[GRASS-SVN] r51217 - in grass-addons/grass6/vector: . v.trimesh
svn_grass at osgeo.org
svn_grass at osgeo.org
Sat Mar 31 04:56:38 EDT 2012
Author: amuriy
Date: 2012-03-31 01:56:38 -0700 (Sat, 31 Mar 2012)
New Revision: 51217
Added:
grass-addons/grass6/vector/v.trimesh/
grass-addons/grass6/vector/v.trimesh/Makefile
grass-addons/grass6/vector/v.trimesh/description.html
grass-addons/grass6/vector/v.trimesh/triangle.c
grass-addons/grass6/vector/v.trimesh/triangle.h
grass-addons/grass6/vector/v.trimesh/v.trimesh.c
grass-addons/grass6/vector/v.trimesh/v.trimesh.tmp.html
Modified:
grass-addons/grass6/vector/Makefile
Log:
<v.trimesh> added to grass6/vector; grass6/vector/Makefile edited
Modified: grass-addons/grass6/vector/Makefile
===================================================================
--- grass-addons/grass6/vector/Makefile 2012-03-31 07:58:03 UTC (rev 51216)
+++ grass-addons/grass6/vector/Makefile 2012-03-31 08:56:38 UTC (rev 51217)
@@ -2,10 +2,10 @@
SUBDIRS = \
adehabitat \
- net.analyze \
v.autokrige \
v.curvature \
v.db.calc \
+ v.eqsm \
v.in.gama \
v.in.geoplot \
v.in.gshhs \
@@ -25,6 +25,9 @@
v.surf.icw \
v.swathwidth \
v.transect.kia \
+ v.transects \
+ v.trimesh \
+ v.vect.stats \
v.what.rast.buffer
include $(MODULE_TOPDIR)/include/Make/Dir.make
Added: grass-addons/grass6/vector/v.trimesh/Makefile
===================================================================
--- grass-addons/grass6/vector/v.trimesh/Makefile (rev 0)
+++ grass-addons/grass6/vector/v.trimesh/Makefile 2012-03-31 08:56:38 UTC (rev 51217)
@@ -0,0 +1,14 @@
+
+#MODULE_TOPDIR = ../..
+
+PGM = v.trimesh
+
+LIBES = $(VECTLIB) $(GISLIB)
+DEPENDENCIES= $(VECTDEP) $(GISDEP)
+EXTRA_INC = $(VECT_INC)
+EXTRA_CFLAGS = $(VECT_CFLAGS)
+
+include $(MODULE_TOPDIR)/include/Make/Module.make
+
+default: cmd
+
Added: grass-addons/grass6/vector/v.trimesh/description.html
===================================================================
--- grass-addons/grass6/vector/v.trimesh/description.html (rev 0)
+++ grass-addons/grass6/vector/v.trimesh/description.html 2012-03-31 08:56:38 UTC (rev 51217)
@@ -0,0 +1,47 @@
+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
+<html>
+<head>
+<title>GRASS GIS manual: v.trimesh</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<link rel="stylesheet" href="grassdocs.css" type="text/css">
+</head>
+<body bgcolor="white">
+
+<img src="grass_logo.png" alt="GRASS logo"><hr align=center size=6 noshade>
+
+<h2>NAME</h2>
+<em><b>v.trimesh</b></em> - Create a triangular mesh from a vector map
+<h2>KEYWORDS</h2>
+vector
+<h2>SYNOPSIS</h2>
+<b>v.trimesh</b><br>
+<b>v.trimesh help</b><br>
+<b>v.trimesh</b> [-<b>a</b>] <b>input</b>=<em>name</em> <b>column</b>=<em>string</em> <b>output</b>=<em>name</em> [--<b>overwrite</b>] [--<b>verbose</b>] [--<b>quiet</b>]
+
+<h3>Flags:</h3>
+<DL>
+<DT><b>-a</b></DT>
+<DD>Do not use areal constraint</DD>
+
+<DT><b>--overwrite</b></DT>
+<DD>Allow output files to overwrite existing files</DD>
+<DT><b>--verbose</b></DT>
+<DD>Verbose module output</DD>
+<DT><b>--quiet</b></DT>
+<DD>Quiet module output</DD>
+</DL>
+
+<h3>Parameters:</h3>
+<DL>
+<DT><b>input</b>=<em>name</em></DT>
+<DD>Name of input vector map</DD>
+
+<DT><b>column</b>=<em>string</em></DT>
+<DD>Column name with area constraints/centroid attributes</DD>
+
+<DT><b>output</b>=<em>name</em></DT>
+<DD>Name for output vector map</DD>
+
+</DL>
+</body>
+</html>
Added: grass-addons/grass6/vector/v.trimesh/triangle.c
===================================================================
--- grass-addons/grass6/vector/v.trimesh/triangle.c (rev 0)
+++ grass-addons/grass6/vector/v.trimesh/triangle.c 2012-03-31 08:56:38 UTC (rev 51217)
@@ -0,0 +1,16006 @@
+/*****************************************************************************/
+/* */
+/* 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((unsigned int) size);
+ if (memptr == (VOID *) NULL) {
+ printf("Error: Out of memory.\n");
+ triexit(1);
+ }
+ return(memptr);
+}
+
+#ifdef ANSI_DECLARATORS
+void trifree(VOID *memptr)
+#else /* not ANSI_DECLARATORS */
+void trifree(memptr)
+VOID *memptr;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ free(memptr);
+}
+
+/** **/
+/** **/
+/********* Memory allocation and program exit wrappers end here *********/
+
+/********* User interaction routines begin here *********/
+/** **/
+/** **/
+
+/*****************************************************************************/
+/* */
+/* syntax() Print list of command line switches. */
+/* */
+/*****************************************************************************/
+
+#ifndef TRILIBRARY
+
+void syntax()
+{
+#ifdef CDT_ONLY
+#ifdef REDUCED
+ printf("triangle [-pAcjevngBPNEIOXzo_lQVh] input_file\n");
+#else /* not REDUCED */
+ printf("triangle [-pAcjevngBPNEIOXzo_iFlCQVh] input_file\n");
+#endif /* not REDUCED */
+#else /* not CDT_ONLY */
+#ifdef REDUCED
+ printf("triangle [-prq__a__uAcDjevngBPNEIOXzo_YS__lQVh] input_file\n");
+#else /* not REDUCED */
+ printf("triangle [-prq__a__uAcDjevngBPNEIOXzo_YS__iFlsCQVh] input_file\n");
+#endif /* not REDUCED */
+#endif /* not CDT_ONLY */
+
+ printf(" -p Triangulates a Planar Straight Line Graph (.poly file).\n");
+#ifndef CDT_ONLY
+ printf(" -r Refines a previously generated mesh.\n");
+ printf(
+ " -q Quality mesh generation. A minimum angle may be specified.\n");
+ printf(" -a Applies a maximum triangle area constraint.\n");
+ printf(" -u Applies a user-defined triangle constraint.\n");
+#endif /* not CDT_ONLY */
+ printf(
+ " -A Applies attributes to identify triangles in certain regions.\n");
+ printf(" -c Encloses the convex hull with segments.\n");
+#ifndef CDT_ONLY
+ printf(" -D Conforming Delaunay: all triangles are truly Delaunay.\n");
+#endif /* not CDT_ONLY */
+/*
+ printf(" -w Weighted Delaunay triangulation.\n");
+ printf(" -W Regular triangulation (lower hull of a height field).\n");
+*/
+ printf(" -j Jettison unused vertices from output .node file.\n");
+ printf(" -e Generates an edge list.\n");
+ printf(" -v Generates a Voronoi diagram.\n");
+ printf(" -n Generates a list of triangle neighbors.\n");
+ printf(" -g Generates an .off file for Geomview.\n");
+ printf(" -B Suppresses output of boundary information.\n");
+ printf(" -P Suppresses output of .poly file.\n");
+ printf(" -N Suppresses output of .node file.\n");
+ printf(" -E Suppresses output of .ele file.\n");
+ printf(" -I Suppresses mesh iteration numbers.\n");
+ printf(" -O Ignores holes in .poly file.\n");
+ printf(" -X Suppresses use of exact arithmetic.\n");
+ printf(" -z Numbers all items starting from zero (rather than one).\n");
+ printf(" -o2 Generates second-order subparametric elements.\n");
+#ifndef CDT_ONLY
+ printf(" -Y Suppresses boundary segment splitting.\n");
+ printf(" -S Specifies maximum number of added Steiner points.\n");
+#endif /* not CDT_ONLY */
+#ifndef REDUCED
+ printf(" -i Uses incremental method, rather than divide-and-conquer.\n");
+ printf(" -F Uses Fortune's sweepline algorithm, rather than d-and-c.\n");
+#endif /* not REDUCED */
+ printf(" -l Uses vertical cuts only, rather than alternating cuts.\n");
+#ifndef REDUCED
+#ifndef CDT_ONLY
+ printf(
+ " -s Force segments into mesh by splitting (instead of using CDT).\n");
+#endif /* not CDT_ONLY */
+ printf(" -C Check consistency of final mesh.\n");
+#endif /* not REDUCED */
+ printf(" -Q Quiet: No terminal output except errors.\n");
+ printf(" -V Verbose: Detailed information on what I'm doing.\n");
+ printf(" -h Help: Detailed instructions for Triangle.\n");
+ triexit(0);
+}
+
+#endif /* not TRILIBRARY */
+
+/*****************************************************************************/
+/* */
+/* info() Print out complete instructions. */
+/* */
+/*****************************************************************************/
+
+#ifndef TRILIBRARY
+
+void info()
+{
+ printf("Triangle\n");
+ printf(
+"A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator.\n");
+ printf("Version 1.6\n\n");
+ printf(
+"Copyright 1993, 1995, 1997, 1998, 2002, 2005 Jonathan Richard Shewchuk\n");
+ printf("2360 Woolsey #H / Berkeley, California 94705-1927\n");
+ printf("Bugs/comments to jrs 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 */
+ int i, j, k;
+ char workstring[FILENAMESIZE];
+
+ b->poly = b->refine = b->quality = 0;
+ b->vararea = b->fixedarea = b->usertest = 0;
+ b->regionattrib = b->convex = b->weighted = b->jettison = 0;
+ b->firstnumber = 1;
+ b->edgesout = b->voronoi = b->neighbors = b->geomview = 0;
+ b->nobound = b->nopolywritten = b->nonodewritten = b->noelewritten = 0;
+ b->noiterationnum = 0;
+ b->noholes = b->noexact = 0;
+ b->incremental = b->sweepline = 0;
+ b->dwyer = 1;
+ b->splitseg = 0;
+ b->docheck = 0;
+ b->nobisect = 0;
+ b->conformdel = 0;
+ b->steiner = -1;
+ b->order = 1;
+ b->minangle = 0.0;
+ b->maxarea = -1.0;
+ b->quiet = b->verbose = 0;
+#ifndef TRILIBRARY
+ b->innodefilename[0] = '\0';
+#endif /* not TRILIBRARY */
+
+ for (i = STARTINDEX; i < argc; i++) {
+#ifndef TRILIBRARY
+ if (argv[i][0] == '-') {
+#endif /* not TRILIBRARY */
+ for (j = STARTINDEX; argv[i][j] != '\0'; j++) {
+ if (argv[i][j] == 'p') {
+ b->poly = 1;
+ }
+#ifndef CDT_ONLY
+ if (argv[i][j] == 'r') {
+ b->refine = 1;
+ }
+ if (argv[i][j] == 'q') {
+ b->quality = 1;
+ if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
+ (argv[i][j + 1] == '.')) {
+ k = 0;
+ while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
+ (argv[i][j + 1] == '.')) {
+ j++;
+ workstring[k] = argv[i][j];
+ k++;
+ }
+ workstring[k] = '\0';
+ b->minangle = (REAL) strtod(workstring, (char **) NULL);
+ } else {
+ b->minangle = 20.0;
+ }
+ }
+ if (argv[i][j] == 'a') {
+ b->quality = 1;
+ if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
+ (argv[i][j + 1] == '.')) {
+ b->fixedarea = 1;
+ k = 0;
+ while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
+ (argv[i][j + 1] == '.')) {
+ j++;
+ workstring[k] = argv[i][j];
+ k++;
+ }
+ workstring[k] = '\0';
+ b->maxarea = (REAL) strtod(workstring, (char **) NULL);
+ if (b->maxarea <= 0.0) {
+ printf("Error: Maximum area must be greater than zero.\n");
+ triexit(1);
+ }
+ } else {
+ b->vararea = 1;
+ }
+ }
+ if (argv[i][j] == 'u') {
+ b->quality = 1;
+ b->usertest = 1;
+ }
+#endif /* not CDT_ONLY */
+ if (argv[i][j] == 'A') {
+ b->regionattrib = 1;
+ }
+ if (argv[i][j] == 'c') {
+ b->convex = 1;
+ }
+ if (argv[i][j] == 'w') {
+ b->weighted = 1;
+ }
+ if (argv[i][j] == 'W') {
+ b->weighted = 2;
+ }
+ if (argv[i][j] == 'j') {
+ b->jettison = 1;
+ }
+ if (argv[i][j] == 'z') {
+ b->firstnumber = 0;
+ }
+ if (argv[i][j] == 'e') {
+ b->edgesout = 1;
+ }
+ if (argv[i][j] == 'v') {
+ b->voronoi = 1;
+ }
+ if (argv[i][j] == 'n') {
+ b->neighbors = 1;
+ }
+ if (argv[i][j] == 'g') {
+ b->geomview = 1;
+ }
+ if (argv[i][j] == 'B') {
+ b->nobound = 1;
+ }
+ if (argv[i][j] == 'P') {
+ b->nopolywritten = 1;
+ }
+ if (argv[i][j] == 'N') {
+ b->nonodewritten = 1;
+ }
+ if (argv[i][j] == 'E') {
+ b->noelewritten = 1;
+ }
+#ifndef TRILIBRARY
+ if (argv[i][j] == 'I') {
+ b->noiterationnum = 1;
+ }
+#endif /* not TRILIBRARY */
+ if (argv[i][j] == 'O') {
+ b->noholes = 1;
+ }
+ if (argv[i][j] == 'X') {
+ b->noexact = 1;
+ }
+ if (argv[i][j] == 'o') {
+ if (argv[i][j + 1] == '2') {
+ j++;
+ b->order = 2;
+ }
+ }
+#ifndef CDT_ONLY
+ if (argv[i][j] == 'Y') {
+ b->nobisect++;
+ }
+ if (argv[i][j] == 'S') {
+ b->steiner = 0;
+ while ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) {
+ j++;
+ b->steiner = b->steiner * 10 + (int) (argv[i][j] - '0');
+ }
+ }
+#endif /* not CDT_ONLY */
+#ifndef REDUCED
+ if (argv[i][j] == 'i') {
+ b->incremental = 1;
+ }
+ if (argv[i][j] == 'F') {
+ b->sweepline = 1;
+ }
+#endif /* not REDUCED */
+ if (argv[i][j] == 'l') {
+ b->dwyer = 0;
+ }
+#ifndef REDUCED
+#ifndef CDT_ONLY
+ if (argv[i][j] == 's') {
+ b->splitseg = 1;
+ }
+ if ((argv[i][j] == 'D') || (argv[i][j] == 'L')) {
+ b->quality = 1;
+ b->conformdel = 1;
+ }
+#endif /* not CDT_ONLY */
+ if (argv[i][j] == 'C') {
+ b->docheck = 1;
+ }
+#endif /* not REDUCED */
+ if (argv[i][j] == 'Q') {
+ b->quiet = 1;
+ }
+ if (argv[i][j] == 'V') {
+ b->verbose++;
+ }
+#ifndef TRILIBRARY
+ if ((argv[i][j] == 'h') || (argv[i][j] == 'H') ||
+ (argv[i][j] == '?')) {
+ info();
+ }
+#endif /* not TRILIBRARY */
+ }
+#ifndef TRILIBRARY
+ } else {
+ strncpy(b->innodefilename, argv[i], FILENAMESIZE - 1);
+ b->innodefilename[FILENAMESIZE - 1] = '\0';
+ }
+#endif /* not TRILIBRARY */
+ }
+#ifndef TRILIBRARY
+ if (b->innodefilename[0] == '\0') {
+ syntax();
+ }
+ if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 5], ".node")) {
+ b->innodefilename[strlen(b->innodefilename) - 5] = '\0';
+ }
+ if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 5], ".poly")) {
+ b->innodefilename[strlen(b->innodefilename) - 5] = '\0';
+ b->poly = 1;
+ }
+#ifndef CDT_ONLY
+ if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 4], ".ele")) {
+ b->innodefilename[strlen(b->innodefilename) - 4] = '\0';
+ b->refine = 1;
+ }
+ if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 5], ".area")) {
+ b->innodefilename[strlen(b->innodefilename) - 5] = '\0';
+ b->refine = 1;
+ b->quality = 1;
+ b->vararea = 1;
+ }
+#endif /* not CDT_ONLY */
+#endif /* not TRILIBRARY */
+ b->usesegments = b->poly || b->refine || b->quality || b->convex;
+ b->goodangle = cos(b->minangle * PI / 180.0);
+ if (b->goodangle == 1.0) {
+ b->offconstant = 0.0;
+ } else {
+ b->offconstant = 0.475 * sqrt((1.0 + b->goodangle) / (1.0 - b->goodangle));
+ }
+ b->goodangle *= b->goodangle;
+ if (b->refine && b->noiterationnum) {
+ printf(
+ "Error: You cannot use the -I switch when refining a triangulation.\n");
+ triexit(1);
+ }
+ /* Be careful not to allocate space for element area constraints that */
+ /* will never be assigned any value (other than the default -1.0). */
+ if (!b->refine && !b->poly) {
+ b->vararea = 0;
+ }
+ /* Be careful not to add an extra attribute to each element unless the */
+ /* input supports it (PSLG in, but not refining a preexisting mesh). */
+ if (b->refine || !b->poly) {
+ b->regionattrib = 0;
+ }
+ /* Regular/weighted triangulations are incompatible with PSLGs */
+ /* and meshing. */
+ if (b->weighted && (b->poly || b->quality)) {
+ b->weighted = 0;
+ if (!b->quiet) {
+ printf("Warning: weighted triangulations (-w, -W) are incompatible\n");
+ printf(" with PSLGs (-p) and meshing (-q, -a, -u). Weights ignored.\n"
+ );
+ }
+ }
+ if (b->jettison && b->nonodewritten && !b->quiet) {
+ printf("Warning: -j and -N switches are somewhat incompatible.\n");
+ printf(" If any vertices are jettisoned, you will need the output\n");
+ printf(" .node file to reconstruct the new node indices.");
+ }
+
+#ifndef TRILIBRARY
+ strcpy(b->inpolyfilename, b->innodefilename);
+ strcpy(b->inelefilename, b->innodefilename);
+ strcpy(b->areafilename, b->innodefilename);
+ increment = 0;
+ strcpy(workstring, b->innodefilename);
+ j = 1;
+ while (workstring[j] != '\0') {
+ if ((workstring[j] == '.') && (workstring[j + 1] != '\0')) {
+ increment = j + 1;
+ }
+ j++;
+ }
+ meshnumber = 0;
+ if (increment > 0) {
+ j = increment;
+ do {
+ if ((workstring[j] >= '0') && (workstring[j] <= '9')) {
+ meshnumber = meshnumber * 10 + (int) (workstring[j] - '0');
+ } else {
+ increment = 0;
+ }
+ j++;
+ } while (workstring[j] != '\0');
+ }
+ if (b->noiterationnum) {
+ strcpy(b->outnodefilename, b->innodefilename);
+ strcpy(b->outelefilename, b->innodefilename);
+ strcpy(b->edgefilename, b->innodefilename);
+ strcpy(b->vnodefilename, b->innodefilename);
+ strcpy(b->vedgefilename, b->innodefilename);
+ strcpy(b->neighborfilename, b->innodefilename);
+ strcpy(b->offfilename, b->innodefilename);
+ strcat(b->outnodefilename, ".node");
+ strcat(b->outelefilename, ".ele");
+ strcat(b->edgefilename, ".edge");
+ strcat(b->vnodefilename, ".v.node");
+ strcat(b->vedgefilename, ".v.edge");
+ strcat(b->neighborfilename, ".neigh");
+ strcat(b->offfilename, ".off");
+ } else if (increment == 0) {
+ strcpy(b->outnodefilename, b->innodefilename);
+ strcpy(b->outpolyfilename, b->innodefilename);
+ strcpy(b->outelefilename, b->innodefilename);
+ strcpy(b->edgefilename, b->innodefilename);
+ strcpy(b->vnodefilename, b->innodefilename);
+ strcpy(b->vedgefilename, b->innodefilename);
+ strcpy(b->neighborfilename, b->innodefilename);
+ strcpy(b->offfilename, b->innodefilename);
+ strcat(b->outnodefilename, ".1.node");
+ strcat(b->outpolyfilename, ".1.poly");
+ strcat(b->outelefilename, ".1.ele");
+ strcat(b->edgefilename, ".1.edge");
+ strcat(b->vnodefilename, ".1.v.node");
+ strcat(b->vedgefilename, ".1.v.edge");
+ strcat(b->neighborfilename, ".1.neigh");
+ strcat(b->offfilename, ".1.off");
+ } else {
+ workstring[increment] = '%';
+ workstring[increment + 1] = 'd';
+ workstring[increment + 2] = '\0';
+ sprintf(b->outnodefilename, workstring, meshnumber + 1);
+ strcpy(b->outpolyfilename, b->outnodefilename);
+ strcpy(b->outelefilename, b->outnodefilename);
+ strcpy(b->edgefilename, b->outnodefilename);
+ strcpy(b->vnodefilename, b->outnodefilename);
+ strcpy(b->vedgefilename, b->outnodefilename);
+ strcpy(b->neighborfilename, b->outnodefilename);
+ strcpy(b->offfilename, b->outnodefilename);
+ strcat(b->outnodefilename, ".node");
+ strcat(b->outpolyfilename, ".poly");
+ strcat(b->outelefilename, ".ele");
+ strcat(b->edgefilename, ".edge");
+ strcat(b->vnodefilename, ".v.node");
+ strcat(b->vedgefilename, ".v.edge");
+ strcat(b->neighborfilename, ".neigh");
+ strcat(b->offfilename, ".off");
+ }
+ strcat(b->innodefilename, ".node");
+ strcat(b->inpolyfilename, ".poly");
+ strcat(b->inelefilename, ".ele");
+ strcat(b->areafilename, ".area");
+#endif /* not TRILIBRARY */
+}
+
+/** **/
+/** **/
+/********* User interaction routines begin here *********/
+
+/********* Debugging routines begin here *********/
+/** **/
+/** **/
+
+/*****************************************************************************/
+/* */
+/* printtriangle() Print out the details of an oriented triangle. */
+/* */
+/* I originally wrote this procedure to simplify debugging; it can be */
+/* called directly from the debugger, and presents information about an */
+/* oriented triangle in digestible form. It's also used when the */
+/* highest level of verbosity (`-VVV') is specified. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+void printtriangle(struct mesh *m, struct behavior *b, struct otri *t)
+#else /* not ANSI_DECLARATORS */
+void printtriangle(m, b, t)
+struct mesh *m;
+struct behavior *b;
+struct otri *t;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ struct otri printtri;
+ struct osub printsh;
+ vertex printvertex;
+
+ printf("triangle x%lx with orientation %d:\n", (unsigned long) t->tri,
+ t->orient);
+ decode(t->tri[0], printtri);
+ if (printtri.tri == m->dummytri) {
+ printf(" [0] = Outer space\n");
+ } else {
+ printf(" [0] = x%lx %d\n", (unsigned long) printtri.tri,
+ printtri.orient);
+ }
+ decode(t->tri[1], printtri);
+ if (printtri.tri == m->dummytri) {
+ printf(" [1] = Outer space\n");
+ } else {
+ printf(" [1] = x%lx %d\n", (unsigned long) printtri.tri,
+ printtri.orient);
+ }
+ decode(t->tri[2], printtri);
+ if (printtri.tri == m->dummytri) {
+ printf(" [2] = Outer space\n");
+ } else {
+ printf(" [2] = x%lx %d\n", (unsigned long) printtri.tri,
+ printtri.orient);
+ }
+
+ org(*t, printvertex);
+ if (printvertex == (vertex) NULL)
+ printf(" Origin[%d] = NULL\n", (t->orient + 1) % 3 + 3);
+ else
+ printf(" Origin[%d] = x%lx (%.12g, %.12g)\n",
+ (t->orient + 1) % 3 + 3, (unsigned long) printvertex,
+ printvertex[0], printvertex[1]);
+ dest(*t, printvertex);
+ if (printvertex == (vertex) NULL)
+ printf(" Dest [%d] = NULL\n", (t->orient + 2) % 3 + 3);
+ else
+ printf(" Dest [%d] = x%lx (%.12g, %.12g)\n",
+ (t->orient + 2) % 3 + 3, (unsigned long) printvertex,
+ printvertex[0], printvertex[1]);
+ apex(*t, printvertex);
+ if (printvertex == (vertex) NULL)
+ printf(" Apex [%d] = NULL\n", t->orient + 3);
+ else
+ printf(" Apex [%d] = x%lx (%.12g, %.12g)\n",
+ t->orient + 3, (unsigned long) printvertex,
+ printvertex[0], printvertex[1]);
+
+ if (b->usesegments) {
+ sdecode(t->tri[6], printsh);
+ if (printsh.ss != m->dummysub) {
+ printf(" [6] = x%lx %d\n", (unsigned long) printsh.ss,
+ printsh.ssorient);
+ }
+ sdecode(t->tri[7], printsh);
+ if (printsh.ss != m->dummysub) {
+ printf(" [7] = x%lx %d\n", (unsigned long) printsh.ss,
+ printsh.ssorient);
+ }
+ sdecode(t->tri[8], printsh);
+ if (printsh.ss != m->dummysub) {
+ printf(" [8] = x%lx %d\n", (unsigned long) printsh.ss,
+ printsh.ssorient);
+ }
+ }
+
+ if (b->vararea) {
+ printf(" Area constraint: %.4g\n", areabound(*t));
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* printsubseg() Print out the details of an oriented subsegment. */
+/* */
+/* I originally wrote this procedure to simplify debugging; it can be */
+/* called directly from the debugger, and presents information about an */
+/* oriented subsegment in digestible form. It's also used when the highest */
+/* level of verbosity (`-VVV') is specified. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+void printsubseg(struct mesh *m, struct behavior *b, struct osub *s)
+#else /* not ANSI_DECLARATORS */
+void printsubseg(m, b, s)
+struct mesh *m;
+struct behavior *b;
+struct osub *s;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ struct osub printsh;
+ struct otri printtri;
+ vertex printvertex;
+
+ printf("subsegment x%lx with orientation %d and mark %d:\n",
+ (unsigned long) s->ss, s->ssorient, mark(*s));
+ sdecode(s->ss[0], printsh);
+ if (printsh.ss == m->dummysub) {
+ printf(" [0] = No subsegment\n");
+ } else {
+ printf(" [0] = x%lx %d\n", (unsigned long) printsh.ss,
+ printsh.ssorient);
+ }
+ sdecode(s->ss[1], printsh);
+ if (printsh.ss == m->dummysub) {
+ printf(" [1] = No subsegment\n");
+ } else {
+ printf(" [1] = x%lx %d\n", (unsigned long) printsh.ss,
+ printsh.ssorient);
+ }
+
+ sorg(*s, printvertex);
+ if (printvertex == (vertex) NULL)
+ printf(" Origin[%d] = NULL\n", 2 + s->ssorient);
+ else
+ printf(" Origin[%d] = x%lx (%.12g, %.12g)\n",
+ 2 + s->ssorient, (unsigned long) printvertex,
+ printvertex[0], printvertex[1]);
+ sdest(*s, printvertex);
+ if (printvertex == (vertex) NULL)
+ printf(" Dest [%d] = NULL\n", 3 - s->ssorient);
+ else
+ printf(" Dest [%d] = x%lx (%.12g, %.12g)\n",
+ 3 - s->ssorient, (unsigned long) printvertex,
+ printvertex[0], printvertex[1]);
+
+ decode(s->ss[6], printtri);
+ if (printtri.tri == m->dummytri) {
+ printf(" [6] = Outer space\n");
+ } else {
+ printf(" [6] = x%lx %d\n", (unsigned long) printtri.tri,
+ printtri.orient);
+ }
+ decode(s->ss[7], printtri);
+ if (printtri.tri == m->dummytri) {
+ printf(" [7] = Outer space\n");
+ } else {
+ printf(" [7] = x%lx %d\n", (unsigned long) printtri.tri,
+ printtri.orient);
+ }
+
+ segorg(*s, printvertex);
+ if (printvertex == (vertex) NULL)
+ printf(" Segment origin[%d] = NULL\n", 4 + s->ssorient);
+ else
+ printf(" Segment origin[%d] = x%lx (%.12g, %.12g)\n",
+ 4 + s->ssorient, (unsigned long) printvertex,
+ printvertex[0], printvertex[1]);
+ segdest(*s, printvertex);
+ if (printvertex == (vertex) NULL)
+ printf(" Segment dest [%d] = NULL\n", 5 - s->ssorient);
+ else
+ printf(" Segment dest [%d] = x%lx (%.12g, %.12g)\n",
+ 5 - s->ssorient, (unsigned long) printvertex,
+ printvertex[0], printvertex[1]);
+}
+
+/** **/
+/** **/
+/********* Debugging routines end here *********/
+
+/********* Memory management routines begin here *********/
+/** **/
+/** **/
+
+/*****************************************************************************/
+/* */
+/* poolzero() Set all of a pool's fields to zero. */
+/* */
+/* This procedure should never be called on a pool that has any memory */
+/* allocated to it, as that memory would leak. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+void poolzero(struct memorypool *pool)
+#else /* not ANSI_DECLARATORS */
+void poolzero(pool)
+struct memorypool *pool;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ pool->firstblock = (VOID **) NULL;
+ pool->nowblock = (VOID **) NULL;
+ pool->nextitem = (VOID *) NULL;
+ pool->deaditemstack = (VOID *) NULL;
+ pool->pathblock = (VOID **) NULL;
+ pool->pathitem = (VOID *) NULL;
+ pool->alignbytes = 0;
+ pool->itembytes = 0;
+ pool->itemsperblock = 0;
+ pool->itemsfirstblock = 0;
+ pool->items = 0;
+ pool->maxitems = 0;
+ pool->unallocateditems = 0;
+ pool->pathitemsleft = 0;
+}
+
+/*****************************************************************************/
+/* */
+/* poolrestart() Deallocate all items in a pool. */
+/* */
+/* The pool is returned to its starting state, except that no memory is */
+/* freed to the operating system. Rather, the previously allocated blocks */
+/* are ready to be reused. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+void poolrestart(struct memorypool *pool)
+#else /* not ANSI_DECLARATORS */
+void poolrestart(pool)
+struct memorypool *pool;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ unsigned long alignptr;
+
+ pool->items = 0;
+ pool->maxitems = 0;
+
+ /* Set the currently active block. */
+ pool->nowblock = pool->firstblock;
+ /* Find the first item in the pool. Increment by the size of (VOID *). */
+ alignptr = (unsigned long) (pool->nowblock + 1);
+ /* Align the item on an `alignbytes'-byte boundary. */
+ pool->nextitem = (VOID *)
+ (alignptr + (unsigned long) pool->alignbytes -
+ (alignptr % (unsigned long) pool->alignbytes));
+ /* There are lots of unallocated items left in this block. */
+ pool->unallocateditems = pool->itemsfirstblock;
+ /* The stack of deallocated items is empty. */
+ pool->deaditemstack = (VOID *) NULL;
+}
+
+/*****************************************************************************/
+/* */
+/* poolinit() Initialize a pool of memory for allocation of items. */
+/* */
+/* This routine initializes the machinery for allocating items. A `pool' */
+/* is created whose records have size at least `bytecount'. Items will be */
+/* allocated in `itemcount'-item blocks. Each item is assumed to be a */
+/* collection of words, and either pointers or floating-point values are */
+/* assumed to be the "primary" word type. (The "primary" word type is used */
+/* to determine alignment of items.) If `alignment' isn't zero, all items */
+/* will be `alignment'-byte aligned in memory. `alignment' must be either */
+/* a multiple or a factor of the primary word size; powers of two are safe. */
+/* `alignment' is normally used to create a few unused bits at the bottom */
+/* of each item's pointer, in which information may be stored. */
+/* */
+/* Don't change this routine unless you understand it. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+void poolinit(struct memorypool *pool, int bytecount, int itemcount,
+ int firstitemcount, int alignment)
+#else /* not ANSI_DECLARATORS */
+void poolinit(pool, bytecount, itemcount, firstitemcount, alignment)
+struct memorypool *pool;
+int bytecount;
+int itemcount;
+int firstitemcount;
+int alignment;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ /* Find the proper alignment, which must be at least as large as: */
+ /* - The parameter `alignment'. */
+ /* - sizeof(VOID *), so the stack of dead items can be maintained */
+ /* without unaligned accesses. */
+ if (alignment > sizeof(VOID *)) {
+ pool->alignbytes = alignment;
+ } else {
+ pool->alignbytes = sizeof(VOID *);
+ }
+ pool->itembytes = ((bytecount - 1) / pool->alignbytes + 1) *
+ pool->alignbytes;
+ pool->itemsperblock = itemcount;
+ if (firstitemcount == 0) {
+ pool->itemsfirstblock = itemcount;
+ } else {
+ pool->itemsfirstblock = firstitemcount;
+ }
+
+ /* Allocate a block of items. Space for `itemsfirstblock' items and one */
+ /* pointer (to point to the next block) are allocated, as well as space */
+ /* to ensure alignment of the items. */
+ pool->firstblock = (VOID **)
+ trimalloc(pool->itemsfirstblock * pool->itembytes + (int) sizeof(VOID *) +
+ pool->alignbytes);
+ /* Set the next block pointer to NULL. */
+ *(pool->firstblock) = (VOID *) NULL;
+ poolrestart(pool);
+}
+
+/*****************************************************************************/
+/* */
+/* pooldeinit() Free to the operating system all memory taken by a pool. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+void pooldeinit(struct memorypool *pool)
+#else /* not ANSI_DECLARATORS */
+void pooldeinit(pool)
+struct memorypool *pool;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ while (pool->firstblock != (VOID **) NULL) {
+ pool->nowblock = (VOID **) *(pool->firstblock);
+ trifree((VOID *) pool->firstblock);
+ pool->firstblock = pool->nowblock;
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* poolalloc() Allocate space for an item. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+VOID *poolalloc(struct memorypool *pool)
+#else /* not ANSI_DECLARATORS */
+VOID *poolalloc(pool)
+struct memorypool *pool;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ VOID *newitem;
+ VOID **newblock;
+ unsigned long alignptr;
+
+ /* First check the linked list of dead items. If the list is not */
+ /* empty, allocate an item from the list rather than a fresh one. */
+ if (pool->deaditemstack != (VOID *) NULL) {
+ newitem = pool->deaditemstack; /* Take first item in list. */
+ pool->deaditemstack = * (VOID **) pool->deaditemstack;
+ } else {
+ /* Check if there are any free items left in the current block. */
+ if (pool->unallocateditems == 0) {
+ /* Check if another block must be allocated. */
+ if (*(pool->nowblock) == (VOID *) NULL) {
+ /* Allocate a new block of items, pointed to by the previous block. */
+ newblock = (VOID **) trimalloc(pool->itemsperblock * pool->itembytes +
+ (int) sizeof(VOID *) +
+ pool->alignbytes);
+ *(pool->nowblock) = (VOID *) newblock;
+ /* The next block pointer is NULL. */
+ *newblock = (VOID *) NULL;
+ }
+
+ /* Move to the new block. */
+ pool->nowblock = (VOID **) *(pool->nowblock);
+ /* Find the first item in the block. */
+ /* Increment by the size of (VOID *). */
+ alignptr = (unsigned long) (pool->nowblock + 1);
+ /* Align the item on an `alignbytes'-byte boundary. */
+ pool->nextitem = (VOID *)
+ (alignptr + (unsigned long) pool->alignbytes -
+ (alignptr % (unsigned long) pool->alignbytes));
+ /* There are lots of unallocated items left in this block. */
+ pool->unallocateditems = pool->itemsperblock;
+ }
+
+ /* Allocate a new item. */
+ newitem = pool->nextitem;
+ /* Advance `nextitem' pointer to next free item in block. */
+ pool->nextitem = (VOID *) ((char *) pool->nextitem + pool->itembytes);
+ pool->unallocateditems--;
+ pool->maxitems++;
+ }
+ pool->items++;
+ return newitem;
+}
+
+/*****************************************************************************/
+/* */
+/* pooldealloc() Deallocate space for an item. */
+/* */
+/* The deallocated space is stored in a queue for later reuse. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+void pooldealloc(struct memorypool *pool, VOID *dyingitem)
+#else /* not ANSI_DECLARATORS */
+void pooldealloc(pool, dyingitem)
+struct memorypool *pool;
+VOID *dyingitem;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ /* Push freshly killed item onto stack. */
+ *((VOID **) dyingitem) = pool->deaditemstack;
+ pool->deaditemstack = dyingitem;
+ pool->items--;
+}
+
+/*****************************************************************************/
+/* */
+/* traversalinit() Prepare to traverse the entire list of items. */
+/* */
+/* This routine is used in conjunction with traverse(). */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+void traversalinit(struct memorypool *pool)
+#else /* not ANSI_DECLARATORS */
+void traversalinit(pool)
+struct memorypool *pool;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ unsigned long alignptr;
+
+ /* Begin the traversal in the first block. */
+ pool->pathblock = pool->firstblock;
+ /* Find the first item in the block. Increment by the size of (VOID *). */
+ alignptr = (unsigned long) (pool->pathblock + 1);
+ /* Align with item on an `alignbytes'-byte boundary. */
+ pool->pathitem = (VOID *)
+ (alignptr + (unsigned long) pool->alignbytes -
+ (alignptr % (unsigned long) pool->alignbytes));
+ /* Set the number of items left in the current block. */
+ pool->pathitemsleft = pool->itemsfirstblock;
+}
+
+/*****************************************************************************/
+/* */
+/* traverse() Find the next item in the list. */
+/* */
+/* This routine is used in conjunction with traversalinit(). Be forewarned */
+/* that this routine successively returns all items in the list, including */
+/* deallocated ones on the deaditemqueue. It's up to you to figure out */
+/* which ones are actually dead. Why? I don't want to allocate extra */
+/* space just to demarcate dead items. It can usually be done more */
+/* space-efficiently by a routine that knows something about the structure */
+/* of the item. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+VOID *traverse(struct memorypool *pool)
+#else /* not ANSI_DECLARATORS */
+VOID *traverse(pool)
+struct memorypool *pool;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ VOID *newitem;
+ unsigned long alignptr;
+
+ /* Stop upon exhausting the list of items. */
+ if (pool->pathitem == pool->nextitem) {
+ return (VOID *) NULL;
+ }
+
+ /* Check whether any untraversed items remain in the current block. */
+ if (pool->pathitemsleft == 0) {
+ /* Find the next block. */
+ pool->pathblock = (VOID **) *(pool->pathblock);
+ /* Find the first item in the block. Increment by the size of (VOID *). */
+ alignptr = (unsigned long) (pool->pathblock + 1);
+ /* Align with item on an `alignbytes'-byte boundary. */
+ pool->pathitem = (VOID *)
+ (alignptr + (unsigned long) pool->alignbytes -
+ (alignptr % (unsigned long) pool->alignbytes));
+ /* Set the number of items left in the current block. */
+ pool->pathitemsleft = pool->itemsperblock;
+ }
+
+ newitem = pool->pathitem;
+ /* Find the next item in the block. */
+ pool->pathitem = (VOID *) ((char *) pool->pathitem + pool->itembytes);
+ pool->pathitemsleft--;
+ return newitem;
+}
+
+/*****************************************************************************/
+/* */
+/* dummyinit() Initialize the triangle that fills "outer space" and the */
+/* omnipresent subsegment. */
+/* */
+/* The triangle that fills "outer space," called `dummytri', is pointed to */
+/* by every triangle and subsegment on a boundary (be it outer or inner) of */
+/* the triangulation. Also, `dummytri' points to one of the triangles on */
+/* the convex hull (until the holes and concavities are carved), making it */
+/* possible to find a starting triangle for point location. */
+/* */
+/* The omnipresent subsegment, `dummysub', is pointed to by every triangle */
+/* or subsegment that doesn't have a full complement of real subsegments */
+/* to point to. */
+/* */
+/* `dummytri' and `dummysub' are generally required to fulfill only a few */
+/* invariants: their vertices must remain NULL and `dummytri' must always */
+/* be bonded (at offset zero) to some triangle on the convex hull of the */
+/* mesh, via a boundary edge. Otherwise, the connections of `dummytri' and */
+/* `dummysub' may change willy-nilly. This makes it possible to avoid */
+/* writing a good deal of special-case code (in the edge flip, for example) */
+/* for dealing with the boundary of the mesh, places where no subsegment is */
+/* present, and so forth. Other entities are frequently bonded to */
+/* `dummytri' and `dummysub' as if they were real mesh entities, with no */
+/* harm done. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+void dummyinit(struct mesh *m, struct behavior *b, int trianglebytes,
+ int subsegbytes)
+#else /* not ANSI_DECLARATORS */
+void dummyinit(m, b, trianglebytes, subsegbytes)
+struct mesh *m;
+struct behavior *b;
+int trianglebytes;
+int subsegbytes;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ unsigned long alignptr;
+
+ /* Set up `dummytri', the `triangle' that occupies "outer space." */
+ m->dummytribase = (triangle *) trimalloc(trianglebytes +
+ m->triangles.alignbytes);
+ /* Align `dummytri' on a `triangles.alignbytes'-byte boundary. */
+ alignptr = (unsigned long) m->dummytribase;
+ m->dummytri = (triangle *)
+ (alignptr + (unsigned long) m->triangles.alignbytes -
+ (alignptr % (unsigned long) m->triangles.alignbytes));
+ /* Initialize the three adjoining triangles to be "outer space." These */
+ /* will eventually be changed by various bonding operations, but their */
+ /* values don't really matter, as long as they can legally be */
+ /* dereferenced. */
+ m->dummytri[0] = (triangle) m->dummytri;
+ m->dummytri[1] = (triangle) m->dummytri;
+ m->dummytri[2] = (triangle) m->dummytri;
+ /* Three NULL vertices. */
+ m->dummytri[3] = (triangle) NULL;
+ m->dummytri[4] = (triangle) NULL;
+ m->dummytri[5] = (triangle) NULL;
+
+ if (b->usesegments) {
+ /* Set up `dummysub', the omnipresent subsegment pointed to by any */
+ /* triangle side or subsegment end that isn't attached to a real */
+ /* subsegment. */
+ m->dummysubbase = (subseg *) trimalloc(subsegbytes +
+ m->subsegs.alignbytes);
+ /* Align `dummysub' on a `subsegs.alignbytes'-byte boundary. */
+ alignptr = (unsigned long) m->dummysubbase;
+ m->dummysub = (subseg *)
+ (alignptr + (unsigned long) m->subsegs.alignbytes -
+ (alignptr % (unsigned long) m->subsegs.alignbytes));
+ /* Initialize the two adjoining subsegments to be the omnipresent */
+ /* subsegment. These will eventually be changed by various bonding */
+ /* operations, but their values don't really matter, as long as they */
+ /* can legally be dereferenced. */
+ m->dummysub[0] = (subseg) m->dummysub;
+ m->dummysub[1] = (subseg) m->dummysub;
+ /* Four NULL vertices. */
+ m->dummysub[2] = (subseg) NULL;
+ m->dummysub[3] = (subseg) NULL;
+ m->dummysub[4] = (subseg) NULL;
+ m->dummysub[5] = (subseg) NULL;
+ /* Initialize the two adjoining triangles to be "outer space." */
+ m->dummysub[6] = (subseg) m->dummytri;
+ m->dummysub[7] = (subseg) m->dummytri;
+ /* Set the boundary marker to zero. */
+ * (int *) (m->dummysub + 8) = 0;
+
+ /* Initialize the three adjoining subsegments of `dummytri' to be */
+ /* the omnipresent subsegment. */
+ m->dummytri[6] = (triangle) m->dummysub;
+ m->dummytri[7] = (triangle) m->dummysub;
+ m->dummytri[8] = (triangle) m->dummysub;
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* initializevertexpool() Calculate the size of the vertex data structure */
+/* and initialize its memory pool. */
+/* */
+/* This routine also computes the `vertexmarkindex' and `vertex2triindex' */
+/* indices used to find values within each vertex. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+void initializevertexpool(struct mesh *m, struct behavior *b)
+#else /* not ANSI_DECLARATORS */
+void initializevertexpool(m, b)
+struct mesh *m;
+struct behavior *b;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ int vertexsize;
+
+ /* The index within each vertex at which the boundary marker is found, */
+ /* followed by the vertex type. Ensure the vertex marker is aligned to */
+ /* a sizeof(int)-byte address. */
+ m->vertexmarkindex = ((m->mesh_dim + m->nextras) * sizeof(REAL) +
+ sizeof(int) - 1) /
+ sizeof(int);
+ vertexsize = (m->vertexmarkindex + 2) * sizeof(int);
+ if (b->poly) {
+ /* The index within each vertex at which a triangle pointer is found. */
+ /* Ensure the pointer is aligned to a sizeof(triangle)-byte address. */
+ m->vertex2triindex = (vertexsize + sizeof(triangle) - 1) /
+ sizeof(triangle);
+ vertexsize = (m->vertex2triindex + 1) * sizeof(triangle);
+ }
+
+ /* Initialize the pool of vertices. */
+ poolinit(&m->vertices, vertexsize, VERTEXPERBLOCK,
+ m->invertices > VERTEXPERBLOCK ? m->invertices : VERTEXPERBLOCK,
+ sizeof(REAL));
+}
+
+/*****************************************************************************/
+/* */
+/* initializetrisubpools() Calculate the sizes of the triangle and */
+/* subsegment data structures and initialize */
+/* their memory pools. */
+/* */
+/* This routine also computes the `highorderindex', `elemattribindex', and */
+/* `areaboundindex' indices used to find values within each triangle. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+void initializetrisubpools(struct mesh *m, struct behavior *b)
+#else /* not ANSI_DECLARATORS */
+void initializetrisubpools(m, b)
+struct mesh *m;
+struct behavior *b;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ int trisize;
+
+ /* The index within each triangle at which the extra nodes (above three) */
+ /* associated with high order elements are found. There are three */
+ /* pointers to other triangles, three pointers to corners, and possibly */
+ /* three pointers to subsegments before the extra nodes. */
+ m->highorderindex = 6 + (b->usesegments * 3);
+ /* The number of bytes occupied by a triangle. */
+ trisize = ((b->order + 1) * (b->order + 2) / 2 + (m->highorderindex - 3)) *
+ sizeof(triangle);
+ /* The index within each triangle at which its attributes are found, */
+ /* where the index is measured in REALs. */
+ m->elemattribindex = (trisize + sizeof(REAL) - 1) / sizeof(REAL);
+ /* The index within each triangle at which the maximum area constraint */
+ /* is found, where the index is measured in REALs. Note that if the */
+ /* `regionattrib' flag is set, an additional attribute will be added. */
+ m->areaboundindex = m->elemattribindex + m->eextras + b->regionattrib;
+ /* If triangle attributes or an area bound are needed, increase the number */
+ /* of bytes occupied by a triangle. */
+ if (b->vararea) {
+ trisize = (m->areaboundindex + 1) * sizeof(REAL);
+ } else if (m->eextras + b->regionattrib > 0) {
+ trisize = m->areaboundindex * sizeof(REAL);
+ }
+ /* If a Voronoi diagram or triangle neighbor graph is requested, make */
+ /* sure there's room to store an integer index in each triangle. This */
+ /* integer index can occupy the same space as the subsegment pointers */
+ /* or attributes or area constraint or extra nodes. */
+ if ((b->voronoi || b->neighbors) &&
+ (trisize < 6 * sizeof(triangle) + sizeof(int))) {
+ trisize = 6 * sizeof(triangle) + sizeof(int);
+ }
+
+ /* Having determined the memory size of a triangle, initialize the pool. */
+ poolinit(&m->triangles, trisize, TRIPERBLOCK,
+ (2 * m->invertices - 2) > TRIPERBLOCK ? (2 * m->invertices - 2) :
+ TRIPERBLOCK, 4);
+
+ if (b->usesegments) {
+ /* Initialize the pool of subsegments. Take into account all eight */
+ /* pointers and one boundary marker. */
+ poolinit(&m->subsegs, 8 * sizeof(triangle) + sizeof(int),
+ SUBSEGPERBLOCK, SUBSEGPERBLOCK, 4);
+
+ /* Initialize the "outer space" triangle and omnipresent subsegment. */
+ dummyinit(m, b, m->triangles.itembytes, m->subsegs.itembytes);
+ } else {
+ /* Initialize the "outer space" triangle. */
+ dummyinit(m, b, m->triangles.itembytes, 0);
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* triangledealloc() Deallocate space for a triangle, marking it dead. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+void triangledealloc(struct mesh *m, triangle *dyingtriangle)
+#else /* not ANSI_DECLARATORS */
+void triangledealloc(m, dyingtriangle)
+struct mesh *m;
+triangle *dyingtriangle;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ /* Mark the triangle as dead. This makes it possible to detect dead */
+ /* triangles when traversing the list of all triangles. */
+ killtri(dyingtriangle);
+ pooldealloc(&m->triangles, (VOID *) dyingtriangle);
+}
+
+/*****************************************************************************/
+/* */
+/* triangletraverse() Traverse the triangles, skipping dead ones. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+triangle *triangletraverse(struct mesh *m)
+#else /* not ANSI_DECLARATORS */
+triangle *triangletraverse(m)
+struct mesh *m;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ triangle *newtriangle;
+
+ do {
+ newtriangle = (triangle *) traverse(&m->triangles);
+ if (newtriangle == (triangle *) NULL) {
+ return (triangle *) NULL;
+ }
+ } while (deadtri(newtriangle)); /* Skip dead ones. */
+ return newtriangle;
+}
+
+/*****************************************************************************/
+/* */
+/* subsegdealloc() Deallocate space for a subsegment, marking it dead. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+void subsegdealloc(struct mesh *m, subseg *dyingsubseg)
+#else /* not ANSI_DECLARATORS */
+void subsegdealloc(m, dyingsubseg)
+struct mesh *m;
+subseg *dyingsubseg;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ /* Mark the subsegment as dead. This makes it possible to detect dead */
+ /* subsegments when traversing the list of all subsegments. */
+ killsubseg(dyingsubseg);
+ pooldealloc(&m->subsegs, (VOID *) dyingsubseg);
+}
+
+/*****************************************************************************/
+/* */
+/* subsegtraverse() Traverse the subsegments, skipping dead ones. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+subseg *subsegtraverse(struct mesh *m)
+#else /* not ANSI_DECLARATORS */
+subseg *subsegtraverse(m)
+struct mesh *m;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ subseg *newsubseg;
+
+ do {
+ newsubseg = (subseg *) traverse(&m->subsegs);
+ if (newsubseg == (subseg *) NULL) {
+ return (subseg *) NULL;
+ }
+ } while (deadsubseg(newsubseg)); /* Skip dead ones. */
+ return newsubseg;
+}
+
+/*****************************************************************************/
+/* */
+/* vertexdealloc() Deallocate space for a vertex, marking it dead. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+void vertexdealloc(struct mesh *m, vertex dyingvertex)
+#else /* not ANSI_DECLARATORS */
+void vertexdealloc(m, dyingvertex)
+struct mesh *m;
+vertex dyingvertex;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ /* Mark the vertex as dead. This makes it possible to detect dead */
+ /* vertices when traversing the list of all vertices. */
+ setvertextype(dyingvertex, DEADVERTEX);
+ pooldealloc(&m->vertices, (VOID *) dyingvertex);
+}
+
+/*****************************************************************************/
+/* */
+/* vertextraverse() Traverse the vertices, skipping dead ones. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+vertex vertextraverse(struct mesh *m)
+#else /* not ANSI_DECLARATORS */
+vertex vertextraverse(m)
+struct mesh *m;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ vertex newvertex;
+
+ do {
+ newvertex = (vertex) traverse(&m->vertices);
+ if (newvertex == (vertex) NULL) {
+ return (vertex) NULL;
+ }
+ } while (vertextype(newvertex) == DEADVERTEX); /* Skip dead ones. */
+ return newvertex;
+}
+
+/*****************************************************************************/
+/* */
+/* badsubsegdealloc() Deallocate space for a bad subsegment, marking it */
+/* dead. */
+/* */
+/*****************************************************************************/
+
+#ifndef CDT_ONLY
+
+#ifdef ANSI_DECLARATORS
+void badsubsegdealloc(struct mesh *m, struct badsubseg *dyingseg)
+#else /* not ANSI_DECLARATORS */
+void badsubsegdealloc(m, dyingseg)
+struct mesh *m;
+struct badsubseg *dyingseg;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ /* Set subsegment's origin to NULL. This makes it possible to detect dead */
+ /* badsubsegs when traversing the list of all badsubsegs . */
+ dyingseg->subsegorg = (vertex) NULL;
+ pooldealloc(&m->badsubsegs, (VOID *) dyingseg);
+}
+
+#endif /* not CDT_ONLY */
+
+/*****************************************************************************/
+/* */
+/* badsubsegtraverse() Traverse the bad subsegments, skipping dead ones. */
+/* */
+/*****************************************************************************/
+
+#ifndef CDT_ONLY
+
+#ifdef ANSI_DECLARATORS
+struct badsubseg *badsubsegtraverse(struct mesh *m)
+#else /* not ANSI_DECLARATORS */
+struct badsubseg *badsubsegtraverse(m)
+struct mesh *m;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ struct badsubseg *newseg;
+
+ do {
+ newseg = (struct badsubseg *) traverse(&m->badsubsegs);
+ if (newseg == (struct badsubseg *) NULL) {
+ return (struct badsubseg *) NULL;
+ }
+ } while (newseg->subsegorg == (vertex) NULL); /* Skip dead ones. */
+ return newseg;
+}
+
+#endif /* not CDT_ONLY */
+
+/*****************************************************************************/
+/* */
+/* getvertex() Get a specific vertex, by number, from the list. */
+/* */
+/* The first vertex is number 'firstnumber'. */
+/* */
+/* Note that this takes O(n) time (with a small constant, if VERTEXPERBLOCK */
+/* is large). I don't care to take the trouble to make it work in constant */
+/* time. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+vertex getvertex(struct mesh *m, struct behavior *b, int number)
+#else /* not ANSI_DECLARATORS */
+vertex getvertex(m, b, number)
+struct mesh *m;
+struct behavior *b;
+int number;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ VOID **getblock;
+ char *foundvertex;
+ unsigned long alignptr;
+ int current;
+
+ getblock = m->vertices.firstblock;
+ current = b->firstnumber;
+
+ /* Find the right block. */
+ if (current + m->vertices.itemsfirstblock <= number) {
+ getblock = (VOID **) *getblock;
+ current += m->vertices.itemsfirstblock;
+ while (current + m->vertices.itemsperblock <= number) {
+ getblock = (VOID **) *getblock;
+ current += m->vertices.itemsperblock;
+ }
+ }
+
+ /* Now find the right vertex. */
+ alignptr = (unsigned long) (getblock + 1);
+ foundvertex = (char *) (alignptr + (unsigned long) m->vertices.alignbytes -
+ (alignptr % (unsigned long) m->vertices.alignbytes));
+ return (vertex) (foundvertex + m->vertices.itembytes * (number - current));
+}
+
+/*****************************************************************************/
+/* */
+/* triangledeinit() Free all remaining allocated memory. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+void triangledeinit(struct mesh *m, struct behavior *b)
+#else /* not ANSI_DECLARATORS */
+void triangledeinit(m, b)
+struct mesh *m;
+struct behavior *b;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ pooldeinit(&m->triangles);
+ trifree((VOID *) m->dummytribase);
+ if (b->usesegments) {
+ pooldeinit(&m->subsegs);
+ trifree((VOID *) m->dummysubbase);
+ }
+ pooldeinit(&m->vertices);
+#ifndef CDT_ONLY
+ if (b->quality) {
+ pooldeinit(&m->badsubsegs);
+ if ((b->minangle > 0.0) || b->vararea || b->fixedarea || b->usertest) {
+ pooldeinit(&m->badtriangles);
+ pooldeinit(&m->flipstackers);
+ }
+ }
+#endif /* not CDT_ONLY */
+}
+
+/** **/
+/** **/
+/********* Memory management routines end here *********/
+
+/********* Constructors begin here *********/
+/** **/
+/** **/
+
+/*****************************************************************************/
+/* */
+/* maketriangle() Create a new triangle with orientation zero. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+void maketriangle(struct mesh *m, struct behavior *b, struct otri *newotri)
+#else /* not ANSI_DECLARATORS */
+void maketriangle(m, b, newotri)
+struct mesh *m;
+struct behavior *b;
+struct otri *newotri;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ int i;
+
+ newotri->tri = (triangle *) poolalloc(&m->triangles);
+ /* Initialize the three adjoining triangles to be "outer space". */
+ newotri->tri[0] = (triangle) m->dummytri;
+ newotri->tri[1] = (triangle) m->dummytri;
+ newotri->tri[2] = (triangle) m->dummytri;
+ /* Three NULL vertices. */
+ newotri->tri[3] = (triangle) NULL;
+ newotri->tri[4] = (triangle) NULL;
+ newotri->tri[5] = (triangle) NULL;
+ if (b->usesegments) {
+ /* Initialize the three adjoining subsegments to be the omnipresent */
+ /* subsegment. */
+ newotri->tri[6] = (triangle) m->dummysub;
+ newotri->tri[7] = (triangle) m->dummysub;
+ newotri->tri[8] = (triangle) m->dummysub;
+ }
+ for (i = 0; i < m->eextras; i++) {
+ setelemattribute(*newotri, i, 0.0);
+ }
+ if (b->vararea) {
+ setareabound(*newotri, -1.0);
+ }
+
+ newotri->orient = 0;
+}
+
+/*****************************************************************************/
+/* */
+/* makesubseg() Create a new subsegment with orientation zero. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+void makesubseg(struct mesh *m, struct osub *newsubseg)
+#else /* not ANSI_DECLARATORS */
+void makesubseg(m, newsubseg)
+struct mesh *m;
+struct osub *newsubseg;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ newsubseg->ss = (subseg *) poolalloc(&m->subsegs);
+ /* Initialize the two adjoining subsegments to be the omnipresent */
+ /* subsegment. */
+ newsubseg->ss[0] = (subseg) m->dummysub;
+ newsubseg->ss[1] = (subseg) m->dummysub;
+ /* Four NULL vertices. */
+ newsubseg->ss[2] = (subseg) NULL;
+ newsubseg->ss[3] = (subseg) NULL;
+ newsubseg->ss[4] = (subseg) NULL;
+ newsubseg->ss[5] = (subseg) NULL;
+ /* Initialize the two adjoining triangles to be "outer space." */
+ newsubseg->ss[6] = (subseg) m->dummytri;
+ newsubseg->ss[7] = (subseg) m->dummytri;
+ /* Set the boundary marker to zero. */
+ setmark(*newsubseg, 0);
+
+ newsubseg->ssorient = 0;
+}
+
+/** **/
+/** **/
+/********* Constructors end here *********/
+
+/********* Geometric primitives begin here *********/
+/** **/
+/** **/
+
+/* The adaptive exact arithmetic geometric predicates implemented herein are */
+/* described in detail in my paper, "Adaptive Precision Floating-Point */
+/* Arithmetic and Fast Robust Geometric Predicates." See the header for a */
+/* full citation. */
+
+/* Which of the following two methods of finding the absolute values is */
+/* fastest is compiler-dependent. A few compilers can inline and optimize */
+/* the fabs() call; but most will incur the overhead of a function call, */
+/* which is disastrously slow. A faster way on IEEE machines might be to */
+/* mask the appropriate bit, but that's difficult to do in C without */
+/* forcing the value to be stored to memory (rather than be kept in the */
+/* register to which the optimizer assigned it). */
+
+#define Absolute(a) ((a) >= 0.0 ? (a) : -(a))
+/* #define Absolute(a) fabs(a) */
+
+/* Many of the operations are broken up into two pieces, a main part that */
+/* performs an approximate operation, and a "tail" that computes the */
+/* roundoff error of that operation. */
+/* */
+/* The operations Fast_Two_Sum(), Fast_Two_Diff(), Two_Sum(), Two_Diff(), */
+/* Split(), and Two_Product() are all implemented as described in the */
+/* reference. Each of these macros requires certain variables to be */
+/* defined in the calling routine. The variables `bvirt', `c', `abig', */
+/* `_i', `_j', `_k', `_l', `_m', and `_n' are declared `INEXACT' because */
+/* they store the result of an operation that may incur roundoff error. */
+/* The input parameter `x' (or the highest numbered `x_' parameter) must */
+/* also be declared `INEXACT'. */
+
+#define Fast_Two_Sum_Tail(a, b, x, y) \
+ bvirt = x - a; \
+ y = b - bvirt
+
+#define Fast_Two_Sum(a, b, x, y) \
+ x = (REAL) (a + b); \
+ Fast_Two_Sum_Tail(a, b, x, y)
+
+#define Two_Sum_Tail(a, b, x, y) \
+ bvirt = (REAL) (x - a); \
+ avirt = x - bvirt; \
+ bround = b - bvirt; \
+ around = a - avirt; \
+ y = around + bround
+
+#define Two_Sum(a, b, x, y) \
+ x = (REAL) (a + b); \
+ Two_Sum_Tail(a, b, x, y)
+
+#define Two_Diff_Tail(a, b, x, y) \
+ bvirt = (REAL) (a - x); \
+ avirt = x + bvirt; \
+ bround = bvirt - b; \
+ around = a - avirt; \
+ y = around + bround
+
+#define Two_Diff(a, b, x, y) \
+ x = (REAL) (a - b); \
+ Two_Diff_Tail(a, b, x, y)
+
+#define Split(a, ahi, alo) \
+ c = (REAL) (splitter * a); \
+ abig = (REAL) (c - a); \
+ ahi = c - abig; \
+ alo = a - ahi
+
+#define Two_Product_Tail(a, b, x, y) \
+ Split(a, ahi, alo); \
+ Split(b, bhi, blo); \
+ err1 = x - (ahi * bhi); \
+ err2 = err1 - (alo * bhi); \
+ err3 = err2 - (ahi * blo); \
+ y = (alo * blo) - err3
+
+#define Two_Product(a, b, x, y) \
+ x = (REAL) (a * b); \
+ Two_Product_Tail(a, b, x, y)
+
+/* Two_Product_Presplit() is Two_Product() where one of the inputs has */
+/* already been split. Avoids redundant splitting. */
+
+#define Two_Product_Presplit(a, b, bhi, blo, x, y) \
+ x = (REAL) (a * b); \
+ Split(a, ahi, alo); \
+ err1 = x - (ahi * bhi); \
+ err2 = err1 - (alo * bhi); \
+ err3 = err2 - (ahi * blo); \
+ y = (alo * blo) - err3
+
+/* Square() can be done more quickly than Two_Product(). */
+
+#define Square_Tail(a, x, y) \
+ Split(a, ahi, alo); \
+ err1 = x - (ahi * ahi); \
+ err3 = err1 - ((ahi + ahi) * alo); \
+ y = (alo * alo) - err3
+
+#define Square(a, x, y) \
+ x = (REAL) (a * a); \
+ Square_Tail(a, x, y)
+
+/* Macros for summing expansions of various fixed lengths. These are all */
+/* unrolled versions of Expansion_Sum(). */
+
+#define Two_One_Sum(a1, a0, b, x2, x1, x0) \
+ Two_Sum(a0, b , _i, x0); \
+ Two_Sum(a1, _i, x2, x1)
+
+#define Two_One_Diff(a1, a0, b, x2, x1, x0) \
+ Two_Diff(a0, b , _i, x0); \
+ Two_Sum( a1, _i, x2, x1)
+
+#define Two_Two_Sum(a1, a0, b1, b0, x3, x2, x1, x0) \
+ Two_One_Sum(a1, a0, b0, _j, _0, x0); \
+ Two_One_Sum(_j, _0, b1, x3, x2, x1)
+
+#define Two_Two_Diff(a1, a0, b1, b0, x3, x2, x1, x0) \
+ Two_One_Diff(a1, a0, b0, _j, _0, x0); \
+ Two_One_Diff(_j, _0, b1, x3, x2, x1)
+
+/* Macro for multiplying a two-component expansion by a single component. */
+
+#define Two_One_Product(a1, a0, b, x3, x2, x1, x0) \
+ Split(b, bhi, blo); \
+ Two_Product_Presplit(a0, b, bhi, blo, _i, x0); \
+ Two_Product_Presplit(a1, b, bhi, blo, _j, _0); \
+ Two_Sum(_i, _0, _k, x1); \
+ Fast_Two_Sum(_j, _k, x3, x2)
+
+/*****************************************************************************/
+/* */
+/* exactinit() Initialize the variables used for exact arithmetic. */
+/* */
+/* `epsilon' is the largest power of two such that 1.0 + epsilon = 1.0 in */
+/* floating-point arithmetic. `epsilon' bounds the relative roundoff */
+/* error. It is used for floating-point error analysis. */
+/* */
+/* `splitter' is used to split floating-point numbers into two half- */
+/* length significands for exact multiplication. */
+/* */
+/* I imagine that a highly optimizing compiler might be too smart for its */
+/* own good, and somehow cause this routine to fail, if it pretends that */
+/* floating-point arithmetic is too much like real arithmetic. */
+/* */
+/* Don't change this routine unless you fully understand it. */
+/* */
+/*****************************************************************************/
+
+void exactinit()
+{
+ REAL half;
+ REAL check, lastcheck;
+ int every_other;
+#ifdef LINUX
+ int cword;
+#endif /* LINUX */
+
+#ifdef CPU86
+#ifdef SINGLE
+ _control87(_PC_24, _MCW_PC); /* Set FPU control word for single precision. */
+#else /* not SINGLE */
+ _control87(_PC_53, _MCW_PC); /* Set FPU control word for double precision. */
+#endif /* not SINGLE */
+#endif /* CPU86 */
+#ifdef LINUX
+#ifdef SINGLE
+ /* cword = 4223; */
+ cword = 4210; /* set FPU control word for single precision */
+#else /* not SINGLE */
+ /* cword = 4735; */
+ cword = 4722; /* set FPU control word for double precision */
+#endif /* not SINGLE */
+ _FPU_SETCW(cword);
+#endif /* LINUX */
+
+ every_other = 1;
+ half = 0.5;
+ epsilon = 1.0;
+ splitter = 1.0;
+ check = 1.0;
+ /* Repeatedly divide `epsilon' by two until it is too small to add to */
+ /* one without causing roundoff. (Also check if the sum is equal to */
+ /* the previous sum, for machines that round up instead of using exact */
+ /* rounding. Not that these routines will work on such machines.) */
+ do {
+ lastcheck = check;
+ epsilon *= half;
+ if (every_other) {
+ splitter *= 2.0;
+ }
+ every_other = !every_other;
+ check = 1.0 + epsilon;
+ } while ((check != 1.0) && (check != lastcheck));
+ splitter += 1.0;
+ /* Error bounds for orientation and incircle tests. */
+ resulterrbound = (3.0 + 8.0 * epsilon) * epsilon;
+ ccwerrboundA = (3.0 + 16.0 * epsilon) * epsilon;
+ ccwerrboundB = (2.0 + 12.0 * epsilon) * epsilon;
+ ccwerrboundC = (9.0 + 64.0 * epsilon) * epsilon * epsilon;
+ iccerrboundA = (10.0 + 96.0 * epsilon) * epsilon;
+ iccerrboundB = (4.0 + 48.0 * epsilon) * epsilon;
+ iccerrboundC = (44.0 + 576.0 * epsilon) * epsilon * epsilon;
+ o3derrboundA = (7.0 + 56.0 * epsilon) * epsilon;
+ o3derrboundB = (3.0 + 28.0 * epsilon) * epsilon;
+ o3derrboundC = (26.0 + 288.0 * epsilon) * epsilon * epsilon;
+}
+
+/*****************************************************************************/
+/* */
+/* fast_expansion_sum_zeroelim() Sum two expansions, eliminating zero */
+/* components from the output expansion. */
+/* */
+/* Sets h = e + f. See my Robust Predicates paper for details. */
+/* */
+/* If round-to-even is used (as with IEEE 754), maintains the strongly */
+/* nonoverlapping property. (That is, if e is strongly nonoverlapping, h */
+/* will be also.) Does NOT maintain the nonoverlapping or nonadjacent */
+/* properties. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+int fast_expansion_sum_zeroelim(int elen, REAL *e, int flen, REAL *f, REAL *h)
+#else /* not ANSI_DECLARATORS */
+int fast_expansion_sum_zeroelim(elen, e, flen, f, h) /* h cannot be e or f. */
+int elen;
+REAL *e;
+int flen;
+REAL *f;
+REAL *h;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ REAL Q;
+ INEXACT REAL Qnew;
+ INEXACT REAL hh;
+ INEXACT REAL bvirt;
+ REAL avirt, bround, around;
+ int eindex, findex, hindex;
+ REAL enow, fnow;
+
+ enow = e[0];
+ fnow = f[0];
+ eindex = findex = 0;
+ if ((fnow > enow) == (fnow > -enow)) {
+ Q = enow;
+ enow = e[++eindex];
+ } else {
+ Q = fnow;
+ fnow = f[++findex];
+ }
+ hindex = 0;
+ if ((eindex < elen) && (findex < flen)) {
+ if ((fnow > enow) == (fnow > -enow)) {
+ Fast_Two_Sum(enow, Q, Qnew, hh);
+ enow = e[++eindex];
+ } else {
+ Fast_Two_Sum(fnow, Q, Qnew, hh);
+ fnow = f[++findex];
+ }
+ Q = Qnew;
+ if (hh != 0.0) {
+ h[hindex++] = hh;
+ }
+ while ((eindex < elen) && (findex < flen)) {
+ if ((fnow > enow) == (fnow > -enow)) {
+ Two_Sum(Q, enow, Qnew, hh);
+ enow = e[++eindex];
+ } else {
+ Two_Sum(Q, fnow, Qnew, hh);
+ fnow = f[++findex];
+ }
+ Q = Qnew;
+ if (hh != 0.0) {
+ h[hindex++] = hh;
+ }
+ }
+ }
+ while (eindex < elen) {
+ Two_Sum(Q, enow, Qnew, hh);
+ enow = e[++eindex];
+ Q = Qnew;
+ if (hh != 0.0) {
+ h[hindex++] = hh;
+ }
+ }
+ while (findex < flen) {
+ Two_Sum(Q, fnow, Qnew, hh);
+ fnow = f[++findex];
+ Q = Qnew;
+ if (hh != 0.0) {
+ h[hindex++] = hh;
+ }
+ }
+ if ((Q != 0.0) || (hindex == 0)) {
+ h[hindex++] = Q;
+ }
+ return hindex;
+}
+
+/*****************************************************************************/
+/* */
+/* scale_expansion_zeroelim() Multiply an expansion by a scalar, */
+/* eliminating zero components from the */
+/* output expansion. */
+/* */
+/* Sets h = be. See my Robust Predicates paper for details. */
+/* */
+/* Maintains the nonoverlapping property. If round-to-even is used (as */
+/* with IEEE 754), maintains the strongly nonoverlapping and nonadjacent */
+/* properties as well. (That is, if e has one of these properties, so */
+/* will h.) */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+int scale_expansion_zeroelim(int elen, REAL *e, REAL b, REAL *h)
+#else /* not ANSI_DECLARATORS */
+int scale_expansion_zeroelim(elen, e, b, h) /* e and h cannot be the same. */
+int elen;
+REAL *e;
+REAL b;
+REAL *h;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ INEXACT REAL Q, sum;
+ REAL hh;
+ INEXACT REAL product1;
+ REAL product0;
+ int eindex, hindex;
+ REAL enow;
+ INEXACT REAL bvirt;
+ REAL avirt, bround, around;
+ INEXACT REAL c;
+ INEXACT REAL abig;
+ REAL ahi, alo, bhi, blo;
+ REAL err1, err2, err3;
+
+ Split(b, bhi, blo);
+ Two_Product_Presplit(e[0], b, bhi, blo, Q, hh);
+ hindex = 0;
+ if (hh != 0) {
+ h[hindex++] = hh;
+ }
+ for (eindex = 1; eindex < elen; eindex++) {
+ enow = e[eindex];
+ Two_Product_Presplit(enow, b, bhi, blo, product1, product0);
+ Two_Sum(Q, product0, sum, hh);
+ if (hh != 0) {
+ h[hindex++] = hh;
+ }
+ Fast_Two_Sum(product1, sum, Q, hh);
+ if (hh != 0) {
+ h[hindex++] = hh;
+ }
+ }
+ if ((Q != 0.0) || (hindex == 0)) {
+ h[hindex++] = Q;
+ }
+ return hindex;
+}
+
+/*****************************************************************************/
+/* */
+/* estimate() Produce a one-word estimate of an expansion's value. */
+/* */
+/* See my Robust Predicates paper for details. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+REAL estimate(int elen, REAL *e)
+#else /* not ANSI_DECLARATORS */
+REAL estimate(elen, e)
+int elen;
+REAL *e;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ REAL Q;
+ int eindex;
+
+ Q = e[0];
+ for (eindex = 1; eindex < elen; eindex++) {
+ Q += e[eindex];
+ }
+ return Q;
+}
+
+/*****************************************************************************/
+/* */
+/* counterclockwise() Return a positive value if the points pa, pb, and */
+/* pc occur in counterclockwise order; a negative */
+/* value if they occur in clockwise order; and zero */
+/* if they are collinear. The result is also a rough */
+/* approximation of twice the signed area of the */
+/* triangle defined by the three points. */
+/* */
+/* Uses exact arithmetic if necessary to ensure a correct answer. The */
+/* result returned is the determinant of a matrix. This determinant is */
+/* computed adaptively, in the sense that exact arithmetic is used only to */
+/* the degree it is needed to ensure that the returned value has the */
+/* correct sign. Hence, this function is usually quite fast, but will run */
+/* more slowly when the input points are collinear or nearly so. */
+/* */
+/* See my Robust Predicates paper for details. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+REAL counterclockwiseadapt(vertex pa, vertex pb, vertex pc, REAL detsum)
+#else /* not ANSI_DECLARATORS */
+REAL counterclockwiseadapt(pa, pb, pc, detsum)
+vertex pa;
+vertex pb;
+vertex pc;
+REAL detsum;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ INEXACT REAL acx, acy, bcx, bcy;
+ REAL acxtail, acytail, bcxtail, bcytail;
+ INEXACT REAL detleft, detright;
+ REAL detlefttail, detrighttail;
+ REAL det, errbound;
+ REAL B[4], C1[8], C2[12], D[16];
+ INEXACT REAL B3;
+ int C1length, C2length, Dlength;
+ REAL u[4];
+ INEXACT REAL u3;
+ INEXACT REAL s1, t1;
+ REAL s0, t0;
+
+ INEXACT REAL bvirt;
+ REAL avirt, bround, around;
+ INEXACT REAL c;
+ INEXACT REAL abig;
+ REAL ahi, alo, bhi, blo;
+ REAL err1, err2, err3;
+ INEXACT REAL _i, _j;
+ REAL _0;
+
+ acx = (REAL) (pa[0] - pc[0]);
+ bcx = (REAL) (pb[0] - pc[0]);
+ acy = (REAL) (pa[1] - pc[1]);
+ bcy = (REAL) (pb[1] - pc[1]);
+
+ Two_Product(acx, bcy, detleft, detlefttail);
+ Two_Product(acy, bcx, detright, detrighttail);
+
+ Two_Two_Diff(detleft, detlefttail, detright, detrighttail,
+ B3, B[2], B[1], B[0]);
+ B[3] = B3;
+
+ det = estimate(4, B);
+ errbound = ccwerrboundB * detsum;
+ if ((det >= errbound) || (-det >= errbound)) {
+ return det;
+ }
+
+ Two_Diff_Tail(pa[0], pc[0], acx, acxtail);
+ Two_Diff_Tail(pb[0], pc[0], bcx, bcxtail);
+ Two_Diff_Tail(pa[1], pc[1], acy, acytail);
+ Two_Diff_Tail(pb[1], pc[1], bcy, bcytail);
+
+ if ((acxtail == 0.0) && (acytail == 0.0)
+ && (bcxtail == 0.0) && (bcytail == 0.0)) {
+ return det;
+ }
+
+ errbound = ccwerrboundC * detsum + resulterrbound * Absolute(det);
+ det += (acx * bcytail + bcy * acxtail)
+ - (acy * bcxtail + bcx * acytail);
+ if ((det >= errbound) || (-det >= errbound)) {
+ return det;
+ }
+
+ Two_Product(acxtail, bcy, s1, s0);
+ Two_Product(acytail, bcx, t1, t0);
+ Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
+ u[3] = u3;
+ C1length = fast_expansion_sum_zeroelim(4, B, 4, u, C1);
+
+ Two_Product(acx, bcytail, s1, s0);
+ Two_Product(acy, bcxtail, t1, t0);
+ Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
+ u[3] = u3;
+ C2length = fast_expansion_sum_zeroelim(C1length, C1, 4, u, C2);
+
+ Two_Product(acxtail, bcytail, s1, s0);
+ Two_Product(acytail, bcxtail, t1, t0);
+ Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
+ u[3] = u3;
+ Dlength = fast_expansion_sum_zeroelim(C2length, C2, 4, u, D);
+
+ return(D[Dlength - 1]);
+}
+
+#ifdef ANSI_DECLARATORS
+REAL counterclockwise(struct mesh *m, struct behavior *b,
+ vertex pa, vertex pb, vertex pc)
+#else /* not ANSI_DECLARATORS */
+REAL counterclockwise(m, b, pa, pb, pc)
+struct mesh *m;
+struct behavior *b;
+vertex pa;
+vertex pb;
+vertex pc;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ REAL detleft, detright, det;
+ REAL detsum, errbound;
+
+ m->counterclockcount++;
+
+ detleft = (pa[0] - pc[0]) * (pb[1] - pc[1]);
+ detright = (pa[1] - pc[1]) * (pb[0] - pc[0]);
+ det = detleft - detright;
+
+ if (b->noexact) {
+ return det;
+ }
+
+ if (detleft > 0.0) {
+ if (detright <= 0.0) {
+ return det;
+ } else {
+ detsum = detleft + detright;
+ }
+ } else if (detleft < 0.0) {
+ if (detright >= 0.0) {
+ return det;
+ } else {
+ detsum = -detleft - detright;
+ }
+ } else {
+ return det;
+ }
+
+ errbound = ccwerrboundA * detsum;
+ if ((det >= errbound) || (-det >= errbound)) {
+ return det;
+ }
+
+ return counterclockwiseadapt(pa, pb, pc, detsum);
+}
+
+/*****************************************************************************/
+/* */
+/* incircle() Return a positive value if the point pd lies inside the */
+/* circle passing through pa, pb, and pc; a negative value if */
+/* it lies outside; and zero if the four points are cocircular.*/
+/* The points pa, pb, and pc must be in counterclockwise */
+/* order, or the sign of the result will be reversed. */
+/* */
+/* Uses exact arithmetic if necessary to ensure a correct answer. The */
+/* result returned is the determinant of a matrix. This determinant is */
+/* computed adaptively, in the sense that exact arithmetic is used only to */
+/* the degree it is needed to ensure that the returned value has the */
+/* correct sign. Hence, this function is usually quite fast, but will run */
+/* more slowly when the input points are cocircular or nearly so. */
+/* */
+/* See my Robust Predicates paper for details. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+REAL incircleadapt(vertex pa, vertex pb, vertex pc, vertex pd, REAL permanent)
+#else /* not ANSI_DECLARATORS */
+REAL incircleadapt(pa, pb, pc, pd, permanent)
+vertex pa;
+vertex pb;
+vertex pc;
+vertex pd;
+REAL permanent;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ INEXACT REAL adx, bdx, cdx, ady, bdy, cdy;
+ REAL det, errbound;
+
+ INEXACT REAL bdxcdy1, cdxbdy1, cdxady1, adxcdy1, adxbdy1, bdxady1;
+ REAL bdxcdy0, cdxbdy0, cdxady0, adxcdy0, adxbdy0, bdxady0;
+ REAL bc[4], ca[4], ab[4];
+ INEXACT REAL bc3, ca3, ab3;
+ REAL axbc[8], axxbc[16], aybc[8], ayybc[16], adet[32];
+ int axbclen, axxbclen, aybclen, ayybclen, alen;
+ REAL bxca[8], bxxca[16], byca[8], byyca[16], bdet[32];
+ int bxcalen, bxxcalen, bycalen, byycalen, blen;
+ REAL cxab[8], cxxab[16], cyab[8], cyyab[16], cdet[32];
+ int cxablen, cxxablen, cyablen, cyyablen, clen;
+ REAL abdet[64];
+ int ablen;
+ REAL fin1[1152], fin2[1152];
+ REAL *finnow, *finother, *finswap;
+ int finlength;
+
+ REAL adxtail, bdxtail, cdxtail, adytail, bdytail, cdytail;
+ INEXACT REAL adxadx1, adyady1, bdxbdx1, bdybdy1, cdxcdx1, cdycdy1;
+ REAL adxadx0, adyady0, bdxbdx0, bdybdy0, cdxcdx0, cdycdy0;
+ REAL aa[4], bb[4], cc[4];
+ INEXACT REAL aa3, bb3, cc3;
+ INEXACT REAL ti1, tj1;
+ REAL ti0, tj0;
+ REAL u[4], v[4];
+ INEXACT REAL u3, v3;
+ REAL temp8[8], temp16a[16], temp16b[16], temp16c[16];
+ REAL temp32a[32], temp32b[32], temp48[48], temp64[64];
+ int temp8len, temp16alen, temp16blen, temp16clen;
+ int temp32alen, temp32blen, temp48len, temp64len;
+ REAL axtbb[8], axtcc[8], aytbb[8], aytcc[8];
+ int axtbblen, axtcclen, aytbblen, aytcclen;
+ REAL bxtaa[8], bxtcc[8], bytaa[8], bytcc[8];
+ int bxtaalen, bxtcclen, bytaalen, bytcclen;
+ REAL cxtaa[8], cxtbb[8], cytaa[8], cytbb[8];
+ int cxtaalen, cxtbblen, cytaalen, cytbblen;
+ REAL axtbc[8], aytbc[8], bxtca[8], bytca[8], cxtab[8], cytab[8];
+ int axtbclen, aytbclen, bxtcalen, bytcalen, cxtablen, cytablen;
+ REAL axtbct[16], aytbct[16], bxtcat[16], bytcat[16], cxtabt[16], cytabt[16];
+ int axtbctlen, aytbctlen, bxtcatlen, bytcatlen, cxtabtlen, cytabtlen;
+ REAL axtbctt[8], aytbctt[8], bxtcatt[8];
+ REAL bytcatt[8], cxtabtt[8], cytabtt[8];
+ int axtbcttlen, aytbcttlen, bxtcattlen, bytcattlen, cxtabttlen, cytabttlen;
+ REAL abt[8], bct[8], cat[8];
+ int abtlen, bctlen, catlen;
+ REAL abtt[4], bctt[4], catt[4];
+ int abttlen, bcttlen, cattlen;
+ INEXACT REAL abtt3, bctt3, catt3;
+ REAL negate;
+
+ INEXACT REAL bvirt;
+ REAL avirt, bround, around;
+ INEXACT REAL c;
+ INEXACT REAL abig;
+ REAL ahi, alo, bhi, blo;
+ REAL err1, err2, err3;
+ INEXACT REAL _i, _j;
+ REAL _0;
+
+ adx = (REAL) (pa[0] - pd[0]);
+ bdx = (REAL) (pb[0] - pd[0]);
+ cdx = (REAL) (pc[0] - pd[0]);
+ ady = (REAL) (pa[1] - pd[1]);
+ bdy = (REAL) (pb[1] - pd[1]);
+ cdy = (REAL) (pc[1] - pd[1]);
+
+ Two_Product(bdx, cdy, bdxcdy1, bdxcdy0);
+ Two_Product(cdx, bdy, cdxbdy1, cdxbdy0);
+ Two_Two_Diff(bdxcdy1, bdxcdy0, cdxbdy1, cdxbdy0, bc3, bc[2], bc[1], bc[0]);
+ bc[3] = bc3;
+ axbclen = scale_expansion_zeroelim(4, bc, adx, axbc);
+ axxbclen = scale_expansion_zeroelim(axbclen, axbc, adx, axxbc);
+ aybclen = scale_expansion_zeroelim(4, bc, ady, aybc);
+ ayybclen = scale_expansion_zeroelim(aybclen, aybc, ady, ayybc);
+ alen = fast_expansion_sum_zeroelim(axxbclen, axxbc, ayybclen, ayybc, adet);
+
+ Two_Product(cdx, ady, cdxady1, cdxady0);
+ Two_Product(adx, cdy, adxcdy1, adxcdy0);
+ Two_Two_Diff(cdxady1, cdxady0, adxcdy1, adxcdy0, ca3, ca[2], ca[1], ca[0]);
+ ca[3] = ca3;
+ bxcalen = scale_expansion_zeroelim(4, ca, bdx, bxca);
+ bxxcalen = scale_expansion_zeroelim(bxcalen, bxca, bdx, bxxca);
+ bycalen = scale_expansion_zeroelim(4, ca, bdy, byca);
+ byycalen = scale_expansion_zeroelim(bycalen, byca, bdy, byyca);
+ blen = fast_expansion_sum_zeroelim(bxxcalen, bxxca, byycalen, byyca, bdet);
+
+ Two_Product(adx, bdy, adxbdy1, adxbdy0);
+ Two_Product(bdx, ady, bdxady1, bdxady0);
+ Two_Two_Diff(adxbdy1, adxbdy0, bdxady1, bdxady0, ab3, ab[2], ab[1], ab[0]);
+ ab[3] = ab3;
+ cxablen = scale_expansion_zeroelim(4, ab, cdx, cxab);
+ cxxablen = scale_expansion_zeroelim(cxablen, cxab, cdx, cxxab);
+ cyablen = scale_expansion_zeroelim(4, ab, cdy, cyab);
+ cyyablen = scale_expansion_zeroelim(cyablen, cyab, cdy, cyyab);
+ clen = fast_expansion_sum_zeroelim(cxxablen, cxxab, cyyablen, cyyab, cdet);
+
+ ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
+ finlength = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, fin1);
+
+ det = estimate(finlength, fin1);
+ errbound = iccerrboundB * permanent;
+ if ((det >= errbound) || (-det >= errbound)) {
+ return det;
+ }
+
+ Two_Diff_Tail(pa[0], pd[0], adx, adxtail);
+ Two_Diff_Tail(pa[1], pd[1], ady, adytail);
+ Two_Diff_Tail(pb[0], pd[0], bdx, bdxtail);
+ Two_Diff_Tail(pb[1], pd[1], bdy, bdytail);
+ Two_Diff_Tail(pc[0], pd[0], cdx, cdxtail);
+ Two_Diff_Tail(pc[1], pd[1], cdy, cdytail);
+ if ((adxtail == 0.0) && (bdxtail == 0.0) && (cdxtail == 0.0)
+ && (adytail == 0.0) && (bdytail == 0.0) && (cdytail == 0.0)) {
+ return det;
+ }
+
+ errbound = iccerrboundC * permanent + resulterrbound * Absolute(det);
+ det += ((adx * adx + ady * ady) * ((bdx * cdytail + cdy * bdxtail)
+ - (bdy * cdxtail + cdx * bdytail))
+ + 2.0 * (adx * adxtail + ady * adytail) * (bdx * cdy - bdy * cdx))
+ + ((bdx * bdx + bdy * bdy) * ((cdx * adytail + ady * cdxtail)
+ - (cdy * adxtail + adx * cdytail))
+ + 2.0 * (bdx * bdxtail + bdy * bdytail) * (cdx * ady - cdy * adx))
+ + ((cdx * cdx + cdy * cdy) * ((adx * bdytail + bdy * adxtail)
+ - (ady * bdxtail + bdx * adytail))
+ + 2.0 * (cdx * cdxtail + cdy * cdytail) * (adx * bdy - ady * bdx));
+ if ((det >= errbound) || (-det >= errbound)) {
+ return det;
+ }
+
+ finnow = fin1;
+ finother = fin2;
+
+ if ((bdxtail != 0.0) || (bdytail != 0.0)
+ || (cdxtail != 0.0) || (cdytail != 0.0)) {
+ Square(adx, adxadx1, adxadx0);
+ Square(ady, adyady1, adyady0);
+ Two_Two_Sum(adxadx1, adxadx0, adyady1, adyady0, aa3, aa[2], aa[1], aa[0]);
+ aa[3] = aa3;
+ }
+ if ((cdxtail != 0.0) || (cdytail != 0.0)
+ || (adxtail != 0.0) || (adytail != 0.0)) {
+ Square(bdx, bdxbdx1, bdxbdx0);
+ Square(bdy, bdybdy1, bdybdy0);
+ Two_Two_Sum(bdxbdx1, bdxbdx0, bdybdy1, bdybdy0, bb3, bb[2], bb[1], bb[0]);
+ bb[3] = bb3;
+ }
+ if ((adxtail != 0.0) || (adytail != 0.0)
+ || (bdxtail != 0.0) || (bdytail != 0.0)) {
+ Square(cdx, cdxcdx1, cdxcdx0);
+ Square(cdy, cdycdy1, cdycdy0);
+ Two_Two_Sum(cdxcdx1, cdxcdx0, cdycdy1, cdycdy0, cc3, cc[2], cc[1], cc[0]);
+ cc[3] = cc3;
+ }
+
+ if (adxtail != 0.0) {
+ axtbclen = scale_expansion_zeroelim(4, bc, adxtail, axtbc);
+ temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, 2.0 * adx,
+ temp16a);
+
+ axtcclen = scale_expansion_zeroelim(4, cc, adxtail, axtcc);
+ temp16blen = scale_expansion_zeroelim(axtcclen, axtcc, bdy, temp16b);
+
+ axtbblen = scale_expansion_zeroelim(4, bb, adxtail, axtbb);
+ temp16clen = scale_expansion_zeroelim(axtbblen, axtbb, -cdy, temp16c);
+
+ temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
+ temp16blen, temp16b, temp32a);
+ temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
+ temp32alen, temp32a, temp48);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
+ temp48, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ if (adytail != 0.0) {
+ aytbclen = scale_expansion_zeroelim(4, bc, adytail, aytbc);
+ temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, 2.0 * ady,
+ temp16a);
+
+ aytbblen = scale_expansion_zeroelim(4, bb, adytail, aytbb);
+ temp16blen = scale_expansion_zeroelim(aytbblen, aytbb, cdx, temp16b);
+
+ aytcclen = scale_expansion_zeroelim(4, cc, adytail, aytcc);
+ temp16clen = scale_expansion_zeroelim(aytcclen, aytcc, -bdx, temp16c);
+
+ temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
+ temp16blen, temp16b, temp32a);
+ temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
+ temp32alen, temp32a, temp48);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
+ temp48, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ if (bdxtail != 0.0) {
+ bxtcalen = scale_expansion_zeroelim(4, ca, bdxtail, bxtca);
+ temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, 2.0 * bdx,
+ temp16a);
+
+ bxtaalen = scale_expansion_zeroelim(4, aa, bdxtail, bxtaa);
+ temp16blen = scale_expansion_zeroelim(bxtaalen, bxtaa, cdy, temp16b);
+
+ bxtcclen = scale_expansion_zeroelim(4, cc, bdxtail, bxtcc);
+ temp16clen = scale_expansion_zeroelim(bxtcclen, bxtcc, -ady, temp16c);
+
+ temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
+ temp16blen, temp16b, temp32a);
+ temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
+ temp32alen, temp32a, temp48);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
+ temp48, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ if (bdytail != 0.0) {
+ bytcalen = scale_expansion_zeroelim(4, ca, bdytail, bytca);
+ temp16alen = scale_expansion_zeroelim(bytcalen, bytca, 2.0 * bdy,
+ temp16a);
+
+ bytcclen = scale_expansion_zeroelim(4, cc, bdytail, bytcc);
+ temp16blen = scale_expansion_zeroelim(bytcclen, bytcc, adx, temp16b);
+
+ bytaalen = scale_expansion_zeroelim(4, aa, bdytail, bytaa);
+ temp16clen = scale_expansion_zeroelim(bytaalen, bytaa, -cdx, temp16c);
+
+ temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
+ temp16blen, temp16b, temp32a);
+ temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
+ temp32alen, temp32a, temp48);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
+ temp48, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ if (cdxtail != 0.0) {
+ cxtablen = scale_expansion_zeroelim(4, ab, cdxtail, cxtab);
+ temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, 2.0 * cdx,
+ temp16a);
+
+ cxtbblen = scale_expansion_zeroelim(4, bb, cdxtail, cxtbb);
+ temp16blen = scale_expansion_zeroelim(cxtbblen, cxtbb, ady, temp16b);
+
+ cxtaalen = scale_expansion_zeroelim(4, aa, cdxtail, cxtaa);
+ temp16clen = scale_expansion_zeroelim(cxtaalen, cxtaa, -bdy, temp16c);
+
+ temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
+ temp16blen, temp16b, temp32a);
+ temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
+ temp32alen, temp32a, temp48);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
+ temp48, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ if (cdytail != 0.0) {
+ cytablen = scale_expansion_zeroelim(4, ab, cdytail, cytab);
+ temp16alen = scale_expansion_zeroelim(cytablen, cytab, 2.0 * cdy,
+ temp16a);
+
+ cytaalen = scale_expansion_zeroelim(4, aa, cdytail, cytaa);
+ temp16blen = scale_expansion_zeroelim(cytaalen, cytaa, bdx, temp16b);
+
+ cytbblen = scale_expansion_zeroelim(4, bb, cdytail, cytbb);
+ temp16clen = scale_expansion_zeroelim(cytbblen, cytbb, -adx, temp16c);
+
+ temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
+ temp16blen, temp16b, temp32a);
+ temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
+ temp32alen, temp32a, temp48);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
+ temp48, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+
+ if ((adxtail != 0.0) || (adytail != 0.0)) {
+ if ((bdxtail != 0.0) || (bdytail != 0.0)
+ || (cdxtail != 0.0) || (cdytail != 0.0)) {
+ Two_Product(bdxtail, cdy, ti1, ti0);
+ Two_Product(bdx, cdytail, tj1, tj0);
+ Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
+ u[3] = u3;
+ negate = -bdy;
+ Two_Product(cdxtail, negate, ti1, ti0);
+ negate = -bdytail;
+ Two_Product(cdx, negate, tj1, tj0);
+ Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
+ v[3] = v3;
+ bctlen = fast_expansion_sum_zeroelim(4, u, 4, v, bct);
+
+ Two_Product(bdxtail, cdytail, ti1, ti0);
+ Two_Product(cdxtail, bdytail, tj1, tj0);
+ Two_Two_Diff(ti1, ti0, tj1, tj0, bctt3, bctt[2], bctt[1], bctt[0]);
+ bctt[3] = bctt3;
+ bcttlen = 4;
+ } else {
+ bct[0] = 0.0;
+ bctlen = 1;
+ bctt[0] = 0.0;
+ bcttlen = 1;
+ }
+
+ if (adxtail != 0.0) {
+ temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, adxtail, temp16a);
+ axtbctlen = scale_expansion_zeroelim(bctlen, bct, adxtail, axtbct);
+ temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, 2.0 * adx,
+ temp32a);
+ temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
+ temp32alen, temp32a, temp48);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
+ temp48, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ if (bdytail != 0.0) {
+ temp8len = scale_expansion_zeroelim(4, cc, adxtail, temp8);
+ temp16alen = scale_expansion_zeroelim(temp8len, temp8, bdytail,
+ temp16a);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
+ temp16a, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ if (cdytail != 0.0) {
+ temp8len = scale_expansion_zeroelim(4, bb, -adxtail, temp8);
+ temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail,
+ temp16a);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
+ temp16a, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+
+ temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, adxtail,
+ temp32a);
+ axtbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adxtail, axtbctt);
+ temp16alen = scale_expansion_zeroelim(axtbcttlen, axtbctt, 2.0 * adx,
+ temp16a);
+ temp16blen = scale_expansion_zeroelim(axtbcttlen, axtbctt, adxtail,
+ temp16b);
+ temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
+ temp16blen, temp16b, temp32b);
+ temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
+ temp32blen, temp32b, temp64);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
+ temp64, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ if (adytail != 0.0) {
+ temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, adytail, temp16a);
+ aytbctlen = scale_expansion_zeroelim(bctlen, bct, adytail, aytbct);
+ temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, 2.0 * ady,
+ temp32a);
+ temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
+ temp32alen, temp32a, temp48);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
+ temp48, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+
+
+ temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, adytail,
+ temp32a);
+ aytbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adytail, aytbctt);
+ temp16alen = scale_expansion_zeroelim(aytbcttlen, aytbctt, 2.0 * ady,
+ temp16a);
+ temp16blen = scale_expansion_zeroelim(aytbcttlen, aytbctt, adytail,
+ temp16b);
+ temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
+ temp16blen, temp16b, temp32b);
+ temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
+ temp32blen, temp32b, temp64);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
+ temp64, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ }
+ if ((bdxtail != 0.0) || (bdytail != 0.0)) {
+ if ((cdxtail != 0.0) || (cdytail != 0.0)
+ || (adxtail != 0.0) || (adytail != 0.0)) {
+ Two_Product(cdxtail, ady, ti1, ti0);
+ Two_Product(cdx, adytail, tj1, tj0);
+ Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
+ u[3] = u3;
+ negate = -cdy;
+ Two_Product(adxtail, negate, ti1, ti0);
+ negate = -cdytail;
+ Two_Product(adx, negate, tj1, tj0);
+ Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
+ v[3] = v3;
+ catlen = fast_expansion_sum_zeroelim(4, u, 4, v, cat);
+
+ Two_Product(cdxtail, adytail, ti1, ti0);
+ Two_Product(adxtail, cdytail, tj1, tj0);
+ Two_Two_Diff(ti1, ti0, tj1, tj0, catt3, catt[2], catt[1], catt[0]);
+ catt[3] = catt3;
+ cattlen = 4;
+ } else {
+ cat[0] = 0.0;
+ catlen = 1;
+ catt[0] = 0.0;
+ cattlen = 1;
+ }
+
+ if (bdxtail != 0.0) {
+ temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, bdxtail, temp16a);
+ bxtcatlen = scale_expansion_zeroelim(catlen, cat, bdxtail, bxtcat);
+ temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, 2.0 * bdx,
+ temp32a);
+ temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
+ temp32alen, temp32a, temp48);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
+ temp48, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ if (cdytail != 0.0) {
+ temp8len = scale_expansion_zeroelim(4, aa, bdxtail, temp8);
+ temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail,
+ temp16a);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
+ temp16a, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ if (adytail != 0.0) {
+ temp8len = scale_expansion_zeroelim(4, cc, -bdxtail, temp8);
+ temp16alen = scale_expansion_zeroelim(temp8len, temp8, adytail,
+ temp16a);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
+ temp16a, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+
+ temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, bdxtail,
+ temp32a);
+ bxtcattlen = scale_expansion_zeroelim(cattlen, catt, bdxtail, bxtcatt);
+ temp16alen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, 2.0 * bdx,
+ temp16a);
+ temp16blen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, bdxtail,
+ temp16b);
+ temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
+ temp16blen, temp16b, temp32b);
+ temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
+ temp32blen, temp32b, temp64);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
+ temp64, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ if (bdytail != 0.0) {
+ temp16alen = scale_expansion_zeroelim(bytcalen, bytca, bdytail, temp16a);
+ bytcatlen = scale_expansion_zeroelim(catlen, cat, bdytail, bytcat);
+ temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, 2.0 * bdy,
+ temp32a);
+ temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
+ temp32alen, temp32a, temp48);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
+ temp48, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+
+
+ temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, bdytail,
+ temp32a);
+ bytcattlen = scale_expansion_zeroelim(cattlen, catt, bdytail, bytcatt);
+ temp16alen = scale_expansion_zeroelim(bytcattlen, bytcatt, 2.0 * bdy,
+ temp16a);
+ temp16blen = scale_expansion_zeroelim(bytcattlen, bytcatt, bdytail,
+ temp16b);
+ temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
+ temp16blen, temp16b, temp32b);
+ temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
+ temp32blen, temp32b, temp64);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
+ temp64, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ }
+ if ((cdxtail != 0.0) || (cdytail != 0.0)) {
+ if ((adxtail != 0.0) || (adytail != 0.0)
+ || (bdxtail != 0.0) || (bdytail != 0.0)) {
+ Two_Product(adxtail, bdy, ti1, ti0);
+ Two_Product(adx, bdytail, tj1, tj0);
+ Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
+ u[3] = u3;
+ negate = -ady;
+ Two_Product(bdxtail, negate, ti1, ti0);
+ negate = -adytail;
+ Two_Product(bdx, negate, tj1, tj0);
+ Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
+ v[3] = v3;
+ abtlen = fast_expansion_sum_zeroelim(4, u, 4, v, abt);
+
+ Two_Product(adxtail, bdytail, ti1, ti0);
+ Two_Product(bdxtail, adytail, tj1, tj0);
+ Two_Two_Diff(ti1, ti0, tj1, tj0, abtt3, abtt[2], abtt[1], abtt[0]);
+ abtt[3] = abtt3;
+ abttlen = 4;
+ } else {
+ abt[0] = 0.0;
+ abtlen = 1;
+ abtt[0] = 0.0;
+ abttlen = 1;
+ }
+
+ if (cdxtail != 0.0) {
+ temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, cdxtail, temp16a);
+ cxtabtlen = scale_expansion_zeroelim(abtlen, abt, cdxtail, cxtabt);
+ temp32alen = scale_expansion_zeroelim(cxtabtlen, cxtabt, 2.0 * cdx,
+ temp32a);
+ temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
+ temp32alen, temp32a, temp48);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
+ temp48, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ if (adytail != 0.0) {
+ temp8len = scale_expansion_zeroelim(4, bb, cdxtail, temp8);
+ temp16alen = scale_expansion_zeroelim(temp8len, temp8, adytail,
+ temp16a);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
+ temp16a, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ if (bdytail != 0.0) {
+ temp8len = scale_expansion_zeroelim(4, aa, -cdxtail, temp8);
+ temp16alen = scale_expansion_zeroelim(temp8len, temp8, bdytail,
+ temp16a);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
+ temp16a, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+
+ temp32alen = scale_expansion_zeroelim(cxtabtlen, cxtabt, cdxtail,
+ temp32a);
+ cxtabttlen = scale_expansion_zeroelim(abttlen, abtt, cdxtail, cxtabtt);
+ temp16alen = scale_expansion_zeroelim(cxtabttlen, cxtabtt, 2.0 * cdx,
+ temp16a);
+ temp16blen = scale_expansion_zeroelim(cxtabttlen, cxtabtt, cdxtail,
+ temp16b);
+ temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
+ temp16blen, temp16b, temp32b);
+ temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
+ temp32blen, temp32b, temp64);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
+ temp64, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ if (cdytail != 0.0) {
+ temp16alen = scale_expansion_zeroelim(cytablen, cytab, cdytail, temp16a);
+ cytabtlen = scale_expansion_zeroelim(abtlen, abt, cdytail, cytabt);
+ temp32alen = scale_expansion_zeroelim(cytabtlen, cytabt, 2.0 * cdy,
+ temp32a);
+ temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
+ temp32alen, temp32a, temp48);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
+ temp48, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+
+
+ temp32alen = scale_expansion_zeroelim(cytabtlen, cytabt, cdytail,
+ temp32a);
+ cytabttlen = scale_expansion_zeroelim(abttlen, abtt, cdytail, cytabtt);
+ temp16alen = scale_expansion_zeroelim(cytabttlen, cytabtt, 2.0 * cdy,
+ temp16a);
+ temp16blen = scale_expansion_zeroelim(cytabttlen, cytabtt, cdytail,
+ temp16b);
+ temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
+ temp16blen, temp16b, temp32b);
+ temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
+ temp32blen, temp32b, temp64);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
+ temp64, finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ }
+
+ return finnow[finlength - 1];
+}
+
+#ifdef ANSI_DECLARATORS
+REAL incircle(struct mesh *m, struct behavior *b,
+ vertex pa, vertex pb, vertex pc, vertex pd)
+#else /* not ANSI_DECLARATORS */
+REAL incircle(m, b, pa, pb, pc, pd)
+struct mesh *m;
+struct behavior *b;
+vertex pa;
+vertex pb;
+vertex pc;
+vertex pd;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ REAL adx, bdx, cdx, ady, bdy, cdy;
+ REAL bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady;
+ REAL alift, blift, clift;
+ REAL det;
+ REAL permanent, errbound;
+
+ m->incirclecount++;
+
+ adx = pa[0] - pd[0];
+ bdx = pb[0] - pd[0];
+ cdx = pc[0] - pd[0];
+ ady = pa[1] - pd[1];
+ bdy = pb[1] - pd[1];
+ cdy = pc[1] - pd[1];
+
+ bdxcdy = bdx * cdy;
+ cdxbdy = cdx * bdy;
+ alift = adx * adx + ady * ady;
+
+ cdxady = cdx * ady;
+ adxcdy = adx * cdy;
+ blift = bdx * bdx + bdy * bdy;
+
+ adxbdy = adx * bdy;
+ bdxady = bdx * ady;
+ clift = cdx * cdx + cdy * cdy;
+
+ det = alift * (bdxcdy - cdxbdy)
+ + blift * (cdxady - adxcdy)
+ + clift * (adxbdy - bdxady);
+
+ if (b->noexact) {
+ return det;
+ }
+
+ permanent = (Absolute(bdxcdy) + Absolute(cdxbdy)) * alift
+ + (Absolute(cdxady) + Absolute(adxcdy)) * blift
+ + (Absolute(adxbdy) + Absolute(bdxady)) * clift;
+ errbound = iccerrboundA * permanent;
+ if ((det > errbound) || (-det > errbound)) {
+ return det;
+ }
+
+ return incircleadapt(pa, pb, pc, pd, permanent);
+}
+
+/*****************************************************************************/
+/* */
+/* orient3d() Return a positive value if the point pd lies below the */
+/* plane passing through pa, pb, and pc; "below" is defined so */
+/* that pa, pb, and pc appear in counterclockwise order when */
+/* viewed from above the plane. Returns a negative value if */
+/* pd lies above the plane. Returns zero if the points are */
+/* coplanar. The result is also a rough approximation of six */
+/* times the signed volume of the tetrahedron defined by the */
+/* four points. */
+/* */
+/* Uses exact arithmetic if necessary to ensure a correct answer. The */
+/* result returned is the determinant of a matrix. This determinant is */
+/* computed adaptively, in the sense that exact arithmetic is used only to */
+/* the degree it is needed to ensure that the returned value has the */
+/* correct sign. Hence, this function is usually quite fast, but will run */
+/* more slowly when the input points are coplanar or nearly so. */
+/* */
+/* See my Robust Predicates paper for details. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+REAL orient3dadapt(vertex pa, vertex pb, vertex pc, vertex pd,
+ REAL aheight, REAL bheight, REAL cheight, REAL dheight,
+ REAL permanent)
+#else /* not ANSI_DECLARATORS */
+REAL orient3dadapt(pa, pb, pc, pd,
+ aheight, bheight, cheight, dheight, permanent)
+vertex pa;
+vertex pb;
+vertex pc;
+vertex pd;
+REAL aheight;
+REAL bheight;
+REAL cheight;
+REAL dheight;
+REAL permanent;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ INEXACT REAL adx, bdx, cdx, ady, bdy, cdy, adheight, bdheight, cdheight;
+ REAL det, errbound;
+
+ INEXACT REAL bdxcdy1, cdxbdy1, cdxady1, adxcdy1, adxbdy1, bdxady1;
+ REAL bdxcdy0, cdxbdy0, cdxady0, adxcdy0, adxbdy0, bdxady0;
+ REAL bc[4], ca[4], ab[4];
+ INEXACT REAL bc3, ca3, ab3;
+ REAL adet[8], bdet[8], cdet[8];
+ int alen, blen, clen;
+ REAL abdet[16];
+ int ablen;
+ REAL *finnow, *finother, *finswap;
+ REAL fin1[192], fin2[192];
+ int finlength;
+
+ REAL adxtail, bdxtail, cdxtail;
+ REAL adytail, bdytail, cdytail;
+ REAL adheighttail, bdheighttail, cdheighttail;
+ INEXACT REAL at_blarge, at_clarge;
+ INEXACT REAL bt_clarge, bt_alarge;
+ INEXACT REAL ct_alarge, ct_blarge;
+ REAL at_b[4], at_c[4], bt_c[4], bt_a[4], ct_a[4], ct_b[4];
+ int at_blen, at_clen, bt_clen, bt_alen, ct_alen, ct_blen;
+ INEXACT REAL bdxt_cdy1, cdxt_bdy1, cdxt_ady1;
+ INEXACT REAL adxt_cdy1, adxt_bdy1, bdxt_ady1;
+ REAL bdxt_cdy0, cdxt_bdy0, cdxt_ady0;
+ REAL adxt_cdy0, adxt_bdy0, bdxt_ady0;
+ INEXACT REAL bdyt_cdx1, cdyt_bdx1, cdyt_adx1;
+ INEXACT REAL adyt_cdx1, adyt_bdx1, bdyt_adx1;
+ REAL bdyt_cdx0, cdyt_bdx0, cdyt_adx0;
+ REAL adyt_cdx0, adyt_bdx0, bdyt_adx0;
+ REAL bct[8], cat[8], abt[8];
+ int bctlen, catlen, abtlen;
+ INEXACT REAL bdxt_cdyt1, cdxt_bdyt1, cdxt_adyt1;
+ INEXACT REAL adxt_cdyt1, adxt_bdyt1, bdxt_adyt1;
+ REAL bdxt_cdyt0, cdxt_bdyt0, cdxt_adyt0;
+ REAL adxt_cdyt0, adxt_bdyt0, bdxt_adyt0;
+ REAL u[4], v[12], w[16];
+ INEXACT REAL u3;
+ int vlength, wlength;
+ REAL negate;
+
+ INEXACT REAL bvirt;
+ REAL avirt, bround, around;
+ INEXACT REAL c;
+ INEXACT REAL abig;
+ REAL ahi, alo, bhi, blo;
+ REAL err1, err2, err3;
+ INEXACT REAL _i, _j, _k;
+ REAL _0;
+
+ adx = (REAL) (pa[0] - pd[0]);
+ bdx = (REAL) (pb[0] - pd[0]);
+ cdx = (REAL) (pc[0] - pd[0]);
+ ady = (REAL) (pa[1] - pd[1]);
+ bdy = (REAL) (pb[1] - pd[1]);
+ cdy = (REAL) (pc[1] - pd[1]);
+ adheight = (REAL) (aheight - dheight);
+ bdheight = (REAL) (bheight - dheight);
+ cdheight = (REAL) (cheight - dheight);
+
+ Two_Product(bdx, cdy, bdxcdy1, bdxcdy0);
+ Two_Product(cdx, bdy, cdxbdy1, cdxbdy0);
+ Two_Two_Diff(bdxcdy1, bdxcdy0, cdxbdy1, cdxbdy0, bc3, bc[2], bc[1], bc[0]);
+ bc[3] = bc3;
+ alen = scale_expansion_zeroelim(4, bc, adheight, adet);
+
+ Two_Product(cdx, ady, cdxady1, cdxady0);
+ Two_Product(adx, cdy, adxcdy1, adxcdy0);
+ Two_Two_Diff(cdxady1, cdxady0, adxcdy1, adxcdy0, ca3, ca[2], ca[1], ca[0]);
+ ca[3] = ca3;
+ blen = scale_expansion_zeroelim(4, ca, bdheight, bdet);
+
+ Two_Product(adx, bdy, adxbdy1, adxbdy0);
+ Two_Product(bdx, ady, bdxady1, bdxady0);
+ Two_Two_Diff(adxbdy1, adxbdy0, bdxady1, bdxady0, ab3, ab[2], ab[1], ab[0]);
+ ab[3] = ab3;
+ clen = scale_expansion_zeroelim(4, ab, cdheight, cdet);
+
+ ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
+ finlength = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, fin1);
+
+ det = estimate(finlength, fin1);
+ errbound = o3derrboundB * permanent;
+ if ((det >= errbound) || (-det >= errbound)) {
+ return det;
+ }
+
+ Two_Diff_Tail(pa[0], pd[0], adx, adxtail);
+ Two_Diff_Tail(pb[0], pd[0], bdx, bdxtail);
+ Two_Diff_Tail(pc[0], pd[0], cdx, cdxtail);
+ Two_Diff_Tail(pa[1], pd[1], ady, adytail);
+ Two_Diff_Tail(pb[1], pd[1], bdy, bdytail);
+ Two_Diff_Tail(pc[1], pd[1], cdy, cdytail);
+ Two_Diff_Tail(aheight, dheight, adheight, adheighttail);
+ Two_Diff_Tail(bheight, dheight, bdheight, bdheighttail);
+ Two_Diff_Tail(cheight, dheight, cdheight, cdheighttail);
+
+ if ((adxtail == 0.0) && (bdxtail == 0.0) && (cdxtail == 0.0) &&
+ (adytail == 0.0) && (bdytail == 0.0) && (cdytail == 0.0) &&
+ (adheighttail == 0.0) &&
+ (bdheighttail == 0.0) &&
+ (cdheighttail == 0.0)) {
+ return det;
+ }
+
+ errbound = o3derrboundC * permanent + resulterrbound * Absolute(det);
+ det += (adheight * ((bdx * cdytail + cdy * bdxtail) -
+ (bdy * cdxtail + cdx * bdytail)) +
+ adheighttail * (bdx * cdy - bdy * cdx)) +
+ (bdheight * ((cdx * adytail + ady * cdxtail) -
+ (cdy * adxtail + adx * cdytail)) +
+ bdheighttail * (cdx * ady - cdy * adx)) +
+ (cdheight * ((adx * bdytail + bdy * adxtail) -
+ (ady * bdxtail + bdx * adytail)) +
+ cdheighttail * (adx * bdy - ady * bdx));
+ if ((det >= errbound) || (-det >= errbound)) {
+ return det;
+ }
+
+ finnow = fin1;
+ finother = fin2;
+
+ if (adxtail == 0.0) {
+ if (adytail == 0.0) {
+ at_b[0] = 0.0;
+ at_blen = 1;
+ at_c[0] = 0.0;
+ at_clen = 1;
+ } else {
+ negate = -adytail;
+ Two_Product(negate, bdx, at_blarge, at_b[0]);
+ at_b[1] = at_blarge;
+ at_blen = 2;
+ Two_Product(adytail, cdx, at_clarge, at_c[0]);
+ at_c[1] = at_clarge;
+ at_clen = 2;
+ }
+ } else {
+ if (adytail == 0.0) {
+ Two_Product(adxtail, bdy, at_blarge, at_b[0]);
+ at_b[1] = at_blarge;
+ at_blen = 2;
+ negate = -adxtail;
+ Two_Product(negate, cdy, at_clarge, at_c[0]);
+ at_c[1] = at_clarge;
+ at_clen = 2;
+ } else {
+ Two_Product(adxtail, bdy, adxt_bdy1, adxt_bdy0);
+ Two_Product(adytail, bdx, adyt_bdx1, adyt_bdx0);
+ Two_Two_Diff(adxt_bdy1, adxt_bdy0, adyt_bdx1, adyt_bdx0,
+ at_blarge, at_b[2], at_b[1], at_b[0]);
+ at_b[3] = at_blarge;
+ at_blen = 4;
+ Two_Product(adytail, cdx, adyt_cdx1, adyt_cdx0);
+ Two_Product(adxtail, cdy, adxt_cdy1, adxt_cdy0);
+ Two_Two_Diff(adyt_cdx1, adyt_cdx0, adxt_cdy1, adxt_cdy0,
+ at_clarge, at_c[2], at_c[1], at_c[0]);
+ at_c[3] = at_clarge;
+ at_clen = 4;
+ }
+ }
+ if (bdxtail == 0.0) {
+ if (bdytail == 0.0) {
+ bt_c[0] = 0.0;
+ bt_clen = 1;
+ bt_a[0] = 0.0;
+ bt_alen = 1;
+ } else {
+ negate = -bdytail;
+ Two_Product(negate, cdx, bt_clarge, bt_c[0]);
+ bt_c[1] = bt_clarge;
+ bt_clen = 2;
+ Two_Product(bdytail, adx, bt_alarge, bt_a[0]);
+ bt_a[1] = bt_alarge;
+ bt_alen = 2;
+ }
+ } else {
+ if (bdytail == 0.0) {
+ Two_Product(bdxtail, cdy, bt_clarge, bt_c[0]);
+ bt_c[1] = bt_clarge;
+ bt_clen = 2;
+ negate = -bdxtail;
+ Two_Product(negate, ady, bt_alarge, bt_a[0]);
+ bt_a[1] = bt_alarge;
+ bt_alen = 2;
+ } else {
+ Two_Product(bdxtail, cdy, bdxt_cdy1, bdxt_cdy0);
+ Two_Product(bdytail, cdx, bdyt_cdx1, bdyt_cdx0);
+ Two_Two_Diff(bdxt_cdy1, bdxt_cdy0, bdyt_cdx1, bdyt_cdx0,
+ bt_clarge, bt_c[2], bt_c[1], bt_c[0]);
+ bt_c[3] = bt_clarge;
+ bt_clen = 4;
+ Two_Product(bdytail, adx, bdyt_adx1, bdyt_adx0);
+ Two_Product(bdxtail, ady, bdxt_ady1, bdxt_ady0);
+ Two_Two_Diff(bdyt_adx1, bdyt_adx0, bdxt_ady1, bdxt_ady0,
+ bt_alarge, bt_a[2], bt_a[1], bt_a[0]);
+ bt_a[3] = bt_alarge;
+ bt_alen = 4;
+ }
+ }
+ if (cdxtail == 0.0) {
+ if (cdytail == 0.0) {
+ ct_a[0] = 0.0;
+ ct_alen = 1;
+ ct_b[0] = 0.0;
+ ct_blen = 1;
+ } else {
+ negate = -cdytail;
+ Two_Product(negate, adx, ct_alarge, ct_a[0]);
+ ct_a[1] = ct_alarge;
+ ct_alen = 2;
+ Two_Product(cdytail, bdx, ct_blarge, ct_b[0]);
+ ct_b[1] = ct_blarge;
+ ct_blen = 2;
+ }
+ } else {
+ if (cdytail == 0.0) {
+ Two_Product(cdxtail, ady, ct_alarge, ct_a[0]);
+ ct_a[1] = ct_alarge;
+ ct_alen = 2;
+ negate = -cdxtail;
+ Two_Product(negate, bdy, ct_blarge, ct_b[0]);
+ ct_b[1] = ct_blarge;
+ ct_blen = 2;
+ } else {
+ Two_Product(cdxtail, ady, cdxt_ady1, cdxt_ady0);
+ Two_Product(cdytail, adx, cdyt_adx1, cdyt_adx0);
+ Two_Two_Diff(cdxt_ady1, cdxt_ady0, cdyt_adx1, cdyt_adx0,
+ ct_alarge, ct_a[2], ct_a[1], ct_a[0]);
+ ct_a[3] = ct_alarge;
+ ct_alen = 4;
+ Two_Product(cdytail, bdx, cdyt_bdx1, cdyt_bdx0);
+ Two_Product(cdxtail, bdy, cdxt_bdy1, cdxt_bdy0);
+ Two_Two_Diff(cdyt_bdx1, cdyt_bdx0, cdxt_bdy1, cdxt_bdy0,
+ ct_blarge, ct_b[2], ct_b[1], ct_b[0]);
+ ct_b[3] = ct_blarge;
+ ct_blen = 4;
+ }
+ }
+
+ bctlen = fast_expansion_sum_zeroelim(bt_clen, bt_c, ct_blen, ct_b, bct);
+ wlength = scale_expansion_zeroelim(bctlen, bct, adheight, w);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
+ finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+
+ catlen = fast_expansion_sum_zeroelim(ct_alen, ct_a, at_clen, at_c, cat);
+ wlength = scale_expansion_zeroelim(catlen, cat, bdheight, w);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
+ finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+
+ abtlen = fast_expansion_sum_zeroelim(at_blen, at_b, bt_alen, bt_a, abt);
+ wlength = scale_expansion_zeroelim(abtlen, abt, cdheight, w);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
+ finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+
+ if (adheighttail != 0.0) {
+ vlength = scale_expansion_zeroelim(4, bc, adheighttail, v);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v,
+ finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ if (bdheighttail != 0.0) {
+ vlength = scale_expansion_zeroelim(4, ca, bdheighttail, v);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v,
+ finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ if (cdheighttail != 0.0) {
+ vlength = scale_expansion_zeroelim(4, ab, cdheighttail, v);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v,
+ finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+
+ if (adxtail != 0.0) {
+ if (bdytail != 0.0) {
+ Two_Product(adxtail, bdytail, adxt_bdyt1, adxt_bdyt0);
+ Two_One_Product(adxt_bdyt1, adxt_bdyt0, cdheight, u3, u[2], u[1], u[0]);
+ u[3] = u3;
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
+ finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ if (cdheighttail != 0.0) {
+ Two_One_Product(adxt_bdyt1, adxt_bdyt0, cdheighttail,
+ u3, u[2], u[1], u[0]);
+ u[3] = u3;
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
+ finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ }
+ if (cdytail != 0.0) {
+ negate = -adxtail;
+ Two_Product(negate, cdytail, adxt_cdyt1, adxt_cdyt0);
+ Two_One_Product(adxt_cdyt1, adxt_cdyt0, bdheight, u3, u[2], u[1], u[0]);
+ u[3] = u3;
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
+ finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ if (bdheighttail != 0.0) {
+ Two_One_Product(adxt_cdyt1, adxt_cdyt0, bdheighttail,
+ u3, u[2], u[1], u[0]);
+ u[3] = u3;
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
+ finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ }
+ }
+ if (bdxtail != 0.0) {
+ if (cdytail != 0.0) {
+ Two_Product(bdxtail, cdytail, bdxt_cdyt1, bdxt_cdyt0);
+ Two_One_Product(bdxt_cdyt1, bdxt_cdyt0, adheight, u3, u[2], u[1], u[0]);
+ u[3] = u3;
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
+ finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ if (adheighttail != 0.0) {
+ Two_One_Product(bdxt_cdyt1, bdxt_cdyt0, adheighttail,
+ u3, u[2], u[1], u[0]);
+ u[3] = u3;
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
+ finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ }
+ if (adytail != 0.0) {
+ negate = -bdxtail;
+ Two_Product(negate, adytail, bdxt_adyt1, bdxt_adyt0);
+ Two_One_Product(bdxt_adyt1, bdxt_adyt0, cdheight, u3, u[2], u[1], u[0]);
+ u[3] = u3;
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
+ finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ if (cdheighttail != 0.0) {
+ Two_One_Product(bdxt_adyt1, bdxt_adyt0, cdheighttail,
+ u3, u[2], u[1], u[0]);
+ u[3] = u3;
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
+ finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ }
+ }
+ if (cdxtail != 0.0) {
+ if (adytail != 0.0) {
+ Two_Product(cdxtail, adytail, cdxt_adyt1, cdxt_adyt0);
+ Two_One_Product(cdxt_adyt1, cdxt_adyt0, bdheight, u3, u[2], u[1], u[0]);
+ u[3] = u3;
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
+ finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ if (bdheighttail != 0.0) {
+ Two_One_Product(cdxt_adyt1, cdxt_adyt0, bdheighttail,
+ u3, u[2], u[1], u[0]);
+ u[3] = u3;
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
+ finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ }
+ if (bdytail != 0.0) {
+ negate = -cdxtail;
+ Two_Product(negate, bdytail, cdxt_bdyt1, cdxt_bdyt0);
+ Two_One_Product(cdxt_bdyt1, cdxt_bdyt0, adheight, u3, u[2], u[1], u[0]);
+ u[3] = u3;
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
+ finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ if (adheighttail != 0.0) {
+ Two_One_Product(cdxt_bdyt1, cdxt_bdyt0, adheighttail,
+ u3, u[2], u[1], u[0]);
+ u[3] = u3;
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u,
+ finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ }
+ }
+
+ if (adheighttail != 0.0) {
+ wlength = scale_expansion_zeroelim(bctlen, bct, adheighttail, w);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
+ finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ if (bdheighttail != 0.0) {
+ wlength = scale_expansion_zeroelim(catlen, cat, bdheighttail, w);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
+ finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+ if (cdheighttail != 0.0) {
+ wlength = scale_expansion_zeroelim(abtlen, abt, cdheighttail, w);
+ finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w,
+ finother);
+ finswap = finnow; finnow = finother; finother = finswap;
+ }
+
+ return finnow[finlength - 1];
+}
+
+#ifdef ANSI_DECLARATORS
+REAL orient3d(struct mesh *m, struct behavior *b,
+ vertex pa, vertex pb, vertex pc, vertex pd,
+ REAL aheight, REAL bheight, REAL cheight, REAL dheight)
+#else /* not ANSI_DECLARATORS */
+REAL orient3d(m, b, pa, pb, pc, pd, aheight, bheight, cheight, dheight)
+struct mesh *m;
+struct behavior *b;
+vertex pa;
+vertex pb;
+vertex pc;
+vertex pd;
+REAL aheight;
+REAL bheight;
+REAL cheight;
+REAL dheight;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ REAL adx, bdx, cdx, ady, bdy, cdy, adheight, bdheight, cdheight;
+ REAL bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady;
+ REAL det;
+ REAL permanent, errbound;
+
+ m->orient3dcount++;
+
+ adx = pa[0] - pd[0];
+ bdx = pb[0] - pd[0];
+ cdx = pc[0] - pd[0];
+ ady = pa[1] - pd[1];
+ bdy = pb[1] - pd[1];
+ cdy = pc[1] - pd[1];
+ adheight = aheight - dheight;
+ bdheight = bheight - dheight;
+ cdheight = cheight - dheight;
+
+ bdxcdy = bdx * cdy;
+ cdxbdy = cdx * bdy;
+
+ cdxady = cdx * ady;
+ adxcdy = adx * cdy;
+
+ adxbdy = adx * bdy;
+ bdxady = bdx * ady;
+
+ det = adheight * (bdxcdy - cdxbdy)
+ + bdheight * (cdxady - adxcdy)
+ + cdheight * (adxbdy - bdxady);
+
+ if (b->noexact) {
+ return det;
+ }
+
+ permanent = (Absolute(bdxcdy) + Absolute(cdxbdy)) * Absolute(adheight)
+ + (Absolute(cdxady) + Absolute(adxcdy)) * Absolute(bdheight)
+ + (Absolute(adxbdy) + Absolute(bdxady)) * Absolute(cdheight);
+ errbound = o3derrboundA * permanent;
+ if ((det > errbound) || (-det > errbound)) {
+ return det;
+ }
+
+ return orient3dadapt(pa, pb, pc, pd, aheight, bheight, cheight, dheight,
+ permanent);
+}
+
+/*****************************************************************************/
+/* */
+/* nonregular() Return a positive value if the point pd is incompatible */
+/* with the circle or plane passing through pa, pb, and pc */
+/* (meaning that pd is inside the circle or below the */
+/* plane); a negative value if it is compatible; and zero if */
+/* the four points are cocircular/coplanar. The points pa, */
+/* pb, and pc must be in counterclockwise order, or the sign */
+/* of the result will be reversed. */
+/* */
+/* If the -w switch is used, the points are lifted onto the parabolic */
+/* lifting map, then they are dropped according to their weights, then the */
+/* 3D orientation test is applied. If the -W switch is used, the points' */
+/* heights are already provided, so the 3D orientation test is applied */
+/* directly. If neither switch is used, the incircle test is applied. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+REAL nonregular(struct mesh *m, struct behavior *b,
+ vertex pa, vertex pb, vertex pc, vertex pd)
+#else /* not ANSI_DECLARATORS */
+REAL nonregular(m, b, pa, pb, pc, pd)
+struct mesh *m;
+struct behavior *b;
+vertex pa;
+vertex pb;
+vertex pc;
+vertex pd;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ if (b->weighted == 0) {
+ return incircle(m, b, pa, pb, pc, pd);
+ } else if (b->weighted == 1) {
+ return orient3d(m, b, pa, pb, pc, pd,
+ pa[0] * pa[0] + pa[1] * pa[1] - pa[2],
+ pb[0] * pb[0] + pb[1] * pb[1] - pb[2],
+ pc[0] * pc[0] + pc[1] * pc[1] - pc[2],
+ pd[0] * pd[0] + pd[1] * pd[1] - pd[2]);
+ } else {
+ return orient3d(m, b, pa, pb, pc, pd, pa[2], pb[2], pc[2], pd[2]);
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* findcircumcenter() Find the circumcenter of a triangle. */
+/* */
+/* The result is returned both in terms of x-y coordinates and xi-eta */
+/* (barycentric) coordinates. The xi-eta coordinate system is defined in */
+/* terms of the triangle: the origin of the triangle is the origin of the */
+/* coordinate system; the destination of the triangle is one unit along the */
+/* xi axis; and the apex of the triangle is one unit along the eta axis. */
+/* This procedure also returns the square of the length of the triangle's */
+/* shortest edge. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+void findcircumcenter(struct mesh *m, struct behavior *b,
+ vertex torg, vertex tdest, vertex tapex,
+ vertex circumcenter, REAL *xi, REAL *eta, int offcenter)
+#else /* not ANSI_DECLARATORS */
+void findcircumcenter(m, b, torg, tdest, tapex, circumcenter, xi, eta,
+ offcenter)
+struct mesh *m;
+struct behavior *b;
+vertex torg;
+vertex tdest;
+vertex tapex;
+vertex circumcenter;
+REAL *xi;
+REAL *eta;
+int offcenter;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ REAL xdo, ydo, xao, yao;
+ REAL dodist, aodist, dadist;
+ REAL denominator;
+ REAL dx, dy, dxoff, dyoff;
+
+ m->circumcentercount++;
+
+ /* Compute the circumcenter of the triangle. */
+ xdo = tdest[0] - torg[0];
+ ydo = tdest[1] - torg[1];
+ xao = tapex[0] - torg[0];
+ yao = tapex[1] - torg[1];
+ dodist = xdo * xdo + ydo * ydo;
+ aodist = xao * xao + yao * yao;
+ dadist = (tdest[0] - tapex[0]) * (tdest[0] - tapex[0]) +
+ (tdest[1] - tapex[1]) * (tdest[1] - tapex[1]);
+ if (b->noexact) {
+ denominator = 0.5 / (xdo * yao - xao * ydo);
+ } else {
+ /* Use the counterclockwise() routine to ensure a positive (and */
+ /* reasonably accurate) result, avoiding any possibility of */
+ /* division by zero. */
+ denominator = 0.5 / counterclockwise(m, b, tdest, tapex, torg);
+ /* Don't count the above as an orientation test. */
+ m->counterclockcount--;
+ }
+ dx = (yao * dodist - ydo * aodist) * denominator;
+ dy = (xdo * aodist - xao * dodist) * denominator;
+
+ /* Find the (squared) length of the triangle's shortest edge. This */
+ /* serves as a conservative estimate of the insertion radius of the */
+ /* circumcenter's parent. The estimate is used to ensure that */
+ /* the algorithm terminates even if very small angles appear in */
+ /* the input PSLG. */
+ if ((dodist < aodist) && (dodist < dadist)) {
+ if (offcenter && (b->offconstant > 0.0)) {
+ /* Find the position of the off-center, as described by Alper Ungor. */
+ dxoff = 0.5 * xdo - b->offconstant * ydo;
+ dyoff = 0.5 * ydo + b->offconstant * xdo;
+ /* If the off-center is closer to the origin than the */
+ /* circumcenter, use the off-center instead. */
+ if (dxoff * dxoff + dyoff * dyoff < dx * dx + dy * dy) {
+ dx = dxoff;
+ dy = dyoff;
+ }
+ }
+ } else if (aodist < dadist) {
+ if (offcenter && (b->offconstant > 0.0)) {
+ dxoff = 0.5 * xao + b->offconstant * yao;
+ dyoff = 0.5 * yao - b->offconstant * xao;
+ /* If the off-center is closer to the origin than the */
+ /* circumcenter, use the off-center instead. */
+ if (dxoff * dxoff + dyoff * dyoff < dx * dx + dy * dy) {
+ dx = dxoff;
+ dy = dyoff;
+ }
+ }
+ } else {
+ if (offcenter && (b->offconstant > 0.0)) {
+ dxoff = 0.5 * (tapex[0] - tdest[0]) -
+ b->offconstant * (tapex[1] - tdest[1]);
+ dyoff = 0.5 * (tapex[1] - tdest[1]) +
+ b->offconstant * (tapex[0] - tdest[0]);
+ /* If the off-center is closer to the destination than the */
+ /* circumcenter, use the off-center instead. */
+ if (dxoff * dxoff + dyoff * dyoff <
+ (dx - xdo) * (dx - xdo) + (dy - ydo) * (dy - ydo)) {
+ dx = xdo + dxoff;
+ dy = ydo + dyoff;
+ }
+ }
+ }
+
+ circumcenter[0] = torg[0] + dx;
+ circumcenter[1] = torg[1] + dy;
+
+ /* To interpolate vertex attributes for the new vertex inserted at */
+ /* the circumcenter, define a coordinate system with a xi-axis, */
+ /* directed from the triangle's origin to its destination, and */
+ /* an eta-axis, directed from its origin to its apex. */
+ /* Calculate the xi and eta coordinates of the circumcenter. */
+ *xi = (yao * dx - xao * dy) * (2.0 * denominator);
+ *eta = (xdo * dy - ydo * dx) * (2.0 * denominator);
+}
+
+/** **/
+/** **/
+/********* Geometric primitives end here *********/
+
+/*****************************************************************************/
+/* */
+/* triangleinit() Initialize some variables. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+void triangleinit(struct mesh *m)
+#else /* not ANSI_DECLARATORS */
+void triangleinit(m)
+struct mesh *m;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ poolzero(&m->vertices);
+ poolzero(&m->triangles);
+ poolzero(&m->subsegs);
+ poolzero(&m->viri);
+ poolzero(&m->badsubsegs);
+ poolzero(&m->badtriangles);
+ poolzero(&m->flipstackers);
+ poolzero(&m->splaynodes);
+
+ m->recenttri.tri = (triangle *) NULL; /* No triangle has been visited yet. */
+ m->undeads = 0; /* No eliminated input vertices yet. */
+ m->samples = 1; /* Point location should take at least one sample. */
+ m->checksegments = 0; /* There are no segments in the triangulation yet. */
+ m->checkquality = 0; /* The quality triangulation stage has not begun. */
+ m->incirclecount = m->counterclockcount = m->orient3dcount = 0;
+ m->hyperbolacount = m->circletopcount = m->circumcentercount = 0;
+ randomseed = 1;
+
+ exactinit(); /* Initialize exact arithmetic constants. */
+}
+
+/*****************************************************************************/
+/* */
+/* randomnation() Generate a random number between 0 and `choices' - 1. */
+/* */
+/* This is a simple linear congruential random number generator. Hence, it */
+/* is a bad random number generator, but good enough for most randomized */
+/* geometric algorithms. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+unsigned long randomnation(unsigned int choices)
+#else /* not ANSI_DECLARATORS */
+unsigned long randomnation(choices)
+unsigned int choices;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ randomseed = (randomseed * 1366l + 150889l) % 714025l;
+ return randomseed / (714025l / choices + 1);
+}
+
+/********* Mesh quality testing routines begin here *********/
+/** **/
+/** **/
+
+/*****************************************************************************/
+/* */
+/* checkmesh() Test the mesh for topological consistency. */
+/* */
+/*****************************************************************************/
+
+#ifndef REDUCED
+
+#ifdef ANSI_DECLARATORS
+void checkmesh(struct mesh *m, struct behavior *b)
+#else /* not ANSI_DECLARATORS */
+void checkmesh(m, b)
+struct mesh *m;
+struct behavior *b;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ struct otri triangleloop;
+ struct otri oppotri, oppooppotri;
+ vertex triorg, tridest, triapex;
+ vertex oppoorg, oppodest;
+ int horrors;
+ int saveexact;
+ triangle ptr; /* Temporary variable used by sym(). */
+
+ /* Temporarily turn on exact arithmetic if it's off. */
+ saveexact = b->noexact;
+ b->noexact = 0;
+ if (!b->quiet) {
+ printf(" Checking consistency of mesh...\n");
+ }
+ horrors = 0;
+ /* Run through the list of triangles, checking each one. */
+ traversalinit(&m->triangles);
+ triangleloop.tri = triangletraverse(m);
+ while (triangleloop.tri != (triangle *) NULL) {
+ /* Check all three edges of the triangle. */
+ for (triangleloop.orient = 0; triangleloop.orient < 3;
+ triangleloop.orient++) {
+ org(triangleloop, triorg);
+ dest(triangleloop, tridest);
+ if (triangleloop.orient == 0) { /* Only test for inversion once. */
+ /* Test if the triangle is flat or inverted. */
+ apex(triangleloop, triapex);
+ if (counterclockwise(m, b, triorg, tridest, triapex) <= 0.0) {
+ printf(" !! !! Inverted ");
+ printtriangle(m, b, &triangleloop);
+ horrors++;
+ }
+ }
+ /* Find the neighboring triangle on this edge. */
+ sym(triangleloop, oppotri);
+ if (oppotri.tri != m->dummytri) {
+ /* Check that the triangle's neighbor knows it's a neighbor. */
+ sym(oppotri, oppooppotri);
+ if ((triangleloop.tri != oppooppotri.tri)
+ || (triangleloop.orient != oppooppotri.orient)) {
+ printf(" !! !! Asymmetric triangle-triangle bond:\n");
+ if (triangleloop.tri == oppooppotri.tri) {
+ printf(" (Right triangle, wrong orientation)\n");
+ }
+ printf(" First ");
+ printtriangle(m, b, &triangleloop);
+ printf(" Second (nonreciprocating) ");
+ printtriangle(m, b, &oppotri);
+ horrors++;
+ }
+ /* Check that both triangles agree on the identities */
+ /* of their shared vertices. */
+ org(oppotri, oppoorg);
+ dest(oppotri, oppodest);
+ if ((triorg != oppodest) || (tridest != oppoorg)) {
+ printf(" !! !! Mismatched edge coordinates between two triangles:\n"
+ );
+ printf(" First mismatched ");
+ printtriangle(m, b, &triangleloop);
+ printf(" Second mismatched ");
+ printtriangle(m, b, &oppotri);
+ horrors++;
+ }
+ }
+ }
+ triangleloop.tri = triangletraverse(m);
+ }
+ if (horrors == 0) {
+ if (!b->quiet) {
+ printf(" In my studied opinion, the mesh appears to be consistent.\n");
+ }
+ } else if (horrors == 1) {
+ printf(" !! !! !! !! Precisely one festering wound discovered.\n");
+ } else {
+ printf(" !! !! !! !! %d abominations witnessed.\n", horrors);
+ }
+ /* Restore the status of exact arithmetic. */
+ b->noexact = saveexact;
+}
+
+#endif /* not REDUCED */
+
+/*****************************************************************************/
+/* */
+/* checkdelaunay() Ensure that the mesh is (constrained) Delaunay. */
+/* */
+/*****************************************************************************/
+
+#ifndef REDUCED
+
+#ifdef ANSI_DECLARATORS
+void checkdelaunay(struct mesh *m, struct behavior *b)
+#else /* not ANSI_DECLARATORS */
+void checkdelaunay(m, b)
+struct mesh *m;
+struct behavior *b;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ struct otri triangleloop;
+ struct otri oppotri;
+ struct osub opposubseg;
+ vertex triorg, tridest, triapex;
+ vertex oppoapex;
+ int shouldbedelaunay;
+ int horrors;
+ int saveexact;
+ triangle ptr; /* Temporary variable used by sym(). */
+ subseg sptr; /* Temporary variable used by tspivot(). */
+
+ /* Temporarily turn on exact arithmetic if it's off. */
+ saveexact = b->noexact;
+ b->noexact = 0;
+ if (!b->quiet) {
+ printf(" Checking Delaunay property of mesh...\n");
+ }
+ horrors = 0;
+ /* Run through the list of triangles, checking each one. */
+ traversalinit(&m->triangles);
+ triangleloop.tri = triangletraverse(m);
+ while (triangleloop.tri != (triangle *) NULL) {
+ /* Check all three edges of the triangle. */
+ for (triangleloop.orient = 0; triangleloop.orient < 3;
+ triangleloop.orient++) {
+ org(triangleloop, triorg);
+ dest(triangleloop, tridest);
+ apex(triangleloop, triapex);
+ sym(triangleloop, oppotri);
+ apex(oppotri, oppoapex);
+ /* Only test that the edge is locally Delaunay if there is an */
+ /* adjoining triangle whose pointer is larger (to ensure that */
+ /* each pair isn't tested twice). */
+ shouldbedelaunay = (oppotri.tri != m->dummytri) &&
+ !deadtri(oppotri.tri) && (triangleloop.tri < oppotri.tri) &&
+ (triorg != m->infvertex1) && (triorg != m->infvertex2) &&
+ (triorg != m->infvertex3) &&
+ (tridest != m->infvertex1) && (tridest != m->infvertex2) &&
+ (tridest != m->infvertex3) &&
+ (triapex != m->infvertex1) && (triapex != m->infvertex2) &&
+ (triapex != m->infvertex3) &&
+ (oppoapex != m->infvertex1) && (oppoapex != m->infvertex2) &&
+ (oppoapex != m->infvertex3);
+ if (m->checksegments && shouldbedelaunay) {
+ /* If a subsegment separates the triangles, then the edge is */
+ /* constrained, so no local Delaunay test should be done. */
+ tspivot(triangleloop, opposubseg);
+ if (opposubseg.ss != m->dummysub){
+ shouldbedelaunay = 0;
+ }
+ }
+ if (shouldbedelaunay) {
+ if (nonregular(m, b, triorg, tridest, triapex, oppoapex) > 0.0) {
+ if (!b->weighted) {
+ printf(" !! !! Non-Delaunay pair of triangles:\n");
+ printf(" First non-Delaunay ");
+ printtriangle(m, b, &triangleloop);
+ printf(" Second non-Delaunay ");
+ } else {
+ printf(" !! !! Non-regular pair of triangles:\n");
+ printf(" First non-regular ");
+ printtriangle(m, b, &triangleloop);
+ printf(" Second non-regular ");
+ }
+ printtriangle(m, b, &oppotri);
+ horrors++;
+ }
+ }
+ }
+ triangleloop.tri = triangletraverse(m);
+ }
+ if (horrors == 0) {
+ if (!b->quiet) {
+ printf(
+ " By virtue of my perceptive intelligence, I declare the mesh Delaunay.\n");
+ }
+ } else if (horrors == 1) {
+ printf(
+ " !! !! !! !! Precisely one terrifying transgression identified.\n");
+ } else {
+ printf(" !! !! !! !! %d obscenities viewed with horror.\n", horrors);
+ }
+ /* Restore the status of exact arithmetic. */
+ b->noexact = saveexact;
+}
+
+#endif /* not REDUCED */
+
+/*****************************************************************************/
+/* */
+/* enqueuebadtriang() Add a bad triangle data structure to the end of a */
+/* queue. */
+/* */
+/* The queue is actually a set of 4096 queues. I use multiple queues to */
+/* give priority to smaller angles. I originally implemented a heap, but */
+/* the queues are faster by a larger margin than I'd suspected. */
+/* */
+/*****************************************************************************/
+
+#ifndef CDT_ONLY
+
+#ifdef ANSI_DECLARATORS
+void enqueuebadtriang(struct mesh *m, struct behavior *b,
+ struct badtriang *badtri)
+#else /* not ANSI_DECLARATORS */
+void enqueuebadtriang(m, b, badtri)
+struct mesh *m;
+struct behavior *b;
+struct badtriang *badtri;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ REAL length, multiplier;
+ int exponent, expincrement;
+ int queuenumber;
+ int posexponent;
+ int i;
+
+ if (b->verbose > 2) {
+ printf(" Queueing bad triangle:\n");
+ printf(" (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
+ badtri->triangorg[0], badtri->triangorg[1],
+ badtri->triangdest[0], badtri->triangdest[1],
+ badtri->triangapex[0], badtri->triangapex[1]);
+ }
+
+ /* Determine the appropriate queue to put the bad triangle into. */
+ /* Recall that the key is the square of its shortest edge length. */
+ if (badtri->key >= 1.0) {
+ length = badtri->key;
+ posexponent = 1;
+ } else {
+ /* `badtri->key' is 2.0 to a negative exponent, so we'll record that */
+ /* fact and use the reciprocal of `badtri->key', which is > 1.0. */
+ length = 1.0 / badtri->key;
+ posexponent = 0;
+ }
+ /* `length' is approximately 2.0 to what exponent? The following code */
+ /* determines the answer in time logarithmic in the exponent. */
+ exponent = 0;
+ while (length > 2.0) {
+ /* Find an approximation by repeated squaring of two. */
+ expincrement = 1;
+ multiplier = 0.5;
+ while (length * multiplier * multiplier > 1.0) {
+ expincrement *= 2;
+ multiplier *= multiplier;
+ }
+ /* Reduce the value of `length', then iterate if necessary. */
+ exponent += expincrement;
+ length *= multiplier;
+ }
+ /* `length' is approximately squareroot(2.0) to what exponent? */
+ exponent = 2.0 * exponent + (length > SQUAREROOTTWO);
+ /* `exponent' is now in the range 0...2047 for IEEE double precision. */
+ /* Choose a queue in the range 0...4095. The shortest edges have the */
+ /* highest priority (queue 4095). */
+ if (posexponent) {
+ queuenumber = 2047 - exponent;
+ } else {
+ queuenumber = 2048 + exponent;
+ }
+
+ /* Are we inserting into an empty queue? */
+ if (m->queuefront[queuenumber] == (struct badtriang *) NULL) {
+ /* Yes, we are inserting into an empty queue. */
+ /* Will this become the highest-priority queue? */
+ if (queuenumber > m->firstnonemptyq) {
+ /* Yes, this is the highest-priority queue. */
+ m->nextnonemptyq[queuenumber] = m->firstnonemptyq;
+ m->firstnonemptyq = queuenumber;
+ } else {
+ /* No, this is not the highest-priority queue. */
+ /* Find the queue with next higher priority. */
+ i = queuenumber + 1;
+ while (m->queuefront[i] == (struct badtriang *) NULL) {
+ i++;
+ }
+ /* Mark the newly nonempty queue as following a higher-priority queue. */
+ m->nextnonemptyq[queuenumber] = m->nextnonemptyq[i];
+ m->nextnonemptyq[i] = queuenumber;
+ }
+ /* Put the bad triangle at the beginning of the (empty) queue. */
+ m->queuefront[queuenumber] = badtri;
+ } else {
+ /* Add the bad triangle to the end of an already nonempty queue. */
+ m->queuetail[queuenumber]->nexttriang = badtri;
+ }
+ /* Maintain a pointer to the last triangle of the queue. */
+ m->queuetail[queuenumber] = badtri;
+ /* Newly enqueued bad triangle has no successor in the queue. */
+ badtri->nexttriang = (struct badtriang *) NULL;
+}
+
+#endif /* not CDT_ONLY */
+
+/*****************************************************************************/
+/* */
+/* enqueuebadtri() Add a bad triangle to the end of a queue. */
+/* */
+/* Allocates a badtriang data structure for the triangle, then passes it to */
+/* enqueuebadtriang(). */
+/* */
+/*****************************************************************************/
+
+#ifndef CDT_ONLY
+
+#ifdef ANSI_DECLARATORS
+void enqueuebadtri(struct mesh *m, struct behavior *b, struct otri *enqtri,
+ REAL minedge, vertex enqapex, vertex enqorg, vertex enqdest)
+#else /* not ANSI_DECLARATORS */
+void enqueuebadtri(m, b, enqtri, minedge, enqapex, enqorg, enqdest)
+struct mesh *m;
+struct behavior *b;
+struct otri *enqtri;
+REAL minedge;
+vertex enqapex;
+vertex enqorg;
+vertex enqdest;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ struct badtriang *newbad;
+
+ /* Allocate space for the bad triangle. */
+ newbad = (struct badtriang *) poolalloc(&m->badtriangles);
+ newbad->poortri = encode(*enqtri);
+ newbad->key = minedge;
+ newbad->triangapex = enqapex;
+ newbad->triangorg = enqorg;
+ newbad->triangdest = enqdest;
+ enqueuebadtriang(m, b, newbad);
+}
+
+#endif /* not CDT_ONLY */
+
+/*****************************************************************************/
+/* */
+/* dequeuebadtriang() Remove a triangle from the front of the queue. */
+/* */
+/*****************************************************************************/
+
+#ifndef CDT_ONLY
+
+#ifdef ANSI_DECLARATORS
+struct badtriang *dequeuebadtriang(struct mesh *m)
+#else /* not ANSI_DECLARATORS */
+struct badtriang *dequeuebadtriang(m)
+struct mesh *m;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ struct badtriang *result;
+
+ /* If no queues are nonempty, return NULL. */
+ if (m->firstnonemptyq < 0) {
+ return (struct badtriang *) NULL;
+ }
+ /* Find the first triangle of the highest-priority queue. */
+ result = m->queuefront[m->firstnonemptyq];
+ /* Remove the triangle from the queue. */
+ m->queuefront[m->firstnonemptyq] = result->nexttriang;
+ /* If this queue is now empty, note the new highest-priority */
+ /* nonempty queue. */
+ if (result == m->queuetail[m->firstnonemptyq]) {
+ m->firstnonemptyq = m->nextnonemptyq[m->firstnonemptyq];
+ }
+ return result;
+}
+
+#endif /* not CDT_ONLY */
+
+/*****************************************************************************/
+/* */
+/* checkseg4encroach() Check a subsegment to see if it is encroached; add */
+/* it to the list if it is. */
+/* */
+/* A subsegment is encroached if there is a vertex in its diametral lens. */
+/* For Ruppert's algorithm (-D switch), the "diametral lens" is the */
+/* diametral circle. For Chew's algorithm (default), the diametral lens is */
+/* just big enough to enclose two isosceles triangles whose bases are the */
+/* subsegment. Each of the two isosceles triangles has two angles equal */
+/* to `b->minangle'. */
+/* */
+/* Chew's algorithm does not require diametral lenses at all--but they save */
+/* time. Any vertex inside a subsegment's diametral lens implies that the */
+/* triangle adjoining the subsegment will be too skinny, so it's only a */
+/* matter of time before the encroaching vertex is deleted by Chew's */
+/* algorithm. It's faster to simply not insert the doomed vertex in the */
+/* first place, which is why I use diametral lenses with Chew's algorithm. */
+/* */
+/* Returns a nonzero value if the subsegment is encroached. */
+/* */
+/*****************************************************************************/
+
+#ifndef CDT_ONLY
+
+#ifdef ANSI_DECLARATORS
+int checkseg4encroach(struct mesh *m, struct behavior *b,
+ struct osub *testsubseg)
+#else /* not ANSI_DECLARATORS */
+int checkseg4encroach(m, b, testsubseg)
+struct mesh *m;
+struct behavior *b;
+struct osub *testsubseg;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ struct otri neighbortri;
+ struct osub testsym;
+ struct badsubseg *encroachedseg;
+ REAL dotproduct;
+ int encroached;
+ int sides;
+ vertex eorg, edest, eapex;
+ triangle ptr; /* Temporary variable used by stpivot(). */
+
+ encroached = 0;
+ sides = 0;
+
+ sorg(*testsubseg, eorg);
+ sdest(*testsubseg, edest);
+ /* Check one neighbor of the subsegment. */
+ stpivot(*testsubseg, neighbortri);
+ /* Does the neighbor exist, or is this a boundary edge? */
+ if (neighbortri.tri != m->dummytri) {
+ sides++;
+ /* Find a vertex opposite this subsegment. */
+ apex(neighbortri, eapex);
+ /* Check whether the apex is in the diametral lens of the subsegment */
+ /* (the diametral circle if `conformdel' is set). A dot product */
+ /* of two sides of the triangle is used to check whether the angle */
+ /* at the apex is greater than (180 - 2 `minangle') degrees (for */
+ /* lenses; 90 degrees for diametral circles). */
+ dotproduct = (eorg[0] - eapex[0]) * (edest[0] - eapex[0]) +
+ (eorg[1] - eapex[1]) * (edest[1] - eapex[1]);
+ if (dotproduct < 0.0) {
+ if (b->conformdel ||
+ (dotproduct * dotproduct >=
+ (2.0 * b->goodangle - 1.0) * (2.0 * b->goodangle - 1.0) *
+ ((eorg[0] - eapex[0]) * (eorg[0] - eapex[0]) +
+ (eorg[1] - eapex[1]) * (eorg[1] - eapex[1])) *
+ ((edest[0] - eapex[0]) * (edest[0] - eapex[0]) +
+ (edest[1] - eapex[1]) * (edest[1] - eapex[1])))) {
+ encroached = 1;
+ }
+ }
+ }
+ /* Check the other neighbor of the subsegment. */
+ ssym(*testsubseg, testsym);
+ stpivot(testsym, neighbortri);
+ /* Does the neighbor exist, or is this a boundary edge? */
+ if (neighbortri.tri != m->dummytri) {
+ sides++;
+ /* Find the other vertex opposite this subsegment. */
+ apex(neighbortri, eapex);
+ /* Check whether the apex is in the diametral lens of the subsegment */
+ /* (or the diametral circle, if `conformdel' is set). */
+ dotproduct = (eorg[0] - eapex[0]) * (edest[0] - eapex[0]) +
+ (eorg[1] - eapex[1]) * (edest[1] - eapex[1]);
+ if (dotproduct < 0.0) {
+ if (b->conformdel ||
+ (dotproduct * dotproduct >=
+ (2.0 * b->goodangle - 1.0) * (2.0 * b->goodangle - 1.0) *
+ ((eorg[0] - eapex[0]) * (eorg[0] - eapex[0]) +
+ (eorg[1] - eapex[1]) * (eorg[1] - eapex[1])) *
+ ((edest[0] - eapex[0]) * (edest[0] - eapex[0]) +
+ (edest[1] - eapex[1]) * (edest[1] - eapex[1])))) {
+ encroached += 2;
+ }
+ }
+ }
+
+ if (encroached && (!b->nobisect || ((b->nobisect == 1) && (sides == 2)))) {
+ if (b->verbose > 2) {
+ printf(
+ " Queueing encroached subsegment (%.12g, %.12g) (%.12g, %.12g).\n",
+ eorg[0], eorg[1], edest[0], edest[1]);
+ }
+ /* Add the subsegment to the list of encroached subsegments. */
+ /* Be sure to get the orientation right. */
+ encroachedseg = (struct badsubseg *) poolalloc(&m->badsubsegs);
+ if (encroached == 1) {
+ encroachedseg->encsubseg = sencode(*testsubseg);
+ encroachedseg->subsegorg = eorg;
+ encroachedseg->subsegdest = edest;
+ } else {
+ encroachedseg->encsubseg = sencode(testsym);
+ encroachedseg->subsegorg = edest;
+ encroachedseg->subsegdest = eorg;
+ }
+ }
+
+ return encroached;
+}
+
+#endif /* not CDT_ONLY */
+
+/*****************************************************************************/
+/* */
+/* testtriangle() Test a triangle for quality and size. */
+/* */
+/* Tests a triangle to see if it satisfies the minimum angle condition and */
+/* the maximum area condition. Triangles that aren't up to spec are added */
+/* to the bad triangle queue. */
+/* */
+/*****************************************************************************/
+
+#ifndef CDT_ONLY
+
+#ifdef ANSI_DECLARATORS
+void testtriangle(struct mesh *m, struct behavior *b, struct otri *testtri)
+#else /* not ANSI_DECLARATORS */
+void testtriangle(m, b, testtri)
+struct mesh *m;
+struct behavior *b;
+struct otri *testtri;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ struct otri tri1, tri2;
+ struct osub testsub;
+ vertex torg, tdest, tapex;
+ vertex base1, base2;
+ vertex org1, dest1, org2, dest2;
+ vertex joinvertex;
+ REAL dxod, dyod, dxda, dyda, dxao, dyao;
+ REAL dxod2, dyod2, dxda2, dyda2, dxao2, dyao2;
+ REAL apexlen, orglen, destlen, minedge;
+ REAL angle;
+ REAL area;
+ REAL dist1, dist2;
+ subseg sptr; /* Temporary variable used by tspivot(). */
+ triangle ptr; /* Temporary variable used by oprev() and dnext(). */
+
+ org(*testtri, torg);
+ dest(*testtri, tdest);
+ apex(*testtri, tapex);
+ dxod = torg[0] - tdest[0];
+ dyod = torg[1] - tdest[1];
+ dxda = tdest[0] - tapex[0];
+ dyda = tdest[1] - tapex[1];
+ dxao = tapex[0] - torg[0];
+ dyao = tapex[1] - torg[1];
+ dxod2 = dxod * dxod;
+ dyod2 = dyod * dyod;
+ dxda2 = dxda * dxda;
+ dyda2 = dyda * dyda;
+ dxao2 = dxao * dxao;
+ dyao2 = dyao * dyao;
+ /* Find the lengths of the triangle's three edges. */
+ apexlen = dxod2 + dyod2;
+ orglen = dxda2 + dyda2;
+ destlen = dxao2 + dyao2;
+
+ if ((apexlen < orglen) && (apexlen < destlen)) {
+ /* The edge opposite the apex is shortest. */
+ minedge = apexlen;
+ /* Find the square of the cosine of the angle at the apex. */
+ angle = dxda * dxao + dyda * dyao;
+ angle = angle * angle / (orglen * destlen);
+ base1 = torg;
+ base2 = tdest;
+ otricopy(*testtri, tri1);
+ } else if (orglen < destlen) {
+ /* The edge opposite the origin is shortest. */
+ minedge = orglen;
+ /* Find the square of the cosine of the angle at the origin. */
+ angle = dxod * dxao + dyod * dyao;
+ angle = angle * angle / (apexlen * destlen);
+ base1 = tdest;
+ base2 = tapex;
+ lnext(*testtri, tri1);
+ } else {
+ /* The edge opposite the destination is shortest. */
+ minedge = destlen;
+ /* Find the square of the cosine of the angle at the destination. */
+ angle = dxod * dxda + dyod * dyda;
+ angle = angle * angle / (apexlen * orglen);
+ base1 = tapex;
+ base2 = torg;
+ lprev(*testtri, tri1);
+ }
+
+ if (b->vararea || b->fixedarea || b->usertest) {
+ /* Check whether the area is larger than permitted. */
+ area = 0.5 * (dxod * dyda - dyod * dxda);
+ if (b->fixedarea && (area > b->maxarea)) {
+ /* Add this triangle to the list of bad triangles. */
+ enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest);
+ return;
+ }
+
+ /* Nonpositive area constraints are treated as unconstrained. */
+ if ((b->vararea) && (area > areabound(*testtri)) &&
+ (areabound(*testtri) > 0.0)) {
+ /* Add this triangle to the list of bad triangles. */
+ enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest);
+ return;
+ }
+
+ if (b->usertest) {
+ /* Check whether the user thinks this triangle is too large. */
+ if (triunsuitable(torg, tdest, tapex, area)) {
+ enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest);
+ return;
+ }
+ }
+ }
+
+ /* Check whether the angle is smaller than permitted. */
+ if (angle > b->goodangle) {
+ /* Use the rules of Miller, Pav, and Walkington to decide that certain */
+ /* triangles should not be split, even if they have bad angles. */
+ /* A skinny triangle is not split if its shortest edge subtends a */
+ /* small input angle, and both endpoints of the edge lie on a */
+ /* concentric circular shell. For convenience, I make a small */
+ /* adjustment to that rule: I check if the endpoints of the edge */
+ /* both lie in segment interiors, equidistant from the apex where */
+ /* the two segments meet. */
+ /* First, check if both points lie in segment interiors. */
+ if ((vertextype(base1) == SEGMENTVERTEX) &&
+ (vertextype(base2) == SEGMENTVERTEX)) {
+ /* Check if both points lie in a common segment. If they do, the */
+ /* skinny triangle is enqueued to be split as usual. */
+ tspivot(tri1, testsub);
+ if (testsub.ss == m->dummysub) {
+ /* No common segment. Find a subsegment that contains `torg'. */
+ otricopy(tri1, tri2);
+ do {
+ oprevself(tri1);
+ tspivot(tri1, testsub);
+ } while (testsub.ss == m->dummysub);
+ /* Find the endpoints of the containing segment. */
+ segorg(testsub, org1);
+ segdest(testsub, dest1);
+ /* Find a subsegment that contains `tdest'. */
+ do {
+ dnextself(tri2);
+ tspivot(tri2, testsub);
+ } while (testsub.ss == m->dummysub);
+ /* Find the endpoints of the containing segment. */
+ segorg(testsub, org2);
+ segdest(testsub, dest2);
+ /* Check if the two containing segments have an endpoint in common. */
+ joinvertex = (vertex) NULL;
+ if ((dest1[0] == org2[0]) && (dest1[1] == org2[1])) {
+ joinvertex = dest1;
+ } else if ((org1[0] == dest2[0]) && (org1[1] == dest2[1])) {
+ joinvertex = org1;
+ }
+ if (joinvertex != (vertex) NULL) {
+ /* Compute the distance from the common endpoint (of the two */
+ /* segments) to each of the endpoints of the shortest edge. */
+ dist1 = ((base1[0] - joinvertex[0]) * (base1[0] - joinvertex[0]) +
+ (base1[1] - joinvertex[1]) * (base1[1] - joinvertex[1]));
+ dist2 = ((base2[0] - joinvertex[0]) * (base2[0] - joinvertex[0]) +
+ (base2[1] - joinvertex[1]) * (base2[1] - joinvertex[1]));
+ /* If the two distances are equal, don't split the triangle. */
+ if ((dist1 < 1.001 * dist2) && (dist1 > 0.999 * dist2)) {
+ /* Return now to avoid enqueueing the bad triangle. */
+ return;
+ }
+ }
+ }
+ }
+
+ /* Add this triangle to the list of bad triangles. */
+ enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest);
+ }
+}
+
+#endif /* not CDT_ONLY */
+
+/** **/
+/** **/
+/********* Mesh quality testing routines end here *********/
+
+/********* Point location routines begin here *********/
+/** **/
+/** **/
+
+/*****************************************************************************/
+/* */
+/* makevertexmap() Construct a mapping from vertices to triangles to */
+/* improve the speed of point location for segment */
+/* insertion. */
+/* */
+/* Traverses all the triangles, and provides each corner of each triangle */
+/* with a pointer to that triangle. Of course, pointers will be */
+/* overwritten by other pointers because (almost) each vertex is a corner */
+/* of several triangles, but in the end every vertex will point to some */
+/* triangle that contains it. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+void makevertexmap(struct mesh *m, struct behavior *b)
+#else /* not ANSI_DECLARATORS */
+void makevertexmap(m, b)
+struct mesh *m;
+struct behavior *b;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ struct otri triangleloop;
+ vertex triorg;
+
+ if (b->verbose) {
+ printf(" Constructing mapping from vertices to triangles.\n");
+ }
+ traversalinit(&m->triangles);
+ triangleloop.tri = triangletraverse(m);
+ while (triangleloop.tri != (triangle *) NULL) {
+ /* Check all three vertices of the triangle. */
+ for (triangleloop.orient = 0; triangleloop.orient < 3;
+ triangleloop.orient++) {
+ org(triangleloop, triorg);
+ setvertex2tri(triorg, encode(triangleloop));
+ }
+ triangleloop.tri = triangletraverse(m);
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* preciselocate() Find a triangle or edge containing a given point. */
+/* */
+/* Begins its search from `searchtri'. It is important that `searchtri' */
+/* be a handle with the property that `searchpoint' is strictly to the left */
+/* of the edge denoted by `searchtri', or is collinear with that edge and */
+/* does not intersect that edge. (In particular, `searchpoint' should not */
+/* be the origin or destination of that edge.) */
+/* */
+/* These conditions are imposed because preciselocate() is normally used in */
+/* one of two situations: */
+/* */
+/* (1) To try to find the location to insert a new point. Normally, we */
+/* know an edge that the point is strictly to the left of. In the */
+/* incremental Delaunay algorithm, that edge is a bounding box edge. */
+/* In Ruppert's Delaunay refinement algorithm for quality meshing, */
+/* that edge is the shortest edge of the triangle whose circumcenter */
+/* is being inserted. */
+/* */
+/* (2) To try to find an existing point. In this case, any edge on the */
+/* convex hull is a good starting edge. You must screen out the */
+/* possibility that the vertex sought is an endpoint of the starting */
+/* edge before you call preciselocate(). */
+/* */
+/* On completion, `searchtri' is a triangle that contains `searchpoint'. */
+/* */
+/* This implementation differs from that given by Guibas and Stolfi. It */
+/* walks from triangle to triangle, crossing an edge only if `searchpoint' */
+/* is on the other side of the line containing that edge. After entering */
+/* a triangle, there are two edges by which one can leave that triangle. */
+/* If both edges are valid (`searchpoint' is on the other side of both */
+/* edges), one of the two is chosen by drawing a line perpendicular to */
+/* the entry edge (whose endpoints are `forg' and `fdest') passing through */
+/* `fapex'. Depending on which side of this perpendicular `searchpoint' */
+/* falls on, an exit edge is chosen. */
+/* */
+/* This implementation is empirically faster than the Guibas and Stolfi */
+/* point location routine (which I originally used), which tends to spiral */
+/* in toward its target. */
+/* */
+/* Returns ONVERTEX if the point lies on an existing vertex. `searchtri' */
+/* is a handle whose origin is the existing vertex. */
+/* */
+/* Returns ONEDGE if the point lies on a mesh edge. `searchtri' is a */
+/* handle whose primary edge is the edge on which the point lies. */
+/* */
+/* Returns INTRIANGLE if the point lies strictly within a triangle. */
+/* `searchtri' is a handle on the triangle that contains the point. */
+/* */
+/* Returns OUTSIDE if the point lies outside the mesh. `searchtri' is a */
+/* handle whose primary edge the point is to the right of. This might */
+/* occur when the circumcenter of a triangle falls just slightly outside */
+/* the mesh due to floating-point roundoff error. It also occurs when */
+/* seeking a hole or region point that a foolish user has placed outside */
+/* the mesh. */
+/* */
+/* If `stopatsubsegment' is nonzero, the search will stop if it tries to */
+/* walk through a subsegment, and will return OUTSIDE. */
+/* */
+/* WARNING: This routine is designed for convex triangulations, and will */
+/* not generally work after the holes and concavities have been carved. */
+/* However, it can still be used to find the circumcenter of a triangle, as */
+/* long as the search is begun from the triangle in question. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+enum locateresult preciselocate(struct mesh *m, struct behavior *b,
+ vertex searchpoint, struct otri *searchtri,
+ int stopatsubsegment)
+#else /* not ANSI_DECLARATORS */
+enum locateresult preciselocate(m, b, searchpoint, searchtri, stopatsubsegment)
+struct mesh *m;
+struct behavior *b;
+vertex searchpoint;
+struct otri *searchtri;
+int stopatsubsegment;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ struct otri backtracktri;
+ struct osub checkedge;
+ vertex forg, fdest, fapex;
+ REAL orgorient, destorient;
+ int moveleft;
+ triangle ptr; /* Temporary variable used by sym(). */
+ subseg sptr; /* Temporary variable used by tspivot(). */
+
+ if (b->verbose > 2) {
+ printf(" Searching for point (%.12g, %.12g).\n",
+ searchpoint[0], searchpoint[1]);
+ }
+ /* Where are we? */
+ org(*searchtri, forg);
+ dest(*searchtri, fdest);
+ apex(*searchtri, fapex);
+ while (1) {
+ if (b->verbose > 2) {
+ printf(" At (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
+ forg[0], forg[1], fdest[0], fdest[1], fapex[0], fapex[1]);
+ }
+ /* Check whether the apex is the point we seek. */
+ if ((fapex[0] == searchpoint[0]) && (fapex[1] == searchpoint[1])) {
+ lprevself(*searchtri);
+ return ONVERTEX;
+ }
+ /* Does the point lie on the other side of the line defined by the */
+ /* triangle edge opposite the triangle's destination? */
+ destorient = counterclockwise(m, b, forg, fapex, searchpoint);
+ /* Does the point lie on the other side of the line defined by the */
+ /* triangle edge opposite the triangle's origin? */
+ orgorient = counterclockwise(m, b, fapex, fdest, searchpoint);
+ if (destorient > 0.0) {
+ if (orgorient > 0.0) {
+ /* Move left if the inner product of (fapex - searchpoint) and */
+ /* (fdest - forg) is positive. This is equivalent to drawing */
+ /* a line perpendicular to the line (forg, fdest) and passing */
+ /* through `fapex', and determining which side of this line */
+ /* `searchpoint' falls on. */
+ moveleft = (fapex[0] - searchpoint[0]) * (fdest[0] - forg[0]) +
+ (fapex[1] - searchpoint[1]) * (fdest[1] - forg[1]) > 0.0;
+ } else {
+ moveleft = 1;
+ }
+ } else {
+ if (orgorient > 0.0) {
+ moveleft = 0;
+ } else {
+ /* The point we seek must be on the boundary of or inside this */
+ /* triangle. */
+ if (destorient == 0.0) {
+ lprevself(*searchtri);
+ return ONEDGE;
+ }
+ if (orgorient == 0.0) {
+ lnextself(*searchtri);
+ return ONEDGE;
+ }
+ return INTRIANGLE;
+ }
+ }
+
+ /* Move to another triangle. Leave a trace `backtracktri' in case */
+ /* floating-point roundoff or some such bogey causes us to walk */
+ /* off a boundary of the triangulation. */
+ if (moveleft) {
+ lprev(*searchtri, backtracktri);
+ fdest = fapex;
+ } else {
+ lnext(*searchtri, backtracktri);
+ forg = fapex;
+ }
+ sym(backtracktri, *searchtri);
+
+ if (m->checksegments && stopatsubsegment) {
+ /* Check for walking through a subsegment. */
+ tspivot(backtracktri, checkedge);
+ if (checkedge.ss != m->dummysub) {
+ /* Go back to the last triangle. */
+ otricopy(backtracktri, *searchtri);
+ return OUTSIDE;
+ }
+ }
+ /* Check for walking right out of the triangulation. */
+ if (searchtri->tri == m->dummytri) {
+ /* Go back to the last triangle. */
+ otricopy(backtracktri, *searchtri);
+ return OUTSIDE;
+ }
+
+ apex(*searchtri, fapex);
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* locate() Find a triangle or edge containing a given point. */
+/* */
+/* Searching begins from one of: the input `searchtri', a recently */
+/* encountered triangle `recenttri', or from a triangle chosen from a */
+/* random sample. The choice is made by determining which triangle's */
+/* origin is closest to the point we are searching for. Normally, */
+/* `searchtri' should be a handle on the convex hull of the triangulation. */
+/* */
+/* Details on the random sampling method can be found in the Mucke, Saias, */
+/* and Zhu paper cited in the header of this code. */
+/* */
+/* On completion, `searchtri' is a triangle that contains `searchpoint'. */
+/* */
+/* Returns ONVERTEX if the point lies on an existing vertex. `searchtri' */
+/* is a handle whose origin is the existing vertex. */
+/* */
+/* Returns ONEDGE if the point lies on a mesh edge. `searchtri' is a */
+/* handle whose primary edge is the edge on which the point lies. */
+/* */
+/* Returns INTRIANGLE if the point lies strictly within a triangle. */
+/* `searchtri' is a handle on the triangle that contains the point. */
+/* */
+/* Returns OUTSIDE if the point lies outside the mesh. `searchtri' is a */
+/* handle whose primary edge the point is to the right of. This might */
+/* occur when the circumcenter of a triangle falls just slightly outside */
+/* the mesh due to floating-point roundoff error. It also occurs when */
+/* seeking a hole or region point that a foolish user has placed outside */
+/* the mesh. */
+/* */
+/* WARNING: This routine is designed for convex triangulations, and will */
+/* not generally work after the holes and concavities have been carved. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+enum locateresult locate(struct mesh *m, struct behavior *b,
+ vertex searchpoint, struct otri *searchtri)
+#else /* not ANSI_DECLARATORS */
+enum locateresult locate(m, b, searchpoint, searchtri)
+struct mesh *m;
+struct behavior *b;
+vertex searchpoint;
+struct otri *searchtri;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ VOID **sampleblock;
+ char *firsttri;
+ struct otri sampletri;
+ vertex torg, tdest;
+ unsigned long alignptr;
+ REAL searchdist, dist;
+ REAL ahead;
+ long samplesperblock, totalsamplesleft, samplesleft;
+ long population, totalpopulation;
+ triangle ptr; /* Temporary variable used by sym(). */
+
+ if (b->verbose > 2) {
+ printf(" Randomly sampling for a triangle near point (%.12g, %.12g).\n",
+ searchpoint[0], searchpoint[1]);
+ }
+ /* Record the distance from the suggested starting triangle to the */
+ /* point we seek. */
+ org(*searchtri, torg);
+ searchdist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) +
+ (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]);
+ if (b->verbose > 2) {
+ printf(" Boundary triangle has origin (%.12g, %.12g).\n",
+ torg[0], torg[1]);
+ }
+
+ /* If a recently encountered triangle has been recorded and has not been */
+ /* deallocated, test it as a good starting point. */
+ if (m->recenttri.tri != (triangle *) NULL) {
+ if (!deadtri(m->recenttri.tri)) {
+ org(m->recenttri, torg);
+ if ((torg[0] == searchpoint[0]) && (torg[1] == searchpoint[1])) {
+ otricopy(m->recenttri, *searchtri);
+ return ONVERTEX;
+ }
+ dist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) +
+ (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]);
+ if (dist < searchdist) {
+ otricopy(m->recenttri, *searchtri);
+ searchdist = dist;
+ if (b->verbose > 2) {
+ printf(" Choosing recent triangle with origin (%.12g, %.12g).\n",
+ torg[0], torg[1]);
+ }
+ }
+ }
+ }
+
+ /* The number of random samples taken is proportional to the cube root of */
+ /* the number of triangles in the mesh. The next bit of code assumes */
+ /* that the number of triangles increases monotonically (or at least */
+ /* doesn't decrease enough to matter). */
+ while (SAMPLEFACTOR * m->samples * m->samples * m->samples <
+ m->triangles.items) {
+ m->samples++;
+ }
+
+ /* We'll draw ceiling(samples * TRIPERBLOCK / maxitems) random samples */
+ /* from each block of triangles (except the first)--until we meet the */
+ /* sample quota. The ceiling means that blocks at the end might be */
+ /* neglected, but I don't care. */
+ samplesperblock = (m->samples * TRIPERBLOCK - 1) / m->triangles.maxitems + 1;
+ /* We'll draw ceiling(samples * itemsfirstblock / maxitems) random samples */
+ /* from the first block of triangles. */
+ samplesleft = (m->samples * m->triangles.itemsfirstblock - 1) /
+ m->triangles.maxitems + 1;
+ totalsamplesleft = m->samples;
+ population = m->triangles.itemsfirstblock;
+ totalpopulation = m->triangles.maxitems;
+ sampleblock = m->triangles.firstblock;
+ sampletri.orient = 0;
+ while (totalsamplesleft > 0) {
+ /* If we're in the last block, `population' needs to be corrected. */
+ if (population > totalpopulation) {
+ population = totalpopulation;
+ }
+ /* Find a pointer to the first triangle in the block. */
+ alignptr = (unsigned long) (sampleblock + 1);
+ firsttri = (char *) (alignptr +
+ (unsigned long) m->triangles.alignbytes -
+ (alignptr %
+ (unsigned long) m->triangles.alignbytes));
+
+ /* Choose `samplesleft' randomly sampled triangles in this block. */
+ do {
+ sampletri.tri = (triangle *) (firsttri +
+ (randomnation((unsigned int) population) *
+ m->triangles.itembytes));
+ if (!deadtri(sampletri.tri)) {
+ org(sampletri, torg);
+ dist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) +
+ (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]);
+ if (dist < searchdist) {
+ otricopy(sampletri, *searchtri);
+ searchdist = dist;
+ if (b->verbose > 2) {
+ printf(" Choosing triangle with origin (%.12g, %.12g).\n",
+ torg[0], torg[1]);
+ }
+ }
+ }
+
+ samplesleft--;
+ totalsamplesleft--;
+ } while ((samplesleft > 0) && (totalsamplesleft > 0));
+
+ if (totalsamplesleft > 0) {
+ sampleblock = (VOID **) *sampleblock;
+ samplesleft = samplesperblock;
+ totalpopulation -= population;
+ population = TRIPERBLOCK;
+ }
+ }
+
+ /* Where are we? */
+ org(*searchtri, torg);
+ dest(*searchtri, tdest);
+ /* Check the starting triangle's vertices. */
+ if ((torg[0] == searchpoint[0]) && (torg[1] == searchpoint[1])) {
+ return ONVERTEX;
+ }
+ if ((tdest[0] == searchpoint[0]) && (tdest[1] == searchpoint[1])) {
+ lnextself(*searchtri);
+ return ONVERTEX;
+ }
+ /* Orient `searchtri' to fit the preconditions of calling preciselocate(). */
+ ahead = counterclockwise(m, b, torg, tdest, searchpoint);
+ if (ahead < 0.0) {
+ /* Turn around so that `searchpoint' is to the left of the */
+ /* edge specified by `searchtri'. */
+ symself(*searchtri);
+ } else if (ahead == 0.0) {
+ /* Check if `searchpoint' is between `torg' and `tdest'. */
+ if (((torg[0] < searchpoint[0]) == (searchpoint[0] < tdest[0])) &&
+ ((torg[1] < searchpoint[1]) == (searchpoint[1] < tdest[1]))) {
+ return ONEDGE;
+ }
+ }
+ return preciselocate(m, b, searchpoint, searchtri, 0);
+}
+
+/** **/
+/** **/
+/********* Point location routines end here *********/
+
+/********* Mesh transformation routines begin here *********/
+/** **/
+/** **/
+
+/*****************************************************************************/
+/* */
+/* insertsubseg() Create a new subsegment and insert it between two */
+/* triangles. */
+/* */
+/* The new subsegment is inserted at the edge described by the handle */
+/* `tri'. Its vertices are properly initialized. The marker `subsegmark' */
+/* is applied to the subsegment and, if appropriate, its vertices. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+void insertsubseg(struct mesh *m, struct behavior *b, struct otri *tri,
+ int subsegmark)
+#else /* not ANSI_DECLARATORS */
+void insertsubseg(m, b, tri, subsegmark)
+struct mesh *m;
+struct behavior *b;
+struct otri *tri; /* Edge at which to insert the new subsegment. */
+int subsegmark; /* Marker for the new subsegment. */
+#endif /* not ANSI_DECLARATORS */
+
+{
+ struct otri oppotri;
+ struct osub newsubseg;
+ vertex triorg, tridest;
+ triangle ptr; /* Temporary variable used by sym(). */
+ subseg sptr; /* Temporary variable used by tspivot(). */
+
+ org(*tri, triorg);
+ dest(*tri, tridest);
+ /* Mark vertices if possible. */
+ if (vertexmark(triorg) == 0) {
+ setvertexmark(triorg, subsegmark);
+ }
+ if (vertexmark(tridest) == 0) {
+ setvertexmark(tridest, subsegmark);
+ }
+ /* Check if there's already a subsegment here. */
+ tspivot(*tri, newsubseg);
+ if (newsubseg.ss == m->dummysub) {
+ /* Make new subsegment and initialize its vertices. */
+ makesubseg(m, &newsubseg);
+ setsorg(newsubseg, tridest);
+ setsdest(newsubseg, triorg);
+ setsegorg(newsubseg, tridest);
+ setsegdest(newsubseg, triorg);
+ /* Bond new subsegment to the two triangles it is sandwiched between. */
+ /* Note that the facing triangle `oppotri' might be equal to */
+ /* `dummytri' (outer space), but the new subsegment is bonded to it */
+ /* all the same. */
+ tsbond(*tri, newsubseg);
+ sym(*tri, oppotri);
+ ssymself(newsubseg);
+ tsbond(oppotri, newsubseg);
+ setmark(newsubseg, subsegmark);
+ if (b->verbose > 2) {
+ printf(" Inserting new ");
+ printsubseg(m, b, &newsubseg);
+ }
+ } else {
+ if (mark(newsubseg) == 0) {
+ setmark(newsubseg, subsegmark);
+ }
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* Terminology */
+/* */
+/* A "local transformation" replaces a small set of triangles with another */
+/* set of triangles. This may or may not involve inserting or deleting a */
+/* vertex. */
+/* */
+/* The term "casing" is used to describe the set of triangles that are */
+/* attached to the triangles being transformed, but are not transformed */
+/* themselves. Think of the casing as a fixed hollow structure inside */
+/* which all the action happens. A "casing" is only defined relative to */
+/* a single transformation; each occurrence of a transformation will */
+/* involve a different casing. */
+/* */
+/*****************************************************************************/
+
+/*****************************************************************************/
+/* */
+/* flip() Transform two triangles to two different triangles by flipping */
+/* an edge counterclockwise within a quadrilateral. */
+/* */
+/* Imagine the original triangles, abc and bad, oriented so that the */
+/* shared edge ab lies in a horizontal plane, with the vertex b on the left */
+/* and the vertex a on the right. The vertex c lies below the edge, and */
+/* the vertex d lies above the edge. The `flipedge' handle holds the edge */
+/* ab of triangle abc, and is directed left, from vertex a to vertex b. */
+/* */
+/* The triangles abc and bad are deleted and replaced by the triangles cdb */
+/* and dca. The triangles that represent abc and bad are NOT deallocated; */
+/* they are reused for dca and cdb, respectively. Hence, any handles that */
+/* may have held the original triangles are still valid, although not */
+/* directed as they were before. */
+/* */
+/* Upon completion of this routine, the `flipedge' handle holds the edge */
+/* dc of triangle dca, and is directed down, from vertex d to vertex c. */
+/* (Hence, the two triangles have rotated counterclockwise.) */
+/* */
+/* WARNING: This transformation is geometrically valid only if the */
+/* quadrilateral adbc is convex. Furthermore, this transformation is */
+/* valid only if there is not a subsegment between the triangles abc and */
+/* bad. This routine does not check either of these preconditions, and */
+/* it is the responsibility of the calling routine to ensure that they are */
+/* met. If they are not, the streets shall be filled with wailing and */
+/* gnashing of teeth. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+void flip(struct mesh *m, struct behavior *b, struct otri *flipedge)
+#else /* not ANSI_DECLARATORS */
+void flip(m, b, flipedge)
+struct mesh *m;
+struct behavior *b;
+struct otri *flipedge; /* Handle for the triangle abc. */
+#endif /* not ANSI_DECLARATORS */
+
+{
+ struct otri botleft, botright;
+ struct otri topleft, topright;
+ struct otri top;
+ struct otri botlcasing, botrcasing;
+ struct otri toplcasing, toprcasing;
+ struct osub botlsubseg, botrsubseg;
+ struct osub toplsubseg, toprsubseg;
+ vertex leftvertex, rightvertex, botvertex;
+ vertex farvertex;
+ triangle ptr; /* Temporary variable used by sym(). */
+ subseg sptr; /* Temporary variable used by tspivot(). */
+
+ /* Identify the vertices of the quadrilateral. */
+ org(*flipedge, rightvertex);
+ dest(*flipedge, leftvertex);
+ apex(*flipedge, botvertex);
+ sym(*flipedge, top);
+#ifdef SELF_CHECK
+ if (top.tri == m->dummytri) {
+ printf("Internal error in flip(): Attempt to flip on boundary.\n");
+ lnextself(*flipedge);
+ return;
+ }
+ if (m->checksegments) {
+ tspivot(*flipedge, toplsubseg);
+ if (toplsubseg.ss != m->dummysub) {
+ printf("Internal error in flip(): Attempt to flip a segment.\n");
+ lnextself(*flipedge);
+ return;
+ }
+ }
+#endif /* SELF_CHECK */
+ apex(top, farvertex);
+
+ /* Identify the casing of the quadrilateral. */
+ lprev(top, topleft);
+ sym(topleft, toplcasing);
+ lnext(top, topright);
+ sym(topright, toprcasing);
+ lnext(*flipedge, botleft);
+ sym(botleft, botlcasing);
+ lprev(*flipedge, botright);
+ sym(botright, botrcasing);
+ /* Rotate the quadrilateral one-quarter turn counterclockwise. */
+ bond(topleft, botlcasing);
+ bond(botleft, botrcasing);
+ bond(botright, toprcasing);
+ bond(topright, toplcasing);
+
+ if (m->checksegments) {
+ /* Check for subsegments and rebond them to the quadrilateral. */
+ tspivot(topleft, toplsubseg);
+ tspivot(botleft, botlsubseg);
+ tspivot(botright, botrsubseg);
+ tspivot(topright, toprsubseg);
+ if (toplsubseg.ss == m->dummysub) {
+ tsdissolve(topright);
+ } else {
+ tsbond(topright, toplsubseg);
+ }
+ if (botlsubseg.ss == m->dummysub) {
+ tsdissolve(topleft);
+ } else {
+ tsbond(topleft, botlsubseg);
+ }
+ if (botrsubseg.ss == m->dummysub) {
+ tsdissolve(botleft);
+ } else {
+ tsbond(botleft, botrsubseg);
+ }
+ if (toprsubseg.ss == m->dummysub) {
+ tsdissolve(botright);
+ } else {
+ tsbond(botright, toprsubseg);
+ }
+ }
+
+ /* New vertex assignments for the rotated quadrilateral. */
+ setorg(*flipedge, farvertex);
+ setdest(*flipedge, botvertex);
+ setapex(*flipedge, rightvertex);
+ setorg(top, botvertex);
+ setdest(top, farvertex);
+ setapex(top, leftvertex);
+ if (b->verbose > 2) {
+ printf(" Edge flip results in left ");
+ printtriangle(m, b, &top);
+ printf(" and right ");
+ printtriangle(m, b, flipedge);
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* unflip() Transform two triangles to two different triangles by */
+/* flipping an edge clockwise within a quadrilateral. Reverses */
+/* the flip() operation so that the data structures representing */
+/* the triangles are back where they were before the flip(). */
+/* */
+/* Imagine the original triangles, abc and bad, oriented so that the */
+/* shared edge ab lies in a horizontal plane, with the vertex b on the left */
+/* and the vertex a on the right. The vertex c lies below the edge, and */
+/* the vertex d lies above the edge. The `flipedge' handle holds the edge */
+/* ab of triangle abc, and is directed left, from vertex a to vertex b. */
+/* */
+/* The triangles abc and bad are deleted and replaced by the triangles cdb */
+/* and dca. The triangles that represent abc and bad are NOT deallocated; */
+/* they are reused for cdb and dca, respectively. Hence, any handles that */
+/* may have held the original triangles are still valid, although not */
+/* directed as they were before. */
+/* */
+/* Upon completion of this routine, the `flipedge' handle holds the edge */
+/* cd of triangle cdb, and is directed up, from vertex c to vertex d. */
+/* (Hence, the two triangles have rotated clockwise.) */
+/* */
+/* WARNING: This transformation is geometrically valid only if the */
+/* quadrilateral adbc is convex. Furthermore, this transformation is */
+/* valid only if there is not a subsegment between the triangles abc and */
+/* bad. This routine does not check either of these preconditions, and */
+/* it is the responsibility of the calling routine to ensure that they are */
+/* met. If they are not, the streets shall be filled with wailing and */
+/* gnashing of teeth. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+void unflip(struct mesh *m, struct behavior *b, struct otri *flipedge)
+#else /* not ANSI_DECLARATORS */
+void unflip(m, b, flipedge)
+struct mesh *m;
+struct behavior *b;
+struct otri *flipedge; /* Handle for the triangle abc. */
+#endif /* not ANSI_DECLARATORS */
+
+{
+ struct otri botleft, botright;
+ struct otri topleft, topright;
+ struct otri top;
+ struct otri botlcasing, botrcasing;
+ struct otri toplcasing, toprcasing;
+ struct osub botlsubseg, botrsubseg;
+ struct osub toplsubseg, toprsubseg;
+ vertex leftvertex, rightvertex, botvertex;
+ vertex farvertex;
+ triangle ptr; /* Temporary variable used by sym(). */
+ subseg sptr; /* Temporary variable used by tspivot(). */
+
+ /* Identify the vertices of the quadrilateral. */
+ org(*flipedge, rightvertex);
+ dest(*flipedge, leftvertex);
+ apex(*flipedge, botvertex);
+ sym(*flipedge, top);
+#ifdef SELF_CHECK
+ if (top.tri == m->dummytri) {
+ printf("Internal error in unflip(): Attempt to flip on boundary.\n");
+ lnextself(*flipedge);
+ return;
+ }
+ if (m->checksegments) {
+ tspivot(*flipedge, toplsubseg);
+ if (toplsubseg.ss != m->dummysub) {
+ printf("Internal error in unflip(): Attempt to flip a subsegment.\n");
+ lnextself(*flipedge);
+ return;
+ }
+ }
+#endif /* SELF_CHECK */
+ apex(top, farvertex);
+
+ /* Identify the casing of the quadrilateral. */
+ lprev(top, topleft);
+ sym(topleft, toplcasing);
+ lnext(top, topright);
+ sym(topright, toprcasing);
+ lnext(*flipedge, botleft);
+ sym(botleft, botlcasing);
+ lprev(*flipedge, botright);
+ sym(botright, botrcasing);
+ /* Rotate the quadrilateral one-quarter turn clockwise. */
+ bond(topleft, toprcasing);
+ bond(botleft, toplcasing);
+ bond(botright, botlcasing);
+ bond(topright, botrcasing);
+
+ if (m->checksegments) {
+ /* Check for subsegments and rebond them to the quadrilateral. */
+ tspivot(topleft, toplsubseg);
+ tspivot(botleft, botlsubseg);
+ tspivot(botright, botrsubseg);
+ tspivot(topright, toprsubseg);
+ if (toplsubseg.ss == m->dummysub) {
+ tsdissolve(botleft);
+ } else {
+ tsbond(botleft, toplsubseg);
+ }
+ if (botlsubseg.ss == m->dummysub) {
+ tsdissolve(botright);
+ } else {
+ tsbond(botright, botlsubseg);
+ }
+ if (botrsubseg.ss == m->dummysub) {
+ tsdissolve(topright);
+ } else {
+ tsbond(topright, botrsubseg);
+ }
+ if (toprsubseg.ss == m->dummysub) {
+ tsdissolve(topleft);
+ } else {
+ tsbond(topleft, toprsubseg);
+ }
+ }
+
+ /* New vertex assignments for the rotated quadrilateral. */
+ setorg(*flipedge, botvertex);
+ setdest(*flipedge, farvertex);
+ setapex(*flipedge, leftvertex);
+ setorg(top, farvertex);
+ setdest(top, botvertex);
+ setapex(top, rightvertex);
+ if (b->verbose > 2) {
+ printf(" Edge unflip results in left ");
+ printtriangle(m, b, flipedge);
+ printf(" and right ");
+ printtriangle(m, b, &top);
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* insertvertex() Insert a vertex into a Delaunay triangulation, */
+/* performing flips as necessary to maintain the Delaunay */
+/* property. */
+/* */
+/* The point `insertvertex' is located. If `searchtri.tri' is not NULL, */
+/* the search for the containing triangle begins from `searchtri'. If */
+/* `searchtri.tri' is NULL, a full point location procedure is called. */
+/* If `insertvertex' is found inside a triangle, the triangle is split into */
+/* three; if `insertvertex' lies on an edge, the edge is split in two, */
+/* thereby splitting the two adjacent triangles into four. Edge flips are */
+/* used to restore the Delaunay property. If `insertvertex' lies on an */
+/* existing vertex, no action is taken, and the value DUPLICATEVERTEX is */
+/* returned. On return, `searchtri' is set to a handle whose origin is the */
+/* existing vertex. */
+/* */
+/* Normally, the parameter `splitseg' is set to NULL, implying that no */
+/* subsegment should be split. In this case, if `insertvertex' is found to */
+/* lie on a segment, no action is taken, and the value VIOLATINGVERTEX is */
+/* returned. On return, `searchtri' is set to a handle whose primary edge */
+/* is the violated subsegment. */
+/* */
+/* If the calling routine wishes to split a subsegment by inserting a */
+/* vertex in it, the parameter `splitseg' should be that subsegment. In */
+/* this case, `searchtri' MUST be the triangle handle reached by pivoting */
+/* from that subsegment; no point location is done. */
+/* */
+/* `segmentflaws' and `triflaws' are flags that indicate whether or not */
+/* there should be checks for the creation of encroached subsegments or bad */
+/* quality triangles. If a newly inserted vertex encroaches upon */
+/* subsegments, these subsegments are added to the list of subsegments to */
+/* be split if `segmentflaws' is set. If bad triangles are created, these */
+/* are added to the queue if `triflaws' is set. */
+/* */
+/* If a duplicate vertex or violated segment does not prevent the vertex */
+/* from being inserted, the return value will be ENCROACHINGVERTEX if the */
+/* vertex encroaches upon a subsegment (and checking is enabled), or */
+/* SUCCESSFULVERTEX otherwise. In either case, `searchtri' is set to a */
+/* handle whose origin is the newly inserted vertex. */
+/* */
+/* insertvertex() does not use flip() for reasons of speed; some */
+/* information can be reused from edge flip to edge flip, like the */
+/* locations of subsegments. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+enum insertvertexresult insertvertex(struct mesh *m, struct behavior *b,
+ vertex newvertex, struct otri *searchtri,
+ struct osub *splitseg,
+ int segmentflaws, int triflaws)
+#else /* not ANSI_DECLARATORS */
+enum insertvertexresult insertvertex(m, b, newvertex, searchtri, splitseg,
+ segmentflaws, triflaws)
+struct mesh *m;
+struct behavior *b;
+vertex newvertex;
+struct otri *searchtri;
+struct osub *splitseg;
+int segmentflaws;
+int triflaws;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ struct otri horiz;
+ struct otri top;
+ struct otri botleft, botright;
+ struct otri topleft, topright;
+ struct otri newbotleft, newbotright;
+ struct otri newtopright;
+ struct otri botlcasing, botrcasing;
+ struct otri toplcasing, toprcasing;
+ struct otri testtri;
+ struct osub botlsubseg, botrsubseg;
+ struct osub toplsubseg, toprsubseg;
+ struct osub brokensubseg;
+ struct osub checksubseg;
+ struct osub rightsubseg;
+ struct osub newsubseg;
+ struct badsubseg *encroached;
+ struct flipstacker *newflip;
+ vertex first;
+ vertex leftvertex, rightvertex, botvertex, topvertex, farvertex;
+ vertex segmentorg, segmentdest;
+ REAL attrib;
+ REAL area;
+ enum insertvertexresult success;
+ enum locateresult intersect;
+ int doflip;
+ int mirrorflag;
+ int enq;
+ int i;
+ triangle ptr; /* Temporary variable used by sym(). */
+ subseg sptr; /* Temporary variable used by spivot() and tspivot(). */
+
+ if (b->verbose > 1) {
+ printf(" Inserting (%.12g, %.12g).\n", newvertex[0], newvertex[1]);
+ }
+
+ if (splitseg == (struct osub *) NULL) {
+ /* Find the location of the vertex to be inserted. Check if a good */
+ /* starting triangle has already been provided by the caller. */
+ if (searchtri->tri == m->dummytri) {
+ /* Find a boundary triangle. */
+ horiz.tri = m->dummytri;
+ horiz.orient = 0;
+ symself(horiz);
+ /* Search for a triangle containing `newvertex'. */
+ intersect = locate(m, b, newvertex, &horiz);
+ } else {
+ /* Start searching from the triangle provided by the caller. */
+ otricopy(*searchtri, horiz);
+ intersect = preciselocate(m, b, newvertex, &horiz, 1);
+ }
+ } else {
+ /* The calling routine provides the subsegment in which */
+ /* the vertex is inserted. */
+ otricopy(*searchtri, horiz);
+ intersect = ONEDGE;
+ }
+
+ if (intersect == ONVERTEX) {
+ /* There's already a vertex there. Return in `searchtri' a triangle */
+ /* whose origin is the existing vertex. */
+ otricopy(horiz, *searchtri);
+ otricopy(horiz, m->recenttri);
+ return DUPLICATEVERTEX;
+ }
+ if ((intersect == ONEDGE) || (intersect == OUTSIDE)) {
+ /* The vertex falls on an edge or boundary. */
+ if (m->checksegments && (splitseg == (struct osub *) NULL)) {
+ /* Check whether the vertex falls on a subsegment. */
+ tspivot(horiz, brokensubseg);
+ if (brokensubseg.ss != m->dummysub) {
+ /* The vertex falls on a subsegment, and hence will not be inserted. */
+ if (segmentflaws) {
+ enq = b->nobisect != 2;
+ if (enq && (b->nobisect == 1)) {
+ /* This subsegment may be split only if it is an */
+ /* internal boundary. */
+ sym(horiz, testtri);
+ enq = testtri.tri != m->dummytri;
+ }
+ if (enq) {
+ /* Add the subsegment to the list of encroached subsegments. */
+ encroached = (struct badsubseg *) poolalloc(&m->badsubsegs);
+ encroached->encsubseg = sencode(brokensubseg);
+ sorg(brokensubseg, encroached->subsegorg);
+ sdest(brokensubseg, encroached->subsegdest);
+ if (b->verbose > 2) {
+ printf(
+ " Queueing encroached subsegment (%.12g, %.12g) (%.12g, %.12g).\n",
+ encroached->subsegorg[0], encroached->subsegorg[1],
+ encroached->subsegdest[0], encroached->subsegdest[1]);
+ }
+ }
+ }
+ /* Return a handle whose primary edge contains the vertex, */
+ /* which has not been inserted. */
+ otricopy(horiz, *searchtri);
+ otricopy(horiz, m->recenttri);
+ return VIOLATINGVERTEX;
+ }
+ }
+
+ /* Insert the vertex on an edge, dividing one triangle into two (if */
+ /* the edge lies on a boundary) or two triangles into four. */
+ lprev(horiz, botright);
+ sym(botright, botrcasing);
+ sym(horiz, topright);
+ /* Is there a second triangle? (Or does this edge lie on a boundary?) */
+ mirrorflag = topright.tri != m->dummytri;
+ if (mirrorflag) {
+ lnextself(topright);
+ sym(topright, toprcasing);
+ maketriangle(m, b, &newtopright);
+ } else {
+ /* Splitting a boundary edge increases the number of boundary edges. */
+ m->hullsize++;
+ }
+ maketriangle(m, b, &newbotright);
+
+ /* Set the vertices of changed and new triangles. */
+ org(horiz, rightvertex);
+ dest(horiz, leftvertex);
+ apex(horiz, botvertex);
+ setorg(newbotright, botvertex);
+ setdest(newbotright, rightvertex);
+ setapex(newbotright, newvertex);
+ setorg(horiz, newvertex);
+ for (i = 0; i < m->eextras; i++) {
+ /* Set the element attributes of a new triangle. */
+ setelemattribute(newbotright, i, elemattribute(botright, i));
+ }
+ if (b->vararea) {
+ /* Set the area constraint of a new triangle. */
+ setareabound(newbotright, areabound(botright));
+ }
+ if (mirrorflag) {
+ dest(topright, topvertex);
+ setorg(newtopright, rightvertex);
+ setdest(newtopright, topvertex);
+ setapex(newtopright, newvertex);
+ setorg(topright, newvertex);
+ for (i = 0; i < m->eextras; i++) {
+ /* Set the element attributes of another new triangle. */
+ setelemattribute(newtopright, i, elemattribute(topright, i));
+ }
+ if (b->vararea) {
+ /* Set the area constraint of another new triangle. */
+ setareabound(newtopright, areabound(topright));
+ }
+ }
+
+ /* There may be subsegments that need to be bonded */
+ /* to the new triangle(s). */
+ if (m->checksegments) {
+ tspivot(botright, botrsubseg);
+ if (botrsubseg.ss != m->dummysub) {
+ tsdissolve(botright);
+ tsbond(newbotright, botrsubseg);
+ }
+ if (mirrorflag) {
+ tspivot(topright, toprsubseg);
+ if (toprsubseg.ss != m->dummysub) {
+ tsdissolve(topright);
+ tsbond(newtopright, toprsubseg);
+ }
+ }
+ }
+
+ /* Bond the new triangle(s) to the surrounding triangles. */
+ bond(newbotright, botrcasing);
+ lprevself(newbotright);
+ bond(newbotright, botright);
+ lprevself(newbotright);
+ if (mirrorflag) {
+ bond(newtopright, toprcasing);
+ lnextself(newtopright);
+ bond(newtopright, topright);
+ lnextself(newtopright);
+ bond(newtopright, newbotright);
+ }
+
+ if (splitseg != (struct osub *) NULL) {
+ /* Split the subsegment into two. */
+ setsdest(*splitseg, newvertex);
+ segorg(*splitseg, segmentorg);
+ segdest(*splitseg, segmentdest);
+ ssymself(*splitseg);
+ spivot(*splitseg, rightsubseg);
+ insertsubseg(m, b, &newbotright, mark(*splitseg));
+ tspivot(newbotright, newsubseg);
+ setsegorg(newsubseg, segmentorg);
+ setsegdest(newsubseg, segmentdest);
+ sbond(*splitseg, newsubseg);
+ ssymself(newsubseg);
+ sbond(newsubseg, rightsubseg);
+ ssymself(*splitseg);
+ /* Transfer the subsegment's boundary marker to the vertex */
+ /* if required. */
+ if (vertexmark(newvertex) == 0) {
+ setvertexmark(newvertex, mark(*splitseg));
+ }
+ }
+
+ if (m->checkquality) {
+ poolrestart(&m->flipstackers);
+ m->lastflip = (struct flipstacker *) poolalloc(&m->flipstackers);
+ m->lastflip->flippedtri = encode(horiz);
+ m->lastflip->prevflip = (struct flipstacker *) &insertvertex;
+ }
+
+#ifdef SELF_CHECK
+ if (counterclockwise(m, b, rightvertex, leftvertex, botvertex) < 0.0) {
+ printf("Internal error in insertvertex():\n");
+ printf(
+ " Clockwise triangle prior to edge vertex insertion (bottom).\n");
+ }
+ if (mirrorflag) {
+ if (counterclockwise(m, b, leftvertex, rightvertex, topvertex) < 0.0) {
+ printf("Internal error in insertvertex():\n");
+ printf(" Clockwise triangle prior to edge vertex insertion (top).\n");
+ }
+ if (counterclockwise(m, b, rightvertex, topvertex, newvertex) < 0.0) {
+ printf("Internal error in insertvertex():\n");
+ printf(
+ " Clockwise triangle after edge vertex insertion (top right).\n");
+ }
+ if (counterclockwise(m, b, topvertex, leftvertex, newvertex) < 0.0) {
+ printf("Internal error in insertvertex():\n");
+ printf(
+ " Clockwise triangle after edge vertex insertion (top left).\n");
+ }
+ }
+ if (counterclockwise(m, b, leftvertex, botvertex, newvertex) < 0.0) {
+ printf("Internal error in insertvertex():\n");
+ printf(
+ " Clockwise triangle after edge vertex insertion (bottom left).\n");
+ }
+ if (counterclockwise(m, b, botvertex, rightvertex, newvertex) < 0.0) {
+ printf("Internal error in insertvertex():\n");
+ printf(
+ " Clockwise triangle after edge vertex insertion (bottom right).\n");
+ }
+#endif /* SELF_CHECK */
+ if (b->verbose > 2) {
+ printf(" Updating bottom left ");
+ printtriangle(m, b, &botright);
+ if (mirrorflag) {
+ printf(" Updating top left ");
+ printtriangle(m, b, &topright);
+ printf(" Creating top right ");
+ printtriangle(m, b, &newtopright);
+ }
+ printf(" Creating bottom right ");
+ printtriangle(m, b, &newbotright);
+ }
+
+ /* Position `horiz' on the first edge to check for */
+ /* the Delaunay property. */
+ lnextself(horiz);
+ } else {
+ /* Insert the vertex in a triangle, splitting it into three. */
+ lnext(horiz, botleft);
+ lprev(horiz, botright);
+ sym(botleft, botlcasing);
+ sym(botright, botrcasing);
+ maketriangle(m, b, &newbotleft);
+ maketriangle(m, b, &newbotright);
+
+ /* Set the vertices of changed and new triangles. */
+ org(horiz, rightvertex);
+ dest(horiz, leftvertex);
+ apex(horiz, botvertex);
+ setorg(newbotleft, leftvertex);
+ setdest(newbotleft, botvertex);
+ setapex(newbotleft, newvertex);
+ setorg(newbotright, botvertex);
+ setdest(newbotright, rightvertex);
+ setapex(newbotright, newvertex);
+ setapex(horiz, newvertex);
+ for (i = 0; i < m->eextras; i++) {
+ /* Set the element attributes of the new triangles. */
+ attrib = elemattribute(horiz, i);
+ setelemattribute(newbotleft, i, attrib);
+ setelemattribute(newbotright, i, attrib);
+ }
+ if (b->vararea) {
+ /* Set the area constraint of the new triangles. */
+ area = areabound(horiz);
+ setareabound(newbotleft, area);
+ setareabound(newbotright, area);
+ }
+
+ /* There may be subsegments that need to be bonded */
+ /* to the new triangles. */
+ if (m->checksegments) {
+ tspivot(botleft, botlsubseg);
+ if (botlsubseg.ss != m->dummysub) {
+ tsdissolve(botleft);
+ tsbond(newbotleft, botlsubseg);
+ }
+ tspivot(botright, botrsubseg);
+ if (botrsubseg.ss != m->dummysub) {
+ tsdissolve(botright);
+ tsbond(newbotright, botrsubseg);
+ }
+ }
+
+ /* Bond the new triangles to the surrounding triangles. */
+ bond(newbotleft, botlcasing);
+ bond(newbotright, botrcasing);
+ lnextself(newbotleft);
+ lprevself(newbotright);
+ bond(newbotleft, newbotright);
+ lnextself(newbotleft);
+ bond(botleft, newbotleft);
+ lprevself(newbotright);
+ bond(botright, newbotright);
+
+ if (m->checkquality) {
+ poolrestart(&m->flipstackers);
+ m->lastflip = (struct flipstacker *) poolalloc(&m->flipstackers);
+ m->lastflip->flippedtri = encode(horiz);
+ m->lastflip->prevflip = (struct flipstacker *) NULL;
+ }
+
+#ifdef SELF_CHECK
+ if (counterclockwise(m, b, rightvertex, leftvertex, botvertex) < 0.0) {
+ printf("Internal error in insertvertex():\n");
+ printf(" Clockwise triangle prior to vertex insertion.\n");
+ }
+ if (counterclockwise(m, b, rightvertex, leftvertex, newvertex) < 0.0) {
+ printf("Internal error in insertvertex():\n");
+ printf(" Clockwise triangle after vertex insertion (top).\n");
+ }
+ if (counterclockwise(m, b, leftvertex, botvertex, newvertex) < 0.0) {
+ printf("Internal error in insertvertex():\n");
+ printf(" Clockwise triangle after vertex insertion (left).\n");
+ }
+ if (counterclockwise(m, b, botvertex, rightvertex, newvertex) < 0.0) {
+ printf("Internal error in insertvertex():\n");
+ printf(" Clockwise triangle after vertex insertion (right).\n");
+ }
+#endif /* SELF_CHECK */
+ if (b->verbose > 2) {
+ printf(" Updating top ");
+ printtriangle(m, b, &horiz);
+ printf(" Creating left ");
+ printtriangle(m, b, &newbotleft);
+ printf(" Creating right ");
+ printtriangle(m, b, &newbotright);
+ }
+ }
+
+ /* The insertion is successful by default, unless an encroached */
+ /* subsegment is found. */
+ success = SUCCESSFULVERTEX;
+ /* Circle around the newly inserted vertex, checking each edge opposite */
+ /* it for the Delaunay property. Non-Delaunay edges are flipped. */
+ /* `horiz' is always the edge being checked. `first' marks where to */
+ /* stop circling. */
+ org(horiz, first);
+ rightvertex = first;
+ dest(horiz, leftvertex);
+ /* Circle until finished. */
+ while (1) {
+ /* By default, the edge will be flipped. */
+ doflip = 1;
+
+ if (m->checksegments) {
+ /* Check for a subsegment, which cannot be flipped. */
+ tspivot(horiz, checksubseg);
+ if (checksubseg.ss != m->dummysub) {
+ /* The edge is a subsegment and cannot be flipped. */
+ doflip = 0;
+#ifndef CDT_ONLY
+ if (segmentflaws) {
+ /* Does the new vertex encroach upon this subsegment? */
+ if (checkseg4encroach(m, b, &checksubseg)) {
+ success = ENCROACHINGVERTEX;
+ }
+ }
+#endif /* not CDT_ONLY */
+ }
+ }
+
+ if (doflip) {
+ /* Check if the edge is a boundary edge. */
+ sym(horiz, top);
+ if (top.tri == m->dummytri) {
+ /* The edge is a boundary edge and cannot be flipped. */
+ doflip = 0;
+ } else {
+ /* Find the vertex on the other side of the edge. */
+ apex(top, farvertex);
+ /* In the incremental Delaunay triangulation algorithm, any of */
+ /* `leftvertex', `rightvertex', and `farvertex' could be vertices */
+ /* of the triangular bounding box. These vertices must be */
+ /* treated as if they are infinitely distant, even though their */
+ /* "coordinates" are not. */
+ if ((leftvertex == m->infvertex1) || (leftvertex == m->infvertex2) ||
+ (leftvertex == m->infvertex3)) {
+ /* `leftvertex' is infinitely distant. Check the convexity of */
+ /* the boundary of the triangulation. 'farvertex' might be */
+ /* infinite as well, but trust me, this same condition should */
+ /* be applied. */
+ doflip = counterclockwise(m, b, newvertex, rightvertex, farvertex)
+ > 0.0;
+ } else if ((rightvertex == m->infvertex1) ||
+ (rightvertex == m->infvertex2) ||
+ (rightvertex == m->infvertex3)) {
+ /* `rightvertex' is infinitely distant. Check the convexity of */
+ /* the boundary of the triangulation. 'farvertex' might be */
+ /* infinite as well, but trust me, this same condition should */
+ /* be applied. */
+ doflip = counterclockwise(m, b, farvertex, leftvertex, newvertex)
+ > 0.0;
+ } else if ((farvertex == m->infvertex1) ||
+ (farvertex == m->infvertex2) ||
+ (farvertex == m->infvertex3)) {
+ /* `farvertex' is infinitely distant and cannot be inside */
+ /* the circumcircle of the triangle `horiz'. */
+ doflip = 0;
+ } else {
+ /* Test whether the edge is locally Delaunay. */
+ doflip = incircle(m, b, leftvertex, newvertex, rightvertex,
+ farvertex) > 0.0;
+ }
+ if (doflip) {
+ /* We made it! Flip the edge `horiz' by rotating its containing */
+ /* quadrilateral (the two triangles adjacent to `horiz'). */
+ /* Identify the casing of the quadrilateral. */
+ lprev(top, topleft);
+ sym(topleft, toplcasing);
+ lnext(top, topright);
+ sym(topright, toprcasing);
+ lnext(horiz, botleft);
+ sym(botleft, botlcasing);
+ lprev(horiz, botright);
+ sym(botright, botrcasing);
+ /* Rotate the quadrilateral one-quarter turn counterclockwise. */
+ bond(topleft, botlcasing);
+ bond(botleft, botrcasing);
+ bond(botright, toprcasing);
+ bond(topright, toplcasing);
+ if (m->checksegments) {
+ /* Check for subsegments and rebond them to the quadrilateral. */
+ tspivot(topleft, toplsubseg);
+ tspivot(botleft, botlsubseg);
+ tspivot(botright, botrsubseg);
+ tspivot(topright, toprsubseg);
+ if (toplsubseg.ss == m->dummysub) {
+ tsdissolve(topright);
+ } else {
+ tsbond(topright, toplsubseg);
+ }
+ if (botlsubseg.ss == m->dummysub) {
+ tsdissolve(topleft);
+ } else {
+ tsbond(topleft, botlsubseg);
+ }
+ if (botrsubseg.ss == m->dummysub) {
+ tsdissolve(botleft);
+ } else {
+ tsbond(botleft, botrsubseg);
+ }
+ if (toprsubseg.ss == m->dummysub) {
+ tsdissolve(botright);
+ } else {
+ tsbond(botright, toprsubseg);
+ }
+ }
+ /* New vertex assignments for the rotated quadrilateral. */
+ setorg(horiz, farvertex);
+ setdest(horiz, newvertex);
+ setapex(horiz, rightvertex);
+ setorg(top, newvertex);
+ setdest(top, farvertex);
+ setapex(top, leftvertex);
+ for (i = 0; i < m->eextras; i++) {
+ /* Take the average of the two triangles' attributes. */
+ attrib = 0.5 * (elemattribute(top, i) + elemattribute(horiz, i));
+ setelemattribute(top, i, attrib);
+ setelemattribute(horiz, i, attrib);
+ }
+ if (b->vararea) {
+ if ((areabound(top) <= 0.0) || (areabound(horiz) <= 0.0)) {
+ area = -1.0;
+ } else {
+ /* Take the average of the two triangles' area constraints. */
+ /* This prevents small area constraints from migrating a */
+ /* long, long way from their original location due to flips. */
+ area = 0.5 * (areabound(top) + areabound(horiz));
+ }
+ setareabound(top, area);
+ setareabound(horiz, area);
+ }
+
+ if (m->checkquality) {
+ newflip = (struct flipstacker *) poolalloc(&m->flipstackers);
+ newflip->flippedtri = encode(horiz);
+ newflip->prevflip = m->lastflip;
+ m->lastflip = newflip;
+ }
+
+#ifdef SELF_CHECK
+ if (newvertex != (vertex) NULL) {
+ if (counterclockwise(m, b, leftvertex, newvertex, rightvertex) <
+ 0.0) {
+ printf("Internal error in insertvertex():\n");
+ printf(" Clockwise triangle prior to edge flip (bottom).\n");
+ }
+ /* The following test has been removed because constrainededge() */
+ /* sometimes generates inverted triangles that insertvertex() */
+ /* removes. */
+/*
+ if (counterclockwise(m, b, rightvertex, farvertex, leftvertex) <
+ 0.0) {
+ printf("Internal error in insertvertex():\n");
+ printf(" Clockwise triangle prior to edge flip (top).\n");
+ }
+*/
+ if (counterclockwise(m, b, farvertex, leftvertex, newvertex) <
+ 0.0) {
+ printf("Internal error in insertvertex():\n");
+ printf(" Clockwise triangle after edge flip (left).\n");
+ }
+ if (counterclockwise(m, b, newvertex, rightvertex, farvertex) <
+ 0.0) {
+ printf("Internal error in insertvertex():\n");
+ printf(" Clockwise triangle after edge flip (right).\n");
+ }
+ }
+#endif /* SELF_CHECK */
+ if (b->verbose > 2) {
+ printf(" Edge flip results in left ");
+ lnextself(topleft);
+ printtriangle(m, b, &topleft);
+ printf(" and right ");
+ printtriangle(m, b, &horiz);
+ }
+ /* On the next iterations, consider the two edges that were */
+ /* exposed (this is, are now visible to the newly inserted */
+ /* vertex) by the edge flip. */
+ lprevself(horiz);
+ leftvertex = farvertex;
+ }
+ }
+ }
+ if (!doflip) {
+ /* The handle `horiz' is accepted as locally Delaunay. */
+#ifndef CDT_ONLY
+ if (triflaws) {
+ /* Check the triangle `horiz' for quality. */
+ testtriangle(m, b, &horiz);
+ }
+#endif /* not CDT_ONLY */
+ /* Look for the next edge around the newly inserted vertex. */
+ lnextself(horiz);
+ sym(horiz, testtri);
+ /* Check for finishing a complete revolution about the new vertex, or */
+ /* falling outside of the triangulation. The latter will happen */
+ /* when a vertex is inserted at a boundary. */
+ if ((leftvertex == first) || (testtri.tri == m->dummytri)) {
+ /* We're done. Return a triangle whose origin is the new vertex. */
+ lnext(horiz, *searchtri);
+ lnext(horiz, m->recenttri);
+ return success;
+ }
+ /* Finish finding the next edge around the newly inserted vertex. */
+ lnext(testtri, horiz);
+ rightvertex = leftvertex;
+ dest(horiz, leftvertex);
+ }
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* triangulatepolygon() Find the Delaunay triangulation of a polygon that */
+/* has a certain "nice" shape. This includes the */
+/* polygons that result from deletion of a vertex or */
+/* insertion of a segment. */
+/* */
+/* This is a conceptually difficult routine. The starting assumption is */
+/* that we have a polygon with n sides. n - 1 of these sides are currently */
+/* represented as edges in the mesh. One side, called the "base", need not */
+/* be. */
+/* */
+/* Inside the polygon is a structure I call a "fan", consisting of n - 1 */
+/* triangles that share a common origin. For each of these triangles, the */
+/* edge opposite the origin is one of the sides of the polygon. The */
+/* primary edge of each triangle is the edge directed from the origin to */
+/* the destination; note that this is not the same edge that is a side of */
+/* the polygon. `firstedge' is the primary edge of the first triangle. */
+/* From there, the triangles follow in counterclockwise order about the */
+/* polygon, until `lastedge', the primary edge of the last triangle. */
+/* `firstedge' and `lastedge' are probably connected to other triangles */
+/* beyond the extremes of the fan, but their identity is not important, as */
+/* long as the fan remains connected to them. */
+/* */
+/* Imagine the polygon oriented so that its base is at the bottom. This */
+/* puts `firstedge' on the far right, and `lastedge' on the far left. */
+/* The right vertex of the base is the destination of `firstedge', and the */
+/* left vertex of the base is the apex of `lastedge'. */
+/* */
+/* The challenge now is to find the right sequence of edge flips to */
+/* transform the fan into a Delaunay triangulation of the polygon. Each */
+/* edge flip effectively removes one triangle from the fan, committing it */
+/* to the polygon. The resulting polygon has one fewer edge. If `doflip' */
+/* is set, the final flip will be performed, resulting in a fan of one */
+/* (useless?) triangle. If `doflip' is not set, the final flip is not */
+/* performed, resulting in a fan of two triangles, and an unfinished */
+/* triangular polygon that is not yet filled out with a single triangle. */
+/* On completion of the routine, `lastedge' is the last remaining triangle, */
+/* or the leftmost of the last two. */
+/* */
+/* Although the flips are performed in the order described above, the */
+/* decisions about what flips to perform are made in precisely the reverse */
+/* order. The recursive triangulatepolygon() procedure makes a decision, */
+/* uses up to two recursive calls to triangulate the "subproblems" */
+/* (polygons with fewer edges), and then performs an edge flip. */
+/* */
+/* The "decision" it makes is which vertex of the polygon should be */
+/* connected to the base. This decision is made by testing every possible */
+/* vertex. Once the best vertex is found, the two edges that connect this */
+/* vertex to the base become the bases for two smaller polygons. These */
+/* are triangulated recursively. Unfortunately, this approach can take */
+/* O(n^2) time not only in the worst case, but in many common cases. It's */
+/* rarely a big deal for vertex deletion, where n is rarely larger than */
+/* ten, but it could be a big deal for segment insertion, especially if */
+/* there's a lot of long segments that each cut many triangles. I ought to */
+/* code a faster algorithm some day. */
+/* */
+/* The `edgecount' parameter is the number of sides of the polygon, */
+/* including its base. `triflaws' is a flag that determines whether the */
+/* new triangles should be tested for quality, and enqueued if they are */
+/* bad. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+void triangulatepolygon(struct mesh *m, struct behavior *b,
+ struct otri *firstedge, struct otri *lastedge,
+ int edgecount, int doflip, int triflaws)
+#else /* not ANSI_DECLARATORS */
+void triangulatepolygon(m, b, firstedge, lastedge, edgecount, doflip, triflaws)
+struct mesh *m;
+struct behavior *b;
+struct otri *firstedge;
+struct otri *lastedge;
+int edgecount;
+int doflip;
+int triflaws;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ struct otri testtri;
+ struct otri besttri;
+ struct otri tempedge;
+ vertex leftbasevertex, rightbasevertex;
+ vertex testvertex;
+ vertex bestvertex;
+ int bestnumber;
+ int i;
+ triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */
+
+ /* Identify the base vertices. */
+ apex(*lastedge, leftbasevertex);
+ dest(*firstedge, rightbasevertex);
+ if (b->verbose > 2) {
+ printf(" Triangulating interior polygon at edge\n");
+ printf(" (%.12g, %.12g) (%.12g, %.12g)\n", leftbasevertex[0],
+ leftbasevertex[1], rightbasevertex[0], rightbasevertex[1]);
+ }
+ /* Find the best vertex to connect the base to. */
+ onext(*firstedge, besttri);
+ dest(besttri, bestvertex);
+ otricopy(besttri, testtri);
+ bestnumber = 1;
+ for (i = 2; i <= edgecount - 2; i++) {
+ onextself(testtri);
+ dest(testtri, testvertex);
+ /* Is this a better vertex? */
+ if (incircle(m, b, leftbasevertex, rightbasevertex, bestvertex,
+ testvertex) > 0.0) {
+ otricopy(testtri, besttri);
+ bestvertex = testvertex;
+ bestnumber = i;
+ }
+ }
+ if (b->verbose > 2) {
+ printf(" Connecting edge to (%.12g, %.12g)\n", bestvertex[0],
+ bestvertex[1]);
+ }
+ if (bestnumber > 1) {
+ /* Recursively triangulate the smaller polygon on the right. */
+ oprev(besttri, tempedge);
+ triangulatepolygon(m, b, firstedge, &tempedge, bestnumber + 1, 1,
+ triflaws);
+ }
+ if (bestnumber < edgecount - 2) {
+ /* Recursively triangulate the smaller polygon on the left. */
+ sym(besttri, tempedge);
+ triangulatepolygon(m, b, &besttri, lastedge, edgecount - bestnumber, 1,
+ triflaws);
+ /* Find `besttri' again; it may have been lost to edge flips. */
+ sym(tempedge, besttri);
+ }
+ if (doflip) {
+ /* Do one final edge flip. */
+ flip(m, b, &besttri);
+#ifndef CDT_ONLY
+ if (triflaws) {
+ /* Check the quality of the newly committed triangle. */
+ sym(besttri, testtri);
+ testtriangle(m, b, &testtri);
+ }
+#endif /* not CDT_ONLY */
+ }
+ /* Return the base triangle. */
+ otricopy(besttri, *lastedge);
+}
+
+/*****************************************************************************/
+/* */
+/* deletevertex() Delete a vertex from a Delaunay triangulation, ensuring */
+/* that the triangulation remains Delaunay. */
+/* */
+/* The origin of `deltri' is deleted. The union of the triangles adjacent */
+/* to this vertex is a polygon, for which the Delaunay triangulation is */
+/* found. Two triangles are removed from the mesh. */
+/* */
+/* Only interior vertices that do not lie on segments or boundaries may be */
+/* deleted. */
+/* */
+/*****************************************************************************/
+
+#ifndef CDT_ONLY
+
+#ifdef ANSI_DECLARATORS
+void deletevertex(struct mesh *m, struct behavior *b, struct otri *deltri)
+#else /* not ANSI_DECLARATORS */
+void deletevertex(m, b, deltri)
+struct mesh *m;
+struct behavior *b;
+struct otri *deltri;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ struct otri countingtri;
+ struct otri firstedge, lastedge;
+ struct otri deltriright;
+ struct otri lefttri, righttri;
+ struct otri leftcasing, rightcasing;
+ struct osub leftsubseg, rightsubseg;
+ vertex delvertex;
+ vertex neworg;
+ int edgecount;
+ triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */
+ subseg sptr; /* Temporary variable used by tspivot(). */
+
+ org(*deltri, delvertex);
+ if (b->verbose > 1) {
+ printf(" Deleting (%.12g, %.12g).\n", delvertex[0], delvertex[1]);
+ }
+ vertexdealloc(m, delvertex);
+
+ /* Count the degree of the vertex being deleted. */
+ onext(*deltri, countingtri);
+ edgecount = 1;
+ while (!otriequal(*deltri, countingtri)) {
+#ifdef SELF_CHECK
+ if (countingtri.tri == m->dummytri) {
+ printf("Internal error in deletevertex():\n");
+ printf(" Attempt to delete boundary vertex.\n");
+ internalerror();
+ }
+#endif /* SELF_CHECK */
+ edgecount++;
+ onextself(countingtri);
+ }
+
+#ifdef SELF_CHECK
+ if (edgecount < 3) {
+ printf("Internal error in deletevertex():\n Vertex has degree %d.\n",
+ edgecount);
+ internalerror();
+ }
+#endif /* SELF_CHECK */
+ if (edgecount > 3) {
+ /* Triangulate the polygon defined by the union of all triangles */
+ /* adjacent to the vertex being deleted. Check the quality of */
+ /* the resulting triangles. */
+ onext(*deltri, firstedge);
+ oprev(*deltri, lastedge);
+ triangulatepolygon(m, b, &firstedge, &lastedge, edgecount, 0,
+ !b->nobisect);
+ }
+ /* Splice out two triangles. */
+ lprev(*deltri, deltriright);
+ dnext(*deltri, lefttri);
+ sym(lefttri, leftcasing);
+ oprev(deltriright, righttri);
+ sym(righttri, rightcasing);
+ bond(*deltri, leftcasing);
+ bond(deltriright, rightcasing);
+ tspivot(lefttri, leftsubseg);
+ if (leftsubseg.ss != m->dummysub) {
+ tsbond(*deltri, leftsubseg);
+ }
+ tspivot(righttri, rightsubseg);
+ if (rightsubseg.ss != m->dummysub) {
+ tsbond(deltriright, rightsubseg);
+ }
+
+ /* Set the new origin of `deltri' and check its quality. */
+ org(lefttri, neworg);
+ setorg(*deltri, neworg);
+ if (!b->nobisect) {
+ testtriangle(m, b, deltri);
+ }
+
+ /* Delete the two spliced-out triangles. */
+ triangledealloc(m, lefttri.tri);
+ triangledealloc(m, righttri.tri);
+}
+
+#endif /* not CDT_ONLY */
+
+/*****************************************************************************/
+/* */
+/* undovertex() Undo the most recent vertex insertion. */
+/* */
+/* Walks through the list of transformations (flips and a vertex insertion) */
+/* in the reverse of the order in which they were done, and undoes them. */
+/* The inserted vertex is removed from the triangulation and deallocated. */
+/* Two triangles (possibly just one) are also deallocated. */
+/* */
+/*****************************************************************************/
+
+#ifndef CDT_ONLY
+
+#ifdef ANSI_DECLARATORS
+void undovertex(struct mesh *m, struct behavior *b)
+#else /* not ANSI_DECLARATORS */
+void undovertex(m, b)
+struct mesh *m;
+struct behavior *b;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ struct otri fliptri;
+ struct otri botleft, botright, topright;
+ struct otri botlcasing, botrcasing, toprcasing;
+ struct otri gluetri;
+ struct osub botlsubseg, botrsubseg, toprsubseg;
+ vertex botvertex, rightvertex;
+ triangle ptr; /* Temporary variable used by sym(). */
+ subseg sptr; /* Temporary variable used by tspivot(). */
+
+ /* Walk through the list of transformations (flips and a vertex insertion) */
+ /* in the reverse of the order in which they were done, and undo them. */
+ while (m->lastflip != (struct flipstacker *) NULL) {
+ /* Find a triangle involved in the last unreversed transformation. */
+ decode(m->lastflip->flippedtri, fliptri);
+
+ /* We are reversing one of three transformations: a trisection of one */
+ /* triangle into three (by inserting a vertex in the triangle), a */
+ /* bisection of two triangles into four (by inserting a vertex in an */
+ /* edge), or an edge flip. */
+ if (m->lastflip->prevflip == (struct flipstacker *) NULL) {
+ /* Restore a triangle that was split into three triangles, */
+ /* so it is again one triangle. */
+ dprev(fliptri, botleft);
+ lnextself(botleft);
+ onext(fliptri, botright);
+ lprevself(botright);
+ sym(botleft, botlcasing);
+ sym(botright, botrcasing);
+ dest(botleft, botvertex);
+
+ setapex(fliptri, botvertex);
+ lnextself(fliptri);
+ bond(fliptri, botlcasing);
+ tspivot(botleft, botlsubseg);
+ tsbond(fliptri, botlsubseg);
+ lnextself(fliptri);
+ bond(fliptri, botrcasing);
+ tspivot(botright, botrsubseg);
+ tsbond(fliptri, botrsubseg);
+
+ /* Delete the two spliced-out triangles. */
+ triangledealloc(m, botleft.tri);
+ triangledealloc(m, botright.tri);
+ } else if (m->lastflip->prevflip == (struct flipstacker *) &insertvertex) {
+ /* Restore two triangles that were split into four triangles, */
+ /* so they are again two triangles. */
+ lprev(fliptri, gluetri);
+ sym(gluetri, botright);
+ lnextself(botright);
+ sym(botright, botrcasing);
+ dest(botright, rightvertex);
+
+ setorg(fliptri, rightvertex);
+ bond(gluetri, botrcasing);
+ tspivot(botright, botrsubseg);
+ tsbond(gluetri, botrsubseg);
+
+ /* Delete the spliced-out triangle. */
+ triangledealloc(m, botright.tri);
+
+ sym(fliptri, gluetri);
+ if (gluetri.tri != m->dummytri) {
+ lnextself(gluetri);
+ dnext(gluetri, topright);
+ sym(topright, toprcasing);
+
+ setorg(gluetri, rightvertex);
+ bond(gluetri, toprcasing);
+ tspivot(topright, toprsubseg);
+ tsbond(gluetri, toprsubseg);
+
+ /* Delete the spliced-out triangle. */
+ triangledealloc(m, topright.tri);
+ }
+
+ /* This is the end of the list, sneakily encoded. */
+ m->lastflip->prevflip = (struct flipstacker *) NULL;
+ } else {
+ /* Undo an edge flip. */
+ unflip(m, b, &fliptri);
+ }
+
+ /* Go on and process the next transformation. */
+ m->lastflip = m->lastflip->prevflip;
+ }
+}
+
+#endif /* not CDT_ONLY */
+
+/** **/
+/** **/
+/********* Mesh transformation routines end here *********/
+
+/********* Divide-and-conquer Delaunay triangulation begins here *********/
+/** **/
+/** **/
+
+/*****************************************************************************/
+/* */
+/* The divide-and-conquer bounding box */
+/* */
+/* I originally implemented the divide-and-conquer and incremental Delaunay */
+/* triangulations using the edge-based data structure presented by Guibas */
+/* and Stolfi. Switching to a triangle-based data structure doubled the */
+/* speed. However, I had to think of a few extra tricks to maintain the */
+/* elegance of the original algorithms. */
+/* */
+/* The "bounding box" used by my variant of the divide-and-conquer */
+/* algorithm uses one triangle for each edge of the convex hull of the */
+/* triangulation. These bounding triangles all share a common apical */
+/* vertex, which is represented by NULL and which represents nothing. */
+/* The bounding triangles are linked in a circular fan about this NULL */
+/* vertex, and the edges on the convex hull of the triangulation appear */
+/* opposite the NULL vertex. You might find it easiest to imagine that */
+/* the NULL vertex is a point in 3D space behind the center of the */
+/* triangulation, and that the bounding triangles form a sort of cone. */
+/* */
+/* This bounding box makes it easy to represent degenerate cases. For */
+/* instance, the triangulation of two vertices is a single edge. This edge */
+/* is represented by two bounding box triangles, one on each "side" of the */
+/* edge. These triangles are also linked together in a fan about the NULL */
+/* vertex. */
+/* */
+/* The bounding box also makes it easy to traverse the convex hull, as the */
+/* divide-and-conquer algorithm needs to do. */
+/* */
+/*****************************************************************************/
+
+/*****************************************************************************/
+/* */
+/* vertexsort() Sort an array of vertices by x-coordinate, using the */
+/* y-coordinate as a secondary key. */
+/* */
+/* Uses quicksort. Randomized O(n log n) time. No, I did not make any of */
+/* the usual quicksort mistakes. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+void vertexsort(vertex *sortarray, int arraysize)
+#else /* not ANSI_DECLARATORS */
+void vertexsort(sortarray, arraysize)
+vertex *sortarray;
+int arraysize;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ int left, right;
+ int pivot;
+ REAL pivotx, pivoty;
+ vertex temp;
+
+ if (arraysize == 2) {
+ /* Recursive base case. */
+ if ((sortarray[0][0] > sortarray[1][0]) ||
+ ((sortarray[0][0] == sortarray[1][0]) &&
+ (sortarray[0][1] > sortarray[1][1]))) {
+ temp = sortarray[1];
+ sortarray[1] = sortarray[0];
+ sortarray[0] = temp;
+ }
+ return;
+ }
+ /* Choose a random pivot to split the array. */
+ pivot = (int) randomnation((unsigned int) arraysize);
+ pivotx = sortarray[pivot][0];
+ pivoty = sortarray[pivot][1];
+ /* Split the array. */
+ left = -1;
+ right = arraysize;
+ while (left < right) {
+ /* Search for a vertex whose x-coordinate is too large for the left. */
+ do {
+ left++;
+ } while ((left <= right) && ((sortarray[left][0] < pivotx) ||
+ ((sortarray[left][0] == pivotx) &&
+ (sortarray[left][1] < pivoty))));
+ /* Search for a vertex whose x-coordinate is too small for the right. */
+ do {
+ right--;
+ } while ((left <= right) && ((sortarray[right][0] > pivotx) ||
+ ((sortarray[right][0] == pivotx) &&
+ (sortarray[right][1] > pivoty))));
+ if (left < right) {
+ /* Swap the left and right vertices. */
+ temp = sortarray[left];
+ sortarray[left] = sortarray[right];
+ sortarray[right] = temp;
+ }
+ }
+ if (left > 1) {
+ /* Recursively sort the left subset. */
+ vertexsort(sortarray, left);
+ }
+ if (right < arraysize - 2) {
+ /* Recursively sort the right subset. */
+ vertexsort(&sortarray[right + 1], arraysize - right - 1);
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* vertexmedian() An order statistic algorithm, almost. Shuffles an */
+/* array of vertices so that the first `median' vertices */
+/* occur lexicographically before the remaining vertices. */
+/* */
+/* Uses the x-coordinate as the primary key if axis == 0; the y-coordinate */
+/* if axis == 1. Very similar to the vertexsort() procedure, but runs in */
+/* randomized linear time. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+void vertexmedian(vertex *sortarray, int arraysize, int median, int axis)
+#else /* not ANSI_DECLARATORS */
+void vertexmedian(sortarray, arraysize, median, axis)
+vertex *sortarray;
+int arraysize;
+int median;
+int axis;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ int left, right;
+ int pivot;
+ REAL pivot1, pivot2;
+ vertex temp;
+
+ if (arraysize == 2) {
+ /* Recursive base case. */
+ if ((sortarray[0][axis] > sortarray[1][axis]) ||
+ ((sortarray[0][axis] == sortarray[1][axis]) &&
+ (sortarray[0][1 - axis] > sortarray[1][1 - axis]))) {
+ temp = sortarray[1];
+ sortarray[1] = sortarray[0];
+ sortarray[0] = temp;
+ }
+ return;
+ }
+ /* Choose a random pivot to split the array. */
+ pivot = (int) randomnation((unsigned int) arraysize);
+ pivot1 = sortarray[pivot][axis];
+ pivot2 = sortarray[pivot][1 - axis];
+ /* Split the array. */
+ left = -1;
+ right = arraysize;
+ while (left < right) {
+ /* Search for a vertex whose x-coordinate is too large for the left. */
+ do {
+ left++;
+ } while ((left <= right) && ((sortarray[left][axis] < pivot1) ||
+ ((sortarray[left][axis] == pivot1) &&
+ (sortarray[left][1 - axis] < pivot2))));
+ /* Search for a vertex whose x-coordinate is too small for the right. */
+ do {
+ right--;
+ } while ((left <= right) && ((sortarray[right][axis] > pivot1) ||
+ ((sortarray[right][axis] == pivot1) &&
+ (sortarray[right][1 - axis] > pivot2))));
+ if (left < right) {
+ /* Swap the left and right vertices. */
+ temp = sortarray[left];
+ sortarray[left] = sortarray[right];
+ sortarray[right] = temp;
+ }
+ }
+ /* Unlike in vertexsort(), at most one of the following */
+ /* conditionals is true. */
+ if (left > median) {
+ /* Recursively shuffle the left subset. */
+ vertexmedian(sortarray, left, median, axis);
+ }
+ if (right < median - 1) {
+ /* Recursively shuffle the right subset. */
+ vertexmedian(&sortarray[right + 1], arraysize - right - 1,
+ median - right - 1, axis);
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* alternateaxes() Sorts the vertices as appropriate for the divide-and- */
+/* conquer algorithm with alternating cuts. */
+/* */
+/* Partitions by x-coordinate if axis == 0; by y-coordinate if axis == 1. */
+/* For the base case, subsets containing only two or three vertices are */
+/* always sorted by x-coordinate. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+void alternateaxes(vertex *sortarray, int arraysize, int axis)
+#else /* not ANSI_DECLARATORS */
+void alternateaxes(sortarray, arraysize, axis)
+vertex *sortarray;
+int arraysize;
+int axis;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ int divider;
+
+ divider = arraysize >> 1;
+ if (arraysize <= 3) {
+ /* Recursive base case: subsets of two or three vertices will be */
+ /* handled specially, and should always be sorted by x-coordinate. */
+ axis = 0;
+ }
+ /* Partition with a horizontal or vertical cut. */
+ vertexmedian(sortarray, arraysize, divider, axis);
+ /* Recursively partition the subsets with a cross cut. */
+ if (arraysize - divider >= 2) {
+ if (divider >= 2) {
+ alternateaxes(sortarray, divider, 1 - axis);
+ }
+ alternateaxes(&sortarray[divider], arraysize - divider, 1 - axis);
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* mergehulls() Merge two adjacent Delaunay triangulations into a */
+/* single Delaunay triangulation. */
+/* */
+/* This is similar to the algorithm given by Guibas and Stolfi, but uses */
+/* a triangle-based, rather than edge-based, data structure. */
+/* */
+/* The algorithm walks up the gap between the two triangulations, knitting */
+/* them together. As they are merged, some of their bounding triangles */
+/* are converted into real triangles of the triangulation. The procedure */
+/* pulls each hull's bounding triangles apart, then knits them together */
+/* like the teeth of two gears. The Delaunay property determines, at each */
+/* step, whether the next "tooth" is a bounding triangle of the left hull */
+/* or the right. When a bounding triangle becomes real, its apex is */
+/* changed from NULL to a real vertex. */
+/* */
+/* Only two new triangles need to be allocated. These become new bounding */
+/* triangles at the top and bottom of the seam. They are used to connect */
+/* the remaining bounding triangles (those that have not been converted */
+/* into real triangles) into a single fan. */
+/* */
+/* On entry, `farleft' and `innerleft' are bounding triangles of the left */
+/* triangulation. The origin of `farleft' is the leftmost vertex, and */
+/* the destination of `innerleft' is the rightmost vertex of the */
+/* triangulation. Similarly, `innerright' and `farright' are bounding */
+/* triangles of the right triangulation. The origin of `innerright' and */
+/* destination of `farright' are the leftmost and rightmost vertices. */
+/* */
+/* On completion, the origin of `farleft' is the leftmost vertex of the */
+/* merged triangulation, and the destination of `farright' is the rightmost */
+/* vertex. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+void mergehulls(struct mesh *m, struct behavior *b, struct otri *farleft,
+ struct otri *innerleft, struct otri *innerright,
+ struct otri *farright, int axis)
+#else /* not ANSI_DECLARATORS */
+void mergehulls(m, b, farleft, innerleft, innerright, farright, axis)
+struct mesh *m;
+struct behavior *b;
+struct otri *farleft;
+struct otri *innerleft;
+struct otri *innerright;
+struct otri *farright;
+int axis;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ struct otri leftcand, rightcand;
+ struct otri baseedge;
+ struct otri nextedge;
+ struct otri sidecasing, topcasing, outercasing;
+ struct otri checkedge;
+ vertex innerleftdest;
+ vertex innerrightorg;
+ vertex innerleftapex, innerrightapex;
+ vertex farleftpt, farrightpt;
+ vertex farleftapex, farrightapex;
+ vertex lowerleft, lowerright;
+ vertex upperleft, upperright;
+ vertex nextapex;
+ vertex checkvertex;
+ int changemade;
+ int badedge;
+ int leftfinished, rightfinished;
+ triangle ptr; /* Temporary variable used by sym(). */
+
+ dest(*innerleft, innerleftdest);
+ apex(*innerleft, innerleftapex);
+ org(*innerright, innerrightorg);
+ apex(*innerright, innerrightapex);
+ /* Special treatment for horizontal cuts. */
+ if (b->dwyer && (axis == 1)) {
+ org(*farleft, farleftpt);
+ apex(*farleft, farleftapex);
+ dest(*farright, farrightpt);
+ apex(*farright, farrightapex);
+ /* The pointers to the extremal vertices are shifted to point to the */
+ /* topmost and bottommost vertex of each hull, rather than the */
+ /* leftmost and rightmost vertices. */
+ while (farleftapex[1] < farleftpt[1]) {
+ lnextself(*farleft);
+ symself(*farleft);
+ farleftpt = farleftapex;
+ apex(*farleft, farleftapex);
+ }
+ sym(*innerleft, checkedge);
+ apex(checkedge, checkvertex);
+ while (checkvertex[1] > innerleftdest[1]) {
+ lnext(checkedge, *innerleft);
+ innerleftapex = innerleftdest;
+ innerleftdest = checkvertex;
+ sym(*innerleft, checkedge);
+ apex(checkedge, checkvertex);
+ }
+ while (innerrightapex[1] < innerrightorg[1]) {
+ lnextself(*innerright);
+ symself(*innerright);
+ innerrightorg = innerrightapex;
+ apex(*innerright, innerrightapex);
+ }
+ sym(*farright, checkedge);
+ apex(checkedge, checkvertex);
+ while (checkvertex[1] > farrightpt[1]) {
+ lnext(checkedge, *farright);
+ farrightapex = farrightpt;
+ farrightpt = checkvertex;
+ sym(*farright, checkedge);
+ apex(checkedge, checkvertex);
+ }
+ }
+ /* Find a line tangent to and below both hulls. */
+ do {
+ changemade = 0;
+ /* Make innerleftdest the "bottommost" vertex of the left hull. */
+ if (counterclockwise(m, b, innerleftdest, innerleftapex, innerrightorg) >
+ 0.0) {
+ lprevself(*innerleft);
+ symself(*innerleft);
+ innerleftdest = innerleftapex;
+ apex(*innerleft, innerleftapex);
+ changemade = 1;
+ }
+ /* Make innerrightorg the "bottommost" vertex of the right hull. */
+ if (counterclockwise(m, b, innerrightapex, innerrightorg, innerleftdest) >
+ 0.0) {
+ lnextself(*innerright);
+ symself(*innerright);
+ innerrightorg = innerrightapex;
+ apex(*innerright, innerrightapex);
+ changemade = 1;
+ }
+ } while (changemade);
+ /* Find the two candidates to be the next "gear tooth." */
+ sym(*innerleft, leftcand);
+ sym(*innerright, rightcand);
+ /* Create the bottom new bounding triangle. */
+ maketriangle(m, b, &baseedge);
+ /* Connect it to the bounding boxes of the left and right triangulations. */
+ bond(baseedge, *innerleft);
+ lnextself(baseedge);
+ bond(baseedge, *innerright);
+ lnextself(baseedge);
+ setorg(baseedge, innerrightorg);
+ setdest(baseedge, innerleftdest);
+ /* Apex is intentionally left NULL. */
+ if (b->verbose > 2) {
+ printf(" Creating base bounding ");
+ printtriangle(m, b, &baseedge);
+ }
+ /* Fix the extreme triangles if necessary. */
+ org(*farleft, farleftpt);
+ if (innerleftdest == farleftpt) {
+ lnext(baseedge, *farleft);
+ }
+ dest(*farright, farrightpt);
+ if (innerrightorg == farrightpt) {
+ lprev(baseedge, *farright);
+ }
+ /* The vertices of the current knitting edge. */
+ lowerleft = innerleftdest;
+ lowerright = innerrightorg;
+ /* The candidate vertices for knitting. */
+ apex(leftcand, upperleft);
+ apex(rightcand, upperright);
+ /* Walk up the gap between the two triangulations, knitting them together. */
+ while (1) {
+ /* Have we reached the top? (This isn't quite the right question, */
+ /* because even though the left triangulation might seem finished now, */
+ /* moving up on the right triangulation might reveal a new vertex of */
+ /* the left triangulation. And vice-versa.) */
+ leftfinished = counterclockwise(m, b, upperleft, lowerleft, lowerright) <=
+ 0.0;
+ rightfinished = counterclockwise(m, b, upperright, lowerleft, lowerright)
+ <= 0.0;
+ if (leftfinished && rightfinished) {
+ /* Create the top new bounding triangle. */
+ maketriangle(m, b, &nextedge);
+ setorg(nextedge, lowerleft);
+ setdest(nextedge, lowerright);
+ /* Apex is intentionally left NULL. */
+ /* Connect it to the bounding boxes of the two triangulations. */
+ bond(nextedge, baseedge);
+ lnextself(nextedge);
+ bond(nextedge, rightcand);
+ lnextself(nextedge);
+ bond(nextedge, leftcand);
+ if (b->verbose > 2) {
+ printf(" Creating top bounding ");
+ printtriangle(m, b, &nextedge);
+ }
+ /* Special treatment for horizontal cuts. */
+ if (b->dwyer && (axis == 1)) {
+ org(*farleft, farleftpt);
+ apex(*farleft, farleftapex);
+ dest(*farright, farrightpt);
+ apex(*farright, farrightapex);
+ sym(*farleft, checkedge);
+ apex(checkedge, checkvertex);
+ /* The pointers to the extremal vertices are restored to the */
+ /* leftmost and rightmost vertices (rather than topmost and */
+ /* bottommost). */
+ while (checkvertex[0] < farleftpt[0]) {
+ lprev(checkedge, *farleft);
+ farleftapex = farleftpt;
+ farleftpt = checkvertex;
+ sym(*farleft, checkedge);
+ apex(checkedge, checkvertex);
+ }
+ while (farrightapex[0] > farrightpt[0]) {
+ lprevself(*farright);
+ symself(*farright);
+ farrightpt = farrightapex;
+ apex(*farright, farrightapex);
+ }
+ }
+ return;
+ }
+ /* Consider eliminating edges from the left triangulation. */
+ if (!leftfinished) {
+ /* What vertex would be exposed if an edge were deleted? */
+ lprev(leftcand, nextedge);
+ symself(nextedge);
+ apex(nextedge, nextapex);
+ /* If nextapex is NULL, then no vertex would be exposed; the */
+ /* triangulation would have been eaten right through. */
+ if (nextapex != (vertex) NULL) {
+ /* Check whether the edge is Delaunay. */
+ badedge = incircle(m, b, lowerleft, lowerright, upperleft, nextapex) >
+ 0.0;
+ while (badedge) {
+ /* Eliminate the edge with an edge flip. As a result, the */
+ /* left triangulation will have one more boundary triangle. */
+ lnextself(nextedge);
+ sym(nextedge, topcasing);
+ lnextself(nextedge);
+ sym(nextedge, sidecasing);
+ bond(nextedge, topcasing);
+ bond(leftcand, sidecasing);
+ lnextself(leftcand);
+ sym(leftcand, outercasing);
+ lprevself(nextedge);
+ bond(nextedge, outercasing);
+ /* Correct the vertices to reflect the edge flip. */
+ setorg(leftcand, lowerleft);
+ setdest(leftcand, NULL);
+ setapex(leftcand, nextapex);
+ setorg(nextedge, NULL);
+ setdest(nextedge, upperleft);
+ setapex(nextedge, nextapex);
+ /* Consider the newly exposed vertex. */
+ upperleft = nextapex;
+ /* What vertex would be exposed if another edge were deleted? */
+ otricopy(sidecasing, nextedge);
+ apex(nextedge, nextapex);
+ if (nextapex != (vertex) NULL) {
+ /* Check whether the edge is Delaunay. */
+ badedge = incircle(m, b, lowerleft, lowerright, upperleft,
+ nextapex) > 0.0;
+ } else {
+ /* Avoid eating right through the triangulation. */
+ badedge = 0;
+ }
+ }
+ }
+ }
+ /* Consider eliminating edges from the right triangulation. */
+ if (!rightfinished) {
+ /* What vertex would be exposed if an edge were deleted? */
+ lnext(rightcand, nextedge);
+ symself(nextedge);
+ apex(nextedge, nextapex);
+ /* If nextapex is NULL, then no vertex would be exposed; the */
+ /* triangulation would have been eaten right through. */
+ if (nextapex != (vertex) NULL) {
+ /* Check whether the edge is Delaunay. */
+ badedge = incircle(m, b, lowerleft, lowerright, upperright, nextapex) >
+ 0.0;
+ while (badedge) {
+ /* Eliminate the edge with an edge flip. As a result, the */
+ /* right triangulation will have one more boundary triangle. */
+ lprevself(nextedge);
+ sym(nextedge, topcasing);
+ lprevself(nextedge);
+ sym(nextedge, sidecasing);
+ bond(nextedge, topcasing);
+ bond(rightcand, sidecasing);
+ lprevself(rightcand);
+ sym(rightcand, outercasing);
+ lnextself(nextedge);
+ bond(nextedge, outercasing);
+ /* Correct the vertices to reflect the edge flip. */
+ setorg(rightcand, NULL);
+ setdest(rightcand, lowerright);
+ setapex(rightcand, nextapex);
+ setorg(nextedge, upperright);
+ setdest(nextedge, NULL);
+ setapex(nextedge, nextapex);
+ /* Consider the newly exposed vertex. */
+ upperright = nextapex;
+ /* What vertex would be exposed if another edge were deleted? */
+ otricopy(sidecasing, nextedge);
+ apex(nextedge, nextapex);
+ if (nextapex != (vertex) NULL) {
+ /* Check whether the edge is Delaunay. */
+ badedge = incircle(m, b, lowerleft, lowerright, upperright,
+ nextapex) > 0.0;
+ } else {
+ /* Avoid eating right through the triangulation. */
+ badedge = 0;
+ }
+ }
+ }
+ }
+ if (leftfinished || (!rightfinished &&
+ (incircle(m, b, upperleft, lowerleft, lowerright, upperright) >
+ 0.0))) {
+ /* Knit the triangulations, adding an edge from `lowerleft' */
+ /* to `upperright'. */
+ bond(baseedge, rightcand);
+ lprev(rightcand, baseedge);
+ setdest(baseedge, lowerleft);
+ lowerright = upperright;
+ sym(baseedge, rightcand);
+ apex(rightcand, upperright);
+ } else {
+ /* Knit the triangulations, adding an edge from `upperleft' */
+ /* to `lowerright'. */
+ bond(baseedge, leftcand);
+ lnext(leftcand, baseedge);
+ setorg(baseedge, lowerright);
+ lowerleft = upperleft;
+ sym(baseedge, leftcand);
+ apex(leftcand, upperleft);
+ }
+ if (b->verbose > 2) {
+ printf(" Connecting ");
+ printtriangle(m, b, &baseedge);
+ }
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* divconqrecurse() Recursively form a Delaunay triangulation by the */
+/* divide-and-conquer method. */
+/* */
+/* Recursively breaks down the problem into smaller pieces, which are */
+/* knitted together by mergehulls(). The base cases (problems of two or */
+/* three vertices) are handled specially here. */
+/* */
+/* On completion, `farleft' and `farright' are bounding triangles such that */
+/* the origin of `farleft' is the leftmost vertex (breaking ties by */
+/* choosing the highest leftmost vertex), and the destination of */
+/* `farright' is the rightmost vertex (breaking ties by choosing the */
+/* lowest rightmost vertex). */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+void divconqrecurse(struct mesh *m, struct behavior *b, vertex *sortarray,
+ int vertices, int axis,
+ struct otri *farleft, struct otri *farright)
+#else /* not ANSI_DECLARATORS */
+void divconqrecurse(m, b, sortarray, vertices, axis, farleft, farright)
+struct mesh *m;
+struct behavior *b;
+vertex *sortarray;
+int vertices;
+int axis;
+struct otri *farleft;
+struct otri *farright;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ struct otri midtri, tri1, tri2, tri3;
+ struct otri innerleft, innerright;
+ REAL area;
+ int divider;
+
+ if (b->verbose > 2) {
+ printf(" Triangulating %d vertices.\n", vertices);
+ }
+ if (vertices == 2) {
+ /* The triangulation of two vertices is an edge. An edge is */
+ /* represented by two bounding triangles. */
+ maketriangle(m, b, farleft);
+ setorg(*farleft, sortarray[0]);
+ setdest(*farleft, sortarray[1]);
+ /* The apex is intentionally left NULL. */
+ maketriangle(m, b, farright);
+ setorg(*farright, sortarray[1]);
+ setdest(*farright, sortarray[0]);
+ /* The apex is intentionally left NULL. */
+ bond(*farleft, *farright);
+ lprevself(*farleft);
+ lnextself(*farright);
+ bond(*farleft, *farright);
+ lprevself(*farleft);
+ lnextself(*farright);
+ bond(*farleft, *farright);
+ if (b->verbose > 2) {
+ printf(" Creating ");
+ printtriangle(m, b, farleft);
+ printf(" Creating ");
+ printtriangle(m, b, farright);
+ }
+ /* Ensure that the origin of `farleft' is sortarray[0]. */
+ lprev(*farright, *farleft);
+ return;
+ } else if (vertices == 3) {
+ /* The triangulation of three vertices is either a triangle (with */
+ /* three bounding triangles) or two edges (with four bounding */
+ /* triangles). In either case, four triangles are created. */
+ maketriangle(m, b, &midtri);
+ maketriangle(m, b, &tri1);
+ maketriangle(m, b, &tri2);
+ maketriangle(m, b, &tri3);
+ area = counterclockwise(m, b, sortarray[0], sortarray[1], sortarray[2]);
+ if (area == 0.0) {
+ /* Three collinear vertices; the triangulation is two edges. */
+ setorg(midtri, sortarray[0]);
+ setdest(midtri, sortarray[1]);
+ setorg(tri1, sortarray[1]);
+ setdest(tri1, sortarray[0]);
+ setorg(tri2, sortarray[2]);
+ setdest(tri2, sortarray[1]);
+ setorg(tri3, sortarray[1]);
+ setdest(tri3, sortarray[2]);
+ /* All apices are intentionally left NULL. */
+ bond(midtri, tri1);
+ bond(tri2, tri3);
+ lnextself(midtri);
+ lprevself(tri1);
+ lnextself(tri2);
+ lprevself(tri3);
+ bond(midtri, tri3);
+ bond(tri1, tri2);
+ lnextself(midtri);
+ lprevself(tri1);
+ lnextself(tri2);
+ lprevself(tri3);
+ bond(midtri, tri1);
+ bond(tri2, tri3);
+ /* Ensure that the origin of `farleft' is sortarray[0]. */
+ otricopy(tri1, *farleft);
+ /* Ensure that the destination of `farright' is sortarray[2]. */
+ otricopy(tri2, *farright);
+ } else {
+ /* The three vertices are not collinear; the triangulation is one */
+ /* triangle, namely `midtri'. */
+ setorg(midtri, sortarray[0]);
+ setdest(tri1, sortarray[0]);
+ setorg(tri3, sortarray[0]);
+ /* Apices of tri1, tri2, and tri3 are left NULL. */
+ if (area > 0.0) {
+ /* The vertices are in counterclockwise order. */
+ setdest(midtri, sortarray[1]);
+ setorg(tri1, sortarray[1]);
+ setdest(tri2, sortarray[1]);
+ setapex(midtri, sortarray[2]);
+ setorg(tri2, sortarray[2]);
+ setdest(tri3, sortarray[2]);
+ } else {
+ /* The vertices are in clockwise order. */
+ setdest(midtri, sortarray[2]);
+ setorg(tri1, sortarray[2]);
+ setdest(tri2, sortarray[2]);
+ setapex(midtri, sortarray[1]);
+ setorg(tri2, sortarray[1]);
+ setdest(tri3, sortarray[1]);
+ }
+ /* The topology does not depend on how the vertices are ordered. */
+ bond(midtri, tri1);
+ lnextself(midtri);
+ bond(midtri, tri2);
+ lnextself(midtri);
+ bond(midtri, tri3);
+ lprevself(tri1);
+ lnextself(tri2);
+ bond(tri1, tri2);
+ lprevself(tri1);
+ lprevself(tri3);
+ bond(tri1, tri3);
+ lnextself(tri2);
+ lprevself(tri3);
+ bond(tri2, tri3);
+ /* Ensure that the origin of `farleft' is sortarray[0]. */
+ otricopy(tri1, *farleft);
+ /* Ensure that the destination of `farright' is sortarray[2]. */
+ if (area > 0.0) {
+ otricopy(tri2, *farright);
+ } else {
+ lnext(*farleft, *farright);
+ }
+ }
+ if (b->verbose > 2) {
+ printf(" Creating ");
+ printtriangle(m, b, &midtri);
+ printf(" Creating ");
+ printtriangle(m, b, &tri1);
+ printf(" Creating ");
+ printtriangle(m, b, &tri2);
+ printf(" Creating ");
+ printtriangle(m, b, &tri3);
+ }
+ return;
+ } else {
+ /* Split the vertices in half. */
+ divider = vertices >> 1;
+ /* Recursively triangulate each half. */
+ divconqrecurse(m, b, sortarray, divider, 1 - axis, farleft, &innerleft);
+ divconqrecurse(m, b, &sortarray[divider], vertices - divider, 1 - axis,
+ &innerright, farright);
+ if (b->verbose > 1) {
+ printf(" Joining triangulations with %d and %d vertices.\n", divider,
+ vertices - divider);
+ }
+ /* Merge the two triangulations into one. */
+ mergehulls(m, b, farleft, &innerleft, &innerright, farright, axis);
+ }
+}
+
+#ifdef ANSI_DECLARATORS
+long removeghosts(struct mesh *m, struct behavior *b, struct otri *startghost)
+#else /* not ANSI_DECLARATORS */
+long removeghosts(m, b, startghost)
+struct mesh *m;
+struct behavior *b;
+struct otri *startghost;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ struct otri searchedge;
+ struct otri dissolveedge;
+ struct otri deadtriangle;
+ vertex markorg;
+ long hullsize;
+ triangle ptr; /* Temporary variable used by sym(). */
+
+ if (b->verbose) {
+ printf(" Removing ghost triangles.\n");
+ }
+ /* Find an edge on the convex hull to start point location from. */
+ lprev(*startghost, searchedge);
+ symself(searchedge);
+ m->dummytri[0] = encode(searchedge);
+ /* Remove the bounding box and count the convex hull edges. */
+ otricopy(*startghost, dissolveedge);
+ hullsize = 0;
+ do {
+ hullsize++;
+ lnext(dissolveedge, deadtriangle);
+ lprevself(dissolveedge);
+ symself(dissolveedge);
+ /* If no PSLG is involved, set the boundary markers of all the vertices */
+ /* on the convex hull. If a PSLG is used, this step is done later. */
+ if (!b->poly) {
+ /* Watch out for the case where all the input vertices are collinear. */
+ if (dissolveedge.tri != m->dummytri) {
+ org(dissolveedge, markorg);
+ if (vertexmark(markorg) == 0) {
+ setvertexmark(markorg, 1);
+ }
+ }
+ }
+ /* Remove a bounding triangle from a convex hull triangle. */
+ dissolve(dissolveedge);
+ /* Find the next bounding triangle. */
+ sym(deadtriangle, dissolveedge);
+ /* Delete the bounding triangle. */
+ triangledealloc(m, deadtriangle.tri);
+ } while (!otriequal(dissolveedge, *startghost));
+ return hullsize;
+}
+
+/*****************************************************************************/
+/* */
+/* divconqdelaunay() Form a Delaunay triangulation by the divide-and- */
+/* conquer method. */
+/* */
+/* Sorts the vertices, calls a recursive procedure to triangulate them, and */
+/* removes the bounding box, setting boundary markers as appropriate. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+long divconqdelaunay(struct mesh *m, struct behavior *b)
+#else /* not ANSI_DECLARATORS */
+long divconqdelaunay(m, b)
+struct mesh *m;
+struct behavior *b;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ vertex *sortarray;
+ struct otri hullleft, hullright;
+ int divider;
+ int i, j;
+
+ if (b->verbose) {
+ printf(" Sorting vertices.\n");
+ }
+
+ /* Allocate an array of pointers to vertices for sorting. */
+ sortarray = (vertex *) trimalloc(m->invertices * (int) sizeof(vertex));
+ traversalinit(&m->vertices);
+ for (i = 0; i < m->invertices; i++) {
+ sortarray[i] = vertextraverse(m);
+ }
+ /* Sort the vertices. */
+ vertexsort(sortarray, m->invertices);
+ /* Discard duplicate vertices, which can really mess up the algorithm. */
+ i = 0;
+ for (j = 1; j < m->invertices; j++) {
+ if ((sortarray[i][0] == sortarray[j][0])
+ && (sortarray[i][1] == sortarray[j][1])) {
+ if (!b->quiet) {
+ printf(
+"Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n",
+ sortarray[j][0], sortarray[j][1]);
+ }
+ setvertextype(sortarray[j], UNDEADVERTEX);
+ m->undeads++;
+ } else {
+ i++;
+ sortarray[i] = sortarray[j];
+ }
+ }
+ i++;
+ if (b->dwyer) {
+ /* Re-sort the array of vertices to accommodate alternating cuts. */
+ divider = i >> 1;
+ if (i - divider >= 2) {
+ if (divider >= 2) {
+ alternateaxes(sortarray, divider, 1);
+ }
+ alternateaxes(&sortarray[divider], i - divider, 1);
+ }
+ }
+
+ if (b->verbose) {
+ printf(" Forming triangulation.\n");
+ }
+
+ /* Form the Delaunay triangulation. */
+ divconqrecurse(m, b, sortarray, i, 0, &hullleft, &hullright);
+ trifree((VOID *) sortarray);
+
+ return removeghosts(m, b, &hullleft);
+}
+
+/** **/
+/** **/
+/********* Divide-and-conquer Delaunay triangulation ends here *********/
+
+/********* Incremental Delaunay triangulation begins here *********/
+/** **/
+/** **/
+
+/*****************************************************************************/
+/* */
+/* boundingbox() Form an "infinite" bounding triangle to insert vertices */
+/* into. */
+/* */
+/* The vertices at "infinity" are assigned finite coordinates, which are */
+/* used by the point location routines, but (mostly) ignored by the */
+/* Delaunay edge flip routines. */
+/* */
+/*****************************************************************************/
+
+#ifndef REDUCED
+
+#ifdef ANSI_DECLARATORS
+void boundingbox(struct mesh *m, struct behavior *b)
+#else /* not ANSI_DECLARATORS */
+void boundingbox(m, b)
+struct mesh *m;
+struct behavior *b;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ struct otri inftri; /* Handle for the triangular bounding box. */
+ REAL width;
+
+ if (b->verbose) {
+ printf(" Creating triangular bounding box.\n");
+ }
+ /* Find the width (or height, whichever is larger) of the triangulation. */
+ width = m->xmax - m->xmin;
+ if (m->ymax - m->ymin > width) {
+ width = m->ymax - m->ymin;
+ }
+ if (width == 0.0) {
+ width = 1.0;
+ }
+ /* Create the vertices of the bounding box. */
+ m->infvertex1 = (vertex) trimalloc(m->vertices.itembytes);
+ m->infvertex2 = (vertex) trimalloc(m->vertices.itembytes);
+ m->infvertex3 = (vertex) trimalloc(m->vertices.itembytes);
+ m->infvertex1[0] = m->xmin - 50.0 * width;
+ m->infvertex1[1] = m->ymin - 40.0 * width;
+ m->infvertex2[0] = m->xmax + 50.0 * width;
+ m->infvertex2[1] = m->ymin - 40.0 * width;
+ m->infvertex3[0] = 0.5 * (m->xmin + m->xmax);
+ m->infvertex3[1] = m->ymax + 60.0 * width;
+
+ /* Create the bounding box. */
+ maketriangle(m, b, &inftri);
+ setorg(inftri, m->infvertex1);
+ setdest(inftri, m->infvertex2);
+ setapex(inftri, m->infvertex3);
+ /* Link dummytri to the bounding box so we can always find an */
+ /* edge to begin searching (point location) from. */
+ m->dummytri[0] = (triangle) inftri.tri;
+ if (b->verbose > 2) {
+ printf(" Creating ");
+ printtriangle(m, b, &inftri);
+ }
+}
+
+#endif /* not REDUCED */
+
+/*****************************************************************************/
+/* */
+/* removebox() Remove the "infinite" bounding triangle, setting boundary */
+/* markers as appropriate. */
+/* */
+/* The triangular bounding box has three boundary triangles (one for each */
+/* side of the bounding box), and a bunch of triangles fanning out from */
+/* the three bounding box vertices (one triangle for each edge of the */
+/* convex hull of the inner mesh). This routine removes these triangles. */
+/* */
+/* Returns the number of edges on the convex hull of the triangulation. */
+/* */
+/*****************************************************************************/
+
+#ifndef REDUCED
+
+#ifdef ANSI_DECLARATORS
+long removebox(struct mesh *m, struct behavior *b)
+#else /* not ANSI_DECLARATORS */
+long removebox(m, b)
+struct mesh *m;
+struct behavior *b;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ struct otri deadtriangle;
+ struct otri searchedge;
+ struct otri checkedge;
+ struct otri nextedge, finaledge, dissolveedge;
+ vertex markorg;
+ long hullsize;
+ triangle ptr; /* Temporary variable used by sym(). */
+
+ if (b->verbose) {
+ printf(" Removing triangular bounding box.\n");
+ }
+ /* Find a boundary triangle. */
+ nextedge.tri = m->dummytri;
+ nextedge.orient = 0;
+ symself(nextedge);
+ /* Mark a place to stop. */
+ lprev(nextedge, finaledge);
+ lnextself(nextedge);
+ symself(nextedge);
+ /* Find a triangle (on the boundary of the vertex set) that isn't */
+ /* a bounding box triangle. */
+ lprev(nextedge, searchedge);
+ symself(searchedge);
+ /* Check whether nextedge is another boundary triangle */
+ /* adjacent to the first one. */
+ lnext(nextedge, checkedge);
+ symself(checkedge);
+ if (checkedge.tri == m->dummytri) {
+ /* Go on to the next triangle. There are only three boundary */
+ /* triangles, and this next triangle cannot be the third one, */
+ /* so it's safe to stop here. */
+ lprevself(searchedge);
+ symself(searchedge);
+ }
+ /* Find a new boundary edge to search from, as the current search */
+ /* edge lies on a bounding box triangle and will be deleted. */
+ m->dummytri[0] = encode(searchedge);
+ hullsize = -2l;
+ while (!otriequal(nextedge, finaledge)) {
+ hullsize++;
+ lprev(nextedge, dissolveedge);
+ symself(dissolveedge);
+ /* If not using a PSLG, the vertices should be marked now. */
+ /* (If using a PSLG, markhull() will do the job.) */
+ if (!b->poly) {
+ /* Be careful! One must check for the case where all the input */
+ /* vertices are collinear, and thus all the triangles are part of */
+ /* the bounding box. Otherwise, the setvertexmark() call below */
+ /* will cause a bad pointer reference. */
+ if (dissolveedge.tri != m->dummytri) {
+ org(dissolveedge, markorg);
+ if (vertexmark(markorg) == 0) {
+ setvertexmark(markorg, 1);
+ }
+ }
+ }
+ /* Disconnect the bounding box triangle from the mesh triangle. */
+ dissolve(dissolveedge);
+ lnext(nextedge, deadtriangle);
+ sym(deadtriangle, nextedge);
+ /* Get rid of the bounding box triangle. */
+ triangledealloc(m, deadtriangle.tri);
+ /* Do we need to turn the corner? */
+ if (nextedge.tri == m->dummytri) {
+ /* Turn the corner. */
+ otricopy(dissolveedge, nextedge);
+ }
+ }
+ triangledealloc(m, finaledge.tri);
+
+ trifree((VOID *) m->infvertex1); /* Deallocate the bounding box vertices. */
+ trifree((VOID *) m->infvertex2);
+ trifree((VOID *) m->infvertex3);
+
+ return hullsize;
+}
+
+#endif /* not REDUCED */
+
+/*****************************************************************************/
+/* */
+/* incrementaldelaunay() Form a Delaunay triangulation by incrementally */
+/* inserting vertices. */
+/* */
+/* Returns the number of edges on the convex hull of the triangulation. */
+/* */
+/*****************************************************************************/
+
+#ifndef REDUCED
+
+#ifdef ANSI_DECLARATORS
+long incrementaldelaunay(struct mesh *m, struct behavior *b)
+#else /* not ANSI_DECLARATORS */
+long incrementaldelaunay(m, b)
+struct mesh *m;
+struct behavior *b;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ struct otri starttri;
+ vertex vertexloop;
+
+ /* Create a triangular bounding box. */
+ boundingbox(m, b);
+ if (b->verbose) {
+ printf(" Incrementally inserting vertices.\n");
+ }
+ traversalinit(&m->vertices);
+ vertexloop = vertextraverse(m);
+ while (vertexloop != (vertex) NULL) {
+ starttri.tri = m->dummytri;
+ if (insertvertex(m, b, vertexloop, &starttri, (struct osub *) NULL, 0, 0)
+ == DUPLICATEVERTEX) {
+ if (!b->quiet) {
+ printf(
+"Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n",
+ vertexloop[0], vertexloop[1]);
+ }
+ setvertextype(vertexloop, UNDEADVERTEX);
+ m->undeads++;
+ }
+ vertexloop = vertextraverse(m);
+ }
+ /* Remove the bounding box. */
+ return removebox(m, b);
+}
+
+#endif /* not REDUCED */
+
+/** **/
+/** **/
+/********* Incremental Delaunay triangulation ends here *********/
+
+/********* Sweepline Delaunay triangulation begins here *********/
+/** **/
+/** **/
+
+#ifndef REDUCED
+
+#ifdef ANSI_DECLARATORS
+void eventheapinsert(struct event **heap, int heapsize, struct event *newevent)
+#else /* not ANSI_DECLARATORS */
+void eventheapinsert(heap, heapsize, newevent)
+struct event **heap;
+int heapsize;
+struct event *newevent;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ REAL eventx, eventy;
+ int eventnum;
+ int parent;
+ int notdone;
+
+ eventx = newevent->xkey;
+ eventy = newevent->ykey;
+ eventnum = heapsize;
+ notdone = eventnum > 0;
+ while (notdone) {
+ parent = (eventnum - 1) >> 1;
+ if ((heap[parent]->ykey < eventy) ||
+ ((heap[parent]->ykey == eventy)
+ && (heap[parent]->xkey <= eventx))) {
+ notdone = 0;
+ } else {
+ heap[eventnum] = heap[parent];
+ heap[eventnum]->heapposition = eventnum;
+
+ eventnum = parent;
+ notdone = eventnum > 0;
+ }
+ }
+ heap[eventnum] = newevent;
+ newevent->heapposition = eventnum;
+}
+
+#endif /* not REDUCED */
+
+#ifndef REDUCED
+
+#ifdef ANSI_DECLARATORS
+void eventheapify(struct event **heap, int heapsize, int eventnum)
+#else /* not ANSI_DECLARATORS */
+void eventheapify(heap, heapsize, eventnum)
+struct event **heap;
+int heapsize;
+int eventnum;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ struct event *thisevent;
+ REAL eventx, eventy;
+ int leftchild, rightchild;
+ int smallest;
+ int notdone;
+
+ thisevent = heap[eventnum];
+ eventx = thisevent->xkey;
+ eventy = thisevent->ykey;
+ leftchild = 2 * eventnum + 1;
+ notdone = leftchild < heapsize;
+ while (notdone) {
+ if ((heap[leftchild]->ykey < eventy) ||
+ ((heap[leftchild]->ykey == eventy)
+ && (heap[leftchild]->xkey < eventx))) {
+ smallest = leftchild;
+ } else {
+ smallest = eventnum;
+ }
+ rightchild = leftchild + 1;
+ if (rightchild < heapsize) {
+ if ((heap[rightchild]->ykey < heap[smallest]->ykey) ||
+ ((heap[rightchild]->ykey == heap[smallest]->ykey)
+ && (heap[rightchild]->xkey < heap[smallest]->xkey))) {
+ smallest = rightchild;
+ }
+ }
+ if (smallest == eventnum) {
+ notdone = 0;
+ } else {
+ heap[eventnum] = heap[smallest];
+ heap[eventnum]->heapposition = eventnum;
+ heap[smallest] = thisevent;
+ thisevent->heapposition = smallest;
+
+ eventnum = smallest;
+ leftchild = 2 * eventnum + 1;
+ notdone = leftchild < heapsize;
+ }
+ }
+}
+
+#endif /* not REDUCED */
+
+#ifndef REDUCED
+
+#ifdef ANSI_DECLARATORS
+void eventheapdelete(struct event **heap, int heapsize, int eventnum)
+#else /* not ANSI_DECLARATORS */
+void eventheapdelete(heap, heapsize, eventnum)
+struct event **heap;
+int heapsize;
+int eventnum;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ struct event *moveevent;
+ REAL eventx, eventy;
+ int parent;
+ int notdone;
+
+ moveevent = heap[heapsize - 1];
+ if (eventnum > 0) {
+ eventx = moveevent->xkey;
+ eventy = moveevent->ykey;
+ do {
+ parent = (eventnum - 1) >> 1;
+ if ((heap[parent]->ykey < eventy) ||
+ ((heap[parent]->ykey == eventy)
+ && (heap[parent]->xkey <= eventx))) {
+ notdone = 0;
+ } else {
+ heap[eventnum] = heap[parent];
+ heap[eventnum]->heapposition = eventnum;
+
+ eventnum = parent;
+ notdone = eventnum > 0;
+ }
+ } while (notdone);
+ }
+ heap[eventnum] = moveevent;
+ moveevent->heapposition = eventnum;
+ eventheapify(heap, heapsize - 1, eventnum);
+}
+
+#endif /* not REDUCED */
+
+#ifndef REDUCED
+
+#ifdef ANSI_DECLARATORS
+void createeventheap(struct mesh *m, struct event ***eventheap,
+ struct event **events, struct event **freeevents)
+#else /* not ANSI_DECLARATORS */
+void createeventheap(m, eventheap, events, freeevents)
+struct mesh *m;
+struct event ***eventheap;
+struct event **events;
+struct event **freeevents;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ vertex thisvertex;
+ int maxevents;
+ int i;
+
+ maxevents = (3 * m->invertices) / 2;
+ *eventheap = (struct event **) trimalloc(maxevents *
+ (int) sizeof(struct event *));
+ *events = (struct event *) trimalloc(maxevents * (int) sizeof(struct event));
+ traversalinit(&m->vertices);
+ for (i = 0; i < m->invertices; i++) {
+ thisvertex = vertextraverse(m);
+ (*events)[i].eventptr = (VOID *) thisvertex;
+ (*events)[i].xkey = thisvertex[0];
+ (*events)[i].ykey = thisvertex[1];
+ eventheapinsert(*eventheap, i, *events + i);
+ }
+ *freeevents = (struct event *) NULL;
+ for (i = maxevents - 1; i >= m->invertices; i--) {
+ (*events)[i].eventptr = (VOID *) *freeevents;
+ *freeevents = *events + i;
+ }
+}
+
+#endif /* not REDUCED */
+
+#ifndef REDUCED
+
+#ifdef ANSI_DECLARATORS
+int rightofhyperbola(struct mesh *m, struct otri *fronttri, vertex newsite)
+#else /* not ANSI_DECLARATORS */
+int rightofhyperbola(m, fronttri, newsite)
+struct mesh *m;
+struct otri *fronttri;
+vertex newsite;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ vertex leftvertex, rightvertex;
+ REAL dxa, dya, dxb, dyb;
+
+ m->hyperbolacount++;
+
+ dest(*fronttri, leftvertex);
+ apex(*fronttri, rightvertex);
+ if ((leftvertex[1] < rightvertex[1]) ||
+ ((leftvertex[1] == rightvertex[1]) &&
+ (leftvertex[0] < rightvertex[0]))) {
+ if (newsite[0] >= rightvertex[0]) {
+ return 1;
+ }
+ } else {
+ if (newsite[0] <= leftvertex[0]) {
+ return 0;
+ }
+ }
+ dxa = leftvertex[0] - newsite[0];
+ dya = leftvertex[1] - newsite[1];
+ dxb = rightvertex[0] - newsite[0];
+ dyb = rightvertex[1] - newsite[1];
+ return dya * (dxb * dxb + dyb * dyb) > dyb * (dxa * dxa + dya * dya);
+}
+
+#endif /* not REDUCED */
+
+#ifndef REDUCED
+
+#ifdef ANSI_DECLARATORS
+REAL circletop(struct mesh *m, vertex pa, vertex pb, vertex pc, REAL ccwabc)
+#else /* not ANSI_DECLARATORS */
+REAL circletop(m, pa, pb, pc, ccwabc)
+struct mesh *m;
+vertex pa;
+vertex pb;
+vertex pc;
+REAL ccwabc;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ REAL xac, yac, xbc, ybc, xab, yab;
+ REAL aclen2, bclen2, ablen2;
+
+ m->circletopcount++;
+
+ xac = pa[0] - pc[0];
+ yac = pa[1] - pc[1];
+ xbc = pb[0] - pc[0];
+ ybc = pb[1] - pc[1];
+ xab = pa[0] - pb[0];
+ yab = pa[1] - pb[1];
+ aclen2 = xac * xac + yac * yac;
+ bclen2 = xbc * xbc + ybc * ybc;
+ ablen2 = xab * xab + yab * yab;
+ return pc[1] + (xac * bclen2 - xbc * aclen2 + sqrt(aclen2 * bclen2 * ablen2))
+ / (2.0 * ccwabc);
+}
+
+#endif /* not REDUCED */
+
+#ifndef REDUCED
+
+#ifdef ANSI_DECLARATORS
+void check4deadevent(struct otri *checktri, struct event **freeevents,
+ struct event **eventheap, int *heapsize)
+#else /* not ANSI_DECLARATORS */
+void check4deadevent(checktri, freeevents, eventheap, heapsize)
+struct otri *checktri;
+struct event **freeevents;
+struct event **eventheap;
+int *heapsize;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ struct event *deadevent;
+ vertex eventvertex;
+ int eventnum;
+
+ org(*checktri, eventvertex);
+ if (eventvertex != (vertex) NULL) {
+ deadevent = (struct event *) eventvertex;
+ eventnum = deadevent->heapposition;
+ deadevent->eventptr = (VOID *) *freeevents;
+ *freeevents = deadevent;
+ eventheapdelete(eventheap, *heapsize, eventnum);
+ (*heapsize)--;
+ setorg(*checktri, NULL);
+ }
+}
+
+#endif /* not REDUCED */
+
+#ifndef REDUCED
+
+#ifdef ANSI_DECLARATORS
+struct splaynode *splay(struct mesh *m, struct splaynode *splaytree,
+ vertex searchpoint, struct otri *searchtri)
+#else /* not ANSI_DECLARATORS */
+struct splaynode *splay(m, splaytree, searchpoint, searchtri)
+struct mesh *m;
+struct splaynode *splaytree;
+vertex searchpoint;
+struct otri *searchtri;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ struct splaynode *child, *grandchild;
+ struct splaynode *lefttree, *righttree;
+ struct splaynode *leftright;
+ vertex checkvertex;
+ int rightofroot, rightofchild;
+
+ if (splaytree == (struct splaynode *) NULL) {
+ return (struct splaynode *) NULL;
+ }
+ dest(splaytree->keyedge, checkvertex);
+ if (checkvertex == splaytree->keydest) {
+ rightofroot = rightofhyperbola(m, &splaytree->keyedge, searchpoint);
+ if (rightofroot) {
+ otricopy(splaytree->keyedge, *searchtri);
+ child = splaytree->rchild;
+ } else {
+ child = splaytree->lchild;
+ }
+ if (child == (struct splaynode *) NULL) {
+ return splaytree;
+ }
+ dest(child->keyedge, checkvertex);
+ if (checkvertex != child->keydest) {
+ child = splay(m, child, searchpoint, searchtri);
+ if (child == (struct splaynode *) NULL) {
+ if (rightofroot) {
+ splaytree->rchild = (struct splaynode *) NULL;
+ } else {
+ splaytree->lchild = (struct splaynode *) NULL;
+ }
+ return splaytree;
+ }
+ }
+ rightofchild = rightofhyperbola(m, &child->keyedge, searchpoint);
+ if (rightofchild) {
+ otricopy(child->keyedge, *searchtri);
+ grandchild = splay(m, child->rchild, searchpoint, searchtri);
+ child->rchild = grandchild;
+ } else {
+ grandchild = splay(m, child->lchild, searchpoint, searchtri);
+ child->lchild = grandchild;
+ }
+ if (grandchild == (struct splaynode *) NULL) {
+ if (rightofroot) {
+ splaytree->rchild = child->lchild;
+ child->lchild = splaytree;
+ } else {
+ splaytree->lchild = child->rchild;
+ child->rchild = splaytree;
+ }
+ return child;
+ }
+ if (rightofchild) {
+ if (rightofroot) {
+ splaytree->rchild = child->lchild;
+ child->lchild = splaytree;
+ } else {
+ splaytree->lchild = grandchild->rchild;
+ grandchild->rchild = splaytree;
+ }
+ child->rchild = grandchild->lchild;
+ grandchild->lchild = child;
+ } else {
+ if (rightofroot) {
+ splaytree->rchild = grandchild->lchild;
+ grandchild->lchild = splaytree;
+ } else {
+ splaytree->lchild = child->rchild;
+ child->rchild = splaytree;
+ }
+ child->lchild = grandchild->rchild;
+ grandchild->rchild = child;
+ }
+ return grandchild;
+ } else {
+ lefttree = splay(m, splaytree->lchild, searchpoint, searchtri);
+ righttree = splay(m, splaytree->rchild, searchpoint, searchtri);
+
+ pooldealloc(&m->splaynodes, (VOID *) splaytree);
+ if (lefttree == (struct splaynode *) NULL) {
+ return righttree;
+ } else if (righttree == (struct splaynode *) NULL) {
+ return lefttree;
+ } else if (lefttree->rchild == (struct splaynode *) NULL) {
+ lefttree->rchild = righttree->lchild;
+ righttree->lchild = lefttree;
+ return righttree;
+ } else if (righttree->lchild == (struct splaynode *) NULL) {
+ righttree->lchild = lefttree->rchild;
+ lefttree->rchild = righttree;
+ return lefttree;
+ } else {
+/* printf("Holy Toledo!!!\n"); */
+ leftright = lefttree->rchild;
+ while (leftright->rchild != (struct splaynode *) NULL) {
+ leftright = leftright->rchild;
+ }
+ leftright->rchild = righttree;
+ return lefttree;
+ }
+ }
+}
+
+#endif /* not REDUCED */
+
+#ifndef REDUCED
+
+#ifdef ANSI_DECLARATORS
+struct splaynode *splayinsert(struct mesh *m, struct splaynode *splayroot,
+ struct otri *newkey, vertex searchpoint)
+#else /* not ANSI_DECLARATORS */
+struct splaynode *splayinsert(m, splayroot, newkey, searchpoint)
+struct mesh *m;
+struct splaynode *splayroot;
+struct otri *newkey;
+vertex searchpoint;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ struct splaynode *newsplaynode;
+
+ newsplaynode = (struct splaynode *) poolalloc(&m->splaynodes);
+ otricopy(*newkey, newsplaynode->keyedge);
+ dest(*newkey, newsplaynode->keydest);
+ if (splayroot == (struct splaynode *) NULL) {
+ newsplaynode->lchild = (struct splaynode *) NULL;
+ newsplaynode->rchild = (struct splaynode *) NULL;
+ } else if (rightofhyperbola(m, &splayroot->keyedge, searchpoint)) {
+ newsplaynode->lchild = splayroot;
+ newsplaynode->rchild = splayroot->rchild;
+ splayroot->rchild = (struct splaynode *) NULL;
+ } else {
+ newsplaynode->lchild = splayroot->lchild;
+ newsplaynode->rchild = splayroot;
+ splayroot->lchild = (struct splaynode *) NULL;
+ }
+ return newsplaynode;
+}
+
+#endif /* not REDUCED */
+
+#ifndef REDUCED
+
+#ifdef ANSI_DECLARATORS
+struct splaynode *circletopinsert(struct mesh *m, struct behavior *b,
+ struct splaynode *splayroot,
+ struct otri *newkey,
+ vertex pa, vertex pb, vertex pc, REAL topy)
+#else /* not ANSI_DECLARATORS */
+struct splaynode *circletopinsert(m, b, splayroot, newkey, pa, pb, pc, topy)
+struct mesh *m;
+struct behavior *b;
+struct splaynode *splayroot;
+struct otri *newkey;
+vertex pa;
+vertex pb;
+vertex pc;
+REAL topy;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ REAL ccwabc;
+ REAL xac, yac, xbc, ybc;
+ REAL aclen2, bclen2;
+ REAL searchpoint[2];
+ struct otri dummytri;
+
+ ccwabc = counterclockwise(m, b, pa, pb, pc);
+ xac = pa[0] - pc[0];
+ yac = pa[1] - pc[1];
+ xbc = pb[0] - pc[0];
+ ybc = pb[1] - pc[1];
+ aclen2 = xac * xac + yac * yac;
+ bclen2 = xbc * xbc + ybc * ybc;
+ searchpoint[0] = pc[0] - (yac * bclen2 - ybc * aclen2) / (2.0 * ccwabc);
+ searchpoint[1] = topy;
+ return splayinsert(m, splay(m, splayroot, (vertex) searchpoint, &dummytri),
+ newkey, (vertex) searchpoint);
+}
+
+#endif /* not REDUCED */
+
+#ifndef REDUCED
+
+#ifdef ANSI_DECLARATORS
+struct splaynode *frontlocate(struct mesh *m, struct splaynode *splayroot,
+ struct otri *bottommost, vertex searchvertex,
+ struct otri *searchtri, int *farright)
+#else /* not ANSI_DECLARATORS */
+struct splaynode *frontlocate(m, splayroot, bottommost, searchvertex,
+ searchtri, farright)
+struct mesh *m;
+struct splaynode *splayroot;
+struct otri *bottommost;
+vertex searchvertex;
+struct otri *searchtri;
+int *farright;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ int farrightflag;
+ triangle ptr; /* Temporary variable used by onext(). */
+
+ otricopy(*bottommost, *searchtri);
+ splayroot = splay(m, splayroot, searchvertex, searchtri);
+
+ farrightflag = 0;
+ while (!farrightflag && rightofhyperbola(m, searchtri, searchvertex)) {
+ onextself(*searchtri);
+ farrightflag = otriequal(*searchtri, *bottommost);
+ }
+ *farright = farrightflag;
+ return splayroot;
+}
+
+#endif /* not REDUCED */
+
+#ifndef REDUCED
+
+#ifdef ANSI_DECLARATORS
+long sweeplinedelaunay(struct mesh *m, struct behavior *b)
+#else /* not ANSI_DECLARATORS */
+long sweeplinedelaunay(m, b)
+struct mesh *m;
+struct behavior *b;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ struct event **eventheap;
+ struct event *events;
+ struct event *freeevents;
+ struct event *nextevent;
+ struct event *newevent;
+ struct splaynode *splayroot;
+ struct otri bottommost;
+ struct otri searchtri;
+ struct otri fliptri;
+ struct otri lefttri, righttri, farlefttri, farrighttri;
+ struct otri inserttri;
+ vertex firstvertex, secondvertex;
+ vertex nextvertex, lastvertex;
+ vertex connectvertex;
+ vertex leftvertex, midvertex, rightvertex;
+ REAL lefttest, righttest;
+ int heapsize;
+ int check4events, farrightflag;
+ triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */
+
+ poolinit(&m->splaynodes, sizeof(struct splaynode), SPLAYNODEPERBLOCK,
+ SPLAYNODEPERBLOCK, 0);
+ splayroot = (struct splaynode *) NULL;
+
+ if (b->verbose) {
+ printf(" Placing vertices in event heap.\n");
+ }
+ createeventheap(m, &eventheap, &events, &freeevents);
+ heapsize = m->invertices;
+
+ if (b->verbose) {
+ printf(" Forming triangulation.\n");
+ }
+ maketriangle(m, b, &lefttri);
+ maketriangle(m, b, &righttri);
+ bond(lefttri, righttri);
+ lnextself(lefttri);
+ lprevself(righttri);
+ bond(lefttri, righttri);
+ lnextself(lefttri);
+ lprevself(righttri);
+ bond(lefttri, righttri);
+ firstvertex = (vertex) eventheap[0]->eventptr;
+ eventheap[0]->eventptr = (VOID *) freeevents;
+ freeevents = eventheap[0];
+ eventheapdelete(eventheap, heapsize, 0);
+ heapsize--;
+ do {
+ if (heapsize == 0) {
+ printf("Error: Input vertices are all identical.\n");
+ triexit(1);
+ }
+ secondvertex = (vertex) eventheap[0]->eventptr;
+ eventheap[0]->eventptr = (VOID *) freeevents;
+ freeevents = eventheap[0];
+ eventheapdelete(eventheap, heapsize, 0);
+ heapsize--;
+ if ((firstvertex[0] == secondvertex[0]) &&
+ (firstvertex[1] == secondvertex[1])) {
+ if (!b->quiet) {
+ printf(
+"Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n",
+ secondvertex[0], secondvertex[1]);
+ }
+ setvertextype(secondvertex, UNDEADVERTEX);
+ m->undeads++;
+ }
+ } while ((firstvertex[0] == secondvertex[0]) &&
+ (firstvertex[1] == secondvertex[1]));
+ setorg(lefttri, firstvertex);
+ setdest(lefttri, secondvertex);
+ setorg(righttri, secondvertex);
+ setdest(righttri, firstvertex);
+ lprev(lefttri, bottommost);
+ lastvertex = secondvertex;
+ while (heapsize > 0) {
+ nextevent = eventheap[0];
+ eventheapdelete(eventheap, heapsize, 0);
+ heapsize--;
+ check4events = 1;
+ if (nextevent->xkey < m->xmin) {
+ decode(nextevent->eventptr, fliptri);
+ oprev(fliptri, farlefttri);
+ check4deadevent(&farlefttri, &freeevents, eventheap, &heapsize);
+ onext(fliptri, farrighttri);
+ check4deadevent(&farrighttri, &freeevents, eventheap, &heapsize);
+
+ if (otriequal(farlefttri, bottommost)) {
+ lprev(fliptri, bottommost);
+ }
+ flip(m, b, &fliptri);
+ setapex(fliptri, NULL);
+ lprev(fliptri, lefttri);
+ lnext(fliptri, righttri);
+ sym(lefttri, farlefttri);
+
+ if (randomnation(SAMPLERATE) == 0) {
+ symself(fliptri);
+ dest(fliptri, leftvertex);
+ apex(fliptri, midvertex);
+ org(fliptri, rightvertex);
+ splayroot = circletopinsert(m, b, splayroot, &lefttri, leftvertex,
+ midvertex, rightvertex, nextevent->ykey);
+ }
+ } else {
+ nextvertex = (vertex) nextevent->eventptr;
+ if ((nextvertex[0] == lastvertex[0]) &&
+ (nextvertex[1] == lastvertex[1])) {
+ if (!b->quiet) {
+ printf(
+"Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n",
+ nextvertex[0], nextvertex[1]);
+ }
+ setvertextype(nextvertex, UNDEADVERTEX);
+ m->undeads++;
+ check4events = 0;
+ } else {
+ lastvertex = nextvertex;
+
+ splayroot = frontlocate(m, splayroot, &bottommost, nextvertex,
+ &searchtri, &farrightflag);
+/*
+ otricopy(bottommost, searchtri);
+ farrightflag = 0;
+ while (!farrightflag && rightofhyperbola(m, &searchtri, nextvertex)) {
+ onextself(searchtri);
+ farrightflag = otriequal(searchtri, bottommost);
+ }
+*/
+
+ check4deadevent(&searchtri, &freeevents, eventheap, &heapsize);
+
+ otricopy(searchtri, farrighttri);
+ sym(searchtri, farlefttri);
+ maketriangle(m, b, &lefttri);
+ maketriangle(m, b, &righttri);
+ dest(farrighttri, connectvertex);
+ setorg(lefttri, connectvertex);
+ setdest(lefttri, nextvertex);
+ setorg(righttri, nextvertex);
+ setdest(righttri, connectvertex);
+ bond(lefttri, righttri);
+ lnextself(lefttri);
+ lprevself(righttri);
+ bond(lefttri, righttri);
+ lnextself(lefttri);
+ lprevself(righttri);
+ bond(lefttri, farlefttri);
+ bond(righttri, farrighttri);
+ if (!farrightflag && otriequal(farrighttri, bottommost)) {
+ otricopy(lefttri, bottommost);
+ }
+
+ if (randomnation(SAMPLERATE) == 0) {
+ splayroot = splayinsert(m, splayroot, &lefttri, nextvertex);
+ } else if (randomnation(SAMPLERATE) == 0) {
+ lnext(righttri, inserttri);
+ splayroot = splayinsert(m, splayroot, &inserttri, nextvertex);
+ }
+ }
+ }
+ nextevent->eventptr = (VOID *) freeevents;
+ freeevents = nextevent;
+
+ if (check4events) {
+ apex(farlefttri, leftvertex);
+ dest(lefttri, midvertex);
+ apex(lefttri, rightvertex);
+ lefttest = counterclockwise(m, b, leftvertex, midvertex, rightvertex);
+ if (lefttest > 0.0) {
+ newevent = freeevents;
+ freeevents = (struct event *) freeevents->eventptr;
+ newevent->xkey = m->xminextreme;
+ newevent->ykey = circletop(m, leftvertex, midvertex, rightvertex,
+ lefttest);
+ newevent->eventptr = (VOID *) encode(lefttri);
+ eventheapinsert(eventheap, heapsize, newevent);
+ heapsize++;
+ setorg(lefttri, newevent);
+ }
+ apex(righttri, leftvertex);
+ org(righttri, midvertex);
+ apex(farrighttri, rightvertex);
+ righttest = counterclockwise(m, b, leftvertex, midvertex, rightvertex);
+ if (righttest > 0.0) {
+ newevent = freeevents;
+ freeevents = (struct event *) freeevents->eventptr;
+ newevent->xkey = m->xminextreme;
+ newevent->ykey = circletop(m, leftvertex, midvertex, rightvertex,
+ righttest);
+ newevent->eventptr = (VOID *) encode(farrighttri);
+ eventheapinsert(eventheap, heapsize, newevent);
+ heapsize++;
+ setorg(farrighttri, newevent);
+ }
+ }
+ }
+
+ pooldeinit(&m->splaynodes);
+ lprevself(bottommost);
+ return removeghosts(m, b, &bottommost);
+}
+
+#endif /* not REDUCED */
+
+/** **/
+/** **/
+/********* Sweepline Delaunay triangulation ends here *********/
+
+/********* General mesh construction routines begin here *********/
+/** **/
+/** **/
+
+/*****************************************************************************/
+/* */
+/* delaunay() Form a Delaunay triangulation. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+long delaunay(struct mesh *m, struct behavior *b)
+#else /* not ANSI_DECLARATORS */
+long delaunay(m, b)
+struct mesh *m;
+struct behavior *b;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ long hulledges;
+
+ m->eextras = 0;
+ initializetrisubpools(m, b);
+
+#ifdef REDUCED
+ if (!b->quiet) {
+ printf(
+ "Constructing Delaunay triangulation by divide-and-conquer method.\n");
+ }
+ hulledges = divconqdelaunay(m, b);
+#else /* not REDUCED */
+ if (!b->quiet) {
+ printf("Constructing Delaunay triangulation ");
+ if (b->incremental) {
+ printf("by incremental method.\n");
+ } else if (b->sweepline) {
+ printf("by sweepline method.\n");
+ } else {
+ printf("by divide-and-conquer method.\n");
+ }
+ }
+ if (b->incremental) {
+ hulledges = incrementaldelaunay(m, b);
+ } else if (b->sweepline) {
+ hulledges = sweeplinedelaunay(m, b);
+ } else {
+ hulledges = divconqdelaunay(m, b);
+ }
+#endif /* not REDUCED */
+
+ if (m->triangles.items == 0) {
+ /* The input vertices were all collinear, so there are no triangles. */
+ return 0l;
+ } else {
+ return hulledges;
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* reconstruct() Reconstruct a triangulation from its .ele (and possibly */
+/* .poly) file. Used when the -r switch is used. */
+/* */
+/* Reads an .ele file and reconstructs the original mesh. If the -p switch */
+/* is used, this procedure will also read a .poly file and reconstruct the */
+/* subsegments of the original mesh. If the -a switch is used, this */
+/* procedure will also read an .area file and set a maximum area constraint */
+/* on each triangle. */
+/* */
+/* Vertices that are not corners of triangles, such as nodes on edges of */
+/* subparametric elements, are discarded. */
+/* */
+/* This routine finds the adjacencies between triangles (and subsegments) */
+/* by forming one stack of triangles for each vertex. Each triangle is on */
+/* three different stacks simultaneously. Each triangle's subsegment */
+/* pointers are used to link the items in each stack. This memory-saving */
+/* feature makes the code harder to read. The most important thing to keep */
+/* in mind is that each triangle is removed from a stack precisely when */
+/* the corresponding pointer is adjusted to refer to a subsegment rather */
+/* than the next triangle of the stack. */
+/* */
+/*****************************************************************************/
+
+#ifndef CDT_ONLY
+
+#ifdef TRILIBRARY
+
+#ifdef ANSI_DECLARATORS
+int reconstruct(struct mesh *m, struct behavior *b, int *trianglelist,
+ REAL *triangleattriblist, REAL *trianglearealist,
+ int elements, int corners, int attribs,
+ int *segmentlist,int *segmentmarkerlist, int numberofsegments)
+#else /* not ANSI_DECLARATORS */
+int reconstruct(m, b, trianglelist, triangleattriblist, trianglearealist,
+ elements, corners, attribs, segmentlist, segmentmarkerlist,
+ numberofsegments)
+struct mesh *m;
+struct behavior *b;
+int *trianglelist;
+REAL *triangleattriblist;
+REAL *trianglearealist;
+int elements;
+int corners;
+int attribs;
+int *segmentlist;
+int *segmentmarkerlist;
+int numberofsegments;
+#endif /* not ANSI_DECLARATORS */
+
+#else /* not TRILIBRARY */
+
+#ifdef ANSI_DECLARATORS
+long reconstruct(struct mesh *m, struct behavior *b, char *elefilename,
+ char *areafilename, char *polyfilename, FILE *polyfile)
+#else /* not ANSI_DECLARATORS */
+long reconstruct(m, b, elefilename, areafilename, polyfilename, polyfile)
+struct mesh *m;
+struct behavior *b;
+char *elefilename;
+char *areafilename;
+char *polyfilename;
+FILE *polyfile;
+#endif /* not ANSI_DECLARATORS */
+
+#endif /* not TRILIBRARY */
+
+{
+#ifdef TRILIBRARY
+ int vertexindex;
+ int attribindex;
+#else /* not TRILIBRARY */
+ FILE *elefile;
+ FILE *areafile;
+ char inputline[INPUTLINESIZE];
+ char *stringptr;
+ int areaelements;
+#endif /* not TRILIBRARY */
+ struct otri triangleloop;
+ struct otri triangleleft;
+ struct otri checktri;
+ struct otri checkleft;
+ struct otri checkneighbor;
+ struct osub subsegloop;
+ triangle *vertexarray;
+ triangle *prevlink;
+ triangle nexttri;
+ vertex tdest, tapex;
+ vertex checkdest, checkapex;
+ vertex shorg;
+ vertex killvertex;
+ vertex segmentorg, segmentdest;
+ REAL area;
+ int corner[3];
+ int end[2];
+ int killvertexindex;
+ int incorners;
+ int segmentmarkers;
+ int boundmarker;
+ int aroundvertex;
+ long hullsize;
+ int notfound;
+ long elementnumber, segmentnumber;
+ int i, j;
+ triangle ptr; /* Temporary variable used by sym(). */
+
+#ifdef TRILIBRARY
+ m->inelements = elements;
+ incorners = corners;
+ if (incorners < 3) {
+ printf("Error: Triangles must have at least 3 vertices.\n");
+ triexit(1);
+ }
+ m->eextras = attribs;
+#else /* not TRILIBRARY */
+ /* Read the triangles from an .ele file. */
+ if (!b->quiet) {
+ printf("Opening %s.\n", elefilename);
+ }
+ elefile = fopen(elefilename, "r");
+ if (elefile == (FILE *) NULL) {
+ printf(" Error: Cannot access file %s.\n", elefilename);
+ triexit(1);
+ }
+ /* Read number of triangles, number of vertices per triangle, and */
+ /* number of triangle attributes from .ele file. */
+ stringptr = readline(inputline, elefile, elefilename);
+ m->inelements = (int) strtol(stringptr, &stringptr, 0);
+ stringptr = findfield(stringptr);
+ if (*stringptr == '\0') {
+ incorners = 3;
+ } else {
+ incorners = (int) strtol(stringptr, &stringptr, 0);
+ if (incorners < 3) {
+ printf("Error: Triangles in %s must have at least 3 vertices.\n",
+ elefilename);
+ triexit(1);
+ }
+ }
+ stringptr = findfield(stringptr);
+ if (*stringptr == '\0') {
+ m->eextras = 0;
+ } else {
+ m->eextras = (int) strtol(stringptr, &stringptr, 0);
+ }
+#endif /* not TRILIBRARY */
+
+ initializetrisubpools(m, b);
+
+ /* Create the triangles. */
+ for (elementnumber = 1; elementnumber <= m->inelements; elementnumber++) {
+ maketriangle(m, b, &triangleloop);
+ /* Mark the triangle as living. */
+ triangleloop.tri[3] = (triangle) triangleloop.tri;
+ }
+
+ segmentmarkers = 0;
+ if (b->poly) {
+#ifdef TRILIBRARY
+ m->insegments = numberofsegments;
+ segmentmarkers = segmentmarkerlist != (int *) NULL;
+#else /* not TRILIBRARY */
+ /* Read number of segments and number of segment */
+ /* boundary markers from .poly file. */
+ stringptr = readline(inputline, polyfile, b->inpolyfilename);
+ m->insegments = (int) strtol(stringptr, &stringptr, 0);
+ stringptr = findfield(stringptr);
+ if (*stringptr != '\0') {
+ segmentmarkers = (int) strtol(stringptr, &stringptr, 0);
+ }
+#endif /* not TRILIBRARY */
+
+ /* Create the subsegments. */
+ for (segmentnumber = 1; segmentnumber <= m->insegments; segmentnumber++) {
+ makesubseg(m, &subsegloop);
+ /* Mark the subsegment as living. */
+ subsegloop.ss[2] = (subseg) subsegloop.ss;
+ }
+ }
+
+#ifdef TRILIBRARY
+ vertexindex = 0;
+ attribindex = 0;
+#else /* not TRILIBRARY */
+ if (b->vararea) {
+ /* Open an .area file, check for consistency with the .ele file. */
+ if (!b->quiet) {
+ printf("Opening %s.\n", areafilename);
+ }
+ areafile = fopen(areafilename, "r");
+ if (areafile == (FILE *) NULL) {
+ printf(" Error: Cannot access file %s.\n", areafilename);
+ triexit(1);
+ }
+ stringptr = readline(inputline, areafile, areafilename);
+ areaelements = (int) strtol(stringptr, &stringptr, 0);
+ if (areaelements != m->inelements) {
+ printf("Error: %s and %s disagree on number of triangles.\n",
+ elefilename, areafilename);
+ triexit(1);
+ }
+ }
+#endif /* not TRILIBRARY */
+
+ if (!b->quiet) {
+ printf("Reconstructing mesh.\n");
+ }
+ /* Allocate a temporary array that maps each vertex to some adjacent */
+ /* triangle. I took care to allocate all the permanent memory for */
+ /* triangles and subsegments first. */
+ vertexarray = (triangle *) trimalloc(m->vertices.items *
+ (int) sizeof(triangle));
+ /* Each vertex is initially unrepresented. */
+ for (i = 0; i < m->vertices.items; i++) {
+ vertexarray[i] = (triangle) m->dummytri;
+ }
+
+ if (b->verbose) {
+ printf(" Assembling triangles.\n");
+ }
+ /* Read the triangles from the .ele file, and link */
+ /* together those that share an edge. */
+ traversalinit(&m->triangles);
+ triangleloop.tri = triangletraverse(m);
+ elementnumber = b->firstnumber;
+ while (triangleloop.tri != (triangle *) NULL) {
+#ifdef TRILIBRARY
+ /* Copy the triangle's three corners. */
+ for (j = 0; j < 3; j++) {
+ corner[j] = trianglelist[vertexindex++];
+ if ((corner[j] < b->firstnumber) ||
+ (corner[j] >= b->firstnumber + m->invertices)) {
+ printf("Error: Triangle %ld has an invalid vertex index.\n",
+ elementnumber);
+ triexit(1);
+ }
+ }
+#else /* not TRILIBRARY */
+ /* Read triangle number and the triangle's three corners. */
+ stringptr = readline(inputline, elefile, elefilename);
+ for (j = 0; j < 3; j++) {
+ stringptr = findfield(stringptr);
+ if (*stringptr == '\0') {
+ printf("Error: Triangle %ld is missing vertex %d in %s.\n",
+ elementnumber, j + 1, elefilename);
+ triexit(1);
+ } else {
+ corner[j] = (int) strtol(stringptr, &stringptr, 0);
+ if ((corner[j] < b->firstnumber) ||
+ (corner[j] >= b->firstnumber + m->invertices)) {
+ printf("Error: Triangle %ld has an invalid vertex index.\n",
+ elementnumber);
+ triexit(1);
+ }
+ }
+ }
+#endif /* not TRILIBRARY */
+
+ /* Find out about (and throw away) extra nodes. */
+ for (j = 3; j < incorners; j++) {
+#ifdef TRILIBRARY
+ killvertexindex = trianglelist[vertexindex++];
+#else /* not TRILIBRARY */
+ stringptr = findfield(stringptr);
+ if (*stringptr != '\0') {
+ killvertexindex = (int) strtol(stringptr, &stringptr, 0);
+#endif /* not TRILIBRARY */
+ if ((killvertexindex >= b->firstnumber) &&
+ (killvertexindex < b->firstnumber + m->invertices)) {
+ /* Delete the non-corner vertex if it's not already deleted. */
+ killvertex = getvertex(m, b, killvertexindex);
+ if (vertextype(killvertex) != DEADVERTEX) {
+ vertexdealloc(m, killvertex);
+ }
+ }
+#ifndef TRILIBRARY
+ }
+#endif /* not TRILIBRARY */
+ }
+
+ /* Read the triangle's attributes. */
+ for (j = 0; j < m->eextras; j++) {
+#ifdef TRILIBRARY
+ setelemattribute(triangleloop, j, triangleattriblist[attribindex++]);
+#else /* not TRILIBRARY */
+ stringptr = findfield(stringptr);
+ if (*stringptr == '\0') {
+ setelemattribute(triangleloop, j, 0);
+ } else {
+ setelemattribute(triangleloop, j,
+ (REAL) strtod(stringptr, &stringptr));
+ }
+#endif /* not TRILIBRARY */
+ }
+
+ if (b->vararea) {
+#ifdef TRILIBRARY
+ area = trianglearealist[elementnumber - b->firstnumber];
+#else /* not TRILIBRARY */
+ /* Read an area constraint from the .area file. */
+ stringptr = readline(inputline, areafile, areafilename);
+ stringptr = findfield(stringptr);
+ if (*stringptr == '\0') {
+ area = -1.0; /* No constraint on this triangle. */
+ } else {
+ area = (REAL) strtod(stringptr, &stringptr);
+ }
+#endif /* not TRILIBRARY */
+ setareabound(triangleloop, area);
+ }
+
+ /* Set the triangle's vertices. */
+ triangleloop.orient = 0;
+ setorg(triangleloop, getvertex(m, b, corner[0]));
+ setdest(triangleloop, getvertex(m, b, corner[1]));
+ setapex(triangleloop, getvertex(m, b, corner[2]));
+ /* Try linking the triangle to others that share these vertices. */
+ for (triangleloop.orient = 0; triangleloop.orient < 3;
+ triangleloop.orient++) {
+ /* Take the number for the origin of triangleloop. */
+ aroundvertex = corner[triangleloop.orient];
+ /* Look for other triangles having this vertex. */
+ nexttri = vertexarray[aroundvertex - b->firstnumber];
+ /* Link the current triangle to the next one in the stack. */
+ triangleloop.tri[6 + triangleloop.orient] = nexttri;
+ /* Push the current triangle onto the stack. */
+ vertexarray[aroundvertex - b->firstnumber] = encode(triangleloop);
+ decode(nexttri, checktri);
+ if (checktri.tri != m->dummytri) {
+ dest(triangleloop, tdest);
+ apex(triangleloop, tapex);
+ /* Look for other triangles that share an edge. */
+ do {
+ dest(checktri, checkdest);
+ apex(checktri, checkapex);
+ if (tapex == checkdest) {
+ /* The two triangles share an edge; bond them together. */
+ lprev(triangleloop, triangleleft);
+ bond(triangleleft, checktri);
+ }
+ if (tdest == checkapex) {
+ /* The two triangles share an edge; bond them together. */
+ lprev(checktri, checkleft);
+ bond(triangleloop, checkleft);
+ }
+ /* Find the next triangle in the stack. */
+ nexttri = checktri.tri[6 + checktri.orient];
+ decode(nexttri, checktri);
+ } while (checktri.tri != m->dummytri);
+ }
+ }
+ triangleloop.tri = triangletraverse(m);
+ elementnumber++;
+ }
+
+#ifdef TRILIBRARY
+ vertexindex = 0;
+#else /* not TRILIBRARY */
+ fclose(elefile);
+ if (b->vararea) {
+ fclose(areafile);
+ }
+#endif /* not TRILIBRARY */
+
+ hullsize = 0; /* Prepare to count the boundary edges. */
+ if (b->poly) {
+ if (b->verbose) {
+ printf(" Marking segments in triangulation.\n");
+ }
+ /* Read the segments from the .poly file, and link them */
+ /* to their neighboring triangles. */
+ boundmarker = 0;
+ traversalinit(&m->subsegs);
+ subsegloop.ss = subsegtraverse(m);
+ segmentnumber = b->firstnumber;
+ while (subsegloop.ss != (subseg *) NULL) {
+#ifdef TRILIBRARY
+ end[0] = segmentlist[vertexindex++];
+ end[1] = segmentlist[vertexindex++];
+ if (segmentmarkers) {
+ boundmarker = segmentmarkerlist[segmentnumber - b->firstnumber];
+ }
+#else /* not TRILIBRARY */
+ /* Read the endpoints of each segment, and possibly a boundary marker. */
+ stringptr = readline(inputline, polyfile, b->inpolyfilename);
+ /* Skip the first (segment number) field. */
+ stringptr = findfield(stringptr);
+ if (*stringptr == '\0') {
+ printf("Error: Segment %ld has no endpoints in %s.\n", segmentnumber,
+ polyfilename);
+ triexit(1);
+ } else {
+ end[0] = (int) strtol(stringptr, &stringptr, 0);
+ }
+ stringptr = findfield(stringptr);
+ if (*stringptr == '\0') {
+ printf("Error: Segment %ld is missing its second endpoint in %s.\n",
+ segmentnumber, polyfilename);
+ triexit(1);
+ } else {
+ end[1] = (int) strtol(stringptr, &stringptr, 0);
+ }
+ if (segmentmarkers) {
+ stringptr = findfield(stringptr);
+ if (*stringptr == '\0') {
+ boundmarker = 0;
+ } else {
+ boundmarker = (int) strtol(stringptr, &stringptr, 0);
+ }
+ }
+#endif /* not TRILIBRARY */
+ for (j = 0; j < 2; j++) {
+ if ((end[j] < b->firstnumber) ||
+ (end[j] >= b->firstnumber + m->invertices)) {
+ printf("Error: Segment %ld has an invalid vertex index.\n",
+ segmentnumber);
+ triexit(1);
+ }
+ }
+
+ /* set the subsegment's vertices. */
+ subsegloop.ssorient = 0;
+ segmentorg = getvertex(m, b, end[0]);
+ segmentdest = getvertex(m, b, end[1]);
+ setsorg(subsegloop, segmentorg);
+ setsdest(subsegloop, segmentdest);
+ setsegorg(subsegloop, segmentorg);
+ setsegdest(subsegloop, segmentdest);
+ setmark(subsegloop, boundmarker);
+ /* Try linking the subsegment to triangles that share these vertices. */
+ for (subsegloop.ssorient = 0; subsegloop.ssorient < 2;
+ subsegloop.ssorient++) {
+ /* Take the number for the destination of subsegloop. */
+ aroundvertex = end[1 - subsegloop.ssorient];
+ /* Look for triangles having this vertex. */
+ prevlink = &vertexarray[aroundvertex - b->firstnumber];
+ nexttri = vertexarray[aroundvertex - b->firstnumber];
+ decode(nexttri, checktri);
+ sorg(subsegloop, shorg);
+ notfound = 1;
+ /* Look for triangles having this edge. Note that I'm only */
+ /* comparing each triangle's destination with the subsegment; */
+ /* each triangle's apex is handled through a different vertex. */
+ /* Because each triangle appears on three vertices' lists, each */
+ /* occurrence of a triangle on a list can (and does) represent */
+ /* an edge. In this way, most edges are represented twice, and */
+ /* every triangle-subsegment bond is represented once. */
+ while (notfound && (checktri.tri != m->dummytri)) {
+ dest(checktri, checkdest);
+ if (shorg == checkdest) {
+ /* We have a match. Remove this triangle from the list. */
+ *prevlink = checktri.tri[6 + checktri.orient];
+ /* Bond the subsegment to the triangle. */
+ tsbond(checktri, subsegloop);
+ /* Check if this is a boundary edge. */
+ sym(checktri, checkneighbor);
+ if (checkneighbor.tri == m->dummytri) {
+ /* The next line doesn't insert a subsegment (because there's */
+ /* already one there), but it sets the boundary markers of */
+ /* the existing subsegment and its vertices. */
+ insertsubseg(m, b, &checktri, 1);
+ hullsize++;
+ }
+ notfound = 0;
+ }
+ /* Find the next triangle in the stack. */
+ prevlink = &checktri.tri[6 + checktri.orient];
+ nexttri = checktri.tri[6 + checktri.orient];
+ decode(nexttri, checktri);
+ }
+ }
+ subsegloop.ss = subsegtraverse(m);
+ segmentnumber++;
+ }
+ }
+
+ /* Mark the remaining edges as not being attached to any subsegment. */
+ /* Also, count the (yet uncounted) boundary edges. */
+ for (i = 0; i < m->vertices.items; i++) {
+ /* Search the stack of triangles adjacent to a vertex. */
+ nexttri = vertexarray[i];
+ decode(nexttri, checktri);
+ while (checktri.tri != m->dummytri) {
+ /* Find the next triangle in the stack before this */
+ /* information gets overwritten. */
+ nexttri = checktri.tri[6 + checktri.orient];
+ /* No adjacent subsegment. (This overwrites the stack info.) */
+ tsdissolve(checktri);
+ sym(checktri, checkneighbor);
+ if (checkneighbor.tri == m->dummytri) {
+ insertsubseg(m, b, &checktri, 1);
+ hullsize++;
+ }
+ decode(nexttri, checktri);
+ }
+ }
+
+ trifree((VOID *) vertexarray);
+ return hullsize;
+}
+
+#endif /* not CDT_ONLY */
+
+/** **/
+/** **/
+/********* General mesh construction routines end here *********/
+
+/********* Segment insertion begins here *********/
+/** **/
+/** **/
+
+/*****************************************************************************/
+/* */
+/* finddirection() Find the first triangle on the path from one point */
+/* to another. */
+/* */
+/* Finds the triangle that intersects a line segment drawn from the */
+/* origin of `searchtri' to the point `searchpoint', and returns the result */
+/* in `searchtri'. The origin of `searchtri' does not change, even though */
+/* the triangle returned may differ from the one passed in. This routine */
+/* is used to find the direction to move in to get from one point to */
+/* another. */
+/* */
+/* The return value notes whether the destination or apex of the found */
+/* triangle is collinear with the two points in question. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+enum finddirectionresult finddirection(struct mesh *m, struct behavior *b,
+ struct otri *searchtri,
+ vertex searchpoint)
+#else /* not ANSI_DECLARATORS */
+enum finddirectionresult finddirection(m, b, searchtri, searchpoint)
+struct mesh *m;
+struct behavior *b;
+struct otri *searchtri;
+vertex searchpoint;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ struct otri checktri;
+ vertex startvertex;
+ vertex leftvertex, rightvertex;
+ REAL leftccw, rightccw;
+ int leftflag, rightflag;
+ triangle ptr; /* Temporary variable used by onext() and oprev(). */
+
+ org(*searchtri, startvertex);
+ dest(*searchtri, rightvertex);
+ apex(*searchtri, leftvertex);
+ /* Is `searchpoint' to the left? */
+ leftccw = counterclockwise(m, b, searchpoint, startvertex, leftvertex);
+ leftflag = leftccw > 0.0;
+ /* Is `searchpoint' to the right? */
+ rightccw = counterclockwise(m, b, startvertex, searchpoint, rightvertex);
+ rightflag = rightccw > 0.0;
+ if (leftflag && rightflag) {
+ /* `searchtri' faces directly away from `searchpoint'. We could go left */
+ /* or right. Ask whether it's a triangle or a boundary on the left. */
+ onext(*searchtri, checktri);
+ if (checktri.tri == m->dummytri) {
+ leftflag = 0;
+ } else {
+ rightflag = 0;
+ }
+ }
+ while (leftflag) {
+ /* Turn left until satisfied. */
+ onextself(*searchtri);
+ if (searchtri->tri == m->dummytri) {
+ printf("Internal error in finddirection(): Unable to find a\n");
+ printf(" triangle leading from (%.12g, %.12g) to", startvertex[0],
+ startvertex[1]);
+ printf(" (%.12g, %.12g).\n", searchpoint[0], searchpoint[1]);
+ internalerror();
+ }
+ apex(*searchtri, leftvertex);
+ rightccw = leftccw;
+ leftccw = counterclockwise(m, b, searchpoint, startvertex, leftvertex);
+ leftflag = leftccw > 0.0;
+ }
+ while (rightflag) {
+ /* Turn right until satisfied. */
+ oprevself(*searchtri);
+ if (searchtri->tri == m->dummytri) {
+ printf("Internal error in finddirection(): Unable to find a\n");
+ printf(" triangle leading from (%.12g, %.12g) to", startvertex[0],
+ startvertex[1]);
+ printf(" (%.12g, %.12g).\n", searchpoint[0], searchpoint[1]);
+ internalerror();
+ }
+ dest(*searchtri, rightvertex);
+ leftccw = rightccw;
+ rightccw = counterclockwise(m, b, startvertex, searchpoint, rightvertex);
+ rightflag = rightccw > 0.0;
+ }
+ if (leftccw == 0.0) {
+ return LEFTCOLLINEAR;
+ } else if (rightccw == 0.0) {
+ return RIGHTCOLLINEAR;
+ } else {
+ return WITHIN;
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* segmentintersection() Find the intersection of an existing segment */
+/* and a segment that is being inserted. Insert */
+/* a vertex at the intersection, splitting an */
+/* existing subsegment. */
+/* */
+/* The segment being inserted connects the apex of splittri to endpoint2. */
+/* splitsubseg is the subsegment being split, and MUST adjoin splittri. */
+/* Hence, endpoints of the subsegment being split are the origin and */
+/* destination of splittri. */
+/* */
+/* On completion, splittri is a handle having the newly inserted */
+/* intersection point as its origin, and endpoint1 as its destination. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+void segmentintersection(struct mesh *m, struct behavior *b,
+ struct otri *splittri, struct osub *splitsubseg,
+ vertex endpoint2)
+#else /* not ANSI_DECLARATORS */
+void segmentintersection(m, b, splittri, splitsubseg, endpoint2)
+struct mesh *m;
+struct behavior *b;
+struct otri *splittri;
+struct osub *splitsubseg;
+vertex endpoint2;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ struct osub opposubseg;
+ vertex endpoint1;
+ vertex torg, tdest;
+ vertex leftvertex, rightvertex;
+ vertex newvertex;
+ enum insertvertexresult success;
+ enum finddirectionresult collinear;
+ REAL ex, ey;
+ REAL tx, ty;
+ REAL etx, ety;
+ REAL split, denom;
+ int i;
+ triangle ptr; /* Temporary variable used by onext(). */
+ subseg sptr; /* Temporary variable used by snext(). */
+
+ /* Find the other three segment endpoints. */
+ apex(*splittri, endpoint1);
+ org(*splittri, torg);
+ dest(*splittri, tdest);
+ /* Segment intersection formulae; see the Antonio reference. */
+ tx = tdest[0] - torg[0];
+ ty = tdest[1] - torg[1];
+ ex = endpoint2[0] - endpoint1[0];
+ ey = endpoint2[1] - endpoint1[1];
+ etx = torg[0] - endpoint2[0];
+ ety = torg[1] - endpoint2[1];
+ denom = ty * ex - tx * ey;
+ if (denom == 0.0) {
+ printf("Internal error in segmentintersection():");
+ printf(" Attempt to find intersection of parallel segments.\n");
+ internalerror();
+ }
+ split = (ey * etx - ex * ety) / denom;
+ /* Create the new vertex. */
+ newvertex = (vertex) poolalloc(&m->vertices);
+ /* Interpolate its coordinate and attributes. */
+ for (i = 0; i < 2 + m->nextras; i++) {
+ newvertex[i] = torg[i] + split * (tdest[i] - torg[i]);
+ }
+ setvertexmark(newvertex, mark(*splitsubseg));
+ setvertextype(newvertex, INPUTVERTEX);
+ if (b->verbose > 1) {
+ printf(
+ " Splitting subsegment (%.12g, %.12g) (%.12g, %.12g) at (%.12g, %.12g).\n",
+ torg[0], torg[1], tdest[0], tdest[1], newvertex[0], newvertex[1]);
+ }
+ /* Insert the intersection vertex. This should always succeed. */
+ success = insertvertex(m, b, newvertex, splittri, splitsubseg, 0, 0);
+ if (success != SUCCESSFULVERTEX) {
+ printf("Internal error in segmentintersection():\n");
+ printf(" Failure to split a segment.\n");
+ internalerror();
+ }
+ /* Record a triangle whose origin is the new vertex. */
+ setvertex2tri(newvertex, encode(*splittri));
+ if (m->steinerleft > 0) {
+ m->steinerleft--;
+ }
+
+ /* Divide the segment into two, and correct the segment endpoints. */
+ ssymself(*splitsubseg);
+ spivot(*splitsubseg, opposubseg);
+ sdissolve(*splitsubseg);
+ sdissolve(opposubseg);
+ do {
+ setsegorg(*splitsubseg, newvertex);
+ snextself(*splitsubseg);
+ } while (splitsubseg->ss != m->dummysub);
+ do {
+ setsegorg(opposubseg, newvertex);
+ snextself(opposubseg);
+ } while (opposubseg.ss != m->dummysub);
+
+ /* Inserting the vertex may have caused edge flips. We wish to rediscover */
+ /* the edge connecting endpoint1 to the new intersection vertex. */
+ collinear = finddirection(m, b, splittri, endpoint1);
+ dest(*splittri, rightvertex);
+ apex(*splittri, leftvertex);
+ if ((leftvertex[0] == endpoint1[0]) && (leftvertex[1] == endpoint1[1])) {
+ onextself(*splittri);
+ } else if ((rightvertex[0] != endpoint1[0]) ||
+ (rightvertex[1] != endpoint1[1])) {
+ printf("Internal error in segmentintersection():\n");
+ printf(" Topological inconsistency after splitting a segment.\n");
+ internalerror();
+ }
+ /* `splittri' should have destination endpoint1. */
+}
+
+/*****************************************************************************/
+/* */
+/* scoutsegment() Scout the first triangle on the path from one endpoint */
+/* to another, and check for completion (reaching the */
+/* second endpoint), a collinear vertex, or the */
+/* intersection of two segments. */
+/* */
+/* Returns one if the entire segment is successfully inserted, and zero if */
+/* the job must be finished by conformingedge() or constrainededge(). */
+/* */
+/* If the first triangle on the path has the second endpoint as its */
+/* destination or apex, a subsegment is inserted and the job is done. */
+/* */
+/* If the first triangle on the path has a destination or apex that lies on */
+/* the segment, a subsegment is inserted connecting the first endpoint to */
+/* the collinear vertex, and the search is continued from the collinear */
+/* vertex. */
+/* */
+/* If the first triangle on the path has a subsegment opposite its origin, */
+/* then there is a segment that intersects the segment being inserted. */
+/* Their intersection vertex is inserted, splitting the subsegment. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+int scoutsegment(struct mesh *m, struct behavior *b, struct otri *searchtri,
+ vertex endpoint2, int newmark)
+#else /* not ANSI_DECLARATORS */
+int scoutsegment(m, b, searchtri, endpoint2, newmark)
+struct mesh *m;
+struct behavior *b;
+struct otri *searchtri;
+vertex endpoint2;
+int newmark;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ struct otri crosstri;
+ struct osub crosssubseg;
+ vertex leftvertex, rightvertex;
+ enum finddirectionresult collinear;
+ subseg sptr; /* Temporary variable used by tspivot(). */
+
+ collinear = finddirection(m, b, searchtri, endpoint2);
+ dest(*searchtri, rightvertex);
+ apex(*searchtri, leftvertex);
+ if (((leftvertex[0] == endpoint2[0]) && (leftvertex[1] == endpoint2[1])) ||
+ ((rightvertex[0] == endpoint2[0]) && (rightvertex[1] == endpoint2[1]))) {
+ /* The segment is already an edge in the mesh. */
+ if ((leftvertex[0] == endpoint2[0]) && (leftvertex[1] == endpoint2[1])) {
+ lprevself(*searchtri);
+ }
+ /* Insert a subsegment, if there isn't already one there. */
+ insertsubseg(m, b, searchtri, newmark);
+ return 1;
+ } else if (collinear == LEFTCOLLINEAR) {
+ /* We've collided with a vertex between the segment's endpoints. */
+ /* Make the collinear vertex be the triangle's origin. */
+ lprevself(*searchtri);
+ insertsubseg(m, b, searchtri, newmark);
+ /* Insert the remainder of the segment. */
+ return scoutsegment(m, b, searchtri, endpoint2, newmark);
+ } else if (collinear == RIGHTCOLLINEAR) {
+ /* We've collided with a vertex between the segment's endpoints. */
+ insertsubseg(m, b, searchtri, newmark);
+ /* Make the collinear vertex be the triangle's origin. */
+ lnextself(*searchtri);
+ /* Insert the remainder of the segment. */
+ return scoutsegment(m, b, searchtri, endpoint2, newmark);
+ } else {
+ lnext(*searchtri, crosstri);
+ tspivot(crosstri, crosssubseg);
+ /* Check for a crossing segment. */
+ if (crosssubseg.ss == m->dummysub) {
+ return 0;
+ } else {
+ /* Insert a vertex at the intersection. */
+ segmentintersection(m, b, &crosstri, &crosssubseg, endpoint2);
+ otricopy(crosstri, *searchtri);
+ insertsubseg(m, b, searchtri, newmark);
+ /* Insert the remainder of the segment. */
+ return scoutsegment(m, b, searchtri, endpoint2, newmark);
+ }
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* conformingedge() Force a segment into a conforming Delaunay */
+/* triangulation by inserting a vertex at its midpoint, */
+/* and recursively forcing in the two half-segments if */
+/* necessary. */
+/* */
+/* Generates a sequence of subsegments connecting `endpoint1' to */
+/* `endpoint2'. `newmark' is the boundary marker of the segment, assigned */
+/* to each new splitting vertex and subsegment. */
+/* */
+/* Note that conformingedge() does not always maintain the conforming */
+/* Delaunay property. Once inserted, segments are locked into place; */
+/* vertices inserted later (to force other segments in) may render these */
+/* fixed segments non-Delaunay. The conforming Delaunay property will be */
+/* restored by enforcequality() by splitting encroached subsegments. */
+/* */
+/*****************************************************************************/
+
+#ifndef REDUCED
+#ifndef CDT_ONLY
+
+#ifdef ANSI_DECLARATORS
+void conformingedge(struct mesh *m, struct behavior *b,
+ vertex endpoint1, vertex endpoint2, int newmark)
+#else /* not ANSI_DECLARATORS */
+void conformingedge(m, b, endpoint1, endpoint2, newmark)
+struct mesh *m;
+struct behavior *b;
+vertex endpoint1;
+vertex endpoint2;
+int newmark;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ struct otri searchtri1, searchtri2;
+ struct osub brokensubseg;
+ vertex newvertex;
+ vertex midvertex1, midvertex2;
+ enum insertvertexresult success;
+ int i;
+ subseg sptr; /* Temporary variable used by tspivot(). */
+
+ if (b->verbose > 2) {
+ printf("Forcing segment into triangulation by recursive splitting:\n");
+ printf(" (%.12g, %.12g) (%.12g, %.12g)\n", endpoint1[0], endpoint1[1],
+ endpoint2[0], endpoint2[1]);
+ }
+ /* Create a new vertex to insert in the middle of the segment. */
+ newvertex = (vertex) poolalloc(&m->vertices);
+ /* Interpolate coordinates and attributes. */
+ for (i = 0; i < 2 + m->nextras; i++) {
+ newvertex[i] = 0.5 * (endpoint1[i] + endpoint2[i]);
+ }
+ setvertexmark(newvertex, newmark);
+ setvertextype(newvertex, SEGMENTVERTEX);
+ /* No known triangle to search from. */
+ searchtri1.tri = m->dummytri;
+ /* Attempt to insert the new vertex. */
+ success = insertvertex(m, b, newvertex, &searchtri1, (struct osub *) NULL,
+ 0, 0);
+ if (success == DUPLICATEVERTEX) {
+ if (b->verbose > 2) {
+ printf(" Segment intersects existing vertex (%.12g, %.12g).\n",
+ newvertex[0], newvertex[1]);
+ }
+ /* Use the vertex that's already there. */
+ vertexdealloc(m, newvertex);
+ org(searchtri1, newvertex);
+ } else {
+ if (success == VIOLATINGVERTEX) {
+ if (b->verbose > 2) {
+ printf(" Two segments intersect at (%.12g, %.12g).\n",
+ newvertex[0], newvertex[1]);
+ }
+ /* By fluke, we've landed right on another segment. Split it. */
+ tspivot(searchtri1, brokensubseg);
+ success = insertvertex(m, b, newvertex, &searchtri1, &brokensubseg,
+ 0, 0);
+ if (success != SUCCESSFULVERTEX) {
+ printf("Internal error in conformingedge():\n");
+ printf(" Failure to split a segment.\n");
+ internalerror();
+ }
+ }
+ /* The vertex has been inserted successfully. */
+ if (m->steinerleft > 0) {
+ m->steinerleft--;
+ }
+ }
+ otricopy(searchtri1, searchtri2);
+ /* `searchtri1' and `searchtri2' are fastened at their origins to */
+ /* `newvertex', and will be directed toward `endpoint1' and `endpoint2' */
+ /* respectively. First, we must get `searchtri2' out of the way so it */
+ /* won't be invalidated during the insertion of the first half of the */
+ /* segment. */
+ finddirection(m, b, &searchtri2, endpoint2);
+ if (!scoutsegment(m, b, &searchtri1, endpoint1, newmark)) {
+ /* The origin of searchtri1 may have changed if a collision with an */
+ /* intervening vertex on the segment occurred. */
+ org(searchtri1, midvertex1);
+ conformingedge(m, b, midvertex1, endpoint1, newmark);
+ }
+ if (!scoutsegment(m, b, &searchtri2, endpoint2, newmark)) {
+ /* The origin of searchtri2 may have changed if a collision with an */
+ /* intervening vertex on the segment occurred. */
+ org(searchtri2, midvertex2);
+ conformingedge(m, b, midvertex2, endpoint2, newmark);
+ }
+}
+
+#endif /* not CDT_ONLY */
+#endif /* not REDUCED */
+
+/*****************************************************************************/
+/* */
+/* delaunayfixup() Enforce the Delaunay condition at an edge, fanning out */
+/* recursively from an existing vertex. Pay special */
+/* attention to stacking inverted triangles. */
+/* */
+/* This is a support routine for inserting segments into a constrained */
+/* Delaunay triangulation. */
+/* */
+/* The origin of fixuptri is treated as if it has just been inserted, and */
+/* the local Delaunay condition needs to be enforced. It is only enforced */
+/* in one sector, however, that being the angular range defined by */
+/* fixuptri. */
+/* */
+/* This routine also needs to make decisions regarding the "stacking" of */
+/* triangles. (Read the description of constrainededge() below before */
+/* reading on here, so you understand the algorithm.) If the position of */
+/* the new vertex (the origin of fixuptri) indicates that the vertex before */
+/* it on the polygon is a reflex vertex, then "stack" the triangle by */
+/* doing nothing. (fixuptri is an inverted triangle, which is how stacked */
+/* triangles are identified.) */
+/* */
+/* Otherwise, check whether the vertex before that was a reflex vertex. */
+/* If so, perform an edge flip, thereby eliminating an inverted triangle */
+/* (popping it off the stack). The edge flip may result in the creation */
+/* of a new inverted triangle, depending on whether or not the new vertex */
+/* is visible to the vertex three edges behind on the polygon. */
+/* */
+/* If neither of the two vertices behind the new vertex are reflex */
+/* vertices, fixuptri and fartri, the triangle opposite it, are not */
+/* inverted; hence, ensure that the edge between them is locally Delaunay. */
+/* */
+/* `leftside' indicates whether or not fixuptri is to the left of the */
+/* segment being inserted. (Imagine that the segment is pointing up from */
+/* endpoint1 to endpoint2.) */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+void delaunayfixup(struct mesh *m, struct behavior *b,
+ struct otri *fixuptri, int leftside)
+#else /* not ANSI_DECLARATORS */
+void delaunayfixup(m, b, fixuptri, leftside)
+struct mesh *m;
+struct behavior *b;
+struct otri *fixuptri;
+int leftside;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ struct otri neartri;
+ struct otri fartri;
+ struct osub faredge;
+ vertex nearvertex, leftvertex, rightvertex, farvertex;
+ triangle ptr; /* Temporary variable used by sym(). */
+ subseg sptr; /* Temporary variable used by tspivot(). */
+
+ lnext(*fixuptri, neartri);
+ sym(neartri, fartri);
+ /* Check if the edge opposite the origin of fixuptri can be flipped. */
+ if (fartri.tri == m->dummytri) {
+ return;
+ }
+ tspivot(neartri, faredge);
+ if (faredge.ss != m->dummysub) {
+ return;
+ }
+ /* Find all the relevant vertices. */
+ apex(neartri, nearvertex);
+ org(neartri, leftvertex);
+ dest(neartri, rightvertex);
+ apex(fartri, farvertex);
+ /* Check whether the previous polygon vertex is a reflex vertex. */
+ if (leftside) {
+ if (counterclockwise(m, b, nearvertex, leftvertex, farvertex) <= 0.0) {
+ /* leftvertex is a reflex vertex too. Nothing can */
+ /* be done until a convex section is found. */
+ return;
+ }
+ } else {
+ if (counterclockwise(m, b, farvertex, rightvertex, nearvertex) <= 0.0) {
+ /* rightvertex is a reflex vertex too. Nothing can */
+ /* be done until a convex section is found. */
+ return;
+ }
+ }
+ if (counterclockwise(m, b, rightvertex, leftvertex, farvertex) > 0.0) {
+ /* fartri is not an inverted triangle, and farvertex is not a reflex */
+ /* vertex. As there are no reflex vertices, fixuptri isn't an */
+ /* inverted triangle, either. Hence, test the edge between the */
+ /* triangles to ensure it is locally Delaunay. */
+ if (incircle(m, b, leftvertex, farvertex, rightvertex, nearvertex) <=
+ 0.0) {
+ return;
+ }
+ /* Not locally Delaunay; go on to an edge flip. */
+ } /* else fartri is inverted; remove it from the stack by flipping. */
+ flip(m, b, &neartri);
+ lprevself(*fixuptri); /* Restore the origin of fixuptri after the flip. */
+ /* Recursively process the two triangles that result from the flip. */
+ delaunayfixup(m, b, fixuptri, leftside);
+ delaunayfixup(m, b, &fartri, leftside);
+}
+
+/*****************************************************************************/
+/* */
+/* constrainededge() Force a segment into a constrained Delaunay */
+/* triangulation by deleting the triangles it */
+/* intersects, and triangulating the polygons that */
+/* form on each side of it. */
+/* */
+/* Generates a single subsegment connecting `endpoint1' to `endpoint2'. */
+/* The triangle `starttri' has `endpoint1' as its origin. `newmark' is the */
+/* boundary marker of the segment. */
+/* */
+/* To insert a segment, every triangle whose interior intersects the */
+/* segment is deleted. The union of these deleted triangles is a polygon */
+/* (which is not necessarily monotone, but is close enough), which is */
+/* divided into two polygons by the new segment. This routine's task is */
+/* to generate the Delaunay triangulation of these two polygons. */
+/* */
+/* You might think of this routine's behavior as a two-step process. The */
+/* first step is to walk from endpoint1 to endpoint2, flipping each edge */
+/* encountered. This step creates a fan of edges connected to endpoint1, */
+/* including the desired edge to endpoint2. The second step enforces the */
+/* Delaunay condition on each side of the segment in an incremental manner: */
+/* proceeding along the polygon from endpoint1 to endpoint2 (this is done */
+/* independently on each side of the segment), each vertex is "enforced" */
+/* as if it had just been inserted, but affecting only the previous */
+/* vertices. The result is the same as if the vertices had been inserted */
+/* in the order they appear on the polygon, so the result is Delaunay. */
+/* */
+/* In truth, constrainededge() interleaves these two steps. The procedure */
+/* walks from endpoint1 to endpoint2, and each time an edge is encountered */
+/* and flipped, the newly exposed vertex (at the far end of the flipped */
+/* edge) is "enforced" upon the previously flipped edges, usually affecting */
+/* only one side of the polygon (depending upon which side of the segment */
+/* the vertex falls on). */
+/* */
+/* The algorithm is complicated by the need to handle polygons that are not */
+/* convex. Although the polygon is not necessarily monotone, it can be */
+/* triangulated in a manner similar to the stack-based algorithms for */
+/* monotone polygons. For each reflex vertex (local concavity) of the */
+/* polygon, there will be an inverted triangle formed by one of the edge */
+/* flips. (An inverted triangle is one with negative area - that is, its */
+/* vertices are arranged in clockwise order - and is best thought of as a */
+/* wrinkle in the fabric of the mesh.) Each inverted triangle can be */
+/* thought of as a reflex vertex pushed on the stack, waiting to be fixed */
+/* later. */
+/* */
+/* A reflex vertex is popped from the stack when a vertex is inserted that */
+/* is visible to the reflex vertex. (However, if the vertex behind the */
+/* reflex vertex is not visible to the reflex vertex, a new inverted */
+/* triangle will take its place on the stack.) These details are handled */
+/* by the delaunayfixup() routine above. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+void constrainededge(struct mesh *m, struct behavior *b,
+ struct otri *starttri, vertex endpoint2, int newmark)
+#else /* not ANSI_DECLARATORS */
+void constrainededge(m, b, starttri, endpoint2, newmark)
+struct mesh *m;
+struct behavior *b;
+struct otri *starttri;
+vertex endpoint2;
+int newmark;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ struct otri fixuptri, fixuptri2;
+ struct osub crosssubseg;
+ vertex endpoint1;
+ vertex farvertex;
+ REAL area;
+ int collision;
+ int done;
+ triangle ptr; /* Temporary variable used by sym() and oprev(). */
+ subseg sptr; /* Temporary variable used by tspivot(). */
+
+ org(*starttri, endpoint1);
+ lnext(*starttri, fixuptri);
+ flip(m, b, &fixuptri);
+ /* `collision' indicates whether we have found a vertex directly */
+ /* between endpoint1 and endpoint2. */
+ collision = 0;
+ done = 0;
+ do {
+ org(fixuptri, farvertex);
+ /* `farvertex' is the extreme point of the polygon we are "digging" */
+ /* to get from endpoint1 to endpoint2. */
+ if ((farvertex[0] == endpoint2[0]) && (farvertex[1] == endpoint2[1])) {
+ oprev(fixuptri, fixuptri2);
+ /* Enforce the Delaunay condition around endpoint2. */
+ delaunayfixup(m, b, &fixuptri, 0);
+ delaunayfixup(m, b, &fixuptri2, 1);
+ done = 1;
+ } else {
+ /* Check whether farvertex is to the left or right of the segment */
+ /* being inserted, to decide which edge of fixuptri to dig */
+ /* through next. */
+ area = counterclockwise(m, b, endpoint1, endpoint2, farvertex);
+ if (area == 0.0) {
+ /* We've collided with a vertex between endpoint1 and endpoint2. */
+ collision = 1;
+ oprev(fixuptri, fixuptri2);
+ /* Enforce the Delaunay condition around farvertex. */
+ delaunayfixup(m, b, &fixuptri, 0);
+ delaunayfixup(m, b, &fixuptri2, 1);
+ done = 1;
+ } else {
+ if (area > 0.0) { /* farvertex is to the left of the segment. */
+ oprev(fixuptri, fixuptri2);
+ /* Enforce the Delaunay condition around farvertex, on the */
+ /* left side of the segment only. */
+ delaunayfixup(m, b, &fixuptri2, 1);
+ /* Flip the edge that crosses the segment. After the edge is */
+ /* flipped, one of its endpoints is the fan vertex, and the */
+ /* destination of fixuptri is the fan vertex. */
+ lprevself(fixuptri);
+ } else { /* farvertex is to the right of the segment. */
+ delaunayfixup(m, b, &fixuptri, 0);
+ /* Flip the edge that crosses the segment. After the edge is */
+ /* flipped, one of its endpoints is the fan vertex, and the */
+ /* destination of fixuptri is the fan vertex. */
+ oprevself(fixuptri);
+ }
+ /* Check for two intersecting segments. */
+ tspivot(fixuptri, crosssubseg);
+ if (crosssubseg.ss == m->dummysub) {
+ flip(m, b, &fixuptri); /* May create inverted triangle at left. */
+ } else {
+ /* We've collided with a segment between endpoint1 and endpoint2. */
+ collision = 1;
+ /* Insert a vertex at the intersection. */
+ segmentintersection(m, b, &fixuptri, &crosssubseg, endpoint2);
+ done = 1;
+ }
+ }
+ }
+ } while (!done);
+ /* Insert a subsegment to make the segment permanent. */
+ insertsubseg(m, b, &fixuptri, newmark);
+ /* If there was a collision with an interceding vertex, install another */
+ /* segment connecting that vertex with endpoint2. */
+ if (collision) {
+ /* Insert the remainder of the segment. */
+ if (!scoutsegment(m, b, &fixuptri, endpoint2, newmark)) {
+ constrainededge(m, b, &fixuptri, endpoint2, newmark);
+ }
+ }
+}
+
+/*****************************************************************************/
+/* */
+/* insertsegment() Insert a PSLG segment into a triangulation. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+void insertsegment(struct mesh *m, struct behavior *b,
+ vertex endpoint1, vertex endpoint2, int newmark)
+#else /* not ANSI_DECLARATORS */
+void insertsegment(m, b, endpoint1, endpoint2, newmark)
+struct mesh *m;
+struct behavior *b;
+vertex endpoint1;
+vertex endpoint2;
+int newmark;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ struct otri searchtri1, searchtri2;
+ triangle encodedtri;
+ vertex checkvertex;
+ triangle ptr; /* Temporary variable used by sym(). */
+
+ if (b->verbose > 1) {
+ printf(" Connecting (%.12g, %.12g) to (%.12g, %.12g).\n",
+ endpoint1[0], endpoint1[1], endpoint2[0], endpoint2[1]);
+ }
+
+ /* Find a triangle whose origin is the segment's first endpoint. */
+ checkvertex = (vertex) NULL;
+ encodedtri = vertex2tri(endpoint1);
+ if (encodedtri != (triangle) NULL) {
+ decode(encodedtri, searchtri1);
+ org(searchtri1, checkvertex);
+ }
+ if (checkvertex != endpoint1) {
+ /* Find a boundary triangle to search from. */
+ searchtri1.tri = m->dummytri;
+ searchtri1.orient = 0;
+ symself(searchtri1);
+ /* Search for the segment's first endpoint by point location. */
+ if (locate(m, b, endpoint1, &searchtri1) != ONVERTEX) {
+ printf(
+ "Internal error in insertsegment(): Unable to locate PSLG vertex\n");
+ printf(" (%.12g, %.12g) in triangulation.\n",
+ endpoint1[0], endpoint1[1]);
+ internalerror();
+ }
+ }
+ /* Remember this triangle to improve subsequent point location. */
+ otricopy(searchtri1, m->recenttri);
+ /* Scout the beginnings of a path from the first endpoint */
+ /* toward the second. */
+ if (scoutsegment(m, b, &searchtri1, endpoint2, newmark)) {
+ /* The segment was easily inserted. */
+ return;
+ }
+ /* The first endpoint may have changed if a collision with an intervening */
+ /* vertex on the segment occurred. */
+ org(searchtri1, endpoint1);
+
+ /* Find a triangle whose origin is the segment's second endpoint. */
+ checkvertex = (vertex) NULL;
+ encodedtri = vertex2tri(endpoint2);
+ if (encodedtri != (triangle) NULL) {
+ decode(encodedtri, searchtri2);
+ org(searchtri2, checkvertex);
+ }
+ if (checkvertex != endpoint2) {
+ /* Find a boundary triangle to search from. */
+ searchtri2.tri = m->dummytri;
+ searchtri2.orient = 0;
+ symself(searchtri2);
+ /* Search for the segment's second endpoint by point location. */
+ if (locate(m, b, endpoint2, &searchtri2) != ONVERTEX) {
+ printf(
+ "Internal error in insertsegment(): Unable to locate PSLG vertex\n");
+ printf(" (%.12g, %.12g) in triangulation.\n",
+ endpoint2[0], endpoint2[1]);
+ internalerror();
+ }
+ }
+ /* Remember this triangle to improve subsequent point location. */
+ otricopy(searchtri2, m->recenttri);
+ /* Scout the beginnings of a path from the second endpoint */
+ /* toward the first. */
+ if (scoutsegment(m, b, &searchtri2, endpoint1, newmark)) {
+ /* The segment was easily inserted. */
+ return;
+ }
+ /* The second endpoint may have changed if a collision with an intervening */
+ /* vertex on the segment occurred. */
+ org(searchtri2, endpoint2);
+
+#ifndef REDUCED
+#ifndef CDT_ONLY
+ if (b->splitseg) {
+ /* Insert vertices to force the segment into the triangulation. */
+ conformingedge(m, b, endpoint1, endpoint2, newmark);
+ } else {
+#endif /* not CDT_ONLY */
+#endif /* not REDUCED */
+ /* Insert the segment directly into the triangulation. */
+ constrainededge(m, b, &searchtri1, endpoint2, newmark);
+#ifndef REDUCED
+#ifndef CDT_ONLY
+ }
+#endif /* not CDT_ONLY */
+#endif /* not REDUCED */
+}
+
+/*****************************************************************************/
+/* */
+/* markhull() Cover the convex hull of a triangulation with subsegments. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+void markhull(struct mesh *m, struct behavior *b)
+#else /* not ANSI_DECLARATORS */
+void markhull(m, b)
+struct mesh *m;
+struct behavior *b;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ struct otri hulltri;
+ struct otri nexttri;
+ struct otri starttri;
+ triangle ptr; /* Temporary variable used by sym() and oprev(). */
+
+ /* Find a triangle handle on the hull. */
+ hulltri.tri = m->dummytri;
+ hulltri.orient = 0;
+ symself(hulltri);
+ /* Remember where we started so we know when to stop. */
+ otricopy(hulltri, starttri);
+ /* Go once counterclockwise around the convex hull. */
+ do {
+ /* Create a subsegment if there isn't already one here. */
+ insertsubseg(m, b, &hulltri, 1);
+ /* To find the next hull edge, go clockwise around the next vertex. */
+ lnextself(hulltri);
+ oprev(hulltri, nexttri);
+ while (nexttri.tri != m->dummytri) {
+ otricopy(nexttri, hulltri);
+ oprev(hulltri, nexttri);
+ }
+ } while (!otriequal(hulltri, starttri));
+}
+
+/*****************************************************************************/
+/* */
+/* formskeleton() Create the segments of a triangulation, including PSLG */
+/* segments and edges on the convex hull. */
+/* */
+/* The PSLG segments are read from a .poly file. The return value is the */
+/* number of segments in the file. */
+/* */
+/*****************************************************************************/
+
+#ifdef TRILIBRARY
+
+#ifdef ANSI_DECLARATORS
+void formskeleton(struct mesh *m, struct behavior *b, int *segmentlist,
+ int *segmentmarkerlist, int numberofsegments)
+#else /* not ANSI_DECLARATORS */
+void formskeleton(m, b, segmentlist, segmentmarkerlist, numberofsegments)
+struct mesh *m;
+struct behavior *b;
+int *segmentlist;
+int *segmentmarkerlist;
+int numberofsegments;
+#endif /* not ANSI_DECLARATORS */
+
+#else /* not TRILIBRARY */
+
+#ifdef ANSI_DECLARATORS
+void formskeleton(struct mesh *m, struct behavior *b,
+ FILE *polyfile, char *polyfilename)
+#else /* not ANSI_DECLARATORS */
+void formskeleton(m, b, polyfile, polyfilename)
+struct mesh *m;
+struct behavior *b;
+FILE *polyfile;
+char *polyfilename;
+#endif /* not ANSI_DECLARATORS */
+
+#endif /* not TRILIBRARY */
+
+{
+#ifdef TRILIBRARY
+ char polyfilename[6];
+ int index;
+#else /* not TRILIBRARY */
+ char inputline[INPUTLINESIZE];
+ char *stringptr;
+#endif /* not TRILIBRARY */
+ vertex endpoint1, endpoint2;
+ int segmentmarkers;
+ int end1, end2;
+ int boundmarker;
+ int i;
+
+ if (b->poly) {
+ if (!b->quiet) {
+ printf("Recovering segments in Delaunay triangulation.\n");
+ }
+#ifdef TRILIBRARY
+ strcpy(polyfilename, "input");
+ m->insegments = numberofsegments;
+ segmentmarkers = segmentmarkerlist != (int *) NULL;
+ index = 0;
+#else /* not TRILIBRARY */
+ /* Read the segments from a .poly file. */
+ /* Read number of segments and number of boundary markers. */
+ stringptr = readline(inputline, polyfile, polyfilename);
+ m->insegments = (int) strtol(stringptr, &stringptr, 0);
+ stringptr = findfield(stringptr);
+ if (*stringptr == '\0') {
+ segmentmarkers = 0;
+ } else {
+ segmentmarkers = (int) strtol(stringptr, &stringptr, 0);
+ }
+#endif /* not TRILIBRARY */
+ /* If the input vertices are collinear, there is no triangulation, */
+ /* so don't try to insert segments. */
+ if (m->triangles.items == 0) {
+ return;
+ }
+
+ /* If segments are to be inserted, compute a mapping */
+ /* from vertices to triangles. */
+ if (m->insegments > 0) {
+ makevertexmap(m, b);
+ if (b->verbose) {
+ printf(" Recovering PSLG segments.\n");
+ }
+ }
+
+ boundmarker = 0;
+ /* Read and insert the segments. */
+ for (i = 0; i < m->insegments; i++) {
+#ifdef TRILIBRARY
+ end1 = segmentlist[index++];
+ end2 = segmentlist[index++];
+ if (segmentmarkers) {
+ boundmarker = segmentmarkerlist[i];
+ }
+#else /* not TRILIBRARY */
+ stringptr = readline(inputline, polyfile, b->inpolyfilename);
+ stringptr = findfield(stringptr);
+ if (*stringptr == '\0') {
+ printf("Error: Segment %d has no endpoints in %s.\n",
+ b->firstnumber + i, polyfilename);
+ triexit(1);
+ } else {
+ end1 = (int) strtol(stringptr, &stringptr, 0);
+ }
+ stringptr = findfield(stringptr);
+ if (*stringptr == '\0') {
+ printf("Error: Segment %d is missing its second endpoint in %s.\n",
+ b->firstnumber + i, polyfilename);
+ triexit(1);
+ } else {
+ end2 = (int) strtol(stringptr, &stringptr, 0);
+ }
+ if (segmentmarkers) {
+ stringptr = findfield(stringptr);
+ if (*stringptr == '\0') {
+ boundmarker = 0;
+ } else {
+ boundmarker = (int) strtol(stringptr, &stringptr, 0);
+ }
+ }
+#endif /* not TRILIBRARY */
+ if ((end1 < b->firstnumber) ||
+ (end1 >= b->firstnumber + m->invertices)) {
+ if (!b->quiet) {
+ printf("Warning: Invalid first endpoint of segment %d in %s.\n",
+ b->firstnumber + i, polyfilename);
+ }
+ } else if ((end2 < b->firstnumber) ||
+ (end2 >= b->firstnumber + m->invertices)) {
+ if (!b->quiet) {
+ printf("Warning: Invalid second endpoint of segment %d in %s.\n",
+ b->firstnumber + i, polyfilename);
+ }
+ } else {
+ /* Find the vertices numbered `end1' and `end2'. */
+ endpoint1 = getvertex(m, b, end1);
+ endpoint2 = getvertex(m, b, end2);
+ if ((endpoint1[0] == endpoint2[0]) && (endpoint1[1] == endpoint2[1])) {
+ if (!b->quiet) {
+ printf("Warning: Endpoints of segment %d are coincident in %s.\n",
+ b->firstnumber + i, polyfilename);
+ }
+ } else {
+ insertsegment(m, b, endpoint1, endpoint2, boundmarker);
+ }
+ }
+ }
+ } else {
+ m->insegments = 0;
+ }
+ if (b->convex || !b->poly) {
+ /* Enclose the convex hull with subsegments. */
+ if (b->verbose) {
+ printf(" Enclosing convex hull with segments.\n");
+ }
+ markhull(m, b);
+ }
+}
+
+/** **/
+/** **/
+/********* Segment insertion ends here *********/
+
+/********* Carving out holes and concavities begins here *********/
+/** **/
+/** **/
+
+/*****************************************************************************/
+/* */
+/* infecthull() Virally infect all of the triangles of the convex hull */
+/* that are not protected by subsegments. Where there are */
+/* subsegments, set boundary markers as appropriate. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+void infecthull(struct mesh *m, struct behavior *b)
+#else /* not ANSI_DECLARATORS */
+void infecthull(m, b)
+struct mesh *m;
+struct behavior *b;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ struct otri hulltri;
+ struct otri nexttri;
+ struct otri starttri;
+ struct osub hullsubseg;
+ triangle **deadtriangle;
+ vertex horg, hdest;
+ triangle ptr; /* Temporary variable used by sym(). */
+ subseg sptr; /* Temporary variable used by tspivot(). */
+
+ if (b->verbose) {
+ printf(" Marking concavities (external triangles) for elimination.\n");
+ }
+ /* Find a triangle handle on the hull. */
+ hulltri.tri = m->dummytri;
+ hulltri.orient = 0;
+ symself(hulltri);
+ /* Remember where we started so we know when to stop. */
+ otricopy(hulltri, starttri);
+ /* Go once counterclockwise around the convex hull. */
+ do {
+ /* Ignore triangles that are already infected. */
+ if (!infected(hulltri)) {
+ /* Is the triangle protected by a subsegment? */
+ tspivot(hulltri, hullsubseg);
+ if (hullsubseg.ss == m->dummysub) {
+ /* The triangle is not protected; infect it. */
+ if (!infected(hulltri)) {
+ infect(hulltri);
+ deadtriangle = (triangle **) poolalloc(&m->viri);
+ *deadtriangle = hulltri.tri;
+ }
+ } else {
+ /* The triangle is protected; set boundary markers if appropriate. */
+ if (mark(hullsubseg) == 0) {
+ setmark(hullsubseg, 1);
+ org(hulltri, horg);
+ dest(hulltri, hdest);
+ if (vertexmark(horg) == 0) {
+ setvertexmark(horg, 1);
+ }
+ if (vertexmark(hdest) == 0) {
+ setvertexmark(hdest, 1);
+ }
+ }
+ }
+ }
+ /* To find the next hull edge, go clockwise around the next vertex. */
+ lnextself(hulltri);
+ oprev(hulltri, nexttri);
+ while (nexttri.tri != m->dummytri) {
+ otricopy(nexttri, hulltri);
+ oprev(hulltri, nexttri);
+ }
+ } while (!otriequal(hulltri, starttri));
+}
+
+/*****************************************************************************/
+/* */
+/* plague() Spread the virus from all infected triangles to any neighbors */
+/* not protected by subsegments. Delete all infected triangles. */
+/* */
+/* This is the procedure that actually creates holes and concavities. */
+/* */
+/* This procedure operates in two phases. The first phase identifies all */
+/* the triangles that will die, and marks them as infected. They are */
+/* marked to ensure that each triangle is added to the virus pool only */
+/* once, so the procedure will terminate. */
+/* */
+/* The second phase actually eliminates the infected triangles. It also */
+/* eliminates orphaned vertices. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+void plague(struct mesh *m, struct behavior *b)
+#else /* not ANSI_DECLARATORS */
+void plague(m, b)
+struct mesh *m;
+struct behavior *b;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ struct otri testtri;
+ struct otri neighbor;
+ triangle **virusloop;
+ triangle **deadtriangle;
+ struct osub neighborsubseg;
+ vertex testvertex;
+ vertex norg, ndest;
+ vertex deadorg, deaddest, deadapex;
+ int killorg;
+ triangle ptr; /* Temporary variable used by sym() and onext(). */
+ subseg sptr; /* Temporary variable used by tspivot(). */
+
+ if (b->verbose) {
+ printf(" Marking neighbors of marked triangles.\n");
+ }
+ /* Loop through all the infected triangles, spreading the virus to */
+ /* their neighbors, then to their neighbors' neighbors. */
+ traversalinit(&m->viri);
+ virusloop = (triangle **) traverse(&m->viri);
+ while (virusloop != (triangle **) NULL) {
+ testtri.tri = *virusloop;
+ /* A triangle is marked as infected by messing with one of its pointers */
+ /* to subsegments, setting it to an illegal value. Hence, we have to */
+ /* temporarily uninfect this triangle so that we can examine its */
+ /* adjacent subsegments. */
+ uninfect(testtri);
+ if (b->verbose > 2) {
+ /* Assign the triangle an orientation for convenience in */
+ /* checking its vertices. */
+ testtri.orient = 0;
+ org(testtri, deadorg);
+ dest(testtri, deaddest);
+ apex(testtri, deadapex);
+ printf(" Checking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
+ deadorg[0], deadorg[1], deaddest[0], deaddest[1],
+ deadapex[0], deadapex[1]);
+ }
+ /* Check each of the triangle's three neighbors. */
+ for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
+ /* Find the neighbor. */
+ sym(testtri, neighbor);
+ /* Check for a subsegment between the triangle and its neighbor. */
+ tspivot(testtri, neighborsubseg);
+ /* Check if the neighbor is nonexistent or already infected. */
+ if ((neighbor.tri == m->dummytri) || infected(neighbor)) {
+ if (neighborsubseg.ss != m->dummysub) {
+ /* There is a subsegment separating the triangle from its */
+ /* neighbor, but both triangles are dying, so the subsegment */
+ /* dies too. */
+ subsegdealloc(m, neighborsubseg.ss);
+ if (neighbor.tri != m->dummytri) {
+ /* Make sure the subsegment doesn't get deallocated again */
+ /* later when the infected neighbor is visited. */
+ uninfect(neighbor);
+ tsdissolve(neighbor);
+ infect(neighbor);
+ }
+ }
+ } else { /* The neighbor exists and is not infected. */
+ if (neighborsubseg.ss == m->dummysub) {
+ /* There is no subsegment protecting the neighbor, so */
+ /* the neighbor becomes infected. */
+ if (b->verbose > 2) {
+ org(neighbor, deadorg);
+ dest(neighbor, deaddest);
+ apex(neighbor, deadapex);
+ printf(
+ " Marking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
+ deadorg[0], deadorg[1], deaddest[0], deaddest[1],
+ deadapex[0], deadapex[1]);
+ }
+ infect(neighbor);
+ /* Ensure that the neighbor's neighbors will be infected. */
+ deadtriangle = (triangle **) poolalloc(&m->viri);
+ *deadtriangle = neighbor.tri;
+ } else { /* The neighbor is protected by a subsegment. */
+ /* Remove this triangle from the subsegment. */
+ stdissolve(neighborsubseg);
+ /* The subsegment becomes a boundary. Set markers accordingly. */
+ if (mark(neighborsubseg) == 0) {
+ setmark(neighborsubseg, 1);
+ }
+ org(neighbor, norg);
+ dest(neighbor, ndest);
+ if (vertexmark(norg) == 0) {
+ setvertexmark(norg, 1);
+ }
+ if (vertexmark(ndest) == 0) {
+ setvertexmark(ndest, 1);
+ }
+ }
+ }
+ }
+ /* Remark the triangle as infected, so it doesn't get added to the */
+ /* virus pool again. */
+ infect(testtri);
+ virusloop = (triangle **) traverse(&m->viri);
+ }
+
+ if (b->verbose) {
+ printf(" Deleting marked triangles.\n");
+ }
+
+ traversalinit(&m->viri);
+ virusloop = (triangle **) traverse(&m->viri);
+ while (virusloop != (triangle **) NULL) {
+ testtri.tri = *virusloop;
+
+ /* Check each of the three corners of the triangle for elimination. */
+ /* This is done by walking around each vertex, checking if it is */
+ /* still connected to at least one live triangle. */
+ for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
+ org(testtri, testvertex);
+ /* Check if the vertex has already been tested. */
+ if (testvertex != (vertex) NULL) {
+ killorg = 1;
+ /* Mark the corner of the triangle as having been tested. */
+ setorg(testtri, NULL);
+ /* Walk counterclockwise about the vertex. */
+ onext(testtri, neighbor);
+ /* Stop upon reaching a boundary or the starting triangle. */
+ while ((neighbor.tri != m->dummytri) &&
+ (!otriequal(neighbor, testtri))) {
+ if (infected(neighbor)) {
+ /* Mark the corner of this triangle as having been tested. */
+ setorg(neighbor, NULL);
+ } else {
+ /* A live triangle. The vertex survives. */
+ killorg = 0;
+ }
+ /* Walk counterclockwise about the vertex. */
+ onextself(neighbor);
+ }
+ /* If we reached a boundary, we must walk clockwise as well. */
+ if (neighbor.tri == m->dummytri) {
+ /* Walk clockwise about the vertex. */
+ oprev(testtri, neighbor);
+ /* Stop upon reaching a boundary. */
+ while (neighbor.tri != m->dummytri) {
+ if (infected(neighbor)) {
+ /* Mark the corner of this triangle as having been tested. */
+ setorg(neighbor, NULL);
+ } else {
+ /* A live triangle. The vertex survives. */
+ killorg = 0;
+ }
+ /* Walk clockwise about the vertex. */
+ oprevself(neighbor);
+ }
+ }
+ if (killorg) {
+ if (b->verbose > 1) {
+ printf(" Deleting vertex (%.12g, %.12g)\n",
+ testvertex[0], testvertex[1]);
+ }
+ setvertextype(testvertex, UNDEADVERTEX);
+ m->undeads++;
+ }
+ }
+ }
+
+ /* Record changes in the number of boundary edges, and disconnect */
+ /* dead triangles from their neighbors. */
+ for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
+ sym(testtri, neighbor);
+ if (neighbor.tri == m->dummytri) {
+ /* There is no neighboring triangle on this edge, so this edge */
+ /* is a boundary edge. This triangle is being deleted, so this */
+ /* boundary edge is deleted. */
+ m->hullsize--;
+ } else {
+ /* Disconnect the triangle from its neighbor. */
+ dissolve(neighbor);
+ /* There is a neighboring triangle on this edge, so this edge */
+ /* becomes a boundary edge when this triangle is deleted. */
+ m->hullsize++;
+ }
+ }
+ /* Return the dead triangle to the pool of triangles. */
+ triangledealloc(m, testtri.tri);
+ virusloop = (triangle **) traverse(&m->viri);
+ }
+ /* Empty the virus pool. */
+ poolrestart(&m->viri);
+}
+
+/*****************************************************************************/
+/* */
+/* regionplague() Spread regional attributes and/or area constraints */
+/* (from a .poly file) throughout the mesh. */
+/* */
+/* This procedure operates in two phases. The first phase spreads an */
+/* attribute and/or an area constraint through a (segment-bounded) region. */
+/* The triangles are marked to ensure that each triangle is added to the */
+/* virus pool only once, so the procedure will terminate. */
+/* */
+/* The second phase uninfects all infected triangles, returning them to */
+/* normal. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+void regionplague(struct mesh *m, struct behavior *b,
+ REAL attribute, REAL area)
+#else /* not ANSI_DECLARATORS */
+void regionplague(m, b, attribute, area)
+struct mesh *m;
+struct behavior *b;
+REAL attribute;
+REAL area;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ struct otri testtri;
+ struct otri neighbor;
+ triangle **virusloop;
+ triangle **regiontri;
+ struct osub neighborsubseg;
+ vertex regionorg, regiondest, regionapex;
+ triangle ptr; /* Temporary variable used by sym() and onext(). */
+ subseg sptr; /* Temporary variable used by tspivot(). */
+
+ if (b->verbose > 1) {
+ printf(" Marking neighbors of marked triangles.\n");
+ }
+ /* Loop through all the infected triangles, spreading the attribute */
+ /* and/or area constraint to their neighbors, then to their neighbors' */
+ /* neighbors. */
+ traversalinit(&m->viri);
+ virusloop = (triangle **) traverse(&m->viri);
+ while (virusloop != (triangle **) NULL) {
+ testtri.tri = *virusloop;
+ /* A triangle is marked as infected by messing with one of its pointers */
+ /* to subsegments, setting it to an illegal value. Hence, we have to */
+ /* temporarily uninfect this triangle so that we can examine its */
+ /* adjacent subsegments. */
+ uninfect(testtri);
+ if (b->regionattrib) {
+ /* Set an attribute. */
+ setelemattribute(testtri, m->eextras, attribute);
+ }
+ if (b->vararea) {
+ /* Set an area constraint. */
+ setareabound(testtri, area);
+ }
+ if (b->verbose > 2) {
+ /* Assign the triangle an orientation for convenience in */
+ /* checking its vertices. */
+ testtri.orient = 0;
+ org(testtri, regionorg);
+ dest(testtri, regiondest);
+ apex(testtri, regionapex);
+ printf(" Checking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
+ regionorg[0], regionorg[1], regiondest[0], regiondest[1],
+ regionapex[0], regionapex[1]);
+ }
+ /* Check each of the triangle's three neighbors. */
+ for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
+ /* Find the neighbor. */
+ sym(testtri, neighbor);
+ /* Check for a subsegment between the triangle and its neighbor. */
+ tspivot(testtri, neighborsubseg);
+ /* Make sure the neighbor exists, is not already infected, and */
+ /* isn't protected by a subsegment. */
+ if ((neighbor.tri != m->dummytri) && !infected(neighbor)
+ && (neighborsubseg.ss == m->dummysub)) {
+ if (b->verbose > 2) {
+ org(neighbor, regionorg);
+ dest(neighbor, regiondest);
+ apex(neighbor, regionapex);
+ printf(" Marking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
+ regionorg[0], regionorg[1], regiondest[0], regiondest[1],
+ regionapex[0], regionapex[1]);
+ }
+ /* Infect the neighbor. */
+ infect(neighbor);
+ /* Ensure that the neighbor's neighbors will be infected. */
+ regiontri = (triangle **) poolalloc(&m->viri);
+ *regiontri = neighbor.tri;
+ }
+ }
+ /* Remark the triangle as infected, so it doesn't get added to the */
+ /* virus pool again. */
+ infect(testtri);
+ virusloop = (triangle **) traverse(&m->viri);
+ }
+
+ /* Uninfect all triangles. */
+ if (b->verbose > 1) {
+ printf(" Unmarking marked triangles.\n");
+ }
+ traversalinit(&m->viri);
+ virusloop = (triangle **) traverse(&m->viri);
+ while (virusloop != (triangle **) NULL) {
+ testtri.tri = *virusloop;
+ uninfect(testtri);
+ virusloop = (triangle **) traverse(&m->viri);
+ }
+ /* Empty the virus pool. */
+ poolrestart(&m->viri);
+}
+
+/*****************************************************************************/
+/* */
+/* carveholes() Find the holes and infect them. Find the area */
+/* constraints and infect them. Infect the convex hull. */
+/* Spread the infection and kill triangles. Spread the */
+/* area constraints. */
+/* */
+/* This routine mainly calls other routines to carry out all these */
+/* functions. */
+/* */
+/*****************************************************************************/
+
+#ifdef ANSI_DECLARATORS
+void carveholes(struct mesh *m, struct behavior *b, REAL *holelist, int holes,
+ REAL *regionlist, int regions)
+#else /* not ANSI_DECLARATORS */
+void carveholes(m, b, holelist, holes, regionlist, regions)
+struct mesh *m;
+struct behavior *b;
+REAL *holelist;
+int holes;
+REAL *regionlist;
+int regions;
+#endif /* not ANSI_DECLARATORS */
+
+{
+ struct otri searchtri;
+ struct otri triangleloop;
+ struct otri *regiontris;
+ triangle **holetri;
+ triangle **regiontri;
+ vertex searchorg, searchdest;
+ enum locateresult intersect;
+ int i;
+ triangle ptr; /* Temporary variable used by sym(). */
+
+ if (!(b->quiet || (b->noholes && b->convex))) {
+ printf("Removing unwanted triangles.\n");
+ if (b->verbose && (holes > 0)) {
+ printf(" Marking holes for elimination.\n");
+ }
+ }
+
+ if (regions > 0) {
+ /* Allocate storage for the triangles in which region points fall. */
+ regiontris = (struct otri *) trimalloc(regions *
+ (int) sizeof(struct otri));
+ } else {
+ regiontris = (struct otri *) NULL;
+ }
+
+ if (((holes > 0) && !b->noholes) || !b->convex || (regions > 0)) {
+ /* Initialize a pool of viri to be used for holes, concavities, */
+ /* regional attributes, and/or regional area constraints. */
+ poolinit(&m->viri, sizeof(triangle *), VIRUSPERBLOCK, VIRUSPERBLOCK, 0);
+ }
+
+ if (!b->convex) {
+ /* Mark as infected any unprotected triangles on the boundary. */
+ /* This is one way by which concavities are created. */
+ infecthull(m, b);
+ }
+
+ if ((holes > 0) && !b->noholes) {
+ /* Infect each triangle in which a hole lies. */
+ for (i = 0; i < 2 * holes; i += 2) {
+ /* Ignore holes that aren't within the bounds of the mesh. */
+ if ((holelist[i] >= m->xmin) && (holelist[i] <= m->xmax)
+ && (holelist[i + 1] >= m->ymin) && (holelist[i + 1] <= m->ymax)) {
+ /* Start searching from some triangle on the outer boundary. */
+ searchtri.tri = m->dummytri;
+ searchtri.orient = 0;
+ symself(searchtri);
+ /* Ensure that the hole is to the left of this boundary edge; */
+ /* otherwise, locate() will falsely report that the hole */
+ /* falls within the starting triangle. */
+ org(searchtri, searchorg);
+ dest(searchtri, searchdest);
+ if (counterclockwise(m, b, searchorg, searchdest, &holelist[i]) >
+ 0.0) {
+ /* Find a triangle that contains the hole. */
+ intersect = locate(m, b, &holelist[i], &searchtri);
+ if ((intersect != OUTSIDE) && (!infected(searchtri))) {
+ /* Infect the triangle. This is done by marking the triangle */
+ /* as infected and including the triangle in the virus pool. */
+ infect(searchtri);
+ holetri = (triangle **) poolalloc(&m->viri);
+ *holetri = searchtri.tri;
+ }
+ }
+ }
+ }
+ }
+
+ /* Now, we have to find all the regions BEFORE we carve the holes, because */
+ /* locate() won't work when the triangulation is no longer convex. */
+ /* (Incidentally, this is the reason why regional attributes and area */
+ /* constraints can't be used when refining a preexisting mesh, which */
+ /* might not be convex; they can only be used with a freshly */
+ /* triangulated PSLG.) */
+ if (regions > 0) {
+ /* Find the starting triangle for each region. */
+ for (i = 0; i < regions; i++) {
+ regiontris[i].tri = m->dummytri;
+ /* Ignore region points that aren't within the bounds of the mesh. */
+ if ((regionlist[4 * i] >= m->xmin) && (regionlist[4 * i] <= m->xmax) &&
+ (regionlist[4 * i + 1] >= m->ymin) &&
+ (regionlist[4 * i + 1] <= m->ymax)) {
+ /* Start searching from some triangle on the outer boundary. */
+ searchtri.tri = m->dummytri;
+ searchtri.orient = 0;
+ symself(searchtri);
+ /* Ensure that the region point is to the left of this boundary */
+ /* edge; otherwise, locate() will falsely report that the */
+ /* region point falls within the starting triangle. */
+ org(searchtri, searchorg);
+ dest(searchtri, searchdest);
+ if (counterclockwise(m, b, searchorg, searchdest, ®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 */
+}
Added: grass-addons/grass6/vector/v.trimesh/triangle.h
===================================================================
--- grass-addons/grass6/vector/v.trimesh/triangle.h (rev 0)
+++ grass-addons/grass6/vector/v.trimesh/triangle.h 2012-03-31 08:56:38 UTC (rev 51217)
@@ -0,0 +1,289 @@
+/*****************************************************************************/
+/* */
+/* (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 */
Added: grass-addons/grass6/vector/v.trimesh/v.trimesh.c
===================================================================
--- grass-addons/grass6/vector/v.trimesh/v.trimesh.c (rev 0)
+++ grass-addons/grass6/vector/v.trimesh/v.trimesh.c 2012-03-31 08:56:38 UTC (rev 51217)
@@ -0,0 +1,399 @@
+/*****************************************************************************/
+/* MODULE: v.trimesh */
+/* AUTHOR: Jaime Carrera-Hernandez, University of Alberta, Edmonton Canada */
+/* jaime.carrera-AT-ualberta.ca */
+/* jaime.carrerah-AT-gmail.com */
+/* PURPOSE: v.trimesh creates a triangular mesh */
+/* using Triangle (by Jonathan Richard Shewchunk) */
+/* */
+/* COPYRIGHT: (C) 2008 by the GRASS development team */
+/* */
+/*****************************************************************************/
+
+
+#ifdef SINGLE
+#define REAL float
+#else /* not SINGLE */
+#define REAL double
+#endif /* not SINGLE */
+
+#include<stdio.h>
+#include<stdlib.h>
+#include<unistd.h>
+#include<grass/gis.h>
+#include<grass/Vect.h>
+#include<grass/glocale.h>
+#include<grass/dbmi.h>
+#include"triangle.h"
+
+int main(int argc, char *argv[])
+{
+ struct Option *input, *output;
+ struct Flag *nomaxarea;
+ struct Map_info Map;
+ struct GModule *module;
+ struct field_info *Fi;
+ dbValue *dbvalue;
+ dbDriver *driver;
+ dbCursor cursor;
+ dbString stmt;
+ dbColumn *col;
+ dbTable *table;
+ char buf[2000];
+ int type, ctype, i, cat, j, firstnode, segments,h;
+ int numberofregions, c, nnodes, nlines;
+ int count, more, of;
+ /* val is used for area constraints... currently set to int values*/
+
+ double *xptr, *yptr, *zptr, x, y, areaconst;
+
+ struct triangulateio in, out;
+ /* I need dynamic allocation */
+ double pointlist[10000];
+ /* regionlist is used for centroids */
+ /* val is for area constraints centroids */
+ double regionlist[40];
+ int val[40];
+ int segmentlist[10000];
+ /* int holelist[30];*/
+ struct line_pnts *Points;
+ struct line_cats *Cats;
+ struct Option *column;
+ /*To determine centroids*/
+ int left,center,right;
+ double xleft,yleft,xcenter,ycenter,xright,yright;
+ double xm1,xm2,ym,m1,m2,b1,b2;
+
+ int area,areas,centroid;
+
+ G_gisinit(argv[0]);
+
+
+ module = G_define_module();
+ module->keywords = _("vector");
+ module->description =
+ _("Create a triangular mesh from a vector map");
+
+ input = G_define_standard_option(G_OPT_V_INPUT);
+
+ column = G_define_option();
+ column->key = "column";
+ column->type= TYPE_STRING;
+ column->required= YES;
+ column->multiple=NO;
+ column->description=_("Column name with area constraints/centroid attributes");
+
+ output = G_define_standard_option(G_OPT_V_OUTPUT);
+
+ nomaxarea = G_define_flag();
+ nomaxarea->key='a';
+ nomaxarea->description=_("Do not use areal constraint");
+ /* The vector map is opened*/
+ if(G_parser(argc,argv))
+ exit(EXIT_FAILURE);
+
+ Vect_set_open_level(2);
+ Vect_open_old(&Map, input->answer, "");
+
+ /* The vector map is now read (boundaries and centroids)*/
+
+ Points = Vect_new_line_struct();
+ Cats = Vect_new_cats_struct();
+
+ areas=Vect_get_num_areas(&Map);
+ printf("areas=%i\n",areas);
+
+ /* Verifying if data were input properly*/
+ if(!column->answer)
+ G_fatal_error ("Please assign a column with areal constraints");
+
+ h=0;
+ c=0;
+ j=0;
+ segments=0;
+
+ for(area=1;area<=areas;area++){
+ centroid=Vect_get_area_centroid(&Map,area);
+ firstnode=j;
+
+ Vect_get_area_points(&Map,area,Points);
+ printf("Reading boundaries for area %i\n",area);
+ xptr=Points->x;
+ yptr=Points->y;
+
+ while(Points->n_points--){
+ pointlist[j*2]=*xptr++;
+ pointlist[j*2+1]=*yptr++;
+ j++;
+ }
+ j--;
+ printf("before reading nodes from boundary\n");
+ for(i=firstnode;i<j;i++){
+ if(i<j-1){
+ segmentlist[i*2]=i;
+ segmentlist[i*2+1]=i+1;
+ }
+ else{
+ segmentlist[i*2]=i;
+ segmentlist[i*2+1]=firstnode;
+ }
+ segments++;
+ }
+ }
+
+
+ /****************************************************************/
+ /* Get area constraints */
+ /****************************************************************/
+
+ c=0;
+ while((type=Vect_read_next_line(&Map,Points,Cats))>0)
+ {
+ if(type == GV_CENTROID && Cats->cat[0] > 0){
+ xptr=Points->x;
+ yptr=Points->y;
+ regionlist[c*2]=*xptr;
+ regionlist[c*2+1]=*yptr;
+ for(i=0;i < Cats->n_cats; i++){
+ Fi= Vect_get_field(&Map,Cats->field[i]);
+ driver = db_start_driver_open_database ( Fi->driver, Fi->database );
+ printf("select %s from %s where %s=%-10d\n",column->answer,Fi->table,Fi->key,Cats->cat[i]);
+
+ sprintf(buf,"select %s from %s where %s=%-10d\n",column->answer,Fi->table,Fi->key,Cats->cat[i]);
+ db_init_string(&stmt);
+ db_append_string(&stmt,buf);
+ if(db_open_select_cursor(driver, &stmt, &cursor, DB_SEQUENTIAL) != DB_OK)
+ G_fatal_error ( "Cannot open select cursor: '%s'", db_get_string(&stmt));
+ table=db_get_cursor_table(&cursor);
+ col=db_get_table_column(table,0); /* first column */
+ ctype= db_sqltype_to_Ctype(db_get_column_sqltype (col));
+ if ( ctype != DB_C_TYPE_INT )
+ G_fatal_error ( "area constraint must be integer");
+
+ dbvalue=db_get_column_value(col);
+ /* fetch the data*/
+ count=0;
+ while(1){
+ if(db_fetch(&cursor, DB_NEXT, &more) != DB_OK)
+ return (-1);
+ if (!more) break;
+ /* somehow it didn't work with double val[c], so only int values are used*/
+ if( count == 0 )
+ val[c] = db_get_value_int ( dbvalue );
+ count ++;
+ }
+ db_close_cursor(&cursor);
+ db_free_string(&stmt);
+
+ printf("c=%i, val[%i]=%i\n",c,c,val[c]);
+ c++;
+ }
+ }
+ }
+ Vect_close(&Map);
+ /*printf("ocas 4\n");*/
+
+ /************************************/
+ /* Creating Triangle's data input : */
+ /************************************/
+
+ in.numberofpoints = j;
+ in.numberofpointattributes = 0;
+
+ in.pointlist = (REAL *) malloc(in.numberofpoints * 2 * sizeof(REAL));
+ /* This is a really dirty way to do it */
+ for(i=0;i<j;i++){
+ for(of=0;of<2;of++){
+ in.pointlist[i*2+of]=pointlist[i*2+of];
+ }
+ }
+
+ in.numberofsegments=segments;
+ in.segmentlist = (int *) malloc(in.numberofsegments * 2 * sizeof(int));
+ for(i=0;i<segments;i++){
+ for(of=0;of<2;of++){
+ in.segmentlist[i*2+of]=segmentlist[i*2+of];
+ /* printf("segmentlist[%i]=%i in.segmentlist[%i]=%i\n",i*2+of,segmentlist[i*2+of],i*2+of,in.segmentlist[i*2+of]);
+ }
+ printf("segment %i= %i--%i\n",i,in.segmentlist[i*2],in.segmentlist[i*2+1]);*/
+ }
+ }
+ in.numberofregions = c;
+ in.regionlist = (REAL *) malloc(in.numberofregions * 4 * sizeof(REAL));
+
+ for(i=0;i<in.numberofregions;i++){
+ in.regionlist[i*4]=regionlist[i*2];
+ in.regionlist[i*4+1]=regionlist[i*2+1];
+ in.regionlist[i*4+2]=0;
+ in.regionlist[i*4+3]=val[i];
+ /*printf("val[%i]=%i",i,val[i]);*/
+ }
+ /* For some reason Triangle doesn't like these lines */
+ /* In case holes are present; so no holes!) */
+ /* Tabernacle!
+ if(h>0){
+ in.numberofholes=h;
+ printf("shouldn't be in...\n");
+ in.holelist=(REAL *) malloc(in.numberofholes * 2 * sizeof(REAL));
+ out.holelist= (int *) NULL;
+ for(i=0;i<in.numberofholes;i++){
+ for(of=0;of<2;of++){
+ in.holelist[i*2+of]=holelist[i*2+of];
+ }
+ }
+ }
+ /* variables need to be initialized for Triangle */
+
+ in.numberofholes=0;
+
+ out.pointlist = (REAL *) NULL;
+ out.trianglelist = (int *) NULL;
+ out.segmentlist = (int *) NULL;
+ out.edgelist= (int *) NULL;
+
+ /* Triangulate the points: read and write a PSLG (p), number everything */
+ /* from zero (z), create a quality mesh (q) and use area constraints (a)*/
+ /* voronoi polygons not needed, thus vorout== NULL*/
+
+ /* Use FLAGS for either constrained Delaunay, area constraints*/
+ printf("number of regions = %i\n",c);
+ printf("calling triangle \n");
+ if(nomaxarea->answer)
+ triangulate("pzqDBeQj", &in, &out, (struct triangulateio *) NULL);
+ else
+ triangulate("pzqDaBeQj", &in, &out, (struct triangulateio *) NULL);
+
+ if (0>Vect_open_new (&Map, output->answer, 0))
+ G_fatal_error(_("Unable to create vector map %s"),output->answer);
+
+ driver=db_start_driver_open_database(Fi->driver,Vect_subst_var(Fi->database,&Map));
+
+ if(driver==NULL)
+ G_fatal_error(_("Cannot open database %s by driver %s"),Vect_subst_var(Fi->database,&Map),Fi->driver);
+
+ printf("driver= %s\n",driver);
+ db_begin_transaction(driver);
+
+ sprintf(buf,"create table %snodes (cat int)",output->answer);
+ db_init_string(&stmt);
+ db_append_string(&stmt,buf);
+ printf("buf=%s\n", buf);
+
+ if(db_execute_immediate(driver,&stmt) != DB_OK)
+ G_fatal_error(_("Cannot create table %s"),db_get_string(&stmt));
+
+
+ sprintf(buf,"%snodes",output->answer);
+ table=buf;
+
+ Vect_map_add_dblink(&Map, 1, NULL, table,"cat",Fi->database,Fi->driver);
+
+ /* Writing the output to GRASS*/
+
+ /*********************/
+ /* Writing NODES */
+ /*********************/
+ for(i=0;i<out.numberofpoints;i++){
+ Vect_reset_line (Points);
+ Vect_reset_cats (Cats);
+ x=out.pointlist[i*2];
+ y=out.pointlist[i*2+1];
+ Vect_append_point (Points,x,y,0);
+ Vect_cat_set (Cats, 1, i+1);
+ Vect_write_line(&Map, GV_POINT, Points, Cats);
+ sprintf(buf,"insert into %snodes values(%i)",output->answer,i+1);
+ db_init_string(&stmt);
+ db_append_string(&stmt,buf);
+ if(db_execute_immediate(driver,&stmt) != DB_OK)
+ G_fatal_error(_("Cannot add values to table %snodes"),output->answer);
+ }
+ /*********************/
+ /* Writing BOUNDARIES */
+ /*********************/
+ for(i=0;i<out.numberofedges;i++){
+ Vect_reset_line (Points);
+ Vect_reset_cats (Cats);
+ for(of=0;of<2;of++){
+ j=out.edgelist[i*2+of];
+ x=out.pointlist[j*2];
+ y=out.pointlist[j*2+1];
+ Vect_append_point (Points,x,y,0);
+ Vect_cat_set (Cats, 1, i+1);
+ Vect_write_line(&Map, GV_BOUNDARY, Points, Cats);
+ }
+ }
+ /*********************/
+ /* Writing CENTROIDS */
+ /*********************/
+ sprintf(buf,"create table %stricentr (cat int)",output->answer);
+ db_init_string(&stmt);
+ db_append_string(&stmt,buf);
+
+ if(db_execute_immediate(driver,&stmt) != DB_OK)
+ G_fatal_error(_("Cannot create table %s"),db_get_string(&stmt));
+
+ sprintf(buf,"%stricentr",output->answer);
+ table=buf;
+
+ Vect_map_add_dblink(&Map, 2, NULL, table,"cat",Fi->database,Fi->driver);
+
+ for(i=0;i<out.numberoftriangles;i++){
+ Vect_reset_line (Points);
+ Vect_reset_cats (Cats);
+ left=out.trianglelist[i*3];
+ center=out.trianglelist[i*3+1];
+ right=out.trianglelist[i*3+2];
+
+ xleft=out.pointlist[left*2];
+ yleft=out.pointlist[left*2+1];
+ xcenter=out.pointlist[center*2];
+ ycenter=out.pointlist[center*2+1];
+ xright=out.pointlist[right*2];
+ yright=out.pointlist[right*2+1];
+
+ xm1=xleft+((xcenter-xleft)/2);
+ ym=yleft+((ycenter-yleft)/2);
+ m1=(yright-ym)/(xright-xm1);
+ b1=yright-(m1*xright);
+
+ xm2=xcenter+((xright-xcenter)/2);
+ ym=ycenter+((yright-ycenter)/2);
+ m2=(yleft-ym)/(xleft-xm2);
+ b2=yleft-(m2*xleft);
+ /* in case a median is a vertical line */
+ if((xright-xm1)==0 || (xleft-xm2)==0 ){
+ if((xright-xm1)==0){
+ x=xm1;
+ y=(m2*x)+b2;
+ }
+ else{
+ x=xm2;
+ y=(m1*x)+b1;
+ }
+ }
+ else{
+ x=(b2-b1)/(m1-m2);
+ y=(m1*x)+b1;
+ }
+
+ Vect_append_point (Points,x,y,0);
+ Vect_cat_set (Cats, 2, i+1);
+ Vect_write_line(&Map, GV_CENTROID, Points, Cats);
+ sprintf(buf,"insert into %stricentr values(%i)",output->answer,i+1);
+ db_init_string(&stmt);
+ db_append_string(&stmt,buf);
+ if(db_execute_immediate(driver,&stmt) != DB_OK){
+ G_fatal_error(_("Cannot add values to table %stricentr"),output->answer);
+ }
+ }
+ db_close_database(driver);
+ db_shutdown_driver(driver);
+ /* Vect_build_partial(&Map,GV_BUILD_NONE,NULL); */
+ /* Vect_build(&Map,stderr); */
+
+ Vect_build_partial(&Map,GV_BUILD_NONE);
+ Vect_build(&Map);
+
+ Vect_close(&Map);
+
+}
Added: grass-addons/grass6/vector/v.trimesh/v.trimesh.tmp.html
===================================================================
--- grass-addons/grass6/vector/v.trimesh/v.trimesh.tmp.html (rev 0)
+++ grass-addons/grass6/vector/v.trimesh/v.trimesh.tmp.html 2012-03-31 08:56:38 UTC (rev 51217)
@@ -0,0 +1,48 @@
+
+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
+<html>
+<head>
+<title>GRASS GIS manual: v.trimesh</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<link rel="stylesheet" href="grassdocs.css" type="text/css">
+</head>
+<body bgcolor="white">
+
+<img src="grass_logo.png" alt="GRASS logo"><hr align=center size=6 noshade>
+
+<h2>NAME</h2>
+<em><b>v.trimesh</b></em> - Create a triangular mesh from a vector map
+<h2>KEYWORDS</h2>
+vector
+<h2>SYNOPSIS</h2>
+<b>v.trimesh</b><br>
+<b>v.trimesh help</b><br>
+<b>v.trimesh</b> [-<b>a</b>] <b>input</b>=<em>name</em> <b>column</b>=<em>string</em> <b>output</b>=<em>name</em> [--<b>overwrite</b>] [--<b>verbose</b>] [--<b>quiet</b>]
+
+<h3>Flags:</h3>
+<DL>
+<DT><b>-a</b></DT>
+<DD>Do not use areal constraint</DD>
+
+<DT><b>--overwrite</b></DT>
+<DD>Allow output files to overwrite existing files</DD>
+<DT><b>--verbose</b></DT>
+<DD>Verbose module output</DD>
+<DT><b>--quiet</b></DT>
+<DD>Quiet module output</DD>
+</DL>
+
+<h3>Parameters:</h3>
+<DL>
+<DT><b>input</b>=<em>name</em></DT>
+<DD>Name of input vector map</DD>
+
+<DT><b>column</b>=<em>string</em></DT>
+<DD>Column name with area constraints/centroid attributes</DD>
+
+<DT><b>output</b>=<em>name</em></DT>
+<DD>Name for output vector map</DD>
+
+</DL>
+</body>
+</html>
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