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#define ANSI_DECLARATORS
/*****************************************************************************/
/* */
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/* 888 888 888 88b 888 888 888 888 888 d888 88b */
/* 888 888 888 o88^o888 888 888 "88888" 888 8888oo888 */
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/* "8oo8D */
/* */
/* A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator. */
/* (triangle.c) */
/* */
/* Version 1.3 */
/* July 19, 1996 */
/* */
/* Copyright 1996 */
/* Jonathan Richard Shewchuk */
/* School of Computer Science */
/* Carnegie Mellon University */
/* 5000 Forbes Avenue */
/* Pittsburgh, Pennsylvania 15213-3891 */
/* jrs@cs.cmu.edu */
/* */
/* This program may be freely redistributed under the condition that the */
/* copyright notices (including this entire header and the copyright */
/* notice printed when the `-h' switch is selected) are not removed, and */
/* no compensation is received. Private, research, and institutional */
/* use is free. You may distribute modified versions of this code UNDER */
/* THE CONDITION THAT THIS CODE AND ANY MODIFICATIONS MADE TO IT IN THE */
/* SAME FILE REMAIN UNDER COPYRIGHT OF THE ORIGINAL AUTHOR, BOTH SOURCE */
/* AND OBJECT CODE ARE MADE FREELY AVAILABLE WITHOUT CHARGE, AND CLEAR */
/* NOTICE IS GIVEN OF THE MODIFICATIONS. Distribution of this code as */
/* part of a commercial system is permissible ONLY BY DIRECT ARRANGEMENT */
/* WITH THE AUTHOR. (If you are not directly supplying this code to a */
/* customer, and you are instead telling them how they can obtain it for */
/* free, then you are not required to make any arrangement with me.) */
/* */
/* Hypertext instructions for Triangle are available on the Web at */
/* */
/* http://www.cs.cmu.edu/~quake/triangle.html */
/* */
/* Some of the references listed below are marked [*]. These are available */
/* for downloading from the Web page */
/* */
/* http://www.cs.cmu.edu/~quake/triangle.research.html */
/* */
/* A paper discussing some aspects of Triangle is available. See Jonathan */
/* Richard Shewchuk, "Triangle: Engineering a 2D Quality Mesh Generator */
/* and Delaunay Triangulator," First Workshop on Applied Computational */
/* Geometry, ACM, May 1996. [*] */
/* */
/* Triangle was created as part of the Archimedes project in the School of */
/* Computer Science at Carnegie Mellon University. Archimedes is a */
/* system for compiling parallel finite element solvers. For further */
/* information, see Anja Feldmann, Omar Ghattas, John R. Gilbert, Gary L. */
/* Miller, David R. O'Hallaron, Eric J. Schwabe, Jonathan R. Shewchuk, */
/* and Shang-Hua Teng, "Automated Parallel Solution of Unstructured PDE */
/* Problems." To appear in Communications of the ACM, we hope. */
/* */
/* The quality mesh generation algorithm is due to Jim Ruppert, "A */
/* Delaunay Refinement Algorithm for Quality 2-Dimensional Mesh */
/* Generation," Journal of Algorithms 18(3):548-585, May 1995. [*] */
/* */
/* My implementation of the divide-and-conquer and incremental Delaunay */
/* triangulation algorithms follows closely the presentation of Guibas */
/* and Stolfi, even though I use a triangle-based data structure instead */
/* of their quad-edge data structure. (In fact, I originally implemented */
/* Triangle using the quad-edge data structure, but switching to a */
/* triangle-based data structure sped Triangle by a factor of two.) The */
/* mesh manipulation primitives and the two aforementioned Delaunay */
/* triangulation algorithms are described by Leonidas J. Guibas and Jorge */
/* Stolfi, "Primitives for the Manipulation of General Subdivisions and */
/* the Computation of Voronoi Diagrams," ACM Transactions on Graphics */
/* 4(2):74-123, April 1985. */
/* */
/* Their O(n log n) divide-and-conquer algorithm is adapted from Der-Tsai */
/* Lee and Bruce J. Schachter, "Two Algorithms for Constructing the */
/* Delaunay Triangulation," International Journal of Computer and */
/* Information Science 9(3):219-242, 1980. The idea to improve the */
/* divide-and-conquer algorithm by alternating between vertical and */
/* horizontal cuts was introduced by Rex A. Dwyer, "A Faster Divide-and- */
/* Conquer Algorithm for Constructing Delaunay Triangulations," */
/* Algorithmica 2(2):137-151, 1987. */
/* */
/* The incremental insertion algorithm was first proposed by C. L. Lawson, */
/* "Software for C1 Surface Interpolation," in Mathematical Software III, */
/* John R. Rice, editor, Academic Press, New York, pp. 161-194, 1977. */
/* For point location, I use the algorithm of Ernst P. Mucke, Isaac */
/* Saias, and Binhai Zhu, "Fast Randomized Point Location Without */
/* Preprocessing in Two- and Three-dimensional Delaunay Triangulations," */
/* Proceedings of the Twelfth Annual Symposium on Computational Geometry, */
/* ACM, May 1996. [*] If I were to randomize the order of point */
/* insertion (I currently don't bother), their result combined with the */
/* result of Leonidas J. Guibas, Donald E. Knuth, and Micha Sharir, */
/* "Randomized Incremental Construction of Delaunay and Voronoi */
/* Diagrams," Algorithmica 7(4):381-413, 1992, would yield an expected */
/* O(n^{4/3}) bound on running time. */
/* */
/* The O(n log n) sweepline Delaunay triangulation algorithm is taken from */
/* Steven Fortune, "A Sweepline Algorithm for Voronoi Diagrams", */
/* Algorithmica 2(2):153-174, 1987. A random sample of edges on the */
/* boundary of the triangulation are maintained in a splay tree for the */
/* purpose of point location. Splay trees are described by Daniel */
/* Dominic Sleator and Robert Endre Tarjan, "Self-Adjusting Binary Search */
/* Trees," Journal of the ACM 32(3):652-686, July 1985. */
/* */
/* The algorithms for exact computation of the signs of determinants are */
/* described in Jonathan Richard Shewchuk, "Adaptive Precision Floating- */
/* Point Arithmetic and Fast Robust Geometric Predicates," Technical */
/* Report CMU-CS-96-140, School of Computer Science, Carnegie Mellon */
/* University, Pittsburgh, Pennsylvania, May 1996. [*] (Submitted to */
/* Discrete & Computational Geometry.) An abbreviated version appears as */
/* Jonathan Richard Shewchuk, "Robust Adaptive Floating-Point Geometric */
/* Predicates," Proceedings of the Twelfth Annual Symposium on Computa- */
/* tional Geometry, ACM, May 1996. [*] Many of the ideas for my exact */
/* arithmetic routines originate with Douglas M. Priest, "Algorithms for */
/* Arbitrary Precision Floating Point Arithmetic," Tenth Symposium on */
/* Computer Arithmetic, 132-143, IEEE Computer Society Press, 1991. [*] */
/* Many of the ideas for the correct evaluation of the signs of */
/* determinants are taken from Steven Fortune and Christopher J. Van Wyk, */
/* "Efficient Exact Arithmetic for Computational Geometry," Proceedings */
/* of the Ninth Annual Symposium on Computational Geometry, ACM, */
/* pp. 163-172, May 1993, and from Steven Fortune, "Numerical Stability */
/* of Algorithms for 2D Delaunay Triangulations," International Journal */
/* of Computational Geometry & Applications 5(1-2):193-213, March-June */
/* 1995. */
/* */
/* For definitions of and results involving Delaunay triangulations, */
/* constrained and conforming versions thereof, and other aspects of */
/* triangular mesh generation, see the excellent survey by Marshall Bern */
/* and David Eppstein, "Mesh Generation and Optimal Triangulation," in */
/* Computing and Euclidean Geometry, Ding-Zhu Du and Frank Hwang, */
/* editors, World Scientific, Singapore, pp. 23-90, 1992. */
/* */
/* The time for incrementally adding PSLG (planar straight line graph) */
/* segments to create a constrained Delaunay triangulation is probably */
/* O(n^2) per segment in the worst case and O(n) per edge in the common */
/* case, where n is the number of triangles that intersect the segment */
/* before it is inserted. This doesn't count point location, which can */
/* be much more expensive. (This note does not apply to conforming */
/* Delaunay triangulations, for which a different method is used to */
/* insert segments.) */
/* */
/* The time for adding segments to a conforming Delaunay triangulation is */
/* not clear, but does not depend upon n alone. In some cases, very */
/* small features (like a point lying next to a segment) can cause a */
/* single segment to be split an arbitrary number of times. Of course, */
/* floating-point precision is a practical barrier to how much this can */
/* happen. */
/* */
/* The time for deleting a point from a Delaunay triangulation is O(n^2) in */
/* the worst case and O(n) in the common case, where n is the degree of */
/* the point being deleted. I could improve this to expected O(n) time */
/* by "inserting" the neighboring vertices in random order, but n is */
/* usually quite small, so it's not worth the bother. (The O(n) time */
/* for random insertion follows from L. Paul Chew, "Building Voronoi */
/* Diagrams for Convex Polygons in Linear Expected Time," Technical */
/* Report PCS-TR90-147, Department of Mathematics and Computer Science, */
/* Dartmouth College, 1990. */
/* */
/* Ruppert's Delaunay refinement algorithm typically generates triangles */
/* at a linear rate (constant time per triangle) after the initial */
/* triangulation is formed. There may be pathological cases where more */
/* time is required, but these never arise in practice. */
/* */
/* The segment intersection formulae are straightforward. If you want to */
/* see them derived, see Franklin Antonio. "Faster Line Segment */
/* Intersection." In Graphics Gems III (David Kirk, editor), pp. 199- */
/* 202. Academic Press, Boston, 1992. */
/* */
/* If you make any improvements to this code, please please please let me */
/* know, so that I may obtain the improvements. Even if you don't change */
/* the code, I'd still love to hear what it's being used for. */
/* */
/* Disclaimer: Neither I nor Carnegie Mellon warrant this code in any way */
/* whatsoever. This code is provided "as-is". Use at your own risk. */
/* */
/*****************************************************************************/
/* For single precision (which will save some memory and reduce paging), */
/* define the symbol SINGLE by using the -DSINGLE compiler switch or by */
/* writing "#define SINGLE" below. */
/* */
/* For double precision (which will allow you to refine meshes to a smaller */
/* edge length), leave SINGLE undefined. */
/* */
/* Double precision uses more memory, but improves the resolution of the */
/* meshes you can generate with Triangle. It also reduces the likelihood */
/* of a floating exception due to overflow. Finally, it is much faster */
/* than single precision on 64-bit architectures like the DEC Alpha. I */
/* recommend double precision unless you want to generate a mesh for which */
/* you do not have enough memory. */
#define SINGLE
#ifdef SINGLE
#define REAL float
#else /* not SINGLE */
#define REAL double
#endif /* not SINGLE */
/* If yours is not a Unix system, define the NO_TIMER compiler switch to */
/* remove the Unix-specific timing code. */
#define NO_TIMER
/* To insert lots of self-checks for internal errors, define the SELF_CHECK */
/* symbol. This will slow down the program significantly. It is best to */
/* define the symbol using the -DSELF_CHECK compiler switch, but you could */
/* write "#define SELF_CHECK" below. If you are modifying this code, I */
/* recommend you turn self-checks on. */
/* #define SELF_CHECK */
/* To compile Triangle as a callable object library (triangle.o), define the */
/* TRILIBRARY symbol. Read the file triangle.h for details on how to call */
/* the procedure triangulate() that results. */
#define TRILIBRARY
/* It is possible to generate a smaller version of Triangle using one or */
/* both of the following symbols. Define the REDUCED symbol to eliminate */
/* all features that are primarily of research interest; specifically, the */
/* -i, -F, -s, and -C switches. Define the CDT_ONLY symbol to eliminate */
/* all meshing algorithms above and beyond constrained Delaunay */
/* triangulation; specifically, the -r, -q, -a, -S, and -s switches. */
/* These reductions are most likely to be useful when generating an object */
/* library (triangle.o) by defining the TRILIBRARY symbol. */
#define REDUCED
#define CDT_ONLY
/* On some machines, the exact arithmetic routines might be defeated by the */
/* use of internal extended precision floating-point registers. Sometimes */
/* this problem can be fixed by defining certain values to be volatile, */
/* thus forcing them to be stored to memory and rounded off. This isn't */
/* a great solution, though, as it slows Triangle down. */
/* */
/* To try this out, write "#define INEXACT volatile" below. Normally, */
/* however, INEXACT should be defined to be nothing. ("#define INEXACT".) */
#define INEXACT /* Nothing */
/* #define INEXACT volatile */
/* Maximum number of characters in a file name (including the null). */
#define FILENAMESIZE 512
/* Maximum number of characters in a line read from a file (including the */
/* null). */
#define INPUTLINESIZE 512
/* For efficiency, a variety of data structures are allocated in bulk. The */
/* following constants determine how many of each structure is allocated */
/* at once. */
#define TRIPERBLOCK 4092 /* Number of triangles allocated at once. */
#define SHELLEPERBLOCK 508 /* Number of shell edges allocated at once. */
#define POINTPERBLOCK 4092 /* Number of points allocated at once. */
#define VIRUSPERBLOCK 1020 /* Number of virus triangles allocated at once. */
/* Number of encroached segments allocated at once. */
#define BADSEGMENTPERBLOCK 252
/* Number of skinny triangles allocated at once. */
#define BADTRIPERBLOCK 4092
/* Number of splay tree nodes allocated at once. */
#define SPLAYNODEPERBLOCK 508
/* The point marker DEADPOINT is an arbitrary number chosen large enough to */
/* (hopefully) not conflict with user boundary markers. Make sure that it */
/* is small enough to fit into your machine's integer size. */
#define DEADPOINT -1073741824
/* The next line is used to outsmart some very stupid compilers. If your */
/* compiler is smarter, feel free to replace the "int" with "void". */
/* Not that it matters. */
#define VOID int
/* Two constants for algorithms based on random sampling. Both constants */
/* have been chosen empirically to optimize their respective algorithms. */
/* Used for the point location scheme of Mucke, Saias, and Zhu, to decide */
/* how large a random sample of triangles to inspect. */
#define SAMPLEFACTOR 11
/* Used in Fortune's sweepline Delaunay algorithm to determine what fraction */
/* of boundary edges should be maintained in the splay tree for point */
/* location on the front. */
#define SAMPLERATE 10
/* A number that speaks for itself, every kissable digit. */
#define PI 3.141592653589793238462643383279502884197169399375105820974944592308
/* Another fave. */
#define SQUAREROOTTWO 1.4142135623730950488016887242096980785696718753769480732
/* And here's one for those of you who are intimidated by math. */
#define ONETHIRD 0.333333333333333333333333333333333333333333333333333333333333
#include <stdio.h>
#include <string.h>
#include <math.h>
#ifndef NO_TIMER
#include <sys/time.h>
#endif /* NO_TIMER */
#ifdef TRILIBRARY
#include "triangle.h"
#endif /* TRILIBRARY */
/* The following obscenity seems to be necessary to ensure that this program */
/* will port to Dec Alphas running OSF/1, because their stdio.h file commits */
/* the unpardonable sin of including stdlib.h. Hence, malloc(), free(), and */
/* exit() may or may not already be defined at this point. I declare these */
/* functions explicitly because some non-ANSI C compilers lack stdlib.h. */
#ifndef _STDLIB_H_
extern void *malloc();
extern void free();
extern void exit();
extern double strtod();
extern long strtol();
#endif /* _STDLIB_H_ */
/* A few forward declarations. */
void poolrestart();
#ifndef TRILIBRARY
char *readline();
char *findfield();
#endif /* not TRILIBRARY */
/* Labels that signify whether a record consists primarily of pointers or of */
/* floating-point words. Used to make decisions about data alignment. */
enum wordtype {POINTER, FLOATINGPOINT};
/* Labels that signify the result of point location. The result of a */
/* search indicates that the point falls in the interior of a triangle, on */
/* an edge, on a vertex, or outside the mesh. */
enum locateresult {INTRIANGLE, ONEDGE, ONVERTEX, OUTSIDE};
/* Labels that signify the result of site insertion. The result indicates */
/* that the point was inserted with complete success, was inserted but */
/* encroaches on a segment, was not inserted because it lies on a segment, */
/* or was not inserted because another point occupies the same location. */
enum insertsiteresult {SUCCESSFULPOINT, ENCROACHINGPOINT, VIOLATINGPOINT,
DUPLICATEPOINT};
/* Labels that signify the result of direction finding. The result */
/* indicates that a segment connecting the two query points falls within */
/* the direction triangle, along the left edge of the direction triangle, */
/* or along the right edge of the direction triangle. */
enum finddirectionresult {WITHIN, LEFTCOLLINEAR, RIGHTCOLLINEAR};
/* Labels that signify the result of the circumcenter computation routine. */
/* The return value indicates which edge of the triangle is shortest. */
enum circumcenterresult {OPPOSITEORG, OPPOSITEDEST, OPPOSITEAPEX};
/*****************************************************************************/
/* */
/* The basic mesh data structures */
/* */
/* There are three: points, triangles, and shell edges (abbreviated */
/* `shelle'). These three data structures, linked by pointers, comprise */
/* the mesh. A point simply represents a point in space and its properties.*/
/* A triangle is a triangle. A shell edge is a special data structure used */
/* to represent impenetrable segments in the mesh (including the outer */
/* boundary, boundaries of holes, and internal boundaries separating two */
/* triangulated regions). Shell edges represent boundaries defined by the */
/* user that triangles may not lie across. */
/* */
/* A triangle consists of a list of three vertices, a list of three */
/* adjoining triangles, a list of three adjoining shell edges (when shell */
/* edges are used), an arbitrary number of optional user-defined floating- */
/* point attributes, and an optional area constraint. The latter is an */
/* upper bound on the permissible area of each triangle in a region, used */
/* for mesh refinement. */
/* */
/* For a triangle on a boundary of the mesh, some or all of the neighboring */
/* triangles may not be present. For a triangle in the interior of the */
/* mesh, often no neighboring shell edges are present. Such absent */
/* triangles and shell edges are never represented by NULL pointers; they */
/* are represented by two special records: `dummytri', the triangle that */
/* fills "outer space", and `dummysh', the omnipresent shell edge. */
/* `dummytri' and `dummysh' are used for several reasons; for instance, */
/* they can be dereferenced and their contents examined without causing the */
/* memory protection exception that would occur if NULL were dereferenced. */
/* */
/* However, it is important to understand that a triangle includes other */
/* information as well. The pointers to adjoining vertices, triangles, and */
/* shell edges are ordered in a way that indicates their geometric relation */
/* to each other. Furthermore, each of these pointers contains orientation */
/* information. Each pointer to an adjoining triangle indicates which face */
/* of that triangle is contacted. Similarly, each pointer to an adjoining */
/* shell edge indicates which side of that shell edge is contacted, and how */
/* the shell edge is oriented relative to the triangle. */
/* */
/* Shell edges are found abutting edges of triangles; either sandwiched */
/* between two triangles, or resting against one triangle on an exterior */
/* boundary or hole boundary. */
/* */
/* A shell edge consists of a list of two vertices, a list of two */
/* adjoining shell edges, and a list of two adjoining triangles. One of */
/* the two adjoining triangles may not be present (though there should */
/* always be one), and neighboring shell edges might not be present. */
/* Shell edges also store a user-defined integer "boundary marker". */
/* Typically, this integer is used to indicate what sort of boundary */
/* conditions are to be applied at that location in a finite element */
/* simulation. */
/* */
/* Like triangles, shell edges maintain information about the relative */
/* orientation of neighboring objects. */
/* */
/* Points are relatively simple. A point is a list of floating point */
/* numbers, starting with the x, and y coordinates, followed by an */
/* arbitrary number of optional user-defined floating-point attributes, */
/* followed by an integer boundary marker. During the segment insertion */
/* phase, there is also a pointer from each point to a triangle that may */
/* contain it. Each pointer is not always correct, but when one is, it */
/* speeds up segment insertion. These pointers are assigned values once */
/* at the beginning of the segment insertion phase, and are not used or */
/* updated at any other time. Edge swapping during segment insertion will */
/* render some of them incorrect. Hence, don't rely upon them for */
/* anything. For the most part, points do not have any information about */
/* what triangles or shell edges they are linked to. */
/* */
/*****************************************************************************/
/*****************************************************************************/
/* */
/* Handles */
/* */
/* The oriented triangle (`triedge') and oriented shell edge (`edge') data */
/* structures defined below do not themselves store any part of the mesh. */
/* The mesh itself is made of `triangle's, `shelle's, and `point's. */
/* */
/* Oriented triangles and oriented shell edges will usually be referred to */
/* as "handles". A handle is essentially a pointer into the mesh; it */
/* allows you to "hold" one particular part of the mesh. Handles are used */
/* to specify the regions in which one is traversing and modifying the mesh.*/
/* A single `triangle' may be held by many handles, or none at all. (The */
/* latter case is not a memory leak, because the triangle is still */
/* connected to other triangles in the mesh.) */
/* */
/* A `triedge' is a handle that holds a triangle. It holds a specific side */
/* of the triangle. An `edge' is a handle that holds a shell edge. It */
/* holds either the left or right side of the edge. */
/* */
/* Navigation about the mesh is accomplished through a set of mesh */
/* manipulation primitives, further below. Many of these primitives take */
/* a handle and produce a new handle that holds the mesh near the first */
/* handle. Other primitives take two handles and glue the corresponding */
/* parts of the mesh together. The exact position of the handles is */
/* important. For instance, when two triangles are glued together by the */
/* bond() primitive, they are glued by the sides on which the handles lie. */
/* */
/* Because points have no information about which triangles they are */
/* attached to, I commonly represent a point by use of a handle whose */
/* origin is the point. A single handle can simultaneously represent a */
/* triangle, an edge, and a point. */
/* */
/*****************************************************************************/
/* The triangle data structure. Each triangle contains three pointers to */
/* adjoining triangles, plus three pointers to vertex points, plus three */
/* pointers to shell edges (defined below; these pointers are usually */
/* `dummysh'). It may or may not also contain user-defined attributes */
/* and/or a floating-point "area constraint". It may also contain extra */
/* pointers for nodes, when the user asks for high-order elements. */
/* Because the size and structure of a `triangle' is not decided until */
/* runtime, I haven't simply defined the type `triangle' to be a struct. */
typedef REAL **triangle; /* Really: typedef triangle *triangle */
/* An oriented triangle: includes a pointer to a triangle and orientation. */
/* The orientation denotes an edge of the triangle. Hence, there are */
/* three possible orientations. By convention, each edge is always */
/* directed to point counterclockwise about the corresponding triangle. */
struct triedge {
triangle *tri;
int orient; /* Ranges from 0 to 2. */
};
/* The shell data structure. Each shell edge contains two pointers to */
/* adjoining shell edges, plus two pointers to vertex points, plus two */
/* pointers to adjoining triangles, plus one shell marker. */
typedef REAL **shelle; /* Really: typedef shelle *shelle */
/* An oriented shell edge: includes a pointer to a shell edge and an */
/* orientation. The orientation denotes a side of the edge. Hence, there */
/* are two possible orientations. By convention, the edge is always */
/* directed so that the "side" denoted is the right side of the edge. */
struct edge {
shelle *sh;
int shorient; /* Ranges from 0 to 1. */
};
/* The point data structure. Each point is actually an array of REALs. */
/* The number of REALs is unknown until runtime. An integer boundary */
/* marker, and sometimes a pointer to a triangle, is appended after the */
/* REALs. */
typedef REAL *point;
/* A queue used to store encroached segments. Each segment's vertices are */
/* stored so that one can check whether a segment is still the same. */
struct badsegment {
struct edge encsegment; /* An encroached segment. */
point segorg, segdest; /* The two vertices. */
struct badsegment *nextsegment; /* Pointer to next encroached segment. */
};
/* A queue used to store bad triangles. The key is the square of the cosine */
/* of the smallest angle of the triangle. Each triangle's vertices are */
/* stored so that one can check whether a triangle is still the same. */
struct badface {
struct triedge badfacetri; /* A bad triangle. */
REAL key; /* cos^2 of smallest (apical) angle. */
point faceorg, facedest, faceapex; /* The three vertices. */
struct badface *nextface; /* Pointer to next bad triangle. */
};
/* A node in a heap used to store events for the sweepline Delaunay */
/* algorithm. Nodes do not point directly to their parents or children in */
/* the heap. Instead, each node knows its position in the heap, and can */
/* look up its parent and children in a separate array. The `eventptr' */
/* points either to a `point' or to a triangle (in encoded format, so that */
/* an orientation is included). In the latter case, the origin of the */
/* oriented triangle is the apex of a "circle event" of the sweepline */
/* algorithm. To distinguish site events from circle events, all circle */
/* events are given an invalid (smaller than `xmin') x-coordinate `xkey'. */
struct event {
REAL xkey, ykey; /* Coordinates of the event. */
VOID *eventptr; /* Can be a point or the location of a circle event. */
int heapposition; /* Marks this event's position in the heap. */
};
/* A node in the splay tree. Each node holds an oriented ghost triangle */
/* that represents a boundary edge of the growing triangulation. When a */
/* circle event covers two boundary edges with a triangle, so that they */
/* are no longer boundary edges, those edges are not immediately deleted */
/* from the tree; rather, they are lazily deleted when they are next */
/* encountered. (Since only a random sample of boundary edges are kept */
/* in the tree, lazy deletion is faster.) `keydest' is used to verify */
/* that a triangle is still the same as when it entered the splay tree; if */
/* it has been rotated (due to a circle event), it no longer represents a */
/* boundary edge and should be deleted. */
struct splaynode {
struct triedge keyedge; /* Lprev of an edge on the front. */
point keydest; /* Used to verify that splay node is still live. */
struct splaynode *lchild, *rchild; /* Children in splay tree. */
};
/* A type used to allocate memory. firstblock is the first block of items. */
/* nowblock is the block from which items are currently being allocated. */
/* nextitem points to the next slab of free memory for an item. */
/* deaditemstack is the head of a linked list (stack) of deallocated items */
/* that can be recycled. unallocateditems is the number of items that */
/* remain to be allocated from nowblock. */
/* */
/* Traversal is the process of walking through the entire list of items, and */
/* is separate from allocation. Note that a traversal will visit items on */
/* the "deaditemstack" stack as well as live items. pathblock points to */
/* the block currently being traversed. pathitem points to the next item */
/* to be traversed. pathitemsleft is the number of items that remain to */
/* be traversed in pathblock. */
/* */
/* itemwordtype is set to POINTER or FLOATINGPOINT, and is used to suggest */
/* what sort of word the record is primarily made up of. alignbytes */
/* determines how new records should be aligned in memory. itembytes and */
/* itemwords are the length of a record in bytes (after rounding up) and */
/* words. itemsperblock is the number of items allocated at once in a */
/* single block. items is the number of currently allocated items. */
/* maxitems is the maximum number of items that have been allocated at */
/* once; it is the current number of items plus the number of records kept */
/* on deaditemstack. */
struct memorypool {
VOID **firstblock, **nowblock;
VOID *nextitem;
VOID *deaditemstack;
VOID **pathblock;
VOID *pathitem;
enum wordtype itemwordtype;
int alignbytes;
int itembytes, itemwords;
int itemsperblock;
long items, maxitems;
int unallocateditems;
int pathitemsleft;
};
/* Variables used to allocate memory for triangles, shell edges, points, */
/* viri (triangles being eaten), bad (encroached) segments, bad (skinny */
/* or too large) triangles, and splay tree nodes. */
static struct memorypool triangles;
static struct memorypool shelles;
static struct memorypool points;
static struct memorypool viri;
static struct memorypool badsegments;
static struct memorypool badtriangles;
static struct memorypool splaynodes;
/* Variables that maintain the bad triangle queues. The tails are pointers */
/* to the pointers that have to be filled in to enqueue an item. */
//static struct badface *queuefront[64];
//static struct badface **queuetail[64];
static REAL xmin, xmax, ymin, ymax; /* x and y bounds. */
static REAL xminextreme; /* Nonexistent x value used as a flag in sweepline. */
static int inpoints; /* Number of input points. */
static int inelements; /* Number of input triangles. */
static int insegments; /* Number of input segments. */
static int holes; /* Number of input holes. */
static int regions; /* Number of input regions. */
static long edges; /* Number of output edges. */
static int mesh_dim; /* Dimension (ought to be 2). */
static int nextras; /* Number of attributes per point. */
static int eextras; /* Number of attributes per triangle. */
static long hullsize; /* Number of edges of convex hull. */
static int triwords; /* Total words per triangle. */
static int shwords; /* Total words per shell edge. */
static int pointmarkindex; /* Index to find boundary marker of a point. */
static int point2triindex; /* Index to find a triangle adjacent to a point. */
static int highorderindex; /* Index to find extra nodes for high-order elements. */
static int elemattribindex; /* Index to find attributes of a triangle. */
static int areaboundindex; /* Index to find area bound of a triangle. */
static int checksegments; /* Are there segments in the triangulation yet? */
static int readnodefile; /* Has a .node file been read? */
static long samples; /* Number of random samples for point location. */
static unsigned long randomseed; /* Current random number seed. */
static REAL splitter; /* Used to split REAL factors for exact multiplication. */
static REAL epsilon; /* Floating-point machine epsilon. */
static REAL resulterrbound;
static REAL ccwerrboundA, ccwerrboundB, ccwerrboundC;
static REAL iccerrboundA, iccerrboundB, iccerrboundC;
static long incirclecount; /* Number of incircle tests performed. */
static long counterclockcount; /* Number of counterclockwise tests performed. */
static long hyperbolacount; /* Number of right-of-hyperbola tests performed. */
static long circumcentercount; /* Number of circumcenter calculations performed. */
static long circletopcount; /* Number of circle top calculations performed. */
/* Switches for the triangulator. */
/* poly: -p switch. refine: -r switch. */
/* quality: -q switch. */
/* minangle: minimum angle bound, specified after -q switch. */
/* goodangle: cosine squared of minangle. */
/* vararea: -a switch without number. */
/* fixedarea: -a switch with number. */
/* maxarea: maximum area bound, specified after -a switch. */
/* regionattrib: -A switch. convex: -c switch. */
/* firstnumber: inverse of -z switch. All items are numbered starting */
/* from firstnumber. */
/* edgesout: -e switch. voronoi: -v switch. */
/* neighbors: -n switch. geomview: -g switch. */
/* nobound: -B switch. nopolywritten: -P switch. */
/* nonodewritten: -N switch. noelewritten: -E switch. */
/* noiterationnum: -I switch. noholes: -O switch. */
/* noexact: -X switch. */
/* order: element order, specified after -o switch. */
/* nobisect: count of how often -Y switch is selected. */
/* steiner: maximum number of Steiner points, specified after -S switch. */
/* steinerleft: number of Steiner points not yet used. */
/* incremental: -i switch. sweepline: -F switch. */
/* dwyer: inverse of -l switch. */
/* splitseg: -s switch. */
/* docheck: -C switch. */
/* quiet: -Q switch. verbose: count of how often -V switch is selected. */
/* useshelles: -p, -r, -q, or -c switch; determines whether shell edges */
/* are used at all. */
/* */
/* Read the instructions to find out the meaning of these switches. */
static int poly, refine, quality, vararea, fixedarea, regionattrib, convex;
static int firstnumber;
static int edgesout, voronoi, neighbors, geomview;
static int nobound, nopolywritten, nonodewritten, noelewritten, noiterationnum;
static int noholes, noexact;
static int incremental, sweepline, dwyer;
static int splitseg;
static int docheck;
static int quiet, verbose;
static int useshelles;
static int order;
static int nobisect;
static int steiner, steinerleft;
static REAL minangle, goodangle;
static REAL maxarea;
/* Variables for file names. */
#ifndef TRILIBRARY
char innodefilename[FILENAMESIZE];
char inelefilename[FILENAMESIZE];
char inpolyfilename[FILENAMESIZE];
char areafilename[FILENAMESIZE];
char outnodefilename[FILENAMESIZE];
char outelefilename[FILENAMESIZE];
char outpolyfilename[FILENAMESIZE];
char edgefilename[FILENAMESIZE];
char vnodefilename[FILENAMESIZE];
char vedgefilename[FILENAMESIZE];
char neighborfilename[FILENAMESIZE];
char offfilename[FILENAMESIZE];
#endif /* not TRILIBRARY */
/* Triangular bounding box points. */
static point infpoint1, infpoint2, infpoint3;
/* Pointer to the `triangle' that occupies all of "outer space". */
static triangle *dummytri;
static triangle *dummytribase; /* Keep base address so we can free() it later. */
/* Pointer to the omnipresent shell edge. Referenced by any triangle or */
/* shell edge that isn't really connected to a shell edge at that */
/* location. */
static shelle *dummysh;
static shelle *dummyshbase; /* Keep base address so we can free() it later. */
/* Pointer to a recently visited triangle. Improves point location if */
/* proximate points are inserted sequentially. */
static struct triedge recenttri;
/*****************************************************************************/
/* */
/* Mesh manipulation primitives. Each triangle contains three pointers to */
/* other triangles, with orientations. Each pointer points not to the */
/* first byte of a triangle, but to one of the first three bytes of a */
/* triangle. It is necessary to extract both the triangle itself and the */
/* orientation. To save memory, I keep both pieces of information in one */
/* pointer. To make this possible, I assume that all triangles are aligned */
/* to four-byte boundaries. The `decode' routine below decodes a pointer, */
/* extracting an orientation (in the range 0 to 2) and a pointer to the */
/* beginning of a triangle. The `encode' routine compresses a pointer to a */
/* triangle and an orientation into a single pointer. My assumptions that */
/* triangles are four-byte-aligned and that the `unsigned long' type is */
/* long enough to hold a pointer are two of the few kludges in this program.*/
/* */
/* Shell edges are manipulated similarly. A pointer to a shell edge */
/* carries both an address and an orientation in the range 0 to 1. */
/* */
/* The other primitives take an oriented triangle or oriented shell edge, */
/* and return an oriented triangle or oriented shell edge or point; or they */
/* change the connections in the data structure. */
/* */
/*****************************************************************************/
/********* Mesh manipulation primitives begin here *********/
/** **/
/** **/
/* Fast lookup arrays to speed some of the mesh manipulation primitives. */
int plus1mod3[3] = {1, 2, 0};
int minus1mod3[3] = {2, 0, 1};
/********* Primitives for triangles *********/
/* */
/* */
/* decode() converts a pointer to an oriented triangle. The orientation is */
/* extracted from the two least significant bits of the pointer. */
#define decode( ptr, triedge ) \
( triedge ).orient = (int) ( (unsigned long) ( ptr ) & (unsigned long) 3l ); \
( triedge ).tri = (triangle *) \
( (unsigned long) ( ptr ) ^ (unsigned long) ( triedge ).orient )
/* encode() compresses an oriented triangle into a single pointer. It */
/* relies on the assumption that all triangles are aligned to four-byte */
/* boundaries, so the two least significant bits of (triedge).tri are zero.*/
#define encode( triedge ) \
(triangle) ( (unsigned long) ( triedge ).tri | (unsigned long) ( triedge ).orient )
/* The following edge manipulation primitives are all described by Guibas */
/* and Stolfi. However, they use an edge-based data structure, whereas I */
/* am using a triangle-based data structure. */
/* sym() finds the abutting triangle, on the same edge. Note that the */
/* edge direction is necessarily reversed, because triangle/edge handles */
/* are always directed counterclockwise around the triangle. */
#define sym( triedge1, triedge2 ) \
ptr = ( triedge1 ).tri[( triedge1 ).orient]; \
decode( ptr, triedge2 );
#define symself( triedge ) \
ptr = ( triedge ).tri[( triedge ).orient]; \
decode( ptr, triedge );
/* lnext() finds the next edge (counterclockwise) of a triangle. */
#define lnext( triedge1, triedge2 ) \
( triedge2 ).tri = ( triedge1 ).tri; \
( triedge2 ).orient = plus1mod3[( triedge1 ).orient]
#define lnextself( triedge ) \
( triedge ).orient = plus1mod3[( triedge ).orient]
/* lprev() finds the previous edge (clockwise) of a triangle. */
#define lprev( triedge1, triedge2 ) \
( triedge2 ).tri = ( triedge1 ).tri; \
( triedge2 ).orient = minus1mod3[( triedge1 ).orient]
#define lprevself( triedge ) \
( triedge ).orient = minus1mod3[( triedge ).orient]
/* onext() spins counterclockwise around a point; that is, it finds the next */
/* edge with the same origin in the counterclockwise direction. This edge */
/* will be part of a different triangle. */
#define onext( triedge1, triedge2 ) \
lprev( triedge1, triedge2 ); \
symself( triedge2 );
#define onextself( triedge ) \
lprevself( triedge ); \
symself( triedge );
/* oprev() spins clockwise around a point; that is, it finds the next edge */
/* with the same origin in the clockwise direction. This edge will be */
/* part of a different triangle. */
#define oprev( triedge1, triedge2 ) \
sym( triedge1, triedge2 ); \
lnextself( triedge2 );
#define oprevself( triedge ) \
symself( triedge ); \
lnextself( triedge );
/* dnext() spins counterclockwise around a point; that is, it finds the next */
/* edge with the same destination in the counterclockwise direction. This */
/* edge will be part of a different triangle. */
#define dnext( triedge1, triedge2 ) \
sym( triedge1, triedge2 ); \
lprevself( triedge2 );
#define dnextself( triedge ) \
symself( triedge ); \
lprevself( triedge );
/* dprev() spins clockwise around a point; that is, it finds the next edge */
/* with the same destination in the clockwise direction. This edge will */
/* be part of a different triangle. */
#define dprev( triedge1, triedge2 ) \
lnext( triedge1, triedge2 ); \
symself( triedge2 );
#define dprevself( triedge ) \
lnextself( triedge ); \
symself( triedge );
/* rnext() moves one edge counterclockwise about the adjacent triangle. */
/* (It's best understood by reading Guibas and Stolfi. It involves */
/* changing triangles twice.) */
#define rnext( triedge1, triedge2 ) \
sym( triedge1, triedge2 ); \
lnextself( triedge2 ); \
symself( triedge2 );
#define rnextself( triedge ) \
symself( triedge ); \
lnextself( triedge ); \
symself( triedge );
/* rnext() moves one edge clockwise about the adjacent triangle. */
/* (It's best understood by reading Guibas and Stolfi. It involves */
/* changing triangles twice.) */
#define rprev( triedge1, triedge2 ) \
sym( triedge1, triedge2 ); \
lprevself( triedge2 ); \
symself( triedge2 );
#define rprevself( triedge ) \
symself( triedge ); \
lprevself( triedge ); \
symself( triedge );
/* These primitives determine or set the origin, destination, or apex of a */
/* triangle. */
#define org( triedge, pointptr ) \
pointptr = (point) ( triedge ).tri[plus1mod3[( triedge ).orient] + 3]
#define dest( triedge, pointptr ) \
pointptr = (point) ( triedge ).tri[minus1mod3[( triedge ).orient] + 3]
#define apex( triedge, pointptr ) \
pointptr = (point) ( triedge ).tri[( triedge ).orient + 3]
#define setorg( triedge, pointptr ) \
( triedge ).tri[plus1mod3[( triedge ).orient] + 3] = (triangle) pointptr
#define setdest( triedge, pointptr ) \
( triedge ).tri[minus1mod3[( triedge ).orient] + 3] = (triangle) pointptr
#define setapex( triedge, pointptr ) \
( triedge ).tri[( triedge ).orient + 3] = (triangle) pointptr
#define setvertices2null( triedge ) \
( triedge ).tri[3] = (triangle) NULL; \
( triedge ).tri[4] = (triangle) NULL; \
( triedge ).tri[5] = (triangle) NULL;
/* Bond two triangles together. */
#define bond( triedge1, triedge2 ) \
( triedge1 ).tri[( triedge1 ).orient] = encode( triedge2 ); \
( triedge2 ).tri[( triedge2 ).orient] = encode( triedge1 )
/* Dissolve a bond (from one side). Note that the other triangle will still */
/* think it's connected to this triangle. Usually, however, the other */
/* triangle is being deleted entirely, or bonded to another triangle, so */
/* it doesn't matter. */
#define dissolve( triedge ) \
( triedge ).tri[( triedge ).orient] = (triangle) dummytri
/* Copy a triangle/edge handle. */
#define triedgecopy( triedge1, triedge2 ) \
( triedge2 ).tri = ( triedge1 ).tri; \
( triedge2 ).orient = ( triedge1 ).orient
/* Test for equality of triangle/edge handles. */
#define triedgeequal( triedge1, triedge2 ) \
( ( ( triedge1 ).tri == ( triedge2 ).tri ) && \
( ( triedge1 ).orient == ( triedge2 ).orient ) )
/* Primitives to infect or cure a triangle with the virus. These rely on */
/* the assumption that all shell edges are aligned to four-byte boundaries.*/
#define infect( triedge ) \
( triedge ).tri[6] = (triangle) \
( (unsigned long) ( triedge ).tri[6] | (unsigned long) 2l )
#define uninfect( triedge ) \
( triedge ).tri[6] = (triangle) \
( (unsigned long) ( triedge ).tri[6] & ~(unsigned long) 2l )
/* Test a triangle for viral infection. */
#define infected( triedge ) \
( ( (unsigned long) ( triedge ).tri[6] & (unsigned long) 2l ) != 0 )
/* Check or set a triangle's attributes. */
#define elemattribute( triedge, attnum ) \
( (REAL *) ( triedge ).tri )[elemattribindex + ( attnum )]
#define setelemattribute( triedge, attnum, value ) \
( (REAL *) ( triedge ).tri )[elemattribindex + ( attnum )] = (REAL)value
/* Check or set a triangle's maximum area bound. */
#define areabound( triedge ) ( (REAL *) ( triedge ).tri )[areaboundindex]
#define setareabound( triedge, value ) \
( (REAL *) ( triedge ).tri )[areaboundindex] = (REAL)value
/********* Primitives for shell edges *********/
/* */
/* */
/* sdecode() converts a pointer to an oriented shell edge. The orientation */
/* is extracted from the least significant bit of the pointer. The two */
/* least significant bits (one for orientation, one for viral infection) */
/* are masked out to produce the real pointer. */
#define sdecode( sptr, edge ) \
( edge ).shorient = (int) ( (unsigned long) ( sptr ) & (unsigned long) 1l ); \
( edge ).sh = (shelle *) \
( (unsigned long) ( sptr ) & ~(unsigned long) 3l )
/* sencode() compresses an oriented shell edge into a single pointer. It */
/* relies on the assumption that all shell edges are aligned to two-byte */
/* boundaries, so the least significant bit of (edge).sh is zero. */
#define sencode( edge ) \
(shelle) ( (unsigned long) ( edge ).sh | (unsigned long) ( edge ).shorient )
/* ssym() toggles the orientation of a shell edge. */
#define ssym( edge1, edge2 ) \
( edge2 ).sh = ( edge1 ).sh; \
( edge2 ).shorient = 1 - ( edge1 ).shorient
#define ssymself( edge ) \
( edge ).shorient = 1 - ( edge ).shorient
/* spivot() finds the other shell edge (from the same segment) that shares */
/* the same origin. */
#define spivot( edge1, edge2 ) \
sptr = ( edge1 ).sh[( edge1 ).shorient]; \
sdecode( sptr, edge2 )
#define spivotself( edge ) \
sptr = ( edge ).sh[( edge ).shorient]; \
sdecode( sptr, edge )
/* snext() finds the next shell edge (from the same segment) in sequence; */
/* one whose origin is the input shell edge's destination. */
#define snext( edge1, edge2 ) \
sptr = ( edge1 ).sh[1 - ( edge1 ).shorient]; \
sdecode( sptr, edge2 )
#define snextself( edge ) \
sptr = ( edge ).sh[1 - ( edge ).shorient]; \
sdecode( sptr, edge )
/* These primitives determine or set the origin or destination of a shell */
/* edge. */
#define sorg( edge, pointptr ) \
pointptr = (point) ( edge ).sh[2 + ( edge ).shorient]
#define sdest( edge, pointptr ) \
pointptr = (point) ( edge ).sh[3 - ( edge ).shorient]
#define setsorg( edge, pointptr ) \
( edge ).sh[2 + ( edge ).shorient] = (shelle) pointptr
#define setsdest( edge, pointptr ) \
( edge ).sh[3 - ( edge ).shorient] = (shelle) pointptr
/* These primitives read or set a shell marker. Shell markers are used to */
/* hold user boundary information. */
#define mark( edge ) ( *(int *) ( ( edge ).sh + 6 ) )
#define setmark( edge, value ) \
*(int *) ( ( edge ).sh + 6 ) = value
/* Bond two shell edges together. */
#define sbond( edge1, edge2 ) \
( edge1 ).sh[( edge1 ).shorient] = sencode( edge2 ); \
( edge2 ).sh[( edge2 ).shorient] = sencode( edge1 )
/* Dissolve a shell edge bond (from one side). Note that the other shell */
/* edge will still think it's connected to this shell edge. */
#define sdissolve( edge ) \
( edge ).sh[( edge ).shorient] = (shelle) dummysh
/* Copy a shell edge. */
#define shellecopy( edge1, edge2 ) \
( edge2 ).sh = ( edge1 ).sh; \
( edge2 ).shorient = ( edge1 ).shorient
/* Test for equality of shell edges. */
#define shelleequal( edge1, edge2 ) \
( ( ( edge1 ).sh == ( edge2 ).sh ) && \
( ( edge1 ).shorient == ( edge2 ).shorient ) )
/********* Primitives for interacting triangles and shell edges *********/
/* */
/* */
/* tspivot() finds a shell edge abutting a triangle. */
#define tspivot( triedge, edge ) \
sptr = (shelle) ( triedge ).tri[6 + ( triedge ).orient]; \
sdecode( sptr, edge )
/* stpivot() finds a triangle abutting a shell edge. It requires that the */
/* variable `ptr' of type `triangle' be defined. */
#define stpivot( edge, triedge ) \
ptr = (triangle) ( edge ).sh[4 + ( edge ).shorient]; \
decode( ptr, triedge )
/* Bond a triangle to a shell edge. */
#define tsbond( triedge, edge ) \
( triedge ).tri[6 + ( triedge ).orient] = (triangle) sencode( edge ); \
( edge ).sh[4 + ( edge ).shorient] = (shelle) encode( triedge )
/* Dissolve a bond (from the triangle side). */
#define tsdissolve( triedge ) \
( triedge ).tri[6 + ( triedge ).orient] = (triangle) dummysh
/* Dissolve a bond (from the shell edge side). */
#define stdissolve( edge ) \
( edge ).sh[4 + ( edge ).shorient] = (shelle) dummytri
/********* Primitives for points *********/
/* */
/* */
#define pointmark( pt ) ( (int *) ( pt ) )[pointmarkindex]
#define setpointmark( pt, value ) \
( (int *) ( pt ) )[pointmarkindex] = value
#define point2tri( pt ) ( (triangle *) ( pt ) )[point2triindex]
#define setpoint2tri( pt, value ) \
( (triangle *) ( pt ) )[point2triindex] = value
/** **/
/** **/
/********* Mesh manipulation primitives end here *********/
/********* User interaction routines begin here *********/
/** **/
/** **/
/*****************************************************************************/
/* */
/* syntax() Print list of command line switches. */
/* */
/*****************************************************************************/
#ifndef TRILIBRARY
void syntax(){
#ifdef CDT_ONLY
#ifdef REDUCED
printf( "triangle [-pAcevngBPNEIOXzo_lQVh] input_file\n" );
#else /* not REDUCED */
printf( "triangle [-pAcevngBPNEIOXzo_iFlCQVh] input_file\n" );
#endif /* not REDUCED */
#else /* not CDT_ONLY */
#ifdef REDUCED
printf( "triangle [-prq__a__AcevngBPNEIOXzo_YS__lQVh] input_file\n" );
#else /* not REDUCED */
printf( "triangle [-prq__a__AcevngBPNEIOXzo_YS__iFlsCQVh] input_file\n" );
#endif /* not REDUCED */
#endif /* not CDT_ONLY */
printf( " -p Triangulates a Planar Straight Line Graph (.poly file).\n" );
#ifndef CDT_ONLY
printf( " -r Refines a previously generated mesh.\n" );
printf(
" -q Quality mesh generation. A minimum angle may be specified.\n" );
printf( " -a Applies a maximum triangle area constraint.\n" );
#endif /* not CDT_ONLY */
printf(
" -A Applies attributes to identify elements in certain regions.\n" );
printf( " -c Encloses the convex hull with segments.\n" );
printf( " -e Generates an edge list.\n" );
printf( " -v Generates a Voronoi diagram.\n" );
printf( " -n Generates a list of triangle neighbors.\n" );
printf( " -g Generates an .off file for Geomview.\n" );
printf( " -B Suppresses output of boundary information.\n" );
printf( " -P Suppresses output of .poly file.\n" );
printf( " -N Suppresses output of .node file.\n" );
printf( " -E Suppresses output of .ele file.\n" );
printf( " -I Suppresses mesh iteration numbers.\n" );
printf( " -O Ignores holes in .poly file.\n" );
printf( " -X Suppresses use of exact arithmetic.\n" );
printf( " -z Numbers all items starting from zero (rather than one).\n" );
printf( " -o2 Generates second-order subparametric elements.\n" );
#ifndef CDT_ONLY
printf( " -Y Suppresses boundary segment splitting.\n" );
printf( " -S Specifies maximum number of added Steiner points.\n" );
#endif /* not CDT_ONLY */
#ifndef REDUCED
printf( " -i Uses incremental method, rather than divide-and-conquer.\n" );
printf( " -F Uses Fortune's sweepline algorithm, rather than d-and-c.\n" );
#endif /* not REDUCED */
printf( " -l Uses vertical cuts only, rather than alternating cuts.\n" );
#ifndef REDUCED
#ifndef CDT_ONLY
printf(
" -s Force segments into mesh by splitting (instead of using CDT).\n" );
#endif /* not CDT_ONLY */
printf( " -C Check consistency of final mesh.\n" );
#endif /* not REDUCED */
printf( " -Q Quiet: No terminal output except errors.\n" );
printf( " -V Verbose: Detailed information on what I'm doing.\n" );
printf( " -h Help: Detailed instructions for Triangle.\n" );
exit( 0 );
}
#endif /* not TRILIBRARY */
/*****************************************************************************/
/* */
/* info() Print out complete instructions. */
/* */
/*****************************************************************************/
#ifndef TRILIBRARY
void info(){
printf( "Triangle\n" );
printf(
"A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator.\n" );
printf( "Version 1.3\n\n" );
printf(
"Copyright 1996 Jonathan Richard Shewchuk (bugs/comments to jrs@cs.cmu.edu)\n"
);
printf( "School of Computer Science / Carnegie Mellon University\n" );
printf( "5000 Forbes Avenue / Pittsburgh, Pennsylvania 15213-3891\n" );
printf(
"Created as part of the Archimedes project (tools for parallel FEM).\n" );
printf(
"Supported in part by NSF Grant CMS-9318163 and an NSERC 1967 Scholarship.\n" );
printf( "There is no warranty whatsoever. Use at your own risk.\n" );
#ifdef SINGLE
printf( "This executable is compiled for single precision arithmetic.\n\n\n" );
#else /* not SINGLE */
printf( "This executable is compiled for double precision arithmetic.\n\n\n" );
#endif /* not SINGLE */
printf(
"Triangle generates exact Delaunay triangulations, constrained Delaunay\n" );
printf(
"triangulations, and quality conforming Delaunay triangulations. The latter\n"
);
printf(
"can be generated with no small angles, and are thus suitable for finite\n" );
printf(
"element analysis. If no command line switches are specified, your .node\n" );
printf(
"input file will be read, and the Delaunay triangulation will be returned in\n"
);
printf( ".node and .ele output files. The command syntax is:\n\n" );
#ifdef CDT_ONLY
#ifdef REDUCED
printf( "triangle [-pAcevngBPNEIOXzo_lQVh] input_file\n\n" );
#else /* not REDUCED */
printf( "triangle [-pAcevngBPNEIOXzo_iFlCQVh] input_file\n\n" );
#endif /* not REDUCED */
#else /* not CDT_ONLY */
#ifdef REDUCED
printf( "triangle [-prq__a__AcevngBPNEIOXzo_YS__lQVh] input_file\n\n" );
#else /* not REDUCED */
printf( "triangle [-prq__a__AcevngBPNEIOXzo_YS__iFlsCQVh] input_file\n\n" );
#endif /* not REDUCED */
#endif /* not CDT_ONLY */
printf(
"Underscores indicate that numbers may optionally follow certain switches;\n" );
printf(
"do not leave any space between a switch and its numeric parameter.\n" );
printf(
"input_file must be a file with extension .node, or extension .poly if the\n" );
printf(
"-p switch is used. If -r is used, you must supply .node and .ele files,\n" );
printf(
"and possibly a .poly file and .area file as well. The formats of these\n" );
printf( "files are described below.\n\n" );
printf( "Command Line Switches:\n\n" );
printf(
" -p Reads a Planar Straight Line Graph (.poly file), which can specify\n"
);
printf(
" points, segments, holes, and regional attributes and area\n" );
printf(
" constraints. Will generate a constrained Delaunay triangulation\n" );
printf(
" fitting the input; or, if -s, -q, or -a is used, a conforming\n" );
printf(
" Delaunay triangulation. If -p is not used, Triangle reads a .node\n"
);
printf( " file by default.\n" );
printf(
" -r Refines a previously generated mesh. The mesh is read from a .node\n"
);
printf(
" file and an .ele file. If -p is also used, a .poly file is read\n" );
printf(
" and used to constrain edges in the mesh. Further details on\n" );
printf( " refinement are given below.\n" );
printf(
" -q Quality mesh generation by Jim Ruppert's Delaunay refinement\n" );
printf(
" algorithm. Adds points to the mesh to ensure that no angles\n" );
printf(
" smaller than 20 degrees occur. An alternative minimum angle may be\n"
);
printf(
" specified after the `q'. If the minimum angle is 20.7 degrees or\n" );
printf(
" smaller, the triangulation algorithm is theoretically guaranteed to\n"
);
printf(
" terminate (assuming infinite precision arithmetic - Triangle may\n" );
printf(
" fail to terminate if you run out of precision). In practice, the\n" );
printf(
" algorithm often succeeds for minimum angles up to 33.8 degrees.\n" );
printf(
" For highly refined meshes, however, it may be necessary to reduce\n" );
printf(
" the minimum angle to well below 20 to avoid problems associated\n" );
printf(
" with insufficient floating-point precision. The specified angle\n" );
printf( " may include a decimal point.\n" );
printf(
" -a Imposes a maximum triangle area. If a number follows the `a', no\n" );
printf(
" triangle will be generated whose area is larger than that number.\n" );
printf(
" If no number is specified, an .area file (if -r is used) or .poly\n" );
printf(
" file (if -r is not used) specifies a number of maximum area\n" );
printf(
" constraints. An .area file contains a separate area constraint for\n"
);
printf(
" each triangle, and is useful for refining a finite element mesh\n" );
printf(
" based on a posteriori error estimates. A .poly file can optionally\n"
);
printf(
" contain an area constraint for each segment-bounded region, thereby\n"
);
printf(
" enforcing triangle densities in a first triangulation. You can\n" );
printf(
" impose both a fixed area constraint and a varying area constraint\n" );
printf(
" by invoking the -a switch twice, once with and once without a\n" );
printf(
" number following. Each area specified may include a decimal point.\n"
);
printf(
" -A Assigns an additional attribute to each triangle that identifies\n" );
printf(
" what segment-bounded region each triangle belongs to. Attributes\n" );
printf(
" are assigned to regions by the .poly file. If a region is not\n" );
printf(
" explicitly marked by the .poly file, triangles in that region are\n" );
printf(
" assigned an attribute of zero. The -A switch has an effect only\n" );
printf( " when the -p switch is used and the -r switch is not.\n" );
printf(
" -c Creates segments on the convex hull of the triangulation. If you\n" );
printf(
" are triangulating a point set, this switch causes a .poly file to\n" );
printf(
" be written, containing all edges in the convex hull. (By default,\n"
);
printf(
" a .poly file is written only if a .poly file is read.) If you are\n"
);
printf(
" triangulating a PSLG, this switch specifies that the interior of\n" );
printf(
" the convex hull of the PSLG should be triangulated. If you do not\n"
);
printf(
" use this switch when triangulating a PSLG, it is assumed that you\n" );
printf(
" have identified the region to be triangulated by surrounding it\n" );
printf(
" with segments of the input PSLG. Beware: if you are not careful,\n"
);
printf(
" this switch can cause the introduction of an extremely thin angle\n" );
printf(
" between a PSLG segment and a convex hull segment, which can cause\n" );
printf(
" overrefinement or failure if Triangle runs out of precision. If\n" );
printf(
" you are refining a mesh, the -c switch works differently; it\n" );
printf(
" generates the set of boundary edges of the mesh, rather than the\n" );
printf( " convex hull.\n" );
printf(
" -e Outputs (to an .edge file) a list of edges of the triangulation.\n" );
printf(
" -v Outputs the Voronoi diagram associated with the triangulation.\n" );
printf( " Does not attempt to detect degeneracies.\n" );
printf(
" -n Outputs (to a .neigh file) a list of triangles neighboring each\n" );
printf( " triangle.\n" );
printf(
" -g Outputs the mesh to an Object File Format (.off) file, suitable for\n"
);
printf( " viewing with the Geometry Center's Geomview package.\n" );
printf(
" -B No boundary markers in the output .node, .poly, and .edge output\n" );
printf(
" files. See the detailed discussion of boundary markers below.\n" );
printf(
" -P No output .poly file. Saves disk space, but you lose the ability\n" );
printf(
" to impose segment constraints on later refinements of the mesh.\n" );
printf( " -N No output .node file.\n" );
printf( " -E No output .ele file.\n" );
printf(
" -I No iteration numbers. Suppresses the output of .node and .poly\n" );
printf(
" files, so your input files won't be overwritten. (If your input is\n"
);
printf(
" a .poly file only, a .node file will be written.) Cannot be used\n" );
printf(
" with the -r switch, because that would overwrite your input .ele\n" );
printf(
" file. Shouldn't be used with the -s, -q, or -a switch if you are\n" );
printf(
" using a .node file for input, because no .node file will be\n" );
printf( " written, so there will be no record of any added points.\n" );
printf( " -O No holes. Ignores the holes in the .poly file.\n" );
printf(
" -X No exact arithmetic. Normally, Triangle uses exact floating-point\n"
);
printf(
" arithmetic for certain tests if it thinks the inexact tests are not\n"
);
printf(
" accurate enough. Exact arithmetic ensures the robustness of the\n" );
printf(
" triangulation algorithms, despite floating-point roundoff error.\n" );
printf(
" Disabling exact arithmetic with the -X switch will cause a small\n" );
printf(
" improvement in speed and create the possibility (albeit small) that\n"
);
printf(
" Triangle will fail to produce a valid mesh. Not recommended.\n" );
printf(
" -z Numbers all items starting from zero (rather than one). Note that\n"
);
printf(
" this switch is normally overrided by the value used to number the\n" );
printf(
" first point of the input .node or .poly file. However, this switch\n"
);
printf( " is useful when calling Triangle from another program.\n" );
printf(
" -o2 Generates second-order subparametric elements with six nodes each.\n"
);
printf(
" -Y No new points on the boundary. This switch is useful when the mesh\n"
);
printf(
" boundary must be preserved so that it conforms to some adjacent\n" );
printf(
" mesh. Be forewarned that you will probably sacrifice some of the\n" );
printf(
" quality of the mesh; Triangle will try, but the resulting mesh may\n"
);
printf(
" contain triangles of poor aspect ratio. Works well if all the\n" );
printf(
" boundary points are closely spaced. Specify this switch twice\n" );
printf(
" (`-YY') to prevent all segment splitting, including internal\n" );
printf( " boundaries.\n" );
printf(
" -S Specifies the maximum number of Steiner points (points that are not\n"
);
printf(
" in the input, but are added to meet the constraints of minimum\n" );
printf(
" angle and maximum area). The default is to allow an unlimited\n" );
printf(
" number. If you specify this switch with no number after it,\n" );
printf(
" the limit is set to zero. Triangle always adds points at segment\n" );
printf(
" intersections, even if it needs to use more points than the limit\n" );
printf(
" you set. When Triangle inserts segments by splitting (-s), it\n" );
printf(
" always adds enough points to ensure that all the segments appear in\n"
);
printf(
" the triangulation, again ignoring the limit. Be forewarned that\n" );
printf(
" the -S switch may result in a conforming triangulation that is not\n"
);
printf(
" truly Delaunay, because Triangle may be forced to stop adding\n" );
printf(
" points when the mesh is in a state where a segment is non-Delaunay\n"
);
printf(
" and needs to be split. If so, Triangle will print a warning.\n" );
printf(
" -i Uses an incremental rather than divide-and-conquer algorithm to\n" );
printf(
" form a Delaunay triangulation. Try it if the divide-and-conquer\n" );
printf( " algorithm fails.\n" );
printf(
" -F Uses Steven Fortune's sweepline algorithm to form a Delaunay\n" );
printf(
" triangulation. Warning: does not use exact arithmetic for all\n" );
printf( " calculations. An exact result is not guaranteed.\n" );
printf(
" -l Uses only vertical cuts in the divide-and-conquer algorithm. By\n" );
printf(
" default, Triangle uses alternating vertical and horizontal cuts,\n" );
printf(
" which usually improve the speed except with point sets that are\n" );
printf(
" small or short and wide. This switch is primarily of theoretical\n" );
printf( " interest.\n" );
printf(
" -s Specifies that segments should be forced into the triangulation by\n"
);
printf(
" recursively splitting them at their midpoints, rather than by\n" );
printf(
" generating a constrained Delaunay triangulation. Segment splitting\n"
);
printf(
" is true to Ruppert's original algorithm, but can create needlessly\n"
);
printf( " small triangles near external small features.\n" );
printf(
" -C Check the consistency of the final mesh. Uses exact arithmetic for\n"
);
printf(
" checking, even if the -X switch is used. Useful if you suspect\n" );
printf( " Triangle is buggy.\n" );
printf(
" -Q Quiet: Suppresses all explanation of what Triangle is doing, unless\n"
);
printf( " an error occurs.\n" );
printf(
" -V Verbose: Gives detailed information about what Triangle is doing.\n" );
printf(
" Add more `V's for increasing amount of detail. `-V' gives\n" );
printf(
" information on algorithmic progress and more detailed statistics.\n" );
printf(
" `-VV' gives point-by-point details, and will print so much that\n" );
printf(
" Triangle will run much more slowly. `-VVV' gives information only\n"
);
printf( " a debugger could love.\n" );
printf( " -h Help: Displays these instructions.\n" );
printf( "\n" );
printf( "Definitions:\n" );
printf( "\n" );
printf(
" A Delaunay triangulation of a point set is a triangulation whose vertices\n"
);
printf(
" are the point set, having the property that no point in the point set\n" );
printf(
" falls in the interior of the circumcircle (circle that passes through all\n"
);
printf( " three vertices) of any triangle in the triangulation.\n\n" );
printf(
" A Voronoi diagram of a point set is a subdivision of the plane into\n" );
printf(
" polygonal regions (some of which may be infinite), where each region is\n" );
printf(
" the set of points in the plane that are closer to some input point than\n" );
printf(
" to any other input point. (The Voronoi diagram is the geometric dual of\n"
);
printf( " the Delaunay triangulation.)\n\n" );
printf(
" A Planar Straight Line Graph (PSLG) is a collection of points and\n" );
printf(
" segments. Segments are simply edges, whose endpoints are points in the\n" );
printf(
" PSLG. The file format for PSLGs (.poly files) is described below.\n" );
printf( "\n" );
printf(
" A constrained Delaunay triangulation of a PSLG is similar to a Delaunay\n" );
printf(
" triangulation, but each PSLG segment is present as a single edge in the\n" );
printf(
" triangulation. (A constrained Delaunay triangulation is not truly a\n" );
printf( " Delaunay triangulation.)\n\n" );
printf(
" A conforming Delaunay triangulation of a PSLG is a true Delaunay\n" );
printf(
" triangulation in which each PSLG segment may have been subdivided into\n" );
printf(
" several edges by the insertion of additional points. These inserted\n" );
printf(
" points are necessary to allow the segments to exist in the mesh while\n" );
printf( " maintaining the Delaunay property.\n\n" );
printf( "File Formats:\n\n" );
printf(
" All files may contain comments prefixed by the character '#'. Points,\n" );
printf(
" triangles, edges, holes, and maximum area constraints must be numbered\n" );
printf(
" consecutively, starting from either 1 or 0. Whichever you choose, all\n" );
printf(
" input files must be consistent; if the nodes are numbered from 1, so must\n"
);
printf(
" be all other objects. Triangle automatically detects your choice while\n" );
printf(
" reading the .node (or .poly) file. (When calling Triangle from another\n" );
printf(
" program, use the -z switch if you wish to number objects from zero.)\n" );
printf( " Examples of these file formats are given below.\n\n" );
printf( " .node files:\n" );
printf(
" First line: <# of points> <dimension (must be 2)> <# of attributes>\n" );
printf(
" <# of boundary markers (0 or 1)>\n"
);
printf(
" Remaining lines: <point #> <x> <y> [attributes] [boundary marker]\n" );
printf( "\n" );
printf(
" The attributes, which are typically floating-point values of physical\n" );
printf(
" quantities (such as mass or conductivity) associated with the nodes of\n"
);
printf(
" a finite element mesh, are copied unchanged to the output mesh. If -s,\n"
);
printf(
" -q, or -a is selected, each new Steiner point added to the mesh will\n" );
printf( " have attributes assigned to it by linear interpolation.\n\n" );
printf(
" If the fourth entry of the first line is `1', the last column of the\n" );
printf(
" remainder of the file is assumed to contain boundary markers. Boundary\n"
);
printf(
" markers are used to identify boundary points and points resting on PSLG\n"
);
printf(
" segments; a complete description appears in a section below. The .node\n"
);
printf(
" file produced by Triangle will contain boundary markers in the last\n" );
printf( " column unless they are suppressed by the -B switch.\n\n" );
printf( " .ele files:\n" );
printf(
" First line: <# of triangles> <points per triangle> <# of attributes>\n" );
printf(
" Remaining lines: <triangle #> <point> <point> <point> ... [attributes]\n"
);
printf( "\n" );
printf(
" Points are indices into the corresponding .node file. The first three\n"
);
printf(
" points are the corners, and are listed in counterclockwise order around\n"
);
printf(
" each triangle. (The remaining points, if any, depend on the type of\n" );
printf(
" finite element used.) The attributes are just like those of .node\n" );
printf(
" files. Because there is no simple mapping from input to output\n" );
printf(
" triangles, an attempt is made to interpolate attributes, which may\n" );
printf(
" result in a good deal of diffusion of attributes among nearby triangles\n"
);
printf(
" as the triangulation is refined. Diffusion does not occur across\n" );
printf(
" segments, so attributes used to identify segment-bounded regions remain\n"
);
printf(
" intact. In output .ele files, all triangles have three points each\n" );
printf(
" unless the -o2 switch is used, in which case they have six, and the\n" );
printf(
" fourth, fifth, and sixth points lie on the midpoints of the edges\n" );
printf( " opposite the first, second, and third corners.\n\n" );
printf( " .poly files:\n" );
printf(
" First line: <# of points> <dimension (must be 2)> <# of attributes>\n" );
printf(
" <# of boundary markers (0 or 1)>\n"
);
printf(
" Following lines: <point #> <x> <y> [attributes] [boundary marker]\n" );
printf( " One line: <# of segments> <# of boundary markers (0 or 1)>\n" );
printf(
" Following lines: <segment #> <endpoint> <endpoint> [boundary marker]\n" );
printf( " One line: <# of holes>\n" );
printf( " Following lines: <hole #> <x> <y>\n" );
printf(
" Optional line: <# of regional attributes and/or area constraints>\n" );
printf(
" Optional following lines: <constraint #> <x> <y> <attrib> <max area>\n" );
printf( "\n" );
printf(
" A .poly file represents a PSLG, as well as some additional information.\n"
);
printf(
" The first section lists all the points, and is identical to the format\n"
);
printf(
" of .node files. <# of points> may be set to zero to indicate that the\n"
);
printf(
" points are listed in a separate .node file; .poly files produced by\n" );
printf(
" Triangle always have this format. This has the advantage that a point\n"
);
printf(
" set may easily be triangulated with or without segments. (The same\n" );
printf(
" effect can be achieved, albeit using more disk space, by making a copy\n"
);
printf(
" of the .poly file with the extension .node; all sections of the file\n" );
printf( " but the first are ignored.)\n\n" );
printf(
" The second section lists the segments. Segments are edges whose\n" );
printf(
" presence in the triangulation is enforced. Each segment is specified\n" );
printf(
" by listing the indices of its two endpoints. This means that you must\n"
);
printf(
" include its endpoints in the point list. If -s, -q, and -a are not\n" );
printf(
" selected, Triangle will produce a constrained Delaunay triangulation,\n" );
printf(
" in which each segment appears as a single edge in the triangulation.\n" );
printf(
" If -q or -a is selected, Triangle will produce a conforming Delaunay\n" );
printf(
" triangulation, in which segments may be subdivided into smaller edges.\n"
);
printf( " Each segment, like each point, may have a boundary marker.\n\n" );
printf(
" The third section lists holes (and concavities, if -c is selected) in\n" );
printf(
" the triangulation. Holes are specified by identifying a point inside\n" );
printf(
" each hole. After the triangulation is formed, Triangle creates holes\n" );
printf(
" by eating triangles, spreading out from each hole point until its\n" );
printf(
" progress is blocked by PSLG segments; you must be careful to enclose\n" );
printf(
" each hole in segments, or your whole triangulation may be eaten away.\n" );
printf(
" If the two triangles abutting a segment are eaten, the segment itself\n" );
printf(
" is also eaten. Do not place a hole directly on a segment; if you do,\n" );
printf( " Triangle will choose one side of the segment arbitrarily.\n\n" );
printf(
" The optional fourth section lists regional attributes (to be assigned\n" );
printf(
" to all triangles in a region) and regional constraints on the maximum\n" );
printf(
" triangle area. Triangle will read this section only if the -A switch\n" );
printf(
" is used or the -a switch is used without a number following it, and the\n"
);
printf(
" -r switch is not used. Regional attributes and area constraints are\n" );
printf(
" propagated in the same manner as holes; you specify a point for each\n" );
printf(
" attribute and/or constraint, and the attribute and/or constraint will\n" );
printf(
" affect the whole region (bounded by segments) containing the point. If\n"
);
printf(
" two values are written on a line after the x and y coordinate, the\n" );
printf(
" former is assumed to be a regional attribute (but will only be applied\n"
);
printf(
" if the -A switch is selected), and the latter is assumed to be a\n" );
printf(
" regional area constraint (but will only be applied if the -a switch is\n"
);
printf(
" selected). You may also specify just one value after the coordinates,\n"
);
printf(
" which can serve as both an attribute and an area constraint, depending\n"
);
printf(
" on the choice of switches. If you are using the -A and -a switches\n" );
printf(
" simultaneously and wish to assign an attribute to some region without\n" );
printf( " imposing an area constraint, use a negative maximum area.\n\n" );
printf(
" When a triangulation is created from a .poly file, you must either\n" );
printf(
" enclose the entire region to be triangulated in PSLG segments, or\n" );
printf(
" use the -c switch, which encloses the convex hull of the input point\n" );
printf(
" set. If you do not use the -c switch, Triangle will eat all triangles\n"
);
printf(
" on the outer boundary that are not protected by segments; if you are\n" );
printf(
" not careful, your whole triangulation may be eaten away. If you do\n" );
printf(
" use the -c switch, you can still produce concavities by appropriate\n" );
printf( " placement of holes just inside the convex hull.\n\n" );
printf(
" An ideal PSLG has no intersecting segments, nor any points that lie\n" );
printf(
" upon segments (except, of course, the endpoints of each segment.) You\n"
);
printf(
" aren't required to make your .poly files ideal, but you should be aware\n"
);
printf(
" of what can go wrong. Segment intersections are relatively safe -\n" );
printf(
" Triangle will calculate the intersection points for you and add them to\n"
);
printf(
" the triangulation - as long as your machine's floating-point precision\n"
);
printf(
" doesn't become a problem. You are tempting the fates if you have three\n"
);
printf(
" segments that cross at the same location, and expect Triangle to figure\n"
);
printf(
" out where the intersection point is. Thanks to floating-point roundoff\n"
);
printf(
" error, Triangle will probably decide that the three segments intersect\n"
);
printf(
" at three different points, and you will find a minuscule triangle in\n" );
printf(
" your output - unless Triangle tries to refine the tiny triangle, uses\n" );
printf(
" up the last bit of machine precision, and fails to terminate at all.\n" );
printf(
" You're better off putting the intersection point in the input files,\n" );
printf(
" and manually breaking up each segment into two. Similarly, if you\n" );
printf(
" place a point at the middle of a segment, and hope that Triangle will\n" );
printf(
" break up the segment at that point, you might get lucky. On the other\n"
);
printf(
" hand, Triangle might decide that the point doesn't lie precisely on the\n"
);
printf(
" line, and you'll have a needle-sharp triangle in your output - or a lot\n"
);
printf( " of tiny triangles if you're generating a quality mesh.\n\n" );
printf(
" When Triangle reads a .poly file, it also writes a .poly file, which\n" );
printf(
" includes all edges that are part of input segments. If the -c switch\n" );
printf(
" is used, the output .poly file will also include all of the edges on\n" );
printf(
" the convex hull. Hence, the output .poly file is useful for finding\n" );
printf(
" edges associated with input segments and setting boundary conditions in\n"
);
printf(
" finite element simulations. More importantly, you will need it if you\n"
);
printf(
" plan to refine the output mesh, and don't want segments to be missing\n" );
printf( " in later triangulations.\n\n" );
printf( " .area files:\n" );
printf( " First line: <# of triangles>\n" );
printf( " Following lines: <triangle #> <maximum area>\n\n" );
printf(
" An .area file associates with each triangle a maximum area that is used\n"
);
printf(
" for mesh refinement. As with other file formats, every triangle must\n" );
printf(
" be represented, and they must be numbered consecutively. A triangle\n" );
printf(
" may be left unconstrained by assigning it a negative maximum area.\n" );
printf( "\n" );
printf( " .edge files:\n" );
printf( " First line: <# of edges> <# of boundary markers (0 or 1)>\n" );
printf(
" Following lines: <edge #> <endpoint> <endpoint> [boundary marker]\n" );
printf( "\n" );
printf(
" Endpoints are indices into the corresponding .node file. Triangle can\n"
);
printf(
" produce .edge files (use the -e switch), but cannot read them. The\n" );
printf(
" optional column of boundary markers is suppressed by the -B switch.\n" );
printf( "\n" );
printf(
" In Voronoi diagrams, one also finds a special kind of edge that is an\n" );
printf(
" infinite ray with only one endpoint. For these edges, a different\n" );
printf( " format is used:\n\n" );
printf( " <edge #> <endpoint> -1 <direction x> <direction y>\n\n" );
printf(
" The `direction' is a floating-point vector that indicates the direction\n"
);
printf( " of the infinite ray.\n\n" );
printf( " .neigh files:\n" );
printf(
" First line: <# of triangles> <# of neighbors per triangle (always 3)>\n"
);
printf(
" Following lines: <triangle #> <neighbor> <neighbor> <neighbor>\n" );
printf( "\n" );
printf(
" Neighbors are indices into the corresponding .ele file. An index of -1\n"
);
printf(
" indicates a mesh boundary, and therefore no neighbor. Triangle can\n" );
printf(
" produce .neigh files (use the -n switch), but cannot read them.\n" );
printf( "\n" );
printf(
" The first neighbor of triangle i is opposite the first corner of\n" );
printf( " triangle i, and so on.\n\n" );
printf( "Boundary Markers:\n\n" );
printf(
" Boundary markers are tags used mainly to identify which output points and\n"
);
printf(
" edges are associated with which PSLG segment, and to identify which\n" );
printf(
" points and edges occur on a boundary of the triangulation. A common use\n"
);
printf(
" is to determine where boundary conditions should be applied to a finite\n" );
printf(
" element mesh. You can prevent boundary markers from being written into\n" );
printf( " files produced by Triangle by using the -B switch.\n\n" );
printf(
" The boundary marker associated with each segment in an output .poly file\n"
);
printf( " or edge in an output .edge file is chosen as follows:\n" );
printf(
" - If an output edge is part or all of a PSLG segment with a nonzero\n" );
printf(
" boundary marker, then the edge is assigned the same marker.\n" );
printf(
" - Otherwise, if the edge occurs on a boundary of the triangulation\n" );
printf(
" (including boundaries of holes), then the edge is assigned the marker\n"
);
printf( " one (1).\n" );
printf( " - Otherwise, the edge is assigned the marker zero (0).\n" );
printf(
" The boundary marker associated with each point in an output .node file is\n"
);
printf( " chosen as follows:\n" );
printf(
" - If a point is assigned a nonzero boundary marker in the input file,\n" );
printf(
" then it is assigned the same marker in the output .node file.\n" );
printf(
" - Otherwise, if the point lies on a PSLG segment (including the\n" );
printf(
" segment's endpoints) with a nonzero boundary marker, then the point\n" );
printf(
" is assigned the same marker. If the point lies on several such\n" );
printf( " segments, one of the markers is chosen arbitrarily.\n" );
printf(
" - Otherwise, if the point occurs on a boundary of the triangulation,\n" );
printf( " then the point is assigned the marker one (1).\n" );
printf( " - Otherwise, the point is assigned the marker zero (0).\n" );
printf( "\n" );
printf(
" If you want Triangle to determine for you which points and edges are on\n" );
printf(
" the boundary, assign them the boundary marker zero (or use no markers at\n"
);
printf(
" all) in your input files. Alternatively, you can mark some of them and\n" );
printf( " leave others marked zero, allowing Triangle to label them.\n\n" );
printf( "Triangulation Iteration Numbers:\n\n" );
printf(
" Because Triangle can read and refine its own triangulations, input\n" );
printf(
" and output files have iteration numbers. For instance, Triangle might\n" );
printf(
" read the files mesh.3.node, mesh.3.ele, and mesh.3.poly, refine the\n" );
printf(
" triangulation, and output the files mesh.4.node, mesh.4.ele, and\n" );
printf( " mesh.4.poly. Files with no iteration number are treated as if\n" );
printf(
" their iteration number is zero; hence, Triangle might read the file\n" );
printf(
" points.node, triangulate it, and produce the files points.1.node and\n" );
printf( " points.1.ele.\n\n" );
printf(
" Iteration numbers allow you to create a sequence of successively finer\n" );
printf(
" meshes suitable for multigrid methods. They also allow you to produce a\n"
);
printf(
" sequence of meshes using error estimate-driven mesh refinement.\n" );
printf( "\n" );
printf(
" If you're not using refinement or quality meshing, and you don't like\n" );
printf(
" iteration numbers, use the -I switch to disable them. This switch will\n" );
printf(
" also disable output of .node and .poly files to prevent your input files\n"
);
printf(
" from being overwritten. (If the input is a .poly file that contains its\n"
);
printf( " own points, a .node file will be written.)\n\n" );
printf( "Examples of How to Use Triangle:\n\n" );
printf(
" `triangle dots' will read points from dots.node, and write their Delaunay\n"
);
printf(
" triangulation to dots.1.node and dots.1.ele. (dots.1.node will be\n" );
printf(
" identical to dots.node.) `triangle -I dots' writes the triangulation to\n"
);
printf(
" dots.ele instead. (No additional .node file is needed, so none is\n" );
printf( " written.)\n\n" );
printf(
" `triangle -pe object.1' will read a PSLG from object.1.poly (and possibly\n"
);
printf(
" object.1.node, if the points are omitted from object.1.poly) and write\n" );
printf( " their constrained Delaunay triangulation to object.2.node and\n" );
printf(
" object.2.ele. The segments will be copied to object.2.poly, and all\n" );
printf( " edges will be written to object.2.edge.\n\n" );
printf(
" `triangle -pq31.5a.1 object' will read a PSLG from object.poly (and\n" );
printf(
" possibly object.node), generate a mesh whose angles are all greater than\n"
);
printf(
" 31.5 degrees and whose triangles all have area smaller than 0.1, and\n" );
printf(
" write the mesh to object.1.node and object.1.ele. Each segment may have\n"
);
printf(
" been broken up into multiple edges; the resulting constrained edges are\n" );
printf( " written to object.1.poly.\n\n" );
printf(
" Here is a sample file `box.poly' describing a square with a square hole:\n"
);
printf( "\n" );
printf(
" # A box with eight points in 2D, no attributes, one boundary marker.\n" );
printf( " 8 2 0 1\n" );
printf( " # Outer box has these vertices:\n" );
printf( " 1 0 0 0\n" );
printf( " 2 0 3 0\n" );
printf( " 3 3 0 0\n" );
printf( " 4 3 3 33 # A special marker for this point.\n" );
printf( " # Inner square has these vertices:\n" );
printf( " 5 1 1 0\n" );
printf( " 6 1 2 0\n" );
printf( " 7 2 1 0\n" );
printf( " 8 2 2 0\n" );
printf( " # Five segments with boundary markers.\n" );
printf( " 5 1\n" );
printf( " 1 1 2 5 # Left side of outer box.\n" );
printf( " 2 5 7 0 # Segments 2 through 5 enclose the hole.\n" );
printf( " 3 7 8 0\n" );
printf( " 4 8 6 10\n" );
printf( " 5 6 5 0\n" );
printf( " # One hole in the middle of the inner square.\n" );
printf( " 1\n" );
printf( " 1 1.5 1.5\n\n" );
printf(
" Note that some segments are missing from the outer square, so one must\n" );
printf(
" use the `-c' switch. After `triangle -pqc box.poly', here is the output\n"
);
printf(
" file `box.1.node', with twelve points. The last four points were added\n" );
printf(
" to meet the angle constraint. Points 1, 2, and 9 have markers from\n" );
printf(
" segment 1. Points 6 and 8 have markers from segment 4. All the other\n" );
printf(
" points but 4 have been marked to indicate that they lie on a boundary.\n" );
printf( "\n" );
printf( " 12 2 0 1\n" );
printf( " 1 0 0 5\n" );
printf( " 2 0 3 5\n" );
printf( " 3 3 0 1\n" );
printf( " 4 3 3 33\n" );
printf( " 5 1 1 1\n" );
printf( " 6 1 2 10\n" );
printf( " 7 2 1 1\n" );
printf( " 8 2 2 10\n" );
printf( " 9 0 1.5 5\n" );
printf( " 10 1.5 0 1\n" );
printf( " 11 3 1.5 1\n" );
printf( " 12 1.5 3 1\n" );
printf( " # Generated by triangle -pqc box.poly\n\n" );
printf( " Here is the output file `box.1.ele', with twelve triangles.\n\n" );
printf( " 12 3 0\n" );
printf( " 1 5 6 9\n" );
printf( " 2 10 3 7\n" );
printf( " 3 6 8 12\n" );
printf( " 4 9 1 5\n" );
printf( " 5 6 2 9\n" );
printf( " 6 7 3 11\n" );
printf( " 7 11 4 8\n" );
printf( " 8 7 5 10\n" );
printf( " 9 12 2 6\n" );
printf( " 10 8 7 11\n" );
printf( " 11 5 1 10\n" );
printf( " 12 8 4 12\n" );
printf( " # Generated by triangle -pqc box.poly\n\n" );
printf(
" Here is the output file `box.1.poly'. Note that segments have been added\n"
);
printf(
" to represent the convex hull, and some segments have been split by newly\n"
);
printf(
" added points. Note also that <# of points> is set to zero to indicate\n" );
printf( " that the points should be read from the .node file.\n\n" );
printf( " 0 2 0 1\n" );
printf( " 12 1\n" );
printf( " 1 1 9 5\n" );
printf( " 2 5 7 1\n" );
printf( " 3 8 7 1\n" );
printf( " 4 6 8 10\n" );
printf( " 5 5 6 1\n" );
printf( " 6 3 10 1\n" );
printf( " 7 4 11 1\n" );
printf( " 8 2 12 1\n" );
printf( " 9 9 2 5\n" );
printf( " 10 10 1 1\n" );
printf( " 11 11 3 1\n" );
printf( " 12 12 4 1\n" );
printf( " 1\n" );
printf( " 1 1.5 1.5\n" );
printf( " # Generated by triangle -pqc box.poly\n\n" );
printf( "Refinement and Area Constraints:\n\n" );
printf(
" The -r switch causes a mesh (.node and .ele files) to be read and\n" );
printf(
" refined. If the -p switch is also used, a .poly file is read and used to\n"
);
printf(
" specify edges that are constrained and cannot be eliminated (although\n" );
printf(
" they can be divided into smaller edges) by the refinement process.\n" );
printf( "\n" );
printf(
" When you refine a mesh, you generally want to impose tighter quality\n" );
printf(
" constraints. One way to accomplish this is to use -q with a larger\n" );
printf(
" angle, or -a followed by a smaller area than you used to generate the\n" );
printf(
" mesh you are refining. Another way to do this is to create an .area\n" );
printf(
" file, which specifies a maximum area for each triangle, and use the -a\n" );
printf(
" switch (without a number following). Each triangle's area constraint is\n"
);
printf(
" applied to that triangle. Area constraints tend to diffuse as the mesh\n" );
printf(
" is refined, so if there are large variations in area constraint between\n" );
printf( " adjacent triangles, you may not get the results you want.\n\n" );
printf(
" If you are refining a mesh composed of linear (three-node) elements, the\n"
);
printf(
" output mesh will contain all the nodes present in the input mesh, in the\n"
);
printf(
" same order, with new nodes added at the end of the .node file. However,\n"
);
printf(
" there is no guarantee that each output element is contained in a single\n" );
printf(
" input element. Often, output elements will overlap two input elements,\n" );
printf(
" and input edges are not present in the output mesh. Hence, a sequence of\n"
);
printf(
" refined meshes will form a hierarchy of nodes, but not a hierarchy of\n" );
printf(
" elements. If you a refining a mesh of higher-order elements, the\n" );
printf(
" hierarchical property applies only to the nodes at the corners of an\n" );
printf( " element; other nodes may not be present in the refined mesh.\n\n" );
printf(
" It is important to understand that maximum area constraints in .poly\n" );
printf(
" files are handled differently from those in .area files. A maximum area\n"
);
printf(
" in a .poly file applies to the whole (segment-bounded) region in which a\n"
);
printf(
" point falls, whereas a maximum area in an .area file applies to only one\n"
);
printf(
" triangle. Area constraints in .poly files are used only when a mesh is\n" );
printf(
" first generated, whereas area constraints in .area files are used only to\n"
);
printf(
" refine an existing mesh, and are typically based on a posteriori error\n" );
printf(
" estimates resulting from a finite element simulation on that mesh.\n" );
printf( "\n" );
printf(
" `triangle -rq25 object.1' will read object.1.node and object.1.ele, then\n"
);
printf(
" refine the triangulation to enforce a 25 degree minimum angle, and then\n" );
printf(
" write the refined triangulation to object.2.node and object.2.ele.\n" );
printf( "\n" );
printf(
" `triangle -rpaa6.2 z.3' will read z.3.node, z.3.ele, z.3.poly, and\n" );
printf(
" z.3.area. After reconstructing the mesh and its segments, Triangle will\n"
);
printf(
" refine the mesh so that no triangle has area greater than 6.2, and\n" );
printf(
" furthermore the triangles satisfy the maximum area constraints in\n" );
printf(
" z.3.area. The output is written to z.4.node, z.4.ele, and z.4.poly.\n" );
printf( "\n" );
printf(
" The sequence `triangle -qa1 x', `triangle -rqa.3 x.1', `triangle -rqa.1\n" );
printf(
" x.2' creates a sequence of successively finer meshes x.1, x.2, and x.3,\n" );
printf( " suitable for multigrid.\n\n" );
printf( "Convex Hulls and Mesh Boundaries:\n\n" );
printf(
" If the input is a point set (rather than a PSLG), Triangle produces its\n" );
printf(
" convex hull as a by-product in the output .poly file if you use the -c\n" );
printf(
" switch. There are faster algorithms for finding a two-dimensional convex\n"
);
printf(
" hull than triangulation, of course, but this one comes for free. If the\n"
);
printf(
" input is an unconstrained mesh (you are using the -r switch but not the\n" );
printf(
" -p switch), Triangle produces a list of its boundary edges (including\n" );
printf( " hole boundaries) as a by-product if you use the -c switch.\n\n" );
printf( "Voronoi Diagrams:\n\n" );
printf(
" The -v switch produces a Voronoi diagram, in files suffixed .v.node and\n" );
printf(
" .v.edge. For example, `triangle -v points' will read points.node,\n" );
printf(
" produce its Delaunay triangulation in points.1.node and points.1.ele,\n" );
printf(
" and produce its Voronoi diagram in points.1.v.node and points.1.v.edge.\n" );
printf(
" The .v.node file contains a list of all Voronoi vertices, and the .v.edge\n"
);
printf(
" file contains a list of all Voronoi edges, some of which may be infinite\n"
);
printf(
" rays. (The choice of filenames makes it easy to run the set of Voronoi\n" );
printf( " vertices through Triangle, if so desired.)\n\n" );
printf(
" This implementation does not use exact arithmetic to compute the Voronoi\n"
);
printf(
" vertices, and does not check whether neighboring vertices are identical.\n"
);
printf(
" Be forewarned that if the Delaunay triangulation is degenerate or\n" );
printf(
" near-degenerate, the Voronoi diagram may have duplicate points, crossing\n"
);
printf(
" edges, or infinite rays whose direction vector is zero. Also, if you\n" );
printf(
" generate a constrained (as opposed to conforming) Delaunay triangulation,\n"
);
printf(
" or if the triangulation has holes, the corresponding Voronoi diagram is\n" );
printf( " likely to have crossing edges and unlikely to make sense.\n\n" );
printf( "Mesh Topology:\n\n" );
printf(
" You may wish to know which triangles are adjacent to a certain Delaunay\n" );
printf(
" edge in an .edge file, which Voronoi regions are adjacent to a certain\n" );
printf(
" Voronoi edge in a .v.edge file, or which Voronoi regions are adjacent to\n"
);
printf(
" each other. All of this information can be found by cross-referencing\n" );
printf(
" output files with the recollection that the Delaunay triangulation and\n" );
printf( " the Voronoi diagrams are planar duals.\n\n" );
printf(
" Specifically, edge i of an .edge file is the dual of Voronoi edge i of\n" );
printf(
" the corresponding .v.edge file, and is rotated 90 degrees counterclock-\n" );
printf(
" wise from the Voronoi edge. Triangle j of an .ele file is the dual of\n" );
printf(
" vertex j of the corresponding .v.node file; and Voronoi region k is the\n" );
printf( " dual of point k of the corresponding .node file.\n\n" );
printf(
" Hence, to find the triangles adjacent to a Delaunay edge, look at the\n" );
printf(
" vertices of the corresponding Voronoi edge; their dual triangles are on\n" );
printf(
" the left and right of the Delaunay edge, respectively. To find the\n" );
printf(
" Voronoi regions adjacent to a Voronoi edge, look at the endpoints of the\n"
);
printf(
" corresponding Delaunay edge; their dual regions are on the right and left\n"
);
printf(
" of the Voronoi edge, respectively. To find which Voronoi regions are\n" );
printf( " adjacent to each other, just read the list of Delaunay edges.\n" );
printf( "\n" );
printf( "Statistics:\n" );
printf( "\n" );
printf(
" After generating a mesh, Triangle prints a count of the number of points,\n"
);
printf(
" triangles, edges, boundary edges, and segments in the output mesh. If\n" );
printf(
" you've forgotten the statistics for an existing mesh, the -rNEP switches\n"
);
printf(
" (or -rpNEP if you've got a .poly file for the existing mesh) will\n" );
printf( " regenerate these statistics without writing any output.\n\n" );
printf(
" The -V switch produces extended statistics, including a rough estimate\n" );
printf(
" of memory use and a histogram of triangle aspect ratios and angles in the\n"
);
printf( " mesh.\n\n" );
printf( "Exact Arithmetic:\n\n" );
printf(
" Triangle uses adaptive exact arithmetic to perform what computational\n" );
printf(
" geometers call the `orientation' and `incircle' tests. If the floating-\n"
);
printf(
" point arithmetic of your machine conforms to the IEEE 754 standard (as\n" );
printf(
" most workstations do), and does not use extended precision internal\n" );
printf(
" registers, then your output is guaranteed to be an absolutely true\n" );
printf( " Delaunay or conforming Delaunay triangulation, roundoff error\n" );
printf(
" notwithstanding. The word `adaptive' implies that these arithmetic\n" );
printf(
" routines compute the result only to the precision necessary to guarantee\n"
);
printf(
" correctness, so they are usually nearly as fast as their approximate\n" );
printf(
" counterparts. The exact tests can be disabled with the -X switch. On\n" );
printf(
" most inputs, this switch will reduce the computation time by about eight\n"
);
printf(
" percent - it's not worth the risk. There are rare difficult inputs\n" );
printf(
" (having many collinear and cocircular points), however, for which the\n" );
printf(
" difference could be a factor of two. These are precisely the inputs most\n"
);
printf( " likely to cause errors if you use the -X switch.\n\n" );
printf(
" Unfortunately, these routines don't solve every numerical problem. Exact\n"
);
printf(
" arithmetic is not used to compute the positions of points, because the\n" );
printf(
" bit complexity of point coordinates would grow without bound. Hence,\n" );
printf(
" segment intersections aren't computed exactly; in very unusual cases,\n" );
printf(
" roundoff error in computing an intersection point might actually lead to\n"
);
printf(
" an inverted triangle and an invalid triangulation. (This is one reason\n" );
printf(
" to compute your own intersection points in your .poly files.) Similarly,\n"
);
printf(
" exact arithmetic is not used to compute the vertices of the Voronoi\n" );
printf( " diagram.\n\n" );
printf(
" Underflow and overflow can also cause difficulties; the exact arithmetic\n"
);
printf(
" routines do not ameliorate out-of-bounds exponents, which can arise\n" );
printf(
" during the orientation and incircle tests. As a rule of thumb, you\n" );
printf(
" should ensure that your input values are within a range such that their\n" );
printf(
" third powers can be taken without underflow or overflow. Underflow can\n" );
printf(
" silently prevent the tests from being performed exactly, while overflow\n" );
printf( " will typically cause a floating exception.\n\n" );
printf( "Calling Triangle from Another Program:\n\n" );
printf( " Read the file triangle.h for details.\n\n" );
printf( "Troubleshooting:\n\n" );
printf( " Please read this section before mailing me bugs.\n\n" );
printf( " `My output mesh has no triangles!'\n\n" );
printf(
" If you're using a PSLG, you've probably failed to specify a proper set\n"
);
printf(
" of bounding segments, or forgotten to use the -c switch. Or you may\n" );
printf(
" have placed a hole badly. To test these possibilities, try again with\n"
);
printf(
" the -c and -O switches. Alternatively, all your input points may be\n" );
printf(
" collinear, in which case you can hardly expect to triangulate them.\n" );
printf( "\n" );
printf( " `Triangle doesn't terminate, or just crashes.'\n" );
printf( "\n" );
printf(
" Bad things can happen when triangles get so small that the distance\n" );
printf(
" between their vertices isn't much larger than the precision of your\n" );
printf(
" machine's arithmetic. If you've compiled Triangle for single-precision\n"
);
printf(
" arithmetic, you might do better by recompiling it for double-precision.\n"
);
printf(
" Then again, you might just have to settle for more lenient constraints\n"
);
printf(
" on the minimum angle and the maximum area than you had planned.\n" );
printf( "\n" );
printf(
" You can minimize precision problems by ensuring that the origin lies\n" );
printf(
" inside your point set, or even inside the densest part of your\n" );
printf(
" mesh. On the other hand, if you're triangulating an object whose x\n" );
printf(
" coordinates all fall between 6247133 and 6247134, you're not leaving\n" );
printf( " much floating-point precision for Triangle to work with.\n\n" );
printf(
" Precision problems can occur covertly if the input PSLG contains two\n" );
printf(
" segments that meet (or intersect) at a very small angle, or if such an\n"
);
printf(
" angle is introduced by the -c switch, which may occur if a point lies\n" );
printf(
" ever-so-slightly inside the convex hull, and is connected by a PSLG\n" );
printf(
" segment to a point on the convex hull. If you don't realize that a\n" );
printf(
" small angle is being formed, you might never discover why Triangle is\n" );
printf(
" crashing. To check for this possibility, use the -S switch (with an\n" );
printf(
" appropriate limit on the number of Steiner points, found by trial-and-\n"
);
printf(
" error) to stop Triangle early, and view the output .poly file with\n" );
printf(
" Show Me (described below). Look carefully for small angles between\n" );
printf(
" segments; zoom in closely, as such segments might look like a single\n" );
printf( " segment from a distance.\n\n" );
printf(
" If some of the input values are too large, Triangle may suffer a\n" );
printf(
" floating exception due to overflow when attempting to perform an\n" );
printf(
" orientation or incircle test. (Read the section on exact arithmetic\n" );
printf(
" above.) Again, I recommend compiling Triangle for double (rather\n" );
printf( " than single) precision arithmetic.\n\n" );
printf(
" `The numbering of the output points doesn't match the input points.'\n" );
printf( "\n" );
printf(
" You may have eaten some of your input points with a hole, or by placing\n"
);
printf( " them outside the area enclosed by segments.\n\n" );
printf(
" `Triangle executes without incident, but when I look at the resulting\n" );
printf(
" mesh, it has overlapping triangles or other geometric inconsistencies.'\n" );
printf( "\n" );
printf(
" If you select the -X switch, Triangle's divide-and-conquer Delaunay\n" );
printf(
" triangulation algorithm occasionally makes mistakes due to floating-\n" );
printf(
" point roundoff error. Although these errors are rare, don't use the -X\n"
);
printf( " switch. If you still have problems, please report the bug.\n" );
printf( "\n" );
printf(
" Strange things can happen if you've taken liberties with your PSLG. Do\n" );
printf(
" you have a point lying in the middle of a segment? Triangle sometimes\n" );
printf(
" copes poorly with that sort of thing. Do you want to lay out a collinear\n"
);
printf(
" row of evenly spaced, segment-connected points? Have you simply defined\n"
);
printf(
" one long segment connecting the leftmost point to the rightmost point,\n" );
printf(
" and a bunch of points lying along it? This method occasionally works,\n" );
printf(
" especially with horizontal and vertical lines, but often it doesn't, and\n"
);
printf(
" you'll have to connect each adjacent pair of points with a separate\n" );
printf( " segment. If you don't like it, tough.\n\n" );
printf(
" Furthermore, if you have segments that intersect other than at their\n" );
printf(
" endpoints, try not to let the intersections fall extremely close to PSLG\n"
);
printf( " points or each other.\n\n" );
printf(
" If you have problems refining a triangulation not produced by Triangle:\n" );
printf(
" Are you sure the triangulation is geometrically valid? Is it formatted\n" );
printf(
" correctly for Triangle? Are the triangles all listed so the first three\n"
);
printf( " points are their corners in counterclockwise order?\n\n" );
printf( "Show Me:\n\n" );
printf(
" Triangle comes with a separate program named `Show Me', whose primary\n" );
printf(
" purpose is to draw meshes on your screen or in PostScript. Its secondary\n"
);
printf(
" purpose is to check the validity of your input files, and do so more\n" );
printf(
" thoroughly than Triangle does. Show Me requires that you have the X\n" );
printf(
" Windows system. If you didn't receive Show Me with Triangle, complain to\n"
);
printf( " whomever you obtained Triangle from, then send me mail.\n\n" );
printf( "Triangle on the Web:\n\n" );
printf(
" To see an illustrated, updated version of these instructions, check out\n" );
printf( "\n" );
printf( " http://www.cs.cmu.edu/~quake/triangle.html\n" );
printf( "\n" );
printf( "A Brief Plea:\n" );
printf( "\n" );
printf(
" If you use Triangle, and especially if you use it to accomplish real\n" );
printf(
" work, I would like very much to hear from you. A short letter or email\n" );
printf(
" (to jrs@cs.cmu.edu) describing how you use Triangle will mean a lot to\n" );
printf(
" me. The more people I know are using this program, the more easily I can\n"
);
printf(
" justify spending time on improvements and on the three-dimensional\n" );
printf(
" successor to Triangle, which in turn will benefit you. Also, I can put\n" );
printf(
" you on a list to receive email whenever a new version of Triangle is\n" );
printf( " available.\n\n" );
printf(
" If you use a mesh generated by Triangle in a publication, please include\n"
);
printf( " an acknowledgment as well.\n\n" );
printf( "Research credit:\n\n" );
printf(
" Of course, I can take credit for only a fraction of the ideas that made\n" );
printf(
" this mesh generator possible. Triangle owes its existence to the efforts\n"
);
printf(
" of many fine computational geometers and other researchers, including\n" );
printf(
" Marshall Bern, L. Paul Chew, Boris Delaunay, Rex A. Dwyer, David\n" );
printf(
" Eppstein, Steven Fortune, Leonidas J. Guibas, Donald E. Knuth, C. L.\n" );
printf(
" Lawson, Der-Tsai Lee, Ernst P. Mucke, Douglas M. Priest, Jim Ruppert,\n" );
printf(
" Isaac Saias, Bruce J. Schachter, Micha Sharir, Jorge Stolfi, Christopher\n"
);
printf(
" J. Van Wyk, David F. Watson, and Binhai Zhu. See the comments at the\n" );
printf( " beginning of the source code for references.\n\n" );
exit( 0 );
}
#endif /* not TRILIBRARY */
/*****************************************************************************/
/* */
/* internalerror() Ask the user to send me the defective product. Exit. */
/* */
/*****************************************************************************/
void internalerror(){
printf( " Please report this bug to jrs@cs.cmu.edu\n" );
printf( " Include the message above, your input data set, and the exact\n" );
printf( " command line you used to run Triangle.\n" );
exit( 1 );
}
/*****************************************************************************/
/* */
/* parsecommandline() Read the command line, identify switches, and set */
/* up options and file names. */
/* */
/* The effects of this routine are felt entirely through global variables. */
/* */
/*****************************************************************************/
void parsecommandline( argc, argv )
int argc;
char **argv;
{
#ifdef TRILIBRARY
#define STARTINDEX 0
#else /* not TRILIBRARY */
#define STARTINDEX 1
int increment;
int meshnumber;
#endif /* not TRILIBRARY */
int i, j;
#ifndef CDT_ONLY
int k;
char workstring[FILENAMESIZE];
#endif
poly = refine = quality = vararea = fixedarea = regionattrib = convex = 0;
firstnumber = 1;
edgesout = voronoi = neighbors = geomview = 0;
nobound = nopolywritten = nonodewritten = noelewritten = noiterationnum = 0;
noholes = noexact = 0;
incremental = sweepline = 0;
dwyer = 1;
splitseg = 0;
docheck = 0;
nobisect = 0;
steiner = -1;
order = 1;
minangle = 0.0;
maxarea = -1.0;
quiet = verbose = 0;
#ifndef TRILIBRARY
innodefilename[0] = '\0';
#endif /* not TRILIBRARY */
for ( i = STARTINDEX; i < argc; i++ ) {
#ifndef TRILIBRARY
if ( argv[i][0] == '-' ) {
#endif /* not TRILIBRARY */
for ( j = STARTINDEX; argv[i][j] != '\0'; j++ ) {
if ( argv[i][j] == 'p' ) {
poly = 1;
}
#ifndef CDT_ONLY
if ( argv[i][j] == 'r' ) {
refine = 1;
}
if ( argv[i][j] == 'q' ) {
quality = 1;
if ( ( ( argv[i][j + 1] >= '0' ) && ( argv[i][j + 1] <= '9' ) ) ||
( argv[i][j + 1] == '.' ) ) {
k = 0;
while ( ( ( argv[i][j + 1] >= '0' ) && ( argv[i][j + 1] <= '9' ) ) ||
( argv[i][j + 1] == '.' ) ) {
j++;
workstring[k] = argv[i][j];
k++;
}
workstring[k] = '\0';
minangle = (REAL) strtod( workstring, (char **) NULL );
}
else {
minangle = 20.0;
}
}
if ( argv[i][j] == 'a' ) {
quality = 1;
if ( ( ( argv[i][j + 1] >= '0' ) && ( argv[i][j + 1] <= '9' ) ) ||
( argv[i][j + 1] == '.' ) ) {
fixedarea = 1;
k = 0;
while ( ( ( argv[i][j + 1] >= '0' ) && ( argv[i][j + 1] <= '9' ) ) ||
( argv[i][j + 1] == '.' ) ) {
j++;
workstring[k] = argv[i][j];
k++;
}
workstring[k] = '\0';
maxarea = (REAL) strtod( workstring, (char **) NULL );
if ( maxarea <= 0.0 ) {
printf( "Error: Maximum area must be greater than zero.\n" );
exit( 1 );
}
}
else {
vararea = 1;
}
}
#endif /* not CDT_ONLY */
if ( argv[i][j] == 'A' ) {
regionattrib = 1;
}
if ( argv[i][j] == 'c' ) {
convex = 1;
}
if ( argv[i][j] == 'z' ) {
firstnumber = 0;
}
if ( argv[i][j] == 'e' ) {
edgesout = 1;
}
if ( argv[i][j] == 'v' ) {
voronoi = 1;
}
if ( argv[i][j] == 'n' ) {
neighbors = 1;
}
if ( argv[i][j] == 'g' ) {
geomview = 1;
}
if ( argv[i][j] == 'B' ) {
nobound = 1;
}
if ( argv[i][j] == 'P' ) {
nopolywritten = 1;
}
if ( argv[i][j] == 'N' ) {
nonodewritten = 1;
}
if ( argv[i][j] == 'E' ) {
noelewritten = 1;
}
#ifndef TRILIBRARY
if ( argv[i][j] == 'I' ) {
noiterationnum = 1;
}
#endif /* not TRILIBRARY */
if ( argv[i][j] == 'O' ) {
noholes = 1;
}
if ( argv[i][j] == 'X' ) {
noexact = 1;
}
if ( argv[i][j] == 'o' ) {
if ( argv[i][j + 1] == '2' ) {
j++;
order = 2;
}
}
#ifndef CDT_ONLY
if ( argv[i][j] == 'Y' ) {
nobisect++;
}
if ( argv[i][j] == 'S' ) {
steiner = 0;
while ( ( argv[i][j + 1] >= '0' ) && ( argv[i][j + 1] <= '9' ) ) {
j++;
steiner = steiner * 10 + (int) ( argv[i][j] - '0' );
}
}
#endif /* not CDT_ONLY */
#ifndef REDUCED
if ( argv[i][j] == 'i' ) {
incremental = 1;
}
if ( argv[i][j] == 'F' ) {
sweepline = 1;
}
#endif /* not REDUCED */
if ( argv[i][j] == 'l' ) {
dwyer = 0;
}
#ifndef REDUCED
#ifndef CDT_ONLY
if ( argv[i][j] == 's' ) {
splitseg = 1;
}
#endif /* not CDT_ONLY */
if ( argv[i][j] == 'C' ) {
docheck = 1;
}
#endif /* not REDUCED */
if ( argv[i][j] == 'Q' ) {
quiet = 1;
}
if ( argv[i][j] == 'V' ) {
verbose++;
}
#ifndef TRILIBRARY
if ( ( argv[i][j] == 'h' ) || ( argv[i][j] == 'H' ) ||
( argv[i][j] == '?' ) ) {
info();
}
#endif /* not TRILIBRARY */
}
#ifndef TRILIBRARY
} else {
strncpy( innodefilename, argv[i], FILENAMESIZE - 1 );
innodefilename[FILENAMESIZE - 1] = '\0';
}
#endif /* not TRILIBRARY */
}
#ifndef TRILIBRARY
if ( innodefilename[0] == '\0' ) {
syntax();
}
if ( !strcmp( &innodefilename[strlen( innodefilename ) - 5], ".node" ) ) {
innodefilename[strlen( innodefilename ) - 5] = '\0';
}
if ( !strcmp( &innodefilename[strlen( innodefilename ) - 5], ".poly" ) ) {
innodefilename[strlen( innodefilename ) - 5] = '\0';
poly = 1;
}
#ifndef CDT_ONLY
if ( !strcmp( &innodefilename[strlen( innodefilename ) - 4], ".ele" ) ) {
innodefilename[strlen( innodefilename ) - 4] = '\0';
refine = 1;
}
if ( !strcmp( &innodefilename[strlen( innodefilename ) - 5], ".area" ) ) {
innodefilename[strlen( innodefilename ) - 5] = '\0';
refine = 1;
quality = 1;
vararea = 1;
}
#endif /* not CDT_ONLY */
#endif /* not TRILIBRARY */
steinerleft = steiner;
useshelles = poly || refine || quality || convex;
goodangle = (REAL)cos( minangle * PI / 180.0 );
goodangle *= goodangle;
if ( refine && noiterationnum ) {
printf(
"Error: You cannot use the -I switch when refining a triangulation.\n" );
exit( 1 );
}
/* Be careful not to allocate space for element area constraints that */
/* will never be assigned any value (other than the default -1.0). */
if ( !refine && !poly ) {
vararea = 0;
}
/* Be careful not to add an extra attribute to each element unless the */
/* input supports it (PSLG in, but not refining a preexisting mesh). */
if ( refine || !poly ) {
regionattrib = 0;
}
#ifndef TRILIBRARY
strcpy( inpolyfilename, innodefilename );
strcpy( inelefilename, innodefilename );
strcpy( areafilename, innodefilename );
increment = 0;
strcpy( workstring, innodefilename );
j = 1;
while ( workstring[j] != '\0' ) {
if ( ( workstring[j] == '.' ) && ( workstring[j + 1] != '\0' ) ) {
increment = j + 1;
}
j++;
}
meshnumber = 0;
if ( increment > 0 ) {
j = increment;
do {
if ( ( workstring[j] >= '0' ) && ( workstring[j] <= '9' ) ) {
meshnumber = meshnumber * 10 + (int) ( workstring[j] - '0' );
}
else {
increment = 0;
}
j++;
} while ( workstring[j] != '\0' );
}
if ( noiterationnum ) {
strcpy( outnodefilename, innodefilename );
strcpy( outelefilename, innodefilename );
strcpy( edgefilename, innodefilename );
strcpy( vnodefilename, innodefilename );
strcpy( vedgefilename, innodefilename );
strcpy( neighborfilename, innodefilename );
strcpy( offfilename, innodefilename );
strcat( outnodefilename, ".node" );
strcat( outelefilename, ".ele" );
strcat( edgefilename, ".edge" );
strcat( vnodefilename, ".v.node" );
strcat( vedgefilename, ".v.edge" );
strcat( neighborfilename, ".neigh" );
strcat( offfilename, ".off" );
}
else if ( increment == 0 ) {
strcpy( outnodefilename, innodefilename );
strcpy( outpolyfilename, innodefilename );
strcpy( outelefilename, innodefilename );
strcpy( edgefilename, innodefilename );
strcpy( vnodefilename, innodefilename );
strcpy( vedgefilename, innodefilename );
strcpy( neighborfilename, innodefilename );
strcpy( offfilename, innodefilename );
strcat( outnodefilename, ".1.node" );
strcat( outpolyfilename, ".1.poly" );
strcat( outelefilename, ".1.ele" );
strcat( edgefilename, ".1.edge" );
strcat( vnodefilename, ".1.v.node" );
strcat( vedgefilename, ".1.v.edge" );
strcat( neighborfilename, ".1.neigh" );
strcat( offfilename, ".1.off" );
}
else {
workstring[increment] = '%';
workstring[increment + 1] = 'd';
workstring[increment + 2] = '\0';
sprintf( outnodefilename, workstring, meshnumber + 1 );
strcpy( outpolyfilename, outnodefilename );
strcpy( outelefilename, outnodefilename );
strcpy( edgefilename, outnodefilename );
strcpy( vnodefilename, outnodefilename );
strcpy( vedgefilename, outnodefilename );
strcpy( neighborfilename, outnodefilename );
strcpy( offfilename, outnodefilename );
strcat( outnodefilename, ".node" );
strcat( outpolyfilename, ".poly" );
strcat( outelefilename, ".ele" );
strcat( edgefilename, ".edge" );
strcat( vnodefilename, ".v.node" );
strcat( vedgefilename, ".v.edge" );
strcat( neighborfilename, ".neigh" );
strcat( offfilename, ".off" );
}
strcat( innodefilename, ".node" );
strcat( inpolyfilename, ".poly" );
strcat( inelefilename, ".ele" );
strcat( areafilename, ".area" );
#endif /* not TRILIBRARY */
}
/** **/
/** **/
/********* User interaction routines begin here *********/
/********* Debugging routines begin here *********/
/** **/
/** **/
/*****************************************************************************/
/* */
/* printtriangle() Print out the details of a triangle/edge handle. */
/* */
/* I originally wrote this procedure to simplify debugging; it can be */
/* called directly from the debugger, and presents information about a */
/* triangle/edge handle in digestible form. It's also used when the */
/* highest level of verbosity (`-VVV') is specified. */
/* */
/*****************************************************************************/
void printtriangle( t )
struct triedge *t;
{
struct triedge printtri;
struct edge printsh;
point printpoint;
printf( "triangle x%lx with orientation %d:\n", (unsigned long) t->tri,
t->orient );
decode( t->tri[0], printtri );
if ( printtri.tri == dummytri ) {
printf( " [0] = Outer space\n" );
}
else {
printf( " [0] = x%lx %d\n", (unsigned long) printtri.tri,
printtri.orient );
}
decode( t->tri[1], printtri );
if ( printtri.tri == dummytri ) {
printf( " [1] = Outer space\n" );
}
else {
printf( " [1] = x%lx %d\n", (unsigned long) printtri.tri,
printtri.orient );
}
decode( t->tri[2], printtri );
if ( printtri.tri == dummytri ) {
printf( " [2] = Outer space\n" );
}
else {
printf( " [2] = x%lx %d\n", (unsigned long) printtri.tri,
printtri.orient );
}
org( *t, printpoint );
if ( printpoint == (point) NULL ) {
printf( " Origin[%d] = NULL\n", ( t->orient + 1 ) % 3 + 3 );
}
else{
printf( " Origin[%d] = x%lx (%.12g, %.12g)\n",
( t->orient + 1 ) % 3 + 3, (unsigned long) printpoint,
printpoint[0], printpoint[1] );
}
dest( *t, printpoint );
if ( printpoint == (point) NULL ) {
printf( " Dest [%d] = NULL\n", ( t->orient + 2 ) % 3 + 3 );
}
else{
printf( " Dest [%d] = x%lx (%.12g, %.12g)\n",
( t->orient + 2 ) % 3 + 3, (unsigned long) printpoint,
printpoint[0], printpoint[1] );
}
apex( *t, printpoint );
if ( printpoint == (point) NULL ) {
printf( " Apex [%d] = NULL\n", t->orient + 3 );
}
else{
printf( " Apex [%d] = x%lx (%.12g, %.12g)\n",
t->orient + 3, (unsigned long) printpoint,
printpoint[0], printpoint[1] );
}
if ( useshelles ) {
sdecode( t->tri[6], printsh );
if ( printsh.sh != dummysh ) {
printf( " [6] = x%lx %d\n", (unsigned long) printsh.sh,
printsh.shorient );
}
sdecode( t->tri[7], printsh );
if ( printsh.sh != dummysh ) {
printf( " [7] = x%lx %d\n", (unsigned long) printsh.sh,
printsh.shorient );
}
sdecode( t->tri[8], printsh );
if ( printsh.sh != dummysh ) {
printf( " [8] = x%lx %d\n", (unsigned long) printsh.sh,
printsh.shorient );
}
}
if ( vararea ) {
printf( " Area constraint: %.4g\n", areabound( *t ) );
}
}
/*****************************************************************************/
/* */
/* printshelle() Print out the details of a shell edge handle. */
/* */
/* I originally wrote this procedure to simplify debugging; it can be */
/* called directly from the debugger, and presents information about a */
/* shell edge handle in digestible form. It's also used when the highest */
/* level of verbosity (`-VVV') is specified. */
/* */
/*****************************************************************************/
void printshelle( s )
struct edge *s;
{
struct edge printsh;
struct triedge printtri;
point printpoint;
printf( "shell edge x%lx with orientation %d and mark %d:\n",
(unsigned long) s->sh, s->shorient, mark( *s ) );
sdecode( s->sh[0], printsh );
if ( printsh.sh == dummysh ) {
printf( " [0] = No shell\n" );
}
else {
printf( " [0] = x%lx %d\n", (unsigned long) printsh.sh,
printsh.shorient );
}
sdecode( s->sh[1], printsh );
if ( printsh.sh == dummysh ) {
printf( " [1] = No shell\n" );
}
else {
printf( " [1] = x%lx %d\n", (unsigned long) printsh.sh,
printsh.shorient );
}
sorg( *s, printpoint );
if ( printpoint == (point) NULL ) {
printf( " Origin[%d] = NULL\n", 2 + s->shorient );
}
else{
printf( " Origin[%d] = x%lx (%.12g, %.12g)\n",
2 + s->shorient, (unsigned long) printpoint,
printpoint[0], printpoint[1] );
}
sdest( *s, printpoint );
if ( printpoint == (point) NULL ) {
printf( " Dest [%d] = NULL\n", 3 - s->shorient );
}
else{
printf( " Dest [%d] = x%lx (%.12g, %.12g)\n",
3 - s->shorient, (unsigned long) printpoint,
printpoint[0], printpoint[1] );
}
decode( s->sh[4], printtri );
if ( printtri.tri == dummytri ) {
printf( " [4] = Outer space\n" );
}
else {
printf( " [4] = x%lx %d\n", (unsigned long) printtri.tri,
printtri.orient );
}
decode( s->sh[5], printtri );
if ( printtri.tri == dummytri ) {
printf( " [5] = Outer space\n" );
}
else {
printf( " [5] = x%lx %d\n", (unsigned long) printtri.tri,
printtri.orient );
}
}
/** **/
/** **/
/********* Debugging routines end here *********/
/********* Memory management routines begin here *********/
/** **/
/** **/
/*****************************************************************************/
/* */
/* poolinit() Initialize a pool of memory for allocation of items. */
/* */
/* This routine initializes the machinery for allocating items. A `pool' */
/* is created whose records have size at least `bytecount'. Items will be */
/* allocated in `itemcount'-item blocks. Each item is assumed to be a */
/* collection of words, and either pointers or floating-point values are */
/* assumed to be the "primary" word type. (The "primary" word type is used */
/* to determine alignment of items.) If `alignment' isn't zero, all items */
/* will be `alignment'-byte aligned in memory. `alignment' must be either */
/* a multiple or a factor of the primary word size; powers of two are safe. */
/* `alignment' is normally used to create a few unused bits at the bottom */
/* of each item's pointer, in which information may be stored. */
/* */
/* Don't change this routine unless you understand it. */
/* */
/*****************************************************************************/
void poolinit( pool, bytecount, itemcount, wtype, alignment )
struct memorypool *pool;
int bytecount;
int itemcount;
enum wordtype wtype;
int alignment;
{
int wordsize;
/* Initialize values in the pool. */
pool->itemwordtype = wtype;
wordsize = ( pool->itemwordtype == POINTER ) ? sizeof( VOID * ) : sizeof( REAL );
/* Find the proper alignment, which must be at least as large as: */
/* - The parameter `alignment'. */
/* - The primary word type, to avoid unaligned accesses. */
/* - sizeof(VOID *), so the stack of dead items can be maintained */
/* without unaligned accesses. */
if ( alignment > wordsize ) {
pool->alignbytes = alignment;
}
else {
pool->alignbytes = wordsize;
}
if ( sizeof( VOID * ) > pool->alignbytes ) {
pool->alignbytes = sizeof( VOID * );
}
pool->itemwords = ( ( bytecount + pool->alignbytes - 1 ) / pool->alignbytes )
* ( pool->alignbytes / wordsize );
pool->itembytes = pool->itemwords * wordsize;
pool->itemsperblock = itemcount;
/* Allocate a block of items. Space for `itemsperblock' items and one */
/* pointer (to point to the next block) are allocated, as well as space */
/* to ensure alignment of the items. */
pool->firstblock = (VOID **) malloc( pool->itemsperblock * pool->itembytes
+ sizeof( VOID * ) + pool->alignbytes );
if ( pool->firstblock == (VOID **) NULL ) {
printf( "Error: Out of memory.\n" );
exit( 1 );
}
/* Set the next block pointer to NULL. */
*( pool->firstblock ) = (VOID *) NULL;
poolrestart( pool );
}
/*****************************************************************************/
/* */
/* poolrestart() Deallocate all items in a pool. */
/* */
/* The pool is returned to its starting state, except that no memory is */
/* freed to the operating system. Rather, the previously allocated blocks */
/* are ready to be reused. */
/* */
/*****************************************************************************/
void poolrestart( pool )
struct memorypool *pool;
{
unsigned long alignptr;
pool->items = 0;
pool->maxitems = 0;
/* Set the currently active block. */
pool->nowblock = pool->firstblock;
/* Find the first item in the pool. Increment by the size of (VOID *). */
alignptr = (unsigned long) ( pool->nowblock + 1 );
/* Align the item on an `alignbytes'-byte boundary. */
pool->nextitem = (VOID *)
( alignptr + (unsigned long) pool->alignbytes
- ( alignptr % (unsigned long) pool->alignbytes ) );
/* There are lots of unallocated items left in this block. */
pool->unallocateditems = pool->itemsperblock;
/* The stack of deallocated items is empty. */
pool->deaditemstack = (VOID *) NULL;
}
/*****************************************************************************/
/* */
/* pooldeinit() Free to the operating system all memory taken by a pool. */
/* */
/*****************************************************************************/
void pooldeinit( pool )
struct memorypool *pool;
{
while ( pool->firstblock != (VOID **) NULL ) {
pool->nowblock = (VOID **) *( pool->firstblock );
free( pool->firstblock );
pool->firstblock = pool->nowblock;
}
}
/*****************************************************************************/
/* */
/* poolalloc() Allocate space for an item. */
/* */
/*****************************************************************************/
VOID *poolalloc( pool )
struct memorypool *pool;
{
VOID *newitem;
VOID **newblock;
unsigned long alignptr;
/* First check the linked list of dead items. If the list is not */
/* empty, allocate an item from the list rather than a fresh one. */
if ( pool->deaditemstack != (VOID *) NULL ) {
newitem = pool->deaditemstack; /* Take first item in list. */
pool->deaditemstack = *(VOID **) pool->deaditemstack;
}
else {
/* Check if there are any free items left in the current block. */
if ( pool->unallocateditems == 0 ) {
/* Check if another block must be allocated. */
if ( *( pool->nowblock ) == (VOID *) NULL ) {
/* Allocate a new block of items, pointed to by the previous block. */
newblock = (VOID **) malloc( pool->itemsperblock * pool->itembytes
+ sizeof( VOID * ) + pool->alignbytes );
if ( newblock == (VOID **) NULL ) {
printf( "Error: Out of memory.\n" );
exit( 1 );
}
*( pool->nowblock ) = (VOID *) newblock;
/* The next block pointer is NULL. */
*newblock = (VOID *) NULL;
}
/* Move to the new block. */
pool->nowblock = (VOID **) *( pool->nowblock );
/* Find the first item in the block. */
/* Increment by the size of (VOID *). */
alignptr = (unsigned long) ( pool->nowblock + 1 );
/* Align the item on an `alignbytes'-byte boundary. */
pool->nextitem = (VOID *)
( alignptr + (unsigned long) pool->alignbytes
- ( alignptr % (unsigned long) pool->alignbytes ) );
/* There are lots of unallocated items left in this block. */
pool->unallocateditems = pool->itemsperblock;
}
/* Allocate a new item. */
newitem = pool->nextitem;
/* Advance `nextitem' pointer to next free item in block. */
if ( pool->itemwordtype == POINTER ) {
pool->nextitem = (VOID *) ( (VOID **) pool->nextitem + pool->itemwords );
}
else {
pool->nextitem = (VOID *) ( (REAL *) pool->nextitem + pool->itemwords );
}
pool->unallocateditems--;
pool->maxitems++;
}
pool->items++;
return newitem;
}
/*****************************************************************************/
/* */
/* pooldealloc() Deallocate space for an item. */
/* */
/* The deallocated space is stored in a queue for later reuse. */
/* */
/*****************************************************************************/
void pooldealloc( pool, dyingitem )
struct memorypool *pool;
VOID *dyingitem;
{
/* Push freshly killed item onto stack. */
*( (VOID **) dyingitem ) = pool->deaditemstack;
pool->deaditemstack = dyingitem;
pool->items--;
}
/*****************************************************************************/
/* */
/* traversalinit() Prepare to traverse the entire list of items. */
/* */
/* This routine is used in conjunction with traverse(). */
/* */
/*****************************************************************************/
void traversalinit( pool )
struct memorypool *pool;
{
unsigned long alignptr;
/* Begin the traversal in the first block. */
pool->pathblock = pool->firstblock;
/* Find the first item in the block. Increment by the size of (VOID *). */
alignptr = (unsigned long) ( pool->pathblock + 1 );
/* Align with item on an `alignbytes'-byte boundary. */
pool->pathitem = (VOID *)
( alignptr + (unsigned long) pool->alignbytes
- ( alignptr % (unsigned long) pool->alignbytes ) );
/* Set the number of items left in the current block. */
pool->pathitemsleft = pool->itemsperblock;
}
/*****************************************************************************/
/* */
/* traverse() Find the next item in the list. */
/* */
/* This routine is used in conjunction with traversalinit(). Be forewarned */
/* that this routine successively returns all items in the list, including */
/* deallocated ones on the deaditemqueue. It's up to you to figure out */
/* which ones are actually dead. Why? I don't want to allocate extra */
/* space just to demarcate dead items. It can usually be done more */
/* space-efficiently by a routine that knows something about the structure */
/* of the item. */
/* */
/*****************************************************************************/
VOID *traverse( pool )
struct memorypool *pool;
{
VOID *newitem;
unsigned long alignptr;
/* Stop upon exhausting the list of items. */
if ( pool->pathitem == pool->nextitem ) {
return (VOID *) NULL;
}
/* Check whether any untraversed items remain in the current block. */
if ( pool->pathitemsleft == 0 ) {
/* Find the next block. */
pool->pathblock = (VOID **) *( pool->pathblock );
/* Find the first item in the block. Increment by the size of (VOID *). */
alignptr = (unsigned long) ( pool->pathblock + 1 );
/* Align with item on an `alignbytes'-byte boundary. */
pool->pathitem = (VOID *)
( alignptr + (unsigned long) pool->alignbytes
- ( alignptr % (unsigned long) pool->alignbytes ) );
/* Set the number of items left in the current block. */
pool->pathitemsleft = pool->itemsperblock;
}
newitem = pool->pathitem;
/* Find the next item in the block. */
if ( pool->itemwordtype == POINTER ) {
pool->pathitem = (VOID *) ( (VOID **) pool->pathitem + pool->itemwords );
}
else {
pool->pathitem = (VOID *) ( (REAL *) pool->pathitem + pool->itemwords );
}
pool->pathitemsleft--;
return newitem;
}
/*****************************************************************************/
/* */
/* dummyinit() Initialize the triangle that fills "outer space" and the */
/* omnipresent shell edge. */
/* */
/* The triangle that fills "outer space", called `dummytri', is pointed to */
/* by every triangle and shell edge on a boundary (be it outer or inner) of */
/* the triangulation. Also, `dummytri' points to one of the triangles on */
/* the convex hull (until the holes and concavities are carved), making it */
/* possible to find a starting triangle for point location. */
/* */
/* The omnipresent shell edge, `dummysh', is pointed to by every triangle */
/* or shell edge that doesn't have a full complement of real shell edges */
/* to point to. */
/* */
/*****************************************************************************/
void dummyinit( trianglewords, shellewords )
int trianglewords;
int shellewords;
{
unsigned long alignptr;
/* `triwords' and `shwords' are used by the mesh manipulation primitives */
/* to extract orientations of triangles and shell edges from pointers. */
triwords = trianglewords; /* Initialize `triwords' once and for all. */
shwords = shellewords; /* Initialize `shwords' once and for all. */
/* Set up `dummytri', the `triangle' that occupies "outer space". */
dummytribase = (triangle *) malloc( triwords * sizeof( triangle )
+ triangles.alignbytes );
if ( dummytribase == (triangle *) NULL ) {
printf( "Error: Out of memory.\n" );
exit( 1 );
}
/* Align `dummytri' on a `triangles.alignbytes'-byte boundary. */
alignptr = (unsigned long) dummytribase;
dummytri = (triangle *)
( alignptr + (unsigned long) triangles.alignbytes
- ( alignptr % (unsigned long) triangles.alignbytes ) );
/* Initialize the three adjoining triangles to be "outer space". These */
/* will eventually be changed by various bonding operations, but their */
/* values don't really matter, as long as they can legally be */
/* dereferenced. */
dummytri[0] = (triangle) dummytri;
dummytri[1] = (triangle) dummytri;
dummytri[2] = (triangle) dummytri;
/* Three NULL vertex points. */
dummytri[3] = (triangle) NULL;
dummytri[4] = (triangle) NULL;
dummytri[5] = (triangle) NULL;
if ( useshelles ) {
/* Set up `dummysh', the omnipresent "shell edge" pointed to by any */
/* triangle side or shell edge end that isn't attached to a real shell */
/* edge. */
dummyshbase = (shelle *) malloc( shwords * sizeof( shelle )
+ shelles.alignbytes );
if ( dummyshbase == (shelle *) NULL ) {
printf( "Error: Out of memory.\n" );
exit( 1 );
}
/* Align `dummysh' on a `shelles.alignbytes'-byte boundary. */
alignptr = (unsigned long) dummyshbase;
dummysh = (shelle *)
( alignptr + (unsigned long) shelles.alignbytes
- ( alignptr % (unsigned long) shelles.alignbytes ) );
/* Initialize the two adjoining shell edges to be the omnipresent shell */
/* edge. These will eventually be changed by various bonding */
/* operations, but their values don't really matter, as long as they */
/* can legally be dereferenced. */
dummysh[0] = (shelle) dummysh;
dummysh[1] = (shelle) dummysh;
/* Two NULL vertex points. */
dummysh[2] = (shelle) NULL;
dummysh[3] = (shelle) NULL;
/* Initialize the two adjoining triangles to be "outer space". */
dummysh[4] = (shelle) dummytri;
dummysh[5] = (shelle) dummytri;
/* Set the boundary marker to zero. */
*(int *) ( dummysh + 6 ) = 0;
/* Initialize the three adjoining shell edges of `dummytri' to be */
/* the omnipresent shell edge. */
dummytri[6] = (triangle) dummysh;
dummytri[7] = (triangle) dummysh;
dummytri[8] = (triangle) dummysh;
}
}
/*****************************************************************************/
/* */
/* initializepointpool() Calculate the size of the point data structure */
/* and initialize its memory pool. */
/* */
/* This routine also computes the `pointmarkindex' and `point2triindex' */
/* indices used to find values within each point. */
/* */
/*****************************************************************************/
void initializepointpool(){
int pointsize;
/* The index within each point at which the boundary marker is found. */
/* Ensure the point marker is aligned to a sizeof(int)-byte address. */
pointmarkindex = ( ( mesh_dim + nextras ) * sizeof( REAL ) + sizeof( int ) - 1 )
/ sizeof( int );
pointsize = ( pointmarkindex + 1 ) * sizeof( int );
if ( poly ) {
/* The index within each point at which a triangle pointer is found. */
/* Ensure the pointer is aligned to a sizeof(triangle)-byte address. */
point2triindex = ( pointsize + sizeof( triangle ) - 1 ) / sizeof( triangle );
pointsize = ( point2triindex + 1 ) * sizeof( triangle );
}
/* Initialize the pool of points. */
poolinit( &points, pointsize, POINTPERBLOCK,
( sizeof( REAL ) >= sizeof( triangle ) ) ? FLOATINGPOINT : POINTER, 0 );
}
/*****************************************************************************/
/* */
/* initializetrisegpools() Calculate the sizes of the triangle and shell */
/* edge data structures and initialize their */
/* memory pools. */
/* */
/* This routine also computes the `highorderindex', `elemattribindex', and */
/* `areaboundindex' indices used to find values within each triangle. */
/* */
/*****************************************************************************/
void initializetrisegpools(){
int trisize;
/* The index within each triangle at which the extra nodes (above three) */
/* associated with high order elements are found. There are three */
/* pointers to other triangles, three pointers to corners, and possibly */
/* three pointers to shell edges before the extra nodes. */
highorderindex = 6 + ( useshelles * 3 );
/* The number of bytes occupied by a triangle. */
trisize = ( ( order + 1 ) * ( order + 2 ) / 2 + ( highorderindex - 3 ) ) *
sizeof( triangle );
/* The index within each triangle at which its attributes are found, */
/* where the index is measured in REALs. */
elemattribindex = ( trisize + sizeof( REAL ) - 1 ) / sizeof( REAL );
/* The index within each triangle at which the maximum area constraint */
/* is found, where the index is measured in REALs. Note that if the */
/* `regionattrib' flag is set, an additional attribute will be added. */
areaboundindex = elemattribindex + eextras + regionattrib;
/* If triangle attributes or an area bound are needed, increase the number */
/* of bytes occupied by a triangle. */
if ( vararea ) {
trisize = ( areaboundindex + 1 ) * sizeof( REAL );
}
else if ( eextras + regionattrib > 0 ) {
trisize = areaboundindex * sizeof( REAL );
}
/* If a Voronoi diagram or triangle neighbor graph is requested, make */
/* sure there's room to store an integer index in each triangle. This */
/* integer index can occupy the same space as the shell edges or */
/* attributes or area constraint or extra nodes. */
if ( ( voronoi || neighbors ) &&
( trisize < 6 * sizeof( triangle ) + sizeof( int ) ) ) {
trisize = 6 * sizeof( triangle ) + sizeof( int );
}
/* Having determined the memory size of a triangle, initialize the pool. */
poolinit( &triangles, trisize, TRIPERBLOCK, POINTER, 4 );
if ( useshelles ) {
/* Initialize the pool of shell edges. */
poolinit( &shelles, 6 * sizeof( triangle ) + sizeof( int ), SHELLEPERBLOCK,
POINTER, 4 );
/* Initialize the "outer space" triangle and omnipresent shell edge. */
dummyinit( triangles.itemwords, shelles.itemwords );
}
else {
/* Initialize the "outer space" triangle. */
dummyinit( triangles.itemwords, 0 );
}
}
/*****************************************************************************/
/* */
/* triangledealloc() Deallocate space for a triangle, marking it dead. */
/* */
/*****************************************************************************/
void triangledealloc( dyingtriangle )
triangle * dyingtriangle;
{
/* Set triangle's vertices to NULL. This makes it possible to */
/* detect dead triangles when traversing the list of all triangles. */
dyingtriangle[3] = (triangle) NULL;
dyingtriangle[4] = (triangle) NULL;
dyingtriangle[5] = (triangle) NULL;
pooldealloc( &triangles, (VOID *) dyingtriangle );
}
/*****************************************************************************/
/* */
/* triangletraverse() Traverse the triangles, skipping dead ones. */
/* */
/*****************************************************************************/
triangle *triangletraverse(){
triangle *newtriangle;
do {
newtriangle = (triangle *) traverse( &triangles );
if ( newtriangle == (triangle *) NULL ) {
return (triangle *) NULL;
}
} while ( newtriangle[3] == (triangle) NULL ); /* Skip dead ones. */
return newtriangle;
}
/*****************************************************************************/
/* */
/* shelledealloc() Deallocate space for a shell edge, marking it dead. */
/* */
/*****************************************************************************/
void shelledealloc( dyingshelle )
shelle * dyingshelle;
{
/* Set shell edge's vertices to NULL. This makes it possible to */
/* detect dead shells when traversing the list of all shells. */
dyingshelle[2] = (shelle) NULL;
dyingshelle[3] = (shelle) NULL;
pooldealloc( &shelles, (VOID *) dyingshelle );
}
/*****************************************************************************/
/* */
/* shelletraverse() Traverse the shell edges, skipping dead ones. */
/* */
/*****************************************************************************/
shelle *shelletraverse(){
shelle *newshelle;
do {
newshelle = (shelle *) traverse( &shelles );
if ( newshelle == (shelle *) NULL ) {
return (shelle *) NULL;
}
} while ( newshelle[2] == (shelle) NULL ); /* Skip dead ones. */
return newshelle;
}
/*****************************************************************************/
/* */
/* pointdealloc() Deallocate space for a point, marking it dead. */
/* */
/*****************************************************************************/
void pointdealloc( dyingpoint )
point dyingpoint;
{
/* Mark the point as dead. This makes it possible to detect dead points */
/* when traversing the list of all points. */
setpointmark( dyingpoint, DEADPOINT );
pooldealloc( &points, (VOID *) dyingpoint );
}
/*****************************************************************************/
/* */
/* pointtraverse() Traverse the points, skipping dead ones. */
/* */
/*****************************************************************************/
point pointtraverse(){
point newpoint;
do {
newpoint = (point) traverse( &points );
if ( newpoint == (point) NULL ) {
return (point) NULL;
}
} while ( pointmark( newpoint ) == DEADPOINT ); /* Skip dead ones. */
return newpoint;
}
/*****************************************************************************/
/* */
/* badsegmentdealloc() Deallocate space for a bad segment, marking it */
/* dead. */
/* */
/*****************************************************************************/
#ifndef CDT_ONLY
void badsegmentdealloc( dyingseg )
struct edge *dyingseg;
{
/* Set segment's orientation to -1. This makes it possible to */
/* detect dead segments when traversing the list of all segments. */
dyingseg->shorient = -1;
pooldealloc( &badsegments, (VOID *) dyingseg );
}
#endif /* not CDT_ONLY */
/*****************************************************************************/
/* */
/* badsegmenttraverse() Traverse the bad segments, skipping dead ones. */
/* */
/*****************************************************************************/
#ifndef CDT_ONLY
struct edge *badsegmenttraverse(){
struct edge *newseg;
do {
newseg = (struct edge *) traverse( &badsegments );
if ( newseg == (struct edge *) NULL ) {
return (struct edge *) NULL;
}
} while ( newseg->shorient == -1 ); /* Skip dead ones. */
return newseg;
}
#endif /* not CDT_ONLY */
/*****************************************************************************/
/* */
/* getpoint() Get a specific point, by number, from the list. */
/* */
/* The first point is number 'firstnumber'. */
/* */
/* Note that this takes O(n) time (with a small constant, if POINTPERBLOCK */
/* is large). I don't care to take the trouble to make it work in constant */
/* time. */
/* */
/*****************************************************************************/
point getpoint( number )
int number;
{
VOID **getblock;
point foundpoint;
unsigned long alignptr;
int current;
getblock = points.firstblock;
current = firstnumber;
/* Find the right block. */
while ( current + points.itemsperblock <= number ) {
getblock = (VOID **) *getblock;
current += points.itemsperblock;
}
/* Now find the right point. */
alignptr = (unsigned long) ( getblock + 1 );
foundpoint = (point) ( alignptr + (unsigned long) points.alignbytes
- ( alignptr % (unsigned long) points.alignbytes ) );
while ( current < number ) {
foundpoint += points.itemwords;
current++;
}
return foundpoint;
}
/*****************************************************************************/
/* */
/* triangledeinit() Free all remaining allocated memory. */
/* */
/*****************************************************************************/
void triangledeinit(){
pooldeinit( &triangles );
free( dummytribase );
if ( useshelles ) {
pooldeinit( &shelles );
free( dummyshbase );
}
pooldeinit( &points );
#ifndef CDT_ONLY
if ( quality ) {
pooldeinit( &badsegments );
if ( ( minangle > 0.0 ) || vararea || fixedarea ) {
pooldeinit( &badtriangles );
}
}
#endif /* not CDT_ONLY */
}
/** **/
/** **/
/********* Memory management routines end here *********/
/********* Constructors begin here *********/
/** **/
/** **/
/*****************************************************************************/
/* */
/* maketriangle() Create a new triangle with orientation zero. */
/* */
/*****************************************************************************/
void maketriangle( newtriedge )
struct triedge *newtriedge;
{
int i;
newtriedge->tri = (triangle *) poolalloc( &triangles );
/* Initialize the three adjoining triangles to be "outer space". */
newtriedge->tri[0] = (triangle) dummytri;
newtriedge->tri[1] = (triangle) dummytri;
newtriedge->tri[2] = (triangle) dummytri;
/* Three NULL vertex points. */
newtriedge->tri[3] = (triangle) NULL;
newtriedge->tri[4] = (triangle) NULL;
newtriedge->tri[5] = (triangle) NULL;
/* Initialize the three adjoining shell edges to be the omnipresent */
/* shell edge. */
if ( useshelles ) {
newtriedge->tri[6] = (triangle) dummysh;
newtriedge->tri[7] = (triangle) dummysh;
newtriedge->tri[8] = (triangle) dummysh;
}
for ( i = 0; i < eextras; i++ ) {
setelemattribute( *newtriedge, i, 0.0 );
}
if ( vararea ) {
setareabound( *newtriedge, -1.0 );
}
newtriedge->orient = 0;
}
/*****************************************************************************/
/* */
/* makeshelle() Create a new shell edge with orientation zero. */
/* */
/*****************************************************************************/
void makeshelle( newedge )
struct edge *newedge;
{
newedge->sh = (shelle *) poolalloc( &shelles );
/* Initialize the two adjoining shell edges to be the omnipresent */
/* shell edge. */
newedge->sh[0] = (shelle) dummysh;
newedge->sh[1] = (shelle) dummysh;
/* Two NULL vertex points. */
newedge->sh[2] = (shelle) NULL;
newedge->sh[3] = (shelle) NULL;
/* Initialize the two adjoining triangles to be "outer space". */
newedge->sh[4] = (shelle) dummytri;
newedge->sh[5] = (shelle) dummytri;
/* Set the boundary marker to zero. */
setmark( *newedge, 0 );
newedge->shorient = 0;
}
/** **/
/** **/
/********* Constructors end here *********/
/********* Determinant evaluation routines begin here *********/
/** **/
/** **/
/* The adaptive exact arithmetic geometric predicates implemented herein are */
/* described in detail in my Technical Report CMU-CS-96-140. The complete */
/* reference is given in the header. */
/* Which of the following two methods of finding the absolute values is */
/* fastest is compiler-dependent. A few compilers can inline and optimize */
/* the fabs() call; but most will incur the overhead of a function call, */
/* which is disastrously slow. A faster way on IEEE machines might be to */
/* mask the appropriate bit, but that's difficult to do in C. */
#define Absolute( a ) ( ( a ) >= 0.0 ? ( a ) : -( a ) )
/* #define Absolute(a) fabs(a) */
/* Many of the operations are broken up into two pieces, a main part that */
/* performs an approximate operation, and a "tail" that computes the */
/* roundoff error of that operation. */
/* */
/* The operations Fast_Two_Sum(), Fast_Two_Diff(), Two_Sum(), Two_Diff(), */
/* Split(), and Two_Product() are all implemented as described in the */
/* reference. Each of these macros requires certain variables to be */
/* defined in the calling routine. The variables `bvirt', `c', `abig', */
/* `_i', `_j', `_k', `_l', `_m', and `_n' are declared `INEXACT' because */
/* they store the result of an operation that may incur roundoff error. */
/* The input parameter `x' (or the highest numbered `x_' parameter) must */
/* also be declared `INEXACT'. */
#define Fast_Two_Sum_Tail( a, b, x, y ) \
bvirt = x - a; \
y = b - bvirt
#define Fast_Two_Sum( a, b, x, y ) \
x = (REAL) ( a + b ); \
Fast_Two_Sum_Tail( a, b, x, y )
#define Two_Sum_Tail( a, b, x, y ) \
bvirt = (REAL) ( x - a ); \
avirt = x - bvirt; \
bround = b - bvirt; \
around = a - avirt; \
y = around + bround
#define Two_Sum( a, b, x, y ) \
x = (REAL) ( a + b ); \
Two_Sum_Tail( a, b, x, y )
#define Two_Diff_Tail( a, b, x, y ) \
bvirt = (REAL) ( a - x ); \
avirt = x + bvirt; \
bround = bvirt - b; \
around = a - avirt; \
y = around + bround
#define Two_Diff( a, b, x, y ) \
x = (REAL) ( a - b ); \
Two_Diff_Tail( a, b, x, y )
#define Split( a, ahi, alo ) \
c = (REAL) ( splitter * a ); \
abig = (REAL) ( c - a ); \
ahi = (REAL)( c - abig ); \
alo = (REAL)( a - ahi )
#define Two_Product_Tail( a, b, x, y ) \
Split( a, ahi, alo ); \
Split( b, bhi, blo ); \
err1 = x - ( ahi * bhi ); \
err2 = err1 - ( alo * bhi ); \
err3 = err2 - ( ahi * blo ); \
y = ( alo * blo ) - err3
#define Two_Product( a, b, x, y ) \
x = (REAL) ( a * b ); \
Two_Product_Tail( a, b, x, y )
/* Two_Product_Presplit() is Two_Product() where one of the inputs has */
/* already been split. Avoids redundant splitting. */
#define Two_Product_Presplit( a, b, bhi, blo, x, y ) \
x = (REAL) ( a * b ); \
Split( a, ahi, alo ); \
err1 = x - ( ahi * bhi ); \
err2 = err1 - ( alo * bhi ); \
err3 = err2 - ( ahi * blo ); \
y = ( alo * blo ) - err3
/* Square() can be done more quickly than Two_Product(). */
#define Square_Tail( a, x, y ) \
Split( a, ahi, alo ); \
err1 = x - ( ahi * ahi ); \
err3 = err1 - ( ( ahi + ahi ) * alo ); \
y = ( alo * alo ) - err3
#define Square( a, x, y ) \
x = (REAL) ( a * a ); \
Square_Tail( a, x, y )
/* Macros for summing expansions of various fixed lengths. These are all */
/* unrolled versions of Expansion_Sum(). */
#define Two_One_Sum( a1, a0, b, x2, x1, x0 ) \
Two_Sum( a0, b, _i, x0 ); \
Two_Sum( a1, _i, x2, x1 )
#define Two_One_Diff( a1, a0, b, x2, x1, x0 ) \
Two_Diff( a0, b, _i, x0 ); \
Two_Sum( a1, _i, x2, x1 )
#define Two_Two_Sum( a1, a0, b1, b0, x3, x2, x1, x0 ) \
Two_One_Sum( a1, a0, b0, _j, _0, x0 ); \
Two_One_Sum( _j, _0, b1, x3, x2, x1 )
#define Two_Two_Diff( a1, a0, b1, b0, x3, x2, x1, x0 ) \
Two_One_Diff( a1, a0, b0, _j, _0, x0 ); \
Two_One_Diff( _j, _0, b1, x3, x2, x1 )
/*****************************************************************************/
/* */
/* exactinit() Initialize the variables used for exact arithmetic. */
/* */
/* `epsilon' is the largest power of two such that 1.0 + epsilon = 1.0 in */
/* floating-point arithmetic. `epsilon' bounds the relative roundoff */
/* error. It is used for floating-point error analysis. */
/* */
/* `splitter' is used to split floating-point numbers into two half- */
/* length significands for exact multiplication. */
/* */
/* I imagine that a highly optimizing compiler might be too smart for its */
/* own good, and somehow cause this routine to fail, if it pretends that */
/* floating-point arithmetic is too much like real arithmetic. */
/* */
/* Don't change this routine unless you fully understand it. */
/* */
/*****************************************************************************/
void exactinit(){
REAL half;
REAL check, lastcheck;
int every_other;
every_other = 1;
half = 0.5;
epsilon = 1.0;
splitter = 1.0;
check = 1.0;
/* Repeatedly divide `epsilon' by two until it is too small to add to */
/* one without causing roundoff. (Also check if the sum is equal to */
/* the previous sum, for machines that round up instead of using exact */
/* rounding. Not that these routines will work on such machines anyway. */
do {
lastcheck = check;
epsilon *= half;
if ( every_other ) {
splitter *= 2.0;
}
every_other = !every_other;
check = (REAL)( 1.0 + epsilon );
} while ( ( check != 1.0 ) && ( check != lastcheck ) );
splitter += 1.0;
if ( verbose > 1 ) {
printf( "Floating point roundoff is of magnitude %.17g\n", epsilon );
printf( "Floating point splitter is %.17g\n", splitter );
}
/* Error bounds for orientation and incircle tests. */
resulterrbound = (REAL)( ( 3.0 + 8.0 * epsilon ) * epsilon );
ccwerrboundA = (REAL)( ( 3.0 + 16.0 * epsilon ) * epsilon );
ccwerrboundB = (REAL)( ( 2.0 + 12.0 * epsilon ) * epsilon );
ccwerrboundC = (REAL)( ( 9.0 + 64.0 * epsilon ) * epsilon * epsilon );
iccerrboundA = (REAL)( ( 10.0 + 96.0 * epsilon ) * epsilon );
iccerrboundB = (REAL)( ( 4.0 + 48.0 * epsilon ) * epsilon );
iccerrboundC = (REAL)( ( 44.0 + 576.0 * epsilon ) * epsilon * epsilon );
}
/*****************************************************************************/
/* */
/* fast_expansion_sum_zeroelim() Sum two expansions, eliminating zero */
/* components from the output expansion. */
/* */
/* Sets h = e + f. See my Robust Predicates paper for details. */
/* */
/* If round-to-even is used (as with IEEE 754), maintains the strongly */
/* nonoverlapping property. (That is, if e is strongly nonoverlapping, h */
/* will be also.) Does NOT maintain the nonoverlapping or nonadjacent */
/* properties. */
/* */
/*****************************************************************************/
int fast_expansion_sum_zeroelim( elen, e, flen, f, h ) /* h cannot be e or f. */
int elen;
REAL *e;
int flen;
REAL *f;
REAL *h;
{
REAL Q;
INEXACT REAL Qnew;
INEXACT REAL hh;
INEXACT REAL bvirt;
REAL avirt, bround, around;
int eindex, findex, hindex;
REAL enow, fnow;
enow = e[0];
fnow = f[0];
eindex = findex = 0;
if ( ( fnow > enow ) == ( fnow > -enow ) ) {
Q = enow;
enow = e[++eindex];
}
else {
Q = fnow;
fnow = f[++findex];
}
hindex = 0;
if ( ( eindex < elen ) && ( findex < flen ) ) {
if ( ( fnow > enow ) == ( fnow > -enow ) ) {
Fast_Two_Sum( enow, Q, Qnew, hh );
enow = e[++eindex];
}
else {
Fast_Two_Sum( fnow, Q, Qnew, hh );
fnow = f[++findex];
}
Q = Qnew;
if ( hh != 0.0 ) {
h[hindex++] = hh;
}
while ( ( eindex < elen ) && ( findex < flen ) ) {
if ( ( fnow > enow ) == ( fnow > -enow ) ) {
Two_Sum( Q, enow, Qnew, hh );
enow = e[++eindex];
}
else {
Two_Sum( Q, fnow, Qnew, hh );
fnow = f[++findex];
}
Q = Qnew;
if ( hh != 0.0 ) {
h[hindex++] = hh;
}
}
}
while ( eindex < elen ) {
Two_Sum( Q, enow, Qnew, hh );
enow = e[++eindex];
Q = Qnew;
if ( hh != 0.0 ) {
h[hindex++] = hh;
}
}
while ( findex < flen ) {
Two_Sum( Q, fnow, Qnew, hh );
fnow = f[++findex];
Q = Qnew;
if ( hh != 0.0 ) {
h[hindex++] = hh;
}
}
if ( ( Q != 0.0 ) || ( hindex == 0 ) ) {
h[hindex++] = Q;
}
return hindex;
}
/*****************************************************************************/
/* */
/* scale_expansion_zeroelim() Multiply an expansion by a scalar, */
/* eliminating zero components from the */
/* output expansion. */
/* */
/* Sets h = be. See my Robust Predicates paper for details. */
/* */
/* Maintains the nonoverlapping property. If round-to-even is used (as */
/* with IEEE 754), maintains the strongly nonoverlapping and nonadjacent */
/* properties as well. (That is, if e has one of these properties, so */
/* will h.) */
/* */
/*****************************************************************************/
int scale_expansion_zeroelim( elen, e, b, h ) /* e and h cannot be the same. */
int elen;
REAL *e;
REAL b;
REAL *h;
{
INEXACT REAL Q, sum;
REAL hh;
INEXACT REAL product1;
REAL product0;
int eindex, hindex;
REAL enow;
INEXACT REAL bvirt;
REAL avirt, bround, around;
INEXACT REAL c;
INEXACT REAL abig;
REAL ahi, alo, bhi, blo;
REAL err1, err2, err3;
Split( b, bhi, blo );
Two_Product_Presplit( e[0], b, bhi, blo, Q, hh );
hindex = 0;
if ( hh != 0 ) {
h[hindex++] = hh;
}
for ( eindex = 1; eindex < elen; eindex++ ) {
enow = e[eindex];
Two_Product_Presplit( enow, b, bhi, blo, product1, product0 );
Two_Sum( Q, product0, sum, hh );
if ( hh != 0 ) {
h[hindex++] = hh;
}
Fast_Two_Sum( product1, sum, Q, hh );
if ( hh != 0 ) {
h[hindex++] = hh;
}
}
if ( ( Q != 0.0 ) || ( hindex == 0 ) ) {
h[hindex++] = Q;
}
return hindex;
}
/*****************************************************************************/
/* */
/* estimate() Produce a one-word estimate of an expansion's value. */
/* */
/* See my Robust Predicates paper for details. */
/* */
/*****************************************************************************/
REAL estimate( elen, e )
int elen;
REAL *e;
{
REAL Q;
int eindex;
Q = e[0];
for ( eindex = 1; eindex < elen; eindex++ ) {
Q += e[eindex];
}
return Q;
}
/*****************************************************************************/
/* */
/* counterclockwise() Return a positive value if the points pa, pb, and */
/* pc occur in counterclockwise order; a negative */
/* value if they occur in clockwise order; and zero */
/* if they are collinear. The result is also a rough */
/* approximation of twice the signed area of the */
/* triangle defined by the three points. */
/* */
/* Uses exact arithmetic if necessary to ensure a correct answer. The */
/* result returned is the determinant of a matrix. This determinant is */
/* computed adaptively, in the sense that exact arithmetic is used only to */
/* the degree it is needed to ensure that the returned value has the */
/* correct sign. Hence, this function is usually quite fast, but will run */
/* more slowly when the input points are collinear or nearly so. */
/* */
/* See my Robust Predicates paper for details. */
/* */
/*****************************************************************************/
REAL counterclockwiseadapt( pa, pb, pc, detsum )
point pa;
point pb;
point pc;
REAL detsum;
{
INEXACT REAL acx, acy, bcx, bcy;
REAL acxtail, acytail, bcxtail, bcytail;
INEXACT REAL detleft, detright;
REAL detlefttail, detrighttail;
REAL det, errbound;
REAL B[4], C1[8], C2[12], D[16];
INEXACT REAL B3;
int C1length, C2length, Dlength;
REAL u[4];
INEXACT REAL u3;
INEXACT REAL s1, t1;
REAL s0, t0;
INEXACT REAL bvirt;
REAL avirt, bround, around;
INEXACT REAL c;
INEXACT REAL abig;
REAL ahi, alo, bhi, blo;
REAL err1, err2, err3;
INEXACT REAL _i, _j;
REAL _0;
acx = (REAL) ( pa[0] - pc[0] );
bcx = (REAL) ( pb[0] - pc[0] );
acy = (REAL) ( pa[1] - pc[1] );
bcy = (REAL) ( pb[1] - pc[1] );
Two_Product( acx, bcy, detleft, detlefttail );
Two_Product( acy, bcx, detright, detrighttail );
Two_Two_Diff( detleft, detlefttail, detright, detrighttail,
B3, B[2], B[1], B[0] );
B[3] = B3;
det = estimate( 4, B );
errbound = (REAL)( ccwerrboundB * detsum );
if ( ( det >= errbound ) || ( -det >= errbound ) ) {
return det;
}
Two_Diff_Tail( pa[0], pc[0], acx, acxtail );
Two_Diff_Tail( pb[0], pc[0], bcx, bcxtail );
Two_Diff_Tail( pa[1], pc[1], acy, acytail );
Two_Diff_Tail( pb[1], pc[1], bcy, bcytail );
if ( ( acxtail == 0.0 ) && ( acytail == 0.0 )
&& ( bcxtail == 0.0 ) && ( bcytail == 0.0 ) ) {
return det;
}
errbound = (REAL)( ccwerrboundC * detsum + resulterrbound * Absolute( det ) );
det += ( acx * bcytail + bcy * acxtail )
- ( acy * bcxtail + bcx * acytail );
if ( ( det >= errbound ) || ( -det >= errbound ) ) {
return det;
}
Two_Product( acxtail, bcy, s1, s0 );
Two_Product( acytail, bcx, t1, t0 );
Two_Two_Diff( s1, s0, t1, t0, u3, u[2], u[1], u[0] );
u[3] = u3;
C1length = fast_expansion_sum_zeroelim( 4, B, 4, u, C1 );
Two_Product( acx, bcytail, s1, s0 );
Two_Product( acy, bcxtail, t1, t0 );
Two_Two_Diff( s1, s0, t1, t0, u3, u[2], u[1], u[0] );
u[3] = u3;
C2length = fast_expansion_sum_zeroelim( C1length, C1, 4, u, C2 );
Two_Product( acxtail, bcytail, s1, s0 );
Two_Product( acytail, bcxtail, t1, t0 );
Two_Two_Diff( s1, s0, t1, t0, u3, u[2], u[1], u[0] );
u[3] = u3;
Dlength = fast_expansion_sum_zeroelim( C2length, C2, 4, u, D );
return( D[Dlength - 1] );
}
REAL counterclockwise( pa, pb, pc )
point pa;
point pb;
point pc;
{
REAL detleft, detright, det;
REAL detsum, errbound;
counterclockcount++;
detleft = ( pa[0] - pc[0] ) * ( pb[1] - pc[1] );
detright = ( pa[1] - pc[1] ) * ( pb[0] - pc[0] );
det = detleft - detright;
if ( noexact ) {
return det;
}
if ( detleft > 0.0 ) {
if ( detright <= 0.0 ) {
return det;
}
else {
detsum = detleft + detright;
}
}
else if ( detleft < 0.0 ) {
if ( detright >= 0.0 ) {
return det;
}
else {
detsum = -detleft - detright;
}
}
else {
return det;
}
errbound = ccwerrboundA * detsum;
if ( ( det >= errbound ) || ( -det >= errbound ) ) {
return det;
}
return counterclockwiseadapt( pa, pb, pc, detsum );
}
/*****************************************************************************/
/* */
/* incircle() Return a positive value if the point pd lies inside the */
/* circle passing through pa, pb, and pc; a negative value if */
/* it lies outside; and zero if the four points are cocircular.*/
/* The points pa, pb, and pc must be in counterclockwise */
/* order, or the sign of the result will be reversed. */
/* */
/* Uses exact arithmetic if necessary to ensure a correct answer. The */
/* result returned is the determinant of a matrix. This determinant is */
/* computed adaptively, in the sense that exact arithmetic is used only to */
/* the degree it is needed to ensure that the returned value has the */
/* correct sign. Hence, this function is usually quite fast, but will run */
/* more slowly when the input points are cocircular or nearly so. */
/* */
/* See my Robust Predicates paper for details. */
/* */
/*****************************************************************************/
REAL incircleadapt( pa, pb, pc, pd, permanent )
point pa;
point pb;
point pc;
point pd;
REAL permanent;
{
INEXACT REAL adx, bdx, cdx, ady, bdy, cdy;
REAL det, errbound;
INEXACT REAL bdxcdy1, cdxbdy1, cdxady1, adxcdy1, adxbdy1, bdxady1;
REAL bdxcdy0, cdxbdy0, cdxady0, adxcdy0, adxbdy0, bdxady0;
REAL bc[4], ca[4], ab[4];
INEXACT REAL bc3, ca3, ab3;
REAL axbc[8], axxbc[16], aybc[8], ayybc[16], adet[32];
int axbclen, axxbclen, aybclen, ayybclen, alen;
REAL bxca[8], bxxca[16], byca[8], byyca[16], bdet[32];
int bxcalen, bxxcalen, bycalen, byycalen, blen;
REAL cxab[8], cxxab[16], cyab[8], cyyab[16], cdet[32];
int cxablen, cxxablen, cyablen, cyyablen, clen;
REAL abdet[64];
int ablen;
REAL fin1[1152], fin2[1152];
REAL *finnow, *finother, *finswap;
int finlength;
REAL adxtail, bdxtail, cdxtail, adytail, bdytail, cdytail;
INEXACT REAL adxadx1, adyady1, bdxbdx1, bdybdy1, cdxcdx1, cdycdy1;
REAL adxadx0, adyady0, bdxbdx0, bdybdy0, cdxcdx0, cdycdy0;
REAL aa[4], bb[4], cc[4];
INEXACT REAL aa3, bb3, cc3;
INEXACT REAL ti1, tj1;
REAL ti0, tj0;
REAL u[4], v[4];
INEXACT REAL u3, v3;
REAL temp8[8], temp16a[16], temp16b[16], temp16c[16];
REAL temp32a[32], temp32b[32], temp48[48], temp64[64];
int temp8len, temp16alen, temp16blen, temp16clen;
int temp32alen, temp32blen, temp48len, temp64len;
REAL axtbb[8], axtcc[8], aytbb[8], aytcc[8];
int axtbblen, axtcclen, aytbblen, aytcclen;
REAL bxtaa[8], bxtcc[8], bytaa[8], bytcc[8];
int bxtaalen, bxtcclen, bytaalen, bytcclen;
REAL cxtaa[8], cxtbb[8], cytaa[8], cytbb[8];
int cxtaalen, cxtbblen, cytaalen, cytbblen;
REAL axtbc[8], aytbc[8], bxtca[8], bytca[8], cxtab[8], cytab[8];
int axtbclen, aytbclen, bxtcalen, bytcalen, cxtablen, cytablen;
REAL axtbct[16], aytbct[16], bxtcat[16], bytcat[16], cxtabt[16], cytabt[16];
int axtbctlen, aytbctlen, bxtcatlen, bytcatlen, cxtabtlen, cytabtlen;
REAL axtbctt[8], aytbctt[8], bxtcatt[8];
REAL bytcatt[8], cxtabtt[8], cytabtt[8];
int axtbcttlen, aytbcttlen, bxtcattlen, bytcattlen, cxtabttlen, cytabttlen;
REAL abt[8], bct[8], cat[8];
int abtlen, bctlen, catlen;
REAL abtt[4], bctt[4], catt[4];
int abttlen, bcttlen, cattlen;
INEXACT REAL abtt3, bctt3, catt3;
REAL negate;
INEXACT REAL bvirt;
REAL avirt, bround, around;
INEXACT REAL c;
INEXACT REAL abig;
REAL ahi, alo, bhi, blo;
REAL err1, err2, err3;
INEXACT REAL _i, _j;
REAL _0;
adx = (REAL) ( pa[0] - pd[0] );
bdx = (REAL) ( pb[0] - pd[0] );
cdx = (REAL) ( pc[0] - pd[0] );
ady = (REAL) ( pa[1] - pd[1] );
bdy = (REAL) ( pb[1] - pd[1] );
cdy = (REAL) ( pc[1] - pd[1] );
Two_Product( bdx, cdy, bdxcdy1, bdxcdy0 );
Two_Product( cdx, bdy, cdxbdy1, cdxbdy0 );
Two_Two_Diff( bdxcdy1, bdxcdy0, cdxbdy1, cdxbdy0, bc3, bc[2], bc[1], bc[0] );
bc[3] = bc3;
axbclen = scale_expansion_zeroelim( 4, bc, adx, axbc );
axxbclen = scale_expansion_zeroelim( axbclen, axbc, adx, axxbc );
aybclen = scale_expansion_zeroelim( 4, bc, ady, aybc );
ayybclen = scale_expansion_zeroelim( aybclen, aybc, ady, ayybc );
alen = fast_expansion_sum_zeroelim( axxbclen, axxbc, ayybclen, ayybc, adet );
Two_Product( cdx, ady, cdxady1, cdxady0 );
Two_Product( adx, cdy, adxcdy1, adxcdy0 );
Two_Two_Diff( cdxady1, cdxady0, adxcdy1, adxcdy0, ca3, ca[2], ca[1], ca[0] );
ca[3] = ca3;
bxcalen = scale_expansion_zeroelim( 4, ca, bdx, bxca );
bxxcalen = scale_expansion_zeroelim( bxcalen, bxca, bdx, bxxca );
bycalen = scale_expansion_zeroelim( 4, ca, bdy, byca );
byycalen = scale_expansion_zeroelim( bycalen, byca, bdy, byyca );
blen = fast_expansion_sum_zeroelim( bxxcalen, bxxca, byycalen, byyca, bdet );
Two_Product( adx, bdy, adxbdy1, adxbdy0 );
Two_Product( bdx, ady, bdxady1, bdxady0 );
Two_Two_Diff( adxbdy1, adxbdy0, bdxady1, bdxady0, ab3, ab[2], ab[1], ab[0] );
ab[3] = ab3;
cxablen = scale_expansion_zeroelim( 4, ab, cdx, cxab );
cxxablen = scale_expansion_zeroelim( cxablen, cxab, cdx, cxxab );
cyablen = scale_expansion_zeroelim( 4, ab, cdy, cyab );
cyyablen = scale_expansion_zeroelim( cyablen, cyab, cdy, cyyab );
clen = fast_expansion_sum_zeroelim( cxxablen, cxxab, cyyablen, cyyab, cdet );
ablen = fast_expansion_sum_zeroelim( alen, adet, blen, bdet, abdet );
finlength = fast_expansion_sum_zeroelim( ablen, abdet, clen, cdet, fin1 );
det = estimate( finlength, fin1 );
errbound = (REAL)( iccerrboundB * permanent );
if ( ( det >= errbound ) || ( -det >= errbound ) ) {
return det;
}
Two_Diff_Tail( pa[0], pd[0], adx, adxtail );
Two_Diff_Tail( pa[1], pd[1], ady, adytail );
Two_Diff_Tail( pb[0], pd[0], bdx, bdxtail );
Two_Diff_Tail( pb[1], pd[1], bdy, bdytail );
Two_Diff_Tail( pc[0], pd[0], cdx, cdxtail );
Two_Diff_Tail( pc[1], pd[1], cdy, cdytail );
if ( ( adxtail == 0.0 ) && ( bdxtail == 0.0 ) && ( cdxtail == 0.0 )
&& ( adytail == 0.0 ) && ( bdytail == 0.0 ) && ( cdytail == 0.0 ) ) {
return det;
}
errbound = (REAL)( iccerrboundC * permanent + resulterrbound * Absolute( det ) );
det += (REAL)( ( ( adx * adx + ady * ady ) * ( ( bdx * cdytail + cdy * bdxtail )
- ( bdy * cdxtail + cdx * bdytail ) )
+ 2.0 * ( adx * adxtail + ady * adytail ) * ( bdx * cdy - bdy * cdx ) )
+ ( ( bdx * bdx + bdy * bdy ) * ( ( cdx * adytail + ady * cdxtail )
- ( cdy * adxtail + adx * cdytail ) )
+ 2.0 * ( bdx * bdxtail + bdy * bdytail ) * ( cdx * ady - cdy * adx ) )
+ ( ( cdx * cdx + cdy * cdy ) * ( ( adx * bdytail + bdy * adxtail )
- ( ady * bdxtail + bdx * adytail ) )
+ 2.0 * ( cdx * cdxtail + cdy * cdytail ) * ( adx * bdy - ady * bdx ) ) );
if ( ( det >= errbound ) || ( -det >= errbound ) ) {
return det;
}
finnow = fin1;
finother = fin2;
if ( ( bdxtail != 0.0 ) || ( bdytail != 0.0 )
|| ( cdxtail != 0.0 ) || ( cdytail != 0.0 ) ) {
Square( adx, adxadx1, adxadx0 );
Square( ady, adyady1, adyady0 );
Two_Two_Sum( adxadx1, adxadx0, adyady1, adyady0, aa3, aa[2], aa[1], aa[0] );
aa[3] = aa3;
}
if ( ( cdxtail != 0.0 ) || ( cdytail != 0.0 )
|| ( adxtail != 0.0 ) || ( adytail != 0.0 ) ) {
Square( bdx, bdxbdx1, bdxbdx0 );
Square( bdy, bdybdy1, bdybdy0 );
Two_Two_Sum( bdxbdx1, bdxbdx0, bdybdy1, bdybdy0, bb3, bb[2], bb[1], bb[0] );
bb[3] = bb3;
}
if ( ( adxtail != 0.0 ) || ( adytail != 0.0 )
|| ( bdxtail != 0.0 ) || ( bdytail != 0.0 ) ) {
Square( cdx, cdxcdx1, cdxcdx0 );
Square( cdy, cdycdy1, cdycdy0 );
Two_Two_Sum( cdxcdx1, cdxcdx0, cdycdy1, cdycdy0, cc3, cc[2], cc[1], cc[0] );
cc[3] = cc3;
}
if ( adxtail != 0.0 ) {
axtbclen = scale_expansion_zeroelim( 4, bc, adxtail, axtbc );
temp16alen = scale_expansion_zeroelim( axtbclen, axtbc, 2.0 * adx,
temp16a );
axtcclen = scale_expansion_zeroelim( 4, cc, adxtail, axtcc );
temp16blen = scale_expansion_zeroelim( axtcclen, axtcc, bdy, temp16b );
axtbblen = scale_expansion_zeroelim( 4, bb, adxtail, axtbb );
temp16clen = scale_expansion_zeroelim( axtbblen, axtbb, -cdy, temp16c );
temp32alen = fast_expansion_sum_zeroelim( temp16alen, temp16a,
temp16blen, temp16b, temp32a );
temp48len = fast_expansion_sum_zeroelim( temp16clen, temp16c,
temp32alen, temp32a, temp48 );
finlength = fast_expansion_sum_zeroelim( finlength, finnow, temp48len,
temp48, finother );
finswap = finnow; finnow = finother; finother = finswap;
}
if ( adytail != 0.0 ) {
aytbclen = scale_expansion_zeroelim( 4, bc, adytail, aytbc );
temp16alen = scale_expansion_zeroelim( aytbclen, aytbc, 2.0 * ady,
temp16a );
aytbblen = scale_expansion_zeroelim( 4, bb, adytail, aytbb );
temp16blen = scale_expansion_zeroelim( aytbblen, aytbb, cdx, temp16b );
aytcclen = scale_expansion_zeroelim( 4, cc, adytail, aytcc );
temp16clen = scale_expansion_zeroelim( aytcclen, aytcc, -bdx, temp16c );
temp32alen = fast_expansion_sum_zeroelim( temp16alen, temp16a,
temp16blen, temp16b, temp32a );
temp48len = fast_expansion_sum_zeroelim( temp16clen, temp16c,
temp32alen, temp32a, temp48 );
finlength = fast_expansion_sum_zeroelim( finlength, finnow, temp48len,
temp48, finother );
finswap = finnow; finnow = finother; finother = finswap;
}
if ( bdxtail != 0.0 ) {
bxtcalen = scale_expansion_zeroelim( 4, ca, bdxtail, bxtca );
temp16alen = scale_expansion_zeroelim( bxtcalen, bxtca, 2.0 * bdx,
temp16a );
bxtaalen = scale_expansion_zeroelim( 4, aa, bdxtail, bxtaa );
temp16blen = scale_expansion_zeroelim( bxtaalen, bxtaa, cdy, temp16b );
bxtcclen = scale_expansion_zeroelim( 4, cc, bdxtail, bxtcc );
temp16clen = scale_expansion_zeroelim( bxtcclen, bxtcc, -ady, temp16c );
temp32alen = fast_expansion_sum_zeroelim( temp16alen, temp16a,
temp16blen, temp16b, temp32a );
temp48len = fast_expansion_sum_zeroelim( temp16clen, temp16c,
temp32alen, temp32a, temp48 );
finlength = fast_expansion_sum_zeroelim( finlength, finnow, temp48len,
temp48, finother );
finswap = finnow; finnow = finother; finother = finswap;
}
if ( bdytail != 0.0 ) {
bytcalen = scale_expansion_zeroelim( 4, ca, bdytail, bytca );
temp16alen = scale_expansion_zeroelim( bytcalen, bytca, 2.0 * bdy,
temp16a );
bytcclen = scale_expansion_zeroelim( 4, cc, bdytail, bytcc );
temp16blen = scale_expansion_zeroelim( bytcclen, bytcc, adx, temp16b );
bytaalen = scale_expansion_zeroelim( 4, aa, bdytail, bytaa );
temp16clen = scale_expansion_zeroelim( bytaalen, bytaa, -cdx, temp16c );
temp32alen = fast_expansion_sum_zeroelim( temp16alen, temp16a,
temp16blen, temp16b, temp32a );
temp48len = fast_expansion_sum_zeroelim( temp16clen, temp16c,
temp32alen, temp32a, temp48 );
finlength = fast_expansion_sum_zeroelim( finlength, finnow, temp48len,
temp48, finother );
finswap = finnow; finnow = finother; finother = finswap;
}
if ( cdxtail != 0.0 ) {
cxtablen = scale_expansion_zeroelim( 4, ab, cdxtail, cxtab );
temp16alen = scale_expansion_zeroelim( cxtablen, cxtab, 2.0 * cdx,
temp16a );
cxtbblen = scale_expansion_zeroelim( 4, bb, cdxtail, cxtbb );
temp16blen = scale_expansion_zeroelim( cxtbblen, cxtbb, ady, temp16b );
cxtaalen = scale_expansion_zeroelim( 4, aa, cdxtail, cxtaa );
temp16clen = scale_expansion_zeroelim( cxtaalen, cxtaa, -bdy, temp16c );
temp32alen = fast_expansion_sum_zeroelim( temp16alen, temp16a,
temp16blen, temp16b, temp32a );
temp48len = fast_expansion_sum_zeroelim( temp16clen, temp16c,
temp32alen, temp32a, temp48 );
finlength = fast_expansion_sum_zeroelim( finlength, finnow, temp48len,
temp48, finother );
finswap = finnow; finnow = finother; finother = finswap;
}
if ( cdytail != 0.0 ) {
cytablen = scale_expansion_zeroelim( 4, ab, cdytail, cytab );
temp16alen = scale_expansion_zeroelim( cytablen, cytab, 2.0 * cdy,
temp16a );
cytaalen = scale_expansion_zeroelim( 4, aa, cdytail, cytaa );
temp16blen = scale_expansion_zeroelim( cytaalen, cytaa, bdx, temp16b );
cytbblen = scale_expansion_zeroelim( 4, bb, cdytail, cytbb );
temp16clen = scale_expansion_zeroelim( cytbblen, cytbb, -adx, temp16c );
temp32alen = fast_expansion_sum_zeroelim( temp16alen, temp16a,
temp16blen, temp16b, temp32a );
temp48len = fast_expansion_sum_zeroelim( temp16clen, temp16c,
temp32alen, temp32a, temp48 );
finlength = fast_expansion_sum_zeroelim( finlength, finnow, temp48len,
temp48, finother );
finswap = finnow; finnow = finother; finother = finswap;
}
if ( ( adxtail != 0.0 ) || ( adytail != 0.0 ) ) {
if ( ( bdxtail != 0.0 ) || ( bdytail != 0.0 )
|| ( cdxtail != 0.0 ) || ( cdytail != 0.0 ) ) {
Two_Product( bdxtail, cdy, ti1, ti0 );
Two_Product( bdx, cdytail, tj1, tj0 );
Two_Two_Sum( ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0] );
u[3] = u3;
negate = -bdy;
Two_Product( cdxtail, negate, ti1, ti0 );
negate = -bdytail;
Two_Product( cdx, negate, tj1, tj0 );
Two_Two_Sum( ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0] );
v[3] = v3;
bctlen = fast_expansion_sum_zeroelim( 4, u, 4, v, bct );
Two_Product( bdxtail, cdytail, ti1, ti0 );
Two_Product( cdxtail, bdytail, tj1, tj0 );
Two_Two_Diff( ti1, ti0, tj1, tj0, bctt3, bctt[2], bctt[1], bctt[0] );
bctt[3] = bctt3;
bcttlen = 4;
}
else {
bct[0] = 0.0;
bctlen = 1;
bctt[0] = 0.0;
bcttlen = 1;
}
if ( adxtail != 0.0 ) {
temp16alen = scale_expansion_zeroelim( axtbclen, axtbc, adxtail, temp16a );
axtbctlen = scale_expansion_zeroelim( bctlen, bct, adxtail, axtbct );
temp32alen = scale_expansion_zeroelim( axtbctlen, axtbct, 2.0 * adx,
temp32a );
temp48len = fast_expansion_sum_zeroelim( temp16alen, temp16a,
temp32alen, temp32a, temp48 );
finlength = fast_expansion_sum_zeroelim( finlength, finnow, temp48len,
temp48, finother );
finswap = finnow; finnow = finother; finother = finswap;
if ( bdytail != 0.0 ) {
temp8len = scale_expansion_zeroelim( 4, cc, adxtail, temp8 );
temp16alen = scale_expansion_zeroelim( temp8len, temp8, bdytail,
temp16a );
finlength = fast_expansion_sum_zeroelim( finlength, finnow, temp16alen,
temp16a, finother );
finswap = finnow; finnow = finother; finother = finswap;
}
if ( cdytail != 0.0 ) {
temp8len = scale_expansion_zeroelim( 4, bb, -adxtail, temp8 );
temp16alen = scale_expansion_zeroelim( temp8len, temp8, cdytail,
temp16a );
finlength = fast_expansion_sum_zeroelim( finlength, finnow, temp16alen,
temp16a, finother );
finswap = finnow; finnow = finother; finother = finswap;
}
temp32alen = scale_expansion_zeroelim( axtbctlen, axtbct, adxtail,
temp32a );
axtbcttlen = scale_expansion_zeroelim( bcttlen, bctt, adxtail, axtbctt );
temp16alen = scale_expansion_zeroelim( axtbcttlen, axtbctt, 2.0 * adx,
temp16a );
temp16blen = scale_expansion_zeroelim( axtbcttlen, axtbctt, adxtail,
temp16b );
temp32blen = fast_expansion_sum_zeroelim( temp16alen, temp16a,
temp16blen, temp16b, temp32b );
temp64len = fast_expansion_sum_zeroelim( temp32alen, temp32a,
temp32blen, temp32b, temp64 );
finlength = fast_expansion_sum_zeroelim( finlength, finnow, temp64len,
temp64, finother );
finswap = finnow; finnow = finother; finother = finswap;
}
if ( adytail != 0.0 ) {
temp16alen = scale_expansion_zeroelim( aytbclen, aytbc, adytail, temp16a );
aytbctlen = scale_expansion_zeroelim( bctlen, bct, adytail, aytbct );
temp32alen = scale_expansion_zeroelim( aytbctlen, aytbct, 2.0 * ady,
temp32a );
temp48len = fast_expansion_sum_zeroelim( temp16alen, temp16a,
temp32alen, temp32a, temp48 );
finlength = fast_expansion_sum_zeroelim( finlength, finnow, temp48len,
temp48, finother );
finswap = finnow; finnow = finother; finother = finswap;
temp32alen = scale_expansion_zeroelim( aytbctlen, aytbct, adytail,
temp32a );
aytbcttlen = scale_expansion_zeroelim( bcttlen, bctt, adytail, aytbctt );
temp16alen = scale_expansion_zeroelim( aytbcttlen, aytbctt, 2.0 * ady,
temp16a );
temp16blen = scale_expansion_zeroelim( aytbcttlen, aytbctt, adytail,
temp16b );
temp32blen = fast_expansion_sum_zeroelim( temp16alen, temp16a,
temp16blen, temp16b, temp32b );
temp64len = fast_expansion_sum_zeroelim( temp32alen, temp32a,
temp32blen, temp32b, temp64 );
finlength = fast_expansion_sum_zeroelim( finlength, finnow, temp64len,
temp64, finother );
finswap = finnow; finnow = finother; finother = finswap;
}
}
if ( ( bdxtail != 0.0 ) || ( bdytail != 0.0 ) ) {
if ( ( cdxtail != 0.0 ) || ( cdytail != 0.0 )
|| ( adxtail != 0.0 ) || ( adytail != 0.0 ) ) {
Two_Product( cdxtail, ady, ti1, ti0 );
Two_Product( cdx, adytail, tj1, tj0 );
Two_Two_Sum( ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0] );
u[3] = u3;
negate = -cdy;
Two_Product( adxtail, negate, ti1, ti0 );
negate = -cdytail;
Two_Product( adx, negate, tj1, tj0 );
Two_Two_Sum( ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0] );
v[3] = v3;
catlen = fast_expansion_sum_zeroelim( 4, u, 4, v, cat );
Two_Product( cdxtail, adytail, ti1, ti0 );
Two_Product( adxtail, cdytail, tj1, tj0 );
Two_Two_Diff( ti1, ti0, tj1, tj0, catt3, catt[2], catt[1], catt[0] );
catt[3] = catt3;
cattlen = 4;
}
else {
cat[0] = 0.0;
catlen = 1;
catt[0] = 0.0;
cattlen = 1;
}
if ( bdxtail != 0.0 ) {
temp16alen = scale_expansion_zeroelim( bxtcalen, bxtca, bdxtail, temp16a );
bxtcatlen = scale_expansion_zeroelim( catlen, cat, bdxtail, bxtcat );
temp32alen = scale_expansion_zeroelim( bxtcatlen, bxtcat, 2.0 * bdx,
temp32a );
temp48len = fast_expansion_sum_zeroelim( temp16alen, temp16a,
temp32alen, temp32a, temp48 );
finlength = fast_expansion_sum_zeroelim( finlength, finnow, temp48len,
temp48, finother );
finswap = finnow; finnow = finother; finother = finswap;
if ( cdytail != 0.0 ) {
temp8len = scale_expansion_zeroelim( 4, aa, bdxtail, temp8 );
temp16alen = scale_expansion_zeroelim( temp8len, temp8, cdytail,
temp16a );
finlength = fast_expansion_sum_zeroelim( finlength, finnow, temp16alen,
temp16a, finother );
finswap = finnow; finnow = finother; finother = finswap;
}
if ( adytail != 0.0 ) {
temp8len = scale_expansion_zeroelim( 4, cc, -bdxtail, temp8 );
temp16alen = scale_expansion_zeroelim( temp8len, temp8, adytail,
temp16a );
finlength = fast_expansion_sum_zeroelim( finlength, finnow, temp16alen,
temp16a, finother );
finswap = finnow; finnow = finother; finother = finswap;
}
temp32alen = scale_expansion_zeroelim( bxtcatlen, bxtcat, bdxtail,
temp32a );
bxtcattlen = scale_expansion_zeroelim( cattlen, catt, bdxtail, bxtcatt );
temp16alen = scale_expansion_zeroelim( bxtcattlen, bxtcatt, 2.0 * bdx,
temp16a );
temp16blen = scale_expansion_zeroelim( bxtcattlen, bxtcatt, bdxtail,
temp16b );
temp32blen = fast_expansion_sum_zeroelim( temp16alen, temp16a,
temp16blen, temp16b, temp32b );
temp64len = fast_expansion_sum_zeroelim( temp32alen, temp32a,
temp32blen, temp32b, temp64 );
finlength = fast_expansion_sum_zeroelim( finlength, finnow, temp64len,
temp64, finother );
finswap = finnow; finnow = finother; finother = finswap;
}
if ( bdytail != 0.0 ) {
temp16alen = scale_expansion_zeroelim( bytcalen, bytca, bdytail, temp16a );
bytcatlen = scale_expansion_zeroelim( catlen, cat, bdytail, bytcat );
temp32alen = scale_expansion_zeroelim( bytcatlen, bytcat, 2.0 * bdy,
temp32a );
temp48len = fast_expansion_sum_zeroelim( temp16alen, temp16a,
temp32alen, temp32a, temp48 );
finlength = fast_expansion_sum_zeroelim( finlength, finnow, temp48len,
temp48, finother );
finswap = finnow; finnow = finother; finother = finswap;
temp32alen = scale_expansion_zeroelim( bytcatlen, bytcat, bdytail,
temp32a );
bytcattlen = scale_expansion_zeroelim( cattlen, catt, bdytail, bytcatt );
temp16alen = scale_expansion_zeroelim( bytcattlen, bytcatt, 2.0 * bdy,
temp16a );
temp16blen = scale_expansion_zeroelim( bytcattlen, bytcatt, bdytail,
temp16b );
temp32blen = fast_expansion_sum_zeroelim( temp16alen, temp16a,
temp16blen, temp16b, temp32b );
temp64len = fast_expansion_sum_zeroelim( temp32alen, temp32a,
temp32blen, temp32b, temp64 );
finlength = fast_expansion_sum_zeroelim( finlength, finnow, temp64len,
temp64, finother );
finswap = finnow; finnow = finother; finother = finswap;
}
}
if ( ( cdxtail != 0.0 ) || ( cdytail != 0.0 ) ) {
if ( ( adxtail != 0.0 ) || ( adytail != 0.0 )
|| ( bdxtail != 0.0 ) || ( bdytail != 0.0 ) ) {
Two_Product( adxtail, bdy, ti1, ti0 );
Two_Product( adx, bdytail, tj1, tj0 );
Two_Two_Sum( ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0] );
u[3] = u3;
negate = -ady;
Two_Product( bdxtail, negate, ti1, ti0 );
negate = -adytail;
Two_Product( bdx, negate, tj1, tj0 );
Two_Two_Sum( ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0] );
v[3] = v3;
abtlen = fast_expansion_sum_zeroelim( 4, u, 4, v, abt );
Two_Product( adxtail, bdytail, ti1, ti0 );
Two_Product( bdxtail, adytail, tj1, tj0 );
Two_Two_Diff( ti1, ti0, tj1, tj0, abtt3, abtt[2], abtt[1], abtt[0] );
abtt[3] = abtt3;
abttlen = 4;
}
else {
abt[0] = 0.0;
abtlen = 1;
abtt[0] = 0.0;
abttlen = 1;
}
if ( cdxtail != 0.0 ) {
temp16alen = scale_expansion_zeroelim( cxtablen, cxtab, cdxtail, temp16a );
cxtabtlen = scale_expansion_zeroelim( abtlen, abt, cdxtail, cxtabt );
temp32alen = scale_expansion_zeroelim( cxtabtlen, cxtabt, 2.0 * cdx,
temp32a );
temp48len = fast_expansion_sum_zeroelim( temp16alen, temp16a,
temp32alen, temp32a, temp48 );
finlength = fast_expansion_sum_zeroelim( finlength, finnow, temp48len,
temp48, finother );
finswap = finnow; finnow = finother; finother = finswap;
if ( adytail != 0.0 ) {
temp8len = scale_expansion_zeroelim( 4, bb, cdxtail, temp8 );
temp16alen = scale_expansion_zeroelim( temp8len, temp8, adytail,
temp16a );
finlength = fast_expansion_sum_zeroelim( finlength, finnow, temp16alen,
temp16a, finother );
finswap = finnow; finnow = finother; finother = finswap;
}
if ( bdytail != 0.0 ) {
temp8len = scale_expansion_zeroelim( 4, aa, -cdxtail, temp8 );
temp16alen = scale_expansion_zeroelim( temp8len, temp8, bdytail,
temp16a );
finlength = fast_expansion_sum_zeroelim( finlength, finnow, temp16alen,
temp16a, finother );
finswap = finnow; finnow = finother; finother = finswap;
}
temp32alen = scale_expansion_zeroelim( cxtabtlen, cxtabt, cdxtail,
temp32a );
cxtabttlen = scale_expansion_zeroelim( abttlen, abtt, cdxtail, cxtabtt );
temp16alen = scale_expansion_zeroelim( cxtabttlen, cxtabtt, 2.0 * cdx,
temp16a );
temp16blen = scale_expansion_zeroelim( cxtabttlen, cxtabtt, cdxtail,
temp16b );
temp32blen = fast_expansion_sum_zeroelim( temp16alen, temp16a,
temp16blen, temp16b, temp32b );
temp64len = fast_expansion_sum_zeroelim( temp32alen, temp32a,
temp32blen, temp32b, temp64 );
finlength = fast_expansion_sum_zeroelim( finlength, finnow, temp64len,
temp64, finother );
finswap = finnow; finnow = finother; finother = finswap;
}
if ( cdytail != 0.0 ) {
temp16alen = scale_expansion_zeroelim( cytablen, cytab, cdytail, temp16a );
cytabtlen = scale_expansion_zeroelim( abtlen, abt, cdytail, cytabt );
temp32alen = scale_expansion_zeroelim( cytabtlen, cytabt, 2.0 * cdy,
temp32a );
temp48len = fast_expansion_sum_zeroelim( temp16alen, temp16a,
temp32alen, temp32a, temp48 );
finlength = fast_expansion_sum_zeroelim( finlength, finnow, temp48len,
temp48, finother );
finswap = finnow; finnow = finother; finother = finswap;
temp32alen = scale_expansion_zeroelim( cytabtlen, cytabt, cdytail,
temp32a );
cytabttlen = scale_expansion_zeroelim( abttlen, abtt, cdytail, cytabtt );
temp16alen = scale_expansion_zeroelim( cytabttlen, cytabtt, 2.0 * cdy,
temp16a );
temp16blen = scale_expansion_zeroelim( cytabttlen, cytabtt, cdytail,
temp16b );
temp32blen = fast_expansion_sum_zeroelim( temp16alen, temp16a,
temp16blen, temp16b, temp32b );
temp64len = fast_expansion_sum_zeroelim( temp32alen, temp32a,
temp32blen, temp32b, temp64 );
finlength = fast_expansion_sum_zeroelim( finlength, finnow, temp64len,
temp64, finother );
finswap = finnow; finnow = finother; finother = finswap;
}
}
return finnow[finlength - 1];
}
REAL incircle( pa, pb, pc, pd )
point pa;
point pb;
point pc;
point pd;
{
REAL adx, bdx, cdx, ady, bdy, cdy;
REAL bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady;
REAL alift, blift, clift;
REAL det;
REAL permanent, errbound;
incirclecount++;
adx = pa[0] - pd[0];
bdx = pb[0] - pd[0];
cdx = pc[0] - pd[0];
ady = pa[1] - pd[1];
bdy = pb[1] - pd[1];
cdy = pc[1] - pd[1];
bdxcdy = bdx * cdy;
cdxbdy = cdx * bdy;
alift = adx * adx + ady * ady;
cdxady = cdx * ady;
adxcdy = adx * cdy;
blift = bdx * bdx + bdy * bdy;
adxbdy = adx * bdy;
bdxady = bdx * ady;
clift = cdx * cdx + cdy * cdy;
det = alift * ( bdxcdy - cdxbdy )
+ blift * ( cdxady - adxcdy )
+ clift * ( adxbdy - bdxady );
if ( noexact ) {
return det;
}
permanent = ( Absolute( bdxcdy ) + Absolute( cdxbdy ) ) * alift
+ ( Absolute( cdxady ) + Absolute( adxcdy ) ) * blift
+ ( Absolute( adxbdy ) + Absolute( bdxady ) ) * clift;
errbound = iccerrboundA * permanent;
if ( ( det > errbound ) || ( -det > errbound ) ) {
return det;
}
return incircleadapt( pa, pb, pc, pd, permanent );
}
/** **/
/** **/
/********* Determinant evaluation routines end here *********/
/*****************************************************************************/
/* */
/* triangleinit() Initialize some variables. */
/* */
/*****************************************************************************/
void triangleinit(){
points.maxitems = triangles.maxitems = shelles.maxitems = viri.maxitems =
badsegments.maxitems = badtriangles.maxitems = splaynodes.maxitems = 0l;
points.itembytes = triangles.itembytes = shelles.itembytes = viri.itembytes =
badsegments.itembytes = badtriangles.itembytes = splaynodes.itembytes = 0;
recenttri.tri = (triangle *) NULL; /* No triangle has been visited yet. */
samples = 1; /* Point location should take at least one sample. */
checksegments = 0; /* There are no segments in the triangulation yet. */
incirclecount = counterclockcount = hyperbolacount = 0;
circumcentercount = circletopcount = 0;
randomseed = 1;
exactinit(); /* Initialize exact arithmetic constants. */
}
/*****************************************************************************/
/* */
/* randomnation() Generate a random number between 0 and `choices' - 1. */
/* */
/* This is a simple linear congruential random number generator. Hence, it */
/* is a bad random number generator, but good enough for most randomized */
/* geometric algorithms. */
/* */
/*****************************************************************************/
unsigned long randomnation( choices )
unsigned int choices;
{
randomseed = ( randomseed * 1366l + 150889l ) % 714025l;
return randomseed / ( 714025l / choices + 1 );
}
/********* Mesh quality testing routines begin here *********/
/** **/
/** **/
/*****************************************************************************/
/* */
/* checkmesh() Test the mesh for topological consistency. */
/* */
/*****************************************************************************/
#ifndef REDUCED
void checkmesh(){
struct triedge triangleloop;
struct triedge oppotri, oppooppotri;
point triorg, tridest, triapex;
point oppoorg, oppodest;
int horrors;
int saveexact;
triangle ptr; /* Temporary variable used by sym(). */
/* Temporarily turn on exact arithmetic if it's off. */
saveexact = noexact;
noexact = 0;
if ( !quiet ) {
printf( " Checking consistency of mesh...\n" );
}
horrors = 0;
/* Run through the list of triangles, checking each one. */
traversalinit( &triangles );
triangleloop.tri = triangletraverse();
while ( triangleloop.tri != (triangle *) NULL ) {
/* Check all three edges of the triangle. */
for ( triangleloop.orient = 0; triangleloop.orient < 3;
triangleloop.orient++ ) {
org( triangleloop, triorg );
dest( triangleloop, tridest );
if ( triangleloop.orient == 0 ) { /* Only test for inversion once. */
/* Test if the triangle is flat or inverted. */
apex( triangleloop, triapex );
if ( counterclockwise( triorg, tridest, triapex ) <= 0.0 ) {
printf( " !! !! Inverted " );
printtriangle( &triangleloop );
horrors++;
}
}
/* Find the neighboring triangle on this edge. */
sym( triangleloop, oppotri );
if ( oppotri.tri != dummytri ) {
/* Check that the triangle's neighbor knows it's a neighbor. */
sym( oppotri, oppooppotri );
if ( ( triangleloop.tri != oppooppotri.tri )
|| ( triangleloop.orient != oppooppotri.orient ) ) {
printf( " !! !! Asymmetric triangle-triangle bond:\n" );
if ( triangleloop.tri == oppooppotri.tri ) {
printf( " (Right triangle, wrong orientation)\n" );
}
printf( " First " );
printtriangle( &triangleloop );
printf( " Second (nonreciprocating) " );
printtriangle( &oppotri );
horrors++;
}
/* Check that both triangles agree on the identities */
/* of their shared vertices. */
org( oppotri, oppoorg );
dest( oppotri, oppodest );
if ( ( triorg != oppodest ) || ( tridest != oppoorg ) ) {
printf( " !! !! Mismatched edge coordinates between two triangles:\n"
);
printf( " First mismatched " );
printtriangle( &triangleloop );
printf( " Second mismatched " );
printtriangle( &oppotri );
horrors++;
}
}
}
triangleloop.tri = triangletraverse();
}
if ( horrors == 0 ) {
if ( !quiet ) {
printf( " In my studied opinion, the mesh appears to be consistent.\n" );
}
}
else if ( horrors == 1 ) {
printf( " !! !! !! !! Precisely one festering wound discovered.\n" );
}
else {
printf( " !! !! !! !! %d abominations witnessed.\n", horrors );
}
/* Restore the status of exact arithmetic. */
noexact = saveexact;
}
#endif /* not REDUCED */
/*****************************************************************************/
/* */
/* checkdelaunay() Ensure that the mesh is (constrained) Delaunay. */
/* */
/*****************************************************************************/
#ifndef REDUCED
void checkdelaunay(){
struct triedge triangleloop;
struct triedge oppotri;
struct edge opposhelle;
point triorg, tridest, triapex;
point oppoapex;
int shouldbedelaunay;
int horrors;
int saveexact;
triangle ptr; /* Temporary variable used by sym(). */
shelle sptr; /* Temporary variable used by tspivot(). */
/* Temporarily turn on exact arithmetic if it's off. */
saveexact = noexact;
noexact = 0;
if ( !quiet ) {
printf( " Checking Delaunay property of mesh...\n" );
}
horrors = 0;
/* Run through the list of triangles, checking each one. */
traversalinit( &triangles );
triangleloop.tri = triangletraverse();
while ( triangleloop.tri != (triangle *) NULL ) {
/* Check all three edges of the triangle. */
for ( triangleloop.orient = 0; triangleloop.orient < 3;
triangleloop.orient++ ) {
org( triangleloop, triorg );
dest( triangleloop, tridest );
apex( triangleloop, triapex );
sym( triangleloop, oppotri );
apex( oppotri, oppoapex );
/* Only test that the edge is locally Delaunay if there is an */
/* adjoining triangle whose pointer is larger (to ensure that */
/* each pair isn't tested twice). */
shouldbedelaunay = ( oppotri.tri != dummytri )
&& ( triapex != (point) NULL ) && ( oppoapex != (point) NULL )
&& ( triangleloop.tri < oppotri.tri );
if ( checksegments && shouldbedelaunay ) {
/* If a shell edge separates the triangles, then the edge is */
/* constrained, so no local Delaunay test should be done. */
tspivot( triangleloop, opposhelle );
if ( opposhelle.sh != dummysh ) {
shouldbedelaunay = 0;
}
}
if ( shouldbedelaunay ) {
if ( incircle( triorg, tridest, triapex, oppoapex ) > 0.0 ) {
printf( " !! !! Non-Delaunay pair of triangles:\n" );
printf( " First non-Delaunay " );
printtriangle( &triangleloop );
printf( " Second non-Delaunay " );
printtriangle( &oppotri );
horrors++;
}
}
}
triangleloop.tri = triangletraverse();
}
if ( horrors == 0 ) {
if ( !quiet ) {
printf(
" By virtue of my perceptive intelligence, I declare the mesh Delaunay.\n" );
}
}
else if ( horrors == 1 ) {
printf(
" !! !! !! !! Precisely one terrifying transgression identified.\n" );
}
else {
printf( " !! !! !! !! %d obscenities viewed with horror.\n", horrors );
}
/* Restore the status of exact arithmetic. */
noexact = saveexact;
}
#endif /* not REDUCED */
/*****************************************************************************/
/* */
/* enqueuebadtri() Add a bad triangle to the end of a queue. */
/* */
/* The queue is actually a set of 64 queues. I use multiple queues to give */
/* priority to smaller angles. I originally implemented a heap, but the */
/* queues are (to my surprise) much faster. */
/* */
/*****************************************************************************/
#ifndef CDT_ONLY
void enqueuebadtri( instri, angle, insapex, insorg, insdest )
struct triedge *instri;
REAL angle;
point insapex;
point insorg;
point insdest;
{
struct badface *newface;
int queuenumber;
if ( verbose > 2 ) {
printf( " Queueing bad triangle:\n" );
printf( " (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", insorg[0],
insorg[1], insdest[0], insdest[1], insapex[0], insapex[1] );
}
/* Allocate space for the bad triangle. */
newface = (struct badface *) poolalloc( &badtriangles );
triedgecopy( *instri, newface->badfacetri );
newface->key = angle;
newface->faceapex = insapex;
newface->faceorg = insorg;
newface->facedest = insdest;
newface->nextface = (struct badface *) NULL;
/* Determine the appropriate queue to put the bad triangle into. */
if ( angle > 0.6 ) {
queuenumber = (int) ( 160.0 * ( angle - 0.6 ) );
if ( queuenumber > 63 ) {
queuenumber = 63;
}
}
else {
/* It's not a bad angle; put the triangle in the lowest-priority queue. */
queuenumber = 0;
}
/* Add the triangle to the end of a queue. */
*queuetail[queuenumber] = newface;
/* Maintain a pointer to the NULL pointer at the end of the queue. */
queuetail[queuenumber] = &newface->nextface;
}
#endif /* not CDT_ONLY */
/*****************************************************************************/
/* */
/* dequeuebadtri() Remove a triangle from the front of the queue. */
/* */
/*****************************************************************************/
#ifndef CDT_ONLY
struct badface *dequeuebadtri(){
struct badface *result;
int queuenumber;
/* Look for a nonempty queue. */
for ( queuenumber = 63; queuenumber >= 0; queuenumber-- ) {
result = queuefront[queuenumber];
if ( result != (struct badface *) NULL ) {
/* Remove the triangle from the queue. */
queuefront[queuenumber] = result->nextface;
/* Maintain a pointer to the NULL pointer at the end of the queue. */
if ( queuefront[queuenumber] == (struct badface *) NULL ) {
queuetail[queuenumber] = &queuefront[queuenumber];
}
return result;
}
}
return (struct badface *) NULL;
}
#endif /* not CDT_ONLY */
/*****************************************************************************/
/* */
/* checkedge4encroach() Check a segment to see if it is encroached; add */
/* it to the list if it is. */
/* */
/* An encroached segment is an unflippable edge that has a point in its */
/* diametral circle (that is, it faces an angle greater than 90 degrees). */
/* This definition is due to Ruppert. */
/* */
/* Returns a nonzero value if the edge is encroached. */
/* */
/*****************************************************************************/
#ifndef CDT_ONLY
int checkedge4encroach( testedge )
struct edge *testedge;
{
struct triedge neighbortri;
struct edge testsym;
struct edge *badedge;
int addtolist;
int sides;
point eorg, edest, eapex;
triangle ptr; /* Temporary variable used by stpivot(). */
addtolist = 0;
sides = 0;
sorg( *testedge, eorg );
sdest( *testedge, edest );
/* Check one neighbor of the shell edge. */
stpivot( *testedge, neighbortri );
/* Does the neighbor exist, or is this a boundary edge? */
if ( neighbortri.tri != dummytri ) {
sides++;
/* Find a vertex opposite this edge. */
apex( neighbortri, eapex );
/* Check whether the vertex is inside the diametral circle of the */
/* shell edge. Pythagoras' Theorem is used to check whether the */
/* angle at the vertex is greater than 90 degrees. */
if ( eapex[0] * ( eorg[0] + edest[0] ) + eapex[1] * ( eorg[1] + edest[1] ) >
eapex[0] * eapex[0] + eorg[0] * edest[0] +
eapex[1] * eapex[1] + eorg[1] * edest[1] ) {
addtolist = 1;
}
}
/* Check the other neighbor of the shell edge. */
ssym( *testedge, testsym );
stpivot( testsym, neighbortri );
/* Does the neighbor exist, or is this a boundary edge? */
if ( neighbortri.tri != dummytri ) {
sides++;
/* Find the other vertex opposite this edge. */
apex( neighbortri, eapex );
/* Check whether the vertex is inside the diametral circle of the */
/* shell edge. Pythagoras' Theorem is used to check whether the */
/* angle at the vertex is greater than 90 degrees. */
if ( eapex[0] * ( eorg[0] + edest[0] ) +
eapex[1] * ( eorg[1] + edest[1] ) >
eapex[0] * eapex[0] + eorg[0] * edest[0] +
eapex[1] * eapex[1] + eorg[1] * edest[1] ) {
addtolist += 2;
}
}
if ( addtolist && ( !nobisect || ( ( nobisect == 1 ) && ( sides == 2 ) ) ) ) {
if ( verbose > 2 ) {
printf( " Queueing encroached segment (%.12g, %.12g) (%.12g, %.12g).\n",
eorg[0], eorg[1], edest[0], edest[1] );
}
/* Add the shell edge to the list of encroached segments. */
/* Be sure to get the orientation right. */
badedge = (struct edge *) poolalloc( &badsegments );
if ( addtolist == 1 ) {
shellecopy( *testedge, *badedge );
}
else {
shellecopy( testsym, *badedge );
}
}
return addtolist;
}
#endif /* not CDT_ONLY */
/*****************************************************************************/
/* */
/* testtriangle() Test a face for quality measures. */
/* */
/* Tests a triangle to see if it satisfies the minimum angle condition and */
/* the maximum area condition. Triangles that aren't up to spec are added */
/* to the bad triangle queue. */
/* */
/*****************************************************************************/
#ifndef CDT_ONLY
void testtriangle( testtri )
struct triedge *testtri;
{
struct triedge sametesttri;
struct edge edge1, edge2;
point torg, tdest, tapex;
point anglevertex;
REAL dxod, dyod, dxda, dyda, dxao, dyao;
REAL dxod2, dyod2, dxda2, dyda2, dxao2, dyao2;
REAL apexlen, orglen, destlen;
REAL angle;
REAL area;
shelle sptr; /* Temporary variable used by tspivot(). */
org( *testtri, torg );
dest( *testtri, tdest );
apex( *testtri, tapex );
dxod = torg[0] - tdest[0];
dyod = torg[1] - tdest[1];
dxda = tdest[0] - tapex[0];
dyda = tdest[1] - tapex[1];
dxao = tapex[0] - torg[0];
dyao = tapex[1] - torg[1];
dxod2 = dxod * dxod;
dyod2 = dyod * dyod;
dxda2 = dxda * dxda;
dyda2 = dyda * dyda;
dxao2 = dxao * dxao;
dyao2 = dyao * dyao;
/* Find the lengths of the triangle's three edges. */
apexlen = dxod2 + dyod2;
orglen = dxda2 + dyda2;
destlen = dxao2 + dyao2;
if ( ( apexlen < orglen ) && ( apexlen < destlen ) ) {
/* The edge opposite the apex is shortest. */
/* Find the square of the cosine of the angle at the apex. */
angle = dxda * dxao + dyda * dyao;
angle = angle * angle / ( orglen * destlen );
anglevertex = tapex;
lnext( *testtri, sametesttri );
tspivot( sametesttri, edge1 );
lnextself( sametesttri );
tspivot( sametesttri, edge2 );
}
else if ( orglen < destlen ) {
/* The edge opposite the origin is shortest. */
/* Find the square of the cosine of the angle at the origin. */
angle = dxod * dxao + dyod * dyao;
angle = angle * angle / ( apexlen * destlen );
anglevertex = torg;
tspivot( *testtri, edge1 );
lprev( *testtri, sametesttri );
tspivot( sametesttri, edge2 );
}
else {
/* The edge opposite the destination is shortest. */
/* Find the square of the cosine of the angle at the destination. */
angle = dxod * dxda + dyod * dyda;
angle = angle * angle / ( apexlen * orglen );
anglevertex = tdest;
tspivot( *testtri, edge1 );
lnext( *testtri, sametesttri );
tspivot( sametesttri, edge2 );
}
/* Check if both edges that form the angle are segments. */
if ( ( edge1.sh != dummysh ) && ( edge2.sh != dummysh ) ) {
/* The angle is a segment intersection. */
if ( ( angle > 0.9924 ) && !quiet ) { /* Roughly 5 degrees. */
if ( angle > 1.0 ) {
/* Beware of a floating exception in acos(). */
angle = 1.0;
}
/* Find the actual angle in degrees, for printing. */
angle = acos( sqrt( angle ) ) * ( 180.0 / PI );
printf(
"Warning: Small angle (%.4g degrees) between segments at point\n",
angle );
printf( " (%.12g, %.12g)\n", anglevertex[0], anglevertex[1] );
}
/* Don't add this bad triangle to the list; there's nothing that */
/* can be done about a small angle between two segments. */
angle = 0.0;
}
/* Check whether the angle is smaller than permitted. */
if ( angle > goodangle ) {
/* Add this triangle to the list of bad triangles. */
enqueuebadtri( testtri, angle, tapex, torg, tdest );
return;
}
if ( vararea || fixedarea ) {
/* Check whether the area is larger than permitted. */
area = 0.5 * ( dxod * dyda - dyod * dxda );
if ( fixedarea && ( area > maxarea ) ) {
/* Add this triangle to the list of bad triangles. */
enqueuebadtri( testtri, angle, tapex, torg, tdest );
}
else if ( vararea ) {
/* Nonpositive area constraints are treated as unconstrained. */
if ( ( area > areabound( *testtri ) ) && ( areabound( *testtri ) > 0.0 ) ) {
/* Add this triangle to the list of bad triangles. */
enqueuebadtri( testtri, angle, tapex, torg, tdest );
}
}
}
}
#endif /* not CDT_ONLY */
/** **/
/** **/
/********* Mesh quality testing routines end here *********/
/********* Point location routines begin here *********/
/** **/
/** **/
/*****************************************************************************/
/* */
/* makepointmap() Construct a mapping from points to triangles to improve */
/* the speed of point location for segment insertion. */
/* */
/* Traverses all the triangles, and provides each corner of each triangle */
/* with a pointer to that triangle. Of course, pointers will be */
/* overwritten by other pointers because (almost) each point is a corner */
/* of several triangles, but in the end every point will point to some */
/* triangle that contains it. */
/* */
/*****************************************************************************/
void makepointmap(){
struct triedge triangleloop;
point triorg;
if ( verbose ) {
printf( " Constructing mapping from points to triangles.\n" );
}
traversalinit( &triangles );
triangleloop.tri = triangletraverse();
while ( triangleloop.tri != (triangle *) NULL ) {
/* Check all three points of the triangle. */
for ( triangleloop.orient = 0; triangleloop.orient < 3;
triangleloop.orient++ ) {
org( triangleloop, triorg );
setpoint2tri( triorg, encode( triangleloop ) );
}
triangleloop.tri = triangletraverse();
}
}
/*****************************************************************************/
/* */
/* preciselocate() Find a triangle or edge containing a given point. */
/* */
/* Begins its search from `searchtri'. It is important that `searchtri' */
/* be a handle with the property that `searchpoint' is strictly to the left */
/* of the edge denoted by `searchtri', or is collinear with that edge and */
/* does not intersect that edge. (In particular, `searchpoint' should not */
/* be the origin or destination of that edge.) */
/* */
/* These conditions are imposed because preciselocate() is normally used in */
/* one of two situations: */
/* */
/* (1) To try to find the location to insert a new point. Normally, we */
/* know an edge that the point is strictly to the left of. In the */
/* incremental Delaunay algorithm, that edge is a bounding box edge. */
/* In Ruppert's Delaunay refinement algorithm for quality meshing, */
/* that edge is the shortest edge of the triangle whose circumcenter */
/* is being inserted. */
/* */
/* (2) To try to find an existing point. In this case, any edge on the */
/* convex hull is a good starting edge. The possibility that the */
/* vertex one seeks is an endpoint of the starting edge must be */
/* screened out before preciselocate() is called. */
/* */
/* On completion, `searchtri' is a triangle that contains `searchpoint'. */
/* */
/* This implementation differs from that given by Guibas and Stolfi. It */
/* walks from triangle to triangle, crossing an edge only if `searchpoint' */
/* is on the other side of the line containing that edge. After entering */
/* a triangle, there are two edges by which one can leave that triangle. */
/* If both edges are valid (`searchpoint' is on the other side of both */
/* edges), one of the two is chosen by drawing a line perpendicular to */
/* the entry edge (whose endpoints are `forg' and `fdest') passing through */
/* `fapex'. Depending on which side of this perpendicular `searchpoint' */
/* falls on, an exit edge is chosen. */
/* */
/* This implementation is empirically faster than the Guibas and Stolfi */
/* point location routine (which I originally used), which tends to spiral */
/* in toward its target. */
/* */
/* Returns ONVERTEX if the point lies on an existing vertex. `searchtri' */
/* is a handle whose origin is the existing vertex. */
/* */
/* Returns ONEDGE if the point lies on a mesh edge. `searchtri' is a */
/* handle whose primary edge is the edge on which the point lies. */
/* */
/* Returns INTRIANGLE if the point lies strictly within a triangle. */
/* `searchtri' is a handle on the triangle that contains the point. */
/* */
/* Returns OUTSIDE if the point lies outside the mesh. `searchtri' is a */
/* handle whose primary edge the point is to the right of. This might */
/* occur when the circumcenter of a triangle falls just slightly outside */
/* the mesh due to floating-point roundoff error. It also occurs when */
/* seeking a hole or region point that a foolish user has placed outside */
/* the mesh. */
/* */
/* WARNING: This routine is designed for convex triangulations, and will */
/* not generally work after the holes and concavities have been carved. */
/* However, it can still be used to find the circumcenter of a triangle, as */
/* long as the search is begun from the triangle in question. */
/* */
/*****************************************************************************/
enum locateresult preciselocate( searchpoint, searchtri )
point searchpoint;
struct triedge *searchtri;
{
struct triedge backtracktri;
point forg, fdest, fapex;
point swappoint;
REAL orgorient, destorient;
int moveleft;
triangle ptr; /* Temporary variable used by sym(). */
if ( verbose > 2 ) {
printf( " Searching for point (%.12g, %.12g).\n",
searchpoint[0], searchpoint[1] );
}
/* Where are we? */
org( *searchtri, forg );
dest( *searchtri, fdest );
apex( *searchtri, fapex );
while ( 1 ) {
if ( verbose > 2 ) {
printf( " At (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
forg[0], forg[1], fdest[0], fdest[1], fapex[0], fapex[1] );
}
/* Check whether the apex is the point we seek. */
if ( ( fapex[0] == searchpoint[0] ) && ( fapex[1] == searchpoint[1] ) ) {
lprevself( *searchtri );
return ONVERTEX;
}
/* Does the point lie on the other side of the line defined by the */
/* triangle edge opposite the triangle's destination? */
destorient = counterclockwise( forg, fapex, searchpoint );
/* Does the point lie on the other side of the line defined by the */
/* triangle edge opposite the triangle's origin? */
orgorient = counterclockwise( fapex, fdest, searchpoint );
if ( destorient > 0.0 ) {
if ( orgorient > 0.0 ) {
/* Move left if the inner product of (fapex - searchpoint) and */
/* (fdest - forg) is positive. This is equivalent to drawing */
/* a line perpendicular to the line (forg, fdest) passing */
/* through `fapex', and determining which side of this line */
/* `searchpoint' falls on. */
moveleft = ( fapex[0] - searchpoint[0] ) * ( fdest[0] - forg[0] ) +
( fapex[1] - searchpoint[1] ) * ( fdest[1] - forg[1] ) > 0.0;
}
else {
moveleft = 1;
}
}
else {
if ( orgorient > 0.0 ) {
moveleft = 0;
}
else {
/* The point we seek must be on the boundary of or inside this */
/* triangle. */
if ( destorient == 0.0 ) {
lprevself( *searchtri );
return ONEDGE;
}
if ( orgorient == 0.0 ) {
lnextself( *searchtri );
return ONEDGE;
}
return INTRIANGLE;
}
}
/* Move to another triangle. Leave a trace `backtracktri' in case */
/* floating-point roundoff or some such bogey causes us to walk */
/* off a boundary of the triangulation. We can just bounce off */
/* the boundary as if it were an elastic band. */
if ( moveleft ) {
lprev( *searchtri, backtracktri );
fdest = fapex;
}
else {
lnext( *searchtri, backtracktri );
forg = fapex;
}
sym( backtracktri, *searchtri );
/* Check for walking off the edge. */
if ( searchtri->tri == dummytri ) {
/* Turn around. */
triedgecopy( backtracktri, *searchtri );
swappoint = forg;
forg = fdest;
fdest = swappoint;
apex( *searchtri, fapex );
/* Check if the point really is beyond the triangulation boundary. */
destorient = counterclockwise( forg, fapex, searchpoint );
orgorient = counterclockwise( fapex, fdest, searchpoint );
if ( ( orgorient < 0.0 ) && ( destorient < 0.0 ) ) {
return OUTSIDE;
}
}
else {
apex( *searchtri, fapex );
}
}
}
/*****************************************************************************/
/* */
/* locate() Find a triangle or edge containing a given point. */
/* */
/* Searching begins from one of: the input `searchtri', a recently */
/* encountered triangle `recenttri', or from a triangle chosen from a */
/* random sample. The choice is made by determining which triangle's */
/* origin is closest to the point we are searcing for. Normally, */
/* `searchtri' should be a handle on the convex hull of the triangulation. */
/* */
/* Details on the random sampling method can be found in the Mucke, Saias, */
/* and Zhu paper cited in the header of this code. */
/* */
/* On completion, `searchtri' is a triangle that contains `searchpoint'. */
/* */
/* Returns ONVERTEX if the point lies on an existing vertex. `searchtri' */
/* is a handle whose origin is the existing vertex. */
/* */
/* Returns ONEDGE if the point lies on a mesh edge. `searchtri' is a */
/* handle whose primary edge is the edge on which the point lies. */
/* */
/* Returns INTRIANGLE if the point lies strictly within a triangle. */
/* `searchtri' is a handle on the triangle that contains the point. */
/* */
/* Returns OUTSIDE if the point lies outside the mesh. `searchtri' is a */
/* handle whose primary edge the point is to the right of. This might */
/* occur when the circumcenter of a triangle falls just slightly outside */
/* the mesh due to floating-point roundoff error. It also occurs when */
/* seeking a hole or region point that a foolish user has placed outside */
/* the mesh. */
/* */
/* WARNING: This routine is designed for convex triangulations, and will */
/* not generally work after the holes and concavities have been carved. */
/* */
/*****************************************************************************/
enum locateresult locate( searchpoint, searchtri )
point searchpoint;
struct triedge *searchtri;
{
VOID **sampleblock;
triangle *firsttri;
struct triedge sampletri;
point torg, tdest;
unsigned long alignptr;
REAL searchdist, dist;
REAL ahead;
long sampleblocks, samplesperblock, samplenum;
long triblocks;
long i, j;
triangle ptr; /* Temporary variable used by sym(). */
if ( verbose > 2 ) {
printf( " Randomly sampling for a triangle near point (%.12g, %.12g).\n",
searchpoint[0], searchpoint[1] );
}
/* Record the distance from the suggested starting triangle to the */
/* point we seek. */
org( *searchtri, torg );
searchdist = ( searchpoint[0] - torg[0] ) * ( searchpoint[0] - torg[0] )
+ ( searchpoint[1] - torg[1] ) * ( searchpoint[1] - torg[1] );
if ( verbose > 2 ) {
printf( " Boundary triangle has origin (%.12g, %.12g).\n",
torg[0], torg[1] );
}
/* If a recently encountered triangle has been recorded and has not been */
/* deallocated, test it as a good starting point. */
if ( recenttri.tri != (triangle *) NULL ) {
if ( recenttri.tri[3] != (triangle) NULL ) {
org( recenttri, torg );
if ( ( torg[0] == searchpoint[0] ) && ( torg[1] == searchpoint[1] ) ) {
triedgecopy( recenttri, *searchtri );
return ONVERTEX;
}
dist = ( searchpoint[0] - torg[0] ) * ( searchpoint[0] - torg[0] )
+ ( searchpoint[1] - torg[1] ) * ( searchpoint[1] - torg[1] );
if ( dist < searchdist ) {
triedgecopy( recenttri, *searchtri );
searchdist = dist;
if ( verbose > 2 ) {
printf( " Choosing recent triangle with origin (%.12g, %.12g).\n",
torg[0], torg[1] );
}
}
}
}
/* The number of random samples taken is proportional to the cube root of */
/* the number of triangles in the mesh. The next bit of code assumes */
/* that the number of triangles increases monotonically. */
while ( SAMPLEFACTOR * samples * samples * samples < triangles.items ) {
samples++;
}
triblocks = ( triangles.maxitems + TRIPERBLOCK - 1 ) / TRIPERBLOCK;
samplesperblock = 1 + ( samples / triblocks );
sampleblocks = samples / samplesperblock;
sampleblock = triangles.firstblock;
sampletri.orient = 0;
for ( i = 0; i < sampleblocks; i++ ) {
alignptr = (unsigned long) ( sampleblock + 1 );
firsttri = (triangle *) ( alignptr + (unsigned long) triangles.alignbytes
- ( alignptr % (unsigned long) triangles.alignbytes ) );
for ( j = 0; j < samplesperblock; j++ ) {
if ( i == triblocks - 1 ) {
samplenum = randomnation( (int)
( triangles.maxitems - ( i * TRIPERBLOCK ) ) );
}
else {
samplenum = randomnation( TRIPERBLOCK );
}
sampletri.tri = (triangle *)
( firsttri + ( samplenum * triangles.itemwords ) );
if ( sampletri.tri[3] != (triangle) NULL ) {
org( sampletri, torg );
dist = ( searchpoint[0] - torg[0] ) * ( searchpoint[0] - torg[0] )
+ ( searchpoint[1] - torg[1] ) * ( searchpoint[1] - torg[1] );
if ( dist < searchdist ) {
triedgecopy( sampletri, *searchtri );
searchdist = dist;
if ( verbose > 2 ) {
printf( " Choosing triangle with origin (%.12g, %.12g).\n",
torg[0], torg[1] );
}
}
}
}
sampleblock = (VOID **) *sampleblock;
}
/* Where are we? */
org( *searchtri, torg );
dest( *searchtri, tdest );
/* Check the starting triangle's vertices. */
if ( ( torg[0] == searchpoint[0] ) && ( torg[1] == searchpoint[1] ) ) {
return ONVERTEX;
}
if ( ( tdest[0] == searchpoint[0] ) && ( tdest[1] == searchpoint[1] ) ) {
lnextself( *searchtri );
return ONVERTEX;
}
/* Orient `searchtri' to fit the preconditions of calling preciselocate(). */
ahead = counterclockwise( torg, tdest, searchpoint );
if ( ahead < 0.0 ) {
/* Turn around so that `searchpoint' is to the left of the */
/* edge specified by `searchtri'. */
symself( *searchtri );
}
else if ( ahead == 0.0 ) {
/* Check if `searchpoint' is between `torg' and `tdest'. */
if ( ( ( torg[0] < searchpoint[0] ) == ( searchpoint[0] < tdest[0] ) )
&& ( ( torg[1] < searchpoint[1] ) == ( searchpoint[1] < tdest[1] ) ) ) {
return ONEDGE;
}
}
return preciselocate( searchpoint, searchtri );
}
/** **/
/** **/
/********* Point location routines end here *********/
/********* Mesh transformation routines begin here *********/
/** **/
/** **/
/*****************************************************************************/
/* */
/* insertshelle() Create a new shell edge and insert it between two */
/* triangles. */
/* */
/* The new shell edge is inserted at the edge described by the handle */
/* `tri'. Its vertices are properly initialized. The marker `shellemark' */
/* is applied to the shell edge and, if appropriate, its vertices. */
/* */
/*****************************************************************************/
void insertshelle( tri, shellemark )
struct triedge *tri; /* Edge at which to insert the new shell edge. */
int shellemark; /* Marker for the new shell edge. */
{
struct triedge oppotri;
struct edge newshelle;
point triorg, tridest;
triangle ptr; /* Temporary variable used by sym(). */
shelle sptr; /* Temporary variable used by tspivot(). */
/* Mark points if possible. */
org( *tri, triorg );
dest( *tri, tridest );
if ( pointmark( triorg ) == 0 ) {
setpointmark( triorg, shellemark );
}
if ( pointmark( tridest ) == 0 ) {
setpointmark( tridest, shellemark );
}
/* Check if there's already a shell edge here. */
tspivot( *tri, newshelle );
if ( newshelle.sh == dummysh ) {
/* Make new shell edge and initialize its vertices. */
makeshelle( &newshelle );
setsorg( newshelle, tridest );
setsdest( newshelle, triorg );
/* Bond new shell edge to the two triangles it is sandwiched between. */
/* Note that the facing triangle `oppotri' might be equal to */
/* `dummytri' (outer space), but the new shell edge is bonded to it */
/* all the same. */
tsbond( *tri, newshelle );
sym( *tri, oppotri );
ssymself( newshelle );
tsbond( oppotri, newshelle );
setmark( newshelle, shellemark );
if ( verbose > 2 ) {
printf( " Inserting new " );
printshelle( &newshelle );
}
}
else {
if ( mark( newshelle ) == 0 ) {
setmark( newshelle, shellemark );
}
}
}
/*****************************************************************************/
/* */
/* Terminology */
/* */
/* A "local transformation" replaces a small set of triangles with another */
/* set of triangles. This may or may not involve inserting or deleting a */
/* point. */
/* */
/* The term "casing" is used to describe the set of triangles that are */
/* attached to the triangles being transformed, but are not transformed */
/* themselves. Think of the casing as a fixed hollow structure inside */
/* which all the action happens. A "casing" is only defined relative to */
/* a single transformation; each occurrence of a transformation will */
/* involve a different casing. */
/* */
/* A "shell" is similar to a "casing". The term "shell" describes the set */
/* of shell edges (if any) that are attached to the triangles being */
/* transformed. However, I sometimes use "shell" to refer to a single */
/* shell edge, so don't get confused. */
/* */
/*****************************************************************************/
/*****************************************************************************/
/* */
/* flip() Transform two triangles to two different triangles by flipping */
/* an edge within a quadrilateral. */
/* */
/* Imagine the original triangles, abc and bad, oriented so that the */
/* shared edge ab lies in a horizontal plane, with the point b on the left */
/* and the point a on the right. The point c lies below the edge, and the */
/* point d lies above the edge. The `flipedge' handle holds the edge ab */
/* of triangle abc, and is directed left, from vertex a to vertex b. */
/* */
/* The triangles abc and bad are deleted and replaced by the triangles cdb */
/* and dca. The triangles that represent abc and bad are NOT deallocated; */
/* they are reused for dca and cdb, respectively. Hence, any handles that */
/* may have held the original triangles are still valid, although not */
/* directed as they were before. */
/* */
/* Upon completion of this routine, the `flipedge' handle holds the edge */
/* dc of triangle dca, and is directed down, from vertex d to vertex c. */
/* (Hence, the two triangles have rotated counterclockwise.) */
/* */
/* WARNING: This transformation is geometrically valid only if the */
/* quadrilateral adbc is convex. Furthermore, this transformation is */
/* valid only if there is not a shell edge between the triangles abc and */
/* bad. This routine does not check either of these preconditions, and */
/* it is the responsibility of the calling routine to ensure that they are */
/* met. If they are not, the streets shall be filled with wailing and */
/* gnashing of teeth. */
/* */
/*****************************************************************************/
void flip( flipedge )
struct triedge *flipedge; /* Handle for the triangle abc. */
{
struct triedge botleft, botright;
struct triedge topleft, topright;
struct triedge top;
struct triedge botlcasing, botrcasing;
struct triedge toplcasing, toprcasing;
struct edge botlshelle, botrshelle;
struct edge toplshelle, toprshelle;
point leftpoint, rightpoint, botpoint;
point farpoint;
triangle ptr; /* Temporary variable used by sym(). */
shelle sptr; /* Temporary variable used by tspivot(). */
/* Identify the vertices of the quadrilateral. */
org( *flipedge, rightpoint );
dest( *flipedge, leftpoint );
apex( *flipedge, botpoint );
sym( *flipedge, top );
#ifdef SELF_CHECK
if ( top.tri == dummytri ) {
printf( "Internal error in flip(): Attempt to flip on boundary.\n" );
lnextself( *flipedge );
return;
}
if ( checksegments ) {
tspivot( *flipedge, toplshelle );
if ( toplshelle.sh != dummysh ) {
printf( "Internal error in flip(): Attempt to flip a segment.\n" );
lnextself( *flipedge );
return;
}
}
#endif /* SELF_CHECK */
apex( top, farpoint );
/* Identify the casing of the quadrilateral. */
lprev( top, topleft );
sym( topleft, toplcasing );
lnext( top, topright );
sym( topright, toprcasing );
lnext( *flipedge, botleft );
sym( botleft, botlcasing );
lprev( *flipedge, botright );
sym( botright, botrcasing );
/* Rotate the quadrilateral one-quarter turn counterclockwise. */
bond( topleft, botlcasing );
bond( botleft, botrcasing );
bond( botright, toprcasing );
bond( topright, toplcasing );
if ( checksegments ) {
/* Check for shell edges and rebond them to the quadrilateral. */
tspivot( topleft, toplshelle );
tspivot( botleft, botlshelle );
tspivot( botright, botrshelle );
tspivot( topright, toprshelle );
if ( toplshelle.sh == dummysh ) {
tsdissolve( topright );
}
else {
tsbond( topright, toplshelle );
}
if ( botlshelle.sh == dummysh ) {
tsdissolve( topleft );
}
else {
tsbond( topleft, botlshelle );
}
if ( botrshelle.sh == dummysh ) {
tsdissolve( botleft );
}
else {
tsbond( botleft, botrshelle );
}
if ( toprshelle.sh == dummysh ) {
tsdissolve( botright );
}
else {
tsbond( botright, toprshelle );
}
}
/* New point assignments for the rotated quadrilateral. */
setorg( *flipedge, farpoint );
setdest( *flipedge, botpoint );
setapex( *flipedge, rightpoint );
setorg( top, botpoint );
setdest( top, farpoint );
setapex( top, leftpoint );
if ( verbose > 2 ) {
printf( " Edge flip results in left " );
lnextself( topleft );
printtriangle( &topleft );
printf( " and right " );
printtriangle( flipedge );
}
}
/*****************************************************************************/
/* */
/* insertsite() Insert a vertex into a Delaunay triangulation, */
/* performing flips as necessary to maintain the Delaunay */
/* property. */
/* */
/* The point `insertpoint' is located. If `searchtri.tri' is not NULL, */
/* the search for the containing triangle begins from `searchtri'. If */
/* `searchtri.tri' is NULL, a full point location procedure is called. */
/* If `insertpoint' is found inside a triangle, the triangle is split into */
/* three; if `insertpoint' lies on an edge, the edge is split in two, */
/* thereby splitting the two adjacent triangles into four. Edge flips are */
/* used to restore the Delaunay property. If `insertpoint' lies on an */
/* existing vertex, no action is taken, and the value DUPLICATEPOINT is */
/* returned. On return, `searchtri' is set to a handle whose origin is the */
/* existing vertex. */
/* */
/* Normally, the parameter `splitedge' is set to NULL, implying that no */
/* segment should be split. In this case, if `insertpoint' is found to */
/* lie on a segment, no action is taken, and the value VIOLATINGPOINT is */
/* returned. On return, `searchtri' is set to a handle whose primary edge */
/* is the violated segment. */
/* */
/* If the calling routine wishes to split a segment by inserting a point in */
/* it, the parameter `splitedge' should be that segment. In this case, */
/* `searchtri' MUST be the triangle handle reached by pivoting from that */
/* segment; no point location is done. */
/* */
/* `segmentflaws' and `triflaws' are flags that indicate whether or not */
/* there should be checks for the creation of encroached segments or bad */
/* quality faces. If a newly inserted point encroaches upon segments, */
/* these segments are added to the list of segments to be split if */
/* `segmentflaws' is set. If bad triangles are created, these are added */
/* to the queue if `triflaws' is set. */
/* */
/* If a duplicate point or violated segment does not prevent the point */
/* from being inserted, the return value will be ENCROACHINGPOINT if the */
/* point encroaches upon a segment (and checking is enabled), or */
/* SUCCESSFULPOINT otherwise. In either case, `searchtri' is set to a */
/* handle whose origin is the newly inserted vertex. */
/* */
/* insertsite() does not use flip() for reasons of speed; some */
/* information can be reused from edge flip to edge flip, like the */
/* locations of shell edges. */
/* */
/*****************************************************************************/
enum insertsiteresult insertsite( insertpoint, searchtri, splitedge,
segmentflaws, triflaws )
point insertpoint;
struct triedge *searchtri;
struct edge *splitedge;
int segmentflaws;
int triflaws;
{
struct triedge horiz;
struct triedge top;
struct triedge botleft, botright;
struct triedge topleft, topright;
struct triedge newbotleft, newbotright;
struct triedge newtopright;
struct triedge botlcasing, botrcasing;
struct triedge toplcasing, toprcasing;
struct triedge testtri;
struct edge botlshelle, botrshelle;
struct edge toplshelle, toprshelle;
struct edge brokenshelle;
struct edge checkshelle;
struct edge rightedge;
struct edge newedge;
struct edge *encroached;
point first;
point leftpoint, rightpoint, botpoint, toppoint, farpoint;
REAL attrib;
REAL area;
enum insertsiteresult success;
enum locateresult intersect;
int doflip;
int mirrorflag;
int i;
triangle ptr; /* Temporary variable used by sym(). */
shelle sptr; /* Temporary variable used by spivot() and tspivot(). */
if ( verbose > 1 ) {
printf( " Inserting (%.12g, %.12g).\n", insertpoint[0], insertpoint[1] );
}
if ( splitedge == (struct edge *) NULL ) {
/* Find the location of the point to be inserted. Check if a good */
/* starting triangle has already been provided by the caller. */
if ( searchtri->tri == (triangle *) NULL ) {
/* Find a boundary triangle. */
horiz.tri = dummytri;
horiz.orient = 0;
symself( horiz );
/* Search for a triangle containing `insertpoint'. */
intersect = locate( insertpoint, &horiz );
}
else {
/* Start searching from the triangle provided by the caller. */
triedgecopy( *searchtri, horiz );
intersect = preciselocate( insertpoint, &horiz );
}
}
else {
/* The calling routine provides the edge in which the point is inserted. */
triedgecopy( *searchtri, horiz );
intersect = ONEDGE;
}
if ( intersect == ONVERTEX ) {
/* There's already a vertex there. Return in `searchtri' a triangle */
/* whose origin is the existing vertex. */
triedgecopy( horiz, *searchtri );
triedgecopy( horiz, recenttri );
return DUPLICATEPOINT;
}
if ( ( intersect == ONEDGE ) || ( intersect == OUTSIDE ) ) {
/* The vertex falls on an edge or boundary. */
if ( checksegments && ( splitedge == (struct edge *) NULL ) ) {
/* Check whether the vertex falls on a shell edge. */
tspivot( horiz, brokenshelle );
if ( brokenshelle.sh != dummysh ) {
/* The vertex falls on a shell edge. */
if ( segmentflaws ) {
if ( nobisect == 0 ) {
/* Add the shell edge to the list of encroached segments. */
encroached = (struct edge *) poolalloc( &badsegments );
shellecopy( brokenshelle, *encroached );
}
else if ( ( nobisect == 1 ) && ( intersect == ONEDGE ) ) {
/* This segment may be split only if it is an internal boundary. */
sym( horiz, testtri );
if ( testtri.tri != dummytri ) {
/* Add the shell edge to the list of encroached segments. */
encroached = (struct edge *) poolalloc( &badsegments );
shellecopy( brokenshelle, *encroached );
}
}
}
/* Return a handle whose primary edge contains the point, */
/* which has not been inserted. */
triedgecopy( horiz, *searchtri );
triedgecopy( horiz, recenttri );
return VIOLATINGPOINT;
}
}
/* Insert the point on an edge, dividing one triangle into two (if */
/* the edge lies on a boundary) or two triangles into four. */
lprev( horiz, botright );
sym( botright, botrcasing );
sym( horiz, topright );
/* Is there a second triangle? (Or does this edge lie on a boundary?) */
mirrorflag = topright.tri != dummytri;
if ( mirrorflag ) {
lnextself( topright );
sym( topright, toprcasing );
maketriangle( &newtopright );
}
else {
/* Splitting the boundary edge increases the number of boundary edges. */
hullsize++;
}
maketriangle( &newbotright );
/* Set the vertices of changed and new triangles. */
org( horiz, rightpoint );
dest( horiz, leftpoint );
apex( horiz, botpoint );
setorg( newbotright, botpoint );
setdest( newbotright, rightpoint );
setapex( newbotright, insertpoint );
setorg( horiz, insertpoint );
for ( i = 0; i < eextras; i++ ) {
/* Set the element attributes of a new triangle. */
setelemattribute( newbotright, i, elemattribute( botright, i ) );
}
if ( vararea ) {
/* Set the area constraint of a new triangle. */
setareabound( newbotright, areabound( botright ) );
}
if ( mirrorflag ) {
dest( topright, toppoint );
setorg( newtopright, rightpoint );
setdest( newtopright, toppoint );
setapex( newtopright, insertpoint );
setorg( topright, insertpoint );
for ( i = 0; i < eextras; i++ ) {
/* Set the element attributes of another new triangle. */
setelemattribute( newtopright, i, elemattribute( topright, i ) );
}
if ( vararea ) {
/* Set the area constraint of another new triangle. */
setareabound( newtopright, areabound( topright ) );
}
}
/* There may be shell edges that need to be bonded */
/* to the new triangle(s). */
if ( checksegments ) {
tspivot( botright, botrshelle );
if ( botrshelle.sh != dummysh ) {
tsdissolve( botright );
tsbond( newbotright, botrshelle );
}
if ( mirrorflag ) {
tspivot( topright, toprshelle );
if ( toprshelle.sh != dummysh ) {
tsdissolve( topright );
tsbond( newtopright, toprshelle );
}
}
}
/* Bond the new triangle(s) to the surrounding triangles. */
bond( newbotright, botrcasing );
lprevself( newbotright );
bond( newbotright, botright );
lprevself( newbotright );
if ( mirrorflag ) {
bond( newtopright, toprcasing );
lnextself( newtopright );
bond( newtopright, topright );
lnextself( newtopright );
bond( newtopright, newbotright );
}
if ( splitedge != (struct edge *) NULL ) {
/* Split the shell edge into two. */
setsdest( *splitedge, insertpoint );
ssymself( *splitedge );
spivot( *splitedge, rightedge );
insertshelle( &newbotright, mark( *splitedge ) );
tspivot( newbotright, newedge );
sbond( *splitedge, newedge );
ssymself( newedge );
sbond( newedge, rightedge );
ssymself( *splitedge );
}
#ifdef SELF_CHECK
if ( counterclockwise( rightpoint, leftpoint, botpoint ) < 0.0 ) {
printf( "Internal error in insertsite():\n" );
printf( " Clockwise triangle prior to edge point insertion (bottom).\n" );
}
if ( mirrorflag ) {
if ( counterclockwise( leftpoint, rightpoint, toppoint ) < 0.0 ) {
printf( "Internal error in insertsite():\n" );
printf( " Clockwise triangle prior to edge point insertion (top).\n" );
}
if ( counterclockwise( rightpoint, toppoint, insertpoint ) < 0.0 ) {
printf( "Internal error in insertsite():\n" );
printf( " Clockwise triangle after edge point insertion (top right).\n"
);
}
if ( counterclockwise( toppoint, leftpoint, insertpoint ) < 0.0 ) {
printf( "Internal error in insertsite():\n" );
printf( " Clockwise triangle after edge point insertion (top left).\n"
);
}
}
if ( counterclockwise( leftpoint, botpoint, insertpoint ) < 0.0 ) {
printf( "Internal error in insertsite():\n" );
printf( " Clockwise triangle after edge point insertion (bottom left).\n"
);
}
if ( counterclockwise( botpoint, rightpoint, insertpoint ) < 0.0 ) {
printf( "Internal error in insertsite():\n" );
printf(
" Clockwise triangle after edge point insertion (bottom right).\n" );
}
#endif /* SELF_CHECK */
if ( verbose > 2 ) {
printf( " Updating bottom left " );
printtriangle( &botright );
if ( mirrorflag ) {
printf( " Updating top left " );
printtriangle( &topright );
printf( " Creating top right " );
printtriangle( &newtopright );
}
printf( " Creating bottom right " );
printtriangle( &newbotright );
}
/* Position `horiz' on the first edge to check for */
/* the Delaunay property. */
lnextself( horiz );
}
else {
/* Insert the point in a triangle, splitting it into three. */
lnext( horiz, botleft );
lprev( horiz, botright );
sym( botleft, botlcasing );
sym( botright, botrcasing );
maketriangle( &newbotleft );
maketriangle( &newbotright );
/* Set the vertices of changed and new triangles. */
org( horiz, rightpoint );
dest( horiz, leftpoint );
apex( horiz, botpoint );
setorg( newbotleft, leftpoint );
setdest( newbotleft, botpoint );
setapex( newbotleft, insertpoint );
setorg( newbotright, botpoint );
setdest( newbotright, rightpoint );
setapex( newbotright, insertpoint );
setapex( horiz, insertpoint );
for ( i = 0; i < eextras; i++ ) {
/* Set the element attributes of the new triangles. */
attrib = elemattribute( horiz, i );
setelemattribute( newbotleft, i, attrib );
setelemattribute( newbotright, i, attrib );
}
if ( vararea ) {
/* Set the area constraint of the new triangles. */
area = areabound( horiz );
setareabound( newbotleft, area );
setareabound( newbotright, area );
}
/* There may be shell edges that need to be bonded */
/* to the new triangles. */
if ( checksegments ) {
tspivot( botleft, botlshelle );
if ( botlshelle.sh != dummysh ) {
tsdissolve( botleft );
tsbond( newbotleft, botlshelle );
}
tspivot( botright, botrshelle );
if ( botrshelle.sh != dummysh ) {
tsdissolve( botright );
tsbond( newbotright, botrshelle );
}
}
/* Bond the new triangles to the surrounding triangles. */
bond( newbotleft, botlcasing );
bond( newbotright, botrcasing );
lnextself( newbotleft );
lprevself( newbotright );
bond( newbotleft, newbotright );
lnextself( newbotleft );
bond( botleft, newbotleft );
lprevself( newbotright );
bond( botright, newbotright );
#ifdef SELF_CHECK
if ( counterclockwise( rightpoint, leftpoint, botpoint ) < 0.0 ) {
printf( "Internal error in insertsite():\n" );
printf( " Clockwise triangle prior to point insertion.\n" );
}
if ( counterclockwise( rightpoint, leftpoint, insertpoint ) < 0.0 ) {
printf( "Internal error in insertsite():\n" );
printf( " Clockwise triangle after point insertion (top).\n" );
}
if ( counterclockwise( leftpoint, botpoint, insertpoint ) < 0.0 ) {
printf( "Internal error in insertsite():\n" );
printf( " Clockwise triangle after point insertion (left).\n" );
}
if ( counterclockwise( botpoint, rightpoint, insertpoint ) < 0.0 ) {
printf( "Internal error in insertsite():\n" );
printf( " Clockwise triangle after point insertion (right).\n" );
}
#endif /* SELF_CHECK */
if ( verbose > 2 ) {
printf( " Updating top " );
printtriangle( &horiz );
printf( " Creating left " );
printtriangle( &newbotleft );
printf( " Creating right " );
printtriangle( &newbotright );
}
}
/* The insertion is successful by default, unless an encroached */
/* edge is found. */
success = SUCCESSFULPOINT;
/* Circle around the newly inserted vertex, checking each edge opposite */
/* it for the Delaunay property. Non-Delaunay edges are flipped. */
/* `horiz' is always the edge being checked. `first' marks where to */
/* stop circling. */
org( horiz, first );
rightpoint = first;
dest( horiz, leftpoint );
/* Circle until finished. */
while ( 1 ) {
/* By default, the edge will be flipped. */
doflip = 1;
if ( checksegments ) {
/* Check for a segment, which cannot be flipped. */
tspivot( horiz, checkshelle );
if ( checkshelle.sh != dummysh ) {
/* The edge is a segment and cannot be flipped. */
doflip = 0;
#ifndef CDT_ONLY
if ( segmentflaws ) {
/* Does the new point encroach upon this segment? */
if ( checkedge4encroach( &checkshelle ) ) {
success = ENCROACHINGPOINT;
}
}
#endif /* not CDT_ONLY */
}
}
if ( doflip ) {
/* Check if the edge is a boundary edge. */
sym( horiz, top );
if ( top.tri == dummytri ) {
/* The edge is a boundary edge and cannot be flipped. */
doflip = 0;
}
else {
/* Find the point on the other side of the edge. */
apex( top, farpoint );
/* In the incremental Delaunay triangulation algorithm, any of */
/* `leftpoint', `rightpoint', and `farpoint' could be vertices */
/* of the triangular bounding box. These vertices must be */
/* treated as if they are infinitely distant, even though their */
/* "coordinates" are not. */
if ( ( leftpoint == infpoint1 ) || ( leftpoint == infpoint2 )
|| ( leftpoint == infpoint3 ) ) {
/* `leftpoint' is infinitely distant. Check the convexity of */
/* the boundary of the triangulation. 'farpoint' might be */
/* infinite as well, but trust me, this same condition */
/* should be applied. */
doflip = counterclockwise( insertpoint, rightpoint, farpoint ) > 0.0;
}
else if ( ( rightpoint == infpoint1 ) || ( rightpoint == infpoint2 )
|| ( rightpoint == infpoint3 ) ) {
/* `rightpoint' is infinitely distant. Check the convexity of */
/* the boundary of the triangulation. 'farpoint' might be */
/* infinite as well, but trust me, this same condition */
/* should be applied. */
doflip = counterclockwise( farpoint, leftpoint, insertpoint ) > 0.0;
}
else if ( ( farpoint == infpoint1 ) || ( farpoint == infpoint2 )
|| ( farpoint == infpoint3 ) ) {
/* `farpoint' is infinitely distant and cannot be inside */
/* the circumcircle of the triangle `horiz'. */
doflip = 0;
}
else {
/* Test whether the edge is locally Delaunay. */
doflip = incircle( leftpoint, insertpoint, rightpoint, farpoint )
> 0.0;
}
if ( doflip ) {
/* We made it! Flip the edge `horiz' by rotating its containing */
/* quadrilateral (the two triangles adjacent to `horiz'). */
/* Identify the casing of the quadrilateral. */
lprev( top, topleft );
sym( topleft, toplcasing );
lnext( top, topright );
sym( topright, toprcasing );
lnext( horiz, botleft );
sym( botleft, botlcasing );
lprev( horiz, botright );
sym( botright, botrcasing );
/* Rotate the quadrilateral one-quarter turn counterclockwise. */
bond( topleft, botlcasing );
bond( botleft, botrcasing );
bond( botright, toprcasing );
bond( topright, toplcasing );
if ( checksegments ) {
/* Check for shell edges and rebond them to the quadrilateral. */
tspivot( topleft, toplshelle );
tspivot( botleft, botlshelle );
tspivot( botright, botrshelle );
tspivot( topright, toprshelle );
if ( toplshelle.sh == dummysh ) {
tsdissolve( topright );
}
else {
tsbond( topright, toplshelle );
}
if ( botlshelle.sh == dummysh ) {
tsdissolve( topleft );
}
else {
tsbond( topleft, botlshelle );
}
if ( botrshelle.sh == dummysh ) {
tsdissolve( botleft );
}
else {
tsbond( botleft, botrshelle );
}
if ( toprshelle.sh == dummysh ) {
tsdissolve( botright );
}
else {
tsbond( botright, toprshelle );
}
}
/* New point assignments for the rotated quadrilateral. */
setorg( horiz, farpoint );
setdest( horiz, insertpoint );
setapex( horiz, rightpoint );
setorg( top, insertpoint );
setdest( top, farpoint );
setapex( top, leftpoint );
for ( i = 0; i < eextras; i++ ) {
/* Take the average of the two triangles' attributes. */
attrib = (REAL)( 0.5 * ( elemattribute( top, i ) + elemattribute( horiz, i ) ) );
setelemattribute( top, i, attrib );
setelemattribute( horiz, i, attrib );
}
if ( vararea ) {
if ( ( areabound( top ) <= 0.0 ) || ( areabound( horiz ) <= 0.0 ) ) {
area = -1.0;
}
else {
/* Take the average of the two triangles' area constraints. */
/* This prevents small area constraints from migrating a */
/* long, long way from their original location due to flips. */
area = (REAL)( 0.5 * ( areabound( top ) + areabound( horiz ) ) );
}
setareabound( top, area );
setareabound( horiz, area );
}
#ifdef SELF_CHECK
if ( insertpoint != (point) NULL ) {
if ( counterclockwise( leftpoint, insertpoint, rightpoint ) < 0.0 ) {
printf( "Internal error in insertsite():\n" );
printf( " Clockwise triangle prior to edge flip (bottom).\n" );
}
/* The following test has been removed because constrainededge() */
/* sometimes generates inverted triangles that insertsite() */
/* removes. */
/*
if (counterclockwise(rightpoint, farpoint, leftpoint) < 0.0) {
printf("Internal error in insertsite():\n");
printf(" Clockwise triangle prior to edge flip (top).\n");
}
*/
if ( counterclockwise( farpoint, leftpoint, insertpoint ) < 0.0 ) {
printf( "Internal error in insertsite():\n" );
printf( " Clockwise triangle after edge flip (left).\n" );
}
if ( counterclockwise( insertpoint, rightpoint, farpoint ) < 0.0 ) {
printf( "Internal error in insertsite():\n" );
printf( " Clockwise triangle after edge flip (right).\n" );
}
}
#endif /* SELF_CHECK */
if ( verbose > 2 ) {
printf( " Edge flip results in left " );
lnextself( topleft );
printtriangle( &topleft );
printf( " and right " );
printtriangle( &horiz );
}
/* On the next iterations, consider the two edges that were */
/* exposed (this is, are now visible to the newly inserted */
/* point) by the edge flip. */
lprevself( horiz );
leftpoint = farpoint;
}
}
}
if ( !doflip ) {
/* The handle `horiz' is accepted as locally Delaunay. */
#ifndef CDT_ONLY
if ( triflaws ) {
/* Check the triangle `horiz' for quality. */
testtriangle( &horiz );
}
#endif /* not CDT_ONLY */
/* Look for the next edge around the newly inserted point. */
lnextself( horiz );
sym( horiz, testtri );
/* Check for finishing a complete revolution about the new point, or */
/* falling off the edge of the triangulation. The latter will */
/* happen when a point is inserted at a boundary. */
if ( ( leftpoint == first ) || ( testtri.tri == dummytri ) ) {
/* We're done. Return a triangle whose origin is the new point. */
lnext( horiz, *searchtri );
lnext( horiz, recenttri );
return success;
}
/* Finish finding the next edge around the newly inserted point. */
lnext( testtri, horiz );
rightpoint = leftpoint;
dest( horiz, leftpoint );
}
}
}
/*****************************************************************************/
/* */
/* triangulatepolygon() Find the Delaunay triangulation of a polygon that */
/* has a certain "nice" shape. This includes the */
/* polygons that result from deletion of a point or */
/* insertion of a segment. */
/* */
/* This is a conceptually difficult routine. The starting assumption is */
/* that we have a polygon with n sides. n - 1 of these sides are currently */
/* represented as edges in the mesh. One side, called the "base", need not */
/* be. */
/* */
/* Inside the polygon is a structure I call a "fan", consisting of n - 1 */
/* triangles that share a common origin. For each of these triangles, the */
/* edge opposite the origin is one of the sides of the polygon. The */
/* primary edge of each triangle is the edge directed from the origin to */
/* the destination; note that this is not the same edge that is a side of */
/* the polygon. `firstedge' is the primary edge of the first triangle. */
/* From there, the triangles follow in counterclockwise order about the */
/* polygon, until `lastedge', the primary edge of the last triangle. */
/* `firstedge' and `lastedge' are probably connected to other triangles */
/* beyond the extremes of the fan, but their identity is not important, as */
/* long as the fan remains connected to them. */
/* */
/* Imagine the polygon oriented so that its base is at the bottom. This */
/* puts `firstedge' on the far right, and `lastedge' on the far left. */
/* The right vertex of the base is the destination of `firstedge', and the */
/* left vertex of the base is the apex of `lastedge'. */
/* */
/* The challenge now is to find the right sequence of edge flips to */
/* transform the fan into a Delaunay triangulation of the polygon. Each */
/* edge flip effectively removes one triangle from the fan, committing it */
/* to the polygon. The resulting polygon has one fewer edge. If `doflip' */
/* is set, the final flip will be performed, resulting in a fan of one */
/* (useless?) triangle. If `doflip' is not set, the final flip is not */
/* performed, resulting in a fan of two triangles, and an unfinished */
/* triangular polygon that is not yet filled out with a single triangle. */
/* On completion of the routine, `lastedge' is the last remaining triangle, */
/* or the leftmost of the last two. */
/* */
/* Although the flips are performed in the order described above, the */
/* decisions about what flips to perform are made in precisely the reverse */
/* order. The recursive triangulatepolygon() procedure makes a decision, */
/* uses up to two recursive calls to triangulate the "subproblems" */
/* (polygons with fewer edges), and then performs an edge flip. */
/* */
/* The "decision" it makes is which vertex of the polygon should be */
/* connected to the base. This decision is made by testing every possible */
/* vertex. Once the best vertex is found, the two edges that connect this */
/* vertex to the base become the bases for two smaller polygons. These */
/* are triangulated recursively. Unfortunately, this approach can take */
/* O(n^2) time not only in the worst case, but in many common cases. It's */
/* rarely a big deal for point deletion, where n is rarely larger than ten, */
/* but it could be a big deal for segment insertion, especially if there's */
/* a lot of long segments that each cut many triangles. I ought to code */
/* a faster algorithm some time. */
/* */
/* The `edgecount' parameter is the number of sides of the polygon, */
/* including its base. `triflaws' is a flag that determines whether the */
/* new triangles should be tested for quality, and enqueued if they are */
/* bad. */
/* */
/*****************************************************************************/
void triangulatepolygon( firstedge, lastedge, edgecount, doflip, triflaws )
struct triedge *firstedge;
struct triedge *lastedge;
int edgecount;
int doflip;
int triflaws;
{
struct triedge testtri;
struct triedge besttri;
struct triedge tempedge;
point leftbasepoint, rightbasepoint;
point testpoint;
point bestpoint;
int bestnumber;
int i;
triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */
/* Identify the base vertices. */
apex( *lastedge, leftbasepoint );
dest( *firstedge, rightbasepoint );
if ( verbose > 2 ) {
printf( " Triangulating interior polygon at edge\n" );
printf( " (%.12g, %.12g) (%.12g, %.12g)\n", leftbasepoint[0],
leftbasepoint[1], rightbasepoint[0], rightbasepoint[1] );
}
/* Find the best vertex to connect the base to. */
onext( *firstedge, besttri );
dest( besttri, bestpoint );
triedgecopy( besttri, testtri );
bestnumber = 1;
for ( i = 2; i <= edgecount - 2; i++ ) {
onextself( testtri );
dest( testtri, testpoint );
/* Is this a better vertex? */
if ( incircle( leftbasepoint, rightbasepoint, bestpoint, testpoint ) > 0.0 ) {
triedgecopy( testtri, besttri );
bestpoint = testpoint;
bestnumber = i;
}
}
if ( verbose > 2 ) {
printf( " Connecting edge to (%.12g, %.12g)\n", bestpoint[0],
bestpoint[1] );
}
if ( bestnumber > 1 ) {
/* Recursively triangulate the smaller polygon on the right. */
oprev( besttri, tempedge );
triangulatepolygon( firstedge, &tempedge, bestnumber + 1, 1, triflaws );
}
if ( bestnumber < edgecount - 2 ) {
/* Recursively triangulate the smaller polygon on the left. */
sym( besttri, tempedge );
triangulatepolygon( &besttri, lastedge, edgecount - bestnumber, 1,
triflaws );
/* Find `besttri' again; it may have been lost to edge flips. */
sym( tempedge, besttri );
}
if ( doflip ) {
/* Do one final edge flip. */
flip( &besttri );
#ifndef CDT_ONLY
if ( triflaws ) {
/* Check the quality of the newly committed triangle. */
sym( besttri, testtri );
testtriangle( &testtri );
}
#endif /* not CDT_ONLY */
}
/* Return the base triangle. */
triedgecopy( besttri, *lastedge );
}
/*****************************************************************************/
/* */
/* deletesite() Delete a vertex from a Delaunay triangulation, ensuring */
/* that the triangulation remains Delaunay. */
/* */
/* The origin of `deltri' is deleted. The union of the triangles adjacent */
/* to this point is a polygon, for which the Delaunay triangulation is */
/* found. Two triangles are removed from the mesh. */
/* */
/* Only interior points that do not lie on segments (shell edges) or */
/* boundaries may be deleted. */
/* */
/*****************************************************************************/
#ifndef CDT_ONLY
void deletesite( deltri )
struct triedge *deltri;
{
struct triedge countingtri;
struct triedge firstedge, lastedge;
struct triedge deltriright;
struct triedge lefttri, righttri;
struct triedge leftcasing, rightcasing;
struct edge leftshelle, rightshelle;
point delpoint;
point neworg;
int edgecount;
triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */
shelle sptr; /* Temporary variable used by tspivot(). */
org( *deltri, delpoint );
if ( verbose > 1 ) {
printf( " Deleting (%.12g, %.12g).\n", delpoint[0], delpoint[1] );
}
pointdealloc( delpoint );
/* Count the degree of the point being deleted. */
onext( *deltri, countingtri );
edgecount = 1;
while ( !triedgeequal( *deltri, countingtri ) ) {
#ifdef SELF_CHECK
if ( countingtri.tri == dummytri ) {
printf( "Internal error in deletesite():\n" );
printf( " Attempt to delete boundary point.\n" );
internalerror();
}
#endif /* SELF_CHECK */
edgecount++;
onextself( countingtri );
}
#ifdef SELF_CHECK
if ( edgecount < 3 ) {
printf( "Internal error in deletesite():\n Point has degree %d.\n",
edgecount );
internalerror();
}
#endif /* SELF_CHECK */
if ( edgecount > 3 ) {
/* Triangulate the polygon defined by the union of all triangles */
/* adjacent to the point being deleted. Check the quality of */
/* the resulting triangles. */
onext( *deltri, firstedge );
oprev( *deltri, lastedge );
triangulatepolygon( &firstedge, &lastedge, edgecount, 0, !nobisect );
}
/* Splice out two triangles. */
lprev( *deltri, deltriright );
dnext( *deltri, lefttri );
sym( lefttri, leftcasing );
oprev( deltriright, righttri );
sym( righttri, rightcasing );
bond( *deltri, leftcasing );
bond( deltriright, rightcasing );
tspivot( lefttri, leftshelle );
if ( leftshelle.sh != dummysh ) {
tsbond( *deltri, leftshelle );
}
tspivot( righttri, rightshelle );
if ( rightshelle.sh != dummysh ) {
tsbond( deltriright, rightshelle );
}
/* Set the new origin of `deltri' and check its quality. */
org( lefttri, neworg );
setorg( *deltri, neworg );
if ( !nobisect ) {
testtriangle( deltri );
}
/* Delete the two spliced-out triangles. */
triangledealloc( lefttri.tri );
triangledealloc( righttri.tri );
}
#endif /* not CDT_ONLY */
/** **/
/** **/
/********* Mesh transformation routines end here *********/
/********* Divide-and-conquer Delaunay triangulation begins here *********/
/** **/
/** **/
/*****************************************************************************/
/* */
/* The divide-and-conquer bounding box */
/* */
/* I originally implemented the divide-and-conquer and incremental Delaunay */
/* triangulations using the edge-based data structure presented by Guibas */
/* and Stolfi. Switching to a triangle-based data structure doubled the */
/* speed. However, I had to think of a few extra tricks to maintain the */
/* elegance of the original algorithms. */
/* */
/* The "bounding box" used by my variant of the divide-and-conquer */
/* algorithm uses one triangle for each edge of the convex hull of the */
/* triangulation. These bounding triangles all share a common apical */
/* vertex, which is represented by NULL and which represents nothing. */
/* The bounding triangles are linked in a circular fan about this NULL */
/* vertex, and the edges on the convex hull of the triangulation appear */
/* opposite the NULL vertex. You might find it easiest to imagine that */
/* the NULL vertex is a point in 3D space behind the center of the */
/* triangulation, and that the bounding triangles form a sort of cone. */
/* */
/* This bounding box makes it easy to represent degenerate cases. For */
/* instance, the triangulation of two vertices is a single edge. This edge */
/* is represented by two bounding box triangles, one on each "side" of the */
/* edge. These triangles are also linked together in a fan about the NULL */
/* vertex. */
/* */
/* The bounding box also makes it easy to traverse the convex hull, as the */
/* divide-and-conquer algorithm needs to do. */
/* */
/*****************************************************************************/
/*****************************************************************************/
/* */
/* pointsort() Sort an array of points by x-coordinate, using the */
/* y-coordinate as a secondary key. */
/* */
/* Uses quicksort. Randomized O(n log n) time. No, I did not make any of */
/* the usual quicksort mistakes. */
/* */
/*****************************************************************************/
void pointsort( sortarray, arraysize )
point * sortarray;
int arraysize;
{
int left, right;
int pivot;
REAL pivotx, pivoty;
point temp;
if ( arraysize == 2 ) {
/* Recursive base case. */
if ( ( sortarray[0][0] > sortarray[1][0] ) ||
( ( sortarray[0][0] == sortarray[1][0] ) &&
( sortarray[0][1] > sortarray[1][1] ) ) ) {
temp = sortarray[1];
sortarray[1] = sortarray[0];
sortarray[0] = temp;
}
return;
}
/* Choose a random pivot to split the array. */
pivot = (int) randomnation( arraysize );
pivotx = sortarray[pivot][0];
pivoty = sortarray[pivot][1];
/* Split the array. */
left = -1;
right = arraysize;
while ( left < right ) {
/* Search for a point whose x-coordinate is too large for the left. */
do {
left++;
} while ( ( left <= right ) && ( ( sortarray[left][0] < pivotx ) ||
( ( sortarray[left][0] == pivotx ) &&
( sortarray[left][1] < pivoty ) ) ) );
/* Search for a point whose x-coordinate is too small for the right. */
do {
right--;
} while ( ( left <= right ) && ( ( sortarray[right][0] > pivotx ) ||
( ( sortarray[right][0] == pivotx ) &&
( sortarray[right][1] > pivoty ) ) ) );
if ( left < right ) {
/* Swap the left and right points. */
temp = sortarray[left];
sortarray[left] = sortarray[right];
sortarray[right] = temp;
}
}
if ( left > 1 ) {
/* Recursively sort the left subset. */
pointsort( sortarray, left );
}
if ( right < arraysize - 2 ) {
/* Recursively sort the right subset. */
pointsort( &sortarray[right + 1], arraysize - right - 1 );
}
}
/*****************************************************************************/
/* */
/* pointmedian() An order statistic algorithm, almost. Shuffles an array */
/* of points so that the first `median' points occur */
/* lexicographically before the remaining points. */
/* */
/* Uses the x-coordinate as the primary key if axis == 0; the y-coordinate */
/* if axis == 1. Very similar to the pointsort() procedure, but runs in */
/* randomized linear time. */
/* */
/*****************************************************************************/
void pointmedian( sortarray, arraysize, median, axis )
point * sortarray;
int arraysize;
int median;
int axis;
{
int left, right;
int pivot;
REAL pivot1, pivot2;
point temp;
if ( arraysize == 2 ) {
/* Recursive base case. */
if ( ( sortarray[0][axis] > sortarray[1][axis] ) ||
( ( sortarray[0][axis] == sortarray[1][axis] ) &&
( sortarray[0][1 - axis] > sortarray[1][1 - axis] ) ) ) {
temp = sortarray[1];
sortarray[1] = sortarray[0];
sortarray[0] = temp;
}
return;
}
/* Choose a random pivot to split the array. */
pivot = (int) randomnation( arraysize );
pivot1 = sortarray[pivot][axis];
pivot2 = sortarray[pivot][1 - axis];
/* Split the array. */
left = -1;
right = arraysize;
while ( left < right ) {
/* Search for a point whose x-coordinate is too large for the left. */
do {
left++;
} while ( ( left <= right ) && ( ( sortarray[left][axis] < pivot1 ) ||
( ( sortarray[left][axis] == pivot1 ) &&
( sortarray[left][1 - axis] < pivot2 ) ) ) );
/* Search for a point whose x-coordinate is too small for the right. */
do {
right--;
} while ( ( left <= right ) && ( ( sortarray[right][axis] > pivot1 ) ||
( ( sortarray[right][axis] == pivot1 ) &&
( sortarray[right][1 - axis] > pivot2 ) ) ) );
if ( left < right ) {
/* Swap the left and right points. */
temp = sortarray[left];
sortarray[left] = sortarray[right];
sortarray[right] = temp;
}
}
/* Unlike in pointsort(), at most one of the following */
/* conditionals is true. */
if ( left > median ) {
/* Recursively shuffle the left subset. */
pointmedian( sortarray, left, median, axis );
}
if ( right < median - 1 ) {
/* Recursively shuffle the right subset. */
pointmedian( &sortarray[right + 1], arraysize - right - 1,
median - right - 1, axis );
}
}
/*****************************************************************************/
/* */
/* alternateaxes() Sorts the points as appropriate for the divide-and- */
/* conquer algorithm with alternating cuts. */
/* */
/* Partitions by x-coordinate if axis == 0; by y-coordinate if axis == 1. */
/* For the base case, subsets containing only two or three points are */
/* always sorted by x-coordinate. */
/* */
/*****************************************************************************/
void alternateaxes( sortarray, arraysize, axis )
point * sortarray;
int arraysize;
int axis;
{
int divider;
divider = arraysize >> 1;
if ( arraysize <= 3 ) {
/* Recursive base case: subsets of two or three points will be */
/* handled specially, and should always be sorted by x-coordinate. */
axis = 0;
}
/* Partition with a horizontal or vertical cut. */
pointmedian( sortarray, arraysize, divider, axis );
/* Recursively partition the subsets with a cross cut. */
if ( arraysize - divider >= 2 ) {
if ( divider >= 2 ) {
alternateaxes( sortarray, divider, 1 - axis );
}
alternateaxes( &sortarray[divider], arraysize - divider, 1 - axis );
}
}
/*****************************************************************************/
/* */
/* mergehulls() Merge two adjacent Delaunay triangulations into a */
/* single Delaunay triangulation. */
/* */
/* This is similar to the algorithm given by Guibas and Stolfi, but uses */
/* a triangle-based, rather than edge-based, data structure. */
/* */
/* The algorithm walks up the gap between the two triangulations, knitting */
/* them together. As they are merged, some of their bounding triangles */
/* are converted into real triangles of the triangulation. The procedure */
/* pulls each hull's bounding triangles apart, then knits them together */
/* like the teeth of two gears. The Delaunay property determines, at each */
/* step, whether the next "tooth" is a bounding triangle of the left hull */
/* or the right. When a bounding triangle becomes real, its apex is */
/* changed from NULL to a real point. */
/* */
/* Only two new triangles need to be allocated. These become new bounding */
/* triangles at the top and bottom of the seam. They are used to connect */
/* the remaining bounding triangles (those that have not been converted */
/* into real triangles) into a single fan. */
/* */
/* On entry, `farleft' and `innerleft' are bounding triangles of the left */
/* triangulation. The origin of `farleft' is the leftmost vertex, and */
/* the destination of `innerleft' is the rightmost vertex of the */
/* triangulation. Similarly, `innerright' and `farright' are bounding */
/* triangles of the right triangulation. The origin of `innerright' and */
/* destination of `farright' are the leftmost and rightmost vertices. */
/* */
/* On completion, the origin of `farleft' is the leftmost vertex of the */
/* merged triangulation, and the destination of `farright' is the rightmost */
/* vertex. */
/* */
/*****************************************************************************/
void mergehulls( farleft, innerleft, innerright, farright, axis )
struct triedge *farleft;
struct triedge *innerleft;
struct triedge *innerright;
struct triedge *farright;
int axis;
{
struct triedge leftcand, rightcand;
struct triedge baseedge;
struct triedge nextedge;
struct triedge sidecasing, topcasing, outercasing;
struct triedge checkedge;
point innerleftdest;
point innerrightorg;
point innerleftapex, innerrightapex;
point farleftpt, farrightpt;
point farleftapex, farrightapex;
point lowerleft, lowerright;
point upperleft, upperright;
point nextapex;
point checkvertex;
int changemade;
int badedge;
int leftfinished, rightfinished;
triangle ptr; /* Temporary variable used by sym(). */
dest( *innerleft, innerleftdest );
apex( *innerleft, innerleftapex );
org( *innerright, innerrightorg );
apex( *innerright, innerrightapex );
/* Special treatment for horizontal cuts. */
if ( dwyer && ( axis == 1 ) ) {
org( *farleft, farleftpt );
apex( *farleft, farleftapex );
dest( *farright, farrightpt );
apex( *farright, farrightapex );
/* The pointers to the extremal points are shifted to point to the */
/* topmost and bottommost point of each hull, rather than the */
/* leftmost and rightmost points. */
while ( farleftapex[1] < farleftpt[1] ) {
lnextself( *farleft );
symself( *farleft );
farleftpt = farleftapex;
apex( *farleft, farleftapex );
}
sym( *innerleft, checkedge );
apex( checkedge, checkvertex );
while ( checkvertex[1] > innerleftdest[1] ) {
lnext( checkedge, *innerleft );
innerleftapex = innerleftdest;
innerleftdest = checkvertex;
sym( *innerleft, checkedge );
apex( checkedge, checkvertex );
}
while ( innerrightapex[1] < innerrightorg[1] ) {
lnextself( *innerright );
symself( *innerright );
innerrightorg = innerrightapex;
apex( *innerright, innerrightapex );
}
sym( *farright, checkedge );
apex( checkedge, checkvertex );
while ( checkvertex[1] > farrightpt[1] ) {
lnext( checkedge, *farright );
farrightapex = farrightpt;
farrightpt = checkvertex;
sym( *farright, checkedge );
apex( checkedge, checkvertex );
}
}
/* Find a line tangent to and below both hulls. */
do {
changemade = 0;
/* Make innerleftdest the "bottommost" point of the left hull. */
if ( counterclockwise( innerleftdest, innerleftapex, innerrightorg ) > 0.0 ) {
lprevself( *innerleft );
symself( *innerleft );
innerleftdest = innerleftapex;
apex( *innerleft, innerleftapex );
changemade = 1;
}
/* Make innerrightorg the "bottommost" point of the right hull. */
if ( counterclockwise( innerrightapex, innerrightorg, innerleftdest ) > 0.0 ) {
lnextself( *innerright );
symself( *innerright );
innerrightorg = innerrightapex;
apex( *innerright, innerrightapex );
changemade = 1;
}
} while ( changemade );
/* Find the two candidates to be the next "gear tooth". */
sym( *innerleft, leftcand );
sym( *innerright, rightcand );
/* Create the bottom new bounding triangle. */
maketriangle( &baseedge );
/* Connect it to the bounding boxes of the left and right triangulations. */
bond( baseedge, *innerleft );
lnextself( baseedge );
bond( baseedge, *innerright );
lnextself( baseedge );
setorg( baseedge, innerrightorg );
setdest( baseedge, innerleftdest );
/* Apex is intentionally left NULL. */
if ( verbose > 2 ) {
printf( " Creating base bounding " );
printtriangle( &baseedge );
}
/* Fix the extreme triangles if necessary. */
org( *farleft, farleftpt );
if ( innerleftdest == farleftpt ) {
lnext( baseedge, *farleft );
}
dest( *farright, farrightpt );
if ( innerrightorg == farrightpt ) {
lprev( baseedge, *farright );
}
/* The vertices of the current knitting edge. */
lowerleft = innerleftdest;
lowerright = innerrightorg;
/* The candidate vertices for knitting. */
apex( leftcand, upperleft );
apex( rightcand, upperright );
/* Walk up the gap between the two triangulations, knitting them together. */
while ( 1 ) {
/* Have we reached the top? (This isn't quite the right question, */
/* because even though the left triangulation might seem finished now, */
/* moving up on the right triangulation might reveal a new point of */
/* the left triangulation. And vice-versa.) */
leftfinished = counterclockwise( upperleft, lowerleft, lowerright ) <= 0.0;
rightfinished = counterclockwise( upperright, lowerleft, lowerright ) <= 0.0;
if ( leftfinished && rightfinished ) {
/* Create the top new bounding triangle. */
maketriangle( &nextedge );
setorg( nextedge, lowerleft );
setdest( nextedge, lowerright );
/* Apex is intentionally left NULL. */
/* Connect it to the bounding boxes of the two triangulations. */
bond( nextedge, baseedge );
lnextself( nextedge );
bond( nextedge, rightcand );
lnextself( nextedge );
bond( nextedge, leftcand );
if ( verbose > 2 ) {
printf( " Creating top bounding " );
printtriangle( &baseedge );
}
/* Special treatment for horizontal cuts. */
if ( dwyer && ( axis == 1 ) ) {
org( *farleft, farleftpt );
apex( *farleft, farleftapex );
dest( *farright, farrightpt );
apex( *farright, farrightapex );
sym( *farleft, checkedge );
apex( checkedge, checkvertex );
/* The pointers to the extremal points are restored to the leftmost */
/* and rightmost points (rather than topmost and bottommost). */
while ( checkvertex[0] < farleftpt[0] ) {
lprev( checkedge, *farleft );
farleftapex = farleftpt;
farleftpt = checkvertex;
sym( *farleft, checkedge );
apex( checkedge, checkvertex );
}
while ( farrightapex[0] > farrightpt[0] ) {
lprevself( *farright );
symself( *farright );
farrightpt = farrightapex;
apex( *farright, farrightapex );
}
}
return;
}
/* Consider eliminating edges from the left triangulation. */
if ( !leftfinished ) {
/* What vertex would be exposed if an edge were deleted? */
lprev( leftcand, nextedge );
symself( nextedge );
apex( nextedge, nextapex );
/* If nextapex is NULL, then no vertex would be exposed; the */
/* triangulation would have been eaten right through. */
if ( nextapex != (point) NULL ) {
/* Check whether the edge is Delaunay. */
badedge = incircle( lowerleft, lowerright, upperleft, nextapex ) > 0.0;
while ( badedge ) {
/* Eliminate the edge with an edge flip. As a result, the */
/* left triangulation will have one more boundary triangle. */
lnextself( nextedge );
sym( nextedge, topcasing );
lnextself( nextedge );
sym( nextedge, sidecasing );
bond( nextedge, topcasing );
bond( leftcand, sidecasing );
lnextself( leftcand );
sym( leftcand, outercasing );
lprevself( nextedge );
bond( nextedge, outercasing );
/* Correct the vertices to reflect the edge flip. */
setorg( leftcand, lowerleft );
setdest( leftcand, NULL );
setapex( leftcand, nextapex );
setorg( nextedge, NULL );
setdest( nextedge, upperleft );
setapex( nextedge, nextapex );
/* Consider the newly exposed vertex. */
upperleft = nextapex;
/* What vertex would be exposed if another edge were deleted? */
triedgecopy( sidecasing, nextedge );
apex( nextedge, nextapex );
if ( nextapex != (point) NULL ) {
/* Check whether the edge is Delaunay. */
badedge = incircle( lowerleft, lowerright, upperleft, nextapex )
> 0.0;
}
else {
/* Avoid eating right through the triangulation. */
badedge = 0;
}
}
}
}
/* Consider eliminating edges from the right triangulation. */
if ( !rightfinished ) {
/* What vertex would be exposed if an edge were deleted? */
lnext( rightcand, nextedge );
symself( nextedge );
apex( nextedge, nextapex );
/* If nextapex is NULL, then no vertex would be exposed; the */
/* triangulation would have been eaten right through. */
if ( nextapex != (point) NULL ) {
/* Check whether the edge is Delaunay. */
badedge = incircle( lowerleft, lowerright, upperright, nextapex ) > 0.0;
while ( badedge ) {
/* Eliminate the edge with an edge flip. As a result, the */
/* right triangulation will have one more boundary triangle. */
lprevself( nextedge );
sym( nextedge, topcasing );
lprevself( nextedge );
sym( nextedge, sidecasing );
bond( nextedge, topcasing );
bond( rightcand, sidecasing );
lprevself( rightcand );
sym( rightcand, outercasing );
lnextself( nextedge );
bond( nextedge, outercasing );
/* Correct the vertices to reflect the edge flip. */
setorg( rightcand, NULL );
setdest( rightcand, lowerright );
setapex( rightcand, nextapex );
setorg( nextedge, upperright );
setdest( nextedge, NULL );
setapex( nextedge, nextapex );
/* Consider the newly exposed vertex. */
upperright = nextapex;
/* What vertex would be exposed if another edge were deleted? */
triedgecopy( sidecasing, nextedge );
apex( nextedge, nextapex );
if ( nextapex != (point) NULL ) {
/* Check whether the edge is Delaunay. */
badedge = incircle( lowerleft, lowerright, upperright, nextapex )
> 0.0;
}
else {
/* Avoid eating right through the triangulation. */
badedge = 0;
}
}
}
}
if ( leftfinished || ( !rightfinished &&
( incircle( upperleft, lowerleft, lowerright, upperright ) > 0.0 ) ) ) {
/* Knit the triangulations, adding an edge from `lowerleft' */
/* to `upperright'. */
bond( baseedge, rightcand );
lprev( rightcand, baseedge );
setdest( baseedge, lowerleft );
lowerright = upperright;
sym( baseedge, rightcand );
apex( rightcand, upperright );
}
else {
/* Knit the triangulations, adding an edge from `upperleft' */
/* to `lowerright'. */
bond( baseedge, leftcand );
lnext( leftcand, baseedge );
setorg( baseedge, lowerright );
lowerleft = upperleft;
sym( baseedge, leftcand );
apex( leftcand, upperleft );
}
if ( verbose > 2 ) {
printf( " Connecting " );
printtriangle( &baseedge );
}
}
}
/*****************************************************************************/
/* */
/* divconqrecurse() Recursively form a Delaunay triangulation by the */
/* divide-and-conquer method. */
/* */
/* Recursively breaks down the problem into smaller pieces, which are */
/* knitted together by mergehulls(). The base cases (problems of two or */
/* three points) are handled specially here. */
/* */
/* On completion, `farleft' and `farright' are bounding triangles such that */
/* the origin of `farleft' is the leftmost vertex (breaking ties by */
/* choosing the highest leftmost vertex), and the destination of */
/* `farright' is the rightmost vertex (breaking ties by choosing the */
/* lowest rightmost vertex). */
/* */
/*****************************************************************************/
void divconqrecurse( sortarray, vertices, axis, farleft, farright )
point * sortarray;
int vertices;
int axis;
struct triedge *farleft;
struct triedge *farright;
{
struct triedge midtri, tri1, tri2, tri3;
struct triedge innerleft, innerright;
REAL area;
int divider;
if ( verbose > 2 ) {
printf( " Triangulating %d points.\n", vertices );
}
if ( vertices == 2 ) {
/* The triangulation of two vertices is an edge. An edge is */
/* represented by two bounding triangles. */
maketriangle( farleft );
setorg( *farleft, sortarray[0] );
setdest( *farleft, sortarray[1] );
/* The apex is intentionally left NULL. */
maketriangle( farright );
setorg( *farright, sortarray[1] );
setdest( *farright, sortarray[0] );
/* The apex is intentionally left NULL. */
bond( *farleft, *farright );
lprevself( *farleft );
lnextself( *farright );
bond( *farleft, *farright );
lprevself( *farleft );
lnextself( *farright );
bond( *farleft, *farright );
if ( verbose > 2 ) {
printf( " Creating " );
printtriangle( farleft );
printf( " Creating " );
printtriangle( farright );
}
/* Ensure that the origin of `farleft' is sortarray[0]. */
lprev( *farright, *farleft );
return;
}
else if ( vertices == 3 ) {
/* The triangulation of three vertices is either a triangle (with */
/* three bounding triangles) or two edges (with four bounding */
/* triangles). In either case, four triangles are created. */
maketriangle( &midtri );
maketriangle( &tri1 );
maketriangle( &tri2 );
maketriangle( &tri3 );
area = counterclockwise( sortarray[0], sortarray[1], sortarray[2] );
if ( area == 0.0 ) {
/* Three collinear points; the triangulation is two edges. */
setorg( midtri, sortarray[0] );
setdest( midtri, sortarray[1] );
setorg( tri1, sortarray[1] );
setdest( tri1, sortarray[0] );
setorg( tri2, sortarray[2] );
setdest( tri2, sortarray[1] );
setorg( tri3, sortarray[1] );
setdest( tri3, sortarray[2] );
/* All apices are intentionally left NULL. */
bond( midtri, tri1 );
bond( tri2, tri3 );
lnextself( midtri );
lprevself( tri1 );
lnextself( tri2 );
lprevself( tri3 );
bond( midtri, tri3 );
bond( tri1, tri2 );
lnextself( midtri );
lprevself( tri1 );
lnextself( tri2 );
lprevself( tri3 );
bond( midtri, tri1 );
bond( tri2, tri3 );
/* Ensure that the origin of `farleft' is sortarray[0]. */
triedgecopy( tri1, *farleft );
/* Ensure that the destination of `farright' is sortarray[2]. */
triedgecopy( tri2, *farright );
}
else {
/* The three points are not collinear; the triangulation is one */
/* triangle, namely `midtri'. */
setorg( midtri, sortarray[0] );
setdest( tri1, sortarray[0] );
setorg( tri3, sortarray[0] );
/* Apices of tri1, tri2, and tri3 are left NULL. */
if ( area > 0.0 ) {
/* The vertices are in counterclockwise order. */
setdest( midtri, sortarray[1] );
setorg( tri1, sortarray[1] );
setdest( tri2, sortarray[1] );
setapex( midtri, sortarray[2] );
setorg( tri2, sortarray[2] );
setdest( tri3, sortarray[2] );
}
else {
/* The vertices are in clockwise order. */
setdest( midtri, sortarray[2] );
setorg( tri1, sortarray[2] );
setdest( tri2, sortarray[2] );
setapex( midtri, sortarray[1] );
setorg( tri2, sortarray[1] );
setdest( tri3, sortarray[1] );
}
/* The topology does not depend on how the vertices are ordered. */
bond( midtri, tri1 );
lnextself( midtri );
bond( midtri, tri2 );
lnextself( midtri );
bond( midtri, tri3 );
lprevself( tri1 );
lnextself( tri2 );
bond( tri1, tri2 );
lprevself( tri1 );
lprevself( tri3 );
bond( tri1, tri3 );
lnextself( tri2 );
lprevself( tri3 );
bond( tri2, tri3 );
/* Ensure that the origin of `farleft' is sortarray[0]. */
triedgecopy( tri1, *farleft );
/* Ensure that the destination of `farright' is sortarray[2]. */
if ( area > 0.0 ) {
triedgecopy( tri2, *farright );
}
else {
lnext( *farleft, *farright );
}
}
if ( verbose > 2 ) {
printf( " Creating " );
printtriangle( &midtri );
printf( " Creating " );
printtriangle( &tri1 );
printf( " Creating " );
printtriangle( &tri2 );
printf( " Creating " );
printtriangle( &tri3 );
}
return;
}
else {
/* Split the vertices in half. */
divider = vertices >> 1;
/* Recursively triangulate each half. */
divconqrecurse( sortarray, divider, 1 - axis, farleft, &innerleft );
divconqrecurse( &sortarray[divider], vertices - divider, 1 - axis,
&innerright, farright );
if ( verbose > 1 ) {
printf( " Joining triangulations with %d and %d vertices.\n", divider,
vertices - divider );
}
/* Merge the two triangulations into one. */
mergehulls( farleft, &innerleft, &innerright, farright, axis );
}
}
long removeghosts( startghost )
struct triedge *startghost;
{
struct triedge searchedge;
struct triedge dissolveedge;
struct triedge deadtri;
point markorg;
long hullsize;
triangle ptr; /* Temporary variable used by sym(). */
if ( verbose ) {
printf( " Removing ghost triangles.\n" );
}
/* Find an edge on the convex hull to start point location from. */
lprev( *startghost, searchedge );
symself( searchedge );
dummytri[0] = encode( searchedge );
/* Remove the bounding box and count the convex hull edges. */
triedgecopy( *startghost, dissolveedge );
hullsize = 0;
do {
hullsize++;
lnext( dissolveedge, deadtri );
lprevself( dissolveedge );
symself( dissolveedge );
/* If no PSLG is involved, set the boundary markers of all the points */
/* on the convex hull. If a PSLG is used, this step is done later. */
if ( !poly ) {
/* Watch out for the case where all the input points are collinear. */
if ( dissolveedge.tri != dummytri ) {
org( dissolveedge, markorg );
if ( pointmark( markorg ) == 0 ) {
setpointmark( markorg, 1 );
}
}
}
/* Remove a bounding triangle from a convex hull triangle. */
dissolve( dissolveedge );
/* Find the next bounding triangle. */
sym( deadtri, dissolveedge );
/* Delete the bounding triangle. */
triangledealloc( deadtri.tri );
} while ( !triedgeequal( dissolveedge, *startghost ) );
return hullsize;
}
/*****************************************************************************/
/* */
/* divconqdelaunay() Form a Delaunay triangulation by the divide-and- */
/* conquer method. */
/* */
/* Sorts the points, calls a recursive procedure to triangulate them, and */
/* removes the bounding box, setting boundary markers as appropriate. */
/* */
/*****************************************************************************/
long divconqdelaunay(){
point *sortarray;
struct triedge hullleft, hullright;
int divider;
int i, j;
/* Allocate an array of pointers to points for sorting. */
sortarray = (point *) malloc( inpoints * sizeof( point ) );
if ( sortarray == (point *) NULL ) {
printf( "Error: Out of memory.\n" );
exit( 1 );
}
traversalinit( &points );
for ( i = 0; i < inpoints; i++ ) {
sortarray[i] = pointtraverse();
}
if ( verbose ) {
printf( " Sorting points.\n" );
}
/* Sort the points. */
pointsort( sortarray, inpoints );
/* Discard duplicate points, which can really mess up the algorithm. */
i = 0;
for ( j = 1; j < inpoints; j++ ) {
if ( ( sortarray[i][0] == sortarray[j][0] )
&& ( sortarray[i][1] == sortarray[j][1] ) ) {
if ( !quiet ) {
printf(
"Warning: A duplicate point at (%.12g, %.12g) appeared and was ignored.\n",
sortarray[j][0], sortarray[j][1] );
}
/* Commented out - would eliminate point from output .node file, but causes
a failure if some segment has this point as an endpoint.
setpointmark(sortarray[j], DEADPOINT);
*/
}
else {
i++;
sortarray[i] = sortarray[j];
}
}
i++;
if ( dwyer ) {
/* Re-sort the array of points to accommodate alternating cuts. */
divider = i >> 1;
if ( i - divider >= 2 ) {
if ( divider >= 2 ) {
alternateaxes( sortarray, divider, 1 );
}
alternateaxes( &sortarray[divider], i - divider, 1 );
}
}
if ( verbose ) {
printf( " Forming triangulation.\n" );
}
/* Form the Delaunay triangulation. */
divconqrecurse( sortarray, i, 0, &hullleft, &hullright );
free( sortarray );
return removeghosts( &hullleft );
}
/** **/
/** **/
/********* Divide-and-conquer Delaunay triangulation ends here *********/
/********* Incremental Delaunay triangulation begins here *********/
/** **/
/** **/
/*****************************************************************************/
/* */
/* boundingbox() Form an "infinite" bounding triangle to insert points */
/* into. */
/* */
/* The points at "infinity" are assigned finite coordinates, which are used */
/* by the point location routines, but (mostly) ignored by the Delaunay */
/* edge flip routines. */
/* */
/*****************************************************************************/
#ifndef REDUCED
void boundingbox(){
struct triedge inftri; /* Handle for the triangular bounding box. */
REAL width;
if ( verbose ) {
printf( " Creating triangular bounding box.\n" );
}
/* Find the width (or height, whichever is larger) of the triangulation. */
width = xmax - xmin;
if ( ymax - ymin > width ) {
width = ymax - ymin;
}
if ( width == 0.0 ) {
width = 1.0;
}
/* Create the vertices of the bounding box. */
infpoint1 = (point) malloc( points.itembytes );
infpoint2 = (point) malloc( points.itembytes );
infpoint3 = (point) malloc( points.itembytes );
if ( ( infpoint1 == (point) NULL ) || ( infpoint2 == (point) NULL )
|| ( infpoint3 == (point) NULL ) ) {
printf( "Error: Out of memory.\n" );
exit( 1 );
}
infpoint1[0] = xmin - 50.0 * width;
infpoint1[1] = ymin - 40.0 * width;
infpoint2[0] = xmax + 50.0 * width;
infpoint2[1] = ymin - 40.0 * width;
infpoint3[0] = 0.5 * ( xmin + xmax );
infpoint3[1] = ymax + 60.0 * width;
/* Create the bounding box. */
maketriangle( &inftri );
setorg( inftri, infpoint1 );
setdest( inftri, infpoint2 );
setapex( inftri, infpoint3 );
/* Link dummytri to the bounding box so we can always find an */
/* edge to begin searching (point location) from. */
dummytri[0] = (triangle) inftri.tri;
if ( verbose > 2 ) {
printf( " Creating " );
printtriangle( &inftri );
}
}
#endif /* not REDUCED */
/*****************************************************************************/
/* */
/* removebox() Remove the "infinite" bounding triangle, setting boundary */
/* markers as appropriate. */
/* */
/* The triangular bounding box has three boundary triangles (one for each */
/* side of the bounding box), and a bunch of triangles fanning out from */
/* the three bounding box vertices (one triangle for each edge of the */
/* convex hull of the inner mesh). This routine removes these triangles. */
/* */
/*****************************************************************************/
#ifndef REDUCED
long removebox(){
struct triedge deadtri;
struct triedge searchedge;
struct triedge checkedge;
struct triedge nextedge, finaledge, dissolveedge;
point markorg;
long hullsize;
triangle ptr; /* Temporary variable used by sym(). */
if ( verbose ) {
printf( " Removing triangular bounding box.\n" );
}
/* Find a boundary triangle. */
nextedge.tri = dummytri;
nextedge.orient = 0;
symself( nextedge );
/* Mark a place to stop. */
lprev( nextedge, finaledge );
lnextself( nextedge );
symself( nextedge );
/* Find a triangle (on the boundary of the point set) that isn't */
/* a bounding box triangle. */
lprev( nextedge, searchedge );
symself( searchedge );
/* Check whether nextedge is another boundary triangle */
/* adjacent to the first one. */
lnext( nextedge, checkedge );
symself( checkedge );
if ( checkedge.tri == dummytri ) {
/* Go on to the next triangle. There are only three boundary */
/* triangles, and this next triangle cannot be the third one, */
/* so it's safe to stop here. */
lprevself( searchedge );
symself( searchedge );
}
/* Find a new boundary edge to search from, as the current search */
/* edge lies on a bounding box triangle and will be deleted. */
dummytri[0] = encode( searchedge );
hullsize = -2l;
while ( !triedgeequal( nextedge, finaledge ) ) {
hullsize++;
lprev( nextedge, dissolveedge );
symself( dissolveedge );
/* If not using a PSLG, the vertices should be marked now. */
/* (If using a PSLG, markhull() will do the job.) */
if ( !poly ) {
/* Be careful! One must check for the case where all the input */
/* points are collinear, and thus all the triangles are part of */
/* the bounding box. Otherwise, the setpointmark() call below */
/* will cause a bad pointer reference. */
if ( dissolveedge.tri != dummytri ) {
org( dissolveedge, markorg );
if ( pointmark( markorg ) == 0 ) {
setpointmark( markorg, 1 );
}
}
}
/* Disconnect the bounding box triangle from the mesh triangle. */
dissolve( dissolveedge );
lnext( nextedge, deadtri );
sym( deadtri, nextedge );
/* Get rid of the bounding box triangle. */
triangledealloc( deadtri.tri );
/* Do we need to turn the corner? */
if ( nextedge.tri == dummytri ) {
/* Turn the corner. */
triedgecopy( dissolveedge, nextedge );
}
}
triangledealloc( finaledge.tri );
free( infpoint1 ); /* Deallocate the bounding box vertices. */
free( infpoint2 );
free( infpoint3 );
return hullsize;
}
#endif /* not REDUCED */
/*****************************************************************************/
/* */
/* incrementaldelaunay() Form a Delaunay triangulation by incrementally */
/* adding vertices. */
/* */
/*****************************************************************************/
#ifndef REDUCED
long incrementaldelaunay(){
struct triedge starttri;
point pointloop;
int i;
/* Create a triangular bounding box. */
boundingbox();
if ( verbose ) {
printf( " Incrementally inserting points.\n" );
}
traversalinit( &points );
pointloop = pointtraverse();
i = 1;
while ( pointloop != (point) NULL ) {
/* Find a boundary triangle to search from. */
starttri.tri = (triangle *) NULL;
if ( insertsite( pointloop, &starttri, (struct edge *) NULL, 0, 0 ) ==
DUPLICATEPOINT ) {
if ( !quiet ) {
printf(
"Warning: A duplicate point at (%.12g, %.12g) appeared and was ignored.\n",
pointloop[0], pointloop[1] );
}
/* Commented out - would eliminate point from output .node file.
setpointmark(pointloop, DEADPOINT);
*/
}
pointloop = pointtraverse();
i++;
}
/* Remove the bounding box. */
return removebox();
}
#endif /* not REDUCED */
/** **/
/** **/
/********* Incremental Delaunay triangulation ends here *********/
/********* Sweepline Delaunay triangulation begins here *********/
/** **/
/** **/
#ifndef REDUCED
void eventheapinsert( heap, heapsize, newevent )
struct event **heap;
int heapsize;
struct event *newevent;
{
REAL eventx, eventy;
int eventnum;
int parent;
int notdone;
eventx = newevent->xkey;
eventy = newevent->ykey;
eventnum = heapsize;
notdone = eventnum > 0;
while ( notdone ) {
parent = ( eventnum - 1 ) >> 1;
if ( ( heap[parent]->ykey < eventy ) ||
( ( heap[parent]->ykey == eventy )
&& ( heap[parent]->xkey <= eventx ) ) ) {
notdone = 0;
}
else {
heap[eventnum] = heap[parent];
heap[eventnum]->heapposition = eventnum;
eventnum = parent;
notdone = eventnum > 0;
}
}
heap[eventnum] = newevent;
newevent->heapposition = eventnum;
}
#endif /* not REDUCED */
#ifndef REDUCED
void eventheapify( heap, heapsize, eventnum )
struct event **heap;
int heapsize;
int eventnum;
{
struct event *thisevent;
REAL eventx, eventy;
int leftchild, rightchild;
int smallest;
int notdone;
thisevent = heap[eventnum];
eventx = thisevent->xkey;
eventy = thisevent->ykey;
leftchild = 2 * eventnum + 1;
notdone = leftchild < heapsize;
while ( notdone ) {
if ( ( heap[leftchild]->ykey < eventy ) ||
( ( heap[leftchild]->ykey == eventy )
&& ( heap[leftchild]->xkey < eventx ) ) ) {
smallest = leftchild;
}
else {
smallest = eventnum;
}
rightchild = leftchild + 1;
if ( rightchild < heapsize ) {
if ( ( heap[rightchild]->ykey < heap[smallest]->ykey ) ||
( ( heap[rightchild]->ykey == heap[smallest]->ykey )
&& ( heap[rightchild]->xkey < heap[smallest]->xkey ) ) ) {
smallest = rightchild;
}
}
if ( smallest == eventnum ) {
notdone = 0;
}
else {
heap[eventnum] = heap[smallest];
heap[eventnum]->heapposition = eventnum;
heap[smallest] = thisevent;
thisevent->heapposition = smallest;
eventnum = smallest;
leftchild = 2 * eventnum + 1;
notdone = leftchild < heapsize;
}
}
}
#endif /* not REDUCED */
#ifndef REDUCED
void eventheapdelete( heap, heapsize, eventnum )
struct event **heap;
int heapsize;
int eventnum;
{
struct event *moveevent;
REAL eventx, eventy;
int parent;
int notdone;
moveevent = heap[heapsize - 1];
if ( eventnum > 0 ) {
eventx = moveevent->xkey;
eventy = moveevent->ykey;
do {
parent = ( eventnum - 1 ) >> 1;
if ( ( heap[parent]->ykey < eventy ) ||
( ( heap[parent]->ykey == eventy )
&& ( heap[parent]->xkey <= eventx ) ) ) {
notdone = 0;
}
else {
heap[eventnum] = heap[parent];
heap[eventnum]->heapposition = eventnum;
eventnum = parent;
notdone = eventnum > 0;
}
} while ( notdone );
}
heap[eventnum] = moveevent;
moveevent->heapposition = eventnum;
eventheapify( heap, heapsize - 1, eventnum );
}
#endif /* not REDUCED */
#ifndef REDUCED
void createeventheap( eventheap, events, freeevents )
struct event ***eventheap;
struct event **events;
struct event **freeevents;
{
point thispoint;
int maxevents;
int i;
maxevents = ( 3 * inpoints ) / 2;
*eventheap = (struct event **) malloc( maxevents * sizeof( struct event * ) );
if ( *eventheap == (struct event **) NULL ) {
printf( "Error: Out of memory.\n" );
exit( 1 );
}
*events = (struct event *) malloc( maxevents * sizeof( struct event ) );
if ( *events == (struct event *) NULL ) {
printf( "Error: Out of memory.\n" );
exit( 1 );
}
traversalinit( &points );
for ( i = 0; i < inpoints; i++ ) {
thispoint = pointtraverse();
( *events )[i].eventptr = (VOID *) thispoint;
( *events )[i].xkey = thispoint[0];
( *events )[i].ykey = thispoint[1];
eventheapinsert( *eventheap, i, *events + i );
}
*freeevents = (struct event *) NULL;
for ( i = maxevents - 1; i >= inpoints; i-- ) {
( *events )[i].eventptr = (VOID *) *freeevents;
*freeevents = *events + i;
}
}
#endif /* not REDUCED */
#ifndef REDUCED
int rightofhyperbola( fronttri, newsite )
struct triedge *fronttri;
point newsite;
{
point leftpoint, rightpoint;
REAL dxa, dya, dxb, dyb;
hyperbolacount++;
dest( *fronttri, leftpoint );
apex( *fronttri, rightpoint );
if ( ( leftpoint[1] < rightpoint[1] )
|| ( ( leftpoint[1] == rightpoint[1] ) && ( leftpoint[0] < rightpoint[0] ) ) ) {
if ( newsite[0] >= rightpoint[0] ) {
return 1;
}
}
else {
if ( newsite[0] <= leftpoint[0] ) {
return 0;
}
}
dxa = leftpoint[0] - newsite[0];
dya = leftpoint[1] - newsite[1];
dxb = rightpoint[0] - newsite[0];
dyb = rightpoint[1] - newsite[1];
return dya * ( dxb * dxb + dyb * dyb ) > dyb * ( dxa * dxa + dya * dya );
}
#endif /* not REDUCED */
#ifndef REDUCED
REAL circletop( pa, pb, pc, ccwabc )
point pa;
point pb;
point pc;
REAL ccwabc;
{
REAL xac, yac, xbc, ybc, xab, yab;
REAL aclen2, bclen2, ablen2;
circletopcount++;
xac = pa[0] - pc[0];
yac = pa[1] - pc[1];
xbc = pb[0] - pc[0];
ybc = pb[1] - pc[1];
xab = pa[0] - pb[0];
yab = pa[1] - pb[1];
aclen2 = xac * xac + yac * yac;
bclen2 = xbc * xbc + ybc * ybc;
ablen2 = xab * xab + yab * yab;
return pc[1] + ( xac * bclen2 - xbc * aclen2 + sqrt( aclen2 * bclen2 * ablen2 ) )
/ ( 2.0 * ccwabc );
}
#endif /* not REDUCED */
#ifndef REDUCED
void check4deadevent( checktri, freeevents, eventheap, heapsize )
struct triedge *checktri;
struct event **freeevents;
struct event **eventheap;
int *heapsize;
{
struct event *deadevent;
point eventpoint;
int eventnum;
org( *checktri, eventpoint );
if ( eventpoint != (point) NULL ) {
deadevent = (struct event *) eventpoint;
eventnum = deadevent->heapposition;
deadevent->eventptr = (VOID *) *freeevents;
*freeevents = deadevent;
eventheapdelete( eventheap, *heapsize, eventnum );
( *heapsize )--;
setorg( *checktri, NULL );
}
}
#endif /* not REDUCED */
#ifndef REDUCED
struct splaynode *splay( splaytree, searchpoint, searchtri )
struct splaynode *splaytree;
point searchpoint;
struct triedge *searchtri;
{
struct splaynode *child, *grandchild;
struct splaynode *lefttree, *righttree;
struct splaynode *leftright;
point checkpoint;
int rightofroot, rightofchild;
if ( splaytree == (struct splaynode *) NULL ) {
return (struct splaynode *) NULL;
}
dest( splaytree->keyedge, checkpoint );
if ( checkpoint == splaytree->keydest ) {
rightofroot = rightofhyperbola( &splaytree->keyedge, searchpoint );
if ( rightofroot ) {
triedgecopy( splaytree->keyedge, *searchtri );
child = splaytree->rchild;
}
else {
child = splaytree->lchild;
}
if ( child == (struct splaynode *) NULL ) {
return splaytree;
}
dest( child->keyedge, checkpoint );
if ( checkpoint != child->keydest ) {
child = splay( child, searchpoint, searchtri );
if ( child == (struct splaynode *) NULL ) {
if ( rightofroot ) {
splaytree->rchild = (struct splaynode *) NULL;
}
else {
splaytree->lchild = (struct splaynode *) NULL;
}
return splaytree;
}
}
rightofchild = rightofhyperbola( &child->keyedge, searchpoint );
if ( rightofchild ) {
triedgecopy( child->keyedge, *searchtri );
grandchild = splay( child->rchild, searchpoint, searchtri );
child->rchild = grandchild;
}
else {
grandchild = splay( child->lchild, searchpoint, searchtri );
child->lchild = grandchild;
}
if ( grandchild == (struct splaynode *) NULL ) {
if ( rightofroot ) {
splaytree->rchild = child->lchild;
child->lchild = splaytree;
}
else {
splaytree->lchild = child->rchild;
child->rchild = splaytree;
}
return child;
}
if ( rightofchild ) {
if ( rightofroot ) {
splaytree->rchild = child->lchild;
child->lchild = splaytree;
}
else {
splaytree->lchild = grandchild->rchild;
grandchild->rchild = splaytree;
}
child->rchild = grandchild->lchild;
grandchild->lchild = child;
}
else {
if ( rightofroot ) {
splaytree->rchild = grandchild->lchild;
grandchild->lchild = splaytree;
}
else {
splaytree->lchild = child->rchild;
child->rchild = splaytree;
}
child->lchild = grandchild->rchild;
grandchild->rchild = child;
}
return grandchild;
}
else {
lefttree = splay( splaytree->lchild, searchpoint, searchtri );
righttree = splay( splaytree->rchild, searchpoint, searchtri );
pooldealloc( &splaynodes, (VOID *) splaytree );
if ( lefttree == (struct splaynode *) NULL ) {
return righttree;
}
else if ( righttree == (struct splaynode *) NULL ) {
return lefttree;
}
else if ( lefttree->rchild == (struct splaynode *) NULL ) {
lefttree->rchild = righttree->lchild;
righttree->lchild = lefttree;
return righttree;
}
else if ( righttree->lchild == (struct splaynode *) NULL ) {
righttree->lchild = lefttree->rchild;
lefttree->rchild = righttree;
return lefttree;
}
else {
/* printf("Holy Toledo!!!\n"); */
leftright = lefttree->rchild;
while ( leftright->rchild != (struct splaynode *) NULL ) {
leftright = leftright->rchild;
}
leftright->rchild = righttree;
return lefttree;
}
}
}
#endif /* not REDUCED */
#ifndef REDUCED
struct splaynode *splayinsert( splayroot, newkey, searchpoint )
struct splaynode *splayroot;
struct triedge *newkey;
point searchpoint;
{
struct splaynode *newsplaynode;
newsplaynode = (struct splaynode *) poolalloc( &splaynodes );
triedgecopy( *newkey, newsplaynode->keyedge );
dest( *newkey, newsplaynode->keydest );
if ( splayroot == (struct splaynode *) NULL ) {
newsplaynode->lchild = (struct splaynode *) NULL;
newsplaynode->rchild = (struct splaynode *) NULL;
}
else if ( rightofhyperbola( &splayroot->keyedge, searchpoint ) ) {
newsplaynode->lchild = splayroot;
newsplaynode->rchild = splayroot->rchild;
splayroot->rchild = (struct splaynode *) NULL;
}
else {
newsplaynode->lchild = splayroot->lchild;
newsplaynode->rchild = splayroot;
splayroot->lchild = (struct splaynode *) NULL;
}
return newsplaynode;
}
#endif /* not REDUCED */
#ifndef REDUCED
struct splaynode *circletopinsert( splayroot, newkey, pa, pb, pc, topy )
struct splaynode *splayroot;
struct triedge *newkey;
point pa;
point pb;
point pc;
REAL topy;
{
REAL ccwabc;
REAL xac, yac, xbc, ybc;
REAL aclen2, bclen2;
REAL searchpoint[2];
struct triedge dummytri;
ccwabc = counterclockwise( pa, pb, pc );
xac = pa[0] - pc[0];
yac = pa[1] - pc[1];
xbc = pb[0] - pc[0];
ybc = pb[1] - pc[1];
aclen2 = xac * xac + yac * yac;
bclen2 = xbc * xbc + ybc * ybc;
searchpoint[0] = pc[0] - ( yac * bclen2 - ybc * aclen2 ) / ( 2.0 * ccwabc );
searchpoint[1] = topy;
return splayinsert( splay( splayroot, (point) searchpoint, &dummytri ), newkey,
(point) searchpoint );
}
#endif /* not REDUCED */
#ifndef REDUCED
struct splaynode *frontlocate( splayroot, bottommost, searchpoint, searchtri,
farright )
struct splaynode *splayroot;
struct triedge *bottommost;
point searchpoint;
struct triedge *searchtri;
int *farright;
{
int farrightflag;
triangle ptr; /* Temporary variable used by onext(). */
triedgecopy( *bottommost, *searchtri );
splayroot = splay( splayroot, searchpoint, searchtri );
farrightflag = 0;
while ( !farrightflag && rightofhyperbola( searchtri, searchpoint ) ) {
onextself( *searchtri );
farrightflag = triedgeequal( *searchtri, *bottommost );
}
*farright = farrightflag;
return splayroot;
}
#endif /* not REDUCED */
#ifndef REDUCED
long sweeplinedelaunay(){
struct event **eventheap;
struct event *events;
struct event *freeevents;
struct event *nextevent;
struct event *newevent;
struct splaynode *splayroot;
struct triedge bottommost;
struct triedge searchtri;
struct triedge fliptri;
struct triedge lefttri, righttri, farlefttri, farrighttri;
struct triedge inserttri;
point firstpoint, secondpoint;
point nextpoint, lastpoint;
point connectpoint;
point leftpoint, midpoint, rightpoint;
REAL lefttest, righttest;
int heapsize;
int check4events, farrightflag;
triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */
poolinit( &splaynodes, sizeof( struct splaynode ), SPLAYNODEPERBLOCK, POINTER,
0 );
splayroot = (struct splaynode *) NULL;
if ( verbose ) {
printf( " Placing points in event heap.\n" );
}
createeventheap( &eventheap, &events, &freeevents );
heapsize = inpoints;
if ( verbose ) {
printf( " Forming triangulation.\n" );
}
maketriangle( &lefttri );
maketriangle( &righttri );
bond( lefttri, righttri );
lnextself( lefttri );
lprevself( righttri );
bond( lefttri, righttri );
lnextself( lefttri );
lprevself( righttri );
bond( lefttri, righttri );
firstpoint = (point) eventheap[0]->eventptr;
eventheap[0]->eventptr = (VOID *) freeevents;
freeevents = eventheap[0];
eventheapdelete( eventheap, heapsize, 0 );
heapsize--;
do {
if ( heapsize == 0 ) {
printf( "Error: Input points are all identical.\n" );
exit( 1 );
}
secondpoint = (point) eventheap[0]->eventptr;
eventheap[0]->eventptr = (VOID *) freeevents;
freeevents = eventheap[0];
eventheapdelete( eventheap, heapsize, 0 );
heapsize--;
if ( ( firstpoint[0] == secondpoint[0] )
&& ( firstpoint[1] == secondpoint[1] ) ) {
printf(
"Warning: A duplicate point at (%.12g, %.12g) appeared and was ignored.\n",
secondpoint[0], secondpoint[1] );
/* Commented out - would eliminate point from output .node file.
setpointmark(secondpoint, DEADPOINT);
*/
}
} while ( ( firstpoint[0] == secondpoint[0] )
&& ( firstpoint[1] == secondpoint[1] ) );
setorg( lefttri, firstpoint );
setdest( lefttri, secondpoint );
setorg( righttri, secondpoint );
setdest( righttri, firstpoint );
lprev( lefttri, bottommost );
lastpoint = secondpoint;
while ( heapsize > 0 ) {
nextevent = eventheap[0];
eventheapdelete( eventheap, heapsize, 0 );
heapsize--;
check4events = 1;
if ( nextevent->xkey < xmin ) {
decode( nextevent->eventptr, fliptri );
oprev( fliptri, farlefttri );
check4deadevent( &farlefttri, &freeevents, eventheap, &heapsize );
onext( fliptri, farrighttri );
check4deadevent( &farrighttri, &freeevents, eventheap, &heapsize );
if ( triedgeequal( farlefttri, bottommost ) ) {
lprev( fliptri, bottommost );
}
flip( &fliptri );
setapex( fliptri, NULL );
lprev( fliptri, lefttri );
lnext( fliptri, righttri );
sym( lefttri, farlefttri );
if ( randomnation( SAMPLERATE ) == 0 ) {
symself( fliptri );
dest( fliptri, leftpoint );
apex( fliptri, midpoint );
org( fliptri, rightpoint );
splayroot = circletopinsert( splayroot, &lefttri, leftpoint, midpoint,
rightpoint, nextevent->ykey );
}
}
else {
nextpoint = (point) nextevent->eventptr;
if ( ( nextpoint[0] == lastpoint[0] ) && ( nextpoint[1] == lastpoint[1] ) ) {
printf(
"Warning: A duplicate point at (%.12g, %.12g) appeared and was ignored.\n",
nextpoint[0], nextpoint[1] );
/* Commented out - would eliminate point from output .node file.
setpointmark(nextpoint, DEADPOINT);
*/
check4events = 0;
}
else {
lastpoint = nextpoint;
splayroot = frontlocate( splayroot, &bottommost, nextpoint, &searchtri,
&farrightflag );
/*
triedgecopy(bottommost, searchtri);
farrightflag = 0;
while (!farrightflag && rightofhyperbola(&searchtri, nextpoint)) {
onextself(searchtri);
farrightflag = triedgeequal(searchtri, bottommost);
}
*/
check4deadevent( &searchtri, &freeevents, eventheap, &heapsize );
triedgecopy( searchtri, farrighttri );
sym( searchtri, farlefttri );
maketriangle( &lefttri );
maketriangle( &righttri );
dest( farrighttri, connectpoint );
setorg( lefttri, connectpoint );
setdest( lefttri, nextpoint );
setorg( righttri, nextpoint );
setdest( righttri, connectpoint );
bond( lefttri, righttri );
lnextself( lefttri );
lprevself( righttri );
bond( lefttri, righttri );
lnextself( lefttri );
lprevself( righttri );
bond( lefttri, farlefttri );
bond( righttri, farrighttri );
if ( !farrightflag && triedgeequal( farrighttri, bottommost ) ) {
triedgecopy( lefttri, bottommost );
}
if ( randomnation( SAMPLERATE ) == 0 ) {
splayroot = splayinsert( splayroot, &lefttri, nextpoint );
}
else if ( randomnation( SAMPLERATE ) == 0 ) {
lnext( righttri, inserttri );
splayroot = splayinsert( splayroot, &inserttri, nextpoint );
}
}
}
nextevent->eventptr = (VOID *) freeevents;
freeevents = nextevent;
if ( check4events ) {
apex( farlefttri, leftpoint );
dest( lefttri, midpoint );
apex( lefttri, rightpoint );
lefttest = counterclockwise( leftpoint, midpoint, rightpoint );
if ( lefttest > 0.0 ) {
newevent = freeevents;
freeevents = (struct event *) freeevents->eventptr;
newevent->xkey = xminextreme;
newevent->ykey = circletop( leftpoint, midpoint, rightpoint,
lefttest );
newevent->eventptr = (VOID *) encode( lefttri );
eventheapinsert( eventheap, heapsize, newevent );
heapsize++;
setorg( lefttri, newevent );
}
apex( righttri, leftpoint );
org( righttri, midpoint );
apex( farrighttri, rightpoint );
righttest = counterclockwise( leftpoint, midpoint, rightpoint );
if ( righttest > 0.0 ) {
newevent = freeevents;
freeevents = (struct event *) freeevents->eventptr;
newevent->xkey = xminextreme;
newevent->ykey = circletop( leftpoint, midpoint, rightpoint,
righttest );
newevent->eventptr = (VOID *) encode( farrighttri );
eventheapinsert( eventheap, heapsize, newevent );
heapsize++;
setorg( farrighttri, newevent );
}
}
}
pooldeinit( &splaynodes );
lprevself( bottommost );
return removeghosts( &bottommost );
}
#endif /* not REDUCED */
/** **/
/** **/
/********* Sweepline Delaunay triangulation ends here *********/
/********* General mesh construction routines begin here *********/
/** **/
/** **/
/*****************************************************************************/
/* */
/* delaunay() Form a Delaunay triangulation. */
/* */
/*****************************************************************************/
long delaunay(){
eextras = 0;
initializetrisegpools();
#ifdef REDUCED
if ( !quiet ) {
printf(
"Constructing Delaunay triangulation by divide-and-conquer method.\n" );
}
return divconqdelaunay();
#else /* not REDUCED */
if ( !quiet ) {
printf( "Constructing Delaunay triangulation " );
if ( incremental ) {
printf( "by incremental method.\n" );
}
else if ( sweepline ) {
printf( "by sweepline method.\n" );
}
else {
printf( "by divide-and-conquer method.\n" );
}
}
if ( incremental ) {
return incrementaldelaunay();
}
else if ( sweepline ) {
return sweeplinedelaunay();
}
else {
return divconqdelaunay();
}
#endif /* not REDUCED */
}
/*****************************************************************************/
/* */
/* reconstruct() Reconstruct a triangulation from its .ele (and possibly */
/* .poly) file. Used when the -r switch is used. */
/* */
/* Reads an .ele file and reconstructs the original mesh. If the -p switch */
/* is used, this procedure will also read a .poly file and reconstruct the */
/* shell edges of the original mesh. If the -a switch is used, this */
/* procedure will also read an .area file and set a maximum area constraint */
/* on each triangle. */
/* */
/* Points that are not corners of triangles, such as nodes on edges of */
/* subparametric elements, are discarded. */
/* */
/* This routine finds the adjacencies between triangles (and shell edges) */
/* by forming one stack of triangles for each vertex. Each triangle is on */
/* three different stacks simultaneously. Each triangle's shell edge */
/* pointers are used to link the items in each stack. This memory-saving */
/* feature makes the code harder to read. The most important thing to keep */
/* in mind is that each triangle is removed from a stack precisely when */
/* the corresponding pointer is adjusted to refer to a shell edge rather */
/* than the next triangle of the stack. */
/* */
/*****************************************************************************/
#ifndef CDT_ONLY
#ifdef TRILIBRARY
int reconstruct( trianglelist, triangleattriblist, trianglearealist, elements,
corners, attribs, segmentlist, segmentmarkerlist,
numberofsegments )
int *trianglelist;
REAL *triangleattriblist;
REAL *trianglearealist;
int elements;
int corners;
int attribs;
int *segmentlist;
int *segmentmarkerlist;
int numberofsegments;
#else /* not TRILIBRARY */
long reconstruct( elefilename, areafilename, polyfilename, polyfile )
char *elefilename;
char *areafilename;
char *polyfilename;
FILE *polyfile;
#endif /* not TRILIBRARY */
{
#ifdef TRILIBRARY
int pointindex;
int attribindex;
#else /* not TRILIBRARY */
FILE *elefile;
FILE *areafile;
char inputline[INPUTLINESIZE];
char *stringptr;
int areaelements;
#endif /* not TRILIBRARY */
struct triedge triangleloop;
struct triedge triangleleft;
struct triedge checktri;
struct triedge checkleft;
struct triedge checkneighbor;
struct edge shelleloop;
triangle *vertexarray;
triangle *prevlink;
triangle nexttri;
point tdest, tapex;
point checkdest, checkapex;
point shorg;
point killpoint;
REAL area;
int corner[3];
int end[2];
int killpointindex;
int incorners;
int segmentmarkers;
int boundmarker;
int aroundpoint;
long hullsize;
int notfound;
int elementnumber, segmentnumber;
int i, j;
triangle ptr; /* Temporary variable used by sym(). */
#ifdef TRILIBRARY
inelements = elements;
incorners = corners;
if ( incorners < 3 ) {
printf( "Error: Triangles must have at least 3 points.\n" );
exit( 1 );
}
eextras = attribs;
#else /* not TRILIBRARY */
/* Read the triangles from an .ele file. */
if ( !quiet ) {
printf( "Opening %s.\n", elefilename );
}
elefile = fopen( elefilename, "r" );
if ( elefile == (FILE *) NULL ) {
printf( " Error: Cannot access file %s.\n", elefilename );
exit( 1 );
}
/* Read number of triangles, number of points per triangle, and */
/* number of triangle attributes from .ele file. */
stringptr = readline( inputline, elefile, elefilename );
inelements = (int) strtol( stringptr, &stringptr, 0 );
stringptr = findfield( stringptr );
if ( *stringptr == '\0' ) {
incorners = 3;
}
else {
incorners = (int) strtol( stringptr, &stringptr, 0 );
if ( incorners < 3 ) {
printf( "Error: Triangles in %s must have at least 3 points.\n",
elefilename );
exit( 1 );
}
}
stringptr = findfield( stringptr );
if ( *stringptr == '\0' ) {
eextras = 0;
}
else {
eextras = (int) strtol( stringptr, &stringptr, 0 );
}
#endif /* not TRILIBRARY */
initializetrisegpools();
/* Create the triangles. */
for ( elementnumber = 1; elementnumber <= inelements; elementnumber++ ) {
maketriangle( &triangleloop );
/* Mark the triangle as living. */
triangleloop.tri[3] = (triangle) triangleloop.tri;
}
if ( poly ) {
#ifdef TRILIBRARY
insegments = numberofsegments;
segmentmarkers = segmentmarkerlist != (int *) NULL;
#else /* not TRILIBRARY */
/* Read number of segments and number of segment */
/* boundary markers from .poly file. */
stringptr = readline( inputline, polyfile, inpolyfilename );
insegments = (int) strtol( stringptr, &stringptr, 0 );
stringptr = findfield( stringptr );
if ( *stringptr == '\0' ) {
segmentmarkers = 0;
}
else {
segmentmarkers = (int) strtol( stringptr, &stringptr, 0 );
}
#endif /* not TRILIBRARY */
/* Create the shell edges. */
for ( segmentnumber = 1; segmentnumber <= insegments; segmentnumber++ ) {
makeshelle( &shelleloop );
/* Mark the shell edge as living. */
shelleloop.sh[2] = (shelle) shelleloop.sh;
}
}
#ifdef TRILIBRARY
pointindex = 0;
attribindex = 0;
#else /* not TRILIBRARY */
if ( vararea ) {
/* Open an .area file, check for consistency with the .ele file. */
if ( !quiet ) {
printf( "Opening %s.\n", areafilename );
}
areafile = fopen( areafilename, "r" );
if ( areafile == (FILE *) NULL ) {
printf( " Error: Cannot access file %s.\n", areafilename );
exit( 1 );
}
stringptr = readline( inputline, areafile, areafilename );
areaelements = (int) strtol( stringptr, &stringptr, 0 );
if ( areaelements != inelements ) {
printf( "Error: %s and %s disagree on number of triangles.\n",
elefilename, areafilename );
exit( 1 );
}
}
#endif /* not TRILIBRARY */
if ( !quiet ) {
printf( "Reconstructing mesh.\n" );
}
/* Allocate a temporary array that maps each point to some adjacent */
/* triangle. I took care to allocate all the permanent memory for */
/* triangles and shell edges first. */
vertexarray = (triangle *) malloc( points.items * sizeof( triangle ) );
if ( vertexarray == (triangle *) NULL ) {
printf( "Error: Out of memory.\n" );
exit( 1 );
}
/* Each point is initially unrepresented. */
for ( i = 0; i < points.items; i++ ) {
vertexarray[i] = (triangle) dummytri;
}
if ( verbose ) {
printf( " Assembling triangles.\n" );
}
/* Read the triangles from the .ele file, and link */
/* together those that share an edge. */
traversalinit( &triangles );
triangleloop.tri = triangletraverse();
elementnumber = firstnumber;
while ( triangleloop.tri != (triangle *) NULL ) {
#ifdef TRILIBRARY
/* Copy the triangle's three corners. */
for ( j = 0; j < 3; j++ ) {
corner[j] = trianglelist[pointindex++];
if ( ( corner[j] < firstnumber ) || ( corner[j] >= firstnumber + inpoints ) ) {
printf( "Error: Triangle %d has an invalid vertex index.\n",
elementnumber );
exit( 1 );
}
}
#else /* not TRILIBRARY */
/* Read triangle number and the triangle's three corners. */
stringptr = readline( inputline, elefile, elefilename );
for ( j = 0; j < 3; j++ ) {
stringptr = findfield( stringptr );
if ( *stringptr == '\0' ) {
printf( "Error: Triangle %d is missing point %d in %s.\n",
elementnumber, j + 1, elefilename );
exit( 1 );
}
else {
corner[j] = (int) strtol( stringptr, &stringptr, 0 );
if ( ( corner[j] < firstnumber ) ||
( corner[j] >= firstnumber + inpoints ) ) {
printf( "Error: Triangle %d has an invalid vertex index.\n",
elementnumber );
exit( 1 );
}
}
}
#endif /* not TRILIBRARY */
/* Find out about (and throw away) extra nodes. */
for ( j = 3; j < incorners; j++ ) {
#ifdef TRILIBRARY
killpointindex = trianglelist[pointindex++];
#else /* not TRILIBRARY */
stringptr = findfield( stringptr );
if ( *stringptr != '\0' ) {
killpointindex = (int) strtol( stringptr, &stringptr, 0 );
#endif /* not TRILIBRARY */
if ( ( killpointindex >= firstnumber ) &&
( killpointindex < firstnumber + inpoints ) ) {
/* Delete the non-corner point if it's not already deleted. */
killpoint = getpoint( killpointindex );
if ( pointmark( killpoint ) != DEADPOINT ) {
pointdealloc( killpoint );
}
}
#ifndef TRILIBRARY
}
#endif /* not TRILIBRARY */
}
/* Read the triangle's attributes. */
for ( j = 0; j < eextras; j++ ) {
#ifdef TRILIBRARY
setelemattribute( triangleloop, j, triangleattriblist[attribindex++] );
#else /* not TRILIBRARY */
stringptr = findfield( stringptr );
if ( *stringptr == '\0' ) {
setelemattribute( triangleloop, j, 0 );
}
else {
setelemattribute( triangleloop, j,
(REAL) strtod( stringptr, &stringptr ) );
}
#endif /* not TRILIBRARY */
}
if ( vararea ) {
#ifdef TRILIBRARY
area = trianglearealist[elementnumber - firstnumber];
#else /* not TRILIBRARY */
/* Read an area constraint from the .area file. */
stringptr = readline( inputline, areafile, areafilename );
stringptr = findfield( stringptr );
if ( *stringptr == '\0' ) {
area = -1.0; /* No constraint on this triangle. */
}
else {
area = (REAL) strtod( stringptr, &stringptr );
}
#endif /* not TRILIBRARY */
setareabound( triangleloop, area );
}
/* Set the triangle's vertices. */
triangleloop.orient = 0;
setorg( triangleloop, getpoint( corner[0] ) );
setdest( triangleloop, getpoint( corner[1] ) );
setapex( triangleloop, getpoint( corner[2] ) );
/* Try linking the triangle to others that share these vertices. */
for ( triangleloop.orient = 0; triangleloop.orient < 3;
triangleloop.orient++ ) {
/* Take the number for the origin of triangleloop. */
aroundpoint = corner[triangleloop.orient];
/* Look for other triangles having this vertex. */
nexttri = vertexarray[aroundpoint - firstnumber];
/* Link the current triangle to the next one in the stack. */
triangleloop.tri[6 + triangleloop.orient] = nexttri;
/* Push the current triangle onto the stack. */
vertexarray[aroundpoint - firstnumber] = encode( triangleloop );
decode( nexttri, checktri );
if ( checktri.tri != dummytri ) {
dest( triangleloop, tdest );
apex( triangleloop, tapex );
/* Look for other triangles that share an edge. */
do {
dest( checktri, checkdest );
apex( checktri, checkapex );
if ( tapex == checkdest ) {
/* The two triangles share an edge; bond them together. */
lprev( triangleloop, triangleleft );
bond( triangleleft, checktri );
}
if ( tdest == checkapex ) {
/* The two triangles share an edge; bond them together. */
lprev( checktri, checkleft );
bond( triangleloop, checkleft );
}
/* Find the next triangle in the stack. */
nexttri = checktri.tri[6 + checktri.orient];
decode( nexttri, checktri );
} while ( checktri.tri != dummytri );
}
}
triangleloop.tri = triangletraverse();
elementnumber++;
}
#ifdef TRILIBRARY
pointindex = 0;
#else /* not TRILIBRARY */
fclose( elefile );
if ( vararea ) {
fclose( areafile );
}
#endif /* not TRILIBRARY */
hullsize = 0; /* Prepare to count the boundary edges. */
if ( poly ) {
if ( verbose ) {
printf( " Marking segments in triangulation.\n" );
}
/* Read the segments from the .poly file, and link them */
/* to their neighboring triangles. */
boundmarker = 0;
traversalinit( &shelles );
shelleloop.sh = shelletraverse();
segmentnumber = firstnumber;
while ( shelleloop.sh != (shelle *) NULL ) {
#ifdef TRILIBRARY
end[0] = segmentlist[pointindex++];
end[1] = segmentlist[pointindex++];
if ( segmentmarkers ) {
boundmarker = segmentmarkerlist[segmentnumber - firstnumber];
}
#else /* not TRILIBRARY */
/* Read the endpoints of each segment, and possibly a boundary marker. */
stringptr = readline( inputline, polyfile, inpolyfilename );
/* Skip the first (segment number) field. */
stringptr = findfield( stringptr );
if ( *stringptr == '\0' ) {
printf( "Error: Segment %d has no endpoints in %s.\n", segmentnumber,
polyfilename );
exit( 1 );
}
else {
end[0] = (int) strtol( stringptr, &stringptr, 0 );
}
stringptr = findfield( stringptr );
if ( *stringptr == '\0' ) {
printf( "Error: Segment %d is missing its second endpoint in %s.\n",
segmentnumber, polyfilename );
exit( 1 );
}
else {
end[1] = (int) strtol( stringptr, &stringptr, 0 );
}
if ( segmentmarkers ) {
stringptr = findfield( stringptr );
if ( *stringptr == '\0' ) {
boundmarker = 0;
}
else {
boundmarker = (int) strtol( stringptr, &stringptr, 0 );
}
}
#endif /* not TRILIBRARY */
for ( j = 0; j < 2; j++ ) {
if ( ( end[j] < firstnumber ) || ( end[j] >= firstnumber + inpoints ) ) {
printf( "Error: Segment %d has an invalid vertex index.\n",
segmentnumber );
exit( 1 );
}
}
/* set the shell edge's vertices. */
shelleloop.shorient = 0;
setsorg( shelleloop, getpoint( end[0] ) );
setsdest( shelleloop, getpoint( end[1] ) );
setmark( shelleloop, boundmarker );
/* Try linking the shell edge to triangles that share these vertices. */
for ( shelleloop.shorient = 0; shelleloop.shorient < 2;
shelleloop.shorient++ ) {
/* Take the number for the destination of shelleloop. */
aroundpoint = end[1 - shelleloop.shorient];
/* Look for triangles having this vertex. */
prevlink = &vertexarray[aroundpoint - firstnumber];
nexttri = vertexarray[aroundpoint - firstnumber];
decode( nexttri, checktri );
sorg( shelleloop, shorg );
notfound = 1;
/* Look for triangles having this edge. Note that I'm only */
/* comparing each triangle's destination with the shell edge; */
/* each triangle's apex is handled through a different vertex. */
/* Because each triangle appears on three vertices' lists, each */
/* occurrence of a triangle on a list can (and does) represent */
/* an edge. In this way, most edges are represented twice, and */
/* every triangle-segment bond is represented once. */
while ( notfound && ( checktri.tri != dummytri ) ) {
dest( checktri, checkdest );
if ( shorg == checkdest ) {
/* We have a match. Remove this triangle from the list. */
*prevlink = checktri.tri[6 + checktri.orient];
/* Bond the shell edge to the triangle. */
tsbond( checktri, shelleloop );
/* Check if this is a boundary edge. */
sym( checktri, checkneighbor );
if ( checkneighbor.tri == dummytri ) {
/* The next line doesn't insert a shell edge (because there's */
/* already one there), but it sets the boundary markers of */
/* the existing shell edge and its vertices. */
insertshelle( &checktri, 1 );
hullsize++;
}
notfound = 0;
}
/* Find the next triangle in the stack. */
prevlink = &checktri.tri[6 + checktri.orient];
nexttri = checktri.tri[6 + checktri.orient];
decode( nexttri, checktri );
}
}
shelleloop.sh = shelletraverse();
segmentnumber++;
}
}
/* Mark the remaining edges as not being attached to any shell edge. */
/* Also, count the (yet uncounted) boundary edges. */
for ( i = 0; i < points.items; i++ ) {
/* Search the stack of triangles adjacent to a point. */
nexttri = vertexarray[i];
decode( nexttri, checktri );
while ( checktri.tri != dummytri ) {
/* Find the next triangle in the stack before this */
/* information gets overwritten. */
nexttri = checktri.tri[6 + checktri.orient];
/* No adjacent shell edge. (This overwrites the stack info.) */
tsdissolve( checktri );
sym( checktri, checkneighbor );
if ( checkneighbor.tri == dummytri ) {
insertshelle( &checktri, 1 );
hullsize++;
}
decode( nexttri, checktri );
}
}
free( vertexarray );
return hullsize;
}
#endif /* not CDT_ONLY */
/** **/
/** **/
/********* General mesh construction routines end here *********/
/********* Segment (shell edge) insertion begins here *********/
/** **/
/** **/
/*****************************************************************************/
/* */
/* finddirection() Find the first triangle on the path from one point */
/* to another. */
/* */
/* Finds the triangle that intersects a line segment drawn from the */
/* origin of `searchtri' to the point `endpoint', and returns the result */
/* in `searchtri'. The origin of `searchtri' does not change, even though */
/* the triangle returned may differ from the one passed in. This routine */
/* is used to find the direction to move in to get from one point to */
/* another. */
/* */
/* The return value notes whether the destination or apex of the found */
/* triangle is collinear with the two points in question. */
/* */
/*****************************************************************************/
enum finddirectionresult finddirection( searchtri, endpoint )
struct triedge *searchtri;
point endpoint;
{
struct triedge checktri;
point startpoint;
point leftpoint, rightpoint;
REAL leftccw, rightccw;
int leftflag, rightflag;
triangle ptr; /* Temporary variable used by onext() and oprev(). */
org( *searchtri, startpoint );
dest( *searchtri, rightpoint );
apex( *searchtri, leftpoint );
/* Is `endpoint' to the left? */
leftccw = counterclockwise( endpoint, startpoint, leftpoint );
leftflag = leftccw > 0.0;
/* Is `endpoint' to the right? */
rightccw = counterclockwise( startpoint, endpoint, rightpoint );
rightflag = rightccw > 0.0;
if ( leftflag && rightflag ) {
/* `searchtri' faces directly away from `endpoint'. We could go */
/* left or right. Ask whether it's a triangle or a boundary */
/* on the left. */
onext( *searchtri, checktri );
if ( checktri.tri == dummytri ) {
leftflag = 0;
}
else {
rightflag = 0;
}
}
while ( leftflag ) {
/* Turn left until satisfied. */
onextself( *searchtri );
if ( searchtri->tri == dummytri ) {
printf( "Internal error in finddirection(): Unable to find a\n" );
printf( " triangle leading from (%.12g, %.12g) to", startpoint[0],
startpoint[1] );
printf( " (%.12g, %.12g).\n", endpoint[0], endpoint[1] );
internalerror();
}
apex( *searchtri, leftpoint );
rightccw = leftccw;
leftccw = counterclockwise( endpoint, startpoint, leftpoint );
leftflag = leftccw > 0.0;
}
while ( rightflag ) {
/* Turn right until satisfied. */
oprevself( *searchtri );
if ( searchtri->tri == dummytri ) {
printf( "Internal error in finddirection(): Unable to find a\n" );
printf( " triangle leading from (%.12g, %.12g) to", startpoint[0],
startpoint[1] );
printf( " (%.12g, %.12g).\n", endpoint[0], endpoint[1] );
internalerror();
}
dest( *searchtri, rightpoint );
leftccw = rightccw;
rightccw = counterclockwise( startpoint, endpoint, rightpoint );
rightflag = rightccw > 0.0;
}
if ( leftccw == 0.0 ) {
return LEFTCOLLINEAR;
}
else if ( rightccw == 0.0 ) {
return RIGHTCOLLINEAR;
}
else {
return WITHIN;
}
}
/*****************************************************************************/
/* */
/* segmentintersection() Find the intersection of an existing segment */
/* and a segment that is being inserted. Insert */
/* a point at the intersection, splitting an */
/* existing shell edge. */
/* */
/* The segment being inserted connects the apex of splittri to endpoint2. */
/* splitshelle is the shell edge being split, and MUST be opposite */
/* splittri. Hence, the edge being split connects the origin and */
/* destination of splittri. */
/* */
/* On completion, splittri is a handle having the newly inserted */
/* intersection point as its origin, and endpoint1 as its destination. */
/* */
/*****************************************************************************/
void segmentintersection( splittri, splitshelle, endpoint2 )
struct triedge *splittri;
struct edge *splitshelle;
point endpoint2;
{
point endpoint1;
point torg, tdest;
point leftpoint, rightpoint;
point newpoint;
enum insertsiteresult success;
enum finddirectionresult collinear;
REAL ex, ey;
REAL tx, ty;
REAL etx, ety;
REAL split, denom;
int i;
triangle ptr; /* Temporary variable used by onext(). */
/* Find the other three segment endpoints. */
apex( *splittri, endpoint1 );
org( *splittri, torg );
dest( *splittri, tdest );
/* Segment intersection formulae; see the Antonio reference. */
tx = tdest[0] - torg[0];
ty = tdest[1] - torg[1];
ex = endpoint2[0] - endpoint1[0];
ey = endpoint2[1] - endpoint1[1];
etx = torg[0] - endpoint2[0];
ety = torg[1] - endpoint2[1];
denom = ty * ex - tx * ey;
if ( denom == 0.0 ) {
printf( "Internal error in segmentintersection():" );
printf( " Attempt to find intersection of parallel segments.\n" );
internalerror();
}
split = ( ey * etx - ex * ety ) / denom;
/* Create the new point. */
newpoint = (point) poolalloc( &points );
/* Interpolate its coordinate and attributes. */
for ( i = 0; i < 2 + nextras; i++ ) {
newpoint[i] = torg[i] + split * ( tdest[i] - torg[i] );
}
setpointmark( newpoint, mark( *splitshelle ) );
if ( verbose > 1 ) {
printf(
" Splitting edge (%.12g, %.12g) (%.12g, %.12g) at (%.12g, %.12g).\n",
torg[0], torg[1], tdest[0], tdest[1], newpoint[0], newpoint[1] );
}
/* Insert the intersection point. This should always succeed. */
success = insertsite( newpoint, splittri, splitshelle, 0, 0 );
if ( success != SUCCESSFULPOINT ) {
printf( "Internal error in segmentintersection():\n" );
printf( " Failure to split a segment.\n" );
internalerror();
}
if ( steinerleft > 0 ) {
steinerleft--;
}
/* Inserting the point may have caused edge flips. We wish to rediscover */
/* the edge connecting endpoint1 to the new intersection point. */
collinear = finddirection( splittri, endpoint1 );
dest( *splittri, rightpoint );
apex( *splittri, leftpoint );
if ( ( leftpoint[0] == endpoint1[0] ) && ( leftpoint[1] == endpoint1[1] ) ) {
onextself( *splittri );
}
else if ( ( rightpoint[0] != endpoint1[0] ) ||
( rightpoint[1] != endpoint1[1] ) ) {
printf( "Internal error in segmentintersection():\n" );
printf( " Topological inconsistency after splitting a segment.\n" );
internalerror();
}
/* `splittri' should have destination endpoint1. */
}
/*****************************************************************************/
/* */
/* scoutsegment() Scout the first triangle on the path from one endpoint */
/* to another, and check for completion (reaching the */
/* second endpoint), a collinear point, and the */
/* intersection of two segments. */
/* */
/* Returns one if the entire segment is successfully inserted, and zero if */
/* the job must be finished by conformingedge() or constrainededge(). */
/* */
/* If the first triangle on the path has the second endpoint as its */
/* destination or apex, a shell edge is inserted and the job is done. */
/* */
/* If the first triangle on the path has a destination or apex that lies on */
/* the segment, a shell edge is inserted connecting the first endpoint to */
/* the collinear point, and the search is continued from the collinear */
/* point. */
/* */
/* If the first triangle on the path has a shell edge opposite its origin, */
/* then there is a segment that intersects the segment being inserted. */
/* Their intersection point is inserted, splitting the shell edge. */
/* */
/* Otherwise, return zero. */
/* */
/*****************************************************************************/
int scoutsegment( searchtri, endpoint2, newmark )
struct triedge *searchtri;
point endpoint2;
int newmark;
{
struct triedge crosstri;
struct edge crossedge;
point leftpoint, rightpoint;
point endpoint1;
enum finddirectionresult collinear;
shelle sptr; /* Temporary variable used by tspivot(). */
collinear = finddirection( searchtri, endpoint2 );
dest( *searchtri, rightpoint );
apex( *searchtri, leftpoint );
if ( ( ( leftpoint[0] == endpoint2[0] ) && ( leftpoint[1] == endpoint2[1] ) ) ||
( ( rightpoint[0] == endpoint2[0] ) && ( rightpoint[1] == endpoint2[1] ) ) ) {
/* The segment is already an edge in the mesh. */
if ( ( leftpoint[0] == endpoint2[0] ) && ( leftpoint[1] == endpoint2[1] ) ) {
lprevself( *searchtri );
}
/* Insert a shell edge, if there isn't already one there. */
insertshelle( searchtri, newmark );
return 1;
}
else if ( collinear == LEFTCOLLINEAR ) {
/* We've collided with a point between the segment's endpoints. */
/* Make the collinear point be the triangle's origin. */
lprevself( *searchtri );
insertshelle( searchtri, newmark );
/* Insert the remainder of the segment. */
return scoutsegment( searchtri, endpoint2, newmark );
}
else if ( collinear == RIGHTCOLLINEAR ) {
/* We've collided with a point between the segment's endpoints. */
insertshelle( searchtri, newmark );
/* Make the collinear point be the triangle's origin. */
lnextself( *searchtri );
/* Insert the remainder of the segment. */
return scoutsegment( searchtri, endpoint2, newmark );
}
else {
lnext( *searchtri, crosstri );
tspivot( crosstri, crossedge );
/* Check for a crossing segment. */
if ( crossedge.sh == dummysh ) {
return 0;
}
else {
org( *searchtri, endpoint1 );
/* Insert a point at the intersection. */
segmentintersection( &crosstri, &crossedge, endpoint2 );
triedgecopy( crosstri, *searchtri );
insertshelle( searchtri, newmark );
/* Insert the remainder of the segment. */
return scoutsegment( searchtri, endpoint2, newmark );
}
}
}
/*****************************************************************************/
/* */
/* conformingedge() Force a segment into a conforming Delaunay */
/* triangulation by inserting a point at its midpoint, */
/* and recursively forcing in the two half-segments if */
/* necessary. */
/* */
/* Generates a sequence of edges connecting `endpoint1' to `endpoint2'. */
/* `newmark' is the boundary marker of the segment, assigned to each new */
/* splitting point and shell edge. */
/* */
/* Note that conformingedge() does not always maintain the conforming */
/* Delaunay property. Once inserted, segments are locked into place; */
/* points inserted later (to force other segments in) may render these */
/* fixed segments non-Delaunay. The conforming Delaunay property will be */
/* restored by enforcequality() by splitting encroached segments. */
/* */
/*****************************************************************************/
#ifndef REDUCED
#ifndef CDT_ONLY
void conformingedge( endpoint1, endpoint2, newmark )
point endpoint1;
point endpoint2;
int newmark;
{
struct triedge searchtri1, searchtri2;
struct edge brokenshelle;
point newpoint;
point midpoint1, midpoint2;
enum insertsiteresult success;
int result1, result2;
int i;
shelle sptr; /* Temporary variable used by tspivot(). */
if ( verbose > 2 ) {
printf( "Forcing segment into triangulation by recursive splitting:\n" );
printf( " (%.12g, %.12g) (%.12g, %.12g)\n", endpoint1[0], endpoint1[1],
endpoint2[0], endpoint2[1] );
}
/* Create a new point to insert in the middle of the segment. */
newpoint = (point) poolalloc( &points );
/* Interpolate coordinates and attributes. */
for ( i = 0; i < 2 + nextras; i++ ) {
newpoint[i] = 0.5 * ( endpoint1[i] + endpoint2[i] );
}
setpointmark( newpoint, newmark );
/* Find a boundary triangle to search from. */
searchtri1.tri = (triangle *) NULL;
/* Attempt to insert the new point. */
success = insertsite( newpoint, &searchtri1, (struct edge *) NULL, 0, 0 );
if ( success == DUPLICATEPOINT ) {
if ( verbose > 2 ) {
printf( " Segment intersects existing point (%.12g, %.12g).\n",
newpoint[0], newpoint[1] );
}
/* Use the point that's already there. */
pointdealloc( newpoint );
org( searchtri1, newpoint );
}
else {
if ( success == VIOLATINGPOINT ) {
if ( verbose > 2 ) {
printf( " Two segments intersect at (%.12g, %.12g).\n",
newpoint[0], newpoint[1] );
}
/* By fluke, we've landed right on another segment. Split it. */
tspivot( searchtri1, brokenshelle );
success = insertsite( newpoint, &searchtri1, &brokenshelle, 0, 0 );
if ( success != SUCCESSFULPOINT ) {
printf( "Internal error in conformingedge():\n" );
printf( " Failure to split a segment.\n" );
internalerror();
}
}
/* The point has been inserted successfully. */
if ( steinerleft > 0 ) {
steinerleft--;
}
}
triedgecopy( searchtri1, searchtri2 );
result1 = scoutsegment( &searchtri1, endpoint1, newmark );
result2 = scoutsegment( &searchtri2, endpoint2, newmark );
if ( !result1 ) {
/* The origin of searchtri1 may have changed if a collision with an */
/* intervening vertex on the segment occurred. */
org( searchtri1, midpoint1 );
conformingedge( midpoint1, endpoint1, newmark );
}
if ( !result2 ) {
/* The origin of searchtri2 may have changed if a collision with an */
/* intervening vertex on the segment occurred. */
org( searchtri2, midpoint2 );
conformingedge( midpoint2, endpoint2, newmark );
}
}
#endif /* not CDT_ONLY */
#endif /* not REDUCED */
/*****************************************************************************/
/* */
/* delaunayfixup() Enforce the Delaunay condition at an edge, fanning out */
/* recursively from an existing point. Pay special */
/* attention to stacking inverted triangles. */
/* */
/* This is a support routine for inserting segments into a constrained */
/* Delaunay triangulation. */
/* */
/* The origin of fixuptri is treated as if it has just been inserted, and */
/* the local Delaunay condition needs to be enforced. It is only enforced */
/* in one sector, however, that being the angular range defined by */
/* fixuptri. */
/* */
/* This routine also needs to make decisions regarding the "stacking" of */
/* triangles. (Read the description of constrainededge() below before */
/* reading on here, so you understand the algorithm.) If the position of */
/* the new point (the origin of fixuptri) indicates that the vertex before */
/* it on the polygon is a reflex vertex, then "stack" the triangle by */
/* doing nothing. (fixuptri is an inverted triangle, which is how stacked */
/* triangles are identified.) */
/* */
/* Otherwise, check whether the vertex before that was a reflex vertex. */
/* If so, perform an edge flip, thereby eliminating an inverted triangle */
/* (popping it off the stack). The edge flip may result in the creation */
/* of a new inverted triangle, depending on whether or not the new vertex */
/* is visible to the vertex three edges behind on the polygon. */
/* */
/* If neither of the two vertices behind the new vertex are reflex */
/* vertices, fixuptri and fartri, the triangle opposite it, are not */
/* inverted; hence, ensure that the edge between them is locally Delaunay. */
/* */
/* `leftside' indicates whether or not fixuptri is to the left of the */
/* segment being inserted. (Imagine that the segment is pointing up from */
/* endpoint1 to endpoint2.) */
/* */
/*****************************************************************************/
void delaunayfixup( fixuptri, leftside )
struct triedge *fixuptri;
int leftside;
{
struct triedge neartri;
struct triedge fartri;
struct edge faredge;
point nearpoint, leftpoint, rightpoint, farpoint;
triangle ptr; /* Temporary variable used by sym(). */
shelle sptr; /* Temporary variable used by tspivot(). */
lnext( *fixuptri, neartri );
sym( neartri, fartri );
/* Check if the edge opposite the origin of fixuptri can be flipped. */
if ( fartri.tri == dummytri ) {
return;
}
tspivot( neartri, faredge );
if ( faredge.sh != dummysh ) {
return;
}
/* Find all the relevant vertices. */
apex( neartri, nearpoint );
org( neartri, leftpoint );
dest( neartri, rightpoint );
apex( fartri, farpoint );
/* Check whether the previous polygon vertex is a reflex vertex. */
if ( leftside ) {
if ( counterclockwise( nearpoint, leftpoint, farpoint ) <= 0.0 ) {
/* leftpoint is a reflex vertex too. Nothing can */
/* be done until a convex section is found. */
return;
}
}
else {
if ( counterclockwise( farpoint, rightpoint, nearpoint ) <= 0.0 ) {
/* rightpoint is a reflex vertex too. Nothing can */
/* be done until a convex section is found. */
return;
}
}
if ( counterclockwise( rightpoint, leftpoint, farpoint ) > 0.0 ) {
/* fartri is not an inverted triangle, and farpoint is not a reflex */
/* vertex. As there are no reflex vertices, fixuptri isn't an */
/* inverted triangle, either. Hence, test the edge between the */
/* triangles to ensure it is locally Delaunay. */
if ( incircle( leftpoint, farpoint, rightpoint, nearpoint ) <= 0.0 ) {
return;
}
/* Not locally Delaunay; go on to an edge flip. */
} /* else fartri is inverted; remove it from the stack by flipping. */
flip( &neartri );
lprevself( *fixuptri ); /* Restore the origin of fixuptri after the flip. */
/* Recursively process the two triangles that result from the flip. */
delaunayfixup( fixuptri, leftside );
delaunayfixup( &fartri, leftside );
}
/*****************************************************************************/
/* */
/* constrainededge() Force a segment into a constrained Delaunay */
/* triangulation by deleting the triangles it */
/* intersects, and triangulating the polygons that */
/* form on each side of it. */
/* */
/* Generates a single edge connecting `endpoint1' to `endpoint2'. The */
/* triangle `starttri' has `endpoint1' as its origin. `newmark' is the */
/* boundary marker of the segment. */
/* */
/* To insert a segment, every triangle whose interior intersects the */
/* segment is deleted. The union of these deleted triangles is a polygon */
/* (which is not necessarily monotone, but is close enough), which is */
/* divided into two polygons by the new segment. This routine's task is */
/* to generate the Delaunay triangulation of these two polygons. */
/* */
/* You might think of this routine's behavior as a two-step process. The */
/* first step is to walk from endpoint1 to endpoint2, flipping each edge */
/* encountered. This step creates a fan of edges connected to endpoint1, */
/* including the desired edge to endpoint2. The second step enforces the */
/* Delaunay condition on each side of the segment in an incremental manner: */
/* proceeding along the polygon from endpoint1 to endpoint2 (this is done */
/* independently on each side of the segment), each vertex is "enforced" */
/* as if it had just been inserted, but affecting only the previous */
/* vertices. The result is the same as if the vertices had been inserted */
/* in the order they appear on the polygon, so the result is Delaunay. */
/* */
/* In truth, constrainededge() interleaves these two steps. The procedure */
/* walks from endpoint1 to endpoint2, and each time an edge is encountered */
/* and flipped, the newly exposed vertex (at the far end of the flipped */
/* edge) is "enforced" upon the previously flipped edges, usually affecting */
/* only one side of the polygon (depending upon which side of the segment */
/* the vertex falls on). */
/* */
/* The algorithm is complicated by the need to handle polygons that are not */
/* convex. Although the polygon is not necessarily monotone, it can be */
/* triangulated in a manner similar to the stack-based algorithms for */
/* monotone polygons. For each reflex vertex (local concavity) of the */
/* polygon, there will be an inverted triangle formed by one of the edge */
/* flips. (An inverted triangle is one with negative area - that is, its */
/* vertices are arranged in clockwise order - and is best thought of as a */
/* wrinkle in the fabric of the mesh.) Each inverted triangle can be */
/* thought of as a reflex vertex pushed on the stack, waiting to be fixed */
/* later. */
/* */
/* A reflex vertex is popped from the stack when a vertex is inserted that */
/* is visible to the reflex vertex. (However, if the vertex behind the */
/* reflex vertex is not visible to the reflex vertex, a new inverted */
/* triangle will take its place on the stack.) These details are handled */
/* by the delaunayfixup() routine above. */
/* */
/*****************************************************************************/
void constrainededge( starttri, endpoint2, newmark )
struct triedge *starttri;
point endpoint2;
int newmark;
{
struct triedge fixuptri, fixuptri2;
struct edge fixupedge;
point endpoint1;
point farpoint;
REAL area;
int collision;
int done;
triangle ptr; /* Temporary variable used by sym() and oprev(). */
shelle sptr; /* Temporary variable used by tspivot(). */
org( *starttri, endpoint1 );
lnext( *starttri, fixuptri );
flip( &fixuptri );
/* `collision' indicates whether we have found a point directly */
/* between endpoint1 and endpoint2. */
collision = 0;
done = 0;
do {
org( fixuptri, farpoint );
/* `farpoint' is the extreme point of the polygon we are "digging" */
/* to get from endpoint1 to endpoint2. */
if ( ( farpoint[0] == endpoint2[0] ) && ( farpoint[1] == endpoint2[1] ) ) {
oprev( fixuptri, fixuptri2 );
/* Enforce the Delaunay condition around endpoint2. */
delaunayfixup( &fixuptri, 0 );
delaunayfixup( &fixuptri2, 1 );
done = 1;
}
else {
/* Check whether farpoint is to the left or right of the segment */
/* being inserted, to decide which edge of fixuptri to dig */
/* through next. */
area = counterclockwise( endpoint1, endpoint2, farpoint );
if ( area == 0.0 ) {
/* We've collided with a point between endpoint1 and endpoint2. */
collision = 1;
oprev( fixuptri, fixuptri2 );
/* Enforce the Delaunay condition around farpoint. */
delaunayfixup( &fixuptri, 0 );
delaunayfixup( &fixuptri2, 1 );
done = 1;
}
else {
if ( area > 0.0 ) { /* farpoint is to the left of the segment. */
oprev( fixuptri, fixuptri2 );
/* Enforce the Delaunay condition around farpoint, on the */
/* left side of the segment only. */
delaunayfixup( &fixuptri2, 1 );
/* Flip the edge that crosses the segment. After the edge is */
/* flipped, one of its endpoints is the fan vertex, and the */
/* destination of fixuptri is the fan vertex. */
lprevself( fixuptri );
}
else { /* farpoint is to the right of the segment. */
delaunayfixup( &fixuptri, 0 );
/* Flip the edge that crosses the segment. After the edge is */
/* flipped, one of its endpoints is the fan vertex, and the */
/* destination of fixuptri is the fan vertex. */
oprevself( fixuptri );
}
/* Check for two intersecting segments. */
tspivot( fixuptri, fixupedge );
if ( fixupedge.sh == dummysh ) {
flip( &fixuptri ); /* May create an inverted triangle on the left. */
}
else {
/* We've collided with a segment between endpoint1 and endpoint2. */
collision = 1;
/* Insert a point at the intersection. */
segmentintersection( &fixuptri, &fixupedge, endpoint2 );
done = 1;
}
}
}
} while ( !done );
/* Insert a shell edge to make the segment permanent. */
insertshelle( &fixuptri, newmark );
/* If there was a collision with an interceding vertex, install another */
/* segment connecting that vertex with endpoint2. */
if ( collision ) {
/* Insert the remainder of the segment. */
if ( !scoutsegment( &fixuptri, endpoint2, newmark ) ) {
constrainededge( &fixuptri, endpoint2, newmark );
}
}
}
/*****************************************************************************/
/* */
/* insertsegment() Insert a PSLG segment into a triangulation. */
/* */
/*****************************************************************************/
void insertsegment( endpoint1, endpoint2, newmark )
point endpoint1;
point endpoint2;
int newmark;
{
struct triedge searchtri1, searchtri2;
triangle encodedtri;
point checkpoint;
triangle ptr; /* Temporary variable used by sym(). */
if ( verbose > 1 ) {
printf( " Connecting (%.12g, %.12g) to (%.12g, %.12g).\n",
endpoint1[0], endpoint1[1], endpoint2[0], endpoint2[1] );
}
/* Find a triangle whose origin is the segment's first endpoint. */
checkpoint = (point) NULL;
encodedtri = point2tri( endpoint1 );
if ( encodedtri != (triangle) NULL ) {
decode( encodedtri, searchtri1 );
org( searchtri1, checkpoint );
}
if ( checkpoint != endpoint1 ) {
/* Find a boundary triangle to search from. */
searchtri1.tri = dummytri;
searchtri1.orient = 0;
symself( searchtri1 );
/* Search for the segment's first endpoint by point location. */
if ( locate( endpoint1, &searchtri1 ) != ONVERTEX ) {
printf(
"Internal error in insertsegment(): Unable to locate PSLG point\n" );
printf( " (%.12g, %.12g) in triangulation.\n",
endpoint1[0], endpoint1[1] );
internalerror();
}
}
/* Remember this triangle to improve subsequent point location. */
triedgecopy( searchtri1, recenttri );
/* Scout the beginnings of a path from the first endpoint */
/* toward the second. */
if ( scoutsegment( &searchtri1, endpoint2, newmark ) ) {
/* The segment was easily inserted. */
return;
}
/* The first endpoint may have changed if a collision with an intervening */
/* vertex on the segment occurred. */
org( searchtri1, endpoint1 );
/* Find a triangle whose origin is the segment's second endpoint. */
checkpoint = (point) NULL;
encodedtri = point2tri( endpoint2 );
if ( encodedtri != (triangle) NULL ) {
decode( encodedtri, searchtri2 );
org( searchtri2, checkpoint );
}
if ( checkpoint != endpoint2 ) {
/* Find a boundary triangle to search from. */
searchtri2.tri = dummytri;
searchtri2.orient = 0;
symself( searchtri2 );
/* Search for the segment's second endpoint by point location. */
if ( locate( endpoint2, &searchtri2 ) != ONVERTEX ) {
printf(
"Internal error in insertsegment(): Unable to locate PSLG point\n" );
printf( " (%.12g, %.12g) in triangulation.\n",
endpoint2[0], endpoint2[1] );
internalerror();
}
}
/* Remember this triangle to improve subsequent point location. */
triedgecopy( searchtri2, recenttri );
/* Scout the beginnings of a path from the second endpoint */
/* toward the first. */
if ( scoutsegment( &searchtri2, endpoint1, newmark ) ) {
/* The segment was easily inserted. */
return;
}
/* The second endpoint may have changed if a collision with an intervening */
/* vertex on the segment occurred. */
org( searchtri2, endpoint2 );
#ifndef REDUCED
#ifndef CDT_ONLY
if ( splitseg ) {
/* Insert vertices to force the segment into the triangulation. */
conformingedge( endpoint1, endpoint2, newmark );
}
else {
#endif /* not CDT_ONLY */
#endif /* not REDUCED */
/* Insert the segment directly into the triangulation. */
constrainededge( &searchtri1, endpoint2, newmark );
#ifndef REDUCED
#ifndef CDT_ONLY
}
#endif /* not CDT_ONLY */
#endif /* not REDUCED */
}
/*****************************************************************************/
/* */
/* markhull() Cover the convex hull of a triangulation with shell edges. */
/* */
/*****************************************************************************/
void markhull(){
struct triedge hulltri;
struct triedge nexttri;
struct triedge starttri;
triangle ptr; /* Temporary variable used by sym() and oprev(). */
/* Find a triangle handle on the hull. */
hulltri.tri = dummytri;
hulltri.orient = 0;
symself( hulltri );
/* Remember where we started so we know when to stop. */
triedgecopy( hulltri, starttri );
/* Go once counterclockwise around the convex hull. */
do {
/* Create a shell edge if there isn't already one here. */
insertshelle( &hulltri, 1 );
/* To find the next hull edge, go clockwise around the next vertex. */
lnextself( hulltri );
oprev( hulltri, nexttri );
while ( nexttri.tri != dummytri ) {
triedgecopy( nexttri, hulltri );
oprev( hulltri, nexttri );
}
} while ( !triedgeequal( hulltri, starttri ) );
}
/*****************************************************************************/
/* */
/* formskeleton() Create the shell edges of a triangulation, including */
/* PSLG edges and edges on the convex hull. */
/* */
/* The PSLG edges are read from a .poly file. The return value is the */
/* number of segments in the file. */
/* */
/*****************************************************************************/
#ifdef TRILIBRARY
int formskeleton( segmentlist, segmentmarkerlist, numberofsegments )
int *segmentlist;
int *segmentmarkerlist;
int numberofsegments;
#else /* not TRILIBRARY */
int formskeleton( polyfile, polyfilename )
FILE * polyfile;
char *polyfilename;
#endif /* not TRILIBRARY */
{
#ifdef TRILIBRARY
char polyfilename[6];
int index;
#else /* not TRILIBRARY */
char inputline[INPUTLINESIZE];
char *stringptr;
#endif /* not TRILIBRARY */
point endpoint1, endpoint2;
int segments;
int segmentmarkers;
int end1, end2;
int boundmarker;
int i;
if ( poly ) {
if ( !quiet ) {
printf( "Inserting segments into Delaunay triangulation.\n" );
}
#ifdef TRILIBRARY
strcpy( polyfilename, "input" );
segments = numberofsegments;
segmentmarkers = segmentmarkerlist != (int *) NULL;
index = 0;
#else /* not TRILIBRARY */
/* Read the segments from a .poly file. */
/* Read number of segments and number of boundary markers. */
stringptr = readline( inputline, polyfile, polyfilename );
segments = (int) strtol( stringptr, &stringptr, 0 );
stringptr = findfield( stringptr );
if ( *stringptr == '\0' ) {
segmentmarkers = 0;
}
else {
segmentmarkers = (int) strtol( stringptr, &stringptr, 0 );
}
#endif /* not TRILIBRARY */
/* If segments are to be inserted, compute a mapping */
/* from points to triangles. */
if ( segments > 0 ) {
if ( verbose ) {
printf( " Inserting PSLG segments.\n" );
}
makepointmap();
}
boundmarker = 0;
/* Read and insert the segments. */
for ( i = 1; i <= segments; i++ ) {
#ifdef TRILIBRARY
end1 = segmentlist[index++];
end2 = segmentlist[index++];
if ( segmentmarkers ) {
boundmarker = segmentmarkerlist[i - 1];
}
#else /* not TRILIBRARY */
stringptr = readline( inputline, polyfile, inpolyfilename );
stringptr = findfield( stringptr );
if ( *stringptr == '\0' ) {
printf( "Error: Segment %d has no endpoints in %s.\n", i,
polyfilename );
exit( 1 );
}
else {
end1 = (int) strtol( stringptr, &stringptr, 0 );
}
stringptr = findfield( stringptr );
if ( *stringptr == '\0' ) {
printf( "Error: Segment %d is missing its second endpoint in %s.\n", i,
polyfilename );
exit( 1 );
}
else {
end2 = (int) strtol( stringptr, &stringptr, 0 );
}
if ( segmentmarkers ) {
stringptr = findfield( stringptr );
if ( *stringptr == '\0' ) {
boundmarker = 0;
}
else {
boundmarker = (int) strtol( stringptr, &stringptr, 0 );
}
}
#endif /* not TRILIBRARY */
if ( ( end1 < firstnumber ) || ( end1 >= firstnumber + inpoints ) ) {
if ( !quiet ) {
printf( "Warning: Invalid first endpoint of segment %d in %s.\n", i,
polyfilename );
}
}
else if ( ( end2 < firstnumber ) || ( end2 >= firstnumber + inpoints ) ) {
if ( !quiet ) {
printf( "Warning: Invalid second endpoint of segment %d in %s.\n", i,
polyfilename );
}
}
else {
endpoint1 = getpoint( end1 );
endpoint2 = getpoint( end2 );
if ( ( endpoint1[0] == endpoint2[0] ) && ( endpoint1[1] == endpoint2[1] ) ) {
if ( !quiet ) {
printf( "Warning: Endpoints of segment %d are coincident in %s.\n",
i, polyfilename );
}
}
else {
insertsegment( endpoint1, endpoint2, boundmarker );
}
}
}
}
else {
segments = 0;
}
if ( convex || !poly ) {
/* Enclose the convex hull with shell edges. */
if ( verbose ) {
printf( " Enclosing convex hull with segments.\n" );
}
markhull();
}
return segments;
}
/** **/
/** **/
/********* Segment (shell edge) insertion ends here *********/
/********* Carving out holes and concavities begins here *********/
/** **/
/** **/
/*****************************************************************************/
/* */
/* infecthull() Virally infect all of the triangles of the convex hull */
/* that are not protected by shell edges. Where there are */
/* shell edges, set boundary markers as appropriate. */
/* */
/*****************************************************************************/
void infecthull(){
struct triedge hulltri;
struct triedge nexttri;
struct triedge starttri;
struct edge hulledge;
triangle **deadtri;
point horg, hdest;
triangle ptr; /* Temporary variable used by sym(). */
shelle sptr; /* Temporary variable used by tspivot(). */
if ( verbose ) {
printf( " Marking concavities (external triangles) for elimination.\n" );
}
/* Find a triangle handle on the hull. */
hulltri.tri = dummytri;
hulltri.orient = 0;
symself( hulltri );
/* Remember where we started so we know when to stop. */
triedgecopy( hulltri, starttri );
/* Go once counterclockwise around the convex hull. */
do {
/* Ignore triangles that are already infected. */
if ( !infected( hulltri ) ) {
/* Is the triangle protected by a shell edge? */
tspivot( hulltri, hulledge );
if ( hulledge.sh == dummysh ) {
/* The triangle is not protected; infect it. */
infect( hulltri );
deadtri = (triangle **) poolalloc( &viri );
*deadtri = hulltri.tri;
}
else {
/* The triangle is protected; set boundary markers if appropriate. */
if ( mark( hulledge ) == 0 ) {
setmark( hulledge, 1 );
org( hulltri, horg );
dest( hulltri, hdest );
if ( pointmark( horg ) == 0 ) {
setpointmark( horg, 1 );
}
if ( pointmark( hdest ) == 0 ) {
setpointmark( hdest, 1 );
}
}
}
}
/* To find the next hull edge, go clockwise around the next vertex. */
lnextself( hulltri );
oprev( hulltri, nexttri );
while ( nexttri.tri != dummytri ) {
triedgecopy( nexttri, hulltri );
oprev( hulltri, nexttri );
}
} while ( !triedgeequal( hulltri, starttri ) );
}
/*****************************************************************************/
/* */
/* plague() Spread the virus from all infected triangles to any neighbors */
/* not protected by shell edges. Delete all infected triangles. */
/* */
/* This is the procedure that actually creates holes and concavities. */
/* */
/* This procedure operates in two phases. The first phase identifies all */
/* the triangles that will die, and marks them as infected. They are */
/* marked to ensure that each triangle is added to the virus pool only */
/* once, so the procedure will terminate. */
/* */
/* The second phase actually eliminates the infected triangles. It also */
/* eliminates orphaned points. */
/* */
/*****************************************************************************/
void plague(){
struct triedge testtri;
struct triedge neighbor;
triangle **virusloop;
triangle **deadtri;
struct edge neighborshelle;
point testpoint;
point norg, ndest;
point deadorg, deaddest, deadapex;
int killorg;
triangle ptr; /* Temporary variable used by sym() and onext(). */
shelle sptr; /* Temporary variable used by tspivot(). */
if ( verbose ) {
printf( " Marking neighbors of marked triangles.\n" );
}
/* Loop through all the infected triangles, spreading the virus to */
/* their neighbors, then to their neighbors' neighbors. */
traversalinit( &viri );
virusloop = (triangle **) traverse( &viri );
while ( virusloop != (triangle **) NULL ) {
testtri.tri = *virusloop;
/* A triangle is marked as infected by messing with one of its shell */
/* edges, setting it to an illegal value. Hence, we have to */
/* temporarily uninfect this triangle so that we can examine its */
/* adjacent shell edges. */
uninfect( testtri );
if ( verbose > 2 ) {
/* Assign the triangle an orientation for convenience in */
/* checking its points. */
testtri.orient = 0;
org( testtri, deadorg );
dest( testtri, deaddest );
apex( testtri, deadapex );
printf( " Checking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
deadorg[0], deadorg[1], deaddest[0], deaddest[1],
deadapex[0], deadapex[1] );
}
/* Check each of the triangle's three neighbors. */
for ( testtri.orient = 0; testtri.orient < 3; testtri.orient++ ) {
/* Find the neighbor. */
sym( testtri, neighbor );
/* Check for a shell between the triangle and its neighbor. */
tspivot( testtri, neighborshelle );
/* Check if the neighbor is nonexistent or already infected. */
if ( ( neighbor.tri == dummytri ) || infected( neighbor ) ) {
if ( neighborshelle.sh != dummysh ) {
/* There is a shell edge separating the triangle from its */
/* neighbor, but both triangles are dying, so the shell */
/* edge dies too. */
shelledealloc( neighborshelle.sh );
if ( neighbor.tri != dummytri ) {
/* Make sure the shell edge doesn't get deallocated again */
/* later when the infected neighbor is visited. */
uninfect( neighbor );
tsdissolve( neighbor );
infect( neighbor );
}
}
}
else { /* The neighbor exists and is not infected. */
if ( neighborshelle.sh == dummysh ) {
/* There is no shell edge protecting the neighbor, so */
/* the neighbor becomes infected. */
if ( verbose > 2 ) {
org( neighbor, deadorg );
dest( neighbor, deaddest );
apex( neighbor, deadapex );
printf(
" Marking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
deadorg[0], deadorg[1], deaddest[0], deaddest[1],
deadapex[0], deadapex[1] );
}
infect( neighbor );
/* Ensure that the neighbor's neighbors will be infected. */
deadtri = (triangle **) poolalloc( &viri );
*deadtri = neighbor.tri;
}
else { /* The neighbor is protected by a shell edge. */
/* Remove this triangle from the shell edge. */
stdissolve( neighborshelle );
/* The shell edge becomes a boundary. Set markers accordingly. */
if ( mark( neighborshelle ) == 0 ) {
setmark( neighborshelle, 1 );
}
org( neighbor, norg );
dest( neighbor, ndest );
if ( pointmark( norg ) == 0 ) {
setpointmark( norg, 1 );
}
if ( pointmark( ndest ) == 0 ) {
setpointmark( ndest, 1 );
}
}
}
}
/* Remark the triangle as infected, so it doesn't get added to the */
/* virus pool again. */
infect( testtri );
virusloop = (triangle **) traverse( &viri );
}
if ( verbose ) {
printf( " Deleting marked triangles.\n" );
}
traversalinit( &viri );
virusloop = (triangle **) traverse( &viri );
while ( virusloop != (triangle **) NULL ) {
testtri.tri = *virusloop;
/* Check each of the three corners of the triangle for elimination. */
/* This is done by walking around each point, checking if it is */
/* still connected to at least one live triangle. */
for ( testtri.orient = 0; testtri.orient < 3; testtri.orient++ ) {
org( testtri, testpoint );
/* Check if the point has already been tested. */
if ( testpoint != (point) NULL ) {
killorg = 1;
/* Mark the corner of the triangle as having been tested. */
setorg( testtri, NULL );
/* Walk counterclockwise about the point. */
onext( testtri, neighbor );
/* Stop upon reaching a boundary or the starting triangle. */
while ( ( neighbor.tri != dummytri )
&& ( !triedgeequal( neighbor, testtri ) ) ) {
if ( infected( neighbor ) ) {
/* Mark the corner of this triangle as having been tested. */
setorg( neighbor, NULL );
}
else {
/* A live triangle. The point survives. */
killorg = 0;
}
/* Walk counterclockwise about the point. */
onextself( neighbor );
}
/* If we reached a boundary, we must walk clockwise as well. */
if ( neighbor.tri == dummytri ) {
/* Walk clockwise about the point. */
oprev( testtri, neighbor );
/* Stop upon reaching a boundary. */
while ( neighbor.tri != dummytri ) {
if ( infected( neighbor ) ) {
/* Mark the corner of this triangle as having been tested. */
setorg( neighbor, NULL );
}
else {
/* A live triangle. The point survives. */
killorg = 0;
}
/* Walk clockwise about the point. */
oprevself( neighbor );
}
}
if ( killorg ) {
if ( verbose > 1 ) {
printf( " Deleting point (%.12g, %.12g)\n",
testpoint[0], testpoint[1] );
}
pointdealloc( testpoint );
}
}
}
/* Record changes in the number of boundary edges, and disconnect */
/* dead triangles from their neighbors. */
for ( testtri.orient = 0; testtri.orient < 3; testtri.orient++ ) {
sym( testtri, neighbor );
if ( neighbor.tri == dummytri ) {
/* There is no neighboring triangle on this edge, so this edge */
/* is a boundary edge. This triangle is being deleted, so this */
/* boundary edge is deleted. */
hullsize--;
}
else {
/* Disconnect the triangle from its neighbor. */
dissolve( neighbor );
/* There is a neighboring triangle on this edge, so this edge */
/* becomes a boundary edge when this triangle is deleted. */
hullsize++;
}
}
/* Return the dead triangle to the pool of triangles. */
triangledealloc( testtri.tri );
virusloop = (triangle **) traverse( &viri );
}
/* Empty the virus pool. */
poolrestart( &viri );
}
/*****************************************************************************/
/* */
/* regionplague() Spread regional attributes and/or area constraints */
/* (from a .poly file) throughout the mesh. */
/* */
/* This procedure operates in two phases. The first phase spreads an */
/* attribute and/or an area constraint through a (segment-bounded) region. */
/* The triangles are marked to ensure that each triangle is added to the */
/* virus pool only once, so the procedure will terminate. */
/* */
/* The second phase uninfects all infected triangles, returning them to */
/* normal. */
/* */
/*****************************************************************************/
void regionplague( attribute, area )
REAL attribute;
REAL area;
{
struct triedge testtri;
struct triedge neighbor;
triangle **virusloop;
triangle **regiontri;
struct edge neighborshelle;
point regionorg, regiondest, regionapex;
triangle ptr; /* Temporary variable used by sym() and onext(). */
shelle sptr; /* Temporary variable used by tspivot(). */
if ( verbose > 1 ) {
printf( " Marking neighbors of marked triangles.\n" );
}
/* Loop through all the infected triangles, spreading the attribute */
/* and/or area constraint to their neighbors, then to their neighbors' */
/* neighbors. */
traversalinit( &viri );
virusloop = (triangle **) traverse( &viri );
while ( virusloop != (triangle **) NULL ) {
testtri.tri = *virusloop;
/* A triangle is marked as infected by messing with one of its shell */
/* edges, setting it to an illegal value. Hence, we have to */
/* temporarily uninfect this triangle so that we can examine its */
/* adjacent shell edges. */
uninfect( testtri );
if ( regionattrib ) {
/* Set an attribute. */
setelemattribute( testtri, eextras, attribute );
}
if ( vararea ) {
/* Set an area constraint. */
setareabound( testtri, area );
}
if ( verbose > 2 ) {
/* Assign the triangle an orientation for convenience in */
/* checking its points. */
testtri.orient = 0;
org( testtri, regionorg );
dest( testtri, regiondest );
apex( testtri, regionapex );
printf( " Checking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
regionorg[0], regionorg[1], regiondest[0], regiondest[1],
regionapex[0], regionapex[1] );
}
/* Check each of the triangle's three neighbors. */
for ( testtri.orient = 0; testtri.orient < 3; testtri.orient++ ) {
/* Find the neighbor. */
sym( testtri, neighbor );
/* Check for a shell between the triangle and its neighbor. */
tspivot( testtri, neighborshelle );
/* Make sure the neighbor exists, is not already infected, and */
/* isn't protected by a shell edge. */
if ( ( neighbor.tri != dummytri ) && !infected( neighbor )
&& ( neighborshelle.sh == dummysh ) ) {
if ( verbose > 2 ) {
org( neighbor, regionorg );
dest( neighbor, regiondest );
apex( neighbor, regionapex );
printf( " Marking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
regionorg[0], regionorg[1], regiondest[0], regiondest[1],
regionapex[0], regionapex[1] );
}
/* Infect the neighbor. */
infect( neighbor );
/* Ensure that the neighbor's neighbors will be infected. */
regiontri = (triangle **) poolalloc( &viri );
*regiontri = neighbor.tri;
}
}
/* Remark the triangle as infected, so it doesn't get added to the */
/* virus pool again. */
infect( testtri );
virusloop = (triangle **) traverse( &viri );
}
/* Uninfect all triangles. */
if ( verbose > 1 ) {
printf( " Unmarking marked triangles.\n" );
}
traversalinit( &viri );
virusloop = (triangle **) traverse( &viri );
while ( virusloop != (triangle **) NULL ) {
testtri.tri = *virusloop;
uninfect( testtri );
virusloop = (triangle **) traverse( &viri );
}
/* Empty the virus pool. */
poolrestart( &viri );
}
/*****************************************************************************/
/* */
/* carveholes() Find the holes and infect them. Find the area */
/* constraints and infect them. Infect the convex hull. */
/* Spread the infection and kill triangles. Spread the */
/* area constraints. */
/* */
/* This routine mainly calls other routines to carry out all these */
/* functions. */
/* */
/*****************************************************************************/
void carveholes( holelist, holes, regionlist, regions )
REAL * holelist;
int holes;
REAL *regionlist;
int regions;
{
struct triedge searchtri;
struct triedge triangleloop;
struct triedge *regiontris;
triangle **holetri;
triangle **regiontri;
point searchorg, searchdest;
enum locateresult intersect;
int i;
triangle ptr; /* Temporary variable used by sym(). */
if ( !( quiet || ( noholes && convex ) ) ) {
printf( "Removing unwanted triangles.\n" );
if ( verbose && ( holes > 0 ) ) {
printf( " Marking holes for elimination.\n" );
}
}
if ( regions > 0 ) {
/* Allocate storage for the triangles in which region points fall. */
regiontris = (struct triedge *) malloc( regions * sizeof( struct triedge ) );
if ( regiontris == (struct triedge *) NULL ) {
printf( "Error: Out of memory.\n" );
exit( 1 );
}
}
if ( ( ( holes > 0 ) && !noholes ) || !convex || ( regions > 0 ) ) {
/* Initialize a pool of viri to be used for holes, concavities, */
/* regional attributes, and/or regional area constraints. */
poolinit( &viri, sizeof( triangle * ), VIRUSPERBLOCK, POINTER, 0 );
}
if ( !convex ) {
/* Mark as infected any unprotected triangles on the boundary. */
/* This is one way by which concavities are created. */
infecthull();
}
if ( ( holes > 0 ) && !noholes ) {
/* Infect each triangle in which a hole lies. */
for ( i = 0; i < 2 * holes; i += 2 ) {
/* Ignore holes that aren't within the bounds of the mesh. */
if ( ( holelist[i] >= xmin ) && ( holelist[i] <= xmax )
&& ( holelist[i + 1] >= ymin ) && ( holelist[i + 1] <= ymax ) ) {
/* Start searching from some triangle on the outer boundary. */
searchtri.tri = dummytri;
searchtri.orient = 0;
symself( searchtri );
/* Ensure that the hole is to the left of this boundary edge; */
/* otherwise, locate() will falsely report that the hole */
/* falls within the starting triangle. */
org( searchtri, searchorg );
dest( searchtri, searchdest );
if ( counterclockwise( searchorg, searchdest, &holelist[i] ) > 0.0 ) {
/* Find a triangle that contains the hole. */
intersect = locate( &holelist[i], &searchtri );
if ( ( intersect != OUTSIDE ) && ( !infected( searchtri ) ) ) {
/* Infect the triangle. This is done by marking the triangle */
/* as infect and including the triangle in the virus pool. */
infect( searchtri );
holetri = (triangle **) poolalloc( &viri );
*holetri = searchtri.tri;
}
}
}
}
}
/* Now, we have to find all the regions BEFORE we carve the holes, because */
/* locate() won't work when the triangulation is no longer convex. */
/* (Incidentally, this is the reason why regional attributes and area */
/* constraints can't be used when refining a preexisting mesh, which */
/* might not be convex; they can only be used with a freshly */
/* triangulated PSLG.) */
if ( regions > 0 ) {
/* Find the starting triangle for each region. */
for ( i = 0; i < regions; i++ ) {
regiontris[i].tri = dummytri;
/* Ignore region points that aren't within the bounds of the mesh. */
if ( ( regionlist[4 * i] >= xmin ) && ( regionlist[4 * i] <= xmax ) &&
( regionlist[4 * i + 1] >= ymin ) && ( regionlist[4 * i + 1] <= ymax ) ) {
/* Start searching from some triangle on the outer boundary. */
searchtri.tri = dummytri;
searchtri.orient = 0;
symself( searchtri );
/* Ensure that the region point is to the left of this boundary */
/* edge; otherwise, locate() will falsely report that the */
/* region point falls within the starting triangle. */
org( searchtri, searchorg );
dest( searchtri, searchdest );
if ( counterclockwise( searchorg, searchdest, &regionlist[4 * i] ) >
0.0 ) {
/* Find a triangle that contains the region point. */
intersect = locate( &regionlist[4 * i], &searchtri );
if ( ( intersect != OUTSIDE ) && ( !infected( searchtri ) ) ) {
/* Record the triangle for processing after the */
/* holes have been carved. */
triedgecopy( searchtri, regiontris[i] );
}
}
}
}
}
if ( viri.items > 0 ) {
/* Carve the holes and concavities. */
plague();
}
/* The virus pool should be empty now. */
if ( regions > 0 ) {
if ( !quiet ) {
if ( regionattrib ) {
if ( vararea ) {
printf( "Spreading regional attributes and area constraints.\n" );
}
else {
printf( "Spreading regional attributes.\n" );
}
}
else {
printf( "Spreading regional area constraints.\n" );
}
}
if ( regionattrib && !refine ) {
/* Assign every triangle a regional attribute of zero. */
traversalinit( &triangles );
triangleloop.orient = 0;
triangleloop.tri = triangletraverse();
while ( triangleloop.tri != (triangle *) NULL ) {
setelemattribute( triangleloop, eextras, 0.0 );
triangleloop.tri = triangletraverse();
}
}
for ( i = 0; i < regions; i++ ) {
if ( regiontris[i].tri != dummytri ) {
/* Make sure the triangle under consideration still exists. */
/* It may have been eaten by the virus. */
if ( regiontris[i].tri[3] != (triangle) NULL ) {
/* Put one triangle in the virus pool. */
infect( regiontris[i] );
regiontri = (triangle **) poolalloc( &viri );
*regiontri = regiontris[i].tri;
/* Apply one region's attribute and/or area constraint. */
regionplague( regionlist[4 * i + 2], regionlist[4 * i + 3] );
/* The virus pool should be empty now. */
}
}
}
if ( regionattrib && !refine ) {
/* Note the fact that each triangle has an additional attribute. */
eextras++;
}
}
/* Free up memory. */
if ( ( ( holes > 0 ) && !noholes ) || !convex || ( regions > 0 ) ) {
pooldeinit( &viri );
}
if ( regions > 0 ) {
free( regiontris );
}
}
/** **/
/** **/
/********* Carving out holes and concavities ends here *********/
/********* Mesh quality maintenance begins here *********/
/** **/
/** **/
/*****************************************************************************/
/* */
/* tallyencs() Traverse the entire list of shell edges, check each edge */
/* to see if it is encroached. If so, add it to the list. */
/* */
/*****************************************************************************/
#ifndef CDT_ONLY
void tallyencs(){
struct edge edgeloop;
int dummy;
traversalinit( &shelles );
edgeloop.shorient = 0;
edgeloop.sh = shelletraverse();
while ( edgeloop.sh != (shelle *) NULL ) {
/* If the segment is encroached, add it to the list. */
dummy = checkedge4encroach( &edgeloop );
edgeloop.sh = shelletraverse();
}
}
#endif /* not CDT_ONLY */
/*****************************************************************************/
/* */
/* precisionerror() Print an error message for precision problems. */
/* */
/*****************************************************************************/
#ifndef CDT_ONLY
void precisionerror(){
printf( "Try increasing the area criterion and/or reducing the minimum\n" );
printf( " allowable angle so that tiny triangles are not created.\n" );
#ifdef SINGLE
printf( "Alternatively, try recompiling me with double precision\n" );
printf( " arithmetic (by removing \"#define SINGLE\" from the\n" );
printf( " source file or \"-DSINGLE\" from the makefile).\n" );
#endif /* SINGLE */
}
#endif /* not CDT_ONLY */
/*****************************************************************************/
/* */
/* repairencs() Find and repair all the encroached segments. */
/* */
/* Encroached segments are repaired by splitting them by inserting a point */
/* at or near their centers. */
/* */
/* `flaws' is a flag that specifies whether one should take note of new */
/* encroached segments and bad triangles that result from inserting points */
/* to repair existing encroached segments. */
/* */
/* When a segment is split, the two resulting subsegments are always */
/* tested to see if they are encroached upon, regardless of the value */
/* of `flaws'. */
/* */
/*****************************************************************************/
#ifndef CDT_ONLY
void repairencs( flaws )
int flaws;
{
struct triedge enctri;
struct triedge testtri;
struct edge *encloop;
struct edge testsh;
point eorg, edest;
point newpoint;
enum insertsiteresult success;
REAL segmentlength, nearestpoweroftwo;
REAL split;
int acuteorg, acutedest;
int dummy;
int i;
triangle ptr; /* Temporary variable used by stpivot(). */
shelle sptr; /* Temporary variable used by snext(). */
while ( ( badsegments.items > 0 ) && ( steinerleft != 0 ) ) {
traversalinit( &badsegments );
encloop = badsegmenttraverse();
while ( ( encloop != (struct edge *) NULL ) && ( steinerleft != 0 ) ) {
/* To decide where to split a segment, we need to know if the */
/* segment shares an endpoint with an adjacent segment. */
/* The concern is that, if we simply split every encroached */
/* segment in its center, two adjacent segments with a small */
/* angle between them might lead to an infinite loop; each */
/* point added to split one segment will encroach upon the */
/* other segment, which must then be split with a point that */
/* will encroach upon the first segment, and so on forever. */
/* To avoid this, imagine a set of concentric circles, whose */
/* radii are powers of two, about each segment endpoint. */
/* These concentric circles determine where the segment is */
/* split. (If both endpoints are shared with adjacent */
/* segments, split the segment in the middle, and apply the */
/* concentric shells for later splittings.) */
/* Is the origin shared with another segment? */
stpivot( *encloop, enctri );
lnext( enctri, testtri );
tspivot( testtri, testsh );
acuteorg = testsh.sh != dummysh;
/* Is the destination shared with another segment? */
lnextself( testtri );
tspivot( testtri, testsh );
acutedest = testsh.sh != dummysh;
/* Now, check the other side of the segment, if there's a triangle */
/* there. */
sym( enctri, testtri );
if ( testtri.tri != dummytri ) {
/* Is the destination shared with another segment? */
lnextself( testtri );
tspivot( testtri, testsh );
acutedest = acutedest || ( testsh.sh != dummysh );
/* Is the origin shared with another segment? */
lnextself( testtri );
tspivot( testtri, testsh );
acuteorg = acuteorg || ( testsh.sh != dummysh );
}
sorg( *encloop, eorg );
sdest( *encloop, edest );
/* Use the concentric circles if exactly one endpoint is shared */
/* with another adjacent segment. */
if ( acuteorg ^ acutedest ) {
segmentlength = sqrt( ( edest[0] - eorg[0] ) * ( edest[0] - eorg[0] )
+ ( edest[1] - eorg[1] ) * ( edest[1] - eorg[1] ) );
/* Find the power of two nearest the segment's length. */
nearestpoweroftwo = 1.0;
while ( segmentlength > SQUAREROOTTWO * nearestpoweroftwo ) {
nearestpoweroftwo *= 2.0;
}
while ( segmentlength < ( 0.5 * SQUAREROOTTWO ) * nearestpoweroftwo ) {
nearestpoweroftwo *= 0.5;
}
/* Where do we split the segment? */
split = 0.5 * nearestpoweroftwo / segmentlength;
if ( acutedest ) {
split = 1.0 - split;
}
}
else {
/* If we're not worried about adjacent segments, split */
/* this segment in the middle. */
split = 0.5;
}
/* Create the new point. */
newpoint = (point) poolalloc( &points );
/* Interpolate its coordinate and attributes. */
for ( i = 0; i < 2 + nextras; i++ ) {
newpoint[i] = ( 1.0 - split ) * eorg[i] + split * edest[i];
}
setpointmark( newpoint, mark( *encloop ) );
if ( verbose > 1 ) {
printf(
" Splitting edge (%.12g, %.12g) (%.12g, %.12g) at (%.12g, %.12g).\n",
eorg[0], eorg[1], edest[0], edest[1], newpoint[0], newpoint[1] );
}
/* Check whether the new point lies on an endpoint. */
if ( ( ( newpoint[0] == eorg[0] ) && ( newpoint[1] == eorg[1] ) )
|| ( ( newpoint[0] == edest[0] ) && ( newpoint[1] == edest[1] ) ) ) {
printf( "Error: Ran out of precision at (%.12g, %.12g).\n",
newpoint[0], newpoint[1] );
printf( "I attempted to split a segment to a smaller size than can\n" );
printf( " be accommodated by the finite precision of floating point\n"
);
printf( " arithmetic.\n" );
precisionerror();
exit( 1 );
}
/* Insert the splitting point. This should always succeed. */
success = insertsite( newpoint, &enctri, encloop, flaws, flaws );
if ( ( success != SUCCESSFULPOINT ) && ( success != ENCROACHINGPOINT ) ) {
printf( "Internal error in repairencs():\n" );
printf( " Failure to split a segment.\n" );
internalerror();
}
if ( steinerleft > 0 ) {
steinerleft--;
}
/* Check the two new subsegments to see if they're encroached. */
dummy = checkedge4encroach( encloop );
snextself( *encloop );
dummy = checkedge4encroach( encloop );
badsegmentdealloc( encloop );
encloop = badsegmenttraverse();
}
}
}
#endif /* not CDT_ONLY */
/*****************************************************************************/
/* */
/* tallyfaces() Test every triangle in the mesh for quality measures. */
/* */
/*****************************************************************************/
#ifndef CDT_ONLY
void tallyfaces(){
struct triedge triangleloop;
if ( verbose ) {
printf( " Making a list of bad triangles.\n" );
}
traversalinit( &triangles );
triangleloop.orient = 0;
triangleloop.tri = triangletraverse();
while ( triangleloop.tri != (triangle *) NULL ) {
/* If the triangle is bad, enqueue it. */
testtriangle( &triangleloop );
triangleloop.tri = triangletraverse();
}
}
#endif /* not CDT_ONLY */
/*****************************************************************************/
/* */
/* findcircumcenter() Find the circumcenter of a triangle. */
/* */
/* The result is returned both in terms of x-y coordinates and xi-eta */
/* coordinates. The xi-eta coordinate system is defined in terms of the */
/* triangle: the origin of the triangle is the origin of the coordinate */
/* system; the destination of the triangle is one unit along the xi axis; */
/* and the apex of the triangle is one unit along the eta axis. */
/* */
/* The return value indicates which edge of the triangle is shortest. */
/* */
/*****************************************************************************/
enum circumcenterresult findcircumcenter( torg, tdest, tapex, circumcenter,
xi, eta )
point torg;
point tdest;
point tapex;
point circumcenter;
REAL *xi;
REAL *eta;
{
REAL xdo, ydo, xao, yao, xad, yad;
REAL dodist, aodist, addist;
REAL denominator;
REAL dx, dy;
circumcentercount++;
/* Compute the circumcenter of the triangle. */
xdo = tdest[0] - torg[0];
ydo = tdest[1] - torg[1];
xao = tapex[0] - torg[0];
yao = tapex[1] - torg[1];
dodist = xdo * xdo + ydo * ydo;
aodist = xao * xao + yao * yao;
if ( noexact ) {
denominator = (REAL)( 0.5 / ( xdo * yao - xao * ydo ) );
}
else {
/* Use the counterclockwise() routine to ensure a positive (and */
/* reasonably accurate) result, avoiding any possibility of */
/* division by zero. */
denominator = (REAL)( 0.5 / counterclockwise( tdest, tapex, torg ) );
/* Don't count the above as an orientation test. */
counterclockcount--;
}
circumcenter[0] = torg[0] - ( ydo * aodist - yao * dodist ) * denominator;
circumcenter[1] = torg[1] + ( xdo * aodist - xao * dodist ) * denominator;
/* To interpolate point attributes for the new point inserted at */
/* the circumcenter, define a coordinate system with a xi-axis, */
/* directed from the triangle's origin to its destination, and */
/* an eta-axis, directed from its origin to its apex. */
/* Calculate the xi and eta coordinates of the circumcenter. */
dx = circumcenter[0] - torg[0];
dy = circumcenter[1] - torg[1];
*xi = (REAL)( ( dx * yao - xao * dy ) * ( 2.0 * denominator ) );
*eta = (REAL)( ( xdo * dy - dx * ydo ) * ( 2.0 * denominator ) );
xad = tapex[0] - tdest[0];
yad = tapex[1] - tdest[1];
addist = xad * xad + yad * yad;
if ( ( addist < dodist ) && ( addist < aodist ) ) {
return OPPOSITEORG;
}
else if ( dodist < aodist ) {
return OPPOSITEAPEX;
}
else {
return OPPOSITEDEST;
}
}
/*****************************************************************************/
/* */
/* splittriangle() Inserts a point at the circumcenter of a triangle. */
/* Deletes the newly inserted point if it encroaches upon */
/* a segment. */
/* */
/*****************************************************************************/
#ifndef CDT_ONLY
void splittriangle( badtri )
struct badface *badtri;
{
point borg, bdest, bapex;
point newpoint;
REAL xi, eta;
enum insertsiteresult success;
enum circumcenterresult shortedge;
int errorflag;
int i;
org( badtri->badfacetri, borg );
dest( badtri->badfacetri, bdest );
apex( badtri->badfacetri, bapex );
/* Make sure that this triangle is still the same triangle it was */
/* when it was tested and determined to be of bad quality. */
/* Subsequent transformations may have made it a different triangle. */
if ( ( borg == badtri->faceorg ) && ( bdest == badtri->facedest ) &&
( bapex == badtri->faceapex ) ) {
if ( verbose > 1 ) {
printf( " Splitting this triangle at its circumcenter:\n" );
printf( " (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", borg[0],
borg[1], bdest[0], bdest[1], bapex[0], bapex[1] );
}
errorflag = 0;
/* Create a new point at the triangle's circumcenter. */
newpoint = (point) poolalloc( &points );
shortedge = findcircumcenter( borg, bdest, bapex, newpoint, &xi, &eta );
/* Check whether the new point lies on a triangle vertex. */
if ( ( ( newpoint[0] == borg[0] ) && ( newpoint[1] == borg[1] ) )
|| ( ( newpoint[0] == bdest[0] ) && ( newpoint[1] == bdest[1] ) )
|| ( ( newpoint[0] == bapex[0] ) && ( newpoint[1] == bapex[1] ) ) ) {
if ( !quiet ) {
printf( "Warning: New point (%.12g, %.12g) falls on existing vertex.\n"
, newpoint[0], newpoint[1] );
errorflag = 1;
}
pointdealloc( newpoint );
}
else {
for ( i = 2; i < 2 + nextras; i++ ) {
/* Interpolate the point attributes at the circumcenter. */
newpoint[i] = borg[i] + xi * ( bdest[i] - borg[i] )
+ eta * ( bapex[i] - borg[i] );
}
/* The new point must be in the interior, and have a marker of zero. */
setpointmark( newpoint, 0 );
/* Ensure that the handle `badtri->badfacetri' represents the shortest */
/* edge of the triangle. This ensures that the circumcenter must */
/* fall to the left of this edge, so point location will work. */
if ( shortedge == OPPOSITEORG ) {
lnextself( badtri->badfacetri );
}
else if ( shortedge == OPPOSITEDEST ) {
lprevself( badtri->badfacetri );
}
/* Insert the circumcenter, searching from the edge of the triangle, */
/* and maintain the Delaunay property of the triangulation. */
success = insertsite( newpoint, &( badtri->badfacetri ),
(struct edge *) NULL, 1, 1 );
if ( success == SUCCESSFULPOINT ) {
if ( steinerleft > 0 ) {
steinerleft--;
}
}
else if ( success == ENCROACHINGPOINT ) {
/* If the newly inserted point encroaches upon a segment, delete it. */
deletesite( &( badtri->badfacetri ) );
}
else if ( success == VIOLATINGPOINT ) {
/* Failed to insert the new point, but some segment was */
/* marked as being encroached. */
pointdealloc( newpoint );
}
else { /* success == DUPLICATEPOINT */
/* Failed to insert the new point because a vertex is already there. */
if ( !quiet ) {
printf(
"Warning: New point (%.12g, %.12g) falls on existing vertex.\n"
, newpoint[0], newpoint[1] );
errorflag = 1;
}
pointdealloc( newpoint );
}
}
if ( errorflag ) {
if ( verbose ) {
printf( " The new point is at the circumcenter of triangle\n" );
printf( " (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
borg[0], borg[1], bdest[0], bdest[1], bapex[0], bapex[1] );
}
printf( "This probably means that I am trying to refine triangles\n" );
printf( " to a smaller size than can be accommodated by the finite\n" );
printf( " precision of floating point arithmetic. (You can be\n" );
printf( " sure of this if I fail to terminate.)\n" );
precisionerror();
}
}
/* Return the bad triangle to the pool. */
pooldealloc( &badtriangles, (VOID *) badtri );
}
#endif /* not CDT_ONLY */
/*****************************************************************************/
/* */
/* enforcequality() Remove all the encroached edges and bad triangles */
/* from the triangulation. */
/* */
/*****************************************************************************/
#ifndef CDT_ONLY
void enforcequality(){
int i;
if ( !quiet ) {
printf( "Adding Steiner points to enforce quality.\n" );
}
/* Initialize the pool of encroached segments. */
poolinit( &badsegments, sizeof( struct edge ), BADSEGMENTPERBLOCK, POINTER, 0 );
if ( verbose ) {
printf( " Looking for encroached segments.\n" );
}
/* Test all segments to see if they're encroached. */
tallyencs();
if ( verbose && ( badsegments.items > 0 ) ) {
printf( " Splitting encroached segments.\n" );
}
/* Note that steinerleft == -1 if an unlimited number */
/* of Steiner points is allowed. */
while ( ( badsegments.items > 0 ) && ( steinerleft != 0 ) ) {
/* Fix the segments without noting newly encroached segments or */
/* bad triangles. The reason we don't want to note newly */
/* encroached segments is because some encroached segments are */
/* likely to be noted multiple times, and would then be blindly */
/* split multiple times. I should fix that some time. */
repairencs( 0 );
/* Now, find all the segments that became encroached while adding */
/* points to split encroached segments. */
tallyencs();
}
/* At this point, if we haven't run out of Steiner points, the */
/* triangulation should be (conforming) Delaunay. */
/* Next, we worry about enforcing triangle quality. */
if ( ( minangle > 0.0 ) || vararea || fixedarea ) {
/* Initialize the pool of bad triangles. */
poolinit( &badtriangles, sizeof( struct badface ), BADTRIPERBLOCK, POINTER,
0 );
/* Initialize the queues of bad triangles. */
for ( i = 0; i < 64; i++ ) {
queuefront[i] = (struct badface *) NULL;
queuetail[i] = &queuefront[i];
}
/* Test all triangles to see if they're bad. */
tallyfaces();
if ( verbose ) {
printf( " Splitting bad triangles.\n" );
}
while ( ( badtriangles.items > 0 ) && ( steinerleft != 0 ) ) {
/* Fix one bad triangle by inserting a point at its circumcenter. */
splittriangle( dequeuebadtri() );
/* Fix any encroached segments that may have resulted. Record */
/* any new bad triangles or encroached segments that result. */
if ( badsegments.items > 0 ) {
repairencs( 1 );
}
}
}
/* At this point, if we haven't run out of Steiner points, the */
/* triangulation should be (conforming) Delaunay and have no */
/* low-quality triangles. */
/* Might we have run out of Steiner points too soon? */
if ( !quiet && ( badsegments.items > 0 ) && ( steinerleft == 0 ) ) {
printf( "\nWarning: I ran out of Steiner points, but the mesh has\n" );
if ( badsegments.items == 1 ) {
printf( " an encroached segment, and therefore might not be truly\n" );
}
else {
printf( " %ld encroached segments, and therefore might not be truly\n",
badsegments.items );
}
printf( " Delaunay. If the Delaunay property is important to you,\n" );
printf( " try increasing the number of Steiner points (controlled by\n" );
printf( " the -S switch) slightly and try again.\n\n" );
}
}
#endif /* not CDT_ONLY */
/** **/
/** **/
/********* Mesh quality maintenance ends here *********/
/*****************************************************************************/
/* */
/* highorder() Create extra nodes for quadratic subparametric elements. */
/* */
/*****************************************************************************/
void highorder(){
struct triedge triangleloop, trisym;
struct edge checkmark;
point newpoint;
point torg, tdest;
int i;
triangle ptr; /* Temporary variable used by sym(). */
shelle sptr; /* Temporary variable used by tspivot(). */
if ( !quiet ) {
printf( "Adding vertices for second-order triangles.\n" );
}
/* The following line ensures that dead items in the pool of nodes */
/* cannot be allocated for the extra nodes associated with high */
/* order elements. This ensures that the primary nodes (at the */
/* corners of elements) will occur earlier in the output files, and */
/* have lower indices, than the extra nodes. */
points.deaditemstack = (VOID *) NULL;
traversalinit( &triangles );
triangleloop.tri = triangletraverse();
/* To loop over the set of edges, loop over all triangles, and look at */
/* the three edges of each triangle. If there isn't another triangle */
/* adjacent to the edge, operate on the edge. If there is another */
/* adjacent triangle, operate on the edge only if the current triangle */
/* has a smaller pointer than its neighbor. This way, each edge is */
/* considered only once. */
while ( triangleloop.tri != (triangle *) NULL ) {
for ( triangleloop.orient = 0; triangleloop.orient < 3;
triangleloop.orient++ ) {
sym( triangleloop, trisym );
if ( ( triangleloop.tri < trisym.tri ) || ( trisym.tri == dummytri ) ) {
org( triangleloop, torg );
dest( triangleloop, tdest );
/* Create a new node in the middle of the edge. Interpolate */
/* its attributes. */
newpoint = (point) poolalloc( &points );
for ( i = 0; i < 2 + nextras; i++ ) {
newpoint[i] = (REAL)( 0.5 * ( torg[i] + tdest[i] ) );
}
/* Set the new node's marker to zero or one, depending on */
/* whether it lies on a boundary. */
setpointmark( newpoint, trisym.tri == dummytri );
if ( useshelles ) {
tspivot( triangleloop, checkmark );
/* If this edge is a segment, transfer the marker to the new node. */
if ( checkmark.sh != dummysh ) {
setpointmark( newpoint, mark( checkmark ) );
}
}
if ( verbose > 1 ) {
printf( " Creating (%.12g, %.12g).\n", newpoint[0], newpoint[1] );
}
/* Record the new node in the (one or two) adjacent elements. */
triangleloop.tri[highorderindex + triangleloop.orient] =
(triangle) newpoint;
if ( trisym.tri != dummytri ) {
trisym.tri[highorderindex + trisym.orient] = (triangle) newpoint;
}
}
}
triangleloop.tri = triangletraverse();
}
}
/********* File I/O routines begin here *********/
/** **/
/** **/
/*****************************************************************************/
/* */
/* readline() Read a nonempty line from a file. */
/* */
/* A line is considered "nonempty" if it contains something that looks like */
/* a number. */
/* */
/*****************************************************************************/
#ifndef TRILIBRARY
char *readline( string, infile, infilename )
char *string;
FILE *infile;
char *infilename;
{
char *result;
/* Search for something that looks like a number. */
do {
result = fgets( string, INPUTLINESIZE, infile );
if ( result == (char *) NULL ) {
printf( " Error: Unexpected end of file in %s.\n", infilename );
exit( 1 );
}
/* Skip anything that doesn't look like a number, a comment, */
/* or the end of a line. */
while ( ( *result != '\0' ) && ( *result != '#' )
&& ( *result != '.' ) && ( *result != '+' ) && ( *result != '-' )
&& ( ( *result < '0' ) || ( *result > '9' ) ) ) {
result++;
}
/* If it's a comment or end of line, read another line and try again. */
} while ( ( *result == '#' ) || ( *result == '\0' ) );
return result;
}
#endif /* not TRILIBRARY */
/*****************************************************************************/
/* */
/* findfield() Find the next field of a string. */
/* */
/* Jumps past the current field by searching for whitespace, then jumps */
/* past the whitespace to find the next field. */
/* */
/*****************************************************************************/
#ifndef TRILIBRARY
char *findfield( string )
char *string;
{
char *result;
result = string;
/* Skip the current field. Stop upon reaching whitespace. */
while ( ( *result != '\0' ) && ( *result != '#' )
&& ( *result != ' ' ) && ( *result != '\t' ) ) {
result++;
}
/* Now skip the whitespace and anything else that doesn't look like a */
/* number, a comment, or the end of a line. */
while ( ( *result != '\0' ) && ( *result != '#' )
&& ( *result != '.' ) && ( *result != '+' ) && ( *result != '-' )
&& ( ( *result < '0' ) || ( *result > '9' ) ) ) {
result++;
}
/* Check for a comment (prefixed with `#'). */
if ( *result == '#' ) {
*result = '\0';
}
return result;
}
#endif /* not TRILIBRARY */
/*****************************************************************************/
/* */
/* readnodes() Read the points from a file, which may be a .node or .poly */
/* file. */
/* */
/*****************************************************************************/
#ifndef TRILIBRARY
void readnodes( nodefilename, polyfilename, polyfile )
char *nodefilename;
char *polyfilename;
FILE **polyfile;
{
FILE *infile;
point pointloop;
char inputline[INPUTLINESIZE];
char *stringptr;
char *infilename;
REAL x, y;
int firstnode;
int nodemarkers;
int currentmarker;
int i, j;
if ( poly ) {
/* Read the points from a .poly file. */
if ( !quiet ) {
printf( "Opening %s.\n", polyfilename );
}
*polyfile = fopen( polyfilename, "r" );
if ( *polyfile == (FILE *) NULL ) {
printf( " Error: Cannot access file %s.\n", polyfilename );
exit( 1 );
}
/* Read number of points, number of dimensions, number of point */
/* attributes, and number of boundary markers. */
stringptr = readline( inputline, *polyfile, polyfilename );
inpoints = (int) strtol( stringptr, &stringptr, 0 );
stringptr = findfield( stringptr );
if ( *stringptr == '\0' ) {
mesh_dim = 2;
}
else {
mesh_dim = (int) strtol( stringptr, &stringptr, 0 );
}
stringptr = findfield( stringptr );
if ( *stringptr == '\0' ) {
nextras = 0;
}
else {
nextras = (int) strtol( stringptr, &stringptr, 0 );
}
stringptr = findfield( stringptr );
if ( *stringptr == '\0' ) {
nodemarkers = 0;
}
else {
nodemarkers = (int) strtol( stringptr, &stringptr, 0 );
}
if ( inpoints > 0 ) {
infile = *polyfile;
infilename = polyfilename;
readnodefile = 0;
}
else {
/* If the .poly file claims there are zero points, that means that */
/* the points should be read from a separate .node file. */
readnodefile = 1;
infilename = innodefilename;
}
}
else {
readnodefile = 1;
infilename = innodefilename;
*polyfile = (FILE *) NULL;
}
if ( readnodefile ) {
/* Read the points from a .node file. */
if ( !quiet ) {
printf( "Opening %s.\n", innodefilename );
}
infile = fopen( innodefilename, "r" );
if ( infile == (FILE *) NULL ) {
printf( " Error: Cannot access file %s.\n", innodefilename );
exit( 1 );
}
/* Read number of points, number of dimensions, number of point */
/* attributes, and number of boundary markers. */
stringptr = readline( inputline, infile, innodefilename );
inpoints = (int) strtol( stringptr, &stringptr, 0 );
stringptr = findfield( stringptr );
if ( *stringptr == '\0' ) {
mesh_dim = 2;
}
else {
mesh_dim = (int) strtol( stringptr, &stringptr, 0 );
}
stringptr = findfield( stringptr );
if ( *stringptr == '\0' ) {
nextras = 0;
}
else {
nextras = (int) strtol( stringptr, &stringptr, 0 );
}
stringptr = findfield( stringptr );
if ( *stringptr == '\0' ) {
nodemarkers = 0;
}
else {
nodemarkers = (int) strtol( stringptr, &stringptr, 0 );
}
}
if ( inpoints < 3 ) {
printf( "Error: Input must have at least three input points.\n" );
exit( 1 );
}
if ( mesh_dim != 2 ) {
printf( "Error: Triangle only works with two-dimensional meshes.\n" );
exit( 1 );
}
initializepointpool();
/* Read the points. */
for ( i = 0; i < inpoints; i++ ) {
pointloop = (point) poolalloc( &points );
stringptr = readline( inputline, infile, infilename );
if ( i == 0 ) {
firstnode = (int) strtol( stringptr, &stringptr, 0 );
if ( ( firstnode == 0 ) || ( firstnode == 1 ) ) {
firstnumber = firstnode;
}
}
stringptr = findfield( stringptr );
if ( *stringptr == '\0' ) {
printf( "Error: Point %d has no x coordinate.\n", firstnumber + i );
exit( 1 );
}
x = (REAL) strtod( stringptr, &stringptr );
stringptr = findfield( stringptr );
if ( *stringptr == '\0' ) {
printf( "Error: Point %d has no y coordinate.\n", firstnumber + i );
exit( 1 );
}
y = (REAL) strtod( stringptr, &stringptr );
pointloop[0] = x;
pointloop[1] = y;
/* Read the point attributes. */
for ( j = 2; j < 2 + nextras; j++ ) {
stringptr = findfield( stringptr );
if ( *stringptr == '\0' ) {
pointloop[j] = 0.0;
}
else {
pointloop[j] = (REAL) strtod( stringptr, &stringptr );
}
}
if ( nodemarkers ) {
/* Read a point marker. */
stringptr = findfield( stringptr );
if ( *stringptr == '\0' ) {
setpointmark( pointloop, 0 );
}
else {
currentmarker = (int) strtol( stringptr, &stringptr, 0 );
setpointmark( pointloop, currentmarker );
}
}
else {
/* If no markers are specified in the file, they default to zero. */
setpointmark( pointloop, 0 );
}
/* Determine the smallest and largest x and y coordinates. */
if ( i == 0 ) {
xmin = xmax = x;
ymin = ymax = y;
}
else {
xmin = ( x < xmin ) ? x : xmin;
xmax = ( x > xmax ) ? x : xmax;
ymin = ( y < ymin ) ? y : ymin;
ymax = ( y > ymax ) ? y : ymax;
}
}
if ( readnodefile ) {
fclose( infile );
}
/* Nonexistent x value used as a flag to mark circle events in sweepline */
/* Delaunay algorithm. */
xminextreme = 10 * xmin - 9 * xmax;
}
#endif /* not TRILIBRARY */
/*****************************************************************************/
/* */
/* transfernodes() Read the points from memory. */
/* */
/*****************************************************************************/
#ifdef TRILIBRARY
void transfernodes( pointlist, pointattriblist, pointmarkerlist, numberofpoints,
numberofpointattribs )
REAL * pointlist;
REAL *pointattriblist;
int *pointmarkerlist;
int numberofpoints;
int numberofpointattribs;
{
point pointloop;
REAL x, y;
int i, j;
int coordindex;
int attribindex;
inpoints = numberofpoints;
mesh_dim = 2;
nextras = numberofpointattribs;
readnodefile = 0;
if ( inpoints < 3 ) {
printf( "Error: Input must have at least three input points.\n" );
exit( 1 );
}
initializepointpool();
/* Read the points. */
coordindex = 0;
attribindex = 0;
for ( i = 0; i < inpoints; i++ ) {
pointloop = (point) poolalloc( &points );
/* Read the point coordinates. */
x = pointloop[0] = pointlist[coordindex++];
y = pointloop[1] = pointlist[coordindex++];
/* Read the point attributes. */
for ( j = 0; j < numberofpointattribs; j++ ) {
pointloop[2 + j] = pointattriblist[attribindex++];
}
if ( pointmarkerlist != (int *) NULL ) {
/* Read a point marker. */
setpointmark( pointloop, pointmarkerlist[i] );
}
else {
/* If no markers are specified, they default to zero. */
setpointmark( pointloop, 0 );
}
x = pointloop[0];
y = pointloop[1];
/* Determine the smallest and largest x and y coordinates. */
if ( i == 0 ) {
xmin = xmax = x;
ymin = ymax = y;
}
else {
xmin = ( x < xmin ) ? x : xmin;
xmax = ( x > xmax ) ? x : xmax;
ymin = ( y < ymin ) ? y : ymin;
ymax = ( y > ymax ) ? y : ymax;
}
}
/* Nonexistent x value used as a flag to mark circle events in sweepline */
/* Delaunay algorithm. */
xminextreme = 10 * xmin - 9 * xmax;
}
#endif /* TRILIBRARY */
/*****************************************************************************/
/* */
/* readholes() Read the holes, and possibly regional attributes and area */
/* constraints, from a .poly file. */
/* */
/*****************************************************************************/
#ifndef TRILIBRARY
void readholes( polyfile, polyfilename, hlist, holes, rlist, regions )
FILE * polyfile;
char *polyfilename;
REAL **hlist;
int *holes;
REAL **rlist;
int *regions;
{
REAL *holelist;
REAL *regionlist;
char inputline[INPUTLINESIZE];
char *stringptr;
int index;
int i;
/* Read the holes. */
stringptr = readline( inputline, polyfile, polyfilename );
*holes = (int) strtol( stringptr, &stringptr, 0 );
if ( *holes > 0 ) {
holelist = (REAL *) malloc( 2 * *holes * sizeof( REAL ) );
*hlist = holelist;
if ( holelist == (REAL *) NULL ) {
printf( "Error: Out of memory.\n" );
exit( 1 );
}
for ( i = 0; i < 2 * *holes; i += 2 ) {
stringptr = readline( inputline, polyfile, polyfilename );
stringptr = findfield( stringptr );
if ( *stringptr == '\0' ) {
printf( "Error: Hole %d has no x coordinate.\n",
firstnumber + ( i >> 1 ) );
exit( 1 );
}
else {
holelist[i] = (REAL) strtod( stringptr, &stringptr );
}
stringptr = findfield( stringptr );
if ( *stringptr == '\0' ) {
printf( "Error: Hole %d has no y coordinate.\n",
firstnumber + ( i >> 1 ) );
exit( 1 );
}
else {
holelist[i + 1] = (REAL) strtod( stringptr, &stringptr );
}
}
}
else {
*hlist = (REAL *) NULL;
}
#ifndef CDT_ONLY
if ( ( regionattrib || vararea ) && !refine ) {
/* Read the area constraints. */
stringptr = readline( inputline, polyfile, polyfilename );
*regions = (int) strtol( stringptr, &stringptr, 0 );
if ( *regions > 0 ) {
regionlist = (REAL *) malloc( 4 * *regions * sizeof( REAL ) );
*rlist = regionlist;
if ( regionlist == (REAL *) NULL ) {
printf( "Error: Out of memory.\n" );
exit( 1 );
}
index = 0;
for ( i = 0; i < *regions; i++ ) {
stringptr = readline( inputline, polyfile, polyfilename );
stringptr = findfield( stringptr );
if ( *stringptr == '\0' ) {
printf( "Error: Region %d has no x coordinate.\n",
firstnumber + i );
exit( 1 );
}
else {
regionlist[index++] = (REAL) strtod( stringptr, &stringptr );
}
stringptr = findfield( stringptr );
if ( *stringptr == '\0' ) {
printf( "Error: Region %d has no y coordinate.\n",
firstnumber + i );
exit( 1 );
}
else {
regionlist[index++] = (REAL) strtod( stringptr, &stringptr );
}
stringptr = findfield( stringptr );
if ( *stringptr == '\0' ) {
printf(
"Error: Region %d has no region attribute or area constraint.\n",
firstnumber + i );
exit( 1 );
}
else {
regionlist[index++] = (REAL) strtod( stringptr, &stringptr );
}
stringptr = findfield( stringptr );
if ( *stringptr == '\0' ) {
regionlist[index] = regionlist[index - 1];
}
else {
regionlist[index] = (REAL) strtod( stringptr, &stringptr );
}
index++;
}
}
}
else {
/* Set `*regions' to zero to avoid an accidental free() later. */
*regions = 0;
*rlist = (REAL *) NULL;
}
#endif /* not CDT_ONLY */
fclose( polyfile );
}
#endif /* not TRILIBRARY */
/*****************************************************************************/
/* */
/* finishfile() Write the command line to the output file so the user */
/* can remember how the file was generated. Close the file. */
/* */
/*****************************************************************************/
#ifndef TRILIBRARY
void finishfile( outfile, argc, argv )
FILE * outfile;
int argc;
char **argv;
{
int i;
fprintf( outfile, "# Generated by" );
for ( i = 0; i < argc; i++ ) {
fprintf( outfile, " " );
fputs( argv[i], outfile );
}
fprintf( outfile, "\n" );
fclose( outfile );
}
#endif /* not TRILIBRARY */
/*****************************************************************************/
/* */
/* writenodes() Number the points and write them to a .node file. */
/* */
/* To save memory, the point numbers are written over the shell markers */
/* after the points are written to a file. */
/* */
/*****************************************************************************/
#ifdef TRILIBRARY
void writenodes( pointlist, pointattriblist, pointmarkerlist )
REAL * *pointlist;
REAL **pointattriblist;
int **pointmarkerlist;
#else /* not TRILIBRARY */
void writenodes( nodefilename, argc, argv )
char *nodefilename;
int argc;
char **argv;
#endif /* not TRILIBRARY */
{
#ifdef TRILIBRARY
REAL *plist;
REAL *palist;
int *pmlist;
int coordindex;
int attribindex;
#else /* not TRILIBRARY */
FILE *outfile;
#endif /* not TRILIBRARY */
point pointloop;
int pointnumber;
int i;
#ifdef TRILIBRARY
if ( !quiet ) {
printf( "Writing points.\n" );
}
/* Allocate memory for output points if necessary. */
if ( *pointlist == (REAL *) NULL ) {
*pointlist = (REAL *) malloc( points.items * 2 * sizeof( REAL ) );
if ( *pointlist == (REAL *) NULL ) {
printf( "Error: Out of memory.\n" );
exit( 1 );
}
}
/* Allocate memory for output point attributes if necessary. */
if ( ( nextras > 0 ) && ( *pointattriblist == (REAL *) NULL ) ) {
*pointattriblist = (REAL *) malloc( points.items * nextras * sizeof( REAL ) );
if ( *pointattriblist == (REAL *) NULL ) {
printf( "Error: Out of memory.\n" );
exit( 1 );
}
}
/* Allocate memory for output point markers if necessary. */
if ( !nobound && ( *pointmarkerlist == (int *) NULL ) ) {
*pointmarkerlist = (int *) malloc( points.items * sizeof( int ) );
if ( *pointmarkerlist == (int *) NULL ) {
printf( "Error: Out of memory.\n" );
exit( 1 );
}
}
plist = *pointlist;
palist = *pointattriblist;
pmlist = *pointmarkerlist;
coordindex = 0;
attribindex = 0;
#else /* not TRILIBRARY */
if ( !quiet ) {
printf( "Writing %s.\n", nodefilename );
}
outfile = fopen( nodefilename, "w" );
if ( outfile == (FILE *) NULL ) {
printf( " Error: Cannot create file %s.\n", nodefilename );
exit( 1 );
}
/* Number of points, number of dimensions, number of point attributes, */
/* and number of boundary markers (zero or one). */
fprintf( outfile, "%ld %d %d %d\n", points.items, mesh_dim, nextras,
1 - nobound );
#endif /* not TRILIBRARY */
traversalinit( &points );
pointloop = pointtraverse();
pointnumber = firstnumber;
while ( pointloop != (point) NULL ) {
#ifdef TRILIBRARY
/* X and y coordinates. */
plist[coordindex++] = pointloop[0];
plist[coordindex++] = pointloop[1];
/* Point attributes. */
for ( i = 0; i < nextras; i++ ) {
palist[attribindex++] = pointloop[2 + i];
}
if ( !nobound ) {
/* Copy the boundary marker. */
pmlist[pointnumber - firstnumber] = pointmark( pointloop );
}
#else /* not TRILIBRARY */
/* Point number, x and y coordinates. */
fprintf( outfile, "%4d %.17g %.17g", pointnumber, pointloop[0],
pointloop[1] );
for ( i = 0; i < nextras; i++ ) {
/* Write an attribute. */
fprintf( outfile, " %.17g", pointloop[i + 2] );
}
if ( nobound ) {
fprintf( outfile, "\n" );
}
else {
/* Write the boundary marker. */
fprintf( outfile, " %d\n", pointmark( pointloop ) );
}
#endif /* not TRILIBRARY */
setpointmark( pointloop, pointnumber );
pointloop = pointtraverse();
pointnumber++;
}
#ifndef TRILIBRARY
finishfile( outfile, argc, argv );
#endif /* not TRILIBRARY */
}
/*****************************************************************************/
/* */
/* numbernodes() Number the points. */
/* */
/* Each point is assigned a marker equal to its number. */
/* */
/* Used when writenodes() is not called because no .node file is written. */
/* */
/*****************************************************************************/
void numbernodes(){
point pointloop;
int pointnumber;
traversalinit( &points );
pointloop = pointtraverse();
pointnumber = firstnumber;
while ( pointloop != (point) NULL ) {
setpointmark( pointloop, pointnumber );
pointloop = pointtraverse();
pointnumber++;
}
}
/*****************************************************************************/
/* */
/* writeelements() Write the triangles to an .ele file. */
/* */
/*****************************************************************************/
#ifdef TRILIBRARY
void writeelements( trianglelist, triangleattriblist )
int **trianglelist;
REAL **triangleattriblist;
#else /* not TRILIBRARY */
void writeelements( elefilename, argc, argv )
char *elefilename;
int argc;
char **argv;
#endif /* not TRILIBRARY */
{
#ifdef TRILIBRARY
int *tlist;
REAL *talist;
int pointindex;
int attribindex;
#else /* not TRILIBRARY */
FILE *outfile;
#endif /* not TRILIBRARY */
struct triedge triangleloop;
point p1, p2, p3;
point mid1, mid2, mid3;
int elementnumber;
int i;
#ifdef TRILIBRARY
if ( !quiet ) {
printf( "Writing triangles.\n" );
}
/* Allocate memory for output triangles if necessary. */
if ( *trianglelist == (int *) NULL ) {
*trianglelist = (int *) malloc( triangles.items *
( ( order + 1 ) * ( order + 2 ) / 2 ) * sizeof( int ) );
if ( *trianglelist == (int *) NULL ) {
printf( "Error: Out of memory.\n" );
exit( 1 );
}
}
/* Allocate memory for output triangle attributes if necessary. */
if ( ( eextras > 0 ) && ( *triangleattriblist == (REAL *) NULL ) ) {
*triangleattriblist = (REAL *) malloc( triangles.items * eextras *
sizeof( REAL ) );
if ( *triangleattriblist == (REAL *) NULL ) {
printf( "Error: Out of memory.\n" );
exit( 1 );
}
}
tlist = *trianglelist;
talist = *triangleattriblist;
pointindex = 0;
attribindex = 0;
#else /* not TRILIBRARY */
if ( !quiet ) {
printf( "Writing %s.\n", elefilename );
}
outfile = fopen( elefilename, "w" );
if ( outfile == (FILE *) NULL ) {
printf( " Error: Cannot create file %s.\n", elefilename );
exit( 1 );
}
/* Number of triangles, points per triangle, attributes per triangle. */
fprintf( outfile, "%ld %d %d\n", triangles.items,
( order + 1 ) * ( order + 2 ) / 2, eextras );
#endif /* not TRILIBRARY */
traversalinit( &triangles );
triangleloop.tri = triangletraverse();
triangleloop.orient = 0;
elementnumber = firstnumber;
while ( triangleloop.tri != (triangle *) NULL ) {
org( triangleloop, p1 );
dest( triangleloop, p2 );
apex( triangleloop, p3 );
if ( order == 1 ) {
#ifdef TRILIBRARY
tlist[pointindex++] = pointmark( p1 );
tlist[pointindex++] = pointmark( p2 );
tlist[pointindex++] = pointmark( p3 );
#else /* not TRILIBRARY */
/* Triangle number, indices for three points. */
fprintf( outfile, "%4d %4d %4d %4d", elementnumber,
pointmark( p1 ), pointmark( p2 ), pointmark( p3 ) );
#endif /* not TRILIBRARY */
}
else {
mid1 = (point) triangleloop.tri[highorderindex + 1];
mid2 = (point) triangleloop.tri[highorderindex + 2];
mid3 = (point) triangleloop.tri[highorderindex];
#ifdef TRILIBRARY
tlist[pointindex++] = pointmark( p1 );
tlist[pointindex++] = pointmark( p2 );
tlist[pointindex++] = pointmark( p3 );
tlist[pointindex++] = pointmark( mid1 );
tlist[pointindex++] = pointmark( mid2 );
tlist[pointindex++] = pointmark( mid3 );
#else /* not TRILIBRARY */
/* Triangle number, indices for six points. */
fprintf( outfile, "%4d %4d %4d %4d %4d %4d %4d", elementnumber,
pointmark( p1 ), pointmark( p2 ), pointmark( p3 ), pointmark( mid1 ),
pointmark( mid2 ), pointmark( mid3 ) );
#endif /* not TRILIBRARY */
}
#ifdef TRILIBRARY
for ( i = 0; i < eextras; i++ ) {
talist[attribindex++] = elemattribute( triangleloop, i );
}
#else /* not TRILIBRARY */
for ( i = 0; i < eextras; i++ ) {
fprintf( outfile, " %.17g", elemattribute( triangleloop, i ) );
}
fprintf( outfile, "\n" );
#endif /* not TRILIBRARY */
triangleloop.tri = triangletraverse();
elementnumber++;
}
#ifndef TRILIBRARY
finishfile( outfile, argc, argv );
#endif /* not TRILIBRARY */
}
/*****************************************************************************/
/* */
/* writepoly() Write the segments and holes to a .poly file. */
/* */
/*****************************************************************************/
#ifdef TRILIBRARY
void writepoly( segmentlist, segmentmarkerlist )
int **segmentlist;
int **segmentmarkerlist;
#else /* not TRILIBRARY */
void writepoly( polyfilename, holelist, holes, regionlist, regions, argc, argv )
char *polyfilename;
REAL *holelist;
int holes;
REAL *regionlist;
int regions;
int argc;
char **argv;
#endif /* not TRILIBRARY */
{
#ifdef TRILIBRARY
int *slist;
int *smlist;
int index;
#else /* not TRILIBRARY */
FILE *outfile;
int i;
#endif /* not TRILIBRARY */
struct edge shelleloop;
point endpoint1, endpoint2;
int shellenumber;
#ifdef TRILIBRARY
if ( !quiet ) {
printf( "Writing segments.\n" );
}
/* Allocate memory for output segments if necessary. */
if ( *segmentlist == (int *) NULL ) {
*segmentlist = (int *) malloc( shelles.items * 2 * sizeof( int ) );
if ( *segmentlist == (int *) NULL ) {
printf( "Error: Out of memory.\n" );
exit( 1 );
}
}
/* Allocate memory for output segment markers if necessary. */
if ( !nobound && ( *segmentmarkerlist == (int *) NULL ) ) {
*segmentmarkerlist = (int *) malloc( shelles.items * sizeof( int ) );
if ( *segmentmarkerlist == (int *) NULL ) {
printf( "Error: Out of memory.\n" );
exit( 1 );
}
}
slist = *segmentlist;
smlist = *segmentmarkerlist;
index = 0;
#else /* not TRILIBRARY */
if ( !quiet ) {
printf( "Writing %s.\n", polyfilename );
}
outfile = fopen( polyfilename, "w" );
if ( outfile == (FILE *) NULL ) {
printf( " Error: Cannot create file %s.\n", polyfilename );
exit( 1 );
}
/* The zero indicates that the points are in a separate .node file. */
/* Followed by number of dimensions, number of point attributes, */
/* and number of boundary markers (zero or one). */
fprintf( outfile, "%d %d %d %d\n", 0, mesh_dim, nextras, 1 - nobound );
/* Number of segments, number of boundary markers (zero or one). */
fprintf( outfile, "%ld %d\n", shelles.items, 1 - nobound );
#endif /* not TRILIBRARY */
traversalinit( &shelles );
shelleloop.sh = shelletraverse();
shelleloop.shorient = 0;
shellenumber = firstnumber;
while ( shelleloop.sh != (shelle *) NULL ) {
sorg( shelleloop, endpoint1 );
sdest( shelleloop, endpoint2 );
#ifdef TRILIBRARY
/* Copy indices of the segment's two endpoints. */
slist[index++] = pointmark( endpoint1 );
slist[index++] = pointmark( endpoint2 );
if ( !nobound ) {
/* Copy the boundary marker. */
smlist[shellenumber - firstnumber] = mark( shelleloop );
}
#else /* not TRILIBRARY */
/* Segment number, indices of its two endpoints, and possibly a marker. */
if ( nobound ) {
fprintf( outfile, "%4d %4d %4d\n", shellenumber,
pointmark( endpoint1 ), pointmark( endpoint2 ) );
}
else {
fprintf( outfile, "%4d %4d %4d %4d\n", shellenumber,
pointmark( endpoint1 ), pointmark( endpoint2 ), mark( shelleloop ) );
}
#endif /* not TRILIBRARY */
shelleloop.sh = shelletraverse();
shellenumber++;
}
#ifndef TRILIBRARY
#ifndef CDT_ONLY
fprintf( outfile, "%d\n", holes );
if ( holes > 0 ) {
for ( i = 0; i < holes; i++ ) {
/* Hole number, x and y coordinates. */
fprintf( outfile, "%4d %.17g %.17g\n", firstnumber + i,
holelist[2 * i], holelist[2 * i + 1] );
}
}
if ( regions > 0 ) {
fprintf( outfile, "%d\n", regions );
for ( i = 0; i < regions; i++ ) {
/* Region number, x and y coordinates, attribute, maximum area. */
fprintf( outfile, "%4d %.17g %.17g %.17g %.17g\n", firstnumber + i,
regionlist[4 * i], regionlist[4 * i + 1],
regionlist[4 * i + 2], regionlist[4 * i + 3] );
}
}
#endif /* not CDT_ONLY */
finishfile( outfile, argc, argv );
#endif /* not TRILIBRARY */
}
/*****************************************************************************/
/* */
/* writeedges() Write the edges to a .edge file. */
/* */
/*****************************************************************************/
#ifdef TRILIBRARY
void writeedges( edgelist, edgemarkerlist )
int **edgelist;
int **edgemarkerlist;
#else /* not TRILIBRARY */
void writeedges( edgefilename, argc, argv )
char *edgefilename;
int argc;
char **argv;
#endif /* not TRILIBRARY */
{
#ifdef TRILIBRARY
int *elist;
int *emlist;
int index;
#else /* not TRILIBRARY */
FILE *outfile;
#endif /* not TRILIBRARY */
struct triedge triangleloop, trisym;
struct edge checkmark;
point p1, p2;
int edgenumber;
triangle ptr; /* Temporary variable used by sym(). */
shelle sptr; /* Temporary variable used by tspivot(). */
#ifdef TRILIBRARY
if ( !quiet ) {
printf( "Writing edges.\n" );
}
/* Allocate memory for edges if necessary. */
if ( *edgelist == (int *) NULL ) {
*edgelist = (int *) malloc( edges * 2 * sizeof( int ) );
if ( *edgelist == (int *) NULL ) {
printf( "Error: Out of memory.\n" );
exit( 1 );
}
}
/* Allocate memory for edge markers if necessary. */
if ( !nobound && ( *edgemarkerlist == (int *) NULL ) ) {
*edgemarkerlist = (int *) malloc( edges * sizeof( int ) );
if ( *edgemarkerlist == (int *) NULL ) {
printf( "Error: Out of memory.\n" );
exit( 1 );
}
}
elist = *edgelist;
emlist = *edgemarkerlist;
index = 0;
#else /* not TRILIBRARY */
if ( !quiet ) {
printf( "Writing %s.\n", edgefilename );
}
outfile = fopen( edgefilename, "w" );
if ( outfile == (FILE *) NULL ) {
printf( " Error: Cannot create file %s.\n", edgefilename );
exit( 1 );
}
/* Number of edges, number of boundary markers (zero or one). */
fprintf( outfile, "%ld %d\n", edges, 1 - nobound );
#endif /* not TRILIBRARY */
traversalinit( &triangles );
triangleloop.tri = triangletraverse();
edgenumber = firstnumber;
/* To loop over the set of edges, loop over all triangles, and look at */
/* the three edges of each triangle. If there isn't another triangle */
/* adjacent to the edge, operate on the edge. If there is another */
/* adjacent triangle, operate on the edge only if the current triangle */
/* has a smaller pointer than its neighbor. This way, each edge is */
/* considered only once. */
while ( triangleloop.tri != (triangle *) NULL ) {
for ( triangleloop.orient = 0; triangleloop.orient < 3;
triangleloop.orient++ ) {
sym( triangleloop, trisym );
if ( ( triangleloop.tri < trisym.tri ) || ( trisym.tri == dummytri ) ) {
org( triangleloop, p1 );
dest( triangleloop, p2 );
#ifdef TRILIBRARY
elist[index++] = pointmark( p1 );
elist[index++] = pointmark( p2 );
#endif /* TRILIBRARY */
if ( nobound ) {
#ifndef TRILIBRARY
/* Edge number, indices of two endpoints. */
fprintf( outfile, "%4d %d %d\n", edgenumber,
pointmark( p1 ), pointmark( p2 ) );
#endif /* not TRILIBRARY */
}
else {
/* Edge number, indices of two endpoints, and a boundary marker. */
/* If there's no shell edge, the boundary marker is zero. */
if ( useshelles ) {
tspivot( triangleloop, checkmark );
if ( checkmark.sh == dummysh ) {
#ifdef TRILIBRARY
emlist[edgenumber - firstnumber] = 0;
#else /* not TRILIBRARY */
fprintf( outfile, "%4d %d %d %d\n", edgenumber,
pointmark( p1 ), pointmark( p2 ), 0 );
#endif /* not TRILIBRARY */
}
else {
#ifdef TRILIBRARY
emlist[edgenumber - firstnumber] = mark( checkmark );
#else /* not TRILIBRARY */
fprintf( outfile, "%4d %d %d %d\n", edgenumber,
pointmark( p1 ), pointmark( p2 ), mark( checkmark ) );
#endif /* not TRILIBRARY */
}
}
else {
#ifdef TRILIBRARY
emlist[edgenumber - firstnumber] = trisym.tri == dummytri;
#else /* not TRILIBRARY */
fprintf( outfile, "%4d %d %d %d\n", edgenumber,
pointmark( p1 ), pointmark( p2 ), trisym.tri == dummytri );
#endif /* not TRILIBRARY */
}
}
edgenumber++;
}
}
triangleloop.tri = triangletraverse();
}
#ifndef TRILIBRARY
finishfile( outfile, argc, argv );
#endif /* not TRILIBRARY */
}
/*****************************************************************************/
/* */
/* writevoronoi() Write the Voronoi diagram to a .v.node and .v.edge */
/* file. */
/* */
/* The Voronoi diagram is the geometric dual of the Delaunay triangulation. */
/* Hence, the Voronoi vertices are listed by traversing the Delaunay */
/* triangles, and the Voronoi edges are listed by traversing the Delaunay */
/* edges. */
/* */
/* WARNING: In order to assign numbers to the Voronoi vertices, this */
/* procedure messes up the shell edges or the extra nodes of every */
/* element. Hence, you should call this procedure last. */
/* */
/*****************************************************************************/
#ifdef TRILIBRARY
void writevoronoi( vpointlist, vpointattriblist, vpointmarkerlist, vedgelist,
vedgemarkerlist, vnormlist )
REAL * *vpointlist;
REAL **vpointattriblist;
int **vpointmarkerlist;
int **vedgelist;
int **vedgemarkerlist;
REAL **vnormlist;
#else /* not TRILIBRARY */
void writevoronoi( vnodefilename, vedgefilename, argc, argv )
char *vnodefilename;
char *vedgefilename;
int argc;
char **argv;
#endif /* not TRILIBRARY */
{
#ifdef TRILIBRARY
REAL *plist;
REAL *palist;
int *elist;
REAL *normlist;
int coordindex;
int attribindex;
#else /* not TRILIBRARY */
FILE *outfile;
#endif /* not TRILIBRARY */
struct triedge triangleloop, trisym;
point torg, tdest, tapex;
REAL circumcenter[2];
REAL xi, eta;
int vnodenumber, vedgenumber;
int p1, p2;
int i;
triangle ptr; /* Temporary variable used by sym(). */
#ifdef TRILIBRARY
if ( !quiet ) {
printf( "Writing Voronoi vertices.\n" );
}
/* Allocate memory for Voronoi vertices if necessary. */
if ( *vpointlist == (REAL *) NULL ) {
*vpointlist = (REAL *) malloc( triangles.items * 2 * sizeof( REAL ) );
if ( *vpointlist == (REAL *) NULL ) {
printf( "Error: Out of memory.\n" );
exit( 1 );
}
}
/* Allocate memory for Voronoi vertex attributes if necessary. */
if ( *vpointattriblist == (REAL *) NULL ) {
*vpointattriblist = (REAL *) malloc( triangles.items * nextras *
sizeof( REAL ) );
if ( *vpointattriblist == (REAL *) NULL ) {
printf( "Error: Out of memory.\n" );
exit( 1 );
}
}
*vpointmarkerlist = (int *) NULL;
plist = *vpointlist;
palist = *vpointattriblist;
coordindex = 0;
attribindex = 0;
#else /* not TRILIBRARY */
if ( !quiet ) {
printf( "Writing %s.\n", vnodefilename );
}
outfile = fopen( vnodefilename, "w" );
if ( outfile == (FILE *) NULL ) {
printf( " Error: Cannot create file %s.\n", vnodefilename );
exit( 1 );
}
/* Number of triangles, two dimensions, number of point attributes, */
/* zero markers. */
fprintf( outfile, "%ld %d %d %d\n", triangles.items, 2, nextras, 0 );
#endif /* not TRILIBRARY */
traversalinit( &triangles );
triangleloop.tri = triangletraverse();
triangleloop.orient = 0;
vnodenumber = firstnumber;
while ( triangleloop.tri != (triangle *) NULL ) {
org( triangleloop, torg );
dest( triangleloop, tdest );
apex( triangleloop, tapex );
findcircumcenter( torg, tdest, tapex, circumcenter, &xi, &eta );
#ifdef TRILIBRARY
/* X and y coordinates. */
plist[coordindex++] = circumcenter[0];
plist[coordindex++] = circumcenter[1];
for ( i = 2; i < 2 + nextras; i++ ) {
/* Interpolate the point attributes at the circumcenter. */
palist[attribindex++] = torg[i] + xi * ( tdest[i] - torg[i] )
+ eta * ( tapex[i] - torg[i] );
}
#else /* not TRILIBRARY */
/* Voronoi vertex number, x and y coordinates. */
fprintf( outfile, "%4d %.17g %.17g", vnodenumber, circumcenter[0],
circumcenter[1] );
for ( i = 2; i < 2 + nextras; i++ ) {
/* Interpolate the point attributes at the circumcenter. */
fprintf( outfile, " %.17g", torg[i] + xi * ( tdest[i] - torg[i] )
+ eta * ( tapex[i] - torg[i] ) );
}
fprintf( outfile, "\n" );
#endif /* not TRILIBRARY */
*(int *) ( triangleloop.tri + 6 ) = vnodenumber;
triangleloop.tri = triangletraverse();
vnodenumber++;
}
#ifndef TRILIBRARY
finishfile( outfile, argc, argv );
#endif /* not TRILIBRARY */
#ifdef TRILIBRARY
if ( !quiet ) {
printf( "Writing Voronoi edges.\n" );
}
/* Allocate memory for output Voronoi edges if necessary. */
if ( *vedgelist == (int *) NULL ) {
*vedgelist = (int *) malloc( edges * 2 * sizeof( int ) );
if ( *vedgelist == (int *) NULL ) {
printf( "Error: Out of memory.\n" );
exit( 1 );
}
}
*vedgemarkerlist = (int *) NULL;
/* Allocate memory for output Voronoi norms if necessary. */
if ( *vnormlist == (REAL *) NULL ) {
*vnormlist = (REAL *) malloc( edges * 2 * sizeof( REAL ) );
if ( *vnormlist == (REAL *) NULL ) {
printf( "Error: Out of memory.\n" );
exit( 1 );
}
}
elist = *vedgelist;
normlist = *vnormlist;
coordindex = 0;
#else /* not TRILIBRARY */
if ( !quiet ) {
printf( "Writing %s.\n", vedgefilename );
}
outfile = fopen( vedgefilename, "w" );
if ( outfile == (FILE *) NULL ) {
printf( " Error: Cannot create file %s.\n", vedgefilename );
exit( 1 );
}
/* Number of edges, zero boundary markers. */
fprintf( outfile, "%ld %d\n", edges, 0 );
#endif /* not TRILIBRARY */
traversalinit( &triangles );
triangleloop.tri = triangletraverse();
vedgenumber = firstnumber;
/* To loop over the set of edges, loop over all triangles, and look at */
/* the three edges of each triangle. If there isn't another triangle */
/* adjacent to the edge, operate on the edge. If there is another */
/* adjacent triangle, operate on the edge only if the current triangle */
/* has a smaller pointer than its neighbor. This way, each edge is */
/* considered only once. */
while ( triangleloop.tri != (triangle *) NULL ) {
for ( triangleloop.orient = 0; triangleloop.orient < 3;
triangleloop.orient++ ) {
sym( triangleloop, trisym );
if ( ( triangleloop.tri < trisym.tri ) || ( trisym.tri == dummytri ) ) {
/* Find the number of this triangle (and Voronoi vertex). */
p1 = *(int *) ( triangleloop.tri + 6 );
if ( trisym.tri == dummytri ) {
org( triangleloop, torg );
dest( triangleloop, tdest );
#ifdef TRILIBRARY
/* Copy an infinite ray. Index of one endpoint, and -1. */
elist[coordindex] = p1;
normlist[coordindex++] = tdest[1] - torg[1];
elist[coordindex] = -1;
normlist[coordindex++] = torg[0] - tdest[0];
#else /* not TRILIBRARY */
/* Write an infinite ray. Edge number, index of one endpoint, -1, */
/* and x and y coordinates of a vector representing the */
/* direction of the ray. */
fprintf( outfile, "%4d %d %d %.17g %.17g\n", vedgenumber,
p1, -1, tdest[1] - torg[1], torg[0] - tdest[0] );
#endif /* not TRILIBRARY */
}
else {
/* Find the number of the adjacent triangle (and Voronoi vertex). */
p2 = *(int *) ( trisym.tri + 6 );
/* Finite edge. Write indices of two endpoints. */
#ifdef TRILIBRARY
elist[coordindex] = p1;
normlist[coordindex++] = 0.0;
elist[coordindex] = p2;
normlist[coordindex++] = 0.0;
#else /* not TRILIBRARY */
fprintf( outfile, "%4d %d %d\n", vedgenumber, p1, p2 );
#endif /* not TRILIBRARY */
}
vedgenumber++;
}
}
triangleloop.tri = triangletraverse();
}
#ifndef TRILIBRARY
finishfile( outfile, argc, argv );
#endif /* not TRILIBRARY */
}
#ifdef TRILIBRARY
void writeneighbors( neighborlist )
int **neighborlist;
#else /* not TRILIBRARY */
void writeneighbors( neighborfilename, argc, argv )
char *neighborfilename;
int argc;
char **argv;
#endif /* not TRILIBRARY */
{
#ifdef TRILIBRARY
int *nlist;
int index;
#else /* not TRILIBRARY */
FILE *outfile;
#endif /* not TRILIBRARY */
struct triedge triangleloop, trisym;
int elementnumber;
int neighbor1, neighbor2, neighbor3;
triangle ptr; /* Temporary variable used by sym(). */
#ifdef TRILIBRARY
if ( !quiet ) {
printf( "Writing neighbors.\n" );
}
/* Allocate memory for neighbors if necessary. */
if ( *neighborlist == (int *) NULL ) {
*neighborlist = (int *) malloc( triangles.items * 3 * sizeof( int ) );
if ( *neighborlist == (int *) NULL ) {
printf( "Error: Out of memory.\n" );
exit( 1 );
}
}
nlist = *neighborlist;
index = 0;
#else /* not TRILIBRARY */
if ( !quiet ) {
printf( "Writing %s.\n", neighborfilename );
}
outfile = fopen( neighborfilename, "w" );
if ( outfile == (FILE *) NULL ) {
printf( " Error: Cannot create file %s.\n", neighborfilename );
exit( 1 );
}
/* Number of triangles, three edges per triangle. */
fprintf( outfile, "%ld %d\n", triangles.items, 3 );
#endif /* not TRILIBRARY */
traversalinit( &triangles );
triangleloop.tri = triangletraverse();
triangleloop.orient = 0;
elementnumber = firstnumber;
while ( triangleloop.tri != (triangle *) NULL ) {
*(int *) ( triangleloop.tri + 6 ) = elementnumber;
triangleloop.tri = triangletraverse();
elementnumber++;
}
*(int *) ( dummytri + 6 ) = -1;
traversalinit( &triangles );
triangleloop.tri = triangletraverse();
elementnumber = 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, "%4d %d %d %d\n", elementnumber,
neighbor1, neighbor2, neighbor3 );
#endif /* not TRILIBRARY */
triangleloop.tri = triangletraverse();
elementnumber++;
}
#ifndef TRILIBRARY
finishfile( outfile, argc, argv );
#endif /* 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
void writeoff( offfilename, argc, argv )
char *offfilename;
int argc;
char **argv;
{
FILE *outfile;
struct triedge triangleloop;
point pointloop;
point p1, p2, p3;
if ( !quiet ) {
printf( "Writing %s.\n", offfilename );
}
outfile = fopen( offfilename, "w" );
if ( outfile == (FILE *) NULL ) {
printf( " Error: Cannot create file %s.\n", offfilename );
exit( 1 );
}
/* Number of points, triangles, and edges. */
fprintf( outfile, "OFF\n%ld %ld %ld\n", points.items, triangles.items,
edges );
/* Write the points. */
traversalinit( &points );
pointloop = pointtraverse();
while ( pointloop != (point) NULL ) {
/* The "0.0" is here because the OFF format uses 3D coordinates. */
fprintf( outfile, " %.17g %.17g %.17g\n", pointloop[0],
pointloop[1], 0.0 );
pointloop = pointtraverse();
}
/* Write the triangles. */
traversalinit( &triangles );
triangleloop.tri = triangletraverse();
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", pointmark( p1 ) - 1,
pointmark( p2 ) - 1, pointmark( p3 ) - 1 );
triangleloop.tri = triangletraverse();
}
finishfile( outfile, argc, argv );
}
#endif /* not TRILIBRARY */
/** **/
/** **/
/********* File I/O routines end here *********/
/*****************************************************************************/
/* */
/* quality_statistics() Print statistics about the quality of the mesh. */
/* */
/*****************************************************************************/
void quality_statistics(){
struct triedge triangleloop;
point 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 = (REAL)( PI / 18.0 );
degconst = (REAL)( 180.0 / PI );
for ( i = 0; i < 8; i++ ) {
cossquaretable[i] = (REAL)( 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 = xmax - xmin + ymax - 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( &triangles );
triangleloop.tri = triangletraverse();
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( 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();
}
shortest = (REAL)sqrt( shortest );
longest = (REAL)sqrt( longest );
minaltitude = (REAL)sqrt( minaltitude );
worstaspect = (REAL)sqrt( worstaspect );
smallestarea *= 2.0;
biggestarea *= 2.0;
if ( smallestangle >= 1.0 ) {
smallestangle = 0.0;
}
else {
smallestangle = (REAL)( degconst * acos( sqrt( smallestangle ) ) );
}
if ( biggestangle >= 1.0 ) {
biggestangle = 180.0;
}
else {
if ( acutebiggest ) {
biggestangle = (REAL)( degconst * acos( sqrt( biggestangle ) ) );
}
else {
biggestangle = (REAL)( 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( " 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(
" (Triangle aspect ratio is longest edge divided by shortest altitude)\n\n" );
printf( " Smallest angle: %15.5g | Largest angle: %15.5g\n\n",
smallestangle, biggestangle );
printf( " Angle histogram:\n" );
for ( i = 0; i < 9; i++ ) {
printf( " %3d - %3d degrees: %8d | %3d - %3d degrees: %8d\n",
i * 10, i * 10 + 10, angletable[i],
i * 10 + 90, i * 10 + 100, angletable[i + 9] );
}
printf( "\n" );
}
/*****************************************************************************/
/* */
/* statistics() Print all sorts of cool facts. */
/* */
/*****************************************************************************/
void statistics(){
printf( "\nStatistics:\n\n" );
printf( " Input points: %d\n", inpoints );
if ( refine ) {
printf( " Input triangles: %d\n", inelements );
}
if ( poly ) {
printf( " Input segments: %d\n", insegments );
if ( !refine ) {
printf( " Input holes: %d\n", holes );
}
}
printf( "\n Mesh points: %ld\n", points.items );
printf( " Mesh triangles: %ld\n", triangles.items );
printf( " Mesh edges: %ld\n", edges );
if ( poly || refine ) {
printf( " Mesh boundary edges: %ld\n", hullsize );
printf( " Mesh segments: %ld\n\n", shelles.items );
}
else {
printf( " Mesh convex hull edges: %ld\n\n", hullsize );
}
if ( verbose ) {
quality_statistics();
printf( "Memory allocation statistics:\n\n" );
printf( " Maximum number of points: %ld\n", points.maxitems );
printf( " Maximum number of triangles: %ld\n", triangles.maxitems );
if ( shelles.maxitems > 0 ) {
printf( " Maximum number of segments: %ld\n", shelles.maxitems );
}
if ( viri.maxitems > 0 ) {
printf( " Maximum number of viri: %ld\n", viri.maxitems );
}
if ( badsegments.maxitems > 0 ) {
printf( " Maximum number of encroached segments: %ld\n",
badsegments.maxitems );
}
if ( badtriangles.maxitems > 0 ) {
printf( " Maximum number of bad triangles: %ld\n",
badtriangles.maxitems );
}
if ( splaynodes.maxitems > 0 ) {
printf( " Maximum number of splay tree nodes: %ld\n",
splaynodes.maxitems );
}
printf( " Approximate heap memory use (bytes): %ld\n\n",
points.maxitems * points.itembytes
+ triangles.maxitems * triangles.itembytes
+ shelles.maxitems * shelles.itembytes
+ viri.maxitems * viri.itembytes
+ badsegments.maxitems * badsegments.itembytes
+ badtriangles.maxitems * badtriangles.itembytes
+ splaynodes.maxitems * splaynodes.itembytes );
printf( "Algorithmic statistics:\n\n" );
printf( " Number of incircle tests: %ld\n", incirclecount );
printf( " Number of orientation tests: %ld\n", counterclockcount );
if ( hyperbolacount > 0 ) {
printf( " Number of right-of-hyperbola tests: %ld\n",
hyperbolacount );
}
if ( circumcentercount > 0 ) {
printf( " Number of circumcenter computations: %ld\n",
circumcentercount );
}
if ( circletopcount > 0 ) {
printf( " Number of circle top computations: %ld\n",
circletopcount );
}
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 points 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
void triangulate( triswitches, in, out, vorout )
char *triswitches;
struct triangulateio *in;
struct triangulateio *out;
struct triangulateio *vorout;
#else /* not TRILIBRARY */
int main( argc, argv )
int argc;
char **argv;
#endif /* not TRILIBRARY */
{
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 /* NO_TIMER */
#ifndef NO_TIMER
gettimeofday( &tv0, &tz );
#endif /* NO_TIMER */
triangleinit();
#ifdef TRILIBRARY
parsecommandline( 1, &triswitches );
#else /* not TRILIBRARY */
parsecommandline( argc, argv );
#endif /* not TRILIBRARY */
#ifdef TRILIBRARY
transfernodes( in->pointlist, in->pointattributelist, in->pointmarkerlist,
in->numberofpoints, in->numberofpointattributes );
#else /* not TRILIBRARY */
readnodes( innodefilename, inpolyfilename, &polyfile );
#endif /* not TRILIBRARY */
#ifndef NO_TIMER
if ( !quiet ) {
gettimeofday( &tv1, &tz );
}
#endif /* NO_TIMER */
#ifdef CDT_ONLY
hullsize = delaunay(); /* Triangulate the points. */
#else /* not CDT_ONLY */
if ( refine ) {
/* Read and reconstruct a mesh. */
#ifdef TRILIBRARY
hullsize = reconstruct( in->trianglelist, in->triangleattributelist,
in->trianglearealist, in->numberoftriangles,
in->numberofcorners, in->numberoftriangleattributes,
in->segmentlist, in->segmentmarkerlist,
in->numberofsegments );
#else /* not TRILIBRARY */
hullsize = reconstruct( inelefilename, areafilename, inpolyfilename,
polyfile );
#endif /* not TRILIBRARY */
}
else {
hullsize = delaunay(); /* Triangulate the points. */
}
#endif /* not CDT_ONLY */
#ifndef NO_TIMER
if ( !quiet ) {
gettimeofday( &tv2, &tz );
if ( 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 /* NO_TIMER */
/* Ensure that no point can be mistaken for a triangular bounding */
/* box point in insertsite(). */
infpoint1 = (point) NULL;
infpoint2 = (point) NULL;
infpoint3 = (point) NULL;
if ( useshelles ) {
checksegments = 1; /* Segments will be introduced next. */
if ( !refine ) {
/* Insert PSLG segments and/or convex hull segments. */
#ifdef TRILIBRARY
insegments = formskeleton( in->segmentlist, in->segmentmarkerlist,
in->numberofsegments );
#else /* not TRILIBRARY */
insegments = formskeleton( polyfile, inpolyfilename );
#endif /* not TRILIBRARY */
}
}
#ifndef NO_TIMER
if ( !quiet ) {
gettimeofday( &tv3, &tz );
if ( useshelles && !refine ) {
printf( "Segment milliseconds: %ld\n",
1000l * ( tv3.tv_sec - tv2.tv_sec )
+ ( tv3.tv_usec - tv2.tv_usec ) / 1000l );
}
}
#endif /* NO_TIMER */
if ( poly ) {
#ifdef TRILIBRARY
holearray = in->holelist;
holes = in->numberofholes;
regionarray = in->regionlist;
regions = in->numberofregions;
#else /* not TRILIBRARY */
readholes( polyfile, inpolyfilename, &holearray, &holes,
&regionarray, &regions );
#endif /* not TRILIBRARY */
if ( !refine ) {
/* Carve out holes and concavities. */
carveholes( holearray, holes, regionarray, 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. */
holes = 0;
regions = 0;
}
#ifndef NO_TIMER
if ( !quiet ) {
gettimeofday( &tv4, &tz );
if ( poly && !refine ) {
printf( "Hole milliseconds: %ld\n", 1000l * ( tv4.tv_sec - tv3.tv_sec )
+ ( tv4.tv_usec - tv3.tv_usec ) / 1000l );
}
}
#endif /* NO_TIMER */
#ifndef CDT_ONLY
if ( quality ) {
enforcequality(); /* Enforce angle and area constraints. */
}
#endif /* not CDT_ONLY */
#ifndef NO_TIMER
if ( !quiet ) {
gettimeofday( &tv5, &tz );
#ifndef CDT_ONLY
if ( 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 /* NO_TIMER */
/* Compute the number of edges. */
edges = ( 3l * triangles.items + hullsize ) / 2l;
if ( order > 1 ) {
highorder(); /* Promote elements to higher polynomial order. */
}
if ( !quiet ) {
printf( "\n" );
}
#ifdef TRILIBRARY
out->numberofpoints = points.items;
out->numberofpointattributes = nextras;
out->numberoftriangles = triangles.items;
out->numberofcorners = ( order + 1 ) * ( order + 2 ) / 2;
out->numberoftriangleattributes = eextras;
out->numberofedges = edges;
if ( useshelles ) {
out->numberofsegments = shelles.items;
}
else {
out->numberofsegments = hullsize;
}
if ( vorout != (struct triangulateio *) NULL ) {
vorout->numberofpoints = triangles.items;
vorout->numberofpointattributes = nextras;
vorout->numberofedges = 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 ( nonodewritten || ( noiterationnum && readnodefile ) ) {
if ( !quiet ) {
#ifdef TRILIBRARY
printf( "NOT writing points.\n" );
#else /* not TRILIBRARY */
printf( "NOT writing a .node file.\n" );
#endif /* not TRILIBRARY */
}
numbernodes(); /* We must remember to number the points. */
}
else {
#ifdef TRILIBRARY
writenodes( &out->pointlist, &out->pointattributelist,
&out->pointmarkerlist );
#else /* not TRILIBRARY */
writenodes( outnodefilename, argc, argv ); /* Numbers the points too. */
#endif /* TRILIBRARY */
}
if ( noelewritten ) {
if ( !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( &out->trianglelist, &out->triangleattributelist );
#else /* not TRILIBRARY */
writeelements( outelefilename, argc, argv );
#endif /* not TRILIBRARY */
}
/* The -c switch (convex switch) causes a PSLG to be written */
/* even if none was read. */
if ( poly || convex ) {
/* If not using iteration numbers, don't overwrite the .poly file. */
if ( nopolywritten || noiterationnum ) {
if ( !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( &out->segmentlist, &out->segmentmarkerlist );
out->numberofholes = holes;
out->numberofregions = regions;
if ( poly ) {
out->holelist = in->holelist;
out->regionlist = in->regionlist;
}
else {
out->holelist = (REAL *) NULL;
out->regionlist = (REAL *) NULL;
}
#else /* not TRILIBRARY */
writepoly( outpolyfilename, holearray, holes, regionarray, regions,
argc, argv );
#endif /* not TRILIBRARY */
}
}
#ifndef TRILIBRARY
#ifndef CDT_ONLY
if ( regions > 0 ) {
free( regionarray );
}
#endif /* not CDT_ONLY */
if ( holes > 0 ) {
free( holearray );
}
if ( geomview ) {
writeoff( offfilename, argc, argv );
}
#endif /* not TRILIBRARY */
if ( edgesout ) {
#ifdef TRILIBRARY
writeedges( &out->edgelist, &out->edgemarkerlist );
#else /* not TRILIBRARY */
writeedges( edgefilename, argc, argv );
#endif /* not TRILIBRARY */
}
if ( voronoi ) {
#ifdef TRILIBRARY
writevoronoi( &vorout->pointlist, &vorout->pointattributelist,
&vorout->pointmarkerlist, &vorout->edgelist,
&vorout->edgemarkerlist, &vorout->normlist );
#else /* not TRILIBRARY */
writevoronoi( vnodefilename, vedgefilename, argc, argv );
#endif /* not TRILIBRARY */
}
if ( neighbors ) {
#ifdef TRILIBRARY
writeneighbors( &out->neighborlist );
#else /* not TRILIBRARY */
writeneighbors( neighborfilename, argc, argv );
#endif /* not TRILIBRARY */
}
if ( !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 /* NO_TIMER */
statistics();
}
#ifndef REDUCED
if ( docheck ) {
checkmesh();
checkdelaunay();
}
#endif /* not REDUCED */
triangledeinit();
#ifndef TRILIBRARY
return 0;
#endif /* not TRILIBRARY */
}
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