ANSI_DECLARATORS */

{
	newsubseg->ss = (subseg *)poolalloc(&m->subsegs);
	/* Initialize the two adjoining subsegments to be the omnipresent */
	/*   subsegment.                                                  */
	newsubseg->ss[0] = (subseg)m->dummysub;
	newsubseg->ss[1] = (subseg)m->dummysub;
	/* Four NULL vertices. */
	newsubseg->ss[2] = (subseg)NULL;
	newsubseg->ss[3] = (subseg)NULL;
	newsubseg->ss[4] = (subseg)NULL;
	newsubseg->ss[5] = (subseg)NULL;
	/* Initialize the two adjoining triangles to be "outer space." */
	newsubseg->ss[6] = (subseg)m->dummytri;
	newsubseg->ss[7] = (subseg)m->dummytri;
	/* Set the boundary marker to zero. */
	setmark(*newsubseg, 0);

	newsubseg->ssorient = 0;
}

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

/********* Geometric primitives begin here                           *********/
/**                                                                         **/
/**                                                                         **/

/* The adaptive exact arithmetic geometric predicates implemented herein are */
/*   described in detail in my paper, "Adaptive Precision Floating-Point     */
/*   Arithmetic and Fast Robust Geometric Predicates."  See the header for a */
/*   full citation.                                                          */

/* Which of the following two methods of finding the absolute values is      */
/*   fastest is compiler-dependent.  A few compilers can inline and optimize */
/*   the fabs() call; but most will incur the overhead of a function call,   */
/*   which is disastrously slow.  A faster way on IEEE machines might be to  */
/*   mask the appropriate bit, but that's difficult to do in C without       */
/*   forcing the value to be stored to memory (rather than be kept in the    */
/*   register to which the optimizer assigned it).                           */

#define Absolute(a)  ((a) >= 0.0 ? (a) : -(a))
/* #define Absolute(a)  fabs(a) */

/* Many of the operations are broken up into two pieces, a main part that    */
/*   performs an approximate operation, and a "tail" that computes the       */
/*   roundoff error of that operation.                                       */
/*                                                                           */
/* The operations Fast_Two_Sum(), Fast_Two_Diff(), Two_Sum(), Two_Diff(),    */
/*   Split(), and Two_Product() are all implemented as described in the      */
/*   reference.  Each of these macros requires certain variables to be       */
/*   defined in the calling routine.  The variables `bvirt', `c', `abig',    */
/*   `_i', `_j', `_k', `_l', `_m', and `_n' are declared `INEXACT' because   */
/*   they store the result of an operation that may incur roundoff error.    */
/*   The input parameter `x' (or the highest numbered `x_' parameter) must   */
/*   also be declared `INEXACT'.                                             */

#define Fast_Two_Sum_Tail(a, b, x, y) \
  bvirt = x - a; \
  y = b - bvirt

#define Fast_Two_Sum(a, b, x, y) \
  x = (REAL) (a + b); \
  Fast_Two_Sum_Tail(a, b, x, y)

#define Two_Sum_Tail(a, b, x, y) \
  bvirt = (REAL) (x - a); \
  avirt = x - bvirt; \
  bround = b - bvirt; \
  around = a - avirt; \
  y = around + bround

#define Two_Sum(a, b, x, y) \
  x = (REAL) (a + b); \
  Two_Sum_Tail(a, b, x, y)

#define Two_Diff_Tail(a, b, x, y) \
  bvirt = (REAL) (a - x); \
  avirt = x + bvirt; \
  bround = bvirt - b; \
  around = a - avirt; \
  y = around + bround

#define Two_Diff(a, b, x, y) \
  x = (REAL) (a - b); \
  Two_Diff_Tail(a, b, x, y)

#define Split(a, ahi, alo) \
  c = (REAL) (splitter * a); \
  abig = (REAL) (c - a); \
  ahi = c - abig; \
  alo = a - ahi

#define Two_Product_Tail(a, b, x, y) \
  Split(a, ahi, alo); \
  Split(b, bhi, blo); \
  err1 = x - (ahi * bhi); \
  err2 = err1 - (alo * bhi); \
  err3 = err2 - (ahi * blo); \
  y = (alo * blo) - err3

#define Two_Product(a, b, x, y) \
  x = (REAL) (a * b); \
  Two_Product_Tail(a, b, x, y)

/* Two_Product_Presplit() is Two_Product() where one of the inputs has       */
/*   already been split.  Avoids redundant splitting.                        */

#define Two_Product_Presplit(a, b, bhi, blo, x, y) \
  x = (REAL) (a * b); \
  Split(a, ahi, alo); \
  err1 = x - (ahi * bhi); \
  err2 = err1 - (alo * bhi); \
  err3 = err2 - (ahi * blo); \
  y = (alo * blo) - err3

/* Square() can be done more quickly than Two_Product().                     */

#define Square_Tail(a, x, y) \
  Split(a, ahi, alo); \
  err1 = x - (ahi * ahi); \
  err3 = err1 - ((ahi + ahi) * alo); \
  y = (alo * alo) - err3

#define Square(a, x, y) \
  x = (REAL) (a * a); \
  Square_Tail(a, x, y)

/* Macros for summing expansions of various fixed lengths.  These are all    */
/*   unrolled versions of Expansion_Sum().                                   */

#define Two_One_Sum(a1, a0, b, x2, x1, x0) \
  Two_Sum(a0, b , _i, x0); \
  Two_Sum(a1, _i, x2, x1)

#define Two_One_Diff(a1, a0, b, x2, x1, x0) \
  Two_Diff(a0, b , _i, x0); \
  Two_Sum( a1, _i, x2, x1)

#define Two_Two_Sum(a1, a0, b1, b0, x3, x2, x1, x0) \
  Two_One_Sum(a1, a0, b0, _j, _0, x0); \
  Two_One_Sum(_j, _0, b1, x3, x2, x1)

#define Two_Two_Diff(a1, a0, b1, b0, x3, x2, x1, x0) \
  Two_One_Diff(a1, a0, b0, _j, _0, x0); \
  Two_One_Diff(_j, _0, b1, x3, x2, x1)

/* Macro for multiplying a two-component expansion by a single component.    */

#define Two_One_Product(a1, a0, b, x3, x2, x1, x0) \
  Split(b, bhi, blo); \
  Two_Product_Presplit(a0, b, bhi, blo, _i, x0); \
  Two_Product_Presplit(a1, b, bhi, blo, _j, _0); \
  Two_Sum(_i, _0, _k, x1); \
  Fast_Two_Sum(_j, _k, x3, x2)

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

void exactinit()
{
	REAL half;
	REAL check, lastcheck;
	int every_other;
#ifdef LINUX
	int cword;
#endif /* LINUX */

#ifdef CPU86
#ifdef SINGLE
	_control87(_PC_24, _MCW_PC); /* Set FPU control word for single precision. */
#else /* not SINGLE */
	_control87(_PC_53, _MCW_PC); /* Set FPU control word for double precision. */
#endif /* not SINGLE */
#endif /* CPU86 */
#ifdef LINUX
#ifdef SINGLE
								 /*  cword = 4223; */
	cword = 4210;                 /* set FPU control word for single precision */
#else /* not SINGLE */
								 /*  cword = 4735; */
	cword = 4722;                 /* set FPU control word for double precision */
#endif /* not SINGLE */
	_FPU_SETCW(cword);
#endif /* LINUX */

	every_other = 1;
	half = 0.5;
	epsilon = 1.0;
	splitter = 1.0;
	check = 1.0;
	/* Repeatedly divide `epsilon' by two until it is too small to add to      */
	/*   one without causing roundoff.  (Also check if the sum is equal to     */
	/*   the previous sum, for machines that round up instead of using exact   */
	/*   rounding.  Not that these routines will work on such machines.)       */
	do {
		lastcheck = check;
		epsilon *= half;
		if (every_other) {
			splitter *= 2.0;
		}
		every_other = !every_other;
		check = 1.0 + epsilon;
	} while ((check != 1.0) && (check != lastcheck));
	splitter += 1.0;
	/* Error bounds for orientation and incircle tests. */
	resulterrbound = (3.0 + 8.0 * epsilon) * epsilon;
	ccwerrboundA = (3.0 + 16.0 * epsilon) * epsilon;
	ccwerrboundB = (2.0 + 12.0 * epsilon) * epsilon;
	ccwerrboundC = (9.0 + 64.0 * epsilon) * epsilon * epsilon;
	iccerrboundA = (10.0 + 96.0 * epsilon) * epsilon;
	iccerrboundB = (4.0 + 48.0 * epsilon) * epsilon;
	iccerrboundC = (44.0 + 576.0 * epsilon) * epsilon * epsilon;
	o3derrboundA = (7.0 + 56.0 * epsilon) * epsilon;
	o3derrboundB = (3.0 + 28.0 * epsilon) * epsilon;
	o3derrboundC = (26.0 + 288.0 * epsilon) * epsilon * epsilon;
}

/*****************************************************************************/
/*                                                                           */
/*  fast_expansion_sum_zeroelim()   Sum two expansions, eliminating zero     */
/*                                  components from the output expansion.    */
/*                                                                           */
/*  Sets h = e + f.  See my Robust Predicates paper for details.             */
/*                                                                           */
/*  If round-to-even is used (as with IEEE 754), maintains the strongly      */
/*  nonoverlapping property.  (That is, if e is strongly nonoverlapping, h   */
/*  will be also.)  Does NOT maintain the nonoverlapping or nonadjacent      */
/*  properties.                                                              */
/*                                                                           */
/*****************************************************************************/

#ifdef ANSI_DECLARATORS
int fast_expansion_sum_zeroelim(int elen, REAL *e, int flen, REAL *f, REAL *h)
#else /* not ANSI_DECLARATORS */
int fast_expansion_sum_zeroelim(elen, e, flen, f, h)  /* h cannot be e or f. */
int elen;
REAL *e;
int flen;
REAL *f;
REAL *h;
#endif /* not ANSI_DECLARATORS */

{
	REAL Q;
	INEXACT REAL Qnew;
	INEXACT REAL hh;
	INEXACT REAL bvirt;
	REAL avirt, bround, around;
	int eindex, findex, hindex;
	REAL enow, fnow;

	enow = e[0];
	fnow = f[0];
	eindex = findex = 0;
	if ((fnow > enow) == (fnow > -enow)) {
		Q = enow;
		enow = e[++eindex];
	}
	else {
		Q = fnow;
		fnow = f[++findex];
	}
	hindex = 0;
	if ((eindex < elen) && (findex < flen)) {
		if ((fnow > enow) == (fnow > -enow)) {
			Fast_Two_Sum(enow, Q, Qnew, hh);
			enow = e[++eindex];
		}
		else {
			Fast_Two_Sum(fnow, Q, Qnew, hh);
			fnow = f[++findex];
		}
		Q = Qnew;
		if (hh != 0.0) {
			h[hindex++] = hh;
		}
		while ((eindex < elen) && (findex < flen)) {
			if ((fnow > enow) == (fnow > -enow)) {
				Two_Sum(Q, enow, Qnew, hh);
				enow = e[++eindex];
			}
			else {
				Two_Sum(Q, fnow, Qnew, hh);
				fnow = f[++findex];
			}
			Q = Qnew;
			if (hh != 0.0) {
				h[hindex++] = hh;
			}
		}
	}
	while (eindex < elen) {
		Two_Sum(Q, enow, Qnew, hh);
		enow = e[++eindex];
		Q = Qnew;
		if (hh != 0.0) {
			h[hindex++] = hh;
		}
	}
	while (findex < flen) {
		Two_Sum(Q, fnow, Qnew, hh);
		fnow = f[++findex];
		Q = Qnew;
		if (hh != 0.0) {
			h[hindex++] = hh;
		}
	}
	if ((Q != 0.0) || (hindex == 0)) {
		h[hindex++] = Q;
	}
	return hindex;
}

/*****************************************************************************/
/*                                                                           */
/*  scale_expansion_zeroelim()   Multiply an expansion by a scalar,          */
/*                               eliminating zero components from the        */
/*                               output expansion.                           */
/*                                                                           */
/*  Sets h = be.  See my Robust Predicates paper for details.                */
/*                                                                           */
/*  Maintains the nonoverlapping property.  If round-to-even is used (as     */
/*  with IEEE 754), maintains the strongly nonoverlapping and nonadjacent    */
/*  properties as well.  (That is, if e has one of these properties, so      */
/*  will h.)                                                                 */
/*                                                                           */
/*****************************************************************************/

#ifdef ANSI_DECLARATORS
int scale_expansion_zeroelim(int elen, REAL *e, REAL b, REAL *h)
#else /* not ANSI_DECLARATORS */
int scale_expansion_zeroelim(elen, e, b, h)   /* e and h cannot be the same. */
int elen;
REAL *e;
REAL b;
REAL *h;
#endif /* not ANSI_DECLARATORS */

{
	INEXACT REAL Q, sum;
	REAL hh;
	INEXACT REAL product1;
	REAL product0;
	int eindex, hindex;
	REAL enow;
	INEXACT REAL bvirt;
	REAL avirt, bround, around;
	INEXACT REAL c;
	INEXACT REAL abig;
	REAL ahi, alo, bhi, blo;
	REAL err1, err2, err3;

	Split(b, bhi, blo);
	Two_Product_Presplit(e[0], b, bhi, blo, Q, hh);
	hindex = 0;
	if (hh != 0) {
		h[hindex++] = hh;
	}
	for (eindex = 1; eindex < elen; eindex++) {
		enow = e[eindex];
		Two_Product_Presplit(enow, b, bhi, blo, product1, product0);
		Two_Sum(Q, product0, sum, hh);
		if (hh != 0) {
			h[hindex++] = hh;
		}
		Fast_Two_Sum(product1, sum, Q, hh);
		if (hh != 0) {
			h[hindex++] = hh;
		}
	}
	if ((Q != 0.0) || (hindex == 0)) {
		h[hindex++] = Q;
	}
	return hindex;
}

/*****************************************************************************/
/*                                                                           */
/*  estimate()   Produce a one-word estimate of an expansion's value.        */
/*                                                                           */
/*  See my Robust Predicates paper for details.                              */
/*                                                                           */
/*****************************************************************************/

#ifdef ANSI_DECLARATORS
REAL estimate(int elen, REAL *e)
#else /* not ANSI_DECLARATORS */
REAL estimate(elen, e)
int elen;
REAL *e;
#endif /* not ANSI_DECLARATORS */

{
	REAL Q;
	int eindex;

	Q = e[0];
	for (eindex = 1; eindex < elen; eindex++) {
		Q += e[eindex];
	}
	return Q;
}

/*****************************************************************************/
/*                                                                           */
/*  counterclockwise()   Return a positive value if the points pa, pb, and   */
/*                       pc occur in counterclockwise order; a negative      */
/*                       value if they occur in clockwise order; and zero    */
/*                       if they are collinear.  The result is also a rough  */
/*                       approximation of twice the signed area of the       */
/*                       triangle defined by the three points.               */
/*                                                                           */
/*  Uses exact arithmetic if necessary to ensure a correct answer.  The      */
/*  result returned is the determinant of a matrix.  This determinant is     */
/*  computed adaptively, in the sense that exact arithmetic is used only to  */
/*  the degree it is needed to ensure that the returned value has the        */
/*  correct sign.  Hence, this function is usually quite fast, but will run  */
/*  more slowly when the input points are collinear or nearly so.            */
/*                                                                           */
/*  See my Robust Predicates paper for details.                              */
/*                                                                           */
/*****************************************************************************/

#ifdef ANSI_DECLARATORS
REAL counterclockwiseadapt(vertex pa, vertex pb, vertex pc, REAL detsum)
#else /* not ANSI_DECLARATORS */
REAL counterclockwiseadapt(pa, pb, pc, detsum)
vertex pa;
vertex pb;
vertex pc;
REAL detsum;
#endif /* not ANSI_DECLARATORS */

{
	INEXACT REAL acx, acy, bcx, bcy;
	REAL acxtail, acytail, bcxtail, bcytail;
	INEXACT REAL detleft, detright;
	REAL detlefttail, detrighttail;
	REAL det, errbound;
	REAL B[4], C1[8], C2[12], D[16];
	INEXACT REAL B3;
	int C1length, C2length, Dlength;
	REAL u[4];
	INEXACT REAL u3;
	INEXACT REAL s1, t1;
	REAL s0, t0;

	INEXACT REAL bvirt;
	REAL avirt, bround, around;
	INEXACT REAL c;
	INEXACT REAL abig;
	REAL ahi, alo, bhi, blo;
	REAL err1, err2, err3;
	INEXACT REAL _i, _j;
	REAL _0;

	acx = (REAL)(pa[0] - pc[0]);
	bcx = (REAL)(pb[0] - pc[0]);
	acy = (REAL)(pa[1] - pc[1]);
	bcy = (REAL)(pb[1] - pc[1]);

	Two_Product(acx, bcy, detleft, detlefttail);
	Two_Product(acy, bcx, detright, detrighttail);

	Two_Two_Diff(detleft, detlefttail, detright, detrighttail,
		B3, B[2], B[1], B[0]);
	B[3] = B3;

	det = estimate(4, B);
	errbound = ccwerrboundB * detsum;
	if ((det >= errbound) || (-det >= errbound)) {
		return det;
	}

	Two_Diff_Tail(pa[0], pc[0], acx, acxtail);
	Two_Diff_Tail(pb[0], pc[0], bcx, bcxtail);
	Two_Diff_Tail(pa[1], pc[1], acy, acytail);
	Two_Diff_Tail(pb[1], pc[1], bcy, bcytail);

	if ((acxtail == 0.0) && (acytail == 0.0)
		&& (bcxtail == 0.0) && (bcytail == 0.0)) {
		return det;
	}

	errbound = ccwerrboundC * detsum + resulterrbound * Absolute(det);
	det += (acx * bcytail + bcy * acxtail)
		- (acy * bcxtail + bcx * acytail);
	if ((det >= errbound) || (-det >= errbound)) {
		return det;
	}

	Two_Product(acxtail, bcy, s1, s0);
	Two_Product(acytail, bcx, t1, t0);
	Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
	u[3] = u3;
	C1length = fast_expansion_sum_zeroelim(4, B, 4, u, C1);

	Two_Product(acx, bcytail, s1, s0);
	Two_Product(acy, bcxtail, t1, t0);
	Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
	u[3] = u3;
	C2length = fast_expansion_sum_zeroelim(C1length, C1, 4, u, C2);

	Two_Product(acxtail, bcytail, s1, s0);
	Two_Product(acytail, bcxtail, t1, t0);
	Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
	u[3] = u3;
	Dlength = fast_expansion_sum_zeroelim(C2length, C2, 4, u, D);

	return(D[Dlength - 1]);
}

#ifdef ANSI_DECLARATORS
REAL counterclockwise(struct mesh *m, struct behavior *b,
	vertex pa, vertex pb, vertex pc)
#else /* not ANSI_DECLARATORS */
REAL counterclockwise(m, b, pa, pb, pc)
struct mesh *m;
struct behavior *b;
vertex pa;
vertex pb;
vertex pc;
#endif /* not ANSI_DECLARATORS */

{
	REAL detleft, detright, det;
	REAL detsum, errbound;

	m->counterclockcount++;

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

	if (b->noexact) {
		return det;
	}

	if (detleft > 0.0) {
		if (detright <= 0.0) {
			return det;
		}
		else {
			detsum = detleft + detright;
		}
	}
	else if (detleft < 0.0) {
		if (detright >= 0.0) {
			return det;
		}
		else {
			detsum = -detleft - detright;
		}
	}
	else {
		return det;
	}

	errbound = ccwerrboundA * detsum;
	if ((det >= errbound) || (-det >= errbound)) {
		return det;
	}

	return counterclockwiseadapt(pa, pb, pc, detsum);
}

/*****************************************************************************/
/*                                                                           */
/*  incircle()   Return a positive value if the point pd lies inside the     */
/*               circle passing through pa, pb, and pc; a negative value if  */
/*               it lies outside; and zero if the four points are cocircular.*/
/*               The points pa, pb, and pc must be in counterclockwise       */
/*               order, or the sign of the result will be reversed.          */
/*                                                                           */
/*  Uses exact arithmetic if necessary to ensure a correct answer.  The      */
/*  result returned is the determinant of a matrix.  This determinant is     */
/*  computed adaptively, in the sense that exact arithmetic is used only to  */
/*  the degree it is needed to ensure that the returned value has the        */
/*  correct sign.  Hence, this function is usually quite fast, but will run  */
/*  more slowly when the input points are cocircular or nearly so.           */
/*                                                                           */
/*  See my Robust Predicates paper for details.                              */
/*                                                                           */
/*****************************************************************************/

#ifdef ANSI_DECLARATORS
REAL incircleadapt(vertex pa, vertex pb, vertex pc, vertex pd, REAL permanent)
#else /* not ANSI_DECLARATORS */
REAL incircleadapt(pa, pb, pc, pd, permanent)
vertex pa;
vertex pb;
vertex pc;
vertex pd;
REAL permanent;
#endif /* not ANSI_DECLARATORS */

{
	INEXACT REAL adx, bdx, cdx, ady, bdy, cdy;
	REAL det, errbound;

	INEXACT REAL bdxcdy1, cdxbdy1, cdxady1, adxcdy1, adxbdy1, bdxady1;
	REAL bdxcdy0, cdxbdy0, cdxady0, adxcdy0, adxbdy0, bdxady0;
	REAL bc[4], ca[4], ab[4];
	INEXACT REAL bc3, ca3, ab3;
	REAL axbc[8], axxbc[16], aybc[8], ayybc[16], adet[32];
	int axbclen, axxbclen, aybclen, ayybclen, alen;
	REAL bxca[8], bxxca[16], byca[8], byyca[16], bdet[32];
	int bxcalen, bxxcalen, bycalen, byycalen, blen;
	REAL cxab[8], cxxab[16], cyab[8], cyyab[16], cdet[32];
	int cxablen, cxxablen, cyablen, cyyablen, clen;
	REAL abdet[64];
	int ablen;
	REAL fin1[1152], fin2[1152];
	REAL *finnow, *finother, *finswap;
	int finlength;

	REAL adxtail, bdxtail, cdxtail, adytail, bdytail, cdytail;
	INEXACT REAL adxadx1, adyady1, bdxbdx1, bdybdy1, cdxcdx1, cdycdy1;
	REAL adxadx0, adyady0, bdxbdx0, bdybdy0, cdxcdx0, cdycdy0;
	REAL aa[4], bb[4], cc[4];
	INEXACT REAL aa3, bb3, cc3;
	INEXACT REAL ti1, tj1;
	REAL ti0, tj0;
	REAL u[4], v[4];
	INEXACT REAL u3, v3;
	REAL temp8[8], temp16a[16], temp16b[16], temp16c[16];
	REAL temp32a[32], temp32b[32], temp48[48], temp64[64];
	int temp8len, temp16alen, temp16blen, temp16clen;
	int temp32alen, temp32blen, temp48len, temp64len;
	REAL axtbb[8], axtcc[8], aytbb[8], aytcc[8];
	int axtbblen, axtcclen, aytbblen, aytcclen;
	REAL bxtaa[8], bxtcc[8], bytaa[8], bytcc[8];
	int bxtaalen, bxtcclen, bytaalen, bytcclen;
	REAL cxtaa[8], cxtbb[8], cytaa[8], cytbb[8];
	int cxtaalen, cxtbblen, cytaalen, cytbblen;
	REAL axtbc[8], aytbc[8], bxtca[8], bytca[8], cxtab[8], cytab[8];
	int axtbclen, aytbclen, bxtcalen, bytcalen, cxtablen, cytablen;
	REAL axtbct[16], aytbct[16], bxtcat[16], bytcat[16], cxtabt[16], cytabt[16];
	int axtbctlen, aytbctlen, bxtcatlen, bytcatlen, cxtabtlen, cytabtlen;
	REAL axtbctt[8], aytbctt[8], bxtcatt[8];
	REAL bytcatt[8], cxtabtt[8], cytabtt[8];
	int axtbcttlen, aytbcttlen, bxtcattlen, bytcattlen, cxtabttlen, cytabttlen;
	REAL abt[8], bct[8], cat[8];
	int abtlen, bctlen, catlen;
	REAL abtt[4], bctt[4], catt[4];
	int abttlen, bcttlen, cattlen;
	INEXACT REAL abtt3, bctt3, catt3;
	REAL negate;

	INEXACT REAL bvirt;
	REAL avirt, bround, around;
	INEXACT REAL c;
	INEXACT REAL abig;
	REAL ahi, alo, bhi, blo;
	REAL err1, err2, err3;
	INEXACT REAL _i, _j;
	REAL _0;

	adx = (REAL)(pa[0] - pd[0]);
	bdx = (REAL)(pb[0] - pd[0]);
	cdx = (REAL)(pc[0] - pd[0]);
	ady = (REAL)(pa[1] - pd[1]);
	bdy = (REAL)(pb[1] - pd[1]);
	cdy = (REAL)(pc[1] - pd[1]);

	Two_Product(bdx, cdy, bdxcdy1, bdxcdy0);
	Two_Product(cdx, bdy, cdxbdy1, cdxbdy0);
	Two_Two_Diff(bdxcdy1, bdxcdy0, cdxbdy1, cdxbdy0, bc3, bc[2], bc[1], bc[0]);
	bc[3] = bc3;
	axbclen = scale_expansion_zeroelim(4, bc, adx, axbc);
	axxbclen = scale_expansion_zeroelim(axbclen, axbc, adx, axxbc);
	aybclen = scale_expansion_zeroelim(4, bc, ady, aybc);
	ayybclen = scale_expansion_zeroelim(aybclen, aybc, ady, ayybc);
	alen = fast_expansion_sum_zeroelim(axxbclen, axxbc, ayybclen, ayybc, adet);

	Two_Product(cdx, ady, cdxady1, cdxady0);
	Two_Product(adx, cdy, adxcdy1, adxcdy0);
	Two_Two_Diff(cdxady1, cdxady0, adxcdy1, adxcdy0, ca3, ca[2], ca[1], ca[0]);
	ca[3] = ca3;
	bxcalen = scale_expansion_zeroelim(4, ca, bdx, bxca);
	bxxcalen = scale_expansion_zeroelim(bxcalen, bxca, bdx, bxxca);
	bycalen = scale_expansion_zeroelim(4, ca, bdy, byca);
	byycalen = scale_expansion_zeroelim(bycalen, byca, bdy, byyca);
	blen = fast_expansion_sum_zeroelim(bxxcalen, bxxca, byycalen, byyca, bdet);

	Two_Product(adx, bdy, adxbdy1, adxbdy0);
	Two_Product(bdx, ady, bdxady1, bdxady0);
	Two_Two_Diff(adxbdy1, adxbdy0, bdxady1, bdxady0, ab3, ab[2], ab[1], ab[0]);
	ab[3] = ab3;
	cxablen = scale_expansion_zeroelim(4, ab, cdx, cxab);
	cxxablen = scale_expansion_zeroelim(cxablen, cxab, cdx, cxxab);
	cyablen = scale_expansion_zeroelim(4, ab, cdy, cyab);
	cyyablen = scale_expansion_zeroelim(cyablen, cyab, cdy, cyyab);
	clen = fast_expansion_sum_zeroelim(cxxablen, cxxab, cyyablen, cyyab, cdet);

	ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
	finlength = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, fin1);

	det = estimate(finlength, fin1);
	errbound = iccerrboundB * permanent;
	if ((det >= errbound) || (-det >= errbound)) {
		return det;
	}

	Two_Diff_Tail(pa[0], pd[0], adx, adxtail);
	Two_Diff_Tail(pa[1], pd[1], ady, adytail);
	Two_Diff_Tail(pb[0], pd[0], bdx, bdxtail);
	Two_Diff_Tail(pb[1], pd[1], bdy, bdytail);
	Two_Diff_Tail(pc[0], pd[0], cdx, cdxtail);
	Two_Diff_Tail(pc[1], pd[1], cdy, cdytail);
	if ((adxtail == 0.0) && (bdxtail == 0.0) && (cdxtail == 0.0)
		&& (adytail == 0.0) && (bdytail == 0.0) && (cdytail == 0.0)) {
		return det;
	}

	errbound = iccerrboundC * permanent + resulterrbound * Absolute(det);
	det += ((adx * adx + ady * ady) * ((bdx * cdytail + cdy * bdxtail)
		- (bdy * cdxtail + cdx * bdytail))
		+ 2.0 * (adx * adxtail + ady * adytail) * (bdx * cdy - bdy * cdx))
		+ ((bdx * bdx + bdy * bdy) * ((cdx * adytail + ady * cdxtail)
			- (cdy * adxtail + adx * cdytail))
			+ 2.0 * (bdx * bdxtail + bdy * bdytail) * (cdx * ady - cdy * adx))
		+ ((cdx * cdx + cdy * cdy) * ((adx * bdytail + bdy * adxtail)
			- (ady * bdxtail + bdx * adytail))
			+ 2.0 * (cdx * cdxtail + cdy * cdytail) * (adx * bdy - ady * bdx));
	if ((det >= errbound) || (-det >= errbound)) {
		return det;
	}

	finnow = fin1;
	finother = fin2;

	if ((bdxtail != 0.0) || (bdytail != 0.0)
		|| (cdxtail != 0.0) || (cdytail != 0.0)) {
		Square(adx, adxadx1, adxadx0);
		Square(ady, adyady1, adyady0);
		Two_Two_Sum(adxadx1, adxadx0, adyady1, adyady0, aa3, aa[2], aa[1], aa[0]);
		aa[3] = aa3;
	}
	if ((cdxtail != 0.0) || (cdytail != 0.0)
		|| (adxtail != 0.0) || (adytail != 0.0)) {
		Square(bdx, bdxbdx1, bdxbdx0);
		Square(bdy, bdybdy1, bdybdy0);
		Two_Two_Sum(bdxbdx1, bdxbdx0, bdybdy1, bdybdy0, bb3, bb[2], bb[1], bb[0]);
		bb[3] = bb3;
	}
	if ((adxtail != 0.0) || (adytail != 0.0)
		|| (bdxtail != 0.0) || (bdytail != 0.0)) {
		Square(cdx, cdxcdx1, cdxcdx0);
		Square(cdy, cdycdy1, cdycdy0);
		Two_Two_Sum(cdxcdx1, cdxcdx0, cdycdy1, cdycdy0, cc3, cc[2], cc[1], cc[0]);
		cc[3] = cc3;
	}

	if (adxtail != 0.0) {
		axtbclen = scale_expansion_zeroelim(4, bc, adxtail, axtbc);
		temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, 2.0 * adx,
			temp16a);

		axtcclen = scale_expansion_zeroelim(4, cc, adxtail, axtcc);
		temp16blen = scale_expansion_zeroelim(axtcclen, axtcc, bdy, temp16b);

		axtbblen = scale_expansion_zeroelim(4, bb, adxtail, axtbb);
		temp16clen = scale_expansion_zeroelim(axtbblen, axtbb, -cdy, temp16c);

		temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
			temp16blen, temp16b, temp32a);
		temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
			temp32alen, temp32a, temp48);
		finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
			temp48, finother);
		finswap = finnow; finnow = finother; finother = finswap;
	}
	if (adytail != 0.0) {
		aytbclen = scale_expansion_zeroelim(4, bc, adytail, aytbc);
		temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, 2.0 * ady,
			temp16a);

		aytbblen = scale_expansion_zeroelim(4, bb, adytail, aytbb);
		temp16blen = scale_expansion_zeroelim(aytbblen, aytbb, cdx, temp16b);

		aytcclen = scale_expansion_zeroelim(4, cc, adytail, aytcc);
		temp16clen = scale_expansion_zeroelim(aytcclen, aytcc, -bdx, temp16c);

		temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
			temp16blen, temp16b, temp32a);
		temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
			temp32alen, temp32a, temp48);
		finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
			temp48, finother);
		finswap = finnow; finnow = finother; finother = finswap;
	}
	if (bdxtail != 0.0) {
		bxtcalen = scale_expansion_zeroelim(4, ca, bdxtail, bxtca);
		temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, 2.0 * bdx,
			temp16a);

		bxtaalen = scale_expansion_zeroelim(4, aa, bdxtail, bxtaa);
		temp16blen = scale_expansion_zeroelim(bxtaalen, bxtaa, cdy, temp16b);

		bxtcclen = scale_expansion_zeroelim(4, cc, bdxtail, bxtcc);
		temp16clen = scale_expansion_zeroelim(bxtcclen, bxtcc, -ady, temp16c);

		temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
			temp16blen, temp16b, temp32a);
		temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
			temp32alen, temp32a, temp48);
		finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
			temp48, finother);
		finswap = finnow; finnow = finother; finother = finswap;
	}
	if (bdytail != 0.0) {
		bytcalen = scale_expansion_zeroelim(4, ca, bdytail, bytca);
		temp16alen = scale_expansion_zeroelim(bytcalen, bytca, 2.0 * bdy,
			temp16a);

		bytcclen = scale_expansion_zeroelim(4, cc, bdytail, bytcc);
		temp16blen = scale_expansion_zeroelim(bytcclen, bytcc, adx, temp16b);

		bytaalen = scale_expansion_zeroelim(4, aa, bdytail, bytaa);
		temp16clen = scale_expansion_zeroelim(bytaalen, bytaa, -cdx, temp16c);

		temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
			temp16blen, temp16b, temp32a);
		temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
			temp32alen, temp32a, temp48);
		finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
			temp48, finother);
		finswap = finnow; finnow = finother; finother = finswap;
	}
	if (cdxtail != 0.0) {
		cxtablen = scale_expansion_zeroelim(4, ab, cdxtail, cxtab);
		temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, 2.0 * cdx,
			temp16a);

		cxtbblen = scale_expansion_zeroelim(4, bb, cdxtail, cxtbb);
		temp16blen = scale_expansion_zeroelim(cxtbblen, cxtbb, ady, temp16b);

		cxtaalen = scale_expansion_zeroelim(4, aa, cdxtail, cxtaa);
		temp16clen = scale_expansion_zeroelim(cxtaalen, cxtaa, -bdy, temp16c);

		temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
			temp16blen, temp16b, temp32a);
		temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
			temp32alen, temp32a, temp48);
		finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
			temp48, finother);
		finswap = finnow; finnow = finother; finother = finswap;
	}
	if (cdytail != 0.0) {
		cytablen = scale_expansion_zeroelim(4, ab, cdytail, cytab);
		temp16alen = scale_expansion_zeroelim(cytablen, cytab, 2.0 * cdy,
			temp16a);

		cytaalen = scale_expansion_zeroelim(4, aa, cdytail, cytaa);
		temp16blen = scale_expansion_zeroelim(cytaalen, cytaa, bdx, temp16b);

		cytbblen = scale_expansion_zeroelim(4, bb, cdytail, cytbb);
		temp16clen = scale_expansion_zeroelim(cytbblen, cytbb, -adx, temp16c);

		temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
			temp16blen, temp16b, temp32a);
		temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
			temp32alen, temp32a, temp48);
		finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
			temp48, finother);
		finswap = finnow; finnow = finother; finother = finswap;
	}

	if ((adxtail != 0.0) || (adytail != 0.0)) {
		if ((bdxtail != 0.0) || (bdytail != 0.0)
			|| (cdxtail != 0.0) || (cdytail != 0.0)) {
			Two_Product(bdxtail, cdy, ti1, ti0);
			Two_Product(bdx, cdytail, tj1, tj0);
			Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
			u[3] = u3;
			negate = -bdy;
			Two_Product(cdxtail, negate, ti1, ti0);
			negate = -bdytail;
			Two_Product(cdx, negate, tj1, tj0);
			Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
			v[3] = v3;
			bctlen = fast_expansion_sum_zeroelim(4, u, 4, v, bct);

			Two_Product(bdxtail, cdytail, ti1, ti0);
			Two_Product(cdxtail, bdytail, tj1, tj0);
			Two_Two_Diff(ti1, ti0, tj1, tj0, bctt3, bctt[2], bctt[1], bctt[0]);
			bctt[3] = bctt3;
			bcttlen = 4;
		}
		else {
			bct[0] = 0.0;
			bctlen = 1;
			bctt[0] = 0.0;
			bcttlen = 1;
		}

		if (adxtail != 0.0) {
			temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, adxtail, temp16a);
			axtbctlen = scale_expansion_zeroelim(bctlen, bct, adxtail, axtbct);
			temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, 2.0 * adx,
				temp32a);
			temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
				temp32alen, temp32a, temp48);
			finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
				temp48, finother);
			finswap = finnow; finnow = finother; finother = finswap;
			if (bdytail != 0.0) {
				temp8len = scale_expansion_zeroelim(4, cc, adxtail, temp8);
				temp16alen = scale_expansion_zeroelim(temp8len, temp8, bdytail,
					temp16a);
				finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
					temp16a, finother);
				finswap = finnow; finnow = finother; finother = finswap;
			}
			if (cdytail != 0.0) {
				temp8len = scale_expansion_zeroelim(4, bb, -adxtail, temp8);
				temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail,
					temp16a);
				finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
					temp16a, finother);
				finswap = finnow; finnow = finother; finother = finswap;
			}

			temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, adxtail,
				temp32a);
			axtbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adxtail, axtbctt);
			temp16alen = scale_expansion_zeroelim(axtbcttlen, axtbctt, 2.0 * adx,
				temp16a);
			temp16blen = scale_expansion_zeroelim(axtbcttlen, axtbctt, adxtail,
				temp16b);
			temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
				temp16blen, temp16b, temp32b);
			temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
				temp32blen, temp32b, temp64);
			finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
				temp64, finother);
			finswap = finnow; finnow = finother; finother = finswap;
		}
		if (adytail != 0.0) {
			temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, adytail, temp16a);
			aytbctlen = scale_expansion_zeroelim(bctlen, bct, adytail, aytbct);
			temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, 2.0 * ady,
				temp32a);
			temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
				temp32alen, temp32a, temp48);
			finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
				temp48, finother);
			finswap = finnow; finnow = finother; finother = finswap;


			temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, adytail,
				temp32a);
			aytbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adytail, aytbctt);
			temp16alen = scale_expansion_zeroelim(aytbcttlen, aytbctt, 2.0 * ady,
				temp16a);
			temp16blen = scale_expansion_zeroelim(aytbcttlen, aytbctt, adytail,
				temp16b);
			temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
				temp16blen, temp16b, temp32b);
			temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
				temp32blen, temp32b, temp64);
			finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
				temp64, finother);
			finswap = finnow; finnow = finother; finother = finswap;
		}
	}
	if ((bdxtail != 0.0) || (bdytail != 0.0)) {
		if ((cdxtail != 0.0) || (cdytail != 0.0)
			|| (adxtail != 0.0) || (adytail != 0.0)) {
			Two_Product(cdxtail, ady, ti1, ti0);
			Two_Product(cdx, adytail, tj1, tj0);
			Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
			u[3] = u3;
			negate = -cdy;
			Two_Product(adxtail, negate, ti1, ti0);
			negate = -cdytail;
			Two_Product(adx, negate, tj1, tj0);
			Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
			v[3] = v3;
			catlen = fast_expansion_sum_zeroelim(4, u, 4, v, cat);

			Two_Product(cdxtail, adytail, ti1, ti0);
			Two_Product(adxtail, cdytail, tj1, tj0);
			Two_Two_Diff(ti1, ti0, tj1, tj0, catt3, catt[2], catt[1], catt[0]);
			catt[3] = catt3;
			cattlen = 4;
		}
		else {
			cat[0] = 0.0;
			catlen = 1;
			catt[0] = 0.0;
			cattlen = 1;
		}

		if (bdxtail != 0.0) {
			temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, bdxtail, temp16a);
			bxtcatlen = scale_expansion_zeroelim(catlen, cat, bdxtail, bxtcat);
			temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, 2.0 * bdx,
				temp32a);
			temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
				temp32alen, temp32a, temp48);
			finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
				temp48, finother);
			finswap = finnow; finnow = finother; finother = finswap;
			if (cdytail != 0.0) {
				temp8len = scale_expansion_zeroelim(4, aa, bdxtail, temp8);
				temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail,
					temp16a);
				finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
					temp16a, finother);
				finswap = finnow; finnow = finother; finother = finswap;
			}
			if (adytail != 0.0) {
				temp8len = scale_expansion_zeroelim(4, cc, -bdxtail, temp8);
				temp16alen = scale_expansion_zeroelim(temp8len, temp8, adytail,
					temp16a);
				finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
					temp16a, finother);
				finswap = finnow; finnow = finother; finother = finswap;
			}

			temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, bdxtail,
				temp32a);
			bxtcattlen = scale_expansion_zeroelim(cattlen, catt, bdxtail, bxtcatt);
			temp16alen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, 2.0 * bdx,
				temp16a);
			temp16blen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, bdxtail,
				temp16b);
			temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
				temp16blen, temp16b, temp32b);
			temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
				temp32blen, temp32b, temp64);
			finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
				temp64, finother);
			finswap = finnow; finnow = finother; finother = finswap;
		}
		if (bdytail != 0.0) {
			temp16alen = scale_expansion_zeroelim(bytcalen, bytca, bdytail, temp16a);
			bytcatlen = scale_expansion_zeroelim(catlen, cat, bdytail, bytcat);
			temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, 2.0 * bdy,
				temp32a);
			temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
				temp32alen, temp32a, temp48);
			finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
				temp48, finother);
			finswap = finnow; finnow = finother; finother = finswap;


			temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, bdytail,
				temp32a);
			bytcattlen = scale_expansion_zeroelim(cattlen, catt, bdytail, bytcatt);
			temp16alen = scale_expansion_zeroelim(bytcattlen, bytcatt, 2.0 * bdy,
				temp16a);
			temp16blen = scale_expansion_zeroelim(bytcattlen, bytcatt, bdytail,
				temp16b);
			temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
				temp16blen, temp16b, temp32b);
			temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
				temp32blen, temp32b, temp64);
			finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
				temp64, finother);
			finswap = finnow; finnow = finother; finother = finswap;
		}
	}
	if ((cdxtail != 0.0) || (cdytail != 0.0)) {
		if ((adxtail != 0.0) || (adytail != 0.0)
			|| (bdxtail != 0.0) || (bdytail != 0.0)) {
			Two_Product(adxtail, bdy, ti1, ti0);
			Two_Product(adx, bdytail, tj1, tj0);
			Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
			u[3] = u3;
			negate = -ady;
			Two_Product(bdxtail, negate, ti1, ti0);
			negate = -adytail;
			Two_Product(bdx, negate, tj1, tj0);
			Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
			v[3] = v3;
			abtlen = fast_expansion_sum_zeroelim(4, u, 4, v, abt);

			Two_Product(adxtail, bdytail, ti1, ti0);
			Two_Product(bdxtail, adytail, tj1, tj0);
			Two_Two_Diff(ti1, ti0, tj1, tj0, abtt3, abtt[2], abtt[1], abtt[0]);
			abtt[3] = abtt3;
			abttlen = 4;
		}
		else {
			abt[0] = 0.0;
			abtlen = 1;
			abtt[0] = 0.0;
			abttlen = 1;
		}

		if (cdxtail != 0.0) {
			temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, cdxtail, temp16a);
			cxtabtlen = scale_expansion_zeroelim(abtlen, abt, cdxtail, cxtabt);
			temp32alen = scale_expansion_zeroelim(cxtabtlen, cxtabt, 2.0 * cdx,
				temp32a);
			temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
				temp32alen, temp32a, temp48);
			finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
				temp48, finother);
			finswap = finnow; finnow = finother; finother = finswap;
			if (adytail != 0.0) {
				temp8len = scale_expansion_zeroelim(4, bb, cdxtail, temp8);
				temp16alen = scale_expansion_zeroelim(temp8len, temp8, adytail,
					temp16a);
				finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
					temp16a, finother);
				finswap = finnow; finnow = finother; finother = finswap;
			}
			if (bdytail != 0.0) {
				temp8len = scale_expansion_zeroelim(4, aa, -cdxtail, temp8);
				temp16alen = scale_expansion_zeroelim(temp8len, temp8, bdytail,
					temp16a);
				finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
					temp16a, finother);
				finswap = finnow; finnow = finother; finother = finswap;
			}

			temp32alen = scale_expansion_zeroelim(cxtabtlen, cxtabt, cdxtail,
				temp32a);
			cxtabttlen = scale_expansion_zeroelim(abttlen, abtt, cdxtail, cxtabtt);
			temp16alen = scale_expansion_zeroelim(cxtabttlen, cxtabtt, 2.0 * cdx,
				temp16a);
			temp16blen = scale_expansion_zeroelim(cxtabttlen, cxtabtt, cdxtail,
				temp16b);
			temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
				temp16blen, temp16b, temp32b);
			temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
				temp32blen, temp32b, temp64);
			finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
				temp64, finother);
			finswap = finnow; finnow = finother; finother = finswap;
		}
		if (cdytail != 0.0) {
			temp16alen = scale_expansion_zeroelim(cytablen, cytab, cdytail, temp16a);
			cytabtlen = scale_expansion_zeroelim(abtlen, abt, cdytail, cytabt);
			temp32alen = scale_expansion_zeroelim(cytabtlen, cytabt, 2.0 * cdy,
				temp32a);
			temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
				temp32alen, temp32a, temp48);
			finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
				temp48, finother);
			finswap = finnow; finnow = finother; finother = finswap;


			temp32alen = scale_expansion_zeroelim(cytabtlen, cytabt, cdytail,
				temp32a);
			cytabttlen = scale_expansion_zeroelim(abttlen, abtt, cdytail, cytabtt);
			temp16alen = scale_expansion_zeroelim(cytabttlen, cytabtt, 2.0 * cdy,
				temp16a);
			temp16blen = scale_expansion_zeroelim(cytabttlen, cytabtt, cdytail,
				temp16b);
			temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
				temp16blen, temp16b, temp32b);
			temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
				temp32blen, temp32b, temp64);
			finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
				temp64, finother);
			finswap = finnow; finnow = finother; finother = finswap;
		}
	}

	return finnow[finlength - 1];
}

#ifdef ANSI_DECLARATORS
REAL incircle(struct mesh *m, struct behavior *b,
	vertex pa, vertex pb, vertex pc, vertex pd)
#else /* not ANSI_DECLARATORS */
REAL incircle(m, b, pa, pb, pc, pd)
struct mesh *m;
struct behavior *b;
vertex pa;
vertex pb;
vertex pc;
vertex pd;
#endif /* not ANSI_DECLARATORS */

{
	REAL adx, bdx, cdx, ady, bdy, cdy;
	REAL bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady;
	REAL alift, blift, clift;
	REAL det;
	REAL permanent, errbound;

	m->incirclecount++;

	adx = pa[0] - pd[0];
	bdx = pb[0] - pd[0];
	cdx = pc[0] - pd[0];
	ady = pa[1] - pd[1];
	bdy = pb[1] - pd[1];
	cdy = pc[1] - pd[1];

	bdxcdy = bdx * cdy;
	cdxbdy = cdx * bdy;
	alift = adx * adx + ady * ady;

	cdxady = cdx * ady;
	adxcdy = adx * cdy;
	blift = bdx * bdx + bdy * bdy;

	adxbdy = adx * bdy;
	bdxady = bdx * ady;
	clift = cdx * cdx + cdy * cdy;

	det = alift * (bdxcdy - cdxbdy)
		+ blift * (cdxady - adxcdy)
		+ clift * (adxbdy - bdxady);

	if (b->noexact) {
		return det;
	}

	permanent = (Absolute(bdxcdy) + Absolute(cdxbdy)) * alift
		+ (Absolute(cdxady) + Absolute(adxcdy)) * blift
		+ (Absolute(adxbdy) + Absolute(bdxady)) * clift;
	errbound = iccerrboundA * permanent;
	if ((det > errbound) || (-det > errbound)) {
		return det;
	}

	return incircleadapt(pa, pb, pc, pd, permanent);
}

/*****************************************************************************/
/*                                                                           */
/*  orient3d()   Return a positive value if the point pd lies below the      */
/*               plane passing through pa, pb, and pc; "below" is defined so */
/*               that pa, pb, and pc appear in counterclockwise order when   */
/*               viewed from above the plane.  Returns a negative value if   */
/*               pd lies above the plane.  Returns zero if the points are    */
/*               coplanar.  The result is also a rough approximation of six  */
/*               times the signed volume of the tetrahedron defined by the   */
/*               four points.                                                */
/*                                                                           */
/*  Uses exact arithmetic if necessary to ensure a correct answer.  The      */
/*  result returned is the determinant of a matrix.  This determinant is     */
/*  computed adaptively, in the sense that exact arithmetic is used only to  */
/*  the degree it is needed to ensure that the returned value has the        */
/*  correct sign.  Hence, this function is usually quite fast, but will run  */
/*  more slowly when the input points are coplanar or nearly so.             */
/*                                                                           */
/*  See my Robust Predicates paper for details.                              */
/*                                                                           */
/*****************************************************************************/

#ifdef ANSI_DECLARATORS
REAL orient3dadapt(vertex pa, vertex pb, vertex pc, vertex pd,
	REAL aheight, REAL bheight, REAL cheight, REAL dheight,
	REAL permanent)
#else /* not ANSI_DECLARATORS */
REAL orient3dadapt(pa, pb, pc, pd,
	aheight, bheight, cheight, dheight, permanent)
	vertex pa;
vertex pb;
vertex pc;
vertex pd;
REAL aheight;
REAL bheight;
REAL cheight;
REAL dheight;
REAL permanent;
#endif /* not ANSI_DECLARATORS */

{
	INEXACT REAL adx, bdx, cdx, ady, bdy, cdy, adheight, bdheight, cdheight;
	REAL det, errbound;

	INEXACT REAL bdxcdy1, cdxbdy1, cdxady1, adxcdy1, adxbdy1, bdxady1;
	REAL bdxcdy0, cdxbdy0, cdxady0, adxcdy0, adxbdy0, bdxady0;
	REAL bc[4], ca[4], ab[4];
	INEXACT REAL bc3, ca3, ab3;
	REAL adet[8], bdet[8], cdet[8];
	int alen, blen, clen;
	REAL abdet[16];
	int ablen;
	REAL *finnow, *finother, *finswap;
	REAL fin1[192], fin2[192];
	int finlength;

	REAL adxtail, bdxtail, cdxtail;
	REAL adytail, bdytail, cdytail;
	REAL adheighttail, bdheighttail, cdheighttail;
	INEXACT REAL at_blarge, at_clarge;
	INEXACT REAL bt_clarge, bt_alarge;
	INEXACT REAL ct_alarge, ct_blarge;
	REAL at_b[4], at_c[4], bt_c[4], bt_a[4], ct_a[4], ct_b[4];
	int at_blen, at_clen, bt_clen, bt_alen, ct_alen, ct_blen;
	INEXACT REAL bdxt_cdy1, cdxt_bdy1, cdxt_ady1;
	INEXACT REAL adxt_cdy1, adxt_bdy1, bdxt_ady1;
	REAL bdxt_cdy0, cdxt_bdy0, cdxt_ady0;
	REAL adxt_cdy0, adxt_bdy0, bdxt_ady0;
	INEXACT REAL bdyt_cdx1, cdyt_bdx1, cdyt_adx1;
	INEXACT REAL adyt_cdx1, adyt_bdx1, bdyt_adx1;
	REAL bdyt_cdx0, cdyt_bdx0, cdyt_adx0;
	REAL adyt_cdx0, adyt_bdx0, bdyt_adx0;
	REAL bct[8], cat[8], abt[8];
	int bctlen, catlen, abtlen;
	INEXACT REAL bdxt_cdyt1, cdxt_bdyt1, cdxt_adyt1;
	INEXACT REAL adxt_cdyt1, adxt_bdyt1, bdxt_adyt1;
	REAL bdxt_cdyt0, cdxt_bdyt0, cdxt_adyt0;
	REAL adxt_cdyt0, adxt_bdyt0, bdxt_adyt0;
	REAL u[4], v[12], w[16];
	INEXACT REAL u3;
	int vlength, wlength;
	REAL negate;

	INEXACT REAL bvirt;
	REAL avirt, bround, around;
	INEXACT REAL c;
	INEXACT REAL abig;
	REAL ahi, alo, bhi, blo;
	REAL err1, err2, err3;
	INEXACT REAL _i, _j, _k;
	REAL _0;

	adx = (REAL)(pa[0] - pd[0]);
	bdx = (REAL)(pb[0] - pd[0]);
	cdx = (REAL)(pc[0] - pd[0]);
	ady = (REAL)(pa[1] - pd[1]);
	bdy = (REAL)(pb[1] - pd[1]);
	cdy = (REAL)(pc[1] - pd[1]);
	adheight = (REAL)(aheight - dheight);
	bdheight = (REAL)(bheight - dheight);
	cdheight = (REAL)(cheight - dheight);

	Two_Product(bdx, cdy, bdxcdy1, bdxcdy0);
	Two_Product(cdx, bdy, cdxbdy1, cdxbdy0);
	Two_Two_Diff(bdxcdy1, bdxcdy0, cdxbdy1, cdxbdy0, bc3, bc[2], bc[1], bc[0]);
	bc[3] = bc3;
	alen = scale_expansion_zeroelim(4, bc, adheight, adet);

	Two_Product(cdx, ady, cdxady1, cdxady0);
	Two_Product(adx, cdy, adxcdy1, adxcdy0);
	Two_Two_Diff(cdxady1, cdxady0, adxcdy1, adxcdy0, ca3, ca[2], ca[1], ca[0]);
	ca[3] = ca3;
	blen = scale_expansion_zeroelim(4, ca, bdheight, bdet);

	Two_Product(adx, bdy, adxbdy1, adxbdy0);
	Two_Product(bdx, ady, bdxady1, bdxady0);
	Two_Two_Diff(adxbdy1, adxbdy0, bdxady1, bdxady0, ab3, ab[2], ab[1], ab[0]);
	ab[3] = ab3;
	clen = scale_expansion_zeroelim(4, ab, cdheight, cdet);

	ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
	finlength = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, fin1);

	det = estimate(finlength, fin1);
	errbound = o3derrboundB * permanent;
	if ((det >= errbound) || (-det >= errbound)) {
		return det;
	}

	Two_Diff_Tail(pa[0], pd[0], adx, adxtail);
	Two_Diff_Tail(pb[0], pd[0], bdx, bdxtail);
	Two_Diff_Tail(pc[0], pd[0], cdx, cdxtail);
	Two_Diff_Tail(pa[1], pd[1], ady, adytail);
	Two_Diff_Tail(pb[1], pd[1], bdy, bdytail);
	Two_Diff_Tail(pc[1], pd[1], cdy, cdytail);
	Two_Diff_Tail(aheight, dheight, adheight, adheighttail);
	Two_Diff_Tail(bheight, dheight, bdheight, bdheighttail);
	Two_Diff_Tail(cheight, dheight, cdheight, cdheighttail);

	if ((adxtail == 0.0) && (bdxtail == 0.0) && (cdxtail == 0.0) &&
		(adytail == 0.0) && (bdytail == 0.0) && (cdytail == 0.0) &&
		(adheighttail == 0.0) &&
		(bdheighttail == 0.0) &&
		(cdheighttail == 0.0)) {
		return det;
	}

	errbound = o3derrboundC * permanent + resulterrbound * Absolute(det);
	det += (adheight * ((bdx * cdytail + cdy * bdxtail) -
		(bdy * cdxtail + cdx * bdytail)) +
		adheighttail * (bdx * cdy - bdy * cdx)) +
		(bdheight * ((cdx * adytail + ady * cdxtail) -
			(cdy * adxtail + adx * cdytail)) +
			bdheighttail * (cdx * ady - cdy * adx)) +
		(cdheight * ((adx * bdytail + bdy * adxtail) -
			(ady * bdxtail + bdx * adytail)) +
			cdheighttail * (adx * bdy - ady * bdx));
	if ((det >= errbound) || (-det >= errbound)) {
		return det;
	}

	finnow = fin1;
	finother = fin2;

	if (adxtail == 0.0) {
		if (adytail == 0.0) {
			at_b[0] = 0.0;
			at_blen = 1;
			at_c[0] = 0.0;
			at_clen = 1;
		}
		else {
			negate = -adytail;
			Two_Product(negate, bdx, at_blarge, at_b[0]);
			at_b[1] = at_blarge;
			at_blen = 2;
			Two_Product(adytail, cdx, at_clarge, at_c[0]);
			at_c[1] = at_clarge;
			at_clen = 2;
		}
	}
	else {
		if (adytail == 0.0) {
			Two_Product(adxtail, bdy, at_blarge, at_b[0]);
			at_b[1] = at_blarge;
			at_blen = 2;
			negate = -adxtail;
			Two_Product(negate, cdy, at_clarge, at_c[0]);
			at_c[1] = at_clarge;
			at_clen = 2;
		}
		else {
			Two_Product(adxtail, bdy, adxt_bdy1, adxt_bdy0);
			Two_Product(adytail, bdx, adyt_bdx1, adyt_bdx0);
			Two_Two_Diff(adxt_bdy1, adxt_bdy0, adyt_bdx1, adyt_bdx0,
				at_blarge, at_b[2], at_b[1], at_b[0]);
			at_b[3] = at_blarge;
			at_blen = 4;
			Two_Product(adytail, cdx, adyt_cdx1, adyt_cdx0);
			Two_Product(adxtail, cdy, adxt_cdy1, adxt_cdy0);
			Two_Two_Diff(adyt_cdx1, adyt_cdx0, adxt_cdy1, adxt_cdy0,
				at_clarge, at_c[2], at_c[1], at_c[0]);
			at_c[3] = at_clarge;
			at_clen = 4;
		}
	}
	if (bdxtail == 0.0) {
		if (bdytail == 0.0) {
			bt_c[0] = 0.0;
			bt_clen = 1;
			bt_a[0] = 0.0;
			bt_alen = 1;
		}
		else {
			negate = -bdytail;
			Two_Product(negate, cdx, bt_clarge, bt_c[0]);
			bt_c[1] = bt_clarge;
			bt_clen = 2;
			Two_Product(bdytail, adx, bt_alarge, bt_a[0]);
			bt_a[1] = bt_alarge;
			bt_alen = 2;
		}
	}
	else {
		if (bdytail == 0.0) {
			Two_Product(bdxtail, cdy, bt_clarge, bt_c[0]);
			bt_c[1] = bt_clarge;
			bt_clen = 2;
			negate = -bdxtail;
			Two_Product(negate, ady, bt_alarge, bt_a[0]);
			bt_a[1] = bt_alarge;
			bt_alen = 2;
		}
		else {
			Two_Product(bdxtail, cdy, bdxt_cdy1, bdxt_cdy0);
			Two_Product(bdytail, cdx, bdyt_cdx1, bdyt_cdx0);
			Two_Two_Diff(bdxt_cdy1, bdxt_cdy0, bdyt_cdx1, bdyt_cdx0,
				bt_clarge, bt_c[2], bt_c[1], bt_c[0]);
			bt_c[3] = bt_clarge;
			bt_clen = 4;
			Two_Product(bdytail, adx, bdyt_adx1, bdyt_adx0);
			Two_Product(bdxtail, ady, bdxt_ady1, bdxt_ady0);
			Two_Two_Diff(bdyt_adx1, bdyt_adx0, bdxt_ady1, bdxt_ady0,
				bt_alarge, bt_a[2], bt_a[1], bt_a[0]);
			bt_a[3] = bt_alarge;
			bt_alen = 4;
		}
	}
	if (cdxtail == 0.0) {
		if (cdytail == 0.0) {
			ct_a[0] = 0.0;
			ct_alen = 1;
			ct_b[0] = 0.0;
			ct_blen = 1;
		}
		else {
			negate = -cdytail;
			Two_Product(negate, adx, ct_alarge, ct_a[0]);
			ct_a[1] = ct_alarge;
			ct_alen = 2;
			Two_Product(cdytail, bdx, ct_blarge, ct_b[0]);
			ct_b[1] = ct_blarge;
			ct_blen = 2;
		}
	}
	else {
		if (cdytail == 0.0) {
			Two_Product(cdxtail, ady, ct_alarge, ct_a[0]);
			ct_a[1] = ct_alarge;
			ct_alen = 2;
			negate = -cdxtail;
			Two_Product(negate, bdy, ct_blarge, ct_b[0]);
			ct_b[1] = ct_blarge;
			ct_blen = 2;
		}
		else {
			Two_Product(cdxtail, ady, cdxt_ady1, cdxt_ady0);
			Two_Product(cdytail, adx, cdyt_adx1, cdyt_adx0);
			Two_Two_Diff(cdxt_ady1, cdxt_ady0, cdyt_adx1, cdyt_adx0,
				ct_alarge, ct_a[2], ct_a[1], ct_a[0]);
			ct_a[3] = ct_alarge;
			ct_alen = 4;
			Two_Product(cdytail, bdx, cdyt_bdx1, cdyt_bdx0);
			Two_Product(cdxtail, bdy, cdxt_bdy1, cdxt_bdy0);
			Two_Two_Diff(cdyt_bdx1, cdyt_bdx0, cdxt_bdy1, cdxt_bdy0,
				ct_blarge, ct_b[2], ct_b[1], ct_b[0]);
			ct_b[3] = ct_blarge;
			ct_blen = 4;
		}
	}

	bctlen = fast_expansion_sum_zeroelim(bt_clen, bt_c, ct_blen, ct_b, bct);
	wlength = scale_expansion_zeroelim(bctlen, bct, adheight, w);
	finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
		finother);
	finswap = finnow; finnow = finother; finother = finswap;

	catlen = fast_expansion_sum_zeroelim(ct_alen, ct_a, at_clen, at_c, cat);
	wlength = scale_expansion_zeroelim(catlen, cat, bdheight, w);
	finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
		finother);
	finswap = finnow; finnow = finother; finother = finswap;

	abtlen = fast_expansion_sum_zeroelim(at_blen, at_b, bt_alen, bt_a, abt);
	wlength = scale_expansion_zeroelim(abtlen, abt, cdheight, w);
	finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
		finother);
	finswap = finnow; finnow = finother; finother = finswap;

	if (adheighttail != 0.0) {
		vlength = scale_expansion_zeroelim(4, bc, adheighttail, v);
		finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v,
			finother);
		finswap = finnow; finnow = finother; finother = finswap;
	}
	if (bdheighttail != 0.0) {
		vlength = scale_expansion_zeroelim(4, ca, bdheighttail, v);
		finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v,
			finother);
		finswap = finnow; finnow = finother; finother = finswap;
	}
	if (cdheighttail != 0.0) {
		vlength = scale_expansion_zeroelim(4, ab, cdheighttail, v);
		finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v,
			finother);
		finswap = finnow; finnow = finother; finother = finswap;
	}

	if (adxtail != 0.0) {
		if (bdytail != 0.0) {
			Two_Product(adxtail, bdytail, adxt_bdyt1, adxt_bdyt0);
			Two_One_Product(adxt_bdyt1, adxt_bdyt0, cdheight, u3, u[2], u[1], u[0]);
			u[3] = u3;
			finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
				finother);
			finswap = finnow; finnow = finother; finother = finswap;
			if (cdheighttail != 0.0) {
				Two_One_Product(adxt_bdyt1, adxt_bdyt0, cdheighttail,
					u3, u[2], u[1], u[0]);
				u[3] = u3;
				finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
					finother);
				finswap = finnow; finnow = finother; finother = finswap;
			}
		}
		if (cdytail != 0.0) {
			negate = -adxtail;
			Two_Product(negate, cdytail, adxt_cdyt1, adxt_cdyt0);
			Two_One_Product(adxt_cdyt1, adxt_cdyt0, bdheight, u3, u[2], u[1], u[0]);
			u[3] = u3;
			finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
				finother);
			finswap = finnow; finnow = finother; finother = finswap;
			if (bdheighttail != 0.0) {
				Two_One_Product(adxt_cdyt1, adxt_cdyt0, bdheighttail,
					u3, u[2], u[1], u[0]);
				u[3] = u3;
				finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
					finother);
				finswap = finnow; finnow = finother; finother = finswap;
			}
		}
	}
	if (bdxtail != 0.0) {
		if (cdytail != 0.0) {
			Two_Product(bdxtail, cdytail, bdxt_cdyt1, bdxt_cdyt0);
			Two_One_Product(bdxt_cdyt1, bdxt_cdyt0, adheight, u3, u[2], u[1], u[0]);
			u[3] = u3;
			finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
				finother);
			finswap = finnow; finnow = finother; finother = finswap;
			if (adheighttail != 0.0) {
				Two_One_Product(bdxt_cdyt1, bdxt_cdyt0, adheighttail,
					u3, u[2], u[1], u[0]);
				u[3] = u3;
				finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
					finother);
				finswap = finnow; finnow = finother; finother = finswap;
			}
		}
		if (adytail != 0.0) {
			negate = -bdxtail;
			Two_Product(negate, adytail, bdxt_adyt1, bdxt_adyt0);
			Two_One_Product(bdxt_adyt1, bdxt_adyt0, cdheight, u3, u[2], u[1], u[0]);
			u[3] = u3;
			finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
				finother);
			finswap = finnow; finnow = finother; finother = finswap;
			if (cdheighttail != 0.0) {
				Two_One_Product(bdxt_adyt1, bdxt_adyt0, cdheighttail,
					u3, u[2], u[1], u[0]);
				u[3] = u3;
				finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
					finother);
				finswap = finnow; finnow = finother; finother = finswap;
			}
		}
	}
	if (cdxtail != 0.0) {
		if (adytail != 0.0) {
			Two_Product(cdxtail, adytail, cdxt_adyt1, cdxt_adyt0);
			Two_One_Product(cdxt_adyt1, cdxt_adyt0, bdheight, u3, u[2], u[1], u[0]);
			u[3] = u3;
			finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
				finother);
			finswap = finnow; finnow = finother; finother = finswap;
			if (bdheighttail != 0.0) {
				Two_One_Product(cdxt_adyt1, cdxt_adyt0, bdheighttail,
					u3, u[2], u[1], u[0]);
				u[3] = u3;
				finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
					finother);
				finswap = finnow; finnow = finother; finother = finswap;
			}
		}
		if (bdytail != 0.0) {
			negate = -cdxtail;
			Two_Product(negate, bdytail, cdxt_bdyt1, cdxt_bdyt0);
			Two_One_Product(cdxt_bdyt1, cdxt_bdyt0, adheight, u3, u[2], u[1], u[0]);
			u[3] = u3;
			finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
				finother);
			finswap = finnow; finnow = finother; finother = finswap;
			if (adheighttail != 0.0) {
				Two_One_Product(cdxt_bdyt1, cdxt_bdyt0, adheighttail,
					u3, u[2], u[1], u[0]);
				u[3] = u3;
				finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
					finother);
				finswap = finnow; finnow = finother; finother = finswap;
			}
		}
	}

	if (adheighttail != 0.0) {
		wlength = scale_expansion_zeroelim(bctlen, bct, adheighttail, w);
		finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
			finother);
		finswap = finnow; finnow = finother; finother = finswap;
	}
	if (bdheighttail != 0.0) {
		wlength = scale_expansion_zeroelim(catlen, cat, bdheighttail, w);
		finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
			finother);
		finswap = finnow; finnow = finother; finother = finswap;
	}
	if (cdheighttail != 0.0) {
		wlength = scale_expansion_zeroelim(abtlen, abt, cdheighttail, w);
		finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
			finother);
		finswap = finnow; finnow = finother; finother = finswap;
	}

	return finnow[finlength - 1];
}

#ifdef ANSI_DECLARATORS
REAL orient3d(struct mesh *m, struct behavior *b,
	vertex pa, vertex pb, vertex pc, vertex pd,
	REAL aheight, REAL bheight, REAL cheight, REAL dheight)
#else /* not ANSI_DECLARATORS */
REAL orient3d(m, b, pa, pb, pc, pd, aheight, bheight, cheight, dheight)
struct mesh *m;
struct behavior *b;
vertex pa;
vertex pb;
vertex pc;
vertex pd;
REAL aheight;
REAL bheight;
REAL cheight;
REAL dheight;
#endif /* not ANSI_DECLARATORS */

{
	REAL adx, bdx, cdx, ady, bdy, cdy, adheight, bdheight, cdheight;
	REAL bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady;
	REAL det;
	REAL permanent, errbound;

	m->orient3dcount++;

	adx = pa[0] - pd[0];
	bdx = pb[0] - pd[0];
	cdx = pc[0] - pd[0];
	ady = pa[1] - pd[1];
	bdy = pb[1] - pd[1];
	cdy = pc[1] - pd[1];
	adheight = aheight - dheight;
	bdheight = bheight - dheight;
	cdheight = cheight - dheight;

	bdxcdy = bdx * cdy;
	cdxbdy = cdx * bdy;

	cdxady = cdx * ady;
	adxcdy = adx * cdy;

	adxbdy = adx * bdy;
	bdxady = bdx * ady;

	det = adheight * (bdxcdy - cdxbdy)
		+ bdheight * (cdxady - adxcdy)
		+ cdheight * (adxbdy - bdxady);

	if (b->noexact) {
		return det;
	}

	permanent = (Absolute(bdxcdy) + Absolute(cdxbdy)) * Absolute(adheight)
		+ (Absolute(cdxady) + Absolute(adxcdy)) * Absolute(bdheight)
		+ (Absolute(adxbdy) + Absolute(bdxady)) * Absolute(cdheight);
	errbound = o3derrboundA * permanent;
	if ((det > errbound) || (-det > errbound)) {
		return det;
	}

	return orient3dadapt(pa, pb, pc, pd, aheight, bheight, cheight, dheight,
		permanent);
}

/*****************************************************************************/
/*                                                                           */
/*  nonregular()   Return a positive value if the point pd is incompatible   */
/*                 with the circle or plane passing through pa, pb, and pc   */
/*                 (meaning that pd is inside the circle or below the        */
/*                 plane); a negative value if it is compatible; and zero if */
/*                 the four points are cocircular/coplanar.  The points pa,  */
/*                 pb, and pc must be in counterclockwise order, or the sign */
/*                 of the result will be reversed.                           */
/*                                                                           */
/*  If the -w switch is used, the points are lifted onto the parabolic       */
/*  lifting map, then they are dropped according to their weights, then the  */
/*  3D orientation test is applied.  If the -W switch is used, the points'   */
/*  heights are already provided, so the 3D orientation test is applied      */
/*  directly.  If neither switch is used, the incircle test is applied.      */
/*                                                                           */
/*****************************************************************************/

#ifdef ANSI_DECLARATORS
REAL nonregular(struct mesh *m, struct behavior *b,
	vertex pa, vertex pb, vertex pc, vertex pd)
#else /* not ANSI_DECLARATORS */
REAL nonregular(m, b, pa, pb, pc, pd)
struct mesh *m;
struct behavior *b;
vertex pa;
vertex pb;
vertex pc;
vertex pd;
#endif /* not ANSI_DECLARATORS */

{
	if (b->weighted == 0) {
		return incircle(m, b, pa, pb, pc, pd);
	}
	else if (b->weighted == 1) {
		return orient3d(m, b, pa, pb, pc, pd,
			pa[0] * pa[0] + pa[1] * pa[1] - pa[2],
			pb[0] * pb[0] + pb[1] * pb[1] - pb[2],
			pc[0] * pc[0] + pc[1] * pc[1] - pc[2],
			pd[0] * pd[0] + pd[1] * pd[1] - pd[2]);
	}
	else {
		return orient3d(m, b, pa, pb, pc, pd, pa[2], pb[2], pc[2], pd[2]);
	}
}

/*****************************************************************************/
/*                                                                           */
/*  findcircumcenter()   Find the circumcenter of a triangle.                */
/*                                                                           */
/*  The result is returned both in terms of x-y coordinates and xi-eta       */
/*  (barycentric) coordinates.  The xi-eta coordinate system is defined in   */
/*  terms of the triangle:  the origin of the triangle is the origin of the  */
/*  coordinate system; the destination of the triangle is one unit along the */
/*  xi axis; and the apex of the triangle is one unit along the eta axis.    */
/*  This procedure also returns the square of the length of the triangle's   */
/*  shortest edge.                                                           */
/*                                                                           */
/*****************************************************************************/

#ifdef ANSI_DECLARATORS
void findcircumcenter(struct mesh *m, struct behavior *b,
	vertex torg, vertex tdest, vertex tapex,
	vertex circumcenter, REAL *xi, REAL *eta, int offcenter)
#else /* not ANSI_DECLARATORS */
void findcircumcenter(m, b, torg, tdest, tapex, circumcenter, xi, eta,
	offcenter)
struct mesh *m;
struct behavior *b;
vertex torg;
vertex tdest;
vertex tapex;
vertex circumcenter;
REAL *xi;
REAL *eta;
int offcenter;
#endif /* not ANSI_DECLARATORS */

{
	REAL xdo, ydo, xao, yao;
	REAL dodist, aodist, dadist;
	REAL denominator;
	REAL dx, dy, dxoff, dyoff;

	m->circumcentercount++;

	/* Compute the circumcenter of the triangle. */
	xdo = tdest[0] - torg[0];
	ydo = tdest[1] - torg[1];
	xao = tapex[0] - torg[0];
	yao = tapex[1] - torg[1];
	dodist = xdo * xdo + ydo * ydo;
	aodist = xao * xao + yao * yao;
	dadist = (tdest[0] - tapex[0]) * (tdest[0] - tapex[0]) +
		(tdest[1] - tapex[1]) * (tdest[1] - tapex[1]);
	if (b->noexact) {
		denominator = 0.5 / (xdo * yao - xao * ydo);
	}
	else {
		/* Use the counterclockwise() routine to ensure a positive (and */
		/*   reasonably accurate) result, avoiding any possibility of   */
		/*   division by zero.                                          */
		denominator = 0.5 / counterclockwise(m, b, tdest, tapex, torg);
		/* Don't count the above as an orientation test. */
		m->counterclockcount--;
	}
	dx = (yao * dodist - ydo * aodist) * denominator;
	dy = (xdo * aodist - xao * dodist) * denominator;

	/* Find the (squared) length of the triangle's shortest edge.  This   */
	/*   serves as a conservative estimate of the insertion radius of the */
	/*   circumcenter's parent.  The estimate is used to ensure that      */
	/*   the algorithm terminates even if very small angles appear in     */
	/*   the input PSLG.                                                  */
	if ((dodist < aodist) && (dodist < dadist)) {
		if (offcenter && (b->offconstant > 0.0)) {
			/* Find the position of the off-center, as described by Alper Ungor. */
			dxoff = 0.5 * xdo - b->offconstant * ydo;
			dyoff = 0.5 * ydo + b->offconstant * xdo;
			/* If the off-center is closer to the origin than the */
			/*   circumcenter, use the off-center instead.        */
			if (dxoff * dxoff + dyoff * dyoff < dx * dx + dy * dy) {
				dx = dxoff;
				dy = dyoff;
			}
		}
	}
	else if (aodist < dadist) {
		if (offcenter && (b->offconstant > 0.0)) {
			dxoff = 0.5 * xao + b->offconstant * yao;
			dyoff = 0.5 * yao - b->offconstant * xao;
			/* If the off-center is closer to the origin than the */
			/*   circumcenter, use the off-center instead.        */
			if (dxoff * dxoff + dyoff * dyoff < dx * dx + dy * dy) {
				dx = dxoff;
				dy = dyoff;
			}
		}
	}
	else {
		if (offcenter && (b->offconstant > 0.0)) {
			dxoff = 0.5 * (tapex[0] - tdest[0]) -
				b->offconstant * (tapex[1] - tdest[1]);
			dyoff = 0.5 * (tapex[1] - tdest[1]) +
				b->offconstant * (tapex[0] - tdest[0]);
			/* If the off-center is closer to the destination than the */
			/*   circumcenter, use the off-center instead.             */
			if (dxoff * dxoff + dyoff * dyoff <
				(dx - xdo) * (dx - xdo) + (dy - ydo) * (dy - ydo)) {
				dx = xdo + dxoff;
				dy = ydo + dyoff;
			}
		}
	}

	circumcenter[0] = torg[0] + dx;
	circumcenter[1] = torg[1] + dy;

	/* To interpolate vertex attributes for the new vertex inserted at */
	/*   the circumcenter, define a coordinate system with a xi-axis,  */
	/*   directed from the triangle's origin to its destination, and   */
	/*   an eta-axis, directed from its origin to its apex.            */
	/*   Calculate the xi and eta coordinates of the circumcenter.     */
	*xi = (yao * dx - xao * dy) * (2.0 * denominator);
	*eta = (xdo * dy - ydo * dx) * (2.0 * denominator);
}

/**                                                                         **/
/**                                                                         **/
/********* Geometric primitives end here                             *********/

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

#ifdef ANSI_DECLARATORS
void triangleinit(struct mesh *m)
#else /* not ANSI_DECLARATORS */
void triangleinit(m)
struct mesh *m;
#endif /* not ANSI_DECLARATORS */

{
	poolzero(&m->vertices);
	poolzero(&m->triangles);
	poolzero(&m->subsegs);
	poolzero(&m->viri);
	poolzero(&m->badsubsegs);
	poolzero(&m->badtriangles);
	poolzero(&m->flipstackers);
	poolzero(&m->splaynodes);

	m->recenttri.tri = (triangle *)NULL; /* No triangle has been visited yet. */
	m->undeads = 0;                       /* No eliminated input vertices yet. */
	m->samples = 1;         /* Point location should take at least one sample. */
	m->checksegments = 0;   /* There are no segments in the triangulation yet. */
	m->checkquality = 0;     /* The quality triangulation stage has not begun. */
	m->incirclecount = m->counterclockcount = m->orient3dcount = 0;
	m->hyperbolacount = m->circletopcount = m->circumcentercount = 0;
	randomseed = 1;

	exactinit();                     /* Initialize exact arithmetic constants. */
}

/*****************************************************************************/
/*                                                                           */
/*  randomnation()   Generate a random number between 0 and `choices' - 1.   */
/*                                                                           */
/*  This is a simple linear congruential random number generator.  Hence, it */
/*  is a bad random number generator, but good enough for most randomized    */
/*  geometric algorithms.                                                    */
/*                                                                           */
/*****************************************************************************/

#ifdef ANSI_DECLARATORS
unsigned long randomnation(unsigned int choices)
#else /* not ANSI_DECLARATORS */
unsigned long randomnation(choices)
unsigned int choices;
#endif /* not ANSI_DECLARATORS */

{
	randomseed = (randomseed * 1366l + 150889l) % 714025l;
	return randomseed / (714025l / choices + 1);
}

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

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

#ifndef REDUCED

#ifdef ANSI_DECLARATORS
void checkmesh(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
void checkmesh(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */

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

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

#endif /* not REDUCED */

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

#ifndef REDUCED

#ifdef ANSI_DECLARATORS
void checkdelaunay(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
void checkdelaunay(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */

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

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

#endif /* not REDUCED */

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

#ifndef CDT_ONLY

#ifdef ANSI_DECLARATORS
void enqueuebadtriang(struct mesh *m, struct behavior *b,
struct badtriang *badtri)
#else /* not ANSI_DECLARATORS */
void enqueuebadtriang(m, b, badtri)
struct mesh *m;
struct behavior *b;
struct badtriang *badtri;
#endif /* not ANSI_DECLARATORS */

{
	REAL length, multiplier;
	int exponent, expincrement;
	int queuenumber;
	int posexponent;
	int i;

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

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

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

#endif /* not CDT_ONLY */

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

#ifndef CDT_ONLY

#ifdef ANSI_DECLARATORS
void enqueuebadtri(struct mesh *m, struct behavior *b, struct otri *enqtri,
	REAL minedge, vertex enqapex, vertex enqorg, vertex enqdest)
#else /* not ANSI_DECLARATORS */
void enqueuebadtri(m, b, enqtri, minedge, enqapex, enqorg, enqdest)
struct mesh *m;
struct behavior *b;
struct otri *enqtri;
REAL minedge;
vertex enqapex;
vertex enqorg;
vertex enqdest;
#endif /* not ANSI_DECLARATORS */

{
	struct badtriang *newbad;

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

#endif /* not CDT_ONLY */

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

#ifndef CDT_ONLY

#ifdef ANSI_DECLARATORS
struct badtriang *dequeuebadtriang(struct mesh *m)
#else /* not ANSI_DECLARATORS */
struct badtriang *dequeuebadtriang(m)
struct mesh *m;
#endif /* not ANSI_DECLARATORS */

{
	struct badtriang *result;

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

#endif /* not CDT_ONLY */

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

#ifndef CDT_ONLY

#ifdef ANSI_DECLARATORS
int checkseg4encroach(struct mesh *m, struct behavior *b,
struct osub *testsubseg)
#else /* not ANSI_DECLARATORS */
int checkseg4encroach(m, b, testsubseg)
struct mesh *m;
struct behavior *b;
struct osub *testsubseg;
#endif /* not ANSI_DECLARATORS */

{
	struct otri neighbortri;
	struct osub testsym;
	struct badsubseg *encroachedseg;
	REAL dotproduct;
	int encroached;
	int sides;
	vertex eorg, edest, eapex;
	triangle ptr;                     /* Temporary variable used by stpivot(). */

	encroached = 0;
	sides = 0;

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

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

	return encroached;
}

#endif /* not CDT_ONLY */

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

#ifndef CDT_ONLY

#ifdef ANSI_DECLARATORS
void testtriangle(struct mesh *m, struct behavior *b, struct otri *testtri)
#else /* not ANSI_DECLARATORS */
void testtriangle(m, b, testtri)
struct mesh *m;
struct behavior *b;
struct otri *testtri;
#endif /* not ANSI_DECLARATORS */

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

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

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

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

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

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

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

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

#endif /* not CDT_ONLY */

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

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

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

#ifdef ANSI_DECLARATORS
void makevertexmap(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
void makevertexmap(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */

{
	struct otri triangleloop;
	vertex triorg;

	if (b->verbose) {
		printf("    Constructing mapping from vertices to triangles.\n");
	}
	traversalinit(&m->triangles);
	triangleloop.tri = triangletraverse(m);
	while (triangleloop.tri != (triangle *)NULL) {
		/* Check all three vertices of the triangle. */
		for (triangleloop.orient = 0; triangleloop.orient < 3;
		triangleloop.orient++) {
			org(triangleloop, triorg);
			setvertex2tri(triorg, encode(triangleloop));
		}
		triangleloop.tri = triangletraverse(m);
	}
}

/*****************************************************************************/
/*                                                                           */
/*  preciselocate()   Find a triangle or edge containing a given point.      */
/*                                                                           */
/*  Begins its search from `searchtri'.  It is important that `searchtri'    */
/*  be a handle with the property that `searchpoint' is strictly to the left */
/*  of the edge denoted by `searchtri', or is collinear with that edge and   */
/*  does not intersect that edge.  (In particular, `searchpoint' should not  */
/*  be the origin or destination of that edge.)                              */
/*                                                                           */
/*  These conditions are imposed because preciselocate() is normally used in */
/*  one of two situations:                                                   */
/*                                                                           */
/*  (1)  To try to find the location to insert a new point.  Normally, we    */
/*       know an edge that the point is strictly to the left of.  In the     */
/*       incremental Delaunay algorithm, that edge is a bounding box edge.   */
/*       In Ruppert's Delaunay refinement algorithm for quality meshing,     */
/*       that edge is the shortest edge of the triangle whose circumcenter   */
/*       is being inserted.                                                  */
/*                                                                           */
/*  (2)  To try to find an existing point.  In this case, any edge on the    */
/*       convex hull is a good starting edge.  You must screen out the       */
/*       possibility that the vertex sought is an endpoint of the starting   */
/*       edge before you call preciselocate().                               */
/*                                                                           */
/*  On completion, `searchtri' is a triangle that contains `searchpoint'.    */
/*                                                                           */
/*  This implementation differs from that given by Guibas and Stolfi.  It    */
/*  walks from triangle to triangle, crossing an edge only if `searchpoint'  */
/*  is on the other side of the line containing that edge.  After entering   */
/*  a triangle, there are two edges by which one can leave that triangle.    */
/*  If both edges are valid (`searchpoint' is on the other side of both      */
/*  edges), one of the two is chosen by drawing a line perpendicular to      */
/*  the entry edge (whose endpoints are `forg' and `fdest') passing through  */
/*  `fapex'.  Depending on which side of this perpendicular `searchpoint'    */
/*  falls on, an exit edge is chosen.                                        */
/*                                                                           */
/*  This implementation is empirically faster than the Guibas and Stolfi     */
/*  point location routine (which I originally used), which tends to spiral  */
/*  in toward its target.                                                    */
/*                                                                           */
/*  Returns ONVERTEX if the point lies on an existing vertex.  `searchtri'   */
/*  is a handle whose origin is the existing vertex.                         */
/*                                                                           */
/*  Returns ONEDGE if the point lies on a mesh edge.  `searchtri' is a       */
/*  handle whose primary edge is the edge on which the point lies.           */
/*                                                                           */
/*  Returns INTRIANGLE if the point lies strictly within a triangle.         */
/*  `searchtri' is a handle on the triangle that contains the point.         */
/*                                                                           */
/*  Returns OUTSIDE if the point lies outside the mesh.  `searchtri' is a    */
/*  handle whose primary edge the point is to the right of.  This might      */
/*  occur when the circumcenter of a triangle falls just slightly outside    */
/*  the mesh due to floating-point roundoff error.  It also occurs when      */
/*  seeking a hole or region point that a foolish user has placed outside    */
/*  the mesh.                                                                */
/*                                                                           */
/*  If `stopatsubsegment' is nonzero, the search will stop if it tries to    */
/*  walk through a subsegment, and will return OUTSIDE.                      */
/*                                                                           */
/*  WARNING:  This routine is designed for convex triangulations, and will   */
/*  not generally work after the holes and concavities have been carved.     */
/*  However, it can still be used to find the circumcenter of a triangle, as */
/*  long as the search is begun from the triangle in question.               */
/*                                                                           */
/*****************************************************************************/

#ifdef ANSI_DECLARATORS
enum locateresult preciselocate(struct mesh *m, struct behavior *b,
	vertex searchpoint, struct otri *searchtri,
	int stopatsubsegment)
#else /* not ANSI_DECLARATORS */
enum locateresult preciselocate(m, b, searchpoint, searchtri, stopatsubsegment)
struct mesh *m;
struct behavior *b;
vertex searchpoint;
struct otri *searchtri;
int stopatsubsegment;
#endif /* not ANSI_DECLARATORS */

{
	struct otri backtracktri;
	struct osub checkedge;
	vertex forg, fdest, fapex;
	REAL orgorient, destorient;
	int moveleft;
	triangle ptr;                         /* Temporary variable used by sym(). */
	subseg sptr;                      /* Temporary variable used by tspivot(). */

	if (b->verbose > 2) {
		printf("  Searching for point (%.12g, %.12g).\n",
			searchpoint[0], searchpoint[1]);
	}
	/* Where are we? */
	org(*searchtri, forg);
	dest(*searchtri, fdest);
	apex(*searchtri, fapex);
	while (1) {
		if (b->verbose > 2) {
			printf("    At (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
				forg[0], forg[1], fdest[0], fdest[1], fapex[0], fapex[1]);
		}
		/* Check whether the apex is the point we seek. */
		if ((fapex[0] == searchpoint[0]) && (fapex[1] == searchpoint[1])) {
			lprevself(*searchtri);
			return ONVERTEX;
		}
		/* Does the point lie on the other side of the line defined by the */
		/*   triangle edge opposite the triangle's destination?            */
		destorient = counterclockwise(m, b, forg, fapex, searchpoint);
		/* Does the point lie on the other side of the line defined by the */
		/*   triangle edge opposite the triangle's origin?                 */
		orgorient = counterclockwise(m, b, fapex, fdest, searchpoint);
		if (destorient > 0.0) {
			if (orgorient > 0.0) {
				/* Move left if the inner product of (fapex - searchpoint) and  */
				/*   (fdest - forg) is positive.  This is equivalent to drawing */
				/*   a line perpendicular to the line (forg, fdest) and passing */
				/*   through `fapex', and determining which side of this line   */
				/*   `searchpoint' falls on.                                    */
				moveleft = (fapex[0] - searchpoint[0]) * (fdest[0] - forg[0]) +
					(fapex[1] - searchpoint[1]) * (fdest[1] - forg[1]) > 0.0;
			}
			else {
				moveleft = 1;
			}
		}
		else {
			if (orgorient > 0.0) {
				moveleft = 0;
			}
			else {
				/* The point we seek must be on the boundary of or inside this */
				/*   triangle.                                                 */
				if (destorient == 0.0) {
					lprevself(*searchtri);
					return ONEDGE;
				}
				if (orgorient == 0.0) {
					lnextself(*searchtri);
					return ONEDGE;
				}
				return INTRIANGLE;
			}
		}

		/* Move to another triangle.  Leave a trace `backtracktri' in case */
		/*   floating-point roundoff or some such bogey causes us to walk  */
		/*   off a boundary of the triangulation.                          */
		if (moveleft) {
			lprev(*searchtri, backtracktri);
			fdest = fapex;
		}
		else {
			lnext(*searchtri, backtracktri);
			forg = fapex;
		}
		sym(backtracktri, *searchtri);

		if (m->checksegments && stopatsubsegment) {
			/* Check for walking through a subsegment. */
			tspivot(backtracktri, checkedge);
			if (checkedge.ss != m->dummysub) {
				/* Go back to the last triangle. */
				otricopy(backtracktri, *searchtri);
				return OUTSIDE;
			}
		}
		/* Check for walking right out of the triangulation. */
		if (searchtri->tri == m->dummytri) {
			/* Go back to the last triangle. */
			otricopy(backtracktri, *searchtri);
			return OUTSIDE;
		}

		apex(*searchtri, fapex);
	}
}

/*****************************************************************************/
/*                                                                           */
/*  locate()   Find a triangle or edge containing a given point.             */
/*                                                                           */
/*  Searching begins from one of:  the input `searchtri', a recently         */
/*  encountered triangle `recenttri', or from a triangle chosen from a       */
/*  random sample.  The choice is made by determining which triangle's       */
/*  origin is closest to the point we are searching for.  Normally,          */
/*  `searchtri' should be a handle on the convex hull of the triangulation.  */
/*                                                                           */
/*  Details on the random sampling method can be found in the Mucke, Saias,  */
/*  and Zhu paper cited in the header of this code.                          */
/*                                                                           */
/*  On completion, `searchtri' is a triangle that contains `searchpoint'.    */
/*                                                                           */
/*  Returns ONVERTEX if the point lies on an existing vertex.  `searchtri'   */
/*  is a handle whose origin is the existing vertex.                         */
/*                                                                           */
/*  Returns ONEDGE if the point lies on a mesh edge.  `searchtri' is a       */
/*  handle whose primary edge is the edge on which the point lies.           */
/*                                                                           */
/*  Returns INTRIANGLE if the point lies strictly within a triangle.         */
/*  `searchtri' is a handle on the triangle that contains the point.         */
/*                                                                           */
/*  Returns OUTSIDE if the point lies outside the mesh.  `searchtri' is a    */
/*  handle whose primary edge the point is to the right of.  This might      */
/*  occur when the circumcenter of a triangle falls just slightly outside    */
/*  the mesh due to floating-point roundoff error.  It also occurs when      */
/*  seeking a hole or region point that a foolish user has placed outside    */
/*  the mesh.                                                                */
/*                                                                           */
/*  WARNING:  This routine is designed for convex triangulations, and will   */
/*  not generally work after the holes and concavities have been carved.     */
/*                                                                           */
/*****************************************************************************/

#ifdef ANSI_DECLARATORS
enum locateresult locate(struct mesh *m, struct behavior *b,
	vertex searchpoint, struct otri *searchtri)
#else /* not ANSI_DECLARATORS */
enum locateresult locate(m, b, searchpoint, searchtri)
struct mesh *m;
struct behavior *b;
vertex searchpoint;
struct otri *searchtri;
#endif /* not ANSI_DECLARATORS */

{
	VOID **sampleblock;
	char *firsttri;
	struct otri sampletri;
	vertex torg, tdest;
	unsigned long alignptr;
	REAL searchdist, dist;
	REAL ahead;
	long samplesperblock, totalsamplesleft, samplesleft;
	long population, totalpopulation;
	triangle ptr;                         /* Temporary variable used by sym(). */

	if (b->verbose > 2) {
		printf("  Randomly sampling for a triangle near point (%.12g, %.12g).\n",
			searchpoint[0], searchpoint[1]);
	}
	/* Record the distance from the suggested starting triangle to the */
	/*   point we seek.                                                */
	org(*searchtri, torg);
	searchdist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) +
		(searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]);
	if (b->verbose > 2) {
		printf("    Boundary triangle has origin (%.12g, %.12g).\n",
			torg[0], torg[1]);
	}

	/* If a recently encountered triangle has been recorded and has not been */
	/*   deallocated, test it as a good starting point.                      */
	if (m->recenttri.tri != (triangle *)NULL) {
		if (!deadtri(m->recenttri.tri)) {
			org(m->recenttri, torg);
			if ((torg[0] == searchpoint[0]) && (torg[1] == searchpoint[1])) {
				otricopy(m->recenttri, *searchtri);
				return ONVERTEX;
			}
			dist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) +
				(searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]);
			if (dist < searchdist) {
				otricopy(m->recenttri, *searchtri);
				searchdist = dist;
				if (b->verbose > 2) {
					printf("    Choosing recent triangle with origin (%.12g, %.12g).\n",
						torg[0], torg[1]);
				}
			}
		}
	}

	/* The number of random samples taken is proportional to the cube root of */
	/*   the number of triangles in the mesh.  The next bit of code assumes   */
	/*   that the number of triangles increases monotonically (or at least    */
	/*   doesn't decrease enough to matter).                                  */
	while (SAMPLEFACTOR * m->samples * m->samples * m->samples <
		m->triangles.items) {
		m->samples++;
	}

	/* We'll draw ceiling(samples * TRIPERBLOCK / maxitems) random samples  */
	/*   from each block of triangles (except the first)--until we meet the */
	/*   sample quota.  The ceiling means that blocks at the end might be   */
	/*   neglected, but I don't care.                                       */
	samplesperblock = (m->samples * TRIPERBLOCK - 1) / m->triangles.maxitems + 1;
	/* We'll draw ceiling(samples * itemsfirstblock / maxitems) random samples */
	/*   from the first block of triangles.                                    */
	samplesleft = (m->samples * m->triangles.itemsfirstblock - 1) /
		m->triangles.maxitems + 1;
	totalsamplesleft = m->samples;
	population = m->triangles.itemsfirstblock;
	totalpopulation = m->triangles.maxitems;
	sampleblock = m->triangles.firstblock;
	sampletri.orient = 0;
	while (totalsamplesleft > 0) {
		/* If we're in the last block, `population' needs to be corrected. */
		if (population > totalpopulation) {
			population = totalpopulation;
		}
		/* Find a pointer to the first triangle in the block. */
		alignptr = (unsigned long)(sampleblock + 1);
		firsttri = (char *)(alignptr +
			(unsigned long)m->triangles.alignbytes -
			(alignptr %
				(unsigned long)m->triangles.alignbytes));

		/* Choose `samplesleft' randomly sampled triangles in this block. */
		do {
			sampletri.tri = (triangle *)(firsttri +
				(randomnation((unsigned int)population) *
					m->triangles.itembytes));
			if (!deadtri(sampletri.tri)) {
				org(sampletri, torg);
				dist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) +
					(searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]);
				if (dist < searchdist) {
					otricopy(sampletri, *searchtri);
					searchdist = dist;
					if (b->verbose > 2) {
						printf("    Choosing triangle with origin (%.12g, %.12g).\n",
							torg[0], torg[1]);
					}
				}
			}

			samplesleft--;
			totalsamplesleft--;
		} while ((samplesleft > 0) && (totalsamplesleft > 0));

		if (totalsamplesleft > 0) {
			sampleblock = (VOID **)*sampleblock;
			samplesleft = samplesperblock;
			totalpopulation -= population;
			population = TRIPERBLOCK;
		}
	}

	/* Where are we? */
	org(*searchtri, torg);
	dest(*searchtri, tdest);
	/* Check the starting triangle's vertices. */
	if ((torg[0] == searchpoint[0]) && (torg[1] == searchpoint[1])) {
		return ONVERTEX;
	}
	if ((tdest[0] == searchpoint[0]) && (tdest[1] == searchpoint[1])) {
		lnextself(*searchtri);
		return ONVERTEX;
	}
	/* Orient `searchtri' to fit the preconditions of calling preciselocate(). */
	ahead = counterclockwise(m, b, torg, tdest, searchpoint);
	if (ahead < 0.0) {
		/* Turn around so that `searchpoint' is to the left of the */
		/*   edge specified by `searchtri'.                        */
		symself(*searchtri);
	}
	else if (ahead == 0.0) {
		/* Check if `searchpoint' is between `torg' and `tdest'. */
		if (((torg[0] < searchpoint[0]) == (searchpoint[0] < tdest[0])) &&
			((torg[1] < searchpoint[1]) == (searchpoint[1] < tdest[1]))) {
			return ONEDGE;
		}
	}
	return preciselocate(m, b, searchpoint, searchtri, 0);
}

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

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

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

#ifdef ANSI_DECLARATORS
void insertsubseg(struct mesh *m, struct behavior *b, struct otri *tri,
	int subsegmark)
#else /* not ANSI_DECLARATORS */
void insertsubseg(m, b, tri, subsegmark)
struct mesh *m;
struct behavior *b;
struct otri *tri;             /* Edge at which to insert the new subsegment. */
int subsegmark;                            /* Marker for the new subsegment. */
#endif /* not ANSI_DECLARATORS */

{
	struct otri oppotri;
	struct osub newsubseg;
	vertex triorg, tridest;
	triangle ptr;                         /* Temporary variable used by sym(). */
	subseg sptr;                      /* Temporary variable used by tspivot(). */

	org(*tri, triorg);
	dest(*tri, tridest);
	/* Mark vertices if possible. */
	if (vertexmark(triorg) == 0) {
		setvertexmark(triorg, subsegmark);
	}
	if (vertexmark(tridest) == 0) {
		setvertexmark(tridest, subsegmark);
	}
	/* Check if there's already a subsegment here. */
	tspivot(*tri, newsubseg);
	if (newsubseg.ss == m->dummysub) {
		/* Make new subsegment and initialize its vertices. */
		makesubseg(m, &newsubseg);
		setsorg(newsubseg, tridest);
		setsdest(newsubseg, triorg);
		setsegorg(newsubseg, tridest);
		setsegdest(newsubseg, triorg);
		/* Bond new subsegment to the two triangles it is sandwiched between. */
		/*   Note that the facing triangle `oppotri' might be equal to        */
		/*   `dummytri' (outer space), but the new subsegment is bonded to it */
		/*   all the same.                                                    */
		tsbond(*tri, newsubseg);
		sym(*tri, oppotri);
		ssymself(newsubseg);
		tsbond(oppotri, newsubseg);
		setmark(newsubseg, subsegmark);
		if (b->verbose > 2) {
			printf("  Inserting new ");
			printsubseg(m, b, &newsubseg);
		}
	}
	else {
		if (mark(newsubseg) == 0) {
			setmark(newsubseg, subsegmark);
		}
	}
}

/*****************************************************************************/
/*                                                                           */
/*  Terminology                                                              */
/*                                                                           */
/*  A "local transformation" replaces a small set of triangles with another  */
/*  set of triangles.  This may or may not involve inserting or deleting a   */
/*  vertex.                                                                  */
/*                                                                           */
/*  The term "casing" is used to describe the set of triangles that are      */
/*  attached to the triangles being transformed, but are not transformed     */
/*  themselves.  Think of the casing as a fixed hollow structure inside      */
/*  which all the action happens.  A "casing" is only defined relative to    */
/*  a single transformation; each occurrence of a transformation will        */
/*  involve a different casing.                                              */
/*                                                                           */
/*****************************************************************************/

/*****************************************************************************/
/*                                                                           */
/*  flip()   Transform two triangles to two different triangles by flipping  */
/*           an edge counterclockwise within a quadrilateral.                */
/*                                                                           */
/*  Imagine the original triangles, abc and bad, oriented so that the        */
/*  shared edge ab lies in a horizontal plane, with the vertex b on the left */
/*  and the vertex a on the right.  The vertex c lies below the edge, and    */
/*  the vertex d lies above the edge.  The `flipedge' handle holds the edge  */
/*  ab of triangle abc, and is directed left, from vertex a to vertex b.     */
/*                                                                           */
/*  The triangles abc and bad are deleted and replaced by the triangles cdb  */
/*  and dca.  The triangles that represent abc and bad are NOT deallocated;  */
/*  they are reused for dca and cdb, respectively.  Hence, any handles that  */
/*  may have held the original triangles are still valid, although not       */
/*  directed as they were before.                                            */
/*                                                                           */
/*  Upon completion of this routine, the `flipedge' handle holds the edge    */
/*  dc of triangle dca, and is directed down, from vertex d to vertex c.     */
/*  (Hence, the two triangles have rotated counterclockwise.)                */
/*                                                                           */
/*  WARNING:  This transformation is geometrically valid only if the         */
/*  quadrilateral adbc is convex.  Furthermore, this transformation is       */
/*  valid only if there is not a subsegment between the triangles abc and    */
/*  bad.  This routine does not check either of these preconditions, and     */
/*  it is the responsibility of the calling routine to ensure that they are  */
/*  met.  If they are not, the streets shall be filled with wailing and      */
/*  gnashing of teeth.                                                       */
/*                                                                           */
/*****************************************************************************/

#ifdef ANSI_DECLARATORS
void flip(struct mesh *m, struct behavior *b, struct otri *flipedge)
#else /* not ANSI_DECLARATORS */
void flip(m, b, flipedge)
struct mesh *m;
struct behavior *b;
struct otri *flipedge;                    /* Handle for the triangle abc. */
#endif /* not ANSI_DECLARATORS */

{
	struct otri botleft, botright;
	struct otri topleft, topright;
	struct otri top;
	struct otri botlcasing, botrcasing;
	struct otri toplcasing, toprcasing;
	struct osub botlsubseg, botrsubseg;
	struct osub toplsubseg, toprsubseg;
	vertex leftvertex, rightvertex, botvertex;
	vertex farvertex;
	triangle ptr;                         /* Temporary variable used by sym(). */
	subseg sptr;                      /* Temporary variable used by tspivot(). */

									  /* Identify the vertices of the quadrilateral. */
	org(*flipedge, rightvertex);
	dest(*flipedge, leftvertex);
	apex(*flipedge, botvertex);
	sym(*flipedge, top);
#ifdef SELF_CHECK
	if (top.tri == m->dummytri) {
		printf("Internal error in flip():  Attempt to flip on boundary.\n");
		lnextself(*flipedge);
		return;
	}
	if (m->checksegments) {
		tspivot(*flipedge, toplsubseg);
		if (toplsubseg.ss != m->dummysub) {
			printf("Internal error in flip():  Attempt to flip a segment.\n");
			lnextself(*flipedge);
			return;
		}
	}
#endif /* SELF_CHECK */
	apex(top, farvertex);

	/* Identify the casing of the quadrilateral. */
	lprev(top, topleft);
	sym(topleft, toplcasing);
	lnext(top, topright);
	sym(topright, toprcasing);
	lnext(*flipedge, botleft);
	sym(botleft, botlcasing);
	lprev(*flipedge, botright);
	sym(botright, botrcasing);
	/* Rotate the quadrilateral one-quarter turn counterclockwise. */
	bond(topleft, botlcasing);
	bond(botleft, botrcasing);
	bond(botright, toprcasing);
	bond(topright, toplcasing);

	if (m->checksegments) {
		/* Check for subsegments and rebond them to the quadrilateral. */
		tspivot(topleft, toplsubseg);
		tspivot(botleft, botlsubseg);
		tspivot(botright, botrsubseg);
		tspivot(topright, toprsubseg);
		if (toplsubseg.ss == m->dummysub) {
			tsdissolve(topright);
		}
		else {
			tsbond(topright, toplsubseg);
		}
		if (botlsubseg.ss == m->dummysub) {
			tsdissolve(topleft);
		}
		else {
			tsbond(topleft, botlsubseg);
		}
		if (botrsubseg.ss == m->dummysub) {
			tsdissolve(botleft);
		}
		else {
			tsbond(botleft, botrsubseg);
		}
		if (toprsubseg.ss == m->dummysub) {
			tsdissolve(botright);
		}
		else {
			tsbond(botright, toprsubseg);
		}
	}

	/* New vertex assignments for the rotated quadrilateral. */
	setorg(*flipedge, farvertex);
	setdest(*flipedge, botvertex);
	setapex(*flipedge, rightvertex);
	setorg(top, botvertex);
	setdest(top, farvertex);
	setapex(top, leftvertex);
	if (b->verbose > 2) {
		printf("  Edge flip results in left ");
		printtriangle(m, b, &top);
		printf("  and right ");
		printtriangle(m, b, flipedge);
	}
}

/*****************************************************************************/
/*                                                                           */
/*  unflip()   Transform two triangles to two different triangles by         */
/*             flipping an edge clockwise within a quadrilateral.  Reverses  */
/*             the flip() operation so that the data structures representing */
/*             the triangles are back where they were before the flip().     */
/*                                                                           */
/*  Imagine the original triangles, abc and bad, oriented so that the        */
/*  shared edge ab lies in a horizontal plane, with the vertex b on the left */
/*  and the vertex a on the right.  The vertex c lies below the edge, and    */
/*  the vertex d lies above the edge.  The `flipedge' handle holds the edge  */
/*  ab of triangle abc, and is directed left, from vertex a to vertex b.     */
/*                                                                           */
/*  The triangles abc and bad are deleted and replaced by the triangles cdb  */
/*  and dca.  The triangles that represent abc and bad are NOT deallocated;  */
/*  they are reused for cdb and dca, respectively.  Hence, any handles that  */
/*  may have held the original triangles are still valid, although not       */
/*  directed as they were before.                                            */
/*                                                                           */
/*  Upon completion of this routine, the `flipedge' handle holds the edge    */
/*  cd of triangle cdb, and is directed up, from vertex c to vertex d.       */
/*  (Hence, the two triangles have rotated clockwise.)                       */
/*                                                                           */
/*  WARNING:  This transformation is geometrically valid only if the         */
/*  quadrilateral adbc is convex.  Furthermore, this transformation is       */
/*  valid only if there is not a subsegment between the triangles abc and    */
/*  bad.  This routine does not check either of these preconditions, and     */
/*  it is the responsibility of the calling routine to ensure that they are  */
/*  met.  If they are not, the streets shall be filled with wailing and      */
/*  gnashing of teeth.                                                       */
/*                                                                           */
/*****************************************************************************/

#ifdef ANSI_DECLARATORS
void unflip(struct mesh *m, struct behavior *b, struct otri *flipedge)
#else /* not ANSI_DECLARATORS */
void unflip(m, b, flipedge)
struct mesh *m;
struct behavior *b;
struct otri *flipedge;                    /* Handle for the triangle abc. */
#endif /* not ANSI_DECLARATORS */

{
	struct otri botleft, botright;
	struct otri topleft, topright;
	struct otri top;
	struct otri botlcasing, botrcasing;
	struct otri toplcasing, toprcasing;
	struct osub botlsubseg, botrsubseg;
	struct osub toplsubseg, toprsubseg;
	vertex leftvertex, rightvertex, botvertex;
	vertex farvertex;
	triangle ptr;                         /* Temporary variable used by sym(). */
	subseg sptr;                      /* Temporary variable used by tspivot(). */

									  /* Identify the vertices of the quadrilateral. */
	org(*flipedge, rightvertex);
	dest(*flipedge, leftvertex);
	apex(*flipedge, botvertex);
	sym(*flipedge, top);
#ifdef SELF_CHECK
	if (top.tri == m->dummytri) {
		printf("Internal error in unflip():  Attempt to flip on boundary.\n");
		lnextself(*flipedge);
		return;
	}
	if (m->checksegments) {
		tspivot(*flipedge, toplsubseg);
		if (toplsubseg.ss != m->dummysub) {
			printf("Internal error in unflip():  Attempt to flip a subsegment.\n");
			lnextself(*flipedge);
			return;
		}
	}
#endif /* SELF_CHECK */
	apex(top, farvertex);

	/* Identify the casing of the quadrilateral. */
	lprev(top, topleft);
	sym(topleft, toplcasing);
	lnext(top, topright);
	sym(topright, toprcasing);
	lnext(*flipedge, botleft);
	sym(botleft, botlcasing);
	lprev(*flipedge, botright);
	sym(botright, botrcasing);
	/* Rotate the quadrilateral one-quarter turn clockwise. */
	bond(topleft, toprcasing);
	bond(botleft, toplcasing);
	bond(botright, botlcasing);
	bond(topright, botrcasing);

	if (m->checksegments) {
		/* Check for subsegments and rebond them to the quadrilateral. */
		tspivot(topleft, toplsubseg);
		tspivot(botleft, botlsubseg);
		tspivot(botright, botrsubseg);
		tspivot(topright, toprsubseg);
		if (toplsubseg.ss == m->dummysub) {
			tsdissolve(botleft);
		}
		else {
			tsbond(botleft, toplsubseg);
		}
		if (botlsubseg.ss == m->dummysub) {
			tsdissolve(botright);
		}
		else {
			tsbond(botright, botlsubseg);
		}
		if (botrsubseg.ss == m->dummysub) {
			tsdissolve(topright);
		}
		else {
			tsbond(topright, botrsubseg);
		}
		if (toprsubseg.ss == m->dummysub) {
			tsdissolve(topleft);
		}
		else {
			tsbond(topleft, toprsubseg);
		}
	}

	/* New vertex assignments for the rotated quadrilateral. */
	setorg(*flipedge, botvertex);
	setdest(*flipedge, farvertex);
	setapex(*flipedge, leftvertex);
	setorg(top, farvertex);
	setdest(top, botvertex);
	setapex(top, rightvertex);
	if (b->verbose > 2) {
		printf("  Edge unflip results in left ");
		printtriangle(m, b, flipedge);
		printf("  and right ");
		printtriangle(m, b, &top);
	}
}

/*****************************************************************************/
/*                                                                           */
/*  insertvertex()   Insert a vertex into a Delaunay triangulation,          */
/*                   performing flips as necessary to maintain the Delaunay  */
/*                   property.                                               */
/*                                                                           */
/*  The point `insertvertex' is located.  If `searchtri.tri' is not NULL,    */
/*  the search for the containing triangle begins from `searchtri'.  If      */
/*  `searchtri.tri' is NULL, a full point location procedure is called.      */
/*  If `insertvertex' is found inside a triangle, the triangle is split into */
/*  three; if `insertvertex' lies on an edge, the edge is split in two,      */
/*  thereby splitting the two adjacent triangles into four.  Edge flips are  */
/*  used to restore the Delaunay property.  If `insertvertex' lies on an     */
/*  existing vertex, no action is taken, and the value DUPLICATEVERTEX is    */
/*  returned.  On return, `searchtri' is set to a handle whose origin is the */
/*  existing vertex.                                                         */
/*                                                                           */
/*  Normally, the parameter `splitseg' is set to NULL, implying that no      */
/*  subsegment should be split.  In this case, if `insertvertex' is found to */
/*  lie on a segment, no action is taken, and the value VIOLATINGVERTEX is   */
/*  returned.  On return, `searchtri' is set to a handle whose primary edge  */
/*  is the violated subsegment.                                              */
/*                                                                           */
/*  If the calling routine wishes to split a subsegment by inserting a       */
/*  vertex in it, the parameter `splitseg' should be that subsegment.  In    */
/*  this case, `searchtri' MUST be the triangle handle reached by pivoting   */
/*  from that subsegment; no point location is done.                         */
/*                                                                           */
/*  `segmentflaws' and `triflaws' are flags that indicate whether or not     */
/*  there should be checks for the creation of encroached subsegments or bad */
/*  quality triangles.  If a newly inserted vertex encroaches upon           */
/*  subsegments, these subsegments are added to the list of subsegments to   */
/*  be split if `segmentflaws' is set.  If bad triangles are created, these  */
/*  are added to the queue if `triflaws' is set.                             */
/*                                                                           */
/*  If a duplicate vertex or violated segment does not prevent the vertex    */
/*  from being inserted, the return value will be ENCROACHINGVERTEX if the   */
/*  vertex encroaches upon a subsegment (and checking is enabled), or        */
/*  SUCCESSFULVERTEX otherwise.  In either case, `searchtri' is set to a     */
/*  handle whose origin is the newly inserted vertex.                        */
/*                                                                           */
/*  insertvertex() does not use flip() for reasons of speed; some            */
/*  information can be reused from edge flip to edge flip, like the          */
/*  locations of subsegments.                                                */
/*                                                                           */
/*****************************************************************************/

#ifdef ANSI_DECLARATORS
enum insertvertexresult insertvertex(struct mesh *m, struct behavior *b,
	vertex newvertex, struct otri *searchtri,
struct osub *splitseg,
	int segmentflaws, int triflaws)
#else /* not ANSI_DECLARATORS */
enum insertvertexresult insertvertex(m, b, newvertex, searchtri, splitseg,
	segmentflaws, triflaws)
struct mesh *m;
struct behavior *b;
vertex newvertex;
struct otri *searchtri;
struct osub *splitseg;
int segmentflaws;
int triflaws;
#endif /* not ANSI_DECLARATORS */

{
	struct otri horiz;
	struct otri top;
	struct otri botleft, botright;
	struct otri topleft, topright;
	struct otri newbotleft, newbotright;
	struct otri newtopright;
	struct otri botlcasing, botrcasing;
	struct otri toplcasing, toprcasing;
	struct otri testtri;
	struct osub botlsubseg, botrsubseg;
	struct osub toplsubseg, toprsubseg;
	struct osub brokensubseg;
	struct osub checksubseg;
	struct osub rightsubseg;
	struct osub newsubseg;
	struct badsubseg *encroached;
	struct flipstacker *newflip;
	vertex first;
	vertex leftvertex, rightvertex, botvertex, topvertex, farvertex;
	vertex segmentorg, segmentdest;
	REAL attrib;
	REAL area;
	enum insertvertexresult success;
	enum locateresult intersect;
	int doflip;
	int mirrorflag;
	int enq;
	int i;
	triangle ptr;                         /* Temporary variable used by sym(). */
	subseg sptr;         /* Temporary variable used by spivot() and tspivot(). */

	if (b->verbose > 1) {
		printf("  Inserting (%.12g, %.12g).\n", newvertex[0], newvertex[1]);
	}

	if (splitseg == (struct osub *) NULL) {
		/* Find the location of the vertex to be inserted.  Check if a good */
		/*   starting triangle has already been provided by the caller.     */
		if (searchtri->tri == m->dummytri) {
			/* Find a boundary triangle. */
			horiz.tri = m->dummytri;
			horiz.orient = 0;
			symself(horiz);
			/* Search for a triangle containing `newvertex'. */
			intersect = locate(m, b, newvertex, &horiz);
		}
		else {
			/* Start searching from the triangle provided by the caller. */
			otricopy(*searchtri, horiz);
			intersect = preciselocate(m, b, newvertex, &horiz, 1);
		}
	}
	else {
		/* The calling routine provides the subsegment in which */
		/*   the vertex is inserted.                             */
		otricopy(*searchtri, horiz);
		intersect = ONEDGE;
	}

	if (intersect == ONVERTEX) {
		/* There's already a vertex there.  Return in `searchtri' a triangle */
		/*   whose origin is the existing vertex.                            */
		otricopy(horiz, *searchtri);
		otricopy(horiz, m->recenttri);
		return DUPLICATEVERTEX;
	}
	if ((intersect == ONEDGE) || (intersect == OUTSIDE)) {
		/* The vertex falls on an edge or boundary. */
		if (m->checksegments && (splitseg == (struct osub *) NULL)) {
			/* Check whether the vertex falls on a subsegment. */
			tspivot(horiz, brokensubseg);
			if (brokensubseg.ss != m->dummysub) {
				/* The vertex falls on a subsegment, and hence will not be inserted. */
				if (segmentflaws) {
					enq = b->nobisect != 2;
					if (enq && (b->nobisect == 1)) {
						/* This subsegment may be split only if it is an */
						/*   internal boundary.                          */
						sym(horiz, testtri);
						enq = testtri.tri != m->dummytri;
					}
					if (enq) {
						/* Add the subsegment to the list of encroached subsegments. */
						encroached = (struct badsubseg *) poolalloc(&m->badsubsegs);
						encroached->encsubseg = sencode(brokensubseg);
						sorg(brokensubseg, encroached->subsegorg);
						sdest(brokensubseg, encroached->subsegdest);
						if (b->verbose > 2) {
							printf(
								"  Queueing encroached subsegment (%.12g, %.12g) (%.12g, %.12g).\n",
								encroached->subsegorg[0], encroached->subsegorg[1],
								encroached->subsegdest[0], encroached->subsegdest[1]);
						}
					}
				}
				/* Return a handle whose primary edge contains the vertex, */
				/*   which has not been inserted.                          */
				otricopy(horiz, *searchtri);
				otricopy(horiz, m->recenttri);
				return VIOLATINGVERTEX;
			}
		}

		/* Insert the vertex on an edge, dividing one triangle into two (if */
		/*   the edge lies on a boundary) or two triangles into four.       */
		lprev(horiz, botright);
		sym(botright, botrcasing);
		sym(horiz, topright);
		/* Is there a second triangle?  (Or does this edge lie on a boundary?) */
		mirrorflag = topright.tri != m->dummytri;
		if (mirrorflag) {
			lnextself(topright);
			sym(topright, toprcasing);
			maketriangle(m, b, &newtopright);
		}
		else {
			/* Splitting a boundary edge increases the number of boundary edges. */
			m->hullsize++;
		}
		maketriangle(m, b, &newbotright);

		/* Set the vertices of changed and new triangles. */
		org(horiz, rightvertex);
		dest(horiz, leftvertex);
		apex(horiz, botvertex);
		setorg(newbotright, botvertex);
		setdest(newbotright, rightvertex);
		setapex(newbotright, newvertex);
		setorg(horiz, newvertex);
		for (i = 0; i < m->eextras; i++) {
			/* Set the element attributes of a new triangle. */
			setelemattribute(newbotright, i, elemattribute(botright, i));
		}
		if (b->vararea) {
			/* Set the area constraint of a new triangle. */
			setareabound(newbotright, areabound(botright));
		}
		if (mirrorflag) {
			dest(topright, topvertex);
			setorg(newtopright, rightvertex);
			setdest(newtopright, topvertex);
			setapex(newtopright, newvertex);
			setorg(topright, newvertex);
			for (i = 0; i < m->eextras; i++) {
				/* Set the element attributes of another new triangle. */
				setelemattribute(newtopright, i, elemattribute(topright, i));
			}
			if (b->vararea) {
				/* Set the area constraint of another new triangle. */
				setareabound(newtopright, areabound(topright));
			}
		}

		/* There may be subsegments that need to be bonded */
		/*   to the new triangle(s).                       */
		if (m->checksegments) {
			tspivot(botright, botrsubseg);
			if (botrsubseg.ss != m->dummysub) {
				tsdissolve(botright);
				tsbond(newbotright, botrsubseg);
			}
			if (mirrorflag) {
				tspivot(topright, toprsubseg);
				if (toprsubseg.ss != m->dummysub) {
					tsdissolve(topright);
					tsbond(newtopright, toprsubseg);
				}
			}
		}

		/* Bond the new triangle(s) to the surrounding triangles. */
		bond(newbotright, botrcasing);
		lprevself(newbotright);
		bond(newbotright, botright);
		lprevself(newbotright);
		if (mirrorflag) {
			bond(newtopright, toprcasing);
			lnextself(newtopright);
			bond(newtopright, topright);
			lnextself(newtopright);
			bond(newtopright, newbotright);
		}

		if (splitseg != (struct osub *) NULL) {
			/* Split the subsegment into two. */
			setsdest(*splitseg, newvertex);
			segorg(*splitseg, segmentorg);
			segdest(*splitseg, segmentdest);
			ssymself(*splitseg);
			spivot(*splitseg, rightsubseg);
			insertsubseg(m, b, &newbotright, mark(*splitseg));
			tspivot(newbotright, newsubseg);
			setsegorg(newsubseg, segmentorg);
			setsegdest(newsubseg, segmentdest);
			sbond(*splitseg, newsubseg);
			ssymself(newsubseg);
			sbond(newsubseg, rightsubseg);
			ssymself(*splitseg);
			/* Transfer the subsegment's boundary marker to the vertex */
			/*   if required.                                          */
			if (vertexmark(newvertex) == 0) {
				setvertexmark(newvertex, mark(*splitseg));
			}
		}

		if (m->checkquality) {
			poolrestart(&m->flipstackers);
			m->lastflip = (struct flipstacker *) poolalloc(&m->flipstackers);
			m->lastflip->flippedtri = encode(horiz);
			m->lastflip->prevflip = (struct flipstacker *) &insertvertex;
		}

#ifdef SELF_CHECK
		if (counterclockwise(m, b, rightvertex, leftvertex, botvertex) < 0.0) {
			printf("Internal error in insertvertex():\n");
			printf(
				"  Clockwise triangle prior to edge vertex insertion (bottom).\n");
		}
		if (mirrorflag) {
			if (counterclockwise(m, b, leftvertex, rightvertex, topvertex) < 0.0) {
				printf("Internal error in insertvertex():\n");
				printf("  Clockwise triangle prior to edge vertex insertion (top).\n");
			}
			if (counterclockwise(m, b, rightvertex, topvertex, newvertex) < 0.0) {
				printf("Internal error in insertvertex():\n");
				printf(
					"  Clockwise triangle after edge vertex insertion (top right).\n");
			}
			if (counterclockwise(m, b, topvertex, leftvertex, newvertex) < 0.0) {
				printf("Internal error in insertvertex():\n");
				printf(
					"  Clockwise triangle after edge vertex insertion (top left).\n");
			}
		}
		if (counterclockwise(m, b, leftvertex, botvertex, newvertex) < 0.0) {
			printf("Internal error in insertvertex():\n");
			printf(
				"  Clockwise triangle after edge vertex insertion (bottom left).\n");
		}
		if (counterclockwise(m, b, botvertex, rightvertex, newvertex) < 0.0) {
			printf("Internal error in insertvertex():\n");
			printf(
				"  Clockwise triangle after edge vertex insertion (bottom right).\n");
		}
#endif /* SELF_CHECK */
		if (b->verbose > 2) {
			printf("  Updating bottom left ");
			printtriangle(m, b, &botright);
			if (mirrorflag) {
				printf("  Updating top left ");
				printtriangle(m, b, &topright);
				printf("  Creating top right ");
				printtriangle(m, b, &newtopright);
			}
			printf("  Creating bottom right ");
			printtriangle(m, b, &newbotright);
		}

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

		/* Set the vertices of changed and new triangles. */
		org(horiz, rightvertex);
		dest(horiz, leftvertex);
		apex(horiz, botvertex);
		setorg(newbotleft, leftvertex);
		setdest(newbotleft, botvertex);
		setapex(newbotleft, newvertex);
		setorg(newbotright, botvertex);
		setdest(newbotright, rightvertex);
		setapex(newbotright, newvertex);
		setapex(horiz, newvertex);
		for (i = 0; i < m->eextras; i++) {
			/* Set the element attributes of the new triangles. */
			attrib = elemattribute(horiz, i);
			setelemattribute(newbotleft, i, attrib);
			setelemattribute(newbotright, i, attrib);
		}
		if (b->vararea) {
			/* Set the area constraint of the new triangles. */
			area = areabound(horiz);
			setareabound(newbotleft, area);
			setareabound(newbotright, area);
		}

		/* There may be subsegments that need to be bonded */
		/*   to the new triangles.                         */
		if (m->checksegments) {
			tspivot(botleft, botlsubseg);
			if (botlsubseg.ss != m->dummysub) {
				tsdissolve(botleft);
				tsbond(newbotleft, botlsubseg);
			}
			tspivot(botright, botrsubseg);
			if (botrsubseg.ss != m->dummysub) {
				tsdissolve(botright);
				tsbond(newbotright, botrsubseg);
			}
		}

		/* Bond the new triangles to the surrounding triangles. */
		bond(newbotleft, botlcasing);
		bond(newbotright, botrcasing);
		lnextself(newbotleft);
		lprevself(newbotright);
		bond(newbotleft, newbotright);
		lnextself(newbotleft);
		bond(botleft, newbotleft);
		lprevself(newbotright);
		bond(botright, newbotright);

		if (m->checkquality) {
			poolrestart(&m->flipstackers);
			m->lastflip = (struct flipstacker *) poolalloc(&m->flipstackers);
			m->lastflip->flippedtri = encode(horiz);
			m->lastflip->prevflip = (struct flipstacker *) NULL;
		}

#ifdef SELF_CHECK
		if (counterclockwise(m, b, rightvertex, leftvertex, botvertex) < 0.0) {
			printf("Internal error in insertvertex():\n");
			printf("  Clockwise triangle prior to vertex insertion.\n");
		}
		if (counterclockwise(m, b, rightvertex, leftvertex, newvertex) < 0.0) {
			printf("Internal error in insertvertex():\n");
			printf("  Clockwise triangle after vertex insertion (top).\n");
		}
		if (counterclockwise(m, b, leftvertex, botvertex, newvertex) < 0.0) {
			printf("Internal error in insertvertex():\n");
			printf("  Clockwise triangle after vertex insertion (left).\n");
		}
		if (counterclockwise(m, b, botvertex, rightvertex, newvertex) < 0.0) {
			printf("Internal error in insertvertex():\n");
			printf("  Clockwise triangle after vertex insertion (right).\n");
		}
#endif /* SELF_CHECK */
		if (b->verbose > 2) {
			printf("  Updating top ");
			printtriangle(m, b, &horiz);
			printf("  Creating left ");
			printtriangle(m, b, &newbotleft);
			printf("  Creating right ");
			printtriangle(m, b, &newbotright);
		}
	}

	/* The insertion is successful by default, unless an encroached */
	/*   subsegment is found.                                       */
	success = SUCCESSFULVERTEX;
	/* Circle around the newly inserted vertex, checking each edge opposite */
	/*   it for the Delaunay property.  Non-Delaunay edges are flipped.     */
	/*   `horiz' is always the edge being checked.  `first' marks where to  */
	/*   stop circling.                                                     */
	org(horiz, first);
	rightvertex = first;
	dest(horiz, leftvertex);
	/* Circle until finished. */
	while (1) {
		/* By default, the edge will be flipped. */
		doflip = 1;

		if (m->checksegments) {
			/* Check for a subsegment, which cannot be flipped. */
			tspivot(horiz, checksubseg);
			if (checksubseg.ss != m->dummysub) {
				/* The edge is a subsegment and cannot be flipped. */
				doflip = 0;
#ifndef CDT_ONLY
				if (segmentflaws) {
					/* Does the new vertex encroach upon this subsegment? */
					if (checkseg4encroach(m, b, &checksubseg)) {
						success = ENCROACHINGVERTEX;
					}
				}
#endif /* not CDT_ONLY */
			}
		}

		if (doflip) {
			/* Check if the edge is a boundary edge. */
			sym(horiz, top);
			if (top.tri == m->dummytri) {
				/* The edge is a boundary edge and cannot be flipped. */
				doflip = 0;
			}
			else {
				/* Find the vertex on the other side of the edge. */
				apex(top, farvertex);
				/* In the incremental Delaunay triangulation algorithm, any of      */
				/*   `leftvertex', `rightvertex', and `farvertex' could be vertices */
				/*   of the triangular bounding box.  These vertices must be        */
				/*   treated as if they are infinitely distant, even though their   */
				/*   "coordinates" are not.                                         */
				if ((leftvertex == m->infvertex1) || (leftvertex == m->infvertex2) ||
					(leftvertex == m->infvertex3)) {
					/* `leftvertex' is infinitely distant.  Check the convexity of  */
					/*   the boundary of the triangulation.  'farvertex' might be   */
					/*   infinite as well, but trust me, this same condition should */
					/*   be applied.                                                */
					doflip = counterclockwise(m, b, newvertex, rightvertex, farvertex)
		> 0.0;
				}
				else if ((rightvertex == m->infvertex1) ||
					(rightvertex == m->infvertex2) ||
					(rightvertex == m->infvertex3)) {
					/* `rightvertex' is infinitely distant.  Check the convexity of */
					/*   the boundary of the triangulation.  'farvertex' might be   */
					/*   infinite as well, but trust me, this same condition should */
					/*   be applied.                                                */
					doflip = counterclockwise(m, b, farvertex, leftvertex, newvertex)
		> 0.0;
				}
				else if ((farvertex == m->infvertex1) ||
					(farvertex == m->infvertex2) ||
					(farvertex == m->infvertex3)) {
					/* `farvertex' is infinitely distant and cannot be inside */
					/*   the circumcircle of the triangle `horiz'.            */
					doflip = 0;
				}
				else {
					/* Test whether the edge is locally Delaunay. */
					doflip = incircle(m, b, leftvertex, newvertex, rightvertex,
						farvertex) > 0.0;
				}
				if (doflip) {
					/* We made it!  Flip the edge `horiz' by rotating its containing */
					/*   quadrilateral (the two triangles adjacent to `horiz').      */
					/* Identify the casing of the quadrilateral. */
					lprev(top, topleft);
					sym(topleft, toplcasing);
					lnext(top, topright);
					sym(topright, toprcasing);
					lnext(horiz, botleft);
					sym(botleft, botlcasing);
					lprev(horiz, botright);
					sym(botright, botrcasing);
					/* Rotate the quadrilateral one-quarter turn counterclockwise. */
					bond(topleft, botlcasing);
					bond(botleft, botrcasing);
					bond(botright, toprcasing);
					bond(topright, toplcasing);
					if (m->checksegments) {
						/* Check for subsegments and rebond them to the quadrilateral. */
						tspivot(topleft, toplsubseg);
						tspivot(botleft, botlsubseg);
						tspivot(botright, botrsubseg);
						tspivot(topright, toprsubseg);
						if (toplsubseg.ss == m->dummysub) {
							tsdissolve(topright);
						}
						else {
							tsbond(topright, toplsubseg);
						}
						if (botlsubseg.ss == m->dummysub) {
							tsdissolve(topleft);
						}
						else {
							tsbond(topleft, botlsubseg);
						}
						if (botrsubseg.ss == m->dummysub) {
							tsdissolve(botleft);
						}
						else {
							tsbond(botleft, botrsubseg);
						}
						if (toprsubseg.ss == m->dummysub) {
							tsdissolve(botright);
						}
						else {
							tsbond(botright, toprsubseg);
						}
					}
					/* New vertex assignments for the rotated quadrilateral. */
					setorg(horiz, farvertex);
					setdest(horiz, newvertex);
					setapex(horiz, rightvertex);
					setorg(top, newvertex);
					setdest(top, farvertex);
					setapex(top, leftvertex);
					for (i = 0; i < m->eextras; i++) {
						/* Take the average of the two triangles' attributes. */
						attrib = 0.5 * (elemattribute(top, i) + elemattribute(horiz, i));
						setelemattribute(top, i, attrib);
						setelemattribute(horiz, i, attrib);
					}
					if (b->vararea) {
						if ((areabound(top) <= 0.0) || (areabound(horiz) <= 0.0)) {
							area = -1.0;
						}
						else {
							/* Take the average of the two triangles' area constraints.    */
							/*   This prevents small area constraints from migrating a     */
							/*   long, long way from their original location due to flips. */
							area = 0.5 * (areabound(top) + areabound(horiz));
						}
						setareabound(top, area);
						setareabound(horiz, area);
					}

					if (m->checkquality) {
						newflip = (struct flipstacker *) poolalloc(&m->flipstackers);
						newflip->flippedtri = encode(horiz);
						newflip->prevflip = m->lastflip;
						m->lastflip = newflip;
					}

#ifdef SELF_CHECK
					if (newvertex != (vertex)NULL) {
						if (counterclockwise(m, b, leftvertex, newvertex, rightvertex) <
							0.0) {
							printf("Internal error in insertvertex():\n");
							printf("  Clockwise triangle prior to edge flip (bottom).\n");
						}
						/* The following test has been removed because constrainededge() */
						/*   sometimes generates inverted triangles that insertvertex()  */
						/*   removes.                                                    */
						/*
						if (counterclockwise(m, b, rightvertex, farvertex, leftvertex) <
						0.0) {
						printf("Internal error in insertvertex():\n");
						printf("  Clockwise triangle prior to edge flip (top).\n");
						}
						*/
						if (counterclockwise(m, b, farvertex, leftvertex, newvertex) <
							0.0) {
							printf("Internal error in insertvertex():\n");
							printf("  Clockwise triangle after edge flip (left).\n");
						}
						if (counterclockwise(m, b, newvertex, rightvertex, farvertex) <
							0.0) {
							printf("Internal error in insertvertex():\n");
							printf("  Clockwise triangle after edge flip (right).\n");
						}
					}
#endif /* SELF_CHECK */
					if (b->verbose > 2) {
						printf("  Edge flip results in left ");
						lnextself(topleft);
						printtriangle(m, b, &topleft);
						printf("  and right ");
						printtriangle(m, b, &horiz);
					}
					/* On the next iterations, consider the two edges that were  */
					/*   exposed (this is, are now visible to the newly inserted */
					/*   vertex) by the edge flip.                               */
					lprevself(horiz);
					leftvertex = farvertex;
				}
			}
		}
		if (!doflip) {
			/* The handle `horiz' is accepted as locally Delaunay. */
#ifndef CDT_ONLY
			if (triflaws) {
				/* Check the triangle `horiz' for quality. */
				testtriangle(m, b, &horiz);
			}
#endif /* not CDT_ONLY */
			/* Look for the next edge around the newly inserted vertex. */
			lnextself(horiz);
			sym(horiz, testtri);
			/* Check for finishing a complete revolution about the new vertex, or */
			/*   falling outside  of the triangulation.  The latter will happen   */
			/*   when a vertex is inserted at a boundary.                         */
			if ((leftvertex == first) || (testtri.tri == m->dummytri)) {
				/* We're done.  Return a triangle whose origin is the new vertex. */
				lnext(horiz, *searchtri);
				lnext(horiz, m->recenttri);
				return success;
			}
			/* Finish finding the next edge around the newly inserted vertex. */
			lnext(testtri, horiz);
			rightvertex = leftvertex;
			dest(horiz, leftvertex);
		}
	}
}

/*****************************************************************************/
/*                                                                           */
/*  triangulatepolygon()   Find the Delaunay triangulation of a polygon that */
/*                         has a certain "nice" shape.  This includes the    */
/*                         polygons that result from deletion of a vertex or */
/*                         insertion of a segment.                           */
/*                                                                           */
/*  This is a conceptually difficult routine.  The starting assumption is    */
/*  that we have a polygon with n sides.  n - 1 of these sides are currently */
/*  represented as edges in the mesh.  One side, called the "base", need not */
/*  be.                                                                      */
/*                                                                           */
/*  Inside the polygon is a structure I call a "fan", consisting of n - 1    */
/*  triangles that share a common origin.  For each of these triangles, the  */
/*  edge opposite the origin is one of the sides of the polygon.  The        */
/*  primary edge of each triangle is the edge directed from the origin to    */
/*  the destination; note that this is not the same edge that is a side of   */
/*  the polygon.  `firstedge' is the primary edge of the first triangle.     */
/*  From there, the triangles follow in counterclockwise order about the     */
/*  polygon, until `lastedge', the primary edge of the last triangle.        */
/*  `firstedge' and `lastedge' are probably connected to other triangles     */
/*  beyond the extremes of the fan, but their identity is not important, as  */
/*  long as the fan remains connected to them.                               */
/*                                                                           */
/*  Imagine the polygon oriented so that its base is at the bottom.  This    */
/*  puts `firstedge' on the far right, and `lastedge' on the far left.       */
/*  The right vertex of the base is the destination of `firstedge', and the  */
/*  left vertex of the base is the apex of `lastedge'.                       */
/*                                                                           */
/*  The challenge now is to find the right sequence of edge flips to         */
/*  transform the fan into a Delaunay triangulation of the polygon.  Each    */
/*  edge flip effectively removes one triangle from the fan, committing it   */
/*  to the polygon.  The resulting polygon has one fewer edge.  If `doflip'  */
/*  is set, the final flip will be performed, resulting in a fan of one      */
/*  (useless?) triangle.  If `doflip' is not set, the final flip is not      */
/*  performed, resulting in a fan of two triangles, and an unfinished        */
/*  triangular polygon that is not yet filled out with a single triangle.    */
/*  On completion of the routine, `lastedge' is the last remaining triangle, */
/*  or the leftmost of the last two.                                         */
/*                                                                           */
/*  Although the flips are performed in the order described above, the       */
/*  decisions about what flips to perform are made in precisely the reverse  */
/*  order.  The recursive triangulatepolygon() procedure makes a decision,   */
/*  uses up to two recursive calls to triangulate the "subproblems"          */
/*  (polygons with fewer edges), and then performs an edge flip.             */
/*                                                                           */
/*  The "decision" it makes is which vertex of the polygon should be         */
/*  connected to the base.  This decision is made by testing every possible  */
/*  vertex.  Once the best vertex is found, the two edges that connect this  */
/*  vertex to the base become the bases for two smaller polygons.  These     */
/*  are triangulated recursively.  Unfortunately, this approach can take     */
/*  O(n^2) time not only in the worst case, but in many common cases.  It's  */
/*  rarely a big deal for vertex deletion, where n is rarely larger than     */
/*  ten, but it could be a big deal for segment insertion, especially if     */
/*  there's a lot of long segments that each cut many triangles.  I ought to */
/*  code a faster algorithm some day.                                        */
/*                                                                           */
/*  The `edgecount' parameter is the number of sides of the polygon,         */
/*  including its base.  `triflaws' is a flag that determines whether the    */
/*  new triangles should be tested for quality, and enqueued if they are     */
/*  bad.                                                                     */
/*                                                                           */
/*****************************************************************************/

#ifdef ANSI_DECLARATORS
void triangulatepolygon(struct mesh *m, struct behavior *b,
struct otri *firstedge, struct otri *lastedge,
	int edgecount, int doflip, int triflaws)
#else /* not ANSI_DECLARATORS */
void triangulatepolygon(m, b, firstedge, lastedge, edgecount, doflip, triflaws)
struct mesh *m;
struct behavior *b;
struct otri *firstedge;
struct otri *lastedge;
int edgecount;
int doflip;
int triflaws;
#endif /* not ANSI_DECLARATORS */

{
	struct otri testtri;
	struct otri besttri;
	struct otri tempedge;
	vertex leftbasevertex, rightbasevertex;
	vertex testvertex;
	vertex bestvertex;
	int bestnumber;
	int i;
	triangle ptr;   /* Temporary variable used by sym(), onext(), and oprev(). */

					/* Identify the base vertices. */
	apex(*lastedge, leftbasevertex);
	dest(*firstedge, rightbasevertex);
	if (b->verbose > 2) {
		printf("  Triangulating interior polygon at edge\n");
		printf("    (%.12g, %.12g) (%.12g, %.12g)\n", leftbasevertex[0],
			leftbasevertex[1], rightbasevertex[0], rightbasevertex[1]);
	}
	/* Find the best vertex to connect the base to. */
	onext(*firstedge, besttri);
	dest(besttri, bestvertex);
	otricopy(besttri, testtri);
	bestnumber = 1;
	for (i = 2; i <= edgecount - 2; i++) {
		onextself(testtri);
		dest(testtri, testvertex);
		/* Is this a better vertex? */
		if (incircle(m, b, leftbasevertex, rightbasevertex, bestvertex,
			testvertex) > 0.0) {
			otricopy(testtri, besttri);
			bestvertex = testvertex;
			bestnumber = i;
		}
	}
	if (b->verbose > 2) {
		printf("    Connecting edge to (%.12g, %.12g)\n", bestvertex[0],
			bestvertex[1]);
	}
	if (bestnumber > 1) {
		/* Recursively triangulate the smaller polygon on the right. */
		oprev(besttri, tempedge);
		triangulatepolygon(m, b, firstedge, &tempedge, bestnumber + 1, 1,
			triflaws);
	}
	if (bestnumber < edgecount - 2) {
		/* Recursively triangulate the smaller polygon on the left. */
		sym(besttri, tempedge);
		triangulatepolygon(m, b, &besttri, lastedge, edgecount - bestnumber, 1,
			triflaws);
		/* Find `besttri' again; it may have been lost to edge flips. */
		sym(tempedge, besttri);
	}
	if (doflip) {
		/* Do one final edge flip. */
		flip(m, b, &besttri);
#ifndef CDT_ONLY
		if (triflaws) {
			/* Check the quality of the newly committed triangle. */
			sym(besttri, testtri);
			testtriangle(m, b, &testtri);
		}
#endif /* not CDT_ONLY */
	}
	/* Return the base triangle. */
	otricopy(besttri, *lastedge);
}

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

#ifndef CDT_ONLY

#ifdef ANSI_DECLARATORS
void deletevertex(struct mesh *m, struct behavior *b, struct otri *deltri)
#else /* not ANSI_DECLARATORS */
void deletevertex(m, b, deltri)
struct mesh *m;
struct behavior *b;
struct otri *deltri;
#endif /* not ANSI_DECLARATORS */

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

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

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

#ifdef SELF_CHECK
	if (edgecount < 3) {
		printf("Internal error in deletevertex():\n  Vertex has degree %d.\n",
			edgecount);
		internalerror();
	}
#endif /* SELF_CHECK */
	if (edgecount > 3) {
		/* Triangulate the polygon defined by the union of all triangles */
		/*   adjacent to the vertex being deleted.  Check the quality of */
		/*   the resulting triangles.                                    */
		onext(*deltri, firstedge);
		oprev(*deltri, lastedge);
		triangulatepolygon(m, b, &firstedge, &lastedge, edgecount, 0,
			!b->nobisect);
	}
	/* Splice out two triangles. */
	lprev(*deltri, deltriright);
	dnext(*deltri, lefttri);
	sym(lefttri, leftcasing);
	oprev(deltriright, righttri);
	sym(righttri, rightcasing);
	bond(*deltri, leftcasing);
	bond(deltriright, rightcasing);
	tspivot(lefttri, leftsubseg);
	if (leftsubseg.ss != m->dummysub) {
		tsbond(*deltri, leftsubseg);
	}
	tspivot(righttri, rightsubseg);
	if (rightsubseg.ss != m->dummysub) {
		tsbond(deltriright, rightsubseg);
	}

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

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

#endif /* not CDT_ONLY */

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

#ifndef CDT_ONLY

#ifdef ANSI_DECLARATORS
void undovertex(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
void undovertex(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */

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

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

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

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

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

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

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

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

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

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

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

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

#endif /* not CDT_ONLY */

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

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

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

/*****************************************************************************/
/*                                                                           */
/*  vertexsort()   Sort an array of vertices by x-coordinate, using the      */
/*                 y-coordinate as a secondary key.                          */
/*                                                                           */
/*  Uses quicksort.  Randomized O(n log n) time.  No, I did not make any of  */
/*  the usual quicksort mistakes.                                            */
/*                                                                           */
/*****************************************************************************/

#ifdef ANSI_DECLARATORS
void vertexsort(vertex *sortarray, int arraysize)
#else /* not ANSI_DECLARATORS */
void vertexsort(sortarray, arraysize)
vertex *sortarray;
int arraysize;
#endif /* not ANSI_DECLARATORS */

{
	int left, right;
	int pivot;
	REAL pivotx, pivoty;
	vertex temp;

	if (arraysize == 2) {
		/* Recursive base case. */
		if ((sortarray[0][0] > sortarray[1][0]) ||
			((sortarray[0][0] == sortarray[1][0]) &&
				(sortarray[0][1] > sortarray[1][1]))) {
			temp = sortarray[1];
			sortarray[1] = sortarray[0];
			sortarray[0] = temp;
		}
		return;
	}
	/* Choose a random pivot to split the array. */
	pivot = (int)randomnation((unsigned int)arraysize);
	pivotx = sortarray[pivot][0];
	pivoty = sortarray[pivot][1];
	/* Split the array. */
	left = -1;
	right = arraysize;
	while (left < right) {
		/* Search for a vertex whose x-coordinate is too large for the left. */
		do {
			left++;
		} while ((left <= right) && ((sortarray[left][0] < pivotx) ||
			((sortarray[left][0] == pivotx) &&
				(sortarray[left][1] < pivoty))));
		/* Search for a vertex whose x-coordinate is too small for the right. */
		do {
			right--;
		} while ((left <= right) && ((sortarray[right][0] > pivotx) ||
			((sortarray[right][0] == pivotx) &&
				(sortarray[right][1] > pivoty))));
		if (left < right) {
			/* Swap the left and right vertices. */
			temp = sortarray[left];
			sortarray[left] = sortarray[right];
			sortarray[right] = temp;
		}
	}
	if (left > 1) {
		/* Recursively sort the left subset. */
		vertexsort(sortarray, left);
	}
	if (right < arraysize - 2) {
		/* Recursively sort the right subset. */
		vertexsort(&sortarray[right + 1], arraysize - right - 1);
	}
}

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

#ifdef ANSI_DECLARATORS
void vertexmedian(vertex *sortarray, int arraysize, int median, int axis)
#else /* not ANSI_DECLARATORS */
void vertexmedian(sortarray, arraysize, median, axis)
vertex *sortarray;
int arraysize;
int median;
int axis;
#endif /* not ANSI_DECLARATORS */

{
	int left, right;
	int pivot;
	REAL pivot1, pivot2;
	vertex temp;

	if (arraysize == 2) {
		/* Recursive base case. */
		if ((sortarray[0][axis] > sortarray[1][axis]) ||
			((sortarray[0][axis] == sortarray[1][axis]) &&
				(sortarray[0][1 - axis] > sortarray[1][1 - axis]))) {
			temp = sortarray[1];
			sortarray[1] = sortarray[0];
			sortarray[0] = temp;
		}
		return;
	}
	/* Choose a random pivot to split the array. */
	pivot = (int)randomnation((unsigned int)arraysize);
	pivot1 = sortarray[pivot][axis];
	pivot2 = sortarray[pivot][1 - axis];
	/* Split the array. */
	left = -1;
	right = arraysize;
	while (left < right) {
		/* Search for a vertex whose x-coordinate is too large for the left. */
		do {
			left++;
		} while ((left <= right) && ((sortarray[left][axis] < pivot1) ||
			((sortarray[left][axis] == pivot1) &&
				(sortarray[left][1 - axis] < pivot2))));
		/* Search for a vertex whose x-coordinate is too small for the right. */
		do {
			right--;
		} while ((left <= right) && ((sortarray[right][axis] > pivot1) ||
			((sortarray[right][axis] == pivot1) &&
				(sortarray[right][1 - axis] > pivot2))));
		if (left < right) {
			/* Swap the left and right vertices. */
			temp = sortarray[left];
			sortarray[left] = sortarray[right];
			sortarray[right] = temp;
		}
	}
	/* Unlike in vertexsort(), at most one of the following */
	/*   conditionals is true.                             */
	if (left > median) {
		/* Recursively shuffle the left subset. */
		vertexmedian(sortarray, left, median, axis);
	}
	if (right < median - 1) {
		/* Recursively shuffle the right subset. */
		vertexmedian(&sortarray[right + 1], arraysize - right - 1,
			median - right - 1, axis);
	}
}

/*****************************************************************************/
/*                                                                           */
/*  alternateaxes()   Sorts the vertices as appropriate for the divide-and-  */
/*                    conquer algorithm with alternating cuts.               */
/*                                                                           */
/*  Partitions by x-coordinate if axis == 0; by y-coordinate if axis == 1.   */
/*  For the base case, subsets containing only two or three vertices are     */
/*  always sorted by x-coordinate.                                           */
/*                                                                           */
/*****************************************************************************/

#ifdef ANSI_DECLARATORS
void alternateaxes(vertex *sortarray, int arraysize, int axis)
#else /* not ANSI_DECLARATORS */
void alternateaxes(sortarray, arraysize, axis)
vertex *sortarray;
int arraysize;
int axis;
#endif /* not ANSI_DECLARATORS */

{
	int divider;

	divider = arraysize >> 1;
	if (arraysize <= 3) {
		/* Recursive base case:  subsets of two or three vertices will be    */
		/*   handled specially, and should always be sorted by x-coordinate. */
		axis = 0;
	}
	/* Partition with a horizontal or vertical cut. */
	vertexmedian(sortarray, arraysize, divider, axis);
	/* Recursively partition the subsets with a cross cut. */
	if (arraysize - divider >= 2) {
		if (divider >= 2) {
			alternateaxes(sortarray, divider, 1 - axis);
		}
		alternateaxes(&sortarray[divider], arraysize - divider, 1 - axis);
	}
}

/*****************************************************************************/
/*                                                                           */
/*  mergehulls()   Merge two adjacent Delaunay triangulations into a         */
/*                 single Delaunay triangulation.                            */
/*                                                                           */
/*  This is similar to the algorithm given by Guibas and Stolfi, but uses    */
/*  a triangle-based, rather than edge-based, data structure.                */
/*                                                                           */
/*  The algorithm walks up the gap between the two triangulations, knitting  */
/*  them together.  As they are merged, some of their bounding triangles     */
/*  are converted into real triangles of the triangulation.  The procedure   */
/*  pulls each hull's bounding triangles apart, then knits them together     */
/*  like the teeth of two gears.  The Delaunay property determines, at each  */
/*  step, whether the next "tooth" is a bounding triangle of the left hull   */
/*  or the right.  When a bounding triangle becomes real, its apex is        */
/*  changed from NULL to a real vertex.                                      */
/*                                                                           */
/*  Only two new triangles need to be allocated.  These become new bounding  */
/*  triangles at the top and bottom of the seam.  They are used to connect   */
/*  the remaining bounding triangles (those that have not been converted     */
/*  into real triangles) into a single fan.                                  */
/*                                                                           */
/*  On entry, `farleft' and `innerleft' are bounding triangles of the left   */
/*  triangulation.  The origin of `farleft' is the leftmost vertex, and      */
/*  the destination of `innerleft' is the rightmost vertex of the            */
/*  triangulation.  Similarly, `innerright' and `farright' are bounding      */
/*  triangles of the right triangulation.  The origin of `innerright' and    */
/*  destination of `farright' are the leftmost and rightmost vertices.       */
/*                                                                           */
/*  On completion, the origin of `farleft' is the leftmost vertex of the     */
/*  merged triangulation, and the destination of `farright' is the rightmost */
/*  vertex.                                                                  */
/*                                                                           */
/*****************************************************************************/

#ifdef ANSI_DECLARATORS
void mergehulls(struct mesh *m, struct behavior *b, struct otri *farleft,
struct otri *innerleft, struct otri *innerright,
struct otri *farright, int axis)
#else /* not ANSI_DECLARATORS */
void mergehulls(m, b, farleft, innerleft, innerright, farright, axis)
struct mesh *m;
struct behavior *b;
struct otri *farleft;
struct otri *innerleft;
struct otri *innerright;
struct otri *farright;
int axis;
#endif /* not ANSI_DECLARATORS */

{
	struct otri leftcand, rightcand;
	struct otri baseedge;
	struct otri nextedge;
	struct otri sidecasing, topcasing, outercasing;
	struct otri checkedge;
	vertex innerleftdest;
	vertex innerrightorg;
	vertex innerleftapex, innerrightapex;
	vertex farleftpt, farrightpt;
	vertex farleftapex, farrightapex;
	vertex lowerleft, lowerright;
	vertex upperleft, upperright;
	vertex nextapex;
	vertex checkvertex;
	int changemade;
	int badedge;
	int leftfinished, rightfinished;
	triangle ptr;                         /* Temporary variable used by sym(). */

	dest(*innerleft, innerleftdest);
	apex(*innerleft, innerleftapex);
	org(*innerright, innerrightorg);
	apex(*innerright, innerrightapex);
	/* Special treatment for horizontal cuts. */
	if (b->dwyer && (axis == 1)) {
		org(*farleft, farleftpt);
		apex(*farleft, farleftapex);
		dest(*farright, farrightpt);
		apex(*farright, farrightapex);
		/* The pointers to the extremal vertices are shifted to point to the */
		/*   topmost and bottommost vertex of each hull, rather than the     */
		/*   leftmost and rightmost vertices.                                */
		while (farleftapex[1] < farleftpt[1]) {
			lnextself(*farleft);
			symself(*farleft);
			farleftpt = farleftapex;
			apex(*farleft, farleftapex);
		}
		sym(*innerleft, checkedge);
		apex(checkedge, checkvertex);
		while (checkvertex[1] > innerleftdest[1]) {
			lnext(checkedge, *innerleft);
			innerleftapex = innerleftdest;
			innerleftdest = checkvertex;
			sym(*innerleft, checkedge);
			apex(checkedge, checkvertex);
		}
		while (innerrightapex[1] < innerrightorg[1]) {
			lnextself(*innerright);
			symself(*innerright);
			innerrightorg = innerrightapex;
			apex(*innerright, innerrightapex);
		}
		sym(*farright, checkedge);
		apex(checkedge, checkvertex);
		while (checkvertex[1] > farrightpt[1]) {
			lnext(checkedge, *farright);
			farrightapex = farrightpt;
			farrightpt = checkvertex;
			sym(*farright, checkedge);
			apex(checkedge, checkvertex);
		}
	}
	/* Find a line tangent to and below both hulls. */
	do {
		changemade = 0;
		/* Make innerleftdest the "bottommost" vertex of the left hull. */
		if (counterclockwise(m, b, innerleftdest, innerleftapex, innerrightorg) >
			0.0) {
			lprevself(*innerleft);
			symself(*innerleft);
			innerleftdest = innerleftapex;
			apex(*innerleft, innerleftapex);
			changemade = 1;
		}
		/* Make innerrightorg the "bottommost" vertex of the right hull. */
		if (counterclockwise(m, b, innerrightapex, innerrightorg, innerleftdest) >
			0.0) {
			lnextself(*innerright);
			symself(*innerright);
			innerrightorg = innerrightapex;
			apex(*innerright, innerrightapex);
			changemade = 1;
		}
	} while (changemade);
	/* Find the two candidates to be the next "gear tooth." */
	sym(*innerleft, leftcand);
	sym(*innerright, rightcand);
	/* Create the bottom new bounding triangle. */
	maketriangle(m, b, &baseedge);
	/* Connect it to the bounding boxes of the left and right triangulations. */
	bond(baseedge, *innerleft);
	lnextself(baseedge);
	bond(baseedge, *innerright);
	lnextself(baseedge);
	setorg(baseedge, innerrightorg);
	setdest(baseedge, innerleftdest);
	/* Apex is intentionally left NULL. */
	if (b->verbose > 2) {
		printf("  Creating base bounding ");
		printtriangle(m, b, &baseedge);
	}
	/* Fix the extreme triangles if necessary. */
	org(*farleft, farleftpt);
	if (innerleftdest == farleftpt) {
		lnext(baseedge, *farleft);
	}
	dest(*farright, farrightpt);
	if (innerrightorg == farrightpt) {
		lprev(baseedge, *farright);
	}
	/* The vertices of the current knitting edge. */
	lowerleft = innerleftdest;
	lowerright = innerrightorg;
	/* The candidate vertices for knitting. */
	apex(leftcand, upperleft);
	apex(rightcand, upperright);
	/* Walk up the gap between the two triangulations, knitting them together. */
	while (1) {
		/* Have we reached the top?  (This isn't quite the right question,       */
		/*   because even though the left triangulation might seem finished now, */
		/*   moving up on the right triangulation might reveal a new vertex of   */
		/*   the left triangulation.  And vice-versa.)                           */
		leftfinished = counterclockwise(m, b, upperleft, lowerleft, lowerright) <=
			0.0;
		rightfinished = counterclockwise(m, b, upperright, lowerleft, lowerright)
			<= 0.0;
		if (leftfinished && rightfinished) {
			/* Create the top new bounding triangle. */
			maketriangle(m, b, &nextedge);
			setorg(nextedge, lowerleft);
			setdest(nextedge, lowerright);
			/* Apex is intentionally left NULL. */
			/* Connect it to the bounding boxes of the two triangulations. */
			bond(nextedge, baseedge);
			lnextself(nextedge);
			bond(nextedge, rightcand);
			lnextself(nextedge);
			bond(nextedge, leftcand);
			if (b->verbose > 2) {
				printf("  Creating top bounding ");
				printtriangle(m, b, &nextedge);
			}
			/* Special treatment for horizontal cuts. */
			if (b->dwyer && (axis == 1)) {
				org(*farleft, farleftpt);
				apex(*farleft, farleftapex);
				dest(*farright, farrightpt);
				apex(*farright, farrightapex);
				sym(*farleft, checkedge);
				apex(checkedge, checkvertex);
				/* The pointers to the extremal vertices are restored to the  */
				/*   leftmost and rightmost vertices (rather than topmost and */
				/*   bottommost).                                             */
				while (checkvertex[0] < farleftpt[0]) {
					lprev(checkedge, *farleft);
					farleftapex = farleftpt;
					farleftpt = checkvertex;
					sym(*farleft, checkedge);
					apex(checkedge, checkvertex);
				}
				while (farrightapex[0] > farrightpt[0]) {
					lprevself(*farright);
					symself(*farright);
					farrightpt = farrightapex;
					apex(*farright, farrightapex);
				}
			}
			return;
		}
		/* Consider eliminating edges from the left triangulation. */
		if (!leftfinished) {
			/* What vertex would be exposed if an edge were deleted? */
			lprev(leftcand, nextedge);
			symself(nextedge);
			apex(nextedge, nextapex);
			/* If nextapex is NULL, then no vertex would be exposed; the */
			/*   triangulation would have been eaten right through.      */
			if (nextapex != (vertex)NULL) {
				/* Check whether the edge is Delaunay. */
				badedge = incircle(m, b, lowerleft, lowerright, upperleft, nextapex) >
					0.0;
				while (badedge) {
					/* Eliminate the edge with an edge flip.  As a result, the    */
					/*   left triangulation will have one more boundary triangle. */
					lnextself(nextedge);
					sym(nextedge, topcasing);
					lnextself(nextedge);
					sym(nextedge, sidecasing);
					bond(nextedge, topcasing);
					bond(leftcand, sidecasing);
					lnextself(leftcand);
					sym(leftcand, outercasing);
					lprevself(nextedge);
					bond(nextedge, outercasing);
					/* Correct the vertices to reflect the edge flip. */
					setorg(leftcand, lowerleft);
					setdest(leftcand, NULL);
					setapex(leftcand, nextapex);
					setorg(nextedge, NULL);
					setdest(nextedge, upperleft);
					setapex(nextedge, nextapex);
					/* Consider the newly exposed vertex. */
					upperleft = nextapex;
					/* What vertex would be exposed if another edge were deleted? */
					otricopy(sidecasing, nextedge);
					apex(nextedge, nextapex);
					if (nextapex != (vertex)NULL) {
						/* Check whether the edge is Delaunay. */
						badedge = incircle(m, b, lowerleft, lowerright, upperleft,
							nextapex) > 0.0;
					}
					else {
						/* Avoid eating right through the triangulation. */
						badedge = 0;
					}
				}
			}
		}
		/* Consider eliminating edges from the right triangulation. */
		if (!rightfinished) {
			/* What vertex would be exposed if an edge were deleted? */
			lnext(rightcand, nextedge);
			symself(nextedge);
			apex(nextedge, nextapex);
			/* If nextapex is NULL, then no vertex would be exposed; the */
			/*   triangulation would have been eaten right through.      */
			if (nextapex != (vertex)NULL) {
				/* Check whether the edge is Delaunay. */
				badedge = incircle(m, b, lowerleft, lowerright, upperright, nextapex) >
					0.0;
				while (badedge) {
					/* Eliminate the edge with an edge flip.  As a result, the     */
					/*   right triangulation will have one more boundary triangle. */
					lprevself(nextedge);
					sym(nextedge, topcasing);
					lprevself(nextedge);
					sym(nextedge, sidecasing);
					bond(nextedge, topcasing);
					bond(rightcand, sidecasing);
					lprevself(rightcand);
					sym(rightcand, outercasing);
					lnextself(nextedge);
					bond(nextedge, outercasing);
					/* Correct the vertices to reflect the edge flip. */
					setorg(rightcand, NULL);
					setdest(rightcand, lowerright);
					setapex(rightcand, nextapex);
					setorg(nextedge, upperright);
					setdest(nextedge, NULL);
					setapex(nextedge, nextapex);
					/* Consider the newly exposed vertex. */
					upperright = nextapex;
					/* What vertex would be exposed if another edge were deleted? */
					otricopy(sidecasing, nextedge);
					apex(nextedge, nextapex);
					if (nextapex != (vertex)NULL) {
						/* Check whether the edge is Delaunay. */
						badedge = incircle(m, b, lowerleft, lowerright, upperright,
							nextapex) > 0.0;
					}
					else {
						/* Avoid eating right through the triangulation. */
						badedge = 0;
					}
				}
			}
		}
		if (leftfinished || (!rightfinished &&
			(incircle(m, b, upperleft, lowerleft, lowerright, upperright) >
				0.0))) {
			/* Knit the triangulations, adding an edge from `lowerleft' */
			/*   to `upperright'.                                       */
			bond(baseedge, rightcand);
			lprev(rightcand, baseedge);
			setdest(baseedge, lowerleft);
			lowerright = upperright;
			sym(baseedge, rightcand);
			apex(rightcand, upperright);
		}
		else {
			/* Knit the triangulations, adding an edge from `upperleft' */
			/*   to `lowerright'.                                       */
			bond(baseedge, leftcand);
			lnext(leftcand, baseedge);
			setorg(baseedge, lowerright);
			lowerleft = upperleft;
			sym(baseedge, leftcand);
			apex(leftcand, upperleft);
		}
		if (b->verbose > 2) {
			printf("  Connecting ");
			printtriangle(m, b, &baseedge);
		}
	}
}

/*****************************************************************************/
/*                                                                           */
/*  divconqrecurse()   Recursively form a Delaunay triangulation by the      */
/*                     divide-and-conquer method.                            */
/*                                                                           */
/*  Recursively breaks down the problem into smaller pieces, which are       */
/*  knitted together by mergehulls().  The base cases (problems of two or    */
/*  three vertices) are handled specially here.                              */
/*                                                                           */
/*  On completion, `farleft' and `farright' are bounding triangles such that */
/*  the origin of `farleft' is the leftmost vertex (breaking ties by         */
/*  choosing the highest leftmost vertex), and the destination of            */
/*  `farright' is the rightmost vertex (breaking ties by choosing the        */
/*  lowest rightmost vertex).                                                */
/*                                                                           */
/*****************************************************************************/

#ifdef ANSI_DECLARATORS
void divconqrecurse(struct mesh *m, struct behavior *b, vertex *sortarray,
	int vertices, int axis,
struct otri *farleft, struct otri *farright)
#else /* not ANSI_DECLARATORS */
void divconqrecurse(m, b, sortarray, vertices, axis, farleft, farright)
struct mesh *m;
struct behavior *b;
vertex *sortarray;
int vertices;
int axis;
struct otri *farleft;
struct otri *farright;
#endif /* not ANSI_DECLARATORS */

{
	struct otri midtri, tri1, tri2, tri3;
	struct otri innerleft, innerright;
	REAL area;
	int divider;

	if (b->verbose > 2) {
		printf("  Triangulating %d vertices.\n", vertices);
	}
	if (vertices == 2) {
		/* The triangulation of two vertices is an edge.  An edge is */
		/*   represented by two bounding triangles.                  */
		maketriangle(m, b, farleft);
		setorg(*farleft, sortarray[0]);
		setdest(*farleft, sortarray[1]);
		/* The apex is intentionally left NULL. */
		maketriangle(m, b, farright);
		setorg(*farright, sortarray[1]);
		setdest(*farright, sortarray[0]);
		/* The apex is intentionally left NULL. */
		bond(*farleft, *farright);
		lprevself(*farleft);
		lnextself(*farright);
		bond(*farleft, *farright);
		lprevself(*farleft);
		lnextself(*farright);
		bond(*farleft, *farright);
		if (b->verbose > 2) {
			printf("  Creating ");
			printtriangle(m, b, farleft);
			printf("  Creating ");
			printtriangle(m, b, farright);
		}
		/* Ensure that the origin of `farleft' is sortarray[0]. */
		lprev(*farright, *farleft);
		return;
	}
	else if (vertices == 3) {
		/* The triangulation of three vertices is either a triangle (with */
		/*   three bounding triangles) or two edges (with four bounding   */
		/*   triangles).  In either case, four triangles are created.     */
		maketriangle(m, b, &midtri);
		maketriangle(m, b, &tri1);
		maketriangle(m, b, &tri2);
		maketriangle(m, b, &tri3);
		area = counterclockwise(m, b, sortarray[0], sortarray[1], sortarray[2]);
		if (area == 0.0) {
			/* Three collinear vertices; the triangulation is two edges. */
			setorg(midtri, sortarray[0]);
			setdest(midtri, sortarray[1]);
			setorg(tri1, sortarray[1]);
			setdest(tri1, sortarray[0]);
			setorg(tri2, sortarray[2]);
			setdest(tri2, sortarray[1]);
			setorg(tri3, sortarray[1]);
			setdest(tri3, sortarray[2]);
			/* All apices are intentionally left NULL. */
			bond(midtri, tri1);
			bond(tri2, tri3);
			lnextself(midtri);
			lprevself(tri1);
			lnextself(tri2);
			lprevself(tri3);
			bond(midtri, tri3);
			bond(tri1, tri2);
			lnextself(midtri);
			lprevself(tri1);
			lnextself(tri2);
			lprevself(tri3);
			bond(midtri, tri1);
			bond(tri2, tri3);
			/* Ensure that the origin of `farleft' is sortarray[0]. */
			otricopy(tri1, *farleft);
			/* Ensure that the destination of `farright' is sortarray[2]. */
			otricopy(tri2, *farright);
		}
		else {
			/* The three vertices are not collinear; the triangulation is one */
			/*   triangle, namely `midtri'.                                   */
			setorg(midtri, sortarray[0]);
			setdest(tri1, sortarray[0]);
			setorg(tri3, sortarray[0]);
			/* Apices of tri1, tri2, and tri3 are left NULL. */
			if (area > 0.0) {
				/* The vertices are in counterclockwise order. */
				setdest(midtri, sortarray[1]);
				setorg(tri1, sortarray[1]);
				setdest(tri2, sortarray[1]);
				setapex(midtri, sortarray[2]);
				setorg(tri2, sortarray[2]);
				setdest(tri3, sortarray[2]);
			}
			else {
				/* The vertices are in clockwise order. */
				setdest(midtri, sortarray[2]);
				setorg(tri1, sortarray[2]);
				setdest(tri2, sortarray[2]);
				setapex(midtri, sortarray[1]);
				setorg(tri2, sortarray[1]);
				setdest(tri3, sortarray[1]);
			}
			/* The topology does not depend on how the vertices are ordered. */
			bond(midtri, tri1);
			lnextself(midtri);
			bond(midtri, tri2);
			lnextself(midtri);
			bond(midtri, tri3);
			lprevself(tri1);
			lnextself(tri2);
			bond(tri1, tri2);
			lprevself(tri1);
			lprevself(tri3);
			bond(tri1, tri3);
			lnextself(tri2);
			lprevself(tri3);
			bond(tri2, tri3);
			/* Ensure that the origin of `farleft' is sortarray[0]. */
			otricopy(tri1, *farleft);
			/* Ensure that the destination of `farright' is sortarray[2]. */
			if (area > 0.0) {
				otricopy(tri2, *farright);
			}
			else {
				lnext(*farleft, *farright);
			}
		}
		if (b->verbose > 2) {
			printf("  Creating ");
			printtriangle(m, b, &midtri);
			printf("  Creating ");
			printtriangle(m, b, &tri1);
			printf("  Creating ");
			printtriangle(m, b, &tri2);
			printf("  Creating ");
			printtriangle(m, b, &tri3);
		}
		return;
	}
	else {
		/* Split the vertices in half. */
		divider = vertices >> 1;
		/* Recursively triangulate each half. */
		divconqrecurse(m, b, sortarray, divider, 1 - axis, farleft, &innerleft);
		divconqrecurse(m, b, &sortarray[divider], vertices - divider, 1 - axis,
			&innerright, farright);
		if (b->verbose > 1) {
			printf("  Joining triangulations with %d and %d vertices.\n", divider,
				vertices - divider);
		}
		/* Merge the two triangulations into one. */
		mergehulls(m, b, farleft, &innerleft, &innerright, farright, axis);
	}
}

#ifdef ANSI_DECLARATORS
long removeghosts(struct mesh *m, struct behavior *b, struct otri *startghost)
#else /* not ANSI_DECLARATORS */
long removeghosts(m, b, startghost)
struct mesh *m;
struct behavior *b;
struct otri *startghost;
#endif /* not ANSI_DECLARATORS */

{
	struct otri searchedge;
	struct otri dissolveedge;
	struct otri deadtriangle;
	vertex markorg;
	long hullsize;
	triangle ptr;                         /* Temporary variable used by sym(). */

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

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

#ifdef ANSI_DECLARATORS
long divconqdelaunay(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
long divconqdelaunay(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */

{
	vertex *sortarray;
	struct otri hullleft, hullright;
	int divider;
	int i, j;

	if (b->verbose) {
		printf("  Sorting vertices.\n");
	}

	/* Allocate an array of pointers to vertices for sorting. */
	sortarray = (vertex *)trimalloc(m->invertices * (int) sizeof(vertex));
	traversalinit(&m->vertices);
	for (i = 0; i < m->invertices; i++) {
		sortarray[i] = vertextraverse(m);
	}
	/* Sort the vertices. */
	vertexsort(sortarray, m->invertices);
	/* Discard duplicate vertices, which can really mess up the algorithm. */
	i = 0;
	for (j = 1; j < m->invertices; j++) {
		if ((sortarray[i][0] == sortarray[j][0])
			&& (sortarray[i][1] == sortarray[j][1])) {
			if (!b->quiet) {
				printf(
					"Warning:  A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n",
					sortarray[j][0], sortarray[j][1]);
			}
			setvertextype(sortarray[j], UNDEADVERTEX);
			m->undeads++;
		}
		else {
			i++;
			sortarray[i] = sortarray[j];
		}
	}
	i++;
	if (b->dwyer) {
		/* Re-sort the array of vertices to accommodate alternating cuts. */
		divider = i >> 1;
		if (i - divider >= 2) {
			if (divider >= 2) {
				alternateaxes(sortarray, divider, 1);
			}
			alternateaxes(&sortarray[divider], i - divider, 1);
		}
	}

	if (b->verbose) {
		printf("  Forming triangulation.\n");
	}

	/* Form the Delaunay triangulation. */
	divconqrecurse(m, b, sortarray, i, 0, &hullleft, &hullright);
	trifree((VOID *)sortarray);

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

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

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

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

#ifndef REDUCED

#ifdef ANSI_DECLARATORS
void boundingbox(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
void boundingbox(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */

{
	struct otri inftri;          /* Handle for the triangular bounding box. */
	REAL width;

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

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

#endif /* not REDUCED */

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

#ifndef REDUCED

#ifdef ANSI_DECLARATORS
long removebox(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
long removebox(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */

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

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

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

	return hullsize;
}

#endif /* not REDUCED */

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

#ifndef REDUCED

#ifdef ANSI_DECLARATORS
long incrementaldelaunay(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
long incrementaldelaunay(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */

{
	struct otri starttri;
	vertex vertexloop;

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

#endif /* not REDUCED */

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

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

#ifndef REDUCED

#ifdef ANSI_DECLARATORS
void eventheapinsert(struct event **heap, int heapsize, struct event *newevent)
#else /* not ANSI_DECLARATORS */
void eventheapinsert(heap, heapsize, newevent)
struct event **heap;
int heapsize;
struct event *newevent;
#endif /* not ANSI_DECLARATORS */

{
	REAL eventx, eventy;
	int eventnum;
	int parent;
	int notdone;

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

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

#endif /* not REDUCED */

#ifndef REDUCED

#ifdef ANSI_DECLARATORS
void eventheapify(struct event **heap, int heapsize, int eventnum)
#else /* not ANSI_DECLARATORS */
void eventheapify(heap, heapsize, eventnum)
struct event **heap;
int heapsize;
int eventnum;
#endif /* not ANSI_DECLARATORS */

{
	struct event *thisevent;
	REAL eventx, eventy;
	int leftchild, rightchild;
	int smallest;
	int notdone;

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

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

#endif /* not REDUCED */

#ifndef REDUCED

#ifdef ANSI_DECLARATORS
void eventheapdelete(struct event **heap, int heapsize, int eventnum)
#else /* not ANSI_DECLARATORS */
void eventheapdelete(heap, heapsize, eventnum)
struct event **heap;
int heapsize;
int eventnum;
#endif /* not ANSI_DECLARATORS */

{
	struct event *moveevent;
	REAL eventx, eventy;
	int parent;
	int notdone;

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

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

#endif /* not REDUCED */

#ifndef REDUCED

#ifdef ANSI_DECLARATORS
void createeventheap(struct mesh *m, struct event ***eventheap,
struct event **events, struct event **freeevents)
#else /* not ANSI_DECLARATORS */
void createeventheap(m, eventheap, events, freeevents)
struct mesh *m;
struct event ***eventheap;
struct event **events;
struct event **freeevents;
#endif /* not ANSI_DECLARATORS */

{
	vertex thisvertex;
	int maxevents;
	int i;

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

#endif /* not REDUCED */

#ifndef REDUCED

#ifdef ANSI_DECLARATORS
int rightofhyperbola(struct mesh *m, struct otri *fronttri, vertex newsite)
#else /* not ANSI_DECLARATORS */
int rightofhyperbola(m, fronttri, newsite)
struct mesh *m;
struct otri *fronttri;
vertex newsite;
#endif /* not ANSI_DECLARATORS */

{
	vertex leftvertex, rightvertex;
	REAL dxa, dya, dxb, dyb;

	m->hyperbolacount++;

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

#endif /* not REDUCED */

#ifndef REDUCED

#ifdef ANSI_DECLARATORS
REAL circletop(struct mesh *m, vertex pa, vertex pb, vertex pc, REAL ccwabc)
#else /* not ANSI_DECLARATORS */
REAL circletop(m, pa, pb, pc, ccwabc)
struct mesh *m;
vertex pa;
vertex pb;
vertex pc;
REAL ccwabc;
#endif /* not ANSI_DECLARATORS */

{
	REAL xac, yac, xbc, ybc, xab, yab;
	REAL aclen2, bclen2, ablen2;

	m->circletopcount++;

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

#endif /* not REDUCED */

#ifndef REDUCED

#ifdef ANSI_DECLARATORS
void check4deadevent(struct otri *checktri, struct event **freeevents,
struct event **eventheap, int *heapsize)
#else /* not ANSI_DECLARATORS */
void check4deadevent(checktri, freeevents, eventheap, heapsize)
struct otri *checktri;
struct event **freeevents;
struct event **eventheap;
int *heapsize;
#endif /* not ANSI_DECLARATORS */

{
	struct event *deadevent;
	vertex eventvertex;
	int eventnum;

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

#endif /* not REDUCED */

#ifndef REDUCED

#ifdef ANSI_DECLARATORS
struct splaynode *splay(struct mesh *m, struct splaynode *splaytree,
	vertex searchpoint, struct otri *searchtri)
#else /* not ANSI_DECLARATORS */
struct splaynode *splay(m, splaytree, searchpoint, searchtri)
struct mesh *m;
struct splaynode *splaytree;
vertex searchpoint;
struct otri *searchtri;
#endif /* not ANSI_DECLARATORS */

{
	struct splaynode *child, *grandchild;
	struct splaynode *lefttree, *righttree;
	struct splaynode *leftright;
	vertex checkvertex;
	int rightofroot, rightofchild;

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

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

#endif /* not REDUCED */

#ifndef REDUCED

#ifdef ANSI_DECLARATORS
struct splaynode *splayinsert(struct mesh *m, struct splaynode *splayroot,
struct otri *newkey, vertex searchpoint)
#else /* not ANSI_DECLARATORS */
struct splaynode *splayinsert(m, splayroot, newkey, searchpoint)
struct mesh *m;
struct splaynode *splayroot;
struct otri *newkey;
vertex searchpoint;
#endif /* not ANSI_DECLARATORS */

{
	struct splaynode *newsplaynode;

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

#endif /* not REDUCED */

#ifndef REDUCED

#ifdef ANSI_DECLARATORS
struct splaynode *circletopinsert(struct mesh *m, struct behavior *b,
struct splaynode *splayroot,
struct otri *newkey,
	vertex pa, vertex pb, vertex pc, REAL topy)
#else /* not ANSI_DECLARATORS */
struct splaynode *circletopinsert(m, b, splayroot, newkey, pa, pb, pc, topy)
struct mesh *m;
struct behavior *b;
struct splaynode *splayroot;
struct otri *newkey;
vertex pa;
vertex pb;
vertex pc;
REAL topy;
#endif /* not ANSI_DECLARATORS */

{
	REAL ccwabc;
	REAL xac, yac, xbc, ybc;
	REAL aclen2, bclen2;
	REAL searchpoint[2];
	struct otri dummytri;

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

#endif /* not REDUCED */

#ifndef REDUCED

#ifdef ANSI_DECLARATORS
struct splaynode *frontlocate(struct mesh *m, struct splaynode *splayroot,
struct otri *bottommost, vertex searchvertex,
struct otri *searchtri, int *farright)
#else /* not ANSI_DECLARATORS */
struct splaynode *frontlocate(m, splayroot, bottommost, searchvertex,
	searchtri, farright)
struct mesh *m;
struct splaynode *splayroot;
struct otri *bottommost;
vertex searchvertex;
struct otri *searchtri;
int *farright;
#endif /* not ANSI_DECLARATORS */

{
	int farrightflag;
	triangle ptr;                       /* Temporary variable used by onext(). */

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

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

#endif /* not REDUCED */

#ifndef REDUCED

#ifdef ANSI_DECLARATORS
long sweeplinedelaunay(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
long sweeplinedelaunay(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */

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

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

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

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

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

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

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

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

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

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

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

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

#endif /* not REDUCED */

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

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

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

#ifdef ANSI_DECLARATORS
long delaunay(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
long delaunay(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */

{
	long hulledges;

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

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

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

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

#ifndef CDT_ONLY

#ifdef TRILIBRARY

#ifdef ANSI_DECLARATORS
int reconstruct(struct mesh *m, struct behavior *b, int *trianglelist,
	REAL *triangleattriblist, REAL *trianglearealist,
	int elements, int corners, int attribs,
	int *segmentlist, int *segmentmarkerlist, int numberofsegments)
#else /* not ANSI_DECLARATORS */
int reconstruct(m, b, trianglelist, triangleattriblist, trianglearealist,
	elements, corners, attribs, segmentlist, segmentmarkerlist,
	numberofsegments)
struct mesh *m;
struct behavior *b;
int *trianglelist;
REAL *triangleattriblist;
REAL *trianglearealist;
int elements;
int corners;
int attribs;
int *segmentlist;
int *segmentmarkerlist;
int numberofsegments;
#endif /* not ANSI_DECLARATORS */

#else /* not TRILIBRARY */

#ifdef ANSI_DECLARATORS
long reconstruct(struct mesh *m, struct behavior *b, char *elefilename,
	char *areafilename, char *polyfilename, FILE *polyfile)
#else /* not ANSI_DECLARATORS */
long reconstruct(m, b, elefilename, areafilename, polyfilename, polyfile)
struct mesh *m;
struct behavior *b;
char *elefilename;
char *areafilename;
char *polyfilename;
FILE *polyfile;
#endif /* not ANSI_DECLARATORS */

#endif /* not TRILIBRARY */

{
#ifdef TRILIBRARY
	int vertexindex;
	int attribindex;
#else /* not TRILIBRARY */
	FILE *elefile;
	FILE *areafile;
	char inputline[INPUTLINESIZE];
	char *stringptr;
	int areaelements;
#endif /* not TRILIBRARY */
	struct otri triangleloop;
	struct otri triangleleft;
	struct otri checktri;
	struct otri checkleft;
	struct otri checkneighbor;
	struct osub subsegloop;
	triangle *vertexarray;
	triangle *prevlink;
	triangle nexttri;
	vertex tdest, tapex;
	vertex checkdest, checkapex;
	vertex shorg;
	vertex killvertex;
	vertex segmentorg, segmentdest;
	REAL area;
	int corner[3];
	int end[2];
	int killvertexindex;
	int incorners;
	int segmentmarkers;
	int boundmarker;
	int aroundvertex;
	long hullsize;
	int notfound;
	long elementnumber, segmentnumber;
	int i, j;
	triangle ptr;                         /* Temporary variable used by sym(). */

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

	initializetrisubpools(m, b);

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

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

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

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

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

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

		/* Find out about (and throw away) extra nodes. */
		for (j = 3; j < incorners; j++) {
#ifdef TRILIBRARY
			killvertexindex = trianglelist[vertexindex++];
#else /* not TRILIBRARY */
			stringptr = findfield(stringptr);
			if (*stringptr != '\0') {
				killvertexindex = (int)strtol(stringptr, &stringptr, 0);
#endif /* not TRILIBRARY */
				if ((killvertexindex >= b->firstnumber) &&
					(killvertexindex < b->firstnumber + m->invertices)) {
					/* Delete the non-corner vertex if it's not already deleted. */
					killvertex = getvertex(m, b, killvertexindex);
					if (vertextype(killvertex) != DEADVERTEX) {
						vertexdealloc(m, killvertex);
					}
				}
#ifndef TRILIBRARY
			}
#endif /* not TRILIBRARY */
		}

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

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

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

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

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

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

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

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

#endif /* not CDT_ONLY */

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

/********* Segment insertion begins here                             *********/
/**                                                                         **/
/**                                                                         **/

/*****************************************************************************/
/*                                                                           */
/*  finddirection()   Find the first triangle on the path from one point     */
/*                    to another.                                            */
/*                                                                           */
/*  Finds the triangle that intersects a line segment drawn from the         */
/*  origin of `searchtri' to the point `searchpoint', and returns the result */
/*  in `searchtri'.  The origin of `searchtri' does not change, even though  */
/*  the triangle returned may differ from the one passed in.  This routine   */
/*  is used to find the direction to move in to get from one point to        */
/*  another.                                                                 */
/*                                                                           */
/*  The return value notes whether the destination or apex of the found      */
/*  triangle is collinear with the two points in question.                   */
/*                                                                           */
/*****************************************************************************/

#ifdef ANSI_DECLARATORS
enum finddirectionresult finddirection(struct mesh *m, struct behavior *b,
struct otri *searchtri,
	vertex searchpoint)
#else /* not ANSI_DECLARATORS */
enum finddirectionresult finddirection(m, b, searchtri, searchpoint)
struct mesh *m;
struct behavior *b;
struct otri *searchtri;
vertex searchpoint;
#endif /* not ANSI_DECLARATORS */

{
	struct otri checktri;
	vertex startvertex;
	vertex leftvertex, rightvertex;
	REAL leftccw, rightccw;
	int leftflag, rightflag;
	triangle ptr;           /* Temporary variable used by onext() and oprev(). */

	org(*searchtri, startvertex);
	dest(*searchtri, rightvertex);
	apex(*searchtri, leftvertex);
	/* Is `searchpoint' to the left? */
	leftccw = counterclockwise(m, b, searchpoint, startvertex, leftvertex);
	leftflag = leftccw > 0.0;
	/* Is `searchpoint' to the right? */
	rightccw = counterclockwise(m, b, startvertex, searchpoint, rightvertex);
	rightflag = rightccw > 0.0;
	if (leftflag && rightflag) {
		/* `searchtri' faces directly away from `searchpoint'.  We could go left */
		/*   or right.  Ask whether it's a triangle or a boundary on the left.   */
		onext(*searchtri, checktri);
		if (checktri.tri == m->dummytri) {
			leftflag = 0;
		}
		else {
			rightflag = 0;
		}
	}
	while (leftflag) {
		/* Turn left until satisfied. */
		onextself(*searchtri);
		if (searchtri->tri == m->dummytri) {
			printf("Internal error in finddirection():  Unable to find a\n");
			printf("  triangle leading from (%.12g, %.12g) to", startvertex[0],
				startvertex[1]);
			printf("  (%.12g, %.12g).\n", searchpoint[0], searchpoint[1]);
			internalerror();
		}
		apex(*searchtri, leftvertex);
		rightccw = leftccw;
		leftccw = counterclockwise(m, b, searchpoint, startvertex, leftvertex);
		leftflag = leftccw > 0.0;
	}
	while (rightflag) {
		/* Turn right until satisfied. */
		oprevself(*searchtri);
		if (searchtri->tri == m->dummytri) {
			printf("Internal error in finddirection():  Unable to find a\n");
			printf("  triangle leading from (%.12g, %.12g) to", startvertex[0],
				startvertex[1]);
			printf("  (%.12g, %.12g).\n", searchpoint[0], searchpoint[1]);
			internalerror();
		}
		dest(*searchtri, rightvertex);
		leftccw = rightccw;
		rightccw = counterclockwise(m, b, startvertex, searchpoint, rightvertex);
		rightflag = rightccw > 0.0;
	}
	if (leftccw == 0.0) {
		return LEFTCOLLINEAR;
	}
	else if (rightccw == 0.0) {
		return RIGHTCOLLINEAR;
	}
	else {
		return WITHIN;
	}
}

/*****************************************************************************/
/*                                                                           */
/*  segmentintersection()   Find the intersection of an existing segment     */
/*                          and a segment that is being inserted.  Insert    */
/*                          a vertex at the intersection, splitting an       */
/*                          existing subsegment.                             */
/*                                                                           */
/*  The segment being inserted connects the apex of splittri to endpoint2.   */
/*  splitsubseg is the subsegment being split, and MUST adjoin splittri.     */
/*  Hence, endpoints of the subsegment being split are the origin and        */
/*  destination of splittri.                                                 */
/*                                                                           */
/*  On completion, splittri is a handle having the newly inserted            */
/*  intersection point as its origin, and endpoint1 as its destination.      */
/*                                                                           */
/*****************************************************************************/

#ifdef ANSI_DECLARATORS
void segmentintersection(struct mesh *m, struct behavior *b,
struct otri *splittri, struct osub *splitsubseg,
	vertex endpoint2)
#else /* not ANSI_DECLARATORS */
void segmentintersection(m, b, splittri, splitsubseg, endpoint2)
struct mesh *m;
struct behavior *b;
struct otri *splittri;
struct osub *splitsubseg;
vertex endpoint2;
#endif /* not ANSI_DECLARATORS */

{
	struct osub opposubseg;
	vertex endpoint1;
	vertex torg, tdest;
	vertex leftvertex, rightvertex;
	vertex newvertex;
	enum insertvertexresult success;
	enum finddirectionresult collinear;
	REAL ex, ey;
	REAL tx, ty;
	REAL etx, ety;
	REAL split, denom;
	int i;
	triangle ptr;                       /* Temporary variable used by onext(). */
	subseg sptr;                        /* Temporary variable used by snext(). */

										/* Find the other three segment endpoints. */
	apex(*splittri, endpoint1);
	org(*splittri, torg);
	dest(*splittri, tdest);
	/* Segment intersection formulae; see the Antonio reference. */
	tx = tdest[0] - torg[0];
	ty = tdest[1] - torg[1];
	ex = endpoint2[0] - endpoint1[0];
	ey = endpoint2[1] - endpoint1[1];
	etx = torg[0] - endpoint2[0];
	ety = torg[1] - endpoint2[1];
	denom = ty * ex - tx * ey;
	if (denom == 0.0) {
		printf("Internal error in segmentintersection():");
		printf("  Attempt to find intersection of parallel segments.\n");
		internalerror();
	}
	split = (ey * etx - ex * ety) / denom;
	/* Create the new vertex. */
	newvertex = (vertex)poolalloc(&m->vertices);
	/* Interpolate its coordinate and attributes. */
	for (i = 0; i < 2 + m->nextras; i++) {
		newvertex[i] = torg[i] + split * (tdest[i] - torg[i]);
	}
	setvertexmark(newvertex, mark(*splitsubseg));
	setvertextype(newvertex, INPUTVERTEX);
	if (b->verbose > 1) {
		printf(
			"  Splitting subsegment (%.12g, %.12g) (%.12g, %.12g) at (%.12g, %.12g).\n",
			torg[0], torg[1], tdest[0], tdest[1], newvertex[0], newvertex[1]);
	}
	/* Insert the intersection vertex.  This should always succeed. */
	success = insertvertex(m, b, newvertex, splittri, splitsubseg, 0, 0);
	if (success != SUCCESSFULVERTEX) {
		printf("Internal error in segmentintersection():\n");
		printf("  Failure to split a segment.\n");
		internalerror();
	}
	/* Record a triangle whose origin is the new vertex. */
	setvertex2tri(newvertex, encode(*splittri));
	if (m->steinerleft > 0) {
		m->steinerleft--;
	}

	/* Divide the segment into two, and correct the segment endpoints. */
	ssymself(*splitsubseg);
	spivot(*splitsubseg, opposubseg);
	sdissolve(*splitsubseg);
	sdissolve(opposubseg);
	do {
		setsegorg(*splitsubseg, newvertex);
		snextself(*splitsubseg);
	} while (splitsubseg->ss != m->dummysub);
	do {
		setsegorg(opposubseg, newvertex);
		snextself(opposubseg);
	} while (opposubseg.ss != m->dummysub);

	/* Inserting the vertex may have caused edge flips.  We wish to rediscover */
	/*   the edge connecting endpoint1 to the new intersection vertex.         */
	collinear = finddirection(m, b, splittri, endpoint1);
	dest(*splittri, rightvertex);
	apex(*splittri, leftvertex);
	if ((leftvertex[0] == endpoint1[0]) && (leftvertex[1] == endpoint1[1])) {
		onextself(*splittri);
	}
	else if ((rightvertex[0] != endpoint1[0]) ||
		(rightvertex[1] != endpoint1[1])) {
		printf("Internal error in segmentintersection():\n");
		printf("  Topological inconsistency after splitting a segment.\n");
		internalerror();
	}
	/* `splittri' should have destination endpoint1. */
}

/*****************************************************************************/
/*                                                                           */
/*  scoutsegment()   Scout the first triangle on the path from one endpoint  */
/*                   to another, and check for completion (reaching the      */
/*                   second endpoint), a collinear vertex, or the            */
/*                   intersection of two segments.                           */
/*                                                                           */
/*  Returns one if the entire segment is successfully inserted, and zero if  */
/*  the job must be finished by conformingedge() or constrainededge().       */
/*                                                                           */
/*  If the first triangle on the path has the second endpoint as its         */
/*  destination or apex, a subsegment is inserted and the job is done.       */
/*                                                                           */
/*  If the first triangle on the path has a destination or apex that lies on */
/*  the segment, a subsegment is inserted connecting the first endpoint to   */
/*  the collinear vertex, and the search is continued from the collinear     */
/*  vertex.                                                                  */
/*                                                                           */
/*  If the first triangle on the path has a subsegment opposite its origin,  */
/*  then there is a segment that intersects the segment being inserted.      */
/*  Their intersection vertex is inserted, splitting the subsegment.         */
/*                                                                           */
/*****************************************************************************/

#ifdef ANSI_DECLARATORS
int scoutsegment(struct mesh *m, struct behavior *b, struct otri *searchtri,
	vertex endpoint2, int newmark)
#else /* not ANSI_DECLARATORS */
int scoutsegment(m, b, searchtri, endpoint2, newmark)
struct mesh *m;
struct behavior *b;
struct otri *searchtri;
vertex endpoint2;
int newmark;
#endif /* not ANSI_DECLARATORS */

{
	struct otri crosstri;
	struct osub crosssubseg;
	vertex leftvertex, rightvertex;
	enum finddirectionresult collinear;
	subseg sptr;                      /* Temporary variable used by tspivot(). */

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

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

#ifndef REDUCED
#ifndef CDT_ONLY

#ifdef ANSI_DECLARATORS
void conformingedge(struct mesh *m, struct behavior *b,
	vertex endpoint1, vertex endpoint2, int newmark)
#else /* not ANSI_DECLARATORS */
void conformingedge(m, b, endpoint1, endpoint2, newmark)
struct mesh *m;
struct behavior *b;
vertex endpoint1;
vertex endpoint2;
int newmark;
#endif /* not ANSI_DECLARATORS */

{
	struct otri searchtri1, searchtri2;
	struct osub brokensubseg;
	vertex newvertex;
	vertex midvertex1, midvertex2;
	enum insertvertexresult success;
	int i;
	subseg sptr;                      /* Temporary variable used by tspivot(). */

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

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

/*****************************************************************************/
/*                                                                           */
/*  delaunayfixup()   Enforce the Delaunay condition at an edge, fanning out */
/*                    recursively from an existing vertex.  Pay special      */
/*                    attention to stacking inverted triangles.              */
/*                                                                           */
/*  This is a support routine for inserting segments into a constrained      */
/*  Delaunay triangulation.                                                  */
/*                                                                           */
/*  The origin of fixuptri is treated as if it has just been inserted, and   */
/*  the local Delaunay condition needs to be enforced.  It is only enforced  */
/*  in one sector, however, that being the angular range defined by          */
/*  fixuptri.                                                                */
/*                                                                           */
/*  This routine also needs to make decisions regarding the "stacking" of    */
/*  triangles.  (Read the description of constrainededge() below before      */
/*  reading on here, so you understand the algorithm.)  If the position of   */
/*  the new vertex (the origin of fixuptri) indicates that the vertex before */
/*  it on the polygon is a reflex vertex, then "stack" the triangle by       */
/*  doing nothing.  (fixuptri is an inverted triangle, which is how stacked  */
/*  triangles are identified.)                                               */
/*                                                                           */
/*  Otherwise, check whether the vertex before that was a reflex vertex.     */
/*  If so, perform an edge flip, thereby eliminating an inverted triangle    */
/*  (popping it off the stack).  The edge flip may result in the creation    */
/*  of a new inverted triangle, depending on whether or not the new vertex   */
/*  is visible to the vertex three edges behind on the polygon.              */
/*                                                                           */
/*  If neither of the two vertices behind the new vertex are reflex          */
/*  vertices, fixuptri and fartri, the triangle opposite it, are not         */
/*  inverted; hence, ensure that the edge between them is locally Delaunay.  */
/*                                                                           */
/*  `leftside' indicates whether or not fixuptri is to the left of the       */
/*  segment being inserted.  (Imagine that the segment is pointing up from   */
/*  endpoint1 to endpoint2.)                                                 */
/*                                                                           */
/*****************************************************************************/

#ifdef ANSI_DECLARATORS
void delaunayfixup(struct mesh *m, struct behavior *b,
struct otri *fixuptri, int leftside)
#else /* not ANSI_DECLARATORS */
void delaunayfixup(m, b, fixuptri, leftside)
struct mesh *m;
struct behavior *b;
struct otri *fixuptri;
int leftside;
#endif /* not ANSI_DECLARATORS */

{
	struct otri neartri;
	struct otri fartri;
	struct osub faredge;
	vertex nearvertex, leftvertex, rightvertex, farvertex;
	triangle ptr;                         /* Temporary variable used by sym(). */
	subseg sptr;                      /* Temporary variable used by tspivot(). */

	lnext(*fixuptri, neartri);
	sym(neartri, fartri);
	/* Check if the edge opposite the origin of fixuptri can be flipped. */
	if (fartri.tri == m->dummytri) {
		return;
	}
	tspivot(neartri, faredge);
	if (faredge.ss != m->dummysub) {
		return;
	}
	/* Find all the relevant vertices. */
	apex(neartri, nearvertex);
	org(neartri, leftvertex);
	dest(neartri, rightvertex);
	apex(fartri, farvertex);
	/* Check whether the previous polygon vertex is a reflex vertex. */
	if (leftside) {
		if (counterclockwise(m, b, nearvertex, leftvertex, farvertex) <= 0.0) {
			/* leftvertex is a reflex vertex too.  Nothing can */
			/*   be done until a convex section is found.      */
			return;
		}
	}
	else {
		if (counterclockwise(m, b, farvertex, rightvertex, nearvertex) <= 0.0) {
			/* rightvertex is a reflex vertex too.  Nothing can */
			/*   be done until a convex section is found.       */
			return;
		}
	}
	if (counterclockwise(m, b, rightvertex, leftvertex, farvertex) > 0.0) {
		/* fartri is not an inverted triangle, and farvertex is not a reflex */
		/*   vertex.  As there are no reflex vertices, fixuptri isn't an     */
		/*   inverted triangle, either.  Hence, test the edge between the    */
		/*   triangles to ensure it is locally Delaunay.                     */
		if (incircle(m, b, leftvertex, farvertex, rightvertex, nearvertex) <=
			0.0) {
			return;
		}
		/* Not locally Delaunay; go on to an edge flip. */
	}        /* else fartri is inverted; remove it from the stack by flipping. */
	flip(m, b, &neartri);
	lprevself(*fixuptri);    /* Restore the origin of fixuptri after the flip. */
							 /* Recursively process the two triangles that result from the flip. */
	delaunayfixup(m, b, fixuptri, leftside);
	delaunayfixup(m, b, &fartri, leftside);
}

/*****************************************************************************/
/*                                                                           */
/*  constrainededge()   Force a segment into a constrained Delaunay          */
/*                      triangulation by deleting the triangles it           */
/*                      intersects, and triangulating the polygons that      */
/*                      form on each side of it.                             */
/*                                                                           */
/*  Generates a single subsegment connecting `endpoint1' to `endpoint2'.     */
/*  The triangle `starttri' has `endpoint1' as its origin.  `newmark' is the */
/*  boundary marker of the segment.                                          */
/*                                                                           */
/*  To insert a segment, every triangle whose interior intersects the        */
/*  segment is deleted.  The union of these deleted triangles is a polygon   */
/*  (which is not necessarily monotone, but is close enough), which is       */
/*  divided into two polygons by the new segment.  This routine's task is    */
/*  to generate the Delaunay triangulation of these two polygons.            */
/*                                                                           */
/*  You might think of this routine's behavior as a two-step process.  The   */
/*  first step is to walk from endpoint1 to endpoint2, flipping each edge    */
/*  encountered.  This step creates a fan of edges connected to endpoint1,   */
/*  including the desired edge to endpoint2.  The second step enforces the   */
/*  Delaunay condition on each side of the segment in an incremental manner: */
/*  proceeding along the polygon from endpoint1 to endpoint2 (this is done   */
/*  independently on each side of the segment), each vertex is "enforced"    */
/*  as if it had just been inserted, but affecting only the previous         */
/*  vertices.  The result is the same as if the vertices had been inserted   */
/*  in the order they appear on the polygon, so the result is Delaunay.      */
/*                                                                           */
/*  In truth, constrainededge() interleaves these two steps.  The procedure  */
/*  walks from endpoint1 to endpoint2, and each time an edge is encountered  */
/*  and flipped, the newly exposed vertex (at the far end of the flipped     */
/*  edge) is "enforced" upon the previously flipped edges, usually affecting */
/*  only one side of the polygon (depending upon which side of the segment   */
/*  the vertex falls on).                                                    */
/*                                                                           */
/*  The algorithm is complicated by the need to handle polygons that are not */
/*  convex.  Although the polygon is not necessarily monotone, it can be     */
/*  triangulated in a manner similar to the stack-based algorithms for       */
/*  monotone polygons.  For each reflex vertex (local concavity) of the      */
/*  polygon, there will be an inverted triangle formed by one of the edge    */
/*  flips.  (An inverted triangle is one with negative area - that is, its   */
/*  vertices are arranged in clockwise order - and is best thought of as a   */
/*  wrinkle in the fabric of the mesh.)  Each inverted triangle can be       */
/*  thought of as a reflex vertex pushed on the stack, waiting to be fixed   */
/*  later.                                                                   */
/*                                                                           */
/*  A reflex vertex is popped from the stack when a vertex is inserted that  */
/*  is visible to the reflex vertex.  (However, if the vertex behind the     */
/*  reflex vertex is not visible to the reflex vertex, a new inverted        */
/*  triangle will take its place on the stack.)  These details are handled   */
/*  by the delaunayfixup() routine above.                                    */
/*                                                                           */
/*****************************************************************************/

#ifdef ANSI_DECLARATORS
void constrainededge(struct mesh *m, struct behavior *b,
struct otri *starttri, vertex endpoint2, int newmark)
#else /* not ANSI_DECLARATORS */
void constrainededge(m, b, starttri, endpoint2, newmark)
struct mesh *m;
struct behavior *b;
struct otri *starttri;
vertex endpoint2;
int newmark;
#endif /* not ANSI_DECLARATORS */

{
	struct otri fixuptri, fixuptri2;
	struct osub crosssubseg;
	vertex endpoint1;
	vertex farvertex;
	REAL area;
	int collision;
	int done;
	triangle ptr;             /* Temporary variable used by sym() and oprev(). */
	subseg sptr;                      /* Temporary variable used by tspivot(). */

	org(*starttri, endpoint1);
	lnext(*starttri, fixuptri);
	flip(m, b, &fixuptri);
	/* `collision' indicates whether we have found a vertex directly */
	/*   between endpoint1 and endpoint2.                            */
	collision = 0;
	done = 0;
	do {
		org(fixuptri, farvertex);
		/* `farvertex' is the extreme point of the polygon we are "digging" */
		/*   to get from endpoint1 to endpoint2.                           */
		if ((farvertex[0] == endpoint2[0]) && (farvertex[1] == endpoint2[1])) {
			oprev(fixuptri, fixuptri2);
			/* Enforce the Delaunay condition around endpoint2. */
			delaunayfixup(m, b, &fixuptri, 0);
			delaunayfixup(m, b, &fixuptri2, 1);
			done = 1;
		}
		else {
			/* Check whether farvertex is to the left or right of the segment */
			/*   being inserted, to decide which edge of fixuptri to dig      */
			/*   through next.                                                */
			area = counterclockwise(m, b, endpoint1, endpoint2, farvertex);
			if (area == 0.0) {
				/* We've collided with a vertex between endpoint1 and endpoint2. */
				collision = 1;
				oprev(fixuptri, fixuptri2);
				/* Enforce the Delaunay condition around farvertex. */
				delaunayfixup(m, b, &fixuptri, 0);
				delaunayfixup(m, b, &fixuptri2, 1);
				done = 1;
			}
			else {
				if (area > 0.0) {        /* farvertex is to the left of the segment. */
					oprev(fixuptri, fixuptri2);
					/* Enforce the Delaunay condition around farvertex, on the */
					/*   left side of the segment only.                        */
					delaunayfixup(m, b, &fixuptri2, 1);
					/* Flip the edge that crosses the segment.  After the edge is */
					/*   flipped, one of its endpoints is the fan vertex, and the */
					/*   destination of fixuptri is the fan vertex.               */
					lprevself(fixuptri);
				}
				else {                /* farvertex is to the right of the segment. */
					delaunayfixup(m, b, &fixuptri, 0);
					/* Flip the edge that crosses the segment.  After the edge is */
					/*   flipped, one of its endpoints is the fan vertex, and the */
					/*   destination of fixuptri is the fan vertex.               */
					oprevself(fixuptri);
				}
				/* Check for two intersecting segments. */
				tspivot(fixuptri, crosssubseg);
				if (crosssubseg.ss == m->dummysub) {
					flip(m, b, &fixuptri);    /* May create inverted triangle at left. */
				}
				else {
					/* We've collided with a segment between endpoint1 and endpoint2. */
					collision = 1;
					/* Insert a vertex at the intersection. */
					segmentintersection(m, b, &fixuptri, &crosssubseg, endpoint2);
					done = 1;
				}
			}
		}
	} while (!done);
	/* Insert a subsegment to make the segment permanent. */
	insertsubseg(m, b, &fixuptri, newmark);
	/* If there was a collision with an interceding vertex, install another */
	/*   segment connecting that vertex with endpoint2.                     */
	if (collision) {
		/* Insert the remainder of the segment. */
		if (!scoutsegment(m, b, &fixuptri, endpoint2, newmark)) {
			constrainededge(m, b, &fixuptri, endpoint2, newmark);
		}
	}
}

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

#ifdef ANSI_DECLARATORS
void insertsegment(struct mesh *m, struct behavior *b,
	vertex endpoint1, vertex endpoint2, int newmark)
#else /* not ANSI_DECLARATORS */
void insertsegment(m, b, endpoint1, endpoint2, newmark)
struct mesh *m;
struct behavior *b;
vertex endpoint1;
vertex endpoint2;
int newmark;
#endif /* not ANSI_DECLARATORS */

{
	struct otri searchtri1, searchtri2;
	triangle encodedtri;
	vertex checkvertex;
	triangle ptr;                         /* Temporary variable used by sym(). */

	if (b->verbose > 1) {
		printf("  Connecting (%.12g, %.12g) to (%.12g, %.12g).\n",
			endpoint1[0], endpoint1[1], endpoint2[0], endpoint2[1]);
	}

	/* Find a triangle whose origin is the segment's first endpoint. */
	checkvertex = (vertex)NULL;
	encodedtri = vertex2tri(endpoint1);
	if (encodedtri != (triangle)NULL) {
		decode(encodedtri, searchtri1);
		org(searchtri1, checkvertex);
	}
	if (checkvertex != endpoint1) {
		/* Find a boundary triangle to search from. */
		searchtri1.tri = m->dummytri;
		searchtri1.orient = 0;
		symself(searchtri1);
		/* Search for the segment's first endpoint by point location. */
		if (locate(m, b, endpoint1, &searchtri1) != ONVERTEX) {
			printf(
				"Internal error in insertsegment():  Unable to locate PSLG vertex\n");
			printf("  (%.12g, %.12g) in triangulation.\n",
				endpoint1[0], endpoint1[1]);
			internalerror();
		}
	}
	/* Remember this triangle to improve subsequent point location. */
	otricopy(searchtri1, m->recenttri);
	/* Scout the beginnings of a path from the first endpoint */
	/*   toward the second.                                   */
	if (scoutsegment(m, b, &searchtri1, endpoint2, newmark)) {
		/* The segment was easily inserted. */
		return;
	}
	/* The first endpoint may have changed if a collision with an intervening */
	/*   vertex on the segment occurred.                                      */
	org(searchtri1, endpoint1);

	/* Find a triangle whose origin is the segment's second endpoint. */
	checkvertex = (vertex)NULL;
	encodedtri = vertex2tri(endpoint2);
	if (encodedtri != (triangle)NULL) {
		decode(encodedtri, searchtri2);
		org(searchtri2, checkvertex);
	}
	if (checkvertex != endpoint2) {
		/* Find a boundary triangle to search from. */
		searchtri2.tri = m->dummytri;
		searchtri2.orient = 0;
		symself(searchtri2);
		/* Search for the segment's second endpoint by point location. */
		if (locate(m, b, endpoint2, &searchtri2) != ONVERTEX) {
			printf(
				"Internal error in insertsegment():  Unable to locate PSLG vertex\n");
			printf("  (%.12g, %.12g) in triangulation.\n",
				endpoint2[0], endpoint2[1]);
			internalerror();
		}
	}
	/* Remember this triangle to improve subsequent point location. */
	otricopy(searchtri2, m->recenttri);
	/* Scout the beginnings of a path from the second endpoint */
	/*   toward the first.                                     */
	if (scoutsegment(m, b, &searchtri2, endpoint1, newmark)) {
		/* The segment was easily inserted. */
		return;
	}
	/* The second endpoint may have changed if a collision with an intervening */
	/*   vertex on the segment occurred.                                       */
	org(searchtri2, endpoint2);

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

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

#ifdef ANSI_DECLARATORS
void markhull(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
void markhull(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */

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

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

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

#ifdef TRILIBRARY

#ifdef ANSI_DECLARATORS
void formskeleton(struct mesh *m, struct behavior *b, int *segmentlist,
	int *segmentmarkerlist, int numberofsegments)
#else /* not ANSI_DECLARATORS */
void formskeleton(m, b, segmentlist, segmentmarkerlist, numberofsegments)
struct mesh *m;
struct behavior *b;
int *segmentlist;
int *segmentmarkerlist;
int numberofsegments;
#endif /* not ANSI_DECLARATORS */

#else /* not TRILIBRARY */

#ifdef ANSI_DECLARATORS
void formskeleton(struct mesh *m, struct behavior *b,
	FILE *polyfile, char *polyfilename)
#else /* not ANSI_DECLARATORS */
void formskeleton(m, b, polyfile, polyfilename)
struct mesh *m;
struct behavior *b;
FILE *polyfile;
char *polyfilename;
#endif /* not ANSI_DECLARATORS */

#endif /* not TRILIBRARY */

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

	if (b->poly) {
		if (!b->quiet) {
			printf("Recovering segments in Delaunay triangulation.\n");
		}
#ifdef TRILIBRARY
		strcpy(polyfilename, "input");
		m->insegments = numberofsegments;
		segmentmarkers = segmentmarkerlist != (int *)NULL;
		index = 0;
#else /* not TRILIBRARY */
		/* Read the segments from a .poly file. */
		/* Read number of segments and number of boundary markers. */
		stringptr = readline(inputline, polyfile, polyfilename);
		m->insegments = (int)strtol(stringptr, &stringptr, 0);
		stringptr = findfield(stringptr);
		if (*stringptr == '\0') {
			segmentmarkers = 0;
		}
		else {
			segmentmarkers = (int)strtol(stringptr, &stringptr, 0);
		}
#endif /* not TRILIBRARY */
		/* If the input vertices are collinear, there is no triangulation, */
		/*   so don't try to insert segments.                              */
		if (m->triangles.items == 0) {
			return;
		}

		/* If segments are to be inserted, compute a mapping */
		/*   from vertices to triangles.                     */
		if (m->insegments > 0) {
			makevertexmap(m, b);
			if (b->verbose) {
				printf("  Recovering PSLG segments.\n");
			}
		}

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

/**                                                                         **/
/**                                                                         **/
/********* Segment insertion ends here                               *********/

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

/*****************************************************************************/
/*                                                                           */
/*  infecthull()   Virally infect all of the triangles of the convex hull    */
/*                 that are not protected by subsegments.  Where there are   */
/*                 subsegments, set boundary markers as appropriate.         */
/*                                                                           */
/*****************************************************************************/

#ifdef ANSI_DECLARATORS
void infecthull(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
void infecthull(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */

{
	struct otri hulltri;
	struct otri nexttri;
	struct otri starttri;
	struct osub hullsubseg;
	triangle **deadtriangle;
	vertex horg, hdest;
	triangle ptr;                         /* Temporary variable used by sym(). */
	subseg sptr;                      /* Temporary variable used by tspivot(). */

	if (b->verbose) {
		printf("  Marking concavities (external triangles) for elimination.\n");
	}
	/* Find a triangle handle on the hull. */
	hulltri.tri = m->dummytri;
	hulltri.orient = 0;
	symself(hulltri);
	/* Remember where we started so we know when to stop. */
	otricopy(hulltri, starttri);
	/* Go once counterclockwise around the convex hull. */
	do {
		/* Ignore triangles that are already infected. */
		if (!infected(hulltri)) {
			/* Is the triangle protected by a subsegment? */
			tspivot(hulltri, hullsubseg);
			if (hullsubseg.ss == m->dummysub) {
				/* The triangle is not protected; infect it. */
				if (!infected(hulltri)) {
					infect(hulltri);
					deadtriangle = (triangle **)poolalloc(&m->viri);
					*deadtriangle = hulltri.tri;
				}
			}
			else {
				/* The triangle is protected; set boundary markers if appropriate. */
				if (mark(hullsubseg) == 0) {
					setmark(hullsubseg, 1);
					org(hulltri, horg);
					dest(hulltri, hdest);
					if (vertexmark(horg) == 0) {
						setvertexmark(horg, 1);
					}
					if (vertexmark(hdest) == 0) {
						setvertexmark(hdest, 1);
					}
				}
			}
		}
		/* To find the next hull edge, go clockwise around the next vertex. */
		lnextself(hulltri);
		oprev(hulltri, nexttri);
		while (nexttri.tri != m->dummytri) {
			otricopy(nexttri, hulltri);
			oprev(hulltri, nexttri);
		}
	} while (!otriequal(hulltri, starttri));
}

/*****************************************************************************/
/*                                                                           */
/*  plague()   Spread the virus from all infected triangles to any neighbors */
/*             not protected by subsegments.  Delete all infected triangles. */
/*                                                                           */
/*  This is the procedure that actually creates holes and concavities.       */
/*                                                                           */
/*  This procedure operates in two phases.  The first phase identifies all   */
/*  the triangles that will die, and marks them as infected.  They are       */
/*  marked to ensure that each triangle is added to the virus pool only      */
/*  once, so the procedure will terminate.                                   */
/*                                                                           */
/*  The second phase actually eliminates the infected triangles.  It also    */
/*  eliminates orphaned vertices.                                            */
/*                                                                           */
/*****************************************************************************/

#ifdef ANSI_DECLARATORS
void plague(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
void plague(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */

{
	struct otri testtri;
	struct otri neighbor;
	triangle **virusloop;
	triangle **deadtriangle;
	struct osub neighborsubseg;
	vertex testvertex;
	vertex norg, ndest;
	vertex deadorg, deaddest, deadapex;
	int killorg;
	triangle ptr;             /* Temporary variable used by sym() and onext(). */
	subseg sptr;                      /* Temporary variable used by tspivot(). */

	if (b->verbose) {
		printf("  Marking neighbors of marked triangles.\n");
	}
	/* Loop through all the infected triangles, spreading the virus to */
	/*   their neighbors, then to their neighbors' neighbors.          */
	traversalinit(&m->viri);
	virusloop = (triangle **)traverse(&m->viri);
	while (virusloop != (triangle **)NULL) {
		testtri.tri = *virusloop;
		/* A triangle is marked as infected by messing with one of its pointers */
		/*   to subsegments, setting it to an illegal value.  Hence, we have to */
		/*   temporarily uninfect this triangle so that we can examine its      */
		/*   adjacent subsegments.                                              */
		uninfect(testtri);
		if (b->verbose > 2) {
			/* Assign the triangle an orientation for convenience in */
			/*   checking its vertices.                              */
			testtri.orient = 0;
			org(testtri, deadorg);
			dest(testtri, deaddest);
			apex(testtri, deadapex);
			printf("    Checking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
				deadorg[0], deadorg[1], deaddest[0], deaddest[1],
				deadapex[0], deadapex[1]);
		}
		/* Check each of the triangle's three neighbors. */
		for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
			/* Find the neighbor. */
			sym(testtri, neighbor);
			/* Check for a subsegment between the triangle and its neighbor. */
			tspivot(testtri, neighborsubseg);
			/* Check if the neighbor is nonexistent or already infected. */
			if ((neighbor.tri == m->dummytri) || infected(neighbor)) {
				if (neighborsubseg.ss != m->dummysub) {
					/* There is a subsegment separating the triangle from its      */
					/*   neighbor, but both triangles are dying, so the subsegment */
					/*   dies too.                                                 */
					subsegdealloc(m, neighborsubseg.ss);
					if (neighbor.tri != m->dummytri) {
						/* Make sure the subsegment doesn't get deallocated again */
						/*   later when the infected neighbor is visited.         */
						uninfect(neighbor);
						tsdissolve(neighbor);
						infect(neighbor);
					}
				}
			}
			else {                   /* The neighbor exists and is not infected. */
				if (neighborsubseg.ss == m->dummysub) {
					/* There is no subsegment protecting the neighbor, so */
					/*   the neighbor becomes infected.                   */
					if (b->verbose > 2) {
						org(neighbor, deadorg);
						dest(neighbor, deaddest);
						apex(neighbor, deadapex);
						printf(
							"    Marking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
							deadorg[0], deadorg[1], deaddest[0], deaddest[1],
							deadapex[0], deadapex[1]);
					}
					infect(neighbor);
					/* Ensure that the neighbor's neighbors will be infected. */
					deadtriangle = (triangle **)poolalloc(&m->viri);
					*deadtriangle = neighbor.tri;
				}
				else {               /* The neighbor is protected by a subsegment. */
									 /* Remove this triangle from the subsegment. */
					stdissolve(neighborsubseg);
					/* The subsegment becomes a boundary.  Set markers accordingly. */
					if (mark(neighborsubseg) == 0) {
						setmark(neighborsubseg, 1);
					}
					org(neighbor, norg);
					dest(neighbor, ndest);
					if (vertexmark(norg) == 0) {
						setvertexmark(norg, 1);
					}
					if (vertexmark(ndest) == 0) {
						setvertexmark(ndest, 1);
					}
				}
			}
		}
		/* Remark the triangle as infected, so it doesn't get added to the */
		/*   virus pool again.                                             */
		infect(testtri);
		virusloop = (triangle **)traverse(&m->viri);
	}

	if (b->verbose) {
		printf("  Deleting marked triangles.\n");
	}

	traversalinit(&m->viri);
	virusloop = (triangle **)traverse(&m->viri);
	while (virusloop != (triangle **)NULL) {
		testtri.tri = *virusloop;

		/* Check each of the three corners of the triangle for elimination. */
		/*   This is done by walking around each vertex, checking if it is  */
		/*   still connected to at least one live triangle.                 */
		for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
			org(testtri, testvertex);
			/* Check if the vertex has already been tested. */
			if (testvertex != (vertex)NULL) {
				killorg = 1;
				/* Mark the corner of the triangle as having been tested. */
				setorg(testtri, NULL);
				/* Walk counterclockwise about the vertex. */
				onext(testtri, neighbor);
				/* Stop upon reaching a boundary or the starting triangle. */
				while ((neighbor.tri != m->dummytri) &&
					(!otriequal(neighbor, testtri))) {
					if (infected(neighbor)) {
						/* Mark the corner of this triangle as having been tested. */
						setorg(neighbor, NULL);
					}
					else {
						/* A live triangle.  The vertex survives. */
						killorg = 0;
					}
					/* Walk counterclockwise about the vertex. */
					onextself(neighbor);
				}
				/* If we reached a boundary, we must walk clockwise as well. */
				if (neighbor.tri == m->dummytri) {
					/* Walk clockwise about the vertex. */
					oprev(testtri, neighbor);
					/* Stop upon reaching a boundary. */
					while (neighbor.tri != m->dummytri) {
						if (infected(neighbor)) {
							/* Mark the corner of this triangle as having been tested. */
							setorg(neighbor, NULL);
						}
						else {
							/* A live triangle.  The vertex survives. */
							killorg = 0;
						}
						/* Walk clockwise about the vertex. */
						oprevself(neighbor);
					}
				}
				if (killorg) {
					if (b->verbose > 1) {
						printf("    Deleting vertex (%.12g, %.12g)\n",
							testvertex[0], testvertex[1]);
					}
					setvertextype(testvertex, UNDEADVERTEX);
					m->undeads++;
				}
			}
		}

		/* Record changes in the number of boundary edges, and disconnect */
		/*   dead triangles from their neighbors.                         */
		for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
			sym(testtri, neighbor);
			if (neighbor.tri == m->dummytri) {
				/* There is no neighboring triangle on this edge, so this edge    */
				/*   is a boundary edge.  This triangle is being deleted, so this */
				/*   boundary edge is deleted.                                    */
				m->hullsize--;
			}
			else {
				/* Disconnect the triangle from its neighbor. */
				dissolve(neighbor);
				/* There is a neighboring triangle on this edge, so this edge */
				/*   becomes a boundary edge when this triangle is deleted.   */
				m->hullsize++;
			}
		}
		/* Return the dead triangle to the pool of triangles. */
		triangledealloc(m, testtri.tri);
		virusloop = (triangle **)traverse(&m->viri);
	}
	/* Empty the virus pool. */
	poolrestart(&m->viri);
}

/*****************************************************************************/
/*                                                                           */
/*  regionplague()   Spread regional attributes and/or area constraints      */
/*                   (from a .poly file) throughout the mesh.                */
/*                                                                           */
/*  This procedure operates in two phases.  The first phase spreads an       */
/*  attribute and/or an area constraint through a (segment-bounded) region.  */
/*  The triangles are marked to ensure that each triangle is added to the    */
/*  virus pool only once, so the procedure will terminate.                   */
/*                                                                           */
/*  The second phase uninfects all infected triangles, returning them to     */
/*  normal.                                                                  */
/*                                                                           */
/*****************************************************************************/

#ifdef ANSI_DECLARATORS
void regionplague(struct mesh *m, struct behavior *b,
	REAL attribute, REAL area)
#else /* not ANSI_DECLARATORS */
void regionplague(m, b, attribute, area)
struct mesh *m;
struct behavior *b;
REAL attribute;
REAL area;
#endif /* not ANSI_DECLARATORS */

{
	struct otri testtri;
	struct otri neighbor;
	triangle **virusloop;
	triangle **regiontri;
	struct osub neighborsubseg;
	vertex regionorg, regiondest, regionapex;
	triangle ptr;             /* Temporary variable used by sym() and onext(). */
	subseg sptr;                      /* Temporary variable used by tspivot(). */

	if (b->verbose > 1) {
		printf("  Marking neighbors of marked triangles.\n");
	}
	/* Loop through all the infected triangles, spreading the attribute      */
	/*   and/or area constraint to their neighbors, then to their neighbors' */
	/*   neighbors.                                                          */
	traversalinit(&m->viri);
	virusloop = (triangle **)traverse(&m->viri);
	while (virusloop != (triangle **)NULL) {
		testtri.tri = *virusloop;
		/* A triangle is marked as infected by messing with one of its pointers */
		/*   to subsegments, setting it to an illegal value.  Hence, we have to */
		/*   temporarily uninfect this triangle so that we can examine its      */
		/*   adjacent subsegments.                                              */
		uninfect(testtri);
		if (b->regionattrib) {
			/* Set an attribute. */
			setelemattribute(testtri, m->eextras, attribute);
		}
		if (b->vararea) {
			/* Set an area constraint. */
			setareabound(testtri, area);
		}
		if (b->verbose > 2) {
			/* Assign the triangle an orientation for convenience in */
			/*   checking its vertices.                              */
			testtri.orient = 0;
			org(testtri, regionorg);
			dest(testtri, regiondest);
			apex(testtri, regionapex);
			printf("    Checking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
				regionorg[0], regionorg[1], regiondest[0], regiondest[1],
				regionapex[0], regionapex[1]);
		}
		/* Check each of the triangle's three neighbors. */
		for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
			/* Find the neighbor. */
			sym(testtri, neighbor);
			/* Check for a subsegment between the triangle and its neighbor. */
			tspivot(testtri, neighborsubseg);
			/* Make sure the neighbor exists, is not already infected, and */
			/*   isn't protected by a subsegment.                          */
			if ((neighbor.tri != m->dummytri) && !infected(neighbor)
				&& (neighborsubseg.ss == m->dummysub)) {
				if (b->verbose > 2) {
					org(neighbor, regionorg);
					dest(neighbor, regiondest);
					apex(neighbor, regionapex);
					printf("    Marking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
						regionorg[0], regionorg[1], regiondest[0], regiondest[1],
						regionapex[0], regionapex[1]);
				}
				/* Infect the neighbor. */
				infect(neighbor);
				/* Ensure that the neighbor's neighbors will be infected. */
				regiontri = (triangle **)poolalloc(&m->viri);
				*regiontri = neighbor.tri;
			}
		}
		/* Remark the triangle as infected, so it doesn't get added to the */
		/*   virus pool again.                                             */
		infect(testtri);
		virusloop = (triangle **)traverse(&m->viri);
	}

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

/*****************************************************************************/
/*                                                                           */
/*  carveholes()   Find the holes and infect them.  Find the area            */
/*                 constraints and infect them.  Infect the convex hull.     */
/*                 Spread the infection and kill triangles.  Spread the      */
/*                 area constraints.                                         */
/*                                                                           */
/*  This routine mainly calls other routines to carry out all these          */
/*  functions.                                                               */
/*                                                                           */
/*****************************************************************************/

#ifdef ANSI_DECLARATORS
void carveholes(struct mesh *m, struct behavior *b, REAL *holelist, int holes,
	REAL *regionlist, int regions)
#else /* not ANSI_DECLARATORS */
void carveholes(m, b, holelist, holes, regionlist, regions)
struct mesh *m;
struct behavior *b;
REAL *holelist;
int holes;
REAL *regionlist;
int regions;
#endif /* not ANSI_DECLARATORS */

{
	struct otri searchtri;
	struct otri triangleloop;
	struct otri *regiontris;
	triangle **holetri;
	triangle **regiontri;
	vertex searchorg, searchdest;
	enum locateresult intersect;
	int i;
	triangle ptr;                         /* Temporary variable used by sym(). */

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

	if (regions > 0) {
		/* Allocate storage for the triangles in which region points fall. */
		regiontris = (struct otri *) trimalloc(regions *
			(int) sizeof(struct otri));
	}
	else {
		regiontris = (struct otri *) NULL;
	}

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

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

	if ((holes > 0) && !b->noholes) {
		/* Infect each triangle in which a hole lies. */
		for (i = 0; i < 2 * holes; i += 2) {
			/* Ignore holes that aren't within the bounds of the mesh. */
			if ((holelist[i] >= m->xmin) && (holelist[i] <= m->xmax)
				&& (holelist[i + 1] >= m->ymin) && (holelist[i + 1] <= m->ymax)) {
				/* Start searching from some triangle on the outer boundary. */
				searchtri.tri = m->dummytri;
				searchtri.orient = 0;
				symself(searchtri);
				/* Ensure that the hole is to the left of this boundary edge; */
				/*   otherwise, locate() will falsely report that the hole    */
				/*   falls within the starting triangle.                      */
				org(searchtri, searchorg);
				dest(searchtri, searchdest);
				if (counterclockwise(m, b, searchorg, searchdest, &holelist[i]) >
					0.0) {
					/* Find a triangle that contains the hole. */
					intersect = locate(m, b, &holelist[i], &searchtri);
					if ((intersect != OUTSIDE) && (!infected(searchtri))) {
						/* Infect the triangle.  This is done by marking the triangle  */
						/*   as infected and including the triangle in the virus pool. */
						infect(searchtri);
						holetri = (triangle **)poolalloc(&m->viri);
						*holetri = searchtri.tri;
					}
				}
			}
		}
	}

	/* Now, we have to find all the regions BEFORE we carve the holes, because */
	/*   locate() won't work when the triangulation is no longer convex.       */
	/*   (Incidentally, this is the reason why regional attributes and area    */
	/*   constraints can't be used when refining a preexisting mesh, which     */
	/*   might not be convex; they can only be used with a freshly             */
	/*   triangulated PSLG.)                                                   */
	if (regions > 0) {
		/* Find the starting triangle for each region. */
		for (i = 0; i < regions; i++) {
			regiontris[i].tri = m->dummytri;
			/* Ignore region points that aren't within the bounds of the mesh. */
			if ((regionlist[4 * i] >= m->xmin) && (regionlist[4 * i] <= m->xmax) &&
				(regionlist[4 * i + 1] >= m->ymin) &&
				(regionlist[4 * i + 1] <= m->ymax)) {
				/* Start searching from some triangle on the outer boundary. */
				searchtri.tri = m->dummytri;
				searchtri.orient = 0;
				symself(searchtri);
				/* Ensure that the region point is to the left of this boundary */
				/*   edge; otherwise, locate() will falsely report that the     */
				/*   region point falls within the starting triangle.           */
				org(searchtri, searchorg);
				dest(searchtri, searchdest);
				if (counterclockwise(m, b, searchorg, searchdest, &regionlist[4 * i]) >
					0.0) {
					/* Find a triangle that contains the region point. */
					intersect = locate(m, b, &regionlist[4 * i], &searchtri);
					if ((intersect != OUTSIDE) && (!infected(searchtri))) {
						/* Record the triangle for processing after the */
						/*   holes have been carved.                    */
						otricopy(searchtri, regiontris[i]);
					}
				}
			}
		}
	}

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

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

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

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

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

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

#ifndef CDT_ONLY

#ifdef ANSI_DECLARATORS
void tallyencs(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
void tallyencs(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */

{
	struct osub subsegloop;
	int dummy;

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

#endif /* not CDT_ONLY */

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

#ifndef CDT_ONLY

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

#endif /* not CDT_ONLY */

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

#ifndef CDT_ONLY

#ifdef ANSI_DECLARATORS
void splitencsegs(struct mesh *m, struct behavior *b, int triflaws)
#else /* not ANSI_DECLARATORS */
void splitencsegs(m, b, triflaws)
struct mesh *m;
struct behavior *b;
int triflaws;
#endif /* not ANSI_DECLARATORS */

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

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

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

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

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

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

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

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

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

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

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

#endif /* not CDT_ONLY */

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

#ifndef CDT_ONLY

#ifdef ANSI_DECLARATORS
void tallyfaces(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
void tallyfaces(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */

{
	struct otri triangleloop;

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

#endif /* not CDT_ONLY */

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

#ifndef CDT_ONLY

#ifdef ANSI_DECLARATORS
void splittriangle(struct mesh *m, struct behavior *b,
struct badtriang *badtri)
#else /* not ANSI_DECLARATORS */
void splittriangle(m, b, badtri)
struct mesh *m;
struct behavior *b;
struct badtriang *badtri;
#endif /* not ANSI_DECLARATORS */

{
	struct otri badotri;
	vertex borg, bdest, bapex;
	vertex newvertex;
	REAL xi, eta;
	enum insertvertexresult success;
	int errorflag;
	int i;

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

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

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

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

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

#endif /* not CDT_ONLY */

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

#ifndef CDT_ONLY

#ifdef ANSI_DECLARATORS
void enforcequality(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
void enforcequality(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */

{
	struct badtriang *badtri;
	int i;

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

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

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

#endif /* not CDT_ONLY */

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

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

#ifdef ANSI_DECLARATORS
void highorder(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
void highorder(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */

{
	struct otri triangleloop, trisym;
	struct osub checkmark;
	vertex newvertex;
	vertex torg, tdest;
	int i;
	triangle ptr;                         /* Temporary variable used by sym(). */
	subseg sptr;                      /* Temporary variable used by tspivot(). */

	if (!b->quiet) {
		printf("Adding vertices for second-order triangles.\n");
	}
	/* The following line ensures that dead items in the pool of nodes    */
	/*   cannot be allocated for the extra nodes associated with high     */
	/*   order elements.  This ensures that the primary nodes (at the     */
	/*   corners of elements) will occur earlier in the output files, and */
	/*   have lower indices, than the extra nodes.                        */
	m->vertices.deaditemstack = (VOID *)NULL;

	traversalinit(&m->triangles);
	triangleloop.tri = triangletraverse(m);
	/* To loop over the set of edges, loop over all triangles, and look at   */
	/*   the three edges of each triangle.  If there isn't another triangle  */
	/*   adjacent to the edge, operate on the edge.  If there is another     */
	/*   adjacent triangle, operate on the edge only if the current triangle */
	/*   has a smaller pointer than its neighbor.  This way, each edge is    */
	/*   considered only once.                                               */
	while (triangleloop.tri != (triangle *)NULL) {
		for (triangleloop.orient = 0; triangleloop.orient < 3;
		triangleloop.orient++) {
			sym(triangleloop, trisym);
			if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) {
				org(triangleloop, torg);
				dest(triangleloop, tdest);
				/* Create a new node in the middle of the edge.  Interpolate */
				/*   its attributes.                                         */
				newvertex = (vertex)poolalloc(&m->vertices);
				for (i = 0; i < 2 + m->nextras; i++) {
					newvertex[i] = 0.5 * (torg[i] + tdest[i]);
				}
				/* Set the new node's marker to zero or one, depending on */
				/*   whether it lies on a boundary.                       */
				setvertexmark(newvertex, trisym.tri == m->dummytri);
				setvertextype(newvertex,
					trisym.tri == m->dummytri ? FREEVERTEX : SEGMENTVERTEX);
				if (b->usesegments) {
					tspivot(triangleloop, checkmark);
					/* If this edge is a segment, transfer the marker to the new node. */
					if (checkmark.ss != m->dummysub) {
						setvertexmark(newvertex, mark(checkmark));
						setvertextype(newvertex, SEGMENTVERTEX);
					}
				}
				if (b->verbose > 1) {
					printf("  Creating (%.12g, %.12g).\n", newvertex[0], newvertex[1]);
				}
				/* Record the new node in the (one or two) adjacent elements. */
				triangleloop.tri[m->highorderindex + triangleloop.orient] =
					(triangle)newvertex;
				if (trisym.tri != m->dummytri) {
					trisym.tri[m->highorderindex + trisym.orient] = (triangle)newvertex;
				}
			}
		}
		triangleloop.tri = triangletraverse(m);
	}
}

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

/*****************************************************************************/
/*                                                                           */
/*  readline()   Read a nonempty line from a file.                           */
/*                                                                           */
/*  A line is considered "nonempty" if it contains something that looks like */
/*  a number.  Comments (prefaced by `#') are ignored.                       */
/*                                                                           */
/*****************************************************************************/

#ifndef TRILIBRARY

#ifdef ANSI_DECLARATORS
char *readline(char *string, FILE *infile, char *infilename)
#else /* not ANSI_DECLARATORS */
char *readline(string, infile, infilename)
char *string;
FILE *infile;
char *infilename;
#endif /* not ANSI_DECLARATORS */

{
	char *result;

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

#endif /* not TRILIBRARY */

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

#ifndef TRILIBRARY

#ifdef ANSI_DECLARATORS
char *findfield(char *string)
#else /* not ANSI_DECLARATORS */
char *findfield(string)
char *string;
#endif /* not ANSI_DECLARATORS */

{
	char *result;

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

#endif /* not TRILIBRARY */

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

#ifndef TRILIBRARY

#ifdef ANSI_DECLARATORS
void readnodes(struct mesh *m, struct behavior *b, char *nodefilename,
	char *polyfilename, FILE **polyfile)
#else /* not ANSI_DECLARATORS */
void readnodes(m, b, nodefilename, polyfilename, polyfile)
struct mesh *m;
struct behavior *b;
char *nodefilename;
char *polyfilename;
FILE **polyfile;
#endif /* not ANSI_DECLARATORS */

{
	FILE *infile;
	vertex vertexloop;
	char inputline[INPUTLINESIZE];
	char *stringptr;
	char *infilename;
	REAL x, y;
	int firstnode;
	int nodemarkers;
	int currentmarker;
	int i, j;

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

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

	if (m->invertices < 3) {
		printf("Error:  Input must have at least three input vertices.\n");
		triexit(1);
	}
	if (m->mesh_dim != 2) {
		printf("Error:  Triangle only works with two-dimensional meshes.\n");
		triexit(1);
	}
	if (m->nextras == 0) {
		b->weighted = 0;
	}

	initializevertexpool(m, b);

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

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

#endif /* not TRILIBRARY */

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

#ifdef TRILIBRARY

#ifdef ANSI_DECLARATORS
void transfernodes(struct mesh *m, struct behavior *b, REAL *pointlist,
	REAL *pointattriblist, int *pointmarkerlist,
	int numberofpoints, int numberofpointattribs)
#else /* not ANSI_DECLARATORS */
void transfernodes(m, b, pointlist, pointattriblist, pointmarkerlist,
	numberofpoints, numberofpointattribs)
struct mesh *m;
struct behavior *b;
REAL *pointlist;
REAL *pointattriblist;
int *pointmarkerlist;
int numberofpoints;
int numberofpointattribs;
#endif /* not ANSI_DECLARATORS */

{
	vertex vertexloop;
	REAL x, y;
	int i, j;
	int coordindex;
	int attribindex;

	m->invertices = numberofpoints;
	m->mesh_dim = 2;
	m->nextras = numberofpointattribs;
	m->readnodefile = 0;
	if (m->invertices < 3) {
		printf("Error:  Input must have at least three input vertices.\n");
		triexit(1);
	}
	if (m->nextras == 0) {
		b->weighted = 0;
	}

	initializevertexpool(m, b);

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

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

#endif /* TRILIBRARY */

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

#ifndef TRILIBRARY

#ifdef ANSI_DECLARATORS
void readholes(struct mesh *m, struct behavior *b,
	FILE *polyfile, char *polyfilename, REAL **hlist, int *holes,
	REAL **rlist, int *regions)
#else /* not ANSI_DECLARATORS */
void readholes(m, b, polyfile, polyfilename, hlist, holes, rlist, regions)
struct mesh *m;
struct behavior *b;
FILE *polyfile;
char *polyfilename;
REAL **hlist;
int *holes;
REAL **rlist;
int *regions;
#endif /* not ANSI_DECLARATORS */

{
	REAL *holelist;
	REAL *regionlist;
	char inputline[INPUTLINESIZE];
	char *stringptr;
	int index;
	int i;

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

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

	fclose(polyfile);
}

#endif /* not TRILIBRARY */

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

#ifndef TRILIBRARY

#ifdef ANSI_DECLARATORS
void finishfile(FILE *outfile, int argc, char **argv)
#else /* not ANSI_DECLARATORS */
void finishfile(outfile, argc, argv)
FILE *outfile;
int argc;
char **argv;
#endif /* not ANSI_DECLARATORS */

{
	int i;

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

#endif /* not TRILIBRARY */

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

#ifdef TRILIBRARY

#ifdef ANSI_DECLARATORS
void writenodes(struct mesh *m, struct behavior *b, REAL **pointlist,
	REAL **pointattriblist, int **pointmarkerlist)
#else /* not ANSI_DECLARATORS */
void writenodes(m, b, pointlist, pointattriblist, pointmarkerlist)
struct mesh *m;
struct behavior *b;
REAL **pointlist;
REAL **pointattriblist;
int **pointmarkerlist;
#endif /* not ANSI_DECLARATORS */

#else /* not TRILIBRARY */

#ifdef ANSI_DECLARATORS
void writenodes(struct mesh *m, struct behavior *b, char *nodefilename,
	int argc, char **argv)
#else /* not ANSI_DECLARATORS */
void writenodes(m, b, nodefilename, argc, argv)
struct mesh *m;
struct behavior *b;
char *nodefilename;
int argc;
char **argv;
#endif /* not ANSI_DECLARATORS */

#endif /* not TRILIBRARY */

{
#ifdef TRILIBRARY
	REAL *plist;
	REAL *palist;
	int *pmlist;
	int coordindex;
	int attribindex;
#else /* not TRILIBRARY */
	FILE *outfile;
#endif /* not TRILIBRARY */
	vertex vertexloop;
	long outvertices;
	int vertexnumber;
	int i;

	if (b->jettison) {
		outvertices = m->vertices.items - m->undeads;
	}
	else {
		outvertices = m->vertices.items;
	}

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

	traversalinit(&m->vertices);
	vertexnumber = b->firstnumber;
	vertexloop = vertextraverse(m);
	while (vertexloop != (vertex)NULL) {
		if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) {
#ifdef TRILIBRARY
			/* X and y coordinates. */
			plist[coordindex++] = vertexloop[0];
			plist[coordindex++] = vertexloop[1];
			/* Vertex attributes. */
			for (i = 0; i < m->nextras; i++) {
				palist[attribindex++] = vertexloop[2 + i];
			}
			if (!b->nobound) {
				/* Copy the boundary marker. */
				pmlist[vertexnumber - b->firstnumber] = vertexmark(vertexloop);
			}
#else /* not TRILIBRARY */
			/* Vertex number, x and y coordinates. */
			fprintf(outfile, "%4d    %.17g  %.17g", vertexnumber, vertexloop[0],
				vertexloop[1]);
			for (i = 0; i < m->nextras; i++) {
				/* Write an attribute. */
				fprintf(outfile, "  %.17g", vertexloop[i + 2]);
			}
			if (b->nobound) {
				fprintf(outfile, "\n");
			}
			else {
				/* Write the boundary marker. */
				fprintf(outfile, "    %d\n", vertexmark(vertexloop));
			}
#endif /* not TRILIBRARY */

			setvertexmark(vertexloop, vertexnumber);
			vertexnumber++;
		}
		vertexloop = vertextraverse(m);
	}

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

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

#ifdef ANSI_DECLARATORS
void numbernodes(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
void numbernodes(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */

{
	vertex vertexloop;
	int vertexnumber;

	traversalinit(&m->vertices);
	vertexnumber = b->firstnumber;
	vertexloop = vertextraverse(m);
	while (vertexloop != (vertex)NULL) {
		setvertexmark(vertexloop, vertexnumber);
		if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) {
			vertexnumber++;
		}
		vertexloop = vertextraverse(m);
	}
}

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

#ifdef TRILIBRARY

#ifdef ANSI_DECLARATORS
void writeelements(struct mesh *m, struct behavior *b,
	int **trianglelist, REAL **triangleattriblist)
#else /* not ANSI_DECLARATORS */
void writeelements(m, b, trianglelist, triangleattriblist)
struct mesh *m;
struct behavior *b;
int **trianglelist;
REAL **triangleattriblist;
#endif /* not ANSI_DECLARATORS */

#else /* not TRILIBRARY */

#ifdef ANSI_DECLARATORS
void writeelements(struct mesh *m, struct behavior *b, char *elefilename,
	int argc, char **argv)
#else /* not ANSI_DECLARATORS */
void writeelements(m, b, elefilename, argc, argv)
struct mesh *m;
struct behavior *b;
char *elefilename;
int argc;
char **argv;
#endif /* not ANSI_DECLARATORS */

#endif /* not TRILIBRARY */

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

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

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

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

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

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

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

#ifdef TRILIBRARY

#ifdef ANSI_DECLARATORS
void writepoly(struct mesh *m, struct behavior *b,
	int **segmentlist, int **segmentmarkerlist)
#else /* not ANSI_DECLARATORS */
void writepoly(m, b, segmentlist, segmentmarkerlist)
struct mesh *m;
struct behavior *b;
int **segmentlist;
int **segmentmarkerlist;
#endif /* not ANSI_DECLARATORS */

#else /* not TRILIBRARY */

#ifdef ANSI_DECLARATORS
void writepoly(struct mesh *m, struct behavior *b, char *polyfilename,
	REAL *holelist, int holes, REAL *regionlist, int regions,
	int argc, char **argv)
#else /* not ANSI_DECLARATORS */
void writepoly(m, b, polyfilename, holelist, holes, regionlist, regions,
	argc, argv)
struct mesh *m;
struct behavior *b;
char *polyfilename;
REAL *holelist;
int holes;
REAL *regionlist;
int regions;
int argc;
char **argv;
#endif /* not ANSI_DECLARATORS */

#endif /* not TRILIBRARY */

{
#ifdef TRILIBRARY
	int *slist;
	int *smlist;
	int index;
#else /* not TRILIBRARY */
	FILE *outfile;
	long holenumber, regionnumber;
#endif /* not TRILIBRARY */
	struct osub subsegloop;
	vertex endpoint1, endpoint2;
	long subsegnumber;

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

	traversalinit(&m->subsegs);
	subsegloop.ss = subsegtraverse(m);
	subsegloop.ssorient = 0;
	subsegnumber = b->firstnumber;
	while (subsegloop.ss != (subseg *)NULL) {
		sorg(subsegloop, endpoint1);
		sdest(subsegloop, endpoint2);
#ifdef TRILIBRARY
		/* Copy indices of the segment's two endpoints. */
		slist[index++] = vertexmark(endpoint1);
		slist[index++] = vertexmark(endpoint2);
		if (!b->nobound) {
			/* Copy the boundary marker. */
			smlist[subsegnumber - b->firstnumber] = mark(subsegloop);
		}
#else /* not TRILIBRARY */
		/* Segment number, indices of its two endpoints, and possibly a marker. */
		if (b->nobound) {
			fprintf(outfile, "%4ld    %4d  %4d\n", subsegnumber,
				vertexmark(endpoint1), vertexmark(endpoint2));
		}
		else {
			fprintf(outfile, "%4ld    %4d  %4d    %4d\n", subsegnumber,
				vertexmark(endpoint1), vertexmark(endpoint2), mark(subsegloop));
		}
#endif /* not TRILIBRARY */

		subsegloop.ss = subsegtraverse(m);
		subsegnumber++;
	}

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

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

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

#ifdef TRILIBRARY

#ifdef ANSI_DECLARATORS
void writeedges(struct mesh *m, struct behavior *b,
	int **edgelist, int **edgemarkerlist)
#else /* not ANSI_DECLARATORS */
void writeedges(m, b, edgelist, edgemarkerlist)
struct mesh *m;
struct behavior *b;
int **edgelist;
int **edgemarkerlist;
#endif /* not ANSI_DECLARATORS */

#else /* not TRILIBRARY */

#ifdef ANSI_DECLARATORS
void writeedges(struct mesh *m, struct behavior *b, char *edgefilename,
	int argc, char **argv)
#else /* not ANSI_DECLARATORS */
void writeedges(m, b, edgefilename, argc, argv)
struct mesh *m;
struct behavior *b;
char *edgefilename;
int argc;
char **argv;
#endif /* not ANSI_DECLARATORS */

#endif /* not TRILIBRARY */

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

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

	traversalinit(&m->triangles);
	triangleloop.tri = triangletraverse(m);
	edgenumber = b->firstnumber;
	/* To loop over the set of edges, loop over all triangles, and look at   */
	/*   the three edges of each triangle.  If there isn't another triangle  */
	/*   adjacent to the edge, operate on the edge.  If there is another     */
	/*   adjacent triangle, operate on the edge only if the current triangle */
	/*   has a smaller pointer than its neighbor.  This way, each edge is    */
	/*   considered only once.                                               */
	while (triangleloop.tri != (triangle *)NULL) {
		for (triangleloop.orient = 0; triangleloop.orient < 3;
		triangleloop.orient++) {
			sym(triangleloop, trisym);
			if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) {
				org(triangleloop, p1);
				dest(triangleloop, p2);
#ifdef TRILIBRARY
				elist[index++] = vertexmark(p1);
				elist[index++] = vertexmark(p2);
#endif /* TRILIBRARY */
				if (b->nobound) {
#ifndef TRILIBRARY
					/* Edge number, indices of two endpoints. */
					fprintf(outfile, "%4ld   %d  %d\n", edgenumber,
						vertexmark(p1), vertexmark(p2));
#endif /* not TRILIBRARY */
				}
				else {
					/* Edge number, indices of two endpoints, and a boundary marker. */
					/*   If there's no subsegment, the boundary marker is zero.      */
					if (b->usesegments) {
						tspivot(triangleloop, checkmark);
						if (checkmark.ss == m->dummysub) {
#ifdef TRILIBRARY
							emlist[edgenumber - b->firstnumber] = 0;
#else /* not TRILIBRARY */
							fprintf(outfile, "%4ld   %d  %d  %d\n", edgenumber,
								vertexmark(p1), vertexmark(p2), 0);
#endif /* not TRILIBRARY */
						}
						else {
#ifdef TRILIBRARY
							emlist[edgenumber - b->firstnumber] = mark(checkmark);
#else /* not TRILIBRARY */
							fprintf(outfile, "%4ld   %d  %d  %d\n", edgenumber,
								vertexmark(p1), vertexmark(p2), mark(checkmark));
#endif /* not TRILIBRARY */
						}
					}
					else {
#ifdef TRILIBRARY
						emlist[edgenumber - b->firstnumber] = trisym.tri == m->dummytri;
#else /* not TRILIBRARY */
						fprintf(outfile, "%4ld   %d  %d  %d\n", edgenumber,
							vertexmark(p1), vertexmark(p2), trisym.tri == m->dummytri);
#endif /* not TRILIBRARY */
					}
				}
				edgenumber++;
			}
		}
		triangleloop.tri = triangletraverse(m);
	}

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

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

#ifdef TRILIBRARY

#ifdef ANSI_DECLARATORS
void writevoronoi(struct mesh *m, struct behavior *b, REAL **vpointlist,
	REAL **vpointattriblist, int **vpointmarkerlist,
	int **vedgelist, int **vedgemarkerlist, REAL **vnormlist)
#else /* not ANSI_DECLARATORS */
void writevoronoi(m, b, vpointlist, vpointattriblist, vpointmarkerlist,
	vedgelist, vedgemarkerlist, vnormlist)
struct mesh *m;
struct behavior *b;
REAL **vpointlist;
REAL **vpointattriblist;
int **vpointmarkerlist;
int **vedgelist;
int **vedgemarkerlist;
REAL **vnormlist;
#endif /* not ANSI_DECLARATORS */

#else /* not TRILIBRARY */

#ifdef ANSI_DECLARATORS
void writevoronoi(struct mesh *m, struct behavior *b, char *vnodefilename,
	char *vedgefilename, int argc, char **argv)
#else /* not ANSI_DECLARATORS */
void writevoronoi(m, b, vnodefilename, vedgefilename, argc, argv)
struct mesh *m;
struct behavior *b;
char *vnodefilename;
char *vedgefilename;
int argc;
char **argv;
#endif /* not ANSI_DECLARATORS */

#endif /* not TRILIBRARY */

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

#ifdef TRILIBRARY
	if (!b->quiet) {
		printf("Writing Voronoi vertices.\n");
	}
	/* Allocate memory for Voronoi vertices if necessary. */
	if (*vpointlist == (REAL *)NULL) {
		*vpointlist = (REAL *)trimalloc((int)(m->triangles.items * 2 *
			sizeof(REAL)));
	}
	/* Allocate memory for Voronoi vertex attributes if necessary. */
	if (*vpointattriblist == (REAL *)NULL) {
		*vpointattriblist = (REAL *)trimalloc((int)(m->triangles.items *
			m->nextras * sizeof(REAL)));
	}
	*vpointmarkerlist = (int *)NULL;
	plist = *vpointlist;
	palist = *vpointattriblist;
	coordindex = 0;
	attribindex = 0;
#else /* not TRILIBRARY */
	if (!b->quiet) {
		printf("Writing %s.\n", vnodefilename);
	}
	outfile = fopen(vnodefilename, "w");
	if (outfile == (FILE *)NULL) {
		printf("  Error:  Cannot create file %s.\n", vnodefilename);
		triexit(1);
	}
	/* Number of triangles, two dimensions, number of vertex attributes, */
	/*   no markers.                                                     */
	fprintf(outfile, "%ld  %d  %d  %d\n", m->triangles.items, 2, m->nextras, 0);
#endif /* not TRILIBRARY */

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

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

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

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

	traversalinit(&m->triangles);
	triangleloop.tri = triangletraverse(m);
	vedgenumber = b->firstnumber;
	/* To loop over the set of edges, loop over all triangles, and look at   */
	/*   the three edges of each triangle.  If there isn't another triangle  */
	/*   adjacent to the edge, operate on the edge.  If there is another     */
	/*   adjacent triangle, operate on the edge only if the current triangle */
	/*   has a smaller pointer than its neighbor.  This way, each edge is    */
	/*   considered only once.                                               */
	while (triangleloop.tri != (triangle *)NULL) {
		for (triangleloop.orient = 0; triangleloop.orient < 3;
		triangleloop.orient++) {
			sym(triangleloop, trisym);
			if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) {
				/* Find the number of this triangle (and Voronoi vertex). */
				p1 = *(int *)(triangleloop.tri + 6);
				if (trisym.tri == m->dummytri) {
					org(triangleloop, torg);
					dest(triangleloop, tdest);
#ifdef TRILIBRARY
					/* Copy an infinite ray.  Index of one endpoint, and -1. */
					elist[coordindex] = p1;
					normlist[coordindex++] = tdest[1] - torg[1];
					elist[coordindex] = -1;
					normlist[coordindex++] = torg[0] - tdest[0];
#else /* not TRILIBRARY */
					/* Write an infinite ray.  Edge number, index of one endpoint, -1, */
					/*   and x and y coordinates of a vector representing the          */
					/*   direction of the ray.                                         */
					fprintf(outfile, "%4ld   %d  %d   %.17g  %.17g\n", vedgenumber,
						p1, -1, tdest[1] - torg[1], torg[0] - tdest[0]);
#endif /* not TRILIBRARY */
				}
				else {
					/* Find the number of the adjacent triangle (and Voronoi vertex). */
					p2 = *(int *)(trisym.tri + 6);
					/* Finite edge.  Write indices of two endpoints. */
#ifdef TRILIBRARY
					elist[coordindex] = p1;
					normlist[coordindex++] = 0.0;
					elist[coordindex] = p2;
					normlist[coordindex++] = 0.0;
#else /* not TRILIBRARY */
					fprintf(outfile, "%4ld   %d  %d\n", vedgenumber, p1, p2);
#endif /* not TRILIBRARY */
				}
				vedgenumber++;
			}
		}
		triangleloop.tri = triangletraverse(m);
	}

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

#ifdef TRILIBRARY

#ifdef ANSI_DECLARATORS
void writeneighbors(struct mesh *m, struct behavior *b, int **neighborlist)
#else /* not ANSI_DECLARATORS */
void writeneighbors(m, b, neighborlist)
struct mesh *m;
struct behavior *b;
int **neighborlist;
#endif /* not ANSI_DECLARATORS */

#else /* not TRILIBRARY */

#ifdef ANSI_DECLARATORS
void writeneighbors(struct mesh *m, struct behavior *b, char *neighborfilename,
	int argc, char **argv)
#else /* not ANSI_DECLARATORS */
void writeneighbors(m, b, neighborfilename, argc, argv)
struct mesh *m;
struct behavior *b;
char *neighborfilename;
int argc;
char **argv;
#endif /* not ANSI_DECLARATORS */

#endif /* not TRILIBRARY */

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

#ifdef TRILIBRARY
	if (!b->quiet) {
		printf("Writing neighbors.\n");
	}
	/* Allocate memory for neighbors if necessary. */
	if (*neighborlist == (int *)NULL) {
		*neighborlist = (int *)trimalloc((int)(m->triangles.items * 3 *
			sizeof(int)));
	}
	nlist = *neighborlist;
	index = 0;
#else /* not TRILIBRARY */
	if (!b->quiet) {
		printf("Writing %s.\n", neighborfilename);
	}
	outfile = fopen(neighborfilename, "w");
	if (outfile == (FILE *)NULL) {
		printf("  Error:  Cannot create file %s.\n", neighborfilename);
		triexit(1);
	}
	/* Number of triangles, three neighbors per triangle. */
	fprintf(outfile, "%ld  %d\n", m->triangles.items, 3);
#endif /* not TRILIBRARY */

	traversalinit(&m->triangles);
	triangleloop.tri = triangletraverse(m);
	triangleloop.orient = 0;
	elementnumber = b->firstnumber;
	while (triangleloop.tri != (triangle *)NULL) {
		*(int *)(triangleloop.tri + 6) = (int)elementnumber;
		triangleloop.tri = triangletraverse(m);
		elementnumber++;
	}
	*(int *)(m->dummytri + 6) = -1;

	traversalinit(&m->triangles);
	triangleloop.tri = triangletraverse(m);
	elementnumber = b->firstnumber;
	while (triangleloop.tri != (triangle *)NULL) {
		triangleloop.orient = 1;
		sym(triangleloop, trisym);
		neighbor1 = *(int *)(trisym.tri + 6);
		triangleloop.orient = 2;
		sym(triangleloop, trisym);
		neighbor2 = *(int *)(trisym.tri + 6);
		triangleloop.orient = 0;
		sym(triangleloop, trisym);
		neighbor3 = *(int *)(trisym.tri + 6);
#ifdef TRILIBRARY
		nlist[index++] = neighbor1;
		nlist[index++] = neighbor2;
		nlist[index++] = neighbor3;
#else /* not TRILIBRARY */
		/* Triangle number, neighboring triangle numbers. */
		fprintf(outfile, "%4ld    %d  %d  %d\n", elementnumber,
			neighbor1, neighbor2, neighbor3);
#endif /* not TRILIBRARY */

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

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

/*****************************************************************************/
/*                                                                           */
/*  writeoff()   Write the triangulation to an .off file.                    */
/*                                                                           */
/*  OFF stands for the Object File Format, a format used by the Geometry     */
/*  Center's Geomview package.                                               */
/*                                                                           */
/*****************************************************************************/

#ifndef TRILIBRARY

#ifdef ANSI_DECLARATORS
void writeoff(struct mesh *m, struct behavior *b, char *offfilename,
	int argc, char **argv)
#else /* not ANSI_DECLARATORS */
void writeoff(m, b, offfilename, argc, argv)
struct mesh *m;
struct behavior *b;
char *offfilename;
int argc;
char **argv;
#endif /* not ANSI_DECLARATORS */

{
	FILE *outfile;
	struct otri triangleloop;
	vertex vertexloop;
	vertex p1, p2, p3;
	long outvertices;

	if (!b->quiet) {
		printf("Writing %s.\n", offfilename);
	}

	if (b->jettison) {
		outvertices = m->vertices.items - m->undeads;
	}
	else {
		outvertices = m->vertices.items;
	}

	outfile = fopen(offfilename, "w");
	if (outfile == (FILE *)NULL) {
		printf("  Error:  Cannot create file %s.\n", offfilename);
		triexit(1);
	}
	/* Number of vertices, triangles, and edges. */
	fprintf(outfile, "OFF\n%ld  %ld  %ld\n", outvertices, m->triangles.items,
		m->edges);

	/* Write the vertices. */
	traversalinit(&m->vertices);
	vertexloop = vertextraverse(m);
	while (vertexloop != (vertex)NULL) {
		if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) {
			/* The "0.0" is here because the OFF format uses 3D coordinates. */
			fprintf(outfile, " %.17g  %.17g  %.17g\n", vertexloop[0], vertexloop[1],
				0.0);
		}
		vertexloop = vertextraverse(m);
	}

	/* Write the triangles. */
	traversalinit(&m->triangles);
	triangleloop.tri = triangletraverse(m);
	triangleloop.orient = 0;
	while (triangleloop.tri != (triangle *)NULL) {
		org(triangleloop, p1);
		dest(triangleloop, p2);
		apex(triangleloop, p3);
		/* The "3" means a three-vertex polygon. */
		fprintf(outfile, " 3   %4d  %4d  %4d\n", vertexmark(p1) - b->firstnumber,
			vertexmark(p2) - b->firstnumber, vertexmark(p3) - b->firstnumber);
		triangleloop.tri = triangletraverse(m);
	}
	finishfile(outfile, argc, argv);
}

#endif /* not TRILIBRARY */

/**                                                                         **/
/**                                                                         **/
/********* File I/O routines end here                                *********/

/*****************************************************************************/
/*                                                                           */
/*  quality_statistics()   Print statistics about the quality of the mesh.   */
/*                                                                           */
/*****************************************************************************/

#ifdef ANSI_DECLARATORS
void quality_statistics(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
void quality_statistics(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */

{
	struct otri triangleloop;
	vertex p[3];
	REAL cossquaretable[8];
	REAL ratiotable[16];
	REAL dx[3], dy[3];
	REAL edgelength[3];
	REAL dotproduct;
	REAL cossquare;
	REAL triarea;
	REAL shortest, longest;
	REAL trilongest2;
	REAL smallestarea, biggestarea;
	REAL triminaltitude2;
	REAL minaltitude;
	REAL triaspect2;
	REAL worstaspect;
	REAL smallestangle, biggestangle;
	REAL radconst, degconst;
	int angletable[18];
	int aspecttable[16];
	int aspectindex;
	int tendegree;
	int acutebiggest;
	int i, ii, j, k;

	printf("Mesh quality statistics:\n\n");
	radconst = PI / 18.0;
	degconst = 180.0 / PI;
	for (i = 0; i < 8; i++) {
		cossquaretable[i] = cos(radconst * (REAL)(i + 1));
		cossquaretable[i] = cossquaretable[i] * cossquaretable[i];
	}
	for (i = 0; i < 18; i++) {
		angletable[i] = 0;
	}

	ratiotable[0] = 1.5;      ratiotable[1] = 2.0;
	ratiotable[2] = 2.5;      ratiotable[3] = 3.0;
	ratiotable[4] = 4.0;      ratiotable[5] = 6.0;
	ratiotable[6] = 10.0;      ratiotable[7] = 15.0;
	ratiotable[8] = 25.0;      ratiotable[9] = 50.0;
	ratiotable[10] = 100.0;      ratiotable[11] = 300.0;
	ratiotable[12] = 1000.0;      ratiotable[13] = 10000.0;
	ratiotable[14] = 100000.0;      ratiotable[15] = 0.0;
	for (i = 0; i < 16; i++) {
		aspecttable[i] = 0;
	}

	worstaspect = 0.0;
	minaltitude = m->xmax - m->xmin + m->ymax - m->ymin;
	minaltitude = minaltitude * minaltitude;
	shortest = minaltitude;
	longest = 0.0;
	smallestarea = minaltitude;
	biggestarea = 0.0;
	worstaspect = 0.0;
	smallestangle = 0.0;
	biggestangle = 2.0;
	acutebiggest = 1;

	traversalinit(&m->triangles);
	triangleloop.tri = triangletraverse(m);
	triangleloop.orient = 0;
	while (triangleloop.tri != (triangle *)NULL) {
		org(triangleloop, p[0]);
		dest(triangleloop, p[1]);
		apex(triangleloop, p[2]);
		trilongest2 = 0.0;

		for (i = 0; i < 3; i++) {
			j = plus1mod3[i];
			k = minus1mod3[i];
			dx[i] = p[j][0] - p[k][0];
			dy[i] = p[j][1] - p[k][1];
			edgelength[i] = dx[i] * dx[i] + dy[i] * dy[i];
			if (edgelength[i] > trilongest2) {
				trilongest2 = edgelength[i];
			}
			if (edgelength[i] > longest) {
				longest = edgelength[i];
			}
			if (edgelength[i] < shortest) {
				shortest = edgelength[i];
			}
		}

		triarea = counterclockwise(m, b, p[0], p[1], p[2]);
		if (triarea < smallestarea) {
			smallestarea = triarea;
		}
		if (triarea > biggestarea) {
			biggestarea = triarea;
		}
		triminaltitude2 = triarea * triarea / trilongest2;
		if (triminaltitude2 < minaltitude) {
			minaltitude = triminaltitude2;
		}
		triaspect2 = trilongest2 / triminaltitude2;
		if (triaspect2 > worstaspect) {
			worstaspect = triaspect2;
		}
		aspectindex = 0;
		while ((triaspect2 > ratiotable[aspectindex] * ratiotable[aspectindex])
			&& (aspectindex < 15)) {
			aspectindex++;
		}
		aspecttable[aspectindex]++;

		for (i = 0; i < 3; i++) {
			j = plus1mod3[i];
			k = minus1mod3[i];
			dotproduct = dx[j] * dx[k] + dy[j] * dy[k];
			cossquare = dotproduct * dotproduct / (edgelength[j] * edgelength[k]);
			tendegree = 8;
			for (ii = 7; ii >= 0; ii--) {
				if (cossquare > cossquaretable[ii]) {
					tendegree = ii;
				}
			}
			if (dotproduct <= 0.0) {
				angletable[tendegree]++;
				if (cossquare > smallestangle) {
					smallestangle = cossquare;
				}
				if (acutebiggest && (cossquare < biggestangle)) {
					biggestangle = cossquare;
				}
			}
			else {
				angletable[17 - tendegree]++;
				if (acutebiggest || (cossquare > biggestangle)) {
					biggestangle = cossquare;
					acutebiggest = 0;
				}
			}
		}
		triangleloop.tri = triangletraverse(m);
	}

	shortest = sqrt(shortest);
	longest = sqrt(longest);
	minaltitude = sqrt(minaltitude);
	worstaspect = sqrt(worstaspect);
	smallestarea *= 0.5;
	biggestarea *= 0.5;
	if (smallestangle >= 1.0) {
		smallestangle = 0.0;
	}
	else {
		smallestangle = degconst * acos(sqrt(smallestangle));
	}
	if (biggestangle >= 1.0) {
		biggestangle = 180.0;
	}
	else {
		if (acutebiggest) {
			biggestangle = degconst * acos(sqrt(biggestangle));
		}
		else {
			biggestangle = 180.0 - degconst * acos(sqrt(biggestangle));
		}
	}

	printf("  Smallest area: %16.5g   |  Largest area: %16.5g\n",
		smallestarea, biggestarea);
	printf("  Shortest edge: %16.5g   |  Longest edge: %16.5g\n",
		shortest, longest);
	printf("  Shortest altitude: %12.5g   |  Largest aspect ratio: %8.5g\n\n",
		minaltitude, worstaspect);

	printf("  Triangle aspect ratio histogram:\n");
	printf("  1.1547 - %-6.6g    :  %8d    | %6.6g - %-6.6g     :  %8d\n",
		ratiotable[0], aspecttable[0], ratiotable[7], ratiotable[8],
		aspecttable[8]);
	for (i = 1; i < 7; i++) {
		printf("  %6.6g - %-6.6g    :  %8d    | %6.6g - %-6.6g     :  %8d\n",
			ratiotable[i - 1], ratiotable[i], aspecttable[i],
			ratiotable[i + 7], ratiotable[i + 8], aspecttable[i + 8]);
	}
	printf("  %6.6g - %-6.6g    :  %8d    | %6.6g -            :  %8d\n",
		ratiotable[6], ratiotable[7], aspecttable[7], ratiotable[14],
		aspecttable[15]);
	printf("  (Aspect ratio is longest edge divided by shortest altitude)\n\n");

	printf("  Smallest angle: %15.5g   |  Largest angle: %15.5g\n\n",
		smallestangle, biggestangle);

	printf("  Angle histogram:\n");
	for (i = 0; i < 9; i++) {
		printf("    %3d - %3d degrees:  %8d    |    %3d - %3d degrees:  %8d\n",
			i * 10, i * 10 + 10, angletable[i],
			i * 10 + 90, i * 10 + 100, angletable[i + 9]);
	}
	printf("\n");
}

/*****************************************************************************/
/*                                                                           */
/*  statistics()   Print all sorts of cool facts.                            */
/*                                                                           */
/*****************************************************************************/

#ifdef ANSI_DECLARATORS
void statistics(struct mesh *m, struct behavior *b)
#else /* not ANSI_DECLARATORS */
void statistics(m, b)
struct mesh *m;
struct behavior *b;
#endif /* not ANSI_DECLARATORS */

{
	printf("\nStatistics:\n\n");
	printf("  Input vertices: %d\n", m->invertices);
	if (b->refine) {
		printf("  Input triangles: %d\n", m->inelements);
	}
	if (b->poly) {
		printf("  Input segments: %d\n", m->insegments);
		if (!b->refine) {
			printf("  Input holes: %d\n", m->holes);
		}
	}

	printf("\n  Mesh vertices: %ld\n", m->vertices.items - m->undeads);
	printf("  Mesh triangles: %ld\n", m->triangles.items);
	printf("  Mesh edges: %ld\n", m->edges);
	printf("  Mesh exterior boundary edges: %ld\n", m->hullsize);
	if (b->poly || b->refine) {
		printf("  Mesh interior boundary edges: %ld\n",
			m->subsegs.items - m->hullsize);
		printf("  Mesh subsegments (constrained edges): %ld\n",
			m->subsegs.items);
	}
	printf("\n");

	if (b->verbose) {
		quality_statistics(m, b);
		printf("Memory allocation statistics:\n\n");
		printf("  Maximum number of vertices: %ld\n", m->vertices.maxitems);
		printf("  Maximum number of triangles: %ld\n", m->triangles.maxitems);
		if (m->subsegs.maxitems > 0) {
			printf("  Maximum number of subsegments: %ld\n", m->subsegs.maxitems);
		}
		if (m->viri.maxitems > 0) {
			printf("  Maximum number of viri: %ld\n", m->viri.maxitems);
		}
		if (m->badsubsegs.maxitems > 0) {
			printf("  Maximum number of encroached subsegments: %ld\n",
				m->badsubsegs.maxitems);
		}
		if (m->badtriangles.maxitems > 0) {
			printf("  Maximum number of bad triangles: %ld\n",
				m->badtriangles.maxitems);
		}
		if (m->flipstackers.maxitems > 0) {
			printf("  Maximum number of stacked triangle flips: %ld\n",
				m->flipstackers.maxitems);
		}
		if (m->splaynodes.maxitems > 0) {
			printf("  Maximum number of splay tree nodes: %ld\n",
				m->splaynodes.maxitems);
		}
		printf("  Approximate heap memory use (bytes): %ld\n\n",
			m->vertices.maxitems * m->vertices.itembytes +
			m->triangles.maxitems * m->triangles.itembytes +
			m->subsegs.maxitems * m->subsegs.itembytes +
			m->viri.maxitems * m->viri.itembytes +
			m->badsubsegs.maxitems * m->badsubsegs.itembytes +
			m->badtriangles.maxitems * m->badtriangles.itembytes +
			m->flipstackers.maxitems * m->flipstackers.itembytes +
			m->splaynodes.maxitems * m->splaynodes.itembytes);

		printf("Algorithmic statistics:\n\n");
		if (!b->weighted) {
			printf("  Number of incircle tests: %ld\n", m->incirclecount);
		}
		else {
			printf("  Number of 3D orientation tests: %ld\n", m->orient3dcount);
		}
		printf("  Number of 2D orientation tests: %ld\n", m->counterclockcount);
		if (m->hyperbolacount > 0) {
			printf("  Number of right-of-hyperbola tests: %ld\n",
				m->hyperbolacount);
		}
		if (m->circletopcount > 0) {
			printf("  Number of circle top computations: %ld\n",
				m->circletopcount);
		}
		if (m->circumcentercount > 0) {
			printf("  Number of triangle circumcenter computations: %ld\n",
				m->circumcentercount);
		}
		printf("\n");
	}
}

/*****************************************************************************/
/*                                                                           */
/*  main() or triangulate()   Gosh, do everything.                           */
/*                                                                           */
/*  The sequence is roughly as follows.  Many of these steps can be skipped, */
/*  depending on the command line switches.                                  */
/*                                                                           */
/*  - Initialize constants and parse the command line.                       */
/*  - Read the vertices from a file and either                               */
/*    - triangulate them (no -r), or                                         */
/*    - read an old mesh from files and reconstruct it (-r).                 */
/*  - Insert the PSLG segments (-p), and possibly segments on the convex     */
/*      hull (-c).                                                           */
/*  - Read the holes (-p), regional attributes (-pA), and regional area      */
/*      constraints (-pa).  Carve the holes and concavities, and spread the  */
/*      regional attributes and area constraints.                            */
/*  - Enforce the constraints on minimum angle (-q) and maximum area (-a).   */
/*      Also enforce the conforming Delaunay property (-q and -a).           */
/*  - Compute the number of edges in the resulting mesh.                     */
/*  - Promote the mesh's linear triangles to higher order elements (-o).     */
/*  - Write the output files and print the statistics.                       */
/*  - Check the consistency and Delaunay property of the mesh (-C).          */
/*                                                                           */
/*****************************************************************************/

#ifdef TRILIBRARY

#ifdef ANSI_DECLARATORS
void triangulate(char *triswitches, struct triangulateio *in,
struct triangulateio *out, struct triangulateio *vorout)
#else /* not ANSI_DECLARATORS */
void triangulate(triswitches, in, out, vorout)
char *triswitches;
struct triangulateio *in;
struct triangulateio *out;
struct triangulateio *vorout;
#endif /* not ANSI_DECLARATORS */

#else /* not TRILIBRARY */

#ifdef ANSI_DECLARATORS
int main(int argc, char **argv)
#else /* not ANSI_DECLARATORS */
int main(argc, argv)
int argc;
char **argv;
#endif /* not ANSI_DECLARATORS */

#endif /* not TRILIBRARY */

{
	struct mesh m;
	struct behavior b;
	REAL *holearray;                                        /* Array of holes. */
	REAL *regionarray;   /* Array of regional attributes and area constraints. */
#ifndef TRILIBRARY
	FILE *polyfile;
#endif /* not TRILIBRARY */
#ifndef NO_TIMER
	/* Variables for timing the performance of Triangle.  The types are */
	/*   defined in sys/time.h.                                         */
	struct timeval tv0, tv1, tv2, tv3, tv4, tv5, tv6;
	struct timezone tz;
#endif /* not NO_TIMER */

#ifndef NO_TIMER
	gettimeofday(&tv0, &tz);
#endif /* not NO_TIMER */

	triangleinit(&m);
#ifdef TRILIBRARY
	parsecommandline(1, &triswitches, &b);
#else /* not TRILIBRARY */
	parsecommandline(argc, argv, &b);
#endif /* not TRILIBRARY */
	m.steinerleft = b.steiner;

#ifdef TRILIBRARY
	transfernodes(&m, &b, in->pointlist, in->pointattributelist,
		in->pointmarkerlist, in->numberofpoints,
		in->numberofpointattributes);
#else /* not TRILIBRARY */
	readnodes(&m, &b, b.innodefilename, b.inpolyfilename, &polyfile);
#endif /* not TRILIBRARY */

#ifndef NO_TIMER
	if (!b.quiet) {
		gettimeofday(&tv1, &tz);
	}
#endif /* not NO_TIMER */

#ifdef CDT_ONLY
	m.hullsize = delaunay(&m, &b);                /* Triangulate the vertices. */
#else /* not CDT_ONLY */
	if (b.refine) {
		/* Read and reconstruct a mesh. */
#ifdef TRILIBRARY
		m.hullsize = reconstruct(&m, &b, in->trianglelist,
			in->triangleattributelist, in->trianglearealist,
			in->numberoftriangles, in->numberofcorners,
			in->numberoftriangleattributes,
			in->segmentlist, in->segmentmarkerlist,
			in->numberofsegments);
#else /* not TRILIBRARY */
		m.hullsize = reconstruct(&m, &b, b.inelefilename, b.areafilename,
			b.inpolyfilename, polyfile);
#endif /* not TRILIBRARY */
	}
	else {
		m.hullsize = delaunay(&m, &b);              /* Triangulate the vertices. */
	}
#endif /* not CDT_ONLY */

#ifndef NO_TIMER
	if (!b.quiet) {
		gettimeofday(&tv2, &tz);
		if (b.refine) {
			printf("Mesh reconstruction");
		}
		else {
			printf("Delaunay");
		}
		printf(" milliseconds:  %ld\n", 1000l * (tv2.tv_sec - tv1.tv_sec) +
			(tv2.tv_usec - tv1.tv_usec) / 1000l);
	}
#endif /* not NO_TIMER */

	/* Ensure that no vertex can be mistaken for a triangular bounding */
	/*   box vertex in insertvertex().                                 */
	m.infvertex1 = (vertex)NULL;
	m.infvertex2 = (vertex)NULL;
	m.infvertex3 = (vertex)NULL;

	if (b.usesegments) {
		m.checksegments = 1;                /* Segments will be introduced next. */
		if (!b.refine) {
			/* Insert PSLG segments and/or convex hull segments. */
#ifdef TRILIBRARY
			formskeleton(&m, &b, in->segmentlist,
				in->segmentmarkerlist, in->numberofsegments);
#else /* not TRILIBRARY */
			formskeleton(&m, &b, polyfile, b.inpolyfilename);
#endif /* not TRILIBRARY */
		}
	}

#ifndef NO_TIMER
	if (!b.quiet) {
		gettimeofday(&tv3, &tz);
		if (b.usesegments && !b.refine) {
			printf("Segment milliseconds:  %ld\n",
				1000l * (tv3.tv_sec - tv2.tv_sec) +
				(tv3.tv_usec - tv2.tv_usec) / 1000l);
		}
	}
#endif /* not NO_TIMER */

	if (b.poly && (m.triangles.items > 0)) {
#ifdef TRILIBRARY
		holearray = in->holelist;
		m.holes = in->numberofholes;
		regionarray = in->regionlist;
		m.regions = in->numberofregions;
#else /* not TRILIBRARY */
		readholes(&m, &b, polyfile, b.inpolyfilename, &holearray, &m.holes,
			&regionarray, &m.regions);
#endif /* not TRILIBRARY */
		if (!b.refine) {
			/* Carve out holes and concavities. */
			carveholes(&m, &b, holearray, m.holes, regionarray, m.regions);
		}
	}
	else {
		/* Without a PSLG, there can be no holes or regional attributes   */
		/*   or area constraints.  The following are set to zero to avoid */
		/*   an accidental free() later.                                  */
		m.holes = 0;
		m.regions = 0;
	}

#ifndef NO_TIMER
	if (!b.quiet) {
		gettimeofday(&tv4, &tz);
		if (b.poly && !b.refine) {
			printf("Hole milliseconds:  %ld\n", 1000l * (tv4.tv_sec - tv3.tv_sec) +
				(tv4.tv_usec - tv3.tv_usec) / 1000l);
		}
	}
#endif /* not NO_TIMER */

#ifndef CDT_ONLY
	if (b.quality && (m.triangles.items > 0)) {
		enforcequality(&m, &b);           /* Enforce angle and area constraints. */
	}
#endif /* not CDT_ONLY */

#ifndef NO_TIMER
	if (!b.quiet) {
		gettimeofday(&tv5, &tz);
#ifndef CDT_ONLY
		if (b.quality) {
			printf("Quality milliseconds:  %ld\n",
				1000l * (tv5.tv_sec - tv4.tv_sec) +
				(tv5.tv_usec - tv4.tv_usec) / 1000l);
		}
#endif /* not CDT_ONLY */
	}
#endif /* not NO_TIMER */

	/* Calculate the number of edges. */
	m.edges = (3l * m.triangles.items + m.hullsize) / 2l;

	if (b.order > 1) {
		highorder(&m, &b);       /* Promote elements to higher polynomial order. */
	}
	if (!b.quiet) {
		printf("\n");
	}

#ifdef TRILIBRARY
	if (b.jettison) {
		out->numberofpoints = m.vertices.items - m.undeads;
	}
	else {
		out->numberofpoints = m.vertices.items;
	}
	out->numberofpointattributes = m.nextras;
	out->numberoftriangles = m.triangles.items;
	out->numberofcorners = (b.order + 1) * (b.order + 2) / 2;
	out->numberoftriangleattributes = m.eextras;
	out->numberofedges = m.edges;
	if (b.usesegments) {
		out->numberofsegments = m.subsegs.items;
	}
	else {
		out->numberofsegments = m.hullsize;
	}
	if (vorout != (struct triangulateio *) NULL) {
		vorout->numberofpoints = m.triangles.items;
		vorout->numberofpointattributes = m.nextras;
		vorout->numberofedges = m.edges;
	}
#endif /* TRILIBRARY */
	/* If not using iteration numbers, don't write a .node file if one was */
	/*   read, because the original one would be overwritten!              */
	if (b.nonodewritten || (b.noiterationnum && m.readnodefile)) {
		if (!b.quiet) {
#ifdef TRILIBRARY
			printf("NOT writing vertices.\n");
#else /* not TRILIBRARY */
			printf("NOT writing a .node file.\n");
#endif /* not TRILIBRARY */
		}
		numbernodes(&m, &b);         /* We must remember to number the vertices. */
	}
	else {
		/* writenodes() numbers the vertices too. */
#ifdef TRILIBRARY
		writenodes(&m, &b, &out->pointlist, &out->pointattributelist,
			&out->pointmarkerlist);
#else /* not TRILIBRARY */
		writenodes(&m, &b, b.outnodefilename, argc, argv);
#endif /* TRILIBRARY */
	}
	if (b.noelewritten) {
		if (!b.quiet) {
#ifdef TRILIBRARY
			printf("NOT writing triangles.\n");
#else /* not TRILIBRARY */
			printf("NOT writing an .ele file.\n");
#endif /* not TRILIBRARY */
		}
	}
	else {
#ifdef TRILIBRARY
		writeelements(&m, &b, &out->trianglelist, &out->triangleattributelist);
#else /* not TRILIBRARY */
		writeelements(&m, &b, b.outelefilename, argc, argv);
#endif /* not TRILIBRARY */
	}
	/* The -c switch (convex switch) causes a PSLG to be written */
	/*   even if none was read.                                  */
	if (b.poly || b.convex) {
		/* If not using iteration numbers, don't overwrite the .poly file. */
		if (b.nopolywritten || b.noiterationnum) {
			if (!b.quiet) {
#ifdef TRILIBRARY
				printf("NOT writing segments.\n");
#else /* not TRILIBRARY */
				printf("NOT writing a .poly file.\n");
#endif /* not TRILIBRARY */
			}
		}
		else {
#ifdef TRILIBRARY
			writepoly(&m, &b, &out->segmentlist, &out->segmentmarkerlist);
			out->numberofholes = m.holes;
			out->numberofregions = m.regions;
			if (b.poly) {
				out->holelist = in->holelist;
				out->regionlist = in->regionlist;
			}
			else {
				out->holelist = (REAL *)NULL;
				out->regionlist = (REAL *)NULL;
			}
#else /* not TRILIBRARY */
			writepoly(&m, &b, b.outpolyfilename, holearray, m.holes, regionarray,
				m.regions, argc, argv);
#endif /* not TRILIBRARY */
		}
	}
#ifndef TRILIBRARY
#ifndef CDT_ONLY
	if (m.regions > 0) {
		trifree((VOID *)regionarray);
	}
#endif /* not CDT_ONLY */
	if (m.holes > 0) {
		trifree((VOID *)holearray);
	}
	if (b.geomview) {
		writeoff(&m, &b, b.offfilename, argc, argv);
	}
#endif /* not TRILIBRARY */
	if (b.edgesout) {
#ifdef TRILIBRARY
		writeedges(&m, &b, &out->edgelist, &out->edgemarkerlist);
#else /* not TRILIBRARY */
		writeedges(&m, &b, b.edgefilename, argc, argv);
#endif /* not TRILIBRARY */
	}
	if (b.voronoi) {
#ifdef TRILIBRARY
		writevoronoi(&m, &b, &vorout->pointlist, &vorout->pointattributelist,
			&vorout->pointmarkerlist, &vorout->edgelist,
			&vorout->edgemarkerlist, &vorout->normlist);
#else /* not TRILIBRARY */
		writevoronoi(&m, &b, b.vnodefilename, b.vedgefilename, argc, argv);
#endif /* not TRILIBRARY */
	}
	if (b.neighbors) {
#ifdef TRILIBRARY
		writeneighbors(&m, &b, &out->neighborlist);
#else /* not TRILIBRARY */
		writeneighbors(&m, &b, b.neighborfilename, argc, argv);
#endif /* not TRILIBRARY */
	}

	if (!b.quiet) {
#ifndef NO_TIMER
		gettimeofday(&tv6, &tz);
		printf("\nOutput milliseconds:  %ld\n",
			1000l * (tv6.tv_sec - tv5.tv_sec) +
			(tv6.tv_usec - tv5.tv_usec) / 1000l);
		printf("Total running milliseconds:  %ld\n",
			1000l * (tv6.tv_sec - tv0.tv_sec) +
			(tv6.tv_usec - tv0.tv_usec) / 1000l);
#endif /* not NO_TIMER */

		statistics(&m, &b);
	}

#ifndef REDUCED
	if (b.docheck) {
		checkmesh(&m, &b);
		checkdelaunay(&m, &b);
	}
#endif /* not REDUCED */

	triangledeinit(&m, &b);
#ifndef TRILIBRARY
	return 0;
#endif /* not TRILIBRARY */
}