+++ /dev/null
-#define ANSI_DECLARATORS
-/*****************************************************************************/
-/* */
-/* 888888888 ,o, / 888 */
-/* 888 88o88o " o8888o 88o8888o o88888o 888 o88888o */
-/* 888 888 888 88b 888 888 888 888 888 d888 88b */
-/* 888 888 888 o88^o888 888 888 "88888" 888 8888oo888 */
-/* 888 888 888 C888 888 888 888 / 888 q888 */
-/* 888 888 888 "88o^888 888 888 Cb 888 "88oooo" */
-/* "8oo8D */
-/* */
-/* A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator. */
-/* (triangle.c) */
-/* */
-/* Version 1.3 */
-/* 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, ®ionlist[4 * i]) >
- 0.0) {
- /* Find a triangle that contains the region point. */
- intersect = locate(®ionlist[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,
- ®ionarray, ®ions);
-#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 */
-}