[SCM] gmt branch, master, updated. upstream/4.5.5-19-gb14a5eb
Francesco Paolo Lovergine
frankie at debian.org
Tue Mar 13 12:54:26 UTC 2012
The following commit has been merged in the master branch:
commit 6ea6d1a5e0e46616da9a2ff6a81ea0c5a8f4a27f
Author: Francesco Paolo Lovergine <frankie at debian.org>
Date: Tue Mar 13 11:19:14 2012 +0100
Removed non-free Triangle sources.
diff --git a/src/triangle.c b/src/triangle.c
deleted file mode 100644
index 3958d42..0000000
--- a/src/triangle.c
+++ /dev/null
@@ -1,16009 +0,0 @@
-/*****************************************************************************/
-/* */
-/* 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 1.6 */
-/* July 28, 2005 */
-/* */
-/* Copyright 1993, 1995, 1997, 1998, 2002, 2005 */
-/* Jonathan Richard Shewchuk */
-/* 2360 Woolsey #H */
-/* Berkeley, California 94705-1927 */
-/* jrs at cs.berkeley.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 */
-/* */
-/* Disclaimer: Neither I nor Carnegie Mellon warrant this code in any way */
-/* whatsoever. This code is provided "as-is". Use at your own risk. */
-/* */
-/* Some of the references listed below are marked with an asterisk. [*] */
-/* These references are available for downloading from the Web page */
-/* */
-/* http://www.cs.cmu.edu/~quake/triangle.research.html */
-/* */
-/* Three papers discussing aspects of Triangle are available. A short */
-/* overview appears in "Triangle: Engineering a 2D Quality Mesh */
-/* Generator and Delaunay Triangulator," in Applied Computational */
-/* Geometry: Towards Geometric Engineering, Ming C. Lin and Dinesh */
-/* Manocha, editors, Lecture Notes in Computer Science volume 1148, */
-/* pages 203-222, Springer-Verlag, Berlin, May 1996 (from the First ACM */
-/* Workshop on Applied Computational Geometry). [*] */
-/* */
-/* The algorithms are discussed in the greatest detail in "Delaunay */
-/* Refinement Algorithms for Triangular Mesh Generation," Computational */
-/* Geometry: Theory and Applications 22(1-3):21-74, May 2002. [*] */
-/* */
-/* More detail about the data structures may be found in my dissertation: */
-/* "Delaunay Refinement Mesh Generation," Ph.D. thesis, Technical Report */
-/* CMU-CS-97-137, School of Computer Science, Carnegie Mellon University, */
-/* Pittsburgh, Pennsylvania, 18 May 1997. [*] */
-/* */
-/* Triangle was created as part of the Quake Project in the School of */
-/* Computer Science at Carnegie Mellon University. For further */
-/* information, see Hesheng Bao, Jacobo Bielak, Omar Ghattas, Loukas F. */
-/* Kallivokas, David R. O'Hallaron, Jonathan R. Shewchuk, and Jifeng Xu, */
-/* "Large-scale Simulation of Elastic Wave Propagation in Heterogeneous */
-/* Media on Parallel Computers," Computer Methods in Applied Mechanics */
-/* and Engineering 152(1-2):85-102, 22 January 1998. */
-/* */
-/* Triangle's Delaunay refinement algorithm for quality mesh generation is */
-/* a hybrid of one due to Jim Ruppert, "A Delaunay Refinement Algorithm */
-/* for Quality 2-Dimensional Mesh Generation," Journal of Algorithms */
-/* 18(3):548-585, May 1995 [*], and one due to L. Paul Chew, "Guaranteed- */
-/* Quality Mesh Generation for Curved Surfaces," Proceedings of the Ninth */
-/* Annual Symposium on Computational Geometry (San Diego, California), */
-/* pages 274-280, Association for Computing Machinery, May 1993, */
-/* http://portal.acm.org/citation.cfm?id=161150 . */
-/* */
-/* The Delaunay refinement algorithm has been modified so that it meshes */
-/* domains with small input angles well, as described in Gary L. Miller, */
-/* Steven E. Pav, and Noel J. Walkington, "When and Why Ruppert's */
-/* Algorithm Works," Twelfth International Meshing Roundtable, pages */
-/* 91-102, Sandia National Laboratories, September 2003. [*] */
-/* */
-/* My implementation of the divide-and-conquer and incremental Delaunay */
-/* triangulation algorithms follows closely the presentation of Guibas */
-/* and Stolfi, even though I use a triangle-based data structure instead */
-/* of their quad-edge data structure. (In fact, I originally implemented */
-/* Triangle using the quad-edge data structure, but the switch to a */
-/* triangle-based data structure sped Triangle by a factor of two.) The */
-/* mesh manipulation primitives and the two aforementioned Delaunay */
-/* triangulation algorithms are described by Leonidas J. Guibas and Jorge */
-/* Stolfi, "Primitives for the Manipulation of General Subdivisions and */
-/* the Computation of Voronoi Diagrams," ACM Transactions on Graphics */
-/* 4(2):74-123, April 1985, http://portal.acm.org/citation.cfm?id=282923 .*/
-/* */
-/* Their O(n log n) divide-and-conquer algorithm is adapted from Der-Tsai */
-/* Lee and Bruce J. Schachter, "Two Algorithms for Constructing the */
-/* Delaunay Triangulation," International Journal of Computer and */
-/* Information Science 9(3):219-242, 1980. Triangle's improvement of the */
-/* divide-and-conquer algorithm by alternating between vertical and */
-/* horizontal cuts was introduced by Rex A. Dwyer, "A Faster Divide-and- */
-/* Conquer Algorithm for Constructing Delaunay Triangulations," */
-/* Algorithmica 2(2):137-151, 1987. */
-/* */
-/* The incremental insertion algorithm was first proposed by C. L. Lawson, */
-/* "Software for C1 Surface Interpolation," in Mathematical Software III, */
-/* John R. Rice, editor, Academic Press, New York, pp. 161-194, 1977. */
-/* For point location, I use the algorithm of Ernst P. Mucke, Isaac */
-/* Saias, and Binhai Zhu, "Fast Randomized Point Location Without */
-/* Preprocessing in Two- and Three-Dimensional Delaunay Triangulations," */
-/* Proceedings of the Twelfth Annual Symposium on Computational Geometry, */
-/* ACM, May 1996. [*] If I were to randomize the order of vertex */
-/* insertion (I currently don't bother), their result combined with the */
-/* result of Kenneth L. Clarkson and Peter W. Shor, "Applications of */
-/* Random Sampling in Computational Geometry II," Discrete & */
-/* Computational Geometry 4(1):387-421, 1989, would yield an expected */
-/* O(n^{4/3}) bound on running time. */
-/* */
-/* The O(n log n) sweepline Delaunay triangulation algorithm is taken from */
-/* Steven Fortune, "A Sweepline Algorithm for Voronoi Diagrams", */
-/* Algorithmica 2(2):153-174, 1987. A random sample of edges on the */
-/* boundary of the triangulation are maintained in a splay tree for the */
-/* purpose of point location. Splay trees are described by Daniel */
-/* Dominic Sleator and Robert Endre Tarjan, "Self-Adjusting Binary Search */
-/* Trees," Journal of the ACM 32(3):652-686, July 1985, */
-/* http://portal.acm.org/citation.cfm?id=3835 . */
-/* */
-/* The algorithms for exact computation of the signs of determinants are */
-/* described in Jonathan Richard Shewchuk, "Adaptive Precision Floating- */
-/* Point Arithmetic and Fast Robust Geometric Predicates," Discrete & */
-/* Computational Geometry 18(3):305-363, October 1997. (Also available */
-/* as Technical Report CMU-CS-96-140, School of Computer Science, */
-/* Carnegie Mellon University, Pittsburgh, Pennsylvania, May 1996.) [*] */
-/* An abbreviated version appears as Jonathan Richard Shewchuk, "Robust */
-/* Adaptive Floating-Point Geometric Predicates," Proceedings of the */
-/* Twelfth Annual Symposium on Computational Geometry, ACM, May 1996. [*] */
-/* Many of the ideas for my exact arithmetic routines originate with */
-/* Douglas M. Priest, "Algorithms for Arbitrary Precision Floating Point */
-/* Arithmetic," Tenth Symposium on Computer Arithmetic, pp. 132-143, IEEE */
-/* Computer Society Press, 1991. [*] Many of the ideas for the correct */
-/* evaluation of the signs of determinants are taken from Steven Fortune */
-/* and Christopher J. Van Wyk, "Efficient Exact Arithmetic for Computa- */
-/* tional Geometry," Proceedings of the Ninth Annual Symposium on */
-/* Computational Geometry, ACM, pp. 163-172, May 1993, and from Steven */
-/* Fortune, "Numerical Stability of Algorithms for 2D Delaunay Triangu- */
-/* lations," International Journal of Computational Geometry & Applica- */
-/* tions 5(1-2):193-213, March-June 1995. */
-/* */
-/* The method of inserting new vertices off-center (not precisely at the */
-/* circumcenter of every poor-quality triangle) is from Alper Ungor, */
-/* "Off-centers: A New Type of Steiner Points for Computing Size-Optimal */
-/* Quality-Guaranteed Delaunay Triangulations," Proceedings of LATIN */
-/* 2004 (Buenos Aires, Argentina), April 2004. */
-/* */
-/* For definitions of and results involving Delaunay triangulations, */
-/* constrained and conforming versions thereof, and other aspects of */
-/* triangular mesh generation, see the excellent survey by Marshall Bern */
-/* and David Eppstein, "Mesh Generation and Optimal Triangulation," in */
-/* Computing and Euclidean Geometry, Ding-Zhu Du and Frank Hwang, */
-/* editors, World Scientific, Singapore, pp. 23-90, 1992. [*] */
-/* */
-/* The time for incrementally adding PSLG (planar straight line graph) */
-/* segments to create a constrained Delaunay triangulation is probably */
-/* O(t^2) per segment in the worst case and O(t) per segment in the */
-/* common case, where t is the number of triangles that intersect the */
-/* segment before it is inserted. This doesn't count point location, */
-/* which can be much more expensive. I could improve this to O(d log d) */
-/* time, but d is usually quite small, so it's not worth the bother. */
-/* (This note does not apply when the -s switch is used, invoking a */
-/* different method is used to insert segments.) */
-/* */
-/* The time for deleting a vertex from a Delaunay triangulation is O(d^2) */
-/* in the worst case and O(d) in the common case, where d is the degree */
-/* of the vertex being deleted. I could improve this to O(d log d) time, */
-/* but d is usually quite small, so it's not worth the bother. */
-/* */
-/* Ruppert's Delaunay refinement algorithm typically generates triangles */
-/* at a linear rate (constant time per triangle) after the initial */
-/* triangulation is formed. There may be pathological cases where */
-/* quadratic time is required, but these never arise in practice. */
-/* */
-/* The geometric predicates (circumcenter calculations, segment */
-/* intersection formulae, etc.) appear in my "Lecture Notes on Geometric */
-/* Robustness" at http://www.cs.berkeley.edu/~jrs/mesh . */
-/* */
-/* If you make any improvements to this code, please please please let me */
-/* know, so that I may obtain the improvements. Even if you don't change */
-/* the code, I'd still love to hear what it's being used for. */
-/* */
-/*****************************************************************************/
-
-/* 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 until your work is debugged. */
-
-/* #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, -u, -D, -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, my exact arithmetic routines might be defeated by the */
-/* use of internal extended precision floating-point registers. The best */
-/* way to solve this problem is to set the floating-point registers to use */
-/* single or double precision internally. On 80x86 processors, this may */
-/* be accomplished by setting the CPU86 symbol for the Microsoft C */
-/* compiler, or the LINUX symbol for the gcc compiler running on Linux. */
-/* */
-/* An inferior solution is to declare certain values as `volatile', thus */
-/* forcing them to be stored to memory and rounded off. Unfortunately, */
-/* this solution might slow Triangle down quite a bit. To use volatile */
-/* values, write "#define INEXACT volatile" below. Normally, however, */
-/* INEXACT should be defined to be nothing. ("#define INEXACT".) */
-/* */
-/* For more discussion, see http://www.cs.cmu.edu/~quake/robust.pc.html . */
-/* For yet more discussion, see Section 5 of my paper, "Adaptive Precision */
-/* Floating-Point Arithmetic and Fast Robust Geometric Predicates" (also */
-/* available as Section 6.6 of my dissertation). */
-
-/* #define CPU86 */
-/* #define LINUX */
-
-#define INEXACT /* Nothing */
-/* #define INEXACT volatile */
-
-/* Maximum number of characters in a file name (including the null). */
-
-#define FILENAMESIZE 2048
-
-/* Maximum number of characters in a line read from a file (including the */
-/* null). */
-
-#define INPUTLINESIZE 1024
-
-/* For efficiency, a variety of data structures are allocated in bulk. The */
-/* following constants determine how many of each structure is allocated */
-/* at once. */
-
-#define TRIPERBLOCK 4092 /* Number of triangles allocated at once. */
-#define SUBSEGPERBLOCK 508 /* Number of subsegments allocated at once. */
-#define VERTEXPERBLOCK 4092 /* Number of vertices allocated at once. */
-#define VIRUSPERBLOCK 1020 /* Number of virus triangles allocated at once. */
-/* Number of encroached subsegments allocated at once. */
-#define BADSUBSEGPERBLOCK 252
-/* Number of skinny triangles allocated at once. */
-#define BADTRIPERBLOCK 4092
-/* Number of flipped triangles allocated at once. */
-#define FLIPSTACKERPERBLOCK 252
-/* Number of splay tree nodes allocated at once. */
-#define SPLAYNODEPERBLOCK 508
-
-/* The vertex types. A DEADVERTEX has been deleted entirely. An */
-/* UNDEADVERTEX is not part of the mesh, but is written to the output */
-/* .node file and affects the node indexing in the other output files. */
-
-#define INPUTVERTEX 0
-#define SEGMENTVERTEX 1
-#define FREEVERTEX 2
-#define DEADVERTEX -32768
-#define UNDEADVERTEX -32767
-
-/* The next line is used to outsmart some very stupid compilers. If your */
-/* compiler is smarter, feel free to replace the "int" with "void". */
-/* Not that it matters. */
-
-#define VOID int
-
-/* Two constants for algorithms based on random sampling. Both constants */
-/* have been chosen empirically to optimize their respective algorithms. */
-
-/* Used for the point location scheme of Mucke, Saias, and Zhu, to decide */
-/* how large a random sample of triangles to inspect. */
-
-#define SAMPLEFACTOR 11
-
-/* Used in Fortune's sweepline Delaunay algorithm to determine what fraction */
-/* of boundary edges should be maintained in the splay tree for point */
-/* location on the front. */
-
-#define SAMPLERATE 10
-
-/* A number that speaks for itself, every kissable digit. */
-
-#define PI 3.141592653589793238462643383279502884197169399375105820974944592308
-
-/* Another fave. */
-
-#define SQUAREROOTTWO 1.4142135623730950488016887242096980785696718753769480732
-
-/* And here's one for those of you who are intimidated by math. */
-
-#define ONETHIRD 0.333333333333333333333333333333333333333333333333333333333333
-
-#include <stdio.h>
-#include <stdlib.h>
-#include <string.h>
-#include <math.h>
-#ifndef NO_TIMER
-#include <sys/time.h>
-#endif /* not NO_TIMER */
-#ifdef CPU86
-#include <float.h>
-#endif /* CPU86 */
-#ifdef LINUX
-#include <fpu_control.h>
-#endif /* LINUX */
-#ifdef TRILIBRARY
-#include "triangle.h"
-#endif /* TRILIBRARY */
-
-/* A few forward declarations. */
-
-#ifndef TRILIBRARY
-char *readline();
-char *findfield();
-#endif /* not TRILIBRARY */
-
-/* Labels that signify the result of point location. The result of a */
-/* search indicates that the point falls in the interior of a triangle, on */
-/* an edge, on a vertex, or outside the mesh. */
-
-enum locateresult {INTRIANGLE, ONEDGE, ONVERTEX, OUTSIDE};
-
-/* Labels that signify the result of vertex insertion. The result indicates */
-/* that the vertex was inserted with complete success, was inserted but */
-/* encroaches upon a subsegment, was not inserted because it lies on a */
-/* segment, or was not inserted because another vertex occupies the same */
-/* location. */
-
-enum insertvertexresult {SUCCESSFULVERTEX, ENCROACHINGVERTEX, VIOLATINGVERTEX,
- DUPLICATEVERTEX};
-
-/* Labels that signify the result of direction finding. The result */
-/* indicates that a segment connecting the two query points falls within */
-/* the direction triangle, along the left edge of the direction triangle, */
-/* or along the right edge of the direction triangle. */
-
-enum finddirectionresult {WITHIN, LEFTCOLLINEAR, RIGHTCOLLINEAR};
-
-/*****************************************************************************/
-/* */
-/* The basic mesh data structures */
-/* */
-/* There are three: vertices, triangles, and subsegments (abbreviated */
-/* `subseg'). These three data structures, linked by pointers, comprise */
-/* the mesh. A vertex simply represents a mesh vertex and its properties. */
-/* A triangle is a triangle. A subsegment is a special data structure used */
-/* to represent an impenetrable edge of the mesh (perhaps on the outer */
-/* boundary, on the boundary of a hole, or part of an internal boundary */
-/* separating two triangulated regions). Subsegments represent boundaries, */
-/* defined by the user, that triangles may not lie across. */
-/* */
-/* A triangle consists of a list of three vertices, a list of three */
-/* adjoining triangles, a list of three adjoining subsegments (when */
-/* segments exist), an arbitrary number of optional user-defined */
-/* floating-point attributes, and an optional area constraint. The latter */
-/* is an upper bound on the permissible area of each triangle in a region, */
-/* used for mesh refinement. */
-/* */
-/* For a triangle on a boundary of the mesh, some or all of the neighboring */
-/* triangles may not be present. For a triangle in the interior of the */
-/* mesh, often no neighboring subsegments are present. Such absent */
-/* triangles and subsegments are never represented by NULL pointers; they */
-/* are represented by two special records: `dummytri', the triangle that */
-/* fills "outer space", and `dummysub', the omnipresent subsegment. */
-/* `dummytri' and `dummysub' are used for several reasons; for instance, */
-/* they can be dereferenced and their contents examined without violating */
-/* protected memory. */
-/* */
-/* However, it is important to understand that a triangle includes other */
-/* information as well. The pointers to adjoining vertices, triangles, and */
-/* subsegments are ordered in a way that indicates their geometric relation */
-/* to each other. Furthermore, each of these pointers contains orientation */
-/* information. Each pointer to an adjoining triangle indicates which face */
-/* of that triangle is contacted. Similarly, each pointer to an adjoining */
-/* subsegment indicates which side of that subsegment is contacted, and how */
-/* the subsegment is oriented relative to the triangle. */
-/* */
-/* The data structure representing a subsegment may be thought to be */
-/* abutting the edge of one or two triangle data structures: either */
-/* sandwiched between two triangles, or resting against one triangle on an */
-/* exterior boundary or hole boundary. */
-/* */
-/* A subsegment consists of a list of four vertices--the vertices of the */
-/* subsegment, and the vertices of the segment it is a part of--a list of */
-/* two adjoining subsegments, and a list of two adjoining triangles. One */
-/* of the two adjoining triangles may not be present (though there should */
-/* always be one), and neighboring subsegments might not be present. */
-/* Subsegments also store a user-defined integer "boundary marker". */
-/* Typically, this integer is used to indicate what boundary conditions are */
-/* to be applied at that location in a finite element simulation. */
-/* */
-/* Like triangles, subsegments maintain information about the relative */
-/* orientation of neighboring objects. */
-/* */
-/* Vertices are relatively simple. A vertex is a list of floating-point */
-/* numbers, starting with the x, and y coordinates, followed by an */
-/* arbitrary number of optional user-defined floating-point attributes, */
-/* followed by an integer boundary marker. During the segment insertion */
-/* phase, there is also a pointer from each vertex to a triangle that may */
-/* contain it. Each pointer is not always correct, but when one is, it */
-/* speeds up segment insertion. These pointers are assigned values once */
-/* at the beginning of the segment insertion phase, and are not used or */
-/* updated except during this phase. Edge flipping during segment */
-/* insertion will render some of them incorrect. Hence, don't rely upon */
-/* them for anything. */
-/* */
-/* Other than the exception mentioned above, vertices have no information */
-/* about what triangles, subfacets, or subsegments they are linked to. */
-/* */
-/*****************************************************************************/
-
-/*****************************************************************************/
-/* */
-/* Handles */
-/* */
-/* The oriented triangle (`otri') and oriented subsegment (`osub') data */
-/* structures defined below do not themselves store any part of the mesh. */
-/* The mesh itself is made of `triangle's, `subseg's, and `vertex's. */
-/* */
-/* Oriented triangles and oriented subsegments will usually be referred to */
-/* as "handles." A handle is essentially a pointer into the mesh; it */
-/* allows you to "hold" one particular part of the mesh. Handles are used */
-/* to specify the regions in which one is traversing and modifying the mesh.*/
-/* A single `triangle' may be held by many handles, or none at all. (The */
-/* latter case is not a memory leak, because the triangle is still */
-/* connected to other triangles in the mesh.) */
-/* */
-/* An `otri' is a handle that holds a triangle. It holds a specific edge */
-/* of the triangle. An `osub' is a handle that holds a subsegment. It */
-/* holds either the left or right side of the subsegment. */
-/* */
-/* Navigation about the mesh is accomplished through a set of mesh */
-/* manipulation primitives, further below. Many of these primitives take */
-/* a handle and produce a new handle that holds the mesh near the first */
-/* handle. Other primitives take two handles and glue the corresponding */
-/* parts of the mesh together. The orientation of the handles is */
-/* important. For instance, when two triangles are glued together by the */
-/* bond() primitive, they are glued at the edges on which the handles lie. */
-/* */
-/* Because vertices have no information about which triangles they are */
-/* attached to, I commonly represent a vertex by use of a handle whose */
-/* origin is the vertex. A single handle can simultaneously represent a */
-/* triangle, an edge, and a vertex. */
-/* */
-/*****************************************************************************/
-
-/* The triangle data structure. Each triangle contains three pointers to */
-/* adjoining triangles, plus three pointers to vertices, plus three */
-/* pointers to subsegments (declared below; these pointers are usually */
-/* `dummysub'). It may or may not also contain user-defined attributes */
-/* and/or a floating-point "area constraint." It may also contain extra */
-/* pointers for nodes, when the user asks for high-order elements. */
-/* Because the size and structure of a `triangle' is not decided until */
-/* runtime, I haven't simply declared the type `triangle' as a struct. */
-
-typedef REAL **triangle; /* Really: typedef triangle *triangle */
-
-/* An oriented triangle: includes a pointer to a triangle and orientation. */
-/* The orientation denotes an edge of the triangle. Hence, there are */
-/* three possible orientations. By convention, each edge always points */
-/* counterclockwise about the corresponding triangle. */
-
-struct otri {
- triangle *tri;
- int orient; /* Ranges from 0 to 2. */
-};
-
-/* The subsegment data structure. Each subsegment contains two pointers to */
-/* adjoining subsegments, plus four pointers to vertices, plus two */
-/* pointers to adjoining triangles, plus one boundary marker, plus one */
-/* segment number. */
-
-typedef REAL **subseg; /* Really: typedef subseg *subseg */
-
-/* An oriented subsegment: includes a pointer to a subsegment and an */
-/* orientation. The orientation denotes a side of the edge. Hence, there */
-/* are two possible orientations. By convention, the edge is always */
-/* directed so that the "side" denoted is the right side of the edge. */
-
-struct osub {
- subseg *ss;
- int ssorient; /* Ranges from 0 to 1. */
-};
-
-/* The vertex data structure. Each vertex is actually an array of REALs. */
-/* The number of REALs is unknown until runtime. An integer boundary */
-/* marker, and sometimes a pointer to a triangle, is appended after the */
-/* REALs. */
-
-typedef REAL *vertex;
-
-/* A queue used to store encroached subsegments. Each subsegment's vertices */
-/* are stored so that we can check whether a subsegment is still the same. */
-
-struct badsubseg {
- subseg encsubseg; /* An encroached subsegment. */
- vertex subsegorg, subsegdest; /* Its two vertices. */
-};
-
-/* A queue used to store bad triangles. The key is the square of the cosine */
-/* of the smallest angle of the triangle. Each triangle's vertices are */
-/* stored so that one can check whether a triangle is still the same. */
-
-struct badtriang {
- triangle poortri; /* A skinny or too-large triangle. */
- REAL key; /* cos^2 of smallest (apical) angle. */
- vertex triangorg, triangdest, triangapex; /* Its three vertices. */
- struct badtriang *nexttriang; /* Pointer to next bad triangle. */
-};
-
-/* A stack of triangles flipped during the most recent vertex insertion. */
-/* The stack is used to undo the vertex insertion if the vertex encroaches */
-/* upon a subsegment. */
-
-struct flipstacker {
- triangle flippedtri; /* A recently flipped triangle. */
- struct flipstacker *prevflip; /* Previous flip in the stack. */
-};
-
-/* A node in a heap used to store events for the sweepline Delaunay */
-/* algorithm. Nodes do not point directly to their parents or children in */
-/* the heap. Instead, each node knows its position in the heap, and can */
-/* look up its parent and children in a separate array. The `eventptr' */
-/* points either to a `vertex' or to a triangle (in encoded format, so */
-/* that an orientation is included). In the latter case, the origin of */
-/* the oriented triangle is the apex of a "circle event" of the sweepline */
-/* algorithm. To distinguish site events from circle events, all circle */
-/* events are given an invalid (smaller than `xmin') x-coordinate `xkey'. */
-
-struct event {
- REAL xkey, ykey; /* Coordinates of the event. */
- VOID *eventptr; /* Can be a vertex or the location of a circle event. */
- int heapposition; /* Marks this event's position in the heap. */
-};
-
-/* A node in the splay tree. Each node holds an oriented ghost triangle */
-/* that represents a boundary edge of the growing triangulation. When a */
-/* circle event covers two boundary edges with a triangle, so that they */
-/* are no longer boundary edges, those edges are not immediately deleted */
-/* from the tree; rather, they are lazily deleted when they are next */
-/* encountered. (Since only a random sample of boundary edges are kept */
-/* in the tree, lazy deletion is faster.) `keydest' is used to verify */
-/* that a triangle is still the same as when it entered the splay tree; if */
-/* it has been rotated (due to a circle event), it no longer represents a */
-/* boundary edge and should be deleted. */
-
-struct splaynode {
- struct otri keyedge; /* Lprev of an edge on the front. */
- vertex keydest; /* Used to verify that splay node is still live. */
- struct splaynode *lchild, *rchild; /* Children in splay tree. */
-};
-
-/* A type used to allocate memory. firstblock is the first block of items. */
-/* nowblock is the block from which items are currently being allocated. */
-/* nextitem points to the next slab of free memory for an item. */
-/* deaditemstack is the head of a linked list (stack) of deallocated items */
-/* that can be recycled. unallocateditems is the number of items that */
-/* remain to be allocated from nowblock. */
-/* */
-/* Traversal is the process of walking through the entire list of items, and */
-/* is separate from allocation. Note that a traversal will visit items on */
-/* the "deaditemstack" stack as well as live items. pathblock points to */
-/* the block currently being traversed. pathitem points to the next item */
-/* to be traversed. pathitemsleft is the number of items that remain to */
-/* be traversed in pathblock. */
-/* */
-/* alignbytes determines how new records should be aligned in memory. */
-/* itembytes is the length of a record in bytes (after rounding up). */
-/* itemsperblock is the number of items allocated at once in a single */
-/* block. itemsfirstblock is the number of items in the first block, */
-/* which can vary from the others. items is the number of currently */
-/* allocated items. maxitems is the maximum number of items that have */
-/* been allocated at once; it is the current number of items plus the */
-/* number of records kept on deaditemstack. */
-
-struct memorypool {
- VOID **firstblock, **nowblock;
- VOID *nextitem;
- VOID *deaditemstack;
- VOID **pathblock;
- VOID *pathitem;
- int alignbytes;
- int itembytes;
- int itemsperblock;
- int itemsfirstblock;
- long items, maxitems;
- int unallocateditems;
- int pathitemsleft;
-};
-
-
-/* Global constants. */
-
-REAL splitter; /* Used to split REAL factors for exact multiplication. */
-REAL epsilon; /* Floating-point machine epsilon. */
-REAL resulterrbound;
-REAL ccwerrboundA, ccwerrboundB, ccwerrboundC;
-REAL iccerrboundA, iccerrboundB, iccerrboundC;
-REAL o3derrboundA, o3derrboundB, o3derrboundC;
-
-/* Random number seed is not constant, but I've made it global anyway. */
-
-unsigned long randomseed; /* Current random number seed. */
-
-
-/* Mesh data structure. Triangle operates on only one mesh, but the mesh */
-/* structure is used (instead of global variables) to allow reentrancy. */
-
-struct mesh {
-
-/* Variables used to allocate memory for triangles, subsegments, vertices, */
-/* viri (triangles being eaten), encroached segments, bad (skinny or too */
-/* large) triangles, and splay tree nodes. */
-
- struct memorypool triangles;
- struct memorypool subsegs;
- struct memorypool vertices;
- struct memorypool viri;
- struct memorypool badsubsegs;
- struct memorypool badtriangles;
- struct memorypool flipstackers;
- struct memorypool splaynodes;
-
-/* Variables that maintain the bad triangle queues. The queues are */
-/* ordered from 4095 (highest priority) to 0 (lowest priority). */
-
- struct badtriang *queuefront[4096];
- struct badtriang *queuetail[4096];
- int nextnonemptyq[4096];
- int firstnonemptyq;
-
-/* Variable that maintains the stack of recently flipped triangles. */
-
- struct flipstacker *lastflip;
-
-/* Other variables. */
-
- REAL xmin, xmax, ymin, ymax; /* x and y bounds. */
- REAL xminextreme; /* Nonexistent x value used as a flag in sweepline. */
- int invertices; /* Number of input vertices. */
- int inelements; /* Number of input triangles. */
- int insegments; /* Number of input segments. */
- int holes; /* Number of input holes. */
- int regions; /* Number of input regions. */
- int undeads; /* Number of input vertices that don't appear in the mesh. */
- long edges; /* Number of output edges. */
- int mesh_dim; /* Dimension (ought to be 2). */
- int nextras; /* Number of attributes per vertex. */
- int eextras; /* Number of attributes per triangle. */
- long hullsize; /* Number of edges in convex hull. */
- int steinerleft; /* Number of Steiner points not yet used. */
- int vertexmarkindex; /* Index to find boundary marker of a vertex. */
- int vertex2triindex; /* Index to find a triangle adjacent to a vertex. */
- int highorderindex; /* Index to find extra nodes for high-order elements. */
- int elemattribindex; /* Index to find attributes of a triangle. */
- int areaboundindex; /* Index to find area bound of a triangle. */
- int checksegments; /* Are there segments in the triangulation yet? */
- int checkquality; /* Has quality triangulation begun yet? */
- int readnodefile; /* Has a .node file been read? */
- long samples; /* Number of random samples for point location. */
-
- long incirclecount; /* Number of incircle tests performed. */
- long counterclockcount; /* Number of counterclockwise tests performed. */
- long orient3dcount; /* Number of 3D orientation tests performed. */
- long hyperbolacount; /* Number of right-of-hyperbola tests performed. */
- long circumcentercount; /* Number of circumcenter calculations performed. */
- long circletopcount; /* Number of circle top calculations performed. */
-
-/* Triangular bounding box vertices. */
-
- vertex infvertex1, infvertex2, infvertex3;
-
-/* Pointer to the `triangle' that occupies all of "outer space." */
-
- triangle *dummytri;
- triangle *dummytribase; /* Keep base address so we can free() it later. */
-
-/* Pointer to the omnipresent subsegment. Referenced by any triangle or */
-/* subsegment that isn't really connected to a subsegment at that */
-/* location. */
-
- subseg *dummysub;
- subseg *dummysubbase; /* Keep base address so we can free() it later. */
-
-/* Pointer to a recently visited triangle. Improves point location if */
-/* proximate vertices are inserted sequentially. */
-
- struct otri recenttri;
-
-}; /* End of `struct mesh'. */
-
-
-/* Data structure for command line switches and file names. This structure */
-/* is used (instead of global variables) to allow reentrancy. */
-
-struct behavior {
-
-/* Switches for the triangulator. */
-/* poly: -p switch. refine: -r switch. */
-/* quality: -q switch. */
-/* minangle: minimum angle bound, specified after -q switch. */
-/* goodangle: cosine squared of minangle. */
-/* offconstant: constant used to place off-center Steiner points. */
-/* vararea: -a switch without number. */
-/* fixedarea: -a switch with number. */
-/* maxarea: maximum area bound, specified after -a switch. */
-/* usertest: -u switch. */
-/* regionattrib: -A switch. convex: -c switch. */
-/* weighted: 1 for -w switch, 2 for -W switch. jettison: -j switch */
-/* firstnumber: inverse of -z switch. All items are numbered starting */
-/* from `firstnumber'. */
-/* edgesout: -e switch. voronoi: -v switch. */
-/* neighbors: -n switch. geomview: -g switch. */
-/* nobound: -B switch. nopolywritten: -P switch. */
-/* nonodewritten: -N switch. noelewritten: -E switch. */
-/* noiterationnum: -I switch. noholes: -O switch. */
-/* noexact: -X switch. */
-/* order: element order, specified after -o switch. */
-/* nobisect: count of how often -Y switch is selected. */
-/* steiner: maximum number of Steiner points, specified after -S switch. */
-/* incremental: -i switch. sweepline: -F switch. */
-/* dwyer: inverse of -l switch. */
-/* splitseg: -s switch. */
-/* conformdel: -D switch. docheck: -C switch. */
-/* quiet: -Q switch. verbose: count of how often -V switch is selected. */
-/* usesegments: -p, -r, -q, or -c switch; determines whether segments are */
-/* used at all. */
-/* */
-/* Read the instructions to find out the meaning of these switches. */
-
- int poly, refine, quality, vararea, fixedarea, usertest;
- int regionattrib, convex, weighted, jettison;
- int firstnumber;
- int edgesout, voronoi, neighbors, geomview;
- int nobound, nopolywritten, nonodewritten, noelewritten, noiterationnum;
- int noholes, noexact, conformdel;
- int incremental, sweepline, dwyer;
- int splitseg;
- int docheck;
- int quiet, verbose;
- int usesegments;
- int order;
- int nobisect;
- int steiner;
- REAL minangle, goodangle, offconstant;
- REAL maxarea;
-
-/* Variables for file names. */
-
-#ifndef TRILIBRARY
- char innodefilename[FILENAMESIZE];
- char inelefilename[FILENAMESIZE];
- char inpolyfilename[FILENAMESIZE];
- char areafilename[FILENAMESIZE];
- char outnodefilename[FILENAMESIZE];
- char outelefilename[FILENAMESIZE];
- char outpolyfilename[FILENAMESIZE];
- char edgefilename[FILENAMESIZE];
- char vnodefilename[FILENAMESIZE];
- char vedgefilename[FILENAMESIZE];
- char neighborfilename[FILENAMESIZE];
- char offfilename[FILENAMESIZE];
-#endif /* not TRILIBRARY */
-
-}; /* End of `struct behavior'. */
-
-
-/*****************************************************************************/
-/* */
-/* Mesh manipulation primitives. Each triangle contains three pointers to */
-/* other triangles, with orientations. Each pointer points not to the */
-/* first byte of a triangle, but to one of the first three bytes of a */
-/* triangle. It is necessary to extract both the triangle itself and the */
-/* orientation. To save memory, I keep both pieces of information in one */
-/* pointer. To make this possible, I assume that all triangles are aligned */
-/* to four-byte boundaries. The decode() routine below decodes a pointer, */
-/* extracting an orientation (in the range 0 to 2) and a pointer to the */
-/* beginning of a triangle. The encode() routine compresses a pointer to a */
-/* triangle and an orientation into a single pointer. My assumptions that */
-/* triangles are four-byte-aligned and that the `unsigned long' type is */
-/* long enough to hold a pointer are two of the few kludges in this program.*/
-/* */
-/* Subsegments are manipulated similarly. A pointer to a subsegment */
-/* carries both an address and an orientation in the range 0 to 1. */
-/* */
-/* The other primitives take an oriented triangle or oriented subsegment, */
-/* and return an oriented triangle or oriented subsegment or vertex; or */
-/* they change the connections in the data structure. */
-/* */
-/* Below, triangles and subsegments are denoted by their vertices. The */
-/* triangle abc has origin (org) a, destination (dest) b, and apex (apex) */
-/* c. These vertices occur in counterclockwise order about the triangle. */
-/* The handle abc may simultaneously denote vertex a, edge ab, and triangle */
-/* abc. */
-/* */
-/* Similarly, the subsegment ab has origin (sorg) a and destination (sdest) */
-/* b. If ab is thought to be directed upward (with b directly above a), */
-/* then the handle ab is thought to grasp the right side of ab, and may */
-/* simultaneously denote vertex a and edge ab. */
-/* */
-/* An asterisk (*) denotes a vertex whose identity is unknown. */
-/* */
-/* Given this notation, a partial list of mesh manipulation primitives */
-/* follows. */
-/* */
-/* */
-/* For triangles: */
-/* */
-/* sym: Find the abutting triangle; same edge. */
-/* sym(abc) -> ba* */
-/* */
-/* lnext: Find the next edge (counterclockwise) of a triangle. */
-/* lnext(abc) -> bca */
-/* */
-/* lprev: Find the previous edge (clockwise) of a triangle. */
-/* lprev(abc) -> cab */
-/* */
-/* onext: Find the next edge counterclockwise with the same origin. */
-/* onext(abc) -> ac* */
-/* */
-/* oprev: Find the next edge clockwise with the same origin. */
-/* oprev(abc) -> a*b */
-/* */
-/* dnext: Find the next edge counterclockwise with the same destination. */
-/* dnext(abc) -> *ba */
-/* */
-/* dprev: Find the next edge clockwise with the same destination. */
-/* dprev(abc) -> cb* */
-/* */
-/* rnext: Find the next edge (counterclockwise) of the adjacent triangle. */
-/* rnext(abc) -> *a* */
-/* */
-/* rprev: Find the previous edge (clockwise) of the adjacent triangle. */
-/* rprev(abc) -> b** */
-/* */
-/* org: Origin dest: Destination apex: Apex */
-/* org(abc) -> a dest(abc) -> b apex(abc) -> c */
-/* */
-/* bond: Bond two triangles together at the resepective handles. */
-/* bond(abc, bad) */
-/* */
-/* */
-/* For subsegments: */
-/* */
-/* ssym: Reverse the orientation of a subsegment. */
-/* ssym(ab) -> ba */
-/* */
-/* spivot: Find adjoining subsegment with the same origin. */
-/* spivot(ab) -> a* */
-/* */
-/* snext: Find next subsegment in sequence. */
-/* snext(ab) -> b* */
-/* */
-/* sorg: Origin sdest: Destination */
-/* sorg(ab) -> a sdest(ab) -> b */
-/* */
-/* sbond: Bond two subsegments together at the respective origins. */
-/* sbond(ab, ac) */
-/* */
-/* */
-/* For interacting tetrahedra and subfacets: */
-/* */
-/* tspivot: Find a subsegment abutting a triangle. */
-/* tspivot(abc) -> ba */
-/* */
-/* stpivot: Find a triangle abutting a subsegment. */
-/* stpivot(ab) -> ba* */
-/* */
-/* tsbond: Bond a triangle to a subsegment. */
-/* tsbond(abc, ba) */
-/* */
-/*****************************************************************************/
-
-/********* Mesh manipulation primitives begin here *********/
-/** **/
-/** **/
-
-/* Fast lookup arrays to speed some of the mesh manipulation primitives. */
-
-int plus1mod3[3] = {1, 2, 0};
-int minus1mod3[3] = {2, 0, 1};
-
-/********* Primitives for triangles *********/
-/* */
-/* */
-
-/* decode() converts a pointer to an oriented triangle. The orientation is */
-/* extracted from the two least significant bits of the pointer. */
-
-#define decode(ptr, otri) \
- (otri).orient = (int) ((unsigned long) (ptr) & (unsigned long) 3l); \
- (otri).tri = (triangle *) \
- ((unsigned long) (ptr) ^ (unsigned long) (otri).orient)
-
-/* encode() compresses an oriented triangle into a single pointer. It */
-/* relies on the assumption that all triangles are aligned to four-byte */
-/* boundaries, so the two least significant bits of (otri).tri are zero. */
-
-#define encode(otri) \
- (triangle) ((unsigned long) (otri).tri | (unsigned long) (otri).orient)
-
-/* The following handle manipulation primitives are all described by Guibas */
-/* and Stolfi. However, Guibas and Stolfi use an edge-based data */
-/* structure, whereas I use a triangle-based data structure. */
-
-/* sym() finds the abutting triangle, on the same edge. Note that the edge */
-/* direction is necessarily reversed, because the handle specified by an */
-/* oriented triangle is directed counterclockwise around the triangle. */
-
-#define sym(otri1, otri2) \
- ptr = (otri1).tri[(otri1).orient]; \
- decode(ptr, otri2);
-
-#define symself(otri) \
- ptr = (otri).tri[(otri).orient]; \
- decode(ptr, otri);
-
-/* lnext() finds the next edge (counterclockwise) of a triangle. */
-
-#define lnext(otri1, otri2) \
- (otri2).tri = (otri1).tri; \
- (otri2).orient = plus1mod3[(otri1).orient]
-
-#define lnextself(otri) \
- (otri).orient = plus1mod3[(otri).orient]
-
-/* lprev() finds the previous edge (clockwise) of a triangle. */
-
-#define lprev(otri1, otri2) \
- (otri2).tri = (otri1).tri; \
- (otri2).orient = minus1mod3[(otri1).orient]
-
-#define lprevself(otri) \
- (otri).orient = minus1mod3[(otri).orient]
-
-/* onext() spins counterclockwise around a vertex; that is, it finds the */
-/* next edge with the same origin in the counterclockwise direction. This */
-/* edge is part of a different triangle. */
-
-#define onext(otri1, otri2) \
- lprev(otri1, otri2); \
- symself(otri2);
-
-#define onextself(otri) \
- lprevself(otri); \
- symself(otri);
-
-/* oprev() spins clockwise around a vertex; that is, it finds the next edge */
-/* with the same origin in the clockwise direction. This edge is part of */
-/* a different triangle. */
-
-#define oprev(otri1, otri2) \
- sym(otri1, otri2); \
- lnextself(otri2);
-
-#define oprevself(otri) \
- symself(otri); \
- lnextself(otri);
-
-/* dnext() spins counterclockwise around a vertex; that is, it finds the */
-/* next edge with the same destination in the counterclockwise direction. */
-/* This edge is part of a different triangle. */
-
-#define dnext(otri1, otri2) \
- sym(otri1, otri2); \
- lprevself(otri2);
-
-#define dnextself(otri) \
- symself(otri); \
- lprevself(otri);
-
-/* dprev() spins clockwise around a vertex; that is, it finds the next edge */
-/* with the same destination in the clockwise direction. This edge is */
-/* part of a different triangle. */
-
-#define dprev(otri1, otri2) \
- lnext(otri1, otri2); \
- symself(otri2);
-
-#define dprevself(otri) \
- lnextself(otri); \
- symself(otri);
-
-/* rnext() moves one edge counterclockwise about the adjacent triangle. */
-/* (It's best understood by reading Guibas and Stolfi. It involves */
-/* changing triangles twice.) */
-
-#define rnext(otri1, otri2) \
- sym(otri1, otri2); \
- lnextself(otri2); \
- symself(otri2);
-
-#define rnextself(otri) \
- symself(otri); \
- lnextself(otri); \
- symself(otri);
-
-/* rprev() moves one edge clockwise about the adjacent triangle. */
-/* (It's best understood by reading Guibas and Stolfi. It involves */
-/* changing triangles twice.) */
-
-#define rprev(otri1, otri2) \
- sym(otri1, otri2); \
- lprevself(otri2); \
- symself(otri2);
-
-#define rprevself(otri) \
- symself(otri); \
- lprevself(otri); \
- symself(otri);
-
-/* These primitives determine or set the origin, destination, or apex of a */
-/* triangle. */
-
-#define org(otri, vertexptr) \
- vertexptr = (vertex) (otri).tri[plus1mod3[(otri).orient] + 3]
-
-#define dest(otri, vertexptr) \
- vertexptr = (vertex) (otri).tri[minus1mod3[(otri).orient] + 3]
-
-#define apex(otri, vertexptr) \
- vertexptr = (vertex) (otri).tri[(otri).orient + 3]
-
-#define setorg(otri, vertexptr) \
- (otri).tri[plus1mod3[(otri).orient] + 3] = (triangle) vertexptr
-
-#define setdest(otri, vertexptr) \
- (otri).tri[minus1mod3[(otri).orient] + 3] = (triangle) vertexptr
-
-#define setapex(otri, vertexptr) \
- (otri).tri[(otri).orient + 3] = (triangle) vertexptr
-
-/* Bond two triangles together. */
-
-#define bond(otri1, otri2) \
- (otri1).tri[(otri1).orient] = encode(otri2); \
- (otri2).tri[(otri2).orient] = encode(otri1)
-
-/* Dissolve a bond (from one side). Note that the other triangle will still */
-/* think it's connected to this triangle. Usually, however, the other */
-/* triangle is being deleted entirely, or bonded to another triangle, so */
-/* it doesn't matter. */
-
-#define dissolve(otri) \
- (otri).tri[(otri).orient] = (triangle) m->dummytri
-
-/* Copy an oriented triangle. */
-
-#define otricopy(otri1, otri2) \
- (otri2).tri = (otri1).tri; \
- (otri2).orient = (otri1).orient
-
-/* Test for equality of oriented triangles. */
-
-#define otriequal(otri1, otri2) \
- (((otri1).tri == (otri2).tri) && \
- ((otri1).orient == (otri2).orient))
-
-/* Primitives to infect or cure a triangle with the virus. These rely on */
-/* the assumption that all subsegments are aligned to four-byte boundaries.*/
-
-#define infect(otri) \
- (otri).tri[6] = (triangle) \
- ((unsigned long) (otri).tri[6] | (unsigned long) 2l)
-
-#define uninfect(otri) \
- (otri).tri[6] = (triangle) \
- ((unsigned long) (otri).tri[6] & ~ (unsigned long) 2l)
-
-/* Test a triangle for viral infection. */
-
-#define infected(otri) \
- (((unsigned long) (otri).tri[6] & (unsigned long) 2l) != 0l)
-
-/* Check or set a triangle's attributes. */
-
-#define elemattribute(otri, attnum) \
- ((REAL *) (otri).tri)[m->elemattribindex + (attnum)]
-
-#define setelemattribute(otri, attnum, value) \
- ((REAL *) (otri).tri)[m->elemattribindex + (attnum)] = value
-
-/* Check or set a triangle's maximum area bound. */
-
-#define areabound(otri) ((REAL *) (otri).tri)[m->areaboundindex]
-
-#define setareabound(otri, value) \
- ((REAL *) (otri).tri)[m->areaboundindex] = value
-
-/* Check or set a triangle's deallocation. Its second pointer is set to */
-/* NULL to indicate that it is not allocated. (Its first pointer is used */
-/* for the stack of dead items.) Its fourth pointer (its first vertex) */
-/* is set to NULL in case a `badtriang' structure points to it. */
-
-#define deadtri(tria) ((tria)[1] == (triangle) NULL)
-
-#define killtri(tria) \
- (tria)[1] = (triangle) NULL; \
- (tria)[3] = (triangle) NULL
-
-/********* Primitives for subsegments *********/
-/* */
-/* */
-
-/* sdecode() converts a pointer to an oriented subsegment. The orientation */
-/* is extracted from the least significant bit of the pointer. The two */
-/* least significant bits (one for orientation, one for viral infection) */
-/* are masked out to produce the real pointer. */
-
-#define sdecode(sptr, osub) \
- (osub).ssorient = (int) ((unsigned long) (sptr) & (unsigned long) 1l); \
- (osub).ss = (subseg *) \
- ((unsigned long) (sptr) & ~ (unsigned long) 3l)
-
-/* sencode() compresses an oriented subsegment into a single pointer. It */
-/* relies on the assumption that all subsegments are aligned to two-byte */
-/* boundaries, so the least significant bit of (osub).ss is zero. */
-
-#define sencode(osub) \
- (subseg) ((unsigned long) (osub).ss | (unsigned long) (osub).ssorient)
-
-/* ssym() toggles the orientation of a subsegment. */
-
-#define ssym(osub1, osub2) \
- (osub2).ss = (osub1).ss; \
- (osub2).ssorient = 1 - (osub1).ssorient
-
-#define ssymself(osub) \
- (osub).ssorient = 1 - (osub).ssorient
-
-/* spivot() finds the other subsegment (from the same segment) that shares */
-/* the same origin. */
-
-#define spivot(osub1, osub2) \
- sptr = (osub1).ss[(osub1).ssorient]; \
- sdecode(sptr, osub2)
-
-#define spivotself(osub) \
- sptr = (osub).ss[(osub).ssorient]; \
- sdecode(sptr, osub)
-
-/* snext() finds the next subsegment (from the same segment) in sequence; */
-/* one whose origin is the input subsegment's destination. */
-
-#define snext(osub1, osub2) \
- sptr = (osub1).ss[1 - (osub1).ssorient]; \
- sdecode(sptr, osub2)
-
-#define snextself(osub) \
- sptr = (osub).ss[1 - (osub).ssorient]; \
- sdecode(sptr, osub)
-
-/* These primitives determine or set the origin or destination of a */
-/* subsegment or the segment that includes it. */
-
-#define sorg(osub, vertexptr) \
- vertexptr = (vertex) (osub).ss[2 + (osub).ssorient]
-
-#define sdest(osub, vertexptr) \
- vertexptr = (vertex) (osub).ss[3 - (osub).ssorient]
-
-#define setsorg(osub, vertexptr) \
- (osub).ss[2 + (osub).ssorient] = (subseg) vertexptr
-
-#define setsdest(osub, vertexptr) \
- (osub).ss[3 - (osub).ssorient] = (subseg) vertexptr
-
-#define segorg(osub, vertexptr) \
- vertexptr = (vertex) (osub).ss[4 + (osub).ssorient]
-
-#define segdest(osub, vertexptr) \
- vertexptr = (vertex) (osub).ss[5 - (osub).ssorient]
-
-#define setsegorg(osub, vertexptr) \
- (osub).ss[4 + (osub).ssorient] = (subseg) vertexptr
-
-#define setsegdest(osub, vertexptr) \
- (osub).ss[5 - (osub).ssorient] = (subseg) vertexptr
-
-/* These primitives read or set a boundary marker. Boundary markers are */
-/* used to hold user-defined tags for setting boundary conditions in */
-/* finite element solvers. */
-
-#define mark(osub) (* (int *) ((osub).ss + 8))
-
-#define setmark(osub, value) \
- * (int *) ((osub).ss + 8) = value
-
-/* Bond two subsegments together. */
-
-#define sbond(osub1, osub2) \
- (osub1).ss[(osub1).ssorient] = sencode(osub2); \
- (osub2).ss[(osub2).ssorient] = sencode(osub1)
-
-/* Dissolve a subsegment bond (from one side). Note that the other */
-/* subsegment will still think it's connected to this subsegment. */
-
-#define sdissolve(osub) \
- (osub).ss[(osub).ssorient] = (subseg) m->dummysub
-
-/* Copy a subsegment. */
-
-#define subsegcopy(osub1, osub2) \
- (osub2).ss = (osub1).ss; \
- (osub2).ssorient = (osub1).ssorient
-
-/* Test for equality of subsegments. */
-
-#define subsegequal(osub1, osub2) \
- (((osub1).ss == (osub2).ss) && \
- ((osub1).ssorient == (osub2).ssorient))
-
-/* Check or set a subsegment's deallocation. Its second pointer is set to */
-/* NULL to indicate that it is not allocated. (Its first pointer is used */
-/* for the stack of dead items.) Its third pointer (its first vertex) */
-/* is set to NULL in case a `badsubseg' structure points to it. */
-
-#define deadsubseg(sub) ((sub)[1] == (subseg) NULL)
-
-#define killsubseg(sub) \
- (sub)[1] = (subseg) NULL; \
- (sub)[2] = (subseg) NULL
-
-/********* Primitives for interacting triangles and subsegments *********/
-/* */
-/* */
-
-/* tspivot() finds a subsegment abutting a triangle. */
-
-#define tspivot(otri, osub) \
- sptr = (subseg) (otri).tri[6 + (otri).orient]; \
- sdecode(sptr, osub)
-
-/* stpivot() finds a triangle abutting a subsegment. It requires that the */
-/* variable `ptr' of type `triangle' be defined. */
-
-#define stpivot(osub, otri) \
- ptr = (triangle) (osub).ss[6 + (osub).ssorient]; \
- decode(ptr, otri)
-
-/* Bond a triangle to a subsegment. */
-
-#define tsbond(otri, osub) \
- (otri).tri[6 + (otri).orient] = (triangle) sencode(osub); \
- (osub).ss[6 + (osub).ssorient] = (subseg) encode(otri)
-
-/* Dissolve a bond (from the triangle side). */
-
-#define tsdissolve(otri) \
- (otri).tri[6 + (otri).orient] = (triangle) m->dummysub
-
-/* Dissolve a bond (from the subsegment side). */
-
-#define stdissolve(osub) \
- (osub).ss[6 + (osub).ssorient] = (subseg) m->dummytri
-
-/********* Primitives for vertices *********/
-/* */
-/* */
-
-#define vertexmark(vx) ((int *) (vx))[m->vertexmarkindex]
-
-#define setvertexmark(vx, value) \
- ((int *) (vx))[m->vertexmarkindex] = value
-
-#define vertextype(vx) ((int *) (vx))[m->vertexmarkindex + 1]
-
-#define setvertextype(vx, value) \
- ((int *) (vx))[m->vertexmarkindex + 1] = value
-
-#define vertex2tri(vx) ((triangle *) (vx))[m->vertex2triindex]
-
-#define setvertex2tri(vx, value) \
- ((triangle *) (vx))[m->vertex2triindex] = value
-
-/** **/
-/** **/
-/********* Mesh manipulation primitives end here *********/
-
-/********* User-defined triangle evaluation routine begins here *********/
-/** **/
-/** **/
-
-/*****************************************************************************/
-/* */
-/* triunsuitable() Determine if a triangle is unsuitable, and thus must */
-/* be further refined. */
-/* */
-/* You may write your own procedure that decides whether or not a selected */
-/* triangle is too big (and needs to be refined). There are two ways to do */
-/* this. */
-/* */
-/* (1) Modify the procedure `triunsuitable' below, then recompile */
-/* Triangle. */
-/* */
-/* (2) Define the symbol EXTERNAL_TEST (either by adding the definition */
-/* to this file, or by using the appropriate compiler switch). This way, */
-/* you can compile triangle.c separately from your test. Write your own */
-/* `triunsuitable' procedure in a separate C file (using the same prototype */
-/* as below). Compile it and link the object code with triangle.o. */
-/* */
-/* This procedure returns 1 if the triangle is too large and should be */
-/* refined; 0 otherwise. */
-/* */
-/*****************************************************************************/
-
-#ifdef EXTERNAL_TEST
-
-int triunsuitable();
-
-#else /* not EXTERNAL_TEST */
-
-#ifdef ANSI_DECLARATORS
-int triunsuitable(vertex triorg, vertex tridest, vertex triapex, REAL area)
-#else /* not ANSI_DECLARATORS */
-int triunsuitable(triorg, tridest, triapex, area)
-vertex triorg; /* The triangle's origin vertex. */
-vertex tridest; /* The triangle's destination vertex. */
-vertex triapex; /* The triangle's apex vertex. */
-REAL area; /* The area of the triangle. */
-#endif /* not ANSI_DECLARATORS */
-
-{
- REAL dxoa, dxda, dxod;
- REAL dyoa, dyda, dyod;
- REAL oalen, dalen, odlen;
- REAL maxlen;
-
- dxoa = triorg[0] - triapex[0];
- dyoa = triorg[1] - triapex[1];
- dxda = tridest[0] - triapex[0];
- dyda = tridest[1] - triapex[1];
- dxod = triorg[0] - tridest[0];
- dyod = triorg[1] - tridest[1];
- /* Find the squares of the lengths of the triangle's three edges. */
- oalen = dxoa * dxoa + dyoa * dyoa;
- dalen = dxda * dxda + dyda * dyda;
- odlen = dxod * dxod + dyod * dyod;
- /* Find the square of the length of the longest edge. */
- maxlen = (dalen > oalen) ? dalen : oalen;
- maxlen = (odlen > maxlen) ? odlen : maxlen;
-
- if (maxlen > 0.05 * (triorg[0] * triorg[0] + triorg[1] * triorg[1]) + 0.02) {
- return 1;
- } else {
- return 0;
- }
-}
-
-#endif /* not EXTERNAL_TEST */
-
-/** **/
-/** **/
-/********* User-defined triangle evaluation routine ends here *********/
-
-/********* Memory allocation and program exit wrappers begin here *********/
-/** **/
-/** **/
-
-#ifdef ANSI_DECLARATORS
-void triexit(int status)
-#else /* not ANSI_DECLARATORS */
-void triexit(status)
-int status;
-#endif /* not ANSI_DECLARATORS */
-
-{
- exit(status);
-}
-
-#ifdef ANSI_DECLARATORS
-VOID *trimalloc(int size)
-#else /* not ANSI_DECLARATORS */
-VOID *trimalloc(size)
-int size;
-#endif /* not ANSI_DECLARATORS */
-
-{
- VOID *memptr;
-
- memptr = (VOID *) malloc((size_t) size);
- if (memptr == (VOID *) NULL) {
- printf("Error: Out of memory.\n");
- triexit(1);
- }
- return(memptr);
-}
-
-#ifdef ANSI_DECLARATORS
-void trifree(VOID *memptr)
-#else /* not ANSI_DECLARATORS */
-void trifree(memptr)
-VOID *memptr;
-#endif /* not ANSI_DECLARATORS */
-
-{
- free(memptr);
-}
-
-/** **/
-/** **/
-/********* Memory allocation and program exit wrappers end here *********/
-
-/********* User interaction routines begin here *********/
-/** **/
-/** **/
-
-/*****************************************************************************/
-/* */
-/* syntax() Print list of command line switches. */
-/* */
-/*****************************************************************************/
-
-#ifndef TRILIBRARY
-
-void syntax()
-{
-#ifdef CDT_ONLY
-#ifdef REDUCED
- printf("triangle [-pAcjevngBPNEIOXzo_lQVh] input_file\n");
-#else /* not REDUCED */
- printf("triangle [-pAcjevngBPNEIOXzo_iFlCQVh] input_file\n");
-#endif /* not REDUCED */
-#else /* not CDT_ONLY */
-#ifdef REDUCED
- printf("triangle [-prq__a__uAcDjevngBPNEIOXzo_YS__lQVh] input_file\n");
-#else /* not REDUCED */
- printf("triangle [-prq__a__uAcDjevngBPNEIOXzo_YS__iFlsCQVh] input_file\n");
-#endif /* not REDUCED */
-#endif /* not CDT_ONLY */
-
- printf(" -p Triangulates a Planar Straight Line Graph (.poly file).\n");
-#ifndef CDT_ONLY
- printf(" -r Refines a previously generated mesh.\n");
- printf(
- " -q Quality mesh generation. A minimum angle may be specified.\n");
- printf(" -a Applies a maximum triangle area constraint.\n");
- printf(" -u Applies a user-defined triangle constraint.\n");
-#endif /* not CDT_ONLY */
- printf(
- " -A Applies attributes to identify triangles in certain regions.\n");
- printf(" -c Encloses the convex hull with segments.\n");
-#ifndef CDT_ONLY
- printf(" -D Conforming Delaunay: all triangles are truly Delaunay.\n");
-#endif /* not CDT_ONLY */
-/*
- printf(" -w Weighted Delaunay triangulation.\n");
- printf(" -W Regular triangulation (lower hull of a height field).\n");
-*/
- printf(" -j Jettison unused vertices from output .node file.\n");
- printf(" -e Generates an edge list.\n");
- printf(" -v Generates a Voronoi diagram.\n");
- printf(" -n Generates a list of triangle neighbors.\n");
- printf(" -g Generates an .off file for Geomview.\n");
- printf(" -B Suppresses output of boundary information.\n");
- printf(" -P Suppresses output of .poly file.\n");
- printf(" -N Suppresses output of .node file.\n");
- printf(" -E Suppresses output of .ele file.\n");
- printf(" -I Suppresses mesh iteration numbers.\n");
- printf(" -O Ignores holes in .poly file.\n");
- printf(" -X Suppresses use of exact arithmetic.\n");
- printf(" -z Numbers all items starting from zero (rather than one).\n");
- printf(" -o2 Generates second-order subparametric elements.\n");
-#ifndef CDT_ONLY
- printf(" -Y Suppresses boundary segment splitting.\n");
- printf(" -S Specifies maximum number of added Steiner points.\n");
-#endif /* not CDT_ONLY */
-#ifndef REDUCED
- printf(" -i Uses incremental method, rather than divide-and-conquer.\n");
- printf(" -F Uses Fortune's sweepline algorithm, rather than d-and-c.\n");
-#endif /* not REDUCED */
- printf(" -l Uses vertical cuts only, rather than alternating cuts.\n");
-#ifndef REDUCED
-#ifndef CDT_ONLY
- printf(
- " -s Force segments into mesh by splitting (instead of using CDT).\n");
-#endif /* not CDT_ONLY */
- printf(" -C Check consistency of final mesh.\n");
-#endif /* not REDUCED */
- printf(" -Q Quiet: No terminal output except errors.\n");
- printf(" -V Verbose: Detailed information on what I'm doing.\n");
- printf(" -h Help: Detailed instructions for Triangle.\n");
- triexit(0);
-}
-
-#endif /* not TRILIBRARY */
-
-/*****************************************************************************/
-/* */
-/* info() Print out complete instructions. */
-/* */
-/*****************************************************************************/
-
-#ifndef TRILIBRARY
-
-void info()
-{
- printf("Triangle\n");
- printf(
-"A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator.\n");
- printf("Version 1.6\n\n");
- printf(
-"Copyright 1993, 1995, 1997, 1998, 2002, 2005 Jonathan Richard Shewchuk\n");
- printf("2360 Woolsey #H / Berkeley, California 94705-1927\n");
- printf("Bugs/comments to jrs at cs.berkeley.edu\n");
- printf(
-"Created as part of the Quake project (tools for earthquake simulation).\n");
- printf(
-"Supported in part by NSF Grant CMS-9318163 and an NSERC 1967 Scholarship.\n");
- printf("There is no warranty whatsoever. Use at your own risk.\n");
-#ifdef SINGLE
- printf("This executable is compiled for single precision arithmetic.\n\n\n");
-#else /* not SINGLE */
- printf("This executable is compiled for double precision arithmetic.\n\n\n");
-#endif /* not SINGLE */
- printf(
-"Triangle generates exact Delaunay triangulations, constrained Delaunay\n");
- printf(
-"triangulations, conforming Delaunay triangulations, Voronoi diagrams, and\n");
- printf(
-"high-quality triangular meshes. The latter can be generated with no small\n"
-);
- printf(
-"or large angles, and are thus suitable for finite element analysis. If no\n"
-);
- printf(
-"command line switch is specified, your .node input file is read, and the\n");
- printf(
-"Delaunay triangulation is returned in .node and .ele output files. The\n");
- printf("command syntax is:\n\n");
- printf("triangle [-prq__a__uAcDjevngBPNEIOXzo_YS__iFlsCQVh] input_file\n\n");
- printf(
-"Underscores indicate that numbers may optionally follow certain switches.\n");
- printf(
-"Do not leave any space between a switch and its numeric parameter.\n");
- printf(
-"input_file must be a file with extension .node, or extension .poly if the\n");
- printf(
-"-p switch is used. If -r is used, you must supply .node and .ele files,\n");
- printf(
-"and possibly a .poly file and an .area file as well. The formats of these\n"
-);
- printf("files are described below.\n\n");
- printf("Command Line Switches:\n\n");
- printf(
-" -p Reads a Planar Straight Line Graph (.poly file), which can specify\n"
-);
- printf(
-" vertices, segments, holes, regional attributes, and regional area\n");
- printf(
-" constraints. Generates a constrained Delaunay triangulation (CDT)\n"
-);
- printf(
-" fitting the input; or, if -s, -q, -a, or -u is used, a conforming\n");
- printf(
-" constrained Delaunay triangulation (CCDT). If you want a truly\n");
- printf(
-" Delaunay (not just constrained Delaunay) triangulation, use -D as\n");
- printf(
-" well. When -p is not used, Triangle reads a .node file by default.\n"
-);
- printf(
-" -r Refines a previously generated mesh. The mesh is read from a .node\n"
-);
- printf(
-" file and an .ele file. If -p is also used, a .poly file is read\n");
- printf(
-" and used to constrain segments in the mesh. If -a is also used\n");
- printf(
-" (with no number following), an .area file is read and used to\n");
- printf(
-" impose area constraints on the mesh. Further details on refinement\n"
-);
- printf(" appear below.\n");
- printf(
-" -q Quality mesh generation by Delaunay refinement (a hybrid of Paul\n");
- printf(
-" Chew's and Jim Ruppert's algorithms). Adds vertices to the mesh to\n"
-);
- printf(
-" ensure that all angles are between 20 and 140 degrees. An\n");
- printf(
-" alternative bound on the minimum angle, replacing 20 degrees, may\n");
- printf(
-" be specified after the `q'. The specified angle may include a\n");
- printf(
-" decimal point, but not exponential notation. Note that a bound of\n"
-);
- printf(
-" theta degrees on the smallest angle also implies a bound of\n");
- printf(
-" (180 - 2 theta) on the largest angle. If the minimum angle is 28.6\n"
-);
- printf(
-" degrees or smaller, Triangle is mathematically guaranteed to\n");
- printf(
-" terminate (assuming infinite precision arithmetic--Triangle may\n");
- printf(
-" fail to terminate if you run out of precision). In practice,\n");
- printf(
-" Triangle often succeeds for minimum angles up to 34 degrees. For\n");
- printf(
-" some meshes, however, you might need to reduce the minimum angle to\n"
-);
- printf(
-" avoid problems associated with insufficient floating-point\n");
- printf(" precision.\n");
- printf(
-" -a Imposes a maximum triangle area. If a number follows the `a', no\n");
- printf(
-" triangle is generated whose area is larger than that number. If no\n"
-);
- printf(
-" number is specified, an .area file (if -r is used) or .poly file\n");
- printf(
-" (if -r is not used) specifies a set of maximum area constraints.\n");
- printf(
-" An .area file contains a separate area constraint for each\n");
- printf(
-" triangle, and is useful for refining a finite element mesh based on\n"
-);
- printf(
-" a posteriori error estimates. A .poly file can optionally contain\n"
-);
- printf(
-" an area constraint for each segment-bounded region, thereby\n");
- printf(
-" controlling triangle densities in a first triangulation of a PSLG.\n"
-);
- printf(
-" You can impose both a fixed area constraint and a varying area\n");
- printf(
-" constraint by invoking the -a switch twice, once with and once\n");
- printf(
-" without a number following. Each area specified may include a\n");
- printf(" decimal point.\n");
- printf(
-" -u Imposes a user-defined constraint on triangle size. There are two\n"
-);
- printf(
-" ways to use this feature. One is to edit the triunsuitable()\n");
- printf(
-" procedure in triangle.c to encode any constraint you like, then\n");
- printf(
-" recompile Triangle. The other is to compile triangle.c with the\n");
- printf(
-" EXTERNAL_TEST symbol set (compiler switch -DEXTERNAL_TEST), then\n");
- printf(
-" link Triangle with a separate object file that implements\n");
- printf(
-" triunsuitable(). In either case, the -u switch causes the user-\n");
- printf(" defined test to be applied to every triangle.\n");
- printf(
-" -A Assigns an additional floating-point attribute to each triangle\n");
- printf(
-" that identifies what segment-bounded region each triangle belongs\n");
- printf(
-" to. Attributes are assigned to regions by the .poly file. If a\n");
- printf(
-" region is not explicitly marked by the .poly file, triangles in\n");
- printf(
-" that region are assigned an attribute of zero. The -A switch has\n");
- printf(
-" an effect only when the -p switch is used and the -r switch is not.\n"
-);
- printf(
-" -c Creates segments on the convex hull of the triangulation. If you\n");
- printf(
-" are triangulating a vertex set, this switch causes a .poly file to\n"
-);
- printf(
-" be written, containing all edges of the convex hull. If you are\n");
- printf(
-" triangulating a PSLG, this switch specifies that the whole convex\n");
- printf(
-" hull of the PSLG should be triangulated, regardless of what\n");
- printf(
-" segments the PSLG has. If you do not use this switch when\n");
- printf(
-" triangulating a PSLG, Triangle assumes that you have identified the\n"
-);
- printf(
-" region to be triangulated by surrounding it with segments of the\n");
- printf(
-" input PSLG. Beware: if you are not careful, this switch can cause\n"
-);
- printf(
-" the introduction of an extremely thin angle between a PSLG segment\n"
-);
- printf(
-" and a convex hull segment, which can cause overrefinement (and\n");
- printf(
-" possibly failure if Triangle runs out of precision). If you are\n");
- printf(
-" refining a mesh, the -c switch works differently: it causes a\n");
- printf(
-" .poly file to be written containing the boundary edges of the mesh\n"
-);
- printf(" (useful if no .poly file was read).\n");
- printf(
-" -D Conforming Delaunay triangulation: use this switch if you want to\n"
-);
- printf(
-" ensure that all the triangles in the mesh are Delaunay, and not\n");
- printf(
-" merely constrained Delaunay; or if you want to ensure that all the\n"
-);
- printf(
-" Voronoi vertices lie within the triangulation. (Some finite volume\n"
-);
- printf(
-" methods have this requirement.) This switch invokes Ruppert's\n");
- printf(
-" original algorithm, which splits every subsegment whose diametral\n");
- printf(
-" circle is encroached. It usually increases the number of vertices\n"
-);
- printf(" and triangles.\n");
- printf(
-" -j Jettisons vertices that are not part of the final triangulation\n");
- printf(
-" from the output .node file. By default, Triangle copies all\n");
- printf(
-" vertices in the input .node file to the output .node file, in the\n");
- printf(
-" same order, so their indices do not change. The -j switch prevents\n"
-);
- printf(
-" duplicated input vertices, or vertices `eaten' by holes, from\n");
- printf(
-" appearing in the output .node file. Thus, if two input vertices\n");
- printf(
-" have exactly the same coordinates, only the first appears in the\n");
- printf(
-" output. If any vertices are jettisoned, the vertex numbering in\n");
- printf(
-" the output .node file differs from that of the input .node file.\n");
- printf(
-" -e Outputs (to an .edge file) a list of edges of the triangulation.\n");
- printf(
-" -v Outputs the Voronoi diagram associated with the triangulation.\n");
- printf(
-" Does not attempt to detect degeneracies, so some Voronoi vertices\n");
- printf(
-" may be duplicated. See the discussion of Voronoi diagrams below.\n");
- printf(
-" -n Outputs (to a .neigh file) a list of triangles neighboring each\n");
- printf(" triangle.\n");
- printf(
-" -g Outputs the mesh to an Object File Format (.off) file, suitable for\n"
-);
- printf(" viewing with the Geometry Center's Geomview package.\n");
- printf(
-" -B No boundary markers in the output .node, .poly, and .edge output\n");
- printf(
-" files. See the detailed discussion of boundary markers below.\n");
- printf(
-" -P No output .poly file. Saves disk space, but you lose the ability\n");
- printf(
-" to maintain constraining segments on later refinements of the mesh.\n"
-);
- printf(" -N No output .node file.\n");
- printf(" -E No output .ele file.\n");
- printf(
-" -I No iteration numbers. Suppresses the output of .node and .poly\n");
- printf(
-" files, so your input files won't be overwritten. (If your input is\n"
-);
- printf(
-" a .poly file only, a .node file is written.) Cannot be used with\n");
- printf(
-" the -r switch, because that would overwrite your input .ele file.\n");
- printf(
-" Shouldn't be used with the -q, -a, -u, or -s switch if you are\n");
- printf(
-" using a .node file for input, because no .node file is written, so\n"
-);
- printf(" there is no record of any added Steiner points.\n");
- printf(" -O No holes. Ignores the holes in the .poly file.\n");
- printf(
-" -X No exact arithmetic. Normally, Triangle uses exact floating-point\n"
-);
- printf(
-" arithmetic for certain tests if it thinks the inexact tests are not\n"
-);
- printf(
-" accurate enough. Exact arithmetic ensures the robustness of the\n");
- printf(
-" triangulation algorithms, despite floating-point roundoff error.\n");
- printf(
-" Disabling exact arithmetic with the -X switch causes a small\n");
- printf(
-" improvement in speed and creates the possibility that Triangle will\n"
-);
- printf(" fail to produce a valid mesh. Not recommended.\n");
- printf(
-" -z Numbers all items starting from zero (rather than one). Note that\n"
-);
- printf(
-" this switch is normally overridden by the value used to number the\n"
-);
- printf(
-" first vertex of the input .node or .poly file. However, this\n");
- printf(
-" switch is useful when calling Triangle from another program.\n");
- printf(
-" -o2 Generates second-order subparametric elements with six nodes each.\n"
-);
- printf(
-" -Y No new vertices on the boundary. This switch is useful when the\n");
- printf(
-" mesh boundary must be preserved so that it conforms to some\n");
- printf(
-" adjacent mesh. Be forewarned that you will probably sacrifice much\n"
-);
- printf(
-" of the quality of the mesh; Triangle will try, but the resulting\n");
- printf(
-" mesh may contain poorly shaped triangles. Works well if all the\n");
- printf(
-" boundary vertices are closely spaced. Specify this switch twice\n");
- printf(
-" (`-YY') to prevent all segment splitting, including internal\n");
- printf(" boundaries.\n");
- printf(
-" -S Specifies the maximum number of Steiner points (vertices that are\n");
- printf(
-" not in the input, but are added to meet the constraints on minimum\n"
-);
- printf(
-" angle and maximum area). The default is to allow an unlimited\n");
- printf(
-" number. If you specify this switch with no number after it,\n");
- printf(
-" the limit is set to zero. Triangle always adds vertices at segment\n"
-);
- printf(
-" intersections, even if it needs to use more vertices than the limit\n"
-);
- printf(
-" you set. When Triangle inserts segments by splitting (-s), it\n");
- printf(
-" always adds enough vertices to ensure that all the segments of the\n"
-);
- printf(" PLSG are recovered, ignoring the limit if necessary.\n");
- printf(
-" -i Uses an incremental rather than a divide-and-conquer algorithm to\n");
- printf(
-" construct a Delaunay triangulation. Try it if the divide-and-\n");
- printf(" conquer algorithm fails.\n");
- printf(
-" -F Uses Steven Fortune's sweepline algorithm to construct a Delaunay\n");
- printf(
-" triangulation. Warning: does not use exact arithmetic for all\n");
- printf(" calculations. An exact result is not guaranteed.\n");
- printf(
-" -l Uses only vertical cuts in the divide-and-conquer algorithm. By\n");
- printf(
-" default, Triangle alternates between vertical and horizontal cuts,\n"
-);
- printf(
-" which usually improve the speed except with vertex sets that are\n");
- printf(
-" small or short and wide. This switch is primarily of theoretical\n");
- printf(" interest.\n");
- printf(
-" -s Specifies that segments should be forced into the triangulation by\n"
-);
- printf(
-" recursively splitting them at their midpoints, rather than by\n");
- printf(
-" generating a constrained Delaunay triangulation. Segment splitting\n"
-);
- printf(
-" is true to Ruppert's original algorithm, but can create needlessly\n"
-);
- printf(
-" small triangles. This switch is primarily of theoretical interest.\n"
-);
- printf(
-" -C Check the consistency of the final mesh. Uses exact arithmetic for\n"
-);
- printf(
-" checking, even if the -X switch is used. Useful if you suspect\n");
- printf(" Triangle is buggy.\n");
- printf(
-" -Q Quiet: Suppresses all explanation of what Triangle is doing,\n");
- printf(" unless an error occurs.\n");
- printf(
-" -V Verbose: Gives detailed information about what Triangle is doing.\n"
-);
- printf(
-" Add more `V's for increasing amount of detail. `-V' is most\n");
- printf(
-" useful; itgives information on algorithmic progress and much more\n");
- printf(
-" detailed statistics. `-VV' gives vertex-by-vertex details, and\n");
- printf(
-" prints so much that Triangle runs much more slowly. `-VVVV' gives\n"
-);
- printf(" information only a debugger could love.\n");
- printf(" -h Help: Displays these instructions.\n");
- printf("\n");
- printf("Definitions:\n");
- printf("\n");
- printf(
-" A Delaunay triangulation of a vertex set is a triangulation whose\n");
- printf(
-" vertices are the vertex set, that covers the convex hull of the vertex\n");
- printf(
-" set. A Delaunay triangulation has the property that no vertex lies\n");
- printf(
-" inside the circumscribing circle (circle that passes through all three\n");
- printf(" vertices) of any triangle in the triangulation.\n\n");
- printf(
-" A Voronoi diagram of a vertex set is a subdivision of the plane into\n");
- printf(
-" polygonal cells (some of which may be unbounded, meaning infinitely\n");
- printf(
-" large), where each cell is the set of points in the plane that are closer\n"
-);
- printf(
-" to some input vertex than to any other input vertex. The Voronoi diagram\n"
-);
- printf(" is a geometric dual of the Delaunay triangulation.\n\n");
- printf(
-" A Planar Straight Line Graph (PSLG) is a set of vertices and segments.\n");
- printf(
-" Segments are simply edges, whose endpoints are all vertices in the PSLG.\n"
-);
- printf(
-" Segments may intersect each other only at their endpoints. The file\n");
- printf(" format for PSLGs (.poly files) is described below.\n\n");
- printf(
-" A constrained Delaunay triangulation (CDT) of a PSLG is similar to a\n");
- printf(
-" Delaunay triangulation, but each PSLG segment is present as a single edge\n"
-);
- printf(
-" of the CDT. (A constrained Delaunay triangulation is not truly a\n");
- printf(
-" Delaunay triangulation, because some of its triangles might not be\n");
- printf(
-" Delaunay.) By definition, a CDT does not have any vertices other than\n");
- printf(
-" those specified in the input PSLG. Depending on context, a CDT might\n");
- printf(
-" cover the convex hull of the PSLG, or it might cover only a segment-\n");
- printf(" bounded region (e.g. a polygon).\n\n");
- printf(
-" A conforming Delaunay triangulation of a PSLG is a triangulation in which\n"
-);
- printf(
-" each triangle is truly Delaunay, and each PSLG segment is represented by\n"
-);
- printf(
-" a linear contiguous sequence of edges of the triangulation. New vertices\n"
-);
- printf(
-" (not part of the PSLG) may appear, and each input segment may have been\n");
- printf(
-" subdivided into shorter edges (subsegments) by these additional vertices.\n"
-);
- printf(
-" The new vertices are frequently necessary to maintain the Delaunay\n");
- printf(" property while ensuring that every segment is represented.\n\n");
- printf(
-" A conforming constrained Delaunay triangulation (CCDT) of a PSLG is a\n");
- printf(
-" triangulation of a PSLG whose triangles are constrained Delaunay. New\n");
- printf(" vertices may appear, and input segments may be subdivided into\n");
- printf(
-" subsegments, but not to guarantee that segments are respected; rather, to\n"
-);
- printf(
-" improve the quality of the triangles. The high-quality meshes produced\n");
- printf(
-" by the -q switch are usually CCDTs, but can be made conforming Delaunay\n");
- printf(" with the -D switch.\n\n");
- printf("File Formats:\n\n");
- printf(
-" All files may contain comments prefixed by the character '#'. Vertices,\n"
-);
- printf(
-" triangles, edges, holes, and maximum area constraints must be numbered\n");
- printf(
-" consecutively, starting from either 1 or 0. Whichever you choose, all\n");
- printf(
-" input files must be consistent; if the vertices are numbered from 1, so\n");
- printf(
-" must be all other objects. Triangle automatically detects your choice\n");
- printf(
-" while reading the .node (or .poly) file. (When calling Triangle from\n");
- printf(
-" another program, use the -z switch if you wish to number objects from\n");
- printf(" zero.) Examples of these file formats are given below.\n\n");
- printf(" .node files:\n");
- printf(
-" First line: <# of vertices> <dimension (must be 2)> <# of attributes>\n"
-);
- printf(
-" <# of boundary markers (0 or 1)>\n"
-);
- printf(
-" Remaining lines: <vertex #> <x> <y> [attributes] [boundary marker]\n");
- printf("\n");
- printf(
-" The attributes, which are typically floating-point values of physical\n");
- printf(
-" quantities (such as mass or conductivity) associated with the nodes of\n"
-);
- printf(
-" a finite element mesh, are copied unchanged to the output mesh. If -q,\n"
-);
- printf(
-" -a, -u, -D, or -s is selected, each new Steiner point added to the mesh\n"
-);
- printf(" has attributes assigned to it by linear interpolation.\n\n");
- printf(
-" If the fourth entry of the first line is `1', the last column of the\n");
- printf(
-" remainder of the file is assumed to contain boundary markers. Boundary\n"
-);
- printf(
-" markers are used to identify boundary vertices and vertices resting on\n"
-);
- printf(
-" PSLG segments; a complete description appears in a section below. The\n"
-);
- printf(
-" .node file produced by Triangle contains boundary markers in the last\n");
- printf(" column unless they are suppressed by the -B switch.\n\n");
- printf(" .ele files:\n");
- printf(
-" First line: <# of triangles> <nodes per triangle> <# of attributes>\n");
- printf(
-" Remaining lines: <triangle #> <node> <node> <node> ... [attributes]\n");
- printf("\n");
- printf(
-" Nodes are indices into the corresponding .node file. The first three\n");
- printf(
-" nodes are the corner vertices, and are listed in counterclockwise order\n"
-);
- printf(
-" around each triangle. (The remaining nodes, if any, depend on the type\n"
-);
- printf(" of finite element used.)\n\n");
- printf(
-" The attributes are just like those of .node files. Because there is no\n"
-);
- printf(
-" simple mapping from input to output triangles, Triangle attempts to\n");
- printf(
-" interpolate attributes, and may cause a lot of diffusion of attributes\n"
-);
- printf(
-" among nearby triangles as the triangulation is refined. Attributes do\n"
-);
- printf(" not diffuse across segments, so attributes used to identify\n");
- printf(" segment-bounded regions remain intact.\n\n");
- printf(
-" In .ele files produced by Triangle, each triangular element has three\n");
- printf(
-" nodes (vertices) unless the -o2 switch is used, in which case\n");
- printf(
-" subparametric quadratic elements with six nodes each are generated.\n");
- printf(
-" The first three nodes are the corners in counterclockwise order, and\n");
- printf(
-" the fourth, fifth, and sixth nodes lie on the midpoints of the edges\n");
- printf(
-" opposite the first, second, and third vertices, respectively.\n");
- printf("\n");
- printf(" .poly files:\n");
- printf(
-" First line: <# of vertices> <dimension (must be 2)> <# of attributes>\n"
-);
- printf(
-" <# of boundary markers (0 or 1)>\n"
-);
- printf(
-" Following lines: <vertex #> <x> <y> [attributes] [boundary marker]\n");
- printf(" One line: <# of segments> <# of boundary markers (0 or 1)>\n");
- printf(
-" Following lines: <segment #> <endpoint> <endpoint> [boundary marker]\n");
- printf(" One line: <# of holes>\n");
- printf(" Following lines: <hole #> <x> <y>\n");
- printf(
-" Optional line: <# of regional attributes and/or area constraints>\n");
- printf(
-" Optional following lines: <region #> <x> <y> <attribute> <max area>\n");
- printf("\n");
- printf(
-" A .poly file represents a PSLG, as well as some additional information.\n"
-);
- printf(
-" The first section lists all the vertices, and is identical to the\n");
- printf(
-" format of .node files. <# of vertices> may be set to zero to indicate\n"
-);
- printf(
-" that the vertices are listed in a separate .node file; .poly files\n");
- printf(
-" produced by Triangle always have this format. A vertex set represented\n"
-);
- printf(
-" this way has the advantage that it may easily be triangulated with or\n");
- printf(
-" without segments (depending on whether the -p switch is invoked).\n");
- printf("\n");
- printf(
-" The second section lists the segments. Segments are edges whose\n");
- printf(
-" presence in the triangulation is enforced. (Depending on the choice of\n"
-);
- printf(
-" switches, segment might be subdivided into smaller edges). Each\n");
- printf(
-" segment is specified by listing the indices of its two endpoints. This\n"
-);
- printf(
-" means that you must include its endpoints in the vertex list. Each\n");
- printf(" segment, like each point, may have a boundary marker.\n\n");
- printf(
-" If -q, -a, -u, and -s are not selected, Triangle produces a constrained\n"
-);
- printf(
-" Delaunay triangulation (CDT), in which each segment appears as a single\n"
-);
- printf(
-" edge in the triangulation. If -q, -a, -u, or -s is selected, Triangle\n"
-);
- printf(
-" produces a conforming constrained Delaunay triangulation (CCDT), in\n");
- printf(
-" which segments may be subdivided into smaller edges. If -D is\n");
- printf(
-" selected, Triangle produces a conforming Delaunay triangulation, so\n");
- printf(
-" that every triangle is Delaunay, and not just constrained Delaunay.\n");
- printf("\n");
- printf(
-" The third section lists holes (and concavities, if -c is selected) in\n");
- printf(
-" the triangulation. Holes are specified by identifying a point inside\n");
- printf(
-" each hole. After the triangulation is formed, Triangle creates holes\n");
- printf(
-" by eating triangles, spreading out from each hole point until its\n");
- printf(
-" progress is blocked by segments in the PSLG. You must be careful to\n");
- printf(
-" enclose each hole in segments, or your whole triangulation might be\n");
- printf(
-" eaten away. If the two triangles abutting a segment are eaten, the\n");
- printf(
-" segment itself is also eaten. Do not place a hole directly on a\n");
- printf(" segment; if you do, Triangle chooses one side of the segment\n");
- printf(" arbitrarily.\n\n");
- printf(
-" The optional fourth section lists regional attributes (to be assigned\n");
- printf(
-" to all triangles in a region) and regional constraints on the maximum\n");
- printf(
-" triangle area. Triangle reads this section only if the -A switch is\n");
- printf(
-" used or the -a switch is used without a number following it, and the -r\n"
-);
- printf(
-" switch is not used. Regional attributes and area constraints are\n");
- printf(
-" propagated in the same manner as holes: you specify a point for each\n");
- printf(
-" attribute and/or constraint, and the attribute and/or constraint\n");
- printf(
-" affects the whole region (bounded by segments) containing the point.\n");
- printf(
-" If two values are written on a line after the x and y coordinate, the\n");
- printf(
-" first such value is assumed to be a regional attribute (but is only\n");
- printf(
-" applied if the -A switch is selected), and the second value is assumed\n"
-);
- printf(
-" to be a regional area constraint (but is only applied if the -a switch\n"
-);
- printf(
-" is selected). You may specify just one value after the coordinates,\n");
- printf(
-" which can serve as both an attribute and an area constraint, depending\n"
-);
- printf(
-" on the choice of switches. If you are using the -A and -a switches\n");
- printf(
-" simultaneously and wish to assign an attribute to some region without\n");
- printf(" imposing an area constraint, use a negative maximum area.\n\n");
- printf(
-" When a triangulation is created from a .poly file, you must either\n");
- printf(
-" enclose the entire region to be triangulated in PSLG segments, or\n");
- printf(
-" use the -c switch, which automatically creates extra segments that\n");
- printf(
-" enclose the convex hull of the PSLG. If you do not use the -c switch,\n"
-);
- printf(
-" Triangle eats all triangles that are not enclosed by segments; if you\n");
- printf(
-" are not careful, your whole triangulation may be eaten away. If you do\n"
-);
- printf(
-" use the -c switch, you can still produce concavities by the appropriate\n"
-);
- printf(
-" placement of holes just inside the boundary of the convex hull.\n");
- printf("\n");
- printf(
-" An ideal PSLG has no intersecting segments, nor any vertices that lie\n");
- printf(
-" upon segments (except, of course, the endpoints of each segment). You\n"
-);
- printf(
-" aren't required to make your .poly files ideal, but you should be aware\n"
-);
- printf(
-" of what can go wrong. Segment intersections are relatively safe--\n");
- printf(
-" Triangle calculates the intersection points for you and adds them to\n");
- printf(
-" the triangulation--as long as your machine's floating-point precision\n");
- printf(
-" doesn't become a problem. You are tempting the fates if you have three\n"
-);
- printf(
-" segments that cross at the same location, and expect Triangle to figure\n"
-);
- printf(
-" out where the intersection point is. Thanks to floating-point roundoff\n"
-);
- printf(
-" error, Triangle will probably decide that the three segments intersect\n"
-);
- printf(
-" at three different points, and you will find a minuscule triangle in\n");
- printf(
-" your output--unless Triangle tries to refine the tiny triangle, uses\n");
- printf(
-" up the last bit of machine precision, and fails to terminate at all.\n");
- printf(
-" You're better off putting the intersection point in the input files,\n");
- printf(
-" and manually breaking up each segment into two. Similarly, if you\n");
- printf(
-" place a vertex at the middle of a segment, and hope that Triangle will\n"
-);
- printf(
-" break up the segment at that vertex, you might get lucky. On the other\n"
-);
- printf(
-" hand, Triangle might decide that the vertex doesn't lie precisely on\n");
- printf(
-" the segment, and you'll have a needle-sharp triangle in your output--or\n"
-);
- printf(" a lot of tiny triangles if you're generating a quality mesh.\n");
- printf("\n");
- printf(
-" When Triangle reads a .poly file, it also writes a .poly file, which\n");
- printf(
-" includes all the subsegments--the edges that are parts of input\n");
- printf(
-" segments. If the -c switch is used, the output .poly file also\n");
- printf(
-" includes all of the edges on the convex hull. Hence, the output .poly\n"
-);
- printf(
-" file is useful for finding edges associated with input segments and for\n"
-);
- printf(
-" setting boundary conditions in finite element simulations. Moreover,\n");
- printf(
-" you will need the output .poly file if you plan to refine the output\n");
- printf(
-" mesh, and don't want segments to be missing in later triangulations.\n");
- printf("\n");
- printf(" .area files:\n");
- printf(" First line: <# of triangles>\n");
- printf(" Following lines: <triangle #> <maximum area>\n");
- printf("\n");
- printf(
-" An .area file associates with each triangle a maximum area that is used\n"
-);
- printf(
-" for mesh refinement. As with other file formats, every triangle must\n");
- printf(
-" be represented, and the triangles must be numbered consecutively. A\n");
- printf(
-" triangle may be left unconstrained by assigning it a negative maximum\n");
- printf(" area.\n\n");
- printf(" .edge files:\n");
- printf(" First line: <# of edges> <# of boundary markers (0 or 1)>\n");
- printf(
-" Following lines: <edge #> <endpoint> <endpoint> [boundary marker]\n");
- printf("\n");
- printf(
-" Endpoints are indices into the corresponding .node file. Triangle can\n"
-);
- printf(
-" produce .edge files (use the -e switch), but cannot read them. The\n");
- printf(
-" optional column of boundary markers is suppressed by the -B switch.\n");
- printf("\n");
- printf(
-" In Voronoi diagrams, one also finds a special kind of edge that is an\n");
- printf(
-" infinite ray with only one endpoint. For these edges, a different\n");
- printf(" format is used:\n\n");
- printf(" <edge #> <endpoint> -1 <direction x> <direction y>\n\n");
- printf(
-" The `direction' is a floating-point vector that indicates the direction\n"
-);
- printf(" of the infinite ray.\n\n");
- printf(" .neigh files:\n");
- printf(
-" First line: <# of triangles> <# of neighbors per triangle (always 3)>\n"
-);
- printf(
-" Following lines: <triangle #> <neighbor> <neighbor> <neighbor>\n");
- printf("\n");
- printf(
-" Neighbors are indices into the corresponding .ele file. An index of -1\n"
-);
- printf(
-" indicates no neighbor (because the triangle is on an exterior\n");
- printf(
-" boundary). The first neighbor of triangle i is opposite the first\n");
- printf(" corner of triangle i, and so on.\n\n");
- printf(
-" Triangle can produce .neigh files (use the -n switch), but cannot read\n"
-);
- printf(" them.\n\n");
- printf("Boundary Markers:\n\n");
- printf(
-" Boundary markers are tags used mainly to identify which output vertices\n");
- printf(
-" and edges are associated with which PSLG segment, and to identify which\n");
- printf(
-" vertices and edges occur on a boundary of the triangulation. A common\n");
- printf(
-" use is to determine where boundary conditions should be applied to a\n");
- printf(
-" finite element mesh. You can prevent boundary markers from being written\n"
-);
- printf(" into files produced by Triangle by using the -B switch.\n\n");
- printf(
-" The boundary marker associated with each segment in an output .poly file\n"
-);
- printf(" and each edge in an output .edge file is chosen as follows:\n");
- printf(
-" - If an output edge is part or all of a PSLG segment with a nonzero\n");
- printf(
-" boundary marker, then the edge is assigned the same marker.\n");
- printf(
-" - Otherwise, if the edge lies on a boundary of the triangulation\n");
- printf(
-" (even the boundary of a hole), then the edge is assigned the marker\n");
- printf(" one (1).\n");
- printf(" - Otherwise, the edge is assigned the marker zero (0).\n");
- printf(
-" The boundary marker associated with each vertex in an output .node file\n");
- printf(" is chosen as follows:\n");
- printf(
-" - If a vertex is assigned a nonzero boundary marker in the input file,\n"
-);
- printf(
-" then it is assigned the same marker in the output .node file.\n");
- printf(
-" - Otherwise, if the vertex lies on a PSLG segment (even if it is an\n");
- printf(
-" endpoint of the segment) with a nonzero boundary marker, then the\n");
- printf(
-" vertex is assigned the same marker. If the vertex lies on several\n");
- printf(" such segments, one of the markers is chosen arbitrarily.\n");
- printf(
-" - Otherwise, if the vertex occurs on a boundary of the triangulation,\n");
- printf(" then the vertex is assigned the marker one (1).\n");
- printf(" - Otherwise, the vertex is assigned the marker zero (0).\n");
- printf("\n");
- printf(
-" If you want Triangle to determine for you which vertices and edges are on\n"
-);
- printf(
-" the boundary, assign them the boundary marker zero (or use no markers at\n"
-);
- printf(
-" all) in your input files. In the output files, all boundary vertices,\n");
- printf(" edges, and segments will be assigned the value one.\n\n");
- printf("Triangulation Iteration Numbers:\n\n");
- printf(
-" Because Triangle can read and refine its own triangulations, input\n");
- printf(
-" and output files have iteration numbers. For instance, Triangle might\n");
- printf(
-" read the files mesh.3.node, mesh.3.ele, and mesh.3.poly, refine the\n");
- printf(
-" triangulation, and output the files mesh.4.node, mesh.4.ele, and\n");
- printf(" mesh.4.poly. Files with no iteration number are treated as if\n");
- printf(
-" their iteration number is zero; hence, Triangle might read the file\n");
- printf(
-" points.node, triangulate it, and produce the files points.1.node and\n");
- printf(" points.1.ele.\n\n");
- printf(
-" Iteration numbers allow you to create a sequence of successively finer\n");
- printf(
-" meshes suitable for multigrid methods. They also allow you to produce a\n"
-);
- printf(
-" sequence of meshes using error estimate-driven mesh refinement.\n");
- printf("\n");
- printf(
-" If you're not using refinement or quality meshing, and you don't like\n");
- printf(
-" iteration numbers, use the -I switch to disable them. This switch also\n");
- printf(
-" disables output of .node and .poly files to prevent your input files from\n"
-);
- printf(
-" being overwritten. (If the input is a .poly file that contains its own\n");
- printf(
-" points, a .node file is written. This can be quite convenient for\n");
- printf(" computing CDTs or quality meshes.)\n\n");
- printf("Examples of How to Use Triangle:\n\n");
- printf(
-" `triangle dots' reads vertices from dots.node, and writes their Delaunay\n"
-);
- printf(
-" triangulation to dots.1.node and dots.1.ele. (dots.1.node is identical\n");
- printf(
-" to dots.node.) `triangle -I dots' writes the triangulation to dots.ele\n");
- printf(
-" instead. (No additional .node file is needed, so none is written.)\n");
- printf("\n");
- printf(
-" `triangle -pe object.1' reads a PSLG from object.1.poly (and possibly\n");
- printf(
-" object.1.node, if the vertices are omitted from object.1.poly) and writes\n"
-);
- printf(
-" its constrained Delaunay triangulation to object.2.node and object.2.ele.\n"
-);
- printf(
-" The segments are copied to object.2.poly, and all edges are written to\n");
- printf(" object.2.edge.\n\n");
- printf(
-" `triangle -pq31.5a.1 object' reads a PSLG from object.poly (and possibly\n"
-);
- printf(
-" object.node), generates a mesh whose angles are all between 31.5 and 117\n"
-);
- printf(
-" degrees and whose triangles all have areas of 0.1 or less, and writes the\n"
-);
- printf(
-" mesh to object.1.node and object.1.ele. Each segment may be broken up\n");
- printf(" into multiple subsegments; these are written to object.1.poly.\n");
- printf("\n");
- printf(
-" Here is a sample file `box.poly' describing a square with a square hole:\n"
-);
- printf("\n");
- printf(
-" # A box with eight vertices in 2D, no attributes, one boundary marker.\n"
-);
- printf(" 8 2 0 1\n");
- printf(" # Outer box has these vertices:\n");
- printf(" 1 0 0 0\n");
- printf(" 2 0 3 0\n");
- printf(" 3 3 0 0\n");
- printf(" 4 3 3 33 # A special marker for this vertex.\n");
- printf(" # Inner square has these vertices:\n");
- printf(" 5 1 1 0\n");
- printf(" 6 1 2 0\n");
- printf(" 7 2 1 0\n");
- printf(" 8 2 2 0\n");
- printf(" # Five segments with boundary markers.\n");
- printf(" 5 1\n");
- printf(" 1 1 2 5 # Left side of outer box.\n");
- printf(" # Square hole has these segments:\n");
- printf(" 2 5 7 0\n");
- printf(" 3 7 8 0\n");
- printf(" 4 8 6 10\n");
- printf(" 5 6 5 0\n");
- printf(" # One hole in the middle of the inner square.\n");
- printf(" 1\n");
- printf(" 1 1.5 1.5\n");
- printf("\n");
- printf(
-" Note that some segments are missing from the outer square, so you must\n");
- printf(
-" use the `-c' switch. After `triangle -pqc box.poly', here is the output\n"
-);
- printf(
-" file `box.1.node', with twelve vertices. The last four vertices were\n");
- printf(
-" added to meet the angle constraint. Vertices 1, 2, and 9 have markers\n");
- printf(
-" from segment 1. Vertices 6 and 8 have markers from segment 4. All the\n");
- printf(
-" other vertices but 4 have been marked to indicate that they lie on a\n");
- printf(" boundary.\n\n");
- printf(" 12 2 0 1\n");
- printf(" 1 0 0 5\n");
- printf(" 2 0 3 5\n");
- printf(" 3 3 0 1\n");
- printf(" 4 3 3 33\n");
- printf(" 5 1 1 1\n");
- printf(" 6 1 2 10\n");
- printf(" 7 2 1 1\n");
- printf(" 8 2 2 10\n");
- printf(" 9 0 1.5 5\n");
- printf(" 10 1.5 0 1\n");
- printf(" 11 3 1.5 1\n");
- printf(" 12 1.5 3 1\n");
- printf(" # Generated by triangle -pqc box.poly\n");
- printf("\n");
- printf(" Here is the output file `box.1.ele', with twelve triangles.\n");
- printf("\n");
- printf(" 12 3 0\n");
- printf(" 1 5 6 9\n");
- printf(" 2 10 3 7\n");
- printf(" 3 6 8 12\n");
- printf(" 4 9 1 5\n");
- printf(" 5 6 2 9\n");
- printf(" 6 7 3 11\n");
- printf(" 7 11 4 8\n");
- printf(" 8 7 5 10\n");
- printf(" 9 12 2 6\n");
- printf(" 10 8 7 11\n");
- printf(" 11 5 1 10\n");
- printf(" 12 8 4 12\n");
- printf(" # Generated by triangle -pqc box.poly\n\n");
- printf(
-" Here is the output file `box.1.poly'. Note that segments have been added\n"
-);
- printf(
-" to represent the convex hull, and some segments have been subdivided by\n");
- printf(
-" newly added vertices. Note also that <# of vertices> is set to zero to\n");
- printf(" indicate that the vertices should be read from the .node file.\n");
- printf("\n");
- printf(" 0 2 0 1\n");
- printf(" 12 1\n");
- printf(" 1 1 9 5\n");
- printf(" 2 5 7 1\n");
- printf(" 3 8 7 1\n");
- printf(" 4 6 8 10\n");
- printf(" 5 5 6 1\n");
- printf(" 6 3 10 1\n");
- printf(" 7 4 11 1\n");
- printf(" 8 2 12 1\n");
- printf(" 9 9 2 5\n");
- printf(" 10 10 1 1\n");
- printf(" 11 11 3 1\n");
- printf(" 12 12 4 1\n");
- printf(" 1\n");
- printf(" 1 1.5 1.5\n");
- printf(" # Generated by triangle -pqc box.poly\n");
- printf("\n");
- printf("Refinement and Area Constraints:\n");
- printf("\n");
- printf(
-" The -r switch causes a mesh (.node and .ele files) to be read and\n");
- printf(
-" refined. If the -p switch is also used, a .poly file is read and used to\n"
-);
- printf(
-" specify edges that are constrained and cannot be eliminated (although\n");
- printf(
-" they can be subdivided into smaller edges) by the refinement process.\n");
- printf("\n");
- printf(
-" When you refine a mesh, you generally want to impose tighter constraints.\n"
-);
- printf(
-" One way to accomplish this is to use -q with a larger angle, or -a\n");
- printf(
-" followed by a smaller area than you used to generate the mesh you are\n");
- printf(
-" refining. Another way to do this is to create an .area file, which\n");
- printf(
-" specifies a maximum area for each triangle, and use the -a switch\n");
- printf(
-" (without a number following). Each triangle's area constraint is applied\n"
-);
- printf(
-" to that triangle. Area constraints tend to diffuse as the mesh is\n");
- printf(
-" refined, so if there are large variations in area constraint between\n");
- printf(
-" adjacent triangles, you may not get the results you want. In that case,\n"
-);
- printf(
-" consider instead using the -u switch and writing a C procedure that\n");
- printf(" determines which triangles are too large.\n\n");
- printf(
-" If you are refining a mesh composed of linear (three-node) elements, the\n"
-);
- printf(
-" output mesh contains all the nodes present in the input mesh, in the same\n"
-);
- printf(
-" order, with new nodes added at the end of the .node file. However, the\n");
- printf(
-" refinement is not hierarchical: there is no guarantee that each output\n");
- printf(
-" element is contained in a single input element. Often, an output element\n"
-);
- printf(
-" can overlap two or three input elements, and some input edges are not\n");
- printf(
-" present in the output mesh. Hence, a sequence of refined meshes forms a\n"
-);
- printf(
-" hierarchy of nodes, but not a hierarchy of elements. If you refine a\n");
- printf(
-" mesh of higher-order elements, the hierarchical property applies only to\n"
-);
- printf(
-" the nodes at the corners of an element; the midpoint nodes on each edge\n");
- printf(" are discarded before the mesh is refined.\n\n");
- printf(
-" Maximum area constraints in .poly files operate differently from those in\n"
-);
- printf(
-" .area files. A maximum area in a .poly file applies to the whole\n");
- printf(
-" (segment-bounded) region in which a point falls, whereas a maximum area\n");
- printf(
-" in an .area file applies to only one triangle. Area constraints in .poly\n"
-);
- printf(
-" files are used only when a mesh is first generated, whereas area\n");
- printf(
-" constraints in .area files are used only to refine an existing mesh, and\n"
-);
- printf(
-" are typically based on a posteriori error estimates resulting from a\n");
- printf(" finite element simulation on that mesh.\n\n");
- printf(
-" `triangle -rq25 object.1' reads object.1.node and object.1.ele, then\n");
- printf(
-" refines the triangulation to enforce a 25 degree minimum angle, and then\n"
-);
- printf(
-" writes the refined triangulation to object.2.node and object.2.ele.\n");
- printf("\n");
- printf(
-" `triangle -rpaa6.2 z.3' reads z.3.node, z.3.ele, z.3.poly, and z.3.area.\n"
-);
- printf(
-" After reconstructing the mesh and its subsegments, Triangle refines the\n");
- printf(
-" mesh so that no triangle has area greater than 6.2, and furthermore the\n");
- printf(
-" triangles satisfy the maximum area constraints in z.3.area. No angle\n");
- printf(
-" bound is imposed at all. The output is written to z.4.node, z.4.ele, and\n"
-);
- printf(" z.4.poly.\n\n");
- printf(
-" The sequence `triangle -qa1 x', `triangle -rqa.3 x.1', `triangle -rqa.1\n");
- printf(
-" x.2' creates a sequence of successively finer meshes x.1, x.2, and x.3,\n");
- printf(" suitable for multigrid.\n\n");
- printf("Convex Hulls and Mesh Boundaries:\n\n");
- printf(
-" If the input is a vertex set (not a PSLG), Triangle produces its convex\n");
- printf(
-" hull as a by-product in the output .poly file if you use the -c switch.\n");
- printf(
-" There are faster algorithms for finding a two-dimensional convex hull\n");
- printf(" than triangulation, of course, but this one comes for free.\n\n");
- printf(
-" If the input is an unconstrained mesh (you are using the -r switch but\n");
- printf(
-" not the -p switch), Triangle produces a list of its boundary edges\n");
- printf(
-" (including hole boundaries) as a by-product when you use the -c switch.\n");
- printf(
-" If you also use the -p switch, the output .poly file contains all the\n");
- printf(" segments from the input .poly file as well.\n\n");
- printf("Voronoi Diagrams:\n\n");
- printf(
-" The -v switch produces a Voronoi diagram, in files suffixed .v.node and\n");
- printf(
-" .v.edge. For example, `triangle -v points' reads points.node, produces\n");
- printf(
-" its Delaunay triangulation in points.1.node and points.1.ele, and\n");
- printf(
-" produces its Voronoi diagram in points.1.v.node and points.1.v.edge. The\n"
-);
- printf(
-" .v.node file contains a list of all Voronoi vertices, and the .v.edge\n");
- printf(
-" file contains a list of all Voronoi edges, some of which may be infinite\n"
-);
- printf(
-" rays. (The choice of filenames makes it easy to run the set of Voronoi\n");
- printf(" vertices through Triangle, if so desired.)\n\n");
- printf(
-" This implementation does not use exact arithmetic to compute the Voronoi\n"
-);
- printf(
-" vertices, and does not check whether neighboring vertices are identical.\n"
-);
- printf(
-" Be forewarned that if the Delaunay triangulation is degenerate or\n");
- printf(
-" near-degenerate, the Voronoi diagram may have duplicate vertices or\n");
- printf(" crossing edges.\n\n");
- printf(
-" The result is a valid Voronoi diagram only if Triangle's output is a true\n"
-);
- printf(
-" Delaunay triangulation. The Voronoi output is usually meaningless (and\n");
- printf(
-" may contain crossing edges and other pathology) if the output is a CDT or\n"
-);
- printf(
-" CCDT, or if it has holes or concavities. If the triangulated domain is\n");
- printf(
-" convex and has no holes, you can use -D switch to force Triangle to\n");
- printf(
-" construct a conforming Delaunay triangulation instead of a CCDT, so the\n");
- printf(" Voronoi diagram will be valid.\n\n");
- printf("Mesh Topology:\n\n");
- printf(
-" You may wish to know which triangles are adjacent to a certain Delaunay\n");
- printf(
-" edge in an .edge file, which Voronoi cells are adjacent to a certain\n");
- printf(
-" Voronoi edge in a .v.edge file, or which Voronoi cells are adjacent to\n");
- printf(
-" each other. All of this information can be found by cross-referencing\n");
- printf(
-" output files with the recollection that the Delaunay triangulation and\n");
- printf(" the Voronoi diagram are planar duals.\n\n");
- printf(
-" Specifically, edge i of an .edge file is the dual of Voronoi edge i of\n");
- printf(
-" the corresponding .v.edge file, and is rotated 90 degrees counterclock-\n");
- printf(
-" wise from the Voronoi edge. Triangle j of an .ele file is the dual of\n");
- printf(
-" vertex j of the corresponding .v.node file. Voronoi cell k is the dual\n");
- printf(" of vertex k of the corresponding .node file.\n\n");
- printf(
-" Hence, to find the triangles adjacent to a Delaunay edge, look at the\n");
- printf(
-" vertices of the corresponding Voronoi edge. If the endpoints of a\n");
- printf(
-" Voronoi edge are Voronoi vertices 2 and 6 respectively, then triangles 2\n"
-);
- printf(
-" and 6 adjoin the left and right sides of the corresponding Delaunay edge,\n"
-);
- printf(
-" respectively. To find the Voronoi cells adjacent to a Voronoi edge, look\n"
-);
- printf(
-" at the endpoints of the corresponding Delaunay edge. If the endpoints of\n"
-);
- printf(
-" a Delaunay edge are input vertices 7 and 12, then Voronoi cells 7 and 12\n"
-);
- printf(
-" adjoin the right and left sides of the corresponding Voronoi edge,\n");
- printf(
-" respectively. To find which Voronoi cells are adjacent to each other,\n");
- printf(" just read the list of Delaunay edges.\n\n");
- printf(
-" Triangle does not write a list of the edges adjoining each Voronoi cell,\n"
-);
- printf(
-" but you can reconstructed it straightforwardly. For instance, to find\n");
- printf(
-" all the edges of Voronoi cell 1, search the output .edge file for every\n");
- printf(
-" edge that has input vertex 1 as an endpoint. The corresponding dual\n");
- printf(
-" edges in the output .v.edge file form the boundary of Voronoi cell 1.\n");
- printf("\n");
- printf(
-" For each Voronoi vertex, the .neigh file gives a list of the three\n");
- printf(
-" Voronoi vertices attached to it. You might find this more convenient\n");
- printf(" than the .v.edge file.\n\n");
- printf("Quadratic Elements:\n\n");
- printf(
-" Triangle generates meshes with subparametric quadratic elements if the\n");
- printf(
-" -o2 switch is specified. Quadratic elements have six nodes per element,\n"
-);
- printf(
-" rather than three. `Subparametric' means that the edges of the triangles\n"
-);
- printf(
-" are always straight, so that subparametric quadratic elements are\n");
- printf(
-" geometrically identical to linear elements, even though they can be used\n"
-);
- printf(
-" with quadratic interpolating functions. The three extra nodes of an\n");
- printf(
-" element fall at the midpoints of the three edges, with the fourth, fifth,\n"
-);
- printf(
-" and sixth nodes appearing opposite the first, second, and third corners\n");
- printf(" respectively.\n\n");
- printf("Domains with Small Angles:\n\n");
- printf(
-" If two input segments adjoin each other at a small angle, clearly the -q\n"
-);
- printf(
-" switch cannot remove the small angle. Moreover, Triangle may have no\n");
- printf(
-" choice but to generate additional triangles whose smallest angles are\n");
- printf(
-" smaller than the specified bound. However, these triangles only appear\n");
- printf(
-" between input segments separated by small angles. Moreover, if you\n");
- printf(
-" request a minimum angle of theta degrees, Triangle will generally produce\n"
-);
- printf(
-" no angle larger than 180 - 2 theta, even if it is forced to compromise on\n"
-);
- printf(" the minimum angle.\n\n");
- printf("Statistics:\n\n");
- printf(
-" After generating a mesh, Triangle prints a count of entities in the\n");
- printf(
-" output mesh, including the number of vertices, triangles, edges, exterior\n"
-);
- printf(
-" boundary edges (i.e. subsegments on the boundary of the triangulation,\n");
- printf(
-" including hole boundaries), interior boundary edges (i.e. subsegments of\n"
-);
- printf(
-" input segments not on the boundary), and total subsegments. If you've\n");
- printf(
-" forgotten the statistics for an existing mesh, run Triangle on that mesh\n"
-);
- printf(
-" with the -rNEP switches to read the mesh and print the statistics without\n"
-);
- printf(
-" writing any files. Use -rpNEP if you've got a .poly file for the mesh.\n");
- printf("\n");
- printf(
-" The -V switch produces extended statistics, including a rough estimate\n");
- printf(
-" of memory use, the number of calls to geometric predicates, and\n");
- printf(
-" histograms of the angles and the aspect ratios of the triangles in the\n");
- printf(" mesh.\n\n");
- printf("Exact Arithmetic:\n\n");
- printf(
-" Triangle uses adaptive exact arithmetic to perform what computational\n");
- printf(
-" geometers call the `orientation' and `incircle' tests. If the floating-\n"
-);
- printf(
-" point arithmetic of your machine conforms to the IEEE 754 standard (as\n");
- printf(
-" most workstations do), and does not use extended precision internal\n");
- printf(
-" floating-point registers, then your output is guaranteed to be an\n");
- printf(
-" absolutely true Delaunay or constrained Delaunay triangulation, roundoff\n"
-);
- printf(
-" error notwithstanding. The word `adaptive' implies that these arithmetic\n"
-);
- printf(
-" routines compute the result only to the precision necessary to guarantee\n"
-);
- printf(
-" correctness, so they are usually nearly as fast as their approximate\n");
- printf(" counterparts.\n\n");
- printf(
-" May CPUs, including Intel x86 processors, have extended precision\n");
- printf(
-" floating-point registers. These must be reconfigured so their precision\n"
-);
- printf(
-" is reduced to memory precision. Triangle does this if it is compiled\n");
- printf(" correctly. See the makefile for details.\n\n");
- printf(
-" The exact tests can be disabled with the -X switch. On most inputs, this\n"
-);
- printf(
-" switch reduces the computation time by about eight percent--it's not\n");
- printf(
-" worth the risk. There are rare difficult inputs (having many collinear\n");
- printf(
-" and cocircular vertices), however, for which the difference in speed\n");
- printf(
-" could be a factor of two. Be forewarned that these are precisely the\n");
- printf(
-" inputs most likely to cause errors if you use the -X switch. Hence, the\n"
-);
- printf(" -X switch is not recommended.\n\n");
- printf(
-" Unfortunately, the exact tests don't solve every numerical problem.\n");
- printf(
-" Exact arithmetic is not used to compute the positions of new vertices,\n");
- printf(
-" because the bit complexity of vertex coordinates would grow without\n");
- printf(
-" bound. Hence, segment intersections aren't computed exactly; in very\n");
- printf(
-" unusual cases, roundoff error in computing an intersection point might\n");
- printf(
-" actually lead to an inverted triangle and an invalid triangulation.\n");
- printf(
-" (This is one reason to specify your own intersection points in your .poly\n"
-);
- printf(
-" files.) Similarly, exact arithmetic is not used to compute the vertices\n"
-);
- printf(" of the Voronoi diagram.\n\n");
- printf(
-" Another pair of problems not solved by the exact arithmetic routines is\n");
- printf(
-" underflow and overflow. If Triangle is compiled for double precision\n");
- printf(
-" arithmetic, I believe that Triangle's geometric predicates work correctly\n"
-);
- printf(
-" if the exponent of every input coordinate falls in the range [-148, 201].\n"
-);
- printf(
-" Underflow can silently prevent the orientation and incircle tests from\n");
- printf(
-" being performed exactly, while overflow typically causes a floating\n");
- printf(" exception.\n\n");
- printf("Calling Triangle from Another Program:\n\n");
- printf(" Read the file triangle.h for details.\n\n");
- printf("Troubleshooting:\n\n");
- printf(" Please read this section before mailing me bugs.\n\n");
- printf(" `My output mesh has no triangles!'\n\n");
- printf(
-" If you're using a PSLG, you've probably failed to specify a proper set\n"
-);
- printf(
-" of bounding segments, or forgotten to use the -c switch. Or you may\n");
- printf(
-" have placed a hole badly, thereby eating all your triangles. To test\n");
- printf(" these possibilities, try again with the -c and -O switches.\n");
- printf(
-" Alternatively, all your input vertices may be collinear, in which case\n"
-);
- printf(" you can hardly expect to triangulate them.\n\n");
- printf(" `Triangle doesn't terminate, or just crashes.'\n\n");
- printf(
-" Bad things can happen when triangles get so small that the distance\n");
- printf(
-" between their vertices isn't much larger than the precision of your\n");
- printf(
-" machine's arithmetic. If you've compiled Triangle for single-precision\n"
-);
- printf(
-" arithmetic, you might do better by recompiling it for double-precision.\n"
-);
- printf(
-" Then again, you might just have to settle for more lenient constraints\n"
-);
- printf(
-" on the minimum angle and the maximum area than you had planned.\n");
- printf("\n");
- printf(
-" You can minimize precision problems by ensuring that the origin lies\n");
- printf(
-" inside your vertex set, or even inside the densest part of your\n");
- printf(
-" mesh. If you're triangulating an object whose x-coordinates all fall\n");
- printf(
-" between 6247133 and 6247134, you're not leaving much floating-point\n");
- printf(" precision for Triangle to work with.\n\n");
- printf(
-" Precision problems can occur covertly if the input PSLG contains two\n");
- printf(
-" segments that meet (or intersect) at an extremely small angle, or if\n");
- printf(
-" such an angle is introduced by the -c switch. If you don't realize\n");
- printf(
-" that a tiny angle is being formed, you might never discover why\n");
- printf(
-" Triangle is crashing. To check for this possibility, use the -S switch\n"
-);
- printf(
-" (with an appropriate limit on the number of Steiner points, found by\n");
- printf(
-" trial-and-error) to stop Triangle early, and view the output .poly file\n"
-);
- printf(
-" with Show Me (described below). Look carefully for regions where dense\n"
-);
- printf(
-" clusters of vertices are forming and for small angles between segments.\n"
-);
- printf(
-" Zoom in closely, as such segments might look like a single segment from\n"
-);
- printf(" a distance.\n\n");
- printf(
-" If some of the input values are too large, Triangle may suffer a\n");
- printf(
-" floating exception due to overflow when attempting to perform an\n");
- printf(
-" orientation or incircle test. (Read the section on exact arithmetic\n");
- printf(
-" above.) Again, I recommend compiling Triangle for double (rather\n");
- printf(" than single) precision arithmetic.\n\n");
- printf(
-" Unexpected problems can arise if you use quality meshing (-q, -a, or\n");
- printf(
-" -u) with an input that is not segment-bounded--that is, if your input\n");
- printf(
-" is a vertex set, or you're using the -c switch. If the convex hull of\n"
-);
- printf(
-" your input vertices has collinear vertices on its boundary, an input\n");
- printf(
-" vertex that you think lies on the convex hull might actually lie just\n");
- printf(
-" inside the convex hull. If so, the vertex and the nearby convex hull\n");
- printf(
-" edge form an extremely thin triangle. When Triangle tries to refine\n");
- printf(
-" the mesh to enforce angle and area constraints, Triangle might generate\n"
-);
- printf(
-" extremely tiny triangles, or it might fail because of insufficient\n");
- printf(" floating-point precision.\n\n");
- printf(
-" `The numbering of the output vertices doesn't match the input vertices.'\n"
-);
- printf("\n");
- printf(
-" You may have had duplicate input vertices, or you may have eaten some\n");
- printf(
-" of your input vertices with a hole, or by placing them outside the area\n"
-);
- printf(
-" enclosed by segments. In any case, you can solve the problem by not\n");
- printf(" using the -j switch.\n\n");
- printf(
-" `Triangle executes without incident, but when I look at the resulting\n");
- printf(
-" mesh, it has overlapping triangles or other geometric inconsistencies.'\n");
- printf("\n");
- printf(
-" If you select the -X switch, Triangle occasionally makes mistakes due\n");
- printf(
-" to floating-point roundoff error. Although these errors are rare,\n");
- printf(
-" don't use the -X switch. If you still have problems, please report the\n"
-);
- printf(" bug.\n\n");
- printf(
-" `Triangle executes without incident, but when I look at the resulting\n");
- printf(" Voronoi diagram, it has overlapping edges or other geometric\n");
- printf(" inconsistencies.'\n");
- printf("\n");
- printf(
-" If your input is a PSLG (-p), you can only expect a meaningful Voronoi\n"
-);
- printf(
-" diagram if the domain you are triangulating is convex and free of\n");
- printf(
-" holes, and you use the -D switch to construct a conforming Delaunay\n");
- printf(" triangulation (instead of a CDT or CCDT).\n\n");
- printf(
-" Strange things can happen if you've taken liberties with your PSLG. Do\n");
- printf(
-" you have a vertex lying in the middle of a segment? Triangle sometimes\n");
- printf(
-" copes poorly with that sort of thing. Do you want to lay out a collinear\n"
-);
- printf(
-" row of evenly spaced, segment-connected vertices? Have you simply\n");
- printf(
-" defined one long segment connecting the leftmost vertex to the rightmost\n"
-);
- printf(
-" vertex, and a bunch of vertices lying along it? This method occasionally\n"
-);
- printf(
-" works, especially with horizontal and vertical lines, but often it\n");
- printf(
-" doesn't, and you'll have to connect each adjacent pair of vertices with a\n"
-);
- printf(" separate segment. If you don't like it, tough.\n\n");
- printf(
-" Furthermore, if you have segments that intersect other than at their\n");
- printf(
-" endpoints, try not to let the intersections fall extremely close to PSLG\n"
-);
- printf(" vertices or each other.\n\n");
- printf(
-" If you have problems refining a triangulation not produced by Triangle:\n");
- printf(
-" Are you sure the triangulation is geometrically valid? Is it formatted\n");
- printf(
-" correctly for Triangle? Are the triangles all listed so the first three\n"
-);
- printf(
-" vertices are their corners in counterclockwise order? Are all of the\n");
- printf(
-" triangles constrained Delaunay? Triangle's Delaunay refinement algorithm\n"
-);
- printf(" assumes that it starts with a CDT.\n\n");
- printf("Show Me:\n\n");
- printf(
-" Triangle comes with a separate program named `Show Me', whose primary\n");
- printf(
-" purpose is to draw meshes on your screen or in PostScript. Its secondary\n"
-);
- printf(
-" purpose is to check the validity of your input files, and do so more\n");
- printf(
-" thoroughly than Triangle does. Unlike Triangle, Show Me requires that\n");
- printf(
-" you have the X Windows system. Sorry, Microsoft Windows users.\n");
- printf("\n");
- printf("Triangle on the Web:\n");
- printf("\n");
- printf(" To see an illustrated version of these instructions, check out\n");
- printf("\n");
- printf(" http://www.cs.cmu.edu/~quake/triangle.html\n");
- printf("\n");
- printf("A Brief Plea:\n");
- printf("\n");
- printf(
-" If you use Triangle, and especially if you use it to accomplish real\n");
- printf(
-" work, I would like very much to hear from you. A short letter or email\n");
- printf(
-" (to jrs at cs.berkeley.edu) describing how you use Triangle will mean a lot\n"
-);
- printf(
-" to me. The more people I know are using this program, the more easily I\n"
-);
- printf(
-" can justify spending time on improvements, which in turn will benefit\n");
- printf(
-" you. Also, I can put you on a list to receive email whenever a new\n");
- printf(" version of Triangle is available.\n\n");
- printf(
-" If you use a mesh generated by Triangle in a publication, please include\n"
-);
- printf(
-" an acknowledgment as well. And please spell Triangle with a capital `T'!\n"
-);
- printf(
-" If you want to include a citation, use `Jonathan Richard Shewchuk,\n");
- printf(
-" ``Triangle: Engineering a 2D Quality Mesh Generator and Delaunay\n");
- printf(
-" Triangulator,'' in Applied Computational Geometry: Towards Geometric\n");
- printf(
-" Engineering (Ming C. Lin and Dinesh Manocha, editors), volume 1148 of\n");
- printf(
-" Lecture Notes in Computer Science, pages 203-222, Springer-Verlag,\n");
- printf(
-" Berlin, May 1996. (From the First ACM Workshop on Applied Computational\n"
-);
- printf(" Geometry.)'\n\n");
- printf("Research credit:\n\n");
- printf(
-" Of course, I can take credit for only a fraction of the ideas that made\n");
- printf(
-" this mesh generator possible. Triangle owes its existence to the efforts\n"
-);
- printf(
-" of many fine computational geometers and other researchers, including\n");
- printf(
-" Marshall Bern, L. Paul Chew, Kenneth L. Clarkson, Boris Delaunay, Rex A.\n"
-);
- printf(
-" Dwyer, David Eppstein, Steven Fortune, Leonidas J. Guibas, Donald E.\n");
- printf(
-" Knuth, Charles L. Lawson, Der-Tsai Lee, Gary L. Miller, Ernst P. Mucke,\n");
- printf(
-" Steven E. Pav, Douglas M. Priest, Jim Ruppert, Isaac Saias, Bruce J.\n");
- printf(
-" Schachter, Micha Sharir, Peter W. Shor, Daniel D. Sleator, Jorge Stolfi,\n"
-);
- printf(" Robert E. Tarjan, Alper Ungor, Christopher J. Van Wyk, Noel J.\n");
- printf(
-" Walkington, and Binhai Zhu. See the comments at the beginning of the\n");
- printf(" source code for references.\n\n");
- triexit(0);
-}
-
-#endif /* not TRILIBRARY */
-
-/*****************************************************************************/
-/* */
-/* internalerror() Ask the user to send me the defective product. Exit. */
-/* */
-/*****************************************************************************/
-
-void internalerror()
-{
- printf(" Please report this bug to jrs at cs.berkeley.edu\n");
- printf(" Include the message above, your input data set, and the exact\n");
- printf(" command line you used to run Triangle.\n");
- triexit(1);
-}
-
-/*****************************************************************************/
-/* */
-/* parsecommandline() Read the command line, identify switches, and set */
-/* up options and file names. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-void parsecommandline(int argc, char **argv, struct behavior *b)
-#else /* not ANSI_DECLARATORS */
-void parsecommandline(argc, argv, b)
-int argc;
-char **argv;
-struct behavior *b;
-#endif /* not ANSI_DECLARATORS */
-
-{
-#ifdef TRILIBRARY
-#define STARTINDEX 0
-#else /* not TRILIBRARY */
-#define STARTINDEX 1
- int increment;
- int meshnumber;
-#endif /* not TRILIBRARY */
-#ifndef CDT_ONLY
- int k;
- char workstring[FILENAMESIZE];
-#endif
- int i, j;
-
- b->poly = b->refine = b->quality = 0;
- b->vararea = b->fixedarea = b->usertest = 0;
- b->regionattrib = b->convex = b->weighted = b->jettison = 0;
- b->firstnumber = 1;
- b->edgesout = b->voronoi = b->neighbors = b->geomview = 0;
- b->nobound = b->nopolywritten = b->nonodewritten = b->noelewritten = 0;
- b->noiterationnum = 0;
- b->noholes = b->noexact = 0;
- b->incremental = b->sweepline = 0;
- b->dwyer = 1;
- b->splitseg = 0;
- b->docheck = 0;
- b->nobisect = 0;
- b->conformdel = 0;
- b->steiner = -1;
- b->order = 1;
- b->minangle = 0.0;
- b->maxarea = -1.0;
- b->quiet = b->verbose = 0;
-#ifndef TRILIBRARY
- b->innodefilename[0] = '\0';
-#endif /* not TRILIBRARY */
-
- for (i = STARTINDEX; i < argc; i++) {
-#ifndef TRILIBRARY
- if (argv[i][0] == '-') {
-#endif /* not TRILIBRARY */
- for (j = STARTINDEX; argv[i][j] != '\0'; j++) {
- if (argv[i][j] == 'p') {
- b->poly = 1;
- }
-#ifndef CDT_ONLY
- if (argv[i][j] == 'r') {
- b->refine = 1;
- }
- if (argv[i][j] == 'q') {
- b->quality = 1;
- if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
- (argv[i][j + 1] == '.')) {
- k = 0;
- while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
- (argv[i][j + 1] == '.')) {
- j++;
- workstring[k] = argv[i][j];
- k++;
- }
- workstring[k] = '\0';
- b->minangle = (REAL) strtod(workstring, (char **) NULL);
- } else {
- b->minangle = 20.0;
- }
- }
- if (argv[i][j] == 'a') {
- b->quality = 1;
- if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
- (argv[i][j + 1] == '.')) {
- b->fixedarea = 1;
- k = 0;
- while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
- (argv[i][j + 1] == '.')) {
- j++;
- workstring[k] = argv[i][j];
- k++;
- }
- workstring[k] = '\0';
- b->maxarea = (REAL) strtod(workstring, (char **) NULL);
- if (b->maxarea <= 0.0) {
- printf("Error: Maximum area must be greater than zero.\n");
- triexit(1);
- }
- } else {
- b->vararea = 1;
- }
- }
- if (argv[i][j] == 'u') {
- b->quality = 1;
- b->usertest = 1;
- }
-#endif /* not CDT_ONLY */
- if (argv[i][j] == 'A') {
- b->regionattrib = 1;
- }
- if (argv[i][j] == 'c') {
- b->convex = 1;
- }
- if (argv[i][j] == 'w') {
- b->weighted = 1;
- }
- if (argv[i][j] == 'W') {
- b->weighted = 2;
- }
- if (argv[i][j] == 'j') {
- b->jettison = 1;
- }
- if (argv[i][j] == 'z') {
- b->firstnumber = 0;
- }
- if (argv[i][j] == 'e') {
- b->edgesout = 1;
- }
- if (argv[i][j] == 'v') {
- b->voronoi = 1;
- }
- if (argv[i][j] == 'n') {
- b->neighbors = 1;
- }
- if (argv[i][j] == 'g') {
- b->geomview = 1;
- }
- if (argv[i][j] == 'B') {
- b->nobound = 1;
- }
- if (argv[i][j] == 'P') {
- b->nopolywritten = 1;
- }
- if (argv[i][j] == 'N') {
- b->nonodewritten = 1;
- }
- if (argv[i][j] == 'E') {
- b->noelewritten = 1;
- }
-#ifndef TRILIBRARY
- if (argv[i][j] == 'I') {
- b->noiterationnum = 1;
- }
-#endif /* not TRILIBRARY */
- if (argv[i][j] == 'O') {
- b->noholes = 1;
- }
- if (argv[i][j] == 'X') {
- b->noexact = 1;
- }
- if (argv[i][j] == 'o') {
- if (argv[i][j + 1] == '2') {
- j++;
- b->order = 2;
- }
- }
-#ifndef CDT_ONLY
- if (argv[i][j] == 'Y') {
- b->nobisect++;
- }
- if (argv[i][j] == 'S') {
- b->steiner = 0;
- while ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) {
- j++;
- b->steiner = b->steiner * 10 + (int) (argv[i][j] - '0');
- }
- }
-#endif /* not CDT_ONLY */
-#ifndef REDUCED
- if (argv[i][j] == 'i') {
- b->incremental = 1;
- }
- if (argv[i][j] == 'F') {
- b->sweepline = 1;
- }
-#endif /* not REDUCED */
- if (argv[i][j] == 'l') {
- b->dwyer = 0;
- }
-#ifndef REDUCED
-#ifndef CDT_ONLY
- if (argv[i][j] == 's') {
- b->splitseg = 1;
- }
- if ((argv[i][j] == 'D') || (argv[i][j] == 'L')) {
- b->quality = 1;
- b->conformdel = 1;
- }
-#endif /* not CDT_ONLY */
- if (argv[i][j] == 'C') {
- b->docheck = 1;
- }
-#endif /* not REDUCED */
- if (argv[i][j] == 'Q') {
- b->quiet = 1;
- }
- if (argv[i][j] == 'V') {
- b->verbose++;
- }
-#ifndef TRILIBRARY
- if ((argv[i][j] == 'h') || (argv[i][j] == 'H') ||
- (argv[i][j] == '?')) {
- info();
- }
-#endif /* not TRILIBRARY */
- }
-#ifndef TRILIBRARY
- } else {
- strncpy(b->innodefilename, argv[i], FILENAMESIZE - 1);
- b->innodefilename[FILENAMESIZE - 1] = '\0';
- }
-#endif /* not TRILIBRARY */
- }
-#ifndef TRILIBRARY
- if (b->innodefilename[0] == '\0') {
- syntax();
- }
- if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 5], ".node")) {
- b->innodefilename[strlen(b->innodefilename) - 5] = '\0';
- }
- if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 5], ".poly")) {
- b->innodefilename[strlen(b->innodefilename) - 5] = '\0';
- b->poly = 1;
- }
-#ifndef CDT_ONLY
- if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 4], ".ele")) {
- b->innodefilename[strlen(b->innodefilename) - 4] = '\0';
- b->refine = 1;
- }
- if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 5], ".area")) {
- b->innodefilename[strlen(b->innodefilename) - 5] = '\0';
- b->refine = 1;
- b->quality = 1;
- b->vararea = 1;
- }
-#endif /* not CDT_ONLY */
-#endif /* not TRILIBRARY */
- b->usesegments = b->poly || b->refine || b->quality || b->convex;
- b->goodangle = cos(b->minangle * PI / 180.0);
- if (b->goodangle == 1.0) {
- b->offconstant = 0.0;
- } else {
- b->offconstant = 0.475 * sqrt((1.0 + b->goodangle) / (1.0 - b->goodangle));
- }
- b->goodangle *= b->goodangle;
- if (b->refine && b->noiterationnum) {
- printf(
- "Error: You cannot use the -I switch when refining a triangulation.\n");
- triexit(1);
- }
- /* Be careful not to allocate space for element area constraints that */
- /* will never be assigned any value (other than the default -1.0). */
- if (!b->refine && !b->poly) {
- b->vararea = 0;
- }
- /* Be careful not to add an extra attribute to each element unless the */
- /* input supports it (PSLG in, but not refining a preexisting mesh). */
- if (b->refine || !b->poly) {
- b->regionattrib = 0;
- }
- /* Regular/weighted triangulations are incompatible with PSLGs */
- /* and meshing. */
- if (b->weighted && (b->poly || b->quality)) {
- b->weighted = 0;
- if (!b->quiet) {
- printf("Warning: weighted triangulations (-w, -W) are incompatible\n");
- printf(" with PSLGs (-p) and meshing (-q, -a, -u). Weights ignored.\n"
- );
- }
- }
- if (b->jettison && b->nonodewritten && !b->quiet) {
- printf("Warning: -j and -N switches are somewhat incompatible.\n");
- printf(" If any vertices are jettisoned, you will need the output\n");
- printf(" .node file to reconstruct the new node indices.");
- }
-
-#ifndef TRILIBRARY
- strcpy(b->inpolyfilename, b->innodefilename);
- strcpy(b->inelefilename, b->innodefilename);
- strcpy(b->areafilename, b->innodefilename);
- increment = 0;
- strcpy(workstring, b->innodefilename);
- j = 1;
- while (workstring[j] != '\0') {
- if ((workstring[j] == '.') && (workstring[j + 1] != '\0')) {
- increment = j + 1;
- }
- j++;
- }
- meshnumber = 0;
- if (increment > 0) {
- j = increment;
- do {
- if ((workstring[j] >= '0') && (workstring[j] <= '9')) {
- meshnumber = meshnumber * 10 + (int) (workstring[j] - '0');
- } else {
- increment = 0;
- }
- j++;
- } while (workstring[j] != '\0');
- }
- if (b->noiterationnum) {
- strcpy(b->outnodefilename, b->innodefilename);
- strcpy(b->outelefilename, b->innodefilename);
- strcpy(b->edgefilename, b->innodefilename);
- strcpy(b->vnodefilename, b->innodefilename);
- strcpy(b->vedgefilename, b->innodefilename);
- strcpy(b->neighborfilename, b->innodefilename);
- strcpy(b->offfilename, b->innodefilename);
- strcat(b->outnodefilename, ".node");
- strcat(b->outelefilename, ".ele");
- strcat(b->edgefilename, ".edge");
- strcat(b->vnodefilename, ".v.node");
- strcat(b->vedgefilename, ".v.edge");
- strcat(b->neighborfilename, ".neigh");
- strcat(b->offfilename, ".off");
- } else if (increment == 0) {
- strcpy(b->outnodefilename, b->innodefilename);
- strcpy(b->outpolyfilename, b->innodefilename);
- strcpy(b->outelefilename, b->innodefilename);
- strcpy(b->edgefilename, b->innodefilename);
- strcpy(b->vnodefilename, b->innodefilename);
- strcpy(b->vedgefilename, b->innodefilename);
- strcpy(b->neighborfilename, b->innodefilename);
- strcpy(b->offfilename, b->innodefilename);
- strcat(b->outnodefilename, ".1.node");
- strcat(b->outpolyfilename, ".1.poly");
- strcat(b->outelefilename, ".1.ele");
- strcat(b->edgefilename, ".1.edge");
- strcat(b->vnodefilename, ".1.v.node");
- strcat(b->vedgefilename, ".1.v.edge");
- strcat(b->neighborfilename, ".1.neigh");
- strcat(b->offfilename, ".1.off");
- } else {
- workstring[increment] = '%';
- workstring[increment + 1] = 'd';
- workstring[increment + 2] = '\0';
- sprintf(b->outnodefilename, workstring, meshnumber + 1);
- strcpy(b->outpolyfilename, b->outnodefilename);
- strcpy(b->outelefilename, b->outnodefilename);
- strcpy(b->edgefilename, b->outnodefilename);
- strcpy(b->vnodefilename, b->outnodefilename);
- strcpy(b->vedgefilename, b->outnodefilename);
- strcpy(b->neighborfilename, b->outnodefilename);
- strcpy(b->offfilename, b->outnodefilename);
- strcat(b->outnodefilename, ".node");
- strcat(b->outpolyfilename, ".poly");
- strcat(b->outelefilename, ".ele");
- strcat(b->edgefilename, ".edge");
- strcat(b->vnodefilename, ".v.node");
- strcat(b->vedgefilename, ".v.edge");
- strcat(b->neighborfilename, ".neigh");
- strcat(b->offfilename, ".off");
- }
- strcat(b->innodefilename, ".node");
- strcat(b->inpolyfilename, ".poly");
- strcat(b->inelefilename, ".ele");
- strcat(b->areafilename, ".area");
-#endif /* not TRILIBRARY */
-}
-
-/** **/
-/** **/
-/********* User interaction routines begin here *********/
-
-/********* Debugging routines begin here *********/
-/** **/
-/** **/
-
-/*****************************************************************************/
-/* */
-/* printtriangle() Print out the details of an oriented triangle. */
-/* */
-/* I originally wrote this procedure to simplify debugging; it can be */
-/* called directly from the debugger, and presents information about an */
-/* oriented triangle in digestible form. It's also used when the */
-/* highest level of verbosity (`-VVV') is specified. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-void printtriangle(struct mesh *m, struct behavior *b, struct otri *t)
-#else /* not ANSI_DECLARATORS */
-void printtriangle(m, b, t)
-struct mesh *m;
-struct behavior *b;
-struct otri *t;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct otri printtri;
- struct osub printsh;
- vertex printvertex;
-
- printf("triangle x%lx with orientation %d:\n", (unsigned long) t->tri,
- t->orient);
- decode(t->tri[0], printtri);
- if (printtri.tri == m->dummytri) {
- printf(" [0] = Outer space\n");
- } else {
- printf(" [0] = x%lx %d\n", (unsigned long) printtri.tri,
- printtri.orient);
- }
- decode(t->tri[1], printtri);
- if (printtri.tri == m->dummytri) {
- printf(" [1] = Outer space\n");
- } else {
- printf(" [1] = x%lx %d\n", (unsigned long) printtri.tri,
- printtri.orient);
- }
- decode(t->tri[2], printtri);
- if (printtri.tri == m->dummytri) {
- printf(" [2] = Outer space\n");
- } else {
- printf(" [2] = x%lx %d\n", (unsigned long) printtri.tri,
- printtri.orient);
- }
-
- org(*t, printvertex);
- if (printvertex == (vertex) NULL)
- printf(" Origin[%d] = NULL\n", (t->orient + 1) % 3 + 3);
- else
- printf(" Origin[%d] = x%lx (%.12g, %.12g)\n",
- (t->orient + 1) % 3 + 3, (unsigned long) printvertex,
- printvertex[0], printvertex[1]);
- dest(*t, printvertex);
- if (printvertex == (vertex) NULL)
- printf(" Dest [%d] = NULL\n", (t->orient + 2) % 3 + 3);
- else
- printf(" Dest [%d] = x%lx (%.12g, %.12g)\n",
- (t->orient + 2) % 3 + 3, (unsigned long) printvertex,
- printvertex[0], printvertex[1]);
- apex(*t, printvertex);
- if (printvertex == (vertex) NULL)
- printf(" Apex [%d] = NULL\n", t->orient + 3);
- else
- printf(" Apex [%d] = x%lx (%.12g, %.12g)\n",
- t->orient + 3, (unsigned long) printvertex,
- printvertex[0], printvertex[1]);
-
- if (b->usesegments) {
- sdecode(t->tri[6], printsh);
- if (printsh.ss != m->dummysub) {
- printf(" [6] = x%lx %d\n", (unsigned long) printsh.ss,
- printsh.ssorient);
- }
- sdecode(t->tri[7], printsh);
- if (printsh.ss != m->dummysub) {
- printf(" [7] = x%lx %d\n", (unsigned long) printsh.ss,
- printsh.ssorient);
- }
- sdecode(t->tri[8], printsh);
- if (printsh.ss != m->dummysub) {
- printf(" [8] = x%lx %d\n", (unsigned long) printsh.ss,
- printsh.ssorient);
- }
- }
-
- if (b->vararea) {
- printf(" Area constraint: %.4g\n", areabound(*t));
- }
-}
-
-/*****************************************************************************/
-/* */
-/* printsubseg() Print out the details of an oriented subsegment. */
-/* */
-/* I originally wrote this procedure to simplify debugging; it can be */
-/* called directly from the debugger, and presents information about an */
-/* oriented subsegment in digestible form. It's also used when the highest */
-/* level of verbosity (`-VVV') is specified. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-void printsubseg(struct mesh *m, struct behavior *b, struct osub *s)
-#else /* not ANSI_DECLARATORS */
-void printsubseg(m, b, s)
-struct mesh *m;
-struct behavior *b;
-struct osub *s;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct osub printsh;
- struct otri printtri;
- vertex printvertex;
-
- printf("subsegment x%lx with orientation %d and mark %d:\n",
- (unsigned long) s->ss, s->ssorient, mark(*s));
- sdecode(s->ss[0], printsh);
- if (printsh.ss == m->dummysub) {
- printf(" [0] = No subsegment\n");
- } else {
- printf(" [0] = x%lx %d\n", (unsigned long) printsh.ss,
- printsh.ssorient);
- }
- sdecode(s->ss[1], printsh);
- if (printsh.ss == m->dummysub) {
- printf(" [1] = No subsegment\n");
- } else {
- printf(" [1] = x%lx %d\n", (unsigned long) printsh.ss,
- printsh.ssorient);
- }
-
- sorg(*s, printvertex);
- if (printvertex == (vertex) NULL)
- printf(" Origin[%d] = NULL\n", 2 + s->ssorient);
- else
- printf(" Origin[%d] = x%lx (%.12g, %.12g)\n",
- 2 + s->ssorient, (unsigned long) printvertex,
- printvertex[0], printvertex[1]);
- sdest(*s, printvertex);
- if (printvertex == (vertex) NULL)
- printf(" Dest [%d] = NULL\n", 3 - s->ssorient);
- else
- printf(" Dest [%d] = x%lx (%.12g, %.12g)\n",
- 3 - s->ssorient, (unsigned long) printvertex,
- printvertex[0], printvertex[1]);
-
- decode(s->ss[6], printtri);
- if (printtri.tri == m->dummytri) {
- printf(" [6] = Outer space\n");
- } else {
- printf(" [6] = x%lx %d\n", (unsigned long) printtri.tri,
- printtri.orient);
- }
- decode(s->ss[7], printtri);
- if (printtri.tri == m->dummytri) {
- printf(" [7] = Outer space\n");
- } else {
- printf(" [7] = x%lx %d\n", (unsigned long) printtri.tri,
- printtri.orient);
- }
-
- segorg(*s, printvertex);
- if (printvertex == (vertex) NULL)
- printf(" Segment origin[%d] = NULL\n", 4 + s->ssorient);
- else
- printf(" Segment origin[%d] = x%lx (%.12g, %.12g)\n",
- 4 + s->ssorient, (unsigned long) printvertex,
- printvertex[0], printvertex[1]);
- segdest(*s, printvertex);
- if (printvertex == (vertex) NULL)
- printf(" Segment dest [%d] = NULL\n", 5 - s->ssorient);
- else
- printf(" Segment dest [%d] = x%lx (%.12g, %.12g)\n",
- 5 - s->ssorient, (unsigned long) printvertex,
- printvertex[0], printvertex[1]);
-}
-
-/** **/
-/** **/
-/********* Debugging routines end here *********/
-
-/********* Memory management routines begin here *********/
-/** **/
-/** **/
-
-/*****************************************************************************/
-/* */
-/* poolzero() Set all of a pool's fields to zero. */
-/* */
-/* This procedure should never be called on a pool that has any memory */
-/* allocated to it, as that memory would leak. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-void poolzero(struct memorypool *pool)
-#else /* not ANSI_DECLARATORS */
-void poolzero(pool)
-struct memorypool *pool;
-#endif /* not ANSI_DECLARATORS */
-
-{
- pool->firstblock = (VOID **) NULL;
- pool->nowblock = (VOID **) NULL;
- pool->nextitem = (VOID *) NULL;
- pool->deaditemstack = (VOID *) NULL;
- pool->pathblock = (VOID **) NULL;
- pool->pathitem = (VOID *) NULL;
- pool->alignbytes = 0;
- pool->itembytes = 0;
- pool->itemsperblock = 0;
- pool->itemsfirstblock = 0;
- pool->items = 0;
- pool->maxitems = 0;
- pool->unallocateditems = 0;
- pool->pathitemsleft = 0;
-}
-
-/*****************************************************************************/
-/* */
-/* poolrestart() Deallocate all items in a pool. */
-/* */
-/* The pool is returned to its starting state, except that no memory is */
-/* freed to the operating system. Rather, the previously allocated blocks */
-/* are ready to be reused. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-void poolrestart(struct memorypool *pool)
-#else /* not ANSI_DECLARATORS */
-void poolrestart(pool)
-struct memorypool *pool;
-#endif /* not ANSI_DECLARATORS */
-
-{
- unsigned long alignptr;
-
- pool->items = 0;
- pool->maxitems = 0;
-
- /* Set the currently active block. */
- pool->nowblock = pool->firstblock;
- /* Find the first item in the pool. Increment by the size of (VOID *). */
- alignptr = (unsigned long) (pool->nowblock + 1);
- /* Align the item on an `alignbytes'-byte boundary. */
- pool->nextitem = (VOID *)
- (alignptr + (unsigned long) pool->alignbytes -
- (alignptr % (unsigned long) pool->alignbytes));
- /* There are lots of unallocated items left in this block. */
- pool->unallocateditems = pool->itemsfirstblock;
- /* The stack of deallocated items is empty. */
- pool->deaditemstack = (VOID *) NULL;
-}
-
-/*****************************************************************************/
-/* */
-/* poolinit() Initialize a pool of memory for allocation of items. */
-/* */
-/* This routine initializes the machinery for allocating items. A `pool' */
-/* is created whose records have size at least `bytecount'. Items will be */
-/* allocated in `itemcount'-item blocks. Each item is assumed to be a */
-/* collection of words, and either pointers or floating-point values are */
-/* assumed to be the "primary" word type. (The "primary" word type is used */
-/* to determine alignment of items.) If `alignment' isn't zero, all items */
-/* will be `alignment'-byte aligned in memory. `alignment' must be either */
-/* a multiple or a factor of the primary word size; powers of two are safe. */
-/* `alignment' is normally used to create a few unused bits at the bottom */
-/* of each item's pointer, in which information may be stored. */
-/* */
-/* Don't change this routine unless you understand it. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-void poolinit(struct memorypool *pool, int bytecount, int itemcount,
- int firstitemcount, int alignment)
-#else /* not ANSI_DECLARATORS */
-void poolinit(pool, bytecount, itemcount, firstitemcount, alignment)
-struct memorypool *pool;
-int bytecount;
-int itemcount;
-int firstitemcount;
-int alignment;
-#endif /* not ANSI_DECLARATORS */
-
-{
- /* Find the proper alignment, which must be at least as large as: */
- /* - The parameter `alignment'. */
- /* - sizeof(VOID *), so the stack of dead items can be maintained */
- /* without unaligned accesses. */
- if (alignment > sizeof(VOID *)) {
- pool->alignbytes = alignment;
- } else {
- pool->alignbytes = sizeof(VOID *);
- }
- pool->itembytes = ((bytecount - 1) / pool->alignbytes + 1) *
- pool->alignbytes;
- pool->itemsperblock = itemcount;
- if (firstitemcount == 0) {
- pool->itemsfirstblock = itemcount;
- } else {
- pool->itemsfirstblock = firstitemcount;
- }
-
- /* Allocate a block of items. Space for `itemsfirstblock' items and one */
- /* pointer (to point to the next block) are allocated, as well as space */
- /* to ensure alignment of the items. */
- pool->firstblock = (VOID **)
- trimalloc(pool->itemsfirstblock * pool->itembytes + (int) sizeof(VOID *) +
- pool->alignbytes);
- /* Set the next block pointer to NULL. */
- *(pool->firstblock) = (VOID *) NULL;
- poolrestart(pool);
-}
-
-/*****************************************************************************/
-/* */
-/* pooldeinit() Free to the operating system all memory taken by a pool. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-void pooldeinit(struct memorypool *pool)
-#else /* not ANSI_DECLARATORS */
-void pooldeinit(pool)
-struct memorypool *pool;
-#endif /* not ANSI_DECLARATORS */
-
-{
- while (pool->firstblock != (VOID **) NULL) {
- pool->nowblock = (VOID **) *(pool->firstblock);
- trifree((VOID *) pool->firstblock);
- pool->firstblock = pool->nowblock;
- }
-}
-
-/*****************************************************************************/
-/* */
-/* poolalloc() Allocate space for an item. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-VOID *poolalloc(struct memorypool *pool)
-#else /* not ANSI_DECLARATORS */
-VOID *poolalloc(pool)
-struct memorypool *pool;
-#endif /* not ANSI_DECLARATORS */
-
-{
- VOID *newitem;
- VOID **newblock;
- unsigned long alignptr;
-
- /* First check the linked list of dead items. If the list is not */
- /* empty, allocate an item from the list rather than a fresh one. */
- if (pool->deaditemstack != (VOID *) NULL) {
- newitem = pool->deaditemstack; /* Take first item in list. */
- pool->deaditemstack = * (VOID **) pool->deaditemstack;
- } else {
- /* Check if there are any free items left in the current block. */
- if (pool->unallocateditems == 0) {
- /* Check if another block must be allocated. */
- if (*(pool->nowblock) == (VOID *) NULL) {
- /* Allocate a new block of items, pointed to by the previous block. */
- newblock = (VOID **) trimalloc(pool->itemsperblock * pool->itembytes +
- (int) sizeof(VOID *) +
- pool->alignbytes);
- *(pool->nowblock) = (VOID *) newblock;
- /* The next block pointer is NULL. */
- *newblock = (VOID *) NULL;
- }
-
- /* Move to the new block. */
- pool->nowblock = (VOID **) *(pool->nowblock);
- /* Find the first item in the block. */
- /* Increment by the size of (VOID *). */
- alignptr = (unsigned long) (pool->nowblock + 1);
- /* Align the item on an `alignbytes'-byte boundary. */
- pool->nextitem = (VOID *)
- (alignptr + (unsigned long) pool->alignbytes -
- (alignptr % (unsigned long) pool->alignbytes));
- /* There are lots of unallocated items left in this block. */
- pool->unallocateditems = pool->itemsperblock;
- }
-
- /* Allocate a new item. */
- newitem = pool->nextitem;
- /* Advance `nextitem' pointer to next free item in block. */
- pool->nextitem = (VOID *) ((char *) pool->nextitem + pool->itembytes);
- pool->unallocateditems--;
- pool->maxitems++;
- }
- pool->items++;
- return newitem;
-}
-
-/*****************************************************************************/
-/* */
-/* pooldealloc() Deallocate space for an item. */
-/* */
-/* The deallocated space is stored in a queue for later reuse. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-void pooldealloc(struct memorypool *pool, VOID *dyingitem)
-#else /* not ANSI_DECLARATORS */
-void pooldealloc(pool, dyingitem)
-struct memorypool *pool;
-VOID *dyingitem;
-#endif /* not ANSI_DECLARATORS */
-
-{
- /* Push freshly killed item onto stack. */
- *((VOID **) dyingitem) = pool->deaditemstack;
- pool->deaditemstack = dyingitem;
- pool->items--;
-}
-
-/*****************************************************************************/
-/* */
-/* traversalinit() Prepare to traverse the entire list of items. */
-/* */
-/* This routine is used in conjunction with traverse(). */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-void traversalinit(struct memorypool *pool)
-#else /* not ANSI_DECLARATORS */
-void traversalinit(pool)
-struct memorypool *pool;
-#endif /* not ANSI_DECLARATORS */
-
-{
- unsigned long alignptr;
-
- /* Begin the traversal in the first block. */
- pool->pathblock = pool->firstblock;
- /* Find the first item in the block. Increment by the size of (VOID *). */
- alignptr = (unsigned long) (pool->pathblock + 1);
- /* Align with item on an `alignbytes'-byte boundary. */
- pool->pathitem = (VOID *)
- (alignptr + (unsigned long) pool->alignbytes -
- (alignptr % (unsigned long) pool->alignbytes));
- /* Set the number of items left in the current block. */
- pool->pathitemsleft = pool->itemsfirstblock;
-}
-
-/*****************************************************************************/
-/* */
-/* traverse() Find the next item in the list. */
-/* */
-/* This routine is used in conjunction with traversalinit(). Be forewarned */
-/* that this routine successively returns all items in the list, including */
-/* deallocated ones on the deaditemqueue. It's up to you to figure out */
-/* which ones are actually dead. Why? I don't want to allocate extra */
-/* space just to demarcate dead items. It can usually be done more */
-/* space-efficiently by a routine that knows something about the structure */
-/* of the item. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-VOID *traverse(struct memorypool *pool)
-#else /* not ANSI_DECLARATORS */
-VOID *traverse(pool)
-struct memorypool *pool;
-#endif /* not ANSI_DECLARATORS */
-
-{
- VOID *newitem;
- unsigned long alignptr;
-
- /* Stop upon exhausting the list of items. */
- if (pool->pathitem == pool->nextitem) {
- return (VOID *) NULL;
- }
-
- /* Check whether any untraversed items remain in the current block. */
- if (pool->pathitemsleft == 0) {
- /* Find the next block. */
- pool->pathblock = (VOID **) *(pool->pathblock);
- /* Find the first item in the block. Increment by the size of (VOID *). */
- alignptr = (unsigned long) (pool->pathblock + 1);
- /* Align with item on an `alignbytes'-byte boundary. */
- pool->pathitem = (VOID *)
- (alignptr + (unsigned long) pool->alignbytes -
- (alignptr % (unsigned long) pool->alignbytes));
- /* Set the number of items left in the current block. */
- pool->pathitemsleft = pool->itemsperblock;
- }
-
- newitem = pool->pathitem;
- /* Find the next item in the block. */
- pool->pathitem = (VOID *) ((char *) pool->pathitem + pool->itembytes);
- pool->pathitemsleft--;
- return newitem;
-}
-
-/*****************************************************************************/
-/* */
-/* dummyinit() Initialize the triangle that fills "outer space" and the */
-/* omnipresent subsegment. */
-/* */
-/* The triangle that fills "outer space," called `dummytri', is pointed to */
-/* by every triangle and subsegment on a boundary (be it outer or inner) of */
-/* the triangulation. Also, `dummytri' points to one of the triangles on */
-/* the convex hull (until the holes and concavities are carved), making it */
-/* possible to find a starting triangle for point location. */
-/* */
-/* The omnipresent subsegment, `dummysub', is pointed to by every triangle */
-/* or subsegment that doesn't have a full complement of real subsegments */
-/* to point to. */
-/* */
-/* `dummytri' and `dummysub' are generally required to fulfill only a few */
-/* invariants: their vertices must remain NULL and `dummytri' must always */
-/* be bonded (at offset zero) to some triangle on the convex hull of the */
-/* mesh, via a boundary edge. Otherwise, the connections of `dummytri' and */
-/* `dummysub' may change willy-nilly. This makes it possible to avoid */
-/* writing a good deal of special-case code (in the edge flip, for example) */
-/* for dealing with the boundary of the mesh, places where no subsegment is */
-/* present, and so forth. Other entities are frequently bonded to */
-/* `dummytri' and `dummysub' as if they were real mesh entities, with no */
-/* harm done. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-void dummyinit(struct mesh *m, struct behavior *b, int trianglebytes,
- int subsegbytes)
-#else /* not ANSI_DECLARATORS */
-void dummyinit(m, b, trianglebytes, subsegbytes)
-struct mesh *m;
-struct behavior *b;
-int trianglebytes;
-int subsegbytes;
-#endif /* not ANSI_DECLARATORS */
-
-{
- unsigned long alignptr;
-
- /* Set up `dummytri', the `triangle' that occupies "outer space." */
- m->dummytribase = (triangle *) trimalloc(trianglebytes +
- m->triangles.alignbytes);
- /* Align `dummytri' on a `triangles.alignbytes'-byte boundary. */
- alignptr = (unsigned long) m->dummytribase;
- m->dummytri = (triangle *)
- (alignptr + (unsigned long) m->triangles.alignbytes -
- (alignptr % (unsigned long) m->triangles.alignbytes));
- /* Initialize the three adjoining triangles to be "outer space." These */
- /* will eventually be changed by various bonding operations, but their */
- /* values don't really matter, as long as they can legally be */
- /* dereferenced. */
- m->dummytri[0] = (triangle) m->dummytri;
- m->dummytri[1] = (triangle) m->dummytri;
- m->dummytri[2] = (triangle) m->dummytri;
- /* Three NULL vertices. */
- m->dummytri[3] = (triangle) NULL;
- m->dummytri[4] = (triangle) NULL;
- m->dummytri[5] = (triangle) NULL;
-
- if (b->usesegments) {
- /* Set up `dummysub', the omnipresent subsegment pointed to by any */
- /* triangle side or subsegment end that isn't attached to a real */
- /* subsegment. */
- m->dummysubbase = (subseg *) trimalloc(subsegbytes +
- m->subsegs.alignbytes);
- /* Align `dummysub' on a `subsegs.alignbytes'-byte boundary. */
- alignptr = (unsigned long) m->dummysubbase;
- m->dummysub = (subseg *)
- (alignptr + (unsigned long) m->subsegs.alignbytes -
- (alignptr % (unsigned long) m->subsegs.alignbytes));
- /* Initialize the two adjoining subsegments to be the omnipresent */
- /* subsegment. These will eventually be changed by various bonding */
- /* operations, but their values don't really matter, as long as they */
- /* can legally be dereferenced. */
- m->dummysub[0] = (subseg) m->dummysub;
- m->dummysub[1] = (subseg) m->dummysub;
- /* Four NULL vertices. */
- m->dummysub[2] = (subseg) NULL;
- m->dummysub[3] = (subseg) NULL;
- m->dummysub[4] = (subseg) NULL;
- m->dummysub[5] = (subseg) NULL;
- /* Initialize the two adjoining triangles to be "outer space." */
- m->dummysub[6] = (subseg) m->dummytri;
- m->dummysub[7] = (subseg) m->dummytri;
- /* Set the boundary marker to zero. */
- * (int *) (m->dummysub + 8) = 0;
-
- /* Initialize the three adjoining subsegments of `dummytri' to be */
- /* the omnipresent subsegment. */
- m->dummytri[6] = (triangle) m->dummysub;
- m->dummytri[7] = (triangle) m->dummysub;
- m->dummytri[8] = (triangle) m->dummysub;
- }
-}
-
-/*****************************************************************************/
-/* */
-/* initializevertexpool() Calculate the size of the vertex data structure */
-/* and initialize its memory pool. */
-/* */
-/* This routine also computes the `vertexmarkindex' and `vertex2triindex' */
-/* indices used to find values within each vertex. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-void initializevertexpool(struct mesh *m, struct behavior *b)
-#else /* not ANSI_DECLARATORS */
-void initializevertexpool(m, b)
-struct mesh *m;
-struct behavior *b;
-#endif /* not ANSI_DECLARATORS */
-
-{
- int vertexsize;
-
- /* The index within each vertex at which the boundary marker is found, */
- /* followed by the vertex type. Ensure the vertex marker is aligned to */
- /* a sizeof(int)-byte address. */
- m->vertexmarkindex = ((m->mesh_dim + m->nextras) * sizeof(REAL) +
- sizeof(int) - 1) /
- sizeof(int);
- vertexsize = (m->vertexmarkindex + 2) * sizeof(int);
- if (b->poly) {
- /* The index within each vertex at which a triangle pointer is found. */
- /* Ensure the pointer is aligned to a sizeof(triangle)-byte address. */
- m->vertex2triindex = (vertexsize + sizeof(triangle) - 1) /
- sizeof(triangle);
- vertexsize = (m->vertex2triindex + 1) * sizeof(triangle);
- }
-
- /* Initialize the pool of vertices. */
- poolinit(&m->vertices, vertexsize, VERTEXPERBLOCK,
- m->invertices > VERTEXPERBLOCK ? m->invertices : VERTEXPERBLOCK,
- sizeof(REAL));
-}
-
-/*****************************************************************************/
-/* */
-/* initializetrisubpools() Calculate the sizes of the triangle and */
-/* subsegment data structures and initialize */
-/* their memory pools. */
-/* */
-/* This routine also computes the `highorderindex', `elemattribindex', and */
-/* `areaboundindex' indices used to find values within each triangle. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-void initializetrisubpools(struct mesh *m, struct behavior *b)
-#else /* not ANSI_DECLARATORS */
-void initializetrisubpools(m, b)
-struct mesh *m;
-struct behavior *b;
-#endif /* not ANSI_DECLARATORS */
-
-{
- int trisize;
-
- /* The index within each triangle at which the extra nodes (above three) */
- /* associated with high order elements are found. There are three */
- /* pointers to other triangles, three pointers to corners, and possibly */
- /* three pointers to subsegments before the extra nodes. */
- m->highorderindex = 6 + (b->usesegments * 3);
- /* The number of bytes occupied by a triangle. */
- trisize = ((b->order + 1) * (b->order + 2) / 2 + (m->highorderindex - 3)) *
- sizeof(triangle);
- /* The index within each triangle at which its attributes are found, */
- /* where the index is measured in REALs. */
- m->elemattribindex = (trisize + sizeof(REAL) - 1) / sizeof(REAL);
- /* The index within each triangle at which the maximum area constraint */
- /* is found, where the index is measured in REALs. Note that if the */
- /* `regionattrib' flag is set, an additional attribute will be added. */
- m->areaboundindex = m->elemattribindex + m->eextras + b->regionattrib;
- /* If triangle attributes or an area bound are needed, increase the number */
- /* of bytes occupied by a triangle. */
- if (b->vararea) {
- trisize = (m->areaboundindex + 1) * sizeof(REAL);
- } else if (m->eextras + b->regionattrib > 0) {
- trisize = m->areaboundindex * sizeof(REAL);
- }
- /* If a Voronoi diagram or triangle neighbor graph is requested, make */
- /* sure there's room to store an integer index in each triangle. This */
- /* integer index can occupy the same space as the subsegment pointers */
- /* or attributes or area constraint or extra nodes. */
- if ((b->voronoi || b->neighbors) &&
- (trisize < 6 * sizeof(triangle) + sizeof(int))) {
- trisize = 6 * sizeof(triangle) + sizeof(int);
- }
-
- /* Having determined the memory size of a triangle, initialize the pool. */
- poolinit(&m->triangles, trisize, TRIPERBLOCK,
- (2 * m->invertices - 2) > TRIPERBLOCK ? (2 * m->invertices - 2) :
- TRIPERBLOCK, 4);
-
- if (b->usesegments) {
- /* Initialize the pool of subsegments. Take into account all eight */
- /* pointers and one boundary marker. */
- poolinit(&m->subsegs, 8 * sizeof(triangle) + sizeof(int),
- SUBSEGPERBLOCK, SUBSEGPERBLOCK, 4);
-
- /* Initialize the "outer space" triangle and omnipresent subsegment. */
- dummyinit(m, b, m->triangles.itembytes, m->subsegs.itembytes);
- } else {
- /* Initialize the "outer space" triangle. */
- dummyinit(m, b, m->triangles.itembytes, 0);
- }
-}
-
-/*****************************************************************************/
-/* */
-/* triangledealloc() Deallocate space for a triangle, marking it dead. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-void triangledealloc(struct mesh *m, triangle *dyingtriangle)
-#else /* not ANSI_DECLARATORS */
-void triangledealloc(m, dyingtriangle)
-struct mesh *m;
-triangle *dyingtriangle;
-#endif /* not ANSI_DECLARATORS */
-
-{
- /* Mark the triangle as dead. This makes it possible to detect dead */
- /* triangles when traversing the list of all triangles. */
- killtri(dyingtriangle);
- pooldealloc(&m->triangles, (VOID *) dyingtriangle);
-}
-
-/*****************************************************************************/
-/* */
-/* triangletraverse() Traverse the triangles, skipping dead ones. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-triangle *triangletraverse(struct mesh *m)
-#else /* not ANSI_DECLARATORS */
-triangle *triangletraverse(m)
-struct mesh *m;
-#endif /* not ANSI_DECLARATORS */
-
-{
- triangle *newtriangle;
-
- do {
- newtriangle = (triangle *) traverse(&m->triangles);
- if (newtriangle == (triangle *) NULL) {
- return (triangle *) NULL;
- }
- } while (deadtri(newtriangle)); /* Skip dead ones. */
- return newtriangle;
-}
-
-/*****************************************************************************/
-/* */
-/* subsegdealloc() Deallocate space for a subsegment, marking it dead. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-void subsegdealloc(struct mesh *m, subseg *dyingsubseg)
-#else /* not ANSI_DECLARATORS */
-void subsegdealloc(m, dyingsubseg)
-struct mesh *m;
-subseg *dyingsubseg;
-#endif /* not ANSI_DECLARATORS */
-
-{
- /* Mark the subsegment as dead. This makes it possible to detect dead */
- /* subsegments when traversing the list of all subsegments. */
- killsubseg(dyingsubseg);
- pooldealloc(&m->subsegs, (VOID *) dyingsubseg);
-}
-
-/*****************************************************************************/
-/* */
-/* subsegtraverse() Traverse the subsegments, skipping dead ones. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-subseg *subsegtraverse(struct mesh *m)
-#else /* not ANSI_DECLARATORS */
-subseg *subsegtraverse(m)
-struct mesh *m;
-#endif /* not ANSI_DECLARATORS */
-
-{
- subseg *newsubseg;
-
- do {
- newsubseg = (subseg *) traverse(&m->subsegs);
- if (newsubseg == (subseg *) NULL) {
- return (subseg *) NULL;
- }
- } while (deadsubseg(newsubseg)); /* Skip dead ones. */
- return newsubseg;
-}
-
-/*****************************************************************************/
-/* */
-/* vertexdealloc() Deallocate space for a vertex, marking it dead. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-void vertexdealloc(struct mesh *m, vertex dyingvertex)
-#else /* not ANSI_DECLARATORS */
-void vertexdealloc(m, dyingvertex)
-struct mesh *m;
-vertex dyingvertex;
-#endif /* not ANSI_DECLARATORS */
-
-{
- /* Mark the vertex as dead. This makes it possible to detect dead */
- /* vertices when traversing the list of all vertices. */
- setvertextype(dyingvertex, DEADVERTEX);
- pooldealloc(&m->vertices, (VOID *) dyingvertex);
-}
-
-/*****************************************************************************/
-/* */
-/* vertextraverse() Traverse the vertices, skipping dead ones. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-vertex vertextraverse(struct mesh *m)
-#else /* not ANSI_DECLARATORS */
-vertex vertextraverse(m)
-struct mesh *m;
-#endif /* not ANSI_DECLARATORS */
-
-{
- vertex newvertex;
-
- do {
- newvertex = (vertex) traverse(&m->vertices);
- if (newvertex == (vertex) NULL) {
- return (vertex) NULL;
- }
- } while (vertextype(newvertex) == DEADVERTEX); /* Skip dead ones. */
- return newvertex;
-}
-
-/*****************************************************************************/
-/* */
-/* badsubsegdealloc() Deallocate space for a bad subsegment, marking it */
-/* dead. */
-/* */
-/*****************************************************************************/
-
-#ifndef CDT_ONLY
-
-#ifdef ANSI_DECLARATORS
-void badsubsegdealloc(struct mesh *m, struct badsubseg *dyingseg)
-#else /* not ANSI_DECLARATORS */
-void badsubsegdealloc(m, dyingseg)
-struct mesh *m;
-struct badsubseg *dyingseg;
-#endif /* not ANSI_DECLARATORS */
-
-{
- /* Set subsegment's origin to NULL. This makes it possible to detect dead */
- /* badsubsegs when traversing the list of all badsubsegs . */
- dyingseg->subsegorg = (vertex) NULL;
- pooldealloc(&m->badsubsegs, (VOID *) dyingseg);
-}
-
-#endif /* not CDT_ONLY */
-
-/*****************************************************************************/
-/* */
-/* badsubsegtraverse() Traverse the bad subsegments, skipping dead ones. */
-/* */
-/*****************************************************************************/
-
-#ifndef CDT_ONLY
-
-#ifdef ANSI_DECLARATORS
-struct badsubseg *badsubsegtraverse(struct mesh *m)
-#else /* not ANSI_DECLARATORS */
-struct badsubseg *badsubsegtraverse(m)
-struct mesh *m;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct badsubseg *newseg;
-
- do {
- newseg = (struct badsubseg *) traverse(&m->badsubsegs);
- if (newseg == (struct badsubseg *) NULL) {
- return (struct badsubseg *) NULL;
- }
- } while (newseg->subsegorg == (vertex) NULL); /* Skip dead ones. */
- return newseg;
-}
-
-#endif /* not CDT_ONLY */
-
-/*****************************************************************************/
-/* */
-/* getvertex() Get a specific vertex, by number, from the list. */
-/* */
-/* The first vertex is number 'firstnumber'. */
-/* */
-/* Note that this takes O(n) time (with a small constant, if VERTEXPERBLOCK */
-/* is large). I don't care to take the trouble to make it work in constant */
-/* time. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-vertex getvertex(struct mesh *m, struct behavior *b, int number)
-#else /* not ANSI_DECLARATORS */
-vertex getvertex(m, b, number)
-struct mesh *m;
-struct behavior *b;
-int number;
-#endif /* not ANSI_DECLARATORS */
-
-{
- VOID **getblock;
- char *foundvertex;
- unsigned long alignptr;
- int current;
-
- getblock = m->vertices.firstblock;
- current = b->firstnumber;
-
- /* Find the right block. */
- if (current + m->vertices.itemsfirstblock <= number) {
- getblock = (VOID **) *getblock;
- current += m->vertices.itemsfirstblock;
- while (current + m->vertices.itemsperblock <= number) {
- getblock = (VOID **) *getblock;
- current += m->vertices.itemsperblock;
- }
- }
-
- /* Now find the right vertex. */
- alignptr = (unsigned long) (getblock + 1);
- foundvertex = (char *) (alignptr + (unsigned long) m->vertices.alignbytes -
- (alignptr % (unsigned long) m->vertices.alignbytes));
- return (vertex) (foundvertex + m->vertices.itembytes * (number - current));
-}
-
-/*****************************************************************************/
-/* */
-/* triangledeinit() Free all remaining allocated memory. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-void triangledeinit(struct mesh *m, struct behavior *b)
-#else /* not ANSI_DECLARATORS */
-void triangledeinit(m, b)
-struct mesh *m;
-struct behavior *b;
-#endif /* not ANSI_DECLARATORS */
-
-{
- pooldeinit(&m->triangles);
- trifree((VOID *) m->dummytribase);
- if (b->usesegments) {
- pooldeinit(&m->subsegs);
- trifree((VOID *) m->dummysubbase);
- }
- pooldeinit(&m->vertices);
-#ifndef CDT_ONLY
- if (b->quality) {
- pooldeinit(&m->badsubsegs);
- if ((b->minangle > 0.0) || b->vararea || b->fixedarea || b->usertest) {
- pooldeinit(&m->badtriangles);
- pooldeinit(&m->flipstackers);
- }
- }
-#endif /* not CDT_ONLY */
-}
-
-/** **/
-/** **/
-/********* Memory management routines end here *********/
-
-/********* Constructors begin here *********/
-/** **/
-/** **/
-
-/*****************************************************************************/
-/* */
-/* maketriangle() Create a new triangle with orientation zero. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-void maketriangle(struct mesh *m, struct behavior *b, struct otri *newotri)
-#else /* not ANSI_DECLARATORS */
-void maketriangle(m, b, newotri)
-struct mesh *m;
-struct behavior *b;
-struct otri *newotri;
-#endif /* not ANSI_DECLARATORS */
-
-{
- int i;
-
- newotri->tri = (triangle *) poolalloc(&m->triangles);
- /* Initialize the three adjoining triangles to be "outer space". */
- newotri->tri[0] = (triangle) m->dummytri;
- newotri->tri[1] = (triangle) m->dummytri;
- newotri->tri[2] = (triangle) m->dummytri;
- /* Three NULL vertices. */
- newotri->tri[3] = (triangle) NULL;
- newotri->tri[4] = (triangle) NULL;
- newotri->tri[5] = (triangle) NULL;
- if (b->usesegments) {
- /* Initialize the three adjoining subsegments to be the omnipresent */
- /* subsegment. */
- newotri->tri[6] = (triangle) m->dummysub;
- newotri->tri[7] = (triangle) m->dummysub;
- newotri->tri[8] = (triangle) m->dummysub;
- }
- for (i = 0; i < m->eextras; i++) {
- setelemattribute(*newotri, i, 0.0);
- }
- if (b->vararea) {
- setareabound(*newotri, -1.0);
- }
-
- newotri->orient = 0;
-}
-
-/*****************************************************************************/
-/* */
-/* makesubseg() Create a new subsegment with orientation zero. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-void makesubseg(struct mesh *m, struct osub *newsubseg)
-#else /* not ANSI_DECLARATORS */
-void makesubseg(m, newsubseg)
-struct mesh *m;
-struct osub *newsubseg;
-#endif /* not ANSI_DECLARATORS */
-
-{
- newsubseg->ss = (subseg *) poolalloc(&m->subsegs);
- /* Initialize the two adjoining subsegments to be the omnipresent */
- /* subsegment. */
- newsubseg->ss[0] = (subseg) m->dummysub;
- newsubseg->ss[1] = (subseg) m->dummysub;
- /* Four NULL vertices. */
- newsubseg->ss[2] = (subseg) NULL;
- newsubseg->ss[3] = (subseg) NULL;
- newsubseg->ss[4] = (subseg) NULL;
- newsubseg->ss[5] = (subseg) NULL;
- /* Initialize the two adjoining triangles to be "outer space." */
- newsubseg->ss[6] = (subseg) m->dummytri;
- newsubseg->ss[7] = (subseg) m->dummytri;
- /* Set the boundary marker to zero. */
- setmark(*newsubseg, 0);
-
- newsubseg->ssorient = 0;
-}
-
-/** **/
-/** **/
-/********* Constructors end here *********/
-
-/********* Geometric primitives begin here *********/
-/** **/
-/** **/
-
-/* The adaptive exact arithmetic geometric predicates implemented herein are */
-/* described in detail in my paper, "Adaptive Precision Floating-Point */
-/* Arithmetic and Fast Robust Geometric Predicates." See the header for a */
-/* full citation. */
-
-/* Which of the following two methods of finding the absolute values is */
-/* fastest is compiler-dependent. A few compilers can inline and optimize */
-/* the fabs() call; but most will incur the overhead of a function call, */
-/* which is disastrously slow. A faster way on IEEE machines might be to */
-/* mask the appropriate bit, but that's difficult to do in C without */
-/* forcing the value to be stored to memory (rather than be kept in the */
-/* register to which the optimizer assigned it). */
-
-#define Absolute(a) ((a) >= 0.0 ? (a) : -(a))
-/* #define Absolute(a) fabs(a) */
-
-/* Many of the operations are broken up into two pieces, a main part that */
-/* performs an approximate operation, and a "tail" that computes the */
-/* roundoff error of that operation. */
-/* */
-/* The operations Fast_Two_Sum(), Fast_Two_Diff(), Two_Sum(), Two_Diff(), */
-/* Split(), and Two_Product() are all implemented as described in the */
-/* reference. Each of these macros requires certain variables to be */
-/* defined in the calling routine. The variables `bvirt', `c', `abig', */
-/* `_i', `_j', `_k', `_l', `_m', and `_n' are declared `INEXACT' because */
-/* they store the result of an operation that may incur roundoff error. */
-/* The input parameter `x' (or the highest numbered `x_' parameter) must */
-/* also be declared `INEXACT'. */
-
-#define Fast_Two_Sum_Tail(a, b, x, y) \
- bvirt = x - a; \
- y = b - bvirt
-
-#define Fast_Two_Sum(a, b, x, y) \
- x = (REAL) (a + b); \
- Fast_Two_Sum_Tail(a, b, x, y)
-
-#define Two_Sum_Tail(a, b, x, y) \
- bvirt = (REAL) (x - a); \
- avirt = x - bvirt; \
- bround = b - bvirt; \
- around = a - avirt; \
- y = around + bround
-
-#define Two_Sum(a, b, x, y) \
- x = (REAL) (a + b); \
- Two_Sum_Tail(a, b, x, y)
-
-#define Two_Diff_Tail(a, b, x, y) \
- bvirt = (REAL) (a - x); \
- avirt = x + bvirt; \
- bround = bvirt - b; \
- around = a - avirt; \
- y = around + bround
-
-#define Two_Diff(a, b, x, y) \
- x = (REAL) (a - b); \
- Two_Diff_Tail(a, b, x, y)
-
-#define Split(a, ahi, alo) \
- c = (REAL) (splitter * a); \
- abig = (REAL) (c - a); \
- ahi = c - abig; \
- alo = a - ahi
-
-#define Two_Product_Tail(a, b, x, y) \
- Split(a, ahi, alo); \
- Split(b, bhi, blo); \
- err1 = x - (ahi * bhi); \
- err2 = err1 - (alo * bhi); \
- err3 = err2 - (ahi * blo); \
- y = (alo * blo) - err3
-
-#define Two_Product(a, b, x, y) \
- x = (REAL) (a * b); \
- Two_Product_Tail(a, b, x, y)
-
-/* Two_Product_Presplit() is Two_Product() where one of the inputs has */
-/* already been split. Avoids redundant splitting. */
-
-#define Two_Product_Presplit(a, b, bhi, blo, x, y) \
- x = (REAL) (a * b); \
- Split(a, ahi, alo); \
- err1 = x - (ahi * bhi); \
- err2 = err1 - (alo * bhi); \
- err3 = err2 - (ahi * blo); \
- y = (alo * blo) - err3
-
-/* Square() can be done more quickly than Two_Product(). */
-
-#define Square_Tail(a, x, y) \
- Split(a, ahi, alo); \
- err1 = x - (ahi * ahi); \
- err3 = err1 - ((ahi + ahi) * alo); \
- y = (alo * alo) - err3
-
-#define Square(a, x, y) \
- x = (REAL) (a * a); \
- Square_Tail(a, x, y)
-
-/* Macros for summing expansions of various fixed lengths. These are all */
-/* unrolled versions of Expansion_Sum(). */
-
-#define Two_One_Sum(a1, a0, b, x2, x1, x0) \
- Two_Sum(a0, b , _i, x0); \
- Two_Sum(a1, _i, x2, x1)
-
-#define Two_One_Diff(a1, a0, b, x2, x1, x0) \
- Two_Diff(a0, b , _i, x0); \
- Two_Sum( a1, _i, x2, x1)
-
-#define Two_Two_Sum(a1, a0, b1, b0, x3, x2, x1, x0) \
- Two_One_Sum(a1, a0, b0, _j, _0, x0); \
- Two_One_Sum(_j, _0, b1, x3, x2, x1)
-
-#define Two_Two_Diff(a1, a0, b1, b0, x3, x2, x1, x0) \
- Two_One_Diff(a1, a0, b0, _j, _0, x0); \
- Two_One_Diff(_j, _0, b1, x3, x2, x1)
-
-/* Macro for multiplying a two-component expansion by a single component. */
-
-#define Two_One_Product(a1, a0, b, x3, x2, x1, x0) \
- Split(b, bhi, blo); \
- Two_Product_Presplit(a0, b, bhi, blo, _i, x0); \
- Two_Product_Presplit(a1, b, bhi, blo, _j, _0); \
- Two_Sum(_i, _0, _k, x1); \
- Fast_Two_Sum(_j, _k, x3, x2)
-
-/*****************************************************************************/
-/* */
-/* exactinit() Initialize the variables used for exact arithmetic. */
-/* */
-/* `epsilon' is the largest power of two such that 1.0 + epsilon = 1.0 in */
-/* floating-point arithmetic. `epsilon' bounds the relative roundoff */
-/* error. It is used for floating-point error analysis. */
-/* */
-/* `splitter' is used to split floating-point numbers into two half- */
-/* length significands for exact multiplication. */
-/* */
-/* I imagine that a highly optimizing compiler might be too smart for its */
-/* own good, and somehow cause this routine to fail, if it pretends that */
-/* floating-point arithmetic is too much like real arithmetic. */
-/* */
-/* Don't change this routine unless you fully understand it. */
-/* */
-/*****************************************************************************/
-
-void exactinit()
-{
- REAL half;
- REAL check, lastcheck;
- int every_other;
-#ifdef LINUX
- int cword;
-#endif /* LINUX */
-
-#ifdef CPU86
-#ifdef SINGLE
- _control87(_PC_24, _MCW_PC); /* Set FPU control word for single precision. */
-#else /* not SINGLE */
- _control87(_PC_53, _MCW_PC); /* Set FPU control word for double precision. */
-#endif /* not SINGLE */
-#endif /* CPU86 */
-#ifdef LINUX
-#ifdef SINGLE
- /* cword = 4223; */
- cword = 4210; /* set FPU control word for single precision */
-#else /* not SINGLE */
- /* cword = 4735; */
- cword = 4722; /* set FPU control word for double precision */
-#endif /* not SINGLE */
- _FPU_SETCW(cword);
-#endif /* LINUX */
-
- every_other = 1;
- half = 0.5;
- epsilon = 1.0;
- splitter = 1.0;
- check = 1.0;
- /* Repeatedly divide `epsilon' by two until it is too small to add to */
- /* one without causing roundoff. (Also check if the sum is equal to */
- /* the previous sum, for machines that round up instead of using exact */
- /* rounding. Not that these routines will work on such machines.) */
- do {
- lastcheck = check;
- epsilon *= half;
- if (every_other) {
- splitter *= 2.0;
- }
- every_other = !every_other;
- check = 1.0 + epsilon;
- } while ((check != 1.0) && (check != lastcheck));
- splitter += 1.0;
- /* Error bounds for orientation and incircle tests. */
- resulterrbound = (3.0 + 8.0 * epsilon) * epsilon;
- ccwerrboundA = (3.0 + 16.0 * epsilon) * epsilon;
- ccwerrboundB = (2.0 + 12.0 * epsilon) * epsilon;
- ccwerrboundC = (9.0 + 64.0 * epsilon) * epsilon * epsilon;
- iccerrboundA = (10.0 + 96.0 * epsilon) * epsilon;
- iccerrboundB = (4.0 + 48.0 * epsilon) * epsilon;
- iccerrboundC = (44.0 + 576.0 * epsilon) * epsilon * epsilon;
- o3derrboundA = (7.0 + 56.0 * epsilon) * epsilon;
- o3derrboundB = (3.0 + 28.0 * epsilon) * epsilon;
- o3derrboundC = (26.0 + 288.0 * epsilon) * epsilon * epsilon;
-}
-
-/*****************************************************************************/
-/* */
-/* fast_expansion_sum_zeroelim() Sum two expansions, eliminating zero */
-/* components from the output expansion. */
-/* */
-/* Sets h = e + f. See my Robust Predicates paper for details. */
-/* */
-/* If round-to-even is used (as with IEEE 754), maintains the strongly */
-/* nonoverlapping property. (That is, if e is strongly nonoverlapping, h */
-/* will be also.) Does NOT maintain the nonoverlapping or nonadjacent */
-/* properties. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-int fast_expansion_sum_zeroelim(int elen, REAL *e, int flen, REAL *f, REAL *h)
-#else /* not ANSI_DECLARATORS */
-int fast_expansion_sum_zeroelim(elen, e, flen, f, h) /* h cannot be e or f. */
-int elen;
-REAL *e;
-int flen;
-REAL *f;
-REAL *h;
-#endif /* not ANSI_DECLARATORS */
-
-{
- REAL Q;
- INEXACT REAL Qnew;
- INEXACT REAL hh;
- INEXACT REAL bvirt;
- REAL avirt, bround, around;
- int eindex, findex, hindex;
- REAL enow, fnow;
-
- enow = e[0];
- fnow = f[0];
- eindex = findex = 0;
- if ((fnow > enow) == (fnow > -enow)) {
- Q = enow;
- enow = e[++eindex];
- } else {
- Q = fnow;
- fnow = f[++findex];
- }
- hindex = 0;
- if ((eindex < elen) && (findex < flen)) {
- if ((fnow > enow) == (fnow > -enow)) {
- Fast_Two_Sum(enow, Q, Qnew, hh);
- enow = e[++eindex];
- } else {
- Fast_Two_Sum(fnow, Q, Qnew, hh);
- fnow = f[++findex];
- }
- Q = Qnew;
- if (hh != 0.0) {
- h[hindex++] = hh;
- }
- while ((eindex < elen) && (findex < flen)) {
- if ((fnow > enow) == (fnow > -enow)) {
- Two_Sum(Q, enow, Qnew, hh);
- enow = e[++eindex];
- } else {
- Two_Sum(Q, fnow, Qnew, hh);
- fnow = f[++findex];
- }
- Q = Qnew;
- if (hh != 0.0) {
- h[hindex++] = hh;
- }
- }
- }
- while (eindex < elen) {
- Two_Sum(Q, enow, Qnew, hh);
- enow = e[++eindex];
- Q = Qnew;
- if (hh != 0.0) {
- h[hindex++] = hh;
- }
- }
- while (findex < flen) {
- Two_Sum(Q, fnow, Qnew, hh);
- fnow = f[++findex];
- Q = Qnew;
- if (hh != 0.0) {
- h[hindex++] = hh;
- }
- }
- if ((Q != 0.0) || (hindex == 0)) {
- h[hindex++] = Q;
- }
- return hindex;
-}
-
-/*****************************************************************************/
-/* */
-/* scale_expansion_zeroelim() Multiply an expansion by a scalar, */
-/* eliminating zero components from the */
-/* output expansion. */
-/* */
-/* Sets h = be. See my Robust Predicates paper for details. */
-/* */
-/* Maintains the nonoverlapping property. If round-to-even is used (as */
-/* with IEEE 754), maintains the strongly nonoverlapping and nonadjacent */
-/* properties as well. (That is, if e has one of these properties, so */
-/* will h.) */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-int scale_expansion_zeroelim(int elen, REAL *e, REAL b, REAL *h)
-#else /* not ANSI_DECLARATORS */
-int scale_expansion_zeroelim(elen, e, b, h) /* e and h cannot be the same. */
-int elen;
-REAL *e;
-REAL b;
-REAL *h;
-#endif /* not ANSI_DECLARATORS */
-
-{
- INEXACT REAL Q, sum;
- REAL hh;
- INEXACT REAL product1;
- REAL product0;
- int eindex, hindex;
- REAL enow;
- INEXACT REAL bvirt;
- REAL avirt, bround, around;
- INEXACT REAL c;
- INEXACT REAL abig;
- REAL ahi, alo, bhi, blo;
- REAL err1, err2, err3;
-
- Split(b, bhi, blo);
- Two_Product_Presplit(e[0], b, bhi, blo, Q, hh);
- hindex = 0;
- if (hh != 0) {
- h[hindex++] = hh;
- }
- for (eindex = 1; eindex < elen; eindex++) {
- enow = e[eindex];
- Two_Product_Presplit(enow, b, bhi, blo, product1, product0);
- Two_Sum(Q, product0, sum, hh);
- if (hh != 0) {
- h[hindex++] = hh;
- }
- Fast_Two_Sum(product1, sum, Q, hh);
- if (hh != 0) {
- h[hindex++] = hh;
- }
- }
- if ((Q != 0.0) || (hindex == 0)) {
- h[hindex++] = Q;
- }
- return hindex;
-}
-
-/*****************************************************************************/
-/* */
-/* estimate() Produce a one-word estimate of an expansion's value. */
-/* */
-/* See my Robust Predicates paper for details. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-REAL estimate(int elen, REAL *e)
-#else /* not ANSI_DECLARATORS */
-REAL estimate(elen, e)
-int elen;
-REAL *e;
-#endif /* not ANSI_DECLARATORS */
-
-{
- REAL Q;
- int eindex;
-
- Q = e[0];
- for (eindex = 1; eindex < elen; eindex++) {
- Q += e[eindex];
- }
- return Q;
-}
-
-/*****************************************************************************/
-/* */
-/* counterclockwise() Return a positive value if the points pa, pb, and */
-/* pc occur in counterclockwise order; a negative */
-/* value if they occur in clockwise order; and zero */
-/* if they are collinear. The result is also a rough */
-/* approximation of twice the signed area of the */
-/* triangle defined by the three points. */
-/* */
-/* Uses exact arithmetic if necessary to ensure a correct answer. The */
-/* result returned is the determinant of a matrix. This determinant is */
-/* computed adaptively, in the sense that exact arithmetic is used only to */
-/* the degree it is needed to ensure that the returned value has the */
-/* correct sign. Hence, this function is usually quite fast, but will run */
-/* more slowly when the input points are collinear or nearly so. */
-/* */
-/* See my Robust Predicates paper for details. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-REAL counterclockwiseadapt(vertex pa, vertex pb, vertex pc, REAL detsum)
-#else /* not ANSI_DECLARATORS */
-REAL counterclockwiseadapt(pa, pb, pc, detsum)
-vertex pa;
-vertex pb;
-vertex pc;
-REAL detsum;
-#endif /* not ANSI_DECLARATORS */
-
-{
- INEXACT REAL acx, acy, bcx, bcy;
- REAL acxtail, acytail, bcxtail, bcytail;
- INEXACT REAL detleft, detright;
- REAL detlefttail, detrighttail;
- REAL det, errbound;
- REAL B[4], C1[8], C2[12], D[16];
- INEXACT REAL B3;
- int C1length, C2length, Dlength;
- REAL u[4];
- INEXACT REAL u3;
- INEXACT REAL s1, t1;
- REAL s0, t0;
-
- INEXACT REAL bvirt;
- REAL avirt, bround, around;
- INEXACT REAL c;
- INEXACT REAL abig;
- REAL ahi, alo, bhi, blo;
- REAL err1, err2, err3;
- INEXACT REAL _i, _j;
- REAL _0;
-
- acx = (REAL) (pa[0] - pc[0]);
- bcx = (REAL) (pb[0] - pc[0]);
- acy = (REAL) (pa[1] - pc[1]);
- bcy = (REAL) (pb[1] - pc[1]);
-
- Two_Product(acx, bcy, detleft, detlefttail);
- Two_Product(acy, bcx, detright, detrighttail);
-
- Two_Two_Diff(detleft, detlefttail, detright, detrighttail,
- B3, B[2], B[1], B[0]);
- B[3] = B3;
-
- det = estimate(4, B);
- errbound = ccwerrboundB * detsum;
- if ((det >= errbound) || (-det >= errbound)) {
- return det;
- }
-
- Two_Diff_Tail(pa[0], pc[0], acx, acxtail);
- Two_Diff_Tail(pb[0], pc[0], bcx, bcxtail);
- Two_Diff_Tail(pa[1], pc[1], acy, acytail);
- Two_Diff_Tail(pb[1], pc[1], bcy, bcytail);
-
- if ((acxtail == 0.0) && (acytail == 0.0)
- && (bcxtail == 0.0) && (bcytail == 0.0)) {
- return det;
- }
-
- errbound = ccwerrboundC * detsum + resulterrbound * Absolute(det);
- det += (acx * bcytail + bcy * acxtail)
- - (acy * bcxtail + bcx * acytail);
- if ((det >= errbound) || (-det >= errbound)) {
- return det;
- }
-
- Two_Product(acxtail, bcy, s1, s0);
- Two_Product(acytail, bcx, t1, t0);
- Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
- u[3] = u3;
- C1length = fast_expansion_sum_zeroelim(4, B, 4, u, C1);
-
- Two_Product(acx, bcytail, s1, s0);
- Two_Product(acy, bcxtail, t1, t0);
- Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
- u[3] = u3;
- C2length = fast_expansion_sum_zeroelim(C1length, C1, 4, u, C2);
-
- Two_Product(acxtail, bcytail, s1, s0);
- Two_Product(acytail, bcxtail, t1, t0);
- Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
- u[3] = u3;
- Dlength = fast_expansion_sum_zeroelim(C2length, C2, 4, u, D);
-
- return(D[Dlength - 1]);
-}
-
-#ifdef ANSI_DECLARATORS
-REAL counterclockwise(struct mesh *m, struct behavior *b,
- vertex pa, vertex pb, vertex pc)
-#else /* not ANSI_DECLARATORS */
-REAL counterclockwise(m, b, pa, pb, pc)
-struct mesh *m;
-struct behavior *b;
-vertex pa;
-vertex pb;
-vertex pc;
-#endif /* not ANSI_DECLARATORS */
-
-{
- REAL detleft, detright, det;
- REAL detsum, errbound;
-
- m->counterclockcount++;
-
- detleft = (pa[0] - pc[0]) * (pb[1] - pc[1]);
- detright = (pa[1] - pc[1]) * (pb[0] - pc[0]);
- det = detleft - detright;
-
- if (b->noexact) {
- return det;
- }
-
- if (detleft > 0.0) {
- if (detright <= 0.0) {
- return det;
- } else {
- detsum = detleft + detright;
- }
- } else if (detleft < 0.0) {
- if (detright >= 0.0) {
- return det;
- } else {
- detsum = -detleft - detright;
- }
- } else {
- return det;
- }
-
- errbound = ccwerrboundA * detsum;
- if ((det >= errbound) || (-det >= errbound)) {
- return det;
- }
-
- return counterclockwiseadapt(pa, pb, pc, detsum);
-}
-
-/*****************************************************************************/
-/* */
-/* incircle() Return a positive value if the point pd lies inside the */
-/* circle passing through pa, pb, and pc; a negative value if */
-/* it lies outside; and zero if the four points are cocircular.*/
-/* The points pa, pb, and pc must be in counterclockwise */
-/* order, or the sign of the result will be reversed. */
-/* */
-/* Uses exact arithmetic if necessary to ensure a correct answer. The */
-/* result returned is the determinant of a matrix. This determinant is */
-/* computed adaptively, in the sense that exact arithmetic is used only to */
-/* the degree it is needed to ensure that the returned value has the */
-/* correct sign. Hence, this function is usually quite fast, but will run */
-/* more slowly when the input points are cocircular or nearly so. */
-/* */
-/* See my Robust Predicates paper for details. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-REAL incircleadapt(vertex pa, vertex pb, vertex pc, vertex pd, REAL permanent)
-#else /* not ANSI_DECLARATORS */
-REAL incircleadapt(pa, pb, pc, pd, permanent)
-vertex pa;
-vertex pb;
-vertex pc;
-vertex pd;
-REAL permanent;
-#endif /* not ANSI_DECLARATORS */
-
-{
- INEXACT REAL adx, bdx, cdx, ady, bdy, cdy;
- REAL det, errbound;
-
- INEXACT REAL bdxcdy1, cdxbdy1, cdxady1, adxcdy1, adxbdy1, bdxady1;
- REAL bdxcdy0, cdxbdy0, cdxady0, adxcdy0, adxbdy0, bdxady0;
- REAL bc[4], ca[4], ab[4];
- INEXACT REAL bc3, ca3, ab3;
- REAL axbc[8], axxbc[16], aybc[8], ayybc[16], adet[32];
- int axbclen, axxbclen, aybclen, ayybclen, alen;
- REAL bxca[8], bxxca[16], byca[8], byyca[16], bdet[32];
- int bxcalen, bxxcalen, bycalen, byycalen, blen;
- REAL cxab[8], cxxab[16], cyab[8], cyyab[16], cdet[32];
- int cxablen, cxxablen, cyablen, cyyablen, clen;
- REAL abdet[64];
- int ablen;
- REAL fin1[1152], fin2[1152];
- REAL *finnow, *finother, *finswap;
- int finlength;
-
- REAL adxtail, bdxtail, cdxtail, adytail, bdytail, cdytail;
- INEXACT REAL adxadx1, adyady1, bdxbdx1, bdybdy1, cdxcdx1, cdycdy1;
- REAL adxadx0, adyady0, bdxbdx0, bdybdy0, cdxcdx0, cdycdy0;
- REAL aa[4], bb[4], cc[4];
- INEXACT REAL aa3, bb3, cc3;
- INEXACT REAL ti1, tj1;
- REAL ti0, tj0;
- REAL u[4], v[4];
- INEXACT REAL u3, v3;
- REAL temp8[8], temp16a[16], temp16b[16], temp16c[16];
- REAL temp32a[32], temp32b[32], temp48[48], temp64[64];
- int temp8len, temp16alen, temp16blen, temp16clen;
- int temp32alen, temp32blen, temp48len, temp64len;
- REAL axtbb[8], axtcc[8], aytbb[8], aytcc[8];
- int axtbblen, axtcclen, aytbblen, aytcclen;
- REAL bxtaa[8], bxtcc[8], bytaa[8], bytcc[8];
- int bxtaalen, bxtcclen, bytaalen, bytcclen;
- REAL cxtaa[8], cxtbb[8], cytaa[8], cytbb[8];
- int cxtaalen, cxtbblen, cytaalen, cytbblen;
- REAL axtbc[8], aytbc[8], bxtca[8], bytca[8], cxtab[8], cytab[8];
- int axtbclen = 0, aytbclen = 0, bxtcalen = 0, bytcalen = 0, cxtablen = 0, cytablen = 0;
- REAL axtbct[16], aytbct[16], bxtcat[16], bytcat[16], cxtabt[16], cytabt[16];
- int axtbctlen, aytbctlen, bxtcatlen, bytcatlen, cxtabtlen, cytabtlen;
- REAL axtbctt[8], aytbctt[8], bxtcatt[8];
- REAL bytcatt[8], cxtabtt[8], cytabtt[8];
- int axtbcttlen, aytbcttlen, bxtcattlen, bytcattlen, cxtabttlen, cytabttlen;
- REAL abt[8], bct[8], cat[8];
- int abtlen, bctlen, catlen;
- REAL abtt[4], bctt[4], catt[4];
- int abttlen, bcttlen, cattlen;
- INEXACT REAL abtt3, bctt3, catt3;
- REAL negate;
-
- INEXACT REAL bvirt;
- REAL avirt, bround, around;
- INEXACT REAL c;
- INEXACT REAL abig;
- REAL ahi, alo, bhi, blo;
- REAL err1, err2, err3;
- INEXACT REAL _i, _j;
- REAL _0;
-
- adx = (REAL) (pa[0] - pd[0]);
- bdx = (REAL) (pb[0] - pd[0]);
- cdx = (REAL) (pc[0] - pd[0]);
- ady = (REAL) (pa[1] - pd[1]);
- bdy = (REAL) (pb[1] - pd[1]);
- cdy = (REAL) (pc[1] - pd[1]);
-
- Two_Product(bdx, cdy, bdxcdy1, bdxcdy0);
- Two_Product(cdx, bdy, cdxbdy1, cdxbdy0);
- Two_Two_Diff(bdxcdy1, bdxcdy0, cdxbdy1, cdxbdy0, bc3, bc[2], bc[1], bc[0]);
- bc[3] = bc3;
- axbclen = scale_expansion_zeroelim(4, bc, adx, axbc);
- axxbclen = scale_expansion_zeroelim(axbclen, axbc, adx, axxbc);
- aybclen = scale_expansion_zeroelim(4, bc, ady, aybc);
- ayybclen = scale_expansion_zeroelim(aybclen, aybc, ady, ayybc);
- alen = fast_expansion_sum_zeroelim(axxbclen, axxbc, ayybclen, ayybc, adet);
-
- Two_Product(cdx, ady, cdxady1, cdxady0);
- Two_Product(adx, cdy, adxcdy1, adxcdy0);
- Two_Two_Diff(cdxady1, cdxady0, adxcdy1, adxcdy0, ca3, ca[2], ca[1], ca[0]);
- ca[3] = ca3;
- bxcalen = scale_expansion_zeroelim(4, ca, bdx, bxca);
- bxxcalen = scale_expansion_zeroelim(bxcalen, bxca, bdx, bxxca);
- bycalen = scale_expansion_zeroelim(4, ca, bdy, byca);
- byycalen = scale_expansion_zeroelim(bycalen, byca, bdy, byyca);
- blen = fast_expansion_sum_zeroelim(bxxcalen, bxxca, byycalen, byyca, bdet);
-
- Two_Product(adx, bdy, adxbdy1, adxbdy0);
- Two_Product(bdx, ady, bdxady1, bdxady0);
- Two_Two_Diff(adxbdy1, adxbdy0, bdxady1, bdxady0, ab3, ab[2], ab[1], ab[0]);
- ab[3] = ab3;
- cxablen = scale_expansion_zeroelim(4, ab, cdx, cxab);
- cxxablen = scale_expansion_zeroelim(cxablen, cxab, cdx, cxxab);
- cyablen = scale_expansion_zeroelim(4, ab, cdy, cyab);
- cyyablen = scale_expansion_zeroelim(cyablen, cyab, cdy, cyyab);
- clen = fast_expansion_sum_zeroelim(cxxablen, cxxab, cyyablen, cyyab, cdet);
-
- ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
- finlength = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, fin1);
-
- det = estimate(finlength, fin1);
- errbound = iccerrboundB * permanent;
- if ((det >= errbound) || (-det >= errbound)) {
- return det;
- }
-
- Two_Diff_Tail(pa[0], pd[0], adx, adxtail);
- Two_Diff_Tail(pa[1], pd[1], ady, adytail);
- Two_Diff_Tail(pb[0], pd[0], bdx, bdxtail);
- Two_Diff_Tail(pb[1], pd[1], bdy, bdytail);
- Two_Diff_Tail(pc[0], pd[0], cdx, cdxtail);
- Two_Diff_Tail(pc[1], pd[1], cdy, cdytail);
- if ((adxtail == 0.0) && (bdxtail == 0.0) && (cdxtail == 0.0)
- && (adytail == 0.0) && (bdytail == 0.0) && (cdytail == 0.0)) {
- return det;
- }
-
- errbound = iccerrboundC * permanent + resulterrbound * Absolute(det);
- det += ((adx * adx + ady * ady) * ((bdx * cdytail + cdy * bdxtail)
- - (bdy * cdxtail + cdx * bdytail))
- + 2.0 * (adx * adxtail + ady * adytail) * (bdx * cdy - bdy * cdx))
- + ((bdx * bdx + bdy * bdy) * ((cdx * adytail + ady * cdxtail)
- - (cdy * adxtail + adx * cdytail))
- + 2.0 * (bdx * bdxtail + bdy * bdytail) * (cdx * ady - cdy * adx))
- + ((cdx * cdx + cdy * cdy) * ((adx * bdytail + bdy * adxtail)
- - (ady * bdxtail + bdx * adytail))
- + 2.0 * (cdx * cdxtail + cdy * cdytail) * (adx * bdy - ady * bdx));
- if ((det >= errbound) || (-det >= errbound)) {
- return det;
- }
-
- finnow = fin1;
- finother = fin2;
-
- if ((bdxtail != 0.0) || (bdytail != 0.0)
- || (cdxtail != 0.0) || (cdytail != 0.0)) {
- Square(adx, adxadx1, adxadx0);
- Square(ady, adyady1, adyady0);
- Two_Two_Sum(adxadx1, adxadx0, adyady1, adyady0, aa3, aa[2], aa[1], aa[0]);
- aa[3] = aa3;
- }
- if ((cdxtail != 0.0) || (cdytail != 0.0)
- || (adxtail != 0.0) || (adytail != 0.0)) {
- Square(bdx, bdxbdx1, bdxbdx0);
- Square(bdy, bdybdy1, bdybdy0);
- Two_Two_Sum(bdxbdx1, bdxbdx0, bdybdy1, bdybdy0, bb3, bb[2], bb[1], bb[0]);
- bb[3] = bb3;
- }
- if ((adxtail != 0.0) || (adytail != 0.0)
- || (bdxtail != 0.0) || (bdytail != 0.0)) {
- Square(cdx, cdxcdx1, cdxcdx0);
- Square(cdy, cdycdy1, cdycdy0);
- Two_Two_Sum(cdxcdx1, cdxcdx0, cdycdy1, cdycdy0, cc3, cc[2], cc[1], cc[0]);
- cc[3] = cc3;
- }
-
- if (adxtail != 0.0) {
- axtbclen = scale_expansion_zeroelim(4, bc, adxtail, axtbc);
- temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, 2.0 * adx,
- temp16a);
-
- axtcclen = scale_expansion_zeroelim(4, cc, adxtail, axtcc);
- temp16blen = scale_expansion_zeroelim(axtcclen, axtcc, bdy, temp16b);
-
- axtbblen = scale_expansion_zeroelim(4, bb, adxtail, axtbb);
- temp16clen = scale_expansion_zeroelim(axtbblen, axtbb, -cdy, temp16c);
-
- temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
- temp16blen, temp16b, temp32a);
- temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
- temp32alen, temp32a, temp48);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
- temp48, finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- if (adytail != 0.0) {
- aytbclen = scale_expansion_zeroelim(4, bc, adytail, aytbc);
- temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, 2.0 * ady,
- temp16a);
-
- aytbblen = scale_expansion_zeroelim(4, bb, adytail, aytbb);
- temp16blen = scale_expansion_zeroelim(aytbblen, aytbb, cdx, temp16b);
-
- aytcclen = scale_expansion_zeroelim(4, cc, adytail, aytcc);
- temp16clen = scale_expansion_zeroelim(aytcclen, aytcc, -bdx, temp16c);
-
- temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
- temp16blen, temp16b, temp32a);
- temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
- temp32alen, temp32a, temp48);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
- temp48, finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- if (bdxtail != 0.0) {
- bxtcalen = scale_expansion_zeroelim(4, ca, bdxtail, bxtca);
- temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, 2.0 * bdx,
- temp16a);
-
- bxtaalen = scale_expansion_zeroelim(4, aa, bdxtail, bxtaa);
- temp16blen = scale_expansion_zeroelim(bxtaalen, bxtaa, cdy, temp16b);
-
- bxtcclen = scale_expansion_zeroelim(4, cc, bdxtail, bxtcc);
- temp16clen = scale_expansion_zeroelim(bxtcclen, bxtcc, -ady, temp16c);
-
- temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
- temp16blen, temp16b, temp32a);
- temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
- temp32alen, temp32a, temp48);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
- temp48, finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- if (bdytail != 0.0) {
- bytcalen = scale_expansion_zeroelim(4, ca, bdytail, bytca);
- temp16alen = scale_expansion_zeroelim(bytcalen, bytca, 2.0 * bdy,
- temp16a);
-
- bytcclen = scale_expansion_zeroelim(4, cc, bdytail, bytcc);
- temp16blen = scale_expansion_zeroelim(bytcclen, bytcc, adx, temp16b);
-
- bytaalen = scale_expansion_zeroelim(4, aa, bdytail, bytaa);
- temp16clen = scale_expansion_zeroelim(bytaalen, bytaa, -cdx, temp16c);
-
- temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
- temp16blen, temp16b, temp32a);
- temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
- temp32alen, temp32a, temp48);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
- temp48, finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- if (cdxtail != 0.0) {
- cxtablen = scale_expansion_zeroelim(4, ab, cdxtail, cxtab);
- temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, 2.0 * cdx,
- temp16a);
-
- cxtbblen = scale_expansion_zeroelim(4, bb, cdxtail, cxtbb);
- temp16blen = scale_expansion_zeroelim(cxtbblen, cxtbb, ady, temp16b);
-
- cxtaalen = scale_expansion_zeroelim(4, aa, cdxtail, cxtaa);
- temp16clen = scale_expansion_zeroelim(cxtaalen, cxtaa, -bdy, temp16c);
-
- temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
- temp16blen, temp16b, temp32a);
- temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
- temp32alen, temp32a, temp48);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
- temp48, finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- if (cdytail != 0.0) {
- cytablen = scale_expansion_zeroelim(4, ab, cdytail, cytab);
- temp16alen = scale_expansion_zeroelim(cytablen, cytab, 2.0 * cdy,
- temp16a);
-
- cytaalen = scale_expansion_zeroelim(4, aa, cdytail, cytaa);
- temp16blen = scale_expansion_zeroelim(cytaalen, cytaa, bdx, temp16b);
-
- cytbblen = scale_expansion_zeroelim(4, bb, cdytail, cytbb);
- temp16clen = scale_expansion_zeroelim(cytbblen, cytbb, -adx, temp16c);
-
- temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
- temp16blen, temp16b, temp32a);
- temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
- temp32alen, temp32a, temp48);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
- temp48, finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
-
- if ((adxtail != 0.0) || (adytail != 0.0)) {
- if ((bdxtail != 0.0) || (bdytail != 0.0)
- || (cdxtail != 0.0) || (cdytail != 0.0)) {
- Two_Product(bdxtail, cdy, ti1, ti0);
- Two_Product(bdx, cdytail, tj1, tj0);
- Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
- u[3] = u3;
- negate = -bdy;
- Two_Product(cdxtail, negate, ti1, ti0);
- negate = -bdytail;
- Two_Product(cdx, negate, tj1, tj0);
- Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
- v[3] = v3;
- bctlen = fast_expansion_sum_zeroelim(4, u, 4, v, bct);
-
- Two_Product(bdxtail, cdytail, ti1, ti0);
- Two_Product(cdxtail, bdytail, tj1, tj0);
- Two_Two_Diff(ti1, ti0, tj1, tj0, bctt3, bctt[2], bctt[1], bctt[0]);
- bctt[3] = bctt3;
- bcttlen = 4;
- } else {
- bct[0] = 0.0;
- bctlen = 1;
- bctt[0] = 0.0;
- bcttlen = 1;
- }
-
- if (adxtail != 0.0) {
- temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, adxtail, temp16a);
- axtbctlen = scale_expansion_zeroelim(bctlen, bct, adxtail, axtbct);
- temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, 2.0 * adx,
- temp32a);
- temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
- temp32alen, temp32a, temp48);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
- temp48, finother);
- finswap = finnow; finnow = finother; finother = finswap;
- if (bdytail != 0.0) {
- temp8len = scale_expansion_zeroelim(4, cc, adxtail, temp8);
- temp16alen = scale_expansion_zeroelim(temp8len, temp8, bdytail,
- temp16a);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
- temp16a, finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- if (cdytail != 0.0) {
- temp8len = scale_expansion_zeroelim(4, bb, -adxtail, temp8);
- temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail,
- temp16a);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
- temp16a, finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
-
- temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, adxtail,
- temp32a);
- axtbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adxtail, axtbctt);
- temp16alen = scale_expansion_zeroelim(axtbcttlen, axtbctt, 2.0 * adx,
- temp16a);
- temp16blen = scale_expansion_zeroelim(axtbcttlen, axtbctt, adxtail,
- temp16b);
- temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
- temp16blen, temp16b, temp32b);
- temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
- temp32blen, temp32b, temp64);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
- temp64, finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- if (adytail != 0.0) {
- temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, adytail, temp16a);
- aytbctlen = scale_expansion_zeroelim(bctlen, bct, adytail, aytbct);
- temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, 2.0 * ady,
- temp32a);
- temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
- temp32alen, temp32a, temp48);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
- temp48, finother);
- finswap = finnow; finnow = finother; finother = finswap;
-
-
- temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, adytail,
- temp32a);
- aytbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adytail, aytbctt);
- temp16alen = scale_expansion_zeroelim(aytbcttlen, aytbctt, 2.0 * ady,
- temp16a);
- temp16blen = scale_expansion_zeroelim(aytbcttlen, aytbctt, adytail,
- temp16b);
- temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
- temp16blen, temp16b, temp32b);
- temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
- temp32blen, temp32b, temp64);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
- temp64, finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- }
- if ((bdxtail != 0.0) || (bdytail != 0.0)) {
- if ((cdxtail != 0.0) || (cdytail != 0.0)
- || (adxtail != 0.0) || (adytail != 0.0)) {
- Two_Product(cdxtail, ady, ti1, ti0);
- Two_Product(cdx, adytail, tj1, tj0);
- Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
- u[3] = u3;
- negate = -cdy;
- Two_Product(adxtail, negate, ti1, ti0);
- negate = -cdytail;
- Two_Product(adx, negate, tj1, tj0);
- Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
- v[3] = v3;
- catlen = fast_expansion_sum_zeroelim(4, u, 4, v, cat);
-
- Two_Product(cdxtail, adytail, ti1, ti0);
- Two_Product(adxtail, cdytail, tj1, tj0);
- Two_Two_Diff(ti1, ti0, tj1, tj0, catt3, catt[2], catt[1], catt[0]);
- catt[3] = catt3;
- cattlen = 4;
- } else {
- cat[0] = 0.0;
- catlen = 1;
- catt[0] = 0.0;
- cattlen = 1;
- }
-
- if (bdxtail != 0.0) {
- temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, bdxtail, temp16a);
- bxtcatlen = scale_expansion_zeroelim(catlen, cat, bdxtail, bxtcat);
- temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, 2.0 * bdx,
- temp32a);
- temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
- temp32alen, temp32a, temp48);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
- temp48, finother);
- finswap = finnow; finnow = finother; finother = finswap;
- if (cdytail != 0.0) {
- temp8len = scale_expansion_zeroelim(4, aa, bdxtail, temp8);
- temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail,
- temp16a);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
- temp16a, finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- if (adytail != 0.0) {
- temp8len = scale_expansion_zeroelim(4, cc, -bdxtail, temp8);
- temp16alen = scale_expansion_zeroelim(temp8len, temp8, adytail,
- temp16a);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
- temp16a, finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
-
- temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, bdxtail,
- temp32a);
- bxtcattlen = scale_expansion_zeroelim(cattlen, catt, bdxtail, bxtcatt);
- temp16alen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, 2.0 * bdx,
- temp16a);
- temp16blen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, bdxtail,
- temp16b);
- temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
- temp16blen, temp16b, temp32b);
- temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
- temp32blen, temp32b, temp64);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
- temp64, finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- if (bdytail != 0.0) {
- temp16alen = scale_expansion_zeroelim(bytcalen, bytca, bdytail, temp16a);
- bytcatlen = scale_expansion_zeroelim(catlen, cat, bdytail, bytcat);
- temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, 2.0 * bdy,
- temp32a);
- temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
- temp32alen, temp32a, temp48);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
- temp48, finother);
- finswap = finnow; finnow = finother; finother = finswap;
-
-
- temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, bdytail,
- temp32a);
- bytcattlen = scale_expansion_zeroelim(cattlen, catt, bdytail, bytcatt);
- temp16alen = scale_expansion_zeroelim(bytcattlen, bytcatt, 2.0 * bdy,
- temp16a);
- temp16blen = scale_expansion_zeroelim(bytcattlen, bytcatt, bdytail,
- temp16b);
- temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
- temp16blen, temp16b, temp32b);
- temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
- temp32blen, temp32b, temp64);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
- temp64, finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- }
- if ((cdxtail != 0.0) || (cdytail != 0.0)) {
- if ((adxtail != 0.0) || (adytail != 0.0)
- || (bdxtail != 0.0) || (bdytail != 0.0)) {
- Two_Product(adxtail, bdy, ti1, ti0);
- Two_Product(adx, bdytail, tj1, tj0);
- Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
- u[3] = u3;
- negate = -ady;
- Two_Product(bdxtail, negate, ti1, ti0);
- negate = -adytail;
- Two_Product(bdx, negate, tj1, tj0);
- Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
- v[3] = v3;
- abtlen = fast_expansion_sum_zeroelim(4, u, 4, v, abt);
-
- Two_Product(adxtail, bdytail, ti1, ti0);
- Two_Product(bdxtail, adytail, tj1, tj0);
- Two_Two_Diff(ti1, ti0, tj1, tj0, abtt3, abtt[2], abtt[1], abtt[0]);
- abtt[3] = abtt3;
- abttlen = 4;
- } else {
- abt[0] = 0.0;
- abtlen = 1;
- abtt[0] = 0.0;
- abttlen = 1;
- }
-
- if (cdxtail != 0.0) {
- temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, cdxtail, temp16a);
- cxtabtlen = scale_expansion_zeroelim(abtlen, abt, cdxtail, cxtabt);
- temp32alen = scale_expansion_zeroelim(cxtabtlen, cxtabt, 2.0 * cdx,
- temp32a);
- temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
- temp32alen, temp32a, temp48);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
- temp48, finother);
- finswap = finnow; finnow = finother; finother = finswap;
- if (adytail != 0.0) {
- temp8len = scale_expansion_zeroelim(4, bb, cdxtail, temp8);
- temp16alen = scale_expansion_zeroelim(temp8len, temp8, adytail,
- temp16a);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
- temp16a, finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- if (bdytail != 0.0) {
- temp8len = scale_expansion_zeroelim(4, aa, -cdxtail, temp8);
- temp16alen = scale_expansion_zeroelim(temp8len, temp8, bdytail,
- temp16a);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
- temp16a, finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
-
- temp32alen = scale_expansion_zeroelim(cxtabtlen, cxtabt, cdxtail,
- temp32a);
- cxtabttlen = scale_expansion_zeroelim(abttlen, abtt, cdxtail, cxtabtt);
- temp16alen = scale_expansion_zeroelim(cxtabttlen, cxtabtt, 2.0 * cdx,
- temp16a);
- temp16blen = scale_expansion_zeroelim(cxtabttlen, cxtabtt, cdxtail,
- temp16b);
- temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
- temp16blen, temp16b, temp32b);
- temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
- temp32blen, temp32b, temp64);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
- temp64, finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- if (cdytail != 0.0) {
- temp16alen = scale_expansion_zeroelim(cytablen, cytab, cdytail, temp16a);
- cytabtlen = scale_expansion_zeroelim(abtlen, abt, cdytail, cytabt);
- temp32alen = scale_expansion_zeroelim(cytabtlen, cytabt, 2.0 * cdy,
- temp32a);
- temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
- temp32alen, temp32a, temp48);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
- temp48, finother);
- finswap = finnow; finnow = finother; finother = finswap;
-
-
- temp32alen = scale_expansion_zeroelim(cytabtlen, cytabt, cdytail,
- temp32a);
- cytabttlen = scale_expansion_zeroelim(abttlen, abtt, cdytail, cytabtt);
- temp16alen = scale_expansion_zeroelim(cytabttlen, cytabtt, 2.0 * cdy,
- temp16a);
- temp16blen = scale_expansion_zeroelim(cytabttlen, cytabtt, cdytail,
- temp16b);
- temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
- temp16blen, temp16b, temp32b);
- temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
- temp32blen, temp32b, temp64);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
- temp64, finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- }
-
- return finnow[finlength - 1];
-}
-
-#ifdef ANSI_DECLARATORS
-REAL incircle(struct mesh *m, struct behavior *b,
- vertex pa, vertex pb, vertex pc, vertex pd)
-#else /* not ANSI_DECLARATORS */
-REAL incircle(m, b, pa, pb, pc, pd)
-struct mesh *m;
-struct behavior *b;
-vertex pa;
-vertex pb;
-vertex pc;
-vertex pd;
-#endif /* not ANSI_DECLARATORS */
-
-{
- REAL adx, bdx, cdx, ady, bdy, cdy;
- REAL bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady;
- REAL alift, blift, clift;
- REAL det;
- REAL permanent, errbound;
-
- m->incirclecount++;
-
- adx = pa[0] - pd[0];
- bdx = pb[0] - pd[0];
- cdx = pc[0] - pd[0];
- ady = pa[1] - pd[1];
- bdy = pb[1] - pd[1];
- cdy = pc[1] - pd[1];
-
- bdxcdy = bdx * cdy;
- cdxbdy = cdx * bdy;
- alift = adx * adx + ady * ady;
-
- cdxady = cdx * ady;
- adxcdy = adx * cdy;
- blift = bdx * bdx + bdy * bdy;
-
- adxbdy = adx * bdy;
- bdxady = bdx * ady;
- clift = cdx * cdx + cdy * cdy;
-
- det = alift * (bdxcdy - cdxbdy)
- + blift * (cdxady - adxcdy)
- + clift * (adxbdy - bdxady);
-
- if (b->noexact) {
- return det;
- }
-
- permanent = (Absolute(bdxcdy) + Absolute(cdxbdy)) * alift
- + (Absolute(cdxady) + Absolute(adxcdy)) * blift
- + (Absolute(adxbdy) + Absolute(bdxady)) * clift;
- errbound = iccerrboundA * permanent;
- if ((det > errbound) || (-det > errbound)) {
- return det;
- }
-
- return incircleadapt(pa, pb, pc, pd, permanent);
-}
-
-/*****************************************************************************/
-/* */
-/* orient3d() Return a positive value if the point pd lies below the */
-/* plane passing through pa, pb, and pc; "below" is defined so */
-/* that pa, pb, and pc appear in counterclockwise order when */
-/* viewed from above the plane. Returns a negative value if */
-/* pd lies above the plane. Returns zero if the points are */
-/* coplanar. The result is also a rough approximation of six */
-/* times the signed volume of the tetrahedron defined by the */
-/* four points. */
-/* */
-/* Uses exact arithmetic if necessary to ensure a correct answer. The */
-/* result returned is the determinant of a matrix. This determinant is */
-/* computed adaptively, in the sense that exact arithmetic is used only to */
-/* the degree it is needed to ensure that the returned value has the */
-/* correct sign. Hence, this function is usually quite fast, but will run */
-/* more slowly when the input points are coplanar or nearly so. */
-/* */
-/* See my Robust Predicates paper for details. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-REAL orient3dadapt(vertex pa, vertex pb, vertex pc, vertex pd,
- REAL aheight, REAL bheight, REAL cheight, REAL dheight,
- REAL permanent)
-#else /* not ANSI_DECLARATORS */
-REAL orient3dadapt(pa, pb, pc, pd,
- aheight, bheight, cheight, dheight, permanent)
-vertex pa;
-vertex pb;
-vertex pc;
-vertex pd;
-REAL aheight;
-REAL bheight;
-REAL cheight;
-REAL dheight;
-REAL permanent;
-#endif /* not ANSI_DECLARATORS */
-
-{
- INEXACT REAL adx, bdx, cdx, ady, bdy, cdy, adheight, bdheight, cdheight;
- REAL det, errbound;
-
- INEXACT REAL bdxcdy1, cdxbdy1, cdxady1, adxcdy1, adxbdy1, bdxady1;
- REAL bdxcdy0, cdxbdy0, cdxady0, adxcdy0, adxbdy0, bdxady0;
- REAL bc[4], ca[4], ab[4];
- INEXACT REAL bc3, ca3, ab3;
- REAL adet[8], bdet[8], cdet[8];
- int alen, blen, clen;
- REAL abdet[16];
- int ablen;
- REAL *finnow, *finother, *finswap;
- REAL fin1[192], fin2[192];
- int finlength;
-
- REAL adxtail, bdxtail, cdxtail;
- REAL adytail, bdytail, cdytail;
- REAL adheighttail, bdheighttail, cdheighttail;
- INEXACT REAL at_blarge, at_clarge;
- INEXACT REAL bt_clarge, bt_alarge;
- INEXACT REAL ct_alarge, ct_blarge;
- REAL at_b[4], at_c[4], bt_c[4], bt_a[4], ct_a[4], ct_b[4];
- int at_blen, at_clen, bt_clen, bt_alen, ct_alen, ct_blen;
- INEXACT REAL bdxt_cdy1, cdxt_bdy1, cdxt_ady1;
- INEXACT REAL adxt_cdy1, adxt_bdy1, bdxt_ady1;
- REAL bdxt_cdy0, cdxt_bdy0, cdxt_ady0;
- REAL adxt_cdy0, adxt_bdy0, bdxt_ady0;
- INEXACT REAL bdyt_cdx1, cdyt_bdx1, cdyt_adx1;
- INEXACT REAL adyt_cdx1, adyt_bdx1, bdyt_adx1;
- REAL bdyt_cdx0, cdyt_bdx0, cdyt_adx0;
- REAL adyt_cdx0, adyt_bdx0, bdyt_adx0;
- REAL bct[8], cat[8], abt[8];
- int bctlen, catlen, abtlen;
- INEXACT REAL bdxt_cdyt1, cdxt_bdyt1, cdxt_adyt1;
- INEXACT REAL adxt_cdyt1, adxt_bdyt1, bdxt_adyt1;
- REAL bdxt_cdyt0, cdxt_bdyt0, cdxt_adyt0;
- REAL adxt_cdyt0, adxt_bdyt0, bdxt_adyt0;
- REAL u[4], v[12], w[16];
- INEXACT REAL u3;
- int vlength, wlength;
- REAL negate;
-
- INEXACT REAL bvirt;
- REAL avirt, bround, around;
- INEXACT REAL c;
- INEXACT REAL abig;
- REAL ahi, alo, bhi, blo;
- REAL err1, err2, err3;
- INEXACT REAL _i, _j, _k;
- REAL _0;
-
- adx = (REAL) (pa[0] - pd[0]);
- bdx = (REAL) (pb[0] - pd[0]);
- cdx = (REAL) (pc[0] - pd[0]);
- ady = (REAL) (pa[1] - pd[1]);
- bdy = (REAL) (pb[1] - pd[1]);
- cdy = (REAL) (pc[1] - pd[1]);
- adheight = (REAL) (aheight - dheight);
- bdheight = (REAL) (bheight - dheight);
- cdheight = (REAL) (cheight - dheight);
-
- Two_Product(bdx, cdy, bdxcdy1, bdxcdy0);
- Two_Product(cdx, bdy, cdxbdy1, cdxbdy0);
- Two_Two_Diff(bdxcdy1, bdxcdy0, cdxbdy1, cdxbdy0, bc3, bc[2], bc[1], bc[0]);
- bc[3] = bc3;
- alen = scale_expansion_zeroelim(4, bc, adheight, adet);
-
- Two_Product(cdx, ady, cdxady1, cdxady0);
- Two_Product(adx, cdy, adxcdy1, adxcdy0);
- Two_Two_Diff(cdxady1, cdxady0, adxcdy1, adxcdy0, ca3, ca[2], ca[1], ca[0]);
- ca[3] = ca3;
- blen = scale_expansion_zeroelim(4, ca, bdheight, bdet);
-
- Two_Product(adx, bdy, adxbdy1, adxbdy0);
- Two_Product(bdx, ady, bdxady1, bdxady0);
- Two_Two_Diff(adxbdy1, adxbdy0, bdxady1, bdxady0, ab3, ab[2], ab[1], ab[0]);
- ab[3] = ab3;
- clen = scale_expansion_zeroelim(4, ab, cdheight, cdet);
-
- ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
- finlength = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, fin1);
-
- det = estimate(finlength, fin1);
- errbound = o3derrboundB * permanent;
- if ((det >= errbound) || (-det >= errbound)) {
- return det;
- }
-
- Two_Diff_Tail(pa[0], pd[0], adx, adxtail);
- Two_Diff_Tail(pb[0], pd[0], bdx, bdxtail);
- Two_Diff_Tail(pc[0], pd[0], cdx, cdxtail);
- Two_Diff_Tail(pa[1], pd[1], ady, adytail);
- Two_Diff_Tail(pb[1], pd[1], bdy, bdytail);
- Two_Diff_Tail(pc[1], pd[1], cdy, cdytail);
- Two_Diff_Tail(aheight, dheight, adheight, adheighttail);
- Two_Diff_Tail(bheight, dheight, bdheight, bdheighttail);
- Two_Diff_Tail(cheight, dheight, cdheight, cdheighttail);
-
- if ((adxtail == 0.0) && (bdxtail == 0.0) && (cdxtail == 0.0) &&
- (adytail == 0.0) && (bdytail == 0.0) && (cdytail == 0.0) &&
- (adheighttail == 0.0) &&
- (bdheighttail == 0.0) &&
- (cdheighttail == 0.0)) {
- return det;
- }
-
- errbound = o3derrboundC * permanent + resulterrbound * Absolute(det);
- det += (adheight * ((bdx * cdytail + cdy * bdxtail) -
- (bdy * cdxtail + cdx * bdytail)) +
- adheighttail * (bdx * cdy - bdy * cdx)) +
- (bdheight * ((cdx * adytail + ady * cdxtail) -
- (cdy * adxtail + adx * cdytail)) +
- bdheighttail * (cdx * ady - cdy * adx)) +
- (cdheight * ((adx * bdytail + bdy * adxtail) -
- (ady * bdxtail + bdx * adytail)) +
- cdheighttail * (adx * bdy - ady * bdx));
- if ((det >= errbound) || (-det >= errbound)) {
- return det;
- }
-
- finnow = fin1;
- finother = fin2;
-
- if (adxtail == 0.0) {
- if (adytail == 0.0) {
- at_b[0] = 0.0;
- at_blen = 1;
- at_c[0] = 0.0;
- at_clen = 1;
- } else {
- negate = -adytail;
- Two_Product(negate, bdx, at_blarge, at_b[0]);
- at_b[1] = at_blarge;
- at_blen = 2;
- Two_Product(adytail, cdx, at_clarge, at_c[0]);
- at_c[1] = at_clarge;
- at_clen = 2;
- }
- } else {
- if (adytail == 0.0) {
- Two_Product(adxtail, bdy, at_blarge, at_b[0]);
- at_b[1] = at_blarge;
- at_blen = 2;
- negate = -adxtail;
- Two_Product(negate, cdy, at_clarge, at_c[0]);
- at_c[1] = at_clarge;
- at_clen = 2;
- } else {
- Two_Product(adxtail, bdy, adxt_bdy1, adxt_bdy0);
- Two_Product(adytail, bdx, adyt_bdx1, adyt_bdx0);
- Two_Two_Diff(adxt_bdy1, adxt_bdy0, adyt_bdx1, adyt_bdx0,
- at_blarge, at_b[2], at_b[1], at_b[0]);
- at_b[3] = at_blarge;
- at_blen = 4;
- Two_Product(adytail, cdx, adyt_cdx1, adyt_cdx0);
- Two_Product(adxtail, cdy, adxt_cdy1, adxt_cdy0);
- Two_Two_Diff(adyt_cdx1, adyt_cdx0, adxt_cdy1, adxt_cdy0,
- at_clarge, at_c[2], at_c[1], at_c[0]);
- at_c[3] = at_clarge;
- at_clen = 4;
- }
- }
- if (bdxtail == 0.0) {
- if (bdytail == 0.0) {
- bt_c[0] = 0.0;
- bt_clen = 1;
- bt_a[0] = 0.0;
- bt_alen = 1;
- } else {
- negate = -bdytail;
- Two_Product(negate, cdx, bt_clarge, bt_c[0]);
- bt_c[1] = bt_clarge;
- bt_clen = 2;
- Two_Product(bdytail, adx, bt_alarge, bt_a[0]);
- bt_a[1] = bt_alarge;
- bt_alen = 2;
- }
- } else {
- if (bdytail == 0.0) {
- Two_Product(bdxtail, cdy, bt_clarge, bt_c[0]);
- bt_c[1] = bt_clarge;
- bt_clen = 2;
- negate = -bdxtail;
- Two_Product(negate, ady, bt_alarge, bt_a[0]);
- bt_a[1] = bt_alarge;
- bt_alen = 2;
- } else {
- Two_Product(bdxtail, cdy, bdxt_cdy1, bdxt_cdy0);
- Two_Product(bdytail, cdx, bdyt_cdx1, bdyt_cdx0);
- Two_Two_Diff(bdxt_cdy1, bdxt_cdy0, bdyt_cdx1, bdyt_cdx0,
- bt_clarge, bt_c[2], bt_c[1], bt_c[0]);
- bt_c[3] = bt_clarge;
- bt_clen = 4;
- Two_Product(bdytail, adx, bdyt_adx1, bdyt_adx0);
- Two_Product(bdxtail, ady, bdxt_ady1, bdxt_ady0);
- Two_Two_Diff(bdyt_adx1, bdyt_adx0, bdxt_ady1, bdxt_ady0,
- bt_alarge, bt_a[2], bt_a[1], bt_a[0]);
- bt_a[3] = bt_alarge;
- bt_alen = 4;
- }
- }
- if (cdxtail == 0.0) {
- if (cdytail == 0.0) {
- ct_a[0] = 0.0;
- ct_alen = 1;
- ct_b[0] = 0.0;
- ct_blen = 1;
- } else {
- negate = -cdytail;
- Two_Product(negate, adx, ct_alarge, ct_a[0]);
- ct_a[1] = ct_alarge;
- ct_alen = 2;
- Two_Product(cdytail, bdx, ct_blarge, ct_b[0]);
- ct_b[1] = ct_blarge;
- ct_blen = 2;
- }
- } else {
- if (cdytail == 0.0) {
- Two_Product(cdxtail, ady, ct_alarge, ct_a[0]);
- ct_a[1] = ct_alarge;
- ct_alen = 2;
- negate = -cdxtail;
- Two_Product(negate, bdy, ct_blarge, ct_b[0]);
- ct_b[1] = ct_blarge;
- ct_blen = 2;
- } else {
- Two_Product(cdxtail, ady, cdxt_ady1, cdxt_ady0);
- Two_Product(cdytail, adx, cdyt_adx1, cdyt_adx0);
- Two_Two_Diff(cdxt_ady1, cdxt_ady0, cdyt_adx1, cdyt_adx0,
- ct_alarge, ct_a[2], ct_a[1], ct_a[0]);
- ct_a[3] = ct_alarge;
- ct_alen = 4;
- Two_Product(cdytail, bdx, cdyt_bdx1, cdyt_bdx0);
- Two_Product(cdxtail, bdy, cdxt_bdy1, cdxt_bdy0);
- Two_Two_Diff(cdyt_bdx1, cdyt_bdx0, cdxt_bdy1, cdxt_bdy0,
- ct_blarge, ct_b[2], ct_b[1], ct_b[0]);
- ct_b[3] = ct_blarge;
- ct_blen = 4;
- }
- }
-
- bctlen = fast_expansion_sum_zeroelim(bt_clen, bt_c, ct_blen, ct_b, bct);
- wlength = scale_expansion_zeroelim(bctlen, bct, adheight, w);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
- finother);
- finswap = finnow; finnow = finother; finother = finswap;
-
- catlen = fast_expansion_sum_zeroelim(ct_alen, ct_a, at_clen, at_c, cat);
- wlength = scale_expansion_zeroelim(catlen, cat, bdheight, w);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
- finother);
- finswap = finnow; finnow = finother; finother = finswap;
-
- abtlen = fast_expansion_sum_zeroelim(at_blen, at_b, bt_alen, bt_a, abt);
- wlength = scale_expansion_zeroelim(abtlen, abt, cdheight, w);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
- finother);
- finswap = finnow; finnow = finother; finother = finswap;
-
- if (adheighttail != 0.0) {
- vlength = scale_expansion_zeroelim(4, bc, adheighttail, v);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v,
- finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- if (bdheighttail != 0.0) {
- vlength = scale_expansion_zeroelim(4, ca, bdheighttail, v);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v,
- finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- if (cdheighttail != 0.0) {
- vlength = scale_expansion_zeroelim(4, ab, cdheighttail, v);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v,
- finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
-
- if (adxtail != 0.0) {
- if (bdytail != 0.0) {
- Two_Product(adxtail, bdytail, adxt_bdyt1, adxt_bdyt0);
- Two_One_Product(adxt_bdyt1, adxt_bdyt0, cdheight, u3, u[2], u[1], u[0]);
- u[3] = u3;
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
- finother);
- finswap = finnow; finnow = finother; finother = finswap;
- if (cdheighttail != 0.0) {
- Two_One_Product(adxt_bdyt1, adxt_bdyt0, cdheighttail,
- u3, u[2], u[1], u[0]);
- u[3] = u3;
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
- finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- }
- if (cdytail != 0.0) {
- negate = -adxtail;
- Two_Product(negate, cdytail, adxt_cdyt1, adxt_cdyt0);
- Two_One_Product(adxt_cdyt1, adxt_cdyt0, bdheight, u3, u[2], u[1], u[0]);
- u[3] = u3;
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
- finother);
- finswap = finnow; finnow = finother; finother = finswap;
- if (bdheighttail != 0.0) {
- Two_One_Product(adxt_cdyt1, adxt_cdyt0, bdheighttail,
- u3, u[2], u[1], u[0]);
- u[3] = u3;
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
- finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- }
- }
- if (bdxtail != 0.0) {
- if (cdytail != 0.0) {
- Two_Product(bdxtail, cdytail, bdxt_cdyt1, bdxt_cdyt0);
- Two_One_Product(bdxt_cdyt1, bdxt_cdyt0, adheight, u3, u[2], u[1], u[0]);
- u[3] = u3;
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
- finother);
- finswap = finnow; finnow = finother; finother = finswap;
- if (adheighttail != 0.0) {
- Two_One_Product(bdxt_cdyt1, bdxt_cdyt0, adheighttail,
- u3, u[2], u[1], u[0]);
- u[3] = u3;
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
- finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- }
- if (adytail != 0.0) {
- negate = -bdxtail;
- Two_Product(negate, adytail, bdxt_adyt1, bdxt_adyt0);
- Two_One_Product(bdxt_adyt1, bdxt_adyt0, cdheight, u3, u[2], u[1], u[0]);
- u[3] = u3;
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
- finother);
- finswap = finnow; finnow = finother; finother = finswap;
- if (cdheighttail != 0.0) {
- Two_One_Product(bdxt_adyt1, bdxt_adyt0, cdheighttail,
- u3, u[2], u[1], u[0]);
- u[3] = u3;
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
- finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- }
- }
- if (cdxtail != 0.0) {
- if (adytail != 0.0) {
- Two_Product(cdxtail, adytail, cdxt_adyt1, cdxt_adyt0);
- Two_One_Product(cdxt_adyt1, cdxt_adyt0, bdheight, u3, u[2], u[1], u[0]);
- u[3] = u3;
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
- finother);
- finswap = finnow; finnow = finother; finother = finswap;
- if (bdheighttail != 0.0) {
- Two_One_Product(cdxt_adyt1, cdxt_adyt0, bdheighttail,
- u3, u[2], u[1], u[0]);
- u[3] = u3;
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
- finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- }
- if (bdytail != 0.0) {
- negate = -cdxtail;
- Two_Product(negate, bdytail, cdxt_bdyt1, cdxt_bdyt0);
- Two_One_Product(cdxt_bdyt1, cdxt_bdyt0, adheight, u3, u[2], u[1], u[0]);
- u[3] = u3;
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
- finother);
- finswap = finnow; finnow = finother; finother = finswap;
- if (adheighttail != 0.0) {
- Two_One_Product(cdxt_bdyt1, cdxt_bdyt0, adheighttail,
- u3, u[2], u[1], u[0]);
- u[3] = u3;
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
- finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- }
- }
-
- if (adheighttail != 0.0) {
- wlength = scale_expansion_zeroelim(bctlen, bct, adheighttail, w);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
- finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- if (bdheighttail != 0.0) {
- wlength = scale_expansion_zeroelim(catlen, cat, bdheighttail, w);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
- finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
- if (cdheighttail != 0.0) {
- wlength = scale_expansion_zeroelim(abtlen, abt, cdheighttail, w);
- finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
- finother);
- finswap = finnow; finnow = finother; finother = finswap;
- }
-
- return finnow[finlength - 1];
-}
-
-#ifdef ANSI_DECLARATORS
-REAL orient3d(struct mesh *m, struct behavior *b,
- vertex pa, vertex pb, vertex pc, vertex pd,
- REAL aheight, REAL bheight, REAL cheight, REAL dheight)
-#else /* not ANSI_DECLARATORS */
-REAL orient3d(m, b, pa, pb, pc, pd, aheight, bheight, cheight, dheight)
-struct mesh *m;
-struct behavior *b;
-vertex pa;
-vertex pb;
-vertex pc;
-vertex pd;
-REAL aheight;
-REAL bheight;
-REAL cheight;
-REAL dheight;
-#endif /* not ANSI_DECLARATORS */
-
-{
- REAL adx, bdx, cdx, ady, bdy, cdy, adheight, bdheight, cdheight;
- REAL bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady;
- REAL det;
- REAL permanent, errbound;
-
- m->orient3dcount++;
-
- adx = pa[0] - pd[0];
- bdx = pb[0] - pd[0];
- cdx = pc[0] - pd[0];
- ady = pa[1] - pd[1];
- bdy = pb[1] - pd[1];
- cdy = pc[1] - pd[1];
- adheight = aheight - dheight;
- bdheight = bheight - dheight;
- cdheight = cheight - dheight;
-
- bdxcdy = bdx * cdy;
- cdxbdy = cdx * bdy;
-
- cdxady = cdx * ady;
- adxcdy = adx * cdy;
-
- adxbdy = adx * bdy;
- bdxady = bdx * ady;
-
- det = adheight * (bdxcdy - cdxbdy)
- + bdheight * (cdxady - adxcdy)
- + cdheight * (adxbdy - bdxady);
-
- if (b->noexact) {
- return det;
- }
-
- permanent = (Absolute(bdxcdy) + Absolute(cdxbdy)) * Absolute(adheight)
- + (Absolute(cdxady) + Absolute(adxcdy)) * Absolute(bdheight)
- + (Absolute(adxbdy) + Absolute(bdxady)) * Absolute(cdheight);
- errbound = o3derrboundA * permanent;
- if ((det > errbound) || (-det > errbound)) {
- return det;
- }
-
- return orient3dadapt(pa, pb, pc, pd, aheight, bheight, cheight, dheight,
- permanent);
-}
-
-/*****************************************************************************/
-/* */
-/* nonregular() Return a positive value if the point pd is incompatible */
-/* with the circle or plane passing through pa, pb, and pc */
-/* (meaning that pd is inside the circle or below the */
-/* plane); a negative value if it is compatible; and zero if */
-/* the four points are cocircular/coplanar. The points pa, */
-/* pb, and pc must be in counterclockwise order, or the sign */
-/* of the result will be reversed. */
-/* */
-/* If the -w switch is used, the points are lifted onto the parabolic */
-/* lifting map, then they are dropped according to their weights, then the */
-/* 3D orientation test is applied. If the -W switch is used, the points' */
-/* heights are already provided, so the 3D orientation test is applied */
-/* directly. If neither switch is used, the incircle test is applied. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-REAL nonregular(struct mesh *m, struct behavior *b,
- vertex pa, vertex pb, vertex pc, vertex pd)
-#else /* not ANSI_DECLARATORS */
-REAL nonregular(m, b, pa, pb, pc, pd)
-struct mesh *m;
-struct behavior *b;
-vertex pa;
-vertex pb;
-vertex pc;
-vertex pd;
-#endif /* not ANSI_DECLARATORS */
-
-{
- if (b->weighted == 0) {
- return incircle(m, b, pa, pb, pc, pd);
- } else if (b->weighted == 1) {
- return orient3d(m, b, pa, pb, pc, pd,
- pa[0] * pa[0] + pa[1] * pa[1] - pa[2],
- pb[0] * pb[0] + pb[1] * pb[1] - pb[2],
- pc[0] * pc[0] + pc[1] * pc[1] - pc[2],
- pd[0] * pd[0] + pd[1] * pd[1] - pd[2]);
- } else {
- return orient3d(m, b, pa, pb, pc, pd, pa[2], pb[2], pc[2], pd[2]);
- }
-}
-
-/*****************************************************************************/
-/* */
-/* findcircumcenter() Find the circumcenter of a triangle. */
-/* */
-/* The result is returned both in terms of x-y coordinates and xi-eta */
-/* (barycentric) coordinates. The xi-eta coordinate system is defined in */
-/* terms of the triangle: the origin of the triangle is the origin of the */
-/* coordinate system; the destination of the triangle is one unit along the */
-/* xi axis; and the apex of the triangle is one unit along the eta axis. */
-/* This procedure also returns the square of the length of the triangle's */
-/* shortest edge. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-void findcircumcenter(struct mesh *m, struct behavior *b,
- vertex torg, vertex tdest, vertex tapex,
- vertex circumcenter, REAL *xi, REAL *eta, int offcenter)
-#else /* not ANSI_DECLARATORS */
-void findcircumcenter(m, b, torg, tdest, tapex, circumcenter, xi, eta,
- offcenter)
-struct mesh *m;
-struct behavior *b;
-vertex torg;
-vertex tdest;
-vertex tapex;
-vertex circumcenter;
-REAL *xi;
-REAL *eta;
-int offcenter;
-#endif /* not ANSI_DECLARATORS */
-
-{
- REAL xdo, ydo, xao, yao;
- REAL dodist, aodist, dadist;
- REAL denominator;
- REAL dx, dy, dxoff, dyoff;
-
- m->circumcentercount++;
-
- /* Compute the circumcenter of the triangle. */
- xdo = tdest[0] - torg[0];
- ydo = tdest[1] - torg[1];
- xao = tapex[0] - torg[0];
- yao = tapex[1] - torg[1];
- dodist = xdo * xdo + ydo * ydo;
- aodist = xao * xao + yao * yao;
- dadist = (tdest[0] - tapex[0]) * (tdest[0] - tapex[0]) +
- (tdest[1] - tapex[1]) * (tdest[1] - tapex[1]);
- if (b->noexact) {
- denominator = 0.5 / (xdo * yao - xao * ydo);
- } else {
- /* Use the counterclockwise() routine to ensure a positive (and */
- /* reasonably accurate) result, avoiding any possibility of */
- /* division by zero. */
- denominator = 0.5 / counterclockwise(m, b, tdest, tapex, torg);
- /* Don't count the above as an orientation test. */
- m->counterclockcount--;
- }
- dx = (yao * dodist - ydo * aodist) * denominator;
- dy = (xdo * aodist - xao * dodist) * denominator;
-
- /* Find the (squared) length of the triangle's shortest edge. This */
- /* serves as a conservative estimate of the insertion radius of the */
- /* circumcenter's parent. The estimate is used to ensure that */
- /* the algorithm terminates even if very small angles appear in */
- /* the input PSLG. */
- if ((dodist < aodist) && (dodist < dadist)) {
- if (offcenter && (b->offconstant > 0.0)) {
- /* Find the position of the off-center, as described by Alper Ungor. */
- dxoff = 0.5 * xdo - b->offconstant * ydo;
- dyoff = 0.5 * ydo + b->offconstant * xdo;
- /* If the off-center is closer to the origin than the */
- /* circumcenter, use the off-center instead. */
- if (dxoff * dxoff + dyoff * dyoff < dx * dx + dy * dy) {
- dx = dxoff;
- dy = dyoff;
- }
- }
- } else if (aodist < dadist) {
- if (offcenter && (b->offconstant > 0.0)) {
- dxoff = 0.5 * xao + b->offconstant * yao;
- dyoff = 0.5 * yao - b->offconstant * xao;
- /* If the off-center is closer to the origin than the */
- /* circumcenter, use the off-center instead. */
- if (dxoff * dxoff + dyoff * dyoff < dx * dx + dy * dy) {
- dx = dxoff;
- dy = dyoff;
- }
- }
- } else {
- if (offcenter && (b->offconstant > 0.0)) {
- dxoff = 0.5 * (tapex[0] - tdest[0]) -
- b->offconstant * (tapex[1] - tdest[1]);
- dyoff = 0.5 * (tapex[1] - tdest[1]) +
- b->offconstant * (tapex[0] - tdest[0]);
- /* If the off-center is closer to the destination than the */
- /* circumcenter, use the off-center instead. */
- if (dxoff * dxoff + dyoff * dyoff <
- (dx - xdo) * (dx - xdo) + (dy - ydo) * (dy - ydo)) {
- dx = xdo + dxoff;
- dy = ydo + dyoff;
- }
- }
- }
-
- circumcenter[0] = torg[0] + dx;
- circumcenter[1] = torg[1] + dy;
-
- /* To interpolate vertex attributes for the new vertex inserted at */
- /* the circumcenter, define a coordinate system with a xi-axis, */
- /* directed from the triangle's origin to its destination, and */
- /* an eta-axis, directed from its origin to its apex. */
- /* Calculate the xi and eta coordinates of the circumcenter. */
- *xi = (yao * dx - xao * dy) * (2.0 * denominator);
- *eta = (xdo * dy - ydo * dx) * (2.0 * denominator);
-}
-
-/** **/
-/** **/
-/********* Geometric primitives end here *********/
-
-/*****************************************************************************/
-/* */
-/* triangleinit() Initialize some variables. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-void triangleinit(struct mesh *m)
-#else /* not ANSI_DECLARATORS */
-void triangleinit(m)
-struct mesh *m;
-#endif /* not ANSI_DECLARATORS */
-
-{
- poolzero(&m->vertices);
- poolzero(&m->triangles);
- poolzero(&m->subsegs);
- poolzero(&m->viri);
- poolzero(&m->badsubsegs);
- poolzero(&m->badtriangles);
- poolzero(&m->flipstackers);
- poolzero(&m->splaynodes);
-
- m->recenttri.tri = (triangle *) NULL; /* No triangle has been visited yet. */
- m->undeads = 0; /* No eliminated input vertices yet. */
- m->samples = 1; /* Point location should take at least one sample. */
- m->checksegments = 0; /* There are no segments in the triangulation yet. */
- m->checkquality = 0; /* The quality triangulation stage has not begun. */
- m->incirclecount = m->counterclockcount = m->orient3dcount = 0;
- m->hyperbolacount = m->circletopcount = m->circumcentercount = 0;
- randomseed = 1;
-
- exactinit(); /* Initialize exact arithmetic constants. */
-}
-
-/*****************************************************************************/
-/* */
-/* randomnation() Generate a random number between 0 and `choices' - 1. */
-/* */
-/* This is a simple linear congruential random number generator. Hence, it */
-/* is a bad random number generator, but good enough for most randomized */
-/* geometric algorithms. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-unsigned long randomnation(unsigned int choices)
-#else /* not ANSI_DECLARATORS */
-unsigned long randomnation(choices)
-unsigned int choices;
-#endif /* not ANSI_DECLARATORS */
-
-{
- randomseed = (randomseed * 1366l + 150889l) % 714025l;
- return randomseed / (714025l / choices + 1);
-}
-
-/********* Mesh quality testing routines begin here *********/
-/** **/
-/** **/
-
-/*****************************************************************************/
-/* */
-/* checkmesh() Test the mesh for topological consistency. */
-/* */
-/*****************************************************************************/
-
-#ifndef REDUCED
-
-#ifdef ANSI_DECLARATORS
-void checkmesh(struct mesh *m, struct behavior *b)
-#else /* not ANSI_DECLARATORS */
-void checkmesh(m, b)
-struct mesh *m;
-struct behavior *b;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct otri triangleloop;
- struct otri oppotri, oppooppotri;
- vertex triorg, tridest, triapex;
- vertex oppoorg, oppodest;
- int horrors;
- int saveexact;
- triangle ptr; /* Temporary variable used by sym(). */
-
- /* Temporarily turn on exact arithmetic if it's off. */
- saveexact = b->noexact;
- b->noexact = 0;
- if (!b->quiet) {
- printf(" Checking consistency of mesh...\n");
- }
- horrors = 0;
- /* Run through the list of triangles, checking each one. */
- traversalinit(&m->triangles);
- triangleloop.tri = triangletraverse(m);
- while (triangleloop.tri != (triangle *) NULL) {
- /* Check all three edges of the triangle. */
- for (triangleloop.orient = 0; triangleloop.orient < 3;
- triangleloop.orient++) {
- org(triangleloop, triorg);
- dest(triangleloop, tridest);
- if (triangleloop.orient == 0) { /* Only test for inversion once. */
- /* Test if the triangle is flat or inverted. */
- apex(triangleloop, triapex);
- if (counterclockwise(m, b, triorg, tridest, triapex) <= 0.0) {
- printf(" !! !! Inverted ");
- printtriangle(m, b, &triangleloop);
- horrors++;
- }
- }
- /* Find the neighboring triangle on this edge. */
- sym(triangleloop, oppotri);
- if (oppotri.tri != m->dummytri) {
- /* Check that the triangle's neighbor knows it's a neighbor. */
- sym(oppotri, oppooppotri);
- if ((triangleloop.tri != oppooppotri.tri)
- || (triangleloop.orient != oppooppotri.orient)) {
- printf(" !! !! Asymmetric triangle-triangle bond:\n");
- if (triangleloop.tri == oppooppotri.tri) {
- printf(" (Right triangle, wrong orientation)\n");
- }
- printf(" First ");
- printtriangle(m, b, &triangleloop);
- printf(" Second (nonreciprocating) ");
- printtriangle(m, b, &oppotri);
- horrors++;
- }
- /* Check that both triangles agree on the identities */
- /* of their shared vertices. */
- org(oppotri, oppoorg);
- dest(oppotri, oppodest);
- if ((triorg != oppodest) || (tridest != oppoorg)) {
- printf(" !! !! Mismatched edge coordinates between two triangles:\n"
- );
- printf(" First mismatched ");
- printtriangle(m, b, &triangleloop);
- printf(" Second mismatched ");
- printtriangle(m, b, &oppotri);
- horrors++;
- }
- }
- }
- triangleloop.tri = triangletraverse(m);
- }
- if (horrors == 0) {
- if (!b->quiet) {
- printf(" In my studied opinion, the mesh appears to be consistent.\n");
- }
- } else if (horrors == 1) {
- printf(" !! !! !! !! Precisely one festering wound discovered.\n");
- } else {
- printf(" !! !! !! !! %d abominations witnessed.\n", horrors);
- }
- /* Restore the status of exact arithmetic. */
- b->noexact = saveexact;
-}
-
-#endif /* not REDUCED */
-
-/*****************************************************************************/
-/* */
-/* checkdelaunay() Ensure that the mesh is (constrained) Delaunay. */
-/* */
-/*****************************************************************************/
-
-#ifndef REDUCED
-
-#ifdef ANSI_DECLARATORS
-void checkdelaunay(struct mesh *m, struct behavior *b)
-#else /* not ANSI_DECLARATORS */
-void checkdelaunay(m, b)
-struct mesh *m;
-struct behavior *b;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct otri triangleloop;
- struct otri oppotri;
- struct osub opposubseg;
- vertex triorg, tridest, triapex;
- vertex oppoapex;
- int shouldbedelaunay;
- int horrors;
- int saveexact;
- triangle ptr; /* Temporary variable used by sym(). */
- subseg sptr; /* Temporary variable used by tspivot(). */
-
- /* Temporarily turn on exact arithmetic if it's off. */
- saveexact = b->noexact;
- b->noexact = 0;
- if (!b->quiet) {
- printf(" Checking Delaunay property of mesh...\n");
- }
- horrors = 0;
- /* Run through the list of triangles, checking each one. */
- traversalinit(&m->triangles);
- triangleloop.tri = triangletraverse(m);
- while (triangleloop.tri != (triangle *) NULL) {
- /* Check all three edges of the triangle. */
- for (triangleloop.orient = 0; triangleloop.orient < 3;
- triangleloop.orient++) {
- org(triangleloop, triorg);
- dest(triangleloop, tridest);
- apex(triangleloop, triapex);
- sym(triangleloop, oppotri);
- apex(oppotri, oppoapex);
- /* Only test that the edge is locally Delaunay if there is an */
- /* adjoining triangle whose pointer is larger (to ensure that */
- /* each pair isn't tested twice). */
- shouldbedelaunay = (oppotri.tri != m->dummytri) &&
- !deadtri(oppotri.tri) && (triangleloop.tri < oppotri.tri) &&
- (triorg != m->infvertex1) && (triorg != m->infvertex2) &&
- (triorg != m->infvertex3) &&
- (tridest != m->infvertex1) && (tridest != m->infvertex2) &&
- (tridest != m->infvertex3) &&
- (triapex != m->infvertex1) && (triapex != m->infvertex2) &&
- (triapex != m->infvertex3) &&
- (oppoapex != m->infvertex1) && (oppoapex != m->infvertex2) &&
- (oppoapex != m->infvertex3);
- if (m->checksegments && shouldbedelaunay) {
- /* If a subsegment separates the triangles, then the edge is */
- /* constrained, so no local Delaunay test should be done. */
- tspivot(triangleloop, opposubseg);
- if (opposubseg.ss != m->dummysub){
- shouldbedelaunay = 0;
- }
- }
- if (shouldbedelaunay) {
- if (nonregular(m, b, triorg, tridest, triapex, oppoapex) > 0.0) {
- if (!b->weighted) {
- printf(" !! !! Non-Delaunay pair of triangles:\n");
- printf(" First non-Delaunay ");
- printtriangle(m, b, &triangleloop);
- printf(" Second non-Delaunay ");
- } else {
- printf(" !! !! Non-regular pair of triangles:\n");
- printf(" First non-regular ");
- printtriangle(m, b, &triangleloop);
- printf(" Second non-regular ");
- }
- printtriangle(m, b, &oppotri);
- horrors++;
- }
- }
- }
- triangleloop.tri = triangletraverse(m);
- }
- if (horrors == 0) {
- if (!b->quiet) {
- printf(
- " By virtue of my perceptive intelligence, I declare the mesh Delaunay.\n");
- }
- } else if (horrors == 1) {
- printf(
- " !! !! !! !! Precisely one terrifying transgression identified.\n");
- } else {
- printf(" !! !! !! !! %d obscenities viewed with horror.\n", horrors);
- }
- /* Restore the status of exact arithmetic. */
- b->noexact = saveexact;
-}
-
-#endif /* not REDUCED */
-
-/*****************************************************************************/
-/* */
-/* enqueuebadtriang() Add a bad triangle data structure to the end of a */
-/* queue. */
-/* */
-/* The queue is actually a set of 4096 queues. I use multiple queues to */
-/* give priority to smaller angles. I originally implemented a heap, but */
-/* the queues are faster by a larger margin than I'd suspected. */
-/* */
-/*****************************************************************************/
-
-#ifndef CDT_ONLY
-
-#ifdef ANSI_DECLARATORS
-void enqueuebadtriang(struct mesh *m, struct behavior *b,
- struct badtriang *badtri)
-#else /* not ANSI_DECLARATORS */
-void enqueuebadtriang(m, b, badtri)
-struct mesh *m;
-struct behavior *b;
-struct badtriang *badtri;
-#endif /* not ANSI_DECLARATORS */
-
-{
- REAL length, multiplier;
- int exponent, expincrement;
- int queuenumber;
- int posexponent;
- int i;
-
- if (b->verbose > 2) {
- printf(" Queueing bad triangle:\n");
- printf(" (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
- badtri->triangorg[0], badtri->triangorg[1],
- badtri->triangdest[0], badtri->triangdest[1],
- badtri->triangapex[0], badtri->triangapex[1]);
- }
-
- /* Determine the appropriate queue to put the bad triangle into. */
- /* Recall that the key is the square of its shortest edge length. */
- if (badtri->key >= 1.0) {
- length = badtri->key;
- posexponent = 1;
- } else {
- /* `badtri->key' is 2.0 to a negative exponent, so we'll record that */
- /* fact and use the reciprocal of `badtri->key', which is > 1.0. */
- length = 1.0 / badtri->key;
- posexponent = 0;
- }
- /* `length' is approximately 2.0 to what exponent? The following code */
- /* determines the answer in time logarithmic in the exponent. */
- exponent = 0;
- while (length > 2.0) {
- /* Find an approximation by repeated squaring of two. */
- expincrement = 1;
- multiplier = 0.5;
- while (length * multiplier * multiplier > 1.0) {
- expincrement *= 2;
- multiplier *= multiplier;
- }
- /* Reduce the value of `length', then iterate if necessary. */
- exponent += expincrement;
- length *= multiplier;
- }
- /* `length' is approximately squareroot(2.0) to what exponent? */
- exponent = 2.0 * exponent + (length > SQUAREROOTTWO);
- /* `exponent' is now in the range 0...2047 for IEEE double precision. */
- /* Choose a queue in the range 0...4095. The shortest edges have the */
- /* highest priority (queue 4095). */
- if (posexponent) {
- queuenumber = 2047 - exponent;
- } else {
- queuenumber = 2048 + exponent;
- }
-
- /* Are we inserting into an empty queue? */
- if (m->queuefront[queuenumber] == (struct badtriang *) NULL) {
- /* Yes, we are inserting into an empty queue. */
- /* Will this become the highest-priority queue? */
- if (queuenumber > m->firstnonemptyq) {
- /* Yes, this is the highest-priority queue. */
- m->nextnonemptyq[queuenumber] = m->firstnonemptyq;
- m->firstnonemptyq = queuenumber;
- } else {
- /* No, this is not the highest-priority queue. */
- /* Find the queue with next higher priority. */
- i = queuenumber + 1;
- while (m->queuefront[i] == (struct badtriang *) NULL) {
- i++;
- }
- /* Mark the newly nonempty queue as following a higher-priority queue. */
- m->nextnonemptyq[queuenumber] = m->nextnonemptyq[i];
- m->nextnonemptyq[i] = queuenumber;
- }
- /* Put the bad triangle at the beginning of the (empty) queue. */
- m->queuefront[queuenumber] = badtri;
- } else {
- /* Add the bad triangle to the end of an already nonempty queue. */
- m->queuetail[queuenumber]->nexttriang = badtri;
- }
- /* Maintain a pointer to the last triangle of the queue. */
- m->queuetail[queuenumber] = badtri;
- /* Newly enqueued bad triangle has no successor in the queue. */
- badtri->nexttriang = (struct badtriang *) NULL;
-}
-
-#endif /* not CDT_ONLY */
-
-/*****************************************************************************/
-/* */
-/* enqueuebadtri() Add a bad triangle to the end of a queue. */
-/* */
-/* Allocates a badtriang data structure for the triangle, then passes it to */
-/* enqueuebadtriang(). */
-/* */
-/*****************************************************************************/
-
-#ifndef CDT_ONLY
-
-#ifdef ANSI_DECLARATORS
-void enqueuebadtri(struct mesh *m, struct behavior *b, struct otri *enqtri,
- REAL minedge, vertex enqapex, vertex enqorg, vertex enqdest)
-#else /* not ANSI_DECLARATORS */
-void enqueuebadtri(m, b, enqtri, minedge, enqapex, enqorg, enqdest)
-struct mesh *m;
-struct behavior *b;
-struct otri *enqtri;
-REAL minedge;
-vertex enqapex;
-vertex enqorg;
-vertex enqdest;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct badtriang *newbad;
-
- /* Allocate space for the bad triangle. */
- newbad = (struct badtriang *) poolalloc(&m->badtriangles);
- newbad->poortri = encode(*enqtri);
- newbad->key = minedge;
- newbad->triangapex = enqapex;
- newbad->triangorg = enqorg;
- newbad->triangdest = enqdest;
- enqueuebadtriang(m, b, newbad);
-}
-
-#endif /* not CDT_ONLY */
-
-/*****************************************************************************/
-/* */
-/* dequeuebadtriang() Remove a triangle from the front of the queue. */
-/* */
-/*****************************************************************************/
-
-#ifndef CDT_ONLY
-
-#ifdef ANSI_DECLARATORS
-struct badtriang *dequeuebadtriang(struct mesh *m)
-#else /* not ANSI_DECLARATORS */
-struct badtriang *dequeuebadtriang(m)
-struct mesh *m;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct badtriang *result;
-
- /* If no queues are nonempty, return NULL. */
- if (m->firstnonemptyq < 0) {
- return (struct badtriang *) NULL;
- }
- /* Find the first triangle of the highest-priority queue. */
- result = m->queuefront[m->firstnonemptyq];
- /* Remove the triangle from the queue. */
- m->queuefront[m->firstnonemptyq] = result->nexttriang;
- /* If this queue is now empty, note the new highest-priority */
- /* nonempty queue. */
- if (result == m->queuetail[m->firstnonemptyq]) {
- m->firstnonemptyq = m->nextnonemptyq[m->firstnonemptyq];
- }
- return result;
-}
-
-#endif /* not CDT_ONLY */
-
-/*****************************************************************************/
-/* */
-/* checkseg4encroach() Check a subsegment to see if it is encroached; add */
-/* it to the list if it is. */
-/* */
-/* A subsegment is encroached if there is a vertex in its diametral lens. */
-/* For Ruppert's algorithm (-D switch), the "diametral lens" is the */
-/* diametral circle. For Chew's algorithm (default), the diametral lens is */
-/* just big enough to enclose two isosceles triangles whose bases are the */
-/* subsegment. Each of the two isosceles triangles has two angles equal */
-/* to `b->minangle'. */
-/* */
-/* Chew's algorithm does not require diametral lenses at all--but they save */
-/* time. Any vertex inside a subsegment's diametral lens implies that the */
-/* triangle adjoining the subsegment will be too skinny, so it's only a */
-/* matter of time before the encroaching vertex is deleted by Chew's */
-/* algorithm. It's faster to simply not insert the doomed vertex in the */
-/* first place, which is why I use diametral lenses with Chew's algorithm. */
-/* */
-/* Returns a nonzero value if the subsegment is encroached. */
-/* */
-/*****************************************************************************/
-
-#ifndef CDT_ONLY
-
-#ifdef ANSI_DECLARATORS
-int checkseg4encroach(struct mesh *m, struct behavior *b,
- struct osub *testsubseg)
-#else /* not ANSI_DECLARATORS */
-int checkseg4encroach(m, b, testsubseg)
-struct mesh *m;
-struct behavior *b;
-struct osub *testsubseg;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct otri neighbortri;
- struct osub testsym;
- struct badsubseg *encroachedseg;
- REAL dotproduct;
- int encroached;
- int sides;
- vertex eorg, edest, eapex;
- triangle ptr; /* Temporary variable used by stpivot(). */
-
- encroached = 0;
- sides = 0;
-
- sorg(*testsubseg, eorg);
- sdest(*testsubseg, edest);
- /* Check one neighbor of the subsegment. */
- stpivot(*testsubseg, neighbortri);
- /* Does the neighbor exist, or is this a boundary edge? */
- if (neighbortri.tri != m->dummytri) {
- sides++;
- /* Find a vertex opposite this subsegment. */
- apex(neighbortri, eapex);
- /* Check whether the apex is in the diametral lens of the subsegment */
- /* (the diametral circle if `conformdel' is set). A dot product */
- /* of two sides of the triangle is used to check whether the angle */
- /* at the apex is greater than (180 - 2 `minangle') degrees (for */
- /* lenses; 90 degrees for diametral circles). */
- dotproduct = (eorg[0] - eapex[0]) * (edest[0] - eapex[0]) +
- (eorg[1] - eapex[1]) * (edest[1] - eapex[1]);
- if (dotproduct < 0.0) {
- if (b->conformdel ||
- (dotproduct * dotproduct >=
- (2.0 * b->goodangle - 1.0) * (2.0 * b->goodangle - 1.0) *
- ((eorg[0] - eapex[0]) * (eorg[0] - eapex[0]) +
- (eorg[1] - eapex[1]) * (eorg[1] - eapex[1])) *
- ((edest[0] - eapex[0]) * (edest[0] - eapex[0]) +
- (edest[1] - eapex[1]) * (edest[1] - eapex[1])))) {
- encroached = 1;
- }
- }
- }
- /* Check the other neighbor of the subsegment. */
- ssym(*testsubseg, testsym);
- stpivot(testsym, neighbortri);
- /* Does the neighbor exist, or is this a boundary edge? */
- if (neighbortri.tri != m->dummytri) {
- sides++;
- /* Find the other vertex opposite this subsegment. */
- apex(neighbortri, eapex);
- /* Check whether the apex is in the diametral lens of the subsegment */
- /* (or the diametral circle, if `conformdel' is set). */
- dotproduct = (eorg[0] - eapex[0]) * (edest[0] - eapex[0]) +
- (eorg[1] - eapex[1]) * (edest[1] - eapex[1]);
- if (dotproduct < 0.0) {
- if (b->conformdel ||
- (dotproduct * dotproduct >=
- (2.0 * b->goodangle - 1.0) * (2.0 * b->goodangle - 1.0) *
- ((eorg[0] - eapex[0]) * (eorg[0] - eapex[0]) +
- (eorg[1] - eapex[1]) * (eorg[1] - eapex[1])) *
- ((edest[0] - eapex[0]) * (edest[0] - eapex[0]) +
- (edest[1] - eapex[1]) * (edest[1] - eapex[1])))) {
- encroached += 2;
- }
- }
- }
-
- if (encroached && (!b->nobisect || ((b->nobisect == 1) && (sides == 2)))) {
- if (b->verbose > 2) {
- printf(
- " Queueing encroached subsegment (%.12g, %.12g) (%.12g, %.12g).\n",
- eorg[0], eorg[1], edest[0], edest[1]);
- }
- /* Add the subsegment to the list of encroached subsegments. */
- /* Be sure to get the orientation right. */
- encroachedseg = (struct badsubseg *) poolalloc(&m->badsubsegs);
- if (encroached == 1) {
- encroachedseg->encsubseg = sencode(*testsubseg);
- encroachedseg->subsegorg = eorg;
- encroachedseg->subsegdest = edest;
- } else {
- encroachedseg->encsubseg = sencode(testsym);
- encroachedseg->subsegorg = edest;
- encroachedseg->subsegdest = eorg;
- }
- }
-
- return encroached;
-}
-
-#endif /* not CDT_ONLY */
-
-/*****************************************************************************/
-/* */
-/* testtriangle() Test a triangle for quality and size. */
-/* */
-/* Tests a triangle to see if it satisfies the minimum angle condition and */
-/* the maximum area condition. Triangles that aren't up to spec are added */
-/* to the bad triangle queue. */
-/* */
-/*****************************************************************************/
-
-#ifndef CDT_ONLY
-
-#ifdef ANSI_DECLARATORS
-void testtriangle(struct mesh *m, struct behavior *b, struct otri *testtri)
-#else /* not ANSI_DECLARATORS */
-void testtriangle(m, b, testtri)
-struct mesh *m;
-struct behavior *b;
-struct otri *testtri;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct otri tri1, tri2;
- struct osub testsub;
- vertex torg, tdest, tapex;
- vertex base1, base2;
- vertex org1, dest1, org2, dest2;
- vertex joinvertex;
- REAL dxod, dyod, dxda, dyda, dxao, dyao;
- REAL dxod2, dyod2, dxda2, dyda2, dxao2, dyao2;
- REAL apexlen, orglen, destlen, minedge;
- REAL angle;
- REAL area;
- REAL dist1, dist2;
- subseg sptr; /* Temporary variable used by tspivot(). */
- triangle ptr; /* Temporary variable used by oprev() and dnext(). */
-
- org(*testtri, torg);
- dest(*testtri, tdest);
- apex(*testtri, tapex);
- dxod = torg[0] - tdest[0];
- dyod = torg[1] - tdest[1];
- dxda = tdest[0] - tapex[0];
- dyda = tdest[1] - tapex[1];
- dxao = tapex[0] - torg[0];
- dyao = tapex[1] - torg[1];
- dxod2 = dxod * dxod;
- dyod2 = dyod * dyod;
- dxda2 = dxda * dxda;
- dyda2 = dyda * dyda;
- dxao2 = dxao * dxao;
- dyao2 = dyao * dyao;
- /* Find the lengths of the triangle's three edges. */
- apexlen = dxod2 + dyod2;
- orglen = dxda2 + dyda2;
- destlen = dxao2 + dyao2;
-
- if ((apexlen < orglen) && (apexlen < destlen)) {
- /* The edge opposite the apex is shortest. */
- minedge = apexlen;
- /* Find the square of the cosine of the angle at the apex. */
- angle = dxda * dxao + dyda * dyao;
- angle = angle * angle / (orglen * destlen);
- base1 = torg;
- base2 = tdest;
- otricopy(*testtri, tri1);
- } else if (orglen < destlen) {
- /* The edge opposite the origin is shortest. */
- minedge = orglen;
- /* Find the square of the cosine of the angle at the origin. */
- angle = dxod * dxao + dyod * dyao;
- angle = angle * angle / (apexlen * destlen);
- base1 = tdest;
- base2 = tapex;
- lnext(*testtri, tri1);
- } else {
- /* The edge opposite the destination is shortest. */
- minedge = destlen;
- /* Find the square of the cosine of the angle at the destination. */
- angle = dxod * dxda + dyod * dyda;
- angle = angle * angle / (apexlen * orglen);
- base1 = tapex;
- base2 = torg;
- lprev(*testtri, tri1);
- }
-
- if (b->vararea || b->fixedarea || b->usertest) {
- /* Check whether the area is larger than permitted. */
- area = 0.5 * (dxod * dyda - dyod * dxda);
- if (b->fixedarea && (area > b->maxarea)) {
- /* Add this triangle to the list of bad triangles. */
- enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest);
- return;
- }
-
- /* Nonpositive area constraints are treated as unconstrained. */
- if ((b->vararea) && (area > areabound(*testtri)) &&
- (areabound(*testtri) > 0.0)) {
- /* Add this triangle to the list of bad triangles. */
- enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest);
- return;
- }
-
- if (b->usertest) {
- /* Check whether the user thinks this triangle is too large. */
- if (triunsuitable(torg, tdest, tapex, area)) {
- enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest);
- return;
- }
- }
- }
-
- /* Check whether the angle is smaller than permitted. */
- if (angle > b->goodangle) {
- /* Use the rules of Miller, Pav, and Walkington to decide that certain */
- /* triangles should not be split, even if they have bad angles. */
- /* A skinny triangle is not split if its shortest edge subtends a */
- /* small input angle, and both endpoints of the edge lie on a */
- /* concentric circular shell. For convenience, I make a small */
- /* adjustment to that rule: I check if the endpoints of the edge */
- /* both lie in segment interiors, equidistant from the apex where */
- /* the two segments meet. */
- /* First, check if both points lie in segment interiors. */
- if ((vertextype(base1) == SEGMENTVERTEX) &&
- (vertextype(base2) == SEGMENTVERTEX)) {
- /* Check if both points lie in a common segment. If they do, the */
- /* skinny triangle is enqueued to be split as usual. */
- tspivot(tri1, testsub);
- if (testsub.ss == m->dummysub) {
- /* No common segment. Find a subsegment that contains `torg'. */
- otricopy(tri1, tri2);
- do {
- oprevself(tri1);
- tspivot(tri1, testsub);
- } while (testsub.ss == m->dummysub);
- /* Find the endpoints of the containing segment. */
- segorg(testsub, org1);
- segdest(testsub, dest1);
- /* Find a subsegment that contains `tdest'. */
- do {
- dnextself(tri2);
- tspivot(tri2, testsub);
- } while (testsub.ss == m->dummysub);
- /* Find the endpoints of the containing segment. */
- segorg(testsub, org2);
- segdest(testsub, dest2);
- /* Check if the two containing segments have an endpoint in common. */
- joinvertex = (vertex) NULL;
- if ((dest1[0] == org2[0]) && (dest1[1] == org2[1])) {
- joinvertex = dest1;
- } else if ((org1[0] == dest2[0]) && (org1[1] == dest2[1])) {
- joinvertex = org1;
- }
- if (joinvertex != (vertex) NULL) {
- /* Compute the distance from the common endpoint (of the two */
- /* segments) to each of the endpoints of the shortest edge. */
- dist1 = ((base1[0] - joinvertex[0]) * (base1[0] - joinvertex[0]) +
- (base1[1] - joinvertex[1]) * (base1[1] - joinvertex[1]));
- dist2 = ((base2[0] - joinvertex[0]) * (base2[0] - joinvertex[0]) +
- (base2[1] - joinvertex[1]) * (base2[1] - joinvertex[1]));
- /* If the two distances are equal, don't split the triangle. */
- if ((dist1 < 1.001 * dist2) && (dist1 > 0.999 * dist2)) {
- /* Return now to avoid enqueueing the bad triangle. */
- return;
- }
- }
- }
- }
-
- /* Add this triangle to the list of bad triangles. */
- enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest);
- }
-}
-
-#endif /* not CDT_ONLY */
-
-/** **/
-/** **/
-/********* Mesh quality testing routines end here *********/
-
-/********* Point location routines begin here *********/
-/** **/
-/** **/
-
-/*****************************************************************************/
-/* */
-/* makevertexmap() Construct a mapping from vertices to triangles to */
-/* improve the speed of point location for segment */
-/* insertion. */
-/* */
-/* Traverses all the triangles, and provides each corner of each triangle */
-/* with a pointer to that triangle. Of course, pointers will be */
-/* overwritten by other pointers because (almost) each vertex is a corner */
-/* of several triangles, but in the end every vertex will point to some */
-/* triangle that contains it. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-void makevertexmap(struct mesh *m, struct behavior *b)
-#else /* not ANSI_DECLARATORS */
-void makevertexmap(m, b)
-struct mesh *m;
-struct behavior *b;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct otri triangleloop;
- vertex triorg;
-
- if (b->verbose) {
- printf(" Constructing mapping from vertices to triangles.\n");
- }
- traversalinit(&m->triangles);
- triangleloop.tri = triangletraverse(m);
- while (triangleloop.tri != (triangle *) NULL) {
- /* Check all three vertices of the triangle. */
- for (triangleloop.orient = 0; triangleloop.orient < 3;
- triangleloop.orient++) {
- org(triangleloop, triorg);
- setvertex2tri(triorg, encode(triangleloop));
- }
- triangleloop.tri = triangletraverse(m);
- }
-}
-
-/*****************************************************************************/
-/* */
-/* preciselocate() Find a triangle or edge containing a given point. */
-/* */
-/* Begins its search from `searchtri'. It is important that `searchtri' */
-/* be a handle with the property that `searchpoint' is strictly to the left */
-/* of the edge denoted by `searchtri', or is collinear with that edge and */
-/* does not intersect that edge. (In particular, `searchpoint' should not */
-/* be the origin or destination of that edge.) */
-/* */
-/* These conditions are imposed because preciselocate() is normally used in */
-/* one of two situations: */
-/* */
-/* (1) To try to find the location to insert a new point. Normally, we */
-/* know an edge that the point is strictly to the left of. In the */
-/* incremental Delaunay algorithm, that edge is a bounding box edge. */
-/* In Ruppert's Delaunay refinement algorithm for quality meshing, */
-/* that edge is the shortest edge of the triangle whose circumcenter */
-/* is being inserted. */
-/* */
-/* (2) To try to find an existing point. In this case, any edge on the */
-/* convex hull is a good starting edge. You must screen out the */
-/* possibility that the vertex sought is an endpoint of the starting */
-/* edge before you call preciselocate(). */
-/* */
-/* On completion, `searchtri' is a triangle that contains `searchpoint'. */
-/* */
-/* This implementation differs from that given by Guibas and Stolfi. It */
-/* walks from triangle to triangle, crossing an edge only if `searchpoint' */
-/* is on the other side of the line containing that edge. After entering */
-/* a triangle, there are two edges by which one can leave that triangle. */
-/* If both edges are valid (`searchpoint' is on the other side of both */
-/* edges), one of the two is chosen by drawing a line perpendicular to */
-/* the entry edge (whose endpoints are `forg' and `fdest') passing through */
-/* `fapex'. Depending on which side of this perpendicular `searchpoint' */
-/* falls on, an exit edge is chosen. */
-/* */
-/* This implementation is empirically faster than the Guibas and Stolfi */
-/* point location routine (which I originally used), which tends to spiral */
-/* in toward its target. */
-/* */
-/* Returns ONVERTEX if the point lies on an existing vertex. `searchtri' */
-/* is a handle whose origin is the existing vertex. */
-/* */
-/* Returns ONEDGE if the point lies on a mesh edge. `searchtri' is a */
-/* handle whose primary edge is the edge on which the point lies. */
-/* */
-/* Returns INTRIANGLE if the point lies strictly within a triangle. */
-/* `searchtri' is a handle on the triangle that contains the point. */
-/* */
-/* Returns OUTSIDE if the point lies outside the mesh. `searchtri' is a */
-/* handle whose primary edge the point is to the right of. This might */
-/* occur when the circumcenter of a triangle falls just slightly outside */
-/* the mesh due to floating-point roundoff error. It also occurs when */
-/* seeking a hole or region point that a foolish user has placed outside */
-/* the mesh. */
-/* */
-/* If `stopatsubsegment' is nonzero, the search will stop if it tries to */
-/* walk through a subsegment, and will return OUTSIDE. */
-/* */
-/* WARNING: This routine is designed for convex triangulations, and will */
-/* not generally work after the holes and concavities have been carved. */
-/* However, it can still be used to find the circumcenter of a triangle, as */
-/* long as the search is begun from the triangle in question. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-enum locateresult preciselocate(struct mesh *m, struct behavior *b,
- vertex searchpoint, struct otri *searchtri,
- int stopatsubsegment)
-#else /* not ANSI_DECLARATORS */
-enum locateresult preciselocate(m, b, searchpoint, searchtri, stopatsubsegment)
-struct mesh *m;
-struct behavior *b;
-vertex searchpoint;
-struct otri *searchtri;
-int stopatsubsegment;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct otri backtracktri;
- struct osub checkedge;
- vertex forg, fdest, fapex;
- REAL orgorient, destorient;
- int moveleft;
- triangle ptr; /* Temporary variable used by sym(). */
- subseg sptr; /* Temporary variable used by tspivot(). */
-
- if (b->verbose > 2) {
- printf(" Searching for point (%.12g, %.12g).\n",
- searchpoint[0], searchpoint[1]);
- }
- /* Where are we? */
- org(*searchtri, forg);
- dest(*searchtri, fdest);
- apex(*searchtri, fapex);
- while (1) {
- if (b->verbose > 2) {
- printf(" At (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
- forg[0], forg[1], fdest[0], fdest[1], fapex[0], fapex[1]);
- }
- /* Check whether the apex is the point we seek. */
- if ((fapex[0] == searchpoint[0]) && (fapex[1] == searchpoint[1])) {
- lprevself(*searchtri);
- return ONVERTEX;
- }
- /* Does the point lie on the other side of the line defined by the */
- /* triangle edge opposite the triangle's destination? */
- destorient = counterclockwise(m, b, forg, fapex, searchpoint);
- /* Does the point lie on the other side of the line defined by the */
- /* triangle edge opposite the triangle's origin? */
- orgorient = counterclockwise(m, b, fapex, fdest, searchpoint);
- if (destorient > 0.0) {
- if (orgorient > 0.0) {
- /* Move left if the inner product of (fapex - searchpoint) and */
- /* (fdest - forg) is positive. This is equivalent to drawing */
- /* a line perpendicular to the line (forg, fdest) and passing */
- /* through `fapex', and determining which side of this line */
- /* `searchpoint' falls on. */
- moveleft = (fapex[0] - searchpoint[0]) * (fdest[0] - forg[0]) +
- (fapex[1] - searchpoint[1]) * (fdest[1] - forg[1]) > 0.0;
- } else {
- moveleft = 1;
- }
- } else {
- if (orgorient > 0.0) {
- moveleft = 0;
- } else {
- /* The point we seek must be on the boundary of or inside this */
- /* triangle. */
- if (destorient == 0.0) {
- lprevself(*searchtri);
- return ONEDGE;
- }
- if (orgorient == 0.0) {
- lnextself(*searchtri);
- return ONEDGE;
- }
- return INTRIANGLE;
- }
- }
-
- /* Move to another triangle. Leave a trace `backtracktri' in case */
- /* floating-point roundoff or some such bogey causes us to walk */
- /* off a boundary of the triangulation. */
- if (moveleft) {
- lprev(*searchtri, backtracktri);
- fdest = fapex;
- } else {
- lnext(*searchtri, backtracktri);
- forg = fapex;
- }
- sym(backtracktri, *searchtri);
-
- if (m->checksegments && stopatsubsegment) {
- /* Check for walking through a subsegment. */
- tspivot(backtracktri, checkedge);
- if (checkedge.ss != m->dummysub) {
- /* Go back to the last triangle. */
- otricopy(backtracktri, *searchtri);
- return OUTSIDE;
- }
- }
- /* Check for walking right out of the triangulation. */
- if (searchtri->tri == m->dummytri) {
- /* Go back to the last triangle. */
- otricopy(backtracktri, *searchtri);
- return OUTSIDE;
- }
-
- apex(*searchtri, fapex);
- }
-}
-
-/*****************************************************************************/
-/* */
-/* locate() Find a triangle or edge containing a given point. */
-/* */
-/* Searching begins from one of: the input `searchtri', a recently */
-/* encountered triangle `recenttri', or from a triangle chosen from a */
-/* random sample. The choice is made by determining which triangle's */
-/* origin is closest to the point we are searching for. Normally, */
-/* `searchtri' should be a handle on the convex hull of the triangulation. */
-/* */
-/* Details on the random sampling method can be found in the Mucke, Saias, */
-/* and Zhu paper cited in the header of this code. */
-/* */
-/* On completion, `searchtri' is a triangle that contains `searchpoint'. */
-/* */
-/* Returns ONVERTEX if the point lies on an existing vertex. `searchtri' */
-/* is a handle whose origin is the existing vertex. */
-/* */
-/* Returns ONEDGE if the point lies on a mesh edge. `searchtri' is a */
-/* handle whose primary edge is the edge on which the point lies. */
-/* */
-/* Returns INTRIANGLE if the point lies strictly within a triangle. */
-/* `searchtri' is a handle on the triangle that contains the point. */
-/* */
-/* Returns OUTSIDE if the point lies outside the mesh. `searchtri' is a */
-/* handle whose primary edge the point is to the right of. This might */
-/* occur when the circumcenter of a triangle falls just slightly outside */
-/* the mesh due to floating-point roundoff error. It also occurs when */
-/* seeking a hole or region point that a foolish user has placed outside */
-/* the mesh. */
-/* */
-/* WARNING: This routine is designed for convex triangulations, and will */
-/* not generally work after the holes and concavities have been carved. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-enum locateresult locate(struct mesh *m, struct behavior *b,
- vertex searchpoint, struct otri *searchtri)
-#else /* not ANSI_DECLARATORS */
-enum locateresult locate(m, b, searchpoint, searchtri)
-struct mesh *m;
-struct behavior *b;
-vertex searchpoint;
-struct otri *searchtri;
-#endif /* not ANSI_DECLARATORS */
-
-{
- VOID **sampleblock;
- char *firsttri;
- struct otri sampletri;
- vertex torg, tdest;
- unsigned long alignptr;
- REAL searchdist, dist;
- REAL ahead;
- long samplesperblock, totalsamplesleft, samplesleft;
- long population, totalpopulation;
- triangle ptr; /* Temporary variable used by sym(). */
-
- if (b->verbose > 2) {
- printf(" Randomly sampling for a triangle near point (%.12g, %.12g).\n",
- searchpoint[0], searchpoint[1]);
- }
- /* Record the distance from the suggested starting triangle to the */
- /* point we seek. */
- org(*searchtri, torg);
- searchdist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) +
- (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]);
- if (b->verbose > 2) {
- printf(" Boundary triangle has origin (%.12g, %.12g).\n",
- torg[0], torg[1]);
- }
-
- /* If a recently encountered triangle has been recorded and has not been */
- /* deallocated, test it as a good starting point. */
- if (m->recenttri.tri != (triangle *) NULL) {
- if (!deadtri(m->recenttri.tri)) {
- org(m->recenttri, torg);
- if ((torg[0] == searchpoint[0]) && (torg[1] == searchpoint[1])) {
- otricopy(m->recenttri, *searchtri);
- return ONVERTEX;
- }
- dist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) +
- (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]);
- if (dist < searchdist) {
- otricopy(m->recenttri, *searchtri);
- searchdist = dist;
- if (b->verbose > 2) {
- printf(" Choosing recent triangle with origin (%.12g, %.12g).\n",
- torg[0], torg[1]);
- }
- }
- }
- }
-
- /* The number of random samples taken is proportional to the cube root of */
- /* the number of triangles in the mesh. The next bit of code assumes */
- /* that the number of triangles increases monotonically (or at least */
- /* doesn't decrease enough to matter). */
- while (SAMPLEFACTOR * m->samples * m->samples * m->samples <
- m->triangles.items) {
- m->samples++;
- }
-
- /* We'll draw ceiling(samples * TRIPERBLOCK / maxitems) random samples */
- /* from each block of triangles (except the first)--until we meet the */
- /* sample quota. The ceiling means that blocks at the end might be */
- /* neglected, but I don't care. */
- samplesperblock = (m->samples * TRIPERBLOCK - 1) / m->triangles.maxitems + 1;
- /* We'll draw ceiling(samples * itemsfirstblock / maxitems) random samples */
- /* from the first block of triangles. */
- samplesleft = (m->samples * m->triangles.itemsfirstblock - 1) /
- m->triangles.maxitems + 1;
- totalsamplesleft = m->samples;
- population = m->triangles.itemsfirstblock;
- totalpopulation = m->triangles.maxitems;
- sampleblock = m->triangles.firstblock;
- sampletri.orient = 0;
- while (totalsamplesleft > 0) {
- /* If we're in the last block, `population' needs to be corrected. */
- if (population > totalpopulation) {
- population = totalpopulation;
- }
- /* Find a pointer to the first triangle in the block. */
- alignptr = (unsigned long) (sampleblock + 1);
- firsttri = (char *) (alignptr +
- (unsigned long) m->triangles.alignbytes -
- (alignptr %
- (unsigned long) m->triangles.alignbytes));
-
- /* Choose `samplesleft' randomly sampled triangles in this block. */
- do {
- sampletri.tri = (triangle *) (firsttri +
- (randomnation((unsigned int) population) *
- m->triangles.itembytes));
- if (!deadtri(sampletri.tri)) {
- org(sampletri, torg);
- dist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) +
- (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]);
- if (dist < searchdist) {
- otricopy(sampletri, *searchtri);
- searchdist = dist;
- if (b->verbose > 2) {
- printf(" Choosing triangle with origin (%.12g, %.12g).\n",
- torg[0], torg[1]);
- }
- }
- }
-
- samplesleft--;
- totalsamplesleft--;
- } while ((samplesleft > 0) && (totalsamplesleft > 0));
-
- if (totalsamplesleft > 0) {
- sampleblock = (VOID **) *sampleblock;
- samplesleft = samplesperblock;
- totalpopulation -= population;
- population = TRIPERBLOCK;
- }
- }
-
- /* Where are we? */
- org(*searchtri, torg);
- dest(*searchtri, tdest);
- /* Check the starting triangle's vertices. */
- if ((torg[0] == searchpoint[0]) && (torg[1] == searchpoint[1])) {
- return ONVERTEX;
- }
- if ((tdest[0] == searchpoint[0]) && (tdest[1] == searchpoint[1])) {
- lnextself(*searchtri);
- return ONVERTEX;
- }
- /* Orient `searchtri' to fit the preconditions of calling preciselocate(). */
- ahead = counterclockwise(m, b, torg, tdest, searchpoint);
- if (ahead < 0.0) {
- /* Turn around so that `searchpoint' is to the left of the */
- /* edge specified by `searchtri'. */
- symself(*searchtri);
- } else if (ahead == 0.0) {
- /* Check if `searchpoint' is between `torg' and `tdest'. */
- if (((torg[0] < searchpoint[0]) == (searchpoint[0] < tdest[0])) &&
- ((torg[1] < searchpoint[1]) == (searchpoint[1] < tdest[1]))) {
- return ONEDGE;
- }
- }
- return preciselocate(m, b, searchpoint, searchtri, 0);
-}
-
-/** **/
-/** **/
-/********* Point location routines end here *********/
-
-/********* Mesh transformation routines begin here *********/
-/** **/
-/** **/
-
-/*****************************************************************************/
-/* */
-/* insertsubseg() Create a new subsegment and insert it between two */
-/* triangles. */
-/* */
-/* The new subsegment is inserted at the edge described by the handle */
-/* `tri'. Its vertices are properly initialized. The marker `subsegmark' */
-/* is applied to the subsegment and, if appropriate, its vertices. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-void insertsubseg(struct mesh *m, struct behavior *b, struct otri *tri,
- int subsegmark)
-#else /* not ANSI_DECLARATORS */
-void insertsubseg(m, b, tri, subsegmark)
-struct mesh *m;
-struct behavior *b;
-struct otri *tri; /* Edge at which to insert the new subsegment. */
-int subsegmark; /* Marker for the new subsegment. */
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct otri oppotri;
- struct osub newsubseg;
- vertex triorg, tridest;
- triangle ptr; /* Temporary variable used by sym(). */
- subseg sptr; /* Temporary variable used by tspivot(). */
-
- org(*tri, triorg);
- dest(*tri, tridest);
- /* Mark vertices if possible. */
- if (vertexmark(triorg) == 0) {
- setvertexmark(triorg, subsegmark);
- }
- if (vertexmark(tridest) == 0) {
- setvertexmark(tridest, subsegmark);
- }
- /* Check if there's already a subsegment here. */
- tspivot(*tri, newsubseg);
- if (newsubseg.ss == m->dummysub) {
- /* Make new subsegment and initialize its vertices. */
- makesubseg(m, &newsubseg);
- setsorg(newsubseg, tridest);
- setsdest(newsubseg, triorg);
- setsegorg(newsubseg, tridest);
- setsegdest(newsubseg, triorg);
- /* Bond new subsegment to the two triangles it is sandwiched between. */
- /* Note that the facing triangle `oppotri' might be equal to */
- /* `dummytri' (outer space), but the new subsegment is bonded to it */
- /* all the same. */
- tsbond(*tri, newsubseg);
- sym(*tri, oppotri);
- ssymself(newsubseg);
- tsbond(oppotri, newsubseg);
- setmark(newsubseg, subsegmark);
- if (b->verbose > 2) {
- printf(" Inserting new ");
- printsubseg(m, b, &newsubseg);
- }
- } else {
- if (mark(newsubseg) == 0) {
- setmark(newsubseg, subsegmark);
- }
- }
-}
-
-/*****************************************************************************/
-/* */
-/* Terminology */
-/* */
-/* A "local transformation" replaces a small set of triangles with another */
-/* set of triangles. This may or may not involve inserting or deleting a */
-/* vertex. */
-/* */
-/* The term "casing" is used to describe the set of triangles that are */
-/* attached to the triangles being transformed, but are not transformed */
-/* themselves. Think of the casing as a fixed hollow structure inside */
-/* which all the action happens. A "casing" is only defined relative to */
-/* a single transformation; each occurrence of a transformation will */
-/* involve a different casing. */
-/* */
-/*****************************************************************************/
-
-/*****************************************************************************/
-/* */
-/* flip() Transform two triangles to two different triangles by flipping */
-/* an edge counterclockwise within a quadrilateral. */
-/* */
-/* Imagine the original triangles, abc and bad, oriented so that the */
-/* shared edge ab lies in a horizontal plane, with the vertex b on the left */
-/* and the vertex a on the right. The vertex c lies below the edge, and */
-/* the vertex d lies above the edge. The `flipedge' handle holds the edge */
-/* ab of triangle abc, and is directed left, from vertex a to vertex b. */
-/* */
-/* The triangles abc and bad are deleted and replaced by the triangles cdb */
-/* and dca. The triangles that represent abc and bad are NOT deallocated; */
-/* they are reused for dca and cdb, respectively. Hence, any handles that */
-/* may have held the original triangles are still valid, although not */
-/* directed as they were before. */
-/* */
-/* Upon completion of this routine, the `flipedge' handle holds the edge */
-/* dc of triangle dca, and is directed down, from vertex d to vertex c. */
-/* (Hence, the two triangles have rotated counterclockwise.) */
-/* */
-/* WARNING: This transformation is geometrically valid only if the */
-/* quadrilateral adbc is convex. Furthermore, this transformation is */
-/* valid only if there is not a subsegment between the triangles abc and */
-/* bad. This routine does not check either of these preconditions, and */
-/* it is the responsibility of the calling routine to ensure that they are */
-/* met. If they are not, the streets shall be filled with wailing and */
-/* gnashing of teeth. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-void flip(struct mesh *m, struct behavior *b, struct otri *flipedge)
-#else /* not ANSI_DECLARATORS */
-void flip(m, b, flipedge)
-struct mesh *m;
-struct behavior *b;
-struct otri *flipedge; /* Handle for the triangle abc. */
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct otri botleft, botright;
- struct otri topleft, topright;
- struct otri top;
- struct otri botlcasing, botrcasing;
- struct otri toplcasing, toprcasing;
- struct osub botlsubseg, botrsubseg;
- struct osub toplsubseg, toprsubseg;
- vertex leftvertex, rightvertex, botvertex;
- vertex farvertex;
- triangle ptr; /* Temporary variable used by sym(). */
- subseg sptr; /* Temporary variable used by tspivot(). */
-
- /* Identify the vertices of the quadrilateral. */
- org(*flipedge, rightvertex);
- dest(*flipedge, leftvertex);
- apex(*flipedge, botvertex);
- sym(*flipedge, top);
-#ifdef SELF_CHECK
- if (top.tri == m->dummytri) {
- printf("Internal error in flip(): Attempt to flip on boundary.\n");
- lnextself(*flipedge);
- return;
- }
- if (m->checksegments) {
- tspivot(*flipedge, toplsubseg);
- if (toplsubseg.ss != m->dummysub) {
- printf("Internal error in flip(): Attempt to flip a segment.\n");
- lnextself(*flipedge);
- return;
- }
- }
-#endif /* SELF_CHECK */
- apex(top, farvertex);
-
- /* Identify the casing of the quadrilateral. */
- lprev(top, topleft);
- sym(topleft, toplcasing);
- lnext(top, topright);
- sym(topright, toprcasing);
- lnext(*flipedge, botleft);
- sym(botleft, botlcasing);
- lprev(*flipedge, botright);
- sym(botright, botrcasing);
- /* Rotate the quadrilateral one-quarter turn counterclockwise. */
- bond(topleft, botlcasing);
- bond(botleft, botrcasing);
- bond(botright, toprcasing);
- bond(topright, toplcasing);
-
- if (m->checksegments) {
- /* Check for subsegments and rebond them to the quadrilateral. */
- tspivot(topleft, toplsubseg);
- tspivot(botleft, botlsubseg);
- tspivot(botright, botrsubseg);
- tspivot(topright, toprsubseg);
- if (toplsubseg.ss == m->dummysub) {
- tsdissolve(topright);
- } else {
- tsbond(topright, toplsubseg);
- }
- if (botlsubseg.ss == m->dummysub) {
- tsdissolve(topleft);
- } else {
- tsbond(topleft, botlsubseg);
- }
- if (botrsubseg.ss == m->dummysub) {
- tsdissolve(botleft);
- } else {
- tsbond(botleft, botrsubseg);
- }
- if (toprsubseg.ss == m->dummysub) {
- tsdissolve(botright);
- } else {
- tsbond(botright, toprsubseg);
- }
- }
-
- /* New vertex assignments for the rotated quadrilateral. */
- setorg(*flipedge, farvertex);
- setdest(*flipedge, botvertex);
- setapex(*flipedge, rightvertex);
- setorg(top, botvertex);
- setdest(top, farvertex);
- setapex(top, leftvertex);
- if (b->verbose > 2) {
- printf(" Edge flip results in left ");
- printtriangle(m, b, &top);
- printf(" and right ");
- printtriangle(m, b, flipedge);
- }
-}
-
-/*****************************************************************************/
-/* */
-/* unflip() Transform two triangles to two different triangles by */
-/* flipping an edge clockwise within a quadrilateral. Reverses */
-/* the flip() operation so that the data structures representing */
-/* the triangles are back where they were before the flip(). */
-/* */
-/* Imagine the original triangles, abc and bad, oriented so that the */
-/* shared edge ab lies in a horizontal plane, with the vertex b on the left */
-/* and the vertex a on the right. The vertex c lies below the edge, and */
-/* the vertex d lies above the edge. The `flipedge' handle holds the edge */
-/* ab of triangle abc, and is directed left, from vertex a to vertex b. */
-/* */
-/* The triangles abc and bad are deleted and replaced by the triangles cdb */
-/* and dca. The triangles that represent abc and bad are NOT deallocated; */
-/* they are reused for cdb and dca, respectively. Hence, any handles that */
-/* may have held the original triangles are still valid, although not */
-/* directed as they were before. */
-/* */
-/* Upon completion of this routine, the `flipedge' handle holds the edge */
-/* cd of triangle cdb, and is directed up, from vertex c to vertex d. */
-/* (Hence, the two triangles have rotated clockwise.) */
-/* */
-/* WARNING: This transformation is geometrically valid only if the */
-/* quadrilateral adbc is convex. Furthermore, this transformation is */
-/* valid only if there is not a subsegment between the triangles abc and */
-/* bad. This routine does not check either of these preconditions, and */
-/* it is the responsibility of the calling routine to ensure that they are */
-/* met. If they are not, the streets shall be filled with wailing and */
-/* gnashing of teeth. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-void unflip(struct mesh *m, struct behavior *b, struct otri *flipedge)
-#else /* not ANSI_DECLARATORS */
-void unflip(m, b, flipedge)
-struct mesh *m;
-struct behavior *b;
-struct otri *flipedge; /* Handle for the triangle abc. */
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct otri botleft, botright;
- struct otri topleft, topright;
- struct otri top;
- struct otri botlcasing, botrcasing;
- struct otri toplcasing, toprcasing;
- struct osub botlsubseg, botrsubseg;
- struct osub toplsubseg, toprsubseg;
- vertex leftvertex, rightvertex, botvertex;
- vertex farvertex;
- triangle ptr; /* Temporary variable used by sym(). */
- subseg sptr; /* Temporary variable used by tspivot(). */
-
- /* Identify the vertices of the quadrilateral. */
- org(*flipedge, rightvertex);
- dest(*flipedge, leftvertex);
- apex(*flipedge, botvertex);
- sym(*flipedge, top);
-#ifdef SELF_CHECK
- if (top.tri == m->dummytri) {
- printf("Internal error in unflip(): Attempt to flip on boundary.\n");
- lnextself(*flipedge);
- return;
- }
- if (m->checksegments) {
- tspivot(*flipedge, toplsubseg);
- if (toplsubseg.ss != m->dummysub) {
- printf("Internal error in unflip(): Attempt to flip a subsegment.\n");
- lnextself(*flipedge);
- return;
- }
- }
-#endif /* SELF_CHECK */
- apex(top, farvertex);
-
- /* Identify the casing of the quadrilateral. */
- lprev(top, topleft);
- sym(topleft, toplcasing);
- lnext(top, topright);
- sym(topright, toprcasing);
- lnext(*flipedge, botleft);
- sym(botleft, botlcasing);
- lprev(*flipedge, botright);
- sym(botright, botrcasing);
- /* Rotate the quadrilateral one-quarter turn clockwise. */
- bond(topleft, toprcasing);
- bond(botleft, toplcasing);
- bond(botright, botlcasing);
- bond(topright, botrcasing);
-
- if (m->checksegments) {
- /* Check for subsegments and rebond them to the quadrilateral. */
- tspivot(topleft, toplsubseg);
- tspivot(botleft, botlsubseg);
- tspivot(botright, botrsubseg);
- tspivot(topright, toprsubseg);
- if (toplsubseg.ss == m->dummysub) {
- tsdissolve(botleft);
- } else {
- tsbond(botleft, toplsubseg);
- }
- if (botlsubseg.ss == m->dummysub) {
- tsdissolve(botright);
- } else {
- tsbond(botright, botlsubseg);
- }
- if (botrsubseg.ss == m->dummysub) {
- tsdissolve(topright);
- } else {
- tsbond(topright, botrsubseg);
- }
- if (toprsubseg.ss == m->dummysub) {
- tsdissolve(topleft);
- } else {
- tsbond(topleft, toprsubseg);
- }
- }
-
- /* New vertex assignments for the rotated quadrilateral. */
- setorg(*flipedge, botvertex);
- setdest(*flipedge, farvertex);
- setapex(*flipedge, leftvertex);
- setorg(top, farvertex);
- setdest(top, botvertex);
- setapex(top, rightvertex);
- if (b->verbose > 2) {
- printf(" Edge unflip results in left ");
- printtriangle(m, b, flipedge);
- printf(" and right ");
- printtriangle(m, b, &top);
- }
-}
-
-/*****************************************************************************/
-/* */
-/* insertvertex() Insert a vertex into a Delaunay triangulation, */
-/* performing flips as necessary to maintain the Delaunay */
-/* property. */
-/* */
-/* The point `insertvertex' is located. If `searchtri.tri' is not NULL, */
-/* the search for the containing triangle begins from `searchtri'. If */
-/* `searchtri.tri' is NULL, a full point location procedure is called. */
-/* If `insertvertex' is found inside a triangle, the triangle is split into */
-/* three; if `insertvertex' lies on an edge, the edge is split in two, */
-/* thereby splitting the two adjacent triangles into four. Edge flips are */
-/* used to restore the Delaunay property. If `insertvertex' lies on an */
-/* existing vertex, no action is taken, and the value DUPLICATEVERTEX is */
-/* returned. On return, `searchtri' is set to a handle whose origin is the */
-/* existing vertex. */
-/* */
-/* Normally, the parameter `splitseg' is set to NULL, implying that no */
-/* subsegment should be split. In this case, if `insertvertex' is found to */
-/* lie on a segment, no action is taken, and the value VIOLATINGVERTEX is */
-/* returned. On return, `searchtri' is set to a handle whose primary edge */
-/* is the violated subsegment. */
-/* */
-/* If the calling routine wishes to split a subsegment by inserting a */
-/* vertex in it, the parameter `splitseg' should be that subsegment. In */
-/* this case, `searchtri' MUST be the triangle handle reached by pivoting */
-/* from that subsegment; no point location is done. */
-/* */
-/* `segmentflaws' and `triflaws' are flags that indicate whether or not */
-/* there should be checks for the creation of encroached subsegments or bad */
-/* quality triangles. If a newly inserted vertex encroaches upon */
-/* subsegments, these subsegments are added to the list of subsegments to */
-/* be split if `segmentflaws' is set. If bad triangles are created, these */
-/* are added to the queue if `triflaws' is set. */
-/* */
-/* If a duplicate vertex or violated segment does not prevent the vertex */
-/* from being inserted, the return value will be ENCROACHINGVERTEX if the */
-/* vertex encroaches upon a subsegment (and checking is enabled), or */
-/* SUCCESSFULVERTEX otherwise. In either case, `searchtri' is set to a */
-/* handle whose origin is the newly inserted vertex. */
-/* */
-/* insertvertex() does not use flip() for reasons of speed; some */
-/* information can be reused from edge flip to edge flip, like the */
-/* locations of subsegments. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-enum insertvertexresult insertvertex(struct mesh *m, struct behavior *b,
- vertex newvertex, struct otri *searchtri,
- struct osub *splitseg,
- int segmentflaws, int triflaws)
-#else /* not ANSI_DECLARATORS */
-enum insertvertexresult insertvertex(m, b, newvertex, searchtri, splitseg,
- segmentflaws, triflaws)
-struct mesh *m;
-struct behavior *b;
-vertex newvertex;
-struct otri *searchtri;
-struct osub *splitseg;
-int segmentflaws;
-int triflaws;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct otri horiz;
- struct otri top;
- struct otri botleft, botright;
- struct otri topleft, topright;
- struct otri newbotleft, newbotright;
- struct otri newtopright;
- struct otri botlcasing, botrcasing;
- struct otri toplcasing, toprcasing;
- struct otri testtri;
- struct osub botlsubseg, botrsubseg;
- struct osub toplsubseg, toprsubseg;
- struct osub brokensubseg;
- struct osub checksubseg;
- struct osub rightsubseg;
- struct osub newsubseg;
- struct badsubseg *encroached;
- struct flipstacker *newflip;
- vertex first;
- vertex leftvertex, rightvertex, botvertex, topvertex, farvertex;
- vertex segmentorg, segmentdest;
- REAL attrib;
- REAL area;
- enum insertvertexresult success;
- enum locateresult intersect;
- int doflip;
- int mirrorflag;
- int enq;
- int i;
- triangle ptr; /* Temporary variable used by sym(). */
- subseg sptr; /* Temporary variable used by spivot() and tspivot(). */
-
- if (b->verbose > 1) {
- printf(" Inserting (%.12g, %.12g).\n", newvertex[0], newvertex[1]);
- }
-
- if (splitseg == (struct osub *) NULL) {
- /* Find the location of the vertex to be inserted. Check if a good */
- /* starting triangle has already been provided by the caller. */
- if (searchtri->tri == m->dummytri) {
- /* Find a boundary triangle. */
- horiz.tri = m->dummytri;
- horiz.orient = 0;
- symself(horiz);
- /* Search for a triangle containing `newvertex'. */
- intersect = locate(m, b, newvertex, &horiz);
- } else {
- /* Start searching from the triangle provided by the caller. */
- otricopy(*searchtri, horiz);
- intersect = preciselocate(m, b, newvertex, &horiz, 1);
- }
- } else {
- /* The calling routine provides the subsegment in which */
- /* the vertex is inserted. */
- otricopy(*searchtri, horiz);
- intersect = ONEDGE;
- }
-
- if (intersect == ONVERTEX) {
- /* There's already a vertex there. Return in `searchtri' a triangle */
- /* whose origin is the existing vertex. */
- otricopy(horiz, *searchtri);
- otricopy(horiz, m->recenttri);
- return DUPLICATEVERTEX;
- }
- if ((intersect == ONEDGE) || (intersect == OUTSIDE)) {
- /* The vertex falls on an edge or boundary. */
- if (m->checksegments && (splitseg == (struct osub *) NULL)) {
- /* Check whether the vertex falls on a subsegment. */
- tspivot(horiz, brokensubseg);
- if (brokensubseg.ss != m->dummysub) {
- /* The vertex falls on a subsegment, and hence will not be inserted. */
- if (segmentflaws) {
- enq = b->nobisect != 2;
- if (enq && (b->nobisect == 1)) {
- /* This subsegment may be split only if it is an */
- /* internal boundary. */
- sym(horiz, testtri);
- enq = testtri.tri != m->dummytri;
- }
- if (enq) {
- /* Add the subsegment to the list of encroached subsegments. */
- encroached = (struct badsubseg *) poolalloc(&m->badsubsegs);
- encroached->encsubseg = sencode(brokensubseg);
- sorg(brokensubseg, encroached->subsegorg);
- sdest(brokensubseg, encroached->subsegdest);
- if (b->verbose > 2) {
- printf(
- " Queueing encroached subsegment (%.12g, %.12g) (%.12g, %.12g).\n",
- encroached->subsegorg[0], encroached->subsegorg[1],
- encroached->subsegdest[0], encroached->subsegdest[1]);
- }
- }
- }
- /* Return a handle whose primary edge contains the vertex, */
- /* which has not been inserted. */
- otricopy(horiz, *searchtri);
- otricopy(horiz, m->recenttri);
- return VIOLATINGVERTEX;
- }
- }
-
- /* Insert the vertex on an edge, dividing one triangle into two (if */
- /* the edge lies on a boundary) or two triangles into four. */
- lprev(horiz, botright);
- sym(botright, botrcasing);
- sym(horiz, topright);
- /* Is there a second triangle? (Or does this edge lie on a boundary?) */
- mirrorflag = topright.tri != m->dummytri;
- if (mirrorflag) {
- lnextself(topright);
- sym(topright, toprcasing);
- maketriangle(m, b, &newtopright);
- } else {
- /* Splitting a boundary edge increases the number of boundary edges. */
- m->hullsize++;
- }
- maketriangle(m, b, &newbotright);
-
- /* Set the vertices of changed and new triangles. */
- org(horiz, rightvertex);
- dest(horiz, leftvertex);
- apex(horiz, botvertex);
- setorg(newbotright, botvertex);
- setdest(newbotright, rightvertex);
- setapex(newbotright, newvertex);
- setorg(horiz, newvertex);
- for (i = 0; i < m->eextras; i++) {
- /* Set the element attributes of a new triangle. */
- setelemattribute(newbotright, i, elemattribute(botright, i));
- }
- if (b->vararea) {
- /* Set the area constraint of a new triangle. */
- setareabound(newbotright, areabound(botright));
- }
- if (mirrorflag) {
- dest(topright, topvertex);
- setorg(newtopright, rightvertex);
- setdest(newtopright, topvertex);
- setapex(newtopright, newvertex);
- setorg(topright, newvertex);
- for (i = 0; i < m->eextras; i++) {
- /* Set the element attributes of another new triangle. */
- setelemattribute(newtopright, i, elemattribute(topright, i));
- }
- if (b->vararea) {
- /* Set the area constraint of another new triangle. */
- setareabound(newtopright, areabound(topright));
- }
- }
-
- /* There may be subsegments that need to be bonded */
- /* to the new triangle(s). */
- if (m->checksegments) {
- tspivot(botright, botrsubseg);
- if (botrsubseg.ss != m->dummysub) {
- tsdissolve(botright);
- tsbond(newbotright, botrsubseg);
- }
- if (mirrorflag) {
- tspivot(topright, toprsubseg);
- if (toprsubseg.ss != m->dummysub) {
- tsdissolve(topright);
- tsbond(newtopright, toprsubseg);
- }
- }
- }
-
- /* Bond the new triangle(s) to the surrounding triangles. */
- bond(newbotright, botrcasing);
- lprevself(newbotright);
- bond(newbotright, botright);
- lprevself(newbotright);
- if (mirrorflag) {
- bond(newtopright, toprcasing);
- lnextself(newtopright);
- bond(newtopright, topright);
- lnextself(newtopright);
- bond(newtopright, newbotright);
- }
-
- if (splitseg != (struct osub *) NULL) {
- /* Split the subsegment into two. */
- setsdest(*splitseg, newvertex);
- segorg(*splitseg, segmentorg);
- segdest(*splitseg, segmentdest);
- ssymself(*splitseg);
- spivot(*splitseg, rightsubseg);
- insertsubseg(m, b, &newbotright, mark(*splitseg));
- tspivot(newbotright, newsubseg);
- setsegorg(newsubseg, segmentorg);
- setsegdest(newsubseg, segmentdest);
- sbond(*splitseg, newsubseg);
- ssymself(newsubseg);
- sbond(newsubseg, rightsubseg);
- ssymself(*splitseg);
- /* Transfer the subsegment's boundary marker to the vertex */
- /* if required. */
- if (vertexmark(newvertex) == 0) {
- setvertexmark(newvertex, mark(*splitseg));
- }
- }
-
- if (m->checkquality) {
- poolrestart(&m->flipstackers);
- m->lastflip = (struct flipstacker *) poolalloc(&m->flipstackers);
- m->lastflip->flippedtri = encode(horiz);
- m->lastflip->prevflip = (struct flipstacker *) &insertvertex;
- }
-
-#ifdef SELF_CHECK
- if (counterclockwise(m, b, rightvertex, leftvertex, botvertex) < 0.0) {
- printf("Internal error in insertvertex():\n");
- printf(
- " Clockwise triangle prior to edge vertex insertion (bottom).\n");
- }
- if (mirrorflag) {
- if (counterclockwise(m, b, leftvertex, rightvertex, topvertex) < 0.0) {
- printf("Internal error in insertvertex():\n");
- printf(" Clockwise triangle prior to edge vertex insertion (top).\n");
- }
- if (counterclockwise(m, b, rightvertex, topvertex, newvertex) < 0.0) {
- printf("Internal error in insertvertex():\n");
- printf(
- " Clockwise triangle after edge vertex insertion (top right).\n");
- }
- if (counterclockwise(m, b, topvertex, leftvertex, newvertex) < 0.0) {
- printf("Internal error in insertvertex():\n");
- printf(
- " Clockwise triangle after edge vertex insertion (top left).\n");
- }
- }
- if (counterclockwise(m, b, leftvertex, botvertex, newvertex) < 0.0) {
- printf("Internal error in insertvertex():\n");
- printf(
- " Clockwise triangle after edge vertex insertion (bottom left).\n");
- }
- if (counterclockwise(m, b, botvertex, rightvertex, newvertex) < 0.0) {
- printf("Internal error in insertvertex():\n");
- printf(
- " Clockwise triangle after edge vertex insertion (bottom right).\n");
- }
-#endif /* SELF_CHECK */
- if (b->verbose > 2) {
- printf(" Updating bottom left ");
- printtriangle(m, b, &botright);
- if (mirrorflag) {
- printf(" Updating top left ");
- printtriangle(m, b, &topright);
- printf(" Creating top right ");
- printtriangle(m, b, &newtopright);
- }
- printf(" Creating bottom right ");
- printtriangle(m, b, &newbotright);
- }
-
- /* Position `horiz' on the first edge to check for */
- /* the Delaunay property. */
- lnextself(horiz);
- } else {
- /* Insert the vertex in a triangle, splitting it into three. */
- lnext(horiz, botleft);
- lprev(horiz, botright);
- sym(botleft, botlcasing);
- sym(botright, botrcasing);
- maketriangle(m, b, &newbotleft);
- maketriangle(m, b, &newbotright);
-
- /* Set the vertices of changed and new triangles. */
- org(horiz, rightvertex);
- dest(horiz, leftvertex);
- apex(horiz, botvertex);
- setorg(newbotleft, leftvertex);
- setdest(newbotleft, botvertex);
- setapex(newbotleft, newvertex);
- setorg(newbotright, botvertex);
- setdest(newbotright, rightvertex);
- setapex(newbotright, newvertex);
- setapex(horiz, newvertex);
- for (i = 0; i < m->eextras; i++) {
- /* Set the element attributes of the new triangles. */
- attrib = elemattribute(horiz, i);
- setelemattribute(newbotleft, i, attrib);
- setelemattribute(newbotright, i, attrib);
- }
- if (b->vararea) {
- /* Set the area constraint of the new triangles. */
- area = areabound(horiz);
- setareabound(newbotleft, area);
- setareabound(newbotright, area);
- }
-
- /* There may be subsegments that need to be bonded */
- /* to the new triangles. */
- if (m->checksegments) {
- tspivot(botleft, botlsubseg);
- if (botlsubseg.ss != m->dummysub) {
- tsdissolve(botleft);
- tsbond(newbotleft, botlsubseg);
- }
- tspivot(botright, botrsubseg);
- if (botrsubseg.ss != m->dummysub) {
- tsdissolve(botright);
- tsbond(newbotright, botrsubseg);
- }
- }
-
- /* Bond the new triangles to the surrounding triangles. */
- bond(newbotleft, botlcasing);
- bond(newbotright, botrcasing);
- lnextself(newbotleft);
- lprevself(newbotright);
- bond(newbotleft, newbotright);
- lnextself(newbotleft);
- bond(botleft, newbotleft);
- lprevself(newbotright);
- bond(botright, newbotright);
-
- if (m->checkquality) {
- poolrestart(&m->flipstackers);
- m->lastflip = (struct flipstacker *) poolalloc(&m->flipstackers);
- m->lastflip->flippedtri = encode(horiz);
- m->lastflip->prevflip = (struct flipstacker *) NULL;
- }
-
-#ifdef SELF_CHECK
- if (counterclockwise(m, b, rightvertex, leftvertex, botvertex) < 0.0) {
- printf("Internal error in insertvertex():\n");
- printf(" Clockwise triangle prior to vertex insertion.\n");
- }
- if (counterclockwise(m, b, rightvertex, leftvertex, newvertex) < 0.0) {
- printf("Internal error in insertvertex():\n");
- printf(" Clockwise triangle after vertex insertion (top).\n");
- }
- if (counterclockwise(m, b, leftvertex, botvertex, newvertex) < 0.0) {
- printf("Internal error in insertvertex():\n");
- printf(" Clockwise triangle after vertex insertion (left).\n");
- }
- if (counterclockwise(m, b, botvertex, rightvertex, newvertex) < 0.0) {
- printf("Internal error in insertvertex():\n");
- printf(" Clockwise triangle after vertex insertion (right).\n");
- }
-#endif /* SELF_CHECK */
- if (b->verbose > 2) {
- printf(" Updating top ");
- printtriangle(m, b, &horiz);
- printf(" Creating left ");
- printtriangle(m, b, &newbotleft);
- printf(" Creating right ");
- printtriangle(m, b, &newbotright);
- }
- }
-
- /* The insertion is successful by default, unless an encroached */
- /* subsegment is found. */
- success = SUCCESSFULVERTEX;
- /* Circle around the newly inserted vertex, checking each edge opposite */
- /* it for the Delaunay property. Non-Delaunay edges are flipped. */
- /* `horiz' is always the edge being checked. `first' marks where to */
- /* stop circling. */
- org(horiz, first);
- rightvertex = first;
- dest(horiz, leftvertex);
- /* Circle until finished. */
- while (1) {
- /* By default, the edge will be flipped. */
- doflip = 1;
-
- if (m->checksegments) {
- /* Check for a subsegment, which cannot be flipped. */
- tspivot(horiz, checksubseg);
- if (checksubseg.ss != m->dummysub) {
- /* The edge is a subsegment and cannot be flipped. */
- doflip = 0;
-#ifndef CDT_ONLY
- if (segmentflaws) {
- /* Does the new vertex encroach upon this subsegment? */
- if (checkseg4encroach(m, b, &checksubseg)) {
- success = ENCROACHINGVERTEX;
- }
- }
-#endif /* not CDT_ONLY */
- }
- }
-
- if (doflip) {
- /* Check if the edge is a boundary edge. */
- sym(horiz, top);
- if (top.tri == m->dummytri) {
- /* The edge is a boundary edge and cannot be flipped. */
- doflip = 0;
- } else {
- /* Find the vertex on the other side of the edge. */
- apex(top, farvertex);
- /* In the incremental Delaunay triangulation algorithm, any of */
- /* `leftvertex', `rightvertex', and `farvertex' could be vertices */
- /* of the triangular bounding box. These vertices must be */
- /* treated as if they are infinitely distant, even though their */
- /* "coordinates" are not. */
- if ((leftvertex == m->infvertex1) || (leftvertex == m->infvertex2) ||
- (leftvertex == m->infvertex3)) {
- /* `leftvertex' is infinitely distant. Check the convexity of */
- /* the boundary of the triangulation. 'farvertex' might be */
- /* infinite as well, but trust me, this same condition should */
- /* be applied. */
- doflip = counterclockwise(m, b, newvertex, rightvertex, farvertex)
- > 0.0;
- } else if ((rightvertex == m->infvertex1) ||
- (rightvertex == m->infvertex2) ||
- (rightvertex == m->infvertex3)) {
- /* `rightvertex' is infinitely distant. Check the convexity of */
- /* the boundary of the triangulation. 'farvertex' might be */
- /* infinite as well, but trust me, this same condition should */
- /* be applied. */
- doflip = counterclockwise(m, b, farvertex, leftvertex, newvertex)
- > 0.0;
- } else if ((farvertex == m->infvertex1) ||
- (farvertex == m->infvertex2) ||
- (farvertex == m->infvertex3)) {
- /* `farvertex' is infinitely distant and cannot be inside */
- /* the circumcircle of the triangle `horiz'. */
- doflip = 0;
- } else {
- /* Test whether the edge is locally Delaunay. */
- doflip = incircle(m, b, leftvertex, newvertex, rightvertex,
- farvertex) > 0.0;
- }
- if (doflip) {
- /* We made it! Flip the edge `horiz' by rotating its containing */
- /* quadrilateral (the two triangles adjacent to `horiz'). */
- /* Identify the casing of the quadrilateral. */
- lprev(top, topleft);
- sym(topleft, toplcasing);
- lnext(top, topright);
- sym(topright, toprcasing);
- lnext(horiz, botleft);
- sym(botleft, botlcasing);
- lprev(horiz, botright);
- sym(botright, botrcasing);
- /* Rotate the quadrilateral one-quarter turn counterclockwise. */
- bond(topleft, botlcasing);
- bond(botleft, botrcasing);
- bond(botright, toprcasing);
- bond(topright, toplcasing);
- if (m->checksegments) {
- /* Check for subsegments and rebond them to the quadrilateral. */
- tspivot(topleft, toplsubseg);
- tspivot(botleft, botlsubseg);
- tspivot(botright, botrsubseg);
- tspivot(topright, toprsubseg);
- if (toplsubseg.ss == m->dummysub) {
- tsdissolve(topright);
- } else {
- tsbond(topright, toplsubseg);
- }
- if (botlsubseg.ss == m->dummysub) {
- tsdissolve(topleft);
- } else {
- tsbond(topleft, botlsubseg);
- }
- if (botrsubseg.ss == m->dummysub) {
- tsdissolve(botleft);
- } else {
- tsbond(botleft, botrsubseg);
- }
- if (toprsubseg.ss == m->dummysub) {
- tsdissolve(botright);
- } else {
- tsbond(botright, toprsubseg);
- }
- }
- /* New vertex assignments for the rotated quadrilateral. */
- setorg(horiz, farvertex);
- setdest(horiz, newvertex);
- setapex(horiz, rightvertex);
- setorg(top, newvertex);
- setdest(top, farvertex);
- setapex(top, leftvertex);
- for (i = 0; i < m->eextras; i++) {
- /* Take the average of the two triangles' attributes. */
- attrib = 0.5 * (elemattribute(top, i) + elemattribute(horiz, i));
- setelemattribute(top, i, attrib);
- setelemattribute(horiz, i, attrib);
- }
- if (b->vararea) {
- if ((areabound(top) <= 0.0) || (areabound(horiz) <= 0.0)) {
- area = -1.0;
- } else {
- /* Take the average of the two triangles' area constraints. */
- /* This prevents small area constraints from migrating a */
- /* long, long way from their original location due to flips. */
- area = 0.5 * (areabound(top) + areabound(horiz));
- }
- setareabound(top, area);
- setareabound(horiz, area);
- }
-
- if (m->checkquality) {
- newflip = (struct flipstacker *) poolalloc(&m->flipstackers);
- newflip->flippedtri = encode(horiz);
- newflip->prevflip = m->lastflip;
- m->lastflip = newflip;
- }
-
-#ifdef SELF_CHECK
- if (newvertex != (vertex) NULL) {
- if (counterclockwise(m, b, leftvertex, newvertex, rightvertex) <
- 0.0) {
- printf("Internal error in insertvertex():\n");
- printf(" Clockwise triangle prior to edge flip (bottom).\n");
- }
- /* The following test has been removed because constrainededge() */
- /* sometimes generates inverted triangles that insertvertex() */
- /* removes. */
-/*
- if (counterclockwise(m, b, rightvertex, farvertex, leftvertex) <
- 0.0) {
- printf("Internal error in insertvertex():\n");
- printf(" Clockwise triangle prior to edge flip (top).\n");
- }
-*/
- if (counterclockwise(m, b, farvertex, leftvertex, newvertex) <
- 0.0) {
- printf("Internal error in insertvertex():\n");
- printf(" Clockwise triangle after edge flip (left).\n");
- }
- if (counterclockwise(m, b, newvertex, rightvertex, farvertex) <
- 0.0) {
- printf("Internal error in insertvertex():\n");
- printf(" Clockwise triangle after edge flip (right).\n");
- }
- }
-#endif /* SELF_CHECK */
- if (b->verbose > 2) {
- printf(" Edge flip results in left ");
- lnextself(topleft);
- printtriangle(m, b, &topleft);
- printf(" and right ");
- printtriangle(m, b, &horiz);
- }
- /* On the next iterations, consider the two edges that were */
- /* exposed (this is, are now visible to the newly inserted */
- /* vertex) by the edge flip. */
- lprevself(horiz);
- leftvertex = farvertex;
- }
- }
- }
- if (!doflip) {
- /* The handle `horiz' is accepted as locally Delaunay. */
-#ifndef CDT_ONLY
- if (triflaws) {
- /* Check the triangle `horiz' for quality. */
- testtriangle(m, b, &horiz);
- }
-#endif /* not CDT_ONLY */
- /* Look for the next edge around the newly inserted vertex. */
- lnextself(horiz);
- sym(horiz, testtri);
- /* Check for finishing a complete revolution about the new vertex, or */
- /* falling outside of the triangulation. The latter will happen */
- /* when a vertex is inserted at a boundary. */
- if ((leftvertex == first) || (testtri.tri == m->dummytri)) {
- /* We're done. Return a triangle whose origin is the new vertex. */
- lnext(horiz, *searchtri);
- lnext(horiz, m->recenttri);
- return success;
- }
- /* Finish finding the next edge around the newly inserted vertex. */
- lnext(testtri, horiz);
- rightvertex = leftvertex;
- dest(horiz, leftvertex);
- }
- }
-}
-
-/*****************************************************************************/
-/* */
-/* triangulatepolygon() Find the Delaunay triangulation of a polygon that */
-/* has a certain "nice" shape. This includes the */
-/* polygons that result from deletion of a vertex or */
-/* insertion of a segment. */
-/* */
-/* This is a conceptually difficult routine. The starting assumption is */
-/* that we have a polygon with n sides. n - 1 of these sides are currently */
-/* represented as edges in the mesh. One side, called the "base", need not */
-/* be. */
-/* */
-/* Inside the polygon is a structure I call a "fan", consisting of n - 1 */
-/* triangles that share a common origin. For each of these triangles, the */
-/* edge opposite the origin is one of the sides of the polygon. The */
-/* primary edge of each triangle is the edge directed from the origin to */
-/* the destination; note that this is not the same edge that is a side of */
-/* the polygon. `firstedge' is the primary edge of the first triangle. */
-/* From there, the triangles follow in counterclockwise order about the */
-/* polygon, until `lastedge', the primary edge of the last triangle. */
-/* `firstedge' and `lastedge' are probably connected to other triangles */
-/* beyond the extremes of the fan, but their identity is not important, as */
-/* long as the fan remains connected to them. */
-/* */
-/* Imagine the polygon oriented so that its base is at the bottom. This */
-/* puts `firstedge' on the far right, and `lastedge' on the far left. */
-/* The right vertex of the base is the destination of `firstedge', and the */
-/* left vertex of the base is the apex of `lastedge'. */
-/* */
-/* The challenge now is to find the right sequence of edge flips to */
-/* transform the fan into a Delaunay triangulation of the polygon. Each */
-/* edge flip effectively removes one triangle from the fan, committing it */
-/* to the polygon. The resulting polygon has one fewer edge. If `doflip' */
-/* is set, the final flip will be performed, resulting in a fan of one */
-/* (useless?) triangle. If `doflip' is not set, the final flip is not */
-/* performed, resulting in a fan of two triangles, and an unfinished */
-/* triangular polygon that is not yet filled out with a single triangle. */
-/* On completion of the routine, `lastedge' is the last remaining triangle, */
-/* or the leftmost of the last two. */
-/* */
-/* Although the flips are performed in the order described above, the */
-/* decisions about what flips to perform are made in precisely the reverse */
-/* order. The recursive triangulatepolygon() procedure makes a decision, */
-/* uses up to two recursive calls to triangulate the "subproblems" */
-/* (polygons with fewer edges), and then performs an edge flip. */
-/* */
-/* The "decision" it makes is which vertex of the polygon should be */
-/* connected to the base. This decision is made by testing every possible */
-/* vertex. Once the best vertex is found, the two edges that connect this */
-/* vertex to the base become the bases for two smaller polygons. These */
-/* are triangulated recursively. Unfortunately, this approach can take */
-/* O(n^2) time not only in the worst case, but in many common cases. It's */
-/* rarely a big deal for vertex deletion, where n is rarely larger than */
-/* ten, but it could be a big deal for segment insertion, especially if */
-/* there's a lot of long segments that each cut many triangles. I ought to */
-/* code a faster algorithm some day. */
-/* */
-/* The `edgecount' parameter is the number of sides of the polygon, */
-/* including its base. `triflaws' is a flag that determines whether the */
-/* new triangles should be tested for quality, and enqueued if they are */
-/* bad. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-void triangulatepolygon(struct mesh *m, struct behavior *b,
- struct otri *firstedge, struct otri *lastedge,
- int edgecount, int doflip, int triflaws)
-#else /* not ANSI_DECLARATORS */
-void triangulatepolygon(m, b, firstedge, lastedge, edgecount, doflip, triflaws)
-struct mesh *m;
-struct behavior *b;
-struct otri *firstedge;
-struct otri *lastedge;
-int edgecount;
-int doflip;
-int triflaws;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct otri testtri;
- struct otri besttri;
- struct otri tempedge;
- vertex leftbasevertex, rightbasevertex;
- vertex testvertex;
- vertex bestvertex;
- int bestnumber;
- int i;
- triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */
-
- /* Identify the base vertices. */
- apex(*lastedge, leftbasevertex);
- dest(*firstedge, rightbasevertex);
- if (b->verbose > 2) {
- printf(" Triangulating interior polygon at edge\n");
- printf(" (%.12g, %.12g) (%.12g, %.12g)\n", leftbasevertex[0],
- leftbasevertex[1], rightbasevertex[0], rightbasevertex[1]);
- }
- /* Find the best vertex to connect the base to. */
- onext(*firstedge, besttri);
- dest(besttri, bestvertex);
- otricopy(besttri, testtri);
- bestnumber = 1;
- for (i = 2; i <= edgecount - 2; i++) {
- onextself(testtri);
- dest(testtri, testvertex);
- /* Is this a better vertex? */
- if (incircle(m, b, leftbasevertex, rightbasevertex, bestvertex,
- testvertex) > 0.0) {
- otricopy(testtri, besttri);
- bestvertex = testvertex;
- bestnumber = i;
- }
- }
- if (b->verbose > 2) {
- printf(" Connecting edge to (%.12g, %.12g)\n", bestvertex[0],
- bestvertex[1]);
- }
- if (bestnumber > 1) {
- /* Recursively triangulate the smaller polygon on the right. */
- oprev(besttri, tempedge);
- triangulatepolygon(m, b, firstedge, &tempedge, bestnumber + 1, 1,
- triflaws);
- }
- if (bestnumber < edgecount - 2) {
- /* Recursively triangulate the smaller polygon on the left. */
- sym(besttri, tempedge);
- triangulatepolygon(m, b, &besttri, lastedge, edgecount - bestnumber, 1,
- triflaws);
- /* Find `besttri' again; it may have been lost to edge flips. */
- sym(tempedge, besttri);
- }
- if (doflip) {
- /* Do one final edge flip. */
- flip(m, b, &besttri);
-#ifndef CDT_ONLY
- if (triflaws) {
- /* Check the quality of the newly committed triangle. */
- sym(besttri, testtri);
- testtriangle(m, b, &testtri);
- }
-#endif /* not CDT_ONLY */
- }
- /* Return the base triangle. */
- otricopy(besttri, *lastedge);
-}
-
-/*****************************************************************************/
-/* */
-/* deletevertex() Delete a vertex from a Delaunay triangulation, ensuring */
-/* that the triangulation remains Delaunay. */
-/* */
-/* The origin of `deltri' is deleted. The union of the triangles adjacent */
-/* to this vertex is a polygon, for which the Delaunay triangulation is */
-/* found. Two triangles are removed from the mesh. */
-/* */
-/* Only interior vertices that do not lie on segments or boundaries may be */
-/* deleted. */
-/* */
-/*****************************************************************************/
-
-#ifndef CDT_ONLY
-
-#ifdef ANSI_DECLARATORS
-void deletevertex(struct mesh *m, struct behavior *b, struct otri *deltri)
-#else /* not ANSI_DECLARATORS */
-void deletevertex(m, b, deltri)
-struct mesh *m;
-struct behavior *b;
-struct otri *deltri;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct otri countingtri;
- struct otri firstedge, lastedge;
- struct otri deltriright;
- struct otri lefttri, righttri;
- struct otri leftcasing, rightcasing;
- struct osub leftsubseg, rightsubseg;
- vertex delvertex;
- vertex neworg;
- int edgecount;
- triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */
- subseg sptr; /* Temporary variable used by tspivot(). */
-
- org(*deltri, delvertex);
- if (b->verbose > 1) {
- printf(" Deleting (%.12g, %.12g).\n", delvertex[0], delvertex[1]);
- }
- vertexdealloc(m, delvertex);
-
- /* Count the degree of the vertex being deleted. */
- onext(*deltri, countingtri);
- edgecount = 1;
- while (!otriequal(*deltri, countingtri)) {
-#ifdef SELF_CHECK
- if (countingtri.tri == m->dummytri) {
- printf("Internal error in deletevertex():\n");
- printf(" Attempt to delete boundary vertex.\n");
- internalerror();
- }
-#endif /* SELF_CHECK */
- edgecount++;
- onextself(countingtri);
- }
-
-#ifdef SELF_CHECK
- if (edgecount < 3) {
- printf("Internal error in deletevertex():\n Vertex has degree %d.\n",
- edgecount);
- internalerror();
- }
-#endif /* SELF_CHECK */
- if (edgecount > 3) {
- /* Triangulate the polygon defined by the union of all triangles */
- /* adjacent to the vertex being deleted. Check the quality of */
- /* the resulting triangles. */
- onext(*deltri, firstedge);
- oprev(*deltri, lastedge);
- triangulatepolygon(m, b, &firstedge, &lastedge, edgecount, 0,
- !b->nobisect);
- }
- /* Splice out two triangles. */
- lprev(*deltri, deltriright);
- dnext(*deltri, lefttri);
- sym(lefttri, leftcasing);
- oprev(deltriright, righttri);
- sym(righttri, rightcasing);
- bond(*deltri, leftcasing);
- bond(deltriright, rightcasing);
- tspivot(lefttri, leftsubseg);
- if (leftsubseg.ss != m->dummysub) {
- tsbond(*deltri, leftsubseg);
- }
- tspivot(righttri, rightsubseg);
- if (rightsubseg.ss != m->dummysub) {
- tsbond(deltriright, rightsubseg);
- }
-
- /* Set the new origin of `deltri' and check its quality. */
- org(lefttri, neworg);
- setorg(*deltri, neworg);
- if (!b->nobisect) {
- testtriangle(m, b, deltri);
- }
-
- /* Delete the two spliced-out triangles. */
- triangledealloc(m, lefttri.tri);
- triangledealloc(m, righttri.tri);
-}
-
-#endif /* not CDT_ONLY */
-
-/*****************************************************************************/
-/* */
-/* undovertex() Undo the most recent vertex insertion. */
-/* */
-/* Walks through the list of transformations (flips and a vertex insertion) */
-/* in the reverse of the order in which they were done, and undoes them. */
-/* The inserted vertex is removed from the triangulation and deallocated. */
-/* Two triangles (possibly just one) are also deallocated. */
-/* */
-/*****************************************************************************/
-
-#ifndef CDT_ONLY
-
-#ifdef ANSI_DECLARATORS
-void undovertex(struct mesh *m, struct behavior *b)
-#else /* not ANSI_DECLARATORS */
-void undovertex(m, b)
-struct mesh *m;
-struct behavior *b;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct otri fliptri;
- struct otri botleft, botright, topright;
- struct otri botlcasing, botrcasing, toprcasing;
- struct otri gluetri;
- struct osub botlsubseg, botrsubseg, toprsubseg;
- vertex botvertex, rightvertex;
- triangle ptr; /* Temporary variable used by sym(). */
- subseg sptr; /* Temporary variable used by tspivot(). */
-
- /* Walk through the list of transformations (flips and a vertex insertion) */
- /* in the reverse of the order in which they were done, and undo them. */
- while (m->lastflip != (struct flipstacker *) NULL) {
- /* Find a triangle involved in the last unreversed transformation. */
- decode(m->lastflip->flippedtri, fliptri);
-
- /* We are reversing one of three transformations: a trisection of one */
- /* triangle into three (by inserting a vertex in the triangle), a */
- /* bisection of two triangles into four (by inserting a vertex in an */
- /* edge), or an edge flip. */
- if (m->lastflip->prevflip == (struct flipstacker *) NULL) {
- /* Restore a triangle that was split into three triangles, */
- /* so it is again one triangle. */
- dprev(fliptri, botleft);
- lnextself(botleft);
- onext(fliptri, botright);
- lprevself(botright);
- sym(botleft, botlcasing);
- sym(botright, botrcasing);
- dest(botleft, botvertex);
-
- setapex(fliptri, botvertex);
- lnextself(fliptri);
- bond(fliptri, botlcasing);
- tspivot(botleft, botlsubseg);
- tsbond(fliptri, botlsubseg);
- lnextself(fliptri);
- bond(fliptri, botrcasing);
- tspivot(botright, botrsubseg);
- tsbond(fliptri, botrsubseg);
-
- /* Delete the two spliced-out triangles. */
- triangledealloc(m, botleft.tri);
- triangledealloc(m, botright.tri);
- } else if (m->lastflip->prevflip == (struct flipstacker *) &insertvertex) {
- /* Restore two triangles that were split into four triangles, */
- /* so they are again two triangles. */
- lprev(fliptri, gluetri);
- sym(gluetri, botright);
- lnextself(botright);
- sym(botright, botrcasing);
- dest(botright, rightvertex);
-
- setorg(fliptri, rightvertex);
- bond(gluetri, botrcasing);
- tspivot(botright, botrsubseg);
- tsbond(gluetri, botrsubseg);
-
- /* Delete the spliced-out triangle. */
- triangledealloc(m, botright.tri);
-
- sym(fliptri, gluetri);
- if (gluetri.tri != m->dummytri) {
- lnextself(gluetri);
- dnext(gluetri, topright);
- sym(topright, toprcasing);
-
- setorg(gluetri, rightvertex);
- bond(gluetri, toprcasing);
- tspivot(topright, toprsubseg);
- tsbond(gluetri, toprsubseg);
-
- /* Delete the spliced-out triangle. */
- triangledealloc(m, topright.tri);
- }
-
- /* This is the end of the list, sneakily encoded. */
- m->lastflip->prevflip = (struct flipstacker *) NULL;
- } else {
- /* Undo an edge flip. */
- unflip(m, b, &fliptri);
- }
-
- /* Go on and process the next transformation. */
- m->lastflip = m->lastflip->prevflip;
- }
-}
-
-#endif /* not CDT_ONLY */
-
-/** **/
-/** **/
-/********* Mesh transformation routines end here *********/
-
-/********* Divide-and-conquer Delaunay triangulation begins here *********/
-/** **/
-/** **/
-
-/*****************************************************************************/
-/* */
-/* The divide-and-conquer bounding box */
-/* */
-/* I originally implemented the divide-and-conquer and incremental Delaunay */
-/* triangulations using the edge-based data structure presented by Guibas */
-/* and Stolfi. Switching to a triangle-based data structure doubled the */
-/* speed. However, I had to think of a few extra tricks to maintain the */
-/* elegance of the original algorithms. */
-/* */
-/* The "bounding box" used by my variant of the divide-and-conquer */
-/* algorithm uses one triangle for each edge of the convex hull of the */
-/* triangulation. These bounding triangles all share a common apical */
-/* vertex, which is represented by NULL and which represents nothing. */
-/* The bounding triangles are linked in a circular fan about this NULL */
-/* vertex, and the edges on the convex hull of the triangulation appear */
-/* opposite the NULL vertex. You might find it easiest to imagine that */
-/* the NULL vertex is a point in 3D space behind the center of the */
-/* triangulation, and that the bounding triangles form a sort of cone. */
-/* */
-/* This bounding box makes it easy to represent degenerate cases. For */
-/* instance, the triangulation of two vertices is a single edge. This edge */
-/* is represented by two bounding box triangles, one on each "side" of the */
-/* edge. These triangles are also linked together in a fan about the NULL */
-/* vertex. */
-/* */
-/* The bounding box also makes it easy to traverse the convex hull, as the */
-/* divide-and-conquer algorithm needs to do. */
-/* */
-/*****************************************************************************/
-
-/*****************************************************************************/
-/* */
-/* vertexsort() Sort an array of vertices by x-coordinate, using the */
-/* y-coordinate as a secondary key. */
-/* */
-/* Uses quicksort. Randomized O(n log n) time. No, I did not make any of */
-/* the usual quicksort mistakes. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-void vertexsort(vertex *sortarray, int arraysize)
-#else /* not ANSI_DECLARATORS */
-void vertexsort(sortarray, arraysize)
-vertex *sortarray;
-int arraysize;
-#endif /* not ANSI_DECLARATORS */
-
-{
- int left, right;
- int pivot;
- REAL pivotx, pivoty;
- vertex temp;
-
- if (arraysize == 2) {
- /* Recursive base case. */
- if ((sortarray[0][0] > sortarray[1][0]) ||
- ((sortarray[0][0] == sortarray[1][0]) &&
- (sortarray[0][1] > sortarray[1][1]))) {
- temp = sortarray[1];
- sortarray[1] = sortarray[0];
- sortarray[0] = temp;
- }
- return;
- }
- /* Choose a random pivot to split the array. */
- pivot = (int) randomnation((unsigned int) arraysize);
- pivotx = sortarray[pivot][0];
- pivoty = sortarray[pivot][1];
- /* Split the array. */
- left = -1;
- right = arraysize;
- while (left < right) {
- /* Search for a vertex whose x-coordinate is too large for the left. */
- do {
- left++;
- } while ((left <= right) && ((sortarray[left][0] < pivotx) ||
- ((sortarray[left][0] == pivotx) &&
- (sortarray[left][1] < pivoty))));
- /* Search for a vertex whose x-coordinate is too small for the right. */
- do {
- right--;
- } while ((left <= right) && ((sortarray[right][0] > pivotx) ||
- ((sortarray[right][0] == pivotx) &&
- (sortarray[right][1] > pivoty))));
- if (left < right) {
- /* Swap the left and right vertices. */
- temp = sortarray[left];
- sortarray[left] = sortarray[right];
- sortarray[right] = temp;
- }
- }
- if (left > 1) {
- /* Recursively sort the left subset. */
- vertexsort(sortarray, left);
- }
- if (right < arraysize - 2) {
- /* Recursively sort the right subset. */
- vertexsort(&sortarray[right + 1], arraysize - right - 1);
- }
-}
-
-/*****************************************************************************/
-/* */
-/* vertexmedian() An order statistic algorithm, almost. Shuffles an */
-/* array of vertices so that the first `median' vertices */
-/* occur lexicographically before the remaining vertices. */
-/* */
-/* Uses the x-coordinate as the primary key if axis == 0; the y-coordinate */
-/* if axis == 1. Very similar to the vertexsort() procedure, but runs in */
-/* randomized linear time. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-void vertexmedian(vertex *sortarray, int arraysize, int median, int axis)
-#else /* not ANSI_DECLARATORS */
-void vertexmedian(sortarray, arraysize, median, axis)
-vertex *sortarray;
-int arraysize;
-int median;
-int axis;
-#endif /* not ANSI_DECLARATORS */
-
-{
- int left, right;
- int pivot;
- REAL pivot1, pivot2;
- vertex temp;
-
- if (arraysize == 2) {
- /* Recursive base case. */
- if ((sortarray[0][axis] > sortarray[1][axis]) ||
- ((sortarray[0][axis] == sortarray[1][axis]) &&
- (sortarray[0][1 - axis] > sortarray[1][1 - axis]))) {
- temp = sortarray[1];
- sortarray[1] = sortarray[0];
- sortarray[0] = temp;
- }
- return;
- }
- /* Choose a random pivot to split the array. */
- pivot = (int) randomnation((unsigned int) arraysize);
- pivot1 = sortarray[pivot][axis];
- pivot2 = sortarray[pivot][1 - axis];
- /* Split the array. */
- left = -1;
- right = arraysize;
- while (left < right) {
- /* Search for a vertex whose x-coordinate is too large for the left. */
- do {
- left++;
- } while ((left <= right) && ((sortarray[left][axis] < pivot1) ||
- ((sortarray[left][axis] == pivot1) &&
- (sortarray[left][1 - axis] < pivot2))));
- /* Search for a vertex whose x-coordinate is too small for the right. */
- do {
- right--;
- } while ((left <= right) && ((sortarray[right][axis] > pivot1) ||
- ((sortarray[right][axis] == pivot1) &&
- (sortarray[right][1 - axis] > pivot2))));
- if (left < right) {
- /* Swap the left and right vertices. */
- temp = sortarray[left];
- sortarray[left] = sortarray[right];
- sortarray[right] = temp;
- }
- }
- /* Unlike in vertexsort(), at most one of the following */
- /* conditionals is true. */
- if (left > median) {
- /* Recursively shuffle the left subset. */
- vertexmedian(sortarray, left, median, axis);
- }
- if (right < median - 1) {
- /* Recursively shuffle the right subset. */
- vertexmedian(&sortarray[right + 1], arraysize - right - 1,
- median - right - 1, axis);
- }
-}
-
-/*****************************************************************************/
-/* */
-/* alternateaxes() Sorts the vertices as appropriate for the divide-and- */
-/* conquer algorithm with alternating cuts. */
-/* */
-/* Partitions by x-coordinate if axis == 0; by y-coordinate if axis == 1. */
-/* For the base case, subsets containing only two or three vertices are */
-/* always sorted by x-coordinate. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-void alternateaxes(vertex *sortarray, int arraysize, int axis)
-#else /* not ANSI_DECLARATORS */
-void alternateaxes(sortarray, arraysize, axis)
-vertex *sortarray;
-int arraysize;
-int axis;
-#endif /* not ANSI_DECLARATORS */
-
-{
- int divider;
-
- divider = arraysize >> 1;
- if (arraysize <= 3) {
- /* Recursive base case: subsets of two or three vertices will be */
- /* handled specially, and should always be sorted by x-coordinate. */
- axis = 0;
- }
- /* Partition with a horizontal or vertical cut. */
- vertexmedian(sortarray, arraysize, divider, axis);
- /* Recursively partition the subsets with a cross cut. */
- if (arraysize - divider >= 2) {
- if (divider >= 2) {
- alternateaxes(sortarray, divider, 1 - axis);
- }
- alternateaxes(&sortarray[divider], arraysize - divider, 1 - axis);
- }
-}
-
-/*****************************************************************************/
-/* */
-/* mergehulls() Merge two adjacent Delaunay triangulations into a */
-/* single Delaunay triangulation. */
-/* */
-/* This is similar to the algorithm given by Guibas and Stolfi, but uses */
-/* a triangle-based, rather than edge-based, data structure. */
-/* */
-/* The algorithm walks up the gap between the two triangulations, knitting */
-/* them together. As they are merged, some of their bounding triangles */
-/* are converted into real triangles of the triangulation. The procedure */
-/* pulls each hull's bounding triangles apart, then knits them together */
-/* like the teeth of two gears. The Delaunay property determines, at each */
-/* step, whether the next "tooth" is a bounding triangle of the left hull */
-/* or the right. When a bounding triangle becomes real, its apex is */
-/* changed from NULL to a real vertex. */
-/* */
-/* Only two new triangles need to be allocated. These become new bounding */
-/* triangles at the top and bottom of the seam. They are used to connect */
-/* the remaining bounding triangles (those that have not been converted */
-/* into real triangles) into a single fan. */
-/* */
-/* On entry, `farleft' and `innerleft' are bounding triangles of the left */
-/* triangulation. The origin of `farleft' is the leftmost vertex, and */
-/* the destination of `innerleft' is the rightmost vertex of the */
-/* triangulation. Similarly, `innerright' and `farright' are bounding */
-/* triangles of the right triangulation. The origin of `innerright' and */
-/* destination of `farright' are the leftmost and rightmost vertices. */
-/* */
-/* On completion, the origin of `farleft' is the leftmost vertex of the */
-/* merged triangulation, and the destination of `farright' is the rightmost */
-/* vertex. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-void mergehulls(struct mesh *m, struct behavior *b, struct otri *farleft,
- struct otri *innerleft, struct otri *innerright,
- struct otri *farright, int axis)
-#else /* not ANSI_DECLARATORS */
-void mergehulls(m, b, farleft, innerleft, innerright, farright, axis)
-struct mesh *m;
-struct behavior *b;
-struct otri *farleft;
-struct otri *innerleft;
-struct otri *innerright;
-struct otri *farright;
-int axis;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct otri leftcand, rightcand;
- struct otri baseedge;
- struct otri nextedge;
- struct otri sidecasing, topcasing, outercasing;
- struct otri checkedge;
- vertex innerleftdest;
- vertex innerrightorg;
- vertex innerleftapex, innerrightapex;
- vertex farleftpt, farrightpt;
- vertex farleftapex, farrightapex;
- vertex lowerleft, lowerright;
- vertex upperleft, upperright;
- vertex nextapex;
- vertex checkvertex;
- int changemade;
- int badedge;
- int leftfinished, rightfinished;
- triangle ptr; /* Temporary variable used by sym(). */
-
- dest(*innerleft, innerleftdest);
- apex(*innerleft, innerleftapex);
- org(*innerright, innerrightorg);
- apex(*innerright, innerrightapex);
- /* Special treatment for horizontal cuts. */
- if (b->dwyer && (axis == 1)) {
- org(*farleft, farleftpt);
- apex(*farleft, farleftapex);
- dest(*farright, farrightpt);
- apex(*farright, farrightapex);
- /* The pointers to the extremal vertices are shifted to point to the */
- /* topmost and bottommost vertex of each hull, rather than the */
- /* leftmost and rightmost vertices. */
- while (farleftapex[1] < farleftpt[1]) {
- lnextself(*farleft);
- symself(*farleft);
- farleftpt = farleftapex;
- apex(*farleft, farleftapex);
- }
- sym(*innerleft, checkedge);
- apex(checkedge, checkvertex);
- while (checkvertex[1] > innerleftdest[1]) {
- lnext(checkedge, *innerleft);
- innerleftapex = innerleftdest;
- innerleftdest = checkvertex;
- sym(*innerleft, checkedge);
- apex(checkedge, checkvertex);
- }
- while (innerrightapex[1] < innerrightorg[1]) {
- lnextself(*innerright);
- symself(*innerright);
- innerrightorg = innerrightapex;
- apex(*innerright, innerrightapex);
- }
- sym(*farright, checkedge);
- apex(checkedge, checkvertex);
- while (checkvertex[1] > farrightpt[1]) {
- lnext(checkedge, *farright);
- farrightapex = farrightpt;
- farrightpt = checkvertex;
- sym(*farright, checkedge);
- apex(checkedge, checkvertex);
- }
- }
- /* Find a line tangent to and below both hulls. */
- do {
- changemade = 0;
- /* Make innerleftdest the "bottommost" vertex of the left hull. */
- if (counterclockwise(m, b, innerleftdest, innerleftapex, innerrightorg) >
- 0.0) {
- lprevself(*innerleft);
- symself(*innerleft);
- innerleftdest = innerleftapex;
- apex(*innerleft, innerleftapex);
- changemade = 1;
- }
- /* Make innerrightorg the "bottommost" vertex of the right hull. */
- if (counterclockwise(m, b, innerrightapex, innerrightorg, innerleftdest) >
- 0.0) {
- lnextself(*innerright);
- symself(*innerright);
- innerrightorg = innerrightapex;
- apex(*innerright, innerrightapex);
- changemade = 1;
- }
- } while (changemade);
- /* Find the two candidates to be the next "gear tooth." */
- sym(*innerleft, leftcand);
- sym(*innerright, rightcand);
- /* Create the bottom new bounding triangle. */
- maketriangle(m, b, &baseedge);
- /* Connect it to the bounding boxes of the left and right triangulations. */
- bond(baseedge, *innerleft);
- lnextself(baseedge);
- bond(baseedge, *innerright);
- lnextself(baseedge);
- setorg(baseedge, innerrightorg);
- setdest(baseedge, innerleftdest);
- /* Apex is intentionally left NULL. */
- if (b->verbose > 2) {
- printf(" Creating base bounding ");
- printtriangle(m, b, &baseedge);
- }
- /* Fix the extreme triangles if necessary. */
- org(*farleft, farleftpt);
- if (innerleftdest == farleftpt) {
- lnext(baseedge, *farleft);
- }
- dest(*farright, farrightpt);
- if (innerrightorg == farrightpt) {
- lprev(baseedge, *farright);
- }
- /* The vertices of the current knitting edge. */
- lowerleft = innerleftdest;
- lowerright = innerrightorg;
- /* The candidate vertices for knitting. */
- apex(leftcand, upperleft);
- apex(rightcand, upperright);
- /* Walk up the gap between the two triangulations, knitting them together. */
- while (1) {
- /* Have we reached the top? (This isn't quite the right question, */
- /* because even though the left triangulation might seem finished now, */
- /* moving up on the right triangulation might reveal a new vertex of */
- /* the left triangulation. And vice-versa.) */
- leftfinished = counterclockwise(m, b, upperleft, lowerleft, lowerright) <=
- 0.0;
- rightfinished = counterclockwise(m, b, upperright, lowerleft, lowerright)
- <= 0.0;
- if (leftfinished && rightfinished) {
- /* Create the top new bounding triangle. */
- maketriangle(m, b, &nextedge);
- setorg(nextedge, lowerleft);
- setdest(nextedge, lowerright);
- /* Apex is intentionally left NULL. */
- /* Connect it to the bounding boxes of the two triangulations. */
- bond(nextedge, baseedge);
- lnextself(nextedge);
- bond(nextedge, rightcand);
- lnextself(nextedge);
- bond(nextedge, leftcand);
- if (b->verbose > 2) {
- printf(" Creating top bounding ");
- printtriangle(m, b, &nextedge);
- }
- /* Special treatment for horizontal cuts. */
- if (b->dwyer && (axis == 1)) {
- org(*farleft, farleftpt);
- apex(*farleft, farleftapex);
- dest(*farright, farrightpt);
- apex(*farright, farrightapex);
- sym(*farleft, checkedge);
- apex(checkedge, checkvertex);
- /* The pointers to the extremal vertices are restored to the */
- /* leftmost and rightmost vertices (rather than topmost and */
- /* bottommost). */
- while (checkvertex[0] < farleftpt[0]) {
- lprev(checkedge, *farleft);
- farleftapex = farleftpt;
- farleftpt = checkvertex;
- sym(*farleft, checkedge);
- apex(checkedge, checkvertex);
- }
- while (farrightapex[0] > farrightpt[0]) {
- lprevself(*farright);
- symself(*farright);
- farrightpt = farrightapex;
- apex(*farright, farrightapex);
- }
- }
- return;
- }
- /* Consider eliminating edges from the left triangulation. */
- if (!leftfinished) {
- /* What vertex would be exposed if an edge were deleted? */
- lprev(leftcand, nextedge);
- symself(nextedge);
- apex(nextedge, nextapex);
- /* If nextapex is NULL, then no vertex would be exposed; the */
- /* triangulation would have been eaten right through. */
- if (nextapex != (vertex) NULL) {
- /* Check whether the edge is Delaunay. */
- badedge = incircle(m, b, lowerleft, lowerright, upperleft, nextapex) >
- 0.0;
- while (badedge) {
- /* Eliminate the edge with an edge flip. As a result, the */
- /* left triangulation will have one more boundary triangle. */
- lnextself(nextedge);
- sym(nextedge, topcasing);
- lnextself(nextedge);
- sym(nextedge, sidecasing);
- bond(nextedge, topcasing);
- bond(leftcand, sidecasing);
- lnextself(leftcand);
- sym(leftcand, outercasing);
- lprevself(nextedge);
- bond(nextedge, outercasing);
- /* Correct the vertices to reflect the edge flip. */
- setorg(leftcand, lowerleft);
- setdest(leftcand, NULL);
- setapex(leftcand, nextapex);
- setorg(nextedge, NULL);
- setdest(nextedge, upperleft);
- setapex(nextedge, nextapex);
- /* Consider the newly exposed vertex. */
- upperleft = nextapex;
- /* What vertex would be exposed if another edge were deleted? */
- otricopy(sidecasing, nextedge);
- apex(nextedge, nextapex);
- if (nextapex != (vertex) NULL) {
- /* Check whether the edge is Delaunay. */
- badedge = incircle(m, b, lowerleft, lowerright, upperleft,
- nextapex) > 0.0;
- } else {
- /* Avoid eating right through the triangulation. */
- badedge = 0;
- }
- }
- }
- }
- /* Consider eliminating edges from the right triangulation. */
- if (!rightfinished) {
- /* What vertex would be exposed if an edge were deleted? */
- lnext(rightcand, nextedge);
- symself(nextedge);
- apex(nextedge, nextapex);
- /* If nextapex is NULL, then no vertex would be exposed; the */
- /* triangulation would have been eaten right through. */
- if (nextapex != (vertex) NULL) {
- /* Check whether the edge is Delaunay. */
- badedge = incircle(m, b, lowerleft, lowerright, upperright, nextapex) >
- 0.0;
- while (badedge) {
- /* Eliminate the edge with an edge flip. As a result, the */
- /* right triangulation will have one more boundary triangle. */
- lprevself(nextedge);
- sym(nextedge, topcasing);
- lprevself(nextedge);
- sym(nextedge, sidecasing);
- bond(nextedge, topcasing);
- bond(rightcand, sidecasing);
- lprevself(rightcand);
- sym(rightcand, outercasing);
- lnextself(nextedge);
- bond(nextedge, outercasing);
- /* Correct the vertices to reflect the edge flip. */
- setorg(rightcand, NULL);
- setdest(rightcand, lowerright);
- setapex(rightcand, nextapex);
- setorg(nextedge, upperright);
- setdest(nextedge, NULL);
- setapex(nextedge, nextapex);
- /* Consider the newly exposed vertex. */
- upperright = nextapex;
- /* What vertex would be exposed if another edge were deleted? */
- otricopy(sidecasing, nextedge);
- apex(nextedge, nextapex);
- if (nextapex != (vertex) NULL) {
- /* Check whether the edge is Delaunay. */
- badedge = incircle(m, b, lowerleft, lowerright, upperright,
- nextapex) > 0.0;
- } else {
- /* Avoid eating right through the triangulation. */
- badedge = 0;
- }
- }
- }
- }
- if (leftfinished || (!rightfinished &&
- (incircle(m, b, upperleft, lowerleft, lowerright, upperright) >
- 0.0))) {
- /* Knit the triangulations, adding an edge from `lowerleft' */
- /* to `upperright'. */
- bond(baseedge, rightcand);
- lprev(rightcand, baseedge);
- setdest(baseedge, lowerleft);
- lowerright = upperright;
- sym(baseedge, rightcand);
- apex(rightcand, upperright);
- } else {
- /* Knit the triangulations, adding an edge from `upperleft' */
- /* to `lowerright'. */
- bond(baseedge, leftcand);
- lnext(leftcand, baseedge);
- setorg(baseedge, lowerright);
- lowerleft = upperleft;
- sym(baseedge, leftcand);
- apex(leftcand, upperleft);
- }
- if (b->verbose > 2) {
- printf(" Connecting ");
- printtriangle(m, b, &baseedge);
- }
- }
-}
-
-/*****************************************************************************/
-/* */
-/* divconqrecurse() Recursively form a Delaunay triangulation by the */
-/* divide-and-conquer method. */
-/* */
-/* Recursively breaks down the problem into smaller pieces, which are */
-/* knitted together by mergehulls(). The base cases (problems of two or */
-/* three vertices) are handled specially here. */
-/* */
-/* On completion, `farleft' and `farright' are bounding triangles such that */
-/* the origin of `farleft' is the leftmost vertex (breaking ties by */
-/* choosing the highest leftmost vertex), and the destination of */
-/* `farright' is the rightmost vertex (breaking ties by choosing the */
-/* lowest rightmost vertex). */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-void divconqrecurse(struct mesh *m, struct behavior *b, vertex *sortarray,
- int vertices, int axis,
- struct otri *farleft, struct otri *farright)
-#else /* not ANSI_DECLARATORS */
-void divconqrecurse(m, b, sortarray, vertices, axis, farleft, farright)
-struct mesh *m;
-struct behavior *b;
-vertex *sortarray;
-int vertices;
-int axis;
-struct otri *farleft;
-struct otri *farright;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct otri midtri, tri1, tri2, tri3;
- struct otri innerleft, innerright;
- REAL area;
- int divider;
-
- if (b->verbose > 2) {
- printf(" Triangulating %d vertices.\n", vertices);
- }
- if (vertices == 2) {
- /* The triangulation of two vertices is an edge. An edge is */
- /* represented by two bounding triangles. */
- maketriangle(m, b, farleft);
- setorg(*farleft, sortarray[0]);
- setdest(*farleft, sortarray[1]);
- /* The apex is intentionally left NULL. */
- maketriangle(m, b, farright);
- setorg(*farright, sortarray[1]);
- setdest(*farright, sortarray[0]);
- /* The apex is intentionally left NULL. */
- bond(*farleft, *farright);
- lprevself(*farleft);
- lnextself(*farright);
- bond(*farleft, *farright);
- lprevself(*farleft);
- lnextself(*farright);
- bond(*farleft, *farright);
- if (b->verbose > 2) {
- printf(" Creating ");
- printtriangle(m, b, farleft);
- printf(" Creating ");
- printtriangle(m, b, farright);
- }
- /* Ensure that the origin of `farleft' is sortarray[0]. */
- lprev(*farright, *farleft);
- return;
- } else if (vertices == 3) {
- /* The triangulation of three vertices is either a triangle (with */
- /* three bounding triangles) or two edges (with four bounding */
- /* triangles). In either case, four triangles are created. */
- maketriangle(m, b, &midtri);
- maketriangle(m, b, &tri1);
- maketriangle(m, b, &tri2);
- maketriangle(m, b, &tri3);
- area = counterclockwise(m, b, sortarray[0], sortarray[1], sortarray[2]);
- if (area == 0.0) {
- /* Three collinear vertices; the triangulation is two edges. */
- setorg(midtri, sortarray[0]);
- setdest(midtri, sortarray[1]);
- setorg(tri1, sortarray[1]);
- setdest(tri1, sortarray[0]);
- setorg(tri2, sortarray[2]);
- setdest(tri2, sortarray[1]);
- setorg(tri3, sortarray[1]);
- setdest(tri3, sortarray[2]);
- /* All apices are intentionally left NULL. */
- bond(midtri, tri1);
- bond(tri2, tri3);
- lnextself(midtri);
- lprevself(tri1);
- lnextself(tri2);
- lprevself(tri3);
- bond(midtri, tri3);
- bond(tri1, tri2);
- lnextself(midtri);
- lprevself(tri1);
- lnextself(tri2);
- lprevself(tri3);
- bond(midtri, tri1);
- bond(tri2, tri3);
- /* Ensure that the origin of `farleft' is sortarray[0]. */
- otricopy(tri1, *farleft);
- /* Ensure that the destination of `farright' is sortarray[2]. */
- otricopy(tri2, *farright);
- } else {
- /* The three vertices are not collinear; the triangulation is one */
- /* triangle, namely `midtri'. */
- setorg(midtri, sortarray[0]);
- setdest(tri1, sortarray[0]);
- setorg(tri3, sortarray[0]);
- /* Apices of tri1, tri2, and tri3 are left NULL. */
- if (area > 0.0) {
- /* The vertices are in counterclockwise order. */
- setdest(midtri, sortarray[1]);
- setorg(tri1, sortarray[1]);
- setdest(tri2, sortarray[1]);
- setapex(midtri, sortarray[2]);
- setorg(tri2, sortarray[2]);
- setdest(tri3, sortarray[2]);
- } else {
- /* The vertices are in clockwise order. */
- setdest(midtri, sortarray[2]);
- setorg(tri1, sortarray[2]);
- setdest(tri2, sortarray[2]);
- setapex(midtri, sortarray[1]);
- setorg(tri2, sortarray[1]);
- setdest(tri3, sortarray[1]);
- }
- /* The topology does not depend on how the vertices are ordered. */
- bond(midtri, tri1);
- lnextself(midtri);
- bond(midtri, tri2);
- lnextself(midtri);
- bond(midtri, tri3);
- lprevself(tri1);
- lnextself(tri2);
- bond(tri1, tri2);
- lprevself(tri1);
- lprevself(tri3);
- bond(tri1, tri3);
- lnextself(tri2);
- lprevself(tri3);
- bond(tri2, tri3);
- /* Ensure that the origin of `farleft' is sortarray[0]. */
- otricopy(tri1, *farleft);
- /* Ensure that the destination of `farright' is sortarray[2]. */
- if (area > 0.0) {
- otricopy(tri2, *farright);
- } else {
- lnext(*farleft, *farright);
- }
- }
- if (b->verbose > 2) {
- printf(" Creating ");
- printtriangle(m, b, &midtri);
- printf(" Creating ");
- printtriangle(m, b, &tri1);
- printf(" Creating ");
- printtriangle(m, b, &tri2);
- printf(" Creating ");
- printtriangle(m, b, &tri3);
- }
- return;
- } else {
- /* Split the vertices in half. */
- divider = vertices >> 1;
- /* Recursively triangulate each half. */
- divconqrecurse(m, b, sortarray, divider, 1 - axis, farleft, &innerleft);
- divconqrecurse(m, b, &sortarray[divider], vertices - divider, 1 - axis,
- &innerright, farright);
- if (b->verbose > 1) {
- printf(" Joining triangulations with %d and %d vertices.\n", divider,
- vertices - divider);
- }
- /* Merge the two triangulations into one. */
- mergehulls(m, b, farleft, &innerleft, &innerright, farright, axis);
- }
-}
-
-#ifdef ANSI_DECLARATORS
-long removeghosts(struct mesh *m, struct behavior *b, struct otri *startghost)
-#else /* not ANSI_DECLARATORS */
-long removeghosts(m, b, startghost)
-struct mesh *m;
-struct behavior *b;
-struct otri *startghost;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct otri searchedge;
- struct otri dissolveedge;
- struct otri deadtriangle;
- vertex markorg;
- long hullsize;
- triangle ptr; /* Temporary variable used by sym(). */
-
- if (b->verbose) {
- printf(" Removing ghost triangles.\n");
- }
- /* Find an edge on the convex hull to start point location from. */
- lprev(*startghost, searchedge);
- symself(searchedge);
- m->dummytri[0] = encode(searchedge);
- /* Remove the bounding box and count the convex hull edges. */
- otricopy(*startghost, dissolveedge);
- hullsize = 0;
- do {
- hullsize++;
- lnext(dissolveedge, deadtriangle);
- lprevself(dissolveedge);
- symself(dissolveedge);
- /* If no PSLG is involved, set the boundary markers of all the vertices */
- /* on the convex hull. If a PSLG is used, this step is done later. */
- if (!b->poly) {
- /* Watch out for the case where all the input vertices are collinear. */
- if (dissolveedge.tri != m->dummytri) {
- org(dissolveedge, markorg);
- if (vertexmark(markorg) == 0) {
- setvertexmark(markorg, 1);
- }
- }
- }
- /* Remove a bounding triangle from a convex hull triangle. */
- dissolve(dissolveedge);
- /* Find the next bounding triangle. */
- sym(deadtriangle, dissolveedge);
- /* Delete the bounding triangle. */
- triangledealloc(m, deadtriangle.tri);
- } while (!otriequal(dissolveedge, *startghost));
- return hullsize;
-}
-
-/*****************************************************************************/
-/* */
-/* divconqdelaunay() Form a Delaunay triangulation by the divide-and- */
-/* conquer method. */
-/* */
-/* Sorts the vertices, calls a recursive procedure to triangulate them, and */
-/* removes the bounding box, setting boundary markers as appropriate. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-long divconqdelaunay(struct mesh *m, struct behavior *b)
-#else /* not ANSI_DECLARATORS */
-long divconqdelaunay(m, b)
-struct mesh *m;
-struct behavior *b;
-#endif /* not ANSI_DECLARATORS */
-
-{
- vertex *sortarray;
- struct otri hullleft, hullright;
- int divider;
- int i, j;
-
- if (b->verbose) {
- printf(" Sorting vertices.\n");
- }
-
- /* Allocate an array of pointers to vertices for sorting. */
- sortarray = (vertex *) trimalloc(m->invertices * (int) sizeof(vertex));
- traversalinit(&m->vertices);
- for (i = 0; i < m->invertices; i++) {
- sortarray[i] = vertextraverse(m);
- }
- /* Sort the vertices. */
- vertexsort(sortarray, m->invertices);
- /* Discard duplicate vertices, which can really mess up the algorithm. */
- i = 0;
- for (j = 1; j < m->invertices; j++) {
- if ((sortarray[i][0] == sortarray[j][0])
- && (sortarray[i][1] == sortarray[j][1])) {
- if (!b->quiet) {
- printf(
-"Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n",
- sortarray[j][0], sortarray[j][1]);
- }
- setvertextype(sortarray[j], UNDEADVERTEX);
- m->undeads++;
- } else {
- i++;
- sortarray[i] = sortarray[j];
- }
- }
- i++;
- if (b->dwyer) {
- /* Re-sort the array of vertices to accommodate alternating cuts. */
- divider = i >> 1;
- if (i - divider >= 2) {
- if (divider >= 2) {
- alternateaxes(sortarray, divider, 1);
- }
- alternateaxes(&sortarray[divider], i - divider, 1);
- }
- }
-
- if (b->verbose) {
- printf(" Forming triangulation.\n");
- }
-
- /* Form the Delaunay triangulation. */
- divconqrecurse(m, b, sortarray, i, 0, &hullleft, &hullright);
- trifree((VOID *) sortarray);
-
- return removeghosts(m, b, &hullleft);
-}
-
-/** **/
-/** **/
-/********* Divide-and-conquer Delaunay triangulation ends here *********/
-
-/********* Incremental Delaunay triangulation begins here *********/
-/** **/
-/** **/
-
-/*****************************************************************************/
-/* */
-/* boundingbox() Form an "infinite" bounding triangle to insert vertices */
-/* into. */
-/* */
-/* The vertices at "infinity" are assigned finite coordinates, which are */
-/* used by the point location routines, but (mostly) ignored by the */
-/* Delaunay edge flip routines. */
-/* */
-/*****************************************************************************/
-
-#ifndef REDUCED
-
-#ifdef ANSI_DECLARATORS
-void boundingbox(struct mesh *m, struct behavior *b)
-#else /* not ANSI_DECLARATORS */
-void boundingbox(m, b)
-struct mesh *m;
-struct behavior *b;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct otri inftri; /* Handle for the triangular bounding box. */
- REAL width;
-
- if (b->verbose) {
- printf(" Creating triangular bounding box.\n");
- }
- /* Find the width (or height, whichever is larger) of the triangulation. */
- width = m->xmax - m->xmin;
- if (m->ymax - m->ymin > width) {
- width = m->ymax - m->ymin;
- }
- if (width == 0.0) {
- width = 1.0;
- }
- /* Create the vertices of the bounding box. */
- m->infvertex1 = (vertex) trimalloc(m->vertices.itembytes);
- m->infvertex2 = (vertex) trimalloc(m->vertices.itembytes);
- m->infvertex3 = (vertex) trimalloc(m->vertices.itembytes);
- m->infvertex1[0] = m->xmin - 50.0 * width;
- m->infvertex1[1] = m->ymin - 40.0 * width;
- m->infvertex2[0] = m->xmax + 50.0 * width;
- m->infvertex2[1] = m->ymin - 40.0 * width;
- m->infvertex3[0] = 0.5 * (m->xmin + m->xmax);
- m->infvertex3[1] = m->ymax + 60.0 * width;
-
- /* Create the bounding box. */
- maketriangle(m, b, &inftri);
- setorg(inftri, m->infvertex1);
- setdest(inftri, m->infvertex2);
- setapex(inftri, m->infvertex3);
- /* Link dummytri to the bounding box so we can always find an */
- /* edge to begin searching (point location) from. */
- m->dummytri[0] = (triangle) inftri.tri;
- if (b->verbose > 2) {
- printf(" Creating ");
- printtriangle(m, b, &inftri);
- }
-}
-
-#endif /* not REDUCED */
-
-/*****************************************************************************/
-/* */
-/* removebox() Remove the "infinite" bounding triangle, setting boundary */
-/* markers as appropriate. */
-/* */
-/* The triangular bounding box has three boundary triangles (one for each */
-/* side of the bounding box), and a bunch of triangles fanning out from */
-/* the three bounding box vertices (one triangle for each edge of the */
-/* convex hull of the inner mesh). This routine removes these triangles. */
-/* */
-/* Returns the number of edges on the convex hull of the triangulation. */
-/* */
-/*****************************************************************************/
-
-#ifndef REDUCED
-
-#ifdef ANSI_DECLARATORS
-long removebox(struct mesh *m, struct behavior *b)
-#else /* not ANSI_DECLARATORS */
-long removebox(m, b)
-struct mesh *m;
-struct behavior *b;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct otri deadtriangle;
- struct otri searchedge;
- struct otri checkedge;
- struct otri nextedge, finaledge, dissolveedge;
- vertex markorg;
- long hullsize;
- triangle ptr; /* Temporary variable used by sym(). */
-
- if (b->verbose) {
- printf(" Removing triangular bounding box.\n");
- }
- /* Find a boundary triangle. */
- nextedge.tri = m->dummytri;
- nextedge.orient = 0;
- symself(nextedge);
- /* Mark a place to stop. */
- lprev(nextedge, finaledge);
- lnextself(nextedge);
- symself(nextedge);
- /* Find a triangle (on the boundary of the vertex set) that isn't */
- /* a bounding box triangle. */
- lprev(nextedge, searchedge);
- symself(searchedge);
- /* Check whether nextedge is another boundary triangle */
- /* adjacent to the first one. */
- lnext(nextedge, checkedge);
- symself(checkedge);
- if (checkedge.tri == m->dummytri) {
- /* Go on to the next triangle. There are only three boundary */
- /* triangles, and this next triangle cannot be the third one, */
- /* so it's safe to stop here. */
- lprevself(searchedge);
- symself(searchedge);
- }
- /* Find a new boundary edge to search from, as the current search */
- /* edge lies on a bounding box triangle and will be deleted. */
- m->dummytri[0] = encode(searchedge);
- hullsize = -2l;
- while (!otriequal(nextedge, finaledge)) {
- hullsize++;
- lprev(nextedge, dissolveedge);
- symself(dissolveedge);
- /* If not using a PSLG, the vertices should be marked now. */
- /* (If using a PSLG, markhull() will do the job.) */
- if (!b->poly) {
- /* Be careful! One must check for the case where all the input */
- /* vertices are collinear, and thus all the triangles are part of */
- /* the bounding box. Otherwise, the setvertexmark() call below */
- /* will cause a bad pointer reference. */
- if (dissolveedge.tri != m->dummytri) {
- org(dissolveedge, markorg);
- if (vertexmark(markorg) == 0) {
- setvertexmark(markorg, 1);
- }
- }
- }
- /* Disconnect the bounding box triangle from the mesh triangle. */
- dissolve(dissolveedge);
- lnext(nextedge, deadtriangle);
- sym(deadtriangle, nextedge);
- /* Get rid of the bounding box triangle. */
- triangledealloc(m, deadtriangle.tri);
- /* Do we need to turn the corner? */
- if (nextedge.tri == m->dummytri) {
- /* Turn the corner. */
- otricopy(dissolveedge, nextedge);
- }
- }
- triangledealloc(m, finaledge.tri);
-
- trifree((VOID *) m->infvertex1); /* Deallocate the bounding box vertices. */
- trifree((VOID *) m->infvertex2);
- trifree((VOID *) m->infvertex3);
-
- return hullsize;
-}
-
-#endif /* not REDUCED */
-
-/*****************************************************************************/
-/* */
-/* incrementaldelaunay() Form a Delaunay triangulation by incrementally */
-/* inserting vertices. */
-/* */
-/* Returns the number of edges on the convex hull of the triangulation. */
-/* */
-/*****************************************************************************/
-
-#ifndef REDUCED
-
-#ifdef ANSI_DECLARATORS
-long incrementaldelaunay(struct mesh *m, struct behavior *b)
-#else /* not ANSI_DECLARATORS */
-long incrementaldelaunay(m, b)
-struct mesh *m;
-struct behavior *b;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct otri starttri;
- vertex vertexloop;
-
- /* Create a triangular bounding box. */
- boundingbox(m, b);
- if (b->verbose) {
- printf(" Incrementally inserting vertices.\n");
- }
- traversalinit(&m->vertices);
- vertexloop = vertextraverse(m);
- while (vertexloop != (vertex) NULL) {
- starttri.tri = m->dummytri;
- if (insertvertex(m, b, vertexloop, &starttri, (struct osub *) NULL, 0, 0)
- == DUPLICATEVERTEX) {
- if (!b->quiet) {
- printf(
-"Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n",
- vertexloop[0], vertexloop[1]);
- }
- setvertextype(vertexloop, UNDEADVERTEX);
- m->undeads++;
- }
- vertexloop = vertextraverse(m);
- }
- /* Remove the bounding box. */
- return removebox(m, b);
-}
-
-#endif /* not REDUCED */
-
-/** **/
-/** **/
-/********* Incremental Delaunay triangulation ends here *********/
-
-/********* Sweepline Delaunay triangulation begins here *********/
-/** **/
-/** **/
-
-#ifndef REDUCED
-
-#ifdef ANSI_DECLARATORS
-void eventheapinsert(struct event **heap, int heapsize, struct event *newevent)
-#else /* not ANSI_DECLARATORS */
-void eventheapinsert(heap, heapsize, newevent)
-struct event **heap;
-int heapsize;
-struct event *newevent;
-#endif /* not ANSI_DECLARATORS */
-
-{
- REAL eventx, eventy;
- int eventnum;
- int parent;
- int notdone;
-
- eventx = newevent->xkey;
- eventy = newevent->ykey;
- eventnum = heapsize;
- notdone = eventnum > 0;
- while (notdone) {
- parent = (eventnum - 1) >> 1;
- if ((heap[parent]->ykey < eventy) ||
- ((heap[parent]->ykey == eventy)
- && (heap[parent]->xkey <= eventx))) {
- notdone = 0;
- } else {
- heap[eventnum] = heap[parent];
- heap[eventnum]->heapposition = eventnum;
-
- eventnum = parent;
- notdone = eventnum > 0;
- }
- }
- heap[eventnum] = newevent;
- newevent->heapposition = eventnum;
-}
-
-#endif /* not REDUCED */
-
-#ifndef REDUCED
-
-#ifdef ANSI_DECLARATORS
-void eventheapify(struct event **heap, int heapsize, int eventnum)
-#else /* not ANSI_DECLARATORS */
-void eventheapify(heap, heapsize, eventnum)
-struct event **heap;
-int heapsize;
-int eventnum;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct event *thisevent;
- REAL eventx, eventy;
- int leftchild, rightchild;
- int smallest;
- int notdone;
-
- thisevent = heap[eventnum];
- eventx = thisevent->xkey;
- eventy = thisevent->ykey;
- leftchild = 2 * eventnum + 1;
- notdone = leftchild < heapsize;
- while (notdone) {
- if ((heap[leftchild]->ykey < eventy) ||
- ((heap[leftchild]->ykey == eventy)
- && (heap[leftchild]->xkey < eventx))) {
- smallest = leftchild;
- } else {
- smallest = eventnum;
- }
- rightchild = leftchild + 1;
- if (rightchild < heapsize) {
- if ((heap[rightchild]->ykey < heap[smallest]->ykey) ||
- ((heap[rightchild]->ykey == heap[smallest]->ykey)
- && (heap[rightchild]->xkey < heap[smallest]->xkey))) {
- smallest = rightchild;
- }
- }
- if (smallest == eventnum) {
- notdone = 0;
- } else {
- heap[eventnum] = heap[smallest];
- heap[eventnum]->heapposition = eventnum;
- heap[smallest] = thisevent;
- thisevent->heapposition = smallest;
-
- eventnum = smallest;
- leftchild = 2 * eventnum + 1;
- notdone = leftchild < heapsize;
- }
- }
-}
-
-#endif /* not REDUCED */
-
-#ifndef REDUCED
-
-#ifdef ANSI_DECLARATORS
-void eventheapdelete(struct event **heap, int heapsize, int eventnum)
-#else /* not ANSI_DECLARATORS */
-void eventheapdelete(heap, heapsize, eventnum)
-struct event **heap;
-int heapsize;
-int eventnum;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct event *moveevent;
- REAL eventx, eventy;
- int parent;
- int notdone;
-
- moveevent = heap[heapsize - 1];
- if (eventnum > 0) {
- eventx = moveevent->xkey;
- eventy = moveevent->ykey;
- do {
- parent = (eventnum - 1) >> 1;
- if ((heap[parent]->ykey < eventy) ||
- ((heap[parent]->ykey == eventy)
- && (heap[parent]->xkey <= eventx))) {
- notdone = 0;
- } else {
- heap[eventnum] = heap[parent];
- heap[eventnum]->heapposition = eventnum;
-
- eventnum = parent;
- notdone = eventnum > 0;
- }
- } while (notdone);
- }
- heap[eventnum] = moveevent;
- moveevent->heapposition = eventnum;
- eventheapify(heap, heapsize - 1, eventnum);
-}
-
-#endif /* not REDUCED */
-
-#ifndef REDUCED
-
-#ifdef ANSI_DECLARATORS
-void createeventheap(struct mesh *m, struct event ***eventheap,
- struct event **events, struct event **freeevents)
-#else /* not ANSI_DECLARATORS */
-void createeventheap(m, eventheap, events, freeevents)
-struct mesh *m;
-struct event ***eventheap;
-struct event **events;
-struct event **freeevents;
-#endif /* not ANSI_DECLARATORS */
-
-{
- vertex thisvertex;
- int maxevents;
- int i;
-
- maxevents = (3 * m->invertices) / 2;
- *eventheap = (struct event **) trimalloc(maxevents *
- (int) sizeof(struct event *));
- *events = (struct event *) trimalloc(maxevents * (int) sizeof(struct event));
- traversalinit(&m->vertices);
- for (i = 0; i < m->invertices; i++) {
- thisvertex = vertextraverse(m);
- (*events)[i].eventptr = (VOID *) thisvertex;
- (*events)[i].xkey = thisvertex[0];
- (*events)[i].ykey = thisvertex[1];
- eventheapinsert(*eventheap, i, *events + i);
- }
- *freeevents = (struct event *) NULL;
- for (i = maxevents - 1; i >= m->invertices; i--) {
- (*events)[i].eventptr = (VOID *) *freeevents;
- *freeevents = *events + i;
- }
-}
-
-#endif /* not REDUCED */
-
-#ifndef REDUCED
-
-#ifdef ANSI_DECLARATORS
-int rightofhyperbola(struct mesh *m, struct otri *fronttri, vertex newsite)
-#else /* not ANSI_DECLARATORS */
-int rightofhyperbola(m, fronttri, newsite)
-struct mesh *m;
-struct otri *fronttri;
-vertex newsite;
-#endif /* not ANSI_DECLARATORS */
-
-{
- vertex leftvertex, rightvertex;
- REAL dxa, dya, dxb, dyb;
-
- m->hyperbolacount++;
-
- dest(*fronttri, leftvertex);
- apex(*fronttri, rightvertex);
- if ((leftvertex[1] < rightvertex[1]) ||
- ((leftvertex[1] == rightvertex[1]) &&
- (leftvertex[0] < rightvertex[0]))) {
- if (newsite[0] >= rightvertex[0]) {
- return 1;
- }
- } else {
- if (newsite[0] <= leftvertex[0]) {
- return 0;
- }
- }
- dxa = leftvertex[0] - newsite[0];
- dya = leftvertex[1] - newsite[1];
- dxb = rightvertex[0] - newsite[0];
- dyb = rightvertex[1] - newsite[1];
- return dya * (dxb * dxb + dyb * dyb) > dyb * (dxa * dxa + dya * dya);
-}
-
-#endif /* not REDUCED */
-
-#ifndef REDUCED
-
-#ifdef ANSI_DECLARATORS
-REAL circletop(struct mesh *m, vertex pa, vertex pb, vertex pc, REAL ccwabc)
-#else /* not ANSI_DECLARATORS */
-REAL circletop(m, pa, pb, pc, ccwabc)
-struct mesh *m;
-vertex pa;
-vertex pb;
-vertex pc;
-REAL ccwabc;
-#endif /* not ANSI_DECLARATORS */
-
-{
- REAL xac, yac, xbc, ybc, xab, yab;
- REAL aclen2, bclen2, ablen2;
-
- m->circletopcount++;
-
- xac = pa[0] - pc[0];
- yac = pa[1] - pc[1];
- xbc = pb[0] - pc[0];
- ybc = pb[1] - pc[1];
- xab = pa[0] - pb[0];
- yab = pa[1] - pb[1];
- aclen2 = xac * xac + yac * yac;
- bclen2 = xbc * xbc + ybc * ybc;
- ablen2 = xab * xab + yab * yab;
- return pc[1] + (xac * bclen2 - xbc * aclen2 + sqrt(aclen2 * bclen2 * ablen2))
- / (2.0 * ccwabc);
-}
-
-#endif /* not REDUCED */
-
-#ifndef REDUCED
-
-#ifdef ANSI_DECLARATORS
-void check4deadevent(struct otri *checktri, struct event **freeevents,
- struct event **eventheap, int *heapsize)
-#else /* not ANSI_DECLARATORS */
-void check4deadevent(checktri, freeevents, eventheap, heapsize)
-struct otri *checktri;
-struct event **freeevents;
-struct event **eventheap;
-int *heapsize;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct event *deadevent;
- vertex eventvertex;
- int eventnum;
-
- org(*checktri, eventvertex);
- if (eventvertex != (vertex) NULL) {
- deadevent = (struct event *) eventvertex;
- eventnum = deadevent->heapposition;
- deadevent->eventptr = (VOID *) *freeevents;
- *freeevents = deadevent;
- eventheapdelete(eventheap, *heapsize, eventnum);
- (*heapsize)--;
- setorg(*checktri, NULL);
- }
-}
-
-#endif /* not REDUCED */
-
-#ifndef REDUCED
-
-#ifdef ANSI_DECLARATORS
-struct splaynode *splay(struct mesh *m, struct splaynode *splaytree,
- vertex searchpoint, struct otri *searchtri)
-#else /* not ANSI_DECLARATORS */
-struct splaynode *splay(m, splaytree, searchpoint, searchtri)
-struct mesh *m;
-struct splaynode *splaytree;
-vertex searchpoint;
-struct otri *searchtri;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct splaynode *child, *grandchild;
- struct splaynode *lefttree, *righttree;
- struct splaynode *leftright;
- vertex checkvertex;
- int rightofroot, rightofchild;
-
- if (splaytree == (struct splaynode *) NULL) {
- return (struct splaynode *) NULL;
- }
- dest(splaytree->keyedge, checkvertex);
- if (checkvertex == splaytree->keydest) {
- rightofroot = rightofhyperbola(m, &splaytree->keyedge, searchpoint);
- if (rightofroot) {
- otricopy(splaytree->keyedge, *searchtri);
- child = splaytree->rchild;
- } else {
- child = splaytree->lchild;
- }
- if (child == (struct splaynode *) NULL) {
- return splaytree;
- }
- dest(child->keyedge, checkvertex);
- if (checkvertex != child->keydest) {
- child = splay(m, child, searchpoint, searchtri);
- if (child == (struct splaynode *) NULL) {
- if (rightofroot) {
- splaytree->rchild = (struct splaynode *) NULL;
- } else {
- splaytree->lchild = (struct splaynode *) NULL;
- }
- return splaytree;
- }
- }
- rightofchild = rightofhyperbola(m, &child->keyedge, searchpoint);
- if (rightofchild) {
- otricopy(child->keyedge, *searchtri);
- grandchild = splay(m, child->rchild, searchpoint, searchtri);
- child->rchild = grandchild;
- } else {
- grandchild = splay(m, child->lchild, searchpoint, searchtri);
- child->lchild = grandchild;
- }
- if (grandchild == (struct splaynode *) NULL) {
- if (rightofroot) {
- splaytree->rchild = child->lchild;
- child->lchild = splaytree;
- } else {
- splaytree->lchild = child->rchild;
- child->rchild = splaytree;
- }
- return child;
- }
- if (rightofchild) {
- if (rightofroot) {
- splaytree->rchild = child->lchild;
- child->lchild = splaytree;
- } else {
- splaytree->lchild = grandchild->rchild;
- grandchild->rchild = splaytree;
- }
- child->rchild = grandchild->lchild;
- grandchild->lchild = child;
- } else {
- if (rightofroot) {
- splaytree->rchild = grandchild->lchild;
- grandchild->lchild = splaytree;
- } else {
- splaytree->lchild = child->rchild;
- child->rchild = splaytree;
- }
- child->lchild = grandchild->rchild;
- grandchild->rchild = child;
- }
- return grandchild;
- } else {
- lefttree = splay(m, splaytree->lchild, searchpoint, searchtri);
- righttree = splay(m, splaytree->rchild, searchpoint, searchtri);
-
- pooldealloc(&m->splaynodes, (VOID *) splaytree);
- if (lefttree == (struct splaynode *) NULL) {
- return righttree;
- } else if (righttree == (struct splaynode *) NULL) {
- return lefttree;
- } else if (lefttree->rchild == (struct splaynode *) NULL) {
- lefttree->rchild = righttree->lchild;
- righttree->lchild = lefttree;
- return righttree;
- } else if (righttree->lchild == (struct splaynode *) NULL) {
- righttree->lchild = lefttree->rchild;
- lefttree->rchild = righttree;
- return lefttree;
- } else {
-/* printf("Holy Toledo!!!\n"); */
- leftright = lefttree->rchild;
- while (leftright->rchild != (struct splaynode *) NULL) {
- leftright = leftright->rchild;
- }
- leftright->rchild = righttree;
- return lefttree;
- }
- }
-}
-
-#endif /* not REDUCED */
-
-#ifndef REDUCED
-
-#ifdef ANSI_DECLARATORS
-struct splaynode *splayinsert(struct mesh *m, struct splaynode *splayroot,
- struct otri *newkey, vertex searchpoint)
-#else /* not ANSI_DECLARATORS */
-struct splaynode *splayinsert(m, splayroot, newkey, searchpoint)
-struct mesh *m;
-struct splaynode *splayroot;
-struct otri *newkey;
-vertex searchpoint;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct splaynode *newsplaynode;
-
- newsplaynode = (struct splaynode *) poolalloc(&m->splaynodes);
- otricopy(*newkey, newsplaynode->keyedge);
- dest(*newkey, newsplaynode->keydest);
- if (splayroot == (struct splaynode *) NULL) {
- newsplaynode->lchild = (struct splaynode *) NULL;
- newsplaynode->rchild = (struct splaynode *) NULL;
- } else if (rightofhyperbola(m, &splayroot->keyedge, searchpoint)) {
- newsplaynode->lchild = splayroot;
- newsplaynode->rchild = splayroot->rchild;
- splayroot->rchild = (struct splaynode *) NULL;
- } else {
- newsplaynode->lchild = splayroot->lchild;
- newsplaynode->rchild = splayroot;
- splayroot->lchild = (struct splaynode *) NULL;
- }
- return newsplaynode;
-}
-
-#endif /* not REDUCED */
-
-#ifndef REDUCED
-
-#ifdef ANSI_DECLARATORS
-struct splaynode *circletopinsert(struct mesh *m, struct behavior *b,
- struct splaynode *splayroot,
- struct otri *newkey,
- vertex pa, vertex pb, vertex pc, REAL topy)
-#else /* not ANSI_DECLARATORS */
-struct splaynode *circletopinsert(m, b, splayroot, newkey, pa, pb, pc, topy)
-struct mesh *m;
-struct behavior *b;
-struct splaynode *splayroot;
-struct otri *newkey;
-vertex pa;
-vertex pb;
-vertex pc;
-REAL topy;
-#endif /* not ANSI_DECLARATORS */
-
-{
- REAL ccwabc;
- REAL xac, yac, xbc, ybc;
- REAL aclen2, bclen2;
- REAL searchpoint[2];
- struct otri dummytri;
-
- ccwabc = counterclockwise(m, b, pa, pb, pc);
- xac = pa[0] - pc[0];
- yac = pa[1] - pc[1];
- xbc = pb[0] - pc[0];
- ybc = pb[1] - pc[1];
- aclen2 = xac * xac + yac * yac;
- bclen2 = xbc * xbc + ybc * ybc;
- searchpoint[0] = pc[0] - (yac * bclen2 - ybc * aclen2) / (2.0 * ccwabc);
- searchpoint[1] = topy;
- return splayinsert(m, splay(m, splayroot, (vertex) searchpoint, &dummytri),
- newkey, (vertex) searchpoint);
-}
-
-#endif /* not REDUCED */
-
-#ifndef REDUCED
-
-#ifdef ANSI_DECLARATORS
-struct splaynode *frontlocate(struct mesh *m, struct splaynode *splayroot,
- struct otri *bottommost, vertex searchvertex,
- struct otri *searchtri, int *farright)
-#else /* not ANSI_DECLARATORS */
-struct splaynode *frontlocate(m, splayroot, bottommost, searchvertex,
- searchtri, farright)
-struct mesh *m;
-struct splaynode *splayroot;
-struct otri *bottommost;
-vertex searchvertex;
-struct otri *searchtri;
-int *farright;
-#endif /* not ANSI_DECLARATORS */
-
-{
- int farrightflag;
- triangle ptr; /* Temporary variable used by onext(). */
-
- otricopy(*bottommost, *searchtri);
- splayroot = splay(m, splayroot, searchvertex, searchtri);
-
- farrightflag = 0;
- while (!farrightflag && rightofhyperbola(m, searchtri, searchvertex)) {
- onextself(*searchtri);
- farrightflag = otriequal(*searchtri, *bottommost);
- }
- *farright = farrightflag;
- return splayroot;
-}
-
-#endif /* not REDUCED */
-
-#ifndef REDUCED
-
-#ifdef ANSI_DECLARATORS
-long sweeplinedelaunay(struct mesh *m, struct behavior *b)
-#else /* not ANSI_DECLARATORS */
-long sweeplinedelaunay(m, b)
-struct mesh *m;
-struct behavior *b;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct event **eventheap;
- struct event *events;
- struct event *freeevents;
- struct event *nextevent;
- struct event *newevent;
- struct splaynode *splayroot;
- struct otri bottommost;
- struct otri searchtri;
- struct otri fliptri;
- struct otri lefttri, righttri, farlefttri, farrighttri;
- struct otri inserttri;
- vertex firstvertex, secondvertex;
- vertex nextvertex, lastvertex;
- vertex connectvertex;
- vertex leftvertex, midvertex, rightvertex;
- REAL lefttest, righttest;
- int heapsize;
- int check4events, farrightflag;
- triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */
-
- poolinit(&m->splaynodes, sizeof(struct splaynode), SPLAYNODEPERBLOCK,
- SPLAYNODEPERBLOCK, 0);
- splayroot = (struct splaynode *) NULL;
-
- if (b->verbose) {
- printf(" Placing vertices in event heap.\n");
- }
- createeventheap(m, &eventheap, &events, &freeevents);
- heapsize = m->invertices;
-
- if (b->verbose) {
- printf(" Forming triangulation.\n");
- }
- maketriangle(m, b, &lefttri);
- maketriangle(m, b, &righttri);
- bond(lefttri, righttri);
- lnextself(lefttri);
- lprevself(righttri);
- bond(lefttri, righttri);
- lnextself(lefttri);
- lprevself(righttri);
- bond(lefttri, righttri);
- firstvertex = (vertex) eventheap[0]->eventptr;
- eventheap[0]->eventptr = (VOID *) freeevents;
- freeevents = eventheap[0];
- eventheapdelete(eventheap, heapsize, 0);
- heapsize--;
- do {
- if (heapsize == 0) {
- printf("Error: Input vertices are all identical.\n");
- triexit(1);
- }
- secondvertex = (vertex) eventheap[0]->eventptr;
- eventheap[0]->eventptr = (VOID *) freeevents;
- freeevents = eventheap[0];
- eventheapdelete(eventheap, heapsize, 0);
- heapsize--;
- if ((firstvertex[0] == secondvertex[0]) &&
- (firstvertex[1] == secondvertex[1])) {
- if (!b->quiet) {
- printf(
-"Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n",
- secondvertex[0], secondvertex[1]);
- }
- setvertextype(secondvertex, UNDEADVERTEX);
- m->undeads++;
- }
- } while ((firstvertex[0] == secondvertex[0]) &&
- (firstvertex[1] == secondvertex[1]));
- setorg(lefttri, firstvertex);
- setdest(lefttri, secondvertex);
- setorg(righttri, secondvertex);
- setdest(righttri, firstvertex);
- lprev(lefttri, bottommost);
- lastvertex = secondvertex;
- while (heapsize > 0) {
- nextevent = eventheap[0];
- eventheapdelete(eventheap, heapsize, 0);
- heapsize--;
- check4events = 1;
- if (nextevent->xkey < m->xmin) {
- decode(nextevent->eventptr, fliptri);
- oprev(fliptri, farlefttri);
- check4deadevent(&farlefttri, &freeevents, eventheap, &heapsize);
- onext(fliptri, farrighttri);
- check4deadevent(&farrighttri, &freeevents, eventheap, &heapsize);
-
- if (otriequal(farlefttri, bottommost)) {
- lprev(fliptri, bottommost);
- }
- flip(m, b, &fliptri);
- setapex(fliptri, NULL);
- lprev(fliptri, lefttri);
- lnext(fliptri, righttri);
- sym(lefttri, farlefttri);
-
- if (randomnation(SAMPLERATE) == 0) {
- symself(fliptri);
- dest(fliptri, leftvertex);
- apex(fliptri, midvertex);
- org(fliptri, rightvertex);
- splayroot = circletopinsert(m, b, splayroot, &lefttri, leftvertex,
- midvertex, rightvertex, nextevent->ykey);
- }
- } else {
- nextvertex = (vertex) nextevent->eventptr;
- if ((nextvertex[0] == lastvertex[0]) &&
- (nextvertex[1] == lastvertex[1])) {
- if (!b->quiet) {
- printf(
-"Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n",
- nextvertex[0], nextvertex[1]);
- }
- setvertextype(nextvertex, UNDEADVERTEX);
- m->undeads++;
- check4events = 0;
- } else {
- lastvertex = nextvertex;
-
- splayroot = frontlocate(m, splayroot, &bottommost, nextvertex,
- &searchtri, &farrightflag);
-/*
- otricopy(bottommost, searchtri);
- farrightflag = 0;
- while (!farrightflag && rightofhyperbola(m, &searchtri, nextvertex)) {
- onextself(searchtri);
- farrightflag = otriequal(searchtri, bottommost);
- }
-*/
-
- check4deadevent(&searchtri, &freeevents, eventheap, &heapsize);
-
- otricopy(searchtri, farrighttri);
- sym(searchtri, farlefttri);
- maketriangle(m, b, &lefttri);
- maketriangle(m, b, &righttri);
- dest(farrighttri, connectvertex);
- setorg(lefttri, connectvertex);
- setdest(lefttri, nextvertex);
- setorg(righttri, nextvertex);
- setdest(righttri, connectvertex);
- bond(lefttri, righttri);
- lnextself(lefttri);
- lprevself(righttri);
- bond(lefttri, righttri);
- lnextself(lefttri);
- lprevself(righttri);
- bond(lefttri, farlefttri);
- bond(righttri, farrighttri);
- if (!farrightflag && otriequal(farrighttri, bottommost)) {
- otricopy(lefttri, bottommost);
- }
-
- if (randomnation(SAMPLERATE) == 0) {
- splayroot = splayinsert(m, splayroot, &lefttri, nextvertex);
- } else if (randomnation(SAMPLERATE) == 0) {
- lnext(righttri, inserttri);
- splayroot = splayinsert(m, splayroot, &inserttri, nextvertex);
- }
- }
- }
- nextevent->eventptr = (VOID *) freeevents;
- freeevents = nextevent;
-
- if (check4events) {
- apex(farlefttri, leftvertex);
- dest(lefttri, midvertex);
- apex(lefttri, rightvertex);
- lefttest = counterclockwise(m, b, leftvertex, midvertex, rightvertex);
- if (lefttest > 0.0) {
- newevent = freeevents;
- freeevents = (struct event *) freeevents->eventptr;
- newevent->xkey = m->xminextreme;
- newevent->ykey = circletop(m, leftvertex, midvertex, rightvertex,
- lefttest);
- newevent->eventptr = (VOID *) encode(lefttri);
- eventheapinsert(eventheap, heapsize, newevent);
- heapsize++;
- setorg(lefttri, newevent);
- }
- apex(righttri, leftvertex);
- org(righttri, midvertex);
- apex(farrighttri, rightvertex);
- righttest = counterclockwise(m, b, leftvertex, midvertex, rightvertex);
- if (righttest > 0.0) {
- newevent = freeevents;
- freeevents = (struct event *) freeevents->eventptr;
- newevent->xkey = m->xminextreme;
- newevent->ykey = circletop(m, leftvertex, midvertex, rightvertex,
- righttest);
- newevent->eventptr = (VOID *) encode(farrighttri);
- eventheapinsert(eventheap, heapsize, newevent);
- heapsize++;
- setorg(farrighttri, newevent);
- }
- }
- }
-
- pooldeinit(&m->splaynodes);
- lprevself(bottommost);
- return removeghosts(m, b, &bottommost);
-}
-
-#endif /* not REDUCED */
-
-/** **/
-/** **/
-/********* Sweepline Delaunay triangulation ends here *********/
-
-/********* General mesh construction routines begin here *********/
-/** **/
-/** **/
-
-/*****************************************************************************/
-/* */
-/* delaunay() Form a Delaunay triangulation. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-long delaunay(struct mesh *m, struct behavior *b)
-#else /* not ANSI_DECLARATORS */
-long delaunay(m, b)
-struct mesh *m;
-struct behavior *b;
-#endif /* not ANSI_DECLARATORS */
-
-{
- long hulledges;
-
- m->eextras = 0;
- initializetrisubpools(m, b);
-
-#ifdef REDUCED
- if (!b->quiet) {
- printf(
- "Constructing Delaunay triangulation by divide-and-conquer method.\n");
- }
- hulledges = divconqdelaunay(m, b);
-#else /* not REDUCED */
- if (!b->quiet) {
- printf("Constructing Delaunay triangulation ");
- if (b->incremental) {
- printf("by incremental method.\n");
- } else if (b->sweepline) {
- printf("by sweepline method.\n");
- } else {
- printf("by divide-and-conquer method.\n");
- }
- }
- if (b->incremental) {
- hulledges = incrementaldelaunay(m, b);
- } else if (b->sweepline) {
- hulledges = sweeplinedelaunay(m, b);
- } else {
- hulledges = divconqdelaunay(m, b);
- }
-#endif /* not REDUCED */
-
- if (m->triangles.items == 0) {
- /* The input vertices were all collinear, so there are no triangles. */
- return 0l;
- } else {
- return hulledges;
- }
-}
-
-/*****************************************************************************/
-/* */
-/* reconstruct() Reconstruct a triangulation from its .ele (and possibly */
-/* .poly) file. Used when the -r switch is used. */
-/* */
-/* Reads an .ele file and reconstructs the original mesh. If the -p switch */
-/* is used, this procedure will also read a .poly file and reconstruct the */
-/* subsegments of the original mesh. If the -a switch is used, this */
-/* procedure will also read an .area file and set a maximum area constraint */
-/* on each triangle. */
-/* */
-/* Vertices that are not corners of triangles, such as nodes on edges of */
-/* subparametric elements, are discarded. */
-/* */
-/* This routine finds the adjacencies between triangles (and subsegments) */
-/* by forming one stack of triangles for each vertex. Each triangle is on */
-/* three different stacks simultaneously. Each triangle's subsegment */
-/* pointers are used to link the items in each stack. This memory-saving */
-/* feature makes the code harder to read. The most important thing to keep */
-/* in mind is that each triangle is removed from a stack precisely when */
-/* the corresponding pointer is adjusted to refer to a subsegment rather */
-/* than the next triangle of the stack. */
-/* */
-/*****************************************************************************/
-
-#ifndef CDT_ONLY
-
-#ifdef TRILIBRARY
-
-#ifdef ANSI_DECLARATORS
-int reconstruct(struct mesh *m, struct behavior *b, int *trianglelist,
- REAL *triangleattriblist, REAL *trianglearealist,
- int elements, int corners, int attribs,
- int *segmentlist,int *segmentmarkerlist, int numberofsegments)
-#else /* not ANSI_DECLARATORS */
-int reconstruct(m, b, trianglelist, triangleattriblist, trianglearealist,
- elements, corners, attribs, segmentlist, segmentmarkerlist,
- numberofsegments)
-struct mesh *m;
-struct behavior *b;
-int *trianglelist;
-REAL *triangleattriblist;
-REAL *trianglearealist;
-int elements;
-int corners;
-int attribs;
-int *segmentlist;
-int *segmentmarkerlist;
-int numberofsegments;
-#endif /* not ANSI_DECLARATORS */
-
-#else /* not TRILIBRARY */
-
-#ifdef ANSI_DECLARATORS
-long reconstruct(struct mesh *m, struct behavior *b, char *elefilename,
- char *areafilename, char *polyfilename, FILE *polyfile)
-#else /* not ANSI_DECLARATORS */
-long reconstruct(m, b, elefilename, areafilename, polyfilename, polyfile)
-struct mesh *m;
-struct behavior *b;
-char *elefilename;
-char *areafilename;
-char *polyfilename;
-FILE *polyfile;
-#endif /* not ANSI_DECLARATORS */
-
-#endif /* not TRILIBRARY */
-
-{
-#ifdef TRILIBRARY
- int vertexindex;
- int attribindex;
-#else /* not TRILIBRARY */
- FILE *elefile;
- FILE *areafile;
- char inputline[INPUTLINESIZE];
- char *stringptr;
- int areaelements;
-#endif /* not TRILIBRARY */
- struct otri triangleloop;
- struct otri triangleleft;
- struct otri checktri;
- struct otri checkleft;
- struct otri checkneighbor;
- struct osub subsegloop;
- triangle *vertexarray;
- triangle *prevlink;
- triangle nexttri;
- vertex tdest, tapex;
- vertex checkdest, checkapex;
- vertex shorg;
- vertex killvertex;
- vertex segmentorg, segmentdest;
- REAL area;
- int corner[3];
- int end[2];
- int killvertexindex;
- int incorners;
- int segmentmarkers;
- int boundmarker;
- int aroundvertex;
- long hullsize;
- int notfound;
- long elementnumber, segmentnumber;
- int i, j;
- triangle ptr; /* Temporary variable used by sym(). */
-
-#ifdef TRILIBRARY
- m->inelements = elements;
- incorners = corners;
- if (incorners < 3) {
- printf("Error: Triangles must have at least 3 vertices.\n");
- triexit(1);
- }
- m->eextras = attribs;
-#else /* not TRILIBRARY */
- /* Read the triangles from an .ele file. */
- if (!b->quiet) {
- printf("Opening %s.\n", elefilename);
- }
- elefile = fopen(elefilename, "r");
- if (elefile == (FILE *) NULL) {
- printf(" Error: Cannot access file %s.\n", elefilename);
- triexit(1);
- }
- /* Read number of triangles, number of vertices per triangle, and */
- /* number of triangle attributes from .ele file. */
- stringptr = readline(inputline, elefile, elefilename);
- m->inelements = (int) strtol(stringptr, &stringptr, 0);
- stringptr = findfield(stringptr);
- if (*stringptr == '\0') {
- incorners = 3;
- } else {
- incorners = (int) strtol(stringptr, &stringptr, 0);
- if (incorners < 3) {
- printf("Error: Triangles in %s must have at least 3 vertices.\n",
- elefilename);
- triexit(1);
- }
- }
- stringptr = findfield(stringptr);
- if (*stringptr == '\0') {
- m->eextras = 0;
- } else {
- m->eextras = (int) strtol(stringptr, &stringptr, 0);
- }
-#endif /* not TRILIBRARY */
-
- initializetrisubpools(m, b);
-
- /* Create the triangles. */
- for (elementnumber = 1; elementnumber <= m->inelements; elementnumber++) {
- maketriangle(m, b, &triangleloop);
- /* Mark the triangle as living. */
- triangleloop.tri[3] = (triangle) triangleloop.tri;
- }
-
- segmentmarkers = 0;
- if (b->poly) {
-#ifdef TRILIBRARY
- m->insegments = numberofsegments;
- segmentmarkers = segmentmarkerlist != (int *) NULL;
-#else /* not TRILIBRARY */
- /* Read number of segments and number of segment */
- /* boundary markers from .poly file. */
- stringptr = readline(inputline, polyfile, b->inpolyfilename);
- m->insegments = (int) strtol(stringptr, &stringptr, 0);
- stringptr = findfield(stringptr);
- if (*stringptr != '\0') {
- segmentmarkers = (int) strtol(stringptr, &stringptr, 0);
- }
-#endif /* not TRILIBRARY */
-
- /* Create the subsegments. */
- for (segmentnumber = 1; segmentnumber <= m->insegments; segmentnumber++) {
- makesubseg(m, &subsegloop);
- /* Mark the subsegment as living. */
- subsegloop.ss[2] = (subseg) subsegloop.ss;
- }
- }
-
-#ifdef TRILIBRARY
- vertexindex = 0;
- attribindex = 0;
-#else /* not TRILIBRARY */
- if (b->vararea) {
- /* Open an .area file, check for consistency with the .ele file. */
- if (!b->quiet) {
- printf("Opening %s.\n", areafilename);
- }
- areafile = fopen(areafilename, "r");
- if (areafile == (FILE *) NULL) {
- printf(" Error: Cannot access file %s.\n", areafilename);
- triexit(1);
- }
- stringptr = readline(inputline, areafile, areafilename);
- areaelements = (int) strtol(stringptr, &stringptr, 0);
- if (areaelements != m->inelements) {
- printf("Error: %s and %s disagree on number of triangles.\n",
- elefilename, areafilename);
- triexit(1);
- }
- }
-#endif /* not TRILIBRARY */
-
- if (!b->quiet) {
- printf("Reconstructing mesh.\n");
- }
- /* Allocate a temporary array that maps each vertex to some adjacent */
- /* triangle. I took care to allocate all the permanent memory for */
- /* triangles and subsegments first. */
- vertexarray = (triangle *) trimalloc(m->vertices.items *
- (int) sizeof(triangle));
- /* Each vertex is initially unrepresented. */
- for (i = 0; i < m->vertices.items; i++) {
- vertexarray[i] = (triangle) m->dummytri;
- }
-
- if (b->verbose) {
- printf(" Assembling triangles.\n");
- }
- /* Read the triangles from the .ele file, and link */
- /* together those that share an edge. */
- traversalinit(&m->triangles);
- triangleloop.tri = triangletraverse(m);
- elementnumber = b->firstnumber;
- while (triangleloop.tri != (triangle *) NULL) {
-#ifdef TRILIBRARY
- /* Copy the triangle's three corners. */
- for (j = 0; j < 3; j++) {
- corner[j] = trianglelist[vertexindex++];
- if ((corner[j] < b->firstnumber) ||
- (corner[j] >= b->firstnumber + m->invertices)) {
- printf("Error: Triangle %ld has an invalid vertex index.\n",
- elementnumber);
- triexit(1);
- }
- }
-#else /* not TRILIBRARY */
- /* Read triangle number and the triangle's three corners. */
- stringptr = readline(inputline, elefile, elefilename);
- for (j = 0; j < 3; j++) {
- stringptr = findfield(stringptr);
- if (*stringptr == '\0') {
- printf("Error: Triangle %ld is missing vertex %d in %s.\n",
- elementnumber, j + 1, elefilename);
- triexit(1);
- } else {
- corner[j] = (int) strtol(stringptr, &stringptr, 0);
- if ((corner[j] < b->firstnumber) ||
- (corner[j] >= b->firstnumber + m->invertices)) {
- printf("Error: Triangle %ld has an invalid vertex index.\n",
- elementnumber);
- triexit(1);
- }
- }
- }
-#endif /* not TRILIBRARY */
-
- /* Find out about (and throw away) extra nodes. */
- for (j = 3; j < incorners; j++) {
-#ifdef TRILIBRARY
- killvertexindex = trianglelist[vertexindex++];
-#else /* not TRILIBRARY */
- stringptr = findfield(stringptr);
- if (*stringptr != '\0') {
- killvertexindex = (int) strtol(stringptr, &stringptr, 0);
-#endif /* not TRILIBRARY */
- if ((killvertexindex >= b->firstnumber) &&
- (killvertexindex < b->firstnumber + m->invertices)) {
- /* Delete the non-corner vertex if it's not already deleted. */
- killvertex = getvertex(m, b, killvertexindex);
- if (vertextype(killvertex) != DEADVERTEX) {
- vertexdealloc(m, killvertex);
- }
- }
-#ifndef TRILIBRARY
- }
-#endif /* not TRILIBRARY */
- }
-
- /* Read the triangle's attributes. */
- for (j = 0; j < m->eextras; j++) {
-#ifdef TRILIBRARY
- setelemattribute(triangleloop, j, triangleattriblist[attribindex++]);
-#else /* not TRILIBRARY */
- stringptr = findfield(stringptr);
- if (*stringptr == '\0') {
- setelemattribute(triangleloop, j, 0);
- } else {
- setelemattribute(triangleloop, j,
- (REAL) strtod(stringptr, &stringptr));
- }
-#endif /* not TRILIBRARY */
- }
-
- if (b->vararea) {
-#ifdef TRILIBRARY
- area = trianglearealist[elementnumber - b->firstnumber];
-#else /* not TRILIBRARY */
- /* Read an area constraint from the .area file. */
- stringptr = readline(inputline, areafile, areafilename);
- stringptr = findfield(stringptr);
- if (*stringptr == '\0') {
- area = -1.0; /* No constraint on this triangle. */
- } else {
- area = (REAL) strtod(stringptr, &stringptr);
- }
-#endif /* not TRILIBRARY */
- setareabound(triangleloop, area);
- }
-
- /* Set the triangle's vertices. */
- triangleloop.orient = 0;
- setorg(triangleloop, getvertex(m, b, corner[0]));
- setdest(triangleloop, getvertex(m, b, corner[1]));
- setapex(triangleloop, getvertex(m, b, corner[2]));
- /* Try linking the triangle to others that share these vertices. */
- for (triangleloop.orient = 0; triangleloop.orient < 3;
- triangleloop.orient++) {
- /* Take the number for the origin of triangleloop. */
- aroundvertex = corner[triangleloop.orient];
- /* Look for other triangles having this vertex. */
- nexttri = vertexarray[aroundvertex - b->firstnumber];
- /* Link the current triangle to the next one in the stack. */
- triangleloop.tri[6 + triangleloop.orient] = nexttri;
- /* Push the current triangle onto the stack. */
- vertexarray[aroundvertex - b->firstnumber] = encode(triangleloop);
- decode(nexttri, checktri);
- if (checktri.tri != m->dummytri) {
- dest(triangleloop, tdest);
- apex(triangleloop, tapex);
- /* Look for other triangles that share an edge. */
- do {
- dest(checktri, checkdest);
- apex(checktri, checkapex);
- if (tapex == checkdest) {
- /* The two triangles share an edge; bond them together. */
- lprev(triangleloop, triangleleft);
- bond(triangleleft, checktri);
- }
- if (tdest == checkapex) {
- /* The two triangles share an edge; bond them together. */
- lprev(checktri, checkleft);
- bond(triangleloop, checkleft);
- }
- /* Find the next triangle in the stack. */
- nexttri = checktri.tri[6 + checktri.orient];
- decode(nexttri, checktri);
- } while (checktri.tri != m->dummytri);
- }
- }
- triangleloop.tri = triangletraverse(m);
- elementnumber++;
- }
-
-#ifdef TRILIBRARY
- vertexindex = 0;
-#else /* not TRILIBRARY */
- fclose(elefile);
- if (b->vararea) {
- fclose(areafile);
- }
-#endif /* not TRILIBRARY */
-
- hullsize = 0; /* Prepare to count the boundary edges. */
- if (b->poly) {
- if (b->verbose) {
- printf(" Marking segments in triangulation.\n");
- }
- /* Read the segments from the .poly file, and link them */
- /* to their neighboring triangles. */
- boundmarker = 0;
- traversalinit(&m->subsegs);
- subsegloop.ss = subsegtraverse(m);
- segmentnumber = b->firstnumber;
- while (subsegloop.ss != (subseg *) NULL) {
-#ifdef TRILIBRARY
- end[0] = segmentlist[vertexindex++];
- end[1] = segmentlist[vertexindex++];
- if (segmentmarkers) {
- boundmarker = segmentmarkerlist[segmentnumber - b->firstnumber];
- }
-#else /* not TRILIBRARY */
- /* Read the endpoints of each segment, and possibly a boundary marker. */
- stringptr = readline(inputline, polyfile, b->inpolyfilename);
- /* Skip the first (segment number) field. */
- stringptr = findfield(stringptr);
- if (*stringptr == '\0') {
- printf("Error: Segment %ld has no endpoints in %s.\n", segmentnumber,
- polyfilename);
- triexit(1);
- } else {
- end[0] = (int) strtol(stringptr, &stringptr, 0);
- }
- stringptr = findfield(stringptr);
- if (*stringptr == '\0') {
- printf("Error: Segment %ld is missing its second endpoint in %s.\n",
- segmentnumber, polyfilename);
- triexit(1);
- } else {
- end[1] = (int) strtol(stringptr, &stringptr, 0);
- }
- if (segmentmarkers) {
- stringptr = findfield(stringptr);
- if (*stringptr == '\0') {
- boundmarker = 0;
- } else {
- boundmarker = (int) strtol(stringptr, &stringptr, 0);
- }
- }
-#endif /* not TRILIBRARY */
- for (j = 0; j < 2; j++) {
- if ((end[j] < b->firstnumber) ||
- (end[j] >= b->firstnumber + m->invertices)) {
- printf("Error: Segment %ld has an invalid vertex index.\n",
- segmentnumber);
- triexit(1);
- }
- }
-
- /* set the subsegment's vertices. */
- subsegloop.ssorient = 0;
- segmentorg = getvertex(m, b, end[0]);
- segmentdest = getvertex(m, b, end[1]);
- setsorg(subsegloop, segmentorg);
- setsdest(subsegloop, segmentdest);
- setsegorg(subsegloop, segmentorg);
- setsegdest(subsegloop, segmentdest);
- setmark(subsegloop, boundmarker);
- /* Try linking the subsegment to triangles that share these vertices. */
- for (subsegloop.ssorient = 0; subsegloop.ssorient < 2;
- subsegloop.ssorient++) {
- /* Take the number for the destination of subsegloop. */
- aroundvertex = end[1 - subsegloop.ssorient];
- /* Look for triangles having this vertex. */
- prevlink = &vertexarray[aroundvertex - b->firstnumber];
- nexttri = vertexarray[aroundvertex - b->firstnumber];
- decode(nexttri, checktri);
- sorg(subsegloop, shorg);
- notfound = 1;
- /* Look for triangles having this edge. Note that I'm only */
- /* comparing each triangle's destination with the subsegment; */
- /* each triangle's apex is handled through a different vertex. */
- /* Because each triangle appears on three vertices' lists, each */
- /* occurrence of a triangle on a list can (and does) represent */
- /* an edge. In this way, most edges are represented twice, and */
- /* every triangle-subsegment bond is represented once. */
- while (notfound && (checktri.tri != m->dummytri)) {
- dest(checktri, checkdest);
- if (shorg == checkdest) {
- /* We have a match. Remove this triangle from the list. */
- *prevlink = checktri.tri[6 + checktri.orient];
- /* Bond the subsegment to the triangle. */
- tsbond(checktri, subsegloop);
- /* Check if this is a boundary edge. */
- sym(checktri, checkneighbor);
- if (checkneighbor.tri == m->dummytri) {
- /* The next line doesn't insert a subsegment (because there's */
- /* already one there), but it sets the boundary markers of */
- /* the existing subsegment and its vertices. */
- insertsubseg(m, b, &checktri, 1);
- hullsize++;
- }
- notfound = 0;
- }
- /* Find the next triangle in the stack. */
- prevlink = &checktri.tri[6 + checktri.orient];
- nexttri = checktri.tri[6 + checktri.orient];
- decode(nexttri, checktri);
- }
- }
- subsegloop.ss = subsegtraverse(m);
- segmentnumber++;
- }
- }
-
- /* Mark the remaining edges as not being attached to any subsegment. */
- /* Also, count the (yet uncounted) boundary edges. */
- for (i = 0; i < m->vertices.items; i++) {
- /* Search the stack of triangles adjacent to a vertex. */
- nexttri = vertexarray[i];
- decode(nexttri, checktri);
- while (checktri.tri != m->dummytri) {
- /* Find the next triangle in the stack before this */
- /* information gets overwritten. */
- nexttri = checktri.tri[6 + checktri.orient];
- /* No adjacent subsegment. (This overwrites the stack info.) */
- tsdissolve(checktri);
- sym(checktri, checkneighbor);
- if (checkneighbor.tri == m->dummytri) {
- insertsubseg(m, b, &checktri, 1);
- hullsize++;
- }
- decode(nexttri, checktri);
- }
- }
-
- trifree((VOID *) vertexarray);
- return hullsize;
-}
-
-#endif /* not CDT_ONLY */
-
-/** **/
-/** **/
-/********* General mesh construction routines end here *********/
-
-/********* Segment insertion begins here *********/
-/** **/
-/** **/
-
-/*****************************************************************************/
-/* */
-/* finddirection() Find the first triangle on the path from one point */
-/* to another. */
-/* */
-/* Finds the triangle that intersects a line segment drawn from the */
-/* origin of `searchtri' to the point `searchpoint', and returns the result */
-/* in `searchtri'. The origin of `searchtri' does not change, even though */
-/* the triangle returned may differ from the one passed in. This routine */
-/* is used to find the direction to move in to get from one point to */
-/* another. */
-/* */
-/* The return value notes whether the destination or apex of the found */
-/* triangle is collinear with the two points in question. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-enum finddirectionresult finddirection(struct mesh *m, struct behavior *b,
- struct otri *searchtri,
- vertex searchpoint)
-#else /* not ANSI_DECLARATORS */
-enum finddirectionresult finddirection(m, b, searchtri, searchpoint)
-struct mesh *m;
-struct behavior *b;
-struct otri *searchtri;
-vertex searchpoint;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct otri checktri;
- vertex startvertex;
- vertex leftvertex, rightvertex;
- REAL leftccw, rightccw;
- int leftflag, rightflag;
- triangle ptr; /* Temporary variable used by onext() and oprev(). */
-
- org(*searchtri, startvertex);
- dest(*searchtri, rightvertex);
- apex(*searchtri, leftvertex);
- /* Is `searchpoint' to the left? */
- leftccw = counterclockwise(m, b, searchpoint, startvertex, leftvertex);
- leftflag = leftccw > 0.0;
- /* Is `searchpoint' to the right? */
- rightccw = counterclockwise(m, b, startvertex, searchpoint, rightvertex);
- rightflag = rightccw > 0.0;
- if (leftflag && rightflag) {
- /* `searchtri' faces directly away from `searchpoint'. We could go left */
- /* or right. Ask whether it's a triangle or a boundary on the left. */
- onext(*searchtri, checktri);
- if (checktri.tri == m->dummytri) {
- leftflag = 0;
- } else {
- rightflag = 0;
- }
- }
- while (leftflag) {
- /* Turn left until satisfied. */
- onextself(*searchtri);
- if (searchtri->tri == m->dummytri) {
- printf("Internal error in finddirection(): Unable to find a\n");
- printf(" triangle leading from (%.12g, %.12g) to", startvertex[0],
- startvertex[1]);
- printf(" (%.12g, %.12g).\n", searchpoint[0], searchpoint[1]);
- internalerror();
- }
- apex(*searchtri, leftvertex);
- rightccw = leftccw;
- leftccw = counterclockwise(m, b, searchpoint, startvertex, leftvertex);
- leftflag = leftccw > 0.0;
- }
- while (rightflag) {
- /* Turn right until satisfied. */
- oprevself(*searchtri);
- if (searchtri->tri == m->dummytri) {
- printf("Internal error in finddirection(): Unable to find a\n");
- printf(" triangle leading from (%.12g, %.12g) to", startvertex[0],
- startvertex[1]);
- printf(" (%.12g, %.12g).\n", searchpoint[0], searchpoint[1]);
- internalerror();
- }
- dest(*searchtri, rightvertex);
- leftccw = rightccw;
- rightccw = counterclockwise(m, b, startvertex, searchpoint, rightvertex);
- rightflag = rightccw > 0.0;
- }
- if (leftccw == 0.0) {
- return LEFTCOLLINEAR;
- } else if (rightccw == 0.0) {
- return RIGHTCOLLINEAR;
- } else {
- return WITHIN;
- }
-}
-
-/*****************************************************************************/
-/* */
-/* segmentintersection() Find the intersection of an existing segment */
-/* and a segment that is being inserted. Insert */
-/* a vertex at the intersection, splitting an */
-/* existing subsegment. */
-/* */
-/* The segment being inserted connects the apex of splittri to endpoint2. */
-/* splitsubseg is the subsegment being split, and MUST adjoin splittri. */
-/* Hence, endpoints of the subsegment being split are the origin and */
-/* destination of splittri. */
-/* */
-/* On completion, splittri is a handle having the newly inserted */
-/* intersection point as its origin, and endpoint1 as its destination. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-void segmentintersection(struct mesh *m, struct behavior *b,
- struct otri *splittri, struct osub *splitsubseg,
- vertex endpoint2)
-#else /* not ANSI_DECLARATORS */
-void segmentintersection(m, b, splittri, splitsubseg, endpoint2)
-struct mesh *m;
-struct behavior *b;
-struct otri *splittri;
-struct osub *splitsubseg;
-vertex endpoint2;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct osub opposubseg;
- vertex endpoint1;
- vertex torg, tdest;
- vertex leftvertex, rightvertex;
- vertex newvertex;
- enum insertvertexresult success;
- enum finddirectionresult collinear;
- REAL ex, ey;
- REAL tx, ty;
- REAL etx, ety;
- REAL split, denom;
- int i;
- triangle ptr; /* Temporary variable used by onext(). */
- subseg sptr; /* Temporary variable used by snext(). */
-
- /* Find the other three segment endpoints. */
- apex(*splittri, endpoint1);
- org(*splittri, torg);
- dest(*splittri, tdest);
- /* Segment intersection formulae; see the Antonio reference. */
- tx = tdest[0] - torg[0];
- ty = tdest[1] - torg[1];
- ex = endpoint2[0] - endpoint1[0];
- ey = endpoint2[1] - endpoint1[1];
- etx = torg[0] - endpoint2[0];
- ety = torg[1] - endpoint2[1];
- denom = ty * ex - tx * ey;
- if (denom == 0.0) {
- printf("Internal error in segmentintersection():");
- printf(" Attempt to find intersection of parallel segments.\n");
- internalerror();
- }
- split = (ey * etx - ex * ety) / denom;
- /* Create the new vertex. */
- newvertex = (vertex) poolalloc(&m->vertices);
- /* Interpolate its coordinate and attributes. */
- for (i = 0; i < 2 + m->nextras; i++) {
- newvertex[i] = torg[i] + split * (tdest[i] - torg[i]);
- }
- setvertexmark(newvertex, mark(*splitsubseg));
- setvertextype(newvertex, INPUTVERTEX);
- if (b->verbose > 1) {
- printf(
- " Splitting subsegment (%.12g, %.12g) (%.12g, %.12g) at (%.12g, %.12g).\n",
- torg[0], torg[1], tdest[0], tdest[1], newvertex[0], newvertex[1]);
- }
- /* Insert the intersection vertex. This should always succeed. */
- success = insertvertex(m, b, newvertex, splittri, splitsubseg, 0, 0);
- if (success != SUCCESSFULVERTEX) {
- printf("Internal error in segmentintersection():\n");
- printf(" Failure to split a segment.\n");
- internalerror();
- }
- /* Record a triangle whose origin is the new vertex. */
- setvertex2tri(newvertex, encode(*splittri));
- if (m->steinerleft > 0) {
- m->steinerleft--;
- }
-
- /* Divide the segment into two, and correct the segment endpoints. */
- ssymself(*splitsubseg);
- spivot(*splitsubseg, opposubseg);
- sdissolve(*splitsubseg);
- sdissolve(opposubseg);
- do {
- setsegorg(*splitsubseg, newvertex);
- snextself(*splitsubseg);
- } while (splitsubseg->ss != m->dummysub);
- do {
- setsegorg(opposubseg, newvertex);
- snextself(opposubseg);
- } while (opposubseg.ss != m->dummysub);
-
- /* Inserting the vertex may have caused edge flips. We wish to rediscover */
- /* the edge connecting endpoint1 to the new intersection vertex. */
- collinear = finddirection(m, b, splittri, endpoint1);
- dest(*splittri, rightvertex);
- apex(*splittri, leftvertex);
- if ((leftvertex[0] == endpoint1[0]) && (leftvertex[1] == endpoint1[1])) {
- onextself(*splittri);
- } else if ((rightvertex[0] != endpoint1[0]) ||
- (rightvertex[1] != endpoint1[1])) {
- printf("Internal error in segmentintersection():\n");
- printf(" Topological inconsistency after splitting a segment.\n");
- internalerror();
- }
- /* `splittri' should have destination endpoint1. */
-}
-
-/*****************************************************************************/
-/* */
-/* scoutsegment() Scout the first triangle on the path from one endpoint */
-/* to another, and check for completion (reaching the */
-/* second endpoint), a collinear vertex, or the */
-/* intersection of two segments. */
-/* */
-/* Returns one if the entire segment is successfully inserted, and zero if */
-/* the job must be finished by conformingedge() or constrainededge(). */
-/* */
-/* If the first triangle on the path has the second endpoint as its */
-/* destination or apex, a subsegment is inserted and the job is done. */
-/* */
-/* If the first triangle on the path has a destination or apex that lies on */
-/* the segment, a subsegment is inserted connecting the first endpoint to */
-/* the collinear vertex, and the search is continued from the collinear */
-/* vertex. */
-/* */
-/* If the first triangle on the path has a subsegment opposite its origin, */
-/* then there is a segment that intersects the segment being inserted. */
-/* Their intersection vertex is inserted, splitting the subsegment. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-int scoutsegment(struct mesh *m, struct behavior *b, struct otri *searchtri,
- vertex endpoint2, int newmark)
-#else /* not ANSI_DECLARATORS */
-int scoutsegment(m, b, searchtri, endpoint2, newmark)
-struct mesh *m;
-struct behavior *b;
-struct otri *searchtri;
-vertex endpoint2;
-int newmark;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct otri crosstri;
- struct osub crosssubseg;
- vertex leftvertex, rightvertex;
- enum finddirectionresult collinear;
- subseg sptr; /* Temporary variable used by tspivot(). */
-
- collinear = finddirection(m, b, searchtri, endpoint2);
- dest(*searchtri, rightvertex);
- apex(*searchtri, leftvertex);
- if (((leftvertex[0] == endpoint2[0]) && (leftvertex[1] == endpoint2[1])) ||
- ((rightvertex[0] == endpoint2[0]) && (rightvertex[1] == endpoint2[1]))) {
- /* The segment is already an edge in the mesh. */
- if ((leftvertex[0] == endpoint2[0]) && (leftvertex[1] == endpoint2[1])) {
- lprevself(*searchtri);
- }
- /* Insert a subsegment, if there isn't already one there. */
- insertsubseg(m, b, searchtri, newmark);
- return 1;
- } else if (collinear == LEFTCOLLINEAR) {
- /* We've collided with a vertex between the segment's endpoints. */
- /* Make the collinear vertex be the triangle's origin. */
- lprevself(*searchtri);
- insertsubseg(m, b, searchtri, newmark);
- /* Insert the remainder of the segment. */
- return scoutsegment(m, b, searchtri, endpoint2, newmark);
- } else if (collinear == RIGHTCOLLINEAR) {
- /* We've collided with a vertex between the segment's endpoints. */
- insertsubseg(m, b, searchtri, newmark);
- /* Make the collinear vertex be the triangle's origin. */
- lnextself(*searchtri);
- /* Insert the remainder of the segment. */
- return scoutsegment(m, b, searchtri, endpoint2, newmark);
- } else {
- lnext(*searchtri, crosstri);
- tspivot(crosstri, crosssubseg);
- /* Check for a crossing segment. */
- if (crosssubseg.ss == m->dummysub) {
- return 0;
- } else {
- /* Insert a vertex at the intersection. */
- segmentintersection(m, b, &crosstri, &crosssubseg, endpoint2);
- otricopy(crosstri, *searchtri);
- insertsubseg(m, b, searchtri, newmark);
- /* Insert the remainder of the segment. */
- return scoutsegment(m, b, searchtri, endpoint2, newmark);
- }
- }
-}
-
-/*****************************************************************************/
-/* */
-/* conformingedge() Force a segment into a conforming Delaunay */
-/* triangulation by inserting a vertex at its midpoint, */
-/* and recursively forcing in the two half-segments if */
-/* necessary. */
-/* */
-/* Generates a sequence of subsegments connecting `endpoint1' to */
-/* `endpoint2'. `newmark' is the boundary marker of the segment, assigned */
-/* to each new splitting vertex and subsegment. */
-/* */
-/* Note that conformingedge() does not always maintain the conforming */
-/* Delaunay property. Once inserted, segments are locked into place; */
-/* vertices inserted later (to force other segments in) may render these */
-/* fixed segments non-Delaunay. The conforming Delaunay property will be */
-/* restored by enforcequality() by splitting encroached subsegments. */
-/* */
-/*****************************************************************************/
-
-#ifndef REDUCED
-#ifndef CDT_ONLY
-
-#ifdef ANSI_DECLARATORS
-void conformingedge(struct mesh *m, struct behavior *b,
- vertex endpoint1, vertex endpoint2, int newmark)
-#else /* not ANSI_DECLARATORS */
-void conformingedge(m, b, endpoint1, endpoint2, newmark)
-struct mesh *m;
-struct behavior *b;
-vertex endpoint1;
-vertex endpoint2;
-int newmark;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct otri searchtri1, searchtri2;
- struct osub brokensubseg;
- vertex newvertex;
- vertex midvertex1, midvertex2;
- enum insertvertexresult success;
- int i;
- subseg sptr; /* Temporary variable used by tspivot(). */
-
- if (b->verbose > 2) {
- printf("Forcing segment into triangulation by recursive splitting:\n");
- printf(" (%.12g, %.12g) (%.12g, %.12g)\n", endpoint1[0], endpoint1[1],
- endpoint2[0], endpoint2[1]);
- }
- /* Create a new vertex to insert in the middle of the segment. */
- newvertex = (vertex) poolalloc(&m->vertices);
- /* Interpolate coordinates and attributes. */
- for (i = 0; i < 2 + m->nextras; i++) {
- newvertex[i] = 0.5 * (endpoint1[i] + endpoint2[i]);
- }
- setvertexmark(newvertex, newmark);
- setvertextype(newvertex, SEGMENTVERTEX);
- /* No known triangle to search from. */
- searchtri1.tri = m->dummytri;
- /* Attempt to insert the new vertex. */
- success = insertvertex(m, b, newvertex, &searchtri1, (struct osub *) NULL,
- 0, 0);
- if (success == DUPLICATEVERTEX) {
- if (b->verbose > 2) {
- printf(" Segment intersects existing vertex (%.12g, %.12g).\n",
- newvertex[0], newvertex[1]);
- }
- /* Use the vertex that's already there. */
- vertexdealloc(m, newvertex);
- org(searchtri1, newvertex);
- } else {
- if (success == VIOLATINGVERTEX) {
- if (b->verbose > 2) {
- printf(" Two segments intersect at (%.12g, %.12g).\n",
- newvertex[0], newvertex[1]);
- }
- /* By fluke, we've landed right on another segment. Split it. */
- tspivot(searchtri1, brokensubseg);
- success = insertvertex(m, b, newvertex, &searchtri1, &brokensubseg,
- 0, 0);
- if (success != SUCCESSFULVERTEX) {
- printf("Internal error in conformingedge():\n");
- printf(" Failure to split a segment.\n");
- internalerror();
- }
- }
- /* The vertex has been inserted successfully. */
- if (m->steinerleft > 0) {
- m->steinerleft--;
- }
- }
- otricopy(searchtri1, searchtri2);
- /* `searchtri1' and `searchtri2' are fastened at their origins to */
- /* `newvertex', and will be directed toward `endpoint1' and `endpoint2' */
- /* respectively. First, we must get `searchtri2' out of the way so it */
- /* won't be invalidated during the insertion of the first half of the */
- /* segment. */
- finddirection(m, b, &searchtri2, endpoint2);
- if (!scoutsegment(m, b, &searchtri1, endpoint1, newmark)) {
- /* The origin of searchtri1 may have changed if a collision with an */
- /* intervening vertex on the segment occurred. */
- org(searchtri1, midvertex1);
- conformingedge(m, b, midvertex1, endpoint1, newmark);
- }
- if (!scoutsegment(m, b, &searchtri2, endpoint2, newmark)) {
- /* The origin of searchtri2 may have changed if a collision with an */
- /* intervening vertex on the segment occurred. */
- org(searchtri2, midvertex2);
- conformingedge(m, b, midvertex2, endpoint2, newmark);
- }
-}
-
-#endif /* not CDT_ONLY */
-#endif /* not REDUCED */
-
-/*****************************************************************************/
-/* */
-/* delaunayfixup() Enforce the Delaunay condition at an edge, fanning out */
-/* recursively from an existing vertex. Pay special */
-/* attention to stacking inverted triangles. */
-/* */
-/* This is a support routine for inserting segments into a constrained */
-/* Delaunay triangulation. */
-/* */
-/* The origin of fixuptri is treated as if it has just been inserted, and */
-/* the local Delaunay condition needs to be enforced. It is only enforced */
-/* in one sector, however, that being the angular range defined by */
-/* fixuptri. */
-/* */
-/* This routine also needs to make decisions regarding the "stacking" of */
-/* triangles. (Read the description of constrainededge() below before */
-/* reading on here, so you understand the algorithm.) If the position of */
-/* the new vertex (the origin of fixuptri) indicates that the vertex before */
-/* it on the polygon is a reflex vertex, then "stack" the triangle by */
-/* doing nothing. (fixuptri is an inverted triangle, which is how stacked */
-/* triangles are identified.) */
-/* */
-/* Otherwise, check whether the vertex before that was a reflex vertex. */
-/* If so, perform an edge flip, thereby eliminating an inverted triangle */
-/* (popping it off the stack). The edge flip may result in the creation */
-/* of a new inverted triangle, depending on whether or not the new vertex */
-/* is visible to the vertex three edges behind on the polygon. */
-/* */
-/* If neither of the two vertices behind the new vertex are reflex */
-/* vertices, fixuptri and fartri, the triangle opposite it, are not */
-/* inverted; hence, ensure that the edge between them is locally Delaunay. */
-/* */
-/* `leftside' indicates whether or not fixuptri is to the left of the */
-/* segment being inserted. (Imagine that the segment is pointing up from */
-/* endpoint1 to endpoint2.) */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-void delaunayfixup(struct mesh *m, struct behavior *b,
- struct otri *fixuptri, int leftside)
-#else /* not ANSI_DECLARATORS */
-void delaunayfixup(m, b, fixuptri, leftside)
-struct mesh *m;
-struct behavior *b;
-struct otri *fixuptri;
-int leftside;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct otri neartri;
- struct otri fartri;
- struct osub faredge;
- vertex nearvertex, leftvertex, rightvertex, farvertex;
- triangle ptr; /* Temporary variable used by sym(). */
- subseg sptr; /* Temporary variable used by tspivot(). */
-
- lnext(*fixuptri, neartri);
- sym(neartri, fartri);
- /* Check if the edge opposite the origin of fixuptri can be flipped. */
- if (fartri.tri == m->dummytri) {
- return;
- }
- tspivot(neartri, faredge);
- if (faredge.ss != m->dummysub) {
- return;
- }
- /* Find all the relevant vertices. */
- apex(neartri, nearvertex);
- org(neartri, leftvertex);
- dest(neartri, rightvertex);
- apex(fartri, farvertex);
- /* Check whether the previous polygon vertex is a reflex vertex. */
- if (leftside) {
- if (counterclockwise(m, b, nearvertex, leftvertex, farvertex) <= 0.0) {
- /* leftvertex is a reflex vertex too. Nothing can */
- /* be done until a convex section is found. */
- return;
- }
- } else {
- if (counterclockwise(m, b, farvertex, rightvertex, nearvertex) <= 0.0) {
- /* rightvertex is a reflex vertex too. Nothing can */
- /* be done until a convex section is found. */
- return;
- }
- }
- if (counterclockwise(m, b, rightvertex, leftvertex, farvertex) > 0.0) {
- /* fartri is not an inverted triangle, and farvertex is not a reflex */
- /* vertex. As there are no reflex vertices, fixuptri isn't an */
- /* inverted triangle, either. Hence, test the edge between the */
- /* triangles to ensure it is locally Delaunay. */
- if (incircle(m, b, leftvertex, farvertex, rightvertex, nearvertex) <=
- 0.0) {
- return;
- }
- /* Not locally Delaunay; go on to an edge flip. */
- } /* else fartri is inverted; remove it from the stack by flipping. */
- flip(m, b, &neartri);
- lprevself(*fixuptri); /* Restore the origin of fixuptri after the flip. */
- /* Recursively process the two triangles that result from the flip. */
- delaunayfixup(m, b, fixuptri, leftside);
- delaunayfixup(m, b, &fartri, leftside);
-}
-
-/*****************************************************************************/
-/* */
-/* constrainededge() Force a segment into a constrained Delaunay */
-/* triangulation by deleting the triangles it */
-/* intersects, and triangulating the polygons that */
-/* form on each side of it. */
-/* */
-/* Generates a single subsegment connecting `endpoint1' to `endpoint2'. */
-/* The triangle `starttri' has `endpoint1' as its origin. `newmark' is the */
-/* boundary marker of the segment. */
-/* */
-/* To insert a segment, every triangle whose interior intersects the */
-/* segment is deleted. The union of these deleted triangles is a polygon */
-/* (which is not necessarily monotone, but is close enough), which is */
-/* divided into two polygons by the new segment. This routine's task is */
-/* to generate the Delaunay triangulation of these two polygons. */
-/* */
-/* You might think of this routine's behavior as a two-step process. The */
-/* first step is to walk from endpoint1 to endpoint2, flipping each edge */
-/* encountered. This step creates a fan of edges connected to endpoint1, */
-/* including the desired edge to endpoint2. The second step enforces the */
-/* Delaunay condition on each side of the segment in an incremental manner: */
-/* proceeding along the polygon from endpoint1 to endpoint2 (this is done */
-/* independently on each side of the segment), each vertex is "enforced" */
-/* as if it had just been inserted, but affecting only the previous */
-/* vertices. The result is the same as if the vertices had been inserted */
-/* in the order they appear on the polygon, so the result is Delaunay. */
-/* */
-/* In truth, constrainededge() interleaves these two steps. The procedure */
-/* walks from endpoint1 to endpoint2, and each time an edge is encountered */
-/* and flipped, the newly exposed vertex (at the far end of the flipped */
-/* edge) is "enforced" upon the previously flipped edges, usually affecting */
-/* only one side of the polygon (depending upon which side of the segment */
-/* the vertex falls on). */
-/* */
-/* The algorithm is complicated by the need to handle polygons that are not */
-/* convex. Although the polygon is not necessarily monotone, it can be */
-/* triangulated in a manner similar to the stack-based algorithms for */
-/* monotone polygons. For each reflex vertex (local concavity) of the */
-/* polygon, there will be an inverted triangle formed by one of the edge */
-/* flips. (An inverted triangle is one with negative area - that is, its */
-/* vertices are arranged in clockwise order - and is best thought of as a */
-/* wrinkle in the fabric of the mesh.) Each inverted triangle can be */
-/* thought of as a reflex vertex pushed on the stack, waiting to be fixed */
-/* later. */
-/* */
-/* A reflex vertex is popped from the stack when a vertex is inserted that */
-/* is visible to the reflex vertex. (However, if the vertex behind the */
-/* reflex vertex is not visible to the reflex vertex, a new inverted */
-/* triangle will take its place on the stack.) These details are handled */
-/* by the delaunayfixup() routine above. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-void constrainededge(struct mesh *m, struct behavior *b,
- struct otri *starttri, vertex endpoint2, int newmark)
-#else /* not ANSI_DECLARATORS */
-void constrainededge(m, b, starttri, endpoint2, newmark)
-struct mesh *m;
-struct behavior *b;
-struct otri *starttri;
-vertex endpoint2;
-int newmark;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct otri fixuptri, fixuptri2;
- struct osub crosssubseg;
- vertex endpoint1;
- vertex farvertex;
- REAL area;
- int collision;
- int done;
- triangle ptr; /* Temporary variable used by sym() and oprev(). */
- subseg sptr; /* Temporary variable used by tspivot(). */
-
- org(*starttri, endpoint1);
- lnext(*starttri, fixuptri);
- flip(m, b, &fixuptri);
- /* `collision' indicates whether we have found a vertex directly */
- /* between endpoint1 and endpoint2. */
- collision = 0;
- done = 0;
- do {
- org(fixuptri, farvertex);
- /* `farvertex' is the extreme point of the polygon we are "digging" */
- /* to get from endpoint1 to endpoint2. */
- if ((farvertex[0] == endpoint2[0]) && (farvertex[1] == endpoint2[1])) {
- oprev(fixuptri, fixuptri2);
- /* Enforce the Delaunay condition around endpoint2. */
- delaunayfixup(m, b, &fixuptri, 0);
- delaunayfixup(m, b, &fixuptri2, 1);
- done = 1;
- } else {
- /* Check whether farvertex is to the left or right of the segment */
- /* being inserted, to decide which edge of fixuptri to dig */
- /* through next. */
- area = counterclockwise(m, b, endpoint1, endpoint2, farvertex);
- if (area == 0.0) {
- /* We've collided with a vertex between endpoint1 and endpoint2. */
- collision = 1;
- oprev(fixuptri, fixuptri2);
- /* Enforce the Delaunay condition around farvertex. */
- delaunayfixup(m, b, &fixuptri, 0);
- delaunayfixup(m, b, &fixuptri2, 1);
- done = 1;
- } else {
- if (area > 0.0) { /* farvertex is to the left of the segment. */
- oprev(fixuptri, fixuptri2);
- /* Enforce the Delaunay condition around farvertex, on the */
- /* left side of the segment only. */
- delaunayfixup(m, b, &fixuptri2, 1);
- /* Flip the edge that crosses the segment. After the edge is */
- /* flipped, one of its endpoints is the fan vertex, and the */
- /* destination of fixuptri is the fan vertex. */
- lprevself(fixuptri);
- } else { /* farvertex is to the right of the segment. */
- delaunayfixup(m, b, &fixuptri, 0);
- /* Flip the edge that crosses the segment. After the edge is */
- /* flipped, one of its endpoints is the fan vertex, and the */
- /* destination of fixuptri is the fan vertex. */
- oprevself(fixuptri);
- }
- /* Check for two intersecting segments. */
- tspivot(fixuptri, crosssubseg);
- if (crosssubseg.ss == m->dummysub) {
- flip(m, b, &fixuptri); /* May create inverted triangle at left. */
- } else {
- /* We've collided with a segment between endpoint1 and endpoint2. */
- collision = 1;
- /* Insert a vertex at the intersection. */
- segmentintersection(m, b, &fixuptri, &crosssubseg, endpoint2);
- done = 1;
- }
- }
- }
- } while (!done);
- /* Insert a subsegment to make the segment permanent. */
- insertsubseg(m, b, &fixuptri, newmark);
- /* If there was a collision with an interceding vertex, install another */
- /* segment connecting that vertex with endpoint2. */
- if (collision) {
- /* Insert the remainder of the segment. */
- if (!scoutsegment(m, b, &fixuptri, endpoint2, newmark)) {
- constrainededge(m, b, &fixuptri, endpoint2, newmark);
- }
- }
-}
-
-/*****************************************************************************/
-/* */
-/* insertsegment() Insert a PSLG segment into a triangulation. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-void insertsegment(struct mesh *m, struct behavior *b,
- vertex endpoint1, vertex endpoint2, int newmark)
-#else /* not ANSI_DECLARATORS */
-void insertsegment(m, b, endpoint1, endpoint2, newmark)
-struct mesh *m;
-struct behavior *b;
-vertex endpoint1;
-vertex endpoint2;
-int newmark;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct otri searchtri1, searchtri2;
- triangle encodedtri;
- vertex checkvertex;
- triangle ptr; /* Temporary variable used by sym(). */
-
- if (b->verbose > 1) {
- printf(" Connecting (%.12g, %.12g) to (%.12g, %.12g).\n",
- endpoint1[0], endpoint1[1], endpoint2[0], endpoint2[1]);
- }
-
- /* Find a triangle whose origin is the segment's first endpoint. */
- checkvertex = (vertex) NULL;
- encodedtri = vertex2tri(endpoint1);
- if (encodedtri != (triangle) NULL) {
- decode(encodedtri, searchtri1);
- org(searchtri1, checkvertex);
- }
- if (checkvertex != endpoint1) {
- /* Find a boundary triangle to search from. */
- searchtri1.tri = m->dummytri;
- searchtri1.orient = 0;
- symself(searchtri1);
- /* Search for the segment's first endpoint by point location. */
- if (locate(m, b, endpoint1, &searchtri1) != ONVERTEX) {
- printf(
- "Internal error in insertsegment(): Unable to locate PSLG vertex\n");
- printf(" (%.12g, %.12g) in triangulation.\n",
- endpoint1[0], endpoint1[1]);
- internalerror();
- }
- }
- /* Remember this triangle to improve subsequent point location. */
- otricopy(searchtri1, m->recenttri);
- /* Scout the beginnings of a path from the first endpoint */
- /* toward the second. */
- if (scoutsegment(m, b, &searchtri1, endpoint2, newmark)) {
- /* The segment was easily inserted. */
- return;
- }
- /* The first endpoint may have changed if a collision with an intervening */
- /* vertex on the segment occurred. */
- org(searchtri1, endpoint1);
-
- /* Find a triangle whose origin is the segment's second endpoint. */
- checkvertex = (vertex) NULL;
- encodedtri = vertex2tri(endpoint2);
- if (encodedtri != (triangle) NULL) {
- decode(encodedtri, searchtri2);
- org(searchtri2, checkvertex);
- }
- if (checkvertex != endpoint2) {
- /* Find a boundary triangle to search from. */
- searchtri2.tri = m->dummytri;
- searchtri2.orient = 0;
- symself(searchtri2);
- /* Search for the segment's second endpoint by point location. */
- if (locate(m, b, endpoint2, &searchtri2) != ONVERTEX) {
- printf(
- "Internal error in insertsegment(): Unable to locate PSLG vertex\n");
- printf(" (%.12g, %.12g) in triangulation.\n",
- endpoint2[0], endpoint2[1]);
- internalerror();
- }
- }
- /* Remember this triangle to improve subsequent point location. */
- otricopy(searchtri2, m->recenttri);
- /* Scout the beginnings of a path from the second endpoint */
- /* toward the first. */
- if (scoutsegment(m, b, &searchtri2, endpoint1, newmark)) {
- /* The segment was easily inserted. */
- return;
- }
- /* The second endpoint may have changed if a collision with an intervening */
- /* vertex on the segment occurred. */
- org(searchtri2, endpoint2);
-
-#ifndef REDUCED
-#ifndef CDT_ONLY
- if (b->splitseg) {
- /* Insert vertices to force the segment into the triangulation. */
- conformingedge(m, b, endpoint1, endpoint2, newmark);
- } else {
-#endif /* not CDT_ONLY */
-#endif /* not REDUCED */
- /* Insert the segment directly into the triangulation. */
- constrainededge(m, b, &searchtri1, endpoint2, newmark);
-#ifndef REDUCED
-#ifndef CDT_ONLY
- }
-#endif /* not CDT_ONLY */
-#endif /* not REDUCED */
-}
-
-/*****************************************************************************/
-/* */
-/* markhull() Cover the convex hull of a triangulation with subsegments. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-void markhull(struct mesh *m, struct behavior *b)
-#else /* not ANSI_DECLARATORS */
-void markhull(m, b)
-struct mesh *m;
-struct behavior *b;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct otri hulltri;
- struct otri nexttri;
- struct otri starttri;
- triangle ptr; /* Temporary variable used by sym() and oprev(). */
-
- /* Find a triangle handle on the hull. */
- hulltri.tri = m->dummytri;
- hulltri.orient = 0;
- symself(hulltri);
- /* Remember where we started so we know when to stop. */
- otricopy(hulltri, starttri);
- /* Go once counterclockwise around the convex hull. */
- do {
- /* Create a subsegment if there isn't already one here. */
- insertsubseg(m, b, &hulltri, 1);
- /* To find the next hull edge, go clockwise around the next vertex. */
- lnextself(hulltri);
- oprev(hulltri, nexttri);
- while (nexttri.tri != m->dummytri) {
- otricopy(nexttri, hulltri);
- oprev(hulltri, nexttri);
- }
- } while (!otriequal(hulltri, starttri));
-}
-
-/*****************************************************************************/
-/* */
-/* formskeleton() Create the segments of a triangulation, including PSLG */
-/* segments and edges on the convex hull. */
-/* */
-/* The PSLG segments are read from a .poly file. The return value is the */
-/* number of segments in the file. */
-/* */
-/*****************************************************************************/
-
-#ifdef TRILIBRARY
-
-#ifdef ANSI_DECLARATORS
-void formskeleton(struct mesh *m, struct behavior *b, int *segmentlist,
- int *segmentmarkerlist, int numberofsegments)
-#else /* not ANSI_DECLARATORS */
-void formskeleton(m, b, segmentlist, segmentmarkerlist, numberofsegments)
-struct mesh *m;
-struct behavior *b;
-int *segmentlist;
-int *segmentmarkerlist;
-int numberofsegments;
-#endif /* not ANSI_DECLARATORS */
-
-#else /* not TRILIBRARY */
-
-#ifdef ANSI_DECLARATORS
-void formskeleton(struct mesh *m, struct behavior *b,
- FILE *polyfile, char *polyfilename)
-#else /* not ANSI_DECLARATORS */
-void formskeleton(m, b, polyfile, polyfilename)
-struct mesh *m;
-struct behavior *b;
-FILE *polyfile;
-char *polyfilename;
-#endif /* not ANSI_DECLARATORS */
-
-#endif /* not TRILIBRARY */
-
-{
-#ifdef TRILIBRARY
- char polyfilename[6];
- int index;
-#else /* not TRILIBRARY */
- char inputline[INPUTLINESIZE];
- char *stringptr;
-#endif /* not TRILIBRARY */
- vertex endpoint1, endpoint2;
- int segmentmarkers;
- int end1, end2;
- int boundmarker;
- int i;
-
- if (b->poly) {
- if (!b->quiet) {
- printf("Recovering segments in Delaunay triangulation.\n");
- }
-#ifdef TRILIBRARY
- strcpy(polyfilename, "input");
- m->insegments = numberofsegments;
- segmentmarkers = segmentmarkerlist != (int *) NULL;
- index = 0;
-#else /* not TRILIBRARY */
- /* Read the segments from a .poly file. */
- /* Read number of segments and number of boundary markers. */
- stringptr = readline(inputline, polyfile, polyfilename);
- m->insegments = (int) strtol(stringptr, &stringptr, 0);
- stringptr = findfield(stringptr);
- if (*stringptr == '\0') {
- segmentmarkers = 0;
- } else {
- segmentmarkers = (int) strtol(stringptr, &stringptr, 0);
- }
-#endif /* not TRILIBRARY */
- /* If the input vertices are collinear, there is no triangulation, */
- /* so don't try to insert segments. */
- if (m->triangles.items == 0) {
- return;
- }
-
- /* If segments are to be inserted, compute a mapping */
- /* from vertices to triangles. */
- if (m->insegments > 0) {
- makevertexmap(m, b);
- if (b->verbose) {
- printf(" Recovering PSLG segments.\n");
- }
- }
-
- boundmarker = 0;
- /* Read and insert the segments. */
- for (i = 0; i < m->insegments; i++) {
-#ifdef TRILIBRARY
- end1 = segmentlist[index++];
- end2 = segmentlist[index++];
- if (segmentmarkers) {
- boundmarker = segmentmarkerlist[i];
- }
-#else /* not TRILIBRARY */
- stringptr = readline(inputline, polyfile, b->inpolyfilename);
- stringptr = findfield(stringptr);
- if (*stringptr == '\0') {
- printf("Error: Segment %d has no endpoints in %s.\n",
- b->firstnumber + i, polyfilename);
- triexit(1);
- } else {
- end1 = (int) strtol(stringptr, &stringptr, 0);
- }
- stringptr = findfield(stringptr);
- if (*stringptr == '\0') {
- printf("Error: Segment %d is missing its second endpoint in %s.\n",
- b->firstnumber + i, polyfilename);
- triexit(1);
- } else {
- end2 = (int) strtol(stringptr, &stringptr, 0);
- }
- if (segmentmarkers) {
- stringptr = findfield(stringptr);
- if (*stringptr == '\0') {
- boundmarker = 0;
- } else {
- boundmarker = (int) strtol(stringptr, &stringptr, 0);
- }
- }
-#endif /* not TRILIBRARY */
- if ((end1 < b->firstnumber) ||
- (end1 >= b->firstnumber + m->invertices)) {
- if (!b->quiet) {
- printf("Warning: Invalid first endpoint of segment %d in %s.\n",
- b->firstnumber + i, polyfilename);
- }
- } else if ((end2 < b->firstnumber) ||
- (end2 >= b->firstnumber + m->invertices)) {
- if (!b->quiet) {
- printf("Warning: Invalid second endpoint of segment %d in %s.\n",
- b->firstnumber + i, polyfilename);
- }
- } else {
- /* Find the vertices numbered `end1' and `end2'. */
- endpoint1 = getvertex(m, b, end1);
- endpoint2 = getvertex(m, b, end2);
- if ((endpoint1[0] == endpoint2[0]) && (endpoint1[1] == endpoint2[1])) {
- if (!b->quiet) {
- printf("Warning: Endpoints of segment %d are coincident in %s.\n",
- b->firstnumber + i, polyfilename);
- }
- } else {
- insertsegment(m, b, endpoint1, endpoint2, boundmarker);
- }
- }
- }
- } else {
- m->insegments = 0;
- }
- if (b->convex || !b->poly) {
- /* Enclose the convex hull with subsegments. */
- if (b->verbose) {
- printf(" Enclosing convex hull with segments.\n");
- }
- markhull(m, b);
- }
-}
-
-/** **/
-/** **/
-/********* Segment insertion ends here *********/
-
-/********* Carving out holes and concavities begins here *********/
-/** **/
-/** **/
-
-/*****************************************************************************/
-/* */
-/* infecthull() Virally infect all of the triangles of the convex hull */
-/* that are not protected by subsegments. Where there are */
-/* subsegments, set boundary markers as appropriate. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-void infecthull(struct mesh *m, struct behavior *b)
-#else /* not ANSI_DECLARATORS */
-void infecthull(m, b)
-struct mesh *m;
-struct behavior *b;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct otri hulltri;
- struct otri nexttri;
- struct otri starttri;
- struct osub hullsubseg;
- triangle **deadtriangle;
- vertex horg, hdest;
- triangle ptr; /* Temporary variable used by sym(). */
- subseg sptr; /* Temporary variable used by tspivot(). */
-
- if (b->verbose) {
- printf(" Marking concavities (external triangles) for elimination.\n");
- }
- /* Find a triangle handle on the hull. */
- hulltri.tri = m->dummytri;
- hulltri.orient = 0;
- symself(hulltri);
- /* Remember where we started so we know when to stop. */
- otricopy(hulltri, starttri);
- /* Go once counterclockwise around the convex hull. */
- do {
- /* Ignore triangles that are already infected. */
- if (!infected(hulltri)) {
- /* Is the triangle protected by a subsegment? */
- tspivot(hulltri, hullsubseg);
- if (hullsubseg.ss == m->dummysub) {
- /* The triangle is not protected; infect it. */
- if (!infected(hulltri)) {
- infect(hulltri);
- deadtriangle = (triangle **) poolalloc(&m->viri);
- *deadtriangle = hulltri.tri;
- }
- } else {
- /* The triangle is protected; set boundary markers if appropriate. */
- if (mark(hullsubseg) == 0) {
- setmark(hullsubseg, 1);
- org(hulltri, horg);
- dest(hulltri, hdest);
- if (vertexmark(horg) == 0) {
- setvertexmark(horg, 1);
- }
- if (vertexmark(hdest) == 0) {
- setvertexmark(hdest, 1);
- }
- }
- }
- }
- /* To find the next hull edge, go clockwise around the next vertex. */
- lnextself(hulltri);
- oprev(hulltri, nexttri);
- while (nexttri.tri != m->dummytri) {
- otricopy(nexttri, hulltri);
- oprev(hulltri, nexttri);
- }
- } while (!otriequal(hulltri, starttri));
-}
-
-/*****************************************************************************/
-/* */
-/* plague() Spread the virus from all infected triangles to any neighbors */
-/* not protected by subsegments. Delete all infected triangles. */
-/* */
-/* This is the procedure that actually creates holes and concavities. */
-/* */
-/* This procedure operates in two phases. The first phase identifies all */
-/* the triangles that will die, and marks them as infected. They are */
-/* marked to ensure that each triangle is added to the virus pool only */
-/* once, so the procedure will terminate. */
-/* */
-/* The second phase actually eliminates the infected triangles. It also */
-/* eliminates orphaned vertices. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-void plague(struct mesh *m, struct behavior *b)
-#else /* not ANSI_DECLARATORS */
-void plague(m, b)
-struct mesh *m;
-struct behavior *b;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct otri testtri;
- struct otri neighbor;
- triangle **virusloop;
- triangle **deadtriangle;
- struct osub neighborsubseg;
- vertex testvertex;
- vertex norg, ndest;
- vertex deadorg, deaddest, deadapex;
- int killorg;
- triangle ptr; /* Temporary variable used by sym() and onext(). */
- subseg sptr; /* Temporary variable used by tspivot(). */
-
- if (b->verbose) {
- printf(" Marking neighbors of marked triangles.\n");
- }
- /* Loop through all the infected triangles, spreading the virus to */
- /* their neighbors, then to their neighbors' neighbors. */
- traversalinit(&m->viri);
- virusloop = (triangle **) traverse(&m->viri);
- while (virusloop != (triangle **) NULL) {
- testtri.tri = *virusloop;
- /* A triangle is marked as infected by messing with one of its pointers */
- /* to subsegments, setting it to an illegal value. Hence, we have to */
- /* temporarily uninfect this triangle so that we can examine its */
- /* adjacent subsegments. */
- uninfect(testtri);
- if (b->verbose > 2) {
- /* Assign the triangle an orientation for convenience in */
- /* checking its vertices. */
- testtri.orient = 0;
- org(testtri, deadorg);
- dest(testtri, deaddest);
- apex(testtri, deadapex);
- printf(" Checking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
- deadorg[0], deadorg[1], deaddest[0], deaddest[1],
- deadapex[0], deadapex[1]);
- }
- /* Check each of the triangle's three neighbors. */
- for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
- /* Find the neighbor. */
- sym(testtri, neighbor);
- /* Check for a subsegment between the triangle and its neighbor. */
- tspivot(testtri, neighborsubseg);
- /* Check if the neighbor is nonexistent or already infected. */
- if ((neighbor.tri == m->dummytri) || infected(neighbor)) {
- if (neighborsubseg.ss != m->dummysub) {
- /* There is a subsegment separating the triangle from its */
- /* neighbor, but both triangles are dying, so the subsegment */
- /* dies too. */
- subsegdealloc(m, neighborsubseg.ss);
- if (neighbor.tri != m->dummytri) {
- /* Make sure the subsegment doesn't get deallocated again */
- /* later when the infected neighbor is visited. */
- uninfect(neighbor);
- tsdissolve(neighbor);
- infect(neighbor);
- }
- }
- } else { /* The neighbor exists and is not infected. */
- if (neighborsubseg.ss == m->dummysub) {
- /* There is no subsegment protecting the neighbor, so */
- /* the neighbor becomes infected. */
- if (b->verbose > 2) {
- org(neighbor, deadorg);
- dest(neighbor, deaddest);
- apex(neighbor, deadapex);
- printf(
- " Marking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
- deadorg[0], deadorg[1], deaddest[0], deaddest[1],
- deadapex[0], deadapex[1]);
- }
- infect(neighbor);
- /* Ensure that the neighbor's neighbors will be infected. */
- deadtriangle = (triangle **) poolalloc(&m->viri);
- *deadtriangle = neighbor.tri;
- } else { /* The neighbor is protected by a subsegment. */
- /* Remove this triangle from the subsegment. */
- stdissolve(neighborsubseg);
- /* The subsegment becomes a boundary. Set markers accordingly. */
- if (mark(neighborsubseg) == 0) {
- setmark(neighborsubseg, 1);
- }
- org(neighbor, norg);
- dest(neighbor, ndest);
- if (vertexmark(norg) == 0) {
- setvertexmark(norg, 1);
- }
- if (vertexmark(ndest) == 0) {
- setvertexmark(ndest, 1);
- }
- }
- }
- }
- /* Remark the triangle as infected, so it doesn't get added to the */
- /* virus pool again. */
- infect(testtri);
- virusloop = (triangle **) traverse(&m->viri);
- }
-
- if (b->verbose) {
- printf(" Deleting marked triangles.\n");
- }
-
- traversalinit(&m->viri);
- virusloop = (triangle **) traverse(&m->viri);
- while (virusloop != (triangle **) NULL) {
- testtri.tri = *virusloop;
-
- /* Check each of the three corners of the triangle for elimination. */
- /* This is done by walking around each vertex, checking if it is */
- /* still connected to at least one live triangle. */
- for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
- org(testtri, testvertex);
- /* Check if the vertex has already been tested. */
- if (testvertex != (vertex) NULL) {
- killorg = 1;
- /* Mark the corner of the triangle as having been tested. */
- setorg(testtri, NULL);
- /* Walk counterclockwise about the vertex. */
- onext(testtri, neighbor);
- /* Stop upon reaching a boundary or the starting triangle. */
- while ((neighbor.tri != m->dummytri) &&
- (!otriequal(neighbor, testtri))) {
- if (infected(neighbor)) {
- /* Mark the corner of this triangle as having been tested. */
- setorg(neighbor, NULL);
- } else {
- /* A live triangle. The vertex survives. */
- killorg = 0;
- }
- /* Walk counterclockwise about the vertex. */
- onextself(neighbor);
- }
- /* If we reached a boundary, we must walk clockwise as well. */
- if (neighbor.tri == m->dummytri) {
- /* Walk clockwise about the vertex. */
- oprev(testtri, neighbor);
- /* Stop upon reaching a boundary. */
- while (neighbor.tri != m->dummytri) {
- if (infected(neighbor)) {
- /* Mark the corner of this triangle as having been tested. */
- setorg(neighbor, NULL);
- } else {
- /* A live triangle. The vertex survives. */
- killorg = 0;
- }
- /* Walk clockwise about the vertex. */
- oprevself(neighbor);
- }
- }
- if (killorg) {
- if (b->verbose > 1) {
- printf(" Deleting vertex (%.12g, %.12g)\n",
- testvertex[0], testvertex[1]);
- }
- setvertextype(testvertex, UNDEADVERTEX);
- m->undeads++;
- }
- }
- }
-
- /* Record changes in the number of boundary edges, and disconnect */
- /* dead triangles from their neighbors. */
- for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
- sym(testtri, neighbor);
- if (neighbor.tri == m->dummytri) {
- /* There is no neighboring triangle on this edge, so this edge */
- /* is a boundary edge. This triangle is being deleted, so this */
- /* boundary edge is deleted. */
- m->hullsize--;
- } else {
- /* Disconnect the triangle from its neighbor. */
- dissolve(neighbor);
- /* There is a neighboring triangle on this edge, so this edge */
- /* becomes a boundary edge when this triangle is deleted. */
- m->hullsize++;
- }
- }
- /* Return the dead triangle to the pool of triangles. */
- triangledealloc(m, testtri.tri);
- virusloop = (triangle **) traverse(&m->viri);
- }
- /* Empty the virus pool. */
- poolrestart(&m->viri);
-}
-
-/*****************************************************************************/
-/* */
-/* regionplague() Spread regional attributes and/or area constraints */
-/* (from a .poly file) throughout the mesh. */
-/* */
-/* This procedure operates in two phases. The first phase spreads an */
-/* attribute and/or an area constraint through a (segment-bounded) region. */
-/* The triangles are marked to ensure that each triangle is added to the */
-/* virus pool only once, so the procedure will terminate. */
-/* */
-/* The second phase uninfects all infected triangles, returning them to */
-/* normal. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-void regionplague(struct mesh *m, struct behavior *b,
- REAL attribute, REAL area)
-#else /* not ANSI_DECLARATORS */
-void regionplague(m, b, attribute, area)
-struct mesh *m;
-struct behavior *b;
-REAL attribute;
-REAL area;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct otri testtri;
- struct otri neighbor;
- triangle **virusloop;
- triangle **regiontri;
- struct osub neighborsubseg;
- vertex regionorg, regiondest, regionapex;
- triangle ptr; /* Temporary variable used by sym() and onext(). */
- subseg sptr; /* Temporary variable used by tspivot(). */
-
- if (b->verbose > 1) {
- printf(" Marking neighbors of marked triangles.\n");
- }
- /* Loop through all the infected triangles, spreading the attribute */
- /* and/or area constraint to their neighbors, then to their neighbors' */
- /* neighbors. */
- traversalinit(&m->viri);
- virusloop = (triangle **) traverse(&m->viri);
- while (virusloop != (triangle **) NULL) {
- testtri.tri = *virusloop;
- /* A triangle is marked as infected by messing with one of its pointers */
- /* to subsegments, setting it to an illegal value. Hence, we have to */
- /* temporarily uninfect this triangle so that we can examine its */
- /* adjacent subsegments. */
- uninfect(testtri);
- if (b->regionattrib) {
- /* Set an attribute. */
- setelemattribute(testtri, m->eextras, attribute);
- }
- if (b->vararea) {
- /* Set an area constraint. */
- setareabound(testtri, area);
- }
- if (b->verbose > 2) {
- /* Assign the triangle an orientation for convenience in */
- /* checking its vertices. */
- testtri.orient = 0;
- org(testtri, regionorg);
- dest(testtri, regiondest);
- apex(testtri, regionapex);
- printf(" Checking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
- regionorg[0], regionorg[1], regiondest[0], regiondest[1],
- regionapex[0], regionapex[1]);
- }
- /* Check each of the triangle's three neighbors. */
- for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
- /* Find the neighbor. */
- sym(testtri, neighbor);
- /* Check for a subsegment between the triangle and its neighbor. */
- tspivot(testtri, neighborsubseg);
- /* Make sure the neighbor exists, is not already infected, and */
- /* isn't protected by a subsegment. */
- if ((neighbor.tri != m->dummytri) && !infected(neighbor)
- && (neighborsubseg.ss == m->dummysub)) {
- if (b->verbose > 2) {
- org(neighbor, regionorg);
- dest(neighbor, regiondest);
- apex(neighbor, regionapex);
- printf(" Marking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
- regionorg[0], regionorg[1], regiondest[0], regiondest[1],
- regionapex[0], regionapex[1]);
- }
- /* Infect the neighbor. */
- infect(neighbor);
- /* Ensure that the neighbor's neighbors will be infected. */
- regiontri = (triangle **) poolalloc(&m->viri);
- *regiontri = neighbor.tri;
- }
- }
- /* Remark the triangle as infected, so it doesn't get added to the */
- /* virus pool again. */
- infect(testtri);
- virusloop = (triangle **) traverse(&m->viri);
- }
-
- /* Uninfect all triangles. */
- if (b->verbose > 1) {
- printf(" Unmarking marked triangles.\n");
- }
- traversalinit(&m->viri);
- virusloop = (triangle **) traverse(&m->viri);
- while (virusloop != (triangle **) NULL) {
- testtri.tri = *virusloop;
- uninfect(testtri);
- virusloop = (triangle **) traverse(&m->viri);
- }
- /* Empty the virus pool. */
- poolrestart(&m->viri);
-}
-
-/*****************************************************************************/
-/* */
-/* carveholes() Find the holes and infect them. Find the area */
-/* constraints and infect them. Infect the convex hull. */
-/* Spread the infection and kill triangles. Spread the */
-/* area constraints. */
-/* */
-/* This routine mainly calls other routines to carry out all these */
-/* functions. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-void carveholes(struct mesh *m, struct behavior *b, REAL *holelist, int holes,
- REAL *regionlist, int regions)
-#else /* not ANSI_DECLARATORS */
-void carveholes(m, b, holelist, holes, regionlist, regions)
-struct mesh *m;
-struct behavior *b;
-REAL *holelist;
-int holes;
-REAL *regionlist;
-int regions;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct otri searchtri;
- struct otri triangleloop;
- struct otri *regiontris;
- triangle **holetri;
- triangle **regiontri;
- vertex searchorg, searchdest;
- enum locateresult intersect;
- int i;
- triangle ptr; /* Temporary variable used by sym(). */
-
- if (!(b->quiet || (b->noholes && b->convex))) {
- printf("Removing unwanted triangles.\n");
- if (b->verbose && (holes > 0)) {
- printf(" Marking holes for elimination.\n");
- }
- }
-
- if (regions > 0) {
- /* Allocate storage for the triangles in which region points fall. */
- regiontris = (struct otri *) trimalloc(regions *
- (int) sizeof(struct otri));
- } else {
- regiontris = (struct otri *) NULL;
- }
-
- if (((holes > 0) && !b->noholes) || !b->convex || (regions > 0)) {
- /* Initialize a pool of viri to be used for holes, concavities, */
- /* regional attributes, and/or regional area constraints. */
- poolinit(&m->viri, sizeof(triangle *), VIRUSPERBLOCK, VIRUSPERBLOCK, 0);
- }
-
- if (!b->convex) {
- /* Mark as infected any unprotected triangles on the boundary. */
- /* This is one way by which concavities are created. */
- infecthull(m, b);
- }
-
- if ((holes > 0) && !b->noholes) {
- /* Infect each triangle in which a hole lies. */
- for (i = 0; i < 2 * holes; i += 2) {
- /* Ignore holes that aren't within the bounds of the mesh. */
- if ((holelist[i] >= m->xmin) && (holelist[i] <= m->xmax)
- && (holelist[i + 1] >= m->ymin) && (holelist[i + 1] <= m->ymax)) {
- /* Start searching from some triangle on the outer boundary. */
- searchtri.tri = m->dummytri;
- searchtri.orient = 0;
- symself(searchtri);
- /* Ensure that the hole is to the left of this boundary edge; */
- /* otherwise, locate() will falsely report that the hole */
- /* falls within the starting triangle. */
- org(searchtri, searchorg);
- dest(searchtri, searchdest);
- if (counterclockwise(m, b, searchorg, searchdest, &holelist[i]) >
- 0.0) {
- /* Find a triangle that contains the hole. */
- intersect = locate(m, b, &holelist[i], &searchtri);
- if ((intersect != OUTSIDE) && (!infected(searchtri))) {
- /* Infect the triangle. This is done by marking the triangle */
- /* as infected and including the triangle in the virus pool. */
- infect(searchtri);
- holetri = (triangle **) poolalloc(&m->viri);
- *holetri = searchtri.tri;
- }
- }
- }
- }
- }
-
- /* Now, we have to find all the regions BEFORE we carve the holes, because */
- /* locate() won't work when the triangulation is no longer convex. */
- /* (Incidentally, this is the reason why regional attributes and area */
- /* constraints can't be used when refining a preexisting mesh, which */
- /* might not be convex; they can only be used with a freshly */
- /* triangulated PSLG.) */
- if (regions > 0) {
- /* Find the starting triangle for each region. */
- for (i = 0; i < regions; i++) {
- regiontris[i].tri = m->dummytri;
- /* Ignore region points that aren't within the bounds of the mesh. */
- if ((regionlist[4 * i] >= m->xmin) && (regionlist[4 * i] <= m->xmax) &&
- (regionlist[4 * i + 1] >= m->ymin) &&
- (regionlist[4 * i + 1] <= m->ymax)) {
- /* Start searching from some triangle on the outer boundary. */
- searchtri.tri = m->dummytri;
- searchtri.orient = 0;
- symself(searchtri);
- /* Ensure that the region point is to the left of this boundary */
- /* edge; otherwise, locate() will falsely report that the */
- /* region point falls within the starting triangle. */
- org(searchtri, searchorg);
- dest(searchtri, searchdest);
- if (counterclockwise(m, b, searchorg, searchdest, ®ionlist[4 * i]) >
- 0.0) {
- /* Find a triangle that contains the region point. */
- intersect = locate(m, b, ®ionlist[4 * i], &searchtri);
- if ((intersect != OUTSIDE) && (!infected(searchtri))) {
- /* Record the triangle for processing after the */
- /* holes have been carved. */
- otricopy(searchtri, regiontris[i]);
- }
- }
- }
- }
- }
-
- if (m->viri.items > 0) {
- /* Carve the holes and concavities. */
- plague(m, b);
- }
- /* The virus pool should be empty now. */
-
- if (regions > 0) {
- if (!b->quiet) {
- if (b->regionattrib) {
- if (b->vararea) {
- printf("Spreading regional attributes and area constraints.\n");
- } else {
- printf("Spreading regional attributes.\n");
- }
- } else {
- printf("Spreading regional area constraints.\n");
- }
- }
- if (b->regionattrib && !b->refine) {
- /* Assign every triangle a regional attribute of zero. */
- traversalinit(&m->triangles);
- triangleloop.orient = 0;
- triangleloop.tri = triangletraverse(m);
- while (triangleloop.tri != (triangle *) NULL) {
- setelemattribute(triangleloop, m->eextras, 0.0);
- triangleloop.tri = triangletraverse(m);
- }
- }
- for (i = 0; i < regions; i++) {
- if (regiontris[i].tri != m->dummytri) {
- /* Make sure the triangle under consideration still exists. */
- /* It may have been eaten by the virus. */
- if (!deadtri(regiontris[i].tri)) {
- /* Put one triangle in the virus pool. */
- infect(regiontris[i]);
- regiontri = (triangle **) poolalloc(&m->viri);
- *regiontri = regiontris[i].tri;
- /* Apply one region's attribute and/or area constraint. */
- regionplague(m, b, regionlist[4 * i + 2], regionlist[4 * i + 3]);
- /* The virus pool should be empty now. */
- }
- }
- }
- if (b->regionattrib && !b->refine) {
- /* Note the fact that each triangle has an additional attribute. */
- m->eextras++;
- }
- }
-
- /* Free up memory. */
- if (((holes > 0) && !b->noholes) || !b->convex || (regions > 0)) {
- pooldeinit(&m->viri);
- }
- if (regions > 0) {
- trifree((VOID *) regiontris);
- }
-}
-
-/** **/
-/** **/
-/********* Carving out holes and concavities ends here *********/
-
-/********* Mesh quality maintenance begins here *********/
-/** **/
-/** **/
-
-/*****************************************************************************/
-/* */
-/* tallyencs() Traverse the entire list of subsegments, and check each */
-/* to see if it is encroached. If so, add it to the list. */
-/* */
-/*****************************************************************************/
-
-#ifndef CDT_ONLY
-
-#ifdef ANSI_DECLARATORS
-void tallyencs(struct mesh *m, struct behavior *b)
-#else /* not ANSI_DECLARATORS */
-void tallyencs(m, b)
-struct mesh *m;
-struct behavior *b;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct osub subsegloop;
- int dummy;
-
- traversalinit(&m->subsegs);
- subsegloop.ssorient = 0;
- subsegloop.ss = subsegtraverse(m);
- while (subsegloop.ss != (subseg *) NULL) {
- /* If the segment is encroached, add it to the list. */
- dummy = checkseg4encroach(m, b, &subsegloop);
- subsegloop.ss = subsegtraverse(m);
- }
-}
-
-#endif /* not CDT_ONLY */
-
-/*****************************************************************************/
-/* */
-/* precisionerror() Print an error message for precision problems. */
-/* */
-/*****************************************************************************/
-
-#ifndef CDT_ONLY
-
-void precisionerror()
-{
- printf("Try increasing the area criterion and/or reducing the minimum\n");
- printf(" allowable angle so that tiny triangles are not created.\n");
-#ifdef SINGLE
- printf("Alternatively, try recompiling me with double precision\n");
- printf(" arithmetic (by removing \"#define SINGLE\" from the\n");
- printf(" source file or \"-DSINGLE\" from the makefile).\n");
-#endif /* SINGLE */
-}
-
-#endif /* not CDT_ONLY */
-
-/*****************************************************************************/
-/* */
-/* splitencsegs() Split all the encroached subsegments. */
-/* */
-/* Each encroached subsegment is repaired by splitting it - inserting a */
-/* vertex at or near its midpoint. Newly inserted vertices may encroach */
-/* upon other subsegments; these are also repaired. */
-/* */
-/* `triflaws' is a flag that specifies whether one should take note of new */
-/* bad triangles that result from inserting vertices to repair encroached */
-/* subsegments. */
-/* */
-/*****************************************************************************/
-
-#ifndef CDT_ONLY
-
-#ifdef ANSI_DECLARATORS
-void splitencsegs(struct mesh *m, struct behavior *b, int triflaws)
-#else /* not ANSI_DECLARATORS */
-void splitencsegs(m, b, triflaws)
-struct mesh *m;
-struct behavior *b;
-int triflaws;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct otri enctri;
- struct otri testtri;
- struct osub testsh;
- struct osub currentenc;
- struct badsubseg *encloop;
- vertex eorg, edest, eapex;
- vertex newvertex;
- enum insertvertexresult success;
- REAL segmentlength, nearestpoweroftwo;
- REAL split;
- REAL multiplier, divisor;
- int acuteorg, acuteorg2, acutedest, acutedest2;
- int dummy;
- int i;
- triangle ptr; /* Temporary variable used by stpivot(). */
- subseg sptr; /* Temporary variable used by snext(). */
-
- /* Note that steinerleft == -1 if an unlimited number */
- /* of Steiner points is allowed. */
- while ((m->badsubsegs.items > 0) && (m->steinerleft != 0)) {
- traversalinit(&m->badsubsegs);
- encloop = badsubsegtraverse(m);
- while ((encloop != (struct badsubseg *) NULL) && (m->steinerleft != 0)) {
- sdecode(encloop->encsubseg, currentenc);
- sorg(currentenc, eorg);
- sdest(currentenc, edest);
- /* Make sure that this segment is still the same segment it was */
- /* when it was determined to be encroached. If the segment was */
- /* enqueued multiple times (because several newly inserted */
- /* vertices encroached it), it may have already been split. */
- if (!deadsubseg(currentenc.ss) &&
- (eorg == encloop->subsegorg) && (edest == encloop->subsegdest)) {
- /* To decide where to split a segment, we need to know if the */
- /* segment shares an endpoint with an adjacent segment. */
- /* The concern is that, if we simply split every encroached */
- /* segment in its center, two adjacent segments with a small */
- /* angle between them might lead to an infinite loop; each */
- /* vertex added to split one segment will encroach upon the */
- /* other segment, which must then be split with a vertex that */
- /* will encroach upon the first segment, and so on forever. */
- /* To avoid this, imagine a set of concentric circles, whose */
- /* radii are powers of two, about each segment endpoint. */
- /* These concentric circles determine where the segment is */
- /* split. (If both endpoints are shared with adjacent */
- /* segments, split the segment in the middle, and apply the */
- /* concentric circles for later splittings.) */
-
- /* Is the origin shared with another segment? */
- stpivot(currentenc, enctri);
- lnext(enctri, testtri);
- tspivot(testtri, testsh);
- acuteorg = testsh.ss != m->dummysub;
- /* Is the destination shared with another segment? */
- lnextself(testtri);
- tspivot(testtri, testsh);
- acutedest = testsh.ss != m->dummysub;
-
- /* If we're using Chew's algorithm (rather than Ruppert's) */
- /* to define encroachment, delete free vertices from the */
- /* subsegment's diametral circle. */
- if (!b->conformdel && !acuteorg && !acutedest) {
- apex(enctri, eapex);
- while ((vertextype(eapex) == FREEVERTEX) &&
- ((eorg[0] - eapex[0]) * (edest[0] - eapex[0]) +
- (eorg[1] - eapex[1]) * (edest[1] - eapex[1]) < 0.0)) {
- deletevertex(m, b, &testtri);
- stpivot(currentenc, enctri);
- apex(enctri, eapex);
- lprev(enctri, testtri);
- }
- }
-
- /* Now, check the other side of the segment, if there's a triangle */
- /* there. */
- sym(enctri, testtri);
- if (testtri.tri != m->dummytri) {
- /* Is the destination shared with another segment? */
- lnextself(testtri);
- tspivot(testtri, testsh);
- acutedest2 = testsh.ss != m->dummysub;
- acutedest = acutedest || acutedest2;
- /* Is the origin shared with another segment? */
- lnextself(testtri);
- tspivot(testtri, testsh);
- acuteorg2 = testsh.ss != m->dummysub;
- acuteorg = acuteorg || acuteorg2;
-
- /* Delete free vertices from the subsegment's diametral circle. */
- if (!b->conformdel && !acuteorg2 && !acutedest2) {
- org(testtri, eapex);
- while ((vertextype(eapex) == FREEVERTEX) &&
- ((eorg[0] - eapex[0]) * (edest[0] - eapex[0]) +
- (eorg[1] - eapex[1]) * (edest[1] - eapex[1]) < 0.0)) {
- deletevertex(m, b, &testtri);
- sym(enctri, testtri);
- apex(testtri, eapex);
- lprevself(testtri);
- }
- }
- }
-
- /* Use the concentric circles if exactly one endpoint is shared */
- /* with another adjacent segment. */
- if (acuteorg || acutedest) {
- segmentlength = sqrt((edest[0] - eorg[0]) * (edest[0] - eorg[0]) +
- (edest[1] - eorg[1]) * (edest[1] - eorg[1]));
- /* Find the power of two that most evenly splits the segment. */
- /* The worst case is a 2:1 ratio between subsegment lengths. */
- nearestpoweroftwo = 1.0;
- while (segmentlength > 3.0 * nearestpoweroftwo) {
- nearestpoweroftwo *= 2.0;
- }
- while (segmentlength < 1.5 * nearestpoweroftwo) {
- nearestpoweroftwo *= 0.5;
- }
- /* Where do we split the segment? */
- split = nearestpoweroftwo / segmentlength;
- if (acutedest) {
- split = 1.0 - split;
- }
- } else {
- /* If we're not worried about adjacent segments, split */
- /* this segment in the middle. */
- split = 0.5;
- }
-
- /* Create the new vertex. */
- newvertex = (vertex) poolalloc(&m->vertices);
- /* Interpolate its coordinate and attributes. */
- for (i = 0; i < 2 + m->nextras; i++) {
- newvertex[i] = eorg[i] + split * (edest[i] - eorg[i]);
- }
-
- if (!b->noexact) {
- /* Roundoff in the above calculation may yield a `newvertex' */
- /* that is not precisely collinear with `eorg' and `edest'. */
- /* Improve collinearity by one step of iterative refinement. */
- multiplier = counterclockwise(m, b, eorg, edest, newvertex);
- divisor = ((eorg[0] - edest[0]) * (eorg[0] - edest[0]) +
- (eorg[1] - edest[1]) * (eorg[1] - edest[1]));
- if ((multiplier != 0.0) && (divisor != 0.0)) {
- multiplier = multiplier / divisor;
- /* Watch out for NANs. */
- if (multiplier == multiplier) {
- newvertex[0] += multiplier * (edest[1] - eorg[1]);
- newvertex[1] += multiplier * (eorg[0] - edest[0]);
- }
- }
- }
-
- setvertexmark(newvertex, mark(currentenc));
- setvertextype(newvertex, SEGMENTVERTEX);
- if (b->verbose > 1) {
- printf(
- " Splitting subsegment (%.12g, %.12g) (%.12g, %.12g) at (%.12g, %.12g).\n",
- eorg[0], eorg[1], edest[0], edest[1],
- newvertex[0], newvertex[1]);
- }
- /* Check whether the new vertex lies on an endpoint. */
- if (((newvertex[0] == eorg[0]) && (newvertex[1] == eorg[1])) ||
- ((newvertex[0] == edest[0]) && (newvertex[1] == edest[1]))) {
- printf("Error: Ran out of precision at (%.12g, %.12g).\n",
- newvertex[0], newvertex[1]);
- printf("I attempted to split a segment to a smaller size than\n");
- printf(" can be accommodated by the finite precision of\n");
- printf(" floating point arithmetic.\n");
- precisionerror();
- triexit(1);
- }
- /* Insert the splitting vertex. This should always succeed. */
- success = insertvertex(m, b, newvertex, &enctri, ¤tenc,
- 1, triflaws);
- if ((success != SUCCESSFULVERTEX) && (success != ENCROACHINGVERTEX)) {
- printf("Internal error in splitencsegs():\n");
- printf(" Failure to split a segment.\n");
- internalerror();
- }
- if (m->steinerleft > 0) {
- m->steinerleft--;
- }
- /* Check the two new subsegments to see if they're encroached. */
- dummy = checkseg4encroach(m, b, ¤tenc);
- snextself(currentenc);
- dummy = checkseg4encroach(m, b, ¤tenc);
- }
-
- badsubsegdealloc(m, encloop);
- encloop = badsubsegtraverse(m);
- }
- }
-}
-
-#endif /* not CDT_ONLY */
-
-/*****************************************************************************/
-/* */
-/* tallyfaces() Test every triangle in the mesh for quality measures. */
-/* */
-/*****************************************************************************/
-
-#ifndef CDT_ONLY
-
-#ifdef ANSI_DECLARATORS
-void tallyfaces(struct mesh *m, struct behavior *b)
-#else /* not ANSI_DECLARATORS */
-void tallyfaces(m, b)
-struct mesh *m;
-struct behavior *b;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct otri triangleloop;
-
- if (b->verbose) {
- printf(" Making a list of bad triangles.\n");
- }
- traversalinit(&m->triangles);
- triangleloop.orient = 0;
- triangleloop.tri = triangletraverse(m);
- while (triangleloop.tri != (triangle *) NULL) {
- /* If the triangle is bad, enqueue it. */
- testtriangle(m, b, &triangleloop);
- triangleloop.tri = triangletraverse(m);
- }
-}
-
-#endif /* not CDT_ONLY */
-
-/*****************************************************************************/
-/* */
-/* splittriangle() Inserts a vertex at the circumcenter of a triangle. */
-/* Deletes the newly inserted vertex if it encroaches */
-/* upon a segment. */
-/* */
-/*****************************************************************************/
-
-#ifndef CDT_ONLY
-
-#ifdef ANSI_DECLARATORS
-void splittriangle(struct mesh *m, struct behavior *b,
- struct badtriang *badtri)
-#else /* not ANSI_DECLARATORS */
-void splittriangle(m, b, badtri)
-struct mesh *m;
-struct behavior *b;
-struct badtriang *badtri;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct otri badotri;
- vertex borg, bdest, bapex;
- vertex newvertex;
- REAL xi, eta;
- enum insertvertexresult success;
- int errorflag;
- int i;
-
- decode(badtri->poortri, badotri);
- org(badotri, borg);
- dest(badotri, bdest);
- apex(badotri, bapex);
- /* Make sure that this triangle is still the same triangle it was */
- /* when it was tested and determined to be of bad quality. */
- /* Subsequent transformations may have made it a different triangle. */
- if (!deadtri(badotri.tri) && (borg == badtri->triangorg) &&
- (bdest == badtri->triangdest) && (bapex == badtri->triangapex)) {
- if (b->verbose > 1) {
- printf(" Splitting this triangle at its circumcenter:\n");
- printf(" (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", borg[0],
- borg[1], bdest[0], bdest[1], bapex[0], bapex[1]);
- }
-
- errorflag = 0;
- /* Create a new vertex at the triangle's circumcenter. */
- newvertex = (vertex) poolalloc(&m->vertices);
- findcircumcenter(m, b, borg, bdest, bapex, newvertex, &xi, &eta, 1);
-
- /* Check whether the new vertex lies on a triangle vertex. */
- if (((newvertex[0] == borg[0]) && (newvertex[1] == borg[1])) ||
- ((newvertex[0] == bdest[0]) && (newvertex[1] == bdest[1])) ||
- ((newvertex[0] == bapex[0]) && (newvertex[1] == bapex[1]))) {
- if (!b->quiet) {
- printf(
- "Warning: New vertex (%.12g, %.12g) falls on existing vertex.\n",
- newvertex[0], newvertex[1]);
- errorflag = 1;
- }
- vertexdealloc(m, newvertex);
- } else {
- for (i = 2; i < 2 + m->nextras; i++) {
- /* Interpolate the vertex attributes at the circumcenter. */
- newvertex[i] = borg[i] + xi * (bdest[i] - borg[i])
- + eta * (bapex[i] - borg[i]);
- }
- /* The new vertex must be in the interior, and therefore is a */
- /* free vertex with a marker of zero. */
- setvertexmark(newvertex, 0);
- setvertextype(newvertex, FREEVERTEX);
-
- /* Ensure that the handle `badotri' does not represent the longest */
- /* edge of the triangle. This ensures that the circumcenter must */
- /* fall to the left of this edge, so point location will work. */
- /* (If the angle org-apex-dest exceeds 90 degrees, then the */
- /* circumcenter lies outside the org-dest edge, and eta is */
- /* negative. Roundoff error might prevent eta from being */
- /* negative when it should be, so I test eta against xi.) */
- if (eta < xi) {
- lprevself(badotri);
- }
-
- /* Insert the circumcenter, searching from the edge of the triangle, */
- /* and maintain the Delaunay property of the triangulation. */
- success = insertvertex(m, b, newvertex, &badotri, (struct osub *) NULL,
- 1, 1);
- if (success == SUCCESSFULVERTEX) {
- if (m->steinerleft > 0) {
- m->steinerleft--;
- }
- } else if (success == ENCROACHINGVERTEX) {
- /* If the newly inserted vertex encroaches upon a subsegment, */
- /* delete the new vertex. */
- undovertex(m, b);
- if (b->verbose > 1) {
- printf(" Rejecting (%.12g, %.12g).\n", newvertex[0], newvertex[1]);
- }
- vertexdealloc(m, newvertex);
- } else if (success == VIOLATINGVERTEX) {
- /* Failed to insert the new vertex, but some subsegment was */
- /* marked as being encroached. */
- vertexdealloc(m, newvertex);
- } else { /* success == DUPLICATEVERTEX */
- /* Couldn't insert the new vertex because a vertex is already there. */
- if (!b->quiet) {
- printf(
- "Warning: New vertex (%.12g, %.12g) falls on existing vertex.\n",
- newvertex[0], newvertex[1]);
- errorflag = 1;
- }
- vertexdealloc(m, newvertex);
- }
- }
- if (errorflag) {
- if (b->verbose) {
- printf(" The new vertex is at the circumcenter of triangle\n");
- printf(" (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
- borg[0], borg[1], bdest[0], bdest[1], bapex[0], bapex[1]);
- }
- printf("This probably means that I am trying to refine triangles\n");
- printf(" to a smaller size than can be accommodated by the finite\n");
- printf(" precision of floating point arithmetic. (You can be\n");
- printf(" sure of this if I fail to terminate.)\n");
- precisionerror();
- }
- }
-}
-
-#endif /* not CDT_ONLY */
-
-/*****************************************************************************/
-/* */
-/* enforcequality() Remove all the encroached subsegments and bad */
-/* triangles from the triangulation. */
-/* */
-/*****************************************************************************/
-
-#ifndef CDT_ONLY
-
-#ifdef ANSI_DECLARATORS
-void enforcequality(struct mesh *m, struct behavior *b)
-#else /* not ANSI_DECLARATORS */
-void enforcequality(m, b)
-struct mesh *m;
-struct behavior *b;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct badtriang *badtri;
- int i;
-
- if (!b->quiet) {
- printf("Adding Steiner points to enforce quality.\n");
- }
- /* Initialize the pool of encroached subsegments. */
- poolinit(&m->badsubsegs, sizeof(struct badsubseg), BADSUBSEGPERBLOCK,
- BADSUBSEGPERBLOCK, 0);
- if (b->verbose) {
- printf(" Looking for encroached subsegments.\n");
- }
- /* Test all segments to see if they're encroached. */
- tallyencs(m, b);
- if (b->verbose && (m->badsubsegs.items > 0)) {
- printf(" Splitting encroached subsegments.\n");
- }
- /* Fix encroached subsegments without noting bad triangles. */
- splitencsegs(m, b, 0);
- /* At this point, if we haven't run out of Steiner points, the */
- /* triangulation should be (conforming) Delaunay. */
-
- /* Next, we worry about enforcing triangle quality. */
- if ((b->minangle > 0.0) || b->vararea || b->fixedarea || b->usertest) {
- /* Initialize the pool of bad triangles. */
- poolinit(&m->badtriangles, sizeof(struct badtriang), BADTRIPERBLOCK,
- BADTRIPERBLOCK, 0);
- /* Initialize the queues of bad triangles. */
- for (i = 0; i < 4096; i++) {
- m->queuefront[i] = (struct badtriang *) NULL;
- }
- m->firstnonemptyq = -1;
- /* Test all triangles to see if they're bad. */
- tallyfaces(m, b);
- /* Initialize the pool of recently flipped triangles. */
- poolinit(&m->flipstackers, sizeof(struct flipstacker), FLIPSTACKERPERBLOCK,
- FLIPSTACKERPERBLOCK, 0);
- m->checkquality = 1;
- if (b->verbose) {
- printf(" Splitting bad triangles.\n");
- }
- while ((m->badtriangles.items > 0) && (m->steinerleft != 0)) {
- /* Fix one bad triangle by inserting a vertex at its circumcenter. */
- badtri = dequeuebadtriang(m);
- splittriangle(m, b, badtri);
- if (m->badsubsegs.items > 0) {
- /* Put bad triangle back in queue for another try later. */
- enqueuebadtriang(m, b, badtri);
- /* Fix any encroached subsegments that resulted. */
- /* Record any new bad triangles that result. */
- splitencsegs(m, b, 1);
- } else {
- /* Return the bad triangle to the pool. */
- pooldealloc(&m->badtriangles, (VOID *) badtri);
- }
- }
- }
- /* At this point, if the "-D" switch was selected and we haven't run out */
- /* of Steiner points, the triangulation should be (conforming) Delaunay */
- /* and have no low-quality triangles. */
-
- /* Might we have run out of Steiner points too soon? */
- if (!b->quiet && b->conformdel && (m->badsubsegs.items > 0) &&
- (m->steinerleft == 0)) {
- printf("\nWarning: I ran out of Steiner points, but the mesh has\n");
- if (m->badsubsegs.items == 1) {
- printf(" one encroached subsegment, and therefore might not be truly\n"
- );
- } else {
- printf(" %ld encroached subsegments, and therefore might not be truly\n"
- , m->badsubsegs.items);
- }
- printf(" Delaunay. If the Delaunay property is important to you,\n");
- printf(" try increasing the number of Steiner points (controlled by\n");
- printf(" the -S switch) slightly and try again.\n\n");
- }
-}
-
-#endif /* not CDT_ONLY */
-
-/** **/
-/** **/
-/********* Mesh quality maintenance ends here *********/
-
-/*****************************************************************************/
-/* */
-/* highorder() Create extra nodes for quadratic subparametric elements. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-void highorder(struct mesh *m, struct behavior *b)
-#else /* not ANSI_DECLARATORS */
-void highorder(m, b)
-struct mesh *m;
-struct behavior *b;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct otri triangleloop, trisym;
- struct osub checkmark;
- vertex newvertex;
- vertex torg, tdest;
- int i;
- triangle ptr; /* Temporary variable used by sym(). */
- subseg sptr; /* Temporary variable used by tspivot(). */
-
- if (!b->quiet) {
- printf("Adding vertices for second-order triangles.\n");
- }
- /* The following line ensures that dead items in the pool of nodes */
- /* cannot be allocated for the extra nodes associated with high */
- /* order elements. This ensures that the primary nodes (at the */
- /* corners of elements) will occur earlier in the output files, and */
- /* have lower indices, than the extra nodes. */
- m->vertices.deaditemstack = (VOID *) NULL;
-
- traversalinit(&m->triangles);
- triangleloop.tri = triangletraverse(m);
- /* To loop over the set of edges, loop over all triangles, and look at */
- /* the three edges of each triangle. If there isn't another triangle */
- /* adjacent to the edge, operate on the edge. If there is another */
- /* adjacent triangle, operate on the edge only if the current triangle */
- /* has a smaller pointer than its neighbor. This way, each edge is */
- /* considered only once. */
- while (triangleloop.tri != (triangle *) NULL) {
- for (triangleloop.orient = 0; triangleloop.orient < 3;
- triangleloop.orient++) {
- sym(triangleloop, trisym);
- if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) {
- org(triangleloop, torg);
- dest(triangleloop, tdest);
- /* Create a new node in the middle of the edge. Interpolate */
- /* its attributes. */
- newvertex = (vertex) poolalloc(&m->vertices);
- for (i = 0; i < 2 + m->nextras; i++) {
- newvertex[i] = 0.5 * (torg[i] + tdest[i]);
- }
- /* Set the new node's marker to zero or one, depending on */
- /* whether it lies on a boundary. */
- setvertexmark(newvertex, trisym.tri == m->dummytri);
- setvertextype(newvertex,
- trisym.tri == m->dummytri ? FREEVERTEX : SEGMENTVERTEX);
- if (b->usesegments) {
- tspivot(triangleloop, checkmark);
- /* If this edge is a segment, transfer the marker to the new node. */
- if (checkmark.ss != m->dummysub) {
- setvertexmark(newvertex, mark(checkmark));
- setvertextype(newvertex, SEGMENTVERTEX);
- }
- }
- if (b->verbose > 1) {
- printf(" Creating (%.12g, %.12g).\n", newvertex[0], newvertex[1]);
- }
- /* Record the new node in the (one or two) adjacent elements. */
- triangleloop.tri[m->highorderindex + triangleloop.orient] =
- (triangle) newvertex;
- if (trisym.tri != m->dummytri) {
- trisym.tri[m->highorderindex + trisym.orient] = (triangle) newvertex;
- }
- }
- }
- triangleloop.tri = triangletraverse(m);
- }
-}
-
-/********* File I/O routines begin here *********/
-/** **/
-/** **/
-
-/*****************************************************************************/
-/* */
-/* readline() Read a nonempty line from a file. */
-/* */
-/* A line is considered "nonempty" if it contains something that looks like */
-/* a number. Comments (prefaced by `#') are ignored. */
-/* */
-/*****************************************************************************/
-
-#ifndef TRILIBRARY
-
-#ifdef ANSI_DECLARATORS
-char *readline(char *string, FILE *infile, char *infilename)
-#else /* not ANSI_DECLARATORS */
-char *readline(string, infile, infilename)
-char *string;
-FILE *infile;
-char *infilename;
-#endif /* not ANSI_DECLARATORS */
-
-{
- char *result;
-
- /* Search for something that looks like a number. */
- do {
- result = fgets(string, INPUTLINESIZE, infile);
- if (result == (char *) NULL) {
- printf(" Error: Unexpected end of file in %s.\n", infilename);
- triexit(1);
- }
- /* Skip anything that doesn't look like a number, a comment, */
- /* or the end of a line. */
- while ((*result != '\0') && (*result != '#')
- && (*result != '.') && (*result != '+') && (*result != '-')
- && ((*result < '0') || (*result > '9'))) {
- result++;
- }
- /* If it's a comment or end of line, read another line and try again. */
- } while ((*result == '#') || (*result == '\0'));
- return result;
-}
-
-#endif /* not TRILIBRARY */
-
-/*****************************************************************************/
-/* */
-/* findfield() Find the next field of a string. */
-/* */
-/* Jumps past the current field by searching for whitespace, then jumps */
-/* past the whitespace to find the next field. */
-/* */
-/*****************************************************************************/
-
-#ifndef TRILIBRARY
-
-#ifdef ANSI_DECLARATORS
-char *findfield(char *string)
-#else /* not ANSI_DECLARATORS */
-char *findfield(string)
-char *string;
-#endif /* not ANSI_DECLARATORS */
-
-{
- char *result;
-
- result = string;
- /* Skip the current field. Stop upon reaching whitespace. */
- while ((*result != '\0') && (*result != '#')
- && (*result != ' ') && (*result != '\t')) {
- result++;
- }
- /* Now skip the whitespace and anything else that doesn't look like a */
- /* number, a comment, or the end of a line. */
- while ((*result != '\0') && (*result != '#')
- && (*result != '.') && (*result != '+') && (*result != '-')
- && ((*result < '0') || (*result > '9'))) {
- result++;
- }
- /* Check for a comment (prefixed with `#'). */
- if (*result == '#') {
- *result = '\0';
- }
- return result;
-}
-
-#endif /* not TRILIBRARY */
-
-/*****************************************************************************/
-/* */
-/* readnodes() Read the vertices from a file, which may be a .node or */
-/* .poly file. */
-/* */
-/*****************************************************************************/
-
-#ifndef TRILIBRARY
-
-#ifdef ANSI_DECLARATORS
-void readnodes(struct mesh *m, struct behavior *b, char *nodefilename,
- char *polyfilename, FILE **polyfile)
-#else /* not ANSI_DECLARATORS */
-void readnodes(m, b, nodefilename, polyfilename, polyfile)
-struct mesh *m;
-struct behavior *b;
-char *nodefilename;
-char *polyfilename;
-FILE **polyfile;
-#endif /* not ANSI_DECLARATORS */
-
-{
- FILE *infile;
- vertex vertexloop;
- char inputline[INPUTLINESIZE];
- char *stringptr;
- char *infilename;
- REAL x, y;
- int firstnode;
- int nodemarkers;
- int currentmarker;
- int i, j;
-
- if (b->poly) {
- /* Read the vertices from a .poly file. */
- if (!b->quiet) {
- printf("Opening %s.\n", polyfilename);
- }
- *polyfile = fopen(polyfilename, "r");
- if (*polyfile == (FILE *) NULL) {
- printf(" Error: Cannot access file %s.\n", polyfilename);
- triexit(1);
- }
- /* Read number of vertices, number of dimensions, number of vertex */
- /* attributes, and number of boundary markers. */
- stringptr = readline(inputline, *polyfile, polyfilename);
- m->invertices = (int) strtol(stringptr, &stringptr, 0);
- stringptr = findfield(stringptr);
- if (*stringptr == '\0') {
- m->mesh_dim = 2;
- } else {
- m->mesh_dim = (int) strtol(stringptr, &stringptr, 0);
- }
- stringptr = findfield(stringptr);
- if (*stringptr == '\0') {
- m->nextras = 0;
- } else {
- m->nextras = (int) strtol(stringptr, &stringptr, 0);
- }
- stringptr = findfield(stringptr);
- if (*stringptr == '\0') {
- nodemarkers = 0;
- } else {
- nodemarkers = (int) strtol(stringptr, &stringptr, 0);
- }
- if (m->invertices > 0) {
- infile = *polyfile;
- infilename = polyfilename;
- m->readnodefile = 0;
- } else {
- /* If the .poly file claims there are zero vertices, that means that */
- /* the vertices should be read from a separate .node file. */
- m->readnodefile = 1;
- infilename = nodefilename;
- }
- } else {
- m->readnodefile = 1;
- infilename = nodefilename;
- *polyfile = (FILE *) NULL;
- }
-
- if (m->readnodefile) {
- /* Read the vertices from a .node file. */
- if (!b->quiet) {
- printf("Opening %s.\n", nodefilename);
- }
- infile = fopen(nodefilename, "r");
- if (infile == (FILE *) NULL) {
- printf(" Error: Cannot access file %s.\n", nodefilename);
- triexit(1);
- }
- /* Read number of vertices, number of dimensions, number of vertex */
- /* attributes, and number of boundary markers. */
- stringptr = readline(inputline, infile, nodefilename);
- m->invertices = (int) strtol(stringptr, &stringptr, 0);
- stringptr = findfield(stringptr);
- if (*stringptr == '\0') {
- m->mesh_dim = 2;
- } else {
- m->mesh_dim = (int) strtol(stringptr, &stringptr, 0);
- }
- stringptr = findfield(stringptr);
- if (*stringptr == '\0') {
- m->nextras = 0;
- } else {
- m->nextras = (int) strtol(stringptr, &stringptr, 0);
- }
- stringptr = findfield(stringptr);
- if (*stringptr == '\0') {
- nodemarkers = 0;
- } else {
- nodemarkers = (int) strtol(stringptr, &stringptr, 0);
- }
- }
-
- if (m->invertices < 3) {
- printf("Error: Input must have at least three input vertices.\n");
- triexit(1);
- }
- if (m->mesh_dim != 2) {
- printf("Error: Triangle only works with two-dimensional meshes.\n");
- triexit(1);
- }
- if (m->nextras == 0) {
- b->weighted = 0;
- }
-
- initializevertexpool(m, b);
-
- /* Read the vertices. */
- for (i = 0; i < m->invertices; i++) {
- vertexloop = (vertex) poolalloc(&m->vertices);
- stringptr = readline(inputline, infile, infilename);
- if (i == 0) {
- firstnode = (int) strtol(stringptr, &stringptr, 0);
- if ((firstnode == 0) || (firstnode == 1)) {
- b->firstnumber = firstnode;
- }
- }
- stringptr = findfield(stringptr);
- if (*stringptr == '\0') {
- printf("Error: Vertex %d has no x coordinate.\n", b->firstnumber + i);
- triexit(1);
- }
- x = (REAL) strtod(stringptr, &stringptr);
- stringptr = findfield(stringptr);
- if (*stringptr == '\0') {
- printf("Error: Vertex %d has no y coordinate.\n", b->firstnumber + i);
- triexit(1);
- }
- y = (REAL) strtod(stringptr, &stringptr);
- vertexloop[0] = x;
- vertexloop[1] = y;
- /* Read the vertex attributes. */
- for (j = 2; j < 2 + m->nextras; j++) {
- stringptr = findfield(stringptr);
- if (*stringptr == '\0') {
- vertexloop[j] = 0.0;
- } else {
- vertexloop[j] = (REAL) strtod(stringptr, &stringptr);
- }
- }
- if (nodemarkers) {
- /* Read a vertex marker. */
- stringptr = findfield(stringptr);
- if (*stringptr == '\0') {
- setvertexmark(vertexloop, 0);
- } else {
- currentmarker = (int) strtol(stringptr, &stringptr, 0);
- setvertexmark(vertexloop, currentmarker);
- }
- } else {
- /* If no markers are specified in the file, they default to zero. */
- setvertexmark(vertexloop, 0);
- }
- setvertextype(vertexloop, INPUTVERTEX);
- /* Determine the smallest and largest x and y coordinates. */
- if (i == 0) {
- m->xmin = m->xmax = x;
- m->ymin = m->ymax = y;
- } else {
- m->xmin = (x < m->xmin) ? x : m->xmin;
- m->xmax = (x > m->xmax) ? x : m->xmax;
- m->ymin = (y < m->ymin) ? y : m->ymin;
- m->ymax = (y > m->ymax) ? y : m->ymax;
- }
- }
- if (m->readnodefile) {
- fclose(infile);
- }
-
- /* Nonexistent x value used as a flag to mark circle events in sweepline */
- /* Delaunay algorithm. */
- m->xminextreme = 10 * m->xmin - 9 * m->xmax;
-}
-
-#endif /* not TRILIBRARY */
-
-/*****************************************************************************/
-/* */
-/* transfernodes() Read the vertices from memory. */
-/* */
-/*****************************************************************************/
-
-#ifdef TRILIBRARY
-
-#ifdef ANSI_DECLARATORS
-void transfernodes(struct mesh *m, struct behavior *b, REAL *pointlist,
- REAL *pointattriblist, int *pointmarkerlist,
- int numberofpoints, int numberofpointattribs)
-#else /* not ANSI_DECLARATORS */
-void transfernodes(m, b, pointlist, pointattriblist, pointmarkerlist,
- numberofpoints, numberofpointattribs)
-struct mesh *m;
-struct behavior *b;
-REAL *pointlist;
-REAL *pointattriblist;
-int *pointmarkerlist;
-int numberofpoints;
-int numberofpointattribs;
-#endif /* not ANSI_DECLARATORS */
-
-{
- vertex vertexloop;
- REAL x, y;
- int i, j;
- int coordindex;
- int attribindex;
-
- m->invertices = numberofpoints;
- m->mesh_dim = 2;
- m->nextras = numberofpointattribs;
- m->readnodefile = 0;
- if (m->invertices < 3) {
- printf("Error: Input must have at least three input vertices.\n");
- triexit(1);
- }
- if (m->nextras == 0) {
- b->weighted = 0;
- }
-
- initializevertexpool(m, b);
-
- /* Read the vertices. */
- coordindex = 0;
- attribindex = 0;
- for (i = 0; i < m->invertices; i++) {
- vertexloop = (vertex) poolalloc(&m->vertices);
- /* Read the vertex coordinates. */
- x = vertexloop[0] = pointlist[coordindex++];
- y = vertexloop[1] = pointlist[coordindex++];
- /* Read the vertex attributes. */
- for (j = 0; j < numberofpointattribs; j++) {
- vertexloop[2 + j] = pointattriblist[attribindex++];
- }
- if (pointmarkerlist != (int *) NULL) {
- /* Read a vertex marker. */
- setvertexmark(vertexloop, pointmarkerlist[i]);
- } else {
- /* If no markers are specified, they default to zero. */
- setvertexmark(vertexloop, 0);
- }
- setvertextype(vertexloop, INPUTVERTEX);
- /* Determine the smallest and largest x and y coordinates. */
- if (i == 0) {
- m->xmin = m->xmax = x;
- m->ymin = m->ymax = y;
- } else {
- m->xmin = (x < m->xmin) ? x : m->xmin;
- m->xmax = (x > m->xmax) ? x : m->xmax;
- m->ymin = (y < m->ymin) ? y : m->ymin;
- m->ymax = (y > m->ymax) ? y : m->ymax;
- }
- }
-
- /* Nonexistent x value used as a flag to mark circle events in sweepline */
- /* Delaunay algorithm. */
- m->xminextreme = 10 * m->xmin - 9 * m->xmax;
-}
-
-#endif /* TRILIBRARY */
-
-/*****************************************************************************/
-/* */
-/* readholes() Read the holes, and possibly regional attributes and area */
-/* constraints, from a .poly file. */
-/* */
-/*****************************************************************************/
-
-#ifndef TRILIBRARY
-
-#ifdef ANSI_DECLARATORS
-void readholes(struct mesh *m, struct behavior *b,
- FILE *polyfile, char *polyfilename, REAL **hlist, int *holes,
- REAL **rlist, int *regions)
-#else /* not ANSI_DECLARATORS */
-void readholes(m, b, polyfile, polyfilename, hlist, holes, rlist, regions)
-struct mesh *m;
-struct behavior *b;
-FILE *polyfile;
-char *polyfilename;
-REAL **hlist;
-int *holes;
-REAL **rlist;
-int *regions;
-#endif /* not ANSI_DECLARATORS */
-
-{
- REAL *holelist;
- REAL *regionlist;
- char inputline[INPUTLINESIZE];
- char *stringptr;
- int index;
- int i;
-
- /* Read the holes. */
- stringptr = readline(inputline, polyfile, polyfilename);
- *holes = (int) strtol(stringptr, &stringptr, 0);
- if (*holes > 0) {
- holelist = (REAL *) trimalloc(2 * *holes * (int) sizeof(REAL));
- *hlist = holelist;
- for (i = 0; i < 2 * *holes; i += 2) {
- stringptr = readline(inputline, polyfile, polyfilename);
- stringptr = findfield(stringptr);
- if (*stringptr == '\0') {
- printf("Error: Hole %d has no x coordinate.\n",
- b->firstnumber + (i >> 1));
- triexit(1);
- } else {
- holelist[i] = (REAL) strtod(stringptr, &stringptr);
- }
- stringptr = findfield(stringptr);
- if (*stringptr == '\0') {
- printf("Error: Hole %d has no y coordinate.\n",
- b->firstnumber + (i >> 1));
- triexit(1);
- } else {
- holelist[i + 1] = (REAL) strtod(stringptr, &stringptr);
- }
- }
- } else {
- *hlist = (REAL *) NULL;
- }
-
-#ifndef CDT_ONLY
- if ((b->regionattrib || b->vararea) && !b->refine) {
- /* Read the area constraints. */
- stringptr = readline(inputline, polyfile, polyfilename);
- *regions = (int) strtol(stringptr, &stringptr, 0);
- if (*regions > 0) {
- regionlist = (REAL *) trimalloc(4 * *regions * (int) sizeof(REAL));
- *rlist = regionlist;
- index = 0;
- for (i = 0; i < *regions; i++) {
- stringptr = readline(inputline, polyfile, polyfilename);
- stringptr = findfield(stringptr);
- if (*stringptr == '\0') {
- printf("Error: Region %d has no x coordinate.\n",
- b->firstnumber + i);
- triexit(1);
- } else {
- regionlist[index++] = (REAL) strtod(stringptr, &stringptr);
- }
- stringptr = findfield(stringptr);
- if (*stringptr == '\0') {
- printf("Error: Region %d has no y coordinate.\n",
- b->firstnumber + i);
- triexit(1);
- } else {
- regionlist[index++] = (REAL) strtod(stringptr, &stringptr);
- }
- stringptr = findfield(stringptr);
- if (*stringptr == '\0') {
- printf(
- "Error: Region %d has no region attribute or area constraint.\n",
- b->firstnumber + i);
- triexit(1);
- } else {
- regionlist[index++] = (REAL) strtod(stringptr, &stringptr);
- }
- stringptr = findfield(stringptr);
- if (*stringptr == '\0') {
- regionlist[index] = regionlist[index - 1];
- } else {
- regionlist[index] = (REAL) strtod(stringptr, &stringptr);
- }
- index++;
- }
- }
- } else {
- /* Set `*regions' to zero to avoid an accidental free() later. */
- *regions = 0;
- *rlist = (REAL *) NULL;
- }
-#endif /* not CDT_ONLY */
-
- fclose(polyfile);
-}
-
-#endif /* not TRILIBRARY */
-
-/*****************************************************************************/
-/* */
-/* finishfile() Write the command line to the output file so the user */
-/* can remember how the file was generated. Close the file. */
-/* */
-/*****************************************************************************/
-
-#ifndef TRILIBRARY
-
-#ifdef ANSI_DECLARATORS
-void finishfile(FILE *outfile, int argc, char **argv)
-#else /* not ANSI_DECLARATORS */
-void finishfile(outfile, argc, argv)
-FILE *outfile;
-int argc;
-char **argv;
-#endif /* not ANSI_DECLARATORS */
-
-{
- int i;
-
- fprintf(outfile, "# Generated by");
- for (i = 0; i < argc; i++) {
- fprintf(outfile, " ");
- fputs(argv[i], outfile);
- }
- fprintf(outfile, "\n");
- fclose(outfile);
-}
-
-#endif /* not TRILIBRARY */
-
-/*****************************************************************************/
-/* */
-/* writenodes() Number the vertices and write them to a .node file. */
-/* */
-/* To save memory, the vertex numbers are written over the boundary markers */
-/* after the vertices are written to a file. */
-/* */
-/*****************************************************************************/
-
-#ifdef TRILIBRARY
-
-#ifdef ANSI_DECLARATORS
-void writenodes(struct mesh *m, struct behavior *b, REAL **pointlist,
- REAL **pointattriblist, int **pointmarkerlist)
-#else /* not ANSI_DECLARATORS */
-void writenodes(m, b, pointlist, pointattriblist, pointmarkerlist)
-struct mesh *m;
-struct behavior *b;
-REAL **pointlist;
-REAL **pointattriblist;
-int **pointmarkerlist;
-#endif /* not ANSI_DECLARATORS */
-
-#else /* not TRILIBRARY */
-
-#ifdef ANSI_DECLARATORS
-void writenodes(struct mesh *m, struct behavior *b, char *nodefilename,
- int argc, char **argv)
-#else /* not ANSI_DECLARATORS */
-void writenodes(m, b, nodefilename, argc, argv)
-struct mesh *m;
-struct behavior *b;
-char *nodefilename;
-int argc;
-char **argv;
-#endif /* not ANSI_DECLARATORS */
-
-#endif /* not TRILIBRARY */
-
-{
-#ifdef TRILIBRARY
- REAL *plist;
- REAL *palist;
- int *pmlist;
- int coordindex;
- int attribindex;
-#else /* not TRILIBRARY */
- FILE *outfile;
-#endif /* not TRILIBRARY */
- vertex vertexloop;
- long outvertices;
- int vertexnumber;
- int i;
-
- if (b->jettison) {
- outvertices = m->vertices.items - m->undeads;
- } else {
- outvertices = m->vertices.items;
- }
-
-#ifdef TRILIBRARY
- if (!b->quiet) {
- printf("Writing vertices.\n");
- }
- /* Allocate memory for output vertices if necessary. */
- if (*pointlist == (REAL *) NULL) {
- *pointlist = (REAL *) trimalloc((int) (outvertices * 2 * sizeof(REAL)));
- }
- /* Allocate memory for output vertex attributes if necessary. */
- if ((m->nextras > 0) && (*pointattriblist == (REAL *) NULL)) {
- *pointattriblist = (REAL *) trimalloc((int) (outvertices * m->nextras *
- sizeof(REAL)));
- }
- /* Allocate memory for output vertex markers if necessary. */
- if (!b->nobound && (*pointmarkerlist == (int *) NULL)) {
- *pointmarkerlist = (int *) trimalloc((int) (outvertices * sizeof(int)));
- }
- plist = *pointlist;
- palist = *pointattriblist;
- pmlist = *pointmarkerlist;
- coordindex = 0;
- attribindex = 0;
-#else /* not TRILIBRARY */
- if (!b->quiet) {
- printf("Writing %s.\n", nodefilename);
- }
- outfile = fopen(nodefilename, "w");
- if (outfile == (FILE *) NULL) {
- printf(" Error: Cannot create file %s.\n", nodefilename);
- triexit(1);
- }
- /* Number of vertices, number of dimensions, number of vertex attributes, */
- /* and number of boundary markers (zero or one). */
- fprintf(outfile, "%ld %d %d %d\n", outvertices, m->mesh_dim,
- m->nextras, 1 - b->nobound);
-#endif /* not TRILIBRARY */
-
- traversalinit(&m->vertices);
- vertexnumber = b->firstnumber;
- vertexloop = vertextraverse(m);
- while (vertexloop != (vertex) NULL) {
- if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) {
-#ifdef TRILIBRARY
- /* X and y coordinates. */
- plist[coordindex++] = vertexloop[0];
- plist[coordindex++] = vertexloop[1];
- /* Vertex attributes. */
- for (i = 0; i < m->nextras; i++) {
- palist[attribindex++] = vertexloop[2 + i];
- }
- if (!b->nobound) {
- /* Copy the boundary marker. */
- pmlist[vertexnumber - b->firstnumber] = vertexmark(vertexloop);
- }
-#else /* not TRILIBRARY */
- /* Vertex number, x and y coordinates. */
- fprintf(outfile, "%4d %.17g %.17g", vertexnumber, vertexloop[0],
- vertexloop[1]);
- for (i = 0; i < m->nextras; i++) {
- /* Write an attribute. */
- fprintf(outfile, " %.17g", vertexloop[i + 2]);
- }
- if (b->nobound) {
- fprintf(outfile, "\n");
- } else {
- /* Write the boundary marker. */
- fprintf(outfile, " %d\n", vertexmark(vertexloop));
- }
-#endif /* not TRILIBRARY */
-
- setvertexmark(vertexloop, vertexnumber);
- vertexnumber++;
- }
- vertexloop = vertextraverse(m);
- }
-
-#ifndef TRILIBRARY
- finishfile(outfile, argc, argv);
-#endif /* not TRILIBRARY */
-}
-
-/*****************************************************************************/
-/* */
-/* numbernodes() Number the vertices. */
-/* */
-/* Each vertex is assigned a marker equal to its number. */
-/* */
-/* Used when writenodes() is not called because no .node file is written. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-void numbernodes(struct mesh *m, struct behavior *b)
-#else /* not ANSI_DECLARATORS */
-void numbernodes(m, b)
-struct mesh *m;
-struct behavior *b;
-#endif /* not ANSI_DECLARATORS */
-
-{
- vertex vertexloop;
- int vertexnumber;
-
- traversalinit(&m->vertices);
- vertexnumber = b->firstnumber;
- vertexloop = vertextraverse(m);
- while (vertexloop != (vertex) NULL) {
- setvertexmark(vertexloop, vertexnumber);
- if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) {
- vertexnumber++;
- }
- vertexloop = vertextraverse(m);
- }
-}
-
-/*****************************************************************************/
-/* */
-/* writeelements() Write the triangles to an .ele file. */
-/* */
-/*****************************************************************************/
-
-#ifdef TRILIBRARY
-
-#ifdef ANSI_DECLARATORS
-void writeelements(struct mesh *m, struct behavior *b,
- int **trianglelist, REAL **triangleattriblist)
-#else /* not ANSI_DECLARATORS */
-void writeelements(m, b, trianglelist, triangleattriblist)
-struct mesh *m;
-struct behavior *b;
-int **trianglelist;
-REAL **triangleattriblist;
-#endif /* not ANSI_DECLARATORS */
-
-#else /* not TRILIBRARY */
-
-#ifdef ANSI_DECLARATORS
-void writeelements(struct mesh *m, struct behavior *b, char *elefilename,
- int argc, char **argv)
-#else /* not ANSI_DECLARATORS */
-void writeelements(m, b, elefilename, argc, argv)
-struct mesh *m;
-struct behavior *b;
-char *elefilename;
-int argc;
-char **argv;
-#endif /* not ANSI_DECLARATORS */
-
-#endif /* not TRILIBRARY */
-
-{
-#ifdef TRILIBRARY
- int *tlist;
- REAL *talist;
- int vertexindex;
- int attribindex;
-#else /* not TRILIBRARY */
- FILE *outfile;
-#endif /* not TRILIBRARY */
- struct otri triangleloop;
- vertex p1, p2, p3;
- vertex mid1, mid2, mid3;
- long elementnumber;
- int i;
-
-#ifdef TRILIBRARY
- if (!b->quiet) {
- printf("Writing triangles.\n");
- }
- /* Allocate memory for output triangles if necessary. */
- if (*trianglelist == (int *) NULL) {
- *trianglelist = (int *) trimalloc((int) (m->triangles.items *
- ((b->order + 1) * (b->order + 2) /
- 2) * sizeof(int)));
- }
- /* Allocate memory for output triangle attributes if necessary. */
- if ((m->eextras > 0) && (*triangleattriblist == (REAL *) NULL)) {
- *triangleattriblist = (REAL *) trimalloc((int) (m->triangles.items *
- m->eextras *
- sizeof(REAL)));
- }
- tlist = *trianglelist;
- talist = *triangleattriblist;
- vertexindex = 0;
- attribindex = 0;
-#else /* not TRILIBRARY */
- if (!b->quiet) {
- printf("Writing %s.\n", elefilename);
- }
- outfile = fopen(elefilename, "w");
- if (outfile == (FILE *) NULL) {
- printf(" Error: Cannot create file %s.\n", elefilename);
- triexit(1);
- }
- /* Number of triangles, vertices per triangle, attributes per triangle. */
- fprintf(outfile, "%ld %d %d\n", m->triangles.items,
- (b->order + 1) * (b->order + 2) / 2, m->eextras);
-#endif /* not TRILIBRARY */
-
- traversalinit(&m->triangles);
- triangleloop.tri = triangletraverse(m);
- triangleloop.orient = 0;
- elementnumber = b->firstnumber;
- while (triangleloop.tri != (triangle *) NULL) {
- org(triangleloop, p1);
- dest(triangleloop, p2);
- apex(triangleloop, p3);
- if (b->order == 1) {
-#ifdef TRILIBRARY
- tlist[vertexindex++] = vertexmark(p1);
- tlist[vertexindex++] = vertexmark(p2);
- tlist[vertexindex++] = vertexmark(p3);
-#else /* not TRILIBRARY */
- /* Triangle number, indices for three vertices. */
- fprintf(outfile, "%4ld %4d %4d %4d", elementnumber,
- vertexmark(p1), vertexmark(p2), vertexmark(p3));
-#endif /* not TRILIBRARY */
- } else {
- mid1 = (vertex) triangleloop.tri[m->highorderindex + 1];
- mid2 = (vertex) triangleloop.tri[m->highorderindex + 2];
- mid3 = (vertex) triangleloop.tri[m->highorderindex];
-#ifdef TRILIBRARY
- tlist[vertexindex++] = vertexmark(p1);
- tlist[vertexindex++] = vertexmark(p2);
- tlist[vertexindex++] = vertexmark(p3);
- tlist[vertexindex++] = vertexmark(mid1);
- tlist[vertexindex++] = vertexmark(mid2);
- tlist[vertexindex++] = vertexmark(mid3);
-#else /* not TRILIBRARY */
- /* Triangle number, indices for six vertices. */
- fprintf(outfile, "%4ld %4d %4d %4d %4d %4d %4d", elementnumber,
- vertexmark(p1), vertexmark(p2), vertexmark(p3), vertexmark(mid1),
- vertexmark(mid2), vertexmark(mid3));
-#endif /* not TRILIBRARY */
- }
-
-#ifdef TRILIBRARY
- for (i = 0; i < m->eextras; i++) {
- talist[attribindex++] = elemattribute(triangleloop, i);
- }
-#else /* not TRILIBRARY */
- for (i = 0; i < m->eextras; i++) {
- fprintf(outfile, " %.17g", elemattribute(triangleloop, i));
- }
- fprintf(outfile, "\n");
-#endif /* not TRILIBRARY */
-
- triangleloop.tri = triangletraverse(m);
- elementnumber++;
- }
-
-#ifndef TRILIBRARY
- finishfile(outfile, argc, argv);
-#endif /* not TRILIBRARY */
-}
-
-/*****************************************************************************/
-/* */
-/* writepoly() Write the segments and holes to a .poly file. */
-/* */
-/*****************************************************************************/
-
-#ifdef TRILIBRARY
-
-#ifdef ANSI_DECLARATORS
-void writepoly(struct mesh *m, struct behavior *b,
- int **segmentlist, int **segmentmarkerlist)
-#else /* not ANSI_DECLARATORS */
-void writepoly(m, b, segmentlist, segmentmarkerlist)
-struct mesh *m;
-struct behavior *b;
-int **segmentlist;
-int **segmentmarkerlist;
-#endif /* not ANSI_DECLARATORS */
-
-#else /* not TRILIBRARY */
-
-#ifdef ANSI_DECLARATORS
-void writepoly(struct mesh *m, struct behavior *b, char *polyfilename,
- REAL *holelist, int holes, REAL *regionlist, int regions,
- int argc, char **argv)
-#else /* not ANSI_DECLARATORS */
-void writepoly(m, b, polyfilename, holelist, holes, regionlist, regions,
- argc, argv)
-struct mesh *m;
-struct behavior *b;
-char *polyfilename;
-REAL *holelist;
-int holes;
-REAL *regionlist;
-int regions;
-int argc;
-char **argv;
-#endif /* not ANSI_DECLARATORS */
-
-#endif /* not TRILIBRARY */
-
-{
-#ifdef TRILIBRARY
- int *slist;
- int *smlist;
- int index;
-#else /* not TRILIBRARY */
- FILE *outfile;
- long holenumber, regionnumber;
-#endif /* not TRILIBRARY */
- struct osub subsegloop;
- vertex endpoint1, endpoint2;
- long subsegnumber;
-
-#ifdef TRILIBRARY
- if (!b->quiet) {
- printf("Writing segments.\n");
- }
- /* Allocate memory for output segments if necessary. */
- if (*segmentlist == (int *) NULL) {
- *segmentlist = (int *) trimalloc((int) (m->subsegs.items * 2 *
- sizeof(int)));
- }
- /* Allocate memory for output segment markers if necessary. */
- if (!b->nobound && (*segmentmarkerlist == (int *) NULL)) {
- *segmentmarkerlist = (int *) trimalloc((int) (m->subsegs.items *
- sizeof(int)));
- }
- slist = *segmentlist;
- smlist = *segmentmarkerlist;
- index = 0;
-#else /* not TRILIBRARY */
- if (!b->quiet) {
- printf("Writing %s.\n", polyfilename);
- }
- outfile = fopen(polyfilename, "w");
- if (outfile == (FILE *) NULL) {
- printf(" Error: Cannot create file %s.\n", polyfilename);
- triexit(1);
- }
- /* The zero indicates that the vertices are in a separate .node file. */
- /* Followed by number of dimensions, number of vertex attributes, */
- /* and number of boundary markers (zero or one). */
- fprintf(outfile, "%d %d %d %d\n", 0, m->mesh_dim, m->nextras,
- 1 - b->nobound);
- /* Number of segments, number of boundary markers (zero or one). */
- fprintf(outfile, "%ld %d\n", m->subsegs.items, 1 - b->nobound);
-#endif /* not TRILIBRARY */
-
- traversalinit(&m->subsegs);
- subsegloop.ss = subsegtraverse(m);
- subsegloop.ssorient = 0;
- subsegnumber = b->firstnumber;
- while (subsegloop.ss != (subseg *) NULL) {
- sorg(subsegloop, endpoint1);
- sdest(subsegloop, endpoint2);
-#ifdef TRILIBRARY
- /* Copy indices of the segment's two endpoints. */
- slist[index++] = vertexmark(endpoint1);
- slist[index++] = vertexmark(endpoint2);
- if (!b->nobound) {
- /* Copy the boundary marker. */
- smlist[subsegnumber - b->firstnumber] = mark(subsegloop);
- }
-#else /* not TRILIBRARY */
- /* Segment number, indices of its two endpoints, and possibly a marker. */
- if (b->nobound) {
- fprintf(outfile, "%4ld %4d %4d\n", subsegnumber,
- vertexmark(endpoint1), vertexmark(endpoint2));
- } else {
- fprintf(outfile, "%4ld %4d %4d %4d\n", subsegnumber,
- vertexmark(endpoint1), vertexmark(endpoint2), mark(subsegloop));
- }
-#endif /* not TRILIBRARY */
-
- subsegloop.ss = subsegtraverse(m);
- subsegnumber++;
- }
-
-#ifndef TRILIBRARY
-#ifndef CDT_ONLY
- fprintf(outfile, "%d\n", holes);
- if (holes > 0) {
- for (holenumber = 0; holenumber < holes; holenumber++) {
- /* Hole number, x and y coordinates. */
- fprintf(outfile, "%4ld %.17g %.17g\n", b->firstnumber + holenumber,
- holelist[2 * holenumber], holelist[2 * holenumber + 1]);
- }
- }
- if (regions > 0) {
- fprintf(outfile, "%d\n", regions);
- for (regionnumber = 0; regionnumber < regions; regionnumber++) {
- /* Region number, x and y coordinates, attribute, maximum area. */
- fprintf(outfile, "%4ld %.17g %.17g %.17g %.17g\n",
- b->firstnumber + regionnumber,
- regionlist[4 * regionnumber], regionlist[4 * regionnumber + 1],
- regionlist[4 * regionnumber + 2],
- regionlist[4 * regionnumber + 3]);
- }
- }
-#endif /* not CDT_ONLY */
-
- finishfile(outfile, argc, argv);
-#endif /* not TRILIBRARY */
-}
-
-/*****************************************************************************/
-/* */
-/* writeedges() Write the edges to an .edge file. */
-/* */
-/*****************************************************************************/
-
-#ifdef TRILIBRARY
-
-#ifdef ANSI_DECLARATORS
-void writeedges(struct mesh *m, struct behavior *b,
- int **edgelist, int **edgemarkerlist)
-#else /* not ANSI_DECLARATORS */
-void writeedges(m, b, edgelist, edgemarkerlist)
-struct mesh *m;
-struct behavior *b;
-int **edgelist;
-int **edgemarkerlist;
-#endif /* not ANSI_DECLARATORS */
-
-#else /* not TRILIBRARY */
-
-#ifdef ANSI_DECLARATORS
-void writeedges(struct mesh *m, struct behavior *b, char *edgefilename,
- int argc, char **argv)
-#else /* not ANSI_DECLARATORS */
-void writeedges(m, b, edgefilename, argc, argv)
-struct mesh *m;
-struct behavior *b;
-char *edgefilename;
-int argc;
-char **argv;
-#endif /* not ANSI_DECLARATORS */
-
-#endif /* not TRILIBRARY */
-
-{
-#ifdef TRILIBRARY
- int *elist;
- int *emlist;
- int index;
-#else /* not TRILIBRARY */
- FILE *outfile;
-#endif /* not TRILIBRARY */
- struct otri triangleloop, trisym;
- struct osub checkmark;
- vertex p1, p2;
- long edgenumber;
- triangle ptr; /* Temporary variable used by sym(). */
- subseg sptr; /* Temporary variable used by tspivot(). */
-
-#ifdef TRILIBRARY
- if (!b->quiet) {
- printf("Writing edges.\n");
- }
- /* Allocate memory for edges if necessary. */
- if (*edgelist == (int *) NULL) {
- *edgelist = (int *) trimalloc((int) (m->edges * 2 * sizeof(int)));
- }
- /* Allocate memory for edge markers if necessary. */
- if (!b->nobound && (*edgemarkerlist == (int *) NULL)) {
- *edgemarkerlist = (int *) trimalloc((int) (m->edges * sizeof(int)));
- }
- elist = *edgelist;
- emlist = *edgemarkerlist;
- index = 0;
-#else /* not TRILIBRARY */
- if (!b->quiet) {
- printf("Writing %s.\n", edgefilename);
- }
- outfile = fopen(edgefilename, "w");
- if (outfile == (FILE *) NULL) {
- printf(" Error: Cannot create file %s.\n", edgefilename);
- triexit(1);
- }
- /* Number of edges, number of boundary markers (zero or one). */
- fprintf(outfile, "%ld %d\n", m->edges, 1 - b->nobound);
-#endif /* not TRILIBRARY */
-
- traversalinit(&m->triangles);
- triangleloop.tri = triangletraverse(m);
- edgenumber = b->firstnumber;
- /* To loop over the set of edges, loop over all triangles, and look at */
- /* the three edges of each triangle. If there isn't another triangle */
- /* adjacent to the edge, operate on the edge. If there is another */
- /* adjacent triangle, operate on the edge only if the current triangle */
- /* has a smaller pointer than its neighbor. This way, each edge is */
- /* considered only once. */
- while (triangleloop.tri != (triangle *) NULL) {
- for (triangleloop.orient = 0; triangleloop.orient < 3;
- triangleloop.orient++) {
- sym(triangleloop, trisym);
- if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) {
- org(triangleloop, p1);
- dest(triangleloop, p2);
-#ifdef TRILIBRARY
- elist[index++] = vertexmark(p1);
- elist[index++] = vertexmark(p2);
-#endif /* TRILIBRARY */
- if (b->nobound) {
-#ifndef TRILIBRARY
- /* Edge number, indices of two endpoints. */
- fprintf(outfile, "%4ld %d %d\n", edgenumber,
- vertexmark(p1), vertexmark(p2));
-#endif /* not TRILIBRARY */
- } else {
- /* Edge number, indices of two endpoints, and a boundary marker. */
- /* If there's no subsegment, the boundary marker is zero. */
- if (b->usesegments) {
- tspivot(triangleloop, checkmark);
- if (checkmark.ss == m->dummysub) {
-#ifdef TRILIBRARY
- emlist[edgenumber - b->firstnumber] = 0;
-#else /* not TRILIBRARY */
- fprintf(outfile, "%4ld %d %d %d\n", edgenumber,
- vertexmark(p1), vertexmark(p2), 0);
-#endif /* not TRILIBRARY */
- } else {
-#ifdef TRILIBRARY
- emlist[edgenumber - b->firstnumber] = mark(checkmark);
-#else /* not TRILIBRARY */
- fprintf(outfile, "%4ld %d %d %d\n", edgenumber,
- vertexmark(p1), vertexmark(p2), mark(checkmark));
-#endif /* not TRILIBRARY */
- }
- } else {
-#ifdef TRILIBRARY
- emlist[edgenumber - b->firstnumber] = trisym.tri == m->dummytri;
-#else /* not TRILIBRARY */
- fprintf(outfile, "%4ld %d %d %d\n", edgenumber,
- vertexmark(p1), vertexmark(p2), trisym.tri == m->dummytri);
-#endif /* not TRILIBRARY */
- }
- }
- edgenumber++;
- }
- }
- triangleloop.tri = triangletraverse(m);
- }
-
-#ifndef TRILIBRARY
- finishfile(outfile, argc, argv);
-#endif /* not TRILIBRARY */
-}
-
-/*****************************************************************************/
-/* */
-/* writevoronoi() Write the Voronoi diagram to a .v.node and .v.edge */
-/* file. */
-/* */
-/* The Voronoi diagram is the geometric dual of the Delaunay triangulation. */
-/* Hence, the Voronoi vertices are listed by traversing the Delaunay */
-/* triangles, and the Voronoi edges are listed by traversing the Delaunay */
-/* edges. */
-/* */
-/* WARNING: In order to assign numbers to the Voronoi vertices, this */
-/* procedure messes up the subsegments or the extra nodes of every */
-/* element. Hence, you should call this procedure last. */
-/* */
-/*****************************************************************************/
-
-#ifdef TRILIBRARY
-
-#ifdef ANSI_DECLARATORS
-void writevoronoi(struct mesh *m, struct behavior *b, REAL **vpointlist,
- REAL **vpointattriblist, int **vpointmarkerlist,
- int **vedgelist, int **vedgemarkerlist, REAL **vnormlist)
-#else /* not ANSI_DECLARATORS */
-void writevoronoi(m, b, vpointlist, vpointattriblist, vpointmarkerlist,
- vedgelist, vedgemarkerlist, vnormlist)
-struct mesh *m;
-struct behavior *b;
-REAL **vpointlist;
-REAL **vpointattriblist;
-int **vpointmarkerlist;
-int **vedgelist;
-int **vedgemarkerlist;
-REAL **vnormlist;
-#endif /* not ANSI_DECLARATORS */
-
-#else /* not TRILIBRARY */
-
-#ifdef ANSI_DECLARATORS
-void writevoronoi(struct mesh *m, struct behavior *b, char *vnodefilename,
- char *vedgefilename, int argc, char **argv)
-#else /* not ANSI_DECLARATORS */
-void writevoronoi(m, b, vnodefilename, vedgefilename, argc, argv)
-struct mesh *m;
-struct behavior *b;
-char *vnodefilename;
-char *vedgefilename;
-int argc;
-char **argv;
-#endif /* not ANSI_DECLARATORS */
-
-#endif /* not TRILIBRARY */
-
-{
-#ifdef TRILIBRARY
- REAL *plist;
- REAL *palist;
- int *elist;
- REAL *normlist;
- int coordindex;
- int attribindex;
-#else /* not TRILIBRARY */
- FILE *outfile;
-#endif /* not TRILIBRARY */
- struct otri triangleloop, trisym;
- vertex torg, tdest, tapex;
- REAL circumcenter[2];
- REAL xi, eta;
- long vnodenumber, vedgenumber;
- int p1, p2;
- int i;
- triangle ptr; /* Temporary variable used by sym(). */
-
-#ifdef TRILIBRARY
- if (!b->quiet) {
- printf("Writing Voronoi vertices.\n");
- }
- /* Allocate memory for Voronoi vertices if necessary. */
- if (*vpointlist == (REAL *) NULL) {
- *vpointlist = (REAL *) trimalloc((int) (m->triangles.items * 2 *
- sizeof(REAL)));
- }
- /* Allocate memory for Voronoi vertex attributes if necessary. */
- if (*vpointattriblist == (REAL *) NULL) {
- *vpointattriblist = (REAL *) trimalloc((int) (m->triangles.items *
- m->nextras * sizeof(REAL)));
- }
- *vpointmarkerlist = (int *) NULL;
- plist = *vpointlist;
- palist = *vpointattriblist;
- coordindex = 0;
- attribindex = 0;
-#else /* not TRILIBRARY */
- if (!b->quiet) {
- printf("Writing %s.\n", vnodefilename);
- }
- outfile = fopen(vnodefilename, "w");
- if (outfile == (FILE *) NULL) {
- printf(" Error: Cannot create file %s.\n", vnodefilename);
- triexit(1);
- }
- /* Number of triangles, two dimensions, number of vertex attributes, */
- /* no markers. */
- fprintf(outfile, "%ld %d %d %d\n", m->triangles.items, 2, m->nextras, 0);
-#endif /* not TRILIBRARY */
-
- traversalinit(&m->triangles);
- triangleloop.tri = triangletraverse(m);
- triangleloop.orient = 0;
- vnodenumber = b->firstnumber;
- while (triangleloop.tri != (triangle *) NULL) {
- org(triangleloop, torg);
- dest(triangleloop, tdest);
- apex(triangleloop, tapex);
- findcircumcenter(m, b, torg, tdest, tapex, circumcenter, &xi, &eta, 0);
-#ifdef TRILIBRARY
- /* X and y coordinates. */
- plist[coordindex++] = circumcenter[0];
- plist[coordindex++] = circumcenter[1];
- for (i = 2; i < 2 + m->nextras; i++) {
- /* Interpolate the vertex attributes at the circumcenter. */
- palist[attribindex++] = torg[i] + xi * (tdest[i] - torg[i])
- + eta * (tapex[i] - torg[i]);
- }
-#else /* not TRILIBRARY */
- /* Voronoi vertex number, x and y coordinates. */
- fprintf(outfile, "%4ld %.17g %.17g", vnodenumber, circumcenter[0],
- circumcenter[1]);
- for (i = 2; i < 2 + m->nextras; i++) {
- /* Interpolate the vertex attributes at the circumcenter. */
- fprintf(outfile, " %.17g", torg[i] + xi * (tdest[i] - torg[i])
- + eta * (tapex[i] - torg[i]));
- }
- fprintf(outfile, "\n");
-#endif /* not TRILIBRARY */
-
- * (int *) (triangleloop.tri + 6) = (int) vnodenumber;
- triangleloop.tri = triangletraverse(m);
- vnodenumber++;
- }
-
-#ifndef TRILIBRARY
- finishfile(outfile, argc, argv);
-#endif /* not TRILIBRARY */
-
-#ifdef TRILIBRARY
- if (!b->quiet) {
- printf("Writing Voronoi edges.\n");
- }
- /* Allocate memory for output Voronoi edges if necessary. */
- if (*vedgelist == (int *) NULL) {
- *vedgelist = (int *) trimalloc((int) (m->edges * 2 * sizeof(int)));
- }
- *vedgemarkerlist = (int *) NULL;
- /* Allocate memory for output Voronoi norms if necessary. */
- if (*vnormlist == (REAL *) NULL) {
- *vnormlist = (REAL *) trimalloc((int) (m->edges * 2 * sizeof(REAL)));
- }
- elist = *vedgelist;
- normlist = *vnormlist;
- coordindex = 0;
-#else /* not TRILIBRARY */
- if (!b->quiet) {
- printf("Writing %s.\n", vedgefilename);
- }
- outfile = fopen(vedgefilename, "w");
- if (outfile == (FILE *) NULL) {
- printf(" Error: Cannot create file %s.\n", vedgefilename);
- triexit(1);
- }
- /* Number of edges, zero boundary markers. */
- fprintf(outfile, "%ld %d\n", m->edges, 0);
-#endif /* not TRILIBRARY */
-
- traversalinit(&m->triangles);
- triangleloop.tri = triangletraverse(m);
- vedgenumber = b->firstnumber;
- /* To loop over the set of edges, loop over all triangles, and look at */
- /* the three edges of each triangle. If there isn't another triangle */
- /* adjacent to the edge, operate on the edge. If there is another */
- /* adjacent triangle, operate on the edge only if the current triangle */
- /* has a smaller pointer than its neighbor. This way, each edge is */
- /* considered only once. */
- while (triangleloop.tri != (triangle *) NULL) {
- for (triangleloop.orient = 0; triangleloop.orient < 3;
- triangleloop.orient++) {
- sym(triangleloop, trisym);
- if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) {
- /* Find the number of this triangle (and Voronoi vertex). */
- p1 = * (int *) (triangleloop.tri + 6);
- if (trisym.tri == m->dummytri) {
- org(triangleloop, torg);
- dest(triangleloop, tdest);
-#ifdef TRILIBRARY
- /* Copy an infinite ray. Index of one endpoint, and -1. */
- elist[coordindex] = p1;
- normlist[coordindex++] = tdest[1] - torg[1];
- elist[coordindex] = -1;
- normlist[coordindex++] = torg[0] - tdest[0];
-#else /* not TRILIBRARY */
- /* Write an infinite ray. Edge number, index of one endpoint, -1, */
- /* and x and y coordinates of a vector representing the */
- /* direction of the ray. */
- fprintf(outfile, "%4ld %d %d %.17g %.17g\n", vedgenumber,
- p1, -1, tdest[1] - torg[1], torg[0] - tdest[0]);
-#endif /* not TRILIBRARY */
- } else {
- /* Find the number of the adjacent triangle (and Voronoi vertex). */
- p2 = * (int *) (trisym.tri + 6);
- /* Finite edge. Write indices of two endpoints. */
-#ifdef TRILIBRARY
- elist[coordindex] = p1;
- normlist[coordindex++] = 0.0;
- elist[coordindex] = p2;
- normlist[coordindex++] = 0.0;
-#else /* not TRILIBRARY */
- fprintf(outfile, "%4ld %d %d\n", vedgenumber, p1, p2);
-#endif /* not TRILIBRARY */
- }
- vedgenumber++;
- }
- }
- triangleloop.tri = triangletraverse(m);
- }
-
-#ifndef TRILIBRARY
- finishfile(outfile, argc, argv);
-#endif /* not TRILIBRARY */
-}
-
-#ifdef TRILIBRARY
-
-#ifdef ANSI_DECLARATORS
-void writeneighbors(struct mesh *m, struct behavior *b, int **neighborlist)
-#else /* not ANSI_DECLARATORS */
-void writeneighbors(m, b, neighborlist)
-struct mesh *m;
-struct behavior *b;
-int **neighborlist;
-#endif /* not ANSI_DECLARATORS */
-
-#else /* not TRILIBRARY */
-
-#ifdef ANSI_DECLARATORS
-void writeneighbors(struct mesh *m, struct behavior *b, char *neighborfilename,
- int argc, char **argv)
-#else /* not ANSI_DECLARATORS */
-void writeneighbors(m, b, neighborfilename, argc, argv)
-struct mesh *m;
-struct behavior *b;
-char *neighborfilename;
-int argc;
-char **argv;
-#endif /* not ANSI_DECLARATORS */
-
-#endif /* not TRILIBRARY */
-
-{
-#ifdef TRILIBRARY
- int *nlist;
- int index;
-#else /* not TRILIBRARY */
- FILE *outfile;
-#endif /* not TRILIBRARY */
- struct otri triangleloop, trisym;
- long elementnumber;
- int neighbor1, neighbor2, neighbor3;
- triangle ptr; /* Temporary variable used by sym(). */
-
-#ifdef TRILIBRARY
- if (!b->quiet) {
- printf("Writing neighbors.\n");
- }
- /* Allocate memory for neighbors if necessary. */
- if (*neighborlist == (int *) NULL) {
- *neighborlist = (int *) trimalloc((int) (m->triangles.items * 3 *
- sizeof(int)));
- }
- nlist = *neighborlist;
- index = 0;
-#else /* not TRILIBRARY */
- if (!b->quiet) {
- printf("Writing %s.\n", neighborfilename);
- }
- outfile = fopen(neighborfilename, "w");
- if (outfile == (FILE *) NULL) {
- printf(" Error: Cannot create file %s.\n", neighborfilename);
- triexit(1);
- }
- /* Number of triangles, three neighbors per triangle. */
- fprintf(outfile, "%ld %d\n", m->triangles.items, 3);
-#endif /* not TRILIBRARY */
-
- traversalinit(&m->triangles);
- triangleloop.tri = triangletraverse(m);
- triangleloop.orient = 0;
- elementnumber = b->firstnumber;
- while (triangleloop.tri != (triangle *) NULL) {
- * (int *) (triangleloop.tri + 6) = (int) elementnumber;
- triangleloop.tri = triangletraverse(m);
- elementnumber++;
- }
- * (int *) (m->dummytri + 6) = -1;
-
- traversalinit(&m->triangles);
- triangleloop.tri = triangletraverse(m);
- elementnumber = b->firstnumber;
- while (triangleloop.tri != (triangle *) NULL) {
- triangleloop.orient = 1;
- sym(triangleloop, trisym);
- neighbor1 = * (int *) (trisym.tri + 6);
- triangleloop.orient = 2;
- sym(triangleloop, trisym);
- neighbor2 = * (int *) (trisym.tri + 6);
- triangleloop.orient = 0;
- sym(triangleloop, trisym);
- neighbor3 = * (int *) (trisym.tri + 6);
-#ifdef TRILIBRARY
- nlist[index++] = neighbor1;
- nlist[index++] = neighbor2;
- nlist[index++] = neighbor3;
-#else /* not TRILIBRARY */
- /* Triangle number, neighboring triangle numbers. */
- fprintf(outfile, "%4ld %d %d %d\n", elementnumber,
- neighbor1, neighbor2, neighbor3);
-#endif /* not TRILIBRARY */
-
- triangleloop.tri = triangletraverse(m);
- elementnumber++;
- }
-
-#ifndef TRILIBRARY
- finishfile(outfile, argc, argv);
-#endif /* not TRILIBRARY */
-}
-
-/*****************************************************************************/
-/* */
-/* writeoff() Write the triangulation to an .off file. */
-/* */
-/* OFF stands for the Object File Format, a format used by the Geometry */
-/* Center's Geomview package. */
-/* */
-/*****************************************************************************/
-
-#ifndef TRILIBRARY
-
-#ifdef ANSI_DECLARATORS
-void writeoff(struct mesh *m, struct behavior *b, char *offfilename,
- int argc, char **argv)
-#else /* not ANSI_DECLARATORS */
-void writeoff(m, b, offfilename, argc, argv)
-struct mesh *m;
-struct behavior *b;
-char *offfilename;
-int argc;
-char **argv;
-#endif /* not ANSI_DECLARATORS */
-
-{
- FILE *outfile;
- struct otri triangleloop;
- vertex vertexloop;
- vertex p1, p2, p3;
- long outvertices;
-
- if (!b->quiet) {
- printf("Writing %s.\n", offfilename);
- }
-
- if (b->jettison) {
- outvertices = m->vertices.items - m->undeads;
- } else {
- outvertices = m->vertices.items;
- }
-
- outfile = fopen(offfilename, "w");
- if (outfile == (FILE *) NULL) {
- printf(" Error: Cannot create file %s.\n", offfilename);
- triexit(1);
- }
- /* Number of vertices, triangles, and edges. */
- fprintf(outfile, "OFF\n%ld %ld %ld\n", outvertices, m->triangles.items,
- m->edges);
-
- /* Write the vertices. */
- traversalinit(&m->vertices);
- vertexloop = vertextraverse(m);
- while (vertexloop != (vertex) NULL) {
- if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) {
- /* The "0.0" is here because the OFF format uses 3D coordinates. */
- fprintf(outfile, " %.17g %.17g %.17g\n", vertexloop[0], vertexloop[1],
- 0.0);
- }
- vertexloop = vertextraverse(m);
- }
-
- /* Write the triangles. */
- traversalinit(&m->triangles);
- triangleloop.tri = triangletraverse(m);
- triangleloop.orient = 0;
- while (triangleloop.tri != (triangle *) NULL) {
- org(triangleloop, p1);
- dest(triangleloop, p2);
- apex(triangleloop, p3);
- /* The "3" means a three-vertex polygon. */
- fprintf(outfile, " 3 %4d %4d %4d\n", vertexmark(p1) - b->firstnumber,
- vertexmark(p2) - b->firstnumber, vertexmark(p3) - b->firstnumber);
- triangleloop.tri = triangletraverse(m);
- }
- finishfile(outfile, argc, argv);
-}
-
-#endif /* not TRILIBRARY */
-
-/** **/
-/** **/
-/********* File I/O routines end here *********/
-
-/*****************************************************************************/
-/* */
-/* quality_statistics() Print statistics about the quality of the mesh. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-void quality_statistics(struct mesh *m, struct behavior *b)
-#else /* not ANSI_DECLARATORS */
-void quality_statistics(m, b)
-struct mesh *m;
-struct behavior *b;
-#endif /* not ANSI_DECLARATORS */
-
-{
- struct otri triangleloop;
- vertex p[3];
- REAL cossquaretable[8];
- REAL ratiotable[16];
- REAL dx[3], dy[3];
- REAL edgelength[3];
- REAL dotproduct;
- REAL cossquare;
- REAL triarea;
- REAL shortest, longest;
- REAL trilongest2;
- REAL smallestarea, biggestarea;
- REAL triminaltitude2;
- REAL minaltitude;
- REAL triaspect2;
- REAL worstaspect;
- REAL smallestangle, biggestangle;
- REAL radconst, degconst;
- int angletable[18];
- int aspecttable[16];
- int aspectindex;
- int tendegree;
- int acutebiggest;
- int i, ii, j, k;
-
- printf("Mesh quality statistics:\n\n");
- radconst = PI / 18.0;
- degconst = 180.0 / PI;
- for (i = 0; i < 8; i++) {
- cossquaretable[i] = cos(radconst * (REAL) (i + 1));
- cossquaretable[i] = cossquaretable[i] * cossquaretable[i];
- }
- for (i = 0; i < 18; i++) {
- angletable[i] = 0;
- }
-
- ratiotable[0] = 1.5; ratiotable[1] = 2.0;
- ratiotable[2] = 2.5; ratiotable[3] = 3.0;
- ratiotable[4] = 4.0; ratiotable[5] = 6.0;
- ratiotable[6] = 10.0; ratiotable[7] = 15.0;
- ratiotable[8] = 25.0; ratiotable[9] = 50.0;
- ratiotable[10] = 100.0; ratiotable[11] = 300.0;
- ratiotable[12] = 1000.0; ratiotable[13] = 10000.0;
- ratiotable[14] = 100000.0; ratiotable[15] = 0.0;
- for (i = 0; i < 16; i++) {
- aspecttable[i] = 0;
- }
-
- worstaspect = 0.0;
- minaltitude = m->xmax - m->xmin + m->ymax - m->ymin;
- minaltitude = minaltitude * minaltitude;
- shortest = minaltitude;
- longest = 0.0;
- smallestarea = minaltitude;
- biggestarea = 0.0;
- worstaspect = 0.0;
- smallestangle = 0.0;
- biggestangle = 2.0;
- acutebiggest = 1;
-
- traversalinit(&m->triangles);
- triangleloop.tri = triangletraverse(m);
- triangleloop.orient = 0;
- while (triangleloop.tri != (triangle *) NULL) {
- org(triangleloop, p[0]);
- dest(triangleloop, p[1]);
- apex(triangleloop, p[2]);
- trilongest2 = 0.0;
-
- for (i = 0; i < 3; i++) {
- j = plus1mod3[i];
- k = minus1mod3[i];
- dx[i] = p[j][0] - p[k][0];
- dy[i] = p[j][1] - p[k][1];
- edgelength[i] = dx[i] * dx[i] + dy[i] * dy[i];
- if (edgelength[i] > trilongest2) {
- trilongest2 = edgelength[i];
- }
- if (edgelength[i] > longest) {
- longest = edgelength[i];
- }
- if (edgelength[i] < shortest) {
- shortest = edgelength[i];
- }
- }
-
- triarea = counterclockwise(m, b, p[0], p[1], p[2]);
- if (triarea < smallestarea) {
- smallestarea = triarea;
- }
- if (triarea > biggestarea) {
- biggestarea = triarea;
- }
- triminaltitude2 = triarea * triarea / trilongest2;
- if (triminaltitude2 < minaltitude) {
- minaltitude = triminaltitude2;
- }
- triaspect2 = trilongest2 / triminaltitude2;
- if (triaspect2 > worstaspect) {
- worstaspect = triaspect2;
- }
- aspectindex = 0;
- while ((triaspect2 > ratiotable[aspectindex] * ratiotable[aspectindex])
- && (aspectindex < 15)) {
- aspectindex++;
- }
- aspecttable[aspectindex]++;
-
- for (i = 0; i < 3; i++) {
- j = plus1mod3[i];
- k = minus1mod3[i];
- dotproduct = dx[j] * dx[k] + dy[j] * dy[k];
- cossquare = dotproduct * dotproduct / (edgelength[j] * edgelength[k]);
- tendegree = 8;
- for (ii = 7; ii >= 0; ii--) {
- if (cossquare > cossquaretable[ii]) {
- tendegree = ii;
- }
- }
- if (dotproduct <= 0.0) {
- angletable[tendegree]++;
- if (cossquare > smallestangle) {
- smallestangle = cossquare;
- }
- if (acutebiggest && (cossquare < biggestangle)) {
- biggestangle = cossquare;
- }
- } else {
- angletable[17 - tendegree]++;
- if (acutebiggest || (cossquare > biggestangle)) {
- biggestangle = cossquare;
- acutebiggest = 0;
- }
- }
- }
- triangleloop.tri = triangletraverse(m);
- }
-
- shortest = sqrt(shortest);
- longest = sqrt(longest);
- minaltitude = sqrt(minaltitude);
- worstaspect = sqrt(worstaspect);
- smallestarea *= 0.5;
- biggestarea *= 0.5;
- if (smallestangle >= 1.0) {
- smallestangle = 0.0;
- } else {
- smallestangle = degconst * acos(sqrt(smallestangle));
- }
- if (biggestangle >= 1.0) {
- biggestangle = 180.0;
- } else {
- if (acutebiggest) {
- biggestangle = degconst * acos(sqrt(biggestangle));
- } else {
- biggestangle = 180.0 - degconst * acos(sqrt(biggestangle));
- }
- }
-
- printf(" Smallest area: %16.5g | Largest area: %16.5g\n",
- smallestarea, biggestarea);
- printf(" Shortest edge: %16.5g | Longest edge: %16.5g\n",
- shortest, longest);
- printf(" Shortest altitude: %12.5g | Largest aspect ratio: %8.5g\n\n",
- minaltitude, worstaspect);
-
- printf(" Triangle aspect ratio histogram:\n");
- printf(" 1.1547 - %-6.6g : %8d | %6.6g - %-6.6g : %8d\n",
- ratiotable[0], aspecttable[0], ratiotable[7], ratiotable[8],
- aspecttable[8]);
- for (i = 1; i < 7; i++) {
- printf(" %6.6g - %-6.6g : %8d | %6.6g - %-6.6g : %8d\n",
- ratiotable[i - 1], ratiotable[i], aspecttable[i],
- ratiotable[i + 7], ratiotable[i + 8], aspecttable[i + 8]);
- }
- printf(" %6.6g - %-6.6g : %8d | %6.6g - : %8d\n",
- ratiotable[6], ratiotable[7], aspecttable[7], ratiotable[14],
- aspecttable[15]);
- printf(" (Aspect ratio is longest edge divided by shortest altitude)\n\n");
-
- printf(" Smallest angle: %15.5g | Largest angle: %15.5g\n\n",
- smallestangle, biggestangle);
-
- printf(" Angle histogram:\n");
- for (i = 0; i < 9; i++) {
- printf(" %3d - %3d degrees: %8d | %3d - %3d degrees: %8d\n",
- i * 10, i * 10 + 10, angletable[i],
- i * 10 + 90, i * 10 + 100, angletable[i + 9]);
- }
- printf("\n");
-}
-
-/*****************************************************************************/
-/* */
-/* statistics() Print all sorts of cool facts. */
-/* */
-/*****************************************************************************/
-
-#ifdef ANSI_DECLARATORS
-void statistics(struct mesh *m, struct behavior *b)
-#else /* not ANSI_DECLARATORS */
-void statistics(m, b)
-struct mesh *m;
-struct behavior *b;
-#endif /* not ANSI_DECLARATORS */
-
-{
- printf("\nStatistics:\n\n");
- printf(" Input vertices: %d\n", m->invertices);
- if (b->refine) {
- printf(" Input triangles: %d\n", m->inelements);
- }
- if (b->poly) {
- printf(" Input segments: %d\n", m->insegments);
- if (!b->refine) {
- printf(" Input holes: %d\n", m->holes);
- }
- }
-
- printf("\n Mesh vertices: %ld\n", m->vertices.items - m->undeads);
- printf(" Mesh triangles: %ld\n", m->triangles.items);
- printf(" Mesh edges: %ld\n", m->edges);
- printf(" Mesh exterior boundary edges: %ld\n", m->hullsize);
- if (b->poly || b->refine) {
- printf(" Mesh interior boundary edges: %ld\n",
- m->subsegs.items - m->hullsize);
- printf(" Mesh subsegments (constrained edges): %ld\n",
- m->subsegs.items);
- }
- printf("\n");
-
- if (b->verbose) {
- quality_statistics(m, b);
- printf("Memory allocation statistics:\n\n");
- printf(" Maximum number of vertices: %ld\n", m->vertices.maxitems);
- printf(" Maximum number of triangles: %ld\n", m->triangles.maxitems);
- if (m->subsegs.maxitems > 0) {
- printf(" Maximum number of subsegments: %ld\n", m->subsegs.maxitems);
- }
- if (m->viri.maxitems > 0) {
- printf(" Maximum number of viri: %ld\n", m->viri.maxitems);
- }
- if (m->badsubsegs.maxitems > 0) {
- printf(" Maximum number of encroached subsegments: %ld\n",
- m->badsubsegs.maxitems);
- }
- if (m->badtriangles.maxitems > 0) {
- printf(" Maximum number of bad triangles: %ld\n",
- m->badtriangles.maxitems);
- }
- if (m->flipstackers.maxitems > 0) {
- printf(" Maximum number of stacked triangle flips: %ld\n",
- m->flipstackers.maxitems);
- }
- if (m->splaynodes.maxitems > 0) {
- printf(" Maximum number of splay tree nodes: %ld\n",
- m->splaynodes.maxitems);
- }
- printf(" Approximate heap memory use (bytes): %ld\n\n",
- m->vertices.maxitems * m->vertices.itembytes +
- m->triangles.maxitems * m->triangles.itembytes +
- m->subsegs.maxitems * m->subsegs.itembytes +
- m->viri.maxitems * m->viri.itembytes +
- m->badsubsegs.maxitems * m->badsubsegs.itembytes +
- m->badtriangles.maxitems * m->badtriangles.itembytes +
- m->flipstackers.maxitems * m->flipstackers.itembytes +
- m->splaynodes.maxitems * m->splaynodes.itembytes);
-
- printf("Algorithmic statistics:\n\n");
- if (!b->weighted) {
- printf(" Number of incircle tests: %ld\n", m->incirclecount);
- } else {
- printf(" Number of 3D orientation tests: %ld\n", m->orient3dcount);
- }
- printf(" Number of 2D orientation tests: %ld\n", m->counterclockcount);
- if (m->hyperbolacount > 0) {
- printf(" Number of right-of-hyperbola tests: %ld\n",
- m->hyperbolacount);
- }
- if (m->circletopcount > 0) {
- printf(" Number of circle top computations: %ld\n",
- m->circletopcount);
- }
- if (m->circumcentercount > 0) {
- printf(" Number of triangle circumcenter computations: %ld\n",
- m->circumcentercount);
- }
- printf("\n");
- }
-}
-
-/*****************************************************************************/
-/* */
-/* main() or triangulate() Gosh, do everything. */
-/* */
-/* The sequence is roughly as follows. Many of these steps can be skipped, */
-/* depending on the command line switches. */
-/* */
-/* - Initialize constants and parse the command line. */
-/* - Read the vertices from a file and either */
-/* - triangulate them (no -r), or */
-/* - read an old mesh from files and reconstruct it (-r). */
-/* - Insert the PSLG segments (-p), and possibly segments on the convex */
-/* hull (-c). */
-/* - Read the holes (-p), regional attributes (-pA), and regional area */
-/* constraints (-pa). Carve the holes and concavities, and spread the */
-/* regional attributes and area constraints. */
-/* - Enforce the constraints on minimum angle (-q) and maximum area (-a). */
-/* Also enforce the conforming Delaunay property (-q and -a). */
-/* - Compute the number of edges in the resulting mesh. */
-/* - Promote the mesh's linear triangles to higher order elements (-o). */
-/* - Write the output files and print the statistics. */
-/* - Check the consistency and Delaunay property of the mesh (-C). */
-/* */
-/*****************************************************************************/
-
-#ifdef TRILIBRARY
-
-#ifdef ANSI_DECLARATORS
-void triangulate(char *triswitches, struct triangulateio *in,
- struct triangulateio *out, struct triangulateio *vorout)
-#else /* not ANSI_DECLARATORS */
-void triangulate(triswitches, in, out, vorout)
-char *triswitches;
-struct triangulateio *in;
-struct triangulateio *out;
-struct triangulateio *vorout;
-#endif /* not ANSI_DECLARATORS */
-
-#else /* not TRILIBRARY */
-
-#ifdef ANSI_DECLARATORS
-int main(int argc, char **argv)
-#else /* not ANSI_DECLARATORS */
-int main(argc, argv)
-int argc;
-char **argv;
-#endif /* not ANSI_DECLARATORS */
-
-#endif /* not TRILIBRARY */
-
-{
- struct mesh m;
- struct behavior b;
- REAL *holearray; /* Array of holes. */
- REAL *regionarray; /* Array of regional attributes and area constraints. */
-#ifndef TRILIBRARY
- FILE *polyfile;
-#endif /* not TRILIBRARY */
-#ifndef NO_TIMER
- /* Variables for timing the performance of Triangle. The types are */
- /* defined in sys/time.h. */
- struct timeval tv0, tv1, tv2, tv3, tv4, tv5, tv6;
- struct timezone tz;
-#endif /* not NO_TIMER */
-
-#ifndef NO_TIMER
- gettimeofday(&tv0, &tz);
-#endif /* not NO_TIMER */
-
- triangleinit(&m);
-#ifdef TRILIBRARY
- parsecommandline(1, &triswitches, &b);
-#else /* not TRILIBRARY */
- parsecommandline(argc, argv, &b);
-#endif /* not TRILIBRARY */
- m.steinerleft = b.steiner;
-
-#ifdef TRILIBRARY
- transfernodes(&m, &b, in->pointlist, in->pointattributelist,
- in->pointmarkerlist, in->numberofpoints,
- in->numberofpointattributes);
-#else /* not TRILIBRARY */
- readnodes(&m, &b, b.innodefilename, b.inpolyfilename, &polyfile);
-#endif /* not TRILIBRARY */
-
-#ifndef NO_TIMER
- if (!b.quiet) {
- gettimeofday(&tv1, &tz);
- }
-#endif /* not NO_TIMER */
-
-#ifdef CDT_ONLY
- m.hullsize = delaunay(&m, &b); /* Triangulate the vertices. */
-#else /* not CDT_ONLY */
- if (b.refine) {
- /* Read and reconstruct a mesh. */
-#ifdef TRILIBRARY
- m.hullsize = reconstruct(&m, &b, in->trianglelist,
- in->triangleattributelist, in->trianglearealist,
- in->numberoftriangles, in->numberofcorners,
- in->numberoftriangleattributes,
- in->segmentlist, in->segmentmarkerlist,
- in->numberofsegments);
-#else /* not TRILIBRARY */
- m.hullsize = reconstruct(&m, &b, b.inelefilename, b.areafilename,
- b.inpolyfilename, polyfile);
-#endif /* not TRILIBRARY */
- } else {
- m.hullsize = delaunay(&m, &b); /* Triangulate the vertices. */
- }
-#endif /* not CDT_ONLY */
-
-#ifndef NO_TIMER
- if (!b.quiet) {
- gettimeofday(&tv2, &tz);
- if (b.refine) {
- printf("Mesh reconstruction");
- } else {
- printf("Delaunay");
- }
- printf(" milliseconds: %ld\n", 1000l * (tv2.tv_sec - tv1.tv_sec) +
- (tv2.tv_usec - tv1.tv_usec) / 1000l);
- }
-#endif /* not NO_TIMER */
-
- /* Ensure that no vertex can be mistaken for a triangular bounding */
- /* box vertex in insertvertex(). */
- m.infvertex1 = (vertex) NULL;
- m.infvertex2 = (vertex) NULL;
- m.infvertex3 = (vertex) NULL;
-
- if (b.usesegments) {
- m.checksegments = 1; /* Segments will be introduced next. */
- if (!b.refine) {
- /* Insert PSLG segments and/or convex hull segments. */
-#ifdef TRILIBRARY
- formskeleton(&m, &b, in->segmentlist,
- in->segmentmarkerlist, in->numberofsegments);
-#else /* not TRILIBRARY */
- formskeleton(&m, &b, polyfile, b.inpolyfilename);
-#endif /* not TRILIBRARY */
- }
- }
-
-#ifndef NO_TIMER
- if (!b.quiet) {
- gettimeofday(&tv3, &tz);
- if (b.usesegments && !b.refine) {
- printf("Segment milliseconds: %ld\n",
- 1000l * (tv3.tv_sec - tv2.tv_sec) +
- (tv3.tv_usec - tv2.tv_usec) / 1000l);
- }
- }
-#endif /* not NO_TIMER */
-
- if (b.poly && (m.triangles.items > 0)) {
-#ifdef TRILIBRARY
- holearray = in->holelist;
- m.holes = in->numberofholes;
- regionarray = in->regionlist;
- m.regions = in->numberofregions;
-#else /* not TRILIBRARY */
- readholes(&m, &b, polyfile, b.inpolyfilename, &holearray, &m.holes,
- ®ionarray, &m.regions);
-#endif /* not TRILIBRARY */
- if (!b.refine) {
- /* Carve out holes and concavities. */
- carveholes(&m, &b, holearray, m.holes, regionarray, m.regions);
- }
- } else {
- /* Without a PSLG, there can be no holes or regional attributes */
- /* or area constraints. The following are set to zero to avoid */
- /* an accidental free() later. */
- m.holes = 0;
- m.regions = 0;
- }
-
-#ifndef NO_TIMER
- if (!b.quiet) {
- gettimeofday(&tv4, &tz);
- if (b.poly && !b.refine) {
- printf("Hole milliseconds: %ld\n", 1000l * (tv4.tv_sec - tv3.tv_sec) +
- (tv4.tv_usec - tv3.tv_usec) / 1000l);
- }
- }
-#endif /* not NO_TIMER */
-
-#ifndef CDT_ONLY
- if (b.quality && (m.triangles.items > 0)) {
- enforcequality(&m, &b); /* Enforce angle and area constraints. */
- }
-#endif /* not CDT_ONLY */
-
-#ifndef NO_TIMER
- if (!b.quiet) {
- gettimeofday(&tv5, &tz);
-#ifndef CDT_ONLY
- if (b.quality) {
- printf("Quality milliseconds: %ld\n",
- 1000l * (tv5.tv_sec - tv4.tv_sec) +
- (tv5.tv_usec - tv4.tv_usec) / 1000l);
- }
-#endif /* not CDT_ONLY */
- }
-#endif /* not NO_TIMER */
-
- /* Calculate the number of edges. */
- m.edges = (3l * m.triangles.items + m.hullsize) / 2l;
-
- if (b.order > 1) {
- highorder(&m, &b); /* Promote elements to higher polynomial order. */
- }
- if (!b.quiet) {
- printf("\n");
- }
-
-#ifdef TRILIBRARY
- if (b.jettison) {
- out->numberofpoints = m.vertices.items - m.undeads;
- } else {
- out->numberofpoints = m.vertices.items;
- }
- out->numberofpointattributes = m.nextras;
- out->numberoftriangles = m.triangles.items;
- out->numberofcorners = (b.order + 1) * (b.order + 2) / 2;
- out->numberoftriangleattributes = m.eextras;
- out->numberofedges = m.edges;
- if (b.usesegments) {
- out->numberofsegments = m.subsegs.items;
- } else {
- out->numberofsegments = m.hullsize;
- }
- if (vorout != (struct triangulateio *) NULL) {
- vorout->numberofpoints = m.triangles.items;
- vorout->numberofpointattributes = m.nextras;
- vorout->numberofedges = m.edges;
- }
-#endif /* TRILIBRARY */
- /* If not using iteration numbers, don't write a .node file if one was */
- /* read, because the original one would be overwritten! */
- if (b.nonodewritten || (b.noiterationnum && m.readnodefile)) {
- if (!b.quiet) {
-#ifdef TRILIBRARY
- printf("NOT writing vertices.\n");
-#else /* not TRILIBRARY */
- printf("NOT writing a .node file.\n");
-#endif /* not TRILIBRARY */
- }
- numbernodes(&m, &b); /* We must remember to number the vertices. */
- } else {
- /* writenodes() numbers the vertices too. */
-#ifdef TRILIBRARY
- writenodes(&m, &b, &out->pointlist, &out->pointattributelist,
- &out->pointmarkerlist);
-#else /* not TRILIBRARY */
- writenodes(&m, &b, b.outnodefilename, argc, argv);
-#endif /* TRILIBRARY */
- }
- if (b.noelewritten) {
- if (!b.quiet) {
-#ifdef TRILIBRARY
- printf("NOT writing triangles.\n");
-#else /* not TRILIBRARY */
- printf("NOT writing an .ele file.\n");
-#endif /* not TRILIBRARY */
- }
- } else {
-#ifdef TRILIBRARY
- writeelements(&m, &b, &out->trianglelist, &out->triangleattributelist);
-#else /* not TRILIBRARY */
- writeelements(&m, &b, b.outelefilename, argc, argv);
-#endif /* not TRILIBRARY */
- }
- /* The -c switch (convex switch) causes a PSLG to be written */
- /* even if none was read. */
- if (b.poly || b.convex) {
- /* If not using iteration numbers, don't overwrite the .poly file. */
- if (b.nopolywritten || b.noiterationnum) {
- if (!b.quiet) {
-#ifdef TRILIBRARY
- printf("NOT writing segments.\n");
-#else /* not TRILIBRARY */
- printf("NOT writing a .poly file.\n");
-#endif /* not TRILIBRARY */
- }
- } else {
-#ifdef TRILIBRARY
- writepoly(&m, &b, &out->segmentlist, &out->segmentmarkerlist);
- out->numberofholes = m.holes;
- out->numberofregions = m.regions;
- if (b.poly) {
- out->holelist = in->holelist;
- out->regionlist = in->regionlist;
- } else {
- out->holelist = (REAL *) NULL;
- out->regionlist = (REAL *) NULL;
- }
-#else /* not TRILIBRARY */
- writepoly(&m, &b, b.outpolyfilename, holearray, m.holes, regionarray,
- m.regions, argc, argv);
-#endif /* not TRILIBRARY */
- }
- }
-#ifndef TRILIBRARY
-#ifndef CDT_ONLY
- if (m.regions > 0) {
- trifree((VOID *) regionarray);
- }
-#endif /* not CDT_ONLY */
- if (m.holes > 0) {
- trifree((VOID *) holearray);
- }
- if (b.geomview) {
- writeoff(&m, &b, b.offfilename, argc, argv);
- }
-#endif /* not TRILIBRARY */
- if (b.edgesout) {
-#ifdef TRILIBRARY
- writeedges(&m, &b, &out->edgelist, &out->edgemarkerlist);
-#else /* not TRILIBRARY */
- writeedges(&m, &b, b.edgefilename, argc, argv);
-#endif /* not TRILIBRARY */
- }
- if (b.voronoi) {
-#ifdef TRILIBRARY
- writevoronoi(&m, &b, &vorout->pointlist, &vorout->pointattributelist,
- &vorout->pointmarkerlist, &vorout->edgelist,
- &vorout->edgemarkerlist, &vorout->normlist);
-#else /* not TRILIBRARY */
- writevoronoi(&m, &b, b.vnodefilename, b.vedgefilename, argc, argv);
-#endif /* not TRILIBRARY */
- }
- if (b.neighbors) {
-#ifdef TRILIBRARY
- writeneighbors(&m, &b, &out->neighborlist);
-#else /* not TRILIBRARY */
- writeneighbors(&m, &b, b.neighborfilename, argc, argv);
-#endif /* not TRILIBRARY */
- }
-
- if (!b.quiet) {
-#ifndef NO_TIMER
- gettimeofday(&tv6, &tz);
- printf("\nOutput milliseconds: %ld\n",
- 1000l * (tv6.tv_sec - tv5.tv_sec) +
- (tv6.tv_usec - tv5.tv_usec) / 1000l);
- printf("Total running milliseconds: %ld\n",
- 1000l * (tv6.tv_sec - tv0.tv_sec) +
- (tv6.tv_usec - tv0.tv_usec) / 1000l);
-#endif /* not NO_TIMER */
-
- statistics(&m, &b);
- }
-
-#ifndef REDUCED
- if (b.docheck) {
- checkmesh(&m, &b);
- checkdelaunay(&m, &b);
- }
-#endif /* not REDUCED */
-
- triangledeinit(&m, &b);
-#ifndef TRILIBRARY
- return 0;
-#endif /* not TRILIBRARY */
-}
diff --git a/src/triangle.h b/src/triangle.h
deleted file mode 100644
index 9df1f39..0000000
--- a/src/triangle.h
+++ /dev/null
@@ -1,289 +0,0 @@
-/*****************************************************************************/
-/* */
-/* (triangle.h) */
-/* */
-/* Include file for programs that call Triangle. */
-/* */
-/* Accompanies Triangle Version 1.6 */
-/* July 28, 2005 */
-/* */
-/* Copyright 1996, 2005 */
-/* Jonathan Richard Shewchuk */
-/* 2360 Woolsey #H */
-/* Berkeley, California 94705-1927 */
-/* jrs at cs.berkeley.edu */
-/* */
-/*****************************************************************************/
-
-/*****************************************************************************/
-/* */
-/* How to call Triangle from another program */
-/* */
-/* */
-/* If you haven't read Triangle's instructions (run "triangle -h" to read */
-/* them), you won't understand what follows. */
-/* */
-/* Triangle must be compiled into an object file (triangle.o) with the */
-/* TRILIBRARY symbol defined (generally by using the -DTRILIBRARY compiler */
-/* switch). The makefile included with Triangle will do this for you if */
-/* you run "make trilibrary". The resulting object file can be called via */
-/* the procedure triangulate(). */
-/* */
-/* If the size of the object file is important to you, you may wish to */
-/* generate a reduced version of triangle.o. The REDUCED symbol gets rid */
-/* of all features that are primarily of research interest. Specifically, */
-/* the -DREDUCED switch eliminates Triangle's -i, -F, -s, and -C switches. */
-/* The CDT_ONLY symbol gets rid of all meshing algorithms above and beyond */
-/* constrained Delaunay triangulation. Specifically, the -DCDT_ONLY switch */
-/* eliminates Triangle's -r, -q, -a, -u, -D, -Y, -S, and -s switches. */
-/* */
-/* IMPORTANT: These definitions (TRILIBRARY, REDUCED, CDT_ONLY) must be */
-/* made in the makefile or in triangle.c itself. Putting these definitions */
-/* in this file (triangle.h) will not create the desired effect. */
-/* */
-/* */
-/* The calling convention for triangulate() follows. */
-/* */
-/* void triangulate(triswitches, in, out, vorout) */
-/* char *triswitches; */
-/* struct triangulateio *in; */
-/* struct triangulateio *out; */
-/* struct triangulateio *vorout; */
-/* */
-/* `triswitches' is a string containing the command line switches you wish */
-/* to invoke. No initial dash is required. Some suggestions: */
-/* */
-/* - You'll probably find it convenient to use the `z' switch so that */
-/* points (and other items) are numbered from zero. This simplifies */
-/* indexing, because the first item of any type always starts at index */
-/* [0] of the corresponding array, whether that item's number is zero or */
-/* one. */
-/* - You'll probably want to use the `Q' (quiet) switch in your final code, */
-/* but you can take advantage of Triangle's printed output (including the */
-/* `V' switch) while debugging. */
-/* - If you are not using the `q', `a', `u', `D', `j', or `s' switches, */
-/* then the output points will be identical to the input points, except */
-/* possibly for the boundary markers. If you don't need the boundary */
-/* markers, you should use the `N' (no nodes output) switch to save */
-/* memory. (If you do need boundary markers, but need to save memory, a */
-/* good nasty trick is to set out->pointlist equal to in->pointlist */
-/* before calling triangulate(), so that Triangle overwrites the input */
-/* points with identical copies.) */
-/* - The `I' (no iteration numbers) and `g' (.off file output) switches */
-/* have no effect when Triangle is compiled with TRILIBRARY defined. */
-/* */
-/* `in', `out', and `vorout' are descriptions of the input, the output, */
-/* and the Voronoi output. If the `v' (Voronoi output) switch is not used, */
-/* `vorout' may be NULL. `in' and `out' may never be NULL. */
-/* */
-/* Certain fields of the input and output structures must be initialized, */
-/* as described below. */
-/* */
-/*****************************************************************************/
-
-/*****************************************************************************/
-/* */
-/* The `triangulateio' structure. */
-/* */
-/* Used to pass data into and out of the triangulate() procedure. */
-/* */
-/* */
-/* Arrays are used to store points, triangles, markers, and so forth. In */
-/* all cases, the first item in any array is stored starting at index [0]. */
-/* However, that item is item number `1' unless the `z' switch is used, in */
-/* which case it is item number `0'. Hence, you may find it easier to */
-/* index points (and triangles in the neighbor list) if you use the `z' */
-/* switch. Unless, of course, you're calling Triangle from a Fortran */
-/* program. */
-/* */
-/* Description of fields (except the `numberof' fields, which are obvious): */
-/* */
-/* `pointlist': An array of point coordinates. The first point's x */
-/* coordinate is at index [0] and its y coordinate at index [1], followed */
-/* by the coordinates of the remaining points. Each point occupies two */
-/* REALs. */
-/* `pointattributelist': An array of point attributes. Each point's */
-/* attributes occupy `numberofpointattributes' REALs. */
-/* `pointmarkerlist': An array of point markers; one int per point. */
-/* */
-/* `trianglelist': An array of triangle corners. The first triangle's */
-/* first corner is at index [0], followed by its other two corners in */
-/* counterclockwise order, followed by any other nodes if the triangle */
-/* represents a nonlinear element. Each triangle occupies */
-/* `numberofcorners' ints. */
-/* `triangleattributelist': An array of triangle attributes. Each */
-/* triangle's attributes occupy `numberoftriangleattributes' REALs. */
-/* `trianglearealist': An array of triangle area constraints; one REAL per */
-/* triangle. Input only. */
-/* `neighborlist': An array of triangle neighbors; three ints per */
-/* triangle. Output only. */
-/* */
-/* `segmentlist': An array of segment endpoints. The first segment's */
-/* endpoints are at indices [0] and [1], followed by the remaining */
-/* segments. Two ints per segment. */
-/* `segmentmarkerlist': An array of segment markers; one int per segment. */
-/* */
-/* `holelist': An array of holes. The first hole's x and y coordinates */
-/* are at indices [0] and [1], followed by the remaining holes. Two */
-/* REALs per hole. Input only, although the pointer is copied to the */
-/* output structure for your convenience. */
-/* */
-/* `regionlist': An array of regional attributes and area constraints. */
-/* The first constraint's x and y coordinates are at indices [0] and [1], */
-/* followed by the regional attribute at index [2], followed by the */
-/* maximum area at index [3], followed by the remaining area constraints. */
-/* Four REALs per area constraint. Note that each regional attribute is */
-/* used only if you select the `A' switch, and each area constraint is */
-/* used only if you select the `a' switch (with no number following), but */
-/* omitting one of these switches does not change the memory layout. */
-/* Input only, although the pointer is copied to the output structure for */
-/* your convenience. */
-/* */
-/* `edgelist': An array of edge endpoints. The first edge's endpoints are */
-/* at indices [0] and [1], followed by the remaining edges. Two ints per */
-/* edge. Output only. */
-/* `edgemarkerlist': An array of edge markers; one int per edge. Output */
-/* only. */
-/* `normlist': An array of normal vectors, used for infinite rays in */
-/* Voronoi diagrams. The first normal vector's x and y magnitudes are */
-/* at indices [0] and [1], followed by the remaining vectors. For each */
-/* finite edge in a Voronoi diagram, the normal vector written is the */
-/* zero vector. Two REALs per edge. Output only. */
-/* */
-/* */
-/* Any input fields that Triangle will examine must be initialized. */
-/* Furthermore, for each output array that Triangle will write to, you */
-/* must either provide space by setting the appropriate pointer to point */
-/* to the space you want the data written to, or you must initialize the */
-/* pointer to NULL, which tells Triangle to allocate space for the results. */
-/* The latter option is preferable, because Triangle always knows exactly */
-/* how much space to allocate. The former option is provided mainly for */
-/* people who need to call Triangle from Fortran code, though it also makes */
-/* possible some nasty space-saving tricks, like writing the output to the */
-/* same arrays as the input. */
-/* */
-/* Triangle will not free() any input or output arrays, including those it */
-/* allocates itself; that's up to you. You should free arrays allocated by */
-/* Triangle by calling the trifree() procedure defined below. (By default, */
-/* trifree() just calls the standard free() library procedure, but */
-/* applications that call triangulate() may replace trimalloc() and */
-/* trifree() in triangle.c to use specialized memory allocators.) */
-/* */
-/* Here's a guide to help you decide which fields you must initialize */
-/* before you call triangulate(). */
-/* */
-/* `in': */
-/* */
-/* - `pointlist' must always point to a list of points; `numberofpoints' */
-/* and `numberofpointattributes' must be properly set. */
-/* `pointmarkerlist' must either be set to NULL (in which case all */
-/* markers default to zero), or must point to a list of markers. If */
-/* `numberofpointattributes' is not zero, `pointattributelist' must */
-/* point to a list of point attributes. */
-/* - If the `r' switch is used, `trianglelist' must point to a list of */
-/* triangles, and `numberoftriangles', `numberofcorners', and */
-/* `numberoftriangleattributes' must be properly set. If */
-/* `numberoftriangleattributes' is not zero, `triangleattributelist' */
-/* must point to a list of triangle attributes. If the `a' switch is */
-/* used (with no number following), `trianglearealist' must point to a */
-/* list of triangle area constraints. `neighborlist' may be ignored. */
-/* - If the `p' switch is used, `segmentlist' must point to a list of */
-/* segments, `numberofsegments' must be properly set, and */
-/* `segmentmarkerlist' must either be set to NULL (in which case all */
-/* markers default to zero), or must point to a list of markers. */
-/* - If the `p' switch is used without the `r' switch, then */
-/* `numberofholes' and `numberofregions' must be properly set. If */
-/* `numberofholes' is not zero, `holelist' must point to a list of */
-/* holes. If `numberofregions' is not zero, `regionlist' must point to */
-/* a list of region constraints. */
-/* - If the `p' switch is used, `holelist', `numberofholes', */
-/* `regionlist', and `numberofregions' is copied to `out'. (You can */
-/* nonetheless get away with not initializing them if the `r' switch is */
-/* used.) */
-/* - `edgelist', `edgemarkerlist', `normlist', and `numberofedges' may be */
-/* ignored. */
-/* */
-/* `out': */
-/* */
-/* - `pointlist' must be initialized (NULL or pointing to memory) unless */
-/* the `N' switch is used. `pointmarkerlist' must be initialized */
-/* unless the `N' or `B' switch is used. If `N' is not used and */
-/* `in->numberofpointattributes' is not zero, `pointattributelist' must */
-/* be initialized. */
-/* - `trianglelist' must be initialized unless the `E' switch is used. */
-/* `neighborlist' must be initialized if the `n' switch is used. If */
-/* the `E' switch is not used and (`in->numberofelementattributes' is */
-/* not zero or the `A' switch is used), `elementattributelist' must be */
-/* initialized. `trianglearealist' may be ignored. */
-/* - `segmentlist' must be initialized if the `p' or `c' switch is used, */
-/* and the `P' switch is not used. `segmentmarkerlist' must also be */
-/* initialized under these circumstances unless the `B' switch is used. */
-/* - `edgelist' must be initialized if the `e' switch is used. */
-/* `edgemarkerlist' must be initialized if the `e' switch is used and */
-/* the `B' switch is not. */
-/* - `holelist', `regionlist', `normlist', and all scalars may be ignored.*/
-/* */
-/* `vorout' (only needed if `v' switch is used): */
-/* */
-/* - `pointlist' must be initialized. If `in->numberofpointattributes' */
-/* is not zero, `pointattributelist' must be initialized. */
-/* `pointmarkerlist' may be ignored. */
-/* - `edgelist' and `normlist' must both be initialized. */
-/* `edgemarkerlist' may be ignored. */
-/* - Everything else may be ignored. */
-/* */
-/* After a call to triangulate(), the valid fields of `out' and `vorout' */
-/* will depend, in an obvious way, on the choice of switches used. Note */
-/* that when the `p' switch is used, the pointers `holelist' and */
-/* `regionlist' are copied from `in' to `out', but no new space is */
-/* allocated; be careful that you don't free() the same array twice. On */
-/* the other hand, Triangle will never copy the `pointlist' pointer (or any */
-/* others); new space is allocated for `out->pointlist', or if the `N' */
-/* switch is used, `out->pointlist' remains uninitialized. */
-/* */
-/* All of the meaningful `numberof' fields will be properly set; for */
-/* instance, `numberofedges' will represent the number of edges in the */
-/* triangulation whether or not the edges were written. If segments are */
-/* not used, `numberofsegments' will indicate the number of boundary edges. */
-/* */
-/*****************************************************************************/
-
-struct triangulateio {
- REAL *pointlist; /* In / out */
- REAL *pointattributelist; /* In / out */
- int *pointmarkerlist; /* In / out */
- int numberofpoints; /* In / out */
- int numberofpointattributes; /* In / out */
-
- int *trianglelist; /* In / out */
- REAL *triangleattributelist; /* In / out */
- REAL *trianglearealist; /* In only */
- int *neighborlist; /* Out only */
- int numberoftriangles; /* In / out */
- int numberofcorners; /* In / out */
- int numberoftriangleattributes; /* In / out */
-
- int *segmentlist; /* In / out */
- int *segmentmarkerlist; /* In / out */
- int numberofsegments; /* In / out */
-
- REAL *holelist; /* In / pointer to array copied out */
- int numberofholes; /* In / copied out */
-
- REAL *regionlist; /* In / pointer to array copied out */
- int numberofregions; /* In / copied out */
-
- int *edgelist; /* Out only */
- int *edgemarkerlist; /* Not used with Voronoi diagram; out only */
- REAL *normlist; /* Used only with Voronoi diagram; out only */
- int numberofedges; /* Out only */
-};
-
-#ifdef ANSI_DECLARATORS
-void triangulate(char *, struct triangulateio *, struct triangulateio *,
- struct triangulateio *);
-void trifree(VOID *memptr);
-#else /* not ANSI_DECLARATORS */
-void triangulate();
-void trifree();
-#endif /* not ANSI_DECLARATORS */
--
Generic Mapping Tools
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